Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,4,Mod(1,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.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: | \(20.6506685020\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 350.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −5.00000 | −0.962250 | −0.481125 | − | 0.876652i | \(-0.659772\pi\) | ||||
−0.481125 | + | 0.876652i | \(0.659772\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 10.0000 | 0.680414 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.0274101 | −0.0137051 | − | 0.999906i | \(-0.504363\pi\) | ||||
−0.0137051 | + | 0.999906i | \(0.504363\pi\) | |||||||
\(12\) | −20.0000 | −0.481125 | ||||||||
\(13\) | −7.00000 | −0.149342 | −0.0746712 | − | 0.997208i | \(-0.523791\pi\) | ||||
−0.0746712 | + | 0.997208i | \(0.523791\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 51.0000 | 0.727607 | 0.363803 | − | 0.931476i | \(-0.381478\pi\) | ||||
0.363803 | + | 0.931476i | \(0.381478\pi\) | |||||||
\(18\) | 4.00000 | 0.0523783 | ||||||||
\(19\) | 30.0000 | 0.362235 | 0.181118 | − | 0.983461i | \(-0.442029\pi\) | ||||
0.181118 | + | 0.983461i | \(0.442029\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −35.0000 | −0.363696 | ||||||||
\(22\) | 2.00000 | 0.0193819 | ||||||||
\(23\) | 50.0000 | 0.453292 | 0.226646 | − | 0.973977i | \(-0.427224\pi\) | ||||
0.226646 | + | 0.973977i | \(0.427224\pi\) | |||||||
\(24\) | 40.0000 | 0.340207 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 14.0000 | 0.105601 | ||||||||
\(27\) | 145.000 | 1.03353 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | 79.0000 | 0.505860 | 0.252930 | − | 0.967485i | \(-0.418606\pi\) | ||||
0.252930 | + | 0.967485i | \(0.418606\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −212.000 | −1.22827 | −0.614134 | − | 0.789202i | \(-0.710495\pi\) | ||||
−0.614134 | + | 0.789202i | \(0.710495\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 5.00000 | 0.0263754 | ||||||||
\(34\) | −102.000 | −0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.00000 | −0.0370370 | ||||||||
\(37\) | 190.000 | 0.844211 | 0.422106 | − | 0.906547i | \(-0.361291\pi\) | ||||
0.422106 | + | 0.906547i | \(0.361291\pi\) | |||||||
\(38\) | −60.0000 | −0.256139 | ||||||||
\(39\) | 35.0000 | 0.143705 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −308.000 | −1.17321 | −0.586604 | − | 0.809874i | \(-0.699535\pi\) | ||||
−0.586604 | + | 0.809874i | \(0.699535\pi\) | |||||||
\(42\) | 70.0000 | 0.257172 | ||||||||
\(43\) | −422.000 | −1.49661 | −0.748307 | − | 0.663353i | \(-0.769133\pi\) | ||||
−0.748307 | + | 0.663353i | \(0.769133\pi\) | |||||||
\(44\) | −4.00000 | −0.0137051 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −100.000 | −0.320526 | ||||||||
\(47\) | −121.000 | −0.375525 | −0.187762 | − | 0.982214i | \(-0.560123\pi\) | ||||
−0.187762 | + | 0.982214i | \(0.560123\pi\) | |||||||
\(48\) | −80.0000 | −0.240563 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −255.000 | −0.700140 | ||||||||
\(52\) | −28.0000 | −0.0746712 | ||||||||
\(53\) | −664.000 | −1.72089 | −0.860447 | − | 0.509539i | \(-0.829816\pi\) | ||||
−0.860447 | + | 0.509539i | \(0.829816\pi\) | |||||||
\(54\) | −290.000 | −0.730815 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | −150.000 | −0.348561 | ||||||||
\(58\) | −158.000 | −0.357697 | ||||||||
\(59\) | 628.000 | 1.38574 | 0.692870 | − | 0.721063i | \(-0.256346\pi\) | ||||
0.692870 | + | 0.721063i | \(0.256346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −684.000 | −1.43569 | −0.717846 | − | 0.696202i | \(-0.754872\pi\) | ||||
−0.717846 | + | 0.696202i | \(0.754872\pi\) | |||||||
\(62\) | 424.000 | 0.868517 | ||||||||
\(63\) | −14.0000 | −0.0279974 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −10.0000 | −0.0186502 | ||||||||
\(67\) | −1056.00 | −1.92554 | −0.962768 | − | 0.270328i | \(-0.912868\pi\) | ||||
−0.962768 | + | 0.270328i | \(0.912868\pi\) | |||||||
\(68\) | 204.000 | 0.363803 | ||||||||
\(69\) | −250.000 | −0.436181 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 744.000 | 1.24361 | 0.621807 | − | 0.783171i | \(-0.286399\pi\) | ||||
0.621807 | + | 0.783171i | \(0.286399\pi\) | |||||||
\(72\) | 16.0000 | 0.0261891 | ||||||||
\(73\) | −726.000 | −1.16400 | −0.581999 | − | 0.813189i | \(-0.697729\pi\) | ||||
−0.581999 | + | 0.813189i | \(0.697729\pi\) | |||||||
\(74\) | −380.000 | −0.596947 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 120.000 | 0.181118 | ||||||||
\(77\) | −7.00000 | −0.0103601 | ||||||||
\(78\) | −70.0000 | −0.101615 | ||||||||
\(79\) | −407.000 | −0.579634 | −0.289817 | − | 0.957082i | \(-0.593594\pi\) | ||||
−0.289817 | + | 0.957082i | \(0.593594\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | 616.000 | 0.829583 | ||||||||
\(83\) | −644.000 | −0.851665 | −0.425832 | − | 0.904802i | \(-0.640019\pi\) | ||||
−0.425832 | + | 0.904802i | \(0.640019\pi\) | |||||||
\(84\) | −140.000 | −0.181848 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 844.000 | 1.05827 | ||||||||
\(87\) | −395.000 | −0.486764 | ||||||||
\(88\) | 8.00000 | 0.00969094 | ||||||||
\(89\) | −880.000 | −1.04809 | −0.524044 | − | 0.851691i | \(-0.675577\pi\) | ||||
−0.524044 | + | 0.851691i | \(0.675577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −49.0000 | −0.0564461 | ||||||||
\(92\) | 200.000 | 0.226646 | ||||||||
\(93\) | 1060.00 | 1.18190 | ||||||||
\(94\) | 242.000 | 0.265536 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 160.000 | 0.170103 | ||||||||
\(97\) | 1351.00 | 1.41416 | 0.707079 | − | 0.707135i | \(-0.250013\pi\) | ||||
0.707079 | + | 0.707135i | \(0.250013\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 2.00000 | 0.00203038 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 54.0000 | 0.0532000 | 0.0266000 | − | 0.999646i | \(-0.491532\pi\) | ||||
0.0266000 | + | 0.999646i | \(0.491532\pi\) | |||||||
\(102\) | 510.000 | 0.495074 | ||||||||
\(103\) | 1027.00 | 0.982459 | 0.491230 | − | 0.871030i | \(-0.336548\pi\) | ||||
0.491230 | + | 0.871030i | \(0.336548\pi\) | |||||||
\(104\) | 56.0000 | 0.0528005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1328.00 | 1.21686 | ||||||||
\(107\) | −314.000 | −0.283697 | −0.141848 | − | 0.989888i | \(-0.545305\pi\) | ||||
−0.141848 | + | 0.989888i | \(0.545305\pi\) | |||||||
\(108\) | 580.000 | 0.516764 | ||||||||
\(109\) | −1611.00 | −1.41565 | −0.707825 | − | 0.706388i | \(-0.750323\pi\) | ||||
−0.707825 | + | 0.706388i | \(0.750323\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −950.000 | −0.812342 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | −366.000 | −0.304694 | −0.152347 | − | 0.988327i | \(-0.548683\pi\) | ||||
−0.152347 | + | 0.988327i | \(0.548683\pi\) | |||||||
\(114\) | 300.000 | 0.246470 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 316.000 | 0.252930 | ||||||||
\(117\) | 14.0000 | 0.0110624 | ||||||||
\(118\) | −1256.00 | −0.979866 | ||||||||
