Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(1,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("108.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{41}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.70156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.1 |
$q$-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 | ||||||||
\(5\) | −57.6281 | −1.03088 | −0.515442 | − | 0.856925i | \(-0.672372\pi\) | ||||
−0.515442 | + | 0.856925i | \(0.672372\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −188.884 | −1.45697 | −0.728485 | − | 0.685061i | \(-0.759775\pi\) | ||||
−0.728485 | + | 0.685061i | \(0.759775\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 704.025 | 1.75431 | 0.877155 | − | 0.480207i | \(-0.159439\pi\) | ||||
0.877155 | + | 0.480207i | \(0.159439\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 795.537 | 1.30558 | 0.652788 | − | 0.757541i | \(-0.273599\pi\) | ||||
0.652788 | + | 0.757541i | \(0.273599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −180.562 | −0.151532 | −0.0757661 | − | 0.997126i | \(-0.524140\pi\) | ||||
−0.0757661 | + | 0.997126i | \(0.524140\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −661.769 | −0.420554 | −0.210277 | − | 0.977642i | \(-0.567437\pi\) | ||||
−0.210277 | + | 0.977642i | \(0.567437\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3632.51 | 1.43182 | 0.715909 | − | 0.698194i | \(-0.246013\pi\) | ||||
0.715909 | + | 0.698194i | \(0.246013\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 196.000 | 0.0627200 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8021.87 | 1.77125 | 0.885626 | − | 0.464398i | \(-0.153729\pi\) | ||||
0.885626 | + | 0.464398i | \(0.153729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3003.88 | −0.561407 | −0.280704 | − | 0.959795i | \(-0.590568\pi\) | ||||
−0.280704 | + | 0.959795i | \(0.590568\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10885.0 | 1.50197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1520.31 | −0.182570 | −0.0912848 | − | 0.995825i | \(-0.529097\pi\) | ||||
−0.0912848 | + | 0.995825i | \(0.529097\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3461.57 | 0.321598 | 0.160799 | − | 0.986987i | \(-0.448593\pi\) | ||||
0.160799 | + | 0.986987i | \(0.448593\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11815.8 | 0.974519 | 0.487260 | − | 0.873257i | \(-0.337997\pi\) | ||||
0.487260 | + | 0.873257i | \(0.337997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5979.82 | −0.394861 | −0.197430 | − | 0.980317i | \(-0.563260\pi\) | ||||
−0.197430 | + | 0.980317i | \(0.563260\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18870.3 | 1.12276 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13819.2 | 0.675761 | 0.337880 | − | 0.941189i | \(-0.390290\pi\) | ||||
0.337880 | + | 0.941189i | \(0.390290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −40571.6 | −1.80849 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 22640.2 | 0.846739 | 0.423370 | − | 0.905957i | \(-0.360847\pi\) | ||||
0.423370 | + | 0.905957i | \(0.360847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37404.2 | −1.28705 | −0.643526 | − | 0.765424i | \(-0.722529\pi\) | ||||
−0.643526 | + | 0.765424i | \(0.722529\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −45845.3 | −1.34590 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 70964.7 | 1.93132 | 0.965662 | − | 0.259802i | \(-0.0836573\pi\) | ||||
0.965662 | + | 0.259802i | \(0.0836573\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −67767.0 | −1.59541 | −0.797705 | − | 0.603048i | \(-0.793953\pi\) | ||||
−0.797705 | + | 0.603048i | \(0.793953\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −31562.4 | −0.693208 | −0.346604 | − | 0.938012i | \(-0.612665\pi\) | ||||
−0.346604 | + | 0.938012i | \(0.612665\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −132979. | −2.55598 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 62791.6 | 1.13197 | 0.565984 | − | 0.824416i | \(-0.308496\pi\) | ||||
0.565984 | + | 0.824416i | \(0.308496\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 93431.5 | 1.48867 | 0.744334 | − | 0.667807i | \(-0.232767\pi\) | ||||
0.744334 | + | 0.667807i | \(0.232767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10405.5 | 0.156212 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −68793.1 | −0.920598 | −0.460299 | − | 0.887764i | \(-0.652258\pi\) | ||||
−0.460299 | + | 0.887764i | \(0.652258\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −150265. | −1.90219 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 38136.5 | 0.433542 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 117774. | 1.27093 | 0.635463 | − | 0.772132i | \(-0.280809\pi\) | ||||
0.635463 | + | 0.772132i | \(0.280809\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −161886. | −1.57908 | −0.789542 | − | 0.613697i | \(-0.789682\pi\) | ||||
−0.789542 | + | 0.613697i | \(0.789682\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 59324.6 | 0.550987 | 0.275494 | − | 0.961303i | \(-0.411159\pi\) | ||||
