Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(881,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.k (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: | \(9.39040727770\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 19 x^{14} - 42 x^{13} + 65 x^{12} - 48 x^{11} - 94 x^{10} + 444 x^{9} - 962 x^{8} + 1332 x^{7} - 846 x^{6} - 1296 x^{5} + 5265 x^{4} - 10206 x^{3} + 13851 x^{2} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.13 | ||
Root | \(-1.70742 - 0.291063i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.881 |
Dual form | 1176.2.k.a.881.14 |
$q$-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 \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.33314 | − | 1.10578i | 0.769687 | − | 0.638421i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.145339 | 0.0649974 | 0.0324987 | − | 0.999472i | \(-0.489654\pi\) | ||||
0.0324987 | + | 0.999472i | \(0.489654\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.554510 | − | 2.94831i | 0.184837 | − | 0.982769i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.46977i | − | 0.744665i | −0.928099 | − | 0.372332i | \(-0.878558\pi\) | ||
0.928099 | − | 0.372332i | \(-0.121442\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.04143i | − | 0.566191i | −0.959092 | − | 0.283096i | \(-0.908639\pi\) | ||
0.959092 | − | 0.283096i | \(-0.0913613\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.193756 | − | 0.160712i | 0.0500276 | − | 0.0414957i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.75684 | 0.426096 | 0.213048 | − | 0.977042i | \(-0.431661\pi\) | ||||
0.213048 | + | 0.977042i | \(0.431661\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.25299i | − | 0.975702i | −0.872927 | − | 0.487851i | \(-0.837781\pi\) | ||
0.872927 | − | 0.487851i | \(-0.162219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.61812i | 1.79700i | 0.438971 | + | 0.898501i | \(0.355343\pi\) | ||||
−0.438971 | + | 0.898501i | \(0.644657\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97888 | −0.995775 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.52094 | − | 4.54366i | −0.485154 | − | 0.874429i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.08790i | − | 1.31619i | −0.752935 | − | 0.658095i | \(-0.771363\pi\) | ||
0.752935 | − | 0.658095i | \(-0.228637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.60050i | − | 0.646669i | −0.946285 | − | 0.323334i | \(-0.895196\pi\) | ||
0.946285 | − | 0.323334i | \(-0.104804\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.73102 | − | 3.29255i | −0.475410 | − | 0.573159i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.86986 | 0.964999 | 0.482499 | − | 0.875896i | \(-0.339729\pi\) | ||||
0.482499 | + | 0.875896i | \(0.339729\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.25737 | − | 2.72151i | −0.361468 | − | 0.435790i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.33255 | 0.832804 | 0.416402 | − | 0.909181i | \(-0.363291\pi\) | ||||
0.416402 | + | 0.909181i | \(0.363291\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.19692 | −1.40252 | −0.701258 | − | 0.712907i | \(-0.747378\pi\) | ||||
−0.701258 | + | 0.712907i | \(0.747378\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0805917 | − | 0.428503i | 0.0120139 | − | 0.0638774i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.30380 | 1.35710 | 0.678549 | − | 0.734555i | \(-0.262609\pi\) | ||||
0.678549 | + | 0.734555i | \(0.262609\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.34211 | − | 1.94267i | 0.327960 | − | 0.272029i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 5.19128i | − | 0.713077i | −0.934281 | − | 0.356539i | \(-0.883957\pi\) | ||
0.934281 | − | 0.356539i | \(-0.116043\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.358953i | − | 0.0484013i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.70286 | − | 5.66982i | −0.622909 | − | 0.750985i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.2060 | 1.45889 | 0.729447 | − | 0.684037i | \(-0.239777\pi\) | ||||
0.729447 | + | 0.684037i | \(0.239777\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.38498i | 0.689476i | 0.938699 | + | 0.344738i | \(0.112032\pi\) | ||||
−0.938699 | + | 0.344738i | \(0.887968\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.296699i | − | 0.0368009i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.14835 | −0.628971 | −0.314485 | − | 0.949262i | \(-0.601832\pi\) | ||||
−0.314485 | + | 0.949262i | \(0.601832\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.52973 | + | 11.4891i | 1.14724 | + | 1.38313i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.79323i | 0.924886i | 0.886649 | + | 0.462443i | \(0.153027\pi\) | ||||
−0.886649 | + | 0.462443i | \(0.846973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.0496i | − | 1.52734i | −0.645604 | − | 0.763672i | \(-0.723394\pi\) | ||
0.645604 | − | 0.763672i | \(-0.276606\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.63753 | + | 5.50553i | −0.766435 | + | 0.635724i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.72151 | −0.643720 | −0.321860 | − | 0.946787i | \(-0.604308\pi\) | ||||
−0.321860 | + | 0.946787i | \(0.604308\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.38504 | − | 3.26973i | −0.931671 | − | 0.363304i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.9818 | −1.75423 | −0.877115 | − | 0.480280i | \(-0.840535\pi\) | ||||
−0.877115 | + | 0.480280i | \(0.840535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.255336 | 0.0276951 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.83764 | − | 9.44914i | −0.840283 | − | 1.01305i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.68504 | 0.920612 | 0.460306 | − | 0.887760i | \(-0.347740\pi\) | ||||
0.460306 | + | 0.887760i | \(0.347740\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.98135 | − | 4.79996i | −0.412847 | − | 0.497733i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.618123i | − | 0.0634181i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.65337i | 0.675547i | 0.941227 | + | 0.337774i | \(0.109674\pi\) | ||||
−0.941227 | + | 0.337774i | \(0.890326\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.28165 | − | 1.36951i | −0.731834 | − | 0.137641i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.1271 | 1.60471 | 0.802355 | − | 0.596847i | \(-0.203580\pi\) | ||||
0.802355 | + | 0.596847i | \(0.203580\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 0.170125i | − | 0.0167629i | −0.999965 | − | 0.00838147i | \(-0.997332\pi\) | ||
0.999965 | − | 0.00838147i | \(-0.00266794\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.97324i | 0.674129i | 0.941482 | + | 0.337064i | \(0.109434\pi\) | ||||
