Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,5,Mod(257,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("688.257");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(71.1185346017\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 142x^{10} + 7173x^{8} + 157368x^{6} + 1510016x^{4} + 5098688x^{2} + 90352 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.8 | ||
Root | \(4.43775i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.257 |
Dual form | 688.5.b.d.257.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).
\(n\) | \(431\) | \(433\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 6.93950i | 0.771055i | 0.922696 | + | 0.385528i | \(0.125981\pi\) | ||||
−0.922696 | + | 0.385528i | \(0.874019\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 22.3554i | 0.894216i | 0.894480 | + | 0.447108i | \(0.147546\pi\) | ||||
−0.894480 | + | 0.447108i | \(0.852454\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 51.9837i | − | 1.06089i | −0.847719 | − | 0.530446i | \(-0.822024\pi\) | ||
0.847719 | − | 0.530446i | \(-0.177976\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 32.8434 | 0.405474 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25.0158 | 0.206742 | 0.103371 | − | 0.994643i | \(-0.467037\pi\) | ||||
0.103371 | + | 0.994643i | \(0.467037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −38.7510 | −0.229296 | −0.114648 | − | 0.993406i | \(-0.536574\pi\) | ||||
−0.114648 | + | 0.993406i | \(0.536574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −155.135 | −0.689490 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 111.381 | 0.385402 | 0.192701 | − | 0.981257i | \(-0.438275\pi\) | ||||
0.192701 | + | 0.981257i | \(0.438275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 238.930i | 0.661856i | 0.943656 | + | 0.330928i | \(0.107362\pi\) | ||||
−0.943656 | + | 0.330928i | \(0.892638\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 360.741 | 0.818007 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −823.523 | −1.55675 | −0.778377 | − | 0.627797i | \(-0.783957\pi\) | ||||
−0.778377 | + | 0.627797i | \(0.783957\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 125.236 | 0.200377 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 790.016i | 1.08370i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 424.840i | − | 0.505160i | −0.967576 | − | 0.252580i | \(-0.918721\pi\) | ||
0.967576 | − | 0.252580i | \(-0.0812791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1447.58 | 1.50632 | 0.753162 | − | 0.657835i | \(-0.228528\pi\) | ||||
0.753162 | + | 0.657835i | \(0.228528\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 173.597i | 0.159409i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1162.12 | 0.948668 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 626.677i | − | 0.457763i | −0.973454 | − | 0.228881i | \(-0.926493\pi\) | ||
0.973454 | − | 0.228881i | \(-0.0735068\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 268.912i | − | 0.176800i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 580.694 | 0.345446 | 0.172723 | − | 0.984970i | \(-0.444744\pi\) | ||||
0.172723 | + | 0.984970i | \(0.444744\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 528.728 | + | 1771.79i | 0.285953 | + | 0.958244i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 734.227i | 0.362581i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 170.609 | 0.0772336 | 0.0386168 | − | 0.999254i | \(-0.487705\pi\) | ||||
0.0386168 | + | 0.999254i | \(0.487705\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −301.309 | −0.125493 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 772.930i | 0.297167i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4308.39 | 1.53378 | 0.766890 | − | 0.641779i | \(-0.221803\pi\) | ||||
0.766890 | + | 0.641779i | \(0.221803\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 559.237i | 0.184872i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1658.05 | −0.510327 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 65.4372 | 0.0187984 | 0.00939919 | − | 0.999956i | \(-0.497008\pi\) | ||||
0.00939919 | + | 0.999956i | \(0.497008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3896.58i | 1.04719i | 0.851968 | + | 0.523594i | \(0.175409\pi\) | ||||
−0.851968 | + | 0.523594i | \(0.824591\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1707.32i | − | 0.430164i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 866.294i | − | 0.205040i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5449.76 | 1.21403 | 0.607013 | − | 0.794692i | \(-0.292368\pi\) | ||||
0.607013 | + | 0.794692i | \(0.292368\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 5714.84i | − | 1.20034i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5845.23i | 1.15954i | 0.814781 | + | 0.579769i | \(0.196857\pi\) | ||||
−0.814781 | + | 0.579769i | \(0.803143\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4773.87i | 0.895828i | 0.894077 | + | 0.447914i | \(0.147833\pi\) | ||||
−0.894077 | + | 0.447914i | \(0.852167\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 869.073i | 0.154502i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1300.41i | − | 0.219331i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10139.3 | −1.62463 | −0.812316 | − | 0.583217i | \(-0.801794\pi\) | ||||
−0.812316 | + | 0.583217i | \(0.801794\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2822.00 | −0.430117 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4438.95 | −0.644353 | −0.322176 | − | 0.946680i | \(-0.604414\pi\) | ||||
−0.322176 | + | 0.946680i | \(0.604414\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2489.97i | 0.344633i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2948.17 | 0.389506 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9870.51i | 1.24612i | 0.782174 | + | 0.623060i | \(0.214111\pi\) | ||||
−0.782174 | + | 0.623060i | \(0.785889\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2014.42i | 0.243258i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10045.5i | 1.16146i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5341.37 | −0.591842 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7761.47 | −0.824899 | −0.412449 | − | 0.910981i | \(-0.635327\pi\) | ||||
−0.412449 | + | 0.910981i | \(0.635327\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 821.602 | 0.0838284 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7907.71 | −0.775190 | −0.387595 | − | 0.921830i | \(-0.626694\pi\) | ||||
−0.387595 | + | 0.921830i | \(0.626694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11579.3 | −1.09146 | −0.545728 | − | 0.837962i | \(-0.683747\pi\) | ||||
−0.545728 | + | 0.837962i | \(0.683747\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8064.51i | 0.731475i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6463.42 | 0.564540 | 0.282270 | − | 0.959335i | \(-0.408913\pi\) | ||||
