Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 223.4 | ||
Character | \(\chi\) | \(=\) | 384.223 |
Dual form | 384.7.l.a.31.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −11.0227 | + | 11.0227i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 15.5658 | − | 15.5658i | 0.124526 | − | 0.124526i | −0.642097 | − | 0.766623i | \(-0.721935\pi\) |
0.766623 | + | 0.642097i | \(0.221935\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.2991 | −0.0300266 | −0.0150133 | − | 0.999887i | \(-0.504779\pi\) | ||||
−0.0150133 | + | 0.999887i | \(0.504779\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 243.000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1309.74 | + | 1309.74i | 0.984027 | + | 0.984027i | 0.999874 | − | 0.0158475i | \(-0.00504461\pi\) |
−0.0158475 | + | 0.999874i | \(0.505045\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1999.54 | − | 1999.54i | −0.910123 | − | 0.910123i | 0.0861580 | − | 0.996281i | \(-0.472541\pi\) |
−0.996281 | + | 0.0861580i | \(0.972541\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 343.155i | 0.101675i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1800.59 | −0.366495 | −0.183247 | − | 0.983067i | \(-0.558661\pi\) | ||||
−0.183247 | + | 0.983067i | \(0.558661\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1703.06 | − | 1703.06i | 0.248296 | − | 0.248296i | −0.571975 | − | 0.820271i | \(-0.693823\pi\) |
0.820271 | + | 0.571975i | \(0.193823\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 113.524 | − | 113.524i | 0.0122583 | − | 0.0122583i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5649.07 | −0.464295 | −0.232147 | − | 0.972681i | \(-0.574575\pi\) | ||||
−0.232147 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15140.4i | 0.968986i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2678.52 | + | 2678.52i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 11764.6 | + | 11764.6i | 0.482373 | + | 0.482373i | 0.905889 | − | 0.423516i | \(-0.139204\pi\) |
−0.423516 | + | 0.905889i | \(0.639204\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 32237.2i | − | 1.08211i | −0.840986 | − | 0.541057i | \(-0.818024\pi\) | ||
0.840986 | − | 0.541057i | \(-0.181976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −28873.7 | −0.803455 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −160.314 | + | 160.314i | −0.00373911 | + | 0.00373911i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 49520.9 | − | 49520.9i | 0.977651 | − | 0.977651i | −0.0221048 | − | 0.999756i | \(-0.507037\pi\) |
0.999756 | + | 0.0221048i | \(0.00703675\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 44080.7 | 0.743113 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 87389.3i | 1.26796i | 0.773348 | + | 0.633982i | \(0.218580\pi\) | ||||
−0.773348 | + | 0.633982i | \(0.781420\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7129.74 | + | 7129.74i | 0.0896744 | + | 0.0896744i | 0.750521 | − | 0.660847i | \(-0.229803\pi\) |
−0.660847 | + | 0.750521i | \(0.729803\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3782.49 | − | 3782.49i | −0.0415088 | − | 0.0415088i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 79423.3i | 0.764987i | 0.923958 | + | 0.382494i | \(0.124935\pi\) | ||||
−0.923958 | + | 0.382494i | \(0.875065\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −117543. | −0.999098 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19847.3 | − | 19847.3i | 0.149621 | − | 0.149621i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −58057.5 | + | 58057.5i | −0.389970 | + | 0.389970i | −0.874677 | − | 0.484707i | \(-0.838926\pi\) |
0.484707 | + | 0.874677i | \(0.338926\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 40774.3 | 0.245075 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 37544.8i | 0.202733i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9265.40 | + | 9265.40i | 0.0451137 | + | 0.0451137i | 0.729304 | − | 0.684190i | \(-0.239844\pi\) |
−0.684190 | + | 0.729304i | \(0.739844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31233.4 | − | 31233.4i | −0.137604 | − | 0.137604i | 0.634950 | − | 0.772553i | \(-0.281021\pi\) |
−0.772553 | + | 0.634950i | \(0.781021\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2502.69i | 0.0100089i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −62249.0 | −0.226669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 140680. | − | 140680.i | 0.467742 | − | 0.467742i | −0.433440 | − | 0.901182i | \(-0.642700\pi\) |
0.901182 | + | 0.433440i | \(0.142700\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 62268.0 | − | 62268.0i | 0.189547 | − | 0.189547i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −445186. | −1.24385 | −0.621923 | − | 0.783079i | \(-0.713648\pi\) | ||||
−0.621923 | + | 0.783079i | \(0.713648\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 674960.i | 1.73504i | 0.497402 | + | 0.867520i | \(0.334287\pi\) | ||||
−0.497402 | + | 0.867520i | \(0.665713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −166888. | − | 166888.i | −0.395587 | − | 0.395587i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13489.2 | − | 13489.2i | −0.0295470 | − | 0.0295470i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 171535.i | 0.347914i | 0.984753 | + | 0.173957i | \(0.0556553\pi\) | ||||
−0.984753 | + | 0.173957i | \(0.944345\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −59049.0 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 709618. | − | 709618.i | 1.24105 | − | 1.24105i | 0.281488 | − | 0.959565i | \(-0.409172\pi\) |
0.959565 | − | 0.281488i | \(-0.0908278\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28027.6 | + | 28027.6i | −0.0456383 | + | 0.0456383i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −259355. | −0.393856 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 549423.i | − | 0.779358i | −0.920951 | − | 0.389679i | \(-0.872586\pi\) | ||
0.920951 | − | 0.389679i | \(-0.127414\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20593.5 | + | 20593.5i | 0.0273279 | + | 0.0273279i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 355342. | + | 355342.i | 0.441771 | + | 0.441771i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 53019.2i | − | 0.0618389i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −675921. | −0.740595 | −0.370297 | − | 0.928913i | \(-0.620744\pi\) | ||||
−0.370297 | + | 0.928913i | \(0.620744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 318267. | − | 318267.i | 0.328009 | − | 0.328009i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −196185. | + | 196185.i | −0.190415 | + | 0.190415i | −0.795875 | − | 0.605460i | \(-0.792989\pi\) |
0.605460 | + | 0.795875i | \(0.292989\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.82223e6 | −1.66759 | −0.833797 | − | 0.552071i | \(-0.813838\pi\) | ||||
−0.833797 | + | 0.552071i | \(0.813838\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 3534.19i | − | 0.00305297i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.18982e6 | − | 1.18982e6i | −0.971248 | − | 0.971248i | 0.0283501 | − | 0.999598i | \(-0.490975\pi\) |
−0.999598 | + | 0.0283501i | \(0.990975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −895661. | − | 895661.i | −0.691615 | − | 0.691615i | 0.270972 | − | 0.962587i | \(-0.412655\pi\) |
−0.962587 | + | 0.270972i | \(0.912655\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.09171e6i | 0.798249i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.27050e6 | −1.57357 | −0.786784 | − | 0.617228i | \(-0.788256\pi\) | ||||
