Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.14 | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.6.c.d.146.13 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.7583i | 1.90181i | 0.309478 | + | 0.950907i | \(0.399846\pi\) | ||||
−0.309478 | + | 0.950907i | \(0.600154\pi\) | |||||||
\(3\) | 14.9806 | + | 4.31048i | 0.961009 | + | 0.276518i | ||||
\(4\) | −83.7406 | −2.61689 | ||||||||
\(5\) | −26.3120 | −0.470683 | −0.235342 | − | 0.971913i | \(-0.575621\pi\) | ||||
−0.235342 | + | 0.971913i | \(0.575621\pi\) | |||||||
\(6\) | −46.3734 | + | 161.166i | −0.525885 | + | 1.82766i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 556.640i | − | 3.07503i | ||||||
\(9\) | 205.839 | + | 129.148i | 0.847076 | + | 0.531472i | ||||
\(10\) | − | 283.072i | − | 0.895151i | ||||||
\(11\) | − | 604.422i | − | 1.50612i | −0.657954 | − | 0.753058i | \(-0.728578\pi\) | ||
0.657954 | − | 0.753058i | \(-0.271422\pi\) | |||||||
\(12\) | −1254.49 | − | 360.963i | −2.51486 | − | 0.723618i | ||||
\(13\) | − | 732.880i | − | 1.20275i | −0.798968 | − | 0.601374i | \(-0.794620\pi\) | ||
0.798968 | − | 0.601374i | \(-0.205380\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −394.170 | − | 113.417i | −0.452331 | − | 0.130152i | ||||
\(16\) | 3308.79 | 3.23124 | ||||||||
\(17\) | −1696.88 | −1.42406 | −0.712030 | − | 0.702149i | \(-0.752224\pi\) | ||||
−0.712030 | + | 0.702149i | \(0.752224\pi\) | |||||||
\(18\) | −1389.41 | + | 2214.48i | −1.01076 | + | 1.61098i | ||||
\(19\) | − | 211.839i | − | 0.134624i | −0.997732 | − | 0.0673120i | \(-0.978558\pi\) | ||
0.997732 | − | 0.0673120i | \(-0.0214423\pi\) | |||||||
\(20\) | 2203.38 | 1.23173 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6502.54 | 2.86435 | ||||||||
\(23\) | − | 966.176i | − | 0.380835i | −0.981703 | − | 0.190417i | \(-0.939016\pi\) | ||
0.981703 | − | 0.190417i | \(-0.0609842\pi\) | |||||||
\(24\) | 2399.39 | − | 8338.83i | 0.850301 | − | 2.95513i | ||||
\(25\) | −2432.68 | −0.778457 | ||||||||
\(26\) | 7884.53 | 2.28740 | ||||||||
\(27\) | 2526.92 | + | 2821.98i | 0.667086 | + | 0.744981i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 764.382i | 0.168778i | 0.996433 | + | 0.0843889i | \(0.0268938\pi\) | ||||
−0.996433 | + | 0.0843889i | \(0.973106\pi\) | |||||||
\(30\) | 1220.18 | − | 4240.60i | 0.247525 | − | 0.860248i | ||||
\(31\) | − | 79.9439i | − | 0.0149410i | −0.999972 | − | 0.00747052i | \(-0.997622\pi\) | ||
0.999972 | − | 0.00747052i | \(-0.00237796\pi\) | |||||||
\(32\) | 17784.4i | 3.07019i | ||||||||
\(33\) | 2605.35 | − | 9054.63i | 0.416468 | − | 1.44739i | ||||
\(34\) | − | 18255.5i | − | 2.70830i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −17237.1 | − | 10814.9i | −2.21671 | − | 1.39081i | ||||
\(37\) | −643.992 | −0.0773350 | −0.0386675 | − | 0.999252i | \(-0.512311\pi\) | ||||
−0.0386675 | + | 0.999252i | \(0.512311\pi\) | |||||||
\(38\) | 2279.03 | 0.256030 | ||||||||
\(39\) | 3159.07 | − | 10979.0i | 0.332581 | − | 1.15585i | ||||
\(40\) | 14646.3i | 1.44737i | ||||||||
\(41\) | −5200.75 | −0.483177 | −0.241589 | − | 0.970379i | \(-0.577668\pi\) | ||||
−0.241589 | + | 0.970379i | \(0.577668\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5841.96 | 0.481823 | 0.240912 | − | 0.970547i | \(-0.422554\pi\) | ||||
0.240912 | + | 0.970547i | \(0.422554\pi\) | |||||||
\(44\) | 50614.7i | 3.94135i | ||||||||
\(45\) | −5416.04 | − | 3398.13i | −0.398704 | − | 0.250155i | ||||
\(46\) | 10394.4 | 0.724277 | ||||||||
\(47\) | −10774.3 | −0.711449 | −0.355724 | − | 0.934591i | \(-0.615766\pi\) | ||||
−0.355724 | + | 0.934591i | \(0.615766\pi\) | |||||||
\(48\) | 49567.9 | + | 14262.5i | 3.10525 | + | 0.893496i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 26171.5i | − | 1.48048i | ||||||
\(51\) | −25420.3 | − | 7314.37i | −1.36854 | − | 0.393778i | ||||
\(52\) | 61371.9i | 3.14747i | ||||||||
\(53\) | 9768.69i | 0.477691i | 0.971058 | + | 0.238845i | \(0.0767689\pi\) | ||||
−0.971058 | + | 0.238845i | \(0.923231\pi\) | |||||||
\(54\) | −30359.7 | + | 27185.3i | −1.41681 | + | 1.26867i | ||||
\(55\) | 15903.5i | 0.708904i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 913.130 | − | 3173.49i | 0.0372259 | − | 0.129375i | ||||
\(58\) | −8223.44 | −0.320984 | ||||||||
\(59\) | −10491.3 | −0.392374 | −0.196187 | − | 0.980566i | \(-0.562856\pi\) | ||||
−0.196187 | + | 0.980566i | \(0.562856\pi\) | |||||||
\(60\) | 33008.1 | + | 9497.64i | 1.18370 | + | 0.340595i | ||||
\(61\) | − | 47115.9i | − | 1.62122i | −0.585585 | − | 0.810611i | \(-0.699135\pi\) | ||
0.585585 | − | 0.810611i | \(-0.300865\pi\) | |||||||
\(62\) | 860.059 | 0.0284151 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −85448.6 | −2.60769 | ||||||||
\(65\) | 19283.5i | 0.566113i | ||||||||
\(66\) | 97412.3 | + | 28029.1i | 2.75267 | + | 0.792044i | ||||
\(67\) | 48582.8 | 1.32219 | 0.661097 | − | 0.750300i | \(-0.270091\pi\) | ||||
0.661097 | + | 0.750300i | \(0.270091\pi\) | |||||||
\(68\) | 142098. | 3.72662 | ||||||||
\(69\) | 4164.69 | − | 14473.9i | 0.105308 | − | 0.365986i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 28803.7i | 0.678113i | 0.940766 | + | 0.339056i | \(0.110108\pi\) | ||||
−0.940766 | + | 0.339056i | \(0.889892\pi\) | |||||||
\(72\) | 71888.8 | − | 114579.i | 1.63429 | − | 2.60479i | ||||
\(73\) | − | 72915.2i | − | 1.60144i | −0.599038 | − | 0.800721i | \(-0.704450\pi\) | ||
0.599038 | − | 0.800721i | \(-0.295550\pi\) | |||||||
\(74\) | − | 6928.25i | − | 0.147077i | ||||||
\(75\) | −36443.1 | − | 10486.0i | −0.748104 | − | 0.215257i | ||||
\(76\) | 17739.6i | 0.352297i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 118115. | + | 33986.2i | 2.19821 | + | 0.632508i | ||||
\(79\) | −70838.8 | −1.27704 | −0.638518 | − | 0.769607i | \(-0.720452\pi\) | ||||
−0.638518 | + | 0.769607i | \(0.720452\pi\) | |||||||
\(80\) | −87060.9 | −1.52089 | ||||||||
\(81\) | 25690.7 | + | 53167.4i | 0.435075 | + | 0.900394i | ||||
\(82\) | − | 55951.1i | − | 0.918913i | ||||||
\(83\) | −33914.5 | −0.540368 | −0.270184 | − | 0.962809i | \(-0.587085\pi\) | ||||
−0.270184 | + | 0.962809i | \(0.587085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 44648.2 | 0.670281 | ||||||||
\(86\) | 62849.5i | 0.916338i | ||||||||
\(87\) | −3294.86 | + | 11450.9i | −0.0466701 | + | 0.162197i | ||||
\(88\) | −336446. | −4.63136 | ||||||||
\(89\) | −84328.4 | −1.12849 | −0.564247 | − | 0.825606i | \(-0.690833\pi\) | ||||
−0.564247 | + | 0.825606i | \(0.690833\pi\) | |||||||
\(90\) | 36558.1 | − | 58267.3i | 0.475748 | − | 0.758261i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 80908.2i | 0.996605i | ||||||||
\(93\) | 344.597 | − | 1197.61i | 0.00413147 | − | 0.0143585i | ||||
\(94\) | − | 115913.i | − | 1.35304i | ||||||
\(95\) | 5573.91i | 0.0633652i | ||||||||
\(96\) | −76659.6 | + | 266422.i | −0.848962 | + | 2.95048i | ||||
\(97\) | − | 17034.2i | − | 0.183819i | −0.995767 | − | 0.0919097i | \(-0.970703\pi\) | ||
0.995767 | − | 0.0919097i | \(-0.0292971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 78059.7 | − | 124414.i | 0.800459 | − | 1.27580i | ||||
\(100\) | 203714. | 2.03714 | ||||||||
\(101\) | −120183. | −1.17230 | −0.586151 | − | 0.810202i | \(-0.699357\pi\) | ||||
−0.586151 | + | 0.810202i | \(0.699357\pi\) | |||||||
\(102\) | 78690.1 | − | 273479.i | 0.748892 | − | 2.60270i | ||||
\(103\) | − | 94611.9i | − | 0.878725i | −0.898310 | − | 0.439362i | \(-0.855204\pi\) | ||
0.898310 | − | 0.439362i | \(-0.144796\pi\) | |||||||
\(104\) | −407951. | −3.69849 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −105094. | −0.908479 | ||||||||
\(107\) | − | 17922.6i | − | 0.151335i | −0.997133 | − | 0.0756677i | \(-0.975891\pi\) | ||
0.997133 | − | 0.0756677i | \(-0.0241088\pi\) | |||||||
\(108\) | −211606. | − | 236315.i | −1.74569 | − | 1.94954i | ||||
\(109\) | 66214.4 | 0.533809 | 0.266905 | − | 0.963723i | \(-0.413999\pi\) | ||||
0.266905 | + | 0.963723i | \(0.413999\pi\) | |||||||
\(110\) | −171095. | −1.34820 | ||||||||
\(111\) | −9647.42 | − | 2775.92i | −0.0743196 | − | 0.0213845i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 138434.i | − | 1.01988i | −0.860211 | − | 0.509938i | \(-0.829668\pi\) | ||
0.860211 | − | 0.509938i | \(-0.170332\pi\) | |||||||
\(114\) | 34141.3 | + | 9823.71i | 0.246047 | + | 0.0707968i | ||||
