Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,7,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), 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: | \(0.920216334479\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-15}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.2 | ||
Root | \(0.500000 + 1.93649i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.7.b.a.3.1 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | + | 7.74597i | 0.250000 | + | 0.968246i | ||||
\(3\) | − | 30.9839i | − | 1.14755i | −0.819013 | − | 0.573775i | \(-0.805478\pi\) | ||
0.819013 | − | 0.573775i | \(-0.194522\pi\) | |||||||
\(4\) | −56.0000 | + | 30.9839i | −0.875000 | + | 0.484123i | ||||
\(5\) | 10.0000 | 0.0800000 | 0.0400000 | − | 0.999200i | \(-0.487264\pi\) | ||||
0.0400000 | + | 0.999200i | \(0.487264\pi\) | |||||||
\(6\) | 240.000 | − | 61.9677i | 1.11111 | − | 0.286888i | ||||
\(7\) | 309.839i | 0.903320i | 0.892190 | + | 0.451660i | \(0.149168\pi\) | ||||
−0.892190 | + | 0.451660i | \(0.850832\pi\) | |||||||
\(8\) | −352.000 | − | 371.806i | −0.687500 | − | 0.726184i | ||||
\(9\) | −231.000 | −0.316872 | ||||||||
\(10\) | 20.0000 | + | 77.4597i | 0.0200000 | + | 0.0774597i | ||||
\(11\) | − | 960.500i | − | 0.721638i | −0.932636 | − | 0.360819i | \(-0.882497\pi\) | ||
0.932636 | − | 0.360819i | \(-0.117503\pi\) | |||||||
\(12\) | 960.000 | + | 1735.10i | 0.555556 | + | 1.00411i | ||||
\(13\) | 1466.00 | 0.667274 | 0.333637 | − | 0.942702i | \(-0.391724\pi\) | ||||
0.333637 | + | 0.942702i | \(0.391724\pi\) | |||||||
\(14\) | −2400.00 | + | 619.677i | −0.874636 | + | 0.225830i | ||||
\(15\) | − | 309.839i | − | 0.0918040i | ||||||
\(16\) | 2176.00 | − | 3470.19i | 0.531250 | − | 0.847215i | ||||
\(17\) | −4766.00 | −0.970079 | −0.485040 | − | 0.874492i | \(-0.661195\pi\) | ||||
−0.485040 | + | 0.874492i | \(0.661195\pi\) | |||||||
\(18\) | −462.000 | − | 1789.32i | −0.0792181 | − | 0.306810i | ||||
\(19\) | 7529.08i | 1.09769i | 0.835923 | + | 0.548847i | \(0.184933\pi\) | ||||
−0.835923 | + | 0.548847i | \(0.815067\pi\) | |||||||
\(20\) | −560.000 | + | 309.839i | −0.0700000 | + | 0.0387298i | ||||
\(21\) | 9600.00 | 1.03661 | ||||||||
\(22\) | 7440.00 | − | 1921.00i | 0.698723 | − | 0.180409i | ||||
\(23\) | − | 10472.5i | − | 0.860734i | −0.902654 | − | 0.430367i | \(-0.858384\pi\) | ||
0.902654 | − | 0.430367i | \(-0.141616\pi\) | |||||||
\(24\) | −11520.0 | + | 10906.3i | −0.833333 | + | 0.788941i | ||||
\(25\) | −15525.0 | −0.993600 | ||||||||
\(26\) | 2932.00 | + | 11355.6i | 0.166818 | + | 0.646085i | ||||
\(27\) | − | 15430.0i | − | 0.783923i | ||||||
\(28\) | −9600.00 | − | 17351.0i | −0.437318 | − | 0.790405i | ||||
\(29\) | 25498.0 | 1.04547 | 0.522736 | − | 0.852495i | \(-0.324911\pi\) | ||||
0.522736 | + | 0.852495i | \(0.324911\pi\) | |||||||
\(30\) | 2400.00 | − | 619.677i | 0.0888889 | − | 0.0229510i | ||||
\(31\) | 41890.2i | 1.40614i | 0.711123 | + | 0.703068i | \(0.248187\pi\) | ||||
−0.711123 | + | 0.703068i | \(0.751813\pi\) | |||||||
\(32\) | 31232.0 | + | 9914.84i | 0.953125 | + | 0.302577i | ||||
\(33\) | −29760.0 | −0.828116 | ||||||||
\(34\) | −9532.00 | − | 36917.3i | −0.242520 | − | 0.939275i | ||||
\(35\) | 3098.39i | 0.0722656i | ||||||||
\(36\) | 12936.0 | − | 7157.27i | 0.277263 | − | 0.153405i | ||||
\(37\) | 1994.00 | 0.0393659 | 0.0196829 | − | 0.999806i | \(-0.493734\pi\) | ||||
0.0196829 | + | 0.999806i | \(0.493734\pi\) | |||||||
\(38\) | −58320.0 | + | 15058.2i | −1.06284 | + | 0.274423i | ||||
\(39\) | − | 45422.3i | − | 0.765730i | ||||||
\(40\) | −3520.00 | − | 3718.06i | −0.0550000 | − | 0.0580948i | ||||
\(41\) | 29362.0 | 0.426024 | 0.213012 | − | 0.977050i | \(-0.431673\pi\) | ||||
0.213012 | + | 0.977050i | \(0.431673\pi\) | |||||||
\(42\) | 19200.0 | + | 74361.3i | 0.259151 | + | 1.00369i | ||||
\(43\) | − | 21533.8i | − | 0.270841i | −0.990788 | − | 0.135421i | \(-0.956761\pi\) | ||
0.990788 | − | 0.135421i | \(-0.0432386\pi\) | |||||||
\(44\) | 29760.0 | + | 53788.0i | 0.349361 | + | 0.631433i | ||||
\(45\) | −2310.00 | −0.0253498 | ||||||||
\(46\) | 81120.0 | − | 20945.1i | 0.833402 | − | 0.215183i | ||||
\(47\) | − | 7560.06i | − | 0.0728168i | −0.999337 | − | 0.0364084i | \(-0.988408\pi\) | ||
0.999337 | − | 0.0364084i | \(-0.0115917\pi\) | |||||||
\(48\) | −107520. | − | 67420.9i | −0.972222 | − | 0.609636i | ||||
\(49\) | 21649.0 | 0.184013 | ||||||||
\(50\) | −31050.0 | − | 120256.i | −0.248400 | − | 0.962049i | ||||
\(51\) | 147669.i | 1.11322i | ||||||||
\(52\) | −82096.0 | + | 45422.3i | −0.583864 | + | 0.323042i | ||||
\(53\) | −192854. | −1.29539 | −0.647696 | − | 0.761899i | \(-0.724267\pi\) | ||||
−0.647696 | + | 0.761899i | \(0.724267\pi\) | |||||||
\(54\) | 119520. | − | 30859.9i | 0.759031 | − | 0.195981i | ||||
\(55\) | − | 9605.00i | − | 0.0577310i | ||||||
\(56\) | 115200. | − | 109063.i | 0.655977 | − | 0.621032i | ||||
\(57\) | 233280. | 1.25966 | ||||||||
\(58\) | 50996.0 | + | 197507.i | 0.261368 | + | 1.01227i | ||||
\(59\) | − | 78420.2i | − | 0.381831i | −0.981606 | − | 0.190916i | \(-0.938854\pi\) | ||
0.981606 | − | 0.190916i | \(-0.0611457\pi\) | |||||||
\(60\) | 9600.00 | + | 17351.0i | 0.0444444 | + | 0.0803285i | ||||
\(61\) | −10918.0 | −0.0481009 | −0.0240505 | − | 0.999711i | \(-0.507656\pi\) | ||||
−0.0240505 | + | 0.999711i | \(0.507656\pi\) | |||||||
\(62\) | −324480. | + | 83780.4i | −1.36149 | + | 0.351534i | ||||
\(63\) | − | 71572.7i | − | 0.286237i | ||||||
\(64\) | −14336.0 | + | 261752.i | −0.0546875 | + | 0.998504i | ||||
\(65\) | 14660.0 | 0.0533819 | ||||||||
\(66\) | −59520.0 | − | 230520.i | −0.207029 | − | 0.801820i | ||||
\(67\) | − | 394146.i | − | 1.31049i | −0.755418 | − | 0.655243i | \(-0.772566\pi\) | ||
0.755418 | − | 0.655243i | \(-0.227434\pi\) | |||||||
\(68\) | 266896. | − | 147669.i | 0.848819 | − | 0.469638i | ||||
\(69\) | −324480. | −0.987735 | ||||||||
\(70\) | −24000.0 | + | 6196.77i | −0.0699708 | + | 0.0180664i | ||||
\(71\) | 532241.i | 1.48708i | 0.668694 | + | 0.743538i | \(0.266854\pi\) | ||||
−0.668694 | + | 0.743538i | \(0.733146\pi\) | |||||||
\(72\) | 81312.0 | + | 85887.3i | 0.217850 | + | 0.230108i | ||||
\(73\) | 288626. | 0.741937 | 0.370968 | − | 0.928646i | \(-0.379026\pi\) | ||||
0.370968 | + | 0.928646i | \(0.379026\pi\) | |||||||
\(74\) | 3988.00 | + | 15445.5i | 0.00984147 | + | 0.0381159i | ||||
\(75\) | 481025.i | 1.14021i | ||||||||
\(76\) | −233280. | − | 421628.i | −0.531419 | − | 0.960482i | ||||
\(77\) | 297600. | 0.651870 | ||||||||
\(78\) | 351840. | − | 90844.7i | 0.741415 | − | 0.191433i | ||||
\(79\) | − | 310706.i | − | 0.630186i | −0.949061 | − | 0.315093i | \(-0.897964\pi\) | ||
0.949061 | − | 0.315093i | \(-0.102036\pi\) | |||||||
\(80\) | 21760.0 | − | 34701.9i | 0.0425000 | − | 0.0677772i | ||||
\(81\) | −646479. | −1.21646 | ||||||||
\(82\) | 58724.0 | + | 227437.i | 0.106506 | + | 0.412496i | ||||
\(83\) | − | 204153.i | − | 0.357043i | −0.983936 | − | 0.178522i | \(-0.942869\pi\) | ||
0.983936 | − | 0.178522i | \(-0.0571314\pi\) | |||||||
\(84\) | −537600. | + | 297445.i | −0.907029 | + | 0.501844i | ||||
\(85\) | −47660.0 | −0.0776064 | ||||||||
\(86\) | 166800. | − | 43067.6i | 0.262241 | − | 0.0677104i | ||||
\(87\) | − | 790027.i | − | 1.19973i | ||||||
\(88\) | −357120. | + | 338096.i | −0.524042 | + | 0.496126i | ||||
\(89\) | 310738. | 0.440783 | 0.220391 | − | 0.975412i | \(-0.429267\pi\) | ||||
0.220391 | + | 0.975412i | \(0.429267\pi\) | |||||||
\(90\) | −4620.00 | − | 17893.2i | −0.00633745 | − | 0.0245448i | ||||
\(91\) | 454223.i | 0.602761i | ||||||||
\(92\) | 324480. | + | 586463.i | 0.416701 | + | 0.753142i | ||||
\(93\) | 1.29792e6 | 1.61361 | ||||||||
\(94\) | 58560.0 | − | 15120.1i | 0.0705046 | − | 0.0182042i | ||||
\(95\) | 75290.8i | 0.0878155i | ||||||||
\(96\) | 307200. | − | 967688.i | 0.347222 | − | 1.09376i | ||||
\(97\) | −1.45709e6 | −1.59650 | −0.798252 | − | 0.602324i | \(-0.794242\pi\) | ||||
−0.798252 | + | 0.602324i | \(0.794242\pi\) | |||||||
\(98\) | 43298.0 | + | 167692.i | 0.0460034 | + | 0.178170i | ||||
\(99\) | 221875.i | 0.228667i | ||||||||
\(100\) | 869400. | − | 481025.i | 0.869400 | − | 0.481025i | ||||
\(101\) | −639158. | −0.620360 | −0.310180 | − | 0.950678i | \(-0.600389\pi\) | ||||
−0.310180 | + | 0.950678i | \(0.600389\pi\) | |||||||
\(102\) | −1.14384e6 | + | 295338.i | −1.07787 | + | 0.278304i | ||||
\(103\) | 1.38913e6i | 1.27125i | 0.771997 | + | 0.635626i | \(0.219258\pi\) | ||||
−0.771997 | + | 0.635626i | \(0.780742\pi\) | |||||||
\(104\) | −516032. | − | 545068.i | −0.458751 | − | 0.484564i | ||||
\(105\) | 96000.0 | 0.0829284 | ||||||||
\(106\) | −385708. | − | 1.49384e6i | −0.323848 | − | 1.25426i | ||||
\(107\) | − | 1.14935e6i | − | 0.938209i | −0.883143 | − | 0.469105i | \(-0.844577\pi\) | ||
0.883143 | − | 0.469105i | \(-0.155423\pi\) | |||||||
\(108\) | 478080. | + | 864078.i | 0.379515 | + | 0.685933i | ||||
\(109\) | 1.53574e6 | 1.18587 | 0.592936 | − | 0.805250i | \(-0.297969\pi\) | ||||
0.592936 | + | 0.805250i | \(0.297969\pi\) | |||||||
\(110\) | 74400.0 | − | 19210.0i | 0.0558978 | − | 0.0144328i | ||||
\(111\) | − | 61781.8i | − | 0.0451743i | ||||||
\(112\) | 1.07520e6 | + | 674209.i | 0.765306 | + | 0.479889i | ||||
\(113\) | −601694. | −0.417004 | −0.208502 | − | 0.978022i | \(-0.566859\pi\) | ||||
−0.208502 | + | 0.978022i | \(0.566859\pi\) | |||||||
\(114\) | 466560. | + | 1.80698e6i | 0.314915 | + | 1.21966i | ||||
\(115\) | − | 104725.i | − | 0.0688587i | ||||||
