Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [242,6,Mod(1,242)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(242, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("242.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 242 = 2 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 242.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: | \(38.8128843947\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 242.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.0641500 | 0.0320750 | − | 0.999485i | \(-0.489788\pi\) | ||||
0.0320750 | + | 0.999485i | \(0.489788\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −51.0000 | −0.912316 | −0.456158 | − | 0.889899i | \(-0.650775\pi\) | ||||
−0.456158 | + | 0.889899i | \(0.650775\pi\) | |||||||
\(6\) | 4.00000 | 0.0453609 | ||||||||
\(7\) | 166.000 | 1.28045 | 0.640226 | − | 0.768187i | \(-0.278841\pi\) | ||||
0.640226 | + | 0.768187i | \(0.278841\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | −242.000 | −0.995885 | ||||||||
\(10\) | −204.000 | −0.645105 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 16.0000 | 0.0320750 | ||||||||
\(13\) | −692.000 | −1.13566 | −0.567829 | − | 0.823146i | \(-0.692217\pi\) | ||||
−0.567829 | + | 0.823146i | \(0.692217\pi\) | |||||||
\(14\) | 664.000 | 0.905416 | ||||||||
\(15\) | −51.0000 | −0.0585251 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 738.000 | 0.619347 | 0.309674 | − | 0.950843i | \(-0.399780\pi\) | ||||
0.309674 | + | 0.950843i | \(0.399780\pi\) | |||||||
\(18\) | −968.000 | −0.704197 | ||||||||
\(19\) | −1424.00 | −0.904953 | −0.452476 | − | 0.891776i | \(-0.649459\pi\) | ||||
−0.452476 | + | 0.891776i | \(0.649459\pi\) | |||||||
\(20\) | −816.000 | −0.456158 | ||||||||
\(21\) | 166.000 | 0.0821410 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1779.00 | −0.701223 | −0.350612 | − | 0.936521i | \(-0.614026\pi\) | ||||
−0.350612 | + | 0.936521i | \(0.614026\pi\) | |||||||
\(24\) | 64.0000 | 0.0226805 | ||||||||
\(25\) | −524.000 | −0.167680 | ||||||||
\(26\) | −2768.00 | −0.803032 | ||||||||
\(27\) | −485.000 | −0.128036 | ||||||||
\(28\) | 2656.00 | 0.640226 | ||||||||
\(29\) | 2064.00 | 0.455737 | 0.227869 | − | 0.973692i | \(-0.426824\pi\) | ||||
0.227869 | + | 0.973692i | \(0.426824\pi\) | |||||||
\(30\) | −204.000 | −0.0413835 | ||||||||
\(31\) | 6245.00 | 1.16715 | 0.583577 | − | 0.812058i | \(-0.301653\pi\) | ||||
0.583577 | + | 0.812058i | \(0.301653\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2952.00 | 0.437944 | ||||||||
\(35\) | −8466.00 | −1.16818 | ||||||||
\(36\) | −3872.00 | −0.497942 | ||||||||
\(37\) | −14785.0 | −1.77549 | −0.887743 | − | 0.460340i | \(-0.847727\pi\) | ||||
−0.887743 | + | 0.460340i | \(0.847727\pi\) | |||||||
\(38\) | −5696.00 | −0.639898 | ||||||||
\(39\) | −692.000 | −0.0728525 | ||||||||
\(40\) | −3264.00 | −0.322552 | ||||||||
\(41\) | −5304.00 | −0.492770 | −0.246385 | − | 0.969172i | \(-0.579243\pi\) | ||||
−0.246385 | + | 0.969172i | \(0.579243\pi\) | |||||||
\(42\) | 664.000 | 0.0580824 | ||||||||
\(43\) | −17798.0 | −1.46791 | −0.733956 | − | 0.679197i | \(-0.762328\pi\) | ||||
−0.733956 | + | 0.679197i | \(0.762328\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 12342.0 | 0.908561 | ||||||||
\(46\) | −7116.00 | −0.495840 | ||||||||
\(47\) | −17184.0 | −1.13470 | −0.567348 | − | 0.823478i | \(-0.692031\pi\) | ||||
−0.567348 | + | 0.823478i | \(0.692031\pi\) | |||||||
\(48\) | 256.000 | 0.0160375 | ||||||||
\(49\) | 10749.0 | 0.639555 | ||||||||
\(50\) | −2096.00 | −0.118568 | ||||||||
\(51\) | 738.000 | 0.0397311 | ||||||||
\(52\) | −11072.0 | −0.567829 | ||||||||
\(53\) | −30726.0 | −1.50251 | −0.751253 | − | 0.660014i | \(-0.770550\pi\) | ||||
−0.751253 | + | 0.660014i | \(0.770550\pi\) | |||||||
\(54\) | −1940.00 | −0.0905352 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10624.0 | 0.452708 | ||||||||
\(57\) | −1424.00 | −0.0580528 | ||||||||
\(58\) | 8256.00 | 0.322255 | ||||||||
\(59\) | −34989.0 | −1.30858 | −0.654292 | − | 0.756242i | \(-0.727033\pi\) | ||||
−0.654292 | + | 0.756242i | \(0.727033\pi\) | |||||||
\(60\) | −816.000 | −0.0292625 | ||||||||
\(61\) | 45940.0 | 1.58076 | 0.790381 | − | 0.612616i | \(-0.209883\pi\) | ||||
0.790381 | + | 0.612616i | \(0.209883\pi\) | |||||||
\(62\) | 24980.0 | 0.825303 | ||||||||
\(63\) | −40172.0 | −1.27518 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 35292.0 | 1.03608 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25343.0 | 0.689717 | 0.344859 | − | 0.938655i | \(-0.387927\pi\) | ||||
0.344859 | + | 0.938655i | \(0.387927\pi\) | |||||||
\(68\) | 11808.0 | 0.309674 | ||||||||
\(69\) | −1779.00 | −0.0449835 | ||||||||
\(70\) | −33864.0 | −0.826025 | ||||||||
\(71\) | 13311.0 | 0.313375 | 0.156688 | − | 0.987648i | \(-0.449918\pi\) | ||||
0.156688 | + | 0.987648i | \(0.449918\pi\) | |||||||
\(72\) | −15488.0 | −0.352098 | ||||||||
\(73\) | 53260.0 | 1.16975 | 0.584876 | − | 0.811123i | \(-0.301143\pi\) | ||||
0.584876 | + | 0.811123i | \(0.301143\pi\) | |||||||
\(74\) | −59140.0 | −1.25546 | ||||||||
\(75\) | −524.000 | −0.0107567 | ||||||||
\(76\) | −22784.0 | −0.452476 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −2768.00 | −0.0515145 | ||||||||
\(79\) | −77234.0 | −1.39233 | −0.696163 | − | 0.717884i | \(-0.745111\pi\) | ||||
−0.696163 | + | 0.717884i | \(0.745111\pi\) | |||||||
\(80\) | −13056.0 | −0.228079 | ||||||||
\(81\) | 58321.0 | 0.987671 | ||||||||
\(82\) | −21216.0 | −0.348441 | ||||||||
\(83\) | −55014.0 | −0.876553 | −0.438276 | − | 0.898840i | \(-0.644411\pi\) | ||||
−0.438276 | + | 0.898840i | \(0.644411\pi\) | |||||||
\(84\) | 2656.00 | 0.0410705 | ||||||||
\(85\) | −37638.0 | −0.565040 | ||||||||
\(86\) | −71192.0 | −1.03797 | ||||||||
\(87\) | 2064.00 | 0.0292356 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 125415. | 1.67832 | 0.839159 | − | 0.543886i | \(-0.183047\pi\) | ||||
0.839159 | + | 0.543886i | \(0.183047\pi\) | |||||||
\(90\) | 49368.0 | 0.642450 | ||||||||
\(91\) | −114872. | −1.45416 | ||||||||
\(92\) | −28464.0 | −0.350612 | ||||||||
\(93\) | 6245.00 | 0.0748730 | ||||||||
\(94\) | −68736.0 | −0.802351 | ||||||||
\(95\) | 72624.0 | 0.825603 | ||||||||
\(96\) | 1024.00 | 0.0113402 | ||||||||
\(97\) | −88807.0 | −0.958336 | −0.479168 | − | 0.877723i | \(-0.659062\pi\) | ||||
−0.479168 | + | 0.877723i | \(0.659062\pi\) | |||||||
\(98\) | 42996.0 | 0.452234 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8384.00 | −0.0838400 | ||||||||
\(101\) | −1482.00 | −0.0144559 | −0.00722794 | − | 0.999974i | \(-0.502301\pi\) | ||||
−0.00722794 | + | 0.999974i | \(0.502301\pi\) | |||||||
\(102\) | 2952.00 | 0.0280942 | ||||||||
\(103\) | −117496. | −1.09126 | −0.545632 | − | 0.838025i | \(-0.683710\pi\) | ||||
−0.545632 | + | 0.838025i | \(0.683710\pi\) | |||||||
\(104\) | −44288.0 | −0.401516 | ||||||||
\(105\) | −8466.00 | −0.0749385 | ||||||||
\(106\) | −122904. | −1.06243 | ||||||||
\(107\) | 79362.0 | 0.670121 | 0.335060 | − | 0.942197i | \(-0.391243\pi\) | ||||
0.335060 | + | 0.942197i | \(0.391243\pi\) | |||||||
\(108\) | −7760.00 | −0.0640180 | ||||||||
\(109\) | −87842.0 | −0.708167 | −0.354084 | − | 0.935214i | \(-0.615207\pi\) | ||||
−0.354084 | + | 0.935214i | \(0.615207\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −14785.0 | −0.113897 | ||||||||
\(112\) | 42496.0 | 0.320113 | ||||||||
\(113\) | −47247.0 | −0.348079 | −0.174040 | − | 0.984739i | \(-0.555682\pi\) | ||||
−0.174040 | + | 0.984739i | \(0.555682\pi\) | |||||||
\(114\) | −5696.00 | −0.0410495 | ||||||||
\(115\) | 90729.0 | 0.639737 | ||||||||
\(116\) | 33024.0 | 0.227869 | ||||||||
\(117\) | 167464. | 1.13098 | ||||||||
\(118\) | −139956. | −0.925308 | ||||||||
\(119\) | 122508. | 0.793044 | ||||||||
\(120\) | −3264.00 | −0.0206917 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 183760. | 1.11777 | ||||||||
\(123\) | −5304.00 | −0.0316112 | ||||||||
\(124\) | 99920.0 | 0.583577 | ||||||||
\(125\) | 186099. | 1.06529 | ||||||||
\(126\) | −160688. | −0.901690 | ||||||||
\(127\) | 239416. | 1.31718 | 0.658588 | − | 0.752504i | \(-0.271154\pi\) | ||||
0.658588 | + | 0.752504i | \(0.271154\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | −17798.0 | −0.0941666 | ||||||||
\(130\) | 141168. | 0.732618 | ||||||||
\(131\) | 98142.0 | 0.499662 | 0.249831 | − | 0.968289i | \(-0.419625\pi\) | ||||
0.249831 | + | 0.968289i | \(0.419625\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −236384. | −1.15875 | ||||||||
\(134\) | 101372. | 0.487704 | ||||||||
\(135\) | 24735.0 | 0.116809 | ||||||||
\(136\) | 47232.0 | 0.218972 | ||||||||
\(137\) | 400137. | 1.82141 | 0.910704 | − | 0.413059i | \(-0.135540\pi\) | ||||
0.910704 | + | 0.413059i | \(0.135540\pi\) | |||||||
\(138\) | −7116.00 | −0.0318081 | ||||||||
\(139\) | −205766. | −0.903310 | −0.451655 | − | 0.892193i | \(-0.649166\pi\) | ||||
−0.451655 | + | 0.892193i | \(0.649166\pi\) | |||||||
\(140\) | −135456. | −0.584088 | ||||||||
\(141\) | −17184.0 | −0.0727908 | ||||||||
\(142\) | 53244.0 | 0.221590 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −61952.0 | −0.248971 | ||||||||
\(145\) | −105264. | −0.415776 | ||||||||
\(146\) | 213040. | 0.827140 | ||||||||
\(147\) | 10749.0 | 0.0410275 | ||||||||
\(148\) | −236560. | −0.887743 | ||||||||
\(149\) | −87726.0 | −0.323715 | −0.161857 | − | 0.986814i | \(-0.551748\pi\) | ||||
−0.161857 | + | 0.986814i | \(0.551748\pi\) | |||||||
\(150\) | −2096.00 | −0.00760612 | ||||||||
\(151\) | 432778. | 1.54462 | 0.772312 | − | 0.635243i | \(-0.219100\pi\) | ||||
0.772312 | + | 0.635243i | \(0.219100\pi\) | |||||||
\(152\) | −91136.0 | −0.319949 | ||||||||
\(153\) | −178596. | −0.616798 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −318495. | −1.06481 | ||||||||
\(156\) | −11072.0 | −0.0364263 | ||||||||
\(157\) | −34075.0 | −0.110328 | −0.0551641 | − | 0.998477i | \(-0.517568\pi\) | ||||
−0.0551641 | + | 0.998477i | \(0.517568\pi\) | |||||||
\(158\) | −308936. | −0.984523 | ||||||||
\(159\) | −30726.0 | −0.0963858 | ||||||||
\(160\) | −52224.0 | −0.161276 | ||||||||
\(161\) | −295314. | −0.897882 | ||||||||
\(162\) | 233284. | 0.698389 | ||||||||
\(163\) | 45020.0 | 0.132720 | 0.0663600 | − | 0.997796i | \(-0.478861\pi\) | ||||
0.0663600 | + | 0.997796i | \(0.478861\pi\) | |||||||
\(164\) | −84864.0 | −0.246385 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −220056. | −0.619816 | ||||||||
\(167\) | −482556. | −1.33893 | −0.669463 | − | 0.742845i | \(-0.733476\pi\) | ||||
−0.669463 | + | 0.742845i | \(0.733476\pi\) | |||||||
\(168\) | 10624.0 | 0.0290412 | ||||||||
\(169\) | 107571. | 0.289720 | ||||||||
\(170\) | −150552. | −0.399544 | ||||||||
\(171\) | 344608. | 0.901229 | ||||||||
\(172\) | −284768. | −0.733956 | ||||||||
\(173\) | 766254. | 1.94651 | 0.973257 | − | 0.229719i | \(-0.0737808\pi\) | ||||
0.973257 | + | 0.229719i | \(0.0737808\pi\) | |||||||
\(174\) | 8256.00 | 0.0206727 | ||||||||
\(175\) | −86984.0 | −0.214706 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −34989.0 | −0.0839457 | ||||||||
\(178\) | 501660. | 1.18675 | ||||||||
\(179\) | 303399. | 0.707753 | 0.353876 | − | 0.935292i | \(-0.384863\pi\) | ||||
0.353876 | + | 0.935292i | \(0.384863\pi\) | |||||||
\(180\) | 197472. | 0.454281 | ||||||||
\(181\) | −285181. | −0.647030 | −0.323515 | − | 0.946223i | \(-0.604865\pi\) | ||||
−0.323515 | + | 0.946223i | \(0.604865\pi\) | |||||||
\(182\) | −459488. | −1.02824 | ||||||||
\(183\) | 45940.0 | 0.101406 | ||||||||
\(184\) | −113856. | −0.247920 | ||||||||
\(185\) | 754035. | 1.61980 | ||||||||
\(186\) | 24980.0 | 0.0529432 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −274944. | −0.567348 | ||||||||
\(189\) | −80510.0 | −0.163944 | ||||||||
\(190\) | 290496. | 0.583789 | ||||||||
\(191\) | 767067. | 1.52142 | 0.760711 | − | 0.649090i | \(-0.224850\pi\) | ||||
0.760711 | + | 0.649090i | \(0.224850\pi\) | |||||||
\(192\) | 4096.00 | 0.00801875 | ||||||||
\(193\) | −411668. | −0.795525 | −0.397763 | − | 0.917488i | \(-0.630213\pi\) | ||||
−0.397763 | + | 0.917488i | \(0.630213\pi\) | |||||||
\(194\) | −355228. | −0.677646 | ||||||||
\(195\) | 35292.0 | 0.0664645 | ||||||||
\(196\) | 171984. | 0.319777 | ||||||||
\(197\) | 759258. | 1.39387 | 0.696937 | − | 0.717132i | \(-0.254545\pi\) | ||||
0.696937 | + | 0.717132i | \(0.254545\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −46600.0 | −0.0834167 | −0.0417084 | − | 0.999130i | \(-0.513280\pi\) | ||||
−0.0417084 | + | 0.999130i | \(0.513280\pi\) | |||||||
\(200\) | −33536.0 | −0.0592838 | ||||||||
\(201\) | 25343.0 | 0.0442454 | ||||||||
\(202\) | −5928.00 | −0.0102219 | ||||||||
\(203\) | 342624. | 0.583549 | ||||||||
\(204\) | 11808.0 | 0.0198656 | ||||||||
\(205\) | 270504. | 0.449561 | ||||||||
\(206\) | −469984. | −0.771641 | ||||||||
\(207\) | 430518. | 0.698338 | ||||||||
\(208\) | −177152. | −0.283915 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −33864.0 | −0.0529895 | ||||||||
\(211\) | 932428. | 1.44181 | 0.720907 | − | 0.693032i | \(-0.243726\pi\) | ||||
0.720907 | + | 0.693032i | \(0.243726\pi\) | |||||||
\(212\) | −491616. | −0.751253 | ||||||||
\(213\) | 13311.0 | 0.0201030 | ||||||||
\(214\) | 317448. | 0.473847 | ||||||||
\(215\) | 907698. | 1.33920 | ||||||||
\(216\) | −31040.0 | −0.0452676 | ||||||||
\(217\) | 1.03667e6 | 1.49448 | ||||||||
\(218\) | −351368. | −0.500750 | ||||||||
\(219\) | 53260.0 | 0.0750397 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −510696. | −0.703367 | ||||||||
\(222\) | −59140.0 | −0.0805376 | ||||||||
\(223\) | 169745. | 0.228578 | 0.114289 | − | 0.993448i | \(-0.463541\pi\) | ||||
0.114289 | + | 0.993448i | \(0.463541\pi\) | |||||||
\(224\) | 169984. | 0.226354 | ||||||||
\(225\) | 126808. | 0.166990 | ||||||||
\(226\) | −188988. | −0.246129 | ||||||||
\(227\) | −198078. | −0.255136 | −0.127568 | − | 0.991830i | \(-0.540717\pi\) | ||||
−0.127568 | + | 0.991830i | \(0.540717\pi\) | |||||||
\(228\) | −22784.0 | −0.0290264 | ||||||||
\(229\) | −849997. | −1.07110 | −0.535548 | − | 0.844505i | \(-0.679895\pi\) | ||||
−0.535548 | + | 0.844505i | \(0.679895\pi\) | |||||||
\(230\) | 362916. | 0.452362 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 132096. | 0.161128 | ||||||||
\(233\) | 401832. | 0.484903 | 0.242451 | − | 0.970164i | \(-0.422048\pi\) | ||||
0.242451 | + | 0.970164i | \(0.422048\pi\) | |||||||
\(234\) | 669856. | 0.799727 | ||||||||
\(235\) | 876384. | 1.03520 | ||||||||
\(236\) | −559824. | −0.654292 | ||||||||
\(237\) | −77234.0 | −0.0893177 | ||||||||
\(238\) | 490032. | 0.560766 | ||||||||
\(239\) | −855174. | −0.968411 | −0.484206 | − | 0.874954i | \(-0.660891\pi\) | ||||
−0.484206 | + | 0.874954i | \(0.660891\pi\) | |||||||
\(240\) | −13056.0 | −0.0146313 | ||||||||
\(241\) | −1.12546e6 | −1.24821 | −0.624107 | − | 0.781339i | \(-0.714537\pi\) | ||||
−0.624107 | + | 0.781339i | \(0.714537\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 176176. | 0.191395 | ||||||||
\(244\) | 735040. | 0.790381 | ||||||||
\(245\) | −548199. | −0.583476 | ||||||||
\(246\) | −21216.0 | −0.0223525 | ||||||||
\(247\) | 985408. | 1.02772 | ||||||||
\(248\) | 399680. | 0.412651 | ||||||||
\(249\) | −55014.0 | −0.0562309 | ||||||||
\(250\) | 744396. | 0.753276 | ||||||||
\(251\) | −1.19751e6 | −1.19976 | −0.599882 | − | 0.800088i | \(-0.704786\pi\) | ||||
−0.599882 | + | 0.800088i | \(0.704786\pi\) | |||||||
\(252\) | −642752. | −0.637591 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 957664. | 0.931384 | ||||||||
\(255\) | −37638.0 | −0.0362473 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 37758.0 | 0.0356596 | 0.0178298 | − | 0.999841i | \(-0.494324\pi\) | ||||
0.0178298 | + | 0.999841i | \(0.494324\pi\) | |||||||
\(258\) | −71192.0 | −0.0665858 | ||||||||
\(259\) | −2.45431e6 | −2.27342 | ||||||||
\(260\) | 564672. | 0.518040 | ||||||||
\(261\) | −499488. | −0.453862 | ||||||||
\(262\) | 392568. | 0.353315 | ||||||||
\(263\) | 631254. | 0.562749 | 0.281375 | − | 0.959598i | \(-0.409210\pi\) | ||||
0.281375 | + | 0.959598i | \(0.409210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.56703e6 | 1.37076 | ||||||||
\(266\) | −945536. | −0.819359 | ||||||||
\(267\) | 125415. | 0.107664 | ||||||||
\(268\) | 405488. | 0.344859 | ||||||||
\(269\) | −1.08034e6 | −0.910292 | −0.455146 | − | 0.890417i | \(-0.650413\pi\) | ||||
−0.455146 | + | 0.890417i | \(0.650413\pi\) | |||||||
\(270\) | 98940.0 | 0.0825967 | ||||||||
\(271\) | 816100. | 0.675025 | 0.337513 | − | 0.941321i | \(-0.390414\pi\) | ||||
0.337513 | + | 0.941321i | \(0.390414\pi\) | |||||||
\(272\) | 188928. | 0.154837 | ||||||||
\(273\) | −114872. | −0.0932841 | ||||||||
\(274\) | 1.60055e6 | 1.28793 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −28464.0 | −0.0224917 | ||||||||
\(277\) | −1.68820e6 | −1.32198 | −0.660989 | − | 0.750396i | \(-0.729863\pi\) | ||||
−0.660989 | + | 0.750396i | \(0.729863\pi\) | |||||||
\(278\) | −823064. | −0.638736 | ||||||||
\(279\) | −1.51129e6 | −1.16235 | ||||||||
\(280\) | −541824. | −0.413012 | ||||||||
\(281\) | 879042. | 0.664116 | 0.332058 | − | 0.943259i | \(-0.392257\pi\) | ||||
0.332058 | + | 0.943259i | \(0.392257\pi\) | |||||||
\(282\) | −68736.0 | −0.0514709 | ||||||||
\(283\) | −1.54027e6 | −1.14322 | −0.571611 | − | 0.820525i | \(-0.693681\pi\) | ||||
−0.571611 | + | 0.820525i | \(0.693681\pi\) | |||||||
\(284\) | 212976. | 0.156688 | ||||||||
\(285\) | 72624.0 | 0.0529624 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −880464. | −0.630967 | ||||||||
\(288\) | −247808. | −0.176049 | ||||||||
\(289\) | −875213. | −0.616409 | ||||||||
\(290\) | −421056. | −0.293998 | ||||||||
\(291\) | −88807.0 | −0.0614773 | ||||||||
\(292\) | 852160. | 0.584876 | ||||||||
\(293\) | −720840. | −0.490535 | −0.245267 | − | 0.969455i | \(-0.578876\pi\) | ||||
−0.245267 | + | 0.969455i | \(0.578876\pi\) | |||||||
\(294\) | 42996.0 | 0.0290108 | ||||||||
\(295\) | 1.78444e6 | 1.19384 | ||||||||
\(296\) | −946240. | −0.627729 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −350904. | −0.228901 | ||||||||
\(299\) | 1.23107e6 | 0.796350 | ||||||||
\(300\) | −8384.00 | −0.00537834 | ||||||||
\(301\) | −2.95447e6 | −1.87959 | ||||||||
\(302\) | 1.73111e6 | 1.09221 | ||||||||
\(303\) | −1482.00 | −0.000927346 0 | ||||||||
\(304\) | −364544. | −0.226238 | ||||||||
\(305\) | −2.34294e6 | −1.44215 | ||||||||
\(306\) | −714384. | −0.436142 | ||||||||
\(307\) | 1.03905e6 | 0.629201 | 0.314601 | − | 0.949224i | \(-0.398129\pi\) | ||||
0.314601 | + | 0.949224i | \(0.398129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −117496. | −0.0700046 | ||||||||
\(310\) | −1.27398e6 | −0.752937 | ||||||||
\(311\) | −1.25135e6 | −0.733630 | −0.366815 | − | 0.930294i | \(-0.619552\pi\) | ||||
−0.366815 | + | 0.930294i | \(0.619552\pi\) | |||||||
\(312\) | −44288.0 | −0.0257573 | ||||||||
\(313\) | −1.44336e6 | −0.832749 | −0.416375 | − | 0.909193i | \(-0.636699\pi\) | ||||
−0.416375 | + | 0.909193i | \(0.636699\pi\) | |||||||
\(314\) | −136300. | −0.0780139 | ||||||||
\(315\) | 2.04877e6 | 1.16337 | ||||||||
\(316\) | −1.23574e6 | −0.696163 | ||||||||
\(317\) | −2.01208e6 | −1.12460 | −0.562298 | − | 0.826934i | \(-0.690083\pi\) | ||||
−0.562298 | + | 0.826934i | \(0.690083\pi\) | |||||||
\(318\) | −122904. | −0.0681551 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −208896. | −0.114039 | ||||||||
\(321\) | 79362.0 | 0.0429883 | ||||||||
\(322\) | −1.18126e6 | −0.634899 | ||||||||
\(323\) | −1.05091e6 | −0.560480 | ||||||||
\(324\) | 933136. | 0.493836 | ||||||||
\(325\) | 362608. | 0.190427 | ||||||||
\(326\) | 180080. | 0.0938472 | ||||||||
\(327\) | −87842.0 | −0.0454290 | ||||||||
\(328\) | −339456. | −0.174220 | ||||||||
\(329\) | −2.85254e6 | −1.45292 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.01734e6 | 1.01207 | 0.506033 | − | 0.862514i | \(-0.331112\pi\) | ||||
0.506033 | + | 0.862514i | \(0.331112\pi\) | |||||||
\(332\) | −880224. | −0.438276 | ||||||||
\(333\) | 3.57797e6 | 1.76818 | ||||||||
\(334\) | −1.93022e6 | −0.946764 | ||||||||
\(335\) | −1.29249e6 | −0.629240 | ||||||||
\(336\) | 42496.0 | 0.0205352 | ||||||||
\(337\) | −264122. | −0.126686 | −0.0633432 | − | 0.997992i | \(-0.520176\pi\) | ||||
−0.0633432 | + | 0.997992i | \(0.520176\pi\) | |||||||
\(338\) | 430284. | 0.204863 | ||||||||
\(339\) | −47247.0 | −0.0223293 | ||||||||
\(340\) | −602208. | −0.282520 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 1.37843e6 | 0.637265 | ||||||||
\(343\) | −1.00563e6 | −0.461532 | ||||||||
\(344\) | −1.13907e6 | −0.518985 | ||||||||
\(345\) | 90729.0 | 0.0410392 | ||||||||
\(346\) | 3.06502e6 | 1.37639 | ||||||||
\(347\) | 1.71049e6 | 0.762601 | 0.381300 | − | 0.924451i | \(-0.375476\pi\) | ||||
0.381300 | + | 0.924451i | \(0.375476\pi\) | |||||||
\(348\) | 33024.0 | 0.0146178 | ||||||||
\(349\) | −218822. | −0.0961673 | −0.0480836 | − | 0.998843i | \(-0.515311\pi\) | ||||
−0.0480836 | + | 0.998843i | \(0.515311\pi\) | |||||||
\(350\) | −347936. | −0.151820 | ||||||||
\(351\) | 335620. | 0.145405 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.68192e6 | 1.57267 | 0.786334 | − | 0.617802i | \(-0.211977\pi\) | ||||
0.786334 | + | 0.617802i | \(0.211977\pi\) | |||||||
\(354\) | −139956. | −0.0593586 | ||||||||
\(355\) | −678861. | −0.285897 | ||||||||
\(356\) | 2.00664e6 | 0.839159 | ||||||||
\(357\) | 122508. | 0.0508738 | ||||||||
\(358\) | 1.21360e6 | 0.500457 | ||||||||
\(359\) | −1.88528e6 | −0.772042 | −0.386021 | − | 0.922490i | \(-0.626151\pi\) | ||||
−0.386021 | + | 0.922490i | \(0.626151\pi\) | |||||||
\(360\) | 789888. | 0.321225 | ||||||||
\(361\) | −448323. | −0.181060 | ||||||||
\(362\) | −1.14072e6 | −0.457519 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.83795e6 | −0.727078 | ||||||||
\(365\) | −2.71626e6 | −1.06718 | ||||||||
\(366\) | 183760. | 0.0717048 | ||||||||
\(367\) | −3.11666e6 | −1.20788 | −0.603940 | − | 0.797029i | \(-0.706404\pi\) | ||||
−0.603940 | + | 0.797029i | \(0.706404\pi\) | |||||||
\(368\) | −455424. | −0.175306 | ||||||||
\(369\) | 1.28357e6 | 0.490742 | ||||||||
\(370\) | 3.01614e6 | 1.14537 | ||||||||
\(371\) | −5.10052e6 | −1.92389 | ||||||||
\(372\) | 99920.0 | 0.0374365 | ||||||||
\(373\) | −1.39441e6 | −0.518943 | −0.259471 | − | 0.965751i | \(-0.583548\pi\) | ||||
−0.259471 | + | 0.965751i | \(0.583548\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 186099. | 0.0683386 | ||||||||
\(376\) | −1.09978e6 | −0.401176 | ||||||||
\(377\) | −1.42829e6 | −0.517562 | ||||||||
\(378\) | −322040. | −0.115926 | ||||||||
\(379\) | −4.26036e6 | −1.52352 | −0.761759 | − | 0.647860i | \(-0.775664\pi\) | ||||
−0.761759 | + | 0.647860i | \(0.775664\pi\) | |||||||
\(380\) | 1.16198e6 | 0.412801 | ||||||||
\(381\) | 239416. | 0.0844969 | ||||||||
\(382\) | 3.06827e6 | 1.07581 | ||||||||
\(383\) | 201765. | 0.0702828 | 0.0351414 | − | 0.999382i | \(-0.488812\pi\) | ||||
0.0351414 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(384\) | 16384.0 | 0.00567012 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.64667e6 | −0.562521 | ||||||||
\(387\) | 4.30712e6 | 1.46187 | ||||||||
\(388\) | −1.42091e6 | −0.479168 | ||||||||
\(389\) | 1.94882e6 | 0.652977 | 0.326489 | − | 0.945201i | \(-0.394135\pi\) | ||||
0.326489 | + | 0.945201i | \(0.394135\pi\) | |||||||
\(390\) | 141168. | 0.0469975 | ||||||||
\(391\) | −1.31290e6 | −0.434301 | ||||||||
\(392\) | 687936. | 0.226117 | ||||||||
\(393\) | 98142.0 | 0.0320534 | ||||||||
\(394\) | 3.03703e6 | 0.985618 | ||||||||
\(395\) | 3.93893e6 | 1.27024 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.46826e6 | −0.467548 | −0.233774 | − | 0.972291i | \(-0.575108\pi\) | ||||
−0.233774 | + | 0.972291i | \(0.575108\pi\) | |||||||
\(398\) | −186400. | −0.0589845 | ||||||||
\(399\) | −236384. | −0.0743337 | ||||||||
\(400\) | −134144. | −0.0419200 | ||||||||
\(401\) | 2.24618e6 | 0.697563 | 0.348781 | − | 0.937204i | \(-0.386596\pi\) | ||||
0.348781 | + | 0.937204i | \(0.386596\pi\) | |||||||
\(402\) | 101372. | 0.0312862 | ||||||||
\(403\) | −4.32154e6 | −1.32549 | ||||||||
\(404\) | −23712.0 | −0.00722794 | ||||||||
\(405\) | −2.97437e6 | −0.901068 | ||||||||
\(406\) | 1.37050e6 | 0.412632 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 47232.0 | 0.0140471 | ||||||||
\(409\) | 3.61488e6 | 1.06853 | 0.534263 | − | 0.845318i | \(-0.320589\pi\) | ||||
0.534263 | + | 0.845318i | \(0.320589\pi\) | |||||||
\(410\) | 1.08202e6 | 0.317888 | ||||||||
\(411\) | 400137. | 0.116843 | ||||||||
\(412\) | −1.87994e6 | −0.545632 | ||||||||
\(413\) | −5.80817e6 | −1.67558 | ||||||||
\(414\) | 1.72207e6 | 0.493799 | ||||||||
\(415\) | 2.80571e6 | 0.799693 | ||||||||
\(416\) | −708608. | −0.200758 | ||||||||
\(417\) | −205766. | −0.0579473 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.81239e6 | −1.06087 | −0.530435 | − | 0.847726i | \(-0.677971\pi\) | ||||
−0.530435 | + | 0.847726i | \(0.677971\pi\) | |||||||
\(420\) | −135456. | −0.0374693 | ||||||||
\(421\) | 1.97346e6 | 0.542655 | 0.271327 | − | 0.962487i | \(-0.412537\pi\) | ||||
0.271327 | + | 0.962487i | \(0.412537\pi\) | |||||||
\(422\) | 3.72971e6 | 1.01952 | ||||||||
\(423\) | 4.15853e6 | 1.13003 | ||||||||
\(424\) | −1.96646e6 | −0.531216 | ||||||||
\(425\) | −386712. | −0.103852 | ||||||||
\(426\) | 53244.0 | 0.0142150 | ||||||||
\(427\) | 7.62604e6 | 2.02409 | ||||||||
\(428\) | 1.26979e6 | 0.335060 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.63079e6 | 0.946957 | ||||||||
\(431\) | 2.08359e6 | 0.540280 | 0.270140 | − | 0.962821i | \(-0.412930\pi\) | ||||
0.270140 | + | 0.962821i | \(0.412930\pi\) | |||||||
\(432\) | −124160. | −0.0320090 | ||||||||
\(433\) | −72691.0 | −0.0186321 | −0.00931603 | − | 0.999957i | \(-0.502965\pi\) | ||||
−0.00931603 | + | 0.999957i | \(0.502965\pi\) | |||||||
\(434\) | 4.14668e6 | 1.05676 | ||||||||
\(435\) | −105264. | −0.0266721 | ||||||||
\(436\) | −1.40547e6 | −0.354084 | ||||||||
\(437\) | 2.53330e6 | 0.634574 | ||||||||
\(438\) | 213040. | 0.0530611 | ||||||||
\(439\) | −594392. | −0.147201 | −0.0736007 | − | 0.997288i | \(-0.523449\pi\) | ||||
−0.0736007 | + | 0.997288i | \(0.523449\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.60126e6 | −0.636923 | ||||||||
\(442\) | −2.04278e6 | −0.497355 | ||||||||
\(443\) | 4.56651e6 | 1.10554 | 0.552770 | − | 0.833334i | \(-0.313571\pi\) | ||||
0.552770 | + | 0.833334i | \(0.313571\pi\) | |||||||
\(444\) | −236560. | −0.0569487 | ||||||||
\(445\) | −6.39616e6 | −1.53116 | ||||||||
\(446\) | 678980. | 0.161629 | ||||||||
\(447\) | −87726.0 | −0.0207663 | ||||||||
\(448\) | 679936. | 0.160056 | ||||||||
\(449\) | −5.44382e6 | −1.27435 | −0.637174 | − | 0.770720i | \(-0.719897\pi\) | ||||
−0.637174 | + | 0.770720i | \(0.719897\pi\) | |||||||
\(450\) | 507232. | 0.118080 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −755952. | −0.174040 | ||||||||
\(453\) | 432778. | 0.0990877 | ||||||||
\(454\) | −792312. | −0.180408 | ||||||||
\(455\) | 5.85847e6 | 1.32665 | ||||||||
\(456\) | −91136.0 | −0.0205247 | ||||||||
\(457\) | −6.70312e6 | −1.50137 | −0.750683 | − | 0.660662i | \(-0.770276\pi\) | ||||
−0.750683 | + | 0.660662i | \(0.770276\pi\) | |||||||
\(458\) | −3.39999e6 | −0.757380 | ||||||||
\(459\) | −357930. | −0.0792988 | ||||||||
\(460\) | 1.45166e6 | 0.319869 | ||||||||
\(461\) | 1.25994e6 | 0.276120 | 0.138060 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138060 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.02308e6 | −1.08897 | −0.544487 | − | 0.838769i | \(-0.683276\pi\) | ||||
−0.544487 | + | 0.838769i | \(0.683276\pi\) | |||||||
\(464\) | 528384. | 0.113934 | ||||||||
\(465\) | −318495. | −0.0683078 | ||||||||
\(466\) | 1.60733e6 | 0.342878 | ||||||||
\(467\) | −2.35660e6 | −0.500028 | −0.250014 | − | 0.968242i | \(-0.580435\pi\) | ||||
−0.250014 | + | 0.968242i | \(0.580435\pi\) | |||||||
\(468\) | 2.67942e6 | 0.565492 | ||||||||
\(469\) | 4.20694e6 | 0.883149 | ||||||||
\(470\) | 3.50554e6 | 0.731998 | ||||||||
\(471\) | −34075.0 | −0.00707756 | ||||||||
\(472\) | −2.23930e6 | −0.462654 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −308936. | −0.0631572 | ||||||||
\(475\) | 746176. | 0.151743 | ||||||||
\(476\) | 1.96013e6 | 0.396522 | ||||||||
\(477\) | 7.43569e6 | 1.49632 | ||||||||
\(478\) | −3.42070e6 | −0.684770 | ||||||||
\(479\) | 6.72258e6 | 1.33874 | 0.669371 | − | 0.742928i | \(-0.266563\pi\) | ||||
0.669371 | + | 0.742928i | \(0.266563\pi\) | |||||||
\(480\) | −52224.0 | −0.0103459 | ||||||||
\(481\) | 1.02312e7 | 2.01634 | ||||||||
\(482\) | −4.50186e6 | −0.882620 | ||||||||
\(483\) | −295314. | −0.0575992 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.52916e6 | 0.874305 | ||||||||
\(486\) | 704704. | 0.135337 | ||||||||
\(487\) | 1.96001e6 | 0.374487 | 0.187243 | − | 0.982314i | \(-0.440045\pi\) | ||||
0.187243 | + | 0.982314i | \(0.440045\pi\) | |||||||
\(488\) | 2.94016e6 | 0.558884 | ||||||||
\(489\) | 45020.0 | 0.00851399 | ||||||||
\(490\) | −2.19280e6 | −0.412580 | ||||||||
\(491\) | 579624. | 0.108503 | 0.0542516 | − | 0.998527i | \(-0.482723\pi\) | ||||
0.0542516 | + | 0.998527i | \(0.482723\pi\) | |||||||
\(492\) | −84864.0 | −0.0158056 | ||||||||
\(493\) | 1.52323e6 | 0.282260 | ||||||||
