Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,6,Mod(1,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("912.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.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: | \(146.270043669\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 4725x^{4} + 92430x^{3} + 1610577x^{2} - 16081740x - 24661341 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 456) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(34.8797\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −80.1366 | −1.43353 | −0.716764 | − | 0.697316i | \(-0.754377\pi\) | ||||
−0.716764 | + | 0.697316i | \(0.754377\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 221.037 | 1.70498 | 0.852490 | − | 0.522744i | \(-0.175092\pi\) | ||||
0.852490 | + | 0.522744i | \(0.175092\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.83714 | −0.0170370 | −0.00851849 | − | 0.999964i | \(-0.502712\pi\) | ||||
−0.00851849 | + | 0.999964i | \(0.502712\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1037.03 | 1.70190 | 0.850948 | − | 0.525251i | \(-0.176028\pi\) | ||||
0.850948 | + | 0.525251i | \(0.176028\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −721.230 | −0.827647 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 89.8390 | 0.0753950 | 0.0376975 | − | 0.999289i | \(-0.487998\pi\) | ||||
0.0376975 | + | 0.999289i | \(0.487998\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1989.33 | 0.984370 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1939.48 | −0.764480 | −0.382240 | − | 0.924063i | \(-0.624847\pi\) | ||||
−0.382240 | + | 0.924063i | \(0.624847\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3296.88 | 1.05500 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8952.03 | 1.97664 | 0.988318 | − | 0.152407i | \(-0.0487024\pi\) | ||||
0.988318 | + | 0.152407i | \(0.0487024\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 152.627 | 0.0285251 | 0.0142626 | − | 0.999898i | \(-0.495460\pi\) | ||||
0.0142626 | + | 0.999898i | \(0.495460\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −61.5342 | −0.00983631 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17713.1 | −2.44413 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2971.83 | −0.356878 | −0.178439 | − | 0.983951i | \(-0.557105\pi\) | ||||
−0.178439 | + | 0.983951i | \(0.557105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9333.27 | 0.982590 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −13839.3 | −1.28574 | −0.642870 | − | 0.765975i | \(-0.722257\pi\) | ||||
−0.642870 | + | 0.765975i | \(0.722257\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12954.7 | 1.06846 | 0.534229 | − | 0.845339i | \(-0.320602\pi\) | ||||
0.534229 | + | 0.845339i | \(0.320602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6491.07 | −0.477842 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 23530.5 | 1.55377 | 0.776883 | − | 0.629645i | \(-0.216799\pi\) | ||||
0.776883 | + | 0.629645i | \(0.216799\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 32050.2 | 1.90695 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 808.551 | 0.0435293 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5834.26 | 0.285296 | 0.142648 | − | 0.989773i | \(-0.454438\pi\) | ||||
0.142648 | + | 0.989773i | \(0.454438\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 547.905 | 0.0244230 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3249.00 | −0.132453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5031.13 | 0.188164 | 0.0940818 | − | 0.995564i | \(-0.470008\pi\) | ||||
0.0940818 | + | 0.995564i | \(0.470008\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −56361.1 | −1.93934 | −0.969672 | − | 0.244408i | \(-0.921406\pi\) | ||||
−0.969672 | + | 0.244408i | \(0.921406\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 17904.0 | 0.568326 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −83104.1 | −2.43971 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −48315.2 | −1.31491 | −0.657456 | − | 0.753493i | \(-0.728368\pi\) | ||||
−0.657456 | + | 0.753493i | \(0.728368\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −17455.3 | −0.441373 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −73547.4 | −1.73150 | −0.865748 | − | 0.500480i | \(-0.833157\pi\) | ||||
−0.865748 | + | 0.500480i | \(0.833157\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 59881.4 | 1.31518 | 0.657589 | − | 0.753377i | \(-0.271576\pi\) | ||||
0.657589 | + | 0.753377i | \(0.271576\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 29671.9 | 0.609105 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1511.26 | −0.0290477 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 34028.2 | 0.613439 | 0.306720 | − | 0.951800i | \(-0.400769\pi\) | ||||
0.306720 | + | 0.951800i | \(0.400769\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −76249.7 | −1.21491 | −0.607453 | − | 0.794356i | \(-0.707809\pi\) | ||||
−0.607453 | + | 0.794356i | \(0.707809\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7199.39 | −0.108081 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 80568.3 | 1.14121 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −18300.9 | −0.244905 | −0.122453 | − | 0.992474i | \(-0.539076\pi\) | ||||
−0.122453 | + | 0.992474i | \(0.539076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 229222. | 2.90170 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1373.64 | 0.0164690 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28929.3 | 0.328874 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 55155.8 | 0.595199 | 0.297599 | − | 0.954691i | \(-0.403814\pi\) | ||||
0.297599 | + | 0.954691i | \(0.403814\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −553.808 | −0.00567899 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2327.63 | −0.0227045 | −0.0113522 | − | 0.999936i | \(-0.503614\pi\) | ||||
−0.0113522 | + | 0.999936i | \(0.503614\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −39962.2 | −0.371156 | −0.185578 | − | 0.982630i | \(-0.559416\pi\) | ||||
−0.185578 | + | 0.982630i | \(0.559416\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −159418. | −1.41112 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −27485.4 | −0.232083 | −0.116041 | − | 0.993244i | \(-0.537021\pi\) | ||||
−0.116041 | + | 0.993244i | \(0.537021\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 141384. | 1.13982 | 0.569908 | − | 0.821709i | \(-0.306979\pi\) | ||||
