Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2700,2,Mod(593,2700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2700, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2700.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2700 = 2^{2} \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2700.j (of order \(4\), degree \(2\), 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: | \(21.5596085457\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.1 | ||
Root | \(-1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2700.1457 |
Dual form | 2700.2.j.a.593.1 |
$q$-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 \(\left(\mathbb{Z}/2700\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1351\) | \(2377\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | − | 2.44949i | −0.925820 | − | 0.925820i | 0.0716124 | − | 0.997433i | \(-0.477186\pi\) |
−0.997433 | + | 0.0716124i | \(0.977186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.00000i | − | 1.80907i | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||
0.426401 | − | 0.904534i | \(-0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | + | 2.44949i | −0.679366 | + | 0.679366i | −0.959857 | − | 0.280491i | \(-0.909503\pi\) |
0.280491 | + | 0.959857i | \(0.409503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.67423 | + | 3.67423i | −0.891133 | + | 0.891133i | −0.994630 | − | 0.103497i | \(-0.966997\pi\) |
0.103497 | + | 0.994630i | \(0.466997\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.00000i | − | 0.229416i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) | ||
0.993399 | − | 0.114708i | \(-0.0365932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.67423 | + | 3.67423i | 0.766131 | + | 0.766131i | 0.977423 | − | 0.211292i | \(-0.0677671\pi\) |
−0.211292 | + | 0.977423i | \(0.567767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.00000 | −0.898027 | −0.449013 | − | 0.893525i | \(-0.648224\pi\) | ||||
−0.449013 | + | 0.893525i | \(0.648224\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.89898 | + | 4.89898i | 0.805387 | + | 0.805387i | 0.983932 | − | 0.178545i | \(-0.0571389\pi\) |
−0.178545 | + | 0.983932i | \(0.557139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.34847 | − | 7.34847i | 1.12063 | − | 1.12063i | 0.128984 | − | 0.991647i | \(-0.458828\pi\) |
0.991647 | − | 0.128984i | \(-0.0411717\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.34847 | + | 7.34847i | −1.07188 | + | 1.07188i | −0.0746766 | + | 0.997208i | \(0.523792\pi\) |
−0.997208 | + | 0.0746766i | \(0.976208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.67423 | + | 3.67423i | 0.504695 | + | 0.504695i | 0.912893 | − | 0.408198i | \(-0.133843\pi\) |
−0.408198 | + | 0.912893i | \(0.633843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.00000 | 0.640184 | 0.320092 | − | 0.947386i | \(-0.396286\pi\) | ||||
0.320092 | + | 0.947386i | \(0.396286\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.89898 | + | 4.89898i | 0.598506 | + | 0.598506i | 0.939915 | − | 0.341409i | \(-0.110904\pi\) |
−0.341409 | + | 0.939915i | \(0.610904\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000i | 0.712069i | 0.934473 | + | 0.356034i | \(0.115871\pi\) | ||||
−0.934473 | + | 0.356034i | \(0.884129\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.44949 | + | 2.44949i | −0.286691 | + | 0.286691i | −0.835770 | − | 0.549079i | \(-0.814979\pi\) |
0.549079 | + | 0.835770i | \(0.314979\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.6969 | + | 14.6969i | −1.67487 | + | 1.67487i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.00000i | − | 0.562544i | −0.959628 | − | 0.281272i | \(-0.909244\pi\) | ||
0.959628 | − | 0.281272i | \(-0.0907563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.0227 | + | 11.0227i | 1.20990 | + | 1.20990i | 0.971059 | + | 0.238840i | \(0.0767671\pi\) |
0.238840 | + | 0.971059i | \(0.423233\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.0000 | 1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.89898 | − | 4.89898i | −0.497416 | − | 0.497416i | 0.413217 | − | 0.910633i | \(-0.364405\pi\) |
−0.910633 | + | 0.413217i | \(0.864405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0000i | 1.19404i | 0.802225 | + | 0.597022i | \(0.203650\pi\) | ||||
−0.802225 | + | 0.597022i | \(0.796350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.89898 | + | 4.89898i | −0.482711 | + | 0.482711i | −0.905996 | − | 0.423286i | \(-0.860877\pi\) |
0.423286 | + | 0.905996i | \(0.360877\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.34847 | + | 7.34847i | −0.710403 | + | 0.710403i | −0.966620 | − | 0.256216i | \(-0.917524\pi\) |
0.256216 | + | 0.966620i | \(0.417524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.0000i | − | 1.05361i | −0.849987 | − | 0.526804i | \(-0.823390\pi\) | ||
0.849987 | − | 0.526804i | \(-0.176610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.0000 | 1.65006 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −25.0000 | −2.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.6969 | − | 14.6969i | −1.30414 | − | 1.30414i | −0.925573 | − | 0.378570i | \(-0.876416\pi\) |
−0.378570 | − | 0.925573i | \(-0.623584\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12.0000i | − | 1.04844i | −0.851581 | − | 0.524222i | \(-0.824356\pi\) | ||
0.851581 | − | 0.524222i | \(-0.175644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.44949 | + | 2.44949i | −0.212398 | + | 0.212398i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.0227 | + | 11.0227i | −0.941733 | + | 0.941733i | −0.998394 | − | 0.0566604i | \(-0.981955\pi\) |
0.0566604 | + | 0.998394i | \(0.481955\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0000i | 1.69638i | 0.529694 | + | 0.848189i | \(0.322307\pi\) | ||||
−0.529694 | + | 0.848189i | \(0.677693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.6969 | + | 14.6969i | 1.22902 | + | 1.22902i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | 0.325515 | 0.162758 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162758 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.34847 | − | 7.34847i | −0.586472 | − | 0.586472i | 0.350202 | − | 0.936674i | \(-0.386113\pi\) |
−0.936674 | + | 0.350202i | \(0.886113\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 18.0000i | − | 1.41860i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.89898 | + | 4.89898i | −0.383718 | + | 0.383718i | −0.872440 | − | 0.488722i | \(-0.837463\pi\) |
0.488722 | + | 0.872440i | \(0.337463\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.67423 | + | 3.67423i | −0.284321 | + | 0.284321i | −0.834829 | − | 0.550509i | \(-0.814434\pi\) |
0.550509 | + | 0.834829i | \(0.314434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000i | 0.0769231i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.67423 | − | 3.67423i | −0.279347 | − | 0.279347i | 0.553501 | − | 0.832848i | \(-0.313291\pi\) |
−0.832848 | + | 0.553501i | \(0.813291\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.0000 | −1.79384 | −0.896922 | − | 0.442189i | \(-0.854202\pi\) | ||||
−0.896922 | + | 0.442189i | \(0.854202\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.0000 | 1.41226 | 0.706129 | − | 0.708083i | \(-0.250440\pi\) | ||||
0.706129 | + | 0.708083i | \(0.250440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.0454 | + | 22.0454i | 1.61212 | + | 1.61212i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000i | 0.868290i | 0.900843 | + | 0.434145i | \(0.142949\pi\) | ||||
−0.900843 | + | 0.434145i | \(0.857051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.1464 | − | 17.1464i | 1.23423 | − | 1.23423i | 0.271902 | − | 0.962325i | \(-0.412347\pi\) |
0.962325 | − | 0.271902i | \(-0.0876526\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.3712 | + | 18.3712i | −1.30889 | + | 1.30889i | −0.386676 | + | 0.922215i | \(0.626377\pi\) |
−0.922215 | + | 0.386676i | \(0.873623\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.00000i | − | 0.567105i | −0.958957 | − | 0.283552i | \(-0.908487\pi\) | ||
0.958957 | − | 0.283552i | \(-0.0915130\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.6969 | + | 14.6969i | 1.03152 | + | 1.03152i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.0000 | −1.72107 | −0.860535 | − | 0.509390i | \(-0.829871\pi\) | ||||
−0.860535 | + | 0.509390i | \(0.829871\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.2474 | + | 12.2474i | 0.831411 | + | 0.831411i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 18.0000i | − | 1.21081i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.6969 | + | 14.6969i | −0.984180 | + | 0.984180i | −0.999877 | − | 0.0156970i | \(-0.995003\pi\) |
