Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(589,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.g (of order \(2\), degree \(1\), 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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 589.4 | ||
Root | \(-1.69230i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.589 |
Dual form | 1470.2.g.k.589.8 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.18183 | − | 0.489528i | 0.975742 | − | 0.218924i | ||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.489528 | − | 2.18183i | −0.154802 | − | 0.689954i | ||||
\(11\) | −2.39327 | −0.721598 | −0.360799 | − | 0.932644i | \(-0.617496\pi\) | ||||
−0.360799 | + | 0.932644i | \(0.617496\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 3.80748i | 1.05601i | 0.849243 | + | 0.528003i | \(0.177059\pi\) | ||||
−0.849243 | + | 0.528003i | \(0.822941\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.489528 | + | 2.18183i | 0.126396 | + | 0.563345i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 1.97038i | − | 0.477888i | −0.971033 | − | 0.238944i | \(-0.923199\pi\) | ||
0.971033 | − | 0.238944i | \(-0.0768012\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 4.17113 | 0.956924 | 0.478462 | − | 0.878108i | \(-0.341194\pi\) | ||||
0.478462 | + | 0.878108i | \(0.341194\pi\) | |||||||
\(20\) | −2.18183 | + | 0.489528i | −0.487871 | + | 0.109462i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.39327i | 0.510247i | ||||||||
\(23\) | 8.17113i | 1.70380i | 0.523705 | + | 0.851900i | \(0.324549\pi\) | ||||
−0.523705 | + | 0.851900i | \(0.675451\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.52072 | − | 2.13613i | 0.904145 | − | 0.427226i | ||||
\(26\) | 3.80748 | 0.746709 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.16246 | 1.70143 | 0.850713 | − | 0.525631i | \(-0.176171\pi\) | ||||
0.850713 | + | 0.525631i | \(0.176171\pi\) | |||||||
\(30\) | 2.18183 | − | 0.489528i | 0.398345 | − | 0.0893752i | ||||
\(31\) | 1.60673 | 0.288577 | 0.144289 | − | 0.989536i | \(-0.453911\pi\) | ||||
0.144289 | + | 0.989536i | \(0.453911\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | − | 2.39327i | − | 0.416615i | ||||||
\(34\) | −1.97038 | −0.337918 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | − | 1.26358i | − | 0.207732i | −0.994591 | − | 0.103866i | \(-0.966879\pi\) | ||
0.994591 | − | 0.103866i | \(-0.0331213\pi\) | |||||||
\(38\) | − | 4.17113i | − | 0.676647i | ||||||
\(39\) | −3.80748 | −0.609685 | ||||||||
\(40\) | 0.489528 | + | 2.18183i | 0.0774012 | + | 0.344977i | ||||
\(41\) | −3.19208 | −0.498519 | −0.249259 | − | 0.968437i | \(-0.580187\pi\) | ||||
−0.249259 | + | 0.968437i | \(0.580187\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.90755i | 0.748394i | 0.927349 | + | 0.374197i | \(0.122082\pi\) | ||||
−0.927349 | + | 0.374197i | \(0.877918\pi\) | |||||||
\(44\) | 2.39327 | 0.360799 | ||||||||
\(45\) | −2.18183 | + | 0.489528i | −0.325247 | + | 0.0729745i | ||||
\(46\) | 8.17113 | 1.20477 | ||||||||
\(47\) | − | 3.00868i | − | 0.438860i | −0.975628 | − | 0.219430i | \(-0.929580\pi\) | ||
0.975628 | − | 0.219430i | \(-0.0704198\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.13613 | − | 4.52072i | −0.302094 | − | 0.639327i | ||||
\(51\) | 1.97038 | 0.275909 | ||||||||
\(52\) | − | 3.80748i | − | 0.528003i | ||||||
\(53\) | 12.1711i | 1.67183i | 0.548856 | + | 0.835917i | \(0.315064\pi\) | ||||
−0.548856 | + | 0.835917i | \(0.684936\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −5.22170 | + | 1.17157i | −0.704093 | + | 0.157975i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.17113i | 0.552480i | ||||||||
\(58\) | − | 9.16246i | − | 1.20309i | ||||||
\(59\) | −13.0414 | −1.69785 | −0.848926 | − | 0.528512i | \(-0.822750\pi\) | ||||
−0.848926 | + | 0.528512i | \(0.822750\pi\) | |||||||
\(60\) | −0.489528 | − | 2.18183i | −0.0631978 | − | 0.281672i | ||||
\(61\) | 13.0910 | 1.67612 | 0.838062 | − | 0.545574i | \(-0.183688\pi\) | ||||
0.838062 | + | 0.545574i | \(0.183688\pi\) | |||||||
\(62\) | − | 1.60673i | − | 0.204055i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.86387 | + | 8.30726i | 0.231185 | + | 1.03039i | ||||
\(66\) | −2.39327 | −0.294591 | ||||||||
\(67\) | 5.77786i | 0.705878i | 0.935646 | + | 0.352939i | \(0.114818\pi\) | ||||
−0.935646 | + | 0.352939i | \(0.885182\pi\) | |||||||
\(68\) | 1.97038i | 0.238944i | ||||||||
\(69\) | −8.17113 | −0.983689 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.94032 | 0.823665 | 0.411832 | − | 0.911260i | \(-0.364889\pi\) | ||||
0.411832 | + | 0.911260i | \(0.364889\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | − | 0.506664i | − | 0.0593005i | −0.999560 | − | 0.0296503i | \(-0.990561\pi\) | ||
0.999560 | − | 0.0296503i | \(-0.00943935\pi\) | |||||||
\(74\) | −1.26358 | −0.146889 | ||||||||
\(75\) | 2.13613 | + | 4.52072i | 0.246659 | + | 0.522008i | ||||
\(76\) | −4.17113 | −0.478462 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3.80748i | 0.431113i | ||||||||
\(79\) | 12.4260 | 1.39804 | 0.699020 | − | 0.715103i | \(-0.253620\pi\) | ||||
0.699020 | + | 0.715103i | \(0.253620\pi\) | |||||||
\(80\) | 2.18183 | − | 0.489528i | 0.243935 | − | 0.0547309i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.19208i | 0.352506i | ||||||||
\(83\) | − | 1.89887i | − | 0.208429i | −0.994555 | − | 0.104214i | \(-0.966767\pi\) | ||
0.994555 | − | 0.104214i | \(-0.0332328\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.964557 | − | 4.29903i | −0.104621 | − | 0.466295i | ||||
\(86\) | 4.90755 | 0.529195 | ||||||||
\(87\) | 9.16246i | 0.982319i | ||||||||
\(88\) | − | 2.39327i | − | 0.255123i | ||||||
\(89\) | −1.97949 | −0.209826 | −0.104913 | − | 0.994481i | \(-0.533456\pi\) | ||||
−0.104913 | + | 0.994481i | \(0.533456\pi\) | |||||||
\(90\) | 0.489528 | + | 2.18183i | 0.0516008 | + | 0.229985i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 8.17113i | − | 0.851900i | ||||||
\(93\) | 1.60673i | 0.166610i | ||||||||
\(94\) | −3.00868 | −0.310321 | ||||||||
\(95\) | 9.10069 | − | 2.04189i | 0.933711 | − | 0.209493i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | − | 12.0624i | − | 1.22475i | −0.790567 | − | 0.612375i | \(-0.790214\pi\) | ||
0.790567 | − | 0.612375i | \(-0.209786\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.39327 | 0.240533 | ||||||||
\(100\) | −4.52072 | + | 2.13613i | −0.452072 | + | 0.213613i | ||||
\(101\) | 7.86672 | 0.782768 | 0.391384 | − | 0.920227i | \(-0.371996\pi\) | ||||
0.391384 | + | 0.920227i | \(0.371996\pi\) | |||||||
\(102\) | − | 1.97038i | − | 0.195097i | ||||||
\(103\) | 5.89887i | 0.581233i | 0.956840 | + | 0.290617i | \(0.0938604\pi\) | ||||
−0.956840 | + | 0.290617i | \(0.906140\pi\) | |||||||
\(104\) | −3.80748 | −0.373354 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.1711 | 1.18217 | ||||||||
\(107\) | − | 3.75798i | − | 0.363298i | −0.983363 | − | 0.181649i | \(-0.941857\pi\) | ||
0.983363 | − | 0.181649i | \(-0.0581434\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −7.14257 | −0.684135 | −0.342067 | − | 0.939675i | \(-0.611127\pi\) | ||||
−0.342067 | + | 0.939675i | \(0.611127\pi\) | |||||||
\(110\) | 1.17157 | + | 5.22170i | 0.111705 | + | 0.497869i | ||||
\(111\) | 1.26358 | 0.119934 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 17.3837i | − | 1.63532i | −0.575700 | − | 0.817661i | \(-0.695270\pi\) | ||
0.575700 | − | 0.817661i | \(-0.304730\pi\) | |||||||
\(114\) | 4.17113 | 0.390663 | ||||||||
\(115\) | 4.00000 | + | 17.8280i | 0.373002 | + | 1.66247i | ||||
\(116\) | −9.16246 | −0.850713 | ||||||||
\(117\) | − | 3.80748i | − | 0.352002i | ||||||
\(118\) | 13.0414i | 1.20056i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.18183 | + | 0.489528i | −0.199173 | + | 0.0446876i | ||||
