Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,6,Mod(1,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, 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("448.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.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: | \(71.8519512762\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{345}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 86 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(9.78709\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.1 |
$q$-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 | ||||||||
\(3\) | 21.5742 | 1.38398 | 0.691992 | − | 0.721905i | \(-0.256733\pi\) | ||||
0.691992 | + | 0.721905i | \(0.256733\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.7225 | 0.263365 | 0.131682 | − | 0.991292i | \(-0.457962\pi\) | ||||
0.131682 | + | 0.991292i | \(0.457962\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 222.445 | 0.915412 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −58.5549 | −0.145909 | −0.0729545 | − | 0.997335i | \(-0.523243\pi\) | ||||
−0.0729545 | + | 0.997335i | \(0.523243\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1179.39 | −1.93553 | −0.967765 | − | 0.251853i | \(-0.918960\pi\) | ||||
−0.967765 | + | 0.251853i | \(0.918960\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 317.626 | 0.364492 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1496.55 | 1.25594 | 0.627972 | − | 0.778236i | \(-0.283885\pi\) | ||||
0.627972 | + | 0.778236i | \(0.283885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −498.838 | −0.317012 | −0.158506 | − | 0.987358i | \(-0.550668\pi\) | ||||
−0.158506 | + | 0.987358i | \(0.550668\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1057.13 | −0.523097 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1889.34 | −0.744716 | −0.372358 | − | 0.928089i | \(-0.621451\pi\) | ||||
−0.372358 | + | 0.928089i | \(0.621451\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2908.25 | −0.930639 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −443.456 | −0.117069 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1914.54 | −0.422737 | −0.211369 | − | 0.977406i | \(-0.567792\pi\) | ||||
−0.211369 | + | 0.977406i | \(0.567792\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 794.577 | 0.148502 | 0.0742509 | − | 0.997240i | \(-0.476343\pi\) | ||||
0.0742509 | + | 0.997240i | \(0.476343\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1263.27 | −0.201936 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −721.404 | −0.0995424 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2987.93 | −0.358811 | −0.179406 | − | 0.983775i | \(-0.557417\pi\) | ||||
−0.179406 | + | 0.983775i | \(0.557417\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −25444.4 | −2.67874 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11941.3 | 1.10941 | 0.554704 | − | 0.832047i | \(-0.312831\pi\) | ||||
0.554704 | + | 0.832047i | \(0.312831\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9820.19 | −0.809933 | −0.404966 | − | 0.914332i | \(-0.632717\pi\) | ||||
−0.404966 | + | 0.914332i | \(0.632717\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3274.95 | 0.241087 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −19636.0 | −1.29660 | −0.648302 | − | 0.761383i | \(-0.724521\pi\) | ||||
−0.648302 | + | 0.761383i | \(0.724521\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 32286.9 | 1.73821 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19875.0 | 0.971889 | 0.485945 | − | 0.873990i | \(-0.338476\pi\) | ||||
0.485945 | + | 0.873990i | \(0.338476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −862.077 | −0.0384272 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10762.0 | −0.438739 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −35838.6 | −1.34036 | −0.670180 | − | 0.742199i | \(-0.733783\pi\) | ||||
−0.670180 | + | 0.742199i | \(0.733783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −49975.9 | −1.71964 | −0.859818 | − | 0.510601i | \(-0.829423\pi\) | ||||
−0.859818 | + | 0.510601i | \(0.829423\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10899.8 | −0.345993 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −17363.6 | −0.509750 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −48176.2 | −1.31113 | −0.655565 | − | 0.755139i | \(-0.727569\pi\) | ||||
−0.655565 | + | 0.755139i | \(0.727569\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −40761.0 | −1.03068 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 77179.1 | 1.81699 | 0.908497 | − | 0.417891i | \(-0.137230\pi\) | ||||
0.908497 | + | 0.417891i | \(0.137230\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −59667.3 | −1.31048 | −0.655238 | − | 0.755422i | \(-0.727432\pi\) | ||||
−0.655238 | + | 0.755422i | \(0.727432\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −62743.0 | −1.28799 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2869.19 | 0.0551484 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 60743.1 | 1.09504 | 0.547519 | − | 0.836793i | \(-0.315572\pi\) | ||||
0.547519 | + | 0.836793i | \(0.315572\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −63621.3 | −1.07743 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 46134.2 | 0.735068 | 0.367534 | − | 0.930010i | \(-0.380202\pi\) | ||||
0.367534 | + | 0.930010i | \(0.380202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22033.1 | 0.330771 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −41304.7 | −0.585061 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 78668.7 | 1.05275 | 0.526377 | − | 0.850251i | \(-0.323550\pi\) | ||||
0.526377 | + | 0.850251i | \(0.323550\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 57790.2 | 0.731562 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 17142.3 | 0.205524 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7344.15 | −0.0834897 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −43573.3 | −0.470209 | −0.235104 | − | 0.971970i | \(-0.575543\pi\) | ||||
−0.235104 | + | 0.971970i | \(0.575543\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −13025.3 | −0.133567 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 164188. | 1.60154 | 0.800772 | − | 0.598970i | \(-0.204423\pi\) | ||||
0.800772 | + | 0.598970i | \(0.204423\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 164547. | 1.52825 | 0.764127 | − | 0.645065i | \(-0.223170\pi\) | ||||
0.764127 | + | 0.645065i | \(0.223170\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −15563.7 | −0.137765 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 185426. | 1.56571 | 0.782854 | − | 0.622206i | \(-0.213763\pi\) | ||||
