Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [725,6,Mod(1,725)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(725, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("725.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 725 = 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 725.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: | \(116.278269364\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(4.90786\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 725.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.90786 | 0.690818 | 0.345409 | − | 0.938452i | \(-0.387740\pi\) | ||||
0.345409 | + | 0.938452i | \(0.387740\pi\) | |||||||
\(3\) | −29.3989 | −1.88594 | −0.942972 | − | 0.332873i | \(-0.891982\pi\) | ||||
−0.942972 | + | 0.332873i | \(0.891982\pi\) | |||||||
\(4\) | −16.7287 | −0.522771 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −114.887 | −1.30284 | ||||||||
\(7\) | 138.793 | 1.07059 | 0.535293 | − | 0.844666i | \(-0.320201\pi\) | ||||
0.535293 | + | 0.844666i | \(0.320201\pi\) | |||||||
\(8\) | −190.425 | −1.05196 | ||||||||
\(9\) | 621.298 | 2.55678 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 557.286 | 1.38866 | 0.694330 | − | 0.719656i | \(-0.255701\pi\) | ||||
0.694330 | + | 0.719656i | \(0.255701\pi\) | |||||||
\(12\) | 491.805 | 0.985916 | ||||||||
\(13\) | 41.1854 | 0.0675903 | 0.0337952 | − | 0.999429i | \(-0.489241\pi\) | ||||
0.0337952 | + | 0.999429i | \(0.489241\pi\) | |||||||
\(14\) | 542.382 | 0.739580 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −208.835 | −0.203940 | ||||||||
\(17\) | 1643.99 | 1.37968 | 0.689838 | − | 0.723964i | \(-0.257682\pi\) | ||||
0.689838 | + | 0.723964i | \(0.257682\pi\) | |||||||
\(18\) | 2427.94 | 1.76627 | ||||||||
\(19\) | 258.134 | 0.164044 | 0.0820221 | − | 0.996631i | \(-0.473862\pi\) | ||||
0.0820221 | + | 0.996631i | \(0.473862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4080.36 | −2.01907 | ||||||||
\(22\) | 2177.79 | 0.959311 | ||||||||
\(23\) | 2828.17 | 1.11477 | 0.557385 | − | 0.830254i | \(-0.311805\pi\) | ||||
0.557385 | + | 0.830254i | \(0.311805\pi\) | |||||||
\(24\) | 5598.28 | 1.98393 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 160.946 | 0.0466926 | ||||||||
\(27\) | −11121.6 | −2.93600 | ||||||||
\(28\) | −2321.82 | −0.559671 | ||||||||
\(29\) | 841.000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5980.62 | −1.11774 | −0.558872 | − | 0.829254i | \(-0.688766\pi\) | ||||
−0.558872 | + | 0.829254i | \(0.688766\pi\) | |||||||
\(32\) | 5277.49 | 0.911072 | ||||||||
\(33\) | −16383.6 | −2.61894 | ||||||||
\(34\) | 6424.48 | 0.953105 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10393.5 | −1.33661 | ||||||||
\(37\) | 3327.01 | 0.399531 | 0.199765 | − | 0.979844i | \(-0.435982\pi\) | ||||
0.199765 | + | 0.979844i | \(0.435982\pi\) | |||||||
\(38\) | 1008.75 | 0.113325 | ||||||||
\(39\) | −1210.81 | −0.127472 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3895.80 | −0.361940 | −0.180970 | − | 0.983489i | \(-0.557924\pi\) | ||||
−0.180970 | + | 0.983489i | \(0.557924\pi\) | |||||||
\(42\) | −15945.5 | −1.39481 | ||||||||
\(43\) | 3589.20 | 0.296023 | 0.148012 | − | 0.988986i | \(-0.452713\pi\) | ||||
0.148012 | + | 0.988986i | \(0.452713\pi\) | |||||||
\(44\) | −9322.64 | −0.725951 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 11052.1 | 0.770103 | ||||||||
\(47\) | 7502.91 | 0.495433 | 0.247717 | − | 0.968833i | \(-0.420320\pi\) | ||||
0.247717 | + | 0.968833i | \(0.420320\pi\) | |||||||
\(48\) | 6139.52 | 0.384619 | ||||||||
\(49\) | 2456.45 | 0.146156 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −48331.6 | −2.60199 | ||||||||
\(52\) | −688.976 | −0.0353342 | ||||||||
\(53\) | −9015.58 | −0.440863 | −0.220432 | − | 0.975402i | \(-0.570747\pi\) | ||||
−0.220432 | + | 0.975402i | \(0.570747\pi\) | |||||||
\(54\) | −43461.5 | −2.02824 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −26429.6 | −1.12621 | ||||||||
\(57\) | −7588.86 | −0.309378 | ||||||||
\(58\) | 3286.51 | 0.128282 | ||||||||
\(59\) | 39101.0 | 1.46237 | 0.731187 | − | 0.682177i | \(-0.238967\pi\) | ||||
0.731187 | + | 0.682177i | \(0.238967\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3951.11 | 0.135955 | 0.0679773 | − | 0.997687i | \(-0.478345\pi\) | ||||
0.0679773 | + | 0.997687i | \(0.478345\pi\) | |||||||
\(62\) | −23371.4 | −0.772157 | ||||||||
\(63\) | 86231.7 | 2.73726 | ||||||||
\(64\) | 27306.4 | 0.833325 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −64024.8 | −1.80921 | ||||||||
\(67\) | −62985.3 | −1.71416 | −0.857082 | − | 0.515180i | \(-0.827725\pi\) | ||||
−0.857082 | + | 0.515180i | \(0.827725\pi\) | |||||||
\(68\) | −27501.8 | −0.721254 | ||||||||
\(69\) | −83145.1 | −2.10239 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7121.60 | 0.167661 | 0.0838304 | − | 0.996480i | \(-0.473285\pi\) | ||||
0.0838304 | + | 0.996480i | \(0.473285\pi\) | |||||||
\(72\) | −118310. | −2.68963 | ||||||||
\(73\) | 13910.9 | 0.305525 | 0.152763 | − | 0.988263i | \(-0.451183\pi\) | ||||
0.152763 | + | 0.988263i | \(0.451183\pi\) | |||||||
\(74\) | 13001.5 | 0.276003 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4318.23 | −0.0857575 | ||||||||
\(77\) | 77347.2 | 1.48668 | ||||||||
\(78\) | −4731.66 | −0.0880596 | ||||||||
\(79\) | −37581.7 | −0.677499 | −0.338749 | − | 0.940877i | \(-0.610004\pi\) | ||||
−0.338749 | + | 0.940877i | \(0.610004\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 175987. | 2.98035 | ||||||||
\(82\) | −15224.2 | −0.250035 | ||||||||
\(83\) | 74905.7 | 1.19349 | 0.596746 | − | 0.802430i | \(-0.296460\pi\) | ||||
0.596746 | + | 0.802430i | \(0.296460\pi\) | |||||||
\(84\) | 68259.0 | 1.05551 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14026.1 | 0.204498 | ||||||||
\(87\) | −24724.5 | −0.350211 | ||||||||
\(88\) | −106121. | −1.46081 | ||||||||
\(89\) | 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 | ||||||||
\(92\) | −47311.5 | −0.582769 | ||||||||
\(93\) | 175824. | 2.10800 | ||||||||
\(94\) | 29320.3 | 0.342254 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −155153. | −1.71823 | ||||||||
\(97\) | 25501.5 | 0.275193 | 0.137596 | − | 0.990488i | \(-0.456062\pi\) | ||||
0.137596 | + | 0.990488i | \(0.456062\pi\) | |||||||
\(98\) | 9599.44 | 0.100967 | ||||||||
\(99\) | 346241. | 3.55050 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −29590.5 | −0.288635 | −0.144317 | − | 0.989531i | \(-0.546099\pi\) | ||||
−0.144317 | + | 0.989531i | \(0.546099\pi\) | |||||||
\(102\) | −188873. | −1.79750 | ||||||||
\(103\) | −170152. | −1.58032 | −0.790159 | − | 0.612902i | \(-0.790002\pi\) | ||||
−0.790159 | + | 0.612902i | \(0.790002\pi\) | |||||||
\(104\) | −7842.71 | −0.0711021 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −35231.6 | −0.304556 | ||||||||
