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: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 204 x^{8} + 42 x^{7} + 12958 x^{6} + 5872 x^{5} - 259871 x^{4} - 149461 x^{3} + \cdots - 43712 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{7}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(9.27510\) 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 | ||||||||
\(3\) | 9.27510 | 1.78499 | 0.892497 | − | 0.451054i | \(-0.148952\pi\) | ||||
0.892497 | + | 0.451054i | \(0.148952\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −33.0838 | −1.78636 | −0.893179 | − | 0.449701i | \(-0.851530\pi\) | ||||
−0.893179 | + | 0.449701i | \(0.851530\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 59.0275 | 2.18620 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 54.6419 | 1.49774 | 0.748871 | − | 0.662716i | \(-0.230596\pi\) | ||||
0.748871 | + | 0.662716i | \(0.230596\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 86.7693 | 1.85119 | 0.925595 | − | 0.378514i | \(-0.123565\pi\) | ||||
0.925595 | + | 0.378514i | \(0.123565\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −46.3755 | −0.798273 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 77.8072 | 1.11006 | 0.555030 | − | 0.831830i | \(-0.312707\pi\) | ||||
0.555030 | + | 0.831830i | \(0.312707\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −138.051 | −1.66690 | −0.833452 | − | 0.552592i | \(-0.813639\pi\) | ||||
−0.833452 | + | 0.552592i | \(0.813639\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −306.856 | −3.18864 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 297.058 | 2.11736 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −212.229 | −1.35896 | −0.679481 | − | 0.733693i | \(-0.737795\pi\) | ||||
−0.679481 | + | 0.733693i | \(0.737795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 147.641 | 0.855393 | 0.427696 | − | 0.903922i | \(-0.359325\pi\) | ||||
0.427696 | + | 0.903922i | \(0.359325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 506.810 | 2.67346 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 165.419 | 0.798884 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −185.803 | −0.825562 | −0.412781 | − | 0.910830i | \(-0.635443\pi\) | ||||
−0.412781 | + | 0.910830i | \(0.635443\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 804.794 | 3.30436 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 322.883 | 1.22990 | 0.614950 | − | 0.788566i | \(-0.289176\pi\) | ||||
0.614950 | + | 0.788566i | \(0.289176\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.59490 | −0.0127492 | −0.00637461 | − | 0.999980i | \(-0.502029\pi\) | ||||
−0.00637461 | + | 0.999980i | \(0.502029\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −295.137 | −0.977700 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18.6351 | 0.0578341 | 0.0289170 | − | 0.999582i | \(-0.490794\pi\) | ||||
0.0289170 | + | 0.999582i | \(0.490794\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 751.539 | 2.19108 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 721.670 | 1.98145 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.84351 | −0.0177364 | −0.00886820 | − | 0.999961i | \(-0.502823\pi\) | ||||
−0.00886820 | + | 0.999961i | \(0.502823\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −273.210 | −0.669811 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1280.44 | −2.97541 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −414.113 | −0.913779 | −0.456889 | − | 0.889524i | \(-0.651036\pi\) | ||||
−0.456889 | + | 0.889524i | \(0.651036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 258.968 | 0.543564 | 0.271782 | − | 0.962359i | \(-0.412387\pi\) | ||||
0.271782 | + | 0.962359i | \(0.412387\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1952.85 | −3.90534 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −433.847 | −0.827878 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 490.096 | 0.893653 | 0.446826 | − | 0.894621i | \(-0.352554\pi\) | ||||
0.446826 | + | 0.894621i | \(0.352554\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −213.327 | −0.372197 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 821.332 | 1.37288 | 0.686438 | − | 0.727189i | \(-0.259173\pi\) | ||||
0.686438 | + | 0.727189i | \(0.259173\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.4667 | 0.0183845 | 0.00919227 | − | 0.999958i | \(-0.497074\pi\) | ||||
0.00919227 | + | 0.999958i | \(0.497074\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 231.877 | 0.356999 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1807.76 | −2.67550 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −214.872 | −0.306012 | −0.153006 | − | 0.988225i | \(-0.548895\pi\) | ||||
−0.153006 | + | 0.988225i | \(0.548895\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1161.50 | 1.59328 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 793.747 | 1.04970 | 0.524850 | − | 0.851195i | \(-0.324122\pi\) | ||||
0.524850 | + | 0.851195i | \(0.324122\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −389.036 | −0.496434 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1968.44 | −2.42574 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −192.788 | −0.229612 | −0.114806 | − | 0.993388i | \(-0.536625\pi\) | ||||
−0.114806 | + | 0.993388i | \(0.536625\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2870.66 | −3.30689 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1369.39 | 1.52687 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 690.257 | 0.745462 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1135.34 | 1.18842 | 0.594208 | − | 0.804312i | \(-0.297466\pi\) | ||||
0.594208 | + | 0.804312i | \(0.297466\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3225.38 | 3.27437 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1974.69 | 1.94543 | 0.972717 | − | 0.231995i | \(-0.0745253\pi\) | ||||
0.972717 | + | 0.231995i | \(0.0745253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −263.452 | −0.252026 | −0.126013 | − | 0.992029i | \(-0.540218\pi\) | ||||
−0.126013 | + | 0.992029i | \(0.540218\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1534.28 | 1.42600 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 544.724 | 0.492154 | 0.246077 | − | 0.969250i | \(-0.420858\pi\) | ||||
0.246077 | + | 0.969250i | \(0.420858\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1850.62 | 1.62621 | 0.813105 | − | 0.582117i | \(-0.197775\pi\) | ||||
0.813105 | + | 0.582117i | \(0.197775\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1723.34 | −1.47362 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −70.8472 | −0.0589800 | −0.0294900 | − | 0.999565i | \(-0.509388\pi\) | ||||
−0.0294900 | + | 0.999565i | \(0.509388\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 115.000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5121.77 | 4.04708 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2574.16 | −1.98296 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1654.74 | 1.24323 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2994.77 | 2.19536 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1399.71 | −0.977982 | −0.488991 | − | 0.872289i | \(-0.662635\pi\) | ||||
−0.488991 | + | 0.872289i | \(0.662635\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −33.3430 | −0.0227573 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1676.24 | −1.11797 | −0.558984 | − | 0.829178i | \(-0.688809\pi\) | ||||
−0.558984 | + | 0.829178i | \(0.688809\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4567.27 | 2.97769 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1485.29 | −0.946914 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 136.256 | 0.0849718 | 0.0424859 | − | 0.999097i | \(-0.486472\pi\) | ||||
0.0424859 | + | 0.999097i | \(0.486472\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1640.19 | 1.00086 | 0.500430 | − | 0.865777i | \(-0.333175\pi\) | ||||
0.500430 | + | 0.865777i | \(0.333175\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 172.842 | 0.103234 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4741.25 | 2.77261 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1061.14 | 0.607746 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6970.60 | 3.91106 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −30.6106 | −0.0168303 | −0.00841516 | − | 0.999965i | \(-0.502679\pi\) | ||||
−0.00841516 | + | 0.999965i | \(0.502679\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2601.86 | 1.40223 | 0.701113 | − | 0.713050i | \(-0.252687\pi\) | ||||
0.701113 | + | 0.713050i | \(0.252687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4592.76 | 2.42682 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −738.207 | −0.382543 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 134.723 | 0.0684845 | 0.0342422 | − | 0.999414i | \(-0.489098\pi\) | ||||
0.0342422 | + | 0.999414i | \(0.489098\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −63.4743 | −0.0316593 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 760.928 | 0.372481 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 926.826 | 0.445366 | 0.222683 | − | 0.974891i | \(-0.428519\pi\) | ||||
0.222683 | + | 0.974891i | \(0.428519\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2534.05 | −1.19561 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1934.24 | −0.896266 | −0.448133 | − | 0.893967i | \(-0.647911\pi\) | ||||
−0.448133 | + | 0.893967i | \(0.647911\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5331.92 | 2.42691 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8148.83 | −3.64419 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1627.32 | −0.715162 | −0.357581 | − | 0.933882i | \(-0.616398\pi\) | ||||
−0.357581 | + | 0.933882i | \(0.616398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −827.095 | −0.357272 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3840.94 | −1.63109 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 220.784 | 0.0921910 | 0.0460955 | − | 0.998937i | \(-0.485322\pi\) | ||||
0.0460955 | + | 0.998937i | \(0.485322\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2748.79 | −1.12882 | −0.564408 | − | 0.825496i | \(-0.690895\pi\) | ||||
−0.564408 | + | 0.825496i | \(0.690895\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2401.95 | 0.970259 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 929.014 | 0.369203 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4251.54 | 1.66258 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9827.81 | −3.78237 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1759.57 | −0.666586 | −0.333293 | − | 0.942823i | \(-0.608160\pi\) | ||||
−0.333293 | + | 0.942823i | \(0.608160\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3951.63 | 1.47381 | 0.736904 | − | 0.675998i | \(-0.236287\pi\) | ||||
0.736904 | + | 0.675998i | \(0.236287\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4023.97 | −1.47776 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2655.95 | −0.960551 | −0.480276 | − | 0.877118i | \(-0.659463\pi\) | ||||
−0.480276 | + | 0.877118i | \(0.659463\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4229.06 | −1.50648 | −0.753241 | − | 0.657745i | \(-0.771510\pi\) | ||||
−0.753241 | + | 0.657745i | \(0.771510\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4545.69 | 1.59516 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7021.34 | 2.42759 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1614.42 | −0.550028 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1357.63 | −0.455855 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7543.40 | −2.49659 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 88.7870 | 0.0289685 | 0.0144842 | − | 0.999895i | \(-0.495389\pi\) | ||||
0.0144842 | + | 0.999895i | \(0.495389\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7617.93 | 2.45057 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.9745 | 0.00570163 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4884.54 | −1.52804 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 106.354 | 0.0328163 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6751.28 | 2.05493 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4580.03 | 1.37534 | 0.687672 | − | 0.726022i | \(-0.258633\pi\) | ||||
0.687672 | + | 0.726022i | \(0.258633\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1475.69 | 0.437241 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 230.581 | 0.0674195 | 0.0337097 | − | 0.999432i | \(-0.489268\pi\) | ||||
0.0337097 | + | 0.999432i | \(0.489268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1673.24 | 0.482841 | 0.241421 | − | 0.970421i | \(-0.422387\pi\) | ||||
0.241421 | + | 0.970421i | \(0.422387\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −16767.2 | −4.77576 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4138.22 | 1.16354 | 0.581768 | − | 0.813355i | \(-0.302361\pi\) | ||||
