Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, 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("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.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: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 119x^{3} + 206x^{2} + 1428x - 1320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.28026\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.28026 | −0.756650 | −0.378325 | − | 0.925673i | \(-0.623500\pi\) | ||||
−0.378325 | + | 0.925673i | \(0.623500\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −13.6794 | −0.427482 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −38.5223 | −0.436852 | ||||||||
\(7\) | 202.127 | 1.55912 | 0.779558 | − | 0.626330i | \(-0.215444\pi\) | ||||
0.779558 | + | 0.626330i | \(0.215444\pi\) | |||||||
\(8\) | 195.520 | 1.08010 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 107.006 | 0.338384 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −123.115 | −0.246807 | ||||||||
\(13\) | −636.662 | −1.04484 | −0.522421 | − | 0.852688i | \(-0.674971\pi\) | ||||
−0.522421 | + | 0.852688i | \(0.674971\pi\) | |||||||
\(14\) | −865.154 | −1.17970 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | −399.133 | −0.389778 | ||||||||
\(17\) | −1203.76 | −1.01022 | −0.505110 | − | 0.863055i | \(-0.668548\pi\) | ||||
−0.505110 | + | 0.863055i | \(0.668548\pi\) | |||||||
\(18\) | −346.701 | −0.252217 | ||||||||
\(19\) | 1153.75 | 0.733207 | 0.366603 | − | 0.930377i | \(-0.380521\pi\) | ||||
0.366603 | + | 0.930377i | \(0.380521\pi\) | |||||||
\(20\) | 341.985 | 0.191176 | ||||||||
\(21\) | 1819.14 | 0.900156 | ||||||||
\(22\) | 517.911 | 0.228138 | ||||||||
\(23\) | 932.834 | 0.367693 | 0.183846 | − | 0.982955i | \(-0.441145\pi\) | ||||
0.183846 | + | 0.982955i | \(0.441145\pi\) | |||||||
\(24\) | 1759.68 | 0.623598 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 2725.07 | 0.790579 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −2764.97 | −0.666493 | ||||||||
\(29\) | 1806.72 | 0.398930 | 0.199465 | − | 0.979905i | \(-0.436080\pi\) | ||||
0.199465 | + | 0.979905i | \(0.436080\pi\) | |||||||
\(30\) | 963.058 | 0.195366 | ||||||||
\(31\) | 4326.37 | 0.808573 | 0.404286 | − | 0.914632i | \(-0.367520\pi\) | ||||
0.404286 | + | 0.914632i | \(0.367520\pi\) | |||||||
\(32\) | −4548.24 | −0.785178 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 5152.39 | 0.764383 | ||||||||
\(35\) | −5053.16 | −0.697258 | ||||||||
\(36\) | −1108.03 | −0.142494 | ||||||||
\(37\) | 6690.43 | 0.803434 | 0.401717 | − | 0.915764i | \(-0.368414\pi\) | ||||
0.401717 | + | 0.915764i | \(0.368414\pi\) | |||||||
\(38\) | −4938.33 | −0.554780 | ||||||||
\(39\) | −5729.95 | −0.603239 | ||||||||
\(40\) | −4887.99 | −0.483037 | ||||||||
\(41\) | 13597.5 | 1.26328 | 0.631640 | − | 0.775262i | \(-0.282382\pi\) | ||||
0.631640 | + | 0.775262i | \(0.282382\pi\) | |||||||
\(42\) | −7786.38 | −0.681102 | ||||||||
\(43\) | 5496.81 | 0.453356 | 0.226678 | − | 0.973970i | \(-0.427213\pi\) | ||||
0.226678 | + | 0.973970i | \(0.427213\pi\) | |||||||
\(44\) | 1655.21 | 0.128891 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | −3992.77 | −0.278214 | ||||||||
\(47\) | −9481.06 | −0.626055 | −0.313027 | − | 0.949744i | \(-0.601343\pi\) | ||||
−0.313027 | + | 0.949744i | \(0.601343\pi\) | |||||||
\(48\) | −3592.19 | −0.225038 | ||||||||
\(49\) | 24048.2 | 1.43084 | ||||||||
\(50\) | −2675.16 | −0.151330 | ||||||||
\(51\) | −10833.8 | −0.583251 | ||||||||
\(52\) | 8709.15 | 0.446650 | ||||||||
\(53\) | 28001.9 | 1.36930 | 0.684648 | − | 0.728874i | \(-0.259956\pi\) | ||||
0.684648 | + | 0.728874i | \(0.259956\pi\) | |||||||
\(54\) | −3120.31 | −0.145617 | ||||||||
\(55\) | 3025.00 | 0.134840 | ||||||||
\(56\) | 39519.7 | 1.68401 | ||||||||
\(57\) | 10383.7 | 0.423317 | ||||||||
\(58\) | −7733.23 | −0.301850 | ||||||||
\(59\) | 23054.7 | 0.862242 | 0.431121 | − | 0.902294i | \(-0.358118\pi\) | ||||
0.431121 | + | 0.902294i | \(0.358118\pi\) | |||||||
\(60\) | 3077.87 | 0.110375 | ||||||||
\(61\) | −3225.94 | −0.111002 | −0.0555011 | − | 0.998459i | \(-0.517676\pi\) | ||||
−0.0555011 | + | 0.998459i | \(0.517676\pi\) | |||||||
\(62\) | −18518.0 | −0.611806 | ||||||||
\(63\) | 16372.3 | 0.519705 | ||||||||
\(64\) | 32239.9 | 0.983882 | ||||||||
\(65\) | 15916.5 | 0.467267 | ||||||||
\(66\) | 4661.20 | 0.131716 | ||||||||
\(67\) | 56889.2 | 1.54826 | 0.774128 | − | 0.633029i | \(-0.218189\pi\) | ||||
0.774128 | + | 0.633029i | \(0.218189\pi\) | |||||||
\(68\) | 16466.7 | 0.431851 | ||||||||
\(69\) | 8395.51 | 0.212287 | ||||||||
\(70\) | 21628.8 | 0.527580 | ||||||||
\(71\) | −61686.0 | −1.45225 | −0.726124 | − | 0.687564i | \(-0.758680\pi\) | ||||
−0.726124 | + | 0.687564i | \(0.758680\pi\) | |||||||
\(72\) | 15837.1 | 0.360034 | ||||||||
\(73\) | 32580.0 | 0.715557 | 0.357779 | − | 0.933806i | \(-0.383534\pi\) | ||||
0.357779 | + | 0.933806i | \(0.383534\pi\) | |||||||
\(74\) | −28636.8 | −0.607918 | ||||||||
\(75\) | 5625.00 | 0.115470 | ||||||||
\(76\) | −15782.6 | −0.313432 | ||||||||
\(77\) | −24457.3 | −0.470091 | ||||||||
\(78\) | 24525.7 | 0.456441 | ||||||||
\(79\) | 52398.7 | 0.944611 | 0.472305 | − | 0.881435i | \(-0.343422\pi\) | ||||
0.472305 | + | 0.881435i | \(0.343422\pi\) | |||||||
\(80\) | 9978.32 | 0.174314 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −58200.8 | −0.955860 | ||||||||
\(83\) | −9259.82 | −0.147539 | −0.0737696 | − | 0.997275i | \(-0.523503\pi\) | ||||
−0.0737696 | + | 0.997275i | \(0.523503\pi\) | |||||||
\(84\) | −24884.7 | −0.384800 | ||||||||
\(85\) | 30093.9 | 0.451785 | ||||||||
\(86\) | −23527.8 | −0.343032 | ||||||||
\(87\) | 16260.5 | 0.230322 | ||||||||
\(88\) | −23657.9 | −0.325663 | ||||||||
\(89\) | −32806.6 | −0.439021 | −0.219511 | − | 0.975610i | \(-0.570446\pi\) | ||||
−0.219511 | + | 0.975610i | \(0.570446\pi\) | |||||||
\(90\) | 8667.52 | 0.112795 | ||||||||
\(91\) | −128686. | −1.62903 | ||||||||
\(92\) | −12760.6 | −0.157182 | ||||||||
\(93\) | 38937.3 | 0.466830 | ||||||||
\(94\) | 40581.4 | 0.473704 | ||||||||
\(95\) | −28843.7 | −0.327900 | ||||||||
\(96\) | −40934.1 | −0.453323 | ||||||||
\(97\) | 30708.3 | 0.331380 | 0.165690 | − | 0.986178i | \(-0.447015\pi\) | ||||
0.165690 | + | 0.986178i | \(0.447015\pi\) | |||||||
\(98\) | −102932. | −1.08265 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | −8549.63 | −0.0854963 | ||||||||
\(101\) | −109736. | −1.07040 | −0.535201 | − | 0.844725i | \(-0.679764\pi\) | ||||
−0.535201 | + | 0.844725i | \(0.679764\pi\) | |||||||
\(102\) | 46371.5 | 0.441317 | ||||||||
\(103\) | 192972. | 1.79226 | 0.896130 | − | 0.443792i | \(-0.146367\pi\) | ||||
0.896130 | + | 0.443792i | \(0.146367\pi\) | |||||||
\(104\) | −124480. | −1.12854 | ||||||||
\(105\) | −45478.5 | −0.402562 | ||||||||
\(106\) | −119855. | −1.03608 | ||||||||
\(107\) | −145055. | −1.22482 | −0.612412 | − | 0.790539i | \(-0.709801\pi\) | ||||
−0.612412 | + | 0.790539i | \(0.709801\pi\) | |||||||
\(108\) | −9972.29 | −0.0822689 | ||||||||
\(109\) | 221636. | 1.78679 | 0.893396 | − | 0.449271i | \(-0.148316\pi\) | ||||
0.893396 | + | 0.449271i | \(0.148316\pi\) | |||||||
\(110\) | −12947.8 | −0.102027 | ||||||||
\(111\) | 60213.9 | 0.463863 | ||||||||
\(112\) | −80675.3 | −0.607709 | ||||||||
