Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3100,3,Mod(1301,3100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3100.1301");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 3100.d (of order \(2\), degree \(1\), 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: | \(84.4688819517\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.9 | ||
Character | \(\chi\) | \(=\) | 3100.1301 |
Dual form | 3100.3.d.g.1301.14 |
$q$-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 \(\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times\).
\(n\) | \(1551\) | \(1801\) | \(2977\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − | 0.957337i | − | 0.319112i | −0.987189 | − | 0.159556i | \(-0.948994\pi\) | ||
0.987189 | − | 0.159556i | \(-0.0510063\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.5381 | 1.79115 | 0.895576 | − | 0.444909i | \(-0.146764\pi\) | ||||
0.895576 | + | 0.444909i | \(0.146764\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 8.08351 | 0.898167 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.45459i | − | 0.586781i | −0.955993 | − | 0.293390i | \(-0.905216\pi\) | ||
0.955993 | − | 0.293390i | \(-0.0947836\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.62883i | − | 0.356064i | −0.984025 | − | 0.178032i | \(-0.943027\pi\) | ||
0.984025 | − | 0.178032i | \(-0.0569730\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 27.9754i | 1.64561i | 0.568323 | + | 0.822805i | \(0.307592\pi\) | ||||
−0.568323 | + | 0.822805i | \(0.692408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.3169 | −0.964047 | −0.482023 | − | 0.876158i | \(-0.660098\pi\) | ||||
−0.482023 | + | 0.876158i | \(0.660098\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 12.0031i | − | 0.571579i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 17.4106i | − | 0.756982i | −0.925605 | − | 0.378491i | \(-0.876443\pi\) | ||
0.925605 | − | 0.378491i | \(-0.123557\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 16.3547i | − | 0.605729i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 34.0557i | − | 1.17433i | −0.809466 | − | 0.587167i | \(-0.800243\pi\) | ||
0.809466 | − | 0.587167i | \(-0.199757\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.55941 | − | 29.7949i | −0.276110 | − | 0.961126i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.17922 | −0.187249 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.2841i | − | 0.277950i | −0.990296 | − | 0.138975i | \(-0.955619\pi\) | ||
0.990296 | − | 0.138975i | \(-0.0443807\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.43135 | −0.113624 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 34.2069 | 0.834315 | 0.417157 | − | 0.908834i | \(-0.363026\pi\) | ||||
0.417157 | + | 0.908834i | \(0.363026\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 82.1464i | − | 1.91038i | −0.295990 | − | 0.955191i | \(-0.595650\pi\) | ||
0.295990 | − | 0.955191i | \(-0.404350\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.35672 | 0.0501431 | 0.0250715 | − | 0.999686i | \(-0.492019\pi\) | ||||
0.0250715 | + | 0.999686i | \(0.492019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 108.203 | 2.20822 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 26.7819 | 0.525135 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 63.9636i | − | 1.20686i | −0.797416 | − | 0.603430i | \(-0.793800\pi\) | ||
0.797416 | − | 0.603430i | \(-0.206200\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.5354i | 0.307639i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −49.0778 | −0.831827 | −0.415914 | − | 0.909404i | \(-0.636538\pi\) | ||||
−0.415914 | + | 0.909404i | \(0.636538\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 44.7523i | − | 0.733644i | −0.930291 | − | 0.366822i | \(-0.880446\pi\) | ||
0.930291 | − | 0.366822i | \(-0.119554\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 101.352 | 1.60875 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −54.9369 | −0.819954 | −0.409977 | − | 0.912096i | \(-0.634463\pi\) | ||||
−0.409977 | + | 0.912096i | \(0.634463\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.6678 | −0.241562 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 23.8443 | 0.335836 | 0.167918 | − | 0.985801i | \(-0.446296\pi\) | ||||
0.167918 | + | 0.985801i | \(0.446296\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 123.706i | 1.69460i | 0.531116 | + | 0.847299i | \(0.321773\pi\) | ||||
−0.531116 | + | 0.847299i | \(0.678227\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 80.9281i | − | 1.05101i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 94.2940i | 1.19359i | 0.802392 | + | 0.596797i | \(0.203560\pi\) | ||||
−0.802392 | + | 0.596797i | \(0.796440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 57.0946 | 0.704872 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 24.1863i | 0.291401i | 0.989329 | + | 0.145701i | \(0.0465436\pi\) | ||||
−0.989329 | + | 0.145701i | \(0.953456\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −32.6028 | −0.374744 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 21.0604i | 0.236633i | 0.992976 | + | 0.118317i | \(0.0377498\pi\) | ||||
−0.992976 | + | 0.118317i | \(0.962250\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 58.0366i | − | 0.637765i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28.5238 | + | 8.19424i | −0.306707 | + | 0.0881101i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 115.185 | 1.18748 | 0.593739 | − | 0.804657i | \(-0.297651\pi\) | ||||
0.593739 | + | 0.804657i | \(0.297651\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 52.1757i | − | 0.527027i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −150.722 | −1.49230 | −0.746149 | − | 0.665779i | \(-0.768099\pi\) | ||||
−0.746149 | + | 0.665779i | \(0.768099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −159.678 | −1.55027 | −0.775136 | − | 0.631794i | \(-0.782319\pi\) | ||||
−0.775136 | + | 0.631794i | \(0.782319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 97.5647 | 0.911820 | 0.455910 | − | 0.890026i | \(-0.349314\pi\) | ||||
0.455910 | + | 0.890026i | \(0.349314\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 78.7375 | 0.722362 | 0.361181 | − | 0.932496i | \(-0.382374\pi\) | ||||
0.361181 | + | 0.932496i | \(0.382374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.84539 | −0.0886972 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9312 | 0.0967367 | 0.0483683 | − | 0.998830i | \(-0.484598\pi\) | ||||
0.0483683 | + | 0.998830i | \(0.484598\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 37.4172i | − | 0.319805i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 350.757i | 2.94754i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 79.3383 | 0.655688 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 32.7475i | − | 0.266240i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 190.929i | − | 1.50338i | −0.659517 | − | 0.751690i | \(-0.729239\pi\) | ||
0.659517 | − | 0.751690i | \(-0.270761\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −78.6418 | −0.609626 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −72.8934 | −0.556438 | −0.278219 | − | 0.960518i | \(-0.589744\pi\) | ||||
−0.278219 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −229.658 | −1.72675 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 132.645i | − | 0.968215i | −0.875008 | − | 0.484108i | \(-0.839144\pi\) | ||
0.875008 | − | 0.484108i | \(-0.160856\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 28.6204i | 0.205902i | 0.994686 | + | 0.102951i | \(0.0328285\pi\) | ||||
−0.994686 | + | 0.102951i | \(0.967171\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 2.25618i | − | 0.0160013i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29.8772 | −0.208932 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 103.587i | − | 0.704672i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −200.836 | −1.34789 | −0.673947 | − | 0.738779i | \(-0.735402\pi\) | ||||
−0.673947 | + | 0.738779i | \(0.735402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 148.996i | 0.986727i | 0.869823 | + | 0.493364i | \(0.164233\pi\) | ||||
−0.869823 | + | 0.493364i | \(0.835767\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 226.139i | 1.47803i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 120.126 | 0.765133 | 0.382567 | − | 0.923928i | \(-0.375040\pi\) | ||||
0.382567 | + | 0.923928i | \(0.375040\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −61.2347 | −0.385124 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 218.295i | − | 1.35587i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 172.918 | 1.06085 | 0.530423 | − | 0.847733i | \(-0.322033\pi\) | ||||
0.530423 | + | 0.847733i | \(0.322033\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 61.6481i | − | 0.369150i | −0.982818 | − | 0.184575i | \(-0.940909\pi\) | ||
0.982818 | − | 0.184575i | \(-0.0590909\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 147.574 | 0.873218 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −148.065 | −0.865875 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 194.170 | 1.12237 | 0.561184 | − | 0.827691i | \(-0.310346\pi\) | ||||
0.561184 | + | 0.827691i | \(0.310346\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 46.9840i | 0.265446i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 326.091i | 1.82174i | 0.412693 | + | 0.910870i | \(0.364588\pi\) | ||||
−0.412693 | + | 0.910870i | \(0.635412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 202.064i | 1.11637i | 0.829715 | + | 0.558187i | \(0.188503\pi\) | ||||
−0.829715 | + | 0.558187i | \(0.811497\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −42.8430 | −0.234115 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 180.570 | 0.965613 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 205.056i | − | 1.08495i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 245.447 | 1.28506 | 0.642531 | − | 0.766260i | \(-0.277884\pi\) | ||||
0.642531 | + | 0.766260i | \(0.277884\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 139.941 | 0.725085 | 0.362542 | − | 0.931967i | \(-0.381909\pi\) | ||||
0.362542 | + | 0.931967i | \(0.381909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 264.058i | − | 1.34039i | −0.742183 | − | 0.670197i | \(-0.766209\pi\) | ||
0.742183 | − | 0.670197i | \(-0.233791\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 105.641i | − | 0.530859i | −0.964130 | − | 0.265429i | \(-0.914486\pi\) | ||
0.964130 | − | 0.265429i | \(-0.0855137\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 52.5931i | 0.261657i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 426.992i | − | 2.10341i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 140.739i | − | 0.679897i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 118.228i | 0.565684i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 232.697 | 1.10283 | 0.551414 | − | 0.834232i | \(-0.314088\pi\) | ||||
0.551414 | + | 0.834232i | \(0.314088\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 22.8271i | − | 0.107169i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −107.318 | − | 373.570i | −0.494555 | − | 1.72152i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 118.428 | 0.540767 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 129.493 | 0.585943 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 280.489i | − | 1.25780i | −0.777487 | − | 0.628899i | \(-0.783506\pi\) | ||
0.777487 | − | 0.628899i | \(-0.216494\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −61.4774 | −0.270825 | −0.135413 | − | 0.990789i | \(-0.543236\pi\) | ||||
−0.135413 | + | 0.990789i | \(0.543236\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.9507i | − | 0.0871211i | −0.999051 | − | 0.0435605i | \(-0.986130\pi\) | ||
