Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(37,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.37");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(17.4841103551\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5090x^{6} + 8905881x^{4} + 5831691048x^{2} + 827887219200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.7 | ||
Root | \(40.3415i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.37 |
Dual form | 76.7.c.b.37.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 40.3415i | 1.49413i | 0.664751 | + | 0.747065i | \(0.268538\pi\) | ||||
−0.664751 | + | 0.747065i | \(0.731462\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −186.796 | −1.49437 | −0.747183 | − | 0.664618i | \(-0.768594\pi\) | ||||
−0.747183 | + | 0.664618i | \(0.768594\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 202.293 | 0.589775 | 0.294888 | − | 0.955532i | \(-0.404718\pi\) | ||||
0.294888 | + | 0.955532i | \(0.404718\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −898.437 | −1.23242 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1591.27 | −1.19555 | −0.597773 | − | 0.801666i | \(-0.703947\pi\) | ||||
−0.597773 | + | 0.801666i | \(0.703947\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 143.277i | 0.0652146i | 0.999468 | + | 0.0326073i | \(0.0103811\pi\) | ||||
−0.999468 | + | 0.0326073i | \(0.989619\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 7535.62i | − | 2.23278i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4771.21 | 0.971141 | 0.485570 | − | 0.874198i | \(-0.338612\pi\) | ||||
0.485570 | + | 0.874198i | \(0.338612\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1010.48 | − | 6784.16i | −0.147321 | − | 0.989089i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8160.80i | 0.881201i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7737.11 | 0.635910 | 0.317955 | − | 0.948106i | \(-0.397004\pi\) | ||||
0.317955 | + | 0.948106i | \(0.397004\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19267.6 | 1.23313 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 6835.36i | − | 0.347272i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8820.72i | 0.361668i | 0.983514 | + | 0.180834i | \(0.0578796\pi\) | ||||
−0.983514 | + | 0.180834i | \(0.942120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 51550.3i | − | 1.73040i | −0.501428 | − | 0.865199i | \(-0.667192\pi\) | ||
0.501428 | − | 0.865199i | \(-0.332808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 64194.3i | − | 1.78630i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −37787.4 | −0.881340 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 94640.6i | − | 1.86841i | −0.356735 | − | 0.934206i | \(-0.616110\pi\) | ||
0.356735 | − | 0.934206i | \(-0.383890\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5779.99 | −0.0974392 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 78747.2i | 1.14257i | 0.820751 | + | 0.571286i | \(0.193555\pi\) | ||||
−0.820751 | + | 0.571286i | \(0.806445\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −129047. | −1.62308 | −0.811542 | − | 0.584294i | \(-0.801371\pi\) | ||||
−0.811542 | + | 0.584294i | \(0.801371\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 167824. | 1.84169 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −97220.5 | −0.936406 | −0.468203 | − | 0.883621i | \(-0.655098\pi\) | ||||
−0.468203 | + | 0.883621i | \(0.655098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −76726.6 | −0.652165 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 192478.i | 1.45101i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 46143.8i | − | 0.309946i | −0.987919 | − | 0.154973i | \(-0.950471\pi\) | ||
0.987919 | − | 0.154973i | \(-0.0495290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 297243. | 1.78658 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 273683. | − | 40764.1i | 1.47783 | − | 0.220117i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 61729.4i | 0.300563i | 0.988643 | + | 0.150282i | \(0.0480181\pi\) | ||||
−0.988643 | + | 0.150282i | \(0.951982\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −85634.0 | −0.377274 | −0.188637 | − | 0.982047i | \(-0.560407\pi\) | ||||
−0.188637 | + | 0.982047i | \(0.560407\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −181747. | −0.726853 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 26763.5i | − | 0.0974545i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 49044.4i | − | 0.163067i | −0.996671 | − | 0.0815334i | \(-0.974018\pi\) | ||
0.996671 | − | 0.0815334i | \(-0.0259817\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 312127.i | 0.950132i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 408517.i | 1.14139i | 0.821161 | + | 0.570696i | \(0.193327\pi\) | ||||
−0.821161 | + | 0.570696i | \(0.806673\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −130029. | −0.334250 | −0.167125 | − | 0.985936i | \(-0.553448\pi\) | ||||
−0.167125 | + | 0.985936i | \(0.553448\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 777286.i | 1.84246i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −321903. | −0.705103 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 106942.i | − | 0.216904i | −0.994102 | − | 0.108452i | \(-0.965411\pi\) | ||
0.994102 | − | 0.108452i | \(-0.0345893\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −379212. | −0.713554 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12258.3 | −0.0214386 | −0.0107193 | − | 0.999943i | \(-0.503412\pi\) | ||||
−0.0107193 | + | 0.999943i | \(0.503412\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −891242. | −1.45124 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −355841. | −0.540379 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 561920.i | − | 0.797085i | −0.917150 | − | 0.398542i | \(-0.869516\pi\) | ||
0.917150 | − | 0.398542i | \(-0.130484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 28983.8i | 0.0384620i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.07962e6 | 2.58544 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 188753. | + | 1.26725e6i | 0.220152 | + | 1.47806i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 851962.i | − | 0.933480i | −0.884395 | − | 0.466740i | \(-0.845428\pi\) | ||
0.884395 | − | 0.466740i | \(-0.154572\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.42966e6 | 1.47342 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.73735e6 | −1.68625 | −0.843127 | − | 0.537714i | \(-0.819288\pi\) | ||||
−0.843127 | + | 0.537714i | \(0.819288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.34950e6i | − | 1.23498i | −0.786577 | − | 0.617492i | \(-0.788149\pi\) | ||
0.786577 | − | 0.617492i | \(-0.211851\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.52440e6i | − | 1.31684i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.32161e6i | − | 1.07883i | −0.842042 | − | 0.539413i | \(-0.818646\pi\) | ||
