Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [464,6,Mod(1,464)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(464, 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("464.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 464 = 2^{4} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 464.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: | \(74.4180923932\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.90786\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 464.1 |
$q$-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 | ||||||||
\(3\) | −29.3989 | −1.88594 | −0.942972 | − | 0.332873i | \(-0.891982\pi\) | ||||
−0.942972 | + | 0.332873i | \(0.891982\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 64.0801 | 1.14630 | 0.573150 | − | 0.819451i | \(-0.305721\pi\) | ||||
0.573150 | + | 0.819451i | \(0.305721\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 138.793 | 1.07059 | 0.535293 | − | 0.844666i | \(-0.320201\pi\) | ||||
0.535293 | + | 0.844666i | \(0.320201\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 621.298 | 2.55678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −557.286 | −1.38866 | −0.694330 | − | 0.719656i | \(-0.744299\pi\) | ||||
−0.694330 | + | 0.719656i | \(0.744299\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −41.1854 | −0.0675903 | −0.0337952 | − | 0.999429i | \(-0.510759\pi\) | ||||
−0.0337952 | + | 0.999429i | \(0.510759\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1883.89 | −2.16186 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1643.99 | −1.37968 | −0.689838 | − | 0.723964i | \(-0.742318\pi\) | ||||
−0.689838 | + | 0.723964i | \(0.742318\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −258.134 | −0.164044 | −0.0820221 | − | 0.996631i | \(-0.526138\pi\) | ||||
−0.0820221 | + | 0.996631i | \(0.526138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4080.36 | −2.01907 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2828.17 | 1.11477 | 0.557385 | − | 0.830254i | \(-0.311805\pi\) | ||||
0.557385 | + | 0.830254i | \(0.311805\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 981.257 | 0.314002 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11121.6 | −2.93600 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 841.000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5980.62 | 1.11774 | 0.558872 | − | 0.829254i | \(-0.311234\pi\) | ||||
0.558872 | + | 0.829254i | \(0.311234\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16383.6 | 2.61894 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8893.86 | 1.22721 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3327.01 | −0.399531 | −0.199765 | − | 0.979844i | \(-0.564018\pi\) | ||||
−0.199765 | + | 0.979844i | \(0.564018\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1210.81 | 0.127472 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3895.80 | −0.361940 | −0.180970 | − | 0.983489i | \(-0.557924\pi\) | ||||
−0.180970 | + | 0.983489i | \(0.557924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3589.20 | 0.296023 | 0.148012 | − | 0.988986i | \(-0.452713\pi\) | ||||
0.148012 | + | 0.988986i | \(0.452713\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 39812.8 | 2.93084 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7502.91 | 0.495433 | 0.247717 | − | 0.968833i | \(-0.420320\pi\) | ||||
0.247717 | + | 0.968833i | \(0.420320\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2456.45 | 0.146156 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 48331.6 | 2.60199 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9015.58 | 0.440863 | 0.220432 | − | 0.975402i | \(-0.429253\pi\) | ||||
0.220432 | + | 0.975402i | \(0.429253\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −35710.9 | −1.59182 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7588.86 | 0.309378 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −39101.0 | −1.46237 | −0.731187 | − | 0.682177i | \(-0.761033\pi\) | ||||
−0.731187 | + | 0.682177i | \(0.761033\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3951.11 | 0.135955 | 0.0679773 | − | 0.997687i | \(-0.478345\pi\) | ||||
0.0679773 | + | 0.997687i | \(0.478345\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 86231.7 | 2.73726 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2639.16 | −0.0774787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62985.3 | −1.71416 | −0.857082 | − | 0.515180i | \(-0.827725\pi\) | ||||
−0.857082 | + | 0.515180i | \(0.827725\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −83145.1 | −2.10239 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7121.60 | −0.167661 | −0.0838304 | − | 0.996480i | \(-0.526715\pi\) | ||||
−0.0838304 | + | 0.996480i | \(0.526715\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13910.9 | −0.305525 | −0.152763 | − | 0.988263i | \(-0.548817\pi\) | ||||
−0.152763 | + | 0.988263i | \(0.548817\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −28847.9 | −0.592190 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −77347.2 | −1.48668 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 37581.7 | 0.677499 | 0.338749 | − | 0.940877i | \(-0.389996\pi\) | ||||
0.338749 | + | 0.940877i | \(0.389996\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 175987. | 2.98035 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 74905.7 | 1.19349 | 0.596746 | − | 0.802430i | \(-0.296460\pi\) | ||||
0.596746 | + | 0.802430i | \(0.296460\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −105347. | −1.58152 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24724.5 | −0.350211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 102613. | 1.37318 | 0.686590 | − | 0.727045i | \(-0.259107\pi\) | ||||
0.686590 | + | 0.727045i | \(0.259107\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5716.23 | −0.0723613 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −175824. | −2.10800 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16541.2 | −0.188044 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −25501.5 | −0.275193 | −0.137596 | − | 0.990488i | \(-0.543938\pi\) | ||||
−0.137596 | + | 0.990488i | \(0.543938\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −346241. | −3.55050 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −29590.5 | −0.288635 | −0.144317 | − | 0.989531i | \(-0.546099\pi\) | ||||
−0.144317 | + | 0.989531i | \(0.546099\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −170152. | −1.58032 | −0.790159 | − | 0.612902i | \(-0.790002\pi\) | ||||
