Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.24 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.3 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.0460i | 1.77590i | 0.459936 | + | 0.887952i | \(0.347872\pi\) | ||||
−0.459936 | + | 0.887952i | \(0.652128\pi\) | |||||||
\(3\) | − | 9.00000i | − | 0.577350i | ||||||
\(4\) | −68.9227 | −2.15384 | ||||||||
\(5\) | 24.7608 | + | 50.1189i | 0.442935 | + | 0.896554i | ||||
\(6\) | 90.4143 | 1.02532 | ||||||||
\(7\) | − | 29.0524i | − | 0.224098i | −0.993703 | − | 0.112049i | \(-0.964259\pi\) | ||
0.993703 | − | 0.112049i | \(-0.0357413\pi\) | |||||||
\(8\) | − | 370.927i | − | 2.04910i | ||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | −503.496 | + | 248.748i | −1.59219 | + | 0.786611i | ||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 620.305i | 1.24352i | ||||||||
\(13\) | − | 1023.51i | − | 1.67971i | −0.542809 | − | 0.839856i | \(-0.682639\pi\) | ||
0.542809 | − | 0.839856i | \(-0.317361\pi\) | |||||||
\(14\) | 291.862 | 0.397976 | ||||||||
\(15\) | 451.070 | − | 222.848i | 0.517625 | − | 0.255729i | ||||
\(16\) | 1520.82 | 1.48517 | ||||||||
\(17\) | − | 1509.69i | − | 1.26696i | −0.773757 | − | 0.633482i | \(-0.781625\pi\) | ||
0.773757 | − | 0.633482i | \(-0.218375\pi\) | |||||||
\(18\) | − | 813.728i | − | 0.591968i | ||||||
\(19\) | −1643.04 | −1.04415 | −0.522075 | − | 0.852900i | \(-0.674842\pi\) | ||||
−0.522075 | + | 0.852900i | \(0.674842\pi\) | |||||||
\(20\) | −1706.58 | − | 3454.33i | −0.954010 | − | 1.93103i | ||||
\(21\) | −261.472 | −0.129383 | ||||||||
\(22\) | 1215.57i | 0.535455i | ||||||||
\(23\) | − | 1478.11i | − | 0.582622i | −0.956628 | − | 0.291311i | \(-0.905908\pi\) | ||
0.956628 | − | 0.291311i | \(-0.0940915\pi\) | |||||||
\(24\) | −3338.34 | −1.18305 | ||||||||
\(25\) | −1898.80 | + | 2481.97i | −0.607616 | + | 0.794231i | ||||
\(26\) | 10282.2 | 2.98301 | ||||||||
\(27\) | 729.000i | 0.192450i | ||||||||
\(28\) | 2002.37i | 0.482669i | ||||||||
\(29\) | 4572.33 | 1.00958 | 0.504792 | − | 0.863241i | \(-0.331569\pi\) | ||||
0.504792 | + | 0.863241i | \(0.331569\pi\) | |||||||
\(30\) | 2238.73 | + | 4531.46i | 0.454150 | + | 0.919253i | ||||
\(31\) | 7531.62 | 1.40762 | 0.703808 | − | 0.710391i | \(-0.251482\pi\) | ||||
0.703808 | + | 0.710391i | \(0.251482\pi\) | |||||||
\(32\) | 3408.50i | 0.588421i | ||||||||
\(33\) | − | 1089.00i | − | 0.174078i | ||||||
\(34\) | 15166.4 | 2.25001 | ||||||||
\(35\) | 1456.07 | − | 719.362i | 0.200916 | − | 0.0992608i | ||||
\(36\) | 5582.74 | 0.717945 | ||||||||
\(37\) | 4408.40i | 0.529391i | 0.964332 | + | 0.264695i | \(0.0852714\pi\) | ||||
−0.964332 | + | 0.264695i | \(0.914729\pi\) | |||||||
\(38\) | − | 16506.0i | − | 1.85431i | ||||||
\(39\) | −9211.62 | −0.969783 | ||||||||
\(40\) | 18590.4 | − | 9184.46i | 1.83713 | − | 0.907619i | ||||
\(41\) | 5629.62 | 0.523021 | 0.261511 | − | 0.965201i | \(-0.415779\pi\) | ||||
0.261511 | + | 0.965201i | \(0.415779\pi\) | |||||||
\(42\) | − | 2626.75i | − | 0.229771i | ||||||
\(43\) | 2283.11i | 0.188302i | 0.995558 | + | 0.0941510i | \(0.0300137\pi\) | ||||
−0.995558 | + | 0.0941510i | \(0.969986\pi\) | |||||||
\(44\) | −8339.65 | −0.649406 | ||||||||
\(45\) | −2005.63 | − | 4059.63i | −0.147645 | − | 0.298851i | ||||
\(46\) | 14849.1 | 1.03468 | ||||||||
\(47\) | 5980.48i | 0.394904i | 0.980313 | + | 0.197452i | \(0.0632667\pi\) | ||||
−0.980313 | + | 0.197452i | \(0.936733\pi\) | |||||||
\(48\) | − | 13687.3i | − | 0.857464i | ||||||
\(49\) | 15963.0 | 0.949780 | ||||||||
\(50\) | −24934.0 | − | 19075.4i | −1.41048 | − | 1.07907i | ||||
\(51\) | −13587.2 | −0.731482 | ||||||||
\(52\) | 70543.3i | 3.61782i | ||||||||
\(53\) | − | 28498.0i | − | 1.39356i | −0.717287 | − | 0.696778i | \(-0.754616\pi\) | ||
0.717287 | − | 0.696778i | \(-0.245384\pi\) | |||||||
\(54\) | −7323.56 | −0.341773 | ||||||||
\(55\) | 2996.06 | + | 6064.38i | 0.133550 | + | 0.270321i | ||||
\(56\) | −10776.3 | −0.459199 | ||||||||
\(57\) | 14787.3i | 0.602840i | ||||||||
\(58\) | 45933.7i | 1.79292i | ||||||||
\(59\) | −25942.8 | −0.970258 | −0.485129 | − | 0.874443i | \(-0.661227\pi\) | ||||
−0.485129 | + | 0.874443i | \(0.661227\pi\) | |||||||
\(60\) | −31089.0 | + | 15359.3i | −1.11488 | + | 0.550798i | ||||
\(61\) | −51360.7 | −1.76728 | −0.883642 | − | 0.468163i | \(-0.844916\pi\) | ||||
−0.883642 | + | 0.468163i | \(0.844916\pi\) | |||||||
\(62\) | 75662.8i | 2.49979i | ||||||||
\(63\) | 2353.25i | 0.0746992i | ||||||||
\(64\) | 14424.2 | 0.440193 | ||||||||
\(65\) | 51297.3 | − | 25343.0i | 1.50595 | − | 0.744004i | ||||
\(66\) | 10940.1 | 0.309145 | ||||||||
\(67\) | − | 39180.2i | − | 1.06630i | −0.846020 | − | 0.533151i | \(-0.821008\pi\) | ||
0.846020 | − | 0.533151i | \(-0.178992\pi\) | |||||||
\(68\) | 104052.i | 2.72883i | ||||||||
\(69\) | −13303.0 | −0.336377 | ||||||||
\(70\) | 7226.74 | + | 14627.8i | 0.176278 | + | 0.356807i | ||||
\(71\) | 37560.3 | 0.884267 | 0.442133 | − | 0.896949i | \(-0.354222\pi\) | ||||
0.442133 | + | 0.896949i | \(0.354222\pi\) | |||||||
\(72\) | 30045.1i | 0.683034i | ||||||||
\(73\) | − | 58687.6i | − | 1.28896i | −0.764621 | − | 0.644480i | \(-0.777074\pi\) | ||
0.764621 | − | 0.644480i | \(-0.222926\pi\) | |||||||
\(74\) | −44286.9 | −0.940147 | ||||||||
\(75\) | 22337.7 | + | 17089.2i | 0.458549 | + | 0.350808i | ||||
\(76\) | 113242. | 2.24893 | ||||||||
\(77\) | − | 3515.34i | − | 0.0675680i | ||||||
\(78\) | − | 92540.2i | − | 1.72224i | ||||||
\(79\) | 8274.06 | 0.149160 | 0.0745798 | − | 0.997215i | \(-0.476238\pi\) | ||||
0.0745798 | + | 0.997215i | \(0.476238\pi\) | |||||||
\(80\) | 37656.7 | + | 76221.5i | 0.657835 | + | 1.33154i | ||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 56555.3i | 0.928836i | ||||||||
\(83\) | 21355.4i | 0.340261i | 0.985422 | + | 0.170130i | \(0.0544188\pi\) | ||||
−0.985422 | + | 0.170130i | \(0.945581\pi\) | |||||||
\(84\) | 18021.4 | 0.278669 | ||||||||
\(85\) | 75663.8 | − | 37381.1i | 1.13590 | − | 0.561183i | ||||
\(86\) | −22936.2 | −0.334406 | ||||||||
\(87\) | − | 41150.9i | − | 0.582883i | ||||||
\(88\) | − | 44882.1i | − | 0.617827i | ||||||
\(89\) | −78385.8 | −1.04897 | −0.524484 | − | 0.851420i | \(-0.675742\pi\) | ||||
−0.524484 | + | 0.851420i | \(0.675742\pi\) | |||||||
\(90\) | 40783.1 | − | 20148.6i | 0.530731 | − | 0.262204i | ||||
\(91\) | −29735.5 | −0.376420 | ||||||||
\(92\) | 101875.i | 1.25487i | ||||||||
\(93\) | − | 67784.5i | − | 0.812687i | ||||||
\(94\) | −60080.1 | −0.701312 | ||||||||
\(95\) | −40682.9 | − | 82347.1i | −0.462491 | − | 0.936136i | ||||
\(96\) | 30676.5 | 0.339725 | ||||||||
\(97\) | 64574.7i | 0.696840i | 0.937339 | + | 0.348420i | \(0.113282\pi\) | ||||
−0.937339 | + | 0.348420i | \(0.886718\pi\) | |||||||
\(98\) | 160364.i | 1.68672i | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 130871. | − | 171064.i | 1.30871 | − | 1.71064i | ||||
\(101\) | 48364.4 | 0.471762 | 0.235881 | − | 0.971782i | \(-0.424203\pi\) | ||||
0.235881 | + | 0.971782i | \(0.424203\pi\) | |||||||
\(102\) | − | 136497.i | − | 1.29904i | ||||||
\(103\) | − | 121923.i | − | 1.13238i | −0.824273 | − | 0.566192i | \(-0.808416\pi\) | ||
0.824273 | − | 0.566192i | \(-0.191584\pi\) | |||||||
\(104\) | −379648. | −3.44190 | ||||||||
\(105\) | −6474.26 | − | 13104.7i | −0.0573082 | − | 0.115999i | ||||
\(106\) | 286291. | 2.47482 | ||||||||
\(107\) | − | 191883.i | − | 1.62023i | −0.586269 | − | 0.810117i | \(-0.699404\pi\) | ||
0.586269 | − | 0.810117i | \(-0.300596\pi\) | |||||||
\(108\) | − | 50244.7i | − | 0.414506i | ||||||
\(109\) | 15660.0 | 0.126248 | 0.0631240 | − | 0.998006i | \(-0.479894\pi\) | ||||
0.0631240 | + | 0.998006i | \(0.479894\pi\) | |||||||
\(110\) | −60923.0 | + | 30098.5i | −0.480064 | + | 0.237172i | ||||
\(111\) | 39675.6 | 0.305644 | ||||||||
\(112\) | − | 44183.4i | − | 0.332823i | ||||||
\(113\) | 15119.6i | 0.111389i | 0.998448 | + | 0.0556947i | \(0.0177374\pi\) | ||||
−0.998448 | + | 0.0556947i | \(0.982263\pi\) | |||||||
\(114\) | −148554. | −1.07059 | ||||||||
\(115\) | 74081.2 | − | 36599.3i | 0.522352 | − | 0.258064i | ||||
\(116\) | −315137. | −2.17448 | ||||||||
\(117\) | 82904.6i | 0.559904i | ||||||||
