Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2366,2,Mod(337,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2366.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.d (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: | \(18.8926051182\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.6 | ||
Root | \(1.24698i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2366.337 |
Dual form | 2366.2.d.p.337.3 |
$q$-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 \(\left(\mathbb{Z}/2366\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(2199\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 2.24698 | 1.29729 | 0.648647 | − | 0.761089i | \(-0.275335\pi\) | ||||
0.648647 | + | 0.761089i | \(0.275335\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.69202i | 0.756695i | 0.925664 | + | 0.378348i | \(0.123508\pi\) | ||||
−0.925664 | + | 0.378348i | \(0.876492\pi\) | |||||||
\(6\) | 2.24698i | 0.917326i | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 2.04892 | 0.682972 | ||||||||
\(10\) | −1.69202 | −0.535064 | ||||||||
\(11\) | − 0.445042i | − 0.134185i | −0.997747 | − | 0.0670926i | \(-0.978628\pi\) | ||||
0.997747 | − | 0.0670926i | \(-0.0213723\pi\) | |||||||
\(12\) | −2.24698 | −0.648647 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 3.80194i | 0.981656i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.15883 | 0.523594 | 0.261797 | − | 0.965123i | \(-0.415685\pi\) | ||||
0.261797 | + | 0.965123i | \(0.415685\pi\) | |||||||
\(18\) | 2.04892i | 0.482934i | ||||||||
\(19\) | 6.35690i | 1.45837i | 0.684316 | + | 0.729186i | \(0.260101\pi\) | ||||
−0.684316 | + | 0.729186i | \(0.739899\pi\) | |||||||
\(20\) | − 1.69202i | − 0.378348i | ||||||||
\(21\) | 2.24698i | 0.490331i | ||||||||
\(22\) | 0.445042 | 0.0948832 | ||||||||
\(23\) | 0.911854 | 0.190135 | 0.0950674 | − | 0.995471i | \(-0.469693\pi\) | ||||
0.0950674 | + | 0.995471i | \(0.469693\pi\) | |||||||
\(24\) | − 2.24698i | − 0.458663i | ||||||||
\(25\) | 2.13706 | 0.427413 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.13706 | −0.411278 | ||||||||
\(28\) | − 1.00000i | − 0.188982i | ||||||||
\(29\) | 3.58211 | 0.665180 | 0.332590 | − | 0.943071i | \(-0.392077\pi\) | ||||
0.332590 | + | 0.943071i | \(0.392077\pi\) | |||||||
\(30\) | −3.80194 | −0.694136 | ||||||||
\(31\) | 8.89977i | 1.59845i | 0.601034 | + | 0.799223i | \(0.294755\pi\) | ||||
−0.601034 | + | 0.799223i | \(0.705245\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 1.00000i | − 0.174078i | ||||||||
\(34\) | 2.15883i | 0.370237i | ||||||||
\(35\) | −1.69202 | −0.286004 | ||||||||
\(36\) | −2.04892 | −0.341486 | ||||||||
\(37\) | − 10.8019i | − 1.77583i | −0.460010 | − | 0.887914i | \(-0.652154\pi\) | ||||
0.460010 | − | 0.887914i | \(-0.347846\pi\) | |||||||
\(38\) | −6.35690 | −1.03122 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.69202 | 0.267532 | ||||||||
\(41\) | 2.41789i | 0.377612i | 0.982014 | + | 0.188806i | \(0.0604617\pi\) | ||||
−0.982014 | + | 0.188806i | \(0.939538\pi\) | |||||||
\(42\) | −2.24698 | −0.346716 | ||||||||
\(43\) | −4.63102 | −0.706224 | −0.353112 | − | 0.935581i | \(-0.614877\pi\) | ||||
−0.353112 | + | 0.935581i | \(0.614877\pi\) | |||||||
\(44\) | 0.445042i | 0.0670926i | ||||||||
\(45\) | 3.46681i | 0.516802i | ||||||||
\(46\) | 0.911854i | 0.134446i | ||||||||
\(47\) | 9.75063i | 1.42228i | 0.703053 | + | 0.711138i | \(0.251820\pi\) | ||||
−0.703053 | + | 0.711138i | \(0.748180\pi\) | |||||||
\(48\) | 2.24698 | 0.324324 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 2.13706i | 0.302226i | ||||||||
\(51\) | 4.85086 | 0.679256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.74094 | −1.20066 | −0.600330 | − | 0.799752i | \(-0.704964\pi\) | ||||
−0.600330 | + | 0.799752i | \(0.704964\pi\) | |||||||
\(54\) | − 2.13706i | − 0.290817i | ||||||||
\(55\) | 0.753020 | 0.101537 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 14.2838i | 1.89194i | ||||||||
\(58\) | 3.58211i | 0.470353i | ||||||||
\(59\) | 10.1468i | 1.32099i | 0.750828 | + | 0.660497i | \(0.229655\pi\) | ||||
−0.750828 | + | 0.660497i | \(0.770345\pi\) | |||||||
\(60\) | − 3.80194i | − 0.490828i | ||||||||
\(61\) | 1.37867 | 0.176520 | 0.0882601 | − | 0.996097i | \(-0.471869\pi\) | ||||
0.0882601 | + | 0.996097i | \(0.471869\pi\) | |||||||
\(62\) | −8.89977 | −1.13027 | ||||||||
\(63\) | 2.04892i | 0.258139i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 6.23490i | 0.761714i | 0.924634 | + | 0.380857i | \(0.124371\pi\) | ||||
−0.924634 | + | 0.380857i | \(0.875629\pi\) | |||||||
\(68\) | −2.15883 | −0.261797 | ||||||||
\(69\) | 2.04892 | 0.246661 | ||||||||
\(70\) | − 1.69202i | − 0.202235i | ||||||||
\(71\) | − 5.76271i | − 0.683908i | −0.939717 | − | 0.341954i | \(-0.888911\pi\) | ||||
0.939717 | − | 0.341954i | \(-0.111089\pi\) | |||||||
\(72\) | − 2.04892i | − 0.241467i | ||||||||
\(73\) | 9.93661i | 1.16299i | 0.813549 | + | 0.581496i | \(0.197532\pi\) | ||||
−0.813549 | + | 0.581496i | \(0.802468\pi\) | |||||||
\(74\) | 10.8019 | 1.25570 | ||||||||
\(75\) | 4.80194 | 0.554480 | ||||||||
\(76\) | − 6.35690i | − 0.729186i | ||||||||
\(77\) | 0.445042 | 0.0507172 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.30127 | −0.708949 | −0.354474 | − | 0.935066i | \(-0.615340\pi\) | ||||
−0.354474 | + | 0.935066i | \(0.615340\pi\) | |||||||
\(80\) | 1.69202i | 0.189174i | ||||||||
\(81\) | −10.9487 | −1.21652 | ||||||||
\(82\) | −2.41789 | −0.267012 | ||||||||
\(83\) | − 2.91185i | − 0.319617i | −0.987148 | − | 0.159809i | \(-0.948912\pi\) | ||||
0.987148 | − | 0.159809i | \(-0.0510878\pi\) | |||||||
\(84\) | − 2.24698i | − 0.245166i | ||||||||
\(85\) | 3.65279i | 0.396201i | ||||||||
\(86\) | − 4.63102i | − 0.499376i | ||||||||
\(87\) | 8.04892 | 0.862935 | ||||||||
\(88\) | −0.445042 | −0.0474416 | ||||||||
\(89\) | − 18.1075i | − 1.91939i | −0.281037 | − | 0.959697i | \(-0.590678\pi\) | ||||
0.281037 | − | 0.959697i | \(-0.409322\pi\) | |||||||
\(90\) | −3.46681 | −0.365434 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.911854 | −0.0950674 | ||||||||
\(93\) | 19.9976i | 2.07366i | ||||||||
\(94\) | −9.75063 | −1.00570 | ||||||||
\(95\) | −10.7560 | −1.10354 | ||||||||
\(96\) | 2.24698i | 0.229331i | ||||||||
\(97\) | − 3.30798i | − 0.335874i | −0.985798 | − | 0.167937i | \(-0.946289\pi\) | ||||
0.985798 | − | 0.167937i | \(-0.0537106\pi\) | |||||||
\(98\) | − 1.00000i | − 0.101015i | ||||||||
\(99\) | − 0.911854i | − 0.0916448i | ||||||||
\(100\) | −2.13706 | −0.213706 | ||||||||
\(101\) | −2.08815 | −0.207778 | −0.103889 | − | 0.994589i | \(-0.533129\pi\) | ||||
−0.103889 | + | 0.994589i | \(0.533129\pi\) | |||||||
\(102\) | 4.85086i | 0.480306i | ||||||||
\(103\) | 11.3013 | 1.11355 | 0.556774 | − | 0.830664i | \(-0.312039\pi\) | ||||
0.556774 | + | 0.830664i | \(0.312039\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.80194 | −0.371031 | ||||||||
\(106\) | − 8.74094i | − 0.848995i | ||||||||
\(107\) | −7.13467 | −0.689735 | −0.344867 | − | 0.938651i | \(-0.612076\pi\) | ||||
−0.344867 | + | 0.938651i | \(0.612076\pi\) | |||||||
\(108\) | 2.13706 | 0.205639 | ||||||||
\(109\) | − 6.57002i | − 0.629294i | −0.949209 | − | 0.314647i | \(-0.898114\pi\) | ||||
0.949209 | − | 0.314647i | \(-0.101886\pi\) | |||||||
\(110\) | 0.753020i | 0.0717977i | ||||||||
\(111\) | − 24.2717i | − 2.30377i | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 10.6015 | 0.997304 | 0.498652 | − | 0.866802i | \(-0.333829\pi\) | ||||
0.498652 | + | 0.866802i | \(0.333829\pi\) | |||||||
\(114\) | −14.2838 | −1.33780 | ||||||||
\(115\) | 1.54288i | 0.143874i | ||||||||
\(116\) | −3.58211 | −0.332590 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.1468 | −0.934084 | ||||||||
\(119\) | 2.15883i | 0.197900i | ||||||||
\(120\) | 3.80194 | 0.347068 | ||||||||
\(121\) | 10.8019 | 0.981994 | ||||||||
\(122\) | 1.37867i | 0.124819i | ||||||||
\(123\) | 5.43296i | 0.489874i | ||||||||
\(124\) | − 8.89977i | − 0.799223i | ||||||||
\(125\) | 12.0761i | 1.08012i | ||||||||
\(126\) | −2.04892 | −0.182532 | ||||||||
\(127\) | 21.5646 | 1.91355 | 0.956776 | − | 0.290824i | \(-0.0939295\pi\) | ||||
0.956776 | + | 0.290824i | \(0.0939295\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −10.4058 | −0.916181 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.14675 | 0.274933 | 0.137467 | − | 0.990506i | \(-0.456104\pi\) | ||||
0.137467 | + | 0.990506i | \(0.456104\pi\) | |||||||
\(132\) | 1.00000i | 0.0870388i | ||||||||
\(133\) | −6.35690 | −0.551213 | ||||||||
\(134\) | −6.23490 | −0.538613 | ||||||||
\(135\) | − 3.61596i | − 0.311212i | ||||||||
\(136\) | − 2.15883i | − 0.185118i | ||||||||
\(137\) | 3.93362i | 0.336072i | 0.985781 | + | 0.168036i | \(0.0537425\pi\) | ||||
−0.985781 | + | 0.168036i | \(0.946257\pi\) | |||||||
\(138\) | 2.04892i | 0.174415i | ||||||||
\(139\) | −11.2078 | −0.950629 | −0.475315 | − | 0.879816i | \(-0.657666\pi\) | ||||
−0.475315 | + | 0.879816i | \(0.657666\pi\) | |||||||
\(140\) | 1.69202 | 0.143002 | ||||||||
\(141\) | 21.9095i | 1.84511i | ||||||||
\(142\) | 5.76271 | 0.483596 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.04892 | 0.170743 | ||||||||
\(145\) | 6.06100i | 0.503339i | ||||||||
\(146\) | −9.93661 | −0.822360 | ||||||||
\(147\) | −2.24698 | −0.185328 | ||||||||
\(148\) | 10.8019i | 0.887914i | ||||||||
\(149\) | − 21.8726i | − 1.79188i | −0.444180 | − | 0.895938i | \(-0.646505\pi\) | ||||
0.444180 | − | 0.895938i | \(-0.353495\pi\) | |||||||
\(150\) | 4.80194i | 0.392077i | ||||||||
\(151\) | − 18.3002i | − 1.48925i | −0.667483 | − | 0.744625i | \(-0.732628\pi\) | ||||
0.667483 | − | 0.744625i | \(-0.267372\pi\) | |||||||
\(152\) | 6.35690 | 0.515612 | ||||||||
\(153\) | 4.42327 | 0.357600 | ||||||||
\(154\) | 0.445042i | 0.0358625i | ||||||||
\(155\) | −15.0586 | −1.20954 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.8442 | −0.865457 | −0.432729 | − | 0.901524i | \(-0.642449\pi\) | ||||
−0.432729 | + | 0.901524i | \(0.642449\pi\) | |||||||
\(158\) | − 6.30127i | − 0.501302i | ||||||||
\(159\) | −19.6407 | −1.55761 | ||||||||
\(160\) | −1.69202 | −0.133766 | ||||||||
\(161\) | 0.911854i | 0.0718642i | ||||||||
\(162\) | − 10.9487i | − 0.860210i | ||||||||
\(163\) | − 14.4058i | − 1.12835i | −0.825655 | − | 0.564175i | \(-0.809194\pi\) | ||||
0.825655 | − | 0.564175i | \(-0.190806\pi\) | |||||||
\(164\) | − 2.41789i | − 0.188806i | ||||||||
\(165\) | 1.69202 | 0.131724 | ||||||||
\(166\) | 2.91185 | 0.226004 | ||||||||
\(167\) | 13.6963i | 1.05985i | 0.848043 | + | 0.529927i | \(0.177781\pi\) | ||||
−0.848043 | + | 0.529927i | \(0.822219\pi\) | |||||||
\(168\) | 2.24698 | 0.173358 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −3.65279 | −0.280156 | ||||||||
\(171\) | 13.0248i | 0.996028i | ||||||||
\(172\) | 4.63102 | 0.353112 | ||||||||
\(173\) | 4.47650 | 0.340342 | 0.170171 | − | 0.985415i | \(-0.445568\pi\) | ||||
0.170171 | + | 0.985415i | \(0.445568\pi\) | |||||||
\(174\) | 8.04892i | 0.610187i | ||||||||
\(175\) | 2.13706i | 0.161547i | ||||||||
\(176\) | − 0.445042i | − 0.0335463i | ||||||||
\(177\) | 22.7995i | 1.71372i | ||||||||
\(178\) | 18.1075 | 1.35722 | ||||||||
\(179\) | 23.0737 | 1.72461 | 0.862304 | − | 0.506392i | \(-0.169021\pi\) | ||||
0.862304 | + | 0.506392i | \(0.169021\pi\) | |||||||
\(180\) | − 3.46681i | − 0.258401i | ||||||||
\(181\) | −8.46980 | −0.629555 | −0.314777 | − | 0.949165i | \(-0.601930\pi\) | ||||
−0.314777 | + | 0.949165i | \(0.601930\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.09783 | 0.228999 | ||||||||
\(184\) | − 0.911854i | − 0.0672228i | ||||||||
\(185\) | 18.2771 | 1.34376 | ||||||||
\(186\) | −19.9976 | −1.46630 | ||||||||
\(187\) | − 0.960771i | − 0.0702586i | ||||||||
\(188\) | − 9.75063i | − 0.711138i | ||||||||
\(189\) | − 2.13706i | − 0.155448i | ||||||||
\(190\) | − 10.7560i | − 0.780323i | ||||||||
\(191\) | 19.7235 | 1.42714 | 0.713570 | − | 0.700583i | \(-0.247077\pi\) | ||||
0.713570 | + | 0.700583i | \(0.247077\pi\) | |||||||
\(192\) | −2.24698 | −0.162162 | ||||||||
\(193\) | 9.15883i | 0.659267i | 0.944109 | + | 0.329634i | \(0.106925\pi\) | ||||
−0.944109 | + | 0.329634i | \(0.893075\pi\) | |||||||
\(194\) | 3.30798 | 0.237499 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 3.73019i | 0.265765i | 0.991132 | + | 0.132882i | \(0.0424232\pi\) | ||||
−0.991132 | + | 0.132882i | \(0.957577\pi\) | |||||||
\(198\) | 0.911854 | 0.0648026 | ||||||||
\(199\) | −19.5918 | −1.38883 | −0.694413 | − | 0.719577i | \(-0.744336\pi\) | ||||
−0.694413 | + | 0.719577i | \(0.744336\pi\) | |||||||
\(200\) | − 2.13706i | − 0.151113i | ||||||||
\(201\) | 14.0097i | 0.988167i | ||||||||
\(202\) | − 2.08815i | − 0.146921i | ||||||||
\(203\) | 3.58211i | 0.251414i | ||||||||
\(204\) | −4.85086 | −0.339628 | ||||||||
\(205\) | −4.09113 | −0.285737 | ||||||||
\(206\) | 11.3013i | 0.787397i | ||||||||
\(207\) | 1.86831 | 0.129857 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.82908 | 0.195692 | ||||||||
\(210\) | − 3.80194i | − 0.262359i | ||||||||
\(211\) | 23.3860 | 1.60996 | 0.804978 | − | 0.593305i | \(-0.202177\pi\) | ||||
0.804978 | + | 0.593305i | \(0.202177\pi\) | |||||||
\(212\) | 8.74094 | 0.600330 | ||||||||
\(213\) | − 12.9487i | − 0.887230i | ||||||||
\(214\) | − 7.13467i | − 0.487716i | ||||||||
\(215\) | − 7.83579i | − 0.534396i | ||||||||
\(216\) | 2.13706i | 0.145409i | ||||||||
\(217\) | −8.89977 | −0.604156 | ||||||||
\(218\) | 6.57002 | 0.444978 | ||||||||
\(219\) | 22.3274i | 1.50874i | ||||||||
\(220\) | −0.753020 | −0.0507686 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 24.2717 | 1.62901 | ||||||||
\(223\) | − 21.7482i | − 1.45637i | −0.685381 | − | 0.728185i | \(-0.740364\pi\) | ||||
0.685381 | − | 0.728185i | \(-0.259636\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 4.37867 | 0.291911 | ||||||||
\(226\) | 10.6015i | 0.705200i | ||||||||
\(227\) | 6.55927i | 0.435354i | 0.976021 | + | 0.217677i | \(0.0698479\pi\) | ||||
−0.976021 | + | 0.217677i | \(0.930152\pi\) | |||||||
\(228\) | − 14.2838i | − 0.945969i | ||||||||
\(229\) | 0.948690i | 0.0626912i | 0.999509 | + | 0.0313456i | \(0.00997925\pi\) | ||||
−0.999509 | + | 0.0313456i | \(0.990021\pi\) | |||||||
\(230\) | −1.54288 | −0.101734 | ||||||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | − 3.58211i | − 0.235177i | ||||||||
\(233\) | 15.4765 | 1.01390 | 0.506950 | − | 0.861976i | \(-0.330773\pi\) | ||||
0.506950 | + | 0.861976i | \(0.330773\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.4983 | −1.07623 | ||||||||
\(236\) | − 10.1468i | − 0.660497i | ||||||||
\(237\) | −14.1588 | −0.919715 | ||||||||
\(238\) | −2.15883 | −0.139936 | ||||||||
\(239\) | 25.3448i | 1.63942i | 0.572779 | + | 0.819710i | \(0.305865\pi\) | ||||
−0.572779 | + | 0.819710i | \(0.694135\pi\) | |||||||
\(240\) | 3.80194i | 0.245414i | ||||||||
\(241\) | 28.2664i | 1.82080i | 0.413733 | + | 0.910398i | \(0.364225\pi\) | ||||
−0.413733 | + | 0.910398i | \(0.635775\pi\) | |||||||
\(242\) | 10.8019i | 0.694375i | ||||||||
\(243\) | −18.1903 | −1.16691 | ||||||||
\(244\) | −1.37867 | −0.0882601 | ||||||||
\(245\) | − 1.69202i | − 0.108099i | ||||||||
\(246\) | −5.43296 | −0.346393 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.89977 | 0.565136 | ||||||||
\(249\) | − 6.54288i | − 0.414638i | ||||||||
\(250\) | −12.0761 | −0.763757 | ||||||||
\(251\) | 13.7235 | 0.866218 | 0.433109 | − | 0.901341i | \(-0.357416\pi\) | ||||
0.433109 | + | 0.901341i | \(0.357416\pi\) | |||||||
\(252\) | − 2.04892i | − 0.129070i | ||||||||
\(253\) | − 0.405813i | − 0.0255133i | ||||||||
\(254\) | 21.5646i | 1.35309i | ||||||||
\(255\) | 8.20775i | 0.513989i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.3502 | 0.832762 | 0.416381 | − | 0.909190i | \(-0.363298\pi\) | ||||
0.416381 | + | 0.909190i | \(0.363298\pi\) | |||||||
\(258\) | − 10.4058i | − 0.647838i | ||||||||
\(259\) | 10.8019 | 0.671200 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.33944 | 0.454300 | ||||||||
\(262\) | 3.14675i | 0.194407i | ||||||||
\(263\) | 19.3153 | 1.19103 | 0.595515 | − | 0.803344i | \(-0.296948\pi\) | ||||
0.595515 | + | 0.803344i | \(0.296948\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | − 14.7899i | − 0.908534i | ||||||||
\(266\) | − 6.35690i | − 0.389766i | ||||||||
\(267\) | − 40.6872i | − 2.49002i | ||||||||
\(268\) | − 6.23490i | − 0.380857i | ||||||||
\(269\) | 24.2935 | 1.48120 | 0.740601 | − | 0.671946i | \(-0.234541\pi\) | ||||
0.740601 | + | 0.671946i | \(0.234541\pi\) | |||||||
\(270\) | 3.61596 | 0.220060 | ||||||||
\(271\) | − 29.0368i | − 1.76386i | −0.471378 | − | 0.881931i | \(-0.656243\pi\) | ||||
0.471378 | − | 0.881931i | \(-0.343757\pi\) | |||||||
\(272\) | 2.15883 | 0.130899 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.93362 | −0.237639 | ||||||||
\(275\) | − 0.951083i | − 0.0573524i | ||||||||
\(276\) | −2.04892 | −0.123330 | ||||||||
\(277\) | −1.19029 | −0.0715177 | −0.0357589 | − | 0.999360i | \(-0.511385\pi\) | ||||
−0.0357589 | + | 0.999360i | \(0.511385\pi\) | |||||||
\(278\) | − 11.2078i | − 0.672196i | ||||||||
\(279\) | 18.2349i | 1.09169i | ||||||||
\(280\) | 1.69202i | 0.101118i | ||||||||
\(281\) | − 21.2325i | − 1.26663i | −0.773896 | − | 0.633313i | \(-0.781695\pi\) | ||||
0.773896 | − | 0.633313i | \(-0.218305\pi\) | |||||||
\(282\) | −21.9095 | −1.30469 | ||||||||
\(283\) | −11.6756 | −0.694044 | −0.347022 | − | 0.937857i | \(-0.612807\pi\) | ||||
−0.347022 | + | 0.937857i | \(0.612807\pi\) | |||||||
\(284\) | 5.76271i | 0.341954i | ||||||||
\(285\) | −24.1685 | −1.43162 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.41789 | −0.142724 | ||||||||
\(288\) | 2.04892i | 0.120734i | ||||||||
\(289\) | −12.3394 | −0.725849 | ||||||||
\(290\) | −6.06100 | −0.355914 | ||||||||
\(291\) | − 7.43296i | − 0.435728i | ||||||||
\(292\) | − 9.93661i | − 0.581496i | ||||||||
\(293\) | − 14.4101i | − 0.841848i | −0.907096 | − | 0.420924i | \(-0.861706\pi\) | ||||
0.907096 | − | 0.420924i | \(-0.138294\pi\) | |||||||
\(294\) | − 2.24698i | − 0.131047i | ||||||||
\(295\) | −17.1685 | −0.999590 | ||||||||
\(296\) | −10.8019 | −0.627850 | ||||||||
\(297\) | 0.951083i | 0.0551874i | ||||||||
\(298\) | 21.8726 | 1.26705 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.80194 | −0.277240 | ||||||||
\(301\) | − 4.63102i | − 0.266928i | ||||||||
\(302\) | 18.3002 | 1.05306 | ||||||||
\(303\) | −4.69202 | −0.269550 | ||||||||
\(304\) | 6.35690i | 0.364593i | ||||||||
\(305\) | 2.33273i | 0.133572i | ||||||||
\(306\) | 4.42327i | 0.252862i | ||||||||
\(307\) | − 2.55257i | − 0.145683i | −0.997344 | − | 0.0728413i | \(-0.976793\pi\) | ||||
0.997344 | − | 0.0728413i | \(-0.0232067\pi\) | |||||||
\(308\) | −0.445042 | −0.0253586 | ||||||||
\(309\) | 25.3937 | 1.44460 | ||||||||
\(310\) | − 15.0586i | − 0.855271i | ||||||||
\(311\) | 1.63533 | 0.0927313 | 0.0463657 | − | 0.998925i | \(-0.485236\pi\) | ||||
0.0463657 | + | 0.998925i | \(0.485236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.7724 | −0.721939 | −0.360969 | − | 0.932578i | \(-0.617554\pi\) | ||||
−0.360969 | + | 0.932578i | \(0.617554\pi\) | |||||||
\(314\) | − 10.8442i | − 0.611971i | ||||||||
\(315\) | −3.46681 | −0.195333 | ||||||||
\(316\) | 6.30127 | 0.354474 | ||||||||
\(317\) | − 10.9041i | − 0.612434i | −0.951962 | − | 0.306217i | \(-0.900937\pi\) | ||||
0.951962 | − | 0.306217i | \(-0.0990634\pi\) | |||||||
\(318\) | − 19.6407i | − 1.10140i | ||||||||
\(319\) | − 1.59419i | − 0.0892573i | ||||||||
\(320\) | − 1.69202i | − 0.0945869i | ||||||||
\(321\) | −16.0315 | −0.894789 | ||||||||
\(322\) | −0.911854 | −0.0508156 | ||||||||
\(323\) | 13.7235i | 0.763595i | ||||||||
\(324\) | 10.9487 | 0.608261 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 14.4058 | 0.797864 | ||||||||
\(327\) | − 14.7627i | − 0.816380i | ||||||||
\(328\) | 2.41789 | 0.133506 | ||||||||
\(329\) | −9.75063 | −0.537569 | ||||||||
\(330\) | 1.69202i | 0.0931427i | ||||||||
\(331\) | 9.94869i | 0.546829i | 0.961896 | + | 0.273415i | \(0.0881531\pi\) | ||||
−0.961896 | + | 0.273415i | \(0.911847\pi\) | |||||||
\(332\) | 2.91185i | 0.159809i | ||||||||
\(333\) | − 22.1323i | − 1.21284i | ||||||||
\(334\) | −13.6963 | −0.749430 | ||||||||
\(335\) | −10.5496 | −0.576385 | ||||||||
\(336\) | 2.24698i | 0.122583i | ||||||||
\(337\) | −8.06829 | −0.439508 | −0.219754 | − | 0.975555i | \(-0.570525\pi\) | ||||
−0.219754 | + | 0.975555i | \(0.570525\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.8213 | 1.29380 | ||||||||
\(340\) | − 3.65279i | − 0.198101i | ||||||||
\(341\) | 3.96077 | 0.214488 | ||||||||
\(342\) | −13.0248 | −0.704298 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 4.63102i | 0.249688i | ||||||||
\(345\) | 3.46681i | 0.186647i | ||||||||
\(346\) | 4.47650i | 0.240658i | ||||||||
\(347\) | −33.1769 | −1.78103 | −0.890514 | − | 0.454955i | \(-0.849655\pi\) | ||||
−0.890514 | + | 0.454955i | \(0.849655\pi\) | |||||||
\(348\) | −8.04892 | −0.431467 | ||||||||
\(349\) | − 24.6872i | − 1.32148i | −0.750616 | − | 0.660739i | \(-0.770243\pi\) | ||||
0.750616 | − | 0.660739i | \(-0.229757\pi\) | |||||||
\(350\) | −2.13706 | −0.114231 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.445042 | 0.0237208 | ||||||||
\(353\) | 22.5754i | 1.20157i | 0.799412 | + | 0.600784i | \(0.205145\pi\) | ||||
−0.799412 | + | 0.600784i | \(0.794855\pi\) | |||||||
\(354\) | −22.7995 | −1.21178 | ||||||||
\(355\) | 9.75063 | 0.517510 | ||||||||
\(356\) | 18.1075i | 0.959697i | ||||||||
\(357\) | 4.85086i | 0.256734i | ||||||||
\(358\) | 23.0737i | 1.21948i | ||||||||
\(359\) | − 2.30798i | − 0.121810i | −0.998144 | − | 0.0609052i | \(-0.980601\pi\) | ||||
0.998144 | − | 0.0609052i | \(-0.0193987\pi\) | |||||||
\(360\) | 3.46681 | 0.182717 | ||||||||
\(361\) | −21.4101 | −1.12685 | ||||||||
\(362\) | − 8.46980i | − 0.445163i | ||||||||
\(363\) | 24.2717 | 1.27394 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.8130 | −0.880030 | ||||||||
\(366\) | 3.09783i | 0.161926i | ||||||||
\(367\) | 25.1685 | 1.31379 | 0.656893 | − | 0.753984i | \(-0.271870\pi\) | ||||
0.656893 | + | 0.753984i | \(0.271870\pi\) | |||||||
\(368\) | 0.911854 | 0.0475337 | ||||||||
\(369\) | 4.95407i | 0.257898i | ||||||||
\(370\) | 18.2771i | 0.950182i | ||||||||
\(371\) | − 8.74094i | − 0.453807i | ||||||||
\(372\) | − 19.9976i | − 1.03683i | ||||||||
\(373\) | 11.6407 | 0.602733 | 0.301367 | − | 0.953508i | \(-0.402557\pi\) | ||||
0.301367 | + | 0.953508i | \(0.402557\pi\) | |||||||
\(374\) | 0.960771 | 0.0496803 | ||||||||
\(375\) | 27.1347i | 1.40123i | ||||||||
\(376\) | 9.75063 | 0.502850 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.13706 | 0.109919 | ||||||||
\(379\) | − 16.5623i | − 0.850746i | −0.905018 | − | 0.425373i | \(-0.860143\pi\) | ||||
0.905018 | − | 0.425373i | \(-0.139857\pi\) | |||||||
\(380\) | 10.7560 | 0.551771 | ||||||||
\(381\) | 48.4553 | 2.48244 | ||||||||
\(382\) | 19.7235i | 1.00914i | ||||||||
\(383\) | − 7.39506i | − 0.377870i | −0.981990 | − | 0.188935i | \(-0.939496\pi\) | ||||
0.981990 | − | 0.188935i | \(-0.0605035\pi\) | |||||||
\(384\) | − 2.24698i | − 0.114666i | ||||||||
\(385\) | 0.753020i | 0.0383775i | ||||||||
\(386\) | −9.15883 | −0.466172 | ||||||||
\(387\) | −9.48858 | −0.482332 | ||||||||
\(388\) | 3.30798i | 0.167937i | ||||||||
\(389\) | −23.4674 | −1.18984 | −0.594922 | − | 0.803783i | \(-0.702817\pi\) | ||||
−0.594922 | + | 0.803783i | \(0.702817\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.96854 | 0.0995534 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | 7.07069 | 0.356669 | ||||||||
\(394\) | −3.73019 | −0.187924 | ||||||||
\(395\) | − 10.6619i | − 0.536458i | ||||||||
\(396\) | 0.911854i | 0.0458224i | ||||||||
\(397\) | 0.0499823i | 0.00250854i | 0.999999 | + | 0.00125427i | \(0.000399246\pi\) | ||||
−0.999999 | + | 0.00125427i | \(0.999601\pi\) | |||||||
\(398\) | − 19.5918i | − 0.982048i | ||||||||
\(399\) | −14.2838 | −0.715085 | ||||||||
\(400\) | 2.13706 | 0.106853 | ||||||||
\(401\) | − 4.84010i | − 0.241703i | −0.992671 | − | 0.120852i | \(-0.961437\pi\) | ||||
0.992671 | − | 0.120852i | \(-0.0385625\pi\) | |||||||
\(402\) | −14.0097 | −0.698740 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.08815 | 0.103889 | ||||||||
\(405\) | − 18.5254i | − 0.920535i | ||||||||
\(406\) | −3.58211 | −0.177777 | ||||||||
\(407\) | −4.80731 | −0.238290 | ||||||||
\(408\) | − 4.85086i | − 0.240153i | ||||||||
\(409\) | 29.8866i | 1.47780i | 0.673816 | + | 0.738899i | \(0.264654\pi\) | ||||
−0.673816 | + | 0.738899i | \(0.735346\pi\) | |||||||
\(410\) | − 4.09113i | − 0.202047i | ||||||||
\(411\) | 8.83877i | 0.435985i | ||||||||
\(412\) | −11.3013 | −0.556774 | ||||||||
\(413\) | −10.1468 | −0.499289 | ||||||||
\(414\) | 1.86831i | 0.0918226i | ||||||||
\(415\) | 4.92692 | 0.241853 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.1836 | −1.23325 | ||||||||
\(418\) | 2.82908i | 0.138375i | ||||||||
\(419\) | 8.13898 | 0.397615 | 0.198808 | − | 0.980039i | \(-0.436293\pi\) | ||||
0.198808 | + | 0.980039i | \(0.436293\pi\) | |||||||
\(420\) | 3.80194 | 0.185516 | ||||||||
\(421\) | − 17.0398i | − 0.830470i | −0.909714 | − | 0.415235i | \(-0.863699\pi\) | ||||
0.909714 | − | 0.415235i | \(-0.136301\pi\) | |||||||
\(422\) | 23.3860i | 1.13841i | ||||||||
\(423\) | 19.9782i | 0.971375i | ||||||||
\(424\) | 8.74094i | 0.424498i | ||||||||
\(425\) | 4.61356 | 0.223791 | ||||||||
\(426\) | 12.9487 | 0.627366 | ||||||||
\(427\) | 1.37867i | 0.0667183i | ||||||||
\(428\) | 7.13467 | 0.344867 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.83579 | 0.377875 | ||||||||
\(431\) | − 6.95779i | − 0.335145i | −0.985860 | − | 0.167572i | \(-0.946407\pi\) | ||||
0.985860 | − | 0.167572i | \(-0.0535928\pi\) | |||||||
\(432\) | −2.13706 | −0.102820 | ||||||||
\(433\) | 6.80731 | 0.327139 | 0.163569 | − | 0.986532i | \(-0.447699\pi\) | ||||
0.163569 | + | 0.986532i | \(0.447699\pi\) | |||||||
\(434\) | − 8.89977i | − 0.427203i | ||||||||
\(435\) | 13.6189i | 0.652978i | ||||||||
\(436\) | 6.57002i | 0.314647i | ||||||||
\(437\) | 5.79656i | 0.277287i | ||||||||
\(438\) | −22.3274 | −1.06684 | ||||||||
\(439\) | −26.3351 | −1.25691 | −0.628453 | − | 0.777847i | \(-0.716312\pi\) | ||||
−0.628453 | + | 0.777847i | \(0.716312\pi\) | |||||||
\(440\) | − 0.753020i | − 0.0358988i | ||||||||
\(441\) | −2.04892 | −0.0975675 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.32437 | 0.347991 | 0.173996 | − | 0.984746i | \(-0.444332\pi\) | ||||
0.173996 | + | 0.984746i | \(0.444332\pi\) | |||||||
\(444\) | 24.2717i | 1.15189i | ||||||||
\(445\) | 30.6383 | 1.45240 | ||||||||
\(446\) | 21.7482 | 1.02981 | ||||||||
\(447\) | − 49.1473i | − 2.32459i | ||||||||
\(448\) | − 1.00000i | − 0.0472456i | ||||||||
\(449\) | 41.4228i | 1.95486i | 0.211253 | + | 0.977431i | \(0.432245\pi\) | ||||
−0.211253 | + | 0.977431i | \(0.567755\pi\) | |||||||
\(450\) | 4.37867i | 0.206412i | ||||||||
\(451\) | 1.07606 | 0.0506699 | ||||||||
\(452\) | −10.6015 | −0.498652 | ||||||||
\(453\) | − 41.1202i | − 1.93200i | ||||||||
\(454\) | −6.55927 | −0.307842 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 14.2838 | 0.668901 | ||||||||
\(457\) | 11.7125i | 0.547886i | 0.961746 | + | 0.273943i | \(0.0883280\pi\) | ||||
−0.961746 | + | 0.273943i | \(0.911672\pi\) | |||||||
\(458\) | −0.948690 | −0.0443294 | ||||||||
\(459\) | −4.61356 | −0.215343 | ||||||||
\(460\) | − 1.54288i | − 0.0719370i | ||||||||
\(461\) | − 20.6461i | − 0.961584i | −0.876835 | − | 0.480792i | \(-0.840349\pi\) | ||||
0.876835 | − | 0.480792i | \(-0.159651\pi\) | |||||||
\(462\) | 1.00000i | 0.0465242i | ||||||||
\(463\) | − 10.9312i | − 0.508017i | −0.967202 | − | 0.254009i | \(-0.918251\pi\) | ||||
0.967202 | − | 0.254009i | \(-0.0817492\pi\) | |||||||
\(464\) | 3.58211 | 0.166295 | ||||||||
\(465\) | −33.8364 | −1.56912 | ||||||||
\(466\) | 15.4765i | 0.716935i | ||||||||
\(467\) | −15.4450 | −0.714711 | −0.357356 | − | 0.933968i | \(-0.616322\pi\) | ||||
−0.357356 | + | 0.933968i | \(0.616322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.23490 | −0.287901 | ||||||||
\(470\) | − 16.4983i | − 0.761008i | ||||||||
\(471\) | −24.3666 | −1.12275 | ||||||||
\(472\) | 10.1468 | 0.467042 | ||||||||
\(473\) | 2.06100i | 0.0947648i | ||||||||
\(474\) | − 14.1588i | − 0.650337i | ||||||||
\(475\) | 13.5851i | 0.623327i | ||||||||
\(476\) | − 2.15883i | − 0.0989500i | ||||||||
\(477\) | −17.9095 | −0.820018 | ||||||||
\(478\) | −25.3448 | −1.15924 | ||||||||
\(479\) | − 25.2828i | − 1.15520i | −0.816321 | − | 0.577599i | \(-0.803990\pi\) | ||||
0.816321 | − | 0.577599i | \(-0.196010\pi\) | |||||||
\(480\) | −3.80194 | −0.173534 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28.2664 | −1.28750 | ||||||||
\(483\) | 2.04892i | 0.0932290i | ||||||||
\(484\) | −10.8019 | −0.490997 | ||||||||
\(485\) | 5.59717 | 0.254154 | ||||||||
\(486\) | − 18.1903i | − 0.825128i | ||||||||
\(487\) | 1.01938i | 0.0461924i | 0.999733 | + | 0.0230962i | \(0.00735240\pi\) | ||||
−0.999733 | + | 0.0230962i | \(0.992648\pi\) | |||||||
\(488\) | − 1.37867i | − 0.0624093i | ||||||||
\(489\) | − 32.3696i | − 1.46380i | ||||||||
\(490\) | 1.69202 | 0.0764377 | ||||||||
\(491\) | 36.7198 | 1.65714 | 0.828570 | − | 0.559886i | \(-0.189155\pi\) | ||||
0.828570 | + | 0.559886i | \(0.189155\pi\) | |||||||
\(492\) | − 5.43296i | − 0.244937i | ||||||||
\(493\) | 7.73317 | 0.348284 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.54288 | 0.0693471 | ||||||||
\(496\) | 8.89977i | 0.399612i | ||||||||
\(497\) | 5.76271 | 0.258493 | ||||||||
\(498\) | 6.54288 | 0.293193 | ||||||||
\(499\) | − 41.4685i | − 1.85638i | −0.372102 | − | 0.928192i | \(-0.621363\pi\) | ||||
0.372102 | − | 0.928192i | \(-0.378637\pi\) | |||||||
\(500\) | − 12.0761i | − 0.540058i | ||||||||
\(501\) | 30.7754i | 1.37494i | ||||||||
\(502\) | 13.7235i | 0.612509i | ||||||||
\(503\) | −2.15346 | −0.0960179 | −0.0480089 | − | 0.998847i | \(-0.515288\pi\) | ||||
−0.0480089 | + | 0.998847i | \(0.515288\pi\) | |||||||
\(504\) | 2.04892 | 0.0912660 | ||||||||
\(505\) | − 3.53319i | − 0.157225i | ||||||||
\(506\) | 0.405813 | 0.0180406 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −21.5646 | −0.956776 | ||||||||
\(509\) | − 7.62565i | − 0.338001i | −0.985616 | − | 0.169000i | \(-0.945946\pi\) | ||||
0.985616 | − | 0.169000i | \(-0.0540539\pi\) | |||||||
\(510\) | −8.20775 | −0.363445 | ||||||||
\(511\) | −9.93661 | −0.439570 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 13.5851i | − 0.599796i | ||||||||
\(514\) | 13.3502i | 0.588852i | ||||||||
\(515\) | 19.1220i | 0.842616i | ||||||||
\(516\) | 10.4058 | 0.458090 | ||||||||
\(517\) | 4.33944 | 0.190848 | ||||||||
\(518\) | 10.8019i | 0.474610i | ||||||||
\(519\) | 10.0586 | 0.441524 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.8377 | 0.912917 | 0.456458 | − | 0.889745i | \(-0.349118\pi\) | ||||
0.456458 | + | 0.889745i | \(0.349118\pi\) | |||||||
\(522\) | 7.33944i | 0.321238i | ||||||||
\(523\) | 38.3491 | 1.67689 | 0.838445 | − | 0.544986i | \(-0.183465\pi\) | ||||
0.838445 | + | 0.544986i | \(0.183465\pi\) | |||||||
\(524\) | −3.14675 | −0.137467 | ||||||||
\(525\) | 4.80194i | 0.209574i | ||||||||
\(526\) | 19.3153i | 0.842186i | ||||||||
\(527\) | 19.2131i | 0.836937i | ||||||||
\(528\) | − 1.00000i | − 0.0435194i | ||||||||
\(529\) | −22.1685 | −0.963849 | ||||||||
\(530\) | 14.7899 | 0.642430 | ||||||||
\(531\) | 20.7899i | 0.902203i | ||||||||
\(532\) | 6.35690 | 0.275606 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 40.6872 | 1.76071 | ||||||||
\(535\) | − 12.0720i | − 0.521919i | ||||||||
\(536\) | 6.23490 | 0.269307 | ||||||||
\(537\) | 51.8461 | 2.23732 | ||||||||
\(538\) | 24.2935i | 1.04737i | ||||||||
\(539\) | 0.445042i | 0.0191693i | ||||||||
\(540\) | 3.61596i | 0.155606i | ||||||||
\(541\) | 5.46740i | 0.235062i | 0.993069 | + | 0.117531i | \(0.0374980\pi\) | ||||
−0.993069 | + | 0.117531i | \(0.962502\pi\) | |||||||
\(542\) | 29.0368 | 1.24724 | ||||||||
\(543\) | −19.0315 | −0.816718 | ||||||||
\(544\) | 2.15883i | 0.0925592i | ||||||||
\(545\) | 11.1166 | 0.476184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.26636 | −0.267930 | −0.133965 | − | 0.990986i | \(-0.542771\pi\) | ||||
−0.133965 | + | 0.990986i | \(0.542771\pi\) | |||||||
\(548\) | − 3.93362i | − 0.168036i | ||||||||
\(549\) | 2.82477 | 0.120558 | ||||||||
\(550\) | 0.951083 | 0.0405543 | ||||||||
\(551\) | 22.7711i | 0.970080i | ||||||||
\(552\) | − 2.04892i | − 0.0872077i | ||||||||
\(553\) | − 6.30127i | − 0.267957i | ||||||||
\(554\) | − 1.19029i | − 0.0505707i | ||||||||
\(555\) | 41.0683 | 1.74325 | ||||||||
\(556\) | 11.2078 | 0.475315 | ||||||||
\(557\) | 23.1371i | 0.980349i | 0.871624 | + | 0.490174i | \(0.163067\pi\) | ||||
−0.871624 | + | 0.490174i | \(0.836933\pi\) | |||||||
\(558\) | −18.2349 | −0.771945 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1.69202 | −0.0715010 | ||||||||
\(561\) | − 2.15883i | − 0.0911460i | ||||||||
\(562\) | 21.2325 | 0.895639 | ||||||||
\(563\) | −1.21685 | −0.0512841 | −0.0256420 | − | 0.999671i | \(-0.508163\pi\) | ||||
−0.0256420 | + | 0.999671i | \(0.508163\pi\) | |||||||
\(564\) | − 21.9095i | − 0.922555i | ||||||||
\(565\) | 17.9379i | 0.754655i | ||||||||
\(566\) | − 11.6756i | − 0.490763i | ||||||||
\(567\) | − 10.9487i | − 0.459802i | ||||||||
\(568\) | −5.76271 | −0.241798 | ||||||||
\(569\) | 28.5816 | 1.19820 | 0.599102 | − | 0.800673i | \(-0.295524\pi\) | ||||
0.599102 | + | 0.800673i | \(0.295524\pi\) | |||||||
\(570\) | − 24.1685i | − 1.01231i | ||||||||
\(571\) | 32.1825 | 1.34680 | 0.673398 | − | 0.739280i | \(-0.264834\pi\) | ||||
0.673398 | + | 0.739280i | \(0.264834\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 44.3183 | 1.85142 | ||||||||
\(574\) | − 2.41789i | − 0.100921i | ||||||||
\(575\) | 1.94869 | 0.0812660 | ||||||||
\(576\) | −2.04892 | −0.0853716 | ||||||||
\(577\) | − 2.94810i | − 0.122731i | −0.998115 | − | 0.0613655i | \(-0.980454\pi\) | ||||
0.998115 | − | 0.0613655i | \(-0.0195455\pi\) | |||||||
\(578\) | − 12.3394i | − 0.513253i | ||||||||
\(579\) | 20.5797i | 0.855264i | ||||||||
\(580\) | − 6.06100i | − 0.251669i | ||||||||
\(581\) | 2.91185 | 0.120804 | ||||||||
\(582\) | 7.43296 | 0.308106 | ||||||||
\(583\) | 3.89008i | 0.161111i | ||||||||
\(584\) | 9.93661 | 0.411180 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.4101 | 0.595277 | ||||||||
\(587\) | 2.77538i | 0.114552i | 0.998358 | + | 0.0572761i | \(0.0182415\pi\) | ||||
−0.998358 | + | 0.0572761i | \(0.981758\pi\) | |||||||
\(588\) | 2.24698 | 0.0926639 | ||||||||
\(589\) | −56.5749 | −2.33113 | ||||||||
\(590\) | − 17.1685i | − 0.706817i | ||||||||
\(591\) | 8.38165i | 0.344775i | ||||||||
\(592\) | − 10.8019i | − 0.443957i | ||||||||
\(593\) | − 21.5241i | − 0.883888i | −0.897043 | − | 0.441944i | \(-0.854289\pi\) | ||||
0.897043 | − | 0.441944i | \(-0.145711\pi\) | |||||||
\(594\) | −0.951083 | −0.0390234 | ||||||||
\(595\) | −3.65279 | −0.149750 | ||||||||
\(596\) | 21.8726i | 0.895938i | ||||||||
\(597\) | −44.0224 | −1.80172 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23.3230 | 0.952954 | 0.476477 | − | 0.879187i | \(-0.341914\pi\) | ||||
0.476477 | + | 0.879187i | \(0.341914\pi\) | |||||||
\(600\) | − 4.80194i | − 0.196038i | ||||||||
\(601\) | 15.7429 | 0.642165 | 0.321082 | − | 0.947051i | \(-0.395953\pi\) | ||||
0.321082 | + | 0.947051i | \(0.395953\pi\) | |||||||
\(602\) | 4.63102 | 0.188746 | ||||||||
\(603\) | 12.7748i | 0.520230i | ||||||||
\(604\) | 18.3002i | 0.744625i | ||||||||
\(605\) | 18.2771i | 0.743070i | ||||||||
\(606\) | − 4.69202i | − 0.190600i | ||||||||
\(607\) | −19.7845 | −0.803027 | −0.401514 | − | 0.915853i | \(-0.631516\pi\) | ||||
−0.401514 | + | 0.915853i | \(0.631516\pi\) | |||||||
\(608\) | −6.35690 | −0.257806 | ||||||||
\(609\) | 8.04892i | 0.326159i | ||||||||
\(610\) | −2.33273 | −0.0944496 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −4.42327 | −0.178800 | ||||||||
\(613\) | − 7.24996i | − 0.292823i | −0.989224 | − | 0.146412i | \(-0.953228\pi\) | ||||
0.989224 | − | 0.146412i | \(-0.0467724\pi\) | |||||||
\(614\) | 2.55257 | 0.103013 | ||||||||
\(615\) | −9.19269 | −0.370685 | ||||||||
\(616\) | − 0.445042i | − 0.0179312i | ||||||||
\(617\) | − 36.7415i | − 1.47916i | −0.673070 | − | 0.739579i | \(-0.735025\pi\) | ||||
0.673070 | − | 0.739579i | \(-0.264975\pi\) | |||||||
\(618\) | 25.3937i | 1.02149i | ||||||||
\(619\) | 17.4959i | 0.703219i | 0.936147 | + | 0.351609i | \(0.114365\pi\) | ||||
−0.936147 | + | 0.351609i | \(0.885635\pi\) | |||||||
\(620\) | 15.0586 | 0.604768 | ||||||||
\(621\) | −1.94869 | −0.0781982 | ||||||||
\(622\) | 1.63533i | 0.0655709i | ||||||||
\(623\) | 18.1075 | 0.725463 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.74764 | −0.389906 | ||||||||
\(626\) | − 12.7724i | − 0.510488i | ||||||||
\(627\) | 6.35690 | 0.253870 | ||||||||
\(628\) | 10.8442 | 0.432729 | ||||||||
\(629\) | − 23.3196i | − 0.929813i | ||||||||
\(630\) | − 3.46681i | − 0.138121i | ||||||||
\(631\) | − 31.4644i | − 1.25258i | −0.779591 | − | 0.626289i | \(-0.784573\pi\) | ||||
0.779591 | − | 0.626289i | \(-0.215427\pi\) | |||||||
\(632\) | 6.30127i | 0.250651i | ||||||||
\(633\) | 52.5478 | 2.08859 | ||||||||
\(634\) | 10.9041 | 0.433057 | ||||||||
\(635\) | 36.4878i | 1.44798i | ||||||||
\(636\) | 19.6407 | 0.778805 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.59419 | 0.0631145 | ||||||||
\(639\) | − 11.8073i | − 0.467090i | ||||||||
\(640\) | 1.69202 | 0.0668830 | ||||||||
\(641\) | 24.6799 | 0.974799 | 0.487400 | − | 0.873179i | \(-0.337946\pi\) | ||||
0.487400 | + | 0.873179i | \(0.337946\pi\) | |||||||
\(642\) | − 16.0315i | − 0.632711i | ||||||||
\(643\) | − 11.1588i | − 0.440061i | −0.975493 | − | 0.220031i | \(-0.929384\pi\) | ||||
0.975493 | − | 0.220031i | \(-0.0706158\pi\) | |||||||
\(644\) | − 0.911854i | − 0.0359321i | ||||||||
\(645\) | − 17.6069i | − 0.693269i | ||||||||
\(646\) | −13.7235 | −0.539943 | ||||||||
\(647\) | −14.8791 | −0.584956 | −0.292478 | − | 0.956272i | \(-0.594480\pi\) | ||||
−0.292478 | + | 0.956272i | \(0.594480\pi\) | |||||||
\(648\) | 10.9487i | 0.430105i | ||||||||
\(649\) | 4.51573 | 0.177258 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −19.9976 | −0.783768 | ||||||||
\(652\) | 14.4058i | 0.564175i | ||||||||
\(653\) | −5.13600 | −0.200987 | −0.100494 | − | 0.994938i | \(-0.532042\pi\) | ||||
−0.100494 | + | 0.994938i | \(0.532042\pi\) | |||||||
\(654\) | 14.7627 | 0.577268 | ||||||||
\(655\) | 5.32437i | 0.208040i | ||||||||
\(656\) | 2.41789i | 0.0944029i | ||||||||
\(657\) | 20.3593i | 0.794292i | ||||||||
\(658\) | − 9.75063i | − 0.380119i | ||||||||
\(659\) | 8.42998 | 0.328385 | 0.164193 | − | 0.986428i | \(-0.447498\pi\) | ||||
0.164193 | + | 0.986428i | \(0.447498\pi\) | |||||||
\(660\) | −1.69202 | −0.0658618 | ||||||||
\(661\) | − 20.3793i | − 0.792661i | −0.918108 | − | 0.396331i | \(-0.870283\pi\) | ||||
0.918108 | − | 0.396331i | \(-0.129717\pi\) | |||||||
\(662\) | −9.94869 | −0.386667 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.91185 | −0.113002 | ||||||||
\(665\) | − 10.7560i | − 0.417100i | ||||||||
\(666\) | 22.1323 | 0.857608 | ||||||||
\(667\) | 3.26636 | 0.126474 | ||||||||
\(668\) | − 13.6963i | − 0.529927i | ||||||||
\(669\) | − 48.8678i | − 1.88934i | ||||||||
\(670\) | − 10.5496i | − 0.407566i | ||||||||
\(671\) | − 0.613564i | − 0.0236864i | ||||||||
\(672\) | −2.24698 | −0.0866791 | ||||||||
\(673\) | −21.6383 | −0.834096 | −0.417048 | − | 0.908884i | \(-0.636935\pi\) | ||||
−0.417048 | + | 0.908884i | \(0.636935\pi\) | |||||||
\(674\) | − 8.06829i | − 0.310779i | ||||||||
\(675\) | −4.56704 | −0.175785 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.5351 | 1.55789 | 0.778945 | − | 0.627092i | \(-0.215755\pi\) | ||||
0.778945 | + | 0.627092i | \(0.215755\pi\) | |||||||
\(678\) | 23.8213i | 0.914852i | ||||||||
\(679\) | 3.30798 | 0.126949 | ||||||||
\(680\) | 3.65279 | 0.140078 | ||||||||
\(681\) | 14.7385i | 0.564782i | ||||||||
\(682\) | 3.96077i | 0.151666i | ||||||||
\(683\) | − 21.6969i | − 0.830210i | −0.909774 | − | 0.415105i | \(-0.863745\pi\) | ||||
0.909774 | − | 0.415105i | \(-0.136255\pi\) | |||||||
\(684\) | − 13.0248i | − 0.498014i | ||||||||
\(685\) | −6.65578 | −0.254304 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 2.13169i | 0.0813289i | ||||||||
\(688\) | −4.63102 | −0.176556 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −3.46681 | −0.131979 | ||||||||
\(691\) | 28.0610i | 1.06749i | 0.845645 | + | 0.533745i | \(0.179216\pi\) | ||||
−0.845645 | + | 0.533745i | \(0.820784\pi\) | |||||||
\(692\) | −4.47650 | −0.170171 | ||||||||
\(693\) | 0.911854 | 0.0346385 | ||||||||
\(694\) | − 33.1769i | − 1.25938i | ||||||||
\(695\) | − 18.9638i | − 0.719336i | ||||||||
\(696\) | − 8.04892i | − 0.305093i | ||||||||
\(697\) | 5.21983i | 0.197715i | ||||||||
\(698\) | 24.6872 | 0.934426 | ||||||||
\(699\) | 34.7754 | 1.31533 | ||||||||
\(700\) | − 2.13706i | − 0.0807734i | ||||||||
\(701\) | 13.7380 | 0.518875 | 0.259438 | − | 0.965760i | \(-0.416463\pi\) | ||||
0.259438 | + | 0.965760i | \(0.416463\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.6668 | 2.58982 | ||||||||
\(704\) | 0.445042i | 0.0167731i | ||||||||
\(705\) | −37.0713 | −1.39619 | ||||||||
\(706\) | −22.5754 | −0.849636 | ||||||||
\(707\) | − 2.08815i | − 0.0785328i | ||||||||
\(708\) | − 22.7995i | − 0.856859i | ||||||||
\(709\) | 23.0586i | 0.865984i | 0.901398 | + | 0.432992i | \(0.142542\pi\) | ||||
−0.901398 | + | 0.432992i | \(0.857458\pi\) | |||||||
\(710\) | 9.75063i | 0.365935i | ||||||||
\(711\) | −12.9108 | −0.484192 | ||||||||
\(712\) | −18.1075 | −0.678608 | ||||||||
\(713\) | 8.11529i | 0.303920i | ||||||||
\(714\) | −4.85086 | −0.181539 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.0737 | −0.862304 | ||||||||
\(717\) | 56.9493i | 2.12681i | ||||||||
\(718\) | 2.30798 | 0.0861330 | ||||||||
\(719\) | −22.8750 | −0.853094 | −0.426547 | − | 0.904465i | \(-0.640270\pi\) | ||||
−0.426547 | + | 0.904465i | \(0.640270\pi\) | |||||||
\(720\) | 3.46681i | 0.129200i | ||||||||
\(721\) | 11.3013i | 0.420881i | ||||||||
\(722\) | − 21.4101i | − 0.796802i | ||||||||
\(723\) | 63.5139i | 2.36211i | ||||||||
\(724\) | 8.46980 | 0.314777 | ||||||||
\(725\) | 7.65519 | 0.284306 | ||||||||
\(726\) | 24.2717i | 0.900809i | ||||||||
\(727\) | −9.76377 | −0.362118 | −0.181059 | − | 0.983472i | \(-0.557953\pi\) | ||||
−0.181059 | + | 0.983472i | \(0.557953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.02715 | −0.297302 | ||||||||
\(730\) | − 16.8130i | − 0.622275i | ||||||||
\(731\) | −9.99761 | −0.369775 | ||||||||
\(732\) | −3.09783 | −0.114499 | ||||||||
\(733\) | 2.65519i | 0.0980715i | 0.998797 | + | 0.0490358i | \(0.0156148\pi\) | ||||
−0.998797 | + | 0.0490358i | \(0.984385\pi\) | |||||||
\(734\) | 25.1685i | 0.928987i | ||||||||
\(735\) | − 3.80194i | − 0.140237i | ||||||||
\(736\) | 0.911854i | 0.0336114i | ||||||||
\(737\) | 2.77479 | 0.102211 | ||||||||
\(738\) | −4.95407 | −0.182362 | ||||||||
\(739\) | − 0.135144i | − 0.00497137i | −0.999997 | − | 0.00248568i | \(-0.999209\pi\) | ||||
0.999997 | − | 0.00248568i | \(-0.000791218\pi\) | |||||||
\(740\) | −18.2771 | −0.671880 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.74094 | 0.320890 | ||||||||
\(743\) | − 38.1943i | − 1.40121i | −0.713547 | − | 0.700607i | \(-0.752913\pi\) | ||||
0.713547 | − | 0.700607i | \(-0.247087\pi\) | |||||||
\(744\) | 19.9976 | 0.733148 | ||||||||
\(745\) | 37.0090 | 1.35590 | ||||||||
\(746\) | 11.6407i | 0.426197i | ||||||||
\(747\) | − 5.96615i | − 0.218290i | ||||||||
\(748\) | 0.960771i | 0.0351293i | ||||||||
\(749\) | − 7.13467i | − 0.260695i | ||||||||
\(750\) | −27.1347 | −0.990818 | ||||||||
\(751\) | −31.9614 | −1.16629 | −0.583143 | − | 0.812369i | \(-0.698177\pi\) | ||||
−0.583143 | + | 0.812369i | \(0.698177\pi\) | |||||||
\(752\) | 9.75063i | 0.355569i | ||||||||
\(753\) | 30.8364 | 1.12374 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.9643 | 1.12691 | ||||||||
\(756\) | 2.13706i | 0.0777242i | ||||||||
\(757\) | −51.4258 | −1.86910 | −0.934551 | − | 0.355829i | \(-0.884198\pi\) | ||||
−0.934551 | + | 0.355829i | \(0.884198\pi\) | |||||||
\(758\) | 16.5623 | 0.601568 | ||||||||
\(759\) | − 0.911854i | − 0.0330982i | ||||||||
\(760\) | 10.7560i | 0.390161i | ||||||||
\(761\) | − 29.4782i | − 1.06858i | −0.845301 | − | 0.534291i | \(-0.820579\pi\) | ||||
0.845301 | − | 0.534291i | \(-0.179421\pi\) | |||||||
\(762\) | 48.4553i | 1.75535i | ||||||||
\(763\) | 6.57002 | 0.237851 | ||||||||
\(764\) | −19.7235 | −0.713570 | ||||||||
\(765\) | 7.48427i | 0.270594i | ||||||||
\(766\) | 7.39506 | 0.267194 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.24698 | 0.0810809 | ||||||||
\(769\) | − 24.7114i | − 0.891116i | −0.895253 | − | 0.445558i | \(-0.853005\pi\) | ||||
0.895253 | − | 0.445558i | \(-0.146995\pi\) | |||||||
\(770\) | −0.753020 | −0.0271370 | ||||||||
\(771\) | 29.9976 | 1.08034 | ||||||||
\(772\) | − 9.15883i | − 0.329634i | ||||||||
\(773\) | − 22.3032i | − 0.802190i | −0.916036 | − | 0.401095i | \(-0.868630\pi\) | ||||
0.916036 | − | 0.401095i | \(-0.131370\pi\) | |||||||
\(774\) | − 9.48858i | − 0.341060i | ||||||||
\(775\) | 19.0194i | 0.683196i | ||||||||
\(776\) | −3.30798 | −0.118750 | ||||||||
\(777\) | 24.2717 | 0.870744 | ||||||||
\(778\) | − 23.4674i | − 0.841347i | ||||||||
\(779\) | −15.3703 | −0.550698 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.56465 | −0.0917703 | ||||||||
\(782\) | 1.96854i | 0.0703949i | ||||||||
\(783\) | −7.65519 | −0.273574 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | − 18.3485i | − 0.654887i | ||||||||
\(786\) | 7.07069i | 0.252203i | ||||||||
\(787\) | 16.4896i | 0.587792i | 0.955837 | + | 0.293896i | \(0.0949520\pi\) | ||||
−0.955837 | + | 0.293896i | \(0.905048\pi\) | |||||||
\(788\) | − 3.73019i | − 0.132882i | ||||||||
\(789\) | 43.4010 | 1.54512 | ||||||||
\(790\) | 10.6619 | 0.379333 | ||||||||
\(791\) | 10.6015i | 0.376945i | ||||||||
\(792\) | −0.911854 | −0.0324013 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.0499823 | −0.00177380 | ||||||||
\(795\) | − 33.2325i | − 1.17864i | ||||||||
\(796\) | 19.5918 | 0.694413 | ||||||||
\(797\) | 1.00106 | 0.0354595 | 0.0177298 | − | 0.999843i | \(-0.494356\pi\) | ||||
0.0177298 | + | 0.999843i | \(0.494356\pi\) | |||||||
\(798\) | − 14.2838i | − 0.505642i | ||||||||
\(799\) | 21.0500i | 0.744695i | ||||||||
\(800\) | 2.13706i | 0.0755566i | ||||||||
\(801\) | − 37.1008i | − 1.31089i | ||||||||
\(802\) | 4.84010 | 0.170910 | ||||||||
\(803\) | 4.42221 | 0.156056 | ||||||||
\(804\) | − 14.0097i | − 0.494084i | ||||||||
\(805\) | −1.54288 | −0.0543793 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 54.5870 | 1.92155 | ||||||||
\(808\) | 2.08815i | 0.0734607i | ||||||||
\(809\) | −49.9172 | −1.75500 | −0.877498 | − | 0.479580i | \(-0.840789\pi\) | ||||
−0.877498 | + | 0.479580i | \(0.840789\pi\) | |||||||
\(810\) | 18.5254 | 0.650917 | ||||||||
\(811\) | 32.9554i | 1.15722i | 0.815604 | + | 0.578610i | \(0.196405\pi\) | ||||
−0.815604 | + | 0.578610i | \(0.803595\pi\) | |||||||
\(812\) | − 3.58211i | − 0.125707i | ||||||||
\(813\) | − 65.2452i | − 2.28825i | ||||||||
\(814\) | − 4.80731i | − 0.168496i | ||||||||
\(815\) | 24.3749 | 0.853817 | ||||||||
\(816\) | 4.85086 | 0.169814 | ||||||||
\(817\) | − 29.4389i | − 1.02994i | ||||||||
\(818\) | −29.8866 | −1.04496 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.09113 | 0.142868 | ||||||||
\(821\) | 29.3129i | 1.02303i | 0.859275 | + | 0.511513i | \(0.170915\pi\) | ||||
−0.859275 | + | 0.511513i | \(0.829085\pi\) | |||||||
\(822\) | −8.83877 | −0.308288 | ||||||||
\(823\) | 11.3013 | 0.393938 | 0.196969 | − | 0.980410i | \(-0.436890\pi\) | ||||
0.196969 | + | 0.980410i | \(0.436890\pi\) | |||||||
\(824\) | − 11.3013i | − 0.393699i | ||||||||
\(825\) | − 2.13706i | − 0.0744030i | ||||||||
\(826\) | − 10.1468i | − 0.353051i | ||||||||
\(827\) | 32.8568i | 1.14254i | 0.820761 | + | 0.571272i | \(0.193550\pi\) | ||||
−0.820761 | + | 0.571272i | \(0.806450\pi\) | |||||||
\(828\) | −1.86831 | −0.0649284 | ||||||||
\(829\) | −36.6853 | −1.27413 | −0.637067 | − | 0.770809i | \(-0.719852\pi\) | ||||
−0.637067 | + | 0.770809i | \(0.719852\pi\) | |||||||
\(830\) | 4.92692i | 0.171016i | ||||||||
\(831\) | −2.67456 | −0.0927796 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.15883 | −0.0747992 | ||||||||
\(834\) | − 25.1836i | − 0.872036i | ||||||||
\(835\) | −23.1745 | −0.801986 | ||||||||
\(836\) | −2.82908 | −0.0978459 | ||||||||
\(837\) | − 19.0194i | − 0.657406i | ||||||||
\(838\) | 8.13898i | 0.281156i | ||||||||
\(839\) | 23.7687i | 0.820586i | 0.911954 | + | 0.410293i | \(0.134574\pi\) | ||||
−0.911954 | + | 0.410293i | \(0.865426\pi\) | |||||||
\(840\) | 3.80194i | 0.131179i | ||||||||
\(841\) | −16.1685 | −0.557535 | ||||||||
\(842\) | 17.0398 | 0.587231 | ||||||||
\(843\) | − 47.7090i | − 1.64319i | ||||||||
\(844\) | −23.3860 | −0.804978 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −19.9782 | −0.686866 | ||||||||
\(847\) | 10.8019i | 0.371159i | ||||||||
\(848\) | −8.74094 | −0.300165 | ||||||||
\(849\) | −26.2349 | −0.900379 | ||||||||
\(850\) | 4.61356i | 0.158244i | ||||||||
\(851\) | − 9.84979i | − 0.337646i | ||||||||
\(852\) | 12.9487i | 0.443615i | ||||||||
\(853\) | − 33.6437i | − 1.15194i | −0.817471 | − | 0.575969i | \(-0.804625\pi\) | ||||
0.817471 | − | 0.575969i | \(-0.195375\pi\) | |||||||
\(854\) | −1.37867 | −0.0471770 | ||||||||
\(855\) | −22.0382 | −0.753689 | ||||||||
\(856\) | 7.13467i | 0.243858i | ||||||||
\(857\) | 35.2646 | 1.20461 | 0.602307 | − | 0.798264i | \(-0.294248\pi\) | ||||
0.602307 | + | 0.798264i | \(0.294248\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.80433 | 0.334519 | 0.167260 | − | 0.985913i | \(-0.446508\pi\) | ||||
0.167260 | + | 0.985913i | \(0.446508\pi\) | |||||||
\(860\) | 7.83579i | 0.267198i | ||||||||
\(861\) | −5.43296 | −0.185155 | ||||||||
\(862\) | 6.95779 | 0.236983 | ||||||||
\(863\) | 34.2586i | 1.16618i | 0.812409 | + | 0.583088i | \(0.198156\pi\) | ||||
−0.812409 | + | 0.583088i | \(0.801844\pi\) | |||||||
\(864\) | − 2.13706i | − 0.0727044i | ||||||||
\(865\) | 7.57434i | 0.257535i | ||||||||
\(866\) | 6.80731i | 0.231322i | ||||||||
\(867\) | −27.7265 | −0.941640 | ||||||||
\(868\) | 8.89977 | 0.302078 | ||||||||
\(869\) | 2.80433i | 0.0951304i | ||||||||
\(870\) | −13.6189 | −0.461725 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.57002 | −0.222489 | ||||||||
\(873\) | − 6.77777i | − 0.229393i | ||||||||
\(874\) | −5.79656 | −0.196072 | ||||||||
\(875\) | −12.0761 | −0.408245 | ||||||||
\(876\) | − 22.3274i | − 0.754371i | ||||||||
\(877\) | − 28.5174i | − 0.962964i | −0.876456 | − | 0.481482i | \(-0.840099\pi\) | ||||
0.876456 | − | 0.481482i | \(-0.159901\pi\) | |||||||
\(878\) | − 26.3351i | − 0.888767i | ||||||||
\(879\) | − 32.3793i | − 1.09213i | ||||||||
\(880\) | 0.753020 | 0.0253843 | ||||||||
\(881\) | 55.3193 | 1.86376 | 0.931878 | − | 0.362773i | \(-0.118170\pi\) | ||||
0.931878 | + | 0.362773i | \(0.118170\pi\) | |||||||
\(882\) | − 2.04892i | − 0.0689906i | ||||||||
\(883\) | −0.815938 | −0.0274585 | −0.0137293 | − | 0.999906i | \(-0.504370\pi\) | ||||
−0.0137293 | + | 0.999906i | \(0.504370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −38.5773 | −1.29676 | ||||||||
\(886\) | 7.32437i | 0.246067i | ||||||||
\(887\) | 39.8713 | 1.33875 | 0.669374 | − | 0.742926i | \(-0.266563\pi\) | ||||
0.669374 | + | 0.742926i | \(0.266563\pi\) | |||||||
\(888\) | −24.2717 | −0.814506 | ||||||||
\(889\) | 21.5646i | 0.723255i | ||||||||
\(890\) | 30.6383i | 1.02700i | ||||||||
\(891\) | 4.87263i | 0.163239i | ||||||||
\(892\) | 21.7482i | 0.728185i | ||||||||
\(893\) | −61.9837 | −2.07421 | ||||||||
\(894\) | 49.1473 | 1.64373 | ||||||||
\(895\) | 39.0411i | 1.30500i | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −41.4228 | −1.38230 | ||||||||
\(899\) | 31.8799i | 1.06325i | ||||||||
\(900\) | −4.37867 | −0.145956 | ||||||||
\(901\) | −18.8702 | −0.628659 | ||||||||
\(902\) | 1.07606i | 0.0358290i | ||||||||
\(903\) | − 10.4058i | − 0.346284i | ||||||||
\(904\) | − 10.6015i | − 0.352600i | ||||||||
\(905\) | − 14.3311i | − 0.476381i | ||||||||
\(906\) | 41.1202 | 1.36613 | ||||||||
\(907\) | −5.54719 | −0.184191 | −0.0920957 | − | 0.995750i | \(-0.529357\pi\) | ||||
−0.0920957 | + | 0.995750i | \(0.529357\pi\) | |||||||
\(908\) | − 6.55927i | − 0.217677i | ||||||||
\(909\) | −4.27844 | −0.141907 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.3357 | 0.408701 | 0.204350 | − | 0.978898i | \(-0.434492\pi\) | ||||
0.204350 | + | 0.978898i | \(0.434492\pi\) | |||||||
\(912\) | 14.2838i | 0.472984i | ||||||||
\(913\) | −1.29590 | −0.0428879 | ||||||||
\(914\) | −11.7125 | −0.387414 | ||||||||
\(915\) | 5.24160i | 0.173282i | ||||||||
\(916\) | − 0.948690i | − 0.0313456i | ||||||||
\(917\) | 3.14675i | 0.103915i | ||||||||
\(918\) | − 4.61356i | − 0.152270i | ||||||||
\(919\) | 5.22223 | 0.172265 | 0.0861327 | − | 0.996284i | \(-0.472549\pi\) | ||||
0.0861327 | + | 0.996284i | \(0.472549\pi\) | |||||||
\(920\) | 1.54288 | 0.0508671 | ||||||||
\(921\) | − 5.73556i | − 0.188993i | ||||||||
\(922\) | 20.6461 | 0.679943 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −1.00000 | −0.0328976 | ||||||||
\(925\) | − 23.0844i | − 0.759011i | ||||||||
\(926\) | 10.9312 | 0.359223 | ||||||||
\(927\) | 23.1554 | 0.760522 | ||||||||
\(928\) | 3.58211i | 0.117588i | ||||||||
\(929\) | 10.9957i | 0.360757i | 0.983597 | + | 0.180378i | \(0.0577322\pi\) | ||||
−0.983597 | + | 0.180378i | \(0.942268\pi\) | |||||||
\(930\) | − 33.8364i | − 1.10954i | ||||||||
\(931\) | − 6.35690i | − 0.208339i | ||||||||
\(932\) | −15.4765 | −0.506950 | ||||||||
\(933\) | 3.67456 | 0.120300 | ||||||||
\(934\) | − 15.4450i | − 0.505377i | ||||||||
\(935\) | 1.62565 | 0.0531643 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.5190 | −0.702994 | −0.351497 | − | 0.936189i | \(-0.614327\pi\) | ||||
−0.351497 | + | 0.936189i | \(0.614327\pi\) | |||||||
\(938\) | − 6.23490i | − 0.203577i | ||||||||
\(939\) | −28.6993 | −0.936567 | ||||||||
\(940\) | 16.4983 | 0.538114 | ||||||||
\(941\) | − 11.2784i | − 0.367667i | −0.982957 | − | 0.183833i | \(-0.941149\pi\) | ||||
0.982957 | − | 0.183833i | \(-0.0588507\pi\) | |||||||
\(942\) | − 24.3666i | − 0.793906i | ||||||||
\(943\) | 2.20477i | 0.0717971i | ||||||||
\(944\) | 10.1468i | 0.330249i | ||||||||
\(945\) | 3.61596 | 0.117627 | ||||||||
\(946\) | −2.06100 | −0.0670089 | ||||||||
\(947\) | 1.92154i | 0.0624417i | 0.999513 | + | 0.0312209i | \(0.00993953\pi\) | ||||
−0.999513 | + | 0.0312209i | \(0.990060\pi\) | |||||||
\(948\) | 14.1588 | 0.459858 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −13.5851 | −0.440758 | ||||||||
\(951\) | − 24.5013i | − 0.794508i | ||||||||
\(952\) | 2.15883 | 0.0699682 | ||||||||
\(953\) | −32.0538 | −1.03833 | −0.519163 | − | 0.854676i | \(-0.673756\pi\) | ||||
−0.519163 | + | 0.854676i | \(0.673756\pi\) | |||||||
\(954\) | − 17.9095i | − 0.579840i | ||||||||
\(955\) | 33.3726i | 1.07991i | ||||||||
\(956\) | − 25.3448i | − 0.819710i | ||||||||
\(957\) | − 3.58211i | − 0.115793i | ||||||||
\(958\) | 25.2828 | 0.816849 | ||||||||
\(959\) | −3.93362 | −0.127023 | ||||||||
\(960\) | − 3.80194i | − 0.122707i | ||||||||
\(961\) | −48.2059 | −1.55503 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.6183 | −0.471070 | ||||||||
\(964\) | − 28.2664i | − 0.910398i | ||||||||
\(965\) | −15.4969 | −0.498864 | ||||||||
\(966\) | −2.04892 | −0.0659228 | ||||||||
\(967\) | 47.5080i | 1.52775i | 0.645362 | + | 0.763876i | \(0.276706\pi\) | ||||
−0.645362 | + | 0.763876i | \(0.723294\pi\) | |||||||
\(968\) | − 10.8019i | − 0.347187i | ||||||||
\(969\) | 30.8364i | 0.990607i | ||||||||
\(970\) | 5.59717i | 0.179714i | ||||||||
\(971\) | 36.0224 | 1.15601 | 0.578006 | − | 0.816032i | \(-0.303831\pi\) | ||||
0.578006 | + | 0.816032i | \(0.303831\pi\) | |||||||
\(972\) | 18.1903 | 0.583454 | ||||||||
\(973\) | − 11.2078i | − 0.359304i | ||||||||
\(974\) | −1.01938 | −0.0326630 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.37867 | 0.0441300 | ||||||||
\(977\) | − 28.2620i | − 0.904183i | −0.891972 | − | 0.452091i | \(-0.850678\pi\) | ||||
0.891972 | − | 0.452091i | \(-0.149322\pi\) | |||||||
\(978\) | 32.3696 | 1.03506 | ||||||||
\(979\) | −8.05861 | −0.257554 | ||||||||
\(980\) | 1.69202i | 0.0540496i | ||||||||
\(981\) | − 13.4614i | − 0.429791i | ||||||||
\(982\) | 36.7198i | 1.17177i | ||||||||
\(983\) | − 8.60196i | − 0.274360i | −0.990546 | − | 0.137180i | \(-0.956196\pi\) | ||||
0.990546 | − | 0.137180i | \(-0.0438038\pi\) | |||||||
\(984\) | 5.43296 | 0.173196 | ||||||||
\(985\) | −6.31155 | −0.201103 | ||||||||
\(986\) | 7.73317i | 0.246274i | ||||||||
\(987\) | −21.9095 | −0.697386 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.22282 | −0.134278 | ||||||||
\(990\) | 1.54288i | 0.0490358i | ||||||||
\(991\) | −17.8549 | −0.567180 | −0.283590 | − | 0.958946i | \(-0.591525\pi\) | ||||
−0.283590 | + | 0.958946i | \(0.591525\pi\) | |||||||
\(992\) | −8.89977 | −0.282568 | ||||||||
\(993\) | 22.3545i | 0.709399i | ||||||||
\(994\) | 5.76271i | 0.182782i | ||||||||
\(995\) | − 33.1497i | − 1.05092i | ||||||||
\(996\) | 6.54288i | 0.207319i | ||||||||
\(997\) | −36.3247 | −1.15041 | −0.575207 | − | 0.818008i | \(-0.695079\pi\) | ||||
−0.575207 | + | 0.818008i | \(0.695079\pi\) | |||||||
\(998\) | 41.4685 | 1.31266 | ||||||||
\(999\) | 23.0844i | 0.730359i |
(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 | 2366.2.d.p.337.6 | 6 | ||
13.5 | odd | 4 | 2366.2.a.bd.1.3 | yes | 3 | ||
13.8 | odd | 4 | 2366.2.a.y.1.3 | ✓ | 3 | ||
13.12 | even | 2 | inner | 2366.2.d.p.337.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2366.2.a.y.1.3 | ✓ | 3 | 13.8 | odd | 4 | ||
2366.2.a.bd.1.3 | yes | 3 | 13.5 | odd | 4 | ||
2366.2.d.p.337.3 | 6 | 13.12 | even | 2 | inner | ||
2366.2.d.p.337.6 | 6 | 1.1 | even | 1 | trivial |