0.999051 | − | 0.0435605i | \(-0.0138701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −77.4754 | −0.335391 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 330.871 | 1.42005 | 0.710024 | − | 0.704177i | \(-0.248684\pi\) | ||||
0.710024 | + | 0.704177i | \(0.248684\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 90.2711 | 0.380891 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 139.998i | 0.585766i | 0.956148 | + | 0.292883i | \(0.0946147\pi\) | ||||
−0.956148 | + | 0.292883i | \(0.905385\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 246.036i | − | 1.02089i | −0.859909 | − | 0.510447i | \(-0.829480\pi\) | ||
0.859909 | − | 0.510447i | \(-0.170520\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 201.851i | − | 0.830662i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 84.7858i | 0.343262i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.1544 | 0.0929897 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 138.762i | − | 0.552835i | −0.961038 | − | 0.276417i | \(-0.910853\pi\) | ||
0.961038 | − | 0.276417i | \(-0.0891472\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −112.378 | −0.444183 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −86.1950 | −0.335389 | −0.167695 | − | 0.985839i | \(-0.553632\pi\) | ||||
−0.167695 | + | 0.985839i | \(0.553632\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 128.943i | − | 0.497850i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 275.289i | − | 1.05475i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 111.985i | 0.425799i | 0.977074 | + | 0.212900i | \(0.0682907\pi\) | ||||
−0.977074 | + | 0.212900i | \(0.931709\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.1619 | 0.0755126 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 389.223i | 1.44693i | 0.690363 | + | 0.723463i | \(0.257451\pi\) | ||||
−0.690363 | + | 0.723463i | \(0.742549\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 142.880i | − | 0.527234i | −0.964627 | − | 0.263617i | \(-0.915084\pi\) | ||
0.964627 | − | 0.263617i | \(-0.0849155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −55.5606 | −0.203519 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 235.632i | − | 0.850658i | −0.905039 | − | 0.425329i | \(-0.860158\pi\) | ||
0.905039 | − | 0.425329i | \(-0.139842\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −69.1900 | − | 240.847i | −0.247993 | − | 0.863252i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 316.317 | 1.12568 | 0.562842 | − | 0.826565i | \(-0.309708\pi\) | ||||
0.562842 | + | 0.826565i | \(0.309708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −327.084 | −1.15577 | −0.577887 | − | 0.816117i | \(-0.696123\pi\) | ||||
−0.577887 | + | 0.816117i | \(0.696123\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 428.888 | 1.49438 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −493.622 | −1.70803 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 110.271i | − | 0.378939i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 99.5877 | 0.339890 | 0.169945 | − | 0.985454i | \(-0.445641\pi\) | ||||
0.169945 | + | 0.985454i | \(0.445641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −105.563 | −0.355430 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −80.5907 | −0.269534 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1029.96i | − | 3.42178i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 144.292i | 0.476211i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −73.6388 | −0.239866 | −0.119933 | − | 0.992782i | \(-0.538268\pi\) | ||||
−0.119933 | + | 0.992782i | \(0.538268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 152.866i | 0.494711i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −554.949 | −1.78440 | −0.892201 | − | 0.451640i | \(-0.850839\pi\) | ||||
−0.892201 | + | 0.451640i | \(0.850839\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 283.035i | − | 0.904265i | −0.891951 | − | 0.452133i | \(-0.850663\pi\) | ||
0.891951 | − | 0.452133i | \(-0.149337\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −457.252 | −1.44243 | −0.721217 | − | 0.692709i | \(-0.756417\pi\) | ||||
−0.721217 | + | 0.692709i | \(0.756417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −219.816 | −0.689077 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 93.4023i | − | 0.290973i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 512.422i | − | 1.58645i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 75.3783i | − | 0.230515i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.5488 | 0.0898139 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 203.608i | 0.615131i | 0.951527 | + | 0.307565i | \(0.0995143\pi\) | ||||
−0.951527 | + | 0.307565i | \(0.900486\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 83.1319i | − | 0.249645i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 123.808i | − | 0.367383i | −0.982984 | − | 0.183691i | \(-0.941195\pi\) | ||
0.982984 | − | 0.183691i | \(-0.0588047\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 10.4649i | − | 0.0308699i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −192.314 | + | 55.2475i | −0.563970 | + | 0.162016i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 742.291 | 2.16411 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 656.462i | 1.89182i | 0.324428 | + | 0.945911i | \(0.394828\pi\) | ||||
−0.324428 | + | 0.945911i | \(0.605172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8273 | 0.0310239 | 0.0155120 | − | 0.999880i | \(-0.495062\pi\) | ||||
0.0155120 | + | 0.999880i | \(0.495062\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −75.7030 | −0.215678 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 86.1215i | − | 0.243970i | −0.992532 | − | 0.121985i | \(-0.961074\pi\) | ||
