Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,4,Mod(1,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.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: | \(115.053724511\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1950.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 25.0000 | 1.34987 | 0.674937 | − | 0.737876i | \(-0.264171\pi\) | ||||
0.674937 | + | 0.737876i | \(0.264171\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21.0000 | −0.575613 | −0.287806 | − | 0.957689i | \(-0.592926\pi\) | ||||
−0.287806 | + | 0.957689i | \(0.592926\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | −13.0000 | −0.277350 | ||||||||
\(14\) | −50.0000 | −0.954504 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −123.000 | −1.75482 | −0.877408 | − | 0.479744i | \(-0.840729\pi\) | ||||
−0.877408 | + | 0.479744i | \(0.840729\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | 146.000 | 1.76288 | 0.881439 | − | 0.472297i | \(-0.156575\pi\) | ||||
0.881439 | + | 0.472297i | \(0.156575\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 75.0000 | 0.779350 | ||||||||
\(22\) | 42.0000 | 0.407020 | ||||||||
\(23\) | −99.0000 | −0.897519 | −0.448759 | − | 0.893653i | \(-0.648134\pi\) | ||||
−0.448759 | + | 0.893653i | \(0.648134\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 26.0000 | 0.196116 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 100.000 | 0.674937 | ||||||||
\(29\) | −246.000 | −1.57521 | −0.787604 | − | 0.616181i | \(-0.788679\pi\) | ||||
−0.787604 | + | 0.616181i | \(0.788679\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 182.000 | 1.05446 | 0.527228 | − | 0.849724i | \(-0.323231\pi\) | ||||
0.527228 | + | 0.849724i | \(0.323231\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −63.0000 | −0.332330 | ||||||||
\(34\) | 246.000 | 1.24084 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 295.000 | 1.31075 | 0.655374 | − | 0.755304i | \(-0.272511\pi\) | ||||
0.655374 | + | 0.755304i | \(0.272511\pi\) | |||||||
\(38\) | −292.000 | −1.24654 | ||||||||
\(39\) | −39.0000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000 | 0.0342820 | 0.0171410 | − | 0.999853i | \(-0.494544\pi\) | ||||
0.0171410 | + | 0.999853i | \(0.494544\pi\) | |||||||
\(42\) | −150.000 | −0.551083 | ||||||||
\(43\) | −452.000 | −1.60301 | −0.801504 | − | 0.597989i | \(-0.795967\pi\) | ||||
−0.801504 | + | 0.597989i | \(0.795967\pi\) | |||||||
\(44\) | −84.0000 | −0.287806 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 198.000 | 0.634641 | ||||||||
\(47\) | −390.000 | −1.21037 | −0.605185 | − | 0.796085i | \(-0.706901\pi\) | ||||
−0.605185 | + | 0.796085i | \(0.706901\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 282.000 | 0.822157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −369.000 | −1.01314 | ||||||||
\(52\) | −52.0000 | −0.138675 | ||||||||
\(53\) | −315.000 | −0.816388 | −0.408194 | − | 0.912895i | \(-0.633841\pi\) | ||||
−0.408194 | + | 0.912895i | \(0.633841\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −200.000 | −0.477252 | ||||||||
\(57\) | 438.000 | 1.01780 | ||||||||
\(58\) | 492.000 | 1.11384 | ||||||||
\(59\) | −24.0000 | −0.0529582 | −0.0264791 | − | 0.999649i | \(-0.508430\pi\) | ||||
−0.0264791 | + | 0.999649i | \(0.508430\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −727.000 | −1.52595 | −0.762974 | − | 0.646429i | \(-0.776262\pi\) | ||||
−0.762974 | + | 0.646429i | \(0.776262\pi\) | |||||||
\(62\) | −364.000 | −0.745614 | ||||||||
\(63\) | 225.000 | 0.449958 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 126.000 | 0.234993 | ||||||||
\(67\) | −596.000 | −1.08676 | −0.543381 | − | 0.839487i | \(-0.682856\pi\) | ||||
−0.543381 | + | 0.839487i | \(0.682856\pi\) | |||||||
\(68\) | −492.000 | −0.877408 | ||||||||
\(69\) | −297.000 | −0.518183 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 771.000 | 1.28874 | 0.644372 | − | 0.764712i | \(-0.277119\pi\) | ||||
0.644372 | + | 0.764712i | \(0.277119\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −326.000 | −0.522677 | −0.261338 | − | 0.965247i | \(-0.584164\pi\) | ||||
−0.261338 | + | 0.965247i | \(0.584164\pi\) | |||||||
\(74\) | −590.000 | −0.926839 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 584.000 | 0.881439 | ||||||||
\(77\) | −525.000 | −0.777004 | ||||||||
\(78\) | 78.0000 | 0.113228 | ||||||||
\(79\) | −889.000 | −1.26608 | −0.633040 | − | 0.774119i | \(-0.718193\pi\) | ||||
−0.633040 | + | 0.774119i | \(0.718193\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −18.0000 | −0.0242411 | ||||||||
\(83\) | 96.0000 | 0.126956 | 0.0634781 | − | 0.997983i | \(-0.479781\pi\) | ||||
0.0634781 | + | 0.997983i | \(0.479781\pi\) | |||||||
\(84\) | 300.000 | 0.389675 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 904.000 | 1.13350 | ||||||||
\(87\) | −738.000 | −0.909447 | ||||||||
\(88\) | 168.000 | 0.203510 | ||||||||
\(89\) | 795.000 | 0.946852 | 0.473426 | − | 0.880834i | \(-0.343017\pi\) | ||||
0.473426 | + | 0.880834i | \(0.343017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −325.000 | −0.374387 | ||||||||
\(92\) | −396.000 | −0.448759 | ||||||||
\(93\) | 546.000 | 0.608791 | ||||||||
\(94\) | 780.000 | 0.855860 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −983.000 | −1.02895 | −0.514477 | − | 0.857504i | \(-0.672014\pi\) | ||||
−0.514477 | + | 0.857504i | \(0.672014\pi\) | |||||||
\(98\) | −564.000 | −0.581353 | ||||||||
\(99\) | −189.000 | −0.191871 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −732.000 | −0.721156 | −0.360578 | − | 0.932729i | \(-0.617420\pi\) | ||||
−0.360578 | + | 0.932729i | \(0.617420\pi\) | |||||||
\(102\) | 738.000 | 0.716401 | ||||||||
\(103\) | 1600.00 | 1.53061 | 0.765304 | − | 0.643669i | \(-0.222588\pi\) | ||||
0.765304 | + | 0.643669i | \(0.222588\pi\) | |||||||
\(104\) | 104.000 | 0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 630.000 | 0.577274 | ||||||||
\(107\) | −1011.00 | −0.913430 | −0.456715 | − | 0.889613i | \(-0.650974\pi\) | ||||
−0.456715 | + | 0.889613i | \(0.650974\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 1100.00 | 0.966614 | 0.483307 | − | 0.875451i | \(-0.339436\pi\) | ||||
0.483307 | + | 0.875451i | \(0.339436\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 885.000 | 0.756761 | ||||||||
\(112\) | 400.000 | 0.337468 | ||||||||
\(113\) | 1770.00 | 1.47352 | 0.736759 | − | 0.676155i | \(-0.236355\pi\) | ||||
0.736759 | + | 0.676155i | \(0.236355\pi\) | |||||||
\(114\) | −876.000 | −0.719692 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −984.000 | −0.787604 | ||||||||
\(117\) | −117.000 | −0.0924500 | ||||||||
\(118\) | 48.0000 | 0.0374471 | ||||||||
\(119\) | −3075.00 | −2.36878 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −890.000 | −0.668670 | ||||||||