−0.941482 | + | 0.337064i | \(0.890566\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.35512 | 0.129797 | 0.0648984 | − | 0.997892i | \(-0.479328\pi\) | ||||
0.0648984 | + | 0.997892i | \(0.479328\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.82532 | − | 6.49076i | 0.742747 | − | 0.616076i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000i | 0.376288i | 0.982141 | + | 0.188144i | \(0.0602472\pi\) | ||||
−0.982141 | + | 0.188144i | \(0.939753\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.25255i | 0.116800i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.01877 | − | 1.13199i | −0.556435 | − | 0.104653i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.90022 | 0.445474 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.10902 | − | 5.89662i | 0.640999 | − | 0.531680i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.45032 | −0.129720 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.33399 | −0.650787 | −0.325393 | − | 0.945579i | \(-0.605497\pi\) | ||||
−0.325393 | + | 0.945579i | \(0.605497\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.2608 | + | 10.1697i | −1.07950 | + | 0.895396i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.09665 | −0.532667 | −0.266333 | − | 0.963881i | \(-0.585812\pi\) | ||||
−0.266333 | + | 0.963881i | \(0.585812\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.366389 | − | 0.660370i | −0.0315338 | − | 0.0568356i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.0724i | 1.71490i | 0.514566 | + | 0.857451i | \(0.327953\pi\) | ||||
−0.514566 | + | 0.857451i | \(0.672047\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 0.117694i | − | 0.00998266i | −0.999988 | − | 0.00499133i | \(-0.998411\pi\) | ||
0.999988 | − | 0.00499133i | \(-0.00158880\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.4032 | − | 10.2879i | 1.04454 | − | 0.866401i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.04187 | −0.421623 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.03014i | − | 0.0855489i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.95707i | 0.733792i | 0.930262 | + | 0.366896i | \(0.119579\pi\) | ||||
−0.930262 | + | 0.366896i | \(0.880421\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.74263 | −0.223192 | −0.111596 | − | 0.993754i | \(-0.535596\pi\) | ||||
−0.111596 | + | 0.993754i | \(0.535596\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.974184 | − | 5.17970i | 0.0787581 | − | 0.418754i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.523291i | − | 0.0420318i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.5450i | 1.08101i | 0.841342 | + | 0.540504i | \(0.181766\pi\) | ||||
−0.841342 | + | 0.540504i | \(0.818234\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.74040 | − | 6.92069i | −0.455244 | − | 0.548846i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.04857 | −0.317108 | −0.158554 | − | 0.987350i | \(-0.550683\pi\) | ||||
−0.158554 | + | 0.987350i | \(0.550683\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.396923 | − | 0.478534i | −0.0309004 | − | 0.0372538i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.70521 | 0.286717 | 0.143359 | − | 0.989671i | \(-0.454210\pi\) | ||||
0.143359 | + | 0.989671i | \(0.454210\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.83256 | 0.679428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.5391 | − | 2.35832i | −0.958890 | − | 0.180346i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.4740 | 1.70867 | 0.854333 | − | 0.519726i | \(-0.173966\pi\) | ||||
0.854333 | + | 0.519726i | \(0.173966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.9391 | − | 12.3913i | 1.12289 | − | 0.931389i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3.67858i | − | 0.274950i | −0.990505 | − | 0.137475i | \(-0.956101\pi\) | ||
0.990505 | − | 0.137475i | \(-0.0438986\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.01062i | − | 0.595425i | −0.954656 | − | 0.297712i | \(-0.903776\pi\) | ||
0.954656 | − | 0.297712i | \(-0.0962237\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.95459 | + | 7.17892i | 0.440176 | + | 0.530681i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.853117 | 0.0627224 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 4.33899i | − | 0.317298i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.12159i | − | 0.0811554i | −0.999176 | − | 0.0405777i | \(-0.987080\pi\) | ||
0.999176 | − | 0.0405777i | \(-0.0129198\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3684 | 1.32219 | 0.661094 | − | 0.750303i | \(-0.270092\pi\) | ||||
0.661094 | + | 0.750303i | \(0.270092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.328083 | − | 0.395540i | −0.0234945 | − | 0.0283252i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.296699i | − | 0.0211389i | −0.999944 | − | 0.0105695i | \(-0.996636\pi\) | ||
0.999944 | − | 0.0105695i | \(-0.00336442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.3518i | 1.93892i | 0.245251 | + | 0.969460i | \(0.421130\pi\) | ||||
−0.245251 | + | 0.969460i | \(0.578870\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.86346 | + | 5.69293i | −0.484111 | + | 0.401548i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.775025 | 0.0541301 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.4089 | + | 4.77884i | 1.76604 | + | 0.332152i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5039 | −0.726571 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.0295 | 1.44773 | 0.723864 | − | 0.689942i | \(-0.242364\pi\) | ||||
0.723864 | + | 0.689942i | \(0.242364\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.61758 | + | 10.3894i | 0.590467 | + | 0.711873i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.33667 | −0.0911599 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.4300 | − | 17.3970i | −0.975089 | − | 1.17558i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 3.58646i | − | 0.241252i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.89447i | − | 0.461688i | −0.972991 | − | 0.230844i | \(-0.925851\pi\) | ||
0.972991 | − | 0.230844i | \(-0.0741487\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.76084 | + | 14.6793i | −0.184056 | + | 0.978617i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.4147 | −0.890363 | −0.445182 | − | 0.895440i | \(-0.646861\pi\) | ||||
−0.445182 | + | 0.895440i | \(0.646861\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.36254i | − | 0.420448i | −0.977653 | − | 0.210224i | \(-0.932581\pi\) | ||
0.977653 | − | 0.210224i | \(-0.0674194\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.95707i | 0.324748i | 0.986729 | + | 0.162374i | \(0.0519152\pi\) | ||||
−0.986729 | + | 0.162374i | \(0.948085\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.35220 | 0.0882079 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.62755 | + | 6.32672i | −0.495463 | + | 0.410964i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.3756i | 1.12394i | 0.827159 | + | 0.561968i | \(0.189956\pi\) | ||||
−0.827159 | + | 0.561968i | \(0.810044\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.5060i | − | 0.934416i | −0.884147 | − | 0.467208i | \(-0.845260\pi\) | ||
0.884147 | − | 0.467208i | \(-0.154740\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7940 | + | 4.91299i | −0.949036 | + | 0.315168i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.68218 | −0.552434 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.3059 | + | 17.6723i | −1.35021 | + | 1.11994i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.49783 | −0.220781 | −0.110391 | − | 0.993888i | \(-0.535210\pi\) | ||||
−0.110391 | + | 0.993888i | \(0.535210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.2848 | 1.33816 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.340398 | − | 0.282345i | 0.0213166 | − | 0.0176811i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.9356 | −0.994036 | −0.497018 | − | 0.867740i | \(-0.665572\pi\) | ||||
−0.497018 | + | 0.867740i | \(0.665572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.8973 | − | 3.93031i | −1.29351 | − | 0.243280i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.3578i | 0.885342i | 0.896684 | + | 0.442671i | \(0.145969\pi\) | ||||
−0.896684 | + | 0.442671i | \(0.854031\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.754493i | − | 0.0463482i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.5784 | − | 9.60373i | 0.708584 | − | 0.587739i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.36422 | −0.449004 | −0.224502 | − | 0.974474i | \(-0.572076\pi\) | ||||
−0.224502 | + | 0.974474i | \(0.572076\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5327i | 0.761309i | 0.924717 | + | 0.380654i | \(0.124301\pi\) | ||||
−0.924717 | + | 0.380654i | \(0.875699\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.2967i | 0.741519i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.4817 | 1.95164 | 0.975819 | − | 0.218580i | \(-0.0701425\pi\) | ||||
0.975819 | + | 0.218580i | \(0.0701425\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.6154 | − | 1.99651i | −0.635526 | − | 0.119528i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1758i | 0.607037i | 0.952826 | + | 0.303518i | \(0.0981614\pi\) | ||||
−0.952826 | + | 0.303518i | \(0.901839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.37024i | 0.0814523i | 0.999170 | + | 0.0407261i | \(0.0129671\pi\) | ||||
−0.999170 | + | 0.0407261i | \(0.987033\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.683507 | − | 0.824043i | −0.0404874 | − | 0.0488121i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.9135 | −0.818442 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.35715 | + | 8.86986i | 0.431284 | + | 0.519960i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 16.9961 | 0.992923 | 0.496461 | − | 0.868059i | \(-0.334632\pi\) | ||||
0.496461 | + | 0.868059i | \(0.334632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.62866 | 0.0948243 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −11.2218 | + | 6.22614i | −0.651156 | + | 0.361277i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.5933 | 1.01745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 21.4997 | − | 17.8330i | 1.23513 | − | 1.02448i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.782645i | 0.0448141i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.9023i | 1.19296i | 0.802629 | + | 0.596479i | \(0.203434\pi\) | ||||
−0.802629 | + | 0.596479i | \(0.796566\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.188121 | − | 0.226800i | −0.0107018 | − | 0.0129022i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.4808 | 0.651017 | 0.325508 | − | 0.945539i | \(-0.394465\pi\) | ||||
0.325508 | + | 0.945539i | \(0.394465\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.89777i | 0.559455i | 0.960079 | + | 0.279728i | \(0.0902442\pi\) | ||||
−0.960079 | + | 0.279728i | \(0.909756\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.63430i | 0.372619i | 0.982491 | + | 0.186310i | \(0.0596527\pi\) | ||||
−0.982491 | + | 0.186310i | \(0.940347\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.5055 | −0.980120 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.71086 | + | 9.29629i | 0.430378 | + | 0.518868i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.47181i | − | 0.415742i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.1640i | 0.563799i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.80656 | − | 1.49846i | 0.0999029 | − | 0.0828650i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7307 | 0.809675 | 0.404837 | − | 0.914389i | \(-0.367328\pi\) | ||||
0.404837 | + | 0.914389i | \(0.367328\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.25489 | − | 17.3061i | 0.178367 | − | 0.948371i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.748254 | −0.0408815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.7209 | −1.67347 | −0.836737 | − | 0.547605i | \(-0.815540\pi\) | ||||
−0.836737 | + | 0.547605i | \(0.815540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.42311 | + | 5.33255i | 0.240230 | + | 0.289624i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.89242 | −0.481551 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.38504 | + | 1.66982i | 0.0745679 | + | 0.0898998i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.7575i | 0.899590i | 0.893132 | + | 0.449795i | \(0.148503\pi\) | ||||
−0.893132 | + | 0.449795i | \(0.851497\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.12385i | 0.167216i | 0.996499 | + | 0.0836080i | \(0.0266443\pi\) | ||||
−0.996499 | + | 0.0836080i | \(0.973356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.27558 | + | 5.14632i | −0.495094 | + | 0.274690i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.4901 | −1.88895 | −0.944473 | − | 0.328590i | \(-0.893426\pi\) | ||||
−0.944473 | + | 0.328590i | \(0.893426\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.13266i | 0.0601152i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 6.26791i | − | 0.330807i | −0.986226 | − | 0.165404i | \(-0.947107\pi\) | ||
0.986226 | − | 0.165404i | \(-0.0528927\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.912103 | 0.0480054 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.53266 | − | 5.41855i | 0.342876 | − | 0.284400i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.89662i | − | 0.0992734i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.8381i | 0.878944i | 0.898256 | + | 0.439472i | \(0.144834\pi\) | ||||
