Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,6,Mod(1,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, 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("392.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.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: | \(62.8704573667\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 167x^{3} - 387x^{2} + 1720x + 2340 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.94609\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 392.1 |
$q$-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 | ||||||||
\(3\) | 14.6817 | 0.941831 | 0.470915 | − | 0.882178i | \(-0.343924\pi\) | ||||
0.470915 | + | 0.882178i | \(0.343924\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −72.1603 | −1.29084 | −0.645421 | − | 0.763827i | \(-0.723318\pi\) | ||||
−0.645421 | + | 0.763827i | \(0.723318\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −27.4480 | −0.112955 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −246.305 | −0.613750 | −0.306875 | − | 0.951750i | \(-0.599283\pi\) | ||||
−0.306875 | + | 0.951750i | \(0.599283\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1130.90 | −1.85594 | −0.927971 | − | 0.372652i | \(-0.878448\pi\) | ||||
−0.927971 | + | 0.372652i | \(0.878448\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1059.43 | −1.21576 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1644.26 | 1.37991 | 0.689953 | − | 0.723855i | \(-0.257631\pi\) | ||||
0.689953 | + | 0.723855i | \(0.257631\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1646.23 | 1.04618 | 0.523091 | − | 0.852277i | \(-0.324779\pi\) | ||||
0.523091 | + | 0.852277i | \(0.324779\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −469.033 | −0.184878 | −0.0924388 | − | 0.995718i | \(-0.529466\pi\) | ||||
−0.0924388 | + | 0.995718i | \(0.529466\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2082.11 | 0.666275 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3970.63 | −1.04822 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5816.06 | 1.28420 | 0.642102 | − | 0.766620i | \(-0.278063\pi\) | ||||
0.642102 | + | 0.766620i | \(0.278063\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5738.00 | 1.07240 | 0.536199 | − | 0.844092i | \(-0.319860\pi\) | ||||
0.536199 | + | 0.844092i | \(0.319860\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3616.17 | −0.578048 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 435.509 | 0.0522990 | 0.0261495 | − | 0.999658i | \(-0.491675\pi\) | ||||
0.0261495 | + | 0.999658i | \(0.491675\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16603.5 | −1.74798 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11216.3 | 1.04205 | 0.521027 | − | 0.853540i | \(-0.325549\pi\) | ||||
0.521027 | + | 0.853540i | \(0.325549\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6147.31 | 0.507007 | 0.253504 | − | 0.967334i | \(-0.418417\pi\) | ||||
0.253504 | + | 0.967334i | \(0.418417\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1980.66 | 0.145807 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −14621.2 | −0.965472 | −0.482736 | − | 0.875766i | \(-0.660357\pi\) | ||||
−0.482736 | + | 0.875766i | \(0.660357\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 24140.6 | 1.29964 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 26805.9 | 1.31081 | 0.655405 | − | 0.755277i | \(-0.272498\pi\) | ||||
0.655405 | + | 0.755277i | \(0.272498\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17773.4 | 0.792254 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 24169.5 | 0.985327 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 25054.0 | 0.937018 | 0.468509 | − | 0.883459i | \(-0.344791\pi\) | ||||
0.468509 | + | 0.883459i | \(0.344791\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15745.8 | 0.541800 | 0.270900 | − | 0.962607i | \(-0.412679\pi\) | ||||
0.270900 | + | 0.962607i | \(0.412679\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 81605.8 | 2.39573 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20233.0 | 0.550646 | 0.275323 | − | 0.961352i | \(-0.411215\pi\) | ||||
0.275323 | + | 0.961352i | \(0.411215\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6886.20 | −0.174123 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −69564.9 | −1.63774 | −0.818869 | − | 0.573980i | \(-0.805399\pi\) | ||||
−0.818869 | + | 0.573980i | \(0.805399\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10481.2 | 0.230200 | 0.115100 | − | 0.993354i | \(-0.463281\pi\) | ||||
0.115100 | + | 0.993354i | \(0.463281\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 30568.9 | 0.627518 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −90425.7 | −1.63014 | −0.815068 | − | 0.579365i | \(-0.803301\pi\) | ||||
−0.815068 | + | 0.579365i | \(0.803301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −51625.7 | −0.874286 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 30880.2 | 0.492023 | 0.246011 | − | 0.969267i | \(-0.420880\pi\) | ||||
0.246011 | + | 0.969267i | \(0.420880\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −118651. | −1.78124 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 85389.5 | 1.20950 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16493.6 | −0.220719 | −0.110359 | − | 0.993892i | \(-0.535200\pi\) | ||||
−0.110359 | + | 0.993892i | \(0.535200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 84243.5 | 1.01002 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −118793. | −1.35046 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 103206. | 1.11372 | 0.556860 | − | 0.830606i | \(-0.312006\pi\) | ||||
0.556860 | + | 0.830606i | \(0.312006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6760.59 | 0.0693260 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 45622.9 | 0.445020 | 0.222510 | − | 0.974930i | \(-0.428575\pi\) | ||||
0.222510 | + | 0.974930i | \(0.428575\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 110143. | 1.02297 | 0.511484 | − | 0.859293i | \(-0.329096\pi\) | ||||
