Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1960,2,Mod(361,1960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1960, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1960.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1960.q (of order \(3\), degree \(2\), 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: | \(15.6506787962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1960.361 |
Dual form | 1960.2.q.p.961.1 |
$q$-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 \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1081\) | \(1177\) | \(1471\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.20711 | + | 2.09077i | −0.696923 | + | 1.20711i | 0.272605 | + | 0.962126i | \(0.412115\pi\) |
−0.969528 | + | 0.244981i | \(0.921218\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.41421 | − | 2.44949i | −0.471405 | − | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.414214 | −0.114882 | −0.0574411 | − | 0.998349i | \(-0.518294\pi\) | ||||
−0.0574411 | + | 0.998349i | \(0.518294\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.41421 | −0.623347 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.20711 | + | 2.09077i | −0.292766 | + | 0.507086i | −0.974463 | − | 0.224549i | \(-0.927909\pi\) |
0.681696 | + | 0.731635i | \(0.261242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | − | 1.73205i | −0.229416 | − | 0.397360i | 0.728219 | − | 0.685344i | \(-0.240348\pi\) |
−0.957635 | + | 0.287984i | \(0.907015\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.12132 | − | 5.40629i | −0.650840 | − | 1.12729i | −0.982919 | − | 0.184037i | \(-0.941083\pi\) |
0.332079 | − | 0.943252i | \(-0.392250\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.414214 | −0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12132 | + | 8.87039i | −0.919816 | + | 1.59317i | −0.120124 | + | 0.992759i | \(0.538329\pi\) |
−0.799693 | + | 0.600410i | \(0.795004\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.20711 | + | 2.09077i | 0.210130 | + | 0.363956i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.94975 | − | 10.3053i | −0.978132 | − | 1.69418i | −0.669185 | − | 0.743096i | \(-0.733357\pi\) |
−0.308948 | − | 0.951079i | \(-0.599977\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.500000 | − | 0.866025i | 0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.58579 | 0.716180 | 0.358090 | − | 0.933687i | \(-0.383428\pi\) | ||||
0.358090 | + | 0.933687i | \(0.383428\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6569 | −1.77765 | −0.888827 | − | 0.458243i | \(-0.848479\pi\) | ||||
−0.888827 | + | 0.458243i | \(0.848479\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.41421 | − | 2.44949i | 0.210819 | − | 0.365148i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.79289 | − | 6.56948i | −0.553250 | − | 0.958258i | −0.998037 | − | 0.0626213i | \(-0.980054\pi\) |
0.444787 | − | 0.895636i | \(-0.353279\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.91421 | − | 5.04757i | −0.408072 | − | 0.706801i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.29289 | + | 5.70346i | −0.452314 | + | 0.783430i | −0.998529 | − | 0.0542143i | \(-0.982735\pi\) |
0.546216 | + | 0.837645i | \(0.316068\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.82843 | 0.639541 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.878680 | + | 1.52192i | −0.114394 | + | 0.198137i | −0.917537 | − | 0.397649i | \(-0.869826\pi\) |
0.803143 | + | 0.595786i | \(0.203159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.41421 | + | 5.91359i | 0.437145 | + | 0.757158i | 0.997468 | − | 0.0711166i | \(-0.0226562\pi\) |
−0.560323 | + | 0.828274i | \(0.689323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.207107 | − | 0.358719i | −0.0256884 | − | 0.0444937i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.707107 | − | 1.22474i | 0.0863868 | − | 0.149626i | −0.819594 | − | 0.572944i | \(-0.805801\pi\) |
0.905981 | + | 0.423318i | \(0.139135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.0711 | 1.81434 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.48528 | −0.294949 | −0.147474 | − | 0.989066i | \(-0.547114\pi\) | ||||
−0.147474 | + | 0.989066i | \(0.547114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.41421 | − | 9.37769i | 0.633686 | − | 1.09758i | −0.353106 | − | 0.935583i | \(-0.614875\pi\) |
0.986792 | − | 0.161993i | \(-0.0517921\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.20711 | − | 2.09077i | −0.139385 | − | 0.241421i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.67157 | + | 2.89525i | 0.188067 | + | 0.325741i | 0.944606 | − | 0.328208i | \(-0.106445\pi\) |
−0.756539 | + | 0.653949i | \(0.773111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.74264 | − | 8.21449i | 0.526960 | − | 0.912722i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.3137 | −1.24184 | −0.620920 | − | 0.783874i | \(-0.713241\pi\) | ||||
−0.620920 | + | 0.783874i | \(0.713241\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.41421 | −0.261858 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.20711 | + | 2.09077i | −0.129415 | + | 0.224154i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.82843 | − | 8.36308i | −0.511812 | − | 0.886485i | −0.999906 | − | 0.0136937i | \(-0.995641\pi\) |
0.488094 | − | 0.872791i | \(-0.337692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −12.3640 | − | 21.4150i | −1.28208 | − | 2.22063i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | − | 1.73205i | 0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.0711 | 1.42870 | 0.714350 | − | 0.699788i | \(-0.246722\pi\) | ||||
0.714350 | + | 0.699788i | \(0.246722\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | −0.284268 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.24264 | + | 9.08052i | −0.521662 | + | 0.903546i | 0.478020 | + | 0.878349i | \(0.341355\pi\) |
−0.999683 | + | 0.0251967i | \(0.991979\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.37868 | − | 5.85204i | −0.332911 | − | 0.576619i | 0.650170 | − | 0.759789i | \(-0.274698\pi\) |
−0.983081 | + | 0.183170i | \(0.941364\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.24264 | + | 12.5446i | 0.700173 | + | 1.21273i | 0.968406 | + | 0.249380i | \(0.0802269\pi\) |
−0.268233 | + | 0.963354i | \(0.586440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.15685 | − | 15.8601i | 0.877068 | − | 1.51913i | 0.0225237 | − | 0.999746i | \(-0.492830\pi\) |
0.854544 | − | 0.519379i | \(-0.173837\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.7279 | 2.72673 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.07107 | −0.853334 | −0.426667 | − | 0.904409i | \(-0.640312\pi\) | ||||