0.0156970 | + | 0.999877i | \(0.495003\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.67423 | − | 3.67423i | 0.243868 | − | 0.243868i | −0.574581 | − | 0.818448i | \(-0.694835\pi\) |
0.818448 | + | 0.574581i | \(0.194835\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000i | 0.330409i | 0.986259 | + | 0.165205i | \(0.0528285\pi\) | ||||
−0.986259 | + | 0.165205i | \(0.947172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.6969 | − | 14.6969i | −0.962828 | − | 0.962828i | 0.0365050 | − | 0.999333i | \(-0.488378\pi\) |
−0.999333 | + | 0.0365050i | \(0.988378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.0000 | 1.48156 | 0.740780 | − | 0.671748i | \(-0.234456\pi\) | ||||
0.740780 | + | 0.671748i | \(0.234456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.44949 | + | 2.44949i | 0.155857 | + | 0.155857i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.0454 | − | 22.0454i | 1.38598 | − | 1.38598i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.67423 | − | 3.67423i | 0.229192 | − | 0.229192i | −0.583163 | − | 0.812355i | \(-0.698185\pi\) |
0.812355 | + | 0.583163i | \(0.198185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 24.0000i | − | 1.49129i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.34847 | + | 7.34847i | 0.453126 | + | 0.453126i | 0.896391 | − | 0.443265i | \(-0.146180\pi\) |
−0.443265 | + | 0.896391i | \(0.646180\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.0000 | 1.46331 | 0.731653 | − | 0.681677i | \(-0.238749\pi\) | ||||
0.731653 | + | 0.681677i | \(0.238749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.0000 | 1.03268 | 0.516338 | − | 0.856385i | \(-0.327295\pi\) | ||||
0.516338 | + | 0.856385i | \(0.327295\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.34847 | − | 7.34847i | −0.441527 | − | 0.441527i | 0.450998 | − | 0.892525i | \(-0.351068\pi\) |
−0.892525 | + | 0.450998i | \(0.851068\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0000i | − | 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.34847 | − | 7.34847i | 0.436821 | − | 0.436821i | −0.454120 | − | 0.890941i | \(-0.650046\pi\) |
0.890941 | + | 0.454120i | \(0.150046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.6969 | − | 14.6969i | 0.867533 | − | 0.867533i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 10.0000i | − | 0.588235i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.67423 | − | 3.67423i | −0.214651 | − | 0.214651i | 0.591589 | − | 0.806240i | \(-0.298501\pi\) |
−0.806240 | + | 0.591589i | \(0.798501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.0000 | −1.04097 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −36.0000 | −2.07501 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0000i | 1.70114i | 0.525859 | + | 0.850572i | \(0.323744\pi\) | ||||
−0.525859 | + | 0.850572i | \(0.676256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.5959 | + | 19.5959i | −1.10763 | + | 1.10763i | −0.114165 | + | 0.993462i | \(0.536419\pi\) |
−0.993462 | + | 0.114165i | \(0.963581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0227 | + | 11.0227i | −0.619097 | + | 0.619097i | −0.945300 | − | 0.326203i | \(-0.894231\pi\) |
0.326203 | + | 0.945300i | \(0.394231\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0000i | 2.01561i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.67423 | + | 3.67423i | 0.204440 | + | 0.204440i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.0000 | 1.98474 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.2474 | − | 12.2474i | −0.667161 | − | 0.667161i | 0.289897 | − | 0.957058i | \(-0.406379\pi\) |
−0.957058 | + | 0.289897i | \(0.906379\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.0000i | 1.62459i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.89898 | + | 4.89898i | −0.264520 | + | 0.264520i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.34847 | − | 7.34847i | 0.394486 | − | 0.394486i | −0.481797 | − | 0.876283i | \(-0.660016\pi\) |
0.876283 | + | 0.481797i | \(0.160016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.0000i | 1.23116i | 0.788074 | + | 0.615581i | \(0.211079\pi\) | ||||
−0.788074 | + | 0.615581i | \(0.788921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.6969 | − | 14.6969i | −0.782239 | − | 0.782239i | 0.197969 | − | 0.980208i | \(-0.436565\pi\) |
−0.980208 | + | 0.197969i | \(0.936565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.2474 | − | 12.2474i | −0.639312 | − | 0.639312i | 0.311074 | − | 0.950386i | \(-0.399311\pi\) |