0.569908 | + | 0.821709i | \(0.306979\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −26746.5 | −0.206044 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −89708.4 | −0.660902 | −0.330451 | − | 0.943823i | \(-0.607201\pi\) | ||||
−0.330451 | + | 0.943823i | \(0.607201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 155424. | 1.09590 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 83999.4 | 0.567298 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19857.7 | 0.128547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −161004. | −0.999710 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −124553. | −0.742323 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13773.8 | −0.0788456 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 264999. | 1.45792 | 0.728962 | − | 0.684554i | \(-0.240003\pi\) | ||||
0.728962 | + | 0.684554i | \(0.240003\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 116593. | 0.616875 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 143573. | 0.730961 | 0.365480 | − | 0.930819i | \(-0.380905\pi\) | ||||
0.365480 | + | 0.930819i | \(0.380905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −79794.2 | −0.391149 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −58419.6 | −0.275882 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 201383. | 0.916690 | 0.458345 | − | 0.888774i | \(-0.348442\pi\) | ||||
0.458345 | + | 0.888774i | \(0.348442\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 449847. | 1.97482 | 0.987411 | − | 0.158174i | \(-0.0505608\pi\) | ||||
0.987411 | + | 0.158174i | \(0.0505608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 211774. | 0.897068 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7090.31 | −0.0289952 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −717386. | −2.83356 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 288452. | 1.10098 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 262602. | 0.969021 | 0.484510 | − | 0.874786i | \(-0.338998\pi\) | ||||
0.484510 | + | 0.874786i | \(0.338998\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 318671. | 1.13737 | 0.568683 | − | 0.822557i | \(-0.307453\pi\) | ||||
0.568683 | + | 0.822557i | \(0.307453\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7276.96 | 0.0251317 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12231.0 | −0.0408916 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 435520. | 1.41013 | 0.705065 | − | 0.709143i | \(-0.250918\pi\) | ||||
0.705065 | + | 0.709143i | \(0.250918\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 52508.3 | 0.164716 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −428697. | −1.30342 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 341902. | 1.00794 | 0.503968 | − | 0.863722i | \(-0.331873\pi\) | ||||
0.503968 | + | 0.863722i | \(0.331873\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4931.15 | 0.0141006 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 105364. | 0.292348 | 0.146174 | − | 0.989259i | \(-0.453304\pi\) | ||||
0.146174 | + | 0.989259i | \(0.453304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 704138. | 1.89645 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −29241.0 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −487341. | −1.23799 | −0.618996 | − | 0.785394i | \(-0.712460\pi\) | ||||
−0.618996 | + | 0.785394i | \(0.712460\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 728731. | 1.79876 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 45280.2 | 0.108636 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 586070. | 1.36715 | 0.683576 | − | 0.729879i | \(-0.260424\pi\) | ||||
0.683576 | + | 0.729879i | \(0.260424\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −143643. | −0.325903 | −0.162951 | − | 0.986634i | \(-0.552101\pi\) | ||||
−0.162951 | + | 0.986634i | \(0.552101\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −507250. | −1.11968 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 238153. | 0.511595 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −614.241 | −0.00128450 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 161136. | 0.328123 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −912988. | −1.81085 | −0.905424 | − | 0.424509i | \(-0.860447\pi\) | ||||
−0.905424 | + | 0.424509i | \(0.860447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 160240. | 0.309654 | 0.154827 | − | 0.987942i | \(-0.450518\pi\) | ||||
0.154827 | + | 0.987942i | \(0.450518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −747937. | −1.40857 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 47620.7 | 0.0874240 | 0.0437120 | − | 0.999044i | \(-0.486082\pi\) | ||||
0.0437120 | + | 0.999044i | \(0.486082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −647040. | −1.15824 | −0.579120 | − | 0.815242i | \(-0.696604\pi\) | ||||
−0.579120 | + | 0.815242i | \(0.696604\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −434837. | −0.759165 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.97873e6 | 3.37012 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.10903e6 | 1.84314 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −157098. | −0.254827 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2468.21 | 0.00390855 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 797079. | 1.23252 | 0.616261 | − | 0.787542i | \(-0.288646\pi\) | ||||
0.616261 | + | 0.787542i | \(0.288646\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −661927. | −0.999680 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.03815e6 | −1.53167 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 33736.2 | 0.0486348 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 538933. | 0.759319 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 93165.7 | 0.128314 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 698425. | 0.940497 | 0.470249 | − | 0.882534i | \(-0.344164\pi\) | ||||
0.470249 | + | 0.882534i | \(0.344164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 267047. | 0.351667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 809651. | 1.04288 | 0.521438 | − | 0.853289i | \(-0.325396\pi\) | ||||
0.521438 | + | 0.853289i | \(0.325396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 244499. | 0.308098 | 0.154049 | − | 0.988063i | \(-0.450769\pi\) | ||||
0.154049 | + | 0.988063i | \(0.450769\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13601.3 | −0.0167707 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 263509. | 0.317984 | 0.158992 | − | 0.987280i | \(-0.449176\pi\) | ||||
