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: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 176x^{6} + 272x^{5} + 9055x^{4} - 15851x^{3} - 118840x^{2} + 149572x - 33248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.292443\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29244 | −0.228474 | −0.114237 | − | 0.993454i | \(-0.536442\pi\) | ||||
−0.114237 | + | 0.993454i | \(0.536442\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −30.3296 | −0.947800 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −11.6320 | −0.131909 | ||||||||
\(7\) | −91.7671 | −0.707851 | −0.353926 | − | 0.935274i | \(-0.615153\pi\) | ||||
−0.353926 | + | 0.935274i | \(0.615153\pi\) | |||||||
\(8\) | 80.5574 | 0.445021 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −272.966 | −0.547212 | ||||||||
\(13\) | −70.3337 | −0.115426 | −0.0577132 | − | 0.998333i | \(-0.518381\pi\) | ||||
−0.0577132 | + | 0.998333i | \(0.518381\pi\) | |||||||
\(14\) | 118.604 | 0.161725 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 866.431 | 0.846124 | ||||||||
\(17\) | 1175.46 | 0.986471 | 0.493235 | − | 0.869896i | \(-0.335814\pi\) | ||||
0.493235 | + | 0.869896i | \(0.335814\pi\) | |||||||
\(18\) | −104.688 | −0.0761579 | ||||||||
\(19\) | −961.502 | −0.611035 | −0.305517 | − | 0.952186i | \(-0.598829\pi\) | ||||
−0.305517 | + | 0.952186i | \(0.598829\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −825.904 | −0.408678 | ||||||||
\(22\) | 156.386 | 0.0688874 | ||||||||
\(23\) | −1303.06 | −0.513625 | −0.256813 | − | 0.966461i | \(-0.582672\pi\) | ||||
−0.256813 | + | 0.966461i | \(0.582672\pi\) | |||||||
\(24\) | 725.017 | 0.256933 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 90.9024 | 0.0263719 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 2783.26 | 0.670901 | ||||||||
\(29\) | −3346.41 | −0.738898 | −0.369449 | − | 0.929251i | \(-0.620454\pi\) | ||||
−0.369449 | + | 0.929251i | \(0.620454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6451.89 | 1.20582 | 0.602911 | − | 0.797809i | \(-0.294008\pi\) | ||||
0.602911 | + | 0.797809i | \(0.294008\pi\) | |||||||
\(32\) | −3697.65 | −0.638338 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −1519.21 | −0.225383 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2456.70 | −0.315933 | ||||||||
\(37\) | 13216.4 | 1.58711 | 0.793557 | − | 0.608496i | \(-0.208227\pi\) | ||||
0.793557 | + | 0.608496i | \(0.208227\pi\) | |||||||
\(38\) | 1242.69 | 0.139605 | ||||||||
\(39\) | −633.004 | −0.0666415 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18467.9 | 1.71577 | 0.857883 | − | 0.513844i | \(-0.171779\pi\) | ||||
0.857883 | + | 0.513844i | \(0.171779\pi\) | |||||||
\(42\) | 1067.43 | 0.0933722 | ||||||||
\(43\) | −19255.1 | −1.58809 | −0.794044 | − | 0.607861i | \(-0.792028\pi\) | ||||
−0.794044 | + | 0.607861i | \(0.792028\pi\) | |||||||
\(44\) | 3669.88 | 0.285772 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1684.14 | 0.117350 | ||||||||
\(47\) | −17064.0 | −1.12677 | −0.563387 | − | 0.826193i | \(-0.690502\pi\) | ||||
−0.563387 | + | 0.826193i | \(0.690502\pi\) | |||||||
\(48\) | 7797.88 | 0.488510 | ||||||||
\(49\) | −8385.80 | −0.498947 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10579.1 | 0.569539 | ||||||||
\(52\) | 2133.19 | 0.109401 | ||||||||
\(53\) | 31237.8 | 1.52753 | 0.763767 | − | 0.645491i | \(-0.223347\pi\) | ||||
0.763767 | + | 0.645491i | \(0.223347\pi\) | |||||||
\(54\) | −942.191 | −0.0439698 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7392.52 | −0.315009 | ||||||||
\(57\) | −8653.52 | −0.352781 | ||||||||
\(58\) | 4325.05 | 0.168819 | ||||||||
\(59\) | 43403.2 | 1.62327 | 0.811637 | − | 0.584162i | \(-0.198577\pi\) | ||||
0.811637 | + | 0.584162i | \(0.198577\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3568.78 | −0.122799 | −0.0613996 | − | 0.998113i | \(-0.519556\pi\) | ||||
−0.0613996 | + | 0.998113i | \(0.519556\pi\) | |||||||
\(62\) | −8338.70 | −0.275499 | ||||||||
\(63\) | −7433.14 | −0.235950 | ||||||||
\(64\) | −22946.8 | −0.700280 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1407.47 | 0.0397722 | ||||||||
\(67\) | −70764.0 | −1.92586 | −0.962932 | − | 0.269745i | \(-0.913061\pi\) | ||||
−0.962932 | + | 0.269745i | \(0.913061\pi\) | |||||||
\(68\) | −35651.1 | −0.934977 | ||||||||
\(69\) | −11727.6 | −0.296542 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 41227.7 | 0.970607 | 0.485304 | − | 0.874346i | \(-0.338709\pi\) | ||||
0.485304 | + | 0.874346i | \(0.338709\pi\) | |||||||
\(72\) | 6525.15 | 0.148340 | ||||||||
\(73\) | 41255.5 | 0.906097 | 0.453048 | − | 0.891486i | \(-0.350336\pi\) | ||||
0.453048 | + | 0.891486i | \(0.350336\pi\) | |||||||
\(74\) | −17081.4 | −0.362614 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 29162.0 | 0.579139 | ||||||||
\(77\) | 11103.8 | 0.213425 | ||||||||
\(78\) | 818.121 | 0.0152258 | ||||||||
\(79\) | −57458.9 | −1.03583 | −0.517916 | − | 0.855431i | \(-0.673292\pi\) | ||||
−0.517916 | + | 0.855431i | \(0.673292\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −23868.7 | −0.392008 | ||||||||
\(83\) | 17233.5 | 0.274587 | 0.137293 | − | 0.990530i | \(-0.456160\pi\) | ||||
0.137293 | + | 0.990530i | \(0.456160\pi\) | |||||||
\(84\) | 25049.3 | 0.387345 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24886.1 | 0.362836 | ||||||||
\(87\) | −30117.7 | −0.426603 | ||||||||
\(88\) | −9747.45 | −0.134179 | ||||||||
\(89\) | −24409.7 | −0.326654 | −0.163327 | − | 0.986572i | \(-0.552223\pi\) | ||||
−0.163327 | + | 0.986572i | \(0.552223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6454.32 | 0.0817047 | ||||||||
\(92\) | 39521.4 | 0.486814 | ||||||||
\(93\) | 58067.0 | 0.696181 | ||||||||
\(94\) | 22054.3 | 0.257438 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −33278.9 | −0.368545 | ||||||||
\(97\) | 126547. | 1.36560 | 0.682799 | − | 0.730606i | \(-0.260762\pi\) | ||||
0.682799 | + | 0.730606i | \(0.260762\pi\) | |||||||
\(98\) | 10838.2 | 0.113996 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −89974.7 | −0.877641 | −0.438820 | − | 0.898575i | \(-0.644604\pi\) | ||||
−0.438820 | + | 0.898575i | \(0.644604\pi\) | |||||||
\(102\) | −13672.9 | −0.130125 | ||||||||
\(103\) | −106257. | −0.986876 | −0.493438 | − | 0.869781i | \(-0.664260\pi\) | ||||
−0.493438 | + | 0.869781i | \(0.664260\pi\) | |||||||
\(104\) | −5665.91 | −0.0513672 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −40373.1 | −0.349002 | ||||||||
\(107\) | −90929.4 | −0.767794 | −0.383897 | − | 0.923376i | \(-0.625418\pi\) | ||||
−0.383897 | + | 0.923376i | \(0.625418\pi\) | |||||||
\(108\) | −22110.3 | −0.182404 | ||||||||
\(109\) | 46968.1 | 0.378649 | 0.189324 | − | 0.981915i | \(-0.439370\pi\) | ||||
0.189324 | + | 0.981915i | \(0.439370\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 118947. | 0.916320 | ||||||||
\(112\) | −79509.9 | −0.598930 | ||||||||
\(113\) | −137709. | −1.01453 | −0.507267 | − | 0.861789i | \(-0.669344\pi\) | ||||
