Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(6.89650425196\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 173x^{6} + 462x^{5} + 9118x^{4} - 14192x^{3} - 167688x^{2} + 106368x + 681984 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(2.58275\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.582753 | 0.103017 | 0.0515085 | − | 0.998673i | \(-0.483597\pi\) | ||||
0.0515085 | + | 0.998673i | \(0.483597\pi\) | |||||||
\(3\) | 3.05838 | 0.196195 | 0.0980976 | − | 0.995177i | \(-0.468724\pi\) | ||||
0.0980976 | + | 0.995177i | \(0.468724\pi\) | |||||||
\(4\) | −31.6604 | −0.989387 | ||||||||
\(5\) | 27.7074 | 0.495645 | 0.247822 | − | 0.968805i | \(-0.420285\pi\) | ||||
0.247822 | + | 0.968805i | \(0.420285\pi\) | |||||||
\(6\) | 1.78228 | 0.0202115 | ||||||||
\(7\) | −103.690 | −0.799819 | −0.399910 | − | 0.916555i | \(-0.630958\pi\) | ||||
−0.399910 | + | 0.916555i | \(0.630958\pi\) | |||||||
\(8\) | −37.0983 | −0.204941 | ||||||||
\(9\) | −233.646 | −0.961507 | ||||||||
\(10\) | 16.1466 | 0.0510599 | ||||||||
\(11\) | −158.323 | −0.394515 | −0.197257 | − | 0.980352i | \(-0.563203\pi\) | ||||
−0.197257 | + | 0.980352i | \(0.563203\pi\) | |||||||
\(12\) | −96.8296 | −0.194113 | ||||||||
\(13\) | −578.882 | −0.950017 | −0.475009 | − | 0.879981i | \(-0.657555\pi\) | ||||
−0.475009 | + | 0.879981i | \(0.657555\pi\) | |||||||
\(14\) | −60.4256 | −0.0823950 | ||||||||
\(15\) | 84.7398 | 0.0972432 | ||||||||
\(16\) | 991.514 | 0.968275 | ||||||||
\(17\) | 253.871 | 0.213055 | 0.106527 | − | 0.994310i | \(-0.466027\pi\) | ||||
0.106527 | + | 0.994310i | \(0.466027\pi\) | |||||||
\(18\) | −136.158 | −0.0990517 | ||||||||
\(19\) | −3092.51 | −1.96529 | −0.982645 | − | 0.185494i | \(-0.940612\pi\) | ||||
−0.982645 | + | 0.185494i | \(0.940612\pi\) | |||||||
\(20\) | −877.227 | −0.490385 | ||||||||
\(21\) | −317.124 | −0.156921 | ||||||||
\(22\) | −92.2633 | −0.0406417 | ||||||||
\(23\) | 4163.45 | 1.64109 | 0.820547 | − | 0.571579i | \(-0.193669\pi\) | ||||
0.820547 | + | 0.571579i | \(0.193669\pi\) | |||||||
\(24\) | −113.461 | −0.0402084 | ||||||||
\(25\) | −2357.30 | −0.754336 | ||||||||
\(26\) | −337.345 | −0.0978680 | ||||||||
\(27\) | −1457.77 | −0.384839 | ||||||||
\(28\) | 3282.87 | 0.791331 | ||||||||
\(29\) | 6771.63 | 1.49520 | 0.747598 | − | 0.664151i | \(-0.231207\pi\) | ||||
0.747598 | + | 0.664151i | \(0.231207\pi\) | |||||||
\(30\) | 49.3823 | 0.0100177 | ||||||||
\(31\) | 6264.06 | 1.17072 | 0.585358 | − | 0.810775i | \(-0.300954\pi\) | ||||
0.585358 | + | 0.810775i | \(0.300954\pi\) | |||||||
\(32\) | 1764.95 | 0.304690 | ||||||||
\(33\) | −484.213 | −0.0774019 | ||||||||
\(34\) | 147.944 | 0.0219483 | ||||||||
\(35\) | −2872.98 | −0.396426 | ||||||||
\(36\) | 7397.34 | 0.951303 | ||||||||
\(37\) | −3294.82 | −0.395665 | −0.197833 | − | 0.980236i | \(-0.563390\pi\) | ||||
−0.197833 | + | 0.980236i | \(0.563390\pi\) | |||||||
\(38\) | −1802.17 | −0.202459 | ||||||||
\(39\) | −1770.44 | −0.186389 | ||||||||
\(40\) | −1027.90 | −0.101578 | ||||||||
\(41\) | −6150.84 | −0.571445 | −0.285723 | − | 0.958312i | \(-0.592234\pi\) | ||||
−0.285723 | + | 0.958312i | \(0.592234\pi\) | |||||||
\(42\) | −184.805 | −0.0161655 | ||||||||
\(43\) | −1849.00 | −0.152499 | ||||||||
\(44\) | 5012.58 | 0.390328 | ||||||||
\(45\) | −6473.73 | −0.476566 | ||||||||
\(46\) | 2426.26 | 0.169061 | ||||||||
\(47\) | 8157.17 | 0.538635 | 0.269318 | − | 0.963051i | \(-0.413202\pi\) | ||||
0.269318 | + | 0.963051i | \(0.413202\pi\) | |||||||
\(48\) | 3032.43 | 0.189971 | ||||||||
\(49\) | −6055.38 | −0.360289 | ||||||||
\(50\) | −1373.72 | −0.0777095 | ||||||||
\(51\) | 776.436 | 0.0418004 | ||||||||
\(52\) | 18327.6 | 0.939935 | ||||||||
\(53\) | −30457.8 | −1.48939 | −0.744697 | − | 0.667403i | \(-0.767406\pi\) | ||||
−0.744697 | + | 0.667403i | \(0.767406\pi\) | |||||||
\(54\) | −849.517 | −0.0396449 | ||||||||
\(55\) | −4386.72 | −0.195539 | ||||||||
\(56\) | 3846.72 | 0.163916 | ||||||||
\(57\) | −9458.07 | −0.385581 | ||||||||
\(58\) | 3946.19 | 0.154031 | ||||||||
\(59\) | −45236.1 | −1.69182 | −0.845912 | − | 0.533322i | \(-0.820943\pi\) | ||||
−0.845912 | + | 0.533322i | \(0.820943\pi\) | |||||||
\(60\) | −2682.90 | −0.0962112 | ||||||||
\(61\) | −7251.18 | −0.249508 | −0.124754 | − | 0.992188i | \(-0.539814\pi\) | ||||
−0.124754 | + | 0.992188i | \(0.539814\pi\) | |||||||
\(62\) | 3650.40 | 0.120604 | ||||||||
\(63\) | 24226.8 | 0.769032 | ||||||||
\(64\) | −30699.9 | −0.936887 | ||||||||
\(65\) | −16039.3 | −0.470871 | ||||||||
\(66\) | −282.176 | −0.00797372 | ||||||||
\(67\) | 19685.7 | 0.535751 | 0.267876 | − | 0.963454i | \(-0.413678\pi\) | ||||
0.267876 | + | 0.963454i | \(0.413678\pi\) | |||||||
\(68\) | −8037.67 | −0.210794 | ||||||||
\(69\) | 12733.4 | 0.321975 | ||||||||
\(70\) | −1674.24 | −0.0408387 | ||||||||
\(71\) | −48132.2 | −1.13316 | −0.566579 | − | 0.824008i | \(-0.691733\pi\) | ||||
−0.566579 | + | 0.824008i | \(0.691733\pi\) | |||||||
\(72\) | 8667.87 | 0.197052 | ||||||||
\(73\) | 42502.1 | 0.933475 | 0.466738 | − | 0.884396i | \(-0.345429\pi\) | ||||
0.466738 | + | 0.884396i | \(0.345429\pi\) | |||||||
\(74\) | −1920.07 | −0.0407603 | ||||||||
\(75\) | −7209.53 | −0.147997 | ||||||||
\(76\) | 97910.0 | 1.94443 | ||||||||
\(77\) | 16416.5 | 0.315540 | ||||||||
\(78\) | −1031.73 | −0.0192012 | ||||||||
\(79\) | −65151.9 | −1.17452 | −0.587258 | − | 0.809400i | \(-0.699793\pi\) | ||||
−0.587258 | + | 0.809400i | \(0.699793\pi\) | |||||||
\(80\) | 27472.3 | 0.479921 | ||||||||
\(81\) | 52317.6 | 0.886004 | ||||||||
\(82\) | −3584.42 | −0.0588686 | ||||||||
\(83\) | 70403.6 | 1.12176 | 0.560880 | − | 0.827897i | \(-0.310463\pi\) | ||||
0.560880 | + | 0.827897i | \(0.310463\pi\) | |||||||
\(84\) | 10040.3 | 0.155255 | ||||||||
\(85\) | 7034.12 | 0.105600 | ||||||||
\(86\) | −1077.51 | −0.0157100 | ||||||||
\(87\) | 20710.2 | 0.293350 | ||||||||
\(88\) | 5873.52 | 0.0808522 | ||||||||
\(89\) | 29645.1 | 0.396714 | 0.198357 | − | 0.980130i | \(-0.436439\pi\) | ||||
0.198357 | + | 0.980130i | \(0.436439\pi\) | |||||||
\(90\) | −3772.58 | −0.0490945 | ||||||||
\(91\) | 60024.2 | 0.759842 | ||||||||
\(92\) | −131816. | −1.62368 | ||||||||
\(93\) | 19157.9 | 0.229689 | ||||||||
\(94\) | 4753.61 | 0.0554887 | ||||||||
\(95\) | −85685.3 | −0.974086 | ||||||||
\(96\) | 5397.90 | 0.0597787 | ||||||||
\(97\) | −89440.4 | −0.965171 | −0.482585 | − | 0.875849i | \(-0.660302\pi\) | ||||
−0.482585 | + | 0.875849i | \(0.660302\pi\) | |||||||
\(98\) | −3528.79 | −0.0371160 | ||||||||
\(99\) | 36991.6 | 0.379329 | ||||||||
\(100\) | 74633.1 | 0.746331 | ||||||||
\(101\) | −28633.0 | −0.279295 | −0.139647 | − | 0.990201i | \(-0.544597\pi\) | ||||
−0.139647 | + | 0.990201i | \(0.544597\pi\) | |||||||
\(102\) | 452.470 | 0.00430615 | ||||||||
\(103\) | 30124.9 | 0.279790 | 0.139895 | − | 0.990166i | \(-0.455324\pi\) | ||||
0.139895 | + | 0.990166i | \(0.455324\pi\) | |||||||
\(104\) | 21475.5 | 0.194697 | ||||||||
\(105\) | −8786.67 | −0.0777770 | ||||||||
\(106\) | −17749.4 | −0.153433 | ||||||||
\(107\) | 83073.3 | 0.701459 | 0.350729 | − | 0.936477i | \(-0.385934\pi\) | ||||
0.350729 | + | 0.936477i | \(0.385934\pi\) | |||||||
\(108\) | 46153.5 | 0.380754 | ||||||||
\(109\) | 58783.5 | 0.473903 | 0.236951 | − | 0.971522i | \(-0.423852\pi\) | ||||
0.236951 | + | 0.971522i | \(0.423852\pi\) | |||||||