0.842042 | − | 0.539413i | \(-0.181354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.99638e6i | 1.54157i | 0.637093 | + | 0.770787i | \(0.280137\pi\) | ||||
−0.637093 | + | 0.770787i | \(0.719863\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.81795e6 | 2.79165 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.42114e6i | − | 0.984920i | −0.870335 | − | 0.492460i | \(-0.836098\pi\) | ||
0.870335 | − | 0.492460i | \(-0.163902\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.44526e6 | −0.950282 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 128725.i | − | 0.0803721i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 965182. | 0.572754 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 760581. | 0.429328 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.17678e6 | −1.70715 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −680431. | −0.348381 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.62081e6i | 1.76764i | 0.467823 | + | 0.883822i | \(0.345039\pi\) | ||||
−0.467823 | + | 0.883822i | \(0.654961\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 5.20593e6i | − | 2.42510i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.12259e6 | −1.83382 | −0.916909 | − | 0.399096i | \(-0.869324\pi\) | ||||
−0.916909 | + | 0.399096i | \(0.869324\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −204412. | − | 1.37239e6i | −0.0868864 | − | 0.583340i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.27682e6i | 0.518952i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.08355e6 | 1.19920 | 0.599598 | − | 0.800302i | \(-0.295327\pi\) | ||||
0.599598 | + | 0.800302i | \(0.295327\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.59964e6 | −0.595631 | −0.297816 | − | 0.954623i | \(-0.596258\pi\) | ||||
−0.297816 | + | 0.954623i | \(0.596258\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 3.92202e6i | − | 1.39911i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 227992.i | − | 0.0779671i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 1.64767e6i | − | 0.540464i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 3.09527e6i | − | 0.974420i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.38080e6 | 1.02202 | 0.511011 | − | 0.859574i | \(-0.329271\pi\) | ||||
0.511011 | + | 0.859574i | \(0.329271\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.08302e6i | 0.895458i | 0.894169 | + | 0.447729i | \(0.147767\pi\) | ||||
−0.894169 | + | 0.447729i | \(0.852233\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.28664e6 | −1.19686 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.62938e6i | 2.58585i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.24712e6 | 0.839072 | 0.419536 | − | 0.907739i | \(-0.362193\pi\) | ||||
0.419536 | + | 0.907739i | \(0.362193\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.86151e6 | 0.463099 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.56516e6 | 0.375044 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.32461e6 | −0.536769 | −0.268385 | − | 0.963312i | \(-0.586490\pi\) | ||||
−0.268385 | + | 0.963312i | \(0.586490\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.19912e7i | 2.66939i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 274073.i | − | 0.0588460i | −0.999567 | − | 0.0294230i | \(-0.990633\pi\) | ||
0.999567 | − | 0.0294230i | \(-0.00936698\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.80628e6 | 0.995747 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 907850. | + | 6.09514e6i | 0.181562 | + | 1.21898i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.32755e6i | 0.449532i | 0.974413 | + | 0.224766i | \(0.0721617\pi\) | ||||
−0.974413 | + | 0.224766i | \(0.927838\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.89771e6 | 0.727269 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.49026e6 | −0.449081 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 6.83222e6i | − | 1.19125i | −0.803263 | − | 0.595625i | \(-0.796905\pi\) | ||
0.803263 | − | 0.595625i | \(-0.203095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.40294e6i | − | 1.58573i | −0.609400 | − | 0.792863i | \(-0.708590\pi\) | ||
0.609400 | − | 0.792863i | \(-0.291410\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.45460e6i | − | 0.563696i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.76785e7i | 2.79209i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.59229e6 | −1.16104 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.38275e6i | − | 0.204813i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.12644e7 | −1.61662 | −0.808309 | − | 0.588759i | \(-0.799617\pi\) | ||||
−0.808309 | + | 0.588759i | \(0.799617\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.26456e6i | 0.175901i | 0.996125 | + | 0.0879504i | \(0.0280317\pi\) | ||||
−0.996125 | + | 0.0879504i | \(0.971968\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.07968e6 | 0.145610 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.92683e6 | −0.775218 | −0.387609 | − | 0.921824i | \(-0.626699\pi\) | ||||
−0.387609 | + | 0.921824i | \(0.626699\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.49979e6 | 0.697889 | 0.348945 | − | 0.937143i | \(-0.386540\pi\) | ||||
0.348945 | + | 0.937143i | \(0.386540\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.97853e6 | 0.243643 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.78437e6i | 0.213303i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.47096e7i | − | 1.70742i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.95131e6 | −0.783711 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.60794e6 | + | 1.07954e7i | 0.176129 | + | 1.18250i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.20580e7i | − | 1.28359i | −0.766876 | − | 0.641795i | \(-0.778190\pi\) | ||
0.766876 | − | 0.641795i | \(-0.221810\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.64802e7 | −1.70539 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.41053e7 | 2.42548 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.04283e7i | − | 1.02055i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 5.24556e6i | − | 0.499412i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 683603.i | 0.0633326i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.50611e7i | 1.35813i | 0.734077 | + | 0.679066i | \(0.237615\pi\) | ||||
−0.734077 | + | 0.679066i | \(0.762385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.73108e7 | −1.51974 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.46485e7i | 1.25232i | 0.779694 | + | 0.626161i | \(0.215375\pi\) | ||||
−0.779694 | + | 0.626161i | \(0.784625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.69472e7 | 1.41121 | 0.705603 | − | 0.708607i | \(-0.250676\pi\) | ||||
