Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(301,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.m (of order \(5\), degree \(4\), 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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 601.4 | ||
Character | \(\chi\) | \(=\) | 1500.601 |
Dual form | 1500.2.m.d.901.4 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.809017 | + | 0.587785i | 0.467086 | + | 0.339358i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.957526 | 0.361911 | 0.180955 | − | 0.983491i | \(-0.442081\pi\) | ||||
0.180955 | + | 0.983491i | \(0.442081\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.309017 | + | 0.951057i | 0.103006 | + | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.67360 | + | 5.15082i | −0.504611 | + | 1.55303i | 0.296814 | + | 0.954935i | \(0.404076\pi\) |
−0.801424 | + | 0.598096i | \(0.795924\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.625052 | + | 1.92371i | 0.173358 | + | 0.533542i | 0.999555 | − | 0.0298404i | \(-0.00949990\pi\) |
−0.826196 | + | 0.563382i | \(0.809500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.520090 | + | 0.377867i | −0.126140 | + | 0.0916463i | −0.649067 | − | 0.760732i | \(-0.724840\pi\) |
0.522926 | + | 0.852378i | \(0.324840\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.07829 | − | 2.96305i | 0.935625 | − | 0.679771i | −0.0117388 | − | 0.999931i | \(-0.503737\pi\) |
0.947364 | + | 0.320160i | \(0.103737\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.774655 | + | 0.562820i | 0.169044 | + | 0.122817i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.08762 | + | 3.34734i | −0.226784 | + | 0.697969i | 0.771322 | + | 0.636445i | \(0.219596\pi\) |
−0.998106 | + | 0.0615235i | \(0.980404\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.309017 | + | 0.951057i | −0.0594703 | + | 0.183031i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.20405 | − | 5.96059i | −1.52345 | − | 1.10685i | −0.959742 | − | 0.280882i | \(-0.909373\pi\) |
−0.563712 | − | 0.825972i | \(-0.690627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.98671 | + | 2.16997i | −0.536429 | + | 0.389738i | −0.822757 | − | 0.568393i | \(-0.807565\pi\) |
0.286328 | + | 0.958132i | \(0.407565\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.38155 | + | 3.18338i | −0.762730 | + | 0.554156i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.49663 | + | 10.7615i | 0.574842 | + | 1.76918i | 0.636717 | + | 0.771097i | \(0.280292\pi\) |
−0.0618753 | + | 0.998084i | \(0.519708\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.625052 | + | 1.92371i | −0.100088 | + | 0.308040i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.08859 | + | 3.35035i | 0.170010 | + | 0.523237i | 0.999370 | − | 0.0354770i | \(-0.0112950\pi\) |
−0.829361 | + | 0.558714i | \(0.811295\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.766348 | −0.116867 | −0.0584335 | − | 0.998291i | \(-0.518611\pi\) | ||||
−0.0584335 | + | 0.998291i | \(0.518611\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.99186 | + | 2.90026i | 0.582273 | + | 0.423046i | 0.839543 | − | 0.543293i | \(-0.182823\pi\) |
−0.257270 | + | 0.966340i | \(0.582823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.08314 | −0.869021 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.642866 | −0.0900193 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.81069 | + | 3.49517i | 0.660799 | + | 0.480099i | 0.866933 | − | 0.498425i | \(-0.166088\pi\) |
−0.206134 | + | 0.978524i | \(0.566088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.04105 | 0.667703 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.45818 | + | 4.48783i | 0.189839 | + | 0.584265i | 0.999998 | − | 0.00194529i | \(-0.000619206\pi\) |
−0.810159 | + | 0.586210i | \(0.800619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.34263 | − | 4.13219i | 0.171906 | − | 0.529073i | −0.827572 | − | 0.561359i | \(-0.810279\pi\) |
0.999479 | + | 0.0322858i | \(0.0102787\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.295892 | + | 0.910662i | 0.0372789 | + | 0.114733i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.70005 | − | 5.59441i | 0.940711 | − | 0.683466i | −0.00788103 | − | 0.999969i | \(-0.502509\pi\) |
0.948592 | + | 0.316503i | \(0.102509\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.84742 | + | 2.06877i | −0.342789 | + | 0.249051i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.66368 | + | 7.02107i | 1.14687 | + | 0.833248i | 0.988061 | − | 0.154062i | \(-0.0492354\pi\) |
0.158806 | + | 0.987310i | \(0.449235\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.67890 | − | 5.16713i | 0.196500 | − | 0.604766i | −0.803455 | − | 0.595365i | \(-0.797007\pi\) |
0.999956 | − | 0.00940128i | \(-0.00299256\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.60252 | + | 4.93205i | −0.182624 | + | 0.562059i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.58637 | − | 6.96491i | −1.07855 | − | 0.783613i | −0.101122 | − | 0.994874i | \(-0.532243\pi\) |
−0.977430 | + | 0.211261i | \(0.932243\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.12784 | + | 0.819420i | −0.123796 | + | 0.0899431i | −0.647960 | − | 0.761674i | \(-0.724378\pi\) |
0.524164 | + | 0.851617i | \(0.324378\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.13367 | − | 9.64444i | −0.335965 | − | 1.03399i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.527839 | + | 1.62452i | −0.0559508 | + | 0.172199i | −0.975127 | − | 0.221649i | \(-0.928856\pi\) |
0.919176 | + | 0.393847i | \(0.128856\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.598504 | + | 1.84200i | 0.0627402 | + | 0.193095i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.69178 | −0.382819 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.8018 | + | 8.57451i | 1.19829 | + | 0.870610i | 0.994116 | − | 0.108325i | \(-0.0345486\pi\) |
0.204176 | + | 0.978934i | \(0.434549\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.41590 | −0.544318 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.2832 | −1.02322 | −0.511610 | − | 0.859218i | \(-0.670951\pi\) | ||||
−0.511610 | + | 0.859218i | \(0.670951\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.3140 | + | 8.22008i | 1.11480 | + | 0.809949i | 0.983413 | − | 0.181383i | \(-0.0580573\pi\) |
0.131386 | + | 0.991331i | \(0.458057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.06727 | −0.876566 | −0.438283 | − | 0.898837i | \(-0.644413\pi\) | ||||
−0.438283 | + | 0.898837i | \(0.644413\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.734025 | + | 2.25910i | 0.0703068 | + | 0.216382i | 0.980036 | − | 0.198820i | \(-0.0637109\pi\) |
−0.909729 | + | 0.415202i | \(0.863711\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.49663 | + | 10.7615i | −0.331885 | + | 1.02144i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.15238 | + | 12.7797i | 0.390623 | + | 1.20221i | 0.932318 | + | 0.361638i | \(0.117782\pi\) |
