Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,6,Mod(1,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.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: | \(80.8334451857\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{177}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(7.15207\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −35.5207 | −0.635413 | −0.317707 | − | 0.948189i | \(-0.602913\pi\) | ||||
−0.317707 | + | 0.948189i | \(0.602913\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −565.825 | −1.40994 | −0.704969 | − | 0.709238i | \(-0.749039\pi\) | ||||
−0.704969 | + | 0.709238i | \(0.749039\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 983.594 | 1.61420 | 0.807100 | − | 0.590415i | \(-0.201036\pi\) | ||||
0.807100 | + | 0.590415i | \(0.201036\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −200.175 | −0.167992 | −0.0839959 | − | 0.996466i | \(-0.526768\pi\) | ||||
−0.0839959 | + | 0.996466i | \(0.526768\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 828.747 | 0.526669 | 0.263335 | − | 0.964705i | \(-0.415178\pi\) | ||||
0.263335 | + | 0.964705i | \(0.415178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4435.43 | −1.74830 | −0.874149 | − | 0.485657i | \(-0.838580\pi\) | ||||
−0.874149 | + | 0.485657i | \(0.838580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1863.28 | −0.596250 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3717.74 | 0.820889 | 0.410444 | − | 0.911886i | \(-0.365374\pi\) | ||||
0.410444 | + | 0.911886i | \(0.365374\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 992.462 | 0.185485 | 0.0927427 | − | 0.995690i | \(-0.470437\pi\) | ||||
0.0927427 | + | 0.995690i | \(0.470437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1740.51 | −0.240164 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8359.69 | −1.00389 | −0.501945 | − | 0.864900i | \(-0.667382\pi\) | ||||
−0.501945 | + | 0.864900i | \(0.667382\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13473.0 | 1.25171 | 0.625855 | − | 0.779940i | \(-0.284750\pi\) | ||||
0.625855 | + | 0.779940i | \(0.284750\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 298.798 | 0.0246437 | 0.0123218 | − | 0.999924i | \(-0.496078\pi\) | ||||
0.0123218 | + | 0.999924i | \(0.496078\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18736.5 | 1.23721 | 0.618606 | − | 0.785701i | \(-0.287698\pi\) | ||||
0.618606 | + | 0.785701i | \(0.287698\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −16036.4 | −0.784181 | −0.392090 | − | 0.919927i | \(-0.628248\pi\) | ||||
−0.392090 | + | 0.919927i | \(0.628248\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 20098.5 | 0.895894 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12749.2 | −0.476817 | −0.238408 | − | 0.971165i | \(-0.576626\pi\) | ||||
−0.238408 | + | 0.971165i | \(0.576626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34975.9 | −1.20350 | −0.601748 | − | 0.798686i | \(-0.705529\pi\) | ||||
−0.601748 | + | 0.798686i | \(0.705529\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −34937.9 | −1.02568 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11978.9 | 0.326009 | 0.163004 | − | 0.986625i | \(-0.447882\pi\) | ||||
0.163004 | + | 0.986625i | \(0.447882\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12924.9 | 0.304285 | 0.152143 | − | 0.988359i | \(-0.451383\pi\) | ||||
0.152143 | + | 0.988359i | \(0.451383\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 81177.2 | 1.78290 | 0.891450 | − | 0.453119i | \(-0.149689\pi\) | ||||
0.891450 | + | 0.453119i | \(0.149689\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27725.4 | −0.532907 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 46998.8 | 0.847265 | 0.423632 | − | 0.905834i | \(-0.360755\pi\) | ||||
0.423632 | + | 0.905834i | \(0.360755\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 111544. | 1.77726 | 0.888632 | − | 0.458621i | \(-0.151656\pi\) | ||||
0.888632 | + | 0.458621i | \(0.151656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7110.36 | 0.106744 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 34726.8 | 0.464719 | 0.232359 | − | 0.972630i | \(-0.425355\pi\) | ||||
0.232359 | + | 0.972630i | \(0.425355\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 48196.1 | 0.610110 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −29437.7 | −0.334653 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 92655.6 | 0.999867 | 0.499933 | − | 0.866064i | \(-0.333358\pi\) | ||||
0.499933 | + | 0.866064i | \(0.333358\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 154765. | 1.50963 | 0.754814 | − | 0.655939i | \(-0.227727\pi\) | ||||
0.754814 | + | 0.655939i | \(0.227727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −197146. | −1.83102 | −0.915512 | − | 0.402290i | \(-0.868214\pi\) | ||||
−0.915512 | + | 0.402290i | \(0.868214\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −63901.3 | −0.539573 | −0.269786 | − | 0.962920i | \(-0.586953\pi\) | ||||
−0.269786 | + | 0.962920i | \(0.586953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 66910.4 | 0.539421 | 0.269710 | − | 0.962941i | \(-0.413072\pi\) | ||||
0.269710 | + | 0.962941i | \(0.413072\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 100524. | 0.740580 | 0.370290 | − | 0.928916i | \(-0.379258\pi\) | ||||
0.370290 | + | 0.928916i | \(0.379258\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 157549. | 1.11089 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9808.58 | −0.0634949 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 159107. | 0.987928 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 177187. | 1.01428 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −155009. | −0.852800 | −0.426400 | − | 0.904535i | \(-0.640218\pi\) | ||||
−0.426400 | + | 0.904535i | \(0.640218\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70396.8 | 0.358405 | 0.179203 | − | 0.983812i | \(-0.442648\pi\) | ||||
0.179203 | + | 0.983812i | \(0.442648\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 40608.6 | 0.199062 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −175732. | −0.799925 | −0.399962 | − | 0.916532i | \(-0.630977\pi\) | ||||
−0.399962 | + | 0.916532i | \(0.630977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 44017.9 | 0.193238 | 0.0966189 | − | 0.995321i | \(-0.469197\pi\) | ||||
0.0966189 | + | 0.995321i | \(0.469197\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −556542. | −2.27592 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −132057. | −0.521603 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 121136. | 0.447001 | 0.223500 | − | 0.974704i | \(-0.428252\pi\) | ||||
0.223500 | + | 0.974704i | \(0.428252\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 398463. | 1.42215 | 0.711075 | − | 0.703116i | \(-0.248209\pi\) | ||||
0.711075 | + | 0.703116i | \(0.248209\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −35252.9 | −0.117860 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −136739. | −0.442733 | −0.221367 | − | 0.975191i | \(-0.571052\pi\) | ||||
−0.221367 | + | 0.975191i | \(0.571052\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −217336. | −0.660795 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 642409. | 1.89384 | 0.946919 | − | 0.321473i | \(-0.104178\pi\) | ||||
0.946919 | + | 0.321473i | \(0.104178\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 290841. | 0.806984 | 0.403492 | − | 0.914983i | \(-0.367796\pi\) | ||||
0.403492 | + | 0.914983i | \(0.367796\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 596163. | 1.60564 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 562234. | 1.42824 | 0.714121 | − | 0.700022i | \(-0.246827\pi\) | ||||
0.714121 | + | 0.700022i | \(0.246827\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −91300.8 | −0.225361 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 312167. | 0.728207 | 0.364103 | − | 0.931359i | \(-0.381375\pi\) | ||||
0.364103 | + | 0.931359i | \(0.381375\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 254232. | 0.576811 | 0.288405 | − | 0.957508i | \(-0.406875\pi\) | ||||
0.288405 | + | 0.957508i | \(0.406875\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 296942. | 0.637884 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 113264. | 0.236858 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 189060. | 0.374986 | 0.187493 | − | 0.982266i | \(-0.439964\pi\) | ||||
0.187493 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 660426. | 1.27624 | 0.638118 | − | 0.769939i | \(-0.279713\pi\) | ||||
0.638118 | + | 0.769939i | \(0.279713\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 786619. | 1.44410 | 0.722052 | − | 0.691838i | \(-0.243199\pi\) | ||||
0.722052 | + | 0.691838i | \(0.243199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 360530. | 0.645370 | 0.322685 | − | 0.946506i | \(-0.395414\pi\) | ||||
0.322685 | + | 0.946506i | \(0.395414\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 182169. | 0.310267 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −478569. | −0.795353 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −468926. | −0.742571 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.13491e6 | −1.75491 | −0.877455 | − | 0.479658i | \(-0.840761\pi\) | ||||
−0.877455 | + | 0.479658i | \(0.840761\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10613.5 | −0.0156589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 48630.7 | 0.0701069 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −196891. | −0.271172 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −783934. | −1.05564 | −0.527822 | − | 0.849355i | \(-0.676991\pi\) | ||||
−0.527822 | + | 0.849355i | \(0.676991\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −600754. | −0.773806 | −0.386903 | − | 0.922120i | \(-0.626455\pi\) | ||||
−0.386903 | + | 0.922120i | \(0.626455\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.47992e6 | 1.86487 | 0.932435 | − | 0.361337i | \(-0.117680\pi\) | ||||
0.932435 | + | 0.361337i | \(0.117680\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.04350e6 | 1.25922 | 0.629610 | − | 0.776911i | \(-0.283215\pi\) | ||||
