Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1500,2,Mod(557,1500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1500, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1500.557");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1500 = 2^{2} \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1500.i (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: | \(11.9775603032\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 557.9 | ||
Character | \(\chi\) | \(=\) | 1500.557 |
Dual form | 1500.2.i.a.1193.9 |
$q$-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 \(\left(\mathbb{Z}/1500\mathbb{Z}\right)^\times\).
\(n\) | \(751\) | \(877\) | \(1001\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.190209 | − | 1.72157i | 0.109817 | − | 0.993952i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.111556 | − | 0.111556i | −0.0421643 | − | 0.0421643i | 0.685710 | − | 0.727875i | \(-0.259492\pi\) |
−0.727875 | + | 0.685710i | \(0.759492\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.92764 | − | 0.654920i | −0.975880 | − | 0.218307i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.01268i | 0.305334i | 0.988278 | + | 0.152667i | \(0.0487862\pi\) | ||||
−0.988278 | + | 0.152667i | \(0.951214\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.98178 | − | 2.98178i | 0.826996 | − | 0.826996i | −0.160104 | − | 0.987100i | \(-0.551183\pi\) |
0.987100 | + | 0.160104i | \(0.0511830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.27381 | − | 1.27381i | 0.308944 | − | 0.308944i | −0.535556 | − | 0.844500i | \(-0.679898\pi\) |
0.844500 | + | 0.535556i | \(0.179898\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.73740i | − | 1.08683i | −0.839463 | − | 0.543417i | \(-0.817130\pi\) | ||
0.839463 | − | 0.543417i | \(-0.182870\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.213271 | + | 0.170833i | −0.0465396 | + | 0.0372789i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.327375 | + | 0.327375i | 0.0682623 | + | 0.0682623i | 0.740414 | − | 0.672151i | \(-0.234630\pi\) |
−0.672151 | + | 0.740414i | \(0.734630\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.68436 | + | 4.91558i | −0.324155 | + | 0.946004i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.26999 | −1.16431 | −0.582154 | − | 0.813079i | \(-0.697790\pi\) | ||||
−0.582154 | + | 0.813079i | \(0.697790\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.35442 | −0.602471 | −0.301235 | − | 0.953550i | \(-0.597399\pi\) | ||||
−0.301235 | + | 0.953550i | \(0.597399\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.74340 | + | 0.192621i | 0.303487 | + | 0.0335310i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.73128 | − | 1.73128i | −0.284621 | − | 0.284621i | 0.550328 | − | 0.834949i | \(-0.314503\pi\) |
−0.834949 | + | 0.550328i | \(0.814503\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.56619 | − | 5.70051i | −0.731175 | − | 0.912813i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.46847i | − | 0.854032i | −0.904244 | − | 0.427016i | \(-0.859565\pi\) | ||
0.904244 | − | 0.427016i | \(-0.140435\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.13594 | − | 3.13594i | 0.478227 | − | 0.478227i | −0.426337 | − | 0.904564i | \(-0.640196\pi\) |
0.904564 | + | 0.426337i | \(0.140196\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.07024 | − | 6.07024i | 0.885435 | − | 0.885435i | −0.108646 | − | 0.994081i | \(-0.534651\pi\) |
0.994081 | + | 0.108646i | \(0.0346514\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 6.97511i | − | 0.996444i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.95067 | − | 2.43525i | −0.273148 | − | 0.341003i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.90038 | − | 4.90038i | −0.673119 | − | 0.673119i | 0.285315 | − | 0.958434i | \(-0.407902\pi\) |
−0.958434 | + | 0.285315i | \(0.907902\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.15579 | − | 0.901098i | −1.08026 | − | 0.119353i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.3166 | −1.86387 | −0.931934 | − | 0.362627i | \(-0.881880\pi\) | ||||
−0.931934 | + | 0.362627i | \(0.881880\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.26526 | 0.290037 | 0.145019 | − | 0.989429i | \(-0.453676\pi\) | ||||
0.145019 | + | 0.989429i | \(0.453676\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.253536 | + | 0.399657i | 0.0319426 | + | 0.0503520i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.84691 | + | 5.84691i | 0.714314 | + | 0.714314i | 0.967435 | − | 0.253121i | \(-0.0814571\pi\) |
−0.253121 | + | 0.967435i | \(0.581457\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.625870 | − | 0.501330i | 0.0753459 | − | 0.0603531i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.4796i | 1.59974i | 0.600176 | + | 0.799868i | \(0.295097\pi\) | ||||
−0.600176 | + | 0.799868i | \(0.704903\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.11772 | + | 6.11772i | −0.716025 | + | 0.716025i | −0.967789 | − | 0.251764i | \(-0.918989\pi\) |
0.251764 | + | 0.967789i | \(0.418989\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.112971 | − | 0.112971i | 0.0128742 | − | 0.0128742i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.81117i | − | 0.766316i | −0.923683 | − | 0.383158i | \(-0.874836\pi\) | ||
0.923683 | − | 0.383158i | \(-0.125164\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.14216 | + | 3.83474i | 0.904685 | + | 0.426082i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.18778 | + | 3.18778i | 0.349904 | + | 0.349904i | 0.860074 | − | 0.510170i | \(-0.170417\pi\) |
−0.510170 | + | 0.860074i | \(0.670417\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.19261 | + | 10.7943i | −0.127861 | + | 1.15727i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.7359 | −1.45600 | −0.728002 | − | 0.685575i | \(-0.759551\pi\) | ||||
−0.728002 | + | 0.685575i | \(0.759551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.665271 | −0.0697394 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.638042 | + | 5.77488i | −0.0661618 | + | 0.598827i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.71608 | − | 7.71608i | −0.783450 | − | 0.783450i | 0.196962 | − | 0.980411i | \(-0.436893\pi\) |
−0.980411 | + | 0.196962i | \(0.936893\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.663223 | − | 2.96476i | 0.0666564 | − | 0.297969i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 14.7314i | − | 1.46582i | −0.680323 | − | 0.732912i | \(-0.738161\pi\) | ||
0.680323 | − | 0.732912i | \(-0.261839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.5549 | + | 13.5549i | −1.33560 | + | 1.33560i | −0.435331 | + | 0.900270i | \(0.643369\pi\) |
−0.900270 | + | 0.435331i | \(0.856631\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.8294 | − | 12.8294i | 1.24026 | − | 1.24026i | 0.280368 | − | 0.959893i | \(-0.409544\pi\) |
0.959893 | − | 0.280368i | \(-0.0904564\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.32624i | − | 0.701726i | −0.936427 | − | 0.350863i | \(-0.885888\pi\) | ||
0.936427 | − | 0.350863i | \(-0.114112\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.30984 | + | 2.65123i | −0.314156 | + | 0.251643i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.08982 | + | 9.08982i | 0.855098 | + | 0.855098i | 0.990756 | − | 0.135658i | \(-0.0433148\pi\) |
−0.135658 | + | 0.990756i | \(0.543315\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.6824 | + | 6.77675i | −0.987587 | + | 0.626510i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.284203 | −0.0260528 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.97448 | 0.906771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.41439 | − | 1.04016i | −0.848867 | − | 0.0937876i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.44135 | + | 8.44135i | 0.749048 | + | 0.749048i | 0.974301 | − | 0.225252i | \(-0.0723206\pi\) |
−0.225252 | + | 0.974301i | \(0.572321\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.80227 | − | 5.99525i | −0.422817 | − | 0.527852i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.59898i | 0.489185i | 0.969626 | + | 0.244592i | \(0.0786542\pi\) | ||||
−0.969626 | + | 0.244592i | \(0.921346\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.528486 | + | 0.528486i | −0.0458256 | + | 0.0458256i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.37098 | − | 9.37098i | 0.800617 | − | 0.800617i | −0.182575 | − | 0.983192i | \(-0.558443\pi\) |
0.983192 | + | 0.182575i | \(0.0584432\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.01703i | 0.595176i | 0.954694 | + | 0.297588i | \(0.0961822\pi\) | ||||
−0.954694 | + | 0.297588i | \(0.903818\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.29575 | − | 11.6050i | −0.782843 | − | 0.977316i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.01958 | + | 3.01958i | 0.252510 | + | 0.252510i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0082 | − | 1.32673i | −0.990418 | − | 0.109427i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.9750 | 1.14488 | 0.572438 | − | 0.819948i | \(-0.305998\pi\) | ||||
0.572438 | + | 0.819948i | \(0.305998\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8568 | −1.04627 | −0.523134 | − | 0.852250i | \(-0.675237\pi\) | ||||
−0.523134 | + | 0.852250i | \(0.675237\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.56350 | + | 2.89502i | −0.368937 | + | 0.234048i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.34487 | − | 5.34487i | −0.426567 | − | 0.426567i | 0.460890 | − | 0.887457i | \(-0.347530\pi\) |
−0.887457 | + | 0.460890i | \(0.847530\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.36846 | + | 7.50427i | −0.742967 | + | 0.595127i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 0.0730414i | − | 0.00575646i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2821 | − | 11.2821i | 0.883681 | − | 0.883681i | −0.110225 | − | 0.993907i | \(-0.535157\pi\) |
0.993907 | + | 0.110225i | \(0.0351572\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.235499 | + | 0.235499i | −0.0182234 | + | 0.0182234i | −0.716160 | − | 0.697936i | \(-0.754102\pi\) |
0.697936 | + | 0.716160i | \(0.254102\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.78198i | − | 0.367844i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.10261 | + | 13.8694i | −0.237263 | + | 1.06062i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8099 | − | 13.8099i | −1.04995 | − | 1.04995i | −0.998685 | − | 0.0512637i | \(-0.983675\pi\) |
−0.0512637 | − | 0.998685i | \(-0.516325\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.72316 | + | 24.6472i | −0.204685 | + | 1.85260i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.29535 | 0.620023 | 0.310012 | − | 0.950733i | \(-0.399667\pi\) | ||||
0.310012 | + | 0.950733i | \(0.399667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.45245 | −0.107960 | −0.0539798 | − | 0.998542i | \(-0.517191\pi\) | ||||
−0.0539798 | + | 0.998542i | \(0.517191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.430874 | − | 3.89982i | 0.0318511 | − | 0.288283i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.28996 | + | 1.28996i | 0.0943313 | + | 0.0943313i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.736264 | − | 0.360463i | 0.0535553 | − | 0.0262198i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.756375i | − | 0.0547294i | −0.999626 | − | 0.0273647i | \(-0.991288\pi\) | ||
0.999626 | − | 0.0273647i | \(-0.00871154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.72724 | − | 5.72724i | 0.412256 | − | 0.412256i | −0.470268 | − | 0.882524i | \(-0.655843\pi\) |
0.882524 | + | 0.470268i | \(0.155843\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1795 | − | 14.1795i | 1.01025 | − | 1.01025i | 0.0102995 | − | 0.999947i | \(-0.496722\pi\) |
0.999947 | − | 0.0102995i | \(-0.00327848\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.28331i | 0.587188i | 0.955930 | + | 0.293594i | \(0.0948514\pi\) | ||||
−0.955930 | + | 0.293594i | \(0.905149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.1780 | − | 8.95376i | 0.788437 | − | 0.631549i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.699456 | + | 0.699456i | 0.0490922 | + | 0.0490922i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.744031 | − | 1.17284i | −0.0517137 | − | 0.0815180i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.79746 | 0.331847 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.66629 | −0.458926 | −0.229463 | − | 0.973317i | \(-0.573697\pi\) | ||||
−0.229463 | + | 0.973317i | \(0.573697\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 23.2062 | + | 2.56395i | 1.59006 | + | 0.175679i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.374206 | + | 0.374206i | 0.0254028 | + | 0.0254028i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.36846 | + | 11.6958i | 0.633062 | + | 0.790326i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 7.59644i | − | 0.510992i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.04773 | + | 5.04773i | −0.338021 | + | 0.338021i | −0.855622 | − | 0.517601i | \(-0.826825\pi\) |
0.517601 | + | 0.855622i | \(0.326825\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.772665 | + | 0.772665i | −0.0512836 | + | 0.0512836i | −0.732283 | − | 0.681000i | \(-0.761545\pi\) |
0.681000 | + | 0.732283i | \(0.261545\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.3034i | 1.53993i | 0.638086 | + | 0.769965i | \(0.279727\pi\) | ||||
−0.638086 | + | 0.769965i | \(0.720273\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.172999 | − | 0.215975i | −0.0113825 | − | 0.0142101i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.85432 | − | 8.85432i | −0.580066 | − | 0.580066i | 0.354856 | − | 0.934921i | \(-0.384530\pi\) |
−0.934921 | + | 0.354856i | \(0.884530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.7259 | − | 1.29555i | −0.761682 | − | 0.0841549i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.1633 | 0.980833 | 0.490416 | − | 0.871488i | \(-0.336845\pi\) | ||||
0.490416 | + | 0.871488i | \(0.336845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.8748 | 1.47350 | 0.736748 | − | 0.676168i | \(-0.236360\pi\) | ||||
0.736748 | + | 0.676168i | \(0.236360\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.15051 | − | 13.2879i | 0.522855 | − | 0.852422i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.1259 | − | 14.1259i | −0.898807 | − | 0.898807i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.09434 | − | 4.88165i | 0.386213 | − | 0.309362i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.6541i | 1.05120i | 0.850732 | + | 0.525599i | \(0.176159\pi\) | ||||
−0.850732 | + | 0.525599i | \(0.823841\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.331525 | + | 0.331525i | −0.0208428 | + | 0.0208428i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.9350 | − | 13.9350i | 0.869239 | − | 0.869239i | −0.123149 | − | 0.992388i | \(-0.539299\pi\) |
0.992388 | + | 0.123149i | \(0.0392993\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.386271i | 0.0240017i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.3563 | + | 4.10634i | 1.13623 | + | 0.254176i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.65365 | + | 9.65365i | 0.595270 | + | 0.595270i | 0.939050 | − | 0.343780i | \(-0.111708\pi\) |
−0.343780 | + | 0.939050i | \(0.611708\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.61270 | + | 23.6474i | −0.159895 | + | 1.44720i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 17.8779 | 1.09004 | 0.545019 | − | 0.838424i | \(-0.316522\pi\) | ||||
0.545019 | + | 0.838424i | \(0.316522\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.292812 | −0.0177871 | −0.00889354 | − | 0.999960i | \(-0.502831\pi\) | ||||
−0.00889354 | + | 0.999960i | \(0.502831\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.126541 | + | 1.14531i | −0.00765860 | + | 0.0693176i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3176 | + | 20.3176i | 1.22077 | + | 1.22077i | 0.967360 | + | 0.253407i | \(0.0815512\pi\) |
0.253407 | + | 0.967360i | \(0.418449\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.82052 | + | 2.19687i | 0.587939 | + | 0.131523i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 4.00557i | − | 0.238952i | −0.992837 | − | 0.119476i | \(-0.961878\pi\) | ||
0.992837 | − | 0.119476i | \(-0.0381215\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.3664 | − | 18.3664i | 1.09177 | − | 1.09177i | 0.0964266 | − | 0.995340i | \(-0.469259\pi\) |
0.995340 | − | 0.0964266i | \(-0.0307413\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.610042 | + | 0.610042i | −0.0360096 | + | 0.0360096i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.7548i | 0.809107i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.7515 | + | 11.8161i | −0.864747 | + | 0.692675i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.71430 | + | 5.71430i | 0.333833 | + | 0.333833i | 0.854040 | − | 0.520207i | \(-0.174145\pi\) |
−0.520207 | + | 0.854040i | \(0.674145\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.97790 | − | 1.70571i | −0.288847 | − | 0.0989755i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.95232 | 0.112905 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.699668 | −0.0403282 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.3611 | − | 2.80204i | −1.45696 | − | 0.160973i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.5326 | − | 17.5326i | −1.00064 | − | 1.00064i | −1.00000 | 0.000639219i | \(-0.999797\pi\) | |
−0.000639219 | − | 1.00000i | \(-0.500203\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.7575 | + | 25.9140i | 1.18085 | + | 1.47420i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.32645i | − | 0.0752158i | −0.999293 | − | 0.0376079i | \(-0.988026\pi\) | ||
0.999293 | − | 0.0376079i | \(-0.0119738\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.7435 | − | 16.7435i | 0.946398 | − | 0.946398i | −0.0522368 | − | 0.998635i | \(-0.516635\pi\) |
0.998635 | + | 0.0522368i | \(0.0166351\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.09524 | − | 5.09524i | 0.286177 | − | 0.286177i | −0.549389 | − | 0.835567i | \(-0.685140\pi\) |
0.835567 | + | 0.549389i | \(0.185140\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.34948i | − | 0.355503i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −19.6464 | − | 24.5270i | −1.09656 | − | 1.36896i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.03455 | − | 6.03455i | −0.335771 | − | 0.335771i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.6127 | − | 1.39352i | −0.697482 | − | 0.0770618i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.35435 | −0.0746675 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.0928 | −1.21433 | −0.607166 | − | 0.794575i | \(-0.707694\pi\) | ||||
−0.607166 | + | 0.794575i | \(0.707694\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.93472 | + | 6.20242i | 0.215621 | + | 0.339891i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4942 | + | 13.4942i | 0.735074 | + | 0.735074i | 0.971620 | − | 0.236546i | \(-0.0760155\pi\) |
−0.236546 | + | 0.971620i | \(0.576016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3778 | − | 13.9198i | 0.943831 | − | 0.756021i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.39694i | − | 0.183955i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.55901 | + | 1.55901i | −0.0841787 | + | 0.0841787i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.8697 | − | 20.8697i | 1.12035 | − | 1.12035i | 0.128657 | − | 0.991689i | \(-0.458933\pi\) |
0.991689 | − | 0.128657i | \(-0.0410668\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.6420i | 1.58670i | 0.608765 | + | 0.793351i | \(0.291665\pi\) | ||||
−0.608765 | + | 0.793351i | \(0.708335\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.63478 | + | 19.6795i | 0.514267 | + | 1.05042i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.7804 | − | 20.7804i | −1.10603 | − | 1.10603i | −0.993667 | − | 0.112361i | \(-0.964159\pi\) |
−0.112361 | − | 0.993667i | \(-0.535841\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.0540581 | + | 0.489277i | −0.00286106 | + | 0.0258953i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.6237 | 0.982919 | 0.491460 | − | 0.870900i | \(-0.336463\pi\) | ||||
0.491460 | + | 0.870900i | \(0.336463\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.44294 | −0.181207 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.89724 | − | 17.1718i | 0.0995793 | − | 0.901287i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.84287 | + | 6.84287i | 0.357195 | + | 0.357195i | 0.862778 | − | 0.505583i | \(-0.168723\pi\) |
−0.505583 | + | 0.862778i | \(0.668723\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.58141 | + | 16.0097i | −0.186441 | + | 0.833433i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.09334i | 0.0567631i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0133 | + | 16.0133i | −0.829135 | + | 0.829135i | −0.987397 | − | 0.158262i | \(-0.949411\pi\) |
0.158262 | + | 0.987397i | \(0.449411\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.6957 | + | 18.6957i | −0.962878 | + | 0.962878i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1990i | 0.729354i | 0.931134 | + | 0.364677i | \(0.118821\pi\) | ||||
−0.931134 | + | 0.364677i | \(0.881179\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.1380 | − | 12.9268i | 0.826777 | − | 0.662259i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.1293 | + | 27.1293i | 1.38624 | + | 1.38624i | 0.833063 | + | 0.553178i | \(0.186585\pi\) |
0.553178 | + | 0.833063i | \(0.313415\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.2347 | + | 7.12712i | −0.571092 | + | 0.362292i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.2242 | 0.873300 | 0.436650 | − | 0.899631i | \(-0.356165\pi\) | ||||
0.436650 | + | 0.899631i | \(0.356165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.834027 | 0.0421785 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.63906 | + | 1.06498i | 0.486226 | + | 0.0537211i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.79625 | − | 5.79625i | −0.290906 | − | 0.290906i | 0.546532 | − | 0.837438i | \(-0.315948\pi\) |
−0.837438 | + | 0.546532i | \(0.815948\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.809306 | + | 1.01035i | 0.0405160 | + | 0.0505809i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 7.77803i | − | 0.388416i | −0.980960 | − | 0.194208i | \(-0.937786\pi\) | ||
0.980960 | − | 0.194208i | \(-0.0622137\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.0021 | + | 10.0021i | −0.498241 | + | 0.498241i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.75323 | − | 1.75323i | 0.0869045 | − | 0.0869045i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 19.2912i | − | 0.953889i | −0.878933 | − | 0.476945i | \(-0.841744\pi\) | ||
0.878933 | − | 0.476945i | \(-0.158256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.3504 | − | 17.9153i | −0.707853 | − | 0.883697i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.59711 | + | 1.59711i | 0.0785887 | + | 0.0785887i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.0803 | + | 1.33470i | 0.591577 | + | 0.0653608i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.19138 | −0.107056 | −0.0535279 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535279 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.5045 | 0.999330 | 0.499665 | − | 0.866219i | \(-0.333456\pi\) | ||||
0.499665 | + | 0.866219i | \(0.333456\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −21.7470 | + | 13.7960i | −1.05737 | + | 0.670782i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.252704 | − | 0.252704i | −0.0122292 | − | 0.0122292i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.77279 | − | 4.62408i | 0.278713 | − | 0.223253i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 5.55384i | − | 0.267519i | −0.991014 | − | 0.133759i | \(-0.957295\pi\) | ||
0.991014 | − | 0.133759i | \(-0.0427049\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.1045 | + | 17.1045i | −0.821989 | + | 0.821989i | −0.986393 | − | 0.164404i | \(-0.947430\pi\) |
0.164404 | + | 0.986393i | \(0.447430\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.55090 | − | 1.55090i | 0.0741898 | − | 0.0741898i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 31.0964i | 1.48415i | 0.670316 | + | 0.742076i | \(0.266159\pi\) | ||||
−0.670316 | + | 0.742076i | \(0.733841\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.56814 | + | 20.4206i | −0.217530 | + | 0.972410i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11.0690 | + | 11.0690i | 0.525904 | + | 0.525904i | 0.919348 | − | 0.393445i | \(-0.128717\pi\) |
−0.393445 | + | 0.919348i | \(0.628717\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.65817 | − | 24.0590i | 0.125727 | − | 1.13795i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.7897 | −0.886740 | −0.443370 | − | 0.896339i | \(-0.646217\pi\) | ||||
−0.443370 | + | 0.896339i | \(0.646217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.53780 | 0.260765 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.44548 | + | 22.1339i | −0.114899 | + | 1.03994i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.53453 | − | 9.53453i | −0.446006 | − | 0.446006i | 0.448018 | − | 0.894025i | \(-0.352130\pi\) |
−0.894025 | + | 0.448018i | \(0.852130\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.11597 | + | 8.40707i | 0.192117 | + | 0.392409i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.6739i | 0.683431i | 0.939803 | + | 0.341716i | \(0.111008\pi\) | ||||
−0.939803 | + | 0.341716i | \(0.888992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.6442 | + | 12.6442i | −0.587626 | + | 0.587626i | −0.936988 | − | 0.349362i | \(-0.886398\pi\) |
0.349362 | + | 0.936988i | \(0.386398\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.94101 | + | 4.94101i | −0.228643 | + | 0.228643i | −0.812125 | − | 0.583483i | \(-0.801690\pi\) |
0.583483 | + | 0.812125i | \(0.301690\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.30452i | − | 0.0602371i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.2182 | + | 8.18495i | −0.470832 | + | 0.377143i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.17570 | + | 3.17570i | 0.146019 | + | 0.146019i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.1372 | + | 17.5559i | 0.509937 | + | 0.803829i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.4964 | 0.936502 | 0.468251 | − | 0.883595i | \(-0.344884\pi\) | ||||
0.468251 | + | 0.883595i | \(0.344884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3246 | −0.470761 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.125746 | − | 0.0138932i | −0.00572165 | − | 0.000632160i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.549665 | + | 0.549665i | 0.0249077 | + | 0.0249077i | 0.719451 | − | 0.694543i | \(-0.244394\pi\) |
−0.694543 | + | 0.719451i | \(0.744394\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.2770 | − | 21.5689i | −0.781293 | − | 0.975380i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.7709i | 1.16302i | 0.813538 | + | 0.581512i | \(0.197539\pi\) | ||||
−0.813538 | + | 0.581512i | \(0.802461\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.98678 | + | 7.98678i | −0.359706 | + | 0.359706i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.50374 | − | 1.50374i | 0.0674517 | − | 0.0674517i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 10.0170i | − | 0.448424i | −0.974540 | − | 0.224212i | \(-0.928019\pi\) | ||
0.974540 | − | 0.224212i | \(-0.0719808\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.360634 | + | 0.450223i | 0.0161120 | + | 0.0201145i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.5378 | − | 16.5378i | −0.737385 | − | 0.737385i | 0.234686 | − | 0.972071i | \(-0.424594\pi\) |
−0.972071 | + | 0.234686i | \(0.924594\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.23253 | − | 0.909577i | −0.365619 | − | 0.0403957i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 35.9439 | 1.59318 | 0.796592 | − | 0.604518i | \(-0.206634\pi\) | ||||
0.796592 | + | 0.604518i | \(0.206634\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.36494 | 0.0603814 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23.2871 | + | 7.97947i | 1.02815 | + | 0.352302i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.14720 | + | 6.14720i | 0.270353 | + | 0.270353i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.4016 | + | 21.1480i | −1.15890 | + | 0.928296i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 41.3270i | − | 1.81057i | −0.424807 | − | 0.905284i | \(-0.639658\pi\) | ||
0.424807 | − | 0.905284i | \(-0.360342\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.87037 | + | 4.87037i | −0.212966 | + | 0.212966i | −0.805526 | − | 0.592560i | \(-0.798117\pi\) |
0.592560 | + | 0.805526i | \(0.298117\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.27289 | + | 4.27289i | −0.186130 | + | 0.186130i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.7857i | − | 0.990681i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 41.9140 | + | 9.37625i | 1.81891 | + | 0.406895i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.3058 | − | 16.3058i | −0.706281 | − | 0.706281i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.57785 | − | 14.2811i | 0.0680894 | − | 0.616273i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.06354 | 0.304248 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3745 | 1.13393 | 0.566964 | − | 0.823743i | \(-0.308118\pi\) | ||||
0.566964 | + | 0.823743i | \(0.308118\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.276269 | + | 2.50050i | −0.0118559 | + | 0.107307i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.17137 | − | 4.17137i | −0.178355 | − | 0.178355i | 0.612283 | − | 0.790638i | \(-0.290251\pi\) |
−0.790638 | + | 0.612283i | \(0.790251\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.63187 | − | 1.48356i | −0.283041 | − | 0.0633170i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29.7034i | 1.26541i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.759828 | + | 0.759828i | −0.0323112 | + | 0.0323112i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.76492 | + | 5.76492i | −0.244267 | + | 0.244267i | −0.818613 | − | 0.574346i | \(-0.805257\pi\) |
0.574346 | + | 0.818613i | \(0.305257\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18.7014i | − | 0.790983i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.46613 | − | 1.97540i | 0.104120 | − | 0.0834015i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.4526 | + | 17.4526i | 0.735541 | + | 0.735541i | 0.971712 | − | 0.236171i | \(-0.0758924\pi\) |
−0.236171 | + | 0.971712i | \(0.575892\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.480520 | − | 1.33610i | −0.0201799 | − | 0.0561108i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.4348 | −1.23397 | −0.616986 | − | 0.786974i | \(-0.711646\pi\) | ||||
−0.616986 | + | 0.786974i | \(0.711646\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.35011 | 0.140198 | 0.0700989 | − | 0.997540i | \(-0.477669\pi\) | ||||
0.0700989 | + | 0.997540i | \(0.477669\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.30216 | − | 0.143870i | −0.0543983 | − | 0.00601024i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24.5318 | + | 24.5318i | 1.02127 | + | 1.02127i | 0.999769 | + | 0.0215023i | \(0.00684493\pi\) |
0.0215023 | + | 0.999769i | \(0.493155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.77049 | − | 10.9492i | −0.364489 | − | 0.455035i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.711233i | − | 0.0295069i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.96251 | − | 4.96251i | 0.205526 | − | 0.205526i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.58383 | + | 9.58383i | −0.395567 | + | 0.395567i | −0.876666 | − | 0.481099i | \(-0.840238\pi\) |
0.481099 | + | 0.876666i | \(0.340238\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.8912i | 0.654786i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.7140 | − | 27.1081i | −0.893194 | − | 1.11508i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.9983 | − | 26.9983i | −1.10869 | − | 1.10869i | −0.993323 | − | 0.115365i | \(-0.963196\pi\) |
−0.115365 | − | 0.993323i | \(-0.536804\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.2603 | + | 1.57556i | 0.583636 | + | 0.0644835i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.0022 | −1.63445 | −0.817223 | − | 0.576322i | \(-0.804487\pi\) | ||||
−0.817223 | + | 0.576322i | \(0.804487\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.8170 | −1.46101 | −0.730504 | − | 0.682909i | \(-0.760715\pi\) | ||||
−0.730504 | + | 0.682909i | \(0.760715\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.2884 | − | 20.9469i | −0.541145 | − | 0.853024i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11.6563 | − | 11.6563i | −0.473114 | − | 0.473114i | 0.429807 | − | 0.902921i | \(-0.358582\pi\) |
−0.902921 | + | 0.429807i | \(0.858582\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.33721 | − | 1.07112i | 0.0541865 | − | 0.0434041i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 36.2002i | − | 1.46450i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.9028 | − | 26.9028i | 1.08659 | − | 1.08659i | 0.0907173 | − | 0.995877i | \(-0.471084\pi\) |
0.995877 | − | 0.0907173i | \(-0.0289160\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.86030 | + | 1.86030i | −0.0748927 | + | 0.0748927i | −0.743561 | − | 0.668668i | \(-0.766865\pi\) |
0.668668 | + | 0.743561i | \(0.266865\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 15.5836i | − | 0.626359i | −0.949694 | − | 0.313180i | \(-0.898606\pi\) | ||
0.949694 | − | 0.313180i | \(-0.101394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.16065 | + | 1.05782i | −0.0867040 | + | 0.0424489i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.53233 | + | 1.53233i | 0.0613914 | + | 0.0613914i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.912522 | − | 8.25919i | 0.0364426 | − | 0.329840i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.41065 | −0.175864 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.6912 | −1.65970 | −0.829851 | − | 0.557986i | \(-0.811574\pi\) | ||||
−0.829851 | + | 0.557986i | \(0.811574\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.26799 | + | 11.4765i | −0.0503981 | + | 0.456150i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.7982 | − | 20.7982i | −0.824055 | − | 0.824055i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.82806 | − | 39.4635i | 0.349233 | − | 1.56115i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3178i | 0.447026i | 0.974701 | + | 0.223513i | \(0.0717526\pi\) | ||||
−0.974701 | + | 0.223513i | \(0.928247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.7923 | − | 17.7923i | 0.701660 | − | 0.701660i | −0.263107 | − | 0.964767i | \(-0.584747\pi\) |
0.964767 | + | 0.263107i | \(0.0847472\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.8246 | + | 11.8246i | −0.464874 | + | 0.464874i | −0.900249 | − | 0.435375i | \(-0.856616\pi\) |
0.435375 | + | 0.900249i | \(0.356616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.4982i | − | 0.569103i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.715401 | − | 0.573046i | 0.0280388 | − | 0.0224594i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.1676 | + | 28.1676i | 1.10228 | + | 1.10228i | 0.994135 | + | 0.108148i | \(0.0344920\pi\) |
0.108148 | + | 0.994135i | \(0.465508\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 21.9171 | − | 13.9039i | 0.855067 | − | 0.542442i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.7953 | −0.887977 | −0.443989 | − | 0.896032i | \(-0.646437\pi\) | ||||
−0.443989 | + | 0.896032i | \(0.646437\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.25051 | 0.0875346 | 0.0437673 | − | 0.999042i | \(-0.486064\pi\) | ||||
0.0437673 | + | 0.999042i | \(0.486064\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.0778 | − | 1.44491i | −0.507901 | − | 0.0561158i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.05264 | − | 2.05264i | −0.0794784 | − | 0.0794784i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.72992 | + | 9.65017i | 0.298856 | + | 0.373097i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.29398i | 0.0885582i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.293887 | + | 0.293887i | −0.0113285 | + | 0.0113285i | −0.712748 | − | 0.701420i | \(-0.752550\pi\) |
0.701420 | + | 0.712748i | \(0.252550\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.36621 | + | 8.36621i | −0.321540 | + | 0.321540i | −0.849358 | − | 0.527818i | \(-0.823010\pi\) |
0.527818 | + | 0.849358i | \(0.323010\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.72155i | 0.0660672i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.18323 | + | 1.47717i | 0.0453416 | + | 0.0566052i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.10728 | + | 2.10728i | 0.0806327 | + | 0.0806327i | 0.746273 | − | 0.665640i | \(-0.231841\pi\) |
−0.665640 | + | 0.746273i | \(0.731841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40.1185 | + | 4.43252i | 1.53062 | + | 0.169111i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.2237 | −1.11333 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.1968 | 1.11070 | 0.555350 | − | 0.831617i | \(-0.312584\pi\) | ||||
0.555350 | + | 0.831617i | \(0.312584\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.404724 | + | 0.256751i | −0.0153742 | + | 0.00975315i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.96580 | − | 6.96580i | −0.263848 | − | 0.263848i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.9275 | + | 13.5592i | −0.640259 | + | 0.512856i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.88318i | 0.222205i | 0.993809 | + | 0.111102i | \(0.0354381\pi\) | ||||
−0.993809 | + | 0.111102i | \(0.964562\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.20178 | + | 8.20178i | −0.309336 | + | 0.309336i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.64337 | + | 1.64337i | −0.0618055 | + | 0.0618055i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 30.4817i | − | 1.14476i | −0.819987 | − | 0.572382i | \(-0.806019\pi\) | ||
0.819987 | − | 0.572382i | \(-0.193981\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.46077 | + | 19.9407i | −0.167292 | + | 0.747833i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.09815 | − | 1.09815i | −0.0411261 | − | 0.0411261i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.88420 | − | 26.1048i | 0.107713 | − | 0.974900i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.1170 | −1.42152 | −0.710762 | − | 0.703433i | \(-0.751649\pi\) | ||||
−0.710762 | + | 0.703433i | \(0.751649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.02426 | 0.112629 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.35100 | − | 39.3807i | 0.161816 | − | 1.46458i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.08333 | − | 9.08333i | −0.336882 | − | 0.336882i | 0.518310 | − | 0.855193i | \(-0.326561\pi\) |
−0.855193 | + | 0.518310i | \(0.826561\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.3259 | − | 16.5592i | −0.789847 | − | 0.613304i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 7.98919i | − | 0.295491i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.6105 | − | 11.6105i | 0.428845 | − | 0.428845i | −0.459390 | − | 0.888235i | \(-0.651932\pi\) |
0.888235 | + | 0.459390i | \(0.151932\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.92104 | + | 5.92104i | −0.218104 | + | 0.218104i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.77501i | 0.175652i | 0.996136 | + | 0.0878258i | \(0.0279919\pi\) | ||||
−0.996136 | + | 0.0878258i | \(0.972008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −27.0056 | + | 21.6319i | −0.992075 | + | 0.794666i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.9192 | + | 34.9192i | 1.28106 | + | 1.28106i | 0.940064 | + | 0.340999i | \(0.110765\pi\) |
0.340999 | + | 0.940064i | \(0.389235\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.24493 | − | 11.4204i | −0.265078 | − | 0.417851i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.86239 | −0.104589 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.5575 | 0.969097 | 0.484548 | − | 0.874764i | \(-0.338984\pi\) | ||||
0.484548 | + | 0.874764i | \(0.338984\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 28.6713 | + | 3.16777i | 1.04484 | + | 0.115440i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0325 | + | 30.0325i | 1.09155 | + | 1.09155i | 0.995363 | + | 0.0961876i | \(0.0306649\pi\) |
0.0961876 | + | 0.995363i | \(0.469335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.507686 | + | 0.633805i | 0.0184278 | + | 0.0230057i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.7650i | 0.390230i | 0.980780 | + | 0.195115i | \(0.0625080\pi\) | ||||
−0.980780 | + | 0.195115i | \(0.937492\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.817287 | + | 0.817287i | −0.0295878 | + | 0.0295878i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.6890 | + | 42.6890i | −1.54141 | + | 1.54141i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 53.3247i | − | 1.92294i | −0.274913 | − | 0.961469i | \(-0.588649\pi\) | ||
0.274913 | − | 0.961469i | \(-0.411351\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.3395 | − | 26.6407i | −0.768524 | − | 0.959440i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −35.5162 | − | 35.5162i | −1.27743 | − | 1.27743i | −0.942101 | − | 0.335330i | \(-0.891152\pi\) |
−0.335330 | − | 0.942101i | \(-0.608848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.664994 | + | 0.0734723i | 0.0238565 | + | 0.00263581i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.9063 | −0.928191 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.6505 | −0.488454 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.5609 | − | 30.8206i | 0.377416 | − | 1.10144i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0977 | + | 28.0977i | 1.00157 | + | 1.00157i | 0.999999 | + | 0.00157487i | \(0.000501296\pi\) |
0.00157487 | + | 0.999999i | \(0.499499\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.4557 | − | 14.7833i | 0.657040 | − | 0.526298i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.02805i | − | 0.0721092i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.75450 | − | 6.75450i | 0.239859 | − | 0.239859i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.3304 | + | 25.3304i | −0.897248 | + | 0.897248i | −0.995192 | − | 0.0979442i | \(-0.968773\pi\) |
0.0979442 | + | 0.995192i | \(0.468773\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.4647i | − | 0.547100i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 40.2138 | + | 8.99592i | 1.42089 | + | 0.317855i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.19528 | − | 6.19528i | −0.218627 | − | 0.218627i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.40055 | − | 30.7782i | 0.119705 | − | 1.08344i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.2296 | −1.02766 | −0.513829 | − | 0.857893i | \(-0.671773\pi\) | ||||
−0.513829 | + | 0.857893i | \(0.671773\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.97765 | 0.139674 | 0.0698371 | − | 0.997558i | \(-0.477752\pi\) | ||||
0.0698371 | + | 0.997558i | \(0.477752\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.0556957 | + | 0.504098i | −0.00195333 | + | 0.0176795i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.8562 | − | 14.8562i | −0.519753 | − | 0.519753i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.94768 | + | 0.435699i | 0.0680573 | + | 0.0152246i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5.75434i | − | 0.200828i | −0.994946 | − | 0.100414i | \(-0.967983\pi\) | ||
0.994946 | − | 0.100414i | \(-0.0320167\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.3410 | − | 16.3410i | 0.569612 | − | 0.569612i | −0.362408 | − | 0.932020i | \(-0.618045\pi\) |
0.932020 | + | 0.362408i | \(0.118045\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.9312 | − | 18.9312i | 0.658302 | − | 0.658302i | −0.296676 | − | 0.954978i | \(-0.595878\pi\) |
0.954978 | + | 0.296676i | \(0.0958781\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.0338i | 0.799997i | 0.916516 | + | 0.399999i | \(0.130989\pi\) | ||||
−0.916516 | + | 0.399999i | \(0.869011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 38.8429 | − | 31.1137i | 1.34744 | − | 1.07932i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.88497 | − | 8.88497i | −0.307846 | − | 0.307846i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.65004 | − | 16.4889i | 0.195294 | − | 0.569940i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.4801 | −0.568957 | −0.284479 | − | 0.958682i | \(-0.591820\pi\) | ||||
−0.284479 | + | 0.958682i | \(0.591820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.3128 | 0.355613 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.89589 | − | 0.761897i | −0.237507 | − | 0.0262411i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.11272 | − | 1.11272i | −0.0382334 | − | 0.0382334i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.1256 | − | 35.1125i | −0.965268 | − | 1.20506i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1.13356i | − | 0.0388578i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.51307 | − | 1.51307i | 0.0518066 | − | 0.0518066i | −0.680729 | − | 0.732535i | \(-0.738337\pi\) |
0.732535 | + | 0.680729i | \(0.238337\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.46476 | − | 2.46476i | 0.0841947 | − | 0.0841947i | −0.663755 | − | 0.747950i | \(-0.731038\pi\) |
0.747950 | + | 0.663755i | \(0.231038\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 18.9804i | − | 0.647601i | −0.946125 | − | 0.323801i | \(-0.895039\pi\) | ||
0.946125 | − | 0.323801i | \(-0.104961\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.934198 | + | 1.16627i | 0.0318374 | + | 0.0397463i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.1114 | − | 18.1114i | −0.616518 | − | 0.616518i | 0.328118 | − | 0.944637i | \(-0.393585\pi\) |
−0.944637 | + | 0.328118i | \(0.893585\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.6799 | + | 2.61630i | 0.804213 | + | 0.0888540i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.89752 | 0.233982 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.8683 | 1.18147 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.5365 | + | 27.6433i | 0.593521 | + | 0.935585i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6363 | − | 22.6363i | −0.764375 | − | 0.764375i | 0.212735 | − | 0.977110i | \(-0.431763\pi\) |
−0.977110 | + | 0.212735i | \(0.931763\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.9245 | − | 8.75069i | 0.368475 | − | 0.295153i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.3924i | 0.653345i | 0.945138 | + | 0.326673i | \(0.105927\pi\) | ||||
−0.945138 | + | 0.326673i | \(0.894073\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.25483 | − | 7.25483i | 0.244144 | − | 0.244144i | −0.574418 | − | 0.818562i | \(-0.694772\pi\) |
0.818562 | + | 0.574418i | \(0.194772\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.8434 | + | 21.8434i | −0.733431 | + | 0.733431i | −0.971298 | − | 0.237867i | \(-0.923552\pi\) |
0.237867 | + | 0.971298i | \(0.423552\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.88337i | − | 0.0631662i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.88336 | + | 8.24539i | −0.130097 | + | 0.276231i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −28.7571 | − | 28.7571i | −0.962320 | − | 0.962320i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.371349 | − | 3.36106i | 0.0123990 | − | 0.112222i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 21.0322 | 0.701462 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.4843 | −0.415912 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.133083 | + | 1.20453i | −0.00442874 | + | 0.0400843i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.4881 | + | 12.4881i | 0.414662 | + | 0.414662i | 0.883359 | − | 0.468697i | \(-0.155276\pi\) |
−0.468697 | + | 0.883359i | \(0.655276\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.64785 | + | 43.1281i | −0.319999 | + | 1.43047i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.91275i | 0.195898i | 0.995191 | + | 0.0979490i | \(0.0312282\pi\) | ||||
−0.995191 | + | 0.0979490i | \(0.968772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.22819 | + | 3.22819i | −0.106838 | + | 0.106838i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.624601 | − | 0.624601i | 0.0206261 | − | 0.0206261i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.6407i | − | 1.01074i | −0.862902 | − | 0.505372i | \(-0.831355\pi\) | ||
0.862902 | − | 0.505372i | \(-0.168645\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.5186 | + | 26.8488i | −1.10447 | + | 0.884699i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40.1932 | + | 40.1932i | 1.32298 | + | 1.32298i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 48.5612 | − | 30.8065i | 1.59496 | − | 1.01182i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −40.1327 | −1.31671 | −0.658356 | − | 0.752707i | \(-0.728748\pi\) | ||||
−0.658356 | + | 0.752707i | \(0.728748\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.0439 | −1.08297 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.28358 | − | 0.252302i | −0.0747609 | − | 0.00826001i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.6008 | − | 35.6008i | −1.16303 | − | 1.16303i | −0.983809 | − | 0.179218i | \(-0.942643\pi\) |
−0.179218 | − | 0.983809i | \(-0.557357\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.6404 | − | 32.0099i | −0.836743 | − | 1.04460i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.16398i | − | 0.135742i | −0.997694 | − | 0.0678709i | \(-0.978379\pi\) | ||
0.997694 | − | 0.0678709i | \(-0.0216206\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.79024 | − | 1.79024i | 0.0582982 | − | 0.0582982i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.58663 | + | 4.58663i | −0.149046 | + | 0.149046i | −0.777692 | − | 0.628646i | \(-0.783609\pi\) |
0.628646 | + | 0.777692i | \(0.283609\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.4833i | 1.18430i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.80268 | − | 9.74100i | −0.253019 | − | 0.315874i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.72806 | − | 3.72806i | −0.120764 | − | 0.120764i | 0.644142 | − | 0.764906i | \(-0.277214\pi\) |
−0.764906 | + | 0.644142i | \(0.777214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.9311 | − | 1.20773i | −0.353353 | − | 0.0390404i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.09078 | −0.0675149 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.7479 | −0.637029 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.9619 | + | 29.1575i | −1.48110 | + | 0.939589i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.3290 | + | 36.3290i | 1.16826 | + | 1.16826i | 0.982617 | + | 0.185646i | \(0.0594379\pi\) |
0.185646 | + | 0.982617i | \(0.440562\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.5368 | + | 9.24110i | −0.370614 | + | 0.296867i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.57600i | 0.178942i | 0.995989 | + | 0.0894712i | \(0.0285177\pi\) | ||||
−0.995989 | + | 0.0894712i | \(0.971482\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.782793 | − | 0.782793i | 0.0250952 | − | 0.0250952i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −37.4734 | + | 37.4734i | −1.19888 | + | 1.19888i | −0.224376 | + | 0.974503i | \(0.572035\pi\) |
−0.974503 | + | 0.224376i | \(0.927965\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 13.9101i | − | 0.444568i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.79810 | + | 21.4486i | −0.153191 | + | 0.684801i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.11736 | + | 3.11736i | 0.0994284 | + | 0.0994284i | 0.755071 | − | 0.655643i | \(-0.227602\pi\) |
−0.655643 | + | 0.755071i | \(0.727602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.257609 | + | 2.33161i | −0.00819979 | + | 0.0742159i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.05326 | 0.0652897 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.5731 | 0.621759 | 0.310880 | − | 0.950449i | \(-0.399376\pi\) | ||||
0.310880 | + | 0.950449i | \(0.399376\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.20226 | + | 38.0345i | −0.133355 | + | 1.20699i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.5349 | + | 24.5349i | 0.777029 | + | 0.777029i | 0.979324 | − | 0.202296i | \(-0.0648402\pi\) |
−0.202296 | + | 0.979324i | \(0.564840\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.4264 | − | 5.59416i | 0.361514 | − | 0.176991i |
(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.i.a.557.9 | yes | 32 | |
3.2 | odd | 2 | inner | 1500.2.i.a.557.16 | yes | 32 | |
5.2 | odd | 4 | inner | 1500.2.i.a.1193.1 | yes | 32 | |
5.3 | odd | 4 | inner | 1500.2.i.a.1193.16 | yes | 32 | |
5.4 | even | 2 | inner | 1500.2.i.a.557.8 | yes | 32 | |
15.2 | even | 4 | inner | 1500.2.i.a.1193.8 | yes | 32 | |
15.8 | even | 4 | inner | 1500.2.i.a.1193.9 | yes | 32 | |
15.14 | odd | 2 | inner | 1500.2.i.a.557.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1500.2.i.a.557.1 | ✓ | 32 | 15.14 | odd | 2 | inner | |
1500.2.i.a.557.8 | yes | 32 | 5.4 | even | 2 | inner | |
1500.2.i.a.557.9 | yes | 32 | 1.1 | even | 1 | trivial | |
1500.2.i.a.557.16 | yes | 32 | 3.2 | odd | 2 | inner | |
1500.2.i.a.1193.1 | yes | 32 | 5.2 | odd | 4 | inner | |
1500.2.i.a.1193.8 | yes | 32 | 15.2 | even | 4 | inner | |
1500.2.i.a.1193.9 | yes | 32 | 15.8 | even | 4 | inner | |
1500.2.i.a.1193.16 | yes | 32 | 5.3 | odd | 4 | inner |