−0.507267 | + | 0.861789i | \(0.669344\pi\) | |||||||
\(114\) | 11184.2 | 0.0806013 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 101495. | 0.700327 | ||||||||
\(117\) | −5697.03 | −0.0384755 | ||||||||
\(118\) | −56096.2 | −0.370876 | ||||||||
\(119\) | −107868. | −0.698274 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 4612.45 | 0.0280564 | ||||||||
\(123\) | 166211. | 0.990598 | ||||||||
\(124\) | −195683. | −1.14288 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9606.90 | 0.0539085 | ||||||||
\(127\) | 25160.6 | 0.138424 | 0.0692120 | − | 0.997602i | \(-0.477952\pi\) | ||||
0.0692120 | + | 0.997602i | \(0.477952\pi\) | |||||||
\(128\) | 147982. | 0.798334 | ||||||||
\(129\) | −173296. | −0.916883 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −217042. | −1.10501 | −0.552505 | − | 0.833510i | \(-0.686328\pi\) | ||||
−0.552505 | + | 0.833510i | \(0.686328\pi\) | |||||||
\(132\) | 33028.9 | 0.164991 | ||||||||
\(133\) | 88234.2 | 0.432522 | ||||||||
\(134\) | 91458.5 | 0.440009 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 94691.8 | 0.439000 | ||||||||
\(137\) | 24093.9 | 0.109675 | 0.0548373 | − | 0.998495i | \(-0.482536\pi\) | ||||
0.0548373 | + | 0.998495i | \(0.482536\pi\) | |||||||
\(138\) | 15157.2 | 0.0677520 | ||||||||
\(139\) | −359804. | −1.57953 | −0.789766 | − | 0.613408i | \(-0.789798\pi\) | ||||
−0.789766 | + | 0.613408i | \(0.789798\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −153576. | −0.650543 | ||||||||
\(142\) | −53284.5 | −0.221758 | ||||||||
\(143\) | 8510.38 | 0.0348024 | ||||||||
\(144\) | 70180.9 | 0.282041 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −53320.4 | −0.207019 | ||||||||
\(147\) | −75472.2 | −0.288067 | ||||||||
\(148\) | −400847. | −1.50427 | ||||||||
\(149\) | −307960. | −1.13639 | −0.568197 | − | 0.822892i | \(-0.692359\pi\) | ||||
−0.568197 | + | 0.822892i | \(0.692359\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −531554. | −1.89716 | −0.948582 | − | 0.316531i | \(-0.897482\pi\) | ||||
−0.948582 | + | 0.316531i | \(0.897482\pi\) | |||||||
\(152\) | −77456.1 | −0.271924 | ||||||||
\(153\) | 95212.0 | 0.328824 | ||||||||
\(154\) | −14351.1 | −0.0487621 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 19198.7 | 0.0631628 | ||||||||
\(157\) | −428858. | −1.38856 | −0.694280 | − | 0.719705i | \(-0.744277\pi\) | ||||
−0.694280 | + | 0.719705i | \(0.744277\pi\) | |||||||
\(158\) | 74262.3 | 0.236660 | ||||||||
\(159\) | 281140. | 0.881923 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 119578. | 0.363570 | ||||||||
\(162\) | −8479.72 | −0.0253860 | ||||||||
\(163\) | 20926.3 | 0.0616912 | 0.0308456 | − | 0.999524i | \(-0.490180\pi\) | ||||
0.0308456 | + | 0.999524i | \(0.490180\pi\) | |||||||
\(164\) | −560124. | −1.62620 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22273.4 | −0.0627358 | ||||||||
\(167\) | 550264. | 1.52679 | 0.763396 | − | 0.645931i | \(-0.223531\pi\) | ||||
0.763396 | + | 0.645931i | \(0.223531\pi\) | |||||||
\(168\) | −66532.7 | −0.181870 | ||||||||
\(169\) | −366346. | −0.986677 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −77881.6 | −0.203678 | ||||||||
\(172\) | 583999. | 1.50519 | ||||||||
\(173\) | 586340. | 1.48948 | 0.744740 | − | 0.667355i | \(-0.232574\pi\) | ||||
0.744740 | + | 0.667355i | \(0.232574\pi\) | |||||||
\(174\) | 38925.4 | 0.0974676 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −104838. | −0.255116 | ||||||||
\(177\) | 390629. | 0.937198 | ||||||||
\(178\) | 31548.2 | 0.0746318 | ||||||||
\(179\) | 556686. | 1.29861 | 0.649303 | − | 0.760530i | \(-0.275061\pi\) | ||||
0.649303 | + | 0.760530i | \(0.275061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 399427. | 0.906235 | 0.453117 | − | 0.891451i | \(-0.350312\pi\) | ||||
0.453117 | + | 0.891451i | \(0.350312\pi\) | |||||||
\(182\) | −8341.85 | −0.0186674 | ||||||||
\(183\) | −32119.0 | −0.0708981 | ||||||||
\(184\) | −104972. | −0.228574 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −75048.3 | −0.159059 | ||||||||
\(187\) | −142230. | −0.297432 | ||||||||
\(188\) | 517545. | 1.06796 | ||||||||
\(189\) | −66898.2 | −0.136226 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −615748. | −1.22129 | −0.610646 | − | 0.791903i | \(-0.709090\pi\) | ||||
−0.610646 | + | 0.791903i | \(0.709090\pi\) | |||||||
\(192\) | −206521. | −0.404307 | ||||||||
\(193\) | 422687. | 0.816819 | 0.408409 | − | 0.912799i | \(-0.366084\pi\) | ||||
0.408409 | + | 0.912799i | \(0.366084\pi\) | |||||||
\(194\) | −163555. | −0.312003 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 254338. | 0.472902 | ||||||||
\(197\) | 116768. | 0.214367 | 0.107184 | − | 0.994239i | \(-0.465817\pi\) | ||||
0.107184 | + | 0.994239i | \(0.465817\pi\) | |||||||
\(198\) | 12667.2 | 0.0229625 | ||||||||
\(199\) | −674634. | −1.20764 | −0.603818 | − | 0.797123i | \(-0.706354\pi\) | ||||
−0.603818 | + | 0.797123i | \(0.706354\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −636876. | −1.11190 | ||||||||
\(202\) | 116287. | 0.200518 | ||||||||
\(203\) | 307090. | 0.523030 | ||||||||
\(204\) | −320860. | −0.539809 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 137331. | 0.225475 | ||||||||
\(207\) | −105548. | −0.171208 | ||||||||
\(208\) | −60939.3 | −0.0976651 | ||||||||
\(209\) | 116342. | 0.184234 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 347243. | 0.536941 | 0.268471 | − | 0.963288i | \(-0.413482\pi\) | ||||
0.268471 | + | 0.963288i | \(0.413482\pi\) | |||||||
\(212\) | −947431. | −1.44780 | ||||||||
\(213\) | 371050. | 0.560380 | ||||||||
\(214\) | 117521. | 0.175421 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 58726.4 | 0.0856444 | ||||||||
\(217\) | −592072. | −0.853542 | ||||||||
\(218\) | −60703.6 | −0.0865113 | ||||||||
\(219\) | 371299. | 0.523135 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −82674.2 | −0.113865 | ||||||||
\(222\) | −153733. | −0.209355 | ||||||||
\(223\) | 314163. | 0.423051 | 0.211525 | − | 0.977373i | \(-0.432157\pi\) | ||||
0.211525 | + | 0.977373i | \(0.432157\pi\) | |||||||
\(224\) | 339323. | 0.451849 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 177981. | 0.231795 | ||||||||
\(227\) | −1.03995e6 | −1.33952 | −0.669759 | − | 0.742579i | \(-0.733602\pi\) | ||||
−0.669759 | + | 0.742579i | \(0.733602\pi\) | |||||||
\(228\) | 262458. | 0.334366 | ||||||||
\(229\) | −192732. | −0.242866 | −0.121433 | − | 0.992600i | \(-0.538749\pi\) | ||||
−0.121433 | + | 0.992600i | \(0.538749\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 99934.4 | 0.123221 | ||||||||
\(232\) | −269578. | −0.328825 | ||||||||
\(233\) | −644411. | −0.777631 | −0.388815 | − | 0.921316i | \(-0.627116\pi\) | ||||
−0.388815 | + | 0.921316i | \(0.627116\pi\) | |||||||
\(234\) | 7363.09 | 0.00879064 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.31640e6 | −1.53854 | ||||||||
\(237\) | −517130. | −0.598038 | ||||||||
\(238\) | 139414. | 0.159537 | ||||||||
\(239\) | −605351. | −0.685508 | −0.342754 | − | 0.939425i | \(-0.611360\pi\) | ||||