0.275494 | + | 0.961303i | \(0.411159\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 21124.1 | 0.178369 | 0.0891845 | − | 0.996015i | \(-0.471574\pi\) | ||||
0.0891845 | + | 0.996015i | \(0.471574\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −168898. | −1.36162 | −0.680812 | − | 0.732458i | \(-0.738373\pi\) | ||||
−0.680812 | + | 0.732458i | \(0.738373\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 61274.0 | 0.451419 | 0.225710 | − | 0.974195i | \(-0.427530\pi\) | ||||
0.225710 | + | 0.974195i | \(0.427530\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −209335. | −1.47604 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 34105.4 | 0.220778 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 334600. | 2.07760 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 168793. | 0.966226 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 23607.7 | 0.129881 | 0.0649404 | − | 0.997889i | \(-0.479314\pi\) | ||||
0.0649404 | + | 0.997889i | \(0.479314\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 206849. | 1.05311 | 0.526557 | − | 0.850140i | \(-0.323483\pi\) | ||||
0.526557 | + | 0.850140i | \(0.323483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 124998. | 0.612736 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 191495. | 0.871678 | 0.435839 | − | 0.900025i | \(-0.356452\pi\) | ||||
0.435839 | + | 0.900025i | \(0.356452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 250418. | 1.09933 | 0.549666 | − | 0.835385i | \(-0.314755\pi\) | ||||
0.549666 | + | 0.835385i | \(0.314755\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 560078. | 2.29039 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −462285. | −1.82595 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −200857. | −0.741177 | −0.370588 | − | 0.928797i | \(-0.620844\pi\) | ||||
−0.370588 | + | 0.928797i | \(0.620844\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23263.1 | −0.0830283 | −0.0415141 | − | 0.999138i | \(-0.513218\pi\) | ||||
−0.0415141 | + | 0.999138i | \(0.513218\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 173108. | 0.578745 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −523985. | −1.69656 | −0.848281 | − | 0.529546i | \(-0.822362\pi\) | ||||
−0.848281 | + | 0.529546i | \(0.822362\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −686125. | −2.08612 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 194530. | 0.573479 | 0.286739 | − | 0.958009i | \(-0.407429\pi\) | ||||
0.286739 | + | 0.958009i | \(0.407429\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 462757. | 1.28399 | 0.641995 | − | 0.766709i | \(-0.278107\pi\) | ||||
0.641995 | + | 0.766709i | \(0.278107\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 261587. | 0.704529 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −39891.8 | −0.101337 | −0.0506685 | − | 0.998716i | \(-0.516135\pi\) | ||||
−0.0506685 | + | 0.998716i | \(0.516135\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −37021.3 | −0.0913812 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 221514. | 0.516736 | 0.258368 | − | 0.966047i | \(-0.416815\pi\) | ||||
0.258368 | + | 0.966047i | \(0.416815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 800588. | 1.81640 | 0.908202 | − | 0.418532i | \(-0.137455\pi\) | ||||
0.908202 | + | 0.418532i | \(0.137455\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 87612.8 | 0.188208 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −127120. | −0.265834 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 70550.6 | 0.139932 | 0.0699661 | − | 0.997549i | \(-0.477711\pi\) | ||||
0.0699661 | + | 0.997549i | \(0.477711\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −458196. | −0.885437 | −0.442719 | − | 0.896661i | \(-0.645986\pi\) | ||||
−0.442719 | + | 0.896661i | \(0.645986\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −605955. | −1.11244 | −0.556218 | − | 0.831037i | \(-0.687748\pi\) | ||||
−0.556218 | + | 0.831037i | \(0.687748\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −108129. | −0.193557 | −0.0967783 | − | 0.995306i | \(-0.530854\pi\) | ||||
−0.0967783 | + | 0.995306i | \(0.530854\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.51521e6 | −2.58066 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −199484. | −0.331530 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −465902. | −0.737783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 274922. | 0.425113 | 0.212556 | − | 0.977149i | \(-0.431821\pi\) | ||||
0.212556 | + | 0.977149i | \(0.431821\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −680920. | −1.00462 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 567385. | 0.817954 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −143644. | −0.197837 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −503846. | −0.678478 | −0.339239 | − | 0.940700i | \(-0.610170\pi\) | ||||
−0.339239 | + | 0.940700i | \(0.610170\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −389725. | −0.501989 | −0.250994 | − | 0.967989i | \(-0.580758\pi\) | ||||
−0.250994 | + | 0.967989i | \(0.580758\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −931505. | −1.17381 | −0.586903 | − | 0.809657i | \(-0.699653\pi\) | ||||
