Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,10,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(91.1613430010\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −23.3610 | −1.03242 | −0.516209 | − | 0.856463i | \(-0.672657\pi\) | ||||
−0.516209 | + | 0.856463i | \(0.672657\pi\) | |||||||
\(3\) | −81.0000 | −0.577350 | ||||||||
\(4\) | 33.7344 | 0.0658874 | ||||||||
\(5\) | 477.585 | 0.341732 | 0.170866 | − | 0.985294i | \(-0.445343\pi\) | ||||
0.170866 | + | 0.985294i | \(0.445343\pi\) | |||||||
\(6\) | 1892.24 | 0.596067 | ||||||||
\(7\) | 1570.96 | 0.247300 | 0.123650 | − | 0.992326i | \(-0.460540\pi\) | ||||
0.123650 | + | 0.992326i | \(0.460540\pi\) | |||||||
\(8\) | 11172.7 | 0.964395 | ||||||||
\(9\) | 6561.00 | 0.333333 | ||||||||
\(10\) | −11156.8 | −0.352810 | ||||||||
\(11\) | −48168.1 | −0.991955 | −0.495978 | − | 0.868335i | \(-0.665190\pi\) | ||||
−0.495978 | + | 0.868335i | \(0.665190\pi\) | |||||||
\(12\) | −2732.48 | −0.0380401 | ||||||||
\(13\) | 60042.1 | 0.583057 | 0.291528 | − | 0.956562i | \(-0.405836\pi\) | ||||
0.291528 | + | 0.956562i | \(0.405836\pi\) | |||||||
\(14\) | −36699.1 | −0.255317 | ||||||||
\(15\) | −38684.4 | −0.197299 | ||||||||
\(16\) | −278278. | −1.06155 | ||||||||
\(17\) | 65961.2 | 0.191544 | 0.0957720 | − | 0.995403i | \(-0.469468\pi\) | ||||
0.0957720 | + | 0.995403i | \(0.469468\pi\) | |||||||
\(18\) | −153271. | −0.344139 | ||||||||
\(19\) | −314381. | −0.553433 | −0.276716 | − | 0.960952i | \(-0.589246\pi\) | ||||
−0.276716 | + | 0.960952i | \(0.589246\pi\) | |||||||
\(20\) | 16111.0 | 0.0225158 | ||||||||
\(21\) | −127248. | −0.142779 | ||||||||
\(22\) | 1.12525e6 | 1.02411 | ||||||||
\(23\) | −1.21197e6 | −0.903060 | −0.451530 | − | 0.892256i | \(-0.649122\pi\) | ||||
−0.451530 | + | 0.892256i | \(0.649122\pi\) | |||||||
\(24\) | −904992. | −0.556794 | ||||||||
\(25\) | −1.72504e6 | −0.883219 | ||||||||
\(26\) | −1.40264e6 | −0.601958 | ||||||||
\(27\) | −531441. | −0.192450 | ||||||||
\(28\) | 52995.3 | 0.0162939 | ||||||||
\(29\) | 5.11139e6 | 1.34199 | 0.670993 | − | 0.741464i | \(-0.265868\pi\) | ||||
0.670993 | + | 0.741464i | \(0.265868\pi\) | |||||||
\(30\) | 903704. | 0.203695 | ||||||||
\(31\) | 2.37877e6 | 0.462620 | 0.231310 | − | 0.972880i | \(-0.425699\pi\) | ||||
0.231310 | + | 0.972880i | \(0.425699\pi\) | |||||||
\(32\) | 780396. | 0.131565 | ||||||||
\(33\) | 3.90161e6 | 0.572706 | ||||||||
\(34\) | −1.54092e6 | −0.197753 | ||||||||
\(35\) | 750267. | 0.0845102 | ||||||||
\(36\) | 221331. | 0.0219625 | ||||||||
\(37\) | 1.04291e6 | 0.0914830 | 0.0457415 | − | 0.998953i | \(-0.485435\pi\) | ||||
0.0457415 | + | 0.998953i | \(0.485435\pi\) | |||||||
\(38\) | 7.34424e6 | 0.571374 | ||||||||
\(39\) | −4.86341e6 | −0.336628 | ||||||||
\(40\) | 5.33593e6 | 0.329565 | ||||||||
\(41\) | −9.06456e6 | −0.500979 | −0.250490 | − | 0.968119i | \(-0.580592\pi\) | ||||
−0.250490 | + | 0.968119i | \(0.580592\pi\) | |||||||
\(42\) | 2.97263e6 | 0.147407 | ||||||||
\(43\) | 3.58131e7 | 1.59747 | 0.798736 | − | 0.601681i | \(-0.205502\pi\) | ||||
0.798736 | + | 0.601681i | \(0.205502\pi\) | |||||||
\(44\) | −1.62492e6 | −0.0653574 | ||||||||
\(45\) | 3.13343e6 | 0.113911 | ||||||||
\(46\) | 2.83128e7 | 0.932336 | ||||||||
\(47\) | 3.00013e7 | 0.896808 | 0.448404 | − | 0.893831i | \(-0.351993\pi\) | ||||
0.448404 | + | 0.893831i | \(0.351993\pi\) | |||||||
\(48\) | 2.25405e7 | 0.612884 | ||||||||
\(49\) | −3.78857e7 | −0.938843 | ||||||||
\(50\) | 4.02985e7 | 0.911852 | ||||||||
\(51\) | −5.34286e6 | −0.110588 | ||||||||
\(52\) | 2.02548e6 | 0.0384161 | ||||||||
\(53\) | −2.45832e7 | −0.427954 | −0.213977 | − | 0.976839i | \(-0.568642\pi\) | ||||
−0.213977 | + | 0.976839i | \(0.568642\pi\) | |||||||
\(54\) | 1.24150e7 | 0.198689 | ||||||||
\(55\) | −2.30043e7 | −0.338983 | ||||||||
\(56\) | 1.75519e7 | 0.238495 | ||||||||
\(57\) | 2.54649e7 | 0.319525 | ||||||||
\(58\) | −1.19407e8 | −1.38549 | ||||||||
\(59\) | −1.21174e7 | −0.130189 | ||||||||
\(60\) | −1.30499e6 | −0.0129995 | ||||||||
\(61\) | 6.49807e7 | 0.600897 | 0.300448 | − | 0.953798i | \(-0.402864\pi\) | ||||
0.300448 | + | 0.953798i | \(0.402864\pi\) | |||||||
\(62\) | −5.55703e7 | −0.477618 | ||||||||
\(63\) | 1.03071e7 | 0.0824333 | ||||||||
\(64\) | 1.24248e8 | 0.925716 | ||||||||
\(65\) | 2.86752e7 | 0.199249 | ||||||||
\(66\) | −9.11454e7 | −0.591272 | ||||||||
\(67\) | 2.82563e8 | 1.71309 | 0.856543 | − | 0.516076i | \(-0.172608\pi\) | ||||
0.856543 | + | 0.516076i | \(0.172608\pi\) | |||||||
\(68\) | 2.22516e6 | 0.0126203 | ||||||||
\(69\) | 9.81696e7 | 0.521382 | ||||||||
\(70\) | −1.75269e7 | −0.0872499 | ||||||||
\(71\) | −6.33502e7 | −0.295860 | −0.147930 | − | 0.988998i | \(-0.547261\pi\) | ||||
−0.147930 | + | 0.988998i | \(0.547261\pi\) | |||||||
\(72\) | 7.33044e7 | 0.321465 | ||||||||
\(73\) | 3.82696e8 | 1.57725 | 0.788626 | − | 0.614873i | \(-0.210793\pi\) | ||||
0.788626 | + | 0.614873i | \(0.210793\pi\) | |||||||
\(74\) | −2.43634e7 | −0.0944487 | ||||||||
\(75\) | 1.39728e8 | 0.509927 | ||||||||
\(76\) | −1.06054e7 | −0.0364643 | ||||||||
\(77\) | −7.56701e7 | −0.245310 | ||||||||
\(78\) | 1.13614e8 | 0.347541 | ||||||||
\(79\) | −5.56447e8 | −1.60732 | −0.803660 | − | 0.595089i | \(-0.797117\pi\) | ||||
−0.803660 | + | 0.595089i | \(0.797117\pi\) | |||||||
\(80\) | −1.32901e8 | −0.362764 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 2.11757e8 | 0.517220 | ||||||||
\(83\) | 4.81897e7 | 0.111456 | 0.0557279 | − | 0.998446i | \(-0.482252\pi\) | ||||
0.0557279 | + | 0.998446i | \(0.482252\pi\) | |||||||
\(84\) | −4.29262e6 | −0.00940731 | ||||||||
\(85\) | 3.15021e7 | 0.0654567 | ||||||||
\(86\) | −8.36627e8 | −1.64926 | ||||||||
\(87\) | −4.14023e8 | −0.774796 | ||||||||
\(88\) | −5.38169e8 | −0.956637 | ||||||||
\(89\) | 1.06126e9 | 1.79294 | 0.896471 | − | 0.443103i | \(-0.146122\pi\) | ||||
0.896471 | + | 0.443103i | \(0.146122\pi\) | |||||||
\(90\) | −7.32000e7 | −0.117603 | ||||||||
\(91\) | 9.43237e7 | 0.144190 | ||||||||
\(92\) | −4.08850e7 | −0.0595003 | ||||||||
\(93\) | −1.92680e8 | −0.267094 | ||||||||
\(94\) | −7.00858e8 | −0.925880 | ||||||||
\(95\) | −1.50144e8 | −0.189126 | ||||||||
\(96\) | −6.32120e7 | −0.0759590 | ||||||||
\(97\) | 1.41946e6 | 0.00162799 | 0.000813994 | − | 1.00000i | \(-0.499741\pi\) | ||||
0.000813994 | 1.00000i | \(0.499741\pi\) | ||||||||
\(98\) | 8.85046e8 | 0.969278 | ||||||||
\(99\) | −3.16031e8 | −0.330652 | ||||||||
\(100\) | −5.81930e7 | −0.0581930 | ||||||||
\(101\) | −1.20629e9 | −1.15347 | −0.576736 | − | 0.816931i | \(-0.695674\pi\) | ||||
−0.576736 | + | 0.816931i | \(0.695674\pi\) | |||||||
\(102\) | 1.24814e8 | 0.114173 | ||||||||
\(103\) | −1.98483e9 | −1.73762 | −0.868811 | − | 0.495144i | \(-0.835115\pi\) | ||||
−0.868811 | + | 0.495144i | \(0.835115\pi\) | |||||||
\(104\) | 6.70835e8 | 0.562297 | ||||||||
\(105\) | −6.07716e7 | −0.0487920 | ||||||||
\(106\) | 5.74287e8 | 0.441827 | ||||||||
\(107\) | −1.19300e9 | −0.879859 | −0.439930 | − | 0.898032i | \(-0.644997\pi\) | ||||
−0.439930 | + | 0.898032i | \(0.644997\pi\) | |||||||
\(108\) | −1.79278e7 | −0.0126800 | ||||||||
\(109\) | −1.66774e9 | −1.13164 | −0.565821 | − | 0.824528i | \(-0.691441\pi\) | ||||
−0.565821 | + | 0.824528i | \(0.691441\pi\) | |||||||
\(110\) | 5.37403e8 | 0.349972 | ||||||||
\(111\) | −8.44760e7 | −0.0528177 | ||||||||
\(112\) | −4.37163e8 | −0.262520 | ||||||||
\(113\) | 2.96330e9 | 1.70971 | 0.854857 | − | 0.518864i | \(-0.173645\pi\) | ||||
0.854857 | + | 0.518864i | \(0.173645\pi\) | |||||||
\(114\) | −5.94883e8 | −0.329883 | ||||||||
\(115\) | −5.78819e8 | −0.308605 | ||||||||
\(116\) | 1.72429e8 | 0.0884200 | ||||||||
\(117\) | 3.93936e8 | 0.194352 | ||||||||
\(118\) | 2.83073e8 | 0.134409 | ||||||||
\(119\) | 1.03622e8 | 0.0473688 | ||||||||
\(120\) | −4.32211e8 | −0.190274 | ||||||||
\(121\) | −3.77854e7 | −0.0160247 | ||||||||
\(122\) | −1.51801e9 | −0.620377 | ||||||||
\(123\) | 7.34230e8 | 0.289240 | ||||||||
\(124\) | 8.02463e7 | 0.0304809 | ||||||||
\(125\) | −1.75663e9 | −0.643556 | ||||||||
\(126\) | −2.40783e8 | −0.0851056 | ||||||||
\(127\) | −1.29615e9 | −0.442120 | −0.221060 | − | 0.975260i | \(-0.570952\pi\) | ||||
−0.221060 | + | 0.975260i | \(0.570952\pi\) | |||||||
\(128\) | −3.30210e9 | −1.08729 | ||||||||
\(129\) | −2.90086e9 | −0.922301 | ||||||||
\(130\) | −6.69880e8 | −0.205708 | ||||||||
\(131\) | 1.95690e9 | 0.580562 | 0.290281 | − | 0.956941i | \(-0.406251\pi\) | ||||
0.290281 | + | 0.956941i | \(0.406251\pi\) | |||||||
\(132\) | 1.31618e8 | 0.0377341 | ||||||||
\(133\) | −4.93880e8 | −0.136864 | ||||||||
\(134\) | −6.60095e9 | −1.76862 | ||||||||
\(135\) | −2.53808e8 | −0.0657663 | ||||||||
\(136\) | 7.36968e8 | 0.184724 | ||||||||
\(137\) | 1.14427e9 | 0.277515 | 0.138757 | − | 0.990326i | \(-0.455689\pi\) | ||||
0.138757 | + | 0.990326i | \(0.455689\pi\) | |||||||
\(138\) | −2.29334e9 | −0.538284 | ||||||||
\(139\) | −8.49846e9 | −1.93096 | −0.965481 | − | 0.260474i | \(-0.916121\pi\) | ||||
−0.965481 | + | 0.260474i | \(0.916121\pi\) | |||||||
\(140\) | 2.53098e7 | 0.00556816 | ||||||||
\(141\) | −2.43010e9 | −0.517772 | ||||||||
\(142\) | 1.47992e9 | 0.305451 | ||||||||
\(143\) | −2.89211e9 | −0.578366 | ||||||||
\(144\) | −1.82578e9 | −0.353849 | ||||||||
\(145\) | 2.44112e9 | 0.458600 | ||||||||
\(146\) | −8.94014e9 | −1.62838 | ||||||||
\(147\) | 3.06874e9 | 0.542041 | ||||||||
\(148\) | 3.51820e7 | 0.00602758 | ||||||||
\(149\) | 2.92284e9 | 0.485811 | 0.242905 | − | 0.970050i | \(-0.421900\pi\) | ||||
0.242905 | + | 0.970050i | \(0.421900\pi\) | |||||||
\(150\) | −3.26418e9 | −0.526458 | ||||||||
\(151\) | 1.67412e9 | 0.262054 | 0.131027 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131027 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(152\) | −3.51250e9 | −0.533728 | ||||||||
\(153\) | 4.32772e8 | 0.0638480 | ||||||||
\(154\) | 1.76773e9 | 0.253263 | ||||||||
\(155\) | 1.13606e9 | 0.158092 | ||||||||
\(156\) | −1.64064e8 | −0.0221795 | ||||||||
\(157\) | −7.62113e9 | −1.00108 | −0.500542 | − | 0.865712i | \(-0.666866\pi\) | ||||
−0.500542 | + | 0.865712i | \(0.666866\pi\) | |||||||
\(158\) | 1.29991e10 | 1.65943 | ||||||||
\(159\) | 1.99124e9 | 0.247079 | ||||||||
\(160\) | 3.72705e8 | 0.0449599 | ||||||||
\(161\) | −1.90396e9 | −0.223327 | ||||||||
\(162\) | −1.00561e9 | −0.114713 | ||||||||
\(163\) | −1.78418e10 | −1.97968 | −0.989839 | − | 0.142193i | \(-0.954585\pi\) | ||||
−0.989839 | + | 0.142193i | \(0.954585\pi\) | |||||||
\(164\) | −3.05787e8 | −0.0330082 | ||||||||
\(165\) | 1.86335e9 | 0.195712 | ||||||||
\(166\) | −1.12576e9 | −0.115069 | ||||||||
\(167\) | 1.14867e10 | 1.14280 | 0.571400 | − | 0.820672i | \(-0.306400\pi\) | ||||
0.571400 | + | 0.820672i | \(0.306400\pi\) | |||||||
\(168\) | −1.42171e9 | −0.137695 | ||||||||
\(169\) | −6.99945e9 | −0.660045 | ||||||||
\(170\) | −7.35919e8 | −0.0675787 | ||||||||
\(171\) | −2.06265e9 | −0.184478 | ||||||||
\(172\) | 1.20813e9 | 0.105253 | ||||||||
\(173\) | −8.09192e9 | −0.686822 | −0.343411 | − | 0.939185i | \(-0.611582\pi\) | ||||
−0.343411 | + | 0.939185i | \(0.611582\pi\) | |||||||
\(174\) | 9.67197e9 | 0.799914 | ||||||||
\(175\) | −2.70996e9 | −0.218420 | ||||||||
\(176\) | 1.34041e10 | 1.05301 | ||||||||
\(177\) | 9.81506e8 | 0.0751646 | ||||||||
\(178\) | −2.47920e10 | −1.85107 | ||||||||
\(179\) | −1.44994e10 | −1.05563 | −0.527814 | − | 0.849360i | \(-0.676988\pi\) | ||||
−0.527814 | + | 0.849360i | \(0.676988\pi\) | |||||||
\(180\) | 1.05704e8 | 0.00750528 | ||||||||
\(181\) | 1.31916e10 | 0.913574 | 0.456787 | − | 0.889576i | \(-0.349000\pi\) | ||||
0.456787 | + | 0.889576i | \(0.349000\pi\) | |||||||
\(182\) | −2.20349e9 | −0.148864 | ||||||||
\(183\) | −5.26343e9 | −0.346928 | ||||||||
\(184\) | −1.35410e10 | −0.870907 | ||||||||
\(185\) | 4.98079e8 | 0.0312627 | ||||||||
\(186\) | 4.50120e9 | 0.275753 | ||||||||
\(187\) | −3.17722e9 | −0.190003 | ||||||||
\(188\) | 1.01207e9 | 0.0590883 | ||||||||
\(189\) | −8.34872e8 | −0.0475929 | ||||||||
\(190\) | 3.50750e9 | 0.195257 | ||||||||
\(191\) | 1.40593e10 | 0.764387 | 0.382193 | − | 0.924082i | \(-0.375169\pi\) | ||||
0.382193 | + | 0.924082i | \(0.375169\pi\) | |||||||
\(192\) | −1.00641e10 | −0.534463 | ||||||||
\(193\) | 2.42504e10 | 1.25809 | 0.629044 | − | 0.777369i | \(-0.283446\pi\) | ||||
0.629044 | + | 0.777369i | \(0.283446\pi\) | |||||||
\(194\) | −3.31600e7 | −0.00168076 | ||||||||
\(195\) | −2.32269e9 | −0.115036 | ||||||||
\(196\) | −1.27805e9 | −0.0618579 | ||||||||
\(197\) | 2.25575e10 | 1.06707 | 0.533536 | − | 0.845777i | \(-0.320863\pi\) | ||||
0.533536 | + | 0.845777i | \(0.320863\pi\) | |||||||
\(198\) | 7.38278e9 | 0.341371 | ||||||||
\(199\) | −2.75426e10 | −1.24499 | −0.622495 | − | 0.782624i | \(-0.713881\pi\) | ||||
−0.622495 | + | 0.782624i | \(0.713881\pi\) | |||||||
\(200\) | −1.92734e10 | −0.851772 | ||||||||
\(201\) | −2.28876e10 | −0.989050 | ||||||||
\(202\) | 2.81802e10 | 1.19087 | ||||||||
\(203\) | 8.02979e9 | 0.331873 | ||||||||
\(204\) | −1.80238e8 | −0.00728636 | ||||||||
\(205\) | −4.32910e9 | −0.171201 | ||||||||
\(206\) | 4.63675e10 | 1.79395 | ||||||||
\(207\) | −7.95174e9 | −0.301020 | ||||||||
\(208\) | −1.67084e10 | −0.618941 | ||||||||
\(209\) | 1.51431e10 | 0.548981 | ||||||||
\(210\) | 1.41968e9 | 0.0503738 | ||||||||
\(211\) | −3.44676e10 | −1.19713 | −0.598563 | − | 0.801076i | \(-0.704261\pi\) | ||||
−0.598563 | + | 0.801076i | \(0.704261\pi\) | |||||||
\(212\) | −8.29298e8 | −0.0281968 | ||||||||
\(213\) | 5.13137e9 | 0.170815 | ||||||||
\(214\) | 2.78696e10 | 0.908383 | ||||||||
\(215\) | 1.71038e10 | 0.545907 | ||||||||
\(216\) | −5.93765e9 | −0.185598 | ||||||||
\(217\) | 3.73695e9 | 0.114406 | ||||||||
\(218\) | 3.89600e10 | 1.16833 | ||||||||
\(219\) | −3.09984e10 | −0.910627 | ||||||||
\(220\) | −7.76037e8 | −0.0223347 | ||||||||
\(221\) | 3.96045e9 | 0.111681 | ||||||||
\(222\) | 1.97344e9 | 0.0545300 | ||||||||
\(223\) | 1.69066e10 | 0.457808 | 0.228904 | − | 0.973449i | \(-0.426486\pi\) | ||||
0.228904 | + | 0.973449i | \(0.426486\pi\) | |||||||
\(224\) | 1.22597e9 | 0.0325360 | ||||||||
\(225\) | −1.13180e10 | −0.294406 | ||||||||
\(226\) | −6.92256e10 | −1.76514 | ||||||||
\(227\) | 1.99018e10 | 0.497482 | 0.248741 | − | 0.968570i | \(-0.419983\pi\) | ||||
0.248741 | + | 0.968570i | \(0.419983\pi\) | |||||||
\(228\) | 8.59041e8 | 0.0210527 | ||||||||
\(229\) | 1.05069e10 | 0.252473 | 0.126236 | − | 0.992000i | \(-0.459710\pi\) | ||||
0.126236 | + | 0.992000i | \(0.459710\pi\) | |||||||
\(230\) | 1.35218e10 | 0.318609 | ||||||||
\(231\) | 6.12928e9 | 0.141630 | ||||||||
\(232\) | 5.71083e10 | 1.29420 | ||||||||
\(233\) | 3.44694e10 | 0.766183 | 0.383092 | − | 0.923710i | \(-0.374859\pi\) | ||||
0.383092 | + | 0.923710i | \(0.374859\pi\) | |||||||
\(234\) | −9.20272e9 | −0.200653 | ||||||||
\(235\) | 1.43282e10 | 0.306468 | ||||||||
\(236\) | −4.08771e8 | −0.00857781 | ||||||||
\(237\) | 4.50722e10 | 0.927986 | ||||||||
\(238\) | −2.42072e9 | −0.0489044 | ||||||||
