Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,76,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, 76, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 76);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 76 \) |
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: | \(35.6228392822\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3 x^{5} + \cdots - 67\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 11\cdot 13\cdot 19 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.60397e9\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.25000e11 | −0.643108 | −0.321554 | − | 0.946891i | \(-0.604205\pi\) | ||||
−0.321554 | + | 0.946891i | \(0.604205\pi\) | |||||||
\(3\) | 1.35148e17 | 0.173286 | 0.0866430 | − | 0.996239i | \(-0.472386\pi\) | ||||
0.0866430 | + | 0.996239i | \(0.472386\pi\) | |||||||
\(4\) | −2.21540e22 | −0.586413 | ||||||||
\(5\) | 1.80927e26 | 1.11206 | 0.556030 | − | 0.831162i | \(-0.312324\pi\) | ||||
0.556030 | + | 0.831162i | \(0.312324\pi\) | |||||||
\(6\) | −1.68935e28 | −0.111442 | ||||||||
\(7\) | 2.76229e31 | 0.562461 | 0.281230 | − | 0.959640i | \(-0.409258\pi\) | ||||
0.281230 | + | 0.959640i | \(0.409258\pi\) | |||||||
\(8\) | 7.49160e33 | 1.02023 | ||||||||
\(9\) | −5.90002e35 | −0.969972 | ||||||||
\(10\) | −2.26158e37 | −0.715175 | ||||||||
\(11\) | 7.60456e38 | 0.674293 | 0.337146 | − | 0.941452i | \(-0.390538\pi\) | ||||
0.337146 | + | 0.941452i | \(0.390538\pi\) | |||||||
\(12\) | −2.99408e39 | −0.101617 | ||||||||
\(13\) | 2.57727e41 | 0.434795 | 0.217397 | − | 0.976083i | \(-0.430243\pi\) | ||||
0.217397 | + | 0.976083i | \(0.430243\pi\) | |||||||
\(14\) | −3.45284e42 | −0.361723 | ||||||||
\(15\) | 2.44520e43 | 0.192705 | ||||||||
\(16\) | −9.94899e43 | −0.0697076 | ||||||||
\(17\) | −1.39330e46 | −1.00510 | −0.502551 | − | 0.864548i | \(-0.667605\pi\) | ||||
−0.502551 | + | 0.864548i | \(0.667605\pi\) | |||||||
\(18\) | 7.37500e46 | 0.623796 | ||||||||
\(19\) | −1.16447e48 | −1.29679 | −0.648394 | − | 0.761305i | \(-0.724559\pi\) | ||||
−0.648394 | + | 0.761305i | \(0.724559\pi\) | |||||||
\(20\) | −4.00827e48 | −0.652126 | ||||||||
\(21\) | 3.73318e48 | 0.0974666 | ||||||||
\(22\) | −9.50567e49 | −0.433643 | ||||||||
\(23\) | 9.81970e50 | 0.845872 | 0.422936 | − | 0.906160i | \(-0.361000\pi\) | ||||
0.422936 | + | 0.906160i | \(0.361000\pi\) | |||||||
\(24\) | 1.01248e51 | 0.176792 | ||||||||
\(25\) | 6.26484e51 | 0.236679 | ||||||||
\(26\) | −3.22158e52 | −0.279620 | ||||||||
\(27\) | −1.61944e53 | −0.341369 | ||||||||
\(28\) | −6.11958e53 | −0.329834 | ||||||||
\(29\) | 3.47815e54 | 0.502832 | 0.251416 | − | 0.967879i | \(-0.419104\pi\) | ||||
0.251416 | + | 0.967879i | \(0.419104\pi\) | |||||||
\(30\) | −3.05649e54 | −0.123930 | ||||||||
\(31\) | 1.19579e56 | 1.41773 | 0.708863 | − | 0.705346i | \(-0.249209\pi\) | ||||
0.708863 | + | 0.705346i | \(0.249209\pi\) | |||||||
\(32\) | −2.70588e56 | −0.975405 | ||||||||
\(33\) | 1.02774e56 | 0.116846 | ||||||||
\(34\) | 1.74162e57 | 0.646388 | ||||||||
\(35\) | 4.99772e57 | 0.625490 | ||||||||
\(36\) | 1.30709e58 | 0.568804 | ||||||||
\(37\) | 1.03750e59 | 1.61593 | 0.807963 | − | 0.589233i | \(-0.200570\pi\) | ||||
0.807963 | + | 0.589233i | \(0.200570\pi\) | |||||||
\(38\) | 1.45558e59 | 0.833974 | ||||||||
\(39\) | 3.48314e58 | 0.0753439 | ||||||||
\(40\) | 1.35543e60 | 1.13456 | ||||||||
\(41\) | 4.07748e60 | 1.35207 | 0.676033 | − | 0.736872i | \(-0.263698\pi\) | ||||
0.676033 | + | 0.736872i | \(0.263698\pi\) | |||||||
\(42\) | −4.66646e59 | −0.0626815 | ||||||||
\(43\) | 2.20097e61 | 1.22334 | 0.611670 | − | 0.791113i | \(-0.290498\pi\) | ||||
0.611670 | + | 0.791113i | \(0.290498\pi\) | |||||||
\(44\) | −1.68472e61 | −0.395414 | ||||||||
\(45\) | −1.06747e62 | −1.07867 | ||||||||
\(46\) | −1.22746e62 | −0.543987 | ||||||||
\(47\) | −4.37785e62 | −0.866146 | −0.433073 | − | 0.901359i | \(-0.642571\pi\) | ||||
−0.433073 | + | 0.901359i | \(0.642571\pi\) | |||||||
\(48\) | −1.34459e61 | −0.0120793 | ||||||||
\(49\) | −1.64884e63 | −0.683638 | ||||||||
\(50\) | −7.83102e62 | −0.152210 | ||||||||
\(51\) | −1.88302e63 | −0.174170 | ||||||||
\(52\) | −5.70970e63 | −0.254969 | ||||||||
\(53\) | 7.68796e64 | 1.68061 | 0.840303 | − | 0.542117i | \(-0.182377\pi\) | ||||
0.840303 | + | 0.542117i | \(0.182377\pi\) | |||||||
\(54\) | 2.02429e64 | 0.219537 | ||||||||
\(55\) | 1.37587e65 | 0.749855 | ||||||||
\(56\) | 2.06939e65 | 0.573841 | ||||||||
\(57\) | −1.57376e65 | −0.224715 | ||||||||
\(58\) | −4.34767e65 | −0.323375 | ||||||||
\(59\) | −3.79588e66 | −1.48717 | −0.743587 | − | 0.668639i | \(-0.766877\pi\) | ||||
−0.743587 | + | 0.668639i | \(0.766877\pi\) | |||||||
\(60\) | −5.41711e65 | −0.113004 | ||||||||
\(61\) | 5.02447e66 | 0.563925 | 0.281962 | − | 0.959425i | \(-0.409015\pi\) | ||||
0.281962 | + | 0.959425i | \(0.409015\pi\) | |||||||
\(62\) | −1.49473e67 | −0.911750 | ||||||||
\(63\) | −1.62975e67 | −0.545571 | ||||||||
\(64\) | 3.75820e67 | 0.696998 | ||||||||
\(65\) | 4.66298e67 | 0.483518 | ||||||||
\(66\) | −1.28468e67 | −0.0751443 | ||||||||
\(67\) | 3.39062e68 | 1.12843 | 0.564214 | − | 0.825629i | \(-0.309179\pi\) | ||||
0.564214 | + | 0.825629i | \(0.309179\pi\) | |||||||
\(68\) | 3.08672e68 | 0.589404 | ||||||||
\(69\) | 1.32712e68 | 0.146578 | ||||||||
\(70\) | −6.24713e68 | −0.402258 | ||||||||
\(71\) | −3.17915e69 | −1.20261 | −0.601303 | − | 0.799021i | \(-0.705352\pi\) | ||||
−0.601303 | + | 0.799021i | \(0.705352\pi\) | |||||||
\(72\) | −4.42005e69 | −0.989598 | ||||||||
\(73\) | 7.11742e69 | 0.949982 | 0.474991 | − | 0.879991i | \(-0.342451\pi\) | ||||
0.474991 | + | 0.879991i | \(0.342451\pi\) | |||||||
\(74\) | −1.29687e70 | −1.03921 | ||||||||
\(75\) | 8.46682e68 | 0.0410131 | ||||||||
\(76\) | 2.57978e70 | 0.760453 | ||||||||
\(77\) | 2.10060e70 | 0.379263 | ||||||||
\(78\) | −4.35391e69 | −0.0484542 | ||||||||
\(79\) | 9.47303e70 | 0.653842 | 0.326921 | − | 0.945052i | \(-0.393989\pi\) | ||||
0.326921 | + | 0.945052i | \(0.393989\pi\) | |||||||
\(80\) | −1.80004e70 | −0.0775190 | ||||||||
\(81\) | 3.36992e71 | 0.910818 | ||||||||
\(82\) | −5.09684e71 | −0.869523 | ||||||||
\(83\) | −1.43323e71 | −0.155198 | −0.0775992 | − | 0.996985i | \(-0.524725\pi\) | ||||
−0.0775992 | + | 0.996985i | \(0.524725\pi\) | |||||||
\(84\) | −8.27051e70 | −0.0571556 | ||||||||
\(85\) | −2.52086e72 | −1.11773 | ||||||||
\(86\) | −2.75120e72 | −0.786739 | ||||||||
\(87\) | 4.70066e71 | 0.0871338 | ||||||||
\(88\) | 5.69703e72 | 0.687937 | ||||||||
\(89\) | 9.94475e72 | 0.786083 | 0.393042 | − | 0.919521i | \(-0.371423\pi\) | ||||
0.393042 | + | 0.919521i | \(0.371423\pi\) | |||||||
\(90\) | 1.33434e73 | 0.693699 | ||||||||
\(91\) | 7.11916e72 | 0.244555 | ||||||||
\(92\) | −2.17546e73 | −0.496030 | ||||||||
\(93\) | 1.61609e73 | 0.245672 | ||||||||
\(94\) | 5.47229e73 | 0.557025 | ||||||||
\(95\) | −2.10685e74 | −1.44211 | ||||||||
\(96\) | −3.65695e73 | −0.169024 | ||||||||
\(97\) | −7.42743e73 | −0.232755 | −0.116377 | − | 0.993205i | \(-0.537128\pi\) | ||||
−0.116377 | + | 0.993205i | \(0.537128\pi\) | |||||||
\(98\) | 2.06105e74 | 0.439653 | ||||||||
\(99\) | −4.48671e74 | −0.654045 | ||||||||
\(100\) | −1.38791e74 | −0.138791 | ||||||||
\(101\) | 1.42243e74 | 0.0979445 | 0.0489722 | − | 0.998800i | \(-0.484405\pi\) | ||||
0.0489722 | + | 0.998800i | \(0.484405\pi\) | |||||||
\(102\) | 2.35377e74 | 0.112010 | ||||||||
\(103\) | 4.64143e75 | 1.53199 | 0.765996 | − | 0.642846i | \(-0.222246\pi\) | ||||
0.765996 | + | 0.642846i | \(0.222246\pi\) | |||||||
\(104\) | 1.93079e75 | 0.443592 | ||||||||
\(105\) | 6.75434e74 | 0.108389 | ||||||||
\(106\) | −9.60991e75 | −1.08081 | ||||||||