\(122\) | 1454.00 | 1.07901 | ||||||||
\(123\) | 27.0000 | 0.0197927 | ||||||||
\(124\) | 728.000 | 0.527228 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −450.000 | −0.318168 | ||||||||
\(127\) | −2666.00 | −1.86275 | −0.931375 | − | 0.364061i | \(-0.881390\pi\) | ||||
−0.931375 | + | 0.364061i | \(0.881390\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −1356.00 | −0.925497 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 582.000 | 0.388165 | 0.194082 | − | 0.980985i | \(-0.437827\pi\) | ||||
0.194082 | + | 0.980985i | \(0.437827\pi\) | |||||||
\(132\) | −252.000 | −0.166165 | ||||||||
\(133\) | 3650.00 | 2.37966 | ||||||||
\(134\) | 1192.00 | 0.768456 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 984.000 | 0.620421 | ||||||||
\(137\) | −270.000 | −0.168377 | −0.0841885 | − | 0.996450i | \(-0.526830\pi\) | ||||
−0.0841885 | + | 0.996450i | \(0.526830\pi\) | |||||||
\(138\) | 594.000 | 0.366410 | ||||||||
\(139\) | −7.00000 | −0.00427146 | −0.00213573 | − | 0.999998i | \(-0.500680\pi\) | ||||
−0.00213573 | + | 0.999998i | \(0.500680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1170.00 | −0.698807 | ||||||||
\(142\) | −1542.00 | −0.911280 | ||||||||
\(143\) | 273.000 | 0.159646 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 652.000 | 0.369588 | ||||||||
\(147\) | 846.000 | 0.474673 | ||||||||
\(148\) | 1180.00 | 0.655374 | ||||||||
\(149\) | 3099.00 | 1.70389 | 0.851946 | − | 0.523629i | \(-0.175422\pi\) | ||||
0.851946 | + | 0.523629i | \(0.175422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2860.00 | −1.54135 | −0.770674 | − | 0.637230i | \(-0.780080\pi\) | ||||
−0.770674 | + | 0.637230i | \(0.780080\pi\) | |||||||
\(152\) | −1168.00 | −0.623272 | ||||||||
\(153\) | −1107.00 | −0.584939 | ||||||||
\(154\) | 1050.00 | 0.549425 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −156.000 | −0.0800641 | ||||||||
\(157\) | 2734.00 | 1.38979 | 0.694895 | − | 0.719111i | \(-0.255451\pi\) | ||||
0.694895 | + | 0.719111i | \(0.255451\pi\) | |||||||
\(158\) | 1778.00 | 0.895254 | ||||||||
\(159\) | −945.000 | −0.471342 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2475.00 | −1.21154 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | 853.000 | 0.409890 | 0.204945 | − | 0.978773i | \(-0.434298\pi\) | ||||
0.204945 | + | 0.978773i | \(0.434298\pi\) | |||||||
\(164\) | 36.0000 | 0.0171410 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −192.000 | −0.0897716 | ||||||||
\(167\) | −2556.00 | −1.18437 | −0.592183 | − | 0.805803i | \(-0.701734\pi\) | ||||
−0.592183 | + | 0.805803i | \(0.701734\pi\) | |||||||
\(168\) | −600.000 | −0.275542 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1314.00 | 0.587626 | ||||||||
\(172\) | −1808.00 | −0.801504 | ||||||||
\(173\) | 1134.00 | 0.498361 | 0.249180 | − | 0.968457i | \(-0.419839\pi\) | ||||
0.249180 | + | 0.968457i | \(0.419839\pi\) | |||||||
\(174\) | 1476.00 | 0.643076 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −336.000 | −0.143903 | ||||||||
\(177\) | −72.0000 | −0.0305754 | ||||||||
\(178\) | −1590.00 | −0.669525 | ||||||||
\(179\) | 498.000 | 0.207946 | 0.103973 | − | 0.994580i | \(-0.466845\pi\) | ||||
0.103973 | + | 0.994580i | \(0.466845\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1901.00 | 0.780664 | 0.390332 | − | 0.920674i | \(-0.372360\pi\) | ||||
0.390332 | + | 0.920674i | \(0.372360\pi\) | |||||||
\(182\) | 650.000 | 0.264732 | ||||||||
\(183\) | −2181.00 | −0.881006 | ||||||||
\(184\) | 792.000 | 0.317321 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1092.00 | −0.430480 | ||||||||
\(187\) | 2583.00 | 1.01009 | ||||||||
\(188\) | −1560.00 | −0.605185 | ||||||||
\(189\) | 675.000 | 0.259783 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2340.00 | 0.886474 | 0.443237 | − | 0.896405i | \(-0.353830\pi\) | ||||
0.443237 | + | 0.896405i | \(0.353830\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | −1685.00 | −0.628440 | −0.314220 | − | 0.949350i | \(-0.601743\pi\) | ||||
−0.314220 | + | 0.949350i | \(0.601743\pi\) | |||||||
\(194\) | 1966.00 | 0.727580 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1128.00 | 0.411079 | ||||||||
\(197\) | −1992.00 | −0.720427 | −0.360214 | − | 0.932870i | \(-0.617296\pi\) | ||||
−0.360214 | + | 0.932870i | \(0.617296\pi\) | |||||||
\(198\) | 378.000 | 0.135673 | ||||||||
\(199\) | −4732.00 | −1.68564 | −0.842821 | − | 0.538195i | \(-0.819107\pi\) | ||||
−0.842821 | + | 0.538195i | \(0.819107\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1788.00 | −0.627442 | ||||||||
\(202\) | 1464.00 | 0.509934 | ||||||||
\(203\) | −6150.00 | −2.12633 | ||||||||
\(204\) | −1476.00 | −0.506572 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3200.00 | −1.08230 | ||||||||
\(207\) | −891.000 | −0.299173 | ||||||||
\(208\) | −208.000 | −0.0693375 | ||||||||
\(209\) | −3066.00 | −1.01474 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4012.00 | −1.30899 | −0.654496 | − | 0.756065i | \(-0.727119\pi\) | ||||
−0.654496 | + | 0.756065i | \(0.727119\pi\) | |||||||
\(212\) | −1260.00 | −0.408194 | ||||||||
\(213\) | 2313.00 | 0.744057 | ||||||||
\(214\) | 2022.00 | 0.645893 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 4550.00 | 1.42338 | ||||||||
\(218\) | −2200.00 | −0.683499 | ||||||||
\(219\) | −978.000 | −0.301768 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1599.00 | 0.486699 | ||||||||
\(222\) | −1770.00 | −0.535111 | ||||||||
\(223\) | 1096.00 | 0.329119 | 0.164560 | − | 0.986367i | \(-0.447380\pi\) | ||||
0.164560 | + | 0.986367i | \(0.447380\pi\) | |||||||
\(224\) | −800.000 | −0.238626 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3540.00 | −1.04193 | ||||||||
\(227\) | −6138.00 | −1.79468 | −0.897342 | − | 0.441335i | \(-0.854505\pi\) | ||||
−0.897342 | + | 0.441335i | \(0.854505\pi\) | |||||||
\(228\) | 1752.00 | 0.508899 | ||||||||
\(229\) | −1294.00 | −0.373406 | −0.186703 | − | 0.982416i | \(-0.559780\pi\) | ||||
−0.186703 | + | 0.982416i | \(0.559780\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1575.00 | −0.448603 | ||||||||
\(232\) | 1968.00 | 0.556920 | ||||||||
\(233\) | −873.000 | −0.245460 | −0.122730 | − | 0.992440i | \(-0.539165\pi\) | ||||
−0.122730 | + | 0.992440i | \(0.539165\pi\) | |||||||
\(234\) | 234.000 | 0.0653720 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −96.0000 | −0.0264791 | ||||||||
\(237\) | −2667.00 | −0.730972 | ||||||||
\(238\) | 6150.00 | 1.67498 | ||||||||
\(239\) | 5163.00 | 1.39735 | 0.698675 | − | 0.715439i | \(-0.253773\pi\) | ||||
0.698675 | + | 0.715439i | \(0.253773\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2482.00 | −0.663401 | −0.331701 | − | 0.943385i | \(-0.607622\pi\) | ||||
−0.331701 | + | 0.943385i | \(0.607622\pi\) | |||||||
