Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,52,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, 52, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 52);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 52 \) |
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: | \(16.4731353414\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 495735060514x^{2} - 23954614981416598x + 48979992255622025570313 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{10}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(644100.\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27049e7 | −0.267737 | −0.133868 | − | 0.990999i | \(-0.542740\pi\) | ||||
−0.133868 | + | 0.990999i | \(0.542740\pi\) | |||||||
\(3\) | −5.15198e11 | −0.351061 | −0.175530 | − | 0.984474i | \(-0.556164\pi\) | ||||
−0.175530 | + | 0.984474i | \(0.556164\pi\) | |||||||
\(4\) | −2.09038e15 | −0.928317 | ||||||||
\(5\) | −3.83602e17 | −0.575633 | −0.287817 | − | 0.957686i | \(-0.592929\pi\) | ||||
−0.287817 | + | 0.957686i | \(0.592929\pi\) | |||||||
\(6\) | 6.54557e18 | 0.0939919 | ||||||||
\(7\) | −2.02239e21 | −0.569988 | −0.284994 | − | 0.958529i | \(-0.591992\pi\) | ||||
−0.284994 | + | 0.958529i | \(0.591992\pi\) | |||||||
\(8\) | 5.51672e22 | 0.516281 | ||||||||
\(9\) | −1.88826e24 | −0.876756 | ||||||||
\(10\) | 4.87365e24 | 0.154118 | ||||||||
\(11\) | −2.47031e25 | −0.0687444 | −0.0343722 | − | 0.999409i | \(-0.510943\pi\) | ||||
−0.0343722 | + | 0.999409i | \(0.510943\pi\) | |||||||
\(12\) | 1.07696e27 | 0.325896 | ||||||||
\(13\) | −1.34161e27 | −0.0527314 | −0.0263657 | − | 0.999652i | \(-0.508393\pi\) | ||||
−0.0263657 | + | 0.999652i | \(0.508393\pi\) | |||||||
\(14\) | 2.56944e28 | 0.152607 | ||||||||
\(15\) | 1.97631e29 | 0.202082 | ||||||||
\(16\) | 4.00623e30 | 0.790090 | ||||||||
\(17\) | 3.03892e31 | 1.27724 | 0.638618 | − | 0.769524i | \(-0.279506\pi\) | ||||
0.638618 | + | 0.769524i | \(0.279506\pi\) | |||||||
\(18\) | 2.39903e31 | 0.234740 | ||||||||
\(19\) | 7.39260e32 | 1.82214 | 0.911068 | − | 0.412257i | \(-0.135259\pi\) | ||||
0.911068 | + | 0.412257i | \(0.135259\pi\) | |||||||
\(20\) | 8.01876e32 | 0.534370 | ||||||||
\(21\) | 1.04193e33 | 0.200100 | ||||||||
\(22\) | 3.13851e32 | 0.0184054 | ||||||||
\(23\) | −7.84569e34 | −1.48106 | −0.740528 | − | 0.672026i | \(-0.765424\pi\) | ||||
−0.740528 | + | 0.672026i | \(0.765424\pi\) | |||||||
\(24\) | −2.84221e34 | −0.181246 | ||||||||
\(25\) | −2.96939e35 | −0.668646 | ||||||||
\(26\) | 1.70450e34 | 0.0141181 | ||||||||
\(27\) | 2.08241e36 | 0.658856 | ||||||||
\(28\) | 4.22758e36 | 0.529129 | ||||||||
\(29\) | 1.79754e37 | 0.919451 | 0.459726 | − | 0.888061i | \(-0.347948\pi\) | ||||
0.459726 | + | 0.888061i | \(0.347948\pi\) | |||||||
\(30\) | −2.51089e36 | −0.0541049 | ||||||||
\(31\) | −9.27311e37 | −0.865969 | −0.432984 | − | 0.901401i | \(-0.642539\pi\) | ||||
−0.432984 | + | 0.901401i | \(0.642539\pi\) | |||||||
\(32\) | −1.75124e38 | −0.727817 | ||||||||
\(33\) | 1.27270e37 | 0.0241335 | ||||||||
\(34\) | −3.86093e38 | −0.341963 | ||||||||
\(35\) | 7.75794e38 | 0.328104 | ||||||||
\(36\) | 3.94720e39 | 0.813908 | ||||||||
\(37\) | 6.86089e39 | 0.703456 | 0.351728 | − | 0.936102i | \(-0.385594\pi\) | ||||
0.351728 | + | 0.936102i | \(0.385594\pi\) | |||||||
\(38\) | −9.39226e39 | −0.487853 | ||||||||
\(39\) | 6.91193e38 | 0.0185119 | ||||||||
\(40\) | −2.11623e40 | −0.297189 | ||||||||
\(41\) | −1.74971e41 | −1.30912 | −0.654559 | − | 0.756011i | \(-0.727146\pi\) | ||||
−0.654559 | + | 0.756011i | \(0.727146\pi\) | |||||||
\(42\) | −1.32377e40 | −0.0535742 | ||||||||
\(43\) | 5.07001e41 | 1.12606 | 0.563032 | − | 0.826435i | \(-0.309635\pi\) | ||||
0.563032 | + | 0.826435i | \(0.309635\pi\) | |||||||
\(44\) | 5.16389e40 | 0.0638166 | ||||||||
\(45\) | 7.24343e41 | 0.504690 | ||||||||
\(46\) | 9.96791e41 | 0.396533 | ||||||||
\(47\) | −2.50083e42 | −0.574895 | −0.287448 | − | 0.957796i | \(-0.592807\pi\) | ||||
−0.287448 | + | 0.957796i | \(0.592807\pi\) | |||||||
\(48\) | −2.06400e42 | −0.277369 | ||||||||
\(49\) | −8.49918e42 | −0.675114 | ||||||||
\(50\) | 3.77259e42 | 0.179021 | ||||||||
\(51\) | −1.56564e43 | −0.448388 | ||||||||
\(52\) | 2.80447e42 | 0.0489515 | ||||||||
\(53\) | 1.56292e44 | 1.67843 | 0.839215 | − | 0.543800i | \(-0.183015\pi\) | ||||
0.839215 | + | 0.543800i | \(0.183015\pi\) | |||||||
\(54\) | −2.64569e43 | −0.176400 | ||||||||
\(55\) | 9.47615e42 | 0.0395716 | ||||||||
\(56\) | −1.11570e44 | −0.294274 | ||||||||
\(57\) | −3.80866e44 | −0.639680 | ||||||||
\(58\) | −2.28376e44 | −0.246171 | ||||||||
\(59\) | −5.63890e44 | −0.393068 | −0.196534 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196534 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(60\) | −4.13125e44 | −0.187596 | ||||||||
\(61\) | 3.98784e45 | 1.18803 | 0.594014 | − | 0.804454i | \(-0.297542\pi\) | ||||
0.594014 | + | 0.804454i | \(0.297542\pi\) | |||||||
\(62\) | 1.17814e45 | 0.231852 | ||||||||
\(63\) | 3.81881e45 | 0.499740 | ||||||||
\(64\) | −6.79628e45 | −0.595226 | ||||||||
\(65\) | 5.14643e44 | 0.0303540 | ||||||||
\(66\) | −1.61696e44 | −0.00646141 | ||||||||
\(67\) | −1.33985e46 | −0.364879 | −0.182439 | − | 0.983217i | \(-0.558399\pi\) | ||||
−0.182439 | + | 0.983217i | \(0.558399\pi\) | |||||||
\(68\) | −6.35251e46 | −1.18568 | ||||||||
\(69\) | 4.04208e46 | 0.519940 | ||||||||
\(70\) | −9.85643e45 | −0.0878455 | ||||||||
\(71\) | 2.44343e47 | 1.51674 | 0.758370 | − | 0.651824i | \(-0.225996\pi\) | ||||
0.758370 | + | 0.651824i | \(0.225996\pi\) | |||||||
\(72\) | −1.04170e47 | −0.452653 | ||||||||
\(73\) | 1.85599e47 | 0.567339 | 0.283669 | − | 0.958922i | \(-0.408448\pi\) | ||||
0.283669 | + | 0.958922i | \(0.408448\pi\) | |||||||
\(74\) | −8.71673e46 | −0.188341 | ||||||||
\(75\) | 1.52982e47 | 0.234735 | ||||||||
\(76\) | −1.54534e48 | −1.69152 | ||||||||
\(77\) | 4.99593e46 | 0.0391835 | ||||||||
\(78\) | −8.78157e45 | −0.00495633 | ||||||||
\(79\) | 1.63316e48 | 0.666097 | 0.333048 | − | 0.942910i | \(-0.391923\pi\) | ||||
0.333048 | + | 0.942910i | \(0.391923\pi\) | |||||||
\(80\) | −1.53680e48 | −0.454802 | ||||||||
\(81\) | 2.99389e48 | 0.645458 | ||||||||
\(82\) | 2.22300e48 | 0.350499 | ||||||||
\(83\) | 5.04167e48 | 0.583556 | 0.291778 | − | 0.956486i | \(-0.405753\pi\) | ||||
0.291778 | + | 0.956486i | \(0.405753\pi\) | |||||||
\(84\) | −2.17804e48 | −0.185757 | ||||||||
\(85\) | −1.16574e49 | −0.735220 | ||||||||
\(86\) | −6.44142e48 | −0.301489 | ||||||||
\(87\) | −9.26087e48 | −0.322783 | ||||||||
\(88\) | −1.36280e48 | −0.0354915 | ||||||||
\(89\) | 1.69379e48 | 0.0330685 | 0.0165342 | − | 0.999863i | \(-0.494737\pi\) | ||||
0.0165342 | + | 0.999863i | \(0.494737\pi\) | |||||||
\(90\) | −9.20274e48 | −0.135124 | ||||||||
\(91\) | 2.71326e48 | 0.0300563 | ||||||||
\(92\) | 1.64005e50 | 1.37489 | ||||||||
\(93\) | 4.77749e49 | 0.304008 | ||||||||
\(94\) | 3.17729e49 | 0.153921 | ||||||||
\(95\) | −2.83582e50 | −1.04888 | ||||||||
\(96\) | 9.02238e49 | 0.255508 | ||||||||
\(97\) | −6.10891e50 | −1.32826 | −0.664132 | − | 0.747615i | \(-0.731199\pi\) | ||||
−0.664132 | + | 0.747615i | \(0.731199\pi\) | |||||||
\(98\) | 1.07982e50 | 0.180753 | ||||||||
\(99\) | 4.66459e49 | 0.0602721 | ||||||||
\(100\) | 6.20716e50 | 0.620716 | ||||||||
\(101\) | −6.28480e50 | −0.487636 | −0.243818 | − | 0.969821i | \(-0.578400\pi\) | ||||
−0.243818 | + | 0.969821i | \(0.578400\pi\) | |||||||
\(102\) | 1.98914e50 | 0.120050 | ||||||||
\(103\) | 2.80053e51 | 1.31793 | 0.658963 | − | 0.752175i | \(-0.270995\pi\) | ||||
0.658963 | + | 0.752175i | \(0.270995\pi\) | |||||||
\(104\) | −7.40127e49 | −0.0272243 | ||||||||