\(113\) | 105834. | 0.779705 | 0.389853 | − | 0.920877i | \(-0.372526\pi\) | ||||
0.389853 | + | 0.920877i | \(0.372526\pi\) | |||||||
\(114\) | −44445.0 | −0.320303 | ||||||||
\(115\) | −23320.9 | −0.164437 | ||||||||
\(116\) | −24714.9 | −0.170535 | ||||||||
\(117\) | −51569.6 | −0.348280 | ||||||||
\(118\) | −98679.9 | −0.652415 | ||||||||
\(119\) | −243311. | −1.57505 | ||||||||
\(120\) | −43991.9 | −0.278881 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 13807.8 | 0.0839898 | ||||||||
\(123\) | 122377. | 0.729355 | ||||||||
\(124\) | −59182.2 | −0.345650 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −70077.4 | −0.393235 | ||||||||
\(127\) | −240397. | −1.32257 | −0.661285 | − | 0.750134i | \(-0.729989\pi\) | ||||
−0.661285 | + | 0.750134i | \(0.729989\pi\) | |||||||
\(128\) | 7548.69 | 0.0407236 | ||||||||
\(129\) | 49471.3 | 0.261745 | ||||||||
\(130\) | −68126.9 | −0.353557 | ||||||||
\(131\) | −175704. | −0.894548 | −0.447274 | − | 0.894397i | \(-0.647605\pi\) | ||||
−0.447274 | + | 0.894397i | \(0.647605\pi\) | |||||||
\(132\) | 14896.9 | 0.0744150 | ||||||||
\(133\) | 233203. | 1.14315 | ||||||||
\(134\) | −243500. | −1.17149 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | −235358. | −1.09114 | ||||||||
\(137\) | −223760. | −1.01855 | −0.509273 | − | 0.860605i | \(-0.670086\pi\) | ||||
−0.509273 | + | 0.860605i | \(0.670086\pi\) | |||||||
\(138\) | −35934.9 | −0.160627 | ||||||||
\(139\) | 179526. | 0.788116 | 0.394058 | − | 0.919085i | \(-0.371071\pi\) | ||||
0.394058 | + | 0.919085i | \(0.371071\pi\) | |||||||
\(140\) | 69124.3 | 0.298065 | ||||||||
\(141\) | −85329.6 | −0.361453 | ||||||||
\(142\) | 264032. | 1.09884 | ||||||||
\(143\) | 77036.0 | 0.315031 | ||||||||
\(144\) | −32329.8 | −0.129926 | ||||||||
\(145\) | −45168.0 | −0.178407 | ||||||||
\(146\) | −139451. | −0.541426 | ||||||||
\(147\) | 216433. | 0.826097 | ||||||||
\(148\) | −91521.2 | −0.343453 | ||||||||
\(149\) | 475283. | 1.75383 | 0.876914 | − | 0.480648i | \(-0.159598\pi\) | ||||
0.876914 | + | 0.480648i | \(0.159598\pi\) | |||||||
\(150\) | −24076.4 | −0.0873704 | ||||||||
\(151\) | 263838. | 0.941661 | 0.470830 | − | 0.882224i | \(-0.343954\pi\) | ||||
0.470830 | + | 0.882224i | \(0.343954\pi\) | |||||||
\(152\) | 225580. | 0.791939 | ||||||||
\(153\) | −97504.3 | −0.336740 | ||||||||
\(154\) | 104684. | 0.355694 | ||||||||
\(155\) | −108159. | −0.361605 | ||||||||
\(156\) | 78382.4 | 0.257874 | ||||||||
\(157\) | −100955. | −0.326873 | −0.163437 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163437 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(158\) | −224280. | −0.714739 | ||||||||
\(159\) | 252017. | 0.790563 | ||||||||
\(160\) | 113706. | 0.351142 | ||||||||
\(161\) | 188551. | 0.573275 | ||||||||
\(162\) | −28082.8 | −0.0840722 | ||||||||
\(163\) | −560105. | −1.65120 | −0.825601 | − | 0.564254i | \(-0.809164\pi\) | ||||
−0.825601 | + | 0.564254i | \(0.809164\pi\) | |||||||
\(164\) | −186006. | −0.540028 | ||||||||
\(165\) | 27225.0 | 0.0778499 | ||||||||
\(166\) | 39634.4 | 0.111635 | ||||||||
\(167\) | 442671. | 1.22826 | 0.614129 | − | 0.789206i | \(-0.289507\pi\) | ||||
0.614129 | + | 0.789206i | \(0.289507\pi\) | |||||||
\(168\) | 355677. | 0.972261 | ||||||||
\(169\) | 34044.9 | 0.0916929 | ||||||||
\(170\) | −128810. | −0.341843 | ||||||||
\(171\) | 93453.5 | 0.244402 | ||||||||
\(172\) | −75193.1 | −0.193801 | ||||||||
\(173\) | 345516. | 0.877715 | 0.438857 | − | 0.898557i | \(-0.355383\pi\) | ||||
0.438857 | + | 0.898557i | \(0.355383\pi\) | |||||||
\(174\) | −69599.1 | −0.174273 | ||||||||
\(175\) | 126329. | 0.311823 | ||||||||
\(176\) | 48295.1 | 0.117523 | ||||||||
\(177\) | 207492. | 0.497815 | ||||||||
\(178\) | 140420. | 0.332185 | ||||||||
\(179\) | −323189. | −0.753917 | −0.376959 | − | 0.926230i | \(-0.623030\pi\) | ||||
−0.376959 | + | 0.926230i | \(0.623030\pi\) | |||||||
\(180\) | 27700.8 | 0.0637252 | ||||||||
\(181\) | −73649.6 | −0.167099 | −0.0835495 | − | 0.996504i | \(-0.526626\pi\) | ||||
−0.0835495 | + | 0.996504i | \(0.526626\pi\) | |||||||
\(182\) | 550810. | 1.23260 | ||||||||
\(183\) | −29033.5 | −0.0640872 | ||||||||
\(184\) | 182387. | 0.397146 | ||||||||
\(185\) | −167261. | −0.359306 | ||||||||
\(186\) | −166662. | −0.353227 | ||||||||
\(187\) | 145655. | 0.304593 | ||||||||
\(188\) | 129695. | 0.267627 | ||||||||
\(189\) | 147350. | 0.300052 | ||||||||
\(190\) | 123458. | 0.248105 | ||||||||
\(191\) | −993310. | −1.97016 | −0.985079 | − | 0.172100i | \(-0.944945\pi\) | ||||
−0.985079 | + | 0.172100i | \(0.944945\pi\) | |||||||
\(192\) | 290159. | 0.568045 | ||||||||
\(193\) | −135815. | −0.262455 | −0.131227 | − | 0.991352i | \(-0.541892\pi\) | ||||
−0.131227 | + | 0.991352i | \(0.541892\pi\) | |||||||
\(194\) | −131440. | −0.250739 | ||||||||
\(195\) | 143249. | 0.269777 | ||||||||
\(196\) | −328965. | −0.611658 | ||||||||
\(197\) | 236510. | 0.434194 | 0.217097 | − | 0.976150i | \(-0.430341\pi\) | ||||
0.217097 | + | 0.976150i | \(0.430341\pi\) | |||||||
\(198\) | 41950.8 | 0.0760461 | ||||||||
\(199\) | −635807. | −1.13813 | −0.569066 | − | 0.822292i | \(-0.692695\pi\) | ||||
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(200\) | 122200. | 0.216021 | ||||||||
\(201\) | 512003. | 0.893886 | ||||||||
\(202\) | 469700. | 0.809919 | ||||||||
\(203\) | 365186. | 0.621977 | ||||||||
\(204\) | 148200. | 0.249329 | ||||||||
\(205\) | −339937. | −0.564956 | ||||||||
\(206\) | −825969. | −1.35611 | ||||||||
\(207\) | 75559.6 | 0.122564 | ||||||||
\(208\) | 254112. | 0.407256 | ||||||||
\(209\) | −139603. | −0.221070 | ||||||||
\(210\) | 194660. | 0.304598 | ||||||||
\(211\) | −753940. | −1.16582 | −0.582909 | − | 0.812537i | \(-0.698086\pi\) | ||||
−0.582909 | + | 0.812537i | \(0.698086\pi\) | |||||||
\(212\) | −383049. | −0.585348 | ||||||||
\(213\) | −555174. | −0.838456 | ||||||||
\(214\) | 620873. | 0.926763 | ||||||||
\(215\) | −137420. | −0.202747 | ||||||||
\(216\) | 142534. | 0.207866 | ||||||||
\(217\) | 874474. | 1.26066 | ||||||||
\(218\) | −948658. | −1.35197 | ||||||||
\(219\) | 293220. | 0.413127 | ||||||||
\(220\) | −41380.2 | −0.0576416 | ||||||||
\(221\) | 766386. | 1.05552 | ||||||||
\(222\) | −257731. | −0.350981 | ||||||||
\(223\) | 1.17395e6 | 1.58084 | 0.790420 | − | 0.612565i | \(-0.209862\pi\) | ||||
0.790420 | + | 0.612565i | \(0.209862\pi\) | |||||||
\(224\) | −919319. | −1.22418 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −452998. | −0.589964 | ||||||||
\(227\) | 465701. | 0.599850 | 0.299925 | − | 0.953963i | \(-0.403038\pi\) | ||||
0.299925 | + | 0.953963i | \(0.403038\pi\) | |||||||
\(228\) | −142043. | −0.180960 | ||||||||
\(229\) | −1.01256e6 | −1.27595 | −0.637973 | − | 0.770059i | \(-0.720227\pi\) | ||||
−0.637973 | + | 0.770059i | \(0.720227\pi\) | |||||||
\(230\) | 99819.2 | 0.124421 | ||||||||
\(231\) | −220116. | −0.271407 | ||||||||
\(232\) | 353249. | 0.430885 | ||||||||
\(233\) | 1.02468e6 | 1.23651 | 0.618255 | − | 0.785977i | \(-0.287840\pi\) | ||||
0.618255 | + | 0.785977i | \(0.287840\pi\) | |||||||
\(234\) | 220731. | 0.263526 | ||||||||
\(235\) | 237027. | 0.279980 | ||||||||
\(236\) | −315374. | −0.368592 | ||||||||
\(237\) | 471588. | 0.545371 | ||||||||
\(238\) | 1.04143e6 | 1.19176 | ||||||||
\(239\) | 776375. | 0.879178 | 0.439589 | − | 0.898199i | \(-0.355124\pi\) | ||||