\(115\) | 25422.0i | 0.179253i | ||||||||
\(116\) | − | 64009.8i | − | 0.441674i | ||||||
\(117\) | 94649.8 | − | 150856.i | 0.639227 | − | 1.01882i | ||||
\(118\) | − | 112869.i | − | 0.746223i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −63132.7 | + | 219411.i | −0.400222 | + | 1.39093i | ||||
\(121\) | −204275. | −1.26839 | ||||||||
\(122\) | 506886. | 3.08326 | ||||||||
\(123\) | −77910.6 | − | 22417.8i | −0.464338 | − | 0.133607i | ||||
\(124\) | 6694.55i | 0.0390992i | ||||||||
\(125\) | 146234. | 0.837090 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 207046. | 1.13909 | 0.569545 | − | 0.821960i | \(-0.307119\pi\) | ||||
0.569545 | + | 0.821960i | \(0.307119\pi\) | |||||||
\(128\) | − | 350178.i | − | 1.88914i | ||||||
\(129\) | 87516.4 | + | 25181.7i | 0.463036 | + | 0.133233i | ||||
\(130\) | −207458. | −1.07664 | ||||||||
\(131\) | 202375. | 1.03033 | 0.515167 | − | 0.857090i | \(-0.327730\pi\) | ||||
0.515167 | + | 0.857090i | \(0.327730\pi\) | |||||||
\(132\) | −218174. | + | 758241.i | −1.08985 | + | 3.78767i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 522667.i | 2.51457i | ||||||||
\(135\) | −66488.2 | − | 74252.0i | −0.313986 | − | 0.350650i | ||||
\(136\) | 944551.i | 4.37903i | ||||||||
\(137\) | − | 1182.37i | − | 0.00538211i | −0.999996 | − | 0.00269106i | \(-0.999143\pi\) | ||
0.999996 | − | 0.00269106i | \(-0.000856591\pi\) | |||||||
\(138\) | 155715. | + | 44804.9i | 0.696037 | + | 0.200275i | ||||
\(139\) | − | 103308.i | − | 0.453519i | −0.973951 | − | 0.226760i | \(-0.927187\pi\) | ||
0.973951 | − | 0.226760i | \(-0.0728132\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −161406. | − | 46442.4i | −0.683709 | − | 0.196728i | ||||
\(142\) | −309878. | −1.28964 | ||||||||
\(143\) | −442969. | −1.81148 | ||||||||
\(144\) | 681080. | + | 427323.i | 2.73711 | + | 1.71732i | ||||
\(145\) | − | 20112.4i | − | 0.0794409i | ||||||
\(146\) | 784443. | 3.04564 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 53928.3 | 0.202378 | ||||||||
\(149\) | − | 383207.i | − | 1.41406i | −0.707184 | − | 0.707029i | \(-0.750035\pi\) | ||
0.707184 | − | 0.707029i | \(-0.249965\pi\) | |||||||
\(150\) | 112812. | − | 392065.i | 0.409379 | − | 1.42276i | ||||
\(151\) | 411512. | 1.46872 | 0.734361 | − | 0.678759i | \(-0.237482\pi\) | ||||
0.734361 | + | 0.678759i | \(0.237482\pi\) | |||||||
\(152\) | −117918. | −0.413973 | ||||||||
\(153\) | −349285. | − | 219148.i | −1.20629 | − | 0.756848i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2103.48i | 0.00703250i | ||||||||
\(156\) | −264543. | + | 919390.i | −0.870330 | + | 3.02474i | ||||
\(157\) | 560413.i | 1.81451i | 0.420582 | + | 0.907255i | \(0.361826\pi\) | ||||
−0.420582 | + | 0.907255i | \(0.638174\pi\) | |||||||
\(158\) | − | 762103.i | − | 2.42868i | ||||||
\(159\) | −42107.8 | + | 146341.i | −0.132090 | + | 0.459065i | ||||
\(160\) | − | 467944.i | − | 1.44509i | ||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −571990. | + | 276388.i | −1.71238 | + | 0.827432i | ||||
\(163\) | 575063. | 1.69530 | 0.847650 | − | 0.530556i | \(-0.178017\pi\) | ||||
0.847650 | + | 0.530556i | \(0.178017\pi\) | |||||||
\(164\) | 435514. | 1.26442 | ||||||||
\(165\) | −68552.0 | + | 238245.i | −0.196024 | + | 0.681263i | ||||
\(166\) | − | 364861.i | − | 1.02768i | ||||||
\(167\) | −101689. | −0.282151 | −0.141076 | − | 0.989999i | \(-0.545056\pi\) | ||||
−0.141076 | + | 0.989999i | \(0.545056\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −165821. | −0.446604 | ||||||||
\(170\) | 480338.i | 1.27475i | ||||||||
\(171\) | 27358.6 | − | 43604.9i | 0.0715489 | − | 0.114037i | ||||
\(172\) | −489210. | −1.26088 | ||||||||
\(173\) | −741653. | −1.88402 | −0.942011 | − | 0.335583i | \(-0.891067\pi\) | ||||
−0.942011 | + | 0.335583i | \(0.891067\pi\) | |||||||
\(174\) | −123192. | − | 35447.0i | −0.308469 | − | 0.0887578i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.99991e6i | − | 4.86663i | ||||||
\(177\) | −157167. | − | 45222.7i | −0.377075 | − | 0.108499i | ||||
\(178\) | − | 907229.i | − | 2.14618i | ||||||
\(179\) | 383196.i | 0.893900i | 0.894559 | + | 0.446950i | \(0.147490\pi\) | ||||
−0.894559 | + | 0.446950i | \(0.852510\pi\) | |||||||
\(180\) | 453543. | + | 284562.i | 1.04337 | + | 0.654629i | ||||
\(181\) | 549563.i | 1.24687i | 0.781875 | + | 0.623435i | \(0.214264\pi\) | ||||
−0.781875 | + | 0.623435i | \(0.785736\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 203092. | − | 705826.i | 0.448297 | − | 1.55801i | ||||
\(184\) | −537813. | −1.17108 | ||||||||
\(185\) | 16944.7 | 0.0364003 | ||||||||
\(186\) | 12884.2 | + | 3707.27i | 0.0273072 | + | 0.00785728i | ||||
\(187\) | 1.02563e6i | 2.14480i | ||||||||
\(188\) | 902245. | 1.86179 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −59965.7 | −0.120509 | ||||||||
\(191\) | − | 477.490i | − | 0.000947068i | −1.00000 | 0.000473534i | \(-0.999849\pi\) | |||
1.00000 | 0.000473534i | \(-0.000150731\pi\) | ||||||||
\(192\) | −1.28008e6 | − | 368325.i | −2.50601 | − | 0.721071i | ||||
\(193\) | −853061. | −1.64849 | −0.824246 | − | 0.566232i | \(-0.808401\pi\) | ||||
−0.824246 | + | 0.566232i | \(0.808401\pi\) | |||||||
\(194\) | 183258. | 0.349590 | ||||||||
\(195\) | −83121.4 | + | 288880.i | −0.156540 | + | 0.544040i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 859613.i | 1.57811i | 0.614322 | + | 0.789056i | \(0.289430\pi\) | ||||
−0.614322 | + | 0.789056i | \(0.710570\pi\) | |||||||
\(198\) | 1.33848e6 | + | 839788.i | 2.42632 | + | 1.52232i | ||||
\(199\) | − | 468982.i | − | 0.839506i | −0.907638 | − | 0.419753i | \(-0.862117\pi\) | ||
0.907638 | − | 0.419753i | \(-0.137883\pi\) | |||||||
\(200\) | 1.35413e6i | 2.39378i | ||||||||
\(201\) | 727802. | + | 209415.i | 1.27064 | + | 0.365610i | ||||
\(202\) | − | 1.29296e6i | − | 2.22950i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 2.12872e6 | + | 612510.i | 3.58131 | + | 1.03048i | ||||
\(205\) | 136842. | 0.227423 | ||||||||
\(206\) | 1.01786e6 | 1.67117 | ||||||||
\(207\) | 124779. | − | 198877.i | 0.202403 | − | 0.322596i | ||||
\(208\) | − | 2.42495e6i | − | 3.88637i | ||||||
\(209\) | −128040. | −0.202759 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −961141. | −1.48621 | −0.743106 | − | 0.669174i | \(-0.766648\pi\) | ||||
−0.743106 | + | 0.669174i | \(0.766648\pi\) | |||||||
\(212\) | − | 818037.i | − | 1.25007i | ||||||
\(213\) | −124158. | + | 431498.i | −0.187510 | + | 0.651672i | ||||
\(214\) | 192816. | 0.287812 | ||||||||
\(215\) | −153714. | −0.226786 | ||||||||
\(216\) | 1.57083e6 | − | 1.40658e6i | 2.29084 | − | 2.05131i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 712353.i | 1.01521i | ||||||||
\(219\) | 314300. | − | 1.09232e6i | 0.442827 | − | 1.53900i | ||||
\(220\) | − | 1.33177e6i | − | 1.85513i | ||||||
\(221\) | 1.24361e6i | 1.71279i | ||||||||
\(222\) | 29864.1 | − | 103790.i | 0.0406693 | − | 0.141342i | ||||
\(223\) | 74345.3i | 0.100113i | 0.998746 | + | 0.0500566i | \(0.0159402\pi\) | ||||
−0.998746 | + | 0.0500566i | \(0.984060\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −500741. | − | 314175.i | −0.659413 | − | 0.413728i | ||||
\(226\) | 1.48931e6 | 1.93961 | ||||||||
\(227\) | −1.00173e6 | −1.29029 | −0.645146 | − | 0.764060i | \(-0.723203\pi\) | ||||
−0.645146 | + | 0.764060i | \(0.723203\pi\) | |||||||
\(228\) | −76466.1 | + | 265750.i | −0.0974163 | + | 0.338560i | ||||
\(229\) | − | 185220.i | − | 0.233400i | −0.993167 | − | 0.116700i | \(-0.962768\pi\) | ||
0.993167 | − | 0.116700i | \(-0.0372316\pi\) | |||||||
\(230\) | −273497. | −0.340905 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 425486. | 0.518997 | ||||||||
\(233\) | − | 483434.i | − | 0.583375i | −0.956514 | − | 0.291687i | \(-0.905783\pi\) | ||
0.956514 | − | 0.291687i | \(-0.0942167\pi\) | |||||||
\(234\) | 1.62295e6 | + | 1.01827e6i | 1.93760 | + | 1.21569i | ||||
\(235\) | 283493. | 0.334867 | ||||||||
\(236\) | 878551. | 1.02680 | ||||||||
\(237\) | −1.06121e6 | − | 305349.i | −1.22724 | − | 0.353123i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 305349.i | 0.345782i | 0.984941 | + | 0.172891i | \(0.0553108\pi\) | ||||
−0.984941 | + | 0.172891i | \(0.944689\pi\) | |||||||
\(240\) | −1.30423e6 | − | 375275.i | −1.46159 | − | 0.420553i | ||||