−0.586903 | + | 0.809657i | \(0.699653\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 967962. | 1.16807 | 0.584034 | − | 0.811729i | \(-0.301473\pi\) | ||||
0.584034 | + | 0.811729i | \(0.301473\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 344606. | 0.407055 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 335896. | 0.380373 | 0.190187 | − | 0.981748i | \(-0.439091\pi\) | ||||
0.190187 | + | 0.981748i | \(0.439091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −547142. | −0.606817 | −0.303408 | − | 0.952861i | \(-0.598125\pi\) | ||||
−0.303408 | + | 0.952861i | \(0.598125\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.08746e6 | −1.15744 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −526462. | −0.549066 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 36479.6 | 0.0365482 | 0.0182741 | − | 0.999833i | \(-0.494183\pi\) | ||||
0.0182741 | + | 0.999833i | \(0.494183\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.55738e6 | 2.51185 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.19968e6 | 1.13301 | 0.566505 | − | 0.824058i | \(-0.308295\pi\) | ||||
0.566505 | + | 0.824058i | \(0.308295\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 287163. | 0.265999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −878508. | −0.783171 | −0.391585 | − | 0.920142i | \(-0.628073\pi\) | ||||
−0.391585 | + | 0.920142i | \(0.628073\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −796374. | −0.696630 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 434159. | 0.365820 | 0.182910 | − | 0.983130i | \(-0.441448\pi\) | ||||
0.182910 | + | 0.983130i | \(0.441448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 799583. | 0.661364 | 0.330682 | − | 0.943742i | \(-0.392721\pi\) | ||||
0.330682 | + | 0.943742i | \(0.392721\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 137989. | 0.110030 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.63042e6 | 1.27674 | 0.638368 | − | 0.769731i | \(-0.279610\pi\) | ||||
0.638368 | + | 0.769731i | \(0.279610\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.53698e6 | 1.91669 | 0.958344 | − | 0.285617i | \(-0.0921984\pi\) | ||||
0.958344 | + | 0.285617i | \(0.0921984\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.07324e6 | −1.53880 | −0.769402 | − | 0.638765i | \(-0.779445\pi\) | ||||
−0.769402 | + | 0.638765i | \(0.779445\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −653836. | −0.468559 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.38725e6 | −0.977038 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −666768. | −0.453739 | −0.226869 | − | 0.973925i | \(-0.572849\pi\) | ||||
−0.226869 | + | 0.973925i | \(0.572849\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.30471e6 | −0.872889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.88980e6 | 1.86935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.23181e6 | −1.41985 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.15554e6 | 1.32680 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 811069. | 0.491148 | 0.245574 | − | 0.969378i | \(-0.421024\pi\) | ||||
0.245574 | + | 0.969378i | \(0.421024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 985037. | 0.577500 | 0.288750 | − | 0.957405i | \(-0.406760\pi\) | ||||
0.288750 | + | 0.957405i | \(0.406760\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 783184. | 0.451859 | 0.225929 | − | 0.974144i | \(-0.427458\pi\) | ||||
0.225929 | + | 0.974144i | \(0.427458\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.66519e6 | 1.48963 | 0.744817 | − | 0.667268i | \(-0.232537\pi\) | ||||
0.744817 | + | 0.667268i | \(0.232537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.64760e6 | 3.10733 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 119491. | 0.0637275 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 155925. | 0.0818857 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.12950e6 | 0.575300 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.34153e6 | −1.17471 | −0.587353 | − | 0.809331i | \(-0.699830\pi\) | ||||
−0.587353 | + | 0.809331i | \(0.699830\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.08956e6 | −1.99097 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −710742. | −0.340908 | −0.170454 | − | 0.985366i | \(-0.554523\pi\) | ||||
−0.170454 | + | 0.985366i | \(0.554523\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.11480e6 | −0.984882 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −389725. | −0.178864 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −702187. | −0.313061 | −0.156531 | − | 0.987673i | \(-0.550031\pi\) | ||||
−0.156531 | + | 0.987673i | \(0.550031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −138699. | −0.0609553 | −0.0304776 | − | 0.999535i | \(-0.509703\pi\) | ||||
−0.0304776 | + | 0.999535i | \(0.509703\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −55094.1 | −0.0235325 | −0.0117663 | − | 0.999931i | \(-0.503745\pi\) | ||||