−0.950386 | + | 0.311074i | \(0.899311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 18.0000i | − | 0.934513i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.4949 | + | 24.4949i | −1.26830 | + | 1.26830i | −0.321331 | + | 0.946967i | \(0.604130\pi\) |
−0.946967 | + | 0.321331i | \(0.895870\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.6969 | − | 14.6969i | 0.756931 | − | 0.756931i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 19.0000i | − | 0.975964i | −0.872854 | − | 0.487982i | \(-0.837733\pi\) | ||
0.872854 | − | 0.487982i | \(-0.162267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.67423 | − | 3.67423i | −0.187745 | − | 0.187745i | 0.606976 | − | 0.794720i | \(-0.292383\pi\) |
−0.794720 | + | 0.606976i | \(0.792383\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.0000 | 0.912636 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0000 | −1.36545 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.34847 | − | 7.34847i | −0.368809 | − | 0.368809i | 0.498234 | − | 0.867043i | \(-0.333982\pi\) |
−0.867043 | + | 0.498234i | \(0.833982\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.0000i | 1.79775i | 0.438201 | + | 0.898877i | \(0.355616\pi\) | ||||
−0.438201 | + | 0.898877i | \(0.644384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.2474 | − | 12.2474i | 0.610089 | − | 0.610089i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 29.3939 | − | 29.3939i | 1.45700 | − | 1.45700i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0000i | 0.543915i | 0.962309 | + | 0.271957i | \(0.0876710\pi\) | ||||
−0.962309 | + | 0.271957i | \(0.912329\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.6969 | − | 14.6969i | −0.723189 | − | 0.723189i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.0000 | −0.879358 | −0.439679 | − | 0.898155i | \(-0.644908\pi\) | ||||
−0.439679 | + | 0.898155i | \(0.644908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0000 | 0.633581 | 0.316791 | − | 0.948495i | \(-0.397395\pi\) | ||||
0.316791 | + | 0.948495i | \(0.397395\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.2474 | − | 12.2474i | −0.592696 | − | 0.592696i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000i | 0.289010i | 0.989504 | + | 0.144505i | \(0.0461589\pi\) | ||||
−0.989504 | + | 0.144505i | \(0.953841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.34847 | + | 7.34847i | −0.353145 | + | 0.353145i | −0.861278 | − | 0.508133i | \(-0.830336\pi\) |
0.508133 | + | 0.861278i | \(0.330336\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.67423 | − | 3.67423i | 0.175762 | − | 0.175762i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 35.0000i | − | 1.67046i | −0.549902 | − | 0.835229i | \(-0.685335\pi\) | ||
0.549902 | − | 0.835229i | \(-0.314665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.67423 | + | 3.67423i | 0.174568 | + | 0.174568i | 0.788983 | − | 0.614415i | \(-0.210608\pi\) |
−0.614415 | + | 0.788983i | \(0.710608\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.0000 | 1.69517 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.6969 | + | 14.6969i | 0.687494 | + | 0.687494i | 0.961677 | − | 0.274184i | \(-0.0884076\pi\) |
−0.274184 | + | 0.961677i | \(0.588408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12.0000i | − | 0.558896i | −0.960161 | − | 0.279448i | \(-0.909849\pi\) | ||
0.960161 | − | 0.279448i | \(-0.0901514\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.5959 | − | 19.5959i | 0.910700 | − | 0.910700i | −0.0856277 | − | 0.996327i | \(-0.527290\pi\) |
0.996327 | + | 0.0856277i | \(0.0272896\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.3712 | − | 18.3712i | 0.850117 | − | 0.850117i | −0.140031 | − | 0.990147i | \(-0.544720\pi\) |
0.990147 | + | 0.140031i | \(0.0447201\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 24.0000i | − | 1.10822i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −44.0908 | − | 44.0908i | −2.02730 | − | 2.02730i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.0000 | −1.37073 | −0.685367 | − | 0.728197i | \(-0.740358\pi\) | ||||
−0.685367 | + | 0.728197i | \(0.740358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | −1.09431 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.2474 | + | 12.2474i | 0.554985 | + | 0.554985i | 0.927875 | − | 0.372890i | \(-0.121633\pi\) |