\(242\) | 1780.00 | 0.472821 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −2908.00 | −0.762974 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −54.0000 | −0.0139956 | ||||||||
\(247\) | −1898.00 | −0.488935 | ||||||||
\(248\) | −1456.00 | −0.372807 | ||||||||
\(249\) | 288.000 | 0.0732982 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5172.00 | 1.30061 | 0.650306 | − | 0.759672i | \(-0.274641\pi\) | ||||
0.650306 | + | 0.759672i | \(0.274641\pi\) | |||||||
\(252\) | 900.000 | 0.224979 | ||||||||
\(253\) | 2079.00 | 0.516623 | ||||||||
\(254\) | 5332.00 | 1.31716 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −198.000 | −0.0480580 | −0.0240290 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240290 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(258\) | 2712.00 | 0.654425 | ||||||||
\(259\) | 7375.00 | 1.76934 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2214.00 | −0.525070 | ||||||||
\(262\) | −1164.00 | −0.274474 | ||||||||
\(263\) | 2568.00 | 0.602090 | 0.301045 | − | 0.953610i | \(-0.402665\pi\) | ||||
0.301045 | + | 0.953610i | \(0.402665\pi\) | |||||||
\(264\) | 504.000 | 0.117496 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7300.00 | −1.68268 | ||||||||
\(267\) | 2385.00 | 0.546665 | ||||||||
\(268\) | −2384.00 | −0.543381 | ||||||||
\(269\) | −6924.00 | −1.56938 | −0.784691 | − | 0.619887i | \(-0.787178\pi\) | ||||
−0.784691 | + | 0.619887i | \(0.787178\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 254.000 | 0.0569351 | 0.0284675 | − | 0.999595i | \(-0.490937\pi\) | ||||
0.0284675 | + | 0.999595i | \(0.490937\pi\) | |||||||
\(272\) | −1968.00 | −0.438704 | ||||||||
\(273\) | −975.000 | −0.216153 | ||||||||
\(274\) | 540.000 | 0.119061 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1188.00 | −0.259091 | ||||||||
\(277\) | −6590.00 | −1.42944 | −0.714720 | − | 0.699411i | \(-0.753446\pi\) | ||||
−0.714720 | + | 0.699411i | \(0.753446\pi\) | |||||||
\(278\) | 14.0000 | 0.00302037 | ||||||||
\(279\) | 1638.00 | 0.351486 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2370.00 | 0.503140 | 0.251570 | − | 0.967839i | \(-0.419053\pi\) | ||||
0.251570 | + | 0.967839i | \(0.419053\pi\) | |||||||
\(282\) | 2340.00 | 0.494131 | ||||||||
\(283\) | 6280.00 | 1.31911 | 0.659553 | − | 0.751658i | \(-0.270745\pi\) | ||||
0.659553 | + | 0.751658i | \(0.270745\pi\) | |||||||
\(284\) | 3084.00 | 0.644372 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −546.000 | −0.112887 | ||||||||
\(287\) | 225.000 | 0.0462764 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | 10216.0 | 2.07938 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2949.00 | −0.594067 | ||||||||
\(292\) | −1304.00 | −0.261338 | ||||||||
\(293\) | 3588.00 | 0.715403 | 0.357702 | − | 0.933836i | \(-0.383560\pi\) | ||||
0.357702 | + | 0.933836i | \(0.383560\pi\) | |||||||
\(294\) | −1692.00 | −0.335644 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2360.00 | −0.463420 | ||||||||
\(297\) | −567.000 | −0.110777 | ||||||||
\(298\) | −6198.00 | −1.20483 | ||||||||
\(299\) | 1287.00 | 0.248927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11300.0 | −2.16386 | ||||||||
\(302\) | 5720.00 | 1.08990 | ||||||||
\(303\) | −2196.00 | −0.416359 | ||||||||
\(304\) | 2336.00 | 0.440720 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2214.00 | 0.413614 | ||||||||
\(307\) | 6469.00 | 1.20262 | 0.601312 | − | 0.799015i | \(-0.294645\pi\) | ||||
0.601312 | + | 0.799015i | \(0.294645\pi\) | |||||||
\(308\) | −2100.00 | −0.388502 | ||||||||
\(309\) | 4800.00 | 0.883697 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1536.00 | 0.280060 | 0.140030 | − | 0.990147i | \(-0.455280\pi\) | ||||
0.140030 | + | 0.990147i | \(0.455280\pi\) | |||||||
\(312\) | 312.000 | 0.0566139 | ||||||||
\(313\) | −1514.00 | −0.273407 | −0.136703 | − | 0.990612i | \(-0.543651\pi\) | ||||
−0.136703 | + | 0.990612i | \(0.543651\pi\) | |||||||
\(314\) | −5468.00 | −0.982730 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3556.00 | −0.633040 | ||||||||
\(317\) | 2724.00 | 0.482634 | 0.241317 | − | 0.970446i | \(-0.422421\pi\) | ||||
0.241317 | + | 0.970446i | \(0.422421\pi\) | |||||||
\(318\) | 1890.00 | 0.333289 | ||||||||
\(319\) | 5166.00 | 0.906710 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3033.00 | −0.527369 | ||||||||
\(322\) | 4950.00 | 0.856685 | ||||||||
\(323\) | −17958.0 | −3.09353 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1706.00 | −0.289836 | ||||||||
\(327\) | 3300.00 | 0.558075 | ||||||||
\(328\) | −72.0000 | −0.0121205 | ||||||||
\(329\) | −9750.00 | −1.63384 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1100.00 | 0.182663 | 0.0913315 | − | 0.995821i | \(-0.470888\pi\) | ||||
0.0913315 | + | 0.995821i | \(0.470888\pi\) | |||||||
\(332\) | 384.000 | 0.0634781 | ||||||||
\(333\) | 2655.00 | 0.436916 | ||||||||
\(334\) | 5112.00 | 0.837474 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1200.00 | 0.194837 | ||||||||
\(337\) | 196.000 | 0.0316819 | 0.0158410 | − | 0.999875i | \(-0.494957\pi\) | ||||
0.0158410 | + | 0.999875i | \(0.494957\pi\) | |||||||
\(338\) | −338.000 | −0.0543928 | ||||||||
\(339\) | 5310.00 | 0.850736 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3822.00 | −0.606959 | ||||||||
\(342\) | −2628.00 | −0.415515 | ||||||||
\(343\) | −1525.00 | −0.240065 | ||||||||
\(344\) | 3616.00 | 0.566749 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2268.00 | −0.352394 | ||||||||
\(347\) | −11055.0 | −1.71027 | −0.855135 | − | 0.518406i | \(-0.826526\pi\) | ||||
−0.855135 | + | 0.518406i | \(0.826526\pi\) | |||||||
\(348\) | −2952.00 | −0.454724 | ||||||||
\(349\) | −11176.0 | −1.71415 | −0.857074 | − | 0.515194i | \(-0.827720\pi\) | ||||
−0.857074 | + | 0.515194i | \(0.827720\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −351.000 | −0.0533761 | ||||||||
\(352\) | 672.000 | 0.101755 | ||||||||
\(353\) | −2130.00 | −0.321157 | −0.160579 | − | 0.987023i | \(-0.551336\pi\) | ||||
−0.160579 | + | 0.987023i | \(0.551336\pi\) | |||||||
\(354\) | 144.000 | 0.0216201 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3180.00 | 0.473426 | ||||||||
\(357\) | −9225.00 | −1.36762 | ||||||||
\(358\) | −996.000 | −0.147040 | ||||||||
\(359\) | 2304.00 | 0.338720 | 0.169360 | − | 0.985554i | \(-0.445830\pi\) | ||||
0.169360 | + | 0.985554i | \(0.445830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14457.0 | 2.10774 | ||||||||
\(362\) | −3802.00 | −0.552013 | ||||||||
\(363\) | −2670.00 | −0.386057 | ||||||||
\(364\) | −1300.00 | −0.187194 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4362.00 | 0.622966 | ||||||||
\(367\) | −13412.0 | −1.90763 | −0.953816 | − | 0.300393i | \(-0.902882\pi\) | ||||
−0.953816 | + | 0.300393i | \(0.902882\pi\) | |||||||
