Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(129,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.129");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 18 x^{10} + 348 x^{9} + 21226 x^{8} - 87824 x^{7} + 205428 x^{6} + 2113880 x^{5} + \cdots + 1072562500 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{46}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.3 | ||
Root | \(-3.92310 - 3.92310i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.129 |
Dual form | 320.6.c.l.129.10 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 16.9825i | − | 1.08943i | −0.838622 | − | 0.544714i | \(-0.816638\pi\) | ||
0.838622 | − | 0.544714i | \(-0.183362\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −12.3893 | − | 54.5115i | −0.221627 | − | 0.975132i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 211.691i | − | 1.63289i | −0.577421 | − | 0.816447i | \(-0.695941\pi\) | ||
0.577421 | − | 0.816447i | \(-0.304059\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −45.4059 | −0.186855 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −520.707 | −1.29751 | −0.648756 | − | 0.760997i | \(-0.724710\pi\) | ||||
−0.648756 | + | 0.760997i | \(0.724710\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 732.105i | 1.20148i | 0.799446 | + | 0.600738i | \(0.205126\pi\) | ||||
−0.799446 | + | 0.600738i | \(0.794874\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −925.743 | + | 210.402i | −1.06234 | + | 0.241447i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2269.82i | − | 1.90488i | −0.304721 | − | 0.952442i | \(-0.598563\pi\) | ||
0.304721 | − | 0.952442i | \(-0.401437\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2033.73 | −1.29244 | −0.646220 | − | 0.763152i | \(-0.723651\pi\) | ||||
−0.646220 | + | 0.763152i | \(0.723651\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3595.05 | −1.77892 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 974.449i | 0.384096i | 0.981386 | + | 0.192048i | \(0.0615129\pi\) | ||||
−0.981386 | + | 0.192048i | \(0.938487\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2818.01 | + | 1350.72i | −0.901763 | + | 0.432231i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3355.65i | − | 0.885863i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5276.32 | 1.16503 | 0.582514 | − | 0.812821i | \(-0.302069\pi\) | ||||
0.582514 | + | 0.812821i | \(0.302069\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2001.75 | 0.374115 | 0.187058 | − | 0.982349i | \(-0.440105\pi\) | ||||
0.187058 | + | 0.982349i | \(0.440105\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8842.91i | 1.41355i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −11539.6 | + | 2622.71i | −1.59229 | + | 0.361893i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3652.25i | − | 0.438587i | −0.975659 | − | 0.219294i | \(-0.929625\pi\) | ||
0.975659 | − | 0.219294i | \(-0.0703752\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12433.0 | 1.30892 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 17113.3 | 1.58992 | 0.794960 | − | 0.606662i | \(-0.207492\pi\) | ||||
0.794960 | + | 0.606662i | \(0.207492\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4073.34i | − | 0.335953i | −0.985791 | − | 0.167977i | \(-0.946277\pi\) | ||
0.985791 | − | 0.167977i | \(-0.0537233\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 562.548 | + | 2475.14i | 0.0414122 | + | 0.182209i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 13335.0i | − | 0.880539i | −0.897866 | − | 0.440270i | \(-0.854883\pi\) | ||
0.897866 | − | 0.440270i | \(-0.145117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −28006.2 | −1.66634 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −38547.2 | −2.07524 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 27482.0i | 1.34388i | 0.740607 | + | 0.671938i | \(0.234538\pi\) | ||||
−0.740607 | + | 0.671938i | \(0.765462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6451.20 | + | 28384.5i | 0.287564 | + | 1.26524i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 34537.9i | 1.40802i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3890.44 | −0.145502 | −0.0727509 | − | 0.997350i | \(-0.523178\pi\) | ||||
−0.0727509 | + | 0.997350i | \(0.523178\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8737.66 | −0.300656 | −0.150328 | − | 0.988636i | \(-0.548033\pi\) | ||||
−0.150328 | + | 0.988636i | \(0.548033\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9612.02i | 0.305115i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 39908.2 | − | 9070.28i | 1.17160 | − | 0.266279i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 40950.5i | − | 1.11448i | −0.830351 | − | 0.557240i | \(-0.811860\pi\) | ||
0.830351 | − | 0.557240i | \(-0.188140\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 16548.6 | 0.418445 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 26897.5 | 0.633236 | 0.316618 | − | 0.948553i | \(-0.397453\pi\) | ||||
0.316618 | + | 0.948553i | \(0.397453\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9824.26i | 0.215771i | 0.994163 | + | 0.107885i | \(0.0344080\pi\) | ||||
−0.994163 | + | 0.107885i | \(0.965592\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 22938.6 | + | 47856.9i | 0.470885 | + | 0.982407i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 110229.i | 2.11870i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 60376.0 | 1.08842 | 0.544210 | − | 0.838949i | \(-0.316829\pi\) | ||||
0.544210 | + | 0.838949i | \(0.316829\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −68020.9 | −1.15194 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2419.27i | 0.0385468i | 0.999814 | + | 0.0192734i | \(0.00613529\pi\) | ||||
−0.999814 | + | 0.0192734i | \(0.993865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −123731. | + | 28121.5i | −1.85751 | + | 0.422173i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 89605.2i | − | 1.26921i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −69364.1 | −0.928239 | −0.464120 | − | 0.885773i | \(-0.653629\pi\) | ||||
−0.464120 | + | 0.885773i | \(0.653629\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 154980. | 1.96188 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 33994.7i | − | 0.407572i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 25196.6 | + | 110862.i | 0.286439 | + | 1.26030i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 76217.3i | 0.822478i | 0.911527 | + | 0.411239i | \(0.134904\pi\) | ||||
−0.911527 | + | 0.411239i | \(0.865096\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 23643.1 | 0.242447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15273.9 | 0.148986 | 0.0744930 | − | 0.997222i | \(-0.476266\pi\) | ||||
0.0744930 | + | 0.997222i | \(0.476266\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 37841.1i | − | 0.351456i | −0.984439 | − | 0.175728i | \(-0.943772\pi\) | ||
0.984439 | − | 0.175728i | \(-0.0562279\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 44540.2 | + | 195972.i | 0.394257 | + | 1.73468i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 159135.i | 1.34371i | 0.740681 | + | 0.671857i | \(0.234503\pi\) | ||||
