Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(33,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 15]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.i (of order \(16\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.08834058349\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{16})\) |
Twist minimal: | no (minimal twist has level 64) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 33.5 | ||
Character | \(\chi\) | \(=\) | 512.33 |
Dual form | 512.2.i.b.481.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{15}{16}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.31138 | − | 0.876237i | 0.757127 | − | 0.505896i | −0.116084 | − | 0.993239i | \(-0.537034\pi\) |
0.873210 | + | 0.487344i | \(0.162034\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.52249 | + | 0.700667i | −1.57531 | + | 0.313348i | −0.903900 | − | 0.427743i | \(-0.859309\pi\) |
−0.671405 | + | 0.741091i | \(0.734309\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.02503 | + | 2.47464i | 0.387425 | + | 0.935326i | 0.990484 | + | 0.137629i | \(0.0439482\pi\) |
−0.603059 | + | 0.797696i | \(0.706052\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.196120 | + | 0.473476i | −0.0653734 | + | 0.157825i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.67900 | + | 2.51280i | −0.506237 | + | 0.757636i | −0.993279 | − | 0.115742i | \(-0.963076\pi\) |
0.487043 | + | 0.873378i | \(0.338076\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.41643 | + | 0.878483i | 1.22490 | + | 0.243647i | 0.764827 | − | 0.644235i | \(-0.222824\pi\) |
0.460070 | + | 0.887882i | \(0.347824\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.00538 | + | 4.00538i | −1.03418 | + | 1.03418i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.12567 | + | 1.12567i | 0.273014 | + | 0.273014i | 0.830312 | − | 0.557298i | \(-0.188162\pi\) |
−0.557298 | + | 0.830312i | \(0.688162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.432994 | + | 2.17681i | −0.0993357 | + | 0.499394i | 0.898800 | + | 0.438359i | \(0.144440\pi\) |
−0.998136 | + | 0.0610352i | \(0.980560\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.51257 | + | 2.34703i | 0.766507 | + | 0.512163i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.52287 | − | 1.87343i | −0.943084 | − | 0.390638i | −0.142457 | − | 0.989801i | \(-0.545500\pi\) |
−0.800627 | + | 0.599163i | \(0.795500\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.29760 | − | 3.02276i | 1.45952 | − | 0.604553i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.08077 | + | 5.43340i | 0.207994 | + | 1.04566i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.43450 | + | 5.14009i | 0.637771 | + | 0.954492i | 0.999751 | + | 0.0223059i | \(0.00710078\pi\) |
−0.361980 | + | 0.932186i | \(0.617899\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.88548i | 0.518248i | 0.965844 | + | 0.259124i | \(0.0834339\pi\) | ||||
−0.965844 | + | 0.259124i | \(0.916566\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.76643i | 0.829730i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.34455 | − | 7.99868i | −0.903394 | − | 1.35202i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.20408 | − | 6.05333i | −0.197950 | − | 0.995162i | −0.944169 | − | 0.329461i | \(-0.893133\pi\) |
0.746219 | − | 0.665700i | \(-0.231867\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.56139 | − | 2.71782i | 1.05066 | − | 0.435199i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.20440 | − | 1.32731i | −0.500443 | − | 0.207290i | 0.118159 | − | 0.992995i | \(-0.462301\pi\) |
−0.618602 | + | 0.785704i | \(0.712301\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.16349 | + | 1.44560i | 0.329929 | + | 0.220452i | 0.709491 | − | 0.704715i | \(-0.248925\pi\) |
−0.379561 | + | 0.925167i | \(0.623925\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.359082 | − | 1.80523i | 0.0535288 | − | 0.269108i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.37708 | − | 2.37708i | −0.346733 | − | 0.346733i | 0.512158 | − | 0.858891i | \(-0.328846\pi\) |
−0.858891 | + | 0.512158i | \(0.828846\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.123405 | + | 0.123405i | −0.0176293 | + | 0.0176293i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.46253 | + | 0.489827i | 0.344823 | + | 0.0685895i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.20051 | − | 4.78991i | 0.439624 | − | 0.657944i | −0.543810 | − | 0.839208i | \(-0.683019\pi\) |
0.983434 | + | 0.181264i | \(0.0580189\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.15361 | − | 10.0277i | 0.560073 | − | 1.35214i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.33958 | + | 3.23403i | 0.177432 | + | 0.428358i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.01300 | + | 0.201498i | −0.131881 | + | 0.0262329i | −0.260590 | − | 0.965450i | \(-0.583917\pi\) |
0.128708 | + | 0.991683i | \(0.458917\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.23513 | − | 1.49347i | 0.286179 | − | 0.191219i | −0.404192 | − | 0.914674i | \(-0.632447\pi\) |
0.690371 | + | 0.723455i | \(0.257447\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.37271 | −0.172945 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −16.1724 | −2.00593 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.1226 | + | 8.10007i | −1.48101 | + | 0.989581i | −0.487840 | + | 0.872933i | \(0.662215\pi\) |
−0.993173 | + | 0.116648i | \(0.962785\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.57278 | + | 1.50632i | −0.911656 | + | 0.181340i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.63617 | + | 11.1927i | 0.550212 | + | 1.32833i | 0.917320 | + | 0.398151i | \(0.130348\pi\) |
−0.367108 | + | 0.930178i | \(0.619652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.99984 | − | 9.65646i | 0.468146 | − | 1.13020i | −0.496826 | − | 0.867850i | \(-0.665501\pi\) |
0.964972 | − | 0.262353i | \(-0.0844986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.92128 | − | 10.3584i | 0.799200 | − | 1.19609i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.93928 | − | 1.57922i | −0.904765 | − | 0.179969i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.05698 | − | 1.05698i | 0.118919 | − | 0.118919i | −0.645143 | − | 0.764062i | \(-0.723202\pi\) |
0.764062 | + | 0.645143i | \(0.223202\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.09110 | + | 5.09110i | 0.565677 | + | 0.565677i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.67409 | − | 8.41620i | 0.183755 | − | 0.923798i | −0.773333 | − | 0.634000i | \(-0.781412\pi\) |
0.957088 | − | 0.289798i | \(-0.0935881\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.75386 | − | 3.17643i | −0.515629 | − | 0.344532i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.00788 | + | 3.73119i | 0.965747 | + | 0.400025i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.40505 | + | 2.23885i | −0.572935 | + | 0.237317i | −0.650290 | − | 0.759686i | \(-0.725352\pi\) |
0.0773551 | + | 0.997004i | \(0.475352\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.35304 | + | 11.8295i | 0.246666 | + | 1.24007i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.52837 | + | 3.78397i | 0.262180 | + | 0.392380i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 7.97117i | − | 0.817825i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.0691i | 1.12389i | 0.827173 | + | 0.561947i | \(0.189948\pi\) | ||||
−0.827173 | + | 0.561947i | \(0.810052\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.860463 | − | 1.28777i | −0.0864798 | − | 0.129426i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.42413 | + | 12.1869i | 0.241210 | + | 1.21264i | 0.891522 | + | 0.452977i | \(0.149638\pi\) |
−0.650313 | + | 0.759667i | \(0.725362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.43691 | + | 3.08047i | −0.732781 | + | 0.303528i | −0.717694 | − | 0.696358i | \(-0.754802\pi\) |
−0.0150867 | + | 0.999886i | \(0.504802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.0175 | − | 5.80623i | −1.36797 | − | 0.566630i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.45543 | − | 3.64520i | −0.527396 | − | 0.352395i | 0.263192 | − | 0.964744i | \(-0.415225\pi\) |
−0.790588 | + | 0.612349i | \(0.790225\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.09534 | − | 10.5340i | 0.200697 | − | 1.00897i | −0.740743 | − | 0.671789i | \(-0.765526\pi\) |
0.941439 | − | 0.337182i | \(-0.109474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.88317 | − | 6.88317i | −0.653321 | − | 0.653321i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.9546 | − | 10.9546i | 1.03052 | − | 1.03052i | 0.0310050 | − | 0.999519i | \(-0.490129\pi\) |
0.999519 | − | 0.0310050i | \(-0.00987077\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.2444 | + | 3.43013i | 1.60805 | + | 0.319861i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.28209 | + | 1.91879i | −0.118529 | + | 0.177392i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.63178 | + | 3.93945i | −0.149585 | + | 0.361129i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.714404 | + | 1.72472i | 0.0649458 | + | 0.156793i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.36523 | + | 1.06721i | −0.483766 | + | 0.0962271i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.65665 | + | 5.78419i | −0.774274 | + | 0.517353i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2036 | 1.17163 | 0.585815 | − | 0.810445i | \(-0.300775\pi\) | ||||
0.585815 | + | 0.810445i | \(0.300775\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.10385 | 0.361324 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.0393 | − | 11.3853i | 1.48873 | − | 0.994739i | 0.496814 | − | 0.867857i | \(-0.334503\pi\) |
0.991918 | − | 0.126881i | \(-0.0404967\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.83065 | + | 1.15979i | −0.505581 | + | 0.100566i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.61400 | − | 18.3818i | −0.655309 | − | 1.58205i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.61344 | − | 6.30941i | 0.223281 | − | 0.539049i | −0.772050 | − | 0.635561i | \(-0.780769\pi\) |
0.995332 | + | 0.0965122i | \(0.0307687\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.07641 | − | 13.5838i | 0.769851 | − | 1.15216i | −0.214634 | − | 0.976695i | \(-0.568856\pi\) |
0.984485 | − | 0.175469i | \(-0.0561443\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.20015 | − | 1.03437i | −0.437932 | − | 0.0871100i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.62262 | + | 9.62262i | −0.804684 | + | 0.804684i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.6995 | − | 15.6995i | −1.30377 | − | 1.30377i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0536992 | + | 0.269964i | −0.00442903 | + | 0.0222663i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.58289 | + | 1.05765i | 0.129675 | + | 0.0866461i | 0.618716 | − | 0.785615i | \(-0.287653\pi\) |
−0.489041 | + | 0.872261i | \(0.662653\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.8207 | − | 5.31052i | −1.04334 | − | 0.432164i | −0.205828 | − | 0.978588i | \(-0.565989\pi\) |
−0.837509 | + | 0.546424i | \(0.815989\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.753741 | + | 0.312210i | −0.0609364 | + | 0.0252407i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.02176 | − | 10.1641i | −0.162392 | − | 0.816399i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.92287 | − | 2.87778i | −0.153462 | − | 0.229672i | 0.746770 | − | 0.665082i | \(-0.231603\pi\) |
−0.900232 | + | 0.435410i | \(0.856603\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 9.08580i | − | 0.720551i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 13.1128i | − | 1.03343i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.50597 | − | 2.25384i | −0.117956 | − | 0.176534i | 0.767793 | − | 0.640698i | \(-0.221355\pi\) |
−0.885749 | + | 0.464164i | \(0.846355\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.33968 | − | 16.7897i | −0.259994 | − | 1.30708i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.45504 | − | 0.602695i | 0.112594 | − | 0.0466380i | −0.325675 | − | 0.945482i | \(-0.605592\pi\) |
0.438269 | + | 0.898844i | \(0.355592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.72270 | + | 2.78464i | 0.517131 | + | 0.214203i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.945748 | − | 0.631929i | −0.0723232 | − | 0.0483248i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.03690 | − | 5.21283i | 0.0788338 | − | 0.396324i | −0.921141 | − | 0.389229i | \(-0.872742\pi\) |
0.999975 | − | 0.00709516i | \(-0.00225848\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.9605 | + | 14.9605i | 1.13091 | + | 1.13091i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.15187 | + | 1.15187i | −0.0865799 | + | 0.0865799i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.4548 | − | 2.27850i | −0.856171 | − | 0.170303i | −0.252559 | − | 0.967581i | \(-0.581272\pi\) |
−0.603612 | + | 0.797279i | \(0.706272\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.32452 | − | 3.47889i | 0.172780 | − | 0.258584i | −0.734966 | − | 0.678104i | \(-0.762802\pi\) |
0.907746 | + | 0.419520i | \(0.137802\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.62248 | − | 3.91701i | 0.119937 | − | 0.289554i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.48274 | + | 20.4791i | 0.623663 | + | 1.50566i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.71856 | + | 0.938579i | −0.345055 | + | 0.0686357i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.3379 | + | 8.24390i | −0.897448 | + | 0.599656i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.8728 | 1.29323 | 0.646617 | − | 0.762815i | \(-0.276183\pi\) | ||||
0.646617 | + | 0.762815i | \(0.276183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.0233 | 1.44131 | 0.720654 | − | 0.693295i | \(-0.243842\pi\) | ||||
0.720654 | + | 0.693295i | \(0.243842\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −21.2081 | + | 14.1708i | −1.51875 | + | 1.01479i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.3511 | − | 3.25244i | 1.16497 | − | 0.231727i | 0.425527 | − | 0.904946i | \(-0.360089\pi\) |
0.739444 | + | 0.673219i | \(0.235089\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.64872 | + | 13.6372i | 0.400427 | + | 0.966716i | 0.987562 | + | 0.157227i | \(0.0502555\pi\) |
−0.587136 | + | 0.809489i | \(0.699744\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.79979 | + | 21.2446i | −0.620689 | + | 1.49848i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.19941 | + | 13.7679i | −0.645672 | + | 0.966317i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.2175 | + | 2.43021i | 0.853305 | + | 0.169733i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.77405 | − | 1.77405i | 0.123305 | − | 0.123305i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.74288 | − | 4.74288i | −0.328072 | − | 0.328072i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.18718 | + | 10.9957i | −0.150572 | + | 0.756975i | 0.829527 | + | 0.558466i | \(0.188610\pi\) |
−0.980099 | + | 0.198509i | \(0.936390\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.8872 | + | 10.6155i | 1.08858 | + | 0.727363i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.63376 | − | 3.57622i | −0.588817 | − | 0.243896i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.14053 | + | 2.95771i | −0.484731 | + | 0.200782i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.21604 | − | 16.1681i | −0.217320 | − | 1.09254i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.98255 | + | 5.96030i | 0.267895 | + | 0.400933i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.50358i | 0.502477i | 0.967925 | + | 0.251239i | \(0.0808379\pi\) | ||||
−0.967925 | + | 0.251239i | \(0.919162\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.04806i | 0.269871i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.7739 | + | 22.1107i | 0.980580 | + | 1.46754i | 0.881343 | + | 0.472478i | \(0.156640\pi\) |
0.0992374 | + | 0.995064i | \(0.468360\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.93523 | + | 14.7564i | 0.193966 | + | 0.975131i | 0.947994 | + | 0.318289i | \(0.103108\pi\) |
−0.754028 | + | 0.656842i | \(0.771892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.7952 | + | 4.88573i | −0.776067 | + | 0.321458i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.7995 | + | 7.37280i | 1.16609 | + | 0.483008i | 0.879897 | − | 0.475165i | \(-0.157612\pi\) |