\(241\) | − | 141408.i | − | 0.156831i | −0.996921 | − | 0.0784157i | \(-0.975014\pi\) | ||
0.996921 | − | 0.0784157i | \(-0.0249861\pi\) | |||||||
\(242\) | − | 2.19765e6i | − | 2.41224i | ||||||
\(243\) | 155687. | + | 907221.i | 0.169136 | + | 0.985593i | ||||
\(244\) | 3.94551e6i | 4.24257i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 241177. | − | 838184.i | 0.254096 | − | 0.883083i | ||||
\(247\) | −155253. | −0.161919 | ||||||||
\(248\) | −44500.0 | −0.0459442 | ||||||||
\(249\) | −508060. | − | 146188.i | −0.519298 | − | 0.149421i | ||||
\(250\) | 1.57322e6i | 1.59199i | ||||||||
\(251\) | 1.49757e6 | 1.50039 | 0.750194 | − | 0.661218i | \(-0.229960\pi\) | ||||
0.750194 | + | 0.661218i | \(0.229960\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −583978. | −0.573582 | ||||||||
\(254\) | 2.22746e6i | 2.16634i | ||||||||
\(255\) | 668860. | + | 192456.i | 0.644146 | + | 0.185345i | ||||
\(256\) | 1.03296e6 | 0.985109 | ||||||||
\(257\) | 408325. | 0.385632 | 0.192816 | − | 0.981235i | \(-0.438238\pi\) | ||||
0.192816 | + | 0.981235i | \(0.438238\pi\) | |||||||
\(258\) | −270912. | + | 941526.i | −0.253384 | + | 0.880609i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 1.61482e6i | − | 1.48146i | ||||||
\(261\) | −98718.2 | + | 157340.i | −0.0897007 | + | 0.142968i | ||||
\(262\) | 2.17721e6i | 1.95950i | ||||||||
\(263\) | − | 777076.i | − | 0.692746i | −0.938097 | − | 0.346373i | \(-0.887413\pi\) | ||
0.938097 | − | 0.346373i | \(-0.112587\pi\) | |||||||
\(264\) | −5.04017e6 | − | 1.45024e6i | −4.45077 | − | 1.28065i | ||||
\(265\) | − | 257034.i | − | 0.224841i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.26329e6 | − | 363496.i | −1.08449 | − | 0.312048i | ||||
\(268\) | −4.06835e6 | −3.46004 | ||||||||
\(269\) | −1.81934e6 | −1.53297 | −0.766483 | − | 0.642264i | \(-0.777995\pi\) | ||||
−0.766483 | + | 0.642264i | \(0.777995\pi\) | |||||||
\(270\) | 798824. | − | 715299.i | 0.666871 | − | 0.597143i | ||||
\(271\) | − | 472882.i | − | 0.391137i | −0.980690 | − | 0.195569i | \(-0.937345\pi\) | ||
0.980690 | − | 0.195569i | \(-0.0626552\pi\) | |||||||
\(272\) | −5.61462e6 | −4.60149 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12720.3 | 0.0102358 | ||||||||
\(275\) | 1.47037e6i | 1.17245i | ||||||||
\(276\) | −348754. | + | 1.21206e6i | −0.275579 | + | 0.957746i | ||||
\(277\) | −623772. | −0.488457 | −0.244229 | − | 0.969718i | \(-0.578535\pi\) | ||||
−0.244229 | + | 0.969718i | \(0.578535\pi\) | |||||||
\(278\) | 1.11141e6 | 0.862509 | ||||||||
\(279\) | 10324.6 | − | 16455.6i | 0.00794075 | − | 0.0126562i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 827985.i | 0.625542i | 0.949828 | + | 0.312771i | \(0.101257\pi\) | ||||
−0.949828 | + | 0.312771i | \(0.898743\pi\) | |||||||
\(282\) | 499640. | − | 1.73645e6i | 0.374140 | − | 1.30029i | ||||
\(283\) | 1.28739e6i | 0.955527i | 0.878488 | + | 0.477764i | \(0.158552\pi\) | ||||
−0.878488 | + | 0.477764i | \(0.841448\pi\) | |||||||
\(284\) | − | 2.41204e6i | − | 1.77455i | ||||||
\(285\) | −24026.3 | + | 83500.8i | −0.0175216 | + | 0.0608946i | ||||
\(286\) | − | 4.76559e6i | − | 3.44510i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.29682e6 | + | 3.66074e6i | −1.63172 | + | 2.60068i | ||||
\(289\) | 1.45954e6 | 1.02795 | ||||||||
\(290\) | 216375. | 0.151082 | ||||||||
\(291\) | 73425.5 | − | 255183.i | 0.0508293 | − | 0.176652i | ||||
\(292\) | 6.10597e6i | 4.19080i | ||||||||
\(293\) | 1.78967e6 | 1.21788 | 0.608940 | − | 0.793217i | \(-0.291595\pi\) | ||||
0.608940 | + | 0.793217i | \(0.291595\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 276048. | 0.184684 | ||||||||
\(296\) | 358472.i | 0.237808i | ||||||||
\(297\) | 1.70567e6 | − | 1.52733e6i | 1.12203 | − | 1.00471i | ||||
\(298\) | 4.12265e6 | 2.68928 | ||||||||
\(299\) | −708092. | −0.458049 | ||||||||
\(300\) | 3.05177e6 | + | 878107.i | 1.95771 | + | 0.563306i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.42716e6i | 2.79324i | ||||||||
\(303\) | −1.80042e6 | − | 518047.i | −1.12659 | − | 0.324162i | ||||
\(304\) | − | 700932.i | − | 0.435003i | ||||||
\(305\) | 1.23971e6i | 0.763082i | ||||||||
\(306\) | 2.35766e6 | − | 3.75770e6i | 1.43938 | − | 2.29413i | ||||
\(307\) | 2.36447e6i | 1.43182i | 0.698195 | + | 0.715908i | \(0.253987\pi\) | ||||
−0.698195 | + | 0.715908i | \(0.746013\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 407823. | − | 1.41735e6i | 0.242983 | − | 0.844462i | ||||
\(310\) | −22629.9 | −0.0133745 | ||||||||
\(311\) | −1.75107e6 | −1.02660 | −0.513302 | − | 0.858208i | \(-0.671578\pi\) | ||||
−0.513302 | + | 0.858208i | \(0.671578\pi\) | |||||||
\(312\) | −6.11137e6 | − | 1.75847e6i | −3.55428 | − | 1.02270i | ||||
\(313\) | − | 1.75907e6i | − | 1.01490i | −0.861682 | − | 0.507449i | \(-0.830588\pi\) | ||
0.861682 | − | 0.507449i | \(-0.169412\pi\) | |||||||
\(314\) | −6.02908e6 | −3.45086 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.93208e6 | 3.34187 | ||||||||
\(317\) | − | 879467.i | − | 0.491554i | −0.969326 | − | 0.245777i | \(-0.920957\pi\) | ||
0.969326 | − | 0.245777i | \(-0.0790431\pi\) | |||||||
\(318\) | −1.57438e6 | − | 453008.i | −0.873056 | − | 0.251210i | ||||
\(319\) | 462009. | 0.254199 | ||||||||
\(320\) | 2.24832e6 | 1.22739 | ||||||||
\(321\) | 77254.9 | − | 268492.i | 0.0418469 | − | 0.145435i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 359466.i | 0.191713i | ||||||||
\(324\) | −2.15136e6 | − | 4.45227e6i | −1.13855 | − | 2.35624i | ||||
\(325\) | 1.78286e6i | 0.936288i | ||||||||
\(326\) | 6.18669e6i | 3.22414i | ||||||||
\(327\) | 991934. | + | 285416.i | 0.512995 | + | 0.147608i | ||||
\(328\) | 2.89495e6i | 1.48579i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.56311e6 | − | 737502.i | −1.29563 | − | 0.372802i | ||||
\(331\) | 450960. | 0.226239 | 0.113120 | − | 0.993581i | \(-0.463916\pi\) | ||||
0.113120 | + | 0.993581i | \(0.463916\pi\) | |||||||
\(332\) | 2.84002e6 | 1.41409 | ||||||||
\(333\) | −132559. | − | 83170.1i | −0.0655086 | − | 0.0411014i | ||||
\(334\) | − | 1.09400e6i | − | 0.536599i | ||||||
\(335\) | −1.27831e6 | −0.622335 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.01453e6 | 0.966273 | 0.483136 | − | 0.875545i | \(-0.339498\pi\) | ||||
0.483136 | + | 0.875545i | \(0.339498\pi\) | |||||||
\(338\) | − | 1.78395e6i | − | 0.849357i | ||||||
\(339\) | 596719. | − | 2.07383e6i | 0.282014 | − | 0.980110i | ||||
\(340\) | −3.73887e6 | −1.75406 | ||||||||
\(341\) | −48319.9 | −0.0225030 | ||||||||
\(342\) | 469114. | + | 294331.i | 0.216877 | + | 0.136073i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 3.25187e6i | − | 1.48162i | ||||||
\(345\) | −109581. | + | 380838.i | −0.0495665 | + | 0.172263i | ||||
\(346\) | − | 7.97892e6i | − | 3.58306i | ||||||
\(347\) | − | 2.27813e6i | − | 1.01568i | −0.861453 | − | 0.507838i | \(-0.830445\pi\) | ||
0.861453 | − | 0.507838i | \(-0.169555\pi\) | |||||||
\(348\) | 275913. | − | 958909.i | 0.122131 | − | 0.424453i | ||||
\(349\) | − | 3.15486e6i | − | 1.38649i | −0.720701 | − | 0.693246i | \(-0.756180\pi\) | ||
0.720701 | − | 0.693246i | \(-0.243820\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.06818e6 | − | 1.85193e6i | 0.896024 | − | 0.802337i | ||||
\(352\) | 1.07493e7 | 4.62406 | ||||||||
\(353\) | 3.04877e6 | 1.30223 | 0.651115 | − | 0.758979i | \(-0.274302\pi\) | ||||
0.651115 | + | 0.758979i | \(0.274302\pi\) | |||||||
\(354\) | 486519. | − | 1.69085e6i | 0.206344 | − | 0.717127i | ||||
\(355\) | − | 757882.i | − | 0.319176i | ||||||
\(356\) | 7.06172e6 | 2.95315 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.12253e6 | −1.70003 | ||||||||
\(359\) | 3.19970e6i | 1.31031i | 0.755496 | + | 0.655154i | \(0.227396\pi\) | ||||
−0.755496 | + | 0.655154i | \(0.772604\pi\) | |||||||
\(360\) | −1.89154e6 | + | 3.01479e6i | −0.769234 | + | 1.22603i | ||||
\(361\) | 2.43122e6 | 0.981876 | ||||||||
\(362\) | −5.91236e6 | −2.37132 | ||||||||
\(363\) | −3.06017e6 | − | 880524.i | −1.21893 | − | 0.350732i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.91854e6i | 0.753771i | ||||||||
\(366\) | 7.59348e6 | + | 2.18492e6i | 2.96304 | + | 0.852577i | ||||
\(367\) | − | 2.78935e6i | − | 1.08103i | −0.841334 | − | 0.540515i | \(-0.818229\pi\) | ||
0.841334 | − | 0.540515i | \(-0.181771\pi\) | |||||||