−0.786784 | + | 0.617228i | \(0.788256\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −87932.4 | + | 87932.4i | −0.0578170 | + | 0.0578170i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −485889. | + | 485889.i | −0.303374 | + | 0.303374i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18544.5 | 0.0110046 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.65928e6i | 0.936618i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −963266. | − | 963266.i | −0.517644 | − | 0.517644i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 478888. | + | 478888.i | 0.245191 | + | 0.245191i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.63397e6i | − | 1.77407i | −0.461705 | − | 0.887034i | \(-0.652762\pi\) | ||
0.461705 | − | 0.887034i | \(-0.347238\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −157178. | −0.0732188 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.91691e6 | + | 1.91691e6i | −0.852685 | + | 0.852685i | −0.990463 | − | 0.137778i | \(-0.956004\pi\) |
0.137778 | + | 0.990463i | \(0.456004\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17540.1 | + | 17540.1i | −0.00745550 | + | 0.00745550i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 83386.6 | 0.0338918 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16843.3i | 0.00655037i | 0.999995 | + | 0.00327519i | \(0.00104253\pi\) | ||||
−0.999995 | + | 0.00327519i | \(0.998957\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.61360e6 | − | 1.61360e6i | −0.600831 | − | 0.600831i | 0.339702 | − | 0.940533i | \(-0.389674\pi\) |
−0.940533 | + | 0.339702i | \(0.889674\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −875459. | − | 875459.i | −0.312305 | − | 0.312305i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 5.23776e6i | − | 1.79117i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 366251. | 0.120136 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.29564e6 | − | 1.29564e6i | 0.407880 | − | 0.407880i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.25465e6 | + | 3.25465e6i | −0.983889 | + | 0.983889i | −0.999872 | − | 0.0159835i | \(-0.994912\pi\) |
0.0159835 | + | 0.999872i | \(0.494912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 534226. | 0.155165 | 0.0775826 | − | 0.996986i | \(-0.475280\pi\) | ||||
0.0775826 | + | 0.996986i | \(0.475280\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 437543.i | 0.122165i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −501799. | − | 501799.i | −0.134752 | − | 0.134752i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.24398e6 | − | 3.24398e6i | −0.838260 | − | 0.838260i | 0.150370 | − | 0.988630i | \(-0.451954\pi\) |
−0.988630 | + | 0.150370i | \(0.951954\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.27990e6i | − | 0.318409i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 58180.5 | 0.0139412 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.38258e6 | + | 1.38258e6i | −0.319247 | + | 0.319247i | −0.848478 | − | 0.529231i | \(-0.822480\pi\) |
0.529231 | + | 0.848478i | \(0.322480\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −449443. | + | 449443.i | −0.100051 | + | 0.100051i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −758120. | −0.162775 | −0.0813877 | − | 0.996683i | \(-0.525935\pi\) | ||||
−0.0813877 | + | 0.996683i | \(0.525935\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.16952e6i | 0.656650i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −413845. | − | 413845.i | −0.0827655 | − | 0.0827655i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.74301e6 | + | 3.74301e6i | 0.722908 | + | 0.722908i | 0.969196 | − | 0.246289i | \(-0.0792112\pi\) |
−0.246289 | + | 0.969196i | \(0.579211\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 155933.i | − | 0.0290954i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −204260. | −0.0368352 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.64678e6 | + | 4.64678e6i | −0.810201 | + | 0.810201i | −0.984664 | − | 0.174463i | \(-0.944181\pi\) |
0.174463 | + | 0.984664i | \(0.444181\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.37439e6 | + | 6.37439e6i | −1.07499 | + | 1.07499i | −0.0780350 | + | 0.996951i | \(0.524865\pi\) |
−0.996951 | + | 0.0780350i | \(0.975135\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 688553. | 0.112353 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 1.54167e6i | − | 0.243487i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.35830e6 | − | 2.35830e6i | −0.360640 | − | 0.360640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −27586.4 | − | 27586.4i | −0.00408610 | − | 0.00408610i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 8.82548e6i | − | 1.26660i | −0.773908 | − | 0.633298i | \(-0.781701\pi\) | ||
0.773908 | − | 0.633298i | \(-0.218299\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.15481e7 | −1.60635 | −0.803175 | − | 0.595743i | \(-0.796858\pi\) | ||||
−0.803175 | + | 0.595743i | \(0.796858\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 686152. | − | 686152.i | 0.0925372 | − | 0.0925372i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.01337e7 | + | 1.01337e7i | −1.32547 | + | 1.32547i | −0.416195 | + | 0.909275i | \(0.636637\pi\) |
−0.909275 | + | 0.416195i | \(0.863363\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.23678e6 | 0.156940 | 0.0784702 | − | 0.996916i | \(-0.474996\pi\) | ||||
0.0784702 | + | 0.996916i | \(0.474996\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.10134e6i | 0.381910i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −121165. | − | 121165.i | −0.0144840 | − | 0.0144840i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.36028e6 | + | 1.36028e6i | 0.157895 | + | 0.157895i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.37272e6i | 0.154765i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.46114e6 | 0.488661 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.18103e6 | − | 1.18103e6i | 0.125722 | − | 0.125722i | −0.641446 | − | 0.767168i | \(-0.721665\pi\) |
0.767168 | + | 0.641446i | \(0.221665\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.90715e6 | − | 4.90715e6i | 0.507798 | − | 0.507798i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 221960. | 0.0223337 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 332016.i | 0.0324922i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.43989e6 | − | 7.43989e6i | −0.708327 | − | 0.708327i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.60035e6 | + | 3.60035e6i | 0.333555 | + | 0.333555i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.20834e7i | 1.08962i | 0.838561 | + | 0.544808i | \(0.183398\pi\) | ||||
−0.838561 | + | 0.544808i | \(0.816602\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.67912e6 | 0.322995 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.40935e7 | − | 1.40935e7i | 1.20488 | − | 1.20488i | 0.232210 | − | 0.972666i | \(-0.425404\pi\) |
0.972666 | − | 0.232210i | \(-0.0745958\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.56390e6 | + | 4.56390e6i | −0.380040 | + | 0.380040i | −0.871117 | − | 0.491076i | \(-0.836604\pi\) |
0.491076 | + | 0.871117i | \(0.336604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 297374. | 0.0241250 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.88250e7i | − | 1.48822i | −0.668056 | − | 0.744111i | \(-0.732873\pi\) | ||
0.668056 | − | 0.744111i | \(-0.267127\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.23629e6 | + | 1.23629e6i | 0.0952612 | + | 0.0952612i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.89078e6 | − | 1.89078e6i | −0.142035 | − | 0.142035i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.87271e7i | − | 1.37176i | −0.727716 | − | 0.685879i | \(-0.759418\pi\) | ||
