Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 109x^{4} + 41x^{3} + 2208x^{2} - 3204x + 560 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(9.72556\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.72556 | 1.54248 | 0.771238 | − | 0.636547i | \(-0.219638\pi\) | ||||
0.771238 | + | 0.636547i | \(0.219638\pi\) | |||||||
\(3\) | 4.73965 | 0.304048 | 0.152024 | − | 0.988377i | \(-0.451421\pi\) | ||||
0.152024 | + | 0.988377i | \(0.451421\pi\) | |||||||
\(4\) | 44.1354 | 1.37923 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 41.3561 | 0.468987 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 105.888 | 0.584955 | ||||||||
\(9\) | −220.536 | −0.907555 | ||||||||
\(10\) | −218.139 | −0.689816 | ||||||||
\(11\) | −679.156 | −1.69234 | −0.846171 | − | 0.532912i | \(-0.821098\pi\) | ||||
−0.846171 | + | 0.532912i | \(0.821098\pi\) | |||||||
\(12\) | 209.186 | 0.419353 | ||||||||
\(13\) | 58.8790 | 0.0966279 | 0.0483139 | − | 0.998832i | \(-0.484615\pi\) | ||||
0.0483139 | + | 0.998832i | \(0.484615\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −118.491 | −0.135975 | ||||||||
\(16\) | −488.399 | −0.476952 | ||||||||
\(17\) | 1427.56 | 1.19804 | 0.599020 | − | 0.800734i | \(-0.295557\pi\) | ||||
0.599020 | + | 0.800734i | \(0.295557\pi\) | |||||||
\(18\) | −1924.30 | −1.39988 | ||||||||
\(19\) | −2197.34 | −1.39641 | −0.698205 | − | 0.715898i | \(-0.746017\pi\) | ||||
−0.698205 | + | 0.715898i | \(0.746017\pi\) | |||||||
\(20\) | −1103.39 | −0.616811 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5926.02 | −2.61040 | ||||||||
\(23\) | −2223.33 | −0.876365 | −0.438182 | − | 0.898886i | \(-0.644378\pi\) | ||||
−0.438182 | + | 0.898886i | \(0.644378\pi\) | |||||||
\(24\) | 501.873 | 0.177855 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 513.753 | 0.149046 | ||||||||
\(27\) | −2197.00 | −0.579989 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2079.59 | 0.459179 | 0.229590 | − | 0.973288i | \(-0.426262\pi\) | ||||
0.229590 | + | 0.973288i | \(0.426262\pi\) | |||||||
\(30\) | −1033.90 | −0.209738 | ||||||||
\(31\) | 3599.58 | 0.672741 | 0.336371 | − | 0.941730i | \(-0.390801\pi\) | ||||
0.336371 | + | 0.941730i | \(0.390801\pi\) | |||||||
\(32\) | −7649.98 | −1.32064 | ||||||||
\(33\) | −3218.96 | −0.514554 | ||||||||
\(34\) | 12456.2 | 1.84795 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9733.43 | −1.25173 | ||||||||
\(37\) | 9181.95 | 1.10263 | 0.551316 | − | 0.834296i | \(-0.314126\pi\) | ||||
0.551316 | + | 0.834296i | \(0.314126\pi\) | |||||||
\(38\) | −19173.0 | −2.15393 | ||||||||
\(39\) | 279.066 | 0.0293796 | ||||||||
\(40\) | −2647.21 | −0.261600 | ||||||||
\(41\) | 10061.1 | 0.934732 | 0.467366 | − | 0.884064i | \(-0.345203\pi\) | ||||
0.467366 | + | 0.884064i | \(0.345203\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −13956.6 | −1.15108 | −0.575542 | − | 0.817772i | \(-0.695209\pi\) | ||||
−0.575542 | + | 0.817772i | \(0.695209\pi\) | |||||||
\(44\) | −29974.8 | −2.33413 | ||||||||
\(45\) | 5513.39 | 0.405871 | ||||||||
\(46\) | −19399.8 | −1.35177 | ||||||||
\(47\) | −16272.5 | −1.07451 | −0.537254 | − | 0.843420i | \(-0.680538\pi\) | ||||
−0.537254 | + | 0.843420i | \(0.680538\pi\) | |||||||
\(48\) | −2314.84 | −0.145017 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 5453.48 | 0.308495 | ||||||||
\(51\) | 6766.12 | 0.364262 | ||||||||
\(52\) | 2598.65 | 0.133272 | ||||||||
\(53\) | 1267.14 | 0.0619634 | 0.0309817 | − | 0.999520i | \(-0.490137\pi\) | ||||
0.0309817 | + | 0.999520i | \(0.490137\pi\) | |||||||
\(54\) | −19170.0 | −0.894619 | ||||||||
\(55\) | 16978.9 | 0.756838 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10414.6 | −0.424576 | ||||||||
\(58\) | 18145.6 | 0.708273 | ||||||||
\(59\) | −13465.7 | −0.503615 | −0.251807 | − | 0.967777i | \(-0.581025\pi\) | ||||
−0.251807 | + | 0.967777i | \(0.581025\pi\) | |||||||
\(60\) | −5229.66 | −0.187540 | ||||||||
\(61\) | 35031.5 | 1.20541 | 0.602703 | − | 0.797965i | \(-0.294090\pi\) | ||||
0.602703 | + | 0.797965i | \(0.294090\pi\) | |||||||
\(62\) | 31408.4 | 1.03769 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −51121.6 | −1.56011 | ||||||||
\(65\) | −1471.98 | −0.0432133 | ||||||||
\(66\) | −28087.2 | −0.793687 | ||||||||
\(67\) | −36919.0 | −1.00476 | −0.502380 | − | 0.864647i | \(-0.667542\pi\) | ||||
−0.502380 | + | 0.864647i | \(0.667542\pi\) | |||||||
\(68\) | 63005.9 | 1.65237 | ||||||||
\(69\) | −10537.8 | −0.266457 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4118.92 | 0.0969700 | 0.0484850 | − | 0.998824i | \(-0.484561\pi\) | ||||
0.0484850 | + | 0.998824i | \(0.484561\pi\) | |||||||
\(72\) | −23352.1 | −0.530879 | ||||||||
\(73\) | −3517.37 | −0.0772521 | −0.0386261 | − | 0.999254i | \(-0.512298\pi\) | ||||
−0.0386261 | + | 0.999254i | \(0.512298\pi\) | |||||||
\(74\) | 80117.7 | 1.70078 | ||||||||
\(75\) | 2962.28 | 0.0608097 | ||||||||
\(76\) | −96980.4 | −1.92597 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 2435.01 | 0.0453173 | ||||||||
\(79\) | −72440.8 | −1.30592 | −0.652959 | − | 0.757394i | \(-0.726472\pi\) | ||||
−0.652959 | + | 0.757394i | \(0.726472\pi\) | |||||||
\(80\) | 12210.0 | 0.213299 | ||||||||
\(81\) | 43177.2 | 0.731210 | ||||||||
\(82\) | 87789.0 | 1.44180 | ||||||||
\(83\) | −42252.6 | −0.673223 | −0.336611 | − | 0.941644i | \(-0.609281\pi\) | ||||
−0.336611 | + | 0.941644i | \(0.609281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −35688.9 | −0.535780 | ||||||||
\(86\) | −121779. | −1.77552 | ||||||||
\(87\) | 9856.51 | 0.139613 | ||||||||
\(88\) | −71914.7 | −0.989944 | ||||||||
\(89\) | 94517.0 | 1.26484 | 0.632419 | − | 0.774627i | \(-0.282062\pi\) | ||||
0.632419 | + | 0.774627i | \(0.282062\pi\) | |||||||
\(90\) | 48107.5 | 0.626046 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −98127.7 | −1.20871 | ||||||||
\(93\) | 17060.8 | 0.204546 | ||||||||
\(94\) | −141987. | −1.65740 | ||||||||
\(95\) | 54933.4 | 0.624493 | ||||||||
\(96\) | −36258.2 | −0.401539 | ||||||||
\(97\) | 85271.1 | 0.920180 | 0.460090 | − | 0.887872i | \(-0.347817\pi\) | ||||
0.460090 | + | 0.887872i | \(0.347817\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 149778. | 1.53589 | ||||||||
\(100\) | 27584.6 | 0.275846 | ||||||||
\(101\) | −180306. | −1.75876 | −0.879380 | − | 0.476121i | \(-0.842042\pi\) | ||||
−0.879380 | + | 0.476121i | \(0.842042\pi\) | |||||||
\(102\) | 59038.2 | 0.561866 | ||||||||
\(103\) | −173368. | −1.61018 | −0.805091 | − | 0.593152i | \(-0.797883\pi\) | ||||
−0.805091 | + | 0.593152i | \(0.797883\pi\) | |||||||
\(104\) | 6234.60 | 0.0565230 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11056.5 | 0.0955770 | ||||||||
\(107\) | 155442. | 1.31253 | 0.656264 | − | 0.754532i | \(-0.272136\pi\) | ||||
0.656264 | + | 0.754532i | \(0.272136\pi\) | |||||||
\(108\) | −96965.3 | −0.799939 | ||||||||
\(109\) | 19088.6 | 0.153889 | 0.0769444 | − | 0.997035i | \(-0.475484\pi\) | ||||
0.0769444 | + | 0.997035i | \(0.475484\pi\) | |||||||
\(110\) | 148151. | 1.16740 | ||||||||
\(111\) | 43519.2 | 0.335254 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 101150. | 0.745197 | 0.372599 | − | 0.927993i | \(-0.378467\pi\) | ||||