0.581768 | + | 0.813355i | \(0.302361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −93.1753 | −0.0258642 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1992.96 | −0.546230 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4784.02 | 1.29478 | 0.647390 | − | 0.762159i | \(-0.275860\pi\) | ||||
0.647390 | + | 0.762159i | \(0.275860\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −67.4103 | −0.0180178 | −0.00900888 | − | 0.999959i | \(-0.502868\pi\) | ||||
−0.00900888 | + | 0.999959i | \(0.502868\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2752.47 | 0.726630 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3757.69 | −0.979879 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11978.6 | −3.08576 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7362.08 | 1.87371 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −216.815 | −0.0545230 | −0.0272615 | − | 0.999628i | \(-0.508679\pi\) | ||||
−0.0272615 | + | 0.999628i | \(0.508679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1256.76 | −0.312301 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3608.35 | −0.886132 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1285.87 | 0.312102 | 0.156051 | − | 0.987749i | \(-0.450124\pi\) | ||||
0.156051 | + | 0.987749i | \(0.450124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6147.07 | 1.47475 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12527.3 | −2.97097 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1238.80 | −0.290447 | −0.145224 | − | 0.989399i | \(-0.546390\pi\) | ||||
−0.145224 | + | 0.989399i | \(0.546390\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 34.2176 | 0.00793196 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1788.13 | −0.409857 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2162.86 | 0.490230 | 0.245115 | − | 0.969494i | \(-0.421174\pi\) | ||||
0.245115 | + | 0.969494i | \(0.421174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4060.78 | 0.910239 | 0.455120 | − | 0.890430i | \(-0.349597\pi\) | ||||
0.455120 | + | 0.890430i | \(0.349597\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26625.7 | −5.90278 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1366.05 | 0.299548 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 373.897 | 0.0811022 | 0.0405511 | − | 0.999177i | \(-0.487089\pi\) | ||||
0.0405511 | + | 0.999177i | \(0.487089\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8714.90 | 1.87006 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3776.83 | −0.801803 | −0.400901 | − | 0.916121i | \(-0.631303\pi\) | ||||
−0.400901 | + | 0.916121i | \(0.631303\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3114.71 | −0.654241 | −0.327121 | − | 0.944983i | \(-0.606078\pi\) | ||||
−0.327121 | + | 0.944983i | \(0.606078\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6402.20 | 1.33065 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10682.2 | −2.19704 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1140.96 | 0.232233 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10530.4 | 2.12131 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 350.402 | 0.0698659 | 0.0349330 | − | 0.999390i | \(-0.488878\pi\) | ||||
0.0349330 | + | 0.999390i | \(0.488878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2070.57 | 0.408654 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16231.8 | 3.17127 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1995.69 | −0.386000 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 118.933 | 0.0227747 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18315.4 | 3.47259 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1294.84 | −0.243089 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5292.26 | 0.983861 | 0.491931 | − | 0.870634i | \(-0.336291\pi\) | ||||
0.491931 | + | 0.870634i | \(0.336291\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2443.54 | −0.449865 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3921.72 | −0.715050 | −0.357525 | − | 0.933904i | \(-0.616379\pi\) | ||||
−0.357525 | + | 0.933904i | \(0.616379\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7396.40 | −1.33569 | −0.667843 | − | 0.744303i | \(-0.732782\pi\) | ||||
−0.667843 | + | 0.744303i | \(0.732782\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9764.27 | 1.74652 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8542.26 | −1.51351 | −0.756753 | − | 0.653701i | \(-0.773215\pi\) | ||||
−0.756753 | + | 0.653701i | \(0.773215\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11596.6 | −2.03537 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5052.37 | 0.878492 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10741.4 | −1.85036 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2169.23 | 0.370238 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17164.7 | 2.90277 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −616.519 | −0.103312 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8197.69 | −1.36129 | −0.680643 | − | 0.732615i | \(-0.738299\pi\) | ||||
−0.680643 | + | 0.732615i | \(0.738299\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10967.5 | −1.80485 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2450.48 | −0.399654 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −79.7920 | −0.0128978 | −0.00644888 | − | 0.999979i | \(-0.502053\pi\) | ||||
−0.00644888 | + | 0.999979i | \(0.502053\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −657.114 | −0.105279 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8067.41 | 1.28116 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13516.0 | −2.12769 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1066.64 | 0.166452 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5432.91 | −0.840501 | −0.420250 | − | 0.907408i | \(-0.638058\pi\) | ||||
−0.420250 | + | 0.907408i | \(0.638058\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5795.96 | −0.888970 | −0.444485 | − | 0.895786i | \(-0.646613\pi\) | ||||
−0.444485 | + | 0.895786i | \(0.646613\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 25775.5 | 3.91965 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 309.167 | 0.0466156 | 0.0233078 | − | 0.999728i | \(-0.492580\pi\) | ||||
0.0233078 | + | 0.999728i | \(0.492580\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4106.66 | −0.613969 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −23875.6 | −3.53958 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6416.01 | −0.943243 | −0.471622 | − | 0.881801i | \(-0.656331\pi\) | ||||
