Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{65}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 16 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(4.53113\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.53113 | 0.800998 | 0.400499 | − | 0.916297i | \(-0.368837\pi\) | ||||
0.400499 | + | 0.916297i | \(0.368837\pi\) | |||||||
\(3\) | 10.5934 | 0.679566 | 0.339783 | − | 0.940504i | \(-0.389646\pi\) | ||||
0.339783 | + | 0.940504i | \(0.389646\pi\) | |||||||
\(4\) | −11.4689 | −0.358402 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 48.0000 | 0.544331 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −196.963 | −1.08808 | ||||||||
\(9\) | −130.780 | −0.538190 | ||||||||
\(10\) | 113.278 | 0.358217 | ||||||||
\(11\) | 90.5195 | 0.225559 | 0.112780 | − | 0.993620i | \(-0.464025\pi\) | ||||
0.112780 | + | 0.993620i | \(0.464025\pi\) | |||||||
\(12\) | −121.494 | −0.243558 | ||||||||
\(13\) | 74.8502 | 0.122838 | 0.0614192 | − | 0.998112i | \(-0.480437\pi\) | ||||
0.0614192 | + | 0.998112i | \(0.480437\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 264.835 | 0.303911 | ||||||||
\(16\) | −525.461 | −0.513146 | ||||||||
\(17\) | −1032.31 | −0.866342 | −0.433171 | − | 0.901312i | \(-0.642605\pi\) | ||||
−0.433171 | + | 0.901312i | \(0.642605\pi\) | |||||||
\(18\) | −592.582 | −0.431089 | ||||||||
\(19\) | 31.6771 | 0.0201308 | 0.0100654 | − | 0.999949i | \(-0.496796\pi\) | ||||
0.0100654 | + | 0.999949i | \(0.496796\pi\) | |||||||
\(20\) | −286.722 | −0.160282 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 410.156 | 0.180672 | ||||||||
\(23\) | −3857.08 | −1.52033 | −0.760167 | − | 0.649728i | \(-0.774883\pi\) | ||||
−0.760167 | + | 0.649728i | \(0.774883\pi\) | |||||||
\(24\) | −2086.51 | −0.739421 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 339.156 | 0.0983934 | ||||||||
\(27\) | −3959.60 | −1.04530 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −866.917 | −0.191418 | −0.0957089 | − | 0.995409i | \(-0.530512\pi\) | ||||
−0.0957089 | + | 0.995409i | \(0.530512\pi\) | |||||||
\(30\) | 1200.00 | 0.243432 | ||||||||
\(31\) | −3526.76 | −0.659131 | −0.329566 | − | 0.944133i | \(-0.606902\pi\) | ||||
−0.329566 | + | 0.944133i | \(0.606902\pi\) | |||||||
\(32\) | 3921.89 | 0.677049 | ||||||||
\(33\) | 958.908 | 0.153282 | ||||||||
\(34\) | −4677.54 | −0.693938 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1499.90 | 0.192888 | ||||||||
\(37\) | −9531.22 | −1.14458 | −0.572288 | − | 0.820053i | \(-0.693944\pi\) | ||||
−0.572288 | + | 0.820053i | \(0.693944\pi\) | |||||||
\(38\) | 143.533 | 0.0161247 | ||||||||
\(39\) | 792.917 | 0.0834769 | ||||||||
\(40\) | −4924.08 | −0.486603 | ||||||||
\(41\) | 14503.9 | 1.34748 | 0.673742 | − | 0.738967i | \(-0.264686\pi\) | ||||
0.673742 | + | 0.738967i | \(0.264686\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9844.30 | −0.811921 | −0.405960 | − | 0.913891i | \(-0.633063\pi\) | ||||
−0.405960 | + | 0.913891i | \(0.633063\pi\) | |||||||
\(44\) | −1038.16 | −0.0808409 | ||||||||
\(45\) | −3269.50 | −0.240686 | ||||||||
\(46\) | −17476.9 | −1.21778 | ||||||||
\(47\) | 16993.5 | 1.12212 | 0.561059 | − | 0.827775i | \(-0.310394\pi\) | ||||
0.561059 | + | 0.827775i | \(0.310394\pi\) | |||||||
\(48\) | −5566.41 | −0.348716 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2831.96 | 0.160200 | ||||||||
\(51\) | −10935.7 | −0.588736 | ||||||||
\(52\) | −858.447 | −0.0440256 | ||||||||
\(53\) | −29621.1 | −1.44848 | −0.724239 | − | 0.689549i | \(-0.757809\pi\) | ||||
−0.724239 | + | 0.689549i | \(0.757809\pi\) | |||||||
\(54\) | −17941.4 | −0.837285 | ||||||||
\(55\) | 2262.99 | 0.100873 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 335.568 | 0.0136802 | ||||||||
\(58\) | −3928.11 | −0.153325 | ||||||||
\(59\) | −50697.4 | −1.89607 | −0.948037 | − | 0.318159i | \(-0.896935\pi\) | ||||
−0.948037 | + | 0.318159i | \(0.896935\pi\) | |||||||
\(60\) | −3037.35 | −0.108922 | ||||||||
\(61\) | 2921.38 | 0.100522 | 0.0502612 | − | 0.998736i | \(-0.483995\pi\) | ||||
0.0502612 | + | 0.998736i | \(0.483995\pi\) | |||||||
\(62\) | −15980.2 | −0.527963 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 34585.3 | 1.05546 | ||||||||
\(65\) | 1871.25 | 0.0549350 | ||||||||
\(66\) | 4344.94 | 0.122779 | ||||||||
\(67\) | −41086.2 | −1.11817 | −0.559086 | − | 0.829109i | \(-0.688848\pi\) | ||||
−0.559086 | + | 0.829109i | \(0.688848\pi\) | |||||||
\(68\) | 11839.5 | 0.310499 | ||||||||
\(69\) | −40859.5 | −1.03317 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 61753.1 | 1.45383 | 0.726914 | − | 0.686729i | \(-0.240954\pi\) | ||||
0.726914 | + | 0.686729i | \(0.240954\pi\) | |||||||
\(72\) | 25758.9 | 0.585592 | ||||||||
\(73\) | 23664.5 | 0.519745 | 0.259872 | − | 0.965643i | \(-0.416320\pi\) | ||||
0.259872 | + | 0.965643i | \(0.416320\pi\) | |||||||
\(74\) | −43187.2 | −0.916802 | ||||||||
\(75\) | 6620.87 | 0.135913 | ||||||||
\(76\) | −363.300 | −0.00721493 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 3592.81 | 0.0668648 | ||||||||
\(79\) | 45191.5 | 0.814683 | 0.407341 | − | 0.913276i | \(-0.366456\pi\) | ||||
0.407341 | + | 0.913276i | \(0.366456\pi\) | |||||||
\(80\) | −13136.5 | −0.229486 | ||||||||
\(81\) | −10166.0 | −0.172162 | ||||||||
\(82\) | 65718.8 | 1.07933 | ||||||||
\(83\) | −39095.9 | −0.622925 | −0.311462 | − | 0.950259i | \(-0.600819\pi\) | ||||
−0.311462 | + | 0.950259i | \(0.600819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −25807.8 | −0.387440 | ||||||||
\(86\) | −44605.8 | −0.650347 | ||||||||
\(87\) | −9183.58 | −0.130081 | ||||||||
\(88\) | −17829.0 | −0.245426 | ||||||||
\(89\) | 41891.1 | 0.560592 | 0.280296 | − | 0.959914i | \(-0.409567\pi\) | ||||
0.280296 | + | 0.959914i | \(0.409567\pi\) | |||||||
\(90\) | −14814.5 | −0.192789 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 44236.3 | 0.544891 | ||||||||
\(93\) | −37360.4 | −0.447923 | ||||||||
\(94\) | 76999.9 | 0.898815 | ||||||||
\(95\) | 791.927 | 0.00900277 | ||||||||
\(96\) | 41546.1 | 0.460099 | ||||||||
\(97\) | −8036.53 | −0.0867240 | −0.0433620 | − | 0.999059i | \(-0.513807\pi\) | ||||
−0.0433620 | + | 0.999059i | \(0.513807\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11838.2 | −0.121394 | ||||||||
\(100\) | −7168.04 | −0.0716804 | ||||||||
\(101\) | −124979. | −1.21908 | −0.609542 | − | 0.792754i | \(-0.708647\pi\) | ||||
−0.609542 | + | 0.792754i | \(0.708647\pi\) | |||||||
\(102\) | −49551.0 | −0.471577 | ||||||||
\(103\) | 76635.1 | 0.711762 | 0.355881 | − | 0.934531i | \(-0.384181\pi\) | ||||
0.355881 | + | 0.934531i | \(0.384181\pi\) | |||||||
\(104\) | −14742.7 | −0.133658 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −134217. | −1.16023 | ||||||||
\(107\) | 135296. | 1.14242 | 0.571209 | − | 0.820804i | \(-0.306474\pi\) | ||||
0.571209 | + | 0.820804i | \(0.306474\pi\) | |||||||
\(108\) | 45412.1 | 0.374638 | ||||||||
\(109\) | −199508. | −1.60840 | −0.804202 | − | 0.594356i | \(-0.797407\pi\) | ||||
−0.804202 | + | 0.594356i | \(0.797407\pi\) | |||||||
\(110\) | 10253.9 | 0.0807992 | ||||||||
\(111\) | −100968. | −0.777814 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 122569. | 0.902991 | 0.451496 | − | 0.892273i | \(-0.350891\pi\) | ||||