\(107\) | 5.79865e75 | 0.458601 | 0.229301 | − | 0.973356i | \(-0.426356\pi\) | ||||
0.229301 | + | 0.973356i | \(0.426356\pi\) | |||||||
\(108\) | 3.58771e75 | 0.200183 | ||||||||
\(109\) | −4.52515e76 | −1.78706 | −0.893531 | − | 0.449001i | \(-0.851780\pi\) | ||||
−0.893531 | + | 0.449001i | \(0.851780\pi\) | |||||||
\(110\) | −1.71983e76 | −0.482237 | ||||||||
\(111\) | 1.40216e76 | 0.280018 | ||||||||
\(112\) | −2.74820e75 | −0.0392078 | ||||||||
\(113\) | 7.93579e76 | 0.811239 | 0.405619 | − | 0.914042i | \(-0.367056\pi\) | ||||
0.405619 | + | 0.914042i | \(0.367056\pi\) | |||||||
\(114\) | 1.96720e76 | 0.144516 | ||||||||
\(115\) | 1.77665e77 | 0.940661 | ||||||||
\(116\) | −7.70550e76 | −0.294867 | ||||||||
\(117\) | −1.52059e77 | −0.421739 | ||||||||
\(118\) | 4.74483e77 | 0.956413 | ||||||||
\(119\) | −3.84869e77 | −0.565330 | ||||||||
\(120\) | 1.83184e77 | 0.196604 | ||||||||
\(121\) | −6.93601e77 | −0.545329 | ||||||||
\(122\) | −6.28056e77 | −0.362664 | ||||||||
\(123\) | 5.51065e77 | 0.234294 | ||||||||
\(124\) | −2.64916e78 | −0.831372 | ||||||||
\(125\) | −3.65562e78 | −0.848859 | ||||||||
\(126\) | 2.03718e78 | 0.350861 | ||||||||
\(127\) | 9.37430e78 | 1.20033 | 0.600163 | − | 0.799878i | \(-0.295102\pi\) | ||||
0.600163 | + | 0.799878i | \(0.295102\pi\) | |||||||
\(128\) | 5.52480e78 | 0.527160 | ||||||||
\(129\) | 2.97457e78 | 0.211988 | ||||||||
\(130\) | −5.82871e78 | −0.310954 | ||||||||
\(131\) | 2.91749e79 | 1.16771 | 0.583857 | − | 0.811857i | \(-0.301543\pi\) | ||||
0.583857 | + | 0.811857i | \(0.301543\pi\) | |||||||
\(132\) | −2.27687e78 | −0.0685197 | ||||||||
\(133\) | −3.21660e79 | −0.729392 | ||||||||
\(134\) | −4.23826e79 | −0.725700 | ||||||||
\(135\) | −2.93001e79 | −0.379623 | ||||||||
\(136\) | −1.04380e80 | −1.02544 | ||||||||
\(137\) | 9.29317e79 | 0.693653 | 0.346827 | − | 0.937929i | \(-0.387259\pi\) | ||||
0.346827 | + | 0.937929i | \(0.387259\pi\) | |||||||
\(138\) | −1.65889e79 | −0.0942653 | ||||||||
\(139\) | 2.02447e80 | 0.877518 | 0.438759 | − | 0.898605i | \(-0.355418\pi\) | ||||
0.438759 | + | 0.898605i | \(0.355418\pi\) | |||||||
\(140\) | −1.10720e80 | −0.366795 | ||||||||
\(141\) | −5.91659e79 | −0.150091 | ||||||||
\(142\) | 3.97393e80 | 0.773405 | ||||||||
\(143\) | 1.95990e80 | 0.293179 | ||||||||
\(144\) | 5.86992e79 | 0.0676144 | ||||||||
\(145\) | 6.29291e80 | 0.559180 | ||||||||
\(146\) | −8.89674e80 | −0.610940 | ||||||||
\(147\) | −2.22838e80 | −0.118465 | ||||||||
\(148\) | −2.29847e81 | −0.947600 | ||||||||
\(149\) | 2.75595e81 | 0.882646 | 0.441323 | − | 0.897348i | \(-0.354509\pi\) | ||||
0.441323 | + | 0.897348i | \(0.354509\pi\) | |||||||
\(150\) | −1.05835e80 | −0.0263759 | ||||||||
\(151\) | −5.55612e81 | −1.07928 | −0.539642 | − | 0.841894i | \(-0.681441\pi\) | ||||
−0.539642 | + | 0.841894i | \(0.681441\pi\) | |||||||
\(152\) | −8.72375e81 | −1.32303 | ||||||||
\(153\) | 8.22049e81 | 0.974920 | ||||||||
\(154\) | −2.62574e81 | −0.243907 | ||||||||
\(155\) | 2.16351e82 | 1.57660 | ||||||||
\(156\) | −7.71656e80 | −0.0441826 | ||||||||
\(157\) | 2.68318e82 | 1.20896 | 0.604481 | − | 0.796619i | \(-0.293380\pi\) | ||||
0.604481 | + | 0.796619i | \(0.293380\pi\) | |||||||
\(158\) | −1.18412e82 | −0.420491 | ||||||||
\(159\) | 1.03901e82 | 0.291226 | ||||||||
\(160\) | −4.89568e82 | −1.08471 | ||||||||
\(161\) | 2.71248e82 | 0.475770 | ||||||||
\(162\) | −4.21238e82 | −0.585754 | ||||||||
\(163\) | −4.12916e82 | −0.455855 | −0.227927 | − | 0.973678i | \(-0.573195\pi\) | ||||
−0.227927 | + | 0.973678i | \(0.573195\pi\) | |||||||
\(164\) | −9.03328e82 | −0.792868 | ||||||||
\(165\) | 1.85947e82 | 0.129939 | ||||||||
\(166\) | 1.79153e82 | 0.0998093 | ||||||||
\(167\) | 1.65503e83 | 0.736103 | 0.368052 | − | 0.929805i | \(-0.380025\pi\) | ||||
0.368052 | + | 0.929805i | \(0.380025\pi\) | |||||||
\(168\) | 2.79675e82 | 0.0994387 | ||||||||
\(169\) | −2.84936e83 | −0.810954 | ||||||||
\(170\) | 3.15106e83 | 0.718823 | ||||||||
\(171\) | 6.87040e83 | 1.25785 | ||||||||
\(172\) | −4.87604e83 | −0.717382 | ||||||||
\(173\) | 2.24737e83 | 0.266039 | 0.133019 | − | 0.991113i | \(-0.457533\pi\) | ||||
0.133019 | + | 0.991113i | \(0.457533\pi\) | |||||||
\(174\) | −5.87580e82 | −0.0560364 | ||||||||
\(175\) | 1.73053e83 | 0.133123 | ||||||||
\(176\) | −7.56578e82 | −0.0470033 | ||||||||
\(177\) | −5.13007e83 | −0.257707 | ||||||||
\(178\) | −1.24309e84 | −0.505536 | ||||||||
\(179\) | −2.15324e84 | −0.709748 | −0.354874 | − | 0.934914i | \(-0.615476\pi\) | ||||
−0.354874 | + | 0.934914i | \(0.615476\pi\) | |||||||
\(180\) | 2.36488e84 | 0.632544 | ||||||||
\(181\) | −5.53508e84 | −1.20275 | −0.601377 | − | 0.798965i | \(-0.705381\pi\) | ||||
−0.601377 | + | 0.798965i | \(0.705381\pi\) | |||||||
\(182\) | −8.89892e83 | −0.157275 | ||||||||
\(183\) | 6.79048e83 | 0.0977203 | ||||||||
\(184\) | 7.35652e84 | 0.862987 | ||||||||
\(185\) | 1.87711e85 | 1.79701 | ||||||||
\(186\) | −2.02011e84 | −0.157994 | ||||||||
\(187\) | −1.05954e85 | −0.677733 | ||||||||
\(188\) | 9.69871e84 | 0.507919 | ||||||||
\(189\) | −4.47336e84 | −0.192006 | ||||||||
\(190\) | 2.63355e85 | 0.927430 | ||||||||
\(191\) | −4.53880e85 | −1.31277 | −0.656387 | − | 0.754424i | \(-0.727916\pi\) | ||||
−0.656387 | + | 0.754424i | \(0.727916\pi\) | |||||||
\(192\) | 5.07915e84 | 0.120780 | ||||||||
\(193\) | −9.26819e85 | −1.81383 | −0.906914 | − | 0.421316i | \(-0.861568\pi\) | ||||
−0.906914 | + | 0.421316i | \(0.861568\pi\) | |||||||
\(194\) | 9.28425e84 | 0.149686 | ||||||||
\(195\) | 6.30194e84 | 0.0837870 | ||||||||
\(196\) | 3.65285e85 | 0.400894 | ||||||||
\(197\) | 4.97463e85 | 0.451105 | 0.225552 | − | 0.974231i | \(-0.427581\pi\) | ||||
0.225552 | + | 0.974231i | \(0.427581\pi\) | |||||||
\(198\) | 5.60836e85 | 0.420621 | ||||||||
\(199\) | −7.14033e85 | −0.443331 | −0.221666 | − | 0.975123i | \(-0.571149\pi\) | ||||
−0.221666 | + | 0.975123i | \(0.571149\pi\) | |||||||
\(200\) | 4.69336e85 | 0.241468 | ||||||||
\(201\) | 4.58236e85 | 0.195541 | ||||||||
\(202\) | −1.77803e85 | −0.0629888 | ||||||||
\(203\) | 9.60764e85 | 0.282823 | ||||||||
\(204\) | 4.17165e85 | 0.102135 | ||||||||
\(205\) | 7.37727e86 | 1.50358 | ||||||||
\(206\) | −5.80177e86 | −0.985235 | ||||||||
\(207\) | −5.79364e86 | −0.820472 | ||||||||
\(208\) | −2.56413e85 | −0.0303085 | ||||||||
\(209\) | −8.85530e86 | −0.874415 | ||||||||
\(210\) | −8.44289e85 | −0.0697056 | ||||||||
\(211\) | 1.15343e87 | 0.796892 | 0.398446 | − | 0.917192i | \(-0.369550\pi\) | ||||
0.398446 | + | 0.917192i | \(0.369550\pi\) | |||||||
\(212\) | −1.70319e87 | −0.985529 | ||||||||
\(213\) | −4.29657e86 | −0.208395 | ||||||||
\(214\) | −7.24828e86 | −0.294930 | ||||||||
\(215\) | 3.98215e87 | 1.36043 | ||||||||
\(216\) | −1.21322e87 | −0.348276 | ||||||||
\(217\) | 3.30312e87 | 0.797415 | ||||||||
\(218\) | 5.65642e87 | 1.14927 | ||||||||
\(219\) | 9.61907e86 | 0.164619 | ||||||||
\(220\) | −3.04811e87 | −0.439724 | ||||||||
\(221\) | −3.59091e87 | −0.437013 | ||||||||
\(222\) | −1.75269e87 | −0.180081 | ||||||||
\(223\) | −2.95594e87 | −0.256604 | −0.128302 | − | 0.991735i | \(-0.540953\pi\) | ||||
−0.128302 | + | 0.991735i | \(0.540953\pi\) | |||||||
\(224\) | −7.47442e87 | −0.548627 | ||||||||
\(225\) | −3.69626e87 | −0.229572 | ||||||||
\(226\) | −9.91971e87 | −0.521714 | ||||||||
\(227\) | −9.67879e87 | −0.431371 | −0.215686 | − | 0.976463i | \(-0.569199\pi\) | ||||
−0.215686 | + | 0.976463i | \(0.569199\pi\) | |||||||
\(228\) | 3.48652e87 | 0.131776 | ||||||||
\(229\) | 4.56764e88 | 1.46508 | 0.732540 | − | 0.680723i | \(-0.238334\pi\) | ||||
0.732540 | + | 0.680723i | \(0.238334\pi\) | |||||||
\(230\) | −2.22081e88 | −0.604946 | ||||||||