\(116\) | −1.42789e6 | + | 790027.i | −0.914787 | + | 0.506137i | ||||
\(117\) | −338646. | −0.211441 | ||||||||
\(118\) | 607440. | − | 156840.i | 0.369707 | − | 0.0954579i | ||||
\(119\) | − | 1.47669e6i | − | 0.876292i | ||||||
\(120\) | −115200. | + | 109063.i | −0.0666667 | + | 0.0631153i | ||||
\(121\) | 849001. | 0.479239 | ||||||||
\(122\) | −21836.0 | − | 84570.5i | −0.0120252 | − | 0.0465735i | ||||
\(123\) | − | 909748.i | − | 0.488884i | ||||||
\(124\) | −1.29792e6 | − | 2.34585e6i | −0.680743 | − | 1.23037i | ||||
\(125\) | −311500. | −0.159488 | ||||||||
\(126\) | 554400. | − | 143145.i | 0.277148 | − | 0.0715593i | ||||
\(127\) | 1.67462e6i | 0.817531i | 0.912640 | + | 0.408765i | \(0.134041\pi\) | ||||
−0.912640 | + | 0.408765i | \(0.865959\pi\) | |||||||
\(128\) | −2.05619e6 | + | 412457.i | −0.980469 | + | 0.196675i | ||||
\(129\) | −667200. | −0.310804 | ||||||||
\(130\) | 29320.0 | + | 113556.i | 0.0133455 | + | 0.0516868i | ||||
\(131\) | 2.84454e6i | 1.26531i | 0.774433 | + | 0.632656i | \(0.218035\pi\) | ||||
−0.774433 | + | 0.632656i | \(0.781965\pi\) | |||||||
\(132\) | 1.66656e6 | − | 922080.i | 0.724601 | − | 0.400910i | ||||
\(133\) | −2.33280e6 | −0.991568 | ||||||||
\(134\) | 3.05304e6 | − | 788292.i | 1.26887 | − | 0.327622i | ||||
\(135\) | − | 154300.i | − | 0.0627139i | ||||||
\(136\) | 1.67763e6 | + | 1.77203e6i | 0.666930 | + | 0.704456i | ||||
\(137\) | 3.81003e6 | 1.48172 | 0.740862 | − | 0.671658i | \(-0.234417\pi\) | ||||
0.740862 | + | 0.671658i | \(0.234417\pi\) | |||||||
\(138\) | −648960. | − | 2.51341e6i | −0.246934 | − | 0.956371i | ||||
\(139\) | 138839.i | 0.0516971i | 0.999666 | + | 0.0258485i | \(0.00822877\pi\) | ||||
−0.999666 | + | 0.0258485i | \(0.991771\pi\) | |||||||
\(140\) | −96000.0 | − | 173510.i | −0.0349854 | − | 0.0632324i | ||||
\(141\) | −234240. | −0.0835610 | ||||||||
\(142\) | −4.12272e6 | + | 1.06448e6i | −1.43986 | + | 0.371769i | ||||
\(143\) | − | 1.40809e6i | − | 0.481530i | ||||||
\(144\) | −502656. | + | 801615.i | −0.168338 | + | 0.268459i | ||||
\(145\) | 254980. | 0.0836377 | ||||||||
\(146\) | 577252. | + | 2.23569e6i | 0.185484 | + | 0.718377i | ||||
\(147\) | − | 670770.i | − | 0.211165i | ||||||
\(148\) | −111664. | + | 61781.8i | −0.0344451 | + | 0.0190579i | ||||
\(149\) | −3.27426e6 | −0.989816 | −0.494908 | − | 0.868945i | \(-0.664798\pi\) | ||||
−0.494908 | + | 0.868945i | \(0.664798\pi\) | |||||||
\(150\) | −3.72600e6 | + | 962049.i | −1.10400 | + | 0.285052i | ||||
\(151\) | − | 5.59352e6i | − | 1.62463i | −0.583220 | − | 0.812314i | \(-0.698207\pi\) | ||
0.583220 | − | 0.812314i | \(-0.301793\pi\) | |||||||
\(152\) | 2.79936e6 | − | 2.65024e6i | 0.797128 | − | 0.754664i | ||||
\(153\) | 1.10095e6 | 0.307391 | ||||||||
\(154\) | 595200. | + | 2.30520e6i | 0.162967 | + | 0.631170i | ||||
\(155\) | 418902.i | 0.112491i | ||||||||
\(156\) | 1.40736e6 | + | 2.54365e6i | 0.370708 | + | 0.670014i | ||||
\(157\) | 816794. | 0.211064 | 0.105532 | − | 0.994416i | \(-0.466345\pi\) | ||||
0.105532 | + | 0.994416i | \(0.466345\pi\) | |||||||
\(158\) | 2.40672e6 | − | 621412.i | 0.610175 | − | 0.157546i | ||||
\(159\) | 5.97536e6i | 1.48653i | ||||||||
\(160\) | 312320. | + | 99148.4i | 0.0762500 | + | 0.0242061i | ||||
\(161\) | 3.24480e6 | 0.777518 | ||||||||
\(162\) | −1.29296e6 | − | 5.00760e6i | −0.304116 | − | 1.17784i | ||||
\(163\) | − | 1.84593e6i | − | 0.426237i | −0.977026 | − | 0.213119i | \(-0.931638\pi\) | ||
0.977026 | − | 0.213119i | \(-0.0683621\pi\) | |||||||
\(164\) | −1.64427e6 | + | 909748.i | −0.372771 | + | 0.206248i | ||||
\(165\) | −297600. | −0.0662493 | ||||||||
\(166\) | 1.58136e6 | − | 408305.i | 0.345706 | − | 0.0892608i | ||||
\(167\) | 7.96515e6i | 1.71019i | 0.518471 | + | 0.855095i | \(0.326501\pi\) | ||||
−0.518471 | + | 0.855095i | \(0.673499\pi\) | |||||||
\(168\) | −3.37920e6 | − | 3.56934e6i | −0.712666 | − | 0.752766i | ||||
\(169\) | −2.67765e6 | −0.554746 | ||||||||
\(170\) | −95320.0 | − | 369173.i | −0.0194016 | − | 0.0751420i | ||||
\(171\) | − | 1.73922e6i | − | 0.347829i | ||||||
\(172\) | 667200. | + | 1.20589e6i | 0.131121 | + | 0.236986i | ||||
\(173\) | −5.12653e6 | −0.990115 | −0.495057 | − | 0.868860i | \(-0.664853\pi\) | ||||
−0.495057 | + | 0.868860i | \(0.664853\pi\) | |||||||
\(174\) | 6.11952e6 | − | 1.58005e6i | 1.16163 | − | 0.299933i | ||||
\(175\) | − | 4.81025e6i | − | 0.897538i | ||||||
\(176\) | −3.33312e6 | − | 2.09005e6i | −0.611382 | − | 0.383370i | ||||
\(177\) | −2.42976e6 | −0.438171 | ||||||||
\(178\) | 621476. | + | 2.40697e6i | 0.110196 | + | 0.426786i | ||||
\(179\) | − | 2.33411e6i | − | 0.406969i | −0.979078 | − | 0.203485i | \(-0.934773\pi\) | ||
0.979078 | − | 0.203485i | \(-0.0652267\pi\) | |||||||
\(180\) | 129360. | − | 71572.7i | 0.0221811 | − | 0.0122724i | ||||
\(181\) | 9.69156e6 | 1.63440 | 0.817199 | − | 0.576355i | \(-0.195525\pi\) | ||||
0.817199 | + | 0.576355i | \(0.195525\pi\) | |||||||
\(182\) | −3.51840e6 | + | 908447.i | −0.583621 | + | 0.150690i | ||||
\(183\) | 338282.i | 0.0551983i | ||||||||
\(184\) | −3.89376e6 | + | 3.68634e6i | −0.625051 | + | 0.591754i | ||||
\(185\) | 19940.0 | 0.00314927 | ||||||||
\(186\) | 2.59584e6 | + | 1.00536e7i | 0.403403 | + | 1.56237i | ||||
\(187\) | 4.57774e6i | 0.700046i | ||||||||
\(188\) | 234240. | + | 423364.i | 0.0352523 | + | 0.0637147i | ||||
\(189\) | 4.78080e6 | 0.708134 | ||||||||
\(190\) | −583200. | + | 150582.i | −0.0850270 | + | 0.0219539i | ||||
\(191\) | − | 1.14164e7i | − | 1.63844i | −0.573479 | − | 0.819220i | \(-0.694407\pi\) | ||
0.573479 | − | 0.819220i | \(-0.305593\pi\) | |||||||
\(192\) | 8.11008e6 | + | 444185.i | 1.14583 | + | 0.0627567i | ||||
\(193\) | −2.43033e6 | −0.338060 | −0.169030 | − | 0.985611i | \(-0.554064\pi\) | ||||
−0.169030 | + | 0.985611i | \(0.554064\pi\) | |||||||
\(194\) | −2.91417e6 | − | 1.12865e7i | −0.399126 | − | 1.54581i | ||||
\(195\) | − | 454223.i | − | 0.0612584i | ||||||
\(196\) | −1.21234e6 | + | 670770.i | −0.161012 | + | 0.0890851i | ||||
\(197\) | −2.23065e6 | −0.291764 | −0.145882 | − | 0.989302i | \(-0.546602\pi\) | ||||
−0.145882 | + | 0.989302i | \(0.546602\pi\) | |||||||
\(198\) | −1.71864e6 | + | 443751.i | −0.221406 | + | 0.0571668i | ||||
\(199\) | 4.89576e6i | 0.621242i | 0.950534 | + | 0.310621i | \(0.100537\pi\) | ||||
−0.950534 | + | 0.310621i | \(0.899463\pi\) | |||||||
\(200\) | 5.46480e6 | + | 5.77229e6i | 0.683100 | + | 0.721537i | ||||
\(201\) | −1.22122e7 | −1.50385 | ||||||||
\(202\) | −1.27832e6 | − | 4.95090e6i | −0.155090 | − | 0.600661i | ||||
\(203\) | 7.90027e6i | 0.944395i | ||||||||
\(204\) | −4.57536e6 | − | 8.26947e6i | −0.538933 | − | 0.974063i | ||||
\(205\) | 293620. | 0.0340819 | ||||||||
\(206\) | −1.07602e7 | + | 2.77826e6i | −1.23088 | + | 0.317813i | ||||
\(207\) | 2.41916e6i | 0.272743i | ||||||||
\(208\) | 3.19002e6 | − | 5.08730e6i | 0.354489 | − | 0.565324i | ||||
\(209\) | 7.23168e6 | 0.792137 | ||||||||
\(210\) | 192000. | + | 743613.i | 0.0207321 | + | 0.0802951i | ||||
\(211\) | 3.90951e6i | 0.416174i | 0.978110 | + | 0.208087i | \(0.0667238\pi\) | ||||
−0.978110 | + | 0.208087i | \(0.933276\pi\) | |||||||
\(212\) | 1.07998e7 | − | 5.97536e6i | 1.13347 | − | 0.627129i | ||||
\(213\) | 1.64909e7 | 1.70650 | ||||||||
\(214\) | 8.90280e6 | − | 2.29869e6i | 0.908417 | − | 0.234552i | ||||
\(215\) | − | 215338.i | − | 0.0216673i | ||||||
\(216\) | −5.73696e6 | + | 5.43135e6i | −0.569273 | + | 0.538947i | ||||
\(217\) | −1.29792e7 | −1.27019 | ||||||||
\(218\) | 3.07148e6 | + | 1.18958e7i | 0.296468 | + | 1.14822i | ||||
\(219\) | − | 8.94275e6i | − | 0.851410i | ||||||
\(220\) | 297600. | + | 537880.i | 0.0279489 | + | 0.0505146i | ||||
\(221\) | −6.98696e6 | −0.647308 | ||||||||
\(222\) | 478560. | − | 123564.i | 0.0437399 | − | 0.0112936i | ||||
\(223\) | 3.33114e6i | 0.300385i | 0.988657 | + | 0.150192i | \(0.0479893\pi\) | ||||
−0.988657 | + | 0.150192i | \(0.952011\pi\) | |||||||
\(224\) | −3.07200e6 | + | 9.67688e6i | −0.273324 | + | 0.860977i | ||||
\(225\) | 3.58628e6 | 0.314844 | ||||||||
\(226\) | −1.20339e6 | − | 4.66070e6i | −0.104251 | − | 0.403763i | ||||
\(227\) | − | 1.35033e7i | − | 1.15442i | −0.816597 | − | 0.577208i | \(-0.804142\pi\) | ||
0.816597 | − | 0.577208i | \(-0.195858\pi\) | |||||||
\(228\) | −1.30637e7 | + | 7.22792e6i | −1.10220 | + | 0.609830i | ||||
\(229\) | 1.59598e6 | 0.132899 | 0.0664493 | − | 0.997790i | \(-0.478833\pi\) | ||||
0.0664493 | + | 0.997790i | \(0.478833\pi\) | |||||||
\(230\) | 811200. | − | 209451.i | 0.0666721 | − | 0.0172147i | ||||
\(231\) | − | 9.22080e6i | − | 0.748053i | ||||||
\(232\) | −8.97530e6 | − | 9.48032e6i | −0.718762 | − | 0.759205i | ||||
\(233\) | 8.04383e6 | 0.635909 | 0.317954 | − | 0.948106i | \(-0.397004\pi\) | ||||
0.317954 | + | 0.948106i | \(0.397004\pi\) | |||||||
\(234\) | −677292. | − | 2.62314e6i | −0.0528601 | − | 0.204726i | ||||
\(235\) | − | 75600.6i | − | 0.00582535i | ||||||
\(236\) | 2.42976e6 | + | 4.39153e6i | 0.184853 | + | 0.334103i | ||||
\(237\) | −9.62688e6 | −0.723170 | ||||||||
\(238\) | 1.14384e7 | − | 2.95338e6i | 0.848466 | − | 0.219073i | ||||
\(239\) | 1.12532e7i | 0.824296i | 0.911117 | + | 0.412148i | \(0.135221\pi\) | ||||
−0.911117 | + | 0.412148i | \(0.864779\pi\) | |||||||
\(240\) | −1.07520e6 | − | 674209.i | −0.0777778 | − | 0.0487709i | ||||
\(241\) | 5.05104e6 | 0.360853 | 0.180426 | − | 0.983589i | \(-0.442252\pi\) | ||||
0.180426 | + | 0.983589i | \(0.442252\pi\) | |||||||
\(242\) | 1.69800e6 | + | 6.57633e6i | 0.119810 | + | 0.464021i | ||||