0.451496 | + | 0.892273i | \(0.350891\pi\) | |||||||
\(114\) | 1520.50 | 0.0109578 | ||||||||
\(115\) | −96427.0 | −0.679914 | ||||||||
\(116\) | 9942.56 | 0.0686046 | ||||||||
\(117\) | −9788.92 | −0.0661104 | ||||||||
\(118\) | −229716. | −1.51875 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −52162.6 | −0.330679 | ||||||||
\(121\) | −152857. | −0.949123 | ||||||||
\(122\) | 13237.1 | 0.0805183 | ||||||||
\(123\) | 153645. | 0.915704 | ||||||||
\(124\) | 40448.0 | 0.236234 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 40046.2 | 0.220319 | 0.110160 | − | 0.993914i | \(-0.464864\pi\) | ||||
0.110160 | + | 0.993914i | \(0.464864\pi\) | |||||||
\(128\) | 31210.2 | 0.168373 | ||||||||
\(129\) | −104284. | −0.551754 | ||||||||
\(130\) | 8478.89 | 0.0440029 | ||||||||
\(131\) | −211963. | −1.07915 | −0.539576 | − | 0.841937i | \(-0.681415\pi\) | ||||
−0.539576 | + | 0.841937i | \(0.681415\pi\) | |||||||
\(132\) | −10997.6 | −0.0549367 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −186167. | −0.895654 | ||||||||
\(135\) | −98989.9 | −0.467473 | ||||||||
\(136\) | 203328. | 0.942647 | ||||||||
\(137\) | 40980.5 | 0.186542 | 0.0932709 | − | 0.995641i | \(-0.470268\pi\) | ||||
0.0932709 | + | 0.995641i | \(0.470268\pi\) | |||||||
\(138\) | −185140. | −0.827565 | ||||||||
\(139\) | 418948. | 1.83917 | 0.919587 | − | 0.392886i | \(-0.128523\pi\) | ||||
0.919587 | + | 0.392886i | \(0.128523\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 180019. | 0.762554 | ||||||||
\(142\) | 279811. | 1.16451 | ||||||||
\(143\) | 6775.40 | 0.0277073 | ||||||||
\(144\) | 68719.9 | 0.276170 | ||||||||
\(145\) | −21672.9 | −0.0856047 | ||||||||
\(146\) | 107227. | 0.416314 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 109312. | 0.410218 | ||||||||
\(149\) | −64962.7 | −0.239717 | −0.119858 | − | 0.992791i | \(-0.538244\pi\) | ||||
−0.119858 | + | 0.992791i | \(0.538244\pi\) | |||||||
\(150\) | 30000.0 | 0.108866 | ||||||||
\(151\) | 379801. | 1.35554 | 0.677772 | − | 0.735272i | \(-0.262946\pi\) | ||||
0.677772 | + | 0.735272i | \(0.262946\pi\) | |||||||
\(152\) | −6239.22 | −0.0219039 | ||||||||
\(153\) | 135006. | 0.466256 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −88169.1 | −0.294773 | ||||||||
\(156\) | −9093.86 | −0.0299183 | ||||||||
\(157\) | 281546. | 0.911590 | 0.455795 | − | 0.890085i | \(-0.349355\pi\) | ||||
0.455795 | + | 0.890085i | \(0.349355\pi\) | |||||||
\(158\) | 204768. | 0.652559 | ||||||||
\(159\) | −313788. | −0.984337 | ||||||||
\(160\) | 98047.1 | 0.302785 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −46063.3 | −0.137901 | ||||||||
\(163\) | −382587. | −1.12788 | −0.563938 | − | 0.825817i | \(-0.690714\pi\) | ||||
−0.563938 | + | 0.825817i | \(0.690714\pi\) | |||||||
\(164\) | −166343. | −0.482941 | ||||||||
\(165\) | 23972.7 | 0.0685499 | ||||||||
\(166\) | −177148. | −0.498961 | ||||||||
\(167\) | 388635. | 1.07833 | 0.539164 | − | 0.842201i | \(-0.318740\pi\) | ||||
0.539164 | + | 0.842201i | \(0.318740\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −365690. | −0.984911 | ||||||||
\(170\) | −116939. | −0.310339 | ||||||||
\(171\) | −4142.73 | −0.0108342 | ||||||||
\(172\) | 112903. | 0.290994 | ||||||||
\(173\) | 389693. | 0.989936 | 0.494968 | − | 0.868911i | \(-0.335180\pi\) | ||||
0.494968 | + | 0.868911i | \(0.335180\pi\) | |||||||
\(174\) | −41612.0 | −0.104195 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −47564.5 | −0.115745 | ||||||||
\(177\) | −537057. | −1.28851 | ||||||||
\(178\) | 189814. | 0.449033 | ||||||||
\(179\) | −149812. | −0.349473 | −0.174737 | − | 0.984615i | \(-0.555907\pi\) | ||||
−0.174737 | + | 0.984615i | \(0.555907\pi\) | |||||||
\(180\) | 37497.5 | 0.0862623 | ||||||||
\(181\) | 821019. | 1.86276 | 0.931380 | − | 0.364049i | \(-0.118606\pi\) | ||||
0.931380 | + | 0.364049i | \(0.118606\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30947.3 | 0.0683117 | ||||||||
\(184\) | 759702. | 1.65424 | ||||||||
\(185\) | −238281. | −0.511870 | ||||||||
\(186\) | −169285. | −0.358786 | ||||||||
\(187\) | −93444.5 | −0.195411 | ||||||||
\(188\) | −194897. | −0.402170 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3588.32 | 0.00721120 | ||||||||
\(191\) | 286619. | 0.568487 | 0.284244 | − | 0.958752i | \(-0.408258\pi\) | ||||
0.284244 | + | 0.958752i | \(0.408258\pi\) | |||||||
\(192\) | 366376. | 0.717255 | ||||||||
\(193\) | 993573. | 1.92002 | 0.960012 | − | 0.279959i | \(-0.0903209\pi\) | ||||
0.960012 | + | 0.279959i | \(0.0903209\pi\) | |||||||
\(194\) | −36414.6 | −0.0694657 | ||||||||
\(195\) | 19822.9 | 0.0373320 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −38209.0 | −0.0701456 | −0.0350728 | − | 0.999385i | \(-0.511166\pi\) | ||||
−0.0350728 | + | 0.999385i | \(0.511166\pi\) | |||||||
\(198\) | −53640.2 | −0.0972361 | ||||||||
\(199\) | −730487. | −1.30761 | −0.653807 | − | 0.756661i | \(-0.726829\pi\) | ||||
−0.653807 | + | 0.756661i | \(0.726829\pi\) | |||||||
\(200\) | −123102. | −0.217615 | ||||||||
\(201\) | −435242. | −0.759872 | ||||||||
\(202\) | −566296. | −0.976484 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 125420. | 0.211004 | ||||||||
\(205\) | 362596. | 0.602613 | ||||||||
\(206\) | 347244. | 0.570120 | ||||||||
\(207\) | 504429. | 0.818228 | ||||||||
\(208\) | −39330.9 | −0.0630340 | ||||||||
\(209\) | 2867.39 | 0.00454069 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 194286. | 0.300424 | 0.150212 | − | 0.988654i | \(-0.452004\pi\) | ||||
0.150212 | + | 0.988654i | \(0.452004\pi\) | |||||||
\(212\) | 339721. | 0.519138 | ||||||||
\(213\) | 654175. | 0.987972 | ||||||||
\(214\) | 613043. | 0.915075 | ||||||||
\(215\) | −246107. | −0.363102 | ||||||||
\(216\) | 779894. | 1.13737 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −903999. | −1.28833 | ||||||||
\(219\) | 250687. | 0.353201 | ||||||||
\(220\) | −25953.9 | −0.0361531 | ||||||||
\(221\) | −77268.8 | −0.106420 | ||||||||
\(222\) | −457499. | −0.623028 | ||||||||
\(223\) | −1.13569e6 | −1.52931 | −0.764656 | − | 0.644438i | \(-0.777091\pi\) | ||||
−0.764656 | + | 0.644438i | \(0.777091\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −81737.6 | −0.107638 | ||||||||
\(226\) | 555375. | 0.723294 | ||||||||
\(227\) | 143806. | 0.185231 | 0.0926155 | − | 0.995702i | \(-0.470477\pi\) | ||||
0.0926155 | + | 0.995702i | \(0.470477\pi\) | |||||||
\(228\) | −3848.58 | −0.00490302 | ||||||||
\(229\) | 3832.50 | 0.00482940 | 0.00241470 | − | 0.999997i | \(-0.499231\pi\) | ||||
0.00241470 | + | 0.999997i | \(0.499231\pi\) | |||||||
\(230\) | −436923. | −0.544610 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 170751. | 0.208277 | ||||||||
\(233\) | −1.35599e6 | −1.63631 | −0.818157 | − | 0.574995i | \(-0.805004\pi\) | ||||
−0.818157 | + | 0.574995i | \(0.805004\pi\) | |||||||
\(234\) | −44354.8 | −0.0529543 | ||||||||
\(235\) | 424838. | 0.501827 | ||||||||
\(236\) | 581442. | 0.679557 | ||||||||
\(237\) | 478731. | 0.553631 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −478372. | −0.541716 | −0.270858 | − | 0.962619i | \(-0.587307\pi\) | ||||