0.372599 | + | 0.927993i | \(0.378467\pi\) | |||||||
\(114\) | −90873.3 | −0.654899 | ||||||||
\(115\) | 55583.3 | 0.391922 | ||||||||
\(116\) | 91783.5 | 0.633315 | ||||||||
\(117\) | −12984.9 | −0.0876951 | ||||||||
\(118\) | −117496. | −0.776814 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −12546.8 | −0.0795391 | ||||||||
\(121\) | 300202. | 1.86402 | ||||||||
\(122\) | 305669. | 1.85931 | ||||||||
\(123\) | 47686.2 | 0.284204 | ||||||||
\(124\) | 158869. | 0.927866 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −112788. | −0.620514 | −0.310257 | − | 0.950653i | \(-0.600415\pi\) | ||||
−0.310257 | + | 0.950653i | \(0.600415\pi\) | |||||||
\(128\) | −201265. | −1.08578 | ||||||||
\(129\) | −66149.1 | −0.349985 | ||||||||
\(130\) | −12843.8 | −0.0666555 | ||||||||
\(131\) | −183577. | −0.934632 | −0.467316 | − | 0.884090i | \(-0.654779\pi\) | ||||
−0.467316 | + | 0.884090i | \(0.654779\pi\) | |||||||
\(132\) | −142070. | −0.709689 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −322139. | −1.54982 | ||||||||
\(135\) | 54924.9 | 0.259379 | ||||||||
\(136\) | 151162. | 0.700800 | ||||||||
\(137\) | −92212.1 | −0.419746 | −0.209873 | − | 0.977729i | \(-0.567305\pi\) | ||||
−0.209873 | + | 0.977729i | \(0.567305\pi\) | |||||||
\(138\) | −91948.3 | −0.411004 | ||||||||
\(139\) | 424349. | 1.86288 | 0.931442 | − | 0.363889i | \(-0.118551\pi\) | ||||
0.931442 | + | 0.363889i | \(0.118551\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −77125.9 | −0.326703 | ||||||||
\(142\) | 35939.9 | 0.149574 | ||||||||
\(143\) | −39988.1 | −0.163527 | ||||||||
\(144\) | 107709. | 0.432860 | ||||||||
\(145\) | −51989.7 | −0.205351 | ||||||||
\(146\) | −30691.0 | −0.119160 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 405249. | 1.52079 | ||||||||
\(149\) | 137894. | 0.508838 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(150\) | 25847.5 | 0.0937975 | ||||||||
\(151\) | −308590. | −1.10139 | −0.550693 | − | 0.834708i | \(-0.685636\pi\) | ||||
−0.550693 | + | 0.834708i | \(0.685636\pi\) | |||||||
\(152\) | −232672. | −0.816837 | ||||||||
\(153\) | −314828. | −1.08729 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −89989.6 | −0.300859 | ||||||||
\(156\) | 12316.7 | 0.0405212 | ||||||||
\(157\) | −209003. | −0.676710 | −0.338355 | − | 0.941018i | \(-0.609871\pi\) | ||||
−0.338355 | + | 0.941018i | \(0.609871\pi\) | |||||||
\(158\) | −632087. | −2.01435 | ||||||||
\(159\) | 6005.80 | 0.0188399 | ||||||||
\(160\) | 191249. | 0.590609 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 376745. | 1.12787 | ||||||||
\(163\) | −249015. | −0.734103 | −0.367051 | − | 0.930201i | \(-0.619633\pi\) | ||||
−0.367051 | + | 0.930201i | \(0.619633\pi\) | |||||||
\(164\) | 444052. | 1.28921 | ||||||||
\(165\) | 80474.0 | 0.230116 | ||||||||
\(166\) | −368678. | −1.03843 | ||||||||
\(167\) | 550497. | 1.52744 | 0.763720 | − | 0.645548i | \(-0.223371\pi\) | ||||
0.763720 | + | 0.645548i | \(0.223371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −367826. | −0.990663 | ||||||||
\(170\) | −311406. | −0.826428 | ||||||||
\(171\) | 484592. | 1.26732 | ||||||||
\(172\) | −615978. | −1.58761 | ||||||||
\(173\) | −103026. | −0.261717 | −0.130859 | − | 0.991401i | \(-0.541773\pi\) | ||||
−0.130859 | + | 0.991401i | \(0.541773\pi\) | |||||||
\(174\) | 86003.6 | 0.215349 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 331699. | 0.807166 | ||||||||
\(177\) | −63822.6 | −0.153123 | ||||||||
\(178\) | 824714. | 1.95098 | ||||||||
\(179\) | 470596. | 1.09778 | 0.548891 | − | 0.835894i | \(-0.315050\pi\) | ||||
0.548891 | + | 0.835894i | \(0.315050\pi\) | |||||||
\(180\) | 243336. | 0.559790 | ||||||||
\(181\) | −529125. | −1.20050 | −0.600250 | − | 0.799812i | \(-0.704932\pi\) | ||||
−0.600250 | + | 0.799812i | \(0.704932\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 166037. | 0.366502 | ||||||||
\(184\) | −235425. | −0.512634 | ||||||||
\(185\) | −229549. | −0.493112 | ||||||||
\(186\) | 148865. | 0.315507 | ||||||||
\(187\) | −969535. | −2.02749 | ||||||||
\(188\) | −718194. | −1.48200 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 479325. | 0.963266 | ||||||||
\(191\) | 180604. | 0.358215 | 0.179108 | − | 0.983829i | \(-0.442679\pi\) | ||||
0.179108 | + | 0.983829i | \(0.442679\pi\) | |||||||
\(192\) | −242298. | −0.474348 | ||||||||
\(193\) | −512865. | −0.991083 | −0.495541 | − | 0.868584i | \(-0.665030\pi\) | ||||
−0.495541 | + | 0.868584i | \(0.665030\pi\) | |||||||
\(194\) | 744038. | 1.41935 | ||||||||
\(195\) | −6976.65 | −0.0131389 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −28199.0 | −0.0517687 | −0.0258844 | − | 0.999665i | \(-0.508240\pi\) | ||||
−0.0258844 | + | 0.999665i | \(0.508240\pi\) | |||||||
\(198\) | 1.30690e6 | 2.36908 | ||||||||
\(199\) | 934000. | 1.67192 | 0.835958 | − | 0.548794i | \(-0.184913\pi\) | ||||
0.835958 | + | 0.548794i | \(0.184913\pi\) | |||||||
\(200\) | 66180.1 | 0.116991 | ||||||||
\(201\) | −174983. | −0.305496 | ||||||||
\(202\) | −1.57327e6 | −2.71284 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 298625. | 0.502402 | ||||||||
\(205\) | −251528. | −0.418025 | ||||||||
\(206\) | −1.51273e6 | −2.48367 | ||||||||
\(207\) | 490324. | 0.795349 | ||||||||
\(208\) | −28756.5 | −0.0460869 | ||||||||
\(209\) | 1.49234e6 | 2.36320 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −206876. | −0.319893 | −0.159946 | − | 0.987126i | \(-0.551132\pi\) | ||||
−0.159946 | + | 0.987126i | \(0.551132\pi\) | |||||||
\(212\) | 55925.8 | 0.0854619 | ||||||||
\(213\) | 19522.2 | 0.0294836 | ||||||||
\(214\) | 1.35632e6 | 2.02454 | ||||||||
\(215\) | 348914. | 0.514780 | ||||||||
\(216\) | −232636. | −0.339268 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 166559. | 0.237370 | ||||||||
\(219\) | −16671.1 | −0.0234884 | ||||||||
\(220\) | 749371. | 1.04386 | ||||||||
\(221\) | 84053.3 | 0.115764 | ||||||||
\(222\) | 379730. | 0.517121 | ||||||||
\(223\) | 347934. | 0.468527 | 0.234263 | − | 0.972173i | \(-0.424732\pi\) | ||||
0.234263 | + | 0.972173i | \(0.424732\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −137835. | −0.181511 | ||||||||
\(226\) | 882594. | 1.14945 | ||||||||
\(227\) | −792997. | −1.02143 | −0.510713 | − | 0.859751i | \(-0.670619\pi\) | ||||
−0.510713 | + | 0.859751i | \(0.670619\pi\) | |||||||
\(228\) | −459653. | −0.585589 | ||||||||
\(229\) | −275845. | −0.347598 | −0.173799 | − | 0.984781i | \(-0.555604\pi\) | ||||
−0.173799 | + | 0.984781i | \(0.555604\pi\) | |||||||
\(230\) | 484996. | 0.604531 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 220204. | 0.268599 | ||||||||
\(233\) | 1.43590e6 | 1.73275 | 0.866373 | − | 0.499398i | \(-0.166446\pi\) | ||||
0.866373 | + | 0.499398i | \(0.166446\pi\) | |||||||
\(234\) | −113301. | −0.135267 | ||||||||
\(235\) | 406813. | 0.480535 | ||||||||
\(236\) | −594314. | −0.694602 | ||||||||
\(237\) | −343344. | −0.397062 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 127902. | 0.144838 | 0.0724191 | − | 0.997374i | \(-0.476928\pi\) | ||||
