Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.788.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.87740\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.55890 | 1.15946 | 0.579731 | − | 0.814808i | \(-0.303158\pi\) | ||||
0.579731 | + | 0.814808i | \(0.303158\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 11.0192 | 0.344351 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −59.0301 | −0.669415 | ||||||||
\(7\) | 146.487 | 1.12993 | 0.564967 | − | 0.825113i | \(-0.308889\pi\) | ||||
0.564967 | + | 0.825113i | \(0.308889\pi\) | |||||||
\(8\) | −137.611 | −0.760200 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 163.973 | 0.518527 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −99.1731 | −0.198811 | ||||||||
\(13\) | 170.238 | 0.279382 | 0.139691 | − | 0.990195i | \(-0.455389\pi\) | ||||
0.139691 | + | 0.990195i | \(0.455389\pi\) | |||||||
\(14\) | 960.792 | 1.31012 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | −1255.19 | −1.22577 | ||||||||
\(17\) | 1564.81 | 1.31323 | 0.656614 | − | 0.754227i | \(-0.271988\pi\) | ||||
0.656614 | + | 0.754227i | \(0.271988\pi\) | |||||||
\(18\) | 531.271 | 0.386487 | ||||||||
\(19\) | 569.786 | 0.362100 | 0.181050 | − | 0.983474i | \(-0.442050\pi\) | ||||
0.181050 | + | 0.983474i | \(0.442050\pi\) | |||||||
\(20\) | 275.481 | 0.153998 | ||||||||
\(21\) | −1318.38 | −0.652368 | ||||||||
\(22\) | −793.627 | −0.349591 | ||||||||
\(23\) | 3153.25 | 1.24291 | 0.621454 | − | 0.783451i | \(-0.286542\pi\) | ||||
0.621454 | + | 0.783451i | \(0.286542\pi\) | |||||||
\(24\) | 1238.50 | 0.438902 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1116.57 | 0.323932 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 1614.17 | 0.389094 | ||||||||
\(29\) | 3982.58 | 0.879366 | 0.439683 | − | 0.898153i | \(-0.355091\pi\) | ||||
0.439683 | + | 0.898153i | \(0.355091\pi\) | |||||||
\(30\) | −1475.75 | −0.299372 | ||||||||
\(31\) | 2990.78 | 0.558959 | 0.279480 | − | 0.960152i | \(-0.409838\pi\) | ||||
0.279480 | + | 0.960152i | \(0.409838\pi\) | |||||||
\(32\) | −3829.14 | −0.661037 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 10263.5 | 1.52264 | ||||||||
\(35\) | 3662.17 | 0.505322 | ||||||||
\(36\) | 892.558 | 0.114784 | ||||||||
\(37\) | 7858.92 | 0.943753 | 0.471877 | − | 0.881665i | \(-0.343577\pi\) | ||||
0.471877 | + | 0.881665i | \(0.343577\pi\) | |||||||
\(38\) | 3737.17 | 0.419841 | ||||||||
\(39\) | −1532.14 | −0.161301 | ||||||||
\(40\) | −3440.27 | −0.339972 | ||||||||
\(41\) | −5206.60 | −0.483721 | −0.241860 | − | 0.970311i | \(-0.577758\pi\) | ||||
−0.241860 | + | 0.970311i | \(0.577758\pi\) | |||||||
\(42\) | −8647.13 | −0.756395 | ||||||||
\(43\) | 13874.3 | 1.14430 | 0.572149 | − | 0.820149i | \(-0.306110\pi\) | ||||
0.572149 | + | 0.820149i | \(0.306110\pi\) | |||||||
\(44\) | −1333.33 | −0.103826 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | 20681.9 | 1.44110 | ||||||||
\(47\) | 6852.01 | 0.452453 | 0.226226 | − | 0.974075i | \(-0.427361\pi\) | ||||
0.226226 | + | 0.974075i | \(0.427361\pi\) | |||||||
\(48\) | 11296.7 | 0.707701 | ||||||||
\(49\) | 4651.35 | 0.276751 | ||||||||
\(50\) | 4099.32 | 0.231892 | ||||||||
\(51\) | −14083.3 | −0.758192 | ||||||||
\(52\) | 1875.89 | 0.0962054 | ||||||||
\(53\) | −3834.15 | −0.187490 | −0.0937452 | − | 0.995596i | \(-0.529884\pi\) | ||||
−0.0937452 | + | 0.995596i | \(0.529884\pi\) | |||||||
\(54\) | −4781.44 | −0.223138 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | −20158.2 | −0.858976 | ||||||||
\(57\) | −5128.08 | −0.209058 | ||||||||
\(58\) | 26121.4 | 1.01959 | ||||||||
\(59\) | 9649.38 | 0.360885 | 0.180443 | − | 0.983586i | \(-0.442247\pi\) | ||||
0.180443 | + | 0.983586i | \(0.442247\pi\) | |||||||
\(60\) | −2479.33 | −0.0889110 | ||||||||
\(61\) | −21131.8 | −0.727128 | −0.363564 | − | 0.931569i | \(-0.618440\pi\) | ||||
−0.363564 | + | 0.931569i | \(0.618440\pi\) | |||||||
\(62\) | 19616.2 | 0.648092 | ||||||||
\(63\) | 11865.4 | 0.376645 | ||||||||
\(64\) | 15051.2 | 0.459326 | ||||||||
\(65\) | 4255.95 | 0.124943 | ||||||||
\(66\) | 7142.65 | 0.201836 | ||||||||
\(67\) | −43499.9 | −1.18386 | −0.591931 | − | 0.805989i | \(-0.701634\pi\) | ||||
−0.591931 | + | 0.805989i | \(0.701634\pi\) | |||||||
\(68\) | 17243.0 | 0.452211 | ||||||||
\(69\) | −28379.2 | −0.717593 | ||||||||
\(70\) | 24019.8 | 0.585901 | ||||||||
\(71\) | −52607.2 | −1.23851 | −0.619255 | − | 0.785190i | \(-0.712565\pi\) | ||||
−0.619255 | + | 0.785190i | \(0.712565\pi\) | |||||||
\(72\) | −11146.5 | −0.253400 | ||||||||
\(73\) | −64367.9 | −1.41372 | −0.706858 | − | 0.707355i | \(-0.749888\pi\) | ||||
−0.706858 | + | 0.707355i | \(0.749888\pi\) | |||||||
\(74\) | 51545.9 | 1.09425 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | 6278.61 | 0.124689 | ||||||||
\(77\) | −17724.9 | −0.340688 | ||||||||
\(78\) | −10049.2 | −0.187022 | ||||||||
\(79\) | 28935.7 | 0.521635 | 0.260817 | − | 0.965388i | \(-0.416008\pi\) | ||||
0.260817 | + | 0.965388i | \(0.416008\pi\) | |||||||
\(80\) | −31379.8 | −0.548183 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −34149.6 | −0.560855 | ||||||||
\(83\) | −4648.64 | −0.0740681 | −0.0370340 | − | 0.999314i | \(-0.511791\pi\) | ||||
−0.0370340 | + | 0.999314i | \(0.511791\pi\) | |||||||
\(84\) | −14527.5 | −0.224643 | ||||||||
\(85\) | 39120.3 | 0.587293 | ||||||||
\(86\) | 91000.1 | 1.32677 | ||||||||
\(87\) | −35843.2 | −0.507702 | ||||||||
\(88\) | 16650.9 | 0.229209 | ||||||||
\(89\) | −103458. | −1.38448 | −0.692242 | − | 0.721666i | \(-0.743377\pi\) | ||||
−0.692242 | + | 0.721666i | \(0.743377\pi\) | |||||||
\(90\) | 13281.8 | 0.172842 | ||||||||
\(91\) | 24937.6 | 0.315683 | ||||||||
\(92\) | 34746.4 | 0.427996 | ||||||||
\(93\) | −26917.0 | −0.322715 | ||||||||
\(94\) | 44941.6 | 0.524601 | ||||||||
\(95\) | 14244.7 | 0.161936 | ||||||||
\(96\) | 34462.2 | 0.381650 | ||||||||
\(97\) | 75809.5 | 0.818077 | 0.409039 | − | 0.912517i | \(-0.365864\pi\) | ||||
0.409039 | + | 0.912517i | \(0.365864\pi\) | |||||||
\(98\) | 30507.8 | 0.320882 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 6887.02 | 0.0688702 | ||||||||
\(101\) | 35023.6 | 0.341631 | 0.170816 | − | 0.985303i | \(-0.445360\pi\) | ||||
0.170816 | + | 0.985303i | \(0.445360\pi\) | |||||||
\(102\) | −92371.1 | −0.879095 | ||||||||
\(103\) | 16965.7 | 0.157572 | 0.0787859 | − | 0.996892i | \(-0.474896\pi\) | ||||
0.0787859 | + | 0.996892i | \(0.474896\pi\) | |||||||
\(104\) | −23426.6 | −0.212386 | ||||||||
\(105\) | −32959.5 | −0.291748 | ||||||||
\(106\) | −25147.8 | −0.217388 | ||||||||
\(107\) | 12190.4 | 0.102934 | 0.0514671 | − | 0.998675i | \(-0.483610\pi\) | ||||
0.0514671 | + | 0.998675i | \(0.483610\pi\) | |||||||
\(108\) | −8033.02 | −0.0662704 | ||||||||
\(109\) | 12138.7 | 0.0978606 | 0.0489303 | − | 0.998802i | \(-0.484419\pi\) | ||||
0.0489303 | + | 0.998802i | \(0.484419\pi\) | |||||||
\(110\) | −19840.7 | −0.156342 | ||||||||
\(111\) | −70730.3 | −0.544876 | ||||||||
\(112\) | −183869. | −1.38504 | ||||||||
\(113\) | 204649. | 1.50770 | 0.753848 | − | 0.657048i | \(-0.228195\pi\) | ||||
0.753848 | + | 0.657048i | \(0.228195\pi\) | |||||||
\(114\) | −33634.6 | −0.242395 | ||||||||
\(115\) | 78831.2 | 0.555845 | ||||||||
\(116\) | 43885.0 | 0.302810 | ||||||||