−0.270858 | + | 0.962619i | \(0.587307\pi\) | |||||||
\(240\) | −139160. | −0.155951 | ||||||||
\(241\) | 1.31082e6 | 1.45379 | 0.726894 | − | 0.686750i | \(-0.240963\pi\) | ||||
0.726894 | + | 0.686750i | \(0.240963\pi\) | |||||||
\(242\) | −692616. | −0.760246 | ||||||||
\(243\) | 854490. | 0.928307 | ||||||||
\(244\) | −33504.9 | −0.0360275 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 696185. | 0.733477 | ||||||||
\(247\) | 2371.04 | 0.00247284 | ||||||||
\(248\) | 694642. | 0.717186 | ||||||||
\(249\) | −414157. | −0.423318 | ||||||||
\(250\) | 70798.9 | 0.0716434 | ||||||||
\(251\) | −340113. | −0.340753 | −0.170376 | − | 0.985379i | \(-0.554498\pi\) | ||||
−0.170376 | + | 0.985379i | \(0.554498\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −349141. | −0.342925 | ||||||||
\(254\) | 181454. | 0.176475 | ||||||||
\(255\) | −273392. | −0.263291 | ||||||||
\(256\) | −965313. | −0.920594 | ||||||||
\(257\) | 58839.6 | 0.0555696 | 0.0277848 | − | 0.999614i | \(-0.491155\pi\) | ||||
0.0277848 | + | 0.999614i | \(0.491155\pi\) | |||||||
\(258\) | −472526. | −0.441954 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −21461.2 | −0.0196888 | ||||||||
\(261\) | 113376. | 0.103019 | ||||||||
\(262\) | −960433. | −0.864398 | ||||||||
\(263\) | −1380.79 | −0.00123095 | −0.000615473 | − | 1.00000i | \(-0.500196\pi\) | ||||
−0.000615473 | 1.00000i | \(0.500196\pi\) | ||||||||
\(264\) | −188869. | −0.166783 | ||||||||
\(265\) | −740528. | −0.647779 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 443769. | 0.380959 | ||||||||
\(268\) | 471212. | 0.400756 | ||||||||
\(269\) | −886839. | −0.747247 | −0.373624 | − | 0.927580i | \(-0.621885\pi\) | ||||
−0.373624 | + | 0.927580i | \(0.621885\pi\) | |||||||
\(270\) | −448536. | −0.374445 | ||||||||
\(271\) | 376955. | 0.311793 | 0.155897 | − | 0.987773i | \(-0.450173\pi\) | ||||
0.155897 | + | 0.987773i | \(0.450173\pi\) | |||||||
\(272\) | 542441. | 0.444559 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 185688. | 0.149420 | ||||||||
\(275\) | 56574.7 | 0.0451118 | ||||||||
\(276\) | 468613. | 0.370289 | ||||||||
\(277\) | −880363. | −0.689386 | −0.344693 | − | 0.938716i | \(-0.612017\pi\) | ||||
−0.344693 | + | 0.938716i | \(0.612017\pi\) | |||||||
\(278\) | 1.89831e6 | 1.47317 | ||||||||
\(279\) | 461231. | 0.354738 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.08492e6 | 1.57515 | 0.787577 | − | 0.616217i | \(-0.211335\pi\) | ||||
0.787577 | + | 0.616217i | \(0.211335\pi\) | |||||||
\(282\) | 815689. | 0.610804 | ||||||||
\(283\) | −692401. | −0.513915 | −0.256958 | − | 0.966423i | \(-0.582720\pi\) | ||||
−0.256958 | + | 0.966423i | \(0.582720\pi\) | |||||||
\(284\) | −708238. | −0.521055 | ||||||||
\(285\) | 8389.19 | 0.00611798 | ||||||||
\(286\) | 30700.2 | 0.0221935 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −512905. | −0.364381 | ||||||||
\(289\) | −354186. | −0.249452 | ||||||||
\(290\) | −98202.8 | −0.0685692 | ||||||||
\(291\) | −85134.1 | −0.0589347 | ||||||||
\(292\) | −271405. | −0.186278 | ||||||||
\(293\) | −2.27624e6 | −1.54899 | −0.774495 | − | 0.632580i | \(-0.781996\pi\) | ||||
−0.774495 | + | 0.632580i | \(0.781996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.26743e6 | −0.847950 | ||||||||
\(296\) | 1.87730e6 | 1.24539 | ||||||||
\(297\) | −358421. | −0.235777 | ||||||||
\(298\) | −294354. | −0.192013 | ||||||||
\(299\) | −288703. | −0.186755 | ||||||||
\(300\) | −75933.9 | −0.0487116 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.72093e6 | 1.08579 | ||||||||
\(303\) | −1.32395e6 | −0.828448 | ||||||||
\(304\) | −16645.1 | −0.0103300 | ||||||||
\(305\) | 73034.5 | 0.0449550 | ||||||||
\(306\) | 611730. | 0.373470 | ||||||||
\(307\) | 2.65187e6 | 1.60586 | 0.802928 | − | 0.596076i | \(-0.203274\pi\) | ||||
0.802928 | + | 0.596076i | \(0.203274\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 811825. | 0.483689 | ||||||||
\(310\) | −399505. | −0.236112 | ||||||||
\(311\) | −2.57626e6 | −1.51039 | −0.755195 | − | 0.655501i | \(-0.772458\pi\) | ||||
−0.755195 | + | 0.655501i | \(0.772458\pi\) | |||||||
\(312\) | −156175. | −0.0908293 | ||||||||
\(313\) | −2.51549e6 | −1.45131 | −0.725657 | − | 0.688057i | \(-0.758464\pi\) | ||||
−0.725657 | + | 0.688057i | \(0.758464\pi\) | |||||||
\(314\) | 1.27572e6 | 0.730182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −518295. | −0.291984 | ||||||||
\(317\) | −2.30397e6 | −1.28774 | −0.643870 | − | 0.765135i | \(-0.722672\pi\) | ||||
−0.643870 | + | 0.765135i | \(0.722672\pi\) | |||||||
\(318\) | −1.42181e6 | −0.788452 | ||||||||
\(319\) | −78472.9 | −0.0431760 | ||||||||
\(320\) | 864633. | 0.472016 | ||||||||
\(321\) | 1.43324e6 | 0.776349 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32700.7 | −0.0174402 | ||||||||
\(324\) | 116592. | 0.0617031 | ||||||||
\(325\) | 46781.4 | 0.0245677 | ||||||||
\(326\) | −1.73355e6 | −0.903427 | ||||||||
\(327\) | −2.11347e6 | −1.09302 | ||||||||
\(328\) | −2.85672e6 | −1.46617 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 108623. | 0.0549084 | ||||||||
\(331\) | 697305. | 0.349827 | 0.174913 | − | 0.984584i | \(-0.444035\pi\) | ||||
0.174913 | + | 0.984584i | \(0.444035\pi\) | |||||||
\(332\) | 448385. | 0.223258 | ||||||||
\(333\) | 1.24649e6 | 0.615999 | ||||||||
\(334\) | 1.76096e6 | 0.863739 | ||||||||
\(335\) | −1.02715e6 | −0.500062 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.14848e6 | −0.550868 | −0.275434 | − | 0.961320i | \(-0.588822\pi\) | ||||
−0.275434 | + | 0.961320i | \(0.588822\pi\) | |||||||
\(338\) | −1.65699e6 | −0.788911 | ||||||||
\(339\) | 1.29842e6 | 0.613642 | ||||||||
\(340\) | 295987. | 0.138859 | ||||||||
\(341\) | −319241. | −0.148673 | ||||||||
\(342\) | −18771.3 | −0.00867817 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1.93896e6 | 0.883433 | ||||||||
\(345\) | −1.02149e6 | −0.462046 | ||||||||
\(346\) | 1.76575e6 | 0.792937 | ||||||||
\(347\) | −2.43716e6 | −1.08658 | −0.543289 | − | 0.839546i | \(-0.682821\pi\) | ||||
−0.543289 | + | 0.839546i | \(0.682821\pi\) | |||||||
\(348\) | 105325. | 0.0466213 | ||||||||
\(349\) | −896801. | −0.394124 | −0.197062 | − | 0.980391i | \(-0.563140\pi\) | ||||
−0.197062 | + | 0.980391i | \(0.563140\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −296377. | −0.128403 | ||||||||
\(352\) | 355007. | 0.152715 | ||||||||
\(353\) | −4.33422e6 | −1.85129 | −0.925644 | − | 0.378396i | \(-0.876476\pi\) | ||||
−0.925644 | + | 0.378396i | \(0.876476\pi\) | |||||||
\(354\) | −2.43347e6 | −1.03209 | ||||||||
\(355\) | 1.54383e6 | 0.650172 | ||||||||
\(356\) | −480444. | −0.200917 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −678817. | −0.279927 | ||||||||
\(359\) | −3.59167e6 | −1.47082 | −0.735411 | − | 0.677621i | \(-0.763011\pi\) | ||||
−0.735411 | + | 0.677621i | \(0.763011\pi\) | |||||||
\(360\) | 643972. | 0.261885 | ||||||||
\(361\) | −2.47510e6 | −0.999595 | ||||||||
\(362\) | 3.72014e6 | 1.49207 | ||||||||
\(363\) | −1.61928e6 | −0.644992 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 591612. | 0.232437 | ||||||||
\(366\) | 140226. | 0.0547175 | ||||||||
\(367\) | −361791. | −0.140215 | −0.0701073 | − | 0.997539i | \(-0.522334\pi\) | ||||