−0.342754 | + | 0.939425i | \(0.611360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −432527. | −0.479701 | −0.239851 | − | 0.970810i | \(-0.577098\pi\) | ||||
−0.239851 | + | 0.970810i | \(0.577098\pi\) | |||||||
\(242\) | −18922.7 | −0.0207703 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 108240. | 0.116389 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −214819. | −0.226326 | ||||||||
\(247\) | 67626.0 | 0.0705296 | ||||||||
\(248\) | 519748. | 0.536616 | ||||||||
\(249\) | 155102. | 0.158533 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.02207e6 | −1.02400 | −0.511998 | − | 0.858987i | \(-0.671094\pi\) | ||||
−0.511998 | + | 0.858987i | \(0.671094\pi\) | |||||||
\(252\) | 225444. | 0.223634 | ||||||||
\(253\) | 157671. | 0.154864 | ||||||||
\(254\) | −32518.6 | −0.0316263 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 543039. | 0.517882 | ||||||||
\(257\) | −909641. | −0.859087 | −0.429544 | − | 0.903046i | \(-0.641326\pi\) | ||||
−0.429544 | + | 0.903046i | \(0.641326\pi\) | |||||||
\(258\) | 223975. | 0.209484 | ||||||||
\(259\) | −1.21283e6 | −1.12344 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −271059. | −0.246299 | ||||||||
\(262\) | 280515. | 0.252466 | ||||||||
\(263\) | 999592. | 0.891115 | 0.445557 | − | 0.895253i | \(-0.353006\pi\) | ||||
0.445557 | + | 0.895253i | \(0.353006\pi\) | |||||||
\(264\) | −87727.1 | −0.0774682 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −114038. | −0.0988199 | ||||||||
\(267\) | −219687. | −0.188594 | ||||||||
\(268\) | 2.14624e6 | 1.82533 | ||||||||
\(269\) | −2.14720e6 | −1.80922 | −0.904611 | − | 0.426238i | \(-0.859839\pi\) | ||||
−0.904611 | + | 0.426238i | \(0.859839\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −743716. | −0.615154 | −0.307577 | − | 0.951523i | \(-0.599518\pi\) | ||||
−0.307577 | + | 0.951523i | \(0.599518\pi\) | |||||||
\(272\) | 1.01845e6 | 0.834677 | ||||||||
\(273\) | 58088.9 | 0.0471723 | ||||||||
\(274\) | −31140.0 | −0.0250578 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 355693. | 0.281062 | ||||||||
\(277\) | −2.30153e6 | −1.80226 | −0.901131 | − | 0.433547i | \(-0.857262\pi\) | ||||
−0.901131 | + | 0.433547i | \(0.857262\pi\) | |||||||
\(278\) | 465026. | 0.360882 | ||||||||
\(279\) | 522603. | 0.401940 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 974755. | 0.736427 | 0.368214 | − | 0.929741i | \(-0.379970\pi\) | ||||
0.368214 | + | 0.929741i | \(0.379970\pi\) | |||||||
\(282\) | 198488. | 0.148632 | ||||||||
\(283\) | −1.23221e6 | −0.914577 | −0.457289 | − | 0.889318i | \(-0.651179\pi\) | ||||
−0.457289 | + | 0.889318i | \(0.651179\pi\) | |||||||
\(284\) | −1.25042e6 | −0.919941 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10999.2 | −0.00795143 | ||||||||
\(287\) | −1.69475e6 | −1.21451 | ||||||||
\(288\) | −299510. | −0.212779 | ||||||||
\(289\) | −38159.6 | −0.0268757 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.13892e6 | 0.788429 | ||||||||
\(292\) | −1.25126e6 | −0.858798 | ||||||||
\(293\) | 367972. | 0.250407 | 0.125203 | − | 0.992131i | \(-0.460042\pi\) | ||||
0.125203 | + | 0.992131i | \(0.460042\pi\) | |||||||
\(294\) | 97543.5 | 0.0658158 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.06468e6 | 0.706299 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 398021. | 0.259636 | ||||||||
\(299\) | 91649.4 | 0.0592859 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.76698e6 | 1.12413 | ||||||||
\(302\) | 687003. | 0.433452 | ||||||||
\(303\) | −809772. | −0.506706 | ||||||||
\(304\) | −833075. | −0.517011 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −123056. | −0.0751276 | ||||||||
\(307\) | −760172. | −0.460327 | −0.230163 | − | 0.973152i | \(-0.573926\pi\) | ||||
−0.230163 | + | 0.973152i | \(0.573926\pi\) | |||||||
\(308\) | −336774. | −0.202284 | ||||||||
\(309\) | −956309. | −0.569773 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.20267e6 | −1.29136 | −0.645681 | − | 0.763607i | \(-0.723426\pi\) | ||||
−0.645681 | + | 0.763607i | \(0.723426\pi\) | |||||||
\(312\) | −50993.2 | −0.0296569 | ||||||||
\(313\) | −685921. | −0.395743 | −0.197872 | − | 0.980228i | \(-0.563403\pi\) | ||||
−0.197872 | + | 0.980228i | \(0.563403\pi\) | |||||||
\(314\) | 554275. | 0.317250 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.74270e6 | 0.981761 | ||||||||
\(317\) | 1.87909e6 | 1.05027 | 0.525134 | − | 0.851019i | \(-0.324015\pi\) | ||||
0.525134 | + | 0.851019i | \(0.324015\pi\) | |||||||
\(318\) | −363358. | −0.201496 | ||||||||
\(319\) | 404916. | 0.222786 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −818364. | −0.443286 | ||||||||
\(322\) | −154548. | −0.0830663 | ||||||||
\(323\) | −1.13020e6 | −0.602768 | ||||||||
\(324\) | −198992. | −0.105311 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −27046.0 | −0.0140948 | ||||||||
\(327\) | 422713. | 0.218613 | ||||||||
\(328\) | 1.48773e6 | 0.763553 | ||||||||
\(329\) | 1.56592e6 | 0.797588 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.94540e6 | 0.975974 | 0.487987 | − | 0.872851i | \(-0.337731\pi\) | ||||
0.487987 | + | 0.872851i | \(0.337731\pi\) | |||||||
\(332\) | −522686. | −0.260253 | ||||||||
\(333\) | 1.07053e6 | 0.529038 | ||||||||
\(334\) | −711185. | −0.348832 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −715589. | −0.345792 | ||||||||
\(337\) | 1.39092e6 | 0.667154 | 0.333577 | − | 0.942723i | \(-0.391744\pi\) | ||||
0.333577 | + | 0.942723i | \(0.391744\pi\) | |||||||
\(338\) | 473482. | 0.225430 | ||||||||
\(339\) | −1.23938e6 | −0.585742 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −780679. | −0.363569 | ||||||||
\(342\) | 100658. | 0.0465352 | ||||||||
\(343\) | 2.31187e6 | 1.06103 | ||||||||
\(344\) | −1.55114e6 | −0.706733 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −757812. | −0.340307 | ||||||||
\(347\) | −3.23565e6 | −1.44257 | −0.721286 | − | 0.692637i | \(-0.756449\pi\) | ||||
−0.721286 | + | 0.692637i | \(0.756449\pi\) | |||||||
\(348\) | 913458. | 0.404334 | ||||||||
\(349\) | −1.54020e6 | −0.676883 | −0.338442 | − | 0.940987i | \(-0.609900\pi\) | ||||
−0.338442 | + | 0.940987i | \(0.609900\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −51273.3 | −0.0222138 | ||||||||
\(352\) | 447416. | 0.192466 | ||||||||
\(353\) | −696423. | −0.297465 | −0.148733 | − | 0.988877i | \(-0.547519\pi\) | ||||
−0.148733 | + | 0.988877i | \(0.547519\pi\) | |||||||
\(354\) | −504866. | −0.214125 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 740337. | 0.309602 | ||||||||
\(357\) | −970814. | −0.403149 | ||||||||
\(358\) | −719485. | −0.296698 | ||||||||
\(359\) | −2.60283e6 | −1.06588 | −0.532942 | − | 0.846152i | \(-0.678914\pi\) | ||||
−0.532942 | + | 0.846152i | \(0.678914\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.55161e6 | −0.626636 | ||||||||
\(362\) | −516236. | −0.207051 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | −195757. | −0.0774397 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 41512.0 | 0.0161984 | ||||||||