0.511484 | + | 0.859293i | \(0.329096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4785.08 | −0.0404045 | −0.0202022 | − | 0.999796i | \(-0.506431\pi\) | ||||
−0.0202022 | + | 0.999796i | \(0.506431\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −104843. | −0.845229 | −0.422615 | − | 0.906309i | \(-0.638888\pi\) | ||||
−0.422615 | + | 0.906309i | \(0.638888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6394.01 | 0.0492568 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12359.7 | −0.0910570 | −0.0455285 | − | 0.998963i | \(-0.514497\pi\) | ||||
−0.0455285 | + | 0.998963i | \(0.514497\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33845.6 | 0.238648 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 31040.9 | 0.209638 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −100385. | −0.623311 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 164674. | 0.981438 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 75255.4 | 0.430787 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15641.1 | −0.0860517 | −0.0430258 | − | 0.999074i | \(-0.513700\pi\) | ||||
−0.0430258 | + | 0.999074i | \(0.513700\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 90252.9 | 0.477515 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 87498.5 | 0.445474 | 0.222737 | − | 0.974879i | \(-0.428501\pi\) | ||||
0.222737 | + | 0.974879i | \(0.428501\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 286522. | 1.35308 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −351405. | −1.59958 | −0.799791 | − | 0.600278i | \(-0.795056\pi\) | ||||
−0.799791 | + | 0.600278i | \(0.795056\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 401624. | 1.76313 | 0.881563 | − | 0.472067i | \(-0.156492\pi\) | ||||
0.881563 | + | 0.472067i | \(0.156492\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −214664. | −0.909311 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 278545. | 1.13908 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −419688. | −1.65770 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 442998. | 1.63469 | 0.817347 | − | 0.576146i | \(-0.195444\pi\) | ||||
0.817347 | + | 0.576146i | \(0.195444\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 289123. | 1.03191 | 0.515953 | − | 0.856617i | \(-0.327438\pi\) | ||||
0.515953 | + | 0.856617i | \(0.327438\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −45131.8 | −0.155867 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −414055. | −1.38430 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 563102. | 1.82322 | 0.911608 | − | 0.411060i | \(-0.134841\pi\) | ||||
0.911608 | + | 0.411060i | \(0.134841\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 393555. | 1.23456 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 638572. | 1.88253 | 0.941263 | − | 0.337674i | \(-0.109640\pi\) | ||||
0.941263 | + | 0.337674i | \(0.109640\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 260944. | 0.746169 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −72016.8 | −0.199822 | −0.0999108 | − | 0.994996i | \(-0.531856\pi\) | ||||
−0.0999108 | + | 0.994996i | \(0.531856\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 907634. | 2.44452 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −45185.9 | −0.118171 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19019.4 | −0.0483150 | −0.0241575 | − | 0.999708i | \(-0.507690\pi\) | ||||
−0.0241575 | + | 0.999708i | \(0.507690\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 367836. | 0.882512 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −109948. | −0.256482 | −0.128241 | − | 0.991743i | \(-0.540933\pi\) | ||||
−0.128241 | + | 0.991743i | \(0.540933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −781927. | −1.77407 | −0.887033 | − | 0.461706i | \(-0.847238\pi\) | ||||
−0.887033 | + | 0.461706i | \(0.847238\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 231175. | 0.510284 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −31426.5 | −0.0675097 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −404990. | −0.846916 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −877632. | −1.74072 | −0.870360 | − | 0.492415i | \(-0.836114\pi\) | ||||
−0.870360 | + | 0.492415i | \(0.836114\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2524.01 | 0.00487751 | 0.00243876 | − | 0.999997i | \(-0.499224\pi\) | ||||
0.00243876 | + | 0.999997i | \(0.499224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.19811e6 | 2.25637 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −375303. | −0.688996 | −0.344498 | − | 0.938787i | \(-0.611951\pi\) | ||||
−0.344498 | + | 0.938787i | \(0.611951\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 210532. | 0.376864 | 0.188432 | − | 0.982086i | \(-0.439659\pi\) | ||||
0.188432 | + | 0.982086i | \(0.439659\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 297054. | 0.518616 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −809372. | −1.34513 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12874.0 | 0.0208828 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −405476. | −0.642094 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 323898. | 0.500844 | 0.250422 | − | 0.968137i | \(-0.419431\pi\) | ||||
0.250422 | + | 0.968137i | \(0.419431\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.02133e6 | −1.54247 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −443592. | −0.654466 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 153882. | 0.216809 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.85949e6 | −2.56102 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 413352. | 0.556618 | 0.278309 | − | 0.960492i | \(-0.410226\pi\) | ||||
0.278309 | + | 0.960492i | \(0.410226\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −57149.8 | −0.0752590 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 623945. | 0.803677 | 0.401839 | − | 0.915711i | \(-0.368371\pi\) | ||||
0.401839 | + | 0.915711i | \(0.368371\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 441658. | 0.556541 | 0.278271 | − | 0.960503i | \(-0.410239\pi\) | ||||