−0.541696 | + | 0.840575i | \(0.682218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.63641 | + | 1.18892i | −0.151286 | + | 0.109916i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.498000 | + | 0.361818i | −0.0456515 | + | 0.0331678i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14.8308 | − | 10.7752i | −1.34826 | − | 0.979567i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.08859 | + | 3.35035i | −0.0981553 | + | 0.302091i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.40749 | + | 13.5648i | −0.391101 | + | 1.20369i | 0.540855 | + | 0.841116i | \(0.318101\pi\) |
−0.931957 | + | 0.362570i | \(0.881899\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.619989 | − | 0.450448i | −0.0545869 | − | 0.0396597i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.104093 | − | 0.0756282i | 0.00909468 | − | 0.00660767i | −0.583229 | − | 0.812308i | \(-0.698211\pi\) |
0.592323 | + | 0.805700i | \(0.298211\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.90507 | − | 2.83720i | 0.338613 | − | 0.246017i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.23423 | − | 13.0316i | −0.361754 | − | 1.11337i | −0.951989 | − | 0.306133i | \(-0.900965\pi\) |
0.590234 | − | 0.807232i | \(-0.299035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.25318 | − | 22.3230i | 0.615206 | − | 1.89341i | 0.216731 | − | 0.976231i | \(-0.430461\pi\) |
0.398475 | − | 0.917179i | \(-0.369539\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.52476 | + | 4.69272i | 0.128408 | + | 0.395198i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.9548 | −0.916086 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.92137 | − | 3.57558i | −0.405907 | − | 0.294909i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.6938 | −0.876071 | −0.438035 | − | 0.898958i | \(-0.644326\pi\) | ||||
−0.438035 | + | 0.898958i | \(0.644326\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.37520 | 0.600185 | 0.300092 | − | 0.953910i | \(-0.402982\pi\) | ||||
0.300092 | + | 0.953910i | \(0.402982\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.520090 | − | 0.377867i | −0.0420468 | − | 0.0305488i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.0329 | −1.04014 | −0.520070 | − | 0.854124i | \(-0.674094\pi\) | ||||
−0.520070 | + | 0.854124i | \(0.674094\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.83752 | + | 5.65531i | 0.145725 | + | 0.448495i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.04142 | + | 3.20517i | −0.0820755 | + | 0.252603i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.28549 | − | 7.03403i | −0.179014 | − | 0.550948i | 0.820780 | − | 0.571244i | \(-0.193539\pi\) |
−0.999794 | + | 0.0202964i | \(0.993539\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.2827 | − | 11.8301i | 1.25999 | − | 0.915438i | 0.261235 | − | 0.965275i | \(-0.415870\pi\) |
0.998757 | + | 0.0498368i | \(0.0158701\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.20724 | − | 5.23637i | 0.554403 | − | 0.402798i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.07829 | + | 2.96305i | 0.311875 | + | 0.226590i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.686365 | − | 2.11241i | 0.0521833 | − | 0.160604i | −0.921569 | − | 0.388215i | \(-0.873092\pi\) |
0.973752 | + | 0.227612i | \(0.0730916\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.45818 | + | 4.48783i | −0.109604 | + | 0.337326i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0312215 | + | 0.0226837i | 0.00233360 | + | 0.00169546i | 0.588951 | − | 0.808168i | \(-0.299541\pi\) |
−0.586618 | + | 0.809864i | \(0.699541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.118881 | + | 0.0863720i | −0.00883634 | + | 0.00641998i | −0.592195 | − | 0.805795i | \(-0.701738\pi\) |
0.583358 | + | 0.812215i | \(0.301738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.51505 | − | 2.55384i | 0.259840 | − | 0.188785i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.07590 | − | 3.31129i | −0.0786779 | − | 0.242146i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.295892 | + | 0.910662i | −0.0215230 | + | 0.0662409i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.142049 | − | 0.437183i | −0.0102783 | − | 0.0316335i | 0.945786 | − | 0.324791i | \(-0.105294\pi\) |
−0.956064 | + | 0.293158i | \(0.905294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.0231 | 1.36932 | 0.684658 | − | 0.728864i | \(-0.259952\pi\) | ||||
0.684658 | + | 0.728864i | \(0.259952\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.80131 | + | 7.12107i | 0.698315 | + | 0.507355i | 0.879383 | − | 0.476115i | \(-0.157955\pi\) |
−0.181068 | + | 0.983471i | \(0.557955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.4872 | 1.16875 | 0.584375 | − | 0.811484i | \(-0.301340\pi\) | ||||
0.584375 | + | 0.811484i | \(0.301340\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.51778 | 0.671333 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.85559 | − | 5.70742i | −0.551355 | − | 0.400583i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.51960 | −0.244629 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.43672 | + | 25.9656i | 0.583580 | + | 1.79607i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.61985 | − | 17.2961i | 0.386887 | − | 1.19071i | −0.548216 | − | 0.836337i | \(-0.684693\pi\) |
0.935102 | − | 0.354378i | \(-0.115307\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.69120 | + | 11.3603i | 0.252917 | + | 0.778397i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.85985 | + | 2.07780i | −0.194139 | + | 0.141051i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.39542 | − | 3.19346i | 0.297015 | − | 0.215794i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.05199 | − | 0.764316i | −0.0707646 | − | 0.0514135i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.26507 | − | 22.3596i | 0.486505 | − | 1.49731i | −0.343284 | − | 0.939231i | \(-0.611539\pi\) |
0.829789 | − | 0.558077i | \(-0.188461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.08155 | − | 18.7171i | 0.403647 | − | 1.24230i | −0.518373 | − | 0.855154i | \(-0.673462\pi\) |
0.922020 | − | 0.387142i | \(-0.126538\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.29343 | − | 3.11936i | −0.283718 | − | 0.206133i | 0.436819 | − | 0.899549i | \(-0.356105\pi\) |
−0.720538 | + | 0.693416i | \(0.756105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.19545 | + | 3.04817i | −0.276040 | + | 0.200555i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.8253 | + | 13.6774i | −1.23329 | + | 0.896034i | −0.997132 | − | 0.0756813i | \(-0.975887\pi\) |
−0.236154 | + | 0.971716i | \(0.575887\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.66167 | − | 11.2695i | −0.237851 | − | 0.732030i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.65842 | + | 14.3371i | −0.301328 | + | 0.927392i | 0.679694 | + | 0.733496i | \(0.262113\pi\) |