\(243\) | 8.78197e6i | 0.612031i | ||||||||
\(244\) | 611408. | − | 338282.i | 0.0420883 | − | 0.0232868i | ||||
\(245\) | 216490. | 0.0147211 | ||||||||
\(246\) | 7.04688e6 | − | 1.81950e6i | 0.473360 | − | 0.122221i | ||||
\(247\) | 1.10376e7i | 0.732462i | ||||||||
\(248\) | 1.55750e7 | − | 1.47453e7i | 1.02111 | − | 0.966718i | ||||
\(249\) | −6.32544e6 | −0.409725 | ||||||||
\(250\) | −623000. | − | 2.41287e6i | −0.0398720 | − | 0.154424i | ||||
\(251\) | 4.71590e6i | 0.298225i | 0.988820 | + | 0.149112i | \(0.0476416\pi\) | ||||
−0.988820 | + | 0.149112i | \(0.952358\pi\) | |||||||
\(252\) | 2.21760e6 | + | 4.00807e6i | 0.138574 | + | 0.250457i | ||||
\(253\) | −1.00589e7 | −0.621138 | ||||||||
\(254\) | −1.29715e7 | + | 3.34923e6i | −0.791571 | + | 0.204383i | ||||
\(255\) | 1.47669e6i | 0.0890572i | ||||||||
\(256\) | −7.30726e6 | − | 1.51023e7i | −0.435547 | − | 0.900166i | ||||
\(257\) | 2.34552e7 | 1.38178 | 0.690892 | − | 0.722958i | \(-0.257218\pi\) | ||||
0.690892 | + | 0.722958i | \(0.257218\pi\) | |||||||
\(258\) | −1.33440e6 | − | 5.16811e6i | −0.0777011 | − | 0.300935i | ||||
\(259\) | 617818.i | 0.0355600i | ||||||||
\(260\) | −820960. | + | 454223.i | −0.0467091 | + | 0.0258434i | ||||
\(261\) | −5.89004e6 | −0.331281 | ||||||||
\(262\) | −2.20337e7 | + | 5.68907e6i | −1.22513 | + | 0.316328i | ||||
\(263\) | − | 2.16993e7i | − | 1.19283i | −0.802676 | − | 0.596415i | \(-0.796591\pi\) | ||
0.802676 | − | 0.596415i | \(-0.203409\pi\) | |||||||
\(264\) | 1.04755e7 | + | 1.10650e7i | 0.569330 | + | 0.601365i | ||||
\(265\) | −1.92854e6 | −0.103631 | ||||||||
\(266\) | −4.66560e6 | − | 1.80698e7i | −0.247892 | − | 0.960082i | ||||
\(267\) | − | 9.62786e6i | − | 0.505820i | ||||||
\(268\) | 1.22122e7 | + | 2.20722e7i | 0.634436 | + | 1.14668i | ||||
\(269\) | −2.94278e7 | −1.51182 | −0.755911 | − | 0.654674i | \(-0.772806\pi\) | ||||
−0.755911 | + | 0.654674i | \(0.772806\pi\) | |||||||
\(270\) | 1.19520e6 | − | 308599.i | 0.0607225 | − | 0.0156785i | ||||
\(271\) | − | 8.51474e6i | − | 0.427822i | −0.976853 | − | 0.213911i | \(-0.931380\pi\) | ||
0.976853 | − | 0.213911i | \(-0.0686203\pi\) | |||||||
\(272\) | −1.03708e7 | + | 1.65389e7i | −0.515355 | + | 0.821866i | ||||
\(273\) | 1.40736e7 | 0.691699 | ||||||||
\(274\) | 7.62007e6 | + | 2.95124e7i | 0.370431 | + | 1.43467i | ||||
\(275\) | 1.49118e7i | 0.717019i | ||||||||
\(276\) | 1.81709e7 | − | 1.00536e7i | 0.864269 | − | 0.478185i | ||||
\(277\) | 2.76226e7 | 1.29965 | 0.649824 | − | 0.760085i | \(-0.274843\pi\) | ||||
0.649824 | + | 0.760085i | \(0.274843\pi\) | |||||||
\(278\) | −1.07544e6 | + | 277677.i | −0.0500555 | + | 0.0129243i | ||||
\(279\) | − | 9.67663e6i | − | 0.445566i | ||||||
\(280\) | 1.15200e6 | − | 1.09063e6i | 0.0524781 | − | 0.0496826i | ||||
\(281\) | 8.64008e6 | 0.389403 | 0.194701 | − | 0.980863i | \(-0.437626\pi\) | ||||
0.194701 | + | 0.980863i | \(0.437626\pi\) | |||||||
\(282\) | −468480. | − | 1.81442e6i | −0.0208903 | − | 0.0809076i | ||||
\(283\) | − | 1.27350e7i | − | 0.561873i | −0.959726 | − | 0.280937i | \(-0.909355\pi\) | ||
0.959726 | − | 0.280937i | \(-0.0906450\pi\) | |||||||
\(284\) | −1.64909e7 | − | 2.98055e7i | −0.719928 | − | 1.30119i | ||||
\(285\) | 2.33280e6 | 0.100773 | ||||||||
\(286\) | 1.09070e7 | − | 2.81619e6i | 0.466239 | − | 0.120382i | ||||
\(287\) | 9.09748e6i | 0.384836i | ||||||||
\(288\) | −7.21459e6 | − | 2.29033e6i | −0.302019 | − | 0.0958783i | ||||
\(289\) | −1.42281e6 | −0.0589460 | ||||||||
\(290\) | 509960. | + | 1.97507e6i | 0.0209094 | + | 0.0809819i | ||||
\(291\) | 4.51462e7i | 1.83207i | ||||||||
\(292\) | −1.61631e7 | + | 8.94275e6i | −0.649195 | + | 0.359189i | ||||
\(293\) | −4.45415e7 | −1.77077 | −0.885385 | − | 0.464859i | \(-0.846105\pi\) | ||||
−0.885385 | + | 0.464859i | \(0.846105\pi\) | |||||||
\(294\) | 5.19576e6 | − | 1.34154e6i | 0.204459 | − | 0.0527912i | ||||
\(295\) | − | 784202.i | − | 0.0305465i | ||||||
\(296\) | −701888. | − | 741382.i | −0.0270640 | − | 0.0285869i | ||||
\(297\) | −1.48205e7 | −0.565709 | ||||||||
\(298\) | −6.54852e6 | − | 2.53623e7i | −0.247454 | − | 0.958386i | ||||
\(299\) | − | 1.53528e7i | − | 0.574345i | ||||||
\(300\) | −1.49040e7 | − | 2.69374e7i | −0.552000 | − | 0.997681i | ||||
\(301\) | 6.67200e6 | 0.244656 | ||||||||
\(302\) | 4.33272e7 | − | 1.11870e7i | 1.57304 | − | 0.406157i | ||||
\(303\) | 1.98036e7i | 0.711895i | ||||||||
\(304\) | 2.61274e7 | + | 1.63833e7i | 0.929983 | + | 0.583150i | ||||
\(305\) | −109180. | −0.00384808 | ||||||||
\(306\) | 2.20189e6 | + | 8.52789e6i | 0.0768479 | + | 0.297630i | ||||
\(307\) | − | 4.89051e7i | − | 1.69020i | −0.534606 | − | 0.845102i | \(-0.679540\pi\) | ||
0.534606 | − | 0.845102i | \(-0.320460\pi\) | |||||||
\(308\) | −1.66656e7 | + | 9.22080e6i | −0.570386 | + | 0.315585i | ||||
\(309\) | 4.30406e7 | 1.45883 | ||||||||
\(310\) | −3.24480e6 | + | 837804.i | −0.108919 | + | 0.0281227i | ||||
\(311\) | 5.00220e7i | 1.66295i | 0.555559 | + | 0.831477i | \(0.312504\pi\) | ||||
−0.555559 | + | 0.831477i | \(0.687496\pi\) | |||||||
\(312\) | −1.68883e7 | + | 1.59887e7i | −0.556061 | + | 0.526440i | ||||
\(313\) | 1.12719e6 | 0.0367589 | 0.0183795 | − | 0.999831i | \(-0.494149\pi\) | ||||
0.0183795 | + | 0.999831i | \(0.494149\pi\) | |||||||
\(314\) | 1.63359e6 | + | 6.32686e6i | 0.0527659 | + | 0.204362i | ||||
\(315\) | − | 715727.i | − | 0.0228990i | ||||||
\(316\) | 9.62688e6 | + | 1.73995e7i | 0.305087 | + | 0.551413i | ||||
\(317\) | 3.44882e7 | 1.08266 | 0.541330 | − | 0.840810i | \(-0.317921\pi\) | ||||
0.541330 | + | 0.840810i | \(0.317921\pi\) | |||||||
\(318\) | −4.62850e7 | + | 1.19507e7i | −1.43932 | + | 0.371632i | ||||
\(319\) | − | 2.44908e7i | − | 0.754452i | ||||||
\(320\) | −143360. | + | 2.61752e6i | −0.00437500 | + | 0.0798803i | ||||
\(321\) | −3.56112e7 | −1.07664 | ||||||||
\(322\) | 6.48960e6 | + | 2.51341e7i | 0.194379 | + | 0.752828i | ||||
\(323\) | − | 3.58836e7i | − | 1.06485i | ||||||
\(324\) | 3.62028e7 | − | 2.00304e7i | 1.06441 | − | 0.588918i | ||||
\(325\) | −2.27596e7 | −0.663003 | ||||||||
\(326\) | 1.42985e7 | − | 3.69185e6i | 0.412702 | − | 0.106559i | ||||
\(327\) | − | 4.75831e7i | − | 1.36085i | ||||||
\(328\) | −1.03354e7 | − | 1.09170e7i | −0.292891 | − | 0.309372i | ||||
\(329\) | 2.34240e6 | 0.0657769 | ||||||||
\(330\) | −595200. | − | 2.30520e6i | −0.0165623 | − | 0.0641456i | ||||
\(331\) | 4.02696e7i | 1.11044i | 0.831705 | + | 0.555218i | \(0.187365\pi\) | ||||
−0.831705 | + | 0.555218i | \(0.812635\pi\) | |||||||
\(332\) | 6.32544e6 | + | 1.14326e7i | 0.172853 | + | 0.312413i | ||||
\(333\) | −460614. | −0.0124740 | ||||||||
\(334\) | −6.16978e7 | + | 1.59303e7i | −1.65588 | + | 0.427547i | ||||
\(335\) | − | 3.94146e6i | − | 0.104839i | ||||||
\(336\) | 2.08896e7 | − | 3.33139e7i | 0.550696 | − | 0.878228i | ||||
\(337\) | −3.42531e7 | −0.894973 | −0.447487 | − | 0.894291i | \(-0.647681\pi\) | ||||
−0.447487 | + | 0.894291i | \(0.647681\pi\) | |||||||
\(338\) | −5.35531e6 | − | 2.07410e7i | −0.138687 | − | 0.537131i | ||||
\(339\) | 1.86428e7i | 0.478533i | ||||||||
\(340\) | 2.66896e6 | − | 1.47669e6i | 0.0679056 | − | 0.0375710i | ||||
\(341\) | 4.02355e7 | 1.01472 | ||||||||
\(342\) | 1.34719e7 | − | 3.47843e6i | 0.336784 | − | 0.0869572i | ||||
\(343\) | 4.31599e7i | 1.06954i | ||||||||
\(344\) | −8.00640e6 | + | 7.57989e6i | −0.196681 | + | 0.186203i | ||||
\(345\) | −3.24480e6 | −0.0790188 | ||||||||
\(346\) | −1.02531e7 | − | 3.97100e7i | −0.247529 | − | 0.958674i | ||||
\(347\) | 5.45496e7i | 1.30558i | 0.757539 | + | 0.652790i | \(0.226401\pi\) | ||||
−0.757539 | + | 0.652790i | \(0.773599\pi\) | |||||||
\(348\) | 2.44781e7 | + | 4.42415e7i | 0.580817 | + | 1.04976i | ||||
\(349\) | 4.70009e7 | 1.10568 | 0.552840 | − | 0.833287i | \(-0.313544\pi\) | ||||
0.552840 | + | 0.833287i | \(0.313544\pi\) | |||||||
\(350\) | 3.72600e7 | − | 9.62049e6i | 0.869038 | − | 0.224385i | ||||
\(351\) | − | 2.26203e7i | − | 0.523091i | ||||||
\(352\) | 9.52320e6 | − | 2.99983e7i | 0.218351 | − | 0.687811i | ||||
\(353\) | −1.27231e7 | −0.289248 | −0.144624 | − | 0.989487i | \(-0.546197\pi\) | ||||
−0.144624 | + | 0.989487i | \(0.546197\pi\) | |||||||
\(354\) | −4.85952e6 | − | 1.88208e7i | −0.109543 | − | 0.424257i | ||||
\(355\) | 5.32241e6i | 0.118966i | ||||||||
\(356\) | −1.74013e7 | + | 9.62786e6i | −0.385685 | + | 0.213393i | ||||
\(357\) | −4.57536e7 | −1.00559 | ||||||||
\(358\) | 1.80799e7 | − | 4.66822e6i | 0.394046 | − | 0.101742i | ||||
\(359\) | − | 2.02153e7i | − | 0.436915i | −0.975846 | − | 0.218457i | \(-0.929898\pi\) | ||
0.975846 | − | 0.218457i | \(-0.0701025\pi\) | |||||||
\(360\) | 813120. | + | 858873.i | 0.0174280 | + | 0.0184086i | ||||
\(361\) | −9.64116e6 | −0.204931 | ||||||||
\(362\) | 1.93831e7 | + | 7.50705e7i | 0.408600 | + | 1.58250i | ||||
\(363\) | − | 2.63053e7i | − | 0.549951i | ||||||
\(364\) | −1.40736e7 | − | 2.54365e7i | −0.291811 | − | 0.527416i | ||||
\(365\) | 2.88626e6 | 0.0593549 | ||||||||
\(366\) | −2.62032e6 | + | 676564.i | −0.0534455 | + | 0.0137996i | ||||
\(367\) | − | 1.11057e7i | − | 0.224672i | −0.993670 | − | 0.112336i | \(-0.964167\pi\) | ||
0.993670 | − | 0.112336i | \(-0.0358333\pi\) | |||||||
\(368\) | −3.63418e7 | − | 2.27883e7i | −0.729227 | − | 0.457265i | ||||
\(369\) | −6.78262e6 | −0.134995 | ||||||||
\(370\) | 39880.0 | + | 154455.i | 0.000787318 | + | 0.00304927i | ||||
\(371\) | − | 5.97536e7i | − | 1.17015i | ||||||
\(372\) | −7.26835e7 | + | 4.02146e7i | −1.41191 | + | 0.781186i | ||||