\(118\) | − | 260622.i | − | 1.72309i | ||||||
\(119\) | −43860.0 | −0.283924 | ||||||||
\(120\) | −82660.2 | − | 167314.i | −0.524014 | − | 1.06067i | ||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | − | 515971.i | − | 3.13853i | ||||||
\(123\) | − | 50666.6i | − | 0.301966i | ||||||
\(124\) | −519099. | −3.03177 | ||||||||
\(125\) | −171409. | − | 33710.1i | −0.981205 | − | 0.192968i | ||||
\(126\) | −23640.8 | −0.132659 | ||||||||
\(127\) | − | 223751.i | − | 1.23099i | −0.788140 | − | 0.615496i | \(-0.788956\pi\) | ||
0.788140 | − | 0.615496i | \(-0.211044\pi\) | |||||||
\(128\) | 253978.i | 1.37016i | ||||||||
\(129\) | 20548.0 | 0.108716 | ||||||||
\(130\) | 254597. | + | 515334.i | 1.32128 | + | 2.67443i | ||||
\(131\) | 269255. | 1.37084 | 0.685418 | − | 0.728149i | \(-0.259619\pi\) | ||||
0.685418 | + | 0.728149i | \(0.259619\pi\) | |||||||
\(132\) | 75056.9i | 0.374935i | ||||||||
\(133\) | 47734.1i | 0.233991i | ||||||||
\(134\) | 393606. | 1.89365 | ||||||||
\(135\) | −36536.7 | + | 18050.7i | −0.172542 | + | 0.0852430i | ||||
\(136\) | −559983. | −2.59614 | ||||||||
\(137\) | 172187.i | 0.783790i | 0.920010 | + | 0.391895i | \(0.128180\pi\) | ||||
−0.920010 | + | 0.391895i | \(0.871820\pi\) | |||||||
\(138\) | − | 133642.i | − | 0.597374i | ||||||
\(139\) | 350209. | 1.53741 | 0.768707 | − | 0.639601i | \(-0.220901\pi\) | ||||
0.768707 | + | 0.639601i | \(0.220901\pi\) | |||||||
\(140\) | −100357. | + | 49580.4i | −0.432739 | + | 0.213791i | ||||
\(141\) | 53824.4 | 0.227998 | ||||||||
\(142\) | 377332.i | 1.57037i | ||||||||
\(143\) | − | 123845.i | − | 0.506452i | ||||||
\(144\) | −123186. | −0.495057 | ||||||||
\(145\) | 113215. | + | 229160.i | 0.447180 | + | 0.905146i | ||||
\(146\) | 589578. | 2.28907 | ||||||||
\(147\) | − | 143667.i | − | 0.548356i | ||||||
\(148\) | − | 303839.i | − | 1.14022i | ||||||
\(149\) | −519184. | −1.91582 | −0.957912 | − | 0.287062i | \(-0.907322\pi\) | ||||
−0.957912 | + | 0.287062i | \(0.907322\pi\) | |||||||
\(150\) | −171679. | + | 224406.i | −0.623000 | + | 0.814340i | ||||
\(151\) | −230203. | −0.821617 | −0.410808 | − | 0.911722i | \(-0.634753\pi\) | ||||
−0.410808 | + | 0.911722i | \(0.634753\pi\) | |||||||
\(152\) | 609446.i | 2.13957i | ||||||||
\(153\) | 122285.i | 0.422321i | ||||||||
\(154\) | 35315.2 | 0.119994 | ||||||||
\(155\) | 186489. | + | 377476.i | 0.623483 | + | 1.26200i | ||||
\(156\) | 634890. | 2.08875 | ||||||||
\(157\) | − | 328864.i | − | 1.06480i | −0.846494 | − | 0.532399i | \(-0.821291\pi\) | ||
0.846494 | − | 0.532399i | \(-0.178709\pi\) | |||||||
\(158\) | 83121.5i | 0.264893i | ||||||||
\(159\) | −256482. | −0.804569 | ||||||||
\(160\) | −170830. | + | 84397.2i | −0.527551 | + | 0.260632i | ||||
\(161\) | −42942.7 | −0.130564 | ||||||||
\(162\) | 65912.0i | 0.197323i | ||||||||
\(163\) | 246382.i | 0.726341i | 0.931723 | + | 0.363171i | \(0.118306\pi\) | ||||
−0.931723 | + | 0.363171i | \(0.881694\pi\) | |||||||
\(164\) | −388009. | −1.12650 | ||||||||
\(165\) | 54579.4 | − | 26964.6i | 0.156070 | − | 0.0771052i | ||||
\(166\) | −214537. | −0.604270 | ||||||||
\(167\) | − | 581413.i | − | 1.61322i | −0.591084 | − | 0.806610i | \(-0.701300\pi\) | ||
0.591084 | − | 0.806610i | \(-0.298700\pi\) | |||||||
\(168\) | 96986.9i | 0.265118i | ||||||||
\(169\) | −676286. | −1.82143 | ||||||||
\(170\) | 375532. | + | 760120.i | 0.996608 | + | 2.01725i | ||||
\(171\) | 133086. | 0.348050 | ||||||||
\(172\) | − | 157358.i | − | 0.405572i | ||||||
\(173\) | 264650.i | 0.672290i | 0.941810 | + | 0.336145i | \(0.109123\pi\) | ||||
−0.941810 | + | 0.336145i | \(0.890877\pi\) | |||||||
\(174\) | 413404. | 1.03515 | ||||||||
\(175\) | 72107.3 | + | 55164.8i | 0.177985 | + | 0.136165i | ||||
\(176\) | 184019. | 0.447796 | ||||||||
\(177\) | 233485.i | 0.560179i | ||||||||
\(178\) | − | 787466.i | − | 1.86287i | ||||||
\(179\) | 13886.5 | 0.0323937 | 0.0161969 | − | 0.999869i | \(-0.494844\pi\) | ||||
0.0161969 | + | 0.999869i | \(0.494844\pi\) | |||||||
\(180\) | 138233. | + | 279801.i | 0.318003 | + | 0.643676i | ||||
\(181\) | −752593. | −1.70751 | −0.853756 | − | 0.520673i | \(-0.825681\pi\) | ||||
−0.853756 | + | 0.520673i | \(0.825681\pi\) | |||||||
\(182\) | − | 298724.i | − | 0.668485i | ||||||
\(183\) | 462246.i | 1.02034i | ||||||||
\(184\) | −548271. | −1.19385 | ||||||||
\(185\) | −220944. | + | 109156.i | −0.474627 | + | 0.234486i | ||||
\(186\) | 680966. | 1.44325 | ||||||||
\(187\) | − | 182672.i | − | 0.382004i | ||||||
\(188\) | − | 412191.i | − | 0.850558i | ||||||
\(189\) | 21179.2 | 0.0431276 | ||||||||
\(190\) | 827261. | − | 408702.i | 1.66249 | − | 0.821340i | ||||
\(191\) | −25416.1 | −0.0504110 | −0.0252055 | − | 0.999682i | \(-0.508024\pi\) | ||||
−0.0252055 | + | 0.999682i | \(0.508024\pi\) | |||||||
\(192\) | − | 129818.i | − | 0.254145i | ||||||
\(193\) | 489822.i | 0.946553i | 0.880914 | + | 0.473277i | \(0.156929\pi\) | ||||
−0.880914 | + | 0.473277i | \(0.843071\pi\) | |||||||
\(194\) | −648719. | −1.23752 | ||||||||
\(195\) | −228087. | − | 461676.i | −0.429551 | − | 0.869462i | ||||
\(196\) | −1.10021e6 | −2.04567 | ||||||||
\(197\) | − | 324827.i | − | 0.596329i | −0.954515 | − | 0.298164i | \(-0.903626\pi\) | ||
0.954515 | − | 0.298164i | \(-0.0963744\pi\) | |||||||
\(198\) | − | 98461.1i | − | 0.178485i | ||||||
\(199\) | 398516. | 0.713368 | 0.356684 | − | 0.934225i | \(-0.383907\pi\) | ||||
0.356684 | + | 0.934225i | \(0.383907\pi\) | |||||||
\(200\) | 920630. | + | 704316.i | 1.62746 | + | 1.24507i | ||||
\(201\) | −352622. | −0.615629 | ||||||||
\(202\) | 485870.i | 0.837803i | ||||||||
\(203\) | − | 132837.i | − | 0.226245i | ||||||
\(204\) | 936465. | 1.57549 | ||||||||
\(205\) | 139394. | + | 282150.i | 0.231665 | + | 0.468917i | ||||
\(206\) | 1.22485e6 | 2.01101 | ||||||||
\(207\) | 119727.i | 0.194207i | ||||||||
\(208\) | − | 1.55657e6i | − | 2.49466i | ||||||
\(209\) | −198807. | −0.314823 | ||||||||
\(210\) | 131650. | − | 65040.6i | 0.206002 | − | 0.101774i | ||||
\(211\) | −868645. | −1.34319 | −0.671593 | − | 0.740920i | \(-0.734390\pi\) | ||||
−0.671593 | + | 0.740920i | \(0.734390\pi\) | |||||||
\(212\) | 1.96416e6i | 3.00149i | ||||||||
\(213\) | − | 338043.i | − | 0.510532i | ||||||
\(214\) | 1.92766e6 | 2.87738 | ||||||||
\(215\) | −114427. | + | 56531.6i | −0.168823 | + | 0.0834057i | ||||
\(216\) | 270406. | 0.394350 | ||||||||
\(217\) | − | 218812.i | − | 0.315443i | ||||||
\(218\) | 157320.i | 0.224204i | ||||||||
\(219\) | −528189. | −0.744181 | ||||||||
\(220\) | −206497. | − | 417974.i | −0.287645 | − | 0.582227i | ||||
\(221\) | −1.54518e6 | −2.12814 | ||||||||
\(222\) | 398582.i | 0.542794i | ||||||||
\(223\) | 48571.9i | 0.0654068i | 0.999465 | + | 0.0327034i | \(0.0104117\pi\) | ||||
−0.999465 | + | 0.0327034i | \(0.989588\pi\) | |||||||
\(224\) | 99025.1 | 0.131864 | ||||||||
\(225\) | 153803. | − | 201040.i | 0.202539 | − | 0.264744i | ||||
\(226\) | −151892. | −0.197817 | ||||||||
\(227\) | 78669.6i | 0.101331i | 0.998716 | + | 0.0506655i | \(0.0161342\pi\) | ||||
−0.998716 | + | 0.0506655i | \(0.983866\pi\) | |||||||
\(228\) | − | 1.01918e6i | − | 1.29842i | ||||||
\(229\) | 324090. | 0.408391 | 0.204196 | − | 0.978930i | \(-0.434542\pi\) | ||||
0.204196 | + | 0.978930i | \(0.434542\pi\) | |||||||
\(230\) | 367677. | + | 744222.i | 0.458297 | + | 0.927647i | ||||
\(231\) | −31638.1 | −0.0390104 | ||||||||
\(232\) | − | 1.69600e6i | − | 2.06874i | ||||||
\(233\) | − | 1.26828e6i | − | 1.53048i | −0.643747 | − | 0.765238i | \(-0.722621\pi\) | ||
0.643747 | − | 0.765238i | \(-0.277379\pi\) | |||||||
\(234\) | −832862. | −0.994336 | ||||||||
\(235\) | −299735. | + | 148082.i | −0.354053 | + | 0.174917i | ||||
\(236\) | 1.78805e6 | 2.08978 | ||||||||
\(237\) | − | 74466.6i | − | 0.0861173i | ||||||
\(238\) | − | 440619.i | − | 0.504221i | ||||||
\(239\) | 1.35381e6 | 1.53307 | 0.766535 | − | 0.642202i | \(-0.221979\pi\) | ||||
0.766535 | + | 0.642202i | \(0.221979\pi\) | |||||||
\(240\) | 685994. | − | 338910.i | 0.768762 | − | 0.379801i | ||||
\(241\) | 1.14198e6 | 1.26653 | 0.633264 | − | 0.773936i | \(-0.281715\pi\) | ||||
0.633264 | + | 0.773936i | \(0.281715\pi\) | |||||||
\(242\) | 147084.i | 0.161446i | ||||||||