−0.0117663 | + | 0.999931i | \(0.503745\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.90528e6 | 1.64468 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.94311e6 | −0.795722 | −0.397861 | − | 0.917446i | \(-0.630247\pi\) | ||||
−0.397861 | + | 0.917446i | \(0.630247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03816e6 | −0.823134 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.81888e6 | 0.714616 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.49593e6 | −0.579758 | −0.289879 | − | 0.957063i | \(-0.593615\pi\) | ||||
−0.289879 | + | 0.957063i | \(0.593615\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.61023e6 | −0.984564 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.71696e6 | −0.638982 | −0.319491 | − | 0.947589i | \(-0.603512\pi\) | ||||
−0.319491 | + | 0.947589i | \(0.603512\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.38170e6 | 2.31251 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.54794e6 | −1.26876 | −0.634378 | − | 0.773023i | \(-0.718744\pi\) | ||||
−0.634378 | + | 0.773023i | \(0.718744\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.75302e6 | −0.958987 | −0.479493 | − | 0.877545i | \(-0.659180\pi\) | ||||
−0.479493 | + | 0.877545i | \(0.659180\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.66335e6 | 2.63492 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.95371e6 | −0.989679 | −0.494839 | − | 0.868984i | \(-0.664773\pi\) | ||||
−0.494839 | + | 0.868984i | \(0.664773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −655895. | −0.216966 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.61856e6 | −1.16693 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.21949e6 | −0.706767 | −0.353383 | − | 0.935479i | \(-0.614969\pi\) | ||||
−0.353383 | + | 0.935479i | \(0.614969\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.43822e6 | −1.37831 | −0.689157 | − | 0.724612i | \(-0.742019\pi\) | ||||
−0.689157 | + | 0.724612i | \(0.742019\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.38970e6 | −0.732960 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.07034e6 | −0.320284 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −331601. | −0.0980184 | −0.0490092 | − | 0.998798i | \(-0.515606\pi\) | ||||
−0.0490092 | + | 0.998798i | \(0.515606\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.27637e6 | −1.23367 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.38428e6 | −1.53464 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.49486e6 | −0.694243 | −0.347121 | − | 0.937820i | \(-0.612841\pi\) | ||||
−0.347121 | + | 0.937820i | \(0.612841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.55155e6 | 1.25157 | 0.625784 | − | 0.779997i | \(-0.284779\pi\) | ||||
0.625784 | + | 0.779997i | \(0.284779\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −35390.2 | −0.00950410 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.06508e6 | 1.87520 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −614314. | −0.159293 | −0.0796466 | − | 0.996823i | \(-0.525379\pi\) | ||||
−0.0796466 | + | 0.996823i | \(0.525379\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.42759e6 | 0.622236 | 0.311118 | − | 0.950371i | \(-0.399297\pi\) | ||||
0.311118 | + | 0.950371i | \(0.399297\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.40388e6 | −0.602157 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.31800e6 | −0.574054 | −0.287027 | − | 0.957923i | \(-0.592667\pi\) | ||||
−0.287027 | + | 0.957923i | \(0.592667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.23648e6 | 1.26774 | 0.633870 | − | 0.773439i | \(-0.281465\pi\) | ||||
0.633870 | + | 0.773439i | \(0.281465\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.96442e6 | 0.949029 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 985716. | 0.230747 | 0.115373 | − | 0.993322i | \(-0.463194\pi\) | ||||
0.115373 | + | 0.993322i | \(0.463194\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.43703e6 | 0.564183 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.65946e6 | 1.96093 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.09496e6 | −1.14117 | −0.570585 | − | 0.821238i | \(-0.693284\pi\) | ||||
−0.570585 | + | 0.821238i | \(0.693284\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.89512e6 | −1.94939 | −0.974697 | − | 0.223531i | \(-0.928242\pi\) | ||||
−0.974697 | + | 0.223531i | \(0.928242\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.26267e6 | 0.707327 | 0.353664 | − | 0.935373i | \(-0.384936\pi\) | ||||
0.353664 | + | 0.935373i | \(0.384936\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.63482e6 | 0.346879 | 0.173439 | − | 0.984845i | \(-0.444512\pi\) | ||||
0.173439 | + | 0.984845i | \(0.444512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.34041e7 | −2.81388 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.31859e6 | 1.70961 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −129707. | −0.0263772 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.57113e6 | 1.70687 | 0.853433 | − | 0.521203i | \(-0.174517\pi\) | ||||
0.853433 | + | 0.521203i | \(0.174517\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.20947e6 | −0.238359 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.78709e6 | −1.31018 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.12742e6 | −0.979662 | −0.489831 | − | 0.871817i | \(-0.662942\pi\) | ||||