0.0724191 | + | 0.997374i | \(0.476928\pi\) | |||||||
\(240\) | 57871.0 | 0.0648534 | ||||||||
\(241\) | 602677. | 0.668409 | 0.334204 | − | 0.942501i | \(-0.391532\pi\) | ||||
0.334204 | + | 0.942501i | \(0.391532\pi\) | |||||||
\(242\) | 2.61943e6 | 2.87521 | ||||||||
\(243\) | 738515. | 0.802312 | ||||||||
\(244\) | 1.54613e6 | 1.66253 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 416089. | 0.438377 | ||||||||
\(247\) | −129377. | −0.134932 | ||||||||
\(248\) | 381154. | 0.393524 | ||||||||
\(249\) | −200263. | −0.204692 | ||||||||
\(250\) | −136337. | −0.137963 | ||||||||
\(251\) | −756978. | −0.758401 | −0.379201 | − | 0.925314i | \(-0.623801\pi\) | ||||
−0.379201 | + | 0.925314i | \(0.623801\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.50999e6 | 1.48311 | ||||||||
\(254\) | −984135. | −0.957128 | ||||||||
\(255\) | −169153. | −0.162903 | ||||||||
\(256\) | −120261. | −0.114689 | ||||||||
\(257\) | 606610. | 0.572898 | 0.286449 | − | 0.958096i | \(-0.407525\pi\) | ||||
0.286449 | + | 0.958096i | \(0.407525\pi\) | |||||||
\(258\) | −577188. | −0.539844 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −64966.3 | −0.0596011 | ||||||||
\(261\) | −458624. | −0.416730 | ||||||||
\(262\) | −1.60181e6 | −1.44165 | ||||||||
\(263\) | −1.41962e6 | −1.26556 | −0.632780 | − | 0.774331i | \(-0.718086\pi\) | ||||
−0.632780 | + | 0.774331i | \(0.718086\pi\) | |||||||
\(264\) | −340850. | −0.300991 | ||||||||
\(265\) | −31678.5 | −0.0277109 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 447977. | 0.384572 | ||||||||
\(268\) | −1.62943e6 | −1.38580 | ||||||||
\(269\) | −496984. | −0.418756 | −0.209378 | − | 0.977835i | \(-0.567144\pi\) | ||||
−0.209378 | + | 0.977835i | \(0.567144\pi\) | |||||||
\(270\) | 479250. | 0.400086 | ||||||||
\(271\) | 155568. | 0.128676 | 0.0643378 | − | 0.997928i | \(-0.479506\pi\) | ||||
0.0643378 | + | 0.997928i | \(0.479506\pi\) | |||||||
\(272\) | −697218. | −0.571408 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −804602. | −0.647448 | ||||||||
\(275\) | −424473. | −0.338468 | ||||||||
\(276\) | −465091. | −0.367506 | ||||||||
\(277\) | −1.77069e6 | −1.38657 | −0.693285 | − | 0.720663i | \(-0.743837\pi\) | ||||
−0.693285 | + | 0.720663i | \(0.743837\pi\) | |||||||
\(278\) | 3.70268e6 | 2.87345 | ||||||||
\(279\) | −793837. | −0.610549 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.38775e6 | −1.80394 | −0.901972 | − | 0.431794i | \(-0.857881\pi\) | ||||
−0.901972 | + | 0.431794i | \(0.857881\pi\) | |||||||
\(282\) | −672967. | −0.503931 | ||||||||
\(283\) | −193515. | −0.143631 | −0.0718156 | − | 0.997418i | \(-0.522879\pi\) | ||||
−0.0718156 | + | 0.997418i | \(0.522879\pi\) | |||||||
\(284\) | 181790. | 0.133744 | ||||||||
\(285\) | 260365. | 0.189876 | ||||||||
\(286\) | −348918. | −0.252237 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.68709e6 | 1.19855 | ||||||||
\(289\) | 618065. | 0.435301 | ||||||||
\(290\) | −453639. | −0.316749 | ||||||||
\(291\) | 404155. | 0.279779 | ||||||||
\(292\) | −155240. | −0.106549 | ||||||||
\(293\) | −66529.2 | −0.0452734 | −0.0226367 | − | 0.999744i | \(-0.507206\pi\) | ||||
−0.0226367 | + | 0.999744i | \(0.507206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 336642. | 0.225223 | ||||||||
\(296\) | 972261. | 0.644991 | ||||||||
\(297\) | 1.49210e6 | 0.981540 | ||||||||
\(298\) | 1.20320e6 | 0.784870 | ||||||||
\(299\) | −130908. | −0.0846813 | ||||||||
\(300\) | 130741. | 0.0838706 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.69262e6 | −1.69886 | ||||||||
\(303\) | −854586. | −0.534748 | ||||||||
\(304\) | 1.07318e6 | 0.666020 | ||||||||
\(305\) | −875786. | −0.539074 | ||||||||
\(306\) | −2.74705e6 | −1.67711 | ||||||||
\(307\) | 1.08295e6 | 0.655787 | 0.327893 | − | 0.944715i | \(-0.393661\pi\) | ||||
0.327893 | + | 0.944715i | \(0.393661\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −821701. | −0.489573 | ||||||||
\(310\) | −785210. | −0.464068 | ||||||||
\(311\) | −1.48395e6 | −0.869999 | −0.435000 | − | 0.900431i | \(-0.643251\pi\) | ||||
−0.435000 | + | 0.900431i | \(0.643251\pi\) | |||||||
\(312\) | 29549.8 | 0.0171857 | ||||||||
\(313\) | −2.59381e6 | −1.49650 | −0.748251 | − | 0.663416i | \(-0.769106\pi\) | ||||
−0.748251 | + | 0.663416i | \(0.769106\pi\) | |||||||
\(314\) | −1.82367e6 | −1.04381 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.19721e6 | −1.80116 | ||||||||
\(317\) | −2.77640e6 | −1.55180 | −0.775898 | − | 0.630858i | \(-0.782703\pi\) | ||||
−0.775898 | + | 0.630858i | \(0.782703\pi\) | |||||||
\(318\) | 52404.0 | 0.0290601 | ||||||||
\(319\) | −1.41237e6 | −0.777088 | ||||||||
\(320\) | 1.27804e6 | 0.697701 | ||||||||
\(321\) | 736739. | 0.399072 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.13683e6 | −1.67295 | ||||||||
\(324\) | 1.90564e6 | 1.00851 | ||||||||
\(325\) | 36799.4 | 0.0193256 | ||||||||
\(326\) | −2.17280e6 | −1.13234 | ||||||||
\(327\) | 90473.1 | 0.0467897 | ||||||||
\(328\) | 1.06535e6 | 0.546776 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 702181. | 0.354948 | ||||||||
\(331\) | −1.99398e6 | −1.00035 | −0.500174 | − | 0.865925i | \(-0.666731\pi\) | ||||
−0.500174 | + | 0.865925i | \(0.666731\pi\) | |||||||
\(332\) | −1.86484e6 | −0.928530 | ||||||||
\(333\) | −2.02495e6 | −1.00070 | ||||||||
\(334\) | 4.80340e6 | 2.35604 | ||||||||
\(335\) | 922974. | 0.449343 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −19232.2 | −0.00922473 | −0.00461236 | − | 0.999989i | \(-0.501468\pi\) | ||||
−0.00461236 | + | 0.999989i | \(0.501468\pi\) | |||||||
\(338\) | −3.20949e6 | −1.52807 | ||||||||
\(339\) | 479417. | 0.226576 | ||||||||
\(340\) | −1.57515e6 | −0.738965 | ||||||||
\(341\) | −2.44468e6 | −1.13851 | ||||||||
\(342\) | 4.22833e6 | 1.95481 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.47783e6 | −0.673333 | ||||||||
\(345\) | 263445. | 0.119163 | ||||||||
\(346\) | −898961. | −0.403692 | ||||||||
\(347\) | −2.23061e6 | −0.994489 | −0.497245 | − | 0.867610i | \(-0.665655\pi\) | ||||
−0.497245 | + | 0.867610i | \(0.665655\pi\) | |||||||
\(348\) | 435021. | 0.192558 | ||||||||
\(349\) | −313791. | −0.137904 | −0.0689520 | − | 0.997620i | \(-0.521966\pi\) | ||||
−0.0689520 | + | 0.997620i | \(0.521966\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −129357. | −0.0560431 | ||||||||
\(352\) | 5.19553e6 | 2.23498 | ||||||||
\(353\) | 1.47348e6 | 0.629370 | 0.314685 | − | 0.949196i | \(-0.398101\pi\) | ||||
0.314685 | + | 0.949196i | \(0.398101\pi\) | |||||||
\(354\) | −556888. | −0.236189 | ||||||||
\(355\) | −102973. | −0.0433663 | ||||||||
\(356\) | 4.17155e6 | 1.74450 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.10622e6 | 1.69330 | ||||||||
\(359\) | −1.21115e6 | −0.495977 | −0.247988 | − | 0.968763i | \(-0.579769\pi\) | ||||
−0.247988 | + | 0.968763i | \(0.579769\pi\) | |||||||
\(360\) | 583803. | 0.237416 | ||||||||
\(361\) | 2.35219e6 | 0.949960 | ||||||||
\(362\) | −4.61692e6 | −1.85174 | ||||||||
\(363\) | 1.42285e6 | 0.566753 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 87934.1 | 0.0345482 | ||||||||
\(366\) | 1.44876e6 | 0.565321 | ||||||||