0.727716 | − | 0.685879i | \(-0.240582\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.72390e6 | 0.266040 | 0.133020 | − | 0.991113i | \(-0.457533\pi\) | ||||
0.133020 | + | 0.991113i | \(0.457533\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 650880. | − | 650880.i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.82965e6 | + | 1.82965e6i | −0.124414 | + | 0.124414i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.81070e6 | −0.451961 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.56438e7i | 1.01332i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.06030e7 | + | 1.06030e7i | 0.670513 | + | 0.670513i | 0.957834 | − | 0.287321i | \(-0.0927648\pi\) |
−0.287321 | + | 0.957834i | \(0.592765\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.39881e6 | − | 7.39881e6i | −0.456878 | − | 0.456878i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 617880.i | − | 0.0372635i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.38806e6 | 0.0817730 | 0.0408865 | − | 0.999164i | \(-0.486982\pi\) | ||||
0.0408865 | + | 0.999164i | \(0.486982\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −510023. | + | 510023.i | −0.0293555 | + | 0.0293555i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.85880e6 | − | 2.85880e6i | 0.160791 | − | 0.160791i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.75571e6 | −0.426338 | −0.213169 | − | 0.977015i | \(-0.568379\pi\) | ||||
−0.213169 | + | 0.977015i | \(0.568379\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.80742e6i | 0.0971231i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.05613e6 | + | 6.05613e6i | 0.318171 | + | 0.318171i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.01455e6 | − | 7.01455e6i | −0.360365 | − | 0.360365i | 0.503582 | − | 0.863947i | \(-0.332015\pi\) |
−0.863947 | + | 0.503582i | \(0.832015\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.58375e7i | 1.80065i | 0.435216 | + | 0.900326i | \(0.356672\pi\) | ||||
−0.435216 | + | 0.900326i | \(0.643328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −453993. | −0.0223132 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.98300e7 | + | 1.98300e7i | −0.953509 | + | 0.953509i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.43034e7 | − | 1.43034e7i | 0.672976 | − | 0.672976i | −0.285425 | − | 0.958401i | \(-0.592135\pi\) |
0.958401 | + | 0.285425i | \(0.0921347\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.83365e6 | −0.360705 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.53217e7i | 0.690539i | 0.938504 | + | 0.345270i | \(0.112213\pi\) | ||||
−0.938504 | + | 0.345270i | \(0.887787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.25052e7 | − | 2.25052e7i | −0.992942 | − | 0.992942i | 0.00703372 | − | 0.999975i | \(-0.497761\pi\) |
−0.999975 | + | 0.00703372i | \(0.997761\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 584414. | + | 584414.i | 0.0252456 | + | 0.0252456i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 900033.i | − | 0.0380726i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.08955e7 | −0.865682 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.45047e6 | − | 7.45047e6i | 0.302346 | − | 0.302346i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.66381e7 | − | 2.66381e7i | 1.05901 | − | 1.05901i | 0.0608658 | − | 0.998146i | \(-0.480614\pi\) |
0.998146 | − | 0.0608658i | \(-0.0193862\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 288447. | 0.0112357 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.01632e6i | 0.267818i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.12956e7 | + | 1.12956e7i | 0.422565 | + | 0.422565i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −73430.1 | − | 73430.1i | −0.00269262 | − | 0.00269262i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 4.32498e6i | − | 0.155473i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −972346. | −0.0342706 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.12747e6 | − | 2.12747e6i | 0.0735273 | − | 0.0735273i | −0.669387 | − | 0.742914i | \(-0.733443\pi\) |
0.742914 | + | 0.669387i | \(0.233443\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.00858e7 | − | 2.00858e7i | 0.680792 | − | 0.680792i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.09965e7 | 0.698018 | 0.349009 | − | 0.937119i | \(-0.386518\pi\) | ||||
0.349009 | + | 0.937119i | \(0.386518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.90976e7i | − | 1.27502i | −0.770442 | − | 0.637511i | \(-0.779964\pi\) | ||
0.770442 | − | 0.637511i | \(-0.220036\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 38956.4 | + | 38956.4i | 0.00124637 | + | 0.00124637i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.72393e7 | + | 3.72393e7i | 1.16902 | + | 1.16902i | 0.982439 | + | 0.186585i | \(0.0597421\pi\) |
0.186585 | + | 0.982439i | \(0.440258\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.08171e7i | 0.949336i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.62301e7 | 0.793021 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.06652e6 | + | 3.06652e6i | −0.0909992 | + | 0.0909992i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.02739e7 | − | 3.02739e7i | 0.881897 | − | 0.881897i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.97452e7 | 0.564701 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 817991.i | − | 0.0229700i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.89023e7 | + | 4.89023e7i | 1.34848 | + | 1.34848i | 0.887312 | + | 0.461170i | \(0.152570\pi\) |
0.461170 | + | 0.887312i | \(0.347430\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.20336e7 | − | 1.20336e7i | −0.325884 | − | 0.325884i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 4.37958e6i | − | 0.116493i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.08256e7 | −0.544136 | −0.272068 | − | 0.962278i | \(-0.587708\pi\) | ||||
−0.272068 | + | 0.962278i | \(0.587708\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.50270e7 | − | 2.50270e7i | 0.642407 | − | 0.642407i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.22224e7 | − | 4.22224e7i | 1.06483 | − | 1.06483i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.42227e6 | 0.0600261 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 1.93850e6i | − | 0.0472073i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.19435e6 | + | 1.19435e6i | 0.0285854 | + | 0.0285854i | 0.721255 | − | 0.692670i | \(-0.243566\pi\) |
−0.692670 | + | 0.721255i | \(0.743566\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.69344e7 | − | 2.69344e7i | −0.633622 | − | 0.633622i | 0.315352 | − | 0.948975i | \(-0.397877\pi\) |
−0.948975 | + | 0.315352i | \(0.897877\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 1.07116e7i | − | 0.247704i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.91191e7 | 1.11667 | 0.558337 | − | 0.829615i | \(-0.311440\pi\) | ||||
0.558337 | + | 0.829615i | \(0.311440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.92968e6 | + | 6.92968e6i | −0.154892 | + | 0.154892i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −204410. | + | 204410.i | −0.00449260 | + | 0.00449260i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.41281e7 | −0.737613 | −0.368806 | − | 0.929506i | \(-0.620233\pi\) | ||||
−0.368806 | + | 0.929506i | \(0.620233\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.12450e7i | 0.876698i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.82897e7 | − | 1.82897e7i | −0.382373 | − | 0.382373i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.05063e7 | + | 1.05063e7i | 0.216058 | + | 0.216058i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.40637e7i | 1.90293i | 0.307751 | + | 0.951467i | \(0.400424\pi\) | ||||