−0.740681 | + | 0.671857i | \(0.765497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 93740.1 | 0.755717 | 0.377858 | − | 0.925863i | \(-0.376661\pi\) | ||||
0.377858 | + | 0.925863i | \(0.376661\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −62024.3 | −0.477809 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 145638.i | 1.07295i | 0.843916 | + | 0.536476i | \(0.180245\pi\) | ||||
−0.843916 | + | 0.536476i | \(0.819755\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 53118.7 | − | 12072.8i | 0.374544 | − | 0.0851259i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 33241.9i | − | 0.224502i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −480500. | −3.11047 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 110084. | 0.683537 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 290628.i | − | 1.73210i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 108543. | + | 136879.i | 0.621337 | + | 0.783544i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8018.59i | − | 0.0441153i | −0.999757 | − | 0.0220576i | \(-0.992978\pi\) | ||
0.999757 | − | 0.0220576i | \(-0.00702173\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −69175.5 | −0.365997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −110408. | −0.562110 | −0.281055 | − | 0.959692i | \(-0.590684\pi\) | ||||
−0.281055 | + | 0.959692i | \(0.590684\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 430524.i | 2.11042i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −182921. | + | 41574.2i | −0.863833 | + | 0.196331i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 4536.88i | − | 0.0206517i | −0.999947 | − | 0.0103259i | \(-0.996713\pi\) | ||
0.999947 | − | 0.0103259i | \(-0.00328688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6371.93 | −0.0279727 | −0.0139863 | − | 0.999902i | \(-0.504452\pi\) | ||||
−0.0139863 | + | 0.999902i | \(0.504452\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −226462. | −0.959285 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 381212.i | − | 1.55893i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −65370.0 | − | 287620.i | −0.258201 | − | 1.13606i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 475615.i | 1.81536i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −232367. | −0.857450 | −0.428725 | − | 0.903435i | \(-0.641037\pi\) | ||||
−0.428725 | + | 0.903435i | \(0.641037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −234269. | −0.836128 | −0.418064 | − | 0.908418i | \(-0.637291\pi\) | ||||
−0.418064 | + | 0.908418i | \(0.637291\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 103063.i | 0.355938i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −24800.3 | − | 109118.i | −0.0829140 | − | 0.364812i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 661.264i | 0.00214105i | 0.999999 | + | 0.00107052i | \(0.000340758\pi\) | ||||
−0.999999 | + | 0.00107052i | \(0.999659\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 466714. | 1.46406 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 206282. | 0.627187 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 388467.i | − | 1.14521i | −0.819831 | − | 0.572606i | \(-0.805933\pi\) | ||
0.819831 | − | 0.572606i | \(-0.194067\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 482040. | − | 109558.i | 1.37839 | − | 0.313280i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 35545.3i | − | 0.0986258i | −0.998783 | − | 0.0493129i | \(-0.984297\pi\) | ||
0.998783 | − | 0.0493129i | \(-0.0157031\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −164685. | −0.443544 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 92343.4 | 0.241499 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 469613.i | − | 1.19296i | −0.802629 | − | 0.596479i | \(-0.796566\pi\) | ||
0.802629 | − | 0.596479i | \(-0.203434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 285936. | + | 596548.i | 0.705787 | + | 1.47248i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 66069.4i | 0.158514i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 25442.9 | 0.0593518 | 0.0296759 | − | 0.999560i | \(-0.490552\pi\) | ||||
0.0296759 | + | 0.999560i | \(0.490552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 131312. | 0.297926 | 0.148963 | − | 0.988843i | \(-0.452406\pi\) | ||||
0.148963 | + | 0.988843i | \(0.452406\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 148387.i | 0.327544i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −199090. | + | 45248.9i | −0.427680 | + | 0.0972027i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.18191e6i | 2.47161i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −710361. | −1.44652 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 165447. | 0.328152 | 0.164076 | − | 0.986448i | \(-0.447536\pi\) | ||||
0.164076 | + | 0.986448i | \(0.447536\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 501316.i | − | 0.968765i | −0.874856 | − | 0.484383i | \(-0.839044\pi\) | ||
0.874856 | − | 0.484383i | \(-0.160956\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −154036. | − | 677741.i | −0.290092 | − | 1.27637i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 142169.i | 0.261000i | 0.991448 | + | 0.130500i | \(0.0416583\pi\) | ||||
−0.991448 | + | 0.130500i | \(0.958342\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 946508. | 1.69430 | 0.847152 | − | 0.531350i | \(-0.178315\pi\) | ||||
0.847152 | + | 0.531350i | \(0.178315\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −695443. | −1.21415 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.11695e6i | − | 1.90237i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −212023. | − | 932874.i | −0.352369 | − | 1.55038i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 44245.7i | − | 0.0717704i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.05898e6 | 1.67696 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −946154. | −1.46304 | −0.731519 | − | 0.681821i | \(-0.761188\pi\) | ||||
−0.731519 | + | 0.681821i | \(0.761188\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 456787.i | − | 0.689866i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −222044. | + | 50465.9i | −0.327599 | + | 0.0744563i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 423753.i | − | 0.610890i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 166841. | 0.235067 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.66174e6 | 2.28867 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 459405.i | − | 0.618633i | −0.950959 | − | 0.309317i | \(-0.899900\pi\) | ||
0.950959 | − | 0.309317i | \(-0.100100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 127954. | − | 61330.6i | 0.168499 | − | 0.0807646i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 493138.i | 0.635190i | 0.948226 | + | 0.317595i | \(0.102875\pi\) | ||||
−0.948226 | + | 0.317595i | \(0.897125\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −210901. | −0.265760 | −0.132880 | − | 0.991132i | \(-0.542423\pi\) | ||||
−0.132880 | + | 0.991132i | \(0.542423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.87197e6 | 2.30817 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 7304.87i | − | 0.00881501i | −0.999990 | − | 0.00440750i | \(-0.998597\pi\) | ||