\(231\) | 2.83892e87 | 0.0657210 | ||||||||
\(232\) | 2.60569e88 | 0.513007 | ||||||||
\(233\) | 1.95700e88 | 0.327902 | 0.163951 | − | 0.986468i | \(-0.447576\pi\) | ||||
0.163951 | + | 0.986468i | \(0.447576\pi\) | |||||||
\(234\) | 1.90074e88 | 0.271223 | ||||||||
\(235\) | −7.92072e88 | −0.963207 | ||||||||
\(236\) | 8.40941e88 | 0.872098 | ||||||||
\(237\) | 1.28026e88 | 0.113302 | ||||||||
\(238\) | 4.81084e88 | 0.363568 | ||||||||
\(239\) | −5.75419e88 | −0.371589 | −0.185795 | − | 0.982589i | \(-0.559486\pi\) | ||||
−0.185795 | + | 0.982589i | \(0.559486\pi\) | |||||||
\(240\) | −2.43273e87 | −0.0134330 | ||||||||
\(241\) | −3.37052e89 | −1.59242 | −0.796210 | − | 0.605020i | \(-0.793165\pi\) | ||||
−0.796210 | + | 0.605020i | \(0.793165\pi\) | |||||||
\(242\) | 8.66999e88 | 0.350705 | ||||||||
\(243\) | 1.44049e89 | 0.499201 | ||||||||
\(244\) | −1.11312e89 | −0.330693 | ||||||||
\(245\) | −2.98320e89 | −0.760247 | ||||||||
\(246\) | −6.88829e88 | −0.150676 | ||||||||
\(247\) | −3.00116e89 | −0.563837 | ||||||||
\(248\) | 8.95839e89 | 1.44641 | ||||||||
\(249\) | −1.93699e88 | −0.0268937 | ||||||||
\(250\) | 4.56951e89 | 0.545908 | ||||||||
\(251\) | 8.76805e89 | 0.901858 | 0.450929 | − | 0.892560i | \(-0.351093\pi\) | ||||
0.450929 | + | 0.892560i | \(0.351093\pi\) | |||||||
\(252\) | 3.61056e89 | 0.319930 | ||||||||
\(253\) | 7.46746e89 | 0.570365 | ||||||||
\(254\) | −1.17178e90 | −0.771939 | ||||||||
\(255\) | −3.40689e89 | −0.193688 | ||||||||
\(256\) | −2.11041e90 | −1.03602 | ||||||||
\(257\) | −1.45805e90 | −0.618416 | −0.309208 | − | 0.950995i | \(-0.600064\pi\) | ||||
−0.309208 | + | 0.950995i | \(0.600064\pi\) | |||||||
\(258\) | −3.71820e89 | −0.136331 | ||||||||
\(259\) | 2.86586e90 | 0.908895 | ||||||||
\(260\) | −1.03304e90 | −0.283541 | ||||||||
\(261\) | −2.05211e90 | −0.487733 | ||||||||
\(262\) | −3.64685e90 | −0.750965 | ||||||||
\(263\) | −1.04913e90 | −0.187280 | −0.0936398 | − | 0.995606i | \(-0.529850\pi\) | ||||
−0.0936398 | + | 0.995606i | \(0.529850\pi\) | |||||||
\(264\) | 7.69944e89 | 0.119210 | ||||||||
\(265\) | 1.39096e91 | 1.86894 | ||||||||
\(266\) | 4.02074e90 | 0.469078 | ||||||||
\(267\) | 1.34402e90 | 0.136217 | ||||||||
\(268\) | −7.51159e90 | −0.661724 | ||||||||
\(269\) | 1.36688e90 | 0.104717 | 0.0523587 | − | 0.998628i | \(-0.483326\pi\) | ||||
0.0523587 | + | 0.998628i | \(0.483326\pi\) | |||||||
\(270\) | 3.66249e90 | 0.244138 | ||||||||
\(271\) | −3.50139e90 | −0.203185 | −0.101593 | − | 0.994826i | \(-0.532394\pi\) | ||||
−0.101593 | + | 0.994826i | \(0.532394\pi\) | |||||||
\(272\) | 1.38619e90 | 0.0700631 | ||||||||
\(273\) | 9.62142e89 | 0.0423780 | ||||||||
\(274\) | −1.16164e91 | −0.446094 | ||||||||
\(275\) | 4.76414e90 | 0.159591 | ||||||||
\(276\) | −2.94010e90 | −0.0859551 | ||||||||
\(277\) | 3.00814e90 | 0.0767903 | 0.0383951 | − | 0.999263i | \(-0.487775\pi\) | ||||
0.0383951 | + | 0.999263i | \(0.487775\pi\) | |||||||
\(278\) | −2.53058e91 | −0.564338 | ||||||||
\(279\) | −7.05519e91 | −1.37515 | ||||||||
\(280\) | 3.74409e91 | 0.638146 | ||||||||
\(281\) | −1.95826e91 | −0.292000 | −0.146000 | − | 0.989285i | \(-0.546640\pi\) | ||||
−0.146000 | + | 0.989285i | \(0.546640\pi\) | |||||||
\(282\) | 7.39571e90 | 0.0965247 | ||||||||
\(283\) | 7.34668e91 | 0.839653 | 0.419826 | − | 0.907604i | \(-0.362091\pi\) | ||||
0.419826 | + | 0.907604i | \(0.362091\pi\) | |||||||
\(284\) | 7.04311e91 | 0.705224 | ||||||||
\(285\) | −2.84737e91 | −0.249897 | ||||||||
\(286\) | −2.44987e91 | −0.188546 | ||||||||
\(287\) | 1.12632e92 | 0.760483 | ||||||||
\(288\) | 1.59648e92 | 0.946115 | ||||||||
\(289\) | 1.96546e90 | 0.0102281 | ||||||||
\(290\) | −7.86611e91 | −0.359613 | ||||||||
\(291\) | −1.00380e91 | −0.0403331 | ||||||||
\(292\) | −1.57680e92 | −0.557081 | ||||||||
\(293\) | −3.78620e92 | −1.17670 | −0.588352 | − | 0.808605i | \(-0.700223\pi\) | ||||
−0.588352 | + | 0.808605i | \(0.700223\pi\) | |||||||
\(294\) | 2.78547e91 | 0.0761857 | ||||||||
\(295\) | −6.86777e92 | −1.65383 | ||||||||
\(296\) | 7.77250e92 | 1.64862 | ||||||||
\(297\) | −1.23151e92 | −0.230182 | ||||||||
\(298\) | −3.44493e92 | −0.567637 | ||||||||
\(299\) | 2.53080e92 | 0.367781 | ||||||||
\(300\) | −1.87574e91 | −0.0240506 | ||||||||
\(301\) | 6.07971e92 | 0.688080 | ||||||||
\(302\) | 6.94513e92 | 0.694096 | ||||||||
\(303\) | 1.92239e91 | 0.0169724 | ||||||||
\(304\) | 1.15853e92 | 0.0903959 | ||||||||
\(305\) | 9.09062e92 | 0.627119 | ||||||||
\(306\) | −1.02756e93 | −0.626978 | ||||||||
\(307\) | 1.04256e92 | 0.0562878 | 0.0281439 | − | 0.999604i | \(-0.491040\pi\) | ||||
0.0281439 | + | 0.999604i | \(0.491040\pi\) | |||||||
\(308\) | −4.65367e92 | −0.222405 | ||||||||
\(309\) | 6.27282e92 | 0.265473 | ||||||||
\(310\) | −2.70438e93 | −1.01392 | ||||||||
\(311\) | 2.13035e93 | 0.707843 | 0.353921 | − | 0.935275i | \(-0.384848\pi\) | ||||
0.353921 | + | 0.935275i | \(0.384848\pi\) | |||||||
\(312\) | 2.60943e92 | 0.0768684 | ||||||||
\(313\) | −2.58095e91 | −0.00674322 | −0.00337161 | − | 0.999994i | \(-0.501073\pi\) | ||||
−0.00337161 | + | 0.999994i | \(0.501073\pi\) | |||||||
\(314\) | −3.35396e93 | −0.777493 | ||||||||
\(315\) | −2.94867e93 | −0.606708 | ||||||||
\(316\) | −2.09866e93 | −0.383421 | ||||||||
\(317\) | 1.87491e93 | 0.304269 | 0.152135 | − | 0.988360i | \(-0.451385\pi\) | ||||
0.152135 | + | 0.988360i | \(0.451385\pi\) | |||||||
\(318\) | −1.29876e93 | −0.187289 | ||||||||
\(319\) | 2.64498e93 | 0.339056 | ||||||||
\(320\) | 6.79961e93 | 0.775104 | ||||||||
\(321\) | 7.83678e92 | 0.0794692 | ||||||||
\(322\) | −3.39059e93 | −0.305971 | ||||||||
\(323\) | 1.62246e94 | 1.30340 | ||||||||
\(324\) | −7.46574e93 | −0.534115 | ||||||||
\(325\) | 1.61462e93 | 0.102907 | ||||||||
\(326\) | 5.16143e93 | 0.293164 | ||||||||
\(327\) | −6.11567e93 | −0.309673 | ||||||||
\(328\) | 3.05469e94 | 1.37942 | ||||||||
\(329\) | −1.20929e94 | −0.487173 | ||||||||
\(330\) | −2.32433e93 | −0.0835650 | ||||||||
\(331\) | −5.42826e94 | −1.74225 | −0.871125 | − | 0.491061i | \(-0.836609\pi\) | ||||
−0.871125 | + | 0.491061i | \(0.836609\pi\) | |||||||
\(332\) | 3.17518e93 | 0.0910103 | ||||||||
\(333\) | −6.12124e94 | −1.56740 | ||||||||
\(334\) | −2.06878e94 | −0.473394 | ||||||||
\(335\) | 6.13454e94 | 1.25488 | ||||||||
\(336\) | −3.71414e92 | −0.00679416 | ||||||||
\(337\) | 1.16963e94 | 0.191393 | 0.0956965 | − | 0.995411i | \(-0.469492\pi\) | ||||
0.0956965 | + | 0.995411i | \(0.469492\pi\) | |||||||
\(338\) | 3.56169e94 | 0.521530 | ||||||||
\(339\) | 1.07251e94 | 0.140576 | ||||||||
\(340\) | 5.58471e94 | 0.655453 | ||||||||
\(341\) | 9.09348e94 | 0.955962 | ||||||||
\(342\) | −8.58797e94 | −0.808931 | ||||||||
\(343\) | −1.12168e95 | −0.946980 | ||||||||
\(344\) | 1.64888e95 | 1.24809 | ||||||||
\(345\) | 2.40111e94 | 0.163003 | ||||||||
\(346\) | −2.80920e94 | −0.171092 | ||||||||
\(347\) | 7.78575e94 | 0.425545 | 0.212772 | − | 0.977102i | \(-0.431751\pi\) | ||||
0.212772 | + | 0.977102i | \(0.431751\pi\) | |||||||
\(348\) | −1.04139e94 | −0.0510964 | ||||||||
\(349\) | −3.88388e95 | −1.71125 | −0.855623 | − | 0.517600i | \(-0.826826\pi\) | ||||
−0.855623 | + | 0.517600i | \(0.826826\pi\) | |||||||
\(350\) | −2.16315e94 | −0.0856121 | ||||||||
\(351\) | −4.17373e94 | −0.148425 | ||||||||
\(352\) | −2.05771e95 | −0.657708 | ||||||||
\(353\) | 6.23918e95 | 1.79298 | 0.896492 | − | 0.443060i | \(-0.146107\pi\) | ||||
0.896492 | + | 0.443060i | \(0.146107\pi\) | |||||||
\(354\) | 6.41256e94 | 0.165733 | ||||||||
\(355\) | −5.75195e95 | −1.33737 | ||||||||
\(356\) | −2.20316e95 | −0.460969 | ||||||||
\(357\) | −5.20144e94 | −0.0979638 | ||||||||
\(358\) | 2.69154e95 | 0.456444 | ||||||||
