Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,52,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, 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("2.1");
S:= CuspForms(chi, 52);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 52 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(32.9462706828\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 313153613520 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{5}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(559602.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.35544e7 | 0.707107 | ||||||||
\(3\) | 2.70751e11 | 0.184493 | 0.0922463 | − | 0.995736i | \(-0.470595\pi\) | ||||
0.0922463 | + | 0.995736i | \(0.470595\pi\) | |||||||
\(4\) | 1.12590e15 | 0.500000 | ||||||||
\(5\) | 5.90004e17 | 0.885359 | 0.442680 | − | 0.896680i | \(-0.354028\pi\) | ||||
0.442680 | + | 0.896680i | \(0.354028\pi\) | |||||||
\(6\) | 9.08491e18 | 0.130456 | ||||||||
\(7\) | −5.92711e21 | −1.67049 | −0.835243 | − | 0.549881i | \(-0.814673\pi\) | ||||
−0.835243 | + | 0.549881i | \(0.814673\pi\) | |||||||
\(8\) | 3.77789e22 | 0.353553 | ||||||||
\(9\) | −2.08039e24 | −0.965962 | ||||||||
\(10\) | 1.97972e25 | 0.626043 | ||||||||
\(11\) | −2.67424e26 | −0.744196 | −0.372098 | − | 0.928194i | \(-0.621361\pi\) | ||||
−0.372098 | + | 0.928194i | \(0.621361\pi\) | |||||||
\(12\) | 3.04839e26 | 0.0922463 | ||||||||
\(13\) | 1.41683e28 | 0.556882 | 0.278441 | − | 0.960453i | \(-0.410182\pi\) | ||||
0.278441 | + | 0.960453i | \(0.410182\pi\) | |||||||
\(14\) | −1.98881e29 | −1.18121 | ||||||||
\(15\) | 1.59744e29 | 0.163342 | ||||||||
\(16\) | 1.26765e30 | 0.250000 | ||||||||
\(17\) | −1.60476e31 | −0.674471 | −0.337235 | − | 0.941420i | \(-0.609492\pi\) | ||||
−0.337235 | + | 0.941420i | \(0.609492\pi\) | |||||||
\(18\) | −6.98062e31 | −0.683039 | ||||||||
\(19\) | −4.18466e32 | −1.03144 | −0.515719 | − | 0.856758i | \(-0.672475\pi\) | ||||
−0.515719 | + | 0.856758i | \(0.672475\pi\) | |||||||
\(20\) | 6.64285e32 | 0.442680 | ||||||||
\(21\) | −1.60477e33 | −0.308192 | ||||||||
\(22\) | −8.97327e33 | −0.526226 | ||||||||
\(23\) | 6.82511e34 | 1.28840 | 0.644198 | − | 0.764859i | \(-0.277191\pi\) | ||||
0.644198 | + | 0.764859i | \(0.277191\pi\) | |||||||
\(24\) | 1.02287e34 | 0.0652280 | ||||||||
\(25\) | −9.59850e34 | −0.216139 | ||||||||
\(26\) | 4.75411e35 | 0.393775 | ||||||||
\(27\) | −1.14638e36 | −0.362705 | ||||||||
\(28\) | −6.67333e36 | −0.835243 | ||||||||
\(29\) | −6.03711e36 | −0.308802 | −0.154401 | − | 0.988008i | \(-0.549345\pi\) | ||||
−0.154401 | + | 0.988008i | \(0.549345\pi\) | |||||||
\(30\) | 5.36013e36 | 0.115500 | ||||||||
\(31\) | −7.93779e37 | −0.741270 | −0.370635 | − | 0.928779i | \(-0.620860\pi\) | ||||
−0.370635 | + | 0.928779i | \(0.620860\pi\) | |||||||
\(32\) | 4.25353e37 | 0.176777 | ||||||||
\(33\) | −7.24055e37 | −0.137299 | ||||||||
\(34\) | −5.38469e38 | −0.476923 | ||||||||
\(35\) | −3.49702e39 | −1.47898 | ||||||||
\(36\) | −2.34231e39 | −0.482981 | ||||||||
\(37\) | −1.71766e40 | −1.76113 | −0.880567 | − | 0.473921i | \(-0.842838\pi\) | ||||
−0.880567 | + | 0.473921i | \(0.842838\pi\) | |||||||
\(38\) | −1.40414e40 | −0.729337 | ||||||||
\(39\) | 3.83610e39 | 0.102741 | ||||||||
\(40\) | 2.22897e40 | 0.313022 | ||||||||
\(41\) | −2.28639e41 | −1.71065 | −0.855326 | − | 0.518090i | \(-0.826643\pi\) | ||||
−0.855326 | + | 0.518090i | \(0.826643\pi\) | |||||||
\(42\) | −5.38473e40 | −0.217925 | ||||||||
\(43\) | 6.51175e41 | 1.44628 | 0.723140 | − | 0.690702i | \(-0.242698\pi\) | ||||
0.723140 | + | 0.690702i | \(0.242698\pi\) | |||||||
\(44\) | −3.01093e41 | −0.372098 | ||||||||
\(45\) | −1.22744e42 | −0.855224 | ||||||||
\(46\) | 2.29013e42 | 0.911034 | ||||||||
\(47\) | 5.04013e42 | 1.15863 | 0.579317 | − | 0.815103i | \(-0.303319\pi\) | ||||
0.579317 | + | 0.815103i | \(0.303319\pi\) | |||||||
\(48\) | 3.43218e41 | 0.0461231 | ||||||||
\(49\) | 2.25414e43 | 1.79052 | ||||||||
\(50\) | −3.22072e42 | −0.152833 | ||||||||
\(51\) | −4.34492e42 | −0.124435 | ||||||||
\(52\) | 1.59521e43 | 0.278441 | ||||||||
\(53\) | −9.15542e43 | −0.983204 | −0.491602 | − | 0.870820i | \(-0.663589\pi\) | ||||
−0.491602 | + | 0.870820i | \(0.663589\pi\) | |||||||
\(54\) | −3.84663e43 | −0.256471 | ||||||||
\(55\) | −1.57781e44 | −0.658881 | ||||||||
\(56\) | −2.23920e44 | −0.590606 | ||||||||
\(57\) | −1.13300e44 | −0.190293 | ||||||||
\(58\) | −2.02572e44 | −0.218356 | ||||||||
\(59\) | 6.44776e44 | 0.449452 | 0.224726 | − | 0.974422i | \(-0.427851\pi\) | ||||
0.224726 | + | 0.974422i | \(0.427851\pi\) | |||||||
\(60\) | 1.79856e44 | 0.0816711 | ||||||||
\(61\) | −2.22244e45 | −0.662093 | −0.331047 | − | 0.943614i | \(-0.607402\pi\) | ||||
−0.331047 | + | 0.943614i | \(0.607402\pi\) | |||||||
\(62\) | −2.66348e45 | −0.524157 | ||||||||
\(63\) | 1.23307e46 | 1.61363 | ||||||||
\(64\) | 1.42725e45 | 0.125000 | ||||||||
\(65\) | 8.35937e45 | 0.493041 | ||||||||
\(66\) | −2.42953e45 | −0.0970848 | ||||||||
\(67\) | 5.61205e46 | 1.52832 | 0.764159 | − | 0.645028i | \(-0.223154\pi\) | ||||
0.764159 | + | 0.645028i | \(0.223154\pi\) | |||||||
\(68\) | −1.80680e46 | −0.337235 | ||||||||
\(69\) | 1.84791e46 | 0.237700 | ||||||||
\(70\) | −1.17340e47 | −1.04580 | ||||||||
\(71\) | −1.91073e47 | −1.18608 | −0.593038 | − | 0.805175i | \(-0.702072\pi\) | ||||
−0.593038 | + | 0.805175i | \(0.702072\pi\) | |||||||
\(72\) | −7.85948e46 | −0.341519 | ||||||||
\(73\) | 2.40551e47 | 0.735316 | 0.367658 | − | 0.929961i | \(-0.380160\pi\) | ||||
0.367658 | + | 0.929961i | \(0.380160\pi\) | |||||||
\(74\) | −5.76350e47 | −1.24531 | ||||||||
\(75\) | −2.59881e46 | −0.0398761 | ||||||||
\(76\) | −4.71150e47 | −0.515719 | ||||||||
\(77\) | 1.58505e48 | 1.24317 | ||||||||
\(78\) | 1.28718e47 | 0.0726486 | ||||||||
\(79\) | 1.22693e48 | 0.500413 | 0.250206 | − | 0.968193i | \(-0.419502\pi\) | ||||
0.250206 | + | 0.968193i | \(0.419502\pi\) | |||||||
\(80\) | 7.47918e47 | 0.221340 | ||||||||
\(81\) | 4.17013e48 | 0.899046 | ||||||||
\(82\) | −7.67184e48 | −1.20961 | ||||||||
\(83\) | 8.82136e48 | 1.02104 | 0.510522 | − | 0.859865i | \(-0.329452\pi\) | ||||
0.510522 | + | 0.859865i | \(0.329452\pi\) | |||||||
\(84\) | −1.80681e48 | −0.154096 | ||||||||
\(85\) | −9.46815e48 | −0.597149 | ||||||||
\(86\) | 2.18498e49 | 1.02267 | ||||||||
\(87\) | −1.63456e48 | −0.0569716 | ||||||||
\(88\) | −1.01030e49 | −0.263113 | ||||||||
\(89\) | −5.56843e49 | −1.08715 | −0.543573 | − | 0.839362i | \(-0.682929\pi\) | ||||
−0.543573 | + | 0.839362i | \(0.682929\pi\) | |||||||
\(90\) | −4.11859e49 | −0.604735 | ||||||||
\(91\) | −8.39773e49 | −0.930264 | ||||||||
\(92\) | 7.68439e49 | 0.644198 | ||||||||
\(93\) | −2.14917e49 | −0.136759 | ||||||||
\(94\) | 1.69119e50 | 0.819278 | ||||||||
\(95\) | −2.46896e50 | −0.913193 | ||||||||
\(96\) | 1.15165e49 | 0.0326140 | ||||||||
\(97\) | 5.94385e50 | 1.29238 | 0.646188 | − | 0.763178i | \(-0.276362\pi\) | ||||
0.646188 | + | 0.763178i | \(0.276362\pi\) | |||||||
\(98\) | 7.56363e50 | 1.26609 | ||||||||
\(99\) | 5.56346e50 | 0.718865 | ||||||||
\(100\) | −1.08070e50 | −0.108070 | ||||||||
\(101\) | −1.51456e51 | −1.17514 | −0.587571 | − | 0.809172i | \(-0.699916\pi\) | ||||
−0.587571 | + | 0.809172i | \(0.699916\pi\) | |||||||
\(102\) | −1.45791e50 | −0.0879887 | ||||||||
\(103\) | −8.50653e50 | −0.400316 | −0.200158 | − | 0.979764i | \(-0.564146\pi\) | ||||
−0.200158 | + | 0.979764i | \(0.564146\pi\) | |||||||
\(104\) | 5.35265e50 | 0.196888 | ||||||||
\(105\) | −9.46822e50 | −0.272861 | ||||||||
\(106\) | −3.07205e51 | −0.695230 | ||||||||
\(107\) | −2.42869e51 | −0.432599 | −0.216299 | − | 0.976327i | \(-0.569399\pi\) | ||||
−0.216299 | + | 0.976327i | \(0.569399\pi\) | |||||||
\(108\) | −1.29071e51 | −0.181353 | ||||||||
\(109\) | 9.70083e51 | 1.07754 | 0.538770 | − | 0.842453i | \(-0.318889\pi\) | ||||
0.538770 | + | 0.842453i | \(0.318889\pi\) | |||||||
\(110\) | −5.29426e51 | −0.465899 | ||||||||
\(111\) | −4.65058e51 | −0.324916 | ||||||||
\(112\) | −7.51350e51 | −0.417622 | ||||||||
\(113\) | 2.32574e52 | 1.03053 | 0.515265 | − | 0.857031i | \(-0.327693\pi\) | ||||
0.515265 | + | 0.857031i | \(0.327693\pi\) | |||||||
\(114\) | −3.80172e51 | −0.134557 | ||||||||
\(115\) | 4.02684e52 | 1.14069 | ||||||||
\(116\) | −6.79718e51 | −0.154401 | ||||||||
\(117\) | −2.94756e52 | −0.537927 | ||||||||
\(118\) | 2.16351e52 | 0.317810 | ||||||||
\(119\) | 9.51160e52 | 1.12669 | ||||||||
\(120\) | 6.03497e51 | 0.0577502 | ||||||||
\(121\) | −5.76143e52 | −0.446173 | ||||||||
\(122\) | −7.45727e52 | −0.468171 | ||||||||
\(123\) | −6.19043e52 | −0.315603 | ||||||||
\(124\) | −8.93716e52 | −0.370635 | ||||||||
\(125\) | −3.18646e53 | −1.07672 | ||||||||
\(126\) | 4.13749e53 | 1.14101 | ||||||||
\(127\) | −8.04886e53 | −1.81443 | −0.907213 | − | 0.420671i | \(-0.861795\pi\) | ||||
−0.907213 | + | 0.420671i | \(0.861795\pi\) | |||||||
\(128\) | 4.78905e52 | 0.0883883 | ||||||||
\(129\) | 1.76307e53 | 0.266828 | ||||||||
\(130\) | 2.80494e53 | 0.348633 | ||||||||
\(131\) | 3.68828e53 | 0.377056 | 0.188528 | − | 0.982068i | \(-0.439628\pi\) | ||||
0.188528 | + | 0.982068i | \(0.439628\pi\) | |||||||
\(132\) | −8.15213e52 | −0.0686493 | ||||||||
\(133\) | 2.48029e54 | 1.72300 | ||||||||
\(134\) | 1.88309e54 | 1.08068 | ||||||||
\(135\) | −6.76371e53 | −0.321125 | ||||||||
\(136\) | −6.06262e53 | −0.238461 | ||||||||
\(137\) | −5.14641e54 | −1.67931 | −0.839654 | − | 0.543122i | \(-0.817242\pi\) | ||||
−0.839654 | + | 0.543122i | \(0.817242\pi\) | |||||||
\(138\) | 6.20055e53 | 0.168079 | ||||||||
\(139\) | 5.59390e54 | 1.26136 | 0.630678 | − | 0.776045i | \(-0.282777\pi\) | ||||
0.630678 | + | 0.776045i | \(0.282777\pi\) | |||||||
\(140\) | −3.93729e54 | −0.739490 | ||||||||
\(141\) | 1.36462e54 | 0.213759 | ||||||||
\(142\) | −6.41136e54 | −0.838682 | ||||||||
\(143\) | −3.78896e54 | −0.414429 | ||||||||
\(144\) | −2.63720e54 | −0.241491 | ||||||||
\(145\) | −3.56191e54 | −0.273401 | ||||||||
\(146\) | 8.07155e54 | 0.519947 | ||||||||
\(147\) | 6.10311e54 | 0.330338 | ||||||||
\(148\) | −1.93391e55 | −0.880567 | ||||||||
\(149\) | 1.41490e55 | 0.542596 | 0.271298 | − | 0.962495i | \(-0.412547\pi\) | ||||
0.271298 | + | 0.962495i | \(0.412547\pi\) | |||||||
\(150\) | −8.72016e53 | −0.0281966 | ||||||||
\(151\) | 1.21063e55 | 0.330444 | 0.165222 | − | 0.986256i | \(-0.447166\pi\) | ||||
0.165222 | + | 0.986256i | \(0.447166\pi\) | |||||||
\(152\) | −1.58092e55 | −0.364668 | ||||||||
\(153\) | 3.33853e55 | 0.651513 | ||||||||
\(154\) | 5.31855e55 | 0.879053 | ||||||||
\(155\) | −4.68332e55 | −0.656290 | ||||||||
\(156\) | 4.31906e54 | 0.0513703 | ||||||||
\(157\) | 1.15196e56 | 1.16412 | 0.582060 | − | 0.813146i | \(-0.302247\pi\) | ||||
0.582060 | + | 0.813146i | \(0.302247\pi\) | |||||||
\(158\) | 4.11689e55 | 0.353845 | ||||||||
\(159\) | −2.47884e55 | −0.181394 | ||||||||
\(160\) | 2.50960e55 | 0.156511 | ||||||||
\(161\) | −4.04531e56 | −2.15225 | ||||||||
\(162\) | 1.39926e56 | 0.635722 | ||||||||
\(163\) | −2.58863e56 | −1.00528 | −0.502640 | − | 0.864496i | \(-0.667638\pi\) | ||||
−0.502640 | + | 0.864496i | \(0.667638\pi\) | |||||||
\(164\) | −2.57424e56 | −0.855326 | ||||||||
\(165\) | −4.27195e55 | −0.121559 | ||||||||
\(166\) | 2.95996e56 | 0.721987 | ||||||||
\(167\) | 2.51396e56 | 0.526125 | 0.263062 | − | 0.964779i | \(-0.415267\pi\) | ||||
0.263062 | + | 0.964779i | \(0.415267\pi\) | |||||||
\(168\) | −6.06266e55 | −0.108962 | ||||||||
\(169\) | −4.46566e56 | −0.689882 | ||||||||
\(170\) | −3.17698e56 | −0.422248 | ||||||||
\(171\) | 8.70571e56 | 0.996330 | ||||||||
\(172\) | 7.33158e56 | 0.723140 | ||||||||
\(173\) | 1.45880e57 | 1.24114 | 0.620568 | − | 0.784153i | \(-0.286902\pi\) | ||||
0.620568 | + | 0.784153i | \(0.286902\pi\) | |||||||
\(174\) | −5.48466e55 | −0.0402850 | ||||||||
\(175\) | 5.68914e56 | 0.361057 | ||||||||
\(176\) | −3.39000e56 | −0.186049 | ||||||||
\(177\) | 1.74574e56 | 0.0829205 | ||||||||
\(178\) | −1.86845e57 | −0.768728 | ||||||||
\(179\) | −1.87738e57 | −0.669576 | −0.334788 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334788 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(180\) | −1.38197e57 | −0.427612 | ||||||||
\(181\) | 3.52839e57 | 0.947923 | 0.473962 | − | 0.880546i | \(-0.342824\pi\) | ||||
0.473962 | + | 0.880546i | \(0.342824\pi\) | |||||||
\(182\) | −2.81781e57 | −0.657796 | ||||||||
\(183\) | −6.01729e56 | −0.122151 | ||||||||
\(184\) | 2.57845e57 | 0.455517 | ||||||||
\(185\) | −1.01342e58 | −1.55924 | ||||||||
\(186\) | −7.21141e56 | −0.0967031 | ||||||||
\(187\) | 4.29152e57 | 0.501938 | ||||||||
\(188\) | 5.67468e57 | 0.579317 | ||||||||
\(189\) | 6.79474e57 | 0.605894 | ||||||||
\(190\) | −8.28446e57 | −0.645725 | ||||||||
\(191\) | −7.54559e57 | −0.514449 | −0.257224 | − | 0.966352i | \(-0.582808\pi\) | ||||
−0.257224 | + | 0.966352i | \(0.582808\pi\) | |||||||
\(192\) | 3.86429e56 | 0.0230616 | ||||||||
\(193\) | −3.90265e57 | −0.204009 | −0.102004 | − | 0.994784i | \(-0.532526\pi\) | ||||
−0.102004 | + | 0.994784i | \(0.532526\pi\) | |||||||
\(194\) | 1.99443e58 | 0.913848 | ||||||||
\(195\) | 2.26331e57 | 0.0909624 | ||||||||
\(196\) | 2.53793e58 | 0.895262 | ||||||||
\(197\) | 5.55147e57 | 0.171996 | 0.0859981 | − | 0.996295i | \(-0.472592\pi\) | ||||
0.0859981 | + | 0.996295i | \(0.472592\pi\) | |||||||
\(198\) | 1.86679e58 | 0.508314 | ||||||||
\(199\) | −1.39534e58 | −0.334138 | −0.167069 | − | 0.985945i | \(-0.553430\pi\) | ||||
−0.167069 | + | 0.985945i | \(0.553430\pi\) | |||||||
\(200\) | −3.62621e57 | −0.0764167 | ||||||||
\(201\) | 1.51947e58 | 0.281963 | ||||||||
\(202\) | −5.08201e58 | −0.830951 | ||||||||
\(203\) | 3.57826e58 | 0.515849 | ||||||||
\(204\) | −4.89194e57 | −0.0622174 | ||||||||
\(205\) | −1.34898e59 | −1.51454 | ||||||||
\(206\) | −2.85432e58 | −0.283066 | ||||||||
\(207\) | −1.41989e59 | −1.24454 | ||||||||
\(208\) | 1.79605e58 | 0.139221 | ||||||||
\(209\) | 1.11908e59 | 0.767592 | ||||||||
\(210\) | −3.17701e58 | −0.192942 | ||||||||
\(211\) | 1.98069e59 | 1.06565 | 0.532825 | − | 0.846226i | \(-0.321130\pi\) | ||||
0.532825 | + | 0.846226i | \(0.321130\pi\) | |||||||
\(212\) | −1.03081e59 | −0.491602 | ||||||||
\(213\) | −5.17334e58 | −0.218822 | ||||||||
\(214\) | −8.14933e58 | −0.305894 | ||||||||
\(215\) | 3.84196e59 | 1.28048 | ||||||||
\(216\) | −4.33092e58 | −0.128236 | ||||||||
\(217\) | 4.70481e59 | 1.23828 | ||||||||
\(218\) | 3.25506e59 | 0.761935 | ||||||||
\(219\) | 6.51295e58 | 0.135660 | ||||||||
\(220\) | −1.77646e59 | −0.329440 | ||||||||
\(221\) | −2.27368e59 | −0.375601 | ||||||||
\(222\) | −1.56048e59 | −0.229750 | ||||||||
\(223\) | −1.05167e60 | −1.38072 | −0.690360 | − | 0.723466i | \(-0.742548\pi\) | ||||
−0.690360 | + | 0.723466i | \(0.742548\pi\) | |||||||
\(224\) | −2.52111e59 | −0.295303 | ||||||||
\(225\) | 1.99686e59 | 0.208782 | ||||||||
\(226\) | 7.80389e59 | 0.728695 | ||||||||
\(227\) | −2.32315e59 | −0.193829 | −0.0969145 | − | 0.995293i | \(-0.530897\pi\) | ||||
−0.0969145 | + | 0.995293i | \(0.530897\pi\) | |||||||
\(228\) | −1.27565e59 | −0.0951463 | ||||||||
\(229\) | −2.08303e60 | −1.38960 | −0.694800 | − | 0.719203i | \(-0.744507\pi\) | ||||
−0.694800 | + | 0.719203i | \(0.744507\pi\) | |||||||
\(230\) | 1.35118e60 | 0.806592 | ||||||||
\(231\) | 4.29155e59 | 0.229355 | ||||||||
\(232\) | −2.28075e59 | −0.109178 | ||||||||
\(233\) | −2.17828e60 | −0.934410 | −0.467205 | − | 0.884149i | \(-0.654739\pi\) | ||||
−0.467205 | + | 0.884149i | \(0.654739\pi\) | |||||||
\(234\) | −9.89038e59 | −0.380372 | ||||||||
\(235\) | 2.97369e60 | 1.02581 | ||||||||
\(236\) | 7.25954e59 | 0.224726 | ||||||||
\(237\) | 3.32193e59 | 0.0923225 | ||||||||
\(238\) | 3.19156e60 | 0.796693 | ||||||||
\(239\) | −1.01088e59 | −0.0226754 | −0.0113377 | − | 0.999936i | \(-0.503609\pi\) | ||||
−0.0113377 | + | 0.999936i | \(0.503609\pi\) | |||||||
\(240\) | 2.02500e59 | 0.0408355 | ||||||||
\(241\) | −5.46605e59 | −0.0991378 | −0.0495689 | − | 0.998771i | \(-0.515785\pi\) | ||||
−0.0495689 | + | 0.998771i | \(0.515785\pi\) | |||||||
\(242\) | −1.93321e60 | −0.315492 | ||||||||
\(243\) | 3.59803e60 | 0.528573 | ||||||||
\(244\) | −2.50224e60 | −0.331047 | ||||||||
\(245\) | 1.32995e61 | 1.58526 | ||||||||
\(246\) | −2.07716e60 | −0.223165 | ||||||||
\(247\) | −5.92896e60 | −0.574389 | ||||||||
\(248\) | −2.99881e60 | −0.262079 | ||||||||
\(249\) | 2.38840e60 | 0.188375 | ||||||||
\(250\) | −1.06920e61 | −0.761356 | ||||||||
\(251\) | −3.50691e60 | −0.225551 | −0.112776 | − | 0.993620i | \(-0.535974\pi\) | ||||
−0.112776 | + | 0.993620i | \(0.535974\pi\) | |||||||
\(252\) | 1.38831e61 | 0.806813 | ||||||||
\(253\) | −1.82520e61 | −0.958819 | ||||||||
\(254\) | −2.70075e61 | −1.28299 | ||||||||
\(255\) | −2.56352e60 | −0.110170 | ||||||||
\(256\) | 1.60694e60 | 0.0625000 | ||||||||
\(257\) | −5.05435e61 | −1.77980 | −0.889900 | − | 0.456157i | \(-0.849226\pi\) | ||||
−0.889900 | + | 0.456157i | \(0.849226\pi\) | |||||||
\(258\) | 5.91587e60 | 0.188676 | ||||||||
\(259\) | 1.01807e62 | 2.94195 | ||||||||
\(260\) | 9.41181e60 | 0.246520 | ||||||||
\(261\) | 1.25595e61 | 0.298291 | ||||||||
\(262\) | 1.23758e61 | 0.266619 | ||||||||
\(263\) | 1.44972e61 | 0.283408 | 0.141704 | − | 0.989909i | \(-0.454742\pi\) | ||||
0.141704 | + | 0.989909i | \(0.454742\pi\) | |||||||
\(264\) | −2.73540e60 | −0.0485424 | ||||||||
\(265\) | −5.40173e61 | −0.870489 | ||||||||
\(266\) | 8.32248e61 | 1.21835 | ||||||||
\(267\) | −1.50766e61 | −0.200570 | ||||||||
\(268\) | 6.31860e61 | 0.764159 | ||||||||
\(269\) | −1.34234e61 | −0.147632 | −0.0738158 | − | 0.997272i | \(-0.523518\pi\) | ||||
−0.0738158 | + | 0.997272i | \(0.523518\pi\) | |||||||
\(270\) | −2.26952e61 | −0.227069 | ||||||||
\(271\) | −8.45578e61 | −0.769905 | −0.384952 | − | 0.922936i | \(-0.625782\pi\) | ||||
−0.384952 | + | 0.922936i | \(0.625782\pi\) | |||||||
\(272\) | −2.03428e61 | −0.168618 | ||||||||
\(273\) | −2.27370e61 | −0.171627 | ||||||||
\(274\) | −1.72685e62 | −1.18745 | ||||||||
\(275\) | 2.56687e61 | 0.160850 | ||||||||
\(276\) | 2.08056e61 | 0.118850 | ||||||||
\(277\) | −1.96004e62 | −1.02101 | −0.510506 | − | 0.859874i | \(-0.670542\pi\) | ||||
−0.510506 | + | 0.859874i | \(0.670542\pi\) | |||||||
\(278\) | 1.87700e62 | 0.891913 | ||||||||
\(279\) | 1.65137e62 | 0.716039 | ||||||||
\(280\) | −1.32113e62 | −0.522898 | ||||||||
\(281\) | −2.29277e61 | −0.0828608 | −0.0414304 | − | 0.999141i | \(-0.513191\pi\) | ||||
−0.0414304 | + | 0.999141i | \(0.513191\pi\) | |||||||
\(282\) | 4.57891e61 | 0.151151 | ||||||||
\(283\) | −2.92760e61 | −0.0882992 | −0.0441496 | − | 0.999025i | \(-0.514058\pi\) | ||||
−0.0441496 | + | 0.999025i | \(0.514058\pi\) | |||||||
\(284\) | −2.15130e62 | −0.593038 | ||||||||
\(285\) | −6.68475e61 | −0.168477 | ||||||||
\(286\) | −1.27136e62 | −0.293046 | ||||||||
\(287\) | 1.35517e63 | 2.85762 | ||||||||
\(288\) | −8.84899e61 | −0.170760 | ||||||||
\(289\) | −3.08576e62 | −0.545089 | ||||||||
\(290\) | −1.19518e62 | −0.193323 | ||||||||
\(291\) | 1.60931e62 | 0.238434 | ||||||||
\(292\) | 2.70836e62 | 0.367658 | ||||||||
\(293\) | −4.39216e62 | −0.546454 | −0.273227 | − | 0.961950i | \(-0.588091\pi\) | ||||
−0.273227 | + | 0.961950i | \(0.588091\pi\) | |||||||
\(294\) | 2.04786e62 | 0.233584 | ||||||||
\(295\) | 3.80420e62 | 0.397926 | ||||||||
\(296\) | −6.48913e62 | −0.622655 | ||||||||
\(297\) | 3.06571e62 | 0.269924 | ||||||||
\(298\) | 4.74762e62 | 0.383673 | ||||||||
\(299\) | 9.67004e62 | 0.717485 | ||||||||
\(300\) | −2.92600e61 | −0.0199380 | ||||||||
\(301\) | −3.85959e63 | −2.41599 | ||||||||
\(302\) | 4.06219e62 | 0.233659 | ||||||||
\(303\) | −4.10069e62 | −0.216805 | ||||||||
\(304\) | −5.30468e62 | −0.257859 | ||||||||
\(305\) | −1.31125e63 | −0.586190 | ||||||||
\(306\) | 1.12022e63 | 0.460690 | ||||||||
\(307\) | −2.38716e63 | −0.903342 | −0.451671 | − | 0.892185i | \(-0.649172\pi\) | ||||
−0.451671 | + | 0.892185i | \(0.649172\pi\) | |||||||
\(308\) | 1.78461e63 | 0.621584 | ||||||||
\(309\) | −2.30316e62 | −0.0738554 | ||||||||
\(310\) | −1.57146e63 | −0.464067 | ||||||||
\(311\) | 4.89938e63 | 1.33276 | 0.666379 | − | 0.745614i | \(-0.267844\pi\) | ||||
0.666379 | + | 0.745614i | \(0.267844\pi\) | |||||||
\(312\) | 1.44924e62 | 0.0363243 | ||||||||
\(313\) | −1.11505e63 | −0.257580 | −0.128790 | − | 0.991672i | \(-0.541109\pi\) | ||||
−0.128790 | + | 0.991672i | \(0.541109\pi\) | |||||||
\(314\) | 3.86535e63 | 0.823158 | ||||||||
\(315\) | 7.27515e63 | 1.42864 | ||||||||
\(316\) | 1.38140e63 | 0.250206 | ||||||||
\(317\) | −2.45255e63 | −0.409833 | −0.204917 | − | 0.978779i | \(-0.565692\pi\) | ||||
−0.204917 | + | 0.978779i | \(0.565692\pi\) | |||||||
\(318\) | −8.31762e62 | −0.128265 | ||||||||
\(319\) | 1.61447e63 | 0.229809 | ||||||||
\(320\) | 8.42081e62 | 0.110670 | ||||||||
\(321\) | −6.57571e62 | −0.0798113 | ||||||||
\(322\) | −1.35738e64 | −1.52187 | ||||||||
\(323\) | 6.71538e63 | 0.695675 | ||||||||
\(324\) | 4.69515e63 | 0.449523 | ||||||||
\(325\) | −1.35995e63 | −0.120364 | ||||||||
\(326\) | −8.68602e63 | −0.710840 | ||||||||
\(327\) | 2.62651e63 | 0.198798 | ||||||||
\(328\) | −8.63773e63 | −0.604807 | ||||||||
\(329\) | −2.98734e64 | −1.93548 | ||||||||
\(330\) | −1.43343e63 | −0.0859549 | ||||||||
\(331\) | −1.52520e64 | −0.846666 | −0.423333 | − | 0.905974i | \(-0.639140\pi\) | ||||
−0.423333 | + | 0.905974i | \(0.639140\pi\) | |||||||
\(332\) | 9.93197e63 | 0.510522 | ||||||||
\(333\) | 3.57339e64 | 1.70119 | ||||||||
\(334\) | 8.43546e63 | 0.372026 | ||||||||
\(335\) | 3.31113e64 | 1.35311 | ||||||||
\(336\) | −2.03429e63 | −0.0770481 | ||||||||
\(337\) | −2.16648e64 | −0.760664 | −0.380332 | − | 0.924850i | \(-0.624190\pi\) | ||||
−0.380332 | + | 0.924850i | \(0.624190\pi\) | |||||||
\(338\) | −1.49843e64 | −0.487820 | ||||||||
\(339\) | 6.29698e63 | 0.190125 | ||||||||
\(340\) | −1.06602e64 | −0.298574 | ||||||||
\(341\) | 2.12276e64 | 0.551650 | ||||||||
\(342\) | 2.92115e64 | 0.704512 | ||||||||
\(343\) | −5.89872e64 | −1.32056 | ||||||||
\(344\) | 2.46007e64 | 0.511337 | ||||||||
\(345\) | 1.09027e64 | 0.210450 | ||||||||
\(346\) | 4.89491e64 | 0.877615 | ||||||||
\(347\) | 5.29970e64 | 0.882774 | 0.441387 | − | 0.897317i | \(-0.354487\pi\) | ||||
0.441387 | + | 0.897317i | \(0.354487\pi\) | |||||||
\(348\) | −1.84035e63 | −0.0284858 | ||||||||
\(349\) | −1.00163e65 | −1.44099 | −0.720494 | − | 0.693461i | \(-0.756085\pi\) | ||||
−0.720494 | + | 0.693461i | \(0.756085\pi\) | |||||||
\(350\) | 1.90896e64 | 0.255306 | ||||||||
\(351\) | −1.62424e64 | −0.201984 | ||||||||
\(352\) | −1.13750e64 | −0.131556 | ||||||||
\(353\) | 6.03904e64 | 0.649700 | 0.324850 | − | 0.945766i | \(-0.394686\pi\) | ||||
0.324850 | + | 0.945766i | \(0.394686\pi\) | |||||||
\(354\) | 5.85774e63 | 0.0586336 | ||||||||
\(355\) | −1.12734e65 | −1.05010 | ||||||||
\(356\) | −6.26949e64 | −0.543573 | ||||||||
\(357\) | 2.57528e64 | 0.207867 | ||||||||
\(358\) | −6.29944e64 | −0.473462 | ||||||||
\(359\) | −7.01548e64 | −0.491076 | −0.245538 | − | 0.969387i | \(-0.578965\pi\) | ||||
−0.245538 | + | 0.969387i | \(0.578965\pi\) | |||||||
\(360\) | −4.63712e64 | −0.302367 | ||||||||
\(361\) | 1.05121e64 | 0.0638637 | ||||||||
\(362\) | 1.18393e65 | 0.670283 | ||||||||
\(363\) | −1.55991e64 | −0.0823156 | ||||||||
\(364\) | −9.45500e64 | −0.465132 | ||||||||
\(365\) | 1.41926e65 | 0.651019 | ||||||||
\(366\) | −2.01907e64 | −0.0863740 | ||||||||
\(367\) | −1.18243e65 | −0.471836 | −0.235918 | − | 0.971773i | \(-0.575810\pi\) | ||||
−0.235918 | + | 0.971773i | \(0.575810\pi\) | |||||||
\(368\) | 8.65185e64 | 0.322099 | ||||||||
\(369\) | 4.75657e65 | 1.65243 | ||||||||
\(370\) | −3.40049e65 | −1.10255 | ||||||||
\(371\) | 5.42652e65 | 1.64243 | ||||||||
\(372\) | −2.41975e64 | −0.0683794 | ||||||||
\(373\) | 7.20138e64 | 0.190038 | 0.0950190 | − | 0.995475i | \(-0.469709\pi\) | ||||
0.0950190 | + | 0.995475i | \(0.469709\pi\) | |||||||
\(374\) | 1.44000e65 | 0.354924 | ||||||||
\(375\) | −8.62738e64 | −0.198647 | ||||||||
\(376\) | 1.90411e65 | 0.409639 | ||||||||
\(377\) | −8.55357e64 | −0.171966 | ||||||||
\(378\) | 2.27994e65 | 0.428432 | ||||||||
\(379\) | −6.43875e65 | −1.13110 | −0.565551 | − | 0.824714i | \(-0.691336\pi\) | ||||
−0.565551 | + | 0.824714i | \(0.691336\pi\) | |||||||
\(380\) | −2.77980e65 | −0.456596 | ||||||||
\(381\) | −2.17924e65 | −0.334748 | ||||||||
\(382\) | −2.53188e65 | −0.363770 | ||||||||
\(383\) | −1.01890e66 | −1.36950 | −0.684751 | − | 0.728777i | \(-0.740089\pi\) | ||||
−0.684751 | + | 0.728777i | \(0.740089\pi\) | |||||||
\(384\) | 1.29664e64 | 0.0163070 | ||||||||
\(385\) | 9.35186e65 | 1.10065 | ||||||||
\(386\) | −1.30951e65 | −0.144256 | ||||||||
\(387\) | −1.35470e66 | −1.39705 | ||||||||
\(388\) | 6.69218e65 | 0.646188 | ||||||||
\(389\) | 3.06541e65 | 0.277188 | 0.138594 | − | 0.990349i | \(-0.455742\pi\) | ||||
0.138594 | + | 0.990349i | \(0.455742\pi\) | |||||||
\(390\) | 7.59441e64 | 0.0643201 | ||||||||
\(391\) | −1.09527e66 | −0.868986 | ||||||||
\(392\) | 8.51589e65 | 0.633046 | ||||||||
\(393\) | 9.98608e64 | 0.0695641 | ||||||||
\(394\) | 1.86276e65 | 0.121620 | ||||||||
\(395\) | 7.23892e65 | 0.443045 | ||||||||
\(396\) | 6.26390e65 | 0.359433 | ||||||||
\(397\) | 3.60543e66 | 1.93999 | 0.969993 | − | 0.243131i | \(-0.0781745\pi\) | ||||
0.969993 | + | 0.243131i | \(0.0781745\pi\) | |||||||
\(398\) | −4.68198e65 | −0.236271 | ||||||||
\(399\) | 6.71543e65 | 0.317881 | ||||||||
\(400\) | −1.21675e65 | −0.0540348 | ||||||||
\(401\) | −4.04832e66 | −1.68691 | −0.843457 | − | 0.537196i | \(-0.819483\pi\) | ||||
−0.843457 | + | 0.537196i | \(0.819483\pi\) | |||||||
\(402\) | 5.09849e65 | 0.199378 | ||||||||
\(403\) | −1.12465e66 | −0.412800 | ||||||||
\(404\) | −1.70524e66 | −0.587571 | ||||||||
\(405\) | 2.46039e66 | 0.795979 | ||||||||
\(406\) | 1.20066e66 | 0.364760 | ||||||||
\(407\) | 4.59343e66 | 1.31063 | ||||||||
\(408\) | −1.64146e65 | −0.0439944 | ||||||||
\(409\) | −2.76141e65 | −0.0695324 | −0.0347662 | − | 0.999395i | \(-0.511069\pi\) | ||||
−0.0347662 | + | 0.999395i | \(0.511069\pi\) | |||||||
\(410\) | −4.52642e66 | −1.07094 | ||||||||
\(411\) | −1.39340e66 | −0.309820 | ||||||||
\(412\) | −9.57750e65 | −0.200158 | ||||||||
\(413\) | −3.82166e66 | −0.750803 | ||||||||
\(414\) | −4.76435e66 | −0.880025 | ||||||||
\(415\) | 5.20463e66 | 0.903990 | ||||||||
\(416\) | 6.02654e65 | 0.0984438 | ||||||||
\(417\) | 1.51456e66 | 0.232711 | ||||||||
\(418\) | 3.75500e66 | 0.542769 | ||||||||
\(419\) | −1.14203e67 | −1.55317 | −0.776585 | − | 0.630013i | \(-0.783050\pi\) | ||||
−0.776585 | + | 0.630013i | \(0.783050\pi\) | |||||||
\(420\) | −1.06603e66 | −0.136430 | ||||||||
\(421\) | 6.12212e66 | 0.737409 | 0.368705 | − | 0.929547i | \(-0.379801\pi\) | ||||
0.368705 | + | 0.929547i | \(0.379801\pi\) | |||||||
\(422\) | 6.64610e66 | 0.753528 | ||||||||
\(423\) | −1.04854e67 | −1.11920 | ||||||||
\(424\) | −3.45882e66 | −0.347615 | ||||||||
\(425\) | 1.54033e66 | 0.145779 | ||||||||
\(426\) | −1.73589e66 | −0.154731 | ||||||||
\(427\) | 1.31726e67 | 1.10602 | ||||||||
\(428\) | −2.73446e66 | −0.216299 | ||||||||
\(429\) | −1.02587e66 | −0.0764591 | ||||||||
\(430\) | 1.28915e67 | 0.905434 | ||||||||
\(431\) | 1.51854e67 | 1.00521 | 0.502604 | − | 0.864517i | \(-0.332375\pi\) | ||||
0.502604 | + | 0.864517i | \(0.332375\pi\) | |||||||
\(432\) | −1.45321e66 | −0.0906764 | ||||||||
\(433\) | 1.75181e66 | 0.103050 | 0.0515248 | − | 0.998672i | \(-0.483592\pi\) | ||||
0.0515248 | + | 0.998672i | \(0.483592\pi\) | |||||||
\(434\) | 1.57867e67 | 0.875597 | ||||||||
\(435\) | −9.64393e65 | −0.0504404 | ||||||||
\(436\) | 1.09222e67 | 0.538770 | ||||||||
\(437\) | −2.85607e67 | −1.32890 | ||||||||
\(438\) | 2.18538e66 | 0.0959264 | ||||||||
\(439\) | 1.63861e66 | 0.0678626 | 0.0339313 | − | 0.999424i | \(-0.489197\pi\) | ||||
0.0339313 | + | 0.999424i | \(0.489197\pi\) | |||||||
\(440\) | −5.96081e66 | −0.232949 | ||||||||
\(441\) | −4.68948e67 | −1.72958 | ||||||||
\(442\) | −7.62921e66 | −0.265590 | ||||||||
\(443\) | 2.54855e67 | 0.837526 | 0.418763 | − | 0.908095i | \(-0.362464\pi\) | ||||
0.418763 | + | 0.908095i | \(0.362464\pi\) | |||||||
\(444\) | −5.23609e66 | −0.162458 | ||||||||
\(445\) | −3.28539e67 | −0.962514 | ||||||||
\(446\) | −3.52882e67 | −0.976316 | ||||||||
\(447\) | 3.83087e66 | 0.100105 | ||||||||
\(448\) | −8.45945e66 | −0.208811 | ||||||||
\(449\) | 3.94691e66 | 0.0920398 | 0.0460199 | − | 0.998941i | \(-0.485346\pi\) | ||||
0.0460199 | + | 0.998941i | \(0.485346\pi\) | |||||||
\(450\) | 6.70035e66 | 0.147631 | ||||||||
\(451\) | 6.11435e67 | 1.27306 | ||||||||
\(452\) | 2.61855e67 | 0.515265 | ||||||||
\(453\) | 3.27779e66 | 0.0609645 | ||||||||
\(454\) | −7.79521e66 | −0.137058 | ||||||||
\(455\) | −4.95469e67 | −0.823618 | ||||||||
\(456\) | −4.28036e66 | −0.0672786 | ||||||||
\(457\) | 9.44235e67 | 1.40351 | 0.701757 | − | 0.712416i | \(-0.252399\pi\) | ||||
0.701757 | + | 0.712416i | \(0.252399\pi\) | |||||||
\(458\) | −6.98947e67 | −0.982595 | ||||||||
\(459\) | 1.83967e67 | 0.244634 | ||||||||
\(460\) | 4.53381e67 | 0.570347 | ||||||||
\(461\) | 6.24242e67 | 0.742984 | 0.371492 | − | 0.928436i | \(-0.378846\pi\) | ||||
0.371492 | + | 0.928436i | \(0.378846\pi\) | |||||||
\(462\) | 1.44001e67 | 0.162179 | ||||||||
\(463\) | 1.16253e68 | 1.23905 | 0.619525 | − | 0.784977i | \(-0.287325\pi\) | ||||
0.619525 | + | 0.784977i | \(0.287325\pi\) | |||||||
\(464\) | −7.65294e66 | −0.0772004 | ||||||||
\(465\) | −1.26802e67 | −0.121081 | ||||||||
\(466\) | −7.30909e67 | −0.660727 | ||||||||
\(467\) | 3.38070e67 | 0.289352 | 0.144676 | − | 0.989479i | \(-0.453786\pi\) | ||||
0.144676 | + | 0.989479i | \(0.453786\pi\) | |||||||
\(468\) | −3.31866e67 | −0.268964 | ||||||||
\(469\) | −3.32632e68 | −2.55303 | ||||||||
\(470\) | 9.97806e67 | 0.725355 | ||||||||
\(471\) | 3.11896e67 | 0.214772 | ||||||||
\(472\) | 2.43590e67 | 0.158905 | ||||||||
\(473\) | −1.74140e68 | −1.07631 | ||||||||
\(474\) | 1.11465e67 | 0.0652818 | ||||||||
\(475\) | 4.01664e67 | 0.222934 | ||||||||
\(476\) | 1.07091e68 | 0.563347 | ||||||||
\(477\) | 1.90468e68 | 0.949738 | ||||||||
\(478\) | −3.39196e66 | −0.0160339 | ||||||||
\(479\) | −2.32823e68 | −1.04345 | −0.521724 | − | 0.853115i | \(-0.674711\pi\) | ||||
−0.521724 | + | 0.853115i | \(0.674711\pi\) | |||||||
\(480\) | 6.79477e66 | 0.0288751 | ||||||||
\(481\) | −2.43363e68 | −0.980745 | ||||||||
\(482\) | −1.83410e67 | −0.0701010 | ||||||||
\(483\) | −1.09527e68 | −0.397074 | ||||||||
\(484\) | −6.48679e67 | −0.223086 | ||||||||
\(485\) | 3.50689e68 | 1.14422 | ||||||||
\(486\) | 1.20730e68 | 0.373757 | ||||||||
\(487\) | 5.88848e67 | 0.172988 | 0.0864938 | − | 0.996252i | \(-0.472434\pi\) | ||||
0.0864938 | + | 0.996252i | \(0.472434\pi\) | |||||||
\(488\) | −8.39614e67 | −0.234085 | ||||||||
\(489\) | −7.00877e67 | −0.185467 | ||||||||
\(490\) | 4.46257e68 | 1.12095 | ||||||||
\(491\) | −2.11706e68 | −0.504841 | −0.252420 | − | 0.967618i | \(-0.581227\pi\) | ||||
−0.252420 | + | 0.967618i | \(0.581227\pi\) | |||||||
\(492\) | −6.96980e67 | −0.157801 | ||||||||
\(493\) | 9.68812e67 | 0.208278 | ||||||||
\(494\) | −1.98943e68 | −0.406155 | ||||||||
\(495\) | 3.28246e68 | 0.636454 | ||||||||
\(496\) | −1.00623e68 | −0.185317 | ||||||||
\(497\) | 1.13251e69 | 1.98132 | ||||||||
\(498\) | 8.01413e67 | 0.133201 | ||||||||
\(499\) | −4.72866e67 | −0.0746748 | −0.0373374 | − | 0.999303i | \(-0.511888\pi\) | ||||
−0.0373374 | + | 0.999303i | \(0.511888\pi\) | |||||||
\(500\) | −3.58763e68 | −0.538360 | ||||||||
\(501\) | 6.80659e67 | 0.0970661 | ||||||||
\(502\) | −1.17673e68 | −0.159489 | ||||||||
\(503\) | −3.67158e68 | −0.473009 | −0.236505 | − | 0.971630i | \(-0.576002\pi\) | ||||
−0.236505 | + | 0.971630i | \(0.576002\pi\) | |||||||
\(504\) | 4.65840e68 | 0.570503 | ||||||||
\(505\) | −8.93594e68 | −1.04042 | ||||||||
\(506\) | −6.12435e68 | −0.677988 | ||||||||
\(507\) | −1.20908e68 | −0.127278 | ||||||||
\(508\) | −9.06221e68 | −0.907213 | ||||||||
\(509\) | 1.22746e69 | 1.16870 | 0.584351 | − | 0.811501i | \(-0.301349\pi\) | ||||
0.584351 | + | 0.811501i | \(0.301349\pi\) | |||||||
\(510\) | −8.60173e67 | −0.0779016 | ||||||||
\(511\) | −1.42577e69 | −1.22834 | ||||||||
\(512\) | 5.39199e67 | 0.0441942 | ||||||||
\(513\) | 4.79722e68 | 0.374108 | ||||||||
\(514\) | −1.69596e69 | −1.25851 | ||||||||
\(515\) | −5.01888e68 | −0.354424 | ||||||||
\(516\) | 1.98504e68 | 0.133414 | ||||||||
\(517\) | −1.34785e69 | −0.862250 | ||||||||
\(518\) | 3.41609e69 | 2.08027 | ||||||||
\(519\) | 3.94971e68 | 0.228980 | ||||||||
\(520\) | 3.15808e68 | 0.174316 | ||||||||
\(521\) | 2.83740e69 | 1.49128 | 0.745640 | − | 0.666349i | \(-0.232144\pi\) | ||||
0.745640 | + | 0.666349i | \(0.232144\pi\) | |||||||
\(522\) | 4.21428e68 | 0.210924 | ||||||||
\(523\) | −1.04293e69 | −0.497122 | −0.248561 | − | 0.968616i | \(-0.579958\pi\) | ||||
−0.248561 | + | 0.968616i | \(0.579958\pi\) | |||||||
\(524\) | 4.15264e68 | 0.188528 | ||||||||
\(525\) | 1.54034e68 | 0.0666124 | ||||||||
\(526\) | 4.86445e68 | 0.200400 | ||||||||
\(527\) | 1.27383e69 | 0.499965 | ||||||||
\(528\) | −9.17849e67 | −0.0343246 | ||||||||
\(529\) | 1.85200e69 | 0.659966 | ||||||||
\(530\) | −1.81252e69 | −0.615529 | ||||||||
\(531\) | −1.34138e69 | −0.434153 | ||||||||
\(532\) | 2.79256e69 | 0.861501 | ||||||||
\(533\) | −3.23943e69 | −0.952632 | ||||||||
\(534\) | −5.05887e68 | −0.141825 | ||||||||
\(535\) | −1.43293e69 | −0.383005 | ||||||||
\(536\) | 2.12017e69 | 0.540342 | ||||||||
\(537\) | −5.08304e68 | −0.123532 | ||||||||
\(538\) | −4.50414e68 | −0.104391 | ||||||||
\(539\) | −6.02810e69 | −1.33250 | ||||||||
\(540\) | −7.61526e68 | −0.160562 | ||||||||
\(541\) | −1.50880e69 | −0.303459 | −0.151730 | − | 0.988422i | \(-0.548484\pi\) | ||||
−0.151730 | + | 0.988422i | \(0.548484\pi\) | |||||||
\(542\) | −2.83729e69 | −0.544405 | ||||||||
\(543\) | 9.55317e68 | 0.174885 | ||||||||
\(544\) | −6.82590e68 | −0.119231 | ||||||||
\(545\) | 5.72352e69 | 0.954009 | ||||||||
\(546\) | −7.62926e68 | −0.121358 | ||||||||
\(547\) | 4.40510e69 | 0.668773 | 0.334387 | − | 0.942436i | \(-0.391471\pi\) | ||||
0.334387 | + | 0.942436i | \(0.391471\pi\) | |||||||
\(548\) | −5.79435e69 | −0.839654 | ||||||||
\(549\) | 4.62354e69 | 0.639557 | ||||||||
\(550\) | 8.61299e68 | 0.113738 | ||||||||
\(551\) | 2.52632e69 | 0.318510 | ||||||||
\(552\) | 6.98120e68 | 0.0840395 | ||||||||
\(553\) | −7.27214e69 | −0.835933 | ||||||||
\(554\) | −6.57681e69 | −0.721965 | ||||||||
\(555\) | −2.74386e69 | −0.287668 | ||||||||
\(556\) | 6.29817e69 | 0.630678 | ||||||||
\(557\) | 2.55341e69 | 0.244238 | 0.122119 | − | 0.992515i | \(-0.461031\pi\) | ||||
0.122119 | + | 0.992515i | \(0.461031\pi\) | |||||||
\(558\) | 5.54107e69 | 0.506316 | ||||||||
\(559\) | 9.22607e69 | 0.805407 | ||||||||
\(560\) | −4.43299e69 | −0.369745 | ||||||||
\(561\) | 1.16194e69 | 0.0926039 | ||||||||
\(562\) | −7.69325e68 | −0.0585914 | ||||||||
\(563\) | 2.20159e70 | 1.60240 | 0.801201 | − | 0.598395i | \(-0.204195\pi\) | ||||
0.801201 | + | 0.598395i | \(0.204195\pi\) | |||||||
\(564\) | 1.53643e69 | 0.106880 | ||||||||
\(565\) | 1.37220e70 | 0.912390 | ||||||||
\(566\) | −9.82338e68 | −0.0624370 | ||||||||
\(567\) | −2.47168e70 | −1.50184 | ||||||||
\(568\) | −7.21855e69 | −0.419341 | ||||||||
\(569\) | −2.89847e70 | −1.60993 | −0.804965 | − | 0.593323i | \(-0.797816\pi\) | ||||
−0.804965 | + | 0.593323i | \(0.797816\pi\) | |||||||
\(570\) | −2.24303e69 | −0.119131 | ||||||||
\(571\) | 1.91490e70 | 0.972581 | 0.486291 | − | 0.873797i | \(-0.338350\pi\) | ||||
0.486291 | + | 0.873797i | \(0.338350\pi\) | |||||||
\(572\) | −4.26598e69 | −0.207215 | ||||||||
\(573\) | −2.04298e69 | −0.0949120 | ||||||||
\(574\) | 4.54719e70 | 2.02064 | ||||||||
\(575\) | −6.55108e69 | −0.278473 | ||||||||
\(576\) | −2.96923e69 | −0.120745 | ||||||||
\(577\) | −3.95868e70 | −1.54017 | −0.770083 | − | 0.637944i | \(-0.779785\pi\) | ||||
−0.770083 | + | 0.637944i | \(0.779785\pi\) | |||||||
\(578\) | −1.03541e70 | −0.385436 | ||||||||
\(579\) | −1.05665e69 | −0.0376381 | ||||||||
\(580\) | −4.01036e69 | −0.136700 | ||||||||
\(581\) | −5.22851e70 | −1.70564 | ||||||||
\(582\) | 5.39994e69 | 0.168598 | ||||||||
\(583\) | 2.44838e70 | 0.731696 | ||||||||
\(584\) | 9.08776e69 | 0.259973 | ||||||||
\(585\) | −1.73907e70 | −0.476259 | ||||||||
\(586\) | −1.47376e70 | −0.386401 | ||||||||
\(587\) | 1.26116e70 | 0.316592 | 0.158296 | − | 0.987392i | \(-0.449400\pi\) | ||||
0.158296 | + | 0.987392i | \(0.449400\pi\) | |||||||
\(588\) | 6.87149e69 | 0.165169 | ||||||||
\(589\) | 3.32169e70 | 0.764574 | ||||||||
\(590\) | 1.27648e70 | 0.281376 | ||||||||
\(591\) | 1.50307e69 | 0.0317320 | ||||||||
\(592\) | −2.17739e70 | −0.440284 | ||||||||
\(593\) | 5.89249e70 | 1.14131 | 0.570656 | − | 0.821189i | \(-0.306689\pi\) | ||||
0.570656 | + | 0.821189i | \(0.306689\pi\) | |||||||
\(594\) | 1.02868e70 | 0.190865 | ||||||||
\(595\) | 5.61188e70 | 0.997529 | ||||||||
\(596\) | 1.59304e70 | 0.271298 | ||||||||
\(597\) | −3.77790e69 | −0.0616460 | ||||||||
\(598\) | 3.24473e70 | 0.507339 | ||||||||
\(599\) | 5.88782e70 | 0.882208 | 0.441104 | − | 0.897456i | \(-0.354587\pi\) | ||||
0.441104 | + | 0.897456i | \(0.354587\pi\) | |||||||
\(600\) | −9.81802e68 | −0.0140983 | ||||||||
\(601\) | 3.71667e70 | 0.511511 | 0.255755 | − | 0.966742i | \(-0.417676\pi\) | ||||
0.255755 | + | 0.966742i | \(0.417676\pi\) | |||||||
\(602\) | −1.29506e71 | −1.70836 | ||||||||
\(603\) | −1.16752e71 | −1.47630 | ||||||||
\(604\) | 1.36304e70 | 0.165222 | ||||||||
\(605\) | −3.39926e70 | −0.395023 | ||||||||
\(606\) | −1.37596e70 | −0.153304 | ||||||||
\(607\) | −1.80800e70 | −0.193146 | −0.0965731 | − | 0.995326i | \(-0.530788\pi\) | ||||
−0.0965731 | + | 0.995326i | \(0.530788\pi\) | |||||||
\(608\) | −1.77996e70 | −0.182334 | ||||||||
\(609\) | 9.68819e69 | 0.0951703 | ||||||||
\(610\) | −4.39982e70 | −0.414499 | ||||||||
\(611\) | 7.14102e70 | 0.645222 | ||||||||
\(612\) | 3.75885e70 | 0.325757 | ||||||||
\(613\) | −1.17454e71 | −0.976397 | −0.488198 | − | 0.872733i | \(-0.662346\pi\) | ||||
−0.488198 | + | 0.872733i | \(0.662346\pi\) | |||||||
\(614\) | −8.00997e70 | −0.638759 | ||||||||
\(615\) | −3.65238e70 | −0.279422 | ||||||||
\(616\) | 5.98816e70 | 0.439526 | ||||||||
\(617\) | 6.20543e70 | 0.437019 | 0.218509 | − | 0.975835i | \(-0.429881\pi\) | ||||
0.218509 | + | 0.975835i | \(0.429881\pi\) | |||||||
\(618\) | −7.72811e69 | −0.0522236 | ||||||||
\(619\) | −8.66432e70 | −0.561853 | −0.280927 | − | 0.959729i | \(-0.590642\pi\) | ||||
−0.280927 | + | 0.959729i | \(0.590642\pi\) | |||||||
\(620\) | −5.27295e70 | −0.328145 | ||||||||
\(621\) | −7.82419e70 | −0.467308 | ||||||||
\(622\) | 1.64396e71 | 0.942402 | ||||||||
\(623\) | 3.30047e71 | 1.81606 | ||||||||
\(624\) | 4.86283e69 | 0.0256852 | ||||||||
\(625\) | −1.45376e71 | −0.737145 | ||||||||
\(626\) | −3.74148e70 | −0.182137 | ||||||||
\(627\) | 3.02992e70 | 0.141615 | ||||||||
\(628\) | 1.29700e71 | 0.582060 | ||||||||
\(629\) | 2.75643e71 | 1.18783 | ||||||||
\(630\) | 2.44113e71 | 1.01020 | ||||||||
\(631\) | −4.75034e71 | −1.88789 | −0.943944 | − | 0.330107i | \(-0.892915\pi\) | ||||
−0.943944 | + | 0.330107i | \(0.892915\pi\) | |||||||
\(632\) | 4.63521e70 | 0.176923 | ||||||||
\(633\) | 5.36276e70 | 0.196604 | ||||||||
\(634\) | −8.22940e70 | −0.289796 | ||||||||
\(635\) | −4.74885e71 | −1.60642 | ||||||||
\(636\) | −2.79093e70 | −0.0906969 | ||||||||
\(637\) | 3.19374e71 | 0.997111 | ||||||||
\(638\) | 5.41726e70 | 0.162499 | ||||||||
\(639\) | 3.97507e71 | 1.14570 | ||||||||
\(640\) | 2.82556e70 | 0.0782554 | ||||||||
\(641\) | 3.18961e71 | 0.848904 | 0.424452 | − | 0.905450i | \(-0.360467\pi\) | ||||
0.424452 | + | 0.905450i | \(0.360467\pi\) | |||||||
\(642\) | −2.20644e70 | −0.0564351 | ||||||||
\(643\) | −3.61532e71 | −0.888724 | −0.444362 | − | 0.895847i | \(-0.646570\pi\) | ||||
−0.444362 | + | 0.895847i | \(0.646570\pi\) | |||||||
\(644\) | −4.55462e71 | −1.07612 | ||||||||
\(645\) | 1.04022e71 | 0.236238 | ||||||||
\(646\) | 2.25331e71 | 0.491916 | ||||||||
\(647\) | −8.45895e71 | −1.77524 | −0.887621 | − | 0.460575i | \(-0.847643\pi\) | ||||
−0.887621 | + | 0.460575i | \(0.847643\pi\) | |||||||
\(648\) | 1.57543e71 | 0.317861 | ||||||||
\(649\) | −1.72429e71 | −0.334480 | ||||||||
\(650\) | −4.56323e70 | −0.0851102 | ||||||||
\(651\) | 1.27384e71 | 0.228454 | ||||||||
\(652\) | −2.91454e71 | −0.502640 | ||||||||
\(653\) | 2.78198e71 | 0.461389 | 0.230695 | − | 0.973026i | \(-0.425900\pi\) | ||||
0.230695 | + | 0.973026i | \(0.425900\pi\) | |||||||
\(654\) | 8.81312e70 | 0.140571 | ||||||||
\(655\) | 2.17610e71 | 0.333830 | ||||||||
\(656\) | −2.89834e71 | −0.427663 | ||||||||
\(657\) | −5.00439e71 | −0.710288 | ||||||||
\(658\) | −1.00238e72 | −1.36859 | ||||||||
\(659\) | 1.17155e72 | 1.53881 | 0.769404 | − | 0.638762i | \(-0.220553\pi\) | ||||
0.769404 | + | 0.638762i | \(0.220553\pi\) | |||||||
\(660\) | −4.80979e70 | −0.0607793 | ||||||||
\(661\) | 3.69963e70 | 0.0449802 | 0.0224901 | − | 0.999747i | \(-0.492841\pi\) | ||||
0.0224901 | + | 0.999747i | \(0.492841\pi\) | |||||||
\(662\) | −5.11771e71 | −0.598683 | ||||||||
\(663\) | −6.15602e70 | −0.0692956 | ||||||||
\(664\) | 3.33261e71 | 0.360993 | ||||||||
\(665\) | 1.46338e72 | 1.52548 | ||||||||
\(666\) | 1.19903e72 | 1.20292 | ||||||||
\(667\) | −4.12039e71 | −0.397859 | ||||||||
\(668\) | 2.83047e71 | 0.263062 | ||||||||
\(669\) | −2.84741e71 | −0.254732 | ||||||||
\(670\) | 1.11103e72 | 0.956794 | ||||||||
\(671\) | 5.94334e71 | 0.492727 | ||||||||
\(672\) | −6.82595e70 | −0.0544812 | ||||||||
\(673\) | −8.02511e71 | −0.616690 | −0.308345 | − | 0.951275i | \(-0.599775\pi\) | ||||
−0.308345 | + | 0.951275i | \(0.599775\pi\) | |||||||
\(674\) | −7.26951e71 | −0.537870 | ||||||||
\(675\) | 1.10036e71 | 0.0783948 | ||||||||
\(676\) | −5.02789e71 | −0.344941 | ||||||||
\(677\) | 2.75308e72 | 1.81890 | 0.909448 | − | 0.415817i | \(-0.136504\pi\) | ||||
0.909448 | + | 0.415817i | \(0.136504\pi\) | |||||||
\(678\) | 2.11291e71 | 0.134439 | ||||||||
\(679\) | −3.52299e72 | −2.15890 | ||||||||
\(680\) | −3.57697e71 | −0.211124 | ||||||||
\(681\) | −6.28997e70 | −0.0357600 | ||||||||
\(682\) | 7.12279e71 | 0.390075 | ||||||||
\(683\) | −7.59014e71 | −0.400426 | −0.200213 | − | 0.979752i | \(-0.564163\pi\) | ||||
−0.200213 | + | 0.979752i | \(0.564163\pi\) | |||||||
\(684\) | 9.80176e71 | 0.498165 | ||||||||
\(685\) | −3.03640e72 | −1.48679 | ||||||||
\(686\) | −1.97928e72 | −0.933776 | ||||||||
\(687\) | −5.63982e71 | −0.256371 | ||||||||
\(688\) | 8.25462e71 | 0.361570 | ||||||||
\(689\) | −1.29717e72 | −0.547529 | ||||||||
\(690\) | 3.65835e71 | 0.148810 | ||||||||
\(691\) | 2.56440e71 | 0.100530 | 0.0502651 | − | 0.998736i | \(-0.483993\pi\) | ||||
0.0502651 | + | 0.998736i | \(0.483993\pi\) | |||||||
\(692\) | 1.64246e72 | 0.620568 | ||||||||
\(693\) | −3.29752e72 | −1.20085 | ||||||||
\(694\) | 1.77828e72 | 0.624216 | ||||||||
\(695\) | 3.30042e72 | 1.11675 | ||||||||
\(696\) | −6.17518e70 | −0.0201425 | ||||||||
\(697\) | 3.66911e72 | 1.15378 | ||||||||
\(698\) | −3.36092e72 | −1.01893 | ||||||||
\(699\) | −5.89772e71 | −0.172392 | ||||||||
\(700\) | 6.40540e71 | 0.180529 | ||||||||
\(701\) | −2.26409e72 | −0.615295 | −0.307647 | − | 0.951500i | \(-0.599542\pi\) | ||||
−0.307647 | + | 0.951500i | \(0.599542\pi\) | |||||||
\(702\) | −5.45003e71 | −0.142824 | ||||||||
\(703\) | 7.18781e72 | 1.81650 | ||||||||
\(704\) | −3.81681e71 | −0.0930245 | ||||||||
\(705\) | 8.05132e71 | 0.189254 | ||||||||
\(706\) | 2.02636e72 | 0.459407 | ||||||||
\(707\) | 8.97694e72 | 1.96306 | ||||||||
\(708\) | 1.96553e71 | 0.0414602 | ||||||||
\(709\) | −1.99310e72 | −0.405555 | −0.202778 | − | 0.979225i | \(-0.564997\pi\) | ||||
−0.202778 | + | 0.979225i | \(0.564997\pi\) | |||||||
\(710\) | −3.78273e72 | −0.742535 | ||||||||
\(711\) | −2.55249e72 | −0.483380 | ||||||||
\(712\) | −2.10369e72 | −0.384364 | ||||||||
\(713\) | −5.41763e72 | −0.955050 | ||||||||
\(714\) | 8.64120e71 | 0.146984 | ||||||||
\(715\) | −2.23550e72 | −0.366919 | ||||||||
\(716\) | −2.11374e72 | −0.334788 | ||||||||
\(717\) | −2.73698e70 | −0.00418344 | ||||||||
\(718\) | −2.35401e72 | −0.347244 | ||||||||
\(719\) | 3.49023e72 | 0.496899 | 0.248449 | − | 0.968645i | \(-0.420079\pi\) | ||||
0.248449 | + | 0.968645i | \(0.420079\pi\) | |||||||
\(720\) | −1.55596e72 | −0.213806 | ||||||||
\(721\) | 5.04191e72 | 0.668723 | ||||||||
\(722\) | 3.52726e71 | 0.0451584 | ||||||||
\(723\) | −1.47994e71 | −0.0182902 | ||||||||
\(724\) | 3.97262e72 | 0.473962 | ||||||||
\(725\) | 5.79472e71 | 0.0667441 | ||||||||
\(726\) | −5.23420e71 | −0.0582059 | ||||||||
\(727\) | −4.54890e72 | −0.488403 | −0.244202 | − | 0.969724i | \(-0.578526\pi\) | ||||
−0.244202 | + | 0.969724i | \(0.578526\pi\) | |||||||
\(728\) | −3.17257e72 | −0.328898 | ||||||||
\(729\) | −8.00702e72 | −0.801528 | ||||||||
\(730\) | 4.76224e72 | 0.460340 | ||||||||
\(731\) | −1.04498e73 | −0.975473 | ||||||||
\(732\) | −6.77486e71 | −0.0610756 | ||||||||
\(733\) | −1.23171e72 | −0.107240 | −0.0536202 | − | 0.998561i | \(-0.517076\pi\) | ||||
−0.0536202 | + | 0.998561i | \(0.517076\pi\) | |||||||
\(734\) | −3.96758e72 | −0.333639 | ||||||||
\(735\) | 3.60086e72 | 0.292468 | ||||||||
\(736\) | 2.90308e72 | 0.227758 | ||||||||
\(737\) | −1.50080e73 | −1.13737 | ||||||||
\(738\) | 1.59604e73 | 1.16844 | ||||||||
\(739\) | 2.26780e73 | 1.60388 | 0.801940 | − | 0.597404i | \(-0.203801\pi\) | ||||
0.801940 | + | 0.597404i | \(0.203801\pi\) | |||||||
\(740\) | −1.14101e73 | −0.779618 | ||||||||
\(741\) | −1.60528e72 | −0.105971 | ||||||||
\(742\) | 1.82084e73 | 1.16137 | ||||||||
\(743\) | 2.66153e72 | 0.164028 | 0.0820138 | − | 0.996631i | \(-0.473865\pi\) | ||||
0.0820138 | + | 0.996631i | \(0.473865\pi\) | |||||||
\(744\) | −8.11933e71 | −0.0483515 | ||||||||
\(745\) | 8.34797e72 | 0.480392 | ||||||||
\(746\) | 2.41638e72 | 0.134377 | ||||||||
\(747\) | −1.83518e73 | −0.986289 | ||||||||
\(748\) | 4.83182e72 | 0.250969 | ||||||||
\(749\) | 1.43951e73 | 0.722651 | ||||||||
\(750\) | −2.89487e72 | −0.140465 | ||||||||
\(751\) | 2.46245e72 | 0.115491 | 0.0577457 | − | 0.998331i | \(-0.481609\pi\) | ||||
0.0577457 | + | 0.998331i | \(0.481609\pi\) | |||||||
\(752\) | 6.38912e72 | 0.289658 | ||||||||
\(753\) | −9.49502e71 | −0.0416125 | ||||||||
\(754\) | −2.87010e72 | −0.121598 | ||||||||
\(755\) | 7.14274e72 | 0.292562 | ||||||||
\(756\) | 7.65020e72 | 0.302947 | ||||||||
\(757\) | 1.10950e73 | 0.424796 | 0.212398 | − | 0.977183i | \(-0.431873\pi\) | ||||
0.212398 | + | 0.977183i | \(0.431873\pi\) | |||||||
\(758\) | −2.16048e73 | −0.799809 | ||||||||
\(759\) | −4.94175e72 | −0.176895 | ||||||||
\(760\) | −9.32748e72 | −0.322862 | ||||||||
\(761\) | −9.14926e72 | −0.306251 | −0.153125 | − | 0.988207i | \(-0.548934\pi\) | ||||
−0.153125 | + | 0.988207i | \(0.548934\pi\) | |||||||
\(762\) | −7.31232e72 | −0.236703 | ||||||||
\(763\) | −5.74979e73 | −1.80001 | ||||||||
\(764\) | −8.49557e72 | −0.257224 | ||||||||
\(765\) | 1.96974e73 | 0.576823 | ||||||||
\(766\) | −3.41886e73 | −0.968384 | ||||||||
\(767\) | 9.13541e72 | 0.250292 | ||||||||
\(768\) | 4.35081e71 | 0.0115308 | ||||||||
\(769\) | −3.24419e72 | −0.0831735 | −0.0415867 | − | 0.999135i | \(-0.513241\pi\) | ||||
−0.0415867 | + | 0.999135i | \(0.513241\pi\) | |||||||
\(770\) | 3.13796e73 | 0.778278 | ||||||||
\(771\) | −1.36847e73 | −0.328360 | ||||||||
\(772\) | −4.39399e72 | −0.102004 | ||||||||
\(773\) | −9.02670e72 | −0.202746 | −0.101373 | − | 0.994849i | \(-0.532324\pi\) | ||||
−0.101373 | + | 0.994849i | \(0.532324\pi\) | |||||||
\(774\) | −4.54561e73 | −0.987865 | ||||||||
\(775\) | 7.61909e72 | 0.160217 | ||||||||
\(776\) | 2.24552e73 | 0.456924 | ||||||||
\(777\) | 2.75645e73 | 0.542768 | ||||||||
\(778\) | 1.02858e73 | 0.196001 | ||||||||
\(779\) | 9.56775e73 | 1.76443 | ||||||||
\(780\) | 2.54826e72 | 0.0454812 | ||||||||
\(781\) | 5.10976e73 | 0.882672 | ||||||||
\(782\) | −3.67511e73 | −0.614466 | ||||||||
\(783\) | 6.92084e72 | 0.112004 | ||||||||
\(784\) | 2.85746e73 | 0.447631 | ||||||||
\(785\) | 6.79663e73 | 1.03066 | ||||||||
\(786\) | 3.35077e72 | 0.0491892 | ||||||||
\(787\) | −8.00870e73 | −1.13817 | −0.569084 | − | 0.822279i | \(-0.692702\pi\) | ||||
−0.569084 | + | 0.822279i | \(0.692702\pi\) | |||||||
\(788\) | 6.25040e72 | 0.0859981 | ||||||||
\(789\) | 3.92513e72 | 0.0522867 | ||||||||
\(790\) | 2.42898e73 | 0.313280 | ||||||||
\(791\) | −1.37849e74 | −1.72149 | ||||||||
\(792\) | 2.10182e73 | 0.254157 | ||||||||
\(793\) | −3.14883e73 | −0.368708 | ||||||||
\(794\) | 1.20978e74 | 1.37178 | ||||||||
\(795\) | −1.46253e73 | −0.160599 | ||||||||
\(796\) | −1.57101e73 | −0.167069 | ||||||||
\(797\) | −9.52170e72 | −0.0980680 | −0.0490340 | − | 0.998797i | \(-0.515614\pi\) | ||||
−0.0490340 | + | 0.998797i | \(0.515614\pi\) | |||||||
\(798\) | 2.25332e73 | 0.224776 | ||||||||
\(799\) | −8.08820e73 | −0.781464 | ||||||||
\(800\) | −4.08275e72 | −0.0382084 | ||||||||
\(801\) | 1.15845e74 | 1.05014 | ||||||||
\(802\) | −1.35839e74 | −1.19283 | ||||||||
\(803\) | −6.43291e73 | −0.547219 | ||||||||
\(804\) | 1.71077e73 | 0.140982 | ||||||||
\(805\) | −2.38675e74 | −1.90551 | ||||||||
\(806\) | −3.77371e73 | −0.291894 | ||||||||
\(807\) | −3.63440e72 | −0.0272369 | ||||||||
\(808\) | −5.72183e73 | −0.415476 | ||||||||
\(809\) | 2.01261e74 | 1.41603 | 0.708016 | − | 0.706197i | \(-0.249591\pi\) | ||||
0.708016 | + | 0.706197i | \(0.249591\pi\) | |||||||
\(810\) | 8.25571e73 | 0.562842 | ||||||||
\(811\) | 1.25620e74 | 0.829900 | 0.414950 | − | 0.909844i | \(-0.363799\pi\) | ||||
0.414950 | + | 0.909844i | \(0.363799\pi\) | |||||||
\(812\) | 4.02876e73 | 0.257925 | ||||||||
\(813\) | −2.28942e73 | −0.142042 | ||||||||
\(814\) | 1.54130e74 | 0.926755 | ||||||||
\(815\) | −1.52730e74 | −0.890034 | ||||||||
\(816\) | −5.50784e72 | −0.0311087 | ||||||||
\(817\) | −2.72494e74 | −1.49175 | ||||||||
\(818\) | −9.26577e72 | −0.0491668 | ||||||||
\(819\) | 1.74705e74 | 0.898600 | ||||||||
\(820\) | −1.51881e74 | −0.757271 | ||||||||
\(821\) | 1.17682e74 | 0.568799 | 0.284400 | − | 0.958706i | \(-0.408206\pi\) | ||||
0.284400 | + | 0.958706i | \(0.408206\pi\) | |||||||
\(822\) | −4.67547e73 | −0.219076 | ||||||||
\(823\) | 4.09028e74 | 1.85805 | 0.929025 | − | 0.370018i | \(-0.120649\pi\) | ||||
0.929025 | + | 0.370018i | \(0.120649\pi\) | |||||||
\(824\) | −3.21368e73 | −0.141533 | ||||||||
\(825\) | 6.94984e72 | 0.0296756 | ||||||||
\(826\) | −1.28234e74 | −0.530898 | ||||||||
\(827\) | −2.32690e73 | −0.0934086 | −0.0467043 | − | 0.998909i | \(-0.514872\pi\) | ||||
−0.0467043 | + | 0.998909i | \(0.514872\pi\) | |||||||
\(828\) | −1.59865e74 | −0.622271 | ||||||||
\(829\) | 4.64969e74 | 1.75503 | 0.877513 | − | 0.479553i | \(-0.159201\pi\) | ||||
0.877513 | + | 0.479553i | \(0.159201\pi\) | |||||||
\(830\) | 1.74638e74 | 0.639217 | ||||||||
\(831\) | −5.30684e73 | −0.188369 | ||||||||
\(832\) | 2.02217e73 | 0.0696103 | ||||||||
\(833\) | −3.61735e74 | −1.20766 | ||||||||
\(834\) | 5.08201e73 | 0.164551 | ||||||||
\(835\) | 1.48325e74 | 0.465810 | ||||||||
\(836\) | 1.25997e74 | 0.383796 | ||||||||
\(837\) | 9.09975e73 | 0.268863 | ||||||||
\(838\) | −3.83201e74 | −1.09826 | ||||||||
\(839\) | 1.05353e74 | 0.292898 | 0.146449 | − | 0.989218i | \(-0.453216\pi\) | ||||
0.146449 | + | 0.989218i | \(0.453216\pi\) | |||||||
\(840\) | −3.57699e73 | −0.0964709 | ||||||||
\(841\) | −3.45760e74 | −0.904641 | ||||||||
\(842\) | 2.05424e74 | 0.521427 | ||||||||
\(843\) | −6.20770e72 | −0.0152872 | ||||||||
\(844\) | 2.23006e74 | 0.532825 | ||||||||
\(845\) | −2.63476e74 | −0.610793 | ||||||||
\(846\) | −3.51832e74 | −0.791391 | ||||||||
\(847\) | 3.41486e74 | 0.745325 | ||||||||
\(848\) | −1.16059e74 | −0.245801 | ||||||||
\(849\) | −7.92651e72 | −0.0162906 | ||||||||
\(850\) | 5.16849e73 | 0.103082 | ||||||||
\(851\) | −1.17232e75 | −2.26904 | ||||||||
\(852\) | −5.82466e73 | −0.109411 | ||||||||
\(853\) | −8.76449e74 | −1.59781 | −0.798907 | − | 0.601454i | \(-0.794588\pi\) | ||||
−0.798907 | + | 0.601454i | \(0.794588\pi\) | |||||||
\(854\) | 4.42000e74 | 0.782073 | ||||||||
\(855\) | 5.13640e74 | 0.882110 | ||||||||
\(856\) | −9.17533e73 | −0.152947 | ||||||||
\(857\) | −1.75132e74 | −0.283370 | −0.141685 | − | 0.989912i | \(-0.545252\pi\) | ||||
−0.141685 | + | 0.989912i | \(0.545252\pi\) | |||||||
\(858\) | −3.44223e73 | −0.0540648 | ||||||||
\(859\) | 4.14489e74 | 0.631956 | 0.315978 | − | 0.948766i | \(-0.397667\pi\) | ||||
0.315978 | + | 0.948766i | \(0.397667\pi\) | |||||||
\(860\) | 4.32566e74 | 0.640238 | ||||||||
\(861\) | 3.66913e74 | 0.527210 | ||||||||
\(862\) | 5.09537e74 | 0.710789 | ||||||||
\(863\) | 1.46481e74 | 0.198383 | 0.0991917 | − | 0.995068i | \(-0.468374\pi\) | ||||
0.0991917 | + | 0.995068i | \(0.468374\pi\) | |||||||
\(864\) | −4.87618e73 | −0.0641179 | ||||||||
\(865\) | 8.60695e74 | 1.09885 | ||||||||
\(866\) | 5.87810e73 | 0.0728670 | ||||||||
\(867\) | −8.35475e73 | −0.100565 | ||||||||
\(868\) | 5.29715e74 | 0.619141 | ||||||||
\(869\) | −3.28110e74 | −0.372405 | ||||||||
\(870\) | −3.23597e73 | −0.0356667 | ||||||||
\(871\) | 7.95134e74 | 0.851093 | ||||||||
\(872\) | 3.66487e74 | 0.380968 | ||||||||
\(873\) | −1.23655e75 | −1.24839 | ||||||||
\(874\) | −9.58339e74 | −0.939675 | ||||||||
\(875\) | 1.88865e75 | 1.79865 | ||||||||
\(876\) | 7.33293e73 | 0.0678302 | ||||||||
\(877\) | −5.01962e74 | −0.451005 | −0.225503 | − | 0.974243i | \(-0.572402\pi\) | ||||
−0.225503 | + | 0.974243i | \(0.572402\pi\) | |||||||
\(878\) | 5.49826e73 | 0.0479861 | ||||||||
\(879\) | −1.18918e74 | −0.100817 | ||||||||
\(880\) | −2.00011e74 | −0.164720 | ||||||||
\(881\) | −1.02163e75 | −0.817349 | −0.408675 | − | 0.912680i | \(-0.634009\pi\) | ||||
−0.408675 | + | 0.912680i | \(0.634009\pi\) | |||||||
\(882\) | −1.57353e75 | −1.22300 | ||||||||
\(883\) | −1.42175e75 | −1.07356 | −0.536780 | − | 0.843722i | \(-0.680359\pi\) | ||||
−0.536780 | + | 0.843722i | \(0.680359\pi\) | |||||||
\(884\) | −2.55994e74 | −0.187800 | ||||||||
\(885\) | 1.02999e74 | 0.0734144 | ||||||||
\(886\) | 8.55152e74 | 0.592221 | ||||||||
\(887\) | −3.69071e74 | −0.248346 | −0.124173 | − | 0.992261i | \(-0.539628\pi\) | ||||
−0.124173 | + | 0.992261i | \(0.539628\pi\) | |||||||
\(888\) | −1.75694e74 | −0.114875 | ||||||||
\(889\) | 4.77064e75 | 3.03097 | ||||||||
\(890\) | −1.10239e75 | −0.680600 | ||||||||
\(891\) | −1.11519e75 | −0.669066 | ||||||||
\(892\) | −1.18408e75 | −0.690360 | ||||||||
\(893\) | −2.10912e75 | −1.19506 | ||||||||
\(894\) | 1.28543e74 | 0.0707849 | ||||||||
\(895\) | −1.10766e75 | −0.592815 | ||||||||
\(896\) | −2.83852e74 | −0.147652 | ||||||||
\(897\) | 2.61818e74 | 0.132371 | ||||||||
\(898\) | 1.32436e74 | 0.0650820 | ||||||||
\(899\) | 4.79213e74 | 0.228905 | ||||||||
\(900\) | 2.24827e74 | 0.104391 | ||||||||
\(901\) | 1.46923e75 | 0.663143 | ||||||||
\(902\) | 2.05164e75 | 0.900189 | ||||||||
\(903\) | −1.04499e75 | −0.445732 | ||||||||
\(904\) | 8.78640e74 | 0.364348 | ||||||||
\(905\) | 2.08176e75 | 0.839253 | ||||||||
\(906\) | 1.09984e74 | 0.0431084 | ||||||||
\(907\) | 2.44006e75 | 0.929853 | 0.464927 | − | 0.885349i | \(-0.346081\pi\) | ||||
0.464927 | + | 0.885349i | \(0.346081\pi\) | |||||||
\(908\) | −2.61564e74 | −0.0969145 | ||||||||
\(909\) | 3.15087e75 | 1.13514 | ||||||||
\(910\) | −1.66252e75 | −0.582386 | ||||||||
\(911\) | −4.25501e75 | −1.44938 | −0.724690 | − | 0.689076i | \(-0.758017\pi\) | ||||
−0.724690 | + | 0.689076i | \(0.758017\pi\) | |||||||
\(912\) | −1.43625e74 | −0.0475731 | ||||||||
\(913\) | −2.35904e75 | −0.759856 | ||||||||
\(914\) | 3.16833e75 | 0.992435 | ||||||||
\(915\) | −3.55022e74 | −0.108148 | ||||||||
\(916\) | −2.34528e75 | −0.694800 | ||||||||
\(917\) | −2.18608e75 | −0.629867 | ||||||||
\(918\) | 6.17292e74 | 0.172983 | ||||||||
\(919\) | 4.21824e75 | 1.14970 | 0.574851 | − | 0.818258i | \(-0.305060\pi\) | ||||
0.574851 | + | 0.818258i | \(0.305060\pi\) | |||||||
\(920\) | 1.52130e75 | 0.403296 | ||||||||
\(921\) | −6.46326e74 | −0.166660 | ||||||||
\(922\) | 2.09461e75 | 0.525369 | ||||||||
\(923\) | −2.70719e75 | −0.660504 | ||||||||
\(924\) | 4.83186e74 | 0.114678 | ||||||||
\(925\) | 1.64869e75 | 0.380650 | ||||||||
\(926\) | 3.90080e75 | 0.876141 | ||||||||
\(927\) | 1.76969e75 | 0.386691 | ||||||||
\(928\) | −2.56790e74 | −0.0545890 | ||||||||
\(929\) | −8.38446e75 | −1.73410 | −0.867050 | − | 0.498221i | \(-0.833987\pi\) | ||||
−0.867050 | + | 0.498221i | \(0.833987\pi\) | |||||||
\(930\) | −4.25476e74 | −0.0856170 | ||||||||
\(931\) | −9.43279e75 | −1.84681 | ||||||||
\(932\) | −2.45252e75 | −0.467205 | ||||||||
\(933\) | 1.32651e75 | 0.245884 | ||||||||
\(934\) | 1.13438e75 | 0.204603 | ||||||||
\(935\) | 2.53201e75 | 0.444396 | ||||||||
\(936\) | −1.11356e75 | −0.190186 | ||||||||
\(937\) | 3.50330e75 | 0.582261 | 0.291131 | − | 0.956683i | \(-0.405969\pi\) | ||||
0.291131 | + | 0.956683i | \(0.405969\pi\) | |||||||
\(938\) | −1.11613e76 | −1.80527 | ||||||||
\(939\) | −3.01901e74 | −0.0475217 | ||||||||
\(940\) | 3.34808e75 | 0.512903 | ||||||||
\(941\) | 1.26513e76 | 1.88625 | 0.943127 | − | 0.332433i | \(-0.107870\pi\) | ||||
0.943127 | + | 0.332433i | \(0.107870\pi\) | |||||||
\(942\) | 1.04655e75 | 0.151866 | ||||||||
\(943\) | −1.56048e76 | −2.20400 | ||||||||
\(944\) | 8.17351e74 | 0.112363 | ||||||||
\(945\) | 4.00892e75 | 0.536434 | ||||||||
\(946\) | −5.84317e75 | −0.761069 | ||||||||
\(947\) | 5.93978e75 | 0.753088 | 0.376544 | − | 0.926399i | \(-0.377112\pi\) | ||||
0.376544 | + | 0.926399i | \(0.377112\pi\) | |||||||
\(948\) | 3.74016e74 | 0.0461612 | ||||||||
\(949\) | 3.40821e75 | 0.409484 | ||||||||
\(950\) | 1.34776e75 | 0.157638 | ||||||||
\(951\) | −6.64033e74 | −0.0756112 | ||||||||
\(952\) | 3.59338e75 | 0.398347 | ||||||||
\(953\) | 7.28890e75 | 0.786671 | 0.393335 | − | 0.919395i | \(-0.371321\pi\) | ||||
0.393335 | + | 0.919395i | \(0.371321\pi\) | |||||||
\(954\) | 6.39106e75 | 0.671567 | ||||||||
\(955\) | −4.45192e75 | −0.455472 | ||||||||
\(956\) | −1.13815e74 | −0.0113377 | ||||||||
\(957\) | 4.37120e74 | 0.0423980 | ||||||||
\(958\) | −7.81225e75 | −0.737828 | ||||||||
\(959\) | 3.05033e76 | 2.80526 | ||||||||
\(960\) | 2.27995e74 | 0.0204178 | ||||||||
\(961\) | −5.16606e75 | −0.450519 | ||||||||
\(962\) | −8.16592e75 | −0.693491 | ||||||||
\(963\) | 5.05261e75 | 0.417874 | ||||||||
\(964\) | −6.15423e74 | −0.0495689 | ||||||||
\(965\) | −2.30258e75 | −0.180621 | ||||||||
\(966\) | −3.67513e75 | −0.280774 | ||||||||
\(967\) | −2.01514e74 | −0.0149945 | −0.00749723 | − | 0.999972i | \(-0.502386\pi\) | ||||
−0.00749723 | + | 0.999972i | \(0.502386\pi\) | |||||||
\(968\) | −2.17661e75 | −0.157746 | ||||||||
\(969\) | 1.81820e75 | 0.128347 | ||||||||
\(970\) | 1.17672e76 | 0.809084 | ||||||||
\(971\) | −2.14332e76 | −1.43548 | −0.717740 | − | 0.696311i | \(-0.754823\pi\) | ||||
−0.717740 | + | 0.696311i | \(0.754823\pi\) | |||||||
\(972\) | 4.05102e75 | 0.264286 | ||||||||
\(973\) | −3.31557e76 | −2.10708 | ||||||||
\(974\) | 1.97585e75 | 0.122321 | ||||||||
\(975\) | −3.68208e74 | −0.0222063 | ||||||||
\(976\) | −2.81728e75 | −0.165523 | ||||||||
\(977\) | −2.17676e76 | −1.24595 | −0.622973 | − | 0.782243i | \(-0.714076\pi\) | ||||
−0.622973 | + | 0.782243i | \(0.714076\pi\) | |||||||
\(978\) | −2.35175e75 | −0.131145 | ||||||||
\(979\) | 1.48913e76 | 0.809049 | ||||||||
\(980\) | 1.49739e76 | 0.792628 | ||||||||
\(981\) | −2.01815e76 | −1.04086 | ||||||||
\(982\) | −7.10366e75 | −0.356976 | ||||||||
\(983\) | 2.22369e75 | 0.108883 | 0.0544414 | − | 0.998517i | \(-0.482662\pi\) | ||||
0.0544414 | + | 0.998517i | \(0.482662\pi\) | |||||||
\(984\) | −2.33868e75 | −0.111582 | ||||||||
\(985\) | 3.27539e75 | 0.152279 | ||||||||
\(986\) | 3.25079e75 | 0.147275 | ||||||||
\(987\) | −8.08826e75 | −0.357082 | ||||||||
\(988\) | −6.67542e75 | −0.287195 | ||||||||
\(989\) | 4.44434e76 | 1.86338 | ||||||||
\(990\) | 1.10141e76 | 0.450041 | ||||||||
\(991\) | 2.17380e76 | 0.865646 | 0.432823 | − | 0.901479i | \(-0.357517\pi\) | ||||
0.432823 | + | 0.901479i | \(0.357517\pi\) | |||||||
\(992\) | −3.37636e75 | −0.131039 | ||||||||
\(993\) | −4.12949e75 | −0.156204 | ||||||||
\(994\) | 3.80008e76 | 1.40101 | ||||||||
\(995\) | −8.23255e75 | −0.295832 | ||||||||
\(996\) | 2.68909e75 | 0.0941874 | ||||||||
\(997\) | −4.09289e76 | −1.39734 | −0.698672 | − | 0.715442i | \(-0.746225\pi\) | ||||
−0.698672 | + | 0.715442i | \(0.746225\pi\) | |||||||
\(998\) | −1.58668e75 | −0.0528031 | ||||||||
\(999\) | 1.96909e76 | 0.638773 |
(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 | 2.52.a.b.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.52.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |