Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.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: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} - 217 x^{10} + 520 x^{9} + 16022 x^{8} - 37368 x^{7} - 509640 x^{6} + 989168 x^{5} + \cdots + 14751072 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{17} \) |
Twist minimal: | no (minimal twist has level 928) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(8.22268\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 | ||||||||
\(3\) | −9.22268 | −1.77491 | −0.887453 | − | 0.460898i | \(-0.847527\pi\) | ||||
−0.887453 | + | 0.460898i | \(0.847527\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −9.91795 | −0.887089 | −0.443544 | − | 0.896252i | \(-0.646279\pi\) | ||||
−0.443544 | + | 0.896252i | \(0.646279\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.1458 | −0.979779 | −0.489890 | − | 0.871784i | \(-0.662963\pi\) | ||||
−0.489890 | + | 0.871784i | \(0.662963\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 58.0578 | 2.15029 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −30.3346 | −0.831476 | −0.415738 | − | 0.909485i | \(-0.636477\pi\) | ||||
−0.415738 | + | 0.909485i | \(0.636477\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.5792 | 0.823073 | 0.411536 | − | 0.911393i | \(-0.364992\pi\) | ||||
0.411536 | + | 0.911393i | \(0.364992\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 91.4701 | 1.57450 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 59.0959 | 0.843109 | 0.421555 | − | 0.906803i | \(-0.361485\pi\) | ||||
0.421555 | + | 0.906803i | \(0.361485\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.7598 | −0.612900 | −0.306450 | − | 0.951887i | \(-0.599141\pi\) | ||||
−0.306450 | + | 0.951887i | \(0.599141\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 167.353 | 1.73902 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 155.842 | 1.41284 | 0.706418 | − | 0.707795i | \(-0.250310\pi\) | ||||
0.706418 | + | 0.707795i | \(0.250310\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −26.6342 | −0.213073 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −286.437 | −2.04166 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −241.283 | −1.39793 | −0.698964 | − | 0.715157i | \(-0.746355\pi\) | ||||
−0.698964 | + | 0.715157i | \(0.746355\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 279.767 | 1.47579 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 179.969 | 0.869151 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −371.714 | −1.65160 | −0.825802 | − | 0.563960i | \(-0.809277\pi\) | ||||
−0.825802 | + | 0.563960i | \(0.809277\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −355.804 | −1.46088 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 61.4490 | 0.234066 | 0.117033 | − | 0.993128i | \(-0.462662\pi\) | ||||
0.117033 | + | 0.993128i | \(0.462662\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −369.530 | −1.31053 | −0.655265 | − | 0.755399i | \(-0.727443\pi\) | ||||
−0.655265 | + | 0.755399i | \(0.727443\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −575.815 | −1.90750 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −281.699 | −0.874255 | −0.437127 | − | 0.899400i | \(-0.644004\pi\) | ||||
−0.437127 | + | 0.899400i | \(0.644004\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.7311 | −0.0400322 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −545.023 | −1.49644 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 374.175 | 0.969753 | 0.484876 | − | 0.874583i | \(-0.338865\pi\) | ||||
0.484876 | + | 0.874583i | \(0.338865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 300.857 | 0.737593 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 468.141 | 1.08784 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 129.028 | 0.284713 | 0.142357 | − | 0.989815i | \(-0.454532\pi\) | ||||
0.142357 | + | 0.989815i | \(0.454532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −463.061 | −0.971948 | −0.485974 | − | 0.873973i | \(-0.661535\pi\) | ||||
−0.485974 | + | 0.873973i | \(0.661535\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1053.50 | −2.10681 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −382.627 | −0.730139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −970.507 | −1.76965 | −0.884823 | − | 0.465927i | \(-0.845721\pi\) | ||||
−0.884823 | + | 0.465927i | \(0.845721\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1437.28 | −2.50765 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 241.521 | 0.403708 | 0.201854 | − | 0.979416i | \(-0.435303\pi\) | ||||
0.201854 | + | 0.979416i | \(0.435303\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 565.154 | 0.906113 | 0.453057 | − | 0.891482i | \(-0.350334\pi\) | ||||
0.453057 | + | 0.891482i | \(0.350334\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 245.639 | 0.378185 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 550.445 | 0.814663 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 424.422 | 0.604446 | 0.302223 | − | 0.953237i | \(-0.402271\pi\) | ||||
0.302223 | + | 0.953237i | \(0.402271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1074.15 | 1.47346 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 161.180 | 0.213154 | 0.106577 | − | 0.994304i | \(-0.466011\pi\) | ||||
0.106577 | + | 0.994304i | \(0.466011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −586.110 | −0.747913 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 267.458 | 0.329592 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1138.20 | −1.35561 | −0.677806 | − | 0.735241i | \(-0.737069\pi\) | ||||
−0.677806 | + | 0.735241i | \(0.737069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −700.050 | −0.806430 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2225.28 | 2.48119 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 503.433 | 0.543696 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1449.36 | −1.51712 | −0.758558 | − | 0.651606i | \(-0.774096\pi\) | ||||
−0.758558 | + | 0.651606i | \(0.774096\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1761.16 | −1.78791 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −979.900 | −0.965383 | −0.482692 | − | 0.875790i | \(-0.660341\pi\) | ||||
−0.482692 | + | 0.875790i | \(0.660341\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −375.174 | −0.358903 | −0.179451 | − | 0.983767i | \(-0.557432\pi\) | ||||
−0.179451 | + | 0.983767i | \(0.557432\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1659.80 | −1.54266 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 779.197 | 0.703999 | 0.351999 | − | 0.936000i | \(-0.385502\pi\) | ||||