\(121\) | −5.27226 | −0.479296 | ||||||||
\(122\) | − | 13.0910i | − | 1.18520i | ||||||
\(123\) | − | 3.19208i | − | 0.287820i | ||||||
\(124\) | −1.60673 | −0.144289 | ||||||||
\(125\) | 8.81774 | − | 6.87368i | 0.788682 | − | 0.614801i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.4434i | 1.63659i | 0.574801 | + | 0.818293i | \(0.305079\pi\) | ||||
−0.574801 | + | 0.818293i | \(0.694921\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −4.90755 | −0.432086 | ||||||||
\(130\) | 8.30726 | − | 1.86387i | 0.728595 | − | 0.163472i | ||||
\(131\) | 0.615405 | 0.0537682 | 0.0268841 | − | 0.999639i | \(-0.491441\pi\) | ||||
0.0268841 | + | 0.999639i | \(0.491441\pi\) | |||||||
\(132\) | 2.39327i | 0.208307i | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 5.77786 | 0.499131 | ||||||||
\(135\) | −0.489528 | − | 2.18183i | −0.0421319 | − | 0.187782i | ||||
\(136\) | 1.97038 | 0.168959 | ||||||||
\(137\) | 7.82799i | 0.668790i | 0.942433 | + | 0.334395i | \(0.108532\pi\) | ||||
−0.942433 | + | 0.334395i | \(0.891468\pi\) | |||||||
\(138\) | 8.17113i | 0.695573i | ||||||||
\(139\) | 6.15378 | 0.521957 | 0.260979 | − | 0.965345i | \(-0.415955\pi\) | ||||
0.260979 | + | 0.965345i | \(0.415955\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00868 | 0.253376 | ||||||||
\(142\) | − | 6.94032i | − | 0.582419i | ||||||
\(143\) | − | 9.11233i | − | 0.762012i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 19.9909 | − | 4.48528i | 1.66015 | − | 0.372482i | ||||
\(146\) | −0.506664 | −0.0419318 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.26358i | 0.103866i | ||||||||
\(149\) | 7.53584 | 0.617360 | 0.308680 | − | 0.951166i | \(-0.400113\pi\) | ||||
0.308680 | + | 0.951166i | \(0.400113\pi\) | |||||||
\(150\) | 4.52072 | − | 2.13613i | 0.369116 | − | 0.174414i | ||||
\(151\) | 9.04145 | 0.735783 | 0.367891 | − | 0.929869i | \(-0.380080\pi\) | ||||
0.367891 | + | 0.929869i | \(0.380080\pi\) | |||||||
\(152\) | 4.17113i | 0.338324i | ||||||||
\(153\) | 1.97038i | 0.159296i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.50560 | − | 0.786540i | 0.281577 | − | 0.0631764i | ||||
\(156\) | 3.80748 | 0.304843 | ||||||||
\(157\) | 22.6640i | 1.80879i | 0.426700 | + | 0.904393i | \(0.359676\pi\) | ||||
−0.426700 | + | 0.904393i | \(0.640324\pi\) | |||||||
\(158\) | − | 12.4260i | − | 0.988563i | ||||||
\(159\) | −12.1711 | −0.965234 | ||||||||
\(160\) | −0.489528 | − | 2.18183i | −0.0387006 | − | 0.172488i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 10.2039i | 0.799232i | 0.916683 | + | 0.399616i | \(0.130856\pi\) | ||||
−0.916683 | + | 0.399616i | \(0.869144\pi\) | |||||||
\(164\) | 3.19208 | 0.249259 | ||||||||
\(165\) | −1.17157 | − | 5.22170i | −0.0912068 | − | 0.406509i | ||||
\(166\) | −1.89887 | −0.147381 | ||||||||
\(167\) | − | 25.2498i | − | 1.95389i | −0.213492 | − | 0.976945i | \(-0.568484\pi\) | ||
0.213492 | − | 0.976945i | \(-0.431516\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.49693 | −0.115148 | ||||||||
\(170\) | −4.29903 | + | 0.964557i | −0.329720 | + | 0.0739781i | ||||
\(171\) | −4.17113 | −0.318975 | ||||||||
\(172\) | − | 4.90755i | − | 0.374197i | ||||||
\(173\) | − | 12.5348i | − | 0.953002i | −0.879174 | − | 0.476501i | \(-0.841905\pi\) | ||
0.879174 | − | 0.476501i | \(-0.158095\pi\) | |||||||
\(174\) | 9.16246 | 0.694604 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.39327 | −0.180399 | ||||||||
\(177\) | − | 13.0414i | − | 0.980255i | ||||||
\(178\) | 1.97949i | 0.148369i | ||||||||
\(179\) | −22.9196 | −1.71309 | −0.856544 | − | 0.516074i | \(-0.827393\pi\) | ||||
−0.856544 | + | 0.516074i | \(0.827393\pi\) | |||||||
\(180\) | 2.18183 | − | 0.489528i | 0.162624 | − | 0.0364873i | ||||
\(181\) | 19.6181 | 1.45820 | 0.729102 | − | 0.684405i | \(-0.239938\pi\) | ||||
0.729102 | + | 0.684405i | \(0.239938\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.0910i | 0.967711i | ||||||||
\(184\) | −8.17113 | −0.602384 | ||||||||
\(185\) | −0.618560 | − | 2.75692i | −0.0454774 | − | 0.202693i | ||||
\(186\) | 1.60673 | 0.117811 | ||||||||
\(187\) | 4.71565i | 0.344843i | ||||||||
\(188\) | 3.00868i | 0.219430i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.04189 | − | 9.10069i | −0.148134 | − | 0.660233i | ||||
\(191\) | −19.7269 | −1.42739 | −0.713693 | − | 0.700459i | \(-0.752979\pi\) | ||||
−0.713693 | + | 0.700459i | \(0.752979\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | − | 4.78654i | − | 0.344543i | −0.985050 | − | 0.172271i | \(-0.944889\pi\) | ||
0.985050 | − | 0.172271i | \(-0.0551106\pi\) | |||||||
\(194\) | −12.0624 | −0.866029 | ||||||||
\(195\) | −8.30726 | + | 1.86387i | −0.594896 | + | 0.133475i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 17.1997i | − | 1.22543i | −0.790305 | − | 0.612714i | \(-0.790078\pi\) | ||
0.790305 | − | 0.612714i | \(-0.209922\pi\) | |||||||
\(198\) | − | 2.39327i | − | 0.170082i | ||||||
\(199\) | −15.5056 | −1.09916 | −0.549582 | − | 0.835440i | \(-0.685213\pi\) | ||||
−0.549582 | + | 0.835440i | \(0.685213\pi\) | |||||||
\(200\) | 2.13613 | + | 4.52072i | 0.151047 | + | 0.319663i | ||||
\(201\) | −5.77786 | −0.407539 | ||||||||
\(202\) | − | 7.86672i | − | 0.553501i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.97038 | −0.137954 | ||||||||
\(205\) | −6.96456 | + | 1.56261i | −0.486426 | + | 0.109138i | ||||
\(206\) | 5.89887 | 0.410994 | ||||||||
\(207\) | − | 8.17113i | − | 0.567933i | ||||||
\(208\) | 3.80748i | 0.264001i | ||||||||
\(209\) | −9.98265 | −0.690514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8980 | −1.64521 | −0.822603 | − | 0.568616i | \(-0.807479\pi\) | ||||
−0.822603 | + | 0.568616i | \(0.807479\pi\) | |||||||
\(212\) | − | 12.1711i | − | 0.835917i | ||||||
\(213\) | 6.94032i | 0.475543i | ||||||||
\(214\) | −3.75798 | −0.256890 | ||||||||
\(215\) | 2.40238 | + | 10.7074i | 0.163841 | + | 0.730240i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.14257i | 0.483756i | ||||||||
\(219\) | 0.506664 | 0.0342372 | ||||||||
\(220\) | 5.22170 | − | 1.17157i | 0.352047 | − | 0.0789874i | ||||
\(221\) | 7.50219 | 0.504652 | ||||||||
\(222\) | − | 1.26358i | − | 0.0848062i | ||||||
\(223\) | 0.870315i | 0.0582806i | 0.999575 | + | 0.0291403i | \(0.00927696\pi\) | ||||
−0.999575 | + | 0.0291403i | \(0.990723\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.52072 | + | 2.13613i | −0.301382 | + | 0.142409i | ||||
\(226\) | −17.3837 | −1.15635 | ||||||||
\(227\) | − | 14.6854i | − | 0.974705i | −0.873205 | − | 0.487353i | \(-0.837963\pi\) | ||
0.873205 | − | 0.487353i | \(-0.162037\pi\) | |||||||
\(228\) | − | 4.17113i | − | 0.276240i | ||||||
\(229\) | −24.0379 | −1.58847 | −0.794233 | − | 0.607613i | \(-0.792127\pi\) | ||||
−0.794233 | + | 0.607613i | \(0.792127\pi\) | |||||||
\(230\) | 17.8280 | − | 4.00000i | 1.17554 | − | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.16246i | 0.601545i | ||||||||
\(233\) | 10.5445i | 0.690794i | 0.938457 | + | 0.345397i | \(0.112256\pi\) | ||||
−0.938457 | + | 0.345397i | \(0.887744\pi\) | |||||||
\(234\) | −3.80748 | −0.248903 | ||||||||
\(235\) | −1.47283 | − | 6.56440i | −0.0960769 | − | 0.428215i | ||||
\(236\) | 13.0414 | 0.848926 | ||||||||
\(237\) | 12.4260i | 0.807158i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.01289 | 0.259572 | 0.129786 | − | 0.991542i | \(-0.458571\pi\) | ||||
0.129786 | + | 0.991542i | \(0.458571\pi\) | |||||||
\(240\) | 0.489528 | + | 2.18183i | 0.0315989 | + | 0.140836i | ||||
\(241\) | 0.543899 | 0.0350356 | 0.0175178 | − | 0.999847i | \(-0.494424\pi\) | ||||
0.0175178 | + | 0.999847i | \(0.494424\pi\) | |||||||
\(242\) | 5.27226i | 0.338914i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −13.0910 | −0.838062 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.19208 | −0.203519 | ||||||||