\(117\) | 13789.3 | 0.0931273 | ||||||||
\(118\) | 63289.3 | 0.418433 | ||||||||
\(119\) | 229224. | 1.48386 | ||||||||
\(120\) | 30962.4 | 0.196283 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −138601. | −0.843077 | ||||||||
\(123\) | 46859.4 | 0.279276 | ||||||||
\(124\) | 32956.1 | 0.192478 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 77824.2 | 0.436705 | ||||||||
\(127\) | −112241. | −0.617506 | −0.308753 | − | 0.951142i | \(-0.599912\pi\) | ||||
−0.308753 | + | 0.951142i | \(0.599912\pi\) | |||||||
\(128\) | 221252. | 1.19361 | ||||||||
\(129\) | −124869. | −0.660661 | ||||||||
\(130\) | 27914.4 | 0.144867 | ||||||||
\(131\) | −11679.0 | −0.0594602 | −0.0297301 | − | 0.999558i | \(-0.509465\pi\) | ||||
−0.0297301 | + | 0.999558i | \(0.509465\pi\) | |||||||
\(132\) | 11999.9 | 0.0599438 | ||||||||
\(133\) | 83466.1 | 0.409149 | ||||||||
\(134\) | −285311. | −1.37264 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | −215335. | −0.998315 | ||||||||
\(137\) | −384935. | −1.75221 | −0.876105 | − | 0.482121i | \(-0.839867\pi\) | ||||
−0.876105 | + | 0.482121i | \(0.839867\pi\) | |||||||
\(138\) | −186137. | −0.832021 | ||||||||
\(139\) | −310605. | −1.36355 | −0.681775 | − | 0.731562i | \(-0.738792\pi\) | ||||
−0.681775 | + | 0.731562i | \(0.738792\pi\) | |||||||
\(140\) | 40354.3 | 0.174008 | ||||||||
\(141\) | −61668.0 | −0.261224 | ||||||||
\(142\) | −345046. | −1.43600 | ||||||||
\(143\) | −20598.8 | −0.0842368 | ||||||||
\(144\) | −101671. | −0.408591 | ||||||||
\(145\) | 99564.5 | 0.393264 | ||||||||
\(146\) | −422183. | −1.63915 | ||||||||
\(147\) | −41862.2 | −0.159782 | ||||||||
\(148\) | 86599.2 | 0.324982 | ||||||||
\(149\) | 285203. | 1.05242 | 0.526209 | − | 0.850355i | \(-0.323613\pi\) | ||||
0.526209 | + | 0.850355i | \(0.323613\pi\) | |||||||
\(150\) | −36893.8 | −0.133883 | ||||||||
\(151\) | −522357. | −1.86434 | −0.932170 | − | 0.362020i | \(-0.882087\pi\) | ||||
−0.932170 | + | 0.362020i | \(0.882087\pi\) | |||||||
\(152\) | −78408.8 | −0.275268 | ||||||||
\(153\) | 126750. | 0.437743 | ||||||||
\(154\) | −116256. | −0.395015 | ||||||||
\(155\) | 74769.5 | 0.249974 | ||||||||
\(156\) | −16883.0 | −0.0555442 | ||||||||
\(157\) | −2221.66 | −0.00719330 | −0.00359665 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359665 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(158\) | 189787. | 0.604816 | ||||||||
\(159\) | 34507.3 | 0.108248 | ||||||||
\(160\) | −95728.4 | −0.295625 | ||||||||
\(161\) | 461909. | 1.40440 | ||||||||
\(162\) | 43033.0 | 0.128829 | ||||||||
\(163\) | 250146. | 0.737436 | 0.368718 | − | 0.929541i | \(-0.379797\pi\) | ||||
0.368718 | + | 0.929541i | \(0.379797\pi\) | |||||||
\(164\) | −57372.7 | −0.166570 | ||||||||
\(165\) | 27225.0 | 0.0778499 | ||||||||
\(166\) | −30490.0 | −0.0858791 | ||||||||
\(167\) | −42083.4 | −0.116767 | −0.0583834 | − | 0.998294i | \(-0.518595\pi\) | ||||
−0.0583834 | + | 0.998294i | \(0.518595\pi\) | |||||||
\(168\) | 181423. | 0.495930 | ||||||||
\(169\) | −342312. | −0.921946 | ||||||||
\(170\) | 256586. | 0.680944 | ||||||||
\(171\) | 46152.7 | 0.120700 | ||||||||
\(172\) | 152884. | 0.394040 | ||||||||
\(173\) | −117206. | −0.297737 | −0.148869 | − | 0.988857i | \(-0.547563\pi\) | ||||
−0.148869 | + | 0.988857i | \(0.547563\pi\) | |||||||
\(174\) | −235092. | −0.588661 | ||||||||
\(175\) | 91554.2 | 0.225987 | ||||||||
\(176\) | 151878. | 0.369585 | ||||||||
\(177\) | −86844.4 | −0.208357 | ||||||||
\(178\) | −678569. | −1.60526 | ||||||||
\(179\) | 582985. | 1.35996 | 0.679978 | − | 0.733233i | \(-0.261989\pi\) | ||||
0.679978 | + | 0.733233i | \(0.261989\pi\) | |||||||
\(180\) | 22313.9 | 0.0513328 | ||||||||
\(181\) | 235291. | 0.533837 | 0.266919 | − | 0.963719i | \(-0.413994\pi\) | ||||
0.266919 | + | 0.963719i | \(0.413994\pi\) | |||||||
\(182\) | 163563. | 0.366022 | ||||||||
\(183\) | 190186. | 0.419808 | ||||||||
\(184\) | −433921. | −0.944858 | ||||||||
\(185\) | 196473. | 0.422059 | ||||||||
\(186\) | −176546. | −0.374176 | ||||||||
\(187\) | −189342. | −0.395953 | ||||||||
\(188\) | 75503.8 | 0.155802 | ||||||||
\(189\) | −106789. | −0.217456 | ||||||||
\(190\) | 93429.4 | 0.187758 | ||||||||
\(191\) | 591788. | 1.17377 | 0.586885 | − | 0.809670i | \(-0.300354\pi\) | ||||
0.586885 | + | 0.809670i | \(0.300354\pi\) | |||||||
\(192\) | −135461. | −0.265192 | ||||||||
\(193\) | −540825. | −1.04511 | −0.522557 | − | 0.852605i | \(-0.675022\pi\) | ||||
−0.522557 | + | 0.852605i | \(0.675022\pi\) | |||||||
\(194\) | 497227. | 0.948529 | ||||||||
\(195\) | −38303.5 | −0.0721361 | ||||||||
\(196\) | 51254.3 | 0.0952994 | ||||||||
\(197\) | 481711. | 0.884344 | 0.442172 | − | 0.896930i | \(-0.354208\pi\) | ||||
0.442172 | + | 0.896930i | \(0.354208\pi\) | |||||||
\(198\) | −64283.8 | −0.116530 | ||||||||
\(199\) | −1.01427e6 | −1.81560 | −0.907801 | − | 0.419401i | \(-0.862240\pi\) | ||||
−0.907801 | + | 0.419401i | \(0.862240\pi\) | |||||||
\(200\) | −86006.8 | −0.152040 | ||||||||
\(201\) | 391499. | 0.683503 | ||||||||
\(202\) | 229717. | 0.396108 | ||||||||
\(203\) | 583395. | 0.993625 | ||||||||
\(204\) | −155187. | −0.261084 | ||||||||
\(205\) | −130165. | −0.216326 | ||||||||
\(206\) | 111276. | 0.182699 | ||||||||
\(207\) | 255413. | 0.414302 | ||||||||
\(208\) | −213681. | −0.342459 | ||||||||
\(209\) | −68944.2 | −0.109177 | ||||||||
\(210\) | −216178. | −0.338270 | ||||||||
\(211\) | 619718. | 0.958270 | 0.479135 | − | 0.877741i | \(-0.340950\pi\) | ||||
0.479135 | + | 0.877741i | \(0.340950\pi\) | |||||||
\(212\) | −42249.3 | −0.0645625 | ||||||||
\(213\) | 473465. | 0.715054 | ||||||||
\(214\) | 79955.8 | 0.119348 | ||||||||
\(215\) | 346857. | 0.511746 | ||||||||
\(216\) | 100318. | 0.146301 | ||||||||
\(217\) | 438109. | 0.631587 | ||||||||
\(218\) | 79616.9 | 0.113466 | ||||||||
\(219\) | 579311. | 0.816210 | ||||||||
\(220\) | −33333.2 | −0.0464323 | ||||||||
\(221\) | 266391. | 0.366892 | ||||||||
\(222\) | −463913. | −0.631763 | ||||||||
\(223\) | 894252. | 1.20420 | 0.602099 | − | 0.798422i | \(-0.294331\pi\) | ||||
0.602099 | + | 0.798422i | \(0.294331\pi\) | |||||||
\(224\) | −560918. | −0.746928 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 1.34227e6 | 1.74812 | ||||||||
\(227\) | 851468. | 1.09674 | 0.548370 | − | 0.836236i | \(-0.315249\pi\) | ||||
0.548370 | + | 0.836236i | \(0.315249\pi\) | |||||||
\(228\) | −56507.5 | −0.0719894 | ||||||||
\(229\) | 137840. | 0.173695 | 0.0868475 | − | 0.996222i | \(-0.472321\pi\) | ||||
0.0868475 | + | 0.996222i | \(0.472321\pi\) | |||||||
\(230\) | 517047. | 0.644481 | ||||||||
\(231\) | 159524. | 0.196696 | ||||||||
\(232\) | −548046. | −0.668494 | ||||||||
\(233\) | −1.31590e6 | −1.58793 | −0.793965 | − | 0.607963i | \(-0.791987\pi\) | ||||
−0.793965 | + | 0.607963i | \(0.791987\pi\) | |||||||
\(234\) | 90442.6 | 0.107977 | ||||||||
\(235\) | 171300. | 0.202343 | ||||||||
\(236\) | 106329. | 0.124271 | ||||||||
\(237\) | −260422. | −0.301166 | ||||||||
\(238\) | 1.50346e6 | 1.72048 | ||||||||
\(239\) | 1.11778e6 | 1.26579 | 0.632896 | − | 0.774237i | \(-0.281866\pi\) | ||||
0.632896 | + | 0.774237i | \(0.281866\pi\) | |||||||
\(240\) | 282418. | 0.316493 | ||||||||
\(241\) | −471581. | −0.523015 | −0.261507 | − | 0.965201i | \(-0.584220\pi\) | ||||