−0.372890 | + | 0.927875i | \(0.621633\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12.0000i | − | 0.541552i | −0.962642 | − | 0.270776i | \(-0.912720\pi\) | ||
0.962642 | − | 0.270776i | \(-0.0872803\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.0454 | − | 22.0454i | 0.992875 | − | 0.992875i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.6969 | − | 14.6969i | 0.659248 | − | 0.659248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.0000i | 0.581960i | 0.956729 | + | 0.290980i | \(0.0939813\pi\) | ||||
−0.956729 | + | 0.290980i | \(0.906019\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.3712 | + | 18.3712i | 0.819130 | + | 0.819130i | 0.985982 | − | 0.166852i | \(-0.0533602\pi\) |
−0.166852 | + | 0.985982i | \(0.553360\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | 0.530849 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 44.0908 | + | 44.0908i | 1.93911 | + | 1.93911i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 18.0000i | − | 0.788594i | −0.918983 | − | 0.394297i | \(-0.870988\pi\) | ||
0.918983 | − | 0.394297i | \(-0.129012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.44949 | + | 2.44949i | −0.107109 | + | 0.107109i | −0.758630 | − | 0.651521i | \(-0.774131\pi\) |
0.651521 | + | 0.758630i | \(0.274131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.3712 | − | 18.3712i | 0.800261 | − | 0.800261i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.00000i | 0.173913i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −14.6969 | − | 14.6969i | −0.636595 | − | 0.636595i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 30.0000 | 1.29219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.2474 | − | 12.2474i | −0.523663 | − | 0.523663i | 0.395013 | − | 0.918676i | \(-0.370740\pi\) |
−0.918676 | + | 0.395013i | \(0.870740\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000i | 0.255609i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.2474 | + | 12.2474i | −0.520814 | + | 0.520814i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.0000i | 1.52264i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.34847 | + | 7.34847i | 0.309701 | + | 0.309701i | 0.844794 | − | 0.535092i | \(-0.179723\pi\) |
−0.535092 | + | 0.844794i | \(0.679723\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.00000 | −0.292941 | −0.146470 | − | 0.989215i | \(-0.546791\pi\) | ||||
−0.146470 | + | 0.989215i | \(0.546791\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.44949 | + | 2.44949i | 0.101974 | + | 0.101974i | 0.756253 | − | 0.654279i | \(-0.227028\pi\) |
−0.654279 | + | 0.756253i | \(0.727028\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 54.0000i | − | 2.24030i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.0454 | − | 22.0454i | 0.913027 | − | 0.913027i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.0681 | − | 33.0681i | 1.36487 | − | 1.36487i | 0.497273 | − | 0.867594i | \(-0.334335\pi\) |
0.867594 | − | 0.497273i | \(-0.165665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00000i | 0.206021i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.7196 | − | 25.7196i | −1.05618 | − | 1.05618i | −0.998325 | − | 0.0578541i | \(-0.981574\pi\) |
−0.0578541 | − | 0.998325i | \(-0.518426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.00000 | −0.245153 | −0.122577 | − | 0.992459i | \(-0.539116\pi\) | ||||
−0.122577 | + | 0.992459i | \(0.539116\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.2474 | + | 12.2474i | 0.497109 | + | 0.497109i | 0.910537 | − | 0.413428i | \(-0.135669\pi\) |
−0.413428 | + | 0.910537i | \(0.635669\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 36.0000i | − | 1.45640i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.5959 | + | 19.5959i | −0.791472 | + | 0.791472i | −0.981733 | − | 0.190262i | \(-0.939066\pi\) |
0.190262 | + | 0.981733i | \(0.439066\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.7196 | − | 25.7196i | 1.03543 | − | 1.03543i | 0.0360851 | − | 0.999349i | \(-0.488511\pi\) |
0.999349 | − | 0.0360851i | \(-0.0114887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.6969 | − | 14.6969i | −0.588820 | − | 0.588820i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −36.0000 | −1.43541 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.00000 | −0.0398094 | −0.0199047 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199047 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.2474 | − | 12.2474i | −0.485262 | − | 0.485262i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.0000i | 0.947943i | 0.880540 | + | 0.473972i | \(0.157180\pi\) | ||||