0.629610 | + | 0.776911i | \(0.283215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −665534. | −0.786141 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −262948. | −0.297767 | −0.148883 | − | 0.988855i | \(-0.547568\pi\) | ||||
−0.148883 | + | 0.988855i | \(0.547568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.79946e6 | −1.99571 | −0.997857 | − | 0.0654284i | \(-0.979159\pi\) | ||||
−0.997857 | + | 0.0654284i | \(0.979159\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −85285.1 | −0.0907733 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 815150. | 0.850149 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.06631e6 | −1.06831 | −0.534156 | − | 0.845386i | \(-0.679370\pi\) | ||||
−0.534156 | + | 0.845386i | \(0.679370\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.50967e6 | 2.46499 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −675178. | −0.637654 | −0.318827 | − | 0.947813i | \(-0.603289\pi\) | ||||
−0.318827 | + | 0.947813i | \(0.603289\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −409625. | −0.379434 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −301937. | −0.269170 | −0.134585 | − | 0.990902i | \(-0.542970\pi\) | ||||
−0.134585 | + | 0.990902i | \(0.542970\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 569622. | 0.498279 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 817428. | 0.688762 | 0.344381 | − | 0.938830i | \(-0.388089\pi\) | ||||
0.344381 | + | 0.938830i | \(0.388089\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 896619. | 0.741626 | 0.370813 | − | 0.928708i | \(-0.379079\pi\) | ||||
0.370813 | + | 0.928708i | \(0.379079\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.05429e6 | 0.840676 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −909620. | −0.712296 | −0.356148 | − | 0.934430i | \(-0.615910\pi\) | ||||
−0.356148 | + | 0.934430i | \(0.615910\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −762090. | −0.575758 | −0.287879 | − | 0.957667i | \(-0.592950\pi\) | ||||
−0.287879 | + | 0.957667i | \(0.592950\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 931060. | 0.691054 | 0.345527 | − | 0.938409i | \(-0.387700\pi\) | ||||
0.345527 | + | 0.938409i | \(0.387700\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 660175. | 0.473102 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.37979e6 | −0.971779 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −204188. | −0.138951 | −0.0694755 | − | 0.997584i | \(-0.522133\pi\) | ||||
−0.0694755 | + | 0.997584i | \(0.522133\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 452859. | 0.302976 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.36266e6 | −2.82210 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14641.1 | 0.00931444 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.24237e6 | 0.764717 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.00786e6 | −0.610314 | −0.305157 | − | 0.952302i | \(-0.598709\pi\) | ||||
−0.305157 | + | 0.952302i | \(0.598709\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.77736e6 | −1.04202 | −0.521009 | − | 0.853551i | \(-0.674444\pi\) | ||||
−0.521009 | + | 0.853551i | \(0.674444\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.73100e6 | −0.998705 | −0.499352 | − | 0.866399i | \(-0.666429\pi\) | ||||
−0.499352 | + | 0.866399i | \(0.666429\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.22072e6 | 1.24121 | 0.620605 | − | 0.784123i | \(-0.286887\pi\) | ||||
0.620605 | + | 0.784123i | \(0.286887\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.10359e6 | −1.15740 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −165895. | −0.0884761 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.83271e6 | −0.962467 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 918089. | 0.467622 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.45218e6 | −1.23022 | −0.615109 | − | 0.788442i | \(-0.710888\pi\) | ||||
−0.615109 | + | 0.788442i | \(0.710888\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −425498. | −0.207150 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.06932e6 | −0.992549 | −0.496275 | − | 0.868166i | \(-0.665299\pi\) | ||||
−0.496275 | + | 0.868166i | \(0.665299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −561560. | −0.261523 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.21939e6 | 0.989487 | 0.494743 | − | 0.869039i | \(-0.335262\pi\) | ||||
0.494743 | + | 0.869039i | \(0.335262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.92580e6 | 1.28582 | 0.642911 | − | 0.765941i | \(-0.277727\pi\) | ||||
0.642911 | + | 0.765941i | \(0.277727\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.03319e6 | 1.29558 | 0.647788 | − | 0.761821i | \(-0.275694\pi\) | ||||
0.647788 | + | 0.761821i | \(0.275694\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −459101. | −0.193347 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.66596e6 | −1.50125 | −0.750623 | − | 0.660731i | \(-0.770246\pi\) | ||||
−0.750623 | + | 0.660731i | \(0.770246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.78928e6 | −0.722619 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.88347e6 | −1.13288 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.47355e6 | −1.34620 | −0.673098 | − | 0.739553i | \(-0.735037\pi\) | ||||