−0.261507 | + | 0.965201i | \(0.584220\pi\) | |||||||
\(242\) | 96028.9 | 0.105406 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −232856. | −0.250387 | ||||||||
\(245\) | 116284. | 0.123767 | ||||||||
\(246\) | 307346. | 0.323810 | ||||||||
\(247\) | 96999.3 | 0.101164 | ||||||||
\(248\) | −411564. | −0.424921 | ||||||||
\(249\) | 41837.8 | 0.0427632 | ||||||||
\(250\) | 102483. | 0.103705 | ||||||||
\(251\) | 1.76541e6 | 1.76873 | 0.884363 | − | 0.466799i | \(-0.154593\pi\) | ||||
0.884363 | + | 0.466799i | \(0.154593\pi\) | |||||||
\(252\) | 130748. | 0.129698 | ||||||||
\(253\) | −381543. | −0.374751 | ||||||||
\(254\) | −736176. | −0.715974 | ||||||||
\(255\) | −352083. | −0.339074 | ||||||||
\(256\) | 969531. | 0.924617 | ||||||||
\(257\) | −19920.1 | −0.0188130 | −0.00940652 | − | 0.999956i | \(-0.502994\pi\) | ||||
−0.00940652 | + | 0.999956i | \(0.502994\pi\) | |||||||
\(258\) | −819001. | −0.766011 | ||||||||
\(259\) | 1.15123e6 | 1.06638 | ||||||||
\(260\) | 46897.3 | 0.0430244 | ||||||||
\(261\) | 322589. | 0.293122 | ||||||||
\(262\) | −76601.2 | −0.0689418 | ||||||||
\(263\) | −2.18348e6 | −1.94652 | −0.973262 | − | 0.229697i | \(-0.926227\pi\) | ||||
−0.973262 | + | 0.229697i | \(0.926227\pi\) | |||||||
\(264\) | −149858. | −0.132334 | ||||||||
\(265\) | −95853.7 | −0.0838483 | ||||||||
\(266\) | 547446. | 0.474392 | ||||||||
\(267\) | 931119. | 0.799332 | ||||||||
\(268\) | −479335. | −0.407664 | ||||||||
\(269\) | 839300. | 0.707190 | 0.353595 | − | 0.935399i | \(-0.384959\pi\) | ||||
0.353595 | + | 0.935399i | \(0.384959\pi\) | |||||||
\(270\) | −119536. | −0.0997906 | ||||||||
\(271\) | 1.42641e6 | 1.17984 | 0.589918 | − | 0.807463i | \(-0.299160\pi\) | ||||
0.589918 | + | 0.807463i | \(0.299160\pi\) | |||||||
\(272\) | −1.96414e6 | −1.60972 | ||||||||
\(273\) | −224438. | −0.182260 | ||||||||
\(274\) | −2.52475e6 | −2.03162 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | −312717. | −0.247104 | ||||||||
\(277\) | −1.30448e6 | −1.02150 | −0.510749 | − | 0.859730i | \(-0.670632\pi\) | ||||
−0.510749 | + | 0.859730i | \(0.670632\pi\) | |||||||
\(278\) | −2.03723e6 | −1.58098 | ||||||||
\(279\) | 242253. | 0.186320 | ||||||||
\(280\) | −503954. | −0.384146 | ||||||||
\(281\) | −580646. | −0.438678 | −0.219339 | − | 0.975649i | \(-0.570390\pi\) | ||||
−0.219339 | + | 0.975649i | \(0.570390\pi\) | |||||||
\(282\) | −404475. | −0.302879 | ||||||||
\(283\) | −601974. | −0.446799 | −0.223399 | − | 0.974727i | \(-0.571715\pi\) | ||||
−0.223399 | + | 0.974727i | \(0.571715\pi\) | |||||||
\(284\) | −579691. | −0.426482 | ||||||||
\(285\) | −128202. | −0.0934937 | ||||||||
\(286\) | −135106. | −0.0976693 | ||||||||
\(287\) | −762698. | −0.546572 | ||||||||
\(288\) | −310160. | −0.220346 | ||||||||
\(289\) | 1.02878e6 | 0.724567 | ||||||||
\(290\) | 653034. | 0.455975 | ||||||||
\(291\) | −682286. | −0.472317 | ||||||||
\(292\) | −709285. | −0.486815 | ||||||||
\(293\) | −2.40993e6 | −1.63996 | −0.819982 | − | 0.572389i | \(-0.806017\pi\) | ||||
−0.819982 | + | 0.572389i | \(0.806017\pi\) | |||||||
\(294\) | −274570. | −0.185261 | ||||||||
\(295\) | 241234. | 0.161393 | ||||||||
\(296\) | −1.08147e6 | −0.717441 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | 1.87062e6 | 1.22024 | ||||||||
\(299\) | 536803. | 0.347246 | ||||||||
\(300\) | −61983.2 | −0.0397622 | ||||||||
\(301\) | 2.03240e6 | 1.29298 | ||||||||
\(302\) | −3.42609e6 | −2.16163 | ||||||||
\(303\) | −315213. | −0.197241 | ||||||||
\(304\) | −715191. | −0.443852 | ||||||||
\(305\) | −528294. | −0.325182 | ||||||||
\(306\) | 831340. | 0.507546 | ||||||||
\(307\) | −1.83380e6 | −1.11047 | −0.555235 | − | 0.831694i | \(-0.687371\pi\) | ||||
−0.555235 | + | 0.831694i | \(0.687371\pi\) | |||||||
\(308\) | −195315. | −0.117316 | ||||||||
\(309\) | −152691. | −0.0909742 | ||||||||
\(310\) | 490406. | 0.289835 | ||||||||
\(311\) | 2.27507e6 | 1.33381 | 0.666906 | − | 0.745142i | \(-0.267618\pi\) | ||||
0.666906 | + | 0.745142i | \(0.267618\pi\) | |||||||
\(312\) | 210839. | 0.122621 | ||||||||
\(313\) | 159585. | 0.0920728 | 0.0460364 | − | 0.998940i | \(-0.485341\pi\) | ||||
0.0460364 | + | 0.998940i | \(0.485341\pi\) | |||||||
\(314\) | −14571.6 | −0.00834035 | ||||||||
\(315\) | 296636. | 0.168441 | ||||||||
\(316\) | 318849. | 0.179625 | ||||||||
\(317\) | −1.24338e6 | −0.694955 | −0.347477 | − | 0.937688i | \(-0.612962\pi\) | ||||
−0.347477 | + | 0.937688i | \(0.612962\pi\) | |||||||
\(318\) | 226330. | 0.125509 | ||||||||
\(319\) | −481892. | −0.265139 | ||||||||
\(320\) | 376280. | 0.205417 | ||||||||
\(321\) | −109714. | −0.0594290 | ||||||||
\(322\) | 3.02962e6 | 1.62835 | ||||||||
\(323\) | 891609. | 0.475519 | ||||||||
\(324\) | 72297.2 | 0.0382612 | ||||||||
\(325\) | 106399. | 0.0558764 | ||||||||
\(326\) | 1.64068e6 | 0.855029 | ||||||||
\(327\) | −109249. | −0.0564998 | ||||||||
\(328\) | 716485. | 0.367724 | ||||||||
\(329\) | 1.00373e6 | 0.511242 | ||||||||
\(330\) | 178566. | 0.0902640 | ||||||||
\(331\) | −958448. | −0.480838 | −0.240419 | − | 0.970669i | \(-0.577285\pi\) | ||||
−0.240419 | + | 0.970669i | \(0.577285\pi\) | |||||||
\(332\) | −51224.5 | −0.0255054 | ||||||||
\(333\) | 636573. | 0.314584 | ||||||||
\(334\) | −276021. | −0.135387 | ||||||||
\(335\) | −1.08750e6 | −0.529439 | ||||||||
\(336\) | 1.65482e6 | 0.799655 | ||||||||
\(337\) | −1.51074e6 | −0.724626 | −0.362313 | − | 0.932056i | \(-0.618013\pi\) | ||||
−0.362313 | + | 0.932056i | \(0.618013\pi\) | |||||||
\(338\) | −2.24519e6 | −1.06896 | ||||||||
\(339\) | −1.84184e6 | −0.870469 | ||||||||
\(340\) | 431076. | 0.202235 | ||||||||
\(341\) | −361884. | −0.168533 | ||||||||
\(342\) | 302711. | 0.139947 | ||||||||
\(343\) | −1.78064e6 | −0.817224 | ||||||||
\(344\) | −1.90925e6 | −0.869896 | ||||||||
\(345\) | −709481. | −0.320917 | ||||||||
\(346\) | −768741. | −0.345215 | ||||||||
\(347\) | −1.93847e6 | −0.864243 | −0.432122 | − | 0.901815i | \(-0.642235\pi\) | ||||
−0.432122 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(348\) | −394965. | −0.174828 | ||||||||
\(349\) | −1.62462e6 | −0.713985 | −0.356992 | − | 0.934107i | \(-0.616198\pi\) | ||||
−0.356992 | + | 0.934107i | \(0.616198\pi\) | |||||||
\(350\) | 600495. | 0.262023 | ||||||||
\(351\) | −124103. | −0.0537671 | ||||||||
\(352\) | 463325. | 0.199310 | ||||||||
\(353\) | −23347.5 | −0.00997249 | −0.00498624 | − | 0.999988i | \(-0.501587\pi\) | ||||
−0.00498624 | + | 0.999988i | \(0.501587\pi\) | |||||||
\(354\) | −569604. | −0.241582 | ||||||||
\(355\) | −1.31518e6 | −0.553878 | ||||||||
\(356\) | −1.14002e6 | −0.476748 | ||||||||
\(357\) | −2.06302e6 | −0.856707 | ||||||||
\(358\) | 3.82374e6 | 1.57682 | ||||||||
\(359\) | 3.63918e6 | 1.49028 | 0.745139 | − | 0.666909i | \(-0.232383\pi\) | ||||
0.745139 | + | 0.666909i | \(0.232383\pi\) | |||||||
\(360\) | −278662. | −0.113324 | ||||||||
\(361\) | −2.15144e6 | −0.868884 | ||||||||
\(362\) | 1.54325e6 | 0.618964 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 274793. | 0.108706 | ||||||||
\(365\) | −1.60920e6 | −0.632233 | ||||||||
\(366\) | 1.24741e6 | 0.486751 | ||||||||
\(367\) | 2.24713e6 | 0.870890 | 0.435445 | − | 0.900215i | \(-0.356591\pi\) | ||||
0.435445 | + | 0.900215i | \(0.356591\pi\) | |||||||
\(368\) | −3.95793e6 | −1.52352 | ||||||||