\(110\) | −2556.38 | −0.0201439 | ||||||||
\(111\) | −10076.8 | −0.0776276 | ||||||||
\(112\) | −102810. | −0.774445 | ||||||||
\(113\) | −232647. | −1.71396 | −0.856981 | − | 0.515347i | \(-0.827663\pi\) | ||||
−0.856981 | + | 0.515347i | \(0.827663\pi\) | |||||||
\(114\) | −5511.72 | −0.0397214 | ||||||||
\(115\) | 115358. | 0.813400 | ||||||||
\(116\) | −214392. | −1.47933 | ||||||||
\(117\) | 135254. | 0.913449 | ||||||||
\(118\) | −26361.5 | −0.174287 | ||||||||
\(119\) | −26323.9 | −0.170405 | ||||||||
\(120\) | −3143.70 | −0.0199291 | ||||||||
\(121\) | −135985. | −0.844358 | ||||||||
\(122\) | −4225.64 | −0.0257036 | ||||||||
\(123\) | −18811.6 | −0.112115 | ||||||||
\(124\) | −198323. | −1.15829 | ||||||||
\(125\) | −151900. | −0.869528 | ||||||||
\(126\) | 14118.2 | 0.0792234 | ||||||||
\(127\) | 109116. | 0.600313 | 0.300156 | − | 0.953890i | \(-0.402961\pi\) | ||||
0.300156 | + | 0.953890i | \(0.402961\pi\) | |||||||
\(128\) | −74368.9 | −0.401205 | ||||||||
\(129\) | −5654.95 | −0.0299195 | ||||||||
\(130\) | −9346.94 | −0.0485078 | ||||||||
\(131\) | 139424. | 0.709839 | 0.354920 | − | 0.934897i | \(-0.384508\pi\) | ||||
0.354920 | + | 0.934897i | \(0.384508\pi\) | |||||||
\(132\) | 15330.4 | 0.0765805 | ||||||||
\(133\) | 320662. | 1.57188 | ||||||||
\(134\) | 11471.9 | 0.0551915 | ||||||||
\(135\) | −40390.9 | −0.190743 | ||||||||
\(136\) | −9418.19 | −0.0436637 | ||||||||
\(137\) | −64194.6 | −0.292211 | −0.146106 | − | 0.989269i | \(-0.546674\pi\) | ||||
−0.146106 | + | 0.989269i | \(0.546674\pi\) | |||||||
\(138\) | 7420.43 | 0.0331689 | ||||||||
\(139\) | −281632. | −1.23636 | −0.618181 | − | 0.786036i | \(-0.712130\pi\) | ||||
−0.618181 | + | 0.786036i | \(0.712130\pi\) | |||||||
\(140\) | 90959.7 | 0.392219 | ||||||||
\(141\) | 24947.7 | 0.105678 | ||||||||
\(142\) | −28049.2 | −0.116735 | ||||||||
\(143\) | 91650.4 | 0.374796 | ||||||||
\(144\) | −231664. | −0.931004 | ||||||||
\(145\) | 187624. | 0.741086 | ||||||||
\(146\) | 24768.2 | 0.0961639 | ||||||||
\(147\) | −18519.7 | −0.0706871 | ||||||||
\(148\) | 104315. | 0.391466 | ||||||||
\(149\) | 225391. | 0.831710 | 0.415855 | − | 0.909431i | \(-0.363482\pi\) | ||||
0.415855 | + | 0.909431i | \(0.363482\pi\) | |||||||
\(150\) | −4201.37 | −0.0152462 | ||||||||
\(151\) | 388390. | 1.38620 | 0.693099 | − | 0.720842i | \(-0.256245\pi\) | ||||
0.693099 | + | 0.720842i | \(0.256245\pi\) | |||||||
\(152\) | 114727. | 0.402768 | ||||||||
\(153\) | −59316.1 | −0.204854 | ||||||||
\(154\) | 9566.78 | 0.0325060 | ||||||||
\(155\) | 173561. | 0.580259 | ||||||||
\(156\) | 56052.9 | 0.184411 | ||||||||
\(157\) | −369612. | −1.19673 | −0.598366 | − | 0.801223i | \(-0.704183\pi\) | ||||
−0.598366 | + | 0.801223i | \(0.704183\pi\) | |||||||
\(158\) | −37967.4 | −0.120995 | ||||||||
\(159\) | −93151.7 | −0.292212 | ||||||||
\(160\) | 48902.2 | 0.151018 | ||||||||
\(161\) | −431708. | −1.31258 | ||||||||
\(162\) | 30488.2 | 0.0912735 | ||||||||
\(163\) | 522204. | 1.53947 | 0.769735 | − | 0.638363i | \(-0.220388\pi\) | ||||
0.769735 | + | 0.638363i | \(0.220388\pi\) | |||||||
\(164\) | 194738. | 0.565381 | ||||||||
\(165\) | −13416.3 | −0.0383638 | ||||||||
\(166\) | 41027.9 | 0.115560 | ||||||||
\(167\) | −17232.5 | −0.0478141 | −0.0239071 | − | 0.999714i | \(-0.507611\pi\) | ||||
−0.0239071 | + | 0.999714i | \(0.507611\pi\) | |||||||
\(168\) | 11764.7 | 0.0321595 | ||||||||
\(169\) | −36189.0 | −0.0974674 | ||||||||
\(170\) | 4099.15 | 0.0108786 | ||||||||
\(171\) | 722553. | 1.88964 | ||||||||
\(172\) | 58540.1 | 0.150880 | ||||||||
\(173\) | −571643. | −1.45214 | −0.726072 | − | 0.687618i | \(-0.758656\pi\) | ||||
−0.726072 | + | 0.687618i | \(0.758656\pi\) | |||||||
\(174\) | 12068.9 | 0.0302201 | ||||||||
\(175\) | 244429. | 0.603333 | ||||||||
\(176\) | −156980. | −0.381999 | ||||||||
\(177\) | −138349. | −0.331928 | ||||||||
\(178\) | 17275.7 | 0.0408683 | ||||||||
\(179\) | −191963. | −0.447802 | −0.223901 | − | 0.974612i | \(-0.571879\pi\) | ||||
−0.223901 | + | 0.974612i | \(0.571879\pi\) | |||||||
\(180\) | 204961. | 0.471509 | ||||||||
\(181\) | 110804. | 0.251396 | 0.125698 | − | 0.992069i | \(-0.459883\pi\) | ||||
0.125698 | + | 0.992069i | \(0.459883\pi\) | |||||||
\(182\) | 34979.3 | 0.0782767 | ||||||||
\(183\) | −22176.9 | −0.0489522 | ||||||||
\(184\) | −154457. | −0.336327 | ||||||||
\(185\) | −91290.9 | −0.196109 | ||||||||
\(186\) | 11164.3 | 0.0236619 | ||||||||
\(187\) | −40193.8 | −0.0840533 | ||||||||
\(188\) | −258259. | −0.532919 | ||||||||
\(189\) | 151156. | 0.307801 | ||||||||
\(190\) | −49933.3 | −0.100348 | ||||||||
\(191\) | 295668. | 0.586437 | 0.293218 | − | 0.956046i | \(-0.405274\pi\) | ||||
0.293218 | + | 0.956046i | \(0.405274\pi\) | |||||||
\(192\) | −93892.0 | −0.183813 | ||||||||
\(193\) | −375944. | −0.726491 | −0.363246 | − | 0.931693i | \(-0.618331\pi\) | ||||
−0.363246 | + | 0.931693i | \(0.618331\pi\) | |||||||
\(194\) | −52121.6 | −0.0994291 | ||||||||
\(195\) | −49054.3 | −0.0923827 | ||||||||
\(196\) | 191716. | 0.356466 | ||||||||
\(197\) | −732825. | −1.34535 | −0.672674 | − | 0.739939i | \(-0.734854\pi\) | ||||
−0.672674 | + | 0.739939i | \(0.734854\pi\) | |||||||
\(198\) | 21557.0 | 0.0390773 | ||||||||
\(199\) | 589939. | 1.05603 | 0.528013 | − | 0.849236i | \(-0.322937\pi\) | ||||
0.528013 | + | 0.849236i | \(0.322937\pi\) | |||||||
\(200\) | 87451.8 | 0.154594 | ||||||||
\(201\) | 60206.3 | 0.105112 | ||||||||
\(202\) | −16685.9 | −0.0287722 | ||||||||
\(203\) | −702150. | −1.19589 | ||||||||
\(204\) | −24582.3 | −0.0413568 | ||||||||
\(205\) | −170424. | −0.283234 | ||||||||
\(206\) | 17555.3 | 0.0288231 | ||||||||
\(207\) | −972774. | −1.57792 | ||||||||
\(208\) | −573969. | −0.919878 | ||||||||
\(209\) | 489616. | 0.775336 | ||||||||
\(210\) | −5120.45 | −0.00801236 | ||||||||
\(211\) | −371450. | −0.574374 | −0.287187 | − | 0.957875i | \(-0.592720\pi\) | ||||
−0.287187 | + | 0.957875i | \(0.592720\pi\) | |||||||
\(212\) | 964307. | 1.47359 | ||||||||
\(213\) | −147207. | −0.222320 | ||||||||
\(214\) | 48411.2 | 0.0722622 | ||||||||
\(215\) | −51231.0 | −0.0755851 | ||||||||
\(216\) | 54080.6 | 0.0788692 | ||||||||
\(217\) | −649520. | −0.936361 | ||||||||
\(218\) | 34256.2 | 0.0488201 | ||||||||
\(219\) | 129988. | 0.183143 | ||||||||
\(220\) | 138885. | 0.193464 | ||||||||
\(221\) | −146962. | −0.202406 | ||||||||
\(222\) | −5872.30 | −0.00799697 | ||||||||
\(223\) | −835552. | −1.12515 | −0.562576 | − | 0.826746i | \(-0.690190\pi\) | ||||
−0.562576 | + | 0.826746i | \(0.690190\pi\) | |||||||
\(224\) | −183008. | −0.243697 | ||||||||
\(225\) | 550775. | 0.725300 | ||||||||
\(226\) | −135576. | −0.176567 | ||||||||
\(227\) | −363342. | −0.468006 | −0.234003 | − | 0.972236i | \(-0.575182\pi\) | ||||
−0.234003 | + | 0.972236i | \(0.575182\pi\) | |||||||
\(228\) | 299446. | 0.381489 | ||||||||
\(229\) | −106091. | −0.133688 | −0.0668438 | − | 0.997763i | \(-0.521293\pi\) | ||||
−0.0668438 | + | 0.997763i | \(0.521293\pi\) | |||||||
\(230\) | 67225.3 | 0.0837941 | ||||||||
\(231\) | 50208.0 | 0.0619075 | ||||||||
\(232\) | −251216. | −0.306427 | ||||||||
\(233\) | 713760. | 0.861315 | 0.430658 | − | 0.902515i | \(-0.358282\pi\) | ||||
0.430658 | + | 0.902515i | \(0.358282\pi\) | |||||||
\(234\) | 78819.4 | 0.0941008 | ||||||||
\(235\) | 226014. | 0.266972 | ||||||||
\(236\) | 1.43219e6 | 1.67387 | ||||||||