0.439589 | + | 0.898199i | \(0.355124\pi\) | |||||||
\(240\) | 89804.9 | 0.100640 | ||||||||
\(241\) | 919762. | 1.02008 | 0.510038 | − | 0.860152i | \(-0.329631\pi\) | ||||
0.510038 | + | 0.860152i | \(0.329631\pi\) | |||||||
\(242\) | −62667.2 | −0.0687863 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 44128.9 | 0.0474514 | ||||||||
\(245\) | −601204. | −0.639892 | ||||||||
\(246\) | −523807. | −0.551866 | ||||||||
\(247\) | −734546. | −0.766084 | ||||||||
\(248\) | 845890. | 0.873342 | ||||||||
\(249\) | −83338.4 | −0.0851818 | ||||||||
\(250\) | 66879.0 | 0.0676768 | ||||||||
\(251\) | −293678. | −0.294230 | −0.147115 | − | 0.989119i | \(-0.546999\pi\) | ||||
−0.147115 | + | 0.989119i | \(0.546999\pi\) | |||||||
\(252\) | −223963. | −0.222164 | ||||||||
\(253\) | −112873. | −0.110864 | ||||||||
\(254\) | 1.02896e6 | 1.00072 | ||||||||
\(255\) | 270845. | 0.260838 | ||||||||
\(256\) | −1.06399e6 | −1.01470 | ||||||||
\(257\) | 469223. | 0.443145 | 0.221573 | − | 0.975144i | \(-0.428881\pi\) | ||||
0.221573 | + | 0.975144i | \(0.428881\pi\) | |||||||
\(258\) | −211750. | −0.198049 | ||||||||
\(259\) | 1.35231e6 | 1.25265 | ||||||||
\(260\) | −217729. | −0.199748 | ||||||||
\(261\) | 146344. | 0.132977 | ||||||||
\(262\) | 752059. | 0.676859 | ||||||||
\(263\) | −1.22481e6 | −1.09189 | −0.545947 | − | 0.837820i | \(-0.683830\pi\) | ||||
−0.545947 | + | 0.837820i | \(0.683830\pi\) | |||||||
\(264\) | −212921. | −0.188022 | ||||||||
\(265\) | −700046. | −0.612367 | ||||||||
\(266\) | −998168. | −0.864967 | ||||||||
\(267\) | −295259. | −0.253469 | ||||||||
\(268\) | −778210. | −0.661851 | ||||||||
\(269\) | 1.49623e6 | 1.26072 | 0.630358 | − | 0.776305i | \(-0.282908\pi\) | ||||
0.630358 | + | 0.776305i | \(0.282908\pi\) | |||||||
\(270\) | 78007.7 | 0.0651220 | ||||||||
\(271\) | −1.18393e6 | −0.979269 | −0.489634 | − | 0.871928i | \(-0.662870\pi\) | ||||
−0.489634 | + | 0.871928i | \(0.662870\pi\) | |||||||
\(272\) | 480459. | 0.393762 | ||||||||
\(273\) | −1.15818e6 | −0.940520 | ||||||||
\(274\) | 957749. | 0.770682 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | −114846. | −0.0907490 | ||||||||
\(277\) | −234080. | −0.183301 | −0.0916505 | − | 0.995791i | \(-0.529214\pi\) | ||||
−0.0916505 | + | 0.995791i | \(0.529214\pi\) | |||||||
\(278\) | −768417. | −0.596328 | ||||||||
\(279\) | 350436. | 0.269524 | ||||||||
\(280\) | −987993. | −0.753110 | ||||||||
\(281\) | −868631. | −0.656250 | −0.328125 | − | 0.944634i | \(-0.606417\pi\) | ||||
−0.328125 | + | 0.944634i | \(0.606417\pi\) | |||||||
\(282\) | 365232. | 0.273493 | ||||||||
\(283\) | 2.15404e6 | 1.59877 | 0.799387 | − | 0.600816i | \(-0.205158\pi\) | ||||
0.799387 | + | 0.600816i | \(0.205158\pi\) | |||||||
\(284\) | 843828. | 0.620809 | ||||||||
\(285\) | −259593. | −0.189313 | ||||||||
\(286\) | −329734. | −0.238368 | ||||||||
\(287\) | 2.74842e6 | 1.96960 | ||||||||
\(288\) | −368407. | −0.261726 | ||||||||
\(289\) | 29173.0 | 0.0205464 | ||||||||
\(290\) | 193331. | 0.134991 | ||||||||
\(291\) | 276375. | 0.191323 | ||||||||
\(292\) | −445676. | −0.305888 | ||||||||
\(293\) | −660182. | −0.449257 | −0.224628 | − | 0.974445i | \(-0.572117\pi\) | ||||
−0.224628 | + | 0.974445i | \(0.572117\pi\) | |||||||
\(294\) | −926390. | −0.625066 | ||||||||
\(295\) | −576367. | −0.385606 | ||||||||
\(296\) | 1.30811e6 | 0.867791 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −2.03433e6 | −1.32703 | ||||||||
\(299\) | −593900. | −0.384180 | ||||||||
\(300\) | −76946.7 | −0.0493613 | ||||||||
\(301\) | 1.11105e6 | 0.706835 | ||||||||
\(302\) | −1.12929e6 | −0.712507 | ||||||||
\(303\) | −987627. | −0.617997 | ||||||||
\(304\) | −460498. | −0.285788 | ||||||||
\(305\) | 80648.5 | 0.0496417 | ||||||||
\(306\) | 417343. | 0.254794 | ||||||||
\(307\) | 2.74311e6 | 1.66111 | 0.830554 | − | 0.556938i | \(-0.188024\pi\) | ||||
0.830554 | + | 0.556938i | \(0.188024\pi\) | |||||||
\(308\) | 334562. | 0.200955 | ||||||||
\(309\) | 1.73675e6 | 1.03476 | ||||||||
\(310\) | 462949. | 0.273608 | ||||||||
\(311\) | −1.34303e6 | −0.787381 | −0.393690 | − | 0.919243i | \(-0.628802\pi\) | ||||
−0.393690 | + | 0.919243i | \(0.628802\pi\) | |||||||
\(312\) | −1.12032e6 | −0.651561 | ||||||||
\(313\) | −3.41274e6 | −1.96898 | −0.984492 | − | 0.175430i | \(-0.943868\pi\) | ||||
−0.984492 | + | 0.175430i | \(0.943868\pi\) | |||||||
\(314\) | 432114. | 0.247329 | ||||||||
\(315\) | −409306. | −0.232419 | ||||||||
\(316\) | −716783. | −0.403804 | ||||||||
\(317\) | 1.74045e6 | 0.972775 | 0.486387 | − | 0.873743i | \(-0.338314\pi\) | ||||
0.486387 | + | 0.873743i | \(0.338314\pi\) | |||||||
\(318\) | −1.07870e6 | −0.598179 | ||||||||
\(319\) | −218613. | −0.120282 | ||||||||
\(320\) | −805997. | −0.440006 | ||||||||
\(321\) | −1.30550e6 | −0.707153 | ||||||||
\(322\) | −807045. | −0.433769 | ||||||||
\(323\) | −1.38883e6 | −0.740701 | ||||||||
\(324\) | −89750.6 | −0.0474979 | ||||||||
\(325\) | −397913. | −0.208968 | ||||||||
\(326\) | 2.39739e6 | 1.24938 | ||||||||
\(327\) | 1.99472e6 | 1.03160 | ||||||||
\(328\) | 2.65858e6 | 1.36447 | ||||||||
\(329\) | −1.91637e6 | −0.976092 | ||||||||
\(330\) | −116530. | −0.0589051 | ||||||||
\(331\) | 1.12360e6 | 0.563693 | 0.281847 | − | 0.959459i | \(-0.409053\pi\) | ||||
0.281847 | + | 0.959459i | \(0.409053\pi\) | |||||||
\(332\) | 126669. | 0.0630703 | ||||||||
\(333\) | 541925. | 0.267811 | ||||||||
\(334\) | −1.89474e6 | −0.929361 | ||||||||
\(335\) | −1.42223e6 | −0.692401 | ||||||||
\(336\) | −726078. | −0.350861 | ||||||||
\(337\) | −2.21997e6 | −1.06481 | −0.532406 | − | 0.846489i | \(-0.678712\pi\) | ||||
−0.532406 | + | 0.846489i | \(0.678712\pi\) | |||||||
\(338\) | −145721. | −0.0693794 | ||||||||
\(339\) | 952509. | 0.450163 | ||||||||
\(340\) | −411667. | −0.193130 | ||||||||
\(341\) | −523490. | −0.243794 | ||||||||
\(342\) | −400005. | −0.184927 | ||||||||
\(343\) | 1.46363e6 | 0.671732 | ||||||||
\(344\) | 1.07473e6 | 0.489671 | ||||||||
\(345\) | −209888. | −0.0949378 | ||||||||
\(346\) | −1.47890e6 | −0.664122 | ||||||||
\(347\) | −1.63788e6 | −0.730228 | −0.365114 | − | 0.930963i | \(-0.618970\pi\) | ||||
−0.365114 | + | 0.930963i | \(0.618970\pi\) | |||||||
\(348\) | −222434. | −0.0984584 | ||||||||
\(349\) | 2.02682e6 | 0.890742 | 0.445371 | − | 0.895346i | \(-0.353072\pi\) | ||||
0.445371 | + | 0.895346i | \(0.353072\pi\) | |||||||
\(350\) | −540721. | −0.235941 | ||||||||
\(351\) | −464126. | −0.201080 | ||||||||
\(352\) | 550337. | 0.236740 | ||||||||
\(353\) | −1.06927e6 | −0.456719 | −0.228359 | − | 0.973577i | \(-0.573336\pi\) | ||||
−0.228359 | + | 0.973577i | \(0.573336\pi\) | |||||||
\(354\) | −888119. | −0.376672 | ||||||||
\(355\) | 1.54215e6 | 0.649465 | ||||||||
\(356\) | 448774. | 0.187673 | ||||||||
\(357\) | −2.18980e6 | −0.909356 | ||||||||
\(358\) | 1.38333e6 | 0.570451 | ||||||||
\(359\) | −2.61188e6 | −1.06959 | −0.534794 | − | 0.844982i | \(-0.679611\pi\) | ||||
−0.534794 | + | 0.844982i | \(0.679611\pi\) | |||||||
\(360\) | −395927. | −0.161012 | ||||||||
\(361\) | −1.14497e6 | −0.462408 | ||||||||
\(362\) | 315239. | 0.126435 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 1.76035e6 | 0.696379 | ||||||||
\(365\) | −814501. | −0.320007 | ||||||||
\(366\) | 124271. | 0.0484915 | ||||||||
\(367\) | −2.28492e6 | −0.885535 | −0.442767 | − | 0.896636i | \(-0.646003\pi\) | ||||