0.351999 | + | 0.936000i | \(0.385502\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 146.498 | 0.128734 | 0.0643669 | − | 0.997926i | \(-0.479497\pi\) | ||||
0.0643669 | + | 0.997926i | \(0.479497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3428.20 | 2.93144 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −209.441 | −0.174359 | −0.0871795 | − | 0.996193i | \(-0.527785\pi\) | ||||
−0.0871795 | + | 0.996193i | \(0.527785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1545.63 | −1.25331 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2239.83 | 1.76985 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1072.34 | −0.826061 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −410.811 | −0.308648 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −566.725 | −0.415446 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1503.90 | 1.07610 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2328.39 | −1.62686 | −0.813429 | − | 0.581664i | \(-0.802402\pi\) | ||||
−0.813429 | + | 0.581664i | \(0.802402\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3408.06 | 2.32607 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2293.89 | −1.52991 | −0.764955 | − | 0.644084i | \(-0.777239\pi\) | ||||
−0.764955 | + | 0.644084i | \(0.777239\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 921.075 | 0.600506 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2840.87 | 1.81113 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1579.37 | −0.984927 | −0.492463 | − | 0.870333i | \(-0.663903\pi\) | ||||
−0.492463 | + | 0.870333i | \(0.663903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1220.98 | 0.745054 | 0.372527 | − | 0.928021i | \(-0.378491\pi\) | ||||
0.372527 | + | 0.928021i | \(0.378491\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2598.02 | 1.55172 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1170.29 | −0.684365 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 287.621 | 0.164728 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 126.637 | 0.0710534 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −400.388 | −0.220141 | −0.110071 | − | 0.993924i | \(-0.535108\pi\) | ||||
−0.110071 | + | 0.993924i | \(0.535108\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 611.484 | 0.329549 | 0.164774 | − | 0.986331i | \(-0.447310\pi\) | ||||
0.164774 | + | 0.986331i | \(0.447310\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3430.98 | 1.81293 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2393.04 | 1.24009 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2219.20 | 1.12810 | 0.564048 | − | 0.825742i | \(-0.309243\pi\) | ||||
0.564048 | + | 0.825742i | \(0.309243\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3450.90 | −1.72122 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2827.87 | −1.38427 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3384.80 | −1.62649 | −0.813245 | − | 0.581922i | \(-0.802301\pi\) | ||||
−0.813245 | + | 0.581922i | \(0.802301\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2774.71 | −1.30916 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1469.18 | −0.680769 | −0.340384 | − | 0.940286i | \(-0.610557\pi\) | ||||
−0.340384 | + | 0.940286i | \(0.610557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −708.644 | −0.322551 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2947.00 | −1.31791 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2494.19 | 1.09613 | 0.548063 | − | 0.836437i | \(-0.315365\pi\) | ||||
0.548063 | + | 0.836437i | \(0.315365\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 483.298 | 0.208765 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1189.99 | −0.505339 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1681.66 | −0.702197 | −0.351099 | − | 0.936339i | \(-0.614192\pi\) | ||||
−0.351099 | + | 0.936339i | \(0.614192\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3463.28 | 1.42223 | 0.711115 | − | 0.703076i | \(-0.248191\pi\) | ||||
0.711115 | + | 0.703076i | \(0.248191\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4270.66 | 1.72512 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3686.64 | 1.46512 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1792.65 | −0.701025 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5197.61 | 2.00037 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2962.78 | 1.12240 | 0.561202 | − | 0.827679i | \(-0.310339\pi\) | ||||
0.561202 | + | 0.827679i | \(0.310339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3212.73 | 1.19822 | 0.599112 | − | 0.800665i | \(-0.295520\pi\) | ||||
0.599112 | + | 0.800665i | \(0.295520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3528.85 | 1.29593 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 40.3205 | 0.0145823 | 0.00729115 | − | 0.999973i | \(-0.497679\pi\) | ||||
0.00729115 | + | 0.999973i | \(0.497679\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −492.569 | −0.175464 | −0.0877319 | − | 0.996144i | \(-0.527962\pi\) | ||||
−0.0877319 | + | 0.996144i | \(0.527962\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8950.68 | 3.14096 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 526.227 | 0.181940 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −609.449 | −0.207638 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9047.83 | 3.03801 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1539.78 | 0.509611 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2004.02 | 0.653850 | 0.326925 | − | 0.945050i | \(-0.393988\pi\) | ||||
0.326925 | + | 0.945050i | \(0.393988\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2227.47 | −0.716544 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3664.98 | 1.16256 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4378.27 | 1.36966 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5212.23 | −1.60827 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2279.87 | 0.693941 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1975.53 | 0.593234 | 0.296617 | − | 0.954996i | \(-0.404141\pi\) | ||||
0.296617 | + | 0.954996i | \(0.404141\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1546.32 | −0.458170 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5304.20 | −1.55089 | −0.775446 | − | 0.631414i | \(-0.782475\pi\) | ||||
−0.775446 | + | 0.631414i | \(0.782475\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2463.70 | 0.710944 | 0.355472 | − | 0.934687i | \(-0.384320\pi\) | ||||