0.286189 | + | 0.958173i | \(0.407612\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0388 | + | 6.70771i | 0.654859 | + | 0.437563i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.459937 | − | 2.31226i | 0.0298761 | − | 0.150198i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.71028 | − | 6.71028i | −0.434052 | − | 0.434052i | 0.455952 | − | 0.890004i | \(-0.349299\pi\) |
−0.890004 | + | 0.455952i | \(0.849299\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.62074 | − | 2.62074i | 0.168816 | − | 0.168816i | −0.617643 | − | 0.786459i | \(-0.711912\pi\) |
0.786459 | + | 0.617643i | \(0.211912\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.16281 | − | 1.02695i | −0.331194 | − | 0.0658787i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.348228 | − | 0.521160i | 0.0222475 | − | 0.0332957i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.82458 | + | 9.23335i | −0.243352 | + | 0.587504i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.17922 | − | 12.5037i | −0.328220 | − | 0.792393i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.80701 | + | 0.757262i | −0.240296 | + | 0.0477979i | −0.313769 | − | 0.949499i | \(-0.601592\pi\) |
0.0734728 | + | 0.997297i | \(0.476592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.3014 | − | 8.21956i | 0.773385 | − | 0.516759i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.01743 | −0.564693 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.79248 | −0.298947 | −0.149473 | − | 0.988766i | \(-0.547758\pi\) | ||||
−0.149473 | + | 0.988766i | \(0.547758\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.7456 | − | 9.18451i | 0.854110 | − | 0.570698i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.10729 | + | 0.618078i | −0.192336 | + | 0.0382581i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.53072 | + | 13.3523i | 0.341039 | + | 0.823340i | 0.997611 | + | 0.0690772i | \(0.0220055\pi\) |
−0.656573 | + | 0.754263i | \(0.727995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.91764 | + | 19.1149i | −0.486377 | + | 1.17422i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.12633 | + | 7.67209i | −0.313726 | + | 0.469524i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.3558 | − | 2.45771i | −0.753344 | − | 0.149849i | −0.196543 | − | 0.980495i | \(-0.562971\pi\) |
−0.556801 | + | 0.830646i | \(0.687971\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.16587 | − | 1.16587i | 0.0708213 | − | 0.0708213i | −0.670809 | − | 0.741630i | \(-0.734053\pi\) |
0.741630 | + | 0.670809i | \(0.234053\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 13.4512 | + | 13.4512i | 0.814105 | + | 0.814105i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.65705 | + | 23.4126i | −0.280831 | + | 1.41183i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.28458 | + | 5.53558i | 0.497772 | + | 0.332601i | 0.778983 | − | 0.627045i | \(-0.215736\pi\) |
−0.281211 | + | 0.959646i | \(0.590736\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.36621 | − | 0.565902i | −0.0817927 | − | 0.0338797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.78965 | + | 0.741299i | −0.106762 | + | 0.0442222i | −0.435425 | − | 0.900225i | \(-0.643402\pi\) |
0.328663 | + | 0.944447i | \(0.393402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.18457 | + | 10.9826i | 0.129859 | + | 0.652845i | 0.989801 | + | 0.142454i | \(0.0454993\pi\) |
−0.859943 | + | 0.510391i | \(0.829501\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.98464 | − | 10.4532i | −0.413734 | − | 0.619197i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 9.29026i | − | 0.548387i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.4658i | − | 0.850927i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.69913 | + | 14.5158i | 0.568573 | + | 0.850930i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.0277262 | + | 0.139389i | 0.00161978 | + | 0.00814318i | 0.981587 | − | 0.191017i | \(-0.0611786\pi\) |
−0.979967 | + | 0.199160i | \(0.936179\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.42710 | − | 1.41955i | 0.199534 | − | 0.0826495i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.4676 | − | 6.40690i | −0.897523 | − | 0.371766i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.3292 | − | 12.2472i | −1.06000 | − | 0.708271i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.35969 | + | 6.83564i | −0.0783714 | + | 0.394000i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.8576 | + | 13.8576i | 0.796097 | + | 0.796097i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.82680 | + | 6.82680i | −0.390901 | + | 0.390901i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.97782 | − | 0.393412i | −0.112880 | − | 0.0224532i | 0.138327 | − | 0.990387i | \(-0.455828\pi\) |
−0.251207 | + | 0.967933i | \(0.580828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.05341 | + | 10.5562i | −0.401254 | + | 0.600520i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.97814 | + | 14.4325i | −0.338989 | + | 0.818392i | 0.658824 | + | 0.752297i | \(0.271054\pi\) |
−0.997813 | + | 0.0660951i | \(0.978946\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3839 | − | 29.8974i | −0.699981 | − | 1.68990i | −0.723635 | − | 0.690183i | \(-0.757530\pi\) |
0.0236544 | − | 0.999720i | \(-0.492470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.83536 | − | 0.961813i | 0.272442 | − | 0.0541920i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.23554 | − | 1.49374i | 0.125560 | − | 0.0838968i | −0.491204 | − | 0.871045i | \(-0.663443\pi\) |
0.616765 | + | 0.787148i | \(0.288443\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.6825 | −1.04602 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3482 | −0.577581 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.93777 | + | 1.96295i | −0.163462 | + | 0.109222i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.8848 | − | 6.93902i | 1.93506 | − | 0.384907i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.48247 | − | 15.6501i | −0.358481 | − | 0.865450i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.44584 | − | 8.31900i | 0.189975 | − | 0.458641i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.656286 | + | 0.982201i | −0.0360727 | + | 0.0539866i | −0.849068 | − | 0.528284i | \(-0.822836\pi\) |
0.812995 | + | 0.582271i | \(0.197836\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.10225 | + | 0.617076i | 0.170002 | + | 0.0338156i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 37.0263 | − | 37.0263i | 2.02296 | − | 2.02296i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.1614 | + | 23.1614i | 1.26168 | + | 1.26168i | 0.950278 | + | 0.311402i | \(0.100798\pi\) |
0.311402 | + | 0.950278i | \(0.399202\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.76684 | − | 23.9645i | 0.258899 | − | 1.30158i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.25063 | − | 4.84472i | −0.392644 | − | 0.262356i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8906 | + | 6.99631i | 0.912006 | + | 0.377765i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 25.6196 | − | 10.6120i | 1.37931 | − | 0.571330i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.47211 | − | 12.4281i | −0.132710 | − | 0.667176i | −0.988666 | − | 0.150129i | \(-0.952031\pi\) |
0.855957 | − | 0.517047i | \(-0.172969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.6597 | − | 21.9398i | −0.784716 | − | 1.17441i | −0.981027 | − | 0.193869i | \(-0.937896\pi\) |
0.196312 | − | 0.980542i | \(-0.437104\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.9457i | 1.33150i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.76818i | 0.413458i | 0.978398 | + | 0.206729i | \(0.0662819\pi\) | ||||
−0.978398 | + | 0.206729i | \(0.933718\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.1732 | − | 36.1778i | −1.28298 | − | 1.92012i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.31202 | + | 6.59595i | 0.0694393 | + | 0.349095i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.48329 | + | 2.27125i | −0.289397 | + | 0.119872i | −0.522659 | − | 0.852542i | \(-0.675060\pi\) |