\(119\) | 357.000 | 0.275010 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1330.00 | −0.999249 | ||||||||
\(122\) | 1368.00 | 1.01519 | ||||||||
\(123\) | 1540.00 | 1.12892 | ||||||||
\(124\) | −848.000 | −0.614134 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 28.0000 | 0.0197971 | ||||||||
\(127\) | −604.000 | −0.422018 | −0.211009 | − | 0.977484i | \(-0.567675\pi\) | ||||
−0.211009 | + | 0.977484i | \(0.567675\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 2110.00 | 1.44012 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2914.00 | 1.94349 | 0.971746 | − | 0.236030i | \(-0.0758465\pi\) | ||||
0.971746 | + | 0.236030i | \(0.0758465\pi\) | |||||||
\(132\) | 20.0000 | 0.0131877 | ||||||||
\(133\) | 210.000 | 0.136912 | ||||||||
\(134\) | 2112.00 | 1.36156 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −408.000 | −0.257248 | ||||||||
\(137\) | −2568.00 | −1.60145 | −0.800726 | − | 0.599030i | \(-0.795553\pi\) | ||||
−0.800726 | + | 0.599030i | \(0.795553\pi\) | |||||||
\(138\) | 500.000 | 0.308426 | ||||||||
\(139\) | 1274.00 | 0.777405 | 0.388702 | − | 0.921363i | \(-0.372923\pi\) | ||||
0.388702 | + | 0.921363i | \(0.372923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 605.000 | 0.361349 | ||||||||
\(142\) | −1488.00 | −0.879368 | ||||||||
\(143\) | 7.00000 | 0.00409349 | ||||||||
\(144\) | −32.0000 | −0.0185185 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1452.00 | 0.823071 | ||||||||
\(147\) | −245.000 | −0.137464 | ||||||||
\(148\) | 760.000 | 0.422106 | ||||||||
\(149\) | 594.000 | 0.326593 | 0.163297 | − | 0.986577i | \(-0.447787\pi\) | ||||
0.163297 | + | 0.986577i | \(0.447787\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1527.00 | −0.822950 | −0.411475 | − | 0.911421i | \(-0.634986\pi\) | ||||
−0.411475 | + | 0.911421i | \(0.634986\pi\) | |||||||
\(152\) | −240.000 | −0.128070 | ||||||||
\(153\) | −102.000 | −0.0538968 | ||||||||
\(154\) | 14.0000 | 0.00732566 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 140.000 | 0.0718524 | ||||||||
\(157\) | −530.000 | −0.269418 | −0.134709 | − | 0.990885i | \(-0.543010\pi\) | ||||
−0.134709 | + | 0.990885i | \(0.543010\pi\) | |||||||
\(158\) | 814.000 | 0.409863 | ||||||||
\(159\) | 3320.00 | 1.65593 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 350.000 | 0.171328 | ||||||||
\(162\) | 1342.00 | 0.650849 | ||||||||
\(163\) | 3662.00 | 1.75969 | 0.879847 | − | 0.475258i | \(-0.157645\pi\) | ||||
0.879847 | + | 0.475258i | \(0.157645\pi\) | |||||||
\(164\) | −1232.00 | −0.586604 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1288.00 | 0.602218 | ||||||||
\(167\) | 315.000 | 0.145961 | 0.0729803 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729803 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(168\) | 280.000 | 0.128586 | ||||||||
\(169\) | −2148.00 | −0.977697 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −60.0000 | −0.0268322 | ||||||||
\(172\) | −1688.00 | −0.748307 | ||||||||
\(173\) | 1251.00 | 0.549779 | 0.274890 | − | 0.961476i | \(-0.411359\pi\) | ||||
0.274890 | + | 0.961476i | \(0.411359\pi\) | |||||||
\(174\) | 790.000 | 0.344194 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.0000 | −0.00685253 | ||||||||
\(177\) | −3140.00 | −1.33343 | ||||||||
\(178\) | 1760.00 | 0.741110 | ||||||||
\(179\) | −148.000 | −0.0617991 | −0.0308996 | − | 0.999522i | \(-0.509837\pi\) | ||||
−0.0308996 | + | 0.999522i | \(0.509837\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1344.00 | −0.551927 | −0.275963 | − | 0.961168i | \(-0.588997\pi\) | ||||
−0.275963 | + | 0.961168i | \(0.588997\pi\) | |||||||
\(182\) | 98.0000 | 0.0399134 | ||||||||
\(183\) | 3420.00 | 1.38150 | ||||||||
\(184\) | −400.000 | −0.160263 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2120.00 | −0.835731 | ||||||||
\(187\) | −51.0000 | −0.0199438 | ||||||||
\(188\) | −484.000 | −0.187762 | ||||||||
\(189\) | 1015.00 | 0.390637 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −561.000 | −0.212526 | −0.106263 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106263 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(192\) | −320.000 | −0.120281 | ||||||||
\(193\) | −3016.00 | −1.12485 | −0.562426 | − | 0.826848i | \(-0.690132\pi\) | ||||
−0.562426 | + | 0.826848i | \(0.690132\pi\) | |||||||
\(194\) | −2702.00 | −0.999960 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 3232.00 | 1.16889 | 0.584443 | − | 0.811435i | \(-0.301313\pi\) | ||||
0.584443 | + | 0.811435i | \(0.301313\pi\) | |||||||
\(198\) | −4.00000 | −0.00143570 | ||||||||
\(199\) | −1164.00 | −0.414642 | −0.207321 | − | 0.978273i | \(-0.566474\pi\) | ||||
−0.207321 | + | 0.978273i | \(0.566474\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5280.00 | 1.85285 | ||||||||
\(202\) | −108.000 | −0.0376181 | ||||||||
\(203\) | 553.000 | 0.191197 | ||||||||
\(204\) | −1020.00 | −0.350070 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2054.00 | −0.694704 | ||||||||
\(207\) | −100.000 | −0.0335772 | ||||||||
\(208\) | −112.000 | −0.0373356 | ||||||||
\(209\) | −30.0000 | −0.00992892 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 569.000 | 0.185647 | 0.0928236 | − | 0.995683i | \(-0.470411\pi\) | ||||
0.0928236 | + | 0.995683i | \(0.470411\pi\) | |||||||
\(212\) | −2656.00 | −0.860447 | ||||||||
\(213\) | −3720.00 | −1.19667 | ||||||||
\(214\) | 628.000 | 0.200604 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1160.00 | −0.365407 | ||||||||
\(217\) | −1484.00 | −0.464242 | ||||||||
\(218\) | 3222.00 | 1.00102 | ||||||||
\(219\) | 3630.00 | 1.12006 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −357.000 | −0.108663 | ||||||||
\(222\) | 1900.00 | 0.574413 | ||||||||
\(223\) | −693.000 | −0.208102 | −0.104051 | − | 0.994572i | \(-0.533180\pi\) | ||||
−0.104051 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 732.000 | 0.215451 | ||||||||
\(227\) | 4279.00 | 1.25113 | 0.625567 | − | 0.780171i | \(-0.284868\pi\) | ||||
0.625567 | + | 0.780171i | \(0.284868\pi\) | |||||||
\(228\) | −600.000 | −0.174281 | ||||||||
\(229\) | −3316.00 | −0.956888 | −0.478444 | − | 0.878118i | \(-0.658799\pi\) | ||||
−0.478444 | + | 0.878118i | \(0.658799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 35.0000 | 0.00996897 | ||||||||
\(232\) | −632.000 | −0.178848 | ||||||||
\(233\) | −3912.00 | −1.09993 | −0.549965 | − | 0.835188i | \(-0.685359\pi\) | ||||
−0.549965 | + | 0.835188i | \(0.685359\pi\) | |||||||
\(234\) | −28.0000 | −0.00782230 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2512.00 | 0.692870 | ||||||||
\(237\) | 2035.00 | 0.557753 | ||||||||
\(238\) | −714.000 | −0.194461 | ||||||||
\(239\) | −5451.00 | −1.47530 | −0.737648 | − | 0.675185i | \(-0.764064\pi\) | ||||
−0.737648 | + | 0.675185i | \(0.764064\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 250.000 | 0.0668212 | 0.0334106 | − | 0.999442i | \(-0.489363\pi\) | ||||
0.0334106 | + | 0.999442i | \(0.489363\pi\) | |||||||