−0.307751 | + | 0.951467i | \(0.599576\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.12356e7 | 0.422654 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 597942. | − | 597942.i | 0.0117095 | − | 0.0117095i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.53429e7 | + | 6.53429e7i | −1.25913 | + | 1.25913i | −0.307626 | + | 0.951507i | \(0.599535\pi\) |
−0.951507 | + | 0.307626i | \(0.900465\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.05573e7 | −0.200198 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.70476e7i | − | 0.878038i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.30308e7 | + | 7.30308e7i | 1.34149 | + | 1.34149i | 0.894575 | + | 0.446918i | \(0.147478\pi\) |
0.446918 | + | 0.894575i | \(0.352522\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.00562e7 | + | 4.00562e7i | 0.724260 | + | 0.724260i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.34668e6i | 0.148565i | 0.997237 | + | 0.0742827i | \(0.0236667\pi\) | ||||
−0.997237 | + | 0.0742827i | \(0.976333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −419940. | −0.00735877 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.73253e6 | − | 1.73253e6i | 0.0298915 | − | 0.0298915i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.74528e7 | + | 2.74528e7i | −0.466377 | + | 0.466377i | −0.900739 | − | 0.434361i | \(-0.856974\pi\) |
0.434361 | + | 0.900739i | \(0.356974\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.01716e7 | 0.170161 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 4.22591e7i | − | 0.696214i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.67008e6 | + | 2.67008e6i | 0.0433244 | + | 0.0433244i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.93307e7 | − | 3.93307e7i | −0.628579 | − | 0.628579i | 0.319131 | − | 0.947710i | \(-0.396609\pi\) |
−0.947710 | + | 0.319131i | \(0.896609\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 386678.i | − | 0.00608739i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.95571e7 | 0.923635 | 0.461817 | − | 0.886975i | \(-0.347198\pi\) | ||||
0.461817 | + | 0.886975i | \(0.347198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.44597e7 | + | 6.44597e7i | −0.984857 | + | 0.984857i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −919145. | + | 919145.i | −0.0138363 | + | 0.0138363i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.29719e8 | 1.92407 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.56064e7i | − | 0.666586i | −0.942823 | − | 0.333293i | \(-0.891840\pi\) | ||
0.942823 | − | 0.333293i | \(-0.108160\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −185659. | − | 185659.i | −0.00267418 | − | 0.00267418i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −95425.5 | − | 95425.5i | −0.00135461 | − | 0.00135461i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.20915e7i | − | 0.309088i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.55725e7 | 0.490576 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.90997e7 | − | 6.90997e7i | 0.939364 | − | 0.939364i | −0.0589000 | − | 0.998264i | \(-0.518759\pi\) |
0.998264 | + | 0.0589000i | \(0.0187593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.73557e6 | − | 3.73557e6i | 0.0500623 | − | 0.0500623i | −0.681632 | − | 0.731695i | \(-0.738730\pi\) |
0.731695 | + | 0.681632i | \(0.238730\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.92999e7 | 0.254996 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 2.72616e7i | − | 0.355128i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 321677. | + | 321677.i | 0.00413177 | + | 0.00413177i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.77343e7 | + | 5.77343e7i | 0.731243 | + | 0.731243i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.26388e7i | 0.657467i | 0.944423 | + | 0.328734i | \(0.106622\pi\) | ||||
−0.944423 | + | 0.328734i | \(0.893378\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.50617e7 | 0.555065 | 0.277532 | − | 0.960716i | \(-0.410483\pi\) | ||||
0.277532 | + | 0.960716i | \(0.410483\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.03707e6 | + | 4.03707e6i | −0.0490455 | + | 0.0490455i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.62073e6 | + | 9.62073e6i | −0.115283 | + | 0.115283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.13040e7 | 0.724595 | 0.362298 | − | 0.932062i | \(-0.381992\pi\) | ||||
0.362298 | + | 0.932062i | \(0.381992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.85629e7i | 0.333033i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.20176e7 | − | 2.20176e7i | −0.253255 | − | 0.253255i | 0.569049 | − | 0.822304i | \(-0.307312\pi\) |
−0.822304 | + | 0.569049i | \(0.807312\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.55221e6 | − | 8.55221e6i | −0.0970506 | − | 0.0970506i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 7.17502e7i | − | 0.803342i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.18241e7 | 0.572523 | 0.286262 | − | 0.958151i | \(-0.407587\pi\) | ||||
0.286262 | + | 0.958151i | \(0.407587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.14457e8 | + | 1.14457e8i | −1.24771 | + | 1.24771i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.88862e6 | + | 5.88862e6i | −0.0633459 | + | 0.0633459i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 641110. | 0.00680610 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.31182e7i | − | 0.346991i | −0.984835 | − | 0.173495i | \(-0.944494\pi\) | ||
0.984835 | − | 0.173495i | \(-0.0555061\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.82290e6 | − | 4.82290e6i | −0.0498736 | − | 0.0498736i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.62828e7 | − | 1.62828e7i | −0.166199 | − | 0.166199i | 0.619108 | − | 0.785306i | \(-0.287494\pi\) |
−0.785306 | + | 0.619108i | \(0.787494\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.56709e7i | − | 0.460147i | −0.973173 | − | 0.230074i | \(-0.926103\pi\) | ||
0.973173 | − | 0.230074i | \(-0.0738967\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.10624e7 | 0.110024 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.27710e7 | − | 5.27710e7i | 0.518137 | − | 0.518137i | −0.398870 | − | 0.917007i | \(-0.630598\pi\) |
0.917007 | + | 0.398870i | \(0.130598\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.44888e6 | + | 1.44888e6i | −0.0140447 | + | 0.0140447i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.15148e7 | 0.684437 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.86762e7i | 0.176484i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.57851e7 | + | 2.57851e7i | 0.240596 | + | 0.240596i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.41080e7 | + | 1.41080e7i | 0.129990 | + | 0.129990i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 8.65283e7i | − | 0.787320i | −0.919256 | − | 0.393660i | \(-0.871209\pi\) | ||
0.919256 | − | 0.393660i | \(-0.128791\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.98038e8 | −1.77957 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −641306. | + | 641306.i | −0.00569147 | + | 0.00569147i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.05213e7 | + | 1.05213e7i | −0.0922236 | + | 0.0922236i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.04559e8 | −0.905263 | −0.452632 | − | 0.891698i | \(-0.649515\pi\) | ||||
−0.452632 | + | 0.891698i | \(0.649515\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.04795e7i | − | 0.260664i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.07335e7 | − | 5.07335e7i | −0.428598 | − | 0.428598i | 0.459553 | − | 0.888151i | \(-0.348010\pi\) |
−0.888151 | + | 0.459553i | \(0.848010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.11832e7 | − | 2.11832e7i | −0.176787 | − | 0.176787i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 9.90816e6i | − | 0.0816916i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.58503e6 | 0.0373485 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.06158e8 | + | 1.06158e8i | −0.854379 | + | 0.854379i | −0.990669 | − | 0.136290i | \(-0.956482\pi\) |
0.136290 | + | 0.990669i | \(0.456482\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.35654e6 | − | 8.35654e6i | 0.0664528 | − | 0.0664528i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.26794e8 | −0.996310 | −0.498155 | − | 0.867088i | \(-0.665989\pi\) | ||||
−0.498155 | + | 0.867088i | \(0.665989\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.10755e6i | 0.0474234i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.49367e7 | − | 3.49367e7i | −0.268076 | − | 0.268076i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −241668. | − | 241668.i | −0.00183259 | − | 0.00183259i | 0.706190 | − | 0.708022i | \(-0.250412\pi\) |
−0.708022 | + | 0.706190i | \(0.750412\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 6.95150e6i | − | 0.0520974i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.12338e6 | 0.0675777 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.83644e7 | + | 2.83644e7i | −0.207660 | + | 0.207660i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.04024e8 | + | 1.04024e8i | −0.752768 | + | 0.752768i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.25162e7 | −0.590252 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.33312e8i | 1.64977i | 0.565301 | + | 0.824885i | \(0.308760\pi\) | ||||
−0.565301 | + | 0.824885i | \(0.691240\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.17256e8 | + | 1.17256e8i | 0.819652 | + | 0.819652i | 0.986057 | − | 0.166405i | \(-0.0532160\pi\) |
−0.166405 | + | 0.986057i | \(0.553216\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.71880e6 | + | 1.71880e6i | 0.0118781 | + | 0.0118781i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.80460e7i | 0.396589i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.16124e8 | −0.784431 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.25149e6 | − | 2.25149e6i | 0.0150379 | − | 0.0150379i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.74738e8 | − | 1.74738e8i | 1.15400 | − | 1.15400i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.70410e7 | −0.241892 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.02440e8i | − | 0.661527i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.53951e8 | − | 1.53951e8i | −0.983140 | − | 0.983140i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.79653e8 | − | 1.79653e8i | −1.13460 | − | 1.13460i | −0.989403 | − | 0.145197i | \(-0.953618\pi\) |
−0.145197 | − | 0.989403i | \(-0.546382\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.40526e8i | − | 0.877722i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.78834e7 | −0.172249 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.98185e7 | − | 3.98185e7i | 0.243289 | − | 0.243289i | −0.574920 | − | 0.818209i | \(-0.694967\pi\) |
0.818209 | + | 0.574920i | \(0.194967\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.58971e6 | + | 7.58971e6i | −0.0458679 | + | 0.0458679i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00717e7 | 0.239543 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.76666e6i | − | 0.0104467i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.69933e7 | + | 1.69933e7i | 0.0994031 | + | 0.0994031i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.27259e7 | + | 3.27259e7i | 0.189377 | + | 0.189377i | 0.795427 | − | 0.606050i | \(-0.207247\pi\) |
−0.606050 | + | 0.795427i | \(0.707247\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 2.85124e7i | − | 0.163230i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.19897e7 | 0.294462 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.04641e8 | − | 1.04641e8i | 0.586376 | − | 0.586376i | −0.350272 | − | 0.936648i | \(-0.613911\pi\) |
0.936648 | + | 0.350272i | \(0.113911\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.53421e7 | + | 3.53421e7i | −0.195951 | + | 0.195951i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 608153. | 0.00333629 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.76056e8i | 0.955684i | 0.878446 | + | 0.477842i | \(0.158581\pi\) | ||||
−0.878446 | + | 0.477842i | \(0.841419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.10539e8 | − | 1.10539e8i | −0.593754 | − | 0.593754i | 0.344889 | − | 0.938643i | \(-0.387917\pi\) |
−0.938643 | + | 0.344889i | \(0.887917\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.72807e7 | + | 9.72807e7i | 0.517086 | + | 0.517086i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8.55293e7i | − | 0.449895i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.03195e8 | −1.05775 | −0.528877 | − | 0.848698i | \(-0.677387\pi\) | ||||
−0.528877 | + | 0.848698i | \(0.677387\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.27292e8 | − | 1.27292e8i | 0.655790 | − | 0.655790i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.30844e6 | + | 7.30844e6i | −0.0372646 | + | 0.0372646i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.52081e8 | −0.767482 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.51265e7i | 0.0755563i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.05167e8 | − | 2.05167e8i | −1.01436 | − | 1.01436i | −0.999895 | − | 0.0144688i | \(-0.995394\pi\) |
−0.0144688 | − | 0.999895i | \(-0.504606\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.49021e7 | − | 5.49021e7i | −0.268685 | − | 0.268685i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2.23402e8i | − | 1.08224i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.11010e7 | 0.149146 | 0.0745728 | − | 0.997216i | \(-0.476241\pi\) | ||||
0.0745728 | + | 0.997216i | \(0.476241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 288660. | − | 288660.i | 0.00137036 | − | 0.00137036i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.36327e7 | + | 1.36327e7i | −0.0640706 | + | 0.0640706i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.95480e8 | −0.909541 | −0.454770 | − | 0.890609i | \(-0.650279\pi\) | ||||
−0.454770 | + | 0.890609i | \(0.650279\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.46859e7i | − | 0.297979i | −0.988839 | − | 0.148990i | \(-0.952398\pi\) | ||
0.988839 | − | 0.148990i | \(-0.0476021\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.41851e7 | − | 3.41851e7i | −0.155914 | − | 0.155914i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.58280e7 | + | 2.58280e7i | 0.116634 | + | 0.116634i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.99248e8i | 1.78516i | 0.450893 | + | 0.892578i | \(0.351106\pi\) | ||||
−0.450893 | + | 0.892578i | \(0.648894\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.67113e6 | 0.0118262 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.58810e8 | − | 1.58810e8i | 0.696233 | − | 0.696233i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.95990e8 | + | 2.95990e8i | −1.28498 | + | 1.28498i | −0.347177 | + | 0.937800i | \(0.612860\pi\) |
−0.937800 | + | 0.347177i | \(0.887140\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.99880e7 | −0.128921 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.85247e8i | 0.788671i | 0.918967 | + | 0.394335i | \(0.129025\pi\) | ||||
−0.918967 | + | 0.394335i | \(0.870975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.32171e7 | − | 5.32171e7i | −0.224378 | − | 0.224378i | 0.585961 | − | 0.810339i | \(-0.300717\pi\) |
−0.810339 | + | 0.585961i | \(0.800717\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.51311e7 | − | 1.51311e7i | −0.0631825 | − | 0.0631825i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.65858e6i | 0.0234015i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.21660e8 | −0.907921 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.91739e7 | + | 4.91739e7i | −0.199495 | + | 0.199495i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.91668e7 | + | 8.91668e7i | −0.358304 | + | 0.358304i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.30000e7 | −0.370165 | −0.185082 | − | 0.982723i | \(-0.559255\pi\) | ||||
−0.185082 | + | 0.982723i | \(0.559255\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.60362e7i | 0.102652i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.65657e7 | − | 5.65657e7i | −0.220918 | − | 0.220918i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.35032e8 | + | 2.35032e8i | 0.909303 | + | 0.909303i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.08180e8i | 0.414615i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.74473e8 | −1.80151 | −0.900756 | − | 0.434326i | \(-0.856986\pi\) | ||||
−0.900756 | + | 0.434326i | \(0.856986\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.92710e8 | − | 1.92710e8i | 0.724890 | − | 0.724890i | −0.244707 | − | 0.969597i | \(-0.578692\pi\) |
0.969597 | + | 0.244707i | \(0.0786918\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.44660e6 | + | 2.44660e6i | −0.00911768 | + | 0.00911768i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.21114e8 | 0.447179 | 0.223589 | − | 0.974683i | \(-0.428223\pi\) | ||||
0.223589 | + | 0.974683i | \(0.428223\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.42705e7i | 0.0887861i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.65971e6 | − | 3.65971e6i | −0.0132649 | − | 0.0132649i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.00270e8 | − | 2.00270e8i | −0.719244 | − | 0.719244i | 0.249207 | − | 0.968450i | \(-0.419830\pi\) |
−0.968450 | + | 0.249207i | \(0.919830\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.96766e7i | 0.212364i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.64015e8 | 0.578347 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.29275e7 | − | 5.29275e7i | 0.184938 | − | 0.184938i | −0.608566 | − | 0.793503i | \(-0.708255\pi\) |
0.793503 | + | 0.608566i | \(0.208255\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.26348e6 | + | 9.26348e6i | −0.0320752 | + | 0.0320752i | −0.722963 | − | 0.690887i | \(-0.757220\pi\) |
0.690887 | + | 0.722963i | \(0.257220\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.93712e7 | −0.272347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 546051.i | 0.00185681i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.64590e7 | − | 6.64590e7i | −0.223963 | − | 0.223963i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.33191e8 | − | 1.33191e8i | −0.444834 | − | 0.444834i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.18152e7i | − | 0.270811i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.11352e8 | −0.365304 | −0.182652 | − | 0.983178i | \(-0.558468\pi\) | ||||
−0.182652 | + | 0.983178i | \(0.558468\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.05538e7 | + | 4.05538e7i | −0.131862 | + | 0.131862i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.72222e8 | − | 1.72222e8i | 0.555039 | − | 0.555039i | −0.372852 | − | 0.927891i | \(-0.621620\pi\) |
0.927891 | + | 0.372852i | \(0.121620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.96139e6 | 0.0222375 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.10698e8i | 0.983777i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.99546e8 | + | 2.99546e8i | 0.940160 | + | 0.940160i | 0.998308 | − | 0.0581483i | \(-0.0185196\pi\) |
−0.0581483 | + | 0.998308i | \(0.518520\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 262180. | + | 262180.i | 0.000815695 | + | 0.000815695i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 1.00613e8i | − | 0.310302i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.32177e8 | 0.709841 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.31649e7 | + | 1.31649e7i | −0.0399008 | + | 0.0399008i | −0.726776 | − | 0.686875i | \(-0.758982\pi\) |
0.686875 | + | 0.726776i | \(0.258982\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.27787e6 | + | 3.27787e6i | −0.00984900 | + | 0.00984900i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.02341e7 | −0.149639 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.57352e8i | − | 0.464702i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.07503e8 | + | 2.07503e8i | 0.607564 | + | 0.607564i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.88418e7 | − | 5.88418e7i | −0.170817 | − | 0.170817i | 0.616521 | − | 0.787338i | \(-0.288542\pi\) |
−0.787338 | + | 0.616521i | \(0.788542\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.68675e8i | − | 0.485494i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.72545e7 | −0.0777804 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.02053e6 | − | 2.02053e6i | 0.00571752 | − | 0.00571752i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.03453e8 | + | 1.03453e8i | −0.290272 | + | 0.290272i | −0.837188 | − | 0.546915i | \(-0.815802\pi\) |
0.546915 | + | 0.837188i | \(0.315802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.16830e7 | 0.115971 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.82111e8i | 0.502419i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.15299e7 | − | 8.15299e7i | −0.223048 | − | 0.223048i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.06424e8 | + | 2.06424e8i | 0.560018 | + | 0.560018i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 2.43205e8i | − | 0.654314i | −0.944970 | − | 0.327157i | \(-0.893909\pi\) | ||
0.944970 | − | 0.327157i | \(-0.106091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.87673e7 | 0.0500722 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.10475e7 | + | 4.10475e7i | −0.108610 | + | 0.108610i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.78121e8 | + | 1.78121e8i | −0.467413 | + | 0.467413i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.48848e7 | −0.116814 | −0.0584071 | − | 0.998293i | \(-0.518602\pi\) | ||||
−0.0584071 | + | 0.998293i | \(0.518602\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.43489e7i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.28377e7 | − | 1.28377e7i | −0.0328652 | − | 0.0328652i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.55826e8 | + | 2.55826e8i | 0.649579 | + | 0.649579i | 0.952891 | − | 0.303312i | \(-0.0980925\pi\) |
−0.303312 | + | 0.952891i | \(0.598092\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 4.03354e7i | − | 0.101584i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.68507e8 | 0.920542 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.81372e8 | + | 2.81372e8i | −0.697184 | + | 0.697184i | −0.963802 | − | 0.266619i | \(-0.914094\pi\) |
0.266619 | + | 0.963802i | \(0.414094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.50723e7 | − | 7.50723e7i | 0.184512 | − | 0.184512i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.35968e8 | 0.331489 | 0.165744 | − | 0.986169i | \(-0.446997\pi\) | ||||
0.165744 | + | 0.986169i | \(0.446997\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.01323e8i | 0.245040i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.72437e8 | − | 1.72437e8i | −0.413684 | − | 0.413684i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.22541e7 | + | 1.22541e7i | 0.0291633 | + | 0.0291633i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.87723e7i | 0.0915382i | 0.998952 | + | 0.0457691i | \(0.0145738\pi\) | ||||
−0.998952 | + | 0.0457691i | \(0.985426\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.33747e8 | −0.547471 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.31566e6 | − | 8.31566e6i | 0.0193222 | − | 0.0193222i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.20208e8 | − | 4.20208e8i | 0.968672 | − | 0.968672i | −0.0308517 | − | 0.999524i | \(-0.509822\pi\) |
0.999524 | + | 0.0308517i | \(0.00982196\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.63110e8 | 0.373040 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 5.17271e8i | − | 1.17372i | −0.809689 | − | 0.586860i | \(-0.800364\pi\) | ||
0.809689 | − | 0.586860i | \(-0.199636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.22453e6 | + | 9.22453e6i | 0.0207669 | + | 0.0207669i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.81071e6 | + | 6.81071e6i | 0.0152128 | + | 0.0152128i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.70531e7i | − | 0.0821180i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.94158e8 | 1.30654 | 0.653270 | − | 0.757125i | \(-0.273397\pi\) | ||||
0.653270 | + | 0.757125i | \(0.273397\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.53002e7 | + | 1.53002e7i | −0.0333837 | + | 0.0333837i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.95585e8 | + | 2.95585e8i | −0.639948 | + | 0.639948i | −0.950542 | − | 0.310595i | \(-0.899472\pi\) |
0.310595 | + | 0.950542i | \(0.399472\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.88085e8 | 1.04855 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.12437e7i | − | 0.0239687i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.48830e8 | + | 1.48830e8i | 0.314831 | + | 0.314831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.83078e8 | − | 5.83078e8i | −1.22398 | − | 1.22398i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.30233e7i | 0.131285i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.00990e8 | −0.208771 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.97521e8 | + | 1.97521e8i | −0.405218 | + | 0.405218i | −0.880067 | − | 0.474849i | \(-0.842503\pi\) |
0.474849 | + | 0.880067i | \(0.342503\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.54889e7 | − | 8.54889e7i | 0.174052 | − | 0.174052i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.33841e7 | 0.0472489 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.24905e8i | 0.250472i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.99227e7 | − | 1.99227e7i | −0.0396503 | − | 0.0396503i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.31312e8 | + | 4.31312e8i | 0.851954 | + | 0.851954i | 0.990374 | − | 0.138419i | \(-0.0442022\pi\) |
−0.138419 | + | 0.990374i | \(0.544202\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1.43009e8i | − | 0.280364i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.33510e8 | −0.259786 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.84022e8 | + | 8.84022e8i | −1.70733 | + | 1.70733i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 905627. | − | 905627.i | 0.00173605 | − | 0.00173605i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.54639e8 | 0.294237 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.32321e8i | − | 1.00538i | −0.864468 | − | 0.502688i | \(-0.832345\pi\) | ||
0.864468 | − | 0.502688i | \(-0.167655\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.63456e7 | + | 9.63456e7i | 0.180622 | + | 0.180622i | 0.791627 | − | 0.611005i | \(-0.209235\pi\) |
−0.611005 | + | 0.791627i | \(0.709235\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.95026e8 | − | 3.95026e8i | −0.735113 | − | 0.735113i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.30418e7i | 0.0795093i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.42848e7 | 0.0445316 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.00423e6 | − | 5.00423e6i | 0.00910931 | − | 0.00910931i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.51953e8 | − | 2.51953e8i | 0.455293 | − | 0.455293i | −0.441814 | − | 0.897107i | \(-0.645665\pi\) |
0.897107 | + | 0.441814i | \(0.145665\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.42435e8 | 1.51125 | 0.755626 | − | 0.655004i | \(-0.227333\pi\) | ||||
0.755626 | + | 0.655004i | \(0.227333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 4.37160e8i | − | 0.778537i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.58922e8 | + | 1.58922e8i | 0.280975 | + | 0.280975i | 0.833498 | − | 0.552523i | \(-0.186335\pi\) |
−0.552523 | + | 0.833498i | \(0.686335\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.73710e8 | + | 1.73710e8i | 0.304902 | + | 0.304902i | 0.842928 | − | 0.538026i | \(-0.180830\pi\) |
−0.538026 | + | 0.842928i | \(0.680830\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.15324e8i | 0.549483i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.11646e8 | 0.366164 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.18008e7 | + | 1.18008e7i | −0.0202698 | + | 0.0202698i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.63480e7 | − | 8.63480e7i | 0.147257 | − | 0.147257i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.40758e8 | −0.238335 | −0.119168 | − | 0.992874i | \(-0.538023\pi\) | ||||
−0.119168 | + | 0.992874i | \(0.538023\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 3.18012e8i | − | 0.534633i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.68887e8 | − | 1.68887e8i | −0.281911 | − | 0.281911i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.93362e7 | + | 4.93362e7i | 0.0817702 | + | 0.0817702i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.70891e7i | − | 0.0281235i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.96136e8 | 0.810733 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.79747e8 | + | 2.79747e8i | −0.453918 | + | 0.453918i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.21132e8 | − | 2.21132e8i | 0.356291 | − | 0.356291i | −0.506153 | − | 0.862444i | \(-0.668933\pi\) |
0.862444 | + | 0.506153i | \(0.168933\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.28837e7 | −0.0206130 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.00862e9i | − | 1.60245i | −0.598365 | − | 0.801224i | \(-0.704183\pi\) | ||
0.598365 | − | 0.801224i | \(-0.295817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.56398e8 | + | 6.56398e8i | 1.03559 | + | 1.03559i | 0.999343 | + | 0.0362465i | \(0.0115402\pi\) |
0.0362465 | + | 0.999343i | \(0.488460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.92080e6 | + | 9.92080e6i | 0.0155431 | + | 0.0155431i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.27673e8i | 0.198641i | 0.995056 | + | 0.0993204i | \(0.0316669\pi\) | ||||
−0.995056 | + | 0.0993204i | \(0.968333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.16526e8 | 0.180042 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.30324e8 | − | 2.30324e8i | 0.353413 | − | 0.353413i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.24666e8 | + | 2.24666e8i | −0.342356 | + | 0.342356i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.62589e8 | −0.851407 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.64249e8i | 0.246865i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.93213e6 | − | 4.93213e6i | −0.00736225 | − | 0.00736225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.52901e8 | − | 2.52901e8i | −0.374931 | − | 0.374931i | 0.494339 | − | 0.869269i | \(-0.335410\pi\) |
−0.869269 | + | 0.494339i | \(0.835410\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.87248e8i | 0.864679i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.24837e9 | 1.82564 | 0.912819 | − | 0.408365i | \(-0.133901\pi\) | ||||
0.912819 | + | 0.408365i | \(0.133901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.14023e8 | − | 9.14023e8i | 1.32762 | − | 1.32762i | 0.420185 | − | 0.907438i | \(-0.361965\pi\) |
0.907438 | − | 0.420185i | \(-0.138035\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.17946e6 | + | 3.17946e6i | −0.00458695 | + | 0.00458695i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.29976e8 | 0.329542 | 0.164771 | − | 0.986332i | \(-0.447311\pi\) | ||||
0.164771 | + | 0.986332i | \(0.447311\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.74267e7i | 0.0532692i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.73388e7 | − | 7.73388e7i | −0.109336 | − | 0.109336i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.35263e8 | + | 1.35263e8i | 0.189944 | + | 0.189944i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.44662e8i | 0.201783i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.49015e8 | −0.345023 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.79258e8 | − | 3.79258e8i | 0.521982 | − | 0.521982i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.04538e8 | − | 1.04538e8i | 0.142922 | − | 0.142922i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.61880e6 | 0.00219851 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.98445e8i | 0.267728i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.51748e8 | − | 4.51748e8i | −0.605444 | − | 0.605444i | 0.336308 | − | 0.941752i | \(-0.390822\pi\) |
−0.941752 | + | 0.336308i | \(0.890822\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.76729e7 | + | 4.76729e7i | 0.0634717 | + | 0.0634717i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.67087e8i | 0.750058i | 0.927013 | + | 0.375029i | \(0.122367\pi\) | ||||
−0.927013 | + | 0.375029i | \(0.877633\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.85883e9 | 2.44246 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.07179e7 | − | 1.07179e7i | 0.0139909 | − | 0.0139909i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.97425e7 | − | 1.97425e7i | 0.0256032 | − | 0.0256032i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.38744e8 | −1.08065 | −0.540323 | − | 0.841458i | \(-0.681698\pi\) | ||||
−0.540323 | + | 0.841458i | \(0.681698\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.69010e7i | 0.0600348i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.90168e8 | + | 8.90168e8i | 1.13205 | + | 1.13205i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.49768e8 | + | 7.49768e8i | 0.947330 | + | 0.947330i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.42801e8i | 0.555865i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.36976e9 | −1.70842 | −0.854212 | − | 0.519924i | \(-0.825960\pi\) | ||||
−0.854212 | + | 0.519924i | \(0.825960\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.00183e8 | + | 2.00183e8i | −0.248072 | + | 0.248072i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.31439e8 | + | 2.31439e8i | −0.284964 | + | 0.284964i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.34177e7 | −0.0898186 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.89998e8i | 0.838743i | 0.907815 | + | 0.419371i | \(0.137749\pi\) | ||||
−0.907815 | + | 0.419371i | \(0.862251\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.30962e8 | + | 4.30962e8i | 0.520525 | + | 0.520525i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.06002e8 | + | 1.06002e8i | 0.127218 | + | 0.127218i | 0.767849 | − | 0.640631i | \(-0.221327\pi\) |
−0.640631 | + | 0.767849i | \(0.721327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.93668e8i | − | 0.588708i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −858809. | −0.00101766 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.85082e8 | + | 1.85082e8i | −0.217928 | + | 0.217928i | −0.807625 | − | 0.589696i | \(-0.799247\pi\) |
0.589696 | + | 0.807625i | \(0.299247\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.34961e9 | − | 1.34961e9i | 1.57910 | − | 1.57910i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.20955e8 | −0.954504 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 7.03272e8i | − | 0.812540i | −0.913753 | − | 0.406270i | \(-0.866829\pi\) | ||
0.913753 | − | 0.406270i | \(-0.133171\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.37376e8 | − | 1.37376e8i | −0.157725 | − | 0.157725i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.39688e8 | − | 3.39688e8i | −0.387565 | − | 0.387565i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 173471.i | − | 0.000196685i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.51736e8 | −0.170970 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.89126e8 | + | 2.89126e8i | −0.323749 | + | 0.323749i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.79756e8 | + | 1.79756e8i | −0.200033 | + | 0.200033i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.58827e8 | 0.618013 | 0.309007 | − | 0.951060i | \(-0.400003\pi\) | ||||
0.309007 | + | 0.951060i | \(0.400003\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6.76026e7i | − | 0.0743006i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.38035e8 | + | 2.38035e8i | 0.260006 | + | 0.260006i | 0.825056 | − | 0.565051i | \(-0.191143\pi\) |
−0.565051 | + | 0.825056i | \(0.691143\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.66187e7 | + | 1.66187e7i | 0.0180409 | + | 0.0180409i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.67400e8i | 0.720066i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.76599e8 | −1.04721 | −0.523603 | − | 0.851962i | \(-0.675413\pi\) | ||||
−0.523603 | + | 0.851962i | \(0.675413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.19601e8 | − | 7.19601e8i | 0.766909 | − | 0.766909i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.17646e8 | + | 2.17646e8i | −0.230538 | + | 0.230538i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.57271e9 | 1.65573 | 0.827863 | − | 0.560930i | \(-0.189556\pi\) | ||||
0.827863 | + | 0.560930i | \(0.189556\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.15479e8i | 0.330112i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.01647e6 | + | 9.01647e6i | 0.00937745 | + | 0.00937745i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.02764e7 | − | 4.02764e7i | −0.0416353 | − | 0.0416353i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.47817e8i | 0.973875i | 0.873437 | + | 0.486938i | \(0.161886\pi\) | ||||
−0.873437 | + | 0.486938i | \(0.838114\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.07807e9 | −1.10103 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.92515e7 | − | 1.92515e7i | 0.0195432 | − | 0.0195432i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.42772e8 | − | 5.42772e8i | 0.547686 | − | 0.547686i | −0.378085 | − | 0.925771i | \(-0.623417\pi\) |
0.925771 | + | 0.378085i | \(0.123417\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.65285e8 | 0.266083 |
(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 | 384.7.l.a.223.4 | 48 | ||
4.3 | odd | 2 | 384.7.l.b.223.21 | 48 | |||
8.3 | odd | 2 | 48.7.l.a.19.15 | ✓ | 48 | ||
8.5 | even | 2 | 192.7.l.a.175.21 | 48 | |||
16.3 | odd | 4 | 192.7.l.a.79.21 | 48 | |||
16.5 | even | 4 | 384.7.l.b.31.21 | 48 | |||
16.11 | odd | 4 | inner | 384.7.l.a.31.4 | 48 | ||
16.13 | even | 4 | 48.7.l.a.43.15 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.7.l.a.19.15 | ✓ | 48 | 8.3 | odd | 2 | ||
48.7.l.a.43.15 | yes | 48 | 16.13 | even | 4 | ||
192.7.l.a.79.21 | 48 | 16.3 | odd | 4 | |||
192.7.l.a.175.21 | 48 | 8.5 | even | 2 | |||
384.7.l.a.31.4 | 48 | 16.11 | odd | 4 | inner | ||
384.7.l.a.223.4 | 48 | 1.1 | even | 1 | trivial | ||
384.7.l.b.31.21 | 48 | 16.5 | even | 4 | |||
384.7.l.b.223.21 | 48 | 4.3 | odd | 2 |