0.233262 | + | 0.972414i | \(0.425060\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0027 | + | 5.38589i | 0.684352 | + | 0.283468i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.44812 | + | 1.63578i | 0.128493 | + | 0.0858564i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.32342 | + | 36.8173i | −0.383326 | + | 1.92711i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.0480 | − | 24.0480i | −1.25530 | − | 1.25530i | −0.953313 | − | 0.301985i | \(-0.902351\pi\) |
−0.301985 | − | 0.953313i | \(-0.597649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.25690 | − | 1.25690i | 0.0654314 | − | 0.0654314i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.1339 | + | 3.01032i | 0.785713 | + | 0.156288i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.521412 | + | 0.780348i | −0.0269977 | + | 0.0404049i | −0.844723 | − | 0.535204i | \(-0.820235\pi\) |
0.817725 | + | 0.575609i | \(0.195235\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.28385 | + | 15.1706i | −0.324497 | + | 0.783404i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.6528 | + | 25.7180i | 0.548645 | + | 1.32455i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.2135 | − | 5.01528i | 1.29513 | − | 0.257618i | 0.501044 | − | 0.865422i | \(-0.332950\pi\) |
0.794087 | + | 0.607804i | \(0.207950\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.3149 | − | 11.5695i | 0.887072 | − | 0.592722i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.1379 | −1.84656 | −0.923279 | − | 0.384130i | \(-0.874501\pi\) | ||||
−0.923279 | + | 0.384130i | \(0.874501\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.0725 | 1.48167 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.10876 | + | 0.740850i | −0.0563615 | + | 0.0376595i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.2404 | + | 3.42934i | −0.874125 | + | 0.173874i | −0.611711 | − | 0.791081i | \(-0.709518\pi\) |
−0.262414 | + | 0.964955i | \(0.584518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.98238 | − | 7.20010i | −0.150825 | − | 0.364125i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.3688 | − | 29.8610i | 0.623924 | − | 1.50629i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.98260 | + | 4.46378i | −0.150071 | + | 0.224597i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.70636 | − | 1.33398i | −0.336583 | − | 0.0669505i | 0.0239055 | − | 0.999714i | \(-0.492390\pi\) |
−0.360488 | + | 0.932764i | \(0.617390\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.62996 | + | 6.62996i | −0.331913 | + | 0.331913i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.0108 | − | 14.0108i | −0.699666 | − | 0.699666i | 0.264672 | − | 0.964338i | \(-0.414736\pi\) |
−0.964338 | + | 0.264672i | \(0.914736\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.53485 | + | 12.7435i | −0.126270 | + | 0.634801i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.5005 | − | 14.3662i | −1.06837 | − | 0.713861i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.2324 | + | 7.13791i | 0.854180 | + | 0.353813i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.5325 | + | 8.50486i | −1.01527 | + | 0.420538i | −0.827374 | − | 0.561651i | \(-0.810166\pi\) |
−0.187895 | + | 0.982189i | \(0.560166\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.10132 | − | 10.5640i | −0.103650 | − | 0.521086i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.53699 | − | 2.30027i | −0.0756304 | − | 0.113189i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.8189i | 1.51284i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 25.7667i | − | 1.26180i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.2124 | + | 18.2772i | 0.596615 | + | 0.892898i | 0.999753 | − | 0.0222415i | \(-0.00708026\pi\) |
−0.403137 | + | 0.915140i | \(0.632080\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.62271 | + | 13.1853i | 0.127823 | + | 0.642610i | 0.990574 | + | 0.136980i | \(0.0437397\pi\) |
−0.862751 | + | 0.505630i | \(0.831260\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.59169 | − | 0.659298i | 0.0773904 | − | 0.0320562i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.6173 | + | 4.81203i | 0.563521 | + | 0.233418i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.98686 | + | 4.00029i | 0.289725 | + | 0.193588i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.18723 | + | 21.0506i | −0.202161 | + | 1.01633i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.2500 | + | 11.2500i | 0.541893 | + | 0.541893i | 0.924084 | − | 0.382190i | \(-0.124830\pi\) |
−0.382190 | + | 0.924084i | \(0.624830\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.8833 | + | 17.8833i | −0.859418 | + | 0.859418i | −0.991269 | − | 0.131851i | \(-0.957908\pi\) |
0.131851 | + | 0.991269i | \(0.457908\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −34.3445 | − | 6.83154i | −1.64669 | − | 0.327547i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.03648 | − | 9.03424i | 0.288764 | − | 0.432166i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.70310 | − | 18.5969i | 0.367649 | − | 0.887583i | −0.626485 | − | 0.779433i | \(-0.715507\pi\) |
0.994135 | − | 0.108150i | \(-0.0344928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0342272 | − | 0.0826318i | −0.00162987 | − | 0.00393485i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.1776 | − | 4.61031i | 1.10120 | − | 0.219043i | 0.389153 | − | 0.921173i | \(-0.372768\pi\) |
0.712048 | + | 0.702130i | \(0.247768\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.4706 | − | 11.6735i | 0.828184 | − | 0.553375i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.00252 | 0.142014 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.3135 | −1.19462 | −0.597310 | − | 0.802010i | \(-0.703764\pi\) | ||||
−0.597310 | + | 0.802010i | \(0.703764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.71543 | − | 5.82346i | 0.410394 | − | 0.274216i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −21.4661 | + | 4.26988i | −1.00857 | + | 0.200617i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −16.5771 | − | 40.0207i | −0.777148 | − | 1.87620i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.63458 | + | 3.94622i | −0.0764624 | + | 0.184596i | −0.957489 | − | 0.288471i | \(-0.906853\pi\) |
0.881026 | + | 0.473067i | \(0.156853\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.89960 | + | 7.33277i | −0.228694 | + | 0.342264i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.97319 | + | 1.18814i | 0.278199 | + | 0.0553372i | 0.332218 | − | 0.943203i | \(-0.392203\pi\) |
−0.0540188 | + | 0.998540i | \(0.517203\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.21551 | + | 4.21551i | −0.195912 | + | 0.195912i | −0.798245 | − | 0.602333i | \(-0.794238\pi\) |
0.602333 | + | 0.798245i | \(0.294238\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −11.5575 | − | 11.5575i | −0.535964 | − | 0.535964i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.66305 | − | 33.4974i | 0.308329 | − | 1.55007i | −0.446882 | − | 0.894593i | \(-0.647466\pi\) |
0.755211 | − | 0.655482i | \(-0.227534\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.4708 | − | 21.6963i | −1.49936 | − | 1.00184i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.04324 | − | 2.08898i | −0.232380 | − | 0.0962551i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.26499 | + | 3.00926i | −0.334045 | + | 0.138366i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.42016 | + | 17.1943i | 0.156928 | + | 0.788929i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.64022 | + | 2.45476i | 0.0751005 | + | 0.112396i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 19.6175i | − | 0.896347i | −0.893947 | − | 0.448174i | \(-0.852075\pi\) | ||
0.893947 | − | 0.448174i | \(-0.147925\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 27.7919i | − | 1.26720i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.4899 | − | 17.1959i | −0.522809 | − | 0.782439i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.75573 | − | 38.9907i | −0.352170 | − | 1.77048i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.3985 | − | 16.3194i | 1.78532 | − | 0.739502i | 0.794013 | − | 0.607901i | \(-0.207988\pi\) |
