Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,6,Mod(1,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.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: | \(144.345437832\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | no (minimal twist has level 300) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.64575\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 147.745 | 1.13964 | 0.569820 | − | 0.821769i | \(-0.307013\pi\) | ||||
0.569820 | + | 0.821769i | \(0.307013\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −662.235 | −1.65018 | −0.825089 | − | 0.565003i | \(-0.808875\pi\) | ||||
−0.825089 | + | 0.565003i | \(0.808875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 629.980 | 1.03388 | 0.516938 | − | 0.856023i | \(-0.327072\pi\) | ||||
0.516938 | + | 0.856023i | \(0.327072\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1082.24 | 0.908237 | 0.454119 | − | 0.890941i | \(-0.349954\pi\) | ||||
0.454119 | + | 0.890941i | \(0.349954\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2521.20 | −1.60222 | −0.801111 | − | 0.598516i | \(-0.795757\pi\) | ||||
−0.801111 | + | 0.598516i | \(0.795757\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1802.24 | 0.710382 | 0.355191 | − | 0.934794i | \(-0.384416\pi\) | ||||
0.355191 | + | 0.934794i | \(0.384416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6237.53 | −1.37727 | −0.688633 | − | 0.725110i | \(-0.741789\pi\) | ||||
−0.688633 | + | 0.725110i | \(0.741789\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5617.75 | 1.04992 | 0.524962 | − | 0.851126i | \(-0.324080\pi\) | ||||
0.524962 | + | 0.851126i | \(0.324080\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1199.41 | 0.144034 | 0.0720168 | − | 0.997403i | \(-0.477056\pi\) | ||||
0.0720168 | + | 0.997403i | \(0.477056\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10016.2 | −0.930561 | −0.465281 | − | 0.885163i | \(-0.654047\pi\) | ||||
−0.465281 | + | 0.885163i | \(0.654047\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10734.6 | −0.885350 | −0.442675 | − | 0.896682i | \(-0.645970\pi\) | ||||
−0.442675 | + | 0.896682i | \(0.645970\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3803.65 | 0.251163 | 0.125581 | − | 0.992083i | \(-0.459920\pi\) | ||||
0.125581 | + | 0.992083i | \(0.459920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5021.61 | 0.298781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −15800.9 | −0.772668 | −0.386334 | − | 0.922359i | \(-0.626259\pi\) | ||||
−0.386334 | + | 0.922359i | \(0.626259\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1734.24 | −0.0648602 | −0.0324301 | − | 0.999474i | \(-0.510325\pi\) | ||||
−0.0324301 | + | 0.999474i | \(0.510325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11199.7 | 0.385374 | 0.192687 | − | 0.981260i | \(-0.438280\pi\) | ||||
0.192687 | + | 0.981260i | \(0.438280\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 48604.8 | 1.32279 | 0.661396 | − | 0.750037i | \(-0.269964\pi\) | ||||
0.661396 | + | 0.750037i | \(0.269964\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −68965.9 | −1.62364 | −0.811818 | − | 0.583911i | \(-0.801522\pi\) | ||||
−0.811818 | + | 0.583911i | \(0.801522\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −80654.7 | −1.77142 | −0.885712 | − | 0.464235i | \(-0.846329\pi\) | ||||
−0.885712 | + | 0.464235i | \(0.846329\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −97842.0 | −1.88061 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 82056.9 | 1.47927 | 0.739635 | − | 0.673008i | \(-0.234998\pi\) | ||||
0.739635 | + | 0.673008i | \(0.234998\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 85683.4 | 1.36522 | 0.682608 | − | 0.730785i | \(-0.260846\pi\) | ||||
0.682608 | + | 0.730785i | \(0.260846\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −25845.6 | −0.345870 | −0.172935 | − | 0.984933i | \(-0.555325\pi\) | ||||
−0.172935 | + | 0.984933i | \(0.555325\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 93076.5 | 1.17825 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9935.27 | −0.107214 | −0.0536068 | − | 0.998562i | \(-0.517072\pi\) | ||||
−0.0536068 | + | 0.998562i | \(0.517072\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −44176.5 | −0.430911 | −0.215456 | − | 0.976514i | \(-0.569124\pi\) | ||||
−0.215456 | + | 0.976514i | \(0.569124\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 131554. | 1.22183 | 0.610914 | − | 0.791697i | \(-0.290802\pi\) | ||||