−0.0701073 | + | 0.997539i | \(0.522334\pi\) | |||||||
\(368\) | 2.02674e6 | 0.780152 | ||||||||
\(369\) | −1.89682e6 | −0.725202 | ||||||||
\(370\) | −1.07968e6 | −0.410006 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 428481. | 0.160537 | ||||||||
\(373\) | −3.08325e6 | −1.14746 | −0.573729 | − | 0.819045i | \(-0.694504\pi\) | ||||
−0.573729 | + | 0.819045i | \(0.694504\pi\) | |||||||
\(374\) | −423409. | −0.156524 | ||||||||
\(375\) | 165522. | 0.0607822 | ||||||||
\(376\) | −3.34710e6 | −1.22095 | ||||||||
\(377\) | −64888.9 | −0.0235135 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.04227e6 | −1.80313 | −0.901567 | − | 0.432639i | \(-0.857582\pi\) | ||||
−0.901567 | + | 0.432639i | \(0.857582\pi\) | |||||||
\(380\) | −9082.51 | −0.00322661 | ||||||||
\(381\) | 424225. | 0.149721 | ||||||||
\(382\) | 1.29871e6 | 0.455357 | ||||||||
\(383\) | 3.11928e6 | 1.08657 | 0.543285 | − | 0.839548i | \(-0.317180\pi\) | ||||
0.543285 | + | 0.839548i | \(0.317180\pi\) | |||||||
\(384\) | 330622. | 0.114420 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.50201e6 | 1.53794 | ||||||||
\(387\) | 1.28744e6 | 0.436968 | ||||||||
\(388\) | 92169.9 | 0.0310821 | ||||||||
\(389\) | −1.64560e6 | −0.551378 | −0.275689 | − | 0.961247i | \(-0.588906\pi\) | ||||
−0.275689 | + | 0.961247i | \(0.588906\pi\) | |||||||
\(390\) | 89820.2 | 0.0299028 | ||||||||
\(391\) | 3.98171e6 | 1.31713 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.24541e6 | −0.733355 | ||||||||
\(394\) | −173130. | −0.0561865 | ||||||||
\(395\) | 1.12979e6 | 0.364337 | ||||||||
\(396\) | 135770. | 0.0435078 | ||||||||
\(397\) | −3.72727e6 | −1.18690 | −0.593451 | − | 0.804870i | \(-0.702235\pi\) | ||||
−0.593451 | + | 0.804870i | \(0.702235\pi\) | |||||||
\(398\) | −3.30993e6 | −1.04740 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −328413. | −0.102629 | ||||||||
\(401\) | 4.84820e6 | 1.50564 | 0.752818 | − | 0.658229i | \(-0.228694\pi\) | ||||
0.752818 | + | 0.658229i | \(0.228694\pi\) | |||||||
\(402\) | −1.97214e6 | −0.608656 | ||||||||
\(403\) | −263979. | −0.0809667 | ||||||||
\(404\) | 1.43337e6 | 0.436923 | ||||||||
\(405\) | −254149. | −0.0769930 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −862761. | −0.258169 | ||||||||
\(408\) | 2.15393e6 | 0.640591 | ||||||||
\(409\) | 3.03126e6 | 0.896014 | 0.448007 | − | 0.894030i | \(-0.352134\pi\) | ||||
0.448007 | + | 0.894030i | \(0.352134\pi\) | |||||||
\(410\) | 1.64297e6 | 0.482692 | ||||||||
\(411\) | 434123. | 0.126768 | ||||||||
\(412\) | −878918. | −0.255097 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.28563e6 | 0.655399 | ||||||||
\(415\) | −977396. | −0.278580 | ||||||||
\(416\) | 293554. | 0.0831676 | ||||||||
\(417\) | 4.43808e6 | 1.24984 | ||||||||
\(418\) | 12992.5 | 0.00363708 | ||||||||
\(419\) | −1.66905e6 | −0.464444 | −0.232222 | − | 0.972663i | \(-0.574600\pi\) | ||||
−0.232222 | + | 0.972663i | \(0.574600\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.76031e6 | −0.484043 | −0.242022 | − | 0.970271i | \(-0.577810\pi\) | ||||
−0.242022 | + | 0.970271i | \(0.577810\pi\) | |||||||
\(422\) | 880335. | 0.240639 | ||||||||
\(423\) | −2.22242e6 | −0.603913 | ||||||||
\(424\) | 5.83427e6 | 1.57606 | ||||||||
\(425\) | −645196. | −0.173268 | ||||||||
\(426\) | 2.96415e6 | 0.791364 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.55169e6 | −0.409445 | ||||||||
\(429\) | 71774.4 | 0.0188290 | ||||||||
\(430\) | −1.11514e6 | −0.290844 | ||||||||
\(431\) | −648832. | −0.168244 | −0.0841219 | − | 0.996455i | \(-0.526809\pi\) | ||||
−0.0841219 | + | 0.996455i | \(0.526809\pi\) | |||||||
\(432\) | 2.08061e6 | 0.536392 | ||||||||
\(433\) | 360993. | 0.0925293 | 0.0462646 | − | 0.998929i | \(-0.485268\pi\) | ||||
0.0462646 | + | 0.998929i | \(0.485268\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −229590. | −0.0581740 | ||||||||
\(436\) | 2.28814e6 | 0.576455 | ||||||||
\(437\) | −122181. | −0.0306055 | ||||||||
\(438\) | 1.13590e6 | 0.282913 | ||||||||
\(439\) | −1.07021e6 | −0.265038 | −0.132519 | − | 0.991180i | \(-0.542307\pi\) | ||||
−0.132519 | + | 0.991180i | \(0.542307\pi\) | |||||||
\(440\) | −445725. | −0.109758 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −350115. | −0.0852423 | ||||||||
\(443\) | −797145. | −0.192987 | −0.0964935 | − | 0.995334i | \(-0.530763\pi\) | ||||
−0.0964935 | + | 0.995334i | \(0.530763\pi\) | |||||||
\(444\) | 1.15799e6 | 0.278770 | ||||||||
\(445\) | 1.04728e6 | 0.250704 | ||||||||
\(446\) | −5.14594e6 | −1.22498 | ||||||||
\(447\) | −688175. | −0.162903 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.40103e6 | 1.49842 | 0.749211 | − | 0.662331i | \(-0.230433\pi\) | ||||
0.749211 | + | 0.662331i | \(0.230433\pi\) | |||||||
\(450\) | −370364. | −0.0862178 | ||||||||
\(451\) | 1.31288e6 | 0.303937 | ||||||||
\(452\) | −1.40572e6 | −0.323634 | ||||||||
\(453\) | 4.02338e6 | 0.921181 | ||||||||
\(454\) | 651605. | 0.148370 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −66094.4 | −0.0148851 | ||||||||
\(457\) | 5.91843e6 | 1.32561 | 0.662806 | − | 0.748791i | \(-0.269366\pi\) | ||||
0.662806 | + | 0.748791i | \(0.269366\pi\) | |||||||
\(458\) | 17365.5 | 0.00386834 | ||||||||
\(459\) | 4.08755e6 | 0.905588 | ||||||||
\(460\) | 1.10591e6 | 0.243683 | ||||||||
\(461\) | 8.84337e6 | 1.93805 | 0.969026 | − | 0.246960i | \(-0.0794315\pi\) | ||||
0.969026 | + | 0.246960i | \(0.0794315\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.76858e6 | −1.46739 | −0.733695 | − | 0.679479i | \(-0.762206\pi\) | ||||
−0.733695 | + | 0.679479i | \(0.762206\pi\) | |||||||
\(464\) | 455531. | 0.0982252 | ||||||||
\(465\) | −934009. | −0.200317 | ||||||||
\(466\) | −6.14416e6 | −1.31068 | ||||||||
\(467\) | 1.04740e6 | 0.222239 | 0.111120 | − | 0.993807i | \(-0.464556\pi\) | ||||
0.111120 | + | 0.993807i | \(0.464556\pi\) | |||||||
\(468\) | 112268. | 0.0236941 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1.92500e6 | 0.401962 | ||||||||
\(471\) | 2.98252e6 | 0.619486 | ||||||||
\(472\) | 9.98551e6 | 2.06308 | ||||||||
\(473\) | −891101. | −0.183136 | ||||||||
\(474\) | 2.16919e6 | 0.443457 | ||||||||
\(475\) | 19798.2 | 0.00402616 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.87386e6 | 0.779556 | ||||||||
\(478\) | −2.16757e6 | −0.433913 | ||||||||
\(479\) | 9.37725e6 | 1.86740 | 0.933699 | − | 0.358060i | \(-0.116562\pi\) | ||||
0.933699 | + | 0.358060i | \(0.116562\pi\) | |||||||
\(480\) | 1.03865e6 | 0.205763 | ||||||||
\(481\) | −713414. | −0.140598 | ||||||||
\(482\) | 5.93950e6 | 1.16448 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.75310e6 | 0.340168 | ||||||||
\(485\) | −200913. | −0.0387841 | ||||||||
\(486\) | 3.87181e6 | 0.743572 | ||||||||
\(487\) | −2.88960e6 | −0.552098 | −0.276049 | − | 0.961144i | \(-0.589025\pi\) | ||||
−0.276049 | + | 0.961144i | \(0.589025\pi\) | |||||||
\(488\) | −575404. | −0.109376 | ||||||||
\(489\) | −4.05290e6 | −0.766467 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.04845e6 | −0.196265 | −0.0981324 | − | 0.995173i | \(-0.531287\pi\) | ||||
−0.0981324 | + | 0.995173i | \(0.531287\pi\) | |||||||
