Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,6,Mod(1,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, 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("525.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.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: | \(84.2015054018\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.00000 | −0.883883 | −0.441942 | − | 0.897044i | \(-0.645710\pi\) | ||||
−0.441942 | + | 0.897044i | \(0.645710\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −7.00000 | −0.218750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 45.0000 | 0.510310 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 195.000 | 1.07723 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 52.0000 | 0.129575 | 0.0647876 | − | 0.997899i | \(-0.479363\pi\) | ||||
0.0647876 | + | 0.997899i | \(0.479363\pi\) | |||||||
\(12\) | 63.0000 | 0.126295 | ||||||||
\(13\) | 770.000 | 1.26367 | 0.631833 | − | 0.775104i | \(-0.282303\pi\) | ||||
0.631833 | + | 0.775104i | \(0.282303\pi\) | |||||||
\(14\) | −245.000 | −0.334077 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −751.000 | −0.733398 | ||||||||
\(17\) | 2022.00 | 1.69691 | 0.848455 | − | 0.529267i | \(-0.177533\pi\) | ||||
0.848455 | + | 0.529267i | \(0.177533\pi\) | |||||||
\(18\) | −405.000 | −0.294628 | ||||||||
\(19\) | 1732.00 | 1.10069 | 0.550344 | − | 0.834938i | \(-0.314497\pi\) | ||||
0.550344 | + | 0.834938i | \(0.314497\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −441.000 | −0.218218 | ||||||||
\(22\) | −260.000 | −0.114529 | ||||||||
\(23\) | 576.000 | 0.227040 | 0.113520 | − | 0.993536i | \(-0.463787\pi\) | ||||
0.113520 | + | 0.993536i | \(0.463787\pi\) | |||||||
\(24\) | −1755.00 | −0.621941 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3850.00 | −1.11693 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −343.000 | −0.0826797 | ||||||||
\(29\) | 5518.00 | 1.21839 | 0.609196 | − | 0.793020i | \(-0.291492\pi\) | ||||
0.609196 | + | 0.793020i | \(0.291492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6336.00 | 1.18416 | 0.592081 | − | 0.805879i | \(-0.298307\pi\) | ||||
0.592081 | + | 0.805879i | \(0.298307\pi\) | |||||||
\(32\) | −2485.00 | −0.428994 | ||||||||
\(33\) | −468.000 | −0.0748102 | ||||||||
\(34\) | −10110.0 | −1.49987 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −567.000 | −0.0729167 | ||||||||
\(37\) | 7338.00 | 0.881198 | 0.440599 | − | 0.897704i | \(-0.354766\pi\) | ||||
0.440599 | + | 0.897704i | \(0.354766\pi\) | |||||||
\(38\) | −8660.00 | −0.972879 | ||||||||
\(39\) | −6930.00 | −0.729578 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3262.00 | −0.303057 | −0.151528 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151528 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(42\) | 2205.00 | 0.192879 | ||||||||
\(43\) | −5420.00 | −0.447021 | −0.223511 | − | 0.974701i | \(-0.571752\pi\) | ||||
−0.223511 | + | 0.974701i | \(0.571752\pi\) | |||||||
\(44\) | −364.000 | −0.0283446 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2880.00 | −0.200677 | ||||||||
\(47\) | −864.000 | −0.0570518 | −0.0285259 | − | 0.999593i | \(-0.509081\pi\) | ||||
−0.0285259 | + | 0.999593i | \(0.509081\pi\) | |||||||
\(48\) | 6759.00 | 0.423428 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18198.0 | −0.979712 | ||||||||
\(52\) | −5390.00 | −0.276427 | ||||||||
\(53\) | −4182.00 | −0.204500 | −0.102250 | − | 0.994759i | \(-0.532604\pi\) | ||||
−0.102250 | + | 0.994759i | \(0.532604\pi\) | |||||||
\(54\) | 3645.00 | 0.170103 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9555.00 | 0.407156 | ||||||||
\(57\) | −15588.0 | −0.635482 | ||||||||
\(58\) | −27590.0 | −1.07692 | ||||||||
\(59\) | −11220.0 | −0.419626 | −0.209813 | − | 0.977741i | \(-0.567286\pi\) | ||||
−0.209813 | + | 0.977741i | \(0.567286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −45602.0 | −1.56913 | −0.784566 | − | 0.620046i | \(-0.787114\pi\) | ||||
−0.784566 | + | 0.620046i | \(0.787114\pi\) | |||||||
\(62\) | −31680.0 | −1.04666 | ||||||||
\(63\) | 3969.00 | 0.125988 | ||||||||
\(64\) | 36457.0 | 1.11258 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2340.00 | 0.0661235 | ||||||||
\(67\) | −1396.00 | −0.0379925 | −0.0189963 | − | 0.999820i | \(-0.506047\pi\) | ||||
−0.0189963 | + | 0.999820i | \(0.506047\pi\) | |||||||
\(68\) | −14154.0 | −0.371199 | ||||||||
\(69\) | −5184.00 | −0.131082 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 18720.0 | 0.440717 | 0.220359 | − | 0.975419i | \(-0.429277\pi\) | ||||
0.220359 | + | 0.975419i | \(0.429277\pi\) | |||||||
\(72\) | 15795.0 | 0.359078 | ||||||||
\(73\) | −46362.0 | −1.01825 | −0.509126 | − | 0.860692i | \(-0.670031\pi\) | ||||
−0.509126 | + | 0.860692i | \(0.670031\pi\) | |||||||
\(74\) | −36690.0 | −0.778876 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12124.0 | −0.240775 | ||||||||
\(77\) | 2548.00 | 0.0489748 | ||||||||
\(78\) | 34650.0 | 0.644862 | ||||||||
\(79\) | 97424.0 | 1.75630 | 0.878149 | − | 0.478387i | \(-0.158778\pi\) | ||||
0.878149 | + | 0.478387i | \(0.158778\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 16310.0 | 0.267867 | ||||||||
\(83\) | 81228.0 | 1.29423 | 0.647114 | − | 0.762394i | \(-0.275976\pi\) | ||||
0.647114 | + | 0.762394i | \(0.275976\pi\) | |||||||
\(84\) | 3087.00 | 0.0477352 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 27100.0 | 0.395115 | ||||||||
\(87\) | −49662.0 | −0.703438 | ||||||||
\(88\) | 10140.0 | 0.139583 | ||||||||
\(89\) | −3182.00 | −0.0425819 | −0.0212910 | − | 0.999773i | \(-0.506778\pi\) | ||||
−0.0212910 | + | 0.999773i | \(0.506778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 37730.0 | 0.477621 | ||||||||
\(92\) | −4032.00 | −0.0496651 | ||||||||
\(93\) | −57024.0 | −0.683676 | ||||||||
\(94\) | 4320.00 | 0.0504271 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 22365.0 | 0.247680 | ||||||||
\(97\) | −4914.00 | −0.0530281 | −0.0265140 | − | 0.999648i | \(-0.508441\pi\) | ||||
−0.0265140 | + | 0.999648i | \(0.508441\pi\) | |||||||
\(98\) | −12005.0 | −0.126269 | ||||||||
\(99\) | 4212.00 | 0.0431917 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −166354. | −1.62267 | −0.811334 | − | 0.584583i | \(-0.801258\pi\) | ||||
−0.811334 | + | 0.584583i | \(0.801258\pi\) | |||||||
\(102\) | 90990.0 | 0.865951 | ||||||||
\(103\) | −157160. | −1.45965 | −0.729825 | − | 0.683634i | \(-0.760399\pi\) | ||||
−0.729825 | + | 0.683634i | \(0.760399\pi\) | |||||||
\(104\) | 150150. | 1.36126 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 20910.0 | 0.180755 | ||||||||
\(107\) | 6764.00 | 0.0571142 | 0.0285571 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285571 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(108\) | 5103.00 | 0.0420985 | ||||||||
\(109\) | 178398. | 1.43821 | 0.719107 | − | 0.694899i | \(-0.244551\pi\) | ||||
0.719107 | + | 0.694899i | \(0.244551\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −66042.0 | −0.508760 | ||||||||
\(112\) | −36799.0 | −0.277199 | ||||||||
\(113\) | 45134.0 | 0.332512 | 0.166256 | − | 0.986083i | \(-0.446832\pi\) | ||||
0.166256 | + | 0.986083i | \(0.446832\pi\) | |||||||