0.999990 | − | 0.00440750i | \(-0.00140296\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −726912. | + | 165212.i | −0.858642 | + | 0.195151i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.02534e6i | − | 1.18576i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −868906. | −0.983962 | −0.491981 | − | 0.870606i | \(-0.663727\pi\) | ||||
−0.491981 | + | 0.870606i | \(0.663727\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 359511. | 0.398722 | 0.199361 | − | 0.979926i | \(-0.436113\pi\) | ||||
0.199361 | + | 0.979926i | \(0.436113\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 339745.i | 0.369094i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 346977. | + | 1.52666e6i | 0.369306 | + | 1.62490i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.48891e6i | − | 1.55283i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 41085.2 | 0.0419940 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 999037. | 1.00092 | 0.500458 | − | 0.865761i | \(-0.333165\pi\) | ||||
0.500458 | + | 0.865761i | \(0.333165\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 507402.i | − | 0.498369i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 477573. | + | 2.10127e6i | 0.459928 | + | 2.02363i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.58468e6i | − | 1.49661i | −0.663354 | − | 0.748306i | \(-0.730868\pi\) | ||
0.663354 | − | 0.748306i | \(-0.269132\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −773149. | −0.716166 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −239576. | −0.217692 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.84241e6i | 1.64247i | 0.570589 | + | 0.821236i | \(0.306715\pi\) | ||||
−0.570589 | + | 0.821236i | \(0.693285\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.49809e6 | − | 340484.i | 1.31046 | − | 0.297839i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.17798e6i | 1.01125i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.28997e6 | −1.08693 | −0.543464 | − | 0.839433i | \(-0.682887\pi\) | ||||
−0.543464 | + | 0.839433i | \(0.682887\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.88685e6 | −1.56068 | −0.780339 | − | 0.625357i | \(-0.784953\pi\) | ||||
−0.780339 | + | 0.625357i | \(0.784953\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2.63195e6i | − | 2.13733i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.46736e6 | − | 703329.i | 1.17005 | − | 0.560824i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 593570.i | − | 0.464807i | −0.972619 | − | 0.232404i | \(-0.925341\pi\) | ||
0.972619 | − | 0.232404i | \(-0.0746590\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −90891.1 | −0.0699054 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 643035. | 0.485813 | 0.242906 | − | 0.970050i | \(-0.421899\pi\) | ||||
0.242906 | + | 0.970050i | \(0.421899\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.62977e6i | − | 1.20965i | −0.796358 | − | 0.604825i | \(-0.793243\pi\) | ||
0.796358 | − | 0.604825i | \(-0.206757\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.88271e6 | − | 427901.i | 1.37301 | − | 0.312055i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 3.62274e6i | − | 2.59617i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.73221e6 | −2.62858 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.29436e6 | 0.896032 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 266348.i | − | 0.181251i | −0.995885 | − | 0.0906254i | \(-0.971113\pi\) | ||
0.995885 | − | 0.0906254i | \(-0.0288866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48199.8 | + | 212074.i | 0.0322471 | + | 0.141883i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.74731e6i | 1.14942i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −713399. | −0.461482 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −862289. | −0.548576 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 259389.i | − | 0.162310i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 108254. | + | 476303.i | 0.0666335 | + | 0.293179i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.64753e6i | − | 0.997672i | −0.866696 | − | 0.498836i | \(-0.833761\pi\) | ||
0.866696 | − | 0.498836i | \(-0.166239\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −642638. | −0.382886 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.04162e6 | −1.78322 | −0.891609 | − | 0.452806i | \(-0.850423\pi\) | ||||
−0.891609 | + | 0.452806i | \(0.850423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.02897e6i | 1.74757i | 0.486314 | + | 0.873784i | \(0.338341\pi\) | ||||
−0.486314 | + | 0.873784i | \(0.661659\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 523966. | − | 119086.i | 0.297527 | − | 0.0676217i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.07750e6i | − | 1.16116i | −0.814202 | − | 0.580582i | \(-0.802825\pi\) | ||
0.814202 | − | 0.580582i | \(-0.197175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.74741e6 | −1.51164 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.70251e6 | 1.46388 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.61620e6i | 2.46195i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −988870. | − | 2.06308e6i | −0.519315 | − | 1.08345i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 1.59194e6i | − | 0.823300i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.82291e6 | −1.43783 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.75626e6 | −1.88446 | −0.942228 | − | 0.334973i | \(-0.891273\pi\) | ||||
−0.942228 | + | 0.334973i | \(0.891273\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 165833.i | 0.0819524i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.23228e6 | + | 507349.i | −1.08677 | + | 0.246999i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.79503e6i | − | 0.860985i | −0.902594 | − | 0.430493i | \(-0.858340\pi\) | ||
0.902594 | − | 0.430493i | \(-0.141660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.47331e6 | 1.16890 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.04232e6 | −0.485419 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.37077e6i | 1.08806i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −205026. | − | 902089.i | −0.0927387 | − | 0.408039i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.73738e6i | 0.774591i | 0.921956 | + | 0.387295i | \(0.126591\pi\) | ||||
−0.921956 | + | 0.387295i | \(0.873409\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.63164e6 | 1.59602 | 0.798012 | − | 0.602642i | \(-0.205885\pi\) | ||||
0.798012 | + | 0.602642i | \(0.205885\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.45669e6 | 1.06434 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 655592.i | 0.280025i | 0.990150 | + | 0.140012i | \(0.0447143\pi\) | ||||
−0.990150 | + | 0.140012i | \(0.955286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −333241. | − | 1.46622e6i | −0.140342 | − | 0.617489i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.16010e6i | 3.38864i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.17606e6 | −0.481609 | −0.240805 | − | 0.970574i | \(-0.577411\pi\) | ||||
