Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1457,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.s (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1793.5 | ||
Character | \(\chi\) | \(=\) | 2100.1793 |
Dual form | 2100.2.s.b.1457.5 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.587996 | + | 1.62919i | −0.339479 | + | 0.940613i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.30852 | − | 1.91591i | −0.769507 | − | 0.638638i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.43430i | − | 0.733968i | −0.930227 | − | 0.366984i | \(-0.880390\pi\) | ||
0.930227 | − | 0.366984i | \(-0.119610\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.98864 | + | 2.98864i | 0.828900 | + | 0.828900i | 0.987365 | − | 0.158465i | \(-0.0506544\pi\) |
−0.158465 | + | 0.987365i | \(0.550654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.94659 | − | 4.94659i | −1.19973 | − | 1.19973i | −0.974249 | − | 0.225477i | \(-0.927606\pi\) |
−0.225477 | − | 0.974249i | \(-0.572394\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.61006i | 0.369373i | 0.982798 | + | 0.184686i | \(0.0591269\pi\) | ||||
−0.982798 | + | 0.184686i | \(0.940873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.736236 | + | 1.56779i | 0.160660 | + | 0.342119i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.57981 | + | 2.57981i | −0.537928 | + | 0.537928i | −0.922920 | − | 0.384992i | \(-0.874204\pi\) |
0.384992 | + | 0.922920i | \(0.374204\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.47879 | − | 2.63447i | 0.861943 | − | 0.507005i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41040 | 0.261905 | 0.130953 | − | 0.991389i | \(-0.458196\pi\) | ||||
0.130953 | + | 0.991389i | \(0.458196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.99675 | −1.61586 | −0.807932 | − | 0.589276i | \(-0.799413\pi\) | ||||
−0.807932 | + | 0.589276i | \(0.799413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.96593 | + | 1.43136i | 0.690380 | + | 0.249167i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.11006 | + | 7.11006i | −1.16889 | + | 1.16889i | −0.186416 | + | 0.982471i | \(0.559687\pi\) |
−0.982471 | + | 0.186416i | \(0.940313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.62637 | + | 3.11176i | −1.06107 | + | 0.498280i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.49343i | − | 0.701755i | −0.936421 | − | 0.350878i | \(-0.885883\pi\) | ||
0.936421 | − | 0.350878i | \(-0.114117\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.69565 | − | 4.69565i | −0.716080 | − | 0.716080i | 0.251720 | − | 0.967800i | \(-0.419004\pi\) |
−0.967800 | + | 0.251720i | \(0.919004\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.89003 | − | 6.89003i | −1.00501 | − | 1.00501i | −0.999987 | − | 0.00502726i | \(-0.998400\pi\) |
−0.00502726 | − | 0.999987i | \(-0.501600\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.9675 | − | 5.15037i | 1.53576 | − | 0.721196i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.78938 | + | 8.78938i | −1.20731 | + | 1.20731i | −0.235421 | + | 0.971893i | \(0.575647\pi\) |
−0.971893 | + | 0.235421i | \(0.924353\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.62309 | − | 0.946707i | −0.347437 | − | 0.125394i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.56655 | −0.464325 | −0.232162 | − | 0.972677i | \(-0.574580\pi\) | ||||
−0.232162 | + | 0.972677i | \(0.574580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.83984 | 1.13183 | 0.565913 | − | 0.824465i | \(-0.308524\pi\) | ||||
0.565913 | + | 0.824465i | \(0.308524\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.98713 | + | 0.277616i | −0.376343 | + | 0.0349764i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.03073 | − | 6.03073i | 0.736771 | − | 0.736771i | −0.235180 | − | 0.971952i | \(-0.575568\pi\) |
0.971952 | + | 0.235180i | \(0.0755681\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.68609 | − | 5.71992i | −0.323367 | − | 0.688598i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.71253i | 0.559274i | 0.960106 | + | 0.279637i | \(0.0902141\pi\) | ||||
−0.960106 | + | 0.279637i | \(0.909786\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.52517 | − | 7.52517i | −0.880755 | − | 0.880755i | 0.112857 | − | 0.993611i | \(-0.464000\pi\) |
−0.993611 | + | 0.112857i | \(0.964000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.72131 | − | 1.72131i | −0.196161 | − | 0.196161i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.16138i | 0.130665i | 0.997864 | + | 0.0653327i | \(0.0208109\pi\) | ||||
−0.997864 | + | 0.0653327i | \(0.979189\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.65855 | + | 8.84586i | 0.184283 | + | 0.982873i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.94830 | + | 2.94830i | −0.323618 | + | 0.323618i | −0.850153 | − | 0.526535i | \(-0.823491\pi\) |
0.526535 | + | 0.850153i | \(0.323491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.829310 | + | 2.29781i | −0.0889114 | + | 0.246351i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.172323 | −0.0182662 | −0.00913311 | − | 0.999958i | \(-0.502907\pi\) | ||||
−0.00913311 | + | 0.999958i | \(0.502907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.22658 | 0.443066 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.29005 | − | 14.6574i | 0.548552 | − | 1.51990i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.38212 | − | 9.38212i | 0.952610 | − | 0.952610i | −0.0463165 | − | 0.998927i | \(-0.514748\pi\) |
0.998927 | + | 0.0463165i | \(0.0147483\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.66390 | + | 5.61963i | −0.468740 | + | 0.564794i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.13144i | − | 0.709604i | −0.934941 | − | 0.354802i | \(-0.884548\pi\) | ||
0.934941 | − | 0.354802i | \(-0.115452\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.42462 | − | 8.42462i | −0.830103 | − | 0.830103i | 0.157428 | − | 0.987531i | \(-0.449680\pi\) |
−0.987531 | + | 0.157428i | \(0.949680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.58306 | − | 2.58306i | −0.249714 | − | 0.249714i | 0.571139 | − | 0.820853i | \(-0.306502\pi\) |
−0.820853 | + | 0.571139i | \(0.806502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.15884i | 0.110997i | 0.998459 | + | 0.0554985i | \(0.0176748\pi\) | ||||
−0.998459 | + | 0.0554985i | \(0.982325\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.40296 | − | 15.7643i | −0.702658 | − | 1.49628i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.85511 | + | 1.85511i | −0.174514 | + | 0.174514i | −0.788959 | − | 0.614445i | \(-0.789380\pi\) |