−0.673098 | + | 0.739553i | \(0.735037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −785782. | −0.296392 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 581430. | 0.216384 | 0.108192 | − | 0.994130i | \(-0.465494\pi\) | ||||
0.108192 | + | 0.994130i | \(0.465494\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.65675e6 | 1.32508 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.83859e6 | 0.657486 | 0.328743 | − | 0.944419i | \(-0.393375\pi\) | ||||
0.328743 | + | 0.944419i | \(0.393375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −139133. | −0.0484655 | −0.0242328 | − | 0.999706i | \(-0.507714\pi\) | ||||
−0.0242328 | + | 0.999706i | \(0.507714\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 984825. | 0.338616 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.21985e6 | −0.743788 | −0.371894 | − | 0.928275i | \(-0.621292\pi\) | ||||
−0.371894 | + | 0.928275i | \(0.621292\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 887862. | 0.293700 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.66943e6 | −0.538363 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 505998. | 0.161129 | 0.0805643 | − | 0.996749i | \(-0.474328\pi\) | ||||
0.0805643 | + | 0.996749i | \(0.474328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.06663e6 | −0.641802 | −0.320901 | − | 0.947113i | \(-0.603986\pi\) | ||||
−0.320901 | + | 0.947113i | \(0.603986\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 976180. | 0.299411 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.73012e6 | 1.41542 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.96711e6 | 1.76383 | 0.881913 | − | 0.471411i | \(-0.156255\pi\) | ||||
0.881913 | + | 0.471411i | \(0.156255\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −624709. | −0.180220 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.96213e6 | −1.12930 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 569081. | 0.158358 | 0.0791788 | − | 0.996860i | \(-0.474770\pi\) | ||||
0.0791788 | + | 0.996860i | \(0.474770\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −171377. | −0.0471247 | −0.0235623 | − | 0.999722i | \(-0.507501\pi\) | ||||
−0.0235623 | + | 0.999722i | \(0.507501\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 372983. | 0.100165 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.71382e6 | −0.454879 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.75930e6 | −1.23410 | −0.617049 | − | 0.786924i | \(-0.711672\pi\) | ||||
−0.617049 | + | 0.786924i | \(0.711672\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 623369. | 0.159781 | 0.0798906 | − | 0.996804i | \(-0.474543\pi\) | ||||
0.0798906 | + | 0.996804i | \(0.474543\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.67585e6 | −0.920775 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.24578e6 | −1.29912 | −0.649559 | − | 0.760311i | \(-0.725046\pi\) | ||||
−0.649559 | + | 0.760311i | \(0.725046\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.64926e6 | −1.36767 | −0.683837 | − | 0.729635i | \(-0.739690\pi\) | ||||
−0.683837 | + | 0.729635i | \(0.739690\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.23352e6 | −0.295288 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −812156. | −0.190118 | −0.0950591 | − | 0.995472i | \(-0.530304\pi\) | ||||
−0.0950591 | + | 0.995472i | \(0.530304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.62334e6 | −1.76483 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.71196e6 | −0.387672 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −926920. | −0.207612 | −0.103806 | − | 0.994598i | \(-0.533102\pi\) | ||||
−0.103806 | + | 0.994598i | \(0.533102\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.67043e6 | 0.804386 | 0.402193 | − | 0.915555i | \(-0.368248\pi\) | ||||
0.402193 | + | 0.915555i | \(0.368248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.70462e6 | −0.586345 | −0.293173 | − | 0.956060i | \(-0.594711\pi\) | ||||
−0.293173 | + | 0.956060i | \(0.594711\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.24431e6 | 1.74929 | 0.874645 | − | 0.484763i | \(-0.161094\pi\) | ||||
0.874645 | + | 0.484763i | \(0.161094\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 586965. | 0.123220 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −169067. | −0.0347461 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.54419e6 | −0.314027 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.55003e6 | 0.507816 | 0.253908 | − | 0.967228i | \(-0.418284\pi\) | ||||
0.253908 | + | 0.967228i | \(0.418284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.22253e6 | −1.62048 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.29119e6 | −0.635328 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.66815e6 | 1.46510 | 0.732552 | − | 0.680711i | \(-0.238329\pi\) | ||||
0.732552 | + | 0.680711i | \(0.238329\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.33268e6 | −1.74704 | −0.873519 | − | 0.486790i | \(-0.838168\pi\) | ||||