\(373\) | 687146. | 0.0132411 | 0.00662053 | − | 0.999978i | \(-0.497893\pi\) | ||||
0.00662053 | + | 0.999978i | \(0.497893\pi\) | |||||||
\(374\) | −3.54590e7 | + | 9.15548e6i | −0.677817 | + | 0.175011i | ||||
\(375\) | 9.65147e6i | 0.183021i | ||||||||
\(376\) | −2.81088e6 | + | 2.66114e6i | −0.0528785 | + | 0.0500616i | ||||
\(377\) | 3.73801e7 | 0.697615 | ||||||||
\(378\) | 9.56160e6 | + | 3.70319e7i | 0.177033 | + | 0.685647i | ||||
\(379\) | 1.48499e7i | 0.272775i | 0.990656 | + | 0.136388i | \(0.0435492\pi\) | ||||
−0.990656 | + | 0.136388i | \(0.956451\pi\) | |||||||
\(380\) | −2.33280e6 | − | 4.21628e6i | −0.0425135 | − | 0.0768385i | ||||
\(381\) | 5.18861e7 | 0.938158 | ||||||||
\(382\) | 8.84314e7 | − | 2.28329e7i | 1.58641 | − | 0.409610i | ||||
\(383\) | − | 3.35885e7i | − | 0.597853i | −0.954276 | − | 0.298926i | \(-0.903372\pi\) | ||
0.954276 | − | 0.298926i | \(-0.0966285\pi\) | |||||||
\(384\) | 1.27795e7 | + | 6.37088e7i | 0.225694 | + | 1.12514i | ||||
\(385\) | 2.97600e6 | 0.0521496 | ||||||||
\(386\) | −4.86067e6 | − | 1.88253e7i | −0.0845150 | − | 0.327325i | ||||
\(387\) | 4.97430e6i | 0.0858222i | ||||||||
\(388\) | 8.15968e7 | − | 4.51462e7i | 1.39694 | − | 0.772904i | ||||
\(389\) | −1.01122e8 | −1.71789 | −0.858946 | − | 0.512066i | \(-0.828880\pi\) | ||||
−0.858946 | + | 0.512066i | \(0.828880\pi\) | |||||||
\(390\) | 3.51840e6 | − | 908447.i | 0.0593132 | − | 0.0153146i | ||||
\(391\) | 4.99122e7i | 0.834980i | ||||||||
\(392\) | −7.62045e6 | − | 8.04924e6i | −0.126509 | − | 0.133628i | ||||
\(393\) | 8.81347e7 | 1.45201 | ||||||||
\(394\) | −4.46129e6 | − | 1.72785e7i | −0.0729410 | − | 0.282499i | ||||
\(395\) | − | 3.10706e6i | − | 0.0504149i | ||||||
\(396\) | −6.87456e6 | − | 1.24250e7i | −0.110703 | − | 0.200084i | ||||
\(397\) | −3.48266e7 | −0.556595 | −0.278297 | − | 0.960495i | \(-0.589770\pi\) | ||||
−0.278297 | + | 0.960495i | \(0.589770\pi\) | |||||||
\(398\) | −3.79224e7 | + | 9.79152e6i | −0.601515 | + | 0.155311i | ||||
\(399\) | 7.22792e7i | 1.13787i | ||||||||
\(400\) | −3.37824e7 | + | 5.38747e7i | −0.527850 | + | 0.841793i | ||||
\(401\) | −6.88398e7 | −1.06760 | −0.533798 | − | 0.845612i | \(-0.679236\pi\) | ||||
−0.533798 | + | 0.845612i | \(0.679236\pi\) | |||||||
\(402\) | −2.44243e7 | − | 9.45950e7i | −0.375962 | − | 1.45610i | ||||
\(403\) | 6.14110e7i | 0.938277i | ||||||||
\(404\) | 3.57928e7 | − | 1.98036e7i | 0.542815 | − | 0.300331i | ||||
\(405\) | −6.46479e6 | −0.0973171 | ||||||||
\(406\) | −6.11952e7 | + | 1.58005e7i | −0.914406 | + | 0.236099i | ||||
\(407\) | − | 1.91524e6i | − | 0.0284079i | ||||||
\(408\) | 5.49043e7 | − | 5.19795e7i | 0.808399 | − | 0.765335i | ||||
\(409\) | 4.59959e7 | 0.672278 | 0.336139 | − | 0.941812i | \(-0.390879\pi\) | ||||
0.336139 | + | 0.941812i | \(0.390879\pi\) | |||||||
\(410\) | 587240. | + | 2.27437e6i | 0.00852048 | + | 0.0329997i | ||||
\(411\) | − | 1.18050e8i | − | 1.70035i | ||||||
\(412\) | −4.30406e7 | − | 7.77913e7i | −0.615442 | − | 1.11234i | ||||
\(413\) | 2.42976e7 | 0.344916 | ||||||||
\(414\) | −1.87387e7 | + | 4.83832e6i | −0.264082 | + | 0.0681857i | ||||
\(415\) | − | 2.04153e6i | − | 0.0285635i | ||||||
\(416\) | 4.57861e7 | + | 1.45352e7i | 0.635995 | + | 0.201902i | ||||
\(417\) | 4.30176e6 | 0.0593250 | ||||||||
\(418\) | 1.44634e7 | + | 5.60164e7i | 0.198034 | + | 0.766983i | ||||
\(419\) | 2.71153e7i | 0.368615i | 0.982869 | + | 0.184307i | \(0.0590042\pi\) | ||||
−0.982869 | + | 0.184307i | \(0.940996\pi\) | |||||||
\(420\) | −5.37600e6 | + | 2.97445e6i | −0.0725624 | + | 0.0401475i | ||||
\(421\) | −9.42078e7 | −1.26253 | −0.631263 | − | 0.775569i | \(-0.717463\pi\) | ||||
−0.631263 | + | 0.775569i | \(0.717463\pi\) | |||||||
\(422\) | −3.02830e7 | + | 7.81903e6i | −0.402959 | + | 0.104044i | ||||
\(423\) | 1.74637e6i | 0.0230737i | ||||||||
\(424\) | 6.78846e7 | + | 7.17044e7i | 0.890582 | + | 0.940693i | ||||
\(425\) | 7.39922e7 | 0.963871 | ||||||||
\(426\) | 3.29818e7 | + | 1.27738e8i | 0.426624 | + | 1.65231i | ||||
\(427\) | − | 3.38282e6i | − | 0.0434505i | ||||||
\(428\) | 3.56112e7 | + | 6.43634e7i | 0.454209 | + | 0.820933i | ||||
\(429\) | −4.36282e7 | −0.552580 | ||||||||
\(430\) | 1.66800e6 | − | 430676.i | 0.0209793 | − | 0.00541683i | ||||
\(431\) | − | 5.19187e7i | − | 0.648473i | −0.945976 | − | 0.324236i | \(-0.894893\pi\) | ||
0.945976 | − | 0.324236i | \(-0.105107\pi\) | |||||||
\(432\) | −5.35450e7 | − | 3.35756e7i | −0.664152 | − | 0.416459i | ||||
\(433\) | 8.40210e7 | 1.03496 | 0.517481 | − | 0.855695i | \(-0.326870\pi\) | ||||
0.517481 | + | 0.855695i | \(0.326870\pi\) | |||||||
\(434\) | −2.59584e7 | − | 1.00536e8i | −0.317548 | − | 1.22986i | ||||
\(435\) | − | 7.90027e6i | − | 0.0959785i | ||||||
\(436\) | −8.60013e7 | + | 4.75831e7i | −1.03764 | + | 0.574108i | ||||
\(437\) | 7.88486e7 | 0.944822 | ||||||||
\(438\) | 6.92702e7 | − | 1.78855e7i | 0.824374 | − | 0.212852i | ||||
\(439\) | − | 1.48115e8i | − | 1.75068i | −0.483512 | − | 0.875338i | \(-0.660639\pi\) | ||
0.483512 | − | 0.875338i | \(-0.339361\pi\) | |||||||
\(440\) | −3.57120e6 | + | 3.38096e6i | −0.0419234 | + | 0.0396901i | ||||
\(441\) | −5.00092e6 | −0.0583088 | ||||||||
\(442\) | −1.39739e7 | − | 5.41207e7i | −0.161827 | − | 0.626754i | ||||
\(443\) | 8.03735e7i | 0.924489i | 0.886752 | + | 0.462245i | \(0.152956\pi\) | ||||
−0.886752 | + | 0.462245i | \(0.847044\pi\) | |||||||
\(444\) | 1.91424e6 | + | 3.45978e6i | 0.0218699 | + | 0.0395275i | ||||
\(445\) | 3.10738e6 | 0.0352626 | ||||||||
\(446\) | −2.58029e7 | + | 6.66227e6i | −0.290846 | + | 0.0750962i | ||||
\(447\) | 1.01449e8i | 1.13586i | ||||||||
\(448\) | −8.11008e7 | − | 4.44185e6i | −0.901968 | − | 0.0494003i | ||||
\(449\) | −8.80925e7 | −0.973196 | −0.486598 | − | 0.873626i | \(-0.661762\pi\) | ||||
−0.486598 | + | 0.873626i | \(0.661762\pi\) | |||||||
\(450\) | 7.17255e6 | + | 2.77792e7i | 0.0787111 | + | 0.304847i | ||||
\(451\) | − | 2.82022e7i | − | 0.307435i | ||||||
\(452\) | 3.36949e7 | − | 1.86428e7i | 0.364879 | − | 0.201881i | ||||
\(453\) | −1.73309e8 | −1.86434 | ||||||||
\(454\) | 1.04596e8 | − | 2.70066e7i | 1.11776 | − | 0.288604i | ||||
\(455\) | 4.54223e6i | 0.0482209i | ||||||||
\(456\) | −8.21146e7 | − | 8.67350e7i | −0.866015 | − | 0.914745i | ||||
\(457\) | −3.75423e7 | −0.393344 | −0.196672 | − | 0.980469i | \(-0.563013\pi\) | ||||
−0.196672 | + | 0.980469i | \(0.563013\pi\) | |||||||
\(458\) | 3.19196e6 | + | 1.23624e7i | 0.0332247 | + | 0.128679i | ||||
\(459\) | 7.35392e7i | 0.760468i | ||||||||
\(460\) | 3.24480e6 | + | 5.86463e6i | 0.0333361 | + | 0.0602514i | ||||
\(461\) | 1.15260e8 | 1.17646 | 0.588228 | − | 0.808695i | \(-0.299826\pi\) | ||||
0.588228 | + | 0.808695i | \(0.299826\pi\) | |||||||
\(462\) | 7.14240e7 | − | 1.84416e7i | 0.724300 | − | 0.187013i | ||||
\(463\) | − | 1.03415e7i | − | 0.104194i | −0.998642 | − | 0.0520970i | \(-0.983410\pi\) | ||
0.998642 | − | 0.0520970i | \(-0.0165905\pi\) | |||||||
\(464\) | 5.54836e7 | − | 8.84830e7i | 0.555407 | − | 0.885739i | ||||
\(465\) | 1.29792e7 | 0.129089 | ||||||||
\(466\) | 1.60877e7 | + | 6.23072e7i | 0.158977 | + | 0.615716i | ||||
\(467\) | 1.64223e8i | 1.61243i | 0.591620 | + | 0.806217i | \(0.298489\pi\) | ||||
−0.591620 | + | 0.806217i | \(0.701511\pi\) | |||||||
\(468\) | 1.89642e7 | − | 1.04926e7i | 0.185011 | − | 0.102363i | ||||
\(469\) | 1.22122e8 | 1.18379 | ||||||||
\(470\) | 585600. | − | 151201.i | 0.00564037 | − | 0.00145634i | ||||
\(471\) | − | 2.53074e7i | − | 0.242206i | ||||||
\(472\) | −2.91571e7 | + | 2.76039e7i | −0.277280 | + | 0.262509i | ||||
\(473\) | −2.06832e7 | −0.195449 | ||||||||
\(474\) | −1.92538e7 | − | 7.45695e7i | −0.180793 | − | 0.700207i | ||||
\(475\) | − | 1.16889e8i | − | 1.09067i | ||||||
\(476\) | 4.57536e7 | + | 8.26947e7i | 0.424233 | + | 0.766755i | ||||
\(477\) | 4.45493e7 | 0.410474 | ||||||||
\(478\) | −8.71670e7 | + | 2.25064e7i | −0.798121 | + | 0.206074i | ||||
\(479\) | 7.76230e7i | 0.706291i | 0.935568 | + | 0.353146i | \(0.114888\pi\) | ||||
−0.935568 | + | 0.353146i | \(0.885112\pi\) | |||||||
\(480\) | 3.07200e6 | − | 9.67688e6i | 0.0277778 | − | 0.0875007i | ||||
\(481\) | 2.92320e6 | 0.0262678 | ||||||||
\(482\) | 1.01021e7 | + | 3.91252e7i | 0.0902132 | + | 0.349394i | ||||
\(483\) | − | 1.00536e8i | − | 0.892241i | ||||||
\(484\) | −4.75441e7 | + | 2.63053e7i | −0.419334 | + | 0.232011i | ||||
\(485\) | −1.45709e7 | −0.127720 | ||||||||
\(486\) | −6.80249e7 | + | 1.75639e7i | −0.592596 | + | 0.153008i | ||||
\(487\) | − | 1.08071e7i | − | 0.0935670i | −0.998905 | − | 0.0467835i | \(-0.985103\pi\) | ||
0.998905 | − | 0.0467835i | \(-0.0148971\pi\) | |||||||
\(488\) | 3.84314e6 | + | 4.05938e6i | 0.0330694 | + | 0.0349302i | ||||
\(489\) | −5.71939e7 | −0.489129 | ||||||||
\(490\) | 432980. | + | 1.67692e6i | 0.00368027 | + | 0.0142536i | ||||
\(491\) | − | 1.85067e8i | − | 1.56345i | −0.623624 | − | 0.781724i | \(-0.714340\pi\) | ||
0.623624 | − | 0.781724i | \(-0.285660\pi\) | |||||||
\(492\) | 2.81875e7 | + | 5.09459e7i | 0.236680 | + | 0.427774i | ||||
\(493\) | −1.21523e8 | −1.01419 | ||||||||
\(494\) | −8.54971e7 | + | 2.20753e7i | −0.709203 | + | 0.183115i | ||||
\(495\) | 2.21875e6i | 0.0182934i | ||||||||
\(496\) | 1.45367e8 | + | 9.11530e7i | 1.19130 | + | 0.747010i | ||||
\(497\) | −1.64909e8 | −1.34331 | ||||||||
\(498\) | −1.26509e7 | − | 4.89966e7i | −0.102431 | − | 0.396715i | ||||
\(499\) | − | 6.83704e7i | − | 0.550258i | −0.961407 | − | 0.275129i | \(-0.911279\pi\) | ||