\(367\) | 2.43854e6 | 0.945073 | 0.472536 | − | 0.881311i | \(-0.343339\pi\) | ||||
0.472536 | + | 0.881311i | \(0.343339\pi\) | |||||||
\(368\) | 1.08587e6 | 0.417984 | ||||||||
\(369\) | −2.21884e6 | −0.848320 | ||||||||
\(370\) | −2.00294e6 | −0.760614 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 752983. | 0.282116 | ||||||||
\(373\) | −3.48803e6 | −1.29810 | −0.649050 | − | 0.760746i | \(-0.724833\pi\) | ||||
−0.649050 | + | 0.760746i | \(0.724833\pi\) | |||||||
\(374\) | −8.45974e6 | −3.12736 | ||||||||
\(375\) | −74057.0 | −0.0271949 | ||||||||
\(376\) | −1.72307e6 | −0.628539 | ||||||||
\(377\) | 122444. | 0.0443695 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −964503. | −0.344910 | −0.172455 | − | 0.985017i | \(-0.555170\pi\) | ||||
−0.172455 | + | 0.985017i | \(0.555170\pi\) | |||||||
\(380\) | 2.42451e6 | 0.861321 | ||||||||
\(381\) | −534573. | −0.188666 | ||||||||
\(382\) | 1.57587e6 | 0.552539 | ||||||||
\(383\) | 3.36433e6 | 1.17193 | 0.585965 | − | 0.810336i | \(-0.300716\pi\) | ||||
0.585965 | + | 0.810336i | \(0.300716\pi\) | |||||||
\(384\) | −953926. | −0.330131 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.47504e6 | −1.52872 | ||||||||
\(387\) | 3.07792e6 | 1.04467 | ||||||||
\(388\) | 3.76348e6 | 1.26914 | ||||||||
\(389\) | −1.18786e6 | −0.398007 | −0.199003 | − | 0.979999i | \(-0.563770\pi\) | ||||
−0.199003 | + | 0.979999i | \(0.563770\pi\) | |||||||
\(390\) | −60875.2 | −0.0202665 | ||||||||
\(391\) | −3.17394e6 | −1.04992 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −870091. | −0.284173 | ||||||||
\(394\) | −246052. | −0.0798520 | ||||||||
\(395\) | 1.81102e6 | 0.584024 | ||||||||
\(396\) | 6.61052e6 | 2.11835 | ||||||||
\(397\) | 1.63665e6 | 0.521171 | 0.260585 | − | 0.965451i | \(-0.416084\pi\) | ||||
0.260585 | + | 0.965451i | \(0.416084\pi\) | |||||||
\(398\) | 8.14967e6 | 2.57889 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −305249. | −0.0953904 | ||||||||
\(401\) | −892182. | −0.277072 | −0.138536 | − | 0.990357i | \(-0.544240\pi\) | ||||
−0.138536 | + | 0.990357i | \(0.544240\pi\) | |||||||
\(402\) | −1.52682e6 | −0.471220 | ||||||||
\(403\) | 211940. | 0.0650056 | ||||||||
\(404\) | −7.95787e6 | −2.42574 | ||||||||
\(405\) | −1.07943e6 | −0.327007 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.23598e6 | −1.86603 | ||||||||
\(408\) | 716453. | 0.213077 | ||||||||
\(409\) | −3.38800e6 | −1.00146 | −0.500732 | − | 0.865603i | \(-0.666936\pi\) | ||||
−0.500732 | + | 0.865603i | \(0.666936\pi\) | |||||||
\(410\) | −2.19472e6 | −0.644793 | ||||||||
\(411\) | −437053. | −0.127623 | ||||||||
\(412\) | −7.65165e6 | −2.22081 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.27836e6 | 1.22681 | ||||||||
\(415\) | 1.05632e6 | 0.301074 | ||||||||
\(416\) | −450423. | −0.127611 | ||||||||
\(417\) | 2.01126e6 | 0.566407 | ||||||||
\(418\) | 1.30215e7 | 3.64518 | ||||||||
\(419\) | −5.29618e6 | −1.47376 | −0.736882 | − | 0.676022i | \(-0.763703\pi\) | ||||
−0.736882 | + | 0.676022i | \(0.763703\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.38110e6 | 1.47967 | 0.739836 | − | 0.672787i | \(-0.234903\pi\) | ||||
0.739836 | + | 0.672787i | \(0.234903\pi\) | |||||||
\(422\) | −1.80511e6 | −0.493427 | ||||||||
\(423\) | 3.58867e6 | 0.975175 | ||||||||
\(424\) | 134175. | 0.0362458 | ||||||||
\(425\) | 892224. | 0.239608 | ||||||||
\(426\) | 170342. | 0.0454777 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.86049e6 | 1.81028 | ||||||||
\(429\) | −189529. | −0.0497203 | ||||||||
\(430\) | 3.04447e6 | 0.794036 | ||||||||
\(431\) | −6.29797e6 | −1.63308 | −0.816540 | − | 0.577290i | \(-0.804110\pi\) | ||||
−0.816540 | + | 0.577290i | \(0.804110\pi\) | |||||||
\(432\) | 1.07301e6 | 0.276627 | ||||||||
\(433\) | −4.54572e6 | −1.16515 | −0.582577 | − | 0.812775i | \(-0.697956\pi\) | ||||
−0.582577 | + | 0.812775i | \(0.697956\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −246413. | −0.0624367 | ||||||||
\(436\) | 842482. | 0.212248 | ||||||||
\(437\) | 4.88541e6 | 1.22376 | ||||||||
\(438\) | −145464. | −0.0362303 | ||||||||
\(439\) | −2.69494e6 | −0.667402 | −0.333701 | − | 0.942679i | \(-0.608298\pi\) | ||||
−0.333701 | + | 0.942679i | \(0.608298\pi\) | |||||||
\(440\) | 1.79787e6 | 0.442717 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 733412. | 0.178563 | ||||||||
\(443\) | −3.00924e6 | −0.728530 | −0.364265 | − | 0.931295i | \(-0.618680\pi\) | ||||
−0.364265 | + | 0.931295i | \(0.618680\pi\) | |||||||
\(444\) | 1.92074e6 | 0.462393 | ||||||||
\(445\) | −2.36292e6 | −0.565653 | ||||||||
\(446\) | 3.03592e6 | 0.722691 | ||||||||
\(447\) | 653569. | 0.154711 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.52092e6 | 0.824214 | 0.412107 | − | 0.911135i | \(-0.364793\pi\) | ||||
0.412107 | + | 0.911135i | \(0.364793\pi\) | |||||||
\(450\) | −1.20269e6 | −0.279976 | ||||||||
\(451\) | −6.83308e6 | −1.58189 | ||||||||
\(452\) | 4.46431e6 | 1.02780 | ||||||||
\(453\) | −1.46261e6 | −0.334875 | ||||||||
\(454\) | −6.91935e6 | −1.57553 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.10278e6 | −0.248358 | ||||||||
\(457\) | 2.51620e6 | 0.563578 | 0.281789 | − | 0.959476i | \(-0.409072\pi\) | ||||
0.281789 | + | 0.959476i | \(0.409072\pi\) | |||||||
\(458\) | −2.40691e6 | −0.536161 | ||||||||
\(459\) | −3.13634e6 | −0.694850 | ||||||||
\(460\) | 2.45319e6 | 0.540552 | ||||||||
\(461\) | −200800. | −0.0440060 | −0.0220030 | − | 0.999758i | \(-0.507004\pi\) | ||||
−0.0220030 | + | 0.999758i | \(0.507004\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 192190. | 0.0416656 | 0.0208328 | − | 0.999783i | \(-0.493368\pi\) | ||||
0.0208328 | + | 0.999783i | \(0.493368\pi\) | |||||||
\(464\) | −1.01567e6 | −0.219007 | ||||||||
\(465\) | −426519. | −0.0914757 | ||||||||
\(466\) | 1.25290e7 | 2.67272 | ||||||||
\(467\) | 1.49891e6 | 0.318040 | 0.159020 | − | 0.987275i | \(-0.449167\pi\) | ||||
0.159020 | + | 0.987275i | \(0.449167\pi\) | |||||||
\(468\) | −573095. | −0.120952 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.54967e6 | 0.741213 | ||||||||
\(471\) | −990599. | −0.205753 | ||||||||
\(472\) | −1.42586e6 | −0.294592 | ||||||||
\(473\) | 9.47868e6 | 1.94803 | ||||||||
\(474\) | −2.99587e6 | −0.612459 | ||||||||
\(475\) | −1.37334e6 | −0.279282 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −279450. | −0.0562352 | ||||||||
\(478\) | 1.11602e6 | 0.223409 | ||||||||
\(479\) | 7.48400e6 | 1.49037 | 0.745186 | − | 0.666857i | \(-0.232361\pi\) | ||||
0.745186 | + | 0.666857i | \(0.232361\pi\) | |||||||
\(480\) | 906455. | 0.179574 | ||||||||
\(481\) | 540625. | 0.106545 | ||||||||
\(482\) | 5.25870e6 | 1.03100 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.32496e7 | 2.57092 | ||||||||
\(485\) | −2.13178e6 | −0.411517 | ||||||||
\(486\) | 6.44395e6 | 1.23755 | ||||||||
\(487\) | −2.19160e6 | −0.418734 | −0.209367 | − | 0.977837i | \(-0.567140\pi\) | ||||
−0.209367 | + | 0.977837i | \(0.567140\pi\) | |||||||
\(488\) | 3.70942e6 | 0.705109 | ||||||||
\(489\) | −1.18024e6 | −0.223203 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.71570e6 | 0.695564 | 0.347782 | − | 0.937575i | \(-0.386935\pi\) | ||||