0.991303 | − | 0.131601i | \(-0.0420119\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.94980 | − | 1.63606i | −0.178616 | − | 0.0739852i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.04811 | − | 2.03668i | −0.137559 | − | 0.0919141i | 0.484887 | − | 0.874577i | \(-0.338861\pi\) |
−0.622446 | + | 0.782663i | \(0.713861\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.91993 | + | 9.65213i | −0.0864692 | + | 0.434710i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.93327 | + | 3.93327i | 0.176788 | + | 0.176788i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.9457 | + | 22.9457i | −1.02925 | + | 1.02925i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.0620242 | − | 0.0123374i | −0.00277658 | − | 0.000552297i | 0.193702 | − | 0.981060i | \(-0.437951\pi\) |
−0.196478 | + | 0.980508i | \(0.562951\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.38000 | − | 2.06532i | 0.0616540 | − | 0.0922717i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.58180 | − | 23.1325i | 0.427231 | − | 1.03143i | −0.552930 | − | 0.833228i | \(-0.686490\pi\) |
0.980162 | − | 0.198200i | \(-0.0635096\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.0779 | − | 41.2298i | −0.759958 | − | 1.83470i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.2560 | − | 2.23896i | 0.499898 | − | 0.0994359i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.5244 | + | 19.0594i | −1.26432 | + | 0.844792i | −0.993048 | − | 0.117710i | \(-0.962445\pi\) |
−0.271273 | + | 0.962503i | \(0.587445\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.9962 | 1.23848 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.2954 | −0.542857 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.0381 | − | 16.0617i | 1.05924 | − | 0.707764i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.96424 | − | 1.98201i | 0.438227 | − | 0.0871687i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.20791 | − | 7.74457i | −0.140812 | − | 0.339949i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5629 | + | 25.5011i | −0.462769 | + | 1.11722i | 0.504487 | + | 0.863420i | \(0.331682\pi\) |
−0.967256 | + | 0.253804i | \(0.918318\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.36875 | + | 12.5247i | −0.365940 | + | 0.547668i | −0.968054 | − | 0.250742i | \(-0.919325\pi\) |
0.602114 | + | 0.798410i | \(0.294325\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 32.7279 | + | 6.50998i | 1.42836 | + | 0.284119i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.24809 | + | 3.24809i | −0.141489 | + | 0.141489i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.683141 | + | 0.683141i | 0.0297018 | + | 0.0297018i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.103265 | − | 0.519150i | 0.00448133 | − | 0.0225292i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.9860 | − | 8.67697i | −0.562486 | − | 0.375841i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.7708 | + | 9.01774i | 0.941232 | + | 0.389871i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.0181 | + | 7.04913i | −0.734385 | + | 0.304192i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.102895 | − | 0.517290i | −0.00443202 | − | 0.0222813i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.97281 | + | 7.44233i | 0.213798 | + | 0.319971i | 0.922832 | − | 0.385203i | \(-0.125869\pi\) |
−0.709034 | + | 0.705174i | \(0.750869\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 6.59898i | − | 0.283189i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 38.5739i | 1.65232i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.1415 | + | 25.6541i | 0.732920 | + | 1.09689i | 0.991399 | + | 0.130875i | \(0.0417786\pi\) |
−0.258479 | + | 0.966017i | \(0.583221\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.268766 | + | 1.35118i | 0.0114707 | + | 0.0576669i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.6761 | + | 5.25062i | −0.540021 | + | 0.223684i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.69907 | + | 1.53220i | 0.157300 | + | 0.0651559i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 29.0687 | + | 19.4231i | 1.23390 | + | 0.824464i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.97599 | − | 35.0707i | 0.295582 | − | 1.48599i | −0.492440 | − | 0.870346i | \(-0.663895\pi\) |
0.788022 | − | 0.615647i | \(-0.211105\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.28498 | + | 8.28498i | 0.350417 | + | 0.350417i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.36541 | + | 5.36541i | −0.226528 | + | 0.226528i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.7512 | − | 4.32658i | −0.916704 | − | 0.182344i | −0.285876 | − | 0.958267i | \(-0.592285\pi\) |
−0.630828 | + | 0.775923i | \(0.717285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.9120 | + | 46.2631i | −1.30048 | + | 1.94630i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.38010 | + | 17.8171i | −0.309935 | + | 0.748250i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.8493 | − | 33.4353i | −0.580594 | − | 1.40168i | −0.892275 | − | 0.451492i | \(-0.850892\pi\) |
0.311681 | − | 0.950187i | \(-0.399108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.7190 | + | 8.09951i | −1.70404 | + | 0.338954i | −0.948650 | − | 0.316326i | \(-0.897551\pi\) |
−0.755386 | + | 0.655280i | \(0.772551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.4381 | − | 15.6608i | 0.979141 | − | 0.654241i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.6690 | −1.61261 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.4102 | 0.475014 | 0.237507 | − | 0.971386i | \(-0.423670\pi\) | ||||
0.237507 | + | 0.971386i | \(0.423670\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 26.2582 | − | 17.5451i | 1.09125 | − | 0.729151i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.5430 | − | 4.48409i | 0.935243 | − | 0.186031i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.66241 | + | 16.0845i | 0.275929 | + | 0.666151i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.17173 | − | 7.65722i | 0.131135 | − | 0.316587i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.5001 | + | 18.7077i | −0.515934 | + | 0.772150i | −0.994369 | − | 0.105973i | \(-0.966204\pi\) |
0.478435 | + | 0.878123i | \(0.341204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.28115 | − | 1.24940i | −0.258810 | − | 0.0514806i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.5927 | − | 18.5927i | 0.764800 | − | 0.764800i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.24913 | − | 1.24913i | −0.0512956 | − | 0.0512956i | 0.680994 | − | 0.732289i | \(-0.261548\pi\) |
−0.732289 | + | 0.680994i | \(0.761548\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.98767 | − | 15.0200i | 0.122482 | − | 0.615761i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.3570 | + | 12.9340i | 0.792231 | + | 0.529352i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.75750 | + | 1.14220i | 0.112669 | + | 0.0466689i | 0.438306 | − | 0.898826i | \(-0.355579\pi\) |
−0.325637 | + | 0.945495i | \(0.605579\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.5982 | − | 8.94628i | 0.881010 | − | 0.364926i | 0.104121 | − | 0.994565i | \(-0.466797\pi\) |
0.776888 | + | 0.629638i | \(0.216797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.45770 | − | 7.32835i | −0.0593621 | − | 0.298434i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.72494 | − | 5.57476i | −0.151440 | − | 0.226646i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.7172i | − | 1.00324i | −0.865088 | − | 0.501620i | \(-0.832738\pi\) | ||
0.865088 | − | 0.501620i | \(-0.167262\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26.1158i | 1.05827i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.41000 | − | 12.5865i | −0.340232 | − | 0.509193i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.44115 | + | 7.24514i | 0.0582074 | + | 0.292629i | 0.998914 | − | 0.0465930i | \(-0.0148364\pi\) |
−0.940707 | + | 0.339222i | \(0.889836\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 18.1512 | − | 7.51847i | 0.731927 | − | 0.303174i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.89273 | − | 1.61242i | −0.156715 | − | 0.0649136i | 0.302947 | − | 0.953007i | \(-0.402030\pi\) |
−0.459662 | + | 0.888094i | \(0.652030\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.36631 | − | 4.25383i | −0.255884 | − | 0.170976i | 0.421012 | − | 0.907055i | \(-0.361675\pi\) |