−0.471622 | + | 0.881801i | \(0.656331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12199.2 | 1.77857 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15347.9 | 2.21916 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −57.3333 | −0.00822182 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7471.41 | 1.06268 | 0.531341 | − | 0.847158i | \(-0.321688\pi\) | ||||
0.531341 | + | 0.847158i | \(0.321688\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19059.0 | 2.68881 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 226.410 | 0.0316835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5260.07 | 0.730177 | 0.365089 | − | 0.930973i | \(-0.381039\pi\) | ||||
0.365089 | + | 0.930973i | \(0.381039\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1159.39 | −0.159655 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18414.9 | −2.51570 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2919.86 | −0.395733 | −0.197867 | − | 0.980229i | \(-0.563401\pi\) | ||||
−0.197867 | + | 0.980229i | \(0.563401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12982.4 | −1.74569 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1320.08 | 0.176117 | 0.0880583 | − | 0.996115i | \(-0.471934\pi\) | ||||
0.0880583 | + | 0.996115i | \(0.471934\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9038.82 | 1.19652 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −212.198 | −0.0278724 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11445.1 | 1.49175 | 0.745874 | − | 0.666087i | \(-0.232032\pi\) | ||||
0.745874 | + | 0.666087i | \(0.232032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1789.57 | −0.231464 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15547.3 | −1.99557 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1074.36 | 0.136853 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8985.05 | 1.13589 | 0.567943 | − | 0.823068i | \(-0.307739\pi\) | ||||
0.567943 | + | 0.823068i | \(0.307739\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 42361.9 | 5.31515 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5793.76 | −0.721513 | −0.360756 | − | 0.932660i | \(-0.617481\pi\) | ||||
−0.360756 | + | 0.932660i | \(0.617481\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12810.7 | 1.58350 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5807.51 | −0.712536 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10152.6 | −1.23648 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12361.7 | −1.49449 | −0.747244 | − | 0.664550i | \(-0.768623\pi\) | ||||
−0.747244 | + | 0.664550i | \(0.768623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1263.79 | 0.151674 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13700.4 | 1.63234 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3968.74 | −0.469440 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15213.0 | 1.78653 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14854.1 | −1.73191 | −0.865955 | − | 0.500122i | \(-0.833289\pi\) | ||||
−0.865955 | + | 0.500122i | \(0.833289\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11243.5 | 1.30160 | 0.650799 | − | 0.759250i | \(-0.274434\pi\) | ||||
0.650799 | + | 0.759250i | \(0.274434\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1099.98 | 0.126437 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1945.18 | 0.222012 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8567.64 | −0.971001 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43975.5 | 4.94909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11909.7 | −1.33102 | −0.665509 | − | 0.746389i | \(-0.731786\pi\) | ||||
−0.665509 | + | 0.746389i | \(0.731786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4466.68 | 0.495739 | 0.247869 | − | 0.968793i | \(-0.420270\pi\) | ||||
0.247869 | + | 0.968793i | \(0.420270\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9842.22 | 1.08482 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3175.18 | 0.347573 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2376.49 | −0.258369 | −0.129184 | − | 0.991621i | \(-0.541236\pi\) | ||||
−0.129184 | + | 0.991621i | \(0.541236\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 44361.4 | 4.79014 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13887.4 | −1.48941 | −0.744705 | − | 0.667394i | \(-0.767410\pi\) | ||||
−0.744705 | + | 0.667394i | \(0.767410\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 963.941 | 0.102686 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −283.916 | −0.0300420 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2773.98 | −0.291563 | −0.145782 | − | 0.989317i | \(-0.546570\pi\) | ||||
−0.145782 | + | 0.989317i | \(0.546570\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17643.0 | 1.84207 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24132.5 | 2.50296 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 14353.3 | 1.47889 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14117.6 | −1.44506 | −0.722531 | − | 0.691339i | \(-0.757021\pi\) | ||||
−0.722531 | + | 0.691339i | \(0.757021\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 23113.3 | 2.35040 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8221.44 | 0.830609 | 0.415305 | − | 0.909682i | \(-0.363675\pi\) | ||||
0.415305 | + | 0.909682i | \(0.363675\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9887.11 | −0.992426 | −0.496213 | − | 0.868201i | \(-0.665276\pi\) | ||||
−0.496213 | + | 0.868201i | \(0.665276\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6846.94 | −0.682837 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3685.63 | −0.365205 | −0.182603 | − | 0.983187i | \(-0.558452\pi\) | ||||
−0.182603 | + | 0.983187i | \(0.558452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16214.2 | −1.59638 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1249.57 | 0.122244 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −196.432 | −0.0190951 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3451.29 | −0.333381 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −403.955 | −0.0387753 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 522.568 | 0.0498470 | 0.0249235 | − | 0.999689i | \(-0.492066\pi\) | ||||
0.0249235 | + | 0.999689i | \(0.492066\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16122.0 | −1.52827 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7057.68 | 0.664877 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5676.70 | −0.531475 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10610.0 | −0.987240 | −0.493620 | − | 0.869678i | \(-0.664327\pi\) | ||||
