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: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 306 x^{11} - 206 x^{10} + 34574 x^{9} + 39928 x^{8} - 1788312 x^{7} - 2591628 x^{6} + 42852537 x^{5} + 63733360 x^{4} - 448113518 x^{3} + \cdots + 522579400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 5^{7} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-9.04603\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.0460 | −1.77590 | −0.887952 | − | 0.459936i | \(-0.847872\pi\) | ||||
−0.887952 | + | 0.459936i | \(0.847872\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 68.9227 | 2.15384 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 90.4143 | 1.02532 | ||||||||
\(7\) | 29.0524 | 0.224098 | 0.112049 | − | 0.993703i | \(-0.464259\pi\) | ||||
0.112049 | + | 0.993703i | \(0.464259\pi\) | |||||||
\(8\) | −370.927 | −2.04910 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −620.305 | −1.24352 | ||||||||
\(13\) | −1023.51 | −1.67971 | −0.839856 | − | 0.542809i | \(-0.817361\pi\) | ||||
−0.839856 | + | 0.542809i | \(0.817361\pi\) | |||||||
\(14\) | −291.862 | −0.397976 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1520.82 | 1.48517 | ||||||||
\(17\) | 1509.69 | 1.26696 | 0.633482 | − | 0.773757i | \(-0.281625\pi\) | ||||
0.633482 | + | 0.773757i | \(0.281625\pi\) | |||||||
\(18\) | −813.728 | −0.591968 | ||||||||
\(19\) | 1643.04 | 1.04415 | 0.522075 | − | 0.852900i | \(-0.325158\pi\) | ||||
0.522075 | + | 0.852900i | \(0.325158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −261.472 | −0.129383 | ||||||||
\(22\) | −1215.57 | −0.535455 | ||||||||
\(23\) | −1478.11 | −0.582622 | −0.291311 | − | 0.956628i | \(-0.594092\pi\) | ||||
−0.291311 | + | 0.956628i | \(0.594092\pi\) | |||||||
\(24\) | 3338.34 | 1.18305 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 10282.2 | 2.98301 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 2002.37 | 0.482669 | ||||||||
\(29\) | −4572.33 | −1.00958 | −0.504792 | − | 0.863241i | \(-0.668431\pi\) | ||||
−0.504792 | + | 0.863241i | \(0.668431\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7531.62 | 1.40762 | 0.703808 | − | 0.710391i | \(-0.251482\pi\) | ||||
0.703808 | + | 0.710391i | \(0.251482\pi\) | |||||||
\(32\) | −3408.50 | −0.588421 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −15166.4 | −2.25001 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5582.74 | 0.717945 | ||||||||
\(37\) | −4408.40 | −0.529391 | −0.264695 | − | 0.964332i | \(-0.585271\pi\) | ||||
−0.264695 | + | 0.964332i | \(0.585271\pi\) | |||||||
\(38\) | −16506.0 | −1.85431 | ||||||||
\(39\) | 9211.62 | 0.969783 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5629.62 | 0.523021 | 0.261511 | − | 0.965201i | \(-0.415779\pi\) | ||||
0.261511 | + | 0.965201i | \(0.415779\pi\) | |||||||
\(42\) | 2626.75 | 0.229771 | ||||||||
\(43\) | 2283.11 | 0.188302 | 0.0941510 | − | 0.995558i | \(-0.469986\pi\) | ||||
0.0941510 | + | 0.995558i | \(0.469986\pi\) | |||||||
\(44\) | 8339.65 | 0.649406 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14849.1 | 1.03468 | ||||||||
\(47\) | −5980.48 | −0.394904 | −0.197452 | − | 0.980313i | \(-0.563267\pi\) | ||||
−0.197452 | + | 0.980313i | \(0.563267\pi\) | |||||||
\(48\) | −13687.3 | −0.857464 | ||||||||
\(49\) | −15963.0 | −0.949780 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13587.2 | −0.731482 | ||||||||
\(52\) | −70543.3 | −3.61782 | ||||||||
\(53\) | −28498.0 | −1.39356 | −0.696778 | − | 0.717287i | \(-0.745384\pi\) | ||||
−0.696778 | + | 0.717287i | \(0.745384\pi\) | |||||||
\(54\) | 7323.56 | 0.341773 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −10776.3 | −0.459199 | ||||||||
\(57\) | −14787.3 | −0.602840 | ||||||||
\(58\) | 45933.7 | 1.79292 | ||||||||
\(59\) | 25942.8 | 0.970258 | 0.485129 | − | 0.874443i | \(-0.338773\pi\) | ||||
0.485129 | + | 0.874443i | \(0.338773\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −51360.7 | −1.76728 | −0.883642 | − | 0.468163i | \(-0.844916\pi\) | ||||
−0.883642 | + | 0.468163i | \(0.844916\pi\) | |||||||
\(62\) | −75662.8 | −2.49979 | ||||||||
\(63\) | 2353.25 | 0.0746992 | ||||||||
\(64\) | −14424.2 | −0.440193 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 10940.1 | 0.309145 | ||||||||
\(67\) | 39180.2 | 1.06630 | 0.533151 | − | 0.846020i | \(-0.321008\pi\) | ||||
0.533151 | + | 0.846020i | \(0.321008\pi\) | |||||||
\(68\) | 104052. | 2.72883 | ||||||||
\(69\) | 13303.0 | 0.336377 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 37560.3 | 0.884267 | 0.442133 | − | 0.896949i | \(-0.354222\pi\) | ||||
0.442133 | + | 0.896949i | \(0.354222\pi\) | |||||||
\(72\) | −30045.1 | −0.683034 | ||||||||
\(73\) | −58687.6 | −1.28896 | −0.644480 | − | 0.764621i | \(-0.722926\pi\) | ||||
−0.644480 | + | 0.764621i | \(0.722926\pi\) | |||||||
\(74\) | 44286.9 | 0.940147 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 113242. | 2.24893 | ||||||||
\(77\) | 3515.34 | 0.0675680 | ||||||||
\(78\) | −92540.2 | −1.72224 | ||||||||
\(79\) | −8274.06 | −0.149160 | −0.0745798 | − | 0.997215i | \(-0.523762\pi\) | ||||
−0.0745798 | + | 0.997215i | \(0.523762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −56555.3 | −0.928836 | ||||||||
\(83\) | 21355.4 | 0.340261 | 0.170130 | − | 0.985422i | \(-0.445581\pi\) | ||||
0.170130 | + | 0.985422i | \(0.445581\pi\) | |||||||
\(84\) | −18021.4 | −0.278669 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −22936.2 | −0.334406 | ||||||||
\(87\) | 41150.9 | 0.582883 | ||||||||
\(88\) | −44882.1 | −0.617827 | ||||||||
\(89\) | 78385.8 | 1.04897 | 0.524484 | − | 0.851420i | \(-0.324258\pi\) | ||||
0.524484 | + | 0.851420i | \(0.324258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −29735.5 | −0.376420 | ||||||||
\(92\) | −101875. | −1.25487 | ||||||||
\(93\) | −67784.5 | −0.812687 | ||||||||
\(94\) | 60080.1 | 0.701312 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 30676.5 | 0.339725 | ||||||||
\(97\) | −64574.7 | −0.696840 | −0.348420 | − | 0.937339i | \(-0.613282\pi\) | ||||
−0.348420 | + | 0.937339i | \(0.613282\pi\) | |||||||
\(98\) | 160364. | 1.68672 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 48364.4 | 0.471762 | 0.235881 | − | 0.971782i | \(-0.424203\pi\) | ||||
0.235881 | + | 0.971782i | \(0.424203\pi\) | |||||||
\(102\) | 136497. | 1.29904 | ||||||||
\(103\) | −121923. | −1.13238 | −0.566192 | − | 0.824273i | \(-0.691584\pi\) | ||||
−0.566192 | + | 0.824273i | \(0.691584\pi\) | |||||||
\(104\) | 379648. | 3.44190 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 286291. | 2.47482 | ||||||||
\(107\) | 191883. | 1.62023 | 0.810117 | − | 0.586269i | \(-0.199404\pi\) | ||||
0.810117 | + | 0.586269i | \(0.199404\pi\) | |||||||
\(108\) | −50244.7 | −0.414506 | ||||||||
\(109\) | −15660.0 | −0.126248 | −0.0631240 | − | 0.998006i | \(-0.520106\pi\) | ||||
−0.0631240 | + | 0.998006i | \(0.520106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 39675.6 | 0.305644 | ||||||||
\(112\) | 44183.4 | 0.332823 | ||||||||