0.278271 | + | 0.960503i | \(0.410239\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −58664.3 | −0.0707920 | −0.0353960 | − | 0.999373i | \(-0.511269\pi\) | ||||
−0.0353960 | + | 0.999373i | \(0.511269\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.05507e6 | 1.24627 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.32760e6 | −1.53531 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −633286. | −0.717142 | −0.358571 | − | 0.933502i | \(-0.616736\pi\) | ||||
−0.358571 | + | 0.933502i | \(0.616736\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 108888. | 0.120763 | 0.0603817 | − | 0.998175i | \(-0.480768\pi\) | ||||
0.0603817 | + | 0.998175i | \(0.480768\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 206911. | 0.224785 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.86172e6 | −1.94166 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 453374. | 0.463402 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −48619.2 | −0.0487106 | −0.0243553 | − | 0.999703i | \(-0.507753\pi\) | ||||
−0.0243553 | + | 0.999703i | \(0.507753\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 115525. | 0.113469 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.74199e6 | −1.67763 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −591667. | −0.558785 | −0.279393 | − | 0.960177i | \(-0.590133\pi\) | ||||
−0.279393 | + | 0.960177i | \(0.590133\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −159639. | −0.145057 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 926427. | 0.825889 | 0.412945 | − | 0.910756i | \(-0.364500\pi\) | ||||
0.412945 | + | 0.910756i | \(0.364500\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.93432e6 | −1.69205 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −242153. | −0.207880 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.08829e6 | −1.75958 | −0.879792 | − | 0.475359i | \(-0.842318\pi\) | ||||
−0.879792 | + | 0.475359i | \(0.842318\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.15806e6 | 1.78501 | 0.892503 | − | 0.451041i | \(-0.148947\pi\) | ||||
0.892503 | + | 0.451041i | \(0.148947\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −512833. | −0.408926 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 912365. | 0.714446 | 0.357223 | − | 0.934019i | \(-0.383724\pi\) | ||||
0.357223 | + | 0.934019i | \(0.383724\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −157497. | −0.121133 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 357409. | 0.270022 | 0.135011 | − | 0.990844i | \(-0.456893\pi\) | ||||
0.135011 | + | 0.990844i | \(0.456893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.23669e6 | −1.66012 | −0.830062 | − | 0.557671i | \(-0.811695\pi\) | ||||
−0.830062 | + | 0.557671i | \(0.811695\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.74408e6 | −1.27190 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.28375e6 | 0.904138 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.51524e6 | 1.04894 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.18692e6 | 1.48821 | 0.744103 | − | 0.668065i | \(-0.232877\pi\) | ||||
0.744103 | + | 0.668065i | \(0.232877\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.80791e6 | −1.20954 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 977986. | 0.643342 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 530428. | 0.343122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 669822. | 0.419134 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.13622e6 | −0.699379 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 56855.1 | 0.0344289 | 0.0172144 | − | 0.999852i | \(-0.494520\pi\) | ||||
0.0172144 | + | 0.999852i | \(0.494520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.61708e6 | 0.963463 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 699329. | 0.409997 | 0.204999 | − | 0.978762i | \(-0.434281\pi\) | ||||
0.204999 | + | 0.978762i | \(0.434281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.23809e6 | −1.29127 | −0.645636 | − | 0.763646i | \(-0.723408\pi\) | ||||
−0.645636 | + | 0.763646i | \(0.723408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.66782e6 | −1.49110 | −0.745552 | − | 0.666447i | \(-0.767814\pi\) | ||||
−0.745552 | + | 0.666447i | \(0.767814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.43252e6 | −0.788179 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −70253.0 | −0.0380542 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.70684e6 | 1.44363 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.35465e6 | −1.23657 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.53928e6 | −0.796063 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.85083e6 | −0.928530 | −0.464265 | − | 0.885696i | \(-0.653682\pi\) | ||||
−0.464265 | + | 0.885696i | \(0.653682\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11953.9 | −0.00590742 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.46002e6 | −0.710798 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.10700e6 | 0.530972 | 0.265486 | − | 0.964115i | \(-0.414468\pi\) | ||||
0.265486 | + | 0.964115i | \(0.414468\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −181462. | −0.0857603 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.41330e6 | −0.658184 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 496910. | 0.224766 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.22108e6 | 0.990241 | 0.495121 | − | 0.868824i | \(-0.335124\pi\) | ||||
0.495121 | + | 0.868824i | \(0.335124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 114207. | 0.0501913 | 0.0250957 | − | 0.999685i | \(-0.492011\pi\) | ||||
0.0250957 | + | 0.999685i | \(0.492011\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.49038e6 | 1.94543 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −610115. | −0.260600 | −0.130300 | − | 0.991475i | \(-0.541594\pi\) | ||||
−0.130300 | + | 0.991475i | \(0.541594\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.01983e6 | 2.11406 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.37887e6 | −0.564658 | −0.282329 | − | 0.959318i | \(-0.591107\pi\) | ||||