0.347782 | + | 0.937575i | \(0.386935\pi\) | |||||||
\(492\) | 2.10465e6 | 0.391983 | ||||||||
\(493\) | 2.96873e6 | 0.550115 | ||||||||
\(494\) | −1.12889e6 | −0.208129 | ||||||||
\(495\) | −3.74446e6 | −0.686872 | ||||||||
\(496\) | −1.75803e6 | −0.320865 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.74740e6 | −0.315733 | ||||||||
\(499\) | 5.74147e6 | 1.03222 | 0.516109 | − | 0.856523i | \(-0.327380\pi\) | ||||
0.516109 | + | 0.856523i | \(0.327380\pi\) | |||||||
\(500\) | −689616. | −0.123362 | ||||||||
\(501\) | 2.60916e6 | 0.464416 | ||||||||
\(502\) | −6.60506e6 | −1.16982 | ||||||||
\(503\) | 8.85276e6 | 1.56012 | 0.780061 | − | 0.625703i | \(-0.215188\pi\) | ||||
0.780061 | + | 0.625703i | \(0.215188\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.50765e6 | 0.786541 | ||||||||
\(506\) | 1.31755e7 | 2.28766 | ||||||||
\(507\) | −1.74337e6 | −0.301210 | ||||||||
\(508\) | −4.97792e6 | −0.855833 | ||||||||
\(509\) | 478571. | 0.0818751 | 0.0409376 | − | 0.999162i | \(-0.486966\pi\) | ||||
0.0409376 | + | 0.999162i | \(0.486966\pi\) | |||||||
\(510\) | −1.47595e6 | −0.251274 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 5.39114e6 | 0.908879 | ||||||||
\(513\) | 4.82754e6 | 0.809902 | ||||||||
\(514\) | 5.29302e6 | 0.883681 | ||||||||
\(515\) | 4.33419e6 | 0.720095 | ||||||||
\(516\) | −2.91952e6 | −0.482711 | ||||||||
\(517\) | 1.10516e7 | 1.81844 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −488307. | −0.0795747 | ||||||||
\(520\) | −155865. | −0.0252778 | ||||||||
\(521\) | −8.96169e6 | −1.44642 | −0.723212 | − | 0.690626i | \(-0.757335\pi\) | ||||
−0.723212 | + | 0.690626i | \(0.757335\pi\) | |||||||
\(522\) | −4.00175e6 | −0.642796 | ||||||||
\(523\) | 1.08551e7 | 1.73531 | 0.867656 | − | 0.497164i | \(-0.165625\pi\) | ||||
0.867656 | + | 0.497164i | \(0.165625\pi\) | |||||||
\(524\) | −8.10226e6 | −1.28907 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.23870e7 | −1.95210 | ||||||||
\(527\) | 5.13861e6 | 0.805971 | ||||||||
\(528\) | 1.57214e6 | 0.245418 | ||||||||
\(529\) | −1.49313e6 | −0.231984 | ||||||||
\(530\) | −276413. | −0.0427434 | ||||||||
\(531\) | 2.96967e6 | 0.457058 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 592389. | 0.0903211 | ||||||||
\(534\) | 3.90885e6 | 0.593193 | ||||||||
\(535\) | −3.88604e6 | −0.586980 | ||||||||
\(536\) | −3.90929e6 | −0.587740 | ||||||||
\(537\) | 2.23046e6 | 0.333779 | ||||||||
\(538\) | −4.33646e6 | −0.645922 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.42413e6 | 0.357744 | ||||||||
\(541\) | −1.15845e7 | −1.70170 | −0.850852 | − | 0.525405i | \(-0.823914\pi\) | ||||
−0.850852 | + | 0.525405i | \(0.823914\pi\) | |||||||
\(542\) | 1.35742e6 | 0.198479 | ||||||||
\(543\) | −2.50787e6 | −0.365010 | ||||||||
\(544\) | −1.09208e7 | −1.58218 | ||||||||
\(545\) | −477214. | −0.0688212 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 594715. | 0.0849846 | 0.0424923 | − | 0.999097i | \(-0.486470\pi\) | ||||
0.0424923 | + | 0.999097i | \(0.486470\pi\) | |||||||
\(548\) | −4.06982e6 | −0.578927 | ||||||||
\(549\) | −7.72569e6 | −1.09397 | ||||||||
\(550\) | −3.70376e6 | −0.522079 | ||||||||
\(551\) | −4.56956e6 | −0.641202 | ||||||||
\(552\) | −1.11583e6 | −0.155866 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.54502e7 | −2.13875 | ||||||||
\(555\) | −1.08798e6 | −0.149930 | ||||||||
\(556\) | 1.87288e7 | 2.56935 | ||||||||
\(557\) | 4.57366e6 | 0.624634 | 0.312317 | − | 0.949978i | \(-0.398895\pi\) | ||||
0.312317 | + | 0.949978i | \(0.398895\pi\) | |||||||
\(558\) | −6.92667e6 | −0.941758 | ||||||||
\(559\) | −821748. | −0.111227 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.59525e6 | −0.616456 | ||||||||
\(562\) | −2.08345e7 | −2.78254 | ||||||||
\(563\) | 2.88071e6 | 0.383027 | 0.191513 | − | 0.981490i | \(-0.438660\pi\) | ||||
0.191513 | + | 0.981490i | \(0.438660\pi\) | |||||||
\(564\) | −3.40398e6 | −0.450599 | ||||||||
\(565\) | −2.52876e6 | −0.333262 | ||||||||
\(566\) | −1.68853e6 | −0.221548 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 436145. | 0.0567231 | ||||||||
\(569\) | 1.18609e7 | 1.53581 | 0.767903 | − | 0.640566i | \(-0.221300\pi\) | ||||
0.767903 | + | 0.640566i | \(0.221300\pi\) | |||||||
\(570\) | 2.27183e6 | 0.292880 | ||||||||
\(571\) | −3.94838e6 | −0.506791 | −0.253396 | − | 0.967363i | \(-0.581547\pi\) | ||||
−0.253396 | + | 0.967363i | \(0.581547\pi\) | |||||||
\(572\) | −1.76489e6 | −0.225542 | ||||||||
\(573\) | 856000. | 0.108915 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.38958e6 | −0.175273 | ||||||||
\(576\) | 1.12741e7 | 1.41588 | ||||||||
\(577\) | 1.33953e6 | 0.167500 | 0.0837498 | − | 0.996487i | \(-0.473310\pi\) | ||||
0.0837498 | + | 0.996487i | \(0.473310\pi\) | |||||||
\(578\) | 5.39296e6 | 0.671441 | ||||||||
\(579\) | −2.43080e6 | −0.301337 | ||||||||
\(580\) | −2.29459e6 | −0.283227 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.52648e6 | 0.431553 | ||||||||
\(583\) | −860587. | −0.104863 | ||||||||
\(584\) | −372448. | −0.0451890 | ||||||||
\(585\) | 324623. | 0.0392184 | ||||||||
\(586\) | −580504. | −0.0698331 | ||||||||
\(587\) | −1.53600e7 | −1.83990 | −0.919951 | − | 0.392034i | \(-0.871772\pi\) | ||||
−0.919951 | + | 0.392034i | \(0.871772\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.90950e6 | −0.939422 | ||||||||
\(590\) | 2.93739e6 | 0.347402 | ||||||||
\(591\) | −133653. | −0.0157402 | ||||||||
\(592\) | −4.48446e6 | −0.525903 | ||||||||
\(593\) | −963371. | −0.112501 | −0.0562506 | − | 0.998417i | \(-0.517915\pi\) | ||||
−0.0562506 | + | 0.998417i | \(0.517915\pi\) | |||||||
\(594\) | 1.30194e7 | 1.51400 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.08600e6 | 0.701805 | ||||||||
\(597\) | 4.42683e6 | 0.508343 | ||||||||
\(598\) | −1.14224e6 | −0.130619 | ||||||||
\(599\) | −1.39812e6 | −0.159212 | −0.0796062 | − | 0.996826i | \(-0.525366\pi\) | ||||
−0.0796062 | + | 0.996826i | \(0.525366\pi\) | |||||||
\(600\) | 313670. | 0.0355710 | ||||||||
\(601\) | 9.79835e6 | 1.10654 | 0.553270 | − | 0.833002i | \(-0.313380\pi\) | ||||
0.553270 | + | 0.833002i | \(0.313380\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.14195e6 | 0.911875 | ||||||||
\(604\) | −1.36197e7 | −1.51907 | ||||||||
\(605\) | −7.50506e6 | −0.833616 | ||||||||
\(606\) | −7.45674e6 | −0.824836 | ||||||||
\(607\) | −1.05240e7 | −1.15933 | −0.579666 | − | 0.814854i | \(-0.696817\pi\) | ||||
−0.579666 | + | 0.814854i | \(0.696817\pi\) | |||||||
\(608\) | 1.68096e7 | 1.84416 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.64173e6 | −0.831509 | ||||||||
\(611\) | −958110. | −0.103827 | ||||||||
\(612\) | −1.38950e7 | −1.49962 | ||||||||
\(613\) | −1.17388e7 | −1.26175 | −0.630874 | − | 0.775886i | \(-0.717303\pi\) | ||||
−0.630874 | + | 0.775886i | \(0.717303\pi\) | |||||||
\(614\) | 9.44935e6 | 1.01154 | ||||||||
\(615\) | −1.19215e6 | −0.127100 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.83389e6 | −0.722695 | −0.361348 | − | 0.932431i | \(-0.617683\pi\) | ||||
−0.361348 | + | 0.932431i | \(0.617683\pi\) | |||||||
\(618\) | −7.16980e6 | −0.755155 | ||||||||