−0.880540 | + | 0.473972i | \(0.842820\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0454 | + | 22.0454i | −0.869386 | + | 0.869386i | −0.992404 | − | 0.123018i | \(-0.960743\pi\) |
0.123018 | + | 0.992404i | \(0.460743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.0227 | − | 11.0227i | 0.433347 | − | 0.433347i | −0.456418 | − | 0.889765i | \(-0.650868\pi\) |
0.889765 | + | 0.456418i | \(0.150868\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 36.0000i | − | 1.41312i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.67423 | + | 3.67423i | 0.143784 | + | 0.143784i | 0.775335 | − | 0.631551i | \(-0.217581\pi\) |
−0.631551 | + | 0.775335i | \(0.717581\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.0000 | 0.701180 | 0.350590 | − | 0.936529i | \(-0.385981\pi\) | ||||
0.350590 | + | 0.936529i | \(0.385981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.0000 | −1.47803 | −0.739014 | − | 0.673690i | \(-0.764708\pi\) | ||||
−0.739014 | + | 0.673690i | \(0.764708\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.0454 | − | 22.0454i | −0.853602 | − | 0.853602i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 30.0000i | − | 1.15814i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.9444 | − | 26.9444i | 1.03863 | − | 1.03863i | 0.0394065 | − | 0.999223i | \(-0.487453\pi\) |
0.999223 | − | 0.0394065i | \(-0.0125467\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6969 | + | 14.6969i | −0.564849 | + | 0.564849i | −0.930681 | − | 0.365832i | \(-0.880785\pi\) |
0.365832 | + | 0.930681i | \(0.380785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000i | 0.921035i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.7196 | − | 25.7196i | −0.984135 | − | 0.984135i | 0.0157413 | − | 0.999876i | \(-0.494989\pi\) |
−0.999876 | + | 0.0157413i | \(0.994989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.0000 | −0.685745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.0000 | −1.33146 | −0.665731 | − | 0.746191i | \(-0.731880\pi\) | ||||
−0.665731 | + | 0.746191i | \(0.731880\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.0454 | − | 22.0454i | −0.835029 | − | 0.835029i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000i | 0.453234i | 0.973984 | + | 0.226617i | \(0.0727665\pi\) | ||||
−0.973984 | + | 0.226617i | \(0.927233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89898 | − | 4.89898i | 0.184769 | − | 0.184769i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 29.3939 | − | 29.3939i | 1.10547 | − | 1.10547i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.0000i | 0.525781i | 0.964826 | + | 0.262891i | \(0.0846758\pi\) | ||||
−0.964826 | + | 0.262891i | \(0.915324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.3712 | − | 18.3712i | −0.688006 | − | 0.688006i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.0000 | 0.893807 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 54.0000i | 1.99726i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.6969 | + | 14.6969i | −0.542844 | + | 0.542844i | −0.924362 | − | 0.381518i | \(-0.875402\pi\) |
0.381518 | + | 0.924362i | \(0.375402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.3939 | − | 29.3939i | 1.08274 | − | 1.08274i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 7.00000i | − | 0.257499i | −0.991677 | − | 0.128750i | \(-0.958904\pi\) | ||
0.991677 | − | 0.128750i | \(-0.0410963\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.0454 | + | 22.0454i | 0.808768 | + | 0.808768i | 0.984447 | − | 0.175680i | \(-0.0562123\pi\) |
−0.175680 | + | 0.984447i | \(0.556212\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.0000 | 1.31541 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.0000 | 0.912263 | 0.456131 | − | 0.889912i | \(-0.349235\pi\) | ||||
0.456131 | + | 0.889912i | \(0.349235\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.4949 | − | 24.4949i | −0.890282 | − | 0.890282i | 0.104267 | − | 0.994549i | \(-0.466750\pi\) |
−0.994549 | + | 0.104267i | \(0.966750\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000i | 1.08750i | 0.839248 | + | 0.543750i | \(0.182996\pi\) | ||||