0.355472 | + | 0.934687i | \(0.384320\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5076.58 | −1.44595 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3230.57 | −0.908332 | −0.454166 | − | 0.890917i | \(-0.650063\pi\) | ||||
−0.454166 | + | 0.890917i | \(0.650063\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2793.87 | 0.775541 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3914.31 | −1.07283 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4280.39 | −1.15848 | −0.579238 | − | 0.815159i | \(-0.696650\pi\) | ||||
−0.579238 | + | 0.815159i | \(0.696650\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6488.41 | 1.73425 | 0.867127 | − | 0.498087i | \(-0.165964\pi\) | ||||
0.867127 | + | 0.498087i | \(0.165964\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2172.77 | −0.573594 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 136.184 | 0.0355121 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1958.27 | −0.504461 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1486.51 | −0.378328 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 407.291 | 0.102422 | 0.0512111 | − | 0.998688i | \(-0.483692\pi\) | ||||
0.0512111 | + | 0.998688i | \(0.483692\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4727.40 | −1.17474 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5405.51 | 1.32748 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5519.50 | −1.33968 | −0.669839 | − | 0.742507i | \(-0.733637\pi\) | ||||
−0.669839 | + | 0.742507i | \(0.733637\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6745.03 | 1.61821 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1683.68 | −0.399299 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4159.14 | −0.975146 | −0.487573 | − | 0.873082i | \(-0.662118\pi\) | ||||
−0.487573 | + | 0.873082i | \(0.662118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3711.05 | −0.860257 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10497.3 | 2.40608 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3408.03 | −0.772459 | −0.386230 | − | 0.922403i | \(-0.626223\pi\) | ||||
−0.386230 | + | 0.922403i | \(0.626223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7638.65 | 1.71223 | 0.856116 | − | 0.516783i | \(-0.172871\pi\) | ||||
0.856116 | + | 0.516783i | \(0.172871\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6456.33 | 1.43134 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 807.938 | 0.177165 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −254.643 | −0.0552347 | −0.0276173 | − | 0.999619i | \(-0.508792\pi\) | ||||
−0.0276173 | + | 0.999619i | \(0.508792\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14008.4 | −3.00595 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3750.69 | −0.796255 | −0.398128 | − | 0.917330i | \(-0.630340\pi\) | ||||
−0.398128 | + | 0.917330i | \(0.630340\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7621.54 | 1.60090 | 0.800448 | − | 0.599402i | \(-0.204595\pi\) | ||||
0.800448 | + | 0.599402i | \(0.204595\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4643.00 | −0.965010 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1115.04 | −0.229334 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1420.67 | −0.289166 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13367.0 | 2.69274 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3420.15 | 0.681935 | 0.340968 | − | 0.940075i | \(-0.389245\pi\) | ||||
0.340968 | + | 0.940075i | \(0.389245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1279.70 | −0.252566 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8688.95 | 1.69759 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6012.25 | 1.16287 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6705.40 | 1.28403 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9037.31 | 1.71346 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4592.61 | 0.862204 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6813.99 | −1.26676 | −0.633380 | − | 0.773841i | \(-0.718333\pi\) | ||||
−0.633380 | + | 0.773841i | \(0.718333\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3460.11 | 0.637018 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6160.82 | 1.12331 | 0.561653 | − | 0.827373i | \(-0.310166\pi\) | ||||
0.561653 | + | 0.827373i | \(0.310166\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5355.56 | −0.967138 | −0.483569 | − | 0.875306i | \(-0.660660\pi\) | ||||
−0.483569 | + | 0.875306i | \(0.660660\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10448.6 | 1.86893 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1812.38 | −0.321115 | −0.160557 | − | 0.987027i | \(-0.551329\pi\) | ||||
−0.160557 | + | 0.987027i | \(0.551329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 879.704 | 0.154401 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7186.29 | −1.24953 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2999.69 | −0.516741 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1027.53 | −0.175375 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1351.11 | −0.228490 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5111.64 | 0.856577 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10192.2 | −1.69249 | −0.846243 | − | 0.532797i | \(-0.821141\pi\) | ||||
−0.846243 | + | 0.532797i | \(0.821141\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −21580.9 | −3.55143 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9625.45 | 1.56983 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4600.14 | 0.743578 | 0.371789 | − | 0.928317i | \(-0.378745\pi\) | ||||
0.371789 | + | 0.928317i | \(0.378745\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1931.61 | 0.309471 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7319.24 | 1.16234 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6473.16 | 1.01900 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14254.8 | 2.22451 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3833.04 | 0.592992 | 0.296496 | − | 0.955034i | \(-0.404182\pi\) | ||||
0.296496 | + | 0.955034i | \(0.404182\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3398.43 | −0.521243 | −0.260622 | − | 0.965441i | \(-0.583928\pi\) | ||||
−0.260622 | + | 0.965441i | \(0.583928\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11050.5 | −1.68043 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8663.33 | −1.30624 | −0.653119 | − | 0.757255i | \(-0.726540\pi\) | ||||
−0.653119 | + | 0.757255i | \(0.726540\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2395.39 | −0.358125 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9889.85 | 1.46618 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12373.5 | −1.81908 | −0.909540 | − | 0.415616i | \(-0.863566\pi\) | ||||
−0.909540 | + | 0.415616i | \(0.863566\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4282.44 | −0.624354 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3788.78 | 0.547822 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5605.17 | −0.803803 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3507.48 | −0.498880 | −0.249440 | − | 0.968390i | \(-0.580246\pi\) | ||||
−0.249440 | + | 0.968390i | \(0.580246\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3567.60 | 0.503311 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6789.69 | −0.950144 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12460.9 | 1.72976 | 0.864878 | − | 0.501982i | \(-0.167396\pi\) | ||||
0.864878 | + | 0.501982i | \(0.167396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13870.0 | −1.90998 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1118.80 | −0.152841 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11480.8 | 1.55601 | 0.778003 | − | 0.628260i | \(-0.216233\pi\) | ||||
0.778003 | + | 0.628260i | \(0.216233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 21474.0 | 2.88752 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11746.7 | 1.56718 | 0.783591 | − | 0.621278i | \(-0.213386\pi\) | ||||
0.783591 | + | 0.621278i | \(0.213386\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5459.29 | −0.722678 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21454.1 | −2.81802 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2142.34 | −0.279232 | −0.139616 | − | 0.990206i | \(-0.544587\pi\) | ||||
−0.139616 | + | 0.990206i | \(0.544587\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9209.60 | 1.19117 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21155.8 | 2.71544 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4209.40 | −0.536197 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3330.09 | −0.420989 | −0.210494 | − | 0.977595i | \(-0.567507\pi\) | ||||
−0.210494 | + | 0.977595i | \(0.567507\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8494.78 | −1.06584 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2449.26 | −0.305013 | −0.152507 | − | 0.988302i | \(-0.548735\pi\) | ||||
−0.152507 | + | 0.988302i | \(0.548735\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9308.52 | −1.15060 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10653.4 | −1.30709 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11275.8 | 1.37327 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1978.69 | 0.239217 | 0.119608 | − | 0.992821i | \(-0.461836\pi\) | ||||
0.119608 | + | 0.992821i | \(0.461836\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14566.1 | 1.74815 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2341.32 | −0.278956 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1598.57 | −0.189087 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11260.7 | −1.32240 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3715.93 | 0.433258 | 0.216629 | − | 0.976254i | \(-0.430494\pi\) | ||||
0.216629 | + | 0.976254i | \(0.430494\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16124.9 | 1.86670 | 0.933350 | − | 0.358968i | \(-0.116871\pi\) | ||||
0.933350 | + | 0.358968i | \(0.116871\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16354.8 | −1.87990 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1573.97 | −0.179644 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8402.59 | 0.952295 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10793.2 | 1.21468 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6764.83 | −0.756034 | −0.378017 | − | 0.925799i | \(-0.623394\pi\) | ||||
−0.378017 | + | 0.925799i | \(0.623394\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1794.00 | −0.199109 | −0.0995544 | − | 0.995032i | \(-0.531742\pi\) | ||||
−0.0995544 | + | 0.995032i | \(0.531742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2652.63 | −0.292377 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7910.48 | −0.865926 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5513.07 | −0.599372 | −0.299686 | − | 0.954038i | \(-0.596882\pi\) | ||||
−0.299686 | + | 0.954038i | \(0.596882\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −797.195 | −0.0860809 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11355.7 | 1.21789 | 0.608945 | − | 0.793213i | \(-0.291593\pi\) | ||||
0.608945 | + | 0.793213i | \(0.291593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11288.7 | 1.20255 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3692.65 | 0.390730 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3049.12 | −0.320483 | −0.160242 | − | 0.987078i | \(-0.551227\pi\) | ||||
−0.160242 | + | 0.987078i | \(0.551227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1864.03 | −0.194621 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5639.52 | −0.584918 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6943.06 | 0.715375 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12033.7 | −1.23176 | −0.615879 | − | 0.787841i | \(-0.711199\pi\) | ||||
−0.615879 | + | 0.787841i | \(0.711199\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16927.2 | −1.72134 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 629.093 | 0.0635570 | 0.0317785 | − | 0.999495i | \(-0.489883\pi\) | ||||
0.0317785 | + | 0.999495i | \(0.489883\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.68659 | 0.000470420 0 | 0.000235210 | − | 1.00000i | \(-0.499925\pi\) | ||||
0.000235210 | 1.00000i | \(0.499925\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −22070.2 | −2.20104 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −694.076 | −0.0687752 | −0.0343876 | − | 0.999409i | \(-0.510948\pi\) | ||||
−0.0343876 | + | 0.999409i | \(0.510948\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17610.6 | 1.73386 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20466.9 | −2.00227 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11209.5 | 1.08967 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1351.95 | 0.130593 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21723.8 | 2.08525 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10669.7 | 1.01777 | 0.508883 | − | 0.860836i | \(-0.330059\pi\) | ||||
0.508883 | + | 0.860836i | \(0.330059\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14340.4 | −1.35939 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 26080.5 | 2.45694 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14374.7 | 1.34582 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1565.26 | −0.145644 | −0.0728221 | − | 0.997345i | \(-0.523201\pi\) | ||||
−0.0728221 | + | 0.997345i | \(0.523201\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 31216.9 | 2.88687 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15547.9 | 1.42906 | 0.714529 | − | 0.699606i | \(-0.246641\pi\) | ||||
0.714529 | + | 0.699606i | \(0.246641\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1713.78 | −0.156561 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17467.1 | 1.58604 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4382.58 | −0.395545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15465.1 | 1.38740 | 0.693700 | − | 0.720264i | \(-0.255979\pi\) | ||||
0.693700 | + | 0.720264i | \(0.255979\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13549.8 | 1.20830 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6096.03 | 0.540375 | 0.270187 | − | 0.962808i | \(-0.412914\pi\) | ||||
0.270187 | + | 0.962808i | \(0.412914\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9718.60 | 0.856381 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6535.60 | 0.572497 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18928.0 | −1.64827 | −0.824133 | − | 0.566397i | \(-0.808337\pi\) | ||||
−0.824133 | + | 0.566397i | \(0.808337\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10255.2 | −0.887791 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14539.5 | 1.25133 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3720.96 | 0.318379 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8545.22 | 0.726921 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −23003.1 | −1.94552 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20910.7 | −1.75838 | −0.879189 | − | 0.476474i | \(-0.841915\pi\) | ||||
−0.879189 | + | 0.476474i | \(0.841915\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16510.9 | −1.38044 | −0.690220 | − | 0.723600i | \(-0.742486\pi\) | ||||
−0.690220 | + | 0.723600i | \(0.742486\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4457.30 | −0.370538 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14258.9 | −1.17861 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12119.6 | 0.996104 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7491.12 | 0.612216 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2370.66 | 0.192654 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7728.04 | −0.624509 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15509.4 | 1.24633 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 416.526 | 0.0332858 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24189.4 | −1.92234 | −0.961169 | − | 0.275960i | \(-0.911004\pi\) | ||||
−0.961169 | + | 0.275960i | \(0.911004\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −31940.7 | −2.52432 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1452.96 | −0.114198 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8110.28 | −0.633950 | −0.316975 | − | 0.948434i | \(-0.602667\pi\) | ||||
−0.316975 | + | 0.948434i | \(0.602667\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −26884.3 | −2.08997 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1472.03 | 0.113813 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7701.47 | −0.592224 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −34000.7 | −2.60045 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22133.0 | 1.68367 | 0.841835 | − | 0.539735i | \(-0.181475\pi\) | ||||
0.841835 | + | 0.539735i | \(0.181475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14256.2 | −1.07866 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16533.1 | 1.24425 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18464.4 | −1.38220 | −0.691102 | − | 0.722757i | \(-0.742874\pi\) | ||||
−0.691102 | + | 0.722757i | \(0.742874\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2077.23 | 0.154672 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19491.3 | −1.44366 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5538.92 | −0.408091 | −0.204045 | − | 0.978961i | \(-0.565409\pi\) | ||||
−0.204045 | + | 0.978961i | \(0.565409\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11219.3 | 0.822262 | 0.411131 | − | 0.911576i | \(-0.365134\pi\) | ||||
0.411131 | + | 0.911576i | \(0.365134\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27324.8 | −1.99216 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4150.71 | −0.301038 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8239.06 | −0.594448 | −0.297224 | − | 0.954808i | \(-0.596061\pi\) | ||||
−0.297224 | + | 0.954808i | \(0.596061\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29630.0 | −2.12674 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2924.73 | −0.208844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11350.5 | −0.806326 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22214.5 | −1.57001 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6452.46 | 0.453699 | 0.226850 | − | 0.973930i | \(-0.427157\pi\) | ||||
0.226850 | + | 0.973930i | \(0.427157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12247.5 | 0.856790 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −371.863 | −0.0258822 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9937.52 | 0.688171 | 0.344085 | − | 0.938938i | \(-0.388189\pi\) | ||||
0.344085 | + | 0.938938i | \(0.388189\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10635.4 | 0.732790 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4542.81 | 0.311432 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5754.72 | 0.392540 | 0.196270 | − | 0.980550i | \(-0.437117\pi\) | ||||
0.196270 | + | 0.980550i | \(0.437117\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17242.3 | 1.17026 | 0.585132 | − | 0.810938i | \(-0.301043\pi\) | ||||
0.585132 | + | 0.810938i | \(0.301043\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −56345.6 | −3.80525 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4074.40 | 0.273798 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11857.0 | −0.792854 | −0.396427 | − | 0.918066i | \(-0.629750\pi\) | ||||
−0.396427 | + | 0.918066i | \(0.629750\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4853.23 | −0.322927 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10867.7 | −0.719575 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6818.16 | 0.449238 | 0.224619 | − | 0.974447i | \(-0.427886\pi\) | ||||
0.224619 | + | 0.974447i | \(0.427886\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5620.75 | 0.368537 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30340.0 | −1.97965 | −0.989825 | − | 0.142289i | \(-0.954554\pi\) | ||||
−0.989825 | + | 0.142289i | \(0.954554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8090.29 | −0.525325 | −0.262663 | − | 0.964888i | \(-0.584601\pi\) | ||||
−0.262663 | + | 0.964888i | \(0.584601\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −44638.7 | −2.88453 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20653.6 | 1.32820 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11586.3 | −0.741526 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14200.9 | −0.904512 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21966.8 | −1.39248 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12014.9 | −0.758010 | −0.379005 | − | 0.925395i | \(-0.623734\pi\) | ||||
−0.379005 | + | 0.925395i | \(0.623734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18482.4 | −1.16052 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 23092.8 | 1.44317 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −529.733 | −0.0329494 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14022.2 | 0.868089 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2106.54 | 0.129802 | 0.0649011 | − | 0.997892i | \(-0.479327\pi\) | ||||
0.0649011 | + | 0.997892i | \(0.479327\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9074.16 | 0.556532 | 0.278266 | − | 0.960504i | \(-0.410240\pi\) | ||||
0.278266 | + | 0.960504i | \(0.410240\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −33800.9 | −2.06343 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25416.1 | 1.54437 | 0.772187 | − | 0.635395i | \(-0.219163\pi\) | ||||
0.772187 | + | 0.635395i | \(0.219163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3914.03 | −0.236732 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −40379.4 | −2.43102 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18241.8 | −1.09319 | −0.546597 | − | 0.837396i | \(-0.684077\pi\) | ||||
−0.546597 | + | 0.837396i | \(0.684077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22750.7 | 1.35717 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 32811.6 | 1.94841 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6878.96 | 0.406626 | 0.203313 | − | 0.979114i | \(-0.434829\pi\) | ||||
0.203313 | + | 0.979114i | \(0.434829\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26498.4 | −1.55925 | −0.779627 | − | 0.626244i | \(-0.784592\pi\) | ||||
−0.779627 | + | 0.626244i | \(0.784592\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21026.5 | −1.23168 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9135.18 | −0.532703 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4519.41 | −0.262357 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18219.7 | −1.05293 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14046.8 | 0.808151 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1232.11 | 0.0705710 | 0.0352855 | − | 0.999377i | \(-0.488766\pi\) | ||||
0.0352855 | + | 0.999377i | \(0.488766\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7629.00 | 0.435023 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6769.54 | −0.384305 | −0.192153 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192153 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26299.8 | 1.48644 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48919.0 | 2.75269 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14965.1 | −0.838393 | −0.419196 | − | 0.907896i | \(-0.637688\pi\) | ||||
−0.419196 | + | 0.907896i | \(0.637688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15664.2 | 0.873717 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −22722.0 | −1.26186 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14435.4 | 0.798177 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26158.4 | 1.44011 | 0.720053 | − | 0.693919i | \(-0.244117\pi\) | ||||
0.720053 | + | 0.693919i | \(0.244117\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 31957.7 | 1.75176 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12109.7 | −0.660929 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3631.39 | 0.197344 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 29794.5 | 1.61220 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1249.14 | −0.0673031 | −0.0336515 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336515 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18868.1 | 1.01227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −25767.0 | −1.37651 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17781.0 | 0.945863 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16036.0 | −0.849427 | −0.424713 | − | 0.905328i | \(-0.639625\pi\) | ||||
−0.424713 | + | 0.905328i | \(0.639625\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24641.0 | 1.29973 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37602.0 | −1.97504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11606.8 | 0.607093 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 39476.7 | 2.05618 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17662.1 | 0.916111 | 0.458056 | − | 0.888923i | \(-0.348546\pi\) | ||||
0.458056 | + | 0.888923i | \(0.348546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6807.82 | 0.351645 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −59840.5 | −3.07814 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 772.391 | 0.0395667 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −700.740 | −0.0357483 | −0.0178741 | − | 0.999840i | \(-0.505690\pi\) | ||||
−0.0178741 | + | 0.999840i | \(0.505690\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8963.33 | −0.455385 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21837.7 | −1.10492 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31338.0 | −1.57912 | −0.789561 | − | 0.613672i | \(-0.789692\pi\) | ||||
−0.789561 | + | 0.613672i | \(0.789692\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1255.98 | −0.0630307 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29440.0 | 1.47142 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34066.8 | 1.69576 | 0.847880 | − | 0.530188i | \(-0.177879\pi\) | ||||
0.847880 | + | 0.530188i | \(0.177879\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18060.5 | 0.895371 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6009.39 | 0.296720 | 0.148360 | − | 0.988933i | \(-0.452601\pi\) | ||||
0.148360 | + | 0.988933i | \(0.452601\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3971.03 | 0.195285 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9357.75 | 0.458343 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14139.1 | −0.689763 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4761.05 | 0.231336 | 0.115668 | − | 0.993288i | \(-0.463099\pi\) | ||||
0.115668 | + | 0.993288i | \(0.463099\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3756.32 | −0.181790 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6064.67 | −0.292339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28880.1 | −1.38661 | −0.693307 | − | 0.720643i | \(-0.743847\pi\) | ||||
−0.693307 | + | 0.720643i | \(0.743847\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 43599.3 | 2.08505 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14423.5 | 0.687059 | 0.343530 | − | 0.939142i | \(-0.388377\pi\) | ||||
0.343530 | + | 0.939142i | \(0.388377\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2658.32 | −0.126131 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −34028.3 | −1.60823 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4977.82 | 0.234340 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38830.7 | 1.82090 | 0.910449 | − | 0.413621i | \(-0.135736\pi\) | ||||
0.910449 | + | 0.413621i | \(0.135736\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50904.6 | 2.37780 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15417.7 | −0.717380 | −0.358690 | − | 0.933457i | \(-0.616776\pi\) | ||||
−0.358690 | + | 0.933457i | \(0.616776\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6426.39 | 0.297861 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −62207.3 | −2.87217 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3119.14 | −0.143459 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7326.45 | −0.335673 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8306.66 | 0.379126 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −22009.9 | −1.00072 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1122.93 | 0.0508618 | 0.0254309 | − | 0.999677i | \(-0.491904\pi\) | ||||
0.0254309 | + | 0.999677i | \(0.491904\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38358.4 | 1.73079 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3800.47 | 0.170833 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17864.5 | −0.799984 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34225.8 | 1.52687 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17273.1 | 0.767684 | 0.383842 | − | 0.923399i | \(-0.374601\pi\) | ||||
0.383842 | + | 0.923399i | \(0.374601\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16647.2 | −0.737092 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −66081.7 | −2.91496 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17143.7 | −0.753411 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28046.6 | 1.22797 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31431.2 | 1.37104 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 31287.2 | 1.35970 | 0.679851 | − | 0.733351i | \(-0.262045\pi\) | ||||
0.679851 | + | 0.733351i | \(0.262045\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20399.1 | 0.883244 | 0.441622 | − | 0.897201i | \(-0.354403\pi\) | ||||
0.441622 | + | 0.897201i | \(0.354403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −70448.8 | −3.03905 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33570.3 | 1.44284 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18757.3 | 0.803223 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −40643.4 | −1.73406 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9158.81 | 0.389336 | 0.194668 | − | 0.980869i | \(-0.437637\pi\) | ||||
0.194668 | + | 0.980869i | \(0.437637\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20147.5 | −0.853340 | −0.426670 | − | 0.904407i | \(-0.640313\pi\) | ||||
−0.426670 | + | 0.904407i | \(0.640313\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7451.35 | −0.314452 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15491.3 | 0.651372 | 0.325686 | − | 0.945478i | \(-0.394405\pi\) | ||||
0.325686 | + | 0.945478i | \(0.394405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36020.1 | 1.50908 | 0.754542 | − | 0.656252i | \(-0.227859\pi\) | ||||
0.754542 | + | 0.656252i | \(0.227859\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2348.49 | 0.0980363 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −811.449 | −0.0337515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14571.2 | 0.603902 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 69112.4 | 2.85409 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 32919.5 | 1.35460 | 0.677298 | − | 0.735709i | \(-0.263151\pi\) | ||||
0.677298 | + | 0.735709i | \(0.263151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34591.5 | 1.41328 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7028.30 | 0.286131 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7454.48 | 0.302407 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −70291.0 | −2.84144 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −57928.5 | −2.33345 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15790.8 | −0.633842 | −0.316921 | − | 0.948452i | \(-0.602649\pi\) | ||||
−0.316921 | + | 0.948452i | \(0.602649\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29228.2 | 1.16911 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31142.7 | 1.24132 | 0.620661 | − | 0.784079i | \(-0.286864\pi\) | ||||
0.620661 | + | 0.784079i | \(0.286864\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15038.5 | −0.597331 | −0.298665 | − | 0.954358i | \(-0.596541\pi\) | ||||
−0.298665 | + | 0.954358i | \(0.596541\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10283.7 | 0.407045 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28642.7 | 1.12979 | 0.564894 | − | 0.825163i | \(-0.308917\pi\) | ||||
0.564894 | + | 0.825163i | \(0.308917\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −24737.3 | −0.972361 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13102.4 | 0.513243 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12874.7 | −0.502582 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37441.4 | −1.45655 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −84146.7 | −3.26224 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27289.4 | −1.05434 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23442.1 | 0.902603 | 0.451302 | − | 0.892371i | \(-0.350960\pi\) | ||||
