Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [350,5,Mod(349,350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(350, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("350.349");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.d (of order \(2\), degree \(1\), 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: | \(36.1794870793\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.6850489614336.26 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 60x^{6} + 1800x^{4} + 38340x^{2} + 408321 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(1.31383 + 3.17185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 350.349 |
Dual form | 350.5.d.a.349.5 |
$q$-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 \(\left(\mathbb{Z}/350\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.82843i | − | 0.707107i | ||||||
\(3\) | −12.6874 | −1.40971 | −0.704857 | − | 0.709350i | \(-0.748989\pi\) | ||||
−0.704857 | + | 0.709350i | \(0.748989\pi\) | |||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 35.8854i | 0.996818i | ||||||||
\(7\) | −48.5729 | + | 6.45584i | −0.991283 | + | 0.131752i | ||||
\(8\) | 22.6274i | 0.353553i | ||||||||
\(9\) | 79.9706 | 0.987291 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 191.823 | 1.58532 | 0.792659 | − | 0.609666i | \(-0.208696\pi\) | ||||
0.792659 | + | 0.609666i | \(0.208696\pi\) | |||||||
\(12\) | 101.499 | 0.704857 | ||||||||
\(13\) | −48.5729 | −0.287413 | −0.143707 | − | 0.989620i | \(-0.545902\pi\) | ||||
−0.143707 | + | 0.989620i | \(0.545902\pi\) | |||||||
\(14\) | 18.2599 | + | 137.385i | 0.0931627 | + | 0.700943i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | 181.977 | 0.629680 | 0.314840 | − | 0.949145i | \(-0.398049\pi\) | ||||
0.314840 | + | 0.949145i | \(0.398049\pi\) | |||||||
\(18\) | − | 226.191i | − | 0.698120i | ||||||
\(19\) | − | 599.915i | − | 1.66182i | −0.556410 | − | 0.830908i | \(-0.687822\pi\) | ||
0.556410 | − | 0.830908i | \(-0.312178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 616.264 | − | 81.9080i | 1.39742 | − | 0.185732i | ||||
\(22\) | − | 542.558i | − | 1.12099i | ||||||
\(23\) | 469.529i | 0.887578i | 0.896131 | + | 0.443789i | \(0.146366\pi\) | ||||
−0.896131 | + | 0.443789i | \(0.853634\pi\) | |||||||
\(24\) | − | 287.083i | − | 0.498409i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 137.385i | 0.203232i | ||||||||
\(27\) | 13.0609 | 0.0179162 | ||||||||
\(28\) | 388.583 | − | 51.6468i | 0.495641 | − | 0.0658760i | ||||
\(29\) | 338.881 | 0.402951 | 0.201475 | − | 0.979494i | \(-0.435426\pi\) | ||||
0.201475 | + | 0.979494i | \(0.435426\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 267.556i | 0.278414i | 0.990263 | + | 0.139207i | \(0.0444554\pi\) | ||||
−0.990263 | + | 0.139207i | \(0.955545\pi\) | |||||||
\(32\) | − | 181.019i | − | 0.176777i | ||||||
\(33\) | −2433.74 | −2.23484 | ||||||||
\(34\) | − | 514.710i | − | 0.445251i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −639.765 | −0.493645 | ||||||||
\(37\) | − | 668.530i | − | 0.488334i | −0.969733 | − | 0.244167i | \(-0.921485\pi\) | ||
0.969733 | − | 0.244167i | \(-0.0785146\pi\) | |||||||
\(38\) | −1696.82 | −1.17508 | ||||||||
\(39\) | 616.264 | 0.405170 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1323.85i | 0.787534i | 0.919210 | + | 0.393767i | \(0.128828\pi\) | ||||
−0.919210 | + | 0.393767i | \(0.871172\pi\) | |||||||
\(42\) | −231.671 | − | 1743.06i | −0.131333 | − | 0.988128i | ||||
\(43\) | − | 1940.23i | − | 1.04934i | −0.851305 | − | 0.524671i | \(-0.824188\pi\) | ||
0.851305 | − | 0.524671i | \(-0.175812\pi\) | |||||||
\(44\) | −1534.59 | −0.792659 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1328.03 | 0.627613 | ||||||||
\(47\) | −2936.89 | −1.32951 | −0.664755 | − | 0.747062i | \(-0.731464\pi\) | ||||
−0.664755 | + | 0.747062i | \(0.731464\pi\) | |||||||
\(48\) | −811.995 | −0.352428 | ||||||||
\(49\) | 2317.64 | − | 627.158i | 0.965283 | − | 0.261207i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2308.82 | −0.887668 | ||||||||
\(52\) | 388.583 | 0.143707 | ||||||||
\(53\) | 1460.94i | 0.520091i | 0.965596 | + | 0.260046i | \(0.0837376\pi\) | ||||
−0.965596 | + | 0.260046i | \(0.916262\pi\) | |||||||
\(54\) | − | 36.9418i | − | 0.0126687i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −146.079 | − | 1099.08i | −0.0465813 | − | 0.350471i | ||||
\(57\) | 7611.38i | 2.34268i | ||||||||
\(58\) | − | 958.501i | − | 0.284929i | ||||||
\(59\) | 1730.83i | 0.497223i | 0.968603 | + | 0.248612i | \(0.0799743\pi\) | ||||
−0.968603 | + | 0.248612i | \(0.920026\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 246.343i | 0.0662034i | 0.999452 | + | 0.0331017i | \(0.0105385\pi\) | ||||
−0.999452 | + | 0.0331017i | \(0.989461\pi\) | |||||||
\(62\) | 756.763 | 0.196869 | ||||||||
\(63\) | −3884.40 | + | 516.277i | −0.978684 | + | 0.130077i | ||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6883.67i | 1.58027i | ||||||||
\(67\) | − | 1076.59i | − | 0.239828i | −0.992784 | − | 0.119914i | \(-0.961738\pi\) | ||
0.992784 | − | 0.119914i | \(-0.0382619\pi\) | |||||||
\(68\) | −1455.82 | −0.314840 | ||||||||
\(69\) | − | 5957.11i | − | 1.25123i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2276.39 | −0.451574 | −0.225787 | − | 0.974177i | \(-0.572495\pi\) | ||||
−0.225787 | + | 0.974177i | \(0.572495\pi\) | |||||||
\(72\) | 1809.53i | 0.349060i | ||||||||
\(73\) | −7106.94 | −1.33363 | −0.666817 | − | 0.745221i | \(-0.732344\pi\) | ||||
−0.666817 | + | 0.745221i | \(0.732344\pi\) | |||||||
\(74\) | −1890.89 | −0.345305 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4799.32i | 0.830908i | ||||||||
\(77\) | −9317.41 | + | 1238.38i | −1.57150 | + | 0.208869i | ||||
\(78\) | − | 1743.06i | − | 0.286499i | ||||||
\(79\) | −7012.38 | −1.12360 | −0.561799 | − | 0.827274i | \(-0.689891\pi\) | ||||
−0.561799 | + | 0.827274i | \(0.689891\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6643.32 | −1.01255 | ||||||||
\(82\) | 3744.40 | 0.556871 | ||||||||
\(83\) | −1448.36 | −0.210243 | −0.105121 | − | 0.994459i | \(-0.533523\pi\) | ||||
−0.105121 | + | 0.994459i | \(0.533523\pi\) | |||||||
\(84\) | −4930.11 | + | 655.264i | −0.698712 | + | 0.0928662i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5487.81 | −0.741997 | ||||||||
\(87\) | −4299.53 | −0.568045 | ||||||||
\(88\) | 4340.47i | 0.560494i | ||||||||
\(89\) | 2133.73i | 0.269376i | 0.990888 | + | 0.134688i | \(0.0430032\pi\) | ||||
−0.990888 | + | 0.134688i | \(0.956997\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2359.32 | − | 313.579i | 0.284908 | − | 0.0378673i | ||||
\(92\) | − | 3756.23i | − | 0.443789i | ||||||
\(93\) | − | 3394.60i | − | 0.392484i | ||||||
\(94\) | 8306.77i | 0.940105i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2296.67i | 0.249204i | ||||||||
\(97\) | 5898.76 | 0.626928 | 0.313464 | − | 0.949600i | \(-0.398511\pi\) | ||||
0.313464 | + | 0.949600i | \(0.398511\pi\) | |||||||
\(98\) | −1773.87 | − | 6555.29i | −0.184701 | − | 0.682558i | ||||
\(99\) | 15340.2 | 1.56517 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9172.07i | 0.899135i | 0.893246 | + | 0.449567i | \(0.148422\pi\) | ||||
−0.893246 | + | 0.449567i | \(0.851578\pi\) | |||||||
\(102\) | 6530.34i | 0.627676i | ||||||||
\(103\) | 3906.46 | 0.368222 | 0.184111 | − | 0.982905i | \(-0.441059\pi\) | ||||
0.184111 | + | 0.982905i | \(0.441059\pi\) | |||||||
\(104\) | − | 1099.08i | − | 0.101616i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4132.15 | 0.367760 | ||||||||
\(107\) | − | 12141.3i | − | 1.06047i | −0.847852 | − | 0.530233i | \(-0.822104\pi\) | ||
0.847852 | − | 0.530233i | \(-0.177896\pi\) | |||||||
\(108\) | −104.487 | −0.00895809 | ||||||||
\(109\) | −6808.34 | −0.573044 | −0.286522 | − | 0.958074i | \(-0.592499\pi\) | ||||