−0.839248 | + | 0.543750i | \(0.817004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.9444 | + | 26.9444i | −0.975452 | + | 0.975452i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.6969 | + | 14.6969i | −0.530676 | + | 0.530676i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 47.0000i | − | 1.69486i | −0.530904 | − | 0.847432i | \(-0.678148\pi\) | ||
0.530904 | − | 0.847432i | \(-0.321852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.67423 | − | 3.67423i | −0.132153 | − | 0.132153i | 0.637936 | − | 0.770089i | \(-0.279788\pi\) |
−0.770089 | + | 0.637936i | \(0.779788\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.1464 | − | 17.1464i | −0.611204 | − | 0.611204i | 0.332056 | − | 0.943260i | \(-0.392258\pi\) |
−0.943260 | + | 0.332056i | \(0.892258\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.2474 | + | 12.2474i | −0.434920 | + | 0.434920i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.0681 | + | 33.0681i | −1.17133 | + | 1.17133i | −0.189440 | + | 0.981892i | \(0.560667\pi\) |
−0.981892 | + | 0.189440i | \(0.939333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 54.0000i | − | 1.91038i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.6969 | + | 14.6969i | 0.518644 | + | 0.518644i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.0000 | −1.47664 | −0.738321 | − | 0.674450i | \(-0.764381\pi\) | ||||
−0.738321 | + | 0.674450i | \(0.764381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.0000 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.34847 | − | 7.34847i | −0.257090 | − | 0.257090i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.0000i | 0.837606i | 0.908077 | + | 0.418803i | \(0.137550\pi\) | ||||
−0.908077 | + | 0.418803i | \(0.862450\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.44949 | − | 2.44949i | 0.0853838 | − | 0.0853838i | −0.663125 | − | 0.748509i | \(-0.730770\pi\) |
0.748509 | + | 0.663125i | \(0.230770\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.67423 | − | 3.67423i | 0.127766 | − | 0.127766i | −0.640332 | − | 0.768098i | \(-0.721203\pi\) |
0.768098 | + | 0.640332i | \(0.221203\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.0000i | 0.903017i | 0.892267 | + | 0.451509i | \(0.149114\pi\) | ||||
−0.892267 | + | 0.451509i | \(0.850886\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.3712 | − | 18.3712i | −0.636523 | − | 0.636523i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | 0.828572 | 0.414286 | − | 0.910147i | \(-0.364031\pi\) | ||||
0.414286 | + | 0.910147i | \(0.364031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 61.2372 | + | 61.2372i | 2.10414 | + | 2.10414i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.0000i | 1.23406i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.79796 | + | 9.79796i | −0.335476 | + | 0.335476i | −0.854661 | − | 0.519186i | \(-0.826235\pi\) |
0.519186 | + | 0.854661i | \(0.326235\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.4166 | − | 40.4166i | 1.38060 | − | 1.38060i | 0.537060 | − | 0.843544i | \(-0.319535\pi\) |
0.843544 | − | 0.537060i | \(-0.180465\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.0000i | 1.46714i | 0.679613 | + | 0.733571i | \(0.262148\pi\) | ||||
−0.679613 | + | 0.733571i | \(0.737852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.67423 | − | 3.67423i | −0.125072 | − | 0.125072i | 0.641800 | − | 0.766872i | \(-0.278188\pi\) |
−0.766872 | + | 0.641800i | \(0.778188\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.0000 | −1.01768 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | −0.813209 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.2474 | + | 12.2474i | 0.413567 | + | 0.413567i | 0.882979 | − | 0.469412i | \(-0.155534\pi\) |
−0.469412 | + | 0.882979i | \(0.655534\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000i | 1.01073i | 0.862907 | + | 0.505363i | \(0.168641\pi\) | ||||
−0.862907 | + | 0.505363i | \(0.831359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.2474 | − | 12.2474i | 0.412159 | − | 0.412159i | −0.470331 | − | 0.882490i | \(-0.655865\pi\) |
0.882490 | + | 0.470331i | \(0.155865\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.3712 | − | 18.3712i | 0.616844 | − | 0.616844i | −0.327877 | − | 0.944720i | \(-0.606333\pi\) |