\(243\) | − | 59049.0i | − | 0.0641500i | ||||||
\(244\) | 3.53992e6 | 3.80644 | ||||||||
\(245\) | 395256. | + | 800045.i | 0.420691 | + | 0.851529i | ||||
\(246\) | 508998. | 0.536264 | ||||||||
\(247\) | 1.68167e6i | 1.75387i | ||||||||
\(248\) | − | 2.79368e6i | − | 2.88434i | ||||||
\(249\) | 192198. | 0.196449 | ||||||||
\(250\) | 338653. | − | 1.72198e6i | 0.342692 | − | 1.74253i | ||||
\(251\) | −321578. | −0.322183 | −0.161091 | − | 0.986940i | \(-0.551501\pi\) | ||||
−0.161091 | + | 0.986940i | \(0.551501\pi\) | |||||||
\(252\) | − | 162192.i | − | 0.160890i | ||||||
\(253\) | − | 178851.i | − | 0.175667i | ||||||
\(254\) | 2.24781e6 | 2.18612 | ||||||||
\(255\) | −336430. | − | 680974.i | −0.323999 | − | 0.655813i | ||||
\(256\) | −2.08990e6 | −1.99308 | ||||||||
\(257\) | 1.44275e6i | 1.36257i | 0.732018 | + | 0.681286i | \(0.238579\pi\) | ||||
−0.732018 | + | 0.681286i | \(0.761421\pi\) | |||||||
\(258\) | 206425.i | 0.193070i | ||||||||
\(259\) | 128075. | 0.118635 | ||||||||
\(260\) | −3.53555e6 | + | 1.74671e6i | −3.24357 | + | 1.60246i | ||||
\(261\) | −370359. | −0.336528 | ||||||||
\(262\) | 2.70495e6i | 2.43447i | ||||||||
\(263\) | − | 838618.i | − | 0.747610i | −0.927507 | − | 0.373805i | \(-0.878053\pi\) | ||
0.927507 | − | 0.373805i | \(-0.121947\pi\) | |||||||
\(264\) | −403939. | −0.356703 | ||||||||
\(265\) | 1.42829e6 | − | 705634.i | 1.24940 | − | 0.617255i | ||||
\(266\) | −479539. | −0.415546 | ||||||||
\(267\) | 705472.i | 0.605622i | ||||||||
\(268\) | 2.70041e6i | 2.29664i | ||||||||
\(269\) | 415262. | 0.349898 | 0.174949 | − | 0.984577i | \(-0.444024\pi\) | ||||
0.174949 | + | 0.984577i | \(0.444024\pi\) | |||||||
\(270\) | −181337. | − | 367048.i | −0.151383 | − | 0.306418i | ||||
\(271\) | 647209. | 0.535330 | 0.267665 | − | 0.963512i | \(-0.413748\pi\) | ||||
0.267665 | + | 0.963512i | \(0.413748\pi\) | |||||||
\(272\) | − | 2.29595e6i | − | 1.88166i | ||||||
\(273\) | 267620.i | 0.217326i | ||||||||
\(274\) | −1.72980e6 | −1.39193 | ||||||||
\(275\) | −229755. | + | 300318.i | −0.183203 | + | 0.239470i | ||||
\(276\) | 916878. | 0.724501 | ||||||||
\(277\) | 679011.i | 0.531713i | 0.964013 | + | 0.265856i | \(0.0856547\pi\) | ||||
−0.964013 | + | 0.265856i | \(0.914345\pi\) | |||||||
\(278\) | 3.51821e6i | 2.73030i | ||||||||
\(279\) | −610061. | −0.469205 | ||||||||
\(280\) | −266831. | − | 540097.i | −0.203395 | − | 0.411696i | ||||
\(281\) | −1.78685e6 | −1.34997 | −0.674983 | − | 0.737834i | \(-0.735849\pi\) | ||||
−0.674983 | + | 0.737834i | \(0.735849\pi\) | |||||||
\(282\) | 540721.i | 0.404903i | ||||||||
\(283\) | 872555.i | 0.647630i | 0.946120 | + | 0.323815i | \(0.104966\pi\) | ||||
−0.946120 | + | 0.323815i | \(0.895034\pi\) | |||||||
\(284\) | −2.58876e6 | −1.90457 | ||||||||
\(285\) | −741123. | + | 366146.i | −0.540478 | + | 0.267019i | ||||
\(286\) | 1.24415e6 | 0.899411 | ||||||||
\(287\) | − | 163554.i | − | 0.117208i | ||||||
\(288\) | − | 276088.i | − | 0.196140i | ||||||
\(289\) | −859295. | −0.605198 | ||||||||
\(290\) | −2.30215e6 | + | 1.13736e6i | −1.60745 | + | 0.794149i | ||||
\(291\) | 581172. | 0.402321 | ||||||||
\(292\) | 4.04491e6i | 2.77621i | ||||||||
\(293\) | − | 653130.i | − | 0.444458i | −0.974995 | − | 0.222229i | \(-0.928667\pi\) | ||
0.974995 | − | 0.222229i | \(-0.0713332\pi\) | |||||||
\(294\) | 1.44328e6 | 0.973827 | ||||||||
\(295\) | −642366. | − | 1.30023e6i | −0.429762 | − | 0.869888i | ||||
\(296\) | 1.63519e6 | 1.08477 | ||||||||
\(297\) | 88209.0i | 0.0580259i | ||||||||
\(298\) | − | 5.21574e6i | − | 3.40232i | ||||||
\(299\) | −1.51286e6 | −0.978638 | ||||||||
\(300\) | −1.53958e6 | − | 1.17784e6i | −0.987640 | − | 0.755582i | ||||
\(301\) | 66329.8 | 0.0421980 | ||||||||
\(302\) | − | 2.31263e6i | − | 1.45911i | ||||||
\(303\) | − | 435280.i | − | 0.272372i | ||||||
\(304\) | −2.49875e6 | −1.55074 | ||||||||
\(305\) | −1.27173e6 | − | 2.57414e6i | −0.782793 | − | 1.58447i | ||||
\(306\) | −1.22847e6 | −0.750002 | ||||||||
\(307\) | − | 1.87392e6i | − | 1.13476i | −0.823456 | − | 0.567381i | \(-0.807957\pi\) | ||
0.823456 | − | 0.567381i | \(-0.192043\pi\) | |||||||
\(308\) | 242287.i | 0.145530i | ||||||||
\(309\) | −1.09731e6 | −0.653783 | ||||||||
\(310\) | −3.79214e6 | + | 1.87348e6i | −2.24119 | + | 1.10725i | ||||
\(311\) | −1.60626e6 | −0.941705 | −0.470853 | − | 0.882212i | \(-0.656054\pi\) | ||||
−0.470853 | + | 0.882212i | \(0.656054\pi\) | |||||||
\(312\) | 3.41684e6i | 1.98718i | ||||||||
\(313\) | 2.58202e6i | 1.48970i | 0.667234 | + | 0.744849i | \(0.267478\pi\) | ||||
−0.667234 | + | 0.744849i | \(0.732522\pi\) | |||||||
\(314\) | 3.30377e6 | 1.89098 | ||||||||
\(315\) | −117942. | + | 58268.4i | −0.0669718 | + | 0.0330869i | ||||
\(316\) | −570271. | −0.321265 | ||||||||
\(317\) | − | 1.34588e6i | − | 0.752242i | −0.926571 | − | 0.376121i | \(-0.877258\pi\) | ||
0.926571 | − | 0.376121i | \(-0.122742\pi\) | |||||||
\(318\) | − | 2.57662e6i | − | 1.42884i | ||||||
\(319\) | 553252. | 0.304401 | ||||||||
\(320\) | 357156. | + | 722926.i | 0.194977 | + | 0.394656i | ||||
\(321\) | −1.72695e6 | −0.935442 | ||||||||
\(322\) | − | 431403.i | − | 0.231870i | ||||||
\(323\) | 2.48047e6i | 1.32290i | ||||||||
\(324\) | −452202. | −0.239315 | ||||||||
\(325\) | 2.54033e6 | + | 1.94345e6i | 1.33408 | + | 1.02062i | ||||
\(326\) | −2.47516e6 | −1.28991 | ||||||||
\(327\) | − | 140940.i | − | 0.0728893i | ||||||
\(328\) | − | 2.08818e6i | − | 1.07172i | ||||||
\(329\) | 173748. | 0.0884971 | ||||||||
\(330\) | 270887. | + | 548307.i | 0.136931 | + | 0.277165i | ||||
\(331\) | 2.74357e6 | 1.37641 | 0.688203 | − | 0.725518i | \(-0.258400\pi\) | ||||
0.688203 | + | 0.725518i | \(0.258400\pi\) | |||||||
\(332\) | − | 1.47187e6i | − | 0.732865i | ||||||
\(333\) | − | 357080.i | − | 0.176464i | ||||||
\(334\) | 5.84089e6 | 2.86492 | ||||||||
\(335\) | 1.96367e6 | − | 970135.i | 0.955996 | − | 0.472303i | ||||
\(336\) | −397650. | −0.192156 | ||||||||
\(337\) | 3.70365e6i | 1.77646i | 0.459400 | + | 0.888229i | \(0.348064\pi\) | ||||
−0.459400 | + | 0.888229i | \(0.651936\pi\) | |||||||
\(338\) | − | 6.79399e6i | − | 3.23469i | ||||||
\(339\) | 136076. | 0.0643107 | ||||||||
\(340\) | −5.21495e6 | + | 2.57641e6i | −2.44654 | + | 1.20870i | ||||
\(341\) | 911325. | 0.424412 | ||||||||
\(342\) | 1.33698e6i | 0.618103i | ||||||||
\(343\) | − | 952047.i | − | 0.436941i | ||||||
\(344\) | 846866. | 0.385850 | ||||||||
\(345\) | −329393. | − | 666731.i | −0.148993 | − | 0.301580i | ||||
\(346\) | −2.65868e6 | −1.19392 | ||||||||
\(347\) | − | 1.17221e6i | − | 0.522616i | −0.965255 | − | 0.261308i | \(-0.915846\pi\) | ||
0.965255 | − | 0.261308i | \(-0.0841539\pi\) | |||||||
\(348\) | 2.83624e6i | 1.25543i | ||||||||
\(349\) | 360082. | 0.158248 | 0.0791240 | − | 0.996865i | \(-0.474788\pi\) | ||||
0.0791240 | + | 0.996865i | \(0.474788\pi\) | |||||||
\(350\) | −554187. | + | 724392.i | −0.241817 | + | 0.316085i | ||||
\(351\) | 746141. | 0.323261 | ||||||||
\(352\) | 412428.i | 0.177415i | ||||||||
\(353\) | − | 998723.i | − | 0.426588i | −0.976988 | − | 0.213294i | \(-0.931581\pi\) | ||
0.976988 | − | 0.213294i | \(-0.0684192\pi\) | |||||||
\(354\) | −2.34560e6 | −0.994824 | ||||||||
\(355\) | 930025. | + | 1.88248e6i | 0.391673 | + | 0.792793i | ||||
\(356\) | 5.40256e6 | 2.25930 | ||||||||
\(357\) | 394740.i | 0.163923i | ||||||||
\(358\) | 139504.i | 0.0575282i | ||||||||
\(359\) | −1.47706e6 | −0.604871 | −0.302436 | − | 0.953170i | \(-0.597800\pi\) | ||||
−0.302436 | + | 0.953170i | \(0.597800\pi\) | |||||||
\(360\) | −1.50583e6 | + | 743941.i | −0.612376 | + | 0.302540i | ||||
\(361\) | 223465. | 0.0902489 | ||||||||
\(362\) | − | 7.56057e6i | − | 3.03238i | ||||||
\(363\) | − | 131769.i | − | 0.0524864i | ||||||
\(364\) | 2.04945e6 | 0.810746 | ||||||||
\(365\) | 2.94136e6 | − | 1.45316e6i | 1.15562 | − | 0.570926i | ||||
\(366\) | −4.64374e6 | −1.81203 | ||||||||
\(367\) | 3.21905e6i | 1.24756i | 0.781599 | + | 0.623781i | \(0.214404\pi\) | ||||
−0.781599 | + | 0.623781i | \(0.785596\pi\) | |||||||
\(368\) | − | 2.24793e6i | − | 0.865294i | ||||||
\(369\) | −455999. | −0.174340 | ||||||||
\(370\) | −1.09658e6 | − | 2.21961e6i | −0.416424 | − | 0.842892i | ||||