−0.489831 | + | 0.871817i | \(0.662942\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.33990e6 | −1.37400 | −0.687000 | − | 0.726658i | \(-0.741073\pi\) | ||||
−0.687000 | + | 0.726658i | \(0.741073\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.44845e6 | −0.268402 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.28001e7 | 2.32446 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.08886e6 | 1.09467 | 0.547336 | − | 0.836913i | \(-0.315642\pi\) | ||||
0.547336 | + | 0.836913i | \(0.315642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.11508e6 | 1.60635 | 0.803175 | − | 0.595743i | \(-0.203142\pi\) | ||||
0.803175 | + | 0.595743i | \(0.203142\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.32917e6 | 1.62785 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.18164e6 | −0.544323 | −0.272162 | − | 0.962252i | \(-0.587739\pi\) | ||||
−0.272162 | + | 0.962252i | \(0.587739\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.96165e6 | 1.00998 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.41876e6 | −0.568003 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.20994e6 | −0.692708 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27154.5 | −0.00438276 | −0.00219138 | − | 0.999998i | \(-0.500698\pi\) | ||||
−0.00219138 | + | 0.999998i | \(0.500698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.93041e6 | −0.628324 | −0.314162 | − | 0.949369i | \(-0.601724\pi\) | ||||
−0.314162 | + | 0.949369i | \(0.601724\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 542387. | 0.0850713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.75880e6 | 1.05010 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.75381e6 | 0.419871 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.21734e6 | −0.183878 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.32852e7 | 1.96968 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.38180e6 | 1.23124 | 0.615622 | − | 0.788042i | \(-0.288905\pi\) | ||||
0.615622 | + | 0.788042i | \(0.288905\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.73325e6 | 1.40367 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.50548e6 | −1.07253 | −0.536266 | − | 0.844049i | \(-0.680166\pi\) | ||||
−0.536266 | + | 0.844049i | \(0.680166\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.30862e6 | −0.744908 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.18604e7 | −1.64924 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.03110e6 | 0.140820 | 0.0704099 | − | 0.997518i | \(-0.477569\pi\) | ||||
0.0704099 | + | 0.997518i | \(0.477569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.39988e6 | 1.27231 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.31962e7 | 1.75461 | 0.877303 | − | 0.479937i | \(-0.159341\pi\) | ||||
0.877303 | + | 0.479937i | \(0.159341\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.53110e6 | −0.465360 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.49155e6 | −0.452103 | −0.226052 | − | 0.974115i | \(-0.572582\pi\) | ||||
−0.226052 | + | 0.974115i | \(0.572582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.49455e6 | −1.21866 | −0.609332 | − | 0.792915i | \(-0.708562\pi\) | ||||
−0.609332 | + | 0.792915i | \(0.708562\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 711972. | 0.0898036 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.60369e6 | 0.325574 | 0.162787 | − | 0.986661i | \(-0.447952\pi\) | ||||
0.162787 | + | 0.986661i | \(0.447952\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.76477e7 | −2.16895 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.72905e6 | 1.18549 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.04099e6 | −0.603838 | −0.301919 | − | 0.953334i | \(-0.597627\pi\) | ||||
−0.301919 | + | 0.953334i | \(0.597627\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.98787e6 | 0.236102 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.35192e7 | −1.57875 | −0.789374 | − | 0.613912i | \(-0.789595\pi\) | ||||
−0.789374 | + | 0.613912i | \(0.789595\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.96543e6 | −0.227596 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 815784. | 0.0928984 | 0.0464492 | − | 0.998921i | \(-0.485209\pi\) | ||||
0.0464492 | + | 0.998921i | \(0.485209\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.53058e6 | −0.737507 | −0.368753 | − | 0.929527i | \(-0.620215\pi\) | ||||
−0.368753 | + | 0.929527i | \(0.620215\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.92824e7 | −2.14177 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.10096e6 | −0.121284 | −0.0606418 | − | 0.998160i | \(-0.519315\pi\) | ||||
−0.0606418 | + | 0.998160i | \(0.519315\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.75717e6 | −0.515520 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.09992e6 | 0.655651 | 0.327825 | − | 0.944738i | \(-0.393684\pi\) | ||||
0.327825 | + | 0.944738i | \(0.393684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −565825. | −0.0598369 | −0.0299184 | − | 0.999552i | \(-0.509525\pi\) | ||||
