Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (of order \(2\), degree \(1\), 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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.2 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.45 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.20235i | − | 1.84888i | −0.381328 | − | 0.924440i | \(-0.624533\pi\) | ||
0.381328 | − | 0.924440i | \(-0.375467\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.49915i | − | 0.670442i | −0.942140 | − | 0.335221i | \(-0.891189\pi\) | ||
0.942140 | − | 0.335221i | \(-0.108811\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.89750i | 1.09515i | 0.836755 | + | 0.547577i | \(0.184450\pi\) | ||||
−0.836755 | + | 0.547577i | \(0.815550\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.25507 | −2.41836 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.590335i | 0.177993i | 0.996032 | + | 0.0889963i | \(0.0283659\pi\) | ||||
−0.996032 | + | 0.0889963i | \(0.971634\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.18813 | 1.71628 | 0.858139 | − | 0.513417i | \(-0.171621\pi\) | ||||
0.858139 | + | 0.513417i | \(0.171621\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.80082 | −1.23957 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.80163 | − | 1.59611i | 0.922032 | − | 0.387114i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.41715 | −0.554531 | −0.277266 | − | 0.960793i | \(-0.589428\pi\) | ||||
−0.277266 | + | 0.960793i | \(0.589428\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.27883 | 2.02481 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 6.41697i | − | 1.33803i | −0.743249 | − | 0.669015i | \(-0.766716\pi\) | ||
0.743249 | − | 0.669015i | \(-0.233284\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.75254 | 0.550508 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.6262i | 2.62237i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.45965i | − | 1.19953i | −0.800177 | − | 0.599763i | \(-0.795261\pi\) | ||
0.800177 | − | 0.599763i | \(-0.204739\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17429i | 0.210909i | 0.994424 | + | 0.105454i | \(0.0336297\pi\) | ||||
−0.994424 | + | 0.105454i | \(0.966370\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.89046 | 0.329087 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.34380 | 0.734237 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.792669i | 0.130314i | 0.997875 | + | 0.0651570i | \(0.0207548\pi\) | ||||
−0.997875 | + | 0.0651570i | \(0.979245\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 19.8166i | − | 3.17319i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.09509i | − | 0.483372i | −0.970355 | − | 0.241686i | \(-0.922300\pi\) | ||
0.970355 | − | 0.241686i | \(-0.0777003\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.984651 | −0.150158 | −0.0750789 | − | 0.997178i | \(-0.523921\pi\) | ||||
−0.0750789 | + | 0.997178i | \(0.523921\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.8765i | 1.62137i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.2473 | 1.64059 | 0.820295 | − | 0.571940i | \(-0.193809\pi\) | ||||
0.820295 | + | 0.571940i | \(0.193809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.39553 | −0.199362 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.11131 | − | 12.1742i | −0.715727 | − | 1.70473i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.09299 | −0.562216 | −0.281108 | − | 0.959676i | \(-0.590702\pi\) | ||||
−0.281108 | + | 0.959676i | \(0.590702\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.885003 | 0.119334 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.74056i | 1.02526i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.04025i | 1.02945i | 0.857356 | + | 0.514725i | \(0.172106\pi\) | ||||
−0.857356 | + | 0.514725i | \(0.827894\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 21.0216i | − | 2.64847i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 9.27696i | − | 1.15066i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.0346 | −1.59243 | −0.796217 | − | 0.605011i | \(-0.793169\pi\) | ||||
−0.796217 | + | 0.605011i | \(0.793169\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −20.5494 | −2.47386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.20065i | − | 0.854560i | −0.904119 | − | 0.427280i | \(-0.859472\pi\) | ||
0.904119 | − | 0.427280i | \(-0.140528\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.29579i | 0.385743i | 0.981224 | + | 0.192871i | \(0.0617800\pi\) | ||||
−0.981224 | + | 0.192871i | \(0.938220\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 8.81460i | − | 1.01782i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.71050 | −0.194929 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 10.9932i | − | 1.23683i | −0.785852 | − | 0.618414i | \(-0.787775\pi\) | ||
0.785852 | − | 0.618414i | \(-0.212225\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 21.8708 | 2.43009 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.87501 | 0.205809 | 0.102904 | − | 0.994691i | \(-0.467186\pi\) | ||||
0.102904 | + | 0.994691i | \(0.467186\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.39282 | − | 5.69924i | −0.259537 | − | 0.618169i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.6861 | −2.21778 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.40337 | −0.254756 | −0.127378 | − | 0.991854i | \(-0.540656\pi\) | ||||
−0.127378 | + | 0.991854i | \(0.540656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.9301i | 1.87959i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.76049 | 0.389945 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.62367i | 0.371781i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.0905i | − | 1.12607i | −0.826432 | − | 0.563037i | \(-0.809633\pi\) | ||
0.826432 | − | 0.563037i | \(-0.190367\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.28292i | − | 0.430450i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.857720 | −0.0853463 | −0.0426732 | − | 0.999089i | \(-0.513587\pi\) | ||||
−0.0426732 | + | 0.999089i | \(0.513587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.74585 | 0.467623 | 0.233811 | − | 0.972282i | \(-0.424880\pi\) | ||||
0.233811 | + | 0.972282i | \(0.424880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 13.9104i | − | 1.35752i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.06741i | − | 0.489885i | −0.969538 | − | 0.244942i | \(-0.921231\pi\) | ||
0.969538 | − | 0.244942i | \(-0.0787691\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.53677i | − | 0.817674i | −0.912607 | − | 0.408837i | \(-0.865934\pi\) | ||
0.912607 | − | 0.408837i | \(-0.134066\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.53841 | 0.240935 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.83003i | − | 0.642515i | −0.946992 | − | 0.321258i | \(-0.895894\pi\) | ||
0.946992 | − | 0.321258i | \(-0.104106\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.62002 | −0.897072 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −44.8953 | −4.15057 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.62474 | + | 11.0153i | 0.423949 | + | 1.00977i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6515 | 0.968319 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.91157 | −0.893696 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.6222i | − | 1.03953i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −20.7281 | −1.83932 | −0.919660 | − | 0.392716i | \(-0.871536\pi\) | ||||
−0.919660 | + | 0.392716i | \(0.871536\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.15320i | 0.277624i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.975048i | 0.0851904i | 0.999092 | + | 0.0425952i | \(0.0135626\pi\) | ||||
−0.999092 | + | 0.0425952i | \(0.986437\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 7.00369i | − | 0.607297i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.4278 | 1.75815 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.17245 | −0.527348 | −0.263674 | − | 0.964612i | \(-0.584934\pi\) | ||||
−0.263674 | + | 0.964612i | \(0.584934\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.3370i | 1.21605i | 0.793918 | + | 0.608025i | \(0.208038\pi\) | ||||
−0.793918 | + | 0.608025i | \(0.791962\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 36.0179i | − | 3.03325i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.65307i | 0.305485i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.68401 | −0.804213 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.46899i | 0.368596i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.5727 | 0.866146 | 0.433073 | − | 0.901359i | \(-0.357429\pi\) | ||||
0.433073 | + | 0.901359i | \(0.357429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.52537 | −0.693785 | −0.346893 | − | 0.937905i | \(-0.612763\pi\) | ||||
−0.346893 | + | 0.937905i | \(0.612763\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27.5811 | + | 11.5799i | −2.22980 | + | 0.936179i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.76044 | 0.141402 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.33072 | −0.265820 | −0.132910 | − | 0.991128i | \(-0.542432\pi\) | ||||
−0.132910 | + | 0.991128i | \(0.542432\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.1072i | 1.03947i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.5932 | 1.46535 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 18.0669i | − | 1.41511i | −0.706660 | − | 0.707553i | \(-0.749799\pi\) | ||
0.706660 | − | 0.707553i | \(-0.250201\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 2.83409i | − | 0.220634i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.7391i | 1.60484i | 0.596760 | + | 0.802420i | \(0.296455\pi\) | ||||
−0.596760 | + | 0.802420i | \(0.703545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.2929 | 1.94561 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.5366 | 1.34105 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 23.2415i | − | 1.76702i | −0.468413 | − | 0.883509i | \(-0.655174\pi\) | ||
0.468413 | − | 0.883509i | \(-0.344826\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.97549i | 0.602891i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 3.20235i | − | 0.240704i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.61019 | −0.344582 | −0.172291 | − | 0.985046i | \(-0.555117\pi\) | ||||
−0.172291 | + | 0.985046i | \(0.555117\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.3108i | − | 0.989385i | −0.869068 | − | 0.494693i | \(-0.835281\pi\) | ||
0.869068 | − | 0.494693i | \(-0.164719\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 25.7477 | 1.90333 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.18833 | 0.0873680 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.942240 | + | 2.24424i | 0.0689034 | + | 0.164115i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −39.4821 | −2.87190 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.20553 | −0.304301 | −0.152151 | − | 0.988357i | \(-0.548620\pi\) | ||||
−0.152151 | + | 0.988357i | \(0.548620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.59831i | 0.690902i | 0.938437 | + | 0.345451i | \(0.112274\pi\) | ||||
−0.938437 | + | 0.345451i | \(0.887726\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −29.7081 | −2.12744 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.91120i | 0.563649i | 0.959466 | + | 0.281825i | \(0.0909397\pi\) | ||||
−0.959466 | + | 0.281825i | \(0.909060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.5702i | 0.820192i | 0.912042 | + | 0.410096i | \(0.134505\pi\) | ||||
−0.912042 | + | 0.410096i | \(0.865495\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 41.7415i | 2.94422i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.7169 | 1.31367 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.64001 | −0.324073 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 46.5556i | 3.23583i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.42693i | − | 0.0987025i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.58369i | 0.522083i | 0.965328 | + | 0.261041i | \(0.0840659\pi\) | ||||
−0.965328 | + | 0.261041i | \(0.915934\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.0590 | −1.57998 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.47614i | 0.100672i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.40251 | −0.230978 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.5543 | 0.713192 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.5250 | − | 9.87694i | 1.58246 | − | 0.664395i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.38200 | −0.226475 | −0.113238 | − | 0.993568i | \(-0.536122\pi\) | ||||
−0.113238 | + | 0.993568i | \(0.536122\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.9699 | −1.33132 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.0399i | 1.79470i | 0.441316 | + | 0.897352i | \(0.354512\pi\) | ||||
−0.441316 | + | 0.897352i | \(0.645488\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.10125 | 0.535346 | 0.267673 | − | 0.963510i | \(-0.413745\pi\) | ||||
0.267673 | + | 0.963510i | \(0.413745\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.47762i | 0.360401i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.2230i | 1.84895i | 0.381240 | + | 0.924476i | \(0.375497\pi\) | ||||
−0.381240 | + | 0.924476i | \(0.624503\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 16.8615i | − | 1.09992i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −35.2040 | −2.28675 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.85304 | 0.443287 | 0.221643 | − | 0.975128i | \(-0.428858\pi\) | ||||
0.221643 | + | 0.975128i | \(0.428858\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2678i | 0.983485i | 0.870741 | + | 0.491743i | \(0.163640\pi\) | ||||
−0.870741 | + | 0.491743i | \(0.836360\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 29.1594i | − | 1.87057i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.09212i | 0.133660i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.9576 | −0.951730 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 6.00444i | − | 0.380516i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.2257 | 1.08728 | 0.543639 | − | 0.839319i | \(-0.317046\pi\) | ||||
0.543639 | + | 0.839319i | \(0.317046\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.78816 | 0.238160 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −18.2510 | + | 7.66264i | −1.14292 | + | 0.479853i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.3501 | −1.26941 | −0.634704 | − | 0.772756i | \(-0.718878\pi\) | ||||
−0.634704 | + | 0.772756i | \(0.718878\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.29676 | −0.142714 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 46.8652i | 2.90088i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −25.7298 | −1.58657 | −0.793285 | − | 0.608850i | \(-0.791631\pi\) | ||||
−0.793285 | + | 0.608850i | \(0.791631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.13602i | 0.376933i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.69643i | 0.471014i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 18.8539i | − | 1.14954i | −0.818314 | − | 0.574772i | \(-0.805091\pi\) | ||
0.818314 | − | 0.574772i | \(-0.194909\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.01751 | −0.304792 | −0.152396 | − | 0.988320i | \(-0.548699\pi\) | ||||
−0.152396 | + | 0.988320i | \(0.548699\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 57.4186 | 3.47513 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.62492i | 0.0979863i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.7009i | 1.12363i | 0.827263 | + | 0.561814i | \(0.189896\pi\) | ||||
−0.827263 | + | 0.561814i | \(0.810104\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8.51956i | − | 0.510053i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 26.0941 | 1.55664 | 0.778321 | − | 0.627867i | \(-0.216072\pi\) | ||||
0.778321 | + | 0.627867i | \(0.216072\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.86388i | 0.170240i | 0.996371 | + | 0.0851199i | \(0.0271273\pi\) | ||||
−0.996371 | + | 0.0851199i | \(0.972873\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.6043 | 0.687379 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.96803 | 0.529366 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.9049 | − | 12.1357i | 0.700286 | − | 0.713863i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.5158 | −2.08197 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.0831991 | −0.00486054 | −0.00243027 | − | 0.999997i | \(-0.500774\pi\) | ||||
−0.00243027 | + | 0.999997i | \(0.500774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1.49915i | − | 0.0872841i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.04404 | −0.466763 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 39.7090i | − | 2.29643i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 2.85303i | − | 0.164446i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.74672i | 0.157795i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0536 | 0.690186 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.09004 | 0.290504 | 0.145252 | − | 0.989395i | \(-0.453601\pi\) | ||||
0.145252 | + | 0.989395i | \(0.453601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 15.1979i | − | 0.864578i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 11.7670i | − | 0.667246i | −0.942707 | − | 0.333623i | \(-0.891729\pi\) | ||
0.942707 | − | 0.333623i | \(-0.108271\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.63405i | − | 0.205409i | −0.994712 | − | 0.102704i | \(-0.967250\pi\) | ||
0.994712 | − | 0.102704i | \(-0.0327495\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −31.5146 | −1.77565 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.13271i | 0.175950i | 0.996123 | + | 0.0879751i | \(0.0280396\pi\) | ||||
−0.996123 | + | 0.0879751i | \(0.971960\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.81336 | 0.213507 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.2276 | −0.905738 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.18911 | + | 3.85804i | −0.511296 | + | 0.214667i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.0331 | 0.944824 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.3378 | −1.51178 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 32.5892i | 1.79670i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.4901 | 0.961342 | 0.480671 | − | 0.876901i | \(-0.340393\pi\) | ||||
0.480671 | + | 0.876901i | \(0.340393\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 5.75087i | − | 0.315146i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.5409i | 1.06763i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 31.8398i | − | 1.73442i | −0.497940 | − | 0.867211i | \(-0.665910\pi\) | ||
0.497940 | − | 0.867211i | \(-0.334090\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.8722 | −1.18793 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.693225 | −0.0375402 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.2390i | 0.876822i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 30.8067i | 1.65858i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 19.6264i | − | 1.05360i | −0.849989 | − | 0.526800i | \(-0.823392\pi\) | ||
0.849989 | − | 0.526800i | \(-0.176608\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.5184 | −1.41950 | −0.709748 | − | 0.704455i | \(-0.751191\pi\) | ||||
−0.709748 | + | 0.704455i | \(0.751191\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 84.3209i | 4.50072i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.813971 | −0.0433233 | −0.0216617 | − | 0.999765i | \(-0.506896\pi\) | ||||
−0.0216617 | + | 0.999765i | \(0.506896\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.7949 | −0.572933 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.2747 | − | 14.8101i | 1.86694 | − | 0.783831i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.7778 | 1.62439 | 0.812196 | − | 0.583384i | \(-0.198272\pi\) | ||||