\(113\) | 15119.6 | 0.111389 | 0.0556947 | − | 0.998448i | \(-0.482263\pi\) | ||||
0.0556947 | + | 0.998448i | \(0.482263\pi\) | |||||||
\(114\) | 148554. | 1.07059 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −315137. | −2.17448 | ||||||||
\(117\) | −82904.6 | −0.559904 | ||||||||
\(118\) | −260622. | −1.72309 | ||||||||
\(119\) | 43860.0 | 0.283924 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 515971. | 3.13853 | ||||||||
\(123\) | −50666.6 | −0.301966 | ||||||||
\(124\) | 519099. | 3.03177 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −23640.8 | −0.132659 | ||||||||
\(127\) | 223751. | 1.23099 | 0.615496 | − | 0.788140i | \(-0.288956\pi\) | ||||
0.615496 | + | 0.788140i | \(0.288956\pi\) | |||||||
\(128\) | 253978. | 1.37016 | ||||||||
\(129\) | −20548.0 | −0.108716 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 269255. | 1.37084 | 0.685418 | − | 0.728149i | \(-0.259619\pi\) | ||||
0.685418 | + | 0.728149i | \(0.259619\pi\) | |||||||
\(132\) | −75056.9 | −0.374935 | ||||||||
\(133\) | 47734.1 | 0.233991 | ||||||||
\(134\) | −393606. | −1.89365 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −559983. | −2.59614 | ||||||||
\(137\) | −172187. | −0.783790 | −0.391895 | − | 0.920010i | \(-0.628180\pi\) | ||||
−0.391895 | + | 0.920010i | \(0.628180\pi\) | |||||||
\(138\) | −133642. | −0.597374 | ||||||||
\(139\) | −350209. | −1.53741 | −0.768707 | − | 0.639601i | \(-0.779099\pi\) | ||||
−0.768707 | + | 0.639601i | \(0.779099\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 53824.4 | 0.227998 | ||||||||
\(142\) | −377332. | −1.57037 | ||||||||
\(143\) | −123845. | −0.506452 | ||||||||
\(144\) | 123186. | 0.495057 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 589578. | 2.28907 | ||||||||
\(147\) | 143667. | 0.548356 | ||||||||
\(148\) | −303839. | −1.14022 | ||||||||
\(149\) | 519184. | 1.91582 | 0.957912 | − | 0.287062i | \(-0.0926785\pi\) | ||||
0.957912 | + | 0.287062i | \(0.0926785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −230203. | −0.821617 | −0.410808 | − | 0.911722i | \(-0.634753\pi\) | ||||
−0.410808 | + | 0.911722i | \(0.634753\pi\) | |||||||
\(152\) | −609446. | −2.13957 | ||||||||
\(153\) | 122285. | 0.422321 | ||||||||
\(154\) | −35315.2 | −0.119994 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 634890. | 2.08875 | ||||||||
\(157\) | 328864. | 1.06480 | 0.532399 | − | 0.846494i | \(-0.321291\pi\) | ||||
0.532399 | + | 0.846494i | \(0.321291\pi\) | |||||||
\(158\) | 83121.5 | 0.264893 | ||||||||
\(159\) | 256482. | 0.804569 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −42942.7 | −0.130564 | ||||||||
\(162\) | −65912.0 | −0.197323 | ||||||||
\(163\) | 246382. | 0.726341 | 0.363171 | − | 0.931723i | \(-0.381694\pi\) | ||||
0.363171 | + | 0.931723i | \(0.381694\pi\) | |||||||
\(164\) | 388009. | 1.12650 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −214537. | −0.604270 | ||||||||
\(167\) | 581413. | 1.61322 | 0.806610 | − | 0.591084i | \(-0.201300\pi\) | ||||
0.806610 | + | 0.591084i | \(0.201300\pi\) | |||||||
\(168\) | 96986.9 | 0.265118 | ||||||||
\(169\) | 676286. | 1.82143 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 133086. | 0.348050 | ||||||||
\(172\) | 157358. | 0.405572 | ||||||||
\(173\) | 264650. | 0.672290 | 0.336145 | − | 0.941810i | \(-0.390877\pi\) | ||||
0.336145 | + | 0.941810i | \(0.390877\pi\) | |||||||
\(174\) | −413404. | −1.03515 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 184019. | 0.447796 | ||||||||
\(177\) | −233485. | −0.560179 | ||||||||
\(178\) | −787466. | −1.86287 | ||||||||
\(179\) | −13886.5 | −0.0323937 | −0.0161969 | − | 0.999869i | \(-0.505156\pi\) | ||||
−0.0161969 | + | 0.999869i | \(0.505156\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −752593. | −1.70751 | −0.853756 | − | 0.520673i | \(-0.825681\pi\) | ||||
−0.853756 | + | 0.520673i | \(0.825681\pi\) | |||||||
\(182\) | 298724. | 0.668485 | ||||||||
\(183\) | 462246. | 1.02034 | ||||||||
\(184\) | 548271. | 1.19385 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 680966. | 1.44325 | ||||||||
\(187\) | 182672. | 0.382004 | ||||||||
\(188\) | −412191. | −0.850558 | ||||||||
\(189\) | −21179.2 | −0.0431276 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −25416.1 | −0.0504110 | −0.0252055 | − | 0.999682i | \(-0.508024\pi\) | ||||
−0.0252055 | + | 0.999682i | \(0.508024\pi\) | |||||||
\(192\) | 129818. | 0.254145 | ||||||||
\(193\) | 489822. | 0.946553 | 0.473277 | − | 0.880914i | \(-0.343071\pi\) | ||||
0.473277 | + | 0.880914i | \(0.343071\pi\) | |||||||
\(194\) | 648719. | 1.23752 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.10021e6 | −2.04567 | ||||||||
\(197\) | 324827. | 0.596329 | 0.298164 | − | 0.954515i | \(-0.403626\pi\) | ||||
0.298164 | + | 0.954515i | \(0.403626\pi\) | |||||||
\(198\) | −98461.1 | −0.178485 | ||||||||
\(199\) | −398516. | −0.713368 | −0.356684 | − | 0.934225i | \(-0.616093\pi\) | ||||
−0.356684 | + | 0.934225i | \(0.616093\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −352622. | −0.615629 | ||||||||
\(202\) | −485870. | −0.837803 | ||||||||
\(203\) | −132837. | −0.226245 | ||||||||
\(204\) | −936465. | −1.57549 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.22485e6 | 2.01101 | ||||||||
\(207\) | −119727. | −0.194207 | ||||||||
\(208\) | −1.55657e6 | −2.49466 | ||||||||
\(209\) | 198807. | 0.314823 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −868645. | −1.34319 | −0.671593 | − | 0.740920i | \(-0.734390\pi\) | ||||
−0.671593 | + | 0.740920i | \(0.734390\pi\) | |||||||
\(212\) | −1.96416e6 | −3.00149 | ||||||||
\(213\) | −338043. | −0.510532 | ||||||||
\(214\) | −1.92766e6 | −2.87738 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 270406. | 0.394350 | ||||||||
\(217\) | 218812. | 0.315443 | ||||||||
\(218\) | 157320. | 0.224204 | ||||||||
\(219\) | 528189. | 0.744181 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.54518e6 | −2.12814 | ||||||||
\(222\) | −398582. | −0.542794 | ||||||||
\(223\) | 48571.9 | 0.0654068 | 0.0327034 | − | 0.999465i | \(-0.489588\pi\) | ||||
0.0327034 | + | 0.999465i | \(0.489588\pi\) | |||||||
\(224\) | −99025.1 | −0.131864 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −151892. | −0.197817 | ||||||||
\(227\) | −78669.6 | −0.101331 | −0.0506655 | − | 0.998716i | \(-0.516134\pi\) | ||||
−0.0506655 | + | 0.998716i | \(0.516134\pi\) | |||||||
\(228\) | −1.01918e6 | −1.29842 | ||||||||
\(229\) | −324090. | −0.408391 | −0.204196 | − | 0.978930i | \(-0.565458\pi\) | ||||
−0.204196 | + | 0.978930i | \(0.565458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −31638.1 | −0.0390104 | ||||||||
\(232\) | 1.69600e6 | 2.06874 | ||||||||
\(233\) | −1.26828e6 | −1.53048 | −0.765238 | − | 0.643747i | \(-0.777379\pi\) | ||||
−0.765238 | + | 0.643747i | \(0.777379\pi\) | |||||||
\(234\) | 832862. | 0.994336 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.78805e6 | 2.08978 | ||||||||
\(237\) | 74466.6 | 0.0861173 | ||||||||
\(238\) | −440619. | −0.504221 | ||||||||