−0.442767 | + | 0.896636i | \(0.646003\pi\) | |||||||
\(368\) | −372325. | −0.143319 | ||||||||
\(369\) | 1.10140e6 | 0.421093 | ||||||||
\(370\) | 715919. | 0.271869 | ||||||||
\(371\) | 5.65992e6 | 2.13489 | ||||||||
\(372\) | −532639. | −0.199561 | ||||||||
\(373\) | −3.45093e6 | −1.28429 | −0.642146 | − | 0.766582i | \(-0.721956\pi\) | ||||
−0.642146 | + | 0.766582i | \(0.721956\pi\) | |||||||
\(374\) | −623439. | −0.230470 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | −1.85373e6 | −0.676204 | ||||||||
\(377\) | −1.15027e6 | −0.416818 | ||||||||
\(378\) | −630697. | −0.227034 | ||||||||
\(379\) | −1.42060e6 | −0.508011 | −0.254005 | − | 0.967203i | \(-0.581748\pi\) | ||||
−0.254005 | + | 0.967203i | \(0.581748\pi\) | |||||||
\(380\) | 394564. | 0.140171 | ||||||||
\(381\) | −2.16357e6 | −0.763587 | ||||||||
\(382\) | 4.25162e6 | 1.49072 | ||||||||
\(383\) | 1.71667e6 | 0.597985 | 0.298993 | − | 0.954255i | \(-0.403349\pi\) | ||||
0.298993 | + | 0.954255i | \(0.403349\pi\) | |||||||
\(384\) | 67938.2 | 0.0235118 | ||||||||
\(385\) | 611433. | 0.210231 | ||||||||
\(386\) | 581323. | 0.198586 | ||||||||
\(387\) | 445242. | 0.151119 | ||||||||
\(388\) | −420072. | −0.141659 | ||||||||
\(389\) | −3.68417e6 | −1.23443 | −0.617214 | − | 0.786795i | \(-0.711739\pi\) | ||||
−0.617214 | + | 0.786795i | \(0.711739\pi\) | |||||||
\(390\) | −613142. | −0.204126 | ||||||||
\(391\) | −1.12291e6 | −0.371451 | ||||||||
\(392\) | 4.70188e6 | 1.54546 | ||||||||
\(393\) | −1.58134e6 | −0.516468 | ||||||||
\(394\) | −1.01232e6 | −0.328533 | ||||||||
\(395\) | −1.30997e6 | −0.422443 | ||||||||
\(396\) | 134072. | 0.0429635 | ||||||||
\(397\) | −1.65933e6 | −0.528392 | −0.264196 | − | 0.964469i | \(-0.585107\pi\) | ||||
−0.264196 | + | 0.964469i | \(0.585107\pi\) | |||||||
\(398\) | 2.72142e6 | 0.861167 | ||||||||
\(399\) | 2.09883e6 | 0.660000 | ||||||||
\(400\) | −249458. | −0.0779556 | ||||||||
\(401\) | 3.70365e6 | 1.15019 | 0.575093 | − | 0.818088i | \(-0.304966\pi\) | ||||
0.575093 | + | 0.818088i | \(0.304966\pi\) | |||||||
\(402\) | −2.19150e6 | −0.676358 | ||||||||
\(403\) | −2.75443e6 | −0.844830 | ||||||||
\(404\) | 1.50113e6 | 0.457577 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | −1.56309e6 | −0.470619 | ||||||||
\(407\) | −809543. | −0.242244 | ||||||||
\(408\) | −2.11822e6 | −0.629972 | ||||||||
\(409\) | 312275. | 0.0923057 | 0.0461529 | − | 0.998934i | \(-0.485304\pi\) | ||||
0.0461529 | + | 0.998934i | \(0.485304\pi\) | |||||||
\(410\) | 1.45502e6 | 0.427473 | ||||||||
\(411\) | −2.01384e6 | −0.588058 | ||||||||
\(412\) | −2.63974e6 | −0.766158 | ||||||||
\(413\) | 4.65996e6 | 1.34433 | ||||||||
\(414\) | −323414. | −0.0927382 | ||||||||
\(415\) | 231496. | 0.0659816 | ||||||||
\(416\) | 2.89569e6 | 0.820386 | ||||||||
\(417\) | 1.61573e6 | 0.455019 | ||||||||
\(418\) | 597538. | 0.167273 | ||||||||
\(419\) | 4.46928e6 | 1.24366 | 0.621831 | − | 0.783152i | \(-0.286389\pi\) | ||||
0.621831 | + | 0.783152i | \(0.286389\pi\) | |||||||
\(420\) | 622119. | 0.172088 | ||||||||
\(421\) | 1.60241e6 | 0.440624 | 0.220312 | − | 0.975429i | \(-0.429293\pi\) | ||||
0.220312 | + | 0.975429i | \(0.429293\pi\) | |||||||
\(422\) | 3.22706e6 | 0.882116 | ||||||||
\(423\) | −767966. | −0.208685 | ||||||||
\(424\) | 5.47491e6 | 1.47898 | ||||||||
\(425\) | −752348. | −0.202044 | ||||||||
\(426\) | 2.37629e6 | 0.634417 | ||||||||
\(427\) | −652048. | −0.173065 | ||||||||
\(428\) | 1.98427e6 | 0.523590 | ||||||||
\(429\) | 693324. | 0.181883 | ||||||||
\(430\) | 588194. | 0.153408 | ||||||||
\(431\) | −4.62483e6 | −1.19923 | −0.599615 | − | 0.800289i | \(-0.704680\pi\) | ||||
−0.599615 | + | 0.800289i | \(0.704680\pi\) | |||||||
\(432\) | −290968. | −0.0750128 | ||||||||
\(433\) | −10306.9 | −0.00264184 | −0.00132092 | − | 0.999999i | \(-0.500420\pi\) | ||||
−0.00132092 | + | 0.999999i | \(0.500420\pi\) | |||||||
\(434\) | −3.74297e6 | −0.953877 | ||||||||
\(435\) | −406512. | −0.103003 | ||||||||
\(436\) | −3.03185e6 | −0.763820 | ||||||||
\(437\) | 1.07625e6 | 0.269595 | ||||||||
\(438\) | −1.25506e6 | −0.312593 | ||||||||
\(439\) | −5.72201e6 | −1.41706 | −0.708529 | − | 0.705682i | \(-0.750641\pi\) | ||||
−0.708529 | + | 0.705682i | \(0.750641\pi\) | |||||||
\(440\) | 591447. | 0.145641 | ||||||||
\(441\) | 1.94790e6 | 0.476947 | ||||||||
\(442\) | −3.28033e6 | −0.798659 | ||||||||
\(443\) | 6.24922e6 | 1.51292 | 0.756460 | − | 0.654040i | \(-0.226927\pi\) | ||||
0.756460 | + | 0.654040i | \(0.226927\pi\) | |||||||
\(444\) | −823691. | −0.198293 | ||||||||
\(445\) | 820164. | 0.196336 | ||||||||
\(446\) | −5.02481e6 | −1.19614 | ||||||||
\(447\) | 4.27755e6 | 1.01257 | ||||||||
\(448\) | 6.51653e6 | 1.53399 | ||||||||
\(449\) | −2.01905e6 | −0.472641 | −0.236321 | − | 0.971675i | \(-0.575942\pi\) | ||||
−0.236321 | + | 0.971675i | \(0.575942\pi\) | |||||||
\(450\) | −216688. | −0.0504433 | ||||||||
\(451\) | −1.64530e6 | −0.380893 | ||||||||
\(452\) | −1.44775e6 | −0.333310 | ||||||||
\(453\) | 2.37454e6 | 0.543668 | ||||||||
\(454\) | −1.99332e6 | −0.453876 | ||||||||
\(455\) | 3.21716e6 | 0.728524 | ||||||||
\(456\) | 2.03022e6 | 0.457226 | ||||||||
\(457\) | −758581. | −0.169907 | −0.0849536 | − | 0.996385i | \(-0.527074\pi\) | ||||
−0.0849536 | + | 0.996385i | \(0.527074\pi\) | |||||||
\(458\) | 4.33402e6 | 0.965444 | ||||||||
\(459\) | −877539. | −0.194417 | ||||||||
\(460\) | 319016. | 0.0702938 | ||||||||
\(461\) | 5.39608e6 | 1.18257 | 0.591284 | − | 0.806463i | \(-0.298621\pi\) | ||||
0.591284 | + | 0.806463i | \(0.298621\pi\) | |||||||
\(462\) | 942152. | 0.205360 | ||||||||
\(463\) | 227337. | 0.0492852 | 0.0246426 | − | 0.999696i | \(-0.492155\pi\) | ||||
0.0246426 | + | 0.999696i | \(0.492155\pi\) | |||||||
\(464\) | −721122. | −0.155494 | ||||||||
\(465\) | −973433. | −0.208773 | ||||||||
\(466\) | −4.38589e6 | −0.935605 | ||||||||
\(467\) | −1.48953e6 | −0.316051 | −0.158026 | − | 0.987435i | \(-0.550513\pi\) | ||||
−0.158026 | + | 0.987435i | \(0.550513\pi\) | |||||||
\(468\) | 705441. | 0.148883 | ||||||||
\(469\) | 1.14988e7 | 2.41391 | ||||||||
\(470\) | −1.01453e6 | −0.211847 | ||||||||
\(471\) | −908597. | −0.188720 | ||||||||
\(472\) | 4.50764e6 | 0.931310 | ||||||||
\(473\) | −665114. | −0.136692 | ||||||||
\(474\) | −2.01852e6 | −0.412655 | ||||||||
\(475\) | 721092. | 0.146641 | ||||||||
\(476\) | 3.32835e6 | 0.673305 | ||||||||
\(477\) | 2.26815e6 | 0.456432 | ||||||||
\(478\) | −3.32308e6 | −0.665230 | ||||||||
\(479\) | −4.99978e6 | −0.995662 | −0.497831 | − | 0.867274i | \(-0.665870\pi\) | ||||
−0.497831 | + | 0.867274i | \(0.665870\pi\) | |||||||
\(480\) | 1.02335e6 | 0.202732 | ||||||||
\(481\) | −4.25954e6 | −0.839460 | ||||||||
\(482\) | −3.93682e6 | −0.771840 | ||||||||
\(483\) | 1.69696e6 | 0.330981 | ||||||||
\(484\) | −200280. | −0.0388620 | ||||||||
\(485\) | −767708. | −0.148198 | ||||||||
\(486\) | −252745. | −0.0485391 | ||||||||
\(487\) | 1.41748e6 | 0.270828 | 0.135414 | − | 0.990789i | \(-0.456763\pi\) | ||||
0.135414 | + | 0.990789i | \(0.456763\pi\) | |||||||
\(488\) | −630734. | −0.119894 | ||||||||
\(489\) | −5.04094e6 | −0.953322 | ||||||||
\(490\) | 2.57331e6 | 0.484174 | ||||||||
\(491\) | 3.78615e6 | 0.708751 | 0.354376 | − | 0.935103i | \(-0.384693\pi\) | ||||