−0.981022 | + | 0.193897i | \(0.937887\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.84454 | − | 17.9877i | −0.376480 | − | 1.15869i | −0.942475 | − | 0.334278i | \(-0.891508\pi\) |
0.565995 | − | 0.824409i | \(-0.308492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.24921 | + | 5.99340i | 0.524885 | + | 0.381351i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.39408 | −0.0883463 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.56761 | −0.288305 | −0.144153 | − | 0.989555i | \(-0.546046\pi\) | ||||
−0.144153 | + | 0.989555i | \(0.546046\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.4213 | − | 11.2042i | −0.969530 | − | 0.704405i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.2556 | −1.26351 | −0.631754 | − | 0.775169i | \(-0.717665\pi\) | ||||
−0.631754 | + | 0.775169i | \(0.717665\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.34811 | + | 10.3044i | 0.208042 | + | 0.640286i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.13367 | − | 9.64444i | 0.193969 | − | 0.596976i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.51119 | − | 29.2724i | −0.586485 | − | 1.80502i | −0.593223 | − | 0.805038i | \(-0.702145\pi\) |
0.00673789 | − | 0.999977i | \(-0.497855\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.38190 | + | 1.00401i | −0.0845709 | + | 0.0614443i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.5796 | − | 15.6785i | 1.31573 | − | 0.955936i | 0.315758 | − | 0.948840i | \(-0.397741\pi\) |
0.999975 | − | 0.00709610i | \(-0.00225878\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.47342 | + | 3.25013i | 0.271741 | + | 0.197431i | 0.715307 | − | 0.698810i | \(-0.246287\pi\) |
−0.443566 | + | 0.896242i | \(0.646287\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.598504 | + | 1.84200i | −0.0362231 | + | 0.111483i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.55583 | + | 29.4098i | −0.574154 | + | 1.76706i | 0.0648872 | + | 0.997893i | \(0.479331\pi\) |
−0.639041 | + | 0.769172i | \(0.720669\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.98671 | − | 2.16997i | −0.178810 | − | 0.129913i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.6310 | − | 9.90352i | 0.813159 | − | 0.590795i | −0.101586 | − | 0.994827i | \(-0.532392\pi\) |
0.914745 | + | 0.404032i | \(0.132392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.11176 | − | 6.62008i | 0.541638 | − | 0.393523i | −0.283055 | − | 0.959104i | \(-0.591348\pi\) |
0.824693 | + | 0.565581i | \(0.191348\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.04236 | + | 3.20805i | 0.0615285 | + | 0.189365i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.12558 | + | 15.7749i | −0.301505 | + | 0.927936i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.50789 | + | 13.8738i | 0.264257 | + | 0.813299i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.1995 | −0.654284 | −0.327142 | − | 0.944975i | \(-0.606086\pi\) | ||||
−0.327142 | + | 0.944975i | \(0.606086\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.38155 | − | 3.18338i | −0.254243 | − | 0.184719i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.11914 | −0.411710 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.733798 | −0.0422954 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.31931 | − | 6.04433i | −0.477932 | − | 0.347238i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.1289 | 1.37711 | 0.688554 | − | 0.725185i | \(-0.258246\pi\) | ||||
0.688554 | + | 0.725185i | \(0.258246\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.32155 | + | 13.3004i | 0.245844 | + | 0.756632i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.640628 | − | 1.97165i | 0.0363267 | − | 0.111802i | −0.931249 | − | 0.364384i | \(-0.881280\pi\) |
0.967576 | + | 0.252582i | \(0.0812797\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.63272 | − | 8.10268i | −0.148810 | − | 0.457991i | 0.848671 | − | 0.528921i | \(-0.177403\pi\) |
−0.997481 | + | 0.0709303i | \(0.977403\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.0083 | + | 7.99798i | −0.618286 | + | 0.449211i | −0.852322 | − | 0.523017i | \(-0.824806\pi\) |
0.234036 | + | 0.972228i | \(0.424806\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 44.4323 | − | 32.2819i | 2.48773 | − | 1.80744i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.33558 | − | 5.32961i | −0.409432 | − | 0.297470i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.00144 | + | 3.08211i | −0.0557215 | + | 0.171493i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.734025 | + | 2.25910i | −0.0405917 | + | 0.124928i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.82231 | + | 2.77707i | 0.210731 | + | 0.153105i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.3097 | − | 13.3028i | 1.00639 | − | 0.731187i | 0.0429430 | − | 0.999078i | \(-0.486327\pi\) |
0.963449 | + | 0.267891i | \(0.0863266\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.15429 | + | 6.65098i | −0.501652 | + | 0.364471i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1215 | − | 34.2285i | −0.605828 | − | 1.86455i | −0.490997 | − | 0.871161i | \(-0.663367\pi\) |
−0.114831 | − | 0.993385i | \(-0.536633\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.15238 | + | 12.7797i | −0.225526 | + | 0.694098i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.17857 | − | 19.0157i | −0.334588 | − | 1.02976i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.5275 | −0.676419 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.25158 | − | 5.26858i | −0.389285 | − | 0.282832i | 0.375877 | − | 0.926669i | \(-0.377341\pi\) |
−0.765162 | + | 0.643837i | \(0.777341\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8276 | −0.633114 | −0.316557 | − | 0.948573i | \(-0.602527\pi\) | ||||
−0.316557 | + | 0.948573i | \(0.602527\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.02271 | −0.107964 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.6791 | + | 13.5712i | 0.994188 | + | 0.722320i | 0.960834 | − | 0.277124i | \(-0.0893812\pi\) |
0.0333537 | + | 0.999444i | \(0.489381\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.615561 | −0.0325790 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.52607 | + | 20.0852i | 0.344433 | + | 1.06005i | 0.961887 | + | 0.273448i | \(0.0881641\pi\) |
−0.617454 | + | 0.786607i | \(0.711836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.98147 | − | 6.09833i | 0.104288 | − | 0.320965i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.66488 | − | 17.4347i | −0.297329 | − | 0.915085i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.78801 | − | 4.93178i | 0.354331 | − | 0.257437i | −0.396353 | − | 0.918098i | \(-0.629724\pi\) |