0.782854 | + | 0.622206i | \(0.213763\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −190063. | −1.53225 | −0.766127 | − | 0.642689i | \(-0.777819\pi\) | ||||
−0.766127 | + | 0.642689i | \(0.777819\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −64462.1 | −0.496589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −116023. | −0.854769 | −0.427384 | − | 0.904070i | \(-0.640565\pi\) | ||||
−0.427384 | + | 0.904070i | \(0.640565\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −27815.9 | −0.196132 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −262350. | −1.77181 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −73331.2 | −0.474702 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −157622. | −0.978711 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 257624. | 1.53540 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −88824.6 | −0.508462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 71785.5 | 0.394936 | 0.197468 | − | 0.980309i | \(-0.436728\pi\) | ||||
0.197468 | + | 0.980309i | \(0.436728\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −211863. | −1.12093 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2016.22 | 0.0102650 | 0.00513250 | − | 0.999987i | \(-0.498366\pi\) | ||||
0.00513250 | + | 0.999987i | \(0.498366\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24443.1 | 0.119819 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6528.79 | −0.0308318 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −243904. | −1.11024 | −0.555120 | − | 0.831770i | \(-0.687328\pi\) | ||||
−0.555120 | + | 0.831770i | \(0.687328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −209413. | −0.919319 | −0.459660 | − | 0.888095i | \(-0.652029\pi\) | ||||
−0.459660 | + | 0.888095i | \(0.652029\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −423630. | −1.79448 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 69059.3 | 0.282411 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −28186.9 | −0.111334 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 51799.6 | 0.197712 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22954.3 | −0.0847028 | −0.0423514 | − | 0.999103i | \(-0.513485\pi\) | ||||
−0.0423514 | + | 0.999103i | \(0.513485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −276737. | −0.987700 | −0.493850 | − | 0.869547i | \(-0.664411\pi\) | ||||
−0.493850 | + | 0.869547i | \(0.664411\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 332901. | 1.14971 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11698.2 | 0.0391101 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −276692. | −0.895874 | −0.447937 | − | 0.894065i | \(-0.647841\pi\) | ||||
−0.447937 | + | 0.894065i | \(0.647841\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 428786. | 1.34508 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 92577.7 | 0.281476 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −274258. | −0.808518 | −0.404259 | − | 0.914645i | \(-0.632471\pi\) | ||||
−0.404259 | + | 0.914645i | \(0.632471\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18598.6 | −0.0531827 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −215716. | −0.598537 | −0.299268 | − | 0.954169i | \(-0.596743\pi\) | ||||
−0.299268 | + | 0.954169i | \(0.596743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.01967e6 | 2.74628 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −110964. | −0.290196 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −86252.7 | −0.219108 | −0.109554 | − | 0.993981i | \(-0.534942\pi\) | ||||
−0.109554 | + | 0.993981i | \(0.534942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 142504. | 0.351749 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −773189. | −1.85504 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 435822. | 1.01666 | 0.508331 | − | 0.861162i | \(-0.330262\pi\) | ||||
0.508331 | + | 0.861162i | \(0.330262\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −56972.2 | −0.129261 | −0.0646303 | − | 0.997909i | \(-0.520587\pi\) | ||||
−0.0646303 | + | 0.997909i | \(0.520587\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.07819e6 | −2.37995 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −43989.9 | −0.0944981 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −87630.7 | −0.183253 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21729.3 | 0.0442478 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −350077. | −0.694353 | −0.347177 | − | 0.937800i | \(-0.612860\pi\) | ||||
−0.347177 | + | 0.937800i | \(0.612860\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −623227. | −1.20435 | −0.602175 | − | 0.798364i | \(-0.705699\pi\) | ||||
−0.602175 | + | 0.798364i | \(0.705699\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −374606. | −0.705486 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −223265. | −0.409879 | −0.204939 | − | 0.978775i | \(-0.565700\pi\) | ||||
−0.204939 | + | 0.978775i | \(0.565700\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 756375. | 1.35396 | 0.676978 | − | 0.736004i | \(-0.263289\pi\) | ||||
0.676978 | + | 0.736004i | \(0.263289\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.03936e6 | −1.81458 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 93812.7 | 0.159780 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 175806. | 0.292179 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −420274. | −0.681722 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29209.4 | 0.0462549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 30644.3 | 0.0473853 | 0.0236927 | − | 0.999719i | \(-0.492458\pi\) | ||||
0.0236927 | + | 0.999719i | \(0.492458\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.66507e6 | 2.51469 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −144578. | −0.213308 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −38934.3 | −0.0561284 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.28727e6 | −1.81368 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.76503e6 | −2.43092 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 461375. | 0.621286 | 0.310643 | − | 0.950527i | \(-0.399456\pi\) | ||||
0.310643 | + | 0.950527i | \(0.399456\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −646925. | −0.851918 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −346439. | −0.446234 | −0.223117 | − | 0.974792i | \(-0.571623\pi\) | ||||
−0.223117 | + | 0.974792i | \(0.571623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 521650. | 0.657341 | 0.328671 | − | 0.944445i | \(-0.393399\pi\) | ||||
0.328671 | + | 0.944445i | \(0.393399\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 61900.5 | 0.0763245 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 154120. | 0.185981 | 0.0929907 | − | 0.995667i | \(-0.470357\pi\) | ||||