\(371\) | −827935. | −0.312292 | ||||||||
\(372\) | 4.67190e6i | 1.75039i | ||||||||
\(373\) | 4.65790e6i | 1.73348i | 0.498762 | + | 0.866739i | \(0.333788\pi\) | ||||
−0.498762 | + | 0.866739i | \(0.666212\pi\) | |||||||
\(374\) | 1.83513e6 | 0.678403 | ||||||||
\(375\) | −303391. | + | 1.54269e6i | −0.111410 | + | 0.566499i | ||||
\(376\) | 2.21832e6 | 0.809198 | ||||||||
\(377\) | − | 4.67984e6i | − | 1.69581i | ||||||
\(378\) | 212767.i | 0.0765905i | ||||||||
\(379\) | 4.04644e6 | 1.44702 | 0.723510 | − | 0.690314i | \(-0.242528\pi\) | ||||
0.723510 | + | 0.690314i | \(0.242528\pi\) | |||||||
\(380\) | 2.80398e6 | + | 5.67558e6i | 0.996129 | + | 2.01628i | ||||
\(381\) | −2.01376e6 | −0.710714 | ||||||||
\(382\) | − | 255331.i | − | 0.0895252i | ||||||
\(383\) | − | 824148.i | − | 0.287084i | −0.989644 | − | 0.143542i | \(-0.954151\pi\) | ||
0.989644 | − | 0.143542i | \(-0.0458491\pi\) | |||||||
\(384\) | 2.28580e6 | 0.791062 | ||||||||
\(385\) | 176185. | − | 87042.9i | 0.0605783 | − | 0.0299283i | ||||
\(386\) | −4.92077e6 | −1.68099 | ||||||||
\(387\) | − | 184932.i | − | 0.0627674i | ||||||
\(388\) | − | 4.45066e6i | − | 1.50088i | ||||||
\(389\) | 2.54462e6 | 0.852607 | 0.426303 | − | 0.904580i | \(-0.359816\pi\) | ||||
0.426303 | + | 0.904580i | \(0.359816\pi\) | |||||||
\(390\) | 4.63801e6 | − | 2.29137e6i | 1.54408 | − | 0.762841i | ||||
\(391\) | −2.23148e6 | −0.738162 | ||||||||
\(392\) | − | 5.92109e6i | − | 1.94620i | ||||||
\(393\) | − | 2.42330e6i | − | 0.791453i | ||||||
\(394\) | 3.26322e6 | 1.05902 | ||||||||
\(395\) | 204873. | + | 414687.i | 0.0660681 | + | 0.133730i | ||||
\(396\) | 675512. | 0.216469 | ||||||||
\(397\) | − | 5.17776e6i | − | 1.64879i | −0.566015 | − | 0.824395i | \(-0.691516\pi\) | ||
0.566015 | − | 0.824395i | \(-0.308484\pi\) | |||||||
\(398\) | 4.00351e6i | 1.26687i | ||||||||
\(399\) | 429607. | 0.135095 | ||||||||
\(400\) | −2.88773e6 | + | 3.77462e6i | −0.902414 | + | 1.17957i | ||||
\(401\) | −4.82239e6 | −1.49762 | −0.748809 | − | 0.662785i | \(-0.769374\pi\) | ||||
−0.748809 | + | 0.662785i | \(0.769374\pi\) | |||||||
\(402\) | − | 3.54245e6i | − | 1.09330i | ||||||
\(403\) | − | 7.70871e6i | − | 2.36439i | ||||||
\(404\) | −3.33341e6 | −1.01610 | ||||||||
\(405\) | 162456. | + | 328830.i | 0.0492150 | + | 0.0996171i | ||||
\(406\) | 1.33449e6 | 0.401790 | ||||||||
\(407\) | 533416.i | 0.159617i | ||||||||
\(408\) | 5.03985e6i | 1.49888i | ||||||||
\(409\) | 3.68626e6 | 1.08963 | 0.544813 | − | 0.838558i | \(-0.316601\pi\) | ||||
0.544813 | + | 0.838558i | \(0.316601\pi\) | |||||||
\(410\) | −2.83449e6 | + | 1.40036e6i | −0.832751 | + | 0.411414i | ||||
\(411\) | 1.54968e6 | 0.452521 | ||||||||
\(412\) | 8.40329e6i | 2.43897i | ||||||||
\(413\) | 753702.i | 0.217433i | ||||||||
\(414\) | −1.20278e6 | −0.344894 | ||||||||
\(415\) | −1.07031e6 | + | 528777.i | −0.305062 | + | 0.150713i | ||||
\(416\) | 3.48864e6 | 0.988377 | ||||||||
\(417\) | − | 3.15188e6i | − | 0.887626i | ||||||
\(418\) | − | 1.99722e6i | − | 0.559095i | ||||||
\(419\) | −1.31904e6 | −0.367049 | −0.183525 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183525 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(420\) | 446224. | + | 903210.i | 0.123432 | + | 0.249842i | ||||
\(421\) | −3.29518e6 | −0.906095 | −0.453048 | − | 0.891486i | \(-0.649663\pi\) | ||||
−0.453048 | + | 0.891486i | \(0.649663\pi\) | |||||||
\(422\) | − | 8.72643e6i | − | 2.38537i | ||||||
\(423\) | − | 484419.i | − | 0.131635i | ||||||
\(424\) | −1.05707e7 | −2.85553 | ||||||||
\(425\) | 3.74700e6 | + | 2.86659e6i | 1.00626 | + | 0.769828i | ||||
\(426\) | 3.39599e6 | 0.906655 | ||||||||
\(427\) | 1.49215e6i | 0.396044i | ||||||||
\(428\) | 1.32251e7i | 3.48972i | ||||||||
\(429\) | −1.11461e6 | −0.292400 | ||||||||
\(430\) | −567919. | − | 1.14953e6i | −0.148120 | − | 0.299813i | ||||
\(431\) | 1.87137e6 | 0.485251 | 0.242625 | − | 0.970120i | \(-0.421991\pi\) | ||||
0.242625 | + | 0.970120i | \(0.421991\pi\) | |||||||
\(432\) | 1.10867e6i | 0.285821i | ||||||||
\(433\) | − | 4.31194e6i | − | 1.10523i | −0.833437 | − | 0.552615i | \(-0.813630\pi\) | ||
0.833437 | − | 0.552615i | \(-0.186370\pi\) | |||||||
\(434\) | 2.19819e6 | 0.560197 | ||||||||
\(435\) | 2.06244e6 | − | 1.01893e6i | 0.522586 | − | 0.258180i | ||||
\(436\) | −1.07933e6 | −0.271917 | ||||||||
\(437\) | 2.42859e6i | 0.608345i | ||||||||
\(438\) | − | 5.30620e6i | − | 1.32159i | ||||||
\(439\) | −1.13612e6 | −0.281360 | −0.140680 | − | 0.990055i | \(-0.544929\pi\) | ||||
−0.140680 | + | 0.990055i | \(0.544929\pi\) | |||||||
\(440\) | 2.24944e6 | − | 1.11132e6i | 0.553915 | − | 0.273658i | ||||
\(441\) | −1.29300e6 | −0.316593 | ||||||||
\(442\) | − | 1.55230e7i | − | 3.77936i | ||||||
\(443\) | 875875.i | 0.212047i | 0.994364 | + | 0.106024i | \(0.0338119\pi\) | ||||
−0.994364 | + | 0.106024i | \(0.966188\pi\) | |||||||
\(444\) | −2.73455e6 | −0.658306 | ||||||||
\(445\) | −1.94090e6 | − | 3.92860e6i | −0.464625 | − | 0.940456i | ||||
\(446\) | −487955. | −0.116156 | ||||||||
\(447\) | 4.67266e6i | 1.10610i | ||||||||
\(448\) | − | 419059.i | − | 0.0986461i | ||||||
\(449\) | −4.08806e6 | −0.956977 | −0.478489 | − | 0.878094i | \(-0.658815\pi\) | ||||
−0.478489 | + | 0.878094i | \(0.658815\pi\) | |||||||
\(450\) | 2.01965e6 | + | 1.54511e6i | 0.470159 | + | 0.359689i | ||||
\(451\) | 681184. | 0.157697 | ||||||||
\(452\) | − | 1.04208e6i | − | 0.239915i | ||||||
\(453\) | 2.07183e6i | 0.474361i | ||||||||
\(454\) | −790317. | −0.179954 | ||||||||
\(455\) | −736277. | − | 1.49031e6i | −0.166730 | − | 0.337480i | ||||
\(456\) | 5.48501e6 | 1.23528 | ||||||||
\(457\) | 2.85279e6i | 0.638968i | 0.947592 | + | 0.319484i | \(0.103510\pi\) | ||||
−0.947592 | + | 0.319484i | \(0.896490\pi\) | |||||||
\(458\) | 3.25581e6i | 0.725263i | ||||||||
\(459\) | 1.10056e6 | 0.243827 | ||||||||
\(460\) | −5.10588e6 | + | 2.52252e6i | −1.12506 | + | 0.555828i | ||||
\(461\) | 6.16387e6 | 1.35083 | 0.675416 | − | 0.737437i | \(-0.263964\pi\) | ||||
0.675416 | + | 0.737437i | \(0.263964\pi\) | |||||||
\(462\) | − | 317837.i | − | 0.0692787i | ||||||
\(463\) | 4.52412e6i | 0.980804i | 0.871496 | + | 0.490402i | \(0.163150\pi\) | ||||
−0.871496 | + | 0.490402i | \(0.836850\pi\) | |||||||
\(464\) | 6.95366e6 | 1.49940 | ||||||||
\(465\) | 3.39728e6 | − | 1.67840e6i | 0.728617 | − | 0.359968i | ||||
\(466\) | 1.27412e7 | 2.71798 | ||||||||
\(467\) | 2.23084e6i | 0.473344i | 0.971590 | + | 0.236672i | \(0.0760567\pi\) | ||||
−0.971590 | + | 0.236672i | \(0.923943\pi\) | |||||||
\(468\) | − | 5.71401e6i | − | 1.20594i | ||||||
\(469\) | −1.13828e6 | −0.238956 | ||||||||
\(470\) | −1.48763e6 | − | 3.01115e6i | −0.310636 | − | 0.628764i | ||||
\(471\) | −2.95977e6 | −0.614761 | ||||||||
\(472\) | 9.62289e6i | 1.98816i | ||||||||
\(473\) | 276256.i | 0.0567752i | ||||||||
\(474\) | 748093. | 0.152936 | ||||||||
\(475\) | 3.11980e6 | − | 4.07796e6i | 0.634443 | − | 0.829296i | ||||
\(476\) | 3.02295e6 | 0.611525 | ||||||||
\(477\) | 2.30834e6i | 0.464518i | ||||||||
\(478\) | 1.36004e7i | 2.72259i | ||||||||
\(479\) | 6.62215e6 | 1.31874 | 0.659372 | − | 0.751817i | \(-0.270822\pi\) | ||||
0.659372 | + | 0.751817i | \(0.270822\pi\) | |||||||
\(480\) | 759575. | + | 1.53747e6i | 0.150476 | + | 0.304581i | ||||
\(481\) | 4.51205e6 | 0.889224 | ||||||||
\(482\) | 1.14723e7i | 2.24923i | ||||||||
\(483\) | 386484.i | 0.0753813i | ||||||||
\(484\) | −1.00910e6 | −0.195803 | ||||||||
\(485\) | −3.23641e6 | + | 1.59892e6i | −0.624754 | + | 0.308655i | ||||
\(486\) | 593208. | 0.113924 | ||||||||
\(487\) | 2.17583e6i | 0.415721i | 0.978158 | + | 0.207860i | \(0.0666500\pi\) | ||||
−0.978158 | + | 0.207860i | \(0.933350\pi\) | |||||||
\(488\) | 1.90511e7i | 3.62134i | ||||||||
\(489\) | 2.21744e6 | 0.419353 | ||||||||
\(490\) | −8.03728e6 | + | 3.97076e6i | −1.51223 | + | 0.747107i | ||||
\(491\) | 7.67198e6 | 1.43616 | 0.718081 | − | 0.695959i | \(-0.245021\pi\) | ||||
0.718081 | + | 0.695959i | \(0.245021\pi\) | |||||||
\(492\) | 3.49208e6i | 0.650386i | ||||||||
\(493\) | − | 6.90278e6i | − | 1.27911i | ||||||
\(494\) | −1.68941e7 | −3.11471 | ||||||||
\(495\) | −242681. | − | 491215.i | −0.0445167 | − | 0.0901070i | ||||