−0.873519 | + | 0.486790i | \(0.838168\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −744200. | −0.137903 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 633320. | 0.115009 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.19065e6 | −0.214059 | −0.107030 | − | 0.994256i | \(-0.534134\pi\) | ||||
−0.107030 | + | 0.994256i | \(0.534134\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.34213e6 | −0.412753 | −0.206377 | − | 0.978473i | \(-0.566167\pi\) | ||||
−0.206377 | + | 0.978473i | \(0.566167\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.49736e6 | −0.959237 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.69767e6 | 1.14585 | 0.572927 | − | 0.819606i | \(-0.305808\pi\) | ||||
0.572927 | + | 0.819606i | \(0.305808\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.97768e6 | 0.673873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.00275e6 | 1.16346 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.06016e7 | −1.74439 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.81727e6 | −0.938911 | −0.469456 | − | 0.882956i | \(-0.655550\pi\) | ||||
−0.469456 | + | 0.882956i | \(0.655550\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.02571e7 | 1.63972 | 0.819858 | − | 0.572568i | \(-0.194053\pi\) | ||||
0.819858 | + | 0.572568i | \(0.194053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −198666. | −0.0311600 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.32367e7 | 2.05655 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.32519e7 | 2.02051 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.26982e6 | 0.342852 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.35855e6 | −0.201420 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.26601e6 | 0.773550 | 0.386775 | − | 0.922174i | \(-0.373589\pi\) | ||||
0.386775 | + | 0.922174i | \(0.373589\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.37670e6 | −0.342755 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.89900e6 | 0.700066 | 0.350033 | − | 0.936737i | \(-0.386170\pi\) | ||||
0.350033 | + | 0.936737i | \(0.386170\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.08107e6 | 0.432337 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.30294e6 | 0.320236 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.17946e6 | 1.25366 | 0.626829 | − | 0.779157i | \(-0.284352\pi\) | ||||
0.626829 | + | 0.779157i | \(0.284352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 293895. | 0.0397799 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 249472. | 0.0331704 | 0.0165852 | − | 0.999862i | \(-0.494721\pi\) | ||||
0.0165852 | + | 0.999862i | \(0.494721\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.57066e6 | −0.470574 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.31498e7 | −1.70270 | −0.851351 | − | 0.524596i | \(-0.824216\pi\) | ||||
−0.851351 | + | 0.524596i | \(0.824216\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.51038e7 | 1.93863 | 0.969316 | − | 0.245817i | \(-0.0790562\pi\) | ||||
0.969316 | + | 0.245817i | \(0.0790562\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.26445e6 | 1.04242 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −727822. | −0.0910093 | −0.0455046 | − | 0.998964i | \(-0.514490\pi\) | ||||
−0.0455046 | + | 0.998964i | \(0.514490\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.46567e6 | 0.671743 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.07377e6 | 1.10565 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.24256e7 | −1.48841 | −0.744207 | − | 0.667949i | \(-0.767172\pi\) | ||||
−0.744207 | + | 0.667949i | \(0.767172\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 822500. | 0.0976895 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.17981e6 | −0.721669 | −0.360835 | − | 0.932630i | \(-0.617508\pi\) | ||||
−0.360835 | + | 0.932630i | \(0.617508\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 348408. | 0.0403455 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.30603e7 | −1.48726 | −0.743630 | − | 0.668592i | \(-0.766897\pi\) | ||||
−0.743630 | + | 0.668592i | \(0.766897\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.01833e6 | 1.01845 | 0.509225 | − | 0.860633i | \(-0.329932\pi\) | ||||
0.509225 | + | 0.860633i | \(0.329932\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.65158e6 | −0.627742 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.36835e7 | −1.50739 | −0.753694 | − | 0.657226i | \(-0.771730\pi\) | ||||
−0.753694 | + | 0.657226i | \(0.771730\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.84291e7 | 1.99711 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.23266e6 | −0.454949 | −0.227474 | − | 0.973784i | \(-0.573047\pi\) | ||||
−0.227474 | + | 0.973784i | \(0.573047\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.32584e6 | −0.351713 | −0.175856 | − | 0.984416i | \(-0.556269\pi\) | ||||
−0.175856 | + | 0.984416i | \(0.556269\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.19987e7 | −1.25866 | −0.629328 | − | 0.777140i | \(-0.716670\pi\) | ||||