\(242\) | 2660.00 | 0.706576 | ||||||||
\(243\) | −560.000 | −0.147835 | ||||||||
\(244\) | −2736.00 | −0.717846 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3080.00 | −0.798267 | ||||||||
\(247\) | −210.000 | −0.0540971 | ||||||||
\(248\) | 1696.00 | 0.434258 | ||||||||
\(249\) | 3220.00 | 0.819515 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 910.000 | 0.228839 | 0.114420 | − | 0.993432i | \(-0.463499\pi\) | ||||
0.114420 | + | 0.993432i | \(0.463499\pi\) | |||||||
\(252\) | −56.0000 | −0.0139987 | ||||||||
\(253\) | −50.0000 | −0.0124248 | ||||||||
\(254\) | 1208.00 | 0.298412 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 6494.00 | 1.57620 | 0.788102 | − | 0.615544i | \(-0.211064\pi\) | ||||
0.788102 | + | 0.615544i | \(0.211064\pi\) | |||||||
\(258\) | −4220.00 | −1.01832 | ||||||||
\(259\) | 1330.00 | 0.319082 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −158.000 | −0.0374711 | ||||||||
\(262\) | −5828.00 | −1.37426 | ||||||||
\(263\) | −1434.00 | −0.336214 | −0.168107 | − | 0.985769i | \(-0.553765\pi\) | ||||
−0.168107 | + | 0.985769i | \(0.553765\pi\) | |||||||
\(264\) | −40.0000 | −0.00932511 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −420.000 | −0.0968115 | ||||||||
\(267\) | 4400.00 | 1.00852 | ||||||||
\(268\) | −4224.00 | −0.962768 | ||||||||
\(269\) | −5014.00 | −1.13646 | −0.568232 | − | 0.822868i | \(-0.692373\pi\) | ||||
−0.568232 | + | 0.822868i | \(0.692373\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5420.00 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(272\) | 816.000 | 0.181902 | ||||||||
\(273\) | 245.000 | 0.0543153 | ||||||||
\(274\) | 5136.00 | 1.13240 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1000.00 | −0.218090 | ||||||||
\(277\) | −3674.00 | −0.796929 | −0.398464 | − | 0.917184i | \(-0.630457\pi\) | ||||
−0.398464 | + | 0.917184i | \(0.630457\pi\) | |||||||
\(278\) | −2548.00 | −0.549708 | ||||||||
\(279\) | 424.000 | 0.0909829 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7331.00 | 1.55634 | 0.778169 | − | 0.628055i | \(-0.216149\pi\) | ||||
0.778169 | + | 0.628055i | \(0.216149\pi\) | |||||||
\(282\) | −1210.00 | −0.255512 | ||||||||
\(283\) | −271.000 | −0.0569232 | −0.0284616 | − | 0.999595i | \(-0.509061\pi\) | ||||
−0.0284616 | + | 0.999595i | \(0.509061\pi\) | |||||||
\(284\) | 2976.00 | 0.621807 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.0000 | −0.00289454 | ||||||||
\(287\) | −2156.00 | −0.443431 | ||||||||
\(288\) | 64.0000 | 0.0130946 | ||||||||
\(289\) | −2312.00 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6755.00 | −1.36077 | ||||||||
\(292\) | −2904.00 | −0.581999 | ||||||||
\(293\) | −4305.00 | −0.858364 | −0.429182 | − | 0.903218i | \(-0.641198\pi\) | ||||
−0.429182 | + | 0.903218i | \(0.641198\pi\) | |||||||
\(294\) | 490.000 | 0.0972020 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1520.00 | −0.298474 | ||||||||
\(297\) | −145.000 | −0.0283291 | ||||||||
\(298\) | −1188.00 | −0.230936 | ||||||||
\(299\) | −350.000 | −0.0676957 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2954.00 | −0.565667 | ||||||||
\(302\) | 3054.00 | 0.581914 | ||||||||
\(303\) | −270.000 | −0.0511917 | ||||||||
\(304\) | 480.000 | 0.0905588 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 204.000 | 0.0381108 | ||||||||
\(307\) | −2639.00 | −0.490605 | −0.245302 | − | 0.969447i | \(-0.578887\pi\) | ||||
−0.245302 | + | 0.969447i | \(0.578887\pi\) | |||||||
\(308\) | −28.0000 | −0.00518003 | ||||||||
\(309\) | −5135.00 | −0.945372 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8514.00 | −1.55236 | −0.776181 | − | 0.630510i | \(-0.782846\pi\) | ||||
−0.776181 | + | 0.630510i | \(0.782846\pi\) | |||||||
\(312\) | −280.000 | −0.0508073 | ||||||||
\(313\) | −219.000 | −0.0395483 | −0.0197741 | − | 0.999804i | \(-0.506295\pi\) | ||||
−0.0197741 | + | 0.999804i | \(0.506295\pi\) | |||||||
\(314\) | 1060.00 | 0.190507 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1628.00 | −0.289817 | ||||||||
\(317\) | 4026.00 | 0.713321 | 0.356660 | − | 0.934234i | \(-0.383915\pi\) | ||||
0.356660 | + | 0.934234i | \(0.383915\pi\) | |||||||
\(318\) | −6640.00 | −1.17092 | ||||||||
\(319\) | −79.0000 | −0.0138657 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1570.00 | 0.272987 | ||||||||
\(322\) | −700.000 | −0.121147 | ||||||||
\(323\) | 1530.00 | 0.263565 | ||||||||
\(324\) | −2684.00 | −0.460219 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7324.00 | −1.24429 | ||||||||
\(327\) | 8055.00 | 1.36221 | ||||||||
\(328\) | 2464.00 | 0.414792 | ||||||||
\(329\) | −847.000 | −0.141935 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7036.00 | −1.16838 | −0.584190 | − | 0.811617i | \(-0.698588\pi\) | ||||
−0.584190 | + | 0.811617i | \(0.698588\pi\) | |||||||
\(332\) | −2576.00 | −0.425832 | ||||||||
\(333\) | −380.000 | −0.0625341 | ||||||||
\(334\) | −630.000 | −0.103210 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −560.000 | −0.0909241 | ||||||||
\(337\) | −10362.0 | −1.67494 | −0.837469 | − | 0.546485i | \(-0.815966\pi\) | ||||
−0.837469 | + | 0.546485i | \(0.815966\pi\) | |||||||
\(338\) | 4296.00 | 0.691336 | ||||||||
\(339\) | 1830.00 | 0.293192 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 212.000 | 0.0336670 | ||||||||
\(342\) | 120.000 | 0.0189733 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 3376.00 | 0.529133 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2502.00 | −0.388752 | ||||||||
\(347\) | 8422.00 | 1.30293 | 0.651465 | − | 0.758679i | \(-0.274155\pi\) | ||||
0.651465 | + | 0.758679i | \(0.274155\pi\) | |||||||
\(348\) | −1580.00 | −0.243382 | ||||||||
\(349\) | −7350.00 | −1.12733 | −0.563663 | − | 0.826005i | \(-0.690608\pi\) | ||||
−0.563663 | + | 0.826005i | \(0.690608\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1015.00 | −0.154350 | ||||||||
\(352\) | 32.0000 | 0.00484547 | ||||||||
\(353\) | −3057.00 | −0.460928 | −0.230464 | − | 0.973081i | \(-0.574024\pi\) | ||||
−0.230464 | + | 0.973081i | \(0.574024\pi\) | |||||||
\(354\) | 6280.00 | 0.942876 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3520.00 | −0.524044 | ||||||||
\(357\) | −1785.00 | −0.264628 | ||||||||
\(358\) | 296.000 | 0.0436986 | ||||||||
\(359\) | 8392.00 | 1.23374 | 0.616870 | − | 0.787065i | \(-0.288400\pi\) | ||||
0.616870 | + | 0.787065i | \(0.288400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5959.00 | −0.868786 | ||||||||
\(362\) | 2688.00 | 0.390271 | ||||||||
\(363\) | 6650.00 | 0.961527 | ||||||||
\(364\) | −196.000 | −0.0282231 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6840.00 | −0.976865 | ||||||||
\(367\) | −8377.00 | −1.19149 | −0.595744 | − | 0.803175i | \(-0.703143\pi\) | ||||
−0.595744 | + | 0.803175i | \(0.703143\pi\) | |||||||
\(368\) | 800.000 | 0.113323 | ||||||||
\(369\) | 616.000 | 0.0869043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4648.00 | −0.650437 | ||||||||
\(372\) | 4240.00 | 0.590951 | ||||||||