\(496\) | 1.14542e7 | 2.09055 | ||||||||
\(497\) | − | 1.09122e6i | − | 0.198162i | ||||||
\(498\) | 1.93083e6i | 0.348875i | ||||||||
\(499\) | −6.65009e6 | −1.19557 | −0.597787 | − | 0.801655i | \(-0.703953\pi\) | ||||
−0.597787 | + | 0.801655i | \(0.703953\pi\) | |||||||
\(500\) | 1.18140e7 | + | 2.32339e6i | 2.11335 | + | 0.415621i | ||||
\(501\) | −5.23272e6 | −0.931393 | ||||||||
\(502\) | − | 3.23058e6i | − | 0.572165i | ||||||
\(503\) | − | 4.18197e6i | − | 0.736989i | −0.929630 | − | 0.368495i | \(-0.879873\pi\) | ||
0.929630 | − | 0.368495i | \(-0.120127\pi\) | |||||||
\(504\) | 872882. | 0.153066 | ||||||||
\(505\) | 1.19754e6 | + | 2.42397e6i | 0.208960 | + | 0.422959i | ||||
\(506\) | 1.79675e6 | 0.311968 | ||||||||
\(507\) | 6.08657e6i | 1.05161i | ||||||||
\(508\) | 1.54215e7i | 2.65135i | ||||||||
\(509\) | 1.01322e7 | 1.73345 | 0.866725 | − | 0.498787i | \(-0.166221\pi\) | ||||
0.866725 | + | 0.498787i | \(0.166221\pi\) | |||||||
\(510\) | 6.84108e6 | − | 3.37978e6i | 1.16466 | − | 0.575392i | ||||
\(511\) | −1.70502e6 | −0.288853 | ||||||||
\(512\) | − | 1.28679e7i | − | 2.16936i | ||||||
\(513\) | − | 1.19777e6i | − | 0.200947i | ||||||
\(514\) | −1.44939e7 | −2.41980 | ||||||||
\(515\) | 6.11066e6 | − | 3.01893e6i | 1.01524 | − | 0.501573i | ||||
\(516\) | −1.41622e6 | −0.234157 | ||||||||
\(517\) | 723639.i | 0.119068i | ||||||||
\(518\) | 1.28664e6i | 0.210685i | ||||||||
\(519\) | 2.38185e6 | 0.388147 | ||||||||
\(520\) | −9.40042e6 | − | 1.90275e7i | −1.52454 | − | 3.08585i | ||||
\(521\) | −6.42546e6 | −1.03707 | −0.518537 | − | 0.855055i | \(-0.673523\pi\) | ||||
−0.518537 | + | 0.855055i | \(0.673523\pi\) | |||||||
\(522\) | − | 3.72063e6i | − | 0.597641i | ||||||
\(523\) | 1.17398e6i | 0.187674i | 0.995588 | + | 0.0938372i | \(0.0299133\pi\) | ||||
−0.995588 | + | 0.0938372i | \(0.970087\pi\) | |||||||
\(524\) | −1.85578e7 | −2.95256 | ||||||||
\(525\) | 496483. | − | 648965.i | 0.0786151 | − | 0.102760i | ||||
\(526\) | 8.42478e6 | 1.32768 | ||||||||
\(527\) | − | 1.13704e7i | − | 1.78340i | ||||||
\(528\) | − | 1.65617e6i | − | 0.258535i | ||||||
\(529\) | 4.25153e6 | 0.660551 | ||||||||
\(530\) | 7.08882e6 | + | 1.43486e7i | 1.09619 | + | 2.21881i | ||||
\(531\) | 2.10137e6 | 0.323419 | ||||||||
\(532\) | − | 3.28997e6i | − | 0.503979i | ||||||
\(533\) | − | 5.76199e6i | − | 0.878525i | ||||||
\(534\) | −7.08719e6 | −1.07553 | ||||||||
\(535\) | 9.61697e6 | − | 4.75119e6i | 1.45263 | − | 0.717659i | ||||
\(536\) | −1.45330e7 | −2.18496 | ||||||||
\(537\) | − | 124979.i | − | 0.0187025i | ||||||
\(538\) | 4.17174e6i | 0.621386i | ||||||||
\(539\) | 1.93152e6 | 0.286370 | ||||||||
\(540\) | 2.51821e6 | − | 1.24410e6i | 0.371627 | − | 0.183599i | ||||
\(541\) | −5.25283e6 | −0.771614 | −0.385807 | − | 0.922580i | \(-0.626077\pi\) | ||||
−0.385807 | + | 0.922580i | \(0.626077\pi\) | |||||||
\(542\) | 6.50188e6i | 0.950694i | ||||||||
\(543\) | 6.77334e6i | 0.985833i | ||||||||
\(544\) | 5.14576e6 | 0.745508 | ||||||||
\(545\) | 387754. | + | 784860.i | 0.0559197 | + | 0.113188i | ||||
\(546\) | −2.68852e6 | −0.385950 | ||||||||
\(547\) | 1.13849e7i | 1.62689i | 0.581640 | + | 0.813447i | \(0.302411\pi\) | ||||
−0.581640 | + | 0.813447i | \(0.697589\pi\) | |||||||
\(548\) | − | 1.18676e7i | − | 1.68815i | ||||||
\(549\) | 4.16022e6 | 0.589095 | ||||||||
\(550\) | −3.01701e6 | − | 2.30813e6i | −0.425275 | − | 0.325351i | ||||
\(551\) | −7.51249e6 | −1.05416 | ||||||||
\(552\) | 4.93444e6i | 0.689271i | ||||||||
\(553\) | − | 240382.i | − | 0.0334263i | ||||||
\(554\) | −6.82136e6 | −0.944271 | ||||||||
\(555\) | 982400. | + | 1.98849e6i | 0.135380 | + | 0.274026i | ||||
\(556\) | −2.41374e7 | −3.31134 | ||||||||
\(557\) | 4.54355e6i | 0.620522i | 0.950651 | + | 0.310261i | \(0.100416\pi\) | ||||
−0.950651 | + | 0.310261i | \(0.899584\pi\) | |||||||
\(558\) | − | 6.12869e6i | − | 0.833263i | ||||||
\(559\) | 2.33679e6 | 0.316293 | ||||||||
\(560\) | 2.21442e6 | − | 1.09402e6i | 0.298394 | − | 0.147419i | ||||
\(561\) | −1.64405e6 | −0.220550 | ||||||||
\(562\) | − | 1.79508e7i | − | 2.39741i | ||||||
\(563\) | 1.22077e7i | 1.62317i | 0.584237 | + | 0.811583i | \(0.301394\pi\) | ||||
−0.584237 | + | 0.811583i | \(0.698606\pi\) | |||||||
\(564\) | −3.70972e6 | −0.491070 | ||||||||
\(565\) | −757777. | + | 374374.i | −0.0998666 | + | 0.0493383i | ||||
\(566\) | −8.76572e6 | −1.15013 | ||||||||
\(567\) | − | 190613.i | − | 0.0248997i | ||||||
\(568\) | − | 1.39321e7i | − | 1.81195i | ||||||
\(569\) | 1.58948e6 | 0.205814 | 0.102907 | − | 0.994691i | \(-0.467186\pi\) | ||||
0.102907 | + | 0.994691i | \(0.467186\pi\) | |||||||
\(570\) | −3.67832e6 | − | 7.44535e6i | −0.474201 | − | 0.959838i | ||||
\(571\) | −692853. | −0.0889306 | −0.0444653 | − | 0.999011i | \(-0.514158\pi\) | ||||
−0.0444653 | + | 0.999011i | \(0.514158\pi\) | |||||||
\(572\) | 8.53574e6i | 1.09082i | ||||||||
\(573\) | 228745.i | 0.0291048i | ||||||||
\(574\) | 1.64307e6 | 0.208150 | ||||||||
\(575\) | 3.66863e6 | + | 2.80664e6i | 0.462737 | + | 0.354011i | ||||
\(576\) | −1.16836e6 | −0.146731 | ||||||||
\(577\) | 1.24815e7i | 1.56073i | 0.625324 | + | 0.780365i | \(0.284967\pi\) | ||||
−0.625324 | + | 0.780365i | \(0.715033\pi\) | |||||||
\(578\) | − | 8.63250e6i | − | 1.07477i | ||||||
\(579\) | 4.40840e6 | 0.546493 | ||||||||
\(580\) | −7.80306e6 | − | 1.57943e7i | −0.963153 | − | 1.94954i | ||||
\(581\) | 620425. | 0.0762516 | ||||||||
\(582\) | 5.83847e6i | 0.714483i | ||||||||
\(583\) | − | 3.44825e6i | − | 0.420173i | ||||||
\(584\) | −2.17688e7 | −2.64121 | ||||||||
\(585\) | −4.15508e6 | + | 2.05279e6i | −0.501984 | + | 0.248001i | ||||
\(586\) | 6.56136e6 | 0.789314 | ||||||||
\(587\) | − | 9.13291e6i | − | 1.09399i | −0.837135 | − | 0.546996i | \(-0.815771\pi\) | ||
0.837135 | − | 0.546996i | \(-0.184229\pi\) | |||||||
\(588\) | 9.90189e6i | 1.18107i | ||||||||
\(589\) | −1.23747e7 | −1.46976 | ||||||||
\(590\) | 1.30621e7 | − | 6.45323e6i | 1.54484 | − | 0.763216i | ||||
\(591\) | −2.92344e6 | −0.344291 | ||||||||
\(592\) | 6.70436e6i | 0.786236i | ||||||||
\(593\) | − | 1.08272e7i | − | 1.26438i | −0.774813 | − | 0.632191i | \(-0.782156\pi\) | ||
0.774813 | − | 0.632191i | \(-0.217844\pi\) | |||||||
\(594\) | −886150. | −0.103048 | ||||||||
\(595\) | −1.08601e6 | − | 2.19822e6i | −0.125760 | − | 0.254553i | ||||
\(596\) | 3.57836e7 | 4.12637 | ||||||||
\(597\) | − | 3.58665e6i | − | 0.411863i | ||||||
\(598\) | − | 1.51983e7i | − | 1.73797i | ||||||
\(599\) | −7.47502e6 | −0.851227 | −0.425614 | − | 0.904905i | \(-0.639942\pi\) | ||||
−0.425614 | + | 0.904905i | \(0.639942\pi\) | |||||||
\(600\) | 6.33885e6 | − | 8.28567e6i | 0.718840 | − | 0.939614i | ||||
\(601\) | −1.02516e6 | −0.115772 | −0.0578861 | − | 0.998323i | \(-0.518436\pi\) | ||||
−0.0578861 | + | 0.998323i | \(0.518436\pi\) | |||||||
\(602\) | 666351.i | 0.0749397i | ||||||||
\(603\) | 3.17360e6i | 0.355434i | ||||||||
\(604\) | 1.58662e7 | 1.76963 | ||||||||
\(605\) | 362524. | + | 733790.i | 0.0402669 | + | 0.0815049i | ||||
\(606\) | 4.37283e6 | 0.483706 | ||||||||
\(607\) | 1.33264e7i | 1.46805i | 0.679123 | + | 0.734024i | \(0.262360\pi\) | ||||
−0.679123 | + | 0.734024i | \(0.737640\pi\) | |||||||
\(608\) | − | 5.60028e6i | − | 0.614399i | ||||||
\(609\) | −1.19553e6 | −0.130623 | ||||||||
\(610\) | 2.58599e7 | − | 1.27759e7i | 2.81386 | − | 1.39017i | ||||
\(611\) | 6.12110e6 | 0.663325 | ||||||||
\(612\) | − | 8.42819e6i | − | 0.909611i | ||||||
\(613\) | 1.57435e7i | 1.69220i | 0.533027 | + | 0.846098i | \(0.321054\pi\) | ||||
−0.533027 | + | 0.846098i | \(0.678946\pi\) | |||||||
\(614\) | 1.88254e7 | 2.01523 | ||||||||
\(615\) | 2.53935e6 | − | 1.25455e6i | 0.270729 | − | 0.133752i | ||||
\(616\) | −1.30394e6 | −0.138454 | ||||||||
\(617\) | − | 5.87960e6i | − | 0.621777i | −0.950446 | − | 0.310888i | \(-0.899373\pi\) | ||
0.950446 | − | 0.310888i | \(-0.100627\pi\) | |||||||
\(618\) | − | 1.10236e7i | − | 1.16106i | ||||||
\(619\) | 1.81138e6 | 0.190013 | 0.0950063 | − | 0.995477i | \(-0.469713\pi\) | ||||
0.0950063 | + | 0.995477i | \(0.469713\pi\) | |||||||
\(620\) | −1.28533e7 | − | 2.60167e7i | −1.34288 | − | 2.71814i | ||||