0.961407 | − | 0.275129i | \(-0.0887206\pi\) | |||||||
\(500\) | 1.74440e7 | − | 9.65147e6i | 0.139552 | − | 0.0772118i | ||||
\(501\) | 2.46791e8 | 1.96253 | ||||||||
\(502\) | −3.65292e7 | + | 9.43180e6i | −0.288755 | + | 0.0745561i | ||||
\(503\) | 1.31562e7i | 0.103377i | 0.998663 | + | 0.0516887i | \(0.0164604\pi\) | ||||
−0.998663 | + | 0.0516887i | \(0.983540\pi\) | |||||||
\(504\) | −2.66112e7 | + | 2.51936e7i | −0.207861 | + | 0.196788i | ||||
\(505\) | −6.39158e6 | −0.0496288 | ||||||||
\(506\) | −2.01178e7 | − | 7.79157e7i | −0.155284 | − | 0.601414i | ||||
\(507\) | 8.29640e7i | 0.636599i | ||||||||
\(508\) | −5.18861e7 | − | 9.37785e7i | −0.395785 | − | 0.715339i | ||||
\(509\) | 1.34186e8 | 1.01755 | 0.508775 | − | 0.860900i | \(-0.330099\pi\) | ||||
0.508775 | + | 0.860900i | \(0.330099\pi\) | |||||||
\(510\) | −1.14384e7 | + | 2.95338e6i | −0.0862293 | + | 0.0222643i | ||||
\(511\) | 8.94275e7i | 0.670206i | ||||||||
\(512\) | 1.02367e8 | − | 8.68064e7i | 0.762695 | − | 0.646758i | ||||
\(513\) | 1.16173e8 | 0.860508 | ||||||||
\(514\) | 4.69105e7 | + | 1.81683e8i | 0.345446 | + | 1.33791i | ||||
\(515\) | 1.38913e7i | 0.101700i | ||||||||
\(516\) | 3.73632e7 | − | 2.06724e7i | 0.271954 | − | 0.150467i | ||||
\(517\) | −7.26144e6 | −0.0525474 | ||||||||
\(518\) | −4.78560e6 | + | 1.23564e6i | −0.0344308 | + | 0.00888999i | ||||
\(519\) | 1.58840e8i | 1.13621i | ||||||||
\(520\) | −5.16032e6 | − | 5.45068e6i | −0.0367000 | − | 0.0387651i | ||||
\(521\) | −1.98565e8 | −1.40407 | −0.702036 | − | 0.712142i | \(-0.747725\pi\) | ||||
−0.702036 | + | 0.712142i | \(0.747725\pi\) | |||||||
\(522\) | −1.17801e7 | − | 4.56240e7i | −0.0828203 | − | 0.320761i | ||||
\(523\) | 2.15512e8i | 1.50649i | 0.657740 | + | 0.753245i | \(0.271513\pi\) | ||||
−0.657740 | + | 0.753245i | \(0.728487\pi\) | |||||||
\(524\) | −8.81347e7 | − | 1.59294e8i | −0.612566 | − | 1.10715i | ||||
\(525\) | −1.49040e8 | −1.02997 | ||||||||
\(526\) | 1.68082e8 | − | 4.33986e7i | 1.15495 | − | 0.298207i | ||||
\(527\) | − | 1.99649e8i | − | 1.36406i | ||||||
\(528\) | −6.47578e7 | + | 1.03273e8i | −0.439937 | + | 0.701592i | ||||
\(529\) | 3.83616e7 | 0.259137 | ||||||||
\(530\) | −3.85708e6 | − | 1.49384e7i | −0.0259078 | − | 0.100341i | ||||
\(531\) | 1.81151e7i | 0.120992i | ||||||||
\(532\) | 1.30637e8 | − | 7.22792e7i | 0.867622 | − | 0.480041i | ||||
\(533\) | 4.30447e7 | 0.284275 | ||||||||
\(534\) | 7.45771e7 | − | 1.92557e7i | 0.489758 | − | 0.126455i | ||||
\(535\) | − | 1.14935e7i | − | 0.0750567i | ||||||
\(536\) | −1.46546e8 | + | 1.38739e8i | −0.951655 | + | 0.900959i | ||||
\(537\) | −7.23197e7 | −0.467018 | ||||||||
\(538\) | −5.88556e7 | − | 2.27947e8i | −0.377956 | − | 1.46382i | ||||
\(539\) | − | 2.07939e7i | − | 0.132791i | ||||||
\(540\) | 4.78080e6 | + | 8.64078e6i | 0.0303612 | + | 0.0548746i | ||||
\(541\) | 1.44188e7 | 0.0910623 | 0.0455311 | − | 0.998963i | \(-0.485502\pi\) | ||||
0.0455311 | + | 0.998963i | \(0.485502\pi\) | |||||||
\(542\) | 6.59549e7 | − | 1.70295e7i | 0.414237 | − | 0.106956i | ||||
\(543\) | − | 3.00282e8i | − | 1.87556i | ||||||
\(544\) | −1.48852e8 | − | 4.72541e7i | −0.924607 | − | 0.293524i | ||||
\(545\) | 1.53574e7 | 0.0948697 | ||||||||
\(546\) | 2.81472e7 | + | 1.09014e8i | 0.172925 | + | 0.669735i | ||||
\(547\) | 4.24129e7i | 0.259141i | 0.991570 | + | 0.129571i | \(0.0413599\pi\) | ||||
−0.991570 | + | 0.129571i | \(0.958640\pi\) | |||||||
\(548\) | −2.13362e8 | + | 1.18050e8i | −1.29651 | + | 0.717336i | ||||
\(549\) | 2.52206e6 | 0.0152419 | ||||||||
\(550\) | −1.15506e8 | + | 2.98235e7i | −0.694251 | + | 0.179255i | ||||
\(551\) | 1.91976e8i | 1.14761i | ||||||||
\(552\) | 1.14217e8 | + | 1.20644e8i | 0.679068 | + | 0.717278i | ||||
\(553\) | 9.62688e7 | 0.569259 | ||||||||
\(554\) | 5.52453e7 | + | 2.13964e8i | 0.324912 | + | 1.25838i | ||||
\(555\) | − | 617818.i | − | 0.00361395i | ||||||
\(556\) | −4.30176e6 | − | 7.77497e6i | −0.0250277 | − | 0.0452350i | ||||
\(557\) | 8.90848e7 | 0.515511 | 0.257756 | − | 0.966210i | \(-0.417017\pi\) | ||||
0.257756 | + | 0.966210i | \(0.417017\pi\) | |||||||
\(558\) | 7.49549e7 | − | 1.93533e7i | 0.431417 | − | 0.111391i | ||||
\(559\) | − | 3.15685e7i | − | 0.180725i | ||||||
\(560\) | 1.07520e7 | + | 6.74209e6i | 0.0612245 | + | 0.0383911i | ||||
\(561\) | 1.41836e8 | 0.803338 | ||||||||
\(562\) | 1.72802e7 | + | 6.69258e7i | 0.0973507 | + | 0.377037i | ||||
\(563\) | − | 2.41576e8i | − | 1.35372i | −0.736112 | − | 0.676860i | \(-0.763340\pi\) | ||
0.736112 | − | 0.676860i | \(-0.236660\pi\) | |||||||
\(564\) | 1.31174e7 | − | 7.25766e6i | 0.0731159 | − | 0.0404538i | ||||
\(565\) | −6.01694e6 | −0.0333603 | ||||||||
\(566\) | 9.86446e7 | − | 2.54699e7i | 0.544031 | − | 0.140468i | ||||
\(567\) | − | 2.00304e8i | − | 1.09886i | ||||||
\(568\) | 1.97891e8 | − | 1.87349e8i | 1.07989 | − | 1.02236i | ||||
\(569\) | −2.56141e7 | −0.139041 | −0.0695203 | − | 0.997581i | \(-0.522147\pi\) | ||||
−0.0695203 | + | 0.997581i | \(0.522147\pi\) | |||||||
\(570\) | 4.66560e6 | + | 1.80698e7i | 0.0251932 | + | 0.0975728i | ||||
\(571\) | 1.10781e8i | 0.595057i | 0.954713 | + | 0.297528i | \(0.0961623\pi\) | ||||
−0.954713 | + | 0.297528i | \(0.903838\pi\) | |||||||
\(572\) | 4.36282e7 | + | 7.88532e7i | 0.233120 | + | 0.421339i | ||||
\(573\) | −3.53725e8 | −1.88019 | ||||||||
\(574\) | −7.04688e7 | + | 1.81950e7i | −0.372616 | + | 0.0962090i | ||||
\(575\) | 1.62586e8i | 0.855225i | ||||||||
\(576\) | 3.31162e6 | − | 6.04646e7i | 0.0173290 | − | 0.316398i | ||||
\(577\) | 1.07272e8 | 0.558415 | 0.279208 | − | 0.960231i | \(-0.409928\pi\) | ||||
0.279208 | + | 0.960231i | \(0.409928\pi\) | |||||||
\(578\) | −2.84563e6 | − | 1.10211e7i | −0.0147365 | − | 0.0570742i | ||||
\(579\) | 7.53011e7i | 0.387941i | ||||||||
\(580\) | −1.42789e7 | + | 7.90027e6i | −0.0731830 | + | 0.0404909i | ||||
\(581\) | 6.32544e7 | 0.322524 | ||||||||
\(582\) | −3.49701e8 | + | 9.02923e7i | −1.77389 | + | 0.458017i | ||||
\(583\) | 1.85236e8i | 0.934803i | ||||||||
\(584\) | −1.01596e8 | − | 1.07313e8i | −0.510082 | − | 0.538783i | ||||
\(585\) | −3.38646e6 | −0.0169152 | ||||||||
\(586\) | −8.90830e7 | − | 3.45017e8i | −0.442692 | − | 1.71454i | ||||
\(587\) | 2.16397e7i | 0.106988i | 0.998568 | + | 0.0534941i | \(0.0170358\pi\) | ||||
−0.998568 | + | 0.0534941i | \(0.982964\pi\) | |||||||
\(588\) | 2.07830e7 | + | 3.75631e7i | 0.102230 | + | 0.184769i | ||||
\(589\) | −3.15395e8 | −1.54351 | ||||||||
\(590\) | 6.07440e6 | − | 1.56840e6i | 0.0295765 | − | 0.00763663i | ||||
\(591\) | 6.91140e7i | 0.334814i | ||||||||
\(592\) | 4.33894e6 | − | 6.91956e6i | 0.0209131 | − | 0.0333514i | ||||
\(593\) | 2.00341e8 | 0.960738 | 0.480369 | − | 0.877066i | \(-0.340503\pi\) | ||||
0.480369 | + | 0.877066i | \(0.340503\pi\) | |||||||
\(594\) | −2.96410e7 | − | 1.14799e8i | −0.141427 | − | 0.547745i | ||||
\(595\) | − | 1.47669e7i | − | 0.0701033i | ||||||
\(596\) | 1.83359e8 | − | 1.01449e8i | 0.866089 | − | 0.479193i | ||||
\(597\) | 1.51690e8 | 0.712907 | ||||||||
\(598\) | 1.18922e8 | − | 3.07055e7i | 0.556107 | − | 0.143586i | ||||
\(599\) | − | 1.37592e8i | − | 0.640197i | −0.947384 | − | 0.320098i | \(-0.896284\pi\) | ||
0.947384 | − | 0.320098i | \(-0.103716\pi\) | |||||||
\(600\) | 1.78848e8 | − | 1.69321e8i | 0.828000 | − | 0.783892i | ||||
\(601\) | −1.90306e8 | −0.876655 | −0.438327 | − | 0.898815i | \(-0.644429\pi\) | ||||
−0.438327 | + | 0.898815i | \(0.644429\pi\) | |||||||
\(602\) | 1.33440e7 | + | 5.16811e7i | 0.0611641 | + | 0.236888i | ||||
\(603\) | 9.10477e7i | 0.415257i | ||||||||
\(604\) | 1.73309e8 | + | 3.13237e8i | 0.786520 | + | 1.42155i | ||||
\(605\) | 8.49001e6 | 0.0383391 | ||||||||
\(606\) | −1.53398e8 | + | 3.96072e7i | −0.689289 | + | 0.177974i | ||||
\(607\) | 1.25461e8i | 0.560974i | 0.959858 | + | 0.280487i | \(0.0904960\pi\) | ||||
−0.959858 | + | 0.280487i | \(0.909504\pi\) | |||||||
\(608\) | −7.46496e7 | + | 2.35148e8i | −0.332137 | + | 1.04624i | ||||
\(609\) | 2.44781e8 | 1.08374 | ||||||||
\(610\) | −218360. | − | 845705.i | −0.000962019 | − | 0.00372588i | ||||
\(611\) | − | 1.10831e7i | − | 0.0485888i | ||||||
\(612\) | −6.16530e7 | + | 3.41116e7i | −0.268967 | + | 0.148815i | ||||
\(613\) | −9.91111e7 | −0.430270 | −0.215135 | − | 0.976584i | \(-0.569019\pi\) | ||||
−0.215135 | + | 0.976584i | \(0.569019\pi\) | |||||||
\(614\) | 3.78817e8 | − | 9.78102e7i | 1.63653 | − | 0.422551i | ||||
\(615\) | − | 9.09748e6i | − | 0.0391107i | ||||||
\(616\) | −1.04755e8 | − | 1.10650e8i | −0.448160 | − | 0.473378i | ||||
\(617\) | 3.70827e7 | 0.157876 | 0.0789379 | − | 0.996880i | \(-0.474847\pi\) | ||||
0.0789379 | + | 0.996880i | \(0.474847\pi\) | |||||||
\(618\) | 8.60813e7 | + | 3.33391e8i | 0.364706 | + | 1.41250i | ||||
\(619\) | − | 4.05274e8i | − | 1.70874i | −0.519662 | − | 0.854372i | \(-0.673942\pi\) | ||
0.519662 | − | 0.854372i | \(-0.326058\pi\) | |||||||
\(620\) | −1.29792e7 | − | 2.34585e7i | −0.0544594 | − | 0.0984295i | ||||
\(621\) | −1.61591e8 | −0.674749 | ||||||||
\(622\) | −3.87469e8 | + | 1.00044e8i | −1.61015 | + | 0.415738i | ||||
\(623\) | 9.62786e7i | 0.398168i | ||||||||
\(624\) | −1.57624e8 | − | 9.88390e7i | −0.648738 | − | 0.406794i | ||||
\(625\) | 2.39463e8 | 0.980841 | ||||||||
\(626\) | 2.25437e6 | + | 8.73115e6i | 0.00918973 | + | 0.0355917i | ||||
\(627\) | − | 2.24065e8i | − | 0.909017i | ||||||
\(628\) | −4.57405e7 | + | 2.53074e7i | −0.184681 | + | 0.102181i | ||||
\(629\) | −9.50340e6 | −0.0381880 | ||||||||