\(368\) | − | 3.19688e6i | − | 1.23057i | ||||||
\(369\) | −1.07052e6 | − | 671665.i | −0.409288 | − | 0.256795i | ||||
\(370\) | 182296.i | 0.0692266i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −28856.8 | + | 100289.i | −0.0108116 | + | 0.0375746i | ||||
\(373\) | −2.57875e6 | −0.959703 | −0.479852 | − | 0.877350i | \(-0.659310\pi\) | ||||
−0.479852 | + | 0.877350i | \(0.659310\pi\) | |||||||
\(374\) | −1.10340e7 | −4.07901 | ||||||||
\(375\) | 2.19067e6 | + | 630338.i | 0.804451 | + | 0.231470i | ||||
\(376\) | 5.99740e6i | 2.18773i | ||||||||
\(377\) | 560201. | 0.202997 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.95401e6 | 1.05636 | 0.528182 | − | 0.849131i | \(-0.322874\pi\) | ||||
0.528182 | + | 0.849131i | \(0.322874\pi\) | |||||||
\(380\) | − | 466763.i | − | 0.165820i | ||||||
\(381\) | 3.10169e6 | + | 892469.i | 1.09468 | + | 0.314979i | ||||
\(382\) | 5136.97 | 0.00180115 | ||||||||
\(383\) | −3.98378e6 | −1.38771 | −0.693854 | − | 0.720116i | \(-0.744089\pi\) | ||||
−0.693854 | + | 0.720116i | \(0.744089\pi\) | |||||||
\(384\) | 1.50944e6 | − | 5.24590e6i | 0.522381 | − | 1.81548i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.17747e6i | − | 3.13513i | ||||||
\(387\) | 1.20251e6 | + | 754476.i | 0.408141 | + | 0.256075i | ||||
\(388\) | 1.42645e6i | 0.481036i | ||||||||
\(389\) | 623403.i | 0.208879i | 0.994531 | + | 0.104440i | \(0.0333049\pi\) | ||||
−0.994531 | + | 0.104440i | \(0.966695\pi\) | |||||||
\(390\) | −3.10785e6 | − | 894243.i | −1.03466 | − | 0.297711i | ||||
\(391\) | 1.63948e6i | 0.542332i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.03171e6 | + | 872334.i | 0.990161 | + | 0.284906i | ||||
\(394\) | −9.24796e6 | −3.00127 | ||||||||
\(395\) | 1.86391e6 | 0.601079 | ||||||||
\(396\) | −6.53677e6 | + | 1.04185e7i | −2.09472 | + | 3.33862i | ||||
\(397\) | − | 3.52878e6i | − | 1.12370i | −0.827240 | − | 0.561848i | \(-0.810091\pi\) | ||
0.827240 | − | 0.561848i | \(-0.189909\pi\) | |||||||
\(398\) | 5.04544e6 | 1.59658 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.04923e6 | −2.51539 | ||||||||
\(401\) | 1.29986e6i | 0.403679i | 0.979419 | + | 0.201840i | \(0.0646919\pi\) | ||||
−0.979419 | + | 0.201840i | \(0.935308\pi\) | |||||||
\(402\) | −2.25295e6 | + | 7.82989e6i | −0.695323 | + | 2.41652i | ||||
\(403\) | −58589.3 | −0.0179703 | ||||||||
\(404\) | 1.00642e7 | 3.06779 | ||||||||
\(405\) | −675975. | − | 1.39894e6i | −0.204782 | − | 0.423800i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 389243.i | 0.116476i | ||||||||
\(408\) | −4.07147e6 | + | 1.41500e7i | −1.21088 | + | 4.20829i | ||||
\(409\) | 227103.i | 0.0671297i | 0.999437 | + | 0.0335648i | \(0.0106860\pi\) | ||||
−0.999437 | + | 0.0335648i | \(0.989314\pi\) | |||||||
\(410\) | 1.47219e6i | 0.432517i | ||||||||
\(411\) | 5096.60 | − | 17712.7i | 0.00148825 | − | 0.00517226i | ||||
\(412\) | 7.92286e6i | 2.29953i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.13958e6 | + | 1.34241e6i | 0.613518 | + | 0.384933i | ||||
\(415\) | 892356. | 0.254342 | ||||||||
\(416\) | 1.30339e7 | 3.69267 | ||||||||
\(417\) | 445306. | − | 1.54762e6i | 0.125406 | − | 0.435836i | ||||
\(418\) | − | 1.37749e6i | − | 0.385611i | ||||||
\(419\) | 2.43482e6 | 0.677536 | 0.338768 | − | 0.940870i | \(-0.389990\pi\) | ||||
0.338768 | + | 0.940870i | \(0.389990\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 566569. | 0.155793 | 0.0778965 | − | 0.996961i | \(-0.475180\pi\) | ||||
0.0778965 | + | 0.996961i | \(0.475180\pi\) | |||||||
\(422\) | − | 1.03402e7i | − | 2.82650i | ||||||
\(423\) | −2.21777e6 | − | 1.39147e6i | −0.602651 | − | 0.378115i | ||||
\(424\) | 5.43765e6 | 1.46891 | ||||||||
\(425\) | 4.12796e6 | 1.10857 | ||||||||
\(426\) | −4.64217e6 | − | 1.33572e6i | −1.23936 | − | 0.356609i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.50085e6i | 0.396029i | ||||||||
\(429\) | −6.63596e6 | − | 1.90941e6i | −1.74085 | − | 0.500906i | ||||
\(430\) | − | 1.65369e6i | − | 0.431305i | ||||||
\(431\) | − | 4.48198e6i | − | 1.16219i | −0.813836 | − | 0.581094i | \(-0.802625\pi\) | ||
0.813836 | − | 0.581094i | \(-0.197375\pi\) | |||||||
\(432\) | 8.36105e6 | + | 9.33736e6i | 2.15552 | + | 2.40721i | ||||
\(433\) | 1.44259e6i | 0.369762i | 0.982761 | + | 0.184881i | \(0.0591899\pi\) | ||||
−0.982761 | + | 0.184881i | \(0.940810\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 86694.2 | − | 301297.i | 0.0219668 | − | 0.0763434i | ||||
\(436\) | −5.54483e6 | −1.39692 | ||||||||
\(437\) | −204674. | −0.0512695 | ||||||||
\(438\) | 1.17515e7 | + | 3.38133e6i | 2.92689 | + | 0.842174i | ||||
\(439\) | − | 2.95219e6i | − | 0.731110i | −0.930790 | − | 0.365555i | \(-0.880879\pi\) | ||
0.930790 | − | 0.365555i | \(-0.119121\pi\) | |||||||
\(440\) | 8.85255e6 | 2.17990 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.33791e7 | −3.25740 | ||||||||
\(443\) | 31430.0i | 0.00760914i | 0.999993 | + | 0.00380457i | \(0.00121103\pi\) | ||||
−0.999993 | + | 0.00380457i | \(0.998789\pi\) | |||||||
\(444\) | 807881. | + | 232457.i | 0.194487 | + | 0.0559610i | ||||
\(445\) | 2.21885e6 | 0.531163 | ||||||||
\(446\) | −799828. | −0.190397 | ||||||||
\(447\) | 1.65181e6 | − | 5.74068e6i | 0.391012 | − | 1.35892i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.65589e6i | 0.855810i | 0.903824 | + | 0.427905i | \(0.140748\pi\) | ||||
−0.903824 | + | 0.427905i | \(0.859252\pi\) | |||||||
\(450\) | 3.37998e6 | − | 5.38712e6i | 0.786834 | − | 1.25408i | ||||
\(451\) | 3.14345e6i | 0.727721i | ||||||||
\(452\) | 1.15926e7i | 2.66891i | ||||||||
\(453\) | 6.16471e6 | + | 1.77382e6i | 1.41146 | + | 0.406128i | ||||
\(454\) | − | 1.07769e7i | − | 2.45389i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.76649e6 | − | 508285.i | −0.397832 | − | 0.114471i | ||||
\(457\) | 3.57735e6 | 0.801255 | 0.400627 | − | 0.916241i | \(-0.368792\pi\) | ||||
0.400627 | + | 0.916241i | \(0.368792\pi\) | |||||||
\(458\) | 1.99265e6 | 0.443883 | ||||||||
\(459\) | −4.28787e6 | − | 4.78856e6i | −0.949971 | − | 1.06090i | ||||
\(460\) | − | 2.12886e6i | − | 0.469085i | ||||||
\(461\) | −3.57853e6 | −0.784247 | −0.392124 | − | 0.919913i | \(-0.628259\pi\) | ||||
−0.392124 | + | 0.919913i | \(0.628259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 463276. | 0.100436 | 0.0502178 | − | 0.998738i | \(-0.484008\pi\) | ||||
0.0502178 | + | 0.998738i | \(0.484008\pi\) | |||||||
\(464\) | 2.52918e6i | 0.545362i | ||||||||
\(465\) | −9067.03 | + | 31511.5i | −0.00194461 | + | 0.00675829i | ||||
\(466\) | 5.20092e6 | 1.10947 | ||||||||
\(467\) | −5.32694e6 | −1.13028 | −0.565140 | − | 0.824995i | \(-0.691178\pi\) | ||||
−0.565140 | + | 0.824995i | \(0.691178\pi\) | |||||||
\(468\) | −7.92604e6 | + | 1.26328e7i | −1.67279 | + | 2.66614i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.04989e6i | 0.636855i | ||||||||
\(471\) | −2.41565e6 | + | 8.39535e6i | −0.501744 | + | 1.74376i | ||||
\(472\) | 5.83990e6i | 1.20656i | ||||||||
\(473\) | − | 3.53101e6i | − | 0.725682i | ||||||
\(474\) | 3.28503e6 | − | 1.14168e7i | 0.671574 | − | 2.33399i | ||||
\(475\) | 515337.i | 0.104799i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.26160e6 | + | 2.01078e6i | −0.253879 | + | 0.404640i | ||||
\(478\) | −3.28503e6 | −0.657612 | ||||||||
\(479\) | 6.34325e6 | 1.26320 | 0.631602 | − | 0.775293i | \(-0.282398\pi\) | ||||
0.631602 | + | 0.775293i | \(0.282398\pi\) | |||||||
\(480\) | 2.01706e6 | − | 7.01010e6i | 0.399592 | − | 1.38874i | ||||
\(481\) | 471969.i | 0.0930146i | ||||||||
\(482\) | 1.52131e6 | 0.298264 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.71061e7 | 3.31924 | ||||||||
\(485\) | 448203.i | 0.0865207i | ||||||||
\(486\) | −9.76014e6 | + | 1.67492e6i | −1.87441 | + | 0.321665i | ||||
\(487\) | −8.17845e6 | −1.56260 | −0.781301 | − | 0.624154i | \(-0.785444\pi\) | ||||
−0.781301 | + | 0.624154i | \(0.785444\pi\) | |||||||
\(488\) | −2.62266e7 | −4.98531 | ||||||||
\(489\) | 8.61481e6 | + | 2.47880e6i | 1.62920 | + | 0.468780i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 6.14286e6i | − | 1.14992i | −0.818182 | − | 0.574959i | \(-0.805018\pi\) | ||
0.818182 | − | 0.574959i | \(-0.194982\pi\) | |||||||
\(492\) | 6.52428e6 | + | 1.87728e6i | 1.21512 | + | 0.349636i | ||||
\(493\) | − | 1.29706e6i | − | 0.240350i | ||||||
\(494\) | − | 1.67025e6i | − | 0.307939i | ||||||
\(495\) | −2.05391e6 | + | 3.27358e6i | −0.376762 | + | 0.600495i | ||||
\(496\) | − | 264518.i | − | 0.0482782i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.57273e6 | − | 5.46586e6i | 0.284172 | − | 0.987609i | ||||
\(499\) | 4.97666e6 | 0.894718 | 0.447359 | − | 0.894354i | \(-0.352365\pi\) | ||||
0.447359 | + | 0.894354i | \(0.352365\pi\) | |||||||
\(500\) | −1.22457e7 | −2.19058 | ||||||||
\(501\) | −1.52336e6 | − | 438328.i | −0.271150 | − | 0.0780199i | ||||
\(502\) | 1.61113e7i | 2.85346i | ||||||||
\(503\) | 1.01525e6 | 0.178918 | 0.0894588 | − | 0.995991i | \(-0.471486\pi\) | ||||
0.0894588 | + | 0.995991i | \(0.471486\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.16225e6 | 0.551782 | ||||||||
\(506\) | − | 6.28260e6i | − | 1.09085i | ||||||
\(507\) | −2.48410e6 | − | 714768.i | −0.429190 | − | 0.123494i | ||||
\(508\) | −1.73382e7 | −2.98088 | ||||||||
\(509\) | 6.31706e6 | 1.08074 | 0.540369 | − | 0.841428i | \(-0.318284\pi\) | ||||
0.540369 | + | 0.841428i | \(0.318284\pi\) | |||||||
\(510\) | −2.07049e6 | + | 7.19578e6i | −0.352491 | + | 1.22505i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 92813.9i | − | 0.0156472i | ||||||
\(513\) | 597807. | − | 535301.i | 0.100292 | − | 0.0898058i | ||||
\(514\) | 4.39287e6i | 0.733400i | ||||||||
\(515\) | 2.48943e6i | 0.413601i | ||||||||
\(516\) | −7.32868e6 | − | 2.10873e6i | −1.21172 | − | 0.348656i | ||||
\(517\) | 6.51221e6i | 1.07153i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.11104e7 | − | 3.19689e6i | −1.81056 | − | 0.520965i | ||||
\(520\) | 1.07340e7 | 1.74082 | ||||||||
\(521\) | −3.69216e6 | −0.595917 | −0.297959 | − | 0.954579i | \(-0.596306\pi\) | ||||
−0.297959 | + | 0.954579i | \(0.596306\pi\) | |||||||
\(522\) | −1.69271e6 | − | 1.06204e6i | −0.271898 | − | 0.170594i | ||||
\(523\) | − | 3.25116e6i | − | 0.519737i | −0.965644 | − | 0.259869i | \(-0.916321\pi\) | ||
0.965644 | − | 0.259869i | \(-0.0836793\pi\) | |||||||
\(524\) | −1.69470e7 | −2.69628 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.36000e6 | 1.31747 | ||||||||
\(527\) | 135655.i | 0.0212770i | ||||||||
\(528\) | 8.62057e6 | − | 2.99599e7i | 1.34571 | − | 4.67687i | ||||
\(529\) | 5.50285e6 | 0.854965 | ||||||||
\(530\) | 2.76524e6 | 0.427606 | ||||||||
\(531\) | −2.15953e6 | − | 1.35493e6i | −0.332371 | − | 0.208536i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.81153e6i | 0.581141i | ||||||||
\(534\) | 3.91060e6 | − | 1.35909e7i | 0.593458 | − | 2.06250i | ||||
\(535\) | 471578.i | 0.0712310i | ||||||||
\(536\) | − | 2.70431e7i | − | 4.06579i | ||||||
\(537\) | −1.65176e6 | + | 5.74053e6i | −0.247179 | + | 0.859045i | ||||
\(538\) | − | 1.95730e7i | − | 2.91542i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.56777e6 | + | 6.21791e6i | 0.821668 | + | 0.917614i | ||||
\(541\) | 7.51164e6 | 1.10342 | 0.551711 | − | 0.834036i | \(-0.313975\pi\) | ||||
0.551711 | + | 0.834036i | \(0.313975\pi\) | |||||||
\(542\) | 5.08739e6 | 0.743870 | ||||||||
\(543\) | −2.36889e6 | + | 8.23282e6i | −0.344782 | + | 1.19825i | ||||
\(544\) | − | 3.01780e7i | − | 4.37214i | ||||||
\(545\) | −1.74223e6 | −0.251255 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.99855e6 | −1.28589 | −0.642945 | − | 0.765912i | \(-0.722288\pi\) | ||||
−0.642945 | + | 0.765912i | \(0.722288\pi\) | |||||||
\(548\) | 99012.6i | 0.0140844i | ||||||||
\(549\) | 6.08490e6 | − | 9.69830e6i | 0.861634 | − | 1.37330i | ||||
\(550\) | −1.58186e7 | −2.22978 | ||||||||
\(551\) | 161926. | 0.0227216 | ||||||||
\(552\) | −8.05678e6 | − | 2.31823e6i | −1.12542 | − | 0.323824i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 6.71072e6i | − | 0.928955i | ||||||
\(555\) | 253843. | + | 73039.9i | 0.0349810 | + | 0.0100653i | ||||
\(556\) | 8.65105e6i | 1.18681i | ||||||||
\(557\) | 3.95822e6i | 0.540583i | 0.962779 | + | 0.270291i | \(0.0871200\pi\) | ||||
−0.962779 | + | 0.270291i | \(0.912880\pi\) | |||||||
\(558\) | 177034. | + | 111075.i | 0.0240697 | + | 0.0151018i | ||||
\(559\) | − | 4.28146e6i | − | 0.579512i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.42097e6 | + | 1.53646e7i | −0.593076 | + | 2.06117i | ||||
\(562\) | −8.90770e6 | −1.18967 | ||||||||
\(563\) | 7.70908e6 | 1.02502 | 0.512509 | − | 0.858682i | \(-0.328716\pi\) | ||||
0.512509 | + | 0.858682i | \(0.328716\pi\) | |||||||
\(564\) | 1.35162e7 | + | 3.88911e6i | 1.78919 | + | 0.514817i | ||||
\(565\) | 3.64248e6i | 0.480038i | ||||||||
\(566\) | −1.38501e7 | −1.81723 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.60333e7 | 2.08522 | ||||||||
\(569\) | − | 3.88317e6i | − | 0.502812i | −0.967882 | − | 0.251406i | \(-0.919107\pi\) | ||
0.967882 | − | 0.251406i | \(-0.0808930\pi\) | |||||||
\(570\) | −898325. | − | 258481.i | −0.115810 | − | 0.0333228i | ||||
\(571\) | 5.43972e6 | 0.698210 | 0.349105 | − | 0.937084i | \(-0.386486\pi\) | ||||
0.349105 | + | 0.937084i | \(0.386486\pi\) | |||||||
\(572\) | 3.70945e7 | 4.74045 | ||||||||
\(573\) | 2058.21 | − | 7153.11i | 0.000261881 | − | 0.000910141i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.35040e6i | 0.296464i | ||||||||
\(576\) | −1.75887e7 | − | 1.10355e7i | −2.20891 | − | 1.38591i | ||||
\(577\) | − | 7.58538e6i | − | 0.948501i | −0.880390 | − | 0.474251i | \(-0.842719\pi\) | ||
0.880390 | − | 0.474251i | \(-0.157281\pi\) | |||||||
\(578\) | 1.57022e7i | 1.95497i | ||||||||
\(579\) | −1.27794e7 | − | 3.67711e6i | −1.58422 | − | 0.455837i | ||||
\(580\) | 1.68423e6i | 0.207888i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 2.74533e6 | + | 789932.i | 0.335959 | + | 0.0966679i | ||||
\(583\) | 5.90441e6 | 0.719458 | ||||||||
\(584\) | −4.05876e7 | −4.92448 | ||||||||
\(585\) | −2.49042e6 | + | 3.96931e6i | −0.300873 | + | 0.479541i | ||||
\(586\) | 1.92538e7i | 2.31618i | ||||||||
\(587\) | 3.48485e6 | 0.417435 | 0.208718 | − | 0.977976i | \(-0.433071\pi\) | ||||
0.208718 | + | 0.977976i | \(0.433071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16935.3 | −0.00201142 | ||||||||
\(590\) | 2.96980e6i | 0.351235i | ||||||||
\(591\) | −3.70535e6 | + | 1.28776e7i | −0.436376 | + | 1.51658i | ||||
\(592\) | −2.13084e6 | −0.249888 | ||||||||
\(593\) | 1.35189e7 | 1.57872 | 0.789360 | − | 0.613930i | \(-0.210412\pi\) | ||||
0.789360 | + | 0.613930i | \(0.210412\pi\) | |||||||
\(594\) | 1.64314e7 | + | 1.83501e7i | 1.91077 | + | 2.13389i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.20900e7i | 3.70044i | ||||||||
\(597\) | 2.02154e6 | − | 7.02566e6i | 0.232138 | − | 0.806773i | ||||
\(598\) | − | 7.61785e6i | − | 0.871123i | ||||||
\(599\) | − | 3.91308e6i | − | 0.445607i | −0.974863 | − | 0.222804i | \(-0.928479\pi\) | ||
0.974863 | − | 0.222804i | \(-0.0715208\pi\) | |||||||
\(600\) | −5.83695e6 | + | 2.02857e7i | −0.661923 | + | 2.30045i | ||||
\(601\) | 1.14323e7i | 1.29106i | 0.763734 | + | 0.645531i | \(0.223364\pi\) | ||||
−0.763734 | + | 0.645531i | \(0.776636\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.00003e7 | + | 6.27436e6i | 1.12000 | + | 0.702710i | ||||
\(604\) | −3.44603e7 | −3.84349 | ||||||||
\(605\) | 5.37488e6 | 0.597008 | ||||||||
\(606\) | 5.57329e6 | − | 1.93694e7i | 0.616496 | − | 2.14257i | ||||
\(607\) | 1.63986e7i | 1.80648i | 0.429133 | + | 0.903241i | \(0.358819\pi\) | ||||
−0.429133 | + | 0.903241i | \(0.641181\pi\) | |||||||
\(608\) | 3.76744e6 | 0.413321 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.33372e7 | −1.45124 | ||||||||
\(611\) | 7.89626e6i | 0.855694i | ||||||||
\(612\) | 2.92493e7 | + | 1.83516e7i | 3.15673 | + | 1.98059i | ||||
\(613\) | −6.33447e6 | −0.680862 | −0.340431 | − | 0.940270i | \(-0.610573\pi\) | ||||
−0.340431 | + | 0.940270i | \(0.610573\pi\) | |||||||
\(614\) | −2.54376e7 | −2.72305 | ||||||||
\(615\) | 2.04998e6 | + | 589856.i | 0.218556 | + | 0.0628866i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.24609e6i | − | 0.977790i | −0.872343 | − | 0.488895i | \(-0.837400\pi\) | ||
0.872343 | − | 0.488895i | \(-0.162600\pi\) | |||||||
\(618\) | 1.52482e7 | + | 4.38748e6i | 1.60601 | + | 0.462108i | ||||
\(619\) | 1.53014e7i | 1.60511i | 0.596581 | + | 0.802553i | \(0.296526\pi\) | ||||
−0.596581 | + | 0.802553i | \(0.703474\pi\) | |||||||
\(620\) | − | 176147.i | − | 0.0184033i | ||||||
\(621\) | 2.72653e6 | − | 2.44145e6i | 0.283715 | − | 0.254050i | ||||
\(622\) | − | 1.88385e7i | − | 1.95241i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.04527e7 | − | 3.63273e7i | 1.07465 | − | 3.73484i | ||||
\(625\) | 3.75443e6 | 0.384454 | ||||||||
\(626\) | 1.89246e7 | 1.93015 | ||||||||
\(627\) | −1.91813e6 | − | 551916.i | −0.194854 | − | 0.0560666i | ||||
\(628\) | − | 4.69293e7i | − | 4.74838i | ||||||
\(629\) | 1.09278e6 | 0.110130 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.50234e7 | −1.50209 | −0.751043 | − | 0.660253i | \(-0.770449\pi\) | ||||
−0.751043 | + | 0.660253i | \(0.770449\pi\) | |||||||
\(632\) | 3.94317e7i | 3.92693i | ||||||||
\(633\) | −1.43985e7 | − | 4.14298e6i | −1.42826 | − | 0.410964i | ||||
\(634\) | 9.46155e6 | 0.934844 | ||||||||
\(635\) | −5.44780e6 | −0.536150 | ||||||||
\(636\) | 3.52613e6 | − | 1.22547e7i | 0.345666 | − | 1.20132i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.97043e6i | 0.483439i | ||||||||
\(639\) | −3.71993e6 | + | 5.92893e6i | −0.360398 | + | 0.574413i | ||||
\(640\) | 9.21389e6i | 0.889187i | ||||||||
\(641\) | 7.78350e6i | 0.748221i | 0.927384 | + | 0.374110i | \(0.122052\pi\) | ||||
−0.927384 | + | 0.374110i | \(0.877948\pi\) | |||||||
\(642\) | 2.88851e6 | + | 831131.i | 0.276590 | + | 0.0795851i | ||||
\(643\) | 1.30114e7i | 1.24107i | 0.784178 | + | 0.620536i | \(0.213085\pi\) | ||||
−0.784178 | + | 0.620536i | \(0.786915\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.30273e6 | − | 662580.i | −0.217943 | − | 0.0627103i | ||||
\(646\) | −3.86723e6 | −0.364602 | ||||||||
\(647\) | −5.03966e6 | −0.473304 | −0.236652 | − | 0.971594i | \(-0.576050\pi\) | ||||
−0.236652 | + | 0.971594i | \(0.576050\pi\) | |||||||
\(648\) | 2.95951e7 | − | 1.43005e7i | 2.76874 | − | 1.33787i | ||||
\(649\) | 6.34119e6i | 0.590962i | ||||||||
\(650\) | −1.91805e7 | −1.78065 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.81561e7 | −4.43642 | ||||||||
\(653\) | − | 1.32180e7i | − | 1.21306i | −0.795060 | − | 0.606531i | \(-0.792561\pi\) | ||
0.795060 | − | 0.606531i | \(-0.207439\pi\) | |||||||
\(654\) | −3.07059e6 | + | 1.06715e7i | −0.280722 | + | 0.975621i | ||||
\(655\) | −5.32488e6 | −0.484961 | ||||||||
\(656\) | −1.72082e7 | −1.56126 | ||||||||
\(657\) | 9.41683e6 | − | 1.50088e7i | 0.851121 | − | 1.35654i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.02891e7i | − | 1.81991i | −0.414706 | − | 0.909956i | \(-0.636115\pi\) | ||
0.414706 | − | 0.909956i | \(-0.363885\pi\) | |||||||
\(660\) | 5.74059e6 | − | 1.99508e7i | 0.512975 | − | 1.78279i | ||||
\(661\) | 5.77967e6i | 0.514517i | 0.966343 | + | 0.257258i | \(0.0828192\pi\) | ||||
−0.966343 | + | 0.257258i | \(0.917181\pi\) | |||||||
\(662\) | 4.85156e6i | 0.430265i | ||||||||
\(663\) | −5.36056e6 | + | 1.86301e7i | −0.473616 | + | 1.64600i | ||||
\(664\) | 1.88782e7i | 1.66165i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 894767. | − | 1.42611e6i | 0.0781672 | − | 0.124585i | ||||
\(667\) | 738528. | 0.0642765 | ||||||||
\(668\) | 8.51549e6 | 0.738361 | ||||||||
\(669\) | −320464. | + | 1.11374e6i | −0.0276831 | + | 0.0962097i | ||||
\(670\) | − | 1.37524e7i | − | 1.18356i | ||||||
\(671\) | −2.84779e7 | −2.44175 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −959659. | −0.0816732 | −0.0408366 | − | 0.999166i | \(-0.513002\pi\) | ||||
−0.0408366 | + | 0.999166i | \(0.513002\pi\) | |||||||
\(674\) | 2.16729e7i | 1.83767i | ||||||||
\(675\) | −6.14718e6 | − | 6.86498e6i | −0.519298 | − | 0.579936i | ||||
\(676\) | 1.38859e7 | 1.16871 | ||||||||
\(677\) | 6.45075e6 | 0.540927 | 0.270464 | − | 0.962730i | \(-0.412823\pi\) | ||||
0.270464 | + | 0.962730i | \(0.412823\pi\) | |||||||
\(678\) | 2.23109e7 | + | 6.41967e6i | 1.86399 | + | 0.536338i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 2.48530e7i | − | 2.06114i | ||||||
\(681\) | −1.50066e7 | − | 4.31796e6i | −1.23998 | − | 0.356788i | ||||
\(682\) | − | 519839.i | − | 0.0427964i | ||||||
\(683\) | − | 8.28136e6i | − | 0.679282i | −0.940555 | − | 0.339641i | \(-0.889695\pi\) | ||
0.940555 | − | 0.339641i | \(-0.110305\pi\) | |||||||
\(684\) | −2.29102e6 | + | 3.65150e6i | −0.187236 | + | 0.298422i | ||||
\(685\) | 31110.5i | 0.00253327i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 798390. | − | 2.77472e6i | 0.0645392 | − | 0.224299i | ||||
\(688\) | 1.93298e7 | 1.55689 | ||||||||
\(689\) | 7.15929e6 | 0.574542 | ||||||||
\(690\) | −4.09716e6 | − | 1.17891e6i | −0.327613 | − | 0.0942663i | ||||
\(691\) | − | 1.95993e7i | − | 1.56151i | −0.624837 | − | 0.780755i | \(-0.714835\pi\) | ||
0.624837 | − | 0.780755i | \(-0.285165\pi\) | |||||||
\(692\) | 6.21065e7 | 4.93028 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.45088e7 | 1.93163 | ||||||||
\(695\) | 2.71823e6i | 0.213464i | ||||||||
\(696\) | 6.37405e6 | + | 1.83405e6i | 0.498761 | + | 0.143512i | ||||
\(697\) | 8.82504e6 | 0.688074 | ||||||||
\(698\) | 3.39409e7 | 2.63685 | ||||||||
\(699\) | 2.08384e6 | − | 7.24215e6i | 0.161313 | − | 0.560628i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.77783e6i | 0.597810i | 0.954283 | + | 0.298905i | \(0.0966214\pi\) | ||||
−0.954283 | + | 0.298905i | \(0.903379\pi\) | |||||||
\(702\) | 1.99236e7 | + | 2.22500e7i | 1.52589 | + | 1.70407i | ||||
\(703\) | 136423.i | 0.0104112i | ||||||||
\(704\) | 5.16470e7i | 3.92748i | ||||||||
\(705\) | 4.24690e6 | + | 1.22199e6i | 0.321810 | + | 0.0925967i | ||||
\(706\) | 3.27995e7i | 2.47660i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.31613e7 | + | 3.78698e6i | 0.986766 | + | 0.283929i | ||||
\(709\) | −404.312 | −3.02066e−5 | −1.51033e−5 | − | 1.00000i | \(-0.500005\pi\) | ||||
−1.51033e−5 | 1.00000i | \(0.500005\pi\) | ||||||||
\(710\) | 8.15350e6 | 0.607014 | ||||||||
\(711\) | −1.45814e7 | − | 9.14866e6i | −1.08175 | − | 0.678709i | ||||
\(712\) | 4.69406e7i | 3.47015i | ||||||||
\(713\) | −77239.9 | −0.00569007 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.16554e7 | 0.852633 | ||||||||
\(716\) | − | 3.20891e7i | − | 2.33924i | ||||||
\(717\) | −1.31620e6 | + | 4.57433e6i | −0.0956148 | + | 0.332299i | ||||
\(718\) | −3.44233e7 | −2.49196 | ||||||||
\(719\) | 2.28281e6 | 0.164683 | 0.0823413 | − | 0.996604i | \(-0.473760\pi\) | ||||
0.0823413 | + | 0.996604i | \(0.473760\pi\) | |||||||
\(720\) | −1.79206e7 | − | 1.12437e7i | −1.28831 | − | 0.808311i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2.61558e7i | 1.86735i | ||||||||
\(723\) | 609539. | − | 2.11839e6i | 0.0433666 | − | 0.150716i | ||||
\(724\) | − | 4.60208e7i | − | 3.26293i | ||||||
\(725\) | − | 1.85950e6i | − | 0.131386i | ||||||
\(726\) | 9.47293e6 | − | 3.29222e7i | 0.667026 | − | 2.31818i | ||||
\(727\) | − | 1.14126e7i | − | 0.800845i | −0.916331 | − | 0.400422i | \(-0.868863\pi\) | ||
0.916331 | − | 0.400422i | \(-0.131137\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.57827e6 | + | 1.42618e7i | −0.109993 | + | 0.993932i | ||||
\(730\) | −2.06402e7 | −1.43353 | ||||||||
\(731\) | −9.91310e6 | −0.686145 | ||||||||
\(732\) | −1.70071e7 | + | 5.91063e7i | −1.17315 | + | 4.07715i | ||||
\(733\) | − | 1.81527e7i | − | 1.24790i | −0.781464 | − | 0.623951i | \(-0.785527\pi\) | ||
0.781464 | − | 0.623951i | \(-0.214473\pi\) | |||||||
\(734\) | 3.00086e7 | 2.05592 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.71829e7 | 1.16924 | ||||||||
\(737\) | − | 2.93645e7i | − | 1.99138i | ||||||
\(738\) | 7.22596e6 | − | 1.15170e7i | 0.488376 | − | 0.778389i | ||||
\(739\) | 4.72208e6 | 0.318070 | 0.159035 | − | 0.987273i | \(-0.449162\pi\) | ||||
0.159035 | + | 0.987273i | \(0.449162\pi\) | |||||||
\(740\) | −1.41896e6 | −0.0952557 | ||||||||
\(741\) | −2.32579e6 | − | 669215.i | −0.155605 | − | 0.0447734i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 2.37693e7i | − | 1.57959i | −0.613372 | − | 0.789794i | \(-0.710187\pi\) | ||
0.613372 | − | 0.789794i | \(-0.289813\pi\) | |||||||
\(744\) | −666639. | − | 191817.i | −0.0441528 | − | 0.0127044i | ||||
\(745\) | 1.00829e7i | 0.665574i | ||||||||
\(746\) | − | 2.77429e7i | − | 1.82518i | ||||||
\(747\) | −6.98093e6 | − | 4.37997e6i | −0.457733 | − | 0.287190i | ||||
\(748\) | − | 8.58870e7i | − | 5.61272i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −6.78135e6 | + | 2.35679e7i | −0.440213 | + | 1.52992i | ||||
\(751\) | 8.55543e6 | 0.553531 | 0.276765 | − | 0.960937i | \(-0.410737\pi\) | ||||
0.276765 | + | 0.960937i | \(0.410737\pi\) | |||||||
\(752\) | −3.56499e7 | −2.29886 | ||||||||
\(753\) | 2.24346e7 | + | 6.45526e6i | 1.44189 | + | 0.414884i | ||||
\(754\) | 6.02680e6i | 0.386063i | ||||||||
\(755\) | −1.08277e7 | −0.691303 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.81552e7 | 1.15149 | 0.575745 | − | 0.817629i | \(-0.304712\pi\) | ||||
0.575745 | + | 0.817629i | \(0.304712\pi\) | |||||||
\(758\) | 3.17801e7i | 2.00901i | ||||||||
\(759\) | −8.74837e6 | − | 2.51723e6i | −0.551217 | − | 0.158606i | ||||
\(760\) | 3.10266e6 | 0.194850 | ||||||||
\(761\) | 2.00423e7 | 1.25454 | 0.627271 | − | 0.778801i | \(-0.284172\pi\) | ||||
0.627271 | + | 0.778801i | \(0.284172\pi\) | |||||||
\(762\) | −9.60144e6 | + | 3.33688e7i | −0.599030 | + | 2.08187i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 39985.3i | 0.00247838i | ||||||||
\(765\) | 9.19037e6 | + | 5.76622e6i | 0.567779 | + | 0.356236i | ||||
\(766\) | − | 4.28586e7i | − | 2.63916i | ||||||
\(767\) | 7.68890e6i | 0.471928i | ||||||||
\(768\) | 1.54744e7 | + | 4.45257e6i | 0.946699 | + | 0.272400i | ||||
\(769\) | − | 1.58687e7i | − | 0.967666i | −0.875160 | − | 0.483833i | \(-0.839244\pi\) | ||
0.875160 | − | 0.483833i | \(-0.160756\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.11697e6 | + | 1.76008e6i | 0.370596 | + | 0.106634i | ||||
\(772\) | 7.14359e7 | 4.31393 | ||||||||
\(773\) | −213540. | −0.0128538 | −0.00642689 | − | 0.999979i | \(-0.502046\pi\) | ||||
−0.00642689 | + | 0.999979i | \(0.502046\pi\) | |||||||
\(774\) | −8.11686e6 | + | 1.29369e7i | −0.487008 | + | 0.776208i | ||||
\(775\) | 194478.i | 0.0116310i | ||||||||
\(776\) | −9.48190e6 | −0.565251 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.70674e6 | −0.397249 | ||||||||
\(779\) | 1.10172e6i | 0.0650472i | ||||||||
\(780\) | 6.96064e6 | − | 2.41910e7i | 0.409650 | − | 1.42369i | ||||
\(781\) | 1.74096e7 | 1.02132 | ||||||||
\(782\) | −1.76380e7 | −1.03141 | ||||||||
\(783\) | −2.15707e6 | + | 1.93153e6i | −0.125736 | + | 0.112589i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1.47456e7i | − | 0.854059i | ||||||
\(786\) | −9.38481e6 | + | 3.26160e7i | −0.541838 | + | 1.88310i | ||||
\(787\) | 1.33401e6i | 0.0767752i | 0.999263 | + | 0.0383876i | \(0.0122222\pi\) | ||||
−0.999263 | + | 0.0383876i | \(0.987778\pi\) | |||||||
\(788\) | − | 7.19846e7i | − | 4.12975i | ||||||
\(789\) | 3.34957e6 | − | 1.16411e7i | 0.191557 | − | 0.665735i | ||||
\(790\) | 2.00524e7i | 1.14314i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.92538e7 | − | 4.34512e7i | −3.92311 | − | 2.46144i | ||||
\(793\) | −3.45303e7 | −1.94992 | ||||||||
\(794\) | 3.79637e7 | 2.13706 | ||||||||
\(795\) | 1.10794e6 | − | 3.85053e6i | 0.0621725 | − | 0.216074i | ||||
\(796\) | 3.92729e7i | 2.19690i | ||||||||
\(797\) | 1.62474e7 | 0.906019 | 0.453009 | − | 0.891506i | \(-0.350350\pi\) | ||||
0.453009 | + | 0.891506i | \(0.350350\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.82827e7 | 1.01315 | ||||||||
\(800\) | − | 4.32638e7i | − | 2.39001i | ||||||
\(801\) | −1.73581e7 | − | 1.08908e7i | −0.955920 | − | 0.599763i | ||||
\(802\) | −1.39843e7 | −0.767722 | ||||||||
\(803\) | −4.40716e7 | −2.41196 | ||||||||
\(804\) | −6.09466e7 | − | 1.75366e7i | −3.32513 | − | 0.956764i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 630320.i | − | 0.0341762i | ||||||
\(807\) | −2.72549e7 | − | 7.84223e6i | −1.47319 | − | 0.423893i | ||||
\(808\) | 6.68987e7i | 3.60487i | ||||||||
\(809\) | 2.90690e7i | 1.56156i | 0.624807 | + | 0.780779i | \(0.285178\pi\) | ||||
−0.624807 | + | 0.780779i | \(0.714822\pi\) | |||||||
\(810\) | 1.50502e7 | − | 7.27232e6i | 0.805989 | − | 0.389458i | ||||
\(811\) | 9.68866e6i | 0.517263i | 0.965976 | + | 0.258631i | \(0.0832715\pi\) | ||||
−0.965976 | + | 0.258631i | \(0.916728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.03835e6 | − | 7.08407e6i | 0.108156 | − | 0.375886i | ||||
\(814\) | −4.18759e6 | −0.221515 | ||||||||
\(815\) | −1.51310e7 | −0.797949 | ||||||||
\(816\) | −8.41106e7 | − | 2.42017e7i | −4.42207 | − | 1.27239i | ||||
\(817\) | − | 1.23756e6i | − | 0.0648650i | ||||||
\(818\) | −2.44324e6 | −0.127668 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.14592e7 | −0.595143 | ||||||||
\(821\) | − | 4.08927e6i | − | 0.211733i | −0.994380 | − | 0.105866i | \(-0.966238\pi\) | ||
0.994380 | − | 0.105866i | \(-0.0337616\pi\) | |||||||
\(822\) | 190558. | + | 54830.6i | 0.00983667 | + | 0.00283037i | ||||
\(823\) | −1.51161e7 | −0.777931 | −0.388965 | − | 0.921252i | \(-0.627167\pi\) | ||||
−0.388965 | + | 0.921252i | \(0.627167\pi\) | |||||||
\(824\) | −5.26648e7 | −2.70211 | ||||||||
\(825\) | −6.33799e6 | + | 2.20270e7i | −0.324203 | + | 1.12673i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 2.42352e7i | − | 1.23220i | −0.787667 | − | 0.616101i | \(-0.788711\pi\) | ||
0.787667 | − | 0.616101i | \(-0.211289\pi\) | |||||||
\(828\) | −1.04491e7 | + | 1.66541e7i | −0.529668 | + | 0.844200i | ||||
\(829\) | − | 1.29487e6i | − | 0.0654396i | −0.999465 | − | 0.0327198i | \(-0.989583\pi\) | ||
0.999465 | − | 0.0327198i | \(-0.0104169\pi\) | |||||||
\(830\) | 9.60022e6i | 0.483711i | ||||||||
\(831\) | −9.34451e6 | − | 2.68876e6i | −0.469412 | − | 0.135067i | ||||
\(832\) | 6.26236e7i | 3.13639i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.66497e7 | + | 4.79073e6i | 0.828879 | + | 0.238499i | ||||
\(835\) | 2.67564e6 | 0.132804 | ||||||||
\(836\) | 1.07222e7 | 0.530600 | ||||||||
\(837\) | 225600. | − | 202012.i | 0.0111308 | − | 0.00996696i | ||||
\(838\) | 2.61945e7i | 1.28855i | ||||||||
\(839\) | −2.38737e6 | −0.117089 | −0.0585443 | − | 0.998285i | \(-0.518646\pi\) | ||||
−0.0585443 | + | 0.998285i | \(0.518646\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.99269e7 | 0.971514 | ||||||||
\(842\) | 6.09531e6i | 0.296289i | ||||||||
\(843\) | −3.56902e6 | + | 1.24038e7i | −0.172974 | + | 0.601152i | ||||
\(844\) | 8.04865e7 | 3.88926 | ||||||||
\(845\) | 4.36307e6 | 0.210209 | ||||||||
\(846\) | 1.49699e7 | − | 2.38594e7i | 0.719105 | − | 1.14613i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.23226e7i | 1.54353i | ||||||||
\(849\) | −5.54926e6 | + | 1.92859e7i | −0.264220 | + | 0.918270i | ||||
\(850\) | 4.44098e7i | 2.10829i | ||||||||
\(851\) | 622210.i | 0.0294519i | ||||||||
\(852\) | 1.03971e7 | − | 3.61339e7i | 0.490695 | − | 1.70536i | ||||
\(853\) | 8.94330e6i | 0.420848i | 0.977610 | + | 0.210424i | \(0.0674845\pi\) | ||||
−0.977610 | + | 0.210424i | \(0.932516\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −719858. | + | 1.14733e6i | −0.0336768 | + | 0.0536752i | ||||
\(856\) | −9.97642e6 | −0.465361 | ||||||||
\(857\) | 2.97785e7 | 1.38501 | 0.692503 | − | 0.721415i | \(-0.256508\pi\) | ||||
0.692503 | + | 0.721415i | \(0.256508\pi\) | |||||||
\(858\) | 2.05420e7 | − | 7.13916e7i | 0.952630 | − | 3.31077i | ||||
\(859\) | − | 2.15240e7i | − | 0.995268i | −0.867387 | − | 0.497634i | \(-0.834202\pi\) | ||
0.867387 | − | 0.497634i | \(-0.165798\pi\) | |||||||
\(860\) | 1.28721e7 | 0.593475 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.82184e7 | 2.21027 | ||||||||
\(863\) | 2.74455e7i | 1.25442i | 0.778848 | + | 0.627212i | \(0.215804\pi\) | ||||
−0.778848 | + | 0.627212i | \(0.784196\pi\) | |||||||
\(864\) | −5.01874e7 | + | 4.49398e7i | −2.28723 | + | 2.04808i | ||||
\(865\) | 1.95144e7 | 0.886777 | ||||||||
\(866\) | −1.55197e7 | −0.703218 | ||||||||
\(867\) | 2.18649e7 | + | 6.29133e6i | 0.987868 | + | 0.284246i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.28165e7i | 1.92337i | ||||||||
\(870\) | 3.24144e6 | + | 932681.i | 0.145191 | + | 0.0417768i | ||||
\(871\) | − | 3.56054e7i | − | 1.59027i | ||||||
\(872\) | − | 3.68576e7i | − | 1.64148i | ||||||
\(873\) | 2.19992e6 | − | 3.50630e6i | 0.0976949 | − | 0.155709i | ||||
\(874\) | − | 2.20194e6i | − | 0.0975051i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.63197e7 | + | 9.14713e7i | −1.15883 | + | 4.02740i | ||||
\(877\) | 983504. | 0.0431794 | 0.0215897 | − | 0.999767i | \(-0.493127\pi\) | ||||
0.0215897 | + | 0.999767i | \(0.493127\pi\) | |||||||
\(878\) | 3.17605e7 | 1.39044 | ||||||||
\(879\) | 2.68104e7 | + | 7.71435e6i | 1.17039 | + | 0.336765i | ||||
\(880\) | 5.26215e7i | 2.29064i | ||||||||
\(881\) | −2.41287e7 | −1.04736 | −0.523678 | − | 0.851917i | \(-0.675440\pi\) | ||||
−0.523678 | + | 0.851917i | \(0.675440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.21508e7 | −1.38768 | −0.693842 | − | 0.720127i | \(-0.744083\pi\) | ||||
−0.693842 | + | 0.720127i | \(0.744083\pi\) | |||||||
\(884\) | − | 1.04141e8i | − | 4.48218i | ||||||
\(885\) | 4.13537e6 | + | 1.18990e6i | 0.177483 | + | 0.0510684i | ||||
\(886\) | −338133. | −0.0144712 | ||||||||
\(887\) | −1.97916e7 | −0.844641 | −0.422321 | − | 0.906447i | \(-0.638784\pi\) | ||||
−0.422321 | + | 0.906447i | \(0.638784\pi\) | |||||||
\(888\) | −1.54519e6 | + | 5.37014e6i | −0.0657580 | + | 0.228535i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.38710e7i | 1.01017i | ||||||||
\(891\) | 3.21355e7 | − | 1.55281e7i | 1.35610 | − | 0.655274i | ||||
\(892\) | − | 6.22572e6i | − | 0.261986i | ||||||
\(893\) | 2.28242e6i | 0.0957781i | ||||||||
\(894\) | 6.17599e7 | + | 1.77706e7i | 2.58442 | + | 0.743633i | ||||
\(895\) | − | 1.00827e7i | − | 0.420743i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.06077e7 | − | 3.05222e6i | −0.440189 | − | 0.126659i | ||||
\(898\) | −3.93311e7 | −1.62759 | ||||||||
\(899\) | 61107.7 | 0.00252172 | ||||||||
\(900\) | 4.19324e7 | + | 2.63092e7i | 1.72561 | + | 1.08268i | ||||
\(901\) | − | 1.65763e7i | − | 0.680261i | ||||||
\(902\) | −3.38181e7 | −1.38399 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.70581e7 | −3.13615 | ||||||||
\(905\) | − | 1.44601e7i | − | 0.586881i | ||||||
\(906\) | −1.90832e7 | + | 6.63217e7i | −0.772380 | + | 2.68433i | ||||
\(907\) | 2.58958e7 | 1.04523 | 0.522615 | − | 0.852569i | \(-0.324957\pi\) | ||||
0.522615 | + | 0.852569i | \(0.324957\pi\) | |||||||
\(908\) | 8.38858e7 | 3.37656 | ||||||||
\(909\) | −2.47384e7 | − | 1.55213e7i | −0.993028 | − | 0.623045i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 3.95347e6i | − | 0.157827i | −0.996881 | − | 0.0789137i | \(-0.974855\pi\) | ||
0.996881 | − | 0.0789137i | \(-0.0251452\pi\) | |||||||
\(912\) | 3.02136e6 | − | 1.05004e7i | 0.120286 | − | 0.418042i | ||||
\(913\) | 2.04986e7i | 0.813857i | ||||||||
\(914\) | 3.84861e7i | 1.52384i | ||||||||
\(915\) | −5.34376e6 | + | 1.85717e7i | −0.211006 | + | 0.733328i | ||||
\(916\) | 1.55105e7i | 0.610782i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 5.15167e7 | − | 4.61302e7i | 2.01763 | − | 1.80667i | ||||
\(919\) | −2.46305e7 | −0.962022 | −0.481011 | − | 0.876715i | \(-0.659730\pi\) | ||||
−0.481011 | + | 0.876715i | \(0.659730\pi\) | |||||||
\(920\) | 1.41509e7 | 0.551207 | ||||||||
\(921\) | −1.01920e7 | + | 3.54212e7i | −0.395922 | + | 1.37599i | ||||
\(922\) | − | 3.84989e7i | − | 1.49149i | ||||||
\(923\) | 2.11096e7 | 0.815599 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.56663e6 | 0.0602020 | ||||||||
\(926\) | 4.98405e6i | 0.191010i | ||||||||
\(927\) | 1.22189e7 | − | 1.94749e7i | 0.467018 | − | 0.744346i | ||||
\(928\) | −1.35941e7 | −0.518180 | ||||||||
\(929\) | 7.12147e6 | 0.270726 | 0.135363 | − | 0.990796i | \(-0.456780\pi\) | ||||
0.135363 | + | 0.990796i | \(0.456780\pi\) | |||||||
\(930\) | −339010. | − | 97545.7i | −0.0128530 | − | 0.00369829i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.04831e7i | 1.52663i | ||||||||
\(933\) | −2.62322e7 | − | 7.54797e6i | −0.986575 | − | 0.283874i | ||||
\(934\) | − | 5.73088e7i | − | 2.14958i | ||||||
\(935\) | − | 2.69864e7i | − | 1.00952i | ||||||
\(936\) | −8.39724e7 | − | 5.26859e7i | −3.13290 | − | 1.96564i | ||||
\(937\) | 1.08826e6i | 0.0404933i | 0.999795 | + | 0.0202467i | \(0.00644516\pi\) | ||||
−0.999795 | + | 0.0202467i | \(0.993555\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.58245e6 | − | 2.63520e7i | 0.280638 | − | 0.975327i | ||||
\(940\) | −2.37399e7 | −0.876312 | ||||||||
\(941\) | −3.05310e7 | −1.12400 | −0.562000 | − | 0.827137i | \(-0.689968\pi\) | ||||
−0.562000 | + | 0.827137i | \(0.689968\pi\) | |||||||
\(942\) | −9.03195e7 | − | 2.59883e7i | −3.31630 | − | 0.954223i | ||||
\(943\) | 5.02484e6i | 0.184011i | ||||||||
\(944\) | −3.47137e7 | −1.26786 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.79876e7 | 1.38011 | ||||||||
\(947\) | − | 5.78796e6i | − | 0.209725i | −0.994487 | − | 0.104863i | \(-0.966560\pi\) | ||
0.994487 | − | 0.104863i | \(-0.0334403\pi\) | |||||||
\(948\) | 8.88664e7 | + | 2.55702e7i | 3.21157 | + | 0.924086i | ||||
\(949\) | −5.34382e7 | −1.92613 | ||||||||
\(950\) | −5.54414e6 | −0.199308 | ||||||||
\(951\) | 3.79093e6 | − | 1.31750e7i | 0.135923 | − | 0.472388i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.14506e7i | − | 0.408410i | −0.978928 | − | 0.204205i | \(-0.934539\pi\) | ||
0.978928 | − | 0.204205i | \(-0.0654609\pi\) | |||||||
\(954\) | −2.16326e7 | − | 1.35727e7i | −0.769550 | − | 0.482831i | ||||
\(955\) | 12563.7i | 0.000445769i | ||||||||
\(956\) | − | 2.55701e7i | − | 0.904874i | ||||||
\(957\) | 6.92120e6 | + | 1.99148e6i | 0.244288 | + | 0.0702906i | ||||
\(958\) | 6.82425e7i | 2.40238i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.36813e7 | + | 9.69136e6i | 1.17954 | + | 0.339396i | ||||
\(961\) | 2.86228e7 | 0.999777 | ||||||||
\(962\) | −5.07758e6 | −0.176896 | ||||||||
\(963\) | 2.31466e6 | − | 3.68917e6i | 0.0804306 | − | 0.128193i | ||||
\(964\) | 1.18416e7i | 0.410411i | ||||||||
\(965\) | 2.24457e7 | 0.775917 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.20783e7 | −1.10318 | −0.551588 | − | 0.834117i | \(-0.685978\pi\) | ||||
−0.551588 | + | 0.834117i | \(0.685978\pi\) | |||||||
\(968\) | 1.13708e8i | 3.90033i | ||||||||
\(969\) | −1.54947e6 | + | 5.38503e6i | −0.0530120 | + | 0.184238i | ||||
\(970\) | −4.82189e6 | −0.164546 | ||||||||
\(971\) | 3.91845e7 | 1.33373 | 0.666863 | − | 0.745181i | \(-0.267637\pi\) | ||||
0.666863 | + | 0.745181i | \(0.267637\pi\) | |||||||
\(972\) | −1.30373e7 | − | 7.59713e7i | −0.442611 | − | 2.57919i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 8.79861e7i | − | 2.97178i | ||||||
\(975\) | −7.68501e6 | + | 2.67084e7i | −0.258900 | + | 0.899781i | ||||
\(976\) | − | 1.55897e8i | − | 5.23856i | ||||||
\(977\) | − | 2.62234e7i | − | 0.878925i | −0.898261 | − | 0.439462i | \(-0.855169\pi\) | ||
0.898261 | − | 0.439462i | \(-0.144831\pi\) | |||||||
\(978\) | −2.66676e7 | + | 9.26806e7i | −0.891533 | + | 3.09843i | ||||
\(979\) | 5.09700e7i | 1.69964i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.36295e7 | + | 8.55143e6i | 0.452177 | + | 0.283705i | ||||
\(982\) | 6.60866e7 | 2.18693 | ||||||||
\(983\) | −5.16857e7 | −1.70603 | −0.853015 | − | 0.521886i | \(-0.825229\pi\) | ||||
−0.853015 | + | 0.521886i | \(0.825229\pi\) | |||||||
\(984\) | −1.24786e7 | + | 4.33682e7i | −0.410846 | + | 1.42785i | ||||
\(985\) | − | 2.26181e7i | − | 0.742790i | ||||||
\(986\) | 1.39542e7 | 0.457101 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.30010e7 | 0.423724 | ||||||||
\(989\) | − | 5.64437e6i | − | 0.183495i | ||||||
\(990\) | −3.52181e7 | − | 2.20965e7i | −1.14203 | − | 0.716532i | ||||
\(991\) | 8.92621e6 | 0.288724 | 0.144362 | − | 0.989525i | \(-0.453887\pi\) | ||||
0.144362 | + | 0.989525i | \(0.453887\pi\) | |||||||
\(992\) | 1.42176e6 | 0.0458719 | ||||||||
\(993\) | 6.75567e6 | + | 1.94386e6i | 0.217418 | + | 0.0625592i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.23399e7i | 0.395141i | ||||||||
\(996\) | 4.25453e7 | + | 1.22419e7i | 1.35895 | + | 0.391020i | ||||
\(997\) | 2.54875e6i | 0.0812061i | 0.999175 | + | 0.0406031i | \(0.0129279\pi\) | ||||
−0.999175 | + | 0.0406031i | \(0.987072\pi\) | |||||||
\(998\) | 5.35403e7i | 1.70159i | ||||||||
\(999\) | −1.62732e6 | − | 1.81733e6i | −0.0515891 | − | 0.0576131i |
(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 | 147.6.c.d.146.14 | yes | 40 | |
3.2 | odd | 2 | inner | 147.6.c.d.146.27 | yes | 40 | |
7.6 | odd | 2 | inner | 147.6.c.d.146.28 | yes | 40 | |
21.20 | even | 2 | inner | 147.6.c.d.146.13 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.c.d.146.13 | ✓ | 40 | 21.20 | even | 2 | inner | |
147.6.c.d.146.14 | yes | 40 | 1.1 | even | 1 | trivial | |
147.6.c.d.146.27 | yes | 40 | 3.2 | odd | 2 | inner | |
147.6.c.d.146.28 | yes | 40 | 7.6 | odd | 2 | inner |