−0.426667 | + | 0.904409i | \(0.640312\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.12132 | − | 5.40629i | 0.291065 | − | 0.504139i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.585786 | + | 1.01461i | 0.0541560 | + | 0.0938009i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.53553 | + | 9.58783i | −0.499122 | + | 0.864505i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.75736 | 0.333412 | 0.166706 | − | 0.986007i | \(-0.446687\pi\) | ||||
0.166706 | + | 0.986007i | \(0.446687\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 14.0711 | − | 24.3718i | 1.23889 | − | 2.14582i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.1213 | − | 17.5306i | −0.884304 | − | 1.53166i | −0.846509 | − | 0.532374i | \(-0.821300\pi\) |
−0.0377944 | − | 0.999286i | \(-0.512033\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.207107 | − | 0.358719i | −0.0178249 | − | 0.0308737i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.65685 | − | 16.7262i | 0.825041 | − | 1.42901i | −0.0768474 | − | 0.997043i | \(-0.524485\pi\) |
0.901888 | − | 0.431970i | \(-0.142181\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41421 | 0.119952 | 0.0599760 | − | 0.998200i | \(-0.480898\pi\) | ||||
0.0599760 | + | 0.998200i | \(0.480898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.3137 | 1.54229 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.207107 | + | 0.358719i | −0.0173191 | + | 0.0299976i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.500000 | + | 0.866025i | 0.0415227 | + | 0.0719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.58579 | + | 7.94282i | 0.375682 | + | 0.650701i | 0.990429 | − | 0.138024i | \(-0.0440751\pi\) |
−0.614747 | + | 0.788725i | \(0.710742\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.32843 | − | 5.76500i | 0.270864 | − | 0.469149i | −0.698220 | − | 0.715884i | \(-0.746024\pi\) |
0.969083 | + | 0.246734i | \(0.0793574\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.82843 | 0.552046 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.2426 | −0.822709 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.24264 | + | 9.08052i | −0.418408 | + | 0.724704i | −0.995780 | − | 0.0917773i | \(-0.970745\pi\) |
0.577371 | + | 0.816482i | \(0.304079\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.94975 | − | 13.7694i | −0.630456 | − | 1.09198i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.46447 | − | 2.53653i | −0.114706 | − | 0.198676i | 0.802956 | − | 0.596038i | \(-0.203259\pi\) |
−0.917662 | + | 0.397362i | \(0.869926\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.20711 | + | 2.09077i | −0.0939731 | + | 0.162766i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.58579 | 0.587006 | 0.293503 | − | 0.955958i | \(-0.405179\pi\) | ||||
0.293503 | + | 0.955958i | \(0.405179\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8284 | −0.986802 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.82843 | + | 4.89898i | −0.216295 | + | 0.374634i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.86396 | + | 11.8887i | 0.521857 | + | 0.903883i | 0.999677 | + | 0.0254253i | \(0.00809399\pi\) |
−0.477819 | + | 0.878458i | \(0.658573\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.12132 | − | 3.67423i | −0.159448 | − | 0.276172i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.07107 | + | 3.58719i | −0.154799 | + | 0.268120i | −0.932986 | − | 0.359913i | \(-0.882806\pi\) |
0.778187 | + | 0.628033i | \(0.216140\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.5563 | −1.89959 | −0.949794 | − | 0.312875i | \(-0.898708\pi\) | ||||
−0.949794 | + | 0.312875i | \(0.898708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.4853 | −1.21863 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.94975 | − | 10.3053i | 0.437434 | − | 0.757658i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.20711 | + | 2.09077i | 0.0882724 | + | 0.152892i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.91421 | − | 11.9758i | −0.500295 | − | 0.866536i | −1.00000 | 0.000340595i | \(-0.999892\pi\) | |
0.499705 | − | 0.866196i | \(-0.333442\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.343146 | + | 0.594346i | −0.0247002 | + | 0.0427820i | −0.878111 | − | 0.478456i | \(-0.841196\pi\) |
0.853411 | + | 0.521238i | \(0.174530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000 | 0.0716115 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2426 | −0.872252 | −0.436126 | − | 0.899886i | \(-0.643650\pi\) | ||||
−0.436126 | + | 0.899886i | \(0.643650\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.19239 | − | 10.7255i | 0.438967 | − | 0.760313i | −0.558643 | − | 0.829408i | \(-0.688678\pi\) |
0.997610 | + | 0.0690953i | \(0.0220113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.70711 | + | 2.95680i | 0.120410 | + | 0.208556i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.29289 | + | 3.97141i | 0.160143 | + | 0.277375i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.82843 | + | 15.2913i | −0.613618 | + | 1.06282i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.00000 | −0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.1421 | 1.18011 | 0.590057 | − | 0.807362i | \(-0.299105\pi\) | ||||
0.590057 | + | 0.807362i | \(0.299105\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.00000 | − | 5.19615i | 0.205557 | − | 0.356034i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.82843 | − | 10.0951i | −0.397495 | − | 0.688482i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.0711 | + | 22.6398i | 0.883261 | + | 1.52985i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.500000 | − | 0.866025i | 0.0336336 | − | 0.0582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.3848 | −1.16417 | −0.582085 | − | 0.813128i | \(-0.697763\pi\) | ||||
−0.582085 | + | 0.813128i | \(0.697763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | 0.188562 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.792893 | + | 1.37333i | −0.0526262 | + | 0.0911512i | −0.891138 | − | 0.453732i | \(-0.850093\pi\) |
0.838512 | + | 0.544883i | \(0.183426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.05025 | + | 3.55114i | 0.135485 | + | 0.234666i | 0.925782 | − | 0.378057i | \(-0.123408\pi\) |
−0.790298 | + | 0.612723i | \(0.790074\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.75736 | − | 3.04384i | −0.115128 | − | 0.199408i | 0.802703 | − | 0.596379i | \(-0.203395\pi\) |
−0.917831 | + | 0.396971i | \(0.870061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.79289 | − | 6.56948i | 0.247421 | − | 0.428546i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.07107 | −0.524272 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.65685 | −0.301227 | −0.150613 | − | 0.988593i | \(-0.548125\pi\) | ||||
−0.150613 | + | 0.988593i | \(0.548125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.19239 | + | 8.99348i | −0.334471 | + | 0.579321i | −0.983383 | − | 0.181543i | \(-0.941891\pi\) |
0.648912 | + | 0.760863i | \(0.275224\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.8284 | + | 18.7554i | 0.694644 | + | 1.20316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.414214 | + | 0.717439i | 0.0263558 | + | 0.0456495i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.6569 | − | 23.6544i | 0.865468 | − | 1.49903i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.55635 | 0.476953 | 0.238476 | − | 0.971148i | \(-0.423352\pi\) | ||||
0.238476 | + | 0.971148i | \(0.423352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.24264 | −0.392471 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.91421 | − | 5.04757i | 0.182495 | − | 0.316091i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.24264 | − | 9.08052i | −0.327027 | − | 0.566427i | 0.654894 | − | 0.755721i | \(-0.272713\pi\) |
−0.981920 | + | 0.189294i | \(0.939380\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41421 | − | 2.44949i | −0.0875376 | − | 0.151620i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.48528 | + | 16.4290i | −0.584888 | + | 1.01305i | 0.410002 | + | 0.912085i | \(0.365528\pi\) |
−0.994889 | + | 0.100970i | \(0.967805\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.58579 | −0.404562 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.3137 | 1.42678 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.29289 | + | 16.0958i | −0.566598 | + | 0.981376i | 0.430301 | + | 0.902685i | \(0.358407\pi\) |
−0.996899 | + | 0.0786907i | \(0.974926\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.17157 | − | 2.02922i | −0.0711680 | − | 0.123267i | 0.828245 | − | 0.560365i | \(-0.189339\pi\) |
−0.899413 | + | 0.437099i | \(0.856006\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.500000 | + | 0.866025i | 0.0301511 | + | 0.0522233i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.53553 | − | 11.3199i | 0.392682 | − | 0.680145i | −0.600120 | − | 0.799910i | \(-0.704881\pi\) |
0.992802 | + | 0.119764i | \(0.0382139\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.9706 | 1.73442 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.3137 | 1.09250 | 0.546252 | − | 0.837621i | \(-0.316054\pi\) | ||||
0.546252 | + | 0.837621i | \(0.316054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.5208 | + | 21.6867i | −0.744285 | + | 1.28914i | 0.206243 | + | 0.978501i | \(0.433876\pi\) |
−0.950528 | + | 0.310639i | \(0.899457\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.41421 | + | 4.18154i | 0.143006 | + | 0.247693i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.58579 | + | 9.67487i | 0.328576 | + | 0.569110i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.9853 | + | 29.4194i | −0.995695 | + | 1.72459i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.4142 | −1.07577 | −0.537885 | − | 0.843018i | \(-0.680777\pi\) | ||||
−0.537885 | + | 0.843018i | \(0.680777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.75736 | −0.102317 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.207107 | + | 0.358719i | −0.0120176 | + | 0.0208150i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.29289 | + | 2.23936i | 0.0747699 | + | 0.129505i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.6569 | − | 21.9223i | −0.727117 | − | 1.25940i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.41421 | + | 5.91359i | −0.195497 | + | 0.338611i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.9289 | −0.680820 | −0.340410 | − | 0.940277i | \(-0.610566\pi\) | ||||
−0.340410 | + | 0.940277i | \(0.610566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 16.3137 | 0.928054 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.00000 | + | 8.66025i | −0.283524 | + | 0.491078i | −0.972250 | − | 0.233944i | \(-0.924837\pi\) |
0.688726 | + | 0.725022i | \(0.258170\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.8640 | + | 20.5490i | 0.670591 | + | 1.16150i | 0.977737 | + | 0.209835i | \(0.0672926\pi\) |
−0.307146 | + | 0.951662i | \(0.599374\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.17157 | − | 10.6895i | −0.346630 | − | 0.600381i | 0.639018 | − | 0.769191i | \(-0.279341\pi\) |
−0.985649 | + | 0.168811i | \(0.946007\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.500000 | − | 0.866025i | 0.0279946 | − | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −34.9706 | −1.95187 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.82843 | 0.268661 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.207107 | − | 0.358719i | 0.0114882 | − | 0.0198982i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 22.1066 | + | 38.2898i | 1.22250 | + | 2.11743i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.75736 | − | 8.23999i | −0.261488 | − | 0.452911i | 0.705149 | − | 0.709059i | \(-0.250880\pi\) |
−0.966638 | + | 0.256148i | \(0.917547\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.8284 | + | 29.1477i | −0.922192 | + | 1.59728i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.41421 | 0.0772667 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.0711 | −0.712026 | −0.356013 | − | 0.934481i | \(-0.615864\pi\) | ||||
−0.356013 | + | 0.934481i | \(0.615864\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.9497 | − | 18.9655i | 0.594709 | − | 1.03007i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.12132 | + | 8.87039i | 0.277335 | + | 0.480358i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.53553 | + | 13.0519i | 0.405700 | + | 0.702692i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.4350 | + | 25.0022i | −0.774913 | + | 1.34219i | 0.159930 | + | 0.987128i | \(0.448873\pi\) |
−0.934843 | + | 0.355060i | \(0.884460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.68629 | −0.357909 | −0.178954 | − | 0.983857i | \(-0.557271\pi\) | ||||
−0.178954 | + | 0.983857i | \(0.557271\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.171573 | 0.00915788 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.1066 | + | 26.1654i | −0.804043 | + | 1.39264i | 0.112892 | + | 0.993607i | \(0.463989\pi\) |
−0.916935 | + | 0.399037i | \(0.869345\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.24264 | − | 2.15232i | −0.0659525 | − | 0.114233i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.8284 | + | 25.6836i | 0.782614 | + | 1.35553i | 0.930414 | + | 0.366511i | \(0.119448\pi\) |
−0.147799 | + | 0.989017i | \(0.547219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.1421 | −1.26713 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.8284 | 0.566786 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.62132 | + | 9.73641i | −0.293431 | + | 0.508237i | −0.974619 | − | 0.223872i | \(-0.928130\pi\) |