0.750684 | + | 0.660662i | \(0.229724\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.84998 | + | 2.07063i | −0.148364 | + | 0.107793i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.60636 | + | 3.34672i | 0.239150 | + | 0.173753i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.95565 | + | 6.01888i | −0.101260 | + | 0.311646i | −0.988834 | − | 0.149018i | \(-0.952389\pi\) |
0.887575 | + | 0.460664i | \(0.152389\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.33850 | − | 19.5079i | 0.326450 | − | 1.00471i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.1990 | − | 8.86310i | −0.626621 | − | 0.455267i | 0.228607 | − | 0.973519i | \(-0.426583\pi\) |
−0.855228 | + | 0.518252i | \(0.826583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.5389 | + | 8.38354i | −0.591158 | + | 0.429502i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 26.3563 | − | 19.1490i | 1.34674 | − | 0.978466i | 0.347576 | − | 0.937652i | \(-0.387005\pi\) |
0.999167 | − | 0.0408145i | \(-0.0129953\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.236815 | − | 0.728840i | −0.0120380 | − | 0.0370490i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.69084 | + | 5.20388i | −0.0857292 | + | 0.263847i | −0.984727 | − | 0.174106i | \(-0.944296\pi\) |
0.898998 | + | 0.437953i | \(0.144296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.699192 | − | 2.15189i | −0.0353597 | − | 0.108826i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.128666 | 0.00649036 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.5435 | − | 8.38686i | −0.579353 | − | 0.420925i | 0.259138 | − | 0.965840i | \(-0.416562\pi\) |
−0.838491 | + | 0.544916i | \(0.816562\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.82694 | 0.241649 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.8291 | 0.890342 | 0.445171 | − | 0.895446i | \(-0.353143\pi\) | ||||
0.445171 | + | 0.895446i | \(0.353143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.04125 | − | 4.38923i | −0.300936 | − | 0.218643i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −61.2826 | −3.03767 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.42964 | + | 22.8661i | 0.367372 | + | 1.13065i | 0.948482 | + | 0.316830i | \(0.102618\pi\) |
−0.581110 | + | 0.813825i | \(0.697382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.23423 | − | 13.0316i | 0.208859 | − | 0.642802i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.39625 | + | 4.29721i | 0.0687049 | + | 0.211452i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 18.9891 | − | 13.7964i | 0.929898 | − | 0.675611i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.7180 | − | 16.5056i | 1.10984 | − | 0.806349i | 0.127206 | − | 0.991876i | \(-0.459399\pi\) |
0.982639 | + | 0.185527i | \(0.0593992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.3383 | − | 11.8704i | −0.796278 | − | 0.578530i | 0.113542 | − | 0.993533i | \(-0.463780\pi\) |
−0.909820 | + | 0.415003i | \(0.863780\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.52476 | + | 4.69272i | −0.0741362 | + | 0.228168i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.28560 | − | 3.95668i | 0.0622148 | − | 0.191477i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.86261 | − | 6.43907i | −0.427891 | − | 0.310881i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.35912 | − | 2.44055i | 0.161803 | − | 0.117557i | −0.503937 | − | 0.863740i | \(-0.668116\pi\) |
0.665741 | + | 0.746183i | \(0.268116\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.5295 | − | 17.8217i | 1.17881 | − | 0.856456i | 0.186773 | − | 0.982403i | \(-0.440197\pi\) |
0.992037 | + | 0.125947i | \(0.0401970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.48273 | + | 16.8741i | 0.262275 | + | 0.807198i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.984067 | + | 3.02865i | −0.0469670 | + | 0.144549i | −0.971790 | − | 0.235849i | \(-0.924213\pi\) |
0.924823 | + | 0.380398i | \(0.124213\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.87979 | − | 5.78541i | −0.0895140 | − | 0.275496i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.4607 | 1.44723 | 0.723615 | − | 0.690204i | \(-0.242479\pi\) | ||||
0.723615 | + | 0.690204i | \(0.242479\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.65147 | − | 6.28566i | −0.409201 | − | 0.297302i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.35787 | 0.0640820 | 0.0320410 | − | 0.999487i | \(-0.489799\pi\) | ||||
0.0320410 | + | 0.999487i | \(0.489799\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.0789 | −0.898392 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.96666 | + | 4.33503i | 0.280338 | + | 0.203678i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.89208 | 0.462732 | 0.231366 | − | 0.972867i | \(-0.425680\pi\) | ||||
0.231366 | + | 0.972867i | \(0.425680\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.198657 | − | 0.611402i | −0.00927250 | − | 0.0285378i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.51515 | + | 20.0516i | −0.303441 | + | 0.933894i | 0.676814 | + | 0.736154i | \(0.263360\pi\) |
−0.980255 | + | 0.197740i | \(0.936640\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.158879 | − | 0.488978i | −0.00738372 | − | 0.0227248i | 0.947297 | − | 0.320357i | \(-0.103803\pi\) |
−0.954681 | + | 0.297633i | \(0.903803\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.0267 | − | 10.9175i | 0.695352 | − | 0.505202i | −0.183063 | − | 0.983101i | \(-0.558601\pi\) |
0.878415 | + | 0.477899i | \(0.158601\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.37300 | − | 5.35680i | 0.340453 | − | 0.247354i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.5439 | − | 7.66056i | −0.485835 | − | 0.352980i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.28256 | − | 3.94732i | 0.0589723 | − | 0.181498i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.83752 | + | 5.65531i | −0.0841343 | + | 0.258939i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.3847 | − | 13.3573i | −0.840017 | − | 0.610308i | 0.0823581 | − | 0.996603i | \(-0.473755\pi\) |
−0.922376 | + | 0.386294i | \(0.873755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.5165 | + | 13.4530i | −0.844279 | + | 0.613404i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.72648 | + | 1.98090i | −0.124059 | + | 0.0901342i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.21528 | − | 25.2840i | −0.372270 | − | 1.14573i | −0.945302 | − | 0.326196i | \(-0.894233\pi\) |
0.573032 | − | 0.819533i | \(-0.305767\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.28549 | − | 7.03403i | 0.103354 | − | 0.318090i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.66601 | + | 5.12746i | 0.0751860 | + | 0.231399i | 0.981586 | − | 0.191022i | \(-0.0611803\pi\) |