−0.282329 | + | 0.959318i | \(0.591107\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 233989. | 0.0944988 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.47382e6 | −0.587054 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −756328. | −0.297152 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −531415. | −0.205953 | −0.102977 | − | 0.994684i | \(-0.532837\pi\) | ||||
−0.102977 | + | 0.994684i | \(0.532837\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −307865. | −0.117705 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 661371. | 0.246135 | 0.123067 | − | 0.992398i | \(-0.460727\pi\) | ||||
0.123067 | + | 0.992398i | \(0.460727\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.10488e6 | 0.405728 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.57736e6 | −2.38341 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.58043e6 | −1.28037 | −0.640187 | − | 0.768219i | \(-0.721143\pi\) | ||||
−0.640187 | + | 0.768219i | \(0.721143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −229638. | −0.0810461 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.64671e6 | −0.921956 | −0.460978 | − | 0.887412i | \(-0.652501\pi\) | ||||
−0.460978 | + | 0.887412i | \(0.652501\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −168732. | −0.0572689 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.51493e6 | −0.842660 | −0.421330 | − | 0.906907i | \(-0.638437\pi\) | ||||
−0.421330 | + | 0.906907i | \(0.638437\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −771215. | −0.255113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.28463e6 | 0.419561 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.52514e6 | 2.10425 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.14870e6 | 1.00266 | 0.501331 | − | 0.865256i | \(-0.332844\pi\) | ||||
0.501331 | + | 0.865256i | \(0.332844\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.43733e6 | 0.756925 | 0.378462 | − | 0.925617i | \(-0.376453\pi\) | ||||
0.378462 | + | 0.925617i | \(0.376453\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.48908e6 | −1.99031 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.72533e6 | 1.12857 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −107268. | −0.0320985 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.17668e6 | 1.53018 | 0.765091 | − | 0.643922i | \(-0.222694\pi\) | ||||
0.765091 | + | 0.643922i | \(0.222694\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.15922e6 | −1.50654 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.22833e6 | −0.635124 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.89652e6 | 1.66057 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 225726. | 0.0628125 | 0.0314062 | − | 0.999507i | \(-0.490001\pi\) | ||||
0.0314062 | + | 0.999507i | \(0.490001\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.79842e6 | −0.769498 | −0.384749 | − | 0.923021i | \(-0.625712\pi\) | ||||
−0.384749 | + | 0.923021i | \(0.625712\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 401324. | 0.109055 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.42353e6 | 0.919396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.08951e6 | 1.07282 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.41262e6 | 0.884901 | 0.442450 | − | 0.896793i | \(-0.354109\pi\) | ||||
0.442450 | + | 0.896793i | \(0.354109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.63239e6 | 0.418412 | 0.209206 | − | 0.977872i | \(-0.432912\pi\) | ||||
0.209206 | + | 0.977872i | \(0.432912\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.16173e6 | −1.56128 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −772139. | −0.193416 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −170371. | −0.0421924 | −0.0210962 | − | 0.999777i | \(-0.506716\pi\) | ||||
−0.0210962 | + | 0.999777i | \(0.506716\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 700975. | 0.169704 | 0.0848522 | − | 0.996394i | \(-0.472958\pi\) | ||||
0.0848522 | + | 0.996394i | \(0.472958\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.19018e6 | 0.284913 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.50396e6 | 1.53960 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.56769e6 | 0.366983 | 0.183491 | − | 0.983021i | \(-0.441260\pi\) | ||||
0.183491 | + | 0.983021i | \(0.441260\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.76263e6 | −0.639560 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.24482e6 | 0.971881 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.37156e6 | 0.531183 | 0.265591 | − | 0.964086i | \(-0.414433\pi\) | ||||
0.265591 | + | 0.964086i | \(0.414433\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.52877e6 | −1.44644 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22412.1 | −0.00491167 | −0.00245584 | − | 0.999997i | \(-0.500782\pi\) | ||||
−0.00245584 | + | 0.999997i | \(0.500782\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 704311. | 0.152691 | 0.0763453 | − | 0.997081i | \(-0.475675\pi\) | ||||
0.0763453 | + | 0.997081i | \(0.475675\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.07903e6 | −1.30377 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.32159e6 | −0.280418 | −0.140209 | − | 0.990122i | \(-0.544777\pi\) | ||||
−0.140209 | + | 0.990122i | \(0.544777\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.26729e6 | 1.71716 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.51411e6 | −0.311175 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.42764e6 | 0.697045 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −735768. | −0.148062 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.12503e6 | −1.81717 | −0.908585 | − | 0.417700i | \(-0.862836\pi\) | ||||
−0.908585 | + | 0.417700i | \(0.862836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −492516. | −0.0970638 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.44738e6 | −1.43764 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.35483e6 | 1.21418 | 0.607088 | − | 0.794635i | \(-0.292338\pi\) | ||||