−0.0299184 | + | 0.999552i | \(0.509525\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.37509e7 | −1.44246 | −0.721232 | − | 0.692693i | \(-0.756424\pi\) | ||||
−0.721232 | + | 0.692693i | \(0.756424\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.29939e7 | 1.34128 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.03397e7 | −1.05879 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 274511. | 0.0276652 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 420973. | 0.0420902 | 0.0210451 | − | 0.999779i | \(-0.493301\pi\) | ||||
0.0210451 | + | 0.999779i | \(0.493301\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.36047e6 | −0.133892 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.50120e7 | 1.46585 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 314421. | 0.0302251 | 0.0151125 | − | 0.999886i | \(-0.495189\pi\) | ||||
0.0151125 | + | 0.999886i | \(0.495189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.38039e7 | 1.31667 | 0.658333 | − | 0.752727i | \(-0.271262\pi\) | ||||
0.658333 | + | 0.752727i | \(0.271262\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.43225e6 | −0.322343 | −0.161172 | − | 0.986926i | \(-0.551527\pi\) | ||||
−0.161172 | + | 0.986926i | \(0.551527\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.59392e7 | 1.48544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.74961e7 | −1.60568 | −0.802839 | − | 0.596196i | \(-0.796678\pi\) | ||||
−0.802839 | + | 0.596196i | \(0.796678\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.19203e7 | −1.08564 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.20687e7 | 1.08254 | 0.541272 | − | 0.840848i | \(-0.317943\pi\) | ||||
0.541272 | + | 0.840848i | \(0.317943\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −181872. | −0.0161906 | −0.00809529 | − | 0.999967i | \(-0.502577\pi\) | ||||
−0.00809529 | + | 0.999967i | \(0.502577\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.20339e6 | −0.631659 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.91395e7 | 2.53611 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.63335e7 | −2.25789 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.06383e7 | −0.905388 | −0.452694 | − | 0.891666i | \(-0.649537\pi\) | ||||
−0.452694 | + | 0.891666i | \(0.649537\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.67911e6 | 0.727786 | 0.363893 | − | 0.931441i | \(-0.381447\pi\) | ||||
0.363893 | + | 0.931441i | \(0.381447\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.22457e7 | −1.85170 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.67179e7 | −1.37129 | −0.685647 | − | 0.727934i | \(-0.740481\pi\) | ||||
−0.685647 | + | 0.727934i | \(0.740481\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.10355e7 | −0.898598 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.09937e7 | 0.882257 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.85551e6 | −0.307175 | −0.153588 | − | 0.988135i | \(-0.549083\pi\) | ||||
−0.153588 | + | 0.988135i | \(0.549083\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.44311e7 | −1.13328 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −625029. | −0.0487325 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.86020e6 | −0.142976 | −0.0714882 | − | 0.997441i | \(-0.522775\pi\) | ||||
−0.0714882 | + | 0.997441i | \(0.522775\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00610e6 | 0.0767805 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.05777e7 | 2.30068 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.55608e7 | 1.16256 | 0.581281 | − | 0.813703i | \(-0.302552\pi\) | ||||
0.581281 | + | 0.813703i | \(0.302552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.09116e7 | −0.803832 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.22763e7 | −2.36112 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.35632e6 | −0.314266 | −0.157133 | − | 0.987577i | \(-0.550225\pi\) | ||||
−0.157133 | + | 0.987577i | \(0.550225\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.12055e7 | −0.802772 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.57229e6 | 0.111093 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.96155e6 | 0.207818 | 0.103909 | − | 0.994587i | \(-0.466865\pi\) | ||||
0.103909 | + | 0.994587i | \(0.466865\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.13348e6 | −0.147671 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −960851. | −0.0660536 | −0.0330268 | − | 0.999454i | \(-0.510515\pi\) | ||||
−0.0330268 | + | 0.999454i | \(0.510515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.99609e7 | 3.38814 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.36123e7 | 0.916898 | 0.458449 | − | 0.888721i | \(-0.348405\pi\) | ||||
0.458449 | + | 0.888721i | \(0.348405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.73716e6 | 0.381263 | 0.190632 | − | 0.981662i | \(-0.438946\pi\) | ||||
0.190632 | + | 0.981662i | \(0.438946\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.15750e7 | 0.764067 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.99002e6 | −0.259878 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.44092e7 | 1.57926 | 0.789631 | − | 0.613582i | \(-0.210272\pi\) | ||||
