Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + 81977088 x^{5} - 3773728 x^{4} - 1245415104 x^{3} + \cdots - 6400833792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(2.69937\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.69937 | 0.477186 | 0.238593 | − | 0.971120i | \(-0.423314\pi\) | ||||
0.238593 | + | 0.971120i | \(0.423314\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −24.7134 | −0.772294 | ||||||||
\(5\) | −80.3454 | −1.43726 | −0.718631 | − | 0.695392i | \(-0.755231\pi\) | ||||
−0.718631 | + | 0.695392i | \(0.755231\pi\) | |||||||
\(6\) | −24.2943 | −0.275503 | ||||||||
\(7\) | −162.093 | −1.25032 | −0.625159 | − | 0.780498i | \(-0.714966\pi\) | ||||
−0.625159 | + | 0.780498i | \(0.714966\pi\) | |||||||
\(8\) | −153.090 | −0.845713 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −216.882 | −0.685841 | ||||||||
\(11\) | −426.976 | −1.06395 | −0.531975 | − | 0.846760i | \(-0.678550\pi\) | ||||
−0.531975 | + | 0.846760i | \(0.678550\pi\) | |||||||
\(12\) | 222.421 | 0.445884 | ||||||||
\(13\) | −106.245 | −0.174361 | −0.0871807 | − | 0.996193i | \(-0.527786\pi\) | ||||
−0.0871807 | + | 0.996193i | \(0.527786\pi\) | |||||||
\(14\) | −437.550 | −0.596634 | ||||||||
\(15\) | 723.108 | 0.829803 | ||||||||
\(16\) | 377.581 | 0.368732 | ||||||||
\(17\) | −864.470 | −0.725483 | −0.362742 | − | 0.931890i | \(-0.618159\pi\) | ||||
−0.362742 | + | 0.931890i | \(0.618159\pi\) | |||||||
\(18\) | 218.649 | 0.159062 | ||||||||
\(19\) | −676.226 | −0.429742 | −0.214871 | − | 0.976642i | \(-0.568933\pi\) | ||||
−0.214871 | + | 0.976642i | \(0.568933\pi\) | |||||||
\(20\) | 1985.61 | 1.10999 | ||||||||
\(21\) | 1458.84 | 0.721871 | ||||||||
\(22\) | −1152.57 | −0.507702 | ||||||||
\(23\) | 783.598 | 0.308869 | 0.154434 | − | 0.988003i | \(-0.450644\pi\) | ||||
0.154434 | + | 0.988003i | \(0.450644\pi\) | |||||||
\(24\) | 1377.81 | 0.488273 | ||||||||
\(25\) | 3330.38 | 1.06572 | ||||||||
\(26\) | −286.795 | −0.0832027 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 4005.88 | 0.965613 | ||||||||
\(29\) | −2853.46 | −0.630052 | −0.315026 | − | 0.949083i | \(-0.602013\pi\) | ||||
−0.315026 | + | 0.949083i | \(0.602013\pi\) | |||||||
\(30\) | 1951.94 | 0.395970 | ||||||||
\(31\) | −1908.96 | −0.356774 | −0.178387 | − | 0.983960i | \(-0.557088\pi\) | ||||
−0.178387 | + | 0.983960i | \(0.557088\pi\) | |||||||
\(32\) | 5918.13 | 1.02167 | ||||||||
\(33\) | 3842.78 | 0.614272 | ||||||||
\(34\) | −2333.52 | −0.346190 | ||||||||
\(35\) | 13023.5 | 1.79703 | ||||||||
\(36\) | −2001.79 | −0.257431 | ||||||||
\(37\) | 568.886 | 0.0683157 | 0.0341579 | − | 0.999416i | \(-0.489125\pi\) | ||||
0.0341579 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(38\) | −1825.38 | −0.205067 | ||||||||
\(39\) | 956.205 | 0.100668 | ||||||||
\(40\) | 12300.1 | 1.21551 | ||||||||
\(41\) | −5535.95 | −0.514319 | −0.257160 | − | 0.966369i | \(-0.582787\pi\) | ||||
−0.257160 | + | 0.966369i | \(0.582787\pi\) | |||||||
\(42\) | 3937.95 | 0.344467 | ||||||||
\(43\) | −6906.55 | −0.569626 | −0.284813 | − | 0.958583i | \(-0.591932\pi\) | ||||
−0.284813 | + | 0.958583i | \(0.591932\pi\) | |||||||
\(44\) | 10552.0 | 0.821682 | ||||||||
\(45\) | −6507.97 | −0.479087 | ||||||||
\(46\) | 2115.22 | 0.147388 | ||||||||
\(47\) | −2905.40 | −0.191850 | −0.0959250 | − | 0.995389i | \(-0.530581\pi\) | ||||
−0.0959250 | + | 0.995389i | \(0.530581\pi\) | |||||||
\(48\) | −3398.23 | −0.212887 | ||||||||
\(49\) | 9467.29 | 0.563294 | ||||||||
\(50\) | 8989.92 | 0.508547 | ||||||||
\(51\) | 7780.23 | 0.418858 | ||||||||
\(52\) | 2625.68 | 0.134658 | ||||||||
\(53\) | −29299.4 | −1.43275 | −0.716373 | − | 0.697717i | \(-0.754199\pi\) | ||||
−0.716373 | + | 0.697717i | \(0.754199\pi\) | |||||||
\(54\) | −1967.84 | −0.0918344 | ||||||||
\(55\) | 34305.5 | 1.52918 | ||||||||
\(56\) | 24815.0 | 1.05741 | ||||||||
\(57\) | 6086.03 | 0.248112 | ||||||||
\(58\) | −7702.54 | −0.300652 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | −17870.5 | −0.640852 | ||||||||
\(61\) | 15250.0 | 0.524741 | 0.262370 | − | 0.964967i | \(-0.415496\pi\) | ||||
0.262370 | + | 0.964967i | \(0.415496\pi\) | |||||||
\(62\) | −5153.00 | −0.170248 | ||||||||
\(63\) | −13129.6 | −0.416773 | ||||||||
\(64\) | 3892.61 | 0.118793 | ||||||||
\(65\) | 8536.29 | 0.250603 | ||||||||
\(66\) | 10373.1 | 0.293122 | ||||||||
\(67\) | −37501.6 | −1.02062 | −0.510309 | − | 0.859991i | \(-0.670469\pi\) | ||||
−0.510309 | + | 0.859991i | \(0.670469\pi\) | |||||||
\(68\) | 21364.0 | 0.560286 | ||||||||
\(69\) | −7052.38 | −0.178325 | ||||||||
\(70\) | 35155.1 | 0.857519 | ||||||||
\(71\) | 32441.3 | 0.763752 | 0.381876 | − | 0.924214i | \(-0.375278\pi\) | ||||
0.381876 | + | 0.924214i | \(0.375278\pi\) | |||||||
\(72\) | −12400.3 | −0.281904 | ||||||||
\(73\) | −60191.0 | −1.32198 | −0.660989 | − | 0.750396i | \(-0.729863\pi\) | ||||
−0.660989 | + | 0.750396i | \(0.729863\pi\) | |||||||
\(74\) | 1535.63 | 0.0325993 | ||||||||
\(75\) | −29973.4 | −0.615294 | ||||||||
\(76\) | 16711.8 | 0.331887 | ||||||||
\(77\) | 69210.0 | 1.33028 | ||||||||
\(78\) | 2581.15 | 0.0480371 | ||||||||
\(79\) | −54275.0 | −0.978436 | −0.489218 | − | 0.872162i | \(-0.662718\pi\) | ||||
−0.489218 | + | 0.872162i | \(0.662718\pi\) | |||||||
\(80\) | −30336.9 | −0.529964 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −14943.6 | −0.245426 | ||||||||
\(83\) | 59211.9 | 0.943439 | 0.471720 | − | 0.881749i | \(-0.343633\pi\) | ||||
0.471720 | + | 0.881749i | \(0.343633\pi\) | |||||||
\(84\) | −36052.9 | −0.557497 | ||||||||
\(85\) | 69456.1 | 1.04271 | ||||||||
\(86\) | −18643.3 | −0.271817 | ||||||||
\(87\) | 25681.1 | 0.363761 | ||||||||
\(88\) | 65365.9 | 0.899797 | ||||||||
\(89\) | −58121.9 | −0.777794 | −0.388897 | − | 0.921281i | \(-0.627144\pi\) | ||||
−0.388897 | + | 0.921281i | \(0.627144\pi\) | |||||||
\(90\) | −17567.4 | −0.228614 | ||||||||
\(91\) | 17221.6 | 0.218007 | ||||||||
\(92\) | −19365.4 | −0.238537 | ||||||||
\(93\) | 17180.7 | 0.205984 | ||||||||
\(94\) | −7842.76 | −0.0915480 | ||||||||
\(95\) | 54331.6 | 0.617652 | ||||||||
\(96\) | −53263.1 | −0.589860 | ||||||||
\(97\) | 174781. | 1.88610 | 0.943051 | − | 0.332647i | \(-0.107942\pi\) | ||||
0.943051 | + | 0.332647i | \(0.107942\pi\) | |||||||
\(98\) | 25555.7 | 0.268796 | ||||||||
\(99\) | −34585.0 | −0.354650 | ||||||||
\(100\) | −82304.9 | −0.823049 | ||||||||
\(101\) | −178436. | −1.74052 | −0.870258 | − | 0.492596i | \(-0.836048\pi\) | ||||
−0.870258 | + | 0.492596i | \(0.836048\pi\) | |||||||
\(102\) | 21001.7 | 0.199873 | ||||||||
\(103\) | 126990. | 1.17944 | 0.589722 | − | 0.807607i | \(-0.299237\pi\) | ||||
0.589722 | + | 0.807607i | \(0.299237\pi\) | |||||||
\(104\) | 16265.1 | 0.147460 | ||||||||
\(105\) | −117211. | −1.03752 | ||||||||
\(106\) | −79090.0 | −0.683686 | ||||||||
\(107\) | −70204.3 | −0.592795 | −0.296397 | − | 0.955065i | \(-0.595785\pi\) | ||||
−0.296397 | + | 0.955065i | \(0.595785\pi\) | |||||||
\(108\) | 18016.1 | 0.148628 | ||||||||
\(109\) | −50071.5 | −0.403668 | −0.201834 | − | 0.979420i | \(-0.564690\pi\) | ||||
−0.201834 | + | 0.979420i | \(0.564690\pi\) | |||||||
\(110\) | 92603.3 | 0.729700 | ||||||||
\(111\) | −5119.97 | −0.0394421 | ||||||||
\(112\) | −61203.4 | −0.461032 | ||||||||
\(113\) | −103197. | −0.760279 | −0.380139 | − | 0.924929i | \(-0.624124\pi\) | ||||