\(373\) | 1968.00 | 0.273188 | 0.136594 | − | 0.990627i | \(-0.456384\pi\) | ||||
0.136594 | + | 0.990627i | \(0.456384\pi\) | |||||||
\(374\) | 102.000 | 0.0141024 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 968.000 | 0.132768 | ||||||||
\(377\) | −553.000 | −0.0755463 | ||||||||
\(378\) | −2030.00 | −0.276222 | ||||||||
\(379\) | 1052.00 | 0.142579 | 0.0712897 | − | 0.997456i | \(-0.477289\pi\) | ||||
0.0712897 | + | 0.997456i | \(0.477289\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3020.00 | 0.406087 | ||||||||
\(382\) | 1122.00 | 0.150279 | ||||||||
\(383\) | 2308.00 | 0.307920 | 0.153960 | − | 0.988077i | \(-0.450797\pi\) | ||||
0.153960 | + | 0.988077i | \(0.450797\pi\) | |||||||
\(384\) | 640.000 | 0.0850517 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6032.00 | 0.795390 | ||||||||
\(387\) | 844.000 | 0.110860 | ||||||||
\(388\) | 5404.00 | 0.707079 | ||||||||
\(389\) | 2281.00 | 0.297304 | 0.148652 | − | 0.988890i | \(-0.452507\pi\) | ||||
0.148652 | + | 0.988890i | \(0.452507\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2550.00 | 0.329819 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | −14570.0 | −1.87013 | ||||||||
\(394\) | −6464.00 | −0.826527 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 8.00000 | 0.00101519 | ||||||||
\(397\) | 14635.0 | 1.85015 | 0.925075 | − | 0.379784i | \(-0.124002\pi\) | ||||
0.925075 | + | 0.379784i | \(0.124002\pi\) | |||||||
\(398\) | 2328.00 | 0.293196 | ||||||||
\(399\) | −1050.00 | −0.131744 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5641.00 | 0.702489 | 0.351245 | − | 0.936284i | \(-0.385759\pi\) | ||||
0.351245 | + | 0.936284i | \(0.385759\pi\) | |||||||
\(402\) | −10560.0 | −1.31016 | ||||||||
\(403\) | 1484.00 | 0.183433 | ||||||||
\(404\) | 216.000 | 0.0266000 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1106.00 | −0.135197 | ||||||||
\(407\) | −190.000 | −0.0231399 | ||||||||
\(408\) | 2040.00 | 0.247537 | ||||||||
\(409\) | 6410.00 | 0.774949 | 0.387474 | − | 0.921880i | \(-0.373348\pi\) | ||||
0.387474 | + | 0.921880i | \(0.373348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12840.0 | 1.54100 | ||||||||
\(412\) | 4108.00 | 0.491230 | ||||||||
\(413\) | 4396.00 | 0.523760 | ||||||||
\(414\) | 200.000 | 0.0237427 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 224.000 | 0.0264002 | ||||||||
\(417\) | −6370.00 | −0.748058 | ||||||||
\(418\) | 60.0000 | 0.00702080 | ||||||||
\(419\) | 4816.00 | 0.561520 | 0.280760 | − | 0.959778i | \(-0.409413\pi\) | ||||
0.280760 | + | 0.959778i | \(0.409413\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15325.0 | 1.77410 | 0.887048 | − | 0.461676i | \(-0.152752\pi\) | ||||
0.887048 | + | 0.461676i | \(0.152752\pi\) | |||||||
\(422\) | −1138.00 | −0.131272 | ||||||||
\(423\) | 242.000 | 0.0278166 | ||||||||
\(424\) | 5312.00 | 0.608428 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7440.00 | 0.846172 | ||||||||
\(427\) | −4788.00 | −0.542641 | ||||||||
\(428\) | −1256.00 | −0.141848 | ||||||||
\(429\) | −35.0000 | −0.00393896 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1875.00 | 0.209549 | 0.104774 | − | 0.994496i | \(-0.466588\pi\) | ||||
0.104774 | + | 0.994496i | \(0.466588\pi\) | |||||||
\(432\) | 2320.00 | 0.258382 | ||||||||
\(433\) | 13874.0 | 1.53982 | 0.769910 | − | 0.638153i | \(-0.220301\pi\) | ||||
0.769910 | + | 0.638153i | \(0.220301\pi\) | |||||||
\(434\) | 2968.00 | 0.328269 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6444.00 | −0.707825 | ||||||||
\(437\) | 1500.00 | 0.164198 | ||||||||
\(438\) | −7260.00 | −0.792000 | ||||||||
\(439\) | −3442.00 | −0.374209 | −0.187104 | − | 0.982340i | \(-0.559910\pi\) | ||||
−0.187104 | + | 0.982340i | \(0.559910\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −98.0000 | −0.0105820 | ||||||||
\(442\) | 714.000 | 0.0768360 | ||||||||
\(443\) | −16750.0 | −1.79643 | −0.898213 | − | 0.439561i | \(-0.855134\pi\) | ||||
−0.898213 | + | 0.439561i | \(0.855134\pi\) | |||||||
\(444\) | −3800.00 | −0.406171 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1386.00 | 0.147150 | ||||||||
\(447\) | −2970.00 | −0.314264 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 695.000 | 0.0730492 | 0.0365246 | − | 0.999333i | \(-0.488371\pi\) | ||||
0.0365246 | + | 0.999333i | \(0.488371\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 308.000 | 0.0321578 | ||||||||
\(452\) | −1464.00 | −0.152347 | ||||||||
\(453\) | 7635.00 | 0.791884 | ||||||||
\(454\) | −8558.00 | −0.884685 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1200.00 | 0.123235 | ||||||||
\(457\) | −5760.00 | −0.589587 | −0.294794 | − | 0.955561i | \(-0.595251\pi\) | ||||
−0.294794 | + | 0.955561i | \(0.595251\pi\) | |||||||
\(458\) | 6632.00 | 0.676622 | ||||||||
\(459\) | 7395.00 | 0.752002 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13440.0 | 1.35784 | 0.678919 | − | 0.734213i | \(-0.262449\pi\) | ||||
0.678919 | + | 0.734213i | \(0.262449\pi\) | |||||||
\(462\) | −70.0000 | −0.00704912 | ||||||||
\(463\) | 7348.00 | 0.737561 | 0.368780 | − | 0.929517i | \(-0.379775\pi\) | ||||
0.368780 | + | 0.929517i | \(0.379775\pi\) | |||||||
\(464\) | 1264.00 | 0.126465 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7824.00 | 0.777768 | ||||||||
\(467\) | 17925.0 | 1.77617 | 0.888084 | − | 0.459682i | \(-0.152037\pi\) | ||||
0.888084 | + | 0.459682i | \(0.152037\pi\) | |||||||
\(468\) | 56.0000 | 0.00553120 | ||||||||
\(469\) | −7392.00 | −0.727784 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2650.00 | 0.259247 | ||||||||
\(472\) | −5024.00 | −0.489933 | ||||||||
\(473\) | 422.000 | 0.0410224 | ||||||||
\(474\) | −4070.00 | −0.394391 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1428.00 | 0.137505 | ||||||||
\(477\) | 1328.00 | 0.127474 | ||||||||
\(478\) | 10902.0 | 1.04319 | ||||||||
\(479\) | 12346.0 | 1.17767 | 0.588834 | − | 0.808254i | \(-0.299587\pi\) | ||||
0.588834 | + | 0.808254i | \(0.299587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1330.00 | −0.126076 | ||||||||
\(482\) | −500.000 | −0.0472497 | ||||||||
\(483\) | −1750.00 | −0.164861 | ||||||||
\(484\) | −5320.00 | −0.499624 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1120.00 | 0.104535 | ||||||||
\(487\) | −15014.0 | −1.39702 | −0.698511 | − | 0.715600i | \(-0.746153\pi\) | ||||
−0.698511 | + | 0.715600i | \(0.746153\pi\) | |||||||
\(488\) | 5472.00 | 0.507594 | ||||||||
\(489\) | −18310.0 | −1.69327 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4723.00 | −0.434106 | −0.217053 | − | 0.976160i | \(-0.569644\pi\) | ||||
−0.217053 | + | 0.976160i | \(0.569644\pi\) | |||||||
\(492\) | 6160.00 | 0.564460 | ||||||||
\(493\) | 4029.00 | 0.368067 | ||||||||
\(494\) | 420.000 | 0.0382524 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3392.00 | −0.307067 | ||||||||
\(497\) | 5208.00 | 0.470042 | ||||||||
\(498\) | −6440.00 | −0.579485 | ||||||||
