Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1840,4,Mod(1,1840)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1840, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1840.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1840 = 2^{4} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1840.a (trivial) |
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: | yes |
Analytic conductor: | \(108.563514411\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 123x^{6} + 335x^{5} + 4492x^{4} - 7035x^{3} - 45582x^{2} + 36684x + 124632 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(7.24150\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1840.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −5.24150 | −1.00873 | −0.504363 | − | 0.863491i | \(-0.668273\pi\) | ||||
−0.504363 | + | 0.863491i | \(0.668273\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.79432 | 0.204874 | 0.102437 | − | 0.994740i | \(-0.467336\pi\) | ||||
0.102437 | + | 0.994740i | \(0.467336\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.473311 | 0.0175300 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 43.1812 | 1.18360 | 0.591801 | − | 0.806084i | \(-0.298417\pi\) | ||||
0.591801 | + | 0.806084i | \(0.298417\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.2585 | 0.816232 | 0.408116 | − | 0.912930i | \(-0.366186\pi\) | ||||
0.408116 | + | 0.912930i | \(0.366186\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −26.2075 | −0.451116 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −99.6414 | −1.42156 | −0.710782 | − | 0.703412i | \(-0.751659\pi\) | ||||
−0.710782 | + | 0.703412i | \(0.751659\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.85492 | −0.106919 | −0.0534594 | − | 0.998570i | \(-0.517025\pi\) | ||||
−0.0534594 | + | 0.998570i | \(0.517025\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −19.8879 | −0.206662 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 139.040 | 0.991044 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 128.800 | 0.824744 | 0.412372 | − | 0.911016i | \(-0.364700\pi\) | ||||
0.412372 | + | 0.911016i | \(0.364700\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 211.911 | 1.22775 | 0.613876 | − | 0.789402i | \(-0.289609\pi\) | ||||
0.613876 | + | 0.789402i | \(0.289609\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −226.334 | −1.19393 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 18.9716 | 0.0916223 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4971 | −0.0466408 | −0.0233204 | − | 0.999728i | \(-0.507424\pi\) | ||||
−0.0233204 | + | 0.999728i | \(0.507424\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −200.532 | −0.823355 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −196.234 | −0.747479 | −0.373739 | − | 0.927534i | \(-0.621925\pi\) | ||||
−0.373739 | + | 0.927534i | \(0.621925\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 232.370 | 0.824094 | 0.412047 | − | 0.911163i | \(-0.364814\pi\) | ||||
0.412047 | + | 0.911163i | \(0.364814\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.36655 | 0.00783967 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −16.0954 | −0.0499522 | −0.0249761 | − | 0.999688i | \(-0.507951\pi\) | ||||
−0.0249761 | + | 0.999688i | \(0.507951\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −328.603 | −0.958027 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 522.270 | 1.43397 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 187.180 | 0.485117 | 0.242558 | − | 0.970137i | \(-0.422013\pi\) | ||||
0.242558 | + | 0.970137i | \(0.422013\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 215.906 | 0.529323 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 46.4130 | 0.107852 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 111.377 | 0.245763 | 0.122882 | − | 0.992421i | \(-0.460786\pi\) | ||||
0.122882 | + | 0.992421i | \(0.460786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −239.851 | −0.503439 | −0.251720 | − | 0.967800i | \(-0.580996\pi\) | ||||
−0.251720 | + | 0.967800i | \(0.580996\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.79589 | 0.00359144 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 191.293 | 0.365030 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −266.333 | −0.485637 | −0.242819 | − | 0.970072i | \(-0.578072\pi\) | ||||
−0.242819 | + | 0.970072i | \(0.578072\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −120.554 | −0.210334 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 399.020 | 0.666971 | 0.333485 | − | 0.942755i | \(-0.391775\pi\) | ||||
0.333485 | + | 0.942755i | \(0.391775\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −454.380 | −0.728508 | −0.364254 | − | 0.931300i | \(-0.618676\pi\) | ||||
−0.364254 | + | 0.931300i | \(0.618676\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −131.037 | −0.201745 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 163.843 | 0.242489 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 348.030 | 0.495651 | 0.247825 | − | 0.968805i | \(-0.420284\pi\) | ||||
0.247825 | + | 0.968805i | \(0.420284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −741.555 | −1.01722 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −845.864 | −1.11862 | −0.559311 | − | 0.828958i | \(-0.688934\pi\) | ||||
−0.559311 | + | 0.828958i | \(0.688934\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −498.207 | −0.635743 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −675.106 | −0.831942 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 133.390 | 0.158869 | 0.0794343 | − | 0.996840i | \(-0.474689\pi\) | ||||
0.0794343 | + | 0.996840i | \(0.474689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 145.165 | 0.167224 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1110.73 | −1.23847 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −44.2746 | −0.0478155 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1036.04 | −1.08447 | −0.542237 | − | 0.840226i | \(-0.682423\pi\) | ||||
−0.542237 | + | 0.840226i | \(0.682423\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.4381 | 0.0207486 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 765.827 | 0.754482 | 0.377241 | − | 0.926115i | \(-0.376873\pi\) | ||||
0.377241 | + | 0.926115i | \(0.376873\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1248.97 | −1.19481 | −0.597403 | − | 0.801941i | \(-0.703801\pi\) | ||||
−0.597403 | + | 0.801941i | \(0.703801\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −99.4395 | −0.0924219 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −177.538 | −0.160404 | −0.0802022 | − | 0.996779i | \(-0.525557\pi\) | ||||