0.992532 | − | 0.121985i | \(-0.0389260\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 335.793 | 0.940596 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −135.320 | −0.376937 | −0.188468 | − | 0.982079i | \(-0.560352\pi\) | ||||
−0.188468 | + | 0.982079i | \(0.560352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −25.4917 | −0.0706141 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 75.9534i | − | 0.209238i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 570.456i | − | 1.55438i | −0.629268 | − | 0.777189i | \(-0.716645\pi\) | ||
0.629268 | − | 0.777189i | \(-0.283355\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 276.512 | 0.749354 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 801.980i | − | 2.16167i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −151.217 | −0.405409 | −0.202704 | − | 0.979240i | \(-0.564973\pi\) | ||||
−0.202704 | + | 0.979240i | \(0.564973\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −157.638 | −0.418138 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 79.6051 | 0.210040 | 0.105020 | − | 0.994470i | \(-0.466509\pi\) | ||||
0.105020 | + | 0.994470i | \(0.466509\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −182.784 | −0.479747 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 385.132i | 1.00557i | 0.864413 | + | 0.502783i | \(0.167691\pi\) | ||||
−0.864413 | + | 0.502783i | \(0.832309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 664.031i | − | 1.71584i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 37.5291i | 0.0964759i | 0.998836 | + | 0.0482379i | \(0.0153606\pi\) | ||||
−0.998836 | + | 0.0482379i | \(0.984639\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 487.068 | 1.24570 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 69.7835i | 0.177566i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 181.996 | 0.458429 | 0.229215 | − | 0.973376i | \(-0.426384\pi\) | ||||
0.229215 | + | 0.973376i | \(0.426384\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 219.860i | 0.551028i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 199.817i | 0.498298i | 0.968465 | + | 0.249149i | \(0.0801508\pi\) | ||||
−0.968465 | + | 0.249149i | \(0.919849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −137.916 | + | 39.6201i | −0.342222 | + | 0.0983128i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −66.3799 | −0.163096 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 289.651i | 0.708193i | 0.935209 | + | 0.354096i | \(0.115212\pi\) | ||||
−0.935209 | + | 0.354096i | \(0.884788\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −126.986 | −0.308969 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −615.341 | −1.48993 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.3994 | 0.0657060 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 177.037 | 0.422523 | 0.211262 | − | 0.977430i | \(-0.432243\pi\) | ||||
0.211262 | + | 0.977430i | \(0.432243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 539.661 | 1.28186 | 0.640928 | − | 0.767601i | \(-0.278550\pi\) | ||||
0.640928 | + | 0.767601i | \(0.278550\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.0506 | 0.0450369 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 561.107i | − | 1.31407i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 28.6026i | 0.0666726i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −386.168 | −0.895981 | −0.447991 | − | 0.894038i | \(-0.647860\pi\) | ||||
−0.447991 | + | 0.894038i | \(0.647860\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 264.248i | 0.610273i | 0.952309 | + | 0.305137i | \(0.0987021\pi\) | ||||
−0.952309 | + | 0.305137i | \(0.901298\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 318.908i | 0.729766i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 247.325 | 0.563382 | 0.281691 | − | 0.959505i | \(-0.409105\pi\) | ||||
0.281691 | + | 0.959505i | \(0.409105\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 874.660 | 1.98336 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 689.353 | 1.55610 | 0.778051 | − | 0.628202i | \(-0.216209\pi\) | ||||
0.778051 | + | 0.628202i | \(0.216209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 192.268i | 0.430130i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 832.590i | 1.85432i | 0.374665 | + | 0.927160i | \(0.377758\pi\) | ||||
−0.374665 | + | 0.927160i | \(0.622242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 220.792i | − | 0.489560i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 142.639 | 0.314877 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 156.740i | 0.342975i | 0.985186 | + | 0.171488i | \(0.0548574\pi\) | ||||
−0.985186 | + | 0.171488i | \(0.945143\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 457.528 | 0.996793 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 846.609i | 1.83646i | 0.396046 | + | 0.918231i | \(0.370382\pi\) | ||||
−0.396046 | + | 0.918231i | \(0.629618\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 104.757i | 0.226256i | 0.993580 | + | 0.113128i | \(0.0360871\pi\) | ||||
−0.993580 | + | 0.113128i | \(0.963913\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −469.270 | −1.00486 | −0.502430 | − | 0.864618i | \(-0.667561\pi\) | ||||
−0.502430 | + | 0.864618i | \(0.667561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −688.802 | −1.46866 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 115.001i | − | 0.244163i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −530.221 | −1.12098 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 517.050i | − | 1.08396i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −721.582 | −1.50643 | −0.753217 | − | 0.657772i | \(-0.771499\pi\) | ||||
−0.753217 | + | 0.657772i | \(0.771499\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −47.6036 | −0.0989679 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −208.982 | −0.432675 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 508.350i | − | 1.04384i | −0.852995 | − | 0.521919i | \(-0.825216\pi\) | ||