\(499\) | 11227.0 | 1.00719 | 0.503597 | − | 0.863939i | \(-0.332010\pi\) | ||||
0.503597 | + | 0.863939i | \(0.332010\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1575.00 | −0.140451 | ||||||||
\(502\) | −1820.00 | −0.161814 | ||||||||
\(503\) | 4557.00 | 0.403949 | 0.201975 | − | 0.979391i | \(-0.435264\pi\) | ||||
0.201975 | + | 0.979391i | \(0.435264\pi\) | |||||||
\(504\) | 112.000 | 0.00989856 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 100.000 | 0.00878566 | ||||||||
\(507\) | 10740.0 | 0.940789 | ||||||||
\(508\) | −2416.00 | −0.211009 | ||||||||
\(509\) | −14110.0 | −1.22871 | −0.614356 | − | 0.789029i | \(-0.710584\pi\) | ||||
−0.614356 | + | 0.789029i | \(0.710584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5082.00 | −0.439950 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 4350.00 | 0.374380 | ||||||||
\(514\) | −12988.0 | −1.11454 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8440.00 | 0.720059 | ||||||||
\(517\) | 121.000 | 0.0102932 | ||||||||
\(518\) | −2660.00 | −0.225625 | ||||||||
\(519\) | −6255.00 | −0.529025 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1902.00 | 0.159939 | 0.0799694 | − | 0.996797i | \(-0.474518\pi\) | ||||
0.0799694 | + | 0.996797i | \(0.474518\pi\) | |||||||
\(522\) | 316.000 | 0.0264961 | ||||||||
\(523\) | 1972.00 | 0.164875 | 0.0824374 | − | 0.996596i | \(-0.473730\pi\) | ||||
0.0824374 | + | 0.996596i | \(0.473730\pi\) | |||||||
\(524\) | 11656.0 | 0.971746 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2868.00 | 0.237739 | ||||||||
\(527\) | −10812.0 | −0.893697 | ||||||||
\(528\) | 80.0000 | 0.00659385 | ||||||||
\(529\) | −9667.00 | −0.794526 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1256.00 | −0.102647 | ||||||||
\(532\) | 840.000 | 0.0684561 | ||||||||
\(533\) | 2156.00 | 0.175210 | ||||||||
\(534\) | −8800.00 | −0.713133 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8448.00 | 0.680780 | ||||||||
\(537\) | 740.000 | 0.0594662 | ||||||||
\(538\) | 10028.0 | 0.803602 | ||||||||
\(539\) | −49.0000 | −0.00391573 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25033.0 | −1.98938 | −0.994688 | − | 0.102933i | \(-0.967177\pi\) | ||||
−0.994688 | + | 0.102933i | \(0.967177\pi\) | |||||||
\(542\) | −10840.0 | −0.859074 | ||||||||
\(543\) | 6720.00 | 0.531092 | ||||||||
\(544\) | −1632.00 | −0.128624 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −490.000 | −0.0384067 | ||||||||
\(547\) | 236.000 | 0.0184472 | 0.00922361 | − | 0.999957i | \(-0.497064\pi\) | ||||
0.00922361 | + | 0.999957i | \(0.497064\pi\) | |||||||
\(548\) | −10272.0 | −0.800726 | ||||||||
\(549\) | 1368.00 | 0.106348 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2370.00 | 0.183240 | ||||||||
\(552\) | 2000.00 | 0.154213 | ||||||||
\(553\) | −2849.00 | −0.219081 | ||||||||
\(554\) | 7348.00 | 0.563514 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5096.00 | 0.388702 | ||||||||
\(557\) | −15504.0 | −1.17940 | −0.589700 | − | 0.807623i | \(-0.700754\pi\) | ||||
−0.589700 | + | 0.807623i | \(0.700754\pi\) | |||||||
\(558\) | −848.000 | −0.0643346 | ||||||||
\(559\) | 2954.00 | 0.223508 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 255.000 | 0.0191909 | ||||||||
\(562\) | −14662.0 | −1.10050 | ||||||||
\(563\) | 8948.00 | 0.669828 | 0.334914 | − | 0.942249i | \(-0.391293\pi\) | ||||
0.334914 | + | 0.942249i | \(0.391293\pi\) | |||||||
\(564\) | 2420.00 | 0.180674 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 542.000 | 0.0402508 | ||||||||
\(567\) | −4697.00 | −0.347893 | ||||||||
\(568\) | −5952.00 | −0.439684 | ||||||||
\(569\) | 13866.0 | 1.02160 | 0.510802 | − | 0.859698i | \(-0.329348\pi\) | ||||
0.510802 | + | 0.859698i | \(0.329348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9988.00 | 0.732022 | 0.366011 | − | 0.930610i | \(-0.380723\pi\) | ||||
0.366011 | + | 0.930610i | \(0.380723\pi\) | |||||||
\(572\) | 28.0000 | 0.00204675 | ||||||||
\(573\) | 2805.00 | 0.204504 | ||||||||
\(574\) | 4312.00 | 0.313553 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −128.000 | −0.00925926 | ||||||||
\(577\) | 2585.00 | 0.186508 | 0.0932539 | − | 0.995642i | \(-0.470273\pi\) | ||||
0.0932539 | + | 0.995642i | \(0.470273\pi\) | |||||||
\(578\) | 4624.00 | 0.332756 | ||||||||
\(579\) | 15080.0 | 1.08239 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4508.00 | −0.321899 | ||||||||
\(582\) | 13510.0 | 0.962212 | ||||||||
\(583\) | 664.000 | 0.0471699 | ||||||||
\(584\) | 5808.00 | 0.411536 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8610.00 | 0.606955 | ||||||||
\(587\) | −19656.0 | −1.38210 | −0.691048 | − | 0.722809i | \(-0.742851\pi\) | ||||
−0.691048 | + | 0.722809i | \(0.742851\pi\) | |||||||
\(588\) | −980.000 | −0.0687322 | ||||||||
\(589\) | −6360.00 | −0.444922 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16160.0 | −1.12476 | ||||||||
\(592\) | 3040.00 | 0.211053 | ||||||||
\(593\) | −21247.0 | −1.47135 | −0.735674 | − | 0.677335i | \(-0.763135\pi\) | ||||
−0.735674 | + | 0.677335i | \(0.763135\pi\) | |||||||
\(594\) | 290.000 | 0.0200317 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2376.00 | 0.163297 | ||||||||
\(597\) | 5820.00 | 0.398990 | ||||||||
\(598\) | 700.000 | 0.0478681 | ||||||||
\(599\) | −9325.00 | −0.636075 | −0.318038 | − | 0.948078i | \(-0.603024\pi\) | ||||
−0.318038 | + | 0.948078i | \(0.603024\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5362.00 | 0.363928 | 0.181964 | − | 0.983305i | \(-0.441755\pi\) | ||||
0.181964 | + | 0.983305i | \(0.441755\pi\) | |||||||
\(602\) | 5908.00 | 0.399987 | ||||||||
\(603\) | 2112.00 | 0.142632 | ||||||||
\(604\) | −6108.00 | −0.411475 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 540.000 | 0.0361980 | ||||||||
\(607\) | −15731.0 | −1.05190 | −0.525949 | − | 0.850516i | \(-0.676290\pi\) | ||||
−0.525949 | + | 0.850516i | \(0.676290\pi\) | |||||||
\(608\) | −960.000 | −0.0640348 | ||||||||
\(609\) | −2765.00 | −0.183979 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 847.000 | 0.0560818 | ||||||||
\(612\) | −408.000 | −0.0269484 | ||||||||
\(613\) | 13742.0 | 0.905439 | 0.452720 | − | 0.891653i | \(-0.350454\pi\) | ||||
0.452720 | + | 0.891653i | \(0.350454\pi\) | |||||||
\(614\) | 5278.00 | 0.346910 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 56.0000 | 0.00366283 | ||||||||
\(617\) | −18286.0 | −1.19314 | −0.596569 | − | 0.802561i | \(-0.703470\pi\) | ||||
−0.596569 | + | 0.802561i | \(0.703470\pi\) | |||||||
\(618\) | 10270.0 | 0.668479 | ||||||||
\(619\) | 24722.0 | 1.60527 | 0.802634 | − | 0.596472i | \(-0.203431\pi\) | ||||
0.802634 | + | 0.596472i | \(0.203431\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7250.00 | 0.468490 | ||||||||
\(622\) | 17028.0 | 1.09769 | ||||||||
\(623\) | −6160.00 | −0.396140 | ||||||||
\(624\) | 560.000 | 0.0359262 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 438.000 | 0.0279649 | ||||||||
\(627\) | 150.000 | 0.00955410 | ||||||||
\(628\) | −2120.00 | −0.134709 | ||||||||