\(107\) | 200423. | 1.69234 | 0.846169 | − | 0.532915i | \(-0.178903\pi\) | ||||
0.846169 | + | 0.532915i | \(0.178903\pi\) | |||||||
\(108\) | 186049. | 1.53486 | ||||||||
\(109\) | −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 | ||||||||
\(112\) | −28984.7 | −0.218336 | ||||||||
\(113\) | −17299.3 | −0.127448 | −0.0637240 | − | 0.997968i | \(-0.520298\pi\) | ||||
−0.0637240 | + | 0.997968i | \(0.520298\pi\) | |||||||
\(114\) | −29656.2 | −0.213724 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −14068.8 | −0.0970761 | ||||||||
\(117\) | 25588.4 | 0.172814 | ||||||||
\(118\) | 152801. | 1.01023 | ||||||||
\(119\) | 228174. | 1.47706 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 149516. | 0.928378 | ||||||||
\(122\) | 15440.4 | 0.0939199 | ||||||||
\(123\) | 114532. | 0.682599 | ||||||||
\(124\) | 100048. | 0.584323 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 336981. | 1.89095 | ||||||||
\(127\) | −191838. | −1.05542 | −0.527711 | − | 0.849424i | \(-0.676949\pi\) | ||||
−0.527711 | + | 0.849424i | \(0.676949\pi\) | |||||||
\(128\) | −62170.3 | −0.335396 | ||||||||
\(129\) | −105519. | −0.558283 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 112493. | 0.572726 | 0.286363 | − | 0.958121i | \(-0.407554\pi\) | ||||
0.286363 | + | 0.958121i | \(0.407554\pi\) | |||||||
\(132\) | 274076. | 1.36910 | ||||||||
\(133\) | 35827.1 | 0.175623 | ||||||||
\(134\) | −246138. | −1.18417 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −313056. | −1.45136 | ||||||||
\(137\) | 13514.2 | 0.0615162 | 0.0307581 | − | 0.999527i | \(-0.490208\pi\) | ||||
0.0307581 | + | 0.999527i | \(0.490208\pi\) | |||||||
\(138\) | −324919. | −1.45237 | ||||||||
\(139\) | 315337. | 1.38432 | 0.692161 | − | 0.721743i | \(-0.256659\pi\) | ||||
0.692161 | + | 0.721743i | \(0.256659\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −220578. | −0.934359 | ||||||||
\(142\) | 27830.2 | 0.115823 | ||||||||
\(143\) | 22952.0 | 0.0938600 | ||||||||
\(144\) | −129749. | −0.521430 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 54361.7 | 0.211062 | ||||||||
\(147\) | −72216.9 | −0.275642 | ||||||||
\(148\) | −55656.5 | −0.208863 | ||||||||
\(149\) | −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 | \(-0.580999\pi\) | ||||
−0.251729 | + | 0.967798i | \(0.580999\pi\) | |||||||
\(152\) | −49155.0 | −0.172567 | ||||||||
\(153\) | 1.02141e6 | 3.52753 | ||||||||
\(154\) | 302262. | 1.02703 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 20255.2 | 0.0666384 | ||||||||
\(157\) | 335858. | 1.08744 | 0.543721 | − | 0.839266i | \(-0.317015\pi\) | ||||
0.543721 | + | 0.839266i | \(0.317015\pi\) | |||||||
\(158\) | −146864. | −0.468028 | ||||||||
\(159\) | 265049. | 0.831443 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 392529. | 1.19346 | ||||||||
\(162\) | 687732. | 2.05888 | ||||||||
\(163\) | −208039. | −0.613303 | −0.306651 | − | 0.951822i | \(-0.599209\pi\) | ||||
−0.306651 | + | 0.951822i | \(0.599209\pi\) | |||||||
\(164\) | 65171.5 | 0.189212 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 292721. | 0.824486 | ||||||||
\(167\) | −235392. | −0.653131 | −0.326565 | − | 0.945175i | \(-0.605891\pi\) | ||||
−0.326565 | + | 0.945175i | \(0.605891\pi\) | |||||||
\(168\) | 777001. | 2.12397 | ||||||||
\(169\) | −369597. | −0.995432 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 160378. | 0.419425 | ||||||||
\(172\) | −60042.4 | −0.154752 | ||||||||
\(173\) | −126867. | −0.322280 | −0.161140 | − | 0.986932i | \(-0.551517\pi\) | ||||
−0.161140 | + | 0.986932i | \(0.551517\pi\) | |||||||
\(174\) | −96619.8 | −0.241932 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −116381. | −0.283203 | ||||||||
\(177\) | −1.14953e6 | −2.75795 | ||||||||
\(178\) | 400997. | 0.948617 | ||||||||
\(179\) | −582710. | −1.35932 | −0.679658 | − | 0.733529i | \(-0.737872\pi\) | ||||
−0.679658 | + | 0.733529i | \(0.737872\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 469745. | 1.06578 | 0.532888 | − | 0.846186i | \(-0.321107\pi\) | ||||
0.532888 | + | 0.846186i | \(0.321107\pi\) | |||||||
\(182\) | 22338.2 | 0.0499885 | ||||||||
\(183\) | −116158. | −0.256403 | ||||||||
\(184\) | −538553. | −1.17269 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 687095. | 1.45624 | ||||||||
\(187\) | 916172. | 1.91590 | ||||||||
\(188\) | −125514. | −0.258998 | ||||||||
\(189\) | −1.54359e6 | −3.14325 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 808559. | 1.60372 | 0.801860 | − | 0.597512i | \(-0.203844\pi\) | ||||
0.801860 | + | 0.597512i | \(0.203844\pi\) | |||||||
\(192\) | −802779. | −1.57160 | ||||||||
\(193\) | −397971. | −0.769057 | −0.384528 | − | 0.923113i | \(-0.625636\pi\) | ||||
−0.384528 | + | 0.923113i | \(0.625636\pi\) | |||||||
\(194\) | 99656.3 | 0.190108 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −41093.1 | −0.0764062 | ||||||||
\(197\) | 821639. | 1.50840 | 0.754198 | − | 0.656647i | \(-0.228026\pi\) | ||||
0.754198 | + | 0.656647i | \(0.228026\pi\) | |||||||
\(198\) | 1.35306e6 | 2.45275 | ||||||||
\(199\) | 304702. | 0.545435 | 0.272718 | − | 0.962094i | \(-0.412078\pi\) | ||||
0.272718 | + | 0.962094i | \(0.412078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.85170e6 | 3.23282 | ||||||||
\(202\) | −115635. | −0.199394 | ||||||||
\(203\) | 116725. | 0.198803 | ||||||||
\(204\) | 808523. | 1.36024 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −664930. | −1.09171 | ||||||||
\(207\) | 1.75714e6 | 2.85023 | ||||||||
\(208\) | −8600.93 | −0.0137844 | ||||||||
\(209\) | 143854. | 0.227802 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 657135. | 1.01613 | 0.508064 | − | 0.861319i | \(-0.330361\pi\) | ||||
0.508064 | + | 0.861319i | \(0.330361\pi\) | |||||||
\(212\) | 150819. | 0.230470 | ||||||||
\(213\) | −209367. | −0.316199 | ||||||||
\(214\) | 783222. | 1.16910 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.11782e6 | 3.08855 | ||||||||
\(217\) | −830067. | −1.19664 | ||||||||
\(218\) | −315141. | −0.449121 | ||||||||
\(219\) | −408965. | −0.576204 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 67708.4 | 0.0932528 | ||||||||
\(222\) | −382230. | −0.520526 | ||||||||
\(223\) | 899606. | 1.21141 | 0.605703 | − | 0.795690i | \(-0.292892\pi\) | ||||
0.605703 | + | 0.795690i | \(0.292892\pi\) | |||||||
\(224\) | 732478. | 0.975381 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −67603.3 | −0.0880434 | ||||||||
\(227\) | −660017. | −0.850139 | −0.425070 | − | 0.905161i | \(-0.639750\pi\) | ||||
−0.425070 | + | 0.905161i | \(0.639750\pi\) | |||||||
\(228\) | 126951. | 0.161734 | ||||||||
\(229\) | −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 | ||||||||
\(232\) | −160147. | −0.195344 | ||||||||
\(233\) | −24182.1 | −0.0291813 | −0.0145906 | − | 0.999894i | \(-0.504645\pi\) | ||||
−0.0145906 | + | 0.999894i | \(0.504645\pi\) | |||||||
\(234\) | 99995.7 | 0.119383 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −654108. | −0.764486 | ||||||||
\(237\) | 1.10486e6 | 1.27772 | ||||||||
\(238\) | 891672. | 1.02038 | ||||||||
\(239\) | 201571. | 0.228262 | 0.114131 | − | 0.993466i | \(-0.463592\pi\) | ||||
0.114131 | + | 0.993466i | \(0.463592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.01961e6 | −1.13081 | −0.565407 | − | 0.824812i | \(-0.691281\pi\) | ||||
−0.565407 | + | 0.824812i | \(0.691281\pi\) | |||||||
\(242\) | 584288. | 0.641340 | ||||||||
\(243\) | −2.47129e6 | −2.68478 | ||||||||
\(244\) | −66096.7 | −0.0710731 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 447576. | 0.471552 | ||||||||
\(247\) | 10631.3 | 0.0110878 | ||||||||
\(248\) | 1.13886e6 | 1.17582 | ||||||||
\(249\) | −2.20215e6 | −2.25086 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.41854e6 | 1.42121 | 0.710604 | − | 0.703593i | \(-0.248422\pi\) | ||||
0.710604 | + | 0.703593i | \(0.248422\pi\) | |||||||
\(252\) | −1.44254e6 | −1.43096 | ||||||||
\(253\) | 1.57610e6 | 1.54804 | ||||||||
\(254\) | −749676. | −0.729104 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.11676e6 | −1.06502 | ||||||||
\(257\) | 54526.1 | 0.0514958 | 0.0257479 | − | 0.999668i | \(-0.491803\pi\) | ||||
0.0257479 | + | 0.999668i | \(0.491803\pi\) | |||||||
\(258\) | −412351. | −0.385672 | ||||||||
\(259\) | 461765. | 0.427732 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 522512. | 0.474783 | ||||||||
\(262\) | 439606. | 0.395649 | ||||||||
\(263\) | −2.15754e6 | −1.92340 | −0.961702 | − | 0.274098i | \(-0.911621\pi\) | ||||
−0.961702 | + | 0.274098i | \(0.911621\pi\) | |||||||
\(264\) | 3.11984e6 | 2.75501 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 140007. | 0.121324 | ||||||||
\(267\) | −3.01672e6 | −2.58974 | ||||||||
\(268\) | 1.05366e6 | 0.896115 | ||||||||
\(269\) | −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 | \(-0.407739\pi\) | ||||
0.285805 | + | 0.958288i | \(0.407739\pi\) | |||||||
\(272\) | −343322. | −0.281371 | ||||||||
\(273\) | −168051. | −0.136469 | ||||||||
\(274\) | 52811.6 | 0.0424965 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.39091e6 | 1.09907 | ||||||||
\(277\) | −589147. | −0.461343 | −0.230672 | − | 0.973032i | \(-0.574092\pi\) | ||||
−0.230672 | + | 0.973032i | \(0.574092\pi\) | |||||||
\(278\) | 1.23229e6 | 0.956315 | ||||||||
\(279\) | −3.71575e6 | −2.85783 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.20853e6 | −0.913044 | −0.456522 | − | 0.889712i | \(-0.650905\pi\) | ||||
−0.456522 | + | 0.889712i | \(0.650905\pi\) | |||||||
\(282\) | −861985. | −0.645472 | ||||||||
\(283\) | −1.88980e6 | −1.40265 | −0.701325 | − | 0.712842i | \(-0.747408\pi\) | ||||
−0.701325 | + | 0.712842i | \(0.747408\pi\) | |||||||
\(284\) | −119135. | −0.0876481 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 89693.1 | 0.0648402 | ||||||||
\(287\) | −540709. | −0.387489 | ||||||||
\(288\) | 3.27890e6 | 2.32941 | ||||||||
\(289\) | 1.28285e6 | 0.903506 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −749718. | −0.518998 | ||||||||
\(292\) | −232710. | −0.159720 | ||||||||
\(293\) | 2.43906e6 | 1.65979 | 0.829895 | − | 0.557920i | \(-0.188400\pi\) | ||||
0.829895 | + | 0.557920i | \(0.188400\pi\) | |||||||
\(294\) | −282213. | −0.190419 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −633545. | −0.420289 | ||||||||
\(297\) | −6.19789e6 | −4.07711 | ||||||||
\(298\) | −5862.63 | −0.00382430 | ||||||||
\(299\) | 116479. | 0.0753477 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 498154. | 0.316919 | ||||||||
\(302\) | −551243. | −0.347797 | ||||||||
\(303\) | 869929. | 0.544349 | ||||||||
\(304\) | −53907.2 | −0.0334552 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.99152e6 | 2.43688 | ||||||||
\(307\) | 842448. | 0.510149 | 0.255074 | − | 0.966921i | \(-0.417900\pi\) | ||||
0.255074 | + | 0.966921i | \(0.417900\pi\) | |||||||
\(308\) | −1.29392e6 | −0.777194 | ||||||||
\(309\) | 5.00229e6 | 2.98039 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.78495e6 | −1.04647 | −0.523233 | − | 0.852190i | \(-0.675274\pi\) | ||||
−0.523233 | + | 0.852190i | \(0.675274\pi\) | |||||||
\(312\) | 230567. | 0.134095 | ||||||||
\(313\) | −1.79477e6 | −1.03550 | −0.517749 | − | 0.855533i | \(-0.673230\pi\) | ||||
−0.517749 | + | 0.855533i | \(0.673230\pi\) | |||||||
\(314\) | 1.31248e6 | 0.751225 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 628691. | 0.354177 | ||||||||
\(317\) | 1.00473e6 | 0.561564 | 0.280782 | − | 0.959772i | \(-0.409406\pi\) | ||||
0.280782 | + | 0.959772i | \(0.409406\pi\) | |||||||
\(318\) | 1.03577e6 | 0.574376 | ||||||||
\(319\) | 468677. | 0.257868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.89221e6 | −3.19165 | ||||||||
\(322\) | 1.53395e6 | 0.824463 | ||||||||
\(323\) | 424369. | 0.226328 | ||||||||
\(324\) | −2.94403e6 | −1.55804 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −812985. | −0.423680 | ||||||||
\(327\) | 2.37082e6 | 1.22611 | ||||||||
\(328\) | 741856. | 0.380746 | ||||||||
\(329\) | 1.04135e6 | 0.530404 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.52272e6 | 1.76729 | 0.883646 | − | 0.468155i | \(-0.155081\pi\) | ||||
0.883646 | + | 0.468155i | \(0.155081\pi\) | |||||||
\(332\) | −1.25307e6 | −0.623923 | ||||||||
\(333\) | 2.06707e6 | 1.02151 | ||||||||
\(334\) | −919878. | −0.451195 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 852121. | 0.411768 | ||||||||
\(337\) | −2.94676e6 | −1.41342 | −0.706708 | − | 0.707506i | \(-0.749820\pi\) | ||||
−0.706708 | + | 0.707506i | \(0.749820\pi\) | |||||||
\(338\) | −1.44433e6 | −0.687662 | ||||||||
\(339\) | 508582. | 0.240360 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.33291e6 | −1.55217 | ||||||||
\(342\) | 626734. | 0.289746 | ||||||||
\(343\) | −1.99175e6 | −0.914114 | ||||||||
\(344\) | −683471. | −0.311404 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −495777. | −0.222637 | ||||||||
\(347\) | 2.31985e6 | 1.03428 | 0.517138 | − | 0.855902i | \(-0.326997\pi\) | ||||
0.517138 | + | 0.855902i | \(0.326997\pi\) | |||||||
\(348\) | 413608. | 0.183080 | ||||||||
\(349\) | 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 | ||||||||
\(352\) | 2.94107e6 | 1.26517 | ||||||||
\(353\) | 942783. | 0.402694 | 0.201347 | − | 0.979520i | \(-0.435468\pi\) | ||||
0.201347 | + | 0.979520i | \(0.435468\pi\) | |||||||
\(354\) | −4.49220e6 | −1.90524 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.71658e6 | −0.717858 | ||||||||
\(357\) | −6.70808e6 | −2.78566 | ||||||||
\(358\) | −2.27715e6 | −0.939039 | ||||||||
\(359\) | −2.78926e6 | −1.14223 | −0.571113 | − | 0.820871i | \(-0.693488\pi\) | ||||
−0.571113 | + | 0.820871i | \(0.693488\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.40947e6 | −0.973090 | ||||||||
\(362\) | 1.83570e6 | 0.736257 | ||||||||
\(363\) | −4.39562e6 | −1.75087 | ||||||||
\(364\) | −95624.9 | −0.0378284 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −453930. | −0.177128 | ||||||||
\(367\) | 4.20179e6 | 1.62843 | 0.814215 | − | 0.580564i | \(-0.197168\pi\) | ||||
0.814215 | + | 0.580564i | \(0.197168\pi\) | |||||||
\(368\) | −590619. | −0.227346 | ||||||||
\(369\) | −2.42045e6 | −0.925403 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.25130e6 | −0.471982 | ||||||||
\(372\) | −2.94130e6 | −1.10200 | ||||||||
\(373\) | −4.83152e6 | −1.79809 | −0.899045 | − | 0.437856i | \(-0.855738\pi\) | ||||
−0.899045 | + | 0.437856i | \(0.855738\pi\) | |||||||
\(374\) | 3.58027e6 | 1.32354 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.42874e6 | −0.521174 | ||||||||
\(377\) | 34636.9 | 0.0125512 | ||||||||
\(378\) | −6.03214e6 | −2.17141 | ||||||||
\(379\) | 2.03959e6 | 0.729366 | 0.364683 | − | 0.931132i | \(-0.381177\pi\) | ||||
0.364683 | + | 0.931132i | \(0.381177\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.63984e6 | 1.99046 | ||||||||
\(382\) | 3.15973e6 | 1.10788 | ||||||||
\(383\) | −923917. | −0.321837 | −0.160919 | − | 0.986968i | \(-0.551446\pi\) | ||||
−0.160919 | + | 0.986968i | \(0.551446\pi\) | |||||||
\(384\) | 1.82774e6 | 0.632538 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.55521e6 | −0.531278 | ||||||||
\(387\) | 2.22996e6 | 0.756867 | ||||||||
\(388\) | −426606. | −0.143863 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | −467768. | −0.153750 | ||||||||
\(393\) | −3.30717e6 | −1.08013 | ||||||||
\(394\) | 3.21085e6 | 1.04203 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.79214e6 | −1.85610 | ||||||||
\(397\) | 1.00161e6 | 0.318949 | 0.159475 | − | 0.987202i | \(-0.449020\pi\) | ||||
0.159475 | + | 0.987202i | \(0.449020\pi\) | |||||||
\(398\) | 1.19073e6 | 0.376796 | ||||||||
\(399\) | −1.05328e6 | −0.331216 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.53448e6 | 1.71876 | 0.859381 | − | 0.511337i | \(-0.170849\pi\) | ||||
0.859381 | + | 0.511337i | \(0.170849\pi\) | |||||||
\(402\) | 7.23618e6 | 2.23329 | ||||||||
\(403\) | −246314. | −0.0755486 | ||||||||
\(404\) | 495009. | 0.150890 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 456144. | 0.137337 | ||||||||
\(407\) | 1.85410e6 | 0.554812 | ||||||||
\(408\) | 9.20353e6 | 2.73718 | ||||||||
\(409\) | 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 | ||||||||
\(412\) | 2.84642e6 | 0.826144 | ||||||||
\(413\) | 5.42694e6 | 1.56560 | ||||||||
\(414\) | 6.86663e6 | 1.96899 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 217355. | 0.0615796 | ||||||||
\(417\) | −9.27057e6 | −2.61075 | ||||||||
\(418\) | 562161. | 0.157369 | ||||||||
\(419\) | 1.80082e6 | 0.501112 | 0.250556 | − | 0.968102i | \(-0.419387\pi\) | ||||
0.250556 | + | 0.968102i | \(0.419387\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.32654e6 | −0.364766 | −0.182383 | − | 0.983228i | \(-0.558381\pi\) | ||||
−0.182383 | + | 0.983228i | \(0.558381\pi\) | |||||||
\(422\) | 2.56799e6 | 0.701959 | ||||||||
\(423\) | 4.66154e6 | 1.26671 | ||||||||
\(424\) | 1.71679e6 | 0.463769 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −818178. | −0.218436 | ||||||||
\(427\) | 548385. | 0.145551 | ||||||||
\(428\) | −3.35280e6 | −0.884705 | ||||||||
\(429\) | −674765. | −0.177015 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 584408. | 0.151539 | 0.0757693 | − | 0.997125i | \(-0.475859\pi\) | ||||
0.0757693 | + | 0.997125i | \(0.475859\pi\) | |||||||
\(432\) | 2.32257e6 | 0.598769 | ||||||||
\(433\) | 707379. | 0.181315 | 0.0906573 | − | 0.995882i | \(-0.471103\pi\) | ||||
0.0906573 | + | 0.995882i | \(0.471103\pi\) | |||||||
\(434\) | −3.24378e6 | −0.826661 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.34905e6 | 0.339869 | ||||||||
\(437\) | 730045. | 0.182872 | ||||||||
\(438\) | −1.59818e6 | −0.398052 | ||||||||
\(439\) | 5.06180e6 | 1.25356 | 0.626778 | − | 0.779198i | \(-0.284373\pi\) | ||||
0.626778 | + | 0.779198i | \(0.284373\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.52619e6 | 0.373689 | ||||||||
\(442\) | 264595. | 0.0644207 | ||||||||
\(443\) | 3.33111e6 | 0.806453 | 0.403227 | − | 0.915100i | \(-0.367889\pi\) | ||||
0.403227 | + | 0.915100i | \(0.367889\pi\) | |||||||
\(444\) | 1.63624e6 | 0.393904 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.51553e6 | 0.836861 | ||||||||
\(447\) | 44104.8 | 0.0104404 | ||||||||
\(448\) | 3.78993e6 | 0.892146 | ||||||||
\(449\) | 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 | ||||||||
\(452\) | 289395. | 0.0666261 | ||||||||
\(453\) | 4.14702e6 | 0.949491 | ||||||||
\(454\) | −2.57925e6 | −0.587292 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.44511e6 | 0.325452 | ||||||||
\(457\) | 7.55109e6 | 1.69129 | 0.845647 | − | 0.533743i | \(-0.179215\pi\) | ||||
0.845647 | + | 0.533743i | \(0.179215\pi\) | |||||||
\(458\) | −2.43217e6 | −0.541790 | ||||||||
\(459\) | −1.82838e7 | −4.05073 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.97564e6 | 0.432967 | 0.216484 | − | 0.976286i | \(-0.430541\pi\) | ||||
0.216484 | + | 0.976286i | \(0.430541\pi\) | |||||||
\(462\) | −8.88618e6 | −1.93691 | ||||||||
\(463\) | 8.35199e6 | 1.81066 | 0.905331 | − | 0.424707i | \(-0.139623\pi\) | ||||
0.905331 | + | 0.424707i | \(0.139623\pi\) | |||||||
\(464\) | −175630. | −0.0378707 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −94500.2 | −0.0201590 | ||||||||
\(467\) | 856159. | 0.181661 | 0.0908306 | − | 0.995866i | \(-0.471048\pi\) | ||||
0.0908306 | + | 0.995866i | \(0.471048\pi\) | |||||||
\(468\) | −428060. | −0.0903420 | ||||||||
\(469\) | −8.74191e6 | −1.83516 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.87387e6 | −2.05086 | ||||||||
\(472\) | −7.44580e6 | −1.53835 | ||||||||
\(473\) | 2.00021e6 | 0.411076 | ||||||||
\(474\) | 4.31764e6 | 0.882675 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.81705e6 | −0.772165 | ||||||||
\(477\) | −5.60136e6 | −1.12719 | ||||||||
\(478\) | 787709. | 0.157687 | ||||||||
\(479\) | 3.97374e6 | 0.791336 | 0.395668 | − | 0.918394i | \(-0.370513\pi\) | ||||
0.395668 | + | 0.918394i | \(0.370513\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 137024. | 0.0270044 | ||||||||
\(482\) | −3.98449e6 | −0.781186 | ||||||||
\(483\) | −1.15399e7 | −2.25080 | ||||||||
\(484\) | −2.50121e6 | −0.485329 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.65745e6 | −1.85469 | ||||||||
\(487\) | −2.73024e6 | −0.521649 | −0.260824 | − | 0.965386i | \(-0.583994\pi\) | ||||
−0.260824 | + | 0.965386i | \(0.583994\pi\) | |||||||
\(488\) | −752388. | −0.143018 | ||||||||