\(247\) | 15.8815i | 1.01052i | ||||||||
\(248\) | 1.60673i | 0.102027i | ||||||||
\(249\) | 1.89887 | 0.120336 | ||||||||
\(250\) | −6.87368 | − | 8.81774i | −0.434730 | − | 0.557683i | ||||
\(251\) | −4.62829 | −0.292135 | −0.146068 | − | 0.989275i | \(-0.546662\pi\) | ||||
−0.146068 | + | 0.989275i | \(0.546662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 19.5557i | − | 1.22946i | ||||||
\(254\) | 18.4434 | 1.15724 | ||||||||
\(255\) | 4.29903 | − | 0.964557i | 0.269216 | − | 0.0604029i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 25.5671i | − | 1.59483i | −0.603429 | − | 0.797417i | \(-0.706199\pi\) | ||
0.603429 | − | 0.797417i | \(-0.293801\pi\) | |||||||
\(258\) | 4.90755i | 0.305531i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.86387 | − | 8.30726i | −0.115592 | − | 0.515195i | ||||
\(261\) | −9.16246 | −0.567142 | ||||||||
\(262\) | − | 0.615405i | − | 0.0380199i | ||||||
\(263\) | 20.5972i | 1.27008i | 0.772481 | + | 0.635038i | \(0.219016\pi\) | ||||
−0.772481 | + | 0.635038i | \(0.780984\pi\) | |||||||
\(264\) | 2.39327 | 0.147296 | ||||||||
\(265\) | 5.95811 | + | 26.5553i | 0.366004 | + | 1.63128i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1.97949i | − | 0.121143i | ||||||
\(268\) | − | 5.77786i | − | 0.352939i | ||||||
\(269\) | 2.23799 | 0.136453 | 0.0682263 | − | 0.997670i | \(-0.478266\pi\) | ||||
0.0682263 | + | 0.997670i | \(0.478266\pi\) | |||||||
\(270\) | −2.18183 | + | 0.489528i | −0.132782 | + | 0.0297917i | ||||
\(271\) | −19.1616 | −1.16398 | −0.581992 | − | 0.813195i | \(-0.697726\pi\) | ||||
−0.581992 | + | 0.813195i | \(0.697726\pi\) | |||||||
\(272\) | − | 1.97038i | − | 0.119472i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.82799 | 0.472906 | ||||||||
\(275\) | −10.8193 | + | 5.11233i | −0.652429 | + | 0.308285i | ||||
\(276\) | 8.17113 | 0.491844 | ||||||||
\(277\) | − | 3.67674i | − | 0.220914i | −0.993881 | − | 0.110457i | \(-0.964769\pi\) | ||
0.993881 | − | 0.110457i | \(-0.0352314\pi\) | |||||||
\(278\) | − | 6.15378i | − | 0.369079i | ||||||
\(279\) | −1.60673 | −0.0961924 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.8280 | −1.77939 | −0.889694 | − | 0.456557i | \(-0.849083\pi\) | ||||
−0.889694 | + | 0.456557i | \(0.849083\pi\) | |||||||
\(282\) | − | 3.00868i | − | 0.179164i | ||||||
\(283\) | − | 4.28961i | − | 0.254991i | −0.991839 | − | 0.127495i | \(-0.959306\pi\) | ||
0.991839 | − | 0.127495i | \(-0.0406938\pi\) | |||||||
\(284\) | −6.94032 | −0.411832 | ||||||||
\(285\) | 2.04189 | + | 9.10069i | 0.120951 | + | 0.539078i | ||||
\(286\) | −9.11233 | −0.538824 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 13.1176 | 0.771623 | ||||||||
\(290\) | −4.48528 | − | 19.9909i | −0.263385 | − | 1.17391i | ||||
\(291\) | 12.0624 | 0.707110 | ||||||||
\(292\) | 0.506664i | 0.0296503i | ||||||||
\(293\) | − | 24.5940i | − | 1.43680i | −0.695631 | − | 0.718399i | \(-0.744875\pi\) | ||
0.695631 | − | 0.718399i | \(-0.255125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −28.4542 | + | 6.38416i | −1.65667 | + | 0.371700i | ||||
\(296\) | 1.26358 | 0.0734444 | ||||||||
\(297\) | 2.39327i | 0.138872i | ||||||||
\(298\) | − | 7.53584i | − | 0.436540i | ||||||
\(299\) | −31.1115 | −1.79922 | ||||||||
\(300\) | −2.13613 | − | 4.52072i | −0.123330 | − | 0.261004i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 9.04145i | − | 0.520277i | ||||||
\(303\) | 7.86672i | 0.451931i | ||||||||
\(304\) | 4.17113 | 0.239231 | ||||||||
\(305\) | 28.5622 | − | 6.40839i | 1.63547 | − | 0.366943i | ||||
\(306\) | 1.97038 | 0.112639 | ||||||||
\(307\) | 2.14089i | 0.122187i | 0.998132 | + | 0.0610937i | \(0.0194588\pi\) | ||||
−0.998132 | + | 0.0610937i | \(0.980541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.89887 | −0.335575 | ||||||||
\(310\) | −0.786540 | − | 3.50560i | −0.0446724 | − | 0.199105i | ||||
\(311\) | 13.9991 | 0.793817 | 0.396909 | − | 0.917858i | \(-0.370083\pi\) | ||||
0.396909 | + | 0.917858i | \(0.370083\pi\) | |||||||
\(312\) | − | 3.80748i | − | 0.215556i | ||||||
\(313\) | − | 33.0727i | − | 1.86938i | −0.355463 | − | 0.934690i | \(-0.615677\pi\) | ||
0.355463 | − | 0.934690i | \(-0.384323\pi\) | |||||||
\(314\) | 22.6640 | 1.27901 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.4260 | −0.699020 | ||||||||
\(317\) | − | 7.38459i | − | 0.414760i | −0.978260 | − | 0.207380i | \(-0.933506\pi\) | ||
0.978260 | − | 0.207380i | \(-0.0664937\pi\) | |||||||
\(318\) | 12.1711i | 0.682523i | ||||||||
\(319\) | −21.9282 | −1.22775 | ||||||||
\(320\) | −2.18183 | + | 0.489528i | −0.121968 | + | 0.0273655i | ||||
\(321\) | 3.75798 | 0.209750 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 8.21872i | − | 0.457302i | ||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 8.13328 | + | 17.2126i | 0.451153 | + | 0.954782i | ||||
\(326\) | 10.2039 | 0.565142 | ||||||||
\(327\) | − | 7.14257i | − | 0.394985i | ||||||
\(328\) | − | 3.19208i | − | 0.176253i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.22170 | + | 1.17157i | −0.287445 | + | 0.0644930i | ||||
\(331\) | 21.5549 | 1.18476 | 0.592381 | − | 0.805658i | \(-0.298188\pi\) | ||||
0.592381 | + | 0.805658i | \(0.298188\pi\) | |||||||
\(332\) | 1.89887i | 0.104214i | ||||||||
\(333\) | 1.26358i | 0.0692440i | ||||||||
\(334\) | −25.2498 | −1.38161 | ||||||||
\(335\) | 2.82843 | + | 12.6063i | 0.154533 | + | 0.688755i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2549i | 1.21230i | 0.795350 | + | 0.606151i | \(0.207287\pi\) | ||||
−0.795350 | + | 0.606151i | \(0.792713\pi\) | |||||||
\(338\) | 1.49693i | 0.0814222i | ||||||||
\(339\) | 17.3837 | 0.944154 | ||||||||
\(340\) | 0.964557 | + | 4.29903i | 0.0523104 | + | 0.233148i | ||||
\(341\) | −3.84534 | −0.208237 | ||||||||
\(342\) | 4.17113i | 0.225549i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.90755 | −0.264597 | ||||||||
\(345\) | −17.8280 | + | 4.00000i | −0.959827 | + | 0.215353i | ||||
\(346\) | −12.5348 | −0.673874 | ||||||||
\(347\) | 2.14089i | 0.114929i | 0.998348 | + | 0.0574646i | \(0.0183016\pi\) | ||||
−0.998348 | + | 0.0574646i | \(0.981698\pi\) | |||||||
\(348\) | − | 9.16246i | − | 0.491159i | ||||||
\(349\) | 0.906929 | 0.0485468 | 0.0242734 | − | 0.999705i | \(-0.492273\pi\) | ||||
0.0242734 | + | 0.999705i | \(0.492273\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.80748 | 0.203228 | ||||||||
\(352\) | 2.39327i | 0.127562i | ||||||||
\(353\) | − | 13.8866i | − | 0.739109i | −0.929209 | − | 0.369555i | \(-0.879510\pi\) | ||
0.929209 | − | 0.369555i | \(-0.120490\pi\) | |||||||
\(354\) | −13.0414 | −0.693145 | ||||||||
\(355\) | 15.1426 | − | 3.39748i | 0.803684 | − | 0.180320i | ||||
\(356\) | 1.97949 | 0.104913 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9196i | 1.21134i | ||||||||
\(359\) | −18.8565 | −0.995211 | −0.497605 | − | 0.867404i | \(-0.665787\pi\) | ||||
−0.497605 | + | 0.867404i | \(0.665787\pi\) | |||||||
\(360\) | −0.489528 | − | 2.18183i | −0.0258004 | − | 0.114992i | ||||
\(361\) | −1.60164 | −0.0842968 | ||||||||
\(362\) | − | 19.6181i | − | 1.03111i | ||||||
\(363\) | − | 5.27226i | − | 0.276722i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.248026 | − | 1.10545i | −0.0129823 | − | 0.0578620i | ||||
\(366\) | 13.0910 | 0.684275 | ||||||||
\(367\) | − | 31.5722i | − | 1.64806i | −0.566549 | − | 0.824028i | \(-0.691722\pi\) | ||
0.566549 | − | 0.824028i | \(-0.308278\pi\) | |||||||
\(368\) | 8.17113i | 0.425950i | ||||||||
\(369\) | 3.19208 | 0.166173 | ||||||||
\(370\) | −2.75692 | + | 0.618560i | −0.143325 | + | 0.0321574i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 1.60673i | − | 0.0833051i | ||||||
\(373\) | − | 20.9075i | − | 1.08255i | −0.840845 | − | 0.541276i | \(-0.817941\pi\) | ||