\(629\) | 9690.00 | 0.614254 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22181.0 | −1.39938 | −0.699692 | − | 0.714444i | \(-0.746680\pi\) | ||||
−0.699692 | + | 0.714444i | \(0.746680\pi\) | |||||||
\(632\) | 3256.00 | 0.204932 | ||||||||
\(633\) | −2845.00 | −0.178639 | ||||||||
\(634\) | −8052.00 | −0.504394 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13280.0 | 0.827966 | ||||||||
\(637\) | −343.000 | −0.0213346 | ||||||||
\(638\) | 158.000 | 0.00980451 | ||||||||
\(639\) | −1488.00 | −0.0921195 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23598.0 | −1.45408 | −0.727040 | − | 0.686595i | \(-0.759104\pi\) | ||||
−0.727040 | + | 0.686595i | \(0.759104\pi\) | |||||||
\(642\) | −3140.00 | −0.193031 | ||||||||
\(643\) | −13349.0 | −0.818714 | −0.409357 | − | 0.912374i | \(-0.634247\pi\) | ||||
−0.409357 | + | 0.912374i | \(0.634247\pi\) | |||||||
\(644\) | 1400.00 | 0.0856642 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3060.00 | −0.186369 | ||||||||
\(647\) | 24488.0 | 1.48798 | 0.743990 | − | 0.668191i | \(-0.232931\pi\) | ||||
0.743990 | + | 0.668191i | \(0.232931\pi\) | |||||||
\(648\) | 5368.00 | 0.325424 | ||||||||
\(649\) | −628.000 | −0.0379833 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7420.00 | 0.446717 | ||||||||
\(652\) | 14648.0 | 0.879847 | ||||||||
\(653\) | −21622.0 | −1.29576 | −0.647882 | − | 0.761740i | \(-0.724345\pi\) | ||||
−0.647882 | + | 0.761740i | \(0.724345\pi\) | |||||||
\(654\) | −16110.0 | −0.963228 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4928.00 | −0.293302 | ||||||||
\(657\) | 1452.00 | 0.0862221 | ||||||||
\(658\) | 1694.00 | 0.100363 | ||||||||
\(659\) | −2973.00 | −0.175738 | −0.0878692 | − | 0.996132i | \(-0.528006\pi\) | ||||
−0.0878692 | + | 0.996132i | \(0.528006\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18912.0 | 1.11285 | 0.556423 | − | 0.830899i | \(-0.312173\pi\) | ||||
0.556423 | + | 0.830899i | \(0.312173\pi\) | |||||||
\(662\) | 14072.0 | 0.826169 | ||||||||
\(663\) | 1785.00 | 0.104561 | ||||||||
\(664\) | 5152.00 | 0.301109 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 760.000 | 0.0442183 | ||||||||
\(667\) | 3950.00 | 0.229302 | ||||||||
\(668\) | 1260.00 | 0.0729803 | ||||||||
\(669\) | 3465.00 | 0.200246 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 684.000 | 0.0393525 | ||||||||
\(672\) | 1120.00 | 0.0642931 | ||||||||
\(673\) | −688.000 | −0.0394063 | −0.0197032 | − | 0.999806i | \(-0.506272\pi\) | ||||
−0.0197032 | + | 0.999806i | \(0.506272\pi\) | |||||||
\(674\) | 20724.0 | 1.18436 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8592.00 | −0.488848 | ||||||||
\(677\) | −12791.0 | −0.726142 | −0.363071 | − | 0.931761i | \(-0.618272\pi\) | ||||
−0.363071 | + | 0.931761i | \(0.618272\pi\) | |||||||
\(678\) | −3660.00 | −0.207318 | ||||||||
\(679\) | 9457.00 | 0.534501 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21395.0 | −1.20390 | ||||||||
\(682\) | −424.000 | −0.0238062 | ||||||||
\(683\) | 7652.00 | 0.428691 | 0.214345 | − | 0.976758i | \(-0.431238\pi\) | ||||
0.214345 | + | 0.976758i | \(0.431238\pi\) | |||||||
\(684\) | −240.000 | −0.0134161 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 16580.0 | 0.920766 | ||||||||
\(688\) | −6752.00 | −0.374153 | ||||||||
\(689\) | 4648.00 | 0.257002 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2532.00 | −0.139395 | −0.0696974 | − | 0.997568i | \(-0.522203\pi\) | ||||
−0.0696974 | + | 0.997568i | \(0.522203\pi\) | |||||||
\(692\) | 5004.00 | 0.274890 | ||||||||
\(693\) | 14.0000 | 0.000767411 0 | ||||||||
\(694\) | −16844.0 | −0.921311 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3160.00 | 0.172097 | ||||||||
\(697\) | −15708.0 | −0.853634 | ||||||||
\(698\) | 14700.0 | 0.797139 | ||||||||
\(699\) | 19560.0 | 1.05841 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2133.00 | −0.114925 | −0.0574624 | − | 0.998348i | \(-0.518301\pi\) | ||||
−0.0574624 | + | 0.998348i | \(0.518301\pi\) | |||||||
\(702\) | 2030.00 | 0.109142 | ||||||||
\(703\) | 5700.00 | 0.305803 | ||||||||
\(704\) | −64.0000 | −0.00342627 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6114.00 | 0.325926 | ||||||||
\(707\) | 378.000 | 0.0201077 | ||||||||
\(708\) | −12560.0 | −0.666714 | ||||||||
\(709\) | −19153.0 | −1.01454 | −0.507268 | − | 0.861788i | \(-0.669345\pi\) | ||||
−0.507268 | + | 0.861788i | \(0.669345\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 814.000 | 0.0429358 | ||||||||
\(712\) | 7040.00 | 0.370555 | ||||||||
\(713\) | −10600.0 | −0.556765 | ||||||||
\(714\) | 3570.00 | 0.187120 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −592.000 | −0.0308996 | ||||||||
\(717\) | 27255.0 | 1.41960 | ||||||||
\(718\) | −16784.0 | −0.872386 | ||||||||
\(719\) | −21334.0 | −1.10657 | −0.553285 | − | 0.832992i | \(-0.686626\pi\) | ||||
−0.553285 | + | 0.832992i | \(0.686626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7189.00 | 0.371335 | ||||||||
\(722\) | 11918.0 | 0.614324 | ||||||||
\(723\) | −1250.00 | −0.0642988 | ||||||||
\(724\) | −5376.00 | −0.275963 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −13300.0 | −0.679903 | ||||||||
\(727\) | −11480.0 | −0.585653 | −0.292826 | − | 0.956166i | \(-0.594596\pi\) | ||||
−0.292826 | + | 0.956166i | \(0.594596\pi\) | |||||||
\(728\) | 392.000 | 0.0199567 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21522.0 | −1.08895 | ||||||||
\(732\) | 13680.0 | 0.690748 | ||||||||
\(733\) | −19763.0 | −0.995857 | −0.497928 | − | 0.867218i | \(-0.665906\pi\) | ||||
−0.497928 | + | 0.867218i | \(0.665906\pi\) | |||||||
\(734\) | 16754.0 | 0.842509 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1600.00 | −0.0801315 | ||||||||
\(737\) | 1056.00 | 0.0527792 | ||||||||
\(738\) | −1232.00 | −0.0614506 | ||||||||
\(739\) | −40153.0 | −1.99872 | −0.999359 | − | 0.0358110i | \(-0.988599\pi\) | ||||
−0.999359 | + | 0.0358110i | \(0.988599\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1050.00 | 0.0520549 | ||||||||
\(742\) | 9296.00 | 0.459928 | ||||||||
\(743\) | 30896.0 | 1.52552 | 0.762762 | − | 0.646679i | \(-0.223843\pi\) | ||||
0.762762 | + | 0.646679i | \(0.223843\pi\) | |||||||
\(744\) | −8480.00 | −0.417865 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3936.00 | −0.193173 | ||||||||
\(747\) | 1288.00 | 0.0630863 | ||||||||
\(748\) | −204.000 | −0.00997190 | ||||||||
\(749\) | −2198.00 | −0.107227 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11969.0 | 0.581565 | 0.290782 | − | 0.956789i | \(-0.406084\pi\) | ||||
0.290782 | + | 0.956789i | \(0.406084\pi\) | |||||||
\(752\) | −1936.00 | −0.0938812 | ||||||||
\(753\) | −4550.00 | −0.220201 | ||||||||
\(754\) | 1106.00 | 0.0534193 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4060.00 | 0.195318 | ||||||||
\(757\) | 10456.0 | 0.502021 | 0.251010 | − | 0.967984i | \(-0.419237\pi\) | ||||
0.251010 | + | 0.967984i | \(0.419237\pi\) | |||||||