0.0929907 | + | 0.995667i | \(0.470357\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −289091. | −0.341480 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.31048e6 | 1.51551 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −478940. | −0.542358 | −0.271179 | − | 0.962529i | \(-0.587414\pi\) | ||||
−0.271179 | + | 0.962529i | \(0.587414\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 86551.8 | 0.0959917 | 0.0479958 | − | 0.998848i | \(-0.484717\pi\) | ||||
0.0479958 | + | 0.998848i | \(0.484717\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.26482e6 | −1.37408 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 35348.8 | 0.0376235 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 588326. | 0.613586 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 995307. | 1.01732 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.90322e6 | 1.90679 | 0.953397 | − | 0.301719i | \(-0.0975605\pi\) | ||||
0.953397 | + | 0.301719i | \(0.0975605\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 110630. | 0.108661 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 475345. | 0.457782 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −569922. | −0.538248 | −0.269124 | − | 0.963105i | \(-0.586734\pi\) | ||||
−0.269124 | + | 0.963105i | \(0.586734\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 146408. | 0.135618 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −425881. | −0.386978 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.29853e6 | 1.15761 | 0.578806 | − | 0.815465i | \(-0.303519\pi\) | ||||
0.578806 | + | 0.815465i | \(0.303519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 292610. | 0.255961 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.69721e6 | 1.45699 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 53721.5 | 0.0452655 | 0.0226328 | − | 0.999744i | \(-0.492795\pi\) | ||||
0.0226328 | + | 0.999744i | \(0.492795\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −758053. | −0.627013 | −0.313506 | − | 0.949586i | \(-0.601504\pi\) | ||||
−0.313506 | + | 0.949586i | \(0.601504\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.24678e6 | 1.01247 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 170292. | 0.135789 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.07598e6 | −1.62564 | −0.812819 | − | 0.582516i | \(-0.802068\pi\) | ||||
−0.812819 | + | 0.582516i | \(0.802068\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 176750. | 0.135940 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.61195e6 | 1.97333 | 0.986664 | − | 0.162770i | \(-0.0520427\pi\) | ||||
0.986664 | + | 0.162770i | \(0.0520427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −992734. | −0.736829 | −0.368414 | − | 0.929662i | \(-0.620099\pi\) | ||||
−0.368414 | + | 0.929662i | \(0.620099\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −158444. | −0.115548 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −585123. | −0.419317 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 819820. | 0.577396 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −940057. | −0.650762 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −371728. | −0.252962 | −0.126481 | − | 0.991969i | \(-0.540368\pi\) | ||||
−0.126481 | + | 0.991969i | \(0.540368\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −527635. | −0.353003 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 25966.5 | 0.0170814 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.22827e6 | 1.44142 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 481189. | 0.306126 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.54223e6 | 2.21651 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −735772. | −0.452891 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.83906e6 | 1.71921 | 0.859606 | − | 0.510958i | \(-0.170709\pi\) | ||||
0.859606 | + | 0.510958i | \(0.170709\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.54996e6 | 2.11508 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 759362. | 0.445193 | 0.222596 | − | 0.974911i | \(-0.428547\pi\) | ||||
0.222596 | + | 0.974911i | \(0.428547\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.80191e6 | −1.03961 | −0.519806 | − | 0.854284i | \(-0.673996\pi\) | ||||
−0.519806 | + | 0.854284i | \(0.673996\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −160473. | −0.0911223 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 441899. | 0.246987 | 0.123494 | − | 0.992345i | \(-0.460590\pi\) | ||||
0.123494 | + | 0.992345i | \(0.460590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 112106. | 0.0616811 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.00041e6 | 2.16691 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −746538. | −0.398149 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.42997e6 | 1.80128 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.10045e6 | −2.12061 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 962162. | 0.490070 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.15779e6 | 1.58421 | 0.792107 | − | 0.610383i | \(-0.208984\pi\) | ||||
0.792107 | + | 0.610383i | \(0.208984\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −664650. | −0.328460 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −709275. | −0.345305 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.66612e6 | −0.799158 | −0.399579 | − | 0.916699i | \(-0.630844\pi\) | ||||
−0.399579 | + | 0.916699i | \(0.630844\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.50310e6 | −1.18299 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −46526.4 | −0.0216677 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −600104. | −0.271443 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.41953e6 | 1.52455 | 0.762277 | − | 0.647251i | \(-0.224081\pi\) | ||||
0.762277 | + | 0.647251i | \(0.224081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.18396e6 | 1.39928 | 0.699638 | − | 0.714497i | \(-0.253345\pi\) | ||||
0.699638 | + | 0.714497i | \(0.253345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 523009. | 0.226590 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.02506e6 | 1.29210 | 0.646051 | − | 0.763294i | \(-0.276419\pi\) | ||||
0.646051 | + | 0.763294i | \(0.276419\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.13627e6 | 0.478532 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.58206e6 | −0.656980 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.12353e6 | −0.460098 | −0.230049 | − | 0.973179i | \(-0.573889\pi\) | ||||
−0.230049 | + | 0.973179i | \(0.573889\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.22726e6 | −0.899504 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.40057e6 | −1.35452 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −878453. | −0.345133 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.39115e6 | 1.31426 | 0.657131 | − | 0.753777i | \(-0.271770\pi\) | ||||
0.657131 | + | 0.753777i | \(0.271770\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.65628e6 | 1.01557 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −973873. | −0.367340 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.33823e6 | −0.498033 | −0.249017 | − | 0.968499i | \(-0.580107\pi\) | ||||
−0.249017 | + | 0.968499i | \(0.580107\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.91632e6 | −0.703703 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.25800e6 | 0.818221 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.11403e6 | −1.11359 | −0.556795 | − | 0.830650i | \(-0.687969\pi\) | ||||
−0.556795 | + | 0.830650i | \(0.687969\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.54871e6 | 0.546586 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −334533. | −0.116531 | −0.0582656 | − | 0.998301i | \(-0.518557\pi\) | ||||
−0.0582656 | + | 0.998301i | \(0.518557\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 42241.8 | 0.0145241 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.18445e6 | −0.741422 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.59871e6 | −0.535667 | −0.267834 | − | 0.963465i | \(-0.586308\pi\) | ||||
−0.267834 | + | 0.963465i | \(0.586308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.82750e6 | −0.935322 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 43498.2 | 0.0142066 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 894292. | 0.288394 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.20789e6 | 0.703074 | 0.351537 | − | 0.936174i | \(-0.385659\pi\) | ||||
0.351537 | + | 0.936174i | \(0.385659\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 527339. | 0.165828 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.89272e6 | 0.587793 | 0.293897 | − | 0.955837i | \(-0.405048\pi\) | ||||
0.293897 | + | 0.955837i | \(0.405048\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −937118. | −0.287430 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −936667. | −0.283758 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 174958. | 0.0523537 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.14418e6 | 0.338210 | 0.169105 | − | 0.985598i | \(-0.445912\pi\) | ||||
0.169105 | + | 0.985598i | \(0.445912\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.26202e6 | −1.53655 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.75609e6 | 0.506608 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 679212. | 0.193591 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.51791e6 | −1.27232 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.17298e6 | −1.43948 | −0.719740 | − | 0.694244i | \(-0.755739\pi\) | ||||
−0.719740 | + | 0.694244i | \(0.755739\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.40960e6 | 0.387606 | 0.193803 | − | 0.981040i | \(-0.437918\pi\) | ||||
0.193803 | + | 0.981040i | \(0.437918\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.36792e6 | −1.18693 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.35235e6 | −1.16883 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.44882e6 | 0.649961 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.48990e6 | 0.390853 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.17076e6 | 1.60009 | 0.800047 | − | 0.599938i | \(-0.204808\pi\) | ||||
0.800047 | + | 0.599938i | \(0.204808\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 387046. | 0.0992071 | 0.0496036 | − | 0.998769i | \(-0.484204\pi\) | ||||
0.0496036 | + | 0.998769i | \(0.484204\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −608110. | −0.154084 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 942475. | 0.236084 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.32974e6 | 0.824611 | 0.412305 | − | 0.911046i | \(-0.364724\pi\) | ||||
0.412305 | + | 0.911046i | \(0.364724\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 534091. | 0.130773 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.44003e6 | 0.348627 | 0.174314 | − | 0.984690i | \(-0.444229\pi\) | ||||
0.174314 | + | 0.984690i | \(0.444229\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.15820e6 | 0.277258 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −495219. | −0.117227 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.28977e6 | 1.00420 | 0.502098 | − | 0.864811i | \(-0.332562\pi\) | ||||
0.502098 | + | 0.864811i | \(0.332562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −699222. | −0.161873 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.97037e6 | −1.36696 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 850819. | 0.192667 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.27889e6 | −1.18237 | −0.591183 | − | 0.806537i | \(-0.701339\pi\) | ||||
−0.591183 | + | 0.806537i | \(0.701339\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −663656. | −0.147032 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.72322e6 | 0.815955 | 0.407977 | − | 0.912992i | \(-0.366234\pi\) | ||||
0.407977 | + | 0.912992i | \(0.366234\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.04809e6 | 0.227220 | 0.113610 | − | 0.993525i | \(-0.463759\pi\) | ||||
0.113610 | + | 0.993525i | \(0.463759\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 252379. | 0.0541278 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.04244e6 | −1.28210 | −0.641048 | − | 0.767501i | \(-0.721500\pi\) | ||||
−0.641048 | + | 0.767501i | \(0.721500\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.36063e6 | 0.495560 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.96940e6 | −1.23988 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 575021. | 0.118176 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.45074e6 | 0.295024 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.42109e6 | 0.889679 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.06868e6 | −0.411959 | −0.205980 | − | 0.978556i | \(-0.566038\pi\) | ||||
−0.205980 | + | 0.978556i | \(0.566038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.52394e6 | 0.694490 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.99729e6 | 0.389559 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −641509. | −0.123836 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.82966e6 | −0.540645 | −0.270323 | − | 0.962770i | \(-0.587130\pi\) | ||||
−0.270323 | + | 0.962770i | \(0.587130\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.91688e6 | −1.11898 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.44554e6 | 0.832186 | 0.416093 | − | 0.909322i | \(-0.363399\pi\) | ||||