−0.629328 | + | 0.777140i | \(0.716670\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.70162e6 | 0.175647 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −471051. | −0.0482356 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.67340e6 | 0.168645 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.99962e6 | 0.999793 | 0.499896 | − | 0.866085i | \(-0.333371\pi\) | ||||
0.499896 | + | 0.866085i | \(0.333371\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.50602e6 | 0.541880 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.36161e6 | 0.230600 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.16624e6 | 0.304368 | 0.152184 | − | 0.988352i | \(-0.451369\pi\) | ||||
0.152184 | + | 0.988352i | \(0.451369\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 950578. | 0.0906693 | 0.0453346 | − | 0.998972i | \(-0.485565\pi\) | ||||
0.0453346 | + | 0.998972i | \(0.485565\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.14671e7 | 1.07694 | 0.538470 | − | 0.842645i | \(-0.319003\pi\) | ||||
0.538470 | + | 0.842645i | \(0.319003\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.21379e6 | 0.672282 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.80936e6 | 0.257824 | 0.128912 | − | 0.991656i | \(-0.458851\pi\) | ||||
0.128912 | + | 0.991656i | \(0.458851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.50054e6 | −0.227735 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.23794e6 | 0.380138 | 0.190069 | − | 0.981771i | \(-0.439129\pi\) | ||||
0.190069 | + | 0.981771i | \(0.439129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.70903e6 | 0.152141 | 0.0760703 | − | 0.997102i | \(-0.475763\pi\) | ||||
0.0760703 | + | 0.997102i | \(0.475763\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.44244e6 | −0.126487 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.64898e7 | −1.43516 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.97903e7 | 1.69686 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.11371e7 | 0.947836 | 0.473918 | − | 0.880569i | \(-0.342839\pi\) | ||||
0.473918 | + | 0.880569i | \(0.342839\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.09873e6 | −0.679118 | −0.339559 | − | 0.940585i | \(-0.610278\pi\) | ||||
−0.339559 | + | 0.940585i | \(0.610278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.54012e6 | 0.377914 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.49864e7 | 1.22926 | 0.614632 | − | 0.788814i | \(-0.289305\pi\) | ||||
0.614632 | + | 0.788814i | \(0.289305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.24211e6 | 0.508283 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.57733e7 | −1.26582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.18569e7 | 1.74138 | 0.870691 | − | 0.491831i | \(-0.163672\pi\) | ||||
0.870691 | + | 0.491831i | \(0.163672\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.56354e6 | −0.122786 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.69695e6 | −0.210277 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.21819e7 | 0.936307 | 0.468154 | − | 0.883647i | \(-0.344919\pi\) | ||||
0.468154 | + | 0.883647i | \(0.344919\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.92807e6 | −0.528718 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.58349e6 | 0.570585 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.03040e6 | −0.599959 | −0.299980 | − | 0.953946i | \(-0.596980\pi\) | ||||
−0.299980 | + | 0.953946i | \(0.596980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.40199e6 | −0.324284 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.97687e7 | 1.44615 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.76681e7 | 1.27458 | 0.637290 | − | 0.770624i | \(-0.280055\pi\) | ||||
0.637290 | + | 0.770624i | \(0.280055\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.66014e6 | −0.692062 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.92720e6 | −0.489455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.71905e7 | 1.20629 | 0.603146 | − | 0.797631i | \(-0.293914\pi\) | ||||
0.603146 | + | 0.797631i | \(0.293914\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −59811.9 | −0.00413994 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.30219e6 | 0.639478 | 0.319739 | − | 0.947506i | \(-0.396405\pi\) | ||||
0.319739 | + | 0.947506i | \(0.396405\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.77794e6 | −0.459652 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.29625e7 | −0.873129 | −0.436564 | − | 0.899673i | \(-0.643805\pi\) | ||||
−0.436564 | + | 0.899673i | \(0.643805\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.45466e7 | −0.966693 | −0.483347 | − | 0.875429i | \(-0.660579\pi\) | ||||
−0.483347 | + | 0.875429i | \(0.660579\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.30284e6 | −0.284030 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.13116e6 | −0.203939 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.44950e7 | 0.937816 | 0.468908 | − | 0.883247i | \(-0.344648\pi\) | ||||
0.468908 | + | 0.883247i | \(0.344648\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.41537e7 | −0.903653 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.49809e7 | 1.58441 | 0.792207 | − | 0.610252i | \(-0.208932\pi\) | ||||
0.792207 | + | 0.610252i | \(0.208932\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.56594e7 | −0.980196 | −0.490098 | − | 0.871667i | \(-0.663039\pi\) | ||||
−0.490098 | + | 0.871667i | \(0.663039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.27861e6 | 0.203882 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.25400e7 | −0.769677 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.30420e7 | 0.795292 | 0.397646 | − | 0.917539i | \(-0.369827\pi\) | ||||
0.397646 | + | 0.917539i | \(0.369827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.46084e7 | 0.879336 | 0.439668 | − | 0.898160i | \(-0.355096\pi\) | ||||
0.439668 | + | 0.898160i | \(0.355096\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.84924e6 | −0.110596 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.11657e7 | 0.659237 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.31323e6 | −0.429024 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.85705e6 | 0.281319 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.62167e7 | −1.50883 | −0.754416 | − | 0.656396i | \(-0.772080\pi\) | ||||
−0.754416 | + | 0.656396i | \(0.772080\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.92565e6 | 0.279913 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.44021e7 | −1.94268 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.41107e6 | −0.190215 | −0.0951075 | − | 0.995467i | \(-0.530319\pi\) | ||||
−0.0951075 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.75059e6 | −0.207841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.59321e7 | −2.51378 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.71992e6 | 0.419878 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.72606e7 | 0.927225 | 0.463612 | − | 0.886038i | \(-0.346553\pi\) | ||||
0.463612 | + | 0.886038i | \(0.346553\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.42616e7 | 1.29529 | 0.647647 | − | 0.761941i | \(-0.275753\pi\) | ||||
0.647647 | + | 0.761941i | \(0.275753\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.28188e7 | −1.20337 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 247628. | 0.0129791 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.29927e6 | 0.170829 | 0.0854143 | − | 0.996346i | \(-0.472779\pi\) | ||||
0.0854143 | + | 0.996346i | \(0.472779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.15209e7 | 1.10754 | 0.553772 | − | 0.832669i | \(-0.313188\pi\) | ||||
0.553772 | + | 0.832669i | \(0.313188\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.31588e6 | 0.371966 | 0.185983 | − | 0.982553i | \(-0.440453\pi\) | ||||
0.185983 | + | 0.982553i | \(0.440453\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.33238e7 | −1.17873 | −0.589364 | − | 0.807867i | \(-0.700622\pi\) | ||||
−0.589364 | + | 0.807867i | \(0.700622\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −480621. | −0.0239988 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.03309e7 | −0.512768 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.69417e7 | 1.32136 | 0.660678 | − | 0.750669i | \(-0.270269\pi\) | ||||
0.660678 | + | 0.750669i | \(0.270269\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.68954e6 | −0.326142 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.11761e7 | −1.02025 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.79623e6 | 0.373402 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.70788e7 | 1.75510 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.20124e7 | −0.565270 | −0.282635 | − | 0.959228i | \(-0.591208\pi\) | ||||
−0.282635 | + | 0.959228i | \(0.591208\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.71627e6 | 0.126334 | 0.0631672 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631672 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.59580e6 | −0.351229 | −0.175615 | − | 0.984459i | \(-0.556191\pi\) | ||||
−0.175615 | + | 0.984459i | \(0.556191\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.72463e6 | 0.0788260 | 0.0394130 | − | 0.999223i | \(-0.487451\pi\) | ||||
0.0394130 | + | 0.999223i | \(0.487451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.99709e7 | −0.907524 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.65931e7 | −1.19459 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.17823e7 | 0.526243 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.68217e6 | 0.383361 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.20923e6 | 0.316512 | 0.158256 | − | 0.987398i | \(-0.449413\pi\) | ||||
0.158256 | + | 0.987398i | \(0.449413\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.88596e7 | 1.68678 | 0.843391 | − | 0.537301i | \(-0.180556\pi\) | ||||
0.843391 | + | 0.537301i | \(0.180556\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.52433e7 | 0.657927 | 0.328964 | − | 0.944343i | \(-0.393301\pi\) | ||||
0.328964 | + | 0.944343i | \(0.393301\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.66999e6 | 0.113947 | 0.0569733 | − | 0.998376i | \(-0.481855\pi\) | ||||