\(492\) | −1.76213e6 | −0.328191 | ||||||||
\(493\) | 894930. | 0.165833 | ||||||||
\(494\) | 10743.5 | 0.00198074 | ||||||||
\(495\) | −295954. | −0.0542889 | ||||||||
\(496\) | 1.85318e6 | 0.338230 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.87660e6 | −0.339077 | ||||||||
\(499\) | 6.38524e6 | 1.14796 | 0.573979 | − | 0.818870i | \(-0.305399\pi\) | ||||
0.573979 | + | 0.818870i | \(0.305399\pi\) | |||||||
\(500\) | −179201. | −0.0320565 | ||||||||
\(501\) | 4.11696e6 | 0.732795 | ||||||||
\(502\) | −1.54110e6 | −0.272942 | ||||||||
\(503\) | −1.35497e6 | −0.238787 | −0.119394 | − | 0.992847i | \(-0.538095\pi\) | ||||
−0.119394 | + | 0.992847i | \(0.538095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.12448e6 | −0.545191 | ||||||||
\(506\) | −1.58200e6 | −0.274682 | ||||||||
\(507\) | −3.87390e6 | −0.669312 | ||||||||
\(508\) | −459285. | −0.0789628 | ||||||||
\(509\) | −6.43410e6 | −1.10076 | −0.550381 | − | 0.834914i | \(-0.685518\pi\) | ||||
−0.550381 | + | 0.834914i | \(0.685518\pi\) | |||||||
\(510\) | −1.23878e6 | −0.210896 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.37268e6 | −0.905767 | ||||||||
\(513\) | −125429. | −0.0210428 | ||||||||
\(514\) | 266610. | 0.0445111 | ||||||||
\(515\) | 1.91588e6 | 0.318310 | ||||||||
\(516\) | 1.19603e6 | 0.197750 | ||||||||
\(517\) | 1.53825e6 | 0.253104 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.12817e6 | 0.672727 | ||||||||
\(520\) | −368568. | −0.0597736 | ||||||||
\(521\) | −6.16552e6 | −0.995120 | −0.497560 | − | 0.867430i | \(-0.665771\pi\) | ||||
−0.497560 | + | 0.867430i | \(0.665771\pi\) | |||||||
\(522\) | 513719. | 0.0825181 | ||||||||
\(523\) | −7.12400e6 | −1.13886 | −0.569429 | − | 0.822040i | \(-0.692836\pi\) | ||||
−0.569429 | + | 0.822040i | \(0.692836\pi\) | |||||||
\(524\) | 2.43098e6 | 0.386770 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6256.55 | −0.000985985 0 | ||||||||
\(527\) | 3.64072e6 | 0.571033 | ||||||||
\(528\) | −503869. | −0.0786562 | ||||||||
\(529\) | 8.44071e6 | 1.31141 | ||||||||
\(530\) | −3.35543e6 | −0.518870 | ||||||||
\(531\) | 6.63021e6 | 1.02045 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.08562e6 | 0.165523 | ||||||||
\(534\) | 2.01077e6 | 0.305148 | ||||||||
\(535\) | 3.38240e6 | 0.510905 | ||||||||
\(536\) | 8.09246e6 | 1.21666 | ||||||||
\(537\) | −1.58702e6 | −0.237490 | ||||||||
\(538\) | −4.01838e6 | −0.598544 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.13530e6 | 0.167543 | ||||||||
\(541\) | −9.51129e6 | −1.39716 | −0.698580 | − | 0.715532i | \(-0.746184\pi\) | ||||
−0.698580 | + | 0.715532i | \(0.746184\pi\) | |||||||
\(542\) | 1.70803e6 | 0.249746 | ||||||||
\(543\) | 8.69737e6 | 1.26587 | ||||||||
\(544\) | −4.04862e6 | −0.586556 | ||||||||
\(545\) | −4.98771e6 | −0.719300 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.48406e6 | 0.212071 | 0.106036 | − | 0.994362i | \(-0.466184\pi\) | ||||
0.106036 | + | 0.994362i | \(0.466184\pi\) | |||||||
\(548\) | −470001. | −0.0668570 | ||||||||
\(549\) | −382058. | −0.0541002 | ||||||||
\(550\) | 256347. | 0.0361345 | ||||||||
\(551\) | −27461.4 | −0.00385340 | ||||||||
\(552\) | 8.04782e6 | 1.12417 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.98904e6 | −0.552197 | ||||||||
\(555\) | −2.52420e6 | −0.347849 | ||||||||
\(556\) | −4.80486e6 | −0.659164 | ||||||||
\(557\) | −7.72192e6 | −1.05460 | −0.527299 | − | 0.849680i | \(-0.676795\pi\) | ||||
−0.527299 | + | 0.849680i | \(0.676795\pi\) | |||||||
\(558\) | 2.08990e6 | 0.284144 | ||||||||
\(559\) | −736847. | −0.0997351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −989894. | −0.132795 | ||||||||
\(562\) | 9.44703e6 | 1.26169 | ||||||||
\(563\) | −3.41747e6 | −0.454395 | −0.227198 | − | 0.973849i | \(-0.572956\pi\) | ||||
−0.227198 | + | 0.973849i | \(0.572956\pi\) | |||||||
\(564\) | −2.06461e6 | −0.273301 | ||||||||
\(565\) | 3.06422e6 | 0.403830 | ||||||||
\(566\) | −3.13736e6 | −0.411645 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.21631e7 | −1.58188 | ||||||||
\(569\) | −2.42117e6 | −0.313505 | −0.156752 | − | 0.987638i | \(-0.550102\pi\) | ||||
−0.156752 | + | 0.987638i | \(0.550102\pi\) | |||||||
\(570\) | 38012.5 | 0.00490049 | ||||||||
\(571\) | 2.31941e6 | 0.297705 | 0.148853 | − | 0.988859i | \(-0.452442\pi\) | ||||
0.148853 | + | 0.988859i | \(0.452442\pi\) | |||||||
\(572\) | −77706.2 | −0.00993037 | ||||||||
\(573\) | 3.03626e6 | 0.386325 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.41067e6 | −0.304067 | ||||||||
\(576\) | −4.52307e6 | −0.568038 | ||||||||
\(577\) | −2.56645e6 | −0.320917 | −0.160459 | − | 0.987043i | \(-0.551297\pi\) | ||||
−0.160459 | + | 0.987043i | \(0.551297\pi\) | |||||||
\(578\) | −1.60486e6 | −0.199811 | ||||||||
\(579\) | 1.05253e7 | 1.30478 | ||||||||
\(580\) | 248564. | 0.0306809 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −385753. | −0.0472066 | ||||||||
\(583\) | −2.68129e6 | −0.326718 | ||||||||
\(584\) | −4.66103e6 | −0.565522 | ||||||||
\(585\) | −244723. | −0.0295655 | ||||||||
\(586\) | −1.03139e7 | −1.24074 | ||||||||
\(587\) | −2.09851e6 | −0.251371 | −0.125685 | − | 0.992070i | \(-0.540113\pi\) | ||||
−0.125685 | + | 0.992070i | \(0.540113\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −111718. | −0.0132688 | ||||||||
\(590\) | −5.74291e6 | −0.679207 | ||||||||
\(591\) | −404763. | −0.0476686 | ||||||||
\(592\) | 5.00829e6 | 0.587334 | ||||||||
\(593\) | 5.11831e6 | 0.597709 | 0.298854 | − | 0.954299i | \(-0.403396\pi\) | ||||
0.298854 | + | 0.954299i | \(0.403396\pi\) | |||||||
\(594\) | −1.62405e6 | −0.188857 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 745048. | 0.0859150 | ||||||||
\(597\) | −7.73833e6 | −0.888610 | ||||||||
\(598\) | −1.30815e6 | −0.149591 | ||||||||
\(599\) | −2.61775e6 | −0.298099 | −0.149049 | − | 0.988830i | \(-0.547621\pi\) | ||||
−0.149049 | + | 0.988830i | \(0.547621\pi\) | |||||||
\(600\) | −1.30407e6 | −0.147884 | ||||||||
\(601\) | −9.49925e6 | −1.07276 | −0.536381 | − | 0.843976i | \(-0.680209\pi\) | ||||
−0.536381 | + | 0.843976i | \(0.680209\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.37326e6 | 0.601789 | ||||||||
\(604\) | −4.35589e6 | −0.485830 | ||||||||
\(605\) | −3.82143e6 | −0.424461 | ||||||||
\(606\) | −5.99899e6 | −0.663586 | ||||||||
\(607\) | −6.07366e6 | −0.669081 | −0.334541 | − | 0.942381i | \(-0.608581\pi\) | ||||
−0.334541 | + | 0.942381i | \(0.608581\pi\) | |||||||
\(608\) | 124234. | 0.0136295 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 330929. | 0.0360089 | ||||||||
\(611\) | 1.27197e6 | 0.137839 | ||||||||
\(612\) | −1.54837e6 | −0.167107 | ||||||||
\(613\) | −9.20907e6 | −0.989839 | −0.494920 | − | 0.868939i | \(-0.664802\pi\) | ||||
−0.494920 | + | 0.868939i | \(0.664802\pi\) | |||||||
\(614\) | 1.20160e7 | 1.28629 | ||||||||
\(615\) | 3.84112e6 | 0.409515 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.37224e7 | 1.45117 | 0.725585 | − | 0.688133i | \(-0.241569\pi\) | ||||
0.725585 | + | 0.688133i | \(0.241569\pi\) | |||||||
\(618\) | 3.67848e6 | 0.387434 | ||||||||
\(619\) | 6.80356e6 | 0.713690 | 0.356845 | − | 0.934164i | \(-0.383852\pi\) | ||||
0.356845 | + | 0.934164i | \(0.383852\pi\) | |||||||