−0.380139 | + | 0.924929i | \(0.624124\pi\) | |||||||
\(114\) | 16428.5 | 0.118395 | ||||||||
\(115\) | −62958.5 | −0.443925 | ||||||||
\(116\) | 70518.7 | 0.486585 | ||||||||
\(117\) | −8605.85 | −0.0581204 | ||||||||
\(118\) | 9396.51 | 0.0621243 | ||||||||
\(119\) | 140125. | 0.907085 | ||||||||
\(120\) | −110701. | −0.701776 | ||||||||
\(121\) | 21257.2 | 0.131991 | ||||||||
\(122\) | 41165.3 | 0.250399 | ||||||||
\(123\) | 49823.6 | 0.296942 | ||||||||
\(124\) | 47177.0 | 0.275535 | ||||||||
\(125\) | −16501.1 | −0.0944577 | ||||||||
\(126\) | −35441.6 | −0.198878 | ||||||||
\(127\) | −95263.9 | −0.524106 | −0.262053 | − | 0.965053i | \(-0.584400\pi\) | ||||
−0.262053 | + | 0.965053i | \(0.584400\pi\) | |||||||
\(128\) | −178872. | −0.964980 | ||||||||
\(129\) | 62159.0 | 0.328874 | ||||||||
\(130\) | 23042.6 | 0.119584 | ||||||||
\(131\) | −283090. | −1.44127 | −0.720636 | − | 0.693313i | \(-0.756150\pi\) | ||||
−0.720636 | + | 0.693313i | \(0.756150\pi\) | |||||||
\(132\) | −94968.2 | −0.474399 | ||||||||
\(133\) | 109612. | 0.537314 | ||||||||
\(134\) | −101231. | −0.487024 | ||||||||
\(135\) | 58571.8 | 0.276601 | ||||||||
\(136\) | 132342. | 0.613551 | ||||||||
\(137\) | −46840.7 | −0.213217 | −0.106609 | − | 0.994301i | \(-0.533999\pi\) | ||||
−0.106609 | + | 0.994301i | \(0.533999\pi\) | |||||||
\(138\) | −19037.0 | −0.0850943 | ||||||||
\(139\) | 352418. | 1.54711 | 0.773555 | − | 0.633729i | \(-0.218477\pi\) | ||||
0.773555 | + | 0.633729i | \(0.218477\pi\) | |||||||
\(140\) | −321854. | −1.38784 | ||||||||
\(141\) | 26148.6 | 0.110765 | ||||||||
\(142\) | 87571.0 | 0.364451 | ||||||||
\(143\) | 45364.0 | 0.185512 | ||||||||
\(144\) | 30584.1 | 0.122911 | ||||||||
\(145\) | 229262. | 0.905550 | ||||||||
\(146\) | −162478. | −0.630829 | ||||||||
\(147\) | −85205.6 | −0.325218 | ||||||||
\(148\) | −14059.1 | −0.0527598 | ||||||||
\(149\) | −170739. | −0.630040 | −0.315020 | − | 0.949085i | \(-0.602011\pi\) | ||||
−0.315020 | + | 0.949085i | \(0.602011\pi\) | |||||||
\(150\) | −80909.3 | −0.293610 | ||||||||
\(151\) | 51532.5 | 0.183924 | 0.0919620 | − | 0.995763i | \(-0.470686\pi\) | ||||
0.0919620 | + | 0.995763i | \(0.470686\pi\) | |||||||
\(152\) | 103524. | 0.363438 | ||||||||
\(153\) | −70022.1 | −0.241828 | ||||||||
\(154\) | 186823. | 0.634789 | ||||||||
\(155\) | 153376. | 0.512778 | ||||||||
\(156\) | −23631.1 | −0.0777449 | ||||||||
\(157\) | −63321.5 | −0.205023 | −0.102511 | − | 0.994732i | \(-0.532688\pi\) | ||||
−0.102511 | + | 0.994732i | \(0.532688\pi\) | |||||||
\(158\) | −146508. | −0.466896 | ||||||||
\(159\) | 263695. | 0.827197 | ||||||||
\(160\) | −475494. | −1.46840 | ||||||||
\(161\) | −127016. | −0.386184 | ||||||||
\(162\) | 17710.6 | 0.0530206 | ||||||||
\(163\) | 248901. | 0.733765 | 0.366882 | − | 0.930267i | \(-0.380425\pi\) | ||||
0.366882 | + | 0.930267i | \(0.380425\pi\) | |||||||
\(164\) | 136812. | 0.397205 | ||||||||
\(165\) | −308750. | −0.882870 | ||||||||
\(166\) | 159835. | 0.450196 | ||||||||
\(167\) | −693685. | −1.92474 | −0.962368 | − | 0.271750i | \(-0.912398\pi\) | ||||
−0.962368 | + | 0.271750i | \(0.912398\pi\) | |||||||
\(168\) | −223335. | −0.610496 | ||||||||
\(169\) | −360005. | −0.969598 | ||||||||
\(170\) | 187488. | 0.497566 | ||||||||
\(171\) | −54774.3 | −0.143247 | ||||||||
\(172\) | 170684. | 0.439919 | ||||||||
\(173\) | −311888. | −0.792288 | −0.396144 | − | 0.918188i | \(-0.629652\pi\) | ||||
−0.396144 | + | 0.918188i | \(0.629652\pi\) | |||||||
\(174\) | 69322.9 | 0.173581 | ||||||||
\(175\) | −539832. | −1.33249 | ||||||||
\(176\) | −161218. | −0.392312 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | −156893. | −0.371152 | ||||||||
\(179\) | −566672. | −1.32190 | −0.660951 | − | 0.750429i | \(-0.729847\pi\) | ||||
−0.660951 | + | 0.750429i | \(0.729847\pi\) | |||||||
\(180\) | 160834. | 0.369996 | ||||||||
\(181\) | −166371. | −0.377468 | −0.188734 | − | 0.982028i | \(-0.560438\pi\) | ||||
−0.188734 | + | 0.982028i | \(0.560438\pi\) | |||||||
\(182\) | 46487.5 | 0.104030 | ||||||||
\(183\) | −137250. | −0.302959 | ||||||||
\(184\) | −119961. | −0.261214 | ||||||||
\(185\) | −45707.3 | −0.0981876 | ||||||||
\(186\) | 46377.0 | 0.0982925 | ||||||||
\(187\) | 369108. | 0.771878 | ||||||||
\(188\) | 71802.4 | 0.148165 | ||||||||
\(189\) | 118166. | 0.240624 | ||||||||
\(190\) | 146661. | 0.294734 | ||||||||
\(191\) | 57779.2 | 0.114601 | 0.0573005 | − | 0.998357i | \(-0.481751\pi\) | ||||
0.0573005 | + | 0.998357i | \(0.481751\pi\) | |||||||
\(192\) | −35033.5 | −0.0685852 | ||||||||
\(193\) | 1.00421e6 | 1.94058 | 0.970290 | − | 0.241946i | \(-0.0777855\pi\) | ||||
0.970290 | + | 0.241946i | \(0.0777855\pi\) | |||||||
\(194\) | 471799. | 0.900021 | ||||||||
\(195\) | −76826.6 | −0.144686 | ||||||||
\(196\) | −233969. | −0.435029 | ||||||||
\(197\) | 964560. | 1.77078 | 0.885388 | − | 0.464853i | \(-0.153893\pi\) | ||||
0.885388 | + | 0.464853i | \(0.153893\pi\) | |||||||
\(198\) | −93357.8 | −0.169234 | ||||||||
\(199\) | 623260. | 1.11567 | 0.557836 | − | 0.829951i | \(-0.311632\pi\) | ||||
0.557836 | + | 0.829951i | \(0.311632\pi\) | |||||||
\(200\) | −509849. | −0.901294 | ||||||||
\(201\) | 337514. | 0.589254 | ||||||||
\(202\) | −481664. | −0.830550 | ||||||||
\(203\) | 462527. | 0.787765 | ||||||||
\(204\) | −192276. | −0.323482 | ||||||||
\(205\) | 444788. | 0.739211 | ||||||||
\(206\) | 342793. | 0.562813 | ||||||||
\(207\) | 63471.5 | 0.102956 | ||||||||
\(208\) | −40116.1 | −0.0642925 | ||||||||
\(209\) | 288732. | 0.457224 | ||||||||
\(210\) | −316396. | −0.495089 | ||||||||
\(211\) | 800296. | 1.23750 | 0.618749 | − | 0.785589i | \(-0.287640\pi\) | ||||
0.618749 | + | 0.785589i | \(0.287640\pi\) | |||||||
\(212\) | 724088. | 1.10650 | ||||||||
\(213\) | −291972. | −0.440952 | ||||||||
\(214\) | −189507. | −0.282873 | ||||||||
\(215\) | 554909. | 0.818702 | ||||||||
\(216\) | 111603. | 0.162758 | ||||||||
\(217\) | 309431. | 0.446081 | ||||||||
\(218\) | −135161. | −0.192624 | ||||||||
\(219\) | 541719. | 0.763244 | ||||||||
\(220\) | −847806. | −1.18097 | ||||||||
\(221\) | 91845.6 | 0.126496 | ||||||||
\(222\) | −13820.7 | −0.0188212 | ||||||||
\(223\) | −195058. | −0.262664 | −0.131332 | − | 0.991338i | \(-0.541925\pi\) | ||||
−0.131332 | + | 0.991338i | \(0.541925\pi\) | |||||||
\(224\) | −959289. | −1.27741 | ||||||||
\(225\) | 269761. | 0.355240 | ||||||||
\(226\) | −278568. | −0.362794 | ||||||||
\(227\) | −787763. | −1.01468 | −0.507342 | − | 0.861745i | \(-0.669372\pi\) | ||||
−0.507342 | + | 0.861745i | \(0.669372\pi\) | |||||||
\(228\) | −150407. | −0.191615 | ||||||||
\(229\) | 1.12310e6 | 1.41524 | 0.707620 | − | 0.706593i | \(-0.249769\pi\) | ||||
0.707620 | + | 0.706593i | \(0.249769\pi\) | |||||||
\(230\) | −169948. | −0.211835 | ||||||||
\(231\) | −622890. | −0.768035 | ||||||||
\(232\) | 436837. | 0.532843 | ||||||||
\(233\) | 1.17683e6 | 1.42012 | 0.710061 | − | 0.704140i | \(-0.248667\pi\) | ||||
0.710061 | + | 0.704140i | \(0.248667\pi\) | |||||||
\(234\) | −23230.4 | −0.0277342 | ||||||||
\(235\) | 233436. | 0.275739 | ||||||||
\(236\) | −86027.4 | −0.100544 | ||||||||
\(237\) | 488475. | 0.564900 | ||||||||
\(238\) | 378249. | 0.432848 | ||||||||
\(239\) | 46985.5 | 0.0532070 | 0.0266035 | − | 0.999646i | \(-0.491531\pi\) | ||||