−0.898256 | + | 0.439472i | \(0.855166\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.95695 | − | 15.7220i | 0.153933 | − | 0.818454i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.23421 | −0.0639051 | −0.0319526 | − | 0.999489i | \(-0.510173\pi\) | ||||
−0.0319526 | + | 0.999489i | \(0.510173\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.93347 | + | 1.60373i | −0.0998439 | + | 0.0828161i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.4695 | −0.745215 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.3895 | −0.739141 | −0.369571 | − | 0.929203i | \(-0.620495\pi\) | ||||
−0.369571 | + | 0.929203i | \(0.620495\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.77722 | + | 8.10977i | −0.500902 | + | 0.415476i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.91684 | 0.506727 | 0.253364 | − | 0.967371i | \(-0.418463\pi\) | ||||
0.253364 | + | 0.967371i | \(0.418463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.09978 | + | 27.1153i | −0.259236 | + | 1.37835i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 13.2861i | − | 0.673633i | −0.941570 | − | 0.336816i | \(-0.890650\pi\) | ||
0.941570 | − | 0.336816i | \(-0.109350\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.1406i | 0.765695i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.12767 | + | 6.74154i | −0.409987 | + | 0.340066i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.831556 | −0.0418401 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.2961i | 1.21939i | 0.792638 | + | 0.609693i | \(0.208707\pi\) | ||||
−0.792638 | + | 0.609693i | \(0.791293\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.3327i | − | 0.715741i | −0.933771 | − | 0.357870i | \(-0.883503\pi\) | ||
0.933771 | − | 0.357870i | \(-0.116497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.35017 | −0.366138 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.21867 | − | 0.475218i | −0.0605562 | − | 0.0236138i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 14.4972i | − | 0.718600i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.0059i | − | 0.989226i | −0.869113 | − | 0.494613i | \(-0.835310\pi\) | ||
0.869113 | − | 0.494613i | \(-0.164690\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22.1956 | + | 26.7593i | 1.09483 | + | 1.31994i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.32277 | −0.114020 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.130143 | − | 0.156902i | −0.00637314 | − | 0.00768353i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.7445 | 1.35541 | 0.677704 | − | 0.735335i | \(-0.262975\pi\) | ||||
0.677704 | + | 0.735335i | \(0.262975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.53586 | −0.0748533 | −0.0374267 | − | 0.999299i | \(-0.511916\pi\) | ||||
−0.0374267 | + | 0.999299i | \(0.511916\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.15905 | − | 27.4305i | 0.250842 | − | 1.33371i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −8.74708 | −0.424296 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.72151 | + | 5.57519i | −0.324517 | + | 0.269173i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 17.1216i | − | 0.824718i | −0.911021 | − | 0.412359i | \(-0.864705\pi\) | ||
0.911021 | − | 0.412359i | \(-0.135295\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 27.5219i | − | 1.32262i | −0.750113 | − | 0.661310i | \(-0.770001\pi\) | ||
0.750113 | − | 0.661310i | \(-0.229999\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.13911 | − | 1.37332i | −0.0546162 | − | 0.0658459i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.6528 | 1.75334 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 21.9303i | − | 1.04667i | −0.852126 | − | 0.523337i | \(-0.824687\pi\) | ||
0.852126 | − | 0.523337i | \(-0.175313\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 20.5062i | − | 0.974278i | −0.873324 | − | 0.487139i | \(-0.838040\pi\) | ||
0.873324 | − | 0.487139i | \(-0.161960\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.26227 | 0.0598374 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.90453 | + | 11.9410i | 0.468468 | + | 0.564790i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.7692i | 0.885773i | 0.896578 | + | 0.442886i | \(0.146046\pi\) | ||||
−0.896578 | + | 0.442886i | \(0.853954\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13.1702i | − | 0.620160i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.65630 | + | 3.03274i | −0.171788 | + | 0.142491i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.59340 | 0.355204 | 0.177602 | − | 0.984102i | \(-0.443166\pi\) | ||||
0.177602 | + | 0.984102i | \(0.443166\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.42887 | − | 7.98248i | −0.206722 | − | 0.372590i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −29.2727 | −1.36337 | −0.681683 | − | 0.731648i | \(-0.738752\pi\) | ||||
−0.681683 | + | 0.731648i | \(0.738752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.8326 | 0.549906 | 0.274953 | − | 0.961458i | \(-0.411338\pi\) | ||||
0.274953 | + | 0.961458i | \(0.411338\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.578644 | − | 0.697619i | −0.0268340 | − | 0.0323513i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.16565 | −0.239038 | −0.119519 | − | 0.992832i | \(-0.538135\pi\) | ||||
−0.119519 | + | 0.992832i | \(0.538135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.9777 | + | 18.0573i | 0.690138 | + | 0.832038i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.7143i | 1.04440i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.1751i | 0.971580i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.3055 | − | 2.87862i | −0.700790 | − | 0.131803i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.7099 | 0.900569 | 0.450284 | − | 0.892885i | \(-0.351323\pi\) | ||||
0.450284 | + | 0.892885i | \(0.351323\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 11.9829i | − | 0.546373i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.966991i | 0.0439088i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.00720 | −0.226898 | −0.113449 | − | 0.993544i | \(-0.536190\pi\) | ||||
−0.113449 | + | 0.993544i | \(0.536190\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.39730 | + | 4.47682i | −0.244074 | + | 0.202449i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.55902i | 0.160616i | 0.996770 | + | 0.0803081i | \(0.0255904\pi\) | ||||
−0.996770 | + | 0.0803081i | \(0.974410\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 12.4523i | − | 0.560823i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.05830 | − | 0.199043i | −0.0475673 | − | 0.00894633i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.809404 | −0.0362339 | −0.0181170 | − | 0.999836i | \(-0.505767\pi\) | ||||
−0.0181170 | + | 0.999836i | \(0.505767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.93955 | − | 4.09713i | 0.220683 | − | 0.183046i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.47070 | −0.422278 | −0.211139 | − | 0.977456i | \(-0.567717\pi\) | ||||
−0.211139 | + | 0.977456i | \(0.567717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.34390 | 0.104302 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.7750 | − | 9.76685i | 0.522947 | − | 0.433761i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.4881 | −0.464876 | −0.232438 | − | 0.972611i | \(-0.574670\pi\) | ||||
−0.232438 | + | 0.972611i | \(0.574670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −19.3241 | + | 10.7215i | −0.853182 | + | 0.473366i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 0.0247258i | − | 0.00108955i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 22.9783i | − | 1.01058i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.9609 | − | 24.8512i | 1.31514 | − | 1.09085i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.55707 | −0.418703 | −0.209351 | − | 0.977840i | \(-0.567135\pi\) | ||||
−0.209351 | + | 0.977840i | \(0.567135\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 27.7480i | − | 1.21334i | −0.794955 | − | 0.606668i | \(-0.792506\pi\) | ||
0.794955 | − | 0.606668i | \(-0.207494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 6.32549i | − | 0.275543i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −51.2720 | −2.22922 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.21383 | − | 33.0387i | 0.269657 | − | 1.43376i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 10.8860i | − | 0.471526i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.01348i | 0.0438166i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.06769 | − | 4.90405i | −0.175534 | − | 0.211625i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.15555 | −0.0496812 | −0.0248406 | − | 0.999691i | \(-0.507908\pi\) | ||||
−0.0248406 | + | 0.999691i | \(0.507908\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.85797 | − | 10.6793i | −0.380132 | − | 0.458291i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.196951 | 0.00843645 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.1394 | 0.690070 | 0.345035 | − | 0.938590i | \(-0.387867\pi\) | ||||
0.345035 | + | 0.938590i | \(0.387867\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.8766 | + | 2.98603i | 0.677596 | + | 0.127440i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −30.1447 | −1.28421 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.13732 | − | 0.943358i | 0.0482766 | − | 0.0400433i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 37.0744i | − | 1.57089i | −0.618929 | − | 0.785447i | \(-0.712433\pi\) | ||
0.618929 | − | 0.785447i | \(-0.287567\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.7749i | 0.794092i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.79796 | − | 5.78447i | −0.202570 | − | 0.244221i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.5917 | 0.657111 | 0.328556 | − | 0.944485i | \(-0.393438\pi\) | ||||
0.328556 | + | 0.944485i | \(0.393438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.581354i | 0.0244578i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 15.0429i | − | 0.630633i | −0.948987 | − | 0.315316i | \(-0.897889\pi\) | ||
0.948987 | − | 0.315316i | \(-0.102111\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.62668 | 0.235469 | 0.117735 | − | 0.993045i | \(-0.462437\pi\) | ||||
0.117735 | + | 0.993045i | \(0.462437\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.24023 | − | 1.49523i | −0.0518114 | − | 0.0624643i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 42.9086i | − | 1.78941i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22.2024i | − | 0.924297i | −0.886802 | − | 0.462149i | \(-0.847079\pi\) | ||
0.886802 | − | 0.462149i | \(-0.152921\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.4876 | − | 20.3114i | 1.01767 | − | 0.844113i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.8213 | −0.531004 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.874759 | − | 0.164522i | −0.0361668 | − | 0.00680216i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.9245 | 0.863648 | 0.431824 | − | 0.901958i | \(-0.357870\pi\) | ||||
0.431824 | + | 0.901958i | \(0.357870\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.3129 | −0.630956 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.328083 | − | 0.395540i | −0.0134955 | − | 0.0162703i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.1690 | 0.869307 | 0.434654 | − | 0.900598i | \(-0.356871\pi\) | ||||
0.434654 | + | 0.900598i | \(0.356871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 30.2450 | + | 36.4637i | 1.23785 | + | 1.49236i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.29601i | 0.216389i | 0.994130 | + | 0.108195i | \(0.0345070\pi\) | ||||
−0.994130 | + | 0.108195i | \(0.965493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 37.5346i | − | 1.53107i | −0.643396 | − | 0.765533i | \(-0.722475\pi\) | ||
0.643396 | − | 0.765533i | \(-0.277525\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.85481 | + | 15.1789i | −0.116257 | + | 0.618133i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.712191 | 0.0289547 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.5050i | 1.60346i | 0.597687 | + | 0.801729i | \(0.296086\pi\) | ||||
−0.597687 | + | 0.801729i | \(0.703914\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 18.9931i | − | 0.768377i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.3947 | 0.581397 | 0.290699 | − | 0.956815i | \(-0.406112\pi\) | ||||
0.290699 | + | 0.956815i | \(0.406112\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.03321 | − | 0.857006i | 0.0416632 | − | 0.0345578i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.1573i | 0.489435i | 0.969594 | + | 0.244718i | \(0.0786952\pi\) | ||||
−0.969594 | + | 0.244718i | \(0.921305\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.4835i | 0.783107i | 0.920155 | + | 0.391553i | \(0.128062\pi\) | ||||
−0.920155 | + | 0.391553i | \(0.871938\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.1579 | − | 21.7257i | 1.57135 | − | 0.871824i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.6836 | 0.987344 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.0032 | + | 11.6150i | −0.559232 | + | 0.463858i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.3124 | 0.411182 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.3846 | −1.24940 | −0.624701 | − | 0.780864i | \(-0.714779\pi\) | ||||