−0.240805 | + | 0.970574i | \(0.577411\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.65997e6 | 0.670399 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1.86951e6i | − | 0.744665i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 535535. | − | 121716.i | 0.210405 | − | 0.0478206i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 788323.i | − | 0.305520i | −0.988263 | − | 0.152760i | \(-0.951184\pi\) | ||
0.988263 | − | 0.152760i | \(-0.0488161\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −777046. | −0.297085 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.81770e6 | 2.19441 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.14542e6i | 1.17060i | 0.810819 | + | 0.585298i | \(0.199022\pi\) | ||||
−0.810819 | + | 0.585298i | \(0.800978\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.32456e6 | − | 1.84333e6i | 0.853615 | − | 0.676902i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.86282e6i | 1.39975i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.29034e6 | 0.461430 | 0.230715 | − | 0.973021i | \(-0.425894\pi\) | ||||
0.230715 | + | 0.973021i | \(0.425894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −136176. | −0.0480604 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.39221e6i | 0.833303i | 0.909066 | + | 0.416652i | \(0.136796\pi\) | ||||
−0.909066 | + | 0.416652i | \(0.863204\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00875e6 | − | 1.36566e6i | 2.06601 | − | 0.469560i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 184953.i | 0.0627747i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.31206e6 | −1.44481 | −0.722406 | − | 0.691469i | \(-0.756964\pi\) | ||||
−0.722406 | + | 0.691469i | \(0.756964\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.21182e6 | 0.731658 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.87500e6i | 0.612378i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −748017. | − | 3.29119e6i | −0.241223 | − | 1.06135i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.22787e6i | − | 0.709436i | −0.934973 | − | 0.354718i | \(-0.884577\pi\) | ||
0.934973 | − | 0.354718i | \(-0.115423\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.31137e6 | 2.29915 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.52683e6 | −1.40583 | −0.702915 | − | 0.711274i | \(-0.748119\pi\) | ||||
−0.702915 | + | 0.711274i | \(0.748119\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.46549e6i | 0.449490i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 842733. | + | 3.70792e6i | 0.255301 | + | 1.12329i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.90175e6i | 0.569072i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.73728e6 | −1.40030 | −0.700149 | − | 0.713997i | \(-0.746883\pi\) | ||||
−0.700149 | + | 0.713997i | \(0.746883\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −77047.7 | −0.0224986 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 823571.i | 0.237589i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 131878. | − | 29973.1i | 0.0375882 | − | 0.00854301i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 108211.i | 0.0304743i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.14343e6 | 0.318181 | 0.159091 | − | 0.987264i | \(-0.449144\pi\) | ||||
0.159091 | + | 0.987264i | \(0.449144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.03804e6 | 1.66032 | 0.830158 | − | 0.557528i | \(-0.188250\pi\) | ||||
0.830158 | + | 0.557528i | \(0.188250\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 605488.i | 0.164534i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.06589e6 | + | 6.39636e6i | 0.823349 | + | 1.71775i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.84968e6i | 0.490940i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.47394e6 | −1.69834 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 461842. | 0.119757 | 0.0598783 | − | 0.998206i | \(-0.480929\pi\) | ||||
0.0598783 | + | 0.998206i | \(0.480929\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 1.86278e6i | − | 0.477464i | −0.971085 | − | 0.238732i | \(-0.923268\pi\) | ||
0.971085 | − | 0.238732i | \(-0.0767318\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.88451e6 | + | 1.11015e6i | −1.23765 | + | 0.281292i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.98177e6i | − | 0.496420i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.85752e6 | 1.45062 | 0.725308 | − | 0.688424i | \(-0.241697\pi\) | ||||
0.725308 | + | 0.688424i | \(0.241697\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.27164e6 | 0.311365 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.28843e6i | 1.03822i | 0.854708 | + | 0.519109i | \(0.173736\pi\) | ||||
−0.854708 | + | 0.519109i | \(0.826264\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 859374. | + | 3.78114e6i | 0.205723 | + | 0.905155i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.94617e6i | 0.934130i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.93198e6 | −0.686348 | −0.343174 | − | 0.939272i | \(-0.611502\pi\) | ||||
−0.343174 | + | 0.939272i | \(0.611502\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.91103e6 | −2.06294 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.97848e6i | 0.910902i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.92010e6 | − | 8.44821e6i | −0.434806 | − | 1.91309i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.06303e6i | 1.13402i | 0.823712 | + | 0.567009i | \(0.191899\pi\) | ||||
−0.823712 | + | 0.567009i | \(0.808101\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.61670e6 | −1.68747 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.43641e6 | 0.533947 | 0.266974 | − | 0.963704i | \(-0.413976\pi\) | ||||
0.266974 | + | 0.963704i | \(0.413976\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 118770.i | − | 0.0257485i | −0.999917 | − | 0.0128743i | \(-0.995902\pi\) | ||
0.999917 | − | 0.0128743i | \(-0.00409812\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.85310e6 | + | 421172.i | −0.397436 | + | 0.0903289i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 7.00735e6i | − | 1.48683i | −0.668830 | − | 0.743415i | \(-0.733205\pi\) | ||
0.668830 | − | 0.743415i | \(-0.266795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.66887e6 | −1.81983 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11229.9 | 0.00233252 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.12101e6i | 0.435903i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.73108e6 | − | 2.74701e6i | 1.16547 | − | 0.558632i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.24785e6i | − | 0.251110i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.00020e6 | −1.39403 | −0.697014 | − | 0.717058i | \(-0.745488\pi\) | ||||
−0.697014 | + | 0.717058i | \(0.745488\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.67383e6 | 0.526952 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 3.50319e6i | − | 0.683276i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.15472e6 | − | 944281.i | 0.802025 | − | 0.182283i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.44869e6i | 1.80530i | 0.430375 | + | 0.902650i | \(0.358381\pi\) | ||||
−0.430375 | + | 0.902650i | \(0.641619\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.59715e6 | −1.24763 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.54041e6 | −0.288358 | −0.144179 | − | 0.989552i | \(-0.546054\pi\) | ||||
−0.144179 | + | 0.989552i | \(0.546054\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.19763e7i | − | 2.21924i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −292922. | − | 1.28882e6i | −0.0537328 | − | 0.236418i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.69396e6i | − | 1.03401i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.02185e6 | −1.08263 | −0.541313 | − | 0.840821i | \(-0.682073\pi\) | ||||
−0.541313 | + | 0.840821i | \(0.682073\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −603648. | −0.107446 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.84251e6i | − | 0.324705i | −0.986733 | − | 0.162352i | \(-0.948092\pi\) | ||
0.986733 | − | 0.162352i | \(-0.0519082\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −189233. | − | 832601.i | −0.0330193 | − | 0.145281i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.79676e6i | 0.483210i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.12602e6 | −1.21914 | −0.609568 | − | 0.792734i | \(-0.708657\pi\) | ||||
−0.609568 | + | 0.792734i | \(0.708657\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.07971e6 | 0.352331 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.82449e6i | 1.14492i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.06278e6 | + | 468826.i | −0.342716 | + | 0.0778921i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.94363e6i | 1.14251i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.97522e6 | −1.29964 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.26117e6 | −0.364954 | −0.182477 | − | 0.983210i | \(-0.558412\pi\) | ||||
−0.182477 | + | 0.983210i | \(0.558412\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 748790.i | 0.119703i | 0.998207 | + | 0.0598516i | \(0.0190628\pi\) | ||||
−0.998207 | + | 0.0598516i | \(0.980937\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.01309e7 | − | 4.85591e6i | 1.60417 | − | 0.768904i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 4.54360e6i | − | 0.712646i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.48679e6 | 0.852470 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 176649. | 0.0271878 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.25288e7i | 1.91025i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.67470e6 | − | 1.97158e6i | 1.31030 | − | 0.297803i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 432085.i | − | 0.0646596i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.45830e7 | 2.16210 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −278009. | −0.0408381 | −0.0204190 | − | 0.999792i | \(-0.506500\pi\) | ||||
−0.0204190 | + | 0.999792i | \(0.506500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 2.23001e6i | − | 0.324570i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.16138e6 | − | 5.10991e6i | −0.167487 | − | 0.736923i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.06047e6i | − | 0.866040i | −0.901384 | − | 0.433020i | \(-0.857448\pi\) | ||
0.901384 | − | 0.433020i | \(-0.142552\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 396741. | 0.0561792 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.07306e7 | −1.50573 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.27811e7i | − | 1.77727i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 768439. | + | 3.38104e6i | 0.105895 | + | 0.465927i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.37326e6i | 1.14355i | 0.820409 | + | 0.571777i | \(0.193746\pi\) | ||||
−0.820409 | + | 0.571777i | \(0.806254\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.98211e6 | 0.403640 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.00718e7 | 2.69264 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.87244e6i | 1.31266i | 0.754472 | + | 0.656332i | \(0.227893\pi\) | ||||
−0.754472 | + | 0.656332i | \(0.772107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.93897e6 | − | 1.80436e6i | 1.04627 | − | 0.237795i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.43994e7i | 1.88100i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.41803e6 | 0.831038 | 0.415519 | − | 0.909584i | \(-0.363600\pi\) | ||||
0.415519 | + | 0.909584i | \(0.363600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.36965e7 | 1.75801 | 0.879003 | − | 0.476817i | \(-0.158210\pi\) | ||||
0.879003 | + | 0.476817i | \(0.158210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 2.80970e6i | − | 0.357498i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.31621e6 | − | 2.74601e6i | −0.166018 | − | 0.346363i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.49348e6i | − | 0.186749i | −0.995631 | − | 0.0933747i | \(-0.970235\pi\) | ||
0.995631 | − | 0.0933747i | \(-0.0297655\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.51361e6 | −1.05540 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 512137. | 0.0629428 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.43101e7i | − | 1.74369i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.81206e6 | + | 411844.i | −0.218919 | + | 0.0497557i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.27999e7i | − | 1.53324i | −0.642098 | − | 0.766622i | \(-0.721936\pi\) | ||
0.642098 | − | 0.766622i | \(-0.278064\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.07102e6 | −0.483521 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.41439e6 | 0.284341 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.38952e6i | − | 0.746160i | −0.927799 | − | 0.373080i | \(-0.878302\pi\) | ||
0.927799 | − | 0.373080i | \(-0.121698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.95307e6 | + | 2.61928e7i | 0.689364 | + | 3.03312i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 1.60741e7i | − | 1.84582i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.77509e6 | −0.885398 | −0.442699 | − | 0.896670i | \(-0.645979\pi\) | ||||
−0.442699 | + | 0.896670i | \(0.645979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.29871e7 | −1.46665 | −0.733323 | − | 0.679880i | \(-0.762032\pi\) | ||||
−0.733323 | + | 0.679880i | \(0.762032\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.85939e6i | 0.208247i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.36387e6 | − | 6.00086e6i | −0.151490 | − | 0.666538i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.40031e6i | − | 0.705066i | −0.935799 | − | 0.352533i | \(-0.885321\pi\) | ||
0.935799 | − | 0.352533i | \(-0.114679\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.89686e7 | −2.07249 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.76263e6 | 1.05795 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.47519e7i | − | 1.58562i | −0.609471 | − | 0.792808i | \(-0.708618\pi\) | ||
0.609471 | − | 0.792808i | \(-0.291382\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.58426e7 | + | 3.60068e6i | −1.68903 | + | 0.383881i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 979056.i | 0.103537i | 0.998659 | + | 0.0517684i | \(0.0164858\pi\) | ||||
−0.998659 | + | 0.0517684i | \(0.983514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.60371e6 | 0.378027 | 0.189013 | − | 0.981974i | \(-0.439471\pi\) | ||||