0.354376 | + | 0.935103i | \(0.384693\pi\) | |||||||
\(492\) | −1.67405e6 | −0.311786 | ||||||||
\(493\) | −2.17485e6 | −0.403007 | ||||||||
\(494\) | 3.14405e6 | 0.579657 | ||||||||
\(495\) | 245025. | 0.0449467 | ||||||||
\(496\) | −1.72679e6 | −0.315164 | ||||||||
\(497\) | −1.24684e7 | −2.26422 | ||||||||
\(498\) | 356710. | 0.0644528 | ||||||||
\(499\) | 2.47452e6 | 0.444877 | 0.222439 | − | 0.974947i | \(-0.428598\pi\) | ||||
0.222439 | + | 0.974947i | \(0.428598\pi\) | |||||||
\(500\) | 213741. | 0.0382351 | ||||||||
\(501\) | 3.98404e6 | 0.709135 | ||||||||
\(502\) | 1.25702e6 | 0.222629 | ||||||||
\(503\) | 7.81639e6 | 1.37748 | 0.688742 | − | 0.725007i | \(-0.258163\pi\) | ||||
0.688742 | + | 0.725007i | \(0.258163\pi\) | |||||||
\(504\) | 3.20110e6 | 0.561335 | ||||||||
\(505\) | 2.74341e6 | 0.478698 | ||||||||
\(506\) | 483125. | 0.0838848 | ||||||||
\(507\) | 306404. | 0.0529389 | ||||||||
\(508\) | 3.28848e6 | 0.565375 | ||||||||
\(509\) | 1.95144e6 | 0.333856 | 0.166928 | − | 0.985969i | \(-0.446615\pi\) | ||||
0.166928 | + | 0.985969i | \(0.446615\pi\) | |||||||
\(510\) | −1.15929e6 | −0.197363 | ||||||||
\(511\) | 6.58529e6 | 1.11564 | ||||||||
\(512\) | 4.31257e6 | 0.727046 | ||||||||
\(513\) | 841081. | 0.141106 | ||||||||
\(514\) | −2.00839e6 | −0.335306 | ||||||||
\(515\) | −4.82430e6 | −0.801523 | ||||||||
\(516\) | −676738. | −0.111891 | ||||||||
\(517\) | 1.14721e6 | 0.188763 | ||||||||
\(518\) | −5.78825e6 | −0.947814 | ||||||||
\(519\) | 3.10965e6 | 0.506749 | ||||||||
\(520\) | 3.11199e6 | 0.504697 | ||||||||
\(521\) | 1.11720e6 | 0.180317 | 0.0901587 | − | 0.995927i | \(-0.471263\pi\) | ||||
0.0901587 | + | 0.995927i | \(0.471263\pi\) | |||||||
\(522\) | −626392. | −0.100617 | ||||||||
\(523\) | 1.20699e7 | 1.92952 | 0.964760 | − | 0.263130i | \(-0.0847548\pi\) | ||||
0.964760 | + | 0.263130i | \(0.0847548\pi\) | |||||||
\(524\) | 2.40353e6 | 0.382403 | ||||||||
\(525\) | 1.13696e6 | 0.180031 | ||||||||
\(526\) | 5.24252e6 | 0.826181 | ||||||||
\(527\) | −5.20789e6 | −0.816837 | ||||||||
\(528\) | 434656. | 0.0678516 | ||||||||
\(529\) | −5.56616e6 | −0.864802 | ||||||||
\(530\) | 2.99638e6 | 0.463348 | ||||||||
\(531\) | 1.86743e6 | 0.287414 | ||||||||
\(532\) | −3.19008e6 | −0.488677 | ||||||||
\(533\) | −8.65700e6 | −1.31993 | ||||||||
\(534\) | 1.26378e6 | 0.191787 | ||||||||
\(535\) | 3.62638e6 | 0.547758 | ||||||||
\(536\) | 1.11229e7 | 1.67228 | ||||||||
\(537\) | −2.90870e6 | −0.435274 | ||||||||
\(538\) | −6.40424e6 | −0.953920 | ||||||||
\(539\) | −2.90983e6 | −0.431415 | ||||||||
\(540\) | 249307. | 0.0367918 | ||||||||
\(541\) | −1.24911e7 | −1.83488 | −0.917439 | − | 0.397876i | \(-0.869747\pi\) | ||||
−0.917439 | + | 0.397876i | \(0.869747\pi\) | |||||||
\(542\) | 5.06751e6 | 0.740963 | ||||||||
\(543\) | −662846. | −0.0964746 | ||||||||
\(544\) | 5.47497e6 | 0.793203 | ||||||||
\(545\) | −5.54090e6 | −0.799077 | ||||||||
\(546\) | 4.95729e6 | 0.711644 | ||||||||
\(547\) | −6.59022e6 | −0.941742 | −0.470871 | − | 0.882202i | \(-0.656060\pi\) | ||||
−0.470871 | + | 0.882202i | \(0.656060\pi\) | |||||||
\(548\) | 3.06090e6 | 0.435409 | ||||||||
\(549\) | −261301. | −0.0370007 | ||||||||
\(550\) | 323694. | 0.0456277 | ||||||||
\(551\) | 2.08450e6 | 0.292498 | ||||||||
\(552\) | 1.64149e6 | 0.229292 | ||||||||
\(553\) | 1.05912e7 | 1.47276 | ||||||||
\(554\) | 1.00192e6 | 0.138695 | ||||||||
\(555\) | −1.50535e6 | −0.207446 | ||||||||
\(556\) | −2.45581e6 | −0.336905 | ||||||||
\(557\) | 1.15679e7 | 1.57986 | 0.789928 | − | 0.613200i | \(-0.210118\pi\) | ||||
0.789928 | + | 0.613200i | \(0.210118\pi\) | |||||||
\(558\) | −1.49995e6 | −0.203935 | ||||||||
\(559\) | −3.49961e6 | −0.473685 | ||||||||
\(560\) | 2.01688e6 | 0.271776 | ||||||||
\(561\) | 1.31089e6 | 0.175857 | ||||||||
\(562\) | 3.71796e6 | 0.496552 | ||||||||
\(563\) | −1.11114e7 | −1.47740 | −0.738702 | − | 0.674032i | \(-0.764561\pi\) | ||||
−0.738702 | + | 0.674032i | \(0.764561\pi\) | |||||||
\(564\) | 1.16726e6 | 0.154514 | ||||||||
\(565\) | −2.64586e6 | −0.348695 | ||||||||
\(566\) | −9.21983e6 | −1.20971 | ||||||||
\(567\) | 1.32615e6 | 0.173235 | ||||||||
\(568\) | −1.20608e7 | −1.56858 | ||||||||
\(569\) | −4.82882e6 | −0.625260 | −0.312630 | − | 0.949875i | \(-0.601210\pi\) | ||||
−0.312630 | + | 0.949875i | \(0.601210\pi\) | |||||||
\(570\) | 1.11112e6 | 0.143244 | ||||||||
\(571\) | −9.35367e6 | −1.20058 | −0.600291 | − | 0.799782i | \(-0.704948\pi\) | ||||
−0.600291 | + | 0.799782i | \(0.704948\pi\) | |||||||
\(572\) | −1.05381e6 | −0.134670 | ||||||||
\(573\) | −8.93979e6 | −1.13747 | ||||||||
\(574\) | −1.17639e7 | −1.49030 | ||||||||
\(575\) | 583021. | 0.0735385 | ||||||||
\(576\) | 2.61143e6 | 0.327961 | ||||||||
\(577\) | −4.34302e6 | −0.543065 | −0.271533 | − | 0.962429i | \(-0.587530\pi\) | ||||
−0.271533 | + | 0.962429i | \(0.587530\pi\) | |||||||
\(578\) | −124868. | −0.0155464 | ||||||||
\(579\) | −1.22234e6 | −0.151528 | ||||||||
\(580\) | 617872. | 0.0762656 | ||||||||
\(581\) | −1.87166e6 | −0.230031 | ||||||||
\(582\) | −1.18296e6 | −0.144764 | ||||||||
\(583\) | −3.38822e6 | −0.412858 | ||||||||
\(584\) | 6.37003e6 | 0.772876 | ||||||||
\(585\) | 1.28924e6 | 0.155756 | ||||||||
\(586\) | 2.82575e6 | 0.339930 | ||||||||
\(587\) | −1.04623e7 | −1.25324 | −0.626618 | − | 0.779327i | \(-0.715561\pi\) | ||||
−0.626618 | + | 0.779327i | \(0.715561\pi\) | |||||||
\(588\) | −2.96068e6 | −0.353141 | ||||||||
\(589\) | 4.99153e6 | 0.592851 | ||||||||
\(590\) | 2.46700e6 | 0.291769 | ||||||||
\(591\) | 2.12859e6 | 0.250682 | ||||||||
\(592\) | −2.67037e6 | −0.313161 | ||||||||
\(593\) | −1.34068e7 | −1.56562 | −0.782812 | − | 0.622259i | \(-0.786215\pi\) | ||||
−0.782812 | + | 0.622259i | \(0.786215\pi\) | |||||||
\(594\) | 377557. | 0.0439053 | ||||||||
\(595\) | 6.08278e6 | 0.704384 | ||||||||
\(596\) | −6.50159e6 | −0.749729 | ||||||||
\(597\) | −5.72226e6 | −0.657101 | ||||||||
\(598\) | 2.54204e6 | 0.290690 | ||||||||
\(599\) | −6.14928e6 | −0.700256 | −0.350128 | − | 0.936702i | \(-0.613862\pi\) | ||||
−0.350128 | + | 0.936702i | \(0.613862\pi\) | |||||||
\(600\) | 1.09980e6 | 0.124720 | ||||||||
\(601\) | 1.14948e7 | 1.29812 | 0.649060 | − | 0.760737i | \(-0.275162\pi\) | ||||
0.649060 | + | 0.760737i | \(0.275162\pi\) | |||||||
\(602\) | −4.75558e6 | −0.534826 | ||||||||
\(603\) | 4.60802e6 | 0.516085 | ||||||||
\(604\) | −3.60914e6 | −0.402543 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | 4.22730e6 | 0.467607 | ||||||||
\(607\) | −1.71751e7 | −1.89202 | −0.946012 | − | 0.324131i | \(-0.894928\pi\) | ||||
−0.946012 | + | 0.324131i | \(0.894928\pi\) | |||||||
\(608\) | −5.24751e6 | −0.575698 | ||||||||
\(609\) | 3.28668e6 | 0.359099 | ||||||||
\(610\) | −345196. | −0.0375614 | ||||||||
\(611\) | 6.03623e6 | 0.654128 | ||||||||
\(612\) | 1.33380e6 | 0.143950 | ||||||||
\(613\) | 4.69632e6 | 0.504785 | 0.252392 | − | 0.967625i | \(-0.418783\pi\) | ||||
0.252392 | + | 0.967625i | \(0.418783\pi\) | |||||||
\(614\) | −1.17412e7 | −1.25688 | ||||||||
\(615\) | −3.05944e6 | −0.326177 | ||||||||
\(616\) | −4.78188e6 | −0.507747 | ||||||||
\(617\) | −3.73984e6 | −0.395494 | −0.197747 | − | 0.980253i | \(-0.563362\pi\) | ||||
−0.197747 | + | 0.980253i | \(0.563362\pi\) | |||||||
\(618\) | −7.43372e6 | −0.782952 | ||||||||