\(239\) | 2.73381e10 | 0.541974 | 0.270987 | − | 0.962583i | \(-0.412650\pi\) | ||||
0.270987 | + | 0.962583i | \(0.412650\pi\) | |||||||
\(240\) | 1.07650e10 | 0.209442 | ||||||||
\(241\) | −5.47074e9 | −0.104465 | −0.0522323 | − | 0.998635i | \(-0.516634\pi\) | ||||
−0.0522323 | + | 0.998635i | \(0.516634\pi\) | |||||||
\(242\) | 8.82703e8 | 0.0165442 | ||||||||
\(243\) | −3.48678e9 | −0.0641500 | ||||||||
\(244\) | 2.19208e9 | 0.0395915 | ||||||||
\(245\) | −1.80936e10 | −0.320833 | ||||||||
\(246\) | −1.71523e10 | −0.298617 | ||||||||
\(247\) | −1.88761e10 | −0.322683 | ||||||||
\(248\) | 2.65774e10 | 0.446149 | ||||||||
\(249\) | −3.90336e9 | −0.0643490 | ||||||||
\(250\) | 4.10367e10 | 0.664419 | ||||||||
\(251\) | −4.37703e10 | −0.696062 | −0.348031 | − | 0.937483i | \(-0.613150\pi\) | ||||
−0.348031 | + | 0.937483i | \(0.613150\pi\) | |||||||
\(252\) | 3.47702e8 | 0.00543132 | ||||||||
\(253\) | 5.83783e10 | 0.895795 | ||||||||
\(254\) | 3.02794e10 | 0.456453 | ||||||||
\(255\) | −2.55167e9 | −0.0377914 | ||||||||
\(256\) | 1.35256e10 | 0.196823 | ||||||||
\(257\) | 6.50898e10 | 0.930709 | 0.465355 | − | 0.885124i | \(-0.345927\pi\) | ||||
0.465355 | + | 0.885124i | \(0.345927\pi\) | |||||||
\(258\) | 6.77668e10 | 0.952201 | ||||||||
\(259\) | 1.63837e9 | 0.0226237 | ||||||||
\(260\) | 9.67339e8 | 0.0131280 | ||||||||
\(261\) | 3.35358e10 | 0.447329 | ||||||||
\(262\) | −4.57152e10 | −0.599383 | ||||||||
\(263\) | 1.08038e11 | 1.39243 | 0.696215 | − | 0.717833i | \(-0.254866\pi\) | ||||
0.696215 | + | 0.717833i | \(0.254866\pi\) | |||||||
\(264\) | 4.35917e10 | 0.552314 | ||||||||
\(265\) | −1.17406e10 | −0.146245 | ||||||||
\(266\) | 1.15375e10 | 0.141301 | ||||||||
\(267\) | −8.59619e10 | −1.03516 | ||||||||
\(268\) | 9.53209e9 | 0.112871 | ||||||||
\(269\) | −1.42805e11 | −1.66287 | −0.831437 | − | 0.555619i | \(-0.812481\pi\) | ||||
−0.831437 | + | 0.555619i | \(0.812481\pi\) | |||||||
\(270\) | 5.92920e9 | 0.0678984 | ||||||||
\(271\) | −8.54937e10 | −0.962880 | −0.481440 | − | 0.876479i | \(-0.659886\pi\) | ||||
−0.481440 | + | 0.876479i | \(0.659886\pi\) | |||||||
\(272\) | −1.83556e10 | −0.203333 | ||||||||
\(273\) | −7.64022e9 | −0.0832480 | ||||||||
\(274\) | −2.67313e10 | −0.286511 | ||||||||
\(275\) | 8.30917e10 | 0.876114 | ||||||||
\(276\) | 3.31169e9 | 0.0343525 | ||||||||
\(277\) | −9.85414e10 | −1.00568 | −0.502840 | − | 0.864380i | \(-0.667711\pi\) | ||||
−0.502840 | + | 0.864380i | \(0.667711\pi\) | |||||||
\(278\) | 1.98532e11 | 1.99356 | ||||||||
\(279\) | 1.56071e10 | 0.154207 | ||||||||
\(280\) | 8.38254e9 | 0.0815012 | ||||||||
\(281\) | −9.83292e10 | −0.940815 | −0.470407 | − | 0.882449i | \(-0.655893\pi\) | ||||
−0.470407 | + | 0.882449i | \(0.655893\pi\) | |||||||
\(282\) | 5.67695e10 | 0.534557 | ||||||||
\(283\) | 1.36212e11 | 1.26234 | 0.631168 | − | 0.775646i | \(-0.282576\pi\) | ||||
0.631168 | + | 0.775646i | \(0.282576\pi\) | |||||||
\(284\) | −2.13708e9 | −0.0194934 | ||||||||
\(285\) | 1.21616e10 | 0.109192 | ||||||||
\(286\) | 6.75625e10 | 0.597116 | ||||||||
\(287\) | −1.42401e10 | −0.123892 | ||||||||
\(288\) | 5.12018e9 | 0.0438550 | ||||||||
\(289\) | −1.14237e11 | −0.963311 | ||||||||
\(290\) | −5.70270e10 | −0.473467 | ||||||||
\(291\) | −1.14976e8 | −0.000939919 0 | ||||||||
\(292\) | 1.29100e10 | 0.103921 | ||||||||
\(293\) | 2.49642e10 | 0.197885 | 0.0989425 | − | 0.995093i | \(-0.468454\pi\) | ||||
0.0989425 | + | 0.995093i | \(0.468454\pi\) | |||||||
\(294\) | −7.16887e10 | −0.559613 | ||||||||
\(295\) | −5.78707e9 | −0.0444897 | ||||||||
\(296\) | 1.16522e10 | 0.0882257 | ||||||||
\(297\) | 2.55985e10 | 0.190902 | ||||||||
\(298\) | −6.82804e10 | −0.501560 | ||||||||
\(299\) | −7.27692e10 | −0.526535 | ||||||||
\(300\) | 4.71364e9 | 0.0335978 | ||||||||
\(301\) | 5.62609e10 | 0.395055 | ||||||||
\(302\) | −3.91091e10 | −0.270549 | ||||||||
\(303\) | 9.77098e10 | 0.665957 | ||||||||
\(304\) | 8.74853e10 | 0.587495 | ||||||||
\(305\) | 3.10338e10 | 0.205346 | ||||||||
\(306\) | −1.01100e10 | −0.0659178 | ||||||||
\(307\) | −8.15988e10 | −0.524277 | −0.262139 | − | 0.965030i | \(-0.584428\pi\) | ||||
−0.262139 | + | 0.965030i | \(0.584428\pi\) | |||||||
\(308\) | −2.55268e9 | −0.0161629 | ||||||||
\(309\) | 1.60771e11 | 1.00322 | ||||||||
\(310\) | −2.65395e10 | −0.163217 | ||||||||
\(311\) | −8.66559e10 | −0.525263 | −0.262631 | − | 0.964896i | \(-0.584590\pi\) | ||||
−0.262631 | + | 0.964896i | \(0.584590\pi\) | |||||||
\(312\) | −5.43376e10 | −0.324642 | ||||||||
\(313\) | −2.95540e11 | −1.74047 | −0.870236 | − | 0.492636i | \(-0.836034\pi\) | ||||
−0.870236 | + | 0.492636i | \(0.836034\pi\) | |||||||
\(314\) | 1.78037e11 | 1.03354 | ||||||||
\(315\) | 4.92250e9 | 0.0281701 | ||||||||
\(316\) | −1.87714e10 | −0.105902 | ||||||||
\(317\) | −3.28835e11 | −1.82899 | −0.914495 | − | 0.404597i | \(-0.867412\pi\) | ||||
−0.914495 | + | 0.404597i | \(0.867412\pi\) | |||||||
\(318\) | −4.65172e10 | −0.255089 | ||||||||
\(319\) | −2.46206e11 | −1.33119 | ||||||||
\(320\) | 5.93387e10 | 0.316347 | ||||||||
\(321\) | 9.66329e10 | 0.507987 | ||||||||
\(322\) | 4.44782e10 | 0.230567 | ||||||||
\(323\) | −2.07369e10 | −0.106007 | ||||||||
\(324\) | 1.45215e9 | 0.00732082 | ||||||||
\(325\) | −1.03575e11 | −0.514967 | ||||||||
\(326\) | 4.16802e11 | 2.04386 | ||||||||
\(327\) | 1.35087e11 | 0.653354 | ||||||||
\(328\) | −1.01276e11 | −0.483142 | ||||||||
\(329\) | 4.71308e10 | 0.221780 | ||||||||
\(330\) | −4.35297e10 | −0.202056 | ||||||||
\(331\) | 1.82900e10 | 0.0837504 | 0.0418752 | − | 0.999123i | \(-0.486667\pi\) | ||||
0.0418752 | + | 0.999123i | \(0.486667\pi\) | |||||||
\(332\) | 1.62565e9 | 0.00734353 | ||||||||
\(333\) | 6.84255e9 | 0.0304943 | ||||||||
\(334\) | −2.68340e11 | −1.17985 | ||||||||
\(335\) | 1.34948e11 | 0.585416 | ||||||||
\(336\) | 3.54102e10 | 0.151566 | ||||||||
\(337\) | 3.39078e11 | 1.43207 | 0.716037 | − | 0.698062i | \(-0.245954\pi\) | ||||
0.716037 | + | 0.698062i | \(0.245954\pi\) | |||||||
\(338\) | 1.63514e11 | 0.681443 | ||||||||
\(339\) | −2.40028e11 | −0.987104 | ||||||||
\(340\) | 1.06270e9 | 0.00431277 | ||||||||
\(341\) | −1.14581e11 | −0.458899 | ||||||||
\(342\) | 4.81856e10 | 0.190458 | ||||||||
\(343\) | −1.22911e11 | −0.479475 | ||||||||
\(344\) | 4.00130e11 | 1.54059 | ||||||||
\(345\) | 4.68843e10 | 0.178173 | ||||||||
\(346\) | 1.89035e11 | 0.709087 | ||||||||
\(347\) | −4.74641e11 | −1.75745 | −0.878724 | − | 0.477330i | \(-0.841605\pi\) | ||||
−0.878724 | + | 0.477330i | \(0.841605\pi\) | |||||||
\(348\) | −1.39668e10 | −0.0510493 | ||||||||
\(349\) | 2.47333e11 | 0.892417 | 0.446209 | − | 0.894929i | \(-0.352774\pi\) | ||||
0.446209 | + | 0.894929i | \(0.352774\pi\) | |||||||
\(350\) | 6.33074e10 | 0.225501 | ||||||||
\(351\) | −3.19088e10 | −0.112209 | ||||||||
\(352\) | −3.75901e10 | −0.130506 | ||||||||
\(353\) | −1.91987e11 | −0.658090 | −0.329045 | − | 0.944314i | \(-0.606727\pi\) | ||||
−0.329045 | + | 0.944314i | \(0.606727\pi\) | |||||||
\(354\) | −2.29289e10 | −0.0776013 | ||||||||
\(355\) | −3.02551e10 | −0.101105 | ||||||||
\(356\) | 3.58009e10 | 0.118132 | ||||||||
\(357\) | −8.39341e9 | −0.0273484 | ||||||||
\(358\) | 3.38719e11 | 1.08985 | ||||||||
\(359\) | −3.99067e9 | −0.0126800 | −0.00634002 | − | 0.999980i | \(-0.502018\pi\) | ||||
−0.00634002 | + | 0.999980i | \(0.502018\pi\) | |||||||
\(360\) | 3.50091e10 | 0.109855 | ||||||||
\(361\) | −2.23852e11 | −0.693712 | ||||||||
\(362\) | −3.08168e11 | −0.943190 | ||||||||
\(363\) | 3.06062e9 | 0.00925186 | ||||||||
\(364\) | 3.18195e9 | 0.00950029 | ||||||||