−0.493620 | + | 0.869678i | \(0.664327\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8596.41 | 0.794975 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10872.5 | −0.999328 | −0.499664 | − | 0.866219i | \(-0.666543\pi\) | ||||
−0.499664 | + | 0.866219i | \(0.666543\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16512.9 | −1.50853 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16126.9 | −1.46434 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27172.8 | −2.45245 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9152.41 | −0.821079 | −0.410539 | − | 0.911843i | \(-0.634660\pi\) | ||||
−0.410539 | + | 0.911843i | \(0.634660\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17940.3 | −1.59983 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9969.46 | 0.883730 | 0.441865 | − | 0.897082i | \(-0.354317\pi\) | ||||
0.441865 | + | 0.897082i | \(0.354317\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9873.44 | −0.870024 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 49454.1 | 4.33202 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7978.16 | 0.694746 | 0.347373 | − | 0.937727i | \(-0.387074\pi\) | ||||
0.347373 | + | 0.937727i | \(0.387074\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −379.361 | −0.0328414 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −41009.3 | −3.52944 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1317.26 | 0.112709 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1018.26 | 0.0866206 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15093.6 | −1.27656 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7429.85 | −0.624775 | −0.312388 | − | 0.949955i | \(-0.601129\pi\) | ||||
−0.312388 | + | 0.949955i | \(0.601129\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9875.34 | −0.825656 | −0.412828 | − | 0.910809i | \(-0.635459\pi\) | ||||
−0.412828 | + | 0.910809i | \(0.635459\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7671.39 | −0.637728 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11487.6 | 0.949537 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24444.1 | −1.99771 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28016.4 | 2.27678 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2723.62 | −0.220098 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2047.80 | 0.164560 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 41065.5 | 3.28167 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11137.6 | −0.885107 | −0.442554 | − | 0.896742i | \(-0.645927\pi\) | ||||
−0.442554 | + | 0.896742i | \(0.645927\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25495.3 | −2.01493 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9253.08 | −0.727263 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4180.81 | 0.326798 | 0.163399 | − | 0.986560i | \(-0.447754\pi\) | ||||
0.163399 | + | 0.986560i | \(0.447754\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15286.2 | 1.18834 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 29298.5 | 2.26526 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7108.78 | 0.546647 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8616.70 | 0.659024 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25536.3 | 1.94256 | 0.971281 | − | 0.237934i | \(-0.0764703\pi\) | ||||
0.971281 | + | 0.237934i | \(0.0764703\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −311.927 | −0.0236013 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 39433.4 | 2.96770 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12434.8 | −0.930843 | −0.465421 | − | 0.885089i | \(-0.654097\pi\) | ||||
−0.465421 | + | 0.885089i | \(0.654097\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 354.236 | 0.0263767 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −38426.9 | −2.84617 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2063.43 | −0.152027 | −0.0760136 | − | 0.997107i | \(-0.524219\pi\) | ||||
−0.0760136 | + | 0.997107i | \(0.524219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11092.0 | −0.812931 | −0.406466 | − | 0.913666i | \(-0.633239\pi\) | ||||
−0.406466 | + | 0.913666i | \(0.633239\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16320.2 | −1.18985 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −575.000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16235.7 | 1.17141 | 0.585704 | − | 0.810525i | \(-0.300818\pi\) | ||||
0.585704 | + | 0.810525i | \(0.300818\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36651.8 | 2.63074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26260.2 | −1.87514 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −373.943 | −0.0265645 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25608.9 | −1.80991 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17018.6 | −1.19665 | −0.598326 | − | 0.801253i | \(-0.704167\pi\) | ||||
−0.598326 | + | 0.801253i | \(0.704167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20382.1 | −1.42586 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24634.2 | −1.71458 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24478.2 | 1.69511 | 0.847553 | − | 0.530710i | \(-0.178075\pi\) | ||||
0.847553 | + | 0.530710i | \(0.178075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12870.8 | 0.886809 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −39224.9 | −2.68906 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17530.9 | −1.19581 | −0.597906 | − | 0.801566i | \(-0.704000\pi\) | ||||
−0.597906 | + | 0.801566i | \(0.704000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27897.8 | 1.89347 | 0.946735 | − | 0.322014i | \(-0.104360\pi\) | ||||
0.946735 | + | 0.322014i | \(0.104360\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 28929.1 | 1.95371 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8273.71 | −0.555990 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17540.7 | −1.17291 | −0.586455 | − | 0.809982i | \(-0.699477\pi\) | ||||
−0.586455 | + | 0.809982i | \(0.699477\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 65123.6 | 4.33324 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1616.95 | 0.107062 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18165.6 | −1.19690 | −0.598452 | − | 0.801159i | \(-0.704217\pi\) | ||||