0.158992 | + | 0.987280i | \(0.449176\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.88565e6 | −2.22737 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 306254. | 0.354169 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −181693. | −0.205752 | −0.102876 | − | 0.994694i | \(-0.532804\pi\) | ||||
−0.102876 | + | 0.994694i | \(0.532804\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00530e6 | −1.11495 | −0.557474 | − | 0.830194i | \(-0.688229\pi\) | ||||
−0.557474 | + | 0.830194i | \(0.688229\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.56839e6 | −2.73367 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −374368. | −0.390442 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −686247. | −0.701426 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −151883. | −0.152168 | −0.0760841 | − | 0.997101i | \(-0.524242\pi\) | ||||
−0.0760841 | + | 0.997101i | \(0.524242\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13260.5 | 0.0130244 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −64794.5 | −0.0624005 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.47290e6 | 1.39104 | 0.695522 | − | 0.718505i | \(-0.255173\pi\) | ||||
0.695522 | + | 0.718505i | \(0.255173\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −656884. | −0.608470 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 725115. | 0.658879 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −602508. | −0.537123 | −0.268561 | − | 0.963263i | \(-0.586548\pi\) | ||||
−0.268561 | + | 0.963263i | \(0.586548\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −467538. | −0.408980 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −164708. | −0.141396 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.17808e6 | 0.992643 | 0.496321 | − | 0.868139i | \(-0.334684\pi\) | ||||
0.496321 | + | 0.868139i | \(0.334684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −476163. | −0.393851 | −0.196926 | − | 0.980418i | \(-0.563096\pi\) | ||||
−0.196926 | + | 0.980418i | \(0.563096\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.06299e6 | 1.67530 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22541.2 | −0.0179740 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.95601e6 | −1.53170 | −0.765848 | − | 0.643022i | \(-0.777680\pi\) | ||||
−0.765848 | + | 0.643022i | \(0.777680\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12362.8 | 0.00950837 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.46010e6 | −1.85861 | −0.929304 | − | 0.369316i | \(-0.879592\pi\) | ||||
−0.929304 | + | 0.369316i | \(0.879592\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 954640. | 0.708555 | 0.354277 | − | 0.935140i | \(-0.384727\pi\) | ||||
0.354277 | + | 0.935140i | \(0.384727\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 260364. | 0.189875 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.05898e6 | −2.19216 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41179e6 | −0.994316 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 496402. | 0.343638 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 425873. | 0.289808 | 0.144904 | − | 0.989446i | \(-0.453713\pi\) | ||||
0.144904 | + | 0.989446i | \(0.453713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −403178. | −0.269738 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4984.27 | −0.00327877 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.01130e6 | −1.30106 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.86347e6 | 1.82170 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −20948.7 | −0.0131084 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.51659e6 | 2.78010 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.25152e6 | 1.36342 | 0.681711 | − | 0.731622i | \(-0.261236\pi\) | ||||
0.681711 | + | 0.731622i | \(0.261236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −359660. | −0.214287 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.97390e6 | 1.74352 | 0.871758 | − | 0.489937i | \(-0.162980\pi\) | ||||
0.871758 | + | 0.489937i | \(0.162980\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.38952e6 | 0.801683 | 0.400842 | − | 0.916147i | \(-0.368718\pi\) | ||||
0.400842 | + | 0.916147i | \(0.368718\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.43476e6 | −0.814712 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.09173e6 | 0.610193 | 0.305096 | − | 0.952321i | \(-0.401311\pi\) | ||||
0.305096 | + | 0.952321i | \(0.401311\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −61206.3 | −0.0336759 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −247369. | −0.133993 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32431.9 | −0.0172968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.41896e6 | 1.79550 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.27246e6 | 0.658073 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.20109e6 | 2.64914 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.67033e6 | 1.33966 | 0.669830 | − | 0.742514i | \(-0.266367\pi\) | ||||
0.669830 | + | 0.742514i | \(0.266367\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −240719. | −0.118959 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.87182e6 | 1.88496 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −599879. | −0.287732 | −0.143866 | − | 0.989597i | \(-0.545953\pi\) | ||||
−0.143866 | + | 0.989597i | \(0.545953\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −807376. | −0.381572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1043.53 | −0.000485982 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.36930e6 | 1.54634 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.39881e6 | 0.632720 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 369338. | 0.164665 | 0.0823324 | − | 0.996605i | \(-0.473763\pi\) | ||||
0.0823324 | + | 0.996605i | \(0.473763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.23931e6 | −1.42360 | −0.711802 | − | 0.702380i | \(-0.752121\pi\) | ||||
−0.711802 | + | 0.702380i | \(0.752121\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 755995. | 0.327530 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.91385e6 | 1.24460 | 0.622300 | − | 0.782779i | \(-0.286198\pi\) | ||||
0.622300 | + | 0.782779i | \(0.286198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.89384e6 | 2.48215 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 178719. | 0.0742166 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.00994e6 | −1.23260 | −0.616299 | − | 0.787512i | \(-0.711369\pi\) | ||||