0.607088 | + | 0.794635i | \(0.292338\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.37532e6 | 1.77302 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.23640e6 | 0.793037 | 0.396518 | − | 0.918027i | \(-0.370218\pi\) | ||||
0.396518 | + | 0.918027i | \(0.370218\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.56313e6 | 1.77208 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −487846. | −0.0894890 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.32644e6 | 1.13739 | 0.568694 | − | 0.822550i | \(-0.307449\pi\) | ||||
0.568694 | + | 0.822550i | \(0.307449\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.05733e6 | −0.188198 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −725474. | −0.127850 | −0.0639251 | − | 0.997955i | \(-0.520362\pi\) | ||||
−0.0639251 | + | 0.997955i | \(0.520362\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.29216e6 | −0.574451 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.33256e7 | 2.30232 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34453.2 | −0.00589434 | −0.00294717 | − | 0.999996i | \(-0.500938\pi\) | ||||
−0.00294717 | + | 0.999996i | \(0.500938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.53659e6 | −1.09662 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.94792e6 | −1.32049 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.60128e6 | 0.592558 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −279237. | −0.0455046 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.41567e6 | 0.712692 | 0.356346 | − | 0.934354i | \(-0.384022\pi\) | ||||
0.356346 | + | 0.934354i | \(0.384022\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 206472. | 0.0330071 | 0.0165035 | − | 0.999864i | \(-0.494747\pi\) | ||||
0.0165035 | + | 0.999864i | \(0.494747\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.43478e6 | 1.47981 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.21635e6 | −0.965820 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −687684. | −0.105841 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.26845e7 | −1.93399 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 345293. | 0.0521558 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.61423e6 | −0.241562 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 144952. | 0.0212927 | 0.0106464 | − | 0.999943i | \(-0.496611\pi\) | ||||
0.0106464 | + | 0.999943i | \(0.496611\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.14800e7 | −1.67087 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.56552e6 | 1.09106 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.65203e6 | −0.521874 | −0.260937 | − | 0.965356i | \(-0.584031\pi\) | ||||
−0.260937 | + | 0.965356i | \(0.584031\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −432191. | −0.0611990 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.57459e6 | 1.34351 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −461394. | −0.0635827 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.55923e6 | 1.16895 | 0.584476 | − | 0.811411i | \(-0.301300\pi\) | ||||
0.584476 | + | 0.811411i | \(0.301300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.95197e6 | −0.940976 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.94594e6 | −0.797652 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.81296e6 | 0.506981 | 0.253490 | − | 0.967338i | \(-0.418421\pi\) | ||||
0.253490 | + | 0.967338i | \(0.418421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 891883. | 0.117540 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 304441. | 0.0394206 | 0.0197103 | − | 0.999806i | \(-0.493726\pi\) | ||||
0.0197103 | + | 0.999806i | \(0.493726\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.70934e6 | 1.24623 | 0.623117 | − | 0.782129i | \(-0.285866\pi\) | ||||
0.623117 | + | 0.782129i | \(0.285866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.28851e7 | −1.63946 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −976578. | −0.123179 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.17345e7 | 1.46732 | 0.733660 | − | 0.679517i | \(-0.237810\pi\) | ||||
0.733660 | + | 0.679517i | \(0.237810\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 37056.8 | 0.00459379 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.60241e6 | −0.804510 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.23992e6 | −0.270609 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.17417e7 | −1.40648 | −0.703241 | − | 0.710951i | \(-0.748265\pi\) | ||||
−0.703241 | + | 0.710951i | \(0.748265\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.44609e6 | 1.12192 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.51009e6 | −0.648918 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.50643e6 | 0.993369 | 0.496684 | − | 0.867931i | \(-0.334551\pi\) | ||||
0.496684 | + | 0.867931i | \(0.334551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.09096e6 | 0.354943 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.04802e6 | 0.802601 | 0.401301 | − | 0.915946i | \(-0.368558\pi\) | ||||
0.401301 | + | 0.915946i | \(0.368558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.32634e7 | 1.49785 | 0.748923 | − | 0.662657i | \(-0.230571\pi\) | ||||
0.748923 | + | 0.662657i | \(0.230571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −555355. | −0.0621982 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.24380e6 | 0.804597 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.10341e7 | −1.21553 | −0.607765 | − | 0.794117i | \(-0.707934\pi\) | ||||
−0.607765 | + | 0.794117i | \(0.707934\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.65351e7 | 1.79186 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.13671e6 | −0.229665 | −0.114832 | − | 0.993385i | \(-0.536633\pi\) | ||||
−0.114832 | + | 0.993385i | \(0.536633\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.18829e7 | −1.26688 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.02769e7 | 1.08680 | 0.543399 | − | 0.839475i | \(-0.317137\pi\) | ||||
0.543399 | + | 0.839475i | \(0.317137\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.58320e6 | 0.585675 | 0.292838 | − | 0.956162i | \(-0.405400\pi\) | ||||
0.292838 | + | 0.956162i | \(0.405400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.86236e6 | 0.193791 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.19370e7 | −1.22235 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.95307e6 | −0.604744 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 716092. | 0.0721676 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.34087e7 | 1.34064 | 0.670322 | − | 0.742071i | \(-0.266156\pi\) | ||||
0.670322 | + | 0.742071i | \(0.266156\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.75537e6 | 0.471710 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.12867e6 | 0.111079 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.90942e6 | 0.184991 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.03725e6 | 0.0997103 | 0.0498551 | − | 0.998756i | \(-0.484124\pi\) | ||||
0.0498551 | + | 0.998756i | \(0.484124\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.71227e7 | 1.63322 | 0.816608 | − | 0.577192i | \(-0.195852\pi\) | ||||
0.816608 | + | 0.577192i | \(0.195852\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.51268e6 | −0.616397 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.66382e6 | −0.625839 | −0.312919 | − | 0.949780i | \(-0.601307\pi\) | ||||
−0.312919 | + | 0.949780i | \(0.601307\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.17093e6 | −0.575094 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.95841e7 | 1.79730 | 0.898649 | − | 0.438669i | \(-0.144550\pi\) | ||||
0.898649 | + | 0.438669i | \(0.144550\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.31392e6 | −0.575037 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −287689. | −0.0260022 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.56939e7 | 1.40772 | 0.703862 | − | 0.710337i | \(-0.251457\pi\) | ||||
0.703862 | + | 0.710337i | \(0.251457\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.85789e6 | −0.165393 | −0.0826964 | − | 0.996575i | \(-0.526353\pi\) | ||||
−0.0826964 | + | 0.996575i | \(0.526353\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.73005e7 | −2.41205 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.72793e6 | −0.237420 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.06870e6 | 0.524240 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.87826e6 | −0.332530 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.12319e7 | −0.955907 | −0.477953 | − | 0.878385i | \(-0.658621\pi\) | ||||
−0.477953 | + | 0.878385i | \(0.658621\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.26729e6 | −0.698399 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.94349e6 | −0.330681 | −0.165340 | − | 0.986237i | \(-0.552872\pi\) | ||||
−0.165340 | + | 0.986237i | \(0.552872\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.16056e6 | 0.756928 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.27174e7 | −1.04315 | −0.521577 | − | 0.853204i | \(-0.674656\pi\) | ||||
−0.521577 | + | 0.853204i | \(0.674656\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.53575e7 | 2.06481 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.48429e6 | 0.524168 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.03146e7 | −2.43279 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.31891e6 | 0.662783 | 0.331391 | − | 0.943493i | \(-0.392482\pi\) | ||||
0.331391 | + | 0.943493i | \(0.392482\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.89813e7 | −2.27592 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.84426e7 | 1.43793 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −861291. | −0.0666741 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.06600e7 | 0.819337 | 0.409669 | − | 0.912234i | \(-0.365644\pi\) | ||||
0.409669 | + | 0.912234i | \(0.365644\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 716950. | 0.0547143 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.54903e7 | 1.17378 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.24696e7 | −0.931617 | −0.465809 | − | 0.884886i | \(-0.654236\pi\) | ||||
−0.465809 | + | 0.884886i | \(0.654236\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.48201e6 | 0.184132 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.69131e6 | −0.198262 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.00999e7 | −1.47038 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.29771e6 | −0.675426 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34256.9 | −0.00247130 | −0.00123565 | − | 0.999999i | \(-0.500393\pi\) | ||||
−0.00123565 | + | 0.999999i | \(0.500393\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.59865e6 | 0.113739 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.21097e7 | 0.855632 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.37823e6 | −0.658090 | −0.329045 | − | 0.944314i | \(-0.606727\pi\) | ||||
−0.329045 | + | 0.944314i | \(0.606727\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.55829e7 | 1.08600 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.01078e7 | 0.699622 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.55584e6 | 0.313190 | 0.156595 | − | 0.987663i | \(-0.449948\pi\) | ||||
0.156595 | + | 0.987663i | \(0.449948\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.98348e6 | −0.337959 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.44646e7 | 1.64788 | 0.823941 | − | 0.566675i | \(-0.191770\pi\) | ||||
0.823941 | + | 0.566675i | \(0.191770\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.73332e7 | −1.82871 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.06680e6 | 0.336715 | 0.168357 | − | 0.985726i | \(-0.446154\pi\) | ||||
0.168357 | + | 0.985726i | \(0.446154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.19669e7 | −2.11013 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −847601. | −0.0555764 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.12217e7 | −1.37303 | −0.686517 | − | 0.727114i | \(-0.740861\pi\) | ||||