\(367\) | 801086. | 0.310466 | 0.155233 | − | 0.987878i | \(-0.450387\pi\) | ||||
0.155233 | + | 0.987878i | \(0.450387\pi\) | |||||||
\(368\) | −1.12902e6 | −0.434591 | ||||||||
\(369\) | 1.49590e6 | 0.571922 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.86660e6 | −1.08127 | ||||||||
\(372\) | −1.76115e6 | −0.659840 | ||||||||
\(373\) | 1.94463e6 | 0.723712 | 0.361856 | − | 0.932234i | \(-0.382143\pi\) | ||||
0.361856 | + | 0.932234i | \(0.382143\pi\) | |||||||
\(374\) | 183824. | 0.0679554 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.37463e6 | −0.501438 | ||||||||
\(377\) | 235366. | 0.0852884 | ||||||||
\(378\) | 86462.1 | 0.0311241 | ||||||||
\(379\) | −3.33496e6 | −1.19260 | −0.596298 | − | 0.802763i | \(-0.703362\pi\) | ||||
−0.596298 | + | 0.802763i | \(0.703362\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 226445. | 0.0799191 | ||||||||
\(382\) | 795820. | 0.279033 | ||||||||
\(383\) | −2.16994e6 | −0.755875 | −0.377938 | − | 0.925831i | \(-0.623367\pi\) | ||||
−0.377938 | + | 0.925831i | \(0.623367\pi\) | |||||||
\(384\) | 1.33184e6 | 0.460918 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −546299. | −0.186622 | ||||||||
\(387\) | −1.55966e6 | −0.529362 | ||||||||
\(388\) | −3.83812e6 | −1.29431 | ||||||||
\(389\) | −561944. | −0.188286 | −0.0941432 | − | 0.995559i | \(-0.530011\pi\) | ||||
−0.0941432 | + | 0.995559i | \(0.530011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.53170e6 | −0.506676 | ||||||||
\(392\) | −675539. | −0.222042 | ||||||||
\(393\) | −1.95338e6 | −0.637978 | ||||||||
\(394\) | −150916. | −0.0489773 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 297260. | 0.0952575 | ||||||||
\(397\) | 3.98781e6 | 1.26987 | 0.634934 | − | 0.772566i | \(-0.281027\pi\) | ||||
0.634934 | + | 0.772566i | \(0.281027\pi\) | |||||||
\(398\) | 871926. | 0.275913 | ||||||||
\(399\) | 794108. | 0.249717 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.07030e6 | 0.953499 | 0.476750 | − | 0.879039i | \(-0.341815\pi\) | ||||
0.476750 | + | 0.879039i | \(0.341815\pi\) | |||||||
\(402\) | 823126. | 0.254040 | ||||||||
\(403\) | −453786. | −0.139184 | ||||||||
\(404\) | 2.72890e6 | 0.831828 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −396897. | −0.119499 | ||||||||
\(407\) | −1.59918e6 | −0.478533 | ||||||||
\(408\) | 852226. | 0.253457 | ||||||||
\(409\) | −34399.2 | −0.0101681 | −0.00508405 | − | 0.999987i | \(-0.501618\pi\) | ||||
−0.00508405 | + | 0.999987i | \(0.501618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 216845. | 0.0633206 | ||||||||
\(412\) | 3.22272e6 | 0.935361 | ||||||||
\(413\) | −3.98299e6 | −1.14904 | ||||||||
\(414\) | 136415. | 0.0391166 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 260070. | 0.0736811 | ||||||||
\(417\) | −3.23823e6 | −0.911944 | ||||||||
\(418\) | −150365. | −0.0420926 | ||||||||
\(419\) | 3.35733e6 | 0.934241 | 0.467121 | − | 0.884194i | \(-0.345291\pi\) | ||||
0.467121 | + | 0.884194i | \(0.345291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −693515. | −0.190700 | −0.0953499 | − | 0.995444i | \(-0.530397\pi\) | ||||
−0.0953499 | + | 0.995444i | \(0.530397\pi\) | |||||||
\(422\) | −448791. | −0.122677 | ||||||||
\(423\) | −1.38219e6 | −0.375591 | ||||||||
\(424\) | 2.51644e6 | 0.679785 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −479560. | −0.128032 | ||||||||
\(427\) | 327497. | 0.0869235 | ||||||||
\(428\) | 2.75785e6 | 0.727715 | ||||||||
\(429\) | 76593.5 | 0.0200932 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.60068e6 | −0.933666 | −0.466833 | − | 0.884346i | \(-0.654605\pi\) | ||||
−0.466833 | + | 0.884346i | \(0.654605\pi\) | |||||||
\(432\) | 631628. | 0.162837 | ||||||||
\(433\) | 2.17347e6 | 0.557100 | 0.278550 | − | 0.960422i | \(-0.410146\pi\) | ||||
0.278550 | + | 0.960422i | \(0.410146\pi\) | |||||||
\(434\) | 765219. | 0.195012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.42452e6 | −0.358883 | ||||||||
\(437\) | 1.25290e6 | 0.313843 | ||||||||
\(438\) | −479883. | −0.119523 | ||||||||
\(439\) | −6.87194e6 | −1.70184 | −0.850919 | − | 0.525296i | \(-0.823954\pi\) | ||||
−0.850919 | + | 0.525296i | \(0.823954\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −679250. | −0.166316 | ||||||||
\(442\) | 106852. | 0.0260151 | ||||||||
\(443\) | −4.97594e6 | −1.20466 | −0.602332 | − | 0.798246i | \(-0.705762\pi\) | ||||
−0.602332 | + | 0.798246i | \(0.705762\pi\) | |||||||
\(444\) | −3.60762e6 | −0.868488 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −406037. | −0.0966560 | ||||||||
\(447\) | −2.77164e6 | −0.656098 | ||||||||
\(448\) | 2.10576e6 | 0.495694 | ||||||||
\(449\) | −1.82131e6 | −0.426352 | −0.213176 | − | 0.977014i | \(-0.568381\pi\) | ||||
−0.213176 | + | 0.977014i | \(0.568381\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.23462e6 | −0.517323 | ||||||||
\(452\) | 4.17666e6 | 0.961576 | ||||||||
\(453\) | −4.78398e6 | −1.09533 | ||||||||
\(454\) | 1.34408e6 | 0.306045 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −697105. | −0.156995 | ||||||||
\(457\) | 1.52586e6 | 0.341763 | 0.170881 | − | 0.985292i | \(-0.445339\pi\) | ||||
0.170881 | + | 0.985292i | \(0.445339\pi\) | |||||||
\(458\) | 249096. | 0.0554885 | ||||||||
\(459\) | 856908. | 0.189846 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.99516e6 | 1.09470 | 0.547352 | − | 0.836902i | \(-0.315636\pi\) | ||||
0.547352 | + | 0.836902i | \(0.315636\pi\) | |||||||
\(462\) | −129159. | −0.0281528 | ||||||||
\(463\) | 5.20396e6 | 1.12819 | 0.564094 | − | 0.825711i | \(-0.309226\pi\) | ||||
0.564094 | + | 0.825711i | \(0.309226\pi\) | |||||||
\(464\) | −2.89943e6 | −0.625199 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 832865. | 0.177668 | ||||||||
\(467\) | −2.28807e6 | −0.485487 | −0.242744 | − | 0.970090i | \(-0.578047\pi\) | ||||
−0.242744 | + | 0.970090i | \(0.578047\pi\) | |||||||
\(468\) | 172789. | 0.0364671 | ||||||||
\(469\) | 6.49381e6 | 1.36322 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.85973e6 | −0.801686 | ||||||||
\(472\) | 3.49645e6 | 0.722391 | ||||||||
\(473\) | 2.32987e6 | 0.478826 | ||||||||
\(474\) | 668361. | 0.136636 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.27160e6 | 0.661824 | ||||||||
\(477\) | 2.53026e6 | 0.509178 | ||||||||
\(478\) | 782382. | 0.156621 | ||||||||
\(479\) | 1.91319e6 | 0.380996 | 0.190498 | − | 0.981688i | \(-0.438990\pi\) | ||||
0.190498 | + | 0.981688i | \(0.438990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −929557. | −0.183195 | ||||||||
\(482\) | 559017. | 0.109599 | ||||||||
\(483\) | 1.07621e6 | 0.209907 | ||||||||
\(484\) | −444056. | −0.0861636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −76317.5 | −0.0146566 | ||||||||
\(487\) | 5.63300e6 | 1.07626 | 0.538130 | − | 0.842862i | \(-0.319131\pi\) | ||||
0.538130 | + | 0.842862i | \(0.319131\pi\) | |||||||
\(488\) | −287492. | −0.0546482 | ||||||||