−0.286522 | + | 0.958074i | \(0.592499\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8481.92i | 0.688411i | ||||||||
\(112\) | −3108.66 | + | 413.174i | −0.247821 | + | 0.0329380i | ||||
\(113\) | 4764.20i | 0.373107i | 0.982445 | + | 0.186553i | \(0.0597317\pi\) | ||||
−0.982445 | + | 0.186553i | \(0.940268\pi\) | |||||||
\(114\) | 21528.2 | 1.65653 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2711.05 | −0.201475 | ||||||||
\(117\) | −3884.40 | −0.283761 | ||||||||
\(118\) | 4895.54 | 0.351590 | ||||||||
\(119\) | −8839.17 | + | 1174.82i | −0.624191 | + | 0.0829615i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 22155.2 | 1.51323 | ||||||||
\(122\) | 696.763 | 0.0468129 | ||||||||
\(123\) | − | 16796.2i | − | 1.11020i | ||||||
\(124\) | − | 2140.45i | − | 0.139207i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1460.25 | + | 10986.7i | 0.0919787 | + | 0.692034i | ||||
\(127\) | − | 27968.9i | − | 1.73408i | −0.498242 | − | 0.867038i | \(-0.666021\pi\) | ||
0.498242 | − | 0.867038i | \(-0.333979\pi\) | |||||||
\(128\) | 1448.15i | 0.0883883i | ||||||||
\(129\) | 24616.6i | 1.47927i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 24016.5i | − | 1.39948i | −0.714397 | − | 0.699741i | \(-0.753299\pi\) | ||
0.714397 | − | 0.699741i | \(-0.246701\pi\) | |||||||
\(132\) | 19469.9 | 1.11742 | ||||||||
\(133\) | 3872.96 | + | 29139.6i | 0.218947 | + | 1.64733i | ||||
\(134\) | −3045.05 | −0.169584 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4117.68i | 0.222625i | ||||||||
\(137\) | − | 4162.00i | − | 0.221748i | −0.993834 | − | 0.110874i | \(-0.964635\pi\) | ||
0.993834 | − | 0.110874i | \(-0.0353651\pi\) | |||||||
\(138\) | −16849.3 | −0.884754 | ||||||||
\(139\) | − | 26365.8i | − | 1.36462i | −0.731064 | − | 0.682309i | \(-0.760976\pi\) | ||
0.731064 | − | 0.682309i | \(-0.239024\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 37261.5 | 1.87423 | ||||||||
\(142\) | 6438.59i | 0.319311i | ||||||||
\(143\) | −9317.41 | −0.455641 | ||||||||
\(144\) | 5118.12 | 0.246823 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 20101.5i | 0.943022i | ||||||||
\(147\) | −29404.9 | + | 7957.01i | −1.36077 | + | 0.368227i | ||||
\(148\) | 5348.24i | 0.244167i | ||||||||
\(149\) | 6576.57 | 0.296229 | 0.148114 | − | 0.988970i | \(-0.452680\pi\) | ||||
0.148114 | + | 0.988970i | \(0.452680\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22930.4 | −1.00568 | −0.502839 | − | 0.864380i | \(-0.667711\pi\) | ||||
−0.502839 | + | 0.864380i | \(0.667711\pi\) | |||||||
\(152\) | 13574.5 | 0.587540 | ||||||||
\(153\) | 14552.8 | 0.621677 | ||||||||
\(154\) | 3502.67 | + | 26353.6i | 0.147692 | + | 1.11122i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4930.11 | −0.202585 | ||||||||
\(157\) | −37292.9 | −1.51296 | −0.756480 | − | 0.654017i | \(-0.773082\pi\) | ||||
−0.756480 | + | 0.654017i | \(0.773082\pi\) | |||||||
\(158\) | 19834.0i | 0.794504i | ||||||||
\(159\) | − | 18535.5i | − | 0.733180i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3031.21 | − | 22806.4i | −0.116940 | − | 0.879841i | ||||
\(162\) | 18790.2i | 0.715979i | ||||||||
\(163\) | − | 40854.0i | − | 1.53766i | −0.639455 | − | 0.768828i | \(-0.720840\pi\) | ||
0.639455 | − | 0.768828i | \(-0.279160\pi\) | |||||||
\(164\) | − | 10590.8i | − | 0.393767i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4096.58i | 0.148664i | ||||||||
\(167\) | 34774.9 | 1.24690 | 0.623452 | − | 0.781862i | \(-0.285730\pi\) | ||||
0.623452 | + | 0.781862i | \(0.285730\pi\) | |||||||
\(168\) | 1853.37 | + | 13944.5i | 0.0656663 | + | 0.494064i | ||||
\(169\) | −26201.7 | −0.917394 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 47975.6i | − | 1.64070i | ||||||
\(172\) | 15521.9i | 0.524671i | ||||||||
\(173\) | 31600.1 | 1.05583 | 0.527917 | − | 0.849296i | \(-0.322973\pi\) | ||||
0.527917 | + | 0.849296i | \(0.322973\pi\) | |||||||
\(174\) | 12160.9i | 0.401668i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12276.7 | 0.396329 | ||||||||
\(177\) | − | 21959.8i | − | 0.700942i | ||||||
\(178\) | 6035.09 | 0.190478 | ||||||||
\(179\) | −22750.7 | −0.710048 | −0.355024 | − | 0.934857i | \(-0.615527\pi\) | ||||
−0.355024 | + | 0.934857i | \(0.615527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 55434.4i | − | 1.69208i | −0.533116 | − | 0.846042i | \(-0.678979\pi\) | ||
0.533116 | − | 0.846042i | \(-0.321021\pi\) | |||||||
\(182\) | −886.935 | − | 6673.17i | −0.0267762 | − | 0.201460i | ||||
\(183\) | − | 3125.45i | − | 0.0933278i | ||||||
\(184\) | −10624.2 | −0.313806 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9601.37 | −0.277528 | ||||||||
\(187\) | 34907.5 | 0.998242 | ||||||||
\(188\) | 23495.1 | 0.664755 | ||||||||
\(189\) | −634.405 | + | 84.3191i | −0.0177600 | + | 0.00236049i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −50817.6 | −1.39299 | −0.696494 | − | 0.717562i | \(-0.745258\pi\) | ||||
−0.696494 | + | 0.717562i | \(0.745258\pi\) | |||||||
\(192\) | 6495.96 | 0.176214 | ||||||||
\(193\) | 1248.34i | 0.0335134i | 0.999860 | + | 0.0167567i | \(0.00533407\pi\) | ||||
−0.999860 | + | 0.0167567i | \(0.994666\pi\) | |||||||
\(194\) | − | 16684.2i | − | 0.443305i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18541.2 | + | 5017.26i | −0.482641 | + | 0.130603i | ||||
\(197\) | 64454.6i | 1.66082i | 0.557155 | + | 0.830408i | \(0.311893\pi\) | ||||
−0.557155 | + | 0.830408i | \(0.688107\pi\) | |||||||
\(198\) | − | 43388.7i | − | 1.10674i | ||||||
\(199\) | 2352.60i | 0.0594076i | 0.999559 | + | 0.0297038i | \(0.00945641\pi\) | ||||
−0.999559 | + | 0.0297038i | \(0.990544\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13659.1i | 0.338088i | ||||||||
\(202\) | 25942.5 | 0.635784 | ||||||||
\(203\) | −16460.4 | + | 2187.77i | −0.399438 | + | 0.0530895i | ||||
\(204\) | 18470.6 | 0.443834 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 11049.2i | − | 0.260372i | ||||||
\(207\) | 37548.5i | 0.876298i | ||||||||
\(208\) | −3108.66 | −0.0718533 | ||||||||
\(209\) | − | 115078.i | − | 2.63450i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −65056.4 | −1.46125 | −0.730626 | − | 0.682778i | \(-0.760772\pi\) | ||||
−0.730626 | + | 0.682778i | \(0.760772\pi\) | |||||||
\(212\) | − | 11687.5i | − | 0.260046i | ||||||
\(213\) | 28881.5 | 0.636590 | ||||||||
\(214\) | −34340.7 | −0.749863 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 295.534i | 0.00633433i | ||||||||
\(217\) | −1727.30 | − | 12996.0i | −0.0366816 | − | 0.275987i | ||||
\(218\) | 19256.9i | 0.405203i | ||||||||
\(219\) | 90168.7 | 1.88004 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8839.17 | −0.180978 | ||||||||
\(222\) | 23990.5 | 0.486780 | ||||||||
\(223\) | 30412.4 | 0.611563 | 0.305781 | − | 0.952102i | \(-0.401082\pi\) | ||||
0.305781 | + | 0.952102i | \(0.401082\pi\) | |||||||
\(224\) | 1168.63 | + | 8792.63i | 0.0232907 | + | 0.175236i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13475.2 | 0.263826 | ||||||||
\(227\) | −52125.5 | −1.01158 | −0.505788 | − | 0.862658i | \(-0.668798\pi\) | ||||
−0.505788 | + | 0.862658i | \(0.668798\pi\) | |||||||
\(228\) | − | 60891.0i | − | 1.17134i | ||||||
\(229\) | 81280.2i | 1.54994i | 0.632000 | + | 0.774968i | \(0.282234\pi\) | ||||
−0.632000 | + | 0.774968i | \(0.717766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 118214. | − | 15711.9i | 2.21536 | − | 0.294445i | ||||
\(232\) | 7668.01i | 0.142465i | ||||||||
\(233\) | 41718.9i | 0.768459i | 0.923238 | + | 0.384229i | \(0.125533\pi\) | ||||
−0.923238 | + | 0.384229i | \(0.874467\pi\) | |||||||
\(234\) | 10986.7i | 0.200649i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 13846.7i | − | 0.248612i | ||||||
\(237\) | 88968.9 | 1.58395 | ||||||||