0.681188 | + | 0.732108i | \(0.261464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.48528 | − | 11.2328i | −0.337610 | − | 0.584758i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.4142 | − | 19.7700i | −0.591006 | − | 1.02365i | −0.994097 | − | 0.108492i | \(-0.965398\pi\) |
0.403092 | − | 0.915160i | \(-0.367936\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.20711 | − | 2.09077i | 0.0623347 | − | 0.107967i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.414214 | −0.0213331 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.6274 | 1.47049 | 0.735246 | − | 0.677801i | \(-0.237067\pi\) | ||||
0.735246 | + | 0.677801i | \(0.237067\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.53553 | + | 7.85578i | −0.232362 | + | 0.402464i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.4142 | − | 19.7700i | −0.583239 | − | 1.01020i | −0.995092 | − | 0.0989496i | \(-0.968452\pi\) |
0.411853 | − | 0.911250i | \(-0.364882\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.4853 | + | 28.5533i | 0.837994 | + | 1.45145i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.39949 | + | 9.35220i | −0.273765 | + | 0.474175i | −0.969823 | − | 0.243811i | \(-0.921602\pi\) |
0.696058 | + | 0.717986i | \(0.254936\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.0711 | 0.762177 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 48.8701 | 2.46517 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.67157 | + | 2.89525i | −0.0841060 | + | 0.145676i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.79289 | + | 4.83743i | 0.140171 | + | 0.242784i | 0.927561 | − | 0.373672i | \(-0.121901\pi\) |
−0.787390 | + | 0.616456i | \(0.788568\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2279 | + | 21.1794i | 0.610633 | + | 1.05765i | 0.991134 | + | 0.132867i | \(0.0424184\pi\) |
−0.380501 | + | 0.924781i | \(0.624248\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.12132 | − | 3.67423i | 0.105670 | − | 0.183027i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.48528 | 0.471327 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.8995 | −0.589836 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.5563 | − | 28.6764i | 0.818659 | − | 1.41796i | −0.0880119 | − | 0.996119i | \(-0.528051\pi\) |
0.906671 | − | 0.421839i | \(-0.138615\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.3137 | + | 40.3805i | 1.14998 | + | 1.99182i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.65685 | − | 9.79796i | −0.277684 | − | 0.480963i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.70711 | + | 2.95680i | −0.0835974 | + | 0.144795i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.5858 | −1.39651 | −0.698254 | − | 0.715851i | \(-0.746039\pi\) | ||||
−0.698254 | + | 0.715851i | \(0.746039\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.3137 | −1.28245 | −0.641226 | − | 0.767352i | \(-0.721574\pi\) | ||||
−0.641226 | + | 0.767352i | \(0.721574\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.7279 | + | 18.5813i | −0.521609 | + | 0.903454i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.20711 | − | 2.09077i | −0.0585533 | − | 0.101417i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.500000 | − | 0.866025i | −0.0241402 | − | 0.0418121i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.3284 | + | 19.6214i | −0.545671 | + | 0.945130i | 0.452893 | + | 0.891565i | \(0.350392\pi\) |
−0.998564 | + | 0.0535654i | \(0.982941\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.97056 | 0.334984 | 0.167492 | − | 0.985873i | \(-0.446433\pi\) | ||||
0.167492 | + | 0.985873i | \(0.446433\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.41421 | −0.115753 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.24264 | + | 10.8126i | −0.298626 | + | 0.517235i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.87868 | + | 3.25397i | 0.0896645 | + | 0.155303i | 0.907369 | − | 0.420334i | \(-0.138087\pi\) |
−0.817705 | + | 0.575638i | \(0.804754\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.3848 | + | 30.1113i | 0.825976 | + | 1.43063i | 0.901171 | + | 0.433463i | \(0.142709\pi\) |
−0.0751957 | + | 0.997169i | \(0.523958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.82843 | − | 8.36308i | 0.228889 | − | 0.396448i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.1421 | −1.04729 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.4853 | −1.29711 | −0.648555 | − | 0.761168i | \(-0.724626\pi\) | ||||
−0.648555 | + | 0.761168i | \(0.724626\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.29289 | − | 3.97141i | 0.107968 | − | 0.187006i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.03553 | + | 13.9180i | 0.377542 | + | 0.653922i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.46447 | − | 4.26858i | −0.115283 | − | 0.199676i | 0.802610 | − | 0.596504i | \(-0.203444\pi\) |
−0.917893 | + | 0.396828i | \(0.870111\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.500000 | − | 0.866025i | 0.0233380 | − | 0.0404226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.2843 | −1.50363 | −0.751814 | − | 0.659375i | \(-0.770821\pi\) | ||||
−0.751814 | + | 0.659375i | \(0.770821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.4558 | 1.18303 | 0.591517 | − | 0.806293i | \(-0.298529\pi\) | ||||
0.591517 | + | 0.806293i | \(0.298529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.3640 | − | 21.4150i | 0.573365 | − | 0.993097i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.20711 | − | 7.28692i | −0.194682 | − | 0.337199i | 0.752114 | − | 0.659033i | \(-0.229034\pi\) |
−0.946796 | + | 0.321834i | \(0.895701\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.6569 | − | 21.9223i | −0.583197 | − | 1.01013i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.82843 | + | 10.0951i | −0.267991 | + | 0.464175i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | 0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 18.6274 | 0.852891 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.2635 | − | 35.0973i | 0.925861 | − | 1.60364i | 0.135690 | − | 0.990751i | \(-0.456675\pi\) |
0.790171 | − | 0.612887i | \(-0.209992\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.46447 | + | 4.26858i | 0.112370 | + | 0.194631i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.03553 | + | 12.1859i | 0.319467 | + | 0.553333i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.636039 | + | 1.10165i | −0.0288217 | + | 0.0499206i | −0.880076 | − | 0.474832i | \(-0.842509\pi\) |
0.851255 | + | 0.524753i | \(0.175842\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.07107 | 0.319765 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.4853 | −0.518323 | −0.259162 | − | 0.965834i | \(-0.583446\pi\) | ||||