\(359\) | 7.02370e95 | 1.07281 | 0.536407 | − | 0.843960i | \(-0.319781\pi\) | ||||
0.536407 | + | 0.843960i | \(0.319781\pi\) | |||||||
\(360\) | −7.99708e95 | −1.10049 | ||||||||
\(361\) | 5.49651e95 | 0.681659 | ||||||||
\(362\) | 6.91882e95 | 0.773500 | ||||||||
\(363\) | −9.37391e94 | −0.0944979 | ||||||||
\(364\) | −1.57718e95 | −0.143410 | ||||||||
\(365\) | 1.28773e96 | 1.05644 | ||||||||
\(366\) | −8.48807e94 | −0.0628447 | ||||||||
\(367\) | 4.84188e95 | 0.323621 | 0.161810 | − | 0.986822i | \(-0.448267\pi\) | ||||
0.161810 | + | 0.986822i | \(0.448267\pi\) | |||||||
\(368\) | −9.76962e94 | −0.0589637 | ||||||||
\(369\) | −2.40572e96 | −1.31147 | ||||||||
\(370\) | −2.34638e96 | −1.15567 | ||||||||
\(371\) | 2.12363e96 | 0.945275 | ||||||||
\(372\) | −3.58030e95 | −0.144065 | ||||||||
\(373\) | −3.19767e96 | −1.16346 | −0.581732 | − | 0.813380i | \(-0.697625\pi\) | ||||
−0.581732 | + | 0.813380i | \(0.697625\pi\) | |||||||
\(374\) | 1.32442e96 | 0.435855 | ||||||||
\(375\) | −4.94051e95 | −0.147095 | ||||||||
\(376\) | −3.27971e96 | −0.883672 | ||||||||
\(377\) | 8.96413e95 | 0.218629 | ||||||||
\(378\) | 5.59167e95 | 0.123481 | ||||||||
\(379\) | 6.31380e96 | 1.26276 | 0.631380 | − | 0.775474i | \(-0.282489\pi\) | ||||
0.631380 | + | 0.775474i | \(0.282489\pi\) | |||||||
\(380\) | 4.66751e96 | 0.845670 | ||||||||
\(381\) | 1.26692e96 | 0.208000 | ||||||||
\(382\) | 5.67348e96 | 0.844255 | ||||||||
\(383\) | −1.05836e97 | −1.42785 | −0.713923 | − | 0.700225i | \(-0.753083\pi\) | ||||
−0.713923 | + | 0.700225i | \(0.753083\pi\) | |||||||
\(384\) | 7.46667e95 | 0.0913495 | ||||||||
\(385\) | 3.80055e96 | 0.421764 | ||||||||
\(386\) | 1.15852e97 | 1.16649 | ||||||||
\(387\) | −1.29858e97 | −1.18661 | ||||||||
\(388\) | 1.64548e96 | 0.136490 | ||||||||
\(389\) | −6.81840e96 | −0.513538 | −0.256769 | − | 0.966473i | \(-0.582658\pi\) | ||||
−0.256769 | + | 0.966473i | \(0.582658\pi\) | |||||||
\(390\) | −7.87740e95 | −0.0538840 | ||||||||
\(391\) | −1.36818e97 | −0.850187 | ||||||||
\(392\) | −1.23525e97 | −0.697471 | ||||||||
\(393\) | 3.94294e96 | 0.202348 | ||||||||
\(394\) | −6.21826e96 | −0.290109 | ||||||||
\(395\) | 1.71393e97 | 0.727112 | ||||||||
\(396\) | 9.93987e96 | 0.383540 | ||||||||
\(397\) | −3.56797e96 | −0.125250 | −0.0626250 | − | 0.998037i | \(-0.519947\pi\) | ||||
−0.0626250 | + | 0.998037i | \(0.519947\pi\) | |||||||
\(398\) | 8.92539e96 | 0.285110 | ||||||||
\(399\) | −4.34719e96 | −0.126393 | ||||||||
\(400\) | −6.23288e95 | −0.0164983 | ||||||||
\(401\) | −1.50986e97 | −0.363934 | −0.181967 | − | 0.983305i | \(-0.558246\pi\) | ||||
−0.181967 | + | 0.983305i | \(0.558246\pi\) | |||||||
\(402\) | −5.72793e96 | −0.125754 | ||||||||
\(403\) | 3.08188e97 | 0.616420 | ||||||||
\(404\) | −3.15126e96 | −0.0574359 | ||||||||
\(405\) | 6.09710e97 | 1.01288 | ||||||||
\(406\) | −1.20095e97 | −0.181886 | ||||||||
\(407\) | 7.88970e97 | 1.08961 | ||||||||
\(408\) | −1.41068e97 | −0.177694 | ||||||||
\(409\) | −9.27122e96 | −0.106540 | −0.0532700 | − | 0.998580i | \(-0.516964\pi\) | ||||
−0.0532700 | + | 0.998580i | \(0.516964\pi\) | |||||||
\(410\) | −9.22156e97 | −0.966963 | ||||||||
\(411\) | 1.25596e97 | 0.120200 | ||||||||
\(412\) | −1.02827e98 | −0.898379 | ||||||||
\(413\) | −1.04853e98 | −0.836477 | ||||||||
\(414\) | 7.24203e97 | 0.527652 | ||||||||
\(415\) | −2.59310e97 | −0.172590 | ||||||||
\(416\) | −6.97379e97 | −0.424101 | ||||||||
\(417\) | 2.73604e97 | 0.152062 | ||||||||
\(418\) | 1.10691e98 | 0.562343 | ||||||||
\(419\) | −2.22993e98 | −1.03577 | −0.517887 | − | 0.855449i | \(-0.673281\pi\) | ||||
−0.517887 | + | 0.855449i | \(0.673281\pi\) | |||||||
\(420\) | −1.49636e97 | −0.0635605 | ||||||||
\(421\) | 2.56359e98 | 0.996023 | 0.498012 | − | 0.867170i | \(-0.334064\pi\) | ||||
0.498012 | + | 0.867170i | \(0.334064\pi\) | |||||||
\(422\) | −1.44178e98 | −0.512487 | ||||||||
\(423\) | 2.58294e98 | 0.840137 | ||||||||
\(424\) | 5.75951e98 | 1.71461 | ||||||||
\(425\) | −8.72879e97 | −0.237886 | ||||||||
\(426\) | 5.37070e97 | 0.134020 | ||||||||
\(427\) | 1.38790e98 | 0.317185 | ||||||||
\(428\) | −1.28464e98 | −0.268929 | ||||||||
\(429\) | 2.64877e97 | 0.0508038 | ||||||||
\(430\) | −4.97767e98 | −0.874902 | ||||||||
\(431\) | −5.84060e98 | −0.940935 | −0.470468 | − | 0.882417i | \(-0.655915\pi\) | ||||
−0.470468 | + | 0.882417i | \(0.655915\pi\) | |||||||
\(432\) | 1.61118e97 | 0.0237960 | ||||||||
\(433\) | −2.66887e97 | −0.0361436 | −0.0180718 | − | 0.999837i | \(-0.505753\pi\) | ||||
−0.0180718 | + | 0.999837i | \(0.505753\pi\) | |||||||
\(434\) | −4.12888e98 | −0.512823 | ||||||||
\(435\) | 8.50477e97 | 0.0968981 | ||||||||
\(436\) | 1.00250e99 | 1.04796 | ||||||||
\(437\) | −1.14348e99 | −1.09692 | ||||||||
\(438\) | −1.20238e98 | −0.105867 | ||||||||
\(439\) | −1.07199e99 | −0.866509 | −0.433255 | − | 0.901272i | \(-0.642635\pi\) | ||||
−0.433255 | + | 0.901272i | \(0.642635\pi\) | |||||||
\(440\) | 1.03075e99 | 0.765027 | ||||||||
\(441\) | 9.72820e98 | 0.663110 | ||||||||
\(442\) | 4.48862e98 | 0.281046 | ||||||||
\(443\) | −2.88329e98 | −0.165863 | −0.0829315 | − | 0.996555i | \(-0.526428\pi\) | ||||
−0.0829315 | + | 0.996555i | \(0.526428\pi\) | |||||||
\(444\) | −3.10635e98 | −0.164206 | ||||||||
\(445\) | 1.79927e99 | 0.874172 | ||||||||
\(446\) | 3.69491e98 | 0.165024 | ||||||||
\(447\) | 3.72462e98 | 0.152950 | ||||||||
\(448\) | 1.03812e99 | 0.392034 | ||||||||
\(449\) | −3.37230e99 | −1.17135 | −0.585676 | − | 0.810545i | \(-0.699171\pi\) | ||||
−0.585676 | + | 0.810545i | \(0.699171\pi\) | |||||||
\(450\) | 4.62031e98 | 0.147639 | ||||||||
\(451\) | 3.10075e99 | 0.911688 | ||||||||
\(452\) | −1.75810e99 | −0.475721 | ||||||||
\(453\) | −7.50900e98 | −0.187025 | ||||||||
\(454\) | 1.20984e99 | 0.277418 | ||||||||
\(455\) | 1.28805e99 | 0.271960 | ||||||||
\(456\) | −1.17900e99 | −0.229262 | ||||||||
\(457\) | −6.02179e99 | −1.07862 | −0.539310 | − | 0.842107i | \(-0.681315\pi\) | ||||
−0.539310 | + | 0.842107i | \(0.681315\pi\) | |||||||
\(458\) | −5.70953e99 | −0.942205 | ||||||||
\(459\) | 2.25636e99 | 0.343110 | ||||||||
\(460\) | −3.93600e99 | −0.551615 | ||||||||
\(461\) | 8.06561e99 | 1.04196 | 0.520982 | − | 0.853568i | \(-0.325566\pi\) | ||||
0.520982 | + | 0.853568i | \(0.325566\pi\) | |||||||
\(462\) | −3.54864e98 | −0.0422657 | ||||||||
\(463\) | −8.25998e99 | −0.907176 | −0.453588 | − | 0.891211i | \(-0.649856\pi\) | ||||
−0.453588 | + | 0.891211i | \(0.649856\pi\) | |||||||
\(464\) | −3.46041e98 | −0.0350512 | ||||||||
\(465\) | 2.92395e99 | 0.273202 | ||||||||
\(466\) | −2.44624e99 | −0.210876 | ||||||||
\(467\) | 2.12206e100 | 1.68801 | 0.844005 | − | 0.536335i | \(-0.180192\pi\) | ||||
0.844005 | + | 0.536335i | \(0.180192\pi\) | |||||||
\(468\) | 3.36873e99 | 0.247313 | ||||||||
\(469\) | 9.36585e99 | 0.634696 | ||||||||
\(470\) | 9.90086e99 | 0.619446 | ||||||||
\(471\) | 3.62627e99 | 0.209496 | ||||||||
\(472\) | −2.84372e100 | −1.51727 | ||||||||
\(473\) | 1.67374e100 | 0.824889 | ||||||||
\(474\) | −1.60032e99 | −0.0728652 | ||||||||
\(475\) | −7.29523e99 | −0.306922 | ||||||||
\(476\) | 8.52640e99 | 0.331516 | ||||||||
\(477\) | −4.53591e100 | −1.63014 | ||||||||
\(478\) | 7.19271e99 | 0.238972 | ||||||||
\(479\) | −6.07031e100 | −1.86479 | −0.932394 | − | 0.361445i | \(-0.882284\pi\) | ||||
−0.932394 | + | 0.361445i | \(0.882284\pi\) | |||||||
\(480\) | −6.61642e99 | −0.187965 | ||||||||
\(481\) | 2.67391e100 | 0.702597 | ||||||||
\(482\) | 4.21314e100 | 1.02410 | ||||||||
\(483\) | 3.66587e99 | 0.0824442 | ||||||||
\(484\) | 1.53661e100 | 0.319788 | ||||||||
\(485\) | −1.34382e100 | −0.258837 | ||||||||
\(486\) | −1.80061e100 | −0.321040 | ||||||||