0.614445 | + | 0.788959i | \(0.289380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.17337 | − | 12.6253i | −0.108478 | − | 1.16721i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.99554 | −0.641280 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.07420 | 0.461291 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.32065 | + | 2.64211i | 0.660080 | + | 0.238231i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.33168 | + | 2.33168i | −0.206903 | + | 0.206903i | −0.802950 | − | 0.596046i | \(-0.796737\pi\) |
0.596046 | + | 0.802950i | \(0.296737\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.4111 | − | 4.88909i | 0.916649 | − | 0.430460i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.20687i | − | 0.542297i | −0.962538 | − | 0.271148i | \(-0.912597\pi\) | ||
0.962538 | − | 0.271148i | \(-0.0874034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.13848 | + | 1.13848i | 0.0987190 | + | 0.0987190i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.32888 | − | 5.32888i | −0.455277 | − | 0.455277i | 0.441825 | − | 0.897101i | \(-0.354331\pi\) |
−0.897101 | + | 0.441825i | \(0.854331\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1410i | 0.860148i | 0.902794 | + | 0.430074i | \(0.141512\pi\) | ||||
−0.902794 | + | 0.430074i | \(0.858488\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.2765 | − | 7.17387i | 1.28651 | − | 0.604149i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.27524 | − | 7.27524i | 0.608386 | − | 0.608386i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.62919 | + | 0.587996i | 0.134373 | + | 0.0484971i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.9444 | 1.96160 | 0.980799 | − | 0.195021i | \(-0.0624775\pi\) | ||||
0.980799 | + | 0.195021i | \(0.0624775\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.6080 | −1.51430 | −0.757150 | − | 0.653242i | \(-0.773409\pi\) | ||||
−0.757150 | + | 0.653242i | \(0.773409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.94208 | + | 20.8966i | 0.157008 | + | 1.68939i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.47944 | − | 7.47944i | 0.596925 | − | 0.596925i | −0.342568 | − | 0.939493i | \(-0.611297\pi\) |
0.939493 | + | 0.342568i | \(0.111297\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.15146 | − | 19.4877i | −0.725758 | − | 1.54547i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.64840i | 0.287534i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.27351 | − | 7.27351i | −0.569706 | − | 0.569706i | 0.362340 | − | 0.932046i | \(-0.381978\pi\) |
−0.932046 | + | 0.362340i | \(0.881978\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.9727 | + | 10.9727i | 0.849090 | + | 0.849090i | 0.990020 | − | 0.140930i | \(-0.0450092\pi\) |
−0.140930 | + | 0.990020i | \(0.545009\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.86395i | 0.374150i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.08473 | − | 3.71685i | 0.235895 | − | 0.284235i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.631993 | − | 0.631993i | 0.0480496 | − | 0.0480496i | −0.682674 | − | 0.730723i | \(-0.739183\pi\) |
0.730723 | + | 0.682674i | \(0.239183\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.09711 | − | 5.81058i | 0.157629 | − | 0.436750i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.60854 | −0.568689 | −0.284344 | − | 0.958722i | \(-0.591776\pi\) | ||||
−0.284344 | + | 0.958722i | \(0.591776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.5290 | −1.30292 | −0.651461 | − | 0.758682i | \(-0.725844\pi\) | ||||
−0.651461 | + | 0.758682i | \(0.725844\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.19778 | + | 14.4018i | −0.384231 | + | 1.06461i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0415 | + | 12.0415i | −0.880560 | + | 0.880560i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.30413 | − | 5.02984i | 0.0948613 | − | 0.365867i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 5.61285i | − | 0.406132i | −0.979165 | − | 0.203066i | \(-0.934909\pi\) | ||
0.979165 | − | 0.203066i | \(-0.0650905\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.70245 | + | 5.70245i | 0.410471 | + | 0.410471i | 0.881903 | − | 0.471431i | \(-0.156263\pi\) |
−0.471431 | + | 0.881903i | \(0.656263\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.94136 | + | 2.94136i | 0.209563 | + | 0.209563i | 0.804082 | − | 0.594519i | \(-0.202657\pi\) |
−0.594519 | + | 0.804082i | \(0.702657\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 26.1729i | − | 1.85535i | −0.373388 | − | 0.927675i | \(-0.621804\pi\) | ||
0.373388 | − | 0.927675i | \(-0.378196\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.27917 | + | 13.3713i | 0.442898 | + | 0.943136i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.997305 | − | 0.997305i | 0.0699971 | − | 0.0699971i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.8982 | − | 1.01286i | 0.757480 | − | 0.0703984i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.91936 | 0.271108 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.53694 | −0.450021 | −0.225011 | − | 0.974356i | \(-0.572242\pi\) | ||||
−0.225011 | + | 0.974356i | \(0.572242\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.67760 | − | 2.77094i | −0.526061 | − | 0.189862i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.36166 | + | 6.36166i | −0.431858 | + | 0.431858i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.6847 | − | 7.83517i | 1.12745 | − | 0.529452i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 29.5672i | − | 1.98890i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.01848 | + | 5.01848i | 0.336062 | + | 0.336062i | 0.854883 | − | 0.518821i | \(-0.173629\pi\) |
−0.518821 | + | 0.854883i | \(0.673629\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.2157 | − | 12.2157i | −0.810781 | − | 0.810781i | 0.173970 | − | 0.984751i | \(-0.444341\pi\) |
−0.984751 | + | 0.173970i | \(0.944341\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.46947i | − | 0.163187i | −0.996666 | − | 0.0815935i | \(-0.973999\pi\) | ||
0.996666 | − | 0.0815935i | \(-0.0260009\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.81646 | − | 1.79222i | 0.251105 | − | 0.117919i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.3358 | − | 12.3358i | 0.808142 | − | 0.808142i | −0.176210 | − | 0.984353i | \(-0.556384\pi\) |
0.984353 | + | 0.176210i | \(0.0563839\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.89211 | − | 0.682886i | −0.122906 | − | 0.0443582i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.59397 | −0.620582 | −0.310291 | − | 0.950642i | \(-0.600427\pi\) | ||||