0.451302 | + | 0.892371i | \(0.350960\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31542.9 | −1.21037 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48730.1 | 1.86352 | 0.931758 | − | 0.363079i | \(-0.118275\pi\) | ||||
0.931758 | + | 0.363079i | \(0.118275\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37501.4 | 1.42924 | 0.714622 | − | 0.699511i | \(-0.246599\pi\) | ||||
0.714622 | + | 0.699511i | \(0.246599\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11802.3 | 0.448281 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 23885.6 | 0.904170 | 0.452085 | − | 0.891975i | \(-0.350680\pi\) | ||||
0.452085 | + | 0.891975i | \(0.350680\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42250.4 | 1.59396 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32584.0 | −1.22515 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14299.0 | 0.535830 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16678.6 | 0.622911 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −55449.0 | −2.06398 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6997.22 | 0.259589 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22112.2 | 0.817608 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −61841.8 | −2.27903 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −34348.7 | −1.26164 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10117.1 | −0.370380 | −0.185190 | − | 0.982703i | \(-0.559290\pi\) | ||||
−0.185190 | + | 0.982703i | \(0.559290\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −56890.9 | −2.07585 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7387.19 | 0.268659 | 0.134330 | − | 0.990937i | \(-0.457112\pi\) | ||||
0.134330 | + | 0.990937i | \(0.457112\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4889.33 | −0.177232 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −42356.2 | −1.53033 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 41624.4 | 1.49897 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41196.3 | 1.47872 | 0.739359 | − | 0.673312i | \(-0.235129\pi\) | ||||
0.739359 | + | 0.673312i | \(0.235129\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 62843.3 | 2.24838 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9317.69 | 0.332281 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9900.29 | 0.351913 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21781.8 | −0.771745 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42590.3 | −1.50414 | −0.752068 | − | 0.659085i | \(-0.770944\pi\) | ||||
−0.752068 | + | 0.659085i | \(0.770944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 696.985 | 0.0245357 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −56819.3 | −1.99376 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 17779.4 | 0.621871 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −19764.2 | −0.689079 | −0.344539 | − | 0.938772i | \(-0.611965\pi\) | ||||
−0.344539 | + | 0.938772i | \(0.611965\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 49392.6 | 1.71658 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19163.0 | 0.663866 | 0.331933 | − | 0.943303i | \(-0.392299\pi\) | ||||
0.331933 | + | 0.943303i | \(0.392299\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9576.31 | 0.330697 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −51549.7 | −1.77451 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29334.5 | −1.00659 | −0.503297 | − | 0.864114i | \(-0.667880\pi\) | ||||
−0.503297 | + | 0.864114i | \(0.667880\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21803.2 | 0.745797 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16715.0 | 0.569948 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26975.1 | −0.916904 | −0.458452 | − | 0.888719i | \(-0.651596\pi\) | ||||
−0.458452 | + | 0.888719i | \(0.651596\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29384.7 | −0.995672 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8113.23 | −0.274048 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 28658.9 | 0.965011 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28426.7 | 0.954204 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45238.5 | 1.51380 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31863.7 | −1.06293 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12036.6 | −0.400280 | −0.200140 | − | 0.979767i | \(-0.564140\pi\) | ||||
−0.200140 | + | 0.979767i | \(0.564140\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 27665.2 | 0.917167 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43608.2 | 1.44125 | 0.720625 | − | 0.693325i | \(-0.243855\pi\) | ||||
0.720625 | + | 0.693325i | \(0.243855\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22155.7 | −0.729989 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9476.54 | 0.311274 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48826.4 | −1.59887 | −0.799434 | − | 0.600754i | \(-0.794867\pi\) | ||||
−0.799434 | + | 0.600754i | \(0.794867\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34527.0 | 1.12716 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8505.37 | 0.276815 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23279.6 | 0.755345 | 0.377672 | − | 0.925939i | \(-0.376725\pi\) | ||||
0.377672 | + | 0.925939i | \(0.376725\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −399.897 | −0.0129358 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −47143.0 | −1.52034 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −57588.1 | −1.85156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39511.7 | −1.26653 | −0.633264 | − | 0.773936i | \(-0.718285\pi\) | ||||
−0.633264 | + | 0.773936i | \(0.718285\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 93999.3 | 3.00400 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4885.28 | 0.155652 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38690.6 | −1.22903 | −0.614515 | − | 0.788905i | \(-0.710648\pi\) | ||||
−0.614515 | + | 0.788905i | \(0.710648\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 106472. | 3.37201 |
(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 | 1856.4.a.bj.1.2 | 12 | ||
4.3 | odd | 2 | 1856.4.a.bl.1.11 | 12 | |||
8.3 | odd | 2 | 928.4.a.h.1.2 | ✓ | 12 | ||
8.5 | even | 2 | 928.4.a.j.1.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
928.4.a.h.1.2 | ✓ | 12 | 8.3 | odd | 2 | ||
928.4.a.j.1.11 | yes | 12 | 8.5 | even | 2 | ||
1856.4.a.bj.1.2 | 12 | 1.1 | even | 1 | trivial | ||
1856.4.a.bl.1.11 | 12 | 4.3 | odd | 2 |