\(619\) | 1.06954e7 | 1.12194 | 0.560969 | − | 0.827837i | \(-0.310429\pi\) | ||||
0.560969 | + | 0.827837i | \(0.310429\pi\) | |||||||
\(620\) | −3.97173e6 | −0.414954 | ||||||||
\(621\) | 4.88465e6 | 0.508282 | ||||||||
\(622\) | −1.29483e7 | −1.34195 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −136295. | −0.0140126 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −2.26324e7 | −2.30832 | ||||||||
\(627\) | 7.07315e6 | 0.718528 | ||||||||
\(628\) | −9.22442e6 | −0.933340 | ||||||||
\(629\) | 1.31078e7 | 1.32100 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.17826e6 | 0.517739 | 0.258869 | − | 0.965912i | \(-0.416650\pi\) | ||||
0.258869 | + | 0.965912i | \(0.416650\pi\) | |||||||
\(632\) | −7.67063e6 | −0.763903 | ||||||||
\(633\) | −980521. | −0.0972630 | ||||||||
\(634\) | −2.42257e7 | −2.39361 | ||||||||
\(635\) | 2.81969e6 | 0.277502 | ||||||||
\(636\) | 265068. | 0.0259846 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.23237e7 | −1.19864 | ||||||||
\(639\) | −908369. | −0.0880055 | ||||||||
\(640\) | 5.03163e6 | 0.485578 | ||||||||
\(641\) | 2.00548e7 | 1.92785 | 0.963927 | − | 0.266165i | \(-0.0857568\pi\) | ||||
0.963927 | + | 0.266165i | \(0.0857568\pi\) | |||||||
\(642\) | 6.42846e6 | 0.615559 | ||||||||
\(643\) | −1.00964e6 | −0.0963032 | −0.0481516 | − | 0.998840i | \(-0.515333\pi\) | ||||
−0.0481516 | + | 0.998840i | \(0.515333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.65373e6 | 0.156518 | ||||||||
\(646\) | −2.73706e7 | −2.58049 | ||||||||
\(647\) | 2.66309e6 | 0.250107 | 0.125053 | − | 0.992150i | \(-0.460090\pi\) | ||||
0.125053 | + | 0.992150i | \(0.460090\pi\) | |||||||
\(648\) | 4.57196e6 | 0.427725 | ||||||||
\(649\) | 9.14531e6 | 0.852289 | ||||||||
\(650\) | 321095. | 0.0298092 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.09904e7 | −1.01250 | ||||||||
\(653\) | 6.98872e6 | 0.641379 | 0.320689 | − | 0.947184i | \(-0.396085\pi\) | ||||
0.320689 | + | 0.947184i | \(0.396085\pi\) | |||||||
\(654\) | 789429. | 0.0721720 | ||||||||
\(655\) | 4.58943e6 | 0.417980 | ||||||||
\(656\) | −4.91384e6 | −0.445822 | ||||||||
\(657\) | 775705. | 0.0701105 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.22406e7 | 1.09797 | 0.548985 | − | 0.835833i | \(-0.315015\pi\) | ||||
0.548985 | + | 0.835833i | \(0.315015\pi\) | |||||||
\(660\) | 3.55175e6 | 0.317383 | ||||||||
\(661\) | 8.94566e6 | 0.796359 | 0.398180 | − | 0.917307i | \(-0.369642\pi\) | ||||
0.398180 | + | 0.917307i | \(0.369642\pi\) | |||||||
\(662\) | −1.73986e7 | −1.54301 | ||||||||
\(663\) | 398383. | 0.0351979 | ||||||||
\(664\) | −4.47406e6 | −0.393805 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.76688e7 | −1.54355 | ||||||||
\(667\) | −4.62362e6 | −0.402409 | ||||||||
\(668\) | 2.42964e7 | 2.10669 | ||||||||
\(669\) | 1.64908e6 | 0.142455 | ||||||||
\(670\) | 8.05347e6 | 0.693100 | ||||||||
\(671\) | −2.37918e7 | −2.03996 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.40438e6 | −0.715267 | −0.357633 | − | 0.933862i | \(-0.616416\pi\) | ||||
−0.357633 | + | 0.933862i | \(0.616416\pi\) | |||||||
\(674\) | −167811. | −0.0142289 | ||||||||
\(675\) | −1.37312e6 | −0.115998 | ||||||||
\(676\) | −1.62342e7 | −1.36635 | ||||||||
\(677\) | 2.67443e6 | 0.224264 | 0.112132 | − | 0.993693i | \(-0.464232\pi\) | ||||
0.112132 | + | 0.993693i | \(0.464232\pi\) | |||||||
\(678\) | 4.18318e6 | 0.349488 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.77904e6 | −0.313407 | ||||||||
\(681\) | −3.75853e6 | −0.310563 | ||||||||
\(682\) | −2.13312e7 | −1.75612 | ||||||||
\(683\) | 8.95973e6 | 0.734925 | 0.367463 | − | 0.930038i | \(-0.380227\pi\) | ||||
0.367463 | + | 0.930038i | \(0.380227\pi\) | |||||||
\(684\) | 2.13876e7 | 1.74792 | ||||||||
\(685\) | 2.30530e6 | 0.187716 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.30741e6 | −0.105687 | ||||||||
\(688\) | 6.81636e6 | 0.549012 | ||||||||
\(689\) | 74608.0 | 0.00598739 | ||||||||
\(690\) | 2.29871e6 | 0.183807 | ||||||||
\(691\) | −22616.0 | −0.00180186 | −0.000900928 | − | 1.00000i | \(-0.500287\pi\) | ||||
−0.000900928 | 1.00000i | \(0.500287\pi\) | ||||||||
\(692\) | −4.54710e6 | −0.360968 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.94633e7 | −1.53398 | ||||||||
\(695\) | −1.06087e7 | −0.833107 | ||||||||
\(696\) | 1.04369e6 | 0.0816672 | ||||||||
\(697\) | 1.43628e7 | 1.11985 | ||||||||
\(698\) | −2.73800e6 | −0.212714 | ||||||||
\(699\) | 6.80566e6 | 0.526839 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.80427e7 | 1.38677 | 0.693386 | − | 0.720566i | \(-0.256118\pi\) | ||||
0.693386 | + | 0.720566i | \(0.256118\pi\) | |||||||
\(702\) | −1.12871e6 | −0.0864451 | ||||||||
\(703\) | −2.01759e7 | −1.53973 | ||||||||
\(704\) | 3.47195e7 | 2.64023 | ||||||||
\(705\) | 1.92815e6 | 0.146106 | ||||||||
\(706\) | 1.28569e7 | 0.970789 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.81684e6 | −0.211193 | ||||||||
\(709\) | 1.52807e7 | 1.14164 | 0.570819 | − | 0.821076i | \(-0.306626\pi\) | ||||
0.570819 | + | 0.821076i | \(0.306626\pi\) | |||||||
\(710\) | −898497. | −0.0668915 | ||||||||
\(711\) | 1.59758e7 | 1.18519 | ||||||||
\(712\) | 1.00082e7 | 0.739874 | ||||||||
\(713\) | −8.00308e6 | −0.589567 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 999702. | 0.0731317 | ||||||||
\(716\) | 2.07700e7 | 1.51409 | ||||||||
\(717\) | 606211. | 0.0440378 | ||||||||
\(718\) | −1.05679e7 | −0.765032 | ||||||||
\(719\) | 1.45192e7 | 1.04742 | 0.523710 | − | 0.851897i | \(-0.324548\pi\) | ||||
0.523710 | + | 0.851897i | \(0.324548\pi\) | |||||||
\(720\) | −2.69274e6 | −0.193581 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.05242e7 | 1.46529 | ||||||||
\(723\) | 2.85648e6 | 0.203229 | ||||||||
\(724\) | −2.33532e7 | −1.65577 | ||||||||
\(725\) | 1.29974e6 | 0.0918359 | ||||||||
\(726\) | 1.24152e7 | 0.874202 | ||||||||
\(727\) | 1.98706e7 | 1.39436 | 0.697179 | − | 0.716897i | \(-0.254438\pi\) | ||||
0.697179 | + | 0.716897i | \(0.254438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.99176e6 | −0.487268 | ||||||||
\(730\) | 767275. | 0.0532898 | ||||||||
\(731\) | −1.99238e7 | −1.37904 | ||||||||
\(732\) | 7.32810e6 | 0.505491 | ||||||||
\(733\) | −1.58619e7 | −1.09042 | −0.545211 | − | 0.838299i | \(-0.683550\pi\) | ||||
−0.545211 | + | 0.838299i | \(0.683550\pi\) | |||||||
\(734\) | 2.12777e7 | 1.45775 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.70085e7 | 1.15736 | ||||||||
\(737\) | 2.50738e7 | 1.70040 | ||||||||
\(738\) | −1.93606e7 | −1.30851 | ||||||||
\(739\) | 2.51524e7 | 1.69421 | 0.847107 | − | 0.531422i | \(-0.178342\pi\) | ||||
0.847107 | + | 0.531422i | \(0.178342\pi\) | |||||||
\(740\) | −1.01312e7 | −0.680116 | ||||||||
\(741\) | −613202. | −0.0410259 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.30561e6 | 0.485495 | 0.242747 | − | 0.970090i | \(-0.421951\pi\) | ||||
0.242747 | + | 0.970090i | \(0.421951\pi\) | |||||||
\(744\) | 1.80653e6 | 0.119650 | ||||||||
\(745\) | −3.44735e6 | −0.227559 | ||||||||
\(746\) | −3.04350e7 | −2.00229 | ||||||||
\(747\) | 9.31822e6 | 0.610986 | ||||||||
\(748\) | −4.27908e7 | −2.79638 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −646189. | −0.0419475 | ||||||||
\(751\) | −826829. | −0.0534953 | −0.0267477 | − | 0.999642i | \(-0.508515\pi\) | ||||
−0.0267477 | + | 0.999642i | \(0.508515\pi\) | |||||||
\(752\) | 7.94747e6 | 0.512489 | ||||||||
\(753\) | −3.58781e6 | −0.230591 | ||||||||
\(754\) | 1.06839e6 | 0.0684389 | ||||||||
\(755\) | 7.71475e6 | 0.492554 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.70431e6 | 0.298371 | 0.149185 | − | 0.988809i | \(-0.452335\pi\) | ||||
0.149185 | + | 0.988809i | \(0.452335\pi\) | |||||||
\(758\) | −8.41583e6 | −0.532015 | ||||||||
\(759\) | 7.15683e6 | 0.450937 | ||||||||
\(760\) | 5.81680e6 | 0.365301 | ||||||||
\(761\) | −1.42681e6 | −0.0893107 | −0.0446553 | − | 0.999002i | \(-0.514219\pi\) | ||||
−0.0446553 | + | 0.999002i | \(0.514219\pi\) | |||||||
\(762\) | −4.66445e6 | −0.291013 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.97104e6 | 0.494062 | ||||||||
\(765\) | 7.87069e6 | 0.486250 | ||||||||
\(766\) | 2.93557e7 | 1.80767 | ||||||||
\(767\) | −792847. | −0.0486632 | ||||||||
\(768\) | −569993. | −0.0348712 | ||||||||
\(769\) | −9.32444e6 | −0.568600 | −0.284300 | − | 0.958735i | \(-0.591761\pi\) | ||||
−0.284300 | + | 0.958735i | \(0.591761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.87512e6 | 0.174189 | ||||||||
\(772\) | −2.26355e7 | −1.36693 | ||||||||
\(773\) | −1.52132e7 | −0.915741 | −0.457870 | − | 0.889019i | \(-0.651388\pi\) | ||||
−0.457870 | + | 0.889019i | \(0.651388\pi\) | |||||||
\(774\) | 2.68566e7 | 1.61138 | ||||||||
\(775\) | 2.24974e6 | 0.134548 | ||||||||
\(776\) | 9.02921e6 | 0.538264 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.03647e7 | −0.613916 | ||||||||
\(779\) | −2.21077e7 | −1.30527 | ||||||||
\(780\) | −307917. | −0.0181216 | ||||||||
\(781\) | −2.79739e6 | −0.164106 | ||||||||
\(782\) | −2.76944e7 | −1.61948 | ||||||||
\(783\) | −4.56885e6 | −0.266319 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.22507e6 | 0.302634 | ||||||||
\(786\) | −7.59203e6 | −0.438331 | ||||||||
\(787\) | 2.20016e7 | 1.26624 | 0.633122 | − | 0.774052i | \(-0.281773\pi\) | ||||
0.633122 | + | 0.774052i | \(0.281773\pi\) | |||||||
\(788\) | −1.24457e6 | −0.0714011 | ||||||||
\(789\) | −6.72850e6 | −0.384792 | ||||||||
\(790\) | 1.58022e7 | 0.900843 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 1.58598e7 | 0.898428 | ||||||||
\(793\) | 2.06262e6 | 0.116476 | ||||||||
\(794\) | 1.42807e7 | 0.803893 | ||||||||
\(795\) | −150145. | −0.00842545 | ||||||||
\(796\) | 4.12225e7 | 2.30596 | ||||||||
\(797\) | 3.02905e7 | 1.68912 | 0.844559 | − | 0.535462i | \(-0.179862\pi\) | ||||
0.844559 | + | 0.535462i | \(0.179862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.32299e7 | −1.28730 | ||||||||
\(800\) | −4.78124e6 | −0.264128 | ||||||||
\(801\) | −2.08444e7 | −1.14791 | ||||||||
\(802\) | −7.78479e6 | −0.427377 | ||||||||
\(803\) | 2.38884e6 | 0.130737 | ||||||||
\(804\) | −7.72294e6 | −0.421350 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.84930e6 | 0.100269 | ||||||||
\(807\) | −2.35553e6 | −0.127322 | ||||||||
\(808\) | −1.90923e7 | −1.02880 | ||||||||
\(809\) | −1.29572e7 | −0.696050 | −0.348025 | − | 0.937485i | \(-0.613148\pi\) | ||||
−0.348025 | + | 0.937485i | \(0.613148\pi\) | |||||||
\(810\) | −9.41863e6 | −0.504400 | ||||||||
\(811\) | −1.87248e7 | −0.999688 | −0.499844 | − | 0.866115i | \(-0.666609\pi\) | ||||
−0.499844 | + | 0.866115i | \(0.666609\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 737336. | 0.0391236 | ||||||||
\(814\) | −5.44124e7 | −2.87831 | ||||||||
\(815\) | 6.22538e6 | 0.328301 | ||||||||
\(816\) | −3.30457e6 | −0.173736 | ||||||||
\(817\) | 3.06673e7 | 1.60738 | ||||||||
\(818\) | −2.95622e7 | −1.54473 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.11013e7 | −0.576553 | ||||||||
\(821\) | 2.07863e7 | 1.07626 | 0.538132 | − | 0.842861i | \(-0.319130\pi\) | ||||
0.538132 | + | 0.842861i | \(0.319130\pi\) | |||||||
\(822\) | −3.81353e6 | −0.196856 | ||||||||
\(823\) | −2.40815e7 | −1.23932 | −0.619660 | − | 0.784870i | \(-0.712730\pi\) | ||||
−0.619660 | + | 0.784870i | \(0.712730\pi\) | |||||||
\(824\) | −1.83576e7 | −0.941884 | ||||||||
\(825\) | −2.01185e6 | −0.102911 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.53428e6 | −0.0780081 | −0.0390041 | − | 0.999239i | \(-0.512419\pi\) | ||||
−0.0390041 | + | 0.999239i | \(0.512419\pi\) | |||||||
\(828\) | 2.16407e7 | 1.09697 | ||||||||
\(829\) | −1.47802e7 | −0.746952 | −0.373476 | − | 0.927640i | \(-0.621834\pi\) | ||||
−0.373476 | + | 0.927640i | \(0.621834\pi\) | |||||||
\(830\) | 9.21695e6 | 0.464400 | ||||||||
\(831\) | −8.39242e6 | −0.421585 | ||||||||
\(832\) | −3.00999e6 | −0.150750 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.75494e7 | 0.873669 | ||||||||
\(835\) | −1.37624e7 | −0.683092 | ||||||||
\(836\) | 6.58649e7 | 3.25940 | ||||||||
\(837\) | −7.90827e6 | −0.390183 | ||||||||
\(838\) | −4.62121e7 | −2.27324 | ||||||||
\(839\) | 2.41688e6 | 0.118536 | 0.0592681 | − | 0.998242i | \(-0.481123\pi\) | ||||
0.0592681 | + | 0.998242i | \(0.481123\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.61865e7 | −0.789154 | ||||||||
\(842\) | 4.69531e7 | 2.28236 | ||||||||
\(843\) | −1.13171e7 | −0.548486 | ||||||||
\(844\) | −9.13057e6 | −0.441206 | ||||||||
\(845\) | 9.19566e6 | 0.443038 | ||||||||
\(846\) | 3.13132e7 | 1.50418 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −618870. | −0.0295536 | ||||||||
\(849\) | −917194. | −0.0436709 | ||||||||
\(850\) | 7.78515e6 | 0.369590 | ||||||||
\(851\) | −2.04145e7 | −0.966309 | ||||||||
\(852\) | 861621. | 0.0406647 | ||||||||
\(853\) | −3.98657e7 | −1.87598 | −0.937988 | − | 0.346669i | \(-0.887313\pi\) | ||||
−0.937988 | + | 0.346669i | \(0.887313\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.21148e7 | −0.566762 | ||||||||
\(856\) | 1.64595e7 | 0.767770 | ||||||||
\(857\) | 3.36474e7 | 1.56495 | 0.782473 | − | 0.622684i | \(-0.213958\pi\) | ||||
0.782473 | + | 0.622684i | \(0.213958\pi\) | |||||||
\(858\) | −1.65375e6 | −0.0766923 | ||||||||
\(859\) | 8.27879e6 | 0.382811 | 0.191405 | − | 0.981511i | \(-0.438695\pi\) | ||||
0.191405 | + | 0.981511i | \(0.438695\pi\) | |||||||
\(860\) | 1.53995e7 | 0.710001 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.49533e7 | −2.51898 | ||||||||
\(863\) | 1.06111e7 | 0.484990 | 0.242495 | − | 0.970153i | \(-0.422034\pi\) | ||||
0.242495 | + | 0.970153i | \(0.422034\pi\) | |||||||
\(864\) | 1.68070e7 | 0.765958 | ||||||||
\(865\) | 2.57565e6 | 0.117043 | ||||||||
\(866\) | −3.96640e7 | −1.79722 | ||||||||
\(867\) | 2.92941e6 | 0.132353 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.91987e7 | 2.21006 | ||||||||
\(870\) | −2.15009e6 | −0.0963072 | ||||||||
\(871\) | −2.17375e6 | −0.0970879 | ||||||||
\(872\) | 2.02126e6 | 0.0900181 | ||||||||
\(873\) | −1.88053e7 | −0.835113 | ||||||||
\(874\) | 4.26280e7 | 1.88763 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −735784. | −0.0323959 | ||||||||
\(877\) | −1.80051e6 | −0.0790492 | −0.0395246 | − | 0.999219i | \(-0.512584\pi\) | ||||