\(489\) | 188336. | 0.0356174 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.42388e6 | −0.453741 | −0.226871 | − | 0.973925i | \(-0.572849\pi\) | ||||
−0.226871 | + | 0.973925i | \(0.572849\pi\) | |||||||
\(492\) | −5.04112e6 | −0.938889 | ||||||||
\(493\) | −3.93356e6 | −0.728901 | ||||||||
\(494\) | −87402.8 | −0.0161142 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.59012e6 | 1.02027 | ||||||||
\(497\) | −3.78335e6 | −0.687045 | ||||||||
\(498\) | −200460. | −0.0362206 | ||||||||
\(499\) | 6.53921e6 | 1.17564 | 0.587819 | − | 0.808992i | \(-0.299987\pi\) | ||||
0.587819 | + | 0.808992i | \(0.299987\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.95238e6 | 0.881494 | ||||||||
\(502\) | 1.32097e6 | 0.233956 | ||||||||
\(503\) | −7.09673e6 | −1.25066 | −0.625329 | − | 0.780361i | \(-0.715035\pi\) | ||||
−0.625329 | + | 0.780361i | \(0.715035\pi\) | |||||||
\(504\) | −598794. | −0.105003 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −203781. | −0.0353823 | ||||||||
\(507\) | −3.29712e6 | −0.569658 | ||||||||
\(508\) | −763110. | −0.131198 | ||||||||
\(509\) | 1.40802e6 | 0.240887 | 0.120443 | − | 0.992720i | \(-0.461568\pi\) | ||||
0.120443 | + | 0.992720i | \(0.461568\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.78590e6 | −0.641382 | ||||||||
\(512\) | −5.43728e6 | −0.916657 | ||||||||
\(513\) | −700935. | −0.117594 | ||||||||
\(514\) | 1.17566e6 | 0.196279 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.25599e6 | 0.869021 | ||||||||
\(517\) | 2.06475e6 | 0.339735 | ||||||||
\(518\) | 1.56751e6 | 0.256677 | ||||||||
\(519\) | 5.27706e6 | 0.859951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.33371e6 | −0.699465 | −0.349732 | − | 0.936850i | \(-0.613728\pi\) | ||||
−0.349732 | + | 0.936850i | \(0.613728\pi\) | |||||||
\(522\) | 350329. | 0.0562729 | ||||||||
\(523\) | 5.99430e6 | 0.958262 | 0.479131 | − | 0.877743i | \(-0.340952\pi\) | ||||
0.479131 | + | 0.877743i | \(0.340952\pi\) | |||||||
\(524\) | 6.58280e6 | 1.04733 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.29192e6 | −0.203596 | ||||||||
\(527\) | 7.58392e6 | 1.18951 | ||||||||
\(528\) | −943543. | −0.147291 | ||||||||
\(529\) | −4.73837e6 | −0.736189 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.51566e6 | 0.541091 | ||||||||
\(532\) | −2.67611e6 | −0.409944 | ||||||||
\(533\) | −1.29892e6 | −0.198045 | ||||||||
\(534\) | 283933. | 0.0430887 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.70057e6 | −0.857050 | ||||||||
\(537\) | 5.01017e6 | 0.749751 | ||||||||
\(538\) | 2.77513e6 | 0.413360 | ||||||||
\(539\) | 1.01468e6 | 0.150438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.71649e6 | 1.42730 | 0.713652 | − | 0.700501i | \(-0.247040\pi\) | ||||
0.713652 | + | 0.700501i | \(0.247040\pi\) | |||||||
\(542\) | 961211. | 0.140547 | ||||||||
\(543\) | 3.59484e6 | 0.523215 | ||||||||
\(544\) | −4.34643e6 | −0.629702 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −75076.6 | −0.0107776 | ||||||||
\(547\) | 1.18605e7 | 1.69486 | 0.847430 | − | 0.530908i | \(-0.178149\pi\) | ||||
0.847430 | + | 0.530908i | \(0.178149\pi\) | |||||||
\(548\) | −730758. | −0.103950 | ||||||||
\(549\) | −289071. | −0.0409331 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.21758e6 | 0.451492 | ||||||||
\(552\) | −944744. | −0.131967 | ||||||||
\(553\) | 5.27283e6 | 0.733215 | ||||||||
\(554\) | 2.97460e6 | 0.411770 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.09127e7 | 1.49708 | ||||||||
\(557\) | 4.65955e6 | 0.636364 | 0.318182 | − | 0.948030i | \(-0.396928\pi\) | ||||
0.318182 | + | 0.948030i | \(0.396928\pi\) | |||||||
\(558\) | −675435. | −0.0918329 | ||||||||
\(559\) | 1.35428e6 | 0.183307 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.28007e6 | −0.171722 | ||||||||
\(562\) | −1.25982e6 | −0.168254 | ||||||||
\(563\) | 7.30425e6 | 0.971191 | 0.485595 | − | 0.874184i | \(-0.338603\pi\) | ||||
0.485595 | + | 0.874184i | \(0.338603\pi\) | |||||||
\(564\) | 4.65790e6 | 0.616584 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.59257e6 | 0.208957 | ||||||||
\(567\) | −602084. | −0.0786501 | ||||||||
\(568\) | 3.32120e6 | 0.431941 | ||||||||
\(569\) | −3.49414e6 | −0.452439 | −0.226219 | − | 0.974076i | \(-0.572637\pi\) | ||||
−0.226219 | + | 0.974076i | \(0.572637\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.42919e7 | 1.83443 | 0.917213 | − | 0.398396i | \(-0.130433\pi\) | ||||
0.917213 | + | 0.398396i | \(0.130433\pi\) | |||||||
\(572\) | −258116. | −0.0329857 | ||||||||
\(573\) | −5.54174e6 | −0.705114 | ||||||||
\(574\) | 2.19036e6 | 0.277483 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.85869e6 | −0.233427 | ||||||||
\(577\) | 6.93782e6 | 0.867528 | 0.433764 | − | 0.901027i | \(-0.357185\pi\) | ||||
0.433764 | + | 0.901027i | \(0.357185\pi\) | |||||||
\(578\) | 49319.1 | 0.00614039 | ||||||||
\(579\) | 3.80418e6 | 0.471591 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.58147e6 | −0.194366 | ||||||||
\(582\) | −1.47199e6 | −0.180135 | ||||||||
\(583\) | −3.77978e6 | −0.460569 | ||||||||
\(584\) | 3.32344e6 | 0.403232 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −475583. | −0.0572114 | ||||||||
\(587\) | −2.56707e6 | −0.307498 | −0.153749 | − | 0.988110i | \(-0.549135\pi\) | ||||
−0.153749 | + | 0.988110i | \(0.549135\pi\) | |||||||
\(588\) | 2.28904e6 | 0.273030 | ||||||||
\(589\) | −6.20351e6 | −0.736799 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.05091e6 | 0.123765 | ||||||||
\(592\) | 1.14511e7 | 1.34289 | ||||||||
\(593\) | −8.76559e6 | −1.02363 | −0.511817 | − | 0.859095i | \(-0.671027\pi\) | ||||
−0.511817 | + | 0.859095i | \(0.671027\pi\) | |||||||
\(594\) | 114005. | 0.0132574 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.34031e6 | 1.07707 | ||||||||
\(597\) | −6.07171e6 | −0.697229 | ||||||||
\(598\) | −118452. | −0.0135453 | ||||||||
\(599\) | 6.17238e6 | 0.702887 | 0.351444 | − | 0.936209i | \(-0.385691\pi\) | ||||
0.351444 | + | 0.936209i | \(0.385691\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.19370e7 | −1.34806 | −0.674031 | − | 0.738703i | \(-0.735439\pi\) | ||||
−0.674031 | + | 0.738703i | \(0.735439\pi\) | |||||||
\(602\) | −2.28373e6 | −0.256834 | ||||||||
\(603\) | −5.73189e6 | −0.641955 | ||||||||
\(604\) | 1.61218e7 | 1.79813 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.04658e6 | 0.115769 | ||||||||
\(607\) | 2.00634e6 | 0.221021 | 0.110510 | − | 0.993875i | \(-0.464751\pi\) | ||||
0.110510 | + | 0.993875i | \(0.464751\pi\) | |||||||
\(608\) | 3.55530e6 | 0.390047 | ||||||||
\(609\) | 2.76381e6 | 0.301971 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.20018e6 | 0.130059 | ||||||||
\(612\) | −2.88774e6 | −0.311659 | ||||||||
\(613\) | 1.13241e6 | 0.121718 | 0.0608589 | − | 0.998146i | \(-0.480616\pi\) | ||||
0.0608589 | + | 0.998146i | \(0.480616\pi\) | |||||||
\(614\) | 982479. | 0.105173 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 894495. | 0.0949787 | ||||||||
\(617\) | 1.20807e6 | 0.127755 | 0.0638775 | − | 0.997958i | \(-0.479653\pi\) | ||||
0.0638775 | + | 0.997958i | \(0.479653\pi\) | |||||||
\(618\) | 1.23598e6 | 0.130178 | ||||||||
\(619\) | 1.14027e7 | 1.19614 | 0.598071 | − | 0.801443i | \(-0.295934\pi\) | ||||
0.598071 | + | 0.801443i | \(0.295934\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −949934. | −0.0988472 | ||||||||
\(622\) | 2.84682e6 | 0.295042 | ||||||||
\(623\) | 2.24001e6 | 0.231222 | ||||||||
\(624\) | −548454. | −0.0563870 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 886514. | 0.0904170 | ||||||||
\(627\) | 1.04708e6 | 0.106368 | ||||||||
\(628\) | 1.30071e7 | 1.31608 | ||||||||
\(629\) | 1.55353e7 | 1.56564 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.32708e6 | 0.132685 | 0.0663426 | − | 0.997797i | \(-0.478867\pi\) | ||||
0.0663426 | + | 0.997797i | \(0.478867\pi\) | |||||||
\(632\) | −4.62874e6 | −0.460967 | ||||||||
\(633\) | 3.12518e6 | 0.310003 | ||||||||
\(634\) | −2.42862e6 | −0.239959 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.52688e6 | −0.835886 | ||||||||
\(637\) | 589805. | 0.0575917 | ||||||||
\(638\) | −523331. | −0.0509008 | ||||||||
\(639\) | 3.33945e6 | 0.323536 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.61062e6 | −0.923860 | −0.461930 | − | 0.886916i | \(-0.652843\pi\) | ||||
−0.461930 | + | 0.886916i | \(0.652843\pi\) | |||||||
\(642\) | 1.05769e6 | 0.101279 | ||||||||
\(643\) | −1.26822e7 | −1.20967 | −0.604835 | − | 0.796351i | \(-0.706761\pi\) | ||||
−0.604835 | + | 0.796351i | \(0.706761\pi\) | |||||||
\(644\) | −3.62677e6 | −0.344592 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.46072e6 | 0.137717 | ||||||||
\(647\) | 1.27269e7 | 1.19526 | 0.597629 | − | 0.801773i | \(-0.296110\pi\) | ||||
0.597629 | + | 0.801773i | \(0.296110\pi\) | |||||||
\(648\) | 528537. | 0.0494468 | ||||||||
\(649\) | −5.25179e6 | −0.489435 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.32864e6 | −0.492793 | ||||||||
\(652\) | −634685. | −0.0584709 | ||||||||
\(653\) | −7.54035e6 | −0.692004 | −0.346002 | − | 0.938234i | \(-0.612461\pi\) | ||||
−0.346002 | + | 0.938234i | \(0.612461\pi\) | |||||||
\(654\) | −546332. | −0.0499473 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.60012e7 | 1.45175 | ||||||||
\(657\) | 3.34170e6 | 0.302032 | ||||||||
\(658\) | −2.02386e6 | −0.182228 | ||||||||
\(659\) | 1.20388e7 | 1.07987 | 0.539933 | − | 0.841708i | \(-0.318450\pi\) | ||||
0.539933 | + | 0.841708i | \(0.318450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.36439e6 | 0.566569 | 0.283285 | − | 0.959036i | \(-0.408576\pi\) | ||||
0.283285 | + | 0.959036i | \(0.408576\pi\) | |||||||
\(662\) | −2.51432e6 | −0.222985 | ||||||||
\(663\) | −744068. | −0.0657399 | ||||||||
\(664\) | 1.38829e6 | 0.122197 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.38359e6 | −0.120871 | ||||||||
\(667\) | 4.36059e6 | 0.379517 | ||||||||
\(668\) | −1.66893e7 | −1.44709 | ||||||||
\(669\) | 2.82746e6 | 0.244248 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 431823. | 0.0370254 | ||||||||
\(672\) | 3.05390e6 | 0.260875 | ||||||||
\(673\) | 741014. | 0.0630650 | 0.0315325 | − | 0.999503i | \(-0.489961\pi\) | ||||
0.0315325 | + | 0.999503i | \(0.489961\pi\) | |||||||
\(674\) | −1.79768e6 | −0.152427 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.11111e7 | 0.935172 | ||||||||
\(677\) | −1.43961e7 | −1.20718 | −0.603590 | − | 0.797295i | \(-0.706264\pi\) | ||||
−0.603590 | + | 0.797295i | \(0.706264\pi\) | |||||||
\(678\) | 1.60183e6 | 0.133827 | ||||||||
\(679\) | −1.16129e7 | −0.966640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.35956e6 | −0.773371 | ||||||||
\(682\) | 1.00898e6 | 0.0830659 | ||||||||
\(683\) | 7.32070e6 | 0.600484 | 0.300242 | − | 0.953863i | \(-0.402933\pi\) | ||||
0.300242 | + | 0.953863i | \(0.402933\pi\) | |||||||
\(684\) | 2.36212e6 | 0.193046 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.98796e6 | −0.242418 | ||||||||
\(687\) | −1.73459e6 | −0.140219 | ||||||||
\(688\) | −1.66832e7 | −1.34372 | ||||||||
\(689\) | −2.19707e6 | −0.176318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.51860e7 | 1.20989 | 0.604947 | − | 0.796266i | \(-0.293194\pi\) | ||||
0.604947 | + | 0.796266i | \(0.293194\pi\) | |||||||
\(692\) | −1.77835e7 | −1.41173 | ||||||||
\(693\) | 899409. | 0.0711417 | ||||||||
\(694\) | 4.18189e6 | 0.329590 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.42621e6 | −0.189847 | ||||||||
\(697\) | 2.17082e7 | 1.69255 | ||||||||
\(698\) | 1.99062e6 | 0.154650 | ||||||||
\(699\) | −5.79970e6 | −0.448965 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.17236e7 | −0.901089 | −0.450544 | − | 0.892754i | \(-0.648770\pi\) | ||||
−0.450544 | + | 0.892754i | \(0.648770\pi\) | |||||||
\(702\) | 66267.8 | 0.00507528 | ||||||||
\(703\) | −1.27076e7 | −0.969782 | ||||||||
\(704\) | 2.77656e6 | 0.211142 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 900087. | 0.0679630 | ||||||||
\(707\) | 8.25672e6 | 0.621239 | ||||||||
\(708\) | −1.18476e7 | −0.888276 | ||||||||
\(709\) | 6.09002e6 | 0.454991 | 0.227495 | − | 0.973779i | \(-0.426946\pi\) | ||||
0.227495 | + | 0.973779i | \(0.426946\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.65417e6 | −0.345277 | ||||||||
\(712\) | −1.96638e6 | −0.145368 | ||||||||
\(713\) | −8.40723e6 | −0.619340 | ||||||||
\(714\) | 1.25472e6 | 0.0921090 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.68841e7 | −1.23082 | ||||||||
\(717\) | −5.44816e6 | −0.395778 | ||||||||
\(718\) | 3.36401e6 | 0.243527 | ||||||||
\(719\) | 3.50864e6 | 0.253114 | 0.126557 | − | 0.991959i | \(-0.459607\pi\) | ||||
0.126557 | + | 0.991959i | \(0.459607\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.75086e6 | 0.698562 | ||||||||
\(722\) | 2.00537e6 | 0.143170 | ||||||||
\(723\) | −3.89274e6 | −0.276956 | ||||||||
\(724\) | −1.21145e7 | −0.858929 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −170304. | −0.0119918 | ||||||||
\(727\) | 222222. | 0.0155937 | 0.00779687 | − | 0.999970i | \(-0.497518\pi\) | ||||
0.00779687 | + | 0.999970i | \(0.497518\pi\) | |||||||
\(728\) | 519944. | 0.0363603 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.26335e7 | −1.56660 | ||||||||
\(732\) | 974157. | 0.0671972 | ||||||||
\(733\) | 1.95614e6 | 0.134475 | 0.0672373 | − | 0.997737i | \(-0.478582\pi\) | ||||
0.0672373 | + | 0.997737i | \(0.478582\pi\) | |||||||
\(734\) | −1.03536e6 | −0.0709333 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.81828e6 | 0.327867 | ||||||||
\(737\) | 8.56245e6 | 0.580670 | ||||||||
\(738\) | −1.93337e6 | −0.130669 | ||||||||
\(739\) | −3.61998e6 | −0.243834 | −0.121917 | − | 0.992540i | \(-0.538904\pi\) | ||||
−0.121917 | + | 0.992540i | \(0.538904\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 608634. | 0.0407203 | ||||||||
\(742\) | 3.70492e6 | 0.247041 | ||||||||
\(743\) | −4.37060e6 | −0.290449 | −0.145224 | − | 0.989399i | \(-0.546390\pi\) | ||||
−0.145224 | + | 0.989399i | \(0.546390\pi\) | |||||||