\(369\) | −421735. | −0.161240 | ||||||||
\(370\) | 1.28865e6 | 0.489362 | ||||||||
\(371\) | −561651. | −0.211852 | ||||||||
\(372\) | −296605. | −0.111127 | ||||||||
\(373\) | 3.82745e6 | 1.42442 | 0.712208 | − | 0.701968i | \(-0.247695\pi\) | ||||
0.712208 | + | 0.701968i | \(0.247695\pi\) | |||||||
\(374\) | −1.24188e6 | −0.459092 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | −942910. | −0.343954 | ||||||||
\(377\) | 677986. | 0.245679 | ||||||||
\(378\) | −700418. | −0.252132 | ||||||||
\(379\) | −4.26443e6 | −1.52498 | −0.762489 | − | 0.647002i | \(-0.776023\pi\) | ||||
−0.762489 | + | 0.647002i | \(0.776023\pi\) | |||||||
\(380\) | 156965. | 0.0557628 | ||||||||
\(381\) | 1.01017e6 | 0.356517 | ||||||||
\(382\) | 3.88148e6 | 1.36094 | ||||||||
\(383\) | 2.40920e6 | 0.839221 | 0.419611 | − | 0.907704i | \(-0.362167\pi\) | ||||
0.419611 | + | 0.907704i | \(0.362167\pi\) | |||||||
\(384\) | −1.99127e6 | −0.689130 | ||||||||
\(385\) | −443122. | −0.152360 | ||||||||
\(386\) | −3.54722e6 | −1.21177 | ||||||||
\(387\) | 1.12382e6 | 0.381433 | ||||||||
\(388\) | 835362. | 0.281706 | ||||||||
\(389\) | 3.73204e6 | 1.25047 | 0.625233 | − | 0.780438i | \(-0.285004\pi\) | ||||
0.625233 | + | 0.780438i | \(0.285004\pi\) | |||||||
\(390\) | −251229. | −0.0836390 | ||||||||
\(391\) | 4.93424e6 | 1.63222 | ||||||||
\(392\) | −640077. | −0.210386 | ||||||||
\(393\) | 105111. | 0.0343293 | ||||||||
\(394\) | 3.15950e6 | 1.02536 | ||||||||
\(395\) | 723393. | 0.233282 | ||||||||
\(396\) | −107999. | −0.0346086 | ||||||||
\(397\) | −4.89288e6 | −1.55808 | −0.779038 | − | 0.626977i | \(-0.784292\pi\) | ||||
−0.779038 | + | 0.626977i | \(0.784292\pi\) | |||||||
\(398\) | −6.65250e6 | −2.10512 | ||||||||
\(399\) | −751195. | −0.236222 | ||||||||
\(400\) | −784495. | −0.245155 | ||||||||
\(401\) | −3.93524e6 | −1.22211 | −0.611055 | − | 0.791588i | \(-0.709255\pi\) | ||||
−0.611055 | + | 0.791588i | \(0.709255\pi\) | |||||||
\(402\) | 2.56780e6 | 0.792495 | ||||||||
\(403\) | 509144. | 0.156163 | ||||||||
\(404\) | 385933. | 0.117641 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | 3.82643e6 | 1.15207 | ||||||||
\(407\) | −950929. | −0.284552 | ||||||||
\(408\) | 1.93802e6 | 0.576378 | ||||||||
\(409\) | 657037. | 0.194215 | 0.0971073 | − | 0.995274i | \(-0.469041\pi\) | ||||
0.0971073 | + | 0.995274i | \(0.469041\pi\) | |||||||
\(410\) | −853740. | −0.250822 | ||||||||
\(411\) | 3.46442e6 | 1.01164 | ||||||||
\(412\) | 186949. | 0.0542600 | ||||||||
\(413\) | 1.41351e6 | 0.407777 | ||||||||
\(414\) | 1.67523e6 | 0.480368 | ||||||||
\(415\) | −116216. | −0.0331243 | ||||||||
\(416\) | −651864. | −0.184682 | ||||||||
\(417\) | 2.79544e6 | 0.787246 | ||||||||
\(418\) | −452198. | −0.126587 | ||||||||
\(419\) | 4.38504e6 | 1.22022 | 0.610110 | − | 0.792317i | \(-0.291125\pi\) | ||||
0.610110 | + | 0.792317i | \(0.291125\pi\) | |||||||
\(420\) | −363188. | −0.100464 | ||||||||
\(421\) | 2.34058e6 | 0.643604 | 0.321802 | − | 0.946807i | \(-0.395711\pi\) | ||||
0.321802 | + | 0.946807i | \(0.395711\pi\) | |||||||
\(422\) | 4.06467e6 | 1.11108 | ||||||||
\(423\) | 555012. | 0.150818 | ||||||||
\(424\) | 527620. | 0.142530 | ||||||||
\(425\) | 978008. | 0.262646 | ||||||||
\(426\) | 3.10541e6 | 0.829078 | ||||||||
\(427\) | −3.09552e6 | −0.821607 | ||||||||
\(428\) | 134329. | 0.0354455 | ||||||||
\(429\) | 185389. | 0.0486341 | ||||||||
\(430\) | 2.27500e6 | 0.593350 | ||||||||
\(431\) | −2.18215e6 | −0.565838 | −0.282919 | − | 0.959144i | \(-0.591303\pi\) | ||||
−0.282919 | + | 0.959144i | \(0.591303\pi\) | |||||||
\(432\) | 915035. | 0.235900 | ||||||||
\(433\) | −3.61080e6 | −0.925515 | −0.462757 | − | 0.886485i | \(-0.653140\pi\) | ||||
−0.462757 | + | 0.886485i | \(0.653140\pi\) | |||||||
\(434\) | 2.87352e6 | 0.732301 | ||||||||
\(435\) | −896080. | −0.227051 | ||||||||
\(436\) | 133760. | 0.0336984 | ||||||||
\(437\) | 1.79668e6 | 0.450056 | ||||||||
\(438\) | 3.79965e6 | 0.946364 | ||||||||
\(439\) | 6.48191e6 | 1.60525 | 0.802624 | − | 0.596486i | \(-0.203437\pi\) | ||||
0.802624 | + | 0.596486i | \(0.203437\pi\) | |||||||
\(440\) | 416273. | 0.102505 | ||||||||
\(441\) | 376760. | 0.0922503 | ||||||||
\(442\) | 1.74723e6 | 0.425397 | ||||||||
\(443\) | −6.81523e6 | −1.64995 | −0.824976 | − | 0.565167i | \(-0.808812\pi\) | ||||
−0.824976 | + | 0.565167i | \(0.808812\pi\) | |||||||
\(444\) | −779393. | −0.187629 | ||||||||
\(445\) | −2.58644e6 | −0.619160 | ||||||||
\(446\) | 5.86531e6 | 1.39622 | ||||||||
\(447\) | −2.56683e6 | −0.607614 | ||||||||
\(448\) | 2.20480e6 | 0.519008 | ||||||||
\(449\) | −2.98356e6 | −0.698423 | −0.349211 | − | 0.937044i | \(-0.613551\pi\) | ||||
−0.349211 | + | 0.937044i | \(0.613551\pi\) | |||||||
\(450\) | 332045. | 0.0772974 | ||||||||
\(451\) | 629999. | 0.145847 | ||||||||
\(452\) | 2.25508e6 | 0.519177 | ||||||||
\(453\) | 4.70122e6 | 1.07638 | ||||||||
\(454\) | 5.58469e6 | 1.27163 | ||||||||
\(455\) | 623440. | 0.141178 | ||||||||
\(456\) | 705679. | 0.158926 | ||||||||
\(457\) | −6.11184e6 | −1.36893 | −0.684466 | − | 0.729045i | \(-0.739964\pi\) | ||||
−0.684466 | + | 0.729045i | \(0.739964\pi\) | |||||||
\(458\) | 904081. | 0.201393 | ||||||||
\(459\) | −1.14075e6 | −0.252731 | ||||||||
\(460\) | 868659. | 0.191406 | ||||||||
\(461\) | −3.41772e6 | −0.749003 | −0.374502 | − | 0.927226i | \(-0.622186\pi\) | ||||
−0.374502 | + | 0.927226i | \(0.622186\pi\) | |||||||
\(462\) | 1.04630e6 | 0.228062 | ||||||||
\(463\) | −4.60011e6 | −0.997277 | −0.498639 | − | 0.866810i | \(-0.666166\pi\) | ||||
−0.498639 | + | 0.866810i | \(0.666166\pi\) | |||||||
\(464\) | −4.99890e6 | −1.07790 | ||||||||
\(465\) | −672925. | −0.144323 | ||||||||
\(466\) | −8.63083e6 | −1.84114 | ||||||||
\(467\) | 5.03617e6 | 1.06858 | 0.534291 | − | 0.845301i | \(-0.320579\pi\) | ||||
0.534291 | + | 0.845301i | \(0.320579\pi\) | |||||||
\(468\) | 151947. | 0.0320685 | ||||||||
\(469\) | −6.37215e6 | −1.33769 | ||||||||
\(470\) | 1.12354e6 | 0.234609 | ||||||||
\(471\) | 19994.9 | 0.00415305 | ||||||||
\(472\) | −1.32786e6 | −0.274345 | ||||||||
\(473\) | −1.67879e6 | −0.345019 | ||||||||
\(474\) | −1.70808e6 | −0.349190 | ||||||||
\(475\) | 356117. | 0.0724199 | ||||||||
\(476\) | 2.52587e6 | 0.510969 | ||||||||
\(477\) | −310566. | −0.0624968 | ||||||||
\(478\) | 7.33142e6 | 1.46764 | ||||||||
\(479\) | −2.82760e6 | −0.563091 | −0.281545 | − | 0.959548i | \(-0.590847\pi\) | ||||
−0.281545 | + | 0.959548i | \(0.590847\pi\) | |||||||
\(480\) | 861556. | 0.170679 | ||||||||
\(481\) | 1.33789e6 | 0.263668 | ||||||||
\(482\) | −3.09306e6 | −0.606416 | ||||||||
\(483\) | −4.15718e6 | −0.810833 | ||||||||
\(484\) | 161333. | 0.0313046 | ||||||||
\(485\) | 1.89524e6 | 0.365855 | ||||||||
\(486\) | −387297. | −0.0743795 | ||||||||
\(487\) | −5.68931e6 | −1.08702 | −0.543510 | − | 0.839403i | \(-0.682905\pi\) | ||||
−0.543510 | + | 0.839403i | \(0.682905\pi\) | |||||||
\(488\) | 2.90796e6 | 0.552763 | ||||||||
\(489\) | −2.25131e6 | −0.425759 | ||||||||
\(490\) | 762695. | 0.143503 | ||||||||
\(491\) | 3.23715e6 | 0.605981 | 0.302990 | − | 0.952994i | \(-0.402015\pi\) | ||||
0.302990 | + | 0.952994i | \(0.402015\pi\) | |||||||
\(492\) | 516355. | 0.0961690 | ||||||||
\(493\) | 6.23199e6 | 1.15481 | ||||||||