−0.676895 | + | 0.736079i | \(0.736675\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.29093 | − | 26.5993i | 0.212318 | − | 1.06739i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.0807 | − | 11.0807i | −0.443938 | − | 0.443938i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.48653 | + | 1.48653i | −0.0594614 | + | 0.0594614i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.3756 | − | 2.06384i | −0.414362 | − | 0.0824218i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.45863 | − | 8.16942i | 0.217650 | − | 0.325736i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.3902 | − | 25.0842i | 0.413628 | − | 0.998587i | −0.570527 | − | 0.821279i | \(-0.693261\pi\) |
0.984155 | − | 0.177308i | \(-0.0567390\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.76661 | + | 16.3360i | 0.268949 | + | 0.649300i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −46.5095 | + | 9.25132i | −1.84567 | + | 0.367127i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.653421 | + | 0.436602i | −0.0258895 | + | 0.0172988i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.20872 | −0.245613 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.6538 | 1.92171 | 0.960855 | − | 0.277053i | \(-0.0893579\pi\) | ||||
0.960855 | + | 0.277053i | \(0.0893579\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.2613 | + | 16.2109i | −0.956772 | + | 0.639295i | −0.932791 | − | 0.360418i | \(-0.882634\pi\) |
−0.0239813 | + | 0.999712i | \(0.507634\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.4558 | + | 2.87543i | −0.569195 | + | 0.113220i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.55831 | + | 13.4190i | 0.218520 | + | 0.527553i | 0.994684 | − | 0.102978i | \(-0.0328371\pi\) |
−0.776164 | + | 0.630531i | \(0.782837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.19450 | − | 2.88378i | 0.0468883 | − | 0.113198i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.77231 | + | 10.1355i | −0.265428 | + | 0.397241i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.4067 | + | 6.44610i | 1.26817 | + | 0.252255i | 0.782922 | − | 0.622120i | \(-0.213728\pi\) |
0.485251 | + | 0.874375i | \(0.338728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52.0435 | + | 52.0435i | −2.03351 | + | 2.03351i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.78765 | + | 3.78765i | 0.147770 | + | 0.147770i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.862145 | − | 4.33430i | 0.0335844 | − | 0.168840i | −0.960353 | − | 0.278786i | \(-0.910068\pi\) |
0.993938 | + | 0.109946i | \(0.0350679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.3472 | − | 16.9364i | −0.985891 | − | 0.658751i | −0.0455418 | − | 0.998962i | \(-0.514501\pi\) |
−0.940349 | + | 0.340211i | \(0.889501\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.4453 | + | 4.32658i | 0.405661 | + | 0.168030i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.7258 | − | 8.17068i | 0.764933 | − | 0.316845i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.90418 | − | 29.6823i | −0.228611 | − | 1.14930i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.57492 | + | 9.84006i | 0.254201 | + | 0.380439i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.12395i | 0.313622i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.5263i | 1.02251i | 0.859428 | + | 0.511257i | \(0.170820\pi\) | ||||
−0.859428 | + | 0.511257i | \(0.829180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.3109 | + | 36.3838i | 0.935727 | + | 1.40041i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.43408 | − | 27.3189i | −0.208849 | − | 1.04995i | −0.932881 | − | 0.360186i | \(-0.882713\pi\) |
0.724032 | − | 0.689766i | \(-0.242287\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.3920 | + | 11.3461i | −1.05121 | + | 0.435424i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.7485 | + | 16.0502i | 1.48485 | + | 0.615043i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.4771 | + | 21.0323i | 1.20444 | + | 0.804779i | 0.985286 | − | 0.170912i | \(-0.0546713\pi\) |
0.219151 | + | 0.975691i | \(0.429671\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.78503 | + | 24.0560i | −0.182827 | + | 0.919132i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.7793 | + | 16.7793i | 0.640171 | + | 0.640171i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.3427 | − | 18.3427i | 0.698801 | − | 0.698801i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.4829 | − | 5.06887i | −0.969416 | − | 0.192829i | −0.315107 | − | 0.949056i | \(-0.602040\pi\) |
−0.654309 | + | 0.756227i | \(0.727040\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.30478 | − | 3.44934i | 0.0875512 | − | 0.131030i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.4538 | + | 54.2084i | −0.851723 | + | 2.05624i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.11298 | − | 5.10119i | −0.0800348 | − | 0.193221i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29.8023 | − | 5.92804i | 1.12723 | − | 0.224219i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.2742 | + | 20.2286i | −1.14344 | + | 0.764023i | −0.975113 | − | 0.221708i | \(-0.928837\pi\) |
−0.168328 | + | 0.985731i | \(0.553837\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.6983 | 0.516642 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.0422 | 0.717172 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.6734 | + | 18.4908i | −1.04077 | + | 0.695417i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.11157 | − | 1.41458i | 0.267081 | − | 0.0531256i | −0.0597332 | − | 0.998214i | \(-0.519025\pi\) |
0.326814 | + | 0.945089i | \(0.394025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.293159 | + | 0.707747i | 0.0109943 | + | 0.0265426i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.40577 | − | 13.0507i | 0.202448 | − | 0.488752i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 27.1533 | − | 40.6378i | 1.01548 | − | 1.51977i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.6795 | − | 2.91994i | −0.548217 | − | 0.109047i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.9786 | − | 24.9786i | 0.931543 | − | 0.931543i | −0.0662593 | − | 0.997802i | \(-0.521106\pi\) |
0.997802 | + | 0.0662593i | \(0.0211064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.2461 | − | 15.2461i | −0.567795 | − | 0.567795i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.14040 | − | 5.73317i | 0.0424119 | − | 0.213219i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.6009 | + | 27.1287i | 1.50788 | + | 1.00753i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −49.4936 | − | 20.5009i | −1.83562 | − | 0.760337i | −0.961608 | − | 0.274425i | \(-0.911512\pi\) |
−0.874008 | − | 0.485912i | \(-0.838488\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.6258 | + | 11.4430i | −1.02318 | + | 0.423814i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.808107 | + | 4.06263i | 0.0298889 | + | 0.150262i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.9138 | + | 25.3133i | 0.624725 | + | 0.934967i | 0.999968 | + | 0.00804070i | \(0.00255946\pi\) |
−0.375242 | + | 0.926927i | \(0.622441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 0.988571i | − | 0.0364640i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 44.0616i | − | 1.62303i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −23.5325 | − | 35.2188i | −0.865656 | − | 1.29555i | −0.954107 | − | 0.299465i | \(-0.903192\pi\) |
0.0884513 | − | 0.996081i | \(-0.471808\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.07512 | + | 15.4597i | 0.112967 | + | 0.567926i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.7692 | − | 6.11761i | 0.541830 | − | 0.224433i | −0.0949455 | − | 0.995482i | \(-0.530268\pi\) |
0.636776 | + | 0.771049i | \(0.280268\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.31676 | − | 2.61649i | −0.231428 | − | 0.0958607i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.65655 | + | 2.44323i | 0.133786 | + | 0.0893930i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.42858 | − | 17.2367i | 0.125278 | − | 0.629814i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.8491 | − | 27.8491i | −1.01623 | − | 1.01623i | −0.999866 | − | 0.0163606i | \(-0.994792\pi\) |
−0.0163606 | − | 0.999866i | \(-0.505208\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.32890 | + | 4.32890i | −0.157754 | + | 0.157754i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 48.8818 | + | 9.72319i | 1.77899 | + | 0.353863i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.58238 | + | 2.36820i | −0.0575127 | + | 0.0860738i | −0.859111 | − | 0.511789i | \(-0.828983\pi\) |
0.801599 | + | 0.597862i | \(0.203983\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.92960 | − | 21.5580i | 0.324124 | − | 0.782504i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.1275 | + | 24.4500i | 0.367123 | + | 0.886312i | 0.994219 | + | 0.107371i | \(0.0342432\pi\) |
−0.627096 | + | 0.778942i | \(0.715757\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.2155 | − | 5.61242i | 1.02147 | − | 0.203183i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.43629 | − | 1.62788i | 0.0880843 | − | 0.0588560i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.65086 | −0.167933 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.9485 | −1.76513 | −0.882564 | − | 0.470193i | \(-0.844184\pi\) | ||||
−0.882564 | + | 0.470193i | \(0.844184\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.28477 | + | 4.19935i | −0.226341 | + | 0.151236i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.5401 | − | 6.07480i | 1.09845 | − | 0.218495i | 0.387593 | − | 0.921831i | \(-0.373307\pi\) |
0.710858 | + | 0.703335i | \(0.248307\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.72214 | + | 21.0571i | 0.313309 | + | 0.756394i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.97791 | − | 24.0888i | 0.357955 | − | 0.864181i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.27678 | − | 6.40065i | 0.153232 | − | 0.229327i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.9091 | − | 7.14276i | −1.28493 | − | 0.255588i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.2163 | + | 24.2163i | −0.865419 | + | 0.865419i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.78967 | + | 8.78967i | 0.313717 | + | 0.313717i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.20769 | + | 36.2355i | −0.256926 | + | 1.29166i | 0.609674 | + | 0.792652i | \(0.291300\pi\) |
−0.866600 | + | 0.499003i | \(0.833700\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.9527 | + | 12.6638i | 0.674733 | + | 0.450842i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 38.3375 | + | 15.8799i | 1.36313 | + | 0.564625i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.1833 | − | 4.63227i | 0.397130 | − | 0.164497i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.36612 | + | 32.0046i | 0.225783 | + | 1.13509i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.09159 | + | 10.6133i | 0.251197 | + | 0.375943i | 0.935542 | − | 0.353215i | \(-0.114912\pi\) |
−0.684345 | + | 0.729158i | \(0.739912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.35160i | − | 0.189326i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.99825i | − | 0.105938i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.5490 | + | 26.2639i | 0.619291 | + | 0.926834i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.18770 | + | 46.1897i | 0.323824 | + | 1.62797i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.3566 | + | 7.60357i | −0.646185 | + | 0.267658i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.8371 | − | 7.80259i | −0.662277 | − | 0.274324i | 0.0261191 | − | 0.999659i | \(-0.491685\pi\) |
−0.688397 | + | 0.725335i | \(0.741685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.9904 | − | 20.7071i | −1.08822 | − | 0.727126i | −0.124015 | − | 0.992280i | \(-0.539577\pi\) |
−0.964206 | + | 0.265154i | \(0.914577\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.507320 | − | 2.55047i | 0.0177925 | − | 0.0894488i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.88394 | + | 6.88394i | 0.241134 | + | 0.241134i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.08357 | + | 4.08357i | −0.142866 | + | 0.142866i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.06248 | − | 1.20590i | −0.211840 | − | 0.0421377i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.3593 | − | 30.4698i | 0.710544 | − | 1.06340i | −0.283974 | − | 0.958832i | \(-0.591653\pi\) |
0.994517 | − | 0.104571i | \(-0.0333471\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.39690 | − | 10.6151i | 0.153266 | − | 0.370018i | −0.828533 | − | 0.559941i | \(-0.810824\pi\) |
0.981799 | + | 0.189923i | \(0.0608239\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 14.4078 | + | 34.7835i | 0.501615 | + | 1.21101i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.2588 | − | 4.02973i | 0.704467 | − | 0.140127i | 0.170159 | − | 0.985417i | \(-0.445572\pi\) |
0.534309 | + | 0.845289i | \(0.320572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.0650754 | − | 0.0434820i | 0.00226016 | − | 0.00151019i | −0.554440 | − | 0.832224i | \(-0.687067\pi\) |
0.556700 | + | 0.830714i | \(0.312067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.7147 | 0.545138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.277826 | −0.00962612 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.70306 | + | 3.14248i | −0.162756 | + | 0.108750i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.6780 | + | 3.11854i | −0.541910 | + | 0.107793i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.26659 | − | 19.9573i | −0.285394 | − | 0.689003i | 0.714550 | − | 0.699585i | \(-0.246632\pi\) |
−0.999944 | + | 0.0105819i | \(0.996632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.52696 | + | 8.51482i | −0.121619 | + | 0.293615i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.69736 | + | 2.54029i | −0.0584604 | + | 0.0874921i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.6318 | − | 5.09847i | −0.881759 | − | 0.175393i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.53578 | + | 3.53578i | −0.121491 | + | 0.121491i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.4881 | + | 12.4881i | 0.428591 | + | 0.428591i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.89461 | + | 29.6342i | −0.202065 | + | 1.01585i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.9713 | − | 20.0262i | −1.02620 | − | 0.685683i | −0.0759277 | − | 0.997113i | \(-0.524192\pi\) |
−0.950269 | + | 0.311431i | \(0.899192\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.77416 | + | 1.56331i | 0.129073 | + | 0.0534640i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.6508 | − | 7.31122i | 0.602941 | − | 0.249747i | −0.0602657 | − | 0.998182i | \(-0.519195\pi\) |
0.663207 | + | 0.748436i | \(0.269195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.96755 | + | 14.9189i | 0.101252 | + | 0.509026i | 0.997813 | + | 0.0661060i | \(0.0210575\pi\) |
−0.896561 | + | 0.442920i | \(0.853942\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.14047 | − | 12.1831i | −0.277427 | − | 0.415198i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.1695i | 1.87799i | 0.343930 | + | 0.938995i | \(0.388242\pi\) | ||||
−0.343930 | + | 0.938995i | \(0.611758\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.0887i | 0.649034i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.6754 | − | 18.9701i | −0.430480 | − | 0.644259i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.881306 | + | 4.43063i | 0.0298963 | + | 0.150299i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −60.6545 | + | 25.1239i | −2.05520 | + | 0.851291i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.24094 | − | 2.17087i | −0.177379 | − | 0.0734728i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.1871 | − | 15.4931i | −0.783867 | − | 0.523763i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.99284 | + | 40.1827i | −0.269899 | + | 1.35687i | 0.573332 | + | 0.819323i | \(0.305650\pi\) |
−0.843231 | + | 0.537551i | \(0.819350\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.158497 | + | 0.158497i | 0.00534598 | + | 0.00534598i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 41.4201 | − | 41.4201i | 1.39548 | − | 1.39548i | 0.583018 | − | 0.812459i | \(-0.301872\pi\) |