0.189013 | + | 0.981974i | \(0.439471\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.26991e6 | 0.340256 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.46838e7i | 1.51572i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.11673e6 | − | 7.61269e6i | 0.626353 | − | 0.779539i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 1.79841e7i | − | 1.82692i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.28993e6 | −0.835457 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.51546e6 | 0.351486 | 0.175743 | − | 0.984436i | \(-0.443767\pi\) | ||||
0.175743 | + | 0.984436i | \(0.443767\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.60681e7i | 1.59388i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −437106. | + | 99344.9i | −0.0430182 | + | 0.00977713i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.05035e7i | − | 2.00207i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.22130e6 | −0.118324 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.73523e6 | −0.262935 | −0.131468 | − | 0.991320i | \(-0.541969\pi\) | ||||
−0.131468 | + | 0.991320i | \(0.541969\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.57847e7i | − | 1.50560i | −0.658251 | − | 0.752799i | \(-0.728703\pi\) | ||
0.658251 | − | 0.752799i | \(-0.271297\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 857037. | + | 3.77086e6i | 0.0811148 | + | 0.356896i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.62226e6i | 0.434104i | 0.976160 | + | 0.217052i | \(0.0696441\pi\) | ||||
−0.976160 | + | 0.217052i | \(0.930356\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.02578e6 | 0.188790 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.19639e6 | −0.665521 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.60370e6i | 0.422497i | 0.977432 | + | 0.211249i | \(0.0677529\pi\) | ||||
−0.977432 | + | 0.211249i | \(0.932247\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.36788e6 | + | 6.01849e6i | 0.124579 | + | 0.548131i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 446079.i | − | 0.0403179i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.49631e7 | 1.34217 | 0.671087 | − | 0.741378i | \(-0.265828\pi\) | ||||
0.671087 | + | 0.741378i | \(0.265828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.40490e7 | 1.25067 | 0.625333 | − | 0.780358i | \(-0.284963\pi\) | ||||
0.625333 | + | 0.780358i | \(0.284963\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 2.82206e7i | − | 2.49334i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.34685e7 | − | 5.33389e6i | 2.05793 | − | 0.467725i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.14150e6i | 0.447482i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.80185e6 | −0.673957 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.54975e6 | 0.390105 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.81487e7i | − | 1.54457i | −0.635276 | − | 0.772285i | \(-0.719114\pi\) | ||
0.635276 | − | 0.772285i | \(-0.280886\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.53254e6 | + | 9.45624e6i | 0.382897 | + | 0.798839i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3.73842e6i | − | 0.313485i | −0.987640 | − | 0.156743i | \(-0.949901\pi\) | ||
0.987640 | − | 0.156743i | \(-0.0500993\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.61345e7 | 1.34302 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.37472e6 | 0.691994 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.31301e7i | 1.07700i | 0.842624 | + | 0.538502i | \(0.181010\pi\) | ||||
−0.842624 | + | 0.538502i | \(0.818990\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −247312. | + | 56208.9i | −0.0201381 | + | 0.00457698i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.58163e6i | 0.289527i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.01197e7 | −1.61463 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.49754e6 | −0.358327 | −0.179164 | − | 0.983819i | \(-0.557339\pi\) | ||||
−0.179164 | + | 0.983819i | \(0.557339\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 5.00504e6i | − | 0.395890i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 78943.9 | + | 347344.i | 0.00619950 | + | 0.0272770i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.88441e7i | − | 3.02861i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −124055. | −0.00960333 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.36524e7 | 1.04933 | 0.524666 | − | 0.851308i | \(-0.324190\pi\) | ||||
0.524666 | + | 0.851308i | \(0.324190\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.42770e6i | 0.566847i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.80571e6 | + | 1.23448e7i | 0.212603 | + | 0.935429i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 3.23334e6i | − | 0.243278i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.79465e6 | −0.582346 | −0.291173 | − | 0.956670i | \(-0.594046\pi\) | ||||
−0.291173 | + | 0.956670i | \(0.594046\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.74142e6 | −0.203377 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.95060e6i | 0.143696i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.07804e7 | + | 4.72296e6i | −1.52016 | + | 0.345501i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.47562e7i | 1.07196i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.98555e7 | 1.43238 | 0.716191 | − | 0.697904i | \(-0.245884\pi\) | ||||
0.716191 | + | 0.697904i | \(0.245884\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.01064e6 | −0.573890 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 6.10540e6i | − | 0.434379i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.48687e7 | + | 7.12684e6i | −1.05058 | + | 0.503561i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.12828e7i | 1.49346i | 0.665128 | + | 0.746730i | \(0.268377\pi\) | ||||
−0.665128 | + | 0.746730i | \(0.731623\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.07594e7 | −0.749839 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.24572e6 | −0.639952 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 726358.i | 0.0499334i | 0.999688 | + | 0.0249667i | \(0.00794797\pi\) | ||||
−0.999688 | + | 0.0249667i | \(0.992052\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.59265e7 | − | 5.89255e6i | 1.77021 | − | 0.402332i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.13232e7i | 1.44605i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −259167. | −0.0174570 | −0.00872849 | − | 0.999962i | \(-0.502778\pi\) | ||||
−0.00872849 | + | 0.999962i | \(0.502778\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.52854e7 | −1.69170 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.47729e6i | − | 0.363994i | −0.983299 | − | 0.181997i | \(-0.941744\pi\) | ||
0.983299 | − | 0.181997i | \(-0.0582560\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.87887e6 | + | 1.26667e7i | 0.190034 | + | 0.836126i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 109849.i | − | 0.00720268i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.36875e7 | 2.19414 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.96106e7 | −1.26879 | −0.634396 | − | 0.773008i | \(-0.718751\pi\) | ||||
−0.634396 | + | 0.773008i | \(0.718751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.69662e7i | − | 1.09043i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.90244e6 | + | 1.27704e7i | 0.185308 | + | 0.815335i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.92552e6i | 0.375826i | 0.982186 | + | 0.187913i | \(0.0601723\pi\) | ||||
−0.982186 | + | 0.187913i | \(0.939828\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.61696e6 | −0.542937 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.56740e7 | 0.981112 | 0.490556 | − | 0.871410i | \(-0.336794\pi\) | ||||
0.490556 | + | 0.871410i | \(0.336794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.98439e7i | − | 1.23400i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.61812e6 | − | 1.27688e6i | 0.347086 | − | 0.0788854i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.84821e6i | − | 0.174817i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.63779e7 | 1.60851 | 0.804255 | − | 0.594285i | \(-0.202565\pi\) | ||||
0.804255 | + | 0.594285i | \(0.202565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.69119e7 | −1.63045 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.84175e7i | − | 1.10862i | −0.832312 | − | 0.554308i | \(-0.812983\pi\) | ||
0.832312 | − | 0.554308i | \(-0.187017\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.64095e6 | + | 2.70380e6i | −0.337363 | + | 0.161704i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.31300e7i | 0.780212i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.48040e7 | −2.05487 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.40057e7 | −0.821631 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.77055e7i | − | 1.03206i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36046.5 | − | 8192.62i | 0.00208780 | − | 0.000474513i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.66821e7i | − | 0.960091i | −0.877243 | − | 0.480046i | \(-0.840620\pi\) | ||
0.877243 | − | 0.480046i | \(-0.159380\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.12888e7 | 1.78936 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.08304e7 | 1.75201 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.39688e6i | − | 0.361231i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.78227e6 | − | 2.54413e7i | −0.324474 | − | 1.42765i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.61029e7i | 1.45560i | 0.685789 | + | 0.727800i | \(0.259457\pi\) | ||||
−0.685789 | + | 0.727800i | \(0.740543\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.02680e7 | −1.67732 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.14954e6 | 0.173446 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 5.11556e6i | − | 0.279965i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.55570e6 | − | 1.12448e7i | −0.139002 | − | 0.611590i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.19070e7i | 1.18413i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.68998e7 | −0.907844 | −0.453922 | − | 0.891041i | \(-0.649975\pi\) | ||||
−0.453922 | + | 0.891041i | \(0.649975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.50687e6 | 0.240615 | 0.120308 | − | 0.992737i | \(-0.461612\pi\) | ||||
0.120308 | + | 0.992737i | \(0.461612\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.20434e7i | 1.70025i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.11759e7 | + | 4.81285e6i | −1.11673 | + | 0.253810i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.28408e6i | 0.434199i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.03701e6 | −0.366588 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.72987e7 | 0.895684 | 0.447842 | − | 0.894113i | \(-0.352193\pi\) | ||||
0.447842 | + | 0.894113i | \(0.352193\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 4.38452e6i | − | 0.225643i | −0.993615 | − | 0.112822i | \(-0.964011\pi\) | ||
0.993615 | − | 0.112822i | \(-0.0359889\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.19443e7 | − | 2.49194e7i | −0.610978 | − | 1.27468i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.67189e7i | 1.35848i | 0.733914 | + | 0.679242i | \(0.237691\pi\) | ||||
−0.733914 | + | 0.679242i | \(0.762309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.60252e7 | −0.809873 | −0.404936 | − | 0.914345i | \(-0.632706\pi\) | ||||
−0.404936 | + | 0.914345i | \(0.632706\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.00803e7 | −0.506374 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.35689e7i | 3.17418i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.93763e6 | + | 440381.i | −0.0961731 | + | 0.0218581i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 6.71716e6i | − | 0.331415i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.65800e7 | 1.30362 | 0.651808 | − | 0.758384i | \(-0.274011\pi\) | ||||
0.651808 | + | 0.758384i | \(0.274011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.32841e6 | 0.357289 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 1.09204e7i | − | 0.529258i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.04033e6 | + | 8.97722e6i | 0.0983014 | + | 0.432514i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.33039e7i | − | 1.11614i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.76776e7 | −1.31783 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.55893e6 | 0.168459 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.33996e7i | − | 0.630548i | −0.949001 | − | 0.315274i | \(-0.897904\pi\) | ||
0.949001 | − | 0.315274i | \(-0.102096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.14407e6 | − | 5.03378e6i | −0.0535227 | − | 0.235493i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.97622e7i | 1.38425i | 0.721780 | + | 0.692123i | \(0.243324\pi\) | ||||
−0.721780 | + | 0.692123i | \(0.756676\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.89754e6 | −0.318942 | −0.159471 | − | 0.987203i | \(-0.550979\pi\) | ||||
−0.159471 | + | 0.987203i | \(0.550979\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.15233e7 | −2.82834 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.06032e6i | 0.414111i | 0.978329 | + | 0.207055i | \(0.0663880\pi\) | ||||
−0.978329 | + | 0.207055i | \(0.933612\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.55993e7 | + | 5.81819e6i | −1.16329 | + | 0.264392i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.33823e7i | 2.86365i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.14382e7 | −1.41224 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.99801e7 | 1.33902 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 3.46071e6i | − | 0.153684i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.89762e7 | − | 2.29776e7i | 1.27944 | − | 1.01458i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 2.83641e7i | − | 1.24529i | −0.782504 | − | 0.622645i | \(-0.786058\pi\) | ||
0.782504 | − | 0.622645i | \(-0.213942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.52325e6 | −0.197460 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.27391e7 | 0.552966 | 0.276483 | − | 0.961019i | \(-0.410831\pi\) | ||||
0.276483 | + | 0.961019i | \(0.410831\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.72031e6i | 0.117413i | 0.998275 | + | 0.0587066i | \(0.0186976\pi\) | ||||
−0.998275 | + | 0.0587066i | \(0.981302\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.60154e6 | − | 818555.i | 0.154572 | − | 0.0351309i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.83636e6i | 0.249077i | 0.992215 | + | 0.124538i | \(0.0397450\pi\) | ||||
−0.992215 | + | 0.124538i | \(0.960255\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.69747e6 | −0.0720355 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.54189e7 | 1.49466 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.71199e7i | 1.13804i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −315220. | − | 1.38693e6i | −0.0131540 | − | 0.0578759i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.21153e7i | 0.502752i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.05619e7 | 0.435854 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.23792e7 | 2.55993 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.46438e7i | 0.597634i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.62687e6 | − | 7.15803e6i | −0.0660285 | − | 0.290517i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.25967e7i | 0.508439i | 0.967147 | + | 0.254220i | \(0.0818186\pi\) | ||||
−0.967147 | + | 0.254220i | \(0.918181\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −693523. | −0.0278388 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.28644e7 | −0.513561 | −0.256781 | − | 0.966470i | \(-0.582662\pi\) | ||||
−0.256781 | + | 0.966470i | \(0.582662\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.25973e6i | − | 0.0500149i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.08882e6 | − | 1.83842e6i | 0.319398 | − | 0.0725925i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.33723e7i | 0.917865i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.81974e7 | −1.10134 | −0.550669 | − | 0.834724i | \(-0.685627\pi\) | ||||
−0.550669 | + | 0.834724i | \(0.685627\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.79792e7 | −1.08689 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.96918e7i | 0.760818i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.93317e6 | + | 1.02921e7i | 0.189571 | + | 0.395502i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.71821e6i | 0.0656715i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.92018e7 | 1.11012 | 0.555061 | − | 0.831810i | \(-0.312695\pi\) | ||||
0.555061 | + | 0.831810i | \(0.312695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.69571e7 | 2.15364 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.16544e7i | 1.94269i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.44276e7 | − | 1.46430e7i | 2.41014 | − | 0.547775i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.99796e7i | − | 1.11552i | −0.830003 | − | 0.557759i | \(-0.811661\pi\) | ||
0.830003 | − | 0.557759i | \(-0.188339\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.14395e7 | 1.90385 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.20363e7 | −0.443119 | −0.221560 | − | 0.975147i | \(-0.571115\pi\) | ||||
−0.221560 | + | 0.975147i | \(0.571115\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.66761e7i | 0.610681i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.80089e6 | + | 3.87228e7i | 0.320588 | + | 1.41055i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 4.86315e7i | − | 1.76215i | −0.472977 | − | 0.881075i | \(-0.656821\pi\) | ||
0.472977 | − | 0.881075i | \(-0.343179\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.19239e6 | −0.259243 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.52813e7 | −1.26501 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.77941e7i | − | 0.991333i | −0.868513 | − | 0.495667i | \(-0.834924\pi\) | ||
0.868513 | − | 0.495667i | \(-0.165076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.04977e6 | − | 9.01875e6i | −0.0727273 | − | 0.319991i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.66580e7i | 1.64682i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −960419. | −0.0337221 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.46222e7 | −0.860038 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 7.22567e6i | − | 0.251080i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.73275e7 | + | 6.21097e6i | −0.944673 | + | 0.214704i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.24365e7i | − | 1.45940i | −0.683768 | − | 0.729699i | \(-0.739660\pi\) | ||
0.683768 | − | 0.729699i | \(-0.260340\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.83947e7 | 2.68212 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.23502e7 | −0.760736 | −0.380368 | − | 0.924835i | \(-0.624203\pi\) | ||||
−0.380368 | + | 0.924835i | \(0.624203\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.34888e6i | 0.0456764i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.50363e7 | + | 1.67935e7i | −1.18034 | + | 0.565757i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 3.02839e7i | − | 1.01502i | −0.861645 | − | 0.507511i | \(-0.830566\pi\) | ||
0.861645 | − | 0.507511i | \(-0.169434\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.61184e7 | 1.20440 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.25635e6 | −0.141210 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.64282e7i | 0.542257i | 0.962543 | + | 0.271128i | \(0.0873968\pi\) | ||||
−0.962543 | + | 0.271128i | \(0.912603\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.74987e6 | − | 1.76138e6i | 0.254509 | − | 0.0578446i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.79400e7i | 1.56641i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.96926e6 | 0.129038 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.23109e6 | −0.0721660 | −0.0360830 | − | 0.999349i | \(-0.511488\pi\) | ||||
−0.0360830 | + | 0.999349i | \(0.511488\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.37908e7i | 2.05298i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.17266e7 | − | 5.15956e7i | −0.375503 | − | 1.65217i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.30762e7i | − | 1.69107i | −0.533919 | − | 0.845536i | \(-0.679281\pi\) | ||
0.533919 | − | 0.845536i | \(-0.320719\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.22556e7 | −0.388528 |
(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 | 320.6.c.l.129.3 | 12 | ||
4.3 | odd | 2 | inner | 320.6.c.l.129.9 | 12 | ||
5.4 | even | 2 | inner | 320.6.c.l.129.10 | 12 | ||
8.3 | odd | 2 | 160.6.c.d.129.4 | yes | 12 | ||
8.5 | even | 2 | 160.6.c.d.129.10 | yes | 12 | ||
20.19 | odd | 2 | inner | 320.6.c.l.129.4 | 12 | ||
40.3 | even | 4 | 800.6.a.w.1.5 | 6 | |||
40.13 | odd | 4 | 800.6.a.bb.1.2 | 6 | |||
40.19 | odd | 2 | 160.6.c.d.129.9 | yes | 12 | ||
40.27 | even | 4 | 800.6.a.bb.1.1 | 6 | |||
40.29 | even | 2 | 160.6.c.d.129.3 | ✓ | 12 | ||
40.37 | odd | 4 | 800.6.a.w.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.c.d.129.3 | ✓ | 12 | 40.29 | even | 2 | ||
160.6.c.d.129.4 | yes | 12 | 8.3 | odd | 2 | ||
160.6.c.d.129.9 | yes | 12 | 40.19 | odd | 2 | ||
160.6.c.d.129.10 | yes | 12 | 8.5 | even | 2 | ||
320.6.c.l.129.3 | 12 | 1.1 | even | 1 | trivial | ||
320.6.c.l.129.4 | 12 | 20.19 | odd | 2 | inner | ||
320.6.c.l.129.9 | 12 | 4.3 | odd | 2 | inner | ||
320.6.c.l.129.10 | 12 | 5.4 | even | 2 | inner | ||
800.6.a.w.1.5 | 6 | 40.3 | even | 4 | |||
800.6.a.w.1.6 | 6 | 40.37 | odd | 4 | |||
800.6.a.bb.1.1 | 6 | 40.27 | even | 4 | |||
800.6.a.bb.1.2 | 6 | 40.13 | odd | 4 |