\(744\) | 4.67773e6 | 0.309815 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.51333e6 | −0.165349 | ||||||||
\(747\) | 1.39592e6 | 0.0915289 | ||||||||
\(748\) | 4.31378e6 | 0.281906 | ||||||||
\(749\) | 8.34432e6 | 0.543484 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.89727e6 | 0.575648 | 0.287824 | − | 0.957683i | \(-0.407068\pi\) | ||||
0.287824 | + | 0.957683i | \(0.407068\pi\) | |||||||
\(752\) | −1.47848e7 | −0.953390 | ||||||||
\(753\) | −9.19867e6 | −0.591204 | ||||||||
\(754\) | −304197. | −0.0194862 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.02900e6 | 0.129115 | ||||||||
\(757\) | 1.36934e7 | 0.868506 | 0.434253 | − | 0.900791i | \(-0.357012\pi\) | ||||
0.434253 | + | 0.900791i | \(0.357012\pi\) | |||||||
\(758\) | 4.31025e6 | 0.272477 | ||||||||
\(759\) | 1.41904e6 | 0.0894107 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.75245e7 | 1.09694 | 0.548472 | − | 0.836169i | \(-0.315210\pi\) | ||||
0.548472 | + | 0.836169i | \(0.315210\pi\) | |||||||
\(762\) | −292668. | −0.0182594 | ||||||||
\(763\) | −4.31012e6 | −0.268027 | ||||||||
\(764\) | 1.86754e7 | 1.15754 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.80452e6 | 0.172698 | ||||||||
\(767\) | −3.05271e6 | −0.187369 | ||||||||
\(768\) | 4.88735e6 | 0.298999 | ||||||||
\(769\) | −1.68641e7 | −1.02837 | −0.514183 | − | 0.857681i | \(-0.671905\pi\) | ||||
−0.514183 | + | 0.857681i | \(0.671905\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.18677e6 | −0.495994 | ||||||||
\(772\) | −1.28199e7 | −0.774181 | ||||||||
\(773\) | −1.24437e7 | −0.749033 | −0.374516 | − | 0.927220i | \(-0.622191\pi\) | ||||
−0.374516 | + | 0.927220i | \(0.622191\pi\) | |||||||
\(774\) | 2.01577e6 | 0.120945 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.01943e7 | 0.607720 | ||||||||
\(777\) | −1.09155e7 | −0.648618 | ||||||||
\(778\) | 726281. | 0.0430185 | ||||||||
\(779\) | −1.77569e7 | −1.04839 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.98856e6 | −0.292649 | ||||||||
\(782\) | 1.97963e6 | 0.115762 | ||||||||
\(783\) | −2.43953e6 | −0.142201 | ||||||||
\(784\) | −7.26572e6 | −0.422171 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.52463e6 | 0.145761 | ||||||||
\(787\) | 2.62304e7 | 1.50962 | 0.754811 | − | 0.655943i | \(-0.227729\pi\) | ||||
0.754811 | + | 0.655943i | \(0.227729\pi\) | |||||||
\(788\) | −3.54152e6 | −0.203177 | ||||||||
\(789\) | 8.99633e6 | 0.514485 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.26372e7 | 0.718139 | ||||||||
\(792\) | −789544. | −0.0447263 | ||||||||
\(793\) | 251006. | 0.0141743 | ||||||||
\(794\) | −5.15402e6 | −0.290132 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.04614e7 | 1.14460 | ||||||||
\(797\) | 4.99841e6 | 0.278731 | 0.139366 | − | 0.990241i | \(-0.455494\pi\) | ||||
0.139366 | + | 0.990241i | \(0.455494\pi\) | |||||||
\(798\) | −1.02634e6 | −0.0570537 | ||||||||
\(799\) | −2.00580e7 | −1.11153 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.97719e6 | −0.108885 | ||||||||
\(802\) | −3.96819e6 | −0.217850 | ||||||||
\(803\) | −4.99191e6 | −0.273199 | ||||||||
\(804\) | 1.93162e7 | 1.05386 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 586492. | 0.0317998 | ||||||||
\(807\) | −1.93248e7 | −1.04456 | ||||||||
\(808\) | −7.24813e6 | −0.390569 | ||||||||
\(809\) | 2.76591e7 | 1.48582 | 0.742912 | − | 0.669389i | \(-0.233444\pi\) | ||||
0.742912 | + | 0.669389i | \(0.233444\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.72731e7 | −0.922184 | −0.461092 | − | 0.887352i | \(-0.652542\pi\) | ||||
−0.461092 | + | 0.887352i | \(0.652542\pi\) | |||||||
\(812\) | −9.31393e6 | −0.495727 | ||||||||
\(813\) | −6.69344e6 | −0.355159 | ||||||||
\(814\) | 2.06685e6 | 0.109332 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 9.16607e6 | 0.481901 | ||||||||
\(817\) | 1.85138e7 | 0.970377 | ||||||||
\(818\) | 44459.0 | 0.00232315 | ||||||||
\(819\) | 522800. | 0.0272349 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.70950e7 | −0.885139 | −0.442570 | − | 0.896734i | \(-0.645933\pi\) | ||||
−0.442570 | + | 0.896734i | \(0.645933\pi\) | |||||||
\(822\) | −280260. | −0.0144671 | ||||||||
\(823\) | −1.39800e7 | −0.719464 | −0.359732 | − | 0.933056i | \(-0.617132\pi\) | ||||
−0.359732 | + | 0.933056i | \(0.617132\pi\) | |||||||
\(824\) | −8.55976e6 | −0.439181 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.14778e6 | 0.262525 | ||||||||
\(827\) | 2.33121e7 | 1.18527 | 0.592636 | − | 0.805471i | \(-0.298087\pi\) | ||||
0.592636 | + | 0.805471i | \(0.298087\pi\) | |||||||
\(828\) | 3.20123e6 | 0.162271 | ||||||||
\(829\) | −2.71774e7 | −1.37348 | −0.686738 | − | 0.726905i | \(-0.740958\pi\) | ||||
−0.686738 | + | 0.726905i | \(0.740958\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.07138e7 | −1.04054 | ||||||||
\(832\) | 1.61393e6 | 0.0808309 | ||||||||
\(833\) | −9.85714e6 | −0.492196 | ||||||||
\(834\) | 4.18523e6 | 0.208355 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.52860e6 | −0.174617 | ||||||||
\(837\) | 4.70343e6 | 0.232060 | ||||||||
\(838\) | −4.33916e6 | −0.213450 | ||||||||
\(839\) | 6.44081e6 | 0.315890 | 0.157945 | − | 0.987448i | \(-0.449513\pi\) | ||||
0.157945 | + | 0.987448i | \(0.449513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.31268e6 | −0.454030 | ||||||||
\(842\) | 896328. | 0.0435699 | ||||||||
\(843\) | 8.77280e6 | 0.425176 | ||||||||
\(844\) | −1.05317e7 | −0.508913 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.78640e6 | 0.0858127 | ||||||||
\(847\) | −1.34356e6 | −0.0643501 | ||||||||
\(848\) | 2.70654e7 | 1.29248 | ||||||||
\(849\) | −1.10899e7 | −0.528031 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.72218e7 | −0.815182 | ||||||||
\(852\) | −1.12538e7 | −0.531128 | ||||||||
\(853\) | −3.24050e6 | −0.152490 | −0.0762448 | − | 0.997089i | \(-0.524293\pi\) | ||||
−0.0762448 | + | 0.997089i | \(0.524293\pi\) | |||||||
\(854\) | −423271. | −0.0198598 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.32504e6 | −0.341685 | ||||||||
\(857\) | −2.15579e7 | −1.00266 | −0.501331 | − | 0.865255i | \(-0.667156\pi\) | ||||
−0.501331 | + | 0.865255i | \(0.667156\pi\) | |||||||
\(858\) | −98992.7 | −0.00459076 | ||||||||
\(859\) | 3.00808e7 | 1.39093 | 0.695467 | − | 0.718558i | \(-0.255197\pi\) | ||||
0.695467 | + | 0.718558i | \(0.255197\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.52527e7 | −0.701196 | ||||||||
\(862\) | 4.65367e6 | 0.213318 | ||||||||
\(863\) | −3.68726e7 | −1.68530 | −0.842650 | − | 0.538462i | \(-0.819005\pi\) | ||||
−0.842650 | + | 0.538462i | \(0.819005\pi\) | |||||||
\(864\) | −2.69559e6 | −0.122848 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.80908e6 | −0.127283 | ||||||||
\(867\) | −343436. | −0.0155167 | ||||||||
\(868\) | 1.79573e7 | 0.808987 | ||||||||
\(869\) | 6.95252e6 | 0.312315 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.97710e6 | 0.222296 | ||||||||
\(872\) | 3.78363e6 | 0.168507 | ||||||||
\(873\) | 1.02503e7 | 0.455200 | ||||||||