\(238\) | 3322.89 | + | 25000.9i | 0.0586627 | + | 0.441370i | ||||
\(239\) | 3936.55 | 0.0689160 | 0.0344580 | − | 0.999406i | \(-0.489030\pi\) | ||||
0.0344580 | + | 0.999406i | \(0.489030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 70511.5i | − | 1.21402i | −0.794694 | − | 0.607010i | \(-0.792369\pi\) | ||
0.794694 | − | 0.607010i | \(-0.207631\pi\) | |||||||
\(242\) | − | 62664.4i | − | 1.07002i | ||||||
\(243\) | 83228.7 | 1.40949 | ||||||||
\(244\) | − | 1970.74i | − | 0.0331017i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −47506.8 | −0.785028 | ||||||||
\(247\) | 29139.6i | 0.477628i | ||||||||
\(248\) | −6054.11 | −0.0984343 | ||||||||
\(249\) | 18376.0 | 0.296382 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 72042.3i | − | 1.14351i | −0.820424 | − | 0.571755i | \(-0.806263\pi\) | ||
0.820424 | − | 0.571755i | \(-0.193737\pi\) | |||||||
\(252\) | 31075.2 | − | 4130.22i | 0.489342 | − | 0.0650387i | ||||
\(253\) | 90066.6i | 1.40709i | ||||||||
\(254\) | −79108.1 | −1.22618 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | −65615.5 | −0.993436 | −0.496718 | − | 0.867912i | \(-0.665462\pi\) | ||||
−0.496718 | + | 0.867912i | \(0.665462\pi\) | |||||||
\(258\) | 69626.1 | 1.04600 | ||||||||
\(259\) | 4315.92 | + | 32472.4i | 0.0643390 | + | 0.484078i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27100.5 | 0.397829 | ||||||||
\(262\) | −67929.0 | −0.989583 | ||||||||
\(263\) | 38706.1i | 0.559588i | 0.960060 | + | 0.279794i | \(0.0902662\pi\) | ||||
−0.960060 | + | 0.279794i | \(0.909734\pi\) | |||||||
\(264\) | − | 55069.3i | − | 0.790136i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 82419.2 | − | 10954.4i | 1.16484 | − | 0.154819i | ||||
\(267\) | − | 27071.5i | − | 0.379743i | ||||||
\(268\) | 8612.70i | 0.119914i | ||||||||
\(269\) | 87226.9i | 1.20544i | 0.797952 | + | 0.602721i | \(0.205917\pi\) | ||||
−0.797952 | + | 0.602721i | \(0.794083\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 105362.i | 1.43465i | 0.696739 | + | 0.717324i | \(0.254633\pi\) | ||||
−0.696739 | + | 0.717324i | \(0.745367\pi\) | |||||||
\(272\) | 11646.6 | 0.157420 | ||||||||
\(273\) | −29933.7 | + | 3978.50i | −0.401638 | + | 0.0533820i | ||||
\(274\) | −11771.9 | −0.156800 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 47656.9i | 0.625615i | ||||||||
\(277\) | 36178.9i | 0.471515i | 0.971812 | + | 0.235758i | \(0.0757571\pi\) | ||||
−0.971812 | + | 0.235758i | \(0.924243\pi\) | |||||||
\(278\) | −74573.7 | −0.964931 | ||||||||
\(279\) | 21396.6i | 0.274876i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 99142.2 | 1.25558 | 0.627792 | − | 0.778381i | \(-0.283959\pi\) | ||||
0.627792 | + | 0.778381i | \(0.283959\pi\) | |||||||
\(282\) | − | 105391.i | − | 1.32528i | ||||||
\(283\) | −4153.27 | −0.0518581 | −0.0259291 | − | 0.999664i | \(-0.508254\pi\) | ||||
−0.0259291 | + | 0.999664i | \(0.508254\pi\) | |||||||
\(284\) | 18211.1 | 0.225787 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 26353.6i | 0.322187i | ||||||||
\(287\) | −8546.54 | − | 64302.9i | −0.103759 | − | 0.780669i | ||||
\(288\) | − | 14476.2i | − | 0.174530i | ||||||
\(289\) | −50405.2 | −0.603503 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −74840.1 | −0.883788 | ||||||||
\(292\) | 56855.5 | 0.666817 | ||||||||
\(293\) | −20239.4 | −0.235756 | −0.117878 | − | 0.993028i | \(-0.537609\pi\) | ||||
−0.117878 | + | 0.993028i | \(0.537609\pi\) | |||||||
\(294\) | 22505.8 | + | 83169.7i | 0.260376 | + | 0.962211i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 15127.1 | 0.172652 | ||||||||
\(297\) | 2505.39 | 0.0284028 | ||||||||
\(298\) | − | 18601.3i | − | 0.209465i | ||||||
\(299\) | − | 22806.4i | − | 0.255102i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12525.8 | + | 94242.7i | 0.138253 | + | 1.04019i | ||||
\(302\) | 64857.1i | 0.711121i | ||||||||
\(303\) | − | 116370.i | − | 1.26752i | ||||||
\(304\) | − | 38394.6i | − | 0.415454i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 41161.7i | − | 0.439592i | ||||||
\(307\) | −63269.8 | −0.671305 | −0.335652 | − | 0.941986i | \(-0.608957\pi\) | ||||
−0.335652 | + | 0.941986i | \(0.608957\pi\) | |||||||
\(308\) | 74539.3 | − | 9907.05i | 0.785749 | − | 0.104434i | ||||
\(309\) | −49563.0 | −0.519087 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 14375.4i | − | 0.148627i | −0.997235 | − | 0.0743137i | \(-0.976323\pi\) | ||
0.997235 | − | 0.0743137i | \(-0.0236766\pi\) | |||||||
\(312\) | 13944.5i | 0.143249i | ||||||||
\(313\) | 36763.0 | 0.375252 | 0.187626 | − | 0.982241i | \(-0.439921\pi\) | ||||
0.187626 | + | 0.982241i | \(0.439921\pi\) | |||||||
\(314\) | 105480.i | 1.06982i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 56099.0 | 0.561799 | ||||||||
\(317\) | − | 125556.i | − | 1.24945i | −0.780844 | − | 0.624726i | \(-0.785211\pi\) | ||
0.780844 | − | 0.624726i | \(-0.214789\pi\) | |||||||
\(318\) | −52426.4 | −0.518436 | ||||||||
\(319\) | 65005.4 | 0.638804 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 154041.i | 1.49495i | ||||||||
\(322\) | −64506.1 | + | 8573.55i | −0.622142 | + | 0.0826892i | ||||
\(323\) | − | 109171.i | − | 1.04641i | ||||||
\(324\) | 53146.6 | 0.506274 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −115553. | −1.08729 | ||||||||
\(327\) | 86380.2 | 0.807828 | ||||||||
\(328\) | −29955.2 | −0.278435 | ||||||||
\(329\) | 142653. | − | 18960.1i | 1.31792 | − | 0.175165i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5376.54 | 0.0490735 | 0.0245367 | − | 0.999699i | \(-0.492189\pi\) | ||||
0.0245367 | + | 0.999699i | \(0.492189\pi\) | |||||||
\(332\) | 11586.9 | 0.105121 | ||||||||
\(333\) | − | 53462.7i | − | 0.482128i | ||||||
\(334\) | − | 98358.3i | − | 0.881694i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 39440.9 | − | 5242.11i | 0.349356 | − | 0.0464331i | ||||
\(337\) | 2202.27i | 0.0193914i | 0.999953 | + | 0.00969572i | \(0.00308629\pi\) | ||||
−0.999953 | + | 0.00969572i | \(0.996914\pi\) | |||||||
\(338\) | 74109.5i | 0.648695i | ||||||||
\(339\) | − | 60445.4i | − | 0.525974i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 51323.5i | 0.441375i | ||||||||
\(342\) | −135695. | −1.16015 | ||||||||
\(343\) | −108526. | + | 45425.2i | −0.922454 | + | 0.386108i | ||||
\(344\) | 43902.5 | 0.370998 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 89378.5i | − | 0.746587i | ||||||
\(347\) | 222201.i | 1.84538i | 0.385541 | + | 0.922691i | \(0.374015\pi\) | ||||
−0.385541 | + | 0.922691i | \(0.625985\pi\) | |||||||
\(348\) | 34396.2 | 0.284022 | ||||||||
\(349\) | 102679.i | 0.843006i | 0.906827 | + | 0.421503i | \(0.138497\pi\) | ||||
−0.906827 | + | 0.421503i | \(0.861503\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −634.405 | −0.00514935 | ||||||||
\(352\) | − | 34723.7i | − | 0.280247i | ||||||
\(353\) | 62595.6 | 0.502336 | 0.251168 | − | 0.967943i | \(-0.419185\pi\) | ||||
0.251168 | + | 0.967943i | \(0.419185\pi\) | |||||||
\(354\) | −62111.8 | −0.495641 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 17069.8i | − | 0.134688i | ||||||
\(357\) | 112146. | − | 14905.4i | 0.879930 | − | 0.116952i | ||||
\(358\) | 64348.6i | 0.502080i | ||||||||
\(359\) | −95505.9 | −0.741040 | −0.370520 | − | 0.928825i | \(-0.620820\pi\) | ||||
−0.370520 | + | 0.928825i | \(0.620820\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −229577. | −1.76163 | ||||||||
\(362\) | −156792. | −1.19648 | ||||||||
\(363\) | −281092. | −2.13322 | ||||||||
\(364\) | −18874.6 | + | 2508.63i | −0.142454 | + | 0.0189336i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8840.12 | −0.0659927 | ||||||||
\(367\) | 82330.9 | 0.611267 | 0.305633 | − | 0.952149i | \(-0.401132\pi\) | ||||
0.305633 | + | 0.952149i | \(0.401132\pi\) | |||||||
\(368\) | 30049.9i | 0.221895i | ||||||||
\(369\) | 105869.i | 0.777525i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9431.58 | − | 70961.9i | −0.0685230 | − | 0.515558i | ||||
\(372\) | 27156.8i | 0.196242i | ||||||||
\(373\) | − | 130223.i | − | 0.935991i | −0.883731 | − | 0.467995i | \(-0.844976\pi\) | ||
0.883731 | − | 0.467995i | \(-0.155024\pi\) | |||||||
\(374\) | − | 98733.4i | − | 0.705864i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 66454.2i | − | 0.470053i | ||||||
\(377\) | −16460.4 | −0.115813 | ||||||||
\(378\) | 238.491 | + | 1794.37i | 0.00166912 | + | 0.0125582i | ||||
\(379\) | −192349. | −1.33909 | −0.669546 | − | 0.742770i | \(-0.733511\pi\) | ||||
−0.669546 | + | 0.742770i | \(0.733511\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 354853.i | 2.44455i | ||||||||
\(382\) | 143734.i | 0.984992i | ||||||||
\(383\) | −101933. | −0.694891 | −0.347446 | − | 0.937700i | \(-0.612951\pi\) | ||||
−0.347446 | + | 0.937700i | \(0.612951\pi\) | |||||||
\(384\) | − | 18373.3i | − | 0.124602i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3530.84 | 0.0236975 | ||||||||
\(387\) | − | 155162.i | − | 1.03601i | ||||||
\(388\) | −47190.1 | −0.313464 | ||||||||
\(389\) | −191074. | −1.26271 | −0.631353 | − | 0.775495i | \(-0.717500\pi\) | ||||
−0.631353 | + | 0.775495i | \(0.717500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 85443.7i | 0.558890i | ||||||||
\(392\) | 14191.0 | + | 52442.3i | 0.0923506 | + | 0.341279i | ||||
\(393\) | 304708.i | 1.97287i | ||||||||
\(394\) | 182305. | 1.17437 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −122722. | −0.782585 | ||||||||
\(397\) | −201143. | −1.27622 | −0.638108 | − | 0.769947i | \(-0.720283\pi\) | ||||
−0.638108 | + | 0.769947i | \(0.720283\pi\) | |||||||
\(398\) | 6654.16 | 0.0420076 | ||||||||
\(399\) | −49137.9 | − | 369706.i | −0.308653 | − | 2.32226i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −39978.4 | −0.248621 | −0.124310 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124310 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(402\) | 38633.8 | 0.239065 | ||||||||
\(403\) | − | 12996.0i | − | 0.0800200i | ||||||
\(404\) | − | 73376.6i | − | 0.449567i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6187.93 | + | 46557.1i | 0.0375399 | + | 0.282445i | ||||
\(407\) | − | 128240.i | − | 0.774165i | ||||||
\(408\) | − | 52242.7i | − | 0.313838i | ||||||
\(409\) | 80655.7i | 0.482157i | 0.970506 | + | 0.241078i | \(0.0775011\pi\) | ||||
−0.970506 | + | 0.241078i | \(0.922499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 52805.0i | 0.312602i | ||||||||
\(412\) | −31251.7 | −0.184111 | ||||||||
\(413\) | −11174.0 | − | 84071.6i | −0.0655101 | − | 0.492889i | ||||
\(414\) | 106203. | 0.619636 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8792.63i | 0.0508080i | ||||||||
\(417\) | 334514.i | 1.92372i | ||||||||
\(418\) | −325489. | −1.86288 | ||||||||
\(419\) | − | 252034.i | − | 1.43559i | −0.696254 | − | 0.717795i | \(-0.745151\pi\) | ||
0.696254 | − | 0.717795i | \(-0.254849\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −84439.3 | −0.476410 | −0.238205 | − | 0.971215i | \(-0.576559\pi\) | ||||
−0.238205 | + | 0.971215i | \(0.576559\pi\) | |||||||
\(422\) | 184007.i | 1.03326i | ||||||||
\(423\) | −234864. | −1.31261 | ||||||||
\(424\) | −33057.2 | −0.183880 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 81689.1i | − | 0.450137i | ||||||
\(427\) | −1590.35 | − | 11965.6i | −0.00872242 | − | 0.0656263i | ||||
\(428\) | 97130.2i | 0.530233i | ||||||||
\(429\) | 118214. | 0.642323 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −127512. | −0.686431 | −0.343215 | − | 0.939257i | \(-0.611516\pi\) | ||||
−0.343215 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(432\) | 835.898 | 0.00447905 | ||||||||
\(433\) | −233539. | −1.24562 | −0.622808 | − | 0.782375i | \(-0.714008\pi\) | ||||
−0.622808 | + | 0.782375i | \(0.714008\pi\) | |||||||
\(434\) | −36758.2 | + | 4885.55i | −0.195153 | + | 0.0259378i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 54466.7 | 0.286522 | ||||||||
\(437\) | 281678. | 1.47499 | ||||||||
\(438\) | − | 255036.i | − | 1.32939i | ||||||
\(439\) | 304238.i | 1.57864i | 0.613980 | + | 0.789322i | \(0.289568\pi\) | ||||
−0.613980 | + | 0.789322i | \(0.710432\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 185343. | − | 50154.1i | 0.953015 | − | 0.257887i | ||||
\(442\) | 25000.9i | 0.127971i | ||||||||
\(443\) | 87061.0i | 0.443625i | 0.975089 | + | 0.221813i | \(0.0711974\pi\) | ||||
−0.975089 | + | 0.221813i | \(0.928803\pi\) | |||||||
\(444\) | − | 67855.3i | − | 0.344206i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 86019.3i | − | 0.432440i | ||||||
\(447\) | −83439.7 | −0.417597 | ||||||||
\(448\) | 24869.3 | − | 3305.39i | 0.123910 | − | 0.0164690i | ||||
\(449\) | 91141.4 | 0.452088 | 0.226044 | − | 0.974117i | \(-0.427421\pi\) | ||||
0.226044 | + | 0.974117i | \(0.427421\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 253944.i | 1.24849i | ||||||||
\(452\) | − | 38113.6i | − | 0.186553i | ||||||
\(453\) | 290928. | 1.41772 | ||||||||
\(454\) | 147433.i | 0.715292i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −172226. | −0.828263 | ||||||||
\(457\) | − | 411928.i | − | 1.97237i | −0.165634 | − | 0.986187i | \(-0.552967\pi\) | ||
0.165634 | − | 0.986187i | \(-0.447033\pi\) | |||||||
\(458\) | 229895. | 1.09597 | ||||||||
\(459\) | 2376.79 | 0.0112815 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 157397.i | − | 0.740617i | −0.928909 | − | 0.370309i | \(-0.879252\pi\) | ||
0.928909 | − | 0.370309i | \(-0.120748\pi\) | |||||||
\(462\) | −44439.9 | − | 334359.i | −0.208204 | − | 1.56650i | ||||
\(463\) | − | 245557.i | − | 1.14549i | −0.819734 | − | 0.572745i | \(-0.805879\pi\) | ||
0.819734 | − | 0.572745i | \(-0.194121\pi\) | |||||||
\(464\) | 21688.4 | 0.100738 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 117999. | 0.543383 | ||||||||
\(467\) | 33069.2 | 0.151632 | 0.0758158 | − | 0.997122i | \(-0.475844\pi\) | ||||
0.0758158 | + | 0.997122i | \(0.475844\pi\) | |||||||
\(468\) | 31075.2 | 0.141880 | ||||||||
\(469\) | 6950.28 | + | 52292.9i | 0.0315978 | + | 0.237737i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 473151. | 2.13284 | ||||||||
\(472\) | −39164.3 | −0.175795 | ||||||||
\(473\) | − | 372182.i | − | 1.66354i | ||||||
\(474\) | − | 251642.i | − | 1.12002i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 70713.3 | − | 9398.55i | 0.312095 | − | 0.0414808i | ||||
\(477\) | 116832.i | 0.513482i | ||||||||
\(478\) | − | 11134.2i | − | 0.0487309i | ||||||
\(479\) | − | 384277.i | − | 1.67484i | −0.546559 | − | 0.837421i | \(-0.684063\pi\) | ||
0.546559 | − | 0.837421i | \(-0.315937\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32472.4i | 0.140354i | ||||||||
\(482\) | −199437. | −0.858442 | ||||||||
\(483\) | 38458.2 | + | 289354.i | 0.164852 | + | 1.24032i | ||||
\(484\) | −177242. | −0.756615 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 235406.i | − | 0.996657i | ||||||
\(487\) | − | 173526.i | − | 0.731657i | −0.930682 | − | 0.365829i | \(-0.880786\pi\) | ||
0.930682 | − | 0.365829i | \(-0.119214\pi\) | |||||||
\(488\) | −5574.10 | −0.0234064 | ||||||||
\(489\) | 518332.i | 2.16765i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20006.3 | −0.0829858 | −0.0414929 | − | 0.999139i | \(-0.513211\pi\) | ||||
−0.0414929 | + | 0.999139i | \(0.513211\pi\) | |||||||
\(492\) | 134369.i | 0.555099i | ||||||||
\(493\) | 61668.8 | 0.253730 | ||||||||
\(494\) | 82419.2 | 0.337734 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 17123.6i | 0.0696036i | ||||||||
\(497\) | 110571. | − | 14696.0i | 0.447638 | − | 0.0594958i | ||||
\(498\) | − | 51975.1i | − | 0.209574i | ||||||
\(499\) | 428368. | 1.72035 | 0.860174 | − | 0.510000i | \(-0.170355\pi\) | ||||
0.860174 | + | 0.510000i | \(0.170355\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −441204. | −1.75778 | ||||||||
\(502\) | −203766. | −0.808584 | ||||||||
\(503\) | 36793.4 | 0.145423 | 0.0727116 | − | 0.997353i | \(-0.476835\pi\) | ||||
0.0727116 | + | 0.997353i | \(0.476835\pi\) | |||||||
\(504\) | −11682.0 | − | 87893.9i | −0.0459893 | − | 0.346017i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 254747. | 0.994965 | ||||||||
\(507\) | 332432. | 1.29326 | ||||||||
\(508\) | 223751.i | 0.867038i | ||||||||
\(509\) | 137334.i | 0.530080i | 0.964237 | + | 0.265040i | \(0.0853852\pi\) | ||||
−0.964237 | + | 0.265040i | \(0.914615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 345204. | − | 45881.3i | 1.32201 | − | 0.175709i | ||||
\(512\) | − | 11585.2i | − | 0.0441942i | ||||||
\(513\) | − | 7835.43i | − | 0.0297734i | ||||||
\(514\) | 185589.i | 0.702466i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 196932.i | − | 0.739636i | ||||||
\(517\) | −563363. | −2.10769 | ||||||||
\(518\) | 91845.8 | − | 12207.3i | 0.342294 | − | 0.0454945i | ||||
\(519\) | −400923. | −1.48842 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 102775.i | 0.378629i | 0.981916 | + | 0.189315i | \(0.0606266\pi\) | ||||
−0.981916 | + | 0.189315i | \(0.939373\pi\) | |||||||
\(522\) | − | 76651.9i | − | 0.281308i | ||||||
\(523\) | −314194. | −1.14867 | −0.574334 | − | 0.818621i | \(-0.694739\pi\) | ||||
−0.574334 | + | 0.818621i | \(0.694739\pi\) | |||||||
\(524\) | 192132.i | 0.699741i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 109478. | 0.395689 | ||||||||
\(527\) | 48689.2i | 0.175312i | ||||||||
\(528\) | −155760. | −0.558711 | ||||||||
\(529\) | 59383.5 | 0.212204 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 138416.i | 0.490904i | ||||||||
\(532\) | −30983.7 | − | 233117.i | −0.109474 | − | 0.823664i | ||||
\(533\) | − | 64302.9i | − | 0.226348i | ||||||
\(534\) | −76569.7 | −0.268519 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24360.4 | 0.0847919 | ||||||||
\(537\) | 288647. | 1.00096 | ||||||||
\(538\) | 246715. | 0.852376 | ||||||||
\(539\) | 444578. | − | 120303.i | 1.53028 | − | 0.414096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 298384. | 1.01948 | 0.509742 | − | 0.860327i | \(-0.329741\pi\) | ||||
0.509742 | + | 0.860327i | \(0.329741\pi\) | |||||||
\(542\) | 298009. | 1.01445 | ||||||||
\(543\) | 703319.i | 2.38535i | ||||||||
\(544\) | − | 32941.4i | − | 0.111313i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11252.9 | + | 84665.3i | 0.0377468 | + | 0.284001i | ||||
\(547\) | 361462.i | 1.20806i | 0.796963 | + | 0.604029i | \(0.206439\pi\) | ||||
−0.796963 | + | 0.604029i | \(0.793561\pi\) | |||||||
\(548\) | 33296.0i | 0.110874i | ||||||||
\(549\) | 19700.2i | 0.0653620i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 203300.i | − | 0.669629i | ||||||
\(552\) | 134794. | 0.442377 | ||||||||
\(553\) | 340611. | − | 45270.8i | 1.11380 | − | 0.148036i | ||||
\(554\) | 102329. | 0.333412 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 210926.i | 0.682309i | ||||||||
\(557\) | 112424.i | 0.362367i | 0.983449 | + | 0.181183i | \(0.0579928\pi\) | ||||
−0.983449 | + | 0.181183i | \(0.942007\pi\) | |||||||
\(558\) | 60518.8 | 0.194367 | ||||||||
\(559\) | 94242.7i | 0.301595i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −442886. | −1.40724 | ||||||||
\(562\) | − | 280416.i | − | 0.887832i | ||||||
\(563\) | 441530. | 1.39298 | 0.696488 | − | 0.717569i | \(-0.254745\pi\) | ||||
0.696488 | + | 0.717569i | \(0.254745\pi\) | |||||||
\(564\) | −298092. | −0.937113 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 11747.2i | 0.0366692i | ||||||||
\(567\) | 322685. | − | 42888.3i | 1.00372 | − | 0.133405i | ||||
\(568\) | − | 51508.8i | − | 0.159656i | ||||||
\(569\) | −397273. | −1.22706 | −0.613529 | − | 0.789673i | \(-0.710250\pi\) | ||||
−0.613529 | + | 0.789673i | \(0.710250\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −67235.8 | −0.206219 | −0.103109 | − | 0.994670i | \(-0.532879\pi\) | ||||
−0.103109 | + | 0.994670i | \(0.532879\pi\) | |||||||
\(572\) | 74539.3 | 0.227821 | ||||||||
\(573\) | 644744. | 1.96371 | ||||||||
\(574\) | −181876. | + | 24173.3i | −0.552016 | + | 0.0733688i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −40944.9 | −0.123411 | ||||||||
\(577\) | 64756.1 | 0.194504 | 0.0972521 | − | 0.995260i | \(-0.468995\pi\) | ||||
0.0972521 | + | 0.995260i | \(0.468995\pi\) | |||||||
\(578\) | 142567.i | 0.426741i | ||||||||
\(579\) | − | 15838.2i | − | 0.0472443i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 70351.0 | − | 9350.39i | 0.208410 | − | 0.0276999i | ||||
\(582\) | 211680.i | 0.624933i | ||||||||
\(583\) | 280242.i | 0.824510i | ||||||||
\(584\) | − | 160812.i | − | 0.471511i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 57245.8i | 0.166705i | ||||||||
\(587\) | 338967. | 0.983741 | 0.491870 | − | 0.870668i | \(-0.336313\pi\) | ||||
0.491870 | + | 0.870668i | \(0.336313\pi\) | |||||||
\(588\) | 235239. | − | 63656.1i | 0.680386 | − | 0.184113i | ||||
\(589\) | 160511. | 0.462673 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 817763.i | − | 2.34128i | ||||||
\(592\) | − | 42785.9i | − | 0.122084i | ||||||
\(593\) | 255668. | 0.727054 | 0.363527 | − | 0.931584i | \(-0.381572\pi\) | ||||
0.363527 | + | 0.931584i | \(0.381572\pi\) | |||||||
\(594\) | − | 7086.30i | − | 0.0200838i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −52612.6 | −0.148114 | ||||||||
\(597\) | − | 29848.4i | − | 0.0837477i | ||||||
\(598\) | −64506.1 | −0.180384 | ||||||||
\(599\) | −129521. | −0.360982 | −0.180491 | − | 0.983577i | \(-0.557769\pi\) | ||||
−0.180491 | + | 0.983577i | \(0.557769\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 377277.i | − | 1.04451i | −0.852790 | − | 0.522254i | \(-0.825091\pi\) | ||
0.852790 | − | 0.522254i | \(-0.174909\pi\) | |||||||
\(602\) | 266559. | − | 35428.4i | 0.735529 | − | 0.0977595i | ||||
\(603\) | − | 86095.3i | − | 0.236780i | ||||||
\(604\) | 183444. | 0.502839 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −329144. | −0.896274 | ||||||||
\(607\) | −421091. | −1.14287 | −0.571437 | − | 0.820646i | \(-0.693614\pi\) | ||||
−0.571437 | + | 0.820646i | \(0.693614\pi\) | |||||||
\(608\) | −108596. | −0.293770 | ||||||||
\(609\) | 208840. | − | 27757.1i | 0.563093 | − | 0.0748410i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 142653. | 0.382119 | ||||||||
\(612\) | −116423. | −0.310839 | ||||||||
\(613\) | − | 412173.i | − | 1.09688i | −0.836190 | − | 0.548440i | \(-0.815222\pi\) | ||
0.836190 | − | 0.548440i | \(-0.184778\pi\) | |||||||
\(614\) | 178954.i | 0.474684i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −28021.4 | − | 210829.i | −0.0738462 | − | 0.555608i | ||||
\(617\) | − | 262676.i | − | 0.690002i | −0.938602 | − | 0.345001i | \(-0.887879\pi\) | ||
0.938602 | − | 0.345001i | \(-0.112121\pi\) | |||||||
\(618\) | 140185.i | 0.367050i | ||||||||
\(619\) | 373975.i | 0.976026i | 0.872836 | + | 0.488013i | \(0.162278\pi\) | ||||
−0.872836 | + | 0.488013i | \(0.837722\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6132.47i | 0.0159020i | ||||||||
\(622\) | −40659.7 | −0.105095 | ||||||||
\(623\) | −13775.0 | − | 103641.i | −0.0354908 | − | 0.267028i | ||||
\(624\) | 39440.9 | 0.101293 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 103982.i | − | 0.265343i | ||||||
\(627\) | 1.46004e6i | 3.71389i | ||||||||
\(628\) | 298344. | 0.756480 | ||||||||
\(629\) | − | 121657.i | − | 0.307494i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −408746. | −1.02659 | −0.513293 | − | 0.858214i | \(-0.671574\pi\) | ||||
−0.513293 | + | 0.858214i | \(0.671574\pi\) | |||||||
\(632\) | − | 158672.i | − | 0.397252i | ||||||
\(633\) | 825397. | 2.05995 | ||||||||
\(634\) | −355126. | −0.883495 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 148284.i | 0.366590i | ||||||||
\(637\) | −112575. | + | 30462.8i | −0.277435 | + | 0.0750743i | ||||
\(638\) | − | 183863.i | − | 0.451703i | ||||||
\(639\) | −182044. | −0.445835 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −528074. | −1.28522 | −0.642612 | − | 0.766192i | \(-0.722149\pi\) | ||||
−0.642612 | + | 0.766192i | \(0.722149\pi\) | |||||||
\(642\) | 435695. | 1.05709 | ||||||||
\(643\) | −323445. | −0.782310 | −0.391155 | − | 0.920325i | \(-0.627924\pi\) | ||||
−0.391155 | + | 0.920325i | \(0.627924\pi\) | |||||||
\(644\) | 24249.6 | + | 182451.i | 0.0584701 | + | 0.439921i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −308782. | −0.739925 | ||||||||
\(647\) | −592372. | −1.41510 | −0.707548 | − | 0.706665i | \(-0.750199\pi\) | ||||
−0.707548 | + | 0.706665i | \(0.750199\pi\) | |||||||
\(648\) | − | 150321.i | − | 0.357990i | ||||||
\(649\) | 332015.i | 0.788257i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21915.0 | + | 164885.i | 0.0517106 | + | 0.389063i | ||||
\(652\) | 326832.i | 0.768828i | ||||||||
\(653\) | 329810.i | 0.773459i | 0.922193 | + | 0.386730i | \(0.126395\pi\) | ||||
−0.922193 | + | 0.386730i | \(0.873605\pi\) | |||||||
\(654\) | − | 244320.i | − | 0.571221i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 84726.1i | 0.196884i | ||||||||
\(657\) | −568346. | −1.31669 | ||||||||
\(658\) | −53627.2 | − | 403483.i | −0.123861 | − | 0.931910i | ||||
\(659\) | 526737. | 1.21290 | 0.606448 | − | 0.795123i | \(-0.292594\pi\) | ||||
0.606448 | + | 0.795123i | \(0.292594\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 144047.i | − | 0.329686i | −0.986320 | − | 0.164843i | \(-0.947288\pi\) | ||
0.986320 | − | 0.164843i | \(-0.0527117\pi\) | |||||||
\(662\) | − | 15207.2i | − | 0.0347002i | ||||||
\(663\) | 112146. | 0.255128 | ||||||||
\(664\) | − | 32772.7i | − | 0.0743320i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −151215. | −0.340916 | ||||||||
\(667\) | 159115.i | 0.357650i | ||||||||
\(668\) | −278199. | −0.623452 | ||||||||
\(669\) | −385855. | −0.862128 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 47254.3i | 0.104953i | ||||||||
\(672\) | −14826.9 | − | 111556.i | −0.0328332 | − | 0.247032i | ||||
\(673\) | − | 620117.i | − | 1.36913i | −0.728953 | − | 0.684563i | \(-0.759993\pi\) | ||
0.728953 | − | 0.684563i | \(-0.240007\pi\) | |||||||
\(674\) | 6228.95 | 0.0137118 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 209613. | 0.458697 | ||||||||
\(677\) | 626172. | 1.36621 | 0.683103 | − | 0.730322i | \(-0.260630\pi\) | ||||
0.683103 | + | 0.730322i | \(0.260630\pi\) | |||||||
\(678\) | −170965. | −0.371920 | ||||||||
\(679\) | −286520. | + | 38081.5i | −0.621463 | + | 0.0825989i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 661338. | 1.42603 | ||||||||
\(682\) | 145165. | 0.312099 | ||||||||
\(683\) | − | 185558.i | − | 0.397775i | −0.980022 | − | 0.198888i | \(-0.936267\pi\) | ||
0.980022 | − | 0.198888i | \(-0.0637328\pi\) | |||||||
\(684\) | 383805.i | 0.820348i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 128482. | + | 306957.i | 0.273019 | + | 0.652273i | ||||
\(687\) | − | 1.03124e6i | − | 2.18497i | ||||||
\(688\) | − | 124175.i | − | 0.262336i | ||||||
\(689\) | − | 70961.9i | − | 0.149481i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 548881.i | − | 1.14953i | −0.818317 | − | 0.574767i | \(-0.805093\pi\) | ||
0.818317 | − | 0.574767i | \(-0.194907\pi\) | |||||||
\(692\) | −252800. | −0.527917 | ||||||||
\(693\) | −745118. | + | 99034.1i | −1.55153 | + | 0.206214i | ||||
\(694\) | 628478. | 1.30488 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 97287.2i | − | 0.200834i | ||||||
\(697\) | 240910.i | 0.495894i | ||||||||
\(698\) | 290420. | 0.596095 | ||||||||
\(699\) | − | 529305.i | − | 1.08331i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 517501. | 1.05311 | 0.526556 | − | 0.850140i | \(-0.323483\pi\) | ||||
0.526556 | + | 0.850140i | \(0.323483\pi\) | |||||||
\(702\) | 1794.37i | 0.00364114i | ||||||||
\(703\) | −401061. | −0.811522 | ||||||||
\(704\) | −98213.6 | −0.198165 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 177047.i | − | 0.355205i | ||||||
\(707\) | −59213.5 | − | 445514.i | −0.118463 | − | 0.891297i | ||||
\(708\) | 175679.i | 0.350471i | ||||||||
\(709\) | −6035.96 | −0.0120075 | −0.00600377 | − | 0.999982i | \(-0.501911\pi\) | ||||
−0.00600377 | + | 0.999982i | \(0.501911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −560784. | −1.10932 | ||||||||
\(712\) | −48280.7 | −0.0952388 | ||||||||
\(713\) | −125625. | −0.247115 | ||||||||
\(714\) | −42158.9 | − | 317197.i | −0.0826975 | − | 0.622204i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 182005. | 0.355024 | ||||||||
\(717\) | −49944.6 | −0.0971517 | ||||||||
\(718\) | 270132.i | 0.523994i | ||||||||
\(719\) | − | 748658.i | − | 1.44819i | −0.689700 | − | 0.724095i | \(-0.742258\pi\) | ||
0.689700 | − | 0.724095i | \(-0.257742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −189748. | + | 25219.5i | −0.365012 | + | 0.0485139i | ||||
\(722\) | 649343.i | 1.24566i | ||||||||
\(723\) | 894609.i | 1.71142i | ||||||||
\(724\) | 443475.i | 0.846042i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 795049.i | 1.50841i | ||||||||
\(727\) | 370335. | 0.700691 | 0.350345 | − | 0.936621i | \(-0.386064\pi\) | ||||
0.350345 | + | 0.936621i | \(0.386064\pi\) | |||||||
\(728\) | 7095.48 | + | 53385.4i | 0.0133881 | + | 0.100730i | ||||
\(729\) | −517848. | −0.974422 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 353079.i | − | 0.660750i | ||||||
\(732\) | 25003.6i | 0.0466639i | ||||||||
\(733\) | 144545. | 0.269027 | 0.134513 | − | 0.990912i | \(-0.457053\pi\) | ||||
0.134513 | + | 0.990912i | \(0.457053\pi\) | |||||||
\(734\) | − | 232867.i | − | 0.432231i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 84993.8 | 0.156903 | ||||||||
\(737\) | − | 206515.i | − | 0.380203i | ||||||
\(738\) | 299442. | 0.549793 | ||||||||
\(739\) | −4650.26 | −0.00851506 | −0.00425753 | − | 0.999991i | \(-0.501355\pi\) | ||||
−0.00425753 | + | 0.999991i | \(0.501355\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 369706.i | − | 0.673318i | ||||||
\(742\) | −200710. | + | 26676.5i | −0.364554 | + | 0.0484531i | ||||
\(743\) | − | 500204.i | − | 0.906087i | −0.891489 | − | 0.453043i | \(-0.850338\pi\) | ||
0.891489 | − | 0.453043i | \(-0.149662\pi\) | |||||||
\(744\) | 76811.0 | 0.138764 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −368327. | −0.661845 | ||||||||
\(747\) | −115826. | −0.207571 | ||||||||
\(748\) | −279260. | −0.499121 | ||||||||
\(749\) | 78382.2 | + | 589737.i | 0.139718 | + | 1.05122i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 944576. | 1.67478 | 0.837389 | − | 0.546608i | \(-0.184081\pi\) | ||||
0.837389 | + | 0.546608i | \(0.184081\pi\) | |||||||
\(752\) | −187961. | −0.332377 | ||||||||
\(753\) | 914031.i | 1.61202i | ||||||||
\(754\) | 46557.1i | 0.0818924i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5075.24 | − | 674.553i | 0.00888000 | − | 0.00118025i | ||||
\(757\) | − | 654028.i | − | 1.14131i | −0.821189 | − | 0.570656i | \(-0.806689\pi\) | ||
0.821189 | − | 0.570656i | \(-0.193311\pi\) | |||||||
\(758\) | 544044.i | 0.946881i | ||||||||
\(759\) | − | 1.14271e6i | − | 1.98360i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 643673.i | 1.11147i | 0.831361 | + | 0.555733i | \(0.187562\pi\) | ||||
−0.831361 | + | 0.555733i | \(0.812438\pi\) | |||||||
\(762\) | 1.00368e6 | 1.72856 | ||||||||
\(763\) | 330700. | − | 43953.6i | 0.568049 | − | 0.0754997i | ||||
\(764\) | 406541. | 0.696494 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 288310.i | 0.491362i | ||||||||
\(767\) | − | 84071.6i | − | 0.142909i | ||||||
\(768\) | −51967.7 | −0.0881071 | ||||||||
\(769\) | 103697.i | 0.175354i | 0.996149 | + | 0.0876768i | \(0.0279443\pi\) | ||||
−0.996149 | + | 0.0876768i | \(0.972056\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 832491. | 1.40046 | ||||||||
\(772\) | − | 9986.72i | − | 0.0167567i | ||||||
\(773\) | −796380. | −1.33279 | −0.666394 | − | 0.745599i | \(-0.732163\pi\) | ||||
−0.666394 | + | 0.745599i | \(0.732163\pi\) | |||||||
\(774\) | −438863. | −0.732567 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 133474.i | 0.221652i | ||||||||
\(777\) | −54757.9 | − | 411991.i | −0.0906995 | − | 0.682410i | ||||
\(778\) | 540439.i | 0.892868i | ||||||||
\(779\) | 794195. | 1.30874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −436664. | −0.715889 | ||||||||
\(782\) | 241671. | 0.395195 | ||||||||
\(783\) | 4426.10 | 0.00721934 | ||||||||
\(784\) | 148329. | − | 40138.1i | 0.241321 | − | 0.0653017i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 861843. | 1.39503 | ||||||||
\(787\) | −1.16895e6 | −1.88733 | −0.943664 | − | 0.330905i | \(-0.892646\pi\) | ||||
−0.943664 | + | 0.330905i | \(0.892646\pi\) | |||||||
\(788\) | − | 515637.i | − | 0.830408i | ||||||
\(789\) | − | 491081.i | − | 0.788859i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30756.9 | − | 231411.i | −0.0491575 | − | 0.369854i | ||||
\(792\) | 347110.i | 0.553371i | ||||||||
\(793\) | − | 11965.6i | − | 0.0190277i | ||||||
\(794\) | 568919.i | 0.902421i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 18820.8i | − | 0.0297038i | ||||||
\(797\) | 808048. | 1.27210 | 0.636049 | − | 0.771649i | \(-0.280568\pi\) | ||||
0.636049 | + | 0.771649i | \(0.280568\pi\) | |||||||
\(798\) | −1.04569e6 | + | 138983.i | −1.64209 | + | 0.218251i | ||||
\(799\) | −534447. | −0.837165 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 170635.i | 0.265952i | ||||||||
\(802\) | 113076.i | 0.175801i | ||||||||
\(803\) | −1.36328e6 | −2.11423 | ||||||||
\(804\) | − | 109273.i | − | 0.169044i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −36758.2 | −0.0565827 | ||||||||
\(807\) | − | 1.10668e6i | − | 1.69933i | ||||||
\(808\) | −207540. | −0.317892 | ||||||||
\(809\) | 692708. | 1.05841 | 0.529204 | − | 0.848495i | \(-0.322491\pi\) | ||||
0.529204 | + | 0.848495i | \(0.322491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 382267.i | 0.581200i | 0.956845 | + | 0.290600i | \(0.0938548\pi\) | ||||
−0.956845 | + | 0.290600i | \(0.906145\pi\) | |||||||
\(812\) | 131683. | − | 17502.1i | 0.199719 | − | 0.0265448i | ||||
\(813\) | − | 1.33677e6i | − | 2.02244i | ||||||
\(814\) | −362717. | −0.547417 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −147765. | −0.221917 | ||||||||
\(817\) | −1.16398e6 | −1.74381 | ||||||||
\(818\) | 228129. | 0.340936 | ||||||||
\(819\) | 188676. | − | 25077.1i | 0.281287 | − | 0.0373860i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 116392. | 0.172678 | 0.0863392 | − | 0.996266i | \(-0.472483\pi\) | ||||
0.0863392 | + | 0.996266i | \(0.472483\pi\) | |||||||
\(822\) | 149355. | 0.221043 | ||||||||
\(823\) | − | 640526.i | − | 0.945665i | −0.881152 | − | 0.472832i | \(-0.843232\pi\) | ||
0.881152 | − | 0.472832i | \(-0.156768\pi\) | |||||||
\(824\) | 88393.2i | 0.130186i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −237790. | + | 31604.8i | −0.348525 | + | 0.0463227i | ||||
\(827\) | − | 158299.i | − | 0.231455i | −0.993281 | − | 0.115727i | \(-0.963080\pi\) | ||
0.993281 | − | 0.115727i | \(-0.0369199\pi\) | |||||||
\(828\) | − | 300388.i | − | 0.438149i | ||||||
\(829\) | 680501.i | 0.990192i | 0.868838 | + | 0.495096i | \(0.164867\pi\) | ||||
−0.868838 | + | 0.495096i | \(0.835133\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 459017.i | − | 0.664701i | ||||||
\(832\) | 24869.3 | 0.0359267 | ||||||||
\(833\) | 421759. | − | 114129.i | 0.607819 | − | 0.164477i | ||||
\(834\) | 946148. | 1.36028 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 920622.i | 1.31725i | ||||||||
\(837\) | 3494.53i | 0.00498812i | ||||||||
\(838\) | −712859. | −1.01512 | ||||||||
\(839\) | − | 622397.i | − | 0.884186i | −0.896969 | − | 0.442093i | \(-0.854236\pi\) | ||
0.896969 | − | 0.442093i | \(-0.145764\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −592440. | −0.837631 | ||||||||
\(842\) | 238831.i | 0.336873i | ||||||||
\(843\) | −1.25786e6 | −1.77001 | ||||||||
\(844\) | 520451. | 0.730626 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 664297.i | 0.928157i | ||||||||
\(847\) | −1.07614e6 | + | 143031.i | −1.50004 | + | 0.199371i | ||||
\(848\) | 93500.0i | 0.130023i | ||||||||
\(849\) | 52694.2 | 0.0731051 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 313894. | 0.433435 | ||||||||
\(852\) | −231052. | −0.318295 | ||||||||
\(853\) | 826596. | 1.13604 | 0.568022 | − | 0.823013i | \(-0.307709\pi\) | ||||
0.568022 | + | 0.823013i | \(0.307709\pi\) | |||||||
\(854\) | −33843.7 | + | 4498.19i | −0.0464048 | + | 0.00616768i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 274726. | 0.374931 | ||||||||
\(857\) | −539076. | −0.733987 | −0.366994 | − | 0.930223i | \(-0.619613\pi\) | ||||
−0.366994 | + | 0.930223i | \(0.619613\pi\) | |||||||
\(858\) | − | 334359.i | − | 0.454191i | ||||||
\(859\) | − | 499964.i | − | 0.677567i | −0.940864 | − | 0.338783i | \(-0.889985\pi\) | ||
0.940864 | − | 0.338783i | \(-0.110015\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 108433. | + | 815838.i | 0.146271 | + | 1.10052i | ||||
\(862\) | 360659.i | 0.485380i | ||||||||
\(863\) | − | 1.16944e6i | − | 1.57021i | −0.619365 | − | 0.785103i | \(-0.712610\pi\) | ||
0.619365 | − | 0.785103i | \(-0.287390\pi\) | |||||||
\(864\) | − | 2364.28i | − | 0.00316716i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 660548.i | 0.880783i | ||||||||
\(867\) | 639512. | 0.850766 | ||||||||
\(868\) | 13818.4 | + | 103968.i | 0.0183408 | + | 0.137994i | ||||
\(869\) | −1.34514e6 | −1.78126 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52292.9i | 0.0689297i | ||||||||
\(872\) | − | 154055.i | − | 0.202602i | ||||||
\(873\) | 471727. | 0.618960 | ||||||||
\(874\) | − | 796705.i | − | 1.04298i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −721350. | −0.940021 | ||||||||
\(877\) | 187496.i | 0.243777i | 0.992544 | + | 0.121888i | \(0.0388950\pi\) | ||||
−0.992544 | + | 0.121888i | \(0.961105\pi\) | |||||||
\(878\) | 860515. | 1.11627 | ||||||||
\(879\) | 256786. | 0.332349 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 179673.i | − | 0.231489i | −0.993279 | − | 0.115745i | \(-0.963075\pi\) | ||
0.993279 | − | 0.115745i | \(-0.0369254\pi\) | |||||||
\(882\) | −141857. | − | 524230.i | −0.182354 | − | 0.673883i | ||||
\(883\) | 1.04658e6i | 1.34231i | 0.741317 | + | 0.671155i | \(0.234201\pi\) | ||||
−0.741317 | + | 0.671155i | \(0.765799\pi\) | |||||||
\(884\) | 70713.3 | 0.0904892 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 246246. | 0.313691 | ||||||||
\(887\) | 1.30029e6 | 1.65270 | 0.826349 | − | 0.563158i | \(-0.190414\pi\) | ||||
0.826349 | + | 0.563158i | \(0.190414\pi\) | |||||||
\(888\) | −191924. | −0.243390 | ||||||||
\(889\) | 180563. | + | 1.35853e6i | 0.228468 | + | 1.71896i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.27434e6 | −1.60521 | ||||||||
\(892\) | −243299. | −0.305781 | ||||||||
\(893\) | 1.76188e6i | 2.20940i | ||||||||
\(894\) | 236003.i | 0.295286i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9349.06 | − | 70341.0i | −0.0116453 | − | 0.0876178i | ||||
\(897\) | 289354.i | 0.359620i | ||||||||
\(898\) | − | 257787.i | − | 0.319675i | ||||||