0.840845 | − | 0.541276i | \(-0.182059\pi\) | |||||||
\(374\) | 4.71565 | 0.243841 | ||||||||
\(375\) | 6.87368 | + | 8.81774i | 0.354956 | + | 0.455346i | ||||
\(376\) | 3.00868 | 0.155161 | ||||||||
\(377\) | 34.8859i | 1.79672i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.82440 | 0.504646 | 0.252323 | − | 0.967643i | \(-0.418805\pi\) | ||||
0.252323 | + | 0.967643i | \(0.418805\pi\) | |||||||
\(380\) | −9.10069 | + | 2.04189i | −0.466855 | + | 0.104747i | ||||
\(381\) | −18.4434 | −0.944884 | ||||||||
\(382\) | 19.7269i | 1.00931i | ||||||||
\(383\) | 30.6647i | 1.56689i | 0.621461 | + | 0.783445i | \(0.286540\pi\) | ||||
−0.621461 | + | 0.783445i | \(0.713460\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.78654 | −0.243628 | ||||||||
\(387\) | − | 4.90755i | − | 0.249465i | ||||||
\(388\) | 12.0624i | 0.612375i | ||||||||
\(389\) | −23.4476 | −1.18884 | −0.594420 | − | 0.804154i | \(-0.702618\pi\) | ||||
−0.594420 | + | 0.804154i | \(0.702618\pi\) | |||||||
\(390\) | 1.86387 | + | 8.30726i | 0.0943807 | + | 0.420655i | ||||
\(391\) | 16.1002 | 0.814225 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.615405i | 0.0310431i | ||||||||
\(394\) | −17.1997 | −0.866508 | ||||||||
\(395\) | 27.1115 | − | 6.08290i | 1.36413 | − | 0.306064i | ||||
\(396\) | −2.39327 | −0.120266 | ||||||||
\(397\) | 35.3761i | 1.77548i | 0.460349 | + | 0.887738i | \(0.347724\pi\) | ||||
−0.460349 | + | 0.887738i | \(0.652276\pi\) | |||||||
\(398\) | 15.5056i | 0.777226i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.52072 | − | 2.13613i | 0.226036 | − | 0.106806i | ||||
\(401\) | −9.04145 | −0.451508 | −0.225754 | − | 0.974184i | \(-0.572485\pi\) | ||||
−0.225754 | + | 0.974184i | \(0.572485\pi\) | |||||||
\(402\) | 5.77786i | 0.288174i | ||||||||
\(403\) | 6.11760i | 0.304739i | ||||||||
\(404\) | −7.86672 | −0.391384 | ||||||||
\(405\) | 2.18183 | − | 0.489528i | 0.108416 | − | 0.0243248i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.02410i | 0.149899i | ||||||||
\(408\) | 1.97038i | 0.0975484i | ||||||||
\(409\) | 15.4379 | 0.763354 | 0.381677 | − | 0.924296i | \(-0.375347\pi\) | ||||
0.381677 | + | 0.924296i | \(0.375347\pi\) | |||||||
\(410\) | 1.56261 | + | 6.96456i | 0.0771719 | + | 0.343955i | ||||
\(411\) | −7.82799 | −0.386126 | ||||||||
\(412\) | − | 5.89887i | − | 0.290617i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −8.17113 | −0.401589 | ||||||||
\(415\) | −0.929553 | − | 4.14301i | −0.0456299 | − | 0.203373i | ||||
\(416\) | 3.80748 | 0.186677 | ||||||||
\(417\) | 6.15378i | 0.301352i | ||||||||
\(418\) | 9.98265i | 0.488267i | ||||||||
\(419\) | 26.6274 | 1.30083 | 0.650417 | − | 0.759577i | \(-0.274594\pi\) | ||||
0.650417 | + | 0.759577i | \(0.274594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.04591 | 0.245923 | 0.122961 | − | 0.992411i | \(-0.460761\pi\) | ||||
0.122961 | + | 0.992411i | \(0.460761\pi\) | |||||||
\(422\) | 23.8980i | 1.16334i | ||||||||
\(423\) | 3.00868i | 0.146287i | ||||||||
\(424\) | −12.1711 | −0.591083 | ||||||||
\(425\) | −4.20899 | − | 8.90755i | −0.204166 | − | 0.432080i | ||||
\(426\) | 6.94032 | 0.336260 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.75798i | 0.181649i | ||||||||
\(429\) | 9.11233 | 0.439948 | ||||||||
\(430\) | 10.7074 | − | 2.40238i | 0.516357 | − | 0.115853i | ||||
\(431\) | −25.2835 | −1.21786 | −0.608931 | − | 0.793223i | \(-0.708401\pi\) | ||||
−0.608931 | + | 0.793223i | \(0.708401\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | 27.0063i | 1.29784i | 0.760857 | + | 0.648920i | \(0.224779\pi\) | ||||
−0.760857 | + | 0.648920i | \(0.775221\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.48528 | + | 19.9909i | 0.215053 | + | 0.958490i | ||||
\(436\) | 7.14257 | 0.342067 | ||||||||
\(437\) | 34.0829i | 1.63041i | ||||||||
\(438\) | − | 0.506664i | − | 0.0242093i | ||||||
\(439\) | −27.9316 | −1.33310 | −0.666552 | − | 0.745458i | \(-0.732231\pi\) | ||||
−0.666552 | + | 0.745458i | \(0.732231\pi\) | |||||||
\(440\) | −1.17157 | − | 5.22170i | −0.0558525 | − | 0.248935i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 7.50219i | − | 0.356843i | ||||||
\(443\) | 10.7692i | 0.511660i | 0.966722 | + | 0.255830i | \(0.0823487\pi\) | ||||
−0.966722 | + | 0.255830i | \(0.917651\pi\) | |||||||
\(444\) | −1.26358 | −0.0599671 | ||||||||
\(445\) | −4.31891 | + | 0.969018i | −0.204736 | + | 0.0459359i | ||||
\(446\) | 0.870315 | 0.0412106 | ||||||||
\(447\) | 7.53584i | 0.356433i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.1288 | 0.713973 | 0.356986 | − | 0.934110i | \(-0.383804\pi\) | ||||
0.356986 | + | 0.934110i | \(0.383804\pi\) | |||||||
\(450\) | 2.13613 | + | 4.52072i | 0.100698 | + | 0.213109i | ||||
\(451\) | 7.63950 | 0.359730 | ||||||||
\(452\) | 17.3837i | 0.817661i | ||||||||
\(453\) | 9.04145i | 0.424804i | ||||||||
\(454\) | −14.6854 | −0.689221 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.17113 | −0.195331 | ||||||||
\(457\) | − | 21.4711i | − | 1.00437i | −0.864759 | − | 0.502187i | \(-0.832529\pi\) | ||
0.864759 | − | 0.502187i | \(-0.167471\pi\) | |||||||
\(458\) | 24.0379i | 1.12322i | ||||||||
\(459\) | −1.97038 | −0.0919695 | ||||||||
\(460\) | −4.00000 | − | 17.8280i | −0.186501 | − | 0.831234i | ||||
\(461\) | −30.4465 | −1.41804 | −0.709019 | − | 0.705190i | \(-0.750862\pi\) | ||||
−0.709019 | + | 0.705190i | \(0.750862\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 40.2005i | − | 1.86828i | −0.356913 | − | 0.934138i | \(-0.616171\pi\) | ||
0.356913 | − | 0.934138i | \(-0.383829\pi\) | |||||||
\(464\) | 9.16246 | 0.425356 | ||||||||
\(465\) | 0.786540 | + | 3.50560i | 0.0364749 | + | 0.162569i | ||||
\(466\) | 10.5445 | 0.488465 | ||||||||
\(467\) | − | 7.84175i | − | 0.362873i | −0.983403 | − | 0.181437i | \(-0.941925\pi\) | ||
0.983403 | − | 0.181437i | \(-0.0580747\pi\) | |||||||
\(468\) | 3.80748i | 0.176001i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −6.56440 | + | 1.47283i | −0.302793 | + | 0.0679366i | ||||
\(471\) | −22.6640 | −1.04430 | ||||||||
\(472\) | − | 13.0414i | − | 0.600281i | ||||||
\(473\) | − | 11.7451i | − | 0.540040i | ||||||
\(474\) | 12.4260 | 0.570747 | ||||||||
\(475\) | 18.8565 | − | 8.91008i | 0.865198 | − | 0.408823i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 12.1711i | − | 0.557278i | ||||||
\(478\) | − | 4.01289i | − | 0.183545i | ||||||
\(479\) | −27.7745 | −1.26905 | −0.634524 | − | 0.772904i | \(-0.718804\pi\) | ||||
−0.634524 | + | 0.772904i | \(0.718804\pi\) | |||||||
\(480\) | 2.18183 | − | 0.489528i | 0.0995863 | − | 0.0223438i | ||||
\(481\) | 4.81108 | 0.219366 | ||||||||
\(482\) | − | 0.543899i | − | 0.0247739i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.27226 | 0.239648 | ||||||||
\(485\) | −5.90488 | − | 26.3180i | −0.268127 | − | 1.19504i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | − | 12.5263i | − | 0.567620i | −0.958880 | − | 0.283810i | \(-0.908401\pi\) | ||
0.958880 | − | 0.283810i | \(-0.0915986\pi\) | |||||||
\(488\) | 13.0910i | 0.592600i | ||||||||
\(489\) | −10.2039 | −0.461437 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.3924 | −1.10081 | −0.550407 | − | 0.834897i | \(-0.685527\pi\) | ||||
−0.550407 | + | 0.834897i | \(0.685527\pi\) | |||||||
\(492\) | 3.19208i | 0.143910i | ||||||||
\(493\) | − | 18.0535i | − | 0.813090i | ||||||
\(494\) | 15.8815 | 0.714544 | ||||||||
\(495\) | 5.22170 | − | 1.17157i | 0.234698 | − | 0.0526583i | ||||
\(496\) | 1.60673 | 0.0721443 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 1.89887i | − | 0.0850906i | ||||||
\(499\) | 23.6560 | 1.05899 | 0.529493 | − | 0.848314i | \(-0.322382\pi\) | ||||
0.529493 | + | 0.848314i | \(0.322382\pi\) | |||||||
\(500\) | −8.81774 | + | 6.87368i | −0.394341 | + | 0.307400i | ||||
\(501\) | 25.2498 | 1.12808 | ||||||||