\(114\) | 77940.0 | 0.561692 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −38626.0 | −0.266523 | ||||||||
\(117\) | 62370.0 | 0.421222 | ||||||||
\(118\) | 56100.0 | 0.370901 | ||||||||
\(119\) | 99078.0 | 0.641372 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −158347. | −0.983210 | ||||||||
\(122\) | 228010. | 1.38693 | ||||||||
\(123\) | 29358.0 | 0.174970 | ||||||||
\(124\) | −44352.0 | −0.259035 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −19845.0 | −0.111359 | ||||||||
\(127\) | 205056. | 1.12814 | 0.564070 | − | 0.825727i | \(-0.309235\pi\) | ||||
0.564070 | + | 0.825727i | \(0.309235\pi\) | |||||||
\(128\) | −102765. | −0.554396 | ||||||||
\(129\) | 48780.0 | 0.258088 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 72964.0 | 0.371476 | 0.185738 | − | 0.982599i | \(-0.440532\pi\) | ||||
0.185738 | + | 0.982599i | \(0.440532\pi\) | |||||||
\(132\) | 3276.00 | 0.0163647 | ||||||||
\(133\) | 84868.0 | 0.416021 | ||||||||
\(134\) | 6980.00 | 0.0335810 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 394290. | 1.82797 | ||||||||
\(137\) | 94182.0 | 0.428713 | 0.214356 | − | 0.976756i | \(-0.431235\pi\) | ||||
0.214356 | + | 0.976756i | \(0.431235\pi\) | |||||||
\(138\) | 25920.0 | 0.115861 | ||||||||
\(139\) | −47796.0 | −0.209824 | −0.104912 | − | 0.994482i | \(-0.533456\pi\) | ||||
−0.104912 | + | 0.994482i | \(0.533456\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7776.00 | 0.0329389 | ||||||||
\(142\) | −93600.0 | −0.389543 | ||||||||
\(143\) | 40040.0 | 0.163740 | ||||||||
\(144\) | −60831.0 | −0.244466 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 231810. | 0.900016 | ||||||||
\(147\) | −21609.0 | −0.0824786 | ||||||||
\(148\) | −51366.0 | −0.192762 | ||||||||
\(149\) | −124266. | −0.458550 | −0.229275 | − | 0.973362i | \(-0.573636\pi\) | ||||
−0.229275 | + | 0.973362i | \(0.573636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −446296. | −1.59287 | −0.796436 | − | 0.604723i | \(-0.793284\pi\) | ||||
−0.796436 | + | 0.604723i | \(0.793284\pi\) | |||||||
\(152\) | 337740. | 1.18570 | ||||||||
\(153\) | 163782. | 0.565637 | ||||||||
\(154\) | −12740.0 | −0.0432880 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 48510.0 | 0.159595 | ||||||||
\(157\) | 159746. | 0.517227 | 0.258613 | − | 0.965981i | \(-0.416734\pi\) | ||||
0.258613 | + | 0.965981i | \(0.416734\pi\) | |||||||
\(158\) | −487120. | −1.55236 | ||||||||
\(159\) | 37638.0 | 0.118068 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 28224.0 | 0.0858132 | ||||||||
\(162\) | −32805.0 | −0.0982093 | ||||||||
\(163\) | −247252. | −0.728905 | −0.364452 | − | 0.931222i | \(-0.618744\pi\) | ||||
−0.364452 | + | 0.931222i | \(0.618744\pi\) | |||||||
\(164\) | 22834.0 | 0.0662937 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −406140. | −1.14395 | ||||||||
\(167\) | 684488. | 1.89922 | 0.949609 | − | 0.313438i | \(-0.101481\pi\) | ||||
0.949609 | + | 0.313438i | \(0.101481\pi\) | |||||||
\(168\) | −85995.0 | −0.235072 | ||||||||
\(169\) | 221607. | 0.596852 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 140292. | 0.366896 | ||||||||
\(172\) | 37940.0 | 0.0977859 | ||||||||
\(173\) | 610474. | 1.55079 | 0.775393 | − | 0.631479i | \(-0.217552\pi\) | ||||
0.775393 | + | 0.631479i | \(0.217552\pi\) | |||||||
\(174\) | 248310. | 0.621758 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −39052.0 | −0.0950302 | ||||||||
\(177\) | 100980. | 0.242271 | ||||||||
\(178\) | 15910.0 | 0.0376374 | ||||||||
\(179\) | 662252. | 1.54487 | 0.772433 | − | 0.635097i | \(-0.219040\pi\) | ||||
0.772433 | + | 0.635097i | \(0.219040\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 154630. | 0.350830 | 0.175415 | − | 0.984495i | \(-0.443873\pi\) | ||||
0.175415 | + | 0.984495i | \(0.443873\pi\) | |||||||
\(182\) | −188650. | −0.422161 | ||||||||
\(183\) | 410418. | 0.905938 | ||||||||
\(184\) | 112320. | 0.244575 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 285120. | 0.604290 | ||||||||
\(187\) | 105144. | 0.219877 | ||||||||
\(188\) | 6048.00 | 0.0124801 | ||||||||
\(189\) | −35721.0 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 486904. | 0.965739 | 0.482870 | − | 0.875692i | \(-0.339594\pi\) | ||||
0.482870 | + | 0.875692i | \(0.339594\pi\) | |||||||
\(192\) | −328113. | −0.642348 | ||||||||
\(193\) | −620546. | −1.19917 | −0.599585 | − | 0.800311i | \(-0.704668\pi\) | ||||
−0.599585 | + | 0.800311i | \(0.704668\pi\) | |||||||
\(194\) | 24570.0 | 0.0468706 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16807.0 | −0.0312500 | ||||||||
\(197\) | 236570. | 0.434304 | 0.217152 | − | 0.976138i | \(-0.430323\pi\) | ||||
0.217152 | + | 0.976138i | \(0.430323\pi\) | |||||||
\(198\) | −21060.0 | −0.0381764 | ||||||||
\(199\) | 82104.0 | 0.146971 | 0.0734855 | − | 0.997296i | \(-0.476588\pi\) | ||||
0.0734855 | + | 0.997296i | \(0.476588\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12564.0 | 0.0219350 | ||||||||
\(202\) | 831770. | 1.43425 | ||||||||
\(203\) | 270382. | 0.460509 | ||||||||
\(204\) | 127386. | 0.214312 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 785800. | 1.29016 | ||||||||
\(207\) | 46656.0 | 0.0756801 | ||||||||
\(208\) | −578270. | −0.926771 | ||||||||
\(209\) | 90064.0 | 0.142622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 99892.0 | 0.154463 | 0.0772315 | − | 0.997013i | \(-0.475392\pi\) | ||||
0.0772315 | + | 0.997013i | \(0.475392\pi\) | |||||||
\(212\) | 29274.0 | 0.0447345 | ||||||||
\(213\) | −168480. | −0.254448 | ||||||||
\(214\) | −33820.0 | −0.0504823 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −142155. | −0.207314 | ||||||||
\(217\) | 310464. | 0.447571 | ||||||||
\(218\) | −891990. | −1.27121 | ||||||||
\(219\) | 417258. | 0.587888 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.55694e6 | 2.14433 | ||||||||
\(222\) | 330210. | 0.449684 | ||||||||
\(223\) | 186704. | 0.251415 | 0.125708 | − | 0.992067i | \(-0.459880\pi\) | ||||
0.125708 | + | 0.992067i | \(0.459880\pi\) | |||||||
\(224\) | −121765. | −0.162145 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −225670. | −0.293902 | ||||||||
\(227\) | −336372. | −0.433267 | −0.216633 | − | 0.976253i | \(-0.569508\pi\) | ||||
−0.216633 | + | 0.976253i | \(0.569508\pi\) | |||||||
\(228\) | 109116. | 0.139012 | ||||||||
\(229\) | −926314. | −1.16727 | −0.583633 | − | 0.812018i | \(-0.698369\pi\) | ||||
−0.583633 | + | 0.812018i | \(0.698369\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22932.0 | −0.0282756 | ||||||||
\(232\) | 1.07601e6 | 1.31249 | ||||||||
\(233\) | −1.25711e6 | −1.51700 | −0.758499 | − | 0.651675i | \(-0.774067\pi\) | ||||
−0.758499 | + | 0.651675i | \(0.774067\pi\) | |||||||
\(234\) | −311850. | −0.372311 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 78540.0 | 0.0917933 | ||||||||
\(237\) | −876816. | −1.01400 | ||||||||
\(238\) | −495390. | −0.566898 | ||||||||
\(239\) | −347016. | −0.392966 | −0.196483 | − | 0.980507i | \(-0.562952\pi\) | ||||
−0.196483 | + | 0.980507i | \(0.562952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 99170.0 | 0.109986 | 0.0549930 | − | 0.998487i | \(-0.482486\pi\) | ||||
0.0549930 | + | 0.998487i | \(0.482486\pi\) | |||||||
\(242\) | 791735. | 0.869043 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 319214. | 0.343247 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −146790. | −0.154653 | ||||||||
\(247\) | 1.33364e6 | 1.39090 | ||||||||
\(248\) | 1.23552e6 | 1.27562 | ||||||||
\(249\) | −731052. | −0.747222 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 344428. | 0.345076 | 0.172538 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172538 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(252\) | −27783.0 | −0.0275599 | ||||||||
\(253\) | 29952.0 | 0.0294188 | ||||||||
\(254\) | −1.02528e6 | −0.997145 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −652799. | −0.622558 | ||||||||
\(257\) | −295130. | −0.278728 | −0.139364 | − | 0.990241i | \(-0.544506\pi\) | ||||
−0.139364 | + | 0.990241i | \(0.544506\pi\) | |||||||
\(258\) | −243900. | −0.228120 | ||||||||
\(259\) | 359562. | 0.333061 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 446958. | 0.406130 | ||||||||
\(262\) | −364820. | −0.328341 | ||||||||
\(263\) | 1.27246e6 | 1.13437 | 0.567187 | − | 0.823589i | \(-0.308032\pi\) | ||||
0.567187 | + | 0.823589i | \(0.308032\pi\) | |||||||
\(264\) | −91260.0 | −0.0805881 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −424340. | −0.367714 | ||||||||
\(267\) | 28638.0 | 0.0245847 | ||||||||
\(268\) | 9772.00 | 0.00831087 | ||||||||
\(269\) | 276774. | 0.233209 | 0.116604 | − | 0.993178i | \(-0.462799\pi\) | ||||
0.116604 | + | 0.993178i | \(0.462799\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.28994e6 | −1.06695 | −0.533476 | − | 0.845815i | \(-0.679115\pi\) | ||||
−0.533476 | + | 0.845815i | \(0.679115\pi\) | |||||||
\(272\) | −1.51852e6 | −1.24451 | ||||||||
\(273\) | −339570. | −0.275755 | ||||||||
\(274\) | −470910. | −0.378932 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 36288.0 | 0.0286741 | ||||||||
\(277\) | −1.71655e6 | −1.34418 | −0.672089 | − | 0.740470i | \(-0.734603\pi\) | ||||
−0.672089 | + | 0.740470i | \(0.734603\pi\) | |||||||
\(278\) | 238980. | 0.185460 | ||||||||
\(279\) | 513216. | 0.394720 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.47218e6 | −1.11223 | −0.556116 | − | 0.831104i | \(-0.687709\pi\) | ||||
−0.556116 | + | 0.831104i | \(0.687709\pi\) | |||||||
\(282\) | −38880.0 | −0.0291141 | ||||||||
\(283\) | −1.02881e6 | −0.763607 | −0.381804 | − | 0.924244i | \(-0.624697\pi\) | ||||
−0.381804 | + | 0.924244i | \(0.624697\pi\) | |||||||
\(284\) | −131040. | −0.0964069 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −200200. | −0.144727 | ||||||||
\(287\) | −159838. | −0.114545 | ||||||||
\(288\) | −201285. | −0.142998 | ||||||||
\(289\) | 2.66863e6 | 1.87950 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 44226.0 | 0.0306158 | ||||||||
\(292\) | 324534. | 0.222742 | ||||||||
\(293\) | 1.18607e6 | 0.807123 | 0.403562 | − | 0.914952i | \(-0.367772\pi\) | ||||
0.403562 | + | 0.914952i | \(0.367772\pi\) | |||||||
\(294\) | 108045. | 0.0729015 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.43091e6 | 0.949255 | ||||||||
\(297\) | −37908.0 | −0.0249367 | ||||||||
\(298\) | 621330. | 0.405305 | ||||||||
\(299\) | 443520. | 0.286903 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −265580. | −0.168958 | ||||||||
\(302\) | 2.23148e6 | 1.40791 | ||||||||
\(303\) | 1.49719e6 | 0.936848 | ||||||||
\(304\) | −1.30073e6 | −0.807242 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −818910. | −0.499957 | ||||||||
\(307\) | −1.51892e6 | −0.919788 | −0.459894 | − | 0.887974i | \(-0.652113\pi\) | ||||
−0.459894 | + | 0.887974i | \(0.652113\pi\) | |||||||
\(308\) | −17836.0 | −0.0107132 | ||||||||
\(309\) | 1.41444e6 | 0.842730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 212808. | 0.124763 | 0.0623817 | − | 0.998052i | \(-0.480130\pi\) | ||||
0.0623817 | + | 0.998052i | \(0.480130\pi\) | |||||||
\(312\) | −1.35135e6 | −0.785925 | ||||||||
\(313\) | 1894.00 | 0.00109275 | 0.000546373 | − | 1.00000i | \(-0.499826\pi\) | ||||
0.000546373 | 1.00000i | \(0.499826\pi\) | ||||||||
\(314\) | −798730. | −0.457168 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −681968. | −0.384190 | ||||||||
\(317\) | 1.57898e6 | 0.882527 | 0.441263 | − | 0.897378i | \(-0.354530\pi\) | ||||
0.441263 | + | 0.897378i | \(0.354530\pi\) | |||||||
\(318\) | −188190. | −0.104359 | ||||||||
\(319\) | 286936. | 0.157873 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −60876.0 | −0.0329749 | ||||||||
\(322\) | −141120. | −0.0758488 | ||||||||
\(323\) | 3.50210e6 | 1.86777 | ||||||||
\(324\) | −45927.0 | −0.0243056 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.23626e6 | 0.644267 | ||||||||
\(327\) | −1.60558e6 | −0.830354 | ||||||||
\(328\) | −636090. | −0.326463 | ||||||||
\(329\) | −42336.0 | −0.0215635 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.39471e6 | −1.70307 | −0.851535 | − | 0.524298i | \(-0.824328\pi\) | ||||
−0.851535 | + | 0.524298i | \(0.824328\pi\) | |||||||
\(332\) | −568596. | −0.283112 | ||||||||
\(333\) | 594378. | 0.293733 | ||||||||
\(334\) | −3.42244e6 | −1.67869 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 331191. | 0.160041 | ||||||||
\(337\) | −2.02731e6 | −0.972403 | −0.486201 | − | 0.873847i | \(-0.661618\pi\) | ||||
−0.486201 | + | 0.873847i | \(0.661618\pi\) | |||||||
\(338\) | −1.10804e6 | −0.527548 | ||||||||
\(339\) | −406206. | −0.191976 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 329472. | 0.153438 | ||||||||
\(342\) | −701460. | −0.324293 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | −1.05690e6 | −0.481546 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.05237e6 | −1.37071 | ||||||||
\(347\) | −3.48885e6 | −1.55546 | −0.777730 | − | 0.628598i | \(-0.783629\pi\) | ||||
−0.777730 | + | 0.628598i | \(0.783629\pi\) | |||||||
\(348\) | 347634. | 0.153877 | ||||||||
\(349\) | 965566. | 0.424344 | 0.212172 | − | 0.977232i | \(-0.431946\pi\) | ||||
0.212172 | + | 0.977232i | \(0.431946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −561330. | −0.243193 | ||||||||
\(352\) | −129220. | −0.0555870 | ||||||||
\(353\) | −1.15393e6 | −0.492882 | −0.246441 | − | 0.969158i | \(-0.579261\pi\) | ||||
−0.246441 | + | 0.969158i | \(0.579261\pi\) | |||||||
\(354\) | −504900. | −0.214140 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 22274.0 | 0.00931479 | ||||||||
\(357\) | −891702. | −0.370296 | ||||||||
\(358\) | −3.31126e6 | −1.36548 | ||||||||
\(359\) | 1.61110e6 | 0.659762 | 0.329881 | − | 0.944022i | \(-0.392991\pi\) | ||||
0.329881 | + | 0.944022i | \(0.392991\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 523725. | 0.211512 | ||||||||
\(362\) | −773150. | −0.310093 | ||||||||
\(363\) | 1.42512e6 | 0.567657 | ||||||||
\(364\) | −264110. | −0.104480 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.05209e6 | −0.800744 | ||||||||
\(367\) | −3.67747e6 | −1.42523 | −0.712614 | − | 0.701557i | \(-0.752489\pi\) | ||||
−0.712614 | + | 0.701557i | \(0.752489\pi\) | |||||||
\(368\) | −432576. | −0.166511 | ||||||||