\(621\) | 1.07754e6 | 0.112126 | ||||||||
\(622\) | − | 1.61365e7i | − | 1.67238i | ||||||
\(623\) | 2.27730e6i | 0.235071i | ||||||||
\(624\) | −1.40092e7 | −1.44029 | ||||||||
\(625\) | −2.55473e6 | − | 9.42554e6i | −0.261605 | − | 0.965175i | ||||
\(626\) | −2.59390e7 | −2.64556 | ||||||||
\(627\) | 1.78927e6i | 0.181763i | ||||||||
\(628\) | 2.26662e7i | 2.29340i | ||||||||
\(629\) | 6.65529e6 | 0.670719 | ||||||||
\(630\) | −585366. | − | 1.18485e6i | −0.0587592 | − | 0.118936i | ||||
\(631\) | −1.43835e7 | −1.43811 | −0.719054 | − | 0.694954i | \(-0.755425\pi\) | ||||
−0.719054 | + | 0.694954i | \(0.755425\pi\) | |||||||
\(632\) | − | 3.06907e6i | − | 0.305643i | ||||||
\(633\) | 7.81780e6i | 0.775489i | ||||||||
\(634\) | 1.35207e7 | 1.33591 | ||||||||
\(635\) | 1.12141e7 | − | 5.54026e6i | 1.10365 | − | 0.545250i | ||||
\(636\) | 1.76774e7 | 1.73291 | ||||||||
\(637\) | − | 1.63383e7i | − | 1.59536i | ||||||
\(638\) | 5.55798e6i | 0.540587i | ||||||||
\(639\) | −3.04239e6 | −0.294756 | ||||||||
\(640\) | −1.27291e7 | + | 6.28871e6i | −1.22842 | + | 0.606893i | ||||
\(641\) | −3.80867e6 | −0.366124 | −0.183062 | − | 0.983101i | \(-0.558601\pi\) | ||||
−0.183062 | + | 0.983101i | \(0.558601\pi\) | |||||||
\(642\) | − | 1.73490e7i | − | 1.66126i | ||||||
\(643\) | − | 483920.i | − | 0.0461579i | −0.999734 | − | 0.0230789i | \(-0.992653\pi\) | ||
0.999734 | − | 0.0230789i | \(-0.00734691\pi\) | |||||||
\(644\) | 2.95973e6 | 0.281214 | ||||||||
\(645\) | 508785. | + | 1.02984e6i | 0.0481543 | + | 0.0974699i | ||||
\(646\) | −2.49188e7 | −2.34934 | ||||||||
\(647\) | 1.80652e7i | 1.69661i | 0.529506 | + | 0.848306i | \(0.322377\pi\) | ||||
−0.529506 | + | 0.848306i | \(0.677623\pi\) | |||||||
\(648\) | − | 2.43365e6i | − | 0.227678i | ||||||
\(649\) | −3.13908e6 | −0.292544 | ||||||||
\(650\) | −1.95239e7 | + | 2.55202e7i | −1.81252 | + | 2.36920i | ||||
\(651\) | −1.96931e6 | −0.182121 | ||||||||
\(652\) | − | 1.69813e7i | − | 1.56442i | ||||||
\(653\) | − | 2.03744e7i | − | 1.86983i | −0.354871 | − | 0.934915i | \(-0.615475\pi\) | ||
0.354871 | − | 0.934915i | \(-0.384525\pi\) | |||||||
\(654\) | 1.41588e6 | 0.129444 | ||||||||
\(655\) | 6.66698e6 | + | 1.34948e7i | 0.607192 | + | 1.22903i | ||||
\(656\) | 8.56161e6 | 0.776776 | ||||||||
\(657\) | 4.75370e6i | 0.429653i | ||||||||
\(658\) | 1.74547e6i | 0.157162i | ||||||||
\(659\) | 1.37586e7 | 1.23413 | 0.617066 | − | 0.786912i | \(-0.288321\pi\) | ||||
0.617066 | + | 0.786912i | \(0.288321\pi\) | |||||||
\(660\) | −3.76176e6 | + | 1.85847e6i | −0.336149 | + | 0.166072i | ||||
\(661\) | −1.34803e7 | −1.20004 | −0.600019 | − | 0.799985i | \(-0.704840\pi\) | ||||
−0.600019 | + | 0.799985i | \(0.704840\pi\) | |||||||
\(662\) | 2.75620e7i | 2.44437i | ||||||||
\(663\) | 1.39066e7i | 1.22868i | ||||||||
\(664\) | 7.92127e6 | 0.697228 | ||||||||
\(665\) | −2.39238e6 | + | 1.18194e6i | −0.209786 | + | 0.103643i | ||||
\(666\) | 3.58724e6 | 0.313382 | ||||||||
\(667\) | − | 6.75840e6i | − | 0.588206i | ||||||
\(668\) | 4.00726e7i | 3.47461i | ||||||||
\(669\) | 437147. | 0.0377627 | ||||||||
\(670\) | 9.74601e6 | + | 1.97271e7i | 0.838764 | + | 1.69776i | ||||
\(671\) | −6.21465e6 | −0.532856 | ||||||||
\(672\) | − | 891226.i | − | 0.0761315i | ||||||
\(673\) | 680925.i | 0.0579511i | 0.999580 | + | 0.0289755i | \(0.00922449\pi\) | ||||
−0.999580 | + | 0.0289755i | \(0.990776\pi\) | |||||||
\(674\) | −3.72070e7 | −3.15482 | ||||||||
\(675\) | −1.80936e6 | − | 1.38423e6i | −0.152850 | − | 0.116936i | ||||
\(676\) | 4.66115e7 | 3.92307 | ||||||||
\(677\) | 1.36705e7i | 1.14634i | 0.819436 | + | 0.573171i | \(0.194287\pi\) | ||||
−0.819436 | + | 0.573171i | \(0.805713\pi\) | |||||||
\(678\) | 1.36703e6i | 0.114210i | ||||||||
\(679\) | 1.87605e6 | 0.156160 | ||||||||
\(680\) | −1.38657e7 | − | 2.80657e7i | −1.14992 | − | 2.32758i | ||||
\(681\) | 708026. | 0.0585034 | ||||||||
\(682\) | 9.15520e6i | 0.753715i | ||||||||
\(683\) | − | 6.79648e6i | − | 0.557484i | −0.960366 | − | 0.278742i | \(-0.910083\pi\) | ||
0.960366 | − | 0.278742i | \(-0.0899174\pi\) | |||||||
\(684\) | −9.17264e6 | −0.749642 | ||||||||
\(685\) | −8.62983e6 | + | 4.26350e6i | −0.702709 | + | 0.347168i | ||||
\(686\) | 9.56429e6 | 0.775966 | ||||||||
\(687\) | − | 2.91681e6i | − | 0.235785i | ||||||
\(688\) | 3.47218e6i | 0.279661i | ||||||||
\(689\) | −2.91680e7 | −2.34077 | ||||||||
\(690\) | 6.69800e6 | − | 3.30909e6i | 0.535577 | − | 0.264598i | ||||
\(691\) | 9.11491e6 | 0.726202 | 0.363101 | − | 0.931750i | \(-0.381718\pi\) | ||||
0.363101 | + | 0.931750i | \(0.381718\pi\) | |||||||
\(692\) | − | 1.82404e7i | − | 1.44800i | ||||||
\(693\) | 284743.i | 0.0225227i | ||||||||
\(694\) | 1.17761e7 | 0.928116 | ||||||||
\(695\) | 8.67148e6 | + | 1.75521e7i | 0.680975 | + | 1.37837i | ||||
\(696\) | −1.52640e7 | −1.19439 | ||||||||
\(697\) | − | 8.49896e6i | − | 0.662649i | ||||||
\(698\) | 3.61740e6i | 0.281033i | ||||||||
\(699\) | −1.14146e7 | −0.883621 | ||||||||
\(700\) | −4.96983e6 | − | 3.80211e6i | −0.383351 | − | 0.293278i | ||||
\(701\) | −1.03729e7 | −0.797269 | −0.398634 | − | 0.917110i | \(-0.630516\pi\) | ||||
−0.398634 | + | 0.917110i | \(0.630516\pi\) | |||||||
\(702\) | 7.49575e6i | 0.574080i | ||||||||
\(703\) | − | 7.24315e6i | − | 0.552763i | ||||||
\(704\) | 1.74533e6 | 0.132723 | ||||||||
\(705\) | 1.33274e6 | + | 2.69762e6i | 0.100988 | + | 0.204412i | ||||
\(706\) | 1.00332e7 | 0.757579 | ||||||||
\(707\) | − | 1.40510e6i | − | 0.105721i | ||||||
\(708\) | − | 1.60925e7i | − | 1.20653i | ||||||
\(709\) | −1.78828e7 | −1.33604 | −0.668022 | − | 0.744142i | \(-0.732859\pi\) | ||||
−0.668022 | + | 0.744142i | \(0.732859\pi\) | |||||||
\(710\) | −1.89115e7 | + | 9.34306e6i | −1.40792 | + | 0.695574i | ||||
\(711\) | −670199. | −0.0497199 | ||||||||
\(712\) | 2.90754e7i | 2.14944i | ||||||||
\(713\) | − | 1.11326e7i | − | 0.820108i | ||||||
\(714\) | −3.96557e6 | −0.291112 | ||||||||
\(715\) | 6.20697e6 | − | 3.06651e6i | 0.454062 | − | 0.224326i | ||||
\(716\) | −957097. | −0.0697708 | ||||||||
\(717\) | − | 1.21843e7i | − | 0.885119i | ||||||
\(718\) | − | 1.48386e7i | − | 1.07419i | ||||||
\(719\) | 2.62904e7 | 1.89660 | 0.948298 | − | 0.317382i | \(-0.102804\pi\) | ||||
0.948298 | + | 0.317382i | \(0.102804\pi\) | |||||||
\(720\) | −3.05019e6 | − | 6.17394e6i | −0.219278 | − | 0.443845i | ||||
\(721\) | −3.54217e6 | −0.253765 | ||||||||
\(722\) | 2.24494e6i | 0.160273i | ||||||||
\(723\) | − | 1.02778e7i | − | 0.731231i | ||||||
\(724\) | 5.18708e7 | 3.67770 | ||||||||
\(725\) | −8.68194e6 | + | 1.13484e7i | −0.613440 | + | 0.801842i | ||||
\(726\) | 1.32376e6 | 0.0932108 | ||||||||
\(727\) | 1.40763e7i | 0.987763i | 0.869529 | + | 0.493882i | \(0.164422\pi\) | ||||
−0.869529 | + | 0.493882i | \(0.835578\pi\) | |||||||
\(728\) | 1.10297e7i | 0.771322i | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 1.45984e7 | + | 2.95490e7i | 1.01391 | + | 2.05227i | ||||
\(731\) | 3.44677e6 | 0.238572 | ||||||||
\(732\) | − | 3.18593e7i | − | 2.19765i | ||||||
\(733\) | 5.60463e6i | 0.385290i | 0.981269 | + | 0.192645i | \(0.0617065\pi\) | ||||
−0.981269 | + | 0.192645i | \(0.938293\pi\) | |||||||
\(734\) | −3.23387e7 | −2.21555 | ||||||||
\(735\) | 7.20041e6 | − | 3.55731e6i | 0.491630 | − | 0.242886i | ||||
\(736\) | 5.03813e6 | 0.342827 | ||||||||
\(737\) | − | 4.74081e6i | − | 0.321502i | ||||||
\(738\) | − | 4.58098e6i | − | 0.309612i | ||||||
\(739\) | 1.92933e6 | 0.129956 | 0.0649778 | − | 0.997887i | \(-0.479302\pi\) | ||||
0.0649778 | + | 0.997887i | \(0.479302\pi\) | |||||||
\(740\) | 1.52280e7 | − | 7.52330e6i | 1.02227 | − | 0.505044i | ||||
\(741\) | 1.51350e7 | 1.01260 | ||||||||
\(742\) | − | 8.31746e6i | − | 0.554601i | ||||||
\(743\) | 4.43790e6i | 0.294921i | 0.989068 | + | 0.147460i | \(0.0471099\pi\) | ||||
−0.989068 | + | 0.147460i | \(0.952890\pi\) | |||||||
\(744\) | −2.51431e7 | −1.66528 | ||||||||
\(745\) | −1.28554e7 | − | 2.60209e7i | −0.848586 | − | 1.71764i | ||||
\(746\) | −4.67934e7 | −3.07849 | ||||||||
\(747\) | − | 1.72978e6i | − | 0.113420i | ||||||
\(748\) | 1.25903e7i | 0.822774i | ||||||||
\(749\) | −5.57467e6 | −0.363090 | ||||||||
\(750\) | −1.54979e7 | − | 3.04787e6i | −1.00605 | − | 0.197853i | ||||