\(368\) | −1584.00 | −0.224380 | ||||||||
\(369\) | 81.0000 | 0.0114273 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7875.00 | −1.10202 | ||||||||
\(372\) | 2184.00 | 0.304395 | ||||||||
\(373\) | −9056.00 | −1.25711 | −0.628555 | − | 0.777765i | \(-0.716353\pi\) | ||||
−0.628555 | + | 0.777765i | \(0.716353\pi\) | |||||||
\(374\) | −5166.00 | −0.714245 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3120.00 | 0.427930 | ||||||||
\(377\) | 3198.00 | 0.436884 | ||||||||
\(378\) | −1350.00 | −0.183694 | ||||||||
\(379\) | −4066.00 | −0.551072 | −0.275536 | − | 0.961291i | \(-0.588855\pi\) | ||||
−0.275536 | + | 0.961291i | \(0.588855\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7998.00 | −1.07546 | ||||||||
\(382\) | −4680.00 | −0.626831 | ||||||||
\(383\) | −786.000 | −0.104864 | −0.0524318 | − | 0.998625i | \(-0.516697\pi\) | ||||
−0.0524318 | + | 0.998625i | \(0.516697\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3370.00 | 0.444374 | ||||||||
\(387\) | −4068.00 | −0.534336 | ||||||||
\(388\) | −3932.00 | −0.514477 | ||||||||
\(389\) | 8364.00 | 1.09016 | 0.545079 | − | 0.838385i | \(-0.316500\pi\) | ||||
0.545079 | + | 0.838385i | \(0.316500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12177.0 | 1.57498 | ||||||||
\(392\) | −2256.00 | −0.290677 | ||||||||
\(393\) | 1746.00 | 0.224107 | ||||||||
\(394\) | 3984.00 | 0.509419 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −756.000 | −0.0959354 | ||||||||
\(397\) | −7625.00 | −0.963949 | −0.481975 | − | 0.876185i | \(-0.660080\pi\) | ||||
−0.481975 | + | 0.876185i | \(0.660080\pi\) | |||||||
\(398\) | 9464.00 | 1.19193 | ||||||||
\(399\) | 10950.0 | 1.37390 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 954.000 | 0.118804 | 0.0594021 | − | 0.998234i | \(-0.481081\pi\) | ||||
0.0594021 | + | 0.998234i | \(0.481081\pi\) | |||||||
\(402\) | 3576.00 | 0.443668 | ||||||||
\(403\) | −2366.00 | −0.292454 | ||||||||
\(404\) | −2928.00 | −0.360578 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12300.0 | 1.50354 | ||||||||
\(407\) | −6195.00 | −0.754483 | ||||||||
\(408\) | 2952.00 | 0.358200 | ||||||||
\(409\) | 182.000 | 0.0220032 | 0.0110016 | − | 0.999939i | \(-0.496498\pi\) | ||||
0.0110016 | + | 0.999939i | \(0.496498\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −810.000 | −0.0972125 | ||||||||
\(412\) | 6400.00 | 0.765304 | ||||||||
\(413\) | −600.000 | −0.0714869 | ||||||||
\(414\) | 1782.00 | 0.211547 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 416.000 | 0.0490290 | ||||||||
\(417\) | −21.0000 | −0.00246613 | ||||||||
\(418\) | 6132.00 | 0.717526 | ||||||||
\(419\) | −4806.00 | −0.560354 | −0.280177 | − | 0.959948i | \(-0.590393\pi\) | ||||
−0.280177 | + | 0.959948i | \(0.590393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10024.0 | −1.16043 | −0.580214 | − | 0.814464i | \(-0.697031\pi\) | ||||
−0.580214 | + | 0.814464i | \(0.697031\pi\) | |||||||
\(422\) | 8024.00 | 0.925598 | ||||||||
\(423\) | −3510.00 | −0.403456 | ||||||||
\(424\) | 2520.00 | 0.288637 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4626.00 | −0.526128 | ||||||||
\(427\) | −18175.0 | −2.05984 | ||||||||
\(428\) | −4044.00 | −0.456715 | ||||||||
\(429\) | 819.000 | 0.0921718 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11544.0 | −1.29015 | −0.645075 | − | 0.764119i | \(-0.723174\pi\) | ||||
−0.645075 | + | 0.764119i | \(0.723174\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | 268.000 | 0.0297442 | 0.0148721 | − | 0.999889i | \(-0.495266\pi\) | ||||
0.0148721 | + | 0.999889i | \(0.495266\pi\) | |||||||
\(434\) | −9100.00 | −1.00648 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4400.00 | 0.483307 | ||||||||
\(437\) | −14454.0 | −1.58222 | ||||||||
\(438\) | 1956.00 | 0.213382 | ||||||||
\(439\) | −6235.00 | −0.677859 | −0.338930 | − | 0.940812i | \(-0.610065\pi\) | ||||
−0.338930 | + | 0.940812i | \(0.610065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2538.00 | 0.274052 | ||||||||
\(442\) | −3198.00 | −0.344148 | ||||||||
\(443\) | −9363.00 | −1.00418 | −0.502088 | − | 0.864817i | \(-0.667434\pi\) | ||||
−0.502088 | + | 0.864817i | \(0.667434\pi\) | |||||||
\(444\) | 3540.00 | 0.378381 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2192.00 | −0.232722 | ||||||||
\(447\) | 9297.00 | 0.983743 | ||||||||
\(448\) | 1600.00 | 0.168734 | ||||||||
\(449\) | −7023.00 | −0.738165 | −0.369082 | − | 0.929397i | \(-0.620328\pi\) | ||||
−0.369082 | + | 0.929397i | \(0.620328\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −189.000 | −0.0197332 | ||||||||
\(452\) | 7080.00 | 0.736759 | ||||||||
\(453\) | −8580.00 | −0.889897 | ||||||||
\(454\) | 12276.0 | 1.26903 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3504.00 | −0.359846 | ||||||||
\(457\) | −2603.00 | −0.266440 | −0.133220 | − | 0.991086i | \(-0.542532\pi\) | ||||
−0.133220 | + | 0.991086i | \(0.542532\pi\) | |||||||
\(458\) | 2588.00 | 0.264038 | ||||||||
\(459\) | −3321.00 | −0.337715 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10377.0 | 1.04838 | 0.524192 | − | 0.851600i | \(-0.324367\pi\) | ||||
0.524192 | + | 0.851600i | \(0.324367\pi\) | |||||||
\(462\) | 3150.00 | 0.317211 | ||||||||
\(463\) | 11401.0 | 1.14438 | 0.572192 | − | 0.820120i | \(-0.306093\pi\) | ||||
0.572192 | + | 0.820120i | \(0.306093\pi\) | |||||||
\(464\) | −3936.00 | −0.393802 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1746.00 | 0.173566 | ||||||||
\(467\) | 15381.0 | 1.52409 | 0.762043 | − | 0.647527i | \(-0.224197\pi\) | ||||
0.762043 | + | 0.647527i | \(0.224197\pi\) | |||||||
\(468\) | −468.000 | −0.0462250 | ||||||||
\(469\) | −14900.0 | −1.46699 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8202.00 | 0.802395 | ||||||||
\(472\) | 192.000 | 0.0187236 | ||||||||
\(473\) | 9492.00 | 0.922712 | ||||||||
\(474\) | 5334.00 | 0.516875 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12300.0 | −1.18439 | ||||||||
\(477\) | −2835.00 | −0.272129 | ||||||||
\(478\) | −10326.0 | −0.988076 | ||||||||
\(479\) | −1767.00 | −0.168552 | −0.0842759 | − | 0.996442i | \(-0.526858\pi\) | ||||
−0.0842759 | + | 0.996442i | \(0.526858\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3835.00 | −0.363536 | ||||||||
\(482\) | 4964.00 | 0.469095 | ||||||||
\(483\) | −7425.00 | −0.699481 | ||||||||
\(484\) | −3560.00 | −0.334335 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −9893.00 | −0.920523 | −0.460261 | − | 0.887783i | \(-0.652244\pi\) | ||||
−0.460261 | + | 0.887783i | \(0.652244\pi\) | |||||||
\(488\) | 5816.00 | 0.539504 | ||||||||
\(489\) | 2559.00 | 0.236650 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15336.0 | −1.40958 | −0.704790 | − | 0.709416i | \(-0.748959\pi\) | ||||
−0.704790 | + | 0.709416i | \(0.748959\pi\) | |||||||
\(492\) | 108.000 | 0.00989637 | ||||||||
\(493\) | 30258.0 | 2.76420 | ||||||||
\(494\) | 3796.00 | 0.345729 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2912.00 | 0.263614 | ||||||||
\(497\) | 19275.0 | 1.73964 | ||||||||
\(498\) | −576.000 | −0.0518297 | ||||||||
\(499\) | −16450.0 | −1.47576 | −0.737879 | − | 0.674933i | \(-0.764172\pi\) | ||||
−0.737879 | + | 0.674933i | \(0.764172\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7668.00 | −0.683794 | ||||||||
\(502\) | −10344.0 | −0.919672 | ||||||||
\(503\) | −3444.00 | −0.305289 | −0.152645 | − | 0.988281i | \(-0.548779\pi\) | ||||
−0.152645 | + | 0.988281i | \(0.548779\pi\) | |||||||
\(504\) | −1800.00 | −0.159084 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4158.00 | −0.365308 | ||||||||
\(507\) | 507.000 | 0.0444116 | ||||||||
\(508\) | −10664.0 | −0.931375 | ||||||||
\(509\) | 5535.00 | 0.481993 | 0.240997 | − | 0.970526i | \(-0.422526\pi\) | ||||
0.240997 | + | 0.970526i | \(0.422526\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8150.00 | −0.705548 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 3942.00 | 0.339266 | ||||||||
\(514\) | 396.000 | 0.0339821 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5424.00 | −0.462749 | ||||||||
\(517\) | 8190.00 | 0.696704 | ||||||||
\(518\) | −14750.0 | −1.25112 | ||||||||
\(519\) | 3402.00 | 0.287729 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6786.00 | −0.570634 | −0.285317 | − | 0.958433i | \(-0.592099\pi\) | ||||
−0.285317 | + | 0.958433i | \(0.592099\pi\) | |||||||
\(522\) | 4428.00 | 0.371280 | ||||||||
\(523\) | −1928.00 | −0.161196 | −0.0805980 | − | 0.996747i | \(-0.525683\pi\) | ||||
−0.0805980 | + | 0.996747i | \(0.525683\pi\) | |||||||
\(524\) | 2328.00 | 0.194082 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5136.00 | −0.425742 | ||||||||
\(527\) | −22386.0 | −1.85038 | ||||||||
\(528\) | −1008.00 | −0.0830825 | ||||||||
\(529\) | −2366.00 | −0.194460 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −216.000 | −0.0176527 | ||||||||
\(532\) | 14600.0 | 1.18983 | ||||||||
\(533\) | −117.000 | −0.00950813 | ||||||||
\(534\) | −4770.00 | −0.386551 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4768.00 | 0.384228 | ||||||||
\(537\) | 1494.00 | 0.120057 | ||||||||
\(538\) | 13848.0 | 1.10972 | ||||||||
\(539\) | −5922.00 | −0.473244 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15118.0 | −1.20143 | −0.600715 | − | 0.799463i | \(-0.705117\pi\) | ||||
−0.600715 | + | 0.799463i | \(0.705117\pi\) | |||||||
\(542\) | −508.000 | −0.0402592 | ||||||||
\(543\) | 5703.00 | 0.450717 | ||||||||
\(544\) | 3936.00 | 0.310211 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1950.00 | 0.152843 | ||||||||
\(547\) | −3620.00 | −0.282962 | −0.141481 | − | 0.989941i | \(-0.545186\pi\) | ||||
−0.141481 | + | 0.989941i | \(0.545186\pi\) | |||||||
\(548\) | −1080.00 | −0.0841885 | ||||||||
\(549\) | −6543.00 | −0.508649 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35916.0 | −2.77690 | ||||||||
\(552\) | 2376.00 | 0.183205 | ||||||||
\(553\) | −22225.0 | −1.70905 | ||||||||
\(554\) | 13180.0 | 1.01077 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −28.0000 | −0.00213573 | ||||||||
\(557\) | 11886.0 | 0.904176 | 0.452088 | − | 0.891973i | \(-0.350679\pi\) | ||||
0.452088 | + | 0.891973i | \(0.350679\pi\) | |||||||
\(558\) | −3276.00 | −0.248538 | ||||||||
\(559\) | 5876.00 | 0.444594 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7749.00 | 0.583178 | ||||||||
\(562\) | −4740.00 | −0.355774 | ||||||||
\(563\) | 11409.0 | 0.854053 | 0.427027 | − | 0.904239i | \(-0.359561\pi\) | ||||
0.427027 | + | 0.904239i | \(0.359561\pi\) | |||||||
\(564\) | −4680.00 | −0.349403 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12560.0 | −0.932749 | ||||||||
\(567\) | 2025.00 | 0.149986 | ||||||||
\(568\) | −6168.00 | −0.455640 | ||||||||
\(569\) | 11760.0 | 0.866441 | 0.433220 | − | 0.901288i | \(-0.357377\pi\) | ||||
0.433220 | + | 0.901288i | \(0.357377\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4057.00 | −0.297338 | −0.148669 | − | 0.988887i | \(-0.547499\pi\) | ||||
−0.148669 | + | 0.988887i | \(0.547499\pi\) | |||||||
\(572\) | 1092.00 | 0.0798231 | ||||||||
\(573\) | 7020.00 | 0.511806 | ||||||||
\(574\) | −450.000 | −0.0327224 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 5101.00 | 0.368037 | 0.184019 | − | 0.982923i | \(-0.441089\pi\) | ||||
0.184019 | + | 0.982923i | \(0.441089\pi\) | |||||||
\(578\) | −20432.0 | −1.47034 | ||||||||
\(579\) | −5055.00 | −0.362830 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2400.00 | 0.171375 | ||||||||
\(582\) | 5898.00 | 0.420069 | ||||||||
\(583\) | 6615.00 | 0.469923 | ||||||||
\(584\) | 2608.00 | 0.184794 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7176.00 | −0.505867 | ||||||||
\(587\) | 24186.0 | 1.70062 | 0.850309 | − | 0.526283i | \(-0.176415\pi\) | ||||
0.850309 | + | 0.526283i | \(0.176415\pi\) | |||||||
\(588\) | 3384.00 | 0.237336 | ||||||||
\(589\) | 26572.0 | 1.85888 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5976.00 | −0.415939 | ||||||||
\(592\) | 4720.00 | 0.327687 | ||||||||
\(593\) | −72.0000 | −0.00498598 | −0.00249299 | − | 0.999997i | \(-0.500794\pi\) | ||||
−0.00249299 | + | 0.999997i | \(0.500794\pi\) | |||||||
\(594\) | 1134.00 | 0.0783309 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12396.0 | 0.851946 | ||||||||
\(597\) | −14196.0 | −0.973205 | ||||||||
\(598\) | −2574.00 | −0.176018 | ||||||||
\(599\) | −14016.0 | −0.956057 | −0.478029 | − | 0.878344i | \(-0.658648\pi\) | ||||
−0.478029 | + | 0.878344i | \(0.658648\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10739.0 | 0.728873 | 0.364437 | − | 0.931228i | \(-0.381262\pi\) | ||||
0.364437 | + | 0.931228i | \(0.381262\pi\) | |||||||
\(602\) | 22600.0 | 1.53008 | ||||||||
\(603\) | −5364.00 | −0.362254 | ||||||||
\(604\) | −11440.0 | −0.770674 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4392.00 | 0.294411 | ||||||||
\(607\) | −18884.0 | −1.26273 | −0.631366 | − | 0.775485i | \(-0.717505\pi\) | ||||
−0.631366 | + | 0.775485i | \(0.717505\pi\) | |||||||
\(608\) | −4672.00 | −0.311636 | ||||||||
\(609\) | −18450.0 | −1.22764 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5070.00 | 0.335696 | ||||||||
\(612\) | −4428.00 | −0.292469 | ||||||||
\(613\) | 3985.00 | 0.262565 | 0.131283 | − | 0.991345i | \(-0.458090\pi\) | ||||
0.131283 | + | 0.991345i | \(0.458090\pi\) | |||||||
\(614\) | −12938.0 | −0.850383 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4200.00 | 0.274712 | ||||||||
\(617\) | −5034.00 | −0.328462 | −0.164231 | − | 0.986422i | \(-0.552514\pi\) | ||||
−0.164231 | + | 0.986422i | \(0.552514\pi\) | |||||||
\(618\) | −9600.00 | −0.624868 | ||||||||