\(369\) | −264222. | −0.101019 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −204918. | −0.0772939 | ||||||||
\(372\) | 399168. | 0.149554 | ||||||||
\(373\) | −649766. | −0.241816 | −0.120908 | − | 0.992664i | \(-0.538581\pi\) | ||||
−0.120908 | + | 0.992664i | \(0.538581\pi\) | |||||||
\(374\) | −525720. | −0.194346 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −168480. | −0.0614580 | ||||||||
\(377\) | 4.24886e6 | 1.53964 | ||||||||
\(378\) | 178605. | 0.0642931 | ||||||||
\(379\) | 320700. | 0.114683 | 0.0573417 | − | 0.998355i | \(-0.481738\pi\) | ||||
0.0573417 | + | 0.998355i | \(0.481738\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.84550e6 | −0.651332 | ||||||||
\(382\) | −2.43452e6 | −0.853601 | ||||||||
\(383\) | 2.36189e6 | 0.822740 | 0.411370 | − | 0.911469i | \(-0.365050\pi\) | ||||
0.411370 | + | 0.911469i | \(0.365050\pi\) | |||||||
\(384\) | 924885. | 0.320081 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.10273e6 | 1.05993 | ||||||||
\(387\) | −439020. | −0.149007 | ||||||||
\(388\) | 34398.0 | 0.0115999 | ||||||||
\(389\) | −3.53390e6 | −1.18408 | −0.592039 | − | 0.805910i | \(-0.701677\pi\) | ||||
−0.592039 | + | 0.805910i | \(0.701677\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.16467e6 | 0.385267 | ||||||||
\(392\) | 468195. | 0.153890 | ||||||||
\(393\) | −656676. | −0.214472 | ||||||||
\(394\) | −1.18285e6 | −0.383874 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −29484.0 | −0.00944819 | ||||||||
\(397\) | −4.04811e6 | −1.28907 | −0.644534 | − | 0.764575i | \(-0.722949\pi\) | ||||
−0.644534 | + | 0.764575i | \(0.722949\pi\) | |||||||
\(398\) | −410520. | −0.129905 | ||||||||
\(399\) | −763812. | −0.240190 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.07645e6 | 0.644853 | 0.322426 | − | 0.946595i | \(-0.395502\pi\) | ||||
0.322426 | + | 0.946595i | \(0.395502\pi\) | |||||||
\(402\) | −62820.0 | −0.0193880 | ||||||||
\(403\) | 4.87872e6 | 1.49638 | ||||||||
\(404\) | 1.16448e6 | 0.354959 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.35191e6 | −0.407036 | ||||||||
\(407\) | 381576. | 0.114181 | ||||||||
\(408\) | −3.54861e6 | −1.05538 | ||||||||
\(409\) | 2.57431e6 | 0.760945 | 0.380472 | − | 0.924792i | \(-0.375761\pi\) | ||||
0.380472 | + | 0.924792i | \(0.375761\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −847638. | −0.247517 | ||||||||
\(412\) | 1.10012e6 | 0.319299 | ||||||||
\(413\) | −549780. | −0.158604 | ||||||||
\(414\) | −233280. | −0.0668924 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.91345e6 | −0.542105 | ||||||||
\(417\) | 430164. | 0.121142 | ||||||||
\(418\) | −450320. | −0.126061 | ||||||||
\(419\) | 848148. | 0.236013 | 0.118007 | − | 0.993013i | \(-0.462350\pi\) | ||||
0.118007 | + | 0.993013i | \(0.462350\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.43682e6 | 0.395092 | 0.197546 | − | 0.980294i | \(-0.436703\pi\) | ||||
0.197546 | + | 0.980294i | \(0.436703\pi\) | |||||||
\(422\) | −499460. | −0.136527 | ||||||||
\(423\) | −69984.0 | −0.0190173 | ||||||||
\(424\) | −815490. | −0.220295 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 842400. | 0.224903 | ||||||||
\(427\) | −2.23450e6 | −0.593076 | ||||||||
\(428\) | −47348.0 | −0.0124937 | ||||||||
\(429\) | −360360. | −0.0945352 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.35438e6 | 0.610496 | 0.305248 | − | 0.952273i | \(-0.401261\pi\) | ||||
0.305248 | + | 0.952273i | \(0.401261\pi\) | |||||||
\(432\) | 547479. | 0.141143 | ||||||||
\(433\) | 3.78808e6 | 0.970955 | 0.485478 | − | 0.874249i | \(-0.338646\pi\) | ||||
0.485478 | + | 0.874249i | \(0.338646\pi\) | |||||||
\(434\) | −1.55232e6 | −0.395601 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.24879e6 | −0.314609 | ||||||||
\(437\) | 997632. | 0.249900 | ||||||||
\(438\) | −2.08629e6 | −0.519624 | ||||||||
\(439\) | −3.64322e6 | −0.902245 | −0.451123 | − | 0.892462i | \(-0.648976\pi\) | ||||
−0.451123 | + | 0.892462i | \(0.648976\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | −7.78470e6 | −1.89534 | ||||||||
\(443\) | −2.48389e6 | −0.601345 | −0.300672 | − | 0.953728i | \(-0.597211\pi\) | ||||
−0.300672 | + | 0.953728i | \(0.597211\pi\) | |||||||
\(444\) | 462294. | 0.111291 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −933520. | −0.222222 | ||||||||
\(447\) | 1.11839e6 | 0.264744 | ||||||||
\(448\) | 1.78639e6 | 0.420515 | ||||||||
\(449\) | −2.63177e6 | −0.616074 | −0.308037 | − | 0.951374i | \(-0.599672\pi\) | ||||
−0.308037 | + | 0.951374i | \(0.599672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −169624. | −0.0392686 | ||||||||
\(452\) | −315938. | −0.0727371 | ||||||||
\(453\) | 4.01666e6 | 0.919645 | ||||||||
\(454\) | 1.68186e6 | 0.382957 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.03966e6 | −0.684562 | ||||||||
\(457\) | 1.16130e6 | 0.260109 | 0.130054 | − | 0.991507i | \(-0.458485\pi\) | ||||
0.130054 | + | 0.991507i | \(0.458485\pi\) | |||||||
\(458\) | 4.63157e6 | 1.03173 | ||||||||
\(459\) | −1.47404e6 | −0.326571 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.81385e6 | 0.616663 | 0.308332 | − | 0.951279i | \(-0.400229\pi\) | ||||
0.308332 | + | 0.951279i | \(0.400229\pi\) | |||||||
\(462\) | 114660. | 0.0249923 | ||||||||
\(463\) | −6.84299e6 | −1.48352 | −0.741760 | − | 0.670665i | \(-0.766009\pi\) | ||||
−0.741760 | + | 0.670665i | \(0.766009\pi\) | |||||||
\(464\) | −4.14402e6 | −0.893566 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.28557e6 | 1.34085 | ||||||||
\(467\) | −3.34314e6 | −0.709353 | −0.354676 | − | 0.934989i | \(-0.615409\pi\) | ||||
−0.354676 | + | 0.934989i | \(0.615409\pi\) | |||||||
\(468\) | −436590. | −0.0921423 | ||||||||
\(469\) | −68404.0 | −0.0143598 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.43771e6 | −0.298621 | ||||||||
\(472\) | −2.18790e6 | −0.452035 | ||||||||
\(473\) | −281840. | −0.0579228 | ||||||||
\(474\) | 4.38408e6 | 0.896257 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −693546. | −0.140300 | ||||||||
\(477\) | −338742. | −0.0681668 | ||||||||
\(478\) | 1.73508e6 | 0.347336 | ||||||||
\(479\) | −4.28248e6 | −0.852818 | −0.426409 | − | 0.904530i | \(-0.640222\pi\) | ||||
−0.426409 | + | 0.904530i | \(0.640222\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.65026e6 | 1.11354 | ||||||||
\(482\) | −495850. | −0.0972149 | ||||||||
\(483\) | −254016. | −0.0495442 | ||||||||
\(484\) | 1.10843e6 | 0.215077 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 295245. | 0.0567012 | ||||||||
\(487\) | 8.93175e6 | 1.70653 | 0.853266 | − | 0.521477i | \(-0.174619\pi\) | ||||
0.853266 | + | 0.521477i | \(0.174619\pi\) | |||||||
\(488\) | −8.89239e6 | −1.69032 | ||||||||
\(489\) | 2.22527e6 | 0.420833 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.75306e6 | 0.515361 | 0.257681 | − | 0.966230i | \(-0.417042\pi\) | ||||
0.257681 | + | 0.966230i | \(0.417042\pi\) | |||||||
\(492\) | −205506. | −0.0382747 | ||||||||
\(493\) | 1.11574e7 | 2.06750 | ||||||||
\(494\) | −6.66820e6 | −1.22939 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.75834e6 | −0.868462 | ||||||||
\(497\) | 917280. | 0.166575 | ||||||||
\(498\) | 3.65526e6 | 0.660458 | ||||||||
