Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1682,4,Mod(1,1682)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1682, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1682.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1682 = 2 \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1682.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: | \(99.2412126297\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 58) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1682.1 |
$q$-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 | ||||||||
\(3\) | 7.00000 | 1.34715 | 0.673575 | − | 0.739119i | \(-0.264758\pi\) | ||||
0.673575 | + | 0.739119i | \(0.264758\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −15.0000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | −14.0000 | −0.952579 | ||||||||
\(7\) | −18.0000 | −0.971909 | −0.485954 | − | 0.873984i | \(-0.661528\pi\) | ||||
−0.485954 | + | 0.873984i | \(0.661528\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 22.0000 | 0.814815 | ||||||||
\(10\) | 30.0000 | 0.948683 | ||||||||
\(11\) | −27.0000 | −0.740073 | −0.370037 | − | 0.929017i | \(-0.620655\pi\) | ||||
−0.370037 | + | 0.929017i | \(0.620655\pi\) | |||||||
\(12\) | 28.0000 | 0.673575 | ||||||||
\(13\) | −57.0000 | −1.21607 | −0.608037 | − | 0.793909i | \(-0.708043\pi\) | ||||
−0.608037 | + | 0.793909i | \(0.708043\pi\) | |||||||
\(14\) | 36.0000 | 0.687243 | ||||||||
\(15\) | −105.000 | −1.80739 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 44.0000 | 0.627739 | 0.313870 | − | 0.949466i | \(-0.398375\pi\) | ||||
0.313870 | + | 0.949466i | \(0.398375\pi\) | |||||||
\(18\) | −44.0000 | −0.576161 | ||||||||
\(19\) | −152.000 | −1.83533 | −0.917663 | − | 0.397360i | \(-0.869927\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | −60.0000 | −0.670820 | ||||||||
\(21\) | −126.000 | −1.30931 | ||||||||
\(22\) | 54.0000 | 0.523311 | ||||||||
\(23\) | −152.000 | −1.37801 | −0.689004 | − | 0.724757i | \(-0.741952\pi\) | ||||
−0.689004 | + | 0.724757i | \(0.741952\pi\) | |||||||
\(24\) | −56.0000 | −0.476290 | ||||||||
\(25\) | 100.000 | 0.800000 | ||||||||
\(26\) | 114.000 | 0.859894 | ||||||||
\(27\) | −35.0000 | −0.249472 | ||||||||
\(28\) | −72.0000 | −0.485954 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 210.000 | 1.27802 | ||||||||
\(31\) | 173.000 | 1.00231 | 0.501157 | − | 0.865357i | \(-0.332908\pi\) | ||||
0.501157 | + | 0.865357i | \(0.332908\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −189.000 | −0.996990 | ||||||||
\(34\) | −88.0000 | −0.443879 | ||||||||
\(35\) | 270.000 | 1.30395 | ||||||||
\(36\) | 88.0000 | 0.407407 | ||||||||
\(37\) | 120.000 | 0.533186 | 0.266593 | − | 0.963809i | \(-0.414102\pi\) | ||||
0.266593 | + | 0.963809i | \(0.414102\pi\) | |||||||
\(38\) | 304.000 | 1.29777 | ||||||||
\(39\) | −399.000 | −1.63823 | ||||||||
\(40\) | 120.000 | 0.474342 | ||||||||
\(41\) | 314.000 | 1.19606 | 0.598031 | − | 0.801473i | \(-0.295950\pi\) | ||||
0.598031 | + | 0.801473i | \(0.295950\pi\) | |||||||
\(42\) | 252.000 | 0.925820 | ||||||||
\(43\) | −339.000 | −1.20226 | −0.601128 | − | 0.799153i | \(-0.705282\pi\) | ||||
−0.601128 | + | 0.799153i | \(0.705282\pi\) | |||||||
\(44\) | −108.000 | −0.370037 | ||||||||
\(45\) | −330.000 | −1.09319 | ||||||||
\(46\) | 304.000 | 0.974399 | ||||||||
\(47\) | 357.000 | 1.10795 | 0.553977 | − | 0.832532i | \(-0.313110\pi\) | ||||
0.553977 | + | 0.832532i | \(0.313110\pi\) | |||||||
\(48\) | 112.000 | 0.336788 | ||||||||
\(49\) | −19.0000 | −0.0553936 | ||||||||
\(50\) | −200.000 | −0.565685 | ||||||||
\(51\) | 308.000 | 0.845659 | ||||||||
\(52\) | −228.000 | −0.608037 | ||||||||
\(53\) | −59.0000 | −0.152911 | −0.0764554 | − | 0.997073i | \(-0.524360\pi\) | ||||
−0.0764554 | + | 0.997073i | \(0.524360\pi\) | |||||||
\(54\) | 70.0000 | 0.176404 | ||||||||
\(55\) | 405.000 | 0.992913 | ||||||||
\(56\) | 144.000 | 0.343622 | ||||||||
\(57\) | −1064.00 | −2.47246 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −572.000 | −1.26217 | −0.631085 | − | 0.775713i | \(-0.717390\pi\) | ||||
−0.631085 | + | 0.775713i | \(0.717390\pi\) | |||||||
\(60\) | −420.000 | −0.903696 | ||||||||
\(61\) | 420.000 | 0.881565 | 0.440783 | − | 0.897614i | \(-0.354701\pi\) | ||||
0.440783 | + | 0.897614i | \(0.354701\pi\) | |||||||
\(62\) | −346.000 | −0.708743 | ||||||||
\(63\) | −396.000 | −0.791926 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 855.000 | 1.63153 | ||||||||
\(66\) | 378.000 | 0.704979 | ||||||||
\(67\) | 660.000 | 1.20346 | 0.601730 | − | 0.798699i | \(-0.294478\pi\) | ||||
0.601730 | + | 0.798699i | \(0.294478\pi\) | |||||||
\(68\) | 176.000 | 0.313870 | ||||||||
\(69\) | −1064.00 | −1.85638 | ||||||||
\(70\) | −540.000 | −0.922033 | ||||||||
\(71\) | 726.000 | 1.21353 | 0.606763 | − | 0.794883i | \(-0.292468\pi\) | ||||
0.606763 | + | 0.794883i | \(0.292468\pi\) | |||||||
\(72\) | −176.000 | −0.288081 | ||||||||
\(73\) | −1004.00 | −1.60972 | −0.804858 | − | 0.593467i | \(-0.797759\pi\) | ||||
−0.804858 | + | 0.593467i | \(0.797759\pi\) | |||||||
\(74\) | −240.000 | −0.377019 | ||||||||
\(75\) | 700.000 | 1.07772 | ||||||||
\(76\) | −608.000 | −0.917663 | ||||||||
\(77\) | 486.000 | 0.719284 | ||||||||
\(78\) | 798.000 | 1.15841 | ||||||||
\(79\) | −361.000 | −0.514122 | −0.257061 | − | 0.966395i | \(-0.582754\pi\) | ||||
−0.257061 | + | 0.966395i | \(0.582754\pi\) | |||||||
\(80\) | −240.000 | −0.335410 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | −628.000 | −0.845744 | ||||||||
\(83\) | −168.000 | −0.222173 | −0.111087 | − | 0.993811i | \(-0.535433\pi\) | ||||
−0.111087 | + | 0.993811i | \(0.535433\pi\) | |||||||
\(84\) | −504.000 | −0.654654 | ||||||||
\(85\) | −660.000 | −0.842201 | ||||||||
\(86\) | 678.000 | 0.850123 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 216.000 | 0.261655 | ||||||||
\(89\) | −58.0000 | −0.0690785 | −0.0345393 | − | 0.999403i | \(-0.510996\pi\) | ||||
−0.0345393 | + | 0.999403i | \(0.510996\pi\) | |||||||
\(90\) | 660.000 | 0.773001 | ||||||||
\(91\) | 1026.00 | 1.18191 | ||||||||
\(92\) | −608.000 | −0.689004 | ||||||||
\(93\) | 1211.00 | 1.35027 | ||||||||
\(94\) | −714.000 | −0.783441 | ||||||||
\(95\) | 2280.00 | 2.46235 | ||||||||
\(96\) | −224.000 | −0.238145 | ||||||||
\(97\) | 1206.00 | 1.26238 | 0.631189 | − | 0.775629i | \(-0.282567\pi\) | ||||
0.631189 | + | 0.775629i | \(0.282567\pi\) | |||||||
\(98\) | 38.0000 | 0.0391692 | ||||||||
\(99\) | −594.000 | −0.603023 | ||||||||
\(100\) | 400.000 | 0.400000 | ||||||||
\(101\) | −1440.00 | −1.41867 | −0.709333 | − | 0.704873i | \(-0.751004\pi\) | ||||
−0.709333 | + | 0.704873i | \(0.751004\pi\) | |||||||
\(102\) | −616.000 | −0.597971 | ||||||||
\(103\) | 1858.00 | 1.77742 | 0.888710 | − | 0.458471i | \(-0.151603\pi\) | ||||
0.888710 | + | 0.458471i | \(0.151603\pi\) | |||||||
\(104\) | 456.000 | 0.429947 | ||||||||
\(105\) | 1890.00 | 1.75662 | ||||||||
\(106\) | 118.000 | 0.108124 | ||||||||
\(107\) | −1914.00 | −1.72928 | −0.864642 | − | 0.502389i | \(-0.832455\pi\) | ||||
−0.864642 | + | 0.502389i | \(0.832455\pi\) | |||||||
\(108\) | −140.000 | −0.124736 | ||||||||
\(109\) | 989.000 | 0.869074 | 0.434537 | − | 0.900654i | \(-0.356912\pi\) | ||||
0.434537 | + | 0.900654i | \(0.356912\pi\) | |||||||
\(110\) | −810.000 | −0.702095 | ||||||||
\(111\) | 840.000 | 0.718282 | ||||||||
\(112\) | −288.000 | −0.242977 | ||||||||
\(113\) | 278.000 | 0.231434 | 0.115717 | − | 0.993282i | \(-0.463083\pi\) | ||||
0.115717 | + | 0.993282i | \(0.463083\pi\) | |||||||
\(114\) | 2128.00 | 1.74829 | ||||||||
\(115\) | 2280.00 | 1.84879 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1254.00 | −0.990875 | ||||||||
\(118\) | 1144.00 | 0.892489 | ||||||||
\(119\) | −792.000 | −0.610105 | ||||||||
\(120\) | 840.000 | 0.639010 | ||||||||
\(121\) | −602.000 | −0.452292 | ||||||||
\(122\) | −840.000 | −0.623361 | ||||||||
\(123\) | 2198.00 | 1.61128 | ||||||||
\(124\) | 692.000 | 0.501157 | ||||||||
\(125\) | 375.000 | 0.268328 | ||||||||
\(126\) | 792.000 | 0.559976 | ||||||||
\(127\) | 600.000 | 0.419224 | 0.209612 | − | 0.977785i | \(-0.432780\pi\) | ||||
0.209612 | + | 0.977785i | \(0.432780\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −2373.00 | −1.61962 | ||||||||
\(130\) | −1710.00 | −1.15367 | ||||||||
\(131\) | 1652.00 | 1.10180 | 0.550900 | − | 0.834571i | \(-0.314284\pi\) | ||||
0.550900 | + | 0.834571i | \(0.314284\pi\) | |||||||
\(132\) | −756.000 | −0.498495 | ||||||||
\(133\) | 2736.00 | 1.78377 | ||||||||
\(134\) | −1320.00 | −0.850975 | ||||||||
\(135\) | 525.000 | 0.334702 | ||||||||
\(136\) | −352.000 | −0.221939 | ||||||||
\(137\) | 1212.00 | 0.755826 | 0.377913 | − | 0.925841i | \(-0.376642\pi\) | ||||
0.377913 | + | 0.925841i | \(0.376642\pi\) | |||||||
\(138\) | 2128.00 | 1.31266 | ||||||||
\(139\) | 1328.00 | 0.810356 | 0.405178 | − | 0.914238i | \(-0.367210\pi\) | ||||
0.405178 | + | 0.914238i | \(0.367210\pi\) | |||||||
\(140\) | 1080.00 | 0.651976 | ||||||||
\(141\) | 2499.00 | 1.49258 | ||||||||
\(142\) | −1452.00 | −0.858092 | ||||||||
\(143\) | 1539.00 | 0.899984 | ||||||||
\(144\) | 352.000 | 0.203704 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2008.00 | 1.13824 | ||||||||
\(147\) | −133.000 | −0.0746235 | ||||||||
\(148\) | 480.000 | 0.266593 | ||||||||
\(149\) | −1777.00 | −0.977030 | −0.488515 | − | 0.872555i | \(-0.662461\pi\) | ||||
−0.488515 | + | 0.872555i | \(0.662461\pi\) | |||||||
\(150\) | −1400.00 | −0.762063 | ||||||||
\(151\) | −1934.00 | −1.04230 | −0.521148 | − | 0.853466i | \(-0.674496\pi\) | ||||
−0.521148 | + | 0.853466i | \(0.674496\pi\) | |||||||
\(152\) | 1216.00 | 0.648886 | ||||||||
\(153\) | 968.000 | 0.511491 | ||||||||
\(154\) | −972.000 | −0.508610 | ||||||||
\(155\) | −2595.00 | −1.34474 | ||||||||
\(156\) | −1596.00 | −0.819117 | ||||||||
\(157\) | −734.000 | −0.373118 | −0.186559 | − | 0.982444i | \(-0.559734\pi\) | ||||
−0.186559 | + | 0.982444i | \(0.559734\pi\) | |||||||
\(158\) | 722.000 | 0.363539 | ||||||||
\(159\) | −413.000 | −0.205994 | ||||||||
\(160\) | 480.000 | 0.237171 | ||||||||
\(161\) | 2736.00 | 1.33930 | ||||||||
\(162\) | 1678.00 | 0.813803 | ||||||||
\(163\) | 3337.00 | 1.60352 | 0.801761 | − | 0.597645i | \(-0.203897\pi\) | ||||
0.801761 | + | 0.597645i | \(0.203897\pi\) | |||||||
\(164\) | 1256.00 | 0.598031 | ||||||||
\(165\) | 2835.00 | 1.33760 | ||||||||
\(166\) | 336.000 | 0.157100 | ||||||||
\(167\) | −198.000 | −0.0917467 | −0.0458734 | − | 0.998947i | \(-0.514607\pi\) | ||||
−0.0458734 | + | 0.998947i | \(0.514607\pi\) | |||||||
\(168\) | 1008.00 | 0.462910 | ||||||||
\(169\) | 1052.00 | 0.478835 | ||||||||
\(170\) | 1320.00 | 0.595526 | ||||||||
\(171\) | −3344.00 | −1.49545 | ||||||||
\(172\) | −1356.00 | −0.601128 | ||||||||
\(173\) | −2598.00 | −1.14175 | −0.570874 | − | 0.821038i | \(-0.693395\pi\) | ||||
−0.570874 | + | 0.821038i | \(0.693395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1800.00 | −0.777527 | ||||||||
\(176\) | −432.000 | −0.185018 | ||||||||
\(177\) | −4004.00 | −1.70033 | ||||||||
\(178\) | 116.000 | 0.0488459 | ||||||||
\(179\) | −1510.00 | −0.630518 | −0.315259 | − | 0.949006i | \(-0.602091\pi\) | ||||
−0.315259 | + | 0.949006i | \(0.602091\pi\) | |||||||
\(180\) | −1320.00 | −0.546594 | ||||||||
\(181\) | −2865.00 | −1.17654 | −0.588270 | − | 0.808665i | \(-0.700191\pi\) | ||||
−0.588270 | + | 0.808665i | \(0.700191\pi\) | |||||||
\(182\) | −2052.00 | −0.835738 | ||||||||
\(183\) | 2940.00 | 1.18760 | ||||||||
\(184\) | 1216.00 | 0.487200 | ||||||||
\(185\) | −1800.00 | −0.715344 | ||||||||
\(186\) | −2422.00 | −0.954783 | ||||||||
\(187\) | −1188.00 | −0.464573 | ||||||||
\(188\) | 1428.00 | 0.553977 | ||||||||
\(189\) | 630.000 | 0.242464 | ||||||||
\(190\) | −4560.00 | −1.74114 | ||||||||
\(191\) | 1936.00 | 0.733424 | 0.366712 | − | 0.930334i | \(-0.380483\pi\) | ||||
0.366712 | + | 0.930334i | \(0.380483\pi\) | |||||||
\(192\) | 448.000 | 0.168394 | ||||||||
\(193\) | −3850.00 | −1.43590 | −0.717951 | − | 0.696094i | \(-0.754920\pi\) | ||||
−0.717951 | + | 0.696094i | \(0.754920\pi\) | |||||||
\(194\) | −2412.00 | −0.892637 | ||||||||
\(195\) | 5985.00 | 2.19792 | ||||||||
\(196\) | −76.0000 | −0.0276968 | ||||||||
\(197\) | 3034.00 | 1.09728 | 0.548638 | − | 0.836060i | \(-0.315146\pi\) | ||||
0.548638 | + | 0.836060i | \(0.315146\pi\) | |||||||
\(198\) | 1188.00 | 0.426401 | ||||||||
\(199\) | 246.000 | 0.0876305 | 0.0438153 | − | 0.999040i | \(-0.486049\pi\) | ||||
0.0438153 | + | 0.999040i | \(0.486049\pi\) | |||||||
\(200\) | −800.000 | −0.282843 | ||||||||
\(201\) | 4620.00 | 1.62124 | ||||||||
\(202\) | 2880.00 | 1.00315 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1232.00 | 0.422830 | ||||||||
\(205\) | −4710.00 | −1.60469 | ||||||||
\(206\) | −3716.00 | −1.25683 | ||||||||
\(207\) | −3344.00 | −1.12282 | ||||||||
\(208\) | −912.000 | −0.304018 | ||||||||
\(209\) | 4104.00 | 1.35828 | ||||||||
\(210\) | −3780.00 | −1.24212 | ||||||||
\(211\) | 1493.00 | 0.487120 | 0.243560 | − | 0.969886i | \(-0.421685\pi\) | ||||
0.243560 | + | 0.969886i | \(0.421685\pi\) | |||||||
\(212\) | −236.000 | −0.0764554 | ||||||||
\(213\) | 5082.00 | 1.63480 | ||||||||
\(214\) | 3828.00 | 1.22279 | ||||||||
\(215\) | 5085.00 | 1.61300 | ||||||||
\(216\) | 280.000 | 0.0882018 | ||||||||
\(217\) | −3114.00 | −0.974157 | ||||||||
\(218\) | −1978.00 | −0.614528 | ||||||||
\(219\) | −7028.00 | −2.16853 | ||||||||
\(220\) | 1620.00 | 0.496456 | ||||||||
\(221\) | −2508.00 | −0.763377 | ||||||||
\(222\) | −1680.00 | −0.507902 | ||||||||
\(223\) | 1402.00 | 0.421008 | 0.210504 | − | 0.977593i | \(-0.432489\pi\) | ||||
0.210504 | + | 0.977593i | \(0.432489\pi\) | |||||||
\(224\) | 576.000 | 0.171811 | ||||||||
\(225\) | 2200.00 | 0.651852 | ||||||||
\(226\) | −556.000 | −0.163649 | ||||||||
\(227\) | 1166.00 | 0.340926 | 0.170463 | − | 0.985364i | \(-0.445474\pi\) | ||||
0.170463 | + | 0.985364i | \(0.445474\pi\) | |||||||
\(228\) | −4256.00 | −1.23623 | ||||||||
\(229\) | 1466.00 | 0.423039 | 0.211520 | − | 0.977374i | \(-0.432159\pi\) | ||||
0.211520 | + | 0.977374i | \(0.432159\pi\) | |||||||
\(230\) | −4560.00 | −1.30729 | ||||||||
\(231\) | 3402.00 | 0.968983 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 847.000 | 0.238149 | 0.119075 | − | 0.992885i | \(-0.462007\pi\) | ||||
0.119075 | + | 0.992885i | \(0.462007\pi\) | |||||||