0.0569733 | + | 0.998376i | \(0.481855\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.59543e6 | −0.322328 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.55278e7 | 0.651602 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.10884e7 | −0.462712 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.68972e6 | 0.152263 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.21008e6 | 0.131736 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.03048e6 | −0.366513 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.48123e6 | −0.342327 | −0.171163 | − | 0.985243i | \(-0.554753\pi\) | ||||
−0.171163 | + | 0.985243i | \(0.554753\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.89967e7 | 1.55680 | 0.778399 | − | 0.627770i | \(-0.216032\pi\) | ||||
0.778399 | + | 0.627770i | \(0.216032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.31145e7 | −2.50583 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.44944e6 | 0.135464 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.65313e7 | −1.03626 | −0.518130 | − | 0.855302i | \(-0.673372\pi\) | ||||
−0.518130 | + | 0.855302i | \(0.673372\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.27128e7 | 0.491177 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.55765e7 | 0.598569 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.74701e6 | −0.370537 | −0.185269 | − | 0.982688i | \(-0.559316\pi\) | ||||
−0.185269 | + | 0.982688i | \(0.559316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.98982e6 | 0.0752385 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.02322e6 | −0.150503 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.21792e7 | 1.19736 | 0.598682 | − | 0.800987i | \(-0.295691\pi\) | ||||
0.598682 | + | 0.800987i | \(0.295691\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.89802e7 | −1.06691 | −0.533454 | − | 0.845829i | \(-0.679106\pi\) | ||||
−0.533454 | + | 0.845829i | \(0.679106\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.97583e7 | −2.18836 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.99329e6 | 0.144696 | 0.0723479 | − | 0.997379i | \(-0.476951\pi\) | ||||
0.0723479 | + | 0.997379i | \(0.476951\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.98454e7 | 2.87796 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.26669e7 | −1.16513 | −0.582566 | − | 0.812783i | \(-0.697951\pi\) | ||||
−0.582566 | + | 0.812783i | \(0.697951\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.71553e6 | −0.238271 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.61086e6 | −0.302343 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.76442e7 | −0.965595 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.34588e7 | −0.810937 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.51237e6 | −0.327132 | −0.163566 | − | 0.986532i | \(-0.552300\pi\) | ||||
−0.163566 | + | 0.986532i | \(0.552300\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.99431e7 | −1.01917 | −0.509587 | − | 0.860419i | \(-0.670202\pi\) | ||||
−0.509587 | + | 0.860419i | \(0.670202\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.15688e6 | 0.0730370 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.93182e7 | −1.65299 | −0.826496 | − | 0.562943i | \(-0.809669\pi\) | ||||
−0.826496 | + | 0.562943i | \(0.809669\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.96493e7 | −0.655225 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.39536e7 | −1.45081 | −0.725405 | − | 0.688322i | \(-0.758347\pi\) | ||||
−0.725405 | + | 0.688322i | \(0.758347\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.79412e7 | −0.917603 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.32529e6 | −0.0430845 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.45885e7 | 0.795331 | 0.397665 | − | 0.917531i | \(-0.369820\pi\) | ||||
0.397665 | + | 0.917531i | \(0.369820\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.28063e7 | −0.410077 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.71682e7 | −0.865612 | −0.432806 | − | 0.901487i | \(-0.642476\pi\) | ||||
−0.432806 | + | 0.901487i | \(0.642476\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 504.6.a.s.1.1 | 2 | ||
3.2 | odd | 2 | 56.6.a.c.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 1008.6.a.bt.1.1 | 2 | |||
12.11 | even | 2 | 112.6.a.k.1.1 | 2 | |||
21.2 | odd | 6 | 392.6.i.l.361.1 | 4 | |||
21.5 | even | 6 | 392.6.i.g.361.2 | 4 | |||
21.11 | odd | 6 | 392.6.i.l.177.1 | 4 | |||
21.17 | even | 6 | 392.6.i.g.177.2 | 4 | |||
21.20 | even | 2 | 392.6.a.f.1.1 | 2 | |||
24.5 | odd | 2 | 448.6.a.z.1.1 | 2 | |||
24.11 | even | 2 | 448.6.a.q.1.2 | 2 | |||
84.83 | odd | 2 | 784.6.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.a.c.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
112.6.a.k.1.1 | 2 | 12.11 | even | 2 | |||
392.6.a.f.1.1 | 2 | 21.20 | even | 2 | |||
392.6.i.g.177.2 | 4 | 21.17 | even | 6 | |||
392.6.i.g.361.2 | 4 | 21.5 | even | 6 | |||
392.6.i.l.177.1 | 4 | 21.11 | odd | 6 | |||
392.6.i.l.361.1 | 4 | 21.2 | odd | 6 | |||
448.6.a.q.1.2 | 2 | 24.11 | even | 2 | |||
448.6.a.z.1.1 | 2 | 24.5 | odd | 2 | |||
504.6.a.s.1.1 | 2 | 1.1 | even | 1 | trivial | ||
784.6.a.p.1.2 | 2 | 84.83 | odd | 2 | |||
1008.6.a.bt.1.1 | 2 | 4.3 | odd | 2 |