−0.310291 | + | 0.950642i | \(0.600427\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.49641 | −0.289639 | −0.144820 | − | 0.989458i | \(-0.546260\pi\) | ||||
−0.144820 | + | 0.989458i | \(0.546260\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.3868 | − | 2.49923i | −0.987064 | − | 0.160326i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.81189 | + | 4.81189i | −0.306173 | + | 0.306173i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.06976 | − | 6.53694i | −0.194538 | − | 0.414262i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.5516i | 0.855371i | 0.903928 | + | 0.427685i | \(0.140671\pi\) | ||||
−0.903928 | + | 0.427685i | \(0.859329\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.28003 | + | 6.28003i | 0.394822 | + | 0.394822i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.2974 | + | 15.2974i | 0.954228 | + | 0.954228i | 0.998997 | − | 0.0447692i | \(-0.0142552\pi\) |
−0.0447692 | + | 0.998997i | \(0.514255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.0551i | 0.624796i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.25595 | − | 2.70221i | −0.201538 | − | 0.167263i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.8610 | + | 17.8610i | −1.10135 | + | 1.10135i | −0.107107 | + | 0.994247i | \(0.534159\pi\) |
−0.994247 | + | 0.107107i | \(0.965841\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.101325 | − | 0.280747i | 0.00620100 | − | 0.0171815i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.5710 | −1.43715 | −0.718575 | − | 0.695449i | \(-0.755205\pi\) | ||||
−0.718575 | + | 0.695449i | \(0.755205\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.1730 | −1.52915 | −0.764576 | − | 0.644534i | \(-0.777051\pi\) | ||||
−0.764576 | + | 0.644534i | \(0.777051\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.48521 | + | 6.88590i | −0.150412 | + | 0.416754i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.894945 | − | 0.894945i | 0.0537721 | − | 0.0537721i | −0.679709 | − | 0.733481i | \(-0.737894\pi\) |
0.733481 | + | 0.679709i | \(0.237894\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.7692 | + | 17.2370i | 1.24342 | + | 1.03195i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.4798i | 0.684828i | 0.939549 | + | 0.342414i | \(0.111245\pi\) | ||||
−0.939549 | + | 0.342414i | \(0.888755\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.10745 | − | 6.10745i | −0.363050 | − | 0.363050i | 0.501884 | − | 0.864935i | \(-0.332640\pi\) |
−0.864935 | + | 0.501884i | \(0.832640\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.17733 | − | 3.17733i | −0.187552 | − | 0.187552i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.9376i | 1.87868i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.76862 | + | 20.8019i | 0.572647 | + | 1.21943i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.9572 | − | 10.9572i | 0.640129 | − | 0.640129i | −0.310458 | − | 0.950587i | \(-0.600482\pi\) |
0.950587 | + | 0.310458i | \(0.100482\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.41309 | − | 10.9027i | −0.372125 | − | 0.632639i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.4203 | −0.891777 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.64065 | −0.382761 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.6185 | + | 4.19325i | 0.667463 | + | 0.240896i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.403804 | − | 0.403804i | 0.0230463 | − | 0.0230463i | −0.695490 | − | 0.718536i | \(-0.744813\pi\) |
0.718536 | + | 0.695490i | \(0.244813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.6790 | − | 8.77167i | 1.06261 | − | 0.499003i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.8750i | 1.35383i | 0.736062 | + | 0.676914i | \(0.236683\pi\) | ||||
−0.736062 | + | 0.676914i | \(0.763317\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.933579 | + | 0.933579i | 0.0527690 | + | 0.0527690i | 0.732999 | − | 0.680230i | \(-0.238120\pi\) |
−0.680230 | + | 0.732999i | \(0.738120\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.3618 | + | 10.3618i | 0.581974 | + | 0.581974i | 0.935445 | − | 0.353471i | \(-0.114999\pi\) |
−0.353471 | + | 0.935445i | \(0.614999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.43334i | − | 0.192230i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.72713 | − | 2.68947i | 0.319657 | − | 0.150112i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.96430 | − | 7.96430i | 0.443146 | − | 0.443146i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.88798 | − | 0.681395i | −0.104405 | − | 0.0376812i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.74398 | −0.537203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.77630 | 0.0976345 | 0.0488172 | − | 0.998808i | \(-0.484455\pi\) | ||||
0.0488172 | + | 0.998808i | \(0.484455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.0360 | − | 2.79147i | 1.64596 | − | 0.152972i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.85736 | + | 4.85736i | −0.264597 | + | 0.264597i | −0.826919 | − | 0.562321i | \(-0.809908\pi\) |
0.562321 | + | 0.826919i | \(0.309908\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.93153 | − | 4.11312i | −0.104906 | − | 0.223394i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.9008i | 1.18599i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.0503 | + | 13.0503i | 0.700579 | + | 0.700579i | 0.964535 | − | 0.263956i | \(-0.0850272\pi\) |
−0.263956 | + | 0.964535i | \(0.585027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.7209i | 0.841522i | 0.907172 | + | 0.420761i | \(0.138237\pi\) | ||||
−0.907172 | + | 0.420761i | \(0.861763\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.2590 | + | 5.51200i | 1.13472 | + | 0.294209i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.4258 | − | 24.4258i | 1.30005 | − | 1.30005i | 0.371701 | − | 0.928353i | \(-0.378775\pi\) |
0.928353 | − | 0.371701i | \(-0.121225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.11335 | − | 11.3971i | 0.217701 | − | 0.603197i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.3763 | 1.33931 | 0.669655 | − | 0.742673i | \(-0.266442\pi\) | ||||
0.669655 | + | 0.742673i | \(0.266442\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4077 | 0.863564 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.98360 | + | 8.26683i | −0.156599 | + | 0.433896i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.5655 | + | 22.5655i | −1.17791 | + | 1.17791i | −0.197633 | + | 0.980276i | \(0.563326\pi\) |