0.789631 | + | 0.613582i | \(0.210272\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.34061e6 | 0.0855924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.16979e6 | 0.327894 | 0.163947 | − | 0.986469i | \(-0.447577\pi\) | ||||
0.163947 | + | 0.986469i | \(0.447577\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.08433e7 | 0.678732 | 0.339366 | − | 0.940654i | \(-0.389788\pi\) | ||||
0.339366 | + | 0.940654i | \(0.389788\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.19021e7 | 1.98385 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.80111e7 | 1.10548 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.27810e6 | −0.565774 | −0.282887 | − | 0.959153i | \(-0.591292\pi\) | ||||
−0.282887 | + | 0.959153i | \(0.591292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.33311e7 | 0.802450 | 0.401225 | − | 0.915980i | \(-0.368585\pi\) | ||||
0.401225 | + | 0.915980i | \(0.368585\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −588760. | −0.0352115 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.29076e6 | −0.135249 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.77096e7 | −2.79884 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.01963e7 | 1.74896 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.35818e6 | 0.365928 | 0.182964 | − | 0.983120i | \(-0.441431\pi\) | ||||
0.182964 | + | 0.983120i | \(0.441431\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.15737e7 | −0.657704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.97565e7 | −1.68035 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.59152e6 | 0.256042 | 0.128021 | − | 0.991771i | \(-0.459138\pi\) | ||||
0.128021 | + | 0.991771i | \(0.459138\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.07973e6 | 0.0598341 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.22207e7 | −1.21610 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.95401e7 | 2.15054 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.91492e6 | 0.478901 | 0.239451 | − | 0.970909i | \(-0.423033\pi\) | ||||
0.239451 | + | 0.970909i | \(0.423033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.29527e6 | −0.175930 | −0.0879648 | − | 0.996124i | \(-0.528036\pi\) | ||||
−0.0879648 | + | 0.996124i | \(0.528036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.12104e7 | −0.591190 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.81930e6 | −0.409838 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.41824e6 | −0.228766 | −0.114383 | − | 0.993437i | \(-0.536489\pi\) | ||||
−0.114383 | + | 0.993437i | \(0.536489\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.58259e6 | −0.287300 | −0.143650 | − | 0.989629i | \(-0.545884\pi\) | ||||
−0.143650 | + | 0.989629i | \(0.545884\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.18571e7 | 1.11130 | 0.555648 | − | 0.831418i | \(-0.312470\pi\) | ||||
0.555648 | + | 0.831418i | \(0.312470\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.89089e7 | 0.955608 | 0.477804 | − | 0.878466i | \(-0.341433\pi\) | ||||
0.477804 | + | 0.878466i | \(0.341433\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.40727e6 | −0.170135 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.66678e7 | −1.32364 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.05498e7 | 0.517413 | 0.258707 | − | 0.965956i | \(-0.416704\pi\) | ||||
0.258707 | + | 0.965956i | \(0.416704\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.38392e7 | 2.13734 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.50748e7 | −0.726287 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.32007e7 | −3.02701 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.52256e6 | −0.261406 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −641534. | −0.0301889 | −0.0150945 | − | 0.999886i | \(-0.504805\pi\) | ||||
−0.0150945 | + | 0.999886i | \(0.504805\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.21711e7 | 1.49628 | 0.748141 | − | 0.663540i | \(-0.230947\pi\) | ||||
0.748141 | + | 0.663540i | \(0.230947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.44739e6 | 0.0669273 | 0.0334637 | − | 0.999440i | \(-0.489346\pi\) | ||||
0.0334637 | + | 0.999440i | \(0.489346\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.16338e6 | 0.418821 | 0.209411 | − | 0.977828i | \(-0.432845\pi\) | ||||
0.209411 | + | 0.977828i | \(0.432845\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.29889e6 | 0.104467 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.42069e7 | 1.98582 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.64550e7 | 2.52149 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.18823e7 | −1.40776 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.15236e7 | −0.944967 | −0.472483 | − | 0.881340i | \(-0.656642\pi\) | ||||
−0.472483 | + | 0.881340i | \(0.656642\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.58447e7 | −1.98998 | −0.994991 | − | 0.0999625i | \(-0.968128\pi\) | ||||
−0.994991 | + | 0.0999625i | \(0.968128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.10719e7 | −1.34111 | −0.670557 | − | 0.741858i | \(-0.733945\pi\) | ||||