−0.906400 | + | 0.422421i | \(0.861180\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.51915 | 0.293608 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.25323 | + | 6.72286i | 0.415064 | + | 0.301562i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5574 | −0.651677 | −0.325839 | − | 0.945425i | \(-0.605647\pi\) | ||||
−0.325839 | + | 0.945425i | \(0.605647\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 20.1265 | 0.899187 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.4386 | − | 19.9353i | −1.22343 | − | 0.888873i | −0.227049 | − | 0.973883i | \(-0.572908\pi\) |
−0.996380 | + | 0.0850104i | \(0.972908\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.90864 | 0.395647 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.18882 | − | 15.9695i | −0.229990 | − | 0.707838i | −0.997747 | − | 0.0670956i | \(-0.978627\pi\) |
0.767756 | − | 0.640742i | \(-0.221373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.60759 | − | 4.94766i | 0.0711157 | − | 0.218872i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.55777 | + | 4.79432i | 0.0687772 | + | 0.211674i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.6195 | + | 15.7075i | −0.950825 | + | 0.690815i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.79693 | − | 1.30554i | 0.0788763 | − | 0.0573070i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.8271 | + | 10.0460i | 0.605777 | + | 0.440123i | 0.847925 | − | 0.530117i | \(-0.177852\pi\) |
−0.242148 | + | 0.970239i | \(0.577852\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.38135 | + | 19.6398i | −0.279037 | + | 0.858788i | 0.709086 | + | 0.705122i | \(0.249108\pi\) |
−0.988123 | + | 0.153666i | \(0.950892\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.733396 | − | 2.25716i | 0.0319472 | − | 0.0983234i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.58561 | + | 6.23781i | 0.373287 | + | 0.271209i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.81757 | + | 2.77363i | −0.165669 | + | 0.120365i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.76468 | + | 4.18829i | −0.249696 | + | 0.181415i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.0119255 | + | 0.0367031i | 0.000514625 | + | 0.00158385i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.1808 | − | 31.3332i | 0.438517 | − | 1.34962i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.75968 | − | 11.5711i | −0.161641 | − | 0.497480i | 0.837132 | − | 0.547001i | \(-0.184231\pi\) |
−0.998773 | + | 0.0495207i | \(0.984231\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.146945 | −0.00630600 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.03427 | + | 6.56378i | 0.386278 | + | 0.280647i | 0.763928 | − | 0.645301i | \(-0.223268\pi\) |
−0.377651 | + | 0.925948i | \(0.623268\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.34485 | 0.185434 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.1201 | −2.17779 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.17921 | − | 6.66908i | −0.390340 | − | 0.283598i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.9282 | −0.547787 | −0.273894 | − | 0.961760i | \(-0.588312\pi\) | ||||
−0.273894 | + | 0.961760i | \(0.588312\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.479007 | − | 1.47423i | −0.0202598 | − | 0.0623534i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.07590 | − | 3.31129i | 0.0454247 | − | 0.139803i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.80354 | + | 30.1722i | 0.413170 | + | 1.27161i | 0.913878 | + | 0.405989i | \(0.133073\pi\) |
−0.500708 | + | 0.865616i | \(0.666927\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.774655 | + | 0.562820i | −0.0325325 | + | 0.0236362i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.3050 | + | 16.9321i | −0.976997 | + | 0.709830i | −0.957036 | − | 0.289971i | \(-0.906354\pi\) |
−0.0199619 | + | 0.999801i | \(0.506354\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.6999 | + | 10.6801i | 0.615173 | + | 0.446950i | 0.851232 | − | 0.524789i | \(-0.175856\pi\) |
−0.236059 | + | 0.971739i | \(0.575856\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.142049 | − | 0.437183i | 0.00593420 | − | 0.0182636i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.6065 | + | 38.7990i | −0.524817 | + | 1.61522i | 0.239859 | + | 0.970808i | \(0.422899\pi\) |
−0.764677 | + | 0.644414i | \(0.777101\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 15.3900 | + | 11.1815i | 0.639589 | + | 0.464688i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.07993 | + | 0.784616i | −0.0448031 | + | 0.0325514i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.0542 | + | 18.9295i | −1.07905 | + | 0.783979i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.84446 | + | 8.75436i | 0.117404 | + | 0.361331i | 0.992441 | − | 0.122725i | \(-0.0391632\pi\) |
−0.875037 | + | 0.484056i | \(0.839163\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.75094 | + | 17.6996i | −0.236963 | + | 0.729298i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.74377 | + | 11.5221i | 0.153998 | + | 0.473957i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.3856 | 0.508614 | 0.254307 | − | 0.967124i | \(-0.418153\pi\) | ||||
0.254307 | + | 0.967124i | \(0.418153\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.3385 | + | 9.69096i | 0.545907 | + | 0.396625i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.1732 | −0.742536 | −0.371268 | − | 0.928526i | \(-0.621077\pi\) | ||||
−0.371268 | + | 0.928526i | \(0.621077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.8155 | 1.21620 | 0.608099 | − | 0.793861i | \(-0.291932\pi\) | ||||
0.608099 | + | 0.793861i | \(0.291932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.70005 | + | 5.59441i | 0.313570 | + | 0.227822i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.16747 | 0.372096 | 0.186048 | − | 0.982541i | \(-0.440432\pi\) | ||||
0.186048 | + | 0.982541i | \(0.440432\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.00057 | − | 9.23480i | −0.121589 | − | 0.374213i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.08414 | + | 9.49201i | −0.124771 | + | 0.384006i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.34294 | + | 13.3662i | 0.175410 | + | 0.539855i | 0.999652 | − | 0.0263819i | \(-0.00839859\pi\) |
−0.824242 | + | 0.566237i | \(0.808399\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.3141 | − | 21.2980i | 1.18014 | − | 0.857424i | 0.187955 | − | 0.982178i | \(-0.439814\pi\) |
0.992188 | + | 0.124754i | \(0.0398141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.7716 | + | 15.0915i | −0.834882 | + | 0.606577i | −0.920936 | − | 0.389713i | \(-0.872574\pi\) |