−0.980276 | + | 0.197633i | \(0.936674\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.60901 | + | 10.3732i | −0.448167 | + | 0.540006i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.4301i | 0.645337i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.44947 | + | 1.44947i | 0.0750506 | + | 0.0750506i | 0.743636 | − | 0.668585i | \(-0.233100\pi\) |
−0.668585 | + | 0.743636i | \(0.733100\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.21519 | + | 4.21519i | 0.217093 | + | 0.217093i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4529i | 0.742394i | 0.928554 | + | 0.371197i | \(0.121053\pi\) | ||||
−0.928554 | + | 0.371197i | \(0.878947\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.42774 | − | 5.16978i | −0.124377 | − | 0.264856i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.1020 | + | 15.1020i | −0.771675 | + | 0.771675i | −0.978399 | − | 0.206724i | \(-0.933720\pi\) |
0.206724 | + | 0.978399i | \(0.433720\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.84355 | + | 19.8365i | 0.0937131 | + | 1.00834i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.85986 | 0.246405 | 0.123202 | − | 0.992382i | \(-0.460684\pi\) | ||||
0.123202 | + | 0.992382i | \(0.460684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.5226 | 1.29073 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.1122 | + | 3.64961i | 0.510092 | + | 0.184099i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.43039 | − | 5.43039i | 0.272543 | − | 0.272543i | −0.557580 | − | 0.830123i | \(-0.688270\pi\) |
0.830123 | + | 0.557580i | \(0.188270\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.52423 | + | 1.18538i | −0.126369 | + | 0.0593433i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 36.9608i | − | 1.84573i | −0.385119 | − | 0.922867i | \(-0.625840\pi\) | ||
0.385119 | − | 0.922867i | \(-0.374160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.8880 | − | 26.8880i | −1.33939 | − | 1.33939i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.3080 | + | 17.3080i | 0.857926 | + | 0.857926i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.4192i | 1.45469i | 0.686274 | + | 0.727343i | \(0.259245\pi\) | ||||
−0.686274 | + | 0.727343i | \(0.740755\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8151 | − | 5.54840i | 0.582797 | − | 0.273682i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.52193 | + | 2.52193i | −0.124096 | + | 0.124096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.5216 | − | 5.96286i | −0.809067 | − | 0.292002i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.7181 | −1.40297 | −0.701485 | − | 0.712684i | \(-0.747479\pi\) | ||||
−0.701485 | + | 0.712684i | \(0.747479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.98981 | 0.243189 | 0.121594 | − | 0.992580i | \(-0.461199\pi\) | ||||
0.121594 | + | 0.992580i | \(0.461199\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.70509 | + | 29.1065i | 0.131526 | + | 1.41521i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.25071 | − | 6.25071i | 0.302493 | − | 0.302493i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.57494 | + | 16.1306i | 0.365722 | + | 0.778791i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.5003i | 1.80632i | 0.429300 | + | 0.903162i | \(0.358760\pi\) | ||||
−0.429300 | + | 0.903162i | \(0.641240\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.2740 | − | 23.2740i | −1.11848 | − | 1.11848i | −0.991965 | − | 0.126514i | \(-0.959621\pi\) |
−0.126514 | − | 0.991965i | \(-0.540379\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.15364 | − | 4.15364i | −0.198696 | − | 0.198696i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 0.591384i | − | 0.0282252i | −0.999900 | − | 0.0141126i | \(-0.995508\pi\) | ||
0.999900 | − | 0.0141126i | \(-0.00449234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.91591 | + | 2.30852i | −0.0912340 | + | 0.109930i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.5701 | − | 12.5701i | 0.597226 | − | 0.597226i | −0.342348 | − | 0.939573i | \(-0.611222\pi\) |
0.939573 | + | 0.342348i | \(0.111222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.0792 | + | 39.0099i | −0.665922 | + | 1.84511i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.79590 | −0.462297 | −0.231149 | − | 0.972918i | \(-0.574248\pi\) | ||||
−0.231149 | + | 0.972918i | \(0.574248\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.9383 | −0.515066 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.9414 | − | 30.3160i | 0.514073 | − | 1.42437i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.1080 | + | 27.1080i | −1.26806 | + | 1.26806i | −0.320970 | + | 0.947089i | \(0.604009\pi\) |
−0.947089 | + | 0.320970i | \(0.895991\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −35.1864 | − | 9.12308i | −1.64236 | − | 0.425829i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.82113i | 0.317692i | 0.987303 | + | 0.158846i | \(0.0507773\pi\) | ||||
−0.987303 | + | 0.158846i | \(0.949223\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.03568 | + | 9.03568i | 0.419924 | + | 0.419924i | 0.885177 | − | 0.465254i | \(-0.154037\pi\) |
−0.465254 | + | 0.885177i | \(0.654037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.6718 | − | 28.6718i | −1.32677 | − | 1.32677i | −0.908169 | − | 0.418603i | \(-0.862520\pi\) |
−0.418603 | − | 0.908169i | \(-0.637480\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.52874i | − | 0.393821i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.78756 | + | 16.5833i | 0.358832 | + | 0.764119i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4306 | + | 11.4306i | −0.525580 | + | 0.525580i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 37.1302 | − | 3.45079i | 1.70007 | − | 0.158001i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.3227 | 0.974261 | 0.487130 | − | 0.873329i | \(-0.338044\pi\) | ||||
0.487130 | + | 0.873329i | \(0.338044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −42.4988 | −1.93778 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.94394 | − | 2.14525i | −0.270459 | − | 0.0976120i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4319 | − | 11.4319i | 0.518028 | − | 0.518028i | −0.398946 | − | 0.916974i | \(-0.630624\pi\) |
0.916974 | + | 0.398946i | \(0.130624\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 16.1267 | − | 7.57314i | 0.729276 | − | 0.342469i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.48805i | − | 0.157413i | −0.996898 | − | 0.0787067i | \(-0.974921\pi\) | ||