\(365\) | 1.82770e11 | 0.538997 | ||||||||
\(366\) | 1.22959e11 | 0.358175 | ||||||||
\(367\) | −5.84621e11 | −1.68220 | −0.841098 | − | 0.540882i | \(-0.818090\pi\) | ||||
−0.841098 | + | 0.540882i | \(0.818090\pi\) | |||||||
\(368\) | 3.37265e11 | 0.958640 | ||||||||
\(369\) | −5.94726e10 | −0.166993 | ||||||||
\(370\) | −1.16356e10 | −0.0322761 | ||||||||
\(371\) | −3.86192e10 | −0.105833 | ||||||||
\(372\) | −6.49995e9 | −0.0175981 | ||||||||
\(373\) | −5.84664e11 | −1.56393 | −0.781964 | − | 0.623323i | \(-0.785782\pi\) | ||||
−0.781964 | + | 0.623323i | \(0.785782\pi\) | |||||||
\(374\) | 7.42230e10 | 0.196163 | ||||||||
\(375\) | 1.42287e11 | 0.371557 | ||||||||
\(376\) | 3.35196e11 | 0.864877 | ||||||||
\(377\) | 3.06899e11 | 0.782454 | ||||||||
\(378\) | 1.95034e10 | 0.0491358 | ||||||||
\(379\) | 1.81625e11 | 0.452168 | 0.226084 | − | 0.974108i | \(-0.427408\pi\) | ||||
0.226084 | + | 0.974108i | \(0.427408\pi\) | |||||||
\(380\) | −5.06500e9 | −0.0124610 | ||||||||
\(381\) | 1.04988e11 | 0.255258 | ||||||||
\(382\) | −3.28438e11 | −0.789167 | ||||||||
\(383\) | 6.89118e11 | 1.63644 | 0.818218 | − | 0.574908i | \(-0.194962\pi\) | ||||
0.818218 | + | 0.574908i | \(0.194962\pi\) | |||||||
\(384\) | 2.67470e11 | 0.627748 | ||||||||
\(385\) | −3.61389e10 | −0.0838304 | ||||||||
\(386\) | −5.66513e11 | −1.29887 | ||||||||
\(387\) | 2.34970e11 | 0.532491 | ||||||||
\(388\) | 4.78847e7 | 0.000107264 0 | ||||||||
\(389\) | −4.98090e11 | −1.10290 | −0.551449 | − | 0.834209i | \(-0.685925\pi\) | ||||
−0.551449 | + | 0.834209i | \(0.685925\pi\) | |||||||
\(390\) | 5.42603e10 | 0.118766 | ||||||||
\(391\) | −7.99430e10 | −0.172976 | ||||||||
\(392\) | −4.23287e11 | −0.905415 | ||||||||
\(393\) | −1.58509e11 | −0.335188 | ||||||||
\(394\) | −5.26966e11 | −1.10166 | ||||||||
\(395\) | −2.65751e11 | −0.549272 | ||||||||
\(396\) | −1.06611e10 | −0.0217858 | ||||||||
\(397\) | −2.97522e11 | −0.601122 | −0.300561 | − | 0.953763i | \(-0.597174\pi\) | ||||
−0.300561 | + | 0.953763i | \(0.597174\pi\) | |||||||
\(398\) | 6.43421e11 | 1.28535 | ||||||||
\(399\) | 4.00043e10 | 0.0790184 | ||||||||
\(400\) | 4.80040e11 | 0.937578 | ||||||||
\(401\) | −4.84900e11 | −0.936489 | −0.468244 | − | 0.883599i | \(-0.655113\pi\) | ||||
−0.468244 | + | 0.883599i | \(0.655113\pi\) | |||||||
\(402\) | 5.34677e11 | 1.02111 | ||||||||
\(403\) | 1.42826e11 | 0.269734 | ||||||||
\(404\) | −4.06936e10 | −0.0759993 | ||||||||
\(405\) | 2.05585e10 | 0.0379702 | ||||||||
\(406\) | −1.87584e11 | −0.342632 | ||||||||
\(407\) | −5.02351e10 | −0.0907470 | ||||||||
\(408\) | −5.96944e10 | −0.106650 | ||||||||
\(409\) | 4.31529e11 | 0.762527 | 0.381264 | − | 0.924466i | \(-0.375489\pi\) | ||||
0.381264 | + | 0.924466i | \(0.375489\pi\) | |||||||
\(410\) | 1.01132e11 | 0.176751 | ||||||||
\(411\) | −9.26859e10 | −0.160223 | ||||||||
\(412\) | −6.69569e10 | −0.114487 | ||||||||
\(413\) | −1.90359e10 | −0.0321957 | ||||||||
\(414\) | 1.85760e11 | 0.310779 | ||||||||
\(415\) | 2.30147e10 | 0.0380880 | ||||||||
\(416\) | 4.68566e10 | 0.0767098 | ||||||||
\(417\) | 6.88375e11 | 1.11484 | ||||||||
\(418\) | −3.53758e11 | −0.566778 | ||||||||
\(419\) | −4.45084e11 | −0.705471 | −0.352736 | − | 0.935723i | \(-0.614748\pi\) | ||||
−0.352736 | + | 0.935723i | \(0.614748\pi\) | |||||||
\(420\) | −2.05009e9 | −0.00321478 | ||||||||
\(421\) | −2.91834e11 | −0.452758 | −0.226379 | − | 0.974039i | \(-0.572689\pi\) | ||||
−0.226379 | + | 0.974039i | \(0.572689\pi\) | |||||||
\(422\) | 8.05196e11 | 1.23593 | ||||||||
\(423\) | 1.96838e11 | 0.298936 | ||||||||
\(424\) | −2.74662e11 | −0.412716 | ||||||||
\(425\) | −1.13786e11 | −0.169175 | ||||||||
\(426\) | −1.19874e11 | −0.176352 | ||||||||
\(427\) | 1.02082e11 | 0.148602 | ||||||||
\(428\) | −4.02451e10 | −0.0579716 | ||||||||
\(429\) | 2.34261e11 | 0.333920 | ||||||||
\(430\) | −3.99561e11 | −0.563605 | ||||||||
\(431\) | −6.26106e11 | −0.873978 | −0.436989 | − | 0.899467i | \(-0.643955\pi\) | ||||
−0.436989 | + | 0.899467i | \(0.643955\pi\) | |||||||
\(432\) | 1.47888e11 | 0.204295 | ||||||||
\(433\) | −6.10341e11 | −0.834405 | −0.417203 | − | 0.908813i | \(-0.636989\pi\) | ||||
−0.417203 | + | 0.908813i | \(0.636989\pi\) | |||||||
\(434\) | −8.72987e10 | −0.118115 | ||||||||
\(435\) | −1.97731e11 | −0.264773 | ||||||||
\(436\) | −5.62601e10 | −0.0745609 | ||||||||
\(437\) | 3.81020e11 | 0.499783 | ||||||||
\(438\) | 7.24152e11 | 0.940148 | ||||||||
\(439\) | 7.33210e11 | 0.942190 | 0.471095 | − | 0.882083i | \(-0.343859\pi\) | ||||
0.471095 | + | 0.882083i | \(0.343859\pi\) | |||||||
\(440\) | −2.57022e11 | −0.326913 | ||||||||
\(441\) | −2.48568e11 | −0.312948 | ||||||||
\(442\) | −9.25199e10 | −0.115301 | ||||||||
\(443\) | −8.62779e11 | −1.06435 | −0.532173 | − | 0.846636i | \(-0.678624\pi\) | ||||
−0.532173 | + | 0.846636i | \(0.678624\pi\) | |||||||
\(444\) | −2.84974e9 | −0.00348002 | ||||||||
\(445\) | 5.06841e11 | 0.612705 | ||||||||
\(446\) | −3.94954e11 | −0.472650 | ||||||||
\(447\) | −2.36750e11 | −0.280483 | ||||||||
\(448\) | 1.95188e11 | 0.228929 | ||||||||
\(449\) | −3.21480e11 | −0.373289 | −0.186645 | − | 0.982427i | \(-0.559761\pi\) | ||||
−0.186645 | + | 0.982427i | \(0.559761\pi\) | |||||||
\(450\) | 2.64399e11 | 0.303951 | ||||||||
\(451\) | 4.36622e11 | 0.496949 | ||||||||
\(452\) | 9.99652e10 | 0.112649 | ||||||||
\(453\) | −1.35604e11 | −0.151297 | ||||||||
\(454\) | −4.64926e11 | −0.513609 | ||||||||
\(455\) | 4.50476e10 | 0.0492742 | ||||||||
\(456\) | 2.84512e11 | 0.308148 | ||||||||
\(457\) | −1.73149e12 | −1.85693 | −0.928467 | − | 0.371415i | \(-0.878873\pi\) | ||||
−0.928467 | + | 0.371415i | \(0.878873\pi\) | |||||||
\(458\) | −2.45451e11 | −0.260658 | ||||||||
\(459\) | −3.50545e10 | −0.0368627 | ||||||||
\(460\) | −1.95261e10 | −0.0203332 | ||||||||
\(461\) | 7.85929e11 | 0.810455 | 0.405228 | − | 0.914216i | \(-0.367192\pi\) | ||||
0.405228 | + | 0.914216i | \(0.367192\pi\) | |||||||
\(462\) | −1.43186e11 | −0.146221 | ||||||||
\(463\) | −7.57858e11 | −0.766431 | −0.383216 | − | 0.923659i | \(-0.625183\pi\) | ||||
−0.383216 | + | 0.923659i | \(0.625183\pi\) | |||||||
\(464\) | −1.42239e12 | −1.42458 | ||||||||
\(465\) | −9.20212e10 | −0.0912745 | ||||||||
\(466\) | −8.05239e11 | −0.791022 | ||||||||
\(467\) | −2.11064e11 | −0.205347 | −0.102674 | − | 0.994715i | \(-0.532740\pi\) | ||||
−0.102674 | + | 0.994715i | \(0.532740\pi\) | |||||||
\(468\) | 1.32892e10 | 0.0128054 | ||||||||
\(469\) | 4.43895e11 | 0.423646 | ||||||||
\(470\) | −3.34719e11 | −0.316403 | ||||||||
\(471\) | 6.17311e11 | 0.577976 | ||||||||
\(472\) | −1.35384e11 | −0.125554 | ||||||||
\(473\) | −1.72505e12 | −1.58462 | ||||||||
\(474\) | −1.05293e12 | −0.958070 | ||||||||
\(475\) | 5.42319e11 | 0.488803 | ||||||||
\(476\) | 3.49564e9 | 0.00312101 | ||||||||
\(477\) | −1.61290e11 | −0.142651 | ||||||||
\(478\) | −6.38645e11 | −0.559543 | ||||||||
\(479\) | −1.00601e12 | −0.873158 | −0.436579 | − | 0.899666i | \(-0.643810\pi\) | ||||
−0.436579 | + | 0.899666i | \(0.643810\pi\) | |||||||
\(480\) | −3.01891e10 | −0.0259576 | ||||||||
\(481\) | 6.26187e10 | 0.0533397 | ||||||||
\(482\) | 1.27802e11 | 0.107851 | ||||||||
\(483\) | 1.54220e11 | 0.128938 | ||||||||
\(484\) | −1.27467e9 | −0.00105583 | ||||||||
\(485\) | 6.77914e8 | 0.000556335 0 | ||||||||
\(486\) | 8.14546e10 | 0.0662297 | ||||||||
\(487\) | −1.83444e12 | −1.47783 | −0.738914 | − | 0.673800i | \(-0.764661\pi\) | ||||
−0.738914 | + | 0.673800i | \(0.764661\pi\) | |||||||
\(488\) | 7.26012e11 | 0.579502 | ||||||||
\(489\) | 1.44519e12 | 1.14297 | ||||||||
\(490\) | 4.22685e11 | 0.331233 | ||||||||
\(491\) | 1.51402e11 | 0.117562 | 0.0587808 | − | 0.998271i | \(-0.481279\pi\) | ||||
0.0587808 | + | 0.998271i | \(0.481279\pi\) | |||||||
\(492\) | 2.47688e10 | 0.0190573 | ||||||||
\(493\) | 3.37154e11 | 0.257049 | ||||||||
\(494\) | 4.40963e11 | 0.333144 | ||||||||
\(495\) | −1.50931e11 | −0.112994 | ||||||||
\(496\) | −6.61959e11 | −0.491093 | ||||||||
\(497\) | −9.95206e10 | −0.0731660 | ||||||||
\(498\) | 9.11863e10 | 0.0664351 | ||||||||
\(499\) | −1.06835e12 | −0.771366 | −0.385683 | − | 0.922631i | \(-0.626034\pi\) | ||||
−0.385683 | + | 0.922631i | \(0.626034\pi\) | |||||||
\(500\) | −5.92590e10 | −0.0424023 | ||||||||
\(501\) | −9.30421e11 | −0.659796 | ||||||||
\(502\) | 1.02252e12 | 0.718627 | ||||||||
\(503\) | 5.89639e11 | 0.410705 | 0.205353 | − | 0.978688i | \(-0.434166\pi\) | ||||
0.205353 | + | 0.978688i | \(0.434166\pi\) | |||||||
\(504\) | 1.15158e11 | 0.0794982 | ||||||||
\(505\) | −5.76108e11 | −0.394178 | ||||||||
\(506\) | −1.36377e12 | −0.924836 | ||||||||
\(507\) | 5.66955e11 | 0.381077 | ||||||||
\(508\) | −4.37249e10 | −0.0291301 | ||||||||
\(509\) | 1.50529e12 | 0.994009 | 0.497005 | − | 0.867748i | \(-0.334433\pi\) | ||||
0.497005 | + | 0.867748i | \(0.334433\pi\) | |||||||
\(510\) | 5.96094e10 | 0.0390166 | ||||||||
\(511\) | 6.01200e11 | 0.390054 | ||||||||
\(512\) | 1.37471e12 | 0.884088 | ||||||||
\(513\) | 1.67075e11 | 0.106508 | ||||||||
\(514\) | −1.52056e12 | −0.960881 | ||||||||
\(515\) | −9.47924e11 | −0.593801 | ||||||||
\(516\) | −9.78586e10 | −0.0607680 | ||||||||
\(517\) | −1.44510e12 | −0.889593 | ||||||||
\(518\) | −3.82740e10 | −0.0233571 | ||||||||
\(519\) | 6.55445e11 | 0.396537 | ||||||||
\(520\) | 3.20381e11 | 0.192155 | ||||||||
\(521\) | 1.04958e12 | 0.624088 | 0.312044 | − | 0.950068i | \(-0.398986\pi\) | ||||
0.312044 | + | 0.950068i | \(0.398986\pi\) | |||||||
\(522\) | −7.83429e11 | −0.461830 | ||||||||
\(523\) | −2.30838e12 | −1.34912 | −0.674558 | − | 0.738222i | \(-0.735666\pi\) | ||||
−0.674558 | + | 0.738222i | \(0.735666\pi\) | |||||||
\(524\) | 6.60149e10 | 0.0382518 | ||||||||
\(525\) | 2.19507e11 | 0.126105 | ||||||||
\(526\) | −2.52386e12 | −1.43757 | ||||||||
\(527\) | 1.56907e11 | 0.0886121 | ||||||||
\(528\) | −1.08573e12 | −0.607954 | ||||||||
\(529\) | −3.32280e11 | −0.184482 | ||||||||
\(530\) | 2.74271e11 | 0.150986 | ||||||||
\(531\) | −7.95020e10 | −0.0433963 | ||||||||
\(532\) | −1.66607e10 | −0.00901761 | ||||||||
\(533\) | −5.44255e11 | −0.292099 | ||||||||
\(534\) | 2.00815e12 | 1.06871 | ||||||||
\(535\) | −5.69758e11 | −0.300676 | ||||||||
\(536\) | 3.15701e12 | 1.65209 | ||||||||
\(537\) | 1.17445e12 | 0.609467 | ||||||||
\(538\) | 3.33607e12 | 1.71678 | ||||||||
\(539\) | 1.82488e12 | 0.931290 | ||||||||
\(540\) | −8.56206e9 | −0.00433317 | ||||||||
\(541\) | 1.72825e12 | 0.867399 | 0.433699 | − | 0.901058i | \(-0.357208\pi\) | ||||
0.433699 | + | 0.901058i | \(0.357208\pi\) | |||||||
\(542\) | 1.99722e12 | 0.994095 | ||||||||
\(543\) | −1.06852e12 | −0.527452 | ||||||||
\(544\) | 5.14758e10 | 0.0252005 | ||||||||
\(545\) | −7.96487e11 | −0.386718 | ||||||||
\(546\) | 1.78483e11 | 0.0859468 | ||||||||
\(547\) | −1.36998e12 | −0.654292 | −0.327146 | − | 0.944974i | \(-0.606087\pi\) | ||||
−0.327146 | + | 0.944974i | \(0.606087\pi\) | |||||||
\(548\) | 3.86012e10 | 0.0182847 | ||||||||
\(549\) | 4.26338e11 | 0.200299 | ||||||||
\(550\) | −1.94110e12 | −0.904516 | ||||||||
\(551\) | −1.60692e12 | −0.742699 | ||||||||
\(552\) | 1.09682e12 | 0.502818 | ||||||||
\(553\) | −8.74156e11 | −0.397490 | ||||||||
\(554\) | 2.30202e12 | 1.03828 | ||||||||
\(555\) | −4.03444e10 | −0.0180495 | ||||||||
\(556\) | −2.86690e11 | −0.127226 | ||||||||
\(557\) | 2.50228e12 | 1.10151 | 0.550753 | − | 0.834668i | \(-0.314341\pi\) | ||||
0.550753 | + | 0.834668i | \(0.314341\pi\) | |||||||
\(558\) | −3.64597e11 | −0.159206 | ||||||||
\(559\) | 2.15029e12 | 0.931417 | ||||||||
\(560\) | −2.08783e11 | −0.0897115 | ||||||||
\(561\) | 2.57355e11 | 0.109698 | ||||||||
\(562\) | 2.29706e12 | 0.971314 | ||||||||
\(563\) | −1.45935e12 | −0.612167 | −0.306084 | − | 0.952005i | \(-0.599019\pi\) | ||||
−0.306084 | + | 0.952005i | \(0.599019\pi\) | |||||||
\(564\) | −8.19780e10 | −0.0341147 | ||||||||
\(565\) | 1.41523e12 | 0.584264 | ||||||||
\(566\) | −3.18203e12 | −1.30326 | ||||||||
\(567\) | 6.76247e10 | 0.0274778 | ||||||||
\(568\) | −7.07796e11 | −0.285325 | ||||||||
\(569\) | 3.11112e12 | 1.24426 | 0.622131 | − | 0.782913i | \(-0.286267\pi\) | ||||
0.622131 | + | 0.782913i | \(0.286267\pi\) | |||||||
\(570\) | −2.84107e11 | −0.112732 | ||||||||
\(571\) | 4.63281e12 | 1.82382 | 0.911909 | − | 0.410391i | \(-0.134608\pi\) | ||||
0.911909 | + | 0.410391i | \(0.134608\pi\) | |||||||
\(572\) | −9.75635e10 | −0.0381070 | ||||||||
\(573\) | −1.13880e12 | −0.441319 | ||||||||
\(574\) | 3.32661e11 | 0.127908 | ||||||||
\(575\) | 2.09069e12 | 0.797600 | ||||||||
\(576\) | 8.15188e11 | 0.308572 | ||||||||
\(577\) | 3.67714e12 | 1.38108 | 0.690540 | − | 0.723294i | \(-0.257373\pi\) | ||||
0.690540 | + | 0.723294i | \(0.257373\pi\) | |||||||
\(578\) | 2.66869e12 | 0.994540 | ||||||||
\(579\) | −1.96428e12 | −0.726358 | ||||||||
\(580\) | 8.23497e10 | 0.0302159 | ||||||||
\(581\) | 7.57040e10 | 0.0275630 | ||||||||
\(582\) | 2.68596e9 | 0.000970390 0 | ||||||||
\(583\) | 1.18412e12 | 0.424511 | ||||||||
\(584\) | 4.27576e12 | 1.52109 | ||||||||
\(585\) | 1.88138e11 | 0.0664163 | ||||||||
\(586\) | −5.83187e11 | −0.204300 | ||||||||
\(587\) | 3.18227e12 | 1.10628 | 0.553141 | − | 0.833088i | \(-0.313429\pi\) | ||||
0.553141 | + | 0.833088i | \(0.313429\pi\) | |||||||
\(588\) | 1.03522e11 | 0.0357137 | ||||||||
\(589\) | −7.47840e11 | −0.256029 | ||||||||
\(590\) | 1.35191e11 | 0.0459320 | ||||||||
\(591\) | −1.82716e12 | −0.616075 | ||||||||
\(592\) | −2.90220e11 | −0.0971134 | ||||||||
\(593\) | −1.13721e12 | −0.377654 | −0.188827 | − | 0.982010i | \(-0.560469\pi\) | ||||
−0.188827 | + | 0.982010i | \(0.560469\pi\) | |||||||
\(594\) | −5.98005e11 | −0.197091 | ||||||||
\(595\) | 4.94885e10 | 0.0161874 | ||||||||
\(596\) | 9.86002e10 | 0.0320088 | ||||||||
\(597\) | 2.23095e12 | 0.718795 | ||||||||
\(598\) | 1.69996e12 | 0.543605 | ||||||||
\(599\) | 8.18505e8 | 0.000259777 0 | 0.000129888 | − | 1.00000i | \(-0.499959\pi\) | ||||
0.000129888 | 1.00000i | \(0.499959\pi\) | ||||||||
\(600\) | 1.56115e12 | 0.491771 | ||||||||
\(601\) | −8.21445e11 | −0.256828 | −0.128414 | − | 0.991721i | \(-0.540989\pi\) | ||||
−0.128414 | + | 0.991721i | \(0.540989\pi\) | |||||||
\(602\) | −1.31431e12 | −0.407862 | ||||||||
\(603\) | 1.85390e12 | 0.571028 | ||||||||
\(604\) | 5.64754e10 | 0.0172661 | ||||||||
\(605\) | −1.80457e10 | −0.00547615 | ||||||||
\(606\) | −2.28260e12 | −0.687547 | ||||||||
\(607\) | −1.81063e12 | −0.541353 | −0.270676 | − | 0.962670i | \(-0.587247\pi\) | ||||
−0.270676 | + | 0.962670i | \(0.587247\pi\) | |||||||
\(608\) | −2.45342e11 | −0.0728123 | ||||||||
\(609\) | −6.50413e11 | −0.191607 | ||||||||
\(610\) | −7.24979e11 | −0.212003 | ||||||||
\(611\) | 1.80134e12 | 0.522889 | ||||||||
\(612\) | 1.45993e10 | 0.00420678 | ||||||||
\(613\) | 1.14483e12 | 0.327468 | 0.163734 | − | 0.986505i | \(-0.447646\pi\) | ||||
0.163734 | + | 0.986505i | \(0.447646\pi\) | |||||||
\(614\) | 1.90623e12 | 0.541273 | ||||||||
\(615\) | 3.50657e11 | 0.0988427 | ||||||||
\(616\) | −8.45442e11 | −0.236576 | ||||||||
\(617\) | −1.58187e12 | −0.439428 | −0.219714 | − | 0.975564i | \(-0.570512\pi\) | ||||
−0.219714 | + | 0.975564i | \(0.570512\pi\) | |||||||
\(618\) | −3.75577e12 | −1.03574 | ||||||||
\(619\) | −1.91787e12 | −0.525062 | −0.262531 | − | 0.964924i | \(-0.584557\pi\) | ||||
−0.262531 | + | 0.964924i | \(0.584557\pi\) | |||||||
\(620\) | 3.83244e10 | 0.0104163 | ||||||||
\(621\) | 6.44091e11 | 0.173794 | ||||||||
\(622\) | 2.02437e12 | 0.542291 | ||||||||
\(623\) | 1.66719e12 | 0.443394 | ||||||||
\(624\) | 1.35338e12 | 0.357346 | ||||||||
\(625\) | 2.53027e12 | 0.663296 | ||||||||
\(626\) | 6.90410e12 | 1.79689 | ||||||||
\(627\) | −1.22659e12 | −0.316954 | ||||||||
\(628\) | −2.57094e11 | −0.0659589 | ||||||||
\(629\) | 6.87918e10 | 0.0175230 | ||||||||
\(630\) | −1.14994e11 | −0.0290833 | ||||||||
\(631\) | −3.98851e12 | −1.00156 | −0.500782 | − | 0.865573i | \(-0.666954\pi\) | ||||
−0.500782 | + | 0.865573i | \(0.666954\pi\) | |||||||
\(632\) | −6.21704e12 | −1.55009 | ||||||||
\(633\) | 2.79187e12 | 0.691161 | ||||||||
\(634\) | 7.68190e12 | 1.88828 | ||||||||
\(635\) | −6.19024e11 | −0.151086 | ||||||||
\(636\) | 6.71732e10 | 0.0162794 | ||||||||
\(637\) | −2.27474e12 | −0.547398 | ||||||||
\(638\) | 5.75160e12 | 1.37435 | ||||||||
\(639\) | −4.15641e11 | −0.0986198 | ||||||||
\(640\) | −1.57704e12 | −0.371562 | ||||||||
\(641\) | 4.30645e12 | 1.00753 | 0.503765 | − | 0.863841i | \(-0.331948\pi\) | ||||
0.503765 | + | 0.863841i | \(0.331948\pi\) | |||||||
\(642\) | −2.25744e12 | −0.524455 | ||||||||
\(643\) | −2.93311e12 | −0.676674 | −0.338337 | − | 0.941025i | \(-0.609864\pi\) | ||||
−0.338337 | + | 0.941025i | \(0.609864\pi\) | |||||||
\(644\) | −6.42288e10 | −0.0147144 | ||||||||
\(645\) | −1.38541e12 | −0.315180 | ||||||||
\(646\) | 4.84435e11 | 0.109443 | ||||||||
\(647\) | 1.29709e12 | 0.291006 | 0.145503 | − | 0.989358i | \(-0.453520\pi\) | ||||
0.145503 | + | 0.989358i | \(0.453520\pi\) | |||||||
\(648\) | 4.80950e11 | 0.107155 | ||||||||
\(649\) | 5.83670e11 | 0.129142 | ||||||||
\(650\) | 2.41961e12 | 0.531661 | ||||||||
\(651\) | −3.02693e11 | −0.0660523 | ||||||||
\(652\) | −6.01882e11 | −0.130436 | ||||||||
\(653\) | 4.63066e12 | 0.996630 | 0.498315 | − | 0.866996i | \(-0.333952\pi\) | ||||
0.498315 | + | 0.866996i | \(0.333952\pi\) | |||||||
\(654\) | −3.15576e12 | −0.674534 | ||||||||
\(655\) | 9.34588e11 | 0.198397 | ||||||||
\(656\) | 2.52247e12 | 0.531812 | ||||||||
\(657\) | 2.51087e12 | 0.525751 | ||||||||
\(658\) | −1.10102e12 | −0.228970 | ||||||||
\(659\) | 3.08986e11 | 0.0638196 | 0.0319098 | − | 0.999491i | \(-0.489841\pi\) | ||||
0.0319098 | + | 0.999491i | \(0.489841\pi\) | |||||||
\(660\) | 6.28590e10 | 0.0128949 | ||||||||
\(661\) | 5.48364e12 | 1.11728 | 0.558640 | − | 0.829410i | \(-0.311323\pi\) | ||||
0.558640 | + | 0.829410i | \(0.311323\pi\) | |||||||
\(662\) | −4.27271e11 | −0.0864654 | ||||||||
\(663\) | −3.20796e11 | −0.0644790 | ||||||||
\(664\) | 5.38411e11 | 0.107487 | ||||||||
\(665\) | −2.35870e11 | −0.0467708 | ||||||||
\(666\) | −1.59849e11 | −0.0314829 | ||||||||
\(667\) | −6.19485e12 | −1.21189 | ||||||||
\(668\) | 3.87496e11 | 0.0752962 | ||||||||
\(669\) | −1.36943e12 | −0.264316 | ||||||||
\(670\) | −3.15251e12 | −0.604394 | ||||||||
\(671\) | −3.12999e12 | −0.596063 | ||||||||
\(672\) | −9.93036e10 | −0.0187846 | ||||||||
\(673\) | −4.26313e12 | −0.801053 | −0.400526 | − | 0.916285i | \(-0.631173\pi\) | ||||
−0.400526 | + | 0.916285i | \(0.631173\pi\) | |||||||
\(674\) | −7.92120e12 | −1.47850 | ||||||||
\(675\) | 9.16756e11 | 0.169976 | ||||||||
\(676\) | −2.36122e11 | −0.0434887 | ||||||||
\(677\) | 3.55841e11 | 0.0651038 | 0.0325519 | − | 0.999470i | \(-0.489637\pi\) | ||||
0.0325519 | + | 0.999470i | \(0.489637\pi\) | |||||||
\(678\) | 5.60728e12 | 1.01910 | ||||||||
\(679\) | 2.22992e9 | 0.000402601 0 | ||||||||
\(680\) | 3.51965e11 | 0.0631261 | ||||||||
\(681\) | −1.61205e12 | −0.287221 | ||||||||
\(682\) | 2.67671e12 | 0.473775 | ||||||||
\(683\) | −5.38485e12 | −0.946849 | −0.473424 | − | 0.880834i | \(-0.656982\pi\) | ||||
−0.473424 | + | 0.880834i | \(0.656982\pi\) | |||||||
\(684\) | −6.95823e10 | −0.0121548 | ||||||||
\(685\) | 5.46487e11 | 0.0948357 | ||||||||
\(686\) | 2.87131e12 | 0.495019 | ||||||||
\(687\) | −8.51058e11 | −0.145765 | ||||||||
\(688\) | −9.96599e12 | −1.69579 | ||||||||
\(689\) | −1.47603e12 | −0.249521 | ||||||||
\(690\) | −1.09526e12 | −0.183949 | ||||||||
\(691\) | 2.56126e12 | 0.427369 | 0.213684 | − | 0.976903i | \(-0.431454\pi\) | ||||
0.213684 | + | 0.976903i | \(0.431454\pi\) | |||||||
\(692\) | −2.72976e11 | −0.0452529 | ||||||||
\(693\) | −4.96471e11 | −0.0817701 | ||||||||
\(694\) | 1.10881e13 | 1.81442 | ||||||||
\(695\) | −4.05874e12 | −0.659871 | ||||||||
\(696\) | −4.62577e12 | −0.747209 | ||||||||
\(697\) | −5.97910e11 | −0.0959595 | ||||||||
\(698\) | −5.77794e12 | −0.921348 | ||||||||
\(699\) | −2.79203e12 | −0.442356 | ||||||||
\(700\) | −9.14189e10 | −0.0143911 | ||||||||
\(701\) | −6.38644e12 | −0.998914 | −0.499457 | − | 0.866339i | \(-0.666467\pi\) | ||||
−0.499457 | + | 0.866339i | \(0.666467\pi\) | |||||||
\(702\) | 7.45421e11 | 0.115847 | ||||||||
\(703\) | −3.27872e11 | −0.0506297 | ||||||||
\(704\) | −5.98476e12 | −0.918269 | ||||||||
\(705\) | −1.16058e12 | −0.176939 | ||||||||
\(706\) | 4.48500e12 | 0.679425 | ||||||||
\(707\) | −1.89504e12 | −0.285253 | ||||||||
\(708\) | 3.31105e10 | 0.00495240 | ||||||||
\(709\) | 4.71903e12 | 0.701367 | 0.350683 | − | 0.936494i | \(-0.385949\pi\) | ||||
0.350683 | + | 0.936494i | \(0.385949\pi\) | |||||||
\(710\) | 7.06788e11 | 0.104382 | ||||||||
\(711\) | −3.65085e12 | −0.535773 | ||||||||
\(712\) | 1.18572e13 | 1.72910 | ||||||||
\(713\) | −2.88300e12 | −0.417774 | ||||||||
\(714\) | 1.96078e11 | 0.0282350 | ||||||||
\(715\) | −1.38123e12 | −0.197646 | ||||||||
\(716\) | −4.89127e11 | −0.0695526 | ||||||||
\(717\) | −2.21439e12 | −0.312909 | ||||||||
\(718\) | 9.32259e10 | 0.0130911 | ||||||||
\(719\) | −8.71884e12 | −1.21669 | −0.608343 | − | 0.793674i | \(-0.708166\pi\) | ||||
−0.608343 | + | 0.793674i | \(0.708166\pi\) | |||||||
\(720\) | −8.71966e11 | −0.120921 | ||||||||
\(721\) | −3.11808e12 | −0.429714 | ||||||||
\(722\) | 5.22940e12 | 0.716201 | ||||||||
\(723\) | 4.43130e11 | 0.0603127 | ||||||||
\(724\) | 4.45010e11 | 0.0601930 | ||||||||
\(725\) | −8.81734e12 | −1.18527 | ||||||||
\(726\) | −7.14990e10 | −0.00955179 | ||||||||
\(727\) | −1.17664e13 | −1.56220 | −0.781101 | − | 0.624405i | \(-0.785342\pi\) | ||||
−0.781101 | + | 0.624405i | \(0.785342\pi\) | |||||||
\(728\) | 1.05385e12 | 0.139056 | ||||||||
\(729\) | 2.82430e11 | 0.0370370 | ||||||||
\(730\) | −4.26968e12 | −0.556471 | ||||||||
\(731\) | 2.36227e12 | 0.305986 | ||||||||
\(732\) | −1.77559e11 | −0.0228582 | ||||||||
\(733\) | −1.13764e12 | −0.145559 | −0.0727794 | − | 0.997348i | \(-0.523187\pi\) | ||||
−0.0727794 | + | 0.997348i | \(0.523187\pi\) | |||||||
\(734\) | 1.36573e13 | 1.73673 | ||||||||
\(735\) | 1.46558e12 | 0.185233 | ||||||||
\(736\) | −9.45816e11 | −0.118811 | ||||||||
\(737\) | −1.36105e13 | −1.69930 | ||||||||
\(738\) | 1.38934e12 | 0.172407 | ||||||||
\(739\) | 9.77524e12 | 1.20567 | 0.602834 | − | 0.797867i | \(-0.294038\pi\) | ||||
0.602834 | + | 0.797867i | \(0.294038\pi\) | |||||||
\(740\) | 1.68024e10 | 0.00205982 | ||||||||
\(741\) | 1.52896e12 | 0.186301 | ||||||||
\(742\) | 9.02181e11 | 0.109264 | ||||||||
\(743\) | 6.06927e11 | 0.0730612 | 0.0365306 | − | 0.999333i | \(-0.488369\pi\) | ||||
0.0365306 | + | 0.999333i | \(0.488369\pi\) | |||||||
\(744\) | −2.15277e12 | −0.257584 | ||||||||
\(745\) | 1.39590e12 | 0.166017 | ||||||||
\(746\) | 1.36583e13 | 1.61463 | ||||||||
\(747\) | 3.16172e11 | 0.0371519 | ||||||||
\(748\) | −1.07182e11 | −0.0125188 | ||||||||
\(749\) | −1.87415e12 | −0.217589 | ||||||||
\(750\) | −3.32397e12 | −0.383603 | ||||||||
\(751\) | −3.40247e12 | −0.390315 | −0.195157 | − | 0.980772i | \(-0.562522\pi\) | ||||
−0.195157 | + | 0.980772i | \(0.562522\pi\) | |||||||
\(752\) | −8.34869e12 | −0.952003 | ||||||||
\(753\) | 3.54540e12 | 0.401872 | ||||||||
\(754\) | −7.16944e12 | −0.807820 | ||||||||
\(755\) | 7.99535e11 | 0.0895522 | ||||||||
\(756\) | −2.81639e10 | −0.00313577 | ||||||||
\(757\) | 6.46608e11 | 0.0715665 | 0.0357832 | − | 0.999360i | \(-0.488607\pi\) | ||||
0.0357832 | + | 0.999360i | \(0.488607\pi\) | |||||||
\(758\) | −4.24294e12 | −0.466827 | ||||||||
\(759\) | −4.72864e12 | −0.517188 | ||||||||
\(760\) | −1.67752e12 | −0.182392 | ||||||||
\(761\) | −1.30326e13 | −1.40864 | −0.704320 | − | 0.709882i | \(-0.748748\pi\) | ||||
−0.704320 | + | 0.709882i | \(0.748748\pi\) | |||||||
\(762\) | −2.45263e12 | −0.263533 | ||||||||
\(763\) | −2.61995e12 | −0.279855 | ||||||||
\(764\) | 4.74281e11 | 0.0503635 | ||||||||
\(765\) | 2.06685e11 | 0.0218189 | ||||||||
\(766\) | −1.60985e13 | −1.68949 | ||||||||
\(767\) | −7.27552e11 | −0.0759075 | ||||||||
\(768\) | −1.09557e12 | −0.113636 | ||||||||
\(769\) | −3.31464e11 | −0.0341797 | −0.0170898 | − | 0.999854i | \(-0.505440\pi\) | ||||
−0.0170898 | + | 0.999854i | \(0.505440\pi\) | |||||||
\(770\) | 8.44239e11 | 0.0865480 | ||||||||
\(771\) | −5.27228e12 | −0.537345 | ||||||||
\(772\) | 8.18072e11 | 0.0828922 | ||||||||
\(773\) | −1.11690e13 | −1.12514 | −0.562568 | − | 0.826751i | \(-0.690187\pi\) | ||||
−0.562568 | + | 0.826751i | \(0.690187\pi\) | |||||||
\(774\) | −5.48911e12 | −0.549753 | ||||||||
\(775\) | −4.10347e12 | −0.408595 | ||||||||
\(776\) | 1.58593e10 | 0.00157002 | ||||||||
\(777\) | −1.32708e11 | −0.0130618 | ||||||||
\(778\) | 1.16359e13 | 1.13865 | ||||||||
\(779\) | 2.84973e12 | 0.277258 | ||||||||
\(780\) | −7.83545e10 | −0.00757946 | ||||||||
\(781\) | 3.05146e12 | 0.293479 | ||||||||
\(782\) | 1.86755e12 | 0.178583 | ||||||||
\(783\) | −2.71640e12 | −0.258265 | ||||||||
\(784\) | 1.05428e13 | 0.996625 | ||||||||
\(785\) | −3.63973e12 | −0.342102 | ||||||||
\(786\) | 3.70293e12 | 0.346054 | ||||||||
\(787\) | −1.36913e13 | −1.27221 | −0.636105 | − | 0.771602i | \(-0.719456\pi\) | ||||
−0.636105 | + | 0.771602i | \(0.719456\pi\) | |||||||
\(788\) | 7.60964e11 | 0.0703066 | ||||||||
\(789\) | −8.75104e12 | −0.803920 | ||||||||
\(790\) | 6.20819e12 | 0.567079 | ||||||||
\(791\) | 4.65523e12 | 0.422812 | ||||||||
\(792\) | −3.53093e12 | −0.318879 | ||||||||
\(793\) | 3.90157e12 | 0.350357 | ||||||||
\(794\) | 6.95041e12 | 0.620609 | ||||||||
\(795\) | 9.50985e11 | 0.0844349 | ||||||||
\(796\) | −9.29132e11 | −0.0820292 | ||||||||
\(797\) | 1.16938e13 | 1.02658 | 0.513290 | − | 0.858215i | \(-0.328427\pi\) | ||||
0.513290 | + | 0.858215i | \(0.328427\pi\) | |||||||
\(798\) | −9.34538e11 | −0.0815800 | ||||||||
\(799\) | 1.97892e12 | 0.171778 | ||||||||
\(800\) | −1.34621e12 | −0.116201 | ||||||||
\(801\) | 6.96292e12 | 0.597647 | ||||||||
\(802\) | 1.13277e13 | 0.966848 | ||||||||
\(803\) | −1.84337e13 | −1.56456 | ||||||||
\(804\) | −7.72099e11 | −0.0651660 | ||||||||
\(805\) | −9.09301e11 | −0.0763179 | ||||||||
\(806\) | −3.33656e12 | −0.278478 | ||||||||
\(807\) | 1.15672e13 | 0.960061 | ||||||||
\(808\) | −1.34776e13 | −1.11240 | ||||||||
\(809\) | 2.55564e12 | 0.209765 | 0.104882 | − | 0.994485i | \(-0.466553\pi\) | ||||
0.104882 | + | 0.994485i | \(0.466553\pi\) | |||||||
\(810\) | −4.80265e11 | −0.0392011 | ||||||||
\(811\) | 9.70911e12 | 0.788107 | 0.394054 | − | 0.919087i | \(-0.371072\pi\) | ||||
0.394054 | + | 0.919087i | \(0.371072\pi\) | |||||||
\(812\) | 2.70880e11 | 0.0218663 | ||||||||
\(813\) | 6.92499e12 | 0.555919 | ||||||||
\(814\) | 1.17354e12 | 0.0936889 | ||||||||
\(815\) | −8.52098e12 | −0.676519 | ||||||||
\(816\) | 1.48680e12 | 0.117394 | ||||||||
\(817\) | −1.12589e13 | −0.884094 | ||||||||
\(818\) | −1.00809e13 | −0.787247 | ||||||||
\(819\) | 6.18858e11 | 0.0480633 | ||||||||
\(820\) | −1.46039e11 | −0.0112800 | ||||||||
\(821\) | −8.51723e12 | −0.654265 | −0.327133 | − | 0.944978i | \(-0.606082\pi\) | ||||
−0.327133 | + | 0.944978i | \(0.606082\pi\) | |||||||
\(822\) | 2.16523e12 | 0.165417 | ||||||||
\(823\) | 1.00520e13 | 0.763750 | 0.381875 | − | 0.924214i | \(-0.375278\pi\) | ||||
0.381875 | + | 0.924214i | \(0.375278\pi\) | |||||||
\(824\) | −2.21760e13 | −1.67575 | ||||||||
\(825\) | −6.73043e12 | −0.505825 | ||||||||
\(826\) | 4.44696e11 | 0.0332394 | ||||||||
\(827\) | −8.59417e11 | −0.0638895 | −0.0319447 | − | 0.999490i | \(-0.510170\pi\) | ||||
−0.0319447 | + | 0.999490i | \(0.510170\pi\) | |||||||
\(828\) | −2.68247e11 | −0.0198334 | ||||||||
\(829\) | 1.45843e13 | 1.07248 | 0.536242 | − | 0.844064i | \(-0.319844\pi\) | ||||
0.536242 | + | 0.844064i | \(0.319844\pi\) | |||||||
\(830\) | −5.37644e11 | −0.0393227 | ||||||||
\(831\) | 7.98185e12 | 0.580630 | ||||||||
\(832\) | 7.46008e12 | 0.539745 | ||||||||
\(833\) | −2.49899e12 | −0.179830 | ||||||||
\(834\) | −1.60811e13 | −1.15098 | ||||||||
\(835\) | 5.48586e12 | 0.390531 | ||||||||
\(836\) | 5.10844e11 | 0.0361709 | ||||||||
\(837\) | −1.26418e12 | −0.0890313 | ||||||||
\(838\) | 1.03976e13 | 0.728341 | ||||||||
\(839\) | 1.28668e13 | 0.896484 | 0.448242 | − | 0.893912i | \(-0.352050\pi\) | ||||
0.448242 | + | 0.893912i | \(0.352050\pi\) | |||||||
\(840\) | −6.78985e11 | −0.0470548 | ||||||||
\(841\) | 1.16192e13 | 0.800927 | ||||||||
\(842\) | 6.81752e12 | 0.467436 | ||||||||
\(843\) | 7.96467e12 | 0.543180 | ||||||||
\(844\) | −1.16274e12 | −0.0788755 | ||||||||
\(845\) | −3.34283e12 | −0.225558 | ||||||||
\(846\) | −4.59833e12 | −0.308627 | ||||||||
\(847\) | −5.93593e10 | −0.00396291 | ||||||||
\(848\) | 6.84096e12 | 0.454293 | ||||||||
\(849\) | −1.10331e13 | −0.728810 | ||||||||
\(850\) | 2.65814e12 | 0.174660 | ||||||||
\(851\) | −1.26398e12 | −0.0826147 | ||||||||
\(852\) | 1.73103e11 | 0.0112545 | ||||||||
\(853\) | 9.19067e12 | 0.594397 | 0.297198 | − | 0.954816i | \(-0.403948\pi\) | ||||
0.297198 | + | 0.954816i | \(0.403948\pi\) | |||||||
\(854\) | −2.38473e12 | −0.153419 | ||||||||
\(855\) | −9.85092e11 | −0.0630419 | ||||||||
\(856\) | −1.33291e13 | −0.848532 | ||||||||
\(857\) | 6.56735e12 | 0.415888 | 0.207944 | − | 0.978141i | \(-0.433323\pi\) | ||||
0.207944 | + | 0.978141i | \(0.433323\pi\) | |||||||
\(858\) | −5.47256e12 | −0.344745 | ||||||||
\(859\) | −1.15305e13 | −0.722566 | −0.361283 | − | 0.932456i | \(-0.617661\pi\) | ||||
−0.361283 | + | 0.932456i | \(0.617661\pi\) | |||||||
\(860\) | 5.76985e11 | 0.0359684 | ||||||||
\(861\) | 1.15345e12 | 0.0715291 | ||||||||
\(862\) | 1.46264e13 | 0.902311 | ||||||||
\(863\) | −3.57238e12 | −0.219235 | −0.109617 | − | 0.993974i | \(-0.534963\pi\) | ||||
−0.109617 | + | 0.993974i | \(0.534963\pi\) | |||||||
\(864\) | −4.14734e11 | −0.0253197 | ||||||||
\(865\) | −3.86458e12 | −0.234709 | ||||||||
\(866\) | 1.42582e13 | 0.861455 | ||||||||
\(867\) | 9.25320e12 | 0.556168 | ||||||||
\(868\) | 1.26064e11 | 0.00753791 | ||||||||
\(869\) | 2.68030e13 | 1.59439 | ||||||||
\(870\) | 4.61918e12 | 0.273356 | ||||||||
\(871\) | 1.69657e13 | 0.998825 | ||||||||
\(872\) | −1.86332e13 | −1.09135 | ||||||||