\(502\) | 4.62829i | 0.206571i | ||||||||
\(503\) | − | 20.8496i | − | 0.929636i | −0.885406 | − | 0.464818i | \(-0.846120\pi\) | ||
0.885406 | − | 0.464818i | \(-0.153880\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.1638 | − | 3.85098i | 0.763780 | − | 0.171366i | ||||
\(506\) | −19.5557 | −0.869358 | ||||||||
\(507\) | − | 1.49693i | − | 0.0664810i | ||||||
\(508\) | − | 18.4434i | − | 0.818293i | ||||||
\(509\) | −2.59490 | −0.115017 | −0.0575085 | − | 0.998345i | \(-0.518316\pi\) | ||||
−0.0575085 | + | 0.998345i | \(0.518316\pi\) | |||||||
\(510\) | −0.964557 | − | 4.29903i | −0.0427113 | − | 0.190364i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | − | 4.17113i | − | 0.184160i | ||||||
\(514\) | −25.5671 | −1.12772 | ||||||||
\(515\) | 2.88767 | + | 12.8703i | 0.127246 | + | 0.567134i | ||||
\(516\) | 4.90755 | 0.216043 | ||||||||
\(517\) | 7.20057i | 0.316681i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.5348 | 0.550216 | ||||||||
\(520\) | −8.30726 | + | 1.86387i | −0.364298 | + | 0.0817361i | ||||
\(521\) | 24.4884 | 1.07286 | 0.536429 | − | 0.843945i | \(-0.319773\pi\) | ||||
0.536429 | + | 0.843945i | \(0.319773\pi\) | |||||||
\(522\) | 9.16246i | 0.401030i | ||||||||
\(523\) | 21.6257i | 0.945627i | 0.881162 | + | 0.472814i | \(0.156762\pi\) | ||||
−0.881162 | + | 0.472814i | \(0.843238\pi\) | |||||||
\(524\) | −0.615405 | −0.0268841 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.5972 | 0.898080 | ||||||||
\(527\) | − | 3.16587i | − | 0.137907i | ||||||
\(528\) | − | 2.39327i | − | 0.104154i | ||||||
\(529\) | −43.7674 | −1.90293 | ||||||||
\(530\) | 26.5553 | − | 5.95811i | 1.15349 | − | 0.258804i | ||||
\(531\) | 13.0414 | 0.565951 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.1538i | − | 0.526439i | ||||||
\(534\) | −1.97949 | −0.0856611 | ||||||||
\(535\) | −1.83964 | − | 8.19926i | −0.0795344 | − | 0.354485i | ||||
\(536\) | −5.77786 | −0.249566 | ||||||||
\(537\) | − | 22.9196i | − | 0.989052i | ||||||
\(538\) | − | 2.23799i | − | 0.0964865i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.489528 | + | 2.18183i | 0.0210659 | + | 0.0938908i | ||||
\(541\) | 8.01735 | 0.344693 | 0.172346 | − | 0.985036i | \(-0.444865\pi\) | ||||
0.172346 | + | 0.985036i | \(0.444865\pi\) | |||||||
\(542\) | 19.1616i | 0.823060i | ||||||||
\(543\) | 19.6181i | 0.841894i | ||||||||
\(544\) | −1.97038 | −0.0844794 | ||||||||
\(545\) | −15.5839 | + | 3.49649i | −0.667539 | + | 0.149773i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 43.0251i | 1.83962i | 0.392361 | + | 0.919811i | \(0.371658\pi\) | ||||
−0.392361 | + | 0.919811i | \(0.628342\pi\) | |||||||
\(548\) | − | 7.82799i | − | 0.334395i | ||||||
\(549\) | −13.0910 | −0.558708 | ||||||||
\(550\) | 5.11233 | + | 10.8193i | 0.217991 | + | 0.461337i | ||||
\(551\) | 38.2178 | 1.62814 | ||||||||
\(552\) | − | 8.17113i | − | 0.347787i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.67674 | −0.156210 | ||||||||
\(555\) | 2.75692 | − | 0.618560i | 0.117025 | − | 0.0262564i | ||||
\(556\) | −6.15378 | −0.260979 | ||||||||
\(557\) | − | 11.1823i | − | 0.473811i | −0.971533 | − | 0.236906i | \(-0.923867\pi\) | ||
0.971533 | − | 0.236906i | \(-0.0761332\pi\) | |||||||
\(558\) | 1.60673i | 0.0680183i | ||||||||
\(559\) | −18.6854 | −0.790309 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.71565 | −0.199095 | ||||||||
\(562\) | 29.8280i | 1.25822i | ||||||||
\(563\) | − | 26.8694i | − | 1.13241i | −0.824264 | − | 0.566206i | \(-0.808411\pi\) | ||
0.824264 | − | 0.566206i | \(-0.191589\pi\) | |||||||
\(564\) | −3.00868 | −0.126688 | ||||||||
\(565\) | −8.50982 | − | 37.9282i | −0.358011 | − | 1.59565i | ||||
\(566\) | −4.28961 | −0.180306 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.94032i | 0.291210i | ||||||||
\(569\) | 2.61453 | 0.109607 | 0.0548034 | − | 0.998497i | \(-0.482547\pi\) | ||||
0.0548034 | + | 0.998497i | \(0.482547\pi\) | |||||||
\(570\) | 9.10069 | − | 2.04189i | 0.381186 | − | 0.0855253i | ||||
\(571\) | 12.4607 | 0.521466 | 0.260733 | − | 0.965411i | \(-0.416036\pi\) | ||||
0.260733 | + | 0.965411i | \(0.416036\pi\) | |||||||
\(572\) | 9.11233i | 0.381006i | ||||||||
\(573\) | − | 19.7269i | − | 0.824102i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.4546 | + | 36.9394i | 0.727907 | + | 1.54048i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 17.8195i | − | 0.741835i | −0.928666 | − | 0.370918i | \(-0.879043\pi\) | ||
0.928666 | − | 0.370918i | \(-0.120957\pi\) | |||||||
\(578\) | − | 13.1176i | − | 0.545620i | ||||||
\(579\) | 4.78654 | 0.198922 | ||||||||
\(580\) | −19.9909 | + | 4.48528i | −0.830076 | + | 0.186241i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 12.0624i | − | 0.500002i | ||||||
\(583\) | − | 29.1288i | − | 1.20639i | ||||||
\(584\) | 0.506664 | 0.0209659 | ||||||||
\(585\) | −1.86387 | − | 8.30726i | −0.0770615 | − | 0.343463i | ||||
\(586\) | −24.5940 | −1.01597 | ||||||||
\(587\) | 9.55661i | 0.394443i | 0.980359 | + | 0.197222i | \(0.0631919\pi\) | ||||
−0.980359 | + | 0.197222i | \(0.936808\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.70189 | 0.276146 | ||||||||
\(590\) | 6.38416 | + | 28.4542i | 0.262832 | + | 1.17144i | ||||
\(591\) | 17.1997 | 0.707501 | ||||||||
\(592\) | − | 1.26358i | − | 0.0519330i | ||||||
\(593\) | − | 11.6619i | − | 0.478898i | −0.970909 | − | 0.239449i | \(-0.923033\pi\) | ||
0.970909 | − | 0.239449i | \(-0.0769668\pi\) | |||||||
\(594\) | 2.39327 | 0.0981970 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.53584 | −0.308680 | ||||||||
\(597\) | − | 15.5056i | − | 0.634602i | ||||||
\(598\) | 31.1115i | 1.27224i | ||||||||
\(599\) | 33.0977 | 1.35234 | 0.676168 | − | 0.736748i | \(-0.263640\pi\) | ||||
0.676168 | + | 0.736748i | \(0.263640\pi\) | |||||||
\(600\) | −4.52072 | + | 2.13613i | −0.184558 | + | 0.0872071i | ||||
\(601\) | 15.2886 | 0.623633 | 0.311817 | − | 0.950142i | \(-0.399063\pi\) | ||||
0.311817 | + | 0.950142i | \(0.399063\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 5.77786i | − | 0.235293i | ||||||
\(604\) | −9.04145 | −0.367891 | ||||||||
\(605\) | −11.5032 | + | 2.58092i | −0.467670 | + | 0.104929i | ||||
\(606\) | 7.86672 | 0.319564 | ||||||||
\(607\) | 40.1823i | 1.63095i | 0.578794 | + | 0.815474i | \(0.303524\pi\) | ||||
−0.578794 | + | 0.815474i | \(0.696476\pi\) | |||||||
\(608\) | − | 4.17113i | − | 0.169162i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.40839 | − | 28.5622i | −0.259468 | − | 1.15645i | ||||
\(611\) | 11.4555 | 0.463439 | ||||||||
\(612\) | − | 1.97038i | − | 0.0796479i | ||||||
\(613\) | − | 24.8591i | − | 1.00405i | −0.864853 | − | 0.502024i | \(-0.832589\pi\) | ||
0.864853 | − | 0.502024i | \(-0.167411\pi\) | |||||||
\(614\) | 2.14089 | 0.0863995 | ||||||||
\(615\) | −1.56261 | − | 6.96456i | −0.0630106 | − | 0.280838i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.7647i | − | 0.916473i | −0.888830 | − | 0.458237i | \(-0.848481\pi\) | ||
0.888830 | − | 0.458237i | \(-0.151519\pi\) | |||||||
\(618\) | 5.89887i | 0.237288i | ||||||||
\(619\) | −17.8280 | −0.716567 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(620\) | −3.50560 | + | 0.786540i | −0.140788 | + | 0.0315882i | ||||
\(621\) | 8.17113 | 0.327896 | ||||||||
\(622\) | − | 13.9991i | − | 0.561314i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.80748 | −0.152421 | ||||||||
\(625\) | 15.8739 | − | 19.3137i | 0.634956 | − | 0.772548i | ||||
\(626\) | −33.0727 | −1.32185 | ||||||||
\(627\) | − | 9.98265i | − | 0.398669i | ||||||
\(628\) | − | 22.6640i | − | 0.904393i | ||||||
\(629\) | −2.48974 | −0.0992725 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.580705 | 0.0231175 | 0.0115587 | − | 0.999933i | \(-0.496321\pi\) | ||||
0.0115587 | + | 0.999933i | \(0.496321\pi\) | |||||||