\(494\) | 636209. | 0.117296 | ||||||||
\(495\) | −245025. | −0.0449467 | ||||||||
\(496\) | −3.75400e6 | −0.685157 | ||||||||
\(497\) | −7.70626e6 | −1.39943 | ||||||||
\(498\) | 274410. | 0.0495823 | ||||||||
\(499\) | −5.08564e6 | −0.914312 | −0.457156 | − | 0.889386i | \(-0.651132\pi\) | ||||
−0.457156 | + | 0.889386i | \(0.651132\pi\) | |||||||
\(500\) | 172175. | 0.0307997 | ||||||||
\(501\) | 378751. | 0.0674154 | ||||||||
\(502\) | 1.15791e7 | 2.05077 | ||||||||
\(503\) | 9.02252e6 | 1.59004 | 0.795019 | − | 0.606584i | \(-0.207461\pi\) | ||||
0.795019 | + | 0.606584i | \(0.207461\pi\) | |||||||
\(504\) | −1.63281e6 | −0.286325 | ||||||||
\(505\) | 875591. | 0.152782 | ||||||||
\(506\) | −2.50251e6 | −0.434509 | ||||||||
\(507\) | 3.08081e6 | 0.532286 | ||||||||
\(508\) | −1.23681e6 | −0.212639 | ||||||||
\(509\) | 8.98909e6 | 1.53788 | 0.768938 | − | 0.639323i | \(-0.220785\pi\) | ||||
0.768938 | + | 0.639323i | \(0.220785\pi\) | |||||||
\(510\) | −2.30928e6 | −0.393143 | ||||||||
\(511\) | −9.42904e6 | −1.59741 | ||||||||
\(512\) | −720997. | −0.121551 | ||||||||
\(513\) | −415374. | −0.0696861 | ||||||||
\(514\) | −130654. | −0.0218130 | ||||||||
\(515\) | 424143. | 0.0704683 | ||||||||
\(516\) | −1.37596e6 | −0.227499 | ||||||||
\(517\) | −829093. | −0.136420 | ||||||||
\(518\) | 7.55079e6 | 1.23643 | ||||||||
\(519\) | 1.05485e6 | 0.171899 | ||||||||
\(520\) | −585665. | −0.0949819 | ||||||||
\(521\) | −1.11219e7 | −1.79508 | −0.897539 | − | 0.440936i | \(-0.854647\pi\) | ||||
−0.897539 | + | 0.440936i | \(0.854647\pi\) | |||||||
\(522\) | 2.11583e6 | 0.339863 | ||||||||
\(523\) | 3.67510e6 | 0.587510 | 0.293755 | − | 0.955881i | \(-0.405095\pi\) | ||||
0.293755 | + | 0.955881i | \(0.405095\pi\) | |||||||
\(524\) | −128693. | −0.0204752 | ||||||||
\(525\) | −823988. | −0.130474 | ||||||||
\(526\) | −1.43212e7 | −2.25692 | ||||||||
\(527\) | 4.68001e6 | 0.734040 | ||||||||
\(528\) | −1.36690e6 | −0.213380 | ||||||||
\(529\) | 3.50664e6 | 0.544818 | ||||||||
\(530\) | −628695. | −0.0972188 | ||||||||
\(531\) | 781600. | 0.120295 | ||||||||
\(532\) | 919733. | 0.140891 | ||||||||
\(533\) | −886361. | −0.135143 | ||||||||
\(534\) | 6.10712e6 | 0.926795 | ||||||||
\(535\) | 304761. | 0.0460335 | ||||||||
\(536\) | 5.98605e6 | 0.899971 | ||||||||
\(537\) | −5.24687e6 | −0.785171 | ||||||||
\(538\) | 5.50489e6 | 0.819960 | ||||||||
\(539\) | −562814. | −0.0834436 | ||||||||
\(540\) | −200825. | −0.0296370 | ||||||||
\(541\) | −4.31097e6 | −0.633260 | −0.316630 | − | 0.948549i | \(-0.602551\pi\) | ||||
−0.316630 | + | 0.948549i | \(0.602551\pi\) | |||||||
\(542\) | 9.35569e6 | 1.36797 | ||||||||
\(543\) | −2.11762e6 | −0.308211 | ||||||||
\(544\) | −5.99188e6 | −0.868092 | ||||||||
\(545\) | 303469. | 0.0437646 | ||||||||
\(546\) | −1.47207e6 | −0.211323 | ||||||||
\(547\) | −1.80626e6 | −0.258114 | −0.129057 | − | 0.991637i | \(-0.541195\pi\) | ||||
−0.129057 | + | 0.991637i | \(0.541195\pi\) | |||||||
\(548\) | −4.24169e6 | −0.603375 | ||||||||
\(549\) | −1.71167e6 | −0.242376 | ||||||||
\(550\) | −496017. | −0.0699182 | ||||||||
\(551\) | 2.26922e6 | 0.318418 | ||||||||
\(552\) | 3.90529e6 | 0.545514 | ||||||||
\(553\) | 4.23870e6 | 0.589413 | ||||||||
\(554\) | −8.55595e6 | −1.18439 | ||||||||
\(555\) | −1.76826e6 | −0.243676 | ||||||||
\(556\) | −3.42262e6 | −0.469540 | ||||||||
\(557\) | 8.42670e6 | 1.15085 | 0.575426 | − | 0.817854i | \(-0.304836\pi\) | ||||
0.575426 | + | 0.817854i | \(0.304836\pi\) | |||||||
\(558\) | 1.58891e6 | 0.216031 | ||||||||
\(559\) | 2.36193e6 | 0.319696 | ||||||||
\(560\) | −4.59672e6 | −0.619410 | ||||||||
\(561\) | 1.70408e6 | 0.228604 | ||||||||
\(562\) | −3.80840e6 | −0.508630 | ||||||||
\(563\) | −9.19966e6 | −1.22321 | −0.611605 | − | 0.791163i | \(-0.709476\pi\) | ||||
−0.611605 | + | 0.791163i | \(0.709476\pi\) | |||||||
\(564\) | −679534. | −0.0899526 | ||||||||
\(565\) | 5.11623e6 | 0.674262 | ||||||||
\(566\) | −3.94829e6 | −0.518046 | ||||||||
\(567\) | 961099. | 0.125548 | ||||||||
\(568\) | 7.23932e6 | 0.941515 | ||||||||
\(569\) | 5.18644e6 | 0.671566 | 0.335783 | − | 0.941939i | \(-0.390999\pi\) | ||||
0.335783 | + | 0.941939i | \(0.390999\pi\) | |||||||
\(570\) | −840864. | −0.108402 | ||||||||
\(571\) | −3.29390e6 | −0.422786 | −0.211393 | − | 0.977401i | \(-0.567800\pi\) | ||||
−0.211393 | + | 0.977401i | \(0.567800\pi\) | |||||||
\(572\) | −226983. | −0.0290070 | ||||||||
\(573\) | −5.32609e6 | −0.677676 | ||||||||
\(574\) | −5.00246e6 | −0.633730 | ||||||||
\(575\) | 1.97078e6 | 0.248581 | ||||||||
\(576\) | 1.21915e6 | 0.153109 | ||||||||
\(577\) | −1.02043e7 | −1.27598 | −0.637989 | − | 0.770046i | \(-0.720233\pi\) | ||||
−0.637989 | + | 0.770046i | \(0.720233\pi\) | |||||||
\(578\) | 6.74768e6 | 0.840107 | ||||||||
\(579\) | 4.86742e6 | 0.603396 | ||||||||
\(580\) | 1.09712e6 | 0.135421 | ||||||||
\(581\) | −680965. | −0.0836921 | ||||||||
\(582\) | −4.47505e6 | −0.547633 | ||||||||
\(583\) | 463932. | 0.0565305 | ||||||||
\(584\) | 8.85773e6 | 1.07471 | ||||||||
\(585\) | 344732. | 0.0416478 | ||||||||
\(586\) | −1.58065e7 | −1.90148 | ||||||||
\(587\) | −1.33951e7 | −1.60454 | −0.802272 | − | 0.596958i | \(-0.796376\pi\) | ||||
−0.802272 | + | 0.596958i | \(0.796376\pi\) | |||||||
\(588\) | −461289. | −0.0550212 | ||||||||
\(589\) | 1.70411e6 | 0.202399 | ||||||||
\(590\) | 1.58223e6 | 0.187129 | ||||||||
\(591\) | −4.33540e6 | −0.510576 | ||||||||
\(592\) | −9.86445e6 | −1.15683 | ||||||||
\(593\) | 3.76550e6 | 0.439730 | 0.219865 | − | 0.975530i | \(-0.429438\pi\) | ||||
0.219865 | + | 0.975530i | \(0.429438\pi\) | |||||||
\(594\) | 578554. | 0.0672788 | ||||||||
\(595\) | 5.73061e6 | 0.663603 | ||||||||
\(596\) | 3.14272e6 | 0.362401 | ||||||||
\(597\) | 9.12843e6 | 1.04824 | ||||||||
\(598\) | 3.52084e6 | 0.402618 | ||||||||
\(599\) | 1.21252e6 | 0.138077 | 0.0690384 | − | 0.997614i | \(-0.478007\pi\) | ||||
0.0690384 | + | 0.997614i | \(0.478007\pi\) | |||||||
\(600\) | 774061. | 0.0877803 | ||||||||
\(601\) | −7.81714e6 | −0.882799 | −0.441399 | − | 0.897311i | \(-0.645518\pi\) | ||||
−0.441399 | + | 0.897311i | \(0.645518\pi\) | |||||||
\(602\) | 1.33303e7 | 1.49916 | ||||||||
\(603\) | −3.52349e6 | −0.394620 | ||||||||
\(604\) | −5.75597e6 | −0.641987 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | −2.06745e6 | −0.228693 | ||||||||
\(607\) | 5.43853e6 | 0.599114 | 0.299557 | − | 0.954078i | \(-0.403161\pi\) | ||||
0.299557 | + | 0.954078i | \(0.403161\pi\) | |||||||
\(608\) | −2.18179e6 | −0.239361 | ||||||||
\(609\) | −5.25055e6 | −0.573670 | ||||||||
\(610\) | −3.46503e6 | −0.377036 | ||||||||
\(611\) | 1.16647e6 | 0.126407 | ||||||||
\(612\) | 1.39669e6 | 0.150737 | ||||||||
\(613\) | 1.70637e7 | 1.83409 | 0.917045 | − | 0.398783i | \(-0.130567\pi\) | ||||
0.917045 | + | 0.398783i | \(0.130567\pi\) | |||||||
\(614\) | −1.20277e7 | −1.28755 | ||||||||
\(615\) | 1.17149e6 | 0.124896 | ||||||||
\(616\) | 2.43914e6 | 0.258991 | ||||||||
\(617\) | 7.80667e6 | 0.825568 | 0.412784 | − | 0.910829i | \(-0.364556\pi\) | ||||
0.412784 | + | 0.910829i | \(0.364556\pi\) | |||||||
\(618\) | −1.00149e6 | −0.105481 | ||||||||
\(619\) | 7.31658e6 | 0.767506 | 0.383753 | − | 0.923436i | \(-0.374631\pi\) | ||||
0.383753 | + | 0.923436i | \(0.374631\pi\) | |||||||