−0.616299 | + | 0.787512i | \(0.711369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.44904e6 | −0.577183 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.79869e6 | −1.88534 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −144945. | −0.0561744 | −0.0280872 | − | 0.999605i | \(-0.508942\pi\) | ||||
−0.0280872 | + | 0.999605i | \(0.508942\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.12098e6 | −0.428580 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.28958e6 | 0.486424 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.07459e6 | −0.399917 | −0.199959 | − | 0.979804i | \(-0.564081\pi\) | ||||
−0.199959 | + | 0.979804i | \(0.564081\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −123964. | −0.0455215 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.28352e6 | 3.36403 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −348280. | −0.124546 | −0.0622732 | − | 0.998059i | \(-0.519835\pi\) | ||||
−0.0622732 | + | 0.998059i | \(0.519835\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.38499e6 | 0.841733 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −923631. | −0.321737 | −0.160869 | − | 0.986976i | \(-0.551430\pi\) | ||||
−0.160869 | + | 0.986976i | \(0.551430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 121107. | 0.0416407 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.04933e6 | 0.356153 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.16205e6 | 1.05948 | 0.529742 | − | 0.848159i | \(-0.322289\pi\) | ||||
0.529742 | + | 0.848159i | \(0.322289\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −174241. | −0.0576380 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.29216e6 | 0.422021 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.72691e6 | −0.879382 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.50866e6 | −1.43572 | −0.717862 | − | 0.696186i | \(-0.754879\pi\) | ||||
−0.717862 | + | 0.696186i | \(0.754879\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −718148. | −0.225830 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −72297.9 | −0.0224525 | −0.0112262 | − | 0.999937i | \(-0.503573\pi\) | ||||
−0.0112262 | + | 0.999937i | \(0.503573\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 158279. | 0.0485468 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −525776. | −0.159281 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 20318.8 | 0.00608013 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.86659e6 | 1.43852 | 0.719261 | − | 0.694740i | \(-0.244481\pi\) | ||||
0.719261 | + | 0.694740i | \(0.244481\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.81245e6 | 0.529251 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.11206e6 | 0.320815 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.11039e6 | 1.74160 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.04863e6 | 1.14016 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.24133e6 | 0.623692 | 0.311846 | − | 0.950133i | \(-0.399053\pi\) | ||||
0.311846 | + | 0.950133i | \(0.399053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 244516. | 0.0672361 | 0.0336180 | − | 0.999435i | \(-0.489297\pi\) | ||||
0.0336180 | + | 0.999435i | \(0.489297\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.90597e6 | 0.517922 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 296188. | 0.0795418 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.24579e7 | −3.30654 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −63812.8 | −0.0167404 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 91916.4 | 0.0238342 | 0.0119171 | − | 0.999929i | \(-0.496207\pi\) | ||||
0.0119171 | + | 0.999929i | \(0.496207\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.21065e6 | −1.84823 | −0.924113 | − | 0.382120i | \(-0.875194\pi\) | ||||
−0.924113 | + | 0.382120i | \(0.875194\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.45647e6 | −1.63596 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 700153. | 0.175384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −818398. | −0.202677 | −0.101338 | − | 0.994852i | \(-0.532312\pi\) | ||||
−0.101338 | + | 0.994852i | \(0.532312\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.59607e6 | 0.635652 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.01390e6 | 0.245464 | 0.122732 | − | 0.992440i | \(-0.460834\pi\) | ||||
0.122732 | + | 0.992440i | \(0.460834\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.46657e6 | 0.351078 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.36342e6 | 0.559464 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.25379e6 | 0.995773 | 0.497887 | − | 0.867242i | \(-0.334110\pi\) | ||||
0.497887 | + | 0.867242i | \(0.334110\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 94621.0 | 0.0219051 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.86804e6 | 0.656659 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.83690e7 | −4.15966 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 858691. | 0.192330 | 0.0961648 | − | 0.995365i | \(-0.469342\pi\) | ||||
0.0961648 | + | 0.995365i | \(0.469342\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 65492.6 | 0.0145098 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.19905e6 | 0.701083 | 0.350541 | − | 0.936547i | \(-0.385998\pi\) | ||||
0.350541 | + | 0.936547i | \(0.385998\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.68844e6 | −1.01643 | −0.508213 | − | 0.861231i | \(-0.669694\pi\) | ||||
−0.508213 | + | 0.861231i | \(0.669694\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −110079. | −0.0236087 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.89088e6 | 0.401210 | 0.200605 | − | 0.979672i | \(-0.435709\pi\) | ||||
0.200605 | + | 0.979672i | \(0.435709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.06794e7 | −2.24190 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.91968e6 | 0.814139 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −88573.4 | −0.0182033 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.19017e6 | −0.242034 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 472575. | 0.0950987 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.39562e6 | 0.875350 | 0.437675 | − | 0.899133i | \(-0.355802\pi\) | ||||
0.437675 | + | 0.899133i | \(0.355802\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.08188e6 | −0.607369 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.85827e6 | −0.752531 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.42000e6 | −0.853234 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.71164e6 | −0.900222 | −0.450111 | − | 0.892973i | \(-0.648616\pi\) | ||||
