Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,98,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 98, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 98);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 98 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(59.5852992940\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} + \cdots - 60\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{30}\cdot 5^{10}\cdot 7^{8}\cdot 11^{2}\cdot 19 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.29850e12\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.12713e14 | −0.283153 | −0.141576 | − | 0.989927i | \(-0.545217\pi\) | ||||
−0.141576 | + | 0.989927i | \(0.545217\pi\) | |||||||
\(3\) | −2.23668e23 | −1.61891 | −0.809455 | − | 0.587182i | \(-0.800237\pi\) | ||||
−0.809455 | + | 0.587182i | \(0.800237\pi\) | |||||||
\(4\) | −1.45752e29 | −0.919824 | ||||||||
\(5\) | −2.02292e33 | −0.254644 | −0.127322 | − | 0.991861i | \(-0.540638\pi\) | ||||
−0.127322 | + | 0.991861i | \(0.540638\pi\) | |||||||
\(6\) | 2.52104e37 | 0.458399 | ||||||||
\(7\) | −1.81030e41 | −1.86422 | −0.932108 | − | 0.362181i | \(-0.882032\pi\) | ||||
−0.932108 | + | 0.362181i | \(0.882032\pi\) | |||||||
\(8\) | 3.42884e43 | 0.543604 | ||||||||
\(9\) | 3.09393e46 | 1.62087 | ||||||||
\(10\) | 2.28010e47 | 0.0721032 | ||||||||
\(11\) | −4.93878e50 | −1.53488 | −0.767441 | − | 0.641120i | \(-0.778470\pi\) | ||||
−0.767441 | + | 0.641120i | \(0.778470\pi\) | |||||||
\(12\) | 3.26000e52 | 1.48911 | ||||||||
\(13\) | −3.60489e53 | −0.339344 | −0.169672 | − | 0.985501i | \(-0.554271\pi\) | ||||
−0.169672 | + | 0.985501i | \(0.554271\pi\) | |||||||
\(14\) | 2.04045e55 | 0.527858 | ||||||||
\(15\) | 4.52463e56 | 0.412246 | ||||||||
\(16\) | 1.92306e58 | 0.765901 | ||||||||
\(17\) | 4.80220e59 | 1.01081 | 0.505403 | − | 0.862883i | \(-0.331344\pi\) | ||||
0.505403 | + | 0.862883i | \(0.331344\pi\) | |||||||
\(18\) | −3.48727e60 | −0.458954 | ||||||||
\(19\) | 5.41141e61 | 0.517321 | 0.258661 | − | 0.965968i | \(-0.416719\pi\) | ||||
0.258661 | + | 0.965968i | \(0.416719\pi\) | |||||||
\(20\) | 2.94845e62 | 0.234228 | ||||||||
\(21\) | 4.04906e64 | 3.01800 | ||||||||
\(22\) | 5.56667e64 | 0.434606 | ||||||||
\(23\) | 1.09041e66 | 0.985798 | 0.492899 | − | 0.870086i | \(-0.335937\pi\) | ||||
0.492899 | + | 0.870086i | \(0.335937\pi\) | |||||||
\(24\) | −7.66921e66 | −0.880046 | ||||||||
\(25\) | −5.90167e67 | −0.935156 | ||||||||
\(26\) | 4.06320e67 | 0.0960862 | ||||||||
\(27\) | −2.65074e69 | −1.00513 | ||||||||
\(28\) | 2.63855e70 | 1.71475 | ||||||||
\(29\) | 6.44541e70 | 0.763744 | 0.381872 | − | 0.924215i | \(-0.375280\pi\) | ||||
0.381872 | + | 0.924215i | \(0.375280\pi\) | |||||||
\(30\) | −5.09986e70 | −0.116729 | ||||||||
\(31\) | −1.88517e72 | −0.879649 | −0.439824 | − | 0.898084i | \(-0.644959\pi\) | ||||
−0.439824 | + | 0.898084i | \(0.644959\pi\) | |||||||
\(32\) | −7.60075e72 | −0.760471 | ||||||||
\(33\) | 1.10465e74 | 2.48483 | ||||||||
\(34\) | −5.41273e73 | −0.286213 | ||||||||
\(35\) | 3.66210e74 | 0.474712 | ||||||||
\(36\) | −4.50946e75 | −1.49092 | ||||||||
\(37\) | 2.51059e75 | 0.219782 | 0.109891 | − | 0.993944i | \(-0.464950\pi\) | ||||
0.109891 | + | 0.993944i | \(0.464950\pi\) | |||||||
\(38\) | −6.09938e75 | −0.146481 | ||||||||
\(39\) | 8.06299e76 | 0.549367 | ||||||||
\(40\) | −6.93627e76 | −0.138426 | ||||||||
\(41\) | 1.64714e77 | 0.0992460 | 0.0496230 | − | 0.998768i | \(-0.484198\pi\) | ||||
0.0496230 | + | 0.998768i | \(0.484198\pi\) | |||||||
\(42\) | −4.56384e78 | −0.854555 | ||||||||
\(43\) | 3.52284e78 | 0.210704 | 0.105352 | − | 0.994435i | \(-0.466403\pi\) | ||||
0.105352 | + | 0.994435i | \(0.466403\pi\) | |||||||
\(44\) | 7.19838e79 | 1.41182 | ||||||||
\(45\) | −6.25877e79 | −0.412745 | ||||||||
\(46\) | −1.22903e80 | −0.279132 | ||||||||
\(47\) | −9.02851e80 | −0.722553 | −0.361277 | − | 0.932459i | \(-0.617659\pi\) | ||||
−0.361277 | + | 0.932459i | \(0.617659\pi\) | |||||||
\(48\) | −4.30126e81 | −1.23993 | ||||||||
\(49\) | 2.33420e82 | 2.47530 | ||||||||
\(50\) | 6.65197e81 | 0.264792 | ||||||||
\(51\) | −1.07410e83 | −1.63640 | ||||||||
\(52\) | 5.25421e82 | 0.312137 | ||||||||
\(53\) | −1.94973e83 | −0.459828 | −0.229914 | − | 0.973211i | \(-0.573845\pi\) | ||||
−0.229914 | + | 0.973211i | \(0.573845\pi\) | |||||||
\(54\) | 2.98774e83 | 0.284607 | ||||||||
\(55\) | 9.99077e83 | 0.390849 | ||||||||
\(56\) | −6.20723e84 | −1.01339 | ||||||||
\(57\) | −1.21036e85 | −0.837497 | ||||||||
\(58\) | −7.26484e84 | −0.216256 | ||||||||
\(59\) | −6.91580e84 | −0.0898504 | −0.0449252 | − | 0.998990i | \(-0.514305\pi\) | ||||
−0.0449252 | + | 0.998990i | \(0.514305\pi\) | |||||||
\(60\) | −6.59473e85 | −0.379194 | ||||||||
\(61\) | −4.83402e86 | −1.24684 | −0.623421 | − | 0.781886i | \(-0.714258\pi\) | ||||
−0.623421 | + | 0.781886i | \(0.714258\pi\) | |||||||
\(62\) | 2.12484e86 | 0.249075 | ||||||||
\(63\) | −5.60094e87 | −3.02165 | ||||||||
\(64\) | −2.19050e87 | −0.550572 | ||||||||
\(65\) | 7.29242e86 | 0.0864120 | ||||||||
\(66\) | −1.24509e88 | −0.703588 | ||||||||
\(67\) | −1.63992e88 | −0.446884 | −0.223442 | − | 0.974717i | \(-0.571729\pi\) | ||||
−0.223442 | + | 0.974717i | \(0.571729\pi\) | |||||||
\(68\) | −6.99931e88 | −0.929764 | ||||||||
\(69\) | −2.43889e89 | −1.59592 | ||||||||
\(70\) | −4.12768e88 | −0.134416 | ||||||||
\(71\) | 6.96780e89 | 1.14042 | 0.570211 | − | 0.821498i | \(-0.306861\pi\) | ||||
0.570211 | + | 0.821498i | \(0.306861\pi\) | |||||||
\(72\) | 1.06086e90 | 0.881111 | ||||||||
\(73\) | −1.03456e90 | −0.440145 | −0.220072 | − | 0.975484i | \(-0.570629\pi\) | ||||
−0.220072 | + | 0.975484i | \(0.570629\pi\) | |||||||
\(74\) | −2.82977e89 | −0.0622320 | ||||||||
\(75\) | 1.32001e91 | 1.51393 | ||||||||
\(76\) | −7.88723e90 | −0.475845 | ||||||||
\(77\) | 8.94069e91 | 2.86135 | ||||||||
\(78\) | −9.08808e90 | −0.155555 | ||||||||
\(79\) | −7.68512e91 | −0.709147 | −0.354574 | − | 0.935028i | \(-0.615374\pi\) | ||||
−0.354574 | + | 0.935028i | \(0.615374\pi\) | |||||||
\(80\) | −3.89019e91 | −0.195032 | ||||||||
\(81\) | 2.31402e90 | 0.00635102 | ||||||||
\(82\) | −1.85655e91 | −0.0281018 | ||||||||
\(83\) | 1.53118e93 | 1.28748 | 0.643739 | − | 0.765246i | \(-0.277382\pi\) | ||||
0.643739 | + | 0.765246i | \(0.277382\pi\) | |||||||
\(84\) | −5.90159e93 | −2.77603 | ||||||||
\(85\) | −9.71448e92 | −0.257396 | ||||||||
\(86\) | −3.97072e92 | −0.0596615 | ||||||||
\(87\) | −1.44163e94 | −1.23643 | ||||||||
\(88\) | −1.69343e94 | −0.834367 | ||||||||
\(89\) | 6.75125e94 | 1.92295 | 0.961476 | − | 0.274887i | \(-0.0886406\pi\) | ||||
0.961476 | + | 0.274887i | \(0.0886406\pi\) | |||||||
\(90\) | 7.05448e93 | 0.116870 | ||||||||
\(91\) | 6.52595e94 | 0.632610 | ||||||||
\(92\) | −1.58929e95 | −0.906761 | ||||||||
\(93\) | 4.21653e95 | 1.42407 | ||||||||
\(94\) | 1.01763e95 | 0.204593 | ||||||||
\(95\) | −1.09468e95 | −0.131733 | ||||||||
\(96\) | 1.70004e96 | 1.23113 | ||||||||
\(97\) | 1.44090e96 | 0.631254 | 0.315627 | − | 0.948883i | \(-0.397785\pi\) | ||||
0.315627 | + | 0.948883i | \(0.397785\pi\) | |||||||
\(98\) | −2.63096e96 | −0.700888 | ||||||||
\(99\) | −1.52802e97 | −2.48784 | ||||||||
\(100\) | 8.60180e96 | 0.860180 | ||||||||
\(101\) | −8.24946e96 | −0.509142 | −0.254571 | − | 0.967054i | \(-0.581934\pi\) | ||||
−0.254571 | + | 0.967054i | \(0.581934\pi\) | |||||||
\(102\) | 1.21065e97 | 0.463353 | ||||||||
\(103\) | −4.11930e97 | −0.982241 | −0.491120 | − | 0.871092i | \(-0.663412\pi\) | ||||
−0.491120 | + | 0.871092i | \(0.663412\pi\) | |||||||
\(104\) | −1.23606e97 | −0.184469 | ||||||||
\(105\) | −8.19094e97 | −0.768516 | ||||||||
\(106\) | 2.19761e97 | 0.130202 | ||||||||