0.812196 | + | 0.583384i | \(0.198272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1574 | −0.692495 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 34.1099i | − | 1.79030i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.94089 | 0.258618 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.65170i | − | 0.0862179i | −0.999070 | − | 0.0431089i | \(-0.986274\pi\) | ||
0.999070 | − | 0.0431089i | \(-0.0137263\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 22.4551i | 1.16896i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 11.8595i | − | 0.615713i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.2501 | 1.35918 | 0.679589 | − | 0.733593i | \(-0.262158\pi\) | ||||
0.679589 | + | 0.733593i | \(0.262158\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −37.2185 | −1.92196 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 39.9731i | − | 2.05872i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.5132i | − | 0.796860i | −0.917199 | − | 0.398430i | \(-0.869555\pi\) | ||
0.917199 | − | 0.398430i | \(-0.130445\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 66.3787i | 3.40068i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.65909 | 0.135873 | 0.0679367 | − | 0.997690i | \(-0.478358\pi\) | ||||
0.0679367 | + | 0.997690i | \(0.478358\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.56430i | 0.130689i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.14371 | 0.363135 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.5116 | −1.49630 | −0.748148 | − | 0.663532i | \(-0.769057\pi\) | ||||
−0.748148 | + | 0.663532i | \(0.769057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2422 | − | 24.3950i | −0.517970 | − | 1.23371i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.12245 | 0.157507 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.4805 | −0.829222 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 1.50052i | − | 0.0753089i | −0.999291 | − | 0.0376544i | \(-0.988011\pi\) | ||
0.999291 | − | 0.0376544i | \(-0.0119886\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −22.4283 | −1.12282 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 33.6682i | − | 1.68131i | −0.541573 | − | 0.840654i | \(-0.682171\pi\) | ||
0.541573 | − | 0.840654i | \(-0.317829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.26666i | 0.361978i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 32.7877i | − | 1.62923i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.467940 | −0.0231949 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.2070 | −1.14751 | −0.573755 | − | 0.819027i | \(-0.694514\pi\) | ||||
−0.573755 | + | 0.819027i | \(0.694514\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.7664i | 0.975003i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.89750i | 0.142577i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.81093i | − | 0.137983i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 45.9122 | 2.24833 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 16.2702i | − | 0.794850i | −0.917635 | − | 0.397425i | \(-0.869904\pi\) | ||
0.917635 | − | 0.397425i | \(-0.130096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.79891 | 0.380096 | 0.190048 | − | 0.981775i | \(-0.439136\pi\) | ||||
0.190048 | + | 0.981775i | \(0.439136\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −81.6001 | −3.96753 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.4641 | − | 4.39336i | 0.507586 | − | 0.213109i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −23.2967 | −1.12741 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.6984 | 0.564805 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.39257i | 0.356088i | 0.984023 | + | 0.178044i | \(0.0569769\pi\) | ||||
−0.984023 | + | 0.178044i | \(0.943023\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.8433 | 1.43418 | 0.717089 | − | 0.696981i | \(-0.245474\pi\) | ||||
0.717089 | + | 0.696981i | \(0.245474\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.0116i | 1.48689i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.5108i | 0.741980i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3004i | 1.01661i | 0.861176 | + | 0.508307i | \(0.169729\pi\) | ||||
−0.861176 | + | 0.508307i | \(0.830271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.1247 | 0.482128 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.2734 | −1.43833 | −0.719166 | − | 0.694838i | \(-0.755476\pi\) | ||||
−0.719166 | + | 0.694838i | \(0.755476\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.60302i | 0.170799i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 33.8574i | − | 1.60140i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.03317i | − | 0.190337i | −0.995461 | − | 0.0951685i | \(-0.969661\pi\) | ||
0.995461 | − | 0.0951685i | \(-0.0303390\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.82714 | 0.0860366 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.3013i | 1.28273i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 26.8800 | 1.26015 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.7730 | 0.597495 | 0.298748 | − | 0.954332i | \(-0.403431\pi\) | ||||
0.298748 | + | 0.954332i | \(0.403431\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.7490 | + | 51.8020i | 1.01516 | + | 2.41791i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.1186 | 0.471269 | 0.235634 | − | 0.971842i | \(-0.424283\pi\) | ||||
0.235634 | + | 0.971842i | \(0.424283\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.2242 | 0.893422 | 0.446711 | − | 0.894678i | \(-0.352595\pi\) | ||||
0.446711 | + | 0.894678i | \(0.352595\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 5.63756i | − | 0.261435i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.98823 | −0.369651 | −0.184826 | − | 0.982771i | \(-0.559172\pi\) | ||||
−0.184826 | + | 0.982771i | \(0.559172\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 37.7679i | − | 1.74396i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10.6661i | 0.491470i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 0.581274i | − | 0.0267270i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.65329 | −0.305274 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 29.6949 | 1.35964 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 31.4216i | 1.43569i | 0.696202 | + | 0.717846i | \(0.254872\pi\) | ||||
−0.696202 | + | 0.717846i | \(0.745128\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.90514i | 0.223655i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 59.5420i | − | 2.70925i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.6264 | −0.754967 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.3236i | 0.966266i | 0.875547 | + | 0.483133i | \(0.160501\pi\) | ||||
−0.875547 | + | 0.483133i | \(0.839499\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −57.8565 | −2.61636 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.32703 | −0.330664 | −0.165332 | − | 0.986238i | \(-0.552870\pi\) | ||||
−0.165332 | + | 0.986238i | \(0.552870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.3103 | − | 24.5572i | −0.464353 | − | 1.10600i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.42076 | −0.288592 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.8639 | 0.935874 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 37.5609i | − | 1.68146i | −0.541457 | − | 0.840729i | \(-0.682127\pi\) | ||
0.541457 | − | 0.840729i | \(-0.317873\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 66.4139 | 2.96716 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 24.6177i | − | 1.09765i | −0.835937 | − | 0.548825i | \(-0.815075\pi\) | ||
0.835937 | − | 0.548825i | \(-0.184925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.28585i | 0.0572198i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 80.9970i | − | 3.59720i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.0162 | 0.488285 | 0.244143 | − | 0.969739i | \(-0.421493\pi\) | ||||
0.244143 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.54956 | −0.422448 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 32.9366i | − | 1.45419i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 7.11476i | − | 0.313514i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.63969i | 0.292013i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −74.4275 | −3.26701 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 31.0672i | − | 1.36108i | −0.732711 | − | 0.680539i | \(-0.761745\pi\) | ||
0.732711 | − | 0.680539i | \(-0.238255\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.65603 | −0.0724131 | −0.0362066 | − | 0.999344i | \(-0.511527\pi\) | ||||
−0.0362066 | + | 0.999344i | \(0.511527\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 25.5403 | 1.11467 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.87430 | + | 4.46422i | 0.0816457 | + | 0.194465i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.1775 | −0.790326 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.25507 | −0.314843 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 19.1528i | − | 0.829600i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.59682 | −0.328439 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.7635i | 0.637091i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 0.823831i | − | 0.0354849i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 14.3785i | − | 0.618179i | −0.951033 | − | 0.309090i | \(-0.899976\pi\) | ||
0.951033 | − | 0.309090i | \(-0.100024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −42.6260 | −1.82925 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.7979 | −0.548203 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 31.8208i | − | 1.36056i | −0.732953 | − | 0.680279i | \(-0.761858\pi\) | ||
0.732953 | − | 0.680279i | \(-0.238142\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 58.3326i | − | 2.48957i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.6139i | 0.665175i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.8528 | 1.35452 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 3.80546i | − | 0.161533i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.4982 | 1.03802 | 0.519011 | − | 0.854767i | \(-0.326300\pi\) | ||||
0.519011 | + | 0.854767i | \(0.326300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.09315 | −0.257713 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.18684 | − | 3.01739i | 0.303429 | − | 0.127394i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.6707 | 1.20833 | 0.604163 | − | 0.796861i | \(-0.293508\pi\) | ||||
0.604163 | + | 0.796861i | \(0.293508\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.2393 | −0.430769 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 63.3708i | 2.66132i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.9326 | 1.42253 | 0.711265 | − | 0.702924i | \(-0.248123\pi\) | ||||
0.711265 | + | 0.702924i | \(0.248123\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 38.1381i | − | 1.59603i | −0.602637 | − | 0.798016i | \(-0.705883\pi\) | ||
0.602637 | − | 0.798016i | \(-0.294117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 13.4676i | 0.562617i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 17.6630i | − | 0.736596i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.2004 | 1.79845 | 0.899227 | − | 0.437481i | \(-0.144129\pi\) | ||||
0.899227 | + | 0.437481i | \(0.144129\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.7372 | 1.27739 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.43284i | 0.225392i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.41624i | − | 0.100070i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 67.3050i | 2.78272i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −41.9962 | −1.73337 | −0.866684 | − | 0.498857i | \(-0.833753\pi\) | ||||
−0.866684 | + | 0.498857i | \(0.833753\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 2.83843i | − | 0.116956i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 25.3345 | 1.04212 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.6415 | 0.642319 | 0.321160 | − | 0.947025i | \(-0.395927\pi\) | ||||
0.321160 | + | 0.947025i | \(0.395927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 16.5136 | − | 6.93320i | 0.676990 | − | 0.284233i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 37.0520 | 1.51644 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −45.3050 | −1.85111 | −0.925556 | − | 0.378611i | \(-0.876402\pi\) | ||||
−0.925556 | + | 0.378611i | \(0.876402\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.2217i | 0.865650i | 0.901478 | + | 0.432825i | \(0.142483\pi\) | ||||
−0.901478 | + | 0.432825i | \(0.857517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 94.5672 | 3.85107 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 15.9682i | − | 0.649201i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.1740i | 1.02178i | 0.859646 | + | 0.510890i | \(0.170684\pi\) | ||||
−0.859646 | + | 0.510890i | \(0.829316\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 59.9380i | − | 2.42881i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 69.5999 | 2.81571 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −46.0852 | −1.86136 | −0.930681 | − | 0.365831i | \(-0.880785\pi\) | ||||
−0.930681 | + | 0.365831i | \(0.880785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14.8590i | 0.599171i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 9.76642i | − | 0.393181i | −0.980486 | − | 0.196591i | \(-0.937013\pi\) | ||
0.980486 | − | 0.196591i | \(-0.0629870\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.7517i | 0.954661i | 0.878724 | + | 0.477330i | \(0.158395\pi\) | ||||
−0.878724 | + | 0.477330i | \(0.841605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 87.4391 | 3.50881 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.96377i | − | 0.278997i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.66084 | −0.146434 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.56952 | −0.182489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.26519 | + | 3.01344i | 0.0504464 | + | 0.120154i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.4965 | −1.45290 | −0.726452 | − | 0.687217i | \(-0.758832\pi\) | ||||
−0.726452 | + | 0.687217i | \(0.758832\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.2856 | 0.965268 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.0746i | 1.23316i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.63573 | −0.342160 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 52.2412i | 2.06663i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.05177i | 0.318026i | 0.987277 | + | 0.159013i | \(0.0508311\pi\) | ||||
−0.987277 | + | 0.159013i | \(0.949169\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 36.0512i | − | 1.42172i | −0.703333 | − | 0.710860i | \(-0.748306\pi\) | ||
0.703333 | − | 0.710860i | \(-0.251694\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.72713 | 0.186131 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 46.2667 | 1.81893 | 0.909466 | − | 0.415779i | \(-0.136491\pi\) | ||||
0.909466 | + | 0.415779i | \(0.136491\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.590335i | 0.0231727i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.8960i | 0.427050i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.21066i | − | 0.0865098i | −0.999064 | − | 0.0432549i | \(-0.986227\pi\) | ||
0.999064 | − | 0.0432549i | \(-0.0137728\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.46175 | 0.0571152 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 23.9112i | − | 0.932863i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.0082 | −1.05209 | −0.526045 | − | 0.850456i | \(-0.676326\pi\) | ||||
−0.526045 | + | 0.850456i | \(0.676326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.1698 | −0.745619 | −0.372809 | − | 0.927908i | \(-0.621605\pi\) | ||||
−0.372809 | + | 0.927908i | \(0.621605\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −31.6295 | − | 75.3354i | −1.22839 | − | 2.92578i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.4996 | −0.407157 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.4514 | −1.60500 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.8304i | 0.418726i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.74644 | −0.183234 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 41.4412i | 1.59744i | 0.601701 | + | 0.798721i | \(0.294490\pi\) | ||||
−0.601701 | + | 0.798721i | \(0.705510\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 37.5067i | 1.44363i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.0301i | 0.385487i | 0.981249 | + | 0.192744i | \(0.0617386\pi\) | ||||
−0.981249 | + | 0.192744i | \(0.938261\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.1349 | 1.23322 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 86.5914 | 3.31819 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.2890i | − | 0.585017i | −0.956263 | − | 0.292508i | \(-0.905510\pi\) | ||
0.956263 | − | 0.292508i | \(-0.0944900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.25345i | 0.353556i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 25.9431i | − | 0.989790i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25.3280 | −0.964919 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.95101i | 0.226387i | 0.993573 | + | 0.113194i | \(0.0361080\pi\) | ||||
−0.993573 | + | 0.113194i | \(0.963892\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.4098 | 0.471409 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.4934 | 0.815290 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.94011 | − | 11.7664i | −0.187120 | − | 0.445684i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 90.3801 | 3.41849 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.9093 | 0.638657 | 0.319328 | − | 0.947644i | \(-0.396543\pi\) | ||||
0.319328 | + | 0.947644i | \(0.396543\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.91600i | − | 0.0722632i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −53.9964 | −2.03362 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 2.48525i | − | 0.0934673i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.6584i | 0.850955i | 0.904969 | + | 0.425477i | \(0.139894\pi\) | ||||
−0.904969 | + | 0.425477i | \(0.860106\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 79.7562i | 2.99109i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.53539 | 0.282202 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.47651 | 0.204810 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 21.9459i | − | 0.819584i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.00790i | 0.0748820i | 0.999299 | + | 0.0374410i | \(0.0119206\pi\) | ||||
−0.999299 | + | 0.0374410i | \(0.988079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.7511i | 0.512119i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48.8929 | 1.81835 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 17.7804i | − | 0.660349i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.8763 | 1.18223 | 0.591114 | − | 0.806588i | \(-0.298688\pi\) | ||||
0.591114 | + | 0.806588i | \(0.298688\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.7662 | −1.02838 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.74328 | + | 1.57161i | −0.138450 | + | 0.0581282i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.5568 | 0.870090 | 0.435045 | − | 0.900409i | \(-0.356733\pi\) | ||||
0.435045 | + | 0.900409i | \(0.356733\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.69970 | 0.247122 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.69480i | − | 0.283442i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.97202 | 0.219684 | 0.109842 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109842 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 47.8996i | 1.75963i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 14.0233i | − | 0.514464i | −0.966350 | − | 0.257232i | \(-0.917190\pi\) | ||
0.966350 | − | 0.257232i | \(-0.0828104\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 15.8500i | − | 0.580701i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.6033 | −0.497719 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.6828 | 0.536499 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 22.4155i | − | 0.817952i | −0.912545 | − | 0.408976i | \(-0.865886\pi\) | ||
0.912545 | − | 0.408976i | \(-0.134114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 55.1629i | − | 2.01025i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.7808i | 0.465143i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.72469 | −0.208067 | −0.104034 | − | 0.994574i | \(-0.533175\pi\) | ||||
−0.104034 | + | 0.994574i | \(0.533175\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 12.1310i | − | 0.440329i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.4142 | −1.42876 | −0.714382 | − | 0.699756i | \(-0.753292\pi\) | ||||
−0.714382 | + | 0.699756i | \(0.753292\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.7353 | 0.895479 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.3600 | + | 41.3483i | 0.627654 | + | 1.49495i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.18813 | 0.223440 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.7805 | 0.677243 | 0.338621 | − | 0.940923i | \(-0.390039\pi\) | ||||
0.338621 | + | 0.940923i | \(0.390039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 65.1684i | 2.34698i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.6069 | −0.525373 | −0.262686 | − | 0.964881i | \(-0.584608\pi\) | ||||
−0.262686 | + | 0.964881i | \(0.584608\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.23228i | 0.116107i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.35505i | 0.263861i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.48128i | 0.268045i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.25079 | 0.152105 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 88.0207 | 3.14560 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.99326i | 0.178217i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 19.0872i | − | 0.680385i | −0.940356 | − | 0.340193i | \(-0.889508\pi\) | ||
0.940356 | − | 0.340193i | \(-0.110492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 82.3961i | 2.93338i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.7900 | 0.703653 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 49.7541i | 1.76682i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.6497 | 0.696904 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 45.9369 | 1.62717 | 0.813585 | − | 0.581446i | \(-0.197513\pi\) | ||||
0.813585 | + | 0.581446i | \(0.197513\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.7582 | − | 17.9520i | 1.51268 | − | 0.635095i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.4366 | 0.616092 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.94562 | −0.0686594 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 27.8741i | − | 0.982432i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −60.3769 | −2.12537 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.1847i | 0.744815i | 0.928069 | + | 0.372407i | \(0.121468\pi\) | ||||
−0.928069 | + | 0.372407i | \(0.878532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 8.56239i | − | 0.300666i | −0.988635 | − | 0.150333i | \(-0.951965\pi\) | ||
0.988635 | − | 0.150333i | \(-0.0480346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16.0678i | 0.563524i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.0850 | −0.948747 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.38004 | 0.0832672 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 130.084i | − | 4.54551i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.48649i | 0.0518787i | 0.999664 | + | 0.0259394i | \(0.00825769\pi\) | ||||
−0.999664 | + | 0.0259394i | \(0.991742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.24387i | − | 0.0782165i | −0.999235 | − | 0.0391082i | \(-0.987548\pi\) | ||
0.999235 | − | 0.0391082i | \(-0.0124517\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.20357 | 0.181165 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.2912i | − | 0.427407i | −0.976899 | − | 0.213703i | \(-0.931447\pi\) | ||
0.976899 | − | 0.213703i | \(-0.0685526\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.1514 | −1.08193 | −0.540966 | − | 0.841044i | \(-0.681941\pi\) | ||||
−0.540966 | + | 0.841044i | \(0.681941\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 59.8869 | 2.07745 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.30530 | + | 2.22742i | −0.183818 | + | 0.0771757i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 31.0911 | 1.07595 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.0012 | −0.553081 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.1199i | 0.556520i | 0.960506 | + | 0.278260i | \(0.0897577\pi\) | ||||
−0.960506 | + | 0.278260i | \(0.910242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.7271 | −0.438864 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 83.5624i | − | 2.87804i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 37.9180i | − | 1.30442i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.8628i | 1.06046i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.17115 | 0.314753 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.08654 | 0.174364 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.1713i | 0.896089i | 0.894011 | + | 0.448044i | \(0.147879\pi\) | ||||
−0.894011 | + | 0.448044i | \(0.852121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 26.2900i | − | 0.899099i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.85281i | − | 0.0632906i | −0.999499 | − | 0.0316453i | \(-0.989925\pi\) | ||
0.999499 | − | 0.0316453i | \(-0.0100747\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.6434 | 0.431388 | 0.215694 | − | 0.976461i | \(-0.430799\pi\) | ||||
0.215694 | + | 0.976461i | \(0.430799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 28.7188i | − | 0.978735i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.4796 | 0.390771 | 0.195385 | − | 0.980727i | \(-0.437404\pi\) | ||||
0.195385 | + | 0.980727i | \(0.437404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.8426 | −1.18468 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.8627 | − | 38.1236i | −1.31985 | − | 1.29474i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.48965 | 0.220146 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −80.6600 | −2.73306 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 80.4626i | 2.72325i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 33.6755 | 1.13844 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.29481i | 0.145026i | 0.997367 | + | 0.0725128i | \(0.0231018\pi\) | ||||
−0.997367 | + | 0.0725128i | \(0.976898\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.266433i | 0.00898656i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.50320i | 0.185408i | 0.995694 | + | 0.0927038i | \(0.0295510\pi\) | ||||
−0.995694 | + | 0.0927038i | \(0.970449\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7553 | −1.10230 | −0.551152 | − | 0.834405i | \(-0.685812\pi\) | ||||
−0.551152 | + | 0.834405i | \(0.685812\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.80082 | −0.161378 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.34493i | 0.145888i | 0.997336 | + | 0.0729442i | \(0.0232395\pi\) | ||||
−0.997336 | + | 0.0729442i | \(0.976761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 60.0597i | − | 2.01434i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 12.9111i | 0.432538i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −27.1864 | −0.909759 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.91139i | 0.231022i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −127.162 | −4.24583 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.58550 | 0.252991 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.5601 | + | 6.53287i | −0.518381 | + | 0.217642i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.13641 | −0.304041 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.9550 | −0.663325 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.1491i | 1.49915i | 0.661918 | + | 0.749576i | \(0.269742\pi\) | ||||
−0.661918 | + | 0.749576i | \(0.730258\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.22282 | 0.206398 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.6582i | 1.28080i | 0.768040 | + | 0.640402i | \(0.221232\pi\) | ||||
−0.768040 | + | 0.640402i | \(0.778768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.10688i | 0.0366325i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 38.5998i | − | 1.27607i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.82521 | −0.0932965 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.7236 | 0.551659 | 0.275830 | − | 0.961207i | \(-0.411047\pi\) | ||||
0.275830 | + | 0.961207i | \(0.411047\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 16.3001i | − | 0.537106i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 44.5585i | − | 1.46666i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.18185i | 0.0717389i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −34.4315 | −1.13088 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 27.9001i | − | 0.915374i | −0.889114 | − | 0.457687i | \(-0.848678\pi\) | ||
0.889114 | − | 0.457687i | \(-0.151322\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.37320 | 0.110552 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37.6821 | −1.23366 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.36446 | − | 1.41256i | 0.110030 | − | 0.0461958i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.3629 | −0.501883 | −0.250942 | − | 0.968002i | \(-0.580740\pi\) | ||||
−0.250942 | + | 0.968002i | \(0.580740\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.6375 | −0.379776 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.6804i | 0.478567i | 0.970950 | + | 0.239284i | \(0.0769126\pi\) | ||||
−0.970950 | + | 0.239284i | \(0.923087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.8611 | −0.646766 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 59.1897i | 1.92544i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.4847i | 1.21809i | 0.793136 | + | 0.609045i | \(0.208447\pi\) | ||||
−0.793136 | + | 0.609045i | \(0.791553\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.3948i | 0.662042i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.0320 | 0.325311 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.8596 | −1.12921 | −0.564606 | − | 0.825360i | \(-0.690972\pi\) | ||||
−0.564606 | + | 0.825360i | \(0.690972\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.30473i | 0.204016i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 12.2117i | − | 0.394749i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 17.8847i | − | 0.577527i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6210 | 0.955517 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 36.7644i | 1.18472i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.3893 | 0.463209 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −60.2590 | −1.93780 | −0.968899 | − | 0.247458i | \(-0.920405\pi\) | ||||
−0.968899 | + | 0.247458i | \(0.920405\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.3548 | + | 29.4268i | 0.396893 | + | 0.945324i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.0207 | −0.899227 | −0.449613 | − | 0.893223i | \(-0.648438\pi\) | ||||
−0.449613 | + | 0.893223i | \(0.648438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −41.5415 | −1.33176 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 54.5459i | − | 1.74687i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.1381 | −0.932209 | −0.466105 | − | 0.884730i | \(-0.654343\pi\) | ||||
−0.466105 | + | 0.884730i | \(0.654343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.41879i | − | 0.0453448i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 61.9348i | 1.97743i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 24.2661i | − | 0.773968i | −0.922086 | − | 0.386984i | \(-0.873517\pi\) | ||
0.922086 | − | 0.386984i | \(-0.126483\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.8601 | 0.377894 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 104.362 | 3.32188 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.31847i | 0.200916i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 49.1107i | 1.56005i | 0.625747 | + | 0.780026i | \(0.284794\pi\) | ||||
−0.625747 | + | 0.780026i | \(0.715206\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 56.0095i | − | 1.77741i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.3456 | 0.549891 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 29.3639i | − | 0.929965i | −0.885320 | − | 0.464983i | \(-0.846061\pi\) | ||
0.885320 | − | 0.464983i | \(-0.153939\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.8011 | −0.341732 |
(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 | 4012.2.b.b.237.2 | ✓ | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.45 | yes | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.2 | ✓ | 46 | 1.1 | even | 1 | trivial | |
4012.2.b.b.237.45 | yes | 46 | 17.16 | even | 2 | inner |