\(620\) | 1.01120e6 | 0.105647 | ||||||||
\(621\) | 1.52725e7 | 1.58921 | ||||||||
\(622\) | −1.16734e7 | −1.20982 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −416647. | −0.0428358 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.13980e7 | −1.16250 | ||||||||
\(627\) | 30375.4 | 0.00308570 | ||||||||
\(628\) | −3.22901e6 | −0.326716 | ||||||||
\(629\) | 9.83921e6 | 0.991593 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.80897e6 | −0.280850 | −0.140425 | − | 0.990091i | \(-0.544847\pi\) | ||||
−0.140425 | + | 0.990091i | \(0.544847\pi\) | |||||||
\(632\) | −8.90105e6 | −0.886438 | ||||||||
\(633\) | 2.05815e6 | 0.204158 | ||||||||
\(634\) | −1.04396e7 | −1.03148 | ||||||||
\(635\) | 1.00115e6 | 0.0985297 | ||||||||
\(636\) | 3.59880e6 | 0.352788 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −355571. | −0.0345839 | ||||||||
\(639\) | −8.07608e6 | −0.782435 | ||||||||
\(640\) | 780256. | 0.0752986 | ||||||||
\(641\) | −3.83494e6 | −0.368649 | −0.184325 | − | 0.982865i | \(-0.559010\pi\) | ||||
−0.184325 | + | 0.982865i | \(0.559010\pi\) | |||||||
\(642\) | 6.49420e6 | 0.621854 | ||||||||
\(643\) | −1.59562e7 | −1.52195 | −0.760977 | − | 0.648779i | \(-0.775280\pi\) | ||||
−0.760977 | + | 0.648779i | \(0.775280\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.60711e6 | −0.246752 | ||||||||
\(646\) | −148171. | −0.0139695 | ||||||||
\(647\) | 7.48025e6 | 0.702514 | 0.351257 | − | 0.936279i | \(-0.385754\pi\) | ||||
0.351257 | + | 0.936279i | \(0.385754\pi\) | |||||||
\(648\) | 2.00232e6 | 0.187325 | ||||||||
\(649\) | −4.58910e6 | −0.427677 | ||||||||
\(650\) | 211972. | 0.0196787 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.38785e6 | 0.404234 | ||||||||
\(653\) | 2.62102e6 | 0.240540 | 0.120270 | − | 0.992741i | \(-0.461624\pi\) | ||||
0.120270 | + | 0.992741i | \(0.461624\pi\) | |||||||
\(654\) | −9.57641e6 | −0.875504 | ||||||||
\(655\) | −5.29908e6 | −0.482611 | ||||||||
\(656\) | −7.62121e6 | −0.691456 | ||||||||
\(657\) | −3.09485e6 | −0.279721 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.01276e6 | −0.718734 | −0.359367 | − | 0.933196i | \(-0.617007\pi\) | ||||
−0.359367 | + | 0.933196i | \(0.617007\pi\) | |||||||
\(660\) | −274940. | −0.0245685 | ||||||||
\(661\) | 7.21439e6 | 0.642238 | 0.321119 | − | 0.947039i | \(-0.395941\pi\) | ||||
0.321119 | + | 0.947039i | \(0.395941\pi\) | |||||||
\(662\) | 3.15958e6 | 0.280210 | ||||||||
\(663\) | −818539. | −0.0723195 | ||||||||
\(664\) | 7.70044e6 | 0.677790 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.64803e6 | 0.493414 | ||||||||
\(667\) | 3.34377e6 | 0.291019 | ||||||||
\(668\) | −4.45721e6 | −0.386475 | ||||||||
\(669\) | −1.20308e7 | −1.03927 | ||||||||
\(670\) | −4.65417e6 | −0.400549 | ||||||||
\(671\) | 264442. | 0.0226738 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.43323e7 | 1.21977 | 0.609887 | − | 0.792488i | \(-0.291215\pi\) | ||||
0.609887 | + | 0.792488i | \(0.291215\pi\) | |||||||
\(674\) | −5.20390e6 | −0.441244 | ||||||||
\(675\) | −2.47475e6 | −0.209060 | ||||||||
\(676\) | 4.19406e6 | 0.352994 | ||||||||
\(677\) | 4.94781e6 | 0.414898 | 0.207449 | − | 0.978246i | \(-0.433484\pi\) | ||||
0.207449 | + | 0.978246i | \(0.433484\pi\) | |||||||
\(678\) | 5.88330e6 | 0.491526 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.08319e6 | 0.421565 | ||||||||
\(681\) | 1.52340e6 | 0.125877 | ||||||||
\(682\) | −1.44652e6 | −0.119087 | ||||||||
\(683\) | 7.77331e6 | 0.637608 | 0.318804 | − | 0.947821i | \(-0.396719\pi\) | ||||
0.318804 | + | 0.947821i | \(0.396719\pi\) | |||||||
\(684\) | 47512.5 | 0.00388300 | ||||||||
\(685\) | 1.02451e6 | 0.0834241 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 40599.1 | 0.00328190 | ||||||||
\(688\) | 5.17280e6 | 0.416634 | ||||||||
\(689\) | −2.21715e6 | −0.177929 | ||||||||
\(690\) | −4.62849e6 | −0.370098 | ||||||||
\(691\) | 7.69151e6 | 0.612797 | 0.306398 | − | 0.951903i | \(-0.400876\pi\) | ||||
0.306398 | + | 0.951903i | \(0.400876\pi\) | |||||||
\(692\) | −4.46934e6 | −0.354795 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.10431e7 | −0.870347 | ||||||||
\(695\) | 1.04737e7 | 0.822504 | ||||||||
\(696\) | 1.80883e6 | 0.141538 | ||||||||
\(697\) | −1.49725e7 | −1.16738 | ||||||||
\(698\) | −4.06352e6 | −0.315692 | ||||||||
\(699\) | −1.43645e7 | −1.11198 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.53139e7 | 1.17704 | 0.588521 | − | 0.808482i | \(-0.299711\pi\) | ||||
0.588521 | + | 0.808482i | \(0.299711\pi\) | |||||||
\(702\) | −1.34292e6 | −0.102851 | ||||||||
\(703\) | −301921. | −0.0230412 | ||||||||
\(704\) | 3.13065e6 | 0.238069 | ||||||||
\(705\) | 4.50048e6 | 0.341025 | ||||||||
\(706\) | −1.96389e7 | −1.48288 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.15944e6 | 0.461804 | ||||||||
\(709\) | 1.84381e7 | 1.37753 | 0.688764 | − | 0.724986i | \(-0.258154\pi\) | ||||
0.688764 | + | 0.724986i | \(0.258154\pi\) | |||||||
\(710\) | 6.99528e6 | 0.520786 | ||||||||
\(711\) | −5.91015e6 | −0.438454 | ||||||||
\(712\) | −8.25100e6 | −0.609968 | ||||||||
\(713\) | 1.36030e7 | 1.00210 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 169385. | 0.0123911 | ||||||||
\(716\) | 1.71817e6 | 0.125252 | ||||||||
\(717\) | −5.06758e6 | −0.368132 | ||||||||
\(718\) | −1.62743e7 | −1.17813 | ||||||||
\(719\) | 99951.2 | 0.00721051 | 0.00360525 | − | 0.999994i | \(-0.498852\pi\) | ||||
0.00360525 | + | 0.999994i | \(0.498852\pi\) | |||||||
\(720\) | 1.71800e6 | 0.123507 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.12150e7 | −0.800673 | ||||||||
\(723\) | 1.38860e7 | 0.987945 | ||||||||
\(724\) | −9.41616e6 | −0.667617 | ||||||||
\(725\) | −541823. | −0.0382836 | ||||||||
\(726\) | −7.33715e6 | −0.516637 | ||||||||
\(727\) | −1.25198e7 | −0.878538 | −0.439269 | − | 0.898356i | \(-0.644762\pi\) | ||||
−0.439269 | + | 0.898356i | \(0.644762\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.15223e7 | 0.803007 | ||||||||
\(730\) | 2.68067e6 | 0.186181 | ||||||||
\(731\) | 1.01624e7 | 0.703401 | ||||||||
\(732\) | −354931. | −0.0244831 | ||||||||
\(733\) | 1.72341e7 | 1.18476 | 0.592378 | − | 0.805660i | \(-0.298189\pi\) | ||||
0.592378 | + | 0.805660i | \(0.298189\pi\) | |||||||
\(734\) | −1.63932e6 | −0.112312 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.51270e7 | −1.02934 | ||||||||
\(737\) | −3.71910e6 | −0.252214 | ||||||||
\(738\) | −8.59472e6 | −0.580886 | ||||||||
\(739\) | −1.83842e7 | −1.23832 | −0.619160 | − | 0.785265i | \(-0.712527\pi\) | ||||
−0.619160 | + | 0.785265i | \(0.712527\pi\) | |||||||
\(740\) | 2.73281e6 | 0.183455 | ||||||||
\(741\) | 25117.3 | 0.00168046 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.79507e7 | 1.85746 | 0.928732 | − | 0.370752i | \(-0.120900\pi\) | ||||
0.928732 | + | 0.370752i | \(0.120900\pi\) | |||||||
\(744\) | 7.35861e6 | 0.487375 | ||||||||
\(745\) | −1.62407e6 | −0.107205 | ||||||||
\(746\) | −1.39706e7 | −0.919111 | ||||||||
\(747\) | 5.11296e6 | 0.335252 | ||||||||
\(748\) | 1.07170e6 | 0.0700358 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 750000. | 0.0486864 | ||||||||
\(751\) | 1.70136e7 | 1.10077 | 0.550383 | − | 0.834912i | \(-0.314482\pi\) | ||||
0.550383 | + | 0.834912i | \(0.314482\pi\) | |||||||
\(752\) | −8.92944e6 | −0.575810 | ||||||||
\(753\) | −3.60295e6 | −0.231564 | ||||||||
\(754\) | −294020. | −0.0188342 | ||||||||
\(755\) | 9.49502e6 | 0.606218 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.91600e7 | −1.21522 | −0.607611 | − | 0.794234i | \(-0.707872\pi\) | ||||
−0.607611 | + | 0.794234i | \(0.707872\pi\) | |||||||
\(758\) | −2.28472e7 | −1.44431 | ||||||||
\(759\) | −3.69858e6 | −0.233040 | ||||||||
\(760\) | −155980. | −0.00979571 | ||||||||
\(761\) | 2.06404e7 | 1.29198 | 0.645992 | − | 0.763344i | \(-0.276444\pi\) | ||||
0.645992 | + | 0.763344i | \(0.276444\pi\) | |||||||
\(762\) | 1.92222e6 | 0.119926 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −3.28719e6 | −0.203747 | ||||||||
\(765\) | 3.37515e6 | 0.208516 | ||||||||
\(766\) | 1.41339e7 | 0.870341 | ||||||||
\(767\) | −3.79471e6 | −0.232911 | ||||||||
\(768\) | −1.02259e7 | −0.625605 | ||||||||
\(769\) | −1.11748e7 | −0.681432 | −0.340716 | − | 0.940166i | \(-0.610669\pi\) | ||||
−0.340716 | + | 0.940166i | \(0.610669\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 623311. | 0.0377632 | ||||||||
\(772\) | −1.13952e7 | −0.688141 | ||||||||
\(773\) | 3.07555e7 | 1.85129 | 0.925645 | − | 0.378394i | \(-0.123523\pi\) | ||||
0.925645 | + | 0.378394i | \(0.123523\pi\) | |||||||
\(774\) | 5.83355e6 | 0.350010 | ||||||||
\(775\) | −2.20423e6 | −0.131826 | ||||||||
\(776\) | 1.58290e6 | 0.0943624 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.45641e6 | −0.441653 | ||||||||
\(779\) | 459440. | 0.0271259 | ||||||||
\(780\) | −227347. | −0.0133799 | ||||||||
\(781\) | 5.58986e6 | 0.327924 | ||||||||
\(782\) | 1.80417e7 | 1.05502 | ||||||||
\(783\) | 3.43264e6 | 0.200089 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.03864e6 | 0.407675 | ||||||||
\(786\) | −1.01742e7 | −0.587416 | ||||||||
\(787\) | −3.52357e6 | −0.202790 | −0.101395 | − | 0.994846i | \(-0.532331\pi\) | ||||
−0.101395 | + | 0.994846i | \(0.532331\pi\) | |||||||
\(788\) | 438214. | 0.0251403 | ||||||||
\(789\) | −14627.3 | −0.000836509 0 | ||||||||
\(790\) | 5.11921e6 | 0.291833 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.33168e6 | 0.132086 | ||||||||
\(793\) | 218666. | 0.0123480 | ||||||||
\(794\) | −1.68887e7 | −0.950706 | ||||||||
\(795\) | −7.84470e6 | −0.440209 | ||||||||
\(796\) | 8.37786e6 | 0.468652 | ||||||||
\(797\) | 3.57469e6 | 0.199339 | 0.0996695 | − | 0.995021i | \(-0.468221\pi\) | ||||
0.0996695 | + | 0.995021i | \(0.468221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.75426e7 | −0.972139 | ||||||||
\(800\) | 2.45118e6 | 0.135410 | ||||||||
\(801\) | −5.47853e6 | −0.301705 | ||||||||
\(802\) | 2.19678e7 | 1.20601 | ||||||||
\(803\) | 2.14210e6 | 0.117233 | ||||||||
\(804\) | 4.99173e6 | 0.272340 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.19612e6 | −0.0648542 | ||||||||
\(807\) | −9.39463e6 | −0.507804 | ||||||||
\(808\) | 2.46163e7 | 1.32646 | ||||||||
\(809\) | 3.38466e7 | 1.81821 | 0.909104 | − | 0.416569i | \(-0.136767\pi\) | ||||
0.909104 | + | 0.416569i | \(0.136767\pi\) | |||||||
\(810\) | −1.15158e6 | −0.0616712 | ||||||||
\(811\) | −3.21058e7 | −1.71408 | −0.857042 | − | 0.515247i | \(-0.827700\pi\) | ||||
−0.857042 | + | 0.515247i | \(0.827700\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.99323e6 | 0.211884 | ||||||||
\(814\) | −3.90928e6 | −0.206793 | ||||||||
\(815\) | −9.56468e6 | −0.504402 | ||||||||
\(816\) | 5.74628e6 | 0.302108 | ||||||||
\(817\) | −311839. | −0.0163446 | ||||||||
\(818\) | 1.37350e7 | 0.717706 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.15857e6 | −0.215978 | ||||||||
\(821\) | 3.04076e6 | 0.157443 | 0.0787216 | − | 0.996897i | \(-0.474916\pi\) | ||||
0.0787216 | + | 0.996897i | \(0.474916\pi\) | |||||||
\(822\) | 1.96707e6 | 0.101541 | ||||||||
\(823\) | 3.72147e6 | 0.191520 | 0.0957601 | − | 0.995404i | \(-0.469472\pi\) | ||||
0.0957601 | + | 0.995404i | \(0.469472\pi\) | |||||||
\(824\) | −1.50943e7 | −0.774452 | ||||||||
\(825\) | 599318. | 0.0306565 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.77895e6 | −0.446354 | −0.223177 | − | 0.974778i | \(-0.571643\pi\) | ||||
−0.223177 | + | 0.974778i | \(0.571643\pi\) | |||||||
\(828\) | −5.78523e6 | −0.293255 | ||||||||
\(829\) | −6.61553e6 | −0.334332 | −0.167166 | − | 0.985929i | \(-0.553462\pi\) | ||||
−0.167166 | + | 0.985929i | \(0.553462\pi\) | |||||||
\(830\) | −4.42871e6 | −0.223142 | ||||||||
\(831\) | −9.32602e6 | −0.468483 | ||||||||
\(832\) | 2.58872e6 | 0.129651 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.01095e7 | 1.00112 | ||||||||
\(835\) | 9.71588e6 | 0.482243 | ||||||||
\(836\) | −32885.8 | −0.00162739 | ||||||||
\(837\) | 1.39646e7 | 0.688991 | ||||||||
\(838\) | −7.56267e6 | −0.372019 | ||||||||
\(839\) | 4.67110e6 | 0.229094 | 0.114547 | − | 0.993418i | \(-0.463458\pi\) | ||||
0.114547 | + | 0.993418i | \(0.463458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.97596e7 | −0.963359 | ||||||||
\(842\) | −7.97619e6 | −0.387718 | ||||||||
\(843\) | 2.20863e7 | 1.07042 | ||||||||
\(844\) | −2.22824e6 | −0.107673 | ||||||||
\(845\) | −9.14226e6 | −0.440465 | ||||||||
\(846\) | −1.00701e7 | −0.483733 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.55648e7 | 0.743280 | ||||||||
\(849\) | −7.33487e6 | −0.349239 | ||||||||
\(850\) | −2.92347e6 | −0.138788 | ||||||||
\(851\) | 3.67627e7 | 1.74014 | ||||||||
\(852\) | −7.50264e6 | −0.354091 | ||||||||
\(853\) | 3.66146e7 | 1.72299 | 0.861494 | − | 0.507768i | \(-0.169529\pi\) | ||||
0.861494 | + | 0.507768i | \(0.169529\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −103568. | −0.00484520 | ||||||||
\(856\) | −2.66483e7 | −1.24304 | ||||||||
\(857\) | −1.15520e7 | −0.537288 | −0.268644 | − | 0.963240i | \(-0.586575\pi\) | ||||
−0.268644 | + | 0.963240i | \(0.586575\pi\) | |||||||
\(858\) | 325219. | 0.0150820 | ||||||||
\(859\) | −3.53878e7 | −1.63633 | −0.818165 | − | 0.574983i | \(-0.805009\pi\) | ||||
−0.818165 | + | 0.574983i | \(0.805009\pi\) | |||||||
\(860\) | 2.82257e6 | 0.130137 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.93994e6 | −0.134763 | ||||||||
\(863\) | 1.07433e7 | 0.491034 | 0.245517 | − | 0.969392i | \(-0.421042\pi\) | ||||
0.245517 | + | 0.969392i | \(0.421042\pi\) | |||||||
\(864\) | −1.55291e7 | −0.707720 | ||||||||
\(865\) | 9.74232e6 | 0.442713 | ||||||||
\(866\) | 1.63571e6 | 0.0741158 | ||||||||
\(867\) | −3.75203e6 | −0.169519 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.09071e6 | 0.183759 | ||||||||
\(870\) | −1.04030e6 | −0.0465973 | ||||||||
\(871\) | −3.07531e6 | −0.137355 | ||||||||
\(872\) | 3.92958e7 | 1.75007 | ||||||||
\(873\) | 1.05102e6 | 0.0466740 | ||||||||
\(874\) | −553618. | −0.0245150 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.87510e6 | −0.126588 | ||||||||
\(877\) | 4.58293e6 | 0.201208 | 0.100604 | − | 0.994927i | \(-0.467923\pi\) | ||||
0.100604 | + | 0.994927i | \(0.467923\pi\) | |||||||
\(878\) | −4.84927e6 | −0.212295 | ||||||||
\(879\) | −2.41131e7 | −1.05264 | ||||||||
\(880\) | −1.18911e6 | −0.0517626 | ||||||||