0.0860542 | + | 0.996290i | \(0.472574\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.84742 | − | 2.06877i | −0.114263 | − | 0.0830169i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.505419 | + | 1.55552i | −0.0202492 | + | 0.0623206i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.43672 | + | 25.9656i | −0.336930 | + | 1.03696i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.88498 | − | 4.27569i | −0.234650 | − | 0.170483i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.9603 | − | 14.5020i | 0.794608 | − | 0.577317i | −0.114719 | − | 0.993398i | \(-0.536597\pi\) |
0.909327 | + | 0.416081i | \(0.136597\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.7130 | − | 10.6896i | 0.584788 | − | 0.424873i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.80228 | − | 11.7022i | −0.150652 | − | 0.463659i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.69120 | + | 11.3603i | −0.146021 | + | 0.449408i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.25128 | − | 28.4725i | −0.365404 | − | 1.12460i | −0.949728 | − | 0.313077i | \(-0.898640\pi\) |
0.584324 | − | 0.811520i | \(-0.301360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.1343 | −0.399658 | −0.199829 | − | 0.979831i | \(-0.564039\pi\) | ||||
−0.199829 | + | 0.979831i | \(0.564039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.6155 | + | 26.6027i | 1.43950 | + | 1.04586i | 0.988146 | + | 0.153518i | \(0.0490603\pi\) |
0.451358 | + | 0.892343i | \(0.350940\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.5564 | −1.00318 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.53497 | −0.138547 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.6853 | − | 19.3880i | −1.04428 | − | 0.758711i | −0.0731608 | − | 0.997320i | \(-0.523309\pi\) |
−0.971116 | + | 0.238609i | \(0.923309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.43304 | 0.211963 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.789392 | + | 2.42950i | 0.0307504 | + | 0.0946398i | 0.965254 | − | 0.261314i | \(-0.0841559\pi\) |
−0.934503 | + | 0.355954i | \(0.884156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0332 | + | 43.1898i | −0.545829 | + | 1.67989i | 0.173182 | + | 0.984890i | \(0.444595\pi\) |
−0.719011 | + | 0.694999i | \(0.755405\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.401825 | − | 1.23669i | −0.0156056 | − | 0.0480290i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.8750 | − | 20.9789i | 1.11804 | − | 0.812307i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.0202 | − | 13.8190i | 0.735363 | − | 0.534273i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.0372 | + | 13.8313i | 0.734922 | + | 0.533952i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.50508 | + | 10.7875i | −0.135111 | + | 0.415828i | −0.995607 | − | 0.0936282i | \(-0.970153\pi\) |
0.860496 | + | 0.509456i | \(0.170153\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.78000 | − | 14.7113i | 0.183710 | − | 0.565402i | −0.816213 | − | 0.577750i | \(-0.803931\pi\) |
0.999924 | + | 0.0123484i | \(0.00393071\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.3005 | + | 8.21032i | 0.433675 | + | 0.315083i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.9217 | − | 11.5678i | 0.610121 | − | 0.443279i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.49567 | − | 3.99284i | 0.210286 | − | 0.152782i | −0.477657 | − | 0.878546i | \(-0.658514\pi\) |
0.687943 | + | 0.725765i | \(0.258514\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.63995 | − | 5.04724i | −0.0625678 | − | 0.192564i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.71677 | + | 11.4390i | −0.141598 | + | 0.435793i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0774 | + | 40.2482i | 0.497489 | + | 1.53111i | 0.813041 | + | 0.582206i | \(0.197810\pi\) |
−0.315552 | + | 0.948908i | \(0.602190\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.18586 | −0.196995 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.83215 | − | 1.33114i | −0.0693978 | − | 0.0504205i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.2693 | −0.880127 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.2924 | 1.21967 | 0.609834 | − | 0.792529i | \(-0.291236\pi\) | ||||
0.609834 | + | 0.792529i | \(0.291236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 46.1472 | + | 33.5279i | 1.74047 | + | 1.26453i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.84647 | −0.370314 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.667116 | − | 2.05317i | −0.0250541 | − | 0.0771085i | 0.937748 | − | 0.347317i | \(-0.112907\pi\) |
−0.962802 | + | 0.270209i | \(0.912907\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.66167 | − | 11.2695i | 0.137323 | − | 0.422638i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.01524 | − | 12.3576i | −0.150372 | − | 0.462797i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.1959 | + | 8.86084i | −0.455464 | + | 0.330914i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.28757 | + | 0.935472i | −0.0480181 | + | 0.0348872i | −0.611535 | − | 0.791217i | \(-0.709448\pi\) |
0.563517 | + | 0.826104i | \(0.309448\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.8334 | + | 7.87094i | 0.403458 | + | 0.293129i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.84454 | − | 17.9877i | 0.217361 | − | 0.668968i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.414026 | − | 1.27424i | 0.0153554 | − | 0.0472589i | −0.943085 | − | 0.332551i | \(-0.892091\pi\) |
0.958441 | + | 0.285292i | \(0.0920906\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.809017 | − | 0.587785i | −0.0299636 | − | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.398570 | − | 0.289578i | 0.0147416 | − | 0.0107104i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.4759 | + | 25.7748i | −1.31033 | + | 0.952013i | −0.310335 | + | 0.950627i | \(0.600441\pi\) |
−0.999999 | + | 0.00138578i | \(0.999559\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.9290 | + | 49.0244i | 0.586752 | + | 1.80584i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.67584 | − | 17.4684i | 0.208789 | − | 0.642587i | −0.790747 | − | 0.612143i | \(-0.790308\pi\) |
0.999536 | − | 0.0304443i | \(-0.00969221\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.15092 | + | 9.69753i | 0.115752 | + | 0.356248i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.5051 | −0.788947 | −0.394474 | − | 0.918907i | \(-0.629073\pi\) | ||||
−0.394474 | + | 0.918907i | \(0.629073\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.12784 | − | 0.819420i | −0.0412653 | − | 0.0299810i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.68215 | −0.317239 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.02810 | −0.256459 | −0.128230 | − | 0.991745i | \(-0.540929\pi\) | ||||
−0.128230 | + | 0.991745i | \(0.540929\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.69528 | − | 2.68477i | −0.134663 | − | 0.0978386i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.39361 | 0.196034 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.89042 | − | 18.1289i | −0.213809 | − | 0.658036i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.22670 | + | 19.1638i | −0.225718 | + | 0.694688i | 0.772500 | + | 0.635014i | \(0.219006\pi\) |
