Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.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: | \(125.740914733\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{37}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 7) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.54138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-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 | ||||||||
\(3\) | −10.0828 | −0.646810 | −0.323405 | − | 0.946261i | \(-0.604828\pi\) | ||||
−0.323405 | + | 0.946261i | \(0.604828\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 79.8276 | 1.42800 | 0.714000 | − | 0.700146i | \(-0.246882\pi\) | ||||
0.714000 | + | 0.700146i | \(0.246882\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −141.338 | −0.581637 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −351.904 | −0.876884 | −0.438442 | − | 0.898760i | \(-0.644469\pi\) | ||||
−0.438442 | + | 0.898760i | \(0.644469\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 291.683 | 0.478688 | 0.239344 | − | 0.970935i | \(-0.423068\pi\) | ||||
0.239344 | + | 0.970935i | \(0.423068\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −804.883 | −0.923644 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 370.075 | 0.310576 | 0.155288 | − | 0.987869i | \(-0.450369\pi\) | ||||
0.155288 | + | 0.987869i | \(0.450369\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1504.93 | 0.956381 | 0.478190 | − | 0.878256i | \(-0.341293\pi\) | ||||
0.478190 | + | 0.878256i | \(0.341293\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 425.711 | 0.167801 | 0.0839006 | − | 0.996474i | \(-0.473262\pi\) | ||||
0.0839006 | + | 0.996474i | \(0.473262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3247.45 | 1.03918 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3875.19 | 1.02302 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7783.93 | −1.71872 | −0.859358 | − | 0.511374i | \(-0.829137\pi\) | ||||
−0.859358 | + | 0.511374i | \(0.829137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2575.18 | −0.481285 | −0.240643 | − | 0.970614i | \(-0.577358\pi\) | ||||
−0.240643 | + | 0.970614i | \(0.577358\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3548.16 | 0.567177 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 739.618 | 0.0888184 | 0.0444092 | − | 0.999013i | \(-0.485859\pi\) | ||||
0.0444092 | + | 0.999013i | \(0.485859\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2940.97 | −0.309620 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7029.84 | −0.653109 | −0.326554 | − | 0.945178i | \(-0.605888\pi\) | ||||
−0.326554 | + | 0.945178i | \(0.605888\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1835.23 | −0.151363 | −0.0756816 | − | 0.997132i | \(-0.524113\pi\) | ||||
−0.0756816 | + | 0.997132i | \(0.524113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11282.7 | −0.830578 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1532.68 | −0.101206 | −0.0506032 | − | 0.998719i | \(-0.516114\pi\) | ||||
−0.0506032 | + | 0.998719i | \(0.516114\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3731.38 | −0.200883 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9537.46 | −0.466383 | −0.233192 | − | 0.972431i | \(-0.574917\pi\) | ||||
−0.233192 | + | 0.972431i | \(0.574917\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −28091.6 | −1.25219 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15173.8 | −0.618596 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −29674.1 | −1.10981 | −0.554903 | − | 0.831915i | \(-0.687245\pi\) | ||||
−0.554903 | + | 0.831915i | \(0.687245\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 46510.8 | 1.60040 | 0.800201 | − | 0.599732i | \(-0.204726\pi\) | ||||
0.800201 | + | 0.599732i | \(0.204726\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23284.3 | 0.683566 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −26746.1 | −0.727902 | −0.363951 | − | 0.931418i | \(-0.618572\pi\) | ||||
−0.363951 | + | 0.931418i | \(0.618572\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4292.34 | −0.108535 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14388.8 | 0.338748 | 0.169374 | − | 0.985552i | \(-0.445825\pi\) | ||||
0.169374 | + | 0.985552i | \(0.445825\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70095.1 | 1.53950 | 0.769752 | − | 0.638343i | \(-0.220380\pi\) | ||||
0.769752 | + | 0.638343i | \(0.220380\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −32743.3 | −0.672154 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 27085.8 | 0.488285 | 0.244143 | − | 0.969739i | \(-0.421493\pi\) | ||||
0.244143 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4727.49 | −0.0800604 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −79755.4 | −1.27076 | −0.635382 | − | 0.772198i | \(-0.719157\pi\) | ||||
−0.635382 | + | 0.772198i | \(0.719157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29542.2 | 0.443502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 78483.6 | 1.11168 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −43577.3 | −0.583157 | −0.291579 | − | 0.956547i | \(-0.594180\pi\) | ||||
−0.291579 | + | 0.956547i | \(0.594180\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 25964.9 | 0.311300 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 120135. | 1.36571 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −103374. | −1.11553 | −0.557765 | − | 0.829999i | \(-0.688341\pi\) | ||||
−0.557765 | + | 0.829999i | \(0.688341\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 49737.3 | 0.510028 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −28700.2 | −0.279951 | −0.139975 | − | 0.990155i | \(-0.544702\pi\) | ||||
−0.139975 | + | 0.990155i | \(0.544702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 29227.9 | 0.271459 | 0.135730 | − | 0.990746i | \(-0.456662\pi\) | ||||
0.135730 | + | 0.990746i | \(0.456662\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −87858.4 | −0.741863 | −0.370932 | − | 0.928660i | \(-0.620962\pi\) | ||||
−0.370932 | + | 0.928660i | \(0.620962\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 220628. | 1.77867 | 0.889333 | − | 0.457260i | \(-0.151169\pi\) | ||||
0.889333 | + | 0.457260i | \(0.151169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7457.39 | −0.0574486 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 39665.6 | 0.292225 | 0.146113 | − | 0.989268i | \(-0.453324\pi\) | ||||
0.146113 | + | 0.989268i | \(0.453324\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 33983.5 | 0.239620 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −41225.8 | −0.278423 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −37214.9 | −0.231075 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 70880.2 | 0.422437 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9774.87 | 0.0559546 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −51740.3 | −0.284655 | −0.142328 | − | 0.989820i | \(-0.545459\pi\) | ||||
−0.142328 | + | 0.989820i | \(0.545459\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18504.2 | 0.0979031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −166674. | −0.848572 | −0.424286 | − | 0.905528i | \(-0.639475\pi\) | ||||
−0.424286 | + | 0.905528i | \(0.639475\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 309347. | 1.46087 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 28259.4 | 0.128636 | 0.0643178 | − | 0.997929i | \(-0.479513\pi\) | ||||
0.0643178 | + | 0.997929i | \(0.479513\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 336393. | 1.47676 | 0.738380 | − | 0.674384i | \(-0.235591\pi\) | ||||
0.738380 | + | 0.674384i | \(0.235591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15453.7 | 0.0654612 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −102644. | −0.419753 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −621373. | −2.45433 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −355381. | −1.31138 | −0.655691 | − | 0.755030i | \(-0.727622\pi\) | ||||
−0.655691 | + | 0.755030i | \(0.727622\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 358797. | 1.28058 | 0.640290 | − | 0.768133i | \(-0.278814\pi\) | ||||
0.640290 | + | 0.768133i | \(0.278814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −52305.7 | −0.180643 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −205570. | −0.687275 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −458911. | −1.48586 | −0.742932 | − | 0.669367i | \(-0.766565\pi\) | ||||
−0.742932 | + | 0.669367i | \(0.766565\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 96164.0 | 0.301661 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −502441. | −1.48121 | −0.740603 | − | 0.671943i | \(-0.765460\pi\) | ||||
−0.740603 | + | 0.671943i | \(0.765460\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 283241. | 0.809928 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −676652. | −1.87748 | −0.938738 | − | 0.344632i | \(-0.888004\pi\) | ||||
−0.938738 | + | 0.344632i | \(0.888004\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −286214. | −0.770858 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −212703. | −0.556267 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 249160. | 0.632941 | 0.316470 | − | 0.948602i | \(-0.397502\pi\) | ||||
0.316470 | + | 0.948602i | \(0.397502\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 299196. | 0.717833 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −139258. | −0.324853 | −0.162427 | − | 0.986721i | \(-0.551932\pi\) | ||||
−0.162427 | + | 0.986721i | \(0.551932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −306246. | −0.694823 | −0.347412 | − | 0.937713i | \(-0.612939\pi\) | ||||
−0.347412 | + | 0.937713i | \(0.612939\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −468957. | −1.03516 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 59041.9 | 0.126833 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −130231. | −0.272339 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −227494. | −0.451218 | −0.225609 | − | 0.974218i | \(-0.572437\pi\) | ||||
−0.225609 | + | 0.974218i | \(0.572437\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −672374. | −1.29933 | −0.649663 | − | 0.760223i | \(-0.725090\pi\) | ||||
−0.649663 | + | 0.760223i | \(0.725090\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −234770. | −0.442137 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1282.76 | −0.00235493 | −0.00117747 | − | 0.999999i | \(-0.500375\pi\) | ||||
−0.00117747 | + | 0.999999i | \(0.500375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 368898. | 0.660349 | 0.330175 | − | 0.943920i | \(-0.392892\pi\) | ||||
0.330175 | + | 0.943920i | \(0.392892\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 269674. | 0.470814 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −561175. | −0.932640 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −60169.0 | −0.0975994 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −529589. | −0.838635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −502168. | −0.776503 | −0.388251 | − | 0.921553i | \(-0.626921\pi\) | ||||
−0.388251 | + | 0.921553i | \(0.626921\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −145078. | −0.219106 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −146502. | −0.216147 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −706753. | −0.995765 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 107945. | 0.148669 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.17328e6 | −1.57993 | −0.789967 | − | 0.613149i | \(-0.789902\pi\) | ||||
−0.789967 | + | 0.613149i | \(0.789902\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −458988. | −0.604428 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −910159. | −1.17234 | −0.586168 | − | 0.810189i | \(-0.699364\pi\) | ||||
−0.586168 | + | 0.810189i | \(0.699364\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −521924. | −0.657686 | −0.328843 | − | 0.944385i | \(-0.606659\pi\) | ||||
−0.328843 | + | 0.944385i | \(0.606659\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.04279e6 | −1.25836 | −0.629182 | − | 0.777258i | \(-0.716610\pi\) | ||||