−0.259162 | + | 0.965834i | \(0.583446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.20711 | + | 2.09077i | −0.0543654 | + | 0.0941636i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.41421 | − | 2.44949i | −0.0635642 | − | 0.110096i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.3995 | + | 23.2086i | 0.599844 | + | 1.03896i | 0.992844 | + | 0.119421i | \(0.0381039\pi\) |
−0.393000 | + | 0.919539i | \(0.628563\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.15685 | + | 15.8601i | −0.409098 | + | 0.708579i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.0416 | −0.759849 | −0.379924 | − | 0.925018i | \(-0.624050\pi\) | ||||
−0.379924 | + | 0.925018i | \(0.624050\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.4853 | −0.466589 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.4853 | − | 26.8213i | 0.687725 | − | 1.19118i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.12132 | − | 14.0665i | −0.359971 | − | 0.623488i | 0.627984 | − | 0.778226i | \(-0.283880\pi\) |
−0.987956 | + | 0.154738i | \(0.950547\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.414214 | + | 0.717439i | 0.0182880 | + | 0.0316757i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.37868 | − | 5.85204i | 0.148882 | − | 0.257872i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.58579 | −0.333623 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −33.1421 | −1.45478 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.00000 | + | 5.19615i | −0.131432 | + | 0.227648i | −0.924229 | − | 0.381839i | \(-0.875291\pi\) |
0.792797 | + | 0.609486i | \(0.208624\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.75736 | + | 13.4361i | 0.339206 | + | 0.587521i | 0.984284 | − | 0.176595i | \(-0.0565084\pi\) |
−0.645078 | + | 0.764117i | \(0.723175\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.3640 | − | 21.4150i | −0.538583 | − | 0.932852i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.98528 | + | 13.8309i | −0.347186 | + | 0.601344i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.97056 | 0.215704 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.89949 | −0.0822763 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.24264 | + | 12.5446i | −0.313127 | + | 0.542351i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.00000 | − | 8.66025i | −0.215766 | − | 0.373718i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.15685 | + | 10.6640i | 0.264704 | + | 0.458480i | 0.967486 | − | 0.252925i | \(-0.0813925\pi\) |
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.8492 | − | 53.4325i | 1.32387 | − | 2.29301i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.3137 | 0.784473 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.1127 | 1.50131 | 0.750655 | − | 0.660694i | \(-0.229738\pi\) | ||||
0.750655 | + | 0.660694i | \(0.229738\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.65685 | − | 16.7262i | 0.412144 | − | 0.713855i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.00000 | − | 1.73205i | −0.0426014 | − | 0.0737878i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.3640 | + | 24.8791i | 0.609716 | + | 1.05606i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.07107 | + | 1.85514i | −0.0453826 | + | 0.0786050i | −0.887824 | − | 0.460182i | \(-0.847784\pi\) |
0.842442 | + | 0.538787i | \(0.181117\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.82843 | 0.204221 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.82843 | −0.246076 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.9706 | + | 24.1977i | −0.588789 | + | 1.01981i | 0.405602 | + | 0.914050i | \(0.367062\pi\) |
−0.994391 | + | 0.105763i | \(0.966272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.53553 | − | 7.85578i | −0.190811 | − | 0.330495i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.0711 | + | 29.5680i | 0.715656 | + | 1.23955i | 0.962706 | + | 0.270550i | \(0.0872057\pi\) |
−0.247049 | + | 0.969003i | \(0.579461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.7279 | − | 20.3134i | 0.490798 | − | 0.850088i | −0.509146 | − | 0.860680i | \(-0.670039\pi\) |
0.999944 | + | 0.0105929i | \(0.00337187\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.3848 | 1.39467 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.24264 | 0.260336 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.2071 | − | 31.5356i | 0.757972 | − | 1.31285i | −0.185912 | − | 0.982566i | \(-0.559524\pi\) |
0.943883 | − | 0.330279i | \(-0.107143\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.828427 | − | 1.43488i | −0.0344283 | − | 0.0596315i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.29289 | + | 5.70346i | 0.136378 | + | 0.236213i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.585786 | + | 1.01461i | −0.0242193 | + | 0.0419490i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.8579 | −0.571975 | −0.285988 | − | 0.958233i | \(-0.592322\pi\) | ||||
−0.285988 | + | 0.958233i | \(0.592322\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.4853 | 0.844081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.7782 | − | 25.5965i | 0.607893 | − | 1.05290i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.72183 | − | 8.17844i | −0.193902 | − | 0.335848i | 0.752638 | − | 0.658435i | \(-0.228781\pi\) |
−0.946540 | + | 0.322586i | \(0.895448\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.9497 | + | 25.8937i | 0.611852 | + | 1.05976i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.1569 | − | 31.4486i | 0.741869 | − | 1.28495i | −0.209774 | − | 0.977750i | \(-0.567273\pi\) |
0.951643 | − | 0.307205i | \(-0.0993937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.2843 | −0.745831 | −0.372915 | − | 0.927865i | \(-0.621642\pi\) | ||||
−0.372915 | + | 0.927865i | \(0.621642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.00000 | + | 8.66025i | −0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0355 | − | 17.3821i | −0.407330 | − | 0.705516i | 0.587260 | − | 0.809398i | \(-0.300207\pi\) |
−0.994590 | + | 0.103883i | \(0.966873\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.57107 | + | 2.72117i | 0.0635586 | + | 0.110087i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.6569 | + | 25.3864i | −0.591985 | + | 1.02535i | 0.401980 | + | 0.915648i | \(0.368322\pi\) |
−0.993965 | + | 0.109699i | \(0.965011\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −11.0711 | −0.446429 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.4142 | −0.459519 | −0.229759 | − | 0.973247i | \(-0.573794\pi\) | ||||
−0.229759 | + | 0.973247i | \(0.573794\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.53553 | − | 13.0519i | 0.302879 | − | 0.524601i | −0.673908 | − | 0.738815i | \(-0.735386\pi\) |