0.0266035 | + | 0.999646i | \(0.491531\pi\) | |||||||
\(240\) | 273032. | 0.305975 | ||||||||
\(241\) | 1.64514e6 | 1.82457 | 0.912286 | − | 0.409553i | \(-0.134315\pi\) | ||||
0.912286 | + | 0.409553i | \(0.134315\pi\) | |||||||
\(242\) | 57381.1 | 0.0629840 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −376879. | −0.405254 | ||||||||
\(245\) | −760653. | −0.809601 | ||||||||
\(246\) | 134492. | 0.141697 | ||||||||
\(247\) | 71845.6 | 0.0749304 | ||||||||
\(248\) | 292244. | 0.301729 | ||||||||
\(249\) | −532907. | −0.544695 | ||||||||
\(250\) | −44542.5 | −0.0450739 | ||||||||
\(251\) | 26758.5 | 0.0268088 | 0.0134044 | − | 0.999910i | \(-0.495733\pi\) | ||||
0.0134044 | + | 0.999910i | \(0.495733\pi\) | |||||||
\(252\) | 324476. | 0.321871 | ||||||||
\(253\) | −334577. | −0.328621 | ||||||||
\(254\) | −257153. | −0.250096 | ||||||||
\(255\) | −625105. | −0.602009 | ||||||||
\(256\) | −607406. | −0.579268 | ||||||||
\(257\) | 1.46732e6 | 1.38577 | 0.692887 | − | 0.721046i | \(-0.256338\pi\) | ||||
0.692887 | + | 0.721046i | \(0.256338\pi\) | |||||||
\(258\) | 167790. | 0.156934 | ||||||||
\(259\) | −92212.6 | −0.0854164 | ||||||||
\(260\) | −210961. | −0.193539 | ||||||||
\(261\) | −231130. | −0.210017 | ||||||||
\(262\) | −764164. | −0.687754 | ||||||||
\(263\) | 972533. | 0.866991 | 0.433496 | − | 0.901156i | \(-0.357280\pi\) | ||||
0.433496 | + | 0.901156i | \(0.357280\pi\) | |||||||
\(264\) | −588293. | −0.519498 | ||||||||
\(265\) | 2.35407e6 | 2.05923 | ||||||||
\(266\) | 295883. | 0.256399 | ||||||||
\(267\) | 523097. | 0.449060 | ||||||||
\(268\) | 926792. | 0.788216 | ||||||||
\(269\) | −440178. | −0.370892 | −0.185446 | − | 0.982654i | \(-0.559373\pi\) | ||||
−0.185446 | + | 0.982654i | \(0.559373\pi\) | |||||||
\(270\) | 158107. | 0.131990 | ||||||||
\(271\) | 350066. | 0.289552 | 0.144776 | − | 0.989464i | \(-0.453754\pi\) | ||||
0.144776 | + | 0.989464i | \(0.453754\pi\) | |||||||
\(272\) | −326408. | −0.267509 | ||||||||
\(273\) | −154995. | −0.125866 | ||||||||
\(274\) | −126440. | −0.101744 | ||||||||
\(275\) | −1.42199e6 | −1.13387 | ||||||||
\(276\) | 174288. | 0.137720 | ||||||||
\(277\) | −144244. | −0.112953 | −0.0564766 | − | 0.998404i | \(-0.517987\pi\) | ||||
−0.0564766 | + | 0.998404i | \(0.517987\pi\) | |||||||
\(278\) | 951306. | 0.738259 | ||||||||
\(279\) | −154626. | −0.118925 | ||||||||
\(280\) | −1.99377e6 | −1.51977 | ||||||||
\(281\) | −818381. | −0.618287 | −0.309143 | − | 0.951015i | \(-0.600042\pi\) | ||||
−0.309143 | + | 0.951015i | \(0.600042\pi\) | |||||||
\(282\) | 70584.8 | 0.0528553 | ||||||||
\(283\) | 1.15317e6 | 0.855909 | 0.427954 | − | 0.903800i | \(-0.359234\pi\) | ||||
0.427954 | + | 0.903800i | \(0.359234\pi\) | |||||||
\(284\) | −801735. | −0.589841 | ||||||||
\(285\) | −488985. | −0.356601 | ||||||||
\(286\) | 122454. | 0.0885236 | ||||||||
\(287\) | 897341. | 0.643062 | ||||||||
\(288\) | 479368. | 0.340556 | ||||||||
\(289\) | −672549. | −0.473674 | ||||||||
\(290\) | 618863. | 0.432115 | ||||||||
\(291\) | −1.57303e6 | −1.08894 | ||||||||
\(292\) | 1.48752e6 | 1.02096 | ||||||||
\(293\) | −1.43446e6 | −0.976153 | −0.488077 | − | 0.872801i | \(-0.662301\pi\) | ||||
−0.488077 | + | 0.872801i | \(0.662301\pi\) | |||||||
\(294\) | −230001. | −0.155189 | ||||||||
\(295\) | −279682. | −0.187116 | ||||||||
\(296\) | −87091.0 | −0.0577755 | ||||||||
\(297\) | 311265. | 0.204757 | ||||||||
\(298\) | −460889. | −0.300646 | ||||||||
\(299\) | −83253.4 | −0.0538548 | ||||||||
\(300\) | 740745. | 0.475188 | ||||||||
\(301\) | 1.11951e6 | 0.712214 | ||||||||
\(302\) | 139105. | 0.0877659 | ||||||||
\(303\) | 1.60592e6 | 1.00489 | ||||||||
\(304\) | −255330. | −0.158459 | ||||||||
\(305\) | −1.22526e6 | −0.754189 | ||||||||
\(306\) | −189015. | −0.115397 | ||||||||
\(307\) | −1.40814e6 | −0.852705 | −0.426353 | − | 0.904557i | \(-0.640202\pi\) | ||||
−0.426353 | + | 0.904557i | \(0.640202\pi\) | |||||||
\(308\) | −1.71041e6 | −1.02736 | ||||||||
\(309\) | −1.14291e6 | −0.680952 | ||||||||
\(310\) | 414020. | 0.244690 | ||||||||
\(311\) | −405966. | −0.238007 | −0.119003 | − | 0.992894i | \(-0.537970\pi\) | ||||
−0.119003 | + | 0.992894i | \(0.537970\pi\) | |||||||
\(312\) | −146386. | −0.0851359 | ||||||||
\(313\) | −2.28785e6 | −1.31998 | −0.659990 | − | 0.751275i | \(-0.729439\pi\) | ||||
−0.659990 | + | 0.751275i | \(0.729439\pi\) | |||||||
\(314\) | −170928. | −0.0978339 | ||||||||
\(315\) | 1.05490e6 | 0.599011 | ||||||||
\(316\) | 1.34132e6 | 0.755640 | ||||||||
\(317\) | −1.72021e6 | −0.961462 | −0.480731 | − | 0.876868i | \(-0.659629\pi\) | ||||
−0.480731 | + | 0.876868i | \(0.659629\pi\) | |||||||
\(318\) | 711810. | 0.394726 | ||||||||
\(319\) | 1.21836e6 | 0.670344 | ||||||||
\(320\) | −312753. | −0.170737 | ||||||||
\(321\) | 631839. | 0.342250 | ||||||||
\(322\) | −342864. | −0.184281 | ||||||||
\(323\) | 584577. | 0.311771 | ||||||||
\(324\) | −162145. | −0.0858104 | ||||||||
\(325\) | −353836. | −0.185820 | ||||||||
\(326\) | 671875. | 0.350142 | ||||||||
\(327\) | 450643. | 0.233058 | ||||||||
\(328\) | 847501. | 0.434966 | ||||||||
\(329\) | 470947. | 0.239873 | ||||||||
\(330\) | −833429. | −0.421293 | ||||||||
\(331\) | −1.23423e6 | −0.619193 | −0.309597 | − | 0.950868i | \(-0.600194\pi\) | ||||
−0.309597 | + | 0.950868i | \(0.600194\pi\) | |||||||
\(332\) | −1.46333e6 | −0.728612 | ||||||||
\(333\) | 46079.7 | 0.0227719 | ||||||||
\(334\) | −1.87251e6 | −0.918456 | ||||||||
\(335\) | 3.01308e6 | 1.46689 | ||||||||
\(336\) | 550831. | 0.266177 | ||||||||
\(337\) | −1.65283e6 | −0.792781 | −0.396391 | − | 0.918082i | \(-0.629737\pi\) | ||||
−0.396391 | + | 0.918082i | \(0.629737\pi\) | |||||||
\(338\) | −971787. | −0.462678 | ||||||||
\(339\) | 928777. | 0.438947 | ||||||||
\(340\) | −1.71650e6 | −0.805278 | ||||||||
\(341\) | 815082. | 0.379590 | ||||||||
\(342\) | −147856. | −0.0683556 | ||||||||
\(343\) | 1.18972e6 | 0.546021 | ||||||||
\(344\) | 1.05733e6 | 0.481740 | ||||||||
\(345\) | 566626. | 0.256300 | ||||||||
\(346\) | −841900. | −0.378068 | ||||||||
\(347\) | −1708.59 | −0.000761752 0 | −0.000380876 | − | 1.00000i | \(-0.500121\pi\) | ||||
−0.000380876 | 1.00000i | \(0.500121\pi\) | ||||||||
\(348\) | −634668. | −0.280930 | ||||||||
\(349\) | −4.09764e6 | −1.80082 | −0.900410 | − | 0.435042i | \(-0.856734\pi\) | ||||
−0.900410 | + | 0.435042i | \(0.856734\pi\) | |||||||
\(350\) | −1.45721e6 | −0.635845 | ||||||||
\(351\) | 77452.6 | 0.0335559 | ||||||||
\(352\) | −2.52690e6 | −1.08700 | ||||||||
\(353\) | −4.02008e6 | −1.71711 | −0.858555 | − | 0.512721i | \(-0.828637\pi\) | ||||
−0.858555 | + | 0.512721i | \(0.828637\pi\) | |||||||
\(354\) | −84568.6 | −0.0358675 | ||||||||
\(355\) | −2.60651e6 | −1.09771 | ||||||||
\(356\) | 1.43639e6 | 0.600686 | ||||||||
\(357\) | −1.26112e6 | −0.523706 | ||||||||
\(358\) | −1.52966e6 | −0.630793 | ||||||||
\(359\) | −1.72475e6 | −0.706300 | −0.353150 | − | 0.935567i | \(-0.614889\pi\) | ||||
−0.353150 | + | 0.935567i | \(0.614889\pi\) | |||||||
\(360\) | 996309. | 0.405170 | ||||||||
\(361\) | −2.01882e6 | −0.815322 | ||||||||
\(362\) | −449096. | −0.180122 | ||||||||
\(363\) | −191315. | −0.0762048 | ||||||||
\(364\) | −425605. | −0.168366 | ||||||||
\(365\) | 4.83607e6 | 1.90003 | ||||||||
\(366\) | −370488. | −0.144568 | ||||||||