0.996898 | − | 0.0787067i | \(-0.0250790\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.97669 | − | 6.97669i | −0.314214 | − | 0.314214i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.33226 | + | 3.33226i | 0.149472 | + | 0.149472i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 13.2787i | − | 0.594438i | −0.954809 | − | 0.297219i | \(-0.903941\pi\) | ||
0.954809 | − | 0.297219i | \(-0.0960592\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.3284 | + | 11.4247i | −1.08691 | + | 0.510417i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.9159 | − | 23.9159i | 1.06636 | − | 1.06636i | 0.0687200 | − | 0.997636i | \(-0.478108\pi\) |
0.997636 | − | 0.0687200i | \(-0.0218915\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.92431 | − | 2.85998i | −0.351931 | − | 0.127016i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.8408 | 1.18970 | 0.594848 | − | 0.803838i | \(-0.297212\pi\) | ||||
0.594848 | + | 0.803838i | \(0.297212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.6422 | −0.470783 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.24166 | + | 7.21111i | 0.187274 | + | 0.318378i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.7724 | + | 16.7724i | −0.737649 | + | 0.737649i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.658028 | + | 1.40125i | 0.0288842 | + | 0.0615079i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.5361i | 0.812081i | 0.913855 | + | 0.406040i | \(0.133091\pi\) | ||||
−0.913855 | + | 0.406040i | \(0.866909\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.4744 | + | 19.4744i | 0.851554 | + | 0.851554i | 0.990325 | − | 0.138770i | \(-0.0443149\pi\) |
−0.138770 | + | 0.990325i | \(0.544315\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 44.5032 | + | 44.5032i | 1.93859 | + | 1.93859i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.68915i | 0.421267i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.23345 | + | 6.83319i | 0.357301 | + | 0.296535i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.4292 | − | 13.4292i | 0.581685 | − | 0.581685i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.47379 | − | 12.3958i | 0.193058 | − | 0.534916i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.43430 | −0.104853 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −37.9743 | −1.63264 | −0.816321 | − | 0.577599i | \(-0.803990\pi\) | ||||
−0.816321 | + | 0.577599i | \(0.803990\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3070 | − | 28.5581i | 0.442315 | − | 1.22555i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.67326 | − | 4.67326i | 0.199814 | − | 0.199814i | −0.600106 | − | 0.799920i | \(-0.704875\pi\) |
0.799920 | + | 0.600106i | \(0.204875\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.4070 | − | 16.9364i | −0.870948 | − | 0.722826i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.27083i | 0.0967406i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.821219 | + | 0.821219i | 0.0349218 | + | 0.0349218i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.6349 | − | 12.6349i | −0.535360 | − | 0.535360i | 0.386803 | − | 0.922163i | \(-0.373579\pi\) |
−0.922163 | + | 0.386803i | \(0.873579\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 28.0672i | − | 1.18712i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −12.5375 | − | 26.6982i | −0.529335 | − | 1.12720i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.5948 | + | 28.5948i | −1.20513 | + | 1.20513i | −0.232543 | + | 0.972586i | \(0.574705\pi\) |
−0.972586 | + | 0.232543i | \(0.925295\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.42774 | + | 5.08219i | 0.311936 | + | 0.213432i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.9168 | 1.04457 | 0.522283 | − | 0.852772i | \(-0.325080\pi\) | ||||
0.522283 | + | 0.852772i | \(0.325080\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.2337 | 0.595662 | 0.297831 | − | 0.954619i | \(-0.403737\pi\) | ||||
0.297831 | + | 0.954619i | \(0.403737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.14440 | + | 3.30033i | 0.382013 | + | 0.137873i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.8426 | − | 14.8426i | 0.617906 | − | 0.617906i | −0.327088 | − | 0.944994i | \(-0.606067\pi\) |
0.944994 | + | 0.327088i | \(0.106067\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.6434 | + | 5.93736i | −0.525441 | + | 0.246748i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.16953i | 0.172981i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.3960 | + | 21.3960i | 0.886131 | + | 0.886131i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.26590 | + | 2.26590i | 0.0935238 | + | 0.0935238i | 0.752321 | − | 0.658797i | \(-0.228934\pi\) |
−0.658797 | + | 0.752321i | \(0.728934\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 14.4853i | − | 0.596856i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.52154 | + | 3.06253i | −0.268260 | + | 0.125975i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.49972 | + | 8.49972i | −0.349042 | + | 0.349042i | −0.859753 | − | 0.510711i | \(-0.829382\pi\) |
0.510711 | + | 0.859753i | \(0.329382\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 42.6407 | + | 15.3896i | 1.74517 | + | 0.629853i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.6550 | 1.37511 | 0.687553 | − | 0.726135i | \(-0.258685\pi\) | ||||
0.687553 | + | 0.726135i | \(0.258685\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.7503 | 1.78461 | 0.892305 | − | 0.451432i | \(-0.149087\pi\) | ||||
0.892305 | + | 0.451432i | \(0.149087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.4764 | + | 2.36772i | −1.03748 | + | 0.0964210i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.2869 | − | 12.2869i | 0.498708 | − | 0.498708i | −0.412328 | − | 0.911036i | \(-0.635284\pi\) |
0.911036 | + | 0.412328i | \(0.135284\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.03839 | + | 2.21121i | 0.0420776 | + | 0.0896028i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 41.1837i | − | 1.66611i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.8333 | + | 19.8333i | 0.801061 | + | 0.801061i | 0.983261 | − | 0.182201i | \(-0.0583221\pi\) |
−0.182201 | + | 0.983261i | \(0.558322\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.5403 | − | 12.5403i | −0.504852 | − | 0.504852i | 0.408090 | − | 0.912942i | \(-0.366195\pi\) |
−0.912942 | + | 0.408090i | \(0.866195\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 31.4704i | − | 1.26490i | −0.774600 | − | 0.632452i | \(-0.782049\pi\) | ||