\(239\) | −1.35381e6 | −1.53307 | −0.766535 | − | 0.642202i | \(-0.778021\pi\) | ||||
−0.766535 | + | 0.642202i | \(0.778021\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.14198e6 | 1.26653 | 0.633264 | − | 0.773936i | \(-0.281715\pi\) | ||||
0.633264 | + | 0.773936i | \(0.281715\pi\) | |||||||
\(242\) | −147084. | −0.161446 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −3.53992e6 | −3.80644 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 508998. | 0.536264 | ||||||||
\(247\) | −1.68167e6 | −1.75387 | ||||||||
\(248\) | −2.79368e6 | −2.88434 | ||||||||
\(249\) | −192198. | −0.196449 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −321578. | −0.322183 | −0.161091 | − | 0.986940i | \(-0.551501\pi\) | ||||
−0.161091 | + | 0.986940i | \(0.551501\pi\) | |||||||
\(252\) | 162192. | 0.160890 | ||||||||
\(253\) | −178851. | −0.175667 | ||||||||
\(254\) | −2.24781e6 | −2.18612 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.08990e6 | −1.99308 | ||||||||
\(257\) | −1.44275e6 | −1.36257 | −0.681286 | − | 0.732018i | \(-0.738579\pi\) | ||||
−0.681286 | + | 0.732018i | \(0.738579\pi\) | |||||||
\(258\) | 206425. | 0.193070 | ||||||||
\(259\) | −128075. | −0.118635 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −370359. | −0.336528 | ||||||||
\(262\) | −2.70495e6 | −2.43447 | ||||||||
\(263\) | −838618. | −0.747610 | −0.373805 | − | 0.927507i | \(-0.621947\pi\) | ||||
−0.373805 | + | 0.927507i | \(0.621947\pi\) | |||||||
\(264\) | 403939. | 0.356703 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −479539. | −0.415546 | ||||||||
\(267\) | −705472. | −0.605622 | ||||||||
\(268\) | 2.70041e6 | 2.29664 | ||||||||
\(269\) | −415262. | −0.349898 | −0.174949 | − | 0.984577i | \(-0.555976\pi\) | ||||
−0.174949 | + | 0.984577i | \(0.555976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 647209. | 0.535330 | 0.267665 | − | 0.963512i | \(-0.413748\pi\) | ||||
0.267665 | + | 0.963512i | \(0.413748\pi\) | |||||||
\(272\) | 2.29595e6 | 1.88166 | ||||||||
\(273\) | 267620. | 0.217326 | ||||||||
\(274\) | 1.72980e6 | 1.39193 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 916878. | 0.724501 | ||||||||
\(277\) | −679011. | −0.531713 | −0.265856 | − | 0.964013i | \(-0.585655\pi\) | ||||
−0.265856 | + | 0.964013i | \(0.585655\pi\) | |||||||
\(278\) | 3.51821e6 | 2.73030 | ||||||||
\(279\) | 610061. | 0.469205 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.78685e6 | −1.34997 | −0.674983 | − | 0.737834i | \(-0.735849\pi\) | ||||
−0.674983 | + | 0.737834i | \(0.735849\pi\) | |||||||
\(282\) | −540721. | −0.404903 | ||||||||
\(283\) | 872555. | 0.647630 | 0.323815 | − | 0.946120i | \(-0.395034\pi\) | ||||
0.323815 | + | 0.946120i | \(0.395034\pi\) | |||||||
\(284\) | 2.58876e6 | 1.90457 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.24415e6 | 0.899411 | ||||||||
\(287\) | 163554. | 0.117208 | ||||||||
\(288\) | −276088. | −0.196140 | ||||||||
\(289\) | 859295. | 0.605198 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 581172. | 0.402321 | ||||||||
\(292\) | −4.04491e6 | −2.77621 | ||||||||
\(293\) | −653130. | −0.444458 | −0.222229 | − | 0.974995i | \(-0.571333\pi\) | ||||
−0.222229 | + | 0.974995i | \(0.571333\pi\) | |||||||
\(294\) | −1.44328e6 | −0.973827 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.63519e6 | 1.08477 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −5.21574e6 | −3.40232 | ||||||||
\(299\) | 1.51286e6 | 0.978638 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 66329.8 | 0.0421980 | ||||||||
\(302\) | 2.31263e6 | 1.45911 | ||||||||
\(303\) | −435280. | −0.272372 | ||||||||
\(304\) | 2.49875e6 | 1.55074 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.22847e6 | −0.750002 | ||||||||
\(307\) | 1.87392e6 | 1.13476 | 0.567381 | − | 0.823456i | \(-0.307957\pi\) | ||||
0.567381 | + | 0.823456i | \(0.307957\pi\) | |||||||
\(308\) | 242287. | 0.145530 | ||||||||
\(309\) | 1.09731e6 | 0.653783 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.60626e6 | −0.941705 | −0.470853 | − | 0.882212i | \(-0.656054\pi\) | ||||
−0.470853 | + | 0.882212i | \(0.656054\pi\) | |||||||
\(312\) | −3.41684e6 | −1.98718 | ||||||||
\(313\) | 2.58202e6 | 1.48970 | 0.744849 | − | 0.667234i | \(-0.232522\pi\) | ||||
0.744849 | + | 0.667234i | \(0.232522\pi\) | |||||||
\(314\) | −3.30377e6 | −1.89098 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −570271. | −0.321265 | ||||||||
\(317\) | 1.34588e6 | 0.752242 | 0.376121 | − | 0.926571i | \(-0.377258\pi\) | ||||
0.376121 | + | 0.926571i | \(0.377258\pi\) | |||||||
\(318\) | −2.57662e6 | −1.42884 | ||||||||
\(319\) | −553252. | −0.304401 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.72695e6 | −0.935442 | ||||||||
\(322\) | 431403. | 0.231870 | ||||||||
\(323\) | 2.48047e6 | 1.32290 | ||||||||
\(324\) | 452202. | 0.239315 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.47516e6 | −1.28991 | ||||||||
\(327\) | 140940. | 0.0728893 | ||||||||
\(328\) | −2.08818e6 | −1.07172 | ||||||||
\(329\) | −173748. | −0.0884971 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.74357e6 | 1.37641 | 0.688203 | − | 0.725518i | \(-0.258400\pi\) | ||||
0.688203 | + | 0.725518i | \(0.258400\pi\) | |||||||
\(332\) | 1.47187e6 | 0.732865 | ||||||||
\(333\) | −357080. | −0.176464 | ||||||||
\(334\) | −5.84089e6 | −2.86492 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −397650. | −0.192156 | ||||||||
\(337\) | −3.70365e6 | −1.77646 | −0.888229 | − | 0.459400i | \(-0.848064\pi\) | ||||
−0.888229 | + | 0.459400i | \(0.848064\pi\) | |||||||
\(338\) | −6.79399e6 | −3.23469 | ||||||||
\(339\) | −136076. | −0.0643107 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 911325. | 0.424412 | ||||||||
\(342\) | −1.33698e6 | −0.618103 | ||||||||
\(343\) | −952047. | −0.436941 | ||||||||
\(344\) | −846866. | −0.385850 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.65868e6 | −1.19392 | ||||||||
\(347\) | 1.17221e6 | 0.522616 | 0.261308 | − | 0.965255i | \(-0.415846\pi\) | ||||
0.261308 | + | 0.965255i | \(0.415846\pi\) | |||||||
\(348\) | 2.83624e6 | 1.25543 | ||||||||
\(349\) | −360082. | −0.158248 | −0.0791240 | − | 0.996865i | \(-0.525212\pi\) | ||||
−0.0791240 | + | 0.996865i | \(0.525212\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 746141. | 0.323261 | ||||||||
\(352\) | −412428. | −0.177415 | ||||||||
\(353\) | −998723. | −0.426588 | −0.213294 | − | 0.976988i | \(-0.568419\pi\) | ||||
−0.213294 | + | 0.976988i | \(0.568419\pi\) | |||||||
\(354\) | 2.34560e6 | 0.994824 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.40256e6 | 2.25930 | ||||||||
\(357\) | −394740. | −0.163923 | ||||||||
\(358\) | 139504. | 0.0575282 | ||||||||
\(359\) | 1.47706e6 | 0.604871 | 0.302436 | − | 0.953170i | \(-0.402200\pi\) | ||||
0.302436 | + | 0.953170i | \(0.402200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 223465. | 0.0902489 | ||||||||
\(362\) | 7.56057e6 | 3.03238 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −2.04945e6 | −0.810746 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.64374e6 | −1.81203 | ||||||||
\(367\) | −3.21905e6 | −1.24756 | −0.623781 | − | 0.781599i | \(-0.714404\pi\) | ||||
−0.623781 | + | 0.781599i | \(0.714404\pi\) | |||||||
\(368\) | −2.24793e6 | −0.865294 | ||||||||
\(369\) | 455999. | 0.174340 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −827935. | −0.312292 | ||||||||
\(372\) | −4.67190e6 | −1.75039 | ||||||||
\(373\) | 4.65790e6 | 1.73348 | 0.866739 | − | 0.498762i | \(-0.166212\pi\) | ||||
0.866739 | + | 0.498762i | \(0.166212\pi\) | |||||||
\(374\) | −1.83513e6 | −0.678403 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.21832e6 | 0.809198 | ||||||||
\(377\) | 4.67984e6 | 1.69581 | ||||||||
\(378\) | 212767. | 0.0765905 | ||||||||
\(379\) | −4.04644e6 | −1.44702 | −0.723510 | − | 0.690314i | \(-0.757472\pi\) | ||||
−0.723510 | + | 0.690314i | \(0.757472\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.01376e6 | −0.710714 | ||||||||
\(382\) | 255331. | 0.0895252 | ||||||||
\(383\) | −824148. | −0.287084 | −0.143542 | − | 0.989644i | \(-0.545849\pi\) | ||||
−0.143542 | + | 0.989644i | \(0.545849\pi\) | |||||||
\(384\) | −2.28580e6 | −0.791062 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.92077e6 | −1.68099 | ||||||||
\(387\) | 184932. | 0.0627674 | ||||||||
\(388\) | −4.45066e6 | −1.50088 | ||||||||
\(389\) | −2.54462e6 | −0.852607 | −0.426303 | − | 0.904580i | \(-0.640184\pi\) | ||||
−0.426303 | + | 0.904580i | \(0.640184\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.23148e6 | −0.738162 | ||||||||
\(392\) | 5.92109e6 | 1.94620 | ||||||||
\(393\) | −2.42330e6 | −0.791453 | ||||||||
\(394\) | −3.26322e6 | −1.05902 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 675512. | 0.216469 | ||||||||
\(397\) | 5.17776e6 | 1.64879 | 0.824395 | − | 0.566015i | \(-0.191516\pi\) | ||||
0.824395 | + | 0.566015i | \(0.191516\pi\) | |||||||
\(398\) | 4.00351e6 | 1.26687 | ||||||||
\(399\) | −429607. | −0.135095 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.82239e6 | −1.49762 | −0.748809 | − | 0.662785i | \(-0.769374\pi\) | ||||
−0.748809 | + | 0.662785i | \(0.769374\pi\) | |||||||
\(402\) | 3.54245e6 | 1.09330 | ||||||||
\(403\) | −7.70871e6 | −2.36439 | ||||||||
\(404\) | 3.33341e6 | 1.01610 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.33449e6 | 0.401790 | ||||||||
\(407\) | −533416. | −0.159617 | ||||||||
\(408\) | 5.03985e6 | 1.49888 | ||||||||
\(409\) | −3.68626e6 | −1.08963 | −0.544813 | − | 0.838558i | \(-0.683399\pi\) | ||||
−0.544813 | + | 0.838558i | \(0.683399\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.54968e6 | 0.452521 | ||||||||
\(412\) | −8.40329e6 | −2.43897 | ||||||||
\(413\) | 753702. | 0.217433 | ||||||||
\(414\) | 1.20278e6 | 0.344894 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.48864e6 | 0.988377 | ||||||||
\(417\) | 3.15188e6 | 0.887626 | ||||||||
\(418\) | −1.99722e6 | −0.559095 | ||||||||
\(419\) | 1.31904e6 | 0.367049 | 0.183525 | − | 0.983015i | \(-0.441249\pi\) | ||||
0.183525 | + | 0.983015i | \(0.441249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.29518e6 | −0.906095 | −0.453048 | − | 0.891486i | \(-0.649663\pi\) | ||||
−0.453048 | + | 0.891486i | \(0.649663\pi\) | |||||||
\(422\) | 8.72643e6 | 2.38537 | ||||||||
\(423\) | −484419. | −0.131635 | ||||||||
\(424\) | 1.05707e7 | 2.85553 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.39599e6 | 0.906655 | ||||||||
\(427\) | −1.49215e6 | −0.396044 | ||||||||
\(428\) | 1.32251e7 | 3.48972 | ||||||||
\(429\) | 1.11461e6 | 0.292400 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.87137e6 | 0.485251 | 0.242625 | − | 0.970120i | \(-0.421991\pi\) | ||||
0.242625 | + | 0.970120i | \(0.421991\pi\) | |||||||
\(432\) | −1.10867e6 | −0.285821 | ||||||||
\(433\) | −4.31194e6 | −1.10523 | −0.552615 | − | 0.833437i | \(-0.686370\pi\) | ||||
−0.552615 | + | 0.833437i | \(0.686370\pi\) | |||||||
\(434\) | −2.19819e6 | −0.560197 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.07933e6 | −0.271917 | ||||||||
\(437\) | −2.42859e6 | −0.608345 | ||||||||
\(438\) | −5.30620e6 | −1.32159 | ||||||||
\(439\) | 1.13612e6 | 0.281360 | 0.140680 | − | 0.990055i | \(-0.455071\pi\) | ||||
0.140680 | + | 0.990055i | \(0.455071\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.29300e6 | −0.316593 | ||||||||
\(442\) | 1.55230e7 | 3.77936 | ||||||||
\(443\) | 875875. | 0.212047 | 0.106024 | − | 0.994364i | \(-0.466188\pi\) | ||||
0.106024 | + | 0.994364i | \(0.466188\pi\) | |||||||
\(444\) | 2.73455e6 | 0.658306 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −487955. | −0.116156 | ||||||||
\(447\) | −4.67266e6 | −1.10610 | ||||||||
\(448\) | −419059. | −0.0986461 | ||||||||
\(449\) | 4.08806e6 | 0.956977 | 0.478489 | − | 0.878094i | \(-0.341185\pi\) | ||||
0.478489 | + | 0.878094i | \(0.341185\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 681184. | 0.157697 | ||||||||
\(452\) | 1.04208e6 | 0.239915 | ||||||||
\(453\) | 2.07183e6 | 0.474361 | ||||||||
\(454\) | 790317. | 0.179954 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.48501e6 | 1.23528 | ||||||||
\(457\) | −2.85279e6 | −0.638968 | −0.319484 | − | 0.947592i | \(-0.603510\pi\) | ||||
−0.319484 | + | 0.947592i | \(0.603510\pi\) | |||||||
\(458\) | 3.25581e6 | 0.725263 | ||||||||
\(459\) | −1.10056e6 | −0.243827 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.16387e6 | 1.35083 | 0.675416 | − | 0.737437i | \(-0.263964\pi\) | ||||
0.675416 | + | 0.737437i | \(0.263964\pi\) | |||||||
\(462\) | 317837. | 0.0692787 | ||||||||
\(463\) | 4.52412e6 | 0.980804 | 0.490402 | − | 0.871496i | \(-0.336850\pi\) | ||||
0.490402 | + | 0.871496i | \(0.336850\pi\) | |||||||
\(464\) | −6.95366e6 | −1.49940 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.27412e7 | 2.71798 | ||||||||
\(467\) | −2.23084e6 | −0.473344 | −0.236672 | − | 0.971590i | \(-0.576057\pi\) | ||||
−0.236672 | + | 0.971590i | \(0.576057\pi\) | |||||||
\(468\) | −5.71401e6 | −1.20594 | ||||||||
\(469\) | 1.13828e6 | 0.238956 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.95977e6 | −0.614761 | ||||||||
\(472\) | −9.62289e6 | −1.98816 | ||||||||
\(473\) | 276256. | 0.0567752 | ||||||||
\(474\) | −748093. | −0.152936 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.02295e6 | 0.611525 | ||||||||
\(477\) | −2.30834e6 | −0.464518 | ||||||||
\(478\) | 1.36004e7 | 2.72259 | ||||||||
\(479\) | −6.62215e6 | −1.31874 | −0.659372 | − | 0.751817i | \(-0.729178\pi\) | ||||
−0.659372 | + | 0.751817i | \(0.729178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.51205e6 | 0.889224 | ||||||||
\(482\) | −1.14723e7 | −2.24923 | ||||||||
\(483\) | 386484. | 0.0753813 | ||||||||
\(484\) | 1.00910e6 | 0.195803 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 593208. | 0.113924 | ||||||||
\(487\) | −2.17583e6 | −0.415721 | −0.207860 | − | 0.978158i | \(-0.566650\pi\) | ||||
−0.207860 | + | 0.978158i | \(0.566650\pi\) | |||||||
\(488\) | 1.90511e7 | 3.62134 | ||||||||
\(489\) | −2.21744e6 | −0.419353 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.67198e6 | 1.43616 | 0.718081 | − | 0.695959i | \(-0.245021\pi\) | ||||
0.718081 | + | 0.695959i | \(0.245021\pi\) | |||||||
\(492\) | −3.49208e6 | −0.650386 | ||||||||
\(493\) | −6.90278e6 | −1.27911 | ||||||||
\(494\) | 1.68941e7 | 3.11471 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.14542e7 | 2.09055 | ||||||||
\(497\) | 1.09122e6 | 0.198162 | ||||||||
\(498\) | 1.93083e6 | 0.348875 | ||||||||
\(499\) | 6.65009e6 | 1.19557 | 0.597787 | − | 0.801655i | \(-0.296047\pi\) | ||||
0.597787 | + | 0.801655i | \(0.296047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.23272e6 | −0.931393 | ||||||||
\(502\) | 3.23058e6 | 0.572165 | ||||||||
\(503\) | −4.18197e6 | −0.736989 | −0.368495 | − | 0.929630i | \(-0.620127\pi\) | ||||
−0.368495 | + | 0.929630i | \(0.620127\pi\) | |||||||
\(504\) | −872882. | −0.153066 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.79675e6 | 0.311968 | ||||||||
\(507\) | −6.08657e6 | −1.05161 | ||||||||
\(508\) | 1.54215e7 | 2.65135 | ||||||||
\(509\) | −1.01322e7 | −1.73345 | −0.866725 | − | 0.498787i | \(-0.833779\pi\) | ||||
−0.866725 | + | 0.498787i | \(0.833779\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.70502e6 | −0.288853 | ||||||||
\(512\) | 1.28679e7 | 2.16936 | ||||||||
\(513\) | −1.19777e6 | −0.200947 | ||||||||
\(514\) | 1.44939e7 | 2.41980 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.41622e6 | −0.234157 | ||||||||
\(517\) | −723639. | −0.119068 | ||||||||
\(518\) | 1.28664e6 | 0.210685 | ||||||||
\(519\) | −2.38185e6 | −0.388147 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.42546e6 | −1.03707 | −0.518537 | − | 0.855055i | \(-0.673523\pi\) | ||||
−0.518537 | + | 0.855055i | \(0.673523\pi\) | |||||||
\(522\) | 3.72063e6 | 0.597641 | ||||||||
\(523\) | 1.17398e6 | 0.187674 | 0.0938372 | − | 0.995588i | \(-0.470087\pi\) | ||||
0.0938372 | + | 0.995588i | \(0.470087\pi\) | |||||||
\(524\) | 1.85578e7 | 2.95256 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.42478e6 | 1.32768 | ||||||||
\(527\) | 1.13704e7 | 1.78340 | ||||||||
\(528\) | −1.65617e6 | −0.258535 | ||||||||
\(529\) | −4.25153e6 | −0.660551 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.10137e6 | 0.323419 | ||||||||
\(532\) | 3.28997e6 | 0.503979 | ||||||||
\(533\) | −5.76199e6 | −0.878525 | ||||||||
\(534\) | 7.08719e6 | 1.07553 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.45330e7 | −2.18496 | ||||||||
\(537\) | 124979. | 0.0187025 | ||||||||
\(538\) | 4.17174e6 | 0.621386 | ||||||||
\(539\) | −1.93152e6 | −0.286370 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.25283e6 | −0.771614 | −0.385807 | − | 0.922580i | \(-0.626077\pi\) | ||||
−0.385807 | + | 0.922580i | \(0.626077\pi\) | |||||||
\(542\) | −6.50188e6 | −0.950694 | ||||||||
\(543\) | 6.77334e6 | 0.985833 | ||||||||
\(544\) | −5.14576e6 | −0.745508 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.68852e6 | −0.385950 | ||||||||
\(547\) | −1.13849e7 | −1.62689 | −0.813447 | − | 0.581640i | \(-0.802411\pi\) | ||||
−0.813447 | + | 0.581640i | \(0.802411\pi\) | |||||||
\(548\) | −1.18676e7 | −1.68815 | ||||||||
\(549\) | −4.16022e6 | −0.589095 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.51249e6 | −1.05416 | ||||||||
\(552\) | −4.93444e6 | −0.689271 | ||||||||
\(553\) | −240382. | −0.0334263 | ||||||||
\(554\) | 6.82136e6 | 0.944271 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.41374e7 | −3.31134 | ||||||||
\(557\) | −4.54355e6 | −0.620522 | −0.310261 | − | 0.950651i | \(-0.600416\pi\) | ||||
−0.310261 | + | 0.950651i | \(0.600416\pi\) | |||||||
\(558\) | −6.12869e6 | −0.833263 | ||||||||
\(559\) | −2.33679e6 | −0.316293 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.64405e6 | −0.220550 | ||||||||
\(562\) | 1.79508e7 | 2.39741 | ||||||||
\(563\) | 1.22077e7 | 1.62317 | 0.811583 | − | 0.584237i | \(-0.198606\pi\) | ||||
0.811583 | + | 0.584237i | \(0.198606\pi\) | |||||||
\(564\) | 3.70972e6 | 0.491070 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8.76572e6 | −1.15013 | ||||||||
\(567\) | 190613. | 0.0248997 | ||||||||
\(568\) | −1.39321e7 | −1.81195 | ||||||||
\(569\) | −1.58948e6 | −0.205814 | −0.102907 | − | 0.994691i | \(-0.532814\pi\) | ||||
−0.102907 | + | 0.994691i | \(0.532814\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −692853. | −0.0889306 | −0.0444653 | − | 0.999011i | \(-0.514158\pi\) | ||||
−0.0444653 | + | 0.999011i | \(0.514158\pi\) | |||||||
\(572\) | −8.53574e6 | −1.09082 | ||||||||
\(573\) | 228745. | 0.0291048 | ||||||||
\(574\) | −1.64307e6 | −0.208150 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.16836e6 | −0.146731 | ||||||||
\(577\) | −1.24815e7 | −1.56073 | −0.780365 | − | 0.625324i | \(-0.784967\pi\) | ||||
−0.780365 | + | 0.625324i | \(0.784967\pi\) | |||||||
\(578\) | −8.63250e6 | −1.07477 | ||||||||
\(579\) | −4.40840e6 | −0.546493 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 620425. | 0.0762516 | ||||||||
\(582\) | −5.83847e6 | −0.714483 | ||||||||
\(583\) | −3.44825e6 | −0.420173 | ||||||||
\(584\) | 2.17688e7 | 2.64121 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.56136e6 | 0.789314 | ||||||||
\(587\) | 9.13291e6 | 1.09399 | 0.546996 | − | 0.837135i | \(-0.315771\pi\) | ||||
0.546996 | + | 0.837135i | \(0.315771\pi\) | |||||||
\(588\) | 9.90189e6 | 1.18107 | ||||||||
\(589\) | 1.23747e7 | 1.46976 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.92344e6 | −0.344291 | ||||||||
\(592\) | −6.70436e6 | −0.786236 | ||||||||
\(593\) | −1.08272e7 | −1.26438 | −0.632191 | − | 0.774813i | \(-0.717844\pi\) | ||||
−0.632191 | + | 0.774813i | \(0.717844\pi\) | |||||||
\(594\) | 886150. | 0.103048 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.57836e7 | 4.12637 | ||||||||
\(597\) | 3.58665e6 | 0.411863 | ||||||||
\(598\) | −1.51983e7 | −1.73797 | ||||||||
\(599\) | 7.47502e6 | 0.851227 | 0.425614 | − | 0.904905i | \(-0.360058\pi\) | ||||
0.425614 | + | 0.904905i | \(0.360058\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.02516e6 | −0.115772 | −0.0578861 | − | 0.998323i | \(-0.518436\pi\) | ||||
−0.0578861 | + | 0.998323i | \(0.518436\pi\) | |||||||
\(602\) | −666351. | −0.0749397 | ||||||||
\(603\) | 3.17360e6 | 0.355434 | ||||||||
\(604\) | −1.58662e7 | −1.76963 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.37283e6 | 0.483706 | ||||||||
\(607\) | −1.33264e7 | −1.46805 | −0.734024 | − | 0.679123i | \(-0.762360\pi\) | ||||
−0.734024 | + | 0.679123i | \(0.762360\pi\) | |||||||
\(608\) | −5.60028e6 | −0.614399 | ||||||||
\(609\) | 1.19553e6 | 0.130623 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.12110e6 | 0.663325 | ||||||||
\(612\) | 8.42819e6 | 0.909611 | ||||||||
\(613\) | 1.57435e7 | 1.69220 | 0.846098 | − | 0.533027i | \(-0.178946\pi\) | ||||
0.846098 | + | 0.533027i | \(0.178946\pi\) | |||||||
\(614\) | −1.88254e7 | −2.01523 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.30394e6 | −0.138454 | ||||||||
\(617\) | 5.87960e6 | 0.621777 | 0.310888 | − | 0.950446i | \(-0.399373\pi\) | ||||
0.310888 | + | 0.950446i | \(0.399373\pi\) | |||||||
\(618\) | −1.10236e7 | −1.16106 | ||||||||
\(619\) | −1.81138e6 | −0.190013 | −0.0950063 | − | 0.995477i | \(-0.530287\pi\) | ||||
−0.0950063 | + | 0.995477i | \(0.530287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.07754e6 | 0.112126 | ||||||||
\(622\) | 1.61365e7 | 1.67238 | ||||||||
\(623\) | 2.27730e6 | 0.235071 | ||||||||
\(624\) | 1.40092e7 | 1.44029 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.59390e7 | −2.64556 | ||||||||
\(627\) | −1.78927e6 | −0.181763 | ||||||||
\(628\) | 2.26662e7 | 2.29340 | ||||||||
\(629\) | −6.65529e6 | −0.670719 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.43835e7 | −1.43811 | −0.719054 | − | 0.694954i | \(-0.755425\pi\) | ||||
−0.719054 | + | 0.694954i | \(0.755425\pi\) | |||||||
\(632\) | 3.06907e6 | 0.305643 | ||||||||
\(633\) | 7.81780e6 | 0.775489 | ||||||||
\(634\) | −1.35207e7 | −1.33591 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.76774e7 | 1.73291 | ||||||||
\(637\) | 1.63383e7 | 1.59536 | ||||||||
\(638\) | 5.55798e6 | 0.540587 | ||||||||
\(639\) | 3.04239e6 | 0.294756 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.80867e6 | −0.366124 | −0.183062 | − | 0.983101i | \(-0.558601\pi\) | ||||
−0.183062 | + | 0.983101i | \(0.558601\pi\) | |||||||
\(642\) | 1.73490e7 | 1.66126 | ||||||||
\(643\) | −483920. | −0.0461579 | −0.0230789 | − | 0.999734i | \(-0.507347\pi\) | ||||
−0.0230789 | + | 0.999734i | \(0.507347\pi\) | |||||||
\(644\) | −2.95973e6 | −0.281214 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.49188e7 | −2.34934 | ||||||||
\(647\) | −1.80652e7 | −1.69661 | −0.848306 | − | 0.529506i | \(-0.822377\pi\) | ||||
−0.848306 | + | 0.529506i | \(0.822377\pi\) | |||||||
\(648\) | −2.43365e6 | −0.227678 | ||||||||
\(649\) | 3.13908e6 | 0.292544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.96931e6 | −0.182121 | ||||||||
\(652\) | 1.69813e7 | 1.56442 | ||||||||
\(653\) | −2.03744e7 | −1.86983 | −0.934915 | − | 0.354871i | \(-0.884525\pi\) | ||||
−0.934915 | + | 0.354871i | \(0.884525\pi\) | |||||||
\(654\) | −1.41588e6 | −0.129444 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.56161e6 | 0.776776 | ||||||||
\(657\) | −4.75370e6 | −0.429653 | ||||||||
\(658\) | 1.74547e6 | 0.157162 | ||||||||
\(659\) | −1.37586e7 | −1.23413 | −0.617066 | − | 0.786912i | \(-0.711679\pi\) | ||||
−0.617066 | + | 0.786912i | \(0.711679\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.34803e7 | −1.20004 | −0.600019 | − | 0.799985i | \(-0.704840\pi\) | ||||
−0.600019 | + | 0.799985i | \(0.704840\pi\) | |||||||
\(662\) | −2.75620e7 | −2.44437 | ||||||||
\(663\) | 1.39066e7 | 1.22868 | ||||||||
\(664\) | −7.92127e6 | −0.697228 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.58724e6 | 0.313382 | ||||||||
\(667\) | 6.75840e6 | 0.588206 | ||||||||
\(668\) | 4.00726e7 | 3.47461 | ||||||||
\(669\) | −437147. | −0.0377627 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.21465e6 | −0.532856 | ||||||||
\(672\) | 891226. | 0.0761315 | ||||||||
\(673\) | 680925. | 0.0579511 | 0.0289755 | − | 0.999580i | \(-0.490776\pi\) | ||||
0.0289755 | + | 0.999580i | \(0.490776\pi\) | |||||||
\(674\) | 3.72070e7 | 3.15482 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.66115e7 | 3.92307 | ||||||||
\(677\) | −1.36705e7 | −1.14634 | −0.573171 | − | 0.819436i | \(-0.694287\pi\) | ||||
−0.573171 | + | 0.819436i | \(0.694287\pi\) | |||||||
\(678\) | 1.36703e6 | 0.114210 | ||||||||
\(679\) | −1.87605e6 | −0.156160 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 708026. | 0.0585034 | ||||||||
\(682\) | −9.15520e6 | −0.753715 | ||||||||
\(683\) | −6.79648e6 | −0.557484 | −0.278742 | − | 0.960366i | \(-0.589917\pi\) | ||||
−0.278742 | + | 0.960366i | \(0.589917\pi\) | |||||||
\(684\) | 9.17264e6 | 0.749642 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.56429e6 | 0.775966 | ||||||||
\(687\) | 2.91681e6 | 0.235785 | ||||||||
\(688\) | 3.47218e6 | 0.279661 | ||||||||
\(689\) | 2.91680e7 | 2.34077 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.11491e6 | 0.726202 | 0.363101 | − | 0.931750i | \(-0.381718\pi\) | ||||
0.363101 | + | 0.931750i | \(0.381718\pi\) | |||||||
\(692\) | 1.82404e7 | 1.44800 | ||||||||
\(693\) | 284743. | 0.0225227 | ||||||||
\(694\) | −1.17761e7 | −0.928116 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.52640e7 | −1.19439 | ||||||||
\(697\) | 8.49896e6 | 0.662649 | ||||||||
\(698\) | 3.61740e6 | 0.281033 | ||||||||
\(699\) | 1.14146e7 | 0.883621 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.03729e7 | −0.797269 | −0.398634 | − | 0.917110i | \(-0.630516\pi\) | ||||
−0.398634 | + | 0.917110i | \(0.630516\pi\) | |||||||
\(702\) | −7.49575e6 | −0.574080 | ||||||||
\(703\) | −7.24315e6 | −0.552763 | ||||||||
\(704\) | −1.74533e6 | −0.132723 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.00332e7 | 0.757579 | ||||||||
\(707\) | 1.40510e6 | 0.105721 | ||||||||
\(708\) | −1.60925e7 | −1.20653 | ||||||||
\(709\) | 1.78828e7 | 1.33604 | 0.668022 | − | 0.744142i | \(-0.267141\pi\) | ||||
0.668022 | + | 0.744142i | \(0.267141\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −670199. | −0.0497199 | ||||||||
\(712\) | −2.90754e7 | −2.14944 | ||||||||
\(713\) | −1.11326e7 | −0.820108 | ||||||||
\(714\) | 3.96557e6 | 0.291112 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −957097. | −0.0697708 | ||||||||
\(717\) | 1.21843e7 | 0.885119 | ||||||||
\(718\) | −1.48386e7 | −1.07419 | ||||||||
\(719\) | −2.62904e7 | −1.89660 | −0.948298 | − | 0.317382i | \(-0.897196\pi\) | ||||
−0.948298 | + | 0.317382i | \(0.897196\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.54217e6 | −0.253765 | ||||||||
\(722\) | −2.24494e6 | −0.160273 | ||||||||
\(723\) | −1.02778e7 | −0.731231 | ||||||||
\(724\) | −5.18708e7 | −3.67770 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.32376e6 | 0.0932108 | ||||||||
\(727\) | −1.40763e7 | −0.987763 | −0.493882 | − | 0.869529i | \(-0.664422\pi\) | ||||
−0.493882 | + | 0.869529i | \(0.664422\pi\) | |||||||
\(728\) | 1.10297e7 | 0.771322 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.44677e6 | 0.238572 | ||||||||
\(732\) | 3.18593e7 | 2.19765 | ||||||||
\(733\) | 5.60463e6 | 0.385290 | 0.192645 | − | 0.981269i | \(-0.438293\pi\) | ||||
0.192645 | + | 0.981269i | \(0.438293\pi\) | |||||||
\(734\) | 3.23387e7 | 2.21555 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.03813e6 | 0.342827 | ||||||||
\(737\) | 4.74081e6 | 0.321502 | ||||||||
\(738\) | −4.58098e6 | −0.309612 | ||||||||
\(739\) | −1.92933e6 | −0.129956 | −0.0649778 | − | 0.997887i | \(-0.520698\pi\) | ||||
−0.0649778 | + | 0.997887i | \(0.520698\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.51350e7 | 1.01260 | ||||||||
\(742\) | 8.31746e6 | 0.554601 | ||||||||
\(743\) | 4.43790e6 | 0.294921 | 0.147460 | − | 0.989068i | \(-0.452890\pi\) | ||||
0.147460 | + | 0.989068i | \(0.452890\pi\) | |||||||
\(744\) | 2.51431e7 | 1.66528 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.67934e7 | −3.07849 | ||||||||
\(747\) | 1.72978e6 | 0.113420 | ||||||||
\(748\) | 1.25903e7 | 0.822774 | ||||||||
\(749\) | 5.57467e6 | 0.363090 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.11577e7 | −0.721897 | −0.360949 | − | 0.932586i | \(-0.617547\pi\) | ||||
−0.360949 | + | 0.932586i | \(0.617547\pi\) | |||||||
\(752\) | −9.09521e6 | −0.586500 | ||||||||
\(753\) | 2.89420e6 | 0.186012 | ||||||||
\(754\) | −4.70138e7 | −3.01160 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.45973e6 | −0.0928898 | ||||||||
\(757\) | −1.16077e7 | −0.736216 | −0.368108 | − | 0.929783i | \(-0.619994\pi\) | ||||
−0.368108 | + | 0.929783i | \(0.619994\pi\) | |||||||
\(758\) | 4.06506e7 | 2.56977 | ||||||||
\(759\) | 1.60966e6 | 0.101422 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.38952e6 | −0.0869770 | −0.0434885 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434885 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(762\) | 2.02303e7 | 1.26216 | ||||||||
\(763\) | −454960. | −0.0282919 | ||||||||
\(764\) | −1.75175e6 | −0.108577 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.27942e6 | 0.509833 | ||||||||
\(767\) | −2.65528e7 | −1.62975 | ||||||||
\(768\) | 1.88091e7 | 1.15071 | ||||||||
\(769\) | −2.19019e7 | −1.33557 | −0.667784 | − | 0.744355i | \(-0.732757\pi\) | ||||
−0.667784 | + | 0.744355i | \(0.732757\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.29848e7 | 0.786681 | ||||||||
\(772\) | 3.37599e7 | 2.03872 | ||||||||
\(773\) | 9.21665e6 | 0.554784 | 0.277392 | − | 0.960757i | \(-0.410530\pi\) | ||||
0.277392 | + | 0.960757i | \(0.410530\pi\) | |||||||
\(774\) | −1.85783e6 | −0.111469 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.39525e7 | 1.42789 | ||||||||
\(777\) | 1.15267e6 | 0.0684941 | ||||||||
\(778\) | 2.55633e7 | 1.51415 | ||||||||
\(779\) | 9.24966e6 | 0.546113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.54480e6 | 0.266617 | ||||||||
\(782\) | 2.24175e7 | 1.31090 | ||||||||
\(783\) | 3.33323e6 | 0.194294 | ||||||||
\(784\) | −2.42767e7 | −1.41059 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.43445e7 | 1.40554 | ||||||||
\(787\) | 2.18581e7 | 1.25798 | 0.628992 | − | 0.777412i | \(-0.283468\pi\) | ||||
0.628992 | + | 0.777412i | \(0.283468\pi\) | |||||||
\(788\) | 2.23879e7 | 1.28439 | ||||||||
\(789\) | 7.54756e6 | 0.431633 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 439261. | 0.0249621 | ||||||||
\(792\) | −3.63545e6 | −0.205942 | ||||||||
\(793\) | 5.25684e7 | 2.96853 | ||||||||
\(794\) | −5.20159e7 | −2.92809 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.74668e7 | −1.53648 | ||||||||
\(797\) | −2.79333e7 | −1.55767 | −0.778837 | − | 0.627226i | \(-0.784190\pi\) | ||||
−0.778837 | + | 0.627226i | \(0.784190\pi\) | |||||||
\(798\) | 4.31585e6 | 0.239916 | ||||||||
\(799\) | −9.02865e6 | −0.500329 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.34925e6 | 0.349656 | ||||||||
\(802\) | 4.84459e7 | 2.65963 | ||||||||
\(803\) | −7.10120e6 | −0.388636 | ||||||||
\(804\) | −2.43037e7 | −1.32596 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.74419e7 | 4.19893 | ||||||||
\(807\) | 3.73736e6 | 0.202014 | ||||||||
\(808\) | −1.79397e7 | −0.966687 | ||||||||
\(809\) | 1.07778e7 | 0.578974 | 0.289487 | − | 0.957182i | \(-0.406515\pi\) | ||||
0.289487 | + | 0.957182i | \(0.406515\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.71394e7 | −1.44893 | −0.724467 | − | 0.689309i | \(-0.757914\pi\) | ||||
−0.724467 | + | 0.689309i | \(0.757914\pi\) | |||||||
\(812\) | −9.15550e6 | −0.487295 | ||||||||
\(813\) | −5.82488e6 | −0.309073 | ||||||||
\(814\) | 5.35871e6 | 0.283465 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.06636e7 | −1.08638 | ||||||||
\(817\) | 3.75122e6 | 0.196616 | ||||||||
\(818\) | 3.70322e7 | 1.93507 | ||||||||
\(819\) | −2.40858e6 | −0.125473 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.84095e6 | 0.354208 | 0.177104 | − | 0.984192i | \(-0.443327\pi\) | ||||
0.177104 | + | 0.984192i | \(0.443327\pi\) | |||||||
\(822\) | −1.55682e7 | −0.803634 | ||||||||
\(823\) | −1.95930e7 | −1.00833 | −0.504163 | − | 0.863609i | \(-0.668199\pi\) | ||||
−0.504163 | + | 0.863609i | \(0.668199\pi\) | |||||||
\(824\) | 4.52247e7 | 2.32037 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.57171e6 | −0.386139 | ||||||||
\(827\) | 1.86828e7 | 0.949902 | 0.474951 | − | 0.880012i | \(-0.342466\pi\) | ||||
0.474951 | + | 0.880012i | \(0.342466\pi\) | |||||||
\(828\) | −8.25191e6 | −0.418291 | ||||||||
\(829\) | −1.58057e7 | −0.798779 | −0.399390 | − | 0.916781i | \(-0.630778\pi\) | ||||
−0.399390 | + | 0.916781i | \(0.630778\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.11109e6 | 0.306985 | ||||||||
\(832\) | 1.47634e7 | 0.739397 | ||||||||
\(833\) | −2.40991e7 | −1.20334 | ||||||||
\(834\) | −3.16639e7 | −1.57634 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.37023e7 | 0.678077 | ||||||||
\(837\) | −5.49055e6 | −0.270896 | ||||||||
\(838\) | −1.32512e7 | −0.651844 | ||||||||
\(839\) | −3.69461e7 | −1.81202 | −0.906011 | − | 0.423255i | \(-0.860888\pi\) | ||||
−0.906011 | + | 0.423255i | \(0.860888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 395030. | 0.0192593 | ||||||||
\(842\) | 3.31035e7 | 1.60914 | ||||||||
\(843\) | 1.60817e7 | 0.779403 | ||||||||
\(844\) | −5.98694e7 | −2.89300 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.86649e6 | 0.233771 | ||||||||
\(847\) | 425357. | 0.0203725 | ||||||||
\(848\) | −4.33401e7 | −2.06967 | ||||||||
\(849\) | −7.85300e6 | −0.373909 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.51609e6 | 0.308435 | ||||||||
\(852\) | −2.32988e7 | −1.09960 | ||||||||
\(853\) | −2.39478e7 | −1.12692 | −0.563459 | − | 0.826144i | \(-0.690530\pi\) | ||||
−0.563459 | + | 0.826144i | \(0.690530\pi\) | |||||||
\(854\) | 1.49902e7 | 0.703337 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.11746e7 | −3.32002 | ||||||||
\(857\) | 4.09428e6 | 0.190426 | 0.0952129 | − | 0.995457i | \(-0.469647\pi\) | ||||
0.0952129 | + | 0.995457i | \(0.469647\pi\) | |||||||
\(858\) | −1.11974e7 | −0.519275 | ||||||||
\(859\) | −6.51782e6 | −0.301384 | −0.150692 | − | 0.988581i | \(-0.548150\pi\) | ||||
−0.150692 | + | 0.988581i | \(0.548150\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.47199e6 | −0.0676700 | ||||||||
\(862\) | −1.87998e7 | −0.861759 | ||||||||
\(863\) | −8.54609e6 | −0.390607 | −0.195304 | − | 0.980743i | \(-0.562569\pi\) | ||||
−0.195304 | + | 0.980743i | \(0.562569\pi\) | |||||||
\(864\) | 2.48479e6 | 0.113242 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.33178e7 | 1.96278 | ||||||||
\(867\) | −7.73365e6 | −0.349411 | ||||||||
\(868\) | 1.50811e7 | 0.679413 | ||||||||
\(869\) | −1.00116e6 | −0.0449733 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.01015e7 | −1.79108 | ||||||||
\(872\) | 5.80870e6 | 0.258695 | ||||||||
\(873\) | −5.23055e6 | −0.232280 | ||||||||
\(874\) | 2.43977e7 | 1.08036 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.64042e7 | 1.60284 | ||||||||
\(877\) | 3.63188e7 | 1.59453 | 0.797266 | − | 0.603629i | \(-0.206279\pi\) | ||||
0.797266 | + | 0.603629i | \(0.206279\pi\) | |||||||
\(878\) | −1.14135e7 | −0.499668 | ||||||||
\(879\) | 5.87817e6 | 0.256608 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.57431e7 | 0.683364 | 0.341682 | − | 0.939816i | \(-0.389004\pi\) | ||||
0.341682 | + | 0.939816i | \(0.389004\pi\) | |||||||
\(882\) | 1.29895e7 | 0.562240 | ||||||||
\(883\) | −1.30059e7 | −0.561354 | −0.280677 | − | 0.959802i | \(-0.590559\pi\) | ||||
−0.280677 | + | 0.959802i | \(0.590559\pi\) | |||||||
\(884\) | −1.06498e8 | −4.58365 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.79907e6 | −0.376576 | ||||||||
\(887\) | 3.12186e7 | 1.33231 | 0.666154 | − | 0.745814i | \(-0.267939\pi\) | ||||
0.666154 | + | 0.745814i | \(0.267939\pi\) | |||||||
\(888\) | −1.47167e7 | −0.626295 | ||||||||
\(889\) | 6.50050e6 | 0.275862 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 3.34771e6 | 0.140876 | ||||||||
\(893\) | −9.82614e6 | −0.412339 | ||||||||
\(894\) | 4.69416e7 | 1.96433 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.37868e6 | 0.307050 | ||||||||
\(897\) | −1.36158e7 | −0.565017 | ||||||||
\(898\) | −4.10688e7 | −1.69950 | ||||||||
\(899\) | −3.44370e7 | −1.42111 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.30230e7 | −1.76558 | ||||||||
\(902\) | −6.84319e6 | −0.280054 | ||||||||
\(903\) | −596968. | −0.0243631 | ||||||||
\(904\) | −5.60827e6 | −0.228248 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.08137e7 | −0.842419 | ||||||||
\(907\) | −3.59253e7 | −1.45005 | −0.725023 | − | 0.688725i | \(-0.758171\pi\) | ||||
−0.725023 | + | 0.688725i | \(0.758171\pi\) | |||||||
\(908\) | −5.42212e6 | −0.218250 | ||||||||
\(909\) | 3.91752e6 | 0.157254 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.47634e7 | −0.589372 | −0.294686 | − | 0.955594i | \(-0.595215\pi\) | ||||
−0.294686 | + | 0.955594i | \(0.595215\pi\) | |||||||
\(912\) | −2.24888e7 | −0.895321 | ||||||||
\(913\) | 2.58400e6 | 0.102592 | ||||||||
\(914\) | 2.86592e7 | 1.13475 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.23371e7 | −0.879607 | ||||||||
\(917\) | 7.82251e6 | 0.307201 | ||||||||
\(918\) | 1.10563e7 | 0.433014 | ||||||||
\(919\) | −1.26772e7 | −0.495146 | −0.247573 | − | 0.968869i | \(-0.579633\pi\) | ||||
−0.247573 | + | 0.968869i | \(0.579633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.68653e7 | −0.655155 | ||||||||
\(922\) | −6.19224e7 | −2.39895 | ||||||||
\(923\) | −3.84435e7 | −1.48531 | ||||||||
\(924\) | −2.18058e6 | −0.0840220 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.54495e7 | −1.74181 | ||||||||
\(927\) | −9.87580e6 | −0.377462 | ||||||||
\(928\) | 1.55848e7 | 0.594060 | ||||||||
\(929\) | 1.20341e7 | 0.457482 | 0.228741 | − | 0.973487i | \(-0.426539\pi\) | ||||
0.228741 | + | 0.973487i | \(0.426539\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.62277e7 | −0.991713 | ||||||||
\(932\) | −8.74136e7 | −3.29639 | ||||||||
\(933\) | 1.44563e7 | 0.543694 | ||||||||
\(934\) | 2.24111e7 | 0.840614 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.07515e7 | 1.14730 | ||||||||
\(937\) | 4.51344e7 | 1.67942 | 0.839708 | − | 0.543038i | \(-0.182726\pi\) | ||||
0.839708 | + | 0.543038i | \(0.182726\pi\) | |||||||
\(938\) | −1.14352e7 | −0.424362 | ||||||||
\(939\) | −2.32381e7 | −0.860077 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.44095e6 | 0.310754 | 0.155377 | − | 0.987855i | \(-0.450341\pi\) | ||||
0.155377 | + | 0.987855i | \(0.450341\pi\) | |||||||
\(942\) | 2.97340e7 | 1.09176 | ||||||||
\(943\) | −8.32120e6 | −0.304724 | ||||||||
\(944\) | 3.94543e7 | 1.44100 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.77528e6 | −0.100827 | ||||||||
\(947\) | −2.68109e7 | −0.971485 | −0.485743 | − | 0.874102i | \(-0.661451\pi\) | ||||
−0.485743 | + | 0.874102i | \(0.661451\pi\) | |||||||
\(948\) | 5.13244e6 | 0.185483 | ||||||||
\(949\) | 6.00675e7 | 2.16508 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.21129e7 | −0.434307 | ||||||||
\(952\) | −1.62689e7 | −0.581788 | ||||||||
\(953\) | −1.42183e7 | −0.507127 | −0.253563 | − | 0.967319i | \(-0.581603\pi\) | ||||
−0.253563 | + | 0.967319i | \(0.581603\pi\) | |||||||
\(954\) | 2.31896e7 | 0.824940 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.33081e7 | −3.30198 | ||||||||
\(957\) | 4.97926e6 | 0.175746 | ||||||||
\(958\) | 6.65263e7 | 2.34196 | ||||||||
\(959\) | −5.00246e6 | −0.175645 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.80961e7 | 0.981380 | ||||||||
\(962\) | −4.53282e7 | −1.57918 | ||||||||
\(963\) | 1.55425e7 | 0.540078 | ||||||||
\(964\) | 7.87082e7 | 2.72789 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.88263e6 | −0.133870 | ||||||||
\(967\) | −277112. | −0.00952993 | −0.00476496 | − | 0.999989i | \(-0.501517\pi\) | ||||
−0.00476496 | + | 0.999989i | \(0.501517\pi\) | |||||||
\(968\) | −5.43074e6 | −0.186282 | ||||||||
\(969\) | −2.23242e7 | −0.763777 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.77514e6 | 0.264643 | 0.132321 | − | 0.991207i | \(-0.457757\pi\) | ||||
0.132321 | + | 0.991207i | \(0.457757\pi\) | |||||||
\(972\) | −4.06982e6 | −0.138169 | ||||||||
\(973\) | −1.01744e7 | −0.344531 | ||||||||
\(974\) | 2.18584e7 | 0.738280 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.81102e7 | −2.62472 | ||||||||
\(977\) | −4.83351e6 | −0.162004 | −0.0810020 | − | 0.996714i | \(-0.525812\pi\) | ||||
−0.0810020 | + | 0.996714i | \(0.525812\pi\) | |||||||
\(978\) | 2.22765e7 | 0.744731 | ||||||||
\(979\) | 9.48468e6 | 0.316276 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.26846e6 | −0.0420827 | ||||||||
\(982\) | −7.70729e7 | −2.55049 | ||||||||
\(983\) | 9.75876e6 | 0.322115 | 0.161057 | − | 0.986945i | \(-0.448510\pi\) | ||||
0.161057 | + | 0.986945i | \(0.448510\pi\) | |||||||
\(984\) | 1.87936e7 | 0.618760 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.93455e7 | 2.27157 | ||||||||
\(987\) | 1.56373e6 | 0.0510938 | ||||||||
\(988\) | −1.15905e8 | −3.77755 | ||||||||
\(989\) | −3.37468e6 | −0.109709 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.72969e7 | 0.882935 | 0.441468 | − | 0.897277i | \(-0.354458\pi\) | ||||
0.441468 | + | 0.897277i | \(0.354458\pi\) | |||||||
\(992\) | −2.56715e7 | −0.828270 | ||||||||
\(993\) | −2.46922e7 | −0.794668 | ||||||||
\(994\) | −1.09624e7 | −0.351917 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.32468e7 | −0.423120 | ||||||||
\(997\) | −4.85951e7 | −1.54830 | −0.774149 | − | 0.633004i | \(-0.781822\pi\) | ||||
−0.774149 | + | 0.633004i | \(0.781822\pi\) | |||||||
\(998\) | −6.68070e7 | −2.12322 | ||||||||
\(999\) | 3.21372e6 | 0.101881 |
(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.v.1.2 | 13 | ||
5.2 | odd | 4 | 165.6.c.b.34.3 | ✓ | 26 | ||
5.3 | odd | 4 | 165.6.c.b.34.24 | yes | 26 | ||
5.4 | even | 2 | 825.6.a.y.1.12 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.3 | ✓ | 26 | 5.2 | odd | 4 | ||
165.6.c.b.34.24 | yes | 26 | 5.3 | odd | 4 | ||
825.6.a.v.1.2 | 13 | 1.1 | even | 1 | trivial | ||
825.6.a.y.1.12 | 13 | 5.4 | even | 2 |