0.610914 | + | 0.791697i | \(0.290802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −170825. | −1.44242 | −0.721210 | − | 0.692716i | \(-0.756414\pi\) | ||||
−0.721210 | + | 0.692716i | \(0.756414\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −28667.9 | −0.231115 | −0.115558 | − | 0.993301i | \(-0.536866\pi\) | ||||
−0.115558 | + | 0.993301i | \(0.536866\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 85548.0 | 0.630251 | 0.315126 | − | 0.949050i | \(-0.397953\pi\) | ||||
0.315126 | + | 0.949050i | \(0.397953\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 159895. | 1.03506 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 277505. | 1.72308 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 109853. | 0.604368 | 0.302184 | − | 0.953250i | \(-0.402284\pi\) | ||||
0.302184 | + | 0.953250i | \(0.402284\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −390140. | −1.98629 | −0.993145 | − | 0.116892i | \(-0.962707\pi\) | ||||
−0.993145 | + | 0.116892i | \(0.962707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −372494. | −1.82596 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 302596. | 1.37741 | 0.688703 | − | 0.725044i | \(-0.258180\pi\) | ||||
0.688703 | + | 0.725044i | \(0.258180\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 125596. | 0.551367 | 0.275683 | − | 0.961249i | \(-0.411096\pi\) | ||||
0.275683 | + | 0.961249i | \(0.411096\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −417195. | −1.70608 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 84368.4 | 0.311325 | 0.155662 | − | 0.987810i | \(-0.450249\pi\) | ||||
0.155662 | + | 0.987810i | \(0.450249\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −454944. | −1.62374 | −0.811869 | − | 0.583840i | \(-0.801550\pi\) | ||||
−0.811869 | + | 0.583840i | \(0.801550\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −109519. | −0.354602 | −0.177301 | − | 0.984157i | \(-0.556737\pi\) | ||||
−0.177301 | + | 0.984157i | \(0.556737\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 266271. | 0.809580 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −420668. | −1.24014 | −0.620070 | − | 0.784547i | \(-0.712896\pi\) | ||||
−0.620070 | + | 0.784547i | \(0.712896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −207627. | −0.576094 | −0.288047 | − | 0.957616i | \(-0.593006\pi\) | ||||
−0.288047 | + | 0.957616i | \(0.593006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25582.2 | 0.0689003 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −665522. | −1.69063 | −0.845313 | − | 0.534272i | \(-0.820586\pi\) | ||||
−0.845313 | + | 0.534272i | \(0.820586\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −431788. | −1.00725 | −0.503626 | − | 0.863922i | \(-0.668001\pi\) | ||||
−0.503626 | + | 0.863922i | \(0.668001\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −588263. | −1.33467 | −0.667336 | − | 0.744756i | \(-0.732566\pi\) | ||||
−0.667336 | + | 0.744756i | \(0.732566\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −716694. | −1.49875 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −653915. | −1.29699 | −0.648496 | − | 0.761218i | \(-0.724602\pi\) | ||||
−0.648496 | + | 0.761218i | \(0.724602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 293969. | 0.568078 | 0.284039 | − | 0.958813i | \(-0.408326\pi\) | ||||
0.284039 | + | 0.958813i | \(0.408326\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −692255. | −1.27087 | −0.635434 | − | 0.772155i | \(-0.719179\pi\) | ||||
−0.635434 | + | 0.772155i | \(0.719179\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −89145.7 | −0.159576 | −0.0797880 | − | 0.996812i | \(-0.525424\pi\) | ||||
−0.0797880 | + | 0.996812i | \(0.525424\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −921564. | −1.56959 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.66962e6 | 2.64395 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −300548. | −0.464737 | −0.232369 | − | 0.972628i | \(-0.574648\pi\) | ||||
−0.232369 | + | 0.972628i | \(0.574648\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 829994. | 1.19654 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 681787. | 0.939005 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.22316e6 | 1.64710 | 0.823549 | − | 0.567245i | \(-0.191991\pi\) | ||||
0.823549 | + | 0.567245i | \(0.191991\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.35994e6 | 1.75168 | 0.875839 | − | 0.482603i | \(-0.160308\pi\) | ||||