\(881\) | −1.68070e7 | −0.729543 | −0.364772 | − | 0.931097i | \(-0.618853\pi\) | ||||
−0.364772 | + | 0.931097i | \(0.618853\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.28260e6 | −0.228006 | −0.114003 | − | 0.993480i | \(-0.536367\pi\) | ||||
−0.114003 | + | 0.993480i | \(0.536367\pi\) | |||||||
\(884\) | 886186. | 0.0381412 | ||||||||
\(885\) | −1.34264e7 | −0.576238 | ||||||||
\(886\) | −3.61197e6 | −0.154582 | ||||||||
\(887\) | −4.43107e7 | −1.89104 | −0.945518 | − | 0.325569i | \(-0.894444\pi\) | ||||
−0.945518 | + | 0.325569i | \(0.894444\pi\) | |||||||
\(888\) | 1.98870e7 | 0.846322 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.74535e6 | 0.200814 | ||||||||
\(891\) | −920219. | −0.0388326 | ||||||||
\(892\) | 1.30250e7 | 0.548109 | ||||||||
\(893\) | 538305. | 0.0225892 | ||||||||
\(894\) | −3.11821e6 | −0.130485 | ||||||||
\(895\) | −3.74530e6 | −0.156289 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.05834e6 | −0.126913 | ||||||||
\(898\) | 2.90039e7 | 1.20023 | ||||||||
\(899\) | 3.05741e6 | 0.126170 | ||||||||
\(900\) | 937438. | 0.0385777 | ||||||||
\(901\) | 3.05783e7 | 1.25488 | ||||||||
\(902\) | 5.94883e6 | 0.243453 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.41415e7 | −0.982524 | ||||||||
\(905\) | 2.05255e7 | 0.833051 | ||||||||
\(906\) | 1.82304e7 | 0.737865 | ||||||||
\(907\) | −3.95608e7 | −1.59679 | −0.798394 | − | 0.602135i | \(-0.794317\pi\) | ||||
−0.798394 | + | 0.602135i | \(0.794317\pi\) | |||||||
\(908\) | −1.64930e6 | −0.0663872 | ||||||||
\(909\) | 1.63448e7 | 0.656099 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.40982e7 | −0.962030 | −0.481015 | − | 0.876712i | \(-0.659732\pi\) | ||||
−0.481015 | + | 0.876712i | \(0.659732\pi\) | |||||||
\(912\) | −176328. | −0.00701994 | ||||||||
\(913\) | −3.53894e6 | −0.140506 | ||||||||
\(914\) | 2.68172e7 | 1.06181 | ||||||||
\(915\) | 773682. | 0.0305499 | ||||||||
\(916\) | −43954.4 | −0.00173087 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.85212e7 | 0.725375 | ||||||||
\(919\) | −2.24660e7 | −0.877480 | −0.438740 | − | 0.898614i | \(-0.644575\pi\) | ||||
−0.438740 | + | 0.898614i | \(0.644575\pi\) | |||||||
\(920\) | 1.89925e7 | 0.739799 | ||||||||
\(921\) | 2.80923e7 | 1.09129 | ||||||||
\(922\) | 4.00704e7 | 1.55238 | ||||||||
\(923\) | 4.62223e6 | 0.178586 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.95701e6 | −0.228915 | ||||||||
\(926\) | −3.06693e7 | −1.17538 | ||||||||
\(927\) | −1.00224e7 | −0.383063 | ||||||||
\(928\) | −3.39995e6 | −0.129599 | ||||||||
\(929\) | 1.16280e7 | 0.442043 | 0.221021 | − | 0.975269i | \(-0.429061\pi\) | ||||
0.221021 | + | 0.975269i | \(0.429061\pi\) | |||||||
\(930\) | −4.23212e6 | −0.160454 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.55517e7 | 0.586458 | ||||||||
\(933\) | −2.72913e7 | −1.02641 | ||||||||
\(934\) | 4.74591e6 | 0.178013 | ||||||||
\(935\) | −2.33611e6 | −0.0873906 | ||||||||
\(936\) | 1.92806e6 | 0.0719333 | ||||||||
\(937\) | 2.40956e7 | 0.896580 | 0.448290 | − | 0.893888i | \(-0.352033\pi\) | ||||
0.448290 | + | 0.893888i | \(0.352033\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.66475e7 | −0.986264 | ||||||||
\(940\) | −4.87241e6 | −0.179856 | ||||||||
\(941\) | 567590. | 0.0208959 | 0.0104479 | − | 0.999945i | \(-0.496674\pi\) | ||||
0.0104479 | + | 0.999945i | \(0.496674\pi\) | |||||||
\(942\) | 1.35142e7 | 0.496207 | ||||||||
\(943\) | −5.59425e7 | −2.04863 | ||||||||
\(944\) | 2.66395e7 | 0.972962 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.03769e6 | −0.146692 | ||||||||
\(947\) | 9.04501e6 | 0.327743 | 0.163872 | − | 0.986482i | \(-0.447602\pi\) | ||||
0.163872 | + | 0.986482i | \(0.447602\pi\) | |||||||
\(948\) | −5.49050e6 | −0.198423 | ||||||||
\(949\) | 1.77129e6 | 0.0638446 | ||||||||
\(950\) | 89708.1 | 0.00322495 | ||||||||
\(951\) | −2.44068e7 | −0.875105 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.48053e7 | −0.528063 | −0.264032 | − | 0.964514i | \(-0.585052\pi\) | ||||
−0.264032 | + | 0.964514i | \(0.585052\pi\) | |||||||
\(954\) | 1.75529e7 | 0.624423 | ||||||||
\(955\) | 7.16546e6 | 0.254235 | ||||||||
\(956\) | 5.48639e6 | 0.194152 | ||||||||
\(957\) | −831294. | −0.0293410 | ||||||||
\(958\) | 4.24895e7 | 1.49578 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 9.15939e6 | 0.320766 | ||||||||
\(961\) | −1.61911e7 | −0.565546 | ||||||||
\(962\) | −3.23257e6 | −0.112619 | ||||||||
\(963\) | −1.76940e7 | −0.614838 | ||||||||
\(964\) | −1.50336e7 | −0.521041 | ||||||||
\(965\) | 2.48393e7 | 0.858661 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.02304e7 | −0.695726 | −0.347863 | − | 0.937545i | \(-0.613093\pi\) | ||||
−0.347863 | + | 0.937545i | \(0.613093\pi\) | |||||||
\(968\) | 3.01072e7 | 1.03272 | ||||||||
\(969\) | −346411. | −0.0118517 | ||||||||
\(970\) | −910364. | −0.0310660 | ||||||||
\(971\) | 255216. | 0.00868679 | 0.00434340 | − | 0.999991i | \(-0.498617\pi\) | ||||
0.00434340 | + | 0.999991i | \(0.498617\pi\) | |||||||
\(972\) | −9.80004e6 | −0.332707 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.30932e7 | −0.442229 | ||||||||
\(975\) | 495573. | 0.0166954 | ||||||||
\(976\) | −1.53507e6 | −0.0515827 | ||||||||
\(977\) | 3.15610e7 | 1.05783 | 0.528914 | − | 0.848675i | \(-0.322599\pi\) | ||||
0.528914 | + | 0.848675i | \(0.322599\pi\) | |||||||
\(978\) | −1.83642e7 | −0.613938 | ||||||||
\(979\) | 3.79196e6 | 0.126447 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.60917e7 | 0.865627 | ||||||||
\(982\) | −4.75064e6 | −0.157208 | ||||||||
\(983\) | 5.24054e7 | 1.72978 | 0.864892 | − | 0.501958i | \(-0.167387\pi\) | ||||
0.864892 | + | 0.501958i | \(0.167387\pi\) | |||||||
\(984\) | −3.02624e7 | −0.996357 | ||||||||
\(985\) | −955225. | −0.0313701 | ||||||||
\(986\) | 4.05504e6 | 0.132832 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27193.1 | −0.000886270 0 | ||||||||
\(989\) | 3.79702e7 | 1.23439 | ||||||||
\(990\) | −1.34101e6 | −0.0434853 | ||||||||
\(991\) | 3.73103e7 | 1.20683 | 0.603413 | − | 0.797429i | \(-0.293807\pi\) | ||||
0.603413 | + | 0.797429i | \(0.293807\pi\) | |||||||
\(992\) | −1.38316e7 | −0.446264 | ||||||||
\(993\) | 7.38682e6 | 0.237730 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.82622e7 | −0.584783 | ||||||||
\(996\) | 4.74992e6 | 0.151718 | ||||||||
\(997\) | 2.27918e7 | 0.726174 | 0.363087 | − | 0.931755i | \(-0.381723\pi\) | ||||
0.363087 | + | 0.931755i | \(0.381723\pi\) | |||||||
\(998\) | 2.89323e7 | 0.919512 | ||||||||
\(999\) | 3.77398e7 | 1.19643 |
(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 | 245.6.a.c.1.2 | 2 | ||
7.6 | odd | 2 | 35.6.a.b.1.2 | ✓ | 2 | ||
21.20 | even | 2 | 315.6.a.c.1.1 | 2 | |||
28.27 | even | 2 | 560.6.a.l.1.2 | 2 | |||
35.13 | even | 4 | 175.6.b.d.99.1 | 4 | |||
35.27 | even | 4 | 175.6.b.d.99.4 | 4 | |||
35.34 | odd | 2 | 175.6.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.a.b.1.2 | ✓ | 2 | 7.6 | odd | 2 | ||
175.6.a.d.1.1 | 2 | 35.34 | odd | 2 | |||
175.6.b.d.99.1 | 4 | 35.13 | even | 4 | |||
175.6.b.d.99.4 | 4 | 35.27 | even | 4 | |||
245.6.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
315.6.a.c.1.1 | 2 | 21.20 | even | 2 | |||
560.6.a.l.1.2 | 2 | 28.27 | even | 2 |