−0.998218 | + | 0.0596731i | \(0.980994\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.702848 | + | 2.16314i | 0.0254448 | + | 0.0783111i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.72184 | + | 5.61025i | −0.278820 | + | 0.202574i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.0121 | + | 18.1724i | −0.901960 | + | 0.655312i | −0.938969 | − | 0.344003i | \(-0.888217\pi\) |
0.0370088 | + | 0.999315i | \(0.488217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.3871 | − | 11.9059i | −0.590167 | − | 0.428781i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.88584 | + | 30.4255i | −0.355569 | + | 1.09433i | 0.600110 | + | 0.799918i | \(0.295124\pi\) |
−0.955679 | + | 0.294411i | \(0.904876\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.34811 | + | 10.3044i | −0.120113 | + | 0.369669i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.3669 | + | 10.4381i | 0.514747 | + | 0.373985i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.3375 | + | 38.0254i | −1.87278 | + | 1.36066i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.20405 | − | 5.96059i | 0.293189 | − | 0.213014i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.54681 | + | 23.2267i | 0.269015 | + | 0.827942i | 0.990741 | + | 0.135764i | \(0.0433489\pi\) |
−0.721726 | + | 0.692178i | \(0.756651\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.51119 | − | 29.2724i | 0.338607 | − | 1.04213i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.97601 | + | 12.2369i | 0.141371 | + | 0.435094i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.78837 | 0.312084 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.1580 | + | 29.1765i | 1.42247 | + | 1.03348i | 0.991358 | + | 0.131184i | \(0.0418778\pi\) |
0.431110 | + | 0.902300i | \(0.358122\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.17204 | −0.112219 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.70812 | −0.0603535 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 23.8051 | + | 17.2954i | 0.840065 | + | 0.610343i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.6739 | 0.938965 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.82162 | − | 17.9171i | −0.204677 | − | 0.629932i | −0.999726 | − | 0.0233871i | \(-0.992555\pi\) |
0.795049 | − | 0.606545i | \(-0.207445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.77928 | − | 17.7868i | 0.202938 | − | 0.624578i | −0.796854 | − | 0.604172i | \(-0.793504\pi\) |
0.999792 | − | 0.0204064i | \(-0.00649600\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.70869 | + | 5.25882i | 0.0599265 | + | 0.184435i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.12539 | + | 2.27073i | −0.109344 | + | 0.0794428i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.56690 | + | 1.13842i | −0.0547520 | + | 0.0397797i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.7103 | − | 21.5858i | −1.03690 | − | 0.753350i | −0.0672202 | − | 0.997738i | \(-0.521413\pi\) |
−0.969678 | + | 0.244388i | \(0.921413\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.5200 | + | 38.5327i | −0.436421 | + | 1.34317i | 0.455202 | + | 0.890388i | \(0.349567\pi\) |
−0.891623 | + | 0.452779i | \(0.850433\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.45274 | + | 10.6264i | −0.120063 | + | 0.369517i | −0.992969 | − | 0.118371i | \(-0.962233\pi\) |
0.872906 | + | 0.487889i | \(0.162233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.8314 | − | 21.6738i | −1.03609 | − | 0.752762i | −0.0665703 | − | 0.997782i | \(-0.521206\pi\) |
−0.969518 | + | 0.245019i | \(0.921206\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.0175 | + | 18.1763i | −0.867847 | + | 0.630528i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.16378 | − | 2.29862i | 0.109618 | − | 0.0796425i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.14082 | − | 3.51109i | −0.0394326 | − | 0.121361i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.53480 | + | 10.8790i | −0.122035 | + | 0.375585i | −0.993349 | − | 0.115140i | \(-0.963268\pi\) |
0.871314 | + | 0.490725i | \(0.163268\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.8163 | + | 70.2213i | 0.786769 | + | 2.42143i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.8489 | 0.580306 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.2009 | − | 10.3176i | −0.487950 | − | 0.354516i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.2627 | 0.386537 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.8254 | −1.36520 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.9368 | − | 14.4849i | −0.682623 | − | 0.495954i | 0.191604 | − | 0.981472i | \(-0.438631\pi\) |
−0.874227 | + | 0.485518i | \(0.838631\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.2342 | −0.383752 | −0.191876 | − | 0.981419i | \(-0.561457\pi\) | ||||
−0.191876 | + | 0.981419i | \(0.561457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.79573 | − | 14.7597i | −0.163628 | − | 0.503595i | 0.835305 | − | 0.549788i | \(-0.185291\pi\) |
−0.998933 | + | 0.0461922i | \(0.985291\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.04236 | + | 3.20805i | −0.0355235 | + | 0.109330i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.03168 | + | 18.5636i | 0.205321 | + | 0.631912i | 0.999700 | + | 0.0244902i | \(0.00779625\pi\) |
−0.794379 | + | 0.607422i | \(0.792204\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.4189 | + | 9.74943i | −0.455731 | + | 0.331108i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 51.9188 | − | 37.7212i | 1.76123 | − | 1.27960i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.5750 | + | 11.3159i | 0.527738 | + | 0.383424i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.50789 | + | 13.8738i | −0.152569 | + | 0.469559i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.24470 | − | 13.0638i | 0.143333 | − | 0.441134i | −0.853460 | − | 0.521159i | \(-0.825500\pi\) |
0.996793 | + | 0.0800245i | \(0.0254999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.06061 | − | 6.58292i | −0.305607 | − | 0.222036i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.4014 | − | 30.8064i | 1.42854 | − | 1.03789i | 0.438253 | − | 0.898852i | \(-0.355598\pi\) |
0.990286 | − | 0.139042i | \(-0.0444024\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.5119 | + | 9.81699i | −0.454713 | + | 0.330368i | −0.791454 | − | 0.611229i | \(-0.790675\pi\) |
0.336741 | + | 0.941597i | \(0.390675\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 8.00379 | + | 24.6331i | 0.268741 | + | 0.827099i | 0.990808 | + | 0.135276i | \(0.0431922\pi\) |