\(489\) | 6.11611e6 | 1.15665 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.52027e6 | 0.471785 | 0.235892 | − | 0.971779i | \(-0.424199\pi\) | ||||
0.235892 | + | 0.971779i | \(0.424199\pi\) | |||||||
\(492\) | −1.91597e6 | −0.356843 | ||||||||
\(493\) | 1.38260e6 | 0.256199 | ||||||||
\(494\) | 41545.7 | 0.00765965 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.24896e6 | 0.227953 | ||||||||
\(497\) | 988426. | 0.179495 | ||||||||
\(498\) | −8.60568e6 | −1.55493 | ||||||||
\(499\) | 8.63079e6 | 1.55167 | 0.775834 | − | 0.630937i | \(-0.217329\pi\) | ||||
0.775834 | + | 0.630937i | \(0.217329\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.92027e6 | 1.23177 | ||||||||
\(502\) | 5.54345e6 | 0.981795 | ||||||||
\(503\) | 8.02315e6 | 1.41392 | 0.706960 | − | 0.707254i | \(-0.250066\pi\) | ||||
0.706960 | + | 0.707254i | \(0.250066\pi\) | |||||||
\(504\) | −1.64206e7 | −2.87948 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.15916e6 | 1.06941 | ||||||||
\(507\) | 1.08658e7 | 1.87733 | ||||||||
\(508\) | 3.20920e6 | 0.551743 | ||||||||
\(509\) | 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 | ||||||||
\(512\) | −2.37467e6 | −0.400340 | ||||||||
\(513\) | −2.87085e6 | −0.481634 | ||||||||
\(514\) | 213080. | 0.0355742 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.76518e6 | 0.291854 | ||||||||
\(517\) | 4.18126e6 | 0.687988 | ||||||||
\(518\) | 1.80451e6 | 0.295485 | ||||||||
\(519\) | 3.72975e6 | 0.607801 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 381523. | 0.0615781 | 0.0307891 | − | 0.999526i | \(-0.490198\pi\) | ||||
0.0307891 | + | 0.999526i | \(0.490198\pi\) | |||||||
\(522\) | 2.04190e6 | 0.327988 | ||||||||
\(523\) | −1.85496e6 | −0.296538 | −0.148269 | − | 0.988947i | \(-0.547370\pi\) | ||||
−0.148269 | + | 0.988947i | \(0.547370\pi\) | |||||||
\(524\) | −1.88186e6 | −0.299404 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.43137e6 | −1.32872 | ||||||||
\(527\) | −9.83209e6 | −1.54212 | ||||||||
\(528\) | 3.42146e6 | 0.534106 | ||||||||
\(529\) | 1.56219e6 | 0.242713 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.42934e7 | 3.73897 | ||||||||
\(532\) | −599340. | −0.0918108 | ||||||||
\(533\) | −160450. | −0.0244637 | ||||||||
\(534\) | −1.17889e7 | −1.78904 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.19940e7 | 1.80323 | ||||||||
\(537\) | 1.71311e7 | 2.56359 | ||||||||
\(538\) | −500373. | −0.0745312 | ||||||||
\(539\) | 1.36894e6 | 0.202961 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.92237e6 | −0.723071 | −0.361535 | − | 0.932358i | \(-0.617747\pi\) | ||||
−0.361535 | + | 0.932358i | \(0.617747\pi\) | |||||||
\(542\) | 2.70061e6 | 0.394878 | ||||||||
\(543\) | −1.38100e7 | −2.00999 | ||||||||
\(544\) | 8.67615e6 | 1.25698 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −656720. | −0.0942755 | ||||||||
\(547\) | 1.35722e6 | 0.193947 | 0.0969735 | − | 0.995287i | \(-0.469084\pi\) | ||||
0.0969735 | + | 0.995287i | \(0.469084\pi\) | |||||||
\(548\) | −226075. | −0.0321589 | ||||||||
\(549\) | 2.45481e6 | 0.347607 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 217090. | 0.0304622 | ||||||||
\(552\) | 1.58329e7 | 2.21163 | ||||||||
\(553\) | −5.21607e6 | −0.725321 | ||||||||
\(554\) | −2.30230e6 | −0.318704 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.27516e6 | −0.723684 | ||||||||
\(557\) | 629428. | 0.0859623 | 0.0429811 | − | 0.999076i | \(-0.486314\pi\) | ||||
0.0429811 | + | 0.999076i | \(0.486314\pi\) | |||||||
\(558\) | −1.45206e7 | −1.97424 | ||||||||
\(559\) | 147822. | 0.0200083 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.69345e7 | −3.61328 | ||||||||
\(562\) | −4.72276e6 | −0.630747 | ||||||||
\(563\) | 706922. | 0.0939941 | 0.0469971 | − | 0.998895i | \(-0.485035\pi\) | ||||
0.0469971 | + | 0.998895i | \(0.485035\pi\) | |||||||
\(564\) | 3.68997e6 | 0.488455 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7.38506e6 | −0.968975 | ||||||||
\(567\) | 2.44257e7 | 3.19073 | ||||||||
\(568\) | −1.35613e6 | −0.176372 | ||||||||
\(569\) | 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 | \(-0.673221\pi\) | ||||
−0.517725 | + | 0.855547i | \(0.673221\pi\) | |||||||
\(572\) | −383956. | −0.0490673 | ||||||||
\(573\) | −2.37708e7 | −3.02452 | ||||||||
\(574\) | −2.11301e6 | −0.267684 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.69654e7 | 2.13063 | ||||||||
\(577\) | −5.23139e6 | −0.654150 | −0.327075 | − | 0.944998i | \(-0.606063\pi\) | ||||
−0.327075 | + | 0.944998i | \(0.606063\pi\) | |||||||
\(578\) | 5.01319e6 | 0.624158 | ||||||||
\(579\) | 1.16999e7 | 1.45040 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.03964e7 | 1.27774 | ||||||||
\(582\) | −2.92979e6 | −0.358533 | ||||||||
\(583\) | −5.02425e6 | −0.612209 | ||||||||
\(584\) | −2.64897e6 | −0.321400 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.53149e6 | 1.14661 | ||||||||
\(587\) | 1.22738e7 | 1.47022 | 0.735111 | − | 0.677947i | \(-0.237130\pi\) | ||||
0.735111 | + | 0.677947i | \(0.237130\pi\) | |||||||
\(588\) | 1.20809e6 | 0.144098 | ||||||||
\(589\) | −1.54380e6 | −0.183359 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.41553e7 | −2.84475 | ||||||||
\(592\) | −694795. | −0.0814803 | ||||||||
\(593\) | 1.56297e7 | 1.82521 | 0.912607 | − | 0.408838i | \(-0.134066\pi\) | ||||
0.912607 | + | 0.408838i | \(0.134066\pi\) | |||||||
\(594\) | −2.42205e7 | −2.81654 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 25096.6 | 0.00289401 | ||||||||
\(597\) | −8.95793e6 | −1.02866 | ||||||||
\(598\) | 455184. | 0.0520515 | ||||||||
\(599\) | −909739. | −0.103598 | −0.0517988 | − | 0.998658i | \(-0.516495\pi\) | ||||
−0.0517988 | + | 0.998658i | \(0.516495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.28807e7 | −1.45463 | −0.727315 | − | 0.686303i | \(-0.759232\pi\) | ||||
−0.727315 | + | 0.686303i | \(0.759232\pi\) | |||||||
\(602\) | 1.94672e6 | 0.218933 | ||||||||
\(603\) | −3.91327e7 | −4.38274 | ||||||||
\(604\) | 2.35975e6 | 0.263193 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.39956e6 | 0.376046 | ||||||||
\(607\) | −1.39560e7 | −1.53741 | −0.768706 | − | 0.639602i | \(-0.779099\pi\) | ||||
−0.768706 | + | 0.639602i | \(0.779099\pi\) | |||||||
\(608\) | 1.36230e6 | 0.149456 | ||||||||
\(609\) | −3.43159e6 | −0.374931 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 309010. | 0.0334865 | ||||||||
\(612\) | −1.70868e7 | −1.84409 | ||||||||
\(613\) | 4.77628e6 | 0.513380 | 0.256690 | − | 0.966494i | \(-0.417368\pi\) | ||||
0.256690 | + | 0.966494i | \(0.417368\pi\) | |||||||
\(614\) | 3.29216e6 | 0.352420 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.47288e7 | −1.56393 | ||||||||
\(617\) | 5.08319e6 | 0.537556 | 0.268778 | − | 0.963202i | \(-0.413380\pi\) | ||||
0.268778 | + | 0.963202i | \(0.413380\pi\) | |||||||
\(618\) | 1.95482e7 | 2.05891 | ||||||||
\(619\) | 2.45717e6 | 0.257755 | 0.128878 | − | 0.991660i | \(-0.458863\pi\) | ||||
0.128878 | + | 0.991660i | \(0.458863\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.14537e7 | −3.27297 | ||||||||
\(622\) | −6.97533e6 | −0.722917 | ||||||||
\(623\) | 1.42420e7 | 1.47011 | ||||||||
\(624\) | 252858. | 0.0259965 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.01372e6 | −0.715340 | ||||||||
\(627\) | −4.22916e6 | −0.429621 | ||||||||
\(628\) | −5.61845e6 | −0.568483 | ||||||||
\(629\) | 5.46958e6 | 0.551223 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.11683e7 | −1.11664 | −0.558322 | − | 0.829624i | \(-0.688555\pi\) | ||||
−0.558322 | + | 0.829624i | \(0.688555\pi\) | |||||||
\(632\) | 7.15648e6 | 0.712700 | ||||||||
\(633\) | −1.93191e7 | −1.91636 | ||||||||
\(634\) | 3.92632e6 | 0.387938 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.43391e6 | −0.434654 | ||||||||
\(637\) | 101170. | 0.00987874 | ||||||||
\(638\) | 1.83152e6 | 0.178140 | ||||||||
\(639\) | 4.42463e6 | 0.428672 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.24222e6 | −0.888446 | −0.444223 | − | 0.895916i | \(-0.646520\pi\) | ||||
−0.444223 | + | 0.895916i | \(0.646520\pi\) | |||||||
\(642\) | −2.30259e7 | −2.20485 | ||||||||
\(643\) | −1.65662e6 | −0.158014 | −0.0790069 | − | 0.996874i | \(-0.525175\pi\) | ||||
−0.0790069 | + | 0.996874i | \(0.525175\pi\) | |||||||
\(644\) | −6.56649e6 | −0.623905 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.65837e6 | 0.156351 | ||||||||
\(647\) | 1.26223e6 | 0.118544 | 0.0592720 | − | 0.998242i | \(-0.481122\pi\) | ||||
0.0592720 | + | 0.998242i | \(0.481122\pi\) | |||||||
\(648\) | −3.35122e7 | −3.13521 | ||||||||
\(649\) | 2.17904e7 | 2.03074 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.44031e7 | 2.25680 | ||||||||
\(652\) | 3.48021e6 | 0.320617 | ||||||||
\(653\) | −1.64066e7 | −1.50569 | −0.752843 | − | 0.658200i | \(-0.771318\pi\) | ||||
−0.752843 | + | 0.658200i | \(0.771318\pi\) | |||||||
\(654\) | 9.26481e6 | 0.847017 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 813578. | 0.0738141 | ||||||||
\(657\) | 8.64280e6 | 0.781162 | ||||||||
\(658\) | 4.06944e6 | 0.366413 | ||||||||
\(659\) | −2.46135e6 | −0.220780 | −0.110390 | − | 0.993888i | \(-0.535210\pi\) | ||||
−0.110390 | + | 0.993888i | \(0.535210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.29962e7 | −1.15694 | −0.578471 | − | 0.815703i | \(-0.696350\pi\) | ||||
−0.578471 | + | 0.815703i | \(0.696350\pi\) | |||||||
\(662\) | 1.37663e7 | 1.22088 | ||||||||
\(663\) | −1.99055e6 | −0.175869 | ||||||||
\(664\) | −1.42639e7 | −1.25550 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.07780e6 | 0.705679 | ||||||||
\(667\) | 2.37849e6 | 0.207008 | ||||||||
\(668\) | 3.93779e6 | 0.341438 | ||||||||
\(669\) | −2.64475e7 | −2.28464 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.20189e6 | 0.188795 | ||||||||
\(672\) | −2.15341e7 | −1.83951 | ||||||||
\(673\) | 1.00711e7 | 0.857119 | 0.428559 | − | 0.903514i | \(-0.359021\pi\) | ||||
0.428559 | + | 0.903514i | \(0.359021\pi\) | |||||||
\(674\) | −1.15155e7 | −0.976413 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.18286e6 | 0.520382 | ||||||||
\(677\) | −9.82242e6 | −0.823658 | −0.411829 | − | 0.911261i | \(-0.635110\pi\) | ||||
−0.411829 | + | 0.911261i | \(0.635110\pi\) | |||||||
\(678\) | 1.98747e6 | 0.166045 | ||||||||
\(679\) | 3.53943e6 | 0.294618 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.94038e7 | 1.60331 | ||||||||
\(682\) | −1.30245e7 | −1.07226 | ||||||||
\(683\) | 1.66547e7 | 1.36611 | 0.683053 | − | 0.730369i | \(-0.260652\pi\) | ||||
0.683053 | + | 0.730369i | \(0.260652\pi\) | |||||||
\(684\) | −2.68291e6 | −0.219263 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.78349e6 | −0.631486 | ||||||||
\(687\) | 1.82973e7 | 1.47909 | ||||||||
\(688\) | −749548. | −0.0603710 | ||||||||
\(689\) | −371310. | −0.0297981 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.35915e6 | 0.506645 | 0.253323 | − | 0.967382i | \(-0.418477\pi\) | ||||
0.253323 | + | 0.967382i | \(0.418477\pi\) | |||||||
\(692\) | 2.12231e6 | 0.168478 | ||||||||
\(693\) | 4.80557e7 | 3.80112 | ||||||||
\(694\) | 9.06565e6 | 0.714497 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.70816e6 | 0.368407 | ||||||||
\(697\) | −6.40466e6 | −0.499360 | ||||||||
\(698\) | 4.44181e6 | 0.345081 | ||||||||
\(699\) | 710929. | 0.0550342 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −167796. | −0.0128969 | −0.00644846 | − | 0.999979i | \(-0.502053\pi\) | ||||
−0.00644846 | + | 0.999979i | \(0.502053\pi\) | |||||||
\(702\) | −1.78998e6 | −0.137090 | ||||||||
\(703\) | 858814. | 0.0655406 | ||||||||
\(704\) | 1.52175e7 | 1.15721 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.68426e6 | 0.278188 | ||||||||
\(707\) | −4.10695e6 | −0.309009 | ||||||||
\(708\) | 1.92301e7 | 1.44178 | ||||||||
\(709\) | −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 | ||||||||
\(712\) | −1.95400e7 | −1.44453 | ||||||||
\(713\) | −1.69142e7 | −1.24603 | ||||||||
\(714\) | −2.62142e7 | −1.92438 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.74797e6 | 0.710610 | ||||||||
\(717\) | −5.92597e6 | −0.430488 | ||||||||
\(718\) | −1.09000e7 | −0.789071 | ||||||||
\(719\) | −1.06393e7 | −0.767523 | −0.383761 | − | 0.923432i | \(-0.625372\pi\) | ||||
−0.383761 | + | 0.923432i | \(0.625372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.36159e7 | −1.69187 | ||||||||
\(722\) | −9.41585e6 | −0.672228 | ||||||||
\(723\) | 2.99754e7 | 2.13265 | ||||||||
\(724\) | −7.85821e6 | −0.557157 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.71774e7 | −1.20953 | ||||||||
\(727\) | −1.07639e7 | −0.755323 | −0.377661 | − | 0.925944i | \(-0.623272\pi\) | ||||
−0.377661 | + | 0.925944i | \(0.623272\pi\) | |||||||
\(728\) | −1.08851e6 | −0.0761210 | ||||||||
\(729\) | 2.98885e7 | 2.08298 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.90060e6 | 0.408416 | ||||||||
\(732\) | 1.94317e6 | 0.134040 | ||||||||
\(733\) | −8.86456e6 | −0.609393 | −0.304696 | − | 0.952450i | \(-0.598555\pi\) | ||||
−0.304696 | + | 0.952450i | \(0.598555\pi\) | |||||||
\(734\) | 1.64200e7 | 1.12495 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.49256e7 | 1.01564 | ||||||||
\(737\) | −3.51008e7 | −2.38039 | ||||||||
\(738\) | −9.45878e6 | −0.639285 | ||||||||
\(739\) | 1.34276e7 | 0.904457 | 0.452229 | − | 0.891902i | \(-0.350629\pi\) | ||||
0.452229 | + | 0.891902i | \(0.350629\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −312550. | −0.0209110 | ||||||||
\(742\) | −4.88989e6 | −0.326054 | ||||||||
\(743\) | 3.76228e6 | 0.250023 | 0.125011 | − | 0.992155i | \(-0.460103\pi\) | ||||
0.125011 | + | 0.992155i | \(0.460103\pi\) | |||||||
\(744\) | −3.34812e7 | −2.21753 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.88809e7 | −1.24215 | ||||||||
\(747\) | 4.65388e7 | 3.05150 | ||||||||
\(748\) | −1.53263e7 | −1.00158 | ||||||||
\(749\) | 2.78172e7 | 1.81179 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.97179e7 | 1.27574 | 0.637870 | − | 0.770144i | \(-0.279816\pi\) | ||||
0.637870 | + | 0.770144i | \(0.279816\pi\) | |||||||
\(752\) | −1.56687e6 | −0.101039 | ||||||||
\(753\) | −4.17036e7 | −2.68032 | ||||||||
\(754\) | 135356. | 0.00867060 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.58223e7 | 1.64320 | ||||||||
\(757\) | 1.91175e7 | 1.21253 | 0.606264 | − | 0.795264i | \(-0.292668\pi\) | ||||
0.606264 | + | 0.795264i | \(0.292668\pi\) | |||||||
\(758\) | 7.97043e6 | 0.503859 | ||||||||
\(759\) | −4.63356e7 | −2.91951 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.51417e6 | −0.282563 | −0.141282 | − | 0.989969i | \(-0.545122\pi\) | ||||
−0.141282 | + | 0.989969i | \(0.545122\pi\) | |||||||
\(762\) | 2.20397e7 | 1.37505 | ||||||||
\(763\) | −1.11927e7 | −0.696020 | ||||||||
\(764\) | −1.35261e7 | −0.838378 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.61054e6 | −0.222331 | ||||||||
\(767\) | 1.61039e6 | 0.0988423 | ||||||||
\(768\) | 3.28315e7 | 2.00857 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 6.65753e6 | 0.402040 | ||||||||
\(773\) | 1.68649e7 | 1.01516 | 0.507581 | − | 0.861604i | \(-0.330540\pi\) | ||||
0.507581 | + | 0.861604i | \(0.330540\pi\) | |||||||
\(774\) | 8.71436e6 | 0.522857 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.85612e6 | −0.289491 | ||||||||
\(777\) | −1.35754e7 | −0.806679 | ||||||||
\(778\) | −1.32644e7 | −0.785667 | ||||||||
\(779\) | −1.00564e6 | −0.0593742 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.96876e6 | 0.232824 | ||||||||
\(782\) | 1.81695e7 | 1.06249 | ||||||||
\(783\) | −9.35324e6 | −0.545202 | ||||||||
\(784\) | −512991. | −0.0298071 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.29240e7 | −0.746172 | ||||||||
\(787\) | 532946. | 0.0306723 | 0.0153361 | − | 0.999882i | \(-0.495118\pi\) | ||||
0.0153361 | + | 0.999882i | \(0.495118\pi\) | |||||||
\(788\) | −1.37449e7 | −0.788546 | ||||||||
\(789\) | 6.34295e7 | 3.62743 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.40102e6 | −0.136444 | ||||||||
\(792\) | −6.59327e7 | −3.73498 | ||||||||
\(793\) | 162728. | 0.00918922 | ||||||||
\(794\) | 3.91414e6 | 0.220336 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.09726e6 | −0.285137 | ||||||||
\(797\) | −2.74340e6 | −0.152983 | −0.0764916 | − | 0.997070i | \(-0.524372\pi\) | ||||
−0.0764916 | + | 0.997070i | \(0.524372\pi\) | |||||||
\(798\) | −4.11606e6 | −0.228810 | ||||||||
\(799\) | 1.23347e7 | 0.683537 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.37533e7 | 3.51092 | ||||||||
\(802\) | 2.16279e7 | 1.18735 | ||||||||
\(803\) | 7.75233e6 | 0.424271 | ||||||||
\(804\) | −3.09765e7 | −1.69002 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −962560. | −0.0521903 | ||||||||
\(807\) | 3.76433e6 | 0.203471 | ||||||||
\(808\) | 5.63476e6 | 0.303631 | ||||||||
\(809\) | 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 | \(-0.724268\pi\) | ||||
−0.647698 | + | 0.761897i | \(0.724268\pi\) | |||||||
\(812\) | −1.95265e6 | −0.103928 | ||||||||
\(813\) | −2.03168e7 | −1.07802 | ||||||||
\(814\) | 7.24554e6 | 0.383274 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00933e7 | 0.530650 | ||||||||
\(817\) | 926492. | 0.0485609 | ||||||||
\(818\) | 7.55344e6 | 0.394695 | ||||||||
\(819\) | 3.55149e6 | 0.185012 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.65430e6 | −0.137433 | −0.0687167 | − | 0.997636i | \(-0.521890\pi\) | ||||
−0.0687167 | + | 0.997636i | \(0.521890\pi\) | |||||||
\(822\) | −1.55261e6 | −0.0801460 | ||||||||
\(823\) | 1.45761e7 | 0.750137 | 0.375068 | − | 0.926997i | \(-0.377619\pi\) | ||||
0.375068 | + | 0.926997i | \(0.377619\pi\) | |||||||
\(824\) | 3.24012e7 | 1.66243 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.12077e7 | 1.08154 | ||||||||
\(827\) | 2.56966e7 | 1.30651 | 0.653254 | − | 0.757139i | \(-0.273403\pi\) | ||||
0.653254 | + | 0.757139i | \(0.273403\pi\) | |||||||
\(828\) | −2.93945e7 | −1.49001 | ||||||||
\(829\) | 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 | ||||||||
\(832\) | 1.12462e6 | 0.0563247 | ||||||||
\(833\) | 4.03838e6 | 0.201648 | ||||||||
\(834\) | −3.62280e7 | −1.80356 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.40649e6 | −0.119088 | ||||||||
\(837\) | 6.65139e7 | 3.28170 | ||||||||
\(838\) | 7.03734e6 | 0.346177 | ||||||||
\(839\) | −6.91282e6 | −0.339039 | −0.169520 | − | 0.985527i | \(-0.554222\pi\) | ||||
−0.169520 | + | 0.985527i | \(0.554222\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 707281. | 0.0344828 | ||||||||
\(842\) | −5.18392e6 | −0.251987 | ||||||||
\(843\) | 3.55295e7 | 1.72195 | ||||||||
\(844\) | −1.09930e7 | −0.531202 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.82166e7 | 0.875069 | ||||||||
\(847\) | 2.07518e7 | 0.993909 | ||||||||
\(848\) | 1.88276e6 | 0.0899097 | ||||||||
\(849\) | 5.55581e7 | 2.64532 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.40934e6 | 0.445385 | ||||||||
\(852\) | 3.50244e6 | 0.165299 | ||||||||
\(853\) | 2.16826e7 | 1.02033 | 0.510164 | − | 0.860077i | \(-0.329585\pi\) | ||||
0.510164 | + | 0.860077i | \(0.329585\pi\) | |||||||
\(854\) | 2.14301e6 | 0.100549 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.81654e7 | −1.78027 | ||||||||
\(857\) | 2.22637e7 | 1.03549 | 0.517745 | − | 0.855535i | \(-0.326772\pi\) | ||||
0.517745 | + | 0.855535i | \(0.326772\pi\) | |||||||
\(858\) | −2.63688e6 | −0.122285 | ||||||||
\(859\) | −1.56538e7 | −0.723828 | −0.361914 | − | 0.932211i | \(-0.617877\pi\) | ||||
−0.361914 | + | 0.932211i | \(0.617877\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.58963e7 | 0.730781 | ||||||||
\(862\) | 2.28378e6 | 0.104685 | ||||||||
\(863\) | −3.14396e7 | −1.43698 | −0.718489 | − | 0.695538i | \(-0.755166\pi\) | ||||
−0.718489 | + | 0.695538i | \(0.755166\pi\) | |||||||
\(864\) | −5.86940e7 | −2.67491 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.76434e6 | 0.125255 | ||||||||
\(867\) | −3.77144e7 | −1.70396 | ||||||||
\(868\) | 1.38859e7 | 0.625569 | ||||||||
\(869\) | −2.09437e7 | −0.940816 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.59407e6 | −0.115861 | ||||||||
\(872\) | 1.53564e7 | 0.683909 | ||||||||
\(873\) | 1.58440e7 | 0.703608 | ||||||||
\(874\) | 2.85291e6 | 0.126331 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 6.84144e6 | 0.301222 | ||||||||
\(877\) | −9.99092e6 | −0.438638 | −0.219319 | − | 0.975653i | \(-0.570384\pi\) | ||||
−0.219319 | + | 0.975653i | \(0.570384\pi\) | |||||||
\(878\) | 1.97808e7 | 0.865978 | ||||||||
\(879\) | −7.17057e7 | −3.13027 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.37367e6 | −0.103034 | −0.0515169 | − | 0.998672i | \(-0.516406\pi\) | ||||
−0.0515169 | + | 0.998672i | \(0.516406\pi\) | |||||||
\(882\) | 5.96411e6 | 0.258151 | ||||||||
\(883\) | 686405. | 0.0296264 | 0.0148132 | − | 0.999890i | \(-0.495285\pi\) | ||||
0.0148132 | + | 0.999890i | \(0.495285\pi\) | |||||||
\(884\) | −1.13267e6 | −0.0487498 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.30175e7 | 0.557112 | ||||||||
\(887\) | −1.54019e7 | −0.657302 | −0.328651 | − | 0.944451i | \(-0.606594\pi\) | ||||
−0.328651 | + | 0.944451i | \(0.606594\pi\) | |||||||
\(888\) | 1.86256e7 | 0.792641 | ||||||||
\(889\) | −2.66258e7 | −1.12992 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.80750e7 | 4.13870 | ||||||||
\(892\) | −1.50492e7 | −0.633288 | ||||||||
\(893\) | 1.93675e6 | 0.0812729 | ||||||||
\(894\) | 172355. | 0.00721242 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.62879e6 | −0.359071 | ||||||||
\(897\) | −3.42436e6 | −0.142102 | ||||||||
\(898\) | 147728. | 0.00611325 | ||||||||
\(899\) | −5.02970e6 | −0.207560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.48215e7 | −0.608248 | ||||||||
\(902\) | −8.48424e6 | −0.347213 | ||||||||
\(903\) | −1.46452e7 | −0.597691 | ||||||||
\(904\) | 3.29422e6 | 0.134070 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.62060e7 | 0.655926 | ||||||||
\(907\) | 2.67004e7 | 1.07770 | 0.538852 | − | 0.842401i | \(-0.318858\pi\) | ||||
0.538852 | + | 0.842401i | \(0.318858\pi\) | |||||||
\(908\) | 1.10412e7 | 0.444428 | ||||||||
\(909\) | −1.83845e7 | −0.737976 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.90851e7 | 0.761902 | 0.380951 | − | 0.924595i | \(-0.375597\pi\) | ||||
0.380951 | + | 0.924595i | \(0.375597\pi\) | |||||||
\(912\) | 1.58482e6 | 0.0630946 | ||||||||
\(913\) | 4.17439e7 | 1.65736 | ||||||||
\(914\) | 2.95086e7 | 1.16838 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.04116e7 | 0.409995 | ||||||||
\(917\) | 1.56132e7 | 0.613153 | ||||||||
\(918\) | −7.14503e7 | −2.79832 | ||||||||
\(919\) | 3.04815e7 | 1.19055 | 0.595274 | − | 0.803523i | \(-0.297043\pi\) | ||||
0.595274 | + | 0.803523i | \(0.297043\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.47671e7 | −0.962112 | ||||||||
\(922\) | 7.72051e6 | 0.299101 | ||||||||
\(923\) | 293306. | 0.0113322 | ||||||||
\(924\) | 3.80398e7 | 1.46574 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.26384e7 | 1.25084 | ||||||||
\(927\) | −1.05715e8 | −4.04053 | ||||||||
\(928\) | 4.43837e6 | 0.169182 | ||||||||
\(929\) | −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 | ||||||||
\(932\) | 404534. | 0.0152551 | ||||||||
\(933\) | 5.24757e7 | 1.97358 | ||||||||
\(934\) | 3.34575e6 | 0.125495 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.87266e6 | −0.181793 | ||||||||
\(937\) | 3.03413e7 | 1.12898 | 0.564489 | − | 0.825441i | \(-0.309073\pi\) | ||||
0.564489 | + | 0.825441i | \(0.309073\pi\) | |||||||
\(938\) | −3.41621e7 | −1.26776 | ||||||||
\(939\) | 5.27645e7 | 1.95289 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.32048e7 | 1.59059 | 0.795294 | − | 0.606224i | \(-0.207317\pi\) | ||||
0.795294 | + | 0.606224i | \(0.207317\pi\) | |||||||
\(942\) | −3.85857e7 | −1.41677 | ||||||||
\(943\) | −1.10180e7 | −0.403480 | ||||||||
\(944\) | −8.16565e6 | −0.298236 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.81652e6 | 0.283979 | ||||||||
\(947\) | 2.50483e7 | 0.907620 | 0.453810 | − | 0.891099i | \(-0.350065\pi\) | ||||
0.453810 | + | 0.891099i | \(0.350065\pi\) | |||||||
\(948\) | −1.84829e7 | −0.667957 | ||||||||
\(949\) | 572925. | 0.0206506 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.95379e7 | −1.05908 | ||||||||
\(952\) | −4.34500e7 | −1.55381 | ||||||||
\(953\) | −4.30580e7 | −1.53576 | −0.767878 | − | 0.640596i | \(-0.778687\pi\) | ||||
−0.767878 | + | 0.640596i | \(0.778687\pi\) | |||||||
\(954\) | −2.18893e7 | −0.778684 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.37201e6 | −0.119328 | ||||||||
\(957\) | −1.37786e7 | −0.486324 | ||||||||
\(958\) | 1.55288e7 | 0.546669 | ||||||||
\(959\) | 1.87568e6 | 0.0658584 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.13868e6 | 0.249350 | ||||||||
\(962\) | 535471. | 0.0186551 | ||||||||
\(963\) | 1.24522e8 | 4.32694 | ||||||||
\(964\) | 1.70567e7 | 0.591156 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.50965e7 | −1.55489 | ||||||||
\(967\) | 3.26447e7 | 1.12266 | 0.561328 | − | 0.827593i | \(-0.310290\pi\) | ||||
0.561328 | + | 0.827593i | \(0.310290\pi\) | |||||||
\(968\) | −2.84716e7 | −0.976614 | ||||||||
\(969\) | −1.24760e7 | −0.426841 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.02885e6 | −0.307315 | −0.153658 | − | 0.988124i | \(-0.549105\pi\) | ||||
−0.153658 | + | 0.988124i | \(0.549105\pi\) | |||||||
\(972\) | 4.13414e7 | 1.40352 | ||||||||
\(973\) | 4.37665e7 | 1.48204 | ||||||||
\(974\) | −1.06694e7 | −0.360364 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −825128. | −0.0277266 | ||||||||
\(977\) | −8.87743e6 | −0.297544 | −0.148772 | − | 0.988872i | \(-0.547532\pi\) | ||||
−0.148772 | + | 0.988872i | \(0.547532\pi\) | |||||||
\(978\) | 2.39009e7 | 0.799037 | ||||||||
\(979\) | 5.71848e7 | 1.90688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.01033e7 | −1.66224 | ||||||||
\(982\) | 9.84886e6 | 0.325917 | ||||||||
\(983\) | 4.56481e7 | 1.50674 | 0.753371 | − | 0.657596i | \(-0.228427\pi\) | ||||
0.753371 | + | 0.657596i | \(0.228427\pi\) | |||||||
\(984\) | −2.18098e7 | −0.718065 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.40299e6 | 0.176987 | ||||||||
\(987\) | −3.06146e7 | −1.00031 | ||||||||
\(988\) | −177848. | −0.00579638 | ||||||||
\(989\) | 1.01508e7 | 0.329998 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.74121e6 | −0.250395 | −0.125197 | − | 0.992132i | \(-0.539956\pi\) | ||||
−0.125197 | + | 0.992132i | \(0.539956\pi\) | |||||||
\(992\) | −3.15627e7 | −1.01834 | ||||||||
\(993\) | −1.03564e8 | −3.33301 | ||||||||
\(994\) | 3.86263e6 | 0.123999 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.68390e7 | 1.17668 | ||||||||
\(997\) | −5.64996e7 | −1.80014 | −0.900072 | − | 0.435740i | \(-0.856487\pi\) | ||||
−0.900072 | + | 0.435740i | \(0.856487\pi\) | |||||||
\(998\) | 3.37279e7 | 1.07192 | ||||||||
\(999\) | −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 | 725.6.a.b.1.5 | 7 | ||
5.4 | even | 2 | 29.6.a.b.1.3 | ✓ | 7 | ||
15.14 | odd | 2 | 261.6.a.e.1.5 | 7 | |||
20.19 | odd | 2 | 464.6.a.k.1.1 | 7 | |||
145.144 | even | 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 | 5.4 | even | 2 | ||
261.6.a.e.1.5 | 7 | 15.14 | odd | 2 | |||
464.6.a.k.1.1 | 7 | 20.19 | odd | 2 | |||
725.6.a.b.1.5 | 7 | 1.1 | even | 1 | trivial | ||
841.6.a.b.1.5 | 7 | 145.144 | even | 2 |