\(620\) | 823902. | 0.0860788 | ||||||||
\(621\) | −2.29872e6 | −0.239198 | ||||||||
\(622\) | 1.49220e7 | 1.54650 | ||||||||
\(623\) | −1.51552e7 | −1.56438 | ||||||||
\(624\) | 1.92313e6 | 0.197719 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.04670e6 | 0.106755 | ||||||||
\(627\) | 620497. | 0.0630335 | ||||||||
\(628\) | −24481.0 | −0.00247702 | ||||||||
\(629\) | 1.22977e7 | 1.23936 | ||||||||
\(630\) | 1.94560e6 | 0.195300 | ||||||||
\(631\) | −1.18729e7 | −1.18709 | −0.593543 | − | 0.804802i | \(-0.702271\pi\) | ||||
−0.593543 | + | 0.804802i | \(0.702271\pi\) | |||||||
\(632\) | −3.98187e6 | −0.396547 | ||||||||
\(633\) | −5.57746e6 | −0.553257 | ||||||||
\(634\) | −8.15523e6 | −0.805773 | ||||||||
\(635\) | −2.80602e6 | −0.276157 | ||||||||
\(636\) | 380244. | 0.0372752 | ||||||||
\(637\) | 791837. | 0.0773192 | ||||||||
\(638\) | −3.16068e6 | −0.307418 | ||||||||
\(639\) | −4.26118e6 | −0.412837 | ||||||||
\(640\) | 5.53129e6 | 0.533798 | ||||||||
\(641\) | −1.85963e7 | −1.78764 | −0.893821 | − | 0.448424i | \(-0.851985\pi\) | ||||
−0.893821 | + | 0.448424i | \(0.851985\pi\) | |||||||
\(642\) | −719603. | −0.0689057 | ||||||||
\(643\) | −1.18028e7 | −1.12579 | −0.562894 | − | 0.826529i | \(-0.690312\pi\) | ||||
−0.562894 | + | 0.826529i | \(0.690312\pi\) | |||||||
\(644\) | 5.08988e6 | 0.483608 | ||||||||
\(645\) | −3.12171e6 | −0.295457 | ||||||||
\(646\) | 5.84798e6 | 0.551346 | ||||||||
\(647\) | 2.05252e7 | 1.92764 | 0.963821 | − | 0.266551i | \(-0.0858842\pi\) | ||||
0.963821 | + | 0.266551i | \(0.0858842\pi\) | |||||||
\(648\) | −902865. | −0.0844666 | ||||||||
\(649\) | −1.16757e6 | −0.108811 | ||||||||
\(650\) | 697859. | 0.0647865 | ||||||||
\(651\) | −3.94298e6 | −0.364647 | ||||||||
\(652\) | 2.75642e6 | 0.253937 | ||||||||
\(653\) | −5.78511e6 | −0.530919 | −0.265460 | − | 0.964122i | \(-0.585524\pi\) | ||||
−0.265460 | + | 0.964122i | \(0.585524\pi\) | |||||||
\(654\) | −716552. | −0.0655094 | ||||||||
\(655\) | −291974. | −0.0265914 | ||||||||
\(656\) | 6.53528e6 | 0.592932 | ||||||||
\(657\) | −5.21380e6 | −0.471239 | ||||||||
\(658\) | 6.58335e6 | 0.592765 | ||||||||
\(659\) | 1.88598e7 | 1.69170 | 0.845852 | − | 0.533418i | \(-0.179093\pi\) | ||||
0.845852 | + | 0.533418i | \(0.179093\pi\) | |||||||
\(660\) | 299999. | 0.0268077 | ||||||||
\(661\) | −1.12652e7 | −1.00285 | −0.501426 | − | 0.865201i | \(-0.667191\pi\) | ||||
−0.501426 | + | 0.865201i | \(0.667191\pi\) | |||||||
\(662\) | −6.28637e6 | −0.557513 | ||||||||
\(663\) | −2.39751e6 | −0.211825 | ||||||||
\(664\) | 639704. | 0.0563065 | ||||||||
\(665\) | 2.08665e6 | 0.182977 | ||||||||
\(666\) | 4.17522e6 | 0.364749 | ||||||||
\(667\) | 1.25581e7 | 1.09297 | ||||||||
\(668\) | −463727. | −0.0402088 | ||||||||
\(669\) | −8.04827e6 | −0.695244 | ||||||||
\(670\) | −7.13279e6 | −0.613864 | ||||||||
\(671\) | 2.55694e6 | 0.219237 | ||||||||
\(672\) | 5.04826e6 | 0.431239 | ||||||||
\(673\) | 1.51301e7 | 1.28767 | 0.643833 | − | 0.765166i | \(-0.277343\pi\) | ||||
0.643833 | + | 0.765166i | \(0.277343\pi\) | |||||||
\(674\) | −9.90878e6 | −0.840176 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | −3.77201e6 | −0.317473 | ||||||||
\(677\) | −1.12001e7 | −0.939187 | −0.469593 | − | 0.882883i | \(-0.655599\pi\) | ||||
−0.469593 | + | 0.882883i | \(0.655599\pi\) | |||||||
\(678\) | −1.20805e7 | −1.00928 | ||||||||
\(679\) | 1.11051e7 | 0.924373 | ||||||||
\(680\) | −5.38338e6 | −0.446460 | ||||||||
\(681\) | −7.66321e6 | −0.633203 | ||||||||
\(682\) | −2.37356e6 | −0.195407 | ||||||||
\(683\) | 2.12907e7 | 1.74638 | 0.873190 | − | 0.487379i | \(-0.162047\pi\) | ||||
0.873190 | + | 0.487379i | \(0.162047\pi\) | |||||||
\(684\) | 508567. | 0.0415631 | ||||||||
\(685\) | −9.62338e6 | −0.783612 | ||||||||
\(686\) | −1.16791e7 | −0.947539 | ||||||||
\(687\) | −1.24056e6 | −0.100283 | ||||||||
\(688\) | −1.74149e7 | −1.40265 | ||||||||
\(689\) | −652717. | −0.0523814 | ||||||||
\(690\) | −4.65342e6 | −0.372091 | ||||||||
\(691\) | 1.77648e6 | 0.141536 | 0.0707678 | − | 0.997493i | \(-0.477455\pi\) | ||||
0.0707678 | + | 0.997493i | \(0.477455\pi\) | |||||||
\(692\) | −1.29152e6 | −0.102526 | ||||||||
\(693\) | −1.43572e6 | −0.113563 | ||||||||
\(694\) | −1.27143e7 | −1.00206 | ||||||||
\(695\) | −7.76512e6 | −0.609798 | ||||||||
\(696\) | 4.93242e6 | 0.385955 | ||||||||
\(697\) | −8.14735e6 | −0.635235 | ||||||||
\(698\) | −1.06557e7 | −0.827838 | ||||||||
\(699\) | 1.18431e7 | 0.916792 | ||||||||
\(700\) | 1.00886e6 | 0.0778188 | ||||||||
\(701\) | 94420.1 | 0.00725720 | 0.00362860 | − | 0.999993i | \(-0.498845\pi\) | ||||
0.00362860 | + | 0.999993i | \(0.498845\pi\) | |||||||
\(702\) | −813983. | −0.0623408 | ||||||||
\(703\) | 4.47791e6 | 0.341733 | ||||||||
\(704\) | −1.82120e6 | −0.138492 | ||||||||
\(705\) | −1.54170e6 | −0.116823 | ||||||||
\(706\) | −153134. | −0.0115627 | ||||||||
\(707\) | 5.13050e6 | 0.386021 | ||||||||
\(708\) | −956958. | −0.0717480 | ||||||||
\(709\) | −1.46333e7 | −1.09327 | −0.546633 | − | 0.837372i | \(-0.684091\pi\) | ||||
−0.546633 | + | 0.837372i | \(0.684091\pi\) | |||||||
\(710\) | −8.62614e6 | −0.642201 | ||||||||
\(711\) | 2.34379e6 | 0.173878 | ||||||||
\(712\) | 1.42369e7 | 1.05248 | ||||||||
\(713\) | 9.43067e6 | 0.694734 | ||||||||
\(714\) | −1.35311e7 | −0.993319 | ||||||||
\(715\) | −514970. | −0.0376718 | ||||||||
\(716\) | 6.42405e6 | 0.468302 | ||||||||
\(717\) | −1.00600e7 | −0.730805 | ||||||||
\(718\) | 2.38690e7 | 1.72792 | ||||||||
\(719\) | 1.15215e7 | 0.831161 | 0.415580 | − | 0.909556i | \(-0.363578\pi\) | ||||
0.415580 | + | 0.909556i | \(0.363578\pi\) | |||||||
\(720\) | −2.54176e6 | −0.182728 | ||||||||
\(721\) | 2.48525e6 | 0.178046 | ||||||||
\(722\) | −1.41111e7 | −1.00744 | ||||||||
\(723\) | 4.24423e6 | 0.301963 | ||||||||
\(724\) | 2.59273e6 | 0.183827 | ||||||||
\(725\) | 2.48911e6 | 0.175873 | ||||||||
\(726\) | −864260. | −0.0608559 | ||||||||
\(727\) | 1.73993e7 | 1.22095 | 0.610473 | − | 0.792037i | \(-0.290979\pi\) | ||||
0.610473 | + | 0.792037i | \(0.290979\pi\) | |||||||
\(728\) | −3.43168e6 | −0.239982 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.05546e7 | −0.733050 | ||||||||
\(731\) | 2.17107e7 | 1.50272 | ||||||||
\(732\) | 2.09570e6 | 0.144561 | ||||||||
\(733\) | −1.21356e7 | −0.834262 | −0.417131 | − | 0.908846i | \(-0.636964\pi\) | ||||
−0.417131 | + | 0.908846i | \(0.636964\pi\) | |||||||
\(734\) | 1.47387e7 | 1.00976 | ||||||||
\(735\) | −1.04655e6 | −0.0714568 | ||||||||
\(736\) | −1.20742e7 | −0.821608 | ||||||||
\(737\) | 5.26348e6 | 0.356948 | ||||||||
\(738\) | −2.76612e6 | −0.186952 | ||||||||
\(739\) | 1.30600e7 | 0.879692 | 0.439846 | − | 0.898073i | \(-0.355033\pi\) | ||||
0.439846 | + | 0.898073i | \(0.355033\pi\) | |||||||
\(740\) | 2.16498e6 | 0.145337 | ||||||||
\(741\) | −872994. | −0.0584071 | ||||||||
\(742\) | −3.68382e6 | −0.245634 | ||||||||
\(743\) | −2.36143e6 | −0.156929 | −0.0784644 | − | 0.996917i | \(-0.525002\pi\) | ||||
−0.0784644 | + | 0.996917i | \(0.525002\pi\) | |||||||
\(744\) | 3.70407e6 | 0.245328 | ||||||||
\(745\) | 7.13008e6 | 0.470656 | ||||||||
\(746\) | 2.51038e7 | 1.65156 | ||||||||
\(747\) | −376540. | −0.0246894 | ||||||||
\(748\) | −2.08641e6 | −0.136347 | ||||||||
\(749\) | 1.78574e6 | 0.116309 | ||||||||