0.282270 | + | 0.959335i | \(0.408913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3408.56 | 0.286892 | 0.143446 | − | 0.989658i | \(-0.454182\pi\) | ||||
0.143446 | + | 0.989658i | \(0.454182\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4348.82 | 0.352960 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 11268.0i | − | 0.882446i | −0.897397 | − | 0.441223i | \(-0.854545\pi\) | ||
0.897397 | − | 0.441223i | \(-0.145455\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 18410.2i | − | 1.39208i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1272.71 | −0.0929734 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5790.02i | − | 0.408871i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14015.2 | −0.957258 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4029.73i | 0.266358i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 16771.8i | 1.07340i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13207.4 | −0.818860 | −0.409430 | − | 0.912342i | \(-0.634272\pi\) | ||||
−0.409430 | + | 0.912342i | \(0.634272\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12295.3 | + | 3669.10i | −0.738859 | + | 0.220486i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 29457.5i | 1.71653i | 0.513203 | + | 0.858267i | \(0.328459\pi\) | ||||
−0.513203 | + | 0.858267i | \(0.671541\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12420.5 | 0.702158 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17661.1 | −0.969060 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 14241.6i | − | 0.758783i | −0.925236 | − | 0.379392i | \(-0.876133\pi\) | ||
0.925236 | − | 0.379392i | \(-0.123867\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18549.0 | 0.960042 | 0.480021 | − | 0.877257i | \(-0.340629\pi\) | ||||
0.480021 | + | 0.877257i | \(0.340629\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1183.94i | 0.0595513i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −969.385 | −0.0474050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9497.46 | 0.451722 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 2090.94i | − | 0.0967623i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 31018.5i | 1.39717i | 0.715528 | + | 0.698584i | \(0.246186\pi\) | ||||
−0.715528 | + | 0.698584i | \(0.753814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10079.5i | 0.442063i | 0.975267 | + | 0.221032i | \(0.0709424\pi\) | ||||
−0.975267 | + | 0.221032i | \(0.929058\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3658.14 | 0.156271 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 32361.2i | 1.34698i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 27782.4i | − | 1.12712i | −0.826075 | − | 0.563560i | \(-0.809431\pi\) | ||
0.826075 | − | 0.563560i | \(-0.190569\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 29898.0i | 1.18263i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 42809.8i | 1.65155i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23274.3i | 0.875993i | 0.898977 | + | 0.437996i | \(0.144312\pi\) | ||||
−0.898977 | + | 0.437996i | \(0.855688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3880.83 | −0.142546 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 38477.5 | 1.37967 | 0.689833 | − | 0.723968i | \(-0.257684\pi\) | ||||
0.689833 | + | 0.723968i | \(0.257684\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −27059.4 | −0.947423 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7847.26i | 0.268365i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 26454.5 | 0.883909 | 0.441954 | − | 0.897038i | \(-0.354285\pi\) | ||||
0.441954 | + | 0.897038i | \(0.354285\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6510.22i | − | 0.212579i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 454.101i | 0.0144946i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5807.25i | − | 0.181244i | −0.995885 | − | 0.0906222i | \(-0.971114\pi\) | ||
0.995885 | − | 0.0906222i | \(-0.0288856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −63912.2 | −1.95086 | −0.975431 | − | 0.220304i | \(-0.929295\pi\) | ||||
−0.975431 | + | 0.220304i | \(0.929295\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −27040.3 | −0.807439 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14009.6 | 0.409339 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2786.29 | 0.0796788 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 41068.0 | 1.14969 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 58852.6i | − | 1.61324i | −0.591071 | − | 0.806620i | \(-0.701295\pi\) | ||
0.591071 | − | 0.806620i | \(-0.298705\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4293.94 | −0.115277 | −0.0576384 | − | 0.998338i | \(-0.518357\pi\) | ||||
−0.0576384 | + | 0.998338i | \(0.518357\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6011.65 | 0.158097 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 60627.5 | 1.56220 | 0.781101 | − | 0.624405i | \(-0.214658\pi\) | ||||
0.781101 | + | 0.624405i | \(0.214658\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 75910.5i | 1.91688i | 0.285290 | + | 0.958441i | \(0.407910\pi\) | ||||
−0.285290 | + | 0.958441i | \(0.592090\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 37818.6i | 0.936081i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22084.8 | −0.535921 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12981.7i | 0.308903i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −27047.3 | −0.631223 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5977.01i | 0.136833i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 34858.4i | − | 0.782964i | −0.920186 | − | 0.391482i | \(-0.871962\pi\) | ||
0.920186 | − | 0.391482i | \(-0.128038\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −40563.0 | −0.894068 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39609.1 | + | 11819.9i | −0.856877 | + | 0.255704i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 75250.5i | − | 1.59805i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −33128.3 | −0.690733 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4316.13 | −0.0883711 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 69871.4i | 1.40504i | 0.711662 | + | 0.702522i | \(0.247943\pi\) | ||||
−0.711662 | + | 0.702522i | \(0.752057\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4113.16 | 0.0812476 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 5952.36i | − | 0.115515i | −0.998331 | − | 0.0577574i | \(-0.981605\pi\) | ||
0.998331 | − | 0.0577574i | \(-0.0183950\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −31808.4 | −0.606556 | −0.303278 | − | 0.952902i | \(-0.598081\pi\) | ||||