\(751\) | −1.11577e7 | −0.721897 | −0.360949 | − | 0.932586i | \(-0.617547\pi\) | ||||
−0.360949 | + | 0.932586i | \(0.617547\pi\) | |||||||
\(752\) | 9.09521e6i | 0.586500i | ||||||||
\(753\) | 2.89420e6i | 0.186012i | ||||||||
\(754\) | 4.70138e7 | 3.01160 | ||||||||
\(755\) | −5.70003e6 | − | 1.15375e7i | −0.363923 | − | 0.736623i | ||||
\(756\) | −1.45973e6 | −0.0928898 | ||||||||
\(757\) | 1.16077e7i | 0.736216i | 0.929783 | + | 0.368108i | \(0.119994\pi\) | ||||
−0.929783 | + | 0.368108i | \(0.880006\pi\) | |||||||
\(758\) | 4.06506e7i | 2.56977i | ||||||||
\(759\) | −1.60966e6 | −0.101422 | ||||||||
\(760\) | −3.05447e7 | + | 1.50904e7i | −1.91824 | + | 0.947691i | ||||
\(761\) | −1.38952e6 | −0.0869770 | −0.0434885 | − | 0.999054i | \(-0.513847\pi\) | ||||
−0.0434885 | + | 0.999054i | \(0.513847\pi\) | |||||||
\(762\) | − | 2.02303e7i | − | 1.26216i | ||||||
\(763\) | − | 454960.i | − | 0.0282919i | ||||||
\(764\) | 1.75175e6 | 0.108577 | ||||||||
\(765\) | −6.12876e6 | + | 3.02787e6i | −0.378634 | + | 0.187061i | ||||
\(766\) | 8.27942e6 | 0.509833 | ||||||||
\(767\) | 2.65528e7i | 1.62975i | ||||||||
\(768\) | 1.88091e7i | 1.15071i | ||||||||
\(769\) | 2.19019e7 | 1.33557 | 0.667784 | − | 0.744355i | \(-0.267243\pi\) | ||||
0.667784 | + | 0.744355i | \(0.267243\pi\) | |||||||
\(770\) | 874435. | + | 1.76996e6i | 0.0531497 | + | 0.107581i | ||||
\(771\) | 1.29848e7 | 0.786681 | ||||||||
\(772\) | − | 3.37599e7i | − | 2.03872i | ||||||
\(773\) | 9.21665e6i | 0.554784i | 0.960757 | + | 0.277392i | \(0.0894701\pi\) | ||||
−0.960757 | + | 0.277392i | \(0.910530\pi\) | |||||||
\(774\) | 1.85783e6 | 0.111469 | ||||||||
\(775\) | −1.43010e7 | + | 1.86932e7i | −0.855290 | + | 1.11797i | ||||
\(776\) | 2.39525e7 | 1.42789 | ||||||||
\(777\) | − | 1.15267e6i | − | 0.0684941i | ||||||
\(778\) | 2.55633e7i | 1.51415i | ||||||||
\(779\) | −9.24966e6 | −0.546113 | ||||||||
\(780\) | 1.57204e7 | + | 3.18200e7i | 0.925182 | + | 1.87268i | ||||
\(781\) | 4.54480e6 | 0.266617 | ||||||||
\(782\) | − | 2.24175e7i | − | 1.31090i | ||||||
\(783\) | 3.33323e6i | 0.194294i | ||||||||
\(784\) | 2.42767e7 | 1.41059 | ||||||||
\(785\) | 1.64823e7 | − | 8.14294e6i | 0.954648 | − | 0.471636i | ||||
\(786\) | 2.43445e7 | 1.40554 | ||||||||
\(787\) | − | 2.18581e7i | − | 1.25798i | −0.777412 | − | 0.628992i | \(-0.783468\pi\) | ||
0.777412 | − | 0.628992i | \(-0.216532\pi\) | |||||||
\(788\) | 2.23879e7i | 1.28439i | ||||||||
\(789\) | −7.54756e6 | −0.431633 | ||||||||
\(790\) | −4.16595e6 | + | 2.05816e6i | −0.237491 | + | 0.117331i | ||||
\(791\) | 439261. | 0.0249621 | ||||||||
\(792\) | 3.63545e6i | 0.205942i | ||||||||
\(793\) | 5.25684e7i | 2.96853i | ||||||||
\(794\) | 5.20159e7 | 2.92809 | ||||||||
\(795\) | −6.35070e6 | − | 1.28546e7i | −0.356372 | − | 0.721340i | ||||
\(796\) | −2.74668e7 | −1.53648 | ||||||||
\(797\) | 2.79333e7i | 1.55767i | 0.627226 | + | 0.778837i | \(0.284190\pi\) | ||||
−0.627226 | + | 0.778837i | \(0.715810\pi\) | |||||||
\(798\) | 4.31585e6i | 0.239916i | ||||||||
\(799\) | 9.02865e6 | 0.500329 | ||||||||
\(800\) | −8.45979e6 | − | 6.47206e6i | −0.467342 | − | 0.357534i | ||||
\(801\) | 6.34925e6 | 0.349656 | ||||||||
\(802\) | − | 4.84459e7i | − | 2.65963i | ||||||
\(803\) | − | 7.10120e6i | − | 0.388636i | ||||||
\(804\) | 2.43037e7 | 1.32596 | ||||||||
\(805\) | −1.06330e6 | − | 2.15224e6i | −0.0578316 | − | 0.117058i | ||||
\(806\) | 7.74419e7 | 4.19893 | ||||||||
\(807\) | − | 3.73736e6i | − | 0.202014i | ||||||
\(808\) | − | 1.79397e7i | − | 0.966687i | ||||||
\(809\) | −1.07778e7 | −0.578974 | −0.289487 | − | 0.957182i | \(-0.593485\pi\) | ||||
−0.289487 | + | 0.957182i | \(0.593485\pi\) | |||||||
\(810\) | −3.30343e6 | + | 1.63204e6i | −0.176910 | + | 0.0874012i | ||||
\(811\) | −2.71394e7 | −1.44893 | −0.724467 | − | 0.689309i | \(-0.757914\pi\) | ||||
−0.724467 | + | 0.689309i | \(0.757914\pi\) | |||||||
\(812\) | 9.15550e6i | 0.487295i | ||||||||
\(813\) | − | 5.82488e6i | − | 0.309073i | ||||||
\(814\) | −5.35871e6 | −0.283465 | ||||||||
\(815\) | −1.23484e7 | + | 6.10064e6i | −0.651204 | + | 0.321722i | ||||
\(816\) | −2.06636e7 | −1.08638 | ||||||||
\(817\) | − | 3.75122e6i | − | 0.196616i | ||||||
\(818\) | 3.70322e7i | 1.93507i | ||||||||
\(819\) | 2.40858e6 | 0.125473 | ||||||||
\(820\) | −9.60742e6 | − | 1.94466e7i | −0.498968 | − | 1.00997i | ||||
\(821\) | 6.84095e6 | 0.354208 | 0.177104 | − | 0.984192i | \(-0.443327\pi\) | ||||
0.177104 | + | 0.984192i | \(0.443327\pi\) | |||||||
\(822\) | 1.55682e7i | 0.803634i | ||||||||
\(823\) | − | 1.95930e7i | − | 1.00833i | −0.863609 | − | 0.504163i | \(-0.831801\pi\) | ||
0.863609 | − | 0.504163i | \(-0.168199\pi\) | |||||||
\(824\) | −4.52247e7 | −2.32037 | ||||||||
\(825\) | 2.70287e6 | + | 2.06779e6i | 0.138258 | + | 0.105772i | ||||
\(826\) | −7.57171e6 | −0.386139 | ||||||||
\(827\) | − | 1.86828e7i | − | 0.949902i | −0.880012 | − | 0.474951i | \(-0.842466\pi\) | ||
0.880012 | − | 0.474951i | \(-0.157534\pi\) | |||||||
\(828\) | − | 8.25191e6i | − | 0.418291i | ||||||
\(829\) | 1.58057e7 | 0.798779 | 0.399390 | − | 0.916781i | \(-0.369222\pi\) | ||||
0.399390 | + | 0.916781i | \(0.369222\pi\) | |||||||
\(830\) | −5.31211e6 | − | 1.07523e7i | −0.267653 | − | 0.541760i | ||||
\(831\) | 6.11109e6 | 0.306985 | ||||||||
\(832\) | − | 1.47634e7i | − | 0.739397i | ||||||
\(833\) | − | 2.40991e7i | − | 1.20334i | ||||||
\(834\) | 3.16639e7 | 1.57634 | ||||||||
\(835\) | 2.91398e7 | − | 1.43963e7i | 1.44634 | − | 0.714552i | ||||
\(836\) | 1.37023e7 | 0.678077 | ||||||||
\(837\) | 5.49055e6i | 0.270896i | ||||||||
\(838\) | − | 1.32512e7i | − | 0.651844i | ||||||
\(839\) | 3.69461e7 | 1.81202 | 0.906011 | − | 0.423255i | \(-0.139112\pi\) | ||||
0.906011 | + | 0.423255i | \(0.139112\pi\) | |||||||
\(840\) | −4.86087e6 | + | 2.40148e6i | −0.237693 | + | 0.117430i | ||||
\(841\) | 395030. | 0.0192593 | ||||||||
\(842\) | − | 3.31035e7i | − | 1.60914i | ||||||
\(843\) | 1.60817e7i | 0.779403i | ||||||||
\(844\) | 5.98694e7 | 2.89300 | ||||||||
\(845\) | −1.67454e7 | − | 3.38947e7i | −0.806778 | − | 1.63301i | ||||
\(846\) | 4.86649e6 | 0.233771 | ||||||||
\(847\) | − | 425357.i | − | 0.0203725i | ||||||
\(848\) | − | 4.33401e7i | − | 2.06967i | ||||||
\(849\) | 7.85300e6 | 0.373909 | ||||||||
\(850\) | −2.87979e7 | + | 3.76424e7i | −1.36714 | + | 1.78702i | ||||
\(851\) | 6.51609e6 | 0.308435 | ||||||||
\(852\) | 2.32988e7i | 1.09960i | ||||||||
\(853\) | − | 2.39478e7i | − | 1.12692i | −0.826144 | − | 0.563459i | \(-0.809470\pi\) | ||
0.826144 | − | 0.563459i | \(-0.190530\pi\) | |||||||
\(854\) | −1.49902e7 | −0.703337 | ||||||||
\(855\) | 3.29532e6 | + | 6.67011e6i | 0.154164 | + | 0.312045i | ||||
\(856\) | −7.11746e7 | −3.32002 | ||||||||
\(857\) | − | 4.09428e6i | − | 0.190426i | −0.995457 | − | 0.0952129i | \(-0.969647\pi\) | ||
0.995457 | − | 0.0952129i | \(-0.0303532\pi\) | |||||||
\(858\) | − | 1.11974e7i | − | 0.519275i | ||||||
\(859\) | 6.51782e6 | 0.301384 | 0.150692 | − | 0.988581i | \(-0.451850\pi\) | ||||
0.150692 | + | 0.988581i | \(0.451850\pi\) | |||||||
\(860\) | 7.88660e6 | − | 3.89632e6i | 0.363617 | − | 0.179642i | ||||
\(861\) | −1.47199e6 | −0.0676700 | ||||||||
\(862\) | 1.87998e7i | 0.861759i | ||||||||
\(863\) | − | 8.54609e6i | − | 0.390607i | −0.980743 | − | 0.195304i | \(-0.937431\pi\) | ||
0.980743 | − | 0.195304i | \(-0.0625693\pi\) | |||||||
\(864\) | −2.48479e6 | −0.113242 | ||||||||
\(865\) | −1.32639e7 | + | 6.55295e6i | −0.602744 | + | 0.297781i | ||||
\(866\) | 4.33178e7 | 1.96278 | ||||||||
\(867\) | 7.73365e6i | 0.349411i | ||||||||
\(868\) | 1.50811e7i | 0.679413i | ||||||||
\(869\) | 1.00116e6 | 0.0449733 | ||||||||
\(870\) | 1.02362e7 | + | 2.07193e7i | 0.458502 | + | 0.928063i | ||||
\(871\) | −4.01015e7 | −1.79108 | ||||||||
\(872\) | − | 5.80870e6i | − | 0.258695i | ||||||
\(873\) | − | 5.23055e6i | − | 0.232280i | ||||||
\(874\) | −2.43977e7 | −1.08036 | ||||||||
\(875\) | −979360. | + | 4.97986e6i | −0.0432436 | + | 0.219886i | ||||
\(876\) | 3.64042e7 | 1.60284 | ||||||||
\(877\) | − | 3.63188e7i | − | 1.59453i | −0.603629 | − | 0.797266i | \(-0.706279\pi\) | ||
0.603629 | − | 0.797266i | \(-0.293721\pi\) | |||||||
\(878\) | − | 1.14135e7i | − | 0.499668i | ||||||
\(879\) | −5.87817e6 | −0.256608 | ||||||||
\(880\) | 4.55646e6 | + | 9.22281e6i | 0.198345 | + | 0.401473i | ||||
\(881\) | 1.57431e7 | 0.683364 | 0.341682 | − | 0.939816i | \(-0.389004\pi\) | ||||
0.341682 | + | 0.939816i | \(0.389004\pi\) | |||||||
\(882\) | − | 1.29895e7i | − | 0.562240i | ||||||
\(883\) | − | 1.30059e7i | − | 0.561354i | −0.959802 | − | 0.280677i | \(-0.909441\pi\) | ||
0.959802 | − | 0.280677i | \(-0.0905590\pi\) | |||||||
\(884\) | 1.06498e8 | 4.58365 | ||||||||
\(885\) | −1.17020e7 | + | 5.78130e6i | −0.502230 | + | 0.248123i | ||||
\(886\) | −8.79907e6 | −0.376576 | ||||||||
\(887\) | − | 3.12186e7i | − | 1.33231i | −0.745814 | − | 0.666154i | \(-0.767939\pi\) | ||
0.745814 | − | 0.666154i | \(-0.232061\pi\) | |||||||
\(888\) | − | 1.47167e7i | − | 0.626295i | ||||||
\(889\) | −6.50050e6 | −0.275862 | ||||||||
\(890\) | 3.94669e7 | − | 1.94983e7i | 1.67016 | − | 0.825129i | ||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | − | 3.34771e6i | − | 0.140876i | ||||||
\(893\) | − | 9.82614e6i | − | 0.412339i | ||||||
\(894\) | −4.69416e7 | −1.96433 | ||||||||
\(895\) | 343842. | + | 695977.i | 0.0143483 | + | 0.0290427i | ||||
\(896\) | 7.37868e6 | 0.307050 | ||||||||
\(897\) | 1.36158e7i | 0.565017i | ||||||||
\(898\) | − | 4.10688e7i | − | 1.69950i | ||||||
\(899\) | 3.44370e7 | 1.42111 | ||||||||
\(900\) | −1.06005e7 | + | 1.38562e7i | −0.436235 | + | 0.570214i | ||||
\(901\) | −4.30230e7 | −1.76558 | ||||||||
\(902\) | 6.84319e6i | 0.280054i | ||||||||
\(903\) | − | 596968.i | − | 0.0243631i | ||||||
\(904\) | 5.60827e6 | 0.228248 | ||||||||
\(905\) | −1.86348e7 | − | 3.77191e7i | −0.756318 | − | 1.53088i | ||||
\(906\) | −2.08137e7 | −0.842419 | ||||||||
\(907\) | 3.59253e7i | 1.45005i | 0.688725 | + | 0.725023i | \(0.258171\pi\) | ||||
−0.688725 | + | 0.725023i | \(0.741829\pi\) | |||||||
\(908\) | − | 5.42212e6i | − | 0.218250i | ||||||
\(909\) | −3.91752e6 | −0.157254 | ||||||||
\(910\) | 1.49717e7 | − | 7.39666e6i | 0.599333 | − | 0.296096i | ||||
\(911\) | −1.47634e7 | −0.589372 | −0.294686 | − | 0.955594i | \(-0.595215\pi\) | ||||
−0.294686 | + | 0.955594i | \(0.595215\pi\) | |||||||
\(912\) | 2.24888e7i | 0.895321i | ||||||||
\(913\) | 2.58400e6i | 0.102592i | ||||||||
\(914\) | −2.86592e7 | −1.13475 | ||||||||
\(915\) | −2.31673e7 | + | 1.14456e7i | −0.914791 | + | 0.451946i | ||||
\(916\) | −2.23371e7 | −0.879607 | ||||||||
\(917\) | − | 7.82251e6i | − | 0.307201i | ||||||
\(918\) | 1.10563e7i | 0.433014i | ||||||||
\(919\) | 1.26772e7 | 0.495146 | 0.247573 | − | 0.968869i | \(-0.420367\pi\) | ||||
0.247573 | + | 0.968869i | \(0.420367\pi\) | |||||||
\(920\) | −1.35756e7 | − | 2.74787e7i | −0.528799 | − | 1.07035i | ||||
\(921\) | −1.68653e7 | −0.655155 | ||||||||
\(922\) | 6.19224e7i | 2.39895i | ||||||||
\(923\) | − | 3.84435e7i | − | 1.48531i | ||||||
\(924\) | 2.18058e6 | 0.0840220 | ||||||||
\(925\) | −1.09415e7 | − | 8.37067e6i | −0.420458 | − | 0.321666i | ||||
\(926\) | −4.54495e7 | −1.74181 | ||||||||
\(927\) | 9.87580e6i | 0.377462i | ||||||||
\(928\) | 1.55848e7i | 0.594060i | ||||||||
\(929\) | −1.20341e7 | −0.457482 | −0.228741 | − | 0.973487i | \(-0.573461\pi\) | ||||
−0.228741 | + | 0.973487i | \(0.573461\pi\) | |||||||
\(930\) | 1.68613e7 | + | 3.41292e7i | 0.639268 | + | 1.29395i | ||||
\(931\) | −2.62277e7 | −0.991713 | ||||||||
\(932\) | 8.74136e7i | 3.29639i | ||||||||
\(933\) | 1.44563e7i | 0.543694i | ||||||||
\(934\) | −2.24111e7 | −0.840614 | ||||||||
\(935\) | 9.15531e6 | − | 4.52311e6i | 0.342487 | − | 0.169203i | ||||
\(936\) | 3.07515e7 | 1.14730 | ||||||||
\(937\) | − | 4.51344e7i | − | 1.67942i | −0.543038 | − | 0.839708i | \(-0.682726\pi\) | ||
0.543038 | − | 0.839708i | \(-0.317274\pi\) | |||||||
\(938\) | − | 1.14352e7i | − | 0.424362i | ||||||
\(939\) | 2.32381e7 | 0.860077 | ||||||||
\(940\) | 2.06586e7 | − | 1.02062e7i | 0.762571 | − | 0.376742i | ||||
\(941\) | 8.44095e6 | 0.310754 | 0.155377 | − | 0.987855i | \(-0.450341\pi\) | ||||
0.155377 | + | 0.987855i | \(0.450341\pi\) | |||||||
\(942\) | − | 2.97340e7i | − | 1.09176i | ||||||
\(943\) | − | 8.32120e6i | − | 0.304724i | ||||||
\(944\) | −3.94543e7 | −1.44100 | ||||||||
\(945\) | 524415. | + | 1.06148e6i | 0.0191027 | + | 0.0386662i | ||||
\(946\) | −2.77528e6 | −0.100827 | ||||||||
\(947\) | 2.68109e7i | 0.971485i | 0.874102 | + | 0.485743i | \(0.161451\pi\) | ||||
−0.874102 | + | 0.485743i | \(0.838549\pi\) | |||||||
\(948\) | 5.13244e6i | 0.185483i | ||||||||
\(949\) | −6.00675e7 | −2.16508 | ||||||||
\(950\) | 4.09674e7 | + | 3.13416e7i | 1.47275 | + | 1.12671i | ||||
\(951\) | −1.21129e7 | −0.434307 | ||||||||
\(952\) | 1.62689e7i | 0.581788i | ||||||||
\(953\) | − | 1.42183e7i | − | 0.507127i | −0.967319 | − | 0.253563i | \(-0.918397\pi\) | ||
0.967319 | − | 0.253563i | \(-0.0816027\pi\) | |||||||
\(954\) | −2.31896e7 | −0.824940 | ||||||||
\(955\) | −629324. | − | 1.27383e6i | −0.0223288 | − | 0.0451962i | ||||
\(956\) | −9.33081e7 | −3.30198 | ||||||||
\(957\) | − | 4.97926e6i | − | 0.175746i | ||||||
\(958\) | 6.65263e7i | 2.34196i | ||||||||
\(959\) | 5.00246e6 | 0.175645 | ||||||||
\(960\) | 6.50633e6 | − | 3.21440e6i | 0.227855 | − | 0.112570i | ||||
\(961\) | 2.80961e7 | 0.981380 | ||||||||
\(962\) | 4.53282e7i | 1.57918i | ||||||||
\(963\) | 1.55425e7i | 0.540078i | ||||||||
\(964\) | −7.87082e7 | −2.72789 | ||||||||
\(965\) | −2.45493e7 | + | 1.21284e7i | −0.848636 | + | 0.419262i | ||||
\(966\) | −3.88263e6 | −0.133870 | ||||||||
\(967\) | 277112.i | 0.00952993i | 0.999989 | + | 0.00476496i | \(0.00151674\pi\) | ||||
−0.999989 | + | 0.00476496i | \(0.998483\pi\) | |||||||
\(968\) | − | 5.43074e6i | − | 0.186282i | ||||||
\(969\) | 2.23242e7 | 0.763777 | ||||||||
\(970\) | −1.60628e7 | − | 3.25131e7i | −0.548142 | − | 1.10950i | ||||
\(971\) | 7.77514e6 | 0.264643 | 0.132321 | − | 0.991207i | \(-0.457757\pi\) | ||||
0.132321 | + | 0.991207i | \(0.457757\pi\) | |||||||
\(972\) | 4.06982e6i | 0.138169i | ||||||||
\(973\) | − | 1.01744e7i | − | 0.344531i | ||||||
\(974\) | −2.18584e7 | −0.738280 | ||||||||
\(975\) | 1.74910e7 | − | 2.28630e7i | 0.589256 | − | 0.770231i | ||||
\(976\) | −7.81102e7 | −2.62472 | ||||||||
\(977\) | 4.83351e6i | 0.162004i | 0.996714 | + | 0.0810020i | \(0.0258120\pi\) | ||||
−0.996714 | + | 0.0810020i | \(0.974188\pi\) | |||||||
\(978\) | 2.22765e7i | 0.744731i | ||||||||
\(979\) | −9.48468e6 | −0.316276 | ||||||||
\(980\) | −2.72421e7 | − | 5.51413e7i | −0.906100 | − | 1.83405i | ||||
\(981\) | −1.26846e6 | −0.0420827 | ||||||||
\(982\) | 7.70729e7i | 2.55049i | ||||||||
\(983\) | 9.75876e6i | 0.322115i | 0.986945 | + | 0.161057i | \(0.0514904\pi\) | ||||
−0.986945 | + | 0.161057i | \(0.948510\pi\) | |||||||
\(984\) | −1.87936e7 | −0.618760 | ||||||||
\(985\) | 1.62799e7 | − | 8.04298e6i | 0.534641 | − | 0.264135i | ||||
\(986\) | 6.93455e7 | 2.27157 | ||||||||
\(987\) | − | 1.56373e6i | − | 0.0510938i | ||||||
\(988\) | − | 1.15905e8i | − | 3.77755i | ||||||
\(989\) | 3.37468e6 | 0.109709 | ||||||||
\(990\) | 4.93476e6 | − | 2.43798e6i | 0.160021 | − | 0.0790574i | ||||
\(991\) | 2.72969e7 | 0.882935 | 0.441468 | − | 0.897277i | \(-0.354458\pi\) | ||||
0.441468 | + | 0.897277i | \(0.354458\pi\) | |||||||
\(992\) | 2.56715e7i | 0.828270i | ||||||||
\(993\) | − | 2.46922e7i | − | 0.794668i | ||||||
\(994\) | 1.09624e7 | 0.351917 | ||||||||
\(995\) | 9.86760e6 | + | 1.99732e7i | 0.315976 | + | 0.639572i | ||||
\(996\) | −1.32468e7 | −0.423120 | ||||||||
\(997\) | 4.85951e7i | 1.54830i | 0.633004 | + | 0.774149i | \(0.281822\pi\) | ||||
−0.633004 | + | 0.774149i | \(0.718178\pi\) | |||||||
\(998\) | − | 6.68070e7i | − | 2.12322i | ||||||
\(999\) | −3.21372e6 | −0.101881 |
(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 | 165.6.c.b.34.24 | yes | 26 | |
5.2 | odd | 4 | 825.6.a.v.1.2 | 13 | |||
5.3 | odd | 4 | 825.6.a.y.1.12 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.3 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.3 | ✓ | 26 | 5.4 | even | 2 | inner | |
165.6.c.b.34.24 | yes | 26 | 1.1 | even | 1 | trivial | |
825.6.a.v.1.2 | 13 | 5.2 | odd | 4 | |||
825.6.a.y.1.12 | 13 | 5.3 | odd | 4 |