\(619\) | 20954.0 | 1.36060 | 0.680301 | − | 0.732933i | \(-0.261849\pi\) | ||||
0.680301 | + | 0.732933i | \(0.261849\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2673.00 | −0.172728 | ||||||||
\(622\) | −3072.00 | −0.198032 | ||||||||
\(623\) | 19875.0 | 1.27813 | ||||||||
\(624\) | −624.000 | −0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3028.00 | 0.193328 | ||||||||
\(627\) | −9198.00 | −0.585858 | ||||||||
\(628\) | 10936.0 | 0.694895 | ||||||||
\(629\) | −36285.0 | −2.30012 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16724.0 | 1.05511 | 0.527553 | − | 0.849522i | \(-0.323110\pi\) | ||||
0.527553 | + | 0.849522i | \(0.323110\pi\) | |||||||
\(632\) | 7112.00 | 0.447627 | ||||||||
\(633\) | −12036.0 | −0.755747 | ||||||||
\(634\) | −5448.00 | −0.341274 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3780.00 | −0.235671 | ||||||||
\(637\) | −3666.00 | −0.228025 | ||||||||
\(638\) | −10332.0 | −0.641141 | ||||||||
\(639\) | 6939.00 | 0.429582 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20520.0 | −1.26442 | −0.632208 | − | 0.774798i | \(-0.717851\pi\) | ||||
−0.632208 | + | 0.774798i | \(0.717851\pi\) | |||||||
\(642\) | 6066.00 | 0.372906 | ||||||||
\(643\) | 8953.00 | 0.549101 | 0.274550 | − | 0.961573i | \(-0.411471\pi\) | ||||
0.274550 | + | 0.961573i | \(0.411471\pi\) | |||||||
\(644\) | −9900.00 | −0.605768 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 35916.0 | 2.18746 | ||||||||
\(647\) | −17913.0 | −1.08846 | −0.544229 | − | 0.838937i | \(-0.683178\pi\) | ||||
−0.544229 | + | 0.838937i | \(0.683178\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | 504.000 | 0.0304834 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13650.0 | 0.821791 | ||||||||
\(652\) | 3412.00 | 0.204945 | ||||||||
\(653\) | −20718.0 | −1.24159 | −0.620795 | − | 0.783973i | \(-0.713190\pi\) | ||||
−0.620795 | + | 0.783973i | \(0.713190\pi\) | |||||||
\(654\) | −6600.00 | −0.394618 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 144.000 | 0.00857051 | ||||||||
\(657\) | −2934.00 | −0.174226 | ||||||||
\(658\) | 19500.0 | 1.15530 | ||||||||
\(659\) | −32040.0 | −1.89393 | −0.946966 | − | 0.321334i | \(-0.895869\pi\) | ||||
−0.946966 | + | 0.321334i | \(0.895869\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2176.00 | −0.128043 | −0.0640216 | − | 0.997949i | \(-0.520393\pi\) | ||||
−0.0640216 | + | 0.997949i | \(0.520393\pi\) | |||||||
\(662\) | −2200.00 | −0.129162 | ||||||||
\(663\) | 4797.00 | 0.280996 | ||||||||
\(664\) | −768.000 | −0.0448858 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5310.00 | −0.308946 | ||||||||
\(667\) | 24354.0 | 1.41378 | ||||||||
\(668\) | −10224.0 | −0.592183 | ||||||||
\(669\) | 3288.00 | 0.190017 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15267.0 | 0.878355 | ||||||||
\(672\) | −2400.00 | −0.137771 | ||||||||
\(673\) | 30238.0 | 1.73193 | 0.865965 | − | 0.500104i | \(-0.166705\pi\) | ||||
0.865965 | + | 0.500104i | \(0.166705\pi\) | |||||||
\(674\) | −392.000 | −0.0224025 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | 25341.0 | 1.43860 | 0.719301 | − | 0.694698i | \(-0.244462\pi\) | ||||
0.719301 | + | 0.694698i | \(0.244462\pi\) | |||||||
\(678\) | −10620.0 | −0.601561 | ||||||||
\(679\) | −24575.0 | −1.38896 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18414.0 | −1.03616 | ||||||||
\(682\) | 7644.00 | 0.429185 | ||||||||
\(683\) | −6504.00 | −0.364376 | −0.182188 | − | 0.983264i | \(-0.558318\pi\) | ||||
−0.182188 | + | 0.983264i | \(0.558318\pi\) | |||||||
\(684\) | 5256.00 | 0.293813 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3050.00 | 0.169752 | ||||||||
\(687\) | −3882.00 | −0.215586 | ||||||||
\(688\) | −7232.00 | −0.400752 | ||||||||
\(689\) | 4095.00 | 0.226425 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22358.0 | 1.23088 | 0.615440 | − | 0.788184i | \(-0.288978\pi\) | ||||
0.615440 | + | 0.788184i | \(0.288978\pi\) | |||||||
\(692\) | 4536.00 | 0.249180 | ||||||||
\(693\) | −4725.00 | −0.259001 | ||||||||
\(694\) | 22110.0 | 1.20934 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5904.00 | 0.321538 | ||||||||
\(697\) | −1107.00 | −0.0601587 | ||||||||
\(698\) | 22352.0 | 1.21209 | ||||||||
\(699\) | −2619.00 | −0.141716 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2268.00 | −0.122199 | −0.0610993 | − | 0.998132i | \(-0.519461\pi\) | ||||
−0.0610993 | + | 0.998132i | \(0.519461\pi\) | |||||||
\(702\) | 702.000 | 0.0377426 | ||||||||
\(703\) | 43070.0 | 2.31069 | ||||||||
\(704\) | −1344.00 | −0.0719516 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4260.00 | 0.227092 | ||||||||
\(707\) | −18300.0 | −0.973469 | ||||||||
\(708\) | −288.000 | −0.0152877 | ||||||||
\(709\) | 13700.0 | 0.725690 | 0.362845 | − | 0.931849i | \(-0.381805\pi\) | ||||
0.362845 | + | 0.931849i | \(0.381805\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8001.00 | −0.422027 | ||||||||
\(712\) | −6360.00 | −0.334763 | ||||||||
\(713\) | −18018.0 | −0.946395 | ||||||||
\(714\) | 18450.0 | 0.967050 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1992.00 | 0.103973 | ||||||||
\(717\) | 15489.0 | 0.806761 | ||||||||
\(718\) | −4608.00 | −0.239511 | ||||||||
\(719\) | 6540.00 | 0.339222 | 0.169611 | − | 0.985511i | \(-0.445749\pi\) | ||||
0.169611 | + | 0.985511i | \(0.445749\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40000.0 | 2.06613 | ||||||||
\(722\) | −28914.0 | −1.49040 | ||||||||
\(723\) | −7446.00 | −0.383015 | ||||||||
\(724\) | 7604.00 | 0.390332 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5340.00 | 0.272983 | ||||||||
\(727\) | 13822.0 | 0.705130 | 0.352565 | − | 0.935787i | \(-0.385310\pi\) | ||||
0.352565 | + | 0.935787i | \(0.385310\pi\) | |||||||
\(728\) | 2600.00 | 0.132366 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 55596.0 | 2.81299 | ||||||||
\(732\) | −8724.00 | −0.440503 | ||||||||
\(733\) | 21715.0 | 1.09422 | 0.547109 | − | 0.837061i | \(-0.315728\pi\) | ||||
0.547109 | + | 0.837061i | \(0.315728\pi\) | |||||||
\(734\) | 26824.0 | 1.34890 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3168.00 | 0.158660 | ||||||||
\(737\) | 12516.0 | 0.625553 | ||||||||
\(738\) | −162.000 | −0.00808036 | ||||||||
\(739\) | −3310.00 | −0.164764 | −0.0823818 | − | 0.996601i | \(-0.526253\pi\) | ||||
−0.0823818 | + | 0.996601i | \(0.526253\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5694.00 | −0.282287 | ||||||||
\(742\) | 15750.0 | 0.779246 | ||||||||
\(743\) | −11178.0 | −0.551926 | −0.275963 | − | 0.961168i | \(-0.588997\pi\) | ||||
−0.275963 | + | 0.961168i | \(0.588997\pi\) | |||||||
\(744\) | −4368.00 | −0.215240 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18112.0 | 0.888911 | ||||||||
\(747\) | 864.000 | 0.0423188 | ||||||||