\(234\) | 2508.00 | 0.700654 | ||||||||
\(235\) | −5355.00 | −1.48648 | ||||||||
\(236\) | −2288.00 | −0.631085 | ||||||||
\(237\) | −2527.00 | −0.692600 | ||||||||
\(238\) | 1584.00 | 0.431410 | ||||||||
\(239\) | −444.000 | −0.120167 | −0.0600836 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600836 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(240\) | −1680.00 | −0.451848 | ||||||||
\(241\) | 5297.00 | 1.41581 | 0.707904 | − | 0.706309i | \(-0.249641\pi\) | ||||
0.707904 | + | 0.706309i | \(0.249641\pi\) | |||||||
\(242\) | 1204.00 | 0.319818 | ||||||||
\(243\) | −4928.00 | −1.30095 | ||||||||
\(244\) | 1680.00 | 0.440783 | ||||||||
\(245\) | 285.000 | 0.0743183 | ||||||||
\(246\) | −4396.00 | −1.13934 | ||||||||
\(247\) | 8664.00 | 2.23189 | ||||||||
\(248\) | −1384.00 | −0.354371 | ||||||||
\(249\) | −1176.00 | −0.299301 | ||||||||
\(250\) | −750.000 | −0.189737 | ||||||||
\(251\) | −4061.00 | −1.02123 | −0.510614 | − | 0.859810i | \(-0.670582\pi\) | ||||
−0.510614 | + | 0.859810i | \(0.670582\pi\) | |||||||
\(252\) | −1584.00 | −0.395963 | ||||||||
\(253\) | 4104.00 | 1.01983 | ||||||||
\(254\) | −1200.00 | −0.296436 | ||||||||
\(255\) | −4620.00 | −1.13457 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −6843.00 | −1.66091 | −0.830456 | − | 0.557084i | \(-0.811920\pi\) | ||||
−0.830456 | + | 0.557084i | \(0.811920\pi\) | |||||||
\(258\) | 4746.00 | 1.14524 | ||||||||
\(259\) | −2160.00 | −0.518208 | ||||||||
\(260\) | 3420.00 | 0.815767 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3304.00 | −0.779091 | ||||||||
\(263\) | −3191.00 | −0.748158 | −0.374079 | − | 0.927397i | \(-0.622041\pi\) | ||||
−0.374079 | + | 0.927397i | \(0.622041\pi\) | |||||||
\(264\) | 1512.00 | 0.352489 | ||||||||
\(265\) | 885.000 | 0.205151 | ||||||||
\(266\) | −5472.00 | −1.26132 | ||||||||
\(267\) | −406.000 | −0.0930592 | ||||||||
\(268\) | 2640.00 | 0.601730 | ||||||||
\(269\) | −7436.00 | −1.68543 | −0.842715 | − | 0.538359i | \(-0.819044\pi\) | ||||
−0.842715 | + | 0.538359i | \(0.819044\pi\) | |||||||
\(270\) | −1050.00 | −0.236670 | ||||||||
\(271\) | 2755.00 | 0.617544 | 0.308772 | − | 0.951136i | \(-0.400082\pi\) | ||||
0.308772 | + | 0.951136i | \(0.400082\pi\) | |||||||
\(272\) | 704.000 | 0.156935 | ||||||||
\(273\) | 7182.00 | 1.59221 | ||||||||
\(274\) | −2424.00 | −0.534450 | ||||||||
\(275\) | −2700.00 | −0.592059 | ||||||||
\(276\) | −4256.00 | −0.928192 | ||||||||
\(277\) | −2410.00 | −0.522754 | −0.261377 | − | 0.965237i | \(-0.584177\pi\) | ||||
−0.261377 | + | 0.965237i | \(0.584177\pi\) | |||||||
\(278\) | −2656.00 | −0.573008 | ||||||||
\(279\) | 3806.00 | 0.816700 | ||||||||
\(280\) | −2160.00 | −0.461017 | ||||||||
\(281\) | 2235.00 | 0.474480 | 0.237240 | − | 0.971451i | \(-0.423757\pi\) | ||||
0.237240 | + | 0.971451i | \(0.423757\pi\) | |||||||
\(282\) | −4998.00 | −1.05541 | ||||||||
\(283\) | −1648.00 | −0.346161 | −0.173080 | − | 0.984908i | \(-0.555372\pi\) | ||||
−0.173080 | + | 0.984908i | \(0.555372\pi\) | |||||||
\(284\) | 2904.00 | 0.606763 | ||||||||
\(285\) | 15960.0 | 3.31715 | ||||||||
\(286\) | −3078.00 | −0.636384 | ||||||||
\(287\) | −5652.00 | −1.16246 | ||||||||
\(288\) | −704.000 | −0.144040 | ||||||||
\(289\) | −2977.00 | −0.605943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8442.00 | 1.70061 | ||||||||
\(292\) | −4016.00 | −0.804858 | ||||||||
\(293\) | −2878.00 | −0.573838 | −0.286919 | − | 0.957955i | \(-0.592631\pi\) | ||||
−0.286919 | + | 0.957955i | \(0.592631\pi\) | |||||||
\(294\) | 266.000 | 0.0527668 | ||||||||
\(295\) | 8580.00 | 1.69338 | ||||||||
\(296\) | −960.000 | −0.188510 | ||||||||
\(297\) | 945.000 | 0.184628 | ||||||||
\(298\) | 3554.00 | 0.690865 | ||||||||
\(299\) | 8664.00 | 1.67576 | ||||||||
\(300\) | 2800.00 | 0.538860 | ||||||||
\(301\) | 6102.00 | 1.16848 | ||||||||
\(302\) | 3868.00 | 0.737015 | ||||||||
\(303\) | −10080.0 | −1.91116 | ||||||||
\(304\) | −2432.00 | −0.458831 | ||||||||
\(305\) | −6300.00 | −1.18274 | ||||||||
\(306\) | −1936.00 | −0.361679 | ||||||||
\(307\) | −4903.00 | −0.911495 | −0.455748 | − | 0.890109i | \(-0.650628\pi\) | ||||
−0.455748 | + | 0.890109i | \(0.650628\pi\) | |||||||
\(308\) | 1944.00 | 0.359642 | ||||||||
\(309\) | 13006.0 | 2.39445 | ||||||||
\(310\) | 5190.00 | 0.950878 | ||||||||
\(311\) | 32.0000 | 0.00583458 | 0.00291729 | − | 0.999996i | \(-0.499071\pi\) | ||||
0.00291729 | + | 0.999996i | \(0.499071\pi\) | |||||||
\(312\) | 3192.00 | 0.579203 | ||||||||
\(313\) | −5455.00 | −0.985095 | −0.492548 | − | 0.870285i | \(-0.663934\pi\) | ||||
−0.492548 | + | 0.870285i | \(0.663934\pi\) | |||||||
\(314\) | 1468.00 | 0.263834 | ||||||||
\(315\) | 5940.00 | 1.06248 | ||||||||
\(316\) | −1444.00 | −0.257061 | ||||||||
\(317\) | 9552.00 | 1.69241 | 0.846205 | − | 0.532858i | \(-0.178882\pi\) | ||||
0.846205 | + | 0.532858i | \(0.178882\pi\) | |||||||
\(318\) | 826.000 | 0.145660 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −960.000 | −0.167705 | ||||||||
\(321\) | −13398.0 | −2.32961 | ||||||||
\(322\) | −5472.00 | −0.947027 | ||||||||
\(323\) | −6688.00 | −1.15211 | ||||||||
\(324\) | −3356.00 | −0.575446 | ||||||||
\(325\) | −5700.00 | −0.972859 | ||||||||
\(326\) | −6674.00 | −1.13386 | ||||||||
\(327\) | 6923.00 | 1.17077 | ||||||||
\(328\) | −2512.00 | −0.422872 | ||||||||
\(329\) | −6426.00 | −1.07683 | ||||||||
\(330\) | −5670.00 | −0.945828 | ||||||||
\(331\) | 2433.00 | 0.404017 | 0.202009 | − | 0.979384i | \(-0.435253\pi\) | ||||
0.202009 | + | 0.979384i | \(0.435253\pi\) | |||||||
\(332\) | −672.000 | −0.111087 | ||||||||
\(333\) | 2640.00 | 0.434448 | ||||||||
\(334\) | 396.000 | 0.0648747 | ||||||||
\(335\) | −9900.00 | −1.61461 | ||||||||
\(336\) | −2016.00 | −0.327327 | ||||||||
\(337\) | 7460.00 | 1.20585 | 0.602926 | − | 0.797797i | \(-0.294001\pi\) | ||||
0.602926 | + | 0.797797i | \(0.294001\pi\) | |||||||
\(338\) | −2104.00 | −0.338587 | ||||||||
\(339\) | 1946.00 | 0.311776 | ||||||||
\(340\) | −2640.00 | −0.421100 | ||||||||
\(341\) | −4671.00 | −0.741785 | ||||||||
\(342\) | 6688.00 | 1.05744 | ||||||||
\(343\) | 6516.00 | 1.02575 | ||||||||
\(344\) | 2712.00 | 0.425062 | ||||||||
\(345\) | 15960.0 | 2.49060 | ||||||||
\(346\) | 5196.00 | 0.807337 | ||||||||
\(347\) | 4002.00 | 0.619131 | 0.309566 | − | 0.950878i | \(-0.399816\pi\) | ||||
0.309566 | + | 0.950878i | \(0.399816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2167.00 | −0.332369 | −0.166185 | − | 0.986095i | \(-0.553145\pi\) | ||||
−0.166185 | + | 0.986095i | \(0.553145\pi\) | |||||||
\(350\) | 3600.00 | 0.549795 | ||||||||
\(351\) | 1995.00 | 0.303377 | ||||||||
\(352\) | 864.000 | 0.130828 | ||||||||
\(353\) | −2354.00 | −0.354931 | −0.177466 | − | 0.984127i | \(-0.556790\pi\) | ||||
−0.177466 | + | 0.984127i | \(0.556790\pi\) | |||||||
\(354\) | 8008.00 | 1.20232 | ||||||||
\(355\) | −10890.0 | −1.62812 | ||||||||
\(356\) | −232.000 | −0.0345393 | ||||||||
\(357\) | −5544.00 | −0.821904 | ||||||||
\(358\) | 3020.00 | 0.445843 | ||||||||
\(359\) | 3471.00 | 0.510285 | 0.255143 | − | 0.966903i | \(-0.417878\pi\) | ||||
0.255143 | + | 0.966903i | \(0.417878\pi\) | |||||||
\(360\) | 2640.00 | 0.386501 | ||||||||
\(361\) | 16245.0 | 2.36842 | ||||||||
\(362\) | 5730.00 | 0.831940 | ||||||||
\(363\) | −4214.00 | −0.609305 | ||||||||
\(364\) | 4104.00 | 0.590956 | ||||||||
\(365\) | 15060.0 | 2.15966 | ||||||||
\(366\) | −5880.00 | −0.839761 | ||||||||
\(367\) | 10880.0 | 1.54750 | 0.773748 | − | 0.633493i | \(-0.218379\pi\) | ||||
0.773748 | + | 0.633493i | \(0.218379\pi\) | |||||||
\(368\) | −2432.00 | −0.344502 | ||||||||
\(369\) | 6908.00 | 0.974569 | ||||||||
\(370\) | 3600.00 | 0.505825 | ||||||||
\(371\) | 1062.00 | 0.148615 | ||||||||
\(372\) | 4844.00 | 0.675134 | ||||||||
\(373\) | 8827.00 | 1.22532 | 0.612661 | − | 0.790346i | \(-0.290099\pi\) | ||||
0.612661 | + | 0.790346i | \(0.290099\pi\) | |||||||
\(374\) | 2376.00 | 0.328503 | ||||||||
\(375\) | 2625.00 | 0.361478 | ||||||||
\(376\) | −2856.00 | −0.391721 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1260.00 | −0.171448 | ||||||||
\(379\) | 876.000 | 0.118726 | 0.0593629 | − | 0.998236i | \(-0.481093\pi\) | ||||
0.0593629 | + | 0.998236i | \(0.481093\pi\) | |||||||
\(380\) | 9120.00 | 1.23117 | ||||||||
\(381\) | 4200.00 | 0.564757 | ||||||||
\(382\) | −3872.00 | −0.518609 | ||||||||
\(383\) | 5446.00 | 0.726573 | 0.363287 | − | 0.931677i | \(-0.381655\pi\) | ||||
0.363287 | + | 0.931677i | \(0.381655\pi\) | |||||||
\(384\) | −896.000 | −0.119072 | ||||||||
\(385\) | −7290.00 | −0.965020 | ||||||||
\(386\) | 7700.00 | 1.01534 | ||||||||
\(387\) | −7458.00 | −0.979616 | ||||||||
\(388\) | 4824.00 | 0.631189 | ||||||||
\(389\) | 2216.00 | 0.288832 | 0.144416 | − | 0.989517i | \(-0.453870\pi\) | ||||
0.144416 | + | 0.989517i | \(0.453870\pi\) | |||||||
\(390\) | −11970.0 | −1.55417 | ||||||||
\(391\) | −6688.00 | −0.865030 | ||||||||
\(392\) | 152.000 | 0.0195846 | ||||||||
\(393\) | 11564.0 | 1.48429 | ||||||||
\(394\) | −6068.00 | −0.775892 | ||||||||
\(395\) | 5415.00 | 0.689768 | ||||||||
\(396\) | −2376.00 | −0.301511 | ||||||||
\(397\) | 6823.00 | 0.862561 | 0.431280 | − | 0.902218i | \(-0.358062\pi\) | ||||
0.431280 | + | 0.902218i | \(0.358062\pi\) | |||||||
\(398\) | −492.000 | −0.0619641 | ||||||||
\(399\) | 19152.0 | 2.40301 | ||||||||
\(400\) | 1600.00 | 0.200000 | ||||||||
\(401\) | −5589.00 | −0.696013 | −0.348007 | − | 0.937492i | \(-0.613141\pi\) | ||||
−0.348007 | + | 0.937492i | \(0.613141\pi\) | |||||||
\(402\) | −9240.00 | −1.14639 | ||||||||
\(403\) | −9861.00 | −1.21889 | ||||||||
\(404\) | −5760.00 | −0.709333 | ||||||||
\(405\) | 12585.0 | 1.54408 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3240.00 | −0.394597 | ||||||||
\(408\) | −2464.00 | −0.298986 | ||||||||
\(409\) | 8258.00 | 0.998366 | 0.499183 | − | 0.866496i | \(-0.333633\pi\) | ||||
0.499183 | + | 0.866496i | \(0.333633\pi\) | |||||||
\(410\) | 9420.00 | 1.13468 | ||||||||
\(411\) | 8484.00 | 1.01821 | ||||||||
\(412\) | 7432.00 | 0.888710 | ||||||||
\(413\) | 10296.0 | 1.22671 | ||||||||
\(414\) | 6688.00 | 0.793955 | ||||||||
\(415\) | 2520.00 | 0.298077 | ||||||||
\(416\) | 1824.00 | 0.214973 | ||||||||
\(417\) | 9296.00 | 1.09167 | ||||||||
\(418\) | −8208.00 | −0.960446 | ||||||||
\(419\) | 3946.00 | 0.460083 | 0.230041 | − | 0.973181i | \(-0.426114\pi\) | ||||
0.230041 | + | 0.973181i | \(0.426114\pi\) | |||||||
\(420\) | 7560.00 | 0.878310 | ||||||||
\(421\) | −1380.00 | −0.159756 | −0.0798778 | − | 0.996805i | \(-0.525453\pi\) | ||||
−0.0798778 | + | 0.996805i | \(0.525453\pi\) | |||||||
\(422\) | −2986.00 | −0.344446 | ||||||||
\(423\) | 7854.00 | 0.902777 | ||||||||
\(424\) | 472.000 | 0.0540621 | ||||||||
\(425\) | 4400.00 | 0.502191 | ||||||||
\(426\) | −10164.0 | −1.15598 | ||||||||
\(427\) | −7560.00 | −0.856801 | ||||||||
\(428\) | −7656.00 | −0.864642 | ||||||||
\(429\) | 10773.0 | 1.21241 | ||||||||
\(430\) | −10170.0 | −1.14056 | ||||||||
\(431\) | −5820.00 | −0.650440 | −0.325220 | − | 0.945638i | \(-0.605438\pi\) | ||||
−0.325220 | + | 0.945638i | \(0.605438\pi\) | |||||||
\(432\) | −560.000 | −0.0623681 | ||||||||
\(433\) | 14504.0 | 1.60974 | 0.804870 | − | 0.593451i | \(-0.202235\pi\) | ||||
0.804870 | + | 0.593451i | \(0.202235\pi\) | |||||||
\(434\) | 6228.00 | 0.688833 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3956.00 | 0.434537 | ||||||||
\(437\) | 23104.0 | 2.52909 | ||||||||
\(438\) | 14056.0 | 1.53338 | ||||||||
\(439\) | 14912.0 | 1.62121 | 0.810605 | − | 0.585594i | \(-0.199139\pi\) | ||||
0.810605 | + | 0.585594i | \(0.199139\pi\) | |||||||
\(440\) | −3240.00 | −0.351048 | ||||||||
\(441\) | −418.000 | −0.0451355 | ||||||||
\(442\) | 5016.00 | 0.539789 | ||||||||
\(443\) | −7180.00 | −0.770050 | −0.385025 | − | 0.922906i | \(-0.625807\pi\) | ||||
−0.385025 | + | 0.922906i | \(0.625807\pi\) | |||||||
\(444\) | 3360.00 | 0.359141 | ||||||||
\(445\) | 870.000 | 0.0926786 | ||||||||
\(446\) | −2804.00 | −0.297698 | ||||||||
\(447\) | −12439.0 | −1.31621 | ||||||||
\(448\) | −1152.00 | −0.121489 | ||||||||
\(449\) | −1398.00 | −0.146939 | −0.0734696 | − | 0.997297i | \(-0.523407\pi\) | ||||
−0.0734696 | + | 0.997297i | \(0.523407\pi\) | |||||||
\(450\) | −4400.00 | −0.460929 | ||||||||
\(451\) | −8478.00 | −0.885174 | ||||||||
\(452\) | 1112.00 | 0.115717 | ||||||||
\(453\) | −13538.0 | −1.40413 | ||||||||
\(454\) | −2332.00 | −0.241071 | ||||||||
\(455\) | −15390.0 | −1.58570 | ||||||||
\(456\) | 8512.00 | 0.874147 | ||||||||
\(457\) | −5658.00 | −0.579147 | −0.289573 | − | 0.957156i | \(-0.593513\pi\) | ||||
−0.289573 | + | 0.957156i | \(0.593513\pi\) | |||||||
\(458\) | −2932.00 | −0.299134 | ||||||||
\(459\) | −1540.00 | −0.156604 | ||||||||
\(460\) | 9120.00 | 0.924396 | ||||||||
\(461\) | −11410.0 | −1.15275 | −0.576374 | − | 0.817186i | \(-0.695533\pi\) | ||||
−0.576374 | + | 0.817186i | \(0.695533\pi\) | |||||||
\(462\) | −6804.00 | −0.685175 | ||||||||
\(463\) | −2560.00 | −0.256962 | −0.128481 | − | 0.991712i | \(-0.541010\pi\) | ||||
−0.128481 | + | 0.991712i | \(0.541010\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18165.0 | −1.81157 | ||||||||
\(466\) | −1694.00 | −0.168397 | ||||||||
\(467\) | −10395.0 | −1.03003 | −0.515014 | − | 0.857182i | \(-0.672213\pi\) | ||||
−0.515014 | + | 0.857182i | \(0.672213\pi\) | |||||||
\(468\) | −5016.00 | −0.495437 | ||||||||
\(469\) | −11880.0 | −1.16965 | ||||||||
\(470\) | 10710.0 | 1.05110 | ||||||||
\(471\) | −5138.00 | −0.502647 | ||||||||
\(472\) | 4576.00 | 0.446245 | ||||||||
\(473\) | 9153.00 | 0.889758 | ||||||||
\(474\) | 5054.00 | 0.489742 | ||||||||
\(475\) | −15200.0 | −1.46826 | ||||||||
\(476\) | −3168.00 | −0.305053 | ||||||||
\(477\) | −1298.00 | −0.124594 | ||||||||
\(478\) | 888.000 | 0.0849711 | ||||||||
\(479\) | 5627.00 | 0.536752 | 0.268376 | − | 0.963314i | \(-0.413513\pi\) | ||||
0.268376 | + | 0.963314i | \(0.413513\pi\) | |||||||
\(480\) | 3360.00 | 0.319505 | ||||||||
\(481\) | −6840.00 | −0.648393 | ||||||||
\(482\) | −10594.0 | −1.00113 | ||||||||
\(483\) | 19152.0 | 1.80424 | ||||||||
\(484\) | −2408.00 | −0.226146 | ||||||||
\(485\) | −18090.0 | −1.69366 | ||||||||
\(486\) | 9856.00 | 0.919912 | ||||||||
\(487\) | 8738.00 | 0.813053 | 0.406526 | − | 0.913639i | \(-0.366740\pi\) | ||||
0.406526 | + | 0.913639i | \(0.366740\pi\) | |||||||
\(488\) | −3360.00 | −0.311680 | ||||||||
\(489\) | 23359.0 | 2.16019 | ||||||||
\(490\) | −570.000 | −0.0525510 | ||||||||
\(491\) | −3177.00 | −0.292008 | −0.146004 | − | 0.989284i | \(-0.546641\pi\) | ||||
−0.146004 | + | 0.989284i | \(0.546641\pi\) | |||||||
\(492\) | 8792.00 | 0.805638 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −17328.0 | −1.57819 | ||||||||
\(495\) | 8910.00 | 0.809040 | ||||||||
\(496\) | 2768.00 | 0.250578 | ||||||||
\(497\) | −13068.0 | −1.17944 | ||||||||
\(498\) | 2352.00 | 0.211638 | ||||||||
\(499\) | −5816.00 | −0.521763 | −0.260882 | − | 0.965371i | \(-0.584013\pi\) | ||||
−0.260882 | + | 0.965371i | \(0.584013\pi\) | |||||||
\(500\) | 1500.00 | 0.134164 | ||||||||
\(501\) | −1386.00 | −0.123597 | ||||||||
\(502\) | 8122.00 | 0.722117 | ||||||||
\(503\) | 2267.00 | 0.200955 | 0.100478 | − | 0.994939i | \(-0.467963\pi\) | ||||
0.100478 | + | 0.994939i | \(0.467963\pi\) | |||||||
\(504\) | 3168.00 | 0.279988 | ||||||||
\(505\) | 21600.0 | 1.90334 | ||||||||
\(506\) | −8208.00 | −0.721127 | ||||||||
\(507\) | 7364.00 | 0.645063 | ||||||||
\(508\) | 2400.00 | 0.209612 | ||||||||
\(509\) | 6481.00 | 0.564372 | 0.282186 | − | 0.959360i | \(-0.408940\pi\) | ||||
0.282186 | + | 0.959360i | \(0.408940\pi\) | |||||||
\(510\) | 9240.00 | 0.802263 | ||||||||
\(511\) | 18072.0 | 1.56450 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 5320.00 | 0.457863 | ||||||||
\(514\) | 13686.0 | 1.17444 | ||||||||
\(515\) | −27870.0 | −2.38466 | ||||||||
\(516\) | −9492.00 | −0.809810 | ||||||||
\(517\) | −9639.00 | −0.819967 | ||||||||
\(518\) | 4320.00 | 0.366428 | ||||||||
\(519\) | −18186.0 | −1.53811 | ||||||||
\(520\) | −6840.00 | −0.576834 | ||||||||
\(521\) | −21357.0 | −1.79591 | −0.897953 | − | 0.440091i | \(-0.854946\pi\) | ||||
−0.897953 | + | 0.440091i | \(0.854946\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6192.00 | −0.517700 | −0.258850 | − | 0.965917i | \(-0.583344\pi\) | ||||
−0.258850 | + | 0.965917i | \(0.583344\pi\) | |||||||
\(524\) | 6608.00 | 0.550900 | ||||||||
\(525\) | −12600.0 | −1.04745 | ||||||||
\(526\) | 6382.00 | 0.529027 | ||||||||
\(527\) | 7612.00 | 0.629192 | ||||||||
\(528\) | −3024.00 | −0.249248 | ||||||||
\(529\) | 10937.0 | 0.898907 | ||||||||
\(530\) | −1770.00 | −0.145064 | ||||||||
\(531\) | −12584.0 | −1.02844 | ||||||||
\(532\) | 10944.0 | 0.891885 | ||||||||
\(533\) | −17898.0 | −1.45450 | ||||||||
\(534\) | 812.000 | 0.0658028 | ||||||||
\(535\) | 28710.0 | 2.32008 | ||||||||
\(536\) | −5280.00 | −0.425487 | ||||||||
\(537\) | −10570.0 | −0.849403 | ||||||||
\(538\) | 14872.0 | 1.19178 | ||||||||
\(539\) | 513.000 | 0.0409953 | ||||||||
\(540\) | 2100.00 | 0.167351 | ||||||||
\(541\) | 19800.0 | 1.57351 | 0.786755 | − | 0.617266i | \(-0.211760\pi\) | ||||
0.786755 | + | 0.617266i | \(0.211760\pi\) | |||||||
\(542\) | −5510.00 | −0.436669 | ||||||||
\(543\) | −20055.0 | −1.58498 | ||||||||
\(544\) | −1408.00 | −0.110970 | ||||||||
\(545\) | −14835.0 | −1.16598 | ||||||||
\(546\) | −14364.0 | −1.12587 | ||||||||
\(547\) | 10526.0 | 0.822777 | 0.411389 | − | 0.911460i | \(-0.365044\pi\) | ||||
0.411389 | + | 0.911460i | \(0.365044\pi\) | |||||||
\(548\) | 4848.00 | 0.377913 | ||||||||
\(549\) | 9240.00 | 0.718313 | ||||||||
\(550\) | 5400.00 | 0.418649 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 8512.00 | 0.656331 | ||||||||
\(553\) | 6498.00 | 0.499680 | ||||||||
\(554\) | 4820.00 | 0.369643 | ||||||||
\(555\) | −12600.0 | −0.963676 | ||||||||
\(556\) | 5312.00 | 0.405178 | ||||||||
\(557\) | −11834.0 | −0.900220 | −0.450110 | − | 0.892973i | \(-0.648615\pi\) | ||||
−0.450110 | + | 0.892973i | \(0.648615\pi\) | |||||||
\(558\) | −7612.00 | −0.577494 | ||||||||
\(559\) | 19323.0 | 1.46203 | ||||||||
\(560\) | 4320.00 | 0.325988 | ||||||||
\(561\) | −8316.00 | −0.625850 | ||||||||
\(562\) | −4470.00 | −0.335508 | ||||||||
\(563\) | −21771.0 | −1.62973 | −0.814865 | − | 0.579650i | \(-0.803189\pi\) | ||||
−0.814865 | + | 0.579650i | \(0.803189\pi\) | |||||||
\(564\) | 9996.00 | 0.746290 | ||||||||
\(565\) | −4170.00 | −0.310501 | ||||||||
\(566\) | 3296.00 | 0.244772 | ||||||||
\(567\) | 15102.0 | 1.11856 | ||||||||
\(568\) | −5808.00 | −0.429046 | ||||||||
\(569\) | −20778.0 | −1.53086 | −0.765430 | − | 0.643519i | \(-0.777474\pi\) | ||||
−0.765430 | + | 0.643519i | \(0.777474\pi\) | |||||||
\(570\) | −31920.0 | −2.34558 | ||||||||
\(571\) | −5596.00 | −0.410132 | −0.205066 | − | 0.978748i | \(-0.565741\pi\) | ||||
−0.205066 | + | 0.978748i | \(0.565741\pi\) | |||||||
\(572\) | 6156.00 | 0.449992 | ||||||||
\(573\) | 13552.0 | 0.988033 | ||||||||
\(574\) | 11304.0 | 0.821986 | ||||||||
\(575\) | −15200.0 | −1.10241 | ||||||||
\(576\) | 1408.00 | 0.101852 | ||||||||
\(577\) | 14908.0 | 1.07561 | 0.537806 | − | 0.843069i | \(-0.319253\pi\) | ||||
0.537806 | + | 0.843069i | \(0.319253\pi\) | |||||||
\(578\) | 5954.00 | 0.428467 | ||||||||
\(579\) | −26950.0 | −1.93438 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3024.00 | 0.215932 | ||||||||
\(582\) | −16884.0 | −1.20252 | ||||||||
\(583\) | 1593.00 | 0.113165 | ||||||||
\(584\) | 8032.00 | 0.569121 | ||||||||
\(585\) | 18810.0 | 1.32940 | ||||||||
\(586\) | 5756.00 | 0.405765 | ||||||||
\(587\) | 8136.00 | 0.572076 | 0.286038 | − | 0.958218i | \(-0.407662\pi\) | ||||
0.286038 | + | 0.958218i | \(0.407662\pi\) | |||||||
\(588\) | −532.000 | −0.0373118 | ||||||||
\(589\) | −26296.0 | −1.83957 | ||||||||
\(590\) | −17160.0 | −1.19740 | ||||||||
\(591\) | 21238.0 | 1.47820 | ||||||||
\(592\) | 1920.00 | 0.133296 | ||||||||
\(593\) | −3521.00 | −0.243828 | −0.121914 | − | 0.992541i | \(-0.538903\pi\) | ||||
−0.121914 | + | 0.992541i | \(0.538903\pi\) | |||||||
\(594\) | −1890.00 | −0.130552 | ||||||||
\(595\) | 11880.0 | 0.818542 | ||||||||
\(596\) | −7108.00 | −0.488515 | ||||||||
\(597\) | 1722.00 | 0.118052 | ||||||||
\(598\) | −17328.0 | −1.18494 | ||||||||
\(599\) | −7749.00 | −0.528574 | −0.264287 | − | 0.964444i | \(-0.585137\pi\) | ||||
−0.264287 | + | 0.964444i | \(0.585137\pi\) | |||||||
\(600\) | −5600.00 | −0.381032 | ||||||||
\(601\) | −5054.00 | −0.343023 | −0.171512 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171512 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(602\) | −12204.0 | −0.826242 | ||||||||
\(603\) | 14520.0 | 0.980597 | ||||||||
\(604\) | −7736.00 | −0.521148 | ||||||||
\(605\) | 9030.00 | 0.606813 | ||||||||
\(606\) | 20160.0 | 1.35139 | ||||||||
\(607\) | −27389.0 | −1.83144 | −0.915721 | − | 0.401815i | \(-0.868380\pi\) | ||||
−0.915721 | + | 0.401815i | \(0.868380\pi\) | |||||||
\(608\) | 4864.00 | 0.324443 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12600.0 | 0.836326 | ||||||||
\(611\) | −20349.0 | −1.34735 | ||||||||
\(612\) | 3872.00 | 0.255746 | ||||||||
\(613\) | −2375.00 | −0.156485 | −0.0782425 | − | 0.996934i | \(-0.524931\pi\) | ||||
−0.0782425 | + | 0.996934i | \(0.524931\pi\) | |||||||
\(614\) | 9806.00 | 0.644524 | ||||||||
\(615\) | −32970.0 | −2.16175 | ||||||||
\(616\) | −3888.00 | −0.254305 | ||||||||
\(617\) | −3412.00 | −0.222629 | −0.111314 | − | 0.993785i | \(-0.535506\pi\) | ||||
−0.111314 | + | 0.993785i | \(0.535506\pi\) | |||||||
\(618\) | −26012.0 | −1.69313 | ||||||||
\(619\) | −17659.0 | −1.14665 | −0.573324 | − | 0.819329i | \(-0.694346\pi\) | ||||
−0.573324 | + | 0.819329i | \(0.694346\pi\) | |||||||
\(620\) | −10380.0 | −0.672372 | ||||||||
\(621\) | 5320.00 | 0.343775 | ||||||||
\(622\) | −64.0000 | −0.00412567 | ||||||||
\(623\) | 1044.00 | 0.0671380 | ||||||||
\(624\) | −6384.00 | −0.409559 | ||||||||
\(625\) | −18125.0 | −1.16000 | ||||||||
\(626\) | 10910.0 | 0.696568 | ||||||||
\(627\) | 28728.0 | 1.82980 | ||||||||
\(628\) | −2936.00 | −0.186559 | ||||||||
\(629\) | 5280.00 | 0.334702 | ||||||||
\(630\) | −11880.0 | −0.751287 | ||||||||
\(631\) | 12742.0 | 0.803884 | 0.401942 | − | 0.915665i | \(-0.368335\pi\) | ||||
0.401942 | + | 0.915665i | \(0.368335\pi\) | |||||||
\(632\) | 2888.00 | 0.181770 | ||||||||
\(633\) | 10451.0 | 0.656224 | ||||||||
\(634\) | −19104.0 | −1.19671 | ||||||||
\(635\) | −9000.00 | −0.562447 | ||||||||
\(636\) | −1652.00 | −0.102997 | ||||||||
\(637\) | 1083.00 | 0.0673627 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15972.0 | 0.988799 | ||||||||
\(640\) | 1920.00 | 0.118585 | ||||||||
\(641\) | 10988.0 | 0.677067 | 0.338533 | − | 0.940954i | \(-0.390069\pi\) | ||||
0.338533 | + | 0.940954i | \(0.390069\pi\) | |||||||
\(642\) | 26796.0 | 1.64728 | ||||||||
\(643\) | −13190.0 | −0.808962 | −0.404481 | − | 0.914546i | \(-0.632548\pi\) | ||||
−0.404481 | + | 0.914546i | \(0.632548\pi\) | |||||||
\(644\) | 10944.0 | 0.669649 | ||||||||
\(645\) | 35595.0 | 2.17295 | ||||||||
\(646\) | 13376.0 | 0.814662 | ||||||||
\(647\) | 22924.0 | 1.39295 | 0.696473 | − | 0.717583i | \(-0.254752\pi\) | ||||
0.696473 | + | 0.717583i | \(0.254752\pi\) | |||||||
\(648\) | 6712.00 | 0.406902 | ||||||||
\(649\) | 15444.0 | 0.934099 | ||||||||
\(650\) | 11400.0 | 0.687915 | ||||||||
\(651\) | −21798.0 | −1.31234 | ||||||||
\(652\) | 13348.0 | 0.801761 | ||||||||
\(653\) | 10278.0 | 0.615941 | 0.307970 | − | 0.951396i | \(-0.400350\pi\) | ||||
0.307970 | + | 0.951396i | \(0.400350\pi\) | |||||||
\(654\) | −13846.0 | −0.827862 | ||||||||
\(655\) | −24780.0 | −1.47822 | ||||||||
\(656\) | 5024.00 | 0.299016 | ||||||||
\(657\) | −22088.0 | −1.31162 | ||||||||
\(658\) | 12852.0 | 0.761433 | ||||||||
\(659\) | 10607.0 | 0.626996 | 0.313498 | − | 0.949589i | \(-0.398499\pi\) | ||||
0.313498 | + | 0.949589i | \(0.398499\pi\) | |||||||
\(660\) | 11340.0 | 0.668801 | ||||||||
\(661\) | −24698.0 | −1.45331 | −0.726657 | − | 0.687000i | \(-0.758927\pi\) | ||||
−0.726657 | + | 0.687000i | \(0.758927\pi\) | |||||||
\(662\) | −4866.00 | −0.285683 | ||||||||
\(663\) | −17556.0 | −1.02838 | ||||||||
\(664\) | 1344.00 | 0.0785502 | ||||||||
\(665\) | −41040.0 | −2.39318 | ||||||||
\(666\) | −5280.00 | −0.307201 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −792.000 | −0.0458734 | ||||||||
\(669\) | 9814.00 | 0.567162 | ||||||||
\(670\) | 19800.0 | 1.14170 | ||||||||
\(671\) | −11340.0 | −0.652423 | ||||||||
\(672\) | 4032.00 | 0.231455 | ||||||||
\(673\) | 16801.0 | 0.962305 | 0.481152 | − | 0.876637i | \(-0.340218\pi\) | ||||
0.481152 | + | 0.876637i | \(0.340218\pi\) | |||||||
\(674\) | −14920.0 | −0.852666 | ||||||||
\(675\) | −3500.00 | −0.199578 | ||||||||
\(676\) | 4208.00 | 0.239417 | ||||||||
\(677\) | 1258.00 | 0.0714163 | 0.0357082 | − | 0.999362i | \(-0.488631\pi\) | ||||
0.0357082 | + | 0.999362i | \(0.488631\pi\) | |||||||
\(678\) | −3892.00 | −0.220459 | ||||||||
\(679\) | −21708.0 | −1.22692 | ||||||||
\(680\) | 5280.00 | 0.297763 | ||||||||
\(681\) | 8162.00 | 0.459278 | ||||||||
\(682\) | 9342.00 | 0.524522 | ||||||||
\(683\) | −1256.00 | −0.0703653 | −0.0351827 | − | 0.999381i | \(-0.511201\pi\) | ||||
−0.0351827 | + | 0.999381i | \(0.511201\pi\) | |||||||
\(684\) | −13376.0 | −0.747725 | ||||||||
\(685\) | −18180.0 | −1.01405 | ||||||||
\(686\) | −13032.0 | −0.725312 | ||||||||
\(687\) | 10262.0 | 0.569898 | ||||||||
\(688\) | −5424.00 | −0.300564 | ||||||||
\(689\) | 3363.00 | 0.185951 | ||||||||
\(690\) | −31920.0 | −1.76112 | ||||||||
\(691\) | −15996.0 | −0.880632 | −0.440316 | − | 0.897843i | \(-0.645134\pi\) | ||||
−0.440316 | + | 0.897843i | \(0.645134\pi\) | |||||||
\(692\) | −10392.0 | −0.570874 | ||||||||
\(693\) | 10692.0 | 0.586083 | ||||||||
\(694\) | −8004.00 | −0.437792 | ||||||||
\(695\) | −19920.0 | −1.08721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13816.0 | 0.750815 | ||||||||
\(698\) | 4334.00 | 0.235021 | ||||||||
\(699\) | 5929.00 | 0.320823 | ||||||||
\(700\) | −7200.00 | −0.388763 | ||||||||
\(701\) | −189.000 | −0.0101832 | −0.00509161 | − | 0.999987i | \(-0.501621\pi\) | ||||
−0.00509161 | + | 0.999987i | \(0.501621\pi\) | |||||||
\(702\) | −3990.00 | −0.214520 | ||||||||
\(703\) | −18240.0 | −0.978570 | ||||||||
\(704\) | −1728.00 | −0.0925092 | ||||||||
\(705\) | −37485.0 | −2.00251 | ||||||||
\(706\) | 4708.00 | 0.250974 | ||||||||
\(707\) | 25920.0 | 1.37881 | ||||||||
\(708\) | −16016.0 | −0.850167 | ||||||||
\(709\) | 2431.00 | 0.128770 | 0.0643851 | − | 0.997925i | \(-0.479491\pi\) | ||||
0.0643851 | + | 0.997925i | \(0.479491\pi\) | |||||||
\(710\) | 21780.0 | 1.15125 | ||||||||
\(711\) | −7942.00 | −0.418915 | ||||||||
\(712\) | 464.000 | 0.0244229 | ||||||||
\(713\) | −26296.0 | −1.38120 | ||||||||
\(714\) | 11088.0 | 0.581174 | ||||||||
\(715\) | −23085.0 | −1.20745 | ||||||||
\(716\) | −6040.00 | −0.315259 | ||||||||
\(717\) | −3108.00 | −0.161883 | ||||||||
\(718\) | −6942.00 | −0.360826 | ||||||||
\(719\) | −3630.00 | −0.188284 | −0.0941420 | − | 0.995559i | \(-0.530011\pi\) | ||||
−0.0941420 | + | 0.995559i | \(0.530011\pi\) | |||||||
\(720\) | −5280.00 | −0.273297 | ||||||||
\(721\) | −33444.0 | −1.72749 | ||||||||
\(722\) | −32490.0 | −1.67473 | ||||||||
\(723\) | 37079.0 | 1.90731 | ||||||||
\(724\) | −11460.0 | −0.588270 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8428.00 | 0.430844 | ||||||||
\(727\) | 1712.00 | 0.0873378 | 0.0436689 | − | 0.999046i | \(-0.486095\pi\) | ||||
0.0436689 | + | 0.999046i | \(0.486095\pi\) | |||||||
\(728\) | −8208.00 | −0.417869 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | −30120.0 | −1.52711 | ||||||||
\(731\) | −14916.0 | −0.754703 | ||||||||
\(732\) | 11760.0 | 0.593801 | ||||||||
\(733\) | −26584.0 | −1.33957 | −0.669783 | − | 0.742557i | \(-0.733613\pi\) | ||||
−0.669783 | + | 0.742557i | \(0.733613\pi\) | |||||||
\(734\) | −21760.0 | −1.09425 | ||||||||
\(735\) | 1995.00 | 0.100118 | ||||||||
\(736\) | 4864.00 | 0.243600 | ||||||||
\(737\) | −17820.0 | −0.890649 | ||||||||
\(738\) | −13816.0 | −0.689125 | ||||||||
\(739\) | −8125.00 | −0.404442 | −0.202221 | − | 0.979340i | \(-0.564816\pi\) | ||||
−0.202221 | + | 0.979340i | \(0.564816\pi\) | |||||||
\(740\) | −7200.00 | −0.357672 | ||||||||
\(741\) | 60648.0 | 3.00669 | ||||||||
\(742\) | −2124.00 | −0.105087 | ||||||||
\(743\) | 31804.0 | 1.57036 | 0.785179 | − | 0.619269i | \(-0.212571\pi\) | ||||
0.785179 | + | 0.619269i | \(0.212571\pi\) | |||||||
\(744\) | −9688.00 | −0.477392 | ||||||||
\(745\) | 26655.0 | 1.31082 | ||||||||
\(746\) | −17654.0 | −0.866433 | ||||||||
\(747\) | −3696.00 | −0.181030 | ||||||||
\(748\) | −4752.00 | −0.232287 | ||||||||
\(749\) | 34452.0 | 1.68071 | ||||||||
\(750\) | −5250.00 | −0.255604 | ||||||||
\(751\) | 37504.0 | 1.82229 | 0.911145 | − | 0.412085i | \(-0.135199\pi\) | ||||
0.911145 | + | 0.412085i | \(0.135199\pi\) | |||||||
\(752\) | 5712.00 | 0.276988 | ||||||||
\(753\) | −28427.0 | −1.37575 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 29010.0 | 1.39839 | ||||||||
\(756\) | 2520.00 | 0.121232 | ||||||||
\(757\) | 76.0000 | 0.00364897 | 0.00182448 | − | 0.999998i | \(-0.499419\pi\) | ||||
0.00182448 | + | 0.999998i | \(0.499419\pi\) | |||||||
\(758\) | −1752.00 | −0.0839519 | ||||||||
\(759\) | 28728.0 | 1.37386 | ||||||||
\(760\) | −18240.0 | −0.870572 | ||||||||
\(761\) | −23374.0 | −1.11341 | −0.556706 | − | 0.830709i | \(-0.687935\pi\) | ||||
−0.556706 | + | 0.830709i | \(0.687935\pi\) | |||||||
\(762\) | −8400.00 | −0.399344 | ||||||||
\(763\) | −17802.0 | −0.844660 | ||||||||
\(764\) | 7744.00 | 0.366712 | ||||||||
\(765\) | −14520.0 | −0.686238 | ||||||||
\(766\) | −10892.0 | −0.513765 | ||||||||
\(767\) | 32604.0 | 1.53489 | ||||||||
\(768\) | 1792.00 | 0.0841969 | ||||||||
\(769\) | 5448.00 | 0.255475 | 0.127737 | − | 0.991808i | \(-0.459229\pi\) | ||||
0.127737 | + | 0.991808i | \(0.459229\pi\) | |||||||
\(770\) | 14580.0 | 0.682372 | ||||||||
\(771\) | −47901.0 | −2.23750 | ||||||||
\(772\) | −15400.0 | −0.717951 | ||||||||
\(773\) | 16062.0 | 0.747361 | 0.373680 | − | 0.927558i | \(-0.378096\pi\) | ||||
0.373680 | + | 0.927558i | \(0.378096\pi\) | |||||||
\(774\) | 14916.0 | 0.692693 | ||||||||
\(775\) | 17300.0 | 0.801851 | ||||||||
\(776\) | −9648.00 | −0.446318 | ||||||||
\(777\) | −15120.0 | −0.698104 | ||||||||
\(778\) | −4432.00 | −0.204235 | ||||||||
\(779\) | −47728.0 | −2.19516 | ||||||||
\(780\) | 23940.0 | 1.09896 | ||||||||
\(781\) | −19602.0 | −0.898098 | ||||||||
\(782\) | 13376.0 | 0.611669 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −304.000 | −0.0138484 | ||||||||
\(785\) | 11010.0 | 0.500591 | ||||||||
\(786\) | −23128.0 | −1.04955 | ||||||||
\(787\) | 19182.0 | 0.868824 | 0.434412 | − | 0.900714i | \(-0.356956\pi\) | ||||
0.434412 | + | 0.900714i | \(0.356956\pi\) | |||||||
\(788\) | 12136.0 | 0.548638 | ||||||||
\(789\) | −22337.0 | −1.00788 | ||||||||
\(790\) | −10830.0 | −0.487739 | ||||||||
\(791\) | −5004.00 | −0.224933 | ||||||||
\(792\) | 4752.00 | 0.213201 | ||||||||
\(793\) | −23940.0 | −1.07205 | ||||||||
\(794\) | −13646.0 | −0.609922 | ||||||||
\(795\) | 6195.00 | 0.276370 | ||||||||
\(796\) | 984.000 | 0.0438153 | ||||||||
\(797\) | −5556.00 | −0.246931 | −0.123465 | − | 0.992349i | \(-0.539401\pi\) | ||||
−0.123465 | + | 0.992349i | \(0.539401\pi\) | |||||||
\(798\) | −38304.0 | −1.69918 | ||||||||
\(799\) | 15708.0 | 0.695506 | ||||||||
\(800\) | −3200.00 | −0.141421 | ||||||||
\(801\) | −1276.00 | −0.0562862 | ||||||||
\(802\) | 11178.0 | 0.492156 | ||||||||
\(803\) | 27108.0 | 1.19131 | ||||||||
\(804\) | 18480.0 | 0.810621 | ||||||||
\(805\) | −41040.0 | −1.79686 | ||||||||
\(806\) | 19722.0 | 0.861883 | ||||||||
\(807\) | −52052.0 | −2.27053 | ||||||||
\(808\) | 11520.0 | 0.501574 | ||||||||
\(809\) | −2616.00 | −0.113688 | −0.0568440 | − | 0.998383i | \(-0.518104\pi\) | ||||
−0.0568440 | + | 0.998383i | \(0.518104\pi\) | |||||||
\(810\) | −25170.0 | −1.09183 | ||||||||
\(811\) | −9626.00 | −0.416787 | −0.208394 | − | 0.978045i | \(-0.566824\pi\) | ||||
−0.208394 | + | 0.978045i | \(0.566824\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19285.0 | 0.831924 | ||||||||
\(814\) | 6480.00 | 0.279022 | ||||||||
\(815\) | −50055.0 | −2.15135 | ||||||||
\(816\) | 4928.00 | 0.211415 | ||||||||
\(817\) | 51528.0 | 2.20653 | ||||||||
\(818\) | −16516.0 | −0.705952 | ||||||||
\(819\) | 22572.0 | 0.963040 | ||||||||
\(820\) | −18840.0 | −0.802343 | ||||||||
\(821\) | 16007.0 | 0.680448 | 0.340224 | − | 0.940344i | \(-0.389497\pi\) | ||||
0.340224 | + | 0.940344i | \(0.389497\pi\) | |||||||
\(822\) | −16968.0 | −0.719984 | ||||||||
\(823\) | −23216.0 | −0.983304 | −0.491652 | − | 0.870792i | \(-0.663607\pi\) | ||||
−0.491652 | + | 0.870792i | \(0.663607\pi\) | |||||||
\(824\) | −14864.0 | −0.628413 | ||||||||
\(825\) | −18900.0 | −0.797592 | ||||||||
\(826\) | −20592.0 | −0.867418 | ||||||||
\(827\) | 46765.0 | 1.96636 | 0.983179 | − | 0.182644i | \(-0.0584654\pi\) | ||||
0.983179 | + | 0.182644i | \(0.0584654\pi\) | |||||||
\(828\) | −13376.0 | −0.561411 | ||||||||
\(829\) | 37820.0 | 1.58449 | 0.792245 | − | 0.610203i | \(-0.208912\pi\) | ||||
0.792245 | + | 0.610203i | \(0.208912\pi\) | |||||||
\(830\) | −5040.00 | −0.210772 | ||||||||
\(831\) | −16870.0 | −0.704228 | ||||||||
\(832\) | −3648.00 | −0.152009 | ||||||||
\(833\) | −836.000 | −0.0347727 | ||||||||
\(834\) | −18592.0 | −0.771928 | ||||||||
\(835\) | 2970.00 | 0.123091 | ||||||||
\(836\) | 16416.0 | 0.679138 | ||||||||
\(837\) | −6055.00 | −0.250049 | ||||||||
\(838\) | −7892.00 | −0.325328 | ||||||||
\(839\) | −6747.00 | −0.277631 | −0.138815 | − | 0.990318i | \(-0.544329\pi\) | ||||
−0.138815 | + | 0.990318i | \(0.544329\pi\) | |||||||
\(840\) | −15120.0 | −0.621059 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 2760.00 | 0.112964 | ||||||||
\(843\) | 15645.0 | 0.639196 | ||||||||
\(844\) | 5972.00 | 0.243560 | ||||||||
\(845\) | −15780.0 | −0.642424 | ||||||||
\(846\) | −15708.0 | −0.638360 | ||||||||
\(847\) | 10836.0 | 0.439586 | ||||||||
\(848\) | −944.000 | −0.0382277 | ||||||||
\(849\) | −11536.0 | −0.466330 | ||||||||
\(850\) | −8800.00 | −0.355103 | ||||||||
\(851\) | −18240.0 | −0.734735 | ||||||||
\(852\) | 20328.0 | 0.817401 | ||||||||
\(853\) | 13274.0 | 0.532817 | 0.266409 | − | 0.963860i | \(-0.414163\pi\) | ||||
0.266409 | + | 0.963860i | \(0.414163\pi\) | |||||||
\(854\) | 15120.0 | 0.605850 | ||||||||
\(855\) | 50160.0 | 2.00636 | ||||||||
\(856\) | 15312.0 | 0.611394 | ||||||||
\(857\) | 39069.0 | 1.55726 | 0.778630 | − | 0.627483i | \(-0.215915\pi\) | ||||
0.778630 | + | 0.627483i | \(0.215915\pi\) | |||||||
\(858\) | −21546.0 | −0.857306 | ||||||||
\(859\) | −35329.0 | −1.40327 | −0.701636 | − | 0.712536i | \(-0.747547\pi\) | ||||
−0.701636 | + | 0.712536i | \(0.747547\pi\) | |||||||
\(860\) | 20340.0 | 0.806498 | ||||||||
\(861\) | −39564.0 | −1.56601 | ||||||||
\(862\) | 11640.0 | 0.459930 | ||||||||
\(863\) | −36378.0 | −1.43490 | −0.717452 | − | 0.696608i | \(-0.754692\pi\) | ||||
−0.717452 | + | 0.696608i | \(0.754692\pi\) | |||||||
\(864\) | 1120.00 | 0.0441009 | ||||||||
\(865\) | 38970.0 | 1.53181 | ||||||||
\(866\) | −29008.0 | −1.13826 | ||||||||
\(867\) | −20839.0 | −0.816297 | ||||||||
\(868\) | −12456.0 | −0.487079 | ||||||||
\(869\) | 9747.00 | 0.380488 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37620.0 | −1.46350 | ||||||||
\(872\) | −7912.00 | −0.307264 | ||||||||
\(873\) | 26532.0 | 1.02860 | ||||||||
\(874\) | −46208.0 | −1.78834 | ||||||||
\(875\) | −6750.00 | −0.260790 | ||||||||
\(876\) | −28112.0 | −1.08427 | ||||||||
\(877\) | −219.000 | −0.00843227 | −0.00421614 | − | 0.999991i | \(-0.501342\pi\) | ||||
−0.00421614 | + | 0.999991i | \(0.501342\pi\) | |||||||
\(878\) | −29824.0 | −1.14637 | ||||||||
\(879\) | −20146.0 | −0.773046 | ||||||||
\(880\) | 6480.00 | 0.248228 | ||||||||
\(881\) | 5598.00 | 0.214077 | 0.107038 | − | 0.994255i | \(-0.465863\pi\) | ||||
0.107038 | + | 0.994255i | \(0.465863\pi\) | |||||||
\(882\) | 836.000 | 0.0319156 | ||||||||
\(883\) | 5886.00 | 0.224326 | 0.112163 | − | 0.993690i | \(-0.464222\pi\) | ||||
0.112163 | + | 0.993690i | \(0.464222\pi\) | |||||||
\(884\) | −10032.0 | −0.381689 | ||||||||
\(885\) | 60060.0 | 2.28124 | ||||||||
\(886\) | 14360.0 | 0.544507 | ||||||||
\(887\) | 29673.0 | 1.12325 | 0.561624 | − | 0.827392i | \(-0.310177\pi\) | ||||
0.561624 | + | 0.827392i | \(0.310177\pi\) | |||||||
\(888\) | −6720.00 | −0.253951 | ||||||||
\(889\) | −10800.0 | −0.407447 | ||||||||
\(890\) | −1740.00 | −0.0655336 | ||||||||
\(891\) | 22653.0 | 0.851744 | ||||||||
\(892\) | 5608.00 | 0.210504 | ||||||||
\(893\) | −54264.0 | −2.03346 | ||||||||
\(894\) | 24878.0 | 0.930699 | ||||||||
\(895\) | 22650.0 | 0.845928 | ||||||||
\(896\) | 2304.00 | 0.0859054 | ||||||||
\(897\) | 60648.0 | 2.25750 | ||||||||
\(898\) | 2796.00 | 0.103902 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 8800.00 | 0.325926 | ||||||||
\(901\) | −2596.00 | −0.0959881 | ||||||||
\(902\) | 16956.0 | 0.625912 | ||||||||
\(903\) | 42714.0 | 1.57412 | ||||||||
\(904\) | −2224.00 | −0.0818243 | ||||||||
\(905\) | 42975.0 | 1.57849 | ||||||||
\(906\) | 27076.0 | 0.992870 | ||||||||
\(907\) | −13668.0 | −0.500373 | −0.250187 | − | 0.968198i | \(-0.580492\pi\) | ||||
−0.250187 | + | 0.968198i | \(0.580492\pi\) | |||||||
\(908\) | 4664.00 | 0.170463 | ||||||||
\(909\) | −31680.0 | −1.15595 | ||||||||
\(910\) | 30780.0 | 1.12126 | ||||||||
\(911\) | 4963.00 | 0.180496 | 0.0902478 | − | 0.995919i | \(-0.471234\pi\) | ||||
0.0902478 | + | 0.995919i | \(0.471234\pi\) | |||||||
\(912\) | −17024.0 | −0.618115 | ||||||||
\(913\) | 4536.00 | 0.164425 | ||||||||
\(914\) | 11316.0 | 0.409519 | ||||||||
\(915\) | −44100.0 | −1.59333 | ||||||||
\(916\) | 5864.00 | 0.211520 | ||||||||
\(917\) | −29736.0 | −1.07085 | ||||||||
\(918\) | 3080.00 | 0.110735 | ||||||||
\(919\) | 9954.00 | 0.357293 | 0.178646 | − | 0.983913i | \(-0.442828\pi\) | ||||
0.178646 | + | 0.983913i | \(0.442828\pi\) | |||||||
\(920\) | −18240.0 | −0.653647 | ||||||||
\(921\) | −34321.0 | −1.22792 | ||||||||
\(922\) | 22820.0 | 0.815116 | ||||||||
\(923\) | −41382.0 | −1.47574 | ||||||||
\(924\) | 13608.0 | 0.484492 | ||||||||
\(925\) | 12000.0 | 0.426549 | ||||||||
\(926\) | 5120.00 | 0.181699 | ||||||||
\(927\) | 40876.0 | 1.44827 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30930.0 | 1.09234 | 0.546168 | − | 0.837676i | \(-0.316086\pi\) | ||||
0.546168 | + | 0.837676i | \(0.316086\pi\) | |||||||
\(930\) | 36330.0 | 1.28098 | ||||||||
\(931\) | 2888.00 | 0.101665 | ||||||||
\(932\) | 3388.00 | 0.119075 | ||||||||
\(933\) | 224.000 | 0.00786005 | ||||||||
\(934\) | 20790.0 | 0.728340 | ||||||||
\(935\) | 17820.0 | 0.623290 | ||||||||
\(936\) | 10032.0 | 0.350327 | ||||||||
\(937\) | −38770.0 | −1.35172 | −0.675859 | − | 0.737030i | \(-0.736227\pi\) | ||||
−0.675859 | + | 0.737030i | \(0.736227\pi\) | |||||||
\(938\) | 23760.0 | 0.827070 | ||||||||
\(939\) | −38185.0 | −1.32707 | ||||||||
\(940\) | −21420.0 | −0.743238 | ||||||||
\(941\) | −30115.0 | −1.04327 | −0.521637 | − | 0.853167i | \(-0.674678\pi\) | ||||
−0.521637 | + | 0.853167i | \(0.674678\pi\) | |||||||
\(942\) | 10276.0 | 0.355425 | ||||||||
\(943\) | −47728.0 | −1.64818 | ||||||||
\(944\) | −9152.00 | −0.315543 | ||||||||
\(945\) | −9450.00 | −0.325300 | ||||||||
\(946\) | −18306.0 | −0.629154 | ||||||||
\(947\) | −31319.0 | −1.07469 | −0.537345 | − | 0.843363i | \(-0.680573\pi\) | ||||
−0.537345 | + | 0.843363i | \(0.680573\pi\) | |||||||
\(948\) | −10108.0 | −0.346300 | ||||||||
\(949\) | 57228.0 | 1.95753 | ||||||||
\(950\) | 30400.0 | 1.03822 | ||||||||
\(951\) | 66864.0 | 2.27993 | ||||||||
\(952\) | 6336.00 | 0.215705 | ||||||||
\(953\) | 7623.00 | 0.259111 | 0.129556 | − | 0.991572i | \(-0.458645\pi\) | ||||
0.129556 | + | 0.991572i | \(0.458645\pi\) | |||||||
\(954\) | 2596.00 | 0.0881013 | ||||||||
\(955\) | −29040.0 | −0.983992 | ||||||||
\(956\) | −1776.00 | −0.0600836 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11254.0 | −0.379541 | ||||||||
\(959\) | −21816.0 | −0.734594 | ||||||||
\(960\) | −6720.00 | −0.225924 | ||||||||
\(961\) | 138.000 | 0.00463227 | ||||||||
\(962\) | 13680.0 | 0.458483 | ||||||||
\(963\) | −42108.0 | −1.40905 | ||||||||
\(964\) | 21188.0 | 0.707904 | ||||||||
\(965\) | 57750.0 | 1.92646 | ||||||||
\(966\) | −38304.0 | −1.27579 | ||||||||
\(967\) | 6269.00 | 0.208477 | 0.104239 | − | 0.994552i | \(-0.466759\pi\) | ||||
0.104239 | + | 0.994552i | \(0.466759\pi\) | |||||||
\(968\) | 4816.00 | 0.159909 | ||||||||
\(969\) | −46816.0 | −1.55206 | ||||||||
\(970\) | 36180.0 | 1.19760 | ||||||||
\(971\) | 34020.0 | 1.12436 | 0.562180 | − | 0.827015i | \(-0.309963\pi\) | ||||
0.562180 | + | 0.827015i | \(0.309963\pi\) | |||||||
\(972\) | −19712.0 | −0.650476 | ||||||||
\(973\) | −23904.0 | −0.787592 | ||||||||
\(974\) | −17476.0 | −0.574915 | ||||||||
\(975\) | −39900.0 | −1.31059 | ||||||||
\(976\) | 6720.00 | 0.220391 | ||||||||
\(977\) | −51291.0 | −1.67957 | −0.839787 | − | 0.542915i | \(-0.817320\pi\) | ||||
−0.839787 | + | 0.542915i | \(0.817320\pi\) | |||||||
\(978\) | −46718.0 | −1.52748 | ||||||||
\(979\) | 1566.00 | 0.0511232 | ||||||||
\(980\) | 1140.00 | 0.0371591 | ||||||||
\(981\) | 21758.0 | 0.708134 | ||||||||
\(982\) | 6354.00 | 0.206481 | ||||||||
\(983\) | −38687.0 | −1.25526 | −0.627632 | − | 0.778511i | \(-0.715976\pi\) | ||||
−0.627632 | + | 0.778511i | \(0.715976\pi\) | |||||||
\(984\) | −17584.0 | −0.569672 | ||||||||
\(985\) | −45510.0 | −1.47215 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −44982.0 | −1.45065 | ||||||||
\(988\) | 34656.0 | 1.11595 | ||||||||
\(989\) | 51528.0 | 1.65672 | ||||||||
\(990\) | −17820.0 | −0.572078 | ||||||||
\(991\) | −3158.00 | −0.101228 | −0.0506141 | − | 0.998718i | \(-0.516118\pi\) | ||||
−0.0506141 | + | 0.998718i | \(0.516118\pi\) | |||||||
\(992\) | −5536.00 | −0.177186 | ||||||||
\(993\) | 17031.0 | 0.544272 | ||||||||
\(994\) | 26136.0 | 0.833988 | ||||||||
\(995\) | −3690.00 | −0.117569 | ||||||||
\(996\) | −4704.00 | −0.149651 | ||||||||
\(997\) | 21944.0 | 0.697065 | 0.348532 | − | 0.937297i | \(-0.386680\pi\) | ||||
0.348532 | + | 0.937297i | \(0.386680\pi\) | |||||||
\(998\) | 11632.0 | 0.368942 | ||||||||
\(999\) | −4200.00 | −0.133015 |
(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 | 1682.4.a.a.1.1 | 1 | ||
29.28 | even | 2 | 58.4.a.b.1.1 | ✓ | 1 | ||
87.86 | odd | 2 | 522.4.a.b.1.1 | 1 | |||
116.115 | odd | 2 | 464.4.a.b.1.1 | 1 | |||
145.144 | even | 2 | 1450.4.a.d.1.1 | 1 | |||
232.115 | odd | 2 | 1856.4.a.c.1.1 | 1 | |||
232.173 | even | 2 | 1856.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
58.4.a.b.1.1 | ✓ | 1 | 29.28 | even | 2 | ||
464.4.a.b.1.1 | 1 | 116.115 | odd | 2 | |||
522.4.a.b.1.1 | 1 | 87.86 | odd | 2 | |||
1450.4.a.d.1.1 | 1 | 145.144 | even | 2 | |||
1682.4.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1856.4.a.c.1.1 | 1 | 232.115 | odd | 2 | |||
1856.4.a.f.1.1 | 1 | 232.173 | even | 2 |