−0.450111 | + | 0.892973i | \(0.648616\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.07712e6 | 0.581933 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 817691. | 0.153068 | 0.0765342 | − | 0.997067i | \(-0.475615\pi\) | ||||
0.0765342 | + | 0.997067i | \(0.475615\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 804241. | 0.149028 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 44380.3 | 0.00814099 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.62567e7 | −2.95217 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.57253e6 | 1.18163 | 0.590815 | − | 0.806807i | \(-0.298806\pi\) | ||||
0.590815 | + | 0.806807i | \(0.298806\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 948274. | 0.168787 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.81301e6 | −1.20066 | −0.600329 | − | 0.799753i | \(-0.704964\pi\) | ||||
−0.600329 | + | 0.799753i | \(0.704964\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 186529. | 0.0325475 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.33724e6 | 1.09491 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −384616. | −0.0658011 | −0.0329006 | − | 0.999459i | \(-0.510474\pi\) | ||||
−0.0329006 | + | 0.999459i | \(0.510474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.32360e7 | 2.24235 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −263169. | −0.0441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.20244e6 | 0.532063 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −160881. | −0.0264715 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.38607e6 | −0.714755 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.55777e6 | −1.38123 | −0.690615 | − | 0.723222i | \(-0.742660\pi\) | ||||
−0.690615 | + | 0.723222i | \(0.742660\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.00968e6 | 0.161410 | 0.0807051 | − | 0.996738i | \(-0.474283\pi\) | ||||
0.0807051 | + | 0.996738i | \(0.474283\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.55858e6 | 1.03851 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13711.9 | 0.00215065 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.67475e6 | −0.415570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 407522. | 0.0627212 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.43517e7 | −2.18820 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.20259e6 | 0.332697 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.27463e6 | 0.789326 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −219132. | −0.0324888 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 631611. | 0.0927805 | 0.0463902 | − | 0.998923i | \(-0.485228\pi\) | ||||
0.0463902 | + | 0.998923i | \(0.485228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.29279e6 | −0.188160 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.13300e7 | −1.63396 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.90704e6 | 0.558316 | 0.279158 | − | 0.960245i | \(-0.409945\pi\) | ||||
0.279158 | + | 0.960245i | \(0.409945\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.56525e6 | −0.646448 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.23168e6 | −0.453471 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.52148e6 | 1.04590 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.14337e6 | 0.295369 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.44118e6 | −0.469969 | −0.234985 | − | 0.971999i | \(-0.575504\pi\) | ||||
−0.234985 | + | 0.971999i | \(0.575504\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.34345e7 | 1.81841 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5528.17 | −0.000741608 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.40711e7 | −1.87093 | −0.935464 | − | 0.353421i | \(-0.885018\pi\) | ||||
−0.935464 | + | 0.353421i | \(0.885018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.18893e6 | 0.947421 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.45022e6 | 0.189442 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.29191e7 | −1.67283 | −0.836413 | − | 0.548100i | \(-0.815351\pi\) | ||||
−0.836413 | + | 0.548100i | \(0.815351\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.35324e6 | 0.430401 | 0.215201 | − | 0.976570i | \(-0.430959\pi\) | ||||
0.215201 | + | 0.976570i | \(0.430959\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.21689e6 | −1.04549 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.39424e6 | −0.806527 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.54867e6 | −1.19400 | −0.596999 | − | 0.802242i | \(-0.703640\pi\) | ||||
−0.596999 | + | 0.802242i | \(0.703640\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.44216e6 | 0.178779 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.68540e7 | −2.07139 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39889.6 | −0.00486059 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.73143e6 | −0.813238 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 74106.0 | 0.00887683 | 0.00443842 | − | 0.999990i | \(-0.498587\pi\) | ||||
0.00443842 | + | 0.999990i | \(0.498587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −55098.4 | −0.00654411 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 428587. | 0.0504743 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.81239e6 | −0.328427 | −0.164214 | − | 0.986425i | \(-0.552509\pi\) | ||||
−0.164214 | + | 0.986425i | \(0.552509\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.59133e6 | −0.184276 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.82336e6 | −0.668710 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.13698e6 | 0.926608 | 0.463304 | − | 0.886199i | \(-0.346664\pi\) | ||||
0.463304 | + | 0.886199i | \(0.346664\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.80255e6 | −0.994082 | −0.497041 | − | 0.867727i | \(-0.665580\pi\) | ||||
−0.497041 | + | 0.867727i | \(0.665580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.91353e6 | −0.438304 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.29023e7 | 1.43311 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.04706e6 | −0.666150 | −0.333075 | − | 0.942900i | \(-0.608086\pi\) | ||||
−0.333075 | + | 0.942900i | \(0.608086\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.78085e7 | 1.94574 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.44018e7 | 2.64435 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.60257e6 | −0.494708 | −0.247354 | − | 0.968925i | \(-0.579561\pi\) | ||||