−0.598452 | + | 0.801159i | \(0.704217\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14973.9 | −0.981796 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14018.2 | −0.914670 | −0.457335 | − | 0.889294i | \(-0.651196\pi\) | ||||
−0.457335 | + | 0.889294i | \(0.651196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9284.22 | 0.602851 | 0.301425 | − | 0.953490i | \(-0.402538\pi\) | ||||
0.301425 | + | 0.953490i | \(0.402538\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6832.33 | −0.441501 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6378.17 | 0.410170 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −69965.8 | −4.45640 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −14456.8 | −0.916423 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16783.2 | −1.05884 | −0.529421 | − | 0.848359i | \(-0.677591\pi\) | ||||
−0.529421 | + | 0.848359i | \(0.677591\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 823.508 | 0.0517085 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6998.53 | 0.437367 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 65210.5 | 4.05610 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 48481.1 | 3.00138 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −15727.9 | −0.969133 | −0.484566 | − | 0.874755i | \(-0.661023\pi\) | ||||
−0.484566 | + | 0.874755i | \(0.661023\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14597.8 | 0.895304 | 0.447652 | − | 0.894208i | \(-0.352260\pi\) | ||||
0.447652 | + | 0.894208i | \(0.352260\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 166.715 | 0.0101774 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22525.0 | 1.36870 | 0.684349 | − | 0.729155i | \(-0.260086\pi\) | ||||
0.684349 | + | 0.729155i | \(0.260086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22627.9 | −1.36860 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45304.6 | −2.72754 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −37.7999 | −0.00226527 | −0.00113264 | − | 0.999999i | \(-0.500361\pi\) | ||||
−0.00113264 | + | 0.999999i | \(0.500361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8381.21 | 0.499971 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 676.849 | 0.0401924 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28100.6 | 1.66107 | 0.830535 | − | 0.556966i | \(-0.188035\pi\) | ||||
0.830535 | + | 0.556966i | \(0.188035\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9234.91 | −0.543414 | −0.271707 | − | 0.962380i | \(-0.587588\pi\) | ||||
−0.271707 | + | 0.962380i | \(0.587588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 62618.8 | 3.66804 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22836.3 | −1.33166 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4881.26 | 0.283363 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 42480.2 | 2.45498 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14150.5 | 0.814119 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20976.3 | −1.20145 | −0.600725 | − | 0.799456i | \(-0.705121\pi\) | ||||
−0.600725 | + | 0.799456i | \(0.705121\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7426.45 | 0.423473 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21323.0 | 1.21050 | 0.605251 | − | 0.796034i | \(-0.293073\pi\) | ||||
0.605251 | + | 0.796034i | \(0.293073\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −37561.4 | −2.12294 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2138.66 | 0.120343 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15058.2 | 0.843608 | 0.421804 | − | 0.906687i | \(-0.361397\pi\) | ||||
0.421804 | + | 0.906687i | \(0.361397\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −681.280 | −0.0380005 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15519.4 | 0.861868 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −593.807 | −0.0328334 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15327.4 | 0.843821 | 0.421911 | − | 0.906637i | \(-0.361360\pi\) | ||||
0.421911 | + | 0.906637i | \(0.361360\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −106708. | −5.84920 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8200.97 | −0.447598 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25122.6 | 1.36526 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38382.4 | 2.07691 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19724.0 | −1.06272 | −0.531358 | − | 0.847147i | \(-0.678318\pi\) | ||||
−0.531358 | + | 0.847147i | \(0.678318\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25650.3 | 1.37613 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −864.210 | −0.0461674 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −65330.2 | −3.47524 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6024.59 | 0.319123 | 0.159562 | − | 0.987188i | \(-0.448992\pi\) | ||||
0.159562 | + | 0.987188i | \(0.448992\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12683.3 | −0.669004 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3395.75 | −0.178362 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23706.2 | −1.23995 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 44372.3 | 2.31118 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7618.85 | 0.395181 | 0.197591 | − | 0.980285i | \(-0.436688\pi\) | ||||
0.197591 | + | 0.980285i | \(0.436688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8715.99 | 0.450209 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −625.237 | −0.0321616 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5305.72 | −0.271792 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4030.71 | −0.205627 | −0.102813 | − | 0.994701i | \(-0.532784\pi\) | ||||
−0.102813 | + | 0.994701i | \(0.532784\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −5831.08 | −0.296250 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −279.709 | −0.0141524 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4186.96 | −0.210981 | −0.105490 | − | 0.994420i | \(-0.533641\pi\) | ||||
−0.105490 | + | 0.994420i | \(0.533641\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −34853.0 | −1.74908 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 26779.8 | 1.33846 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15299.2 | 0.761556 | 0.380778 | − | 0.924666i | \(-0.375656\pi\) | ||||
0.380778 | + | 0.924666i | \(0.375656\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −111103. | −5.50806 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32208.7 | 1.59034 | 0.795169 | − | 0.606388i | \(-0.207382\pi\) | ||||
0.795169 | + | 0.606388i | \(0.207382\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 153.053 | 0.00752674 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 46852.9 | 2.29486 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18021.6 | −0.879163 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27095.1 | 1.31653 | 0.658265 | − | 0.752787i | \(-0.271291\pi\) | ||||
0.658265 | + | 0.752787i | \(0.271291\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2010.98 | −0.0973232 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13009.3 | −0.627094 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31829.6 | −1.52822 | −0.764112 | − | 0.645083i | \(-0.776823\pi\) | ||||
−0.764112 | + | 0.645083i | \(0.776823\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11656.6 | −0.557455 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7041.33 | 0.335411 | 0.167706 | − | 0.985837i | \(-0.446364\pi\) | ||||
0.167706 | + | 0.985837i | \(0.446364\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −61225.4 | −2.90499 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22963.8 | −1.08531 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35932.3 | −1.69158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16296.5 | 0.764198 | 0.382099 | − | 0.924121i | \(-0.375201\pi\) | ||||
0.382099 | + | 0.924121i | \(0.375201\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11926.6 | 0.557101 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25481.8 | 1.18566 | 0.592830 | − | 0.805327i | \(-0.298010\pi\) | ||||
0.592830 | + | 0.805327i | \(0.298010\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3691.03 | 0.171079 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 57014.7 | 2.63242 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −44574.5 | −2.05012 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 44879.2 | 2.05621 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −63044.3 | −2.87742 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −673.615 | −0.0306272 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22862.8 | −1.03554 | −0.517770 | − | 0.855520i | \(-0.673238\pi\) | ||||
−0.517770 | + | 0.855520i | \(0.673238\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11490.0 | −0.518447 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2343.89 | 0.105359 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22470.5 | 1.00624 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 317.371 | 0.0141585 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9293.68 | −0.413048 | −0.206524 | − | 0.978442i | \(-0.566215\pi\) | ||||
−0.206524 | + | 0.978442i | \(0.566215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1449.94 | 0.0641993 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11379.8 | −0.501979 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 626.561 | 0.0275353 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3804.64 | −0.166579 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20060.8 | 0.875058 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27526.0 | −1.19625 | −0.598123 | − | 0.801405i | \(-0.704086\pi\) | ||||
−0.598123 | + | 0.801405i | \(0.704086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20552.6 | −0.889888 | −0.444944 | − | 0.895558i | \(-0.646776\pi\) | ||||
−0.444944 | + | 0.895558i | \(0.646776\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 37664.1 | 1.62477 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4634.13 | −0.199174 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 496.281 | 0.0212517 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −169448. | −7.22953 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22182.6 | 0.942971 | 0.471486 | − | 0.881874i | \(-0.343718\pi\) | ||||
0.471486 | + | 0.881874i | \(0.343718\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24099.2 | −1.02071 | −0.510355 | − | 0.859964i | \(-0.670486\pi\) | ||||
−0.510355 | + | 0.859964i | \(0.670486\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12670.2 | 0.534692 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 32947.6 | 1.38537 | 0.692685 | − | 0.721240i | \(-0.256428\pi\) | ||||
0.692685 | + | 0.721240i | \(0.256428\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47467.0 | −1.98866 | −0.994329 | − | 0.106352i | \(-0.966083\pi\) | ||||
−0.994329 | + | 0.106352i | \(0.966083\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3467.94 | 0.144767 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 58475.1 | 2.43223 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9671.22 | 0.400822 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 43858.1 | 1.81118 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35808.6 | −1.47348 | −0.736741 | − | 0.676175i | \(-0.763636\pi\) | ||||
−0.736741 | + | 0.676175i | \(0.763636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20652.1 | 0.846778 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −35030.5 | −1.43121 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26659.6 | −1.08535 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −54745.2 | −2.22086 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28889.2 | −1.16782 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4273.46 | 0.172142 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29776.0 | −1.19521 | −0.597604 | − | 0.801791i | \(-0.703880\pi\) | ||||
−0.597604 | + | 0.801791i | \(0.703880\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 40744.1 | 1.62973 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21287.4 | 0.848500 | 0.424250 | − | 0.905545i | \(-0.360538\pi\) | ||||
0.424250 | + | 0.905545i | \(0.360538\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36073.0 | −1.43282 | −0.716412 | − | 0.697677i | \(-0.754217\pi\) | ||||
−0.716412 | + | 0.697677i | \(0.754217\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −99078.5 | −3.92170 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8228.21 | −0.324556 | −0.162278 | − | 0.986745i | \(-0.551884\pi\) | ||||
−0.162278 | + | 0.986745i | \(0.551884\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8136.61 | 0.319830 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10582.5 | 0.414535 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11741.0 | −0.458327 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 42525.3 | 1.65432 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 67016.2 | 2.59812 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4135.48 | 0.159777 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35683.8 | −1.37395 | −0.686977 | − | 0.726679i | \(-0.741063\pi\) | ||||
−0.686977 | + | 0.726679i | \(0.741063\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3250.02 | 0.124710 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14849.8 | 0.567881 | 0.283940 | − | 0.958842i | \(-0.408358\pi\) | ||||
0.283940 | + | 0.958842i | \(0.408358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11821.6 | 0.450542 | 0.225271 | − | 0.974296i | \(-0.427673\pi\) | ||||
0.225271 | + | 0.974296i | \(0.427673\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19204.7 | 0.729445 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11012.0 | −0.416851 | −0.208426 | − | 0.978038i | \(-0.566834\pi\) | ||||
−0.208426 | + | 0.978038i | \(0.566834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 46307.6 | 1.74703 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 63466.7 | 2.38632 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2572.60 | −0.0964039 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1103.92 | −0.0412291 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −18510.3 | −0.689008 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31333.8 | −1.16245 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −532.475 | −0.0196885 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1103.12 | 0.0406527 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 13743.9 | 0.504822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5387.11 | −0.197217 | −0.0986086 | − | 0.995126i | \(-0.531439\pi\) | ||||
−0.0986086 | + | 0.995126i | \(0.531439\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 116561. | 4.25311 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20928.2 | −0.761122 | −0.380561 | − | 0.924756i | \(-0.624269\pi\) | ||||
−0.380561 | + | 0.924756i | \(0.624269\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43371.9 | 1.57218 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12009.8 | −0.433913 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 55456.5 | 1.99709 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 44252.4 | 1.58842 | 0.794208 | − | 0.607647i | \(-0.207886\pi\) | ||||
0.794208 | + | 0.607647i | \(0.207886\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 49086.3 | 1.75619 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 71266.4 | 2.54145 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4645.07 | −0.165112 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15550.9 | −0.550980 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 354.349 | 0.0125143 | 0.00625717 | − | 0.999980i | \(-0.498008\pi\) | ||||
0.00625717 | + | 0.999980i | \(0.498008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −103751. | −3.65231 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36374.4 | −1.27636 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21257.7 | −0.743530 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26221.9 | 0.914228 | 0.457114 | − | 0.889408i | \(-0.348883\pi\) | ||||
0.457114 | + | 0.889408i | \(0.348883\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −68602.4 | −2.38419 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17076.4 | −0.591578 | −0.295789 | − | 0.955253i | \(-0.595583\pi\) | ||||
−0.295789 | + | 0.955253i | \(0.595583\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7426.31 | −0.256452 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 49139.1 | 1.69153 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43933.6 | 1.50755 | 0.753775 | − | 0.657132i | \(-0.228231\pi\) | ||||
0.753775 | + | 0.657132i | \(0.228231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 994.955 | 0.0340333 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −79230.3 | −2.70160 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15779.8 | −0.536366 | −0.268183 | − | 0.963368i | \(-0.586423\pi\) | ||||
−0.268183 | + | 0.963368i | \(0.586423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8797.85 | 0.298106 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −107560. | −3.63313 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4507.87 | −0.151790 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7993.02 | −0.268303 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 32153.7 | 1.07595 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19758.2 | −0.659107 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22495.0 | 0.748076 | 0.374038 | − | 0.927413i | \(-0.377973\pi\) | ||||
0.374038 | + | 0.927413i | \(0.377973\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −99627.5 | −3.30289 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30483.9 | −1.00749 | −0.503745 | − | 0.863852i | \(-0.668045\pi\) | ||||
−0.503745 | + | 0.863852i | \(0.668045\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54263.9 | −1.78789 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 20119.9 | 0.660873 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20890.7 | −0.684087 | −0.342043 | − | 0.939684i | \(-0.611119\pi\) | ||||
−0.342043 | + | 0.939684i | \(0.611119\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10534.3 | −0.343900 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 109237. | 3.55522 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −11588.6 | −0.376011 | −0.188006 | − | 0.982168i | \(-0.560202\pi\) | ||||
−0.188006 | + | 0.982168i | \(0.560202\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13279.8 | 0.429572 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5718.27 | −0.184412 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 82.6827 | 0.00265840 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46035.4 | −1.47564 | −0.737822 | − | 0.674996i | \(-0.764146\pi\) | ||||
−0.737822 | + | 0.674996i | \(0.764146\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −76034.4 | −2.42989 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21145.3 | 0.673719 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −44523.8 | −1.41433 | −0.707163 | − | 0.707050i | \(-0.750025\pi\) | ||||
−0.707163 | + | 0.707050i | \(0.750025\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −55194.2 | −1.74802 |
(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.bb.1.9 | 10 | ||
4.3 | odd | 2 | 920.4.a.g.1.2 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.4.a.g.1.2 | ✓ | 10 | 4.3 | odd | 2 | ||
1840.4.a.bb.1.9 | 10 | 1.1 | even | 1 | trivial |