Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 271 x^{8} + 309 x^{7} + 24456 x^{6} - 33410 x^{5} - 822204 x^{4} + 1367872 x^{3} + \cdots - 7036608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(11.0151\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.0151 | 1.94722 | 0.973610 | − | 0.228220i | \(-0.0732906\pi\) | ||||
0.973610 | + | 0.228220i | \(0.0732906\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 89.3332 | 2.79166 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −99.1362 | −1.12423 | ||||||||
\(7\) | 62.7690 | 0.484173 | 0.242086 | − | 0.970255i | \(-0.422168\pi\) | ||||
0.242086 | + | 0.970255i | \(0.422168\pi\) | |||||||
\(8\) | 631.533 | 3.48876 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −803.999 | −1.61177 | ||||||||
\(13\) | 986.561 | 1.61907 | 0.809535 | − | 0.587071i | \(-0.199719\pi\) | ||||
0.809535 | + | 0.587071i | \(0.199719\pi\) | |||||||
\(14\) | 691.409 | 0.942790 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4097.76 | 4.00171 | ||||||||
\(17\) | 577.936 | 0.485018 | 0.242509 | − | 0.970149i | \(-0.422030\pi\) | ||||
0.242509 | + | 0.970149i | \(0.422030\pi\) | |||||||
\(18\) | 892.226 | 0.649073 | ||||||||
\(19\) | −234.681 | −0.149140 | −0.0745698 | − | 0.997216i | \(-0.523758\pi\) | ||||
−0.0745698 | + | 0.997216i | \(0.523758\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −564.921 | −0.279537 | ||||||||
\(22\) | 1332.83 | 0.587109 | ||||||||
\(23\) | −2024.23 | −0.797885 | −0.398943 | − | 0.916976i | \(-0.630623\pi\) | ||||
−0.398943 | + | 0.916976i | \(0.630623\pi\) | |||||||
\(24\) | −5683.79 | −2.01424 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10867.1 | 3.15268 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 5607.35 | 1.35165 | ||||||||
\(29\) | −6877.68 | −1.51861 | −0.759306 | − | 0.650734i | \(-0.774461\pi\) | ||||
−0.759306 | + | 0.650734i | \(0.774461\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −689.224 | −0.128812 | −0.0644060 | − | 0.997924i | \(-0.520515\pi\) | ||||
−0.0644060 | + | 0.997924i | \(0.520515\pi\) | |||||||
\(32\) | 24928.3 | 4.30346 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 6366.04 | 0.944436 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7235.99 | 0.930554 | ||||||||
\(37\) | 12437.0 | 1.49352 | 0.746761 | − | 0.665092i | \(-0.231608\pi\) | ||||
0.746761 | + | 0.665092i | \(0.231608\pi\) | |||||||
\(38\) | −2585.04 | −0.290408 | ||||||||
\(39\) | −8879.05 | −0.934771 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5372.90 | −0.499170 | −0.249585 | − | 0.968353i | \(-0.580294\pi\) | ||||
−0.249585 | + | 0.968353i | \(0.580294\pi\) | |||||||
\(42\) | −6222.68 | −0.544320 | ||||||||
\(43\) | 13722.5 | 1.13178 | 0.565889 | − | 0.824482i | \(-0.308533\pi\) | ||||
0.565889 | + | 0.824482i | \(0.308533\pi\) | |||||||
\(44\) | 10809.3 | 0.841718 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −22297.2 | −1.55366 | ||||||||
\(47\) | −22652.2 | −1.49577 | −0.747887 | − | 0.663826i | \(-0.768932\pi\) | ||||
−0.747887 | + | 0.663826i | \(0.768932\pi\) | |||||||
\(48\) | −36879.8 | −2.31039 | ||||||||
\(49\) | −12867.1 | −0.765577 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5201.42 | −0.280025 | ||||||||
\(52\) | 88132.7 | 4.51990 | ||||||||
\(53\) | −5321.80 | −0.260237 | −0.130118 | − | 0.991498i | \(-0.541536\pi\) | ||||
−0.130118 | + | 0.991498i | \(0.541536\pi\) | |||||||
\(54\) | −8030.03 | −0.374742 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 39640.7 | 1.68916 | ||||||||
\(57\) | 2112.12 | 0.0861058 | ||||||||
\(58\) | −75758.6 | −2.95707 | ||||||||
\(59\) | 23792.4 | 0.889833 | 0.444916 | − | 0.895572i | \(-0.353233\pi\) | ||||
0.444916 | + | 0.895572i | \(0.353233\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 45926.5 | 1.58030 | 0.790149 | − | 0.612915i | \(-0.210003\pi\) | ||||
0.790149 | + | 0.612915i | \(0.210003\pi\) | |||||||
\(62\) | −7591.90 | −0.250825 | ||||||||
\(63\) | 5084.29 | 0.161391 | ||||||||
\(64\) | 143460. | 4.37806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −11995.5 | −0.338967 | ||||||||
\(67\) | 50509.5 | 1.37463 | 0.687315 | − | 0.726359i | \(-0.258789\pi\) | ||||
0.687315 | + | 0.726359i | \(0.258789\pi\) | |||||||
\(68\) | 51628.9 | 1.35401 | ||||||||
\(69\) | 18218.1 | 0.460659 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −29316.4 | −0.690184 | −0.345092 | − | 0.938569i | \(-0.612152\pi\) | ||||
−0.345092 | + | 0.938569i | \(0.612152\pi\) | |||||||
\(72\) | 51154.1 | 1.16292 | ||||||||
\(73\) | −42433.0 | −0.931959 | −0.465979 | − | 0.884796i | \(-0.654298\pi\) | ||||
−0.465979 | + | 0.884796i | \(0.654298\pi\) | |||||||
\(74\) | 136995. | 2.90822 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −20964.8 | −0.416347 | ||||||||
\(77\) | 7595.05 | 0.145984 | ||||||||
\(78\) | −97804.0 | −1.82020 | ||||||||
\(79\) | 63806.8 | 1.15027 | 0.575134 | − | 0.818059i | \(-0.304950\pi\) | ||||
0.575134 | + | 0.818059i | \(0.304950\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −59183.2 | −0.971994 | ||||||||
\(83\) | −57952.6 | −0.923374 | −0.461687 | − | 0.887043i | \(-0.652756\pi\) | ||||
−0.461687 | + | 0.887043i | \(0.652756\pi\) | |||||||
\(84\) | −50466.2 | −0.780373 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 151155. | 2.20382 | ||||||||
\(87\) | 61899.1 | 0.876771 | ||||||||
\(88\) | 76415.5 | 1.05190 | ||||||||
\(89\) | 75013.4 | 1.00384 | 0.501919 | − | 0.864915i | \(-0.332628\pi\) | ||||
0.501919 | + | 0.864915i | \(0.332628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 61925.5 | 0.783909 | ||||||||
\(92\) | −180831. | −2.22743 | ||||||||
\(93\) | 6203.02 | 0.0743696 | ||||||||
\(94\) | −249517. | −2.91260 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −224355. | −2.48460 | ||||||||
\(97\) | −10869.1 | −0.117291 | −0.0586454 | − | 0.998279i | \(-0.518678\pi\) | ||||
−0.0586454 | + | 0.998279i | \(0.518678\pi\) | |||||||
\(98\) | −141732. | −1.49075 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 112358. | 1.09597 | 0.547987 | − | 0.836487i | \(-0.315394\pi\) | ||||
0.547987 | + | 0.836487i | \(0.315394\pi\) | |||||||
\(102\) | −57294.4 | −0.545270 | ||||||||
\(103\) | 63393.0 | 0.588774 | 0.294387 | − | 0.955686i | \(-0.404885\pi\) | ||||
0.294387 | + | 0.955686i | \(0.404885\pi\) | |||||||
\(104\) | 623046. | 5.64855 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −58620.3 | −0.506738 | ||||||||
\(107\) | 163095. | 1.37715 | 0.688574 | − | 0.725167i | \(-0.258237\pi\) | ||||
0.688574 | + | 0.725167i | \(0.258237\pi\) | |||||||
\(108\) | −65123.9 | −0.537256 | ||||||||
\(109\) | −177552. | −1.43139 | −0.715697 | − | 0.698411i | \(-0.753891\pi\) | ||||
−0.715697 | + | 0.698411i | \(0.753891\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −111933. | −0.862286 | ||||||||
\(112\) | 257212. | 1.93752 | ||||||||
\(113\) | −3009.41 | −0.0221710 | −0.0110855 | − | 0.999939i | \(-0.503529\pi\) | ||||
−0.0110855 | + | 0.999939i | \(0.503529\pi\) | |||||||
\(114\) | 23265.3 | 0.167667 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −614405. | −4.23945 | ||||||||
\(117\) | 79911.5 | 0.539690 | ||||||||
\(118\) | 262077. | 1.73270 | ||||||||
\(119\) | 36276.5 | 0.234832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 505887. | 3.07719 | ||||||||
\(123\) | 48356.1 | 0.288196 | ||||||||
\(124\) | −61570.6 | −0.359599 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 56004.1 | 0.314263 | ||||||||
\(127\) | 151116. | 0.831382 | 0.415691 | − | 0.909506i | \(-0.363540\pi\) | ||||
0.415691 | + | 0.909506i | \(0.363540\pi\) | |||||||
\(128\) | 782528. | 4.22158 | ||||||||
\(129\) | −123502. | −0.653432 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −45401.3 | −0.231148 | −0.115574 | − | 0.993299i | \(-0.536871\pi\) | ||||
−0.115574 | + | 0.993299i | \(0.536871\pi\) | |||||||
\(132\) | −97283.8 | −0.485966 | ||||||||
\(133\) | −14730.7 | −0.0722093 | ||||||||
\(134\) | 556369. | 2.67671 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 364986. | 1.69211 | ||||||||
\(137\) | −297728. | −1.35525 | −0.677624 | − | 0.735408i | \(-0.736990\pi\) | ||||
−0.677624 | + | 0.735408i | \(0.736990\pi\) | |||||||
\(138\) | 200675. | 0.897005 | ||||||||
\(139\) | −214343. | −0.940962 | −0.470481 | − | 0.882410i | \(-0.655920\pi\) | ||||
−0.470481 | + | 0.882410i | \(0.655920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 203870. | 0.863586 | ||||||||
\(142\) | −322924. | −1.34394 | ||||||||
\(143\) | 119374. | 0.488168 | ||||||||
\(144\) | 331918. | 1.33390 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −467405. | −1.81473 | ||||||||
\(147\) | 115803. | 0.442006 | ||||||||
\(148\) | 1.11104e6 | 4.16941 | ||||||||
\(149\) | 234432. | 0.865071 | 0.432536 | − | 0.901617i | \(-0.357619\pi\) | ||||
0.432536 | + | 0.901617i | \(0.357619\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 60872.6 | 0.217260 | 0.108630 | − | 0.994082i | \(-0.465354\pi\) | ||||
0.108630 | + | 0.994082i | \(0.465354\pi\) | |||||||
\(152\) | −148208. | −0.520312 | ||||||||
\(153\) | 46812.8 | 0.161673 | ||||||||
\(154\) | 83660.5 | 0.284262 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −793194. | −2.60956 | ||||||||
\(157\) | 112122. | 0.363029 | 0.181514 | − | 0.983388i | \(-0.441900\pi\) | ||||
0.181514 | + | 0.983388i | \(0.441900\pi\) | |||||||
\(158\) | 702840. | 2.23982 | ||||||||
\(159\) | 47896.2 | 0.150248 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −127059. | −0.386314 | ||||||||
\(162\) | 72270.3 | 0.216358 | ||||||||
\(163\) | 364063. | 1.07327 | 0.536634 | − | 0.843815i | \(-0.319696\pi\) | ||||
0.536634 | + | 0.843815i | \(0.319696\pi\) | |||||||
\(164\) | −479978. | −1.39351 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −638356. | −1.79801 | ||||||||
\(167\) | −599451. | −1.66327 | −0.831635 | − | 0.555323i | \(-0.812595\pi\) | ||||
−0.831635 | + | 0.555323i | \(0.812595\pi\) | |||||||
\(168\) | −356766. | −0.975237 | ||||||||
\(169\) | 602011. | 1.62139 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −19009.1 | −0.0497132 | ||||||||
\(172\) | 1.22587e6 | 3.15954 | ||||||||
\(173\) | −546315. | −1.38780 | −0.693902 | − | 0.720070i | \(-0.744110\pi\) | ||||
−0.693902 | + | 0.720070i | \(0.744110\pi\) | |||||||
\(174\) | 681827. | 1.70727 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 495828. | 1.20656 | ||||||||
\(177\) | −214132. | −0.513745 | ||||||||
\(178\) | 826282. | 1.95469 | ||||||||
\(179\) | −482038. | −1.12447 | −0.562236 | − | 0.826977i | \(-0.690059\pi\) | ||||
−0.562236 | + | 0.826977i | \(0.690059\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −481935. | −1.09343 | −0.546717 | − | 0.837318i | \(-0.684123\pi\) | ||||
−0.546717 | + | 0.837318i | \(0.684123\pi\) | |||||||
\(182\) | 682117. | 1.52644 | ||||||||
\(183\) | −413339. | −0.912385 | ||||||||
\(184\) | −1.27837e6 | −2.78363 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 68327.1 | 0.144814 | ||||||||
\(187\) | 69930.3 | 0.146238 | ||||||||
\(188\) | −2.02359e6 | −4.17570 | ||||||||
\(189\) | −45758.6 | −0.0931790 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −300485. | −0.595990 | −0.297995 | − | 0.954567i | \(-0.596318\pi\) | ||||
−0.297995 | + | 0.954567i | \(0.596318\pi\) | |||||||
\(192\) | −1.29114e6 | −2.52767 | ||||||||
\(193\) | −860084. | −1.66206 | −0.831032 | − | 0.556225i | \(-0.812249\pi\) | ||||
−0.831032 | + | 0.556225i | \(0.812249\pi\) | |||||||
\(194\) | −119724. | −0.228391 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.14945e6 | −2.13723 | ||||||||
\(197\) | −623099. | −1.14391 | −0.571954 | − | 0.820286i | \(-0.693814\pi\) | ||||
−0.571954 | + | 0.820286i | \(0.693814\pi\) | |||||||
\(198\) | 107959. | 0.195703 | ||||||||
\(199\) | −417370. | −0.747116 | −0.373558 | − | 0.927607i | \(-0.621862\pi\) | ||||
−0.373558 | + | 0.927607i | \(0.621862\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −454585. | −0.793643 | ||||||||
\(202\) | 1.23764e6 | 2.13410 | ||||||||
\(203\) | −431705. | −0.735270 | ||||||||
\(204\) | −464660. | −0.781735 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 698283. | 1.14647 | ||||||||
\(207\) | −163963. | −0.265962 | ||||||||
\(208\) | 4.04269e6 | 6.47906 | ||||||||
\(209\) | −28396.3 | −0.0449673 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.24795e6 | 1.92970 | 0.964852 | − | 0.262795i | \(-0.0846441\pi\) | ||||
0.964852 | + | 0.262795i | \(0.0846441\pi\) | |||||||
\(212\) | −475413. | −0.726493 | ||||||||
\(213\) | 263848. | 0.398478 | ||||||||
\(214\) | 1.79651e6 | 2.68161 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −460387. | −0.671412 | ||||||||
\(217\) | −43261.9 | −0.0623672 | ||||||||
\(218\) | −1.95576e6 | −2.78724 | ||||||||
\(219\) | 381897. | 0.538067 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 570169. | 0.785278 | ||||||||
\(222\) | −1.23296e6 | −1.67906 | ||||||||
\(223\) | −399761. | −0.538317 | −0.269159 | − | 0.963096i | \(-0.586746\pi\) | ||||
−0.269159 | + | 0.963096i | \(0.586746\pi\) | |||||||
\(224\) | 1.56472e6 | 2.08362 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −33149.1 | −0.0431718 | ||||||||
\(227\) | 1.14478e6 | 1.47454 | 0.737269 | − | 0.675599i | \(-0.236115\pi\) | ||||
0.737269 | + | 0.675599i | \(0.236115\pi\) | |||||||
\(228\) | 188683. | 0.240378 | ||||||||
\(229\) | 24928.6 | 0.0314130 | 0.0157065 | − | 0.999877i | \(-0.495000\pi\) | ||||
0.0157065 | + | 0.999877i | \(0.495000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −68355.4 | −0.0842836 | ||||||||
\(232\) | −4.34348e6 | −5.29807 | ||||||||
\(233\) | −626233. | −0.755694 | −0.377847 | − | 0.925868i | \(-0.623336\pi\) | ||||
−0.377847 | + | 0.925868i | \(0.623336\pi\) | |||||||
\(234\) | 880236. | 1.05089 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.12545e6 | 2.48411 | ||||||||
\(237\) | −574261. | −0.664108 | ||||||||
\(238\) | 399590. | 0.457270 | ||||||||
\(239\) | −1.05033e6 | −1.18941 | −0.594704 | − | 0.803945i | \(-0.702731\pi\) | ||||
−0.594704 | + | 0.803945i | \(0.702731\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 251724. | 0.279178 | 0.139589 | − | 0.990210i | \(-0.455422\pi\) | ||||
0.139589 | + | 0.990210i | \(0.455422\pi\) | |||||||
\(242\) | 161273. | 0.177020 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 4.10276e6 | 4.41166 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 532649. | 0.561181 | ||||||||
\(247\) | −231527. | −0.241468 | ||||||||
\(248\) | −435268. | −0.449394 | ||||||||
\(249\) | 521574. | 0.533111 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 926617. | 0.928359 | 0.464180 | − | 0.885741i | \(-0.346349\pi\) | ||||
0.464180 | + | 0.885741i | \(0.346349\pi\) | |||||||
\(252\) | 454196. | 0.450549 | ||||||||
\(253\) | −244932. | −0.240571 | ||||||||
\(254\) | 1.66456e6 | 1.61888 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.02893e6 | 3.84228 | ||||||||
\(257\) | 1.37226e6 | 1.29600 | 0.647998 | − | 0.761642i | \(-0.275607\pi\) | ||||
0.647998 | + | 0.761642i | \(0.275607\pi\) | |||||||
\(258\) | −1.36039e6 | −1.27238 | ||||||||
\(259\) | 780659. | 0.723123 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −557092. | −0.506204 | ||||||||
\(262\) | −500101. | −0.450095 | ||||||||
\(263\) | 1.81605e6 | 1.61896 | 0.809482 | − | 0.587144i | \(-0.199748\pi\) | ||||
0.809482 | + | 0.587144i | \(0.199748\pi\) | |||||||
\(264\) | −687739. | −0.607315 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −162260. | −0.140607 | ||||||||
\(267\) | −675120. | −0.579566 | ||||||||
\(268\) | 4.51217e6 | 3.83750 | ||||||||
\(269\) | 1.27139e6 | 1.07127 | 0.535634 | − | 0.844450i | \(-0.320073\pi\) | ||||
0.535634 | + | 0.844450i | \(0.320073\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.44540e6 | 1.19554 | 0.597769 | − | 0.801668i | \(-0.296054\pi\) | ||||
0.597769 | + | 0.801668i | \(0.296054\pi\) | |||||||
\(272\) | 2.36824e6 | 1.94090 | ||||||||
\(273\) | −557329. | −0.452590 | ||||||||
\(274\) | −3.27952e6 | −2.63897 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.62748e6 | 1.28601 | ||||||||
\(277\) | 1.74706e6 | 1.36807 | 0.684034 | − | 0.729450i | \(-0.260224\pi\) | ||||
0.684034 | + | 0.729450i | \(0.260224\pi\) | |||||||
\(278\) | −2.36102e6 | −1.83226 | ||||||||
\(279\) | −55827.1 | −0.0429373 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.84101e6 | −1.39088 | −0.695441 | − | 0.718583i | \(-0.744791\pi\) | ||||
−0.695441 | + | 0.718583i | \(0.744791\pi\) | |||||||
\(282\) | 2.24565e6 | 1.68159 | ||||||||
\(283\) | −986043. | −0.731863 | −0.365931 | − | 0.930642i | \(-0.619249\pi\) | ||||
−0.365931 | + | 0.930642i | \(0.619249\pi\) | |||||||
\(284\) | −2.61893e6 | −1.92676 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.31492e6 | 0.950570 | ||||||||
\(287\) | −337251. | −0.241685 | ||||||||
\(288\) | 2.01919e6 | 1.43449 | ||||||||
\(289\) | −1.08585e6 | −0.764758 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 97821.8 | 0.0677179 | ||||||||
\(292\) | −3.79068e6 | −2.60171 | ||||||||
\(293\) | −1.98564e6 | −1.35124 | −0.675618 | − | 0.737252i | \(-0.736123\pi\) | ||||
−0.675618 | + | 0.737252i | \(0.736123\pi\) | |||||||
\(294\) | 1.27559e6 | 0.860683 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.85438e6 | 5.21054 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 2.58230e6 | 1.68448 | ||||||||
\(299\) | −1.99703e6 | −1.29183 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 861346. | 0.547976 | ||||||||
\(302\) | 670520. | 0.423052 | ||||||||
\(303\) | −1.01122e6 | −0.632761 | ||||||||
\(304\) | −961663. | −0.596814 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 515650. | 0.314812 | ||||||||
\(307\) | −1.13983e6 | −0.690232 | −0.345116 | − | 0.938560i | \(-0.612160\pi\) | ||||
−0.345116 | + | 0.938560i | \(0.612160\pi\) | |||||||
\(308\) | 678490. | 0.407537 | ||||||||
\(309\) | −570537. | −0.339929 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −131904. | −0.0773319 | −0.0386659 | − | 0.999252i | \(-0.512311\pi\) | ||||
−0.0386659 | + | 0.999252i | \(0.512311\pi\) | |||||||
\(312\) | −5.60741e6 | −3.26119 | ||||||||
\(313\) | −2.07325e6 | −1.19616 | −0.598082 | − | 0.801435i | \(-0.704070\pi\) | ||||
−0.598082 | + | 0.801435i | \(0.704070\pi\) | |||||||
\(314\) | 1.23504e6 | 0.706896 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.70006e6 | 3.21116 | ||||||||
\(317\) | 95123.6 | 0.0531667 | 0.0265834 | − | 0.999647i | \(-0.491537\pi\) | ||||
0.0265834 | + | 0.999647i | \(0.491537\pi\) | |||||||
\(318\) | 527583. | 0.292565 | ||||||||
\(319\) | −832199. | −0.457879 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.46785e6 | −0.795096 | ||||||||
\(322\) | −1.39957e6 | −0.752238 | ||||||||
\(323\) | −135630. | −0.0723353 | ||||||||
\(324\) | 586115. | 0.310185 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.01021e6 | 2.08989 | ||||||||
\(327\) | 1.59797e6 | 0.826415 | ||||||||
\(328\) | −3.39316e6 | −1.74148 | ||||||||
\(329\) | −1.42186e6 | −0.724213 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.20153e6 | −1.60616 | −0.803078 | − | 0.595874i | \(-0.796806\pi\) | ||||
−0.803078 | + | 0.595874i | \(0.796806\pi\) | |||||||
\(332\) | −5.17709e6 | −2.57775 | ||||||||
\(333\) | 1.00740e6 | 0.497841 | ||||||||
\(334\) | −6.60304e6 | −3.23875 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.31491e6 | −1.11863 | ||||||||
\(337\) | −2.16577e6 | −1.03881 | −0.519406 | − | 0.854527i | \(-0.673847\pi\) | ||||
−0.519406 | + | 0.854527i | \(0.673847\pi\) | |||||||
\(338\) | 6.63123e6 | 3.15720 | ||||||||
\(339\) | 27084.7 | 0.0128004 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −83396.1 | −0.0388383 | ||||||||
\(342\) | −209388. | −0.0968025 | ||||||||
\(343\) | −1.86261e6 | −0.854844 | ||||||||
\(344\) | 8.66619e6 | 3.94850 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.01773e6 | −2.70236 | ||||||||
\(347\) | 2.76730e6 | 1.23377 | 0.616883 | − | 0.787055i | \(-0.288395\pi\) | ||||
0.616883 | + | 0.787055i | \(0.288395\pi\) | |||||||
\(348\) | 5.52964e6 | 2.44765 | ||||||||
\(349\) | 3.44895e6 | 1.51574 | 0.757868 | − | 0.652408i | \(-0.226241\pi\) | ||||
0.757868 | + | 0.652408i | \(0.226241\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −719203. | −0.311590 | ||||||||
\(352\) | 3.01632e6 | 1.29754 | ||||||||
\(353\) | −4.34110e6 | −1.85423 | −0.927113 | − | 0.374781i | \(-0.877718\pi\) | ||||
−0.927113 | + | 0.374781i | \(0.877718\pi\) | |||||||
\(354\) | −2.35869e6 | −1.00037 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.70118e6 | 2.80238 | ||||||||
\(357\) | −326488. | −0.135580 | ||||||||
\(358\) | −5.30971e6 | −2.18959 | ||||||||
\(359\) | 2.70091e6 | 1.10605 | 0.553024 | − | 0.833166i | \(-0.313474\pi\) | ||||
0.553024 | + | 0.833166i | \(0.313474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.42102e6 | −0.977757 | ||||||||
\(362\) | −5.30858e6 | −2.12915 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 5.53200e6 | 2.18841 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.55298e6 | −1.77661 | ||||||||
\(367\) | −3.59856e6 | −1.39465 | −0.697323 | − | 0.716757i | \(-0.745626\pi\) | ||||
−0.697323 | + | 0.716757i | \(0.745626\pi\) | |||||||
\(368\) | −8.29480e6 | −3.19291 | ||||||||
\(369\) | −435205. | −0.166390 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −334044. | −0.126000 | ||||||||
\(372\) | 554135. | 0.207615 | ||||||||
\(373\) | 4.71222e6 | 1.75369 | 0.876846 | − | 0.480772i | \(-0.159643\pi\) | ||||
0.876846 | + | 0.480772i | \(0.159643\pi\) | |||||||
\(374\) | 770291. | 0.284758 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.43056e7 | −5.21839 | ||||||||
\(377\) | −6.78525e6 | −2.45874 | ||||||||
\(378\) | −504037. | −0.181440 | ||||||||
\(379\) | 2.89500e6 | 1.03526 | 0.517631 | − | 0.855604i | \(-0.326814\pi\) | ||||
0.517631 | + | 0.855604i | \(0.326814\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.36004e6 | −0.479999 | ||||||||
\(382\) | −3.30988e6 | −1.16052 | ||||||||
\(383\) | −691654. | −0.240931 | −0.120465 | − | 0.992718i | \(-0.538439\pi\) | ||||
−0.120465 | + | 0.992718i | \(0.538439\pi\) | |||||||
\(384\) | −7.04275e6 | −2.43733 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.47394e6 | −3.23640 | ||||||||
\(387\) | 1.11152e6 | 0.377259 | ||||||||
\(388\) | −970970. | −0.327436 | ||||||||
\(389\) | −210206. | −0.0704323 | −0.0352161 | − | 0.999380i | \(-0.511212\pi\) | ||||
−0.0352161 | + | 0.999380i | \(0.511212\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.16988e6 | −0.386988 | ||||||||
\(392\) | −8.12596e6 | −2.67091 | ||||||||
\(393\) | 408611. | 0.133453 | ||||||||
\(394\) | −6.86352e6 | −2.22744 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 875555. | 0.280573 | ||||||||
\(397\) | −2.04826e6 | −0.652242 | −0.326121 | − | 0.945328i | \(-0.605742\pi\) | ||||
−0.326121 | + | 0.945328i | \(0.605742\pi\) | |||||||
\(398\) | −4.59738e6 | −1.45480 | ||||||||
\(399\) | 132576. | 0.0416901 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.26605e6 | 0.393179 | 0.196589 | − | 0.980486i | \(-0.437013\pi\) | ||||
0.196589 | + | 0.980486i | \(0.437013\pi\) | |||||||
\(402\) | −5.00732e6 | −1.54540 | ||||||||
\(403\) | −679962. | −0.208556 | ||||||||
\(404\) | 1.00373e7 | 3.05959 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.75529e6 | −1.43173 | ||||||||
\(407\) | 1.50488e6 | 0.450314 | ||||||||
\(408\) | −3.28487e6 | −0.976940 | ||||||||
\(409\) | 2.04510e6 | 0.604514 | 0.302257 | − | 0.953226i | \(-0.402260\pi\) | ||||
0.302257 | + | 0.953226i | \(0.402260\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.67956e6 | 0.782453 | ||||||||
\(412\) | 5.66310e6 | 1.64366 | ||||||||
\(413\) | 1.49343e6 | 0.430832 | ||||||||
\(414\) | −1.80607e6 | −0.517886 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.45933e7 | 6.96760 | ||||||||
\(417\) | 1.92909e6 | 0.543265 | ||||||||
\(418\) | −312790. | −0.0875612 | ||||||||
\(419\) | −1.00407e6 | −0.279401 | −0.139701 | − | 0.990194i | \(-0.544614\pi\) | ||||
−0.139701 | + | 0.990194i | \(0.544614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.99725e6 | −1.37412 | −0.687061 | − | 0.726599i | \(-0.741100\pi\) | ||||
−0.687061 | + | 0.726599i | \(0.741100\pi\) | |||||||
\(422\) | 1.37463e7 | 3.75756 | ||||||||
\(423\) | −1.83483e6 | −0.498591 | ||||||||
\(424\) | −3.36089e6 | −0.907903 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.90632e6 | 0.775924 | ||||||||
\(427\) | 2.88276e6 | 0.765137 | ||||||||
\(428\) | 1.45698e7 | 3.84453 | ||||||||
\(429\) | −1.07437e6 | −0.281844 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −397569. | −0.103091 | −0.0515453 | − | 0.998671i | \(-0.516415\pi\) | ||||
−0.0515453 | + | 0.998671i | \(0.516415\pi\) | |||||||
\(432\) | −2.98726e6 | −0.770130 | ||||||||
\(433\) | −5.89453e6 | −1.51088 | −0.755439 | − | 0.655219i | \(-0.772576\pi\) | ||||
−0.755439 | + | 0.655219i | \(0.772576\pi\) | |||||||
\(434\) | −476536. | −0.121443 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.58613e7 | −3.99597 | ||||||||
\(437\) | 475048. | 0.118996 | ||||||||
\(438\) | 4.20665e6 | 1.04773 | ||||||||
\(439\) | −2.26759e6 | −0.561570 | −0.280785 | − | 0.959771i | \(-0.590595\pi\) | ||||
−0.280785 | + | 0.959771i | \(0.590595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.04223e6 | −0.255192 | ||||||||
\(442\) | 6.28049e6 | 1.52911 | ||||||||
\(443\) | −1.42871e6 | −0.345888 | −0.172944 | − | 0.984932i | \(-0.555328\pi\) | ||||
−0.172944 | + | 0.984932i | \(0.555328\pi\) | |||||||
\(444\) | −9.99934e6 | −2.40721 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.40342e6 | −1.04822 | ||||||||
\(447\) | −2.10989e6 | −0.499449 | ||||||||
\(448\) | 9.00485e6 | 2.11974 | ||||||||
\(449\) | 4.49834e6 | 1.05302 | 0.526510 | − | 0.850169i | \(-0.323500\pi\) | ||||
0.526510 | + | 0.850169i | \(0.323500\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −650120. | −0.150506 | ||||||||
\(452\) | −268840. | −0.0618940 | ||||||||
\(453\) | −547853. | −0.125435 | ||||||||
\(454\) | 1.26099e7 | 2.87125 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.33388e6 | 0.300402 | ||||||||
\(457\) | −5.64865e6 | −1.26518 | −0.632592 | − | 0.774485i | \(-0.718009\pi\) | ||||
−0.632592 | + | 0.774485i | \(0.718009\pi\) | |||||||
\(458\) | 274592. | 0.0611680 | ||||||||
\(459\) | −421315. | −0.0933417 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.44590e6 | −1.85094 | −0.925472 | − | 0.378815i | \(-0.876332\pi\) | ||||
−0.925472 | + | 0.378815i | \(0.876332\pi\) | |||||||
\(462\) | −752944. | −0.164119 | ||||||||
\(463\) | −4.07836e6 | −0.884165 | −0.442082 | − | 0.896974i | \(-0.645760\pi\) | ||||
−0.442082 | + | 0.896974i | \(0.645760\pi\) | |||||||
\(464\) | −2.81830e7 | −6.07705 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.89804e6 | −1.47150 | ||||||||
\(467\) | −3.43895e6 | −0.729682 | −0.364841 | − | 0.931070i | \(-0.618877\pi\) | ||||
−0.364841 | + | 0.931070i | \(0.618877\pi\) | |||||||
\(468\) | 7.13875e6 | 1.50663 | ||||||||
\(469\) | 3.17043e6 | 0.665558 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00910e6 | −0.209595 | ||||||||
\(472\) | 1.50257e7 | 3.10441 | ||||||||
\(473\) | 1.66042e6 | 0.341244 | ||||||||
\(474\) | −6.32556e6 | −1.29316 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.24069e6 | 0.655572 | ||||||||
\(477\) | −431066. | −0.0867456 | ||||||||
\(478\) | −1.15695e7 | −2.31604 | ||||||||
\(479\) | 3.52502e6 | 0.701978 | 0.350989 | − | 0.936380i | \(-0.385845\pi\) | ||||
0.350989 | + | 0.936380i | \(0.385845\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.22699e7 | 2.41812 | ||||||||
\(482\) | 2.77277e6 | 0.543621 | ||||||||
\(483\) | 1.14353e6 | 0.223039 | ||||||||
\(484\) | 1.30793e6 | 0.253787 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −650433. | −0.124914 | ||||||||
\(487\) | −1.06326e6 | −0.203151 | −0.101575 | − | 0.994828i | \(-0.532388\pi\) | ||||
−0.101575 | + | 0.994828i | \(0.532388\pi\) | |||||||
\(488\) | 2.90041e7 | 5.51328 | ||||||||
\(489\) | −3.27657e6 | −0.619651 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.16347e6 | 1.71536 | 0.857682 | − | 0.514180i | \(-0.171904\pi\) | ||||
0.857682 | + | 0.514180i | \(0.171904\pi\) | |||||||
\(492\) | 4.31980e6 | 0.804546 | ||||||||
\(493\) | −3.97486e6 | −0.736554 | ||||||||
\(494\) | −2.55030e6 | −0.470190 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.82427e6 | −0.515469 | ||||||||
\(497\) | −1.84016e6 | −0.334168 | ||||||||
\(498\) | 5.74520e6 | 1.03808 | ||||||||
\(499\) | −4.49589e6 | −0.808285 | −0.404142 | − | 0.914696i | \(-0.632430\pi\) | ||||
−0.404142 | + | 0.914696i | \(0.632430\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.39506e6 | 0.960289 | ||||||||
\(502\) | 1.02068e7 | 1.80772 | ||||||||
\(503\) | −8.70281e6 | −1.53370 | −0.766848 | − | 0.641828i | \(-0.778176\pi\) | ||||
−0.766848 | + | 0.641828i | \(0.778176\pi\) | |||||||
\(504\) | 3.21089e6 | 0.563054 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.69796e6 | −0.468445 | ||||||||
\(507\) | −5.41809e6 | −0.936110 | ||||||||
\(508\) | 1.34997e7 | 2.32094 | ||||||||
\(509\) | 5.96436e6 | 1.02040 | 0.510199 | − | 0.860057i | \(-0.329572\pi\) | ||||
0.510199 | + | 0.860057i | \(0.329572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.66348e6 | −0.451229 | ||||||||
\(512\) | 1.93383e7 | 3.26019 | ||||||||
\(513\) | 171082. | 0.0287019 | ||||||||
\(514\) | 1.51156e7 | 2.52359 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.10328e7 | −1.82416 | ||||||||
\(517\) | −2.74092e6 | −0.450993 | ||||||||
\(518\) | 8.59906e6 | 1.40808 | ||||||||
\(519\) | 4.91683e6 | 0.801248 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.15902e6 | −0.348468 | −0.174234 | − | 0.984704i | \(-0.555745\pi\) | ||||
−0.174234 | + | 0.984704i | \(0.555745\pi\) | |||||||
\(522\) | −6.13644e6 | −0.985690 | ||||||||
\(523\) | 768246. | 0.122814 | 0.0614068 | − | 0.998113i | \(-0.480441\pi\) | ||||
0.0614068 | + | 0.998113i | \(0.480441\pi\) | |||||||
\(524\) | −4.05584e6 | −0.645286 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.00040e7 | 3.15248 | ||||||||
\(527\) | −398327. | −0.0624761 | ||||||||
\(528\) | −4.46246e6 | −0.696609 | ||||||||
\(529\) | −2.33883e6 | −0.363379 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.92718e6 | 0.296611 | ||||||||
\(532\) | −1.31594e6 | −0.201584 | ||||||||
\(533\) | −5.30069e6 | −0.808192 | ||||||||
\(534\) | −7.43654e6 | −1.12854 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.18984e7 | 4.79575 | ||||||||
\(537\) | 4.33834e6 | 0.649214 | ||||||||
\(538\) | 1.40045e7 | 2.08599 | ||||||||
\(539\) | −1.55691e6 | −0.230830 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −518319. | −0.0761385 | −0.0380693 | − | 0.999275i | \(-0.512121\pi\) | ||||
−0.0380693 | + | 0.999275i | \(0.512121\pi\) | |||||||
\(542\) | 1.59212e7 | 2.32797 | ||||||||
\(543\) | 4.33742e6 | 0.631294 | ||||||||
\(544\) | 1.44070e7 | 2.08725 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.13906e6 | −0.881292 | ||||||||
\(547\) | −4.96112e6 | −0.708944 | −0.354472 | − | 0.935067i | \(-0.615339\pi\) | ||||
−0.354472 | + | 0.935067i | \(0.615339\pi\) | |||||||
\(548\) | −2.65970e7 | −3.78340 | ||||||||
\(549\) | 3.72005e6 | 0.526766 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.61406e6 | 0.226485 | ||||||||
\(552\) | 1.15053e7 | 1.60713 | ||||||||
\(553\) | 4.00509e6 | 0.556928 | ||||||||
\(554\) | 1.92441e7 | 2.66393 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.91479e7 | −2.62685 | ||||||||
\(557\) | 9.82979e6 | 1.34248 | 0.671238 | − | 0.741242i | \(-0.265763\pi\) | ||||
0.671238 | + | 0.741242i | \(0.265763\pi\) | |||||||
\(558\) | −614944. | −0.0836084 | ||||||||
\(559\) | 1.35381e7 | 1.83243 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −629372. | −0.0844307 | ||||||||
\(562\) | −2.02790e7 | −2.70835 | ||||||||
\(563\) | −7.66483e6 | −1.01913 | −0.509567 | − | 0.860431i | \(-0.670195\pi\) | ||||
−0.509567 | + | 0.860431i | \(0.670195\pi\) | |||||||
\(564\) | 1.82124e7 | 2.41084 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.08614e7 | −1.42510 | ||||||||
\(567\) | 411827. | 0.0537969 | ||||||||
\(568\) | −1.85143e7 | −2.40788 | ||||||||
\(569\) | −62102.5 | −0.00804134 | −0.00402067 | − | 0.999992i | \(-0.501280\pi\) | ||||
−0.00402067 | + | 0.999992i | \(0.501280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.48638e6 | −0.447491 | −0.223745 | − | 0.974648i | \(-0.571828\pi\) | ||||
−0.223745 | + | 0.974648i | \(0.571828\pi\) | |||||||
\(572\) | 1.06641e7 | 1.36280 | ||||||||
\(573\) | 2.70436e6 | 0.344095 | ||||||||
\(574\) | −3.71487e6 | −0.470613 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.16203e7 | 1.45935 | ||||||||
\(577\) | 9.55413e6 | 1.19468 | 0.597340 | − | 0.801988i | \(-0.296224\pi\) | ||||
0.597340 | + | 0.801988i | \(0.296224\pi\) | |||||||
\(578\) | −1.19607e7 | −1.48915 | ||||||||
\(579\) | 7.74076e6 | 0.959593 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.63763e6 | −0.447073 | ||||||||
\(582\) | 1.07752e6 | 0.131861 | ||||||||
\(583\) | −643938. | −0.0784644 | ||||||||
\(584\) | −2.67978e7 | −3.25138 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.18721e7 | −2.63115 | ||||||||
\(587\) | 5.56273e6 | 0.666335 | 0.333168 | − | 0.942868i | \(-0.391882\pi\) | ||||
0.333168 | + | 0.942868i | \(0.391882\pi\) | |||||||
\(588\) | 1.03451e7 | 1.23393 | ||||||||
\(589\) | 161747. | 0.0192110 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.60789e6 | 0.660436 | ||||||||
\(592\) | 5.09639e7 | 5.97665 | ||||||||
\(593\) | −1.10409e7 | −1.28934 | −0.644669 | − | 0.764462i | \(-0.723005\pi\) | ||||
−0.644669 | + | 0.764462i | \(0.723005\pi\) | |||||||
\(594\) | −971634. | −0.112989 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.09426e7 | 2.41499 | ||||||||
\(597\) | 3.75633e6 | 0.431348 | ||||||||
\(598\) | −2.19975e7 | −2.51548 | ||||||||
\(599\) | −1.47678e6 | −0.168170 | −0.0840852 | − | 0.996459i | \(-0.526797\pi\) | ||||
−0.0840852 | + | 0.996459i | \(0.526797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.70993e6 | −0.870691 | −0.435346 | − | 0.900263i | \(-0.643374\pi\) | ||||
−0.435346 | + | 0.900263i | \(0.643374\pi\) | |||||||
\(602\) | 9.48784e6 | 1.06703 | ||||||||
\(603\) | 4.09127e6 | 0.458210 | ||||||||
\(604\) | 5.43794e6 | 0.606516 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.11387e7 | −1.23212 | ||||||||
\(607\) | −1.55229e7 | −1.71002 | −0.855009 | − | 0.518613i | \(-0.826449\pi\) | ||||
−0.855009 | + | 0.518613i | \(0.826449\pi\) | |||||||
\(608\) | −5.85018e6 | −0.641816 | ||||||||
\(609\) | 3.88535e6 | 0.424509 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.23478e7 | −2.42176 | ||||||||
\(612\) | 4.18194e6 | 0.451335 | ||||||||
\(613\) | −7.98615e6 | −0.858394 | −0.429197 | − | 0.903211i | \(-0.641203\pi\) | ||||
−0.429197 | + | 0.903211i | \(0.641203\pi\) | |||||||
\(614\) | −1.25554e7 | −1.34403 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.79652e6 | 0.509301 | ||||||||
\(617\) | 8.91087e6 | 0.942339 | 0.471170 | − | 0.882043i | \(-0.343832\pi\) | ||||
0.471170 | + | 0.882043i | \(0.343832\pi\) | |||||||
\(618\) | −6.28454e6 | −0.661915 | ||||||||
\(619\) | −4.54740e6 | −0.477019 | −0.238510 | − | 0.971140i | \(-0.576659\pi\) | ||||
−0.238510 | + | 0.971140i | \(0.576659\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.47566e6 | 0.153553 | ||||||||
\(622\) | −1.45295e6 | −0.150582 | ||||||||
\(623\) | 4.70851e6 | 0.486031 | ||||||||
\(624\) | −3.63842e7 | −3.74069 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.28371e7 | −2.32919 | ||||||||
\(627\) | 255567. | 0.0259619 | ||||||||
\(628\) | 1.00162e7 | 1.01345 | ||||||||
\(629\) | 7.18780e6 | 0.724385 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.26569e7 | 1.26548 | 0.632740 | − | 0.774365i | \(-0.281930\pi\) | ||||
0.632740 | + | 0.774365i | \(0.281930\pi\) | |||||||
\(632\) | 4.02961e7 | 4.01301 | ||||||||
\(633\) | −1.12315e7 | −1.11411 | ||||||||
\(634\) | 1.04780e6 | 0.103527 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.27872e6 | 0.419441 | ||||||||
\(637\) | −1.26941e7 | −1.23952 | ||||||||
\(638\) | −9.16679e6 | −0.891590 | ||||||||
\(639\) | −2.37463e6 | −0.230061 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.39088e6 | 0.325963 | 0.162981 | − | 0.986629i | \(-0.447889\pi\) | ||||
0.162981 | + | 0.986629i | \(0.447889\pi\) | |||||||
\(642\) | −1.61686e7 | −1.54823 | ||||||||
\(643\) | −5.58626e6 | −0.532837 | −0.266418 | − | 0.963858i | \(-0.585840\pi\) | ||||
−0.266418 | + | 0.963858i | \(0.585840\pi\) | |||||||
\(644\) | −1.13506e7 | −1.07846 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.49399e6 | −0.140853 | ||||||||
\(647\) | −1.49548e7 | −1.40450 | −0.702248 | − | 0.711932i | \(-0.747820\pi\) | ||||
−0.702248 | + | 0.711932i | \(0.747820\pi\) | |||||||
\(648\) | 4.14349e6 | 0.387640 | ||||||||
\(649\) | 2.87888e6 | 0.268295 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 389357. | 0.0360077 | ||||||||
\(652\) | 3.25229e7 | 2.99620 | ||||||||
\(653\) | −3.85494e6 | −0.353782 | −0.176891 | − | 0.984230i | \(-0.556604\pi\) | ||||
−0.176891 | + | 0.984230i | \(0.556604\pi\) | |||||||
\(654\) | 1.76018e7 | 1.60921 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.20168e7 | −1.99754 | ||||||||
\(657\) | −3.43707e6 | −0.310653 | ||||||||
\(658\) | −1.56619e7 | −1.41020 | ||||||||
\(659\) | −8.60888e6 | −0.772206 | −0.386103 | − | 0.922456i | \(-0.626179\pi\) | ||||
−0.386103 | + | 0.922456i | \(0.626179\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.93015e6 | 0.349869 | 0.174934 | − | 0.984580i | \(-0.444029\pi\) | ||||
0.174934 | + | 0.984580i | \(0.444029\pi\) | |||||||
\(662\) | −3.52653e7 | −3.12754 | ||||||||
\(663\) | −5.13153e6 | −0.453380 | ||||||||
\(664\) | −3.65990e7 | −3.22143 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.10966e7 | 0.969405 | ||||||||
\(667\) | 1.39220e7 | 1.21168 | ||||||||
\(668\) | −5.35509e7 | −4.64329 | ||||||||
\(669\) | 3.59785e6 | 0.310798 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.55711e6 | 0.476478 | ||||||||
\(672\) | −1.40825e7 | −1.20298 | ||||||||
\(673\) | 1.74231e7 | 1.48282 | 0.741408 | − | 0.671054i | \(-0.234158\pi\) | ||||
0.741408 | + | 0.671054i | \(0.234158\pi\) | |||||||
\(674\) | −2.38562e7 | −2.02280 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.37795e7 | 4.52637 | ||||||||
\(677\) | 1.74041e7 | 1.45942 | 0.729711 | − | 0.683756i | \(-0.239655\pi\) | ||||
0.729711 | + | 0.683756i | \(0.239655\pi\) | |||||||
\(678\) | 298342. | 0.0249253 | ||||||||
\(679\) | −682242. | −0.0567890 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.03030e7 | −0.851325 | ||||||||
\(682\) | −918619. | −0.0756266 | ||||||||
\(683\) | −6.21136e6 | −0.509489 | −0.254745 | − | 0.967008i | \(-0.581991\pi\) | ||||
−0.254745 | + | 0.967008i | \(0.581991\pi\) | |||||||
\(684\) | −1.69815e6 | −0.138782 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.05169e7 | −1.66457 | ||||||||
\(687\) | −224358. | −0.0181363 | ||||||||
\(688\) | 5.62313e7 | 4.52905 | ||||||||
\(689\) | −5.25028e6 | −0.421342 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.49150e6 | −0.278174 | −0.139087 | − | 0.990280i | \(-0.544417\pi\) | ||||
−0.139087 | + | 0.990280i | \(0.544417\pi\) | |||||||
\(692\) | −4.88041e7 | −3.87428 | ||||||||
\(693\) | 615199. | 0.0486612 | ||||||||
\(694\) | 3.04822e7 | 2.40241 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.90913e7 | 3.05884 | ||||||||
\(697\) | −3.10519e6 | −0.242106 | ||||||||
\(698\) | 3.79907e7 | 2.95147 | ||||||||
\(699\) | 5.63610e6 | 0.436300 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.84192e6 | 0.756458 | 0.378229 | − | 0.925712i | \(-0.376533\pi\) | ||||
0.378229 | + | 0.925712i | \(0.376533\pi\) | |||||||
\(702\) | −7.92212e6 | −0.606734 | ||||||||
\(703\) | −2.91873e6 | −0.222743 | ||||||||
\(704\) | 1.73587e7 | 1.32003 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.78178e7 | −3.61059 | ||||||||
\(707\) | 7.05260e6 | 0.530641 | ||||||||
\(708\) | −1.91291e7 | −1.43420 | ||||||||
\(709\) | 2.04292e7 | 1.52629 | 0.763144 | − | 0.646228i | \(-0.223655\pi\) | ||||
0.763144 | + | 0.646228i | \(0.223655\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.16835e6 | 0.383423 | ||||||||
\(712\) | 4.73734e7 | 3.50215 | ||||||||
\(713\) | 1.39515e6 | 0.102777 | ||||||||
\(714\) | −3.59631e6 | −0.264005 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.30620e7 | −3.13915 | ||||||||
\(717\) | 9.45296e6 | 0.686705 | ||||||||
\(718\) | 2.97509e7 | 2.15372 | ||||||||
\(719\) | 1.70520e7 | 1.23014 | 0.615069 | − | 0.788474i | \(-0.289128\pi\) | ||||
0.615069 | + | 0.788474i | \(0.289128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.97912e6 | 0.285068 | ||||||||
\(722\) | −2.66679e7 | −1.90391 | ||||||||
\(723\) | −2.26551e6 | −0.161184 | ||||||||
\(724\) | −4.30528e7 | −3.05250 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.45145e6 | −0.102202 | ||||||||
\(727\) | −6.52920e6 | −0.458167 | −0.229084 | − | 0.973407i | \(-0.573573\pi\) | ||||
−0.229084 | + | 0.973407i | \(0.573573\pi\) | |||||||
\(728\) | 3.91080e7 | 2.73487 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.93071e6 | 0.548932 | ||||||||
\(732\) | −3.69248e7 | −2.54707 | ||||||||
\(733\) | −1.96819e7 | −1.35303 | −0.676513 | − | 0.736430i | \(-0.736510\pi\) | ||||
−0.676513 | + | 0.736430i | \(0.736510\pi\) | |||||||
\(734\) | −3.96386e7 | −2.71568 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.04606e7 | −3.43366 | ||||||||
\(737\) | 6.11165e6 | 0.414467 | ||||||||
\(738\) | −4.79384e6 | −0.323998 | ||||||||
\(739\) | 5.50059e6 | 0.370509 | 0.185254 | − | 0.982691i | \(-0.440689\pi\) | ||||
0.185254 | + | 0.982691i | \(0.440689\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.08374e6 | 0.139411 | ||||||||
\(742\) | −3.67954e6 | −0.245349 | ||||||||
\(743\) | 6.56551e6 | 0.436311 | 0.218156 | − | 0.975914i | \(-0.429996\pi\) | ||||
0.218156 | + | 0.975914i | \(0.429996\pi\) | |||||||
\(744\) | 3.91741e6 | 0.259458 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.19057e7 | 3.41482 | ||||||||
\(747\) | −4.69416e6 | −0.307791 | ||||||||
\(748\) | 6.24709e6 | 0.408248 | ||||||||
\(749\) | 1.02373e7 | 0.666777 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.04233e7 | 1.32137 | 0.660687 | − | 0.750662i | \(-0.270265\pi\) | ||||
0.660687 | + | 0.750662i | \(0.270265\pi\) | |||||||
\(752\) | −9.28232e7 | −5.98566 | ||||||||
\(753\) | −8.33956e6 | −0.535989 | ||||||||
\(754\) | −7.47405e7 | −4.78771 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.08776e6 | −0.260124 | ||||||||
\(757\) | 1.28683e7 | 0.816174 | 0.408087 | − | 0.912943i | \(-0.366196\pi\) | ||||
0.408087 | + | 0.912943i | \(0.366196\pi\) | |||||||
\(758\) | 3.18888e7 | 2.01588 | ||||||||
\(759\) | 2.20439e6 | 0.138894 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.16269e7 | 0.727782 | 0.363891 | − | 0.931442i | \(-0.381448\pi\) | ||||
0.363891 | + | 0.931442i | \(0.381448\pi\) | |||||||
\(762\) | −1.49811e7 | −0.934663 | ||||||||
\(763\) | −1.11448e7 | −0.693041 | ||||||||
\(764\) | −2.68432e7 | −1.66380 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.61866e6 | −0.469144 | ||||||||
\(767\) | 2.34727e7 | 1.44070 | ||||||||
\(768\) | −3.62603e7 | −2.21834 | ||||||||
\(769\) | 2.67451e7 | 1.63091 | 0.815453 | − | 0.578823i | \(-0.196488\pi\) | ||||
0.815453 | + | 0.578823i | \(0.196488\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.23503e7 | −0.748243 | ||||||||
\(772\) | −7.68340e7 | −4.63992 | ||||||||
\(773\) | −1.62196e7 | −0.976320 | −0.488160 | − | 0.872754i | \(-0.662332\pi\) | ||||
−0.488160 | + | 0.872754i | \(0.662332\pi\) | |||||||
\(774\) | 1.22435e7 | 0.734606 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.86419e6 | −0.409199 | ||||||||
\(777\) | −7.02593e6 | −0.417495 | ||||||||
\(778\) | −2.31545e6 | −0.137147 | ||||||||
\(779\) | 1.26091e6 | 0.0744461 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.54728e6 | −0.208098 | ||||||||
\(782\) | −1.28863e7 | −0.753551 | ||||||||
\(783\) | 5.01383e6 | 0.292257 | ||||||||
\(784\) | −5.27260e7 | −3.06362 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.50091e6 | 0.259863 | ||||||||
\(787\) | 3.30833e7 | 1.90402 | 0.952011 | − | 0.306063i | \(-0.0990119\pi\) | ||||
0.952011 | + | 0.306063i | \(0.0990119\pi\) | |||||||
\(788\) | −5.56634e7 | −3.19341 | ||||||||
\(789\) | −1.63444e7 | −0.934710 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −188898. | −0.0107346 | ||||||||
\(792\) | 6.18965e6 | 0.350633 | ||||||||
\(793\) | 4.53093e7 | 2.55861 | ||||||||
\(794\) | −2.25619e7 | −1.27006 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.72850e7 | −2.08570 | ||||||||
\(797\) | 6.59997e6 | 0.368041 | 0.184020 | − | 0.982922i | \(-0.441089\pi\) | ||||
0.184020 | + | 0.982922i | \(0.441089\pi\) | |||||||
\(798\) | 1.46034e6 | 0.0811797 | ||||||||
\(799\) | −1.30915e7 | −0.725477 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.07608e6 | 0.334613 | ||||||||
\(802\) | 1.39457e7 | 0.765605 | ||||||||
\(803\) | −5.13439e6 | −0.280996 | ||||||||
\(804\) | −4.06096e7 | −2.21558 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.48987e6 | −0.406104 | ||||||||
\(807\) | −1.14425e7 | −0.618497 | ||||||||
\(808\) | 7.09577e7 | 3.82359 | ||||||||
\(809\) | −2.14723e7 | −1.15347 | −0.576736 | − | 0.816931i | \(-0.695674\pi\) | ||||
−0.576736 | + | 0.816931i | \(0.695674\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.13634e7 | −0.606678 | −0.303339 | − | 0.952883i | \(-0.598101\pi\) | ||||
−0.303339 | + | 0.952883i | \(0.598101\pi\) | |||||||
\(812\) | −3.85656e7 | −2.05263 | ||||||||
\(813\) | −1.30086e7 | −0.690244 | ||||||||
\(814\) | 1.65764e7 | 0.876860 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.13142e7 | −1.12058 | ||||||||
\(817\) | −3.22040e6 | −0.168793 | ||||||||
\(818\) | 2.25271e7 | 1.17712 | ||||||||
\(819\) | 5.01596e6 | 0.261303 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.33658e6 | −0.328093 | −0.164047 | − | 0.986453i | \(-0.552455\pi\) | ||||
−0.164047 | + | 0.986453i | \(0.552455\pi\) | |||||||
\(822\) | 2.95157e7 | 1.52361 | ||||||||
\(823\) | −3.27073e7 | −1.68324 | −0.841619 | − | 0.540071i | \(-0.818397\pi\) | ||||
−0.841619 | + | 0.540071i | \(0.818397\pi\) | |||||||
\(824\) | 4.00348e7 | 2.05409 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.64503e7 | 0.838925 | ||||||||
\(827\) | 3.83082e6 | 0.194773 | 0.0973863 | − | 0.995247i | \(-0.468952\pi\) | ||||
0.0973863 | + | 0.995247i | \(0.468952\pi\) | |||||||
\(828\) | −1.46473e7 | −0.742475 | ||||||||
\(829\) | −2.45814e7 | −1.24228 | −0.621142 | − | 0.783698i | \(-0.713331\pi\) | ||||
−0.621142 | + | 0.783698i | \(0.713331\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.57235e7 | −0.789854 | ||||||||
\(832\) | 1.41532e8 | 7.08838 | ||||||||
\(833\) | −7.43633e6 | −0.371318 | ||||||||
\(834\) | 2.12491e7 | 1.05786 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.53674e6 | −0.125533 | ||||||||
\(837\) | 502444. | 0.0247899 | ||||||||
\(838\) | −1.10599e7 | −0.544055 | ||||||||
\(839\) | 8.44908e6 | 0.414386 | 0.207193 | − | 0.978300i | \(-0.433567\pi\) | ||||
0.207193 | + | 0.978300i | \(0.433567\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.67913e7 | 1.30618 | ||||||||
\(842\) | −5.50453e7 | −2.67572 | ||||||||
\(843\) | 1.65691e7 | 0.803026 | ||||||||
\(844\) | 1.11483e8 | 5.38708 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.02109e7 | −0.970867 | ||||||||
\(847\) | 919001. | 0.0440157 | ||||||||
\(848\) | −2.18074e7 | −1.04139 | ||||||||
\(849\) | 8.87438e6 | 0.422541 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.51754e7 | −1.19166 | ||||||||
\(852\) | 2.35703e7 | 1.11242 | ||||||||
\(853\) | 1.03931e7 | 0.489072 | 0.244536 | − | 0.969640i | \(-0.421364\pi\) | ||||
0.244536 | + | 0.969640i | \(0.421364\pi\) | |||||||
\(854\) | 3.17540e7 | 1.48989 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.03000e8 | 4.80453 | ||||||||
\(857\) | −1.78951e7 | −0.832302 | −0.416151 | − | 0.909295i | \(-0.636621\pi\) | ||||
−0.416151 | + | 0.909295i | \(0.636621\pi\) | |||||||
\(858\) | −1.18343e7 | −0.548812 | ||||||||
\(859\) | −1.57750e7 | −0.729435 | −0.364717 | − | 0.931118i | \(-0.618834\pi\) | ||||
−0.364717 | + | 0.931118i | \(0.618834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.03526e6 | 0.139537 | ||||||||
\(862\) | −4.37928e6 | −0.200740 | ||||||||
\(863\) | 3.34930e7 | 1.53083 | 0.765416 | − | 0.643536i | \(-0.222533\pi\) | ||||
0.765416 | + | 0.643536i | \(0.222533\pi\) | |||||||
\(864\) | −1.81727e7 | −0.828201 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.49290e7 | −2.94201 | ||||||||
\(867\) | 9.77262e6 | 0.441533 | ||||||||
\(868\) | −3.86472e6 | −0.174108 | ||||||||
\(869\) | 7.72062e6 | 0.346819 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.98307e7 | 2.22562 | ||||||||
\(872\) | −1.12130e8 | −4.99379 | ||||||||
\(873\) | −880396. | −0.0390969 | ||||||||
\(874\) | 5.23271e6 | 0.231712 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.41161e7 | 1.50210 | ||||||||
\(877\) | −3.05516e7 | −1.34133 | −0.670665 | − | 0.741760i | \(-0.733991\pi\) | ||||
−0.670665 | + | 0.741760i | \(0.733991\pi\) | |||||||
\(878\) | −2.49778e7 | −1.09350 | ||||||||
\(879\) | 1.78708e7 | 0.780137 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.31867e6 | −0.274275 | −0.137137 | − | 0.990552i | \(-0.543790\pi\) | ||||
−0.137137 | + | 0.990552i | \(0.543790\pi\) | |||||||
\(882\) | −1.14803e7 | −0.496915 | ||||||||
\(883\) | −2.91551e7 | −1.25838 | −0.629191 | − | 0.777251i | \(-0.716614\pi\) | ||||
−0.629191 | + | 0.777251i | \(0.716614\pi\) | |||||||
\(884\) | 5.09351e7 | 2.19223 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.57375e7 | −0.673519 | ||||||||
\(887\) | −1.26078e7 | −0.538061 | −0.269030 | − | 0.963132i | \(-0.586703\pi\) | ||||
−0.269030 | + | 0.963132i | \(0.586703\pi\) | |||||||
\(888\) | −7.06894e7 | −3.00831 | ||||||||
\(889\) | 9.48539e6 | 0.402532 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −3.57119e7 | −1.50280 | ||||||||
\(893\) | 5.31603e6 | 0.223079 | ||||||||
\(894\) | −2.32407e7 | −0.972537 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.91185e7 | 2.04397 | ||||||||
\(897\) | 1.79733e7 | 0.745840 | ||||||||
\(898\) | 4.95499e7 | 2.05046 | ||||||||
\(899\) | 4.74026e6 | 0.195615 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.07566e6 | −0.126219 | ||||||||
\(902\) | −7.16116e6 | −0.293067 | ||||||||
\(903\) | −7.75211e6 | −0.316374 | ||||||||
\(904\) | −1.90054e6 | −0.0773493 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6.03468e6 | −0.244249 | ||||||||
\(907\) | −2.75312e7 | −1.11124 | −0.555618 | − | 0.831437i | \(-0.687518\pi\) | ||||
−0.555618 | + | 0.831437i | \(0.687518\pi\) | |||||||
\(908\) | 1.02267e8 | 4.11641 | ||||||||
\(909\) | 9.10099e6 | 0.365325 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.45616e7 | 0.980531 | 0.490265 | − | 0.871573i | \(-0.336900\pi\) | ||||
0.490265 | + | 0.871573i | \(0.336900\pi\) | |||||||
\(912\) | 8.65497e6 | 0.344571 | ||||||||
\(913\) | −7.01227e6 | −0.278408 | ||||||||
\(914\) | −6.22206e7 | −2.46359 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.22695e6 | 0.0876945 | ||||||||
\(917\) | −2.84979e6 | −0.111915 | ||||||||
\(918\) | −4.64085e6 | −0.181757 | ||||||||
\(919\) | 1.79061e7 | 0.699379 | 0.349690 | − | 0.936866i | \(-0.386287\pi\) | ||||
0.349690 | + | 0.936866i | \(0.386287\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.02585e7 | 0.398505 | ||||||||
\(922\) | −9.30327e7 | −3.60419 | ||||||||
\(923\) | −2.89224e7 | −1.11746 | ||||||||
\(924\) | −6.10641e6 | −0.235291 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.49237e7 | −1.72166 | ||||||||
\(927\) | 5.13483e6 | 0.196258 | ||||||||
\(928\) | −1.71449e8 | −6.53528 | ||||||||
\(929\) | −1.63508e7 | −0.621583 | −0.310791 | − | 0.950478i | \(-0.600594\pi\) | ||||
−0.310791 | + | 0.950478i | \(0.600594\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.01965e6 | 0.114178 | ||||||||
\(932\) | −5.59434e7 | −2.10964 | ||||||||
\(933\) | 1.18714e6 | 0.0446476 | ||||||||
\(934\) | −3.78805e7 | −1.42085 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.04667e7 | 1.88285 | ||||||||
\(937\) | 5.61949e6 | 0.209097 | 0.104548 | − | 0.994520i | \(-0.466660\pi\) | ||||
0.104548 | + | 0.994520i | \(0.466660\pi\) | |||||||
\(938\) | 3.49227e7 | 1.29599 | ||||||||
\(939\) | 1.86592e7 | 0.690605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.03132e6 | 0.185228 | 0.0926142 | − | 0.995702i | \(-0.470478\pi\) | ||||
0.0926142 | + | 0.995702i | \(0.470478\pi\) | |||||||
\(942\) | −1.11153e7 | −0.408127 | ||||||||
\(943\) | 1.08760e7 | 0.398281 | ||||||||
\(944\) | 9.74955e7 | 3.56086 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.82897e7 | 0.664476 | ||||||||
\(947\) | −1.16336e7 | −0.421540 | −0.210770 | − | 0.977536i | \(-0.567597\pi\) | ||||
−0.210770 | + | 0.977536i | \(0.567597\pi\) | |||||||
\(948\) | −5.13006e7 | −1.85396 | ||||||||
\(949\) | −4.18628e7 | −1.50891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −856112. | −0.0306958 | ||||||||
\(952\) | 2.29098e7 | 0.819273 | ||||||||
\(953\) | 1.43027e7 | 0.510135 | 0.255068 | − | 0.966923i | \(-0.417902\pi\) | ||||
0.255068 | + | 0.966923i | \(0.417902\pi\) | |||||||
\(954\) | −4.74825e6 | −0.168913 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.38293e7 | −3.32042 | ||||||||
\(957\) | 7.48979e6 | 0.264356 | ||||||||
\(958\) | 3.88286e7 | 1.36690 | ||||||||
\(959\) | −1.86881e7 | −0.656174 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.81541e7 | −0.983407 | ||||||||
\(962\) | 1.35154e8 | 4.70861 | ||||||||
\(963\) | 1.32107e7 | 0.459049 | ||||||||
\(964\) | 2.24873e7 | 0.779372 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.25961e7 | 0.434305 | ||||||||
\(967\) | 1.87953e7 | 0.646372 | 0.323186 | − | 0.946335i | \(-0.395246\pi\) | ||||
0.323186 | + | 0.946335i | \(0.395246\pi\) | |||||||
\(968\) | 9.24627e6 | 0.317160 | ||||||||
\(969\) | 1.22067e6 | 0.0417628 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.65105e7 | 1.24271 | 0.621355 | − | 0.783529i | \(-0.286582\pi\) | ||||
0.621355 | + | 0.783529i | \(0.286582\pi\) | |||||||
\(972\) | −5.27504e6 | −0.179085 | ||||||||
\(973\) | −1.34541e7 | −0.455588 | ||||||||
\(974\) | −1.17120e7 | −0.395579 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.88196e8 | 6.32390 | ||||||||
\(977\) | 2.62418e7 | 0.879542 | 0.439771 | − | 0.898110i | \(-0.355060\pi\) | ||||
0.439771 | + | 0.898110i | \(0.355060\pi\) | |||||||
\(978\) | −3.60919e7 | −1.20660 | ||||||||
\(979\) | 9.07662e6 | 0.302669 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.43817e7 | −0.477131 | ||||||||
\(982\) | 1.00937e8 | 3.34019 | ||||||||
\(983\) | −4.19211e7 | −1.38372 | −0.691861 | − | 0.722030i | \(-0.743209\pi\) | ||||
−0.691861 | + | 0.722030i | \(0.743209\pi\) | |||||||
\(984\) | 3.05384e7 | 1.00545 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.37836e7 | −1.43423 | ||||||||
\(987\) | 1.27967e7 | 0.418124 | ||||||||
\(988\) | −2.06830e7 | −0.674096 | ||||||||
\(989\) | −2.77774e7 | −0.903029 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.68229e7 | 1.19106 | 0.595530 | − | 0.803333i | \(-0.296942\pi\) | ||||
0.595530 | + | 0.803333i | \(0.296942\pi\) | |||||||
\(992\) | −1.71812e7 | −0.554337 | ||||||||
\(993\) | 2.88138e7 | 0.927315 | ||||||||
\(994\) | −2.02696e7 | −0.650698 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.65938e7 | 1.48826 | ||||||||
\(997\) | 5.96749e6 | 0.190132 | 0.0950658 | − | 0.995471i | \(-0.469694\pi\) | ||||
0.0950658 | + | 0.995471i | \(0.469694\pi\) | |||||||
\(998\) | −4.95228e7 | −1.57391 | ||||||||
\(999\) | −9.06658e6 | −0.287429 |
(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 | 825.6.a.u.1.10 | yes | 10 | |
5.4 | even | 2 | 825.6.a.t.1.1 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.t.1.1 | ✓ | 10 | 5.4 | even | 2 | ||
825.6.a.u.1.10 | yes | 10 | 1.1 | even | 1 | trivial |