−0.624701 | + | 0.780864i | \(0.714779\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.0352 | − | 23.2539i | 1.11430 | − | 0.924261i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.06591 | −0.0422994 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 22.9768 | + | 4.32142i | 0.908950 | + | 0.170953i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 41.5828i | − | 1.64242i | −0.570624 | − | 0.821211i | \(-0.693299\pi\) | ||
0.570624 | − | 0.821211i | \(-0.306701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 13.5290i | − | 0.533531i | −0.963761 | − | 0.266766i | \(-0.914045\pi\) | ||
0.963761 | − | 0.266766i | \(-0.0859549\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.78196 | + | 1.47806i | −0.0701646 | + | 0.0581984i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.0884 | −1.18290 | −0.591449 | − | 0.806343i | \(-0.701444\pi\) | ||||
−0.591449 | + | 0.806343i | \(0.701444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 27.6762i | − | 1.08639i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.2138i | 0.830161i | 0.909785 | + | 0.415081i | \(0.136247\pi\) | ||||
−0.909785 | + | 0.415081i | \(0.863753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.886078 | −0.0346219 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −38.4743 | − | 7.23615i | −1.50103 | − | 0.282309i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.67926i | − | 0.104369i | −0.998637 | − | 0.0521846i | \(-0.983382\pi\) | ||
0.998637 | − | 0.0521846i | \(-0.0166184\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 5.54008i | − | 0.215484i | −0.994179 | − | 0.107742i | \(-0.965638\pi\) | ||
0.994179 | − | 0.107742i | \(-0.0343621\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.96583 | − | 4.78125i | −0.154020 | − | 0.185688i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 61.0844 | 2.36520 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.62376 | − | 9.19128i | −0.294752 | − | 0.355355i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.2997 | 0.513429 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1946 | −0.662804 | −0.331402 | − | 0.943490i | \(-0.607522\pi\) | ||||
−0.331402 | + | 0.943490i | \(0.607522\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 12.5514 | + | 22.6223i | 0.483105 | + | 0.870734i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.4664 | −0.555988 | −0.277994 | − | 0.960583i | \(-0.589670\pi\) | ||||
−0.277994 | + | 0.960583i | \(0.589670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.8836 | + | 14.8337i | −0.685301 | + | 0.568427i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 32.4882i | − | 1.24313i | −0.783363 | − | 0.621564i | \(-0.786498\pi\) | ||
0.783363 | − | 0.621564i | \(-0.213502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.91730i | 0.111464i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.03555 | − | 8.48214i | −0.268423 | − | 0.323614i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.5976 | −0.403738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.4426i | − | 1.23417i | −0.786895 | − | 0.617087i | \(-0.788312\pi\) | ||
0.786895 | − | 0.617087i | \(-0.211688\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.0171055i | − | 0.000648847i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.36842 | 0.354854 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.48142 | + | 6.60845i | 0.207326 | + | 0.249955i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30.3777i | − | 1.14735i | −0.819084 | − | 0.573674i | \(-0.805518\pi\) | ||
0.819084 | − | 0.573674i | \(-0.194482\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 24.9644i | − | 0.941551i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.80267 | − | 1.49523i | 0.0678925 | − | 0.0563138i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.5139 | −1.22108 | −0.610542 | − | 0.791984i | \(-0.709048\pi\) | ||||
−0.610542 | + | 0.791984i | \(0.709048\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.17263 | + | 16.8688i | −0.118983 | + | 0.632628i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.0295 | 1.16207 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.732778 | −0.0274044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.2136 | + | 23.1641i | 0.717545 | + | 0.865079i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.5973 | 0.395214 | 0.197607 | − | 0.980281i | \(-0.436683\pi\) | ||||
0.197607 | + | 0.980281i | \(0.436683\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.0405 | − | 19.3385i | −0.596551 | − | 0.719208i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35.2898i | 1.31063i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 31.3600i | − | 1.16308i | −0.813518 | − | 0.581540i | \(-0.802451\pi\) | ||
0.813518 | − | 0.581540i | \(-0.197549\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.2898 | + | 22.9086i | −0.529251 | + | 0.848466i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −16.1575 | −0.597606 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 3.61634i | − | 0.133573i | −0.997767 | − | 0.0667863i | \(-0.978725\pi\) | ||
0.997767 | − | 0.0667863i | \(-0.0212746\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.7153i | 0.468373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −38.6926 | −1.42333 | −0.711665 | − | 0.702519i | \(-0.752058\pi\) | ||||
−0.711665 | + | 0.702519i | \(0.752058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.5745 | + | 9.60056i | −0.425201 | + | 0.352685i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 45.1194i | − | 1.65527i | −0.561266 | − | 0.827635i | \(-0.689686\pi\) | ||
0.561266 | − | 0.827635i | \(-0.310314\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.30181i | 0.0476945i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.86207 | + | 47.1193i | −0.324246 | + | 1.72400i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.5683 | −0.860018 | −0.430009 | − | 0.902825i | \(-0.641490\pi\) | ||||
−0.430009 | + | 0.902825i | \(0.641490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.66309 | + | 3.86782i | −0.169932 | + | 0.140951i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.398610 | −0.0145069 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.2967 | 0.955770 | 0.477885 | − | 0.878422i | \(-0.341404\pi\) | ||||
0.477885 | + | 0.878422i | \(0.341404\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.3756 | − | 23.5363i | 1.02997 | − | 0.854313i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.9560 | −0.940903 | −0.470452 | − | 0.882426i | \(-0.655909\pi\) | ||||