−0.303278 | + | 0.952902i | \(0.598081\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9024.21 | 0.169116 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 55507.2i | 1.02244i | 0.859450 | + | 0.511220i | \(0.170806\pi\) | ||||
−0.859450 | + | 0.511220i | \(0.829194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3814.03i | 0.0690635i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 70361.9i | − | 1.25268i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 62886.2 | 1.10093 | 0.550465 | − | 0.834859i | \(-0.314451\pi\) | ||||
0.550465 | + | 0.834859i | \(0.314451\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19314.0i | 0.332536i | 0.986081 | + | 0.166268i | \(0.0531717\pi\) | ||||
−0.986081 | + | 0.166268i | \(0.946828\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 44408.0i | 0.752054i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6735.90i | − | 0.112218i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 9258.77i | − | 0.151761i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 30804.1i | − | 0.496832i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 62983.5 | 0.999723 | 0.499862 | − | 0.866105i | \(-0.333384\pi\) | ||||
0.499862 | + | 0.866105i | \(0.333384\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20601.0 | −0.321846 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17279.2 | −0.265731 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 53736.0i | 0.813579i | 0.913522 | + | 0.406789i | \(0.133352\pi\) | ||||
−0.913522 | + | 0.406789i | \(0.866648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −32577.0 | −0.485637 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 13953.2i | − | 0.204829i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 133357.i | − | 1.92798i | −0.265932 | − | 0.963992i | \(-0.585680\pi\) | ||
0.265932 | − | 0.963992i | \(-0.414320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 96315.7i | 1.37153i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −68496.4 | −0.960827 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 61320.3 | 0.847421 | 0.423711 | − | 0.905798i | \(-0.360727\pi\) | ||||
0.423711 | + | 0.905798i | \(0.360727\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −66120.9 | −0.900326 | −0.450163 | − | 0.892946i | \(-0.648634\pi\) | ||||
−0.450163 | + | 0.892946i | \(0.648634\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13979.1 | −0.187565 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3132.86 | 0.0414263 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 62649.4i | 0.816502i | 0.912870 | + | 0.408251i | \(0.133861\pi\) | ||||
−0.912870 | + | 0.408251i | \(0.866139\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 47543.3 | 0.610775 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 110235. | 1.39606 | 0.698032 | − | 0.716066i | \(-0.254059\pi\) | ||||
0.698032 | + | 0.716066i | \(0.254059\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 109263. | 1.36427 | 0.682135 | − | 0.731226i | \(-0.261052\pi\) | ||||
0.682135 | + | 0.731226i | \(0.261052\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 37066.5i | − | 0.456343i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 30186.7i | − | 0.366481i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −71115.2 | −0.851465 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 53860.7i | − | 0.636042i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −137382. | −1.60028 | −0.800139 | − | 0.599814i | \(-0.795241\pi\) | ||||
−0.800139 | + | 0.599814i | \(0.795241\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1462.88i | 0.0168098i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19762.8i | 0.224046i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 31912.3 | 0.356957 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 92104.4 | − | 27485.2i | 1.01659 | − | 0.303366i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 54875.5i | − | 0.597714i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −87109.7 | −0.936412 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13056.1 | 0.138528 | 0.0692639 | − | 0.997598i | \(-0.477935\pi\) | ||||
0.0692639 | + | 0.997598i | \(0.477935\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 80354.2i | − | 0.841573i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 190885. | 1.97356 | 0.986781 | − | 0.162061i | \(-0.0518140\pi\) | ||||
0.986781 | + | 0.162061i | \(0.0518140\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 31940.8i | − | 0.326030i | −0.986624 | − | 0.163015i | \(-0.947878\pi\) | ||
0.986624 | − | 0.163015i | \(-0.0521219\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 38167.9 | 0.384660 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10721.3 | 0.106692 | 0.0533459 | − | 0.998576i | \(-0.483011\pi\) | ||||
0.0533459 | + | 0.998576i | \(0.483011\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 10627.7i | − | 0.104438i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 44852.9i | 0.435291i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26612.3i | 0.255081i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4853.00 | −0.0459456 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 23653.7i | 0.221209i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 8868.89i | − | 0.0819365i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 49144.6i | 0.448560i | 0.974525 | + | 0.224280i | \(0.0720030\pi\) | ||||
−0.974525 | + | 0.224280i | \(0.927997\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 20582.2i | − | 0.185611i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 121832.i | 1.08560i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 113598. | 1.00025 | 0.500127 | − | 0.865952i | \(-0.333287\pi\) | ||||
0.500127 | + | 0.865952i | \(0.333287\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 78194.0 | 0.680415 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36212.2 | 0.311420 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 109150.i | − | 0.927758i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 127757. | 1.07337 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25603.4i | 0.212637i | 0.994332 | + | 0.106319i | \(0.0339063\pi\) | ||||
−0.994332 | + | 0.106319i | \(0.966094\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 4308.53i | − | 0.0353735i | −0.999844 | − | 0.0176867i | \(-0.994370\pi\) | ||
0.999844 | − | 0.0176867i | \(-0.00563016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 30613.9i | − | 0.248487i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 101165. | 0.811856 | 0.405928 | − | 0.913905i | \(-0.366948\pi\) | ||||
0.405928 | + | 0.913905i | \(0.366948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −130673. | −1.03688 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 40179.8 | 0.315262 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3103.18 | −0.0240779 | −0.0120389 | − | 0.999928i | \(-0.503832\pi\) | ||||
−0.0120389 | + | 0.999928i | \(0.503832\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 73233.5 | 0.561947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 97258.5i | − | 0.738099i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −106722. | −0.801064 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −158319. | −1.17544 | −0.587722 | − | 0.809063i | \(-0.699975\pi\) | ||||
−0.587722 | + | 0.809063i | \(0.699975\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19072.0 | 0.140069 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 223966.i | − | 1.62718i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 186262.i | − | 1.33877i | −0.742914 | − | 0.669387i | \(-0.766557\pi\) | ||
0.742914 | − | 0.669387i | \(-0.233443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −116388. | −0.827648 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16463.0i | 0.115831i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31309.9 | −0.217973 | −0.108987 | − | 0.994043i | \(-0.534761\pi\) | ||||
−0.108987 | + | 0.994043i | \(0.534761\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 91652.6i | − | 0.631386i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18588.7i | 0.126722i | 0.997991 | + | 0.0633609i | \(0.0201819\pi\) | ||||
−0.997991 | + | 0.0633609i | \(0.979818\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29071.3 | 0.196129 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17365.2 | + | 58191.6i | 0.115947 | + | 0.388543i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 158939.i | − | 1.05034i | −0.850997 | − | 0.525170i | \(-0.824002\pi\) | ||
0.850997 | − | 0.525170i | \(-0.175998\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −91725.1 | −0.599977 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −204420. | −1.32354 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 226669.i | − | 1.45277i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 97945.4 | 0.621445 | 0.310723 | − | 0.950501i | \(-0.399429\pi\) | ||||
0.310723 | + | 0.950501i | \(0.399429\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 86191.8i | 0.541402i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −252905. | −1.57278 | −0.786392 | − | 0.617727i | \(-0.788054\pi\) | ||||
−0.786392 | + | 0.617727i | \(0.788054\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −56095.0 | −0.345394 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 63086.9i | − | 0.384618i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15676.8i | − | 0.0946386i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 134853.i | 0.806149i | 0.915167 | + | 0.403074i | \(0.132058\pi\) | ||||
−0.915167 | + | 0.403074i | \(0.867942\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 98829.6 | 0.585064 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3401.67i | − | 0.0199431i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 99234.5i | − | 0.576191i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 128720.i | 0.740245i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 10482.5i | − | 0.0597086i | −0.999554 | − | 0.0298543i | \(-0.990496\pi\) | ||
0.999554 | − | 0.0298543i | \(-0.00950433\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 241369.i | − | 1.36181i | −0.732371 | − | 0.680906i | \(-0.761586\pi\) | ||
0.732371 | − | 0.680906i | \(-0.238414\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5603.37 | 0.0313162 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13948.9 | 0.0772258 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 202559. | 1.11095 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 6727.04i | − | 0.0365519i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −59107.4 | −0.318191 | −0.159095 | − | 0.987263i | \(-0.550858\pi\) | ||||
−0.159095 | + | 0.987263i | \(0.550858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 193520.i | − | 1.03216i | −0.856539 | − | 0.516082i | \(-0.827390\pi\) | ||
0.856539 | − | 0.516082i | \(-0.172610\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 65907.6i | 0.348303i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 196764.i | − | 1.03035i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4663.78 | 0.0241997 | 0.0120998 | − | 0.999927i | \(-0.496148\pi\) | ||||
0.0120998 | + | 0.999927i | \(0.496148\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9896.02 | −0.0508843 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −102777. | −0.523708 | −0.261854 | − | 0.965107i | \(-0.584334\pi\) | ||||
−0.261854 | + | 0.965107i | \(0.584334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −220659. | −1.11430 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −215253. | −1.07729 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 222984.i | − | 1.10606i | −0.833160 | − | 0.553032i | \(-0.813471\pi\) | ||
0.833160 | − | 0.553032i | \(-0.186529\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14526.5 | 0.0714180 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −69946.6 | −0.340855 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −45033.2 | −0.217525 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 239772.i | 1.14806i | 0.818833 | + | 0.574032i | \(0.194622\pi\) | ||||
−0.818833 | + | 0.574032i | \(0.805378\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 87993.0i | 0.417660i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 234784. | 1.10476 | 0.552378 | − | 0.833593i | \(-0.313720\pi\) | ||||
0.552378 | + | 0.833593i | \(0.313720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 323705.i | − | 1.51004i | −0.655704 | − | 0.755018i | \(-0.727628\pi\) | ||
0.655704 | − | 0.755018i | \(-0.272372\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −224570. | −1.03860 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 158850.i | 0.728372i | 0.931326 | + | 0.364186i | \(0.118653\pi\) | ||||
−0.931326 | + | 0.364186i | \(0.881347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 283299.i | − | 1.28795i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 192796. | 0.869072 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13226.5 | + | 44322.7i | 0.0591185 | + | 0.198109i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29922.5i | 0.132621i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 141502. | 0.621907 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 50616.7 | 0.220609 | 0.110304 | − | 0.993898i | \(-0.464817\pi\) | ||||
0.110304 | + | 0.993898i | \(0.464817\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24284.3i | 0.104963i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −297079. | −1.27344 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 173511.i | − | 0.737638i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 414555. | 1.74793 | 0.873966 | − | 0.485987i | \(-0.161540\pi\) | ||||
0.873966 | + | 0.485987i | \(0.161540\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −161512. | −0.675439 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 162691.i | 0.674841i | 0.941354 | + | 0.337421i | \(0.109554\pi\) | ||||
−0.941354 | + | 0.337421i | \(0.890446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 47319.2i | − | 0.194690i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18367.2i | 0.0749607i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 303857. | 1.23015 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 202146.i | − | 0.811829i | −0.913911 | − | 0.405914i | \(-0.866953\pi\) | ||
0.913911 | − | 0.405914i | \(-0.133047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 267015.i | 1.06380i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 142571.i | − | 0.563501i | −0.959488 | − | 0.281751i | \(-0.909085\pi\) | ||
0.959488 | − | 0.281751i | \(-0.0909151\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 176780.i | − | 0.693187i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 187778.i | − | 0.730516i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −132370. | −0.510922 | −0.255461 | − | 0.966819i | \(-0.582227\pi\) | ||||
−0.255461 | + | 0.966819i | \(0.582227\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 248164. | 0.950378 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −188758. | −0.717251 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 258859.i | − | 0.975998i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4267.91 | 0.0159674 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 183581.i | 0.681542i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 222159.i | 0.818444i | 0.912435 | + | 0.409222i | \(0.134200\pi\) | ||||
−0.912435 | + | 0.409222i | \(0.865800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 426785.i | 1.56029i | 0.625599 | + | 0.780145i | \(0.284855\pi\) | ||||
−0.625599 | + | 0.780145i | \(0.715145\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 45177.6 | 0.163910 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 161233. | 0.580541 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 398349. | 1.42348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2149.18 | 0.00762225 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22502.5 | −0.0792092 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 144492.i | 0.504821i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 40299.4 | 0.139750 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7537.48 | −0.0259447 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 225636. | 0.770927 | 0.385463 | − | 0.922723i | \(-0.374042\pi\) | ||||
0.385463 | + | 0.922723i | \(0.374042\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 443519.i | − | 1.50422i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 76199.8i | 0.256543i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45128.1 | −0.150825 | −0.0754124 | − | 0.997152i | \(-0.524027\pi\) | ||||
−0.0754124 | + | 0.997152i | \(0.524027\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 127977.i | 0.424607i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 101507. | 0.334343 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 527080.i | 1.72356i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 97219.7i | 0.315623i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 561545. | 1.80998 | 0.904991 | − | 0.425430i | \(-0.139877\pi\) | ||||
0.904991 | + | 0.425430i | \(0.139877\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20488.7 | − | 68658.7i | −0.0655679 | − | 0.219721i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 19335.4i | 0.0614367i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −140409. | −0.442975 | −0.221487 | − | 0.975163i | \(-0.571091\pi\) | ||||
−0.221487 | + | 0.975163i | \(0.571091\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 251900. | 0.789098 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 146698.i | 0.456308i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −434476. | −1.34197 | −0.670983 | − | 0.741473i | \(-0.734128\pi\) | ||||
−0.670983 | + | 0.741473i | \(0.734128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 63191.7i | − | 0.193815i | −0.995293 | − | 0.0969076i | \(-0.969105\pi\) | ||
0.995293 | − | 0.0969076i | \(-0.0308951\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 408407. | 1.24390 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −103134. | −0.311938 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 524185.i | 1.57447i | 0.616656 | + | 0.787233i | \(0.288487\pi\) | ||||
−0.616656 | + | 0.787233i | \(0.711513\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 29797.8i | − | 0.0888847i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 230753.i | 0.683589i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 107778. | 0.317096 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 28452.0i | − | 0.0831383i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 653761.i | − | 1.89733i | −0.316284 | − | 0.948665i | \(-0.602435\pi\) | ||
0.316284 | − | 0.948665i | \(-0.397565\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 345869.i | 0.996969i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 420724.i | 1.20454i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 73594.7i | 0.209285i | 0.994510 | + | 0.104642i | \(0.0333698\pi\) | ||||
−0.994510 | + | 0.104642i | \(0.966630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 129438. | 0.365619 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −526781. | −1.47802 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 219023. | 0.610430 | 0.305215 | − | 0.952283i | \(-0.401272\pi\) | ||||
0.305215 | + | 0.952283i | \(0.401272\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 350767.i | − | 0.971112i | −0.874206 | − | 0.485556i | \(-0.838617\pi\) | ||
0.874206 | − | 0.485556i | \(-0.161383\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 178989. | 0.492256 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 313316.i | − | 0.855996i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 93560.7i | 0.253931i | 0.991907 | + | 0.126966i | \(0.0405238\pi\) | ||||
−0.991907 | + | 0.126966i | \(0.959476\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 153257.i | − | 0.413224i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6611.26 | −0.0177093 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 385616. | 1.02620 | 0.513102 | − | 0.858327i | \(-0.328496\pi\) | ||||
0.513102 | + | 0.858327i | \(0.328496\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −90086.2 | −0.238181 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −262907. | −0.690609 | −0.345304 | − | 0.938491i | \(-0.612224\pi\) | ||||
−0.345304 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −105010. | −0.274063 | −0.137031 | − | 0.990567i | \(-0.543756\pi\) | ||||
−0.137031 | + | 0.990567i | \(0.543756\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 650596.i | − | 1.68705i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 513106. | 1.32200 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −296669. | −0.759472 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −41477.4 | −0.105506 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 69800.1i | − | 0.176423i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 584197.i | 1.46724i | 0.679561 | + | 0.733619i | \(0.262170\pi\) | ||||
−0.679561 | + | 0.733619i | \(0.737830\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 241899. | 0.603709 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 295257.i | − | 0.732238i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 11676.0 | 0.0287751 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 191977.i | 0.470162i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 230667.i | 0.561397i | 0.959796 | + | 0.280699i | \(0.0905661\pi\) | ||||
−0.959796 | + | 0.280699i | \(0.909434\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −205024. | −0.495886 | −0.247943 | − | 0.968775i | \(-0.579755\pi\) | ||||
−0.247943 | + | 0.968775i | \(0.579755\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −82024.3 | − | 274868.i | −0.197162 | − | 0.660700i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 151853.i | − | 0.362757i | −0.983413 | − | 0.181379i | \(-0.941944\pi\) | ||
0.983413 | − | 0.181379i | \(-0.0580560\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1636.96 | 0.00388641 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 522200. | 1.23218 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 165779.i | 0.388780i | 0.980924 | + | 0.194390i | \(0.0622727\pi\) | ||||
−0.980924 | + | 0.194390i | \(0.937727\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −658533. | −1.53495 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 156790.i | 0.363235i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −461726. | −1.06320 | −0.531599 | − | 0.846996i | \(-0.678408\pi\) | ||||
−0.531599 | + | 0.846996i | \(0.678408\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −206270. | −0.472099 | −0.236050 | − | 0.971741i | \(-0.575853\pi\) | ||||
−0.236050 | + | 0.971741i | \(0.575853\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 29951.8i | − | 0.0681390i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 277665.i | 0.627881i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 349865.i | 0.786410i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −484873. | −1.08337 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 97476.0i | 0.216497i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 739539.i | 1.63279i | 0.577492 | + | 0.816397i | \(0.304032\pi\) | ||||
−0.577492 | + | 0.816397i | \(0.695968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 98938.2i | 0.217148i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 248420.i | − | 0.542012i | −0.962578 | − | 0.271006i | \(-0.912644\pi\) | ||
0.962578 | − | 0.271006i | \(-0.0873563\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 403470.i | 0.875129i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 41306.4 | 0.0890682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −536792. | −1.15071 | −0.575354 | − | 0.817905i | \(-0.695136\pi\) | ||||
−0.575354 | + | 0.817905i | \(0.695136\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 318377. | 0.678517 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 220734.i | − | 0.467688i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −166954. | −0.351689 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 253638.i | 0.531199i | 0.964083 | + | 0.265600i | \(0.0855699\pi\) | ||||
−0.964083 | + | 0.265600i | \(0.914430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 42709.9i | − | 0.0889329i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 414670.i | 0.858485i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 64678.5 | 0.133136 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −385192. | −0.788358 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −64810.3 | −0.131889 | −0.0659444 | − | 0.997823i | \(-0.521006\pi\) | ||||
−0.0659444 | + | 0.997823i | \(0.521006\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 149732. | 0.302973 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −26467.5 | −0.0532518 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 411072.i | 0.822393i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −120036. | −0.238792 | −0.119396 | − | 0.992847i | \(-0.538096\pi\) | ||||
−0.119396 | + | 0.992847i | \(0.538096\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −333010. | −0.658746 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.19211e6 | −2.34498 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 21671.0i | − | 0.0423903i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 436398.i | 0.848877i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 332719. | 0.643605 | 0.321802 | − | 0.946807i | \(-0.395711\pi\) | ||||
0.321802 | + | 0.946807i | \(0.395711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 601933.i | 1.15792i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −134030. | −0.256404 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 53205.1i | − | 0.101222i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 582297.i | − | 1.10173i | −0.834594 | − | 0.550866i | \(-0.814298\pi\) | ||
0.834594 | − | 0.550866i | \(-0.185702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −536751. | −1.00999 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58890.4 | + | 197345.i | 0.110207 | + | 0.369309i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 469633.i | − | 0.874079i | −0.899442 | − | 0.437039i | \(-0.856027\pi\) | ||
0.899442 | − | 0.437039i | \(-0.143973\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 46743.7 | 0.0865264 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 136330. | 0.250990 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 755334.i | 1.38309i | 0.722334 | + | 0.691545i | \(0.243070\pi\) | ||||
−0.722334 | + | 0.691545i | \(0.756930\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 64251.2 | 0.117016 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18481.9i | − | 0.0334788i | −0.999860 | − | 0.0167394i | \(-0.994671\pi\) | ||
0.999860 | − | 0.0167394i | \(-0.00532857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −693432. | −1.24937 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −145790. | −0.261268 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 335993.i | − | 0.598916i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 62072.3i | − | 0.110057i | −0.998485 | − | 0.0550286i | \(-0.982475\pi\) | ||
0.998485 | − | 0.0550286i | \(-0.0175250\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 437074.i | 0.770842i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −225331. | −0.395300 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 452452.i | − | 0.789551i | −0.918778 | − | 0.394776i | \(-0.870822\pi\) | ||
0.918778 | − | 0.394776i | \(-0.129178\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 142961.i | − | 0.248161i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 239204.i | 0.413047i | 0.978442 | + | 0.206523i | \(0.0662150\pi\) | ||||
−0.978442 | + | 0.206523i | \(0.933785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 177190.i | − | 0.304361i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 81779.2i | 0.139740i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2535.76 | −0.00431039 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 838340. | 1.41765 | 0.708823 | − | 0.705386i | \(-0.249227\pi\) | ||||
0.708823 | + | 0.705386i | \(0.249227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −372901. | −0.627314 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 520027.i | − | 0.870295i | −0.900359 | − | 0.435148i | \(-0.856696\pi\) | ||
0.900359 | − | 0.435148i | \(-0.143304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 181288. | 0.301833 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 226068.i | − | 0.374453i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 138745.i | 0.228635i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 146223.i | 0.239725i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 335630. | 0.547441 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 621087. | 1.00789 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 297689. | 0.480633 | 0.240316 | − | 0.970695i | \(-0.422749\pi\) | ||||
0.240316 | + | 0.970695i | \(0.422749\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 925429. | 1.48658 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −585751. | −0.936181 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 150996.i | − | 0.240116i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −668383. | −1.05753 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 943410. | 1.48520 | 0.742598 | − | 0.669737i | \(-0.233593\pi\) | ||||
0.742598 | + | 0.669737i | \(0.233593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19002.6 | 0.0297660 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 324181.i | 0.505269i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 119422.i | 0.185205i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −957031. | −1.47684 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 425532.i | 0.653409i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 365446. | 0.558375 | 0.279187 | − | 0.960237i | \(-0.409935\pi\) | ||||
0.279187 | + | 0.960237i | \(0.409935\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 465367.i | − | 0.707544i | −0.935332 | − | 0.353772i | \(-0.884899\pi\) | ||
0.935332 | − | 0.353772i | \(-0.115101\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 458846.i | − | 0.694201i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −520305. | −0.783327 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −423334. | + | 126329.i | −0.634219 | + | 0.189260i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 66160.4i | 0.0986348i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −391246. | −0.580449 | −0.290224 | − | 0.956959i | \(-0.593730\pi\) | ||||
−0.290224 | + | 0.956959i | \(0.593730\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 329039. | 0.485789 | 0.242895 | − | 0.970053i | \(-0.421903\pi\) | ||||
0.242895 | + | 0.970053i | \(0.421903\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 21740.5i | 0.0319420i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42044.1 | 0.0614744 | 0.0307372 | − | 0.999528i | \(-0.490215\pi\) | ||||
0.0307372 | + | 0.999528i | \(0.490215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 591458.i | 0.860626i | 0.902680 | + | 0.430313i | \(0.141597\pi\) | ||||
−0.902680 | + | 0.430313i | \(0.858403\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −434755. | −0.629568 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33560.2 | −0.0483654 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 860181.i | 1.23372i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.14361e6i | 1.63240i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.21494e6i | 1.72597i | 0.505233 | + | 0.862983i | \(0.331407\pi\) | ||||
−0.505233 | + | 0.862983i | \(0.668593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 526792. | 0.744813 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 764973.i | 1.07644i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 604923.i | − | 0.847202i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 728563.i | 1.01555i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 758230.i | 1.05193i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 516083.i | 0.712624i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.22261e6 | −1.68031 | −0.840154 | − | 0.542347i | \(-0.817536\pi\) | ||||
−0.840154 | + | 0.542347i | \(0.817536\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −175429. | −0.239976 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25443.6 | −0.0346432 | −0.0173216 | − | 0.999850i | \(-0.505514\pi\) | ||||
−0.0173216 | + | 0.999850i | \(0.505514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 853100.i | − | 1.15615i | −0.815984 | − | 0.578074i | \(-0.803804\pi\) | ||
0.815984 | − | 0.578074i | \(-0.196196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 209480. | 0.282577 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 657351.i | − | 0.882624i | −0.897354 | − | 0.441312i | \(-0.854513\pi\) | ||
0.897354 | − | 0.441312i | \(-0.145487\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 591401.i | 0.790406i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 493504.i | − | 0.656527i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −253643. | −0.335879 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −211184. | −0.278371 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −254913. | −0.334475 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 871862. | 1.13876 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −853878. | −1.11019 | −0.555094 | − | 0.831788i | \(-0.687318\pi\) | ||||
−0.555094 | + | 0.831788i | \(0.687318\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 953364.i | − | 1.23390i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 170801. | 0.220059 | 0.110030 | − | 0.993928i | \(-0.464905\pi\) | ||||
0.110030 | + | 0.993928i | \(0.464905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 608395. | 0.780304 | 0.390152 | − | 0.920750i | \(-0.372422\pi\) | ||||
0.390152 | + | 0.920750i | \(0.372422\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10151.6 | −0.0129613 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 433884.i | − | 0.551476i | −0.961233 | − | 0.275738i | \(-0.911078\pi\) | ||
0.961233 | − | 0.275738i | \(-0.0889222\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 686570.i | 0.868722i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −70594.4 | −0.0889232 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40763.6i | 0.0511175i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 129824. | 0.162072 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 221455.i | 0.275234i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 614988.i | − | 0.760935i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 479874. | 0.591122 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 190734. | + | 639158.i | 0.233912 | + | 0.783850i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.42878e6i | − | 1.74449i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.51273e6 | 1.83885 | 0.919425 | − | 0.393265i | \(-0.128655\pi\) | ||||
0.919425 | + | 0.393265i | \(0.128655\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −259716. | −0.314319 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.18401e6i | − | 1.42665i | −0.700831 | − | 0.713327i | \(-0.747187\pi\) | ||
0.700831 | − | 0.713327i | \(-0.252813\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −111044. | −0.133215 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 604498.i | − | 0.722025i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.53131e6 | 1.82106 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −367164. | −0.434740 | −0.217370 | − | 0.976089i | \(-0.569748\pi\) | ||||
−0.217370 | + | 0.976089i | \(0.569748\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 90602.9i | 0.106813i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 226508.i | − | 0.265877i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 78482.3i | − | 0.0917251i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −380302. | −0.442557 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1.60017e6i | − | 1.85410i | −0.374936 | − | 0.927051i | \(-0.622335\pi\) | ||
0.374936 | − | 0.927051i | \(-0.377665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 71991.8i | − | 0.0830585i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.32464e6i | 1.52173i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 62288.6i | 0.0712501i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 241683.i | 0.275275i | 0.990483 | + | 0.137638i | \(0.0439510\pi\) | ||||
−0.990483 | + | 0.137638i | \(0.956049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 221653. | 0.251387 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −586773. | −0.662660 | −0.331330 | − | 0.943515i | \(-0.607497\pi\) | ||||
−0.331330 | + | 0.943515i | \(0.607497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −478215. | −0.537774 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 918091.i | 1.02807i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.14388e6 | 1.27550 | 0.637748 | − | 0.770245i | \(-0.279866\pi\) | ||||
0.637748 | + | 0.770245i | \(0.279866\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 184992.i | − | 0.205410i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 74400.7i | 0.0822652i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.25121e6i | 1.37766i | 0.724922 | + | 0.688831i | \(0.241876\pi\) | ||||
−0.724922 | + | 0.688831i | \(0.758124\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.31567e6 | 1.44259 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 73750.8 | 0.0805272 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −740332. | −0.804988 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.17196e6 | 1.26901 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 212280. | 0.228906 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 95992.8i | − | 0.103082i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −687143. | −0.734843 | −0.367421 | − | 0.930055i | \(-0.619759\pi\) | ||||
−0.367421 | + | 0.930055i | \(0.619759\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −184676. | −0.196681 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 288966. | 0.306484 | 0.153242 | − | 0.988189i | \(-0.451029\pi\) | ||||
0.153242 | + | 0.988189i | \(0.451029\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 964245.i | − | 1.01850i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 33677.4i | − | 0.0354266i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.40399e6 | 1.47087 | 0.735434 | − | 0.677597i | \(-0.236978\pi\) | ||||
0.735434 | + | 0.677597i | \(0.236978\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 246918.i | 0.257625i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 111949. | 0.116327 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 308569.i | − | 0.319334i | −0.987171 | − | 0.159667i | \(-0.948958\pi\) | ||
0.987171 | − | 0.159667i | \(-0.0510421\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.35535e6i | 1.39695i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 61545.6 | 0.0631776 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −435419. | − | 1.45911e6i | −0.445159 | − | 1.49175i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 630206.i | 0.641705i | 0.947129 | + | 0.320853i | \(0.103969\pi\) | ||||
−0.947129 | + | 0.320853i | \(0.896031\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −341039. | −0.345864 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.69701e6 | −1.71411 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.44327e6i | − | 1.45197i | −0.687713 | − | 0.725983i | \(-0.741385\pi\) | ||
0.687713 | − | 0.725983i | \(-0.258615\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 495085. | 0.496076 |
(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 | 688.5.b.d.257.8 | 12 | ||
4.3 | odd | 2 | 43.5.b.b.42.10 | yes | 12 | ||
12.11 | even | 2 | 387.5.b.c.343.3 | 12 | |||
43.42 | odd | 2 | inner | 688.5.b.d.257.5 | 12 | ||
172.171 | even | 2 | 43.5.b.b.42.3 | ✓ | 12 | ||
516.515 | odd | 2 | 387.5.b.c.343.10 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.5.b.b.42.3 | ✓ | 12 | 172.171 | even | 2 | ||
43.5.b.b.42.10 | yes | 12 | 4.3 | odd | 2 | ||
387.5.b.c.343.3 | 12 | 12.11 | even | 2 | |||
387.5.b.c.343.10 | 12 | 516.515 | odd | 2 | |||
688.5.b.d.257.5 | 12 | 43.42 | odd | 2 | inner | ||
688.5.b.d.257.8 | 12 | 1.1 | even | 1 | trivial |