\(619\) | −1.04630e7 | −1.09756 | −0.548780 | − | 0.835967i | \(-0.684907\pi\) | ||||
−0.548780 | + | 0.835967i | \(0.684907\pi\) | |||||||
\(620\) | 1.47955e6 | 0.154579 | ||||||||
\(621\) | 680036. | 0.0707625 | ||||||||
\(622\) | 5.74851e6 | 0.595771 | ||||||||
\(623\) | −6.63108e6 | −0.684485 | ||||||||
\(624\) | 2.28701e6 | 0.235129 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.46074e7 | 1.48983 | ||||||||
\(627\) | −1.25643e6 | −0.127635 | ||||||||
\(628\) | 1.38101e6 | 0.139732 | ||||||||
\(629\) | −8.05365e6 | −0.811646 | ||||||||
\(630\) | 1.75194e6 | 0.175860 | ||||||||
\(631\) | 5.70827e6 | 0.570731 | 0.285365 | − | 0.958419i | \(-0.407885\pi\) | ||||
0.285365 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(632\) | 1.02450e7 | 1.02028 | ||||||||
\(633\) | −6.78546e6 | −0.673085 | ||||||||
\(634\) | −7.44955e6 | −0.736050 | ||||||||
\(635\) | 6.00991e6 | 0.591472 | ||||||||
\(636\) | −3.44744e6 | −0.337951 | ||||||||
\(637\) | −1.53105e7 | −1.49500 | ||||||||
\(638\) | 935721. | 0.0910112 | ||||||||
\(639\) | −4.99657e6 | −0.484083 | ||||||||
\(640\) | −188717. | −0.0182122 | ||||||||
\(641\) | −1.24666e7 | −1.19841 | −0.599204 | − | 0.800597i | \(-0.704516\pi\) | ||||
−0.599204 | + | 0.800597i | \(0.704516\pi\) | |||||||
\(642\) | 5.58786e6 | 0.535067 | ||||||||
\(643\) | 1.70621e7 | 1.62744 | 0.813719 | − | 0.581258i | \(-0.197439\pi\) | ||||
0.813719 | + | 0.581258i | \(0.197439\pi\) | |||||||
\(644\) | −2.57926e6 | −0.245065 | ||||||||
\(645\) | −1.23678e6 | −0.117056 | ||||||||
\(646\) | 5.94455e6 | 0.560451 | ||||||||
\(647\) | 1.30654e7 | 1.22705 | 0.613524 | − | 0.789676i | \(-0.289752\pi\) | ||||
0.613524 | + | 0.789676i | \(0.289752\pi\) | |||||||
\(648\) | 1.28280e6 | 0.120011 | ||||||||
\(649\) | −2.78962e6 | −0.259976 | ||||||||
\(650\) | 1.70317e6 | 0.158116 | ||||||||
\(651\) | 7.87027e6 | 0.727842 | ||||||||
\(652\) | 7.66190e6 | 0.705859 | ||||||||
\(653\) | −5.62419e6 | −0.516151 | −0.258076 | − | 0.966125i | \(-0.583088\pi\) | ||||
−0.258076 | + | 0.966125i | \(0.583088\pi\) | |||||||
\(654\) | −8.53792e6 | −0.780563 | ||||||||
\(655\) | 4.39260e6 | 0.400054 | ||||||||
\(656\) | −5.42721e6 | −0.492398 | ||||||||
\(657\) | 2.63898e6 | 0.238519 | ||||||||
\(658\) | 8.20257e6 | 0.738559 | ||||||||
\(659\) | 4.40853e6 | 0.395440 | 0.197720 | − | 0.980259i | \(-0.436646\pi\) | ||||
0.197720 | + | 0.980259i | \(0.436646\pi\) | |||||||
\(660\) | −372422. | −0.0332794 | ||||||||
\(661\) | −8.03899e6 | −0.715645 | −0.357822 | − | 0.933790i | \(-0.616481\pi\) | ||||
−0.357822 | + | 0.933790i | \(0.616481\pi\) | |||||||
\(662\) | −4.80931e6 | −0.426518 | ||||||||
\(663\) | 6.89747e6 | 0.609405 | ||||||||
\(664\) | −1.81048e6 | −0.159358 | ||||||||
\(665\) | −5.83007e6 | −0.511234 | ||||||||
\(666\) | −2.31958e6 | −0.202639 | ||||||||
\(667\) | 1.68537e6 | 0.146683 | ||||||||
\(668\) | −6.05547e6 | −0.525058 | ||||||||
\(669\) | 1.05656e7 | 0.912698 | ||||||||
\(670\) | 6.08751e6 | 0.523905 | ||||||||
\(671\) | 390339. | 0.0334684 | ||||||||
\(672\) | −8.27387e6 | −0.706782 | ||||||||
\(673\) | 1.79122e7 | 1.52445 | 0.762223 | − | 0.647314i | \(-0.224108\pi\) | ||||
0.762223 | + | 0.647314i | \(0.224108\pi\) | |||||||
\(674\) | 9.50205e6 | 0.805689 | ||||||||
\(675\) | 455625. | 0.0384900 | ||||||||
\(676\) | −465714. | −0.0391970 | ||||||||
\(677\) | −7.96540e6 | −0.667937 | −0.333969 | − | 0.942584i | \(-0.608388\pi\) | ||||
−0.333969 | + | 0.942584i | \(0.608388\pi\) | |||||||
\(678\) | −4.07698e6 | −0.340616 | ||||||||
\(679\) | 6.20697e6 | 0.516660 | ||||||||
\(680\) | 5.88395e6 | 0.487974 | ||||||||
\(681\) | 4.19131e6 | 0.346323 | ||||||||
\(682\) | 2.24067e6 | 0.184467 | ||||||||
\(683\) | 1.72633e7 | 1.41602 | 0.708012 | − | 0.706200i | \(-0.249592\pi\) | ||||
0.708012 | + | 0.706200i | \(0.249592\pi\) | |||||||
\(684\) | −1.27839e6 | −0.104477 | ||||||||
\(685\) | 5.59399e6 | 0.455507 | ||||||||
\(686\) | −6.26471e6 | −0.508266 | ||||||||
\(687\) | −9.11305e6 | −0.736668 | ||||||||
\(688\) | −2.19396e6 | −0.176708 | ||||||||
\(689\) | −1.78277e7 | −1.43070 | ||||||||
\(690\) | 898373. | 0.0718347 | ||||||||
\(691\) | −6.08747e6 | −0.485000 | −0.242500 | − | 0.970151i | \(-0.577967\pi\) | ||||
−0.242500 | + | 0.970151i | \(0.577967\pi\) | |||||||
\(692\) | −4.72646e6 | −0.375207 | ||||||||
\(693\) | −1.98104e6 | −0.156697 | ||||||||
\(694\) | 7.01054e6 | 0.552526 | ||||||||
\(695\) | −4.48815e6 | −0.352456 | ||||||||
\(696\) | 3.17924e6 | 0.248772 | ||||||||
\(697\) | −1.63681e7 | −1.27619 | ||||||||
\(698\) | −8.67532e6 | −0.673980 | ||||||||
\(699\) | 9.22211e6 | 0.713900 | ||||||||
\(700\) | −1.72811e6 | −0.133299 | ||||||||
\(701\) | −6.99341e6 | −0.537519 | −0.268760 | − | 0.963207i | \(-0.586614\pi\) | ||||
−0.268760 | + | 0.963207i | \(0.586614\pi\) | |||||||
\(702\) | 1.98658e6 | 0.152147 | ||||||||
\(703\) | 7.71907e6 | 0.589083 | ||||||||
\(704\) | −3.90102e6 | −0.296652 | ||||||||
\(705\) | 2.13324e6 | 0.161647 | ||||||||
\(706\) | 4.57673e6 | 0.345576 | ||||||||
\(707\) | −2.21806e7 | −1.66888 | ||||||||
\(708\) | −2.83837e6 | −0.212807 | ||||||||
\(709\) | −2.18416e7 | −1.63181 | −0.815905 | − | 0.578186i | \(-0.803761\pi\) | ||||
−0.815905 | + | 0.578186i | \(0.803761\pi\) | |||||||
\(710\) | −6.60080e6 | −0.491417 | ||||||||
\(711\) | 4.24430e6 | 0.314870 | ||||||||
\(712\) | −6.41432e6 | −0.474188 | ||||||||
\(713\) | 4.03578e6 | 0.297306 | ||||||||
\(714\) | 9.37291e6 | 0.688064 | ||||||||
\(715\) | −1.92590e6 | −0.140886 | ||||||||
\(716\) | 4.42103e6 | 0.322286 | ||||||||
\(717\) | 6.98738e6 | 0.507594 | ||||||||
\(718\) | 1.11795e7 | 0.809304 | ||||||||
\(719\) | 1.36972e7 | 0.988118 | 0.494059 | − | 0.869428i | \(-0.335513\pi\) | ||||
0.494059 | + | 0.869428i | \(0.335513\pi\) | |||||||
\(720\) | 808244. | 0.0581047 | ||||||||
\(721\) | 3.90047e7 | 2.79434 | ||||||||
\(722\) | 4.90076e6 | 0.349881 | ||||||||
\(723\) | 8.27786e6 | 0.588941 | ||||||||
\(724\) | 1.00748e6 | 0.0714317 | ||||||||
\(725\) | 1.12920e6 | 0.0797859 | ||||||||
\(726\) | −564005. | −0.0397138 | ||||||||
\(727\) | 2.14780e7 | 1.50715 | 0.753577 | − | 0.657359i | \(-0.228327\pi\) | ||||
0.753577 | + | 0.657359i | \(0.228327\pi\) | |||||||
\(728\) | −2.51607e7 | −1.75952 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 3.48627e6 | 0.242133 | ||||||||
\(731\) | −6.61682e6 | −0.457990 | ||||||||
\(732\) | 397161. | 0.0273961 | ||||||||
\(733\) | 1.75804e7 | 1.20856 | 0.604282 | − | 0.796771i | \(-0.293460\pi\) | ||||
0.604282 | + | 0.796771i | \(0.293460\pi\) | |||||||
\(734\) | 9.78004e6 | 0.670040 | ||||||||
\(735\) | −5.41083e6 | −0.369442 | ||||||||
\(736\) | −4.24275e6 | −0.288704 | ||||||||
\(737\) | −6.88359e6 | −0.466817 | ||||||||
\(738\) | −4.71426e6 | −0.318620 | ||||||||
\(739\) | 1.04421e7 | 0.703360 | 0.351680 | − | 0.936120i | \(-0.385611\pi\) | ||||
0.351680 | + | 0.936120i | \(0.385611\pi\) | |||||||
\(740\) | 2.28803e6 | 0.153597 | ||||||||
\(741\) | −6.61091e6 | −0.442299 | ||||||||
\(742\) | −2.42259e7 | −1.61536 | ||||||||
\(743\) | 3.35925e6 | 0.223239 | 0.111620 | − | 0.993751i | \(-0.464396\pi\) | ||||
0.111620 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(744\) | 7.61301e6 | 0.504224 | ||||||||
\(745\) | −1.18821e7 | −0.784335 | ||||||||
\(746\) | 1.47709e7 | 0.971760 | ||||||||
\(747\) | −750046. | −0.0491797 | ||||||||