\(632\) | 12.4260i | 0.494281i | ||||||||
\(633\) | − | 23.8980i | − | 0.949860i | ||||||
\(634\) | −7.38459 | −0.293280 | ||||||||
\(635\) | 9.02856 | + | 40.2403i | 0.358287 | + | 1.59689i | ||||
\(636\) | 12.1711 | 0.482617 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 21.9282i | 0.868147i | ||||||||
\(639\) | −6.94032 | −0.274555 | ||||||||
\(640\) | 0.489528 | + | 2.18183i | 0.0193503 | + | 0.0862442i | ||||
\(641\) | 18.0353 | 0.712352 | 0.356176 | − | 0.934419i | \(-0.384080\pi\) | ||||
0.356176 | + | 0.934419i | \(0.384080\pi\) | |||||||
\(642\) | − | 3.75798i | − | 0.148316i | ||||||
\(643\) | − | 39.3664i | − | 1.55246i | −0.630451 | − | 0.776229i | \(-0.717130\pi\) | ||
0.630451 | − | 0.776229i | \(-0.282870\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.7074 | + | 2.40238i | −0.421604 | + | 0.0945938i | ||||
\(646\) | −8.21872 | −0.323361 | ||||||||
\(647\) | 2.38038i | 0.0935824i | 0.998905 | + | 0.0467912i | \(0.0148995\pi\) | ||||
−0.998905 | + | 0.0467912i | \(0.985100\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 31.2117 | 1.22517 | ||||||||
\(650\) | 17.2126 | − | 8.13328i | 0.675133 | − | 0.319013i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 10.2039i | − | 0.399616i | ||||||
\(653\) | − | 25.1115i | − | 0.982687i | −0.870966 | − | 0.491344i | \(-0.836506\pi\) | ||
0.870966 | − | 0.491344i | \(-0.163494\pi\) | |||||||
\(654\) | −7.14257 | −0.279297 | ||||||||
\(655\) | 1.34271 | − | 0.301258i | 0.0524639 | − | 0.0117711i | ||||
\(656\) | −3.19208 | −0.124630 | ||||||||
\(657\) | 0.506664i | 0.0197668i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.17981 | 0.279686 | 0.139843 | − | 0.990174i | \(-0.455340\pi\) | ||||
0.139843 | + | 0.990174i | \(0.455340\pi\) | |||||||
\(660\) | 1.17157 | + | 5.22170i | 0.0456034 | + | 0.203254i | ||||
\(661\) | −25.0330 | −0.973669 | −0.486835 | − | 0.873494i | \(-0.661849\pi\) | ||||
−0.486835 | + | 0.873494i | \(0.661849\pi\) | |||||||
\(662\) | − | 21.5549i | − | 0.837753i | ||||||
\(663\) | 7.50219i | 0.291361i | ||||||||
\(664\) | 1.89887 | 0.0736906 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.26358 | 0.0489629 | ||||||||
\(667\) | 74.8677i | 2.89889i | ||||||||
\(668\) | 25.2498i | 0.976945i | ||||||||
\(669\) | −0.870315 | −0.0336483 | ||||||||
\(670\) | 12.6063 | − | 2.82843i | 0.487024 | − | 0.109272i | ||||
\(671\) | −31.3302 | −1.20949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 9.67062i | − | 0.372775i | −0.982476 | − | 0.186388i | \(-0.940322\pi\) | ||
0.982476 | − | 0.186388i | \(-0.0596780\pi\) | |||||||
\(674\) | 22.2549 | 0.857227 | ||||||||
\(675\) | −2.13613 | − | 4.52072i | −0.0822197 | − | 0.174003i | ||||
\(676\) | 1.49693 | 0.0575742 | ||||||||
\(677\) | 27.6890i | 1.06418i | 0.846689 | + | 0.532088i | \(0.178592\pi\) | ||||
−0.846689 | + | 0.532088i | \(0.821408\pi\) | |||||||
\(678\) | − | 17.3837i | − | 0.667618i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.29903 | − | 0.964557i | 0.164860 | − | 0.0369891i | ||||
\(681\) | 14.6854 | 0.562746 | ||||||||
\(682\) | 3.84534i | 0.147246i | ||||||||
\(683\) | − | 26.1227i | − | 0.999556i | −0.866154 | − | 0.499778i | \(-0.833415\pi\) | ||
0.866154 | − | 0.499778i | \(-0.166585\pi\) | |||||||
\(684\) | 4.17113 | 0.159487 | ||||||||
\(685\) | 3.83202 | + | 17.0793i | 0.146414 | + | 0.652567i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 24.0379i | − | 0.917101i | ||||||
\(688\) | 4.90755i | 0.187099i | ||||||||
\(689\) | −46.3414 | −1.76547 | ||||||||
\(690\) | 4.00000 | + | 17.8280i | 0.152277 | + | 0.678700i | ||||
\(691\) | 24.7901 | 0.943061 | 0.471530 | − | 0.881850i | \(-0.343702\pi\) | ||||
0.471530 | + | 0.881850i | \(0.343702\pi\) | |||||||
\(692\) | 12.5348i | 0.476501i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.14089 | 0.0812673 | ||||||||
\(695\) | 13.4265 | − | 3.01245i | 0.509295 | − | 0.114269i | ||||
\(696\) | −9.16246 | −0.347302 | ||||||||
\(697\) | 6.28961i | 0.238236i | ||||||||
\(698\) | − | 0.906929i | − | 0.0343278i | ||||||
\(699\) | −10.5445 | −0.398830 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.8817 | 1.43077 | 0.715386 | − | 0.698730i | \(-0.246251\pi\) | ||||
0.715386 | + | 0.698730i | \(0.246251\pi\) | |||||||
\(702\) | − | 3.80748i | − | 0.143704i | ||||||
\(703\) | − | 5.27058i | − | 0.198784i | ||||||
\(704\) | 2.39327 | 0.0901997 | ||||||||
\(705\) | 6.56440 | − | 1.47283i | 0.247230 | − | 0.0554700i | ||||
\(706\) | −13.8866 | −0.522629 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 13.0414i | 0.490128i | ||||||||
\(709\) | 30.9801 | 1.16348 | 0.581741 | − | 0.813374i | \(-0.302372\pi\) | ||||
0.581741 | + | 0.813374i | \(0.302372\pi\) | |||||||
\(710\) | −3.39748 | − | 15.1426i | −0.127505 | − | 0.568291i | ||||
\(711\) | −12.4260 | −0.466013 | ||||||||
\(712\) | − | 1.97949i | − | 0.0741847i | ||||||
\(713\) | 13.1288i | 0.491678i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.46074 | − | 19.8815i | −0.166822 | − | 0.743527i | ||||
\(716\) | 22.9196 | 0.856544 | ||||||||
\(717\) | 4.01289i | 0.149864i | ||||||||
\(718\) | 18.8565i | 0.703720i | ||||||||
\(719\) | 16.7028 | 0.622908 | 0.311454 | − | 0.950261i | \(-0.399184\pi\) | ||||
0.311454 | + | 0.950261i | \(0.399184\pi\) | |||||||
\(720\) | −2.18183 | + | 0.489528i | −0.0813118 | + | 0.0182436i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.60164i | 0.0596068i | ||||||||
\(723\) | 0.543899i | 0.0202278i | ||||||||
\(724\) | −19.6181 | −0.729102 | ||||||||
\(725\) | 41.4210 | − | 19.5722i | 1.53834 | − | 0.726893i | ||||
\(726\) | −5.27226 | −0.195672 | ||||||||
\(727\) | − | 36.1218i | − | 1.33968i | −0.742504 | − | 0.669842i | \(-0.766362\pi\) | ||
0.742504 | − | 0.669842i | \(-0.233638\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −1.10545 | + | 0.248026i | −0.0409146 | + | 0.00917986i | ||||
\(731\) | 9.66974 | 0.357648 | ||||||||
\(732\) | − | 13.0910i | − | 0.483856i | ||||||
\(733\) | − | 7.83860i | − | 0.289525i | −0.989466 | − | 0.144763i | \(-0.953758\pi\) | ||
0.989466 | − | 0.144763i | \(-0.0462419\pi\) | |||||||
\(734\) | −31.5722 | −1.16535 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.17113 | 0.301192 | ||||||||
\(737\) | − | 13.8280i | − | 0.509361i | ||||||
\(738\) | − | 3.19208i | − | 0.117502i | ||||||
\(739\) | 29.7969 | 1.09610 | 0.548048 | − | 0.836447i | \(-0.315371\pi\) | ||||
0.548048 | + | 0.836447i | \(0.315371\pi\) | |||||||
\(740\) | 0.618560 | + | 2.75692i | 0.0227387 | + | 0.101346i | ||||
\(741\) | −15.8815 | −0.583422 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.7487i | 0.431017i | 0.976502 | + | 0.215509i | \(0.0691409\pi\) | ||||
−0.976502 | + | 0.215509i | \(0.930859\pi\) | |||||||
\(744\) | −1.60673 | −0.0589056 | ||||||||
\(745\) | 16.4419 | − | 3.68901i | 0.602384 | − | 0.135155i | ||||
\(746\) | −20.9075 | −0.765480 | ||||||||
\(747\) | 1.89887i | 0.0694762i | ||||||||
\(748\) | − | 4.71565i | − | 0.172421i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.81774 | − | 6.87368i | 0.321978 | − | 0.250991i | ||||
\(751\) | −2.43981 | −0.0890299 | −0.0445150 | − | 0.999009i | \(-0.514174\pi\) | ||||
−0.0445150 | + | 0.999009i | \(0.514174\pi\) | |||||||
\(752\) | − | 3.00868i | − | 0.109715i | ||||||
\(753\) | − | 4.62829i | − | 0.168664i | ||||||
\(754\) | 34.8859 | 1.27047 | ||||||||
\(755\) | 19.7269 | − | 4.42604i | 0.717934 | − | 0.161080i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 17.5039i | − | 0.636188i | −0.948059 | − | 0.318094i | \(-0.896957\pi\) | ||
0.948059 | − | 0.318094i | \(-0.103043\pi\) | |||||||
\(758\) | − | 9.82440i | − | 0.356838i | ||||||
\(759\) | 19.5557 | 0.709828 | ||||||||
\(760\) | 2.04189 | + | 9.10069i | 0.0740670 | + | 0.330117i | ||||
\(761\) | −6.06327 | −0.219793 | −0.109897 | − | 0.993943i | \(-0.535052\pi\) | ||||
−0.109897 | + | 0.993943i | \(0.535052\pi\) | |||||||
\(762\) | 18.4434i | 0.668134i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 19.7269 | 0.713693 | ||||||||
\(765\) | 0.964557 | + | 4.29903i | 0.0348736 | + | 0.155432i | ||||
\(766\) | 30.6647 | 1.10796 | ||||||||
\(767\) | − | 49.6551i | − | 1.79294i | ||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 6.94628 | 0.250489 | 0.125245 | − | 0.992126i | \(-0.460028\pi\) | ||||
0.125245 | + | 0.992126i | \(0.460028\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.5671 | 0.920777 | ||||||||
\(772\) | 4.78654i | 0.172271i | ||||||||
\(773\) | 14.8597i | 0.534466i | 0.963632 | + | 0.267233i | \(0.0861094\pi\) | ||||
−0.963632 | + | 0.267233i | \(0.913891\pi\) | |||||||
\(774\) | −4.90755 | −0.176398 | ||||||||
\(775\) | 7.26358 | − | 3.43218i | 0.260916 | − | 0.123288i | ||||
\(776\) | 12.0624 | 0.433015 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.4476i | 0.840637i | ||||||||
\(779\) | −13.3146 | −0.477045 | ||||||||
\(780\) | 8.30726 | − | 1.86387i | 0.297448 | − | 0.0667373i | ||||
\(781\) | −16.6101 | −0.594355 | ||||||||
\(782\) | − | 16.1002i | − | 0.575744i | ||||||
\(783\) | − | 9.16246i | − | 0.327440i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0947 | + | 49.4490i | 0.395986 | + | 1.76491i | ||||
\(786\) | 0.615405 | 0.0219508 | ||||||||
\(787\) | − | 16.7683i | − | 0.597726i | −0.954296 | − | 0.298863i | \(-0.903393\pi\) | ||
0.954296 | − | 0.298863i | \(-0.0966073\pi\) | |||||||
\(788\) | 17.1997i | 0.612714i | ||||||||
\(789\) | −20.5972 | −0.733279 | ||||||||
\(790\) | −6.08290 | − | 27.1115i | −0.216420 | − | 0.964582i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.39327i | 0.0850411i | ||||||||
\(793\) | 49.8436i | 1.77000i | ||||||||
\(794\) | 35.3761 | 1.25545 | ||||||||
\(795\) | −26.5553 | + | 5.95811i | −0.941819 | + | 0.211312i | ||||
\(796\) | 15.5056 | 0.549582 | ||||||||
\(797\) | 37.5481i | 1.33002i | 0.746833 | + | 0.665011i | \(0.231573\pi\) | ||||
−0.746833 | + | 0.665011i | \(0.768427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.92824 | −0.209726 | ||||||||
\(800\) | −2.13613 | − | 4.52072i | −0.0755236 | − | 0.159832i | ||||
\(801\) | 1.97949 | 0.0699420 | ||||||||
\(802\) | 9.04145i | 0.319265i | ||||||||
\(803\) | 1.21258i | 0.0427911i | ||||||||
\(804\) | 5.77786 | 0.203770 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.11760 | 0.215483 | ||||||||
\(807\) | 2.23799i | 0.0787809i | ||||||||
\(808\) | 7.86672i | 0.276750i | ||||||||
\(809\) | −12.5014 | −0.439526 | −0.219763 | − | 0.975553i | \(-0.570528\pi\) | ||||
−0.219763 | + | 0.975553i | \(0.570528\pi\) | |||||||
\(810\) | −0.489528 | − | 2.18183i | −0.0172003 | − | 0.0766615i | ||||
\(811\) | −30.4470 | −1.06914 | −0.534569 | − | 0.845125i | \(-0.679526\pi\) | ||||
−0.534569 | + | 0.845125i | \(0.679526\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 19.1616i | − | 0.672026i | ||||||
\(814\) | 3.02410 | 0.105995 | ||||||||
\(815\) | 4.99510 | + | 22.2631i | 0.174971 | + | 0.779844i | ||||
\(816\) | 1.97038 | 0.0689771 | ||||||||
\(817\) | 20.4700i | 0.716156i | ||||||||
\(818\) | − | 15.4379i | − | 0.539773i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.96456 | − | 1.56261i | 0.243213 | − | 0.0545688i | ||||
\(821\) | 38.2775 | 1.33589 | 0.667947 | − | 0.744209i | \(-0.267173\pi\) | ||||
0.667947 | + | 0.744209i | \(0.267173\pi\) | |||||||
\(822\) | 7.82799i | 0.273032i | ||||||||
\(823\) | 23.6213i | 0.823386i | 0.911323 | + | 0.411693i | \(0.135062\pi\) | ||||
−0.911323 | + | 0.411693i | \(0.864938\pi\) | |||||||
\(824\) | −5.89887 | −0.205497 | ||||||||
\(825\) | −5.11233 | − | 10.8193i | −0.177989 | − | 0.376680i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.5652i | 1.20195i | 0.799268 | + | 0.600975i | \(0.205221\pi\) | ||||
−0.799268 | + | 0.600975i | \(0.794779\pi\) | |||||||
\(828\) | 8.17113i | 0.283967i | ||||||||
\(829\) | 27.2086 | 0.944992 | 0.472496 | − | 0.881333i | \(-0.343353\pi\) | ||||
0.472496 | + | 0.881333i | \(0.343353\pi\) | |||||||
\(830\) | −4.14301 | + | 0.929553i | −0.143806 | + | 0.0322652i | ||||
\(831\) | 3.67674 | 0.127545 | ||||||||
\(832\) | − | 3.80748i | − | 0.132001i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.15378 | 0.213088 | ||||||||
\(835\) | −12.3605 | − | 55.0907i | −0.427753 | − | 1.90649i | ||||
\(836\) | 9.98265 | 0.345257 | ||||||||
\(837\) | − | 1.60673i | − | 0.0555367i | ||||||
\(838\) | − | 26.6274i | − | 0.919829i | ||||||
\(839\) | 1.49861 | 0.0517377 | 0.0258689 | − | 0.999665i | \(-0.491765\pi\) | ||||
0.0258689 | + | 0.999665i | \(0.491765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54.9507 | 1.89485 | ||||||||
\(842\) | − | 5.04591i | − | 0.173894i | ||||||
\(843\) | − | 29.8280i | − | 1.02733i | ||||||
\(844\) | 23.8980 | 0.822603 | ||||||||
\(845\) | −3.26604 | + | 0.732789i | −0.112355 | + | 0.0252087i | ||||
\(846\) | 3.00868 | 0.103440 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.1711i | 0.417958i | ||||||||
\(849\) | 4.28961 | 0.147219 | ||||||||
\(850\) | −8.90755 | + | 4.20899i | −0.305526 | + | 0.144367i | ||||
\(851\) | 10.3249 | 0.353934 | ||||||||
\(852\) | − | 6.94032i | − | 0.237772i | ||||||
\(853\) | − | 38.9306i | − | 1.33296i | −0.745524 | − | 0.666479i | \(-0.767801\pi\) | ||
0.745524 | − | 0.666479i | \(-0.232199\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.10069 | + | 2.04189i | −0.311237 | + | 0.0698311i | ||||
\(856\) | 3.75798 | 0.128445 | ||||||||
\(857\) | 18.5987i | 0.635319i | 0.948205 | + | 0.317659i | \(0.102897\pi\) | ||||
−0.948205 | + | 0.317659i | \(0.897103\pi\) | |||||||
\(858\) | − | 9.11233i | − | 0.311090i | ||||||
\(859\) | 9.09945 | 0.310469 | 0.155235 | − | 0.987878i | \(-0.450387\pi\) | ||||
0.155235 | + | 0.987878i | \(0.450387\pi\) | |||||||
\(860\) | −2.40238 | − | 10.7074i | −0.0819206 | − | 0.365120i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.2835i | 0.861158i | ||||||||
\(863\) | 10.4616i | 0.356118i | 0.984020 | + | 0.178059i | \(0.0569817\pi\) | ||||
−0.984020 | + | 0.178059i | \(0.943018\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | −6.13613 | − | 27.3487i | −0.208635 | − | 0.929884i | ||||
\(866\) | 27.0063 | 0.917711 | ||||||||
\(867\) | 13.1176i | 0.445497i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29.7389 | −1.00882 | ||||||||
\(870\) | 19.9909 | − | 4.48528i | 0.677755 | − | 0.152065i | ||||
\(871\) | −21.9991 | −0.745412 | ||||||||
\(872\) | − | 7.14257i | − | 0.241878i | ||||||
\(873\) | 12.0624i | 0.408250i | ||||||||
\(874\) | 34.0829 | 1.15287 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.506664 | −0.0171186 | ||||||||
\(877\) | 5.29829i | 0.178910i | 0.995991 | + | 0.0894552i | \(0.0285126\pi\) | ||||
−0.995991 | + | 0.0894552i | \(0.971487\pi\) | |||||||
\(878\) | 27.9316i | 0.942647i | ||||||||
\(879\) | 24.5940 | 0.829536 | ||||||||
\(880\) | −5.22170 | + | 1.17157i | −0.176023 | + | 0.0394937i | ||||
\(881\) | −2.68857 | −0.0905802 | −0.0452901 | − | 0.998974i | \(-0.514421\pi\) | ||||
−0.0452901 | + | 0.998974i | \(0.514421\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 26.4277i | − | 0.889363i | −0.895689 | − | 0.444681i | \(-0.853317\pi\) | ||
0.895689 | − | 0.444681i | \(-0.146683\pi\) | |||||||
\(884\) | −7.50219 | −0.252326 | ||||||||
\(885\) | −6.38416 | − | 28.4542i | −0.214601 | − | 0.956476i | ||||
\(886\) | 10.7692 | 0.361798 | ||||||||
\(887\) | − | 8.18149i | − | 0.274708i | −0.990522 | − | 0.137354i | \(-0.956140\pi\) | ||
0.990522 | − | 0.137354i | \(-0.0438597\pi\) | |||||||
\(888\) | 1.26358i | 0.0424031i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.969018 | + | 4.31891i | 0.0324816 | + | 0.144770i | ||||
\(891\) | −2.39327 | −0.0801776 | ||||||||
\(892\) | − | 0.870315i | − | 0.0291403i | ||||||
\(893\) | − | 12.5496i | − | 0.419956i | ||||||
\(894\) | 7.53584 | 0.252036 | ||||||||
\(895\) | −50.0065 | + | 11.2198i | −1.67153 | + | 0.375036i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 31.1115i | − | 1.03878i | ||||||
\(898\) | − | 15.1288i | − | 0.504855i | ||||||
\(899\) | 14.7216 | 0.490993 | ||||||||
\(900\) | 4.52072 | − | 2.13613i | 0.150691 | − | 0.0712043i | ||||
\(901\) | 23.9818 | 0.798949 | ||||||||
\(902\) | − | 7.63950i | − | 0.254368i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 17.3837 | 0.578174 | ||||||||
\(905\) | 42.8033 | − | 9.60362i | 1.42283 | − | 0.319235i | ||||
\(906\) | 9.04145 | 0.300382 | ||||||||
\(907\) | 3.80028i | 0.126186i | 0.998008 | + | 0.0630932i | \(0.0200965\pi\) | ||||
−0.998008 | + | 0.0630932i | \(0.979903\pi\) | |||||||
\(908\) | 14.6854i | 0.487353i | ||||||||
\(909\) | −7.86672 | −0.260923 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.1590 | 1.29740 | 0.648699 | − | 0.761045i | \(-0.275314\pi\) | ||||
0.648699 | + | 0.761045i | \(0.275314\pi\) | |||||||
\(912\) | 4.17113i | 0.138120i | ||||||||
\(913\) | 4.54452i | 0.150402i | ||||||||
\(914\) | −21.4711 | −0.710200 | ||||||||
\(915\) | 6.40839 | + | 28.5622i | 0.211855 | + | 0.944236i | ||||
\(916\) | 24.0379 | 0.794233 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.97038i | 0.0650323i | ||||||||
\(919\) | 13.8462 | 0.456745 | 0.228372 | − | 0.973574i | \(-0.426660\pi\) | ||||
0.228372 | + | 0.973574i | \(0.426660\pi\) | |||||||
\(920\) | −17.8280 | + | 4.00000i | −0.587771 | + | 0.131876i | ||||
\(921\) | −2.14089 | −0.0705449 | ||||||||
\(922\) | 30.4465i | 1.00270i | ||||||||
\(923\) | 26.4252i | 0.869795i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.69918 | − | 5.71232i | −0.0887485 | − | 0.187820i | ||||
\(926\) | −40.2005 | −1.32107 | ||||||||
\(927\) | − | 5.89887i | − | 0.193744i | ||||||
\(928\) | − | 9.16246i | − | 0.300772i | ||||||
\(929\) | 13.8030 | 0.452862 | 0.226431 | − | 0.974027i | \(-0.427294\pi\) | ||||
0.226431 | + | 0.974027i | \(0.427294\pi\) | |||||||
\(930\) | 3.50560 | − | 0.786540i | 0.114953 | − | 0.0257917i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 10.5445i | − | 0.345397i | ||||||
\(933\) | 13.9991i | 0.458311i | ||||||||
\(934\) | −7.84175 | −0.256590 | ||||||||
\(935\) | 2.30845 | + | 10.2887i | 0.0754942 | + | 0.336478i | ||||
\(936\) | 3.80748 | 0.124451 | ||||||||
\(937\) | 29.1062i | 0.950858i | 0.879754 | + | 0.475429i | \(0.157707\pi\) | ||||
−0.879754 | + | 0.475429i | \(0.842293\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.0727 | 1.07929 | ||||||||
\(940\) | 1.47283 | + | 6.56440i | 0.0480385 | + | 0.214107i | ||||
\(941\) | −26.9934 | −0.879960 | −0.439980 | − | 0.898008i | \(-0.645014\pi\) | ||||
−0.439980 | + | 0.898008i | \(0.645014\pi\) | |||||||
\(942\) | 22.6640i | 0.738434i | ||||||||
\(943\) | − | 26.0829i | − | 0.849376i | ||||||
\(944\) | −13.0414 | −0.424463 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.7451 | −0.381866 | ||||||||
\(947\) | − | 32.5005i | − | 1.05612i | −0.849206 | − | 0.528062i | \(-0.822919\pi\) | ||
0.849206 | − | 0.528062i | \(-0.177081\pi\) | |||||||
\(948\) | − | 12.4260i | − | 0.403579i | ||||||
\(949\) | 1.92911 | 0.0626217 | ||||||||
\(950\) | −8.91008 | − | 18.8565i | −0.289081 | − | 0.611787i | ||||
\(951\) | 7.38459 | 0.239462 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41.4364i | 1.34226i | 0.741342 | + | 0.671128i | \(0.234190\pi\) | ||||
−0.741342 | + | 0.671128i | \(0.765810\pi\) | |||||||
\(954\) | −12.1711 | −0.394055 | ||||||||
\(955\) | −43.0406 | + | 9.65685i | −1.39276 | + | 0.312488i | ||||
\(956\) | −4.01289 | −0.129786 | ||||||||
\(957\) | − | 21.9282i | − | 0.708839i | ||||||
\(958\) | 27.7745i | 0.897352i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.489528 | − | 2.18183i | −0.0157995 | − | 0.0704181i | ||||
\(961\) | −28.4184 | −0.916723 | ||||||||
\(962\) | − | 4.81108i | − | 0.155115i | ||||||
\(963\) | 3.75798i | 0.121099i | ||||||||
\(964\) | −0.543899 | −0.0175178 | ||||||||
\(965\) | −2.34315 | − | 10.4434i | −0.0754285 | − | 0.336185i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.0294i | 0.740577i | 0.928917 | + | 0.370288i | \(0.120741\pi\) | ||||
−0.928917 | + | 0.370288i | \(0.879259\pi\) | |||||||
\(968\) | − | 5.27226i | − | 0.169457i | ||||||
\(969\) | 8.21872 | 0.264023 | ||||||||
\(970\) | −26.3180 | + | 5.90488i | −0.845021 | + | 0.189594i | ||||
\(971\) | −5.06326 | −0.162488 | −0.0812439 | − | 0.996694i | \(-0.525889\pi\) | ||||
−0.0812439 | + | 0.996694i | \(0.525889\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −12.5263 | −0.401368 | ||||||||
\(975\) | −17.2126 | + | 8.13328i | −0.551244 | + | 0.260473i | ||||
\(976\) | 13.0910 | 0.419031 | ||||||||
\(977\) | 29.6213i | 0.947669i | 0.880614 | + | 0.473834i | \(0.157130\pi\) | ||||
−0.880614 | + | 0.473834i | \(0.842870\pi\) | |||||||
\(978\) | 10.2039i | 0.326285i | ||||||||
\(979\) | 4.73747 | 0.151410 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.14257 | 0.228045 | ||||||||
\(982\) | 24.3924i | 0.778393i | ||||||||
\(983\) | − | 8.18149i | − | 0.260949i | −0.991452 | − | 0.130474i | \(-0.958350\pi\) | ||
0.991452 | − | 0.130474i | \(-0.0416501\pi\) | |||||||
\(984\) | 3.19208 | 0.101760 | ||||||||
\(985\) | −8.41973 | − | 37.5267i | −0.268275 | − | 1.19570i | ||||
\(986\) | −18.0535 | −0.574942 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 15.8815i | − | 0.505259i | ||||||
\(989\) | −40.1002 | −1.27511 | ||||||||
\(990\) | −1.17157 | − | 5.22170i | −0.0372350 | − | 0.165956i | ||||
\(991\) | 16.7554 | 0.532254 | 0.266127 | − | 0.963938i | \(-0.414256\pi\) | ||||
0.266127 | + | 0.963938i | \(0.414256\pi\) | |||||||
\(992\) | − | 1.60673i | − | 0.0510137i | ||||||
\(993\) | 21.5549i | 0.684023i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.8305 | + | 7.59043i | −1.07250 | + | 0.240633i | ||||
\(996\) | −1.89887 | −0.0601681 | ||||||||
\(997\) | 4.62390i | 0.146440i | 0.997316 | + | 0.0732202i | \(0.0233276\pi\) | ||||
−0.997316 | + | 0.0732202i | \(0.976672\pi\) | |||||||
\(998\) | − | 23.6560i | − | 0.748817i | ||||||
\(999\) | −1.26358 | −0.0399780 |
(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 | 1470.2.g.k.589.4 | yes | 8 | |
5.2 | odd | 4 | 7350.2.a.du.1.2 | 4 | |||
5.3 | odd | 4 | 7350.2.a.dr.1.2 | 4 | |||
5.4 | even | 2 | inner | 1470.2.g.k.589.8 | yes | 8 | |
7.2 | even | 3 | 1470.2.n.k.949.2 | 16 | |||
7.3 | odd | 6 | 1470.2.n.l.79.7 | 16 | |||
7.4 | even | 3 | 1470.2.n.k.79.6 | 16 | |||
7.5 | odd | 6 | 1470.2.n.l.949.3 | 16 | |||
7.6 | odd | 2 | 1470.2.g.j.589.1 | ✓ | 8 | ||
35.4 | even | 6 | 1470.2.n.k.79.2 | 16 | |||
35.9 | even | 6 | 1470.2.n.k.949.6 | 16 | |||
35.13 | even | 4 | 7350.2.a.ds.1.2 | 4 | |||
35.19 | odd | 6 | 1470.2.n.l.949.7 | 16 | |||
35.24 | odd | 6 | 1470.2.n.l.79.3 | 16 | |||
35.27 | even | 4 | 7350.2.a.dt.1.2 | 4 | |||
35.34 | odd | 2 | 1470.2.g.j.589.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.g.j.589.1 | ✓ | 8 | 7.6 | odd | 2 | ||
1470.2.g.j.589.5 | yes | 8 | 35.34 | odd | 2 | ||
1470.2.g.k.589.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1470.2.g.k.589.8 | yes | 8 | 5.4 | even | 2 | inner | |
1470.2.n.k.79.2 | 16 | 35.4 | even | 6 | |||
1470.2.n.k.79.6 | 16 | 7.4 | even | 3 | |||
1470.2.n.k.949.2 | 16 | 7.2 | even | 3 | |||
1470.2.n.k.949.6 | 16 | 35.9 | even | 6 | |||
1470.2.n.l.79.3 | 16 | 35.24 | odd | 6 | |||
1470.2.n.l.79.7 | 16 | 7.3 | odd | 6 | |||
1470.2.n.l.949.3 | 16 | 7.5 | odd | 6 | |||
1470.2.n.l.949.7 | 16 | 35.19 | odd | 6 | |||
7350.2.a.dr.1.2 | 4 | 5.3 | odd | 4 | |||
7350.2.a.ds.1.2 | 4 | 35.13 | even | 4 | |||
7350.2.a.dt.1.2 | 4 | 35.27 | even | 4 | |||
7350.2.a.du.1.2 | 4 | 5.2 | odd | 4 |