0.852995 | − | 0.521919i | \(-0.174784\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 165.541i | − | 0.338529i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 43.0848i | − | 0.0877492i | −0.999037 | − | 0.0438746i | \(-0.986030\pi\) | ||
0.999037 | − | 0.0438746i | \(-0.0139702\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 952.721 | 1.93250 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 298.962 | 0.601533 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 397.773i | − | 0.797140i | −0.917138 | − | 0.398570i | \(-0.869507\pi\) | ||
0.917138 | − | 0.398570i | \(-0.130493\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −59.0180 | −0.117800 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −759.610 | −1.51016 | −0.755080 | − | 0.655633i | \(-0.772402\pi\) | ||||
−0.755080 | + | 0.655633i | \(0.772402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 141.278i | − | 0.278655i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 705.929i | 1.38689i | 0.720508 | + | 0.693447i | \(0.243909\pi\) | ||||
−0.720508 | + | 0.693447i | \(0.756091\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1551.03i | 3.03528i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 299.567i | 0.583951i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 15.2117i | − | 0.0294230i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 185.886i | − | 0.358162i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 406.342 | 0.779927 | 0.389963 | − | 0.920830i | \(-0.372488\pi\) | ||||
0.389963 | + | 0.920830i | \(0.372488\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 192.449i | − | 0.367971i | −0.982929 | − | 0.183986i | \(-0.941100\pi\) | ||
0.982929 | − | 0.183986i | \(-0.0589000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 833.524 | − | 239.453i | 1.58164 | − | 0.454370i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 225.871 | 0.426978 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −396.721 | −0.747120 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 158.338i | − | 0.297069i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 312.179 | 0.581340 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 698.406i | − | 1.29574i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −577.722 | −1.06788 | −0.533939 | − | 0.845523i | \(-0.679289\pi\) | ||||
−0.533939 | + | 0.845523i | \(0.679289\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 193.443 | 0.356248 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 347.000 | 0.634370 | 0.317185 | − | 0.948364i | \(-0.397262\pi\) | ||||
0.317185 | + | 0.948364i | \(0.397262\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 361.755i | − | 0.658935i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 623.794i | 1.13211i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1182.26i | 2.13791i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 485.901i | 0.872354i | 0.899861 | + | 0.436177i | \(0.143668\pi\) | ||||
−0.899861 | + | 0.436177i | \(0.856332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −380.242 | −0.680218 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 172.866i | − | 0.308139i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 943.562 | 1.67595 | 0.837977 | − | 0.545706i | \(-0.183738\pi\) | ||||
0.837977 | + | 0.545706i | \(0.183738\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 715.856 | 1.26253 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1044.94i | 1.83645i | 0.396062 | + | 0.918224i | \(0.370377\pi\) | ||||
−0.396062 | + | 0.918224i | \(0.629623\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 715.772i | − | 1.25354i | −0.779204 | − | 0.626771i | \(-0.784376\pi\) | ||
0.779204 | − | 0.626771i | \(-0.215624\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 234.975i | − | 0.410079i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −995.223 | −1.72482 | −0.862412 | − | 0.506207i | \(-0.831047\pi\) | ||||
−0.862412 | + | 0.506207i | \(0.831047\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 133.971i | − | 0.231383i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 303.249i | 0.521944i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −412.859 | −0.708163 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 327.196i | 0.557403i | 0.960378 | + | 0.278702i | \(0.0899041\pi\) | ||||
−0.960378 | + | 0.278702i | \(0.910096\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 156.782 | + | 545.750i | 0.266183 | + | 0.926570i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −252.792 | −0.427736 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −845.163 | −1.42523 | −0.712616 | − | 0.701554i | \(-0.752490\pi\) | ||||
−0.712616 | + | 0.701554i | \(0.752490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −101.134 | −0.169403 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 239.373 | 0.399620 | 0.199810 | − | 0.979835i | \(-0.435967\pi\) | ||||
0.199810 | + | 0.979835i | \(0.435967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 387.358i | − | 0.644523i | −0.946651 | − | 0.322262i | \(-0.895557\pi\) | ||
0.946651 | − | 0.322262i | \(-0.104443\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −444.083 | −0.736456 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −728.736 | −1.20055 | −0.600277 | − | 0.799792i | \(-0.704943\pi\) | ||||
−0.600277 | + | 0.799792i | \(0.704943\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −408.776 | −0.671224 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 10.9089i | − | 0.0178541i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 281.663i | 0.459483i | 0.973252 | + | 0.229741i | \(0.0737880\pi\) | ||||
−0.973252 | + | 0.229741i | \(0.926212\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 743.929 | 1.20572 | 0.602860 | − | 0.797847i | \(-0.294028\pi\) | ||||