−0.686517 | + | 0.727114i | \(0.740861\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −713813. | −0.0458772 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.08632e7 | −1.33203 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −184262. | −0.0116868 | −0.00584342 | − | 0.999983i | \(-0.501860\pi\) | ||||
−0.00584342 | + | 0.999983i | \(0.501860\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.69610e6 | 0.106868 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.06343e7 | −0.665650 | −0.332825 | − | 0.942989i | \(-0.608002\pi\) | ||||
−0.332825 | + | 0.942989i | \(0.608002\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.25673e6 | 0.201200 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.83335e7 | −1.73905 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.46176e6 | −0.333056 | −0.166528 | − | 0.986037i | \(-0.553256\pi\) | ||||
−0.166528 | + | 0.986037i | \(0.553256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.68667e6 | −0.526281 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.68523e7 | 1.01440 | 0.507201 | − | 0.861828i | \(-0.330680\pi\) | ||||
0.507201 | + | 0.861828i | \(0.330680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.19471e7 | 0.714511 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.84647e7 | 1.09018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.71342e7 | 1.00516 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.30934e7 | −1.34612 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.06336e7 | −2.35349 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.33846e7 | −0.770317 | −0.385158 | − | 0.922851i | \(-0.625853\pi\) | ||||
−0.385158 | + | 0.922851i | \(0.625853\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.36015e7 | 0.777848 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.78068e7 | −1.00555 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.83991e7 | −1.59362 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.88049e6 | 0.104864 | 0.0524319 | − | 0.998625i | \(-0.483303\pi\) | ||||
0.0524319 | + | 0.998625i | \(0.483303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.40412e7 | −1.33226 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 452716. | 0.0249313 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.58158e6 | −0.141285 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.06596e7 | −1.65723 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.39864e6 | −0.0751337 | −0.0375668 | − | 0.999294i | \(-0.511961\pi\) | ||||
−0.0375668 | + | 0.999294i | \(0.511961\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.91052e7 | 1.55388 | 0.776941 | − | 0.629573i | \(-0.216770\pi\) | ||||
0.776941 | + | 0.629573i | \(0.216770\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.16839e7 | 1.68117 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.60796e7 | −2.43004 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.01199e7 | 0.530422 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.02666e7 | −1.56713 | −0.783566 | − | 0.621309i | \(-0.786601\pi\) | ||||
−0.783566 | + | 0.621309i | \(0.786601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.60589e7 | 0.826447 | 0.413224 | − | 0.910630i | \(-0.364403\pi\) | ||||
0.413224 | + | 0.910630i | \(0.364403\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.52926e6 | −0.385139 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.36135e6 | −0.221747 | −0.110873 | − | 0.993835i | \(-0.535365\pi\) | ||||
−0.110873 | + | 0.993835i | \(0.535365\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.43234e6 | 0.122924 | 0.0614622 | − | 0.998109i | \(-0.480424\pi\) | ||||
0.0614622 | + | 0.998109i | \(0.480424\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.33951e7 | 0.672887 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.19675e6 | 0.257938 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.27835e7 | −1.12410 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.83907e7 | −1.39243 | −0.696213 | − | 0.717836i | \(-0.745133\pi\) | ||||
−0.696213 | + | 0.717836i | \(0.745133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.33154e7 | 0.649178 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.24736e6 | 0.254315 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.54951e7 | −3.15549 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.28384e7 | −1.56356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −204268. | −0.00966890 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.36423e7 | 0.641972 | 0.320986 | − | 0.947084i | \(-0.395986\pi\) | ||||
0.320986 | + | 0.947084i | \(0.395986\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.26063e6 | 0.152541 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.26545e7 | 0.588562 | 0.294281 | − | 0.955719i | \(-0.404920\pi\) | ||||
0.294281 | + | 0.955719i | \(0.404920\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.39148e6 | −0.388021 | −0.194011 | − | 0.980999i | \(-0.562150\pi\) | ||||
−0.194011 | + | 0.980999i | \(0.562150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.08837e7 | −0.954511 | −0.477256 | − | 0.878764i | \(-0.658368\pi\) | ||||
−0.477256 | + | 0.878764i | \(0.658368\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.37245e6 | 0.0623671 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.88476e7 | 0.851545 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.22723e7 | 1.00050 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.28814e7 | −1.02197 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.83280e6 | −0.125800 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.22777e7 | 0.978074 | 0.489037 | − | 0.872263i | \(-0.337348\pi\) | ||||
0.489037 | + | 0.872263i | \(0.337348\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.21076e7 | 1.40164 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.51345e7 | −1.09102 | −0.545508 | − | 0.838106i | \(-0.683663\pi\) | ||||
−0.545508 | + | 0.838106i | \(0.683663\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.23710e7 | 1.39719 | 0.698594 | − | 0.715518i | \(-0.253809\pi\) | ||||
0.698594 | + | 0.715518i | \(0.253809\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.65431e7 | −1.13918 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.96905e7 | 1.26709 | 0.633547 | − | 0.773704i | \(-0.281598\pi\) | ||||