0.812459 | − | 0.583018i | \(-0.198128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.2589 | + | 4.02975i | 0.681766 | + | 0.135612i | 0.523811 | − | 0.851834i | \(-0.324510\pi\) |
0.157955 | + | 0.987446i | \(0.449510\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.25037 | − | 4.86453i | 0.109260 | − | 0.163519i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −18.0495 | + | 43.5752i | −0.606042 | + | 1.46311i | 0.261229 | + | 0.965277i | \(0.415872\pi\) |
−0.867271 | + | 0.497837i | \(0.834128\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.5341 | + | 32.6741i | 0.453918 | + | 1.09585i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.3408 | + | 4.24495i | −0.714944 | + | 0.142211i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.20372 | − | 4.14519i | 0.207600 | − | 0.138714i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 41.9458 | 1.40209 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −34.7679 | −1.16087 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.8317 | + | 9.91020i | −0.494664 | + | 0.330524i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.99454 | − | 1.78912i | 0.299651 | − | 0.0596044i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.20657 | + | 10.1555i | 0.139986 | + | 0.337955i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.75055 | + | 13.8831i | −0.191155 | + | 0.461489i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.0167 | − | 20.9775i | 0.465418 | − | 0.696548i | −0.522305 | − | 0.852758i | \(-0.674928\pi\) |
0.987724 | + | 0.156211i | \(0.0499279\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.24563 | − | 1.24233i | −0.207155 | − | 0.0412056i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.97097 | − | 3.97097i | 0.131564 | − | 0.131564i | −0.638258 | − | 0.769822i | \(-0.720345\pi\) |
0.769822 | + | 0.638258i | \(0.220345\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.3374 | + | 18.3374i | 0.606880 | + | 0.606880i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.97064 | + | 14.9344i | −0.0982064 | + | 0.493717i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.6403 | + | 30.4959i | 1.50718 | + | 1.00706i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.2073 | − | 16.6544i | −1.32632 | − | 0.549378i | −0.396714 | − | 0.917942i | \(-0.629850\pi\) |
−0.929602 | + | 0.368564i | \(0.879850\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.93840 | + | 1.21712i | −0.0968235 | + | 0.0401056i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.6427 | + | 53.5046i | 0.350310 | + | 1.76113i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.0847 | − | 40.5351i | −0.890540 | − | 1.33279i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 4.12534i | − | 0.135494i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 5.16429i | − | 0.169435i | −0.996405 | − | 0.0847174i | \(-0.973001\pi\) | ||
0.996405 | − | 0.0847174i | \(-0.0269987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.215196 | − | 0.322064i | −0.00705277 | − | 0.0105552i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.80667 | + | 24.1648i | 0.157363 | + | 0.791119i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.9634 | − | 6.61227i | 0.522060 | − | 0.216244i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.9512 | − | 5.36457i | −0.423097 | − | 0.175253i | 0.160967 | − | 0.986960i | \(-0.448539\pi\) |
−0.584065 | + | 0.811707i | \(0.698539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −42.4373 | − | 28.3557i | −1.38489 | − | 0.925353i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.17307 | + | 15.9521i | −0.103439 | + | 0.520023i | 0.893973 | + | 0.448121i | \(0.147907\pi\) |
−0.997412 | + | 0.0719017i | \(0.977093\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.0065 | + | 12.0065i | 0.390984 | + | 0.390984i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 37.6838 | − | 37.6838i | 1.22585 | − | 1.22585i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.7095 | + | 8.69436i | 1.42037 | + | 0.282529i | 0.844737 | − | 0.535181i | \(-0.179757\pi\) |
0.575630 | + | 0.817710i | \(0.304757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.1480 | − | 39.1333i | 0.848802 | − | 1.27032i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.62278 | − | 3.91773i | 0.0526221 | − | 0.127041i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.09229 | + | 9.87966i | 0.132562 | + | 0.320033i | 0.976198 | − | 0.216883i | \(-0.0695890\pi\) |
−0.843635 | + | 0.536916i | \(0.819589\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −62.9569 | + | 12.5229i | −2.03724 | + | 0.405232i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.4999 | + | 16.3703i | −0.791970 | + | 0.529177i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.2924 | 0.590691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6740 | 0.731419 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.79583 | − | 1.86812i | 0.0900945 | − | 0.0601992i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −70.5318 | + | 14.0296i | −2.27050 | + | 0.451630i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.17090 | − | 19.7263i | −0.262758 | − | 0.634355i | 0.736349 | − | 0.676602i | \(-0.236548\pi\) |
−0.999107 | + | 0.0422473i | \(0.986548\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.13252 | + | 5.14836i | −0.0685064 | + | 0.165389i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.6361 | − | 18.9113i | 0.405513 | − | 0.606893i | −0.571364 | − | 0.820697i | \(-0.693585\pi\) |
0.976877 | + | 0.213804i | \(0.0685854\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 42.9186 | + | 8.53704i | 1.37591 | + | 0.273685i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 39.6670 | − | 39.6670i | 1.27036 | − | 1.27036i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.39950 | − | 6.39950i | −0.204738 | − | 0.204738i | 0.597288 | − | 0.802027i | \(-0.296245\pi\) |
−0.802027 | + | 0.597288i | \(0.796245\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.44930 | − | 17.3408i | 0.110240 | − | 0.554215i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.57664 | + | 3.05801i | 0.146121 | + | 0.0976349i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.428626 | + | 0.177543i | 0.0136710 | + | 0.00566273i | 0.389508 | − | 0.921023i | \(-0.372645\pi\) |
−0.375837 | + | 0.926686i | \(0.622645\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −55.3178 | + | 22.9134i | −1.76257 | + | 0.730082i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.77060 | − | 13.9288i | −0.0881893 | − | 0.443357i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.07696 | − | 10.5914i | −0.225034 | − | 0.336787i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 44.6212i | − | 1.41744i | −0.705490 | − | 0.708720i | \(-0.749273\pi\) | ||
0.705490 | − | 0.708720i | \(-0.250727\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.86310i | 0.0591238i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.4527 | − | 44.0790i | −0.933713 | − | 1.39740i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.3063 | − | 56.8407i | −0.358075 | − | 1.80016i | −0.568643 | − | 0.822584i | \(-0.692531\pi\) |
0.210568 | − | 0.977579i | \(-0.432469\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 31.5888 | − | 13.0845i | 0.999426 | − | 0.413976i |
(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 | 512.2.i.b.33.5 | 56 | ||
4.3 | odd | 2 | 512.2.i.a.33.3 | 56 | |||
8.3 | odd | 2 | 256.2.i.a.145.5 | 56 | |||
8.5 | even | 2 | 64.2.i.a.13.1 | yes | 56 | ||
24.5 | odd | 2 | 576.2.bd.a.397.7 | 56 | |||
64.5 | even | 16 | inner | 512.2.i.b.481.5 | 56 | ||
64.27 | odd | 16 | 256.2.i.a.113.5 | 56 | |||
64.37 | even | 16 | 64.2.i.a.5.1 | ✓ | 56 | ||
64.59 | odd | 16 | 512.2.i.a.481.3 | 56 | |||
192.101 | odd | 16 | 576.2.bd.a.325.7 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
64.2.i.a.5.1 | ✓ | 56 | 64.37 | even | 16 | ||
64.2.i.a.13.1 | yes | 56 | 8.5 | even | 2 | ||
256.2.i.a.113.5 | 56 | 64.27 | odd | 16 | |||
256.2.i.a.145.5 | 56 | 8.3 | odd | 2 | |||
512.2.i.a.33.3 | 56 | 4.3 | odd | 2 | |||
512.2.i.a.481.3 | 56 | 64.59 | odd | 16 | |||
512.2.i.b.33.5 | 56 | 1.1 | even | 1 | trivial | ||
512.2.i.b.481.5 | 56 | 64.5 | even | 16 | inner | ||
576.2.bd.a.325.7 | 56 | 192.101 | odd | 16 | |||
576.2.bd.a.397.7 | 56 | 24.5 | odd | 2 |