−0.247354 | + | 0.968925i | \(0.579561\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.98129e6 | 1.06414 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.17504e7 | −1.24263 | −0.621314 | − | 0.783562i | \(-0.713401\pi\) | ||||
−0.621314 | + | 0.783562i | \(0.713401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.99190e6 | −0.313849 | −0.156924 | − | 0.987611i | \(-0.550158\pi\) | ||||
−0.156924 | + | 0.987611i | \(0.550158\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.41388e6 | −0.147124 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.04517e6 | −0.417558 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.19896e6 | −0.941974 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22213.9 | 0.00225660 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −266986. | −0.0269068 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.95172e6 | 0.595072 | 0.297536 | − | 0.954711i | \(-0.403835\pi\) | ||||
0.297536 | + | 0.954711i | \(0.403835\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.17371e6 | 0.711597 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.12361e7 | −2.08997 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.32370e7 | 3.24544 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.95734e6 | −0.577165 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.94545e6 | −0.187015 | −0.0935073 | − | 0.995619i | \(-0.529808\pi\) | ||||
−0.0935073 | + | 0.995619i | \(0.529808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.98422e6 | 0.856945 | 0.428472 | − | 0.903555i | \(-0.359052\pi\) | ||||
0.428472 | + | 0.903555i | \(0.359052\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.34335e6 | −0.884307 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.64265e7 | −1.54271 | −0.771356 | − | 0.636404i | \(-0.780421\pi\) | ||||
−0.771356 | + | 0.636404i | \(0.780421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −34398.6 | −0.00320574 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 303626. | 0.0280793 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.64800e6 | −0.334789 | −0.167395 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167395 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.15054e7 | −1.04785 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.85039e6 | 0.438393 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.42986e6 | 0.397353 | 0.198677 | − | 0.980065i | \(-0.436336\pi\) | ||||
0.198677 | + | 0.980065i | \(0.436336\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.30589e6 | −0.116252 | −0.0581262 | − | 0.998309i | \(-0.518513\pi\) | ||||
−0.0581262 | + | 0.998309i | \(0.518513\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 838491. | 0.0740823 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.39444e6 | 0.560723 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.73623e7 | −1.51110 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.28582e6 | 0.542996 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 385349. | 0.0330406 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.74209e7 | 1.48263 | 0.741316 | − | 0.671157i | \(-0.234202\pi\) | ||||
0.741316 | + | 0.671157i | \(0.234202\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.40342e6 | 0.203035 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.47484e6 | −0.542947 | −0.271473 | − | 0.962446i | \(-0.587511\pi\) | ||||
−0.271473 | + | 0.962446i | \(0.587511\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.21915e7 | 1.01480 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.28686e6 | 0.602105 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.44202e7 | 1.18282 | 0.591411 | − | 0.806371i | \(-0.298571\pi\) | ||||
0.591411 | + | 0.806371i | \(0.298571\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.61382e7 | −1.31410 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.20050e6 | 0.177881 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.05030e6 | 0.485544 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.80165e6 | 0.143541 | 0.0717703 | − | 0.997421i | \(-0.477135\pi\) | ||||
0.0717703 | + | 0.997421i | \(0.477135\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −122412. | −0.00968257 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.60492e7 | −2.83096 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.24331e6 | −0.0969384 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.37158e6 | 0.183588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.09790e7 | 0.843857 | 0.421928 | − | 0.906629i | \(-0.361353\pi\) | ||||
0.421928 | + | 0.906629i | \(0.361353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.07283e6 | 0.0818735 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.69709e7 | −1.28597 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −514492. | −0.0387106 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.53321e7 | −1.14548 | −0.572738 | − | 0.819739i | \(-0.694119\pi\) | ||||
−0.572738 | + | 0.819739i | \(0.694119\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.75629e6 | 0.204480 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −296018. | −0.0218069 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 568194. | 0.0415654 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.63524e6 | −0.118791 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.63305e7 | 1.17808 | 0.589042 | − | 0.808103i | \(-0.299505\pi\) | ||||
0.589042 | + | 0.808103i | \(0.299505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.83312e6 | −0.632814 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.04773e6 | −0.643715 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.95138e7 | 2.08535 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 79286.1 | 0.00556367 | 0.00278183 | − | 0.999996i | \(-0.499115\pi\) | ||||
0.00278183 | + | 0.999996i | \(0.499115\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.16384e6 | 0.0805565 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.68148e7 | 1.15593 | 0.577965 | − | 0.816062i | \(-0.303847\pi\) | ||||
0.577965 | + | 0.816062i | \(0.303847\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.31155e7 | −1.57829 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 330338. | 0.0224021 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.23677e7 | 1.50664 | 0.753322 | − | 0.657652i | \(-0.228450\pi\) | ||||
0.753322 | + | 0.657652i | \(0.228450\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.36931e6 | −0.225422 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.54060e7 | −1.02380 | −0.511902 | − | 0.859044i | \(-0.671059\pi\) | ||||
−0.511902 | + | 0.859044i | \(0.671059\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.10441e7 | −1.38912 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.17622e6 | −0.404969 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.07528e6 | −0.395696 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.22337e7 | 0.791512 | 0.395756 | − | 0.918356i | \(-0.370483\pi\) | ||||
0.395756 | + | 0.918356i | \(0.370483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.36694e6 | −0.0878543 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.55372e7 | −1.63045 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.12366e7 | 0.712683 | 0.356341 | − | 0.934356i | \(-0.384024\pi\) | ||||
0.356341 | + | 0.934356i | \(0.384024\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 119345. | 0.00751966 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.50972e7 | 1.57095 | 0.785477 | − | 0.618890i | \(-0.212417\pi\) | ||||
0.785477 | + | 0.618890i | \(0.212417\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.12511e7 | 1.94336 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −583151. | −0.0360269 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.21743e6 | 0.320235 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.70225e7 | −1.64782 | −0.823910 | − | 0.566720i | \(-0.808212\pi\) | ||||
−0.823910 | + | 0.566720i | \(0.808212\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.32561e7 | 0.803119 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.42992e6 | 0.326847 | 0.163424 | − | 0.986556i | \(-0.447746\pi\) | ||||
0.163424 | + | 0.986556i | \(0.447746\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 503193. | 0.0300940 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.91196e6 | −0.351300 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.99598e6 | 0.294969 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 502854. | 0.0294995 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.52603e6 | 0.380404 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.49011e7 | −2.02146 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.63648e6 | −0.209288 | −0.104644 | − | 0.994510i | \(-0.533370\pi\) | ||||
−0.104644 | + | 0.994510i | \(0.533370\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.42257e6 | −0.310108 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.98289e7 | −1.12682 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.84482e7 | −3.30056 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.20784e6 | −0.236125 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.06851e6 | −0.282641 | −0.141320 | − | 0.989964i | \(-0.545135\pi\) | ||||
−0.141320 | + | 0.989964i | \(0.545135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.11395e6 | 0.117146 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.48237e6 | −0.0816350 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −409417. | −0.0224067 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.43543e7 | 1.86849 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.06027e7 | 0.573102 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.93485e7 | −1.03938 | −0.519691 | − | 0.854354i | \(-0.673953\pi\) | ||||
−0.519691 | + | 0.854354i | \(0.673953\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.75853e7 | −0.938854 | −0.469427 | − | 0.882971i | \(-0.655539\pi\) | ||||
−0.469427 | + | 0.882971i | \(0.655539\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.28546e6 | −0.227390 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.73989e7 | −1.44490 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.67666e6 | −0.245121 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.85669e7 | 0.967232 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.24199e6 | −0.0643074 | −0.0321537 | − | 0.999483i | \(-0.510237\pi\) | ||||
−0.0321537 | + | 0.999483i | \(0.510237\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.79887e6 | 0.0925761 | 0.0462881 | − | 0.998928i | \(-0.485261\pi\) | ||||
0.0462881 | + | 0.998928i | \(0.485261\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −202871. | −0.0103773 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.43748e6 | −0.327304 | −0.163652 | − | 0.986518i | \(-0.552327\pi\) | ||||
−0.163652 | + | 0.986518i | \(0.552327\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.46989e7 | 0.742843 | 0.371422 | − | 0.928464i | \(-0.378870\pi\) | ||||
0.371422 | + | 0.928464i | \(0.378870\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.76041e7 | −0.884325 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.87936e6 | 0.143775 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.44350e6 | −0.419089 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 111265. | 0.00548966 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.92855e7 | 0.945859 | 0.472929 | − | 0.881100i | \(-0.343197\pi\) | ||||
0.472929 | + | 0.881100i | \(0.343197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.96277e7 | 2.90709 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.21409e7 | −1.07307 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.64272e7 | −2.71861 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.55878e7 | −1.70448 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.59176e6 | 0.409084 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.76382e6 | 0.272826 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.26519e7 | −1.53651 | −0.768256 | − | 0.640143i | \(-0.778875\pi\) | ||||
−0.768256 | + | 0.640143i | \(0.778875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.34328e6 | 0.109625 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.78009e7 | −1.29303 | −0.646513 | − | 0.762903i | \(-0.723773\pi\) | ||||
−0.646513 | + | 0.762903i | \(0.723773\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.12121e7 | −0.980844 | −0.490422 | − | 0.871485i | \(-0.663157\pi\) | ||||
−0.490422 | + | 0.871485i | \(0.663157\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.75309e7 | −1.26565 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.36175e7 | −1.07946 | −0.539730 | − | 0.841838i | \(-0.681474\pi\) | ||||
−0.539730 | + | 0.841838i | \(0.681474\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.90539e7 | 1.77470 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.27061e7 | −0.574068 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −232656. | −0.0104512 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.01043e7 | −2.23784 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.46762e6 | 0.198400 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.04450e6 | −0.134430 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.13618e7 | 1.81594 | 0.907968 | − | 0.419040i | \(-0.137633\pi\) | ||||
0.907968 | + | 0.419040i | \(0.137633\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.83286e6 | 0.167321 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.56620e7 | 0.679843 | 0.339921 | − | 0.940454i | \(-0.389600\pi\) | ||||
0.339921 | + | 0.940454i | \(0.389600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.53491e6 | −0.152572 | −0.0762862 | − | 0.997086i | \(-0.524306\pi\) | ||||
−0.0762862 | + | 0.997086i | \(0.524306\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.62860e6 | −0.155733 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.43493e7 | 1.89268 | 0.946341 | − | 0.323170i | \(-0.104749\pi\) | ||||
0.946341 | + | 0.323170i | \(0.104749\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.85745e7 | 2.48573 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44858.5 | −0.00189300 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.49450e6 | −0.356458 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.69657e7 | −1.95985 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.81017e7 | −0.751170 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.36632e6 | 0.0563838 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 524144. | 0.0215099 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.57713e7 | 1.05176 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.15111e7 | 0.467190 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.76359e6 | 0.394086 | 0.197043 | − | 0.980395i | \(-0.436866\pi\) | ||||
0.197043 | + | 0.980395i | \(0.436866\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −188538. | −0.00756815 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.16139e7 | −1.26207 | −0.631033 | − | 0.775756i | \(-0.717369\pi\) | ||||
−0.631033 | + | 0.775756i | \(0.717369\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 521330. | 0.0206983 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.06493e7 | 1.60509 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.17349e7 | 1.24627 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.93593e6 | −0.349020 | −0.174510 | − | 0.984655i | \(-0.555834\pi\) | ||||
−0.174510 | + | 0.984655i | \(0.555834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.02637e7 | 0.787172 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.62708e7 | −2.94682 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.79777e6 | −0.376507 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.23694e6 | −0.123719 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.99767e7 | 1.51973 | 0.759866 | − | 0.650079i | \(-0.225264\pi\) | ||||
0.759866 | + | 0.650079i | \(0.225264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.15701e7 | −0.437485 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.67651e7 | 1.00662 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 49223.2 | 0.00184137 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.81200e7 | −1.04633 | −0.523163 | − | 0.852233i | \(-0.675248\pi\) | ||||
−0.523163 | + | 0.852233i | \(0.675248\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.25056e7 | 0.462852 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.50473e6 | −0.0922120 | −0.0461060 | − | 0.998937i | \(-0.514681\pi\) | ||||
−0.0461060 | + | 0.998937i | \(0.514681\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.68410e7 | 0.982923 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.29129e7 | −0.470374 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.47836e6 | 0.307211 | 0.153606 | − | 0.988132i | \(-0.450912\pi\) | ||||
0.153606 | + | 0.988132i | \(0.450912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.20988e7 | 2.23830 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.82557e6 | 0.352295 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.34630e6 | −0.119353 | −0.0596765 | − | 0.998218i | \(-0.519007\pi\) | ||||
−0.0596765 | + | 0.998218i | \(0.519007\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.31638e7 | 2.59590 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −550856. | −0.0194428 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.45131e7 | 1.56294 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.86059e7 | −0.999186 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.22632e6 | −0.0773609 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.28411e7 | −0.443897 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.23247e6 | −0.145555 | −0.0727776 | − | 0.997348i | \(-0.523186\pi\) | ||||
−0.0727776 | + | 0.997348i | \(0.523186\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −291887. | −0.00998631 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.58111e7 | 1.55927 | 0.779637 | − | 0.626231i | \(-0.215403\pi\) | ||||
0.779637 | + | 0.626231i | \(0.215403\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.94327e7 | 3.36703 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.07706e7 | 1.03663 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.45408e7 | 0.487361 | 0.243681 | − | 0.969856i | \(-0.421645\pi\) | ||||
0.243681 | + | 0.969856i | \(0.421645\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 125126. | 0.00417244 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.14521e7 | 0.379938 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.36787e7 | −0.781580 | −0.390790 | − | 0.920480i | \(-0.627798\pi\) | ||||
−0.390790 | + | 0.920480i | \(0.627798\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.81616e6 | −0.125325 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.68098e7 | 1.52948 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.51255e7 | −0.816815 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.16060e7 | −1.34577 | −0.672887 | − | 0.739745i | \(-0.734946\pi\) | ||||
−0.672887 | + | 0.739745i | \(0.734946\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.40330e7 | 0.773453 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.18516e7 | 1.66037 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.76770e6 | −0.0881823 | −0.0440912 | − | 0.999028i | \(-0.514039\pi\) | ||||
−0.0440912 | + | 0.999028i | \(0.514039\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.16647e6 | −0.0686813 |
(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 | 912.6.a.y.1.2 | 6 | ||
4.3 | odd | 2 | 456.6.a.f.1.2 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.6.a.f.1.2 | ✓ | 6 | 4.3 | odd | 2 | ||
912.6.a.y.1.2 | 6 | 1.1 | even | 1 | trivial |