−0.0802022 | + | 0.996779i | \(0.525557\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −156.524 | −0.137544 | −0.0687718 | − | 0.997632i | \(-0.521908\pi\) | ||||
−0.0687718 | + | 0.997632i | \(0.521908\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 55.0205 | 0.0470478 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 827.065 | 0.688529 | 0.344264 | − | 0.938873i | \(-0.388128\pi\) | ||||
0.344264 | + | 0.938873i | \(0.388128\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.1082 | 0.0143086 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −378.071 | −0.291241 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 533.618 | 0.400915 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1028.56 | 0.754002 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1778.94 | 1.24295 | 0.621477 | − | 0.783432i | \(-0.286533\pi\) | ||||
0.621477 | + | 0.783432i | \(0.286533\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1217.97 | −0.831286 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1084.69 | 0.723432 | 0.361716 | − | 0.932288i | \(-0.382191\pi\) | ||||
0.361716 | + | 0.932288i | \(0.382191\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −33.5983 | −0.0219049 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 695.198 | 0.443208 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 789.160 | 0.492135 | 0.246067 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246067 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 929.231 | 0.567024 | 0.283512 | − | 0.958969i | \(-0.408500\pi\) | ||||
0.283512 | + | 0.958969i | \(0.408500\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 84.3639 | 0.0503881 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1652.05 | 0.966094 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 644.001 | 0.368837 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1722.37 | 0.966387 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 781.662 | 0.429773 | 0.214887 | − | 0.976639i | \(-0.431062\pi\) | ||||
0.214887 | + | 0.976639i | \(0.431062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 878.005 | 0.473186 | 0.236593 | − | 0.971609i | \(-0.423969\pi\) | ||||
0.236593 | + | 0.971609i | \(0.423969\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −47.1614 | −0.0249201 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1059.55 | 0.549068 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1975.87 | 1.00441 | 0.502203 | − | 0.864750i | \(-0.332523\pi\) | ||||
0.502203 | + | 0.864750i | \(0.332523\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −981.105 | −0.489350 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 87.2693 | 0.0427191 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1854.76 | 0.891263 | 0.445632 | − | 0.895216i | \(-0.352979\pi\) | ||||
0.445632 | + | 0.895216i | \(0.352979\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1131.67 | −0.533943 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1561.67 | −0.723626 | −0.361813 | − | 0.932251i | \(-0.617842\pi\) | ||||
−0.361813 | + | 0.932251i | \(0.617842\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −733.284 | −0.333766 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.19113 | −0.00187429 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1317.46 | −0.578985 | −0.289493 | − | 0.957180i | \(-0.593487\pi\) | ||||
−0.289493 | + | 0.957180i | \(0.593487\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 94.8579 | 0.0409748 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −583.782 | −0.247908 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1626.90 | −0.679332 | −0.339666 | − | 0.940546i | \(-0.610314\pi\) | ||||
−0.339666 | + | 0.940546i | \(0.610314\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2100.53 | 0.862601 | 0.431301 | − | 0.902208i | \(-0.358055\pi\) | ||||
0.431301 | + | 0.902208i | \(0.358055\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1257.18 | 0.507833 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −52.4854 | −0.0208584 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4302.64 | −1.68257 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 527.560 | 0.203039 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4536.80 | 1.71870 | 0.859350 | − | 0.511388i | \(-0.170869\pi\) | ||||
0.859350 | + | 0.511388i | \(0.170869\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 176.357 | 0.0657743 | 0.0328872 | − | 0.999459i | \(-0.489530\pi\) | ||||
0.0328872 | + | 0.999459i | \(0.489530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1002.66 | −0.368215 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −574.859 | −0.207904 | −0.103952 | − | 0.994582i | \(-0.533149\pi\) | ||||
−0.103952 | + | 0.994582i | \(0.533149\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 27.1335 | 0.00966554 | 0.00483277 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483277 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1395.98 | 0.489876 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 488.708 | 0.168968 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −981.171 | −0.334283 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.8861 | 0.00365526 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −382.366 | −0.126549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1527.16 | −0.498265 | −0.249133 | − | 0.968469i | \(-0.580145\pi\) | ||||
−0.249133 | + | 0.968469i | \(0.580145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2091.46 | −0.672792 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1161.85 | 0.368546 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 804.057 | 0.251534 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2381.63 | 0.734866 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3812.14 | −1.16033 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6000.58 | 1.80192 | 0.900962 | − | 0.433899i | \(-0.142862\pi\) | ||||
0.900962 | + | 0.433899i | \(0.142862\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.8328 | 0.00350601 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3263.02 | −0.954071 | −0.477036 | − | 0.878884i | \(-0.658289\pi\) | ||||
−0.477036 | + | 0.878884i | \(0.658289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5126.41 | 1.47931 | 0.739656 | − | 0.672985i | \(-0.234988\pi\) | ||||
