Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1680,2,Mod(1009,1680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1680.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1680.t (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 840) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1009.3 | ||
Root | \(0.403032 + 0.403032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1680.1009 |
Dual form | 1680.2.t.i.1009.6 |
$q$-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 \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(421\) | \(1121\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.48119 | − | 1.67513i | 0.662410 | − | 0.749141i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.387873 | −0.116948 | −0.0584741 | − | 0.998289i | \(-0.518623\pi\) | ||||
−0.0584741 | + | 0.998289i | \(0.518623\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.96239i | − | 0.821619i | −0.911721 | − | 0.410809i | \(-0.865246\pi\) | ||
0.911721 | − | 0.410809i | \(-0.134754\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.67513 | − | 1.48119i | −0.432517 | − | 0.382443i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.35026i | − | 0.812558i | −0.913749 | − | 0.406279i | \(-0.866826\pi\) | ||
0.913749 | − | 0.406279i | \(-0.133174\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.96239 | −0.679619 | −0.339809 | − | 0.940494i | \(-0.610363\pi\) | ||||
−0.339809 | + | 0.940494i | \(0.610363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.962389i | 0.200672i | 0.994954 | + | 0.100336i | \(0.0319918\pi\) | ||||
−0.994954 | + | 0.100336i | \(0.968008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.612127 | − | 4.96239i | −0.122425 | − | 0.992478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.22425 | −0.227338 | −0.113669 | − | 0.993519i | \(-0.536260\pi\) | ||||
−0.113669 | + | 0.993519i | \(0.536260\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.96239 | −0.532061 | −0.266030 | − | 0.963965i | \(-0.585712\pi\) | ||||
−0.266030 | + | 0.963965i | \(0.585712\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.387873i | 0.0675200i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.67513 | + | 1.48119i | 0.283149 | + | 0.250368i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.92478i | − | 0.974027i | −0.873394 | − | 0.487014i | \(-0.838086\pi\) | ||
0.873394 | − | 0.487014i | \(-0.161914\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.96239 | −0.474362 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.03761 | 0.162048 | 0.0810238 | − | 0.996712i | \(-0.474181\pi\) | ||||
0.0810238 | + | 0.996712i | \(0.474181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.7005i | − | 1.63181i | −0.578183 | − | 0.815907i | \(-0.696238\pi\) | ||
0.578183 | − | 0.815907i | \(-0.303762\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.48119 | + | 1.67513i | −0.220803 | + | 0.249714i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.22425i | 0.470306i | 0.971958 | + | 0.235153i | \(0.0755591\pi\) | ||||
−0.971958 | + | 0.235153i | \(0.924441\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.35026 | −0.469130 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.66291i | − | 0.777861i | −0.921267 | − | 0.388930i | \(-0.872845\pi\) | ||
0.921267 | − | 0.388930i | \(-0.127155\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.574515 | + | 0.649738i | −0.0774677 | + | 0.0876107i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.96239i | 0.392378i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.22425 | 0.419762 | 0.209881 | − | 0.977727i | \(-0.432692\pi\) | ||||
0.209881 | + | 0.977727i | \(0.432692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.6253 | 1.87258 | 0.936289 | − | 0.351231i | \(-0.114237\pi\) | ||||
0.936289 | + | 0.351231i | \(0.114237\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.96239 | − | 4.38787i | −0.615509 | − | 0.544249i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.962389 | 0.115858 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.53690 | −0.657110 | −0.328555 | − | 0.944485i | \(-0.606562\pi\) | ||||
−0.328555 | + | 0.944485i | \(0.606562\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.18664i | 0.724092i | 0.932160 | + | 0.362046i | \(0.117922\pi\) | ||||
−0.932160 | + | 0.362046i | \(0.882078\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.96239 | + | 0.612127i | −0.573007 | + | 0.0706823i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.387873i | − | 0.0442022i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.9248 | −1.56666 | −0.783330 | − | 0.621606i | \(-0.786480\pi\) | ||||
−0.783330 | + | 0.621606i | \(0.786480\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.22425i | − | 0.353908i | −0.984219 | − | 0.176954i | \(-0.943376\pi\) | ||
0.984219 | − | 0.176954i | \(-0.0566244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.61213 | − | 4.96239i | −0.608721 | − | 0.538247i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.22425i | 0.131254i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.73813 | −0.396242 | −0.198121 | − | 0.980178i | \(-0.563484\pi\) | ||||
−0.198121 | + | 0.980178i | \(0.563484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.96239 | 0.310543 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.96239i | 0.307185i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.38787 | + | 4.96239i | −0.450186 | + | 0.509130i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.73813i | 0.785689i | 0.919605 | + | 0.392844i | \(0.128509\pi\) | ||||
−0.919605 | + | 0.392844i | \(0.871491\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.387873 | 0.0389827 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.58769 | −0.755003 | −0.377502 | − | 0.926009i | \(-0.623217\pi\) | ||||
−0.377502 | + | 0.926009i | \(0.623217\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.7005i | − | 1.44849i | −0.689545 | − | 0.724243i | \(-0.742189\pi\) | ||
0.689545 | − | 0.724243i | \(-0.257811\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.48119 | − | 1.67513i | 0.144550 | − | 0.163476i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.4387i | 1.58919i | 0.607143 | + | 0.794593i | \(0.292315\pi\) | ||||
−0.607143 | + | 0.794593i | \(0.707685\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.77575 | 0.265868 | 0.132934 | − | 0.991125i | \(-0.457560\pi\) | ||||
0.132934 | + | 0.991125i | \(0.457560\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.92478 | −0.562355 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.26187i | 0.400923i | 0.979702 | + | 0.200461i | \(0.0642441\pi\) | ||||
−0.979702 | + | 0.200461i | \(0.935756\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.61213 | + | 1.42548i | 0.150332 | + | 0.132927i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.96239i | 0.273873i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.35026 | 0.307118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8496 | −0.986323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 1.03761i | − | 0.0935583i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.21933 | − | 6.32487i | −0.824602 | − | 0.565713i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.5501i | − | 1.29111i | −0.763714 | − | 0.645555i | \(-0.776626\pi\) | ||
0.763714 | − | 0.645555i | \(-0.223374\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.7005 | −0.942129 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.96239i | − | 0.256872i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.67513 | + | 1.48119i | 0.144172 | + | 0.127481i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 10.4387i | − | 0.891835i | −0.895074 | − | 0.445917i | \(-0.852878\pi\) | ||
0.895074 | − | 0.445917i | \(-0.147122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.66291 | 0.480322 | 0.240161 | − | 0.970733i | \(-0.422800\pi\) | ||||
0.240161 | + | 0.970733i | \(0.422800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.22425 | 0.271531 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.14903i | 0.0960868i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.81336 | + | 2.05079i | −0.150591 | + | 0.170308i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.5501 | −1.68353 | −0.841764 | − | 0.539846i | \(-0.818483\pi\) | ||||
−0.841764 | + | 0.539846i | \(0.818483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.7005 | 1.84734 | 0.923671 | − | 0.383186i | \(-0.125173\pi\) | ||||
0.923671 | + | 0.383186i | \(0.125173\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.35026i | 0.270853i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.38787 | + | 4.96239i | −0.352442 | + | 0.398589i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.18664i | 0.174513i | 0.996186 | + | 0.0872565i | \(0.0278100\pi\) | ||||
−0.996186 | + | 0.0872565i | \(0.972190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.66291 | −0.449098 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.962389 | −0.0758468 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.22425i | − | 0.565847i | −0.959142 | − | 0.282924i | \(-0.908696\pi\) | ||
0.959142 | − | 0.282924i | \(-0.0913043\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.649738 | + | 0.574515i | 0.0505821 | + | 0.0447260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 15.8496i | − | 1.22648i | −0.789898 | − | 0.613238i | \(-0.789867\pi\) | ||
0.789898 | − | 0.613238i | \(-0.210133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.22425 | 0.324943 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.96239 | 0.226540 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.9756i | 1.82283i | 0.411490 | + | 0.911414i | \(0.365008\pi\) | ||||
−0.411490 | + | 0.911414i | \(0.634992\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.96239 | − | 0.612127i | 0.375121 | − | 0.0462724i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.22425i | − | 0.242350i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.2374 | 0.914668 | 0.457334 | − | 0.889295i | \(-0.348804\pi\) | ||||
0.457334 | + | 0.889295i | \(0.348804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.70052 | 0.646705 | 0.323352 | − | 0.946279i | \(-0.395190\pi\) | ||||
0.323352 | + | 0.946279i | \(0.395190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 14.6253i | − | 1.08113i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.92478 | − | 8.77575i | −0.729684 | − | 0.645206i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.29948i | 0.0950271i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5369 | 0.979496 | 0.489748 | − | 0.871864i | \(-0.337089\pi\) | ||||
0.489748 | + | 0.871864i | \(0.337089\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 1.92478i | − | 0.138548i | −0.997598 | − | 0.0692742i | \(-0.977932\pi\) | ||
0.997598 | − | 0.0692742i | \(-0.0220684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.38787 | + | 4.96239i | −0.314222 | + | 0.355364i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.1114i | − | 1.43288i | −0.697649 | − | 0.716440i | \(-0.745771\pi\) | ||
0.697649 | − | 0.716440i | \(-0.254229\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.26187 | −0.585668 | −0.292834 | − | 0.956163i | \(-0.594598\pi\) | ||||
−0.292834 | + | 0.956163i | \(0.594598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.22425i | − | 0.0859258i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.53690 | − | 1.73813i | 0.107342 | − | 0.121397i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 0.962389i | − | 0.0668906i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.14903 | 0.0794801 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.1768 | 1.25134 | 0.625671 | − | 0.780087i | \(-0.284825\pi\) | ||||
0.625671 | + | 0.780087i | \(0.284825\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.53690i | 0.379382i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.9248 | − | 15.8496i | −1.22246 | − | 1.08093i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 2.96239i | − | 0.201100i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.18664 | 0.418055 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.92478 | −0.667613 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 21.4010i | − | 1.43312i | −0.697525 | − | 0.716560i | \(-0.745716\pi\) | ||
0.697525 | − | 0.716560i | \(-0.254284\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.612127 | + | 4.96239i | 0.0408085 | + | 0.330826i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.5501i | 1.23121i | 0.788054 | + | 0.615606i | \(0.211089\pi\) | ||||
−0.788054 | + | 0.615606i | \(0.788911\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.5501 | 1.88664 | 0.943321 | − | 0.331881i | \(-0.107683\pi\) | ||||
0.943321 | + | 0.331881i | \(0.107683\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.387873 | −0.0255202 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9624i | 1.24227i | 0.783705 | + | 0.621134i | \(0.213328\pi\) | ||||
−0.783705 | + | 0.621134i | \(0.786672\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.40105 | + | 4.77575i | 0.352325 | + | 0.311535i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.9248i | 0.904511i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.1622 | −1.17482 | −0.587408 | − | 0.809291i | \(-0.699851\pi\) | ||||
−0.587408 | + | 0.809291i | \(0.699851\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.3733 | 0.925865 | 0.462932 | − | 0.886394i | \(-0.346797\pi\) | ||||
0.462932 | + | 0.886394i | \(0.346797\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.48119 | + | 1.67513i | −0.0946300 | + | 0.107020i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.77575i | 0.558387i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.22425 | −0.204329 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.62530 | 0.544424 | 0.272212 | − | 0.962237i | \(-0.412245\pi\) | ||||
0.272212 | + | 0.962237i | \(0.412245\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 0.373285i | − | 0.0234682i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.96239 | + | 5.61213i | −0.310757 | + | 0.351445i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.8251i | 1.73568i | 0.496841 | + | 0.867842i | \(0.334493\pi\) | ||||
−0.496841 | + | 0.867842i | \(0.665507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.92478 | 0.368148 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.22425 | 0.0757794 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.589104i | 0.0363257i | 0.999835 | + | 0.0181629i | \(0.00578173\pi\) | ||||
−0.999835 | + | 0.0181629i | \(0.994218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.48612 | − | 8.38787i | −0.582728 | − | 0.515263i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.73813i | 0.228770i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.7381 | −0.959571 | −0.479786 | − | 0.877386i | \(-0.659286\pi\) | ||||
−0.479786 | + | 0.877386i | \(0.659286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.11283 | 0.432074 | 0.216037 | − | 0.976385i | \(-0.430687\pi\) | ||||
0.216037 | + | 0.976385i | \(0.430687\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.96239i | − | 0.179292i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.237428 | + | 1.92478i | 0.0143174 | + | 0.116068i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.92478i | − | 0.355985i | −0.984032 | − | 0.177993i | \(-0.943040\pi\) | ||
0.984032 | − | 0.177993i | \(-0.0569603\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.96239 | 0.177354 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 29.3258 | 1.74943 | 0.874716 | − | 0.484636i | \(-0.161048\pi\) | ||||
0.874716 | + | 0.484636i | \(0.161048\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.1016i | 0.957139i | 0.878050 | + | 0.478570i | \(0.158845\pi\) | ||||
−0.878050 | + | 0.478570i | \(0.841155\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.96239 | + | 4.38787i | 0.293947 | + | 0.259915i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.03761i | 0.0612483i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.77575 | 0.339750 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.73813 | 0.453617 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.27504i | 0.541854i | 0.962600 | + | 0.270927i | \(0.0873301\pi\) | ||||
−0.962600 | + | 0.270927i | \(0.912670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.77575 | − | 5.40105i | 0.278055 | − | 0.314461i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 0.387873i | − | 0.0225067i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.85097 | 0.164876 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.7005 | 0.616768 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.58769i | 0.435901i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.6629 | − | 24.4993i | 1.24041 | − | 1.40283i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.7005i | 0.610711i | 0.952238 | + | 0.305356i | \(0.0987753\pi\) | ||||
−0.952238 | + | 0.305356i | \(0.901225\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.7005 | −0.836284 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.1016 | −0.686217 | −0.343109 | − | 0.939296i | \(-0.611480\pi\) | ||||
−0.343109 | + | 0.939296i | \(0.611480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.3634i | 1.60320i | 0.597863 | + | 0.801598i | \(0.296017\pi\) | ||||
−0.597863 | + | 0.801598i | \(0.703983\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.67513 | − | 1.48119i | −0.0943829 | − | 0.0834558i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.5125i | 0.983598i | 0.870709 | + | 0.491799i | \(0.163661\pi\) | ||||
−0.870709 | + | 0.491799i | \(0.836339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.474855 | 0.0265868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.4387 | 0.917516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.92478i | 0.552229i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.7005 | + | 1.81336i | −0.815438 | + | 0.100587i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.77575i | − | 0.153499i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.22425 | −0.177759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2243 | 1.05666 | 0.528330 | − | 0.849039i | \(-0.322818\pi\) | ||||
0.528330 | + | 0.849039i | \(0.322818\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.92478i | 0.324676i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 16.0000i | − | 0.871576i | −0.900049 | − | 0.435788i | \(-0.856470\pi\) | ||
0.900049 | − | 0.435788i | \(-0.143530\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.26187 | 0.231473 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.14903 | 0.0622235 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.42548 | − | 1.61213i | 0.0767455 | − | 0.0867940i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 1.11283i | − | 0.0597401i | −0.999554 | − | 0.0298700i | \(-0.990491\pi\) | ||
0.999554 | − | 0.0298700i | \(-0.00950934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 32.0263 | 1.71433 | 0.857166 | − | 0.515041i | \(-0.172223\pi\) | ||||
0.857166 | + | 0.515041i | \(0.172223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.96239 | 0.158121 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.20123i | 0.330058i | 0.986289 | + | 0.165029i | \(0.0527718\pi\) | ||||
−0.986289 | + | 0.165029i | \(0.947228\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.20123 | + | 9.27504i | −0.435276 | + | 0.492268i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.35026i | − | 0.177315i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.68735 | −0.0890549 | −0.0445275 | − | 0.999008i | \(-0.514178\pi\) | ||||
−0.0445275 | + | 0.999008i | \(0.514178\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.2243 | −0.538119 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.8496i | 0.569454i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.3634 | + | 9.16362i | 0.542447 | + | 0.479646i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.84955i | 0.200945i | 0.994940 | + | 0.100473i | \(0.0320355\pi\) | ||||
−0.994940 | + | 0.100473i | \(0.967965\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.03761 | −0.0540159 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.66291 | 0.294004 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 24.8773i | − | 1.28810i | −0.764984 | − | 0.644049i | \(-0.777253\pi\) | ||
0.764984 | − | 0.644049i | \(-0.222747\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.32487 | + | 9.21933i | −0.326615 | + | 0.476084i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.62672i | 0.186785i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.70052 | 0.138717 | 0.0693583 | − | 0.997592i | \(-0.477905\pi\) | ||||
0.0693583 | + | 0.997592i | \(0.477905\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.5501 | −0.745423 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.523730i | 0.0267614i | 0.999910 | + | 0.0133807i | \(0.00425933\pi\) | ||||
−0.999910 | + | 0.0133807i | \(0.995741\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.649738 | − | 0.574515i | −0.0331137 | − | 0.0292800i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.7005i | 0.543938i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.77575 | −0.343544 | −0.171772 | − | 0.985137i | \(-0.554949\pi\) | ||||
−0.171772 | + | 0.985137i | \(0.554949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22425 | 0.163058 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.00000i | − | 0.201773i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.6253 | + | 23.3258i | −1.03777 | + | 1.17365i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.635150i | − | 0.0318773i | −0.999873 | − | 0.0159386i | \(-0.994926\pi\) | ||
0.999873 | − | 0.0159386i | \(-0.00507364\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.96239 | −0.148305 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.3733 | 0.518017 | 0.259009 | − | 0.965875i | \(-0.416604\pi\) | ||||
0.259009 | + | 0.965875i | \(0.416604\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.77575i | 0.437151i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.48119 | − | 1.67513i | 0.0736011 | − | 0.0832379i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.29806i | 0.113911i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.7743 | −0.779991 | −0.389995 | − | 0.920817i | \(-0.627523\pi\) | ||||
−0.389995 | + | 0.920817i | \(0.627523\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4387 | −0.514901 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.22425i | 0.158655i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.40105 | − | 4.77575i | −0.265127 | − | 0.234432i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 5.66291i | − | 0.277314i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.1490 | 1.22861 | 0.614305 | − | 0.789068i | \(-0.289436\pi\) | ||||
0.614305 | + | 0.789068i | \(0.289436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.1768 | 0.983357 | 0.491678 | − | 0.870777i | \(-0.336384\pi\) | ||||
0.491678 | + | 0.870777i | \(0.336384\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 3.22425i | − | 0.156769i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.6253 | + | 2.05079i | −0.806446 | + | 0.0994777i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.6253i | 0.707768i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.14903 | 0.0554757 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.3127 | 1.84546 | 0.922728 | − | 0.385452i | \(-0.125955\pi\) | ||||
0.922728 | + | 0.385452i | \(0.125955\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.8872i | − | 0.619318i | −0.950848 | − | 0.309659i | \(-0.899785\pi\) | ||
0.950848 | − | 0.309659i | \(-0.100215\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.05079 | + | 1.81336i | 0.0983276 | + | 0.0869438i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.85097i | − | 0.136380i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.6629 | −1.41573 | −0.707867 | − | 0.706346i | \(-0.750342\pi\) | ||||
−0.707867 | + | 0.706346i | \(0.750342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.8119i | 1.17885i | 0.807823 | + | 0.589425i | \(0.200646\pi\) | ||||
−0.807823 | + | 0.589425i | \(0.799354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.53690 | + | 6.26187i | −0.262474 | + | 0.296841i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 20.5501i | 0.971985i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.6516 | 1.72970 | 0.864849 | − | 0.502032i | \(-0.167414\pi\) | ||||
0.864849 | + | 0.502032i | \(0.167414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.402462 | −0.0189512 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 22.7005i | − | 1.06656i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.38787 | − | 4.96239i | 0.205707 | − | 0.232640i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 15.4763i | − | 0.723949i | −0.932188 | − | 0.361975i | \(-0.882103\pi\) | ||
0.932188 | − | 0.361975i | \(-0.117897\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.35026 | 0.156377 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.2605 | 1.92169 | 0.960845 | − | 0.277085i | \(-0.0893684\pi\) | ||||
0.960845 | + | 0.277085i | \(0.0893684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.5975i | − | 0.724879i | −0.932007 | − | 0.362440i | \(-0.881944\pi\) | ||
0.932007 | − | 0.362440i | \(-0.118056\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.96239 | + | 4.38787i | 0.230125 | + | 0.203483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 18.5501i | − | 0.858395i | −0.903211 | − | 0.429198i | \(-0.858796\pi\) | ||
0.903211 | − | 0.429198i | \(-0.141204\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.18664 | 0.100755 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.15045i | 0.190838i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.81336 | + | 14.7005i | 0.0832026 | + | 0.674506i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.66291i | 0.259287i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −41.5026 | −1.89630 | −0.948151 | − | 0.317819i | \(-0.897050\pi\) | ||||
−0.948151 | + | 0.317819i | \(0.897050\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5515 | −0.800279 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.962389i | 0.0437902i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.9624 | + | 11.4617i | 0.588592 | + | 0.520448i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 13.6728i | − | 0.619572i | −0.950806 | − | 0.309786i | \(-0.899743\pi\) | ||
0.950806 | − | 0.309786i | \(-0.100257\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.22425 | −0.326692 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.3404 | −1.05334 | −0.526669 | − | 0.850070i | \(-0.676559\pi\) | ||||
−0.526669 | + | 0.850070i | \(0.676559\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.10157i | 0.184725i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.574515 | − | 0.649738i | 0.0258226 | − | 0.0292036i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.53690i | − | 0.248364i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.85097 | −0.306691 | −0.153346 | − | 0.988173i | \(-0.549005\pi\) | ||||
−0.153346 | + | 0.988173i | \(0.549005\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.8496 | −0.708106 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 3.32582i | − | 0.148291i | −0.997247 | − | 0.0741456i | \(-0.976377\pi\) | ||
0.997247 | − | 0.0741456i | \(-0.0236230\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.2388 | + | 12.7104i | −0.500122 | + | 0.565604i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4.22425i | − | 0.187606i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.18664 | 0.274218 | 0.137109 | − | 0.990556i | \(-0.456219\pi\) | ||||
0.137109 | + | 0.990556i | \(0.456219\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.18664 | −0.273681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.96239i | − | 0.130793i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.6253 | − | 21.7743i | −1.08512 | − | 0.959492i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.25060i | − | 0.0550014i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.9756 | 1.05241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4387 | 1.50879 | 0.754393 | − | 0.656424i | \(-0.227932\pi\) | ||||
0.754393 | + | 0.656424i | \(0.227932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 6.59895i | − | 0.288552i | −0.989537 | − | 0.144276i | \(-0.953915\pi\) | ||
0.989537 | − | 0.144276i | \(-0.0460853\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.612127 | − | 4.96239i | −0.0267154 | − | 0.216576i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.92478i | 0.432330i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.0738 | 0.959731 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.22425 | −0.139921 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.07381i | − | 0.133141i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.5369 | + | 24.3488i | 1.19052 | + | 1.05269i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 12.2374i | − | 0.528084i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.387873 | 0.0167069 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.07381 | −0.390113 | −0.195057 | − | 0.980792i | \(-0.562489\pi\) | ||||
−0.195057 | + | 0.980792i | \(0.562489\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 8.70052i | − | 0.373375i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.11142 | − | 4.64974i | 0.176114 | − | 0.199173i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 19.8496i | − | 0.848706i | −0.905497 | − | 0.424353i | \(-0.860502\pi\) | ||
0.905497 | − | 0.424353i | \(-0.139498\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.6253 | −0.624193 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.62672 | 0.154503 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 13.9248i | − | 0.592142i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.77575 | + | 9.92478i | −0.372510 | + | 0.421283i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.785595i | − | 0.0332867i | −0.999861 | − | 0.0166434i | \(-0.994702\pi\) | ||
0.999861 | − | 0.0166434i | \(-0.00529799\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.6991 | −1.34073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.29948 | 0.0548639 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.2228i | 1.35803i | 0.734124 | + | 0.679015i | \(0.237593\pi\) | ||||
−0.734124 | + | 0.679015i | \(0.762407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.13918 | + | 6.31265i | 0.300348 | + | 0.265575i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.0752 | −0.673908 | −0.336954 | − | 0.941521i | \(-0.609397\pi\) | ||||
−0.336954 | + | 0.941521i | \(0.609397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.8496 | 1.66765 | 0.833826 | − | 0.552027i | \(-0.186146\pi\) | ||||
0.833826 | + | 0.552027i | \(0.186146\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 13.5369i | − | 0.565512i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.77575 | − | 0.589104i | 0.199162 | − | 0.0245673i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.1378i | 1.25465i | 0.778757 | + | 0.627326i | \(0.215851\pi\) | ||||
−0.778757 | + | 0.627326i | \(0.784149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.92478 | −0.0799910 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.22425 | 0.133765 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.19649i | 0.0909694i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.96239 | + | 4.38787i | 0.205170 | + | 0.181416i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 33.7743i | − | 1.39402i | −0.717063 | − | 0.697008i | \(-0.754514\pi\) | ||
0.717063 | − | 0.697008i | \(-0.245486\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.77575 | 0.361598 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.1114 | −0.827273 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.19982i | 0.295661i | 0.989013 | + | 0.147831i | \(0.0472290\pi\) | ||||
−0.989013 | + | 0.147831i | \(0.952771\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.96239 | − | 5.61213i | 0.203438 | − | 0.230075i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.26187i | 0.338136i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.5369 | −1.20685 | −0.603423 | − | 0.797422i | \(-0.706197\pi\) | ||||
−0.603423 | + | 0.797422i | \(0.706197\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.59895 | 0.350759 | 0.175379 | − | 0.984501i | \(-0.443885\pi\) | ||||
0.175379 | + | 0.984501i | \(0.443885\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −16.0703 | + | 18.1744i | −0.653351 | + | 0.738895i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.4010i | 1.51806i | 0.651055 | + | 0.759031i | \(0.274327\pi\) | ||||
−0.651055 | + | 0.759031i | \(0.725673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.22425 | −0.0496093 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.55149 | 0.386412 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 14.5990i | − | 0.589646i | −0.955552 | − | 0.294823i | \(-0.904739\pi\) | ||
0.955552 | − | 0.294823i | \(-0.0952607\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.73813 | − | 1.53690i | −0.0700884 | − | 0.0619740i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.8119i | − | 0.918374i | −0.888340 | − | 0.459187i | \(-0.848141\pi\) | ||
0.888340 | − | 0.459187i | \(-0.151859\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.261865 | 0.0105252 | 0.00526262 | − | 0.999986i | \(-0.498325\pi\) | ||||
0.00526262 | + | 0.999986i | \(0.498325\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.962389 | −0.0386193 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.73813i | − | 0.149765i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.2506 | + | 6.07522i | −0.970024 | + | 0.243009i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.14903i | − | 0.0458879i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.8496 | −0.791454 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.92478 | 0.235862 | 0.117931 | − | 0.993022i | \(-0.462374\pi\) | ||||
0.117931 | + | 0.993022i | \(0.462374\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 18.1768i | − | 0.722463i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −24.3733 | − | 21.5515i | −0.967224 | − | 0.855245i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.96239i | 0.117374i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.53690 | 0.219037 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.87732 | 0.271638 | 0.135819 | − | 0.990734i | \(-0.456633\pi\) | ||||
0.135819 | + | 0.990734i | \(0.456633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7005i | 0.421987i | 0.977487 | + | 0.210994i | \(0.0676700\pi\) | ||||
−0.977487 | + | 0.210994i | \(0.932330\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.8496 | + | 17.9248i | −0.624076 | + | 0.705787i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 45.2506i | − | 1.77898i | −0.456950 | − | 0.889492i | \(-0.651058\pi\) | ||
0.456950 | − | 0.889492i | \(-0.348942\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.25060 | −0.0490904 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.96239 | −0.116105 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.0625i | 1.41124i | 0.708592 | + | 0.705618i | \(0.249331\pi\) | ||||
−0.708592 | + | 0.705618i | \(0.750669\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.92478 | − | 6.70052i | 0.231500 | − | 0.261811i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.18664i | − | 0.241364i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 43.4617 | 1.69303 | 0.846513 | − | 0.532367i | \(-0.178698\pi\) | ||||
0.846513 | + | 0.532367i | \(0.178698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.4749 | −0.874171 | −0.437085 | − | 0.899420i | \(-0.643989\pi\) | ||||
−0.437085 | + | 0.899420i | \(0.643989\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.92478i | 0.385446i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.96239 | − | 4.38787i | −0.192433 | − | 0.170154i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.17821i | − | 0.0456204i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.4010 | −0.827412 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.67276 | −0.218995 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.5487i | 1.83287i | 0.400188 | + | 0.916433i | \(0.368945\pi\) | ||||
−0.400188 | + | 0.916433i | \(0.631055\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.96239 | − | 0.612127i | 0.191002 | − | 0.0235608i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.67750i | − | 0.218204i | −0.994031 | − | 0.109102i | \(-0.965202\pi\) | ||
0.994031 | − | 0.109102i | \(-0.0347975\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.73813 | −0.296962 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.5501 | 0.710841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 12.2882i | − | 0.470195i | −0.971972 | − | 0.235098i | \(-0.924459\pi\) | ||
0.971972 | − | 0.235098i | \(-0.0755410\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.4861 | − | 15.4617i | −0.668110 | − | 0.590760i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 28.5501i | − | 1.08925i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.7757 | −0.639105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.81336 | 0.0689834 | 0.0344917 | − | 0.999405i | \(-0.489019\pi\) | ||||
0.0344917 | + | 0.999405i | \(0.489019\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.387873i | 0.0147341i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.38787 | − | 9.48612i | 0.318170 | − | 0.359829i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.47627i | − | 0.131673i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.9624 | 0.717223 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.5778 | 1.11714 | 0.558570 | − | 0.829458i | \(-0.311350\pi\) | ||||
0.558570 | + | 0.829458i | \(0.311350\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.5515i | 0.661967i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.77575 | − | 5.40105i | 0.179865 | − | 0.203415i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 7.58769i | − | 0.285364i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.8021 | −0.781239 | −0.390620 | − | 0.920552i | \(-0.627739\pi\) | ||||
−0.390620 | + | 0.920552i | \(0.627739\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.9248 | 0.522220 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.85097i | − | 0.106770i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.92478 | + | 1.70194i | 0.0719826 | + | 0.0636489i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.1622i | 0.678280i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 19.3258 | 0.720732 | 0.360366 | − | 0.932811i | \(-0.382652\pi\) | ||||
0.360366 | + | 0.932811i | \(0.382652\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.7005 | 0.547476 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 14.3733i | − | 0.534548i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.749399 | + | 6.07522i | 0.0278320 | + | 0.225628i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.6531i | − | 0.803068i | −0.915844 | − | 0.401534i | \(-0.868477\pi\) | ||
0.915844 | − | 0.401534i | \(-0.131523\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.8496 | −1.32594 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 48.0625i | − | 1.77523i | −0.460586 | − | 0.887615i | \(-0.652361\pi\) | ||
0.460586 | − | 0.887615i | \(-0.347639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.67513 | + | 1.48119i | 0.0617881 | + | 0.0546347i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.2981 | −1.11453 | −0.557266 | − | 0.830334i | \(-0.688150\pi\) | ||||
−0.557266 | + | 0.830334i | \(0.688150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.77575 | 0.322385 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.9624i | 1.50276i | 0.659867 | + | 0.751382i | \(0.270612\pi\) | ||||
−0.659867 | + | 0.751382i | \(0.729388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.4387 | + | 34.4241i | −1.11519 | + | 1.26120i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.22425i | 0.117969i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.4387 | −0.600656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.52232 | −0.347474 | −0.173737 | − | 0.984792i | \(-0.555584\pi\) | ||||
−0.173737 | + | 0.984792i | \(0.555584\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 8.62530i | − | 0.314323i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 33.6239 | − | 38.0263i | 1.22370 | − | 1.38392i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 31.3258i | − | 1.13856i | −0.822145 | − | 0.569278i | \(-0.807223\pi\) | ||
0.822145 | − | 0.569278i | \(-0.192777\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.373285 | −0.0135494 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −54.2393 | −1.96617 | −0.983087 | − | 0.183138i | \(-0.941375\pi\) | ||||
−0.983087 | + | 0.183138i | \(0.941375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.77575i | 0.100489i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.61213 | + | 4.96239i | 0.202907 | + | 0.179416i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 9.55149i | − | 0.344884i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.1002 | −1.26574 | −0.632872 | − | 0.774256i | \(-0.718124\pi\) | ||||
−0.632872 | + | 0.774256i | \(0.718124\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 27.8251 | 1.00210 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.8740i | 0.714818i | 0.933948 | + | 0.357409i | \(0.116340\pi\) | ||||
−0.933948 | + | 0.357409i | \(0.883660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.81336 | + | 14.7005i | 0.0651377 | + | 0.528058i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 5.92478i | − | 0.212550i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.07381 | −0.110131 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.14762 | 0.0768478 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.22425i | − | 0.0437513i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.66291 | + | 3.23884i | 0.130735 | + | 0.115599i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.2506i | 0.472333i | 0.971713 | + | 0.236166i | \(0.0758911\pi\) | ||||
−0.971713 | + | 0.236166i | \(0.924109\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.589104 | 0.0209727 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.26187 | −0.151534 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 43.3258i | − | 1.53855i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.38787 | + | 9.48612i | −0.297487 | + | 0.336438i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.7235i | 0.556957i | 0.960443 | + | 0.278478i | \(0.0898300\pi\) | ||||
−0.960443 | + | 0.278478i | \(0.910170\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.8021 | 0.382151 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.73813 | 0.132081 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.39963i | − | 0.0846812i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.42548 | + | 1.61213i | −0.0502417 | + | 0.0568200i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.7381i | 0.554009i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.5040 | 0.650567 | 0.325284 | − | 0.945617i | \(-0.394540\pi\) | ||||
0.325284 | + | 0.945617i | \(0.394540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.6629 | −1.32252 | −0.661262 | − | 0.750155i | \(-0.729979\pi\) | ||||
−0.661262 | + | 0.750155i | \(0.729979\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 7.11283i | − | 0.249458i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1016 | − | 10.7005i | −0.423900 | − | 0.374823i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.6991i | 1.10901i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.96239 | −0.103514 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.9511 | −0.626499 | −0.313249 | − | 0.949671i | \(-0.601418\pi\) | ||||
−0.313249 | + | 0.949671i | \(0.601418\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.1016i | 1.11899i | 0.828834 | + | 0.559495i | \(0.189005\pi\) | ||||
−0.828834 | + | 0.559495i | \(0.810995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.92478 | − | 0.237428i | 0.0670121 | − | 0.00826617i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.8594i | − | 0.899220i | −0.893225 | − | 0.449610i | \(-0.851563\pi\) | ||
0.893225 | − | 0.449610i | \(-0.148437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.8035 | −0.409953 | −0.204976 | − | 0.978767i | \(-0.565712\pi\) | ||||
−0.204976 | + | 0.978767i | \(0.565712\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.92478 | −0.205528 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.35026i | 0.116080i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.5501 | − | 23.4763i | −0.918803 | − | 0.812430i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 2.96239i | − | 0.102395i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.5778 | 0.675902 | 0.337951 | − | 0.941164i | \(-0.390266\pi\) | ||||
0.337951 | + | 0.941164i | \(0.390266\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.5012 | −0.948317 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 29.3258i | − | 1.01004i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.25694 | − | 7.07618i | 0.215245 | − | 0.243428i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.8496i | − | 0.372795i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.1016 | 0.552604 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.70194 | 0.195460 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 40.6155i | − | 1.39065i | −0.718697 | − | 0.695323i | \(-0.755261\pi\) | ||
0.718697 | − | 0.695323i | \(-0.244739\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.38787 | − | 4.96239i | 0.150062 | − | 0.169710i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 29.1246i | − | 0.994877i | −0.867499 | − | 0.497439i | \(-0.834274\pi\) | ||
0.867499 | − | 0.497439i | \(-0.165726\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35.7090 | 1.21837 | 0.609187 | − | 0.793027i | \(-0.291496\pi\) | ||||
0.609187 | + | 0.793027i | \(0.291496\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.03761 | 0.0353617 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 21.1852i | − | 0.721154i | −0.932730 | − | 0.360577i | \(-0.882580\pi\) | ||
0.932730 | − | 0.360577i | \(-0.117420\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.1622 | + | 35.5125i | 1.36556 | + | 1.20746i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 5.77575i | − | 0.196155i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.40105 | 0.183218 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 7.73813i | − | 0.261896i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.32487 | − | 9.21933i | 0.213820 | − | 0.311670i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.4485i | 0.893103i | 0.894758 | + | 0.446551i | \(0.147348\pi\) | ||||
−0.894758 | + | 0.446551i | \(0.852652\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.27504 | 0.312839 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.0362 | −0.877182 | −0.438591 | − | 0.898687i | \(-0.644522\pi\) | ||||
−0.438591 | + | 0.898687i | \(0.644522\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 8.87732i | − | 0.298745i | −0.988781 | − | 0.149373i | \(-0.952275\pi\) | ||
0.988781 | − | 0.149373i | \(-0.0477254\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.40105 | − | 4.77575i | −0.181554 | − | 0.160535i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.17679i | 0.0730896i | 0.999332 | + | 0.0365448i | \(0.0116352\pi\) | ||||
−0.999332 | + | 0.0365448i | \(0.988365\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.5501 | 0.487994 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.387873 | −0.0129942 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 9.55149i | − | 0.319629i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.1260 | − | 20.4993i | 0.605886 | − | 0.685216i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 2.85097i | − | 0.0951911i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.62672 | 0.120958 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.9722 | −0.632057 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 10.7005i | − | 0.356091i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.8872 | − | 14.5745i | 0.428384 | − | 0.484473i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 44.7269i | − | 1.48513i | −0.669773 | − | 0.742566i | \(-0.733609\pi\) | ||
0.669773 | − | 0.742566i | \(-0.266391\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.58769 | 0.251668 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.4631 | −0.876761 | −0.438381 | − | 0.898789i | \(-0.644448\pi\) | ||||
−0.438381 | + | 0.898789i | \(0.644448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.25060i | 0.0413889i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.4993 | − | 21.6629i | −0.809922 | − | 0.716154i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.00000i | 0.132092i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −59.2769 | −1.95537 | −0.977683 | − | 0.210085i | \(-0.932626\pi\) | ||||
−0.977683 | + | 0.210085i | \(0.932626\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.7005 | 0.352594 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.4025i | 0.539894i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.4010 | + | 3.62672i | −0.966700 | + | 0.119246i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.7005i | 0.482829i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.3620 | −0.832101 | −0.416050 | − | 0.909342i | \(-0.636586\pi\) | ||||
−0.416050 | + | 0.909342i | \(0.636586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.96239 | 0.0970884 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.1016i | 0.396188i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.17679 | + | 1.92478i | 0.0711888 | + | 0.0629469i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.85940i | 0.126081i | 0.998011 | + | 0.0630406i | \(0.0200798\pi\) | ||||
−0.998011 | + | 0.0630406i | \(0.979920\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.3634 | 0.925606 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.4861 | 0.896022 | 0.448011 | − | 0.894028i | \(-0.352133\pi\) | ||||
0.448011 | + | 0.894028i | \(0.352133\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.998585i | 0.0325184i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.48119 | + | 1.67513i | −0.0481833 | + | 0.0544920i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 13.8397i | − | 0.449730i | −0.974390 | − | 0.224865i | \(-0.927806\pi\) | ||
0.974390 | − | 0.224865i | \(-0.0721941\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.3272 | 0.594927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.5125 | 0.567881 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 39.2868i | − | 1.27262i | −0.771432 | − | 0.636312i | \(-0.780459\pi\) | ||
0.771432 | − | 0.636312i | \(-0.219541\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.0508 | − | 22.6761i | 0.648828 | − | 0.733781i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.474855i | − | 0.0153499i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.4387 | 0.337082 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2243 | −0.716911 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 16.4387i | − | 0.529728i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.22425 | − | 2.85097i | −0.103792 | − | 0.0917759i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 8.67418i | − | 0.278943i | −0.990226 | − | 0.139471i | \(-0.955460\pi\) | ||
0.990226 | − | 0.139471i | \(-0.0445403\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.92478 | 0.318830 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.9248 | 0.831966 | 0.415983 | − | 0.909372i | \(-0.363438\pi\) | ||||
0.415983 | + | 0.909372i | \(0.363438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.66291i | 0.181545i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.81336 | + | 14.7005i | 0.0580739 | + | 0.470794i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 7.85940i | − | 0.251445i | −0.992065 | − | 0.125722i | \(-0.959875\pi\) | ||
0.992065 | − | 0.125722i | \(-0.0401248\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.44992 | 0.0463397 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.77575 | −0.0886228 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.8510i | 0.601253i | 0.953742 | + | 0.300626i | \(0.0971957\pi\) | ||||
−0.953742 | + | 0.300626i | \(0.902804\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.6893 | − | 29.7889i | −1.07343 | − | 0.949154i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.22425i | 0.102629i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.2981 | 0.327459 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.0738 | 1.36828 | 0.684142 | − | 0.729349i | \(-0.260177\pi\) | ||||
0.684142 | + | 0.729349i | \(0.260177\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 19.2243i | − | 0.610063i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.2374 | + | 13.8397i | −0.387953 | + | 0.438748i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.6155i | 0.779579i | 0.920904 | + | 0.389790i | \(0.127452\pi\) | ||||
−0.920904 | + | 0.389790i | \(0.872548\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.92478 | 0.187452 |
(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 | 1680.2.t.i.1009.3 | 6 | ||
3.2 | odd | 2 | 5040.2.t.ba.1009.2 | 6 | |||
4.3 | odd | 2 | 840.2.t.e.169.6 | yes | 6 | ||
5.2 | odd | 4 | 8400.2.a.dh.1.2 | 3 | |||
5.3 | odd | 4 | 8400.2.a.dk.1.2 | 3 | |||
5.4 | even | 2 | inner | 1680.2.t.i.1009.6 | 6 | ||
12.11 | even | 2 | 2520.2.t.j.1009.2 | 6 | |||
15.14 | odd | 2 | 5040.2.t.ba.1009.1 | 6 | |||
20.3 | even | 4 | 4200.2.a.bo.1.2 | 3 | |||
20.7 | even | 4 | 4200.2.a.bq.1.2 | 3 | |||
20.19 | odd | 2 | 840.2.t.e.169.3 | ✓ | 6 | ||
60.59 | even | 2 | 2520.2.t.j.1009.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
840.2.t.e.169.3 | ✓ | 6 | 20.19 | odd | 2 | ||
840.2.t.e.169.6 | yes | 6 | 4.3 | odd | 2 | ||
1680.2.t.i.1009.3 | 6 | 1.1 | even | 1 | trivial | ||
1680.2.t.i.1009.6 | 6 | 5.4 | even | 2 | inner | ||
2520.2.t.j.1009.1 | 6 | 60.59 | even | 2 | |||
2520.2.t.j.1009.2 | 6 | 12.11 | even | 2 | |||
4200.2.a.bo.1.2 | 3 | 20.3 | even | 4 | |||
4200.2.a.bq.1.2 | 3 | 20.7 | even | 4 | |||
5040.2.t.ba.1009.1 | 6 | 15.14 | odd | 2 | |||
5040.2.t.ba.1009.2 | 6 | 3.2 | odd | 2 | |||
8400.2.a.dh.1.2 | 3 | 5.2 | odd | 4 | |||
8400.2.a.dk.1.2 | 3 | 5.3 | odd | 4 |