\(499\) | 4.80408e6 | 0.863693 | 0.431846 | − | 0.901947i | \(-0.357862\pi\) | ||||
0.431846 | + | 0.901947i | \(0.357862\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.16039e6 | −1.09651 | ||||||||
\(502\) | −1.72214e6 | −0.305007 | ||||||||
\(503\) | 6.02465e6 | 1.06172 | 0.530862 | − | 0.847458i | \(-0.321868\pi\) | ||||
0.530862 | + | 0.847458i | \(0.321868\pi\) | |||||||
\(504\) | 773955. | 0.135719 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −149760. | −0.0260028 | ||||||||
\(507\) | −1.99446e6 | −0.344593 | ||||||||
\(508\) | −1.43539e6 | −0.246781 | ||||||||
\(509\) | −8.42987e6 | −1.44220 | −0.721101 | − | 0.692830i | \(-0.756364\pi\) | ||||
−0.721101 | + | 0.692830i | \(0.756364\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.27174e6 | −0.384863 | ||||||||
\(512\) | 6.55248e6 | 1.10466 | ||||||||
\(513\) | −1.26263e6 | −0.211827 | ||||||||
\(514\) | 1.47565e6 | 0.246363 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −341460. | −0.0564567 | ||||||||
\(517\) | −44928.0 | −0.00739249 | ||||||||
\(518\) | −1.79781e6 | −0.294388 | ||||||||
\(519\) | −5.49427e6 | −0.895347 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.25058e6 | 1.49305 | 0.746525 | − | 0.665357i | \(-0.231721\pi\) | ||||
0.746525 | + | 0.665357i | \(0.231721\pi\) | |||||||
\(522\) | −2.23479e6 | −0.358972 | ||||||||
\(523\) | −5.84494e6 | −0.934385 | −0.467192 | − | 0.884156i | \(-0.654734\pi\) | ||||
−0.467192 | + | 0.884156i | \(0.654734\pi\) | |||||||
\(524\) | −510748. | −0.0812603 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.36232e6 | −1.00265 | ||||||||
\(527\) | 1.28114e7 | 2.00942 | ||||||||
\(528\) | 351468. | 0.0548657 | ||||||||
\(529\) | −6.10457e6 | −0.948453 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −908820. | −0.139875 | ||||||||
\(532\) | −594076. | −0.0910045 | ||||||||
\(533\) | −2.51174e6 | −0.382963 | ||||||||
\(534\) | −143190. | −0.0217300 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −272220. | −0.0409268 | ||||||||
\(537\) | −5.96027e6 | −0.891929 | ||||||||
\(538\) | −1.38387e6 | −0.206129 | ||||||||
\(539\) | 124852. | 0.0185107 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.22533e6 | 1.35515 | 0.677577 | − | 0.735452i | \(-0.263030\pi\) | ||||
0.677577 | + | 0.735452i | \(0.263030\pi\) | |||||||
\(542\) | 6.44968e6 | 0.943061 | ||||||||
\(543\) | −1.39167e6 | −0.202552 | ||||||||
\(544\) | −5.02467e6 | −0.727965 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.69785e6 | 0.243735 | ||||||||
\(547\) | 6.44337e6 | 0.920757 | 0.460378 | − | 0.887723i | \(-0.347714\pi\) | ||||
0.460378 | + | 0.887723i | \(0.347714\pi\) | |||||||
\(548\) | −659274. | −0.0937809 | ||||||||
\(549\) | −3.69376e6 | −0.523044 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.55718e6 | 1.34107 | ||||||||
\(552\) | −1.01088e6 | −0.141206 | ||||||||
\(553\) | 4.77378e6 | 0.663818 | ||||||||
\(554\) | 8.58275e6 | 1.18810 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 334572. | 0.0458989 | ||||||||
\(557\) | −3.74213e6 | −0.511070 | −0.255535 | − | 0.966800i | \(-0.582252\pi\) | ||||
−0.255535 | + | 0.966800i | \(0.582252\pi\) | |||||||
\(558\) | −2.56608e6 | −0.348887 | ||||||||
\(559\) | −4.17340e6 | −0.564886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −946296. | −0.126946 | ||||||||
\(562\) | 7.36091e6 | 0.983084 | ||||||||
\(563\) | 1.46384e7 | 1.94635 | 0.973176 | − | 0.230060i | \(-0.0738923\pi\) | ||||
0.973176 | + | 0.230060i | \(0.0738923\pi\) | |||||||
\(564\) | −54432.0 | −0.00720537 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.14406e6 | 0.674940 | ||||||||
\(567\) | 321489. | 0.0419961 | ||||||||
\(568\) | 3.65040e6 | 0.474755 | ||||||||
\(569\) | 1.41805e7 | 1.83616 | 0.918078 | − | 0.396400i | \(-0.129741\pi\) | ||||
0.918078 | + | 0.396400i | \(0.129741\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.25160e6 | −0.160648 | −0.0803242 | − | 0.996769i | \(-0.525596\pi\) | ||||
−0.0803242 | + | 0.996769i | \(0.525596\pi\) | |||||||
\(572\) | −280280. | −0.0358181 | ||||||||
\(573\) | −4.38214e6 | −0.557570 | ||||||||
\(574\) | 799190. | 0.101244 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.95302e6 | 0.370860 | ||||||||
\(577\) | −5.94378e6 | −0.743230 | −0.371615 | − | 0.928387i | \(-0.621196\pi\) | ||||
−0.371615 | + | 0.928387i | \(0.621196\pi\) | |||||||
\(578\) | −1.33431e7 | −1.66126 | ||||||||
\(579\) | 5.58491e6 | 0.692341 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.98017e6 | 0.489172 | ||||||||
\(582\) | −221130. | −0.0270608 | ||||||||
\(583\) | −217464. | −0.0264982 | ||||||||
\(584\) | −9.04059e6 | −1.09689 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.93033e6 | −0.713403 | ||||||||
\(587\) | 6.46192e6 | 0.774046 | 0.387023 | − | 0.922070i | \(-0.373503\pi\) | ||||
0.387023 | + | 0.922070i | \(0.373503\pi\) | |||||||
\(588\) | 151263. | 0.0180422 | ||||||||
\(589\) | 1.09740e7 | 1.30339 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.12913e6 | −0.250746 | ||||||||
\(592\) | −5.51084e6 | −0.646269 | ||||||||
\(593\) | 2.34605e6 | 0.273969 | 0.136984 | − | 0.990573i | \(-0.456259\pi\) | ||||
0.136984 | + | 0.990573i | \(0.456259\pi\) | |||||||
\(594\) | 189540. | 0.0220412 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 869862. | 0.100308 | ||||||||
\(597\) | −738936. | −0.0848537 | ||||||||
\(598\) | −2.21760e6 | −0.253589 | ||||||||
\(599\) | −1.34959e7 | −1.53686 | −0.768432 | − | 0.639931i | \(-0.778963\pi\) | ||||
−0.768432 | + | 0.639931i | \(0.778963\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.87849e6 | 0.438002 | 0.219001 | − | 0.975725i | \(-0.429720\pi\) | ||||
0.219001 | + | 0.975725i | \(0.429720\pi\) | |||||||
\(602\) | 1.32790e6 | 0.149339 | ||||||||
\(603\) | −113076. | −0.0126642 | ||||||||
\(604\) | 3.12407e6 | 0.348441 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.48593e6 | −0.828065 | ||||||||
\(607\) | 533488. | 0.0587696 | 0.0293848 | − | 0.999568i | \(-0.490645\pi\) | ||||
0.0293848 | + | 0.999568i | \(0.490645\pi\) | |||||||
\(608\) | −4.30402e6 | −0.472188 | ||||||||
\(609\) | −2.43344e6 | −0.265875 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −665280. | −0.0720944 | ||||||||
\(612\) | −1.14647e6 | −0.123733 | ||||||||
\(613\) | −5.14610e6 | −0.553130 | −0.276565 | − | 0.960995i | \(-0.589196\pi\) | ||||
−0.276565 | + | 0.960995i | \(0.589196\pi\) | |||||||
\(614\) | 7.59458e6 | 0.812986 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 496860. | 0.0527573 | ||||||||
\(617\) | 2.37860e6 | 0.251541 | 0.125770 | − | 0.992059i | \(-0.459860\pi\) | ||||
0.125770 | + | 0.992059i | \(0.459860\pi\) | |||||||
\(618\) | −7.07220e6 | −0.744875 | ||||||||
\(619\) | 1.60023e7 | 1.67863 | 0.839317 | − | 0.543642i | \(-0.182955\pi\) | ||||
0.839317 | + | 0.543642i | \(0.182955\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −419904. | −0.0436939 | ||||||||
\(622\) | −1.06404e6 | −0.110276 | ||||||||
\(623\) | −155918. | −0.0160944 | ||||||||
\(624\) | 5.20443e6 | 0.535071 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9470.00 | −0.000965860 0 | ||||||||
\(627\) | −810576. | −0.0823427 | ||||||||
\(628\) | −1.11822e6 | −0.113143 | ||||||||