0.944720 | + | 0.327877i | \(0.106333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 72.0000i | 2.41480i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.34847 | + | 7.34847i | 0.245907 | + | 0.245907i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.0000 | 1.00056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.0000 | −0.899500 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.89898 | + | 4.89898i | 0.162668 | + | 0.162668i | 0.783748 | − | 0.621080i | \(-0.213306\pi\) |
−0.621080 | + | 0.783748i | \(0.713306\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 30.0000i | − | 0.993944i | −0.867766 | − | 0.496972i | \(-0.834445\pi\) | ||
0.867766 | − | 0.496972i | \(-0.165555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 66.1362 | − | 66.1362i | 2.18879 | − | 2.18879i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −29.3939 | + | 29.3939i | −0.970671 | + | 0.970671i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.0000i | − | 0.527791i | −0.964551 | − | 0.263896i | \(-0.914993\pi\) | ||
0.964551 | − | 0.263896i | \(-0.0850075\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.6969 | − | 14.6969i | −0.483756 | − | 0.483756i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.0000 | −1.37798 | −0.688988 | − | 0.724773i | \(-0.741945\pi\) | ||||
−0.688988 | + | 0.724773i | \(0.741945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | 0.163868 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.89898 | + | 4.89898i | 0.160043 | + | 0.160043i | 0.782586 | − | 0.622543i | \(-0.213900\pi\) |
−0.622543 | + | 0.782586i | \(0.713900\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −22.0454 | + | 22.0454i | −0.717897 | + | 0.717897i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.3712 | + | 18.3712i | −0.596983 | + | 0.596983i | −0.939508 | − | 0.342526i | \(-0.888718\pi\) |
0.342526 | + | 0.939508i | \(0.388718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 12.0000i | − | 0.389536i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.6969 | + | 14.6969i | 0.476081 | + | 0.476081i | 0.903876 | − | 0.427795i | \(-0.140710\pi\) |
−0.427795 | + | 0.903876i | \(0.640710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 54.0000 | 1.74375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.00000 | −0.193548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.89898 | + | 4.89898i | 0.157541 | + | 0.157541i | 0.781476 | − | 0.623935i | \(-0.214467\pi\) |
−0.623935 | + | 0.781476i | \(0.714467\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000i | 0.385098i | 0.981287 | + | 0.192549i | \(0.0616755\pi\) | ||||
−0.981287 | + | 0.192549i | \(0.938325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.9898 | − | 48.9898i | 1.57054 | − | 1.57054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −14.6969 | + | 14.6969i | −0.470197 | + | 0.470197i | −0.901978 | − | 0.431782i | \(-0.857885\pi\) |
0.431782 | + | 0.901978i | \(0.357885\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 36.0000i | − | 1.15056i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.3712 | + | 18.3712i | 0.585949 | + | 0.585949i | 0.936532 | − | 0.350582i | \(-0.114016\pi\) |
−0.350582 | + | 0.936532i | \(0.614016\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54.0000 | 1.71710 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.0000 | −1.17534 | −0.587672 | − | 0.809099i | \(-0.699955\pi\) | ||||
−0.587672 | + | 0.809099i | \(0.699955\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.0454 | + | 22.0454i | 0.698185 | + | 0.698185i | 0.964019 | − | 0.265834i | \(-0.0856472\pi\) |
−0.265834 | + | 0.964019i | \(0.585647\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2700.2.j.a.1457.1 | yes | 4 | |
3.2 | odd | 2 | 2700.2.j.g.1457.1 | yes | 4 | ||
5.2 | odd | 4 | 2700.2.j.g.593.2 | yes | 4 | ||
5.3 | odd | 4 | 2700.2.j.g.593.1 | yes | 4 | ||
5.4 | even | 2 | inner | 2700.2.j.a.1457.2 | yes | 4 | |
15.2 | even | 4 | inner | 2700.2.j.a.593.2 | yes | 4 | |
15.8 | even | 4 | inner | 2700.2.j.a.593.1 | ✓ | 4 | |
15.14 | odd | 2 | 2700.2.j.g.1457.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2700.2.j.a.593.1 | ✓ | 4 | 15.8 | even | 4 | inner | |
2700.2.j.a.593.2 | yes | 4 | 15.2 | even | 4 | inner | |
2700.2.j.a.1457.1 | yes | 4 | 1.1 | even | 1 | trivial | |
2700.2.j.a.1457.2 | yes | 4 | 5.4 | even | 2 | inner | |
2700.2.j.g.593.1 | yes | 4 | 5.3 | odd | 4 | ||
2700.2.j.g.593.2 | yes | 4 | 5.2 | odd | 4 | ||
2700.2.j.g.1457.1 | yes | 4 | 3.2 | odd | 2 | ||
2700.2.j.g.1457.2 | yes | 4 | 15.14 | odd | 2 |