\(367\) | −2.48879e6 | −0.964547 | −0.482274 | − | 0.876021i | \(-0.660189\pi\) | ||||
−0.482274 | + | 0.876021i | \(0.660189\pi\) | |||||||
\(368\) | 295872. | 0.113890 | ||||||||
\(369\) | −448412. | −0.171440 | ||||||||
\(370\) | −123381. | −0.0468537 | ||||||||
\(371\) | 4.74924e6 | 1.79139 | ||||||||
\(372\) | −424593. | −0.159080 | ||||||||
\(373\) | 4.73910e6 | 1.76370 | 0.881848 | − | 0.471534i | \(-0.156299\pi\) | ||||
0.881848 | + | 0.471534i | \(0.156299\pi\) | |||||||
\(374\) | 996358. | 0.368329 | ||||||||
\(375\) | 148510. | 0.0545352 | ||||||||
\(376\) | 444789. | 0.162250 | ||||||||
\(377\) | 303166. | 0.109857 | ||||||||
\(378\) | 318974. | 0.114822 | ||||||||
\(379\) | −1.94813e6 | −0.696658 | −0.348329 | − | 0.937372i | \(-0.613251\pi\) | ||||
−0.348329 | + | 0.937372i | \(0.613251\pi\) | |||||||
\(380\) | −1.34272e6 | −0.477009 | ||||||||
\(381\) | 857376. | 0.302593 | ||||||||
\(382\) | 155967. | 0.0546859 | ||||||||
\(383\) | 4.90807e6 | 1.70967 | 0.854837 | − | 0.518896i | \(-0.173657\pi\) | ||||
0.854837 | + | 0.518896i | \(0.173657\pi\) | |||||||
\(384\) | 1.60985e6 | 0.557132 | ||||||||
\(385\) | −5.56070e6 | −1.91195 | ||||||||
\(386\) | 2.71074e6 | 0.926017 | ||||||||
\(387\) | −559431. | −0.189875 | ||||||||
\(388\) | −4.31944e6 | −1.45663 | ||||||||
\(389\) | −3.64955e6 | −1.22283 | −0.611414 | − | 0.791311i | \(-0.709399\pi\) | ||||
−0.611414 | + | 0.791311i | \(0.709399\pi\) | |||||||
\(390\) | −207384. | −0.0690419 | ||||||||
\(391\) | −677397. | −0.224079 | ||||||||
\(392\) | −1.44935e6 | −0.476385 | ||||||||
\(393\) | 2.54781e6 | 0.832119 | ||||||||
\(394\) | 2.60370e6 | 0.844989 | ||||||||
\(395\) | 4.36075e6 | 1.40627 | ||||||||
\(396\) | 854714. | 0.273894 | ||||||||
\(397\) | −3.33365e6 | −1.06156 | −0.530779 | − | 0.847510i | \(-0.678101\pi\) | ||||
−0.530779 | + | 0.847510i | \(0.678101\pi\) | |||||||
\(398\) | 1.68241e6 | 0.532382 | ||||||||
\(399\) | −986506. | −0.310218 | ||||||||
\(400\) | 1.25749e6 | 0.392965 | ||||||||
\(401\) | 184478. | 0.0572906 | 0.0286453 | − | 0.999590i | \(-0.490881\pi\) | ||||
0.0286453 | + | 0.999590i | \(0.490881\pi\) | |||||||
\(402\) | 911076. | 0.281183 | ||||||||
\(403\) | 202818. | 0.0622077 | ||||||||
\(404\) | 4.40975e6 | 1.34419 | ||||||||
\(405\) | −527146. | −0.159696 | ||||||||
\(406\) | 1.24853e6 | 0.375910 | ||||||||
\(407\) | −242900. | −0.0726845 | ||||||||
\(408\) | −1.19108e6 | −0.354234 | ||||||||
\(409\) | −1.84713e6 | −0.545996 | −0.272998 | − | 0.962015i | \(-0.588015\pi\) | ||||
−0.272998 | + | 0.962015i | \(0.588015\pi\) | |||||||
\(410\) | 1.20065e6 | 0.352741 | ||||||||
\(411\) | 421567. | 0.123101 | ||||||||
\(412\) | −3.13836e6 | −0.910877 | ||||||||
\(413\) | −564247. | −0.162778 | ||||||||
\(414\) | 171333. | 0.0491292 | ||||||||
\(415\) | −4.75740e6 | −1.35597 | ||||||||
\(416\) | −628771. | −0.178139 | ||||||||
\(417\) | −3.17176e6 | −0.893224 | ||||||||
\(418\) | 779394. | 0.218181 | ||||||||
\(419\) | 3.58683e6 | 0.998105 | 0.499052 | − | 0.866572i | \(-0.333682\pi\) | ||||
0.499052 | + | 0.866572i | \(0.333682\pi\) | |||||||
\(420\) | 2.89669e6 | 0.801269 | ||||||||
\(421\) | 1.55188e6 | 0.426729 | 0.213364 | − | 0.976973i | \(-0.431558\pi\) | ||||
0.213364 | + | 0.976973i | \(0.431558\pi\) | |||||||
\(422\) | 2.16030e6 | 0.590516 | ||||||||
\(423\) | −235338. | −0.0639500 | ||||||||
\(424\) | 4.48546e6 | 1.21169 | ||||||||
\(425\) | −2.87901e6 | −0.773163 | ||||||||
\(426\) | −788139. | −0.210416 | ||||||||
\(427\) | −2.47192e6 | −0.656092 | ||||||||
\(428\) | 1.73499e6 | 0.457812 | ||||||||
\(429\) | −408276. | −0.107105 | ||||||||
\(430\) | 1.49791e6 | 0.390673 | ||||||||
\(431\) | 3.66890e6 | 0.951356 | 0.475678 | − | 0.879619i | \(-0.342203\pi\) | ||||
0.475678 | + | 0.879619i | \(0.342203\pi\) | |||||||
\(432\) | −275257. | −0.0709624 | ||||||||
\(433\) | −17511.1 | −0.00448842 | −0.00224421 | − | 0.999997i | \(-0.500714\pi\) | ||||
−0.00224421 | + | 0.999997i | \(0.500714\pi\) | |||||||
\(434\) | 835268. | 0.212864 | ||||||||
\(435\) | −2.06336e6 | −0.522819 | ||||||||
\(436\) | 1.23744e6 | 0.311750 | ||||||||
\(437\) | −529889. | −0.132734 | ||||||||
\(438\) | 1.46230e6 | 0.364209 | ||||||||
\(439\) | 6.13137e6 | 1.51844 | 0.759218 | − | 0.650837i | \(-0.225582\pi\) | ||||
0.759218 | + | 0.650837i | \(0.225582\pi\) | |||||||
\(440\) | −5.25185e6 | −1.29324 | ||||||||
\(441\) | 766850. | 0.187765 | ||||||||
\(442\) | 247925. | 0.0603622 | ||||||||
\(443\) | −2.69068e6 | −0.651408 | −0.325704 | − | 0.945472i | \(-0.605601\pi\) | ||||
−0.325704 | + | 0.945472i | \(0.605601\pi\) | |||||||
\(444\) | 126532. | 0.0304609 | ||||||||
\(445\) | 4.66983e6 | 1.11789 | ||||||||
\(446\) | −526532. | −0.125340 | ||||||||
\(447\) | 1.53665e6 | 0.363754 | ||||||||
\(448\) | −630966. | −0.148529 | ||||||||
\(449\) | −4.36660e6 | −1.02218 | −0.511091 | − | 0.859527i | \(-0.670758\pi\) | ||||
−0.511091 | + | 0.859527i | \(0.670758\pi\) | |||||||
\(450\) | 728183. | 0.169516 | ||||||||
\(451\) | 2.36372e6 | 0.547210 | ||||||||
\(452\) | 2.55036e6 | 0.587158 | ||||||||
\(453\) | −463792. | −0.106189 | ||||||||
\(454\) | −2.12646e6 | −0.484193 | ||||||||
\(455\) | −1.38368e6 | −0.313333 | ||||||||
\(456\) | −931713. | −0.209831 | ||||||||
\(457\) | −7.30210e6 | −1.63553 | −0.817763 | − | 0.575555i | \(-0.804786\pi\) | ||||
−0.817763 | + | 0.575555i | \(0.804786\pi\) | |||||||
\(458\) | 3.03167e6 | 0.675332 | ||||||||
\(459\) | 630198. | 0.139619 | ||||||||
\(460\) | 1.55592e6 | 0.342841 | ||||||||
\(461\) | −7.01104e6 | −1.53649 | −0.768246 | − | 0.640155i | \(-0.778870\pi\) | ||||
−0.768246 | + | 0.640155i | \(0.778870\pi\) | |||||||
\(462\) | −1.68141e6 | −0.366495 | ||||||||
\(463\) | 1.31573e6 | 0.285243 | 0.142621 | − | 0.989777i | \(-0.454447\pi\) | ||||
0.142621 | + | 0.989777i | \(0.454447\pi\) | |||||||
\(464\) | −1.07741e6 | −0.232320 | ||||||||
\(465\) | −1.38039e6 | −0.296053 | ||||||||
\(466\) | 3.17671e6 | 0.677662 | ||||||||
\(467\) | 3.13078e6 | 0.664293 | 0.332147 | − | 0.943228i | \(-0.392227\pi\) | ||||
0.332147 | + | 0.943228i | \(0.392227\pi\) | |||||||
\(468\) | 212680. | 0.0448861 | ||||||||
\(469\) | 6.07876e6 | 1.27610 | ||||||||
\(470\) | 630129. | 0.131578 | ||||||||
\(471\) | 569894. | 0.118370 | ||||||||
\(472\) | −532908. | −0.110102 | ||||||||
\(473\) | 2.94893e6 | 0.606054 | ||||||||
\(474\) | 1.31858e6 | 0.269562 | ||||||||
\(475\) | −2.25209e6 | −0.457985 | ||||||||
\(476\) | −3.46296e6 | −0.700536 | ||||||||
\(477\) | −2.37325e6 | −0.477582 | ||||||||
\(478\) | 126831. | 0.0253896 | ||||||||
\(479\) | 7.00448e6 | 1.39488 | 0.697441 | − | 0.716642i | \(-0.254322\pi\) | ||||
0.697441 | + | 0.716642i | \(0.254322\pi\) | |||||||
\(480\) | 4.27945e6 | 0.847782 | ||||||||
\(481\) | −60441.3 | −0.0119116 | ||||||||
\(482\) | 4.44085e6 | 0.870660 | ||||||||
\(483\) | 1.14315e6 | 0.222963 | ||||||||
\(484\) | −525338. | −0.101935 | ||||||||
\(485\) | −1.40429e7 | −2.71082 | ||||||||
\(486\) | −159395. | −0.0306115 | ||||||||
\(487\) | 2.09435e6 | 0.400154 | 0.200077 | − | 0.979780i | \(-0.435881\pi\) | ||||
0.200077 | + | 0.979780i | \(0.435881\pi\) | |||||||
\(488\) | −2.33463e6 | −0.443780 | ||||||||
\(489\) | −2.24011e6 | −0.423639 | ||||||||
\(490\) | −2.05328e6 | −0.386330 | ||||||||
\(491\) | −4.28066e6 | −0.801322 | −0.400661 | − | 0.916226i | \(-0.631219\pi\) | ||||