\(748\) | 10332.0 | 0.505047 | ||||||||
\(749\) | −25275.0 | −1.23302 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16337.0 | 0.793802 | 0.396901 | − | 0.917861i | \(-0.370086\pi\) | ||||
0.396901 | + | 0.917861i | \(0.370086\pi\) | |||||||
\(752\) | −6240.00 | −0.302592 | ||||||||
\(753\) | 15516.0 | 0.750909 | ||||||||
\(754\) | −6396.00 | −0.308924 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2700.00 | 0.129892 | ||||||||
\(757\) | −23096.0 | −1.10890 | −0.554451 | − | 0.832217i | \(-0.687072\pi\) | ||||
−0.554451 | + | 0.832217i | \(0.687072\pi\) | |||||||
\(758\) | 8132.00 | 0.389667 | ||||||||
\(759\) | 6237.00 | 0.298272 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4578.00 | −0.218071 | −0.109036 | − | 0.994038i | \(-0.534776\pi\) | ||||
−0.109036 | + | 0.994038i | \(0.534776\pi\) | |||||||
\(762\) | 15996.0 | 0.760464 | ||||||||
\(763\) | 27500.0 | 1.30481 | ||||||||
\(764\) | 9360.00 | 0.443237 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1572.00 | 0.0741497 | ||||||||
\(767\) | 312.000 | 0.0146880 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | 29036.0 | 1.36159 | 0.680796 | − | 0.732473i | \(-0.261634\pi\) | ||||
0.680796 | + | 0.732473i | \(0.261634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −594.000 | −0.0277463 | ||||||||
\(772\) | −6740.00 | −0.314220 | ||||||||
\(773\) | 37056.0 | 1.72421 | 0.862103 | − | 0.506733i | \(-0.169147\pi\) | ||||
0.862103 | + | 0.506733i | \(0.169147\pi\) | |||||||
\(774\) | 8136.00 | 0.377833 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7864.00 | 0.363790 | ||||||||
\(777\) | 22125.0 | 1.02153 | ||||||||
\(778\) | −16728.0 | −0.770858 | ||||||||
\(779\) | 1314.00 | 0.0604351 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16191.0 | −0.741818 | ||||||||
\(782\) | −24354.0 | −1.11368 | ||||||||
\(783\) | −6642.00 | −0.303149 | ||||||||
\(784\) | 4512.00 | 0.205539 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3492.00 | −0.158468 | ||||||||
\(787\) | 17332.0 | 0.785031 | 0.392515 | − | 0.919745i | \(-0.371605\pi\) | ||||
0.392515 | + | 0.919745i | \(0.371605\pi\) | |||||||
\(788\) | −7968.00 | −0.360214 | ||||||||
\(789\) | 7704.00 | 0.347617 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44250.0 | 1.98906 | ||||||||
\(792\) | 1512.00 | 0.0678366 | ||||||||
\(793\) | 9451.00 | 0.423222 | ||||||||
\(794\) | 15250.0 | 0.681615 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18928.0 | −0.842821 | ||||||||
\(797\) | 30759.0 | 1.36705 | 0.683526 | − | 0.729927i | \(-0.260446\pi\) | ||||
0.683526 | + | 0.729927i | \(0.260446\pi\) | |||||||
\(798\) | −21900.0 | −0.971493 | ||||||||
\(799\) | 47970.0 | 2.12398 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7155.00 | 0.315617 | ||||||||
\(802\) | −1908.00 | −0.0840073 | ||||||||
\(803\) | 6846.00 | 0.300859 | ||||||||
\(804\) | −7152.00 | −0.313721 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4732.00 | 0.206796 | ||||||||
\(807\) | −20772.0 | −0.906083 | ||||||||
\(808\) | 5856.00 | 0.254967 | ||||||||
\(809\) | −30102.0 | −1.30820 | −0.654098 | − | 0.756410i | \(-0.726951\pi\) | ||||
−0.654098 | + | 0.756410i | \(0.726951\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14308.0 | −0.619509 | −0.309755 | − | 0.950817i | \(-0.600247\pi\) | ||||
−0.309755 | + | 0.950817i | \(0.600247\pi\) | |||||||
\(812\) | −24600.0 | −1.06317 | ||||||||
\(813\) | 762.000 | 0.0328715 | ||||||||
\(814\) | 12390.0 | 0.533500 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −5904.00 | −0.253286 | ||||||||
\(817\) | −65992.0 | −2.82591 | ||||||||
\(818\) | −364.000 | −0.0155586 | ||||||||
\(819\) | −2925.00 | −0.124796 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27501.0 | 1.16905 | 0.584526 | − | 0.811375i | \(-0.301281\pi\) | ||||
0.584526 | + | 0.811375i | \(0.301281\pi\) | |||||||
\(822\) | 1620.00 | 0.0687396 | ||||||||
\(823\) | −2288.00 | −0.0969072 | −0.0484536 | − | 0.998825i | \(-0.515429\pi\) | ||||
−0.0484536 | + | 0.998825i | \(0.515429\pi\) | |||||||
\(824\) | −12800.0 | −0.541152 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1200.00 | 0.0505488 | ||||||||
\(827\) | 1422.00 | 0.0597918 | 0.0298959 | − | 0.999553i | \(-0.490482\pi\) | ||||
0.0298959 | + | 0.999553i | \(0.490482\pi\) | |||||||
\(828\) | −3564.00 | −0.149586 | ||||||||
\(829\) | −42298.0 | −1.77210 | −0.886050 | − | 0.463590i | \(-0.846561\pi\) | ||||
−0.886050 | + | 0.463590i | \(0.846561\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19770.0 | −0.825287 | ||||||||
\(832\) | −832.000 | −0.0346688 | ||||||||
\(833\) | −34686.0 | −1.44274 | ||||||||
\(834\) | 42.0000 | 0.00174381 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12264.0 | −0.507368 | ||||||||
\(837\) | 4914.00 | 0.202930 | ||||||||
\(838\) | 9612.00 | 0.396230 | ||||||||
\(839\) | 17595.0 | 0.724013 | 0.362006 | − | 0.932176i | \(-0.382092\pi\) | ||||
0.362006 | + | 0.932176i | \(0.382092\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36127.0 | 1.48128 | ||||||||
\(842\) | 20048.0 | 0.820546 | ||||||||
\(843\) | 7110.00 | 0.290488 | ||||||||
\(844\) | −16048.0 | −0.654496 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7020.00 | 0.285287 | ||||||||
\(847\) | −22250.0 | −0.902620 | ||||||||
\(848\) | −5040.00 | −0.204097 | ||||||||
\(849\) | 18840.0 | 0.761587 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29205.0 | −1.17642 | ||||||||
\(852\) | 9252.00 | 0.372029 | ||||||||
\(853\) | 13633.0 | 0.547227 | 0.273614 | − | 0.961840i | \(-0.411781\pi\) | ||||
0.273614 | + | 0.961840i | \(0.411781\pi\) | |||||||
\(854\) | 36350.0 | 1.45652 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8088.00 | 0.322946 | ||||||||
\(857\) | 29319.0 | 1.16863 | 0.584316 | − | 0.811526i | \(-0.301363\pi\) | ||||
0.584316 | + | 0.811526i | \(0.301363\pi\) | |||||||
\(858\) | −1638.00 | −0.0651753 | ||||||||
\(859\) | −24235.0 | −0.962616 | −0.481308 | − | 0.876551i | \(-0.659838\pi\) | ||||
−0.481308 | + | 0.876551i | \(0.659838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 675.000 | 0.0267177 | ||||||||
\(862\) | 23088.0 | 0.912274 | ||||||||
\(863\) | 7470.00 | 0.294649 | 0.147324 | − | 0.989088i | \(-0.452934\pi\) | ||||
0.147324 | + | 0.989088i | \(0.452934\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −536.000 | −0.0210324 | ||||||||
\(867\) | 30648.0 | 1.20053 | ||||||||
\(868\) | 18200.0 | 0.711692 | ||||||||
\(869\) | 18669.0 | 0.728772 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7748.00 | 0.301413 | ||||||||
\(872\) | −8800.00 | −0.341750 | ||||||||
\(873\) | −8847.00 | −0.342985 | ||||||||
\(874\) | 28908.0 | 1.11880 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3912.00 | −0.150884 | ||||||||
\(877\) | 28762.0 | 1.10744 | 0.553719 | − | 0.832703i | \(-0.313208\pi\) | ||||