\(630\) | 5.54400e6 | − | 1.43145e6i | 0.0221718 | − | 0.00572474i | ||||
\(631\) | − | 2.52648e7i | − | 0.100561i | −0.998735 | − | 0.0502803i | \(-0.983989\pi\) | ||
0.998735 | − | 0.0502803i | \(-0.0160115\pi\) | |||||||
\(632\) | −1.15523e8 | + | 1.09369e8i | −0.457631 | + | 0.433253i | ||||
\(633\) | 1.21132e8 | 0.477581 | ||||||||
\(634\) | 6.89763e7 | + | 2.67144e8i | 0.270665 | + | 1.04828i | ||||
\(635\) | 1.67462e7i | 0.0654025i | ||||||||
\(636\) | −1.85140e8 | − | 3.34620e8i | −0.719662 | − | 1.30071i | ||||
\(637\) | 3.17374e7 | 0.122787 | ||||||||
\(638\) | 1.89705e8 | − | 4.89817e7i | 0.730495 | − | 0.188613i | ||||
\(639\) | − | 1.22948e8i | − | 0.471213i | ||||||
\(640\) | −2.05619e7 | + | 4.12457e6i | −0.0784375 | + | 0.0157340i | ||||
\(641\) | −4.21293e8 | −1.59959 | −0.799797 | − | 0.600270i | \(-0.795060\pi\) | ||||
−0.799797 | + | 0.600270i | \(0.795060\pi\) | |||||||
\(642\) | −7.12224e7 | − | 2.75843e8i | −0.269161 | − | 1.04245i | ||||
\(643\) | 8.17706e7i | 0.307584i | 0.988103 | + | 0.153792i | \(0.0491486\pi\) | ||||
−0.988103 | + | 0.153792i | \(0.950851\pi\) | |||||||
\(644\) | −1.81709e8 | + | 1.00536e8i | −0.680328 | + | 0.376414i | ||||
\(645\) | −6.67200e6 | −0.0248643 | ||||||||
\(646\) | 2.77953e8 | − | 7.17672e7i | 1.03104 | − | 0.266212i | ||||
\(647\) | − | 1.84284e8i | − | 0.680416i | −0.940350 | − | 0.340208i | \(-0.889503\pi\) | ||
0.940350 | − | 0.340208i | \(-0.110497\pi\) | |||||||
\(648\) | 2.27561e8 | + | 2.40365e8i | 0.836319 | + | 0.883377i | ||||
\(649\) | −7.53226e7 | −0.275544 | ||||||||
\(650\) | −4.55193e7 | − | 1.76295e8i | −0.165751 | − | 0.641950i | ||||
\(651\) | 4.02146e8i | 1.45761i | ||||||||
\(652\) | 5.71939e7 | + | 1.03372e8i | 0.206351 | + | 0.372958i | ||||
\(653\) | 6.43842e7 | 0.231228 | 0.115614 | − | 0.993294i | \(-0.463117\pi\) | ||||
0.115614 | + | 0.993294i | \(0.463117\pi\) | |||||||
\(654\) | 3.68577e8 | − | 9.51662e7i | 1.31764 | − | 0.340212i | ||||
\(655\) | 2.84454e7i | 0.101225i | ||||||||
\(656\) | 6.38917e7 | − | 1.01892e8i | 0.226325 | − | 0.360934i | ||||
\(657\) | −6.66726e7 | −0.235099 | ||||||||
\(658\) | 4.68480e6 | + | 1.81442e7i | 0.0164442 | + | 0.0636882i | ||||
\(659\) | 5.38099e8i | 1.88021i | 0.340889 | + | 0.940103i | \(0.389272\pi\) | ||||
−0.340889 | + | 0.940103i | \(0.610728\pi\) | |||||||
\(660\) | 1.66656e7 | − | 9.22080e6i | 0.0579681 | − | 0.0320728i | ||||
\(661\) | 2.83897e8 | 0.983008 | 0.491504 | − | 0.870875i | \(-0.336447\pi\) | ||||
0.491504 | + | 0.870875i | \(0.336447\pi\) | |||||||
\(662\) | −3.11927e8 | + | 8.05393e7i | −1.07518 | + | 0.277609i | ||||
\(663\) | 2.16483e8i | 0.742819i | ||||||||
\(664\) | −7.59053e7 | + | 7.18617e7i | −0.259279 | + | 0.245467i | ||||
\(665\) | −2.33280e7 | −0.0793255 | ||||||||
\(666\) | −921228. | − | 3.56790e6i | −0.00311849 | − | 0.0120779i | ||||
\(667\) | − | 2.67029e8i | − | 0.899872i | ||||||
\(668\) | −2.46791e8 | − | 4.46048e8i | −0.827942 | − | 1.49642i | ||||
\(669\) | 1.03212e8 | 0.344707 | ||||||||
\(670\) | 3.05304e7 | − | 7.88292e6i | 0.101510 | − | 0.0262097i | ||||
\(671\) | 1.04867e7i | 0.0347115i | ||||||||
\(672\) | 2.99827e8 | + | 9.51824e7i | 0.988014 | + | 0.313653i | ||||
\(673\) | 2.77693e8 | 0.911002 | 0.455501 | − | 0.890235i | \(-0.349460\pi\) | ||||
0.455501 | + | 0.890235i | \(0.349460\pi\) | |||||||
\(674\) | −6.85062e7 | − | 2.65323e8i | −0.223743 | − | 0.866554i | ||||
\(675\) | 2.39550e8i | 0.778906i | ||||||||
\(676\) | 1.49949e8 | − | 8.29640e7i | 0.485403 | − | 0.268565i | ||||
\(677\) | −9.23026e7 | −0.297473 | −0.148737 | − | 0.988877i | \(-0.547521\pi\) | ||||
−0.148737 | + | 0.988877i | \(0.547521\pi\) | |||||||
\(678\) | −1.44407e8 | + | 3.72856e7i | −0.463338 | + | 0.119633i | ||||
\(679\) | − | 4.51462e8i | − | 1.44215i | ||||||
\(680\) | 1.67763e7 | + | 1.77203e7i | 0.0533544 | + | 0.0563565i | ||||
\(681\) | −4.18384e8 | −1.32475 | ||||||||
\(682\) | 8.04710e7 | + | 3.11663e8i | 0.253680 | + | 0.982499i | ||||
\(683\) | − | 2.70862e8i | − | 0.850132i | −0.905162 | − | 0.425066i | \(-0.860251\pi\) | ||
0.905162 | − | 0.425066i | \(-0.139749\pi\) | |||||||
\(684\) | 5.38877e7 | + | 9.73962e7i | 0.168392 | + | 0.304350i | ||||
\(685\) | 3.81003e7 | 0.118538 | ||||||||
\(686\) | −3.34315e8 | + | 8.63198e7i | −1.03558 | + | 0.267386i | ||||
\(687\) | − | 4.94496e7i | − | 0.152508i | ||||||
\(688\) | −7.47264e7 | − | 4.68575e7i | −0.229461 | − | 0.143884i | ||||
\(689\) | −2.82724e8 | −0.864380 | ||||||||
\(690\) | −6.48960e6 | − | 2.51341e7i | −0.0197547 | − | 0.0765097i | ||||
\(691\) | − | 1.92568e7i | − | 0.0583645i | −0.999574 | − | 0.0291823i | \(-0.990710\pi\) | ||
0.999574 | − | 0.0291823i | \(-0.00929032\pi\) | |||||||
\(692\) | 2.87086e8 | − | 1.58840e8i | 0.866350 | − | 0.479337i | ||||
\(693\) | −6.87456e7 | −0.206560 | ||||||||
\(694\) | −4.22539e8 | + | 1.09099e8i | −1.26412 | + | 0.326395i | ||||
\(695\) | 1.38839e6i | 0.00413577i | ||||||||
\(696\) | −2.93737e8 | + | 2.78089e8i | −0.871226 | + | 0.824815i | ||||
\(697\) | −1.39939e8 | −0.413277 | ||||||||
\(698\) | 9.40017e7 | + | 3.64067e8i | 0.276420 | + | 1.07057i | ||||
\(699\) | − | 2.49229e8i | − | 0.729738i | ||||||
\(700\) | 1.49040e8 | + | 2.69374e8i | 0.434519 | + | 0.785346i | ||||
\(701\) | 3.52234e8 | 1.02253 | 0.511266 | − | 0.859423i | \(-0.329177\pi\) | ||||
0.511266 | + | 0.859423i | \(0.329177\pi\) | |||||||
\(702\) | 1.75216e8 | − | 4.52407e7i | 0.506481 | − | 0.130773i | ||||
\(703\) | 1.50130e7i | 0.0432117i | ||||||||
\(704\) | 2.51412e8 | + | 1.37697e7i | 0.720558 | + | 0.0394646i | ||||
\(705\) | −2.34240e6 | −0.00668488 | ||||||||
\(706\) | −2.54463e7 | − | 9.85530e7i | −0.0723119 | − | 0.280063i | ||||
\(707\) | − | 1.98036e8i | − | 0.560384i | ||||||
\(708\) | 1.36067e8 | − | 7.52834e7i | 0.383400 | − | 0.212129i | ||||
\(709\) | 4.62733e8 | 1.29835 | 0.649175 | − | 0.760639i | \(-0.275114\pi\) | ||||
0.649175 | + | 0.760639i | \(0.275114\pi\) | |||||||
\(710\) | −4.12272e7 | + | 1.06448e7i | −0.115188 | + | 0.0297415i | ||||
\(711\) | 7.17731e7i | 0.199689i | ||||||||
\(712\) | −1.09380e8 | − | 1.15534e8i | −0.303038 | − | 0.320089i | ||||
\(713\) | 4.38697e8 | 1.21031 | ||||||||
\(714\) | −9.15072e7 | − | 3.54406e8i | −0.251397 | − | 0.973658i | ||||
\(715\) | − | 1.40809e7i | − | 0.0385224i | ||||||
\(716\) | 7.23197e7 | + | 1.30710e8i | 0.197023 | + | 0.356098i | ||||
\(717\) | 3.48668e8 | 0.945921 | ||||||||
\(718\) | 1.56587e8 | − | 4.04306e7i | 0.423041 | − | 0.109229i | ||||
\(719\) | 4.60385e8i | 1.23861i | 0.785150 | + | 0.619305i | \(0.212586\pi\) | ||||
−0.785150 | + | 0.619305i | \(0.787414\pi\) | |||||||
\(720\) | −5.02656e6 | + | 8.01615e6i | −0.0134671 | + | 0.0214767i | ||||
\(721\) | −4.30406e8 | −1.14835 | ||||||||
\(722\) | −1.92823e7 | − | 7.46801e7i | −0.0512327 | − | 0.198424i | ||||
\(723\) | − | 1.56501e8i | − | 0.414097i | ||||||
\(724\) | −5.42727e8 | + | 3.00282e8i | −1.43010 | + | 0.791250i | ||||
\(725\) | −3.95856e8 | −1.03878 | ||||||||
\(726\) | 2.03760e8 | − | 5.26107e7i | 0.532488 | − | 0.137488i | ||||
\(727\) | 4.82173e8i | 1.25487i | 0.778668 | + | 0.627437i | \(0.215896\pi\) | ||||
−0.778668 | + | 0.627437i | \(0.784104\pi\) | |||||||
\(728\) | 1.68883e8 | − | 1.59887e8i | 0.437716 | − | 0.414398i | ||||
\(729\) | −1.99184e8 | −0.514128 | ||||||||
\(730\) | 5.77252e6 | + | 2.23569e7i | 0.0148387 | + | 0.0574702i | ||||
\(731\) | 1.02630e8i | 0.262738i | ||||||||
\(732\) | −1.04813e7 | − | 1.89438e7i | −0.0267227 | − | 0.0482985i | ||||
\(733\) | −5.08270e8 | −1.29057 | −0.645287 | − | 0.763941i | \(-0.723262\pi\) | ||||
−0.645287 | + | 0.763941i | \(0.723262\pi\) | |||||||
\(734\) | 8.60246e7 | − | 2.22115e7i | 0.217538 | − | 0.0561680i | ||||
\(735\) | − | 6.70770e6i | − | 0.0168932i | ||||||
\(736\) | 1.03834e8 | − | 3.27079e8i | 0.260438 | − | 0.820387i | ||||
\(737\) | −3.78577e8 | −0.945696 | ||||||||
\(738\) | −1.35652e7 | − | 5.25380e7i | −0.0337488 | − | 0.130709i | ||||
\(739\) | 1.27767e8i | 0.316582i | 0.987392 | + | 0.158291i | \(0.0505984\pi\) | ||||
−0.987392 | + | 0.158291i | \(0.949402\pi\) | |||||||
\(740\) | −1.11664e6 | + | 617818.i | −0.00275561 | + | 0.00152463i | ||||
\(741\) | 3.41988e8 | 0.840537 | ||||||||
\(742\) | 4.62850e8 | − | 1.19507e8i | 1.13300 | − | 0.292538i | ||||
\(743\) | − | 2.83312e8i | − | 0.690716i | −0.938471 | − | 0.345358i | \(-0.887758\pi\) | ||
0.938471 | − | 0.345358i | \(-0.112242\pi\) | |||||||
\(744\) | −4.56868e8 | − | 4.82575e8i | −1.10936 | − | 1.17178i | ||||
\(745\) | −3.27426e7 | −0.0791853 | ||||||||
\(746\) | 1.37429e6 | + | 5.32261e6i | 0.00331026 | + | 0.0128206i | ||||
\(747\) | 4.71593e7i | 0.113137i | ||||||||
\(748\) | −1.41836e8 | − | 2.56354e8i | −0.338908 | − | 0.612540i | ||||
\(749\) | 3.56112e8 | 0.847503 | ||||||||
\(750\) | −7.47600e7 | + | 1.93029e7i | −0.177209 | + | 0.0457551i | ||||
\(751\) | − | 2.15309e8i | − | 0.508325i | −0.967161 | − | 0.254163i | \(-0.918200\pi\) | ||
0.967161 | − | 0.254163i | \(-0.0817999\pi\) | |||||||
\(752\) | −2.62349e7 | − | 1.64507e7i | −0.0616915 | − | 0.0386839i | ||||
\(753\) | 1.46117e8 | 0.342228 | ||||||||
\(754\) | 7.47601e7 | + | 2.89545e8i | 0.174404 | + | 0.675463i | ||||
\(755\) | − | 5.59352e7i | − | 0.129970i | ||||||
\(756\) | −2.67725e8 | + | 1.48128e8i | −0.619617 | + | 0.342824i | ||||
\(757\) | −3.03985e8 | −0.700753 | −0.350377 | − | 0.936609i | \(-0.613946\pi\) | ||||
−0.350377 | + | 0.936609i | \(0.613946\pi\) | |||||||
\(758\) | −1.15026e8 | + | 2.96997e7i | −0.264113 | + | 0.0681938i | ||||
\(759\) | 3.11663e8i | 0.712787i | ||||||||