−0.400661 | + | 0.916226i | \(0.631219\pi\) | |||||||
\(492\) | −1.23131e6 | −0.229327 | ||||||||
\(493\) | 2.46673e6 | 0.457092 | ||||||||
\(494\) | 193938. | 0.0357557 | ||||||||
\(495\) | 2.77875e6 | 0.509725 | ||||||||
\(496\) | −720789. | −0.131554 | ||||||||
\(497\) | −5.25852e6 | −0.954932 | ||||||||
\(498\) | −1.43851e6 | −0.259921 | ||||||||
\(499\) | −5.62839e6 | −1.01189 | −0.505944 | − | 0.862566i | \(-0.668856\pi\) | ||||
−0.505944 | + | 0.862566i | \(0.668856\pi\) | |||||||
\(500\) | 407798. | 0.0729491 | ||||||||
\(501\) | 6.24316e6 | 1.11125 | ||||||||
\(502\) | 72231.0 | 0.0127928 | ||||||||
\(503\) | −2.46000e6 | −0.433526 | −0.216763 | − | 0.976224i | \(-0.569550\pi\) | ||||
−0.216763 | + | 0.976224i | \(0.569550\pi\) | |||||||
\(504\) | 2.01001e6 | 0.352470 | ||||||||
\(505\) | 1.43365e7 | 2.50158 | ||||||||
\(506\) | −903148. | −0.156813 | ||||||||
\(507\) | 3.24004e6 | 0.559798 | ||||||||
\(508\) | 2.35430e6 | 0.404764 | ||||||||
\(509\) | 7.82777e6 | 1.33919 | 0.669597 | − | 0.742724i | \(-0.266467\pi\) | ||||
0.669597 | + | 0.742724i | \(0.266467\pi\) | |||||||
\(510\) | −1.68739e6 | −0.287270 | ||||||||
\(511\) | 9.75656e6 | 1.65289 | ||||||||
\(512\) | 4.08430e6 | 0.688562 | ||||||||
\(513\) | 492969. | 0.0827039 | ||||||||
\(514\) | 3.96084e6 | 0.661272 | ||||||||
\(515\) | −1.02031e7 | −1.69517 | ||||||||
\(516\) | −1.53616e6 | −0.253987 | ||||||||
\(517\) | 1.24054e6 | 0.204119 | ||||||||
\(518\) | −248916. | −0.0407595 | ||||||||
\(519\) | 2.80699e6 | 0.457428 | ||||||||
\(520\) | −1.30683e6 | −0.211938 | ||||||||
\(521\) | −9.96359e6 | −1.60813 | −0.804066 | − | 0.594541i | \(-0.797334\pi\) | ||||
−0.804066 | + | 0.594541i | \(0.797334\pi\) | |||||||
\(522\) | −623906. | −0.100217 | ||||||||
\(523\) | 4.30575e6 | 0.688327 | 0.344164 | − | 0.938910i | \(-0.388163\pi\) | ||||
0.344164 | + | 0.938910i | \(0.388163\pi\) | |||||||
\(524\) | 6.99611e6 | 1.11309 | ||||||||
\(525\) | 4.85849e6 | 0.769313 | ||||||||
\(526\) | 2.62522e6 | 0.413716 | ||||||||
\(527\) | 1.65024e6 | 0.258834 | ||||||||
\(528\) | 1.45096e6 | 0.226502 | ||||||||
\(529\) | −5.82232e6 | −0.904600 | ||||||||
\(530\) | 6.35451e6 | 0.982636 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | −2.70888e6 | −0.414964 | ||||||||
\(533\) | 588167. | 0.0896774 | ||||||||
\(534\) | 1.41203e6 | 0.214285 | ||||||||
\(535\) | 5.64059e6 | 0.852001 | ||||||||
\(536\) | 5.74114e6 | 0.863149 | ||||||||
\(537\) | 5.10005e6 | 0.763201 | ||||||||
\(538\) | −1.18820e6 | −0.176984 | ||||||||
\(539\) | −4.04230e6 | −0.599317 | ||||||||
\(540\) | −1.44751e6 | −0.213617 | ||||||||
\(541\) | 340272. | 0.0499843 | 0.0249922 | − | 0.999688i | \(-0.492044\pi\) | ||||
0.0249922 | + | 0.999688i | \(0.492044\pi\) | |||||||
\(542\) | 944959. | 0.138170 | ||||||||
\(543\) | 1.49734e6 | 0.217931 | ||||||||
\(544\) | −5.11604e6 | −0.741202 | ||||||||
\(545\) | 4.02301e6 | 0.580176 | ||||||||
\(546\) | −418388. | −0.0600617 | ||||||||
\(547\) | −1.33663e7 | −1.91004 | −0.955021 | − | 0.296540i | \(-0.904167\pi\) | ||||
−0.955021 | + | 0.296540i | \(0.904167\pi\) | |||||||
\(548\) | 1.15759e6 | 0.164666 | ||||||||
\(549\) | 1.23525e6 | 0.174914 | ||||||||
\(550\) | −3.83848e6 | −0.541068 | ||||||||
\(551\) | 1.92958e6 | 0.270760 | ||||||||
\(552\) | 1.07965e6 | 0.150812 | ||||||||
\(553\) | 8.79763e6 | 1.22336 | ||||||||
\(554\) | −389368. | −0.0538996 | ||||||||
\(555\) | 411366. | 0.0566886 | ||||||||
\(556\) | −8.70945e6 | −1.19482 | ||||||||
\(557\) | −5.96149e6 | −0.814174 | −0.407087 | − | 0.913389i | \(-0.633455\pi\) | ||||
−0.407087 | + | 0.913389i | \(0.633455\pi\) | |||||||
\(558\) | −417393. | −0.0567492 | ||||||||
\(559\) | 733787. | 0.0993208 | ||||||||
\(560\) | 4.91741e6 | 0.662623 | ||||||||
\(561\) | −3.32197e6 | −0.445644 | ||||||||
\(562\) | −2.20911e6 | −0.295037 | ||||||||
\(563\) | 7.64380e6 | 1.01634 | 0.508169 | − | 0.861257i | \(-0.330322\pi\) | ||||
0.508169 | + | 0.861257i | \(0.330322\pi\) | |||||||
\(564\) | −646222. | −0.0855428 | ||||||||
\(565\) | 8.29143e6 | 1.09272 | ||||||||
\(566\) | 3.11283e6 | 0.408427 | ||||||||
\(567\) | −1.06350e6 | −0.138924 | ||||||||
\(568\) | −4.96645e6 | −0.645915 | ||||||||
\(569\) | −2.06870e6 | −0.267865 | −0.133933 | − | 0.990990i | \(-0.542761\pi\) | ||||
−0.133933 | + | 0.990990i | \(0.542761\pi\) | |||||||
\(570\) | −1.31995e6 | −0.170165 | ||||||||
\(571\) | 1.48686e6 | 0.190845 | 0.0954224 | − | 0.995437i | \(-0.469580\pi\) | ||||
0.0954224 | + | 0.995437i | \(0.469580\pi\) | |||||||
\(572\) | −1.12110e6 | −0.143270 | ||||||||
\(573\) | −520013. | −0.0661649 | ||||||||
\(574\) | 2.42226e6 | 0.306860 | ||||||||
\(575\) | 2.60968e6 | 0.329168 | ||||||||
\(576\) | 315301. | 0.0395977 | ||||||||
\(577\) | −2.80446e6 | −0.350679 | −0.175340 | − | 0.984508i | \(-0.556102\pi\) | ||||
−0.175340 | + | 0.984508i | \(0.556102\pi\) | |||||||
\(578\) | −1.81546e6 | −0.226030 | ||||||||
\(579\) | −9.03789e6 | −1.12039 | ||||||||
\(580\) | −5.66585e6 | −0.699351 | ||||||||
\(581\) | −9.59786e6 | −1.17960 | ||||||||
\(582\) | −4.24619e6 | −0.519627 | ||||||||
\(583\) | 1.25101e7 | 1.52437 | ||||||||
\(584\) | 9.21466e6 | 1.11801 | ||||||||
\(585\) | 691440. | 0.0835343 | ||||||||
\(586\) | −3.87212e6 | −0.465806 | ||||||||
\(587\) | −6.90944e6 | −0.827652 | −0.413826 | − | 0.910356i | \(-0.635808\pi\) | ||||
−0.413826 | + | 0.910356i | \(0.635808\pi\) | |||||||
\(588\) | 2.10572e6 | 0.251164 | ||||||||
\(589\) | 1.29089e6 | 0.153321 | ||||||||
\(590\) | −754966. | −0.0892888 | ||||||||
\(591\) | −8.68104e6 | −1.02236 | ||||||||
\(592\) | 214801. | 0.0251902 | ||||||||
\(593\) | −4.57203e6 | −0.533915 | −0.266958 | − | 0.963708i | \(-0.586018\pi\) | ||||
−0.266958 | + | 0.963708i | \(0.586018\pi\) | |||||||
\(594\) | 840220. | 0.0977073 | ||||||||
\(595\) | −1.12584e7 | −1.30372 | ||||||||
\(596\) | 4.21955e6 | 0.486576 | ||||||||
\(597\) | −5.60934e6 | −0.644133 | ||||||||
\(598\) | −224732. | −0.0256987 | ||||||||
\(599\) | 3.76968e6 | 0.429277 | 0.214638 | − | 0.976694i | \(-0.431143\pi\) | ||||
0.214638 | + | 0.976694i | \(0.431143\pi\) | |||||||
\(600\) | 4.58864e6 | 0.520362 | ||||||||
\(601\) | 4.52282e6 | 0.510768 | 0.255384 | − | 0.966840i | \(-0.417798\pi\) | ||||
0.255384 | + | 0.966840i | \(0.417798\pi\) | |||||||
\(602\) | 3.02196e6 | 0.339858 | ||||||||
\(603\) | −3.03763e6 | −0.340206 | ||||||||
\(604\) | −1.27354e6 | −0.142043 | ||||||||
\(605\) | −1.70792e6 | −0.189705 | ||||||||
\(606\) | 4.33497e6 | 0.479518 | ||||||||
\(607\) | 5.43182e6 | 0.598376 | 0.299188 | − | 0.954194i | \(-0.403284\pi\) | ||||
0.299188 | + | 0.954194i | \(0.403284\pi\) | |||||||
\(608\) | −4.00199e6 | −0.439053 | ||||||||
\(609\) | −4.16274e6 | −0.454817 | ||||||||
\(610\) | −3.30744e6 | −0.359888 | ||||||||
\(611\) | 308685. | 0.0334512 | ||||||||
\(612\) | 1.73048e6 | 0.186762 | ||||||||
\(613\) | −4.97549e6 | −0.534791 | −0.267396 | − | 0.963587i | \(-0.586163\pi\) | ||||
−0.267396 | + | 0.963587i | \(0.586163\pi\) | |||||||
\(614\) | −3.80108e6 | −0.406899 | ||||||||
\(615\) | −4.00309e6 | −0.426784 | ||||||||
\(616\) | −1.05954e7 | −1.12503 | ||||||||
\(617\) | −1.15456e7 | −1.22097 | −0.610483 | − | 0.792029i | \(-0.709025\pi\) | ||||
−0.610483 | + | 0.792029i | \(0.709025\pi\) | |||||||
\(618\) | −3.08514e6 | −0.324940 | ||||||||