\(748\) | −1.99247e6 | −0.130208 | ||||||||
\(749\) | −2.93195e7 | −1.90964 | ||||||||
\(750\) | 601911. | 0.0390732 | ||||||||
\(751\) | 2.94949e7 | 1.90830 | 0.954152 | − | 0.299322i | \(-0.0967606\pi\) | ||||
0.954152 | + | 0.299322i | \(0.0967606\pi\) | |||||||
\(752\) | 3.78420e6 | 0.244022 | ||||||||
\(753\) | −2.64310e6 | −0.169874 | ||||||||
\(754\) | 4.92345e6 | 0.315385 | ||||||||
\(755\) | −6.59594e6 | −0.421123 | ||||||||
\(756\) | −2.01566e6 | −0.128267 | ||||||||
\(757\) | −1.30403e7 | −0.827083 | −0.413542 | − | 0.910485i | \(-0.635708\pi\) | ||||
−0.413542 | + | 0.910485i | \(0.635708\pi\) | |||||||
\(758\) | 6.08052e6 | 0.384386 | ||||||||
\(759\) | −1.01586e6 | −0.0640071 | ||||||||
\(760\) | −5.63950e6 | −0.354166 | ||||||||
\(761\) | 5.20428e6 | 0.325761 | 0.162880 | − | 0.986646i | \(-0.447922\pi\) | ||||
0.162880 | + | 0.986646i | \(0.447922\pi\) | |||||||
\(762\) | 9.26063e6 | 0.577767 | ||||||||
\(763\) | 4.47985e7 | 2.78581 | ||||||||
\(764\) | 1.35879e7 | 0.842207 | ||||||||
\(765\) | 2.43761e6 | 0.150595 | ||||||||
\(766\) | −7.34780e6 | −0.452465 | ||||||||
\(767\) | −1.46780e7 | −0.900906 | ||||||||
\(768\) | −9.57587e6 | −0.585835 | ||||||||
\(769\) | 2.36072e7 | 1.43956 | 0.719778 | − | 0.694204i | \(-0.244244\pi\) | ||||
0.719778 | + | 0.694204i | \(0.244244\pi\) | |||||||
\(770\) | −2.61709e6 | −0.159071 | ||||||||
\(771\) | 4.22300e6 | 0.255850 | ||||||||
\(772\) | 1.85787e6 | 0.112195 | ||||||||
\(773\) | −1.51766e7 | −0.913536 | −0.456768 | − | 0.889586i | \(-0.650993\pi\) | ||||
−0.456768 | + | 0.889586i | \(0.650993\pi\) | |||||||
\(774\) | −1.90575e6 | −0.114344 | ||||||||
\(775\) | 2.70398e6 | 0.161715 | ||||||||
\(776\) | 6.00408e6 | 0.357925 | ||||||||
\(777\) | 1.21708e7 | 0.723215 | ||||||||
\(778\) | 1.57692e7 | 0.934029 | ||||||||
\(779\) | 1.56881e7 | 0.926245 | ||||||||
\(780\) | −1.95956e6 | −0.115325 | ||||||||
\(781\) | 7.46401e6 | 0.437869 | ||||||||
\(782\) | 4.80632e6 | 0.281058 | ||||||||
\(783\) | 1.31710e6 | 0.0767740 | ||||||||
\(784\) | −9.59841e6 | −0.557711 | ||||||||
\(785\) | 2.52388e6 | 0.146182 | ||||||||
\(786\) | 6.76853e6 | 0.390785 | ||||||||
\(787\) | 1.45626e7 | 0.838110 | 0.419055 | − | 0.907961i | \(-0.362361\pi\) | ||||
0.419055 | + | 0.907961i | \(0.362361\pi\) | |||||||
\(788\) | −3.23532e6 | −0.185610 | ||||||||
\(789\) | −1.10233e7 | −0.630405 | ||||||||
\(790\) | 5.60700e6 | 0.319641 | ||||||||
\(791\) | 2.13919e7 | 1.21565 | ||||||||
\(792\) | −1.91629e6 | −0.108554 | ||||||||
\(793\) | 2.05383e6 | 0.115980 | ||||||||
\(794\) | 7.10235e6 | 0.399807 | ||||||||
\(795\) | −6.30042e6 | −0.353550 | ||||||||
\(796\) | 8.69747e6 | 0.486530 | ||||||||
\(797\) | −924949. | −0.0515789 | −0.0257894 | − | 0.999667i | \(-0.508210\pi\) | ||||
−0.0257894 | + | 0.999667i | \(0.508210\pi\) | |||||||
\(798\) | −8.98351e6 | −0.499389 | ||||||||
\(799\) | 1.14129e7 | 0.632454 | ||||||||
\(800\) | −2.84265e6 | −0.157036 | ||||||||
\(801\) | −2.65733e6 | −0.146340 | ||||||||
\(802\) | −1.58525e7 | −0.870288 | ||||||||
\(803\) | −3.94218e6 | −0.215749 | ||||||||
\(804\) | −7.00389e6 | −0.382120 | ||||||||
\(805\) | −4.71377e6 | −0.256377 | ||||||||
\(806\) | 1.17897e7 | 0.639240 | ||||||||
\(807\) | 1.34661e7 | 0.727875 | ||||||||
\(808\) | −2.14556e7 | −1.15614 | ||||||||
\(809\) | 1.15962e7 | 0.622938 | 0.311469 | − | 0.950256i | \(-0.399179\pi\) | ||||
0.311469 | + | 0.950256i | \(0.399179\pi\) | |||||||
\(810\) | 702069. | 0.0375982 | ||||||||
\(811\) | −1.69320e7 | −0.903974 | −0.451987 | − | 0.892025i | \(-0.649285\pi\) | ||||
−0.451987 | + | 0.892025i | \(0.649285\pi\) | |||||||
\(812\) | −4.99553e6 | −0.265884 | ||||||||
\(813\) | −1.06553e7 | −0.565381 | ||||||||
\(814\) | 3.46505e6 | 0.183294 | ||||||||
\(815\) | 1.40026e7 | 0.738440 | ||||||||
\(816\) | 4.32413e6 | 0.227339 | ||||||||
\(817\) | 6.34192e6 | 0.332404 | ||||||||
\(818\) | −1.33662e6 | −0.0698431 | ||||||||
\(819\) | −1.04236e7 | −0.543009 | ||||||||
\(820\) | 4.65014e6 | 0.241508 | ||||||||
\(821\) | 2.60647e7 | 1.34957 | 0.674783 | − | 0.738016i | \(-0.264237\pi\) | ||||
0.674783 | + | 0.738016i | \(0.264237\pi\) | |||||||
\(822\) | 8.61974e6 | 0.444954 | ||||||||
\(823\) | 1.20408e6 | 0.0619663 | 0.0309831 | − | 0.999520i | \(-0.490136\pi\) | ||||
0.0309831 | + | 0.999520i | \(0.490136\pi\) | |||||||
\(824\) | 3.77298e7 | 1.93583 | ||||||||
\(825\) | −680625. | −0.0348155 | ||||||||
\(826\) | −1.99458e7 | −1.01719 | ||||||||
\(827\) | 3.53147e7 | 1.79553 | 0.897764 | − | 0.440478i | \(-0.145191\pi\) | ||||
0.897764 | + | 0.440478i | \(0.145191\pi\) | |||||||
\(828\) | −1.03361e6 | −0.0523939 | ||||||||
\(829\) | −1.35902e7 | −0.686813 | −0.343406 | − | 0.939187i | \(-0.611581\pi\) | ||||
−0.343406 | + | 0.939187i | \(0.611581\pi\) | |||||||
\(830\) | −990861. | −0.0499249 | ||||||||
\(831\) | −2.10672e6 | −0.105829 | ||||||||
\(832\) | −2.05259e7 | −1.02800 | ||||||||
\(833\) | −2.89481e7 | −1.44547 | ||||||||
\(834\) | −6.91576e6 | −0.344290 | ||||||||
\(835\) | −1.10668e7 | −0.549294 | ||||||||
\(836\) | 1.90969e6 | 0.0945034 | ||||||||
\(837\) | 3.15392e6 | 0.155610 | ||||||||
\(838\) | −1.91296e7 | −0.941016 | ||||||||
\(839\) | 1.01361e7 | 0.497125 | 0.248562 | − | 0.968616i | \(-0.420042\pi\) | ||||
0.248562 | + | 0.968616i | \(0.420042\pi\) | |||||||
\(840\) | −8.89193e6 | −0.434808 | ||||||||
\(841\) | −1.72469e7 | −0.840855 | ||||||||
\(842\) | −6.85871e6 | −0.333398 | ||||||||
\(843\) | −7.81768e6 | −0.378886 | ||||||||
\(844\) | 1.03135e7 | 0.498366 | ||||||||
\(845\) | −851123. | −0.0410063 | ||||||||
\(846\) | 3.28709e6 | 0.157901 | ||||||||
\(847\) | 2.95934e6 | 0.141738 | ||||||||
\(848\) | −1.11765e7 | −0.533721 | ||||||||
\(849\) | 1.93863e7 | 0.923053 | ||||||||
\(850\) | 3.22024e6 | 0.152877 | ||||||||
\(851\) | 6.24107e6 | 0.295417 | ||||||||
\(852\) | 7.59445e6 | 0.358424 | ||||||||
\(853\) | −1.64131e7 | −0.772358 | −0.386179 | − | 0.922424i | \(-0.626205\pi\) | ||||
−0.386179 | + | 0.922424i | \(0.626205\pi\) | |||||||
\(854\) | 2.79093e6 | 0.130950 | ||||||||
\(855\) | −2.33634e6 | −0.109300 | ||||||||
\(856\) | −2.83611e7 | −1.32294 | ||||||||
\(857\) | −1.90891e7 | −0.887839 | −0.443919 | − | 0.896067i | \(-0.646412\pi\) | ||||
−0.443919 | + | 0.896067i | \(0.646412\pi\) | |||||||
\(858\) | −2.96761e6 | −0.137622 | ||||||||
\(859\) | −3.79193e7 | −1.75339 | −0.876694 | − | 0.481049i | \(-0.840256\pi\) | ||||
−0.876694 | + | 0.481049i | \(0.840256\pi\) | |||||||
\(860\) | 1.87983e6 | 0.0866706 | ||||||||
\(861\) | 2.47357e7 | 1.13715 | ||||||||
\(862\) | 1.97954e7 | 0.907396 | ||||||||
\(863\) | −2.22911e7 | −1.01884 | −0.509419 | − | 0.860519i | \(-0.670140\pi\) | ||||
−0.509419 | + | 0.860519i | \(0.670140\pi\) | |||||||
\(864\) | −3.31566e6 | −0.151108 | ||||||||
\(865\) | −8.63791e6 | −0.392526 | ||||||||
\(866\) | 44116.0 | 0.00199895 | ||||||||
\(867\) | 262557. | 0.0118625 | ||||||||
\(868\) | −1.19623e7 | −0.538908 | ||||||||
\(869\) | −6.34024e6 | −0.284811 | ||||||||
\(870\) | 1.73998e6 | 0.0779373 | ||||||||
\(871\) | −3.62192e7 | −1.61768 | ||||||||
\(872\) | 4.33341e7 | 1.92992 | ||||||||
\(873\) | 2.48737e6 | 0.110460 | ||||||||
\(874\) | −4.60664e6 | −0.203989 | ||||||||
\(875\) | −3.15823e6 | −0.139452 | ||||||||
\(876\) | −4.01108e6 | −0.176604 | ||||||||