\(760\) | 2.79936e7 | − | 2.65024e7i | 0.0637702 | − | 0.0603731i | ||||
\(761\) | 8.63611e8 | 1.95959 | 0.979793 | − | 0.200014i | \(-0.0640988\pi\) | ||||
0.979793 | + | 0.200014i | \(0.0640988\pi\) | |||||||
\(762\) | 1.03772e8 | + | 4.01908e8i | 0.234539 | + | 0.908367i | ||||
\(763\) | 4.75831e8i | 1.07122i | ||||||||
\(764\) | 3.53725e8 | + | 6.39321e8i | 0.793206 | + | 1.43364i | ||||
\(765\) | 1.10095e7 | 0.0245913 | ||||||||
\(766\) | 2.60175e8 | − | 6.71770e7i | 0.578868 | − | 0.149463i | ||||
\(767\) | − | 1.14964e8i | − | 0.254786i | ||||||
\(768\) | −4.67927e8 | + | 2.26407e8i | −1.03299 | + | 0.499812i | ||||
\(769\) | −1.97898e7 | −0.0435174 | −0.0217587 | − | 0.999763i | \(-0.506927\pi\) | ||||
−0.0217587 | + | 0.999763i | \(0.506927\pi\) | |||||||
\(770\) | 5.95200e6 | + | 2.30520e7i | 0.0130374 | + | 0.0504936i | ||||
\(771\) | − | 7.26734e8i | − | 1.58567i | ||||||
\(772\) | 1.36099e8 | − | 7.53011e7i | 0.295803 | − | 0.163663i | ||||
\(773\) | −5.64048e8 | −1.22117 | −0.610587 | − | 0.791949i | \(-0.709067\pi\) | ||||
−0.610587 | + | 0.791949i | \(0.709067\pi\) | |||||||
\(774\) | −3.85308e7 | + | 9.94861e6i | −0.0830970 | + | 0.0214555i | ||||
\(775\) | − | 6.50345e8i | − | 1.39714i | ||||||
\(776\) | 5.12894e8 | + | 5.41754e8i | 1.09760 | + | 1.15936i | ||||
\(777\) | 1.91424e7 | 0.0408069 | ||||||||
\(778\) | −2.02244e8 | − | 7.83286e8i | −0.429473 | − | 1.66334i | ||||
\(779\) | 2.21069e8i | 0.467644i | ||||||||
\(780\) | 1.40736e7 | + | 2.54365e7i | 0.0296566 | + | 0.0536011i | ||||
\(781\) | 5.11217e8 | 1.07313 | ||||||||
\(782\) | −3.86618e8 | + | 9.98243e7i | −0.808466 | + | 0.208745i | ||||
\(783\) | − | 3.93433e8i | − | 0.819570i | ||||||
\(784\) | 4.71082e7 | − | 7.51262e7i | 0.0977572 | − | 0.155899i | ||||
\(785\) | 8.16794e6 | 0.0168851 | ||||||||
\(786\) | 1.76269e8 | + | 6.82689e8i | 0.363002 | + | 1.40590i | ||||
\(787\) | 4.04198e8i | 0.829220i | 0.909999 | + | 0.414610i | \(0.136082\pi\) | ||||
−0.909999 | + | 0.414610i | \(0.863918\pi\) | |||||||
\(788\) | 1.24916e8 | − | 6.91140e7i | 0.255294 | − | 0.141250i | ||||
\(789\) | −6.72328e8 | −1.36883 | ||||||||
\(790\) | 2.40672e7 | − | 6.21412e6i | 0.0488140 | − | 0.0126037i | ||||
\(791\) | − | 1.86428e8i | − | 0.376688i | ||||||
\(792\) | 8.24947e7 | − | 7.81002e7i | 0.166054 | − | 0.157209i | ||||
\(793\) | −1.60058e7 | −0.0320965 | ||||||||
\(794\) | −6.96531e7 | − | 2.69765e8i | −0.139149 | − | 0.538921i | ||||
\(795\) | 5.97536e7i | 0.118922i | ||||||||
\(796\) | −1.51690e8 | − | 2.74163e8i | −0.300758 | − | 0.543587i | ||||
\(797\) | −2.15998e7 | −0.0426654 | −0.0213327 | − | 0.999772i | \(-0.506791\pi\) | ||||
−0.0213327 | + | 0.999772i | \(0.506791\pi\) | |||||||
\(798\) | −5.59872e8 | + | 1.44558e8i | −1.10174 | + | 0.284469i | ||||
\(799\) | 3.60313e7i | 0.0706381i | ||||||||
\(800\) | −4.84877e8 | − | 1.53928e8i | −0.947025 | − | 0.300640i | ||||
\(801\) | −7.17805e7 | −0.139672 | ||||||||
\(802\) | −1.37680e8 | − | 5.33231e8i | −0.266899 | − | 1.03369i | ||||
\(803\) | − | 2.77225e8i | − | 0.535410i | ||||||
\(804\) | 6.83881e8 | − | 3.78380e8i | 1.31587 | − | 0.728048i | ||||
\(805\) | 3.24480e7 | 0.0622014 | ||||||||
\(806\) | −4.75688e8 | + | 1.22822e8i | −0.908483 | + | 0.234569i | ||||
\(807\) | 9.11786e8i | 1.73489i | ||||||||
\(808\) | 2.24984e8 | + | 2.37643e8i | 0.426498 | + | 0.450496i | ||||
\(809\) | 6.51310e8 | 1.23011 | 0.615053 | − | 0.788486i | \(-0.289135\pi\) | ||||
0.615053 | + | 0.788486i | \(0.289135\pi\) | |||||||
\(810\) | −1.29296e7 | − | 5.00760e7i | −0.0243293 | − | 0.0942269i | ||||
\(811\) | 5.52891e8i | 1.03652i | 0.855223 | + | 0.518259i | \(0.173420\pi\) | ||||
−0.855223 | + | 0.518259i | \(0.826580\pi\) | |||||||
\(812\) | −2.44781e8 | − | 4.42415e8i | −0.457203 | − | 0.826346i | ||||
\(813\) | −2.63820e8 | −0.490948 | ||||||||
\(814\) | 1.48354e7 | − | 3.83047e6i | 0.0275058 | − | 0.00710198i | ||||
\(815\) | − | 1.84593e7i | − | 0.0340990i | ||||||
\(816\) | 5.12440e8 | + | 3.21328e8i | 0.943133 | + | 0.591396i | ||||
\(817\) | 1.62130e8 | 0.297301 | ||||||||
\(818\) | 9.19917e7 | + | 3.56282e8i | 0.168069 | + | 0.650930i | ||||
\(819\) | − | 1.04926e8i | − | 0.190998i | ||||||
\(820\) | −1.64427e7 | + | 9.09748e6i | −0.0298217 | + | 0.0164998i | ||||
\(821\) | −8.94865e8 | −1.61707 | −0.808534 | − | 0.588450i | \(-0.799738\pi\) | ||||
−0.808534 | + | 0.588450i | \(0.799738\pi\) | |||||||
\(822\) | 9.14408e8 | − | 2.36099e8i | 1.64636 | − | 0.425088i | ||||
\(823\) | 8.44482e8i | 1.51492i | 0.652879 | + | 0.757462i | \(0.273561\pi\) | ||||
−0.652879 | + | 0.757462i | \(0.726439\pi\) | |||||||
\(824\) | 5.16488e8 | − | 4.88974e8i | 0.923163 | − | 0.873985i | ||||
\(825\) | 4.62024e8 | 0.822816 | ||||||||
\(826\) | 4.85952e7 | + | 1.88208e8i | 0.0862290 | + | 0.333963i | ||||
\(827\) | − | 3.11099e7i | − | 0.0550024i | −0.999622 | − | 0.0275012i | \(-0.991245\pi\) | ||
0.999622 | − | 0.0275012i | \(-0.00875501\pi\) | |||||||
\(828\) | −7.49549e7 | − | 1.35473e8i | −0.132041 | − | 0.238650i | ||||
\(829\) | −4.05444e7 | −0.0711652 | −0.0355826 | − | 0.999367i | \(-0.511329\pi\) | ||||
−0.0355826 | + | 0.999367i | \(0.511329\pi\) | |||||||
\(830\) | 1.58136e7 | − | 4.08305e6i | 0.0276565 | − | 0.00714087i | ||||
\(831\) | − | 8.55856e8i | − | 1.49141i | ||||||
\(832\) | −2.10166e7 | + | 3.83728e8i | −0.0364915 | + | 0.666275i | ||||
\(833\) | −1.03179e8 | −0.178508 | ||||||||
\(834\) | 8.60352e6 | + | 3.33213e7i | 0.0148313 | + | 0.0574412i | ||||
\(835\) | 7.96515e7i | 0.136815i | ||||||||
\(836\) | −4.04974e8 | + | 2.24065e8i | −0.693120 | + | 0.383492i | ||||
\(837\) | 6.46364e8 | 1.10230 | ||||||||
\(838\) | −2.10034e8 | + | 5.42306e7i | −0.356910 | + | 0.0921537i | ||||
\(839\) | − | 4.17820e8i | − | 0.707463i | −0.935347 | − | 0.353731i | \(-0.884913\pi\) | ||
0.935347 | − | 0.353731i | \(-0.115087\pi\) | |||||||
\(840\) | −3.37920e7 | − | 3.56934e7i | −0.0570133 | − | 0.0602213i | ||||
\(841\) | 5.53247e7 | 0.0930103 | ||||||||
\(842\) | −1.88416e8 | − | 7.29730e8i | −0.315632 | − | 1.22244i | ||||
\(843\) | − | 2.67703e8i | − | 0.446859i | ||||||
\(844\) | −1.21132e8 | − | 2.18933e8i | −0.201480 | − | 0.364153i | ||||
\(845\) | −2.67765e7 | −0.0443797 | ||||||||
\(846\) | −1.35274e7 | + | 3.49275e6i | −0.0223410 | + | 0.00576841i | ||||
\(847\) | 2.63053e8i | 0.432906i | ||||||||
\(848\) | −4.19650e8 | + | 6.69241e8i | −0.688177 | + | 1.09748i | ||||
\(849\) | −3.94578e8 | −0.644778 | ||||||||
\(850\) | 1.47984e8 | + | 5.73141e8i | 0.240968 | + | 0.933264i | ||||
\(851\) | − | 2.08823e7i | − | 0.0338835i | ||||||
\(852\) | −9.23489e8 | + | 5.10951e8i | −1.49318 | + | 0.826153i | ||||
\(853\) | −4.28994e8 | −0.691201 | −0.345601 | − | 0.938382i | \(-0.612325\pi\) | ||||
−0.345601 | + | 0.938382i | \(0.612325\pi\) | |||||||
\(854\) | 2.62032e7 | − | 6.76564e6i | 0.0420708 | − | 0.0108626i | ||||
\(855\) | − | 1.73922e7i | − | 0.0278263i | ||||||
\(856\) | −4.27334e8 | + | 4.04570e8i | −0.681313 | + | 0.645019i | ||||
\(857\) | 2.20598e8 | 0.350476 | 0.175238 | − | 0.984526i | \(-0.443930\pi\) | ||||
0.175238 | + | 0.984526i | \(0.443930\pi\) | |||||||
\(858\) | −8.72563e7 | − | 3.37942e8i | −0.138145 | − | 0.535033i | ||||
\(859\) | − | 1.14768e9i | − | 1.81068i | −0.424689 | − | 0.905339i | \(-0.639617\pi\) | ||
0.424689 | − | 0.905339i | \(-0.360383\pi\) | |||||||
\(860\) | 6.67200e6 | + | 1.20589e7i | 0.0104896 | + | 0.0189589i | ||||
\(861\) | 2.81875e8 | 0.441619 | ||||||||
\(862\) | 4.02160e8 | − | 1.03837e8i | 0.627881 | − | 0.162118i | ||||
\(863\) | 6.44987e7i | 0.100350i | 0.998740 | + | 0.0501752i | \(0.0159780\pi\) | ||||
−0.998740 | + | 0.0501752i | \(0.984022\pi\) | |||||||
\(864\) | 1.52986e8 | − | 4.81909e8i | 0.237197 | − | 0.747177i | ||||
\(865\) | −5.12653e7 | −0.0792092 | ||||||||
\(866\) | 1.68042e8 | + | 6.50824e8i | 0.258740 | + | 1.00210i | ||||
\(867\) | 4.40842e7i | 0.0676435i | ||||||||
\(868\) | 7.26835e8 | − | 4.02146e8i | 1.11142 | − | 0.614928i | ||||
\(869\) | −2.98433e8 | −0.454766 | ||||||||
\(870\) | 6.11952e7 | − | 1.58005e7i | 0.0929308 | − | 0.0239946i | ||||
\(871\) | − | 5.77818e8i | − | 0.874453i | ||||||
\(872\) | −5.40580e8 | − | 5.70997e8i | −0.815287 | − | 0.861161i | ||||
\(873\) | 3.36587e8 | 0.505888 | ||||||||
\(874\) | 1.57697e8 | + | 6.10759e8i | 0.236205 | + | 0.914820i | ||||
\(875\) | − | 9.65147e7i | − | 0.144069i | ||||||
\(876\) | 2.77081e8 | + | 5.00794e8i | 0.412187 | + | 0.744984i | ||||
\(877\) | 5.15252e8 | 0.763873 | 0.381937 | − | 0.924189i | \(-0.375257\pi\) | ||||
0.381937 | + | 0.924189i | \(0.375257\pi\) | |||||||
\(878\) | 1.14729e9 | − | 2.96230e8i | 1.69508 | − | 0.437669i | ||||
\(879\) | 1.38007e9i | 2.03205i | ||||||||
\(880\) | −3.33312e7 | − | 2.09005e7i | −0.0489106 | − | 0.0306696i | ||||
\(881\) | −1.18519e8 | −0.173324 | −0.0866622 | − | 0.996238i | \(-0.527620\pi\) | ||||
−0.0866622 | + | 0.996238i | \(0.527620\pi\) | |||||||
\(882\) | −1.00018e7 | − | 3.87370e7i | −0.0145772 | − | 0.0564572i | ||||
\(883\) | − | 1.28669e8i | − | 0.186893i | −0.995624 | − | 0.0934466i | \(-0.970212\pi\) | ||
0.995624 | − | 0.0934466i | \(-0.0297884\pi\) | |||||||
\(884\) | 3.91270e8 | − | 2.16483e8i | 0.566395 | − | 0.313377i | ||||
\(885\) | −2.42976e7 | −0.0350537 | ||||||||
\(886\) | −6.22571e8 | + | 1.60747e8i | −0.895133 | + | 0.231122i | ||||
\(887\) | 5.09948e8i | 0.730727i | 0.930865 | + | 0.365363i | \(0.119055\pi\) | ||||
−0.930865 | + | 0.365363i | \(0.880945\pi\) | |||||||
\(888\) | −2.29709e7 | + | 2.17472e7i | −0.0328049 | + | 0.0310574i | ||||