\(874\) | −1.61930e6 | −0.0717049 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.12614e7 | −0.495827 | ||||||||
\(877\) | −1.99151e7 | −0.874348 | −0.437174 | − | 0.899377i | \(-0.644021\pi\) | ||||
−0.437174 | + | 0.899377i | \(0.644021\pi\) | |||||||
\(878\) | 8.88160e6 | 0.388826 | ||||||||
\(879\) | 3.31175e6 | 0.144572 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.96980e7 | 1.28910 | 0.644551 | − | 0.764561i | \(-0.277044\pi\) | ||||
0.644551 | + | 0.764561i | \(0.277044\pi\) | |||||||
\(882\) | 877892. | 0.0379988 | ||||||||
\(883\) | 1.61839e7 | 0.698526 | 0.349263 | − | 0.937025i | \(-0.386432\pi\) | ||||
0.349263 | + | 0.937025i | \(0.386432\pi\) | |||||||
\(884\) | 2.50748e6 | 0.107921 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.43112e6 | 0.275234 | ||||||||
\(887\) | −3.22208e7 | −1.37508 | −0.687540 | − | 0.726147i | \(-0.741309\pi\) | ||||
−0.687540 | + | 0.726147i | \(0.741309\pi\) | |||||||
\(888\) | 9.58209e6 | 0.407782 | ||||||||
\(889\) | −2.30891e6 | −0.0979836 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | −9.52842e6 | −0.400967 | ||||||||
\(893\) | 1.64071e7 | 0.688498 | ||||||||
\(894\) | 3.58219e6 | 0.149901 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.35799e7 | −0.565102 | ||||||||
\(897\) | 824845. | 0.0342288 | ||||||||
\(898\) | 2.35394e6 | 0.0974102 | ||||||||
\(899\) | −2.15907e7 | −0.890979 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.67187e7 | 1.50687 | ||||||||
\(902\) | 2.88812e6 | 0.118195 | ||||||||
\(903\) | 1.59029e7 | 0.649016 | ||||||||
\(904\) | −1.10935e7 | −0.451489 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.18303e6 | 0.250254 | ||||||||
\(907\) | 6.59225e6 | 0.266082 | 0.133041 | − | 0.991111i | \(-0.457526\pi\) | ||||
0.133041 | + | 0.991111i | \(0.457526\pi\) | |||||||
\(908\) | 3.15413e7 | 1.26959 | ||||||||
\(909\) | −7.28795e6 | −0.292547 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.51432e7 | −1.80217 | −0.901086 | − | 0.433640i | \(-0.857229\pi\) | ||||
−0.901086 | + | 0.433640i | \(0.857229\pi\) | |||||||
\(912\) | −7.49767e6 | −0.298497 | ||||||||
\(913\) | −2.08526e6 | −0.0827910 | ||||||||
\(914\) | −1.97209e6 | −0.0780838 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.84550e6 | 0.230188 | ||||||||
\(917\) | 1.99173e7 | 0.782182 | ||||||||
\(918\) | −1.10750e6 | −0.0433749 | ||||||||
\(919\) | −4.40836e7 | −1.72182 | −0.860911 | − | 0.508756i | \(-0.830106\pi\) | ||||
−0.860911 | + | 0.508756i | \(0.830106\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.84155e6 | −0.265770 | ||||||||
\(922\) | −6.45596e6 | −0.250111 | ||||||||
\(923\) | −2.89970e6 | −0.112034 | ||||||||
\(924\) | −3.03097e6 | −0.116789 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.72582e6 | −0.257761 | ||||||||
\(927\) | −8.60678e6 | −0.328959 | ||||||||
\(928\) | 1.23739e7 | 0.471667 | ||||||||
\(929\) | −3.78094e7 | −1.43734 | −0.718672 | − | 0.695349i | \(-0.755250\pi\) | ||||
−0.718672 | + | 0.695349i | \(0.755250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.06296e6 | 0.304874 | ||||||||
\(932\) | 1.95447e7 | 0.737038 | ||||||||
\(933\) | −1.98240e7 | −0.745568 | ||||||||
\(934\) | 2.95721e6 | 0.110921 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −458938. | −0.0171224 | ||||||||
\(937\) | 4.50928e7 | 1.67787 | 0.838935 | − | 0.544231i | \(-0.183179\pi\) | ||||
0.838935 | + | 0.544231i | \(0.183179\pi\) | |||||||
\(938\) | −8.39288e6 | −0.311461 | ||||||||
\(939\) | −6.17329e6 | −0.228482 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.32466e7 | 1.59213 | 0.796063 | − | 0.605213i | \(-0.206912\pi\) | ||||
0.796063 | + | 0.605213i | \(0.206912\pi\) | |||||||
\(942\) | 4.98847e6 | 0.183164 | ||||||||
\(943\) | −2.40649e7 | −0.881261 | ||||||||
\(944\) | 3.76059e7 | 1.37349 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.01122e6 | −0.109399 | ||||||||
\(947\) | −3.10917e7 | −1.12660 | −0.563300 | − | 0.826253i | \(-0.690468\pi\) | ||||
−0.563300 | + | 0.826253i | \(0.690468\pi\) | |||||||
\(948\) | 1.56843e7 | 0.566820 | ||||||||
\(949\) | −2.90165e6 | −0.104588 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.69118e7 | 0.606373 | ||||||||
\(952\) | −8.68959e6 | −0.310747 | ||||||||
\(953\) | 4.53118e7 | 1.61614 | 0.808071 | − | 0.589085i | \(-0.200512\pi\) | ||||
0.808071 | + | 0.589085i | \(0.200512\pi\) | |||||||
\(954\) | −3.27022e6 | −0.116334 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.83601e7 | 0.649725 | ||||||||
\(957\) | 3.64424e6 | 0.128626 | ||||||||
\(958\) | −2.47269e6 | −0.0870476 | ||||||||
\(959\) | −2.21103e6 | −0.0776333 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.29978e7 | 0.454005 | ||||||||
\(962\) | 1.20140e6 | 0.0418552 | ||||||||
\(963\) | −7.36528e6 | −0.255931 | ||||||||
\(964\) | 1.31184e7 | 0.454661 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.39094e6 | −0.0479583 | ||||||||
\(967\) | −3.52998e7 | −1.21396 | −0.606982 | − | 0.794715i | \(-0.707620\pi\) | ||||
−0.606982 | + | 0.794715i | \(0.707620\pi\) | |||||||
\(968\) | 1.17944e6 | 0.0404565 | ||||||||
\(969\) | −1.01718e7 | −0.348008 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.90825e7 | −0.989883 | −0.494941 | − | 0.868926i | \(-0.664810\pi\) | ||||
−0.494941 | + | 0.868926i | \(0.664810\pi\) | |||||||
\(972\) | −1.79093e6 | −0.0608014 | ||||||||
\(973\) | 3.30181e7 | 1.11807 | ||||||||
\(974\) | −7.28033e6 | −0.245897 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.09210e6 | −0.103903 | ||||||||
\(977\) | −2.59538e7 | −0.869890 | −0.434945 | − | 0.900457i | \(-0.643232\pi\) | ||||
−0.434945 | + | 0.900457i | \(0.643232\pi\) | |||||||
\(978\) | −243414. | −0.00813764 | ||||||||
\(979\) | 2.95357e6 | 0.0984898 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.80441e6 | 0.126216 | ||||||||
\(982\) | 3.13273e6 | 0.103668 | ||||||||
\(983\) | 2.55539e7 | 0.843477 | 0.421738 | − | 0.906718i | \(-0.361420\pi\) | ||||
0.421738 | + | 0.906718i | \(0.361420\pi\) | |||||||
\(984\) | 1.33896e7 | 0.440837 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.08390e6 | 0.166535 | ||||||||
\(987\) | 1.40932e7 | 0.460488 | ||||||||
\(988\) | −2.05107e6 | −0.0668479 | ||||||||
\(989\) | 2.50906e7 | 0.815682 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.48265e7 | −1.77340 | −0.886699 | − | 0.462346i | \(-0.847008\pi\) | ||||
−0.886699 | + | 0.462346i | \(0.847008\pi\) | |||||||
\(992\) | −2.38568e7 | −0.769722 | ||||||||
\(993\) | 1.75086e7 | 0.563479 | ||||||||
\(994\) | 4.88976e6 | 0.156972 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.70418e6 | −0.150257 | ||||||||
\(997\) | 2.30540e7 | 0.734527 | 0.367264 | − | 0.930117i | \(-0.380295\pi\) | ||||
0.367264 | + | 0.930117i | \(0.380295\pi\) | |||||||
\(998\) | −8.45155e6 | −0.268603 | ||||||||
\(999\) | 9.63474e6 | 0.305440 |
(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.p.1.5 | ✓ | 8 | |
5.4 | even | 2 | 825.6.a.q.1.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.p.1.5 | ✓ | 8 | 1.1 | even | 1 | trivial | |
825.6.a.q.1.4 | yes | 8 | 5.4 | even | 2 |