\(619\) | −7.93466e6 | −0.832341 | −0.416171 | − | 0.909287i | \(-0.636628\pi\) | ||||
−0.416171 | + | 0.909287i | \(0.636628\pi\) | |||||||
\(620\) | −3.79045e6 | −0.396015 | ||||||||
\(621\) | −571243. | −0.0594418 | ||||||||
\(622\) | −1.09585e6 | −0.113573 | ||||||||
\(623\) | 9.42118e6 | 0.972490 | ||||||||
\(624\) | 361045. | 0.0371193 | ||||||||
\(625\) | −9.08164e6 | −0.929960 | ||||||||
\(626\) | −6.17576e6 | −0.629875 | ||||||||
\(627\) | −2.59859e6 | −0.263979 | ||||||||
\(628\) | 1.56489e6 | 0.158338 | ||||||||
\(629\) | −491784. | −0.0495619 | ||||||||
\(630\) | 2.84757e6 | 0.285840 | ||||||||
\(631\) | 1.48499e6 | 0.148474 | 0.0742370 | − | 0.997241i | \(-0.476348\pi\) | ||||
0.0742370 | + | 0.997241i | \(0.476348\pi\) | |||||||
\(632\) | 8.30899e6 | 0.827476 | ||||||||
\(633\) | −7.20267e6 | −0.714470 | ||||||||
\(634\) | −4.64347e6 | −0.458796 | ||||||||
\(635\) | 7.65402e6 | 0.753278 | ||||||||
\(636\) | −6.51680e6 | −0.638839 | ||||||||
\(637\) | −1.00585e6 | −0.0982168 | ||||||||
\(638\) | 3.28880e6 | 0.319879 | ||||||||
\(639\) | 2.62774e6 | 0.254584 | ||||||||
\(640\) | 1.43716e7 | 1.38693 | ||||||||
\(641\) | −1.80343e7 | −1.73362 | −0.866811 | − | 0.498636i | \(-0.833834\pi\) | ||||
−0.866811 | + | 0.498636i | \(0.833834\pi\) | |||||||
\(642\) | 1.70557e6 | 0.163317 | ||||||||
\(643\) | 6.54380e6 | 0.624170 | 0.312085 | − | 0.950054i | \(-0.398973\pi\) | ||||
0.312085 | + | 0.950054i | \(0.398973\pi\) | |||||||
\(644\) | 3.13900e6 | 0.298248 | ||||||||
\(645\) | −4.99418e6 | −0.472678 | ||||||||
\(646\) | 1.57799e6 | 0.148773 | ||||||||
\(647\) | −3.41879e6 | −0.321078 | −0.160539 | − | 0.987029i | \(-0.551323\pi\) | ||||
−0.160539 | + | 0.987029i | \(0.551323\pi\) | |||||||
\(648\) | −1.00443e6 | −0.0939681 | ||||||||
\(649\) | −1.48630e6 | −0.138515 | ||||||||
\(650\) | −955134. | −0.0886709 | ||||||||
\(651\) | −2.78488e6 | −0.257545 | ||||||||
\(652\) | −6.15118e6 | −0.566682 | ||||||||
\(653\) | −4.85652e6 | −0.445700 | −0.222850 | − | 0.974853i | \(-0.571536\pi\) | ||||
−0.222850 | + | 0.974853i | \(0.571536\pi\) | |||||||
\(654\) | 1.21645e6 | 0.111212 | ||||||||
\(655\) | 2.27450e7 | 2.07149 | ||||||||
\(656\) | −2.09027e6 | −0.189646 | ||||||||
\(657\) | −4.87547e6 | −0.440659 | ||||||||
\(658\) | 1.27126e6 | 0.114464 | ||||||||
\(659\) | 2.71649e6 | 0.243665 | 0.121833 | − | 0.992551i | \(-0.461123\pi\) | ||||
0.121833 | + | 0.992551i | \(0.461123\pi\) | |||||||
\(660\) | 7.63025e6 | 0.681835 | ||||||||
\(661\) | 9.13072e6 | 0.812833 | 0.406417 | − | 0.913688i | \(-0.366778\pi\) | ||||
0.406417 | + | 0.913688i | \(0.366778\pi\) | |||||||
\(662\) | −3.33164e6 | −0.295470 | ||||||||
\(663\) | −826610. | −0.0730327 | ||||||||
\(664\) | −9.06478e6 | −0.797879 | ||||||||
\(665\) | −8.80680e6 | −0.772261 | ||||||||
\(666\) | 124386. | 0.0108664 | ||||||||
\(667\) | −2.23597e6 | −0.194603 | ||||||||
\(668\) | 1.71433e7 | 1.48646 | ||||||||
\(669\) | 1.75552e6 | 0.151649 | ||||||||
\(670\) | 8.13342e6 | 0.699981 | ||||||||
\(671\) | −6.51137e6 | −0.558298 | ||||||||
\(672\) | 8.63360e6 | 0.737512 | ||||||||
\(673\) | 1.84820e7 | 1.57294 | 0.786470 | − | 0.617629i | \(-0.211906\pi\) | ||||
0.786470 | + | 0.617629i | \(0.211906\pi\) | |||||||
\(674\) | −4.46160e6 | −0.378304 | ||||||||
\(675\) | −2.42784e6 | −0.205098 | ||||||||
\(676\) | 8.89695e6 | 0.748815 | ||||||||
\(677\) | −1.19598e6 | −0.100289 | −0.0501444 | − | 0.998742i | \(-0.515968\pi\) | ||||
−0.0501444 | + | 0.998742i | \(0.515968\pi\) | |||||||
\(678\) | 2.50711e6 | 0.209459 | ||||||||
\(679\) | −2.83309e7 | −2.35823 | ||||||||
\(680\) | −1.06331e7 | −0.881833 | ||||||||
\(681\) | 7.08987e6 | 0.585828 | ||||||||
\(682\) | 2.20021e6 | 0.181135 | ||||||||
\(683\) | −3.97416e6 | −0.325982 | −0.162991 | − | 0.986628i | \(-0.552114\pi\) | ||||
−0.162991 | + | 0.986628i | \(0.552114\pi\) | |||||||
\(684\) | 1.35366e6 | 0.110629 | ||||||||
\(685\) | 3.76344e6 | 0.306449 | ||||||||
\(686\) | 3.21149e6 | 0.260553 | ||||||||
\(687\) | −1.01079e7 | −0.817090 | ||||||||
\(688\) | −2.60778e6 | −0.210039 | ||||||||
\(689\) | 3.11292e6 | 0.249816 | ||||||||
\(690\) | 1.52953e6 | 0.122303 | ||||||||
\(691\) | 2.02655e7 | 1.61459 | 0.807296 | − | 0.590147i | \(-0.200930\pi\) | ||||
0.807296 | + | 0.590147i | \(0.200930\pi\) | |||||||
\(692\) | 7.70781e6 | 0.611879 | ||||||||
\(693\) | 5.60601e6 | 0.443425 | ||||||||
\(694\) | −4612.11 | −0.000363497 0 | ||||||||
\(695\) | −2.83152e7 | −2.22360 | ||||||||
\(696\) | −3.93153e6 | −0.307637 | ||||||||
\(697\) | 4.78566e6 | 0.373130 | ||||||||
\(698\) | −1.10611e7 | −0.859326 | ||||||||
\(699\) | −1.05915e7 | −0.819908 | ||||||||
\(700\) | 1.33411e7 | 1.02907 | ||||||||
\(701\) | −4.25157e6 | −0.326779 | −0.163390 | − | 0.986562i | \(-0.552243\pi\) | ||||
−0.163390 | + | 0.986562i | \(0.552243\pi\) | |||||||
\(702\) | 209073. | 0.0160124 | ||||||||
\(703\) | −384695. | −0.0293581 | ||||||||
\(704\) | −1.66205e6 | −0.126390 | ||||||||
\(705\) | −2.10092e6 | −0.159198 | ||||||||
\(706\) | −1.08517e7 | −0.819380 | ||||||||
\(707\) | 2.89233e7 | 2.17620 | ||||||||
\(708\) | 774246. | 0.0580492 | ||||||||
\(709\) | 1.60414e6 | 0.119847 | 0.0599234 | − | 0.998203i | \(-0.480914\pi\) | ||||
0.0599234 | + | 0.998203i | \(0.480914\pi\) | |||||||
\(710\) | −7.03593e6 | −0.523812 | ||||||||
\(711\) | −4.39628e6 | −0.326145 | ||||||||
\(712\) | 8.89791e6 | 0.657791 | ||||||||
\(713\) | −1.49586e6 | −0.110196 | ||||||||
\(714\) | −3.40424e6 | −0.249905 | ||||||||
\(715\) | −3.64479e6 | −0.266629 | ||||||||
\(716\) | 1.40044e7 | 1.02090 | ||||||||
\(717\) | −422869. | −0.0307191 | ||||||||
\(718\) | −4.65573e6 | −0.337036 | ||||||||
\(719\) | 3.70513e6 | 0.267289 | 0.133645 | − | 0.991029i | \(-0.457332\pi\) | ||||
0.133645 | + | 0.991029i | \(0.457332\pi\) | |||||||
\(720\) | −2.45729e6 | −0.176655 | ||||||||
\(721\) | −2.05843e7 | −1.47468 | ||||||||
\(722\) | −5.44953e6 | −0.389060 | ||||||||
\(723\) | −1.48063e7 | −1.05342 | ||||||||
\(724\) | 4.11158e6 | 0.291516 | ||||||||
\(725\) | −9.50309e6 | −0.671460 | ||||||||
\(726\) | −516430. | −0.0363638 | ||||||||
\(727\) | 9.76045e6 | 0.684910 | 0.342455 | − | 0.939534i | \(-0.388742\pi\) | ||||
0.342455 | + | 0.939534i | \(0.388742\pi\) | |||||||
\(728\) | −2.63647e6 | −0.184371 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.30543e7 | 0.906666 | ||||||||
\(731\) | 5.97050e6 | 0.413254 | ||||||||
\(732\) | 3.39191e6 | 0.233973 | ||||||||
\(733\) | 6.56659e6 | 0.451419 | 0.225710 | − | 0.974195i | \(-0.427530\pi\) | ||||
0.225710 | + | 0.974195i | \(0.427530\pi\) | |||||||
\(734\) | −6.71817e6 | −0.460268 | ||||||||
\(735\) | 6.84587e6 | 0.467424 | ||||||||
\(736\) | 4.63743e6 | 0.315561 | ||||||||
\(737\) | 1.60123e7 | 1.08589 | ||||||||
\(738\) | −1.21043e6 | −0.0818086 | ||||||||
\(739\) | −2.02187e7 | −1.36189 | −0.680946 | − | 0.732333i | \(-0.738431\pi\) | ||||
−0.680946 | + | 0.732333i | \(0.738431\pi\) | |||||||
\(740\) | 1.12958e6 | 0.0758297 | ||||||||
\(741\) | −646611. | −0.0432611 | ||||||||
\(742\) | 1.28200e7 | 0.854825 | ||||||||
\(743\) | 5.51074e6 | 0.366216 | 0.183108 | − | 0.983093i | \(-0.441384\pi\) | ||||
0.183108 | + | 0.983093i | \(0.441384\pi\) | |||||||
\(744\) | −2.63020e6 | −0.174203 | ||||||||
\(745\) | 1.37181e7 | 0.905532 | ||||||||
\(746\) | 1.27926e7 | 0.841610 | ||||||||
\(747\) | 4.79616e6 | 0.314480 | ||||||||
\(748\) | −9.12190e6 | −0.596117 | ||||||||
\(749\) | 1.13797e7 | 0.741182 | ||||||||
\(750\) | 400883. | 0.0260234 | ||||||||
\(751\) | −1.06252e6 | −0.0687445 | −0.0343723 | − | 0.999409i | \(-0.510943\pi\) | ||||
−0.0343723 | + | 0.999409i | \(0.510943\pi\) | |||||||
\(752\) | −1.09703e6 | −0.0707412 | ||||||||
\(753\) | −240826. | −0.0154781 | ||||||||
\(754\) | 818356. | 0.0524221 | ||||||||
\(755\) | −4.14040e6 | −0.264347 | ||||||||
\(756\) | −2.92029e6 | −0.185832 | ||||||||
\(757\) | −2.03351e7 | −1.28976 | −0.644878 | − | 0.764285i | \(-0.723092\pi\) | ||||
−0.644878 | + | 0.764285i | \(0.723092\pi\) | |||||||
\(758\) | −5.25872e6 | −0.332435 | ||||||||
\(759\) | 3.01120e6 | 0.189729 | ||||||||
\(760\) | −8.31765e6 | −0.522356 | ||||||||
\(761\) | −4.03059e6 | −0.252294 | −0.126147 | − | 0.992012i | \(-0.540261\pi\) | ||||
−0.126147 | + | 0.992012i | \(0.540261\pi\) | |||||||
\(762\) | 2.31437e6 | 0.144393 | ||||||||
\(763\) | 8.11626e6 | 0.504713 | ||||||||
\(764\) | −1.42792e6 | −0.0885056 | ||||||||
\(765\) | 5.62595e6 | 0.347570 | ||||||||
\(766\) | 1.32487e7 | 0.815832 | ||||||||
\(767\) | −369839. | −0.0226999 | ||||||||
\(768\) | 5.46666e6 | 0.334440 | ||||||||
\(769\) | 1.40981e7 | 0.859697 | 0.429848 | − | 0.902901i | \(-0.358567\pi\) | ||||
0.429848 | + | 0.902901i | \(0.358567\pi\) | |||||||
\(770\) | −1.50104e7 | −0.912357 | ||||||||
\(771\) | −1.32059e7 | −0.800077 | ||||||||
\(772\) | −2.48175e7 | −1.49870 | ||||||||
\(773\) | 2.73980e7 | 1.64919 | 0.824593 | − | 0.565727i | \(-0.191404\pi\) | ||||
0.824593 | + | 0.565727i | \(0.191404\pi\) | |||||||
\(774\) | −1.51011e6 | −0.0906058 | ||||||||
\(775\) | −6.35757e6 | −0.380222 | ||||||||
\(776\) | −2.67573e7 | −1.59510 | ||||||||
\(777\) | 829914. | 0.0493152 | ||||||||
\(778\) | −9.85149e6 | −0.583516 | ||||||||
\(779\) | 3.74355e6 | 0.221024 | ||||||||
\(780\) | 1.89865e6 | 0.111740 | ||||||||
\(781\) | −1.38516e7 | −0.812594 | ||||||||
\(782\) | −1.82855e6 | −0.106927 | ||||||||
\(783\) | 2.08017e6 | 0.121254 | ||||||||
\(784\) | 3.57467e6 | 0.207704 | ||||||||
\(785\) | 5.08759e6 | 0.294671 | ||||||||
\(786\) | 6.87748e6 | 0.397075 | ||||||||
\(787\) | −4.27413e6 | −0.245986 | −0.122993 | − | 0.992408i | \(-0.539249\pi\) | ||||
−0.122993 | + | 0.992408i | \(0.539249\pi\) | |||||||
\(788\) | −2.38376e7 | −1.36756 | ||||||||
\(789\) | −8.75279e6 | −0.500558 | ||||||||
\(790\) | 1.17713e7 | 0.671051 | ||||||||
\(791\) | 1.67276e7 | 0.950590 | ||||||||
\(792\) | 5.29464e6 | 0.299932 | ||||||||
\(793\) | −1.62023e6 | −0.0914945 | ||||||||
\(794\) | −8.99875e6 | −0.506560 | ||||||||
\(795\) | −2.11867e7 | −1.18890 | ||||||||
\(796\) | −1.54029e7 | −0.861626 | ||||||||
\(797\) | −1.91541e7 | −1.06811 | −0.534056 | − | 0.845449i | \(-0.679333\pi\) | ||||
−0.534056 | + | 0.845449i | \(0.679333\pi\) | |||||||
\(798\) | −2.66294e6 | −0.148032 | ||||||||
\(799\) | 2.51163e6 | 0.139184 | ||||||||
\(800\) | 1.97096e7 | 1.08881 | ||||||||
\(801\) | −4.70787e6 | −0.259265 | ||||||||
\(802\) | 497974. | 0.0273383 | ||||||||
\(803\) | 2.57001e7 | 1.40652 | ||||||||
\(804\) | −8.34113e6 | −0.455077 | ||||||||
\(805\) | 1.02052e7 | 0.555047 | ||||||||
\(806\) | 547481. | 0.0296846 | ||||||||
\(807\) | 3.96160e6 | 0.214135 | ||||||||
\(808\) | 2.73168e7 | 1.47198 | ||||||||
\(809\) | 3.40439e6 | 0.182881 | 0.0914405 | − | 0.995811i | \(-0.470853\pi\) | ||||
0.0914405 | + | 0.995811i | \(0.470853\pi\) | |||||||
\(810\) | −1.42296e6 | −0.0762045 | ||||||||
\(811\) | 110790. | 0.00591490 | 0.00295745 | − | 0.999996i | \(-0.499059\pi\) | ||||
0.00295745 | + | 0.999996i | \(0.499059\pi\) | |||||||
\(812\) | −1.14306e7 | −0.608386 | ||||||||
\(813\) | −3.15060e6 | −0.167173 | ||||||||
\(814\) | −655678. | −0.0346840 | ||||||||
\(815\) | −1.99980e7 | −1.05461 | ||||||||
\(816\) | 2.93767e6 | 0.154446 | ||||||||
\(817\) | 4.67039e6 | 0.244792 | ||||||||
\(818\) | −4.98609e6 | −0.260542 | ||||||||
\(819\) | 1.39495e6 | 0.0726690 | ||||||||
\(820\) | −1.09922e7 | −0.570888 | ||||||||
\(821\) | −3.27368e6 | −0.169503 | −0.0847516 | − | 0.996402i | \(-0.527010\pi\) | ||||
−0.0847516 | + | 0.996402i | \(0.527010\pi\) | |||||||
\(822\) | 1.13796e6 | 0.0587421 | ||||||||
\(823\) | 3.40687e7 | 1.75330 | 0.876650 | − | 0.481128i | \(-0.159773\pi\) | ||||
0.876650 | + | 0.481128i | \(0.159773\pi\) | |||||||
\(824\) | −1.94410e7 | −0.997471 | ||||||||
\(825\) | 1.27979e7 | 0.654642 | ||||||||
\(826\) | −1.52311e6 | −0.0776751 | ||||||||
\(827\) | −8.58953e6 | −0.436723 | −0.218361 | − | 0.975868i | \(-0.570071\pi\) | ||||
−0.218361 | + | 0.975868i | \(0.570071\pi\) | |||||||
\(828\) | −1.56860e6 | −0.0795125 | ||||||||
\(829\) | −3.09207e7 | −1.56266 | −0.781328 | − | 0.624121i | \(-0.785457\pi\) | ||||
−0.781328 | + | 0.624121i | \(0.785457\pi\) | |||||||
\(830\) | −1.28420e7 | −0.647049 | ||||||||
\(831\) | 1.29820e6 | 0.0652135 | ||||||||
\(832\) | −413570. | −0.0207129 | ||||||||
\(833\) | −8.18418e6 | −0.408661 | ||||||||
\(834\) | −8.56176e6 | −0.426234 | ||||||||
\(835\) | 5.57344e7 | 2.76635 | ||||||||
\(836\) | −7.13555e6 | −0.353111 | ||||||||
\(837\) | 1.39164e6 | 0.0686613 | ||||||||
\(838\) | 9.68219e6 | 0.476281 | ||||||||
\(839\) | −1.62311e7 | −0.796054 | −0.398027 | − | 0.917374i | \(-0.630305\pi\) | ||||
−0.398027 | + | 0.917374i | \(0.630305\pi\) | |||||||
\(840\) | 1.79439e7 | 0.877442 | ||||||||
\(841\) | −1.23689e7 | −0.603034 | ||||||||
\(842\) | 4.18909e6 | 0.203629 | ||||||||
\(843\) | 7.36543e6 | 0.356968 | ||||||||
\(844\) | −1.97780e7 | −0.955712 | ||||||||
\(845\) | 2.89247e7 | 1.39357 | ||||||||
\(846\) | −635263. | −0.0305160 | ||||||||
\(847\) | −3.44565e6 | −0.165030 | ||||||||
\(848\) | −1.10629e7 | −0.528299 | ||||||||
\(849\) | −1.03785e7 | −0.494159 | ||||||||
\(850\) | −7.77151e6 | −0.368942 | ||||||||
\(851\) | 445778. | 0.0211006 | ||||||||
\(852\) | 7.21561e6 | 0.340545 | ||||||||
\(853\) | 2.71754e7 | 1.27880 | 0.639402 | − | 0.768873i | \(-0.279182\pi\) | ||||
0.639402 | + | 0.768873i | \(0.279182\pi\) | |||||||
\(854\) | −6.67263e6 | −0.313078 | ||||||||
\(855\) | 4.40086e6 | 0.205884 | ||||||||
\(856\) | 1.07476e7 | 0.501334 | ||||||||
\(857\) | 3.35816e7 | 1.56188 | 0.780942 | − | 0.624603i | \(-0.214739\pi\) | ||||
0.780942 | + | 0.624603i | \(0.214739\pi\) | |||||||
\(858\) | −1.10209e6 | −0.0511091 | ||||||||
\(859\) | 2.03318e6 | 0.0940140 | 0.0470070 | − | 0.998895i | \(-0.485032\pi\) | ||||
0.0470070 | + | 0.998895i | \(0.485032\pi\) | |||||||
\(860\) | −1.37137e7 | −0.632278 | ||||||||
\(861\) | −8.07607e6 | −0.371272 | ||||||||
\(862\) | 9.90373e6 | 0.453974 | ||||||||
\(863\) | −5.62968e6 | −0.257310 | −0.128655 | − | 0.991689i | \(-0.541066\pi\) | ||||
−0.128655 | + | 0.991689i | \(0.541066\pi\) | |||||||
\(864\) | −4.31431e6 | −0.196620 | ||||||||
\(865\) | 2.50587e7 | 1.13873 | ||||||||
\(866\) | −47268.9 | −0.00214181 | ||||||||
\(867\) | 6.05294e6 | 0.273476 | ||||||||
\(868\) | −7.64709e6 | −0.344506 | ||||||||
\(869\) | 2.31741e7 | 1.04101 | ||||||||
\(870\) | −5.56977e6 | −0.249482 | ||||||||
\(871\) | 3.98436e6 | 0.177956 | ||||||||
\(872\) | 7.66546e6 | 0.341387 | ||||||||
\(873\) | 1.41573e7 | 0.628701 | ||||||||
\(874\) | −1.43037e6 | −0.0633387 | ||||||||
\(875\) | 2.67472e6 | 0.118102 | ||||||||
\(876\) | −1.33877e7 | −0.589449 | ||||||||
\(877\) | 3.64806e7 | 1.60163 | 0.800816 | − | 0.598910i | \(-0.204399\pi\) | ||||
0.800816 | + | 0.598910i | \(0.204399\pi\) | |||||||
\(878\) | 1.65508e7 | 0.724576 | ||||||||
\(879\) | 1.29101e7 | 0.563582 | ||||||||
\(880\) | 1.29531e7 | 0.563855 | ||||||||
\(881\) | 3.83390e7 | 1.66418 | 0.832091 | − | 0.554640i | \(-0.187144\pi\) | ||||
0.832091 | + | 0.554640i | \(0.187144\pi\) | |||||||
\(882\) | 2.07001e6 | 0.0895987 | ||||||||
\(883\) | −316951. | −0.0136801 | −0.00684006 | − | 0.999977i | \(-0.502177\pi\) | ||||
−0.00684006 | + | 0.999977i | \(0.502177\pi\) | |||||||
\(884\) | −2.26982e6 | −0.0976923 | ||||||||
\(885\) | 2.51714e6 | 0.108031 | ||||||||
\(886\) | −7.26315e6 | −0.310843 | ||||||||
\(887\) | 4.42907e7 | 1.89018 | 0.945092 | − | 0.326805i | \(-0.105972\pi\) | ||||
0.945092 | + | 0.326805i | \(0.105972\pi\) | |||||||
\(888\) | 783819. | 0.0333567 | ||||||||
\(889\) | 1.54417e7 | 0.655299 | ||||||||
\(890\) | 1.26056e7 | 0.533443 | ||||||||
\(891\) | −2.80139e6 | −0.118217 | ||||||||
\(892\) | 4.82054e6 | 0.202854 | ||||||||
\(893\) | 1.96471e6 | 0.0824460 | ||||||||
\(894\) | 4.14800e6 | 0.173578 | ||||||||
\(895\) | 4.55295e7 | 1.89992 | ||||||||
\(896\) | 2.89940e7 | 1.20653 | ||||||||
\(897\) | 749281. | 0.0310931 | ||||||||
\(898\) | −1.17871e7 | −0.487770 | ||||||||
\(899\) | 5.44715e6 | 0.224787 | ||||||||
\(900\) | −6.66670e6 | −0.274350 | ||||||||
\(901\) | 2.53285e7 | 1.03943 | ||||||||
\(902\) | 6.38054e6 | 0.261121 | ||||||||
\(903\) | −1.00756e7 | −0.411197 | ||||||||
\(904\) | 1.57985e7 | 0.642978 | ||||||||
\(905\) | 1.33671e7 | 0.542520 | ||||||||
\(906\) | −1.25195e6 | −0.0506717 | ||||||||
\(907\) | −3.22962e7 | −1.30357 | −0.651783 | − | 0.758405i | \(-0.725979\pi\) | ||||
−0.651783 | + | 0.758405i | \(0.725979\pi\) | |||||||
\(908\) | 1.94683e7 | 0.783635 | ||||||||
\(909\) | −1.44533e7 | −0.580172 | ||||||||
\(910\) | −3.73506e6 | −0.149518 | ||||||||
\(911\) | 1.74012e6 | 0.0694679 | 0.0347340 | − | 0.999397i | \(-0.488942\pi\) | ||||
0.0347340 | + | 0.999397i | \(0.488942\pi\) | |||||||
\(912\) | 2.29797e6 | 0.0914866 | ||||||||
\(913\) | −2.52820e7 | −1.00377 | ||||||||
\(914\) | −1.97111e7 | −0.780449 | ||||||||
\(915\) | 1.10274e7 | 0.435431 | ||||||||
\(916\) | −2.77557e7 | −1.09298 | ||||||||
\(917\) | 4.58870e7 | 1.80205 | ||||||||
\(918\) | 1.70114e6 | 0.0666244 | ||||||||
\(919\) | −2.88435e7 | −1.12657 | −0.563286 | − | 0.826262i | \(-0.690463\pi\) | ||||
−0.563286 | + | 0.826262i | \(0.690463\pi\) | |||||||
\(920\) | 9.63834e6 | 0.375433 | ||||||||
\(921\) | 1.26732e7 | 0.492310 | ||||||||
\(922\) | −1.89254e7 | −0.733192 | ||||||||
\(923\) | −3.44673e6 | −0.133169 | ||||||||
\(924\) | 1.53937e7 | 0.593149 | ||||||||
\(925\) | 1.89460e6 | 0.0728055 | ||||||||
\(926\) | 3.55164e6 | 0.136114 | ||||||||
\(927\) | 1.02862e7 | 0.393148 | ||||||||
\(928\) | −1.68871e7 | −0.643703 | ||||||||
\(929\) | −2.74877e7 | −1.04496 | −0.522479 | − | 0.852652i | \(-0.674993\pi\) | ||||
−0.522479 | + | 0.852652i | \(0.674993\pi\) | |||||||
\(930\) | −3.72618e6 | −0.141272 | ||||||||
\(931\) | −6.40203e6 | −0.242071 | ||||||||
\(932\) | −2.90836e7 | −1.09675 | ||||||||
\(933\) | 3.65370e6 | 0.137413 | ||||||||
\(934\) | 8.45112e6 | 0.316991 | ||||||||
\(935\) | −2.96561e7 | −1.10939 | ||||||||
\(936\) | 1.31747e6 | 0.0491532 | ||||||||
\(937\) | −1.55562e7 | −0.578834 | −0.289417 | − | 0.957203i | \(-0.593461\pi\) | ||||
−0.289417 | + | 0.957203i | \(0.593461\pi\) | |||||||
\(938\) | 1.64088e7 | 0.608935 | ||||||||
\(939\) | 2.05907e7 | 0.762091 | ||||||||
\(940\) | −5.76899e6 | −0.212951 | ||||||||
\(941\) | 3.24594e6 | 0.119499 | 0.0597497 | − | 0.998213i | \(-0.480970\pi\) | ||||
0.0597497 | + | 0.998213i | \(0.480970\pi\) | |||||||
\(942\) | 1.53835e6 | 0.0564845 | ||||||||
\(943\) | −4.33796e6 | −0.158857 | ||||||||
\(944\) | 1.31436e6 | 0.0480048 | ||||||||
\(945\) | −9.49410e6 | −0.345839 | ||||||||
\(946\) | 7.96025e6 | 0.289200 | ||||||||
\(947\) | −1.66618e6 | −0.0603734 | −0.0301867 | − | 0.999544i | \(-0.509610\pi\) | ||||
−0.0301867 | + | 0.999544i | \(0.509610\pi\) | |||||||
\(948\) | −1.20719e7 | −0.436269 | ||||||||
\(949\) | 6.39499e6 | 0.230502 | ||||||||
\(950\) | −6.07922e6 | −0.218544 | ||||||||
\(951\) | 1.54818e7 | 0.555100 | ||||||||
\(952\) | −2.14518e7 | −0.767134 | ||||||||
\(953\) | 9.27492e6 | 0.330810 | 0.165405 | − | 0.986226i | \(-0.447107\pi\) | ||||
0.165405 | + | 0.986226i | \(0.447107\pi\) | |||||||
\(954\) | −6.40629e6 | −0.227895 | ||||||||
\(955\) | −4.64229e6 | −0.164711 | ||||||||
\(956\) | −1.16117e6 | −0.0410914 | ||||||||
\(957\) | −1.09652e7 | −0.387023 | ||||||||
\(958\) | 1.89077e7 | 0.665617 | ||||||||
\(959\) | 7.59258e6 | 0.266589 | ||||||||
\(960\) | 2.81478e6 | 0.0985748 | ||||||||
\(961\) | −2.49850e7 | −0.872712 | ||||||||
\(962\) | −163153. | −0.00568405 | ||||||||
\(963\) | −5.68655e6 | −0.197598 | ||||||||
\(964\) | −4.06571e7 | −1.40911 | ||||||||
\(965\) | −8.06837e7 | −2.78912 | ||||||||
\(966\) | 3.08577e6 | 0.106395 | ||||||||
\(967\) | 3.90239e7 | 1.34204 | 0.671019 | − | 0.741440i | \(-0.265857\pi\) | ||||
0.671019 | + | 0.741440i | \(0.265857\pi\) | |||||||
\(968\) | −3.25428e6 | −0.111626 | ||||||||
\(969\) | −5.26119e6 | −0.180001 | ||||||||
\(970\) | −3.79069e7 | −1.29357 | ||||||||
\(971\) | 1.52419e7 | 0.518791 | 0.259395 | − | 0.965771i | \(-0.416477\pi\) | ||||
0.259395 | + | 0.965771i | \(0.416477\pi\) | |||||||
\(972\) | 1.45930e6 | 0.0495427 | ||||||||
\(973\) | −5.71247e7 | −1.93438 | ||||||||
\(974\) | 5.65343e6 | 0.190948 | ||||||||
\(975\) | 3.18452e6 | 0.107283 | ||||||||
\(976\) | 5.75810e6 | 0.193488 | ||||||||
\(977\) | −4.86169e7 | −1.62949 | −0.814744 | − | 0.579821i | \(-0.803122\pi\) | ||||
−0.814744 | + | 0.579821i | \(0.803122\pi\) | |||||||
\(978\) | −6.04687e6 | −0.202155 | ||||||||
\(979\) | 2.48166e7 | 0.827535 | ||||||||
\(980\) | 1.87983e7 | 0.625250 | ||||||||
\(981\) | −4.05579e6 | −0.134556 | ||||||||
\(982\) | −1.15551e7 | −0.382379 | ||||||||
\(983\) | −5.24218e6 | −0.173033 | −0.0865163 | − | 0.996250i | \(-0.527573\pi\) | ||||
−0.0865163 | + | 0.996250i | \(0.527573\pi\) | |||||||
\(984\) | −7.62751e6 | −0.251128 | ||||||||
\(985\) | −7.74979e7 | −2.54507 | ||||||||
\(986\) | 6.65861e6 | 0.218118 | ||||||||
\(987\) | −4.23852e6 | −0.138491 | ||||||||
\(988\) | −1.77555e6 | −0.0578683 | ||||||||
\(989\) | −5.41196e6 | −0.175940 | ||||||||
\(990\) | 7.50086e6 | 0.243233 | ||||||||
\(991\) | −2.53147e7 | −0.818819 | −0.409409 | − | 0.912351i | \(-0.634265\pi\) | ||||
−0.409409 | + | 0.912351i | \(0.634265\pi\) | |||||||
\(992\) | −1.12975e7 | −0.364505 | ||||||||
\(993\) | 1.11081e7 | 0.357491 | ||||||||
\(994\) | −1.41947e7 | −0.455680 | ||||||||
\(995\) | −5.00760e7 | −1.60351 | ||||||||
\(996\) | 1.31700e7 | 0.420664 | ||||||||
\(997\) | −3.69734e7 | −1.17802 | −0.589008 | − | 0.808127i | \(-0.700481\pi\) | ||||
−0.589008 | + | 0.808127i | \(0.700481\pi\) | |||||||
\(998\) | −1.51931e7 | −0.482859 | ||||||||
\(999\) | −414718. | −0.0131474 |
(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 | 177.6.a.d.1.8 | ✓ | 13 | |
3.2 | odd | 2 | 531.6.a.e.1.6 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.d.1.8 | ✓ | 13 | 1.1 | even | 1 | trivial | |
531.6.a.e.1.6 | 13 | 3.2 | odd | 2 |