\(107\) | 2.93147e98 | 1.10147 | 0.550734 | − | 0.834681i | \(-0.314348\pi\) | ||||
0.550734 | + | 0.834681i | \(0.314348\pi\) | |||||||
\(108\) | 3.86350e98 | 0.924547 | ||||||||
\(109\) | 8.89007e98 | 1.36057 | 0.680284 | − | 0.732949i | \(-0.261857\pi\) | ||||
0.680284 | + | 0.732949i | \(0.261857\pi\) | |||||||
\(110\) | −1.12609e98 | −0.110670 | ||||||||
\(111\) | −5.61539e98 | −0.355808 | ||||||||
\(112\) | −3.48131e99 | −1.42781 | ||||||||
\(113\) | 4.49778e99 | 1.19865 | 0.599326 | − | 0.800505i | \(-0.295435\pi\) | ||||
0.599326 | + | 0.800505i | \(0.295435\pi\) | |||||||
\(114\) | 1.36424e99 | 0.237140 | ||||||||
\(115\) | −2.20580e99 | −0.251028 | ||||||||
\(116\) | −9.39431e99 | −0.702510 | ||||||||
\(117\) | −1.11533e100 | −0.550033 | ||||||||
\(118\) | 7.79504e98 | 0.0254414 | ||||||||
\(119\) | −8.69344e100 | −1.88436 | ||||||||
\(120\) | 1.55142e100 | 0.224099 | ||||||||
\(121\) | 1.40380e101 | 1.35586 | ||||||||
\(122\) | 5.44859e100 | 0.353047 | ||||||||
\(123\) | −3.68412e100 | −0.160670 | ||||||||
\(124\) | 2.74768e101 | 0.809122 | ||||||||
\(125\) | 2.47050e101 | 0.492776 | ||||||||
\(126\) | 6.31302e101 | 0.855590 | ||||||||
\(127\) | −1.65157e102 | −1.52551 | −0.762757 | − | 0.646685i | \(-0.776155\pi\) | ||||
−0.762757 | + | 0.646685i | \(0.776155\pi\) | |||||||
\(128\) | 1.45129e102 | 0.916367 | ||||||||
\(129\) | −7.87947e101 | −0.341111 | ||||||||
\(130\) | −8.21954e100 | −0.0244678 | ||||||||
\(131\) | 4.11864e102 | 0.845466 | 0.422733 | − | 0.906254i | \(-0.361071\pi\) | ||||
0.422733 | + | 0.906254i | \(0.361071\pi\) | |||||||
\(132\) | −1.61005e103 | −2.28561 | ||||||||
\(133\) | −9.79628e102 | −0.964399 | ||||||||
\(134\) | 1.84841e102 | 0.126536 | ||||||||
\(135\) | 5.36223e102 | 0.255952 | ||||||||
\(136\) | 1.64660e103 | 0.549478 | ||||||||
\(137\) | 2.42949e103 | 0.568288 | 0.284144 | − | 0.958782i | \(-0.408291\pi\) | ||||
0.284144 | + | 0.958782i | \(0.408291\pi\) | |||||||
\(138\) | 2.74895e103 | 0.451889 | ||||||||
\(139\) | −3.15734e103 | −0.365682 | −0.182841 | − | 0.983142i | \(-0.558529\pi\) | ||||
−0.182841 | + | 0.983142i | \(0.558529\pi\) | |||||||
\(140\) | −5.33758e103 | −0.436651 | ||||||||
\(141\) | 2.01939e104 | 1.16975 | ||||||||
\(142\) | −7.85365e103 | −0.322914 | ||||||||
\(143\) | 1.78038e104 | 0.520853 | ||||||||
\(144\) | 5.94980e104 | 1.24143 | ||||||||
\(145\) | −1.30386e104 | −0.194483 | ||||||||
\(146\) | 1.16608e104 | 0.124628 | ||||||||
\(147\) | −5.22085e105 | −4.00729 | ||||||||
\(148\) | −3.65924e104 | −0.202161 | ||||||||
\(149\) | 4.81442e105 | 1.91871 | 0.959357 | − | 0.282196i | \(-0.0910627\pi\) | ||||
0.959357 | + | 0.282196i | \(0.0910627\pi\) | |||||||
\(150\) | −1.48783e105 | −0.428675 | ||||||||
\(151\) | −3.18494e105 | −0.664843 | −0.332422 | − | 0.943131i | \(-0.607866\pi\) | ||||
−0.332422 | + | 0.943131i | \(0.607866\pi\) | |||||||
\(152\) | 1.85548e105 | 0.281218 | ||||||||
\(153\) | 1.48577e106 | 1.63839 | ||||||||
\(154\) | −1.00774e106 | −0.810199 | ||||||||
\(155\) | 3.81356e105 | 0.223997 | ||||||||
\(156\) | −1.17520e106 | −0.505321 | ||||||||
\(157\) | 4.16274e106 | 1.31295 | 0.656473 | − | 0.754350i | \(-0.272048\pi\) | ||||
0.656473 | + | 0.754350i | \(0.272048\pi\) | |||||||
\(158\) | 8.66216e105 | 0.200797 | ||||||||
\(159\) | 4.36093e106 | 0.744421 | ||||||||
\(160\) | 1.53757e106 | 0.193650 | ||||||||
\(161\) | −1.97396e107 | −1.83774 | ||||||||
\(162\) | −2.60821e104 | −0.00179831 | ||||||||
\(163\) | −5.63074e106 | −0.288049 | −0.144025 | − | 0.989574i | \(-0.546004\pi\) | ||||
−0.144025 | + | 0.989574i | \(0.546004\pi\) | |||||||
\(164\) | −2.40074e106 | −0.0912889 | ||||||||
\(165\) | −2.23461e107 | −0.632749 | ||||||||
\(166\) | −1.72585e107 | −0.364553 | ||||||||
\(167\) | −1.09978e107 | −0.173603 | −0.0868013 | − | 0.996226i | \(-0.527665\pi\) | ||||
−0.0868013 | + | 0.996226i | \(0.527665\pi\) | |||||||
\(168\) | 1.38836e108 | 1.64060 | ||||||||
\(169\) | −9.98557e107 | −0.884846 | ||||||||
\(170\) | 1.09495e107 | 0.0728824 | ||||||||
\(171\) | 1.67425e108 | 0.838511 | ||||||||
\(172\) | −5.13462e107 | −0.193811 | ||||||||
\(173\) | 1.06059e108 | 0.302213 | 0.151107 | − | 0.988517i | \(-0.451716\pi\) | ||||
0.151107 | + | 0.988517i | \(0.451716\pi\) | |||||||
\(174\) | 1.62491e108 | 0.350099 | ||||||||
\(175\) | 1.06838e109 | 1.74333 | ||||||||
\(176\) | −9.49756e108 | −1.17557 | ||||||||
\(177\) | 1.54684e108 | 0.145460 | ||||||||
\(178\) | −7.60956e108 | −0.544490 | ||||||||
\(179\) | −3.26184e109 | −1.77865 | −0.889326 | − | 0.457274i | \(-0.848826\pi\) | ||||
−0.889326 | + | 0.457274i | \(0.848826\pi\) | |||||||
\(180\) | 9.12228e108 | 0.379653 | ||||||||
\(181\) | −4.33297e109 | −1.37840 | −0.689199 | − | 0.724572i | \(-0.742037\pi\) | ||||
−0.689199 | + | 0.724572i | \(0.742037\pi\) | |||||||
\(182\) | −7.35562e108 | −0.179125 | ||||||||
\(183\) | 1.08121e110 | 2.01852 | ||||||||
\(184\) | 3.73882e109 | 0.535884 | ||||||||
\(185\) | −5.07873e108 | −0.0559663 | ||||||||
\(186\) | −4.75260e109 | −0.403230 | ||||||||
\(187\) | −2.37170e110 | −1.55147 | ||||||||
\(188\) | 1.31592e110 | 0.664622 | ||||||||
\(189\) | 4.79863e110 | 1.87379 | ||||||||
\(190\) | 1.23386e109 | 0.0373006 | ||||||||
\(191\) | −4.22760e109 | −0.0990776 | −0.0495388 | − | 0.998772i | \(-0.515775\pi\) | ||||
−0.0495388 | + | 0.998772i | \(0.515775\pi\) | |||||||
\(192\) | 4.89944e110 | 0.891327 | ||||||||
\(193\) | −3.46389e110 | −0.489817 | −0.244909 | − | 0.969546i | \(-0.578758\pi\) | ||||
−0.244909 | + | 0.969546i | \(0.578758\pi\) | |||||||
\(194\) | −1.62409e110 | −0.178741 | ||||||||
\(195\) | −1.63108e110 | −0.139893 | ||||||||
\(196\) | −3.40214e111 | −2.27684 | ||||||||
\(197\) | −8.47806e110 | −0.443286 | −0.221643 | − | 0.975128i | \(-0.571142\pi\) | ||||
−0.221643 | + | 0.975128i | \(0.571142\pi\) | |||||||
\(198\) | 1.72229e111 | 0.704440 | ||||||||
\(199\) | 1.90688e111 | 0.610871 | 0.305435 | − | 0.952213i | \(-0.401198\pi\) | ||||
0.305435 | + | 0.952213i | \(0.401198\pi\) | |||||||
\(200\) | −2.02359e111 | −0.508355 | ||||||||
\(201\) | 3.66797e111 | 0.723465 | ||||||||
\(202\) | 9.29826e110 | 0.144165 | ||||||||
\(203\) | −1.16681e112 | −1.42378 | ||||||||
\(204\) | 1.56552e112 | 1.50521 | ||||||||
\(205\) | −3.33203e110 | −0.0252724 | ||||||||
\(206\) | 4.64300e111 | 0.278124 | ||||||||
\(207\) | 3.37364e112 | 1.59785 | ||||||||
\(208\) | −6.93242e111 | −0.259904 | ||||||||
\(209\) | −2.67258e112 | −0.794027 | ||||||||
\(210\) | 9.23229e111 | 0.217607 | ||||||||
\(211\) | −2.46773e112 | −0.461954 | −0.230977 | − | 0.972959i | \(-0.574192\pi\) | ||||
−0.230977 | + | 0.972959i | \(0.574192\pi\) | |||||||
\(212\) | 2.84178e112 | 0.422961 | ||||||||
\(213\) | −1.55847e113 | −1.84624 | ||||||||
\(214\) | −3.30416e112 | −0.311884 | ||||||||
\(215\) | −7.12644e111 | −0.0536546 | ||||||||
\(216\) | −9.08894e112 | −0.546395 | ||||||||
\(217\) | 3.41273e113 | 1.63985 | ||||||||
\(218\) | −1.00203e113 | −0.385249 | ||||||||
\(219\) | 2.31397e113 | 0.712555 | ||||||||
\(220\) | −1.45617e113 | −0.359512 | ||||||||
\(221\) | −1.73114e113 | −0.343011 | ||||||||
\(222\) | 6.32930e112 | 0.100748 | ||||||||
\(223\) | 5.71050e113 | 0.730951 | 0.365475 | − | 0.930821i | \(-0.380906\pi\) | ||||
0.365475 | + | 0.930821i | \(0.380906\pi\) | |||||||
\(224\) | 1.37597e114 | 1.41768 | ||||||||
\(225\) | −1.82593e114 | −1.51577 | ||||||||
\(226\) | −5.06960e113 | −0.339402 | ||||||||
\(227\) | 2.37441e114 | 1.28322 | 0.641612 | − | 0.767029i | \(-0.278266\pi\) | ||||
0.641612 | + | 0.767029i | \(0.278266\pi\) | |||||||
\(228\) | 1.76412e114 | 0.770350 | ||||||||
\(229\) | −1.57063e113 | −0.0554694 | −0.0277347 | − | 0.999615i | \(-0.508829\pi\) | ||||
−0.0277347 | + | 0.999615i | \(0.508829\pi\) | |||||||
\(230\) | 2.48624e113 | 0.0710792 | ||||||||
\(231\) | −1.99975e115 | −4.63227 | ||||||||
\(232\) | 2.21003e114 | 0.415174 | ||||||||
\(233\) | 6.20004e114 | 0.945437 | 0.472718 | − | 0.881214i | \(-0.343273\pi\) | ||||
0.472718 | + | 0.881214i | \(0.343273\pi\) | |||||||
\(234\) | 1.25712e114 | 0.155743 | ||||||||
\(235\) | 1.82640e114 | 0.183994 | ||||||||
\(236\) | 1.00799e114 | 0.0826466 | ||||||||
\(237\) | 1.71891e115 | 1.14805 | ||||||||
\(238\) | 9.79868e114 | 0.533562 | ||||||||
\(239\) | −1.24517e115 | −0.553263 | −0.276631 | − | 0.960976i | \(-0.589218\pi\) | ||||
−0.276631 | + | 0.960976i | \(0.589218\pi\) | |||||||
\(240\) | 8.70111e114 | 0.315740 | ||||||||
\(241\) | −1.70475e115 | −0.505631 | −0.252815 | − | 0.967515i | \(-0.581357\pi\) | ||||
−0.252815 | + | 0.967515i | \(0.581357\pi\) | |||||||
\(242\) | −1.58227e115 | −0.383916 | ||||||||
\(243\) | 5.00798e115 | 0.994852 | ||||||||
\(244\) | 7.04568e115 | 1.14688 | ||||||||
\(245\) | −4.72190e115 | −0.630321 | ||||||||
\(246\) | 4.15250e114 | 0.0454943 | ||||||||
\(247\) | −1.95076e115 | −0.175550 | ||||||||
\(248\) | −6.46395e115 | −0.478180 | ||||||||
\(249\) | −3.42476e116 | −2.08431 | ||||||||
\(250\) | −2.78459e115 | −0.139531 | ||||||||
\(251\) | −1.71502e116 | −0.708100 | −0.354050 | − | 0.935226i | \(-0.615196\pi\) | ||||
−0.354050 | + | 0.935226i | \(0.615196\pi\) | |||||||
\(252\) | 8.16349e116 | 2.77939 | ||||||||
\(253\) | −5.38528e116 | −1.51308 | ||||||||
\(254\) | 1.86154e116 | 0.431954 | ||||||||
\(255\) | 2.17282e116 | 0.416701 | ||||||||
\(256\) | 1.83519e116 | 0.291100 | ||||||||
\(257\) | 2.75833e116 | 0.362151 | 0.181075 | − | 0.983469i | \(-0.442042\pi\) | ||||
0.181075 | + | 0.983469i | \(0.442042\pi\) | |||||||
\(258\) | 8.88122e115 | 0.0965866 | ||||||||
\(259\) | −4.54493e116 | −0.409721 | ||||||||
\(260\) | −1.06288e116 | −0.0794838 | ||||||||
\(261\) | 1.99416e117 | 1.23793 | ||||||||
\(262\) | −4.64227e116 | −0.239396 | ||||||||
\(263\) | −2.18680e117 | −0.937465 | −0.468733 | − | 0.883340i | \(-0.655289\pi\) | ||||
−0.468733 | + | 0.883340i | \(0.655289\pi\) | |||||||
\(264\) | 3.78766e117 | 1.35077 | ||||||||
\(265\) | 3.94416e116 | 0.117093 | ||||||||
\(266\) | 1.10417e117 | 0.273072 | ||||||||
\(267\) | −1.51004e118 | −3.11309 | ||||||||
\(268\) | 2.39021e117 | 0.411055 | ||||||||
\(269\) | −5.84841e117 | −0.839562 | −0.419781 | − | 0.907626i | \(-0.637893\pi\) | ||||
−0.419781 | + | 0.907626i | \(0.637893\pi\) | |||||||
\(270\) | −6.04396e116 | −0.0724734 | ||||||||
\(271\) | 7.88052e117 | 0.789850 | 0.394925 | − | 0.918713i | \(-0.370771\pi\) | ||||
0.394925 | + | 0.918713i | \(0.370771\pi\) | |||||||
\(272\) | 9.23491e117 | 0.774178 | ||||||||
\(273\) | −1.45965e118 | −1.02414 | ||||||||
\(274\) | −2.73837e117 | −0.160912 | ||||||||
\(275\) | 2.91470e118 | 1.43535 | ||||||||
\(276\) | 3.55473e118 | 1.46797 | ||||||||
\(277\) | 5.49111e117 | 0.190279 | 0.0951396 | − | 0.995464i | \(-0.469670\pi\) | ||||
0.0951396 | + | 0.995464i | \(0.469670\pi\) | |||||||
\(278\) | 3.55875e117 | 0.103544 | ||||||||
\(279\) | −5.83259e118 | −1.42580 | ||||||||
\(280\) | 1.25567e118 | 0.258055 | ||||||||
\(281\) | −3.87258e118 | −0.669490 | −0.334745 | − | 0.942309i | \(-0.608650\pi\) | ||||
−0.334745 | + | 0.942309i | \(0.608650\pi\) | |||||||
\(282\) | −2.27612e118 | −0.331218 | ||||||||
\(283\) | 1.38783e119 | 1.70097 | 0.850483 | − | 0.526003i | \(-0.176310\pi\) | ||||
0.850483 | + | 0.526003i | \(0.176310\pi\) | |||||||
\(284\) | −1.01557e119 | −1.04899 | ||||||||
\(285\) | 2.44846e118 | 0.213264 | ||||||||
\(286\) | −2.00673e118 | −0.147481 | ||||||||
\(287\) | −2.98182e118 | −0.185016 | ||||||||
\(288\) | −2.35162e119 | −1.23263 | ||||||||
\(289\) | 4.90449e117 | 0.0217294 | ||||||||
\(290\) | 1.46962e118 | 0.0550684 | ||||||||
\(291\) | −3.22283e119 | −1.02194 | ||||||||
\(292\) | 1.50789e119 | 0.404856 | ||||||||
\(293\) | 4.27458e119 | 0.972330 | 0.486165 | − | 0.873867i | \(-0.338395\pi\) | ||||
0.486165 | + | 0.873867i | \(0.338395\pi\) | |||||||
\(294\) | 5.88460e119 | 1.13468 | ||||||||
\(295\) | 1.39901e118 | 0.0228799 | ||||||||
\(296\) | 8.60841e118 | 0.119474 | ||||||||
\(297\) | 1.30914e120 | 1.54276 | ||||||||
\(298\) | −5.42650e119 | −0.543289 | ||||||||
\(299\) | −3.93080e119 | −0.334525 | ||||||||
\(300\) | −1.92395e120 | −1.39255 | ||||||||
\(301\) | −6.37741e119 | −0.392798 | ||||||||
\(302\) | 3.58985e119 | 0.188252 | ||||||||
\(303\) | 1.84514e120 | 0.824256 | ||||||||
\(304\) | 1.04064e120 | 0.396217 | ||||||||
\(305\) | 9.77884e119 | 0.317501 | ||||||||
\(306\) | −1.67466e120 | −0.463914 | ||||||||
\(307\) | −4.81954e120 | −1.13971 | −0.569855 | − | 0.821745i | \(-0.693001\pi\) | ||||
−0.569855 | + | 0.821745i | \(0.693001\pi\) | |||||||
\(308\) | −1.30312e121 | −2.63194 | ||||||||
\(309\) | 9.21355e120 | 1.59016 | ||||||||
\(310\) | −4.29839e119 | −0.0634255 | ||||||||
\(311\) | 1.01240e120 | 0.127783 | 0.0638914 | − | 0.997957i | \(-0.479649\pi\) | ||||
0.0638914 | + | 0.997957i | \(0.479649\pi\) | |||||||
\(312\) | 2.76467e120 | 0.298638 | ||||||||
\(313\) | 1.46458e121 | 1.35461 | 0.677304 | − | 0.735703i | \(-0.263148\pi\) | ||||
0.677304 | + | 0.735703i | \(0.263148\pi\) | |||||||
\(314\) | −4.69197e120 | −0.371764 | ||||||||
\(315\) | 1.13303e121 | 0.769446 | ||||||||
\(316\) | 1.12012e121 | 0.652291 | ||||||||
\(317\) | 1.55068e121 | 0.774726 | 0.387363 | − | 0.921927i | \(-0.373386\pi\) | ||||
0.387363 | + | 0.921927i | \(0.373386\pi\) | |||||||
\(318\) | −4.91536e120 | −0.210785 | ||||||||
\(319\) | −3.18325e121 | −1.17226 | ||||||||
\(320\) | 4.43120e120 | 0.140200 | ||||||||
\(321\) | −6.55675e121 | −1.78318 | ||||||||
\(322\) | 2.22492e121 | 0.520362 | ||||||||
\(323\) | 2.59867e121 | 0.522912 | ||||||||
\(324\) | −3.37273e119 | −0.00584182 | ||||||||
\(325\) | 2.12749e121 | 0.317340 | ||||||||
\(326\) | 6.34660e120 | 0.0815619 | ||||||||
\(327\) | −1.98842e122 | −2.20264 | ||||||||
\(328\) | 5.64777e120 | 0.0539505 | ||||||||
\(329\) | 1.63443e122 | 1.34700 | ||||||||
\(330\) | 2.51871e121 | 0.179165 | ||||||||
\(331\) | −1.72930e121 | −0.106221 | −0.0531106 | − | 0.998589i | \(-0.516914\pi\) | ||||
−0.0531106 | + | 0.998589i | \(0.516914\pi\) | |||||||
\(332\) | −2.23173e122 | −1.18425 | ||||||||
\(333\) | 7.76759e121 | 0.356238 | ||||||||
\(334\) | 1.23960e121 | 0.0491561 | ||||||||
\(335\) | 3.31743e121 | 0.113796 | ||||||||
\(336\) | 7.78658e122 | 2.31149 | ||||||||
\(337\) | 2.48323e122 | 0.638215 | 0.319108 | − | 0.947718i | \(-0.396617\pi\) | ||||
0.319108 | + | 0.947718i | \(0.396617\pi\) | |||||||
\(338\) | 1.12551e122 | 0.250547 | ||||||||
\(339\) | −1.00601e123 | −1.94051 | ||||||||
\(340\) | 1.41591e122 | 0.236759 | ||||||||
\(341\) | 9.31046e122 | 1.35016 | ||||||||
\(342\) | −1.88710e122 | −0.237427 | ||||||||
\(343\) | −2.51850e123 | −2.75028 | ||||||||
\(344\) | 1.20793e122 | 0.114540 | ||||||||
\(345\) | 4.93368e122 | 0.406392 | ||||||||
\(346\) | −1.19543e122 | −0.0855725 | ||||||||
\(347\) | −1.74732e123 | −1.08741 | −0.543705 | − | 0.839277i | \(-0.682979\pi\) | ||||
−0.543705 | + | 0.839277i | \(0.682979\pi\) | |||||||
\(348\) | 2.10121e123 | 1.13730 | ||||||||
\(349\) | −1.75996e122 | −0.0828836 | −0.0414418 | − | 0.999141i | \(-0.513195\pi\) | ||||
−0.0414418 | + | 0.999141i | \(0.513195\pi\) | |||||||
\(350\) | −1.20421e123 | −0.493630 | ||||||||
\(351\) | 9.55563e122 | 0.341086 | ||||||||
\(352\) | 3.75385e123 | 1.16723 | ||||||||
\(353\) | −1.68570e123 | −0.456779 | −0.228390 | − | 0.973570i | \(-0.573346\pi\) | ||||
−0.228390 | + | 0.973570i | \(0.573346\pi\) | |||||||
\(354\) | −1.74350e122 | −0.0411873 | ||||||||
\(355\) | −1.40953e123 | −0.290402 | ||||||||
\(356\) | −9.84008e123 | −1.76878 | ||||||||
\(357\) | 1.94444e124 | 3.05061 | ||||||||
\(358\) | 3.67654e123 | 0.503630 | ||||||||
\(359\) | 8.93132e123 | 1.06865 | 0.534324 | − | 0.845280i | \(-0.320566\pi\) | ||||
0.534324 | + | 0.845280i | \(0.320566\pi\) | |||||||
\(360\) | −2.14603e123 | −0.224370 | ||||||||
\(361\) | −8.01373e123 | −0.732378 | ||||||||
\(362\) | 4.88384e123 | 0.390297 | ||||||||
\(363\) | −3.13985e124 | −2.19502 | ||||||||
\(364\) | −9.51170e123 | −0.581890 | ||||||||
\(365\) | 2.09283e123 | 0.112080 | ||||||||
\(366\) | −1.21867e124 | −0.571551 | ||||||||
\(367\) | −5.31976e123 | −0.218569 | −0.109284 | − | 0.994011i | \(-0.534856\pi\) | ||||
−0.109284 | + | 0.994011i | \(0.534856\pi\) | |||||||
\(368\) | 2.09691e124 | 0.755024 | ||||||||
\(369\) | 5.09613e123 | 0.160865 | ||||||||
\(370\) | 5.72441e122 | 0.0158470 | ||||||||
\(371\) | 3.52961e124 | 0.857219 | ||||||||
\(372\) | −6.14567e124 | −1.30990 | ||||||||
\(373\) | 7.10916e124 | 1.33027 | 0.665135 | − | 0.746723i | \(-0.268374\pi\) | ||||
0.665135 | + | 0.746723i | \(0.268374\pi\) | |||||||
\(374\) | 2.67323e124 | 0.439302 | ||||||||
\(375\) | −5.52572e124 | −0.797761 | ||||||||
\(376\) | −3.09573e124 | −0.392783 | ||||||||
\(377\) | −2.32350e124 | −0.259172 | ||||||||
\(378\) | −5.40871e124 | −0.530568 | ||||||||
\(379\) | 2.11040e125 | 1.82122 | 0.910609 | − | 0.413268i | \(-0.135613\pi\) | ||||
0.910609 | + | 0.413268i | \(0.135613\pi\) | |||||||
\(380\) | 1.59553e124 | 0.121171 | ||||||||
\(381\) | 3.69403e125 | 2.46967 | ||||||||
\(382\) | 4.76507e123 | 0.0280541 | ||||||||
\(383\) | −2.81102e125 | −1.45789 | −0.728943 | − | 0.684574i | \(-0.759988\pi\) | ||||
−0.728943 | + | 0.684574i | \(0.759988\pi\) | |||||||
\(384\) | −3.24606e125 | −1.48352 | ||||||||
\(385\) | −1.80863e125 | −0.728626 | ||||||||
\(386\) | 3.90427e124 | 0.138693 | ||||||||
\(387\) | 1.08994e125 | 0.341524 | ||||||||
\(388\) | −2.10014e125 | −0.580643 | ||||||||
\(389\) | −6.39856e125 | −1.56144 | −0.780722 | − | 0.624878i | \(-0.785149\pi\) | ||||
−0.780722 | + | 0.624878i | \(0.785149\pi\) | |||||||
\(390\) | 1.83845e124 | 0.0396112 | ||||||||
\(391\) | 5.23635e125 | 0.996451 | ||||||||
\(392\) | 8.00359e125 | 1.34558 | ||||||||
\(393\) | −9.21208e125 | −1.36873 | ||||||||
\(394\) | 9.55591e124 | 0.125518 | ||||||||
\(395\) | 1.55464e125 | 0.180580 | ||||||||
\(396\) | 2.22712e126 | 2.28838 | ||||||||
\(397\) | −1.17265e126 | −1.06617 | −0.533086 | − | 0.846061i | \(-0.678968\pi\) | ||||
−0.533086 | + | 0.846061i | \(0.678968\pi\) | |||||||
\(398\) | −2.14931e125 | −0.172970 | ||||||||
\(399\) | 2.19111e126 | 1.56128 | ||||||||
\(400\) | −1.13492e126 | −0.716238 | ||||||||
\(401\) | −1.29718e126 | −0.725266 | −0.362633 | − | 0.931932i | \(-0.618122\pi\) | ||||
−0.362633 | + | 0.931932i | \(0.618122\pi\) | |||||||
\(402\) | −4.13430e125 | −0.204851 | ||||||||
\(403\) | 6.79585e125 | 0.298503 | ||||||||
\(404\) | 1.20238e126 | 0.468321 | ||||||||
\(405\) | −4.68108e123 | −0.00161725 | ||||||||
\(406\) | 1.31516e126 | 0.403148 | ||||||||
\(407\) | −1.23993e126 | −0.337339 | ||||||||
\(408\) | −3.68291e126 | −0.889556 | ||||||||
\(409\) | −4.22786e126 | −0.906860 | −0.453430 | − | 0.891292i | \(-0.649800\pi\) | ||||
−0.453430 | + | 0.891292i | \(0.649800\pi\) | |||||||
\(410\) | 3.75565e124 | 0.00715596 | ||||||||
\(411\) | −5.43400e126 | −0.920007 | ||||||||
\(412\) | 6.00396e126 | 0.903489 | ||||||||
\(413\) | 1.25197e126 | 0.167500 | ||||||||
\(414\) | −3.80254e126 | −0.452436 | ||||||||
\(415\) | −3.09746e126 | −0.327849 | ||||||||
\(416\) | 2.73999e126 | 0.258061 | ||||||||
\(417\) | 7.06196e126 | 0.592007 | ||||||||
\(418\) | 3.01235e126 | 0.224831 | ||||||||
\(419\) | 2.60430e127 | 1.73106 | 0.865528 | − | 0.500860i | \(-0.166983\pi\) | ||||
0.865528 | + | 0.500860i | \(0.166983\pi\) | |||||||
\(420\) | 1.19385e127 | 0.706900 | ||||||||
\(421\) | −1.18108e127 | −0.623156 | −0.311578 | − | 0.950221i | \(-0.600858\pi\) | ||||
−0.311578 | + | 0.950221i | \(0.600858\pi\) | |||||||
\(422\) | 2.78147e126 | 0.130804 | ||||||||
\(423\) | −2.79335e127 | −1.17117 | ||||||||
\(424\) | −6.68532e126 | −0.249965 | ||||||||
\(425\) | −2.83410e127 | −0.945262 | ||||||||
\(426\) | 1.75661e127 | 0.522769 | ||||||||
\(427\) | 8.75103e127 | 2.32438 | ||||||||
\(428\) | −4.27267e127 | −1.01316 | ||||||||
\(429\) | −3.98214e127 | −0.843214 | ||||||||
\(430\) | 8.03245e125 | 0.0151925 | ||||||||
\(431\) | 2.46609e127 | 0.416736 | 0.208368 | − | 0.978051i | \(-0.433185\pi\) | ||||
0.208368 | + | 0.978051i | \(0.433185\pi\) | |||||||
\(432\) | −5.09752e127 | −0.769834 | ||||||||
\(433\) | −3.33591e127 | −0.450351 | −0.225175 | − | 0.974318i | \(-0.572295\pi\) | ||||
−0.225175 | + | 0.974318i | \(0.572295\pi\) | |||||||
\(434\) | −3.84661e127 | −0.464330 | ||||||||
\(435\) | 2.91631e127 | 0.314850 | ||||||||
\(436\) | −1.29575e128 | −1.25148 | ||||||||
\(437\) | 5.90063e127 | 0.509975 | ||||||||
\(438\) | −2.60816e127 | −0.201762 | ||||||||
\(439\) | −9.20962e127 | −0.637841 | −0.318920 | − | 0.947781i | \(-0.603320\pi\) | ||||
−0.318920 | + | 0.947781i | \(0.603320\pi\) | |||||||
\(440\) | 3.42567e127 | 0.212467 | ||||||||
\(441\) | 7.22184e128 | 4.01214 | ||||||||
\(442\) | 1.95123e127 | 0.0971245 | ||||||||
\(443\) | 5.93667e127 | 0.264827 | 0.132414 | − | 0.991195i | \(-0.457727\pi\) | ||||
0.132414 | + | 0.991195i | \(0.457727\pi\) | |||||||
\(444\) | 8.18454e127 | 0.327281 | ||||||||
\(445\) | −1.36572e128 | −0.489669 | ||||||||
\(446\) | −6.43650e127 | −0.206971 | ||||||||
\(447\) | −1.07683e129 | −3.10623 | ||||||||
\(448\) | 3.96546e128 | 1.02638 | ||||||||
\(449\) | 8.64330e127 | 0.200785 | 0.100393 | − | 0.994948i | \(-0.467990\pi\) | ||||
0.100393 | + | 0.994948i | \(0.467990\pi\) | |||||||
\(450\) | 2.05807e128 | 0.429194 | ||||||||
\(451\) | −8.13486e127 | −0.152331 | ||||||||
\(452\) | −6.55560e128 | −1.10255 | ||||||||
\(453\) | 7.12369e128 | 1.07632 | ||||||||
\(454\) | −2.67629e128 | −0.363349 | ||||||||
\(455\) | −1.32015e128 | −0.161091 | ||||||||
\(456\) | −4.15012e128 | −0.455267 | ||||||||
\(457\) | 4.98066e128 | 0.491305 | 0.245653 | − | 0.969358i | \(-0.420998\pi\) | ||||
0.245653 | + | 0.969358i | \(0.420998\pi\) | |||||||
\(458\) | 1.77031e127 | 0.0157063 | ||||||||
\(459\) | −1.27294e129 | −1.01600 | ||||||||
\(460\) | 3.21500e128 | 0.230902 | ||||||||
\(461\) | −1.94114e129 | −1.25477 | −0.627383 | − | 0.778711i | \(-0.715874\pi\) | ||||
−0.627383 | + | 0.778711i | \(0.715874\pi\) | |||||||
\(462\) | 2.25398e129 | 1.31164 | ||||||||
\(463\) | 1.80817e129 | 0.947460 | 0.473730 | − | 0.880670i | \(-0.342907\pi\) | ||||
0.473730 | + | 0.880670i | \(0.342907\pi\) | |||||||
\(464\) | 1.23949e129 | 0.584952 | ||||||||
\(465\) | −8.52971e128 | −0.362632 | ||||||||
\(466\) | −6.98828e128 | −0.267703 | ||||||||
\(467\) | 3.48140e129 | 1.20195 | 0.600974 | − | 0.799269i | \(-0.294780\pi\) | ||||
0.600974 | + | 0.799269i | \(0.294780\pi\) | |||||||
\(468\) | 1.62561e129 | 0.505933 | ||||||||
\(469\) | 2.96875e129 | 0.833087 | ||||||||
\(470\) | −2.05859e128 | −0.0520984 | ||||||||
\(471\) | −9.31072e129 | −2.12554 | ||||||||
\(472\) | −2.37132e128 | −0.0488430 | ||||||||
\(473\) | −1.73986e129 | −0.323406 | ||||||||
\(474\) | −1.93745e129 | −0.325073 | ||||||||
\(475\) | −3.19363e129 | −0.483776 | ||||||||
\(476\) | 1.26709e130 | 1.73328 | ||||||||
\(477\) | −6.03234e129 | −0.745323 | ||||||||
\(478\) | 1.40348e129 | 0.156658 | ||||||||
\(479\) | −1.82246e130 | −1.83816 | −0.919082 | − | 0.394065i | \(-0.871068\pi\) | ||||
−0.919082 | + | 0.394065i | \(0.871068\pi\) | |||||||
\(480\) | −3.43906e129 | −0.313501 | ||||||||
\(481\) | −9.05042e128 | −0.0745817 | ||||||||
\(482\) | 1.92148e129 | 0.143171 | ||||||||
\(483\) | 4.41512e130 | 2.97514 | ||||||||
\(484\) | −2.04607e130 | −1.24715 | ||||||||
\(485\) | −2.91482e129 | −0.160745 | ||||||||
\(486\) | −5.64467e129 | −0.281695 | ||||||||
\(487\) | 1.25932e130 | 0.568828 | 0.284414 | − | 0.958702i | \(-0.408201\pi\) | ||||
0.284414 | + | 0.958702i | \(0.408201\pi\) | |||||||
\(488\) | −1.65751e130 | −0.677788 | ||||||||
\(489\) | 1.25942e130 | 0.466326 | ||||||||
\(490\) | 5.32222e129 | 0.178477 | ||||||||
\(491\) | 3.33258e130 | 1.01234 | 0.506172 | − | 0.862433i | \(-0.331060\pi\) | ||||
0.506172 | + | 0.862433i | \(0.331060\pi\) | |||||||
\(492\) | 5.36968e129 | 0.147789 | ||||||||
\(493\) | 3.09522e130 | 0.771997 | ||||||||
\(494\) | 2.19876e129 | 0.0497075 | ||||||||
\(495\) | 3.09107e130 | 0.633515 | ||||||||
\(496\) | −3.62530e130 | −0.673724 | ||||||||
\(497\) | −1.26138e131 | −2.12599 | ||||||||
\(498\) | 3.86017e130 | 0.590178 | ||||||||
\(499\) | −1.20619e131 | −1.67317 | −0.836586 | − | 0.547835i | \(-0.815452\pi\) | ||||
−0.836586 | + | 0.547835i | \(0.815452\pi\) | |||||||
\(500\) | −3.60081e130 | −0.453268 | ||||||||
\(501\) | 2.45985e130 | 0.281047 | ||||||||
\(502\) | 1.93306e130 | 0.200501 | ||||||||
\(503\) | 9.91612e130 | 0.933887 | 0.466944 | − | 0.884287i | \(-0.345355\pi\) | ||||
0.466944 | + | 0.884287i | \(0.345355\pi\) | |||||||
\(504\) | −1.92047e131 | −1.64258 | ||||||||
\(505\) | 1.66880e130 | 0.129650 | ||||||||
\(506\) | 6.06993e130 | 0.428434 | ||||||||
\(507\) | 2.23345e131 | 1.43249 | ||||||||
\(508\) | 2.40719e131 | 1.40321 | ||||||||
\(509\) | −1.93323e131 | −1.02441 | −0.512203 | − | 0.858864i | \(-0.671170\pi\) | ||||
−0.512203 | + | 0.858864i | \(0.671170\pi\) | |||||||
\(510\) | −2.44906e130 | −0.117990 | ||||||||
\(511\) | 1.87286e131 | 0.820525 | ||||||||
\(512\) | −2.50650e131 | −0.998793 | ||||||||
\(513\) | −1.43442e131 | −0.519977 | ||||||||
\(514\) | −3.10900e130 | −0.102544 | ||||||||
\(515\) | 8.33302e130 | 0.250122 | ||||||||
\(516\) | 1.14845e131 | 0.313762 | ||||||||
\(517\) | 4.45898e131 | 1.10903 | ||||||||
\(518\) | 5.12275e130 | 0.116014 | ||||||||
\(519\) | −2.37221e131 | −0.489256 | ||||||||
\(520\) | 2.50045e130 | 0.0469739 | ||||||||
\(521\) | 8.96380e131 | 1.53413 | 0.767065 | − | 0.641569i | \(-0.221716\pi\) | ||||
0.767065 | + | 0.641569i | \(0.221716\pi\) | |||||||
\(522\) | −2.24769e131 | −0.350523 | ||||||||
\(523\) | −5.60728e131 | −0.796931 | −0.398465 | − | 0.917183i | \(-0.630457\pi\) | ||||
−0.398465 | + | 0.917183i | \(0.630457\pi\) | |||||||
\(524\) | −6.00301e131 | −0.777681 | ||||||||
\(525\) | −2.38962e132 | −2.82230 | ||||||||
\(526\) | 2.46482e131 | 0.265446 | ||||||||
\(527\) | −9.05299e131 | −0.889154 | ||||||||
\(528\) | 2.12430e132 | 1.90314 | ||||||||
\(529\) | −3.45045e130 | −0.0282018 | ||||||||
\(530\) | −4.44560e130 | −0.0331551 | ||||||||
\(531\) | −2.13970e131 | −0.145636 | ||||||||
\(532\) | 1.42783e132 | 0.887078 | ||||||||
\(533\) | −5.93776e130 | −0.0336785 | ||||||||
\(534\) | 1.70201e132 | 0.881480 | ||||||||
\(535\) | −5.93013e131 | −0.280483 | ||||||||
\(536\) | −5.62302e131 | −0.242928 | ||||||||
\(537\) | 7.29570e132 | 2.87948 | ||||||||
\(538\) | 6.59195e131 | 0.237724 | ||||||||
\(539\) | −1.15281e133 | −3.79929 | ||||||||
\(540\) | −7.81556e131 | −0.235430 | ||||||||
\(541\) | 3.84151e132 | 1.05787 | 0.528937 | − | 0.848661i | \(-0.322591\pi\) | ||||
0.528937 | + | 0.848661i | \(0.322591\pi\) | |||||||
\(542\) | −8.88241e131 | −0.223648 | ||||||||
\(543\) | 9.69145e132 | 2.23150 | ||||||||
\(544\) | −3.65004e132 | −0.768689 | ||||||||
\(545\) | −1.79839e132 | −0.346461 | ||||||||
\(546\) | 1.64522e132 | 0.289988 | ||||||||
\(547\) | 5.42767e130 | 0.00875443 | 0.00437721 | − | 0.999990i | \(-0.498607\pi\) | ||||
0.00437721 | + | 0.999990i | \(0.498607\pi\) | |||||||
\(548\) | −3.54104e132 | −0.522725 | ||||||||
\(549\) | −1.49561e133 | −2.02097 | ||||||||
\(550\) | −3.28526e132 | −0.406425 | ||||||||
\(551\) | 3.48787e132 | 0.395101 | ||||||||
\(552\) | −8.36255e132 | −0.867548 | ||||||||
\(553\) | 1.39124e133 | 1.32200 | ||||||||
\(554\) | −6.18922e131 | −0.0538781 | ||||||||
\(555\) | 1.13595e132 | 0.0906043 | ||||||||
\(556\) | 4.60189e132 | 0.336363 | ||||||||
\(557\) | −1.26479e133 | −0.847308 | −0.423654 | − | 0.905824i | \(-0.639253\pi\) | ||||
−0.423654 | + | 0.905824i | \(0.639253\pi\) | |||||||
\(558\) | 6.57411e132 | 0.403718 | ||||||||
\(559\) | −1.26995e132 | −0.0715012 | ||||||||
\(560\) | 7.04242e132 | 0.363582 | ||||||||
\(561\) | 5.30474e133 | 2.51169 | ||||||||
\(562\) | 4.36492e132 | 0.189568 | ||||||||
\(563\) | 5.35021e132 | 0.213164 | 0.106582 | − | 0.994304i | \(-0.466009\pi\) | ||||
0.106582 | + | 0.994304i | \(0.466009\pi\) | |||||||
\(564\) | −2.94330e133 | −1.07596 | ||||||||
\(565\) | −9.09865e132 | −0.305230 | ||||||||
\(566\) | −1.56428e133 | −0.481633 | ||||||||
\(567\) | −4.18907e131 | −0.0118397 | ||||||||
\(568\) | 2.38915e133 | 0.619938 | ||||||||
\(569\) | −5.46524e133 | −1.30216 | −0.651080 | − | 0.759009i | \(-0.725684\pi\) | ||||
−0.651080 | + | 0.759009i | \(0.725684\pi\) | |||||||
\(570\) | −2.75974e132 | −0.0603863 | ||||||||
\(571\) | 4.37356e133 | 0.878990 | 0.439495 | − | 0.898245i | \(-0.355157\pi\) | ||||
0.439495 | + | 0.898245i | \(0.355157\pi\) | |||||||
\(572\) | −2.59494e133 | −0.479093 | ||||||||
\(573\) | 9.45578e132 | 0.160398 | ||||||||
\(574\) | 3.36091e132 | 0.0523878 | ||||||||
\(575\) | −6.43521e133 | −0.921875 | ||||||||
\(576\) | −6.77724e133 | −0.892406 | ||||||||
\(577\) | 8.23104e133 | 0.996387 | 0.498193 | − | 0.867066i | \(-0.333997\pi\) | ||||
0.498193 | + | 0.867066i | \(0.333997\pi\) | |||||||
\(578\) | −5.52802e131 | −0.00615276 | ||||||||
\(579\) | 7.74760e133 | 0.792970 | ||||||||
\(580\) | 1.90040e133 | 0.178890 | ||||||||
\(581\) | −2.77190e134 | −2.40013 | ||||||||
\(582\) | 3.63256e133 | 0.289366 | ||||||||
\(583\) | 9.62932e133 | 0.705782 | ||||||||
\(584\) | −3.54733e133 | −0.239264 | ||||||||
\(585\) | 2.25622e133 | 0.140063 | ||||||||
\(586\) | −4.81802e133 | −0.275318 | ||||||||
\(587\) | 3.26683e133 | 0.171861 | 0.0859307 | − | 0.996301i | \(-0.472614\pi\) | ||||
0.0859307 | + | 0.996301i | \(0.472614\pi\) | |||||||
\(588\) | 7.60950e134 | 3.68600 | ||||||||
\(589\) | −1.02014e134 | −0.455061 | ||||||||
\(590\) | −1.57687e132 | −0.00647850 | ||||||||
\(591\) | 1.89627e134 | 0.717641 | ||||||||
\(592\) | 4.82801e133 | 0.168331 | ||||||||
\(593\) | −5.04630e134 | −1.62114 | −0.810571 | − | 0.585641i | \(-0.800843\pi\) | ||||
−0.810571 | + | 0.585641i | \(0.800843\pi\) | |||||||
\(594\) | −1.47558e134 | −0.436837 | ||||||||
\(595\) | 1.75861e134 | 0.479842 | ||||||||
\(596\) | −7.01712e134 | −1.76488 | ||||||||
\(597\) | −4.26508e134 | −0.988945 | ||||||||
\(598\) | 4.43054e133 | 0.0947216 | ||||||||
\(599\) | −3.75880e134 | −0.741051 | −0.370526 | − | 0.928822i | \(-0.620822\pi\) | ||||
−0.370526 | + | 0.928822i | \(0.620822\pi\) | |||||||
\(600\) | 4.52611e134 | 0.822980 | ||||||||
\(601\) | 6.42928e134 | 1.07833 | 0.539163 | − | 0.842201i | \(-0.318741\pi\) | ||||
0.539163 | + | 0.842201i | \(0.318741\pi\) | |||||||
\(602\) | 7.18820e133 | 0.111222 | ||||||||
\(603\) | −5.07379e134 | −0.724341 | ||||||||
\(604\) | 4.64211e134 | 0.611539 | ||||||||
\(605\) | −2.83978e134 | −0.345262 | ||||||||
\(606\) | −2.07972e134 | −0.233390 | ||||||||
\(607\) | −5.58240e134 | −0.578321 | −0.289161 | − | 0.957281i | \(-0.593376\pi\) | ||||
−0.289161 | + | 0.957281i | \(0.593376\pi\) | |||||||
\(608\) | −4.11308e134 | −0.393408 | ||||||||
\(609\) | 2.60979e135 | 2.30498 | ||||||||
\(610\) | −1.10221e134 | −0.0899013 | ||||||||
\(611\) | 3.25468e134 | 0.245194 | ||||||||
\(612\) | −2.16554e135 | −1.50703 | ||||||||
\(613\) | −7.34401e133 | −0.0472172 | −0.0236086 | − | 0.999721i | \(-0.507516\pi\) | ||||
−0.0236086 | + | 0.999721i | \(0.507516\pi\) | |||||||
\(614\) | 5.43227e134 | 0.322712 | ||||||||
\(615\) | 7.45269e133 | 0.0409138 | ||||||||
\(616\) | 3.06562e135 | 1.55544 | ||||||||
\(617\) | 3.33719e135 | 1.56513 | 0.782566 | − | 0.622568i | \(-0.213911\pi\) | ||||
0.782566 | + | 0.622568i | \(0.213911\pi\) | |||||||
\(618\) | −1.03849e135 | −0.450258 | ||||||||
\(619\) | 8.53749e134 | 0.342242 | 0.171121 | − | 0.985250i | \(-0.445261\pi\) | ||||
0.171121 | + | 0.985250i | \(0.445261\pi\) | |||||||
\(620\) | −5.55834e134 | −0.206038 | ||||||||
\(621\) | −2.89038e135 | −0.990859 | ||||||||
\(622\) | −1.14111e134 | −0.0361821 | ||||||||
\(623\) | −1.22218e136 | −3.58480 | ||||||||
\(624\) | 1.55056e135 | 0.420761 | ||||||||
\(625\) | 3.22471e135 | 0.809674 | ||||||||
\(626\) | −1.65078e135 | −0.383561 | ||||||||
\(627\) | 5.97770e135 | 1.28546 | ||||||||
\(628\) | −6.06728e135 | −1.20768 | ||||||||
\(629\) | 1.20564e135 | 0.222157 | ||||||||
\(630\) | −1.27707e135 | −0.217871 | ||||||||
\(631\) | 6.63301e135 | 1.04782 | 0.523910 | − | 0.851774i | \(-0.324473\pi\) | ||||
0.523910 | + | 0.851774i | \(0.324473\pi\) | |||||||
\(632\) | −2.63510e135 | −0.385495 | ||||||||
\(633\) | 5.51952e135 | 0.747862 | ||||||||
\(634\) | −1.74783e135 | −0.219366 | ||||||||
\(635\) | 3.34099e135 | 0.388463 | ||||||||
\(636\) | −6.35614e135 | −0.684737 | ||||||||
\(637\) | −8.41454e135 | −0.839978 | ||||||||
\(638\) | 3.58795e135 | 0.331928 | ||||||||
\(639\) | 2.15579e136 | 1.84848 | ||||||||
\(640\) | −2.93584e135 | −0.233348 | ||||||||
\(641\) | −3.59662e135 | −0.265021 | −0.132511 | − | 0.991182i | \(-0.542304\pi\) | ||||
−0.132511 | + | 0.991182i | \(0.542304\pi\) | |||||||
\(642\) | 7.39034e135 | 0.504912 | ||||||||
\(643\) | −1.89570e136 | −1.20098 | −0.600492 | − | 0.799631i | \(-0.705029\pi\) | ||||
−0.600492 | + | 0.799631i | \(0.705029\pi\) | |||||||
\(644\) | 2.87709e136 | 1.69040 | ||||||||
\(645\) | 1.59395e135 | 0.0868620 | ||||||||
\(646\) | −2.92905e135 | −0.148064 | ||||||||
\(647\) | 2.63899e135 | 0.123760 | 0.0618801 | − | 0.998084i | \(-0.480290\pi\) | ||||
0.0618801 | + | 0.998084i | \(0.480290\pi\) | |||||||
\(648\) | 7.93440e133 | 0.00345244 | ||||||||
\(649\) | 3.41556e135 | 0.137910 | ||||||||
\(650\) | −2.39797e135 | −0.0898556 | ||||||||
\(651\) | −7.63319e136 | −2.65478 | ||||||||
\(652\) | 8.20691e135 | 0.264955 | ||||||||
\(653\) | −2.55404e136 | −0.765488 | −0.382744 | − | 0.923855i | \(-0.625021\pi\) | ||||
−0.382744 | + | 0.923855i | \(0.625021\pi\) | |||||||
\(654\) | 2.24122e136 | 0.623683 | ||||||||
\(655\) | −8.33169e135 | −0.215293 | ||||||||
\(656\) | 3.16754e135 | 0.0760127 | ||||||||
\(657\) | −3.20084e136 | −0.713418 | ||||||||
\(658\) | −1.84223e136 | −0.381406 | ||||||||
\(659\) | 2.69234e136 | 0.517830 | 0.258915 | − | 0.965900i | \(-0.416635\pi\) | ||||
0.258915 | + | 0.965900i | \(0.416635\pi\) | |||||||
\(660\) | 3.25700e136 | 0.582018 | ||||||||
\(661\) | 4.30762e136 | 0.715265 | 0.357632 | − | 0.933862i | \(-0.383584\pi\) | ||||
0.357632 | + | 0.933862i | \(0.383584\pi\) | |||||||
\(662\) | 1.94915e135 | 0.0300769 | ||||||||
\(663\) | 3.87201e136 | 0.555304 | ||||||||
\(664\) | 5.25018e136 | 0.699877 | ||||||||
\(665\) | 1.98171e136 | 0.245579 | ||||||||
\(666\) | −8.75512e135 | −0.100870 | ||||||||
\(667\) | 7.02811e136 | 0.752897 | ||||||||
\(668\) | 1.60295e136 | 0.159684 | ||||||||
\(669\) | −1.27726e137 | −1.18334 | ||||||||
\(670\) | −3.73919e135 | −0.0322218 | ||||||||
\(671\) | 2.38742e137 | 1.91375 | ||||||||
\(672\) | −3.07759e137 | −2.29510 | ||||||||
\(673\) | −2.61744e137 | −1.81612 | −0.908062 | − | 0.418835i | \(-0.862438\pi\) | ||||
−0.908062 | + | 0.418835i | \(0.862438\pi\) | |||||||
\(674\) | −2.79894e136 | −0.180713 | ||||||||
\(675\) | 1.56438e137 | 0.939957 | ||||||||
\(676\) | 1.45542e137 | 0.813903 | ||||||||
\(677\) | 2.86931e137 | 1.49357 | 0.746787 | − | 0.665064i | \(-0.231596\pi\) | ||||
0.746787 | + | 0.665064i | \(0.231596\pi\) | |||||||
\(678\) | 1.13391e137 | 0.549461 | ||||||||
\(679\) | −2.60846e137 | −1.17679 | ||||||||
\(680\) | −3.33094e136 | −0.139921 | ||||||||
\(681\) | −5.31080e137 | −2.07742 | ||||||||
\(682\) | −1.04941e137 | −0.382301 | ||||||||
\(683\) | 2.07909e137 | 0.705456 | 0.352728 | − | 0.935726i | \(-0.385254\pi\) | ||||
0.352728 | + | 0.935726i | \(0.385254\pi\) | |||||||
\(684\) | −2.44025e137 | −0.771283 | ||||||||
\(685\) | −4.91468e136 | −0.144711 | ||||||||
\(686\) | 2.83868e137 | 0.778749 | ||||||||
\(687\) | 3.51300e136 | 0.0897999 | ||||||||
\(688\) | 6.77463e136 | 0.161379 | ||||||||
\(689\) | 7.02859e136 | 0.156040 | ||||||||
\(690\) | −5.56092e136 | −0.115071 | ||||||||
\(691\) | −6.16036e137 | −1.18828 | −0.594142 | − | 0.804360i | \(-0.702508\pi\) | ||||
−0.594142 | + | 0.804360i | \(0.702508\pi\) | |||||||
\(692\) | −1.54584e137 | −0.277983 | ||||||||
\(693\) | 2.76618e138 | 4.63788 | ||||||||
\(694\) | 1.96947e137 | 0.307903 | ||||||||
\(695\) | 6.38705e136 | 0.0931188 | ||||||||
\(696\) | −4.94312e137 | −0.672129 | ||||||||
\(697\) | 7.90990e136 | 0.100319 | ||||||||
\(698\) | 1.98371e136 | 0.0234687 | ||||||||
\(699\) | −1.38675e138 | −1.53058 | ||||||||
\(700\) | −1.55719e138 | −1.60356 | ||||||||
\(701\) | 2.99195e137 | 0.287495 | 0.143748 | − | 0.989614i | \(-0.454085\pi\) | ||||
0.143748 | + | 0.989614i | \(0.454085\pi\) | |||||||
\(702\) | −1.07705e137 | −0.0965795 | ||||||||
\(703\) | 1.35858e137 | 0.113698 | ||||||||
\(704\) | 1.08184e138 | 0.845062 | ||||||||
\(705\) | −4.08506e137 | −0.297870 | ||||||||
\(706\) | 1.90001e137 | 0.129338 | ||||||||
\(707\) | 1.49340e138 | 0.949151 | ||||||||
\(708\) | −2.25455e137 | −0.133797 | ||||||||
\(709\) | −2.61734e138 | −1.45050 | −0.725250 | − | 0.688486i | \(-0.758276\pi\) | ||||
−0.725250 | + | 0.688486i | \(0.758276\pi\) | |||||||
\(710\) | 1.58873e137 | 0.0822282 | ||||||||
\(711\) | −2.37772e138 | −1.14944 | ||||||||
\(712\) | 2.31489e138 | 1.04532 | ||||||||
\(713\) | −2.05560e138 | −0.867156 | ||||||||
\(714\) | −2.19165e138 | −0.863789 | ||||||||
\(715\) | −3.60157e137 | −0.132632 | ||||||||
\(716\) | 4.75420e138 | 1.63605 | ||||||||
\(717\) | 2.78505e138 | 0.895683 | ||||||||
\(718\) | −1.00668e138 | −0.302591 | ||||||||
\(719\) | −2.46641e138 | −0.692970 | −0.346485 | − | 0.938055i | \(-0.612625\pi\) | ||||
−0.346485 | + | 0.938055i | \(0.612625\pi\) | |||||||
\(720\) | −1.20360e138 | −0.316122 | ||||||||
\(721\) | 7.45718e138 | 1.83111 | ||||||||
\(722\) | 9.03256e137 | 0.207375 | ||||||||
\(723\) | 3.81297e138 | 0.818571 | ||||||||
\(724\) | 6.31539e138 | 1.26788 | ||||||||
\(725\) | −3.80387e138 | −0.714220 | ||||||||
\(726\) | 3.53903e138 | 0.621525 | ||||||||
\(727\) | −7.91554e138 | −1.30035 | −0.650177 | − | 0.759783i | \(-0.725305\pi\) | ||||
−0.650177 | + | 0.759783i | \(0.725305\pi\) | |||||||
\(728\) | 2.23764e138 | 0.343889 | ||||||||
\(729\) | −1.12454e139 | −1.61693 | ||||||||
\(730\) | −2.35890e137 | −0.0317359 | ||||||||
\(731\) | 1.69174e138 | 0.212981 | ||||||||
\(732\) | −1.57589e139 | −1.85669 | ||||||||
\(733\) | −2.05544e138 | −0.226653 | −0.113327 | − | 0.993558i | \(-0.536151\pi\) | ||||
−0.113327 | + | 0.993558i | \(0.536151\pi\) | |||||||
\(734\) | 5.99609e137 | 0.0618883 | ||||||||
\(735\) | 1.05614e139 | 1.02043 | ||||||||
\(736\) | −8.28790e138 | −0.749671 | ||||||||
\(737\) | 8.09920e138 | 0.685913 | ||||||||
\(738\) | −5.74402e137 | −0.0455494 | ||||||||
\(739\) | 7.40954e138 | 0.550220 | 0.275110 | − | 0.961413i | \(-0.411286\pi\) | ||||
0.275110 | + | 0.961413i | \(0.411286\pi\) | |||||||
\(740\) | 7.40235e137 | 0.0514791 | ||||||||
\(741\) | 4.36321e138 | 0.284200 | ||||||||
\(742\) | −3.97834e138 | −0.242724 | ||||||||
\(743\) | −2.68694e139 | −1.53568 | −0.767841 | − | 0.640641i | \(-0.778669\pi\) | ||||
−0.767841 | + | 0.640641i | \(0.778669\pi\) | |||||||
\(744\) | 1.44578e139 | 0.774131 | ||||||||
\(745\) | −9.73920e138 | −0.488589 | ||||||||
\(746\) | −8.01298e138 | −0.376670 | ||||||||
\(747\) | 4.73737e139 | 2.08683 | ||||||||
\(748\) | 3.45681e139 | 1.42708 | ||||||||
\(749\) | −5.30684e139 | −2.05337 | ||||||||
\(750\) | 6.22823e138 | 0.225888 | ||||||||
\(751\) | 1.83639e139 | 0.624350 | 0.312175 | − | 0.950025i | \(-0.398942\pi\) | ||||
0.312175 | + | 0.950025i | \(0.398942\pi\) | |||||||
\(752\) | −1.73623e139 | −0.553405 | ||||||||
\(753\) | 3.83596e139 | 1.14635 | ||||||||
\(754\) | 2.61890e138 | 0.0733852 | ||||||||
\(755\) | 6.44288e138 | 0.169298 | ||||||||
\(756\) | −6.99410e139 | −1.72355 | ||||||||
\(757\) | 5.04230e139 | 1.16541 | 0.582705 | − | 0.812684i | \(-0.301994\pi\) | ||||
0.582705 | + | 0.812684i | \(0.301994\pi\) | |||||||
\(758\) | −2.37870e139 | −0.515683 | ||||||||
\(759\) | 1.20451e140 | 2.44955 | ||||||||
\(760\) | −3.75350e138 | −0.0716105 | ||||||||
\(761\) | −7.69419e139 | −1.37723 | −0.688616 | − | 0.725126i | \(-0.741781\pi\) | ||||
−0.688616 | + | 0.725126i | \(0.741781\pi\) | |||||||
\(762\) | −4.16367e139 | −0.699294 | ||||||||
\(763\) | −1.60937e140 | −2.53639 | ||||||||
\(764\) | 6.16181e138 | 0.0911340 | ||||||||
\(765\) | −3.00559e139 | −0.417206 | ||||||||
\(766\) | 3.16840e139 | 0.412805 | ||||||||
\(767\) | 2.49307e138 | 0.0304902 | ||||||||
\(768\) | −4.10473e139 | −0.471265 | ||||||||
\(769\) | 1.21595e140 | 1.31065 | 0.655326 | − | 0.755346i | \(-0.272531\pi\) | ||||
0.655326 | + | 0.755346i | \(0.272531\pi\) | |||||||
\(770\) | 2.03857e139 | 0.206313 | ||||||||
\(771\) | −6.16949e139 | −0.586289 | ||||||||
\(772\) | 5.04868e139 | 0.450546 | ||||||||
\(773\) | 2.98873e139 | 0.250485 | 0.125243 | − | 0.992126i | \(-0.460029\pi\) | ||||
0.125243 | + | 0.992126i | \(0.460029\pi\) | |||||||
\(774\) | −1.22851e139 | −0.0967036 | ||||||||
\(775\) | 1.11257e140 | 0.822609 | ||||||||
\(776\) | 4.94060e139 | 0.343152 | ||||||||
\(777\) | 1.01655e140 | 0.663302 | ||||||||
\(778\) | 7.21204e139 | 0.442128 | ||||||||
\(779\) | 8.91334e138 | 0.0513421 | ||||||||
\(780\) | 2.37733e139 | 0.128677 | ||||||||
\(781\) | −3.44125e140 | −1.75041 | ||||||||
\(782\) | −5.90207e139 | −0.282148 | ||||||||
\(783\) | −1.70851e140 | −0.767665 | ||||||||
\(784\) | 4.48879e140 | 1.89584 | ||||||||
\(785\) | −8.42091e139 | −0.334334 | ||||||||
\(786\) | 1.03833e140 | 0.387561 | ||||||||
\(787\) | −1.13298e140 | −0.397603 | −0.198801 | − | 0.980040i | \(-0.563705\pi\) | ||||
−0.198801 | + | 0.980040i | \(0.563705\pi\) | |||||||
\(788\) | 1.23569e140 | 0.407746 | ||||||||
\(789\) | 4.89117e140 | 1.51767 | ||||||||
\(790\) | −1.75229e139 | −0.0511318 | ||||||||
\(791\) | −8.14233e140 | −2.23455 | ||||||||
\(792\) | −5.23934e140 | −1.35240 | ||||||||
\(793\) | 1.74261e140 | 0.423108 | ||||||||
\(794\) | 1.32173e140 | 0.301890 | ||||||||
\(795\) | −8.82182e139 | −0.189563 | ||||||||
\(796\) | −2.77932e140 | −0.561894 | ||||||||
\(797\) | −7.10014e140 | −1.35064 | −0.675318 | − | 0.737527i | \(-0.735994\pi\) | ||||
−0.675318 | + | 0.737527i | \(0.735994\pi\) | |||||||
\(798\) | −2.46968e140 | −0.442080 | ||||||||
\(799\) | −4.33567e140 | −0.730362 | ||||||||
\(800\) | 4.48571e140 | 0.711159 | ||||||||
\(801\) | 2.08879e141 | 3.11686 | ||||||||
\(802\) | 1.46209e140 | 0.205361 | ||||||||
\(803\) | 5.10945e140 | 0.675570 | ||||||||
\(804\) | −5.34614e140 | −0.665460 | ||||||||
\(805\) | 3.99317e140 | 0.467970 | ||||||||
\(806\) | −7.65984e139 | −0.0845221 | ||||||||
\(807\) | 1.30810e141 | 1.35917 | ||||||||
\(808\) | −2.82861e140 | −0.276772 | ||||||||
\(809\) | −1.18382e141 | −1.09089 | −0.545445 | − | 0.838147i | \(-0.683639\pi\) | ||||
−0.545445 | + | 0.838147i | \(0.683639\pi\) | |||||||
\(810\) | 5.27621e137 | 0.000457929 0 | ||||||||
\(811\) | −5.08646e140 | −0.415819 | −0.207909 | − | 0.978148i | \(-0.566666\pi\) | ||||
−0.207909 | + | 0.978148i | \(0.566666\pi\) | |||||||
\(812\) | 1.70065e141 | 1.30963 | ||||||||
\(813\) | −1.76262e141 | −1.27870 | ||||||||
\(814\) | 1.39756e140 | 0.0955186 | ||||||||
\(815\) | 1.13905e140 | 0.0733500 | ||||||||
\(816\) | −2.06555e141 | −1.25332 | ||||||||
\(817\) | 1.90635e140 | 0.109002 | ||||||||
\(818\) | 4.76537e140 | 0.256780 | ||||||||
\(819\) | 2.01908e141 | 1.02538 | ||||||||
\(820\) | 4.85650e139 | 0.0232462 | ||||||||
\(821\) | 7.71220e140 | 0.347965 | 0.173982 | − | 0.984749i | \(-0.444336\pi\) | ||||
0.173982 | + | 0.984749i | \(0.444336\pi\) | |||||||
\(822\) | 6.12485e140 | 0.260503 | ||||||||
\(823\) | −7.98625e139 | −0.0320222 | −0.0160111 | − | 0.999872i | \(-0.505097\pi\) | ||||
−0.0160111 | + | 0.999872i | \(0.505097\pi\) | |||||||
\(824\) | −1.41244e141 | −0.533950 | ||||||||
\(825\) | −6.51926e141 | −2.32371 | ||||||||
\(826\) | −1.41114e140 | −0.0474282 | ||||||||
\(827\) | 3.54407e141 | 1.12327 | 0.561637 | − | 0.827384i | \(-0.310172\pi\) | ||||
0.561637 | + | 0.827384i | \(0.310172\pi\) | |||||||
\(828\) | −4.91714e141 | −1.46974 | ||||||||
\(829\) | −9.91560e140 | −0.279527 | −0.139764 | − | 0.990185i | \(-0.544634\pi\) | ||||
−0.139764 | + | 0.990185i | \(0.544634\pi\) | |||||||
\(830\) | 3.49126e140 | 0.0928313 | ||||||||
\(831\) | −1.22819e141 | −0.308045 | ||||||||
\(832\) | 7.89651e140 | 0.186833 | ||||||||
\(833\) | 1.12093e142 | 2.50205 | ||||||||
\(834\) | −7.95978e140 | −0.167628 | ||||||||
\(835\) | 2.22476e140 | 0.0442069 | ||||||||
\(836\) | 3.89533e141 | 0.730365 | ||||||||
\(837\) | 4.99710e141 | 0.884165 | ||||||||
\(838\) | −2.93540e141 | −0.490154 | ||||||||
\(839\) | 1.81126e141 | 0.285448 | 0.142724 | − | 0.989763i | \(-0.454414\pi\) | ||||
0.142724 | + | 0.989763i | \(0.454414\pi\) | |||||||
\(840\) | −2.80854e141 | −0.417768 | ||||||||
\(841\) | −2.96773e141 | −0.416696 | ||||||||
\(842\) | 1.33123e141 | 0.176448 | ||||||||
\(843\) | 8.66173e141 | 1.08384 | ||||||||
\(844\) | 3.59677e141 | 0.424917 | ||||||||
\(845\) | 2.02000e141 | 0.225321 | ||||||||
\(846\) | 3.14849e141 | 0.331619 | ||||||||
\(847\) | −2.54130e142 | −2.52762 | ||||||||
\(848\) | −3.74945e141 | −0.352183 | ||||||||
\(849\) | −3.10414e142 | −2.75371 | ||||||||
\(850\) | 3.19441e141 | 0.267654 | ||||||||
\(851\) | 2.73756e141 | 0.216661 | ||||||||
\(852\) | 2.27151e142 | 1.69822 | ||||||||
\(853\) | 1.81782e142 | 1.28387 | 0.641937 | − | 0.766757i | \(-0.278131\pi\) | ||||
0.641937 | + | 0.766757i | \(0.278131\pi\) | |||||||
\(854\) | −9.86359e141 | −0.658155 | ||||||||
\(855\) | −3.38688e141 | −0.213522 | ||||||||
\(856\) | 1.00515e142 | 0.598762 | ||||||||
\(857\) | −2.44014e142 | −1.37355 | −0.686776 | − | 0.726869i | \(-0.740975\pi\) | ||||
−0.686776 | + | 0.726869i | \(0.740975\pi\) | |||||||
\(858\) | 4.48840e141 | 0.238758 | ||||||||
\(859\) | −2.45966e142 | −1.23653 | −0.618267 | − | 0.785968i | \(-0.712165\pi\) | ||||
−0.618267 | + | 0.785968i | \(0.712165\pi\) | |||||||
\(860\) | 1.03869e141 | 0.0493528 | ||||||||
\(861\) | 6.66937e141 | 0.299524 | ||||||||
\(862\) | −2.77961e141 | −0.118000 | ||||||||
\(863\) | 4.28714e142 | 1.72046 | 0.860230 | − | 0.509907i | \(-0.170320\pi\) | ||||
0.860230 | + | 0.509907i | \(0.170320\pi\) | |||||||
\(864\) | 2.01476e142 | 0.764375 | ||||||||
\(865\) | −2.14550e141 | −0.0769568 | ||||||||
\(866\) | 3.76001e141 | 0.127518 | ||||||||
\(867\) | −1.09698e141 | −0.0351780 | ||||||||
\(868\) | −4.97413e142 | −1.50838 | ||||||||
\(869\) | 3.79551e142 | 1.08846 | ||||||||
\(870\) | −3.28707e141 | −0.0891508 | ||||||||
\(871\) | 5.91174e141 | 0.151647 | ||||||||
\(872\) | 3.04826e142 | 0.739610 | ||||||||
\(873\) | 4.45803e142 | 1.02318 | ||||||||
\(874\) | −6.65080e141 | −0.144401 | ||||||||
\(875\) | −4.47236e142 | −0.918641 | ||||||||
\(876\) | −3.37266e142 | −0.655425 | ||||||||
\(877\) | 7.83172e142 | 1.44005 | 0.720024 | − | 0.693949i | \(-0.244131\pi\) | ||||
0.720024 | + | 0.693949i | \(0.244131\pi\) | |||||||
\(878\) | 1.03805e142 | 0.180606 | ||||||||
\(879\) | −9.56085e142 | −1.57411 | ||||||||
\(880\) | 1.92128e142 | 0.299351 | ||||||||
\(881\) | −7.07567e142 | −1.04336 | −0.521682 | − | 0.853140i | \(-0.674695\pi\) | ||||
−0.521682 | + | 0.853140i | \(0.674695\pi\) | |||||||
\(882\) | −8.13998e142 | −1.13605 | ||||||||
\(883\) | −6.58230e142 | −0.869528 | −0.434764 | − | 0.900544i | \(-0.643168\pi\) | ||||
−0.434764 | + | 0.900544i | \(0.643168\pi\) | |||||||
\(884\) | 2.52318e142 | 0.315510 | ||||||||
\(885\) | −3.12914e141 | −0.0370405 | ||||||||
\(886\) | −6.69143e141 | −0.0749866 | ||||||||
\(887\) | −9.56399e141 | −0.101471 | −0.0507357 | − | 0.998712i | \(-0.516157\pi\) | ||||
−0.0507357 | + | 0.998712i | \(0.516157\pi\) | |||||||
\(888\) | −1.92542e142 | −0.193418 | ||||||||
\(889\) | 2.98984e143 | 2.84389 | ||||||||
\(890\) | 1.53935e142 | 0.138651 | ||||||||
\(891\) | −1.14284e141 | −0.00974806 | ||||||||
\(892\) | −8.32317e142 | −0.672346 | ||||||||
\(893\) | −4.88569e142 | −0.373792 | ||||||||
\(894\) | 1.21373e143 | 0.879537 | ||||||||
\(895\) | 6.59845e142 | 0.452923 | ||||||||
\(896\) | −2.62727e143 | −1.70831 | ||||||||
\(897\) | 8.79193e142 | 0.541565 | ||||||||
\(898\) | −9.74216e141 | −0.0568529 | ||||||||
\(899\) | −1.21507e143 | −0.671826 | ||||||||
\(900\) | 2.66133e143 | 1.39424 | ||||||||
\(901\) | −9.36303e142 | −0.464798 | ||||||||
\(902\) | 9.16908e141 | 0.0431329 | ||||||||
\(903\) | 1.42642e143 | 0.635905 | ||||||||
\(904\) | 1.54221e143 | 0.651592 | ||||||||
\(905\) | 8.76525e142 | 0.351001 | ||||||||
\(906\) | −8.02935e142 | −0.304763 | ||||||||
\(907\) | 4.40941e143 | 1.58645 | 0.793227 | − | 0.608927i | \(-0.208400\pi\) | ||||
0.793227 | + | 0.608927i | \(0.208400\pi\) | |||||||
\(908\) | −3.46076e143 | −1.18034 | ||||||||
\(909\) | −2.55232e143 | −0.825254 | ||||||||
\(910\) | 1.48798e142 | 0.0456132 | ||||||||
\(911\) | 3.14937e143 | 0.915339 | 0.457670 | − | 0.889122i | \(-0.348684\pi\) | ||||
0.457670 | + | 0.889122i | \(0.348684\pi\) | |||||||
\(912\) | −2.32759e143 | −0.641440 | ||||||||
\(913\) | −7.56218e143 | −1.97612 | ||||||||
\(914\) | −5.61388e142 | −0.139114 | ||||||||
\(915\) | −2.18721e143 | −0.514006 | ||||||||
\(916\) | 2.28923e142 | 0.0510221 | ||||||||
\(917\) | −7.45599e143 | −1.57613 | ||||||||
\(918\) | 1.43477e143 | 0.287682 | ||||||||
\(919\) | −4.01749e143 | −0.764103 | −0.382052 | − | 0.924141i | \(-0.624782\pi\) | ||||
−0.382052 | + | 0.924141i | \(0.624782\pi\) | |||||||
\(920\) | −7.56335e142 | −0.136460 | ||||||||
\(921\) | 1.07798e144 | 1.84509 | ||||||||
\(922\) | 2.18793e143 | 0.355291 | ||||||||
\(923\) | −2.51182e143 | −0.386995 | ||||||||
\(924\) | 2.91467e144 | 4.26087 | ||||||||
\(925\) | −1.48167e143 | −0.205531 | ||||||||
\(926\) | −2.03805e143 | −0.268276 | ||||||||
\(927\) | −1.27448e144 | −1.59208 | ||||||||
\(928\) | −4.89900e143 | −0.580805 | ||||||||
\(929\) | 2.87597e143 | 0.323610 | 0.161805 | − | 0.986823i | \(-0.448268\pi\) | ||||
0.161805 | + | 0.986823i | \(0.448268\pi\) | |||||||
\(930\) | 9.61413e142 | 0.102680 | ||||||||
\(931\) | 1.26313e144 | 1.28053 | ||||||||
\(932\) | −9.03669e143 | −0.869636 | ||||||||
\(933\) | −2.26441e143 | −0.206869 | ||||||||
\(934\) | −3.92401e143 | −0.340335 | ||||||||
\(935\) | 4.79777e143 | 0.395072 | ||||||||
\(936\) | −3.82428e143 | −0.299000 | ||||||||
\(937\) | 2.28970e144 | 1.69984 | 0.849921 | − | 0.526910i | \(-0.176650\pi\) | ||||
0.849921 | + | 0.526910i | \(0.176650\pi\) | |||||||
\(938\) | −3.34618e143 | −0.235891 | ||||||||
\(939\) | −3.27580e144 | −2.19299 | ||||||||
\(940\) | −2.66201e143 | −0.169242 | ||||||||
\(941\) | 1.00318e144 | 0.605734 | 0.302867 | − | 0.953033i | \(-0.402056\pi\) | ||||
0.302867 | + | 0.953033i | \(0.402056\pi\) | |||||||
\(942\) | 1.04944e144 | 0.601853 | ||||||||
\(943\) | 1.79605e143 | 0.0978366 | ||||||||
\(944\) | −1.32995e143 | −0.0688165 | ||||||||
\(945\) | −9.70726e143 | −0.477149 | ||||||||
\(946\) | 1.96105e143 | 0.0915733 | ||||||||
\(947\) | −7.02646e143 | −0.311718 | −0.155859 | − | 0.987779i | \(-0.549815\pi\) | ||||
−0.155859 | + | 0.987779i | \(0.549815\pi\) | |||||||
\(948\) | −2.50535e144 | −1.05600 | ||||||||
\(949\) | 3.72947e143 | 0.149360 | ||||||||
\(950\) | 3.59965e143 | 0.136983 | ||||||||
\(951\) | −3.46837e144 | −1.25421 | ||||||||
\(952\) | −2.98084e144 | −1.02435 | ||||||||
\(953\) | 3.95465e144 | 1.29152 | 0.645762 | − | 0.763539i | \(-0.276540\pi\) | ||||
0.645762 | + | 0.763539i | \(0.276540\pi\) | |||||||
\(954\) | 6.79926e143 | 0.211040 | ||||||||
\(955\) | 8.55210e142 | 0.0252295 | ||||||||
\(956\) | 1.81487e144 | 0.508905 | ||||||||
\(957\) | 7.11990e144 | 1.89778 | ||||||||
\(958\) | 2.05415e144 | 0.520482 | ||||||||
\(959\) | −4.39812e144 | −1.05941 | ||||||||
\(960\) | −9.91118e143 | −0.226971 | ||||||||
\(961\) | −1.03899e144 | −0.226218 | ||||||||
\(962\) | 1.02010e143 | 0.0211180 | ||||||||
\(963\) | 9.06975e144 | 1.78534 | ||||||||
\(964\) | 2.48470e144 | 0.465092 | ||||||||
\(965\) | 7.00717e143 | 0.124729 | ||||||||
\(966\) | −4.97644e144 | −0.842419 | ||||||||
\(967\) | −3.61685e144 | −0.582299 | −0.291149 | − | 0.956678i | \(-0.594038\pi\) | ||||
−0.291149 | + | 0.956678i | \(0.594038\pi\) | |||||||
\(968\) | 4.81340e144 | 0.737051 | ||||||||
\(969\) | −5.81239e144 | −0.846547 | ||||||||
\(970\) | 3.28540e143 | 0.0455154 | ||||||||
\(971\) | 3.52227e142 | 0.00464183 | 0.00232092 | − | 0.999997i | \(-0.499261\pi\) | ||||
0.00232092 | + | 0.999997i | \(0.499261\pi\) | |||||||
\(972\) | −7.29924e144 | −0.915089 | ||||||||
\(973\) | 5.71574e144 | 0.681710 | ||||||||
\(974\) | −1.41942e144 | −0.161065 | ||||||||
\(975\) | −4.75851e144 | −0.513744 | ||||||||
\(976\) | −9.29609e144 | −0.954958 | ||||||||
\(977\) | 1.48341e145 | 1.45003 | 0.725013 | − | 0.688735i | \(-0.241834\pi\) | ||||
0.725013 | + | 0.688735i | \(0.241834\pi\) | |||||||
\(978\) | −1.41953e144 | −0.132041 | ||||||||
\(979\) | −3.33429e145 | −2.95150 | ||||||||
\(980\) | 6.88226e144 | 0.579784 | ||||||||
\(981\) | 2.75052e145 | 2.20530 | ||||||||
\(982\) | −3.75626e144 | −0.286648 | ||||||||
\(983\) | 3.00019e144 | 0.217923 | 0.108962 | − | 0.994046i | \(-0.465247\pi\) | ||||
0.108962 | + | 0.994046i | \(0.465247\pi\) | |||||||
\(984\) | −1.26323e144 | −0.0873411 | ||||||||
\(985\) | 1.71504e144 | 0.112880 | ||||||||
\(986\) | −3.48873e144 | −0.218593 | ||||||||
\(987\) | −3.65570e145 | −2.18066 | ||||||||
\(988\) | 2.84326e144 | 0.161475 | ||||||||
\(989\) | 3.84133e144 | 0.207712 | ||||||||
\(990\) | −3.48405e144 | −0.179382 | ||||||||
\(991\) | 3.64914e145 | 1.78903 | 0.894517 | − | 0.447034i | \(-0.147520\pi\) | ||||
0.894517 | + | 0.447034i | \(0.147520\pi\) | |||||||
\(992\) | 1.43287e145 | 0.668947 | ||||||||
\(993\) | 3.86788e144 | 0.171963 | ||||||||
\(994\) | 1.42175e145 | 0.601981 | ||||||||
\(995\) | −3.85747e144 | −0.155555 | ||||||||
\(996\) | 4.99166e145 | 1.91720 | ||||||||
\(997\) | −3.29611e145 | −1.20583 | −0.602916 | − | 0.797804i | \(-0.705995\pi\) | ||||
−0.602916 | + | 0.797804i | \(0.705995\pi\) | |||||||
\(998\) | 1.35954e145 | 0.473764 | ||||||||
\(999\) | −6.65492e144 | −0.220910 |
(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 | 1.98.a.a.1.3 | ✓ | 7 | |
3.2 | odd | 2 | 9.98.a.a.1.5 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.98.a.a.1.3 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.98.a.a.1.5 | 7 | 3.2 | odd | 2 |