\(877\) | 3.18988e7 | 1.40047 | 0.700237 | − | 0.713910i | \(-0.253078\pi\) | ||||
0.700237 | + | 0.713910i | \(0.253078\pi\) | |||||||
\(878\) | 2.44917e7 | 1.07222 | ||||||||
\(879\) | −5.94164e6 | −0.259378 | ||||||||
\(880\) | −1.20738e6 | −0.0525577 | ||||||||
\(881\) | −4.66914e6 | −0.202673 | −0.101337 | − | 0.994852i | \(-0.532312\pi\) | ||||
−0.101337 | + | 0.994852i | \(0.532312\pi\) | |||||||
\(882\) | −8.33751e6 | −0.360882 | ||||||||
\(883\) | −7.83553e6 | −0.338195 | −0.169097 | − | 0.985599i | \(-0.554085\pi\) | ||||
−0.169097 | + | 0.985599i | \(0.554085\pi\) | |||||||
\(884\) | −1.04837e7 | −0.451215 | ||||||||
\(885\) | −5.18730e6 | −0.222630 | ||||||||
\(886\) | −2.67482e7 | −1.14475 | ||||||||
\(887\) | 2.31623e7 | 0.988491 | 0.494245 | − | 0.869322i | \(-0.335444\pi\) | ||||
0.494245 | + | 0.869322i | \(0.335444\pi\) | |||||||
\(888\) | 1.17730e7 | 0.501019 | ||||||||
\(889\) | −4.85905e7 | −2.06204 | ||||||||
\(890\) | −3.51051e6 | −0.148558 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | −1.60590e7 | −0.675780 | ||||||||
\(893\) | −1.09387e7 | −0.459028 | ||||||||
\(894\) | −1.83090e7 | −0.766163 | ||||||||
\(895\) | 8.07972e6 | 0.337162 | ||||||||
\(896\) | 1.52579e6 | 0.0634929 | ||||||||
\(897\) | −5.34510e6 | −0.221807 | ||||||||
\(898\) | 8.64206e6 | 0.357624 | ||||||||
\(899\) | 7.81654e6 | 0.322564 | ||||||||
\(900\) | −692520. | −0.0284988 | ||||||||
\(901\) | −3.37074e7 | −1.38329 | ||||||||
\(902\) | 7.04229e6 | 0.288203 | ||||||||
\(903\) | 9.99946e6 | 0.408091 | ||||||||
\(904\) | 2.06927e7 | 0.842162 | ||||||||
\(905\) | 1.84124e6 | 0.0747289 | ||||||||
\(906\) | −1.01636e7 | −0.411366 | ||||||||
\(907\) | 1.45366e7 | 0.586738 | 0.293369 | − | 0.955999i | \(-0.405223\pi\) | ||||
0.293369 | + | 0.955999i | \(0.405223\pi\) | |||||||
\(908\) | −6.37051e6 | −0.256425 | ||||||||
\(909\) | −8.88864e6 | −0.356801 | ||||||||
\(910\) | −1.37702e7 | −0.551237 | ||||||||
\(911\) | 1.98780e7 | 0.793554 | 0.396777 | − | 0.917915i | \(-0.370129\pi\) | ||||
0.396777 | + | 0.917915i | \(0.370129\pi\) | |||||||
\(912\) | −4.14448e6 | −0.165000 | ||||||||
\(913\) | 1.12044e6 | 0.0444848 | ||||||||
\(914\) | 3.24692e6 | 0.128560 | ||||||||
\(915\) | 725836. | 0.0286607 | ||||||||
\(916\) | 1.38512e7 | 0.545443 | ||||||||
\(917\) | −3.55145e7 | −1.39470 | ||||||||
\(918\) | 3.75609e6 | 0.147106 | ||||||||
\(919\) | 2.87364e7 | 1.12239 | 0.561195 | − | 0.827684i | \(-0.310342\pi\) | ||||
0.561195 | + | 0.827684i | \(0.310342\pi\) | |||||||
\(920\) | −4.55968e6 | −0.177609 | ||||||||
\(921\) | 2.46880e7 | 0.959041 | ||||||||
\(922\) | −2.30966e7 | −0.894790 | ||||||||
\(923\) | 3.92731e7 | 1.51737 | ||||||||
\(924\) | 3.01105e6 | 0.116022 | ||||||||
\(925\) | 4.18152e6 | 0.160687 | ||||||||
\(926\) | −973059. | −0.0372917 | ||||||||
\(927\) | 1.56307e7 | 0.597420 | ||||||||
\(928\) | −8.21740e6 | −0.313231 | ||||||||
\(929\) | 3.50219e7 | 1.33138 | 0.665688 | − | 0.746231i | \(-0.268138\pi\) | ||||
0.665688 | + | 0.746231i | \(0.268138\pi\) | |||||||
\(930\) | 4.16654e6 | 0.157968 | ||||||||
\(931\) | 2.77455e7 | 1.04910 | ||||||||
\(932\) | −1.40170e7 | −0.528585 | ||||||||
\(933\) | −1.20873e7 | −0.454594 | ||||||||
\(934\) | 6.37558e6 | 0.239140 | ||||||||
\(935\) | −3.64136e6 | −0.136218 | ||||||||
\(936\) | −1.00829e7 | −0.376179 | ||||||||
\(937\) | 4.31664e7 | 1.60619 | 0.803095 | − | 0.595851i | \(-0.203185\pi\) | ||||
0.803095 | + | 0.595851i | \(0.203185\pi\) | |||||||
\(938\) | −4.92179e7 | −1.82648 | ||||||||
\(939\) | −3.07146e7 | −1.13679 | ||||||||
\(940\) | −3.24238e6 | −0.119686 | ||||||||
\(941\) | 1.82030e7 | 0.670147 | 0.335073 | − | 0.942192i | \(-0.391239\pi\) | ||||
0.335073 | + | 0.942192i | \(0.391239\pi\) | |||||||
\(942\) | 3.88903e6 | 0.142795 | ||||||||
\(943\) | 1.26842e7 | 0.464498 | ||||||||
\(944\) | −9.20188e6 | −0.336083 | ||||||||
\(945\) | −3.68376e6 | −0.134187 | ||||||||
\(946\) | 2.84686e6 | 0.103428 | ||||||||
\(947\) | 4.35637e7 | 1.57852 | 0.789259 | − | 0.614060i | \(-0.210465\pi\) | ||||
0.789259 | + | 0.614060i | \(0.210465\pi\) | |||||||
\(948\) | −6.45105e6 | −0.233136 | ||||||||
\(949\) | −2.07425e7 | −0.747644 | ||||||||
\(950\) | −3.08646e6 | −0.110956 | ||||||||
\(951\) | 1.56640e7 | 0.561632 | ||||||||
\(952\) | −4.75721e7 | −1.70122 | ||||||||
\(953\) | 2.03171e6 | 0.0724653 | 0.0362326 | − | 0.999343i | \(-0.488464\pi\) | ||||
0.0362326 | + | 0.999343i | \(0.488464\pi\) | |||||||
\(954\) | −9.70826e6 | −0.345359 | ||||||||
\(955\) | 2.48327e7 | 0.881082 | ||||||||
\(956\) | −1.06204e7 | −0.375832 | ||||||||
\(957\) | −1.96752e6 | −0.0694447 | ||||||||
\(958\) | 2.14003e7 | 0.753367 | ||||||||
\(959\) | −4.52278e7 | −1.58803 | ||||||||
\(960\) | −7.25397e6 | −0.254037 | ||||||||
\(961\) | −9.91169e6 | −0.346210 | ||||||||
\(962\) | 1.82319e7 | 0.635177 | ||||||||
\(963\) | −1.17495e7 | −0.408275 | ||||||||
\(964\) | −1.25818e7 | −0.436064 | ||||||||
\(965\) | 3.39538e6 | 0.117373 | ||||||||
\(966\) | −7.26340e6 | −0.250436 | ||||||||
\(967\) | 2.09486e7 | 0.720427 | 0.360213 | − | 0.932870i | \(-0.382704\pi\) | ||||
0.360213 | + | 0.932870i | \(0.382704\pi\) | |||||||
\(968\) | 2.86260e6 | 0.0981912 | ||||||||
\(969\) | −1.24995e7 | −0.427644 | ||||||||
\(970\) | 3.28599e6 | 0.112134 | ||||||||
\(971\) | −2.57967e7 | −0.878043 | −0.439022 | − | 0.898477i | \(-0.644675\pi\) | ||||
−0.439022 | + | 0.898477i | \(0.644675\pi\) | |||||||
\(972\) | −807755. | −0.0274230 | ||||||||
\(973\) | 3.62870e7 | 1.22876 | ||||||||
\(974\) | −6.06717e6 | −0.204922 | ||||||||
\(975\) | −3.58122e6 | −0.120648 | ||||||||
\(976\) | 1.28758e6 | 0.0432662 | ||||||||
\(977\) | −5.53752e6 | −0.185600 | −0.0928002 | − | 0.995685i | \(-0.529582\pi\) | ||||
−0.0928002 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(978\) | 2.15765e7 | 0.721331 | ||||||||
\(979\) | 3.96959e6 | 0.132370 | ||||||||
\(980\) | 8.22411e6 | 0.273542 | ||||||||
\(981\) | 1.79525e7 | 0.595597 | ||||||||
\(982\) | −1.62057e7 | −0.536276 | ||||||||
\(983\) | −2.67527e7 | −0.883048 | −0.441524 | − | 0.897249i | \(-0.645562\pi\) | ||||
−0.441524 | + | 0.897249i | \(0.645562\pi\) | |||||||
\(984\) | 2.39272e7 | 0.787778 | ||||||||
\(985\) | −5.91275e6 | −0.194178 | ||||||||
\(986\) | 9.30893e6 | 0.304935 | ||||||||
\(987\) | −1.72474e7 | −0.563547 | ||||||||
\(988\) | 1.00482e7 | 0.327487 | ||||||||
\(989\) | 5.12761e6 | 0.166696 | ||||||||
\(990\) | −1.04877e6 | −0.0340089 | ||||||||
\(991\) | −4.26868e7 | −1.38073 | −0.690366 | − | 0.723460i | \(-0.742551\pi\) | ||||
−0.690366 | + | 0.723460i | \(0.742551\pi\) | |||||||
\(992\) | −1.96773e7 | −0.634874 | ||||||||
\(993\) | 1.01124e7 | 0.325448 | ||||||||
\(994\) | 5.33679e7 | 1.71322 | ||||||||
\(995\) | 1.58952e7 | 0.508988 | ||||||||
\(996\) | 1.14002e6 | 0.0364137 | ||||||||
\(997\) | 1.07810e7 | 0.343495 | 0.171748 | − | 0.985141i | \(-0.445059\pi\) | ||||
0.171748 | + | 0.985141i | \(0.445059\pi\) | |||||||
\(998\) | −1.05916e7 | −0.336616 | ||||||||
\(999\) | 4.87733e6 | 0.154621 |
(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 | 165.6.a.f.1.2 | ✓ | 5 | |
3.2 | odd | 2 | 495.6.a.j.1.4 | 5 | |||
5.4 | even | 2 | 825.6.a.l.1.4 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.f.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
495.6.a.j.1.4 | 5 | 3.2 | odd | 2 | |||
825.6.a.l.1.4 | 5 | 5.4 | even | 2 |