0.739656 | + | 0.672985i | \(0.234988\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −858.784 | −0.244605 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2624.90 | 0.738039 | 0.369019 | − | 0.929422i | \(-0.379694\pi\) | ||||
0.369019 | + | 0.929422i | \(0.379694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −80.4769 | −0.0223393 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1824.20 | −0.499976 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6773.26 | 1.83316 | 0.916582 | − | 0.399847i | \(-0.130937\pi\) | ||||
0.916582 | + | 0.399847i | \(0.130937\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1440.79 | −0.385100 | −0.192550 | − | 0.981287i | \(-0.561676\pi\) | ||||
−0.192550 | + | 0.981287i | \(0.561676\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 132.792 | 0.0350560 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1643.02 | −0.428443 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −338.776 | −0.0872705 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4433.60 | 1.12838 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −285.672 | −0.0718384 | −0.0359192 | − | 0.999355i | \(-0.511436\pi\) | ||||
−0.0359192 | + | 0.999355i | \(0.511436\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 993.168 | 0.246798 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2611.35 | 0.641291 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1440.79 | −0.349704 | −0.174852 | − | 0.984595i | \(-0.555945\pi\) | ||||
−0.174852 | + | 0.984595i | \(0.555945\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39.8293 | −0.00955548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 60.9625 | 0.0144578 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6216.58 | 1.45753 | 0.728766 | − | 0.684763i | \(-0.240094\pi\) | ||||
0.728766 | + | 0.684763i | \(0.240094\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 935.902 | 0.216951 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −699.163 | −0.160255 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −598.663 | −0.135692 | −0.0678460 | − | 0.997696i | \(-0.521613\pi\) | ||||
−0.0678460 | + | 0.997696i | \(0.521613\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 434.654 | 0.0974292 | 0.0487146 | − | 0.998813i | \(-0.484488\pi\) | ||||
0.0487146 | + | 0.998813i | \(0.484488\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −760.882 | −0.168684 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1079.53 | 0.236721 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2336.84 | −0.506885 | −0.253443 | − | 0.967350i | \(-0.581563\pi\) | ||||
−0.253443 | + | 0.967350i | \(0.581563\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 100.300 | 0.0215225 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1472.16 | 0.312533 | 0.156266 | − | 0.987715i | \(-0.450054\pi\) | ||||
0.156266 | + | 0.987715i | \(0.450054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7135.91 | 1.49889 | 0.749445 | − | 0.662067i | \(-0.230321\pi\) | ||||
0.749445 | + | 0.662067i | \(0.230321\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 232.065 | 0.0482328 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −744.574 | −0.153139 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5015.41 | 1.02085 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5430.41 | 1.09394 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5562.87 | 1.10917 | 0.554584 | − | 0.832127i | \(-0.312877\pi\) | ||||
0.554584 | + | 0.832127i | \(0.312877\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 556.884 | 0.109909 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6003.90 | 1.17300 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 879.947 | 0.170196 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 881.684 | 0.168835 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4014.08 | −0.761066 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1199.26 | −0.225145 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4551.82 | −0.846209 | −0.423104 | − | 0.906081i | \(-0.639060\pi\) | ||||
−0.423104 | + | 0.906081i | \(0.639060\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6546.49 | 1.20523 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3828.02 | 0.697964 | 0.348982 | − | 0.937129i | \(-0.386527\pi\) | ||||
0.348982 | + | 0.937129i | \(0.386527\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6426.24 | 1.16049 | 0.580244 | − | 0.814443i | \(-0.302957\pi\) | ||||
0.580244 | + | 0.814443i | \(0.302957\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.97945 | 0.00160614 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2310.55 | −0.409381 | −0.204690 | − | 0.978827i | \(-0.565619\pi\) | ||||
−0.204690 | + | 0.978827i | \(0.565619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5561.75 | 0.976169 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 930.566 | 0.161804 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 882.317 | 0.151992 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 956.464 | 0.163246 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 820.419 | 0.138744 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −61.0709 | −0.0102339 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4299.86 | −0.714023 | −0.357011 | − | 0.934100i | \(-0.616204\pi\) | ||||
−0.357011 | + | 0.934100i | \(0.616204\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.96838 | −0.000817615 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1331.66 | −0.217184 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8495.93 | 1.37330 | 0.686651 | − | 0.726987i | \(-0.259080\pi\) | ||||
0.686651 | + | 0.726987i | \(0.259080\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4335.06 | −0.694538 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9150.57 | 1.45317 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2548.27 | −0.401148 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −602.772 | −0.0940643 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8208.05 | −1.26983 | −0.634916 | − | 0.772582i | \(-0.718965\pi\) | ||||
−0.634916 | + | 0.772582i | \(0.718965\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8246.78 | 1.26487 | 0.632435 | − | 0.774613i | \(-0.282055\pi\) | ||||
0.632435 | + | 0.774613i | \(0.282055\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5319.45 | 0.808921 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3257.88 | 0.491217 | 0.245609 | − | 0.969369i | \(-0.421012\pi\) | ||||