\(758\) | −2104.00 | −0.100819 | ||||||||
\(759\) | 250.000 | 0.0119558 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28782.0 | −1.37102 | −0.685510 | − | 0.728063i | \(-0.740421\pi\) | ||||
−0.685510 | + | 0.728063i | \(0.740421\pi\) | |||||||
\(762\) | −6040.00 | −0.287147 | ||||||||
\(763\) | −11277.0 | −0.535065 | ||||||||
\(764\) | −2244.00 | −0.106263 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4616.00 | −0.217732 | ||||||||
\(767\) | −4396.00 | −0.206950 | ||||||||
\(768\) | −1280.00 | −0.0601407 | ||||||||
\(769\) | −14630.0 | −0.686048 | −0.343024 | − | 0.939327i | \(-0.611451\pi\) | ||||
−0.343024 | + | 0.939327i | \(0.611451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32470.0 | −1.51670 | ||||||||
\(772\) | −12064.0 | −0.562426 | ||||||||
\(773\) | −24351.0 | −1.13305 | −0.566523 | − | 0.824046i | \(-0.691712\pi\) | ||||
−0.566523 | + | 0.824046i | \(0.691712\pi\) | |||||||
\(774\) | −1688.00 | −0.0783901 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10808.0 | −0.499980 | ||||||||
\(777\) | −6650.00 | −0.307037 | ||||||||
\(778\) | −4562.00 | −0.210226 | ||||||||
\(779\) | −9240.00 | −0.424977 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −744.000 | −0.0340876 | ||||||||
\(782\) | −5100.00 | −0.233217 | ||||||||
\(783\) | 11455.0 | 0.522820 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 29140.0 | 1.32238 | ||||||||
\(787\) | −2329.00 | −0.105489 | −0.0527445 | − | 0.998608i | \(-0.516797\pi\) | ||||
−0.0527445 | + | 0.998608i | \(0.516797\pi\) | |||||||
\(788\) | 12928.0 | 0.584443 | ||||||||
\(789\) | 7170.00 | 0.323522 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2562.00 | −0.115163 | ||||||||
\(792\) | −16.0000 | −0.000717848 0 | ||||||||
\(793\) | 4788.00 | 0.214410 | ||||||||
\(794\) | −29270.0 | −1.30825 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4656.00 | −0.207321 | ||||||||
\(797\) | 11067.0 | 0.491861 | 0.245931 | − | 0.969287i | \(-0.420906\pi\) | ||||
0.245931 | + | 0.969287i | \(0.420906\pi\) | |||||||
\(798\) | 2100.00 | 0.0931569 | ||||||||
\(799\) | −6171.00 | −0.273234 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1760.00 | 0.0776361 | ||||||||
\(802\) | −11282.0 | −0.496735 | ||||||||
\(803\) | 726.000 | 0.0319053 | ||||||||
\(804\) | 21120.0 | 0.926424 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2968.00 | −0.129706 | ||||||||
\(807\) | 25070.0 | 1.09356 | ||||||||
\(808\) | −432.000 | −0.0188090 | ||||||||
\(809\) | −3879.00 | −0.168576 | −0.0842882 | − | 0.996441i | \(-0.526862\pi\) | ||||
−0.0842882 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7518.00 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(812\) | 2212.00 | 0.0955985 | ||||||||
\(813\) | −27100.0 | −1.16905 | ||||||||
\(814\) | 380.000 | 0.0163624 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4080.00 | −0.175035 | ||||||||
\(817\) | −12660.0 | −0.542126 | ||||||||
\(818\) | −12820.0 | −0.547972 | ||||||||
\(819\) | 98.0000 | 0.00418119 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39801.0 | 1.69192 | 0.845959 | − | 0.533248i | \(-0.179029\pi\) | ||||
0.845959 | + | 0.533248i | \(0.179029\pi\) | |||||||
\(822\) | −25680.0 | −1.08965 | ||||||||
\(823\) | 3564.00 | 0.150952 | 0.0754758 | − | 0.997148i | \(-0.475952\pi\) | ||||
0.0754758 | + | 0.997148i | \(0.475952\pi\) | |||||||
\(824\) | −8216.00 | −0.347352 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8792.00 | −0.370354 | ||||||||
\(827\) | −10838.0 | −0.455712 | −0.227856 | − | 0.973695i | \(-0.573172\pi\) | ||||
−0.227856 | + | 0.973695i | \(0.573172\pi\) | |||||||
\(828\) | −400.000 | −0.0167886 | ||||||||
\(829\) | 41956.0 | 1.75777 | 0.878885 | − | 0.477033i | \(-0.158288\pi\) | ||||
0.878885 | + | 0.477033i | \(0.158288\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18370.0 | 0.766845 | ||||||||
\(832\) | −448.000 | −0.0186678 | ||||||||
\(833\) | 2499.00 | 0.103944 | ||||||||
\(834\) | 12740.0 | 0.528957 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −120.000 | −0.00496446 | ||||||||
\(837\) | −30740.0 | −1.26945 | ||||||||
\(838\) | −9632.00 | −0.397055 | ||||||||
\(839\) | −28714.0 | −1.18155 | −0.590773 | − | 0.806838i | \(-0.701177\pi\) | ||||
−0.590773 | + | 0.806838i | \(0.701177\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18148.0 | −0.744106 | ||||||||
\(842\) | −30650.0 | −1.25448 | ||||||||
\(843\) | −36655.0 | −1.49759 | ||||||||
\(844\) | 2276.00 | 0.0928236 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −484.000 | −0.0196693 | ||||||||
\(847\) | −9310.00 | −0.377681 | ||||||||
\(848\) | −10624.0 | −0.430224 | ||||||||
\(849\) | 1355.00 | 0.0547744 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9500.00 | 0.382674 | ||||||||
\(852\) | −14880.0 | −0.598334 | ||||||||
\(853\) | −15442.0 | −0.619841 | −0.309920 | − | 0.950763i | \(-0.600302\pi\) | ||||
−0.309920 | + | 0.950763i | \(0.600302\pi\) | |||||||
\(854\) | 9576.00 | 0.383705 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2512.00 | 0.100302 | ||||||||
\(857\) | 17978.0 | 0.716589 | 0.358295 | − | 0.933609i | \(-0.383358\pi\) | ||||
0.358295 | + | 0.933609i | \(0.383358\pi\) | |||||||
\(858\) | 70.0000 | 0.00278527 | ||||||||
\(859\) | 19308.0 | 0.766916 | 0.383458 | − | 0.923558i | \(-0.374733\pi\) | ||||
0.383458 | + | 0.923558i | \(0.374733\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10780.0 | 0.426692 | ||||||||
\(862\) | −3750.00 | −0.148173 | ||||||||
\(863\) | −17464.0 | −0.688855 | −0.344427 | − | 0.938813i | \(-0.611927\pi\) | ||||
−0.344427 | + | 0.938813i | \(0.611927\pi\) | |||||||
\(864\) | −4640.00 | −0.182704 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −27748.0 | −1.08882 | ||||||||
\(867\) | 11560.0 | 0.452824 | ||||||||
\(868\) | −5936.00 | −0.232121 | ||||||||
\(869\) | 407.000 | 0.0158878 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7392.00 | 0.287564 | ||||||||
\(872\) | 12888.0 | 0.500508 | ||||||||
\(873\) | −2702.00 | −0.104752 | ||||||||
\(874\) | −3000.00 | −0.116106 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14520.0 | 0.560029 | ||||||||
\(877\) | 23962.0 | 0.922622 | 0.461311 | − | 0.887239i | \(-0.347379\pi\) | ||||
0.461311 | + | 0.887239i | \(0.347379\pi\) | |||||||
\(878\) | 6884.00 | 0.264606 | ||||||||
\(879\) | 21525.0 | 0.825962 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35168.0 | −1.34488 | −0.672440 | − | 0.740151i | \(-0.734754\pi\) | ||||
−0.672440 | + | 0.740151i | \(0.734754\pi\) | |||||||
\(882\) | 196.000 | 0.00748261 | ||||||||
\(883\) | 37896.0 | 1.44428 | 0.722142 | − | 0.691745i | \(-0.243158\pi\) | ||||
0.722142 | + | 0.691745i | \(0.243158\pi\) | |||||||
\(884\) | −1428.00 | −0.0543313 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33500.0 | 1.27026 | ||||||||
\(887\) | −30368.0 | −1.14956 | −0.574779 | − | 0.818309i | \(-0.694912\pi\) | ||||
−0.574779 | + | 0.818309i | \(0.694912\pi\) | |||||||
\(888\) | 7600.00 | 0.287206 | ||||||||