0.774600 | − | 0.632452i | \(-0.217951\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.75798 | + | 18.3509i | −0.190931 | + | 0.736395i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.121851 | + | 0.121851i | −0.00488185 | + | 0.00488185i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.30457 | + | 6.38538i | −0.0920355 | + | 0.255008i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 70.3412 | 2.80469 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.7145 | −1.26254 | −0.631268 | − | 0.775565i | \(-0.717465\pi\) | ||||
−0.631268 | + | 0.775565i | \(0.717465\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.84369 | − | 10.6499i | 0.152773 | − | 0.423296i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.98864 | − | 2.98864i | 0.118414 | − | 0.118414i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.02879 | − | 10.8790i | 0.357173 | − | 0.430365i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.4067i | 0.687525i | 0.939057 | + | 0.343762i | \(0.111701\pi\) | ||||
−0.939057 | + | 0.343762i | \(0.888299\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.4684 | − | 16.4684i | −0.649449 | − | 0.649449i | 0.303411 | − | 0.952860i | \(-0.401875\pi\) |
−0.952860 | + | 0.303411i | \(0.901875\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.9808 | + | 11.9808i | 0.471012 | + | 0.471012i | 0.902242 | − | 0.431230i | \(-0.141920\pi\) |
−0.431230 | + | 0.902242i | \(0.641920\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.68204i | 0.340800i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.62373 | − | 14.1050i | −0.259604 | − | 0.552818i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.81877 | + | 7.81877i | −0.305972 | + | 0.305972i | −0.843345 | − | 0.537373i | \(-0.819417\pi\) |
0.537373 | + | 0.843345i | \(0.319417\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.95445 | + | 31.7896i | 0.115264 | + | 1.24023i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.2957 | 1.76447 | 0.882235 | − | 0.470810i | \(-0.156038\pi\) | ||||
0.882235 | + | 0.470810i | \(0.156038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.836250 | −0.0325263 | −0.0162632 | − | 0.999868i | \(-0.505177\pi\) | ||||
−0.0162632 | + | 0.999868i | \(0.505177\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 48.1706 | + | 17.3854i | 1.87079 | + | 0.675192i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.63857 | + | 3.63857i | −0.140886 | + | 0.140886i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.1269 | + | 5.22521i | −0.430191 | + | 0.202018i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 21.5188i | − | 0.830724i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.4215 | + | 27.4215i | 1.05702 | + | 1.05702i | 0.998273 | + | 0.0587488i | \(0.0187111\pi\) |
0.0587488 | + | 0.998273i | \(0.481289\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.26276 | + | 7.26276i | 0.279131 | + | 0.279131i | 0.832762 | − | 0.553631i | \(-0.186758\pi\) |
−0.553631 | + | 0.832762i | \(0.686758\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 13.2683i | − | 0.509192i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.0844 | − | 12.7189i | 1.03788 | − | 0.487388i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.6466 | + | 13.6466i | −0.522171 | + | 0.522171i | −0.918227 | − | 0.396055i | \(-0.870379\pi\) |
0.396055 | + | 0.918227i | \(0.370379\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.02323 | + | 1.45204i | 0.153496 | + | 0.0553986i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −52.5366 | −2.00149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.1089 | −0.384559 | −0.192280 | − | 0.981340i | \(-0.561588\pi\) | ||||
−0.192280 | + | 0.981340i | \(0.561588\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.675801 | + | 7.27156i | 0.0256716 | + | 0.276224i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.2271 | + | 22.2271i | −0.841913 | + | 0.841913i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.8439 | + | 27.3507i | 0.485802 | + | 1.03450i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 36.9379i | − | 1.39512i | −0.716525 | − | 0.697562i | \(-0.754268\pi\) | ||
0.716525 | − | 0.697562i | \(-0.245732\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.4476 | − | 11.4476i | −0.431755 | − | 0.431755i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.04269 | − | 5.04269i | −0.189650 | − | 0.189650i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.5205i | 1.48423i | 0.670275 | + | 0.742113i | \(0.266176\pi\) | ||||
−0.670275 | + | 0.742113i | \(0.733824\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.22510 | − | 2.68107i | 0.0834479 | − | 0.100548i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 23.2099 | − | 23.2099i | 0.869218 | − | 0.869218i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.64121 | − | 15.6304i | 0.210675 | − | 0.583728i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −17.8781 | −0.666740 | −0.333370 | − | 0.942796i | \(-0.608186\pi\) | ||||
−0.333370 | + | 0.942796i | \(0.608186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.9142 | −0.443709 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.64387 | − | 7.32551i | 0.0983266 | − | 0.272439i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1939 | − | 12.1939i | 0.452245 | − | 0.452245i | −0.443854 | − | 0.896099i | \(-0.646389\pi\) |
0.896099 | + | 0.443854i | \(0.146389\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.1191 | − | 23.5985i | 0.485892 | − | 0.874019i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.4549i | 1.71820i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.7602 | − | 21.7602i | −0.803732 | − | 0.803732i | 0.179945 | − | 0.983677i | \(-0.442408\pi\) |
−0.983677 | + | 0.179945i | \(0.942408\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.6806 | − | 14.6806i | −0.540767 | − | 0.540767i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 14.3075i | − | 0.526310i | −0.964754 | − | 0.263155i | \(-0.915237\pi\) | ||
0.964754 | − | 0.263155i | \(-0.0847630\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.01011 | − | 10.6688i | −0.184051 | − | 0.391930i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.38543 | + | 7.38543i | −0.270945 | + | 0.270945i | −0.829481 | − | 0.558535i | \(-0.811363\pi\) |
0.558535 | + | 0.829481i | \(0.311363\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.4549 | − | 1.15753i | 0.455702 | − | 0.0423518i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.65300 | −0.133478 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.5508 | −0.713419 | −0.356710 | − | 0.934215i | \(-0.616101\pi\) | ||||