0.976787 | + | 0.214214i | \(0.0687190\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.29289 | + | 2.23936i | 0.0518820 | + | 0.0898623i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.41421 | − | 4.18154i | 0.0964144 | − | 0.166995i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28.7279 | 1.14546 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.6274 | −1.49792 | −0.748962 | − | 0.662613i | \(-0.769447\pi\) | ||||
−0.748962 | + | 0.662613i | \(0.769447\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.6924 | + | 35.8403i | −0.822449 | + | 1.42452i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.87868 | + | 3.25397i | 0.0745531 | + | 0.129130i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.51472 | + | 6.08767i | 0.139040 | + | 0.240825i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.1421 | + | 27.9590i | −0.637576 | + | 1.10431i | 0.348387 | + | 0.937351i | \(0.386729\pi\) |
−0.985963 | + | 0.166963i | \(0.946604\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.2132 | −1.19149 | −0.595746 | − | 0.803173i | \(-0.703144\pi\) | ||||
−0.595746 | + | 0.803173i | \(0.703144\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.1421 | 1.10810 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.07107 | + | 15.7116i | −0.356620 | + | 0.617685i | −0.987394 | − | 0.158282i | \(-0.949404\pi\) |
0.630773 | + | 0.775967i | \(0.282738\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.878680 | + | 1.52192i | 0.0344912 | + | 0.0597405i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.1421 | + | 19.2987i | 0.436025 | + | 0.755218i | 0.997379 | − | 0.0723580i | \(-0.0230524\pi\) |
−0.561353 | + | 0.827576i | \(0.689719\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1213 | − | 17.5306i | 0.395473 | − | 0.684979i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.6274 | −1.19489 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.4853 | 0.681130 | 0.340565 | − | 0.940221i | \(-0.389382\pi\) | ||||
0.340565 | + | 0.940221i | \(0.389382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.4142 | − | 26.6982i | 0.599543 | − | 1.03844i | −0.393345 | − | 0.919391i | \(-0.628682\pi\) |
0.992888 | − | 0.119049i | \(-0.0379845\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.20711 | + | 2.09077i | 0.0468801 | + | 0.0811988i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.12132 | − | 5.40629i | −0.120858 | − | 0.209332i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.9853 | − | 36.3476i | 0.811338 | − | 1.40528i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.82843 | 0.263609 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 50.8284 | 1.95929 | 0.979646 | − | 0.200733i | \(-0.0643324\pi\) | ||||
0.979646 | + | 0.200733i | \(0.0643324\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.207107 | − | 0.358719i | 0.00797154 | − | 0.0138071i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0355 | − | 31.2385i | −0.693162 | − | 1.20059i | −0.970796 | − | 0.239905i | \(-0.922884\pi\) |
0.277635 | − | 0.960687i | \(-0.410450\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.91421 | − | 3.31552i | −0.0733528 | − | 0.127051i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.58579 | − | 11.4069i | 0.251998 | − | 0.436474i | −0.712078 | − | 0.702101i | \(-0.752246\pi\) |
0.964076 | + | 0.265627i | \(0.0855790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.3137 | 0.737939 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.89949 | −0.377689 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.36396 | − | 2.36245i | 0.0519628 | − | 0.0900022i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.07107 | − | 8.78335i | −0.192913 | − | 0.334134i | 0.753302 | − | 0.657675i | \(-0.228460\pi\) |
−0.946214 | + | 0.323541i | \(0.895127\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.707107 | + | 1.22474i | 0.0268221 | + | 0.0464572i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.53553 | + | 9.58783i | −0.209673 | + | 0.363165i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.48528 | 0.320943 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.1421 | −1.40284 | −0.701420 | − | 0.712749i | \(-0.747450\pi\) | ||||
−0.701420 | + | 0.712749i | \(0.747450\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.8995 | + | 20.6105i | −0.448798 | + | 0.777341i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.15685 | + | 15.8601i | 0.344867 | + | 0.597327i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.6716 | + | 18.4837i | 0.400779 | + | 0.694170i | 0.993820 | − | 0.111002i | \(-0.0354061\pi\) |
−0.593041 | + | 0.805172i | \(0.702073\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.72792 | − | 8.18900i | 0.177311 | − | 0.307112i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 63.9411 | 2.39461 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.414214 | −0.0154907 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.62132 | − | 9.73641i | 0.209932 | − | 0.363613i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.8492 | − | 43.0402i | −0.926720 | − | 1.60513i | −0.788771 | − | 0.614688i | \(-0.789282\pi\) |
−0.137950 | − | 0.990439i | \(-0.544051\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.5355 | − | 21.7122i | −0.466202 | − | 0.807485i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.500000 | + | 0.866025i | −0.0185695 | + | 0.0321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.3137 | 1.53224 | 0.766120 | − | 0.642697i | \(-0.222185\pi\) | ||||
0.766120 | + | 0.642697i | \(0.222185\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0711 | − | 24.3718i | 0.520437 | − | 0.901424i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.3492 | + | 23.1216i | 0.493066 | + | 0.854015i | 0.999968 | − | 0.00798883i | \(-0.00254295\pi\) |
−0.506903 | + | 0.862003i | \(0.669210\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.707107 | − | 1.22474i | −0.0260466 | − | 0.0451141i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.39949 | − | 4.15605i | 0.0882668 | − | 0.152883i | −0.818512 | − | 0.574490i | \(-0.805201\pi\) |
0.906779 | + | 0.421607i | \(0.138534\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.89949 | −0.216431 | −0.108216 | − | 0.994127i | \(-0.534514\pi\) | ||||
−0.108216 | + | 0.994127i | \(0.534514\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.58579 | + | 7.94282i | −0.168010 | + | 0.291002i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.0000 | + | 27.7128i | 0.585409 | + | 1.01396i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.8137 | − | 22.1940i | −0.467579 | − | 0.809870i | 0.531735 | − | 0.846911i | \(-0.321540\pi\) |
−0.999314 | + | 0.0370405i | \(0.988207\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.12132 | + | 15.7986i | −0.332399 | + | 0.575733i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.65685 | 0.242268 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.7696 | −1.33641 | −0.668206 | − | 0.743976i | \(-0.732938\pi\) | ||||