\(750\) | −922346. | −0.0598743 | ||||||||
\(751\) | 4.12172e6 | 0.266673 | 0.133336 | − | 0.991071i | \(-0.457431\pi\) | ||||
0.133336 | + | 0.991071i | \(0.457431\pi\) | |||||||
\(752\) | −8.60058e6 | −0.554604 | ||||||||
\(753\) | −1.58887e7 | −1.02117 | ||||||||
\(754\) | 4.44685e6 | 0.284855 | ||||||||
\(755\) | −1.30589e7 | −0.833759 | ||||||||
\(756\) | −1.17673e6 | −0.0748811 | ||||||||
\(757\) | 4.12364e6 | 0.261542 | 0.130771 | − | 0.991413i | \(-0.458255\pi\) | ||||
0.130771 | + | 0.991413i | \(0.458255\pi\) | |||||||
\(758\) | −2.79700e7 | −1.76815 | ||||||||
\(759\) | 3.43389e6 | 0.216362 | ||||||||
\(760\) | −1.96022e6 | −0.123104 | ||||||||
\(761\) | −2.08230e7 | −1.30341 | −0.651706 | − | 0.758472i | \(-0.725946\pi\) | ||||
−0.651706 | + | 0.758472i | \(0.725946\pi\) | |||||||
\(762\) | 6.62558e6 | 0.413368 | ||||||||
\(763\) | 1.77817e6 | 0.110576 | ||||||||
\(764\) | 6.52105e6 | 0.404189 | ||||||||
\(765\) | 3.16875e6 | 0.195764 | ||||||||
\(766\) | 1.58017e7 | 0.973045 | ||||||||
\(767\) | 1.64269e6 | 0.100825 | ||||||||
\(768\) | −8.72578e6 | −0.533828 | ||||||||
\(769\) | 1.58156e7 | 0.964427 | 0.482213 | − | 0.876054i | \(-0.339833\pi\) | ||||
0.482213 | + | 0.876054i | \(0.339833\pi\) | |||||||
\(770\) | −2.90640e6 | −0.176656 | ||||||||
\(771\) | 179281. | 0.0108617 | ||||||||
\(772\) | −5.95947e6 | −0.359886 | ||||||||
\(773\) | −2.58350e6 | −0.155510 | −0.0777552 | − | 0.996972i | \(-0.524775\pi\) | ||||
−0.0777552 | + | 0.996972i | \(0.524775\pi\) | |||||||
\(774\) | 7.37101e6 | 0.442257 | ||||||||
\(775\) | 1.86924e6 | 0.111792 | ||||||||
\(776\) | −1.04322e7 | −0.621902 | ||||||||
\(777\) | −1.03610e7 | −0.615674 | ||||||||
\(778\) | 2.44781e7 | 1.44987 | ||||||||
\(779\) | −2.96665e6 | −0.175155 | ||||||||
\(780\) | −422076. | −0.0248401 | ||||||||
\(781\) | 6.36547e6 | 0.373425 | ||||||||
\(782\) | 3.23632e7 | 1.89250 | ||||||||
\(783\) | −2.90330e6 | −0.169234 | ||||||||
\(784\) | −5.83834e6 | −0.339234 | ||||||||
\(785\) | −55541.5 | −0.00321694 | ||||||||
\(786\) | 689411. | 0.0398035 | ||||||||
\(787\) | −5.64885e6 | −0.325105 | −0.162552 | − | 0.986700i | \(-0.551973\pi\) | ||||
−0.162552 | + | 0.986700i | \(0.551973\pi\) | |||||||
\(788\) | 5.30809e6 | 0.304525 | ||||||||
\(789\) | 1.96513e7 | 1.12383 | ||||||||
\(790\) | 4.74467e6 | 0.270482 | ||||||||
\(791\) | 2.99784e7 | 1.70360 | ||||||||
\(792\) | 1.34872e6 | 0.0764030 | ||||||||
\(793\) | −3.59743e6 | −0.203146 | ||||||||
\(794\) | −3.20920e7 | −1.80653 | ||||||||
\(795\) | 862683. | 0.0484098 | ||||||||
\(796\) | −1.11765e7 | −0.625204 | ||||||||
\(797\) | −3.72876e6 | −0.207931 | −0.103965 | − | 0.994581i | \(-0.533153\pi\) | ||||
−0.103965 | + | 0.994581i | \(0.533153\pi\) | |||||||
\(798\) | −4.92702e6 | −0.273890 | ||||||||
\(799\) | 1.07221e7 | 0.594173 | ||||||||
\(800\) | −2.39321e6 | −0.132207 | ||||||||
\(801\) | −8.38007e6 | −0.461495 | ||||||||
\(802\) | −2.58109e7 | −1.41699 | ||||||||
\(803\) | 7.78852e6 | 0.426252 | ||||||||
\(804\) | 4.31401e6 | 0.235365 | ||||||||
\(805\) | 1.15477e7 | 0.628068 | ||||||||
\(806\) | 3.33943e6 | 0.181065 | ||||||||
\(807\) | −7.55370e6 | −0.408296 | ||||||||
\(808\) | −4.81963e6 | −0.259708 | ||||||||
\(809\) | 6.35004e6 | 0.341119 | 0.170559 | − | 0.985347i | \(-0.445443\pi\) | ||||
0.170559 | + | 0.985347i | \(0.445443\pi\) | |||||||
\(810\) | 1.07582e6 | 0.0576141 | ||||||||
\(811\) | 1.34156e7 | 0.716241 | 0.358120 | − | 0.933675i | \(-0.383418\pi\) | ||||
0.358120 | + | 0.933675i | \(0.383418\pi\) | |||||||
\(812\) | 6.42856e6 | 0.342156 | ||||||||
\(813\) | −1.28377e7 | −0.681178 | ||||||||
\(814\) | −6.23705e6 | −0.329928 | ||||||||
\(815\) | 6.25365e6 | 0.329791 | ||||||||
\(816\) | 1.76773e7 | 0.929372 | ||||||||
\(817\) | 7.90538e6 | 0.414350 | ||||||||
\(818\) | 4.30945e6 | 0.225184 | ||||||||
\(819\) | 2.01995e6 | 0.105228 | ||||||||
\(820\) | −1.43432e6 | −0.0744922 | ||||||||
\(821\) | 2.40201e7 | 1.24370 | 0.621851 | − | 0.783135i | \(-0.286381\pi\) | ||||
0.621851 | + | 0.783135i | \(0.286381\pi\) | |||||||
\(822\) | 2.27228e7 | 1.17296 | ||||||||
\(823\) | −1.46523e6 | −0.0754058 | −0.0377029 | − | 0.999289i | \(-0.512004\pi\) | ||||
−0.0377029 | + | 0.999289i | \(0.512004\pi\) | |||||||
\(824\) | −2.33466e6 | −0.119786 | ||||||||
\(825\) | 680625. | 0.0348155 | ||||||||
\(826\) | 9.27105e6 | 0.472801 | ||||||||
\(827\) | −2.32918e7 | −1.18424 | −0.592120 | − | 0.805850i | \(-0.701709\pi\) | ||||
−0.592120 | + | 0.805850i | \(0.701709\pi\) | |||||||
\(828\) | 2.81446e6 | 0.142665 | ||||||||
\(829\) | −2.02821e6 | −0.102501 | −0.0512503 | − | 0.998686i | \(-0.516321\pi\) | ||||
−0.0512503 | + | 0.998686i | \(0.516321\pi\) | |||||||
\(830\) | −762250. | −0.0384063 | ||||||||
\(831\) | 1.17403e7 | 0.589762 | ||||||||
\(832\) | 2.56229e6 | 0.128327 | ||||||||
\(833\) | 7.27850e6 | 0.363437 | ||||||||
\(834\) | 1.83350e7 | 0.912781 | ||||||||
\(835\) | −1.05208e6 | −0.0522197 | ||||||||
\(836\) | −759712. | −0.0375953 | ||||||||
\(837\) | −2.18028e6 | −0.107572 | ||||||||
\(838\) | 2.87610e7 | 1.41480 | ||||||||
\(839\) | −3.07518e7 | −1.50822 | −0.754111 | − | 0.656747i | \(-0.771932\pi\) | ||||
−0.754111 | + | 0.656747i | \(0.771932\pi\) | |||||||
\(840\) | 4.53559e6 | 0.221787 | ||||||||
\(841\) | −4.65021e6 | −0.226716 | ||||||||
\(842\) | 1.53517e7 | 0.746234 | ||||||||
\(843\) | 5.22582e6 | 0.253271 | ||||||||
\(844\) | 6.82881e6 | 0.329981 | ||||||||
\(845\) | −8.55780e6 | −0.412307 | ||||||||
\(846\) | 3.64027e6 | 0.174867 | ||||||||
\(847\) | 2.14471e6 | 0.102721 | ||||||||
\(848\) | 4.81259e6 | 0.229821 | ||||||||
\(849\) | 5.41777e6 | 0.257959 | ||||||||
\(850\) | 6.41466e6 | 0.304527 | ||||||||
\(851\) | 2.47811e7 | 1.17300 | ||||||||
\(852\) | 5.21722e6 | 0.246229 | ||||||||
\(853\) | −2.05598e7 | −0.967491 | −0.483745 | − | 0.875209i | \(-0.660724\pi\) | ||||
−0.483745 | + | 0.875209i | \(0.660724\pi\) | |||||||
\(854\) | −2.03032e7 | −0.952621 | ||||||||
\(855\) | 1.15382e6 | 0.0539786 | ||||||||
\(856\) | −1.67753e6 | −0.0782505 | ||||||||
\(857\) | 3.20463e7 | 1.49048 | 0.745240 | − | 0.666796i | \(-0.232335\pi\) | ||||
0.745240 | + | 0.666796i | \(0.232335\pi\) | |||||||
\(858\) | 1.21595e6 | 0.0563894 | ||||||||
\(859\) | 2.34894e6 | 0.108615 | 0.0543075 | − | 0.998524i | \(-0.482705\pi\) | ||||
0.0543075 | + | 0.998524i | \(0.482705\pi\) | |||||||
\(860\) | 3.82210e6 | 0.176220 | ||||||||
\(861\) | 6.86428e6 | 0.315564 | ||||||||
\(862\) | −1.43125e7 | −0.656068 | ||||||||
\(863\) | −1.44887e7 | −0.662219 | −0.331110 | − | 0.943592i | \(-0.607423\pi\) | ||||
−0.331110 | + | 0.943592i | \(0.607423\pi\) | |||||||
\(864\) | 2.79144e6 | 0.127217 | ||||||||
\(865\) | −2.93014e6 | −0.133152 | ||||||||
\(866\) | −2.36829e7 | −1.07310 | ||||||||
\(867\) | −9.25903e6 | −0.418329 | ||||||||
\(868\) | 4.82763e6 | 0.217488 | ||||||||
\(869\) | −3.50122e6 | −0.157279 | ||||||||
\(870\) | −5.87731e6 | −0.263257 | ||||||||
\(871\) | −7.40533e6 | −0.330749 | ||||||||
\(872\) | −1.67042e6 | −0.0743936 | ||||||||
\(873\) | 6.14057e6 | 0.272692 | ||||||||
\(874\) | 1.17842e7 | 0.521823 | ||||||||
\(875\) | 2.28885e6 | 0.101064 | ||||||||
\(876\) | 6.38356e6 | 0.281063 | ||||||||
\(877\) | −3.17684e7 | −1.39475 | −0.697376 | − | 0.716705i | \(-0.745649\pi\) | ||||