0.602860 | + | 0.797847i | \(0.294028\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1082.36i | − | 1.74856i | −0.485418 | − | 0.874282i | \(-0.661333\pi\) | ||
0.485418 | − | 0.874282i | \(-0.338667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −284.745 | −0.458526 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 264.056i | 0.423846i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 113.184 | 0.180517 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 287.703 | 0.457397 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 500.313i | 0.792889i | 0.918059 | + | 0.396445i | \(0.129756\pi\) | ||||
−0.918059 | + | 0.396445i | \(0.870244\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 222.769i | − | 0.351926i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 500.853i | − | 0.786269i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 192.746 | 0.301637 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 167.638i | − | 0.261525i | −0.991414 | − | 0.130763i | \(-0.958257\pi\) | ||
0.991414 | − | 0.130763i | \(-0.0417426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 602.608i | − | 0.937182i | −0.883415 | − | 0.468591i | \(-0.844762\pi\) | ||
0.883415 | − | 0.468591i | \(-0.155238\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 352.530i | − | 0.544869i | −0.962174 | − | 0.272435i | \(-0.912171\pi\) | ||
0.962174 | − | 0.272435i | \(-0.0878289\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 316.777i | 0.488101i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −357.633 | + | 102.740i | −0.549359 | + | 0.157819i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1072.69 | 1.64271 | 0.821354 | − | 0.570418i | \(-0.193219\pi\) | ||||
0.821354 | + | 0.570418i | \(0.193219\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 999.976i | 1.52203i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.8230 | −0.0528422 | −0.0264211 | − | 0.999651i | \(-0.508411\pi\) | ||||
−0.0264211 | + | 0.999651i | \(0.508411\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −701.878 | −1.06184 | −0.530922 | − | 0.847421i | \(-0.678154\pi\) | ||||
−0.530922 | + | 0.847421i | \(0.678154\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 123.969i | − | 0.186982i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −592.930 | −0.888950 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −268.522 | −0.401379 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −288.858 | −0.430488 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1080.02i | − | 1.60479i | −0.596796 | − | 0.802393i | \(-0.703560\pi\) | ||
0.596796 | − | 0.802393i | \(-0.296440\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 651.535i | − | 0.962385i | −0.876615 | − | 0.481193i | \(-0.840204\pi\) | ||
0.876615 | − | 0.481193i | \(-0.159796\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1444.20 | 2.12695 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 58.8546i | 0.0864237i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −733.610 | −1.07410 | −0.537050 | − | 0.843551i | \(-0.680461\pi\) | ||||
−0.537050 | + | 0.843551i | \(0.680461\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −19.0996 | −0.0278014 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −296.077 | −0.429719 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −464.673 | −0.672465 | −0.336232 | − | 0.941779i | \(-0.609153\pi\) | ||||
−0.336232 | + | 0.941779i | \(0.609153\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 654.182i | − | 0.943986i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 956.951i | 1.37296i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 316.755i | − | 0.453155i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1316.24 | 1.87766 | 0.938828 | − | 0.344386i | \(-0.111913\pi\) | ||||
0.938828 | + | 0.344386i | \(0.111913\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 188.373i | 0.267957i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1889.76 | −2.67293 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 924.122i | − | 1.30342i | −0.758470 | − | 0.651708i | \(-0.774053\pi\) | ||
0.758470 | − | 0.651708i | \(-0.225947\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 762.226i | 1.07205i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −518.747 | + | 149.024i | −0.727555 | + | 0.209010i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 134.025 | 0.186925 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 988.873i | − | 1.37535i | −0.726021 | − | 0.687673i | \(-0.758632\pi\) | ||
0.726021 | − | 0.687673i | \(-0.241368\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2002.05 | −2.77677 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −235.539 | −0.325780 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 787.202 | 1.08281 | 0.541404 | − | 0.840762i | \(-0.317893\pi\) | ||||
0.541404 | + | 0.840762i | \(0.317893\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 320.612 | 0.439798 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2298.08 | 3.14375 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −153.102 | −0.208871 | −0.104435 | − | 0.994532i | \(-0.533304\pi\) | ||||
−0.104435 | + | 0.994532i | \(0.533304\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 354.595i | 0.481133i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 643.904i | − | 0.871318i | −0.900112 | − | 0.435659i | \(-0.856515\pi\) | ||
0.900112 | − | 0.435659i | \(-0.143485\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 81.1685 | 0.109539 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 831.462i | − | 1.11906i | −0.828810 | − | 0.559530i | \(-0.810982\pi\) | ||
0.828810 | − | 0.559530i | \(-0.189018\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 195.510i | 0.261727i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1223.27 | 1.63321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1146.18 | 1.52621 | 0.763104 | − | 0.646275i | \(-0.223674\pi\) | ||||