\(105\) | −3.99688e50 | −0.115184 | ||||||||
\(106\) | −1.98569e51 | −0.449377 | ||||||||
\(107\) | −1.63322e50 | −0.0290910 | −0.0145455 | − | 0.999894i | \(-0.504630\pi\) | ||||
−0.0145455 | + | 0.999894i | \(0.504630\pi\) | |||||||
\(108\) | −4.35304e51 | −0.611627 | ||||||||
\(109\) | −1.58683e51 | −0.176260 | −0.0881302 | − | 0.996109i | \(-0.528089\pi\) | ||||
−0.0881302 | + | 0.996109i | \(0.528089\pi\) | |||||||
\(110\) | −1.20394e50 | −0.0105948 | ||||||||
\(111\) | −3.53472e51 | −0.246956 | ||||||||
\(112\) | −8.10217e51 | −0.450341 | ||||||||
\(113\) | 3.37912e52 | 1.49728 | 0.748640 | − | 0.662977i | \(-0.230707\pi\) | ||||
0.748640 | + | 0.662977i | \(0.230707\pi\) | |||||||
\(114\) | 4.83888e51 | 0.171266 | ||||||||
\(115\) | 3.00962e52 | 0.852545 | ||||||||
\(116\) | −3.75754e52 | −0.853542 | ||||||||
\(117\) | 2.53331e51 | 0.0462326 | ||||||||
\(118\) | 7.16419e51 | 0.105239 | ||||||||
\(119\) | −6.14589e52 | −0.728009 | ||||||||
\(120\) | 1.09028e52 | 0.104331 | ||||||||
\(121\) | −1.28520e53 | −0.995274 | ||||||||
\(122\) | −5.06653e52 | −0.318079 | ||||||||
\(123\) | 9.01450e52 | 0.459580 | ||||||||
\(124\) | 1.93844e53 | 0.803893 | ||||||||
\(125\) | 2.84260e53 | 0.960529 | ||||||||
\(126\) | −4.85178e52 | −0.133799 | ||||||||
\(127\) | −3.62929e53 | −0.818137 | −0.409069 | − | 0.912504i | \(-0.634146\pi\) | ||||
−0.409069 | + | 0.912504i | \(0.634146\pi\) | |||||||
\(128\) | 4.80692e53 | 0.887181 | ||||||||
\(129\) | −2.61206e53 | −0.395317 | ||||||||
\(130\) | −6.53852e51 | −0.00812688 | ||||||||
\(131\) | −2.78824e53 | −0.285044 | −0.142522 | − | 0.989792i | \(-0.545521\pi\) | ||||
−0.142522 | + | 0.989792i | \(0.545521\pi\) | |||||||
\(132\) | −2.66043e52 | −0.0224035 | ||||||||
\(133\) | −1.49507e54 | −1.03859 | ||||||||
\(134\) | 1.70227e53 | 0.0976914 | ||||||||
\(135\) | −7.98817e53 | −0.379259 | ||||||||
\(136\) | 1.67649e54 | 0.659414 | ||||||||
\(137\) | 2.86306e54 | 0.934236 | 0.467118 | − | 0.884195i | \(-0.345292\pi\) | ||||
0.467118 | + | 0.884195i | \(0.345292\pi\) | |||||||
\(138\) | −5.13545e53 | −0.139207 | ||||||||
\(139\) | 3.12773e54 | 0.705264 | 0.352632 | − | 0.935762i | \(-0.385287\pi\) | ||||
0.352632 | + | 0.935762i | \(0.385287\pi\) | |||||||
\(140\) | −1.62171e54 | −0.304585 | ||||||||
\(141\) | 1.28842e54 | 0.201823 | ||||||||
\(142\) | −3.10436e54 | −0.406087 | ||||||||
\(143\) | 3.31418e52 | 0.00362499 | ||||||||
\(144\) | −7.56482e54 | −0.692716 | ||||||||
\(145\) | −6.89539e54 | −0.529267 | ||||||||
\(146\) | −2.35802e54 | −0.151897 | ||||||||
\(147\) | 4.37876e54 | 0.237006 | ||||||||
\(148\) | −1.43419e55 | −0.653030 | ||||||||
\(149\) | 4.23740e55 | 1.62499 | 0.812493 | − | 0.582971i | \(-0.198110\pi\) | ||||
0.812493 | + | 0.582971i | \(0.198110\pi\) | |||||||
\(150\) | −1.94363e54 | −0.0628473 | ||||||||
\(151\) | 7.71079e54 | 0.210468 | 0.105234 | − | 0.994447i | \(-0.466441\pi\) | ||||
0.105234 | + | 0.994447i | \(0.466441\pi\) | |||||||
\(152\) | 4.07829e55 | 0.940734 | ||||||||
\(153\) | −5.73828e55 | −1.11983 | ||||||||
\(154\) | −6.34730e53 | −0.0104909 | ||||||||
\(155\) | 3.55718e55 | 0.498480 | ||||||||
\(156\) | −1.44486e54 | −0.0171849 | ||||||||
\(157\) | −1.17035e56 | −1.18270 | −0.591351 | − | 0.806414i | \(-0.701405\pi\) | ||||
−0.591351 | + | 0.806414i | \(0.701405\pi\) | |||||||
\(158\) | −2.07492e55 | −0.178339 | ||||||||
\(159\) | −8.05215e55 | −0.589231 | ||||||||
\(160\) | 6.71781e55 | 0.418956 | ||||||||
\(161\) | 1.58671e56 | 0.844183 | ||||||||
\(162\) | −3.80372e55 | −0.172813 | ||||||||
\(163\) | −1.56667e56 | −0.608405 | −0.304203 | − | 0.952607i | \(-0.598390\pi\) | ||||
−0.304203 | + | 0.952607i | \(0.598390\pi\) | |||||||
\(164\) | 3.65757e56 | 1.21528 | ||||||||
\(165\) | −4.88209e54 | −0.0138920 | ||||||||
\(166\) | −6.40541e55 | −0.156239 | ||||||||
\(167\) | 4.64519e56 | 0.972150 | 0.486075 | − | 0.873917i | \(-0.338428\pi\) | ||||
0.486075 | + | 0.873917i | \(0.338428\pi\) | |||||||
\(168\) | 5.74806e55 | 0.103308 | ||||||||
\(169\) | −6.45508e56 | −0.997219 | ||||||||
\(170\) | 1.48106e56 | 0.196846 | ||||||||
\(171\) | −1.39592e57 | −1.59757 | ||||||||
\(172\) | −1.05983e57 | −1.04534 | ||||||||
\(173\) | 1.75769e57 | 1.49543 | 0.747714 | − | 0.664021i | \(-0.231151\pi\) | ||||
0.747714 | + | 0.664021i | \(0.231151\pi\) | |||||||
\(174\) | 1.17659e56 | 0.0864209 | ||||||||
\(175\) | 6.00526e56 | 0.381120 | ||||||||
\(176\) | −9.89661e55 | −0.0543142 | ||||||||
\(177\) | 2.90515e56 | 0.137991 | ||||||||
\(178\) | −2.15195e55 | −0.00885364 | ||||||||
\(179\) | 3.24188e57 | 1.15623 | 0.578116 | − | 0.815955i | \(-0.303788\pi\) | ||||
0.578116 | + | 0.815955i | \(0.303788\pi\) | |||||||
\(180\) | −1.51415e57 | −0.468513 | ||||||||
\(181\) | 8.53725e56 | 0.229358 | 0.114679 | − | 0.993403i | \(-0.463416\pi\) | ||||
0.114679 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(182\) | −3.44718e55 | −0.00804717 | ||||||||
\(183\) | −2.05453e57 | −0.417070 | ||||||||
\(184\) | −4.32825e57 | −0.764641 | ||||||||
\(185\) | −2.63185e57 | −0.404933 | ||||||||
\(186\) | −6.06977e56 | −0.0813940 | ||||||||
\(187\) | −7.50706e56 | −0.0878029 | ||||||||
\(188\) | 5.22769e57 | 0.533685 | ||||||||
\(189\) | −4.21145e57 | −0.375540 | ||||||||
\(190\) | 3.60289e57 | 0.280824 | ||||||||
\(191\) | 9.24442e57 | 0.630273 | 0.315136 | − | 0.949046i | \(-0.397950\pi\) | ||||
0.315136 | + | 0.949046i | \(0.397950\pi\) | |||||||
\(192\) | 3.50143e57 | 0.208961 | ||||||||
\(193\) | −2.11389e57 | −0.110502 | −0.0552512 | − | 0.998472i | \(-0.517596\pi\) | ||||
−0.0552512 | + | 0.998472i | \(0.517596\pi\) | |||||||
\(194\) | 7.76134e57 | 0.355625 | ||||||||
\(195\) | −2.65143e56 | −0.0106561 | ||||||||
\(196\) | 1.77666e58 | 0.626720 | ||||||||
\(197\) | −2.03837e58 | −0.631531 | −0.315765 | − | 0.948837i | \(-0.602261\pi\) | ||||
−0.315765 | + | 0.948837i | \(0.602261\pi\) | |||||||
\(198\) | −5.92634e56 | −0.0161371 | ||||||||
\(199\) | −4.89566e58 | −1.17235 | −0.586176 | − | 0.810184i | \(-0.699367\pi\) | ||||
−0.586176 | + | 0.810184i | \(0.699367\pi\) | |||||||
\(200\) | −1.63813e58 | −0.345210 | ||||||||
\(201\) | 6.90288e57 | 0.128095 | ||||||||
\(202\) | 7.98480e57 | 0.130558 | ||||||||
\(203\) | −3.63532e58 | −0.524076 | ||||||||
\(204\) | 3.27280e58 | 0.416246 | ||||||||
\(205\) | 6.71194e58 | 0.753572 | ||||||||
\(206\) | −3.55806e58 | −0.352857 | ||||||||
\(207\) | 1.48147e59 | 1.29852 | ||||||||
\(208\) | −5.37478e57 | −0.0416626 | ||||||||
\(209\) | −1.82620e58 | −0.125262 | ||||||||
\(210\) | 5.07801e57 | 0.0308391 | ||||||||
\(211\) | 1.53613e59 | 0.826467 | 0.413234 | − | 0.910625i | \(-0.364399\pi\) | ||||
0.413234 | + | 0.910625i | \(0.364399\pi\) | |||||||
\(212\) | −3.26711e59 | −1.55811 | ||||||||
\(213\) | −1.25885e59 | −0.532468 | ||||||||
\(214\) | 2.07500e57 | 0.00778872 | ||||||||
\(215\) | −1.94487e59 | −0.648200 | ||||||||
\(216\) | 1.14881e59 | 0.340155 | ||||||||
\(217\) | 1.87539e59 | 0.493591 | ||||||||
\(218\) | 2.01606e58 | 0.0471914 | ||||||||
\(219\) | −9.56202e58 | −0.199170 | ||||||||
\(220\) | −1.98088e58 | −0.0367350 | ||||||||
\(221\) | −4.07703e58 | −0.0673505 | ||||||||
\(222\) | 4.49084e58 | 0.0661191 | ||||||||
\(223\) | 8.84276e59 | 1.16095 | 0.580475 | − | 0.814278i | \(-0.302867\pi\) | ||||
0.580475 | + | 0.814278i | \(0.302867\pi\) | |||||||
\(224\) | 3.54171e59 | 0.414847 | ||||||||
\(225\) | 5.60699e59 | 0.586240 | ||||||||
\(226\) | −4.29315e59 | −0.400877 | ||||||||
\(227\) | −1.84839e60 | −1.54218 | −0.771090 | − | 0.636726i | \(-0.780288\pi\) | ||||
−0.771090 | + | 0.636726i | \(0.780288\pi\) | |||||||
\(228\) | 7.96155e59 | 0.593826 | ||||||||