\(494\) | 3.94163e6 | 0.726706 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.59872e6 | 0.291789 | ||||||||
\(497\) | 2.20963e6 | 0.401262 | ||||||||
\(498\) | −220056. | −0.0397612 | ||||||||
\(499\) | 1.36905e6 | 0.246132 | 0.123066 | − | 0.992398i | \(-0.460727\pi\) | ||||
0.123066 | + | 0.992398i | \(0.460727\pi\) | |||||||
\(500\) | 2.97758e6 | 0.532646 | ||||||||
\(501\) | −482556. | −0.0858921 | ||||||||
\(502\) | −4.79005e6 | −0.848361 | ||||||||
\(503\) | −1.83343e6 | −0.323105 | −0.161552 | − | 0.986864i | \(-0.551650\pi\) | ||||
−0.161552 | + | 0.986864i | \(0.551650\pi\) | |||||||
\(504\) | −2.57101e6 | −0.450845 | ||||||||
\(505\) | 75582.0 | 0.0131883 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 107571. | 0.0185855 | ||||||||
\(508\) | 3.83066e6 | 0.658588 | ||||||||
\(509\) | −1.71266e6 | −0.293006 | −0.146503 | − | 0.989210i | \(-0.546802\pi\) | ||||
−0.146503 | + | 0.989210i | \(0.546802\pi\) | |||||||
\(510\) | −150552. | −0.0256307 | ||||||||
\(511\) | 8.84116e6 | 1.49781 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 690640. | 0.115867 | ||||||||
\(514\) | 151032. | 0.0252151 | ||||||||
\(515\) | 5.99230e6 | 0.995578 | ||||||||
\(516\) | −284768. | −0.0470833 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −9.81724e6 | −1.60755 | ||||||||
\(519\) | 766254. | 0.124869 | ||||||||
\(520\) | 2.25869e6 | 0.366309 | ||||||||
\(521\) | −789435. | −0.127415 | −0.0637077 | − | 0.997969i | \(-0.520293\pi\) | ||||
−0.0637077 | + | 0.997969i | \(0.520293\pi\) | |||||||
\(522\) | −1.99795e6 | −0.320929 | ||||||||
\(523\) | −627392. | −0.100296 | −0.0501481 | − | 0.998742i | \(-0.515969\pi\) | ||||
−0.0501481 | + | 0.998742i | \(0.515969\pi\) | |||||||
\(524\) | 1.57027e6 | 0.249831 | ||||||||
\(525\) | −86984.0 | −0.0137734 | ||||||||
\(526\) | 2.52502e6 | 0.397924 | ||||||||
\(527\) | 4.60881e6 | 0.722873 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.27150e6 | −0.508286 | ||||||||
\(530\) | 6.26810e6 | 0.969274 | ||||||||
\(531\) | 8.46734e6 | 1.30320 | ||||||||
\(532\) | −3.78214e6 | −0.579374 | ||||||||
\(533\) | 3.67037e6 | 0.559618 | ||||||||
\(534\) | 501660. | 0.0761301 | ||||||||
\(535\) | −4.04746e6 | −0.611362 | ||||||||
\(536\) | 1.62195e6 | 0.243852 | ||||||||
\(537\) | 303399. | 0.0454024 | ||||||||
\(538\) | −4.32137e6 | −0.643673 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 395760. | 0.0584047 | ||||||||
\(541\) | −3.20895e6 | −0.471379 | −0.235689 | − | 0.971828i | \(-0.575735\pi\) | ||||
−0.235689 | + | 0.971828i | \(0.575735\pi\) | |||||||
\(542\) | 3.26440e6 | 0.477315 | ||||||||
\(543\) | −285181. | −0.0415070 | ||||||||
\(544\) | 755712. | 0.109486 | ||||||||
\(545\) | 4.47994e6 | 0.646072 | ||||||||
\(546\) | −459488. | −0.0659618 | ||||||||
\(547\) | −3.42658e6 | −0.489658 | −0.244829 | − | 0.969566i | \(-0.578732\pi\) | ||||
−0.244829 | + | 0.969566i | \(0.578732\pi\) | |||||||
\(548\) | 6.40219e6 | 0.910704 | ||||||||
\(549\) | −1.11175e7 | −1.57426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.93914e6 | −0.412421 | ||||||||
\(552\) | −113856. | −0.0159041 | ||||||||
\(553\) | −1.28208e7 | −1.78280 | ||||||||
\(554\) | −6.75279e6 | −0.934779 | ||||||||
\(555\) | 754035. | 0.103910 | ||||||||
\(556\) | −3.29226e6 | −0.451655 | ||||||||
\(557\) | −1.05198e7 | −1.43672 | −0.718358 | − | 0.695674i | \(-0.755106\pi\) | ||||
−0.718358 | + | 0.695674i | \(0.755106\pi\) | |||||||
\(558\) | −6.04516e6 | −0.821906 | ||||||||
\(559\) | 1.23162e7 | 1.66705 | ||||||||
\(560\) | −2.16730e6 | −0.292044 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.51617e6 | 0.469601 | ||||||||
\(563\) | −5.47288e6 | −0.727687 | −0.363844 | − | 0.931460i | \(-0.618536\pi\) | ||||
−0.363844 | + | 0.931460i | \(0.618536\pi\) | |||||||
\(564\) | −274944. | −0.0363954 | ||||||||
\(565\) | 2.40960e6 | 0.317558 | ||||||||
\(566\) | −6.16107e6 | −0.808379 | ||||||||
\(567\) | 9.68129e6 | 1.26466 | ||||||||
\(568\) | 851904. | 0.110795 | ||||||||
\(569\) | 1.17787e7 | 1.52516 | 0.762580 | − | 0.646893i | \(-0.223932\pi\) | ||||
0.762580 | + | 0.646893i | \(0.223932\pi\) | |||||||
\(570\) | 290496. | 0.0374501 | ||||||||
\(571\) | 8.35628e6 | 1.07256 | 0.536281 | − | 0.844039i | \(-0.319829\pi\) | ||||
0.536281 | + | 0.844039i | \(0.319829\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 767067. | 0.0975993 | ||||||||
\(574\) | −3.52186e6 | −0.446161 | ||||||||
\(575\) | 932196. | 0.117581 | ||||||||
\(576\) | −991232. | −0.124486 | ||||||||
\(577\) | −1.37758e7 | −1.72258 | −0.861288 | − | 0.508117i | \(-0.830342\pi\) | ||||
−0.861288 | + | 0.508117i | \(0.830342\pi\) | |||||||
\(578\) | −3.50085e6 | −0.435867 | ||||||||
\(579\) | −411668. | −0.0510330 | ||||||||
\(580\) | −1.68422e6 | −0.207888 | ||||||||
\(581\) | −9.13232e6 | −1.12238 | ||||||||
\(582\) | −355228. | −0.0434710 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 3.40864e6 | 0.413570 | ||||||||
\(585\) | −8.54066e6 | −1.03182 | ||||||||
\(586\) | −2.88336e6 | −0.346860 | ||||||||
\(587\) | −1.27093e7 | −1.52239 | −0.761196 | − | 0.648522i | \(-0.775388\pi\) | ||||
−0.761196 | + | 0.648522i | \(0.775388\pi\) | |||||||
\(588\) | 171984. | 0.0205137 | ||||||||
\(589\) | −8.89288e6 | −1.05622 | ||||||||
\(590\) | 7.13776e6 | 0.844173 | ||||||||
\(591\) | 759258. | 0.0894171 | ||||||||
\(592\) | −3.78496e6 | −0.443871 | ||||||||
\(593\) | −1.00825e6 | −0.117742 | −0.0588711 | − | 0.998266i | \(-0.518750\pi\) | ||||
−0.0588711 | + | 0.998266i | \(0.518750\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.24791e6 | −0.723506 | ||||||||
\(596\) | −1.40362e6 | −0.161857 | ||||||||
\(597\) | −46600.0 | −0.00535119 | ||||||||
\(598\) | 4.92427e6 | 0.563105 | ||||||||
\(599\) | 1.05100e7 | 1.19684 | 0.598421 | − | 0.801182i | \(-0.295795\pi\) | ||||
0.598421 | + | 0.801182i | \(0.295795\pi\) | |||||||
\(600\) | −33536.0 | −0.00380306 | ||||||||
\(601\) | 199390. | 0.0225173 | 0.0112587 | − | 0.999937i | \(-0.496416\pi\) | ||||
0.0112587 | + | 0.999937i | \(0.496416\pi\) | |||||||
\(602\) | −1.18179e7 | −1.32907 | ||||||||
\(603\) | −6.13301e6 | −0.686879 | ||||||||
\(604\) | 6.92445e6 | 0.772312 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5928.00 | −0.000655732 0 | ||||||||
\(607\) | −16190.0 | −0.00178351 | −0.000891754 | − | 1.00000i | \(-0.500284\pi\) | ||||
−0.000891754 | 1.00000i | \(0.500284\pi\) | ||||||||
\(608\) | −1.45818e6 | −0.159975 | ||||||||
\(609\) | 342624. | 0.0374347 | ||||||||
\(610\) | −9.37176e6 | −1.01976 | ||||||||
\(611\) | 1.18913e7 | 1.28863 | ||||||||
\(612\) | −2.85754e6 | −0.308399 | ||||||||
\(613\) | 1.15253e7 | 1.23880 | 0.619402 | − | 0.785074i | \(-0.287375\pi\) | ||||
0.619402 | + | 0.785074i | \(0.287375\pi\) | |||||||
\(614\) | 4.15619e6 | 0.444913 | ||||||||
\(615\) | 270504. | 0.0288394 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.69974e7 | 1.79750 | 0.898751 | − | 0.438459i | \(-0.144476\pi\) | ||||
0.898751 | + | 0.438459i | \(0.144476\pi\) | |||||||
\(618\) | −469984. | −0.0495008 | ||||||||
\(619\) | −1.84875e7 | −1.93933 | −0.969663 | − | 0.244445i | \(-0.921394\pi\) | ||||
−0.969663 | + | 0.244445i | \(0.921394\pi\) | |||||||
\(620\) | −5.09592e6 | −0.532407 | ||||||||
\(621\) | 862815. | 0.0897819 | ||||||||
\(622\) | −5.00539e6 | −0.518755 | ||||||||
\(623\) | 2.08189e7 | 2.14901 | ||||||||
\(624\) | −177152. | −0.0182131 | ||||||||
\(625\) | −7.85355e6 | −0.804203 | ||||||||
\(626\) | −5.77344e6 | −0.588842 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −545200. | −0.0551641 | ||||||||
\(629\) | −1.09113e7 | −1.09964 | ||||||||
\(630\) | 8.19509e6 | 0.822626 | ||||||||
\(631\) | −4.54281e6 | −0.454204 | −0.227102 | − | 0.973871i | \(-0.572925\pi\) | ||||
−0.227102 | + | 0.973871i | \(0.572925\pi\) | |||||||
\(632\) | −4.94298e6 | −0.492261 | ||||||||
\(633\) | 932428. | 0.0924924 | ||||||||
\(634\) | −8.04832e6 | −0.795210 | ||||||||
\(635\) | −1.22102e7 | −1.20168 | ||||||||
\(636\) | −491616. | −0.0481929 | ||||||||
\(637\) | −7.43831e6 | −0.726316 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.22126e6 | −0.312086 | ||||||||
\(640\) | −835584. | −0.0806381 | ||||||||
\(641\) | 1.84286e7 | 1.77153 | 0.885764 | − | 0.464136i | \(-0.153635\pi\) | ||||
0.885764 | + | 0.464136i | \(0.153635\pi\) | |||||||
\(642\) | 317448. | 0.0303973 | ||||||||
\(643\) | 9.66604e6 | 0.921979 | 0.460989 | − | 0.887406i | \(-0.347495\pi\) | ||||
0.460989 | + | 0.887406i | \(0.347495\pi\) | |||||||
\(644\) | −4.72502e6 | −0.448941 | ||||||||
\(645\) | 907698. | 0.0859097 | ||||||||
\(646\) | −4.20365e6 | −0.396319 | ||||||||
\(647\) | −4.51430e6 | −0.423965 | −0.211982 | − | 0.977273i | \(-0.567992\pi\) | ||||
−0.211982 | + | 0.977273i | \(0.567992\pi\) | |||||||
\(648\) | 3.73254e6 | 0.349195 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.45043e6 | 0.134652 | ||||||||
\(651\) | 1.03667e6 | 0.0958712 | ||||||||
\(652\) | 720320. | 0.0663600 | ||||||||
\(653\) | −5.37235e6 | −0.493039 | −0.246519 | − | 0.969138i | \(-0.579287\pi\) | ||||
−0.246519 | + | 0.969138i | \(0.579287\pi\) | |||||||
\(654\) | −351368. | −0.0321231 | ||||||||
\(655\) | −5.00524e6 | −0.455850 | ||||||||
\(656\) | −1.35782e6 | −0.123192 | ||||||||
\(657\) | −1.28889e7 | −1.16494 | ||||||||
\(658\) | −1.14102e7 | −1.02737 | ||||||||
\(659\) | −9.87956e6 | −0.886184 | −0.443092 | − | 0.896476i | \(-0.646119\pi\) | ||||
−0.443092 | + | 0.896476i | \(0.646119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.08052e7 | 0.961898 | 0.480949 | − | 0.876748i | \(-0.340292\pi\) | ||||
0.480949 | + | 0.876748i | \(0.340292\pi\) | |||||||
\(662\) | 8.06935e6 | 0.715638 | ||||||||
\(663\) | −510696. | −0.0451210 | ||||||||
\(664\) | −3.52090e6 | −0.309908 | ||||||||
\(665\) | 1.20556e7 | 1.05714 | ||||||||
\(666\) | 1.43119e7 | 1.25029 | ||||||||
\(667\) | −3.67186e6 | −0.319574 | ||||||||
\(668\) | −7.72090e6 | −0.669463 | ||||||||
\(669\) | 169745. | 0.0146633 | ||||||||
\(670\) | −5.16997e6 | −0.444940 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 169984. | 0.0145206 | ||||||||
\(673\) | −1.13275e7 | −0.964042 | −0.482021 | − | 0.876160i | \(-0.660097\pi\) | ||||
−0.482021 | + | 0.876160i | \(0.660097\pi\) | |||||||
\(674\) | −1.05649e6 | −0.0895808 | ||||||||
\(675\) | 254140. | 0.0214691 | ||||||||
\(676\) | 1.72114e6 | 0.144860 | ||||||||
\(677\) | 1.20595e7 | 1.01125 | 0.505624 | − | 0.862754i | \(-0.331262\pi\) | ||||
0.505624 | + | 0.862754i | \(0.331262\pi\) | |||||||
\(678\) | −188988. | −0.0157892 | ||||||||
\(679\) | −1.47420e7 | −1.22710 | ||||||||
\(680\) | −2.40883e6 | −0.199772 | ||||||||
\(681\) | −198078. | −0.0163670 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.14166e6 | −0.421747 | −0.210873 | − | 0.977513i | \(-0.567631\pi\) | ||||
−0.210873 | + | 0.977513i | \(0.567631\pi\) | |||||||
\(684\) | 5.51373e6 | 0.450614 | ||||||||
\(685\) | −2.04070e7 | −1.66170 | ||||||||
\(686\) | −4.02251e6 | −0.326353 | ||||||||
\(687\) | −849997. | −0.0687109 | ||||||||
\(688\) | −4.55629e6 | −0.366978 | ||||||||
\(689\) | 2.12624e7 | 1.70633 | ||||||||
\(690\) | 362916. | 0.0290191 | ||||||||
\(691\) | 1.31243e7 | 1.04563 | 0.522817 | − | 0.852445i | \(-0.324881\pi\) | ||||
0.522817 | + | 0.852445i | \(0.324881\pi\) | |||||||
\(692\) | 1.22601e7 | 0.973257 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.84197e6 | 0.539240 | ||||||||
\(695\) | 1.04941e7 | 0.824104 | ||||||||
\(696\) | 132096. | 0.0103363 | ||||||||
\(697\) | −3.91435e6 | −0.305195 | ||||||||
\(698\) | −875288. | −0.0680005 | ||||||||
\(699\) | 401832. | 0.0311065 | ||||||||
\(700\) | −1.39174e6 | −0.107353 | ||||||||
\(701\) | −3.65956e6 | −0.281277 | −0.140638 | − | 0.990061i | \(-0.544916\pi\) | ||||
−0.140638 | + | 0.990061i | \(0.544916\pi\) | |||||||
\(702\) | 1.34248e6 | 0.102817 | ||||||||
\(703\) | 2.10538e7 | 1.60673 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 876384. | 0.0664082 | ||||||||
\(706\) | 1.47277e7 | 1.11204 | ||||||||
\(707\) | −246012. | −0.0185101 | ||||||||
\(708\) | −559824. | −0.0419728 | ||||||||
\(709\) | 1.02252e7 | 0.763935 | 0.381968 | − | 0.924176i | \(-0.375247\pi\) | ||||
0.381968 | + | 0.924176i | \(0.375247\pi\) | |||||||
\(710\) | −2.71544e6 | −0.202160 | ||||||||
\(711\) | 1.86906e7 | 1.38660 | ||||||||
\(712\) | 8.02656e6 | 0.593375 | ||||||||
\(713\) | −1.11099e7 | −0.818436 | ||||||||
\(714\) | 490032. | 0.0359732 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.85438e6 | 0.353876 | ||||||||
\(717\) | −855174. | −0.0621236 | ||||||||
\(718\) | −7.54114e6 | −0.545916 | ||||||||
\(719\) | 2.41683e7 | 1.74351 | 0.871753 | − | 0.489945i | \(-0.162983\pi\) | ||||
0.871753 | + | 0.489945i | \(0.162983\pi\) | |||||||
\(720\) | 3.15955e6 | 0.227140 | ||||||||
\(721\) | −1.95043e7 | −1.39731 | ||||||||
\(722\) | −1.79329e6 | −0.128029 | ||||||||
\(723\) | −1.12546e6 | −0.0800730 | ||||||||
\(724\) | −4.56290e6 | −0.323515 | ||||||||
\(725\) | −1.08154e6 | −0.0764181 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.68246e7 | 1.18062 | 0.590310 | − | 0.807177i | \(-0.299006\pi\) | ||||
0.590310 | + | 0.807177i | \(0.299006\pi\) | |||||||
\(728\) | −7.35181e6 | −0.514121 | ||||||||
\(729\) | −1.39958e7 | −0.975393 | ||||||||
\(730\) | −1.08650e7 | −0.754613 | ||||||||
\(731\) | −1.31349e7 | −0.909147 | ||||||||
\(732\) | 735040. | 0.0507030 | ||||||||
\(733\) | 5.04168e6 | 0.346590 | 0.173295 | − | 0.984870i | \(-0.444559\pi\) | ||||
0.173295 | + | 0.984870i | \(0.444559\pi\) | |||||||
\(734\) | −1.24666e7 | −0.854101 | ||||||||
\(735\) | −548199. | −0.0374300 | ||||||||
\(736\) | −1.82170e6 | −0.123960 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 5.13427e6 | 0.347007 | ||||||||
\(739\) | 6.26375e6 | 0.421913 | 0.210957 | − | 0.977495i | \(-0.432342\pi\) | ||||
0.210957 | + | 0.977495i | \(0.432342\pi\) | |||||||
\(740\) | 1.20646e7 | 0.809901 | ||||||||
\(741\) | 985408. | 0.0659281 | ||||||||
\(742\) | −2.04021e7 | −1.36039 | ||||||||
\(743\) | −3.63976e6 | −0.241880 | −0.120940 | − | 0.992660i | \(-0.538591\pi\) | ||||
−0.120940 | + | 0.992660i | \(0.538591\pi\) | |||||||
\(744\) | 399680. | 0.0264716 | ||||||||
\(745\) | 4.47403e6 | 0.295330 | ||||||||
\(746\) | −5.57766e6 | −0.366948 | ||||||||
\(747\) | 1.33134e7 | 0.872945 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.31741e7 | 0.858057 | ||||||||
\(750\) | 744396. | 0.0483227 | ||||||||
\(751\) | −1.87370e7 | −1.21227 | −0.606135 | − | 0.795362i | \(-0.707281\pi\) | ||||
−0.606135 | + | 0.795362i | \(0.707281\pi\) | |||||||
\(752\) | −4.39910e6 | −0.283674 | ||||||||
\(753\) | −1.19751e6 | −0.0769649 | ||||||||
\(754\) | −5.71315e6 | −0.365972 | ||||||||
\(755\) | −2.20717e7 | −1.40918 | ||||||||
\(756\) | −1.28816e6 | −0.0819720 | ||||||||
\(757\) | 489242. | 0.0310302 | 0.0155151 | − | 0.999880i | \(-0.495061\pi\) | ||||
0.0155151 | + | 0.999880i | \(0.495061\pi\) | |||||||
\(758\) | −1.70414e7 | −1.07729 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.64794e6 | 0.291895 | ||||||||
\(761\) | −1.46969e7 | −0.919952 | −0.459976 | − | 0.887931i | \(-0.652142\pi\) | ||||
−0.459976 | + | 0.887931i | \(0.652142\pi\) | |||||||
\(762\) | 957664. | 0.0597483 | ||||||||
\(763\) | −1.45818e7 | −0.906774 | ||||||||
\(764\) | 1.22731e7 | 0.760711 | ||||||||
\(765\) | 9.10840e6 | 0.562715 | ||||||||
\(766\) | 807060. | 0.0496974 | ||||||||
\(767\) | 2.42124e7 | 1.48610 | ||||||||
\(768\) | 65536.0 | 0.00400938 | ||||||||
\(769\) | −2.42072e7 | −1.47615 | −0.738073 | − | 0.674721i | \(-0.764264\pi\) | ||||
−0.738073 | + | 0.674721i | \(0.764264\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37758.0 | 0.00228756 | ||||||||
\(772\) | −6.58669e6 | −0.397763 | ||||||||
\(773\) | 1.35260e7 | 0.814181 | 0.407091 | − | 0.913388i | \(-0.366543\pi\) | ||||
0.407091 | + | 0.913388i | \(0.366543\pi\) | |||||||
\(774\) | 1.72285e7 | 1.03370 | ||||||||
\(775\) | −3.27238e6 | −0.195708 | ||||||||
\(776\) | −5.68365e6 | −0.338823 | ||||||||
\(777\) | −2.45431e6 | −0.145840 | ||||||||
\(778\) | 7.79528e6 | 0.461725 | ||||||||
\(779\) | 7.55290e6 | 0.445933 | ||||||||
\(780\) | 564672. | 0.0332323 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.25161e6 | −0.307097 | ||||||||
\(783\) | −1.00104e6 | −0.0583508 | ||||||||
\(784\) | 2.75174e6 | 0.159889 | ||||||||
\(785\) | 1.73782e6 | 0.100654 | ||||||||
\(786\) | 392568. | 0.0226651 | ||||||||
\(787\) | −1.42094e7 | −0.817786 | −0.408893 | − | 0.912582i | \(-0.634085\pi\) | ||||
−0.408893 | + | 0.912582i | \(0.634085\pi\) | |||||||
\(788\) | 1.21481e7 | 0.696937 | ||||||||
\(789\) | 631254. | 0.0361004 | ||||||||
\(790\) | 1.57557e7 | 0.898196 | ||||||||
\(791\) | −7.84300e6 | −0.445698 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.17905e7 | −1.79521 | ||||||||
\(794\) | −5.87303e6 | −0.330606 | ||||||||
\(795\) | 1.56703e6 | 0.0879343 | ||||||||
\(796\) | −745600. | −0.0417084 | ||||||||
\(797\) | −7.93333e6 | −0.442395 | −0.221197 | − | 0.975229i | \(-0.570997\pi\) | ||||
−0.221197 | + | 0.975229i | \(0.570997\pi\) | |||||||
\(798\) | −945536. | −0.0525619 | ||||||||
\(799\) | −1.26818e7 | −0.702771 | ||||||||
\(800\) | −536576. | −0.0296419 | ||||||||
\(801\) | −3.03504e7 | −1.67141 | ||||||||
\(802\) | 8.98471e6 | 0.493251 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 405488. | 0.0221227 | ||||||||
\(805\) | 1.50610e7 | 0.819152 | ||||||||
\(806\) | −1.72862e7 | −0.937262 | ||||||||
\(807\) | −1.08034e6 | −0.0583952 | ||||||||
\(808\) | −94848.0 | −0.00511093 | ||||||||
\(809\) | 1.04685e7 | 0.562359 | 0.281180 | − | 0.959655i | \(-0.409274\pi\) | ||||
0.281180 | + | 0.959655i | \(0.409274\pi\) | |||||||
\(810\) | −1.18975e7 | −0.637151 | ||||||||
\(811\) | −1.19147e7 | −0.636110 | −0.318055 | − | 0.948072i | \(-0.603030\pi\) | ||||
−0.318055 | + | 0.948072i | \(0.603030\pi\) | |||||||
\(812\) | 5.48198e6 | 0.291775 | ||||||||
\(813\) | 816100. | 0.0433029 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.29602e6 | −0.121083 | ||||||||
\(816\) | 188928. | 0.00993278 | ||||||||
\(817\) | 2.53444e7 | 1.32839 | ||||||||
\(818\) | 1.44595e7 | 0.755562 | ||||||||
\(819\) | 2.77990e7 | 1.44817 | ||||||||
\(820\) | 4.32806e6 | 0.224781 | ||||||||
\(821\) | 1.86112e6 | 0.0963645 | 0.0481822 | − | 0.998839i | \(-0.484657\pi\) | ||||
0.0481822 | + | 0.998839i | \(0.484657\pi\) | |||||||
\(822\) | 1.60055e6 | 0.0826208 | ||||||||
\(823\) | 2.30153e7 | 1.18445 | 0.592225 | − | 0.805773i | \(-0.298250\pi\) | ||||
0.592225 | + | 0.805773i | \(0.298250\pi\) | |||||||
\(824\) | −7.51974e6 | −0.385820 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.32327e7 | −1.18481 | ||||||||
\(827\) | 1.68351e7 | 0.855959 | 0.427980 | − | 0.903788i | \(-0.359225\pi\) | ||||
0.427980 | + | 0.903788i | \(0.359225\pi\) | |||||||
\(828\) | 6.88829e6 | 0.349169 | ||||||||
\(829\) | −2.35299e7 | −1.18914 | −0.594570 | − | 0.804044i | \(-0.702678\pi\) | ||||
−0.594570 | + | 0.804044i | \(0.702678\pi\) | |||||||
\(830\) | 1.12229e7 | 0.565468 | ||||||||
\(831\) | −1.68820e6 | −0.0848049 | ||||||||
\(832\) | −2.83443e6 | −0.141957 | ||||||||
\(833\) | 7.93276e6 | 0.396106 | ||||||||
\(834\) | −823064. | −0.0409750 | ||||||||
\(835\) | 2.46104e7 | 1.22152 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.02882e6 | −0.149438 | ||||||||
\(838\) | −1.52496e7 | −0.750148 | ||||||||
\(839\) | 2.91549e7 | 1.42990 | 0.714952 | − | 0.699173i | \(-0.246448\pi\) | ||||
0.714952 | + | 0.699173i | \(0.246448\pi\) | |||||||
\(840\) | −541824. | −0.0264948 | ||||||||
\(841\) | −1.62511e7 | −0.792303 | ||||||||
\(842\) | 7.89385e6 | 0.383715 | ||||||||
\(843\) | 879042. | 0.0426030 | ||||||||
\(844\) | 1.49188e7 | 0.720907 | ||||||||
\(845\) | −5.48612e6 | −0.264316 | ||||||||
\(846\) | 1.66341e7 | 0.799050 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.86586e6 | −0.375627 | ||||||||
\(849\) | −1.54027e6 | −0.0733377 | ||||||||
\(850\) | −1.54685e6 | −0.0734345 | ||||||||
\(851\) | 2.63025e7 | 1.24501 | ||||||||
\(852\) | 212976. | 0.0100515 | ||||||||
\(853\) | 9.49052e6 | 0.446599 | 0.223299 | − | 0.974750i | \(-0.428317\pi\) | ||||
0.223299 | + | 0.974750i | \(0.428317\pi\) | |||||||
\(854\) | 3.05042e7 | 1.43125 | ||||||||
\(855\) | −1.75750e7 | −0.822205 | ||||||||
\(856\) | 5.07917e6 | 0.236924 | ||||||||
\(857\) | 1.81553e6 | 0.0844405 | 0.0422203 | − | 0.999108i | \(-0.486557\pi\) | ||||
0.0422203 | + | 0.999108i | \(0.486557\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.07812e7 | −0.498522 | −0.249261 | − | 0.968436i | \(-0.580188\pi\) | ||||
−0.249261 | + | 0.968436i | \(0.580188\pi\) | |||||||
\(860\) | 1.45232e7 | 0.669600 | ||||||||
\(861\) | −880464. | −0.0404766 | ||||||||
\(862\) | 8.33436e6 | 0.382036 | ||||||||
\(863\) | −2.83355e7 | −1.29510 | −0.647550 | − | 0.762023i | \(-0.724206\pi\) | ||||
−0.647550 | + | 0.762023i | \(0.724206\pi\) | |||||||
\(864\) | −496640. | −0.0226338 | ||||||||
\(865\) | −3.90790e7 | −1.77584 | ||||||||
\(866\) | −290764. | −0.0131749 | ||||||||
\(867\) | −875213. | −0.0395427 | ||||||||
\(868\) | 1.65867e7 | 0.747242 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −421056. | −0.0188600 | ||||||||
\(871\) | −1.75374e7 | −0.783283 | ||||||||
\(872\) | −5.62189e6 | −0.250375 | ||||||||
\(873\) | 2.14913e7 | 0.954392 | ||||||||
\(874\) | 1.01332e7 | 0.448712 | ||||||||
\(875\) | 3.08924e7 | 1.36406 | ||||||||
\(876\) | 852160. | 0.0375198 | ||||||||
\(877\) | 2.68919e7 | 1.18065 | 0.590326 | − | 0.807165i | \(-0.298999\pi\) | ||||
0.590326 | + | 0.807165i | \(0.298999\pi\) | |||||||
\(878\) | −2.37757e6 | −0.104087 | ||||||||
\(879\) | −720840. | −0.0314678 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.92132e7 | −0.833989 | −0.416995 | − | 0.908909i | \(-0.636917\pi\) | ||||
−0.416995 | + | 0.908909i | \(0.636917\pi\) | |||||||
\(882\) | −1.04050e7 | −0.450373 | ||||||||
\(883\) | 1.15931e7 | 0.500378 | 0.250189 | − | 0.968197i | \(-0.419507\pi\) | ||||
0.250189 | + | 0.968197i | \(0.419507\pi\) | |||||||
\(884\) | −8.17114e6 | −0.351683 | ||||||||
\(885\) | 1.78444e6 | 0.0765850 | ||||||||
\(886\) | 1.82660e7 | 0.781735 | ||||||||
\(887\) | −1.31857e7 | −0.562721 | −0.281361 | − | 0.959602i | \(-0.590786\pi\) | ||||
−0.281361 | + | 0.959602i | \(0.590786\pi\) | |||||||
\(888\) | −946240. | −0.0402688 | ||||||||
\(889\) | 3.97431e7 | 1.68658 | ||||||||
\(890\) | −2.55847e7 | −1.08269 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.71592e6 | 0.114289 | ||||||||
\(893\) | 2.44700e7 | 1.02685 | ||||||||
\(894\) | −350904. | −0.0146840 | ||||||||
\(895\) | −1.54733e7 | −0.645694 | ||||||||
\(896\) | 2.71974e6 | 0.113177 | ||||||||
\(897\) | 1.23107e6 | 0.0510859 | ||||||||
\(898\) | −2.17753e7 | −0.901100 | ||||||||
\(899\) | 1.28897e7 | 0.531916 | ||||||||
\(900\) | 2.02893e6 | 0.0834950 | ||||||||
\(901\) | −2.26758e7 | −0.930573 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.95447e6 | −0.120576 | ||||||||
\(904\) | −3.02381e6 | −0.123065 | ||||||||
\(905\) | 1.45442e7 | 0.590295 | ||||||||
\(906\) | 1.73111e6 | 0.0700656 | ||||||||
\(907\) | 2.98195e6 | 0.120360 | 0.0601800 | − | 0.998188i | \(-0.480833\pi\) | ||||
0.0601800 | + | 0.998188i | \(0.480833\pi\) | |||||||
\(908\) | −3.16925e6 | −0.127568 | ||||||||
\(909\) | 358644. | 0.0143964 | ||||||||
\(910\) | 2.34339e7 | 0.938082 | ||||||||
\(911\) | 2.96579e7 | 1.18398 | 0.591989 | − | 0.805946i | \(-0.298343\pi\) | ||||
0.591989 | + | 0.805946i | \(0.298343\pi\) | |||||||
\(912\) | −364544. | −0.0145132 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −2.68125e7 | −1.06163 | ||||||||
\(915\) | −2.34294e6 | −0.0925142 | ||||||||
\(916\) | −1.36000e7 | −0.535548 | ||||||||
\(917\) | 1.62916e7 | 0.639793 | ||||||||
\(918\) | −1.43172e6 | −0.0560727 | ||||||||
\(919\) | −3.18057e7 | −1.24227 | −0.621135 | − | 0.783704i | \(-0.713328\pi\) | ||||
−0.621135 | + | 0.783704i | \(0.713328\pi\) | |||||||
\(920\) | 5.80666e6 | 0.226181 | ||||||||
\(921\) | 1.03905e6 | 0.0403633 | ||||||||
\(922\) | 5.03976e6 | 0.195246 | ||||||||
\(923\) | −9.21121e6 | −0.355887 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.74734e6 | 0.297713 | ||||||||
\(926\) | −2.00923e7 | −0.770021 | ||||||||
\(927\) | 2.84340e7 | 1.08677 | ||||||||
\(928\) | 2.11354e6 | 0.0805638 | ||||||||
\(929\) | −2.33444e7 | −0.887451 | −0.443725 | − | 0.896163i | \(-0.646343\pi\) | ||||
−0.443725 | + | 0.896163i | \(0.646343\pi\) | |||||||
\(930\) | −1.27398e6 | −0.0483009 | ||||||||
\(931\) | −1.53066e7 | −0.578767 | ||||||||
\(932\) | 6.42931e6 | 0.242451 | ||||||||
\(933\) | −1.25135e6 | −0.0470624 | ||||||||
\(934\) | −9.42642e6 | −0.353573 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.07177e7 | 0.399864 | ||||||||
\(937\) | −2.07372e7 | −0.771616 | −0.385808 | − | 0.922579i | \(-0.626077\pi\) | ||||
−0.385808 | + | 0.922579i | \(0.626077\pi\) | |||||||
\(938\) | 1.68278e7 | 0.624481 | ||||||||
\(939\) | −1.44336e6 | −0.0534209 | ||||||||
\(940\) | 1.40221e7 | 0.517601 | ||||||||
\(941\) | −2.69193e7 | −0.991036 | −0.495518 | − | 0.868598i | \(-0.665022\pi\) | ||||
−0.495518 | + | 0.868598i | \(0.665022\pi\) | |||||||
\(942\) | −136300. | −0.00500459 | ||||||||
\(943\) | 9.43582e6 | 0.345542 | ||||||||
\(944\) | −8.95718e6 | −0.327146 | ||||||||
\(945\) | 4.10601e6 | 0.149569 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.01896e7 | 0.369216 | 0.184608 | − | 0.982812i | \(-0.440898\pi\) | ||||
0.184608 | + | 0.982812i | \(0.440898\pi\) | |||||||
\(948\) | −1.23574e6 | −0.0446589 | ||||||||
\(949\) | −3.68559e7 | −1.32844 | ||||||||
\(950\) | 2.98470e6 | 0.107298 | ||||||||
\(951\) | −2.01208e6 | −0.0721429 | ||||||||
\(952\) | 7.84051e6 | 0.280383 | ||||||||
\(953\) | −1.03924e7 | −0.370665 | −0.185333 | − | 0.982676i | \(-0.559336\pi\) | ||||
−0.185333 | + | 0.982676i | \(0.559336\pi\) | |||||||
\(954\) | 2.97428e7 | 1.05806 | ||||||||
\(955\) | −3.91204e7 | −1.38802 | ||||||||
\(956\) | −1.36828e7 | −0.484206 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.68903e7 | 0.946634 | ||||||||
\(959\) | 6.64227e7 | 2.33222 | ||||||||
\(960\) | −208896. | −0.00731564 | ||||||||
\(961\) | 1.03709e7 | 0.362249 | ||||||||
\(962\) | 4.09249e7 | 1.42577 | ||||||||
\(963\) | −1.92056e7 | −0.667363 | ||||||||
\(964\) | −1.80074e7 | −0.624107 | ||||||||
\(965\) | 2.09951e7 | 0.725770 | ||||||||
\(966\) | −1.18126e6 | −0.0407288 | ||||||||
\(967\) | 8.18877e6 | 0.281613 | 0.140806 | − | 0.990037i | \(-0.455030\pi\) | ||||
0.140806 | + | 0.990037i | \(0.455030\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.05091e6 | −0.0359548 | ||||||||
\(970\) | 1.81166e7 | 0.618227 | ||||||||
\(971\) | −1.73274e7 | −0.589775 | −0.294887 | − | 0.955532i | \(-0.595282\pi\) | ||||
−0.294887 | + | 0.955532i | \(0.595282\pi\) | |||||||
\(972\) | 2.81882e6 | 0.0956976 | ||||||||
\(973\) | −3.41572e7 | −1.15664 | ||||||||
\(974\) | 7.84005e6 | 0.264802 | ||||||||
\(975\) | 362608. | 0.0122159 | ||||||||
\(976\) | 1.17606e7 | 0.395190 | ||||||||
\(977\) | −438963. | −0.0147127 | −0.00735634 | − | 0.999973i | \(-0.502342\pi\) | ||||
−0.00735634 | + | 0.999973i | \(0.502342\pi\) | |||||||
\(978\) | 180080. | 0.00602030 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −8.77118e6 | −0.291738 | ||||||||
\(981\) | 2.12578e7 | 0.705253 | ||||||||
\(982\) | 2.31850e6 | 0.0767234 | ||||||||
\(983\) | −2.79124e7 | −0.921326 | −0.460663 | − | 0.887575i | \(-0.652388\pi\) | ||||
−0.460663 | + | 0.887575i | \(0.652388\pi\) | |||||||
\(984\) | −339456. | −0.0111762 | ||||||||
\(985\) | −3.87222e7 | −1.27165 | ||||||||
\(986\) | 6.09293e6 | 0.199588 | ||||||||
\(987\) | −2.85254e6 | −0.0932051 | ||||||||
\(988\) | 1.57665e7 | 0.513859 | ||||||||
\(989\) | 3.16626e7 | 1.02933 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.26846e7 | −1.38066 | −0.690331 | − | 0.723494i | \(-0.742535\pi\) | ||||
−0.690331 | + | 0.723494i | \(0.742535\pi\) | |||||||
\(992\) | 6.39488e6 | 0.206326 | ||||||||
\(993\) | 2.01734e6 | 0.0649240 | ||||||||
\(994\) | 8.83850e6 | 0.283735 | ||||||||
\(995\) | 2.37660e6 | 0.0761024 | ||||||||
\(996\) | −880224. | −0.0281154 | ||||||||
\(997\) | 2.21044e7 | 0.704273 | 0.352137 | − | 0.935949i | \(-0.385455\pi\) | ||||
0.352137 | + | 0.935949i | \(0.385455\pi\) | |||||||
\(998\) | 5.47621e6 | 0.174042 | ||||||||
\(999\) | 7.17072e6 | 0.227326 |
(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 | 242.6.a.d.1.1 | 1 | ||
11.10 | odd | 2 | 22.6.a.b.1.1 | ✓ | 1 | ||
33.32 | even | 2 | 198.6.a.i.1.1 | 1 | |||
44.43 | even | 2 | 176.6.a.b.1.1 | 1 | |||
55.32 | even | 4 | 550.6.b.f.199.1 | 2 | |||
55.43 | even | 4 | 550.6.b.f.199.2 | 2 | |||
55.54 | odd | 2 | 550.6.a.f.1.1 | 1 | |||
77.76 | even | 2 | 1078.6.a.a.1.1 | 1 | |||
88.21 | odd | 2 | 704.6.a.e.1.1 | 1 | |||
88.43 | even | 2 | 704.6.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.6.a.b.1.1 | ✓ | 1 | 11.10 | odd | 2 | ||
176.6.a.b.1.1 | 1 | 44.43 | even | 2 | |||
198.6.a.i.1.1 | 1 | 33.32 | even | 2 | |||
242.6.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
550.6.a.f.1.1 | 1 | 55.54 | odd | 2 | |||
550.6.b.f.199.1 | 2 | 55.32 | even | 4 | |||
550.6.b.f.199.2 | 2 | 55.43 | even | 4 | |||
704.6.a.e.1.1 | 1 | 88.21 | odd | 2 | |||
704.6.a.f.1.1 | 1 | 88.43 | even | 2 | |||
1078.6.a.a.1.1 | 1 | 77.76 | even | 2 |