−0.470452 | + | 0.882426i | \(0.655909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.141586 | − | 0.752810i | 0.00511907 | − | 0.0272179i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 22.8762i | − | 0.826013i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.9215i | 1.33142i | 0.746209 | + | 0.665712i | \(0.231872\pi\) | ||||
−0.746209 | + | 0.665712i | \(0.768128\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −21.2444 | + | 17.6212i | −0.765097 | + | 0.634614i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.5857 | −0.416708 | −0.208354 | − | 0.978054i | \(-0.566811\pi\) | ||||
−0.208354 | + | 0.978054i | \(0.566811\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.9264i | 0.643937i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 22.6793i | − | 0.812569i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.2475 | 0.688730 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32.2050 | + | 17.8681i | −1.15091 | + | 0.638555i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.96861i | 0.0702627i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.9244i | − | 1.06669i | −0.845898 | − | 0.533344i | \(-0.820935\pi\) | ||
0.845898 | − | 0.533344i | \(-0.179065\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.8766 | + | 19.1410i | 0.565221 | + | 0.681436i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.9931 | 0.390375 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.834302 | − | 1.00584i | −0.0295896 | − | 0.0356736i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.2866 | 0.718587 | 0.359293 | − | 0.933225i | \(-0.383018\pi\) | ||||
0.359293 | + | 0.933225i | \(0.383018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3453 | 0.578254 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.81594 | − | 25.6062i | 0.170163 | − | 0.904750i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −32.2297 | −1.13736 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.81751 | + | 8.14319i | −0.345593 | + | 0.286654i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.49001i | 0.0875442i | 0.999042 | + | 0.0437721i | \(0.0139375\pi\) | ||||
−0.999042 | + | 0.0437721i | \(0.986062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.9838i | 0.561269i | 0.959815 | + | 0.280634i | \(0.0905448\pi\) | ||||
−0.959815 | + | 0.280634i | \(0.909455\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.8584 | + | 16.7078i | 0.486036 | + | 0.585970i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.588413 | −0.0206112 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 39.1144i | 1.36844i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.75927i | 0.0962991i | 0.998840 | + | 0.0481495i | \(0.0153324\pi\) | ||||
−0.998840 | + | 0.0481495i | \(0.984668\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.4424 | −0.991440 | −0.495720 | − | 0.868482i | \(-0.665096\pi\) | ||||
−0.495720 | + | 0.868482i | \(0.665096\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.5974 | + | 16.3932i | 0.473401 | + | 0.570738i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.6070i | 1.06431i | 0.846647 | + | 0.532154i | \(0.178617\pi\) | ||||
−0.846647 | + | 0.532154i | \(0.821383\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 10.0620i | − | 0.349469i | −0.984616 | − | 0.174734i | \(-0.944093\pi\) | ||
0.984616 | − | 0.174734i | \(-0.0559067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.3026 | − | 35.9176i | 1.50215 | − | 1.24597i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.538509 | 0.0186359 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.3595 | + | 9.07663i | −0.565465 | + | 0.313734i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.3067 | 0.459400 | 0.229700 | − | 0.973262i | \(-0.426226\pi\) | ||||
0.229700 | + | 0.973262i | \(0.426226\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.2383 | −0.732354 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.2522 | + | 13.5657i | 0.387545 | + | 0.467229i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.28371 | 0.0441610 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.51518 | + | 1.82672i | 0.0520009 | + | 0.0626928i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.5871i | 1.73411i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.4736i | 1.45427i | 0.686495 | + | 0.727134i | \(0.259148\pi\) | ||||
−0.686495 | + | 0.727134i | \(0.740852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.82242 | − | 0.342755i | −0.0623253 | − | 0.0117220i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.55707 | −0.326463 | −0.163232 | − | 0.986588i | \(-0.552192\pi\) | ||||
−0.163232 | + | 0.986588i | \(0.552192\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.11241i | − | 0.0720745i | −0.999350 | − | 0.0360372i | \(-0.988527\pi\) | ||
0.999350 | − | 0.0360372i | \(-0.0114735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 35.2974i | − | 1.20154i | −0.799423 | − | 0.600768i | \(-0.794861\pi\) | ||
0.799423 | − | 0.600768i | \(-0.205139\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.26634 | 0.111059 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.5486 | + | 15.3853i | −0.629945 | + | 0.522511i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.1308i | 0.479356i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5100i | 0.356118i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.6162 | + | 3.68936i | 0.663907 | + | 0.124866i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.7377 | −0.565193 | −0.282596 | − | 0.959239i | \(-0.591196\pi\) | ||||
−0.282596 | + | 0.959239i | \(0.591196\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.6581 | − | 18.7939i | 0.764240 | − | 0.633903i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.6152 | −1.43574 | −0.717871 | − | 0.696176i | \(-0.754883\pi\) | ||||
−0.717871 | + | 0.696176i | \(0.754883\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.2392 | −0.512839 | −0.256419 | − | 0.966566i | \(-0.582543\pi\) | ||||
−0.256419 | + | 0.966566i | \(0.582543\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.17123 | − | 1.80094i | 0.0729850 | − | 0.0605378i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −56.1267 | −1.88455 | −0.942275 | − | 0.334841i | \(-0.891317\pi\) | ||||
−0.942275 | + | 0.334841i | \(0.891317\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.07550 | + | 20.7091i | −0.270539 | + | 0.693782i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 39.5689i | − | 1.32412i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 0.534639i | − | 0.0178710i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.4543 | − | 19.4543i | 0.783116 | − | 0.649560i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −25.5200 | −0.851138 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 9.12024i | − | 0.303839i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.16425i | − | 0.0387011i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40.7249 | 1.35225 | 0.676124 | − | 0.736788i | \(-0.263658\pi\) | ||||