\(629\) | 1.48374e7 | 1.49531 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.23459e7 | 1.23439 | 0.617193 | − | 0.786812i | \(-0.288270\pi\) | ||||
0.617193 | + | 0.786812i | \(0.288270\pi\) | |||||||
\(632\) | 1.89977e7 | 1.89194 | ||||||||
\(633\) | −899028. | −0.0891793 | ||||||||
\(634\) | −7.89489e6 | −0.780051 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −263466. | −0.0258275 | ||||||||
\(637\) | 1.84877e6 | 0.180524 | ||||||||
\(638\) | −1.43468e6 | −0.139541 | ||||||||
\(639\) | 1.51632e6 | 0.146906 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.43755e6 | −0.330449 | −0.165224 | − | 0.986256i | \(-0.552835\pi\) | ||||
−0.165224 | + | 0.986256i | \(0.552835\pi\) | |||||||
\(642\) | 304380. | 0.0291460 | ||||||||
\(643\) | 1.62191e7 | 1.54703 | 0.773515 | − | 0.633778i | \(-0.218497\pi\) | ||||
0.773515 | + | 0.633778i | \(0.218497\pi\) | |||||||
\(644\) | −197568. | −0.0187716 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.75105e7 | −1.65089 | ||||||||
\(647\) | −1.19929e7 | −1.12632 | −0.563160 | − | 0.826348i | \(-0.690415\pi\) | ||||
−0.563160 | + | 0.826348i | \(0.690415\pi\) | |||||||
\(648\) | 1.27940e6 | 0.119693 | ||||||||
\(649\) | −583440. | −0.0543731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.79418e6 | −0.258405 | ||||||||
\(652\) | 1.73076e6 | 0.159448 | ||||||||
\(653\) | −1.58009e6 | −0.145011 | −0.0725053 | − | 0.997368i | \(-0.523099\pi\) | ||||
−0.0725053 | + | 0.997368i | \(0.523099\pi\) | |||||||
\(654\) | 8.02791e6 | 0.733936 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.44976e6 | 0.222262 | ||||||||
\(657\) | −3.75532e6 | −0.339417 | ||||||||
\(658\) | 211680. | 0.0190597 | ||||||||
\(659\) | 6.98358e6 | 0.626419 | 0.313209 | − | 0.949684i | \(-0.398596\pi\) | ||||
0.313209 | + | 0.949684i | \(0.398596\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.69602e6 | 0.329027 | 0.164513 | − | 0.986375i | \(-0.447395\pi\) | ||||
0.164513 | + | 0.986375i | \(0.447395\pi\) | |||||||
\(662\) | 1.69735e7 | 1.50532 | ||||||||
\(663\) | −1.40125e7 | −1.23803 | ||||||||
\(664\) | 1.58395e7 | 1.39418 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.97189e6 | −0.259625 | ||||||||
\(667\) | 3.17837e6 | 0.276624 | ||||||||
\(668\) | −4.79142e6 | −0.415454 | ||||||||
\(669\) | −1.68034e6 | −0.145155 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.37130e6 | −0.203320 | ||||||||
\(672\) | 1.09588e6 | 0.0936142 | ||||||||
\(673\) | −1.84688e6 | −0.157182 | −0.0785908 | − | 0.996907i | \(-0.525042\pi\) | ||||
−0.0785908 | + | 0.996907i | \(0.525042\pi\) | |||||||
\(674\) | 1.01366e7 | 0.859491 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.55125e6 | −0.130561 | ||||||||
\(677\) | 7.68501e6 | 0.644426 | 0.322213 | − | 0.946667i | \(-0.395573\pi\) | ||||
0.322213 | + | 0.946667i | \(0.395573\pi\) | |||||||
\(678\) | 2.03103e6 | 0.169684 | ||||||||
\(679\) | −240786. | −0.0200427 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.02735e6 | 0.250147 | ||||||||
\(682\) | −1.64736e6 | −0.135621 | ||||||||
\(683\) | −7.12180e6 | −0.584168 | −0.292084 | − | 0.956393i | \(-0.594349\pi\) | ||||
−0.292084 | + | 0.956393i | \(0.594349\pi\) | |||||||
\(684\) | −982044. | −0.0802584 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −588245. | −0.0477252 | ||||||||
\(687\) | 8.33683e6 | 0.673921 | ||||||||
\(688\) | 4.07042e6 | 0.327845 | ||||||||
\(689\) | −3.22014e6 | −0.258420 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.23787e6 | −0.257967 | −0.128983 | − | 0.991647i | \(-0.541171\pi\) | ||||
−0.128983 | + | 0.991647i | \(0.541171\pi\) | |||||||
\(692\) | −4.27332e6 | −0.339234 | ||||||||
\(693\) | 206388. | 0.0163249 | ||||||||
\(694\) | 1.74443e7 | 1.37485 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.68409e6 | −0.757767 | ||||||||
\(697\) | −6.59576e6 | −0.514260 | ||||||||
\(698\) | −4.82783e6 | −0.375071 | ||||||||
\(699\) | 1.13140e7 | 0.875839 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.39163e6 | −0.568127 | −0.284063 | − | 0.958805i | \(-0.591683\pi\) | ||||
−0.284063 | + | 0.958805i | \(0.591683\pi\) | |||||||
\(702\) | 2.80665e6 | 0.214954 | ||||||||
\(703\) | 1.27094e7 | 0.969923 | ||||||||
\(704\) | 1.89576e6 | 0.144163 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.76965e6 | 0.435650 | ||||||||
\(707\) | −8.15135e6 | −0.613311 | ||||||||
\(708\) | −706860. | −0.0529969 | ||||||||
\(709\) | −5.33361e6 | −0.398479 | −0.199240 | − | 0.979951i | \(-0.563847\pi\) | ||||
−0.199240 | + | 0.979951i | \(0.563847\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.89134e6 | 0.585433 | ||||||||
\(712\) | −620490. | −0.0458706 | ||||||||
\(713\) | 3.64954e6 | 0.268852 | ||||||||
\(714\) | 4.45851e6 | 0.327299 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.63576e6 | −0.337939 | ||||||||
\(717\) | 3.12314e6 | 0.226879 | ||||||||
\(718\) | −8.05552e6 | −0.583153 | ||||||||
\(719\) | −1.14564e7 | −0.826468 | −0.413234 | − | 0.910625i | \(-0.635601\pi\) | ||||
−0.413234 | + | 0.910625i | \(0.635601\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.70084e6 | −0.551696 | ||||||||
\(722\) | −2.61862e6 | −0.186952 | ||||||||
\(723\) | −892530. | −0.0635005 | ||||||||
\(724\) | −1.08241e6 | −0.0767442 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −7.12562e6 | −0.501742 | ||||||||
\(727\) | 2.49540e7 | 1.75107 | 0.875536 | − | 0.483153i | \(-0.160508\pi\) | ||||
0.875536 | + | 0.483153i | \(0.160508\pi\) | |||||||
\(728\) | 7.35735e6 | 0.514509 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.09592e7 | −0.758555 | ||||||||
\(732\) | −2.87293e6 | −0.198174 | ||||||||
\(733\) | 1.43398e7 | 0.985789 | 0.492894 | − | 0.870089i | \(-0.335939\pi\) | ||||
0.492894 | + | 0.870089i | \(0.335939\pi\) | |||||||
\(734\) | 1.83874e7 | 1.25974 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.43136e6 | −0.0973990 | ||||||||
\(737\) | −72592.0 | −0.00492289 | ||||||||
\(738\) | 1.32111e6 | 0.0892890 | ||||||||
\(739\) | 922932. | 0.0621668 | 0.0310834 | − | 0.999517i | \(-0.490104\pi\) | ||||
0.0310834 | + | 0.999517i | \(0.490104\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.20028e7 | −0.803037 | ||||||||
\(742\) | 1.02459e6 | 0.0683188 | ||||||||
\(743\) | 9.38995e6 | 0.624010 | 0.312005 | − | 0.950081i | \(-0.398999\pi\) | ||||
0.312005 | + | 0.950081i | \(0.398999\pi\) | |||||||
\(744\) | −1.11197e7 | −0.736478 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.24883e6 | 0.213737 | ||||||||
\(747\) | 6.57947e6 | 0.431409 | ||||||||
\(748\) | −736008. | −0.0480982 | ||||||||
\(749\) | 331436. | 0.0215871 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −408032. | −0.0263994 | −0.0131997 | − | 0.999913i | \(-0.504202\pi\) | ||||
−0.0131997 | + | 0.999913i | \(0.504202\pi\) | |||||||
\(752\) | 648864. | 0.0418417 | ||||||||
\(753\) | −3.09985e6 | −0.199229 | ||||||||
\(754\) | −2.12443e7 | −1.36086 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 250047. | 0.0159117 | ||||||||
\(757\) | −2.59605e7 | −1.64654 | −0.823271 | − | 0.567649i | \(-0.807853\pi\) | ||||
−0.823271 | + | 0.567649i | \(0.807853\pi\) | |||||||
\(758\) | −1.60350e6 | −0.101367 | ||||||||
\(759\) | −269568. | −0.0169849 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.83554e7 | 1.14895 | 0.574477 | − | 0.818521i | \(-0.305206\pi\) | ||||
0.574477 | + | 0.818521i | \(0.305206\pi\) | |||||||
\(762\) | 9.22752e6 | 0.575702 | ||||||||
\(763\) | 8.74150e6 | 0.543594 | ||||||||
\(764\) | −3.40833e6 | −0.211255 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.18094e7 | −0.727206 | ||||||||
\(767\) | −8.63940e6 | −0.530268 | ||||||||
\(768\) | 5.87519e6 | 0.359434 | ||||||||
\(769\) | −747166. | −0.0455618 | −0.0227809 | − | 0.999740i | \(-0.507252\pi\) | ||||
−0.0227809 | + | 0.999740i | \(0.507252\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.65617e6 | 0.160924 | ||||||||
\(772\) | 4.34382e6 | 0.262318 | ||||||||
\(773\) | −2.02692e7 | −1.22008 | −0.610038 | − | 0.792372i | \(-0.708846\pi\) | ||||
−0.610038 | + | 0.792372i | \(0.708846\pi\) | |||||||
\(774\) | 2.19510e6 | 0.131705 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −958230. | −0.0571236 | ||||||||
\(777\) | −3.23606e6 | −0.192293 | ||||||||
\(778\) | 1.76695e7 | 1.04659 | ||||||||
\(779\) | −5.64978e6 | −0.333571 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 973440. | 0.0571060 | ||||||||
\(782\) | −5.82336e6 | −0.340531 | ||||||||
\(783\) | −4.02262e6 | −0.234479 | ||||||||
\(784\) | −1.80315e6 | −0.104771 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.28338e6 | 0.189568 | ||||||||
\(787\) | 4.69982e6 | 0.270486 | 0.135243 | − | 0.990812i | \(-0.456819\pi\) | ||||
0.135243 | + | 0.990812i | \(0.456819\pi\) | |||||||
\(788\) | −1.65599e6 | −0.0950041 | ||||||||
\(789\) | −1.14522e7 | −0.654931 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.21157e6 | 0.125678 | ||||||||
\(792\) | 821340. | 0.0465275 | ||||||||
\(793\) | −3.51135e7 | −1.98286 | ||||||||
\(794\) | 2.02406e7 | 1.13939 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −574728. | −0.0321499 | ||||||||
\(797\) | −584710. | −0.0326058 | −0.0163029 | − | 0.999867i | \(-0.505190\pi\) | ||||
−0.0163029 | + | 0.999867i | \(0.505190\pi\) | |||||||
\(798\) | 3.81906e6 | 0.212300 | ||||||||
\(799\) | −1.74701e6 | −0.0968117 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −257742. | −0.0141940 | ||||||||
\(802\) | −1.03822e7 | −0.569975 | ||||||||
\(803\) | −2.41082e6 | −0.131940 | ||||||||
\(804\) | −87948.0 | −0.00479828 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.43936e7 | −1.32263 | ||||||||
\(807\) | −2.49097e6 | −0.134643 | ||||||||
\(808\) | −3.24390e7 | −1.74799 | ||||||||
\(809\) | −1.64013e7 | −0.881061 | −0.440531 | − | 0.897738i | \(-0.645210\pi\) | ||||
−0.440531 | + | 0.897738i | \(0.645210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −304948. | −0.0162807 | −0.00814036 | − | 0.999967i | \(-0.502591\pi\) | ||||
−0.00814036 | + | 0.999967i | \(0.502591\pi\) | |||||||
\(812\) | −1.89267e6 | −0.100736 | ||||||||
\(813\) | 1.16094e7 | 0.616005 | ||||||||
\(814\) | −1.90788e6 | −0.100923 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.36667e7 | 0.718519 | ||||||||
\(817\) | −9.38744e6 | −0.492031 | ||||||||
\(818\) | −1.28716e7 | −0.672587 | ||||||||
\(819\) | 3.05613e6 | 0.159207 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.43428e7 | 1.77819 | 0.889095 | − | 0.457722i | \(-0.151335\pi\) | ||||
0.889095 | + | 0.457722i | \(0.151335\pi\) | |||||||
\(822\) | 4.23819e6 | 0.218777 | ||||||||
\(823\) | −1.56684e7 | −0.806351 | −0.403176 | − | 0.915123i | \(-0.632094\pi\) | ||||
−0.403176 | + | 0.915123i | \(0.632094\pi\) | |||||||
\(824\) | −3.06462e7 | −1.57238 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.74890e6 | 0.140187 | ||||||||
\(827\) | 2.96886e7 | 1.50948 | 0.754738 | − | 0.656026i | \(-0.227764\pi\) | ||||
0.754738 | + | 0.656026i | \(0.227764\pi\) | |||||||
\(828\) | −326592. | −0.0165550 | ||||||||
\(829\) | −2.30708e7 | −1.16594 | −0.582970 | − | 0.812494i | \(-0.698110\pi\) | ||||
−0.582970 | + | 0.812494i | \(0.698110\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.54490e7 | 0.776062 | ||||||||
\(832\) | 2.80719e7 | 1.40593 | ||||||||
\(833\) | 4.85482e6 | 0.242416 | ||||||||
\(834\) | −2.15082e6 | −0.107075 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −630448. | −0.0311985 | ||||||||
\(837\) | −4.61894e6 | −0.227892 | ||||||||
\(838\) | −4.24074e6 | −0.208608 | ||||||||
\(839\) | 2.32642e7 | 1.14100 | 0.570498 | − | 0.821299i | \(-0.306750\pi\) | ||||
0.570498 | + | 0.821299i | \(0.306750\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.93718e6 | 0.484477 | ||||||||
\(842\) | −7.18411e6 | −0.349215 | ||||||||
\(843\) | 1.32496e7 | 0.642148 | ||||||||
\(844\) | −699244. | −0.0337888 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 349920. | 0.0168090 | ||||||||
\(847\) | −7.75900e6 | −0.371619 | ||||||||
\(848\) | 3.14068e6 | 0.149980 | ||||||||
\(849\) | 9.25931e6 | 0.440869 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.22669e6 | 0.200067 | ||||||||
\(852\) | 1.17936e6 | 0.0556605 | ||||||||
\(853\) | −1.91515e7 | −0.901219 | −0.450610 | − | 0.892721i | \(-0.648793\pi\) | ||||
−0.450610 | + | 0.892721i | \(0.648793\pi\) | |||||||
\(854\) | 1.11725e7 | 0.524210 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.31898e6 | 0.0615253 | ||||||||
\(857\) | 5.34683e6 | 0.248682 | 0.124341 | − | 0.992240i | \(-0.460318\pi\) | ||||
0.124341 | + | 0.992240i | \(0.460318\pi\) | |||||||
\(858\) | 1.80180e6 | 0.0835581 | ||||||||
\(859\) | 3.95858e7 | 1.83045 | 0.915223 | − | 0.402948i | \(-0.132014\pi\) | ||||
0.915223 | + | 0.402948i | \(0.132014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.43854e6 | 0.0661325 | ||||||||
\(862\) | −1.17719e7 | −0.539607 | ||||||||
\(863\) | 2.50284e7 | 1.14395 | 0.571973 | − | 0.820272i | \(-0.306178\pi\) | ||||
0.571973 | + | 0.820272i | \(0.306178\pi\) | |||||||
\(864\) | 1.81156e6 | 0.0825600 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.89404e7 | −0.858211 | ||||||||
\(867\) | −2.40176e7 | −1.08513 | ||||||||
\(868\) | −2.17325e6 | −0.0979062 | ||||||||
\(869\) | 5.06605e6 | 0.227573 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.07492e6 | −0.0480099 | ||||||||
\(872\) | 3.47876e7 | 1.54929 | ||||||||
\(873\) | −398034. | −0.0176760 | ||||||||
\(874\) | −4.98816e6 | −0.220883 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.92081e6 | −0.128600 | ||||||||
\(877\) | 5.02589e6 | 0.220655 | 0.110328 | − | 0.993895i | \(-0.464810\pi\) | ||||
0.110328 | + | 0.993895i | \(0.464810\pi\) | |||||||
\(878\) | 1.82161e7 | 0.797480 | ||||||||
\(879\) | −1.06746e7 | −0.465993 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.60490e7 | −1.13071 | −0.565356 | − | 0.824847i | \(-0.691261\pi\) | ||||
−0.565356 | + | 0.824847i | \(0.691261\pi\) | |||||||
\(882\) | −972405. | −0.0420897 | ||||||||
\(883\) | 6.82462e6 | 0.294562 | 0.147281 | − | 0.989095i | \(-0.452948\pi\) | ||||
0.147281 | + | 0.989095i | \(0.452948\pi\) | |||||||
\(884\) | −1.08986e7 | −0.469072 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.24195e7 | 0.531519 | ||||||||
\(887\) | −2.33835e7 | −0.997931 | −0.498965 | − | 0.866622i | \(-0.666287\pi\) | ||||
−0.498965 | + | 0.866622i | \(0.666287\pi\) | |||||||
\(888\) | −1.28782e7 | −0.548053 | ||||||||
\(889\) | 1.00477e7 | 0.426397 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 341172. | 0.0143972 | ||||||||
\(892\) | −1.30693e6 | −0.0549971 | ||||||||
\(893\) | −1.49645e6 | −0.0627961 | ||||||||
\(894\) | −5.59197e6 | −0.234003 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5.03548e6 | −0.209542 | ||||||||
\(897\) | −3.99168e6 | −0.165644 | ||||||||
\(898\) | 1.31589e7 | 0.544537 | ||||||||
\(899\) | 3.49620e7 | 1.44277 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.45600e6 | −0.347019 | ||||||||
\(902\) | 848120. | 0.0347089 | ||||||||
\(903\) | 2.39022e6 | 0.0975480 | ||||||||
\(904\) | 8.80113e6 | 0.358193 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.00833e7 | −0.812859 | ||||||||
\(907\) | −3.95959e7 | −1.59820 | −0.799102 | − | 0.601196i | \(-0.794691\pi\) | ||||
−0.799102 | + | 0.601196i | \(0.794691\pi\) | |||||||
\(908\) | 2.35460e6 | 0.0947771 | ||||||||
\(909\) | −1.34747e7 | −0.540890 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.67570e6 | −0.186660 | −0.0933300 | − | 0.995635i | \(-0.529751\pi\) | ||||
−0.0933300 | + | 0.995635i | \(0.529751\pi\) | |||||||
\(912\) | 1.17066e7 | 0.466062 | ||||||||
\(913\) | 4.22386e6 | 0.167700 | ||||||||
\(914\) | −5.80651e6 | −0.229906 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.48420e6 | 0.255339 | ||||||||
\(917\) | 3.57524e6 | 0.140405 | ||||||||
\(918\) | 7.37019e6 | 0.288650 | ||||||||
\(919\) | −4.92594e6 | −0.192398 | −0.0961990 | − | 0.995362i | \(-0.530669\pi\) | ||||
−0.0961990 | + | 0.995362i | \(0.530669\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.36702e7 | 0.531040 | ||||||||
\(922\) | −1.40692e7 | −0.545058 | ||||||||
\(923\) | 1.44144e7 | 0.556919 | ||||||||
\(924\) | 160524. | 0.00618529 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.42150e7 | 1.31126 | ||||||||
\(927\) | −1.27300e7 | −0.486550 | ||||||||
\(928\) | −1.37122e7 | −0.522683 | ||||||||
\(929\) | −3.23688e7 | −1.23052 | −0.615258 | − | 0.788326i | \(-0.710948\pi\) | ||||
−0.615258 | + | 0.788326i | \(0.710948\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.15853e6 | 0.157241 | ||||||||
\(932\) | 8.79980e6 | 0.331843 | ||||||||
\(933\) | −1.91527e6 | −0.0720321 | ||||||||
\(934\) | 1.67157e7 | 0.626985 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.21622e7 | 0.453754 | ||||||||
\(937\) | 3.32337e7 | 1.23660 | 0.618301 | − | 0.785941i | \(-0.287821\pi\) | ||||
0.618301 | + | 0.785941i | \(0.287821\pi\) | |||||||
\(938\) | 342020. | 0.0126924 | ||||||||
\(939\) | −17046.0 | −0.000630897 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.66426e7 | −0.980852 | −0.490426 | − | 0.871483i | \(-0.663159\pi\) | ||||
−0.490426 | + | 0.871483i | \(0.663159\pi\) | |||||||
\(942\) | 7.18857e6 | 0.263946 | ||||||||
\(943\) | −1.87891e6 | −0.0688061 | ||||||||
\(944\) | 8.42622e6 | 0.307753 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.40920e6 | 0.0511970 | ||||||||
\(947\) | −3.14663e7 | −1.14017 | −0.570086 | − | 0.821585i | \(-0.693090\pi\) | ||||
−0.570086 | + | 0.821585i | \(0.693090\pi\) | |||||||
\(948\) | 6.13771e6 | 0.221812 | ||||||||
\(949\) | −3.56987e7 | −1.28673 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.42108e7 | −0.509527 | ||||||||
\(952\) | 1.93202e7 | 0.690907 | ||||||||
\(953\) | 1.34516e7 | 0.479779 | 0.239890 | − | 0.970800i | \(-0.422889\pi\) | ||||
0.239890 | + | 0.970800i | \(0.422889\pi\) | |||||||
\(954\) | 1.69371e6 | 0.0602515 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.42911e6 | 0.0859613 | ||||||||
\(957\) | −2.58242e6 | −0.0911481 | ||||||||
\(958\) | 2.14124e7 | 0.753792 | ||||||||
\(959\) | 4.61492e6 | 0.162038 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.15157e7 | 0.402238 | ||||||||
\(962\) | −2.82513e7 | −0.984239 | ||||||||
\(963\) | 547884. | 0.0190381 | ||||||||
\(964\) | −694190. | −0.0240595 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.27008e6 | 0.0437913 | ||||||||
\(967\) | 2.84963e7 | 0.979992 | 0.489996 | − | 0.871725i | \(-0.336998\pi\) | ||||
0.489996 | + | 0.871725i | \(0.336998\pi\) | |||||||
\(968\) | −3.08777e7 | −1.05915 | ||||||||
\(969\) | −3.15189e7 | −1.07836 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.81858e7 | 0.618990 | 0.309495 | − | 0.950901i | \(-0.399840\pi\) | ||||
0.309495 | + | 0.950901i | \(0.399840\pi\) | |||||||
\(972\) | 413343. | 0.0140328 | ||||||||
\(973\) | −2.34200e6 | −0.0793059 | ||||||||
\(974\) | −4.46588e7 | −1.50837 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.42471e7 | 1.15080 | ||||||||
\(977\) | −3.20941e7 | −1.07569 | −0.537847 | − | 0.843042i | \(-0.680762\pi\) | ||||
−0.537847 | + | 0.843042i | \(0.680762\pi\) | |||||||
\(978\) | −1.11263e7 | −0.371968 | ||||||||
\(979\) | −165464. | −0.00551756 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.44502e7 | 0.479405 | ||||||||
\(982\) | −1.37653e7 | −0.455519 | ||||||||
\(983\) | −1.56154e7 | −0.515429 | −0.257715 | − | 0.966221i | \(-0.582969\pi\) | ||||
−0.257715 | + | 0.966221i | \(0.582969\pi\) | |||||||
\(984\) | 5.72481e6 | 0.188483 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.57870e7 | −1.82743 | ||||||||
\(987\) | 381024. | 0.0124497 | ||||||||
\(988\) | −9.33548e6 | −0.304260 | ||||||||
\(989\) | −3.12192e6 | −0.101492 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.84499e7 | 1.56714 | 0.783572 | − | 0.621301i | \(-0.213395\pi\) | ||||
0.783572 | + | 0.621301i | \(0.213395\pi\) | |||||||
\(992\) | −1.57450e7 | −0.507998 | ||||||||
\(993\) | 3.05524e7 | 0.983268 | ||||||||
\(994\) | −4.58640e6 | −0.147233 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.11736e6 | 0.163455 | ||||||||
\(997\) | 4.54336e7 | 1.44757 | 0.723784 | − | 0.690027i | \(-0.242401\pi\) | ||||
0.723784 | + | 0.690027i | \(0.242401\pi\) | |||||||
\(998\) | −2.40204e7 | −0.763404 | ||||||||
\(999\) | −5.34940e6 | −0.169587 |
(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 | 525.6.a.b.1.1 | 1 | ||
5.2 | odd | 4 | 525.6.d.c.274.1 | 2 | |||
5.3 | odd | 4 | 525.6.d.c.274.2 | 2 | |||
5.4 | even | 2 | 21.6.a.c.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 63.6.a.b.1.1 | 1 | |||
20.19 | odd | 2 | 336.6.a.i.1.1 | 1 | |||
35.4 | even | 6 | 147.6.e.c.79.1 | 2 | |||
35.9 | even | 6 | 147.6.e.c.67.1 | 2 | |||
35.19 | odd | 6 | 147.6.e.d.67.1 | 2 | |||
35.24 | odd | 6 | 147.6.e.d.79.1 | 2 | |||
35.34 | odd | 2 | 147.6.a.f.1.1 | 1 | |||
60.59 | even | 2 | 1008.6.a.a.1.1 | 1 | |||
105.104 | even | 2 | 441.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.a.c.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
63.6.a.b.1.1 | 1 | 15.14 | odd | 2 | |||
147.6.a.f.1.1 | 1 | 35.34 | odd | 2 | |||
147.6.e.c.67.1 | 2 | 35.9 | even | 6 | |||
147.6.e.c.79.1 | 2 | 35.4 | even | 6 | |||
147.6.e.d.67.1 | 2 | 35.19 | odd | 6 | |||
147.6.e.d.79.1 | 2 | 35.24 | odd | 6 | |||
336.6.a.i.1.1 | 1 | 20.19 | odd | 2 | |||
441.6.a.c.1.1 | 1 | 105.104 | even | 2 | |||
525.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial | ||
525.6.d.c.274.1 | 2 | 5.2 | odd | 4 | |||
525.6.d.c.274.2 | 2 | 5.3 | odd | 4 | |||
1008.6.a.a.1.1 | 1 | 60.59 | even | 2 |