0.763104 | + | 0.646275i | \(0.223674\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −132.842 | −0.176416 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 944.831i | 1.24813i | 0.781374 | + | 0.624063i | \(0.214519\pi\) | ||||
−0.781374 | + | 0.624063i | \(0.785481\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 107.584i | 0.141744i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1198.74i | − | 1.57522i | −0.616174 | − | 0.787610i | \(-0.711318\pi\) | ||
0.616174 | − | 0.787610i | \(-0.288682\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 987.216 | 1.29386 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 227.173i | 0.296184i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −242.061 | −0.314773 | −0.157387 | − | 0.987537i | \(-0.550307\pi\) | ||||
−0.157387 | + | 0.987537i | \(0.550307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 82.5176i | 0.107027i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 643.478i | 0.832443i | 0.909263 | + | 0.416221i | \(0.136646\pi\) | ||||
−0.909263 | + | 0.416221i | \(0.863354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −123.442 | −0.158870 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −626.564 | −0.804318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 153.905i | − | 0.197062i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −556.970 | −0.711328 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 788.278i | 1.00162i | 0.865556 | + | 0.500812i | \(0.166965\pi\) | ||||
−0.865556 | + | 0.500812i | \(0.833035\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 107.208 | 0.135878 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 137.057 | 0.173270 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −207.151 | −0.261224 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 950.849i | 1.19304i | 0.802600 | + | 0.596518i | \(0.203449\pi\) | ||||
−0.802600 | + | 0.596518i | \(0.796551\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 65.9303i | 0.0825160i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 170.241i | 0.212536i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 798.470 | 0.994358 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 372.618 | 0.461732 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.08190i | − | 0.00628171i | −0.999995 | − | 0.00314085i | \(-0.999000\pi\) | ||
0.999995 | − | 0.00314085i | \(-0.000999767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 918.456 | 1.13250 | 0.566249 | − | 0.824234i | \(-0.308394\pi\) | ||||
0.566249 | + | 0.824234i | \(0.308394\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −136.785 | −0.168247 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1504.67i | 1.84170i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 469.139i | − | 0.572819i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 979.982i | − | 1.19364i | −0.802373 | − | 0.596822i | \(-0.796430\pi\) | ||
0.802373 | − | 0.596822i | \(-0.203570\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 418.294i | − | 0.508255i | −0.967171 | − | 0.254128i | \(-0.918212\pi\) | ||
0.967171 | − | 0.254128i | \(-0.0817883\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 484.546i | 0.585908i | 0.956127 | + | 0.292954i | \(0.0946383\pi\) | ||||
−0.956127 | + | 0.292954i | \(0.905362\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1256.49i | 1.51567i | 0.652444 | + | 0.757837i | \(0.273744\pi\) | ||||
−0.652444 | + | 0.757837i | \(0.726256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −225.579 | −0.271455 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3027.02i | 3.63388i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −487.286 | + | 139.986i | −0.582181 | + | 0.167248i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1599.82 | 1.90682 | 0.953408 | − | 0.301685i | \(-0.0975492\pi\) | ||||
0.953408 | + | 0.301685i | \(0.0975492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −318.790 | −0.379061 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 302.822i | − | 0.359219i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 994.748 | 1.17444 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 313.130i | 0.368822i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −179.053 | −0.210403 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −196.356 | −0.230194 | −0.115097 | − | 0.993354i | \(-0.536718\pi\) | ||||
−0.115097 | + | 0.993354i | \(0.536718\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1226.13 | −1.43072 | −0.715360 | − | 0.698756i | \(-0.753737\pi\) | ||||
−0.715360 | + | 0.698756i | \(0.753737\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 732.830i | 0.853120i | 0.904459 | + | 0.426560i | \(0.140275\pi\) | ||||
−0.904459 | + | 0.426560i | \(0.859725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 410.591i | − | 0.476876i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 484.751i | − | 0.561704i | −0.959751 | − | 0.280852i | \(-0.909383\pi\) | ||
0.959751 | − | 0.280852i | \(-0.0906170\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 472.563i | 0.545055i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 608.629 | 0.700378 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 254.294i | 0.291956i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 931.102 | 1.06655 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 676.353 | 0.771212 | 0.385606 | − | 0.922664i | \(-0.373992\pi\) | ||||
0.385606 | + | 0.922664i | \(0.373992\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 95.3390i | − | 0.108463i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1212.48i | 1.37626i | 0.725589 | + | 0.688128i | \(0.241567\pi\) | ||||
−0.725589 | + | 0.688128i | \(0.758433\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 491.333i | 0.556437i | 0.960518 | + | 0.278218i | \(0.0897439\pi\) | ||||
−0.960518 | + | 0.278218i | \(0.910256\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 80.9774 | 0.0912936 | 0.0456468 | − | 0.998958i | \(-0.485465\pi\) | ||||
0.0456468 | + | 0.998958i | \(0.485465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2393.88i | − | 2.69278i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 368.522i | − | 0.413605i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −43.1679 | −0.0483403 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 77.1525i | 0.0860117i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1014.69 | + | 291.497i | −1.12868 | + | 0.324245i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1789.41 | 1.98602 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −986.016 | −1.09193 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1053.61 | 1.16164 | 0.580819 | − | 0.814033i | \(-0.302732\pi\) | ||||
0.580819 | + | 0.814033i | \(0.302732\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1218.36 | −1.34033 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1017.91i | − | 1.11736i | −0.829383 | − | 0.558680i | \(-0.811308\pi\) | ||
0.829383 | − | 0.558680i | \(-0.188692\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 156.113 | 0.170989 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −913.942 | −0.996665 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 404.861 | 0.440545 | 0.220272 | − | 0.975438i | \(-0.429305\pi\) | ||||
0.220272 | + | 0.975438i | \(0.429305\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 70.4971i | 0.0765441i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 110.371i | − | 0.119579i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1290.76 | −1.39240 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 449.751i | − | 0.484124i | −0.970261 | − | 0.242062i | \(-0.922176\pi\) | ||
0.970261 | − | 0.242062i | \(-0.0778237\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1981.94 | −2.12883 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 531.273i | 0.569424i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1095.58 | −1.16924 | −0.584621 | − | 0.811306i | \(-0.698757\pi\) | ||||
−0.584621 | + | 0.811306i | \(0.698757\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −270.960 | −0.288562 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 398.859i | 0.423867i | 0.977284 | + | 0.211934i | \(0.0679761\pi\) | ||||
−0.977284 | + | 0.211934i | \(0.932024\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 595.562i | − | 0.631561i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1697.26i | 1.79225i | 0.443803 | + | 0.896125i | \(0.353629\pi\) | ||||
−0.443803 | + | 0.896125i | \(0.646371\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 572.613 | 0.603386 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 437.744i | 0.460299i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1365.25i | 1.43258i | 0.697801 | + | 0.716292i | \(0.254162\pi\) | ||||
−0.697801 | + | 0.716292i | \(0.745838\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 210.437i | 0.219893i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1663.12i | − | 1.73422i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −814.473 | + | 510.054i | −0.847527 | + | 0.530753i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 788.665 | 0.818967 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 809.773i | − | 0.837407i | −0.908123 | − | 0.418704i | \(-0.862485\pi\) | ||
0.908123 | − | 0.418704i | \(-0.137515\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −490.560 | −0.506254 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −886.258 | −0.912727 | −0.456363 | − | 0.889793i | \(-0.650848\pi\) | ||||
−0.456363 | + | 0.889793i | \(0.650848\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 358.845i | 0.368802i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 648.945 | 0.664222 | 0.332111 | − | 0.943240i | \(-0.392239\pi\) | ||||
0.332111 | + | 0.943240i | \(0.392239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 135.936 | 0.138852 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 636.475 | 0.648802 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 652.183i | 0.663462i | 0.943374 | + | 0.331731i | \(0.107633\pi\) | ||||
−0.943374 | + | 0.331731i | \(0.892367\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 28.2881i | − | 0.0286607i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1430.22 | −1.44613 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1282.72i | 1.29437i | 0.762335 | + | 0.647183i | \(0.224053\pi\) | ||||
−0.762335 | + | 0.647183i | \(0.775947\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 194.922 | 0.196296 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1112.81 | −1.11616 | −0.558080 | − | 0.829787i | \(-0.688462\pi\) | ||||
−0.558080 | + | 0.829787i | \(0.688462\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −168.194 | −0.168362 |
(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 | 3100.3.d.g.1301.9 | yes | 22 | |
5.2 | odd | 4 | 3100.3.f.d.1549.17 | 44 | |||
5.3 | odd | 4 | 3100.3.f.d.1549.28 | 44 | |||
5.4 | even | 2 | 3100.3.d.f.1301.14 | yes | 22 | ||
31.30 | odd | 2 | inner | 3100.3.d.g.1301.14 | yes | 22 | |
155.92 | even | 4 | 3100.3.f.d.1549.27 | 44 | |||
155.123 | even | 4 | 3100.3.f.d.1549.18 | 44 | |||
155.154 | odd | 2 | 3100.3.d.f.1301.9 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3100.3.d.f.1301.9 | ✓ | 22 | 155.154 | odd | 2 | ||
3100.3.d.f.1301.14 | yes | 22 | 5.4 | even | 2 | ||
3100.3.d.g.1301.9 | yes | 22 | 1.1 | even | 1 | trivial | |
3100.3.d.g.1301.14 | yes | 22 | 31.30 | odd | 2 | inner | |
3100.3.f.d.1549.17 | 44 | 5.2 | odd | 4 | |||
3100.3.f.d.1549.18 | 44 | 155.123 | even | 4 | |||
3100.3.f.d.1549.27 | 44 | 155.92 | even | 4 | |||
3100.3.f.d.1549.28 | 44 | 5.3 | odd | 4 |