0.676124 | + | 0.736788i | \(0.263658\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.94266 | − | 47.5478i | 0.296609 | − | 1.57706i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.0308i | 1.02810i | 0.857761 | + | 0.514049i | \(0.171855\pi\) | ||||
−0.857761 | + | 0.514049i | \(0.828145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.4714i | 1.30631i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.865432 | + | 1.04337i | 0.0286103 | + | 0.0344929i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.2356 | −1.69011 | −0.845053 | − | 0.534683i | \(-0.820431\pi\) | ||||
−0.845053 | + | 0.534683i | \(0.820431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.1133 | + | 27.8656i | 0.761609 | + | 0.918204i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.9093 | 0.523662 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −29.2253 | −0.960922 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.501582 | − | 0.0943362i | −0.0164741 | − | 0.00309841i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.74232 | 0.122781 | 0.0613907 | − | 0.998114i | \(-0.480446\pi\) | ||||
0.0613907 | + | 0.998114i | \(0.480446\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.3055 | − | 12.6952i | 0.501079 | − | 0.415623i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.630623i | − | 0.0206236i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.23951i | 0.105830i | 0.998599 | + | 0.0529150i | \(0.0168512\pi\) | ||||
−0.998599 | + | 0.0529150i | \(0.983149\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.9447 | + | 13.1951i | 0.357168 | + | 0.430606i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.0683 | 0.719407 | 0.359703 | − | 0.933067i | \(-0.382878\pi\) | ||||
0.359703 | + | 0.933067i | \(0.382878\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.9566i | 1.49655i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36.2595i | 1.17827i | 0.808033 | + | 0.589137i | \(0.200532\pi\) | ||||
−0.808033 | + | 0.589137i | \(0.799468\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.6399 | −0.864769 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.33606 | + | 8.84443i | 0.237888 | + | 0.286800i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.4656i | − | 0.436192i | −0.975927 | − | 0.218096i | \(-0.930015\pi\) | ||
0.975927 | − | 0.218096i | \(-0.0699846\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 0.163010i | − | 0.00527489i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −23.3372 | + | 19.3572i | −0.754386 | + | 0.625729i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0364 | 0.581820 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.5593 | + | 3.86673i | 0.662513 | + | 0.124604i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.66964 | 0.0859388 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.25940 | −0.297762 | −0.148881 | − | 0.988855i | \(-0.547567\pi\) | ||||
−0.148881 | + | 0.988855i | \(0.547567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.26216 | − | 9.96094i | −0.265419 | − | 0.319992i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 39.9290 | 1.28138 | 0.640691 | − | 0.767798i | \(-0.278648\pi\) | ||||
0.640691 | + | 0.767798i | \(0.278648\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.2392 | + | 13.5501i | 0.359941 | + | 0.433949i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 60.5408i | 1.93687i | 0.249261 | + | 0.968436i | \(0.419812\pi\) | ||||
−0.249261 | + | 0.968436i | \(0.580188\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 21.4501i | − | 0.685548i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.751427 | − | 3.99531i | 0.0239912 | − | 0.127560i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.4054 | −1.25684 | −0.628419 | − | 0.777875i | \(-0.716298\pi\) | ||||
−0.628419 | + | 0.777875i | \(0.716298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 0.0431217i | − | 0.00137397i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 79.2602i | − | 2.52033i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.1015 | 0.956205 | 0.478102 | − | 0.878304i | \(-0.341325\pi\) | ||||
0.478102 | + | 0.878304i | \(0.341325\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.6381 | − | 16.2889i | 0.623196 | − | 0.516914i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.97527i | 0.126025i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.04907i | 0.223246i | 0.993751 | + | 0.111623i | \(0.0356049\pi\) | ||||
−0.993751 | + | 0.111623i | \(0.964395\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −14.7975 | − | 26.6707i | −0.468173 | − | 0.843822i |
(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 | 1176.2.k.a.881.13 | 16 | ||
3.2 | odd | 2 | inner | 1176.2.k.a.881.3 | 16 | ||
4.3 | odd | 2 | 2352.2.k.i.881.4 | 16 | |||
7.2 | even | 3 | 168.2.u.a.17.5 | ✓ | 16 | ||
7.3 | odd | 6 | 168.2.u.a.89.7 | yes | 16 | ||
7.4 | even | 3 | 1176.2.u.b.1097.2 | 16 | |||
7.5 | odd | 6 | 1176.2.u.b.521.4 | 16 | |||
7.6 | odd | 2 | inner | 1176.2.k.a.881.4 | 16 | ||
12.11 | even | 2 | 2352.2.k.i.881.14 | 16 | |||
21.2 | odd | 6 | 168.2.u.a.17.7 | yes | 16 | ||
21.5 | even | 6 | 1176.2.u.b.521.2 | 16 | |||
21.11 | odd | 6 | 1176.2.u.b.1097.4 | 16 | |||
21.17 | even | 6 | 168.2.u.a.89.5 | yes | 16 | ||
21.20 | even | 2 | inner | 1176.2.k.a.881.14 | 16 | ||
28.3 | even | 6 | 336.2.bc.f.257.2 | 16 | |||
28.23 | odd | 6 | 336.2.bc.f.17.4 | 16 | |||
28.27 | even | 2 | 2352.2.k.i.881.13 | 16 | |||
84.23 | even | 6 | 336.2.bc.f.17.2 | 16 | |||
84.59 | odd | 6 | 336.2.bc.f.257.4 | 16 | |||
84.83 | odd | 2 | 2352.2.k.i.881.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.u.a.17.5 | ✓ | 16 | 7.2 | even | 3 | ||
168.2.u.a.17.7 | yes | 16 | 21.2 | odd | 6 | ||
168.2.u.a.89.5 | yes | 16 | 21.17 | even | 6 | ||
168.2.u.a.89.7 | yes | 16 | 7.3 | odd | 6 | ||
336.2.bc.f.17.2 | 16 | 84.23 | even | 6 | |||
336.2.bc.f.17.4 | 16 | 28.23 | odd | 6 | |||
336.2.bc.f.257.2 | 16 | 28.3 | even | 6 | |||
336.2.bc.f.257.4 | 16 | 84.59 | odd | 6 | |||
1176.2.k.a.881.3 | 16 | 3.2 | odd | 2 | inner | ||
1176.2.k.a.881.4 | 16 | 7.6 | odd | 2 | inner | ||
1176.2.k.a.881.13 | 16 | 1.1 | even | 1 | trivial | ||
1176.2.k.a.881.14 | 16 | 21.20 | even | 2 | inner | ||
1176.2.u.b.521.2 | 16 | 21.5 | even | 6 | |||
1176.2.u.b.521.4 | 16 | 7.5 | odd | 6 | |||
1176.2.u.b.1097.2 | 16 | 7.4 | even | 3 | |||
1176.2.u.b.1097.4 | 16 | 21.11 | odd | 6 | |||
2352.2.k.i.881.3 | 16 | 84.83 | odd | 2 | |||
2352.2.k.i.881.4 | 16 | 4.3 | odd | 2 | |||
2352.2.k.i.881.13 | 16 | 28.27 | even | 2 | |||
2352.2.k.i.881.14 | 16 | 12.11 | even | 2 |