\(889\) | −5.18861e8 | −0.738492 | ||||||||
\(890\) | 6.21476e6 | + | 2.40697e7i | 0.00881565 | + | 0.0341429i | ||||
\(891\) | 6.20943e8i | 0.877847i | ||||||||
\(892\) | −1.03212e8 | − | 1.86544e8i | −0.145423 | − | 0.262837i | ||||
\(893\) | 5.69203e7 | 0.0799306 | ||||||||
\(894\) | −7.85823e8 | + | 2.02899e8i | −1.09980 | + | 0.283966i | ||||
\(895\) | − | 2.33411e7i | − | 0.0325576i | ||||||
\(896\) | −1.27795e8 | − | 6.37088e8i | −0.177660 | − | 0.885677i | ||||
\(897\) | −4.75688e8 | −0.659090 | ||||||||
\(898\) | −1.76185e8 | − | 6.82362e8i | −0.243299 | − | 0.942293i | ||||
\(899\) | 1.06812e9i | 1.47007i | ||||||||
\(900\) | −2.00831e8 | + | 1.11117e8i | −0.275489 | + | 0.152423i | ||||
\(901\) | 9.19142e8 | 1.25663 | ||||||||
\(902\) | 2.18453e8 | − | 5.64044e7i | 0.297673 | − | 0.0768588i | ||||
\(903\) | − | 2.06724e8i | − | 0.280756i | ||||||
\(904\) | 2.11796e8 | + | 2.23714e8i | 0.286690 | + | 0.302822i | ||||
\(905\) | 9.69156e7 | 0.130752 | ||||||||
\(906\) | −3.46618e8 | − | 1.34244e9i | −0.466086 | − | 1.80514i | ||||
\(907\) | − | 5.43212e8i | − | 0.728027i | −0.931394 | − | 0.364014i | \(-0.881406\pi\) | ||
0.931394 | − | 0.364014i | \(-0.118594\pi\) | |||||||
\(908\) | 4.18384e8 | + | 7.56185e8i | 0.558879 | + | 1.01011i | ||||
\(909\) | 1.47645e8 | 0.196575 | ||||||||
\(910\) | −3.51840e7 | + | 9.08447e6i | −0.0466897 | + | 0.0120552i | ||||
\(911\) | − | 5.99585e8i | − | 0.793041i | −0.918026 | − | 0.396520i | \(-0.870218\pi\) | ||
0.918026 | − | 0.396520i | \(-0.129782\pi\) | |||||||
\(912\) | 5.07617e8 | − | 8.09527e8i | 0.669194 | − | 1.06720i | ||||
\(913\) | −1.96089e8 | −0.257656 | ||||||||
\(914\) | −7.50846e7 | − | 2.90801e8i | −0.0983359 | − | 0.380853i | ||||
\(915\) | 3.38282e6i | 0.00441586i | ||||||||
\(916\) | −8.93748e7 | + | 4.94496e7i | −0.116286 | + | 0.0643393i | ||||
\(917\) | −8.81347e8 | −1.14298 | ||||||||
\(918\) | −5.69632e8 | + | 1.47078e8i | −0.736320 | + | 0.190117i | ||||
\(919\) | − | 9.66486e8i | − | 1.24523i | −0.782529 | − | 0.622614i | \(-0.786071\pi\) | ||
0.782529 | − | 0.622614i | \(-0.213929\pi\) | |||||||
\(920\) | −3.89376e7 | + | 3.68634e7i | −0.0500041 | + | 0.0473404i | ||||
\(921\) | −1.51527e9 | −1.93959 | ||||||||
\(922\) | 2.30520e8 | + | 8.92800e8i | 0.294114 | + | 1.13910i | ||||
\(923\) | 7.80265e8i | 0.992286i | ||||||||
\(924\) | 2.85696e8 | + | 5.16365e8i | 0.362150 | + | 0.654547i | ||||
\(925\) | −3.09568e7 | −0.0391139 | ||||||||
\(926\) | 8.01053e7 | − | 2.06831e7i | 0.100885 | − | 0.0260485i | ||||
\(927\) | − | 3.20889e8i | − | 0.402825i | ||||||
\(928\) | 7.96354e8 | + | 2.52809e8i | 0.996465 | + | 0.316335i | ||||
\(929\) | 7.22626e8 | 0.901295 | 0.450647 | − | 0.892702i | \(-0.351193\pi\) | ||||
0.450647 | + | 0.892702i | \(0.351193\pi\) | |||||||
\(930\) | 2.59584e7 | + | 1.00536e8i | 0.0322722 | + | 0.124990i | ||||
\(931\) | 1.62997e8i | 0.201990i | ||||||||
\(932\) | −4.50454e8 | + | 2.49229e8i | −0.556420 | + | 0.307858i | ||||
\(933\) | 1.54988e9 | 1.90832 | ||||||||
\(934\) | −1.27206e9 | + | 3.28445e8i | −1.56123 | + | 0.403109i | ||||
\(935\) | 4.57774e7i | 0.0560037i | ||||||||
\(936\) | 1.19203e8 | + | 1.25911e8i | 0.145365 | + | 0.153545i | ||||
\(937\) | −4.12016e8 | −0.500836 | −0.250418 | − | 0.968138i | \(-0.580568\pi\) | ||||
−0.250418 | + | 0.968138i | \(0.580568\pi\) | |||||||
\(938\) | 2.44243e8 | + | 9.45950e8i | 0.295947 | + | 1.14620i | ||||
\(939\) | − | 3.49246e7i | − | 0.0421827i | ||||||
\(940\) | 2.34240e6 | + | 4.23364e6i | 0.00282018 | + | 0.00509718i | ||||
\(941\) | 7.87666e8 | 0.945308 | 0.472654 | − | 0.881248i | \(-0.343296\pi\) | ||||
0.472654 | + | 0.881248i | \(0.343296\pi\) | |||||||
\(942\) | 1.96031e8 | − | 5.06149e7i | 0.234515 | − | 0.0605516i | ||||
\(943\) | − | 3.07495e8i | − | 0.366693i | ||||||
\(944\) | −2.72133e8 | − | 1.70642e8i | −0.323493 | − | 0.202848i | ||||
\(945\) | 4.78080e7 | 0.0566507 | ||||||||
\(946\) | −4.13664e7 | − | 1.60211e8i | −0.0488623 | − | 0.189243i | ||||
\(947\) | − | 5.29504e8i | − | 0.623475i | −0.950168 | − | 0.311738i | \(-0.899089\pi\) | ||
0.950168 | − | 0.311738i | \(-0.100911\pi\) | |||||||
\(948\) | 5.39105e8 | − | 2.98278e8i | 0.632774 | − | 0.350103i | ||||
\(949\) | 4.23126e8 | 0.495075 | ||||||||
\(950\) | 9.05418e8 | − | 2.33778e8i | 1.05603 | − | 0.272667i | ||||
\(951\) | − | 1.06858e9i | − | 1.24241i | ||||||
\(952\) | −5.49043e8 | + | 5.19795e8i | −0.636349 | + | 0.602451i | ||||
\(953\) | 1.18323e9 | 1.36706 | 0.683532 | − | 0.729920i | \(-0.260443\pi\) | ||||
0.683532 | + | 0.729920i | \(0.260443\pi\) | |||||||
\(954\) | 8.90985e7 | + | 3.45077e8i | 0.102618 | + | 0.397440i | ||||
\(955\) | − | 1.14164e8i | − | 0.131075i | ||||||
\(956\) | −3.48668e8 | − | 6.30180e8i | −0.399060 | − | 0.721259i | ||||
\(957\) | −7.58820e8 | −0.865771 | ||||||||
\(958\) | −6.01265e8 | + | 1.55246e8i | −0.683864 | + | 0.176573i | ||||
\(959\) | 1.18050e9i | 1.33847i | ||||||||
\(960\) | 8.11008e7 | + | 4.44185e6i | 0.0916667 | + | 0.00502053i | ||||
\(961\) | −8.67284e8 | −0.977218 | ||||||||
\(962\) | 5.84641e6 | + | 2.26430e7i | 0.00656695 | + | 0.0254337i | ||||
\(963\) | 2.65499e8i | 0.297293i | ||||||||
\(964\) | −2.82858e8 | + | 1.56501e8i | −0.315746 | + | 0.174697i | ||||
\(965\) | −2.43033e7 | −0.0270448 | ||||||||
\(966\) | 7.78752e8 | − | 2.01073e8i | 0.863909 | − | 0.223060i | ||||
\(967\) | 4.78688e8i | 0.529387i | 0.964333 | + | 0.264693i | \(0.0852708\pi\) | ||||
−0.964333 | + | 0.264693i | \(0.914729\pi\) | |||||||
\(968\) | −2.98848e8 | − | 3.15664e8i | −0.329477 | − | 0.348016i | ||||
\(969\) | −1.11181e9 | −1.22197 | ||||||||
\(970\) | −2.91417e7 | − | 1.12865e8i | −0.0319301 | − | 0.123665i | ||||
\(971\) | − | 7.02914e8i | − | 0.767793i | −0.923376 | − | 0.383897i | \(-0.874582\pi\) | ||
0.923376 | − | 0.383897i | \(-0.125418\pi\) | |||||||
\(972\) | −2.72100e8 | − | 4.91791e8i | −0.296298 | − | 0.535527i | ||||
\(973\) | −4.30176e7 | −0.0466990 | ||||||||
\(974\) | 8.37115e7 | − | 2.16142e7i | 0.0905959 | − | 0.0233918i | ||||
\(975\) | 7.05182e8i | 0.760830i | ||||||||
\(976\) | −2.37576e7 | + | 3.78876e7i | −0.0255536 | + | 0.0407518i | ||||
\(977\) | −9.21323e8 | −0.987934 | −0.493967 | − | 0.869481i | \(-0.664454\pi\) | ||||
−0.493967 | + | 0.869481i | \(0.664454\pi\) | |||||||
\(978\) | −1.14388e8 | − | 4.43022e8i | −0.122282 | − | 0.473597i | ||||
\(979\) | − | 2.98464e8i | − | 0.318085i | ||||||
\(980\) | −1.21234e7 | + | 6.70770e6i | −0.0128809 | + | 0.00712681i | ||||
\(981\) | −3.54755e8 | −0.375770 | ||||||||
\(982\) | 1.43352e9 | − | 3.70133e8i | 1.51380 | − | 0.390862i | ||||
\(983\) | 2.44410e8i | 0.257311i | 0.991689 | + | 0.128655i | \(0.0410661\pi\) | ||||
−0.991689 | + | 0.128655i | \(0.958934\pi\) | |||||||
\(984\) | −3.38250e8 | + | 3.20231e8i | −0.355020 | + | 0.336108i | ||||
\(985\) | −2.23065e7 | −0.0233411 | ||||||||
\(986\) | −2.43047e8 | − | 9.41317e8i | −0.253548 | − | 0.981985i | ||||
\(987\) | − | 7.25766e7i | − | 0.0754823i | ||||||
\(988\) | −3.41988e8 | − | 6.18107e8i | −0.354602 | − | 0.640904i | ||||
\(989\) | −2.25514e8 | −0.233122 | ||||||||
\(990\) | −1.71864e7 | + | 4.43751e6i | −0.0177125 | + | 0.00457334i | ||||
\(991\) | 1.78184e9i | 1.83083i | 0.402516 | + | 0.915413i | \(0.368136\pi\) | ||||
−0.402516 | + | 0.915413i | \(0.631864\pi\) | |||||||
\(992\) | −4.15334e8 | + | 1.30831e9i | −0.425464 | + | 1.34022i | ||||
\(993\) | 1.24771e9 | 1.27428 | ||||||||
\(994\) | −3.29818e8 | − | 1.27738e9i | −0.335826 | − | 1.30065i | ||||
\(995\) | 4.89576e7i | 0.0496994i | ||||||||
\(996\) | 3.54225e8 | − | 1.95987e8i | 0.358510 | − | 0.198357i | ||||
\(997\) | 1.36790e9 | 1.38029 | 0.690143 | − | 0.723673i | \(-0.257548\pi\) | ||||
0.690143 | + | 0.723673i | \(0.257548\pi\) | |||||||
\(998\) | 5.29595e8 | − | 1.36741e8i | 0.532785 | − | 0.137565i | ||||
\(999\) | − | 3.07674e7i | − | 0.0308598i |
(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 | 4.7.b.a.3.2 | yes | 2 | |
3.2 | odd | 2 | 36.7.d.c.19.1 | 2 | |||
4.3 | odd | 2 | inner | 4.7.b.a.3.1 | ✓ | 2 | |
5.2 | odd | 4 | 100.7.d.a.99.2 | 4 | |||
5.3 | odd | 4 | 100.7.d.a.99.3 | 4 | |||
5.4 | even | 2 | 100.7.b.c.51.1 | 2 | |||
8.3 | odd | 2 | 64.7.c.c.63.1 | 2 | |||
8.5 | even | 2 | 64.7.c.c.63.2 | 2 | |||
12.11 | even | 2 | 36.7.d.c.19.2 | 2 | |||
16.3 | odd | 4 | 256.7.d.f.127.1 | 4 | |||
16.5 | even | 4 | 256.7.d.f.127.2 | 4 | |||
16.11 | odd | 4 | 256.7.d.f.127.4 | 4 | |||
16.13 | even | 4 | 256.7.d.f.127.3 | 4 | |||
20.3 | even | 4 | 100.7.d.a.99.1 | 4 | |||
20.7 | even | 4 | 100.7.d.a.99.4 | 4 | |||
20.19 | odd | 2 | 100.7.b.c.51.2 | 2 | |||
24.5 | odd | 2 | 576.7.g.h.127.2 | 2 | |||
24.11 | even | 2 | 576.7.g.h.127.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.7.b.a.3.1 | ✓ | 2 | 4.3 | odd | 2 | inner | |
4.7.b.a.3.2 | yes | 2 | 1.1 | even | 1 | trivial | |
36.7.d.c.19.1 | 2 | 3.2 | odd | 2 | |||
36.7.d.c.19.2 | 2 | 12.11 | even | 2 | |||
64.7.c.c.63.1 | 2 | 8.3 | odd | 2 | |||
64.7.c.c.63.2 | 2 | 8.5 | even | 2 | |||
100.7.b.c.51.1 | 2 | 5.4 | even | 2 | |||
100.7.b.c.51.2 | 2 | 20.19 | odd | 2 | |||
100.7.d.a.99.1 | 4 | 20.3 | even | 4 | |||
100.7.d.a.99.2 | 4 | 5.2 | odd | 4 | |||
100.7.d.a.99.3 | 4 | 5.3 | odd | 4 | |||
100.7.d.a.99.4 | 4 | 20.7 | even | 4 | |||
256.7.d.f.127.1 | 4 | 16.3 | odd | 4 | |||
256.7.d.f.127.2 | 4 | 16.5 | even | 4 | |||
256.7.d.f.127.3 | 4 | 16.13 | even | 4 | |||
256.7.d.f.127.4 | 4 | 16.11 | odd | 4 | |||
576.7.g.h.127.1 | 2 | 24.11 | even | 2 | |||
576.7.g.h.127.2 | 2 | 24.5 | odd | 2 |