−0.668206 | + | 0.743976i | \(0.732938\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.53553 | − | 13.0519i | 0.273523 | − | 0.473755i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.22183 | − | 3.84831i | −0.0805411 | − | 0.139501i | 0.822941 | − | 0.568126i | \(-0.192331\pi\) |
−0.903482 | + | 0.428625i | \(0.858998\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.41421 | + | 5.91359i | 0.123441 | + | 0.213806i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.363961 | − | 0.630399i | 0.0131419 | − | 0.0227624i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.4853 | −0.666596 | −0.333298 | − | 0.942821i | \(-0.608162\pi\) | ||||
−0.333298 | + | 0.942821i | \(0.608162\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.3137 | 0.911651 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.6924 | − | 18.5198i | 0.384578 | − | 0.666109i | −0.607132 | − | 0.794601i | \(-0.707680\pi\) |
0.991711 | + | 0.128491i | \(0.0410135\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.12132 | − | 8.87039i | −0.183963 | − | 0.318634i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.58579 | − | 7.94282i | −0.164303 | − | 0.284581i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.24264 | + | 2.15232i | −0.0444652 | + | 0.0770160i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −0.414214 | −0.0148028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.4853 | −0.374236 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.4203 | − | 37.1011i | 0.763552 | − | 1.32251i | −0.177457 | − | 0.984128i | \(-0.556787\pi\) |
0.941009 | − | 0.338382i | \(-0.109879\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.8995 | − | 39.6631i | −0.815244 | − | 1.41204i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.41421 | − | 2.44949i | −0.0502202 | − | 0.0869839i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.94975 | − | 13.7694i | 0.281948 | − | 0.488349i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.9289 | 1.27267 | 0.636334 | − | 0.771414i | \(-0.280450\pi\) | ||||
0.636334 | + | 0.771414i | \(0.280450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.3137 | 0.647892 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.6569 | + | 23.6544i | −0.482541 | + | 0.835786i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.41421 | − | 9.37769i | −0.191063 | − | 0.330932i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.4350 | − | 38.8586i | −0.789750 | − | 1.36789i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.4706 | + | 42.3843i | −0.860339 | + | 1.49015i | 0.0112626 | + | 0.999937i | \(0.496415\pi\) |
−0.871602 | + | 0.490215i | \(0.836918\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.5563 | −1.38901 | −0.694506 | − | 0.719487i | \(-0.744377\pi\) | ||||
−0.694506 | + | 0.719487i | \(0.744377\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.65685 | 0.198395 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.46447 | − | 2.53653i | 0.0512980 | − | 0.0888508i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6569 | + | 20.1903i | 0.407822 | + | 0.706368i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.7426 | − | 18.6068i | −0.374921 | − | 0.649382i | 0.615394 | − | 0.788219i | \(-0.288997\pi\) |
−0.990315 | + | 0.138838i | \(0.955663\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.0208 | − | 31.2130i | 0.628166 | − | 1.08802i | −0.359753 | − | 0.933047i | \(-0.617139\pi\) |
0.987919 | − | 0.154968i | \(-0.0495275\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.41421 | −0.0840521 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.0416 | −1.87921 | −0.939606 | − | 0.342259i | \(-0.888808\pi\) | ||||
−0.939606 | + | 0.342259i | \(0.888808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.70711 | + | 6.42090i | −0.128753 | + | 0.223007i | −0.923194 | − | 0.384335i | \(-0.874431\pi\) |
0.794441 | + | 0.607342i | \(0.207764\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.7782 | + | 27.3286i | 0.547339 | + | 0.948019i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.79289 | + | 6.56948i | 0.131258 | + | 0.227346i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.12132 | − | 3.67423i | 0.0733236 | − | 0.127000i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.75736 | 0.267814 | 0.133907 | − | 0.990994i | \(-0.457248\pi\) | ||||
0.133907 | + | 0.990994i | \(0.457248\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.1066 | + | 38.2898i | −0.761392 | + | 1.31877i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.41421 | − | 11.1097i | −0.220656 | − | 0.382187i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.2279 | − | 52.3563i | −1.03742 | − | 1.79686i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.1421 | + | 64.3321i | −1.27322 | + | 2.20527i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.31371 | 0.318895 | 0.159448 | − | 0.987206i | \(-0.449029\pi\) | ||||
0.159448 | + | 0.987206i | \(0.449029\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.65685 | −0.193460 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.2426 | + | 47.1856i | −0.930591 | + | 1.61183i | −0.148277 | + | 0.988946i | \(0.547373\pi\) |
−0.782314 | + | 0.622885i | \(0.785960\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.7279 | + | 46.2941i | 0.911945 | + | 1.57953i | 0.811314 | + | 0.584611i | \(0.198753\pi\) |
0.100631 | + | 0.994924i | \(0.467914\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.0919 | − | 19.2117i | −0.377572 | − | 0.653974i | 0.613136 | − | 0.789977i | \(-0.289908\pi\) |
−0.990708 | + | 0.136003i | \(0.956574\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.86396 | + | 11.8887i | −0.233382 | + | 0.404229i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.9706 | −0.915968 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.34315 | 0.113408 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.292893 | + | 0.507306i | −0.00992431 | + | 0.0171894i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.8995 | − | 34.4669i | −0.673496 | − | 1.16653i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.4853 | − | 23.3572i | −0.455366 | − | 0.788716i | 0.543344 | − | 0.839510i | \(-0.317158\pi\) |
−0.998709 | + | 0.0507941i | \(0.983825\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.2279 | − | 38.4999i | 0.749729 | − | 1.29857i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.6569 | 0.594875 | 0.297437 | − | 0.954741i | \(-0.403868\pi\) | ||||
0.297437 | + | 0.954741i | \(0.403868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.1127 | 1.18164 | 0.590818 | − | 0.806805i | \(-0.298805\pi\) | ||||