−0.356710 | + | 0.934215i | \(0.616101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.0782 | − | 7.96829i | −0.804573 | − | 0.290381i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.2828 | + | 28.2828i | −1.02796 | + | 1.02796i | −0.0283579 | + | 0.999598i | \(0.509028\pi\) |
−0.999598 | + | 0.0283579i | \(0.990972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.9240 | + | 6.53873i | −0.505409 | + | 0.237341i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 21.8245i | − | 0.791138i | −0.918436 | − | 0.395569i | \(-0.870547\pi\) | ||
0.918436 | − | 0.395569i | \(-0.129453\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.819426 | + | 0.819426i | 0.0296652 | + | 0.0296652i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.6591 | − | 10.6591i | −0.384879 | − | 0.384879i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 21.0365i | − | 0.758595i | −0.925275 | − | 0.379298i | \(-0.876166\pi\) | ||
0.925275 | − | 0.379298i | \(-0.123834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −33.9173 | + | 15.9276i | −1.22150 | + | 0.573619i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.4974 | + | 11.4974i | −0.413533 | + | 0.413533i | −0.882967 | − | 0.469434i | \(-0.844458\pi\) |
0.469434 | + | 0.882967i | \(0.344458\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.3817 | − | 5.91238i | −0.587692 | − | 0.212105i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.23467 | 0.259209 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.4717 | 0.410489 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.31689 | − | 3.71567i | 0.225747 | − | 0.132787i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.7791 | − | 29.7791i | 1.06151 | − | 1.06151i | 0.0635285 | − | 0.997980i | \(-0.479765\pi\) |
0.997980 | − | 0.0635285i | \(-0.0202354\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.5968 | − | 39.6011i | −0.662062 | − | 1.40984i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.62352i | 0.0932817i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.4191 | + | 26.4191i | 0.938170 | + | 0.938170i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.2146 | − | 18.2146i | −0.645194 | − | 0.645194i | 0.306634 | − | 0.951828i | \(-0.400797\pi\) |
−0.951828 | + | 0.306634i | \(0.900797\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 68.1644i | 2.41148i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.397812 | + | 0.330156i | 0.0140560 | + | 0.0116655i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.3185 | + | 18.3185i | −0.646446 | + | 0.646446i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.8597 | − | 38.4017i | 0.487883 | − | 1.35180i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.6294 | −1.14719 | −0.573594 | − | 0.819140i | \(-0.694451\pi\) | ||||
−0.573594 | + | 0.819140i | \(0.694451\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.3733 | 0.820749 | 0.410375 | − | 0.911917i | \(-0.365398\pi\) | ||||
0.410375 | + | 0.911917i | \(0.365398\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.8016 | − | 41.0116i | 0.519115 | − | 1.43834i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.56027 | − | 7.56027i | 0.264500 | − | 0.264500i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.75715 | − | 8.09776i | −0.340942 | − | 0.282958i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.48918i | 0.121773i | 0.998145 | + | 0.0608867i | \(0.0193928\pi\) | ||||
−0.998145 | + | 0.0608867i | \(0.980607\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.0664 | − | 23.0664i | −0.804045 | − | 0.804045i | 0.179680 | − | 0.983725i | \(-0.442494\pi\) |
−0.983725 | + | 0.179680i | \(0.942494\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.1289 | + | 18.1289i | 0.630404 | + | 0.630404i | 0.948169 | − | 0.317765i | \(-0.102932\pi\) |
−0.317765 | + | 0.948169i | \(0.602932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.54620i | 0.262091i | 0.991376 | + | 0.131045i | \(0.0418333\pi\) | ||||
−0.991376 | + | 0.131045i | \(0.958167\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.931812 | + | 1.98426i | 0.0323242 | + | 0.0688332i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.94659 | + | 4.94659i | −0.171389 | + | 0.171389i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.2945 | + | 23.7017i | −1.39278 | + | 0.819250i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.3150 | −0.597780 | −0.298890 | − | 0.954288i | \(-0.596616\pi\) | ||||
−0.298890 | + | 0.954288i | \(0.596616\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.0108 | −0.931406 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.7028 | − | 6.75008i | −0.644159 | − | 0.232485i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.58800 | − | 3.58800i | 0.123285 | − | 0.123285i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.5414 | − | 6.35905i | 0.464738 | − | 0.218242i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 36.6852i | − | 1.25755i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.87944 | − | 4.87944i | −0.167069 | − | 0.167069i | 0.618621 | − | 0.785690i | \(-0.287692\pi\) |
−0.785690 | + | 0.618621i | \(0.787692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.1962 | − | 10.1962i | −0.348296 | − | 0.348296i | 0.511178 | − | 0.859475i | \(-0.329209\pi\) |
−0.859475 | + | 0.511178i | \(0.829209\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 43.7659i | − | 1.49327i | −0.665231 | − | 0.746637i | \(-0.731667\pi\) | ||
0.665231 | − | 0.746637i | \(-0.268333\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.04473 | − | 3.30822i | 0.240084 | − | 0.112744i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.65231 | − | 9.65231i | 0.328569 | − | 0.328569i | −0.523473 | − | 0.852042i | \(-0.675364\pi\) |
0.852042 | + | 0.523473i | \(0.175364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −52.0324 | − | 18.7792i | −1.76711 | − | 0.637774i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.82714 | 0.0959042 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.0474 | 1.22142 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −39.6342 | + | 3.68351i | −1.34141 | + | 0.124668i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.6620 | − | 28.6620i | 0.967848 | − | 0.967848i | −0.0316508 | − | 0.999499i | \(-0.510076\pi\) |
0.999499 | + | 0.0316508i | \(0.0100764\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.4086 | + | 24.2942i | 0.384803 | + | 0.819424i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.5710i | 0.962583i | 0.876561 | + | 0.481291i | \(0.159832\pi\) | ||||
−0.876561 | + | 0.481291i | \(0.840168\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.9387 | − | 21.9387i | −0.738297 | − | 0.738297i | 0.233952 | − | 0.972248i | \(-0.424834\pi\) |