0.553719 | + | 0.832703i | \(0.313208\pi\) | |||||||
\(878\) | 12470.0 | 0.479319 | ||||||||
\(879\) | 10764.0 | 0.413038 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11442.0 | 0.437560 | 0.218780 | − | 0.975774i | \(-0.429792\pi\) | ||||
0.218780 | + | 0.975774i | \(0.429792\pi\) | |||||||
\(882\) | −5076.00 | −0.193784 | ||||||||
\(883\) | 15208.0 | 0.579604 | 0.289802 | − | 0.957087i | \(-0.406411\pi\) | ||||
0.289802 | + | 0.957087i | \(0.406411\pi\) | |||||||
\(884\) | 6396.00 | 0.243349 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18726.0 | 0.710059 | ||||||||
\(887\) | −25461.0 | −0.963807 | −0.481903 | − | 0.876224i | \(-0.660054\pi\) | ||||
−0.481903 | + | 0.876224i | \(0.660054\pi\) | |||||||
\(888\) | −7080.00 | −0.267555 | ||||||||
\(889\) | −66650.0 | −2.51448 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1701.00 | −0.0639570 | ||||||||
\(892\) | 4384.00 | 0.164560 | ||||||||
\(893\) | −56940.0 | −2.13373 | ||||||||
\(894\) | −18594.0 | −0.695611 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3200.00 | −0.119313 | ||||||||
\(897\) | 3861.00 | 0.143718 | ||||||||
\(898\) | 14046.0 | 0.521961 | ||||||||
\(899\) | −44772.0 | −1.66099 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 38745.0 | 1.43261 | ||||||||
\(902\) | 378.000 | 0.0139535 | ||||||||
\(903\) | −33900.0 | −1.24930 | ||||||||
\(904\) | −14160.0 | −0.520967 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 17160.0 | 0.629253 | ||||||||
\(907\) | −27326.0 | −1.00038 | −0.500190 | − | 0.865916i | \(-0.666737\pi\) | ||||
−0.500190 | + | 0.865916i | \(0.666737\pi\) | |||||||
\(908\) | −24552.0 | −0.897342 | ||||||||
\(909\) | −6588.00 | −0.240385 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24420.0 | 0.888113 | 0.444056 | − | 0.895999i | \(-0.353539\pi\) | ||||
0.444056 | + | 0.895999i | \(0.353539\pi\) | |||||||
\(912\) | 7008.00 | 0.254450 | ||||||||
\(913\) | −2016.00 | −0.0730776 | ||||||||
\(914\) | 5206.00 | 0.188402 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5176.00 | −0.186703 | ||||||||
\(917\) | 14550.0 | 0.523973 | ||||||||
\(918\) | 6642.00 | 0.238800 | ||||||||
\(919\) | 32951.0 | 1.18276 | 0.591378 | − | 0.806394i | \(-0.298584\pi\) | ||||
0.591378 | + | 0.806394i | \(0.298584\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19407.0 | 0.694335 | ||||||||
\(922\) | −20754.0 | −0.741320 | ||||||||
\(923\) | −10023.0 | −0.357433 | ||||||||
\(924\) | −6300.00 | −0.224302 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22802.0 | −0.809201 | ||||||||
\(927\) | 14400.0 | 0.510203 | ||||||||
\(928\) | 7872.00 | 0.278460 | ||||||||
\(929\) | 49779.0 | 1.75802 | 0.879008 | − | 0.476808i | \(-0.158206\pi\) | ||||
0.879008 | + | 0.476808i | \(0.158206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41172.0 | 1.44936 | ||||||||
\(932\) | −3492.00 | −0.122730 | ||||||||
\(933\) | 4608.00 | 0.161693 | ||||||||
\(934\) | −30762.0 | −1.07769 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 936.000 | 0.0326860 | ||||||||
\(937\) | 44494.0 | 1.55129 | 0.775643 | − | 0.631171i | \(-0.217426\pi\) | ||||
0.775643 | + | 0.631171i | \(0.217426\pi\) | |||||||
\(938\) | 29800.0 | 1.03732 | ||||||||
\(939\) | −4542.00 | −0.157852 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 41235.0 | 1.42850 | 0.714252 | − | 0.699888i | \(-0.246767\pi\) | ||||
0.714252 | + | 0.699888i | \(0.246767\pi\) | |||||||
\(942\) | −16404.0 | −0.567379 | ||||||||
\(943\) | −891.000 | −0.0307688 | ||||||||
\(944\) | −384.000 | −0.0132396 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18984.0 | −0.652456 | ||||||||
\(947\) | 34536.0 | 1.18508 | 0.592539 | − | 0.805542i | \(-0.298126\pi\) | ||||
0.592539 | + | 0.805542i | \(0.298126\pi\) | |||||||
\(948\) | −10668.0 | −0.365486 | ||||||||
\(949\) | 4238.00 | 0.144964 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8172.00 | 0.278649 | ||||||||
\(952\) | 24600.0 | 0.837490 | ||||||||
\(953\) | 48693.0 | 1.65511 | 0.827556 | − | 0.561384i | \(-0.189731\pi\) | ||||
0.827556 | + | 0.561384i | \(0.189731\pi\) | |||||||
\(954\) | 5670.00 | 0.192425 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20652.0 | 0.698675 | ||||||||
\(957\) | 15498.0 | 0.523489 | ||||||||
\(958\) | 3534.00 | 0.119184 | ||||||||
\(959\) | −6750.00 | −0.227288 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3333.00 | 0.111879 | ||||||||
\(962\) | 7670.00 | 0.257059 | ||||||||
\(963\) | −9099.00 | −0.304477 | ||||||||
\(964\) | −9928.00 | −0.331701 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 14850.0 | 0.494608 | ||||||||
\(967\) | 18088.0 | 0.601521 | 0.300761 | − | 0.953700i | \(-0.402760\pi\) | ||||
0.300761 | + | 0.953700i | \(0.402760\pi\) | |||||||
\(968\) | 7120.00 | 0.236411 | ||||||||
\(969\) | −53874.0 | −1.78605 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 15396.0 | 0.508837 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | −175.000 | −0.00576592 | ||||||||
\(974\) | 19786.0 | 0.650908 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11632.0 | −0.381487 | ||||||||
\(977\) | −29700.0 | −0.972556 | −0.486278 | − | 0.873804i | \(-0.661646\pi\) | ||||
−0.486278 | + | 0.873804i | \(0.661646\pi\) | |||||||
\(978\) | −5118.00 | −0.167337 | ||||||||
\(979\) | −16695.0 | −0.545020 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9900.00 | 0.322205 | ||||||||
\(982\) | 30672.0 | 0.996724 | ||||||||
\(983\) | −54444.0 | −1.76652 | −0.883262 | − | 0.468879i | \(-0.844658\pi\) | ||||
−0.883262 | + | 0.468879i | \(0.844658\pi\) | |||||||
\(984\) | −216.000 | −0.00699779 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −60516.0 | −1.95459 | ||||||||
\(987\) | −29250.0 | −0.943301 | ||||||||
\(988\) | −7592.00 | −0.244467 | ||||||||
\(989\) | 44748.0 | 1.43873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12571.0 | −0.402958 | −0.201479 | − | 0.979493i | \(-0.564575\pi\) | ||||
−0.201479 | + | 0.979493i | \(0.564575\pi\) | |||||||
\(992\) | −5824.00 | −0.186403 | ||||||||
\(993\) | 3300.00 | 0.105461 | ||||||||
\(994\) | −38550.0 | −1.23011 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1152.00 | 0.0366491 | ||||||||
\(997\) | 3796.00 | 0.120582 | 0.0602911 | − | 0.998181i | \(-0.480797\pi\) | ||||
0.0602911 | + | 0.998181i | \(0.480797\pi\) | |||||||
\(998\) | 32900.0 | 1.04352 | ||||||||
\(999\) | 7965.00 | 0.252254 |
(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 | 1950.4.a.g.1.1 | 1 | ||
5.4 | even | 2 | 390.4.a.g.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 1170.4.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.4.a.g.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
1170.4.a.e.1.1 | 1 | 15.14 | odd | 2 | |||
1950.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial |