Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.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: | \(48.1977026600\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 4 x^{14} - 27 x^{13} + 106 x^{12} + 266 x^{11} - 1004 x^{10} - 1105 x^{9} + 4076 x^{8} + \cdots - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.546893\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.453107 | −0.202636 | −0.101318 | − | 0.994854i | \(-0.532306\pi\) | ||||
−0.101318 | + | 0.994854i | \(0.532306\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.17063 | 0.820422 | 0.410211 | − | 0.911991i | \(-0.365455\pi\) | ||||
0.410211 | + | 0.911991i | \(0.365455\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.35442 | −1.61442 | −0.807209 | − | 0.590266i | \(-0.799023\pi\) | ||||
−0.807209 | + | 0.590266i | \(0.799023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.71175 | 0.752105 | 0.376052 | − | 0.926598i | \(-0.377281\pi\) | ||||
0.376052 | + | 0.926598i | \(0.377281\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.453107 | −0.116992 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.07839 | 1.47423 | 0.737113 | − | 0.675770i | \(-0.236189\pi\) | ||||
0.737113 | + | 0.675770i | \(0.236189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.86135 | −0.656439 | −0.328220 | − | 0.944601i | \(-0.606449\pi\) | ||||
−0.328220 | + | 0.944601i | \(0.606449\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.17063 | 0.473671 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.42982 | −1.13220 | −0.566098 | − | 0.824338i | \(-0.691547\pi\) | ||||
−0.566098 | + | 0.824338i | \(0.691547\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.79469 | −0.958939 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.45567 | −1.38448 | −0.692242 | − | 0.721666i | \(-0.743377\pi\) | ||||
−0.692242 | + | 0.721666i | \(0.743377\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.78314 | −1.03868 | −0.519341 | − | 0.854567i | \(-0.673823\pi\) | ||||
−0.519341 | + | 0.854567i | \(0.673823\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.35442 | −0.932084 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.983530 | −0.166247 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.10695 | 0.181981 | 0.0909907 | − | 0.995852i | \(-0.470997\pi\) | ||||
0.0909907 | + | 0.995852i | \(0.470997\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.71175 | 0.434228 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.10245 | −0.953043 | −0.476521 | − | 0.879163i | \(-0.658103\pi\) | ||||
−0.476521 | + | 0.879163i | \(0.658103\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.08829 | 0.928456 | 0.464228 | − | 0.885716i | \(-0.346332\pi\) | ||||
0.464228 | + | 0.885716i | \(0.346332\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.453107 | −0.0675453 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.32792 | −0.485428 | −0.242714 | − | 0.970098i | \(-0.578038\pi\) | ||||
−0.242714 | + | 0.970098i | \(0.578038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.28835 | −0.326907 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.07839 | 0.851145 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.31676 | −0.730313 | −0.365157 | − | 0.930946i | \(-0.618985\pi\) | ||||
−0.365157 | + | 0.930946i | \(0.618985\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.42613 | 0.327139 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.86135 | −0.378995 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.97520 | 0.257150 | 0.128575 | − | 0.991700i | \(-0.458960\pi\) | ||||
0.128575 | + | 0.991700i | \(0.458960\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0797 | −1.80272 | −0.901360 | − | 0.433071i | \(-0.857430\pi\) | ||||
−0.901360 | + | 0.433071i | \(0.857430\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.17063 | 0.273474 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.22872 | −0.152403 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.24688 | 0.396670 | 0.198335 | − | 0.980134i | \(-0.436447\pi\) | ||||
0.198335 | + | 0.980134i | \(0.436447\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.42982 | −0.653673 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.70398 | 0.439581 | 0.219791 | − | 0.975547i | \(-0.429463\pi\) | ||||
0.219791 | + | 0.975547i | \(0.429463\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.73959 | 0.320645 | 0.160322 | − | 0.987065i | \(-0.448747\pi\) | ||||
0.160322 | + | 0.987065i | \(0.448747\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.79469 | −0.553644 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.6225 | −1.32450 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.25178 | 0.253345 | 0.126673 | − | 0.991945i | \(-0.459570\pi\) | ||||
0.126673 | + | 0.991945i | \(0.459570\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.0721083 | 0.00791492 | 0.00395746 | − | 0.999992i | \(-0.498740\pi\) | ||||
0.00395746 | + | 0.999992i | \(0.498740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.75416 | −0.298731 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.45567 | −0.799332 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.49320 | −1.00628 | −0.503139 | − | 0.864206i | \(-0.667821\pi\) | ||||
−0.503139 | + | 0.864206i | \(0.667821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.88622 | 0.617044 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.78314 | −0.599683 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.29650 | 0.133018 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.29553 | −0.233076 | −0.116538 | − | 0.993186i | \(-0.537180\pi\) | ||||
−0.116538 | + | 0.993186i | \(0.537180\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.35442 | −0.538139 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.49019 | 0.347286 | 0.173643 | − | 0.984809i | \(-0.444446\pi\) | ||||
0.173643 | + | 0.984809i | \(0.444446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.8256 | 1.46081 | 0.730404 | − | 0.683016i | \(-0.239332\pi\) | ||||
0.730404 | + | 0.683016i | \(0.239332\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.983530 | −0.0959827 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.2199 | 1.37469 | 0.687345 | − | 0.726331i | \(-0.258776\pi\) | ||||
0.687345 | + | 0.726331i | \(0.258776\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.1497 | 1.45108 | 0.725541 | − | 0.688179i | \(-0.241590\pi\) | ||||
0.725541 | + | 0.688179i | \(0.241590\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.10695 | 0.105067 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.1496 | −1.33108 | −0.665540 | − | 0.746363i | \(-0.731799\pi\) | ||||
−0.665540 | + | 0.746363i | \(0.731799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.46029 | 0.229423 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.71175 | 0.250702 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.1940 | 1.20949 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.6698 | 1.60634 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.10245 | −0.550240 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.43805 | 0.396951 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1939 | −1.52571 | −0.762857 | − | 0.646568i | \(-0.776204\pi\) | ||||
−0.762857 | + | 0.646568i | \(0.776204\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.08829 | 0.536044 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.99301 | 0.873093 | 0.436547 | − | 0.899682i | \(-0.356201\pi\) | ||||
0.436547 | + | 0.899682i | \(0.356201\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.21095 | −0.538557 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.453107 | −0.0389973 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −23.0873 | −1.97248 | −0.986239 | − | 0.165328i | \(-0.947132\pi\) | ||||
−0.986239 | + | 0.165328i | \(0.947132\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.63055 | −0.562396 | −0.281198 | − | 0.959650i | \(-0.590732\pi\) | ||||
−0.281198 | + | 0.959650i | \(0.590732\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.32792 | −0.280262 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.5199 | −1.21421 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.37822 | 0.280546 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.28835 | −0.188740 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.9556 | −1.14328 | −0.571642 | − | 0.820503i | \(-0.693693\pi\) | ||||
−0.571642 | + | 0.820503i | \(0.693693\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.16809 | −0.0950575 | −0.0475287 | − | 0.998870i | \(-0.515135\pi\) | ||||
−0.0475287 | + | 0.998870i | \(0.515135\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.07839 | 0.491409 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.62038 | 0.210474 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.29448 | −0.582163 | −0.291081 | − | 0.956698i | \(-0.594015\pi\) | ||||
−0.291081 | + | 0.956698i | \(0.594015\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.31676 | −0.421647 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.7861 | −0.928878 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0146 | 0.784407 | 0.392203 | − | 0.919879i | \(-0.371713\pi\) | ||||
0.392203 | + | 0.919879i | \(0.371713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.42613 | 0.188874 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.8988 | 0.998137 | 0.499069 | − | 0.866562i | \(-0.333676\pi\) | ||||
0.499069 | + | 0.866562i | \(0.333676\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.64640 | −0.434338 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.86135 | −0.218813 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.0976 | −0.843737 | −0.421868 | − | 0.906657i | \(-0.638626\pi\) | ||||
−0.421868 | + | 0.906657i | \(0.638626\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.4075 | −0.786735 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.97520 | 0.148465 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.9102 | −1.48816 | −0.744081 | − | 0.668090i | \(-0.767112\pi\) | ||||
−0.744081 | + | 0.668090i | \(0.767112\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.2772 | 0.986884 | 0.493442 | − | 0.869779i | \(-0.335739\pi\) | ||||
0.493442 | + | 0.869779i | \(0.335739\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.0797 | −1.04080 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.501567 | −0.0368760 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −32.5462 | −2.38002 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.17063 | 0.157890 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.57891 | −0.693105 | −0.346553 | − | 0.938031i | \(-0.612648\pi\) | ||||
−0.346553 | + | 0.938031i | \(0.612648\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.29142 | −0.164940 | −0.0824701 | − | 0.996594i | \(-0.526281\pi\) | ||||
−0.0824701 | + | 0.996594i | \(0.526281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.22872 | −0.0879901 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.32164 | −0.592893 | −0.296446 | − | 0.955050i | \(-0.595802\pi\) | ||||
−0.296446 | + | 0.955050i | \(0.595802\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0433 | 1.70439 | 0.852193 | − | 0.523227i | \(-0.175272\pi\) | ||||
0.852193 | + | 0.523227i | \(0.175272\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.24688 | 0.229017 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.1835 | −1.13586 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.76507 | 0.193121 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.42982 | −0.377398 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.3209 | 1.05977 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.3329 | 1.33093 | 0.665466 | − | 0.746428i | \(-0.268233\pi\) | ||||
0.665466 | + | 0.746428i | \(0.268233\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.70398 | 0.253792 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.75865 | −0.188138 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.5531 | −0.852158 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.73959 | 0.185124 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.4831 | 1.10877 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.11843 | −0.476686 | −0.238343 | − | 0.971181i | \(-0.576604\pi\) | ||||
−0.238343 | + | 0.971181i | \(0.576604\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.79469 | −0.319646 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.15200 | −0.541068 | −0.270534 | − | 0.962710i | \(-0.587200\pi\) | ||||
−0.270534 | + | 0.962710i | \(0.587200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.40020 | −0.224692 | −0.112346 | − | 0.993669i | \(-0.535836\pi\) | ||||
−0.112346 | + | 0.993669i | \(0.535836\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.6225 | −0.764703 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.36410 | −0.0893651 | −0.0446825 | − | 0.999001i | \(-0.514228\pi\) | ||||
−0.0446825 | + | 0.999001i | \(0.514228\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.50791 | 0.0983650 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.25178 | 0.146269 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.6613 | −0.689621 | −0.344811 | − | 0.938672i | \(-0.612057\pi\) | ||||
−0.344811 | + | 0.938672i | \(0.612057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.96872 | −0.191232 | −0.0956160 | − | 0.995418i | \(-0.530482\pi\) | ||||
−0.0956160 | + | 0.995418i | \(0.530482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.03687 | 0.0662431 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.75928 | −0.493711 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0721083 | 0.00456968 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.703338 | −0.0443943 | −0.0221971 | − | 0.999754i | \(-0.507066\pi\) | ||||
−0.0221971 | + | 0.999754i | \(0.507066\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.0735 | 1.82784 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.75416 | −0.172472 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.4602 | −0.652487 | −0.326243 | − | 0.945286i | \(-0.605783\pi\) | ||||
−0.326243 | + | 0.945286i | \(0.605783\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.40278 | 0.149302 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.45567 | −0.461495 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.1467 | −0.748996 | −0.374498 | − | 0.927228i | \(-0.622185\pi\) | ||||
−0.374498 | + | 0.927228i | \(0.622185\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.40906 | 0.147988 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.49320 | −0.580974 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.974897 | −0.0594405 | −0.0297203 | − | 0.999558i | \(-0.509462\pi\) | ||||
−0.0297203 | + | 0.999558i | \(0.509462\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.06798 | 0.550841 | 0.275420 | − | 0.961324i | \(-0.411183\pi\) | ||||
0.275420 | + | 0.961324i | \(0.411183\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.88622 | 0.356250 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.6728 | 1.54813 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.5217 | −0.872526 | −0.436263 | − | 0.899819i | \(-0.643698\pi\) | ||||
−0.436263 | + | 0.899819i | \(0.643698\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.78314 | −0.346227 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.623745 | 0.0372095 | 0.0186048 | − | 0.999827i | \(-0.494078\pi\) | ||||
0.0186048 | + | 0.999827i | \(0.494078\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −25.1834 | −1.49700 | −0.748498 | − | 0.663137i | \(-0.769225\pi\) | ||||
−0.748498 | + | 0.663137i | \(0.769225\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.29650 | 0.0767980 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.2462 | −0.781897 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.9468 | 1.17334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.29553 | −0.134567 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.37810 | 0.255772 | 0.127886 | − | 0.991789i | \(-0.459181\pi\) | ||||
0.127886 | + | 0.991789i | \(0.459181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.894980 | −0.0521077 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.35442 | −0.310695 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.7243 | −0.851529 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.2155 | 0.761726 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.49019 | 0.200506 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.37961 | 0.365295 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.46257 | 0.197619 | 0.0988096 | − | 0.995106i | \(-0.468497\pi\) | ||||
0.0988096 | + | 0.995106i | \(0.468497\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.8256 | 0.843398 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.24430 | 0.354082 | 0.177041 | − | 0.984203i | \(-0.443347\pi\) | ||||
0.177041 | + | 0.984203i | \(0.443347\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.9415 | 0.901066 | 0.450533 | − | 0.892760i | \(-0.351234\pi\) | ||||
0.450533 | + | 0.892760i | \(0.351234\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.983530 | −0.0554156 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.5258 | 0.647353 | 0.323677 | − | 0.946168i | \(-0.395081\pi\) | ||||
0.323677 | + | 0.946168i | \(0.395081\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 39.9208 | 2.23513 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.2199 | 0.793678 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.3924 | −0.967739 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.0020 | −0.721222 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.1497 | 0.837782 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.22370 | −0.398256 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7940 | 1.14294 | 0.571471 | − | 0.820622i | \(-0.306373\pi\) | ||||
0.571471 | + | 0.820622i | \(0.306373\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.10695 | 0.0606605 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.47119 | −0.0803795 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.98189 | −0.489275 | −0.244637 | − | 0.969615i | \(-0.578669\pi\) | ||||
−0.244637 | + | 0.969615i | \(0.578669\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.1496 | −0.768499 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.9653 | 1.67687 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1616 | −1.08862 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.46029 | 0.132458 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.2501 | 0.550256 | 0.275128 | − | 0.961408i | \(-0.411280\pi\) | ||||
0.275128 | + | 0.961408i | \(0.411280\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.62046 | −0.140270 | −0.0701351 | − | 0.997538i | \(-0.522343\pi\) | ||||
−0.0701351 | + | 0.997538i | \(0.522343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.71175 | 0.144743 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.2356 | 1.60928 | 0.804640 | − | 0.593763i | \(-0.202358\pi\) | ||||
0.804640 | + | 0.593763i | \(0.202358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.67830 | −0.0890749 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.1940 | 0.698298 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.60842 | −0.137667 | −0.0688336 | − | 0.997628i | \(-0.521928\pi\) | ||||
−0.0688336 | + | 0.997628i | \(0.521928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.8127 | −0.569088 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.6698 | 0.927423 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.24133 | −0.0649741 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.4100 | −0.647798 | −0.323899 | − | 0.946092i | \(-0.604994\pi\) | ||||
−0.323899 | + | 0.946092i | \(0.604994\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.10245 | −0.317681 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.5407 | −0.599165 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.2918 | −1.72378 | −0.861892 | − | 0.507091i | \(-0.830721\pi\) | ||||
−0.861892 | + | 0.507091i | \(0.830721\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.43805 | 0.229180 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.2179 | −1.04128 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.23029 | −0.268662 | −0.134331 | − | 0.990937i | \(-0.542889\pi\) | ||||
−0.134331 | + | 0.990937i | \(0.542889\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.1939 | −0.880871 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.1088 | 1.28300 | 0.641501 | − | 0.767123i | \(-0.278312\pi\) | ||||
0.641501 | + | 0.767123i | \(0.278312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.26623 | 0.268392 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.08829 | 0.309485 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.58702 | 0.232571 | 0.116286 | − | 0.993216i | \(-0.462901\pi\) | ||||
0.116286 | + | 0.993216i | \(0.462901\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −33.0045 | −1.66911 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.99301 | 0.504081 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.02030 | −0.0513368 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.0046 | 1.10438 | 0.552189 | − | 0.833719i | \(-0.313793\pi\) | ||||
0.552189 | + | 0.833719i | \(0.313793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.21095 | −0.310936 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.9076 | −1.89302 | −0.946508 | − | 0.322680i | \(-0.895416\pi\) | ||||
−0.946508 | + | 0.322680i | \(0.895416\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.6824 | −0.781198 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.453107 | −0.0225151 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.92707 | −0.293794 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.8490 | −1.17926 | −0.589629 | − | 0.807674i | \(-0.700726\pi\) | ||||
−0.589629 | + | 0.807674i | \(0.700726\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −23.0873 | −1.13881 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.28744 | 0.210971 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.0326728 | −0.00160384 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6.63055 | −0.324699 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.22924 | −0.206612 | −0.103306 | − | 0.994650i | \(-0.532942\pi\) | ||||
−0.103306 | + | 0.994650i | \(0.532942\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8136 | 0.819447 | 0.409723 | − | 0.912210i | \(-0.365625\pi\) | ||||
0.409723 | + | 0.912210i | \(0.365625\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.32792 | −0.161809 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −29.1440 | −1.41369 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.5618 | −1.47899 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.5199 | −0.701025 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.0376 | 0.965178 | 0.482589 | − | 0.875847i | \(-0.339697\pi\) | ||||
0.482589 | + | 0.875847i | \(0.339697\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.9602 | 0.718942 | 0.359471 | − | 0.933156i | \(-0.382957\pi\) | ||||
0.359471 | + | 0.933156i | \(0.382957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.37822 | 0.161973 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.5366 | 0.743217 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.5369 | −1.55290 | −0.776452 | − | 0.630177i | \(-0.782982\pi\) | ||||
−0.776452 | + | 0.630177i | \(0.782982\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.28835 | −0.108969 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.7623 | 0.891425 | 0.445713 | − | 0.895176i | \(-0.352950\pi\) | ||||
0.445713 | + | 0.895176i | \(0.352950\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.30144 | 0.203908 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.9556 | −0.660075 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3823 | 0.867514 | 0.433757 | − | 0.901030i | \(-0.357188\pi\) | ||||
0.433757 | + | 0.901030i | \(0.357188\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.6751 | 1.53861 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.16809 | −0.0548815 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.66709 | −0.125035 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0186 | −0.889653 | −0.444826 | − | 0.895617i | \(-0.646735\pi\) | ||||
−0.444826 | + | 0.895617i | \(0.646735\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.07839 | 0.283715 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.6257 | 1.37980 | 0.689902 | − | 0.723902i | \(-0.257653\pi\) | ||||
0.689902 | + | 0.723902i | \(0.257653\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0705096 | −0.00327686 | −0.00163843 | − | 0.999999i | \(-0.500522\pi\) | ||||
−0.00163843 | + | 0.999999i | \(0.500522\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.62038 | 0.121517 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.88942 | 0.457628 | 0.228814 | − | 0.973470i | \(-0.426515\pi\) | ||||
0.228814 | + | 0.973470i | \(0.426515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.04779 | 0.325437 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.29448 | −0.336112 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.5993 | −1.49892 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 13.7193 | 0.629485 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.31676 | −0.243438 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.8615 | −1.36441 | −0.682203 | − | 0.731162i | \(-0.738978\pi\) | ||||
−0.682203 | + | 0.731162i | \(0.738978\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.00177 | 0.136869 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −11.7861 | −0.536288 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.04012 | 0.0472296 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.45499 | −0.247189 | −0.123595 | − | 0.992333i | \(-0.539442\pi\) | ||||
−0.123595 | + | 0.992333i | \(0.539442\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.0146 | 0.452877 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.0330 | 0.949207 | 0.474604 | − | 0.880200i | \(-0.342591\pi\) | ||||
0.474604 | + | 0.880200i | \(0.342591\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −45.3185 | −2.04104 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.42613 | 0.109046 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.03998 | 0.360642 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.1234 | −0.542720 | −0.271360 | − | 0.962478i | \(-0.587473\pi\) | ||||
−0.271360 | + | 0.962478i | \(0.587473\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.8988 | 0.576275 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.58143 | −0.0703727 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.64640 | −0.250765 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.8830 | 0.615355 | 0.307677 | − | 0.951491i | \(-0.400448\pi\) | ||||
0.307677 | + | 0.951491i | \(0.400448\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.94664 | 0.263064 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.86135 | −0.126332 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.71758 | −0.296012 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 17.8191 | 0.783683 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.0976 | −0.487132 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.5791 | −1.16445 | −0.582226 | − | 0.813027i | \(-0.697818\pi\) | ||||
−0.582226 | + | 0.813027i | \(0.697818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.81327 | −0.429104 | −0.214552 | − | 0.976713i | \(-0.568829\pi\) | ||||
−0.214552 | + | 0.976713i | \(0.568829\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.4075 | −0.454221 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −35.1521 | −1.53125 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.48292 | 0.281866 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.97520 | 0.0857166 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.5483 | −0.716788 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.44315 | −0.278561 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.9102 | −0.859190 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.2528 | 0.527765 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.490807 | 0.0211015 | 0.0105507 | − | 0.999944i | \(-0.496642\pi\) | ||||
0.0105507 | + | 0.999944i | \(0.496642\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.2772 | 0.569778 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.86446 | −0.294041 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −42.3002 | −1.80863 | −0.904314 | − | 0.426868i | \(-0.859617\pi\) | ||||
−0.904314 | + | 0.426868i | \(0.859617\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −14.0797 | −0.600906 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.3333 | 0.908829 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.88779 | 0.207850 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.501567 | −0.0212903 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.6538 | −0.578531 | −0.289265 | − | 0.957249i | \(-0.593411\pi\) | ||||
−0.289265 | + | 0.957249i | \(0.593411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.5099 | 0.698296 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.5462 | −1.37410 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.3148 | 1.31976 | 0.659881 | − | 0.751370i | \(-0.270606\pi\) | ||||
0.659881 | + | 0.751370i | \(0.270606\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.41127 | 0.269724 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.17063 | 0.0911580 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.0677 | 0.925127 | 0.462563 | − | 0.886586i | \(-0.346930\pi\) | ||||
0.462563 | + | 0.886586i | \(0.346930\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.6681 | 1.53451 | 0.767257 | − | 0.641340i | \(-0.221621\pi\) | ||||
0.767257 | + | 0.641340i | \(0.221621\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.57891 | −0.400165 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.0343 | 1.08571 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.2547 | 1.30115 | 0.650575 | − | 0.759442i | \(-0.274528\pi\) | ||||
0.650575 | + | 0.759442i | \(0.274528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.29142 | −0.0952282 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.156521 | 0.00649357 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.4682 | 1.17903 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.22872 | −0.0508011 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.1818 | 0.750442 | 0.375221 | − | 0.926935i | \(-0.377567\pi\) | ||||
0.375221 | + | 0.926935i | \(0.377567\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.5476 | 0.681831 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.32164 | −0.342307 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.4236 | −1.53680 | −0.768402 | − | 0.639968i | \(-0.778948\pi\) | ||||
−0.768402 | + | 0.639968i | \(0.778948\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.97828 | −0.245085 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.0433 | 0.984028 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.5507 | −0.839678 | −0.419839 | − | 0.907599i | \(-0.637914\pi\) | ||||
−0.419839 | + | 0.907599i | \(0.637914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.59515 | 0.146649 | 0.0733247 | − | 0.997308i | \(-0.476639\pi\) | ||||
0.0733247 | + | 0.997308i | \(0.476639\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.24688 | 0.132223 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.00631 | −0.325503 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.24278 | 0.172209 | 0.0861046 | − | 0.996286i | \(-0.472558\pi\) | ||||
0.0861046 | + | 0.996286i | \(0.472558\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −16.1835 | −0.655790 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.02451 | −0.365092 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.3003 | −1.06226 | −0.531130 | − | 0.847290i | \(-0.678232\pi\) | ||||
−0.531130 | + | 0.847290i | \(0.678232\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.76507 | 0.111498 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.1905 | −0.732322 | −0.366161 | − | 0.930552i | \(-0.619328\pi\) | ||||
−0.366161 | + | 0.930552i | \(0.619328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.89833 | 0.0763004 | 0.0381502 | − | 0.999272i | \(-0.487853\pi\) | ||||
0.0381502 | + | 0.999272i | \(0.487853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.42982 | −0.217891 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −20.6063 | −0.825572 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.9626 | 0.878502 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.3209 | 0.611857 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.72847 | 0.268282 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.86232 | 0.193566 | 0.0967829 | − | 0.995306i | \(-0.469145\pi\) | ||||
0.0967829 | + | 0.995306i | \(0.469145\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.3329 | 0.768414 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.79069 | 0.309164 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.20544 | −0.245869 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.70398 | 0.146527 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.1797 | −1.27102 | −0.635512 | − | 0.772091i | \(-0.719211\pi\) | ||||
−0.635512 | + | 0.772091i | \(0.719211\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0389 | 0.790255 | 0.395128 | − | 0.918626i | \(-0.370700\pi\) | ||||
0.395128 | + | 0.918626i | \(0.370700\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.75865 | −0.108622 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.7994 | −0.974966 | −0.487483 | − | 0.873132i | \(-0.662085\pi\) | ||||
−0.487483 | + | 0.873132i | \(0.662085\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5761 | −0.415147 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.5531 | −0.491993 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.457411 | 0.0178999 | 0.00894994 | − | 0.999960i | \(-0.497151\pi\) | ||||
0.00894994 | + | 0.999960i | \(0.497151\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.52791 | −0.176920 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.73959 | 0.106882 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.3180 | −0.830431 | −0.415216 | − | 0.909723i | \(-0.636294\pi\) | ||||
−0.415216 | + | 0.909723i | \(0.636294\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.5620 | −0.488606 | −0.244303 | − | 0.969699i | \(-0.578559\pi\) | ||||
−0.244303 | + | 0.969699i | \(0.578559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.4831 | 0.640150 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.81423 | 0.109131 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.4829 | 1.56751 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.11843 | −0.275215 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 75.3885 | 2.91034 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.3809 | 0.747080 | 0.373540 | − | 0.927614i | \(-0.378144\pi\) | ||||
0.373540 | + | 0.927614i | \(0.378144\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.79469 | −0.184548 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.26226 | 0.0485124 | 0.0242562 | − | 0.999706i | \(-0.492278\pi\) | ||||
0.0242562 | + | 0.999706i | \(0.492278\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.98276 | −0.191221 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.15200 | −0.312385 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.6336 | −0.445149 | −0.222575 | − | 0.974916i | \(-0.571446\pi\) | ||||
−0.222575 | + | 0.974916i | \(0.571446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.4610 | 0.399694 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.40020 | −0.129726 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.4177 | −0.549272 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.7137 | 1.05428 | 0.527139 | − | 0.849779i | \(-0.323265\pi\) | ||||
0.527139 | + | 0.849779i | \(0.323265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −11.6225 | −0.441501 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.00435 | 0.113962 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −37.0931 | −1.40500 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.36410 | −0.0515949 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0567 | 0.681993 | 0.340997 | − | 0.940065i | \(-0.389236\pi\) | ||||
0.340997 | + | 0.940065i | \(0.389236\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.16737 | −0.119460 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.50791 | 0.0567911 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.57591 | 0.284922 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.56909 | 0.359375 | 0.179687 | − | 0.983724i | \(-0.442491\pi\) | ||||
0.179687 | + | 0.983724i | \(0.442491\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.25178 | 0.0844484 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 31.4014 | 1.17599 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.57905 | 0.246043 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.6613 | −0.398153 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6323 | −0.844043 | −0.422021 | − | 0.906586i | \(-0.638679\pi\) | ||||
−0.422021 | + | 0.906586i | \(0.638679\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.1809 | 1.19848 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.96872 | −0.110408 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 35.7477 | 1.32764 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.2755 | 0.640714 | 0.320357 | − | 0.947297i | \(-0.396197\pi\) | ||||
0.320357 | + | 0.947297i | \(0.396197\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.0070 | 1.36875 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.37565 | 0.0508107 | 0.0254053 | − | 0.999677i | \(-0.491912\pi\) | ||||
0.0254053 | + | 0.999677i | \(0.491912\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.03687 | 0.0382455 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.3852 | −0.640391 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 41.6690 | 1.53282 | 0.766409 | − | 0.642353i | \(-0.222042\pi\) | ||||
0.766409 | + | 0.642353i | \(0.222042\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.75928 | −0.285044 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.5159 | −1.08283 | −0.541417 | − | 0.840754i | \(-0.682112\pi\) | ||||
−0.541417 | + | 0.840754i | \(0.682112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.32337 | 0.231670 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.0721083 | 0.00263831 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.8662 | 1.12783 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.0693 | −1.06075 | −0.530377 | − | 0.847762i | \(-0.677950\pi\) | ||||
−0.530377 | + | 0.847762i | \(0.677950\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.703338 | −0.0256310 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.529268 | 0.0192621 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.1987 | 0.843172 | 0.421586 | − | 0.906788i | \(-0.361474\pi\) | ||||
0.421586 | + | 0.906788i | \(0.361474\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.0735 | 1.05530 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.9946 | −1.84855 | −0.924276 | − | 0.381725i | \(-0.875330\pi\) | ||||
−0.924276 | + | 0.381725i | \(0.875330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.8845 | 1.19050 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.75416 | −0.0995770 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.35627 | 0.193404 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.3536 | 0.589726 | 0.294863 | − | 0.955540i | \(-0.404726\pi\) | ||||
0.294863 | + | 0.955540i | \(0.404726\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.4602 | −0.376713 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.7218 | 0.961116 | 0.480558 | − | 0.876963i | \(-0.340434\pi\) | ||||
0.480558 | + | 0.876963i | \(0.340434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.7284 | 0.996032 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.40278 | 0.0861993 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.4613 | 0.625615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.8326 | −0.709668 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.45567 | −0.266444 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.30518 | 0.117967 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.6769 | 1.20045 | 0.600226 | − | 0.799831i | \(-0.295077\pi\) | ||||
0.600226 | + | 0.799831i | \(0.295077\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.1467 | −0.432433 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.7135 | −1.09205 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.1806 | −1.35583 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.40906 | 0.0854407 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −18.1019 | −0.641202 | −0.320601 | − | 0.947214i | \(-0.603885\pi\) | ||||
−0.320601 | + | 0.947214i | \(0.603885\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.2284 | −0.715630 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.49320 | −0.335426 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.6689 | −0.517654 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.34039 | 0.188224 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.974897 | −0.0343180 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.4728 | −1.00105 | −0.500525 | − | 0.865722i | \(-0.666859\pi\) | ||||
−0.500525 | + | 0.865722i | \(0.666859\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.2550 | 1.58912 | 0.794559 | − | 0.607187i | \(-0.207702\pi\) | ||||
0.794559 | + | 0.607187i | \(0.207702\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.06798 | 0.318028 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −4.53770 | −0.158949 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.4208 | −0.609475 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.88622 | 0.205681 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.4969 | 1.41335 | 0.706676 | − | 0.707537i | \(-0.250194\pi\) | ||||
0.706676 | + | 0.707537i | \(0.250194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.1873 | 0.529394 | 0.264697 | − | 0.964332i | \(-0.414728\pi\) | ||||
0.264697 | + | 0.964332i | \(0.414728\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 25.6728 | 0.893812 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.5058 | −0.956471 | −0.478236 | − | 0.878232i | \(-0.658724\pi\) | ||||
−0.478236 | + | 0.878232i | \(0.658724\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.42817 | −0.327454 | −0.163727 | − | 0.986506i | \(-0.552352\pi\) | ||||
−0.163727 | + | 0.986506i | \(0.552352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.5217 | −0.503753 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.9095 | −0.481935 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.84453 | −0.202258 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.78314 | −0.199894 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.2263 | 1.52686 | 0.763431 | − | 0.645890i | \(-0.223513\pi\) | ||||
0.763431 | + | 0.645890i | \(0.223513\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.5871 | 0.916795 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.623745 | 0.0214829 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.55842 | 0.0880125 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.3546 | 1.31788 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.1834 | −0.864291 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.01054 | −0.206039 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.974354 | −0.0333613 | −0.0166806 | − | 0.999861i | \(-0.505310\pi\) | ||||
−0.0166806 | + | 0.999861i | \(0.505310\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.29650 | 0.0443394 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.8334 | 1.53148 | 0.765740 | − | 0.643150i | \(-0.222373\pi\) | ||||
0.765740 | + | 0.643150i | \(0.222373\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.0429 | 1.70744 | 0.853721 | − | 0.520730i | \(-0.174340\pi\) | ||||
0.853721 | + | 0.520730i | \(0.174340\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.2462 | −0.451429 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.7593 | −0.366251 | −0.183126 | − | 0.983090i | \(-0.558622\pi\) | ||||
−0.183126 | + | 0.983090i | \(0.558622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.02842 | 0.170971 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.9468 | 0.677429 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0570 | −0.409005 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.80474 | 0.298337 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.29553 | −0.0776921 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.63337 | 0.325667 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.9714 | −1.24844 | −0.624218 | − | 0.781250i | \(-0.714582\pi\) | ||||
−0.624218 | + | 0.781250i | \(0.714582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.37810 | 0.147670 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.3517 | −0.517211 | −0.258605 | − | 0.965983i | \(-0.583263\pi\) | ||||
−0.258605 | + | 0.965983i | \(0.583263\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.4942 | 0.420462 | 0.210231 | − | 0.977652i | \(-0.432578\pi\) | ||||
0.210231 | + | 0.977652i | \(0.432578\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.894980 | −0.0300844 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.75567 | 0.193256 | 0.0966282 | − | 0.995321i | \(-0.469194\pi\) | ||||
0.0966282 | + | 0.995321i | \(0.469194\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.3217 | −1.25173 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.35442 | −0.179380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.52236 | 0.318654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.02148 | 0.301555 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.7243 | −0.491631 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 43.1172 | 1.43804 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.3173 | −1.07665 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 13.2155 | 0.439783 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.01598 | −0.199978 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.4509 | 1.11072 | 0.555360 | − | 0.831610i | \(-0.312581\pi\) | ||||
0.555360 | + | 0.831610i | \(0.312581\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.49019 | 0.115762 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.2620 | −1.93031 | −0.965153 | − | 0.261686i | \(-0.915721\pi\) | ||||
−0.965153 | + | 0.261686i | \(0.915721\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.386098 | −0.0127780 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.37961 | 0.210903 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.6912 | 0.716305 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.9879 | −0.626352 | −0.313176 | − | 0.949695i | \(-0.601393\pi\) | ||||
−0.313176 | + | 0.949695i | \(0.601393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.46257 | 0.114095 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0443 | 0.330611 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.30749 | −0.174509 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.8256 | 0.486936 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.14313 | −0.103123 | −0.0515614 | − | 0.998670i | \(-0.516420\pi\) | ||||
−0.0515614 | + | 0.998670i | \(0.516420\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.54778 | 0.214595 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.24430 | 0.204429 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.7469 | 0.482276 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.4629 | 0.570489 | 0.285244 | − | 0.958455i | \(-0.407925\pi\) | ||||
0.285244 | + | 0.958455i | \(0.407925\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.9415 | 0.520230 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.1050 | −0.785799 | −0.392899 | − | 0.919581i | \(-0.628528\pi\) | ||||
−0.392899 | + | 0.919581i | \(0.628528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.1352 | 1.07903 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.983530 | −0.0319942 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.56033 | −0.115695 | −0.0578476 | − | 0.998325i | \(-0.518424\pi\) | ||||
−0.0578476 | + | 0.998325i | \(0.518424\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.42909 | 0.241158 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.5258 | 0.373749 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.2055 | 0.784092 | 0.392046 | − | 0.919946i | \(-0.371767\pi\) | ||||
0.392046 | + | 0.919946i | \(0.371767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.34027 | 0.140448 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 39.9208 | 1.29046 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −50.1140 | −1.61826 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.44466 | 0.0788600 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.2199 | 0.458230 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.03826 | 0.0334228 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.3663 | 1.55536 | 0.777678 | − | 0.628662i | \(-0.216397\pi\) | ||||
0.777678 | + | 0.628662i | \(0.216397\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −17.3924 | −0.558725 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.2827 | 1.22855 | 0.614276 | − | 0.789092i | \(-0.289448\pi\) | ||||
0.614276 | + | 0.789092i | \(0.289448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −14.3925 | −0.461402 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.0020 | −0.416398 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.3330 | −1.61030 | −0.805148 | − | 0.593073i | \(-0.797914\pi\) | ||||
−0.805148 | + | 0.593073i | \(0.797914\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 50.8305 | 1.62455 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.1497 | 0.483694 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.9070 | −1.33663 | −0.668313 | − | 0.743880i | \(-0.732983\pi\) | ||||
−0.668313 | + | 0.743880i | \(0.732983\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.77060 | 0.120141 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.22370 | −0.229933 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.0583 | −1.05119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.8646 | −0.980447 | −0.490224 | − | 0.871597i | \(-0.663085\pi\) | ||||
−0.490224 | + | 0.871597i | \(0.663085\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.7940 | 0.659878 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.8942 | −0.345370 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.9030 | −1.23207 | −0.616035 | − | 0.787719i | \(-0.711262\pi\) | ||||
−0.616035 | + | 0.787719i | \(0.711262\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.10695 | 0.0350224 |
(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 | 6036.2.a.g.1.9 | ✓ | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.g.1.9 | ✓ | 15 | 1.1 | even | 1 | trivial |