\(889\) | −4228.00 | −0.159508 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 671.000 | 0.0252293 | ||||||||
\(892\) | −2772.00 | −0.104051 | ||||||||
\(893\) | −3630.00 | −0.136028 | ||||||||
\(894\) | 5940.00 | 0.222218 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 1750.00 | 0.0651402 | ||||||||
\(898\) | −1390.00 | −0.0516536 | ||||||||
\(899\) | −16748.0 | −0.621332 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33864.0 | −1.25213 | ||||||||
\(902\) | −616.000 | −0.0227390 | ||||||||
\(903\) | 14770.0 | 0.544313 | ||||||||
\(904\) | 2928.00 | 0.107725 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15270.0 | −0.559947 | ||||||||
\(907\) | 33874.0 | 1.24010 | 0.620048 | − | 0.784564i | \(-0.287113\pi\) | ||||
0.620048 | + | 0.784564i | \(0.287113\pi\) | |||||||
\(908\) | 17116.0 | 0.625567 | ||||||||
\(909\) | −108.000 | −0.00394074 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24880.0 | 0.904842 | 0.452421 | − | 0.891804i | \(-0.350560\pi\) | ||||
0.452421 | + | 0.891804i | \(0.350560\pi\) | |||||||
\(912\) | −2400.00 | −0.0871403 | ||||||||
\(913\) | 644.000 | 0.0233442 | ||||||||
\(914\) | 11520.0 | 0.416901 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13264.0 | −0.478444 | ||||||||
\(917\) | 20398.0 | 0.734571 | ||||||||
\(918\) | −14790.0 | −0.531746 | ||||||||
\(919\) | −25299.0 | −0.908092 | −0.454046 | − | 0.890978i | \(-0.650020\pi\) | ||||
−0.454046 | + | 0.890978i | \(0.650020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13195.0 | 0.472085 | ||||||||
\(922\) | −26880.0 | −0.960136 | ||||||||
\(923\) | −5208.00 | −0.185724 | ||||||||
\(924\) | 140.000 | 0.00498448 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14696.0 | −0.521534 | ||||||||
\(927\) | −2054.00 | −0.0727748 | ||||||||
\(928\) | −2528.00 | −0.0894242 | ||||||||
\(929\) | 6792.00 | 0.239869 | 0.119934 | − | 0.992782i | \(-0.461732\pi\) | ||||
0.119934 | + | 0.992782i | \(0.461732\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1470.00 | 0.0517479 | ||||||||
\(932\) | −15648.0 | −0.549965 | ||||||||
\(933\) | 42570.0 | 1.49376 | ||||||||
\(934\) | −35850.0 | −1.25594 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −112.000 | −0.00391115 | ||||||||
\(937\) | 43575.0 | 1.51925 | 0.759623 | − | 0.650364i | \(-0.225384\pi\) | ||||
0.759623 | + | 0.650364i | \(0.225384\pi\) | |||||||
\(938\) | 14784.0 | 0.514621 | ||||||||
\(939\) | 1095.00 | 0.0380554 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 45372.0 | 1.57182 | 0.785911 | − | 0.618339i | \(-0.212194\pi\) | ||||
0.785911 | + | 0.618339i | \(0.212194\pi\) | |||||||
\(942\) | −5300.00 | −0.183316 | ||||||||
\(943\) | −15400.0 | −0.531806 | ||||||||
\(944\) | 10048.0 | 0.346435 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −844.000 | −0.0290072 | ||||||||
\(947\) | 39152.0 | 1.34347 | 0.671737 | − | 0.740790i | \(-0.265549\pi\) | ||||
0.671737 | + | 0.740790i | \(0.265549\pi\) | |||||||
\(948\) | 8140.00 | 0.278876 | ||||||||
\(949\) | 5082.00 | 0.173834 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20130.0 | −0.686393 | ||||||||
\(952\) | −2856.00 | −0.0972306 | ||||||||
\(953\) | 18632.0 | 0.633316 | 0.316658 | − | 0.948540i | \(-0.397439\pi\) | ||||
0.316658 | + | 0.948540i | \(0.397439\pi\) | |||||||
\(954\) | −2656.00 | −0.0901375 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21804.0 | −0.737648 | ||||||||
\(957\) | 395.000 | 0.0133423 | ||||||||
\(958\) | −24692.0 | −0.832737 | ||||||||
\(959\) | −17976.0 | −0.605292 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15153.0 | 0.508644 | ||||||||
\(962\) | 2660.00 | 0.0891495 | ||||||||
\(963\) | 628.000 | 0.0210146 | ||||||||
\(964\) | 1000.00 | 0.0334106 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3500.00 | 0.116574 | ||||||||
\(967\) | −48862.0 | −1.62492 | −0.812459 | − | 0.583018i | \(-0.801872\pi\) | ||||
−0.812459 | + | 0.583018i | \(0.801872\pi\) | |||||||
\(968\) | 10640.0 | 0.353288 | ||||||||
\(969\) | −7650.00 | −0.253615 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19896.0 | 0.657562 | 0.328781 | − | 0.944406i | \(-0.393362\pi\) | ||||
0.328781 | + | 0.944406i | \(0.393362\pi\) | |||||||
\(972\) | −2240.00 | −0.0739177 | ||||||||
\(973\) | 8918.00 | 0.293831 | ||||||||
\(974\) | 30028.0 | 0.987843 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10944.0 | −0.358923 | ||||||||
\(977\) | −5130.00 | −0.167987 | −0.0839935 | − | 0.996466i | \(-0.526767\pi\) | ||||
−0.0839935 | + | 0.996466i | \(0.526767\pi\) | |||||||
\(978\) | 36620.0 | 1.19732 | ||||||||
\(979\) | 880.000 | 0.0287282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3222.00 | 0.104863 | ||||||||
\(982\) | 9446.00 | 0.306959 | ||||||||
\(983\) | 11573.0 | 0.375505 | 0.187752 | − | 0.982216i | \(-0.439880\pi\) | ||||
0.187752 | + | 0.982216i | \(0.439880\pi\) | |||||||
\(984\) | −12320.0 | −0.399133 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8058.00 | −0.260263 | ||||||||
\(987\) | 4235.00 | 0.136577 | ||||||||
\(988\) | −840.000 | −0.0270485 | ||||||||
\(989\) | −21100.0 | −0.678403 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34600.0 | 1.10909 | 0.554544 | − | 0.832155i | \(-0.312893\pi\) | ||||
0.554544 | + | 0.832155i | \(0.312893\pi\) | |||||||
\(992\) | 6784.00 | 0.217129 | ||||||||
\(993\) | 35180.0 | 1.12427 | ||||||||
\(994\) | −10416.0 | −0.332370 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 12880.0 | 0.409757 | ||||||||
\(997\) | 15199.0 | 0.482806 | 0.241403 | − | 0.970425i | \(-0.422393\pi\) | ||||
0.241403 | + | 0.970425i | \(0.422393\pi\) | |||||||
\(998\) | −22454.0 | −0.712193 | ||||||||
\(999\) | 27550.0 | 0.872516 |
(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 | 350.4.a.c.1.1 | 1 | ||
5.2 | odd | 4 | 350.4.c.k.99.1 | 2 | |||
5.3 | odd | 4 | 350.4.c.k.99.2 | 2 | |||
5.4 | even | 2 | 70.4.a.e.1.1 | ✓ | 1 | ||
7.6 | odd | 2 | 2450.4.a.r.1.1 | 1 | |||
15.14 | odd | 2 | 630.4.a.b.1.1 | 1 | |||
20.19 | odd | 2 | 560.4.a.f.1.1 | 1 | |||
35.4 | even | 6 | 490.4.e.c.471.1 | 2 | |||
35.9 | even | 6 | 490.4.e.c.361.1 | 2 | |||
35.19 | odd | 6 | 490.4.e.g.361.1 | 2 | |||
35.24 | odd | 6 | 490.4.e.g.471.1 | 2 | |||
35.34 | odd | 2 | 490.4.a.j.1.1 | 1 | |||
40.19 | odd | 2 | 2240.4.a.bc.1.1 | 1 | |||
40.29 | even | 2 | 2240.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.4.a.e.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
350.4.a.c.1.1 | 1 | 1.1 | even | 1 | trivial | ||
350.4.c.k.99.1 | 2 | 5.2 | odd | 4 | |||
350.4.c.k.99.2 | 2 | 5.3 | odd | 4 | |||
490.4.a.j.1.1 | 1 | 35.34 | odd | 2 | |||
490.4.e.c.361.1 | 2 | 35.9 | even | 6 | |||
490.4.e.c.471.1 | 2 | 35.4 | even | 6 | |||
490.4.e.g.361.1 | 2 | 35.19 | odd | 6 | |||
490.4.e.g.471.1 | 2 | 35.24 | odd | 6 | |||
560.4.a.f.1.1 | 1 | 20.19 | odd | 2 | |||
630.4.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
2240.4.a.h.1.1 | 1 | 40.29 | even | 2 | |||
2240.4.a.bc.1.1 | 1 | 40.19 | odd | 2 | |||
2450.4.a.r.1.1 | 1 | 7.6 | odd | 2 |