0.416093 | + | 0.909322i | \(0.363399\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.86522e6 | −0.530934 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −191765. | −0.0351767 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.78177e6 | −0.686759 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.34623e6 | 0.242029 | 0.121015 | − | 0.992651i | \(-0.461385\pi\) | ||||
0.121015 | + | 0.992651i | \(0.461385\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.65389e6 | −0.828365 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.88909e6 | −0.861604 | −0.430802 | − | 0.902446i | \(-0.641769\pi\) | ||||
−0.430802 | + | 0.902446i | \(0.641769\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.41727e6 | 0.421790 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.19986e7 | 3.80081 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.55518e6 | −1.12148 | −0.560738 | − | 0.827993i | \(-0.689483\pi\) | ||||
−0.560738 | + | 0.827993i | \(0.689483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.92370e6 | 0.495313 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 221213. | 0.0371122 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.42254e6 | 0.402488 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.14978e6 | 0.189186 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.86083e6 | −0.303242 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.77290e6 | −0.770349 | −0.385175 | − | 0.922844i | \(-0.625859\pi\) | ||||
−0.385175 | + | 0.922844i | \(0.625859\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 828135. | 0.132387 | 0.0661937 | − | 0.997807i | \(-0.478914\pi\) | ||||
0.0661937 | + | 0.997807i | \(0.478914\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.07441e6 | 0.486814 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.18913e6 | 0.186510 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.86673e6 | −0.445398 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.97212e6 | −1.22698 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.40835e7 | −2.14730 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.72994e6 | 0.412352 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.40251e6 | 1.40705 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −140590. | −0.0208441 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.93356e6 | −1.01851 | −0.509253 | − | 0.860617i | \(-0.670078\pi\) | ||||
−0.509253 | + | 0.860617i | \(0.670078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.22913e6 | −0.178895 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.79820e6 | −0.403541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −559077. | −0.0798920 | −0.0399460 | − | 0.999202i | \(-0.512719\pi\) | ||||
−0.0399460 | + | 0.999202i | \(0.512719\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.11169e7 | −1.57417 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 955047. | 0.134013 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.97641e6 | −0.413885 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −949045. | −0.130784 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.90444e6 | 0.533237 | 0.266619 | − | 0.963802i | \(-0.414094\pi\) | ||||
0.266619 | + | 0.963802i | \(0.414094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.15819e7 | 1.56765 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.89056e6 | −0.253620 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.02307e6 | 0.534918 | 0.267459 | − | 0.963569i | \(-0.413816\pi\) | ||||
0.267459 | + | 0.963569i | \(0.413816\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.70815e6 | −0.225116 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.11745e6 | 0.407231 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.35801e6 | −0.305327 | −0.152663 | − | 0.988278i | \(-0.548785\pi\) | ||||
−0.152663 | + | 0.988278i | \(0.548785\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.76733e6 | 0.996969 | 0.498484 | − | 0.866899i | \(-0.333890\pi\) | ||||
0.498484 | + | 0.866899i | \(0.333890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.55263e6 | −0.960974 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.49467e6 | 0.693062 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.38363e7 | 1.73013 | 0.865066 | − | 0.501657i | \(-0.167276\pi\) | ||||
0.865066 | + | 0.501657i | \(0.167276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.34456e7 | −1.66680 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.26057e6 | −0.277830 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.16378e6 | −0.141807 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.86246e6 | −0.466631 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.13747e6 | −0.256038 | −0.128019 | − | 0.991772i | \(-0.540862\pi\) | ||||
−0.128019 | + | 0.991772i | \(0.540862\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −396365. | −0.0470768 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.81676e6 | −0.567265 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.11381e7 | −1.30069 | −0.650345 | − | 0.759639i | \(-0.725376\pi\) | ||||
−0.650345 | + | 0.759639i | \(0.725376\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.07962e6 | −0.125020 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.63182e7 | 1.87385 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.10044e7 | 1.25314 | 0.626572 | − | 0.779364i | \(-0.284457\pi\) | ||||
0.626572 | + | 0.779364i | \(0.284457\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.28046e6 | 0.144604 | 0.0723019 | − | 0.997383i | \(-0.476965\pi\) | ||||
0.0723019 | + | 0.997383i | \(0.476965\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.07166e7 | −1.20022 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.32060e6 | −0.257758 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.08327e6 | −0.229496 | −0.114748 | − | 0.993395i | \(-0.536606\pi\) | ||||
−0.114748 | + | 0.993395i | \(0.536606\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.02393e6 | 0.221132 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.31585e7 | 2.50962 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.37116e7 | 1.47380 | 0.736899 | − | 0.676003i | \(-0.236289\pi\) | ||||
0.736899 | + | 0.676003i | \(0.236289\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.79287e6 | 0.404371 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.65172e7 | −1.74672 | −0.873361 | − | 0.487073i | \(-0.838064\pi\) | ||||
−0.873361 | + | 0.487073i | \(0.838064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.51321e6 | −0.368534 | −0.184267 | − | 0.982876i | \(-0.558991\pi\) | ||||