\(873\) | 9.31309e9 | 0.000542663 0 | ||||||||
\(874\) | −8.90100e12 | −0.515985 | ||||||||
\(875\) | −2.75960e12 | −0.159151 | ||||||||
\(876\) | −1.04571e12 | −0.0599988 | ||||||||
\(877\) | 3.20992e13 | 1.83230 | 0.916149 | − | 0.400837i | \(-0.131281\pi\) | ||||
0.916149 | + | 0.400837i | \(0.131281\pi\) | |||||||
\(878\) | −1.71285e13 | −0.972734 | ||||||||
\(879\) | −2.02210e12 | −0.114249 | ||||||||
\(880\) | 6.40160e12 | 0.359846 | ||||||||
\(881\) | −2.72871e13 | −1.52604 | −0.763020 | − | 0.646375i | \(-0.776284\pi\) | ||||
−0.763020 | + | 0.646375i | \(0.776284\pi\) | |||||||
\(882\) | 5.80679e12 | 0.323093 | ||||||||
\(883\) | −5.72818e12 | −0.317098 | −0.158549 | − | 0.987351i | \(-0.550682\pi\) | ||||
−0.158549 | + | 0.987351i | \(0.550682\pi\) | |||||||
\(884\) | 1.33603e11 | 0.00735837 | ||||||||
\(885\) | 4.68753e11 | 0.0256861 | ||||||||
\(886\) | 2.01554e13 | 1.09885 | ||||||||
\(887\) | 9.01105e12 | 0.488787 | 0.244393 | − | 0.969676i | \(-0.421411\pi\) | ||||
0.244393 | + | 0.969676i | \(0.421411\pi\) | |||||||
\(888\) | −9.43828e11 | −0.0509371 | ||||||||
\(889\) | −2.03621e12 | −0.109336 | ||||||||
\(890\) | −1.18403e13 | −0.632568 | ||||||||
\(891\) | −2.07348e12 | −0.110217 | ||||||||
\(892\) | 5.70333e11 | 0.0301638 | ||||||||
\(893\) | −9.43183e12 | −0.496323 | ||||||||
\(894\) | 5.53071e12 | 0.289576 | ||||||||
\(895\) | −6.92468e12 | −0.360742 | ||||||||
\(896\) | −5.18747e12 | −0.268887 | ||||||||
\(897\) | 5.89431e12 | 0.303995 | ||||||||
\(898\) | 7.51009e12 | 0.385391 | ||||||||
\(899\) | 1.21588e13 | 0.620830 | ||||||||
\(900\) | −3.81805e11 | −0.0193977 | ||||||||
\(901\) | −1.62154e12 | −0.0819720 | ||||||||
\(902\) | −1.01999e13 | −0.513059 | ||||||||
\(903\) | −4.55713e12 | −0.228085 | ||||||||
\(904\) | 3.31082e13 | 1.64884 | ||||||||
\(905\) | 6.30011e12 | 0.312197 | ||||||||
\(906\) | 3.16784e12 | 0.156202 | ||||||||
\(907\) | −1.01989e12 | −0.0500402 | −0.0250201 | − | 0.999687i | \(-0.507965\pi\) | ||||
−0.0250201 | + | 0.999687i | \(0.507965\pi\) | |||||||
\(908\) | 6.71376e11 | 0.0327778 | ||||||||
\(909\) | −7.91450e12 | −0.384491 | ||||||||
\(910\) | −1.05235e12 | −0.0508716 | ||||||||
\(911\) | −1.10786e13 | −0.532909 | −0.266455 | − | 0.963847i | \(-0.585852\pi\) | ||||
−0.266455 | + | 0.963847i | \(0.585852\pi\) | |||||||
\(912\) | −7.08631e12 | −0.339190 | ||||||||
\(913\) | −2.32120e12 | −0.110559 | ||||||||
\(914\) | 4.04492e13 | 1.91713 | ||||||||
\(915\) | −2.51374e12 | −0.118556 | ||||||||
\(916\) | 3.54443e11 | 0.0166348 | ||||||||
\(917\) | 3.07422e12 | 0.143573 | ||||||||
\(918\) | 8.18907e11 | 0.0380577 | ||||||||
\(919\) | −1.02036e13 | −0.471881 | −0.235941 | − | 0.971767i | \(-0.575817\pi\) | ||||
−0.235941 | + | 0.971767i | \(0.575817\pi\) | |||||||
\(920\) | −6.46699e12 | −0.297617 | ||||||||
\(921\) | 6.60950e12 | 0.302692 | ||||||||
\(922\) | −1.83601e13 | −0.836729 | ||||||||
\(923\) | −3.80368e12 | −0.172503 | ||||||||
\(924\) | 2.06767e11 | 0.00933164 | ||||||||
\(925\) | −1.79906e12 | −0.0807995 | ||||||||
\(926\) | 1.77043e13 | 0.791278 | ||||||||
\(927\) | −1.30225e13 | −0.579207 | ||||||||
\(928\) | 3.98891e12 | 0.176558 | ||||||||
\(929\) | −3.80349e13 | −1.67537 | −0.837686 | − | 0.546152i | \(-0.816092\pi\) | ||||
−0.837686 | + | 0.546152i | \(0.816092\pi\) | |||||||
\(930\) | 2.14970e12 | 0.0942335 | ||||||||
\(931\) | 1.19105e13 | 0.519587 | ||||||||
\(932\) | 1.16280e12 | 0.0504818 | ||||||||
\(933\) | 7.01913e12 | 0.303260 | ||||||||
\(934\) | 4.93066e12 | 0.212004 | ||||||||
\(935\) | −1.51739e12 | −0.0649301 | ||||||||
\(936\) | 4.40135e12 | 0.187432 | ||||||||
\(937\) | 3.02627e13 | 1.28256 | 0.641282 | − | 0.767305i | \(-0.278403\pi\) | ||||
0.641282 | + | 0.767305i | \(0.278403\pi\) | |||||||
\(938\) | −1.03698e13 | −0.437379 | ||||||||
\(939\) | 2.39387e13 | 1.00486 | ||||||||
\(940\) | 4.83351e11 | 0.0201924 | ||||||||
\(941\) | 1.55023e12 | 0.0644531 | 0.0322266 | − | 0.999481i | \(-0.489740\pi\) | ||||
0.0322266 | + | 0.999481i | \(0.489740\pi\) | |||||||
\(942\) | −1.44210e13 | −0.596713 | ||||||||
\(943\) | 1.09860e13 | 0.452414 | ||||||||
\(944\) | 3.37199e12 | 0.138202 | ||||||||
\(945\) | −3.98722e11 | −0.0162640 | ||||||||
\(946\) | 4.02987e13 | 1.63599 | ||||||||
\(947\) | −3.90879e13 | −1.57931 | −0.789654 | − | 0.613552i | \(-0.789740\pi\) | ||||
−0.789654 | + | 0.613552i | \(0.789740\pi\) | |||||||
\(948\) | 1.52048e12 | 0.0611426 | ||||||||
\(949\) | 2.29779e13 | 0.919627 | ||||||||
\(950\) | −1.26691e13 | −0.504649 | ||||||||
\(951\) | 2.66356e13 | 1.05597 | ||||||||
\(952\) | 1.15775e12 | 0.0456822 | ||||||||
\(953\) | −2.78189e13 | −1.09250 | −0.546251 | − | 0.837622i | \(-0.683945\pi\) | ||||
−0.546251 | + | 0.837622i | \(0.683945\pi\) | |||||||
\(954\) | 3.76790e12 | 0.147276 | ||||||||
\(955\) | 6.71450e12 | 0.261215 | ||||||||
\(956\) | 9.22234e11 | 0.0357092 | ||||||||
\(957\) | 1.99427e13 | 0.768563 | ||||||||
\(958\) | 2.35014e13 | 0.901464 | ||||||||
\(959\) | 1.79760e12 | 0.0686294 | ||||||||
\(960\) | −4.80644e12 | −0.182643 | ||||||||
\(961\) | −2.07811e13 | −0.785982 | ||||||||
\(962\) | −1.46283e12 | −0.0550689 | ||||||||
\(963\) | −7.82727e12 | −0.293286 | ||||||||
\(964\) | −1.84552e11 | −0.00688291 | ||||||||
\(965\) | 1.15816e13 | 0.429929 | ||||||||
\(966\) | −3.60274e12 | −0.133118 | ||||||||
\(967\) | 3.01952e12 | 0.111050 | 0.0555250 | − | 0.998457i | \(-0.482317\pi\) | ||||
0.0555250 | + | 0.998457i | \(0.482317\pi\) | |||||||
\(968\) | −4.22167e11 | −0.0154541 | ||||||||
\(969\) | 1.67969e12 | 0.0612030 | ||||||||
\(970\) | −1.58367e10 | −0.000574371 0 | ||||||||
\(971\) | 4.22227e13 | 1.52426 | 0.762130 | − | 0.647424i | \(-0.224154\pi\) | ||||
0.762130 | + | 0.647424i | \(0.224154\pi\) | |||||||
\(972\) | −1.17624e11 | −0.00422668 | ||||||||
\(973\) | −1.33507e13 | −0.477526 | ||||||||
\(974\) | 4.28543e13 | 1.52574 | ||||||||
\(975\) | 8.38956e12 | 0.297316 | ||||||||
\(976\) | −1.80827e13 | −0.637880 | ||||||||
\(977\) | 2.06518e12 | 0.0725159 | 0.0362579 | − | 0.999342i | \(-0.488456\pi\) | ||||
0.0362579 | + | 0.999342i | \(0.488456\pi\) | |||||||
\(978\) | −3.37609e13 | −1.18002 | ||||||||
\(979\) | −5.11188e13 | −1.77852 | ||||||||
\(980\) | −6.10377e11 | −0.0211388 | ||||||||
\(981\) | −1.09420e13 | −0.377214 | ||||||||
\(982\) | −3.53690e12 | −0.121373 | ||||||||
\(983\) | −2.25904e13 | −0.771674 | −0.385837 | − | 0.922567i | \(-0.626087\pi\) | ||||
−0.385837 | + | 0.922567i | \(0.626087\pi\) | |||||||
\(984\) | 8.20336e12 | 0.278942 | ||||||||
\(985\) | 1.07731e13 | 0.364653 | ||||||||
\(986\) | −7.87623e12 | −0.265382 | ||||||||
\(987\) | −3.81759e12 | −0.128045 | ||||||||
\(988\) | −6.36773e11 | −0.0212607 | ||||||||
\(989\) | −4.34044e13 | −1.44261 | ||||||||
\(990\) | 3.52590e12 | 0.116657 | ||||||||
\(991\) | 5.55935e12 | 0.183102 | 0.0915509 | − | 0.995800i | \(-0.470818\pi\) | ||||
0.0915509 | + | 0.995800i | \(0.470818\pi\) | |||||||
\(992\) | 1.85638e12 | 0.0608646 | ||||||||
\(993\) | −1.48149e12 | −0.0483533 | ||||||||
\(994\) | 2.32490e12 | 0.0755379 | ||||||||
\(995\) | −1.31539e13 | −0.425453 | ||||||||
\(996\) | −1.31677e11 | −0.00423979 | ||||||||
\(997\) | 2.57742e13 | 0.826145 | 0.413073 | − | 0.910698i | \(-0.364456\pi\) | ||||
0.413073 | + | 0.910698i | \(0.364456\pi\) | |||||||
\(998\) | 2.49576e13 | 0.796372 | ||||||||
\(999\) | −5.54247e11 | −0.0176059 |
(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 | 177.10.a.b.1.6 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.10.a.b.1.6 | ✓ | 21 | 1.1 | even | 1 | trivial |