0.633547 | + | 0.773704i | \(0.281598\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.27157e7 | 0.536593 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.40700e7 | −1.01006 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.93391e6 | 0.331078 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.78758e6 | 0.323163 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.33725e7 | 1.37718 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.40759e7 | 1.80879 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.64241e7 | 2.29004 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.81102e7 | 1.53824 | 0.769118 | − | 0.639107i | \(-0.220696\pi\) | ||||
0.769118 | + | 0.639107i | \(0.220696\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.25226e6 | −0.0502672 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.69460e7 | 1.47493 | 0.737466 | − | 0.675385i | \(-0.236022\pi\) | ||||
0.737466 | + | 0.675385i | \(0.236022\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.60595e6 | −0.301979 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.66816e7 | −0.658697 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.34431e7 | 0.915643 | 0.457822 | − | 0.889044i | \(-0.348630\pi\) | ||||
0.457822 | + | 0.889044i | \(0.348630\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 834728. | 0.0324262 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.86707e7 | 3.03955 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 906777. | 0.0348455 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.02320e6 | −0.115549 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.13042e7 | −1.19004 | −0.595022 | − | 0.803710i | \(-0.702857\pi\) | ||||
−0.595022 | + | 0.803710i | \(0.702857\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.02673e7 | 0.386148 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.92242e7 | 1.09324 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.12939e7 | −0.420238 | −0.210119 | − | 0.977676i | \(-0.567385\pi\) | ||||
−0.210119 | + | 0.977676i | \(0.567385\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.28590e7 | −1.21616 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.71554e6 | −0.0631578 | −0.0315789 | − | 0.999501i | \(-0.510054\pi\) | ||||
−0.0315789 | + | 0.999501i | \(0.510054\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.26082e6 | −0.192652 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.75601e7 | 1.36098 | 0.680489 | − | 0.732758i | \(-0.261767\pi\) | ||||
0.680489 | + | 0.732758i | \(0.261767\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.18532e7 | −0.427237 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.91681e7 | −1.40437 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.90008e7 | −1.74771 | −0.873857 | − | 0.486182i | \(-0.838389\pi\) | ||||
−0.873857 | + | 0.486182i | \(0.838389\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.33302e7 | 2.24700 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.10319e7 | −0.742331 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.29545e6 | 0.150038 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 131341. | 0.00456388 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −182134. | −0.00629610 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.24075e7 | 1.45840 | 0.729199 | − | 0.684301i | \(-0.239893\pi\) | ||||
0.729199 | + | 0.684301i | \(0.239893\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.97410e7 | 1.35966 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.81684e7 | −0.958770 | −0.479385 | − | 0.877605i | \(-0.659140\pi\) | ||||
−0.479385 | + | 0.877605i | \(0.659140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.45702e7 | −1.16464 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.32664e7 | −1.78532 | −0.892662 | − | 0.450727i | \(-0.851165\pi\) | ||||
−0.892662 | + | 0.450727i | \(0.851165\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.06245e6 | 0.135466 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.87774e6 | 0.0954728 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.89251e7 | −0.954754 | −0.477377 | − | 0.878699i | \(-0.658412\pi\) | ||||
−0.477377 | + | 0.878699i | \(0.658412\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.70820e7 | 0.889386 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.88329e6 | −0.0937342 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.07125e7 | 0.993414 | 0.496707 | − | 0.867918i | \(-0.334542\pi\) | ||||
0.496707 | + | 0.867918i | \(0.334542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.71733e7 | −0.874518 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.51920e7 | −0.486473 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −715992. | −0.0228124 | −0.0114062 | − | 0.999935i | \(-0.503631\pi\) | ||||
−0.0114062 | + | 0.999935i | \(0.503631\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.72925e6 | −0.0548206 |
(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 | 392.6.a.l.1.4 | 5 | ||
4.3 | odd | 2 | 784.6.a.bj.1.2 | 5 | |||
7.2 | even | 3 | 56.6.i.a.25.2 | yes | 10 | ||
7.3 | odd | 6 | 392.6.i.p.177.4 | 10 | |||
7.4 | even | 3 | 56.6.i.a.9.2 | ✓ | 10 | ||
7.5 | odd | 6 | 392.6.i.p.361.4 | 10 | |||
7.6 | odd | 2 | 392.6.a.i.1.2 | 5 | |||
21.2 | odd | 6 | 504.6.s.d.361.1 | 10 | |||
21.11 | odd | 6 | 504.6.s.d.289.1 | 10 | |||
28.11 | odd | 6 | 112.6.i.g.65.4 | 10 | |||
28.23 | odd | 6 | 112.6.i.g.81.4 | 10 | |||
28.27 | even | 2 | 784.6.a.bm.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.i.a.9.2 | ✓ | 10 | 7.4 | even | 3 | ||
56.6.i.a.25.2 | yes | 10 | 7.2 | even | 3 | ||
112.6.i.g.65.4 | 10 | 28.11 | odd | 6 | |||
112.6.i.g.81.4 | 10 | 28.23 | odd | 6 | |||
392.6.a.i.1.2 | 5 | 7.6 | odd | 2 | |||
392.6.a.l.1.4 | 5 | 1.1 | even | 1 | trivial | ||
392.6.i.p.177.4 | 10 | 7.3 | odd | 6 | |||
392.6.i.p.361.4 | 10 | 7.5 | odd | 6 | |||
504.6.s.d.289.1 | 10 | 21.11 | odd | 6 | |||
504.6.s.d.361.1 | 10 | 21.2 | odd | 6 | |||
784.6.a.bj.1.2 | 5 | 4.3 | odd | 2 | |||
784.6.a.bm.1.4 | 5 | 28.27 | even | 2 |