−0.629182 | + | 0.777258i | \(0.716610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −122350. | −0.144523 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −273100. | −0.315828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.53447e6 | 1.73766 | 0.868830 | − | 0.495110i | \(-0.164872\pi\) | ||||
0.868830 | + | 0.495110i | \(0.164872\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00758e6 | 1.11747 | 0.558735 | − | 0.829346i | \(-0.311287\pi\) | ||||
0.558735 | + | 0.829346i | \(0.311287\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −894004. | −0.971234 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 438961. | 0.457808 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 804155. | 0.821942 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8511.89 | 0.00852789 | 0.00426394 | − | 0.999991i | \(-0.498643\pi\) | ||||
0.00426394 | + | 0.999991i | \(0.498643\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −149809. | −0.147142 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −297867. | −0.286862 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 527532. | 0.498214 | 0.249107 | − | 0.968476i | \(-0.419863\pi\) | ||||
0.249107 | + | 0.968476i | \(0.419863\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.10016e6 | 0.999670 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 352085. | 0.313876 | 0.156938 | − | 0.987608i | \(-0.449838\pi\) | ||||
0.156938 | + | 0.987608i | \(0.449838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −761353. | −0.665996 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 439380. | 0.377192 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −479540. | −0.404058 | −0.202029 | − | 0.979380i | \(-0.564754\pi\) | ||||
−0.202029 | + | 0.979380i | \(0.564754\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −977611. | −0.808617 | −0.404308 | − | 0.914623i | \(-0.632488\pi\) | ||||
−0.404308 | + | 0.914623i | \(0.632488\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.14279e6 | −0.911243 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 968723. | 0.758578 | 0.379289 | − | 0.925278i | \(-0.376169\pi\) | ||||
0.379289 | + | 0.925278i | \(0.376169\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 363970. | 0.279934 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −318333. | −0.240501 | −0.120250 | − | 0.992744i | \(-0.538370\pi\) | ||||
−0.120250 | + | 0.992744i | \(0.538370\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.77210e6 | 1.31529 | 0.657646 | − | 0.753327i | \(-0.271552\pi\) | ||||
0.657646 | + | 0.753327i | \(0.271552\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.21129e6 | −0.883356 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.28290e6 | −0.903543 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.04229e6 | 0.721535 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.64148e6 | −1.11703 | −0.558516 | − | 0.829494i | \(-0.688629\pi\) | ||||
−0.558516 | + | 0.829494i | \(0.688629\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.36881e6 | −1.58480 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.36369e6 | −0.897068 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 124172. | 0.0803243 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 289377. | 0.181075 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.71285e6 | 2.28537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −466930. | −0.282752 | −0.141376 | − | 0.989956i | \(-0.545153\pi\) | ||||
−0.141376 | + | 0.989956i | \(0.545153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −294698. | −0.175582 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.43796e6 | −1.42931 | −0.714654 | − | 0.699478i | \(-0.753416\pi\) | ||||
−0.714654 | + | 0.699478i | \(0.753416\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.42094e6 | −1.39676 | −0.698381 | − | 0.715726i | \(-0.746096\pi\) | ||||
−0.698381 | + | 0.715726i | \(0.746096\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.87611e6 | 1.04860 | 0.524301 | − | 0.851533i | \(-0.324327\pi\) | ||||
0.524301 | + | 0.851533i | \(0.324327\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.73919e6 | 1.50711 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 885855. | 0.479844 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 556936. | 0.297029 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 947225. | 0.497445 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.22454e6 | −1.15046 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.08310e6 | 0.543373 | 0.271686 | − | 0.962386i | \(-0.412419\pi\) | ||||
0.271686 | + | 0.962386i | \(0.412419\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −104536. | −0.0516601 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.13507e6 | −1.03944 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.59465e6 | −1.24453 | −0.622263 | − | 0.782809i | \(-0.713786\pi\) | ||||
−0.622263 | + | 0.782809i | \(0.713786\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −399939. | −0.189014 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 906213. | 0.422031 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −342647. | −0.154989 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.87051e6 | 0.833943 | 0.416972 | − | 0.908920i | \(-0.363091\pi\) | ||||
0.416972 | + | 0.908920i | \(0.363091\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.61685e6 | 0.710568 | 0.355284 | − | 0.934758i | \(-0.384384\pi\) | ||||
0.355284 | + | 0.934758i | \(0.384384\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.13033e6 | 0.489706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 578305. | 0.247013 | 0.123507 | − | 0.992344i | \(-0.460586\pi\) | ||||
0.123507 | + | 0.992344i | \(0.460586\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.14862e6 | 0.483733 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.96818e6 | 0.805988 | 0.402994 | − | 0.915203i | \(-0.367970\pi\) | ||||
0.402994 | + | 0.915203i | \(0.367970\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −211299. | −0.0853355 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 375229. | 0.149462 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.59553e6 | 2.19841 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.17452e6 | 0.842749 | 0.421375 | − | 0.906887i | \(-0.361548\pi\) | ||||
0.421375 | + | 0.906887i | \(0.361548\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 993583. | 0.379873 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.38476e6 | 0.515349 | 0.257675 | − | 0.966232i | \(-0.417044\pi\) | ||||
0.257675 | + | 0.966232i | \(0.417044\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −98557.7 | −0.0361920 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.27044e6 | −0.822728 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.37190e6 | −1.20580 | −0.602902 | − | 0.797815i | \(-0.705989\pi\) | ||||
−0.602902 | + | 0.797815i | \(0.705989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 521685. | 0.184118 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.28060e6 | 1.14276 | 0.571382 | − | 0.820685i | \(-0.306408\pi\) | ||||
0.571382 | + | 0.820685i | \(0.306408\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 259388. | 0.0880385 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.94810e6 | −0.987797 | −0.493899 | − | 0.869520i | \(-0.664429\pi\) | ||||
−0.493899 | + | 0.869520i | \(0.664429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 157545. | 0.0521150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.68053e6 | 0.548865 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.16219e6 | 0.697271 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 69270.2 | 0.0220582 | 0.0110291 | − | 0.999939i | \(-0.496489\pi\) | ||||
0.0110291 | + | 0.999939i | \(0.496489\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.34786e6 | −1.03970 | −0.519848 | − | 0.854259i | \(-0.674012\pi\) | ||||
−0.519848 | + | 0.854259i | \(0.674012\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −751134. | −0.230385 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −377384. | −0.114326 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −260274. | −0.0778834 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.91217e6 | −0.860812 | −0.430406 | − | 0.902636i | \(-0.641630\pi\) | ||||
−0.430406 | + | 0.902636i | \(0.641630\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −284933. | −0.0832028 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.36669e6 | −1.81465 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.39177e6 | −0.955183 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.62361e6 | −1.28661 | −0.643304 | − | 0.765611i | \(-0.722437\pi\) | ||||
−0.643304 | + | 0.765611i | \(0.722437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.63042e6 | −0.723303 | −0.361652 | − | 0.932313i | \(-0.617787\pi\) | ||||
−0.361652 | + | 0.932313i | \(0.617787\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 216626. | 0.0588654 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.20180e6 | 0.322746 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.03494e6 | 0.271500 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.54128e6 | −1.95547 | −0.977736 | − | 0.209837i | \(-0.932707\pi\) | ||||
−0.977736 | + | 0.209837i | \(0.932707\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.83558e6 | −1.49577 | −0.747883 | − | 0.663830i | \(-0.768930\pi\) | ||||
−0.747883 | + | 0.663830i | \(0.768930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.26516e6 | 1.58748 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 640663. | 0.160482 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 168104. | 0.0416310 | 0.0208155 | − | 0.999783i | \(-0.493374\pi\) | ||||
0.0208155 | + | 0.999783i | \(0.493374\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.84151e6 | 0.687924 | 0.343962 | − | 0.938984i | \(-0.388231\pi\) | ||||
0.343962 | + | 0.938984i | \(0.388231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.47867e6 | −0.832748 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.58323e6 | 0.848214 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.41567e6 | −0.331396 | −0.165698 | − | 0.986177i | \(-0.552988\pi\) | ||||
−0.165698 | + | 0.986177i | \(0.552988\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.47382e6 | 0.572701 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.61767e6 | −0.828291 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.55727e6 | 0.348799 | 0.174399 | − | 0.984675i | \(-0.444202\pi\) | ||||
0.174399 | + | 0.984675i | \(0.444202\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.43411e6 | 0.317725 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.45345e6 | 0.975987 | 0.487994 | − | 0.872847i | \(-0.337729\pi\) | ||||
0.487994 | + | 0.872847i | \(0.337729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.92263e6 | −1.06720 | −0.533599 | − | 0.845738i | \(-0.679161\pi\) | ||||
−0.533599 | + | 0.845738i | \(0.679161\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.07271e6 | 0.444536 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.09090e6 | 1.08020 | 0.540098 | − | 0.841602i | \(-0.318387\pi\) | ||||
0.540098 | + | 0.841602i | \(0.318387\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.62709e6 | 0.961071 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 645825. | 0.132728 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.88717e6 | 0.993856 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.34800e6 | 0.271266 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.30085e6 | −1.65304 | −0.826521 | − | 0.562907i | \(-0.809683\pi\) | ||||
−0.826521 | + | 0.562907i | \(0.809683\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 215734. | 0.0425163 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.25208e6 | −1.59298 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.63401e6 | −1.64964 | −0.824822 | − | 0.565392i | \(-0.808725\pi\) | ||||
−0.824822 | + | 0.565392i | \(0.808725\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.06599e6 | 0.958059 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −95039.5 | −0.0177910 | −0.00889550 | − | 0.999960i | \(-0.502832\pi\) | ||||
−0.00889550 | + | 0.999960i | \(0.502832\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.88064e6 | −0.533792 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.97041e6 | 0.728320 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.14203e6 | −0.385101 | −0.192551 | − | 0.981287i | \(-0.561676\pi\) | ||||
−0.192551 | + | 0.981287i | \(0.561676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.82252e6 | 1.21437 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.24794e6 | 0.924844 | 0.462422 | − | 0.886660i | \(-0.346981\pi\) | ||||
0.462422 | + | 0.886660i | \(0.346981\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.29107e6 | −0.399769 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.88583e6 | 0.498598 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.05891e7 | 1.81160 | 0.905802 | − | 0.423702i | \(-0.139270\pi\) | ||||
0.905802 | + | 0.423702i | \(0.139270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.83187e6 | 0.978395 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.33319e6 | 0.387644 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 539357. | 0.0887462 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.51222e6 | −0.409392 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.54465e6 | 0.733510 | 0.366755 | − | 0.930318i | \(-0.380469\pi\) | ||||
0.366755 | + | 0.930318i | \(0.380469\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.27197e6 | −0.842789 | −0.421394 | − | 0.906877i | \(-0.638459\pi\) | ||||
−0.421394 | + | 0.906877i | \(0.638459\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −953009. | −0.149476 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.25511e6 | −0.971843 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.19407e6 | 0.645504 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.05048e6 | −0.312635 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.01353e6 | −1.05938 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.40410e6 | 0.210118 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.93445e6 | 0.871741 | 0.435871 | − | 0.900009i | \(-0.356441\pi\) | ||||
0.435871 | + | 0.900009i | \(0.356441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.08781e6 | 0.449418 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.76122e7 | 2.53994 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.82017e6 | 1.26040 | 0.630200 | − | 0.776433i | \(-0.282973\pi\) | ||||
0.630200 | + | 0.776433i | \(0.282973\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.57374e6 | −0.930854 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.17142e7 | −1.64375 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −595306. | −0.0820366 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.18224e6 | −0.161461 | −0.0807304 | − | 0.996736i | \(-0.525725\pi\) | ||||
−0.0807304 | + | 0.996736i | \(0.525725\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −535306. | −0.0724556 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.31309e6 | 0.176151 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.07741e6 | 0.542142 | 0.271071 | − | 0.962559i | \(-0.412622\pi\) | ||||
0.271071 | + | 0.962559i | \(0.412622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.16641e6 | 0.417298 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.17615e6 | 1.05869 | 0.529344 | − | 0.848407i | \(-0.322438\pi\) | ||||
0.529344 | + | 0.848407i | \(0.322438\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.30615e6 | −0.424357 | −0.212179 | − | 0.977231i | \(-0.568056\pi\) | ||||
−0.212179 | + | 0.977231i | \(0.568056\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.29377e6 | 0.291852 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.38247e6 | 0.174376 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.14994e6 | 0.894052 | 0.447026 | − | 0.894521i | \(-0.352483\pi\) | ||||
0.447026 | + | 0.894521i | \(0.352483\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.77939e6 | 0.840416 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.35627e6 | 0.408964 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.29096e6 | −0.397588 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.69191e6 | 1.16095 | 0.580476 | − | 0.814277i | \(-0.302867\pi\) | ||||
0.580476 | + | 0.814277i | \(0.302867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.87545e6 | −0.460292 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12933.7 | 0.00152319 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.63960e6 | −0.775363 | −0.387682 | − | 0.921793i | \(-0.626724\pi\) | ||||
−0.387682 | + | 0.921793i | \(0.626724\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.71951e6 | −0.427120 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.24191e6 | 0.369177 | 0.184588 | − | 0.982816i | \(-0.440905\pi\) | ||||
0.184588 | + | 0.982816i | \(0.440905\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.65076e6 | 0.638147 | 0.319074 | − | 0.947730i | \(-0.396628\pi\) | ||||
0.319074 | + | 0.947730i | \(0.396628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.78023e6 | 0.423375 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.97078e6 | −0.329975 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 235674. | 0.0259621 | 0.0129811 | − | 0.999916i | \(-0.495868\pi\) | ||||
0.0129811 | + | 0.999916i | \(0.495868\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −447057. | −0.0484462 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 788877. | 0.0847926 | 0.0423963 | − | 0.999101i | \(-0.486501\pi\) | ||||
0.0423963 | + | 0.999101i | \(0.486501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.65820e6 | 0.603240 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.67739e7 | 1.77387 | 0.886935 | − | 0.461894i | \(-0.152830\pi\) | ||||
0.886935 | + | 0.461894i | \(0.152830\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.22300e6 | 0.862588 | 0.431294 | − | 0.902211i | \(-0.358057\pi\) | ||||
0.431294 | + | 0.902211i | \(0.358057\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.64971e6 | 0.171664 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.36798e6 | −0.959281 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.33972e6 | 0.542437 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 273714. | 0.0275849 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.94507e6 | 0.594406 | 0.297203 | − | 0.954814i | \(-0.403946\pi\) | ||||
0.297203 | + | 0.954814i | \(0.403946\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.06324e6 | 0.502249 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.13030e6 | −0.406488 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.03368e6 | −0.197029 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.06761e7 | −1.02628 | −0.513141 | − | 0.858304i | \(-0.671518\pi\) | ||||
−0.513141 | + | 0.858304i | \(0.671518\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.13159e6 | −0.298701 | −0.149351 | − | 0.988784i | \(-0.547718\pi\) | ||||
−0.149351 | + | 0.988784i | \(0.547718\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.47715e6 | 0.139806 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.93457e6 | −0.463435 | −0.231717 | − | 0.972783i | \(-0.574434\pi\) | ||||
−0.231717 | + | 0.972783i | \(0.574434\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.04424e7 | 0.973170 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.72224e6 | 0.525150 | 0.262575 | − | 0.964912i | \(-0.415428\pi\) | ||||
0.262575 | + | 0.964912i | \(0.415428\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.33052e7 | −1.21176 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.90710e6 | −0.895433 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −362477. | −0.0325137 | −0.0162569 | − | 0.999868i | \(-0.505175\pi\) | ||||
−0.0162569 | + | 0.999868i | \(0.505175\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.91211e7 | 1.70219 | 0.851096 | − | 0.525011i | \(-0.175939\pi\) | ||||
0.851096 | + | 0.525011i | \(0.175939\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.08838e6 | −0.0961604 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.31370e6 | −0.288403 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.18299e7 | 1.02192 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.63673e7 | −1.40337 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −573374. | −0.0487978 | −0.0243989 | − | 0.999702i | \(-0.507767\pi\) | ||||
−0.0243989 | + | 0.999702i | \(0.507767\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.25845e7 | 1.06310 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.16903e7 | −0.980291 | −0.490146 | − | 0.871641i | \(-0.663056\pi\) | ||||
−0.490146 | + | 0.871641i | \(0.663056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.17691e6 | 0.758279 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.83674e7 | −1.50659 | −0.753297 | − | 0.657681i | \(-0.771538\pi\) | ||||
−0.753297 | + | 0.657681i | \(0.771538\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.25588e6 | 0.183692 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.26244e6 | 0.425398 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.78191e6 | −0.223252 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.35611e7 | 1.87716 | 0.938579 | − | 0.345066i | \(-0.112143\pi\) | ||||
0.938579 | + | 0.345066i | \(0.112143\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.68535e7 | 2.10881 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.60157e6 | −0.202840 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.05142e7 | 0.813921 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.32980e7 | 1.02210 | 0.511048 | − | 0.859552i | \(-0.329257\pi\) | ||||
0.511048 | + | 0.859552i | \(0.329257\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.11307e6 | 0.0849442 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.23363e6 | 0.0934786 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.85353e6 | −0.512034 | −0.256017 | − | 0.966672i | \(-0.582410\pi\) | ||||
−0.256017 | + | 0.966672i | \(0.582410\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.82825e6 | −0.284005 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.09628e6 | −0.0807602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.19384e6 | −0.599408 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.54717e7 | −1.12394 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.65729e7 | 1.91698 | 0.958490 | − | 0.285127i | \(-0.0920357\pi\) | ||||
0.958490 | + | 0.285127i | \(0.0920357\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.01592e7 | −0.722791 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.52779e7 | −1.78606 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.16991e6 | 0.152267 | 0.0761335 | − | 0.997098i | \(-0.475742\pi\) | ||||
0.0761335 | + | 0.997098i | \(0.475742\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.01628e7 | 0.708264 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −679174. | −0.0470097 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.74653e7 | 1.20065 | 0.600324 | − | 0.799757i | \(-0.295038\pi\) | ||||
0.600324 | + | 0.799757i | \(0.295038\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.41203e6 | 0.638285 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.36461e7 | 0.919172 | 0.459586 | − | 0.888133i | \(-0.347998\pi\) | ||||
0.459586 | + | 0.888133i | \(0.347998\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.42594e6 | −0.296114 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.48965e7 | −0.989944 | −0.494972 | − | 0.868909i | \(-0.664822\pi\) | ||||
−0.494972 | + | 0.868909i | \(0.664822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.83692e7 | −1.87265 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.12725e7 | 0.739124 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.53463e7 | 1.63989 | 0.819944 | − | 0.572443i | \(-0.194004\pi\) | ||||
0.819944 | + | 0.572443i | \(0.194004\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −85823.3 | −0.00551592 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.86419e7 | 1.82867 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.66725e7 | −1.69170 | −0.845852 | − | 0.533417i | \(-0.820908\pi\) | ||||
−0.845852 | + | 0.533417i | \(0.820908\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.51049e6 | 0.0951729 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −579829. | −0.0362943 | −0.0181471 | − | 0.999835i | \(-0.505777\pi\) | ||||
−0.0181471 | + | 0.999835i | \(0.505777\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.17544e6 | −0.257958 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.65541e6 | −0.531250 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.52438e7 | −0.929562 | −0.464781 | − | 0.885426i | \(-0.653867\pi\) | ||||
−0.464781 | + | 0.885426i | \(0.653867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.31898e6 | −0.322250 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.94926e7 | 1.17333 | 0.586665 | − | 0.809830i | \(-0.300441\pi\) | ||||
0.586665 | + | 0.809830i | \(0.300441\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.36275e6 | −0.500144 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.05794e7 | −0.624621 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.06345e6 | −0.297043 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.01642e7 | −1.75828 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.66337e7 | −2.12181 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.36277e7 | 0.784305 | 0.392153 | − | 0.919900i | \(-0.371730\pi\) | ||||
0.392153 | + | 0.919900i | \(0.371730\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.54999e6 | −0.203018 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.35664e7 | 0.766093 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.67654e6 | 0.430772 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.62853e6 | −0.202341 | −0.101171 | − | 0.994869i | \(-0.532259\pi\) | ||||
−0.101171 | + | 0.994869i | \(0.532259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −567208. | −0.0314323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.15913e6 | 0.339186 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.46667e7 | −1.34997 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.83509e6 | 0.261349 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.98780e7 | 1.60502 | 0.802509 | − | 0.596640i | \(-0.203498\pi\) | ||||
0.802509 | + | 0.596640i | \(0.203498\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.02643e6 | −0.0547995 | −0.0273998 | − | 0.999625i | \(-0.508723\pi\) | ||||
−0.0273998 | + | 0.999625i | \(0.508723\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.85702e6 | 0.523021 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.01086e7 | −2.11516 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.76189e6 | −0.144761 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.15062e7 | −0.595766 | −0.297883 | − | 0.954602i | \(-0.596281\pi\) | ||||
−0.297883 | + | 0.954602i | \(0.596281\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.51210e7 | 1.29282 | 0.646408 | − | 0.762992i | \(-0.276270\pi\) | ||||
0.646408 | + | 0.762992i | \(0.276270\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.15225e7 | 0.589401 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.14447e6 | 0.109032 | 0.0545162 | − | 0.998513i | \(-0.482638\pi\) | ||||
0.0545162 | + | 0.998513i | \(0.482638\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −818065. | −0.0413430 | −0.0206715 | − | 0.999786i | \(-0.506580\pi\) | ||||
−0.0206715 | + | 0.999786i | \(0.506580\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.76741e6 | −0.490656 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.40155e7 | −2.68104 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.97929e6 | −0.492364 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.11279e7 | −1.03622 | −0.518110 | − | 0.855314i | \(-0.673364\pi\) | ||||
−0.518110 | + | 0.855314i | \(0.673364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.00785e7 | 1.95398 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.20968e6 | 0.155558 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.28478e7 | −1.10079 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.78677e7 | −0.850744 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 314863. | 0.0149038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.89000e7 | 0.889386 | 0.444693 | − | 0.895683i | \(-0.353313\pi\) | ||||
0.444693 | + | 0.895683i | \(0.353313\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.69796e7 | −0.794349 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.72286e7 | −1.73151 | −0.865753 | − | 0.500471i | \(-0.833160\pi\) | ||||
−0.865753 | + | 0.500471i | \(0.833160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.02064e6 | 0.139674 | 0.0698371 | − | 0.997558i | \(-0.477752\pi\) | ||||
0.0698371 | + | 0.997558i | \(0.477752\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.71843e7 | 1.24248 | 0.621242 | − | 0.783619i | \(-0.286629\pi\) | ||||
0.621242 | + | 0.783619i | \(0.286629\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.98899e7 | 0.903839 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.29352e7 | 0.584420 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.53158e6 | −0.428169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.80136e6 | −0.348438 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.46106e7 | 0.648834 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.73868e7 | 0.763344 | 0.381672 | − | 0.924298i | \(-0.375348\pi\) | ||||
0.381672 | + | 0.924298i | \(0.375348\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.65506e7 | 0.722507 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.14472e6 | 0.353538 | 0.176769 | − | 0.984252i | \(-0.443435\pi\) | ||||
0.176769 | + | 0.984252i | \(0.443435\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.10298e7 | 1.33930 | 0.669649 | − | 0.742678i | \(-0.266445\pi\) | ||||
0.669649 | + | 0.742678i | \(0.266445\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.38841e7 | 1.02507 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.47028e7 | −0.627465 | −0.313733 | − | 0.949511i | \(-0.601580\pi\) | ||||
−0.313733 | + | 0.949511i | \(0.601580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.66362e6 | 0.0702037 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.30657e6 | −0.0967918 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.11166e7 | −0.463890 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.25200e6 | −0.0519545 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.00450e7 | 0.827193 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.52958e6 | −0.144848 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.44469e7 | −0.992208 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.30940e7 | −0.528512 | −0.264256 | − | 0.964453i | \(-0.585126\pi\) | ||||
−0.264256 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.05643e6 | 0.162830 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.68695e7 | −1.07266 | −0.536332 | − | 0.844007i | \(-0.680191\pi\) | ||||
−0.536332 | + | 0.844007i | \(0.680191\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.80662e7 | 1.11431 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.74357e7 | −1.47820 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.27317e6 | −0.0497277 | −0.0248638 | − | 0.999691i | \(-0.507915\pi\) | ||||
−0.0248638 | + | 0.999691i | \(0.507915\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.70795e6 | 0.182887 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.19695e6 | 0.162155 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.40187e6 | 0.0922986 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.13101e6 | −0.157891 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.31705e6 | 0.354192 | 0.177096 | − | 0.984194i | \(-0.443330\pi\) | ||||
0.177096 | + | 0.984194i | \(0.443330\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.45814e7 | 0.924490 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.03960e7 | −0.388900 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.18158e7 | −0.439657 | −0.219829 | − | 0.975539i | \(-0.570550\pi\) | ||||
−0.219829 | + | 0.975539i | \(0.570550\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.44097e7 | 0.903439 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.53529e7 | 0.933371 | 0.466685 | − | 0.884423i | \(-0.345448\pi\) | ||||
0.466685 | + | 0.884423i | \(0.345448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.99268e6 | −0.109592 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.64941e7 | −0.960008 | −0.480004 | − | 0.877266i | \(-0.659365\pi\) | ||||
−0.480004 | + | 0.877266i | \(0.659365\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.04455e7 | 0.736941 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.89164e7 | −0.678246 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.88335e7 | −0.671735 | −0.335868 | − | 0.941909i | \(-0.609030\pi\) | ||||
−0.335868 | + | 0.941909i | \(0.609030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.81603e7 | −0.644339 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.76186e7 | −0.974816 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.19976e7 | −0.768365 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.24177e7 | 0.431495 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.36740e7 | −1.85544 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.14956e7 | 1.08314 | 0.541569 | − | 0.840656i | \(-0.317831\pi\) | ||||
0.541569 | + | 0.840656i | \(0.317831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.61545e6 | −0.192121 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.85669e6 | −0.233381 | −0.116691 | − | 0.993168i | \(-0.537229\pi\) | ||||
−0.116691 | + | 0.993168i | \(0.537229\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.55064e6 | −0.321752 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.81471e7 | 0.943402 | 0.471701 | − | 0.881759i | \(-0.343640\pi\) | ||||
0.471701 | + | 0.881759i | \(0.343640\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.53350e7 | 0.511361 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.11831e7 | −1.03454 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.34916e7 | 0.775406 | 0.387703 | − | 0.921784i | \(-0.373269\pi\) | ||||
0.387703 | + | 0.921784i | \(0.373269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −102399. | −0.00336285 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −781278. | −0.0253989 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.14412e6 | 0.0693530 | 0.0346765 | − | 0.999399i | \(-0.488960\pi\) | ||||
0.0346765 | + | 0.999399i | \(0.488960\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.09206e7 | −0.351459 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.94483e7 | 0.942979 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50872e7 | −0.799307 | −0.399654 | − | 0.916666i | \(-0.630870\pi\) | ||||
−0.399654 | + | 0.916666i | \(0.630870\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.86616e6 | 0.0908628 |
(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 | 784.6.a.t.1.1 | 2 | ||
4.3 | odd | 2 | 49.6.a.e.1.2 | 2 | |||
7.3 | odd | 6 | 112.6.i.c.65.1 | 4 | |||
7.5 | odd | 6 | 112.6.i.c.81.1 | 4 | |||
7.6 | odd | 2 | 784.6.a.ba.1.2 | 2 | |||
12.11 | even | 2 | 441.6.a.m.1.1 | 2 | |||
28.3 | even | 6 | 7.6.c.a.2.1 | ✓ | 4 | ||
28.11 | odd | 6 | 49.6.c.f.30.1 | 4 | |||
28.19 | even | 6 | 7.6.c.a.4.1 | yes | 4 | ||
28.23 | odd | 6 | 49.6.c.f.18.1 | 4 | |||
28.27 | even | 2 | 49.6.a.d.1.2 | 2 | |||
84.47 | odd | 6 | 63.6.e.d.46.2 | 4 | |||
84.59 | odd | 6 | 63.6.e.d.37.2 | 4 | |||
84.83 | odd | 2 | 441.6.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.c.a.2.1 | ✓ | 4 | 28.3 | even | 6 | ||
7.6.c.a.4.1 | yes | 4 | 28.19 | even | 6 | ||
49.6.a.d.1.2 | 2 | 28.27 | even | 2 | |||
49.6.a.e.1.2 | 2 | 4.3 | odd | 2 | |||
49.6.c.f.18.1 | 4 | 28.23 | odd | 6 | |||
49.6.c.f.30.1 | 4 | 28.11 | odd | 6 | |||
63.6.e.d.37.2 | 4 | 84.59 | odd | 6 | |||
63.6.e.d.46.2 | 4 | 84.47 | odd | 6 | |||
112.6.i.c.65.1 | 4 | 7.3 | odd | 6 | |||
112.6.i.c.81.1 | 4 | 7.5 | odd | 6 | |||
441.6.a.m.1.1 | 2 | 12.11 | even | 2 | |||
441.6.a.n.1.1 | 2 | 84.83 | odd | 2 | |||
784.6.a.t.1.1 | 2 | 1.1 | even | 1 | trivial | ||
784.6.a.ba.1.2 | 2 | 7.6 | odd | 2 |