\(237\) | −199259. | −0.230435 | ||||||||
\(238\) | −15340.3 | −0.0175547 | ||||||||
\(239\) | −70400.0 | −0.0797220 | −0.0398610 | − | 0.999205i | \(-0.512692\pi\) | ||||
−0.0398610 | + | 0.999205i | \(0.512692\pi\) | |||||||
\(240\) | 84020.6 | 0.0941581 | ||||||||
\(241\) | 44600.6 | 0.0494650 | 0.0247325 | − | 0.999694i | \(-0.492127\pi\) | ||||
0.0247325 | + | 0.999694i | \(0.492127\pi\) | |||||||
\(242\) | −79245.5 | −0.0869833 | ||||||||
\(243\) | 514245. | 0.558668 | ||||||||
\(244\) | 229575. | 0.246860 | ||||||||
\(245\) | −167779. | −0.178576 | ||||||||
\(246\) | −10962.5 | −0.0115497 | ||||||||
\(247\) | 1.79020e6 | 1.86706 | ||||||||
\(248\) | −232386. | −0.239928 | ||||||||
\(249\) | 215321. | 0.220084 | ||||||||
\(250\) | −88520.3 | −0.0895762 | ||||||||
\(251\) | 1.05989e6 | 1.06188 | 0.530942 | − | 0.847408i | \(-0.321838\pi\) | ||||
0.530942 | + | 0.847408i | \(0.321838\pi\) | |||||||
\(252\) | −767030. | −0.760871 | ||||||||
\(253\) | −659170. | −0.647435 | ||||||||
\(254\) | 63587.4 | 0.0618425 | ||||||||
\(255\) | 21513.0 | 0.0207181 | ||||||||
\(256\) | 939058. | 0.895556 | ||||||||
\(257\) | −966091. | −0.912400 | −0.456200 | − | 0.889877i | \(-0.650790\pi\) | ||||
−0.456200 | + | 0.889877i | \(0.650790\pi\) | |||||||
\(258\) | −3295.44 | −0.00308222 | ||||||||
\(259\) | 341640. | 0.316460 | ||||||||
\(260\) | 507811. | 0.465874 | ||||||||
\(261\) | −1.58217e6 | −1.43764 | ||||||||
\(262\) | 81249.8 | 0.0731255 | ||||||||
\(263\) | 855270. | 0.762454 | 0.381227 | − | 0.924481i | \(-0.375502\pi\) | ||||
0.381227 | + | 0.924481i | \(0.375502\pi\) | |||||||
\(264\) | 17963.5 | 0.0158628 | ||||||||
\(265\) | −843907. | −0.738210 | ||||||||
\(266\) | 186867. | 0.161930 | ||||||||
\(267\) | 90665.9 | 0.0778334 | ||||||||
\(268\) | −623256. | −0.530065 | ||||||||
\(269\) | 1.55224e6 | 1.30791 | 0.653955 | − | 0.756533i | \(-0.273108\pi\) | ||||
0.653955 | + | 0.756533i | \(0.273108\pi\) | |||||||
\(270\) | −23537.9 | −0.0196498 | ||||||||
\(271\) | −4177.31 | −0.00345520 | −0.00172760 | − | 0.999999i | \(-0.500550\pi\) | ||||
−0.00172760 | + | 0.999999i | \(0.500550\pi\) | |||||||
\(272\) | 251717. | 0.206296 | ||||||||
\(273\) | 183577. | 0.149077 | ||||||||
\(274\) | −37409.5 | −0.0301027 | ||||||||
\(275\) | 373216. | 0.297597 | ||||||||
\(276\) | −403145. | −0.318558 | ||||||||
\(277\) | −1.59749e6 | −1.25095 | −0.625475 | − | 0.780244i | \(-0.715095\pi\) | ||||
−0.625475 | + | 0.780244i | \(0.715095\pi\) | |||||||
\(278\) | −164122. | −0.127366 | ||||||||
\(279\) | −1.46357e6 | −1.12565 | ||||||||
\(280\) | 106583. | 0.0812439 | ||||||||
\(281\) | 1.60304e6 | 1.21110 | 0.605549 | − | 0.795808i | \(-0.292954\pi\) | ||||
0.605549 | + | 0.795808i | \(0.292954\pi\) | |||||||
\(282\) | 14538.4 | 0.0108866 | ||||||||
\(283\) | 2.04664e6 | 1.51906 | 0.759530 | − | 0.650472i | \(-0.225429\pi\) | ||||
0.759530 | + | 0.650472i | \(0.225429\pi\) | |||||||
\(284\) | 1.52389e6 | 1.12113 | ||||||||
\(285\) | −262058. | −0.191111 | ||||||||
\(286\) | 53409.5 | 0.0386103 | ||||||||
\(287\) | 637780. | 0.457053 | ||||||||
\(288\) | −412374. | −0.292961 | ||||||||
\(289\) | −1.35541e6 | −0.954608 | ||||||||
\(290\) | 109338. | 0.0763446 | ||||||||
\(291\) | −273543. | −0.189362 | ||||||||
\(292\) | −1.34563e6 | −0.923569 | ||||||||
\(293\) | 1.35028e6 | 0.918869 | 0.459434 | − | 0.888212i | \(-0.348052\pi\) | ||||
0.459434 | + | 0.888212i | \(0.348052\pi\) | |||||||
\(294\) | −10792.4 | −0.00728198 | ||||||||
\(295\) | −1.25337e6 | −0.838544 | ||||||||
\(296\) | 122232. | 0.0810880 | ||||||||
\(297\) | 230798. | 0.151824 | ||||||||
\(298\) | 131347. | 0.0856803 | ||||||||
\(299\) | −2.41014e6 | −1.55907 | ||||||||
\(300\) | 228256. | 0.146427 | ||||||||
\(301\) | 191723. | 0.121971 | ||||||||
\(302\) | 226335. | 0.142802 | ||||||||
\(303\) | −87570.6 | −0.0547964 | ||||||||
\(304\) | −3.06626e6 | −1.90294 | ||||||||
\(305\) | −200911. | −0.123667 | ||||||||
\(306\) | −34566.6 | −0.0211035 | ||||||||
\(307\) | −361103. | −0.218668 | −0.109334 | − | 0.994005i | \(-0.534872\pi\) | ||||
−0.109334 | + | 0.994005i | \(0.534872\pi\) | |||||||
\(308\) | −519754. | −0.312192 | ||||||||
\(309\) | 92133.4 | 0.0548935 | ||||||||
\(310\) | 101143. | 0.0597766 | ||||||||
\(311\) | 2.12425e6 | 1.24539 | 0.622694 | − | 0.782466i | \(-0.286038\pi\) | ||||
0.622694 | + | 0.782466i | \(0.286038\pi\) | |||||||
\(312\) | 65680.3 | 0.0381987 | ||||||||
\(313\) | −541717. | −0.312545 | −0.156272 | − | 0.987714i | \(-0.549948\pi\) | ||||
−0.156272 | + | 0.987714i | \(0.549948\pi\) | |||||||
\(314\) | −215392. | −0.123284 | ||||||||
\(315\) | 671261. | 0.381167 | ||||||||
\(316\) | 2.06273e6 | 1.16205 | ||||||||
\(317\) | −3.06921e6 | −1.71545 | −0.857725 | − | 0.514110i | \(-0.828122\pi\) | ||||
−0.857725 | + | 0.514110i | \(0.828122\pi\) | |||||||
\(318\) | −54284.4 | −0.0301028 | ||||||||
\(319\) | −1.07211e6 | −0.589877 | ||||||||
\(320\) | −850614. | −0.464363 | ||||||||
\(321\) | 254070. | 0.137623 | ||||||||
\(322\) | −251579. | −0.135218 | ||||||||
\(323\) | −785100. | −0.418715 | ||||||||
\(324\) | −1.65640e6 | −0.876601 | ||||||||
\(325\) | 1.36460e6 | 0.716632 | ||||||||
\(326\) | 304316. | 0.158592 | ||||||||
\(327\) | 179782. | 0.0929775 | ||||||||
\(328\) | 228185. | 0.117112 | ||||||||
\(329\) | −845817. | −0.430811 | ||||||||
\(330\) | −7818.37 | −0.00395213 | ||||||||
\(331\) | −282184. | −0.141567 | −0.0707836 | − | 0.997492i | \(-0.522550\pi\) | ||||
−0.0707836 | + | 0.997492i | \(0.522550\pi\) | |||||||
\(332\) | −2.22901e6 | −1.10986 | ||||||||
\(333\) | 769823. | 0.380435 | ||||||||
\(334\) | −10042.3 | −0.00492567 | ||||||||
\(335\) | 545438. | 0.265542 | ||||||||
\(336\) | −314432. | −0.151942 | ||||||||
\(337\) | 1.04584e6 | 0.501640 | 0.250820 | − | 0.968034i | \(-0.419300\pi\) | ||||
0.250820 | + | 0.968034i | \(0.419300\pi\) | |||||||
\(338\) | −21089.2 | −0.0100408 | ||||||||
\(339\) | −711523. | −0.336271 | ||||||||
\(340\) | −222703. | −0.104479 | ||||||||
\(341\) | −991746. | −0.461864 | ||||||||
\(342\) | 421070. | 0.194665 | ||||||||
\(343\) | 2.37060e6 | 1.08799 | ||||||||
\(344\) | 68594.7 | 0.0312532 | ||||||||
\(345\) | 352810. | 0.159585 | ||||||||
\(346\) | −333127. | −0.149596 | ||||||||
\(347\) | 1.90831e6 | 0.850796 | 0.425398 | − | 0.905006i | \(-0.360134\pi\) | ||||
0.425398 | + | 0.905006i | \(0.360134\pi\) | |||||||
\(348\) | −655694. | −0.290237 | ||||||||
\(349\) | 1.46350e6 | 0.643175 | 0.321588 | − | 0.946880i | \(-0.395784\pi\) | ||||
0.321588 | + | 0.946880i | \(0.395784\pi\) | |||||||
\(350\) | 142441. | 0.0621536 | ||||||||
\(351\) | 843874. | 0.365603 | ||||||||
\(352\) | −279433. | −0.120205 | ||||||||
\(353\) | 867374. | 0.370484 | 0.185242 | − | 0.982693i | \(-0.440693\pi\) | ||||
0.185242 | + | 0.982693i | \(0.440693\pi\) | |||||||
\(354\) | −80623.4 | −0.0341942 | ||||||||
\(355\) | −1.33362e6 | −0.561643 | ||||||||
\(356\) | −938575. | −0.392504 | ||||||||
\(357\) | −80508.6 | −0.0334327 | ||||||||
\(358\) | −111867. | −0.0461313 | ||||||||
\(359\) | 3.45466e6 | 1.41472 | 0.707359 | − | 0.706855i | \(-0.249887\pi\) | ||||
0.707359 | + | 0.706855i | \(0.249887\pi\) | |||||||
\(360\) | 240164. | 0.0976679 | ||||||||
\(361\) | 7.08751e6 | 2.86237 | ||||||||
\(362\) | 64571.2 | 0.0258981 | ||||||||
\(363\) | −415893. | −0.165659 | ||||||||