−0.697376 | + | 0.716705i | \(0.745649\pi\) | |||||||
\(878\) | 4.25143e7 | 1.86122 | ||||||||
\(879\) | 2.16893e7 | 0.946834 | ||||||||
\(880\) | 3.79696e6 | 0.165283 | ||||||||
\(881\) | 1.06777e7 | 0.463486 | 0.231743 | − | 0.972777i | \(-0.425557\pi\) | ||||
0.231743 | + | 0.972777i | \(0.425557\pi\) | |||||||
\(882\) | 2.47113e6 | 0.106961 | ||||||||
\(883\) | 1.77890e7 | 0.767804 | 0.383902 | − | 0.923374i | \(-0.374580\pi\) | ||||
0.383902 | + | 0.923374i | \(0.374580\pi\) | |||||||
\(884\) | 2.93542e6 | 0.126340 | ||||||||
\(885\) | −2.17111e6 | −0.0931802 | ||||||||
\(886\) | −4.47005e7 | −1.91306 | ||||||||
\(887\) | 3.13731e7 | 1.33890 | 0.669450 | − | 0.742857i | \(-0.266530\pi\) | ||||
0.669450 | + | 0.742857i | \(0.266530\pi\) | |||||||
\(888\) | 9.73326e6 | 0.414215 | ||||||||
\(889\) | −1.64418e7 | −0.697741 | ||||||||
\(890\) | −1.69642e7 | −0.717892 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | 9.85397e6 | 0.414667 | ||||||||
\(893\) | 3.90418e6 | 0.163833 | ||||||||
\(894\) | −1.68356e7 | −0.704505 | ||||||||
\(895\) | 1.45746e7 | 0.608191 | ||||||||
\(896\) | 3.24104e7 | 1.34870 | ||||||||
\(897\) | −4.83123e6 | −0.200482 | ||||||||
\(898\) | −1.95689e7 | −0.809795 | ||||||||
\(899\) | 1.19110e7 | 0.491529 | ||||||||
\(900\) | 557849. | 0.0229567 | ||||||||
\(901\) | −5.99972e6 | −0.246218 | ||||||||
\(902\) | 4.13210e6 | 0.169104 | ||||||||
\(903\) | −1.82916e7 | −0.746504 | ||||||||
\(904\) | −2.81620e7 | −1.14615 | ||||||||
\(905\) | 5.88228e6 | 0.238739 | ||||||||
\(906\) | 3.08348e7 | 1.24802 | ||||||||
\(907\) | −8.46355e6 | −0.341613 | −0.170807 | − | 0.985305i | \(-0.554637\pi\) | ||||
−0.170807 | + | 0.985305i | \(0.554637\pi\) | |||||||
\(908\) | 9.38252e6 | 0.377663 | ||||||||
\(909\) | 2.83691e6 | 0.113877 | ||||||||
\(910\) | 4.08908e6 | 0.163690 | ||||||||
\(911\) | −2.18411e7 | −0.871923 | −0.435961 | − | 0.899965i | \(-0.643592\pi\) | ||||
−0.435961 | + | 0.899965i | \(0.643592\pi\) | |||||||
\(912\) | 6.43672e6 | 0.256258 | ||||||||
\(913\) | 562486. | 0.0223324 | ||||||||
\(914\) | −4.00870e7 | −1.58722 | ||||||||
\(915\) | 4.75464e6 | 0.187744 | ||||||||
\(916\) | 1.51889e6 | 0.0598120 | ||||||||
\(917\) | −1.71081e6 | −0.0671861 | ||||||||
\(918\) | −7.48206e6 | −0.293032 | ||||||||
\(919\) | 4.18752e7 | 1.63557 | 0.817784 | − | 0.575525i | \(-0.195202\pi\) | ||||
0.817784 | + | 0.575525i | \(0.195202\pi\) | |||||||
\(920\) | −1.08480e7 | −0.422553 | ||||||||
\(921\) | 1.65042e7 | 0.641130 | ||||||||
\(922\) | −2.24165e7 | −0.868440 | ||||||||
\(923\) | −8.95575e6 | −0.346017 | ||||||||
\(924\) | 1.75783e6 | 0.0677325 | ||||||||
\(925\) | 4.91183e6 | 0.188751 | ||||||||
\(926\) | −3.01717e7 | −1.15630 | ||||||||
\(927\) | 1.37422e6 | 0.0525240 | ||||||||
\(928\) | −1.52498e7 | −0.581293 | ||||||||
\(929\) | 8.03740e6 | 0.305546 | 0.152773 | − | 0.988261i | \(-0.451180\pi\) | ||||
0.152773 | + | 0.988261i | \(0.451180\pi\) | |||||||
\(930\) | −4.41365e6 | −0.167337 | ||||||||
\(931\) | 2.65028e6 | 0.100211 | ||||||||
\(932\) | −1.45002e7 | −0.546805 | ||||||||
\(933\) | −2.04757e7 | −0.770077 | ||||||||
\(934\) | 3.30317e7 | 1.23898 | ||||||||
\(935\) | −4.73356e6 | −0.177076 | ||||||||
\(936\) | −1.89755e6 | −0.0707953 | ||||||||
\(937\) | −1.78192e6 | −0.0663038 | −0.0331519 | − | 0.999450i | \(-0.510555\pi\) | ||||
−0.0331519 | + | 0.999450i | \(0.510555\pi\) | |||||||
\(938\) | −4.17943e7 | −1.55099 | ||||||||
\(939\) | −1.43627e6 | −0.0531583 | ||||||||
\(940\) | 1.88760e6 | 0.0696770 | ||||||||
\(941\) | 2.97245e7 | 1.09431 | 0.547154 | − | 0.837032i | \(-0.315711\pi\) | ||||
0.547154 | + | 0.837032i | \(0.315711\pi\) | |||||||
\(942\) | 131145. | 0.00481531 | ||||||||
\(943\) | −1.64177e7 | −0.601220 | ||||||||
\(944\) | −1.21118e7 | −0.442364 | ||||||||
\(945\) | −2.66972e6 | −0.0972492 | ||||||||
\(946\) | −1.10110e7 | −0.400036 | ||||||||
\(947\) | 931083. | 0.0337375 | 0.0168688 | − | 0.999858i | \(-0.494630\pi\) | ||||
0.0168688 | + | 0.999858i | \(0.494630\pi\) | |||||||
\(948\) | −2.86965e6 | −0.103707 | ||||||||
\(949\) | −1.09579e7 | −0.394967 | ||||||||
\(950\) | 2.33573e6 | 0.0839681 | ||||||||
\(951\) | 1.11904e7 | 0.401232 | ||||||||
\(952\) | −3.15437e7 | −1.12803 | ||||||||
\(953\) | −2.74983e7 | −0.980784 | −0.490392 | − | 0.871502i | \(-0.663146\pi\) | ||||
−0.490392 | + | 0.871502i | \(0.663146\pi\) | |||||||
\(954\) | −2.03697e6 | −0.0724626 | ||||||||
\(955\) | 1.47947e7 | 0.524926 | ||||||||
\(956\) | 1.23171e7 | 0.435876 | ||||||||
\(957\) | 4.33703e6 | 0.153078 | ||||||||
\(958\) | −1.85459e7 | −0.652882 | ||||||||
\(959\) | −5.63879e7 | −1.97988 | ||||||||
\(960\) | −3.38652e6 | −0.118598 | ||||||||
\(961\) | −1.96844e7 | −0.687565 | ||||||||
\(962\) | 8.77507e6 | 0.305712 | ||||||||
\(963\) | 987424. | 0.0343114 | ||||||||
\(964\) | −5.19646e6 | −0.180101 | ||||||||
\(965\) | −1.35206e7 | −0.467389 | ||||||||
\(966\) | −2.72666e7 | −0.940129 | ||||||||
\(967\) | 4.33623e6 | 0.149123 | 0.0745617 | − | 0.997216i | \(-0.476244\pi\) | ||||
0.0745617 | + | 0.997216i | \(0.476244\pi\) | |||||||
\(968\) | −2.01476e6 | −0.0691091 | ||||||||
\(969\) | −8.02448e6 | −0.274541 | ||||||||
\(970\) | 1.24307e7 | 0.424195 | ||||||||
\(971\) | −5.44123e7 | −1.85204 | −0.926018 | − | 0.377480i | \(-0.876791\pi\) | ||||
−0.926018 | + | 0.377480i | \(0.876791\pi\) | |||||||
\(972\) | −650675. | −0.0220901 | ||||||||
\(973\) | −4.54995e7 | −1.54072 | ||||||||
\(974\) | −3.73157e7 | −1.26036 | ||||||||
\(975\) | −957589. | −0.0322602 | ||||||||
\(976\) | 2.65244e7 | 0.891294 | ||||||||
\(977\) | −3.16213e7 | −1.05985 | −0.529924 | − | 0.848045i | \(-0.677780\pi\) | ||||
−0.529924 | + | 0.848045i | \(0.677780\pi\) | |||||||
\(978\) | −1.47662e7 | −0.493651 | ||||||||
\(979\) | 1.25184e7 | 0.417438 | ||||||||
\(980\) | 1.28136e6 | 0.0426192 | ||||||||
\(981\) | 983239. | 0.0326202 | ||||||||
\(982\) | 2.12321e7 | 0.702611 | ||||||||
\(983\) | 1.31368e7 | 0.433617 | 0.216808 | − | 0.976214i | \(-0.430435\pi\) | ||||
0.216808 | + | 0.976214i | \(0.430435\pi\) | |||||||
\(984\) | −6.44836e6 | −0.212306 | ||||||||
\(985\) | 1.20428e7 | 0.395491 | ||||||||
\(986\) | 4.08750e7 | 1.33895 | ||||||||
\(987\) | −9.03355e6 | −0.295165 | ||||||||
\(988\) | 1.06886e6 | 0.0348359 | ||||||||
\(989\) | 4.37491e7 | 1.42226 | ||||||||
\(990\) | −1.60710e6 | −0.0521139 | ||||||||
\(991\) | −3.53335e7 | −1.14288 | −0.571442 | − | 0.820643i | \(-0.693616\pi\) | ||||
−0.571442 | + | 0.820643i | \(0.693616\pi\) | |||||||
\(992\) | −1.14521e7 | −0.369493 | ||||||||
\(993\) | 8.62603e6 | 0.277612 | ||||||||
\(994\) | −5.05446e7 | −1.62259 | ||||||||
\(995\) | −2.53567e7 | −0.811962 | ||||||||
\(996\) | 461020. | 0.0147256 | ||||||||
\(997\) | 3.72145e7 | 1.18570 | 0.592850 | − | 0.805313i | \(-0.298003\pi\) | ||||
0.592850 | + | 0.805313i | \(0.298003\pi\) | |||||||
\(998\) | −3.33563e7 | −1.06011 | ||||||||
\(999\) | −5.72915e6 | −0.181625 |
(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 | 165.6.a.d.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 495.6.a.c.1.1 | 3 | |||
5.4 | even | 2 | 825.6.a.h.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.d.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
495.6.a.c.1.1 | 3 | 3.2 | odd | 2 | |||
825.6.a.h.1.1 | 3 | 5.4 | even | 2 |