0.245609 | + | 0.969369i | \(0.421012\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1995.10 | 0.298278 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1981.66 | 0.293783 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5424.68 | 0.797503 | 0.398751 | − | 0.917059i | \(-0.369444\pi\) | ||||
0.398751 | + | 0.917059i | \(0.369444\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6780.59 | −0.988568 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2796.96 | −0.404414 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2271.90 | −0.325799 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2547.12 | 0.362286 | 0.181143 | − | 0.983457i | \(-0.442020\pi\) | ||||
0.181143 | + | 0.983457i | \(0.442020\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −92.8797 | −0.0131033 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 710.221 | 0.0993877 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5185.61 | 0.719840 | 0.359920 | − | 0.932983i | \(-0.382804\pi\) | ||||
0.359920 | + | 0.932983i | \(0.382804\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −655.187 | −0.0902233 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4927.70 | 0.673182 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5599.77 | 0.758947 | 0.379473 | − | 0.925203i | \(-0.376105\pi\) | ||||
0.379473 | + | 0.925203i | \(0.376105\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9324.30 | −1.25380 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3208.50 | 0.428059 | 0.214029 | − | 0.976827i | \(-0.431341\pi\) | ||||
0.214029 | + | 0.976827i | \(0.431341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 819.216 | 0.108444 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 109.983 | 0.0144464 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3324.79 | 0.433350 | 0.216675 | − | 0.976244i | \(-0.430479\pi\) | ||||
0.216675 | + | 0.976244i | \(0.430479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2291.75 | −0.296417 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5685.39 | −0.729745 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1740.15 | 0.221662 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1710.76 | −0.216273 | −0.108137 | − | 0.994136i | \(-0.534488\pi\) | ||||
−0.108137 | + | 0.994136i | \(0.534488\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 176.106 | 0.0220960 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14722.7 | 1.83346 | 0.916732 | − | 0.399504i | \(-0.130818\pi\) | ||||
0.916732 | + | 0.399504i | \(0.130818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8107.41 | 1.00213 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3707.78 | −0.454916 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −453.277 | −0.0552042 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6495.40 | −0.785273 | −0.392637 | − | 0.919694i | \(-0.628437\pi\) | ||||
−0.392637 | + | 0.919694i | \(0.628437\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4136.38 | −0.496430 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 422.599 | 0.0503505 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4229.32 | −0.500263 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4870.56 | −0.571972 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6975.87 | −0.813350 | −0.406675 | − | 0.913573i | \(-0.633312\pi\) | ||||
−0.406675 | + | 0.913573i | \(0.633312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14922.5 | 1.72751 | 0.863753 | − | 0.503916i | \(-0.168108\pi\) | ||||
0.863753 | + | 0.503916i | \(0.168108\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.61811 | −0.000875663 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2491.04 | −0.284313 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −910.071 | −0.103141 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8659.22 | −0.974525 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7438.59 | −0.831333 | −0.415666 | − | 0.909517i | \(-0.636452\pi\) | ||||
−0.415666 | + | 0.909517i | \(0.636452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7906.99 | −0.877566 | −0.438783 | − | 0.898593i | \(-0.644590\pi\) | ||||
−0.438783 | + | 0.898593i | \(0.644590\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3375.53 | −0.372056 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −203.663 | −0.0222941 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −144.770 | −0.0157392 | −0.00786960 | − | 0.999969i | \(-0.502505\pi\) | ||||
−0.00786960 | + | 0.999969i | \(0.502505\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −155.531 | −0.0167942 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8993.34 | −0.964529 | −0.482265 | − | 0.876026i | \(-0.660186\pi\) | ||||
−0.482265 | + | 0.876026i | \(0.660186\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 666.950 | 0.0710482 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4097.08 | −0.433524 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13599.3 | 1.42938 | 0.714688 | − | 0.699443i | \(-0.246569\pi\) | ||||
0.714688 | + | 0.699443i | \(0.246569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8473.63 | −0.884718 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4602.06 | −0.477315 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 725.825 | 0.0747851 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8002.87 | 0.819165 | 0.409583 | − | 0.912273i | \(-0.365674\pi\) | ||||
0.409583 | + | 0.912273i | \(0.365674\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13854.1 | −1.40883 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7419.08 | 0.749547 | 0.374773 | − | 0.927116i | \(-0.377720\pi\) | ||||
0.374773 | + | 0.927116i | \(0.377720\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7240.14 | −0.726734 | −0.363367 | − | 0.931646i | \(-0.618373\pi\) | ||||
−0.363367 | + | 0.931646i | \(0.618373\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5553.66 | −0.553859 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10057.2 | −0.996557 | −0.498278 | − | 0.867017i | \(-0.666034\pi\) | ||||
−0.498278 | + | 0.867017i | \(0.666034\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1010.55 | −0.0994944 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10356.5 | −1.01317 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10034.0 | 0.975400 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −221.373 | −0.0213838 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 88.5945 | 0.00850411 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1133.04 | 0.108079 | 0.0540394 | − | 0.998539i | \(-0.482790\pi\) | ||||