−0.184267 | + | 0.982876i | \(0.558991\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 837839. | 0.0871830 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.85477e6 | −0.397904 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.78055e6 | 0.796728 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 630169. | 0.0640160 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.47160e6 | −0.450647 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.54135e6 | −0.853991 | −0.426995 | − | 0.904254i | \(-0.640428\pi\) | ||||
−0.426995 | + | 0.904254i | \(0.640428\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 661126. | 0.0655805 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.05686e6 | 0.104012 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.83172e6 | −0.276504 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.71681e7 | 1.66330 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.95519e6 | −0.956983 | −0.478492 | − | 0.878092i | \(-0.658816\pi\) | ||||
−0.478492 | + | 0.878092i | \(0.658816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.98313e6 | 0.379924 | 0.189962 | − | 0.981791i | \(-0.439163\pi\) | ||||
0.189962 | + | 0.981791i | \(0.439163\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.11915e6 | −0.295214 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.84121e6 | −0.360750 | −0.180375 | − | 0.983598i | \(-0.557731\pi\) | ||||
−0.180375 | + | 0.983598i | \(0.557731\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.09853e6 | 0.195570 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −839975. | −0.0776808 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.84286e7 | −1.69126 | −0.845628 | − | 0.533772i | \(-0.820774\pi\) | ||||
−0.845628 | + | 0.533772i | \(0.820774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29683.8 | 0.00270344 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.32727e7 | −1.19963 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.15854e7 | −1.93619 | −0.968093 | − | 0.250590i | \(-0.919376\pi\) | ||||
−0.968093 | + | 0.250590i | \(0.919376\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.44072e7 | −1.28256 | −0.641278 | − | 0.767308i | \(-0.721596\pi\) | ||||
−0.641278 | + | 0.767308i | \(0.721596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.80790e7 | −3.36435 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 359864. | 0.0315561 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.61723e6 | 0.314819 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.95378e6 | 0.859850 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.92634e6 | 0.250910 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.55230e6 | −0.472536 | −0.236268 | − | 0.971688i | \(-0.575924\pi\) | ||||
−0.236268 | + | 0.971688i | \(0.575924\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.28968e6 | 0.108949 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.92009e6 | 0.831848 | 0.415924 | − | 0.909399i | \(-0.363458\pi\) | ||||
0.415924 | + | 0.909399i | \(0.363458\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.13509e6 | 0.177722 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.47414e6 | −0.617581 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.01291e7 | 0.830846 | 0.415423 | − | 0.909628i | \(-0.363634\pi\) | ||||
0.415423 | + | 0.909628i | \(0.363634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.59088e6 | −0.292398 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.12542e7 | 0.909750 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.34404e7 | −1.88112 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.98747e7 | −1.58345 | −0.791727 | − | 0.610875i | \(-0.790818\pi\) | ||||
−0.791727 | + | 0.610875i | \(0.790818\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 638238. | 0.0504835 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.08309e6 | −0.242116 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.78708e7 | 1.39336 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.32502e6 | 0.257395 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.13147e7 | 1.63826 | 0.819132 | − | 0.573605i | \(-0.194455\pi\) | ||||
0.819132 | + | 0.573605i | \(0.194455\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.49049e6 | 0.113747 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.23690e6 | −0.472602 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.04523e6 | −0.605327 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.83200e6 | −0.734559 | −0.367279 | − | 0.930111i | \(-0.619711\pi\) | ||||
−0.367279 | + | 0.930111i | \(0.619711\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.35120e7 | 1.00241 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.50123e6 | −0.110592 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.01673e6 | 0.0743771 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.03327e7 | −0.750615 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.80674e7 | −1.30338 | −0.651692 | − | 0.758484i | \(-0.725940\pi\) | ||||
−0.651692 | + | 0.758484i | \(0.725940\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.06278e6 | −0.577626 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.86728e6 | 0.132851 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.56797e6 | 0.393416 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.82003e7 | −1.27715 | −0.638576 | − | 0.769559i | \(-0.720476\pi\) | ||||
−0.638576 | + | 0.769559i | \(0.720476\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.18274e7 | −0.824274 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.46965e7 | −1.01723 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.70629e6 | −0.461023 | −0.230512 | − | 0.973070i | \(-0.574040\pi\) | ||||
−0.230512 | + | 0.973070i | \(0.574040\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 762621. | 0.0520703 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.82095e6 | 0.191305 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.16502e7 | −1.45831 | −0.729156 | − | 0.684347i | \(-0.760087\pi\) | ||||
−0.729156 | + | 0.684347i | \(0.760087\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.26926e7 | 0.849193 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.40437e7 | −0.933276 | −0.466638 | − | 0.884448i | \(-0.654535\pi\) | ||||
−0.466638 | + | 0.884448i | \(0.654535\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −337945. | −0.0223077 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.02623e7 | 0.672890 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.08586e6 | −0.591782 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.91381e6 | 0.576718 | 0.288359 | − | 0.957522i | \(-0.406890\pi\) | ||||
0.288359 | + | 0.957522i | \(0.406890\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.10603e7 | 2.63897 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.07427e6 | −0.260125 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.04419e7 | 0.662276 | 0.331138 | − | 0.943582i | \(-0.392567\pi\) | ||||