\(364\) | −1.90039e6 | −0.751778 | ||||||||
\(365\) | 1.17762e6 | 0.462672 | ||||||||
\(366\) | −12923.6 | −0.00504292 | ||||||||
\(367\) | −2.78797e6 | −1.08050 | −0.540248 | − | 0.841506i | \(-0.681670\pi\) | ||||
−0.540248 | + | 0.841506i | \(0.681670\pi\) | |||||||
\(368\) | 4.12811e6 | 1.58903 | ||||||||
\(369\) | 1.43712e6 | 0.549449 | ||||||||
\(370\) | −53200.0 | −0.0202026 | ||||||||
\(371\) | 3.15817e6 | 1.19125 | ||||||||
\(372\) | −606546. | −0.227251 | ||||||||
\(373\) | −1.65578e6 | −0.616212 | −0.308106 | − | 0.951352i | \(-0.599695\pi\) | ||||
−0.308106 | + | 0.951352i | \(0.599695\pi\) | |||||||
\(374\) | −23423.0 | −0.00865892 | ||||||||
\(375\) | −464569. | −0.170597 | ||||||||
\(376\) | −302617. | −0.110388 | ||||||||
\(377\) | −3.91997e6 | −1.42046 | ||||||||
\(378\) | 88086.4 | 0.0317088 | ||||||||
\(379\) | −2.35538e6 | −0.842291 | −0.421146 | − | 0.906993i | \(-0.638372\pi\) | ||||
−0.421146 | + | 0.906993i | \(0.638372\pi\) | |||||||
\(380\) | 2.71283e6 | 0.963749 | ||||||||
\(381\) | 333717. | 0.117779 | ||||||||
\(382\) | 172301. | 0.0604130 | ||||||||
\(383\) | −4.13864e6 | −1.44165 | −0.720827 | − | 0.693115i | \(-0.756238\pi\) | ||||
−0.720827 | + | 0.693115i | \(0.756238\pi\) | |||||||
\(384\) | −227449. | −0.0787146 | ||||||||
\(385\) | 454859. | 0.156396 | ||||||||
\(386\) | −219083. | −0.0748410 | ||||||||
\(387\) | 432012. | 0.146629 | ||||||||
\(388\) | 2.83172e6 | 0.954928 | ||||||||
\(389\) | −5.27781e6 | −1.76840 | −0.884198 | − | 0.467112i | \(-0.845294\pi\) | ||||
−0.884198 | + | 0.467112i | \(0.845294\pi\) | |||||||
\(390\) | −28586.5 | −0.00951700 | ||||||||
\(391\) | 1.05698e6 | 0.349643 | ||||||||
\(392\) | 224644. | 0.0738380 | ||||||||
\(393\) | 426412. | 0.139267 | ||||||||
\(394\) | −427056. | −0.138594 | ||||||||
\(395\) | −1.80519e6 | −0.582143 | ||||||||
\(396\) | −1.17117e6 | −0.375303 | ||||||||
\(397\) | 3.71439e6 | 1.18280 | 0.591401 | − | 0.806378i | \(-0.298575\pi\) | ||||
0.591401 | + | 0.806378i | \(0.298575\pi\) | |||||||
\(398\) | 343789. | 0.108789 | ||||||||
\(399\) | 980707. | 0.308395 | ||||||||
\(400\) | −2.33730e6 | −0.730405 | ||||||||
\(401\) | 3.60034e6 | 1.11810 | 0.559052 | − | 0.829132i | \(-0.311165\pi\) | ||||
0.559052 | + | 0.829132i | \(0.311165\pi\) | |||||||
\(402\) | 35085.4 | 0.0108283 | ||||||||
\(403\) | −3.62615e6 | −1.11220 | ||||||||
\(404\) | 906532. | 0.276331 | ||||||||
\(405\) | 1.44959e6 | 0.439143 | ||||||||
\(406\) | −409180. | −0.123197 | ||||||||
\(407\) | 521647. | 0.156096 | ||||||||
\(408\) | −28804.4 | −0.00856661 | ||||||||
\(409\) | 1.65305e6 | 0.488627 | 0.244314 | − | 0.969696i | \(-0.421437\pi\) | ||||
0.244314 | + | 0.969696i | \(0.421437\pi\) | |||||||
\(410\) | −99314.8 | −0.0291779 | ||||||||
\(411\) | −196331. | −0.0573304 | ||||||||
\(412\) | −953765. | −0.276821 | ||||||||
\(413\) | 4.69053e6 | 1.35315 | ||||||||
\(414\) | −566887. | −0.162553 | ||||||||
\(415\) | 1.95070e6 | 0.555994 | ||||||||
\(416\) | −1.02170e6 | −0.289461 | ||||||||
\(417\) | −861339. | −0.242568 | ||||||||
\(418\) | 285325. | 0.0798728 | ||||||||
\(419\) | 1.25123e6 | 0.348180 | 0.174090 | − | 0.984730i | \(-0.444302\pi\) | ||||
0.174090 | + | 0.984730i | \(0.444302\pi\) | |||||||
\(420\) | 278189. | 0.0769515 | ||||||||
\(421\) | 3.12108e6 | 0.858221 | 0.429111 | − | 0.903252i | \(-0.358827\pi\) | ||||
0.429111 | + | 0.903252i | \(0.358827\pi\) | |||||||
\(422\) | −216464. | −0.0591703 | ||||||||
\(423\) | −1.90589e6 | −0.517902 | ||||||||
\(424\) | 1.12993e6 | 0.305238 | ||||||||
\(425\) | −598451. | −0.160715 | ||||||||
\(426\) | −85785.1 | −0.0229028 | ||||||||
\(427\) | 751875. | 0.199561 | ||||||||
\(428\) | −2.63013e6 | −0.694015 | ||||||||
\(429\) | 280302. | 0.0735331 | ||||||||
\(430\) | −29855.0 | −0.00778656 | ||||||||
\(431\) | 246469. | 0.0639102 | 0.0319551 | − | 0.999489i | \(-0.489827\pi\) | ||||
0.0319551 | + | 0.999489i | \(0.489827\pi\) | |||||||
\(432\) | −1.44540e6 | −0.372630 | ||||||||
\(433\) | −7.56031e6 | −1.93785 | −0.968924 | − | 0.247357i | \(-0.920438\pi\) | ||||
−0.968924 | + | 0.247357i | \(0.920438\pi\) | |||||||
\(434\) | −378510. | −0.0964612 | ||||||||
\(435\) | 573826. | 0.145398 | ||||||||
\(436\) | −1.86111e6 | −0.468873 | ||||||||
\(437\) | −1.28755e7 | −3.22523 | ||||||||
\(438\) | 75750.6 | 0.0188669 | ||||||||
\(439\) | −3.76145e6 | −0.931525 | −0.465763 | − | 0.884910i | \(-0.654220\pi\) | ||||
−0.465763 | + | 0.884910i | \(0.654220\pi\) | |||||||
\(440\) | 162740. | 0.0400740 | ||||||||
\(441\) | 1.41482e6 | 0.346421 | ||||||||
\(442\) | −85642.2 | −0.0208513 | ||||||||
\(443\) | −1.02986e6 | −0.249327 | −0.124664 | − | 0.992199i | \(-0.539785\pi\) | ||||
−0.124664 | + | 0.992199i | \(0.539785\pi\) | |||||||
\(444\) | 319036. | 0.0768038 | ||||||||
\(445\) | 821387. | 0.196629 | ||||||||
\(446\) | −486920. | −0.115910 | ||||||||
\(447\) | 689333. | 0.163177 | ||||||||
\(448\) | 3.18327e6 | 0.749340 | ||||||||
\(449\) | −4.29961e6 | −1.00650 | −0.503249 | − | 0.864141i | \(-0.667862\pi\) | ||||
−0.503249 | + | 0.864141i | \(0.667862\pi\) | |||||||
\(450\) | 320965. | 0.0747183 | ||||||||
\(451\) | 973820. | 0.225443 | ||||||||
\(452\) | 7.36570e6 | 1.69577 | ||||||||
\(453\) | 1.18784e6 | 0.271966 | ||||||||
\(454\) | −211739. | −0.0482126 | ||||||||
\(455\) | 1.66312e6 | 0.376612 | ||||||||
\(456\) | 350878. | 0.0790213 | ||||||||
\(457\) | −1.42831e6 | −0.319913 | −0.159957 | − | 0.987124i | \(-0.551135\pi\) | ||||
−0.159957 | + | 0.987124i | \(0.551135\pi\) | |||||||
\(458\) | −61825.0 | −0.0137721 | ||||||||
\(459\) | −370085. | −0.0819917 | ||||||||
\(460\) | −3.65229e6 | −0.804768 | ||||||||
\(461\) | −3.06394e6 | −0.671472 | −0.335736 | − | 0.941956i | \(-0.608985\pi\) | ||||
−0.335736 | + | 0.941956i | \(0.608985\pi\) | |||||||
\(462\) | 29258.9 | 0.00637753 | ||||||||
\(463\) | −3.51890e6 | −0.762877 | −0.381438 | − | 0.924394i | \(-0.624571\pi\) | ||||
−0.381438 | + | 0.924394i | \(0.624571\pi\) | |||||||
\(464\) | 6.71416e6 | 1.44776 | ||||||||
\(465\) | 530815. | 0.113844 | ||||||||
\(466\) | 415945. | 0.0887302 | ||||||||
\(467\) | −6.90153e6 | −1.46438 | −0.732188 | − | 0.681102i | \(-0.761501\pi\) | ||||
−0.732188 | + | 0.681102i | \(0.761501\pi\) | |||||||
\(468\) | −4.28218e6 | −0.903755 | ||||||||
\(469\) | −2.04121e6 | −0.428504 | ||||||||
\(470\) | 131710. | 0.0275027 | ||||||||
\(471\) | −1.13041e6 | −0.234793 | ||||||||
\(472\) | 1.67818e6 | 0.346724 | ||||||||
\(473\) | 292740. | 0.0601629 | ||||||||
\(474\) | −116119. | −0.0237387 | ||||||||
\(475\) | 7.28997e6 | 1.48249 | ||||||||
\(476\) | 833426. | 0.168597 | ||||||||
\(477\) | 7.11636e6 | 1.43206 | ||||||||
\(478\) | −41025.8 | −0.00821272 | ||||||||
\(479\) | −4.37684e6 | −0.871609 | −0.435805 | − | 0.900041i | \(-0.643536\pi\) | ||||
−0.435805 | + | 0.900041i | \(0.643536\pi\) | |||||||
\(480\) | 149562. | 0.0296290 | ||||||||
\(481\) | 1.90731e6 | 0.375889 | ||||||||
\(482\) | 25991.1 | 0.00509574 | ||||||||
\(483\) | −1.32033e6 | −0.257522 | ||||||||
\(484\) | 4.30533e6 | 0.835398 | ||||||||
\(485\) | −2.47816e6 | −0.478382 | ||||||||
\(486\) | 299677. | 0.0575524 | ||||||||
\(487\) | 4.08443e6 | 0.780385 | 0.390192 | − | 0.920733i | \(-0.372409\pi\) | ||||
0.390192 | + | 0.920733i | \(0.372409\pi\) | |||||||
\(488\) | 269006. | 0.0511343 | ||||||||
\(489\) | 1.59710e6 | 0.302037 | ||||||||
\(490\) | −97773.6 | −0.0183963 | ||||||||
\(491\) | −4.67807e6 | −0.875716 | −0.437858 | − | 0.899044i | \(-0.644263\pi\) | ||||
−0.437858 | + | 0.899044i | \(0.644263\pi\) | |||||||
\(492\) | 595583. | 0.110925 | ||||||||
\(493\) | 1.71912e6 | 0.318559 | ||||||||
\(494\) | 1.04324e6 | 0.192339 | ||||||||
\(495\) | 1.02494e6 | 0.188012 | ||||||||
\(496\) | 6.21090e6 | 1.13357 | ||||||||
\(497\) | 4.99083e6 | 0.906321 | ||||||||
\(498\) | 125479. | 0.0226724 | ||||||||
\(499\) | 9.66466e6 | 1.73754 | 0.868771 | − | 0.495214i | \(-0.164910\pi\) | ||||
0.868771 | + | 0.495214i | \(0.164910\pi\) | |||||||
\(500\) | 4.80922e6 | 0.860300 | ||||||||
\(501\) | −52703.5 | −0.00938091 | ||||||||
\(502\) | 617655. | 0.109392 | ||||||||
\(503\) | −1.03319e7 | −1.82079 | −0.910396 | − | 0.413738i | \(-0.864223\pi\) | ||||
−0.910396 | + | 0.413738i | \(0.864223\pi\) | |||||||
\(504\) | −898772. | −0.157606 | ||||||||
\(505\) | −793345. | −0.138431 | ||||||||
\(506\) | −384133. | −0.0666969 | ||||||||
\(507\) | −110680. | −0.0191227 | ||||||||
\(508\) | −3.45464e6 | −0.593942 | ||||||||
\(509\) | −4.20006e6 | −0.718557 | −0.359278 | − | 0.933230i | \(-0.616977\pi\) | ||||
−0.359278 | + | 0.933230i | \(0.616977\pi\) | |||||||
\(510\) | 12536.8 | 0.00213432 | ||||||||
\(511\) | −4.40704e6 | −0.746611 | ||||||||
\(512\) | 2.92704e6 | 0.493463 | ||||||||
\(513\) | 4.50815e6 | 0.756320 | ||||||||
\(514\) | −562992. | −0.0939928 | ||||||||
\(515\) | 834681. | 0.138676 | ||||||||
\(516\) | 179038. | 0.0296020 | ||||||||
\(517\) | −1.29147e6 | −0.212500 | ||||||||
\(518\) | 199092. | 0.0326008 | ||||||||
\(519\) | −1.74830e6 | −0.284904 | ||||||||
\(520\) | 595030. | 0.0965007 | ||||||||
\(521\) | 6.46853e6 | 1.04403 | 0.522013 | − | 0.852938i | \(-0.325181\pi\) | ||||
0.522013 | + | 0.852938i | \(0.325181\pi\) | |||||||
\(522\) | −922012. | −0.148102 | ||||||||
\(523\) | −3.00248e6 | −0.479983 | −0.239991 | − | 0.970775i | \(-0.577145\pi\) | ||||
−0.239991 | + | 0.970775i | \(0.577145\pi\) | |||||||
\(524\) | −4.41423e6 | −0.702306 | ||||||||
\(525\) | 747556. | 0.118371 | ||||||||
\(526\) | 498411. | 0.0785458 | ||||||||
\(527\) | 1.59027e6 | 0.249427 | ||||||||
\(528\) | −480104. | −0.0749463 | ||||||||
\(529\) | 1.08979e7 | 1.69319 | ||||||||
\(530\) | −491789. | −0.0760482 | ||||||||
\(531\) | 1.05692e7 | 1.62670 | ||||||||
\(532\) | −1.01523e7 | −1.55520 | ||||||||
\(533\) | 3.56061e6 | 0.542883 | ||||||||
\(534\) | 52835.8 | 0.00801817 | ||||||||
\(535\) | 2.30175e6 | 0.347674 | ||||||||
\(536\) | −730304. | −0.109797 | ||||||||
\(537\) | −587098. | −0.0878566 | ||||||||
\(538\) | 904572. | 0.134737 | ||||||||
\(539\) | 958708. | 0.142139 | ||||||||
\(540\) | 1.27879e6 | 0.188719 | ||||||||
\(541\) | −5.21767e6 | −0.766449 | −0.383224 | − | 0.923655i | \(-0.625186\pi\) | ||||
−0.383224 | + | 0.923655i | \(0.625186\pi\) | |||||||
\(542\) | −2434.34 | −0.000355945 0 | ||||||||
\(543\) | 338880. | 0.0493227 | ||||||||
\(544\) | 448071. | 0.0649157 | ||||||||
\(545\) | 1.62874e6 | 0.234887 | ||||||||
\(546\) | 106980. | 0.0153575 | ||||||||
\(547\) | −7.86187e6 | −1.12346 | −0.561730 | − | 0.827321i | \(-0.689864\pi\) | ||||
−0.561730 | + | 0.827321i | \(0.689864\pi\) | |||||||
\(548\) | 2.03243e6 | 0.289110 | ||||||||
\(549\) | 1.69421e6 | 0.239903 | ||||||||
\(550\) | 217492. | 0.0306575 | ||||||||
\(551\) | −2.09413e7 | −2.93850 | ||||||||
\(552\) | −472387. | −0.0659858 | ||||||||
\(553\) | 6.75560e6 | 0.939401 | ||||||||
\(554\) | −930944. | −0.128869 | ||||||||
\(555\) | −279202. | −0.0384757 | ||||||||
\(556\) | 8.91659e6 | 1.22324 | ||||||||
\(557\) | 1.21531e7 | 1.65978 | 0.829889 | − | 0.557929i | \(-0.188404\pi\) | ||||
0.829889 | + | 0.557929i | \(0.188404\pi\) | |||||||
\(558\) | −852902. | −0.115961 | ||||||||
\(559\) | 1.07035e6 | 0.144876 | ||||||||
\(560\) | −2.84860e6 | −0.383850 | ||||||||
\(561\) | −122928. | −0.0164909 | ||||||||
\(562\) | 934177. | 0.124764 | ||||||||
\(563\) | 5.15518e6 | 0.685446 | 0.342723 | − | 0.939437i | \(-0.388651\pi\) | ||||
0.342723 | + | 0.939437i | \(0.388651\pi\) | |||||||
\(564\) | −789856. | −0.104556 | ||||||||
\(565\) | −6.44604e6 | −0.849517 | ||||||||
\(566\) | 1.19268e6 | 0.156489 | ||||||||
\(567\) | −5.42482e6 | −0.708643 | ||||||||
\(568\) | 1.78562e6 | 0.232230 | ||||||||
\(569\) | −1.42079e6 | −0.183972 | −0.0919858 | − | 0.995760i | \(-0.529321\pi\) | ||||
−0.0919858 | + | 0.995760i | \(0.529321\pi\) | |||||||
\(570\) | −152715. | −0.0196877 | ||||||||
\(571\) | −1.14786e7 | −1.47332 | −0.736661 | − | 0.676262i | \(-0.763599\pi\) | ||||
−0.736661 | + | 0.676262i | \(0.763599\pi\) | |||||||
\(572\) | −2.90169e6 | −0.370818 | ||||||||
\(573\) | 904266. | 0.115056 | ||||||||
\(574\) | 371668. | 0.0470842 | ||||||||
\(575\) | −9.81450e6 | −1.23794 | ||||||||
\(576\) | 7.17292e6 | 0.900824 | ||||||||
\(577\) | 1.00683e7 | 1.25897 | 0.629484 | − | 0.777014i | \(-0.283266\pi\) | ||||
0.629484 | + | 0.777014i | \(0.283266\pi\) | |||||||
\(578\) | −789867. | −0.0983409 | ||||||||
\(579\) | −1.14978e6 | −0.142534 | ||||||||
\(580\) | −5.94026e6 | −0.733221 | ||||||||
\(581\) | −7.30015e6 | −0.897205 | ||||||||
\(582\) | −159408. | −0.0195075 | ||||||||
\(583\) | 4.82218e6 | 0.587587 | ||||||||
\(584\) | −1.57675e6 | −0.191307 | ||||||||
\(585\) | 3.74752e6 | 0.452746 | ||||||||
\(586\) | 786877. | 0.0946592 | ||||||||
\(587\) | −1.33560e7 | −1.59985 | −0.799927 | − | 0.600097i | \(-0.795129\pi\) | ||||
−0.799927 | + | 0.600097i | \(0.795129\pi\) | |||||||
\(588\) | 586340. | 0.0699369 | ||||||||
\(589\) | −1.93716e7 | −2.30080 | ||||||||
\(590\) | −730407. | −0.0863843 | ||||||||
\(591\) | −2.24126e6 | −0.263951 | ||||||||
\(592\) | −3.26686e6 | −0.383113 | ||||||||
\(593\) | 1.20725e7 | 1.40981 | 0.704906 | − | 0.709301i | \(-0.250989\pi\) | ||||
0.704906 | + | 0.709301i | \(0.250989\pi\) | |||||||
\(594\) | 134498. | 0.0156405 | ||||||||
\(595\) | −729367. | −0.0844606 | ||||||||
\(596\) | −7.13598e6 | −0.822883 | ||||||||
\(597\) | 1.80426e6 | 0.207187 | ||||||||
\(598\) | −1.40452e6 | −0.160611 | ||||||||
\(599\) | 1.59735e7 | 1.81900 | 0.909502 | − | 0.415700i | \(-0.136463\pi\) | ||||
0.909502 | + | 0.415700i | \(0.136463\pi\) | |||||||
\(600\) | 267461. | 0.0303307 | ||||||||
\(601\) | 7.82358e6 | 0.883526 | 0.441763 | − | 0.897132i | \(-0.354353\pi\) | ||||
0.441763 | + | 0.897132i | \(0.354353\pi\) | |||||||
\(602\) | 111727. | 0.0125651 | ||||||||
\(603\) | −4.59948e6 | −0.515129 | ||||||||
\(604\) | −1.22966e7 | −1.37149 | ||||||||
\(605\) | −3.76778e6 | −0.418502 | ||||||||
\(606\) | −51032.0 | −0.00564496 | ||||||||
\(607\) | 3.67967e6 | 0.405356 | 0.202678 | − | 0.979245i | \(-0.435036\pi\) | ||||
0.202678 | + | 0.979245i | \(0.435036\pi\) | |||||||
\(608\) | −5.45813e6 | −0.598804 | ||||||||
\(609\) | −2.14744e6 | −0.234627 | ||||||||
\(610\) | −117082. | −0.0127398 | ||||||||
\(611\) | −4.72204e6 | −0.511713 | ||||||||
\(612\) | 1.87797e6 | 0.202680 | ||||||||
\(613\) | 4.33193e6 | 0.465619 | 0.232810 | − | 0.972522i | \(-0.425208\pi\) | ||||
0.232810 | + | 0.972522i | \(0.425208\pi\) | |||||||
\(614\) | −210434. | −0.0225265 | ||||||||
\(615\) | −521220. | −0.0555691 | ||||||||
\(616\) | −609025. | −0.0646671 | ||||||||
\(617\) | −6.45241e6 | −0.682353 | −0.341176 | − | 0.939999i | \(-0.610825\pi\) | ||||
−0.341176 | + | 0.939999i | \(0.610825\pi\) | |||||||
\(618\) | 53691.0 | 0.00565497 | ||||||||
\(619\) | 7.05387e6 | 0.739947 | 0.369974 | − | 0.929042i | \(-0.379367\pi\) | ||||
0.369974 | + | 0.929042i | \(0.379367\pi\) | |||||||
\(620\) | −5.49500e6 | −0.574101 | ||||||||
\(621\) | −6.06933e6 | −0.631556 | ||||||||
\(622\) | 1.23791e6 | 0.128296 | ||||||||
\(623\) | −3.07390e6 | −0.317299 | ||||||||
\(624\) | −1.75542e6 | −0.180476 | ||||||||
\(625\) | 3.15781e6 | 0.323359 | ||||||||
\(626\) | −315687. | −0.0321974 | ||||||||
\(627\) | 1.49743e6 | 0.152117 | ||||||||
\(628\) | 1.17021e7 | 1.18403 | ||||||||
\(629\) | −836461. | −0.0842984 | ||||||||
\(630\) | 391179. | 0.0392667 | ||||||||
\(631\) | 1.46818e7 | 1.46793 | 0.733966 | − | 0.679186i | \(-0.237667\pi\) | ||||
0.733966 | + | 0.679186i | \(0.237667\pi\) | |||||||
\(632\) | 2.41702e6 | 0.240706 | ||||||||
\(633\) | −1.13604e6 | −0.112689 | ||||||||
\(634\) | −1.78859e6 | −0.176721 | ||||||||
\(635\) | 3.02331e6 | 0.297542 | ||||||||
\(636\) | 2.94922e6 | 0.289111 | ||||||||
\(637\) | 3.50535e6 | 0.342281 | ||||||||
\(638\) | −624773. | −0.0607674 | ||||||||
\(639\) | 1.12459e7 | 1.08954 | ||||||||
\(640\) | −2.06057e6 | −0.198855 | ||||||||
\(641\) | 3.24675e6 | 0.312107 | 0.156054 | − | 0.987749i | \(-0.450123\pi\) | ||||
0.156054 | + | 0.987749i | \(0.450123\pi\) | |||||||
\(642\) | 148060. | 0.0141775 | ||||||||
\(643\) | −7.57964e6 | −0.722971 | −0.361486 | − | 0.932378i | \(-0.617730\pi\) | ||||
−0.361486 | + | 0.932378i | \(0.617730\pi\) | |||||||
\(644\) | 1.36680e7 | 1.29865 | ||||||||
\(645\) | −156684. | −0.0148294 | ||||||||
\(646\) | −457519. | −0.0431348 | ||||||||
\(647\) | 6.13290e6 | 0.575977 | 0.287988 | − | 0.957634i | \(-0.407014\pi\) | ||||
0.287988 | + | 0.957634i | \(0.407014\pi\) | |||||||
\(648\) | −1.94089e6 | −0.181578 | ||||||||
\(649\) | 7.16193e6 | 0.667449 | ||||||||
\(650\) | 795223. | 0.0738254 | ||||||||
\(651\) | −1.98648e6 | −0.183710 | ||||||||
\(652\) | −1.65332e7 | −1.52313 | ||||||||
\(653\) | −1.13174e6 | −0.103864 | −0.0519318 | − | 0.998651i | \(-0.516538\pi\) | ||||
−0.0519318 | + | 0.998651i | \(0.516538\pi\) | |||||||
\(654\) | 104769. | 0.00957827 | ||||||||
\(655\) | 3.86308e6 | 0.351828 | ||||||||
\(656\) | −6.09864e6 | −0.553316 | ||||||||
\(657\) | −9.93045e6 | −0.897544 | ||||||||
\(658\) | −492902. | −0.0443809 | ||||||||
\(659\) | 1.03411e7 | 0.927586 | 0.463793 | − | 0.885944i | \(-0.346488\pi\) | ||||
0.463793 | + | 0.885944i | \(0.346488\pi\) | |||||||
\(660\) | 424765. | 0.0379567 | ||||||||
\(661\) | −8.30708e6 | −0.739511 | −0.369756 | − | 0.929129i | \(-0.620559\pi\) | ||||
−0.369756 | + | 0.929129i | \(0.620559\pi\) | |||||||
\(662\) | −164444. | −0.0145838 | ||||||||
\(663\) | −449465. | −0.0397111 | ||||||||
\(664\) | −2.61185e6 | −0.229894 | ||||||||
\(665\) | 8.88471e6 | 0.779093 | ||||||||
\(666\) | 448616. | 0.0391913 | ||||||||
\(667\) | 2.81933e7 | 2.45376 | ||||||||
\(668\) | 545587. | 0.0473067 | ||||||||
\(669\) | −2.55544e6 | −0.220750 | ||||||||
\(670\) | 317856. | 0.0273554 | ||||||||
\(671\) | 1.14803e6 | 0.0984344 | ||||||||
\(672\) | −559708. | −0.0478121 | ||||||||
\(673\) | −1.13225e7 | −0.963617 | −0.481809 | − | 0.876276i | \(-0.660020\pi\) | ||||
−0.481809 | + | 0.876276i | \(0.660020\pi\) | |||||||
\(674\) | 609468. | 0.0516775 | ||||||||
\(675\) | 3.43639e6 | 0.290298 | ||||||||
\(676\) | 1.14576e6 | 0.0964331 | ||||||||
\(677\) | 2.12894e7 | 1.78522 | 0.892609 | − | 0.450831i | \(-0.148872\pi\) | ||||
0.892609 | + | 0.450831i | \(0.148872\pi\) | |||||||
\(678\) | −414642. | −0.0346417 | ||||||||
\(679\) | 9.27407e6 | 0.771962 | ||||||||
\(680\) | −260954. | −0.0216417 | ||||||||
\(681\) | −1.11124e6 | −0.0918205 | ||||||||
\(682\) | −577943. | −0.0475799 | ||||||||
\(683\) | −1.18724e7 | −0.973841 | −0.486920 | − | 0.873446i | \(-0.661880\pi\) | ||||
−0.486920 | + | 0.873446i | \(0.661880\pi\) | |||||||
\(684\) | −2.28763e7 | −1.86959 | ||||||||
\(685\) | −1.77866e6 | −0.144833 | ||||||||
\(686\) | 1.38147e6 | 0.112081 | ||||||||
\(687\) | −324468. | −0.0262289 | ||||||||
\(688\) | −1.83331e6 | −0.147661 | ||||||||
\(689\) | 1.76315e7 | 1.41495 | ||||||||
\(690\) | 205601. | 0.0164400 | ||||||||
\(691\) | −1.96927e7 | −1.56896 | −0.784478 | − | 0.620157i | \(-0.787069\pi\) | ||||
−0.784478 | + | 0.620157i | \(0.787069\pi\) | |||||||
\(692\) | 1.80985e7 | 1.43673 | ||||||||
\(693\) | −3.83566e6 | −0.303394 | ||||||||
\(694\) | 1.11207e6 | 0.0876465 | ||||||||
\(695\) | −7.80329e6 | −0.612796 | ||||||||
\(696\) | −768314. | −0.0601195 | ||||||||
\(697\) | −1.56152e6 | −0.121749 | ||||||||
\(698\) | 852859. | 0.0662581 | ||||||||
\(699\) | 2.18295e6 | 0.168986 | ||||||||
\(700\) | −7.73870e6 | −0.596930 | ||||||||
\(701\) | −1.36097e7 | −1.04605 | −0.523027 | − | 0.852316i | \(-0.675197\pi\) | ||||
−0.523027 | + | 0.852316i | \(0.675197\pi\) | |||||||
\(702\) | 491770. | 0.0376634 | ||||||||
\(703\) | 1.01893e7 | 0.777597 | ||||||||
\(704\) | 4.86051e6 | 0.369615 | ||||||||
\(705\) | 691237. | 0.0523786 | ||||||||
\(706\) | 505464. | 0.0381662 | ||||||||
\(707\) | 2.96895e6 | 0.223385 | ||||||||
\(708\) | 4.38019e6 | 0.328405 | ||||||||
\(709\) | 1.30274e7 | 0.973290 | 0.486645 | − | 0.873600i | \(-0.338220\pi\) | ||||
0.486645 | + | 0.873600i | \(0.338220\pi\) | |||||||
\(710\) | −777170. | −0.0578589 | ||||||||
\(711\) | 1.52225e7 | 1.12931 | ||||||||
\(712\) | −1.09978e6 | −0.0813029 | ||||||||
\(713\) | 2.60801e7 | 1.92125 | ||||||||
\(714\) | −46916.6 | −0.00344414 | ||||||||
\(715\) | 2.53939e6 | 0.185765 | ||||||||
\(716\) | 6.07764e6 | 0.443050 | ||||||||
\(717\) | −215310. | −0.0156411 | ||||||||
\(718\) | 2.01321e6 | 0.145740 | ||||||||
\(719\) | −9.11723e6 | −0.657719 | −0.328860 | − | 0.944379i | \(-0.606664\pi\) | ||||
−0.328860 | + | 0.944379i | \(0.606664\pi\) | |||||||
\(720\) | −6.41879e6 | −0.461447 | ||||||||
\(721\) | −3.12365e6 | −0.223781 | ||||||||
\(722\) | 4.13026e6 | 0.294873 | ||||||||
\(723\) | 136406. | 0.00970480 | ||||||||
\(724\) | −3.50809e6 | −0.248728 | ||||||||
\(725\) | −1.59628e7 | −1.12788 | ||||||||
\(726\) | −242363. | −0.0170657 | ||||||||
\(727\) | −1.52424e7 | −1.06959 | −0.534797 | − | 0.844981i | \(-0.679612\pi\) | ||||
−0.534797 | + | 0.844981i | \(0.679612\pi\) | |||||||
\(728\) | −2.22680e6 | −0.155723 | ||||||||
\(729\) | −1.11404e7 | −0.776396 | ||||||||
\(730\) | 686262. | 0.0476631 | ||||||||
\(731\) | −469408. | −0.0324906 | ||||||||
\(732\) | 702128. | 0.0484327 | ||||||||
\(733\) | −1.61394e7 | −1.10950 | −0.554751 | − | 0.832016i | \(-0.687187\pi\) | ||||
−0.554751 | + | 0.832016i | \(0.687187\pi\) | |||||||
\(734\) | −1.62470e6 | −0.111310 | ||||||||
\(735\) | −513132. | −0.0350357 | ||||||||
\(736\) | 7.34828e6 | 0.500025 | ||||||||
\(737\) | −3.11670e6 | −0.211362 | ||||||||
\(738\) | 837486. | 0.0566026 | ||||||||
\(739\) | −9.24471e6 | −0.622704 | −0.311352 | − | 0.950295i | \(-0.600782\pi\) | ||||
−0.311352 | + | 0.950295i | \(0.600782\pi\) | |||||||
\(740\) | 2.89031e6 | 0.194028 | ||||||||
\(741\) | 5.47510e6 | 0.366308 | ||||||||
\(742\) | 1.84043e6 | 0.122719 | ||||||||
\(743\) | −3.89612e6 | −0.258917 | −0.129459 | − | 0.991585i | \(-0.541324\pi\) | ||||
−0.129459 | + | 0.991585i | \(0.541324\pi\) | |||||||
\(744\) | −710724. | −0.0470727 | ||||||||
\(745\) | 6.24501e6 | 0.412233 | ||||||||
\(746\) | −964909. | −0.0634804 | ||||||||
\(747\) | −1.64495e7 | −1.07858 | ||||||||
\(748\) | 1.27255e6 | 0.0831613 | ||||||||
\(749\) | −8.61387e6 | −0.561040 | ||||||||
\(750\) | −270729. | −0.0175744 | ||||||||
\(751\) | −2.36303e7 | −1.52887 | −0.764433 | − | 0.644704i | \(-0.776981\pi\) | ||||
−0.764433 | + | 0.644704i | \(0.776981\pi\) | |||||||
\(752\) | 8.08795e6 | 0.521547 | ||||||||
\(753\) | 3.24155e6 | 0.208337 | ||||||||
\(754\) | −2.28437e6 | −0.146332 | ||||||||
\(755\) | 1.07613e7 | 0.687062 | ||||||||
\(756\) | −4.78565e6 | −0.304535 | ||||||||
\(757\) | 2.86009e6 | 0.181401 | 0.0907005 | − | 0.995878i | \(-0.471089\pi\) | ||||
0.0907005 | + | 0.995878i | \(0.471089\pi\) | |||||||
\(758\) | −1.37260e6 | −0.0867704 | ||||||||
\(759\) | −2.01599e6 | −0.127024 | ||||||||
\(760\) | 3.17878e6 | 0.199630 | ||||||||
\(761\) | −2.90585e7 | −1.81891 | −0.909456 | − | 0.415800i | \(-0.863502\pi\) | ||||
−0.909456 | + | 0.415800i | \(0.863502\pi\) | |||||||
\(762\) | 194475. | 0.0121332 | ||||||||
\(763\) | −6.09526e6 | −0.379036 | ||||||||
\(764\) | −9.36097e6 | −0.580213 | ||||||||
\(765\) | −1.64350e6 | −0.101535 | ||||||||
\(766\) | −2.41180e6 | −0.148515 | ||||||||
\(767\) | 2.61864e7 | 1.60726 | ||||||||
\(768\) | 2.87200e6 | 0.175704 | ||||||||
\(769\) | −1.85731e7 | −1.13258 | −0.566290 | − | 0.824206i | \(-0.691622\pi\) | ||||
−0.566290 | + | 0.824206i | \(0.691622\pi\) | |||||||
\(770\) | 265071. | 0.0161115 | ||||||||
\(771\) | −2.95468e6 | −0.179009 | ||||||||
\(772\) | 1.19026e7 | 0.718781 | ||||||||
\(773\) | 1.38698e7 | 0.834872 | 0.417436 | − | 0.908706i | \(-0.362929\pi\) | ||||
0.417436 | + | 0.908706i | \(0.362929\pi\) | |||||||
\(774\) | 251756. | 0.0151052 | ||||||||
\(775\) | −1.47663e7 | −0.883113 | ||||||||
\(776\) | 3.31808e6 | 0.197803 | ||||||||
\(777\) | 1.04487e6 | 0.0620881 | ||||||||
\(778\) | −3.07566e6 | −0.182175 | ||||||||
\(779\) | 1.90215e7 | 1.12306 | ||||||||
\(780\) | 1.55308e6 | 0.0914023 | ||||||||
\(781\) | 7.62045e6 | 0.447047 | ||||||||
\(782\) | 615958. | 0.0360192 | ||||||||
\(783\) | −9.87145e6 | −0.575409 | ||||||||
\(784\) | −6.00400e6 | −0.348859 | ||||||||
\(785\) | −1.02410e7 | −0.593154 | ||||||||
\(786\) | 248493. | 0.0143469 | ||||||||
\(787\) | −1.95803e7 | −1.12689 | −0.563445 | − | 0.826154i | \(-0.690524\pi\) | ||||
−0.563445 | + | 0.826154i | \(0.690524\pi\) | |||||||
\(788\) | 2.32015e7 | 1.33107 | ||||||||
\(789\) | 2.61574e6 | 0.149590 | ||||||||
\(790\) | −1.05198e6 | −0.0599707 | ||||||||
\(791\) | 2.41232e7 | 1.37086 | ||||||||
\(792\) | −1.37233e6 | −0.0777400 | ||||||||
\(793\) | 4.19757e6 | 0.237037 | ||||||||
\(794\) | 2.16457e6 | 0.121849 | ||||||||
\(795\) | −2.58099e6 | −0.144833 | ||||||||
\(796\) | −1.86777e7 | −1.04482 | ||||||||
\(797\) | −2.66479e7 | −1.48600 | −0.742998 | − | 0.669293i | \(-0.766597\pi\) | ||||
−0.742998 | + | 0.669293i | \(0.766597\pi\) | |||||||
\(798\) | 571510. | 0.0317699 | ||||||||
\(799\) | 2.07087e6 | 0.114759 | ||||||||
\(800\) | −4.16052e6 | −0.229839 | ||||||||
\(801\) | −6.92646e6 | −0.381443 | ||||||||
\(802\) | 2.09811e6 | 0.115184 | ||||||||
\(803\) | −6.72907e6 | −0.368270 | ||||||||
\(804\) | −1.90615e6 | −0.103996 | ||||||||
\(805\) | −1.19615e7 | −0.650573 | ||||||||
\(806\) | −2.11315e6 | −0.114576 | ||||||||
\(807\) | 4.74734e6 | 0.256606 | ||||||||
\(808\) | 1.06223e6 | 0.0572390 | ||||||||
\(809\) | 4.31569e6 | 0.231835 | 0.115917 | − | 0.993259i | \(-0.463019\pi\) | ||||
0.115917 | + | 0.993259i | \(0.463019\pi\) | |||||||
\(810\) | 844750. | 0.0452393 | ||||||||
\(811\) | 1.07890e7 | 0.576007 | 0.288003 | − | 0.957629i | \(-0.407009\pi\) | ||||
0.288003 | + | 0.957629i | \(0.407009\pi\) | |||||||
\(812\) | 2.22304e7 | 1.18320 | ||||||||
\(813\) | −12775.8 | −0.000677894 0 | ||||||||
\(814\) | 303991. | 0.0160805 | ||||||||
\(815\) | 1.44689e7 | 0.763031 | ||||||||
\(816\) | 769847. | 0.0404743 | ||||||||
\(817\) | 5.71805e6 | 0.299704 | ||||||||
\(818\) | 963319. | 0.0503369 | ||||||||
\(819\) | −1.40244e7 | −0.730594 | ||||||||
\(820\) | 5.39568e6 | 0.280228 | ||||||||
\(821\) | −2.12759e7 | −1.10162 | −0.550808 | − | 0.834632i | \(-0.685680\pi\) | ||||
−0.550808 | + | 0.834632i | \(0.685680\pi\) | |||||||
\(822\) | −114413. | −0.00590602 | ||||||||
\(823\) | 7.04803e6 | 0.362717 | 0.181359 | − | 0.983417i | \(-0.441950\pi\) | ||||
0.181359 | + | 0.983417i | \(0.441950\pi\) | |||||||
\(824\) | −1.11758e6 | −0.0573404 | ||||||||
\(825\) | 1.14144e6 | 0.0583870 | ||||||||
\(826\) | 2.73342e6 | 0.139398 | ||||||||
\(827\) | 2.00838e7 | 1.02113 | 0.510566 | − | 0.859839i | \(-0.329436\pi\) | ||||
0.510566 | + | 0.859839i | \(0.329436\pi\) | |||||||
\(828\) | 3.07984e7 | 1.56118 | ||||||||
\(829\) | 2.04193e7 | 1.03194 | 0.515970 | − | 0.856606i | \(-0.327431\pi\) | ||||
0.515970 | + | 0.856606i | \(0.327431\pi\) | |||||||
\(830\) | 1.13678e6 | 0.0572769 | ||||||||
\(831\) | −4.88575e6 | −0.245431 | ||||||||
\(832\) | 1.77716e7 | 0.890059 | ||||||||
\(833\) | −1.53729e6 | −0.0767614 | ||||||||
\(834\) | −501948. | −0.0249887 | ||||||||
\(835\) | −477467. | −0.0236988 | ||||||||
\(836\) | −1.55014e7 | −0.767108 | ||||||||
\(837\) | −9.13153e6 | −0.450537 | ||||||||
\(838\) | 729160. | 0.0358685 | ||||||||
\(839\) | −4.92445e6 | −0.241520 | −0.120760 | − | 0.992682i | \(-0.538533\pi\) | ||||
−0.120760 | + | 0.992682i | \(0.538533\pi\) | |||||||
\(840\) | 325970. | 0.0159397 | ||||||||
\(841\) | 2.53438e7 | 1.23561 | ||||||||
\(842\) | 1.81882e6 | 0.0884114 | ||||||||
\(843\) | 4.90271e6 | 0.237612 | ||||||||
\(844\) | 1.17603e7 | 0.568278 | ||||||||
\(845\) | −1.00270e6 | −0.0483092 | ||||||||
\(846\) | −1.11066e6 | −0.0533528 | ||||||||
\(847\) | 1.41003e7 | 0.675334 | ||||||||
\(848\) | −3.01994e7 | −1.44214 | ||||||||
\(849\) | 6.25940e6 | 0.298032 | ||||||||
\(850\) | −348749. | −0.0165564 | ||||||||
\(851\) | −1.37178e7 | −0.649324 | ||||||||
\(852\) | 4.66062e6 | 0.219961 | ||||||||
\(853\) | −1.25088e7 | −0.588632 | −0.294316 | − | 0.955708i | \(-0.595092\pi\) | ||||
−0.294316 | + | 0.955708i | \(0.595092\pi\) | |||||||
\(854\) | 438157. | 0.0205582 | ||||||||
\(855\) | 2.00201e7 | 0.936591 | ||||||||
\(856\) | −3.08188e6 | −0.143758 | ||||||||
\(857\) | 2.21879e7 | 1.03196 | 0.515982 | − | 0.856600i | \(-0.327427\pi\) | ||||
0.515982 | + | 0.856600i | \(0.327427\pi\) | |||||||
\(858\) | 163347. | 0.00757517 | ||||||||
\(859\) | −1.40835e7 | −0.651218 | −0.325609 | − | 0.945505i | \(-0.605569\pi\) | ||||
−0.325609 | + | 0.945505i | \(0.605569\pi\) | |||||||
\(860\) | 1.62199e6 | 0.0747830 | ||||||||
\(861\) | 1.95058e6 | 0.0896716 | ||||||||
\(862\) | 143631. | 0.00658384 | ||||||||
\(863\) | −7.94491e6 | −0.363130 | −0.181565 | − | 0.983379i | \(-0.558116\pi\) | ||||
−0.181565 | + | 0.983379i | \(0.558116\pi\) | |||||||
\(864\) | −2.57289e6 | −0.117256 | ||||||||
\(865\) | −1.58387e7 | −0.719748 | ||||||||
\(866\) | −4.40579e6 | −0.199632 | ||||||||
\(867\) | −4.14535e6 | −0.187290 | ||||||||
\(868\) | 2.05641e7 | 0.926424 | ||||||||
\(869\) | 1.03151e7 | 0.463364 | ||||||||
\(870\) | 334399. | 0.0149784 | ||||||||
\(871\) | −1.13957e7 | −0.508973 | ||||||||
\(872\) | −2.18077e6 | −0.0971221 | ||||||||
\(873\) | 2.08974e7 | 0.928019 | ||||||||
\(874\) | −7.50323e6 | −0.332253 | ||||||||
\(875\) | 1.57505e7 | 0.695465 | ||||||||
\(876\) | −4.11546e6 | −0.181200 | ||||||||
\(877\) | −4.03970e6 | −0.177358 | −0.0886788 | − | 0.996060i | \(-0.528264\pi\) | ||||
−0.0886788 | + | 0.996060i | \(0.528264\pi\) | |||||||
\(878\) | −2.19200e6 | −0.0959630 | ||||||||
\(879\) | 4.12966e6 | 0.180278 | ||||||||
\(880\) | −4.34950e6 | −0.189336 | ||||||||
\(881\) | −1.99840e7 | −0.867447 | −0.433724 | − | 0.901046i | \(-0.642801\pi\) | ||||
−0.433724 | + | 0.901046i | \(0.642801\pi\) | |||||||
\(882\) | 824489. | 0.0356873 | ||||||||
\(883\) | 1.66868e7 | 0.720230 | 0.360115 | − | 0.932908i | \(-0.382737\pi\) | ||||
0.360115 | + | 0.932908i | \(0.382737\pi\) | |||||||
\(884\) | 4.65286e6 | 0.200258 | ||||||||
\(885\) | −3.83330e6 | −0.164518 | ||||||||
\(886\) | −600155. | −0.0256850 | ||||||||
\(887\) | −1.79964e6 | −0.0768027 | −0.0384014 | − | 0.999262i | \(-0.512227\pi\) | ||||
−0.0384014 | + | 0.999262i | \(0.512227\pi\) | |||||||
\(888\) | 373833. | 0.0159091 | ||||||||
\(889\) | −1.13142e7 | −0.480141 | ||||||||
\(890\) | 478666. | 0.0202562 | ||||||||
\(891\) | −8.28310e6 | −0.349541 | ||||||||
\(892\) | 2.64539e7 | 1.11321 | ||||||||
\(893\) | −2.52261e7 | −1.05858 | ||||||||
\(894\) | 401711. | 0.0168101 | ||||||||
\(895\) | −5.31881e6 | −0.221951 | ||||||||
\(896\) | 7.71131e6 | 0.320892 | ||||||||
\(897\) | −7.37114e6 | −0.305882 | ||||||||
\(898\) | −2.50561e6 | −0.103687 | ||||||||
\(899\) | 4.24179e7 | 1.75045 | ||||||||
\(900\) | −1.74377e7 | −0.717603 | ||||||||
\(901\) | −7.73238e6 | −0.317323 | ||||||||
\(902\) | 567496. | 0.0232245 | ||||||||
\(903\) | 586362. | 0.0239302 | ||||||||
\(904\) | 8.63080e6 | 0.351261 | ||||||||
\(905\) | 3.07008e6 | 0.124603 | ||||||||
\(906\) | 692219. | 0.0280171 | ||||||||
\(907\) | −3.64748e6 | −0.147223 | −0.0736113 | − | 0.997287i | \(-0.523452\pi\) | ||||
−0.0736113 | + | 0.997287i | \(0.523452\pi\) | |||||||
\(908\) | 1.15036e7 | 0.463039 | ||||||||
\(909\) | 6.68999e6 | 0.268544 | ||||||||
\(910\) | 969185. | 0.0387974 | ||||||||
\(911\) | 4.92223e6 | 0.196502 | 0.0982508 | − | 0.995162i | \(-0.468675\pi\) | ||||
0.0982508 | + | 0.995162i | \(0.468675\pi\) | |||||||
\(912\) | −9.37781e6 | −0.373348 | ||||||||
\(913\) | −1.11465e7 | −0.442551 | ||||||||
\(914\) | −832352. | −0.0329565 | ||||||||
\(915\) | −614463. | −0.0242629 | ||||||||
\(916\) | 3.35890e6 | 0.132269 | ||||||||
\(917\) | −1.44569e7 | −0.567743 | ||||||||
\(918\) | −215668. | −0.00844655 | ||||||||
\(919\) | 1.52960e7 | 0.597432 | 0.298716 | − | 0.954342i | \(-0.403442\pi\) | ||||
0.298716 | + | 0.954342i | \(0.403442\pi\) | |||||||
\(920\) | −4.27959e6 | −0.166699 | ||||||||
\(921\) | −1.10439e6 | −0.0429016 | ||||||||
\(922\) | −1.78552e6 | −0.0691731 | ||||||||
\(923\) | 2.78629e7 | 1.07652 | ||||||||
\(924\) | −1.58961e6 | −0.0612505 | ||||||||
\(925\) | 7.76689e6 | 0.298464 | ||||||||
\(926\) | −2.05065e6 | −0.0785893 | ||||||||
\(927\) | −7.03856e6 | −0.269020 | ||||||||
\(928\) | 1.19516e7 | 0.455571 | ||||||||
\(929\) | 3.10755e7 | 1.18135 | 0.590674 | − | 0.806910i | \(-0.298862\pi\) | ||||
0.590674 | + | 0.806910i | \(0.298862\pi\) | |||||||
\(930\) | 309334. | 0.0117279 | ||||||||
\(931\) | 1.87263e7 | 0.708073 | ||||||||
\(932\) | −2.25979e7 | −0.852175 | ||||||||
\(933\) | 6.49676e6 | 0.244339 | ||||||||
\(934\) | −4.02188e6 | −0.150856 | ||||||||
\(935\) | −1.11366e6 | −0.0416606 | ||||||||
\(936\) | −5.01767e6 | −0.187203 | ||||||||
\(937\) | −3.19233e7 | −1.18784 | −0.593922 | − | 0.804523i | \(-0.702421\pi\) | ||||
−0.593922 | + | 0.804523i | \(0.702421\pi\) | |||||||
\(938\) | −1.18952e6 | −0.0441432 | ||||||||
\(939\) | −1.65678e6 | −0.0613198 | ||||||||
\(940\) | −7.15569e6 | −0.264139 | ||||||||
\(941\) | −4.89415e7 | −1.80179 | −0.900894 | − | 0.434040i | \(-0.857088\pi\) | ||||
−0.900894 | + | 0.434040i | \(0.857088\pi\) | |||||||
\(942\) | −658752. | −0.0241877 | ||||||||
\(943\) | −2.56087e7 | −0.937795 | ||||||||
\(944\) | −4.48522e7 | −1.63815 | ||||||||
\(945\) | 4.18813e6 | 0.152560 | ||||||||
\(946\) | 170595. | 0.00619781 | ||||||||
\(947\) | −1.45580e7 | −0.527505 | −0.263753 | − | 0.964590i | \(-0.584960\pi\) | ||||
−0.263753 | + | 0.964590i | \(0.584960\pi\) | |||||||
\(948\) | 6.30863e6 | 0.227989 | ||||||||
\(949\) | −2.46037e7 | −0.886818 | ||||||||
\(950\) | 4.24825e6 | 0.152722 | ||||||||
\(951\) | −9.38680e6 | −0.336563 | ||||||||
\(952\) | 976572. | 0.0349230 | ||||||||
\(953\) | −2.71191e7 | −0.967261 | −0.483631 | − | 0.875272i | \(-0.660682\pi\) | ||||
−0.483631 | + | 0.875272i | \(0.660682\pi\) | |||||||
\(954\) | 4.14708e6 | 0.147527 | ||||||||
\(955\) | 8.19219e6 | 0.290664 | ||||||||
\(956\) | 2.22889e6 | 0.0788759 | ||||||||
\(957\) | −3.27891e6 | −0.115731 | ||||||||
\(958\) | −2.55062e6 | −0.0897907 | ||||||||
\(959\) | 6.65633e6 | 0.233716 | ||||||||
\(960\) | −2.60150e6 | −0.0911059 | ||||||||
\(961\) | 1.06093e7 | 0.370576 | ||||||||
\(962\) | 1.11149e6 | 0.0387229 | ||||||||
\(963\) | −1.94098e7 | −0.674458 | ||||||||
\(964\) | −1.41207e6 | −0.0489401 | ||||||||
\(965\) | −1.04164e7 | −0.360082 | ||||||||
\(966\) | −769424. | −0.0265291 | ||||||||
\(967\) | 1.16883e7 | 0.401963 | 0.200982 | − | 0.979595i | \(-0.435587\pi\) | ||||
0.200982 | + | 0.979595i | \(0.435587\pi\) | |||||||
\(968\) | 5.04480e6 | 0.173044 | ||||||||
\(969\) | −2.40113e6 | −0.0821499 | ||||||||
\(970\) | −1.44415e6 | −0.0492815 | ||||||||
\(971\) | 3.07622e6 | 0.104706 | 0.0523528 | − | 0.998629i | \(-0.483328\pi\) | ||||
0.0523528 | + | 0.998629i | \(0.483328\pi\) | |||||||
\(972\) | −1.62812e7 | −0.552739 | ||||||||
\(973\) | 2.92024e7 | 0.988865 | ||||||||
\(974\) | 2.38021e6 | 0.0803930 | ||||||||
\(975\) | 4.17346e6 | 0.140600 | ||||||||
\(976\) | −7.18964e6 | −0.241592 | ||||||||
\(977\) | 3.81186e7 | 1.27762 | 0.638809 | − | 0.769365i | \(-0.279427\pi\) | ||||
0.638809 | + | 0.769365i | \(0.279427\pi\) | |||||||
\(978\) | 930714. | 0.0311150 | ||||||||
\(979\) | −4.69350e6 | −0.156509 | ||||||||
\(980\) | 5.31195e6 | 0.176680 | ||||||||
\(981\) | −1.37345e7 | −0.455661 | ||||||||
\(982\) | −2.72616e6 | −0.0902137 | ||||||||
\(983\) | −3.14497e7 | −1.03809 | −0.519043 | − | 0.854748i | \(-0.673711\pi\) | ||||
−0.519043 | + | 0.854748i | \(0.673711\pi\) | |||||||
\(984\) | 697878. | 0.0229769 | ||||||||
\(985\) | −2.03047e7 | −0.666815 | ||||||||
\(986\) | 1.00182e6 | 0.0328170 | ||||||||
\(987\) | −2.58683e6 | −0.0845231 | ||||||||
\(988\) | −5.66783e7 | −1.84725 | ||||||||
\(989\) | −7.69821e6 | −0.250264 | ||||||||
\(990\) | 597288. | 0.0193685 | ||||||||
\(991\) | 1.08378e7 | 0.350555 | 0.175277 | − | 0.984519i | \(-0.443918\pi\) | ||||
0.175277 | + | 0.984519i | \(0.443918\pi\) | |||||||
\(992\) | 1.10558e7 | 0.356705 | ||||||||
\(993\) | −863027. | −0.0277748 | ||||||||
\(994\) | 2.90842e6 | 0.0933665 | ||||||||
\(995\) | 1.63457e7 | 0.523414 | ||||||||
\(996\) | −6.81715e6 | −0.217748 | ||||||||
\(997\) | −1.37214e7 | −0.437179 | −0.218590 | − | 0.975817i | \(-0.570146\pi\) | ||||
−0.218590 | + | 0.975817i | \(0.570146\pi\) | |||||||
\(998\) | 5.63211e6 | 0.178997 | ||||||||
\(999\) | 4.80308e6 | 0.152267 |
(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 | 43.6.a.a.1.5 | ✓ | 8 | |
3.2 | odd | 2 | 387.6.a.c.1.4 | 8 | |||
4.3 | odd | 2 | 688.6.a.e.1.4 | 8 | |||
5.4 | even | 2 | 1075.6.a.a.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.a.a.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
387.6.a.c.1.4 | 8 | 3.2 | odd | 2 | |||
688.6.a.e.1.4 | 8 | 4.3 | odd | 2 | |||
1075.6.a.a.1.4 | 8 | 5.4 | even | 2 |