0.0540394 | + | 0.998539i | \(0.482790\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −401.603 | −0.0380697 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −457.422 | −0.0430919 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5180.20 | −0.484992 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7200.83 | 0.670022 | 0.335011 | − | 0.942214i | \(-0.391260\pi\) | ||||
0.335011 | + | 0.942214i | \(0.391260\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9721.71 | −0.899041 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6645.56 | −0.610815 | −0.305407 | − | 0.952222i | \(-0.598793\pi\) | ||||
−0.305407 | + | 0.952222i | \(0.598793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12833.8 | −1.17243 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 102.191 | 0.00927905 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1514.01 | 0.136645 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2027.12 | −0.181857 | −0.0909283 | − | 0.995857i | \(-0.528983\pi\) | ||||
−0.0909283 | + | 0.995857i | \(0.528983\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8185.49 | 0.729941 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7036.81 | −0.623769 | −0.311884 | − | 0.950120i | \(-0.600960\pi\) | ||||
−0.311884 | + | 0.950120i | \(0.600960\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3829.14 | 0.337415 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3843.51 | 0.336679 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13894.3 | 1.20993 | 0.604967 | − | 0.796251i | \(-0.293186\pi\) | ||||
0.604967 | + | 0.796251i | \(0.293186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1724.06 | −0.149252 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1231.18 | −0.105961 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6244.87 | −0.534333 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −695.018 | −0.0591235 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6905.46 | 0.584038 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3685.32 | 0.309898 | 0.154949 | − | 0.987922i | \(-0.450479\pi\) | ||||
0.154949 | + | 0.987922i | \(0.450479\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20979.8 | 1.75408 | 0.877040 | − | 0.480417i | \(-0.159515\pi\) | ||||
0.877040 | + | 0.480417i | \(0.159515\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −497.198 | −0.0413323 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21115.1 | −1.74533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 52.7159 | 0.00430824 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7507.63 | −0.610116 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −887.691 | −0.0717350 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8527.41 | 0.685260 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14189.5 | −1.13392 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18116.8 | 1.43974 | 0.719871 | − | 0.694108i | \(-0.244201\pi\) | ||||
0.719871 | + | 0.694108i | \(0.244201\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11009.9 | −0.870129 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −782.619 | −0.0615114 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9773.99 | −0.763996 | −0.381998 | − | 0.924163i | \(-0.624764\pi\) | ||||
−0.381998 | + | 0.924163i | \(0.624764\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −113.524 | −0.00882530 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1140.51 | −0.0881806 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1320.53 | 0.101546 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 275.102 | 0.0210404 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −22489.7 | −1.71081 | −0.855404 | − | 0.517962i | \(-0.826691\pi\) | ||||
−0.855404 | + | 0.517962i | \(0.826691\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8890.13 | 0.672652 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22552.3 | 1.69725 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21287.5 | 1.59354 | 0.796769 | − | 0.604284i | \(-0.206541\pi\) | ||||
0.796769 | + | 0.604284i | \(0.206541\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4135.33 | 0.307920 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2813.70 | −0.208402 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5816.13 | 0.428515 | 0.214257 | − | 0.976777i | \(-0.431267\pi\) | ||||
0.214257 | + | 0.976777i | \(0.431267\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5290.24 | 0.387723 | 0.193861 | − | 0.981029i | \(-0.437899\pi\) | ||||
0.193861 | + | 0.981029i | \(0.437899\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −23779.7 | −1.73370 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21661.1 | −1.56285 | −0.781425 | − | 0.624000i | \(-0.785507\pi\) | ||||
−0.781425 | + | 0.624000i | \(0.785507\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −924.374 | −0.0663483 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3209.48 | −0.229176 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8082.67 | 0.574186 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 90.5409 | 0.00639898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12966.0 | 0.911697 | 0.455848 | − | 0.890057i | \(-0.349336\pi\) | ||||
0.455848 | + | 0.890057i | \(0.349336\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1876.45 | −0.131270 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3013.12 | 0.209718 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19460.8 | −1.34766 | −0.673828 | − | 0.738888i | \(-0.735351\pi\) | ||||
−0.673828 | + | 0.738888i | \(0.735351\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1890.36 | −0.130247 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −142.220 | −0.00974989 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16995.9 | 1.15932 | 0.579662 | − | 0.814857i | \(-0.303184\pi\) | ||||
0.579662 | + | 0.814857i | \(0.303184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6785.41 | 0.460537 | 0.230268 | − | 0.973127i | \(-0.426040\pi\) | ||||
0.230268 | + | 0.973127i | \(0.426040\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −126.058 | −0.00851324 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2668.09 | 0.179295 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7731.28 | −0.516973 | −0.258487 | − | 0.966015i | \(-0.583224\pi\) | ||||
−0.258487 | + | 0.966015i | \(0.583224\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2561.56 | −0.170443 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −615.786 | −0.0407725 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29237.4 | −1.92640 | −0.963202 | − | 0.268778i | \(-0.913380\pi\) | ||||
−0.963202 | + | 0.268778i | \(0.913380\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5142.81 | 0.337200 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30318.2 | −1.97822 | −0.989111 | − | 0.147171i | \(-0.952983\pi\) | ||||
−0.989111 | + | 0.147171i | \(0.952983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3911.57 | −0.253989 | −0.126995 | − | 0.991903i | \(-0.540533\pi\) | ||||
−0.126995 | + | 0.991903i | \(0.540533\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3197.91 | 0.206647 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 506.124 | 0.0325480 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2004.17 | 0.127654 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1045.94 | 0.0663029 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4531.01 | −0.285859 | −0.142929 | − | 0.989733i | \(-0.545652\pi\) | ||||
−0.142929 | + | 0.989733i | \(0.545652\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8004.60 | 0.502613 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8894.69 | 0.555866 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12571.9 | −0.781972 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 188.860 | 0.0116920 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24798.0 | 1.52802 | 0.764011 | − | 0.645203i | \(-0.223227\pi\) | ||||
0.764011 | + | 0.645203i | \(0.223227\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9422.44 | 0.577893 | 0.288946 | − | 0.957345i | \(-0.406695\pi\) | ||||
0.288946 | + | 0.957345i | \(0.406695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6089.83 | −0.371762 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23562.6 | −1.43175 | −0.715876 | − | 0.698228i | \(-0.753972\pi\) | ||||
−0.715876 | + | 0.698228i | \(0.753972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4809.39 | 0.290886 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4214.46 | −0.253729 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5489.74 | −0.328990 | −0.164495 | − | 0.986378i | \(-0.552599\pi\) | ||||
−0.164495 | + | 0.986378i | \(0.552599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5423.44 | 0.323529 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −215.063 | −0.0127708 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19807.4 | −1.17084 | −0.585421 | − | 0.810729i | \(-0.699071\pi\) | ||||
−0.585421 | + | 0.810729i | \(0.699071\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26356.1 | −1.55089 | −0.775443 | − | 0.631418i | \(-0.782473\pi\) | ||||
−0.775443 | + | 0.631418i | \(0.782473\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19981.3 | 1.17045 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −167.992 | −0.00979615 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2962.40 | 0.171971 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −31452.1 | −1.81765 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10357.1 | −0.595872 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16057.4 | −0.919716 | −0.459858 | − | 0.887992i | \(-0.652100\pi\) | ||||
−0.459858 | + | 0.887992i | \(0.652100\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3475.99 | 0.198209 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2144.76 | −0.121758 | −0.0608788 | − | 0.998145i | \(-0.519390\pi\) | ||||
−0.0608788 | + | 0.998145i | \(0.519390\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3931.07 | −0.222180 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17103.1 | 0.962397 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15697.1 | 0.879401 | 0.439701 | − | 0.898144i | \(-0.355085\pi\) | ||||
0.439701 | + | 0.898144i | \(0.355085\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3945.80 | 0.220089 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26870.1 | −1.49222 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7161.25 | 0.395968 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21654.4 | 1.19215 | 0.596073 | − | 0.802930i | \(-0.296727\pi\) | ||||
0.596073 | + | 0.802930i | \(0.296727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 77.5487 | 0.00425084 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4646.15 | 0.253581 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19553.1 | 1.06259 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13758.4 | −0.744480 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2664.19 | −0.143545 | −0.0717726 | − | 0.997421i | \(-0.522866\pi\) | ||||
−0.0717726 | + | 0.997421i | \(0.522866\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 92.9508 | 0.00498678 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 421.819 | 0.0225342 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2905.79 | 0.154574 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24936.5 | −1.32089 | −0.660444 | − | 0.750875i | \(-0.729632\pi\) | ||||
−0.660444 | + | 0.750875i | \(0.729632\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 164.726 | 0.00868877 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4873.95 | 0.256004 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8260.25 | 0.432050 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −35502.1 | −1.84916 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9849.35 | 0.510874 | 0.255437 | − | 0.966826i | \(-0.417781\pi\) | ||||
0.255437 | + | 0.966826i | \(0.417781\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4739.00 | −0.244784 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7551.87 | 0.388461 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3220.00 | 0.164949 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4212.01 | −0.214876 | −0.107438 | − | 0.994212i | \(-0.534265\pi\) | ||||
−0.107438 | + | 0.994212i | \(0.534265\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19326.0 | 0.981861 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23153.6 | −1.17150 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15633.4 | −0.787765 | −0.393883 | − | 0.919161i | \(-0.628868\pi\) | ||||
−0.393883 | + | 0.919161i | \(0.628868\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8611.87 | 0.432182 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11500.6 | −0.574802 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14148.6 | 0.704282 | 0.352141 | − | 0.935947i | \(-0.385454\pi\) | ||||
0.352141 | + | 0.935947i | \(0.385454\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1775.70 | 0.0880321 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1348.01 | 0.0665594 | 0.0332797 | − | 0.999446i | \(-0.489405\pi\) | ||||
0.0332797 | + | 0.999446i | \(0.489405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3908.31 | 0.192201 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −400.357 | −0.0196095 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −673.636 | −0.0328627 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5148.02 | −0.250138 | −0.125069 | − | 0.992148i | \(-0.539915\pi\) | ||||
−0.125069 | + | 0.992148i | \(0.539915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1497.35 | 0.0724654 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4390.03 | 0.211615 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23323.2 | −1.11981 | −0.559905 | − | 0.828557i | \(-0.689162\pi\) | ||||
−0.559905 | + | 0.828557i | \(0.689162\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5205.69 | −0.248952 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24239.0 | 1.15462 | 0.577308 | − | 0.816527i | \(-0.304103\pi\) | ||||
0.577308 | + | 0.816527i | \(0.304103\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −593.901 | −0.0281791 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −235.807 | −0.0111446 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4261.12 | 0.200600 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33635.3 | −1.57727 | −0.788635 | − | 0.614862i | \(-0.789212\pi\) | ||||
−0.788635 | + | 0.614862i | \(0.789212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7551.89 | 0.352756 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14721.9 | −0.685005 | −0.342502 | − | 0.939517i | \(-0.611275\pi\) | ||||
−0.342502 | + | 0.939517i | \(0.611275\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5297.77 | 0.245551 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 208.765 | 0.00963887 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1737.64 | 0.0799195 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17230.2 | 0.789428 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17908.3 | 0.817358 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9879.36 | 0.449184 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20595.7 | −0.932854 | −0.466427 | − | 0.884560i | \(-0.654459\pi\) | ||||
−0.466427 | + | 0.884560i | \(0.654459\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32584.2 | −1.47025 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3138.15 | 0.141062 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9176.35 | −0.410923 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4905.53 | −0.218844 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5580.16 | 0.248004 | 0.124002 | − | 0.992282i | \(-0.460427\pi\) | ||||
0.124002 | + | 0.992282i | \(0.460427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1603.77 | 0.0710102 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 63.1349 | 0.00278497 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19620.7 | −0.862264 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 436.346 | 0.0191046 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3137.89 | 0.136876 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 23778.2 | 1.03337 | 0.516686 | − | 0.856175i | \(-0.327165\pi\) | ||||
0.516686 | + | 0.856175i | \(0.327165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3367.60 | −0.145811 | −0.0729054 | − | 0.997339i | \(-0.523227\pi\) | ||||
−0.0729054 | + | 0.997339i | \(0.523227\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2278.24 | −0.0982795 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9273.79 | 0.398585 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2057.61 | −0.0881112 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 68.7082 | 0.00293145 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21263.6 | 0.903903 | 0.451952 | − | 0.892043i | \(-0.350728\pi\) | ||||
0.451952 | + | 0.892043i | \(0.350728\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12142.8 | 0.514302 | 0.257151 | − | 0.966371i | \(-0.417216\pi\) | ||||
0.257151 | + | 0.966371i | \(0.417216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5658.36 | −0.238786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15173.2 | 0.637996 | 0.318998 | − | 0.947755i | \(-0.396654\pi\) | ||||
0.318998 | + | 0.947755i | \(0.396654\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33425.0 | −1.40036 | −0.700179 | − | 0.713967i | \(-0.746897\pi\) | ||||
−0.700179 | + | 0.713967i | \(0.746897\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12248.6 | 0.511309 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 32742.5 | 1.36190 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7808.35 | −0.323615 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29464.0 | 1.21676 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27779.9 | 1.14311 | 0.571554 | − | 0.820565i | \(-0.306341\pi\) | ||||
0.571554 | + | 0.820565i | \(0.306341\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7799.53 | −0.319797 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7716.32 | −0.315260 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3666.42 | −0.149265 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2024.71 | 0.0821370 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −37402.8 | −1.51197 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −241.433 | −0.00972528 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42202.3 | 1.69400 | 0.846998 | − | 0.531596i | \(-0.178408\pi\) | ||||
0.846998 | + | 0.531596i | \(0.178408\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −20.9556 | −0.000838208 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5656.66 | 0.225470 | 0.112735 | − | 0.993625i | \(-0.464039\pi\) | ||||
0.112735 | + | 0.993625i | \(0.464039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12080.1 | 0.479824 | 0.239912 | − | 0.970795i | \(-0.422881\pi\) | ||||
0.239912 | + | 0.970795i | \(0.422881\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3902.69 | 0.154475 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37839.4 | −1.49255 | −0.746274 | − | 0.665638i | \(-0.768159\pi\) | ||||
−0.746274 | + | 0.665638i | \(0.768159\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6587.29 | −0.258930 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26288.3 | −1.02975 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15028.3 | 0.586653 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10189.5 | −0.396393 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −490.369 | −0.0190109 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 474.289 | 0.0183245 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13065.2 | −0.503058 | −0.251529 | − | 0.967850i | \(-0.580933\pi\) | ||||
−0.251529 | + | 0.967850i | \(0.580933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29157.8 | −1.11885 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14704.0 | −0.562304 | −0.281152 | − | 0.959663i | \(-0.590716\pi\) | ||||
−0.281152 | + | 0.959663i | \(0.590716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37695.5 | 1.43664 | 0.718322 | − | 0.695711i | \(-0.244911\pi\) | ||||
0.718322 | + | 0.695711i | \(0.244911\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2918.91 | −0.110868 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36116.6 | 1.36717 | 0.683583 | − | 0.729873i | \(-0.260421\pi\) | ||||
0.683583 | + | 0.729873i | \(0.260421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6749.85 | 0.254649 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32021.3 | −1.20399 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 142.523 | 0.00534083 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8134.51 | −0.303806 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4612.24 | −0.171681 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27294.2 | 1.01258 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18650.9 | −0.689625 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4621.35 | −0.170309 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10502.6 | 0.385767 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19109.4 | −0.699579 | −0.349790 | − | 0.936828i | \(-0.613747\pi\) | ||||
−0.349790 | + | 0.936828i | \(0.613747\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 362.474 | 0.0132261 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17435.2 | 0.634086 | 0.317043 | − | 0.948411i | \(-0.397310\pi\) | ||||
0.317043 | + | 0.948411i | \(0.397310\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −36525.4 | −1.32400 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6285.90 | 0.227110 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4115.65 | 0.148212 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37654.4 | −1.35158 | −0.675791 | − | 0.737093i | \(-0.736198\pi\) | ||||
−0.675791 | + | 0.737093i | \(0.736198\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23858.4 | 0.853594 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15265.9 | 0.544403 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −262.427 | −0.00932816 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −591.152 | −0.0209450 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21651.8 | 0.764663 | 0.382332 | − | 0.924025i | \(-0.375121\pi\) | ||||
0.382332 | + | 0.924025i | \(0.375121\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2909.75 | 0.102431 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20064.5 | −0.704055 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21513.2 | −0.752467 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17488.7 | −0.609744 | −0.304872 | − | 0.952393i | \(-0.598614\pi\) | ||||
−0.304872 | + | 0.952393i | \(0.598614\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −33683.1 | −1.17062 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12010.2 | 0.416071 | 0.208036 | − | 0.978121i | \(-0.433293\pi\) | ||||
0.208036 | + | 0.978121i | \(0.433293\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4513.39 | −0.155860 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2637.80 | 0.0908018 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4851.30 | 0.166469 | 0.0832344 | − | 0.996530i | \(-0.473475\pi\) | ||||
0.0832344 | + | 0.996530i | \(0.473475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −17383.9 | −0.594631 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12110.8 | 0.412953 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33419.4 | −1.13595 | −0.567976 | − | 0.823045i | \(-0.692273\pi\) | ||||
−0.567976 | + | 0.823045i | \(0.692273\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22684.0 | 0.768626 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29151.9 | −0.984688 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2994.32 | 0.100826 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15115.3 | 0.507377 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −84.0308 | −0.00281189 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 881.784 | 0.0294152 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29709.5 | 0.987999 | 0.493999 | − | 0.869462i | \(-0.335535\pi\) | ||||
0.493999 | + | 0.869462i | \(0.335535\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4624.66 | −0.153318 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22640.5 | −0.748267 | −0.374134 | − | 0.927375i | \(-0.622060\pi\) | ||||
−0.374134 | + | 0.927375i | \(0.622060\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3525.79 | 0.116168 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5013.30 | −0.164671 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25047.2 | −0.820194 | −0.410097 | − | 0.912042i | \(-0.634505\pi\) | ||||
−0.410097 | + | 0.912042i | \(0.634505\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5759.94 | 0.188037 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −74.0844 | −0.00241115 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14172.5 | 0.459849 | 0.229925 | − | 0.973208i | \(-0.426152\pi\) | ||||
0.229925 | + | 0.973208i | \(0.426152\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2874.29 | −0.0929773 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 320.103 | 0.0103232 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5344.50 | 0.171836 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30020.3 | 0.962285 | 0.481143 | − | 0.876642i | \(-0.340222\pi\) | ||||
0.481143 | + | 0.876642i | \(0.340222\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22537.7 | 0.720254 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 135.667 | 0.00432256 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19801.8 | 0.629016 | 0.314508 | − | 0.949255i | \(-0.398160\pi\) | ||||
0.314508 | + | 0.949255i | \(0.398160\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1459.51 | −0.0462231 |
(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 | 1840.4.a.x.1.2 | 8 | ||
4.3 | odd | 2 | 920.4.a.c.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.4.a.c.1.7 | ✓ | 8 | 4.3 | odd | 2 | ||
1840.4.a.x.1.2 | 8 | 1.1 | even | 1 | trivial |