0.590818 | + | 0.806805i | \(0.298805\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.12132 | − | 3.67423i | 0.0713074 | − | 0.123508i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.14214 | + | 15.8346i | 0.306963 | + | 0.531675i | 0.977696 | − | 0.210023i | \(-0.0673539\pi\) |
−0.670734 | + | 0.741698i | \(0.734021\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.74264 | − | 8.21449i | −0.158884 | − | 0.275196i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.58579 | + | 13.1390i | −0.253849 | + | 0.439679i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.14214 | −0.138456 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.24264 | −0.208436 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.12132 | + | 8.87039i | −0.170806 | + | 0.295844i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.94975 | − | 13.7694i | −0.264844 | − | 0.458724i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.7782 | − | 22.1324i | −0.424761 | − | 0.735707i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.84924 | − | 6.66708i | 0.127812 | − | 0.221377i | −0.795017 | − | 0.606588i | \(-0.792538\pi\) |
0.922829 | + | 0.385211i | \(0.125871\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 29.6569 | 0.983656 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.6863 | 0.685367 | 0.342684 | − | 0.939451i | \(-0.388664\pi\) | ||||
0.342684 | + | 0.939451i | \(0.388664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.65685 | + | 9.79796i | −0.187215 | + | 0.324265i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.24264 | − | 14.2767i | −0.272493 | − | 0.471972i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.2990 | − | 24.7666i | −0.471680 | − | 0.816974i | 0.527795 | − | 0.849372i | \(-0.323019\pi\) |
−0.999475 | + | 0.0323979i | \(0.989686\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.3995 | − | 24.9407i | 0.474479 | − | 0.821823i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.02944 | 0.0338843 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.8995 | 0.391253 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.55635 | + | 16.5521i | −0.313872 | + | 0.543642i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.2635 | + | 29.9012i | 0.566396 | + | 0.981026i | 0.996918 | + | 0.0784462i | \(0.0249959\pi\) |
−0.430523 | + | 0.902580i | \(0.641671\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.0711 | − | 20.9077i | −0.395189 | − | 0.684487i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.20711 | + | 2.09077i | −0.0394766 | + | 0.0683755i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.2132 | 0.464325 | 0.232163 | − | 0.972677i | \(-0.425420\pi\) | ||||
0.232163 | + | 0.972677i | \(0.425420\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −57.2843 | −1.86940 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | \(-0.961269\pi\) |
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −14.3137 | − | 24.7921i | −0.466118 | − | 0.807341i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.94975 | − | 8.57321i | −0.160845 | − | 0.278592i | 0.774327 | − | 0.632786i | \(-0.218089\pi\) |
−0.935172 | + | 0.354194i | \(0.884755\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.24264 | + | 3.88437i | −0.0727992 | + | 0.126092i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.7990 | 0.966298 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.3848 | 1.89127 | 0.945634 | − | 0.325232i | \(-0.105442\pi\) | ||||
0.945634 | + | 0.325232i | \(0.105442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.91421 | − | 11.9758i | 0.223739 | − | 0.387527i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.20711 | + | 2.09077i | 0.0390202 | + | 0.0675850i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −36.9558 | − | 64.0094i | −1.19212 | − | 2.06482i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.4853 | − | 35.4815i | 0.660129 | − | 1.14338i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.686292 | −0.0220925 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.8284 | 0.927060 | 0.463530 | − | 0.886081i | \(-0.346583\pi\) | ||||
0.463530 | + | 0.886081i | \(0.346583\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.82843 | + | 10.0951i | −0.187236 | + | 0.324302i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.0919 | + | 24.4079i | 0.452230 | + | 0.783285i | 0.998524 | − | 0.0543080i | \(-0.0172953\pi\) |
−0.546294 | + | 0.837593i | \(0.683962\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.500000 | + | 0.866025i | 0.0160128 | + | 0.0277350i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0416 | + | 36.4452i | −0.673181 | + | 1.16598i | 0.303815 | + | 0.952731i | \(0.401739\pi\) |
−0.976997 | + | 0.213254i | \(0.931594\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.65685 | −0.308634 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.7990 | −1.65381 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.6924 | + | 28.9121i | −0.532404 | + | 0.922152i | 0.466880 | + | 0.884321i | \(0.345378\pi\) |
−0.999284 | + | 0.0378308i | \(0.987955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.12132 | − | 10.6024i | −0.195041 | − | 0.337822i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 36.3848 | + | 63.0203i | 1.15697 | + | 2.00393i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.65685 | − | 4.60181i | 0.0843978 | − | 0.146181i | −0.820737 | − | 0.571307i | \(-0.806437\pi\) |
0.905134 | + | 0.425125i | \(0.139770\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.9706 | 0.728949 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.3848 | 0.392624 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.44975 | − | 11.1713i | 0.204266 | − | 0.353798i | −0.745633 | − | 0.666357i | \(-0.767853\pi\) |
0.949898 | + | 0.312559i | \(0.101186\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.46447 | + | 4.26858i | 0.0779723 | + | 0.135052i |
(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 | 1960.2.q.p.361.1 | 4 | ||
7.2 | even | 3 | inner | 1960.2.q.p.961.1 | 4 | ||
7.3 | odd | 6 | 1960.2.a.q.1.1 | ✓ | 2 | ||
7.4 | even | 3 | 1960.2.a.u.1.2 | yes | 2 | ||
7.5 | odd | 6 | 1960.2.q.v.961.2 | 4 | |||
7.6 | odd | 2 | 1960.2.q.v.361.2 | 4 | |||
28.3 | even | 6 | 3920.2.a.by.1.2 | 2 | |||
28.11 | odd | 6 | 3920.2.a.bn.1.1 | 2 | |||
35.4 | even | 6 | 9800.2.a.bs.1.1 | 2 | |||
35.24 | odd | 6 | 9800.2.a.ca.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1960.2.a.q.1.1 | ✓ | 2 | 7.3 | odd | 6 | ||
1960.2.a.u.1.2 | yes | 2 | 7.4 | even | 3 | ||
1960.2.q.p.361.1 | 4 | 1.1 | even | 1 | trivial | ||
1960.2.q.p.961.1 | 4 | 7.2 | even | 3 | inner | ||
1960.2.q.v.361.2 | 4 | 7.6 | odd | 2 | |||
1960.2.q.v.961.2 | 4 | 7.5 | odd | 6 | |||
3920.2.a.bn.1.1 | 2 | 28.11 | odd | 6 | |||
3920.2.a.by.1.2 | 2 | 28.3 | even | 6 | |||
9800.2.a.bs.1.1 | 2 | 35.4 | even | 6 | |||
9800.2.a.ca.1.2 | 2 | 35.24 | odd | 6 |