−0.972248 | + | 0.233952i | \(0.924834\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.26720 | − | 5.26720i | −0.176855 | − | 0.176855i | 0.613128 | − | 0.789983i | \(-0.289911\pi\) |
−0.789983 | + | 0.613128i | \(0.789911\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.29750i | 0.110595i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.5335 | − | 4.03741i | 0.721398 | − | 0.135258i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.0934 | − | 11.0934i | 0.371225 | − | 0.371225i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.06704 | − | 25.1225i | 0.302740 | − | 0.838817i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.6890 | −0.423203 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 86.9550 | 2.89689 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.90467 | − | 10.8189i | 0.129939 | − | 0.360030i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.47086 | − | 5.47086i | 0.181657 | − | 0.181657i | −0.610421 | − | 0.792077i | \(-0.709000\pi\) |
0.792077 | + | 0.610421i | \(0.209000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.6632 | + | 16.4631i | −0.453180 | + | 0.546046i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.74155i | 0.256489i | 0.991743 | + | 0.128244i | \(0.0409342\pi\) | ||||
−0.991743 | + | 0.128244i | \(0.959066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.17705 | + | 7.17705i | 0.237526 | + | 0.237526i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.38892 | − | 4.38892i | −0.144935 | − | 0.144935i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.4209i | 0.838557i | 0.907858 | + | 0.419278i | \(0.137717\pi\) | ||||
−0.907858 | + | 0.419278i | \(0.862283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.420438 | + | 0.895308i | 0.0138539 | + | 0.0295014i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.0840 | + | 14.0840i | −0.463582 | + | 0.463582i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.30758 | + | 35.5893i | 0.108635 | + | 1.16891i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.5656 | −1.56058 | −0.780289 | − | 0.625419i | \(-0.784928\pi\) | ||||
−0.780289 | + | 0.625419i | \(0.784928\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.61006 | 0.0527675 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −38.8969 | − | 14.0384i | −1.27343 | − | 0.459596i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.39983 | − | 9.39983i | 0.307079 | − | 0.307079i | −0.536696 | − | 0.843775i | \(-0.680328\pi\) |
0.843775 | + | 0.536696i | \(0.180328\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.06992 | + | 0.972038i | −0.0675492 | + | 0.0317213i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.36091i | 0.239959i | 0.992776 | + | 0.119979i | \(0.0382828\pi\) | ||||
−0.992776 | + | 0.119979i | \(0.961717\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.5922 | + | 11.5922i | 0.377494 | + | 0.377494i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.1921 | + | 15.1921i | 0.493678 | + | 0.493678i | 0.909463 | − | 0.415785i | \(-0.136493\pi\) |
−0.415785 | + | 0.909463i | \(0.636493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 44.9801i | − | 1.46011i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.9739 | + | 10.7886i | −0.744981 | + | 0.349845i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.4626 | − | 17.4626i | 0.565670 | − | 0.565670i | −0.365242 | − | 0.930913i | \(-0.619014\pi\) |
0.930913 | + | 0.365242i | \(0.119014\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.59356 | + | 2.01879i | 0.180814 | + | 0.0652581i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.53617 | −0.243356 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.9414 | 1.61101 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.01413 | + | 10.9120i | 0.0326800 | + | 0.351634i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.0684 | + | 23.0684i | −0.741828 | + | 0.741828i | −0.972930 | − | 0.231101i | \(-0.925767\pi\) |
0.231101 | + | 0.972930i | \(0.425767\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.29239 | + | 17.6583i | 0.266390 | + | 0.567268i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.29785i | 0.0737415i | 0.999320 | + | 0.0368707i | \(0.0117390\pi\) | ||||
−0.999320 | + | 0.0368707i | \(0.988261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.17076 | + | 7.17076i | 0.229884 | + | 0.229884i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.29551 | − | 8.29551i | −0.265397 | − | 0.265397i | 0.561845 | − | 0.827242i | \(-0.310092\pi\) |
−0.827242 | + | 0.561845i | \(0.810092\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.419486i | 0.0134068i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.22024 | − | 2.67521i | 0.0708869 | − | 0.0854130i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.75732 | + | 6.75732i | −0.215525 | + | 0.215525i | −0.806610 | − | 0.591085i | \(-0.798700\pi\) |
0.591085 | + | 0.806610i | \(0.298700\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.72942 | − | 15.8748i | 0.182369 | − | 0.505300i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.2278 | 0.770398 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.89708 | 0.0920287 | 0.0460143 | − | 0.998941i | \(-0.485348\pi\) | ||||
0.0460143 | + | 0.998941i | \(0.485348\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.04446 | + | 2.89394i | −0.0331449 | + | 0.0918363i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.587263 | − | 0.587263i | 0.0185988 | − | 0.0185988i | −0.697746 | − | 0.716345i | \(-0.745814\pi\) |
0.716345 | + | 0.697746i | \(0.245814\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.1132 | + | 50.5757i | −0.414883 | + | 1.60015i |
(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 | 2100.2.s.b.1793.5 | 24 | ||
3.2 | odd | 2 | inner | 2100.2.s.b.1793.11 | 24 | ||
5.2 | odd | 4 | inner | 2100.2.s.b.1457.11 | 24 | ||
5.3 | odd | 4 | 420.2.s.a.197.2 | yes | 24 | ||
5.4 | even | 2 | 420.2.s.a.113.8 | yes | 24 | ||
15.2 | even | 4 | inner | 2100.2.s.b.1457.5 | 24 | ||
15.8 | even | 4 | 420.2.s.a.197.8 | yes | 24 | ||
15.14 | odd | 2 | 420.2.s.a.113.2 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.s.a.113.2 | ✓ | 24 | 15.14 | odd | 2 | ||
420.2.s.a.113.8 | yes | 24 | 5.4 | even | 2 | ||
420.2.s.a.197.2 | yes | 24 | 5.3 | odd | 4 | ||
420.2.s.a.197.8 | yes | 24 | 15.8 | even | 4 | ||
2100.2.s.b.1457.5 | 24 | 15.2 | even | 4 | inner | ||
2100.2.s.b.1457.11 | 24 | 5.2 | odd | 4 | inner | ||
2100.2.s.b.1793.5 | 24 | 1.1 | even | 1 | trivial | ||
2100.2.s.b.1793.11 | 24 | 3.2 | odd | 2 | inner |