−0.0395246 | + | 0.999219i | \(0.512584\pi\) | |||||||
\(878\) | −2.35148e7 | −1.02945 | ||||||||
\(879\) | −315325. | −0.0137653 | ||||||||
\(880\) | −8.29248e6 | −0.360976 | ||||||||
\(881\) | −3.86161e7 | −1.67621 | −0.838105 | − | 0.545508i | \(-0.816337\pi\) | ||||
−0.838105 | + | 0.545508i | \(0.816337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.80155e6 | 0.379890 | 0.189945 | − | 0.981795i | \(-0.439169\pi\) | ||||
0.189945 | + | 0.981795i | \(0.439169\pi\) | |||||||
\(884\) | 3.70972e6 | 0.159665 | ||||||||
\(885\) | 1.59557e6 | 0.0684789 | ||||||||
\(886\) | −2.62573e7 | −1.12374 | ||||||||
\(887\) | 2.76706e7 | 1.18089 | 0.590444 | − | 0.807078i | \(-0.298953\pi\) | ||||
0.590444 | + | 0.807078i | \(0.298953\pi\) | |||||||
\(888\) | 4.60817e6 | 0.196108 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.06178e7 | −0.872505 | ||||||||
\(891\) | −2.93241e7 | −1.23746 | ||||||||
\(892\) | 1.53562e7 | 0.646207 | ||||||||
\(893\) | 3.57562e7 | 1.50045 | ||||||||
\(894\) | 5.70275e6 | 0.238639 | ||||||||
\(895\) | −1.17649e7 | −0.490943 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −620457. | −0.0257472 | ||||||||
\(898\) | 3.07220e7 | 1.27133 | ||||||||
\(899\) | 7.48565e6 | 0.308909 | ||||||||
\(900\) | −6.08340e6 | −0.250346 | ||||||||
\(901\) | 1.80892e6 | 0.0742347 | ||||||||
\(902\) | −5.96224e7 | −2.44002 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.07106e7 | 0.435907 | ||||||||
\(905\) | 1.32281e7 | 0.536880 | ||||||||
\(906\) | −1.27621e7 | −0.516536 | ||||||||
\(907\) | −3.47961e7 | −1.40447 | −0.702235 | − | 0.711945i | \(-0.747815\pi\) | ||||
−0.702235 | + | 0.711945i | \(0.747815\pi\) | |||||||
\(908\) | −3.49993e7 | −1.40878 | ||||||||
\(909\) | 3.97639e7 | 1.59617 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.48752e7 | 0.993049 | 0.496524 | − | 0.868023i | \(-0.334609\pi\) | ||||
0.496524 | + | 0.868023i | \(0.334609\pi\) | |||||||
\(912\) | 5.08648e6 | 0.202502 | ||||||||
\(913\) | 2.86962e7 | 1.13932 | ||||||||
\(914\) | 2.19552e7 | 0.869306 | ||||||||
\(915\) | −4.15092e6 | −0.163905 | ||||||||
\(916\) | −1.21745e7 | −0.479418 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.73663e7 | −1.07179 | ||||||||
\(919\) | −1.88971e7 | −0.738086 | −0.369043 | − | 0.929412i | \(-0.620314\pi\) | ||||
−0.369043 | + | 0.929412i | \(0.620314\pi\) | |||||||
\(920\) | 5.88562e6 | 0.229257 | ||||||||
\(921\) | 5.13280e6 | 0.199391 | ||||||||
\(922\) | −1.75209e6 | −0.0678782 | ||||||||
\(923\) | 242518. | 0.00937000 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.73872e6 | 0.220527 | ||||||||
\(926\) | 1.67696e6 | 0.0642681 | ||||||||
\(927\) | 3.82337e7 | 1.46133 | ||||||||
\(928\) | −1.59088e7 | −0.606412 | ||||||||
\(929\) | −2.29202e7 | −0.871324 | −0.435662 | − | 0.900110i | \(-0.643486\pi\) | ||||
−0.435662 | + | 0.900110i | \(0.643486\pi\) | |||||||
\(930\) | −3.72162e6 | −0.141099 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6.33741e7 | 2.38986 | ||||||||
\(933\) | −7.03341e6 | −0.264522 | ||||||||
\(934\) | 1.30788e7 | 0.490570 | ||||||||
\(935\) | 2.42384e7 | 0.906723 | ||||||||
\(936\) | −1.37495e6 | −0.0512977 | ||||||||
\(937\) | 3.70307e7 | 1.37789 | 0.688943 | − | 0.724815i | \(-0.258075\pi\) | ||||
0.688943 | + | 0.724815i | \(0.258075\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.22937e7 | −0.455009 | ||||||||
\(940\) | 1.79548e7 | 0.662769 | ||||||||
\(941\) | −1.25128e7 | −0.460660 | −0.230330 | − | 0.973113i | \(-0.573981\pi\) | ||||
−0.230330 | + | 0.973113i | \(0.573981\pi\) | |||||||
\(942\) | −8.64353e6 | −0.317369 | ||||||||
\(943\) | −2.23692e7 | −0.819166 | ||||||||
\(944\) | 6.57663e6 | 0.240200 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.27068e7 | 3.00479 | ||||||||
\(947\) | −1.22987e7 | −0.445640 | −0.222820 | − | 0.974860i | \(-0.571526\pi\) | ||||
−0.222820 | + | 0.974860i | \(0.571526\pi\) | |||||||
\(948\) | −1.51536e7 | −0.547641 | ||||||||
\(949\) | −207099. | −0.00746471 | ||||||||
\(950\) | −1.19831e7 | −0.430786 | ||||||||
\(951\) | −1.31592e7 | −0.471821 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.53421e6 | 0.126055 | 0.0630275 | − | 0.998012i | \(-0.479924\pi\) | ||||
0.0630275 | + | 0.998012i | \(0.479924\pi\) | |||||||
\(954\) | −2.43836e6 | −0.0867414 | ||||||||
\(955\) | −4.51510e6 | −0.160199 | ||||||||
\(956\) | 5.64501e6 | 0.199765 | ||||||||
\(957\) | −6.69411e6 | −0.236273 | ||||||||
\(958\) | 6.53021e7 | 2.29886 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.05746e6 | 0.212135 | ||||||||
\(961\) | −1.56721e7 | −0.547419 | ||||||||
\(962\) | 4.71725e6 | 0.164343 | ||||||||
\(963\) | −3.42805e7 | −1.19119 | ||||||||
\(964\) | 2.65994e7 | 0.921890 | ||||||||
\(965\) | 1.28216e7 | 0.443226 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.47189e6 | −0.325740 | −0.162870 | − | 0.986648i | \(-0.552075\pi\) | ||||
−0.162870 | + | 0.986648i | \(0.552075\pi\) | |||||||
\(968\) | 3.17879e7 | 1.09037 | ||||||||
\(969\) | −1.48675e7 | −0.508659 | ||||||||
\(970\) | −1.86010e7 | −0.634755 | ||||||||
\(971\) | 1.18431e7 | 0.403106 | 0.201553 | − | 0.979478i | \(-0.435401\pi\) | ||||
0.201553 | + | 0.979478i | \(0.435401\pi\) | |||||||
\(972\) | 3.25946e7 | 1.10657 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.91229e7 | −0.645887 | ||||||||
\(975\) | 174416. | 0.00587591 | ||||||||
\(976\) | −1.71093e7 | −0.574921 | ||||||||
\(977\) | −7.17342e6 | −0.240431 | −0.120215 | − | 0.992748i | \(-0.538358\pi\) | ||||
−0.120215 | + | 0.992748i | \(0.538358\pi\) | |||||||
\(978\) | −1.02983e7 | −0.344285 | ||||||||
\(979\) | −6.41918e7 | −2.14054 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.20971e6 | −0.139663 | ||||||||
\(982\) | 3.24216e7 | 1.07289 | ||||||||
\(983\) | 3.00611e7 | 0.992251 | 0.496126 | − | 0.868251i | \(-0.334755\pi\) | ||||
0.496126 | + | 0.868251i | \(0.334755\pi\) | |||||||
\(984\) | 5.04940e6 | 0.166246 | ||||||||
\(985\) | 704974. | 0.0231517 | ||||||||
\(986\) | 2.59039e7 | 0.848540 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.71011e6 | −0.186103 | ||||||||
\(989\) | 3.10301e7 | 1.00877 | ||||||||
\(990\) | −3.26725e7 | −1.05948 | ||||||||
\(991\) | −2.55378e7 | −0.826035 | −0.413018 | − | 0.910723i | \(-0.635525\pi\) | ||||
−0.413018 | + | 0.910723i | \(0.635525\pi\) | |||||||
\(992\) | −2.75367e7 | −0.888451 | ||||||||
\(993\) | −9.45077e6 | −0.304154 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.33500e7 | −0.747703 | ||||||||
\(996\) | −8.83867e6 | −0.282318 | ||||||||
\(997\) | −2.42489e7 | −0.772598 | −0.386299 | − | 0.922374i | \(-0.626247\pi\) | ||||
−0.386299 | + | 0.922374i | \(0.626247\pi\) | |||||||
\(998\) | 5.00975e7 | 1.59217 | ||||||||
\(999\) | −2.01727e7 | −0.639515 |
(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 | 245.6.a.i.1.6 | 6 | ||
7.2 | even | 3 | 35.6.e.a.11.1 | ✓ | 12 | ||
7.4 | even | 3 | 35.6.e.a.16.1 | yes | 12 | ||
7.6 | odd | 2 | 245.6.a.h.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.e.a.11.1 | ✓ | 12 | 7.2 | even | 3 | ||
35.6.e.a.16.1 | yes | 12 | 7.4 | even | 3 | ||
245.6.a.h.1.6 | 6 | 7.6 | odd | 2 | |||
245.6.a.i.1.6 | 6 | 1.1 | even | 1 | trivial |