−0.790159 | + | 0.612902i | \(0.790002\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −261470. | −2.31445 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 200423. | 1.69234 | 0.846169 | − | 0.532915i | \(-0.178903\pi\) | ||||
0.846169 | + | 0.532915i | \(0.178903\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −80642.9 | −0.650130 | −0.325065 | − | 0.945692i | \(-0.605386\pi\) | ||||
−0.325065 | + | 0.945692i | \(0.605386\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 97810.6 | 0.753492 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17299.3 | 0.127448 | 0.0637240 | − | 0.997968i | \(-0.479702\pi\) | ||||
0.0637240 | + | 0.997968i | \(0.479702\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 181229. | 1.27786 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −25588.4 | −0.172814 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −228174. | −1.47706 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 149516. | 0.928378 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 114532. | 0.682599 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −137371. | −0.786359 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −191838. | −1.05542 | −0.527711 | − | 0.849424i | \(-0.676949\pi\) | ||||
−0.527711 | + | 0.849424i | \(0.676949\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −105519. | −0.558283 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −112493. | −0.572726 | −0.286363 | − | 0.958121i | \(-0.592446\pi\) | ||||
−0.286363 | + | 0.958121i | \(0.592446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −35827.1 | −0.175623 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −712671. | −3.36554 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13514.2 | −0.0615162 | −0.0307581 | − | 0.999527i | \(-0.509792\pi\) | ||||
−0.0307581 | + | 0.999527i | \(0.509792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −315337. | −1.38432 | −0.692161 | − | 0.721743i | \(-0.743341\pi\) | ||||
−0.692161 | + | 0.721743i | \(0.743341\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −220578. | −0.934359 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22952.0 | 0.0938600 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 53891.3 | 0.212862 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −72216.9 | −0.275642 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1500.22 | −0.00553590 | −0.00276795 | − | 0.999996i | \(-0.500881\pi\) | ||||
−0.00276795 | + | 0.999996i | \(0.500881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 141060. | 0.503457 | 0.251729 | − | 0.967798i | \(-0.419001\pi\) | ||||
0.251729 | + | 0.967798i | \(0.419001\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.02141e6 | −3.52753 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 383239. | 1.28127 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −335858. | −1.08744 | −0.543721 | − | 0.839266i | \(-0.682985\pi\) | ||||
−0.543721 | + | 0.839266i | \(0.682985\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −265049. | −0.831443 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 392529. | 1.19346 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −208039. | −0.613303 | −0.306651 | − | 0.951822i | \(-0.599209\pi\) | ||||
−0.306651 | + | 0.951822i | \(0.599209\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.04986e6 | 3.00208 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −235392. | −0.653131 | −0.326565 | − | 0.945175i | \(-0.605891\pi\) | ||||
−0.326565 | + | 0.945175i | \(0.605891\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −369597. | −0.995432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −160378. | −0.419425 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 126867. | 0.322280 | 0.161140 | − | 0.986932i | \(-0.448483\pi\) | ||||
0.161140 | + | 0.986932i | \(0.448483\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 136191. | 0.336167 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.14953e6 | 2.75795 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 582710. | 1.35932 | 0.679658 | − | 0.733529i | \(-0.262128\pi\) | ||||
0.679658 | + | 0.733529i | \(0.262128\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 469745. | 1.06578 | 0.532888 | − | 0.846186i | \(-0.321107\pi\) | ||||
0.532888 | + | 0.846186i | \(0.321107\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −116158. | −0.256403 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −213195. | −0.457982 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 916172. | 1.91590 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.54359e6 | −3.14325 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −808559. | −1.60372 | −0.801860 | − | 0.597512i | \(-0.796156\pi\) | ||||
−0.801860 | + | 0.597512i | \(0.796156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 397971. | 0.769057 | 0.384528 | − | 0.923113i | \(-0.374364\pi\) | ||||
0.384528 | + | 0.923113i | \(0.374364\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 77588.6 | 0.146121 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −821639. | −1.50840 | −0.754198 | − | 0.656647i | \(-0.771974\pi\) | ||||
−0.754198 | + | 0.656647i | \(0.771974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −304702. | −0.545435 | −0.272718 | − | 0.962094i | \(-0.587922\pi\) | ||||
−0.272718 | + | 0.962094i | \(0.587922\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.85170e6 | 3.23282 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 116725. | 0.198803 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −249643. | −0.414892 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.75714e6 | 2.85023 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 143854. | 0.227802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −657135. | −1.01613 | −0.508064 | − | 0.861319i | \(-0.669639\pi\) | ||||
−0.508064 | + | 0.861319i | \(0.669639\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 209367. | 0.316199 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 229996. | 0.339331 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 830067. | 1.19664 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 408965. | 0.576204 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 67708.4 | 0.0932528 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 899606. | 1.21141 | 0.605703 | − | 0.795690i | \(-0.292892\pi\) | ||||
0.605703 | + | 0.795690i | \(0.292892\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 609653. | 0.802835 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −660017. | −0.850139 | −0.425070 | − | 0.905161i | \(-0.639750\pi\) | ||||
−0.425070 | + | 0.905161i | \(0.639750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −622380. | −0.784273 | −0.392136 | − | 0.919907i | \(-0.628264\pi\) | ||||
−0.392136 | + | 0.919907i | \(0.628264\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.27393e6 | 2.80380 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24182.1 | 0.0291813 | 0.0145906 | − | 0.999894i | \(-0.495355\pi\) | ||||
0.0145906 | + | 0.999894i | \(0.495355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 480787. | 0.567915 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.10486e6 | −1.27772 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −201571. | −0.228262 | −0.114131 | − | 0.993466i | \(-0.536408\pi\) | ||||
−0.114131 | + | 0.993466i | \(0.536408\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.01961e6 | −1.13081 | −0.565407 | − | 0.824812i | \(-0.691281\pi\) | ||||
−0.565407 | + | 0.824812i | \(0.691281\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.47129e6 | −2.68478 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 157409. | 0.167539 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10631.3 | 0.0110878 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.20215e6 | −2.25086 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.41854e6 | −1.42121 | −0.710604 | − | 0.703593i | \(-0.751578\pi\) | ||||
−0.710604 | + | 0.703593i | \(0.751578\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.57610e6 | −1.54804 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.09709e6 | 2.98266 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −54526.1 | −0.0514958 | −0.0257479 | − | 0.999668i | \(-0.508197\pi\) | ||||
−0.0257479 | + | 0.999668i | \(0.508197\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −461765. | −0.427732 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 522512. | 0.474783 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.15754e6 | −1.92340 | −0.961702 | − | 0.274098i | \(-0.911621\pi\) | ||||
−0.961702 | + | 0.274098i | \(0.911621\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 577719. | 0.505361 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.01672e6 | −2.58974 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −128043. | −0.107888 | −0.0539442 | − | 0.998544i | \(-0.517179\pi\) | ||||
−0.0539442 | + | 0.998544i | \(0.517179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −691071. | −0.571610 | −0.285805 | − | 0.958288i | \(-0.592261\pi\) | ||||
−0.285805 | + | 0.958288i | \(0.592261\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 168051. | 0.136469 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −546840. | −0.436042 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 589147. | 0.461343 | 0.230672 | − | 0.973032i | \(-0.425908\pi\) | ||||
0.230672 | + | 0.973032i | \(0.425908\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.71575e6 | 2.85783 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.20853e6 | −0.913044 | −0.456522 | − | 0.889712i | \(-0.650905\pi\) | ||||
−0.456522 | + | 0.889712i | \(0.650905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.88980e6 | −1.40265 | −0.701325 | − | 0.712842i | \(-0.747408\pi\) | ||||
−0.701325 | + | 0.712842i | \(0.747408\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 486295. | 0.354640 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −540709. | −0.387489 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.28285e6 | 0.903506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 749718. | 0.518998 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.43906e6 | −1.65979 | −0.829895 | − | 0.557920i | \(-0.811600\pi\) | ||||
−0.829895 | + | 0.557920i | \(0.811600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.50560e6 | −1.67632 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.19789e6 | 4.07711 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −116479. | −0.0753477 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 498154. | 0.316919 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 869929. | 0.544349 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 253187. | 0.155845 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 842448. | 0.510149 | 0.255074 | − | 0.966921i | \(-0.417900\pi\) | ||||
0.255074 | + | 0.966921i | \(0.417900\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.00229e6 | 2.98039 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.78495e6 | 1.04647 | 0.523233 | − | 0.852190i | \(-0.324726\pi\) | ||||
0.523233 | + | 0.852190i | \(0.324726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.79477e6 | 1.03550 | 0.517749 | − | 0.855533i | \(-0.326770\pi\) | ||||
0.517749 | + | 0.855533i | \(0.326770\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.52574e6 | 3.13772 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.00473e6 | −0.561564 | −0.280782 | − | 0.959772i | \(-0.590594\pi\) | ||||
−0.280782 | + | 0.959772i | \(0.590594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −468677. | −0.257868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.89221e6 | −3.19165 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 424369. | 0.226328 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −40413.4 | −0.0212235 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.37082e6 | 1.22611 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.04135e6 | 0.530404 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.52272e6 | −1.76729 | −0.883646 | − | 0.468155i | \(-0.844919\pi\) | ||||
−0.883646 | + | 0.468155i | \(0.844919\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.06707e6 | −1.02151 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.03610e6 | −1.96494 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.94676e6 | 1.41342 | 0.706708 | − | 0.707506i | \(-0.250180\pi\) | ||||
0.706708 | + | 0.707506i | \(0.250180\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −508582. | −0.240360 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.33291e6 | −1.55217 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.99175e6 | −0.914114 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.32795e6 | −2.40997 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.31985e6 | 1.03428 | 0.517138 | − | 0.855902i | \(-0.326997\pi\) | ||||
0.517138 | + | 0.855902i | \(0.326997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.13664e6 | 0.499526 | 0.249763 | − | 0.968307i | \(-0.419647\pi\) | ||||
0.249763 | + | 0.968307i | \(0.419647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 458046. | 0.198445 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −942783. | −0.402694 | −0.201347 | − | 0.979520i | \(-0.564532\pi\) | ||||
−0.201347 | + | 0.979520i | \(0.564532\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −456352. | −0.192189 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.70808e6 | 2.78566 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.78926e6 | 1.14223 | 0.571113 | − | 0.820871i | \(-0.306512\pi\) | ||||
0.571113 | + | 0.820871i | \(0.306512\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.40947e6 | −0.973090 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.39562e6 | −1.75087 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −891410. | −0.350224 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.20179e6 | 1.62843 | 0.814215 | − | 0.580564i | \(-0.197168\pi\) | ||||
0.814215 | + | 0.580564i | \(0.197168\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.42045e6 | −0.925403 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.25130e6 | 0.471982 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.83152e6 | 1.79809 | 0.899045 | − | 0.437856i | \(-0.144262\pi\) | ||||
0.899045 | + | 0.437856i | \(0.144262\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.03857e6 | 1.48303 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −34636.9 | −0.0125512 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.03959e6 | −0.729366 | −0.364683 | − | 0.931132i | \(-0.618823\pi\) | ||||
−0.364683 | + | 0.931132i | \(0.618823\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.63984e6 | 1.99046 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −923917. | −0.321837 | −0.160919 | − | 0.986968i | \(-0.551446\pi\) | ||||
−0.160919 | + | 0.986968i | \(0.551446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.95642e6 | −1.70418 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.22996e6 | 0.756867 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.39429e6 | −1.13730 | −0.568650 | − | 0.822580i | \(-0.692534\pi\) | ||||
−0.568650 | + | 0.822580i | \(0.692534\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.64948e6 | −1.53802 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.30717e6 | 1.08013 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.40824e6 | 0.776616 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.00161e6 | −0.318949 | −0.159475 | − | 0.987202i | \(-0.550980\pi\) | ||||
−0.159475 | + | 0.987202i | \(0.550980\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.05328e6 | 0.331216 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.53448e6 | 1.71876 | 0.859381 | − | 0.511337i | \(-0.170849\pi\) | ||||
0.859381 | + | 0.511337i | \(0.170849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −246314. | −0.0755486 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.12773e7 | 3.41638 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.85410e6 | 0.554812 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.93289e6 | 0.571345 | 0.285672 | − | 0.958327i | \(-0.407783\pi\) | ||||
0.285672 | + | 0.958327i | \(0.407783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 397304. | 0.116016 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.42694e6 | −1.56560 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.79997e6 | 1.36810 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.27057e6 | 2.61075 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.80082e6 | −0.501112 | −0.250556 | − | 0.968102i | \(-0.580613\pi\) | ||||
−0.250556 | + | 0.968102i | \(0.580613\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.32654e6 | −0.364766 | −0.182383 | − | 0.983228i | \(-0.558381\pi\) | ||||
−0.182383 | + | 0.983228i | \(0.558381\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.66154e6 | 1.26671 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.61318e6 | −0.433221 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 548385. | 0.145551 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −674765. | −0.177015 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −584408. | −0.151539 | −0.0757693 | − | 0.997125i | \(-0.524141\pi\) | ||||
−0.0757693 | + | 0.997125i | \(0.524141\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −707379. | −0.181315 | −0.0906573 | − | 0.995882i | \(-0.528897\pi\) | ||||
−0.0906573 | + | 0.995882i | \(0.528897\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.58435e6 | −0.401447 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −730045. | −0.182872 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.06180e6 | −1.25356 | −0.626778 | − | 0.779198i | \(-0.715627\pi\) | ||||
−0.626778 | + | 0.779198i | \(0.715627\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.52619e6 | 0.373689 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.33111e6 | 0.806453 | 0.403227 | − | 0.915100i | \(-0.367889\pi\) | ||||
0.403227 | + | 0.915100i | \(0.367889\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.57545e6 | 1.57408 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 44104.8 | 0.0104404 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37802.9 | 0.00884930 | 0.00442465 | − | 0.999990i | \(-0.498592\pi\) | ||||
0.00442465 | + | 0.999990i | \(0.498592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.17107e6 | 0.502612 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.14702e6 | −0.949491 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −366297. | −0.0829477 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.55109e6 | −1.69129 | −0.845647 | − | 0.533743i | \(-0.820785\pi\) | ||||
−0.845647 | + | 0.533743i | \(0.820785\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.82838e7 | 4.05073 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.97564e6 | 0.432967 | 0.216484 | − | 0.976286i | \(-0.430541\pi\) | ||||
0.216484 | + | 0.976286i | \(0.430541\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.35199e6 | 1.81066 | 0.905331 | − | 0.424707i | \(-0.139623\pi\) | ||||
0.905331 | + | 0.424707i | \(0.139623\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.12668e7 | −2.41640 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 856159. | 0.181661 | 0.0908306 | − | 0.995866i | \(-0.471048\pi\) | ||||
0.0908306 | + | 0.995866i | \(0.471048\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.74191e6 | −1.83516 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.87387e6 | 2.05086 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.00021e6 | −0.411076 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −253296. | −0.0515102 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.60136e6 | 1.12719 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.97374e6 | −0.791336 | −0.395668 | − | 0.918394i | \(-0.629487\pi\) | ||||
−0.395668 | + | 0.918394i | \(0.629487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 137024. | 0.0270044 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.15399e7 | −2.25080 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.63414e6 | −0.315453 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.73024e6 | −0.521649 | −0.260824 | − | 0.965386i | \(-0.583994\pi\) | ||||
−0.260824 | + | 0.965386i | \(0.583994\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.11611e6 | 1.15665 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.52027e6 | −0.471785 | −0.235892 | − | 0.971779i | \(-0.575801\pi\) | ||||
−0.235892 | + | 0.971779i | \(0.575801\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.38260e6 | −0.256199 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.21871e7 | −4.06994 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −988426. | −0.179495 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.63079e6 | −1.55167 | −0.775834 | − | 0.630937i | \(-0.782671\pi\) | ||||
−0.775834 | + | 0.630937i | \(0.782671\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.92027e6 | 1.23177 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.02315e6 | 1.41392 | 0.706960 | − | 0.707254i | \(-0.250066\pi\) | ||||
0.706960 | + | 0.707254i | \(0.250066\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.89616e6 | −0.330862 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.08658e7 | 1.87733 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.81312e6 | 0.994523 | 0.497261 | − | 0.867601i | \(-0.334339\pi\) | ||||
0.497261 | + | 0.867601i | \(0.334339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.93073e6 | −0.327092 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.87085e6 | 0.481634 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.09034e7 | −1.81152 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.18126e6 | −0.687988 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.72975e6 | −0.607801 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 381523. | 0.0615781 | 0.0307891 | − | 0.999526i | \(-0.490198\pi\) | ||||
0.0307891 | + | 0.999526i | \(0.490198\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.85496e6 | −0.296538 | −0.148269 | − | 0.988947i | \(-0.547370\pi\) | ||||
−0.148269 | + | 0.988947i | \(0.547370\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.00388e6 | −0.633991 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.83209e6 | −1.54212 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.56219e6 | 0.242713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.42934e7 | −3.73897 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 160450. | 0.0244637 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.28431e7 | 1.93993 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.71311e7 | −2.56359 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.36894e6 | −0.202961 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.92237e6 | −0.723071 | −0.361535 | − | 0.932358i | \(-0.617747\pi\) | ||||
−0.361535 | + | 0.932358i | \(0.617747\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.38100e7 | −2.00999 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.16760e6 | −0.745243 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.35722e6 | 0.193947 | 0.0969735 | − | 0.995287i | \(-0.469084\pi\) | ||||
0.0969735 | + | 0.995287i | \(0.469084\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.45481e6 | 0.347607 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −217090. | −0.0304622 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.21607e6 | 0.725321 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.26771e6 | 0.863727 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −629428. | −0.0859623 | −0.0429811 | − | 0.999076i | \(-0.513686\pi\) | ||||
−0.0429811 | + | 0.999076i | \(0.513686\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −147822. | −0.0200083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.69345e7 | −3.61328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 706922. | 0.0939941 | 0.0469971 | − | 0.998895i | \(-0.485035\pi\) | ||||
0.0469971 | + | 0.998895i | \(0.485035\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.10854e6 | 0.146094 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.44257e7 | 3.19073 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.26921e7 | 1.64343 | 0.821716 | − | 0.569898i | \(-0.193017\pi\) | ||||
0.821716 | + | 0.569898i | \(0.193017\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.06713e6 | 1.03545 | 0.517725 | − | 0.855547i | \(-0.326779\pi\) | ||||
0.517725 | + | 0.855547i | \(0.326779\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.37708e7 | 3.02452 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.77516e6 | 0.350040 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.23139e6 | 0.654150 | 0.327075 | − | 0.944998i | \(-0.393937\pi\) | ||||
0.327075 | + | 0.944998i | \(0.393937\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.16999e7 | −1.45040 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.03964e7 | 1.27774 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.02425e6 | −0.612209 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.63971e6 | −0.198096 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.22738e7 | 1.47022 | 0.735111 | − | 0.677947i | \(-0.237130\pi\) | ||||
0.735111 | + | 0.677947i | \(0.237130\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.54380e6 | −0.183359 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.41553e7 | 2.84475 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.56297e7 | −1.82521 | −0.912607 | − | 0.408838i | \(-0.865934\pi\) | ||||
−0.912607 | + | 0.408838i | \(0.865934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.46214e7 | −1.69316 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.95793e6 | 1.02866 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 909739. | 0.103598 | 0.0517988 | − | 0.998658i | \(-0.483505\pi\) | ||||
0.0517988 | + | 0.998658i | \(0.483505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.28807e7 | −1.45463 | −0.727315 | − | 0.686303i | \(-0.759232\pi\) | ||||
−0.727315 | + | 0.686303i | \(0.759232\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.91327e7 | −4.38274 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.58101e6 | 1.06420 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.39560e7 | −1.53741 | −0.768706 | − | 0.639602i | \(-0.779099\pi\) | ||||
−0.768706 | + | 0.639602i | \(0.779099\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.43159e6 | −0.374931 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −309010. | −0.0334865 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.77628e6 | −0.513380 | −0.256690 | − | 0.966494i | \(-0.582632\pi\) | ||||
−0.256690 | + | 0.966494i | \(0.582632\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.33925e6 | 0.782463 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.08319e6 | −0.537556 | −0.268778 | − | 0.963202i | \(-0.586620\pi\) | ||||
−0.268778 | + | 0.963202i | \(0.586620\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.45717e6 | −0.257755 | −0.128878 | − | 0.991660i | \(-0.541137\pi\) | ||||
−0.128878 | + | 0.991660i | \(0.541137\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.14537e7 | −3.27297 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.42420e7 | 1.47011 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.18692e7 | −1.21540 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.22916e6 | −0.429621 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.46958e6 | 0.551223 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.11683e7 | 1.11664 | 0.558322 | − | 0.829624i | \(-0.311445\pi\) | ||||
0.558322 | + | 0.829624i | \(0.311445\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.93191e7 | 1.91636 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.22930e7 | −1.20983 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −101170. | −0.00987874 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.42463e6 | −0.428672 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.24222e6 | −0.888446 | −0.444223 | − | 0.895916i | \(-0.646520\pi\) | ||||
−0.444223 | + | 0.895916i | \(0.646520\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.65662e6 | −0.158014 | −0.0790069 | − | 0.996874i | \(-0.525175\pi\) | ||||
−0.0790069 | + | 0.996874i | \(0.525175\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.76164e6 | −0.639960 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.26223e6 | 0.118544 | 0.0592720 | − | 0.998242i | \(-0.481122\pi\) | ||||
0.0592720 | + | 0.998242i | \(0.481122\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.17904e7 | 2.03074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.44031e7 | −2.25680 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.64066e7 | 1.50569 | 0.752843 | − | 0.658200i | \(-0.228682\pi\) | ||||
0.752843 | + | 0.658200i | \(0.228682\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.20855e6 | −0.656515 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8.64280e6 | −0.781162 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.46135e6 | 0.220780 | 0.110390 | − | 0.993888i | \(-0.464790\pi\) | ||||
0.110390 | + | 0.993888i | \(0.464790\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.29962e7 | −1.15694 | −0.578471 | − | 0.815703i | \(-0.696350\pi\) | ||||
−0.578471 | + | 0.815703i | \(0.696350\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.99055e6 | −0.175869 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.29580e6 | −0.201317 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.37849e6 | 0.207008 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.64475e7 | −2.28464 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.20189e6 | −0.188795 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00711e7 | −0.857119 | −0.428559 | − | 0.903514i | \(-0.640979\pi\) | ||||
−0.428559 | + | 0.903514i | \(0.640979\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.09131e7 | −0.921912 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.82242e6 | 0.823658 | 0.411829 | − | 0.911261i | \(-0.364890\pi\) | ||||
0.411829 | + | 0.911261i | \(0.364890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.53943e6 | −0.294618 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.94038e7 | 1.60331 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.66547e7 | 1.36611 | 0.683053 | − | 0.730369i | \(-0.260652\pi\) | ||||
0.683053 | + | 0.730369i | \(0.260652\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −865992. | −0.0705160 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.82973e7 | 1.47909 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −371310. | −0.0297981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.35915e6 | −0.506645 | −0.253323 | − | 0.967382i | \(-0.581523\pi\) | ||||
−0.253323 | + | 0.967382i | \(0.581523\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −4.80557e7 | −3.80112 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.02068e7 | −1.58685 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.40466e6 | 0.499360 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −710929. | −0.0550342 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −167796. | −0.0128969 | −0.00644846 | − | 0.999979i | \(-0.502053\pi\) | ||||
−0.00644846 | + | 0.999979i | \(0.502053\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 858814. | 0.0655406 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.41346e7 | −1.07105 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.10695e6 | −0.309009 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.01558e7 | −1.50586 | −0.752932 | − | 0.658099i | \(-0.771361\pi\) | ||||
−0.752932 | + | 0.658099i | \(0.771361\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.33494e7 | 1.73222 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.69142e7 | 1.24603 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.47077e6 | 0.107592 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.92597e6 | 0.430488 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.06393e7 | 0.767523 | 0.383761 | − | 0.923432i | \(-0.374628\pi\) | ||||
0.383761 | + | 0.923432i | \(0.374628\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.36159e7 | −1.69187 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.99754e7 | 2.13265 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 825237. | 0.0583087 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.07639e7 | −0.755323 | −0.377661 | − | 0.925944i | \(-0.623272\pi\) | ||||
−0.377661 | + | 0.925944i | \(0.623272\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.98885e7 | 2.08298 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.90060e6 | −0.408416 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.86456e6 | 0.609393 | 0.304696 | − | 0.952450i | \(-0.401445\pi\) | ||||
0.304696 | + | 0.952450i | \(0.401445\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.62767e6 | −0.315968 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.51008e7 | 2.38039 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.34276e7 | −0.904457 | −0.452229 | − | 0.891902i | \(-0.649371\pi\) | ||||
−0.452229 | + | 0.891902i | \(0.649371\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −312550. | −0.0209110 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.76228e6 | 0.250023 | 0.125011 | − | 0.992155i | \(-0.460103\pi\) | ||||
0.125011 | + | 0.992155i | \(0.460103\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −96134.1 | −0.00634580 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.65388e7 | 3.05150 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.78172e7 | 1.81179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.97179e7 | −1.27574 | −0.637870 | − | 0.770144i | \(-0.720184\pi\) | ||||
−0.637870 | + | 0.770144i | \(0.720184\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.17036e7 | 2.68032 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.03915e6 | 0.577112 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.91175e7 | −1.21253 | −0.606264 | − | 0.795264i | \(-0.707332\pi\) | ||||
−0.606264 | + | 0.795264i | \(0.707332\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.63356e7 | 2.91951 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.51417e6 | −0.282563 | −0.141282 | − | 0.989969i | \(-0.545122\pi\) | ||||
−0.141282 | + | 0.989969i | \(0.545122\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.11927e7 | −0.696020 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.54519e7 | −4.04361 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.61039e6 | 0.0988423 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.08251e7 | 1.26990 | 0.634952 | − | 0.772551i | \(-0.281020\pi\) | ||||
0.634952 | + | 0.772551i | \(0.281020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.60301e6 | 0.0971182 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.68649e7 | −1.01516 | −0.507581 | − | 0.861604i | \(-0.669460\pi\) | ||||
−0.507581 | + | 0.861604i | \(0.669460\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.86853e6 | 0.350974 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.35754e7 | 0.806679 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00564e6 | 0.0593742 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.96876e6 | 0.232824 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.35324e6 | −0.545202 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.15218e7 | −1.24654 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 532946. | 0.0306723 | 0.0153361 | − | 0.999882i | \(-0.495118\pi\) | ||||
0.0153361 | + | 0.999882i | \(0.495118\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.34295e7 | 3.62743 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.40102e6 | 0.136444 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −162728. | −0.00918922 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.69843e7 | −0.953083 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.74340e6 | 0.152983 | 0.0764916 | − | 0.997070i | \(-0.475628\pi\) | ||||
0.0764916 | + | 0.997070i | \(0.475628\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.23347e7 | −0.683537 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.37533e7 | 3.51092 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.75233e6 | 0.424271 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.51533e7 | 1.36806 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.76433e6 | 0.203471 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.60884e6 | 0.193864 | 0.0969318 | − | 0.995291i | \(-0.469097\pi\) | ||||
0.0969318 | + | 0.995291i | \(0.469097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.42636e7 | 1.29540 | 0.647698 | − | 0.761897i | \(-0.275732\pi\) | ||||
0.647698 | + | 0.761897i | \(0.275732\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.03168e7 | 1.07802 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.33311e7 | −0.703028 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −926492. | −0.0485609 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.55149e6 | −0.185012 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.65430e6 | −0.137433 | −0.0687167 | − | 0.997636i | \(-0.521890\pi\) | ||||
−0.0687167 | + | 0.997636i | \(0.521890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.45761e7 | 0.750137 | 0.375068 | − | 0.926997i | \(-0.377619\pi\) | ||||
0.375068 | + | 0.926997i | \(0.377619\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.60765e7 | 0.822351 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.56966e7 | 1.30651 | 0.653254 | − | 0.757139i | \(-0.273403\pi\) | ||||
0.653254 | + | 0.757139i | \(0.273403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.04257e6 | 0.254839 | 0.127419 | − | 0.991849i | \(-0.459331\pi\) | ||||
0.127419 | + | 0.991849i | \(0.459331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.73203e7 | −0.870067 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.03838e6 | −0.201648 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50839e7 | −0.748684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.65139e7 | −3.28170 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.91282e6 | 0.339039 | 0.169520 | − | 0.985527i | \(-0.445778\pi\) | ||||
0.169520 | + | 0.985527i | \(0.445778\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 707281. | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.55295e7 | 1.72195 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.36838e7 | −1.14106 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.07518e7 | 0.993909 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.55581e7 | 2.64532 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.40934e6 | −0.445385 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.16826e7 | −1.02033 | −0.510164 | − | 0.860077i | \(-0.670415\pi\) | ||||
−0.510164 | + | 0.860077i | \(0.670415\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.02770e7 | −0.480787 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.22637e7 | −1.03549 | −0.517745 | − | 0.855535i | \(-0.673228\pi\) | ||||
−0.517745 | + | 0.855535i | \(0.673228\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.56538e7 | 0.723828 | 0.361914 | − | 0.932211i | \(-0.382123\pi\) | ||||
0.361914 | + | 0.932211i | \(0.382123\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.58963e7 | 0.730781 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.14396e7 | −1.43698 | −0.718489 | − | 0.695538i | \(-0.755166\pi\) | ||||
−0.718489 | + | 0.695538i | \(0.755166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.12964e6 | 0.369429 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.77144e7 | −1.70396 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.09437e7 | −0.940816 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.59407e6 | 0.115861 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.58440e7 | −0.703608 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.90661e7 | −0.841865 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.99092e6 | 0.438638 | 0.219319 | − | 0.975653i | \(-0.429616\pi\) | ||||
0.219319 | + | 0.975653i | \(0.429616\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.17057e7 | 3.13027 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.37367e6 | −0.103034 | −0.0515169 | − | 0.998672i | \(-0.516406\pi\) | ||||
−0.0515169 | + | 0.998672i | \(0.516406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 686405. | 0.0296264 | 0.0148132 | − | 0.999890i | \(-0.495285\pi\) | ||||
0.0148132 | + | 0.999890i | \(0.495285\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.36619e7 | 3.16144 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.54019e7 | −0.657302 | −0.328651 | − | 0.944451i | \(-0.606594\pi\) | ||||
−0.328651 | + | 0.944451i | \(0.606594\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.66258e7 | −1.12992 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.80750e7 | −4.13870 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.93675e6 | −0.0812729 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.73401e7 | 1.55818 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.42436e6 | 0.142102 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.02970e6 | 0.207560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.48215e7 | −0.608248 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.46452e7 | −0.597691 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.01013e7 | 1.22170 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.67004e7 | 1.07770 | 0.538852 | − | 0.842401i | \(-0.318858\pi\) | ||||
0.538852 | + | 0.842401i | \(0.318858\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.83845e7 | −0.737976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.90851e7 | −0.761902 | −0.380951 | − | 0.924595i | \(-0.624403\pi\) | ||||
−0.380951 | + | 0.924595i | \(0.624403\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.17439e7 | −1.65736 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.44344e6 | −0.293914 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.56132e7 | −0.613153 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.04815e7 | −1.19055 | −0.595274 | − | 0.803523i | \(-0.702957\pi\) | ||||
−0.595274 | + | 0.803523i | \(0.702957\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.47671e7 | −0.962112 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 293306. | 0.0113322 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.26465e6 | −0.125453 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.05715e8 | −4.04053 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.44730e7 | −0.930352 | −0.465176 | − | 0.885218i | \(-0.654009\pi\) | ||||
−0.465176 | + | 0.885218i | \(0.654009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −634092. | −0.0239761 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.24757e7 | −1.97358 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.87084e7 | 2.19620 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.03413e7 | −1.12898 | −0.564489 | − | 0.825441i | \(-0.690927\pi\) | ||||
−0.564489 | + | 0.825441i | \(0.690927\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.27645e7 | −1.95289 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.32048e7 | 1.59059 | 0.795294 | − | 0.606224i | \(-0.207317\pi\) | ||||
0.795294 | + | 0.606224i | \(0.207317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.10180e7 | −0.403480 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.89136e7 | −3.60310 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.50483e7 | 0.907620 | 0.453810 | − | 0.891099i | \(-0.350065\pi\) | ||||
0.453810 | + | 0.891099i | \(0.350065\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 572925. | 0.0206506 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.95379e7 | 1.05908 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.30580e7 | 1.53576 | 0.767878 | − | 0.640596i | \(-0.221313\pi\) | ||||
0.767878 | + | 0.640596i | \(0.221313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.18125e7 | −1.83834 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.37786e7 | 0.486324 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.87568e6 | −0.0658584 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.13868e6 | 0.249350 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.24522e8 | 4.32694 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.55020e7 | 0.881569 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.26447e7 | 1.12266 | 0.561328 | − | 0.827593i | \(-0.310290\pi\) | ||||
0.561328 | + | 0.827593i | \(0.310290\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.24760e7 | −0.426841 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.02885e6 | 0.307315 | 0.153658 | − | 0.988124i | \(-0.450895\pi\) | ||||
0.153658 | + | 0.988124i | \(0.450895\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.37665e7 | −1.48204 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.18811e6 | 0.0400263 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.87743e6 | 0.297544 | 0.148772 | − | 0.988872i | \(-0.452468\pi\) | ||||
0.148772 | + | 0.988872i | \(0.452468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.71848e7 | −1.90688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.01033e7 | −1.66224 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.56481e7 | 1.50674 | 0.753371 | − | 0.657596i | \(-0.228427\pi\) | ||||
0.753371 | + | 0.657596i | \(0.228427\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.26507e7 | −1.72907 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.06146e7 | −1.00031 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.01508e7 | 0.329998 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.74121e6 | 0.250395 | 0.125197 | − | 0.992132i | \(-0.460044\pi\) | ||||
0.125197 | + | 0.992132i | \(0.460044\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.03564e8 | 3.33301 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.95253e7 | −0.625232 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.64996e7 | 1.80014 | 0.900072 | − | 0.435740i | \(-0.143513\pi\) | ||||
0.900072 | + | 0.435740i | \(0.143513\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.70016e7 | 1.17302 |
(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 | 464.6.a.k.1.1 | 7 | ||
4.3 | odd | 2 | 29.6.a.b.1.3 | ✓ | 7 | ||
12.11 | even | 2 | 261.6.a.e.1.5 | 7 | |||
20.19 | odd | 2 | 725.6.a.b.1.5 | 7 | |||
116.115 | odd | 2 | 841.6.a.b.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.a.b.1.3 | ✓ | 7 | 4.3 | odd | 2 | ||
261.6.a.e.1.5 | 7 | 12.11 | even | 2 | |||
464.6.a.k.1.1 | 7 | 1.1 | even | 1 | trivial | ||
725.6.a.b.1.5 | 7 | 20.19 | odd | 2 | |||
841.6.a.b.1.5 | 7 | 116.115 | odd | 2 |