−0.670557 | + | 0.741858i | \(0.733945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.08214e7 | 0.461820 | 0.230910 | − | 0.972975i | \(-0.425830\pi\) | ||||
0.230910 | + | 0.972975i | \(0.425830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.45913e6 | −0.189232 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.95726e6 | 0.166060 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.27654e7 | −0.532694 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.40967e7 | −0.994394 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.49523e6 | −0.102399 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.61364e7 | −1.87250 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.71785e7 | 1.50063 | 0.750316 | − | 0.661080i | \(-0.229901\pi\) | ||||
0.750316 | + | 0.661080i | \(0.229901\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.76509e7 | −1.10386 | −0.551929 | − | 0.833891i | \(-0.686108\pi\) | ||||
−0.551929 | + | 0.833891i | \(0.686108\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.57781e7 | 2.61159 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.90705e7 | −1.53436 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.24727e6 | 0.0877743 | 0.0438872 | − | 0.999036i | \(-0.486026\pi\) | ||||
0.0438872 | + | 0.999036i | \(0.486026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.39112e7 | −2.08293 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −297981. | −0.0114508 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 791805. | 0.0301009 | 0.0150504 | − | 0.999887i | \(-0.495209\pi\) | ||||
0.0150504 | + | 0.999887i | \(0.495209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.24878e7 | −0.472184 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.32571e6 | 0.274044 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.61458e6 | −0.357751 | −0.178876 | − | 0.983872i | \(-0.557246\pi\) | ||||
−0.178876 | + | 0.983872i | \(0.557246\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.50396e7 | 0.553683 | 0.276842 | − | 0.960916i | \(-0.410712\pi\) | ||||
0.276842 | + | 0.960916i | \(0.410712\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.25742e7 | 0.460470 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.55153e7 | −0.562194 | −0.281097 | − | 0.959679i | \(-0.590698\pi\) | ||||
−0.281097 | + | 0.959679i | \(0.590698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.51091e7 | −0.905035 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.16599e7 | 1.84256 | 0.921280 | − | 0.388899i | \(-0.127145\pi\) | ||||
0.921280 | + | 0.388899i | \(0.127145\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.06570e6 | −0.144254 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.61704e7 | −1.27001 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.96059e7 | −0.684822 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2.64050e7 | 0.912782 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.19595e6 | 0.213079 | 0.106540 | − | 0.994308i | \(-0.466023\pi\) | ||||
0.106540 | + | 0.994308i | \(0.466023\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.67480e7 | −1.59116 | −0.795582 | − | 0.605846i | \(-0.792835\pi\) | ||||
−0.795582 | + | 0.605846i | \(0.792835\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.73001e7 | −1.60169 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.63907e6 | 0.155487 | 0.0777435 | − | 0.996973i | \(-0.475228\pi\) | ||||
0.0777435 | + | 0.996973i | \(0.475228\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.84321e7 | −1.61501 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.75449e7 | 0.909197 | 0.454598 | − | 0.890697i | \(-0.349783\pi\) | ||||
0.454598 | + | 0.890697i | \(0.349783\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.49200e7 | 1.14679 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.29209e7 | 1.39533 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.83035e7 | 0.592038 | 0.296019 | − | 0.955182i | \(-0.404341\pi\) | ||||
0.296019 | + | 0.955182i | \(0.404341\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.23125e6 | 0.199534 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.44890e7 | −1.41747 | −0.708736 | − | 0.705473i | \(-0.750734\pi\) | ||||
−0.708736 | + | 0.705473i | \(0.750734\pi\) | |||||||
\(998\) | 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 | 108.6.a.c.1.1 | yes | 2 | |
3.2 | odd | 2 | 108.6.a.b.1.2 | ✓ | 2 | ||
4.3 | odd | 2 | 432.6.a.q.1.1 | 2 | |||
9.2 | odd | 6 | 324.6.e.g.109.1 | 4 | |||
9.4 | even | 3 | 324.6.e.f.217.2 | 4 | |||
9.5 | odd | 6 | 324.6.e.g.217.1 | 4 | |||
9.7 | even | 3 | 324.6.e.f.109.2 | 4 | |||
12.11 | even | 2 | 432.6.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.a.b.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
108.6.a.c.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
324.6.e.f.109.2 | 4 | 9.7 | even | 3 | |||
324.6.e.f.217.2 | 4 | 9.4 | even | 3 | |||
324.6.e.g.109.1 | 4 | 9.2 | odd | 6 | |||
324.6.e.g.217.1 | 4 | 9.5 | odd | 6 | |||
432.6.a.q.1.1 | 2 | 4.3 | odd | 2 | |||
432.6.a.r.1.2 | 2 | 12.11 | even | 2 |