Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 63 x^{10} - 126 x^{9} + 2784 x^{8} - 5290 x^{7} + 62015 x^{6} - 99530 x^{5} + \cdots + 5466244 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.3 | ||
Root | \(-2.55045 - 4.41750i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.79 |
Dual form | 147.6.e.p.67.3 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.69017 | + | 2.92745i | −0.298782 | + | 0.517505i | −0.975858 | − | 0.218408i | \(-0.929914\pi\) |
0.677076 | + | 0.735913i | \(0.263247\pi\) | |||||||
\(3\) | −4.50000 | − | 7.79423i | −0.288675 | − | 0.500000i | ||||
\(4\) | 10.2867 | + | 17.8171i | 0.321459 | + | 0.556783i | ||||
\(5\) | 27.2626 | − | 47.2203i | 0.487689 | − | 0.844702i | −0.512211 | − | 0.858860i | \(-0.671173\pi\) |
0.999900 | + | 0.0141577i | \(0.00450668\pi\) | |||||||
\(6\) | 30.4230 | 0.345004 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −177.715 | −0.981748 | ||||||||
\(9\) | −40.5000 | + | 70.1481i | −0.166667 | + | 0.288675i | ||||
\(10\) | 92.1567 | + | 159.620i | 0.291425 | + | 0.504763i | ||||
\(11\) | −240.956 | − | 417.347i | −0.600420 | − | 1.03996i | −0.992757 | − | 0.120137i | \(-0.961667\pi\) |
0.392337 | − | 0.919821i | \(-0.371667\pi\) | |||||||
\(12\) | 92.5801 | − | 160.354i | 0.185594 | − | 0.321459i | ||||
\(13\) | 512.622 | 0.841277 | 0.420638 | − | 0.907228i | \(-0.361806\pi\) | ||||
0.420638 | + | 0.907228i | \(0.361806\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −490.728 | −0.563135 | ||||||||
\(16\) | −28.8055 | + | 49.8926i | −0.0281304 | + | 0.0487233i | ||||
\(17\) | −295.372 | − | 511.599i | −0.247883 | − | 0.429346i | 0.715055 | − | 0.699068i | \(-0.246402\pi\) |
−0.962938 | + | 0.269722i | \(0.913068\pi\) | |||||||
\(18\) | −136.903 | − | 237.124i | −0.0995939 | − | 0.172502i | ||||
\(19\) | −1225.51 | + | 2122.64i | −0.778811 | + | 1.34894i | 0.153817 | + | 0.988099i | \(0.450844\pi\) |
−0.932627 | + | 0.360841i | \(0.882490\pi\) | |||||||
\(20\) | 1121.77 | 0.627088 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1629.02 | 0.717579 | ||||||||
\(23\) | −887.452 | + | 1537.11i | −0.349804 | + | 0.605879i | −0.986214 | − | 0.165472i | \(-0.947085\pi\) |
0.636410 | + | 0.771351i | \(0.280419\pi\) | |||||||
\(24\) | 799.719 | + | 1385.15i | 0.283406 | + | 0.490874i | ||||
\(25\) | 75.9967 | + | 131.630i | 0.0243189 | + | 0.0421216i | ||||
\(26\) | −866.416 | + | 1500.68i | −0.251358 | + | 0.435365i | ||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4246.44 | −0.937627 | −0.468814 | − | 0.883297i | \(-0.655318\pi\) | ||||
−0.468814 | + | 0.883297i | \(0.655318\pi\) | |||||||
\(30\) | 829.411 | − | 1436.58i | 0.168254 | − | 0.291425i | ||||
\(31\) | −4883.69 | − | 8458.79i | −0.912733 | − | 1.58090i | −0.810187 | − | 0.586171i | \(-0.800635\pi\) |
−0.102545 | − | 0.994728i | \(-0.532699\pi\) | |||||||
\(32\) | −2940.82 | − | 5093.65i | −0.507684 | − | 0.879334i | ||||
\(33\) | −2168.60 | + | 3756.13i | −0.346653 | + | 0.600420i | ||||
\(34\) | 1996.91 | 0.296252 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1666.44 | −0.214306 | ||||||||
\(37\) | 4984.83 | − | 8633.97i | 0.598612 | − | 1.03683i | −0.394414 | − | 0.918933i | \(-0.629052\pi\) |
0.993026 | − | 0.117894i | \(-0.0376143\pi\) | |||||||
\(38\) | −4142.62 | − | 7175.23i | −0.465389 | − | 0.806078i | ||||
\(39\) | −2306.80 | − | 3995.49i | −0.242856 | − | 0.420638i | ||||
\(40\) | −4844.99 | + | 8391.77i | −0.478788 | + | 0.829284i | ||||
\(41\) | −3377.54 | −0.313791 | −0.156896 | − | 0.987615i | \(-0.550149\pi\) | ||||
−0.156896 | + | 0.987615i | \(0.550149\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18223.4 | −1.50300 | −0.751500 | − | 0.659733i | \(-0.770669\pi\) | ||||
−0.751500 | + | 0.659733i | \(0.770669\pi\) | |||||||
\(44\) | 4957.27 | − | 8586.24i | 0.386021 | − | 0.668608i | ||||
\(45\) | 2208.27 | + | 3824.84i | 0.162563 | + | 0.281567i | ||||
\(46\) | −2999.88 | − | 5195.95i | −0.209030 | − | 0.362051i | ||||
\(47\) | −660.320 | + | 1143.71i | −0.0436023 | + | 0.0755214i | −0.887003 | − | 0.461764i | \(-0.847217\pi\) |
0.843401 | + | 0.537285i | \(0.180550\pi\) | |||||||
\(48\) | 518.500 | 0.0324822 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −513.788 | −0.0290642 | ||||||||
\(51\) | −2658.35 | + | 4604.39i | −0.143115 | + | 0.247883i | ||||
\(52\) | 5273.18 | + | 9133.42i | 0.270436 | + | 0.468409i | ||||
\(53\) | −17418.5 | − | 30169.7i | −0.851767 | − | 1.47530i | −0.879612 | − | 0.475691i | \(-0.842198\pi\) |
0.0278456 | − | 0.999612i | \(-0.491135\pi\) | |||||||
\(54\) | −1232.13 | + | 2134.11i | −0.0575006 | + | 0.0995939i | ||||
\(55\) | −26276.3 | −1.17127 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 22059.1 | 0.899293 | ||||||||
\(58\) | 7177.19 | − | 12431.3i | 0.280146 | − | 0.485227i | ||||
\(59\) | −5796.25 | − | 10039.4i | −0.216779 | − | 0.375472i | 0.737043 | − | 0.675846i | \(-0.236222\pi\) |
−0.953821 | + | 0.300374i | \(0.902888\pi\) | |||||||
\(60\) | −5047.96 | − | 8743.32i | −0.181025 | − | 0.313544i | ||||
\(61\) | −15703.1 | + | 27198.5i | −0.540331 | + | 0.935881i | 0.458554 | + | 0.888667i | \(0.348368\pi\) |
−0.998885 | + | 0.0472144i | \(0.984966\pi\) | |||||||
\(62\) | 33016.9 | 1.09083 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 18038.3 | 0.550486 | ||||||||
\(65\) | 13975.4 | − | 24206.2i | 0.410281 | − | 0.710628i | ||||
\(66\) | −7330.59 | − | 12696.9i | −0.207147 | − | 0.358789i | ||||
\(67\) | −13778.0 | − | 23864.1i | −0.374971 | − | 0.649469i | 0.615352 | − | 0.788253i | \(-0.289014\pi\) |
−0.990323 | + | 0.138784i | \(0.955681\pi\) | |||||||
\(68\) | 6076.79 | − | 10525.3i | 0.159368 | − | 0.276034i | ||||
\(69\) | 15974.1 | 0.403919 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −22868.5 | −0.538384 | −0.269192 | − | 0.963086i | \(-0.586757\pi\) | ||||
−0.269192 | + | 0.963086i | \(0.586757\pi\) | |||||||
\(72\) | 7197.47 | − | 12466.4i | 0.163625 | − | 0.283406i | ||||
\(73\) | −7968.20 | − | 13801.3i | −0.175006 | − | 0.303120i | 0.765157 | − | 0.643843i | \(-0.222661\pi\) |
−0.940163 | + | 0.340724i | \(0.889328\pi\) | |||||||
\(74\) | 16850.4 | + | 29185.7i | 0.357709 | + | 0.619570i | ||||
\(75\) | 683.970 | − | 1184.67i | 0.0140405 | − | 0.0243189i | ||||
\(76\) | −50425.6 | −1.00142 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 15595.5 | 0.290243 | ||||||||
\(79\) | −43582.6 | + | 75487.3i | −0.785680 | + | 1.36084i | 0.142912 | + | 0.989735i | \(0.454354\pi\) |
−0.928592 | + | 0.371103i | \(0.878980\pi\) | |||||||
\(80\) | 1570.63 | + | 2720.41i | 0.0274378 | + | 0.0475236i | ||||
\(81\) | −3280.50 | − | 5681.99i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 5708.60 | − | 9887.59i | 0.0937551 | − | 0.162389i | ||||
\(83\) | 90307.5 | 1.43889 | 0.719447 | − | 0.694548i | \(-0.244395\pi\) | ||||
0.719447 | + | 0.694548i | \(0.244395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −32210.5 | −0.483559 | ||||||||
\(86\) | 30800.6 | − | 53348.2i | 0.449069 | − | 0.777811i | ||||
\(87\) | 19109.0 | + | 33097.7i | 0.270670 | + | 0.468814i | ||||
\(88\) | 42821.5 | + | 74169.0i | 0.589461 | + | 1.02098i | ||||
\(89\) | 63284.8 | − | 109612.i | 0.846884 | − | 1.46685i | −0.0370902 | − | 0.999312i | \(-0.511809\pi\) |
0.883975 | − | 0.467535i | \(-0.154858\pi\) | |||||||
\(90\) | −14929.4 | −0.194283 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −36515.7 | −0.449791 | ||||||||
\(93\) | −43953.2 | + | 76129.1i | −0.526966 | + | 0.912733i | ||||
\(94\) | −2232.10 | − | 3866.11i | −0.0260552 | − | 0.0451289i | ||||
\(95\) | 66821.2 | + | 115738.i | 0.759635 | + | 1.31573i | ||||
\(96\) | −26467.4 | + | 45842.8i | −0.293111 | + | 0.507684i | ||||
\(97\) | −16573.1 | −0.178844 | −0.0894219 | − | 0.995994i | \(-0.528502\pi\) | ||||
−0.0894219 | + | 0.995994i | \(0.528502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 39034.8 | 0.400280 | ||||||||
\(100\) | −1563.51 | + | 2708.07i | −0.0156351 | + | 0.0270807i | ||||
\(101\) | 38305.0 | + | 66346.3i | 0.373639 | + | 0.647162i | 0.990122 | − | 0.140206i | \(-0.0447765\pi\) |
−0.616483 | + | 0.787368i | \(0.711443\pi\) | |||||||
\(102\) | −8986.09 | − | 15564.4i | −0.0855205 | − | 0.148126i | ||||
\(103\) | −40217.9 | + | 69659.5i | −0.373531 | + | 0.646974i | −0.990106 | − | 0.140322i | \(-0.955186\pi\) |
0.616575 | + | 0.787296i | \(0.288520\pi\) | |||||||
\(104\) | −91100.8 | −0.825922 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 117760. | 1.01797 | ||||||||
\(107\) | −74021.1 | + | 128208.i | −0.625023 | + | 1.08257i | 0.363513 | + | 0.931589i | \(0.381577\pi\) |
−0.988536 | + | 0.150983i | \(0.951756\pi\) | |||||||
\(108\) | 7498.99 | + | 12988.6i | 0.0618648 | + | 0.107153i | ||||
\(109\) | 62491.1 | + | 108238.i | 0.503793 | + | 0.872594i | 0.999990 | + | 0.00438493i | \(0.00139577\pi\) |
−0.496198 | + | 0.868210i | \(0.665271\pi\) | |||||||
\(110\) | 44411.4 | − | 76922.7i | 0.349955 | − | 0.606140i | ||||
\(111\) | −89726.9 | −0.691218 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −194474. | −1.43273 | −0.716366 | − | 0.697724i | \(-0.754196\pi\) | ||||
−0.716366 | + | 0.697724i | \(0.754196\pi\) | |||||||
\(114\) | −37283.6 | + | 64577.1i | −0.268693 | + | 0.465389i | ||||
\(115\) | 48388.6 | + | 83811.4i | 0.341191 | + | 0.590961i | ||||
\(116\) | −43681.8 | − | 75659.1i | −0.301409 | − | 0.522055i | ||||
\(117\) | −20761.2 | + | 35959.4i | −0.140213 | + | 0.242856i | ||||
\(118\) | 39186.5 | 0.259078 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 87209.8 | 0.552856 | ||||||||
\(121\) | −35593.7 | + | 61650.1i | −0.221009 | + | 0.382799i | ||||
\(122\) | −53081.6 | − | 91940.0i | −0.322882 | − | 0.559249i | ||||
\(123\) | 15198.9 | + | 26325.3i | 0.0905838 | + | 0.156896i | ||||
\(124\) | 100474. | − | 174026.i | 0.586812 | − | 1.01639i | ||||
\(125\) | 178679. | 1.02282 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 239766. | 1.31910 | 0.659551 | − | 0.751660i | \(-0.270746\pi\) | ||||
0.659551 | + | 0.751660i | \(0.270746\pi\) | |||||||
\(128\) | 63618.4 | − | 110190.i | 0.343208 | − | 0.594455i | ||||
\(129\) | 82005.5 | + | 142038.i | 0.433879 | + | 0.751500i | ||||
\(130\) | 47241.6 | + | 81824.8i | 0.245169 | + | 0.424646i | ||||
\(131\) | 174788. | − | 302741.i | 0.889883 | − | 1.54132i | 0.0498711 | − | 0.998756i | \(-0.484119\pi\) |
0.840012 | − | 0.542567i | \(-0.182548\pi\) | |||||||
\(132\) | −89230.8 | −0.445738 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 93148.1 | 0.448138 | ||||||||
\(135\) | 19874.5 | − | 34423.6i | 0.0938558 | − | 0.162563i | ||||
\(136\) | 52492.1 | + | 90919.0i | 0.243359 | + | 0.421509i | ||||
\(137\) | 140483. | + | 243323.i | 0.639472 | + | 1.10760i | 0.985549 | + | 0.169392i | \(0.0541804\pi\) |
−0.346076 | + | 0.938206i | \(0.612486\pi\) | |||||||
\(138\) | −26998.9 | + | 46763.5i | −0.120684 | + | 0.209030i | ||||
\(139\) | 50042.9 | 0.219688 | 0.109844 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109844 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11885.8 | 0.0503476 | ||||||||
\(142\) | 38651.6 | − | 66946.5i | 0.160859 | − | 0.278617i | ||||
\(143\) | −123519. | − | 213941.i | −0.505120 | − | 0.874893i | ||||
\(144\) | −2333.25 | − | 4041.30i | −0.00937680 | − | 0.0162411i | ||||
\(145\) | −115769. | + | 200518.i | −0.457270 | + | 0.792016i | ||||
\(146\) | 53870.3 | 0.209155 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 205109. | 0.769717 | ||||||||
\(149\) | 164406. | − | 284760.i | 0.606671 | − | 1.05079i | −0.385114 | − | 0.922869i | \(-0.625838\pi\) |
0.991785 | − | 0.127916i | \(-0.0408288\pi\) | |||||||
\(150\) | 2312.05 | + | 4004.58i | 0.00839012 | + | 0.0145321i | ||||
\(151\) | −255652. | − | 442802.i | −0.912445 | − | 1.58040i | −0.810600 | − | 0.585600i | \(-0.800859\pi\) |
−0.101844 | − | 0.994800i | \(-0.532474\pi\) | |||||||
\(152\) | 217792. | − | 377226.i | 0.764596 | − | 1.32432i | ||||
\(153\) | 47850.2 | 0.165255 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −532569. | −1.78052 | ||||||||
\(156\) | 47458.6 | − | 82200.8i | 0.156136 | − | 0.270436i | ||||
\(157\) | 37721.1 | + | 65334.8i | 0.122134 | + | 0.211541i | 0.920609 | − | 0.390486i | \(-0.127693\pi\) |
−0.798475 | + | 0.602028i | \(0.794360\pi\) | |||||||
\(158\) | −147324. | − | 255172.i | −0.469494 | − | 0.813187i | ||||
\(159\) | −156766. | + | 271527.i | −0.491768 | + | 0.851767i | ||||
\(160\) | −320698. | −0.990367 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 22178.3 | 0.0663960 | ||||||||
\(163\) | −170376. | + | 295101.i | −0.502274 | + | 0.869963i | 0.497723 | + | 0.867336i | \(0.334170\pi\) |
−0.999997 | + | 0.00262731i | \(0.999164\pi\) | |||||||
\(164\) | −34743.7 | − | 60177.8i | −0.100871 | − | 0.174714i | ||||
\(165\) | 118244. | + | 204804.i | 0.338117 | + | 0.585637i | ||||
\(166\) | −152635. | + | 264371.i | −0.429915 | + | 0.744635i | ||||
\(167\) | −132392. | −0.367342 | −0.183671 | − | 0.982988i | \(-0.558798\pi\) | ||||
−0.183671 | + | 0.982988i | \(0.558798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −108512. | −0.292253 | ||||||||
\(170\) | 54441.0 | − | 94294.6i | 0.144479 | − | 0.250244i | ||||
\(171\) | −99266.1 | − | 171934.i | −0.259604 | − | 0.449647i | ||||
\(172\) | −187459. | − | 324688.i | −0.483153 | − | 0.836845i | ||||
\(173\) | −224661. | + | 389124.i | −0.570706 | + | 0.988492i | 0.425788 | + | 0.904823i | \(0.359997\pi\) |
−0.996494 | + | 0.0836688i | \(0.973336\pi\) | |||||||
\(174\) | −129189. | −0.323485 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 27763.4 | 0.0675602 | ||||||||
\(177\) | −52166.2 | + | 90354.5i | −0.125157 | + | 0.216779i | ||||
\(178\) | 213923. | + | 370526.i | 0.506067 | + | 0.876534i | ||||
\(179\) | 46833.4 | + | 81117.8i | 0.109250 | + | 0.189227i | 0.915467 | − | 0.402393i | \(-0.131822\pi\) |
−0.806216 | + | 0.591621i | \(0.798488\pi\) | |||||||
\(180\) | −45431.6 | + | 78689.9i | −0.104515 | + | 0.181025i | ||||
\(181\) | 399795. | 0.907071 | 0.453535 | − | 0.891238i | \(-0.350163\pi\) | ||||
0.453535 | + | 0.891238i | \(0.350163\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 282655. | 0.623921 | ||||||||
\(184\) | 157714. | − | 273168.i | 0.343420 | − | 0.594820i | ||||
\(185\) | −271799. | − | 470770.i | −0.583873 | − | 1.01130i | ||||
\(186\) | −148576. | − | 257342.i | −0.314896 | − | 0.545416i | ||||
\(187\) | −142343. | + | 246545.i | −0.297668 | + | 0.515576i | ||||
\(188\) | −27170.0 | −0.0560654 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −451755. | −0.907861 | ||||||||
\(191\) | −13911.4 | + | 24095.2i | −0.0275922 | + | 0.0477911i | −0.879492 | − | 0.475914i | \(-0.842117\pi\) |
0.851900 | + | 0.523705i | \(0.175451\pi\) | |||||||
\(192\) | −81172.4 | − | 140595.i | −0.158912 | − | 0.275243i | ||||
\(193\) | 33232.1 | + | 57559.7i | 0.0642192 | + | 0.111231i | 0.896347 | − | 0.443352i | \(-0.146211\pi\) |
−0.832128 | + | 0.554583i | \(0.812878\pi\) | |||||||
\(194\) | 28011.3 | − | 48516.9i | 0.0534353 | − | 0.0925527i | ||||
\(195\) | −251558. | −0.473752 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −492506. | −0.904162 | −0.452081 | − | 0.891977i | \(-0.649318\pi\) | ||||
−0.452081 | + | 0.891977i | \(0.649318\pi\) | |||||||
\(198\) | −65975.3 | + | 114273.i | −0.119596 | + | 0.207147i | ||||
\(199\) | −174603. | − | 302421.i | −0.312549 | − | 0.541351i | 0.666364 | − | 0.745626i | \(-0.267850\pi\) |
−0.978914 | + | 0.204275i | \(0.934516\pi\) | |||||||
\(200\) | −13505.8 | − | 23392.7i | −0.0238751 | − | 0.0413528i | ||||
\(201\) | −124002. | + | 214777.i | −0.216490 | + | 0.374971i | ||||
\(202\) | −258967. | −0.446547 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −109382. | −0.184023 | ||||||||
\(205\) | −92080.7 | + | 159488.i | −0.153033 | + | 0.265060i | ||||
\(206\) | −135950. | − | 235472.i | −0.223208 | − | 0.386608i | ||||
\(207\) | −71883.6 | − | 124506.i | −0.116601 | − | 0.201960i | ||||
\(208\) | −14766.4 | + | 25576.1i | −0.0236655 | + | 0.0409898i | ||||
\(209\) | 1.18117e6 | 1.87046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −218250. | −0.337480 | −0.168740 | − | 0.985661i | \(-0.553970\pi\) | ||||
−0.168740 | + | 0.985661i | \(0.553970\pi\) | |||||||
\(212\) | 358357. | − | 620692.i | 0.547616 | − | 0.948499i | ||||
\(213\) | 102908. | + | 178243.i | 0.155418 | + | 0.269192i | ||||
\(214\) | −250216. | − | 433386.i | −0.373491 | − | 0.646905i | ||||
\(215\) | −496819. | + | 860516.i | −0.732997 | + | 1.26959i | ||||
\(216\) | −129554. | −0.188937 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −422481. | −0.602096 | ||||||||
\(219\) | −71713.8 | + | 124212.i | −0.101040 | + | 0.175006i | ||||
\(220\) | −270296. | − | 468167.i | −0.376516 | − | 0.652145i | ||||
\(221\) | −151414. | − | 262257.i | −0.208538 | − | 0.361199i | ||||
\(222\) | 151653. | − | 262671.i | 0.206523 | − | 0.357709i | ||||
\(223\) | 1.24807e6 | 1.68065 | 0.840324 | − | 0.542084i | \(-0.182365\pi\) | ||||
0.840324 | + | 0.542084i | \(0.182365\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12311.5 | −0.0162126 | ||||||||
\(226\) | 328693. | − | 569313.i | 0.428074 | − | 0.741447i | ||||
\(227\) | 260487. | + | 451176.i | 0.335522 | + | 0.581141i | 0.983585 | − | 0.180446i | \(-0.0577541\pi\) |
−0.648063 | + | 0.761587i | \(0.724421\pi\) | |||||||
\(228\) | 226915. | + | 393029.i | 0.289086 | + | 0.500711i | ||||
\(229\) | 262826. | − | 455227.i | 0.331191 | − | 0.573640i | −0.651554 | − | 0.758602i | \(-0.725883\pi\) |
0.982746 | + | 0.184962i | \(0.0592161\pi\) | |||||||
\(230\) | −327139. | −0.407767 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 754658. | 0.920514 | ||||||||
\(233\) | −105103. | + | 182043.i | −0.126831 | + | 0.219677i | −0.922447 | − | 0.386124i | \(-0.873814\pi\) |
0.795616 | + | 0.605801i | \(0.207147\pi\) | |||||||
\(234\) | −70179.7 | − | 121555.i | −0.0837861 | − | 0.145122i | ||||
\(235\) | 36004.1 | + | 62360.9i | 0.0425287 | + | 0.0736619i | ||||
\(236\) | 119248. | − | 206544.i | 0.139371 | − | 0.241398i | ||||
\(237\) | 784488. | 0.907225 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 805791. | 0.912489 | 0.456244 | − | 0.889855i | \(-0.349194\pi\) | ||||
0.456244 | + | 0.889855i | \(0.349194\pi\) | |||||||
\(240\) | 14135.7 | − | 24483.7i | 0.0158412 | − | 0.0274378i | ||||
\(241\) | −568975. | − | 985493.i | −0.631030 | − | 1.09298i | −0.987341 | − | 0.158609i | \(-0.949299\pi\) |
0.356311 | − | 0.934367i | \(-0.384034\pi\) | |||||||
\(242\) | −120318. | − | 208398.i | −0.132067 | − | 0.228746i | ||||
\(243\) | −29524.5 | + | 51137.9i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −646130. | −0.694777 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −102755. | −0.108259 | ||||||||
\(247\) | −628222. | + | 1.08811e6i | −0.655196 | + | 1.13483i | ||||
\(248\) | 867906. | + | 1.50326e6i | 0.896073 | + | 1.55204i | ||||
\(249\) | −406384. | − | 703877.i | −0.415373 | − | 0.719447i | ||||
\(250\) | −301997. | + | 523074.i | −0.305600 | + | 0.529314i | ||||
\(251\) | −1.16566e6 | −1.16785 | −0.583927 | − | 0.811806i | \(-0.698484\pi\) | ||||
−0.583927 | + | 0.811806i | \(0.698484\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 855346. | 0.840118 | ||||||||
\(254\) | −405244. | + | 701904.i | −0.394124 | + | 0.682643i | ||||
\(255\) | 144947. | + | 251056.i | 0.139592 | + | 0.241780i | ||||
\(256\) | 503664. | + | 872372.i | 0.480332 | + | 0.831959i | ||||
\(257\) | 514406. | − | 890977.i | 0.485817 | − | 0.841460i | −0.514050 | − | 0.857760i | \(-0.671855\pi\) |
0.999867 | + | 0.0162999i | \(0.00518866\pi\) | |||||||
\(258\) | −554411. | −0.518540 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 575043. | 0.527554 | ||||||||
\(261\) | 171981. | − | 297880.i | 0.156271 | − | 0.270670i | ||||
\(262\) | 590841. | + | 1.02337e6i | 0.531762 | + | 0.921039i | ||||
\(263\) | 328673. | + | 569278.i | 0.293004 | + | 0.507499i | 0.974519 | − | 0.224306i | \(-0.0720116\pi\) |
−0.681514 | + | 0.731805i | \(0.738678\pi\) | |||||||
\(264\) | 385394. | − | 667521.i | 0.340326 | − | 0.589461i | ||||
\(265\) | −1.89950e6 | −1.66159 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.13913e6 | −0.977898 | ||||||||
\(268\) | 283459. | − | 490965.i | 0.241076 | − | 0.417555i | ||||
\(269\) | −2737.93 | − | 4742.23i | −0.00230697 | − | 0.00399578i | 0.864870 | − | 0.501997i | \(-0.167401\pi\) |
−0.867177 | + | 0.498001i | \(0.834068\pi\) | |||||||
\(270\) | 67182.3 | + | 116363.i | 0.0560848 | + | 0.0971417i | ||||
\(271\) | 384573. | − | 666101.i | 0.318094 | − | 0.550956i | −0.661996 | − | 0.749507i | \(-0.730290\pi\) |
0.980090 | + | 0.198552i | \(0.0636237\pi\) | |||||||
\(272\) | 34033.4 | 0.0278922 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −949757. | −0.764251 | ||||||||
\(275\) | 36623.7 | − | 63434.0i | 0.0292032 | − | 0.0505814i | ||||
\(276\) | 164321. | + | 284612.i | 0.129843 | + | 0.224895i | ||||
\(277\) | 586918. | + | 1.01657e6i | 0.459598 | + | 0.796047i | 0.998940 | − | 0.0460398i | \(-0.0146601\pi\) |
−0.539341 | + | 0.842087i | \(0.681327\pi\) | |||||||
\(278\) | −84580.8 | + | 146498.i | −0.0656386 | + | 0.113689i | ||||
\(279\) | 791157. | 0.608488 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 837649. | 0.632843 | 0.316422 | − | 0.948619i | \(-0.397519\pi\) | ||||
0.316422 | + | 0.948619i | \(0.397519\pi\) | |||||||
\(282\) | −20088.9 | + | 34795.0i | −0.0150430 | + | 0.0260552i | ||||
\(283\) | 298611. | + | 517209.i | 0.221635 | + | 0.383884i | 0.955305 | − | 0.295623i | \(-0.0955272\pi\) |
−0.733669 | + | 0.679507i | \(0.762194\pi\) | |||||||
\(284\) | −235241. | − | 407450.i | −0.173068 | − | 0.299763i | ||||
\(285\) | 601390. | − | 1.04164e6i | 0.438575 | − | 0.759635i | ||||
\(286\) | 835071. | 0.603682 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 476412. | 0.338456 | ||||||||
\(289\) | 535440. | − | 927408.i | 0.377108 | − | 0.653170i | ||||
\(290\) | −391338. | − | 677818.i | −0.273248 | − | 0.473280i | ||||
\(291\) | 74578.9 | + | 129174.i | 0.0516278 | + | 0.0894219i | ||||
\(292\) | 163933. | − | 283940.i | 0.112515 | − | 0.194881i | ||||
\(293\) | −851321. | −0.579328 | −0.289664 | − | 0.957128i | \(-0.593543\pi\) | ||||
−0.289664 | + | 0.957128i | \(0.593543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −632084. | −0.422883 | ||||||||
\(296\) | −885880. | + | 1.53439e6i | −0.587686 | + | 1.01790i | ||||
\(297\) | −175657. | − | 304246.i | −0.115551 | − | 0.200140i | ||||
\(298\) | 555748. | + | 962584.i | 0.362525 | + | 0.627911i | ||||
\(299\) | −454927. | + | 787957.i | −0.294282 | + | 0.509712i | ||||
\(300\) | 28143.1 | 0.0180538 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.72838e6 | 1.09049 | ||||||||
\(303\) | 344745. | − | 597117.i | 0.215721 | − | 0.373639i | ||||
\(304\) | −70602.8 | − | 122288.i | −0.0438165 | − | 0.0758925i | ||||
\(305\) | 856215. | + | 1.48301e6i | 0.527027 | + | 0.912838i | ||||
\(306\) | −80874.8 | + | 140079.i | −0.0493753 | + | 0.0855205i | ||||
\(307\) | −600906. | −0.363882 | −0.181941 | − | 0.983309i | \(-0.558238\pi\) | ||||
−0.181941 | + | 0.983309i | \(0.558238\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 723923. | 0.431316 | ||||||||
\(310\) | 900129. | − | 1.55907e6i | 0.531987 | − | 0.921428i | ||||
\(311\) | 232933. | + | 403452.i | 0.136562 | + | 0.236533i | 0.926193 | − | 0.377049i | \(-0.123061\pi\) |
−0.789631 | + | 0.613582i | \(0.789728\pi\) | |||||||
\(312\) | 409954. | + | 710061.i | 0.238423 | + | 0.412961i | ||||
\(313\) | 1.48683e6 | − | 2.57526e6i | 0.857827 | − | 1.48580i | −0.0161698 | − | 0.999869i | \(-0.505147\pi\) |
0.873997 | − | 0.485931i | \(-0.161519\pi\) | |||||||
\(314\) | −255019. | −0.145965 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.79328e6 | −1.01026 | ||||||||
\(317\) | −1.27760e6 | + | 2.21288e6i | −0.714082 | + | 1.23683i | 0.249230 | + | 0.968444i | \(0.419822\pi\) |
−0.963312 | + | 0.268383i | \(0.913511\pi\) | |||||||
\(318\) | −529922. | − | 917852.i | −0.293863 | − | 0.508985i | ||||
\(319\) | 1.02320e6 | + | 1.77224e6i | 0.562970 | + | 0.975093i | ||||
\(320\) | 491772. | − | 851774.i | 0.268466 | − | 0.464997i | ||||
\(321\) | 1.33238e6 | 0.721714 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.44792e6 | 0.772216 | ||||||||
\(324\) | 67490.9 | − | 116898.i | 0.0357176 | − | 0.0618648i | ||||
\(325\) | 38957.6 | + | 67476.5i | 0.0204590 | + | 0.0354360i | ||||
\(326\) | −575928. | − | 997537.i | −0.300140 | − | 0.519859i | ||||
\(327\) | 562420. | − | 974140.i | 0.290865 | − | 0.503793i | ||||
\(328\) | 600241. | 0.308064 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −799405. | −0.404093 | ||||||||
\(331\) | −1.28069e6 | + | 2.21822e6i | −0.642502 | + | 1.11285i | 0.342370 | + | 0.939565i | \(0.388770\pi\) |
−0.984872 | + | 0.173281i | \(0.944563\pi\) | |||||||
\(332\) | 928965. | + | 1.60901e6i | 0.462545 | + | 0.801152i | ||||
\(333\) | 403771. | + | 699352.i | 0.199537 | + | 0.345609i | ||||
\(334\) | 223764. | − | 387571.i | 0.109755 | − | 0.190101i | ||||
\(335\) | −1.50249e6 | −0.731477 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.21525e6 | −0.582894 | −0.291447 | − | 0.956587i | \(-0.594137\pi\) | ||||
−0.291447 | + | 0.956587i | \(0.594137\pi\) | |||||||
\(338\) | 183403. | − | 317662.i | 0.0873200 | − | 0.151243i | ||||
\(339\) | 875132. | + | 1.51577e6i | 0.413594 | + | 0.716366i | ||||
\(340\) | −331339. | − | 573896.i | −0.155444 | − | 0.269238i | ||||
\(341\) | −2.35350e6 | + | 4.07639e6i | −1.09605 | + | 1.89841i | ||||
\(342\) | 671105. | 0.310259 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.23858e6 | 1.47557 | ||||||||
\(345\) | 435497. | − | 754303.i | 0.196987 | − | 0.341191i | ||||
\(346\) | −759429. | − | 1.31537e6i | −0.341033 | − | 0.590687i | ||||
\(347\) | −626590. | − | 1.08529e6i | −0.279357 | − | 0.483861i | 0.691868 | − | 0.722024i | \(-0.256788\pi\) |
−0.971225 | + | 0.238163i | \(0.923455\pi\) | |||||||
\(348\) | −393136. | + | 680932.i | −0.174018 | + | 0.301409i | ||||
\(349\) | 450403. | 0.197942 | 0.0989709 | − | 0.995090i | \(-0.468445\pi\) | ||||
0.0989709 | + | 0.995090i | \(0.468445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 373702. | 0.161904 | ||||||||
\(352\) | −1.41721e6 | + | 2.45468e6i | −0.609647 | + | 1.05594i | ||||
\(353\) | −272640. | − | 472227.i | −0.116454 | − | 0.201704i | 0.801906 | − | 0.597450i | \(-0.203819\pi\) |
−0.918360 | + | 0.395746i | \(0.870486\pi\) | |||||||
\(354\) | −176339. | − | 305428.i | −0.0747895 | − | 0.129539i | ||||
\(355\) | −623456. | + | 1.07986e6i | −0.262564 | + | 0.454774i | ||||
\(356\) | 2.60396e6 | 1.08895 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −316625. | −0.130568 | ||||||||
\(359\) | 505793. | − | 876060.i | 0.207127 | − | 0.358755i | −0.743681 | − | 0.668534i | \(-0.766922\pi\) |
0.950808 | + | 0.309780i | \(0.100255\pi\) | |||||||
\(360\) | −392444. | − | 679733.i | −0.159596 | − | 0.276428i | ||||
\(361\) | −1.76569e6 | − | 3.05826e6i | −0.713093 | − | 1.23511i | ||||
\(362\) | −675720. | + | 1.17038e6i | −0.271016 | + | 0.469414i | ||||
\(363\) | 640686. | 0.255199 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −868937. | −0.341394 | ||||||||
\(366\) | −477734. | + | 827460.i | −0.186416 | + | 0.322882i | ||||
\(367\) | 545190. | + | 944298.i | 0.211292 | + | 0.365968i | 0.952119 | − | 0.305727i | \(-0.0988996\pi\) |
−0.740827 | + | 0.671696i | \(0.765566\pi\) | |||||||
\(368\) | −51127.0 | − | 88554.6i | −0.0196803 | − | 0.0340872i | ||||
\(369\) | 136790. | − | 236928.i | 0.0522986 | − | 0.0905838i | ||||
\(370\) | 1.83754e6 | 0.697803 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.80853e6 | −0.677592 | ||||||||
\(373\) | 1.56501e6 | − | 2.71068e6i | 0.582433 | − | 1.00880i | −0.412757 | − | 0.910841i | \(-0.635434\pi\) |
0.995190 | − | 0.0979624i | \(-0.0312325\pi\) | |||||||
\(374\) | −481166. | − | 833404.i | −0.177876 | − | 0.308089i | ||||
\(375\) | −804055. | − | 1.39266e6i | −0.295262 | − | 0.511409i | ||||
\(376\) | 117349. | − | 203254.i | 0.0428065 | − | 0.0741430i | ||||
\(377\) | −2.17682e6 | −0.788804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.27933e6 | −0.457492 | −0.228746 | − | 0.973486i | \(-0.573463\pi\) | ||||
−0.228746 | + | 0.973486i | \(0.573463\pi\) | |||||||
\(380\) | −1.37474e6 | + | 2.38111e6i | −0.488383 | + | 0.845904i | ||||
\(381\) | −1.07895e6 | − | 1.86879e6i | −0.380792 | − | 0.659551i | ||||
\(382\) | −47025.0 | − | 81449.7i | −0.0164881 | − | 0.0285582i | ||||
\(383\) | −653329. | + | 1.13160e6i | −0.227580 | + | 0.394181i | −0.957090 | − | 0.289789i | \(-0.906415\pi\) |
0.729510 | + | 0.683970i | \(0.239748\pi\) | |||||||
\(384\) | −1.14513e6 | −0.396303 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −224671. | −0.0767501 | ||||||||
\(387\) | 738049. | − | 1.27834e6i | 0.250500 | − | 0.433879i | ||||
\(388\) | −170482. | − | 295284.i | −0.0574909 | − | 0.0995772i | ||||
\(389\) | 18244.1 | + | 31599.7i | 0.00611292 | + | 0.0105879i | 0.869066 | − | 0.494697i | \(-0.164721\pi\) |
−0.862953 | + | 0.505285i | \(0.831388\pi\) | |||||||
\(390\) | 425174. | − | 736423.i | 0.141549 | − | 0.245169i | ||||
\(391\) | 1.04851e6 | 0.346842 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.14618e6 | −1.02755 | ||||||||
\(394\) | 832417. | − | 1.44179e6i | 0.270147 | − | 0.467909i | ||||
\(395\) | 2.37636e6 | + | 4.11597e6i | 0.766335 | + | 1.32733i | ||||
\(396\) | 401539. | + | 695485.i | 0.128674 | + | 0.222869i | ||||
\(397\) | −320102. | + | 554433.i | −0.101932 | + | 0.176552i | −0.912481 | − | 0.409120i | \(-0.865836\pi\) |
0.810548 | + | 0.585672i | \(0.199169\pi\) | |||||||
\(398\) | 1.18043e6 | 0.373536 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8756.50 | −0.00273641 | ||||||||
\(401\) | 1.34575e6 | − | 2.33090e6i | 0.417929 | − | 0.723874i | −0.577802 | − | 0.816177i | \(-0.696089\pi\) |
0.995731 | + | 0.0923027i | \(0.0294227\pi\) | |||||||
\(402\) | −419166. | − | 726018.i | −0.129366 | − | 0.224069i | ||||
\(403\) | −2.50349e6 | − | 4.33616e6i | −0.767861 | − | 1.32997i | ||||
\(404\) | −788064. | + | 1.36497e6i | −0.240219 | + | 0.416072i | ||||
\(405\) | −357740. | −0.108375 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.80449e6 | −1.43768 | ||||||||
\(408\) | 472429. | − | 818271.i | 0.140503 | − | 0.243359i | ||||
\(409\) | −1.46286e6 | − | 2.53375e6i | −0.432409 | − | 0.748954i | 0.564672 | − | 0.825316i | \(-0.309003\pi\) |
−0.997080 | + | 0.0763622i | \(0.975669\pi\) | |||||||
\(410\) | −311263. | − | 539124.i | −0.0914467 | − | 0.158390i | ||||
\(411\) | 1.26435e6 | − | 2.18991e6i | 0.369199 | − | 0.639472i | ||||
\(412\) | −1.65484e6 | −0.480299 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 485981. | 0.139354 | ||||||||
\(415\) | 2.46202e6 | − | 4.26435e6i | 0.701733 | − | 1.21544i | ||||
\(416\) | −1.50753e6 | − | 2.61112e6i | −0.427103 | − | 0.739763i | ||||
\(417\) | −225193. | − | 390046.i | −0.0634183 | − | 0.109844i | ||||
\(418\) | −1.99638e6 | + | 3.45782e6i | −0.558858 | + | 0.967971i | ||||
\(419\) | −5.52810e6 | −1.53830 | −0.769150 | − | 0.639068i | \(-0.779320\pi\) | ||||
−0.769150 | + | 0.639068i | \(0.779320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.77477e6 | 1.58792 | 0.793961 | − | 0.607968i | \(-0.208015\pi\) | ||||
0.793961 | + | 0.607968i | \(0.208015\pi\) | |||||||
\(422\) | 368878. | − | 638916.i | 0.100833 | − | 0.174648i | ||||
\(423\) | −53485.9 | − | 92640.3i | −0.0145341 | − | 0.0251738i | ||||
\(424\) | 3.09553e6 | + | 5.36162e6i | 0.836220 | + | 1.44838i | ||||
\(425\) | 44894.6 | − | 77759.6i | 0.0120565 | − | 0.0208825i | ||||
\(426\) | −695729. | −0.185744 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.04573e6 | −0.803677 | ||||||||
\(429\) | −1.11167e6 | + | 1.92547e6i | −0.291631 | + | 0.505120i | ||||
\(430\) | −1.67941e6 | − | 2.90883e6i | −0.438012 | − | 0.758659i | ||||
\(431\) | −1.10482e6 | − | 1.91360e6i | −0.286483 | − | 0.496203i | 0.686485 | − | 0.727144i | \(-0.259153\pi\) |
−0.972968 | + | 0.230941i | \(0.925819\pi\) | |||||||
\(432\) | −20999.2 | + | 36371.7i | −0.00541370 | + | 0.00937680i | ||||
\(433\) | 4.97215e6 | 1.27446 | 0.637228 | − | 0.770676i | \(-0.280081\pi\) | ||||
0.637228 | + | 0.770676i | \(0.280081\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.08385e6 | 0.528010 | ||||||||
\(436\) | −1.28565e6 | + | 2.22681e6i | −0.323897 | + | 0.561006i | ||||
\(437\) | −2.17516e6 | − | 3.76748e6i | −0.544863 | − | 0.943730i | ||||
\(438\) | −242416. | − | 419878.i | −0.0603777 | − | 0.104577i | ||||
\(439\) | 1.43202e6 | − | 2.48034e6i | 0.354641 | − | 0.614257i | −0.632415 | − | 0.774630i | \(-0.717936\pi\) |
0.987056 | + | 0.160373i | \(0.0512697\pi\) | |||||||
\(440\) | 4.66971e6 | 1.14990 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.02366e6 | 0.249230 | ||||||||
\(443\) | 2.83117e6 | − | 4.90373e6i | 0.685419 | − | 1.18718i | −0.287886 | − | 0.957665i | \(-0.592952\pi\) |
0.973305 | − | 0.229516i | \(-0.0737144\pi\) | |||||||
\(444\) | −922992. | − | 1.59867e6i | −0.222198 | − | 0.384858i | ||||
\(445\) | −3.45062e6 | − | 5.97665e6i | −0.826032 | − | 1.43073i | ||||
\(446\) | −2.10944e6 | + | 3.65367e6i | −0.502147 | + | 0.869744i | ||||
\(447\) | −2.95932e6 | −0.700523 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.54480e6 | 1.76617 | 0.883084 | − | 0.469215i | \(-0.155463\pi\) | ||||
0.883084 | + | 0.469215i | \(0.155463\pi\) | |||||||
\(450\) | 20808.4 | − | 36041.2i | 0.00484404 | − | 0.00839012i | ||||
\(451\) | 813837. | + | 1.40961e6i | 0.188407 | + | 0.326330i | ||||
\(452\) | −2.00049e6 | − | 3.46495e6i | −0.460565 | − | 0.797721i | ||||
\(453\) | −2.30087e6 | + | 3.98522e6i | −0.526800 | + | 0.912445i | ||||
\(454\) | −1.76106e6 | −0.400991 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.92025e6 | −0.882879 | ||||||||
\(457\) | 294507. | − | 510101.i | 0.0659638 | − | 0.114253i | −0.831157 | − | 0.556037i | \(-0.812321\pi\) |
0.897121 | + | 0.441785i | \(0.145654\pi\) | |||||||
\(458\) | 888437. | + | 1.53882e6i | 0.197908 | + | 0.342787i | ||||
\(459\) | −215326. | − | 372956.i | −0.0477051 | − | 0.0826277i | ||||
\(460\) | −995516. | + | 1.72428e6i | −0.219358 | + | 0.379939i | ||||
\(461\) | −5.94951e6 | −1.30385 | −0.651927 | − | 0.758282i | \(-0.726039\pi\) | ||||
−0.651927 | + | 0.758282i | \(0.726039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.16083e6 | −0.468456 | −0.234228 | − | 0.972182i | \(-0.575256\pi\) | ||||
−0.234228 | + | 0.972182i | \(0.575256\pi\) | |||||||
\(464\) | 122321. | − | 211866.i | 0.0263758 | − | 0.0456843i | ||||
\(465\) | 2.39656e6 | + | 4.15096e6i | 0.513991 | + | 0.890259i | ||||
\(466\) | −355282. | − | 615366.i | −0.0757893 | − | 0.131271i | ||||
\(467\) | −252883. | + | 438006.i | −0.0536571 | + | 0.0929368i | −0.891606 | − | 0.452811i | \(-0.850421\pi\) |
0.837949 | + | 0.545748i | \(0.183754\pi\) | |||||||
\(468\) | −854255. | −0.180291 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −243412. | −0.0508272 | ||||||||
\(471\) | 339490. | − | 588013.i | 0.0705138 | − | 0.122134i | ||||
\(472\) | 1.03008e6 | + | 1.78415e6i | 0.212822 | + | 0.368619i | ||||
\(473\) | 4.39104e6 | + | 7.60550e6i | 0.902432 | + | 1.56306i | ||||
\(474\) | −1.32591e6 | + | 2.29655e6i | −0.271062 | + | 0.469494i | ||||
\(475\) | −372538. | −0.0757594 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.82179e6 | 0.567845 | ||||||||
\(478\) | −1.36192e6 | + | 2.35891e6i | −0.272635 | + | 0.472218i | ||||
\(479\) | 273534. | + | 473774.i | 0.0544718 | + | 0.0943480i | 0.891976 | − | 0.452084i | \(-0.149319\pi\) |
−0.837504 | + | 0.546432i | \(0.815986\pi\) | |||||||
\(480\) | 1.44314e6 | + | 2.49959e6i | 0.285894 | + | 0.495183i | ||||
\(481\) | 2.55533e6 | − | 4.42596e6i | 0.503599 | − | 0.872258i | ||||
\(482\) | 3.84665e6 | 0.754162 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.46456e6 | −0.284181 | ||||||||
\(485\) | −451826. | + | 782586.i | −0.0872202 | + | 0.151070i | ||||
\(486\) | −99802.6 | − | 172863.i | −0.0191669 | − | 0.0331980i | ||||
\(487\) | −1.18944e6 | − | 2.06018e6i | −0.227259 | − | 0.393625i | 0.729736 | − | 0.683729i | \(-0.239643\pi\) |
−0.956995 | + | 0.290105i | \(0.906310\pi\) | |||||||
\(488\) | 2.79068e6 | − | 4.83359e6i | 0.530469 | − | 0.918799i | ||||
\(489\) | 3.06677e6 | 0.579976 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.19719e6 | −1.34728 | −0.673642 | − | 0.739058i | \(-0.735271\pi\) | ||||
−0.673642 | + | 0.739058i | \(0.735271\pi\) | |||||||
\(492\) | −312693. | + | 541600.i | −0.0582379 | + | 0.100871i | ||||
\(493\) | 1.25428e6 | + | 2.17248e6i | 0.232422 | + | 0.402566i | ||||
\(494\) | −2.12360e6 | − | 3.67818e6i | −0.391521 | − | 0.678134i | ||||
\(495\) | 1.06419e6 | − | 1.84323e6i | 0.195212 | − | 0.338117i | ||||
\(496\) | 562709. | 0.102702 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.74742e6 | 0.496423 | ||||||||
\(499\) | −1.11118e6 | + | 1.92462e6i | −0.199771 | + | 0.346014i | −0.948454 | − | 0.316914i | \(-0.897353\pi\) |
0.748683 | + | 0.662928i | \(0.230687\pi\) | |||||||
\(500\) | 1.83801e6 | + | 3.18353e6i | 0.328794 | + | 0.569488i | ||||
\(501\) | 595764. | + | 1.03189e6i | 0.106042 | + | 0.183671i | ||||
\(502\) | 1.97016e6 | − | 3.41242e6i | 0.348933 | − | 0.604370i | ||||
\(503\) | −305857. | −0.0539013 | −0.0269506 | − | 0.999637i | \(-0.508580\pi\) | ||||
−0.0269506 | + | 0.999637i | \(0.508580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.17719e6 | 0.728879 | ||||||||
\(506\) | −1.44568e6 | + | 2.50398e6i | −0.251012 | + | 0.434766i | ||||
\(507\) | 488302. | + | 845764.i | 0.0843662 | + | 0.146127i | ||||
\(508\) | 2.46640e6 | + | 4.27193e6i | 0.424037 | + | 0.734454i | ||||
\(509\) | 4.53210e6 | − | 7.84983e6i | 0.775363 | − | 1.34297i | −0.159228 | − | 0.987242i | \(-0.550900\pi\) |
0.934590 | − | 0.355726i | \(-0.115766\pi\) | |||||||
\(510\) | −979938. | −0.166830 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 666475. | 0.112359 | ||||||||
\(513\) | −893395. | + | 1.54741e6i | −0.149882 | + | 0.259604i | ||||
\(514\) | 1.73886e6 | + | 3.01180e6i | 0.290307 | + | 0.502826i | ||||
\(515\) | 2.19289e6 | + | 3.79820e6i | 0.364334 | + | 0.631045i | ||||
\(516\) | −1.68713e6 | + | 2.92219e6i | −0.278948 | + | 0.483153i | ||||
\(517\) | 636431. | 0.104719 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.04390e6 | 0.658995 | ||||||||
\(520\) | −2.48365e6 | + | 4.30181e6i | −0.402793 | + | 0.697658i | ||||
\(521\) | −4.22324e6 | − | 7.31487e6i | −0.681635 | − | 1.18063i | −0.974482 | − | 0.224467i | \(-0.927936\pi\) |
0.292847 | − | 0.956159i | \(-0.405397\pi\) | |||||||
\(522\) | 581352. | + | 1.00693e6i | 0.0933820 | + | 0.161742i | ||||
\(523\) | −1.95793e6 | + | 3.39123e6i | −0.312998 | + | 0.542129i | −0.979010 | − | 0.203812i | \(-0.934667\pi\) |
0.666012 | + | 0.745941i | \(0.268000\pi\) | |||||||
\(524\) | 7.19195e6 | 1.14424 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.22204e6 | −0.350178 | ||||||||
\(527\) | −2.88501e6 | + | 4.99698e6i | −0.452502 | + | 0.783756i | ||||
\(528\) | −124935. | − | 216394.i | −0.0195030 | − | 0.0337801i | ||||
\(529\) | 1.64303e6 | + | 2.84581e6i | 0.255274 | + | 0.442147i | ||||
\(530\) | 3.21046e6 | − | 5.56068e6i | 0.496453 | − | 0.859881i | ||||
\(531\) | 938992. | 0.144519 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.73140e6 | −0.263985 | ||||||||
\(534\) | 1.92531e6 | − | 3.33474e6i | 0.292178 | − | 0.506067i | ||||
\(535\) | 4.03602e6 | + | 6.99059e6i | 0.609634 | + | 1.05592i | ||||
\(536\) | 2.44855e6 | + | 4.24102e6i | 0.368127 | + | 0.637615i | ||||
\(537\) | 421501. | − | 730061.i | 0.0630758 | − | 0.109250i | ||||
\(538\) | 18510.2 | 0.00275712 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 817769. | 0.120683 | ||||||||
\(541\) | 1.47401e6 | − | 2.55306e6i | 0.216524 | − | 0.375031i | −0.737219 | − | 0.675654i | \(-0.763861\pi\) |
0.953743 | + | 0.300623i | \(0.0971946\pi\) | |||||||
\(542\) | 1.29999e6 | + | 2.25164e6i | 0.190082 | + | 0.329231i | ||||
\(543\) | −1.79908e6 | − | 3.11610e6i | −0.261849 | − | 0.453535i | ||||
\(544\) | −1.73727e6 | + | 3.00904e6i | −0.251692 | + | 0.435944i | ||||
\(545\) | 6.81469e6 | 0.982776 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.50670e6 | −0.786906 | −0.393453 | − | 0.919345i | \(-0.628720\pi\) | ||||
−0.393453 | + | 0.919345i | \(0.628720\pi\) | |||||||
\(548\) | −2.89020e6 | + | 5.00598e6i | −0.411128 | + | 0.712095i | ||||
\(549\) | −1.27195e6 | − | 2.20308e6i | −0.180110 | − | 0.311960i | ||||
\(550\) | 123800. | + | 214428.i | 0.0174508 | + | 0.0302256i | ||||
\(551\) | 5.20405e6 | − | 9.01368e6i | 0.730234 | − | 1.26480i | ||||
\(552\) | −2.83885e6 | −0.396547 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.96796e6 | −0.549278 | ||||||||
\(555\) | −2.44619e6 | + | 4.23693e6i | −0.337099 | + | 0.583873i | ||||
\(556\) | 514775. | + | 891617.i | 0.0706205 | + | 0.122318i | ||||
\(557\) | 2.48618e6 | + | 4.30618e6i | 0.339542 | + | 0.588105i | 0.984347 | − | 0.176243i | \(-0.0563945\pi\) |
−0.644804 | + | 0.764348i | \(0.723061\pi\) | |||||||
\(558\) | −1.33719e6 | + | 2.31607e6i | −0.181805 | + | 0.314896i | ||||
\(559\) | −9.34174e6 | −1.26444 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.56217e6 | 0.343717 | ||||||||
\(562\) | −1.41577e6 | + | 2.45218e6i | −0.189082 | + | 0.327500i | ||||
\(563\) | −6.56986e6 | − | 1.13793e7i | −0.873544 | − | 1.51302i | −0.858305 | − | 0.513139i | \(-0.828482\pi\) |
−0.0152390 | − | 0.999884i | \(-0.504851\pi\) | |||||||
\(564\) | 122265. | + | 211769.i | 0.0161847 | + | 0.0280327i | ||||
\(565\) | −5.30187e6 | + | 9.18311e6i | −0.698728 | + | 1.21023i | ||||
\(566\) | −2.01880e6 | −0.264882 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.06409e6 | 0.528558 | ||||||||
\(569\) | 6.92946e6 | − | 1.20022e7i | 0.897261 | − | 1.55410i | 0.0662804 | − | 0.997801i | \(-0.478887\pi\) |
0.830981 | − | 0.556301i | \(-0.187780\pi\) | |||||||
\(570\) | 2.03290e6 | + | 3.52108e6i | 0.262077 | + | 0.453930i | ||||
\(571\) | 5.34885e6 | + | 9.26448e6i | 0.686547 | + | 1.18913i | 0.972948 | + | 0.231025i | \(0.0742078\pi\) |
−0.286401 | + | 0.958110i | \(0.592459\pi\) | |||||||
\(572\) | 2.54120e6 | − | 4.40150e6i | 0.324750 | − | 0.562484i | ||||
\(573\) | 250404. | 0.0318607 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −269774. | −0.0340275 | ||||||||
\(576\) | −730552. | + | 1.26535e6i | −0.0917476 | + | 0.158912i | ||||
\(577\) | 2.80949e6 | + | 4.86618e6i | 0.351308 | + | 0.608483i | 0.986479 | − | 0.163888i | \(-0.0524037\pi\) |
−0.635171 | + | 0.772372i | \(0.719070\pi\) | |||||||
\(578\) | 1.80996e6 | + | 3.13495e6i | 0.225346 | + | 0.390311i | ||||
\(579\) | 299089. | − | 518038.i | 0.0370770 | − | 0.0642192i | ||||
\(580\) | −4.76353e6 | −0.587975 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −504203. | −0.0617018 | ||||||||
\(583\) | −8.39416e6 | + | 1.45391e7i | −1.02284 | + | 1.77160i | ||||
\(584\) | 1.41607e6 | + | 2.45271e6i | 0.171812 | + | 0.297587i | ||||
\(585\) | 1.13201e6 | + | 1.96070e6i | 0.136760 | + | 0.236876i | ||||
\(586\) | 1.43887e6 | − | 2.49220e6i | 0.173093 | − | 0.299805i | ||||
\(587\) | −6.86832e6 | −0.822726 | −0.411363 | − | 0.911471i | \(-0.634947\pi\) | ||||
−0.411363 | + | 0.911471i | \(0.634947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.39400e7 | 2.84338 | ||||||||
\(590\) | 1.06833e6 | − | 1.85040e6i | 0.126350 | − | 0.218844i | ||||
\(591\) | 2.21628e6 | + | 3.83871e6i | 0.261009 | + | 0.452081i | ||||
\(592\) | 287181. | + | 497412.i | 0.0336784 | + | 0.0583327i | ||||
\(593\) | −2.03868e6 | + | 3.53110e6i | −0.238075 | + | 0.412357i | −0.960162 | − | 0.279445i | \(-0.909850\pi\) |
0.722087 | + | 0.691802i | \(0.243183\pi\) | |||||||
\(594\) | 1.18755e6 | 0.138098 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.76479e6 | 0.780079 | ||||||||
\(597\) | −1.57143e6 | + | 2.72179e6i | −0.180450 | + | 0.312549i | ||||
\(598\) | −1.53780e6 | − | 2.66356e6i | −0.175852 | − | 0.304585i | ||||
\(599\) | −291496. | − | 504887.i | −0.0331945 | − | 0.0574946i | 0.848951 | − | 0.528472i | \(-0.177235\pi\) |
−0.882145 | + | 0.470977i | \(0.843901\pi\) | |||||||
\(600\) | −121552. | + | 210534.i | −0.0137843 | + | 0.0238751i | ||||
\(601\) | −6.87250e6 | −0.776119 | −0.388060 | − | 0.921634i | \(-0.626855\pi\) | ||||
−0.388060 | + | 0.921634i | \(0.626855\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.23203e6 | 0.249981 | ||||||||
\(604\) | 5.25962e6 | − | 9.10993e6i | 0.586627 | − | 1.01607i | ||||
\(605\) | 1.94076e6 | + | 3.36149e6i | 0.215567 | + | 0.373373i | ||||
\(606\) | 1.16535e6 | + | 2.01845e6i | 0.128907 | + | 0.223273i | ||||
\(607\) | 1.20281e6 | − | 2.08333e6i | 0.132503 | − | 0.229502i | −0.792138 | − | 0.610342i | \(-0.791032\pi\) |
0.924641 | + | 0.380840i | \(0.124365\pi\) | |||||||
\(608\) | 1.44160e7 | 1.58156 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.78858e6 | −0.629865 | ||||||||
\(611\) | −338494. | + | 586289.i | −0.0366816 | + | 0.0635344i | ||||
\(612\) | 492220. | + | 852550.i | 0.0531228 | + | 0.0920114i | ||||
\(613\) | 5.81225e6 | + | 1.00671e7i | 0.624731 | + | 1.08207i | 0.988593 | + | 0.150613i | \(0.0481248\pi\) |
−0.363861 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(614\) | 1.01563e6 | − | 1.75912e6i | 0.108721 | − | 0.188311i | ||||
\(615\) | 1.65745e6 | 0.176707 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.37370e7 | −1.45271 | −0.726353 | − | 0.687322i | \(-0.758786\pi\) | ||||
−0.726353 | + | 0.687322i | \(0.758786\pi\) | |||||||
\(618\) | −1.22355e6 | + | 2.11925e6i | −0.128869 | + | 0.223208i | ||||
\(619\) | −8.20042e6 | − | 1.42035e7i | −0.860220 | − | 1.48994i | −0.871717 | − | 0.490010i | \(-0.836993\pi\) |
0.0114968 | − | 0.999934i | \(-0.496340\pi\) | |||||||
\(620\) | −5.47837e6 | − | 9.48881e6i | −0.572363 | − | 0.991362i | ||||
\(621\) | −646952. | + | 1.12055e6i | −0.0673199 | + | 0.116601i | ||||
\(622\) | −1.57478e6 | −0.163209 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 265794. | 0.0273265 | ||||||||
\(625\) | 4.63377e6 | − | 8.02593e6i | 0.474498 | − | 0.821855i | ||||
\(626\) | 5.02597e6 | + | 8.70523e6i | 0.512606 | + | 0.887860i | ||||
\(627\) | −5.31527e6 | − | 9.20632e6i | −0.539954 | − | 0.935228i | ||||
\(628\) | −776049. | + | 1.34416e6i | −0.0785218 | + | 0.136004i | ||||
\(629\) | −5.88951e6 | −0.593543 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.28252e6 | −0.728129 | −0.364065 | − | 0.931374i | \(-0.618611\pi\) | ||||
−0.364065 | + | 0.931374i | \(0.618611\pi\) | |||||||
\(632\) | 7.74530e6 | − | 1.34153e7i | 0.771340 | − | 1.33600i | ||||
\(633\) | 982124. | + | 1.70109e6i | 0.0974220 | + | 0.168740i | ||||
\(634\) | −4.31873e6 | − | 7.48025e6i | −0.426710 | − | 0.739083i | ||||
\(635\) | 6.53666e6 | − | 1.13218e7i | 0.643312 | − | 1.11425i | ||||
\(636\) | −6.45042e6 | −0.632332 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.91754e6 | −0.672821 | ||||||||
\(639\) | 926175. | − | 1.60418e6i | 0.0897307 | − | 0.155418i | ||||
\(640\) | −3.46881e6 | − | 6.00816e6i | −0.334758 | − | 0.579818i | ||||
\(641\) | 53757.1 | + | 93110.0i | 0.00516762 | + | 0.00895058i | 0.868598 | − | 0.495518i | \(-0.165022\pi\) |
−0.863430 | + | 0.504469i | \(0.831688\pi\) | |||||||
\(642\) | −2.25194e6 | + | 3.90048e6i | −0.215635 | + | 0.373491i | ||||
\(643\) | 9.75913e6 | 0.930858 | 0.465429 | − | 0.885085i | \(-0.345900\pi\) | ||||
0.465429 | + | 0.885085i | \(0.345900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.94274e6 | 0.846392 | ||||||||
\(646\) | −2.44723e6 | + | 4.23872e6i | −0.230724 | + | 0.399626i | ||||
\(647\) | 3.37794e6 | + | 5.85077e6i | 0.317243 | + | 0.549480i | 0.979912 | − | 0.199432i | \(-0.0639097\pi\) |
−0.662669 | + | 0.748912i | \(0.730576\pi\) | |||||||
\(648\) | 582995. | + | 1.00978e6i | 0.0545415 | + | 0.0944687i | ||||
\(649\) | −2.79328e6 | + | 4.83810e6i | −0.260317 | + | 0.450882i | ||||
\(650\) | −263379. | −0.0244511 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.01043e6 | −0.645841 | ||||||||
\(653\) | −1.10173e6 | + | 1.90825e6i | −0.101110 | + | 0.175127i | −0.912142 | − | 0.409874i | \(-0.865573\pi\) |
0.811033 | + | 0.585001i | \(0.198906\pi\) | |||||||
\(654\) | 1.90116e6 | + | 3.29291e6i | 0.173810 | + | 0.301048i | ||||
\(655\) | −9.53036e6 | − | 1.65071e7i | −0.867973 | − | 1.50337i | ||||
\(656\) | 97291.8 | − | 168514.i | 0.00882708 | − | 0.0152889i | ||||
\(657\) | 1.29085e6 | 0.116671 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.39630e7 | −1.25247 | −0.626233 | − | 0.779636i | \(-0.715404\pi\) | ||||
−0.626233 | + | 0.779636i | \(0.715404\pi\) | |||||||
\(660\) | −2.43267e6 | + | 4.21350e6i | −0.217382 | + | 0.376516i | ||||
\(661\) | 25526.4 | + | 44213.1i | 0.00227241 | + | 0.00393593i | 0.867159 | − | 0.498031i | \(-0.165943\pi\) |
−0.864887 | + | 0.501967i | \(0.832610\pi\) | |||||||
\(662\) | −4.32916e6 | − | 7.49833e6i | −0.383936 | − | 0.664997i | ||||
\(663\) | −1.36273e6 | + | 2.36031e6i | −0.120400 | + | 0.208538i | ||||
\(664\) | −1.60490e7 | −1.41263 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.72976e6 | −0.238473 | ||||||||
\(667\) | 3.76851e6 | − | 6.52726e6i | 0.327986 | − | 0.568089i | ||||
\(668\) | −1.36187e6 | − | 2.35883e6i | −0.118085 | − | 0.204530i | ||||
\(669\) | −5.61632e6 | − | 9.72774e6i | −0.485161 | − | 0.840324i | ||||
\(670\) | 2.53946e6 | − | 4.39848e6i | 0.218552 | − | 0.378543i | ||||
\(671\) | 1.51350e7 | 1.29770 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.71688e6 | 0.571650 | 0.285825 | − | 0.958282i | \(-0.407732\pi\) | ||||
0.285825 | + | 0.958282i | \(0.407732\pi\) | |||||||
\(674\) | 2.05397e6 | − | 3.55757e6i | 0.174158 | − | 0.301651i | ||||
\(675\) | 55401.6 | + | 95958.4i | 0.00468018 | + | 0.00810631i | ||||
\(676\) | −1.11622e6 | − | 1.93336e6i | −0.0939474 | − | 0.162722i | ||||
\(677\) | −7.28274e6 | + | 1.26141e7i | −0.610693 | + | 1.05775i | 0.380430 | + | 0.924810i | \(0.375776\pi\) |
−0.991124 | + | 0.132942i | \(0.957558\pi\) | |||||||
\(678\) | −5.91647e6 | −0.494298 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.72429e6 | 0.474733 | ||||||||
\(681\) | 2.34438e6 | − | 4.06058e6i | 0.193714 | − | 0.335522i | ||||
\(682\) | −7.95562e6 | − | 1.37795e7i | −0.654957 | − | 1.13442i | ||||
\(683\) | 812824. | + | 1.40785e6i | 0.0666722 | + | 0.115480i | 0.897435 | − | 0.441148i | \(-0.145428\pi\) |
−0.830762 | + | 0.556627i | \(0.812095\pi\) | |||||||
\(684\) | 2.04224e6 | − | 3.53726e6i | 0.166904 | − | 0.289086i | ||||
\(685\) | 1.53197e7 | 1.24745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.73086e6 | −0.382427 | ||||||||
\(688\) | 524936. | − | 909215.i | 0.0422800 | − | 0.0732311i | ||||
\(689\) | −8.92910e6 | − | 1.54657e7i | −0.716572 | − | 1.24114i | ||||
\(690\) | 1.47212e6 | + | 2.54979e6i | 0.117712 | + | 0.203884i | ||||
\(691\) | 1.40778e6 | − | 2.43834e6i | 0.112160 | − | 0.194267i | −0.804481 | − | 0.593979i | \(-0.797556\pi\) |
0.916641 | + | 0.399711i | \(0.130890\pi\) | |||||||
\(692\) | −9.24407e6 | −0.733834 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.23616e6 | 0.333867 | ||||||||
\(695\) | 1.36430e6 | − | 2.36304e6i | 0.107139 | − | 0.185571i | ||||
\(696\) | −3.39596e6 | − | 5.88198e6i | −0.265729 | − | 0.460257i | ||||
\(697\) | 997630. | + | 1.72795e6i | 0.0777835 | + | 0.134725i | ||||
\(698\) | −761255. | + | 1.31853e6i | −0.0591414 | + | 0.102436i | ||||
\(699\) | 1.89185e6 | 0.146451 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.40996e7 | 1.08371 | 0.541855 | − | 0.840472i | \(-0.317722\pi\) | ||||
0.541855 | + | 0.840472i | \(0.317722\pi\) | |||||||
\(702\) | −631617. | + | 1.09399e6i | −0.0483739 | + | 0.0837861i | ||||
\(703\) | 1.22179e7 | + | 2.11620e7i | 0.932412 | + | 1.61498i | ||||
\(704\) | −4.34643e6 | − | 7.52824e6i | −0.330523 | − | 0.572482i | ||||
\(705\) | 324037. | − | 561249.i | 0.0245540 | − | 0.0425287i | ||||
\(706\) | 1.84323e6 | 0.139177 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.14647e6 | −0.160932 | ||||||||
\(709\) | 4.22472e6 | − | 7.31742e6i | 0.315633 | − | 0.546692i | −0.663939 | − | 0.747787i | \(-0.731117\pi\) |
0.979572 | + | 0.201095i | \(0.0644499\pi\) | |||||||
\(710\) | −2.10749e6 | − | 3.65028e6i | −0.156899 | − | 0.271757i | ||||
\(711\) | −3.53019e6 | − | 6.11448e6i | −0.261893 | − | 0.453613i | ||||
\(712\) | −1.12467e7 | + | 1.94798e7i | −0.831427 | + | 1.44007i | ||||
\(713\) | 1.73361e7 | 1.27711 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.34698e7 | −0.985365 | ||||||||
\(716\) | −963521. | + | 1.66887e6i | −0.0702390 | + | 0.121658i | ||||
\(717\) | −3.62606e6 | − | 6.28052e6i | −0.263413 | − | 0.456244i | ||||
\(718\) | 1.70975e6 | + | 2.96137e6i | 0.123772 | + | 0.214379i | ||||
\(719\) | −9.13284e6 | + | 1.58185e7i | −0.658846 | + | 1.14115i | 0.322069 | + | 0.946716i | \(0.395622\pi\) |
−0.980915 | + | 0.194438i | \(0.937712\pi\) | |||||||
\(720\) | −254442. | −0.0182918 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.19372e7 | 0.852237 | ||||||||
\(723\) | −5.12077e6 | + | 8.86944e6i | −0.364326 | + | 0.631030i | ||||
\(724\) | 4.11257e6 | + | 7.12318e6i | 0.291586 | + | 0.505042i | ||||
\(725\) | −322716. | − | 558960.i | −0.0228021 | − | 0.0394944i | ||||
\(726\) | −1.08287e6 | + | 1.87558e6i | −0.0762488 | + | 0.132067i | ||||
\(727\) | 1.37476e6 | 0.0964700 | 0.0482350 | − | 0.998836i | \(-0.484640\pi\) | ||||
0.0482350 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.46865e6 | − | 2.54377e6i | 0.102002 | − | 0.176673i | ||||
\(731\) | 5.38269e6 | + | 9.32309e6i | 0.372568 | + | 0.645307i | ||||
\(732\) | 2.90759e6 | + | 5.03609e6i | 0.200565 | + | 0.347389i | ||||
\(733\) | −8.23126e6 | + | 1.42570e7i | −0.565857 | + | 0.980093i | 0.431112 | + | 0.902298i | \(0.358121\pi\) |
−0.996969 | + | 0.0777948i | \(0.975212\pi\) | |||||||
\(734\) | −3.68585e6 | −0.252521 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.04393e7 | 0.710360 | ||||||||
\(737\) | −6.63975e6 | + | 1.15004e7i | −0.450280 | + | 0.779909i | ||||
\(738\) | 462397. | + | 800895.i | 0.0312517 | + | 0.0541296i | ||||
\(739\) | −1.36498e6 | − | 2.36422e6i | −0.0919425 | − | 0.159249i | 0.816386 | − | 0.577507i | \(-0.195974\pi\) |
−0.908328 | + | 0.418258i | \(0.862641\pi\) | |||||||
\(740\) | 5.59182e6 | − | 9.68532e6i | 0.375382 | − | 0.650181i | ||||
\(741\) | 1.13080e7 | 0.756555 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.34396e7 | −1.55768 | −0.778839 | − | 0.627224i | \(-0.784191\pi\) | ||||
−0.778839 | + | 0.627224i | \(0.784191\pi\) | |||||||
\(744\) | 7.81115e6 | − | 1.35293e7i | 0.517348 | − | 0.896073i | ||||
\(745\) | −8.96431e6 | − | 1.55266e7i | −0.591734 | − | 1.02491i | ||||
\(746\) | 5.29026e6 | + | 9.16300e6i | 0.348041 | + | 0.602824i | ||||
\(747\) | −3.65745e6 | + | 6.33490e6i | −0.239816 | + | 0.415373i | ||||
\(748\) | −5.85695e6 | −0.382752 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.43595e6 | 0.352876 | ||||||||
\(751\) | −8.97034e6 | + | 1.55371e7i | −0.580376 | + | 1.00524i | 0.415059 | + | 0.909794i | \(0.363761\pi\) |
−0.995435 | + | 0.0954455i | \(0.969572\pi\) | |||||||
\(752\) | −38041.7 | − | 65890.2i | −0.00245310 | − | 0.00424890i | ||||
\(753\) | 5.24548e6 | + | 9.08544e6i | 0.337130 | + | 0.583927i | ||||
\(754\) | 3.67919e6 | − | 6.37254e6i | 0.235680 | − | 0.408210i | ||||
\(755\) | −2.78790e7 | −1.77996 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.30823e7 | −1.46399 | −0.731997 | − | 0.681308i | \(-0.761412\pi\) | ||||
−0.731997 | + | 0.681308i | \(0.761412\pi\) | |||||||
\(758\) | 2.16228e6 | − | 3.74517e6i | 0.136690 | − | 0.236755i | ||||
\(759\) | −3.84906e6 | − | 6.66676e6i | −0.242521 | − | 0.420059i | ||||
\(760\) | −1.18751e7 | − | 2.05684e7i | −0.745770 | − | 1.29171i | ||||
\(761\) | −9.57936e6 | + | 1.65919e7i | −0.599618 | + | 1.03857i | 0.393259 | + | 0.919428i | \(0.371348\pi\) |
−0.992877 | + | 0.119141i | \(0.961986\pi\) | |||||||
\(762\) | 7.29440e6 | 0.455095 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −572407. | −0.0354790 | ||||||||
\(765\) | 1.30452e6 | − | 2.25950e6i | 0.0805932 | − | 0.139592i | ||||
\(766\) | −2.20847e6 | − | 3.82518e6i | −0.135994 | − | 0.235548i | ||||
\(767\) | −2.97128e6 | − | 5.14641e6i | −0.182371 | − | 0.315876i | ||||
\(768\) | 4.53298e6 | − | 7.85135e6i | 0.277320 | − | 0.480332i | ||||
\(769\) | 1.73017e7 | 1.05505 | 0.527526 | − | 0.849539i | \(-0.323120\pi\) | ||||
0.527526 | + | 0.849539i | \(0.323120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.25931e6 | −0.560974 | ||||||||
\(772\) | −683697. | + | 1.18420e6i | −0.0412877 | + | 0.0715123i | ||||
\(773\) | −1.56143e7 | − | 2.70448e7i | −0.939885 | − | 1.62793i | −0.765683 | − | 0.643218i | \(-0.777599\pi\) |
−0.174202 | − | 0.984710i | \(-0.555735\pi\) | |||||||
\(774\) | 2.49485e6 | + | 4.32121e6i | 0.149690 | + | 0.259270i | ||||
\(775\) | 742288. | − | 1.28568e6i | 0.0443934 | − | 0.0768916i | ||||
\(776\) | 2.94529e6 | 0.175580 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −123342. | −0.00730572 | ||||||||
\(779\) | 4.13920e6 | − | 7.16931e6i | 0.244384 | − | 0.423286i | ||||
\(780\) | −2.58770e6 | − | 4.48202e6i | −0.152292 | − | 0.263777i | ||||
\(781\) | 5.51030e6 | + | 9.54412e6i | 0.323257 | + | 0.559897i | ||||
\(782\) | −1.77216e6 | + | 3.06947e6i | −0.103630 | + | 0.179493i | ||||
\(783\) | −3.09566e6 | −0.180446 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.11350e6 | 0.238253 | ||||||||
\(786\) | 5.31757e6 | − | 9.21030e6i | 0.307013 | − | 0.531762i | ||||
\(787\) | 1.24346e7 | + | 2.15373e7i | 0.715638 | + | 1.23952i | 0.962713 | + | 0.270525i | \(0.0871974\pi\) |
−0.247075 | + | 0.968996i | \(0.579469\pi\) | |||||||
\(788\) | −5.06626e6 | − | 8.77501e6i | −0.290651 | − | 0.503422i | ||||
\(789\) | 2.95805e6 | − | 5.12350e6i | 0.169166 | − | 0.293004i | ||||
\(790\) | −1.60657e7 | −0.915868 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.93708e6 | −0.392974 | ||||||||
\(793\) | −8.04974e6 | + | 1.39426e7i | −0.454568 | + | 0.787335i | ||||
\(794\) | −1.08205e6 | − | 1.87417e6i | −0.0609110 | − | 0.105501i | ||||
\(795\) | 8.54773e6 | + | 1.48051e7i | 0.479659 | + | 0.830795i | ||||
\(796\) | 3.59217e6 | − | 6.22182e6i | 0.200943 | − | 0.348044i | ||||
\(797\) | 584574. | 0.0325982 | 0.0162991 | − | 0.999867i | \(-0.494812\pi\) | ||||
0.0162991 | + | 0.999867i | \(0.494812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 780159. | 0.0432331 | ||||||||
\(800\) | 446985. | − | 774200.i | 0.0246927 | − | 0.0427689i | ||||
\(801\) | 5.12607e6 | + | 8.87861e6i | 0.282295 | + | 0.488949i | ||||
\(802\) | 4.54907e6 | + | 7.87922e6i | 0.249739 | + | 0.432561i | ||||
\(803\) | −3.83997e6 | + | 6.65102e6i | −0.210154 | + | 0.363998i | ||||
\(804\) | −5.10226e6 | −0.278370 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.69252e7 | 0.917691 | ||||||||
\(807\) | −24641.3 | + | 42680.1i | −0.00133193 | + | 0.00230697i | ||||
\(808\) | −6.80739e6 | − | 1.17908e7i | −0.366820 | − | 0.635350i | ||||
\(809\) | 5.52762e6 | + | 9.57412e6i | 0.296939 | + | 0.514313i | 0.975434 | − | 0.220292i | \(-0.0707009\pi\) |
−0.678495 | + | 0.734605i | \(0.737368\pi\) | |||||||
\(810\) | 604640. | − | 1.04727e6i | 0.0323806 | − | 0.0560848i | ||||
\(811\) | 1.62780e7 | 0.869060 | 0.434530 | − | 0.900657i | \(-0.356914\pi\) | ||||
0.434530 | + | 0.900657i | \(0.356914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.92232e6 | −0.367304 | ||||||||
\(814\) | 8.12038e6 | − | 1.40649e7i | 0.429551 | − | 0.744005i | ||||
\(815\) | 9.28982e6 | + | 1.60904e7i | 0.489907 | + | 0.848543i | ||||
\(816\) | −153150. | − | 265264.i | −0.00805178 | − | 0.0139461i | ||||
\(817\) | 2.23330e7 | − | 3.86818e7i | 1.17055 | − | 2.02746i | ||||
\(818\) | 9.88989e6 | 0.516783 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.78882e6 | −0.196775 | ||||||||
\(821\) | −1.64287e7 | + | 2.84553e7i | −0.850638 | + | 1.47335i | 0.0299951 | + | 0.999550i | \(0.490451\pi\) |
−0.880633 | + | 0.473798i | \(0.842883\pi\) | |||||||
\(822\) | 4.27390e6 | + | 7.40262e6i | 0.220620 | + | 0.382125i | ||||
\(823\) | −5.30231e6 | − | 9.18386e6i | −0.272876 | − | 0.472635i | 0.696721 | − | 0.717342i | \(-0.254642\pi\) |
−0.969597 | + | 0.244707i | \(0.921308\pi\) | |||||||
\(824\) | 7.14734e6 | − | 1.23796e7i | 0.366713 | − | 0.635166i | ||||
\(825\) | −659226. | −0.0337209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.57582e7 | 0.801203 | 0.400602 | − | 0.916252i | \(-0.368801\pi\) | ||||
0.400602 | + | 0.916252i | \(0.368801\pi\) | |||||||
\(828\) | 1.47889e6 | − | 2.56151e6i | 0.0749651 | − | 0.129843i | ||||
\(829\) | 1.35068e7 | + | 2.33944e7i | 0.682598 | + | 1.18229i | 0.974185 | + | 0.225750i | \(0.0724832\pi\) |
−0.291588 | + | 0.956544i | \(0.594184\pi\) | |||||||
\(830\) | 8.32245e6 | + | 1.44149e7i | 0.419330 | + | 0.726301i | ||||
\(831\) | 5.28227e6 | − | 9.14915e6i | 0.265349 | − | 0.459598i | ||||
\(832\) | 9.24684e6 | 0.463111 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.52245e6 | 0.0757930 | ||||||||
\(835\) | −3.60935e6 | + | 6.25158e6i | −0.179149 | + | 0.310294i | ||||
\(836\) | 1.21503e7 | + | 2.10450e7i | 0.601274 | + | 1.04144i | ||||
\(837\) | −3.56021e6 | − | 6.16646e6i | −0.175655 | − | 0.304244i | ||||
\(838\) | 9.34341e6 | − | 1.61833e7i | 0.459616 | − | 0.796078i | ||||
\(839\) | −3.50490e7 | −1.71898 | −0.859489 | − | 0.511154i | \(-0.829218\pi\) | ||||
−0.859489 | + | 0.511154i | \(0.829218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.47888e6 | −0.120855 | ||||||||
\(842\) | −9.76031e6 | + | 1.69054e7i | −0.474442 | + | 0.821758i | ||||
\(843\) | −3.76942e6 | − | 6.52883e6i | −0.182686 | − | 0.316422i | ||||
\(844\) | −2.24507e6 | − | 3.88857e6i | −0.108486 | − | 0.187903i | ||||
\(845\) | −2.95831e6 | + | 5.12395e6i | −0.142529 | + | 0.246867i | ||||
\(846\) | 361600. | 0.0173701 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00699e6 | 0.0958422 | ||||||||
\(849\) | 2.68749e6 | − | 4.65488e6i | 0.127961 | − | 0.221635i | ||||
\(850\) | 151758. | + | 262853.i | 0.00720453 | + | 0.0124786i | ||||
\(851\) | 8.84758e6 | + | 1.53245e7i | 0.418794 | + | 0.725373i | ||||
\(852\) | −2.11717e6 | + | 3.66705e6i | −0.0999211 | + | 0.173068i | ||||
\(853\) | −538313. | −0.0253316 | −0.0126658 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126658 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.08250e7 | −0.506423 | ||||||||
\(856\) | 1.31547e7 | − | 2.27846e7i | 0.613615 | − | 1.06281i | ||||
\(857\) | 1.84137e6 | + | 3.18935e6i | 0.0856426 | + | 0.148337i | 0.905665 | − | 0.423994i | \(-0.139372\pi\) |
−0.820022 | + | 0.572332i | \(0.806039\pi\) | |||||||
\(858\) | −3.75782e6 | − | 6.50874e6i | −0.174268 | − | 0.301841i | ||||
\(859\) | 9.44416e6 | − | 1.63578e7i | 0.436697 | − | 0.756382i | −0.560735 | − | 0.827995i | \(-0.689481\pi\) |
0.997432 | + | 0.0716134i | \(0.0228148\pi\) | |||||||
\(860\) | −2.04425e7 | −0.942513 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.46931e6 | 0.342383 | ||||||||
\(863\) | −1.39272e7 | + | 2.41226e7i | −0.636557 | + | 1.10255i | 0.349626 | + | 0.936889i | \(0.386308\pi\) |
−0.986183 | + | 0.165659i | \(0.947025\pi\) | |||||||
\(864\) | −2.14386e6 | − | 3.71327e6i | −0.0977038 | − | 0.169228i | ||||
\(865\) | 1.22497e7 | + | 2.12171e7i | 0.556654 | + | 0.964153i | ||||
\(866\) | −8.40376e6 | + | 1.45557e7i | −0.380784 | + | 0.659537i | ||||
\(867\) | −9.63791e6 | −0.435447 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.20059e7 | 1.88695 | ||||||||
\(870\) | −3.52204e6 | + | 6.10036e6i | −0.157760 | + | 0.273248i | ||||
\(871\) | −7.06289e6 | − | 1.22333e7i | −0.315455 | − | 0.546383i | ||||
\(872\) | −1.11056e7 | − | 1.92355e7i | −0.494597 | − | 0.856668i | ||||
\(873\) | 671210. | − | 1.16257e6i | 0.0298073 | − | 0.0516278i | ||||
\(874\) | 1.47055e7 | 0.651180 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.95079e6 | −0.129921 | ||||||||
\(877\) | 8.75262e6 | − | 1.51600e7i | 0.384272 | − | 0.665579i | −0.607396 | − | 0.794399i | \(-0.707786\pi\) |
0.991668 | + | 0.128821i | \(0.0411191\pi\) | |||||||
\(878\) | 4.84072e6 | + | 8.38437e6i | 0.211921 | + | 0.367057i | ||||
\(879\) | 3.83094e6 | + | 6.63539e6i | 0.167237 | + | 0.289664i | ||||
\(880\) | 756904. | − | 1.31100e6i | 0.0329484 | − | 0.0570683i | ||||
\(881\) | −5.66292e6 | −0.245811 | −0.122905 | − | 0.992418i | \(-0.539221\pi\) | ||||
−0.122905 | + | 0.992418i | \(0.539221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.43933e7 | 0.621239 | 0.310620 | − | 0.950534i | \(-0.399463\pi\) | ||||
0.310620 | + | 0.950534i | \(0.399463\pi\) | |||||||
\(884\) | 3.11510e6 | − | 5.39551e6i | 0.134073 | − | 0.232221i | ||||
\(885\) | 2.84438e6 | + | 4.92661e6i | 0.122076 | + | 0.211441i | ||||
\(886\) | 9.57028e6 | + | 1.65762e7i | 0.409582 | + | 0.709416i | ||||
\(887\) | −2.75097e6 | + | 4.76481e6i | −0.117402 | + | 0.203347i | −0.918737 | − | 0.394869i | \(-0.870790\pi\) |
0.801335 | + | 0.598215i | \(0.204123\pi\) | |||||||
\(888\) | 1.59458e7 | 0.678602 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.33285e7 | 0.987214 | ||||||||
\(891\) | −1.58091e6 | + | 2.73822e6i | −0.0667134 | + | 0.115551i | ||||
\(892\) | 1.28385e7 | + | 2.22369e7i | 0.540259 | + | 0.935756i | ||||
\(893\) | −1.61845e6 | − | 2.80324e6i | −0.0679159 | − | 0.117634i | ||||
\(894\) | 5.00173e6 | − | 8.66326e6i | 0.209304 | − | 0.362525i | ||||
\(895\) | 5.10721e6 | 0.213121 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.18869e6 | 0.339808 | ||||||||
\(898\) | −1.27520e7 | + | 2.20870e7i | −0.527699 | + | 0.914001i | ||||
\(899\) | 2.07383e7 | + | 3.59198e7i | 0.855803 | + | 1.48229i | ||||
\(900\) | −126644. | − | 219354.i | −0.00521169 | − | 0.00902692i | ||||
\(901\) | −1.02899e7 | + | 1.78226e7i | −0.422277 | + | 0.731405i | ||||
\(902\) | −5.50208e6 | −0.225170 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.45610e7 | 1.40658 | ||||||||
\(905\) | 1.08995e7 | − | 1.88784e7i | 0.442368 | − | 0.766205i | ||||
\(906\) | −7.77769e6 | − | 1.34714e7i | −0.314797 | − | 0.545244i | ||||
\(907\) | −3.00778e6 | − | 5.20962e6i | −0.121402 | − | 0.210275i | 0.798919 | − | 0.601439i | \(-0.205406\pi\) |
−0.920321 | + | 0.391164i | \(0.872072\pi\) | |||||||
\(908\) | −5.35909e6 | + | 9.28221e6i | −0.215713 | + | 0.373626i | ||||
\(909\) | −6.20542e6 | −0.249093 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.47513e7 | −0.588892 | −0.294446 | − | 0.955668i | \(-0.595135\pi\) | ||||
−0.294446 | + | 0.955668i | \(0.595135\pi\) | |||||||
\(912\) | −635425. | + | 1.10059e6i | −0.0252975 | + | 0.0438165i | ||||
\(913\) | −2.17601e7 | − | 3.76896e7i | −0.863941 | − | 1.49639i | ||||
\(914\) | 995532. | + | 1.72431e6i | 0.0394175 | + | 0.0682732i | ||||
\(915\) | 7.70593e6 | − | 1.33471e7i | 0.304279 | − | 0.527027i | ||||
\(916\) | 1.08144e7 | 0.425858 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.45575e6 | 0.0570137 | ||||||||
\(919\) | 1.77001e7 | − | 3.06574e7i | 0.691331 | − | 1.19742i | −0.280070 | − | 0.959979i | \(-0.590358\pi\) |
0.971402 | − | 0.237442i | \(-0.0763089\pi\) | |||||||
\(920\) | −8.59939e6 | − | 1.48946e7i | −0.334964 | − | 0.580175i | ||||
\(921\) | 2.70408e6 | + | 4.68360e6i | 0.105044 | + | 0.181941i | ||||
\(922\) | 1.00557e7 | − | 1.74169e7i | 0.389568 | − | 0.674751i | ||||
\(923\) | −1.17229e7 | −0.452930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.51532e6 | 0.0582305 | ||||||||
\(926\) | 3.65217e6 | − | 6.32574e6i | 0.139966 | − | 0.242429i | ||||
\(927\) | −3.25765e6 | − | 5.64242e6i | −0.124510 | − | 0.215658i | ||||
\(928\) | 1.24880e7 | + | 2.16299e7i | 0.476018 | + | 0.824487i | ||||
\(929\) | 1.91633e7 | − | 3.31918e7i | 0.728502 | − | 1.26180i | −0.229014 | − | 0.973423i | \(-0.573550\pi\) |
0.957516 | − | 0.288379i | \(-0.0931164\pi\) | |||||||
\(930\) | −1.62023e7 | −0.614285 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.32463e6 | −0.163083 | ||||||||
\(933\) | 2.09640e6 | − | 3.63107e6i | 0.0788442 | − | 0.136562i | ||||
\(934\) | −854828. | − | 1.48061e6i | −0.0320635 | − | 0.0555357i | ||||
\(935\) | 7.76129e6 | + | 1.34429e7i | 0.290339 | + | 0.502881i | ||||
\(936\) | 3.68958e6 | − | 6.39055e6i | 0.137654 | − | 0.238423i | ||||
\(937\) | 1.48693e7 | 0.553274 | 0.276637 | − | 0.960974i | \(-0.410780\pi\) | ||||
0.276637 | + | 0.960974i | \(0.410780\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.67629e7 | −0.990534 | ||||||||
\(940\) | −740726. | + | 1.28297e6i | −0.0273425 | + | 0.0473586i | ||||
\(941\) | 1.75447e6 | + | 3.03883e6i | 0.0645909 | + | 0.111875i | 0.896512 | − | 0.443019i | \(-0.146092\pi\) |
−0.831922 | + | 0.554893i | \(0.812759\pi\) | |||||||
\(942\) | 1.14759e6 | + | 1.98768e6i | 0.0421365 | + | 0.0729825i | ||||
\(943\) | 2.99740e6 | − | 5.19166e6i | 0.109766 | − | 0.190120i | ||||
\(944\) | 667856. | 0.0243923 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.96863e7 | −1.07852 | ||||||||
\(947\) | −1.94887e7 | + | 3.37554e7i | −0.706168 | + | 1.22312i | 0.260100 | + | 0.965582i | \(0.416244\pi\) |
−0.966268 | + | 0.257537i | \(0.917089\pi\) | |||||||
\(948\) | 8.06977e6 | + | 1.39773e7i | 0.291636 | + | 0.505128i | ||||
\(949\) | −4.08468e6 | − | 7.07487e6i | −0.147229 | − | 0.255007i | ||||
\(950\) | 629651. | − | 1.09059e6i | 0.0226355 | − | 0.0392059i | ||||
\(951\) | 2.29969e7 | 0.824551 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.11438e6 | 0.253749 | 0.126875 | − | 0.991919i | \(-0.459505\pi\) | ||||
0.126875 | + | 0.991919i | \(0.459505\pi\) | |||||||
\(954\) | −4.76930e6 | + | 8.26067e6i | −0.169662 | + | 0.293863i | ||||
\(955\) | 758521. | + | 1.31380e6i | 0.0269128 | + | 0.0466144i | ||||
\(956\) | 8.28891e6 | + | 1.43568e7i | 0.293328 | + | 0.508058i | ||||
\(957\) | 9.20884e6 | − | 1.59502e7i | 0.325031 | − | 0.562970i | ||||
\(958\) | −1.84927e6 | −0.0651008 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.85190e6 | −0.309998 | ||||||||
\(961\) | −3.33862e7 | + | 5.78266e7i | −1.16616 | + | 2.01985i | ||||
\(962\) | 8.63787e6 | + | 1.49612e7i | 0.300932 | + | 0.521230i | ||||
\(963\) | −5.99571e6 | − | 1.03849e7i | −0.208341 | − | 0.360857i | ||||
\(964\) | 1.17057e7 | − | 2.02749e7i | 0.405701 | − | 0.702694i | ||||
\(965\) | 3.62398e6 | 0.125276 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.99357e7 | −0.685592 | −0.342796 | − | 0.939410i | \(-0.611374\pi\) | ||||
−0.342796 | + | 0.939410i | \(0.611374\pi\) | |||||||
\(968\) | 6.32555e6 | − | 1.09562e7i | 0.216975 | − | 0.375812i | ||||
\(969\) | −6.51565e6 | − | 1.12854e7i | −0.222920 | − | 0.386108i | ||||
\(970\) | −1.52732e6 | − | 2.64540e6i | −0.0521196 | − | 0.0902738i | ||||
\(971\) | −2.47944e7 | + | 4.29452e7i | −0.843928 | + | 1.46173i | 0.0426206 | + | 0.999091i | \(0.486429\pi\) |
−0.886549 | + | 0.462635i | \(0.846904\pi\) | |||||||
\(972\) | −1.21484e6 | −0.0412432 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.04143e6 | 0.271604 | ||||||||
\(975\) | 350618. | − | 607289.i | 0.0118120 | − | 0.0204590i | ||||
\(976\) | −904671. | − | 1.56694e6i | −0.0303995 | − | 0.0526534i | ||||
\(977\) | 177674. | + | 307740.i | 0.00595508 | + | 0.0103145i | 0.868988 | − | 0.494834i | \(-0.164771\pi\) |
−0.863033 | + | 0.505148i | \(0.831438\pi\) | |||||||
\(978\) | −5.18336e6 | + | 8.97784e6i | −0.173286 | + | 0.300140i | ||||
\(979\) | −6.09953e7 | −2.03395 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.01236e7 | −0.335862 | ||||||||
\(982\) | 1.21644e7 | − | 2.10694e7i | 0.402544 | − | 0.697226i | ||||
\(983\) | 495877. | + | 858884.i | 0.0163678 | + | 0.0283499i | 0.874093 | − | 0.485758i | \(-0.161456\pi\) |
−0.857725 | + | 0.514108i | \(0.828123\pi\) | |||||||
\(984\) | −2.70108e6 | − | 4.67841e6i | −0.0889304 | − | 0.154032i | ||||
\(985\) | −1.34270e7 | + | 2.32563e7i | −0.440950 | + | 0.763748i | ||||
\(986\) | −8.47976e6 | −0.277774 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.58493e7 | −0.842474 | ||||||||
\(989\) | 1.61724e7 | − | 2.80115e7i | 0.525756 | − | 0.910636i | ||||
\(990\) | 3.59732e6 | + | 6.23074e6i | 0.116652 | + | 0.202047i | ||||
\(991\) | −5.33372e6 | − | 9.23828e6i | −0.172523 | − | 0.298818i | 0.766778 | − | 0.641912i | \(-0.221858\pi\) |
−0.939301 | + | 0.343094i | \(0.888525\pi\) | |||||||
\(992\) | −2.87241e7 | + | 4.97515e7i | −0.926759 | + | 1.60519i | ||||
\(993\) | 2.30524e7 | 0.741898 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.90405e7 | −0.609707 | ||||||||
\(996\) | 8.36068e6 | − | 1.44811e7i | 0.267051 | − | 0.462545i | ||||
\(997\) | −2.79142e7 | − | 4.83488e7i | −0.889379 | − | 1.54045i | −0.840611 | − | 0.541639i | \(-0.817804\pi\) |
−0.0487677 | − | 0.998810i | \(-0.515529\pi\) | |||||||
\(998\) | −3.75616e6 | − | 6.50586e6i | −0.119376 | − | 0.206766i | ||||
\(999\) | 3.63394e6 | − | 6.29416e6i | 0.115203 | − | 0.199537i |
(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.e.p.79.3 | 12 | ||
7.2 | even | 3 | 147.6.a.o.1.4 | yes | 6 | ||
7.3 | odd | 6 | 147.6.e.q.67.3 | 12 | |||
7.4 | even | 3 | inner | 147.6.e.p.67.3 | 12 | ||
7.5 | odd | 6 | 147.6.a.n.1.4 | ✓ | 6 | ||
7.6 | odd | 2 | 147.6.e.q.79.3 | 12 | |||
21.2 | odd | 6 | 441.6.a.ba.1.3 | 6 | |||
21.5 | even | 6 | 441.6.a.bb.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.n.1.4 | ✓ | 6 | 7.5 | odd | 6 | ||
147.6.a.o.1.4 | yes | 6 | 7.2 | even | 3 | ||
147.6.e.p.67.3 | 12 | 7.4 | even | 3 | inner | ||
147.6.e.p.79.3 | 12 | 1.1 | even | 1 | trivial | ||
147.6.e.q.67.3 | 12 | 7.3 | odd | 6 | |||
147.6.e.q.79.3 | 12 | 7.6 | odd | 2 | |||
441.6.a.ba.1.3 | 6 | 21.2 | odd | 6 | |||
441.6.a.bb.1.3 | 6 | 21.5 | even | 6 |