0.875839 | + | 0.482603i | \(0.160308\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 171691. | 0.216351 | 0.108176 | − | 0.994132i | \(-0.465499\pi\) | ||||
0.108176 | + | 0.994132i | \(0.465499\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −741362. | −0.894624 | −0.447312 | − | 0.894378i | \(-0.647619\pi\) | ||||
−0.447312 | + | 0.894378i | \(0.647619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 309086. | 0.350013 | 0.175006 | − | 0.984567i | \(-0.444005\pi\) | ||||
0.175006 | + | 0.984567i | \(0.444005\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.44908e6 | −1.60712 | −0.803561 | − | 0.595223i | \(-0.797064\pi\) | ||||
−0.803561 | + | 0.595223i | \(0.797064\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.58830e6 | −1.65650 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.14053e6 | 1.14268 | 0.571338 | − | 0.820715i | \(-0.306425\pi\) | ||||
0.571338 | + | 0.820715i | \(0.306425\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.19350e6 | −1.17226 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −646450. | −0.610523 | −0.305261 | − | 0.952269i | \(-0.598744\pi\) | ||||
−0.305261 | + | 0.952269i | \(0.598744\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 177207. | 0.164147 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.06070e6 | −0.945591 | −0.472795 | − | 0.881172i | \(-0.656755\pi\) | ||||
−0.472795 | + | 0.881172i | \(0.656755\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.19054e6 | 1.84574 | 0.922868 | − | 0.385116i | \(-0.125838\pi\) | ||||
0.922868 | + | 0.385116i | \(0.125838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 874765. | 0.723550 | 0.361775 | − | 0.932265i | \(-0.382171\pi\) | ||||
0.361775 | + | 0.932265i | \(0.382171\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.32986e6 | −1.04137 | −0.520687 | − | 0.853748i | \(-0.674324\pi\) | ||||
−0.520687 | + | 0.853748i | \(0.674324\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.81200e6 | −1.36896 | −0.684482 | − | 0.729030i | \(-0.739971\pi\) | ||||
−0.684482 | + | 0.729030i | \(0.739971\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.98848e6 | −1.47589 | −0.737946 | − | 0.674860i | \(-0.764204\pi\) | ||||
−0.737946 | + | 0.674860i | \(0.764204\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.47985e6 | −1.06051 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −248624. | −0.175105 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.22419e6 | −1.51357 | −0.756785 | − | 0.653664i | \(-0.773231\pi\) | ||||
−0.756785 | + | 0.653664i | \(0.773231\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.13537e6 | 0.734447 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.58599e6 | −1.00898 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −535556. | −0.324309 | −0.162155 | − | 0.986765i | \(-0.551844\pi\) | ||||
−0.162155 | + | 0.986765i | \(0.551844\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.14998e6 | −1.26047 | −0.630236 | − | 0.776403i | \(-0.717042\pi\) | ||||
−0.630236 | + | 0.776403i | \(0.717042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 319986. | 0.184616 | 0.0923081 | − | 0.995730i | \(-0.470576\pi\) | ||||
0.0923081 | + | 0.995730i | \(0.470576\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.04672e6 | −0.585033 | −0.292517 | − | 0.956260i | \(-0.594493\pi\) | ||||
−0.292517 | + | 0.956260i | \(0.594493\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.13071e6 | 2.27273 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.72853e6 | −1.45520 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 561970. | 0.286235 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.47074e6 | −0.737845 | −0.368923 | − | 0.929460i | \(-0.620273\pi\) | ||||
−0.368923 | + | 0.929460i | \(0.620273\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.05286e6 | 0.984657 | 0.492329 | − | 0.870409i | \(-0.336146\pi\) | ||||
0.492329 | + | 0.870409i | \(0.336146\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.72027e6 | −1.73256 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.74123e6 | −0.799138 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.44297e6 | 0.643330 | 0.321665 | − | 0.946854i | \(-0.395758\pi\) | ||||
0.321665 | + | 0.946854i | \(0.395758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.53038e6 | −1.55152 | −0.775761 | − | 0.631027i | \(-0.782634\pi\) | ||||
−0.775761 | + | 0.631027i | \(0.782634\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.46715e6 | 1.05380 | 0.526900 | − | 0.849927i | \(-0.323354\pi\) | ||||
0.526900 | + | 0.849927i | \(0.323354\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.26610e6 | −1.33750 | −0.668748 | − | 0.743489i | \(-0.733170\pi\) | ||||
−0.668748 | + | 0.743489i | \(0.733170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.88033e6 | 1.56711 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.16639e6 | 0.839596 | 0.419798 | − | 0.907617i | \(-0.362101\pi\) | ||||
0.419798 | + | 0.907617i | \(0.362101\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.33451e6 | −0.880564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.68582e6 | −1.74387 | −0.871933 | − | 0.489625i | \(-0.837134\pi\) | ||||
−0.871933 | + | 0.489625i | \(0.837134\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.92952e6 | −1.42392 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.99853e6 | 1.42989 | 0.714944 | − | 0.699182i | \(-0.246452\pi\) | ||||
0.714944 | + | 0.699182i | \(0.246452\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.83762e6 | −0.640115 | −0.320057 | − | 0.947398i | \(-0.603702\pi\) | ||||
−0.320057 | + | 0.947398i | \(0.603702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.57983e6 | −1.19947 | −0.599734 | − | 0.800200i | \(-0.704727\pi\) | ||||
−0.599734 | + | 0.800200i | \(0.704727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.95044e6 | 0.645195 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.43403e6 | 0.775086 | 0.387543 | − | 0.921852i | \(-0.373324\pi\) | ||||
0.387543 | + | 0.921852i | \(0.373324\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.04925e6 | 0.636406 | 0.318203 | − | 0.948023i | \(-0.396921\pi\) | ||||
0.318203 | + | 0.948023i | \(0.396921\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.53907e6 | 1.08549 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −794293. | −0.237681 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.67579e6 | −1.38212 | −0.691061 | − | 0.722796i | \(-0.742856\pi\) | ||||
−0.691061 | + | 0.722796i | \(0.742856\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −256225. | −0.0739173 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.86934e6 | 0.798449 | 0.399225 | − | 0.916853i | \(-0.369279\pi\) | ||||
0.399225 | + | 0.916853i | \(0.369279\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −495614. | −0.136282 | −0.0681410 | − | 0.997676i | \(-0.521707\pi\) | ||||
−0.0681410 | + | 0.997676i | \(0.521707\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.65470e6 | 0.439188 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.66876e6 | −0.951319 | −0.475659 | − | 0.879630i | \(-0.657790\pi\) | ||||
−0.475659 | + | 0.879630i | \(0.657790\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.62199e6 | −0.415746 | −0.207873 | − | 0.978156i | \(-0.566654\pi\) | ||||
−0.207873 | + | 0.978156i | \(0.566654\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.54379e6 | −1.13819 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.66935e6 | 0.908716 | 0.454358 | − | 0.890819i | \(-0.349869\pi\) | ||||
0.454358 | + | 0.890819i | \(0.349869\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.01410e6 | −0.245512 | −0.122756 | − | 0.992437i | \(-0.539173\pi\) | ||||
−0.122756 | + | 0.992437i | \(0.539173\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.43185e6 | 1.27154 | 0.635772 | − | 0.771877i | \(-0.280682\pi\) | ||||
0.635772 | + | 0.771877i | \(0.280682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.63310e6 | 1.53559 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.58390e6 | −1.25068 | −0.625341 | − | 0.780351i | \(-0.715040\pi\) | ||||
−0.625341 | + | 0.780351i | \(0.715040\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 420777. | 0.0922145 | 0.0461073 | − | 0.998936i | \(-0.485318\pi\) | ||||
0.0461073 | + | 0.998936i | \(0.485318\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 512658. | 0.111141 | 0.0555706 | − | 0.998455i | \(-0.482302\pi\) | ||||
0.0555706 | + | 0.998455i | \(0.482302\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.14897e6 | 1.94124 | 0.970621 | − | 0.240612i | \(-0.0773482\pi\) | ||||
0.970621 | + | 0.240612i | \(0.0773482\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.18111e6 | 1.50751 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 7.10884e6 | 1.46098 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.15726e6 | 0.230458 | 0.115229 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115229 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 755606. | 0.148913 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.75578e6 | −0.335465 | −0.167732 | − | 0.985833i | \(-0.553644\pi\) | ||||
−0.167732 | + | 0.985833i | \(0.553644\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.64300e6 | −0.869150 | −0.434575 | − | 0.900636i | \(-0.643101\pi\) | ||||
−0.434575 | + | 0.900636i | \(0.643101\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.75047e6 | −1.25088 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.01894e7 | −1.85036 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.50099e6 | −0.629419 | −0.314709 | − | 0.949188i | \(-0.601907\pi\) | ||||
−0.314709 | + | 0.949188i | \(0.601907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.80449e6 | 1.19916 | 0.599578 | − | 0.800316i | \(-0.295335\pi\) | ||||
0.599578 | + | 0.800316i | \(0.295335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 803645. | 0.137490 | 0.0687448 | − | 0.997634i | \(-0.478101\pi\) | ||||
0.0687448 | + | 0.997634i | \(0.478101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.19163e7 | −2.01879 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.51891e6 | −0.414463 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.15940e6 | 0.832731 | 0.416366 | − | 0.909197i | \(-0.363304\pi\) | ||||
0.416366 | + | 0.909197i | \(0.363304\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.23531e6 | 0.677065 | 0.338533 | − | 0.940955i | \(-0.390069\pi\) | ||||
0.338533 | + | 0.940955i | \(0.390069\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.07972e6 | 0.953580 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.18829e6 | −0.495358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.31003e6 | −0.962085 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.32549e6 | −0.493041 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.22222e6 | −1.20780 | −0.603901 | − | 0.797059i | \(-0.706388\pi\) | ||||
−0.603901 | + | 0.797059i | \(0.706388\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −372072. | −0.0531690 | −0.0265845 | − | 0.999647i | \(-0.508463\pi\) | ||||
−0.0265845 | + | 0.999647i | \(0.508463\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.57260e7 | 2.20668 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.21235e7 | 1.68584 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.23214e7 | 1.68276 | 0.841378 | − | 0.540447i | \(-0.181745\pi\) | ||||
0.841378 | + | 0.540447i | \(0.181745\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.76259e6 | −0.915342 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −577762. | −0.0768207 | −0.0384104 | − | 0.999262i | \(-0.512229\pi\) | ||||
−0.0384104 | + | 0.999262i | \(0.512229\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.41678e6 | −1.08985 | −0.544923 | − | 0.838486i | \(-0.683441\pi\) | ||||
−0.544923 | + | 0.838486i | \(0.683441\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.88483e6 | 1.26876 | 0.634379 | − | 0.773022i | \(-0.281256\pi\) | ||||
0.634379 | + | 0.773022i | \(0.281256\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.80006e6 | 0.600215 | 0.300108 | − | 0.953905i | \(-0.402977\pi\) | ||||
0.300108 | + | 0.953905i | \(0.402977\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.26593e7 | 1.55586 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.04639e7 | 1.27504 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.20764e6 | −0.264443 | −0.132222 | − | 0.991220i | \(-0.542211\pi\) | ||||
−0.132222 | + | 0.991220i | \(0.542211\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.41634e7 | −1.68221 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.87399e6 | 0.569178 | 0.284589 | − | 0.958650i | \(-0.408143\pi\) | ||||
0.284589 | + | 0.958650i | \(0.408143\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.18365e7 | −1.34789 | −0.673945 | − | 0.738781i | \(-0.735402\pi\) | ||||
−0.673945 | + | 0.738781i | \(0.735402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.54130e6 | 0.851648 | 0.425824 | − | 0.904806i | \(-0.359984\pi\) | ||||
0.425824 | + | 0.904806i | \(0.359984\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.89856e6 | 0.539631 | 0.269815 | − | 0.962912i | \(-0.413037\pi\) | ||||
0.269815 | + | 0.962912i | \(0.413037\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.39622e6 | 0.259671 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.92286e6 | 1.06656 | 0.533281 | − | 0.845938i | \(-0.320959\pi\) | ||||
0.533281 | + | 0.845938i | \(0.320959\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.25453e6 | 0.767179 | 0.383589 | − | 0.923504i | \(-0.374688\pi\) | ||||
0.383589 | + | 0.923504i | \(0.374688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.81096e6 | 0.294869 | 0.147434 | − | 0.989072i | \(-0.452898\pi\) | ||||
0.147434 | + | 0.989072i | \(0.452898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.81857e6 | −0.394167 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.29805e6 | 0.130817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.77303e6 | −0.777172 | −0.388586 | − | 0.921413i | \(-0.627036\pi\) | ||||
−0.388586 | + | 0.921413i | \(0.627036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.16351e6 | 0.308902 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.91161e7 | 1.83761 | 0.918807 | − | 0.394708i | \(-0.129154\pi\) | ||||
0.918807 | + | 0.394708i | \(0.129154\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.52558e6 | 0.336282 | 0.168141 | − | 0.985763i | \(-0.446224\pi\) | ||||
0.168141 | + | 0.985763i | \(0.446224\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.43353e7 | 1.34631 | 0.673156 | − | 0.739501i | \(-0.264938\pi\) | ||||
0.673156 | + | 0.739501i | \(0.264938\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.14847e6 | 0.107031 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.62752e6 | 0.700004 | 0.350002 | − | 0.936749i | \(-0.386181\pi\) | ||||
0.350002 | + | 0.936749i | \(0.386181\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 836481. | 0.0750314 | 0.0375157 | − | 0.999296i | \(-0.488056\pi\) | ||||
0.0375157 | + | 0.999296i | \(0.488056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.49009e7 | −1.32650 | −0.663251 | − | 0.748397i | \(-0.730824\pi\) | ||||
−0.663251 | + | 0.748397i | \(0.730824\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.12415e7 | −0.978384 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.41684e6 | −0.635935 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.98768e6 | −0.424484 | −0.212242 | − | 0.977217i | \(-0.568076\pi\) | ||||
−0.212242 | + | 0.977217i | \(0.568076\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.60906e7 | 1.34928 | 0.674639 | − | 0.738148i | \(-0.264299\pi\) | ||||
0.674639 | + | 0.738148i | \(0.264299\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.46789e6 | −0.122185 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.10028e7 | 1.72276 | 0.861380 | − | 0.507961i | \(-0.169601\pi\) | ||||
0.861380 | + | 0.507961i | \(0.169601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.95428e6 | −0.798844 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.42900e6 | −0.671554 | −0.335777 | − | 0.941941i | \(-0.608999\pi\) | ||||
−0.335777 | + | 0.941941i | \(0.608999\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.08399e7 | −0.845170 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.86044e6 | 0.373577 | 0.186788 | − | 0.982400i | \(-0.440192\pi\) | ||||
0.186788 | + | 0.982400i | \(0.440192\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.02395e6 | −0.230774 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.52686e6 | −0.491084 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14126.8 | −0.00105543 | −0.000527714 | − | 1.00000i | \(-0.500168\pi\) | ||||
−0.000527714 | 1.00000i | \(0.500168\pi\) | ||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.01245e7 | 0.745847 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.77010e6 | 0.488397 | 0.244198 | − | 0.969725i | \(-0.421475\pi\) | ||||
0.244198 | + | 0.969725i | \(0.421475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.94364e7 | 1.39244 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.46483e7 | 1.02790 | 0.513949 | − | 0.857821i | \(-0.328182\pi\) | ||||
0.513949 | + | 0.857821i | \(0.328182\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.16174e7 | −0.804108 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.40016e6 | 0.233743 | 0.116872 | − | 0.993147i | \(-0.462713\pi\) | ||||
0.116872 | + | 0.993147i | \(0.462713\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.21878e7 | −2.18284 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.13728e7 | −1.43962 | −0.719812 | − | 0.694169i | \(-0.755772\pi\) | ||||
−0.719812 | + | 0.694169i | \(0.755772\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.95381e7 | 1.29841 | 0.649204 | − | 0.760614i | \(-0.275102\pi\) | ||||
0.649204 | + | 0.760614i | \(0.275102\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.52385e7 | −1.64384 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.50172e7 | 0.971605 | 0.485803 | − | 0.874069i | \(-0.338527\pi\) | ||||
0.485803 | + | 0.874069i | \(0.338527\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.23095e6 | −0.268348 | −0.134174 | − | 0.990958i | \(-0.542838\pi\) | ||||
−0.134174 | + | 0.990958i | \(0.542838\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.72356e6 | −0.170481 | −0.0852405 | − | 0.996360i | \(-0.527166\pi\) | ||||
−0.0852405 | + | 0.996360i | \(0.527166\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.23553e6 | −0.263389 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.09253e6 | −0.0670574 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.69504e7 | 1.64342 | 0.821711 | − | 0.569905i | \(-0.193020\pi\) | ||||
0.821711 | + | 0.569905i | \(0.193020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.40755e7 | −1.44920 | −0.724598 | − | 0.689171i | \(-0.757975\pi\) | ||||
−0.724598 | + | 0.689171i | \(0.757975\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.52529e7 | 1.49097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.56716e7 | 2.67929 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.52790e6 | −0.260591 | −0.130296 | − | 0.991475i | \(-0.541593\pi\) | ||||
−0.130296 | + | 0.991475i | \(0.541593\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.26393e7 | 0.718260 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.05559e6 | 0.398429 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.67415e6 | 0.483705 | 0.241853 | − | 0.970313i | \(-0.422245\pi\) | ||||
0.241853 | + | 0.970313i | \(0.422245\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.11644e6 | 0.228115 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.34124e7 | 2.92316 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.02725e7 | −0.551830 | −0.275915 | − | 0.961182i | \(-0.588981\pi\) | ||||
−0.275915 | + | 0.961182i | \(0.588981\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.51741e7 | −1.34401 | −0.672005 | − | 0.740546i | \(-0.734567\pi\) | ||||
−0.672005 | + | 0.740546i | \(0.734567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.70640e7 | 1.41853 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.66034e6 | 0.293079 | 0.146539 | − | 0.989205i | \(-0.453186\pi\) | ||||
0.146539 | + | 0.989205i | \(0.453186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −445634. | −0.0229339 | −0.0114670 | − | 0.999934i | \(-0.503650\pi\) | ||||
−0.0114670 | + | 0.999934i | \(0.503650\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.37086e7 | 0.696992 | 0.348496 | − | 0.937310i | \(-0.386692\pi\) | ||||
0.348496 | + | 0.937310i | \(0.386692\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.50876e7 | −0.762489 | −0.381244 | − | 0.924474i | \(-0.624504\pi\) | ||||
−0.381244 | + | 0.924474i | \(0.624504\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.43456e6 | 0.271364 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.74393e7 | 0.855310 | 0.427655 | − | 0.903942i | \(-0.359340\pi\) | ||||
0.427655 | + | 0.903942i | \(0.359340\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.83956e7 | 0.896859 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.09999e7 | 1.96370 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.16162e6 | 0.102319 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.83662e7 | 1.33484 | 0.667418 | − | 0.744683i | \(-0.267399\pi\) | ||||
0.667418 | + | 0.744683i | \(0.267399\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.85290e6 | −0.179199 | −0.0895996 | − | 0.995978i | \(-0.528559\pi\) | ||||
−0.0895996 | + | 0.995978i | \(0.528559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.13700e7 | 0.988145 | 0.494073 | − | 0.869421i | \(-0.335508\pi\) | ||||
0.494073 | + | 0.869421i | \(0.335508\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.18358e7 | 1.45509 | 0.727544 | − | 0.686061i | \(-0.240662\pi\) | ||||
0.727544 | + | 0.686061i | \(0.240662\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.43410e7 | −2.44106 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.06200e7 | 1.36760 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.26983e7 | −0.996539 | −0.498269 | − | 0.867022i | \(-0.666031\pi\) | ||||
−0.498269 | + | 0.867022i | \(0.666031\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.72028e7 | −1.18079 | −0.590396 | − | 0.807114i | \(-0.701029\pi\) | ||||
−0.590396 | + | 0.807114i | \(0.701029\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.57028e6 | −0.326746 | −0.163373 | − | 0.986564i | \(-0.552237\pi\) | ||||
−0.163373 | + | 0.986564i | \(0.552237\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.48320e6 | −0.276682 | −0.138341 | − | 0.990385i | \(-0.544177\pi\) | ||||
−0.138341 | + | 0.990385i | \(0.544177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.62302e7 | 0.688762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.58974e6 | −0.402419 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.50408e7 | −1.44602 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.71003e7 | −0.701766 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.32491e7 | 1.74566 | 0.872829 | − | 0.488027i | \(-0.162283\pi\) | ||||
0.872829 | + | 0.488027i | \(0.162283\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.46826e7 | −1.78379 | −0.891893 | − | 0.452247i | \(-0.850623\pi\) | ||||
−0.891893 | + | 0.452247i | \(0.850623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.67426e7 | −2.25285 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.76413e7 | −2.26366 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.73106e7 | −0.676118 | −0.338059 | − | 0.941125i | \(-0.609770\pi\) | ||||
−0.338059 | + | 0.941125i | \(0.609770\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.34471e7 | −1.67864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.98156e6 | 0.189377 | 0.0946883 | − | 0.995507i | \(-0.469815\pi\) | ||||
0.0946883 | + | 0.995507i | \(0.469815\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.26605e7 | −0.478713 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.25149e7 | −1.58195 | −0.790975 | − | 0.611849i | \(-0.790426\pi\) | ||||
−0.790975 | + | 0.611849i | \(0.790426\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.22797e7 | 0.820230 | 0.410115 | − | 0.912034i | \(-0.365489\pi\) | ||||
0.410115 | + | 0.912034i | \(0.365489\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.80516e7 | −0.661054 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.79405e7 | 1.37476 | 0.687381 | − | 0.726297i | \(-0.258760\pi\) | ||||
0.687381 | + | 0.726297i | \(0.258760\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.08109e7 | −1.83143 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.55436e7 | −1.62441 | −0.812204 | − | 0.583374i | \(-0.801732\pi\) | ||||
−0.812204 | + | 0.583374i | \(0.801732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.47071e7 | 1.56975 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.92991e6 | 0.102340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.58055e7 | −0.543552 | −0.271776 | − | 0.962361i | \(-0.587611\pi\) | ||||
−0.271776 | + | 0.962361i | \(0.587611\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.14171e6 | −0.0728976 | −0.0364488 | − | 0.999336i | \(-0.511605\pi\) | ||||
−0.0364488 | + | 0.999336i | \(0.511605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.85563e7 | 0.628360 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.92203e7 | −0.644204 | −0.322102 | − | 0.946705i | \(-0.604389\pi\) | ||||
−0.322102 | + | 0.946705i | \(0.604389\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.71159e7 | 0.570746 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.85343e7 | −0.941853 | −0.470926 | − | 0.882173i | \(-0.656080\pi\) | ||||
−0.470926 | + | 0.882173i | \(0.656080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.93463e7 | −0.628937 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.83531e7 | −1.24056 | −0.620278 | − | 0.784382i | \(-0.712980\pi\) | ||||
−0.620278 | + | 0.784382i | \(0.712980\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.31478e7 | −1.05613 | −0.528064 | − | 0.849205i | \(-0.677082\pi\) | ||||
−0.528064 | + | 0.849205i | \(0.677082\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 900.6.a.n.1.2 | 2 | ||
3.2 | odd | 2 | 300.6.a.g.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 900.6.d.j.649.3 | 4 | |||
5.3 | odd | 4 | 900.6.d.j.649.2 | 4 | |||
5.4 | even | 2 | 900.6.a.r.1.1 | 2 | |||
15.2 | even | 4 | 300.6.d.f.49.4 | 4 | |||
15.8 | even | 4 | 300.6.d.f.49.1 | 4 | |||
15.14 | odd | 2 | 300.6.a.h.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.6.a.g.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
300.6.a.h.1.1 | yes | 2 | 15.14 | odd | 2 | ||
300.6.d.f.49.1 | 4 | 15.8 | even | 4 | |||
300.6.d.f.49.4 | 4 | 15.2 | even | 4 | |||
900.6.a.n.1.2 | 2 | 1.1 | even | 1 | trivial | ||
900.6.a.r.1.1 | 2 | 5.4 | even | 2 | |||
900.6.d.j.649.2 | 4 | 5.3 | odd | 4 | |||
900.6.d.j.649.3 | 4 | 5.2 | odd | 4 |