0.331138 | + | 0.943582i | \(0.392567\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.38676e6 | 0.150385 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.96214e7 | 1.85414 | 0.927072 | − | 0.374883i | \(-0.122317\pi\) | ||||
0.927072 | + | 0.374883i | \(0.122317\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.31307e6 | 0.579138 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.90115e6 | 0.302792 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.22678e7 | 2.59431 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.24042e6 | −0.258579 | −0.129289 | − | 0.991607i | \(-0.541270\pi\) | ||||
−0.129289 | + | 0.991607i | \(0.541270\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.22956e7 | −0.744927 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.37072e7 | 0.825086 | 0.412543 | − | 0.910938i | \(-0.364641\pi\) | ||||
0.412543 | + | 0.910938i | \(0.364641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.31083e6 | −0.138202 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.15864e6 | 0.187693 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.95677e6 | −0.351696 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.51922e6 | −0.265116 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 849016. | 0.0494893 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.07360e6 | −0.235942 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.02427e7 | −0.589491 | −0.294745 | − | 0.955576i | \(-0.595235\pi\) | ||||
−0.294745 | + | 0.955576i | \(0.595235\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.80148e7 | 1.60212 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.68513e6 | 0.323072 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.89413e7 | 3.32841 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.31281e6 | 0.354246 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.00087e7 | −1.67340 | −0.836702 | − | 0.547658i | \(-0.815520\pi\) | ||||
−0.836702 | + | 0.547658i | \(0.815520\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.93863e7 | −1.62846 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.74995e7 | 0.963704 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.49381e6 | 0.191210 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.36298e6 | 0.0741309 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.15900e6 | 0.0626468 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 922081. | 0.0495333 | 0.0247667 | − | 0.999693i | \(-0.492116\pi\) | ||||
0.0247667 | + | 0.999693i | \(0.492116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.49323e7 | 1.33110 | 0.665549 | − | 0.746355i | \(-0.268198\pi\) | ||||
0.665549 | + | 0.746355i | \(0.268198\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.63544e7 | −0.867776 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.03776e6 | −0.212935 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.89868e6 | 0.256758 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.28552e7 | 0.669680 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.06228e6 | 0.417446 | 0.208723 | − | 0.977975i | \(-0.433069\pi\) | ||||
0.208723 | + | 0.977975i | \(0.433069\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.68168e6 | −0.292400 | −0.146200 | − | 0.989255i | \(-0.546704\pi\) | ||||
−0.146200 | + | 0.989255i | \(0.546704\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.67392e6 | 0.187929 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 976611. | 0.0496544 | 0.0248272 | − | 0.999692i | \(-0.492096\pi\) | ||||
0.0248272 | + | 0.999692i | \(0.492096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.94857e6 | 0.250088 | 0.125044 | − | 0.992151i | \(-0.460093\pi\) | ||||
0.125044 | + | 0.992151i | \(0.460093\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.47876e7 | −2.24986 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.59323e6 | 0.179421 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.17588e6 | −0.157633 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −352360. | −0.0173849 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.03716e7 | −0.999125 | −0.499562 | − | 0.866278i | \(-0.666506\pi\) | ||||
−0.499562 | + | 0.866278i | \(0.666506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.68457e7 | −0.821293 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.63507e7 | 2.73105 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.50122e7 | 0.723273 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.72349e6 | 0.369918 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.14174e7 | −1.01976 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.64521e6 | 0.267212 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.41579e7 | −0.666234 | −0.333117 | − | 0.942885i | \(-0.608100\pi\) | ||||
−0.333117 | + | 0.942885i | \(0.608100\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.63367e6 | −0.0764274 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.24397e7 | −0.578575 | −0.289287 | − | 0.957242i | \(-0.593418\pi\) | ||||
−0.289287 | + | 0.957242i | \(0.593418\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.72105e7 | −0.795810 | −0.397905 | − | 0.917427i | \(-0.630263\pi\) | ||||
−0.397905 | + | 0.917427i | \(0.630263\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.26236e7 | −0.580328 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.04374e7 | 0.934113 | 0.467057 | − | 0.884227i | \(-0.345314\pi\) | ||||
0.467057 | + | 0.884227i | \(0.345314\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.26986e6 | −0.0577052 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.76869e7 | 0.799107 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.55681e6 | −0.159776 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.68187e7 | 2.53773 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.69266e6 | −0.430435 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.35241e6 | 0.192181 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.72398e7 | 0.756890 | 0.378445 | − | 0.925624i | \(-0.376459\pi\) | ||||
0.378445 | + | 0.925624i | \(0.376459\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.01972e6 | −0.350096 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.86589e7 | −1.67807 | −0.839034 | − | 0.544080i | \(-0.816879\pi\) | ||||
−0.839034 | + | 0.544080i | \(0.816879\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.29454e7 | 1.42198 | 0.710990 | − | 0.703203i | \(-0.248247\pi\) | ||||
0.710990 | + | 0.703203i | \(0.248247\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.13833e7 | −0.488551 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.61545e7 | 1.54295 | 0.771477 | − | 0.636258i | \(-0.219518\pi\) | ||||