−0.722067 | + | 0.691823i | \(0.756808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.22028 | + | 12.9887i | −0.141544 | + | 0.435627i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.67360 | − | 5.15082i | −0.0560678 | − | 0.172559i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.8736 | 0.832364 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.75950 | − | 4.18452i | −0.192304 | − | 0.139717i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 37.4374 | 1.24861 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.82270 | −0.127353 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.593655 | − | 0.431316i | −0.0197556 | − | 0.0143533i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.74821 | −0.157662 | −0.0788308 | − | 0.996888i | \(-0.525119\pi\) | ||||
−0.0788308 | + | 0.996888i | \(0.525119\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.17769 | − | 9.77994i | −0.105397 | − | 0.324380i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.79559 | + | 11.6816i | −0.125753 | + | 0.387029i | −0.994038 | − | 0.109038i | \(-0.965223\pi\) |
0.868284 | + | 0.496067i | \(0.165223\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.33314 | − | 7.18067i | −0.0772156 | − | 0.237645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0996721 | − | 0.0724160i | 0.00329146 | − | 0.00239139i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.7306 | + | 12.1555i | −0.551893 | + | 0.400974i | −0.828483 | − | 0.560014i | \(-0.810796\pi\) |
0.276590 | + | 0.960988i | \(0.410796\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.5207 | + | 14.1826i | 0.643228 | + | 0.467332i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.46622 | + | 22.9787i | −0.245754 | + | 0.756352i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.32155 | + | 13.3004i | −0.141938 | + | 0.436841i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.4753 | − | 14.1496i | −0.638964 | − | 0.464235i | 0.220530 | − | 0.975380i | \(-0.429221\pi\) |
−0.859494 | + | 0.511145i | \(0.829221\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.8088 | + | 18.0247i | −0.813077 | + | 0.590735i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.67719 | − | 1.21855i | 0.0549086 | − | 0.0398934i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.8438 | − | 42.6067i | −0.452256 | − | 1.39190i | −0.874327 | − | 0.485338i | \(-0.838697\pi\) |
0.422071 | − | 0.906563i | \(-0.361303\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.63272 | − | 8.10268i | 0.0859156 | − | 0.264421i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.5501 | − | 44.7806i | −0.474319 | − | 1.45980i | −0.846874 | − | 0.531794i | \(-0.821518\pi\) |
0.372554 | − | 0.928010i | \(-0.378482\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.3987 | −0.403759 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.5424 | − | 10.5656i | −0.472563 | − | 0.343337i | 0.325876 | − | 0.945412i | \(-0.394341\pi\) |
−0.798439 | + | 0.602075i | \(0.794341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.9895 | 0.356733 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.6070 | −0.441236 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.0854 | + | 21.1318i | 0.942169 | + | 0.684526i | 0.948942 | − | 0.315451i | \(-0.102156\pi\) |
−0.00677250 | + | 0.999977i | \(0.502156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 54.9213 | 1.77535 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.05438 | − | 12.4781i | −0.130923 | − | 0.402939i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.36787 | + | 16.5206i | −0.173157 | + | 0.532923i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.80194 | − | 8.62349i | −0.0902913 | − | 0.277888i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.76589 | + | 5.64225i | −0.249734 | + | 0.181443i | −0.705609 | − | 0.708601i | \(-0.749326\pi\) |
0.455875 | + | 0.890044i | \(0.349326\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.62180 | + | 1.90485i | −0.0842243 | + | 0.0611925i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.5625 | + | 16.3926i | 0.724066 | + | 0.526065i | 0.887681 | − | 0.460460i | \(-0.152315\pi\) |
−0.163615 | + | 0.986524i | \(0.552315\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.94511 | − | 21.3748i | 0.222650 | − | 0.685246i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.5347 | − | 53.9664i | 0.560986 | − | 1.72654i | −0.118601 | − | 0.992942i | \(-0.537841\pi\) |
0.679587 | − | 0.733595i | \(-0.262159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.48423 | − | 5.43761i | −0.239197 | − | 0.173787i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.92170 | + | 1.39620i | −0.0613552 | + | 0.0445772i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.10235 | − | 6.61324i | 0.290320 | − | 0.210930i | −0.433086 | − | 0.901352i | \(-0.642575\pi\) |
0.723406 | + | 0.690423i | \(0.242575\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.45999 | + | 4.49340i | 0.0464721 | + | 0.143026i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.833493 | − | 2.56523i | 0.0265035 | − | 0.0815695i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.6488 | + | 32.7735i | 0.338269 | + | 1.04109i | 0.965089 | + | 0.261921i | \(0.0843561\pi\) |
−0.626820 | + | 0.779164i | \(0.715644\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.6320 | 0.718206 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.4138 | − | 30.0889i | −1.31159 | − | 0.952924i | −0.999996 | − | 0.00270782i | \(-0.999138\pi\) |
−0.311591 | − | 0.950216i | \(-0.600862\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −11.3153 | −0.358001 |
(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 | 1500.2.m.d.601.4 | 24 | ||
5.2 | odd | 4 | 1500.2.o.c.649.5 | 24 | |||
5.3 | odd | 4 | 300.2.o.a.229.2 | yes | 24 | ||
5.4 | even | 2 | 1500.2.m.c.601.3 | 24 | |||
15.8 | even | 4 | 900.2.w.c.829.4 | 24 | |||
25.6 | even | 5 | inner | 1500.2.m.d.901.4 | 24 | ||
25.8 | odd | 20 | 1500.2.o.c.349.5 | 24 | |||
25.9 | even | 10 | 7500.2.a.n.1.5 | 12 | |||
25.12 | odd | 20 | 7500.2.d.g.1249.20 | 24 | |||
25.13 | odd | 20 | 7500.2.d.g.1249.5 | 24 | |||
25.16 | even | 5 | 7500.2.a.m.1.8 | 12 | |||
25.17 | odd | 20 | 300.2.o.a.169.2 | ✓ | 24 | ||
25.19 | even | 10 | 1500.2.m.c.901.3 | 24 | |||
75.17 | even | 20 | 900.2.w.c.469.4 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.169.2 | ✓ | 24 | 25.17 | odd | 20 | ||
300.2.o.a.229.2 | yes | 24 | 5.3 | odd | 4 | ||
900.2.w.c.469.4 | 24 | 75.17 | even | 20 | |||
900.2.w.c.829.4 | 24 | 15.8 | even | 4 | |||
1500.2.m.c.601.3 | 24 | 5.4 | even | 2 | |||
1500.2.m.c.901.3 | 24 | 25.19 | even | 10 | |||
1500.2.m.d.601.4 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.m.d.901.4 | 24 | 25.6 | even | 5 | inner | ||
1500.2.o.c.349.5 | 24 | 25.8 | odd | 20 | |||
1500.2.o.c.649.5 | 24 | 5.2 | odd | 4 | |||
7500.2.a.m.1.8 | 12 | 25.16 | even | 5 | |||
7500.2.a.n.1.5 | 12 | 25.9 | even | 10 | |||
7500.2.d.g.1249.5 | 24 | 25.13 | odd | 20 | |||
7500.2.d.g.1249.20 | 24 | 25.12 | odd | 20 |