\(487\) | −3.82403e100 | −0.631226 | −0.315613 | − | 0.948888i | \(-0.602210\pi\) | ||||
−0.315613 | + | 0.948888i | \(0.602210\pi\) | |||||||
\(488\) | 3.76413e100 | 0.575335 | ||||||||
\(489\) | −5.58049e99 | −0.0789933 | ||||||||
\(490\) | 3.72899e100 | 0.488921 | ||||||||
\(491\) | 1.61347e101 | 1.95977 | 0.979884 | − | 0.199566i | \(-0.0639532\pi\) | ||||
0.979884 | + | 0.199566i | \(0.0639532\pi\) | |||||||
\(492\) | −1.22083e100 | −0.137393 | ||||||||
\(493\) | −4.84610e100 | −0.505397 | ||||||||
\(494\) | 3.75144e100 | 0.362608 | ||||||||
\(495\) | −8.11767e100 | −0.727338 | ||||||||
\(496\) | −1.18969e100 | −0.0988262 | ||||||||
\(497\) | −8.78173e100 | −0.676419 | ||||||||
\(498\) | 2.42122e99 | 0.0172956 | ||||||||
\(499\) | −7.09381e99 | −0.0470012 | −0.0235006 | − | 0.999724i | \(-0.507481\pi\) | ||||
−0.0235006 | + | 0.999724i | \(0.507481\pi\) | |||||||
\(500\) | 8.09868e100 | 0.497782 | ||||||||
\(501\) | 2.23675e100 | 0.127556 | ||||||||
\(502\) | −1.09600e101 | −0.579992 | ||||||||
\(503\) | 2.88098e100 | 0.141495 | 0.0707475 | − | 0.997494i | \(-0.477462\pi\) | ||||
0.0707475 | + | 0.997494i | \(0.477462\pi\) | |||||||
\(504\) | −1.22095e101 | −0.556610 | ||||||||
\(505\) | 2.57356e100 | 0.108920 | ||||||||
\(506\) | −9.33429e100 | −0.366806 | ||||||||
\(507\) | −3.85086e100 | −0.140527 | ||||||||
\(508\) | −2.07679e101 | −0.703886 | ||||||||
\(509\) | 3.40536e100 | 0.107213 | 0.0536063 | − | 0.998562i | \(-0.482928\pi\) | ||||
0.0536063 | + | 0.998562i | \(0.482928\pi\) | |||||||
\(510\) | 4.25860e100 | 0.124562 | ||||||||
\(511\) | 1.96603e101 | 0.534327 | ||||||||
\(512\) | 5.50789e100 | 0.139111 | ||||||||
\(513\) | 1.88579e101 | 0.442683 | ||||||||
\(514\) | 1.82256e101 | 0.397708 | ||||||||
\(515\) | 8.39761e101 | 1.70367 | ||||||||
\(516\) | −6.58988e100 | −0.124312 | ||||||||
\(517\) | −3.32916e101 | −0.584036 | ||||||||
\(518\) | −3.58231e101 | −0.584517 | ||||||||
\(519\) | 3.03728e100 | 0.0461008 | ||||||||
\(520\) | 3.49332e101 | 0.493302 | ||||||||
\(521\) | −2.83196e100 | −0.0372111 | −0.0186055 | − | 0.999827i | \(-0.505923\pi\) | ||||
−0.0186055 | + | 0.999827i | \(0.505923\pi\) | |||||||
\(522\) | 2.56513e101 | 0.313665 | ||||||||
\(523\) | −6.78214e101 | −0.771887 | −0.385943 | − | 0.922522i | \(-0.626124\pi\) | ||||
−0.385943 | + | 0.922522i | \(0.626124\pi\) | |||||||
\(524\) | −6.46343e101 | −0.684762 | ||||||||
\(525\) | 2.33878e100 | 0.0230683 | ||||||||
\(526\) | 1.31141e101 | 0.120441 | ||||||||
\(527\) | −1.66610e102 | −1.42496 | ||||||||
\(528\) | −1.02250e100 | −0.00814502 | ||||||||
\(529\) | −3.83417e101 | −0.284501 | ||||||||
\(530\) | −1.73869e102 | −1.20193 | ||||||||
\(531\) | 2.23957e102 | 1.44252 | ||||||||
\(532\) | 7.12608e101 | 0.427725 | ||||||||
\(533\) | 1.05088e102 | 0.587871 | ||||||||
\(534\) | −1.68001e101 | −0.0876024 | ||||||||
\(535\) | 1.04913e102 | 0.509992 | ||||||||
\(536\) | 2.54011e102 | 1.15126 | ||||||||
\(537\) | −2.91007e101 | −0.122989 | ||||||||
\(538\) | −1.70859e101 | −0.0673445 | ||||||||
\(539\) | −1.25387e102 | −0.460972 | ||||||||
\(540\) | 6.49115e101 | 0.222616 | ||||||||
\(541\) | −1.95501e101 | −0.0625536 | −0.0312768 | − | 0.999511i | \(-0.509957\pi\) | ||||
−0.0312768 | + | 0.999511i | \(0.509957\pi\) | |||||||
\(542\) | 4.37673e101 | 0.130670 | ||||||||
\(543\) | −7.48056e101 | −0.208421 | ||||||||
\(544\) | 3.77010e102 | 0.980380 | ||||||||
\(545\) | −8.18723e102 | −1.98732 | ||||||||
\(546\) | −1.20267e101 | −0.0272536 | ||||||||
\(547\) | 5.36210e102 | 1.13451 | 0.567257 | − | 0.823541i | \(-0.308004\pi\) | ||||
0.567257 | + | 0.823541i | \(0.308004\pi\) | |||||||
\(548\) | −2.05881e102 | −0.406767 | ||||||||
\(549\) | −2.96444e102 | −0.546991 | ||||||||
\(550\) | −5.95515e101 | −0.102634 | ||||||||
\(551\) | −4.05021e102 | −0.652067 | ||||||||
\(552\) | 9.94222e101 | 0.149544 | ||||||||
\(553\) | 2.61672e102 | 0.367760 | ||||||||
\(554\) | −3.76016e101 | −0.0493844 | ||||||||
\(555\) | 2.53688e102 | 0.311397 | ||||||||
\(556\) | −4.48502e102 | −0.514588 | ||||||||
\(557\) | −1.00958e103 | −1.08286 | −0.541430 | − | 0.840746i | \(-0.682117\pi\) | ||||
−0.541430 | + | 0.840746i | \(0.682117\pi\) | |||||||
\(558\) | 8.81896e102 | 0.884372 | ||||||||
\(559\) | 5.67250e102 | 0.531902 | ||||||||
\(560\) | −4.97223e101 | −0.0436014 | ||||||||
\(561\) | −1.43195e102 | −0.117442 | ||||||||
\(562\) | 2.44781e102 | 0.187787 | ||||||||
\(563\) | 1.59566e103 | 1.14518 | 0.572591 | − | 0.819841i | \(-0.305938\pi\) | ||||
0.572591 | + | 0.819841i | \(0.305938\pi\) | |||||||
\(564\) | 1.31076e102 | 0.0880153 | ||||||||
\(565\) | 1.43580e103 | 0.902147 | ||||||||
\(566\) | −9.18332e102 | −0.539987 | ||||||||
\(567\) | 9.30868e102 | 0.512299 | ||||||||
\(568\) | −2.38169e103 | −1.22694 | ||||||||
\(569\) | 6.65325e102 | 0.320866 | 0.160433 | − | 0.987047i | \(-0.448711\pi\) | ||||
0.160433 | + | 0.987047i | \(0.448711\pi\) | |||||||
\(570\) | 3.55919e102 | 0.160711 | ||||||||
\(571\) | −1.13478e103 | −0.479798 | −0.239899 | − | 0.970798i | \(-0.577114\pi\) | ||||
−0.239899 | + | 0.970798i | \(0.577114\pi\) | |||||||
\(572\) | −4.34198e102 | −0.171924 | ||||||||
\(573\) | −6.13412e102 | −0.227485 | ||||||||
\(574\) | −1.40789e103 | −0.489073 | ||||||||
\(575\) | 6.15188e102 | 0.200200 | ||||||||
\(576\) | −2.21735e103 | −0.676068 | ||||||||
\(577\) | −1.02337e103 | −0.292374 | −0.146187 | − | 0.989257i | \(-0.546700\pi\) | ||||
−0.146187 | + | 0.989257i | \(0.546700\pi\) | |||||||
\(578\) | −2.45682e101 | −0.00657778 | ||||||||
\(579\) | −1.25258e103 | −0.314311 | ||||||||
\(580\) | −1.39413e103 | −0.327910 | ||||||||
\(581\) | −3.95899e102 | −0.0872930 | ||||||||
\(582\) | 1.25475e102 | 0.0259385 | ||||||||
\(583\) | 5.84636e103 | 1.13322 | ||||||||
\(584\) | 5.33208e103 | 0.969204 | ||||||||
\(585\) | −2.75117e103 | −0.468999 | ||||||||
\(586\) | 4.73273e103 | 0.756748 | ||||||||
\(587\) | 1.04432e104 | 1.56641 | 0.783206 | − | 0.621763i | \(-0.213583\pi\) | ||||
0.783206 | + | 0.621763i | \(0.213583\pi\) | |||||||
\(588\) | 4.93677e102 | 0.0694693 | ||||||||
\(589\) | −1.39247e104 | −1.83849 | ||||||||
\(590\) | 8.58469e103 | 1.06359 | ||||||||
\(591\) | 6.72313e102 | 0.0781701 | ||||||||
\(592\) | −1.03220e103 | −0.112642 | ||||||||
\(593\) | −9.71824e103 | −0.995489 | −0.497745 | − | 0.867324i | \(-0.665838\pi\) | ||||
−0.497745 | + | 0.867324i | \(0.665838\pi\) | |||||||
\(594\) | 1.53939e103 | 0.148032 | ||||||||
\(595\) | −6.96332e103 | −0.628681 | ||||||||
\(596\) | −6.10555e103 | −0.517595 | ||||||||
\(597\) | −9.65004e102 | −0.0768231 | ||||||||
\(598\) | −3.16349e103 | −0.236523 | ||||||||
\(599\) | 2.58692e104 | 1.81667 | 0.908337 | − | 0.418240i | \(-0.137353\pi\) | ||||
0.908337 | + | 0.418240i | \(0.137353\pi\) | |||||||
\(600\) | 6.34300e102 | 0.0418430 | ||||||||
\(601\) | −2.18067e104 | −1.35144 | −0.675720 | − | 0.737158i | \(-0.736167\pi\) | ||||
−0.675720 | + | 0.737158i | \(0.736167\pi\) | |||||||
\(602\) | −7.59961e103 | −0.442510 | ||||||||
\(603\) | −2.00047e104 | −1.09454 | ||||||||
\(604\) | 1.23091e104 | 0.632906 | ||||||||
\(605\) | −1.25491e104 | −0.606439 | ||||||||
\(606\) | −2.40298e102 | −0.0109151 | ||||||||
\(607\) | 3.95671e104 | 1.68950 | 0.844750 | − | 0.535161i | \(-0.179749\pi\) | ||||
0.844750 | + | 0.535161i | \(0.179749\pi\) | |||||||
\(608\) | 3.15092e104 | 1.26489 | ||||||||
\(609\) | 1.29846e103 | 0.0490093 | ||||||||
\(610\) | −1.13632e104 | −0.403305 | ||||||||
\(611\) | −1.12829e104 | −0.376596 | ||||||||
\(612\) | −1.82117e104 | −0.571705 | ||||||||
\(613\) | 5.60714e102 | 0.0165567 | 0.00827834 | − | 0.999966i | \(-0.497365\pi\) | ||||
0.00827834 | + | 0.999966i | \(0.497365\pi\) | |||||||
\(614\) | −1.30320e103 | −0.0361991 | ||||||||
\(615\) | 9.97026e103 | 0.260549 | ||||||||
\(616\) | 1.57368e104 | 0.386937 | ||||||||
\(617\) | 4.75635e104 | 1.10047 | 0.550237 | − | 0.835009i | \(-0.314537\pi\) | ||||
0.550237 | + | 0.835009i | \(0.314537\pi\) | |||||||
\(618\) | −7.84100e103 | −0.170728 | ||||||||
\(619\) | 3.45849e104 | 0.708740 | 0.354370 | − | 0.935105i | \(-0.384695\pi\) | ||||
0.354370 | + | 0.935105i | \(0.384695\pi\) | |||||||
\(620\) | −4.79305e104 | −0.924536 | ||||||||
\(621\) | −1.59024e104 | −0.288754 | ||||||||
\(622\) | −2.66293e104 | −0.455219 | ||||||||
\(623\) | 2.74702e104 | 0.442141 | ||||||||
\(624\) | −3.46537e102 | −0.00525204 | ||||||||
\(625\) | −8.27230e104 | −1.18066 | ||||||||
\(626\) | 3.22618e102 | 0.00433662 | ||||||||
\(627\) | −1.19678e104 | −0.151524 | ||||||||
\(628\) | −5.94433e104 | −0.708951 | ||||||||
\(629\) | −1.44554e105 | −1.62417 | ||||||||
\(630\) | 3.68582e104 | 0.390179 | ||||||||
\(631\) | 1.13799e105 | 1.13510 | 0.567552 | − | 0.823337i | \(-0.307890\pi\) | ||||
0.567552 | + | 0.823337i | \(0.307890\pi\) | |||||||
\(632\) | 7.09681e104 | 0.667072 | ||||||||
\(633\) | 1.55884e104 | 0.138090 | ||||||||
\(634\) | −2.34363e104 | −0.195678 | ||||||||
\(635\) | 1.69606e105 | 1.33484 | ||||||||
\(636\) | −2.30184e104 | −0.170778 | ||||||||
\(637\) | −4.24951e104 | −0.297242 | ||||||||
\(638\) | −3.30621e104 | −0.218050 | ||||||||
\(639\) | 1.87571e105 | 1.16649 | ||||||||
\(640\) | 9.99586e104 | 0.586234 | ||||||||
\(641\) | −1.25933e105 | −0.696569 | −0.348285 | − | 0.937389i | \(-0.613236\pi\) | ||||
−0.348285 | + | 0.937389i | \(0.613236\pi\) | |||||||
\(642\) | −9.79593e103 | −0.0511072 | ||||||||
\(643\) | 2.15243e105 | 1.05930 | 0.529648 | − | 0.848218i | \(-0.322324\pi\) | ||||
0.529648 | + | 0.848218i | \(0.322324\pi\) | |||||||
\(644\) | −6.00925e104 | −0.278997 | ||||||||
\(645\) | 5.38181e104 | 0.235743 | ||||||||
\(646\) | −2.02806e105 | −0.838228 | ||||||||
\(647\) | −4.52853e105 | −1.76623 | −0.883115 | − | 0.469157i | \(-0.844558\pi\) | ||||
−0.883115 | + | 0.469157i | \(0.844558\pi\) | |||||||
\(648\) | 2.52461e105 | 0.929247 | ||||||||
\(649\) | −2.88660e105 | −1.00279 | ||||||||
\(650\) | −2.01827e104 | −0.0661801 | ||||||||
\(651\) | 4.46411e104 | 0.138181 | ||||||||
\(652\) | 9.14776e104 | 0.267319 | ||||||||
\(653\) | −4.91238e105 | −1.35534 | −0.677669 | − | 0.735367i | \(-0.737010\pi\) | ||||
−0.677669 | + | 0.735367i | \(0.737010\pi\) | |||||||
\(654\) | 7.64456e104 | 0.199153 | ||||||||
\(655\) | 5.27854e105 | 1.29857 | ||||||||
\(656\) | −4.05669e104 | −0.0942492 | ||||||||
\(657\) | −4.19929e105 | −0.921456 | ||||||||
\(658\) | 1.51160e105 | 0.313305 | ||||||||
\(659\) | 1.98171e105 | 0.388005 | 0.194003 | − | 0.981001i | \(-0.437853\pi\) | ||||
0.194003 | + | 0.981001i | \(0.437853\pi\) | |||||||
\(660\) | −4.11947e104 | −0.0761981 | ||||||||
\(661\) | 2.87807e105 | 0.502975 | 0.251487 | − | 0.967861i | \(-0.419080\pi\) | ||||
0.251487 | + | 0.967861i | \(0.419080\pi\) | |||||||
\(662\) | 6.78530e105 | 1.12045 | ||||||||
\(663\) | −4.85305e104 | −0.0757282 | ||||||||
\(664\) | −1.07372e105 | −0.158339 | ||||||||
\(665\) | −5.81971e105 | −0.811128 | ||||||||
\(666\) | 7.65153e105 | 1.00801 | ||||||||
\(667\) | 3.41544e105 | 0.425332 | ||||||||
\(668\) | −3.66656e105 | −0.431660 | ||||||||
\(669\) | −3.99490e104 | −0.0444658 | ||||||||
\(670\) | −7.66815e105 | −0.807023 | ||||||||
\(671\) | 3.82089e105 | 0.380250 | ||||||||
\(672\) | −1.01016e105 | −0.0950693 | ||||||||
\(673\) | 2.37451e105 | 0.211353 | 0.105676 | − | 0.994401i | \(-0.466299\pi\) | ||||
0.105676 | + | 0.994401i | \(0.466299\pi\) | |||||||
\(674\) | −1.46203e105 | −0.123086 | ||||||||
\(675\) | −1.01455e105 | −0.0807947 | ||||||||
\(676\) | 6.31249e105 | 0.475553 | ||||||||
\(677\) | −5.88403e105 | −0.419372 | −0.209686 | − | 0.977769i | \(-0.567244\pi\) | ||||
−0.209686 | + | 0.977769i | \(0.567244\pi\) | |||||||
\(678\) | −1.34063e105 | −0.0904057 | ||||||||
\(679\) | −2.05167e105 | −0.130915 | ||||||||
\(680\) | −1.88852e106 | −1.14035 | ||||||||
\(681\) | −1.30807e105 | −0.0747506 | ||||||||
\(682\) | −1.13668e106 | −0.614787 | ||||||||
\(683\) | 3.15565e105 | 0.161552 | 0.0807760 | − | 0.996732i | \(-0.474260\pi\) | ||||
0.0807760 | + | 0.996732i | \(0.474260\pi\) | |||||||
\(684\) | −1.52207e106 | −0.737618 | ||||||||
\(685\) | 1.68139e106 | 0.771385 | ||||||||
\(686\) | 1.40210e106 | 0.609010 | ||||||||
\(687\) | 6.17309e105 | 0.253878 | ||||||||
\(688\) | −2.18974e105 | −0.0852760 | ||||||||
\(689\) | 1.98140e106 | 0.730719 | ||||||||
\(690\) | −3.00138e105 | −0.104829 | ||||||||
\(691\) | 4.44799e106 | 1.47142 | 0.735710 | − | 0.677296i | \(-0.236849\pi\) | ||||
0.735710 | + | 0.677296i | \(0.236849\pi\) | |||||||
\(692\) | −4.97883e105 | −0.156009 | ||||||||
\(693\) | −1.23936e106 | −0.367875 | ||||||||
\(694\) | −9.73215e105 | −0.273671 | ||||||||
\(695\) | 3.66281e106 | 0.975853 | ||||||||
\(696\) | 3.52154e105 | 0.0888969 | ||||||||
\(697\) | −5.68115e106 | −1.35896 | ||||||||
\(698\) | 4.85483e106 | 1.10052 | ||||||||
\(699\) | 2.64485e105 | 0.0568208 | ||||||||
\(700\) | −3.83382e105 | −0.0780647 | ||||||||
\(701\) | −2.53368e106 | −0.489020 | −0.244510 | − | 0.969647i | \(-0.578627\pi\) | ||||
−0.244510 | + | 0.969647i | \(0.578627\pi\) | |||||||
\(702\) | 5.21715e105 | 0.0954534 | ||||||||
\(703\) | −1.20813e107 | −2.09551 | ||||||||
\(704\) | 2.85795e106 | 0.469981 | ||||||||
\(705\) | −1.07047e106 | −0.166910 | ||||||||
\(706\) | −7.79895e106 | −1.15308 | ||||||||
\(707\) | 3.92916e105 | 0.0550899 | ||||||||
\(708\) | 1.13652e106 | 0.151122 | ||||||||
\(709\) | −1.30039e106 | −0.163998 | −0.0819990 | − | 0.996632i | \(-0.526130\pi\) | ||||
−0.0819990 | + | 0.996632i | \(0.526130\pi\) | |||||||
\(710\) | 7.18991e106 | 0.860074 | ||||||||
\(711\) | −5.58910e106 | −0.634208 | ||||||||
\(712\) | 7.45020e106 | 0.801989 | ||||||||
\(713\) | 1.17423e107 | 1.19921 | ||||||||
\(714\) | 6.50178e105 | 0.0630012 | ||||||||
\(715\) | 3.54599e106 | 0.326033 | ||||||||
\(716\) | 4.77030e106 | 0.416205 | ||||||||
\(717\) | −7.77669e105 | −0.0643912 | ||||||||
\(718\) | −8.77960e106 | −0.689935 | ||||||||
\(719\) | −4.99955e106 | −0.372905 | −0.186452 | − | 0.982464i | \(-0.559699\pi\) | ||||
−0.186452 | + | 0.982464i | \(0.559699\pi\) | |||||||
\(720\) | 1.06203e106 | 0.0751913 | ||||||||
\(721\) | 1.28210e107 | 0.861685 | ||||||||
\(722\) | −6.87061e106 | −0.438380 | ||||||||
\(723\) | −4.55520e106 | −0.275944 | ||||||||
\(724\) | 1.22624e107 | 0.705310 | ||||||||
\(725\) | 2.17900e106 | 0.119010 | ||||||||
\(726\) | 1.17173e106 | 0.0607723 | ||||||||
\(727\) | 1.34392e106 | 0.0661963 | 0.0330981 | − | 0.999452i | \(-0.489463\pi\) | ||||
0.0330981 | + | 0.999452i | \(0.489463\pi\) | |||||||
\(728\) | 5.33338e106 | 0.249503 | ||||||||
\(729\) | −1.85513e107 | −0.824313 | ||||||||
\(730\) | −1.60966e107 | −0.679403 | ||||||||
\(731\) | −3.06661e107 | −1.22958 | ||||||||
\(732\) | −1.50437e106 | −0.0573044 | ||||||||
\(733\) | 2.35888e107 | 0.853703 | 0.426851 | − | 0.904322i | \(-0.359623\pi\) | ||||
0.426851 | + | 0.904322i | \(0.359623\pi\) | |||||||
\(734\) | −6.05233e106 | −0.208123 | ||||||||
\(735\) | −4.03175e106 | −0.131740 | ||||||||
\(736\) | −2.65710e107 | −0.825067 | ||||||||
\(737\) | 2.57842e107 | 0.760890 | ||||||||
\(738\) | 3.00714e107 | 0.843413 | ||||||||
\(739\) | 2.54158e107 | 0.677543 | 0.338771 | − | 0.940869i | \(-0.389989\pi\) | ||||
0.338771 | + | 0.940869i | \(0.389989\pi\) | |||||||
\(740\) | −4.15856e107 | −1.05379 | ||||||||
\(741\) | −4.05602e106 | −0.0977050 | ||||||||
\(742\) | −2.65453e107 | −0.607913 | ||||||||
\(743\) | −1.66703e107 | −0.362964 | −0.181482 | − | 0.983394i | \(-0.558089\pi\) | ||||
−0.181482 | + | 0.983394i | \(0.558089\pi\) | |||||||
\(744\) | 1.21071e107 | 0.250643 | ||||||||
\(745\) | 4.98627e107 | 0.981556 | ||||||||
\(746\) | 3.99708e107 | 0.748233 | ||||||||
\(747\) | 8.45608e106 | 0.150538 | ||||||||
\(748\) | 2.34732e107 | 0.397431 | ||||||||
\(749\) | 1.60175e107 | 0.257945 | ||||||||
\(750\) | 6.17562e106 | 0.0945982 | ||||||||
\(751\) | −4.43790e105 | −0.00646666 | −0.00323333 | − | 0.999995i | \(-0.501029\pi\) | ||||
−0.00323333 | + | 0.999995i | \(0.501029\pi\) | |||||||
\(752\) | 4.35552e106 | 0.0603769 | ||||||||
\(753\) | 1.18499e107 | 0.156279 | ||||||||
\(754\) | −1.12051e107 | −0.140602 | ||||||||
\(755\) | −1.00525e108 | −1.20023 | ||||||||
\(756\) | 9.91029e106 | 0.112595 | ||||||||
\(757\) | 1.15903e108 | 1.25314 | 0.626571 | − | 0.779364i | \(-0.284458\pi\) | ||||
0.626571 | + | 0.779364i | \(0.284458\pi\) | |||||||
\(758\) | −7.89223e107 | −0.812090 | ||||||||
\(759\) | 1.00921e107 | 0.0988364 | ||||||||
\(760\) | −1.57836e108 | −1.47129 | ||||||||
\(761\) | −1.37920e108 | −1.22377 | −0.611887 | − | 0.790945i | \(-0.709589\pi\) | ||||
−0.611887 | + | 0.790945i | \(0.709589\pi\) | |||||||
\(762\) | −1.58365e107 | −0.133766 | ||||||||
\(763\) | −1.24998e108 | −1.00515 | ||||||||
\(764\) | 1.00553e108 | 0.769827 | ||||||||
\(765\) | 1.48731e108 | 1.08417 | ||||||||
\(766\) | 1.32295e108 | 0.918258 | ||||||||
\(767\) | −9.78301e107 | −0.646616 | ||||||||
\(768\) | −2.85218e107 | −0.179528 | ||||||||
\(769\) | 4.00119e107 | 0.239856 | 0.119928 | − | 0.992783i | \(-0.461734\pi\) | ||||
0.119928 | + | 0.992783i | \(0.461734\pi\) | |||||||
\(770\) | −4.75067e107 | −0.271239 | ||||||||
\(771\) | −1.97053e107 | −0.107163 | ||||||||
\(772\) | 2.05328e108 | 1.06365 | ||||||||
\(773\) | 1.87052e108 | 0.923064 | 0.461532 | − | 0.887124i | \(-0.347300\pi\) | ||||
0.461532 | + | 0.887124i | \(0.347300\pi\) | |||||||
\(774\) | 1.62321e108 | 0.763115 | ||||||||
\(775\) | 7.49144e107 | 0.335546 | ||||||||
\(776\) | −5.56433e107 | −0.237464 | ||||||||
\(777\) | 3.87316e107 | 0.157499 | ||||||||
\(778\) | 8.52296e107 | 0.330260 | ||||||||
\(779\) | −4.74812e108 | −1.75334 | ||||||||
\(780\) | −1.39613e107 | −0.0491337 | ||||||||
\(781\) | −2.41761e108 | −0.810909 | ||||||||
\(782\) | 1.71022e108 | 0.546761 | ||||||||
\(783\) | −5.63265e107 | −0.171651 | ||||||||
\(784\) | 1.64043e107 | 0.0476547 | ||||||||
\(785\) | 4.85460e108 | 1.34444 | ||||||||
\(786\) | −4.92866e107 | −0.130132 | ||||||||
\(787\) | −6.55380e108 | −1.64983 | −0.824917 | − | 0.565253i | \(-0.808778\pi\) | ||||
−0.824917 | + | 0.565253i | \(0.808778\pi\) | |||||||
\(788\) | −1.10208e108 | −0.264533 | ||||||||
\(789\) | −1.41789e107 | −0.0324530 | ||||||||
\(790\) | −2.14240e108 | −0.467611 | ||||||||
\(791\) | 2.19209e108 | 0.456290 | ||||||||
\(792\) | −3.36126e108 | −0.667279 | ||||||||
\(793\) | 1.29494e108 | 0.245192 | ||||||||
\(794\) | 4.45995e107 | 0.0805492 | ||||||||
\(795\) | 1.87986e108 | 0.323861 | ||||||||
\(796\) | 1.58187e108 | 0.259975 | ||||||||
\(797\) | −9.83900e106 | −0.0154264 | −0.00771319 | − | 0.999970i | \(-0.502455\pi\) | ||||
−0.00771319 | + | 0.999970i | \(0.502455\pi\) | |||||||
\(798\) | 5.43396e107 | 0.0812846 | ||||||||
\(799\) | 6.09965e108 | 0.870564 | ||||||||
\(800\) | −1.69519e108 | −0.230858 | ||||||||
\(801\) | −5.86742e108 | −0.762479 | ||||||||
\(802\) | 1.88732e108 | 0.234049 | ||||||||
\(803\) | 5.41249e108 | 0.640566 | ||||||||
\(804\) | −1.01518e108 | −0.114668 | ||||||||
\(805\) | 4.90762e108 | 0.529085 | ||||||||
\(806\) | −3.85234e108 | −0.396424 | ||||||||
\(807\) | 1.84731e107 | 0.0181460 | ||||||||
\(808\) | 1.06563e108 | 0.0999263 | ||||||||
\(809\) | 1.09522e109 | 0.980463 | 0.490231 | − | 0.871592i | \(-0.336912\pi\) | ||||
0.490231 | + | 0.871592i | \(0.336912\pi\) | |||||||
\(810\) | −7.62135e108 | −0.651394 | ||||||||
\(811\) | 1.44228e109 | 1.17698 | 0.588488 | − | 0.808506i | \(-0.299724\pi\) | ||||
0.588488 | + | 0.808506i | \(0.299724\pi\) | |||||||
\(812\) | −2.12848e108 | −0.165851 | ||||||||
\(813\) | −4.73208e107 | −0.0352092 | ||||||||
\(814\) | −9.86209e108 | −0.700735 | ||||||||
\(815\) | −7.47077e108 | −0.506938 | ||||||||
\(816\) | 1.87342e107 | 0.0121410 | ||||||||
\(817\) | −2.56297e109 | −1.58641 | ||||||||
\(818\) | 1.15890e108 | 0.0685167 | ||||||||
\(819\) | −4.20032e108 | −0.237211 | ||||||||
\(820\) | −1.63436e109 | −0.881717 | ||||||||
\(821\) | 1.67032e109 | 0.860858 | 0.430429 | − | 0.902624i | \(-0.358362\pi\) | ||||
0.430429 | + | 0.902624i | \(0.358362\pi\) | |||||||
\(822\) | −1.56994e108 | −0.0773018 | ||||||||
\(823\) | −2.67065e109 | −1.25639 | −0.628193 | − | 0.778057i | \(-0.716205\pi\) | ||||
−0.628193 | + | 0.778057i | \(0.716205\pi\) | |||||||
\(824\) | 3.47717e109 | 1.56299 | ||||||||
\(825\) | 6.43865e107 | 0.0276549 | ||||||||
\(826\) | 1.31066e109 | 0.537945 | ||||||||
\(827\) | −3.63648e108 | −0.142634 | −0.0713172 | − | 0.997454i | \(-0.522720\pi\) | ||||
−0.0713172 | + | 0.997454i | \(0.522720\pi\) | |||||||
\(828\) | 1.28353e109 | 0.481135 | ||||||||
\(829\) | −8.52744e108 | −0.305509 | −0.152754 | − | 0.988264i | \(-0.548814\pi\) | ||||
−0.152754 | + | 0.988264i | \(0.548814\pi\) | |||||||
\(830\) | 3.24136e108 | 0.110994 | ||||||||
\(831\) | 4.06545e107 | 0.0133067 | ||||||||
\(832\) | 9.68591e108 | 0.303051 | ||||||||
\(833\) | 2.29733e109 | 0.687125 | ||||||||
\(834\) | −3.42003e108 | −0.0977920 | ||||||||
\(835\) | 2.99440e109 | 0.818591 | ||||||||
\(836\) | 1.96181e109 | 0.512768 | ||||||||
\(837\) | −1.93651e109 | −0.483967 | ||||||||
\(838\) | 2.78740e109 | 0.666115 | ||||||||
\(839\) | −1.65765e109 | −0.378809 | −0.189404 | − | 0.981899i | \(-0.560656\pi\) | ||||
−0.189404 | + | 0.981899i | \(0.560656\pi\) | |||||||
\(840\) | 5.06008e108 | 0.110582 | ||||||||
\(841\) | −3.57490e109 | −0.747160 | ||||||||
\(842\) | −3.20447e109 | −0.640550 | ||||||||
\(843\) | −2.64655e108 | −0.0505995 | ||||||||
\(844\) | −2.55532e109 | −0.467308 | ||||||||
\(845\) | −5.15527e109 | −0.901829 | ||||||||
\(846\) | −3.22866e109 | −0.540299 | ||||||||
\(847\) | −1.91593e109 | −0.306726 | ||||||||
\(848\) | −7.64875e108 | −0.117151 | ||||||||
\(849\) | 9.92891e108 | 0.145500 | ||||||||
\(850\) | 1.09109e109 | 0.152986 | ||||||||
\(851\) | 1.01879e110 | 1.36687 | ||||||||
\(852\) | 9.51865e108 | 0.122205 | ||||||||
\(853\) | −5.77263e109 | −0.709227 | −0.354613 | − | 0.935013i | \(-0.615387\pi\) | ||||
−0.354613 | + | 0.935013i | \(0.615387\pi\) | |||||||
\(854\) | −1.73487e109 | −0.203984 | ||||||||
\(855\) | 1.24304e110 | 1.39880 | ||||||||
\(856\) | 4.34411e109 | 0.467880 | ||||||||
\(857\) | −1.55041e110 | −1.59833 | −0.799164 | − | 0.601113i | \(-0.794724\pi\) | ||||
−0.799164 | + | 0.601113i | \(0.794724\pi\) | |||||||
\(858\) | −3.31096e108 | −0.0326723 | ||||||||
\(859\) | 1.13730e110 | 1.07431 | 0.537156 | − | 0.843483i | \(-0.319499\pi\) | ||||
0.537156 | + | 0.843483i | \(0.319499\pi\) | |||||||
\(860\) | −8.82208e109 | −0.797772 | ||||||||
\(861\) | 1.52220e109 | 0.131781 | ||||||||
\(862\) | 7.30072e109 | 0.605122 | ||||||||
\(863\) | 2.94758e109 | 0.233917 | 0.116958 | − | 0.993137i | \(-0.462686\pi\) | ||||
0.116958 | + | 0.993137i | \(0.462686\pi\) | |||||||
\(864\) | 4.38201e109 | 0.332973 | ||||||||
\(865\) | 4.06610e109 | 0.295851 | ||||||||
\(866\) | 3.33608e108 | 0.0232442 | ||||||||
\(867\) | 2.65629e107 | 0.00177239 | ||||||||
\(868\) | −7.31774e109 | −0.467614 | ||||||||
\(869\) | 7.20382e109 | 0.440881 | ||||||||
\(870\) | −1.06309e109 | −0.0623159 | ||||||||
\(871\) | 8.73854e109 | 0.490634 | ||||||||
\(872\) | −3.39006e110 | −1.82322 | ||||||||
\(873\) | 4.38219e109 | 0.225765 | ||||||||
\(874\) | 1.42934e110 | 0.705435 | ||||||||
\(875\) | −1.00979e110 | −0.477450 | ||||||||
\(876\) | −2.13101e109 | −0.0965344 | ||||||||
\(877\) | −5.57654e109 | −0.242036 | −0.121018 | − | 0.992650i | \(-0.538616\pi\) | ||||
−0.121018 | + | 0.992650i | \(0.538616\pi\) | |||||||
\(878\) | 1.33999e110 | 0.557259 | ||||||||
\(879\) | −5.11698e109 | −0.203906 | ||||||||
\(880\) | −1.36885e109 | −0.0522705 | ||||||||
\(881\) | −5.10259e110 | −1.86721 | −0.933607 | − | 0.358299i | \(-0.883357\pi\) | ||||
−0.933607 | + | 0.358299i | \(0.883357\pi\) | |||||||
\(882\) | −1.21602e110 | −0.426451 | ||||||||
\(883\) | 1.13575e110 | 0.381730 | 0.190865 | − | 0.981616i | \(-0.438871\pi\) | ||||
0.190865 | + | 0.981616i | \(0.438871\pi\) | |||||||
\(884\) | 7.95531e109 | 0.256270 | ||||||||
\(885\) | −9.28168e109 | −0.286585 | ||||||||
\(886\) | 3.60411e109 | 0.106668 | ||||||||
\(887\) | 3.22462e110 | 0.914835 | 0.457417 | − | 0.889252i | \(-0.348775\pi\) | ||||
0.457417 | + | 0.889252i | \(0.348775\pi\) | |||||||
\(888\) | 1.05044e110 | 0.285683 | ||||||||
\(889\) | 2.58945e110 | 0.675136 | ||||||||
\(890\) | −2.24909e110 | −0.562187 | ||||||||
\(891\) | 2.56268e110 | 0.614158 | ||||||||
\(892\) | 6.54860e109 | 0.150476 | ||||||||
\(893\) | 5.09788e110 | 1.12321 | ||||||||
\(894\) | −4.65576e109 | −0.0983635 | ||||||||
\(895\) | −3.89580e110 | −0.789283 | ||||||||
\(896\) | 1.52611e110 | 0.296507 | ||||||||
\(897\) | 3.42034e109 | 0.0637313 | ||||||||
\(898\) | 4.21535e110 | 0.753306 | ||||||||
\(899\) | 4.15914e110 | 0.712878 | ||||||||
\(900\) | 8.18872e109 | 0.134624 | ||||||||
\(901\) | −1.07116e111 | −1.68918 | ||||||||
\(902\) | −3.87592e110 | −0.586313 | ||||||||
\(903\) | 8.21662e109 | 0.119235 | ||||||||
\(904\) | 5.94518e110 | 0.827654 | ||||||||
\(905\) | −1.00145e111 | −1.33754 | ||||||||
\(906\) | 9.38622e109 | 0.120277 | ||||||||
\(907\) | −1.38032e111 | −1.69709 | −0.848547 | − | 0.529120i | \(-0.822522\pi\) | ||||
−0.848547 | + | 0.529120i | \(0.822522\pi\) | |||||||
\(908\) | 2.14424e110 | 0.252962 | ||||||||
\(909\) | −8.39237e109 | −0.0950034 | ||||||||
\(910\) | −1.61005e110 | −0.174899 | ||||||||
\(911\) | 2.99939e110 | 0.312676 | 0.156338 | − | 0.987704i | \(-0.450031\pi\) | ||||
0.156338 | + | 0.987704i | \(0.450031\pi\) | |||||||
\(912\) | 1.56574e109 | 0.0156644 | ||||||||
\(913\) | −1.08991e110 | −0.104649 | ||||||||
\(914\) | 7.52721e110 | 0.693668 | ||||||||
\(915\) | 1.22858e110 | 0.108671 | ||||||||
\(916\) | −1.01192e111 | −0.859142 | ||||||||
\(917\) | 8.05895e110 | 0.656793 | ||||||||
\(918\) | −2.82044e110 | −0.220657 | ||||||||
\(919\) | 2.25950e111 | 1.69700 | 0.848498 | − | 0.529199i | \(-0.177508\pi\) | ||||
0.848498 | + | 0.529199i | \(0.177508\pi\) | |||||||
\(920\) | 1.33099e111 | 0.959694 | ||||||||
\(921\) | 1.40901e109 | 0.00975388 | ||||||||
\(922\) | −1.00820e111 | −0.670095 | ||||||||
\(923\) | −8.19354e110 | −0.522887 | ||||||||
\(924\) | −6.28936e109 | −0.0385396 | ||||||||
\(925\) | 6.49974e110 | 0.382456 | ||||||||
\(926\) | 1.03249e111 | 0.583412 | ||||||||
\(927\) | −2.73845e111 | −1.48599 | ||||||||
\(928\) | −9.41146e110 | −0.490465 | ||||||||
\(929\) | 3.73615e111 | 1.86997 | 0.934985 | − | 0.354688i | \(-0.115413\pi\) | ||||
0.934985 | + | 0.354688i | \(0.115413\pi\) | |||||||
\(930\) | −3.65492e110 | −0.175698 | ||||||||
\(931\) | 1.92003e111 | 0.886534 | ||||||||
\(932\) | −4.33555e110 | −0.192286 | ||||||||
\(933\) | 2.87914e110 | 0.122659 | ||||||||
\(934\) | −2.65257e111 | −1.08557 | ||||||||
\(935\) | −1.91700e111 | −0.753680 | ||||||||
\(936\) | −1.13917e111 | −0.430272 | ||||||||
\(937\) | −2.04035e111 | −0.740405 | −0.370203 | − | 0.928951i | \(-0.620712\pi\) | ||||
−0.370203 | + | 0.928951i | \(0.620712\pi\) | |||||||
\(938\) | −1.17073e111 | −0.408178 | ||||||||
\(939\) | −3.48812e108 | −0.00116851 | ||||||||
\(940\) | 1.75476e111 | 0.564837 | ||||||||
\(941\) | 1.19436e111 | 0.369425 | 0.184712 | − | 0.982793i | \(-0.440865\pi\) | ||||
0.184712 | + | 0.982793i | \(0.440865\pi\) | |||||||
\(942\) | −4.53282e110 | −0.134729 | ||||||||
\(943\) | 4.00397e111 | 1.14367 | ||||||||
\(944\) | 3.77652e110 | 0.103667 | ||||||||
\(945\) | −8.09351e110 | −0.213523 | ||||||||
\(946\) | −2.09217e111 | −0.530493 | ||||||||
\(947\) | −5.14584e111 | −1.25410 | −0.627050 | − | 0.778979i | \(-0.715738\pi\) | ||||
−0.627050 | + | 0.778979i | \(0.715738\pi\) | |||||||
\(948\) | −2.83630e110 | −0.0664416 | ||||||||
\(949\) | 1.83435e111 | 0.413047 | ||||||||
\(950\) | 9.11900e110 | 0.197384 | ||||||||
\(951\) | 2.53391e110 | 0.0527256 | ||||||||
\(952\) | −2.88328e111 | −0.576769 | ||||||||
\(953\) | 8.87914e111 | 1.70760 | 0.853802 | − | 0.520597i | \(-0.174291\pi\) | ||||
0.853802 | + | 0.520597i | \(0.174291\pi\) | |||||||
\(954\) | 5.66987e111 | 1.04836 | ||||||||
\(955\) | −8.21192e111 | −1.45988 | ||||||||
\(956\) | 1.27479e111 | 0.217905 | ||||||||
\(957\) | 3.57465e110 | 0.0587537 | ||||||||
\(958\) | 7.58786e111 | 1.19926 | ||||||||
\(959\) | 2.56704e111 | 0.390153 | ||||||||
\(960\) | 9.18956e110 | 0.134315 | ||||||||
\(961\) | 7.18497e111 | 1.00995 | ||||||||
\(962\) | −3.34237e111 | −0.451845 | ||||||||
\(963\) | −3.42121e111 | −0.444830 | ||||||||
\(964\) | 7.46707e111 | 0.933816 | ||||||||
\(965\) | −1.67687e112 | −2.01709 | ||||||||
\(966\) | −4.58233e110 | −0.0530205 | ||||||||
\(967\) | −1.49205e112 | −1.66070 | −0.830351 | − | 0.557241i | \(-0.811860\pi\) | ||||
−0.830351 | + | 0.557241i | \(0.811860\pi\) | |||||||
\(968\) | −5.19618e111 | −0.556363 | ||||||||
\(969\) | 2.19272e111 | 0.225862 | ||||||||
\(970\) | 1.67977e111 | 0.166460 | ||||||||
\(971\) | −2.06690e111 | −0.197060 | −0.0985299 | − | 0.995134i | \(-0.531414\pi\) | ||||
−0.0985299 | + | 0.995134i | \(0.531414\pi\) | |||||||
\(972\) | −3.19127e111 | −0.292738 | ||||||||
\(973\) | 5.59216e111 | 0.493569 | ||||||||
\(974\) | 4.78002e111 | 0.405946 | ||||||||
\(975\) | 2.18213e110 | 0.0178323 | ||||||||
\(976\) | −4.99884e110 | −0.0393098 | ||||||||
\(977\) | −1.87496e112 | −1.41888 | −0.709439 | − | 0.704767i | \(-0.751051\pi\) | ||||
−0.709439 | + | 0.704767i | \(0.751051\pi\) | |||||||
\(978\) | 6.97559e110 | 0.0508012 | ||||||||
\(979\) | 7.56255e111 | 0.530050 | ||||||||
\(980\) | 6.60900e111 | 0.445818 | ||||||||
\(981\) | 2.66985e112 | 1.73340 | ||||||||
\(982\) | −2.01683e112 | −1.26034 | ||||||||
\(983\) | 7.83556e111 | 0.471317 | 0.235659 | − | 0.971836i | \(-0.424275\pi\) | ||||
0.235659 | + | 0.971836i | \(0.424275\pi\) | |||||||
\(984\) | 4.12836e111 | 0.239035 | ||||||||
\(985\) | 9.00045e111 | 0.501656 | ||||||||
\(986\) | 6.05760e111 | 0.325025 | ||||||||
\(987\) | −1.63433e111 | −0.0844203 | ||||||||
\(988\) | 6.64878e111 | 0.330641 | ||||||||
\(989\) | 2.16129e112 | 1.03479 | ||||||||
\(990\) | 1.01470e112 | 0.467757 | ||||||||
\(991\) | −1.41350e112 | −0.627383 | −0.313692 | − | 0.949525i | \(-0.601566\pi\) | ||||
−0.313692 | + | 0.949525i | \(0.601566\pi\) | |||||||
\(992\) | −3.23567e112 | −1.38286 | ||||||||
\(993\) | −7.33620e111 | −0.301908 | ||||||||
\(994\) | 1.09771e112 | 0.435010 | ||||||||
\(995\) | −1.29188e112 | −0.493011 | ||||||||
\(996\) | 4.29121e110 | 0.0157708 | ||||||||
\(997\) | −4.15637e111 | −0.147111 | −0.0735556 | − | 0.997291i | \(-0.523435\pi\) | ||||
−0.0735556 | + | 0.997291i | \(0.523435\pi\) | |||||||
\(998\) | 8.86724e110 | 0.0302269 | ||||||||
\(999\) | −1.68016e112 | −0.551627 |
(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 | 1.76.a.a.1.3 | ✓ | 6 | |
3.2 | odd | 2 | 9.76.a.c.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.76.a.a.1.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9.76.a.c.1.4 | 6 | 3.2 | odd | 2 |