\(899\) | 90669.8i | 0.112187i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 265858.i | 0.327491i | ||||||||
\(902\) | 718263. | 0.882817 | ||||||||
\(903\) | −158921. | − | 1.19570e6i | −0.194897 | − | 1.46638i | ||||
\(904\) | −107802. | −0.131913 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 822869.i | − | 1.00248i | ||||||
\(907\) | 1.18388e6i | 1.43911i | 0.694435 | + | 0.719556i | \(0.255654\pi\) | ||||
−0.694435 | + | 0.719556i | \(0.744346\pi\) | |||||||
\(908\) | 417004. | 0.505788 | ||||||||
\(909\) | 733496.i | 0.887708i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.30731e6 | −1.57522 | −0.787612 | − | 0.616172i | \(-0.788683\pi\) | ||||
−0.787612 | + | 0.616172i | \(0.788683\pi\) | |||||||
\(912\) | 487128.i | 0.585671i | ||||||||
\(913\) | −277830. | −0.333301 | ||||||||
\(914\) | −1.16511e6 | −1.39468 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 650242.i | − | 0.774968i | ||||||
\(917\) | 155047. | + | 1.16655e6i | 0.184384 | + | 1.38728i | ||||
\(918\) | − | 6722.58i | − | 0.00797720i | ||||||
\(919\) | −698775. | −0.827382 | −0.413691 | − | 0.910417i | \(-0.635761\pi\) | ||||
−0.413691 | + | 0.910417i | \(0.635761\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 802730. | 0.946347 | ||||||||
\(922\) | −445185. | −0.523696 | ||||||||
\(923\) | 110571. | 0.129789 | ||||||||
\(924\) | −945711. | + | 125695.i | −1.10768 | + | 0.147222i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −694541. | −0.809984 | ||||||||
\(927\) | 312402. | 0.363542 | ||||||||
\(928\) | − | 61344.1i | − | 0.0712323i | ||||||
\(929\) | − | 1.39460e6i | − | 1.61591i | −0.589244 | − | 0.807955i | \(-0.700574\pi\) | ||
0.589244 | − | 0.807955i | \(-0.299426\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −376241. | − | 1.39039e6i | −0.434077 | − | 1.60412i | ||||
\(932\) | − | 333751.i | − | 0.384229i | ||||||
\(933\) | 182387.i | 0.209522i | ||||||||
\(934\) | − | 93533.8i | − | 0.107220i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 87893.9i | − | 0.100325i | ||||||
\(937\) | −509380. | −0.580180 | −0.290090 | − | 0.956999i | \(-0.593685\pi\) | ||||
−0.290090 | + | 0.956999i | \(0.593685\pi\) | |||||||
\(938\) | 147907. | − | 19658.4i | 0.168106 | − | 0.0223430i | ||||
\(939\) | −466428. | −0.528997 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.62505e6i | 1.83522i | 0.397486 | + | 0.917608i | \(0.369883\pi\) | ||||
−0.397486 | + | 0.917608i | \(0.630117\pi\) | |||||||
\(942\) | − | 1.33827e6i | − | 1.50814i | ||||||
\(943\) | −621584. | −0.698998 | ||||||||
\(944\) | 110773.i | 0.124306i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.05269e6 | −1.17630 | ||||||||
\(947\) | 1.22462e6i | 1.36553i | 0.730640 | + | 0.682763i | \(0.239222\pi\) | ||||
−0.730640 | + | 0.682763i | \(0.760778\pi\) | |||||||
\(948\) | −711752. | −0.791976 | ||||||||
\(949\) | 345204. | 0.383304 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.59298e6i | 1.76137i | ||||||||
\(952\) | −26583.1 | − | 200007.i | −0.0293313 | − | 0.220685i | ||||
\(953\) | 1.14847e6i | 1.26454i | 0.774749 | + | 0.632269i | \(0.217876\pi\) | ||||
−0.774749 | + | 0.632269i | \(0.782124\pi\) | |||||||
\(954\) | 330451. | 0.363086 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −31492.4 | −0.0344580 | ||||||||
\(957\) | −824750. | −0.900531 | ||||||||
\(958\) | −1.08690e6 | −1.18429 | ||||||||
\(959\) | 26869.2 | + | 202160.i | 0.0292158 | + | 0.219815i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 851935. | 0.922485 | ||||||||
\(962\) | 91845.8 | 0.0992451 | ||||||||
\(963\) | − | 970945.i | − | 1.04699i | ||||||
\(964\) | 564092.i | 0.607010i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 818416. | − | 108776.i | 0.877041 | − | 0.116568i | ||||
\(967\) | − | 733668.i | − | 0.784597i | −0.919838 | − | 0.392298i | \(-0.871680\pi\) | ||
0.919838 | − | 0.392298i | \(-0.128320\pi\) | |||||||
\(968\) | 501315.i | 0.535008i | ||||||||
\(969\) | 1.38510e6i | 1.47514i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 786749.i | 0.834445i | 0.908804 | + | 0.417223i | \(0.136996\pi\) | ||||
−0.908804 | + | 0.417223i | \(0.863004\pi\) | |||||||
\(972\) | −665830. | −0.704743 | ||||||||
\(973\) | 170213. | + | 1.28066e6i | 0.179791 | + | 1.35272i | ||||
\(974\) | −490807. | −0.517360 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15765.9i | 0.0165508i | ||||||||
\(977\) | 837039.i | 0.876913i | 0.898752 | + | 0.438457i | \(0.144475\pi\) | ||||
−0.898752 | + | 0.438457i | \(0.855525\pi\) | |||||||
\(978\) | 1.46606e6 | 1.53276 | ||||||||
\(979\) | 409299.i | 0.427046i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −544467. | −0.565761 | ||||||||
\(982\) | 56586.3i | 0.0586798i | ||||||||
\(983\) | 644129. | 0.666600 | 0.333300 | − | 0.942821i | \(-0.391838\pi\) | ||||
0.333300 | + | 0.942821i | \(0.391838\pi\) | |||||||
\(984\) | 380054. | 0.392514 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 174426.i | − | 0.179414i | ||||||
\(987\) | −1.80990e6 | + | 240554.i | −1.85789 | + | 0.246933i | ||||
\(988\) | − | 233117.i | − | 0.238814i | ||||||
\(989\) | 910996. | 0.931374 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 92517.5 | 0.0942056 | 0.0471028 | − | 0.998890i | \(-0.485001\pi\) | ||||
0.0471028 | + | 0.998890i | \(0.485001\pi\) | |||||||
\(992\) | 48432.8 | 0.0492172 | ||||||||
\(993\) | −68214.4 | −0.0691795 | ||||||||
\(994\) | −41566.6 | − | 312741.i | −0.0420699 | − | 0.316528i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −147008. | −0.148191 | ||||||||
\(997\) | −366383. | −0.368591 | −0.184295 | − | 0.982871i | \(-0.559000\pi\) | ||||
−0.184295 | + | 0.982871i | \(0.559000\pi\) | |||||||
\(998\) | − | 1.21161e6i | − | 1.21647i | ||||||
\(999\) | − | 8731.60i | − | 0.00874909i |
(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 | 350.5.d.a.349.1 | 8 | ||
5.2 | odd | 4 | 350.5.b.a.251.4 | 4 | |||
5.3 | odd | 4 | 14.5.b.a.13.1 | ✓ | 4 | ||
5.4 | even | 2 | inner | 350.5.d.a.349.8 | 8 | ||
7.6 | odd | 2 | inner | 350.5.d.a.349.4 | 8 | ||
15.8 | even | 4 | 126.5.c.a.55.4 | 4 | |||
20.3 | even | 4 | 112.5.c.c.97.4 | 4 | |||
35.3 | even | 12 | 98.5.d.d.19.4 | 8 | |||
35.13 | even | 4 | 14.5.b.a.13.2 | yes | 4 | ||
35.18 | odd | 12 | 98.5.d.d.19.3 | 8 | |||
35.23 | odd | 12 | 98.5.d.d.31.4 | 8 | |||
35.27 | even | 4 | 350.5.b.a.251.3 | 4 | |||
35.33 | even | 12 | 98.5.d.d.31.3 | 8 | |||
35.34 | odd | 2 | inner | 350.5.d.a.349.5 | 8 | ||
40.3 | even | 4 | 448.5.c.f.321.1 | 4 | |||
40.13 | odd | 4 | 448.5.c.e.321.4 | 4 | |||
60.23 | odd | 4 | 1008.5.f.h.433.3 | 4 | |||
105.83 | odd | 4 | 126.5.c.a.55.3 | 4 | |||
140.83 | odd | 4 | 112.5.c.c.97.1 | 4 | |||
280.13 | even | 4 | 448.5.c.e.321.1 | 4 | |||
280.83 | odd | 4 | 448.5.c.f.321.4 | 4 | |||
420.83 | even | 4 | 1008.5.f.h.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.5.b.a.13.1 | ✓ | 4 | 5.3 | odd | 4 | ||
14.5.b.a.13.2 | yes | 4 | 35.13 | even | 4 | ||
98.5.d.d.19.3 | 8 | 35.18 | odd | 12 | |||
98.5.d.d.19.4 | 8 | 35.3 | even | 12 | |||
98.5.d.d.31.3 | 8 | 35.33 | even | 12 | |||
98.5.d.d.31.4 | 8 | 35.23 | odd | 12 | |||
112.5.c.c.97.1 | 4 | 140.83 | odd | 4 | |||
112.5.c.c.97.4 | 4 | 20.3 | even | 4 | |||
126.5.c.a.55.3 | 4 | 105.83 | odd | 4 | |||
126.5.c.a.55.4 | 4 | 15.8 | even | 4 | |||
350.5.b.a.251.3 | 4 | 35.27 | even | 4 | |||
350.5.b.a.251.4 | 4 | 5.2 | odd | 4 | |||
350.5.d.a.349.1 | 8 | 1.1 | even | 1 | trivial | ||
350.5.d.a.349.4 | 8 | 7.6 | odd | 2 | inner | ||
350.5.d.a.349.5 | 8 | 35.34 | odd | 2 | inner | ||
350.5.d.a.349.8 | 8 | 5.4 | even | 2 | inner | ||
448.5.c.e.321.1 | 4 | 280.13 | even | 4 | |||
448.5.c.e.321.4 | 4 | 40.13 | odd | 4 | |||
448.5.c.f.321.1 | 4 | 40.3 | even | 4 | |||
448.5.c.f.321.4 | 4 | 280.83 | odd | 4 | |||
1008.5.f.h.433.2 | 4 | 420.83 | even | 4 | |||
1008.5.f.h.433.3 | 4 | 60.23 | odd | 4 |