0.771477 | + | 0.636258i | \(0.219518\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.51749e6 | −0.149272 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.72534e6 | 0.157207 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.79516e6 | 0.411039 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.41641e6 | 0.267753 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.80732e7 | 1.99490 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.52125e6 | −0.0627772 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.97440e7 | 1.22064 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.03813e7 | 0.423673 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −838774. | −0.0340427 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.15620e7 | 1.67756 | 0.838781 | − | 0.544469i | \(-0.183269\pi\) | ||||
0.838781 | + | 0.544469i | \(0.183269\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.65229e7 | 1.46607 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.55917e6 | −0.381614 | −0.190807 | − | 0.981628i | \(-0.561110\pi\) | ||||
−0.190807 | + | 0.981628i | \(0.561110\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.70138e6 | −0.107253 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.58737e7 | −0.626794 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −98794.6 | −0.00387980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.20453e7 | −0.470469 | −0.235234 | − | 0.971939i | \(-0.575586\pi\) | ||||
−0.235234 | + | 0.971939i | \(0.575586\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.12505e7 | 2.37936 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.10244e7 | −3.51685 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.68963e6 | 0.333924 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.66026e7 | 1.39898 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.42707e7 | −0.922661 | −0.461331 | − | 0.887228i | \(-0.652628\pi\) | ||||
−0.461331 | + | 0.887228i | \(0.652628\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.19771e6 | −0.0452874 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.63826e7 | 0.616140 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.29015e6 | −0.0482625 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.02014e7 | 0.751679 | 0.375840 | − | 0.926685i | \(-0.377354\pi\) | ||||
0.375840 | + | 0.926685i | \(0.377354\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.88747e7 | −1.43881 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.68084e6 | 0.245956 | 0.122978 | − | 0.992409i | \(-0.460756\pi\) | ||||
0.122978 | + | 0.992409i | \(0.460756\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.25612e7 | −0.826195 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 319911. | 0.0116533 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.19373e7 | 1.15724 | 0.578619 | − | 0.815598i | \(-0.303592\pi\) | ||||
0.578619 | + | 0.815598i | \(0.303592\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.03712e7 | 2.53647 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.53361e6 | 0.341827 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.26242e7 | 0.806938 | 0.403469 | − | 0.914993i | \(-0.367804\pi\) | ||||
0.403469 | + | 0.914993i | \(0.367804\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.15402e6 | −0.182868 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.41859e6 | 0.0853657 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.19513e7 | 0.419631 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.79978e7 | −0.977947 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.12470e7 | 1.43327 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.17547e6 | −0.317183 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.38201e7 | −0.819178 | −0.409589 | − | 0.912270i | \(-0.634328\pi\) | ||||
−0.409589 | + | 0.912270i | \(0.634328\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.61059e7 | −0.551032 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.87074e7 | −0.636746 | −0.318373 | − | 0.947965i | \(-0.603136\pi\) | ||||
−0.318373 | + | 0.947965i | \(0.603136\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.02612e7 | 0.347470 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.39987e7 | 2.49294 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.50783e7 | 0.505376 | 0.252688 | − | 0.967548i | \(-0.418685\pi\) | ||||
0.252688 | + | 0.967548i | \(0.418685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.60644e6 | −0.153606 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.22785e7 | −1.40264 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.38312e6 | 0.0786614 | 0.0393307 | − | 0.999226i | \(-0.487477\pi\) | ||||
0.0393307 | + | 0.999226i | \(0.487477\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.28703e6 | −0.107948 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.07579e7 | 0.678250 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.85537e7 | 0.603170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.86331e7 | −1.57307 | −0.786535 | − | 0.617546i | \(-0.788127\pi\) | ||||
−0.786535 | + | 0.617546i | \(0.788127\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.81268e7 | 2.19253 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.11357e7 | 0.356584 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.73445e7 | −0.552617 | −0.276309 | − | 0.961069i | \(-0.589111\pi\) | ||||
−0.276309 | + | 0.961069i | \(0.589111\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.32501e6 | 0.0420056 |
(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 | 448.6.a.v.1.2 | 2 | ||
4.3 | odd | 2 | 448.6.a.t.1.1 | 2 | |||
8.3 | odd | 2 | 112.6.a.i.1.2 | 2 | |||
8.5 | even | 2 | 56.6.a.e.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 504.6.a.i.1.2 | 2 | |||
24.11 | even | 2 | 1008.6.a.bd.1.2 | 2 | |||
56.5 | odd | 6 | 392.6.i.i.361.1 | 4 | |||
56.13 | odd | 2 | 392.6.a.d.1.2 | 2 | |||
56.27 | even | 2 | 784.6.a.u.1.1 | 2 | |||
56.37 | even | 6 | 392.6.i.j.361.2 | 4 | |||
56.45 | odd | 6 | 392.6.i.i.177.1 | 4 | |||
56.53 | even | 6 | 392.6.i.j.177.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.a.e.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
112.6.a.i.1.2 | 2 | 8.3 | odd | 2 | |||
392.6.a.d.1.2 | 2 | 56.13 | odd | 2 | |||
392.6.i.i.177.1 | 4 | 56.45 | odd | 6 | |||
392.6.i.i.361.1 | 4 | 56.5 | odd | 6 | |||
392.6.i.j.177.2 | 4 | 56.53 | even | 6 | |||
392.6.i.j.361.2 | 4 | 56.37 | even | 6 | |||
448.6.a.t.1.1 | 2 | 4.3 | odd | 2 | |||
448.6.a.v.1.2 | 2 | 1.1 | even | 1 | trivial | ||
504.6.a.i.1.2 | 2 | 24.5 | odd | 2 | |||
784.6.a.u.1.1 | 2 | 56.27 | even | 2 | |||
1008.6.a.bd.1.2 | 2 | 24.11 | even | 2 |