0.705603 | + | 0.708607i | \(0.250676\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 1.29860e7i | − | 1.05352i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.81937e6 | −0.301942 | −0.150971 | − | 0.988538i | \(-0.548240\pi\) | ||||
−0.150971 | + | 0.988538i | \(0.548240\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.81604e7 | 1.39933 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.31420e6 | 0.324082 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.51010e7 | 1.83864 | 0.919322 | − | 0.393507i | \(-0.128738\pi\) | ||||
0.919322 | + | 0.393507i | \(0.128738\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 7.55161e6i | − | 0.539496i | −0.962931 | − | 0.269748i | \(-0.913060\pi\) | ||
0.962931 | − | 0.269748i | \(-0.0869404\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 2.02810e7i | − | 1.41342i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.43322e7 | 0.974574 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 972011. | − | 144778.i | 0.0645031 | − | 0.00960750i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 494519.i | − | 0.0320321i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.68658e7 | −1.69894 | −0.849471 | − | 0.527635i | \(-0.823079\pi\) | ||||
−0.849471 | + | 0.527635i | \(0.823079\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.23118e7 | −0.760259 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 3.59541e7i | − | 2.16834i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.72065e7i | − | 1.01366i | −0.862046 | − | 0.506831i | \(-0.830817\pi\) | ||
0.862046 | − | 0.506831i | \(-0.169183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.91451e7i | − | 1.10194i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 7.92486e6i | − | 0.445728i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.35861e6 | −0.404510 | −0.202255 | − | 0.979333i | \(-0.564827\pi\) | ||||
−0.202255 | + | 0.979333i | \(0.564827\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.61947e6i | 0.463173i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.26687e7 | 1.19095 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.68576e7i | 1.37978i | 0.723913 | + | 0.689891i | \(0.242342\pi\) | ||||
−0.723913 | + | 0.689891i | \(0.757658\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.84648e6 | −0.0927762 | −0.0463881 | − | 0.998923i | \(-0.514771\pi\) | ||||
−0.0463881 | + | 0.998923i | \(0.514771\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.16925e6 | −0.0574672 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.06600e7 | −1.47426 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00493e7 | 0.472819 | 0.236410 | − | 0.971653i | \(-0.424029\pi\) | ||||
0.236410 | + | 0.971653i | \(0.424029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.63147e7i | 2.13259i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.79351e7i | 0.808321i | 0.914688 | + | 0.404160i | \(0.132436\pi\) | ||||
−0.914688 | + | 0.404160i | \(0.867564\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.11035e7 | −1.37230 | −0.686151 | − | 0.727460i | \(-0.740701\pi\) | ||||
−0.686151 | + | 0.727460i | \(0.740701\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.11229e7 | + | 7.61457e6i | −2.20841 | + | 0.328936i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.59300e7i | 0.673860i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.37309e6 | −0.0568860 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.43694e7 | 1.39474 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.91396e7i | 1.15846i | 0.815165 | + | 0.579229i | \(0.196646\pi\) | ||||
−0.815165 | + | 0.579229i | \(0.803354\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.15308e7i | − | 0.449152i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.08769e7i | 0.415180i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.10855e6i | 0.0414706i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.61052e7 | −0.957254 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 7.00873e7i | − | 2.51948i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.59961e7 | 0.563785 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.02183e7i | 1.38998i | 0.719020 | + | 0.694989i | \(0.244591\pi\) | ||||
−0.719020 | + | 0.694989i | \(0.755409\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.44409e7 | 1.84523 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.73795e7 | −0.577771 | −0.288885 | − | 0.957364i | \(-0.593285\pi\) | ||||
−0.288885 | + | 0.957364i | \(0.593285\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.25313e7 | 1.06089 | 0.530443 | − | 0.847721i | \(-0.322026\pi\) | ||||
0.530443 | + | 0.847721i | \(0.322026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.39497e7 | 1.08618 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.86504e7i | 0.899400i | 0.893180 | + | 0.449700i | \(0.148469\pi\) | ||||
−0.893180 | + | 0.449700i | \(0.851531\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.40361e7i | − | 0.432390i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.33156e7 | 1.61190 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.82120e6 | − | 3.23687e7i | −0.143070 | − | 0.960544i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.76060e6i | 0.0804181i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.05371e7 | −2.30331 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.96670e7 | −0.552269 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.74259e7i | 1.30777i | 0.756594 | + | 0.653885i | \(0.226862\pi\) | ||||
−0.756594 | + | 0.653885i | \(0.773138\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.50287e7i | 2.30268i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.16129e6i | 0.243681i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.20894e7i | − | 0.577157i | −0.957456 | − | 0.288579i | \(-0.906817\pi\) | ||
0.957456 | − | 0.288579i | \(-0.0931827\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.73309e7 | 1.47160 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.20305e7i | 2.06877i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.93208e7 | −0.974406 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 5.83039e7i | − | 1.41984i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.73262e7 | 0.654019 | 0.327009 | − | 0.945021i | \(-0.393959\pi\) | ||||
0.327009 | + | 0.945021i | \(0.393959\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.12946e7 | 0.971442 | 0.485721 | − | 0.874114i | \(-0.338557\pi\) | ||||
0.485721 | + | 0.874114i | \(0.338557\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 979348. | 0.0226473 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.44872e7 | −1.23871 | −0.619356 | − | 0.785110i | \(-0.712606\pi\) | ||||
−0.619356 | + | 0.785110i | \(0.712606\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 7.63092e7i | − | 1.70566i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.89369e7i | 0.855770i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.80050e7 | −0.389144 | −0.194572 | − | 0.980888i | \(-0.562332\pi\) | ||||
−0.194572 | + | 0.980888i | \(0.562332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.50038e7 | + | 1.37105e7i | −0.956593 | + | 0.291428i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.06830e7i | 0.641472i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.42888e7 | 0.499491 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.33600e7 | −1.68640 | −0.843198 | − | 0.537603i | \(-0.819330\pi\) | ||||
−0.843198 | + | 0.537603i | \(0.819330\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.07494e7i | − | 1.40813i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.33456e6i | − | 0.182798i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 2.46066e7i | − | 0.474159i | −0.971490 | − | 0.237080i | \(-0.923810\pi\) | ||
0.971490 | − | 0.237080i | \(-0.0761902\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 2.74496e7i | − | 0.520526i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.26380e6 | −0.0235860 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.80987e7i | − | 0.332452i | −0.986088 | − | 0.166226i | \(-0.946842\pi\) | ||
0.986088 | − | 0.166226i | \(-0.0531581\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.46069e8 | −2.64109 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.68217e7i | − | 0.833395i | −0.909045 | − | 0.416697i | \(-0.863188\pi\) | ||
0.909045 | − | 0.416697i | \(-0.136812\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.01300e7 | 1.05368 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.15940e8 | 2.00033 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.49752e7 | −0.424288 | −0.212144 | − | 0.977238i | \(-0.568045\pi\) | ||||
−0.212144 | + | 0.977238i | \(0.568045\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.69154e7 | 0.617558 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.66312e8i | − | 2.73996i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.99763e7i | 0.324134i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.03759e6 | 0.0165827 | 0.00829133 | − | 0.999966i | \(-0.497361\pi\) | ||||
0.00829133 | + | 0.999966i | \(0.497361\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.53642e7 | − | 8.24630e6i | 0.871586 | − | 0.129820i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.02883e8i | − | 1.59555i | −0.602953 | − | 0.797777i | \(-0.706009\pi\) | ||
0.602953 | − | 0.797777i | \(-0.293991\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.38595e6 | 0.112847 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.08352e7 | 1.06631 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.50599e8i | 2.23377i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 7.78751e7i | − | 1.13823i | −0.822259 | − | 0.569113i | \(-0.807287\pi\) | ||
0.822259 | − | 0.569113i | \(-0.192713\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.24395e8i | 1.79175i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.24874e7i | 0.177265i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.28980e6 | 0.0320371 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 6.45318e7i | − | 0.889950i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.20628e8 | −1.63986 | −0.819932 | − | 0.572461i | \(-0.805989\pi\) | ||||
−0.819932 | + | 0.572461i | \(0.805989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 9.94059e7i | − | 1.33219i | −0.745867 | − | 0.666095i | \(-0.767965\pi\) | ||
0.745867 | − | 0.666095i | \(-0.232035\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.73465e7 | 1.15405 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.19301e7 | 1.19754 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.73231e7 | −0.222507 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.19753e6 | 0.116493 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 3.81811e7i | − | 0.476888i | −0.971156 | − | 0.238444i | \(-0.923363\pi\) | ||
0.971156 | − | 0.238444i | \(-0.0766373\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.37273e8i | 1.69091i | 0.534043 | + | 0.845457i | \(0.320672\pi\) | ||||
−0.534043 | + | 0.845457i | \(0.679328\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.64696e7 | 0.807524 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.81817e6 | − | 5.24898e7i | −0.0936830 | − | 0.628971i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.17437e6i | 0.108438i | 0.998529 | + | 0.0542192i | \(0.0172670\pi\) | ||||
−0.998529 | + | 0.0542192i | \(0.982733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.89341e7 | 0.803745 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.79271e6 | 0.0206204 | 0.0103102 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103102 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.04964e8i | 1.19114i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.36387e8i | 1.52703i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.43497e6i | 0.0710898i | 0.999368 | + | 0.0355449i | \(0.0113167\pi\) | ||||
−0.999368 | + | 0.0355449i | \(0.988683\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.25308e8i | − | 1.36600i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.24374e8 | −1.33793 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 5.41406e6i | − | 0.0574763i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.28044e8 | −1.34156 | −0.670779 | − | 0.741658i | \(-0.734040\pi\) | ||||
−0.670779 | + | 0.741658i | \(0.734040\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 3.26130e7i | − | 0.337250i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.10758e7 | 0.317190 | 0.158595 | − | 0.987344i | \(-0.449304\pi\) | ||||
0.158595 | + | 0.987344i | \(0.449304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.91490e7 | 0.898201 | 0.449100 | − | 0.893481i | \(-0.351745\pi\) | ||||
0.449100 | + | 0.893481i | \(0.351745\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.88464e8 | −3.86359 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.26320e7 | −0.222214 | −0.111107 | − | 0.993808i | \(-0.535440\pi\) | ||||
−0.111107 | + | 0.993808i | \(0.535440\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 9.92134e6i | − | 0.0961727i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.30994e8i | 1.25368i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.05348e8 | 1.94047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.94695e7 | − | 1.30715e8i | −0.181666 | − | 1.21967i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.14573e7i | 0.381985i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.34746e8 | −1.22605 | −0.613026 | − | 0.790062i | \(-0.710048\pi\) | ||||
−0.613026 | + | 0.790062i | \(0.710048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.35598e7 | 0.121848 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.31410e7i | 0.560364i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.59143e8i | 1.39496i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4.94767e7i | − | 0.428365i | −0.976794 | − | 0.214182i | \(-0.931291\pi\) | ||
0.976794 | − | 0.214182i | \(-0.0687087\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 9.37783e7i | − | 0.802003i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.86984e8 | 1.57965 | 0.789825 | − | 0.613333i | \(-0.210172\pi\) | ||||
0.789825 | + | 0.613333i | \(0.210172\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.20855e7i | 0.351230i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.67054e8 | −2.20183 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.26400e7i | 0.673165i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.68560e6 | −0.0538070 | −0.0269035 | − | 0.999638i | \(-0.508565\pi\) | ||||
−0.0269035 | + | 0.999638i | \(0.508565\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.10565e7 | 0.0879236 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.07046e8 | −0.841139 | −0.420570 | − | 0.907260i | \(-0.638170\pi\) | ||||
−0.420570 | + | 0.907260i | \(0.638170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.24529e8 | 2.51988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.93893e8i | 1.48778i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 8.78261e7i | − | 0.665994i | −0.942928 | − | 0.332997i | \(-0.891940\pi\) | ||
0.942928 | − | 0.332997i | \(-0.108060\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.63039e7 | −0.197132 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.63722e7 | + | 6.90697e6i | −0.343483 | + | 0.0511606i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.52081e8i | 1.84552i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.54704e8 | 1.11952 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.38968e7 | −0.671659 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.29466e7i | 0.374391i | 0.982323 | + | 0.187195i | \(0.0599397\pi\) | ||||
−0.982323 | + | 0.187195i | \(0.940060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.04408e8i | 1.42887i | 0.699701 | + | 0.714436i | \(0.253317\pi\) | ||||
−0.699701 | + | 0.714436i | \(0.746683\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.57239e8i | 1.08663i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.45958e8i | − | 1.68046i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.81730e7 | −0.595619 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 5.54600e7i | − | 0.370422i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.12826e7 | −0.0745124 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.46871e8i | 1.61216i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.75622e8 | 1.77988 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.22093e8 | 0.779693 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.07904e7 | 0.0681469 | 0.0340735 | − | 0.999419i | \(-0.489152\pi\) | ||||
0.0340735 | + | 0.999419i | \(0.489152\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.79329e8 | 2.36928 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 3.72916e8i | − | 2.30368i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.89052e7i | 0.359908i | 0.983675 | + | 0.179954i | \(0.0575949\pi\) | ||||
−0.983675 | + | 0.179954i | \(0.942405\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.69368e7 | 0.464961 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.98411e7 | − | 8.91313e6i | 0.357722 | − | 0.0532814i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.16336e7i | − | 0.127924i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.13176e8 | −4.17175 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.50709e7 | 0.260814 | 0.130407 | − | 0.991461i | \(-0.458372\pi\) | ||||
0.130407 | + | 0.991461i | \(0.458372\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.84893e7i | − | 0.105849i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 3.06285e8i | − | 1.73475i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.83179e8i | − | 1.58685i | −0.608670 | − | 0.793424i | \(-0.708297\pi\) | ||
0.608670 | − | 0.793424i | \(-0.291703\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.65463e8i | 1.47183i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.67119e7 | −0.420837 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.97743e8i | − | 1.61624i | −0.589021 | − | 0.808118i | \(-0.700486\pi\) | ||
0.589021 | − | 0.808118i | \(-0.299514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.51806e7 | 0.242685 | 0.121343 | − | 0.992611i | \(-0.461280\pi\) | ||||
0.121343 | + | 0.992611i | \(0.461280\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 4.54422e8i | − | 2.41544i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.49076e8 | 0.784159 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.15048e8 | −0.598896 | −0.299448 | − | 0.954113i | \(-0.596802\pi\) | ||||
−0.299448 | + | 0.954113i | \(0.596802\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.10143e7 | −0.262819 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.47977e6 | −0.0126440 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.34273e7i | 0.370554i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.40453e7i | 0.120105i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.59622e8 | 0.789183 | 0.394592 | − | 0.918857i | \(-0.370886\pi\) | ||||
0.394592 | + | 0.918857i | \(0.370886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.49726e8 | + | 5.20904e7i | −1.71152 | + | 0.254925i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2.39097e8i | − | 1.15828i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.60997e7 | −0.316983 | −0.158491 | − | 0.987360i | \(-0.550663\pi\) | ||||
−0.158491 | + | 0.987360i | \(0.550663\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.80292e8 | −0.855905 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.21870e8i | 1.04274i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 1.30989e8i | − | 0.609475i | −0.952436 | − | 0.304738i | \(-0.901431\pi\) | ||
0.952436 | − | 0.304738i | \(-0.0985688\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.96588e8i | 1.36625i | 0.730303 | + | 0.683124i | \(0.239379\pi\) | ||||
−0.730303 | + | 0.683124i | \(0.760621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.40634e7i | 0.200967i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.42073e8 | −0.641573 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.29083e7i | 0.325995i | 0.986626 | + | 0.162997i | \(0.0521162\pi\) | ||||
−0.986626 | + | 0.162997i | \(0.947884\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.19841e7 | −0.318702 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.39294e7i | − | 0.0610674i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.92971e8 | 1.70600 | 0.853000 | − | 0.521910i | \(-0.174780\pi\) | ||||
0.853000 | + | 0.521910i | \(0.174780\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.93409e8 | 2.55111 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.27576e8 | −0.968884 | −0.484442 | − | 0.874823i | \(-0.660977\pi\) | ||||
−0.484442 | + | 0.874823i | \(0.660977\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.93252e8 | −0.814804 | −0.407402 | − | 0.913249i | \(-0.633565\pi\) | ||||
−0.407402 | + | 0.913249i | \(0.633565\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 5.28860e7i | − | 0.220834i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1.13672e8i | − | 0.470101i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.73955e8 | −0.712521 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.35504e8 | + | 6.48668e7i | −1.76681 | + | 0.263160i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.51551e8i | − | 1.81449i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.93900e7 | 0.0771773 | 0.0385887 | − | 0.999255i | \(-0.487714\pi\) | ||||
0.0385887 | + | 0.999255i | \(0.487714\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.86436e8 | 1.91785 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 6.76353e8i | − | 2.64151i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.09931e7i | − | 0.0425307i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 3.67027e8i | − | 1.40668i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.28211e8i | 1.24617i | 0.782152 | + | 0.623087i | \(0.214122\pi\) | ||||
−0.782152 | + | 0.623087i | \(0.785878\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.37495e7 | 0.0893349 | 0.0446675 | − | 0.999002i | \(-0.485777\pi\) | ||||
0.0446675 | + | 0.999002i | \(0.485777\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.72446e8i | 3.62398i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.17583e7 | 0.0434143 | 0.0217072 | − | 0.999764i | \(-0.493090\pi\) | ||||
0.0217072 | + | 0.999764i | \(0.493090\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.82282e7i | − | 0.359337i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.20692e8 | 1.52483 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.27271e8 | 0.457079 | 0.228539 | − | 0.973535i | \(-0.426605\pi\) | ||||
0.228539 | + | 0.973535i | \(0.426605\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.70082e8 | 2.74040 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.16823e8 | 0.411937 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.32452e8i | 0.812227i | 0.913823 | + | 0.406114i | \(0.133116\pi\) | ||||
−0.913823 | + | 0.406114i | \(0.866884\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.14463e8i | − | 1.08884i | −0.838812 | − | 0.544421i | \(-0.816750\pi\) | ||
0.838812 | − | 0.544421i | \(-0.183250\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.75776e7 | −0.0946271 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.81833e7 | + | 2.56356e8i | 0.129840 | + | 0.871723i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.82469e7i | 0.229988i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.07587e8 | −2.02923 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.36267e8 | 0.451048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 2.76451e8i | − | 0.906929i | −0.891274 | − | 0.453465i | \(-0.850188\pi\) | ||
0.891274 | − | 0.453465i | \(-0.149812\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 1.31701e8i | − | 0.428232i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.08200e8i | 1.31555i | 0.753215 | + | 0.657775i | \(0.228502\pi\) | ||||
−0.753215 | + | 0.657775i | \(0.771498\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.72346e8i | − | 0.550543i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.90943e8 | −1.87113 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 3.61070e8i | − | 1.13326i | −0.823973 | − | 0.566630i | \(-0.808247\pi\) | ||
0.823973 | − | 0.566630i | \(-0.191753\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.75995e8 | −1.79204 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.83674e8i | 2.10853i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.61133e6 | 0.0202130 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.47750e8 | 1.05398 | 0.526991 | − | 0.849871i | \(-0.323320\pi\) | ||||
0.526991 | + | 0.849871i | \(0.323320\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.89209e8 | 0.868986 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.98806e8 | 0.890091 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.75720e8i | 1.10960i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.54079e8i | − | 0.451141i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.95408e7 | −0.259936 | −0.129968 | − | 0.991518i | \(-0.541487\pi\) | ||||
−0.129968 | + | 0.991518i | \(0.541487\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.42057e8 | + | 9.56321e7i | −1.84802 | + | 0.275257i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.32617e8i | 2.09079i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.51453e8 | −0.994511 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.93298e8 | 0.542362 | 0.271181 | − | 0.962528i | \(-0.412586\pi\) | ||||
0.271181 | + | 0.962528i | \(0.412586\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.60807e7i | 0.267317i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.98851e8i | − | 1.10038i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.25879e7i | 0.116511i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.01261e9i | 2.74717i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.52698e8 | −0.948891 | −0.474445 | − | 0.880285i | \(-0.657351\pi\) | ||||
−0.474445 | + | 0.880285i | \(0.657351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 2.72994e8i | − | 0.728363i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.04643e8 | 0.806077 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.69954e8i | 0.445983i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.02827e8 | −0.527865 | −0.263932 | − | 0.964541i | \(-0.585020\pi\) | ||||
−0.263932 | + | 0.964541i | \(0.585020\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.41719e8 | 1.39827 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.15709e8 | −1.57624 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.60785e8 | −1.17000 | −0.585001 | − | 0.811033i | \(-0.698906\pi\) | ||||
−0.585001 | + | 0.811033i | \(0.698906\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.78183e8i | 1.45614i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.80430e7i | 0.194954i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.61415e8 | −0.647734 | −0.323867 | − | 0.946103i | \(-0.604983\pi\) | ||||
−0.323867 | + | 0.946103i | \(0.604983\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.84055e6 | + | 3.92124e7i | 0.0143549 | + | 0.0963760i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.25053e8i | 0.792480i | 0.918147 | + | 0.396240i | \(0.129685\pi\) | ||||
−0.918147 | + | 0.396240i | \(0.870315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.31519e8 | −1.52728 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.10133e7 | 0.0264215 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.67352e8i | − | 0.636264i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.90899e8i | 0.686787i | 0.939192 | + | 0.343393i | \(0.111576\pi\) | ||||
−0.939192 | + | 0.343393i | \(0.888424\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.08381e9i | − | 2.53844i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5.75895e8i | − | 1.33814i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.60667e8 | 1.75350 | 0.876752 | − | 0.480943i | \(-0.159706\pi\) | ||||
0.876752 | + | 0.480943i | \(0.159706\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 4.96678e8i | − | 1.13593i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.20532e8 | −0.727306 | −0.363653 | − | 0.931534i | \(-0.618471\pi\) | ||||
−0.363653 | + | 0.931534i | \(0.618471\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.03854e8i | 0.909182i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.00726e8 | 1.78854 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.84438e6 | −0.0196011 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.20733e8 | 0.925183 | 0.462592 | − | 0.886571i | \(-0.346920\pi\) | ||||
0.462592 | + | 0.886571i | \(0.346920\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.94136e8 | 1.51454 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.21759e8i | 1.34612i | 0.739588 | + | 0.673060i | \(0.235020\pi\) | ||||
−0.739588 | + | 0.673060i | \(0.764980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 9.93253e8i | − | 2.13381i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.72343e8 | 1.64645 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.34233e8 | − | 7.95722e7i | 1.13010 | − | 0.168325i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 6.50061e8i | − | 1.36459i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.02928e7 | 0.125597 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.06548e8 | −1.25388 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.97860e7i | 0.0405913i | 0.999794 | + | 0.0202956i | \(0.00646075\pi\) | ||||
−0.999794 | + | 0.0202956i | \(0.993539\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 2.96858e8i | − | 0.604390i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 2.87486e8i | − | 0.580881i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1.22693e7i | − | 0.0246038i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.47722e8 | −0.692040 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.31780e8i | 1.05041i | 0.850977 | + | 0.525203i | \(0.176010\pi\) | ||||
−0.850977 | + | 0.525203i | \(0.823990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.63860e8 | −0.909382 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.04850e8i | 0.982347i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.06911e8 | 0.399610 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.92366e8 | −0.560452 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.08348e9 | −2.06157 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.55853e8 | 1.61642 | 0.808209 | − | 0.588896i | \(-0.200437\pi\) | ||||
0.808209 | + | 0.588896i | \(0.200437\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.99910e8i | 1.31214i | 0.754701 | + | 0.656069i | \(0.227782\pi\) | ||||
−0.754701 | + | 0.656069i | \(0.772218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 7.44898e7i | − | 0.138620i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.34228e8 | 0.802130 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.30398e8 | + | 8.75472e8i | 0.239115 | + | 1.60537i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 2.60402e7i | − | 0.0474015i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.84681e8 | 1.05655 | 0.528274 | − | 0.849074i | \(-0.322839\pi\) | ||||
0.528274 | + | 0.849074i | \(0.322839\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.37701e8 | 0.785196 | 0.392598 | − | 0.919710i | \(-0.371576\pi\) | ||||
0.392598 | + | 0.919710i | \(0.371576\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.23687e9i | − | 2.20274i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.36193e8i | − | 0.240790i | −0.992726 | − | 0.120395i | \(-0.961584\pi\) | ||
0.992726 | − | 0.120395i | \(-0.0384162\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.38167e7i | 0.129566i | 0.997899 | + | 0.0647830i | \(0.0206355\pi\) | ||||
−0.997899 | + | 0.0647830i | \(0.979364\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.05403e8i | 0.706454i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.66079e8 | −0.633344 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.11957e7i | 0.0879375i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.52365e8 | −0.600920 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 4.83661e8i | − | 0.818946i | −0.912322 | − | 0.409473i | \(-0.865713\pi\) | ||
0.912322 | − | 0.409473i | \(-0.134287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.17018e8 | 0.869196 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.23527e8 | −1.20774 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8.97793e8 | −1.48801 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.53860e8 | 0.253207 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1.25476e9i | − | 2.05040i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 7.32245e8i | − | 1.18814i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.52710e8 | −0.246048 | −0.123024 | − | 0.992404i | \(-0.539259\pi\) | ||||
−0.123024 | + | 0.992404i | \(0.539259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.69583e8 | − | 1.13855e9i | −0.271321 | − | 1.82160i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.05617e9i | − | 1.67799i | −0.544138 | − | 0.838996i | \(-0.683143\pi\) | ||
0.544138 | − | 0.838996i | \(-0.316857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.53777e8 | 0.558150 | 0.279075 | − | 0.960269i | \(-0.409972\pi\) | ||||
0.279075 | + | 0.960269i | \(0.409972\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.42640e8 | −1.00683 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.01186e8i | − | 0.157431i | −0.996897 | − | 0.0787153i | \(-0.974918\pi\) | ||
0.996897 | − | 0.0787153i | \(-0.0250818\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 4.34776e8i | − | 0.671765i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 5.53925e7i | − | 0.0849951i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.70174e8i | 0.259318i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.02692e6 | 0.0106343 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.65434e8i | 1.15044i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.37646e8 | −0.205466 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1.10266e9i | − | 1.63472i | −0.576127 | − | 0.817360i | \(-0.695437\pi\) | ||
0.576127 | − | 0.817360i | \(-0.304563\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.17553e9 | −1.73089 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.09645e7 | 0.133028 | 0.0665142 | − | 0.997785i | \(-0.478812\pi\) | ||||
0.0665142 | + | 0.997785i | \(0.478812\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.92658e8 | −0.570338 | −0.285169 | − | 0.958477i | \(-0.592050\pi\) | ||||
−0.285169 | + | 0.958477i | \(0.592050\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.65169e8 | 0.671091 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.46247e8i | 0.496152i | 0.968741 | + | 0.248076i | \(0.0797983\pi\) | ||||
−0.968741 | + | 0.248076i | \(0.920202\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.32465e8i | 1.04251i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.03429e8 | 0.853086 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.82390e7 | + | 6.59559e8i | 0.137952 | + | 0.926189i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.27623e9i | 1.78016i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.47205e7 | −0.0619625 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.54711e8 | 0.625830 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.20162e8i | − | 0.301001i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.05312e9i | − | 1.43026i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.75643e9i | 2.36965i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.69987e8i | 0.629888i | 0.949110 | + | 0.314944i | \(0.101986\pi\) | ||||
−0.949110 | + | 0.314944i | \(0.898014\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.56090e9 | 2.07818 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.84138e8i | − | 0.375816i | −0.982187 | − | 0.187908i | \(-0.939829\pi\) | ||
0.982187 | − | 0.187908i | \(-0.0601706\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.95063e7 | 0.0256308 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.45305e8i | 0.842368i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.33971e8 | −1.08154 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.06131e9 | 1.36740 | 0.683700 | − | 0.729763i | \(-0.260370\pi\) | ||||
0.683700 | + | 0.729763i | \(0.260370\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.62247e9 | −2.07681 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.85309e7 | −0.0744355 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.82350e9i | − | 2.30399i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.21244e9i | 1.52203i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.01662e8 | 0.625697 | 0.312848 | − | 0.949803i | \(-0.398717\pi\) | ||||
0.312848 | + | 0.949803i | \(0.398717\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.75304e7 | + | 5.20526e8i | 0.0960778 | + | 0.645049i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 7.01114e8i | − | 0.863264i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.41821e9 | 1.73502 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.16919e8 | −0.749910 | −0.374955 | − | 0.927043i | \(-0.622342\pi\) | ||||
−0.374955 | + | 0.927043i | \(0.622342\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.31236e9i | 1.58510i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.00994e9i | 1.21206i | 0.795441 | + | 0.606031i | \(0.207239\pi\) | ||||
−0.795441 | + | 0.606031i | \(0.792761\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.09276e8i | 0.726572i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.58291e8i | 0.306065i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.91940e8 | 0.814739 | 0.407369 | − | 0.913263i | \(-0.366446\pi\) | ||||
0.407369 | + | 0.913263i | \(0.366446\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.86301e7i | − | 0.0217980i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.15580e9 | −1.34382 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 4.95481e8i | − | 0.572464i | −0.958160 | − | 0.286232i | \(-0.907597\pi\) | ||
0.958160 | − | 0.286232i | \(-0.0924028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.10414e9 | 2.41582 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.66239e8 | 0.646047 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.23781e8 | 0.707256 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.76993e9 | −1.99428 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.18738e9i | 1.32957i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2.36215e8i | − | 0.262860i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.38648e9 | −1.53332 | −0.766661 | − | 0.642052i | \(-0.778083\pi\) | ||||
−0.766661 | + | 0.642052i | \(0.778083\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.30580e9 | − | 1.94494e8i | 1.43518 | − | 0.213765i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.47483e8i | 0.379556i | 0.981827 | + | 0.189778i | \(0.0607769\pi\) | ||||
−0.981827 | + | 0.189778i | \(0.939223\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.23595e8 | −0.351288 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.11367e8 | −0.120155 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.77225e9i | 1.90038i | 0.311664 | + | 0.950192i | \(0.399114\pi\) | ||||
−0.311664 | + | 0.950192i | \(0.600886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.94167e8i | 0.952951i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.79363e9i | − | 1.89987i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.01843e8i | − | 0.212497i | −0.994340 | − | 0.106248i | \(-0.966116\pi\) | ||
0.994340 | − | 0.106248i | \(-0.0338839\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.10711e9 | 1.15846 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 7.93397e8i | − | 0.825161i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.98447e8 | −1.03213 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.84564e8i | 0.806135i | 0.915170 | + | 0.403067i | \(0.132056\pi\) | ||||
−0.915170 | + | 0.403067i | \(0.867944\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.91323e9 | −1.95398 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.02734e9 | −1.04290 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.23743e9 | 1.24863 | 0.624316 | − | 0.781172i | \(-0.285378\pi\) | ||||
0.624316 | + | 0.781172i | \(0.285378\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.46903e8 | −0.648848 |
(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 | 76.7.c.b.37.7 | yes | 8 | |
3.2 | odd | 2 | 684.7.h.c.37.8 | 8 | |||
4.3 | odd | 2 | 304.7.e.c.113.2 | 8 | |||
19.18 | odd | 2 | inner | 76.7.c.b.37.2 | ✓ | 8 | |
57.56 | even | 2 | 684.7.h.c.37.7 | 8 | |||
76.75 | even | 2 | 304.7.e.c.113.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.c.b.37.2 | ✓ | 8 | 19.18 | odd | 2 | inner | |
76.7.c.b.37.7 | yes | 8 | 1.1 | even | 1 | trivial | |
304.7.e.c.113.2 | 8 | 4.3 | odd | 2 | |||
304.7.e.c.113.7 | 8 | 76.75 | even | 2 | |||
684.7.h.c.37.7 | 8 | 57.56 | even | 2 | |||
684.7.h.c.37.8 | 8 | 3.2 | odd | 2 |