\(229\) | −1.13494e60 | −0.757126 | −0.378563 | − | 0.925576i | \(-0.623582\pi\) | ||||
−0.378563 | + | 0.925576i | \(0.623582\pi\) | |||||||
\(230\) | −3.82371e59 | −0.228258 | ||||||||
\(231\) | −2.57389e58 | −0.0137558 | ||||||||
\(232\) | 9.91651e59 | 0.474696 | ||||||||
\(233\) | −1.75626e60 | −0.753376 | −0.376688 | − | 0.926340i | \(-0.622937\pi\) | ||||
−0.376688 | + | 0.926340i | \(0.622937\pi\) | |||||||
\(234\) | −3.21855e58 | −0.0123782 | ||||||||
\(235\) | 9.59324e59 | 0.330929 | ||||||||
\(236\) | 1.17875e60 | 0.364892 | ||||||||
\(237\) | −8.41400e59 | −0.233840 | ||||||||
\(238\) | 7.80832e59 | 0.194915 | ||||||||
\(239\) | 7.46779e60 | 1.67512 | 0.837560 | − | 0.546346i | \(-0.183982\pi\) | ||||
0.837560 | + | 0.546346i | \(0.183982\pi\) | |||||||
\(240\) | 7.91756e59 | 0.159663 | ||||||||
\(241\) | −2.67830e60 | −0.485763 | −0.242882 | − | 0.970056i | \(-0.578093\pi\) | ||||
−0.242882 | + | 0.970056i | \(0.578093\pi\) | |||||||
\(242\) | 1.63284e60 | 0.266471 | ||||||||
\(243\) | −6.02732e60 | −0.885451 | ||||||||
\(244\) | −8.33612e60 | −1.10287 | ||||||||
\(245\) | 3.26031e60 | 0.388618 | ||||||||
\(246\) | −1.14529e60 | −0.123046 | ||||||||
\(247\) | −9.91796e59 | −0.0960838 | ||||||||
\(248\) | −5.11572e60 | −0.447083 | ||||||||
\(249\) | −2.59746e60 | −0.204864 | ||||||||
\(250\) | −3.61151e60 | −0.257169 | ||||||||
\(251\) | 2.75172e61 | 1.76980 | 0.884900 | − | 0.465782i | \(-0.154227\pi\) | ||||
0.884900 | + | 0.465782i | \(0.154227\pi\) | |||||||
\(252\) | −7.98279e60 | −0.463917 | ||||||||
\(253\) | 1.93813e60 | 0.101814 | ||||||||
\(254\) | 4.61099e60 | 0.219045 | ||||||||
\(255\) | 6.00585e60 | 0.258107 | ||||||||
\(256\) | 9.19670e60 | 0.357695 | ||||||||
\(257\) | −4.92610e59 | −0.0173464 | −0.00867318 | − | 0.999962i | \(-0.502761\pi\) | ||||
−0.00867318 | + | 0.999962i | \(0.502761\pi\) | |||||||
\(258\) | 3.31861e60 | 0.105841 | ||||||||
\(259\) | −1.38754e61 | −0.400961 | ||||||||
\(260\) | −1.07580e60 | −0.0281781 | ||||||||
\(261\) | −3.39422e61 | −0.806135 | ||||||||
\(262\) | 3.54245e60 | 0.0763169 | ||||||||
\(263\) | −1.45507e60 | −0.0284454 | −0.0142227 | − | 0.999899i | \(-0.504527\pi\) | ||||
−0.0142227 | + | 0.999899i | \(0.504527\pi\) | |||||||
\(264\) | 7.02112e59 | 0.0124597 | ||||||||
\(265\) | −5.99541e61 | −0.966160 | ||||||||
\(266\) | 1.89948e61 | 0.278070 | ||||||||
\(267\) | −8.72636e59 | −0.0116090 | ||||||||
\(268\) | 2.80080e61 | 0.338723 | ||||||||
\(269\) | 8.25887e60 | 0.0908318 | 0.0454159 | − | 0.998968i | \(-0.485539\pi\) | ||||
0.0454159 | + | 0.998968i | \(0.485539\pi\) | |||||||
\(270\) | 1.01489e61 | 0.101542 | ||||||||
\(271\) | 8.46290e61 | 0.770553 | 0.385276 | − | 0.922801i | \(-0.374106\pi\) | ||||
0.385276 | + | 0.922801i | \(0.374106\pi\) | |||||||
\(272\) | 1.21746e62 | 1.00913 | ||||||||
\(273\) | −1.39786e60 | −0.0105516 | ||||||||
\(274\) | −3.63751e61 | −0.250129 | ||||||||
\(275\) | 7.33529e60 | 0.0459657 | ||||||||
\(276\) | −8.44951e61 | −0.482669 | ||||||||
\(277\) | −2.17621e62 | −1.13362 | −0.566808 | − | 0.823850i | \(-0.691822\pi\) | ||||
−0.566808 | + | 0.823850i | \(0.691822\pi\) | |||||||
\(278\) | −3.97376e61 | −0.188825 | ||||||||
\(279\) | 1.75101e62 | 0.759243 | ||||||||
\(280\) | 4.27984e61 | 0.169394 | ||||||||
\(281\) | −4.49759e62 | −1.62543 | −0.812715 | − | 0.582661i | \(-0.802012\pi\) | ||||
−0.812715 | + | 0.582661i | \(0.802012\pi\) | |||||||
\(282\) | −1.63693e61 | −0.0540355 | ||||||||
\(283\) | 5.28631e62 | 1.59440 | 0.797202 | − | 0.603713i | \(-0.206313\pi\) | ||||
0.797202 | + | 0.603713i | \(0.206313\pi\) | |||||||
\(284\) | −5.10770e62 | −1.40802 | ||||||||
\(285\) | 1.46101e62 | 0.368221 | ||||||||
\(286\) | −4.21065e59 | −0.000970543 0 | ||||||||
\(287\) | 3.53861e62 | 0.746181 | ||||||||
\(288\) | 3.30681e62 | 0.638119 | ||||||||
\(289\) | 3.57400e62 | 0.631334 | ||||||||
\(290\) | 8.76056e61 | 0.141704 | ||||||||
\(291\) | 3.14730e62 | 0.466301 | ||||||||
\(292\) | −3.87973e62 | −0.526670 | ||||||||
\(293\) | −1.35914e63 | −1.69099 | −0.845493 | − | 0.533987i | \(-0.820693\pi\) | ||||
−0.845493 | + | 0.533987i | \(0.820693\pi\) | |||||||
\(294\) | −5.56320e61 | −0.0634552 | ||||||||
\(295\) | 2.16309e62 | 0.226263 | ||||||||
\(296\) | 3.78496e62 | 0.363181 | ||||||||
\(297\) | −5.14419e61 | −0.0452926 | ||||||||
\(298\) | −5.38359e62 | −0.435069 | ||||||||
\(299\) | 1.05258e62 | 0.0780982 | ||||||||
\(300\) | −3.19792e62 | −0.217909 | ||||||||
\(301\) | −1.02535e63 | −0.641843 | ||||||||
\(302\) | −9.79652e61 | −0.0563501 | ||||||||
\(303\) | 3.23791e62 | 0.171190 | ||||||||
\(304\) | 2.96165e63 | 1.43965 | ||||||||
\(305\) | −1.52974e63 | −0.683869 | ||||||||
\(306\) | 7.29046e62 | 0.299818 | ||||||||
\(307\) | 3.47883e63 | 1.31645 | 0.658226 | − | 0.752821i | \(-0.271307\pi\) | ||||
0.658226 | + | 0.752821i | \(0.271307\pi\) | |||||||
\(308\) | −1.04434e62 | −0.0363747 | ||||||||
\(309\) | −1.44283e63 | −0.462672 | ||||||||
\(310\) | −4.51939e62 | −0.133462 | ||||||||
\(311\) | 9.88875e62 | 0.268999 | 0.134500 | − | 0.990914i | \(-0.457057\pi\) | ||||
0.134500 | + | 0.990914i | \(0.457057\pi\) | |||||||
\(312\) | 3.81312e61 | 0.00955737 | ||||||||
\(313\) | −5.32344e63 | −1.22974 | −0.614868 | − | 0.788630i | \(-0.710791\pi\) | ||||
−0.614868 | + | 0.788630i | \(0.710791\pi\) | |||||||
\(314\) | 1.48693e63 | 0.316653 | ||||||||
\(315\) | −1.46491e63 | −0.287667 | ||||||||
\(316\) | −3.41393e63 | −0.618349 | ||||||||
\(317\) | −2.07710e63 | −0.347094 | −0.173547 | − | 0.984826i | \(-0.555523\pi\) | ||||
−0.173547 | + | 0.984826i | \(0.555523\pi\) | |||||||
\(318\) | 1.02302e63 | 0.157759 | ||||||||
\(319\) | −4.44046e62 | −0.0632071 | ||||||||
\(320\) | 2.60707e63 | 0.342632 | ||||||||
\(321\) | 8.41432e61 | 0.0102127 | ||||||||
\(322\) | −2.01590e63 | −0.226019 | ||||||||
\(323\) | 2.24655e64 | 2.32730 | ||||||||
\(324\) | −6.25838e63 | −0.599190 | ||||||||
\(325\) | 3.98375e62 | 0.0352587 | ||||||||
\(326\) | 1.99044e63 | 0.162892 | ||||||||
\(327\) | 8.17532e62 | 0.0618781 | ||||||||
\(328\) | −9.65269e63 | −0.675873 | ||||||||
\(329\) | 5.05766e63 | 0.327683 | ||||||||
\(330\) | 6.20268e61 | 0.00371941 | ||||||||
\(331\) | −1.81346e63 | −0.100669 | −0.0503343 | − | 0.998732i | \(-0.516029\pi\) | ||||
−0.0503343 | + | 0.998732i | \(0.516029\pi\) | |||||||
\(332\) | −1.05390e64 | −0.541725 | ||||||||
\(333\) | −1.29552e64 | −0.616759 | ||||||||
\(334\) | −5.90169e63 | −0.260280 | ||||||||
\(335\) | 5.13969e63 | 0.210036 | ||||||||
\(336\) | 4.17422e63 | 0.158097 | ||||||||
\(337\) | −1.27328e64 | −0.447056 | −0.223528 | − | 0.974698i | \(-0.571757\pi\) | ||||
−0.223528 | + | 0.974698i | \(0.571757\pi\) | |||||||
\(338\) | 8.20115e63 | 0.266992 | ||||||||
\(339\) | −1.74091e64 | −0.525636 | ||||||||
\(340\) | 2.43684e64 | 0.682518 | ||||||||
\(341\) | 2.29074e63 | 0.0595305 | ||||||||
\(342\) | 1.77351e64 | 0.427728 | ||||||||
\(343\) | 4.26491e64 | 0.954794 | ||||||||
\(344\) | 2.79698e64 | 0.581366 | ||||||||
\(345\) | −1.55055e64 | −0.299295 | ||||||||
\(346\) | −2.23313e64 | −0.400381 | ||||||||
\(347\) | −4.50582e64 | −0.750537 | −0.375269 | − | 0.926916i | \(-0.622450\pi\) | ||||
−0.375269 | + | 0.926916i | \(0.622450\pi\) | |||||||
\(348\) | 1.93588e64 | 0.299645 | ||||||||
\(349\) | 6.10318e63 | 0.0878026 | 0.0439013 | − | 0.999036i | \(-0.486021\pi\) | ||||
0.0439013 | + | 0.999036i | \(0.486021\pi\) | |||||||
\(350\) | −7.62966e63 | −0.102040 | ||||||||
\(351\) | −2.79377e63 | −0.0347424 | ||||||||
\(352\) | 4.32611e63 | 0.0500334 | ||||||||
\(353\) | −6.21110e64 | −0.668211 | −0.334106 | − | 0.942536i | \(-0.608434\pi\) | ||||
−0.334106 | + | 0.942536i | \(0.608434\pi\) | |||||||
\(354\) | −3.69098e63 | −0.0369452 | ||||||||
\(355\) | −9.37304e64 | −0.873087 | ||||||||
\(356\) | −3.54067e63 | −0.0306980 | ||||||||
\(357\) | 3.16635e64 | 0.255576 | ||||||||
\(358\) | −4.11879e64 | −0.309566 | ||||||||
\(359\) | −2.08428e64 | −0.145898 | −0.0729488 | − | 0.997336i | \(-0.523241\pi\) | ||||
−0.0729488 | + | 0.997336i | \(0.523241\pi\) | |||||||
\(360\) | 3.99600e64 | 0.260562 | ||||||||
\(361\) | 3.81904e65 | 2.32018 | ||||||||
\(362\) | −1.08465e64 | −0.0614076 | ||||||||
\(363\) | 6.62131e64 | 0.349402 | ||||||||
\(364\) | −5.67175e63 | −0.0279017 | ||||||||
\(365\) | −7.11962e64 | −0.326579 | ||||||||
\(366\) | 2.61027e64 | 0.111665 | ||||||||
\(367\) | −1.66429e65 | −0.664118 | −0.332059 | − | 0.943259i | \(-0.607743\pi\) | ||||
−0.332059 | + | 0.943259i | \(0.607743\pi\) | |||||||
\(368\) | −3.14316e65 | −1.17017 | ||||||||
\(369\) | 3.30392e65 | 1.14778 | ||||||||
\(370\) | 3.34376e64 | 0.108415 | ||||||||
\(371\) | −3.16085e65 | −0.956684 | ||||||||
\(372\) | −9.98678e64 | −0.282215 | ||||||||
\(373\) | 3.79646e64 | 0.100185 | 0.0500925 | − | 0.998745i | \(-0.484048\pi\) | ||||
0.0500925 | + | 0.998745i | \(0.484048\pi\) | |||||||
\(374\) | 9.53768e63 | 0.0235081 | ||||||||
\(375\) | −1.46450e65 | −0.337204 | ||||||||
\(376\) | −1.37964e65 | −0.296808 | ||||||||
\(377\) | −2.41159e64 | −0.0484840 | ||||||||
\(378\) | 5.35063e64 | 0.100546 | ||||||||
\(379\) | 3.34355e65 | 0.587364 | 0.293682 | − | 0.955903i | \(-0.405119\pi\) | ||||
0.293682 | + | 0.955903i | \(0.405119\pi\) | |||||||
\(380\) | 5.92795e65 | 0.973695 | ||||||||
\(381\) | 1.86980e65 | 0.287216 | ||||||||
\(382\) | −1.17450e65 | −0.168747 | ||||||||
\(383\) | 3.02479e65 | 0.406561 | 0.203281 | − | 0.979121i | \(-0.434840\pi\) | ||||
0.203281 | + | 0.979121i | \(0.434840\pi\) | |||||||
\(384\) | −2.47651e65 | −0.311455 | ||||||||
\(385\) | −1.91645e64 | −0.0225553 | ||||||||
\(386\) | 2.68569e64 | 0.0295855 | ||||||||
\(387\) | −9.57352e65 | −0.987284 | ||||||||
\(388\) | 1.27700e66 | 1.23305 | ||||||||
\(389\) | 3.96714e65 | 0.358726 | 0.179363 | − | 0.983783i | \(-0.442596\pi\) | ||||
0.179363 | + | 0.983783i | \(0.442596\pi\) | |||||||
\(390\) | 3.36863e63 | 0.00285303 | ||||||||
\(391\) | −2.38424e66 | −1.89166 | ||||||||
\(392\) | −4.68876e65 | −0.348549 | ||||||||
\(393\) | 1.43650e65 | 0.100068 | ||||||||
\(394\) | 2.58974e65 | 0.169084 | ||||||||
\(395\) | −6.26483e65 | −0.383428 | ||||||||
\(396\) | −9.75079e64 | −0.0559516 | ||||||||
\(397\) | 1.53914e65 | 0.0828174 | 0.0414087 | − | 0.999142i | \(-0.486815\pi\) | ||||
0.0414087 | + | 0.999142i | \(0.486815\pi\) | |||||||
\(398\) | 6.21992e65 | 0.313882 | ||||||||
\(399\) | 7.70260e65 | 0.364610 | ||||||||
\(400\) | −1.18960e66 | −0.528290 | ||||||||
\(401\) | 3.72470e66 | 1.55207 | 0.776033 | − | 0.630693i | \(-0.217229\pi\) | ||||
0.776033 | + | 0.630693i | \(0.217229\pi\) | |||||||
\(402\) | −8.77007e64 | −0.0342956 | ||||||||
\(403\) | 1.24409e65 | 0.0456638 | ||||||||
\(404\) | 1.31376e66 | 0.452681 | ||||||||
\(405\) | −1.14846e66 | −0.371547 | ||||||||
\(406\) | 4.61866e65 | 0.140314 | ||||||||
\(407\) | −1.69485e65 | −0.0483586 | ||||||||
\(408\) | −8.63723e65 | −0.231494 | ||||||||
\(409\) | 1.18361e66 | 0.298033 | 0.149017 | − | 0.988835i | \(-0.452389\pi\) | ||||
0.149017 | + | 0.988835i | \(0.452389\pi\) | |||||||
\(410\) | −8.52749e65 | −0.201759 | ||||||||
\(411\) | −1.47505e66 | −0.327974 | ||||||||
\(412\) | −5.85419e66 | −1.22345 | ||||||||
\(413\) | 1.14041e66 | 0.224044 | ||||||||
\(414\) | −1.88220e66 | −0.347663 | ||||||||
\(415\) | −1.93399e66 | −0.335915 | ||||||||
\(416\) | 2.34948e65 | 0.0383789 | ||||||||
\(417\) | −1.61140e66 | −0.247591 | ||||||||
\(418\) | 2.32018e65 | 0.0335371 | ||||||||
\(419\) | 9.81782e66 | 1.33523 | 0.667617 | − | 0.744505i | \(-0.267314\pi\) | ||||
0.667617 | + | 0.744505i | \(0.267314\pi\) | |||||||
\(420\) | 8.35501e65 | 0.106928 | ||||||||
\(421\) | 4.41844e66 | 0.532201 | 0.266101 | − | 0.963945i | \(-0.414265\pi\) | ||||
0.266101 | + | 0.963945i | \(0.414265\pi\) | |||||||
\(422\) | −1.95165e66 | −0.221276 | ||||||||
\(423\) | 4.72223e66 | 0.504043 | ||||||||
\(424\) | 8.62222e66 | 0.866542 | ||||||||
\(425\) | −9.02372e66 | −0.854019 | ||||||||
\(426\) | 1.59936e66 | 0.142561 | ||||||||
\(427\) | −8.06498e66 | −0.677162 | ||||||||
\(428\) | 3.41406e65 | 0.0270056 | ||||||||
\(429\) | −1.70746e64 | −0.00127259 | ||||||||
\(430\) | 2.47094e66 | 0.173547 | ||||||||
\(431\) | −9.31273e66 | −0.616463 | −0.308231 | − | 0.951311i | \(-0.599737\pi\) | ||||
−0.308231 | + | 0.951311i | \(0.599737\pi\) | |||||||
\(432\) | 8.34261e66 | 0.520555 | ||||||||
\(433\) | −5.53636e66 | −0.325674 | −0.162837 | − | 0.986653i | \(-0.552064\pi\) | ||||
−0.162837 | + | 0.986653i | \(0.552064\pi\) | |||||||
\(434\) | −2.38267e66 | −0.132153 | ||||||||
\(435\) | 3.55249e66 | 0.185805 | ||||||||
\(436\) | 3.31709e66 | 0.163626 | ||||||||
\(437\) | −5.80001e67 | −2.69868 | ||||||||
\(438\) | 1.21485e66 | 0.0533252 | ||||||||
\(439\) | 3.50063e67 | 1.44978 | 0.724888 | − | 0.688867i | \(-0.241891\pi\) | ||||
0.724888 | + | 0.688867i | \(0.241891\pi\) | |||||||
\(440\) | 5.22773e65 | 0.0204301 | ||||||||
\(441\) | 1.60487e67 | 0.591910 | ||||||||
\(442\) | 5.17985e65 | 0.0180322 | ||||||||
\(443\) | 3.49460e67 | 1.14842 | 0.574211 | − | 0.818707i | \(-0.305309\pi\) | ||||
0.574211 | + | 0.818707i | \(0.305309\pi\) | |||||||
\(444\) | 7.38892e66 | 0.229253 | ||||||||
\(445\) | −6.49741e65 | −0.0190353 | ||||||||
\(446\) | −1.12347e67 | −0.310829 | ||||||||
\(447\) | −2.18310e67 | −0.570469 | ||||||||
\(448\) | 1.37447e67 | 0.339272 | ||||||||
\(449\) | 3.38559e67 | 0.789501 | 0.394750 | − | 0.918788i | \(-0.370831\pi\) | ||||
0.394750 | + | 0.918788i | \(0.370831\pi\) | |||||||
\(450\) | −7.12365e66 | −0.156958 | ||||||||
\(451\) | 4.32233e66 | 0.0899945 | ||||||||
\(452\) | −7.06365e67 | −1.38995 | ||||||||
\(453\) | −3.97259e66 | −0.0738872 | ||||||||
\(454\) | 2.34838e67 | 0.412899 | ||||||||
\(455\) | −1.04081e66 | −0.0173014 | ||||||||
\(456\) | −2.10113e67 | −0.330255 | ||||||||
\(457\) | −1.12417e68 | −1.67096 | −0.835482 | − | 0.549517i | \(-0.814812\pi\) | ||||
−0.835482 | + | 0.549517i | \(0.814812\pi\) | |||||||
\(458\) | 1.44194e67 | 0.202710 | ||||||||
\(459\) | 6.32827e67 | 0.841515 | ||||||||
\(460\) | −6.29127e67 | −0.791432 | ||||||||
\(461\) | 3.19451e67 | 0.380216 | 0.190108 | − | 0.981763i | \(-0.439116\pi\) | ||||
0.190108 | + | 0.981763i | \(0.439116\pi\) | |||||||
\(462\) | 3.27012e65 | 0.00368293 | ||||||||
\(463\) | 1.31779e68 | 1.40453 | 0.702263 | − | 0.711918i | \(-0.252173\pi\) | ||||
0.702263 | + | 0.711918i | \(0.252173\pi\) | |||||||
\(464\) | 7.20134e67 | 0.726449 | ||||||||
\(465\) | −1.83266e67 | −0.174997 | ||||||||
\(466\) | 2.23131e67 | 0.201706 | ||||||||
\(467\) | −4.26431e67 | −0.364979 | −0.182490 | − | 0.983208i | \(-0.558416\pi\) | ||||
−0.182490 | + | 0.983208i | \(0.558416\pi\) | |||||||
\(468\) | −5.29559e66 | −0.0429185 | ||||||||
\(469\) | 2.70970e67 | 0.207976 | ||||||||
\(470\) | −1.21882e67 | −0.0886018 | ||||||||
\(471\) | 6.02963e67 | 0.415200 | ||||||||
\(472\) | −3.11082e67 | −0.202934 | ||||||||
\(473\) | −1.25245e67 | −0.0774106 | ||||||||
\(474\) | 1.06899e67 | 0.0626077 | ||||||||
\(475\) | −2.19515e68 | −1.21836 | ||||||||
\(476\) | 1.28473e68 | 0.675823 | ||||||||
\(477\) | −2.95121e68 | −1.47157 | ||||||||
\(478\) | −9.48779e67 | −0.448491 | ||||||||
\(479\) | 1.74665e68 | 0.782801 | 0.391401 | − | 0.920220i | \(-0.371991\pi\) | ||||
0.391401 | + | 0.920220i | \(0.371991\pi\) | |||||||
\(480\) | −3.46101e67 | −0.147079 | ||||||||
\(481\) | −9.20462e66 | −0.0370942 | ||||||||
\(482\) | 3.40277e67 | 0.130057 | ||||||||
\(483\) | −8.17468e67 | −0.296360 | ||||||||
\(484\) | 2.68656e68 | 0.923930 | ||||||||
\(485\) | 2.34339e68 | 0.764593 | ||||||||
\(486\) | 7.65768e67 | 0.237068 | ||||||||
\(487\) | −3.99057e68 | −1.17232 | −0.586161 | − | 0.810195i | \(-0.699361\pi\) | ||||
−0.586161 | + | 0.810195i | \(0.699361\pi\) | |||||||
\(488\) | 2.19998e68 | 0.613357 | ||||||||
\(489\) | 8.07144e67 | 0.213587 | ||||||||
\(490\) | −4.14220e67 | −0.104047 | ||||||||
\(491\) | 1.41320e68 | 0.336997 | 0.168499 | − | 0.985702i | \(-0.446108\pi\) | ||||
0.168499 | + | 0.985702i | \(0.446108\pi\) | |||||||
\(492\) | −1.88438e68 | −0.426636 | ||||||||
\(493\) | 5.46256e68 | 1.17436 | ||||||||
\(494\) | 1.26007e67 | 0.0257252 | ||||||||
\(495\) | −1.78935e67 | −0.0346946 | ||||||||
\(496\) | −3.71502e68 | −0.684193 | ||||||||
\(497\) | −4.94157e68 | −0.864523 | ||||||||
\(498\) | 3.30006e67 | 0.0548496 | ||||||||
\(499\) | 3.57937e68 | 0.565253 | 0.282626 | − | 0.959230i | \(-0.408794\pi\) | ||||
0.282626 | + | 0.959230i | \(0.408794\pi\) | |||||||
\(500\) | −5.94212e68 | −0.891675 | ||||||||
\(501\) | −2.39319e68 | −0.341284 | ||||||||
\(502\) | −3.49604e68 | −0.473840 | ||||||||
\(503\) | −4.56639e68 | −0.588287 | −0.294143 | − | 0.955761i | \(-0.595034\pi\) | ||||
−0.294143 | + | 0.955761i | \(0.595034\pi\) | |||||||
\(504\) | 2.10673e68 | 0.258007 | ||||||||
\(505\) | 2.41086e68 | 0.280700 | ||||||||
\(506\) | −2.46238e67 | −0.0272594 | ||||||||
\(507\) | 3.32565e68 | 0.350085 | ||||||||
\(508\) | 7.58660e68 | 0.759491 | ||||||||
\(509\) | 1.62918e69 | 1.55119 | 0.775596 | − | 0.631230i | \(-0.217450\pi\) | ||||
0.775596 | + | 0.631230i | \(0.217450\pi\) | |||||||
\(510\) | −7.63040e67 | −0.0691047 | ||||||||
\(511\) | −3.75354e68 | −0.323376 | ||||||||
\(512\) | −1.19926e69 | −0.982949 | ||||||||
\(513\) | 1.53944e69 | 1.20052 | ||||||||
\(514\) | 6.25858e66 | 0.00464426 | ||||||||
\(515\) | −1.07429e69 | −0.758643 | ||||||||
\(516\) | 5.46021e68 | 0.366979 | ||||||||
\(517\) | 6.17781e67 | 0.0395208 | ||||||||
\(518\) | 1.76287e68 | 0.107352 | ||||||||
\(519\) | −9.05557e68 | −0.524986 | ||||||||
\(520\) | 2.83914e67 | 0.0156712 | ||||||||
\(521\) | −1.25774e69 | −0.661040 | −0.330520 | − | 0.943799i | \(-0.607224\pi\) | ||||
−0.330520 | + | 0.943799i | \(0.607224\pi\) | |||||||
\(522\) | 4.31234e68 | 0.215832 | ||||||||
\(523\) | −1.98441e69 | −0.945883 | −0.472941 | − | 0.881094i | \(-0.656808\pi\) | ||||
−0.472941 | + | 0.881094i | \(0.656808\pi\) | |||||||
\(524\) | 5.82850e68 | 0.264612 | ||||||||
\(525\) | −3.09390e68 | −0.133796 | ||||||||
\(526\) | 1.84866e67 | 0.00761589 | ||||||||
\(527\) | −2.81802e69 | −1.10605 | ||||||||
\(528\) | 5.09872e67 | 0.0190676 | ||||||||
\(529\) | 3.34927e69 | 1.19352 | ||||||||
\(530\) | 7.61714e68 | 0.258677 | ||||||||
\(531\) | 1.06477e69 | 0.344625 | ||||||||
\(532\) | 3.12528e69 | 0.964145 | ||||||||
\(533\) | 2.34743e68 | 0.0690317 | ||||||||
\(534\) | 1.10868e67 | 0.00310817 | ||||||||
\(535\) | 6.26507e67 | 0.0167457 | ||||||||
\(536\) | −7.39158e68 | −0.188380 | ||||||||
\(537\) | −1.67021e69 | −0.405908 | ||||||||
\(538\) | −1.04929e68 | −0.0243190 | ||||||||
\(539\) | 2.09956e68 | 0.0464103 | ||||||||
\(540\) | 1.66983e69 | 0.352073 | ||||||||
\(541\) | 2.04153e69 | 0.410606 | 0.205303 | − | 0.978698i | \(-0.434182\pi\) | ||||
0.205303 | + | 0.978698i | \(0.434182\pi\) | |||||||
\(542\) | −1.07521e69 | −0.206305 | ||||||||
\(543\) | −4.39837e68 | −0.0805187 | ||||||||
\(544\) | −5.32189e69 | −0.929595 | ||||||||
\(545\) | 6.08712e68 | 0.101461 | ||||||||
\(546\) | 1.77598e67 | 0.00282505 | ||||||||
\(547\) | −1.73926e69 | −0.264050 | −0.132025 | − | 0.991246i | \(-0.542148\pi\) | ||||
−0.132025 | + | 0.991246i | \(0.542148\pi\) | |||||||
\(548\) | −5.98490e69 | −0.867267 | ||||||||
\(549\) | −7.53010e69 | −1.04161 | ||||||||
\(550\) | −9.31945e67 | −0.0123067 | ||||||||
\(551\) | 1.32885e70 | 1.67536 | ||||||||
\(552\) | 2.22991e69 | 0.268435 | ||||||||
\(553\) | −3.30289e69 | −0.379667 | ||||||||
\(554\) | 2.76486e69 | 0.303511 | ||||||||
\(555\) | 1.35593e69 | 0.142156 | ||||||||
\(556\) | −6.53815e69 | −0.654709 | ||||||||
\(557\) | 1.57782e70 | 1.50921 | 0.754604 | − | 0.656180i | \(-0.227829\pi\) | ||||
0.754604 | + | 0.656180i | \(0.227829\pi\) | |||||||
\(558\) | −2.22465e69 | −0.203277 | ||||||||
\(559\) | −6.80195e68 | −0.0593790 | ||||||||
\(560\) | 3.10801e69 | 0.259232 | ||||||||
\(561\) | 3.86762e68 | 0.0308241 | ||||||||
\(562\) | 5.71416e69 | 0.435188 | ||||||||
\(563\) | 1.07629e70 | 0.783370 | 0.391685 | − | 0.920099i | \(-0.371892\pi\) | ||||
0.391685 | + | 0.920099i | \(0.371892\pi\) | |||||||
\(564\) | −2.69330e69 | −0.187356 | ||||||||
\(565\) | −1.29624e70 | −0.861884 | ||||||||
\(566\) | −6.71623e69 | −0.426881 | ||||||||
\(567\) | −6.05482e69 | −0.367903 | ||||||||
\(568\) | 1.34797e70 | 0.783065 | ||||||||
\(569\) | −2.42046e70 | −1.34442 | −0.672210 | − | 0.740361i | \(-0.734655\pi\) | ||||
−0.672210 | + | 0.740361i | \(0.734655\pi\) | |||||||
\(570\) | −1.85620e69 | −0.0985864 | ||||||||
\(571\) | −2.02012e70 | −1.02602 | −0.513012 | − | 0.858382i | \(-0.671470\pi\) | ||||
−0.513012 | + | 0.858382i | \(0.671470\pi\) | |||||||
\(572\) | −6.92791e67 | −0.00336514 | ||||||||
\(573\) | −4.76271e69 | −0.221264 | ||||||||
\(574\) | −4.49579e69 | −0.199780 | ||||||||
\(575\) | 2.32969e70 | 0.990302 | ||||||||
\(576\) | 1.28332e70 | 0.521868 | ||||||||
\(577\) | 2.07089e70 | 0.805699 | 0.402850 | − | 0.915266i | \(-0.368020\pi\) | ||||
0.402850 | + | 0.915266i | \(0.368020\pi\) | |||||||
\(578\) | −4.54075e69 | −0.169031 | ||||||||
\(579\) | 1.08907e69 | 0.0387930 | ||||||||
\(580\) | 1.44140e70 | 0.491327 | ||||||||
\(581\) | −1.01962e70 | −0.332620 | ||||||||
\(582\) | −3.99863e69 | −0.124846 | ||||||||
\(583\) | −3.86090e69 | −0.115383 | ||||||||
\(584\) | 1.02390e70 | 0.292906 | ||||||||
\(585\) | −9.71783e68 | −0.0266130 | ||||||||
\(586\) | 1.72678e70 | 0.452739 | ||||||||
\(587\) | 4.82066e70 | 1.21014 | 0.605070 | − | 0.796173i | \(-0.293145\pi\) | ||||
0.605070 | + | 0.796173i | \(0.293145\pi\) | |||||||
\(588\) | −9.15330e69 | −0.220017 | ||||||||
\(589\) | −6.85524e70 | −1.57791 | ||||||||
\(590\) | −2.74820e69 | −0.0605790 | ||||||||
\(591\) | 1.05017e70 | 0.221706 | ||||||||
\(592\) | 2.74863e70 | 0.555793 | ||||||||
\(593\) | −6.85044e70 | −1.32686 | −0.663428 | − | 0.748240i | \(-0.730899\pi\) | ||||
−0.663428 | + | 0.748240i | \(0.730899\pi\) | |||||||
\(594\) | 6.53567e68 | 0.0121265 | ||||||||
\(595\) | 2.35758e70 | 0.419067 | ||||||||
\(596\) | −8.85779e70 | −1.50850 | ||||||||
\(597\) | 2.52224e70 | 0.411567 | ||||||||
\(598\) | −1.33730e69 | −0.0209097 | ||||||||
\(599\) | −3.61715e70 | −0.541979 | −0.270990 | − | 0.962582i | \(-0.587351\pi\) | ||||
−0.270990 | + | 0.962582i | \(0.587351\pi\) | |||||||
\(600\) | 8.43960e69 | 0.121190 | ||||||||
\(601\) | 6.55680e70 | 0.902387 | 0.451193 | − | 0.892426i | \(-0.350998\pi\) | ||||
0.451193 | + | 0.892426i | \(0.350998\pi\) | |||||||
\(602\) | 1.30271e70 | 0.171845 | ||||||||
\(603\) | 2.52999e70 | 0.319910 | ||||||||
\(604\) | −1.61185e70 | −0.195381 | ||||||||
\(605\) | 4.93004e70 | 0.572913 | ||||||||
\(606\) | −4.11375e69 | −0.0458339 | ||||||||
\(607\) | 1.24140e71 | 1.32617 | 0.663086 | − | 0.748544i | \(-0.269247\pi\) | ||||
0.663086 | + | 0.748544i | \(0.269247\pi\) | |||||||
\(608\) | −1.29463e71 | −1.32618 | ||||||||
\(609\) | 1.87291e70 | 0.183982 | ||||||||
\(610\) | 1.94353e70 | 0.183097 | ||||||||
\(611\) | 3.35513e69 | 0.0303151 | ||||||||
\(612\) | 1.19952e71 | 1.03955 | ||||||||
\(613\) | −7.66168e70 | −0.636916 | −0.318458 | − | 0.947937i | \(-0.603165\pi\) | ||||
−0.318458 | + | 0.947937i | \(0.603165\pi\) | |||||||
\(614\) | −4.41984e70 | −0.352462 | ||||||||
\(615\) | −3.45798e70 | −0.264550 | ||||||||
\(616\) | 2.75612e69 | 0.0202297 | ||||||||
\(617\) | 8.27703e70 | 0.582912 | 0.291456 | − | 0.956584i | \(-0.405860\pi\) | ||||
0.291456 | + | 0.956584i | \(0.405860\pi\) | |||||||
\(618\) | 1.83311e70 | 0.123874 | ||||||||
\(619\) | −1.97805e71 | −1.28270 | −0.641350 | − | 0.767248i | \(-0.721625\pi\) | ||||
−0.641350 | + | 0.767248i | \(0.721625\pi\) | |||||||
\(620\) | −7.43588e70 | −0.462748 | ||||||||
\(621\) | −1.63379e71 | −0.975801 | ||||||||
\(622\) | −1.25636e70 | −0.0720210 | ||||||||
\(623\) | −3.42550e69 | −0.0188486 | ||||||||
\(624\) | 2.76908e69 | 0.0146261 | ||||||||
\(625\) | 2.28244e70 | 0.115734 | ||||||||
\(626\) | 6.76341e70 | 0.329246 | ||||||||
\(627\) | 9.40854e69 | 0.0439744 | ||||||||
\(628\) | 2.44649e71 | 1.09792 | ||||||||
\(629\) | 2.08497e71 | 0.898480 | ||||||||
\(630\) | 1.86115e70 | 0.0770191 | ||||||||
\(631\) | −1.41814e71 | −0.563598 | −0.281799 | − | 0.959473i | \(-0.590931\pi\) | ||||
−0.281799 | + | 0.959473i | \(0.590931\pi\) | |||||||
\(632\) | 9.00968e70 | 0.343893 | ||||||||
\(633\) | −7.91412e70 | −0.290140 | ||||||||
\(634\) | 2.63895e70 | 0.0929297 | ||||||||
\(635\) | 1.39220e71 | 0.470947 | ||||||||
\(636\) | 1.68321e71 | 0.546993 | ||||||||
\(637\) | 1.14026e70 | 0.0355997 | ||||||||
\(638\) | 5.64159e69 | 0.0169229 | ||||||||
\(639\) | −4.61384e71 | −1.32981 | ||||||||
\(640\) | −1.84394e71 | −0.510691 | ||||||||
\(641\) | 3.78805e71 | 1.00818 | 0.504088 | − | 0.863652i | \(-0.331829\pi\) | ||||
0.504088 | + | 0.863652i | \(0.331829\pi\) | |||||||
\(642\) | −1.06903e69 | −0.00273432 | ||||||||
\(643\) | −2.33505e71 | −0.574006 | −0.287003 | − | 0.957930i | \(-0.592659\pi\) | ||||
−0.287003 | + | 0.957930i | \(0.592659\pi\) | |||||||
\(644\) | −3.31683e71 | −0.783670 | ||||||||
\(645\) | 1.00199e71 | 0.227558 | ||||||||
\(646\) | −2.85423e71 | −0.623103 | ||||||||
\(647\) | −2.29082e71 | −0.480764 | −0.240382 | − | 0.970678i | \(-0.577273\pi\) | ||||
−0.240382 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(648\) | 1.65165e71 | 0.333238 | ||||||||
\(649\) | 1.39298e70 | 0.0270212 | ||||||||
\(650\) | −5.06133e69 | −0.00944004 | ||||||||
\(651\) | −9.66196e70 | −0.173281 | ||||||||
\(652\) | 3.27494e71 | 0.564793 | ||||||||
\(653\) | 8.77846e71 | 1.45590 | 0.727951 | − | 0.685629i | \(-0.240473\pi\) | ||||
0.727951 | + | 0.685629i | \(0.240473\pi\) | |||||||
\(654\) | −1.03867e70 | −0.0165671 | ||||||||
\(655\) | 1.06958e71 | 0.164081 | ||||||||
\(656\) | −7.00976e71 | −1.03432 | ||||||||
\(657\) | −3.50460e71 | −0.497418 | ||||||||
\(658\) | −6.42573e70 | −0.0877329 | ||||||||
\(659\) | 9.01191e71 | 1.18369 | 0.591846 | − | 0.806051i | \(-0.298399\pi\) | ||||
0.591846 | + | 0.806051i | \(0.298399\pi\) | |||||||
\(660\) | 1.02055e70 | 0.0128962 | ||||||||
\(661\) | 5.00776e71 | 0.608845 | 0.304422 | − | 0.952537i | \(-0.401537\pi\) | ||||
0.304422 | + | 0.952537i | \(0.401537\pi\) | |||||||
\(662\) | 2.30399e70 | 0.0269527 | ||||||||
\(663\) | 2.10048e70 | 0.0236441 | ||||||||
\(664\) | 2.78135e71 | 0.301279 | ||||||||
\(665\) | 5.73514e71 | 0.597850 | ||||||||
\(666\) | 1.64595e71 | 0.165129 | ||||||||
\(667\) | −1.41029e72 | −1.36176 | ||||||||
\(668\) | −9.71022e71 | −0.902463 | ||||||||
\(669\) | −4.55577e71 | −0.407564 | ||||||||
\(670\) | −6.52995e70 | −0.0562345 | ||||||||
\(671\) | −9.85118e70 | −0.0816703 | ||||||||
\(672\) | −1.82468e71 | −0.145636 | ||||||||
\(673\) | −8.23485e71 | −0.632807 | −0.316404 | − | 0.948625i | \(-0.602475\pi\) | ||||
−0.316404 | + | 0.948625i | \(0.602475\pi\) | |||||||
\(674\) | 1.61770e71 | 0.119693 | ||||||||
\(675\) | −6.18348e71 | −0.440541 | ||||||||
\(676\) | 1.34936e72 | 0.925736 | ||||||||
\(677\) | −1.48471e71 | −0.0980916 | −0.0490458 | − | 0.998797i | \(-0.515618\pi\) | ||||
−0.0490458 | + | 0.998797i | \(0.515618\pi\) | |||||||
\(678\) | 2.21182e71 | 0.140732 | ||||||||
\(679\) | 1.23546e72 | 0.757094 | ||||||||
\(680\) | −6.43104e71 | −0.379581 | ||||||||
\(681\) | 9.52289e71 | 0.541399 | ||||||||
\(682\) | −2.91038e70 | −0.0159385 | ||||||||
\(683\) | −9.71690e71 | −0.512625 | −0.256313 | − | 0.966594i | \(-0.582508\pi\) | ||||
−0.256313 | + | 0.966594i | \(0.582508\pi\) | |||||||
\(684\) | 2.91801e72 | 1.48305 | ||||||||
\(685\) | −1.09828e72 | −0.537778 | ||||||||
\(686\) | −5.41855e71 | −0.255634 | ||||||||
\(687\) | 5.84719e71 | 0.265797 | ||||||||
\(688\) | 2.03116e72 | 0.889691 | ||||||||
\(689\) | −2.09683e71 | −0.0885060 | ||||||||
\(690\) | 1.96997e71 | 0.0801323 | ||||||||
\(691\) | 1.49847e72 | 0.587431 | 0.293715 | − | 0.955893i | \(-0.405108\pi\) | ||||
0.293715 | + | 0.955893i | \(0.405108\pi\) | |||||||
\(692\) | −3.67424e72 | −1.38823 | ||||||||
\(693\) | −9.43364e70 | −0.0343543 | ||||||||
\(694\) | 5.72462e71 | 0.200946 | ||||||||
\(695\) | −1.19980e72 | −0.405974 | ||||||||
\(696\) | −5.10897e71 | −0.166647 | ||||||||
\(697\) | −5.31724e72 | −1.67205 | ||||||||
\(698\) | −7.75405e70 | −0.0235080 | ||||||||
\(699\) | 9.04820e71 | 0.264481 | ||||||||
\(700\) | −1.25533e72 | −0.353800 | ||||||||
\(701\) | −4.77735e71 | −0.129831 | −0.0649153 | − | 0.997891i | \(-0.520678\pi\) | ||||
−0.0649153 | + | 0.997891i | \(0.520678\pi\) | |||||||
\(702\) | 3.54948e70 | 0.00930182 | ||||||||
\(703\) | 5.07199e72 | 1.28179 | ||||||||
\(704\) | 1.67889e71 | 0.0409185 | ||||||||
\(705\) | −4.94242e71 | −0.116176 | ||||||||
\(706\) | 7.89117e71 | 0.178905 | ||||||||
\(707\) | 1.27103e72 | 0.277947 | ||||||||
\(708\) | −6.07288e71 | −0.128099 | ||||||||
\(709\) | 3.39807e72 | 0.691439 | 0.345719 | − | 0.938338i | \(-0.387635\pi\) | ||||
0.345719 | + | 0.938338i | \(0.387635\pi\) | |||||||
\(710\) | 1.19084e72 | 0.233757 | ||||||||
\(711\) | −3.08383e72 | −0.584004 | ||||||||
\(712\) | 9.34416e70 | 0.0170726 | ||||||||
\(713\) | 7.27539e72 | 1.28255 | ||||||||
\(714\) | −4.02283e71 | −0.0684270 | ||||||||
\(715\) | −1.27133e70 | −0.00208667 | ||||||||
\(716\) | −6.77678e72 | −1.07335 | ||||||||
\(717\) | −3.84739e72 | −0.588069 | ||||||||
\(718\) | 2.64807e71 | 0.0390621 | ||||||||
\(719\) | 9.45409e72 | 1.34596 | 0.672981 | − | 0.739659i | \(-0.265013\pi\) | ||||
0.672981 | + | 0.739659i | \(0.265013\pi\) | |||||||
\(720\) | 2.90188e72 | 0.398751 | ||||||||
\(721\) | −5.66378e72 | −0.751202 | ||||||||
\(722\) | −4.85207e72 | −0.621196 | ||||||||
\(723\) | 1.37985e72 | 0.170532 | ||||||||
\(724\) | −1.78461e72 | −0.212917 | ||||||||
\(725\) | −5.33758e72 | −0.614787 | ||||||||
\(726\) | −8.41234e71 | −0.0935477 | ||||||||
\(727\) | −9.75134e72 | −1.04698 | −0.523488 | − | 0.852033i | \(-0.675370\pi\) | ||||
−0.523488 | + | 0.852033i | \(0.675370\pi\) | |||||||
\(728\) | 1.49683e71 | 0.0155175 | ||||||||
\(729\) | −3.34266e72 | −0.334611 | ||||||||
\(730\) | 9.04544e71 | 0.0874373 | ||||||||
\(731\) | 1.54073e73 | 1.43825 | ||||||||
\(732\) | 4.29475e72 | 0.387173 | ||||||||
\(733\) | −7.22486e72 | −0.629040 | −0.314520 | − | 0.949251i | \(-0.601843\pi\) | ||||
−0.314520 | + | 0.949251i | \(0.601843\pi\) | |||||||
\(734\) | 2.11448e72 | 0.177809 | ||||||||
\(735\) | −1.67970e72 | −0.136429 | ||||||||
\(736\) | 1.37397e73 | 1.07794 | ||||||||
\(737\) | 3.30984e71 | 0.0250834 | ||||||||
\(738\) | −4.19762e72 | −0.307302 | ||||||||
\(739\) | 2.75849e72 | 0.195091 | 0.0975456 | − | 0.995231i | \(-0.468901\pi\) | ||||
0.0975456 | + | 0.995231i | \(0.468901\pi\) | |||||||
\(740\) | 5.50159e72 | 0.375906 | ||||||||
\(741\) | 5.10972e71 | 0.0337313 | ||||||||
\(742\) | 4.01584e72 | 0.256140 | ||||||||
\(743\) | 1.34405e73 | 0.828325 | 0.414162 | − | 0.910203i | \(-0.364075\pi\) | ||||
0.414162 | + | 0.910203i | \(0.364075\pi\) | |||||||
\(744\) | 2.63561e72 | 0.156953 | ||||||||
\(745\) | −1.62548e73 | −0.935396 | ||||||||
\(746\) | −4.82338e71 | −0.0268232 | ||||||||
\(747\) | −9.52000e72 | −0.511637 | ||||||||
\(748\) | 1.56926e72 | 0.0815089 | ||||||||
\(749\) | 3.30301e71 | 0.0165815 | ||||||||
\(750\) | 1.86064e72 | 0.0902819 | ||||||||
\(751\) | −3.23615e73 | −1.51778 | −0.758892 | − | 0.651216i | \(-0.774259\pi\) | ||||
−0.758892 | + | 0.651216i | \(0.774259\pi\) | |||||||
\(752\) | −1.00189e73 | −0.454219 | ||||||||
\(753\) | −1.41768e73 | −0.621307 | ||||||||
\(754\) | 3.06391e71 | 0.0129809 | ||||||||
\(755\) | −2.95788e72 | −0.121153 | ||||||||
\(756\) | 8.80355e72 | 0.348620 | ||||||||
\(757\) | 3.58779e73 | 1.37367 | 0.686834 | − | 0.726814i | \(-0.259000\pi\) | ||||
0.686834 | + | 0.726814i | \(0.259000\pi\) | |||||||
\(758\) | −4.24796e72 | −0.157259 | ||||||||
\(759\) | −9.98518e71 | −0.0357430 | ||||||||
\(760\) | −1.56444e73 | −0.541518 | ||||||||
\(761\) | 3.58257e73 | 1.19918 | 0.599592 | − | 0.800306i | \(-0.295330\pi\) | ||||
0.599592 | + | 0.800306i | \(0.295330\pi\) | |||||||
\(762\) | −2.37557e72 | −0.0768983 | ||||||||
\(763\) | 3.20920e72 | 0.100466 | ||||||||
\(764\) | −1.93244e73 | −0.585093 | ||||||||
\(765\) | 2.20122e73 | 0.644609 | ||||||||
\(766\) | −3.84298e72 | −0.108851 | ||||||||
\(767\) | 7.56518e71 | 0.0207271 | ||||||||
\(768\) | −4.73812e72 | −0.125573 | ||||||||
\(769\) | 5.92781e73 | 1.51975 | 0.759876 | − | 0.650068i | \(-0.225259\pi\) | ||||
0.759876 | + | 0.650068i | \(0.225259\pi\) | |||||||
\(770\) | 2.43484e71 | 0.00603889 | ||||||||
\(771\) | 2.53792e71 | 0.00608963 | ||||||||
\(772\) | 4.41885e72 | 0.102581 | ||||||||
\(773\) | −5.75726e73 | −1.29312 | −0.646560 | − | 0.762863i | \(-0.723793\pi\) | ||||
−0.646560 | + | 0.762863i | \(0.723793\pi\) | |||||||
\(774\) | 1.21631e73 | 0.264332 | ||||||||
\(775\) | 2.75354e73 | 0.579026 | ||||||||
\(776\) | −3.37011e73 | −0.685758 | ||||||||
\(777\) | 7.14859e72 | 0.140762 | ||||||||
\(778\) | −5.04023e72 | −0.0960441 | ||||||||
\(779\) | −1.29349e74 | −2.38539 | ||||||||
\(780\) | 5.54251e71 | 0.00989223 | ||||||||
\(781\) | −6.03601e72 | −0.104267 | ||||||||
\(782\) | 3.02916e73 | 0.506466 | ||||||||
\(783\) | 3.74321e73 | 0.605785 | ||||||||
\(784\) | −3.40497e73 | −0.533400 | ||||||||
\(785\) | 4.48950e73 | 0.680803 | ||||||||
\(786\) | −1.82506e72 | −0.0267919 | ||||||||
\(787\) | 1.39652e73 | 0.198469 | 0.0992344 | − | 0.995064i | \(-0.468361\pi\) | ||||
0.0992344 | + | 0.995064i | \(0.468361\pi\) | |||||||
\(788\) | 4.26098e73 | 0.586261 | ||||||||
\(789\) | 7.49650e71 | 0.00998608 | ||||||||
\(790\) | 7.95943e72 | 0.102658 | ||||||||
\(791\) | −6.83390e73 | −0.853431 | ||||||||
\(792\) | 2.57333e72 | 0.0311174 | ||||||||
\(793\) | −5.35011e72 | −0.0626465 | ||||||||
\(794\) | −1.95548e72 | −0.0221733 | ||||||||
\(795\) | 3.08882e73 | 0.339181 | ||||||||
\(796\) | 1.02338e74 | 1.08831 | ||||||||
\(797\) | 9.83821e73 | 1.01328 | 0.506640 | − | 0.862158i | \(-0.330888\pi\) | ||||
0.506640 | + | 0.862158i | \(0.330888\pi\) | |||||||
\(798\) | −9.78611e72 | −0.0976195 | ||||||||
\(799\) | −7.59982e73 | −0.734277 | ||||||||
\(800\) | 5.20012e73 | 0.486652 | ||||||||
\(801\) | −3.19832e72 | −0.0289930 | ||||||||
\(802\) | −4.73222e73 | −0.415545 | ||||||||
\(803\) | −4.58486e72 | −0.0390014 | ||||||||
\(804\) | −1.44297e73 | −0.118912 | ||||||||
\(805\) | −6.08664e73 | −0.485940 | ||||||||
\(806\) | −1.58060e72 | −0.0122259 | ||||||||
\(807\) | −4.25496e72 | −0.0318875 | ||||||||
\(808\) | −3.46715e73 | −0.251758 | ||||||||
\(809\) | −2.22779e74 | −1.56742 | −0.783712 | − | 0.621125i | \(-0.786676\pi\) | ||||
−0.783712 | + | 0.621125i | \(0.786676\pi\) | |||||||
\(810\) | 1.45912e73 | 0.0994769 | ||||||||
\(811\) | −7.69456e73 | −0.508338 | −0.254169 | − | 0.967160i | \(-0.581802\pi\) | ||||
−0.254169 | + | 0.967160i | \(0.581802\pi\) | |||||||
\(812\) | 7.59922e73 | 0.486509 | ||||||||
\(813\) | −4.36007e73 | −0.270511 | ||||||||
\(814\) | 2.15330e72 | 0.0129474 | ||||||||
\(815\) | 6.00977e73 | 0.350218 | ||||||||
\(816\) | −6.27233e73 | −0.354266 | ||||||||
\(817\) | 3.74806e74 | 2.05184 | ||||||||
\(818\) | −1.50377e73 | −0.0797944 | ||||||||
\(819\) | −5.12334e72 | −0.0263520 | ||||||||
\(820\) | −1.40305e74 | −0.699554 | ||||||||
\(821\) | 1.32614e74 | 0.640971 | 0.320486 | − | 0.947253i | \(-0.396154\pi\) | ||||
0.320486 | + | 0.947253i | \(0.396154\pi\) | |||||||
\(822\) | 1.87404e73 | 0.0878106 | ||||||||
\(823\) | 1.51804e73 | 0.0689585 | 0.0344792 | − | 0.999405i | \(-0.489023\pi\) | ||||
0.0344792 | + | 0.999405i | \(0.489023\pi\) | |||||||
\(824\) | 1.54498e74 | 0.680421 | ||||||||
\(825\) | −3.77913e72 | −0.0161367 | ||||||||
\(826\) | −1.44888e73 | −0.0599848 | ||||||||
\(827\) | 3.58794e74 | 1.44031 | 0.720153 | − | 0.693815i | \(-0.244072\pi\) | ||||
0.720153 | + | 0.693815i | \(0.244072\pi\) | |||||||
\(828\) | −3.09685e74 | −1.20544 | ||||||||
\(829\) | −1.78233e74 | −0.672741 | −0.336370 | − | 0.941730i | \(-0.609199\pi\) | ||||
−0.336370 | + | 0.941730i | \(0.609199\pi\) | |||||||
\(830\) | 2.45713e73 | 0.0899367 | ||||||||
\(831\) | 1.12118e74 | 0.397968 | ||||||||
\(832\) | 9.11793e72 | 0.0313871 | ||||||||
\(833\) | −2.58283e74 | −0.862281 | ||||||||
\(834\) | 2.04728e73 | 0.0662891 | ||||||||
\(835\) | −1.78190e74 | −0.559602 | ||||||||
\(836\) | 3.81746e73 | 0.116282 | ||||||||
\(837\) | −1.93104e74 | −0.570548 | ||||||||
\(838\) | −1.24735e74 | −0.357491 | ||||||||
\(839\) | 6.85470e73 | 0.190572 | 0.0952859 | − | 0.995450i | \(-0.469623\pi\) | ||||
0.0952859 | + | 0.995450i | \(0.469623\pi\) | |||||||
\(840\) | −2.20497e73 | −0.0594676 | ||||||||
\(841\) | −5.90927e73 | −0.154609 | ||||||||
\(842\) | −5.61361e73 | −0.142490 | ||||||||
\(843\) | 2.31715e74 | 0.570625 | ||||||||
\(844\) | −3.21110e74 | −0.767224 | ||||||||
\(845\) | 2.47618e74 | 0.574033 | ||||||||
\(846\) | −5.99957e73 | −0.134951 | ||||||||
\(847\) | 2.59917e74 | 0.567294 | ||||||||
\(848\) | 6.26143e74 | 1.32611 | ||||||||
\(849\) | −2.72350e74 | −0.559733 | ||||||||
\(850\) | 1.14646e74 | 0.228652 | ||||||||
\(851\) | −5.38284e74 | −1.04186 | ||||||||
\(852\) | 2.63148e74 | 0.494299 | ||||||||
\(853\) | 2.78536e74 | 0.507787 | 0.253893 | − | 0.967232i | \(-0.418289\pi\) | ||||
0.253893 | + | 0.967232i | \(0.418289\pi\) | |||||||
\(854\) | 1.02465e74 | 0.181301 | ||||||||
\(855\) | 5.35478e74 | 0.919614 | ||||||||
\(856\) | −9.01002e72 | −0.0150191 | ||||||||
\(857\) | −9.69175e74 | −1.56816 | −0.784082 | − | 0.620658i | \(-0.786866\pi\) | ||||
−0.784082 | + | 0.620658i | \(0.786866\pi\) | |||||||
\(858\) | 2.16932e71 | 0.000340720 0 | ||||||||
\(859\) | 8.61964e74 | 1.31421 | 0.657103 | − | 0.753801i | \(-0.271782\pi\) | ||||
0.657103 | + | 0.753801i | \(0.271782\pi\) | |||||||
\(860\) | 4.06552e74 | 0.601735 | ||||||||
\(861\) | −1.82309e74 | −0.261955 | ||||||||
\(862\) | 1.18318e74 | 0.165050 | ||||||||
\(863\) | −9.32304e74 | −1.26265 | −0.631324 | − | 0.775519i | \(-0.717488\pi\) | ||||
−0.631324 | + | 0.775519i | \(0.717488\pi\) | |||||||
\(864\) | −3.64681e74 | −0.479526 | ||||||||
\(865\) | −6.74252e74 | −0.860819 | ||||||||
\(866\) | 7.03392e73 | 0.0871949 | ||||||||
\(867\) | −1.84132e74 | −0.221637 | ||||||||
\(868\) | −3.92028e74 | −0.458209 | ||||||||
\(869\) | −4.03440e73 | −0.0457904 | ||||||||
\(870\) | −4.51342e73 | −0.0497468 | ||||||||
\(871\) | 1.79755e73 | 0.0192406 | ||||||||
\(872\) | −8.75410e73 | −0.0910000 | ||||||||
\(873\) | 1.15352e75 | 1.16456 | ||||||||
\(874\) | 7.36888e74 | 0.722536 | ||||||||
\(875\) | −5.74885e74 | −0.547489 | ||||||||
\(876\) | 1.99883e74 | 0.184893 | ||||||||
\(877\) | −9.43999e74 | −0.848168 | −0.424084 | − | 0.905623i | \(-0.639404\pi\) | ||||
−0.424084 | + | 0.905623i | \(0.639404\pi\) | |||||||
\(878\) | −4.44753e74 | −0.388158 | ||||||||
\(879\) | 7.00226e74 | 0.593639 | ||||||||
\(880\) | 3.79636e73 | 0.0312651 | ||||||||
\(881\) | 5.77938e74 | 0.462376 | 0.231188 | − | 0.972909i | \(-0.425739\pi\) | ||||
0.231188 | + | 0.972909i | \(0.425739\pi\) | |||||||
\(882\) | −2.03898e74 | −0.158476 | ||||||||
\(883\) | 2.23770e75 | 1.68968 | 0.844838 | − | 0.535022i | \(-0.179697\pi\) | ||||
0.844838 | + | 0.535022i | \(0.179697\pi\) | |||||||
\(884\) | 8.52256e73 | 0.0625227 | ||||||||
\(885\) | −1.11442e74 | −0.0794322 | ||||||||
\(886\) | −4.43987e74 | −0.307475 | ||||||||
\(887\) | 8.40500e74 | 0.565568 | 0.282784 | − | 0.959184i | \(-0.408742\pi\) | ||||
0.282784 | + | 0.959184i | \(0.408742\pi\) | |||||||
\(888\) | −1.95001e74 | −0.127499 | ||||||||
\(889\) | 7.33984e74 | 0.466328 | ||||||||
\(890\) | 8.25492e72 | 0.00509645 | ||||||||
\(891\) | −7.39583e73 | −0.0443716 | ||||||||
\(892\) | −1.84848e75 | −1.07773 | ||||||||
\(893\) | −1.84876e75 | −1.04754 | ||||||||
\(894\) | 2.77362e74 | 0.152735 | ||||||||
\(895\) | −1.24359e75 | −0.665566 | ||||||||
\(896\) | −9.72147e74 | −0.505682 | ||||||||
\(897\) | −5.42289e73 | −0.0274172 | ||||||||
\(898\) | −4.30137e74 | −0.211378 | ||||||||
\(899\) | −1.66687e75 | −0.796216 | ||||||||
\(900\) | −1.17208e75 | −0.544216 | ||||||||
\(901\) | 4.74960e75 | 2.14375 | ||||||||
\(902\) | −5.49150e73 | −0.0240948 | ||||||||
\(903\) | 5.28261e74 | 0.225326 | ||||||||
\(904\) | 1.86416e75 | 0.773017 | ||||||||
\(905\) | −3.27491e74 | −0.132026 | ||||||||
\(906\) | 5.04715e73 | 0.0197823 | ||||||||
\(907\) | −4.85471e75 | −1.85002 | −0.925012 | − | 0.379937i | \(-0.875946\pi\) | ||||
−0.925012 | + | 0.379937i | \(0.875946\pi\) | |||||||
\(908\) | 3.86385e75 | 1.43163 | ||||||||
\(909\) | 1.18674e75 | 0.427538 | ||||||||
\(910\) | 1.32234e73 | 0.00463222 | ||||||||
\(911\) | 1.08836e75 | 0.370727 | 0.185364 | − | 0.982670i | \(-0.440654\pi\) | ||||
0.185364 | + | 0.982670i | \(0.440654\pi\) | |||||||
\(912\) | −1.52583e75 | −0.505405 | ||||||||
\(913\) | −1.24545e74 | −0.0401162 | ||||||||
\(914\) | 1.42825e75 | 0.447379 | ||||||||
\(915\) | 7.88121e74 | 0.240080 | ||||||||
\(916\) | 2.37246e75 | 0.702853 | ||||||||
\(917\) | 5.63892e74 | 0.162472 | ||||||||
\(918\) | −8.04004e74 | −0.225304 | ||||||||
\(919\) | −1.86949e75 | −0.509538 | −0.254769 | − | 0.967002i | \(-0.581999\pi\) | ||||
−0.254769 | + | 0.967002i | \(0.581999\pi\) | |||||||
\(920\) | 1.66033e75 | 0.440153 | ||||||||
\(921\) | −1.79229e75 | −0.462154 | ||||||||
\(922\) | −4.05860e74 | −0.101798 | ||||||||
\(923\) | −3.27812e74 | −0.0799799 | ||||||||
\(924\) | 5.38043e73 | 0.0127697 | ||||||||
\(925\) | −2.03726e75 | −0.470363 | ||||||||
\(926\) | −1.67424e75 | −0.376043 | ||||||||
\(927\) | −5.28815e75 | −1.15550 | ||||||||
\(928\) | −3.14793e75 | −0.669193 | ||||||||
\(929\) | 7.68668e75 | 1.58978 | 0.794892 | − | 0.606751i | \(-0.207527\pi\) | ||||
0.794892 | + | 0.606751i | \(0.207527\pi\) | |||||||
\(930\) | 2.32838e74 | 0.0468531 | ||||||||
\(931\) | −6.28311e75 | −1.23015 | ||||||||
\(932\) | 3.67125e75 | 0.699372 | ||||||||
\(933\) | −5.09466e74 | −0.0944352 | ||||||||
\(934\) | 5.41778e74 | 0.0977184 | ||||||||
\(935\) | 2.87972e74 | 0.0505423 | ||||||||
\(936\) | 1.39756e74 | 0.0238690 | ||||||||
\(937\) | 5.84868e74 | 0.0972071 | 0.0486036 | − | 0.998818i | \(-0.484523\pi\) | ||||
0.0486036 | + | 0.998818i | \(0.484523\pi\) | |||||||
\(938\) | −3.44266e74 | −0.0556829 | ||||||||
\(939\) | 2.74263e75 | 0.431712 | ||||||||
\(940\) | −2.00536e75 | −0.307207 | ||||||||
\(941\) | 2.81919e75 | 0.420328 | 0.210164 | − | 0.977666i | \(-0.432600\pi\) | ||||
0.210164 | + | 0.977666i | \(0.432600\pi\) | |||||||
\(942\) | −7.66062e74 | −0.111164 | ||||||||
\(943\) | 1.37277e76 | 1.93888 | ||||||||
\(944\) | −2.25907e75 | −0.310559 | ||||||||
\(945\) | 1.61552e75 | 0.216173 | ||||||||
\(946\) | 1.59123e74 | 0.0207257 | ||||||||
\(947\) | −6.56754e75 | −0.832680 | −0.416340 | − | 0.909209i | \(-0.636687\pi\) | ||||
−0.416340 | + | 0.909209i | \(0.636687\pi\) | |||||||
\(948\) | 1.75885e75 | 0.217078 | ||||||||
\(949\) | −2.49001e74 | −0.0299166 | ||||||||
\(950\) | 2.78892e75 | 0.326201 | ||||||||
\(951\) | 1.07012e75 | 0.121851 | ||||||||
\(952\) | −3.39051e75 | −0.375858 | ||||||||
\(953\) | 4.31977e74 | 0.0466221 | 0.0233110 | − | 0.999728i | \(-0.492579\pi\) | ||||
0.0233110 | + | 0.999728i | \(0.492579\pi\) | |||||||
\(954\) | 3.74950e75 | 0.393994 | ||||||||
\(955\) | −3.54618e75 | −0.362806 | ||||||||
\(956\) | −1.56106e76 | −1.55504 | ||||||||
\(957\) | 2.28772e74 | 0.0221895 | ||||||||
\(958\) | −2.21912e75 | −0.209585 | ||||||||
\(959\) | −5.79024e75 | −0.532503 | ||||||||
\(960\) | −1.34316e75 | −0.120285 | ||||||||
\(961\) | −2.86786e75 | −0.250099 | ||||||||
\(962\) | 1.16944e74 | 0.00993149 | ||||||||
\(963\) | 3.08395e74 | 0.0255057 | ||||||||
\(964\) | 5.59867e75 | 0.450942 | ||||||||
\(965\) | 8.10894e74 | 0.0636089 | ||||||||
\(966\) | 1.03859e75 | 0.0793464 | ||||||||
\(967\) | 1.78694e76 | 1.32964 | 0.664820 | − | 0.747004i | \(-0.268508\pi\) | ||||
0.664820 | + | 0.747004i | \(0.268508\pi\) | |||||||
\(968\) | −7.09007e75 | −0.513842 | ||||||||
\(969\) | −1.15742e76 | −0.817023 | ||||||||
\(970\) | −2.97727e75 | −0.204710 | ||||||||
\(971\) | 1.48969e76 | 0.997715 | 0.498857 | − | 0.866684i | \(-0.333753\pi\) | ||||
0.498857 | + | 0.866684i | \(0.333753\pi\) | |||||||
\(972\) | 1.25994e76 | 0.821979 | ||||||||
\(973\) | −6.32550e75 | −0.401992 | ||||||||
\(974\) | 5.07000e75 | 0.313873 | ||||||||
\(975\) | −2.05242e74 | −0.0123779 | ||||||||
\(976\) | 1.59762e76 | 0.938649 | ||||||||
\(977\) | 3.67383e75 | 0.210285 | 0.105142 | − | 0.994457i | \(-0.466470\pi\) | ||||
0.105142 | + | 0.994457i | \(0.466470\pi\) | |||||||
\(978\) | −1.02547e75 | −0.0571851 | ||||||||
\(979\) | −4.18417e73 | −0.00227327 | ||||||||
\(980\) | −6.81529e75 | −0.360761 | ||||||||
\(981\) | 2.99636e75 | 0.154537 | ||||||||
\(982\) | −1.79547e75 | −0.0902265 | ||||||||
\(983\) | −2.53462e76 | −1.24108 | −0.620538 | − | 0.784176i | \(-0.713086\pi\) | ||||
−0.620538 | + | 0.784176i | \(0.713086\pi\) | |||||||
\(984\) | 4.97305e75 | 0.237273 | ||||||||
\(985\) | 7.81924e75 | 0.363530 | ||||||||
\(986\) | −6.94016e75 | −0.314419 | ||||||||
\(987\) | −2.60570e75 | −0.115037 | ||||||||
\(988\) | 2.07324e75 | 0.0891962 | ||||||||
\(989\) | −3.97777e76 | −1.66776 | ||||||||
\(990\) | 2.27336e74 | 0.00928903 | ||||||||
\(991\) | −1.78337e76 | −0.710173 | −0.355086 | − | 0.934834i | \(-0.615549\pi\) | ||||
−0.355086 | + | 0.934834i | \(0.615549\pi\) | |||||||
\(992\) | 1.62395e76 | 0.630267 | ||||||||
\(993\) | 9.34291e74 | 0.0353408 | ||||||||
\(994\) | 6.27824e75 | 0.231465 | ||||||||
\(995\) | 1.87799e76 | 0.674845 | ||||||||
\(996\) | 5.42968e75 | 0.190178 | ||||||||
\(997\) | −6.38902e75 | −0.218126 | −0.109063 | − | 0.994035i | \(-0.534785\pi\) | ||||
−0.109063 | + | 0.994035i | \(0.534785\pi\) | |||||||
\(998\) | −4.54757e75 | −0.151339 | ||||||||
\(999\) | 1.42872e76 | 0.463476 |
(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 | 1.52.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 9.52.a.b.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.52.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.52.a.b.1.3 | 4 | 3.2 | odd | 2 |