Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [349,2,Mod(348,349)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(349, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("349.348");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 349 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 349.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: | \(2.78677903054\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 348.11 | ||
Character | \(\chi\) | \(=\) | 349.348 |
Dual form | 349.2.b.b.348.16 |
$q$-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 \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.980996i | − | 0.693669i | −0.937926 | − | 0.346835i | \(-0.887257\pi\) | ||
0.937926 | − | 0.346835i | \(-0.112743\pi\) | |||||||
\(3\) | −2.39151 | −1.38074 | −0.690370 | − | 0.723456i | \(-0.742552\pi\) | ||||
−0.690370 | + | 0.723456i | \(0.742552\pi\) | |||||||
\(4\) | 1.03765 | 0.518823 | ||||||||
\(5\) | −1.59459 | −0.713124 | −0.356562 | − | 0.934272i | \(-0.616051\pi\) | ||||
−0.356562 | + | 0.934272i | \(0.616051\pi\) | |||||||
\(6\) | 2.34607i | 0.957777i | ||||||||
\(7\) | − | 3.49225i | − | 1.31995i | −0.751289 | − | 0.659974i | \(-0.770567\pi\) | ||
0.751289 | − | 0.659974i | \(-0.229433\pi\) | |||||||
\(8\) | − | 2.97992i | − | 1.05356i | ||||||
\(9\) | 2.71933 | 0.906445 | ||||||||
\(10\) | 1.56429i | 0.494672i | ||||||||
\(11\) | 5.72888i | 1.72732i | 0.504072 | + | 0.863662i | \(0.331835\pi\) | ||||
−0.504072 | + | 0.863662i | \(0.668165\pi\) | |||||||
\(12\) | −2.48154 | −0.716360 | ||||||||
\(13\) | − | 1.18640i | − | 0.329047i | −0.986373 | − | 0.164524i | \(-0.947391\pi\) | ||
0.986373 | − | 0.164524i | \(-0.0526086\pi\) | |||||||
\(14\) | −3.42589 | −0.915607 | ||||||||
\(15\) | 3.81349 | 0.984639 | ||||||||
\(16\) | −0.847998 | −0.211999 | ||||||||
\(17\) | −7.98398 | −1.93640 | −0.968200 | − | 0.250177i | \(-0.919511\pi\) | ||||
−0.968200 | + | 0.250177i | \(0.919511\pi\) | |||||||
\(18\) | − | 2.66766i | − | 0.628773i | ||||||
\(19\) | −4.33179 | −0.993781 | −0.496890 | − | 0.867813i | \(-0.665525\pi\) | ||||
−0.496890 | + | 0.867813i | \(0.665525\pi\) | |||||||
\(20\) | −1.65462 | −0.369985 | ||||||||
\(21\) | 8.35177i | 1.82251i | ||||||||
\(22\) | 5.62001 | 1.19819 | ||||||||
\(23\) | −4.74560 | −0.989525 | −0.494763 | − | 0.869028i | \(-0.664745\pi\) | ||||
−0.494763 | + | 0.869028i | \(0.664745\pi\) | |||||||
\(24\) | 7.12652i | 1.45469i | ||||||||
\(25\) | −2.45727 | −0.491455 | ||||||||
\(26\) | −1.16385 | −0.228250 | ||||||||
\(27\) | 0.671217 | 0.129176 | ||||||||
\(28\) | − | 3.62372i | − | 0.684819i | ||||||
\(29\) | 3.89895 | 0.724017 | 0.362008 | − | 0.932175i | \(-0.382091\pi\) | ||||
0.362008 | + | 0.932175i | \(0.382091\pi\) | |||||||
\(30\) | − | 3.74102i | − | 0.683014i | ||||||
\(31\) | −7.04162 | −1.26471 | −0.632356 | − | 0.774678i | \(-0.717912\pi\) | ||||
−0.632356 | + | 0.774678i | \(0.717912\pi\) | |||||||
\(32\) | − | 5.12796i | − | 0.906503i | ||||||
\(33\) | − | 13.7007i | − | 2.38499i | ||||||
\(34\) | 7.83226i | 1.34322i | ||||||||
\(35\) | 5.56872i | 0.941286i | ||||||||
\(36\) | 2.82171 | 0.470284 | ||||||||
\(37\) | 4.56742 | 0.750879 | 0.375440 | − | 0.926847i | \(-0.377492\pi\) | ||||
0.375440 | + | 0.926847i | \(0.377492\pi\) | |||||||
\(38\) | 4.24947i | 0.689355i | ||||||||
\(39\) | 2.83728i | 0.454329i | ||||||||
\(40\) | 4.75176i | 0.751319i | ||||||||
\(41\) | 6.92928 | 1.08217 | 0.541086 | − | 0.840967i | \(-0.318013\pi\) | ||||
0.541086 | + | 0.840967i | \(0.318013\pi\) | |||||||
\(42\) | 8.19305 | 1.26422 | ||||||||
\(43\) | − | 3.20900i | − | 0.489368i | −0.969603 | − | 0.244684i | \(-0.921316\pi\) | ||
0.969603 | − | 0.244684i | \(-0.0786842\pi\) | |||||||
\(44\) | 5.94456i | 0.896175i | ||||||||
\(45\) | −4.33623 | −0.646407 | ||||||||
\(46\) | 4.65541i | 0.686403i | ||||||||
\(47\) | 9.60778i | 1.40144i | 0.713437 | + | 0.700720i | \(0.247138\pi\) | ||||
−0.713437 | + | 0.700720i | \(0.752862\pi\) | |||||||
\(48\) | 2.02800 | 0.292716 | ||||||||
\(49\) | −5.19583 | −0.742261 | ||||||||
\(50\) | 2.41058i | 0.340907i | ||||||||
\(51\) | 19.0938 | 2.67367 | ||||||||
\(52\) | − | 1.23106i | − | 0.170717i | ||||||
\(53\) | − | 4.11388i | − | 0.565085i | −0.959255 | − | 0.282543i | \(-0.908822\pi\) | ||
0.959255 | − | 0.282543i | \(-0.0911779\pi\) | |||||||
\(54\) | − | 0.658461i | − | 0.0896052i | ||||||
\(55\) | − | 9.13524i | − | 1.23180i | ||||||
\(56\) | −10.4066 | −1.39064 | ||||||||
\(57\) | 10.3595 | 1.37215 | ||||||||
\(58\) | − | 3.82486i | − | 0.502228i | ||||||
\(59\) | − | 10.5501i | − | 1.37350i | −0.726893 | − | 0.686751i | \(-0.759036\pi\) | ||
0.726893 | − | 0.686751i | \(-0.240964\pi\) | |||||||
\(60\) | 3.95705 | 0.510853 | ||||||||
\(61\) | − | 14.5748i | − | 1.86612i | −0.359726 | − | 0.933058i | \(-0.617130\pi\) | ||
0.359726 | − | 0.933058i | \(-0.382870\pi\) | |||||||
\(62\) | 6.90780i | 0.877291i | ||||||||
\(63\) | − | 9.49660i | − | 1.19646i | ||||||
\(64\) | −6.72650 | −0.840813 | ||||||||
\(65\) | 1.89182i | 0.234651i | ||||||||
\(66\) | −13.4403 | −1.65439 | ||||||||
\(67\) | −2.31537 | −0.282867 | −0.141433 | − | 0.989948i | \(-0.545171\pi\) | ||||
−0.141433 | + | 0.989948i | \(0.545171\pi\) | |||||||
\(68\) | −8.28455 | −1.00465 | ||||||||
\(69\) | 11.3492 | 1.36628 | ||||||||
\(70\) | 5.46290 | 0.652941 | ||||||||
\(71\) | 2.98972i | 0.354814i | 0.984138 | + | 0.177407i | \(0.0567709\pi\) | ||||
−0.984138 | + | 0.177407i | \(0.943229\pi\) | |||||||
\(72\) | − | 8.10340i | − | 0.954994i | ||||||
\(73\) | 5.97802 | 0.699674 | 0.349837 | − | 0.936811i | \(-0.386237\pi\) | ||||
0.349837 | + | 0.936811i | \(0.386237\pi\) | |||||||
\(74\) | − | 4.48062i | − | 0.520862i | ||||||
\(75\) | 5.87660 | 0.678571 | ||||||||
\(76\) | −4.49487 | −0.515597 | ||||||||
\(77\) | 20.0067 | 2.27998 | ||||||||
\(78\) | 2.78336 | 0.315154 | ||||||||
\(79\) | − | 7.16874i | − | 0.806546i | −0.915080 | − | 0.403273i | \(-0.867873\pi\) | ||
0.915080 | − | 0.403273i | \(-0.132127\pi\) | |||||||
\(80\) | 1.35221 | 0.151182 | ||||||||
\(81\) | −9.76323 | −1.08480 | ||||||||
\(82\) | − | 6.79760i | − | 0.750669i | ||||||
\(83\) | −15.6039 | −1.71275 | −0.856374 | − | 0.516356i | \(-0.827288\pi\) | ||||
−0.856374 | + | 0.516356i | \(0.827288\pi\) | |||||||
\(84\) | 8.66618i | 0.945558i | ||||||||
\(85\) | 12.7312 | 1.38089 | ||||||||
\(86\) | −3.14802 | −0.339459 | ||||||||
\(87\) | −9.32439 | −0.999679 | ||||||||
\(88\) | 17.0716 | 1.81984 | ||||||||
\(89\) | − | 13.2842i | − | 1.40812i | −0.710138 | − | 0.704062i | \(-0.751368\pi\) | ||
0.710138 | − | 0.704062i | \(-0.248632\pi\) | |||||||
\(90\) | 4.25383i | 0.448393i | ||||||||
\(91\) | −4.14319 | −0.434325 | ||||||||
\(92\) | −4.92425 | −0.513389 | ||||||||
\(93\) | 16.8401 | 1.74624 | ||||||||
\(94\) | 9.42520 | 0.972135 | ||||||||
\(95\) | 6.90744 | 0.708689 | ||||||||
\(96\) | 12.2636i | 1.25165i | ||||||||
\(97\) | 0.486705i | 0.0494174i | 0.999695 | + | 0.0247087i | \(0.00786583\pi\) | ||||
−0.999695 | + | 0.0247087i | \(0.992134\pi\) | |||||||
\(98\) | 5.09709i | 0.514884i | ||||||||
\(99\) | 15.5787i | 1.56572i | ||||||||
\(100\) | −2.54978 | −0.254978 | ||||||||
\(101\) | 9.78271i | 0.973416i | 0.873565 | + | 0.486708i | \(0.161802\pi\) | ||||
−0.873565 | + | 0.486708i | \(0.838198\pi\) | |||||||
\(102\) | − | 18.7309i | − | 1.85464i | ||||||
\(103\) | 5.00860i | 0.493512i | 0.969078 | + | 0.246756i | \(0.0793646\pi\) | ||||
−0.969078 | + | 0.246756i | \(0.920635\pi\) | |||||||
\(104\) | −3.53537 | −0.346671 | ||||||||
\(105\) | − | 13.3177i | − | 1.29967i | ||||||
\(106\) | −4.03570 | −0.391982 | ||||||||
\(107\) | 18.0456i | 1.74453i | 0.489033 | + | 0.872266i | \(0.337350\pi\) | ||||
−0.489033 | + | 0.872266i | \(0.662650\pi\) | |||||||
\(108\) | 0.696486 | 0.0670194 | ||||||||
\(109\) | 4.49358 | 0.430407 | 0.215204 | − | 0.976569i | \(-0.430959\pi\) | ||||
0.215204 | + | 0.976569i | \(0.430959\pi\) | |||||||
\(110\) | −8.96164 | −0.854458 | ||||||||
\(111\) | −10.9230 | −1.03677 | ||||||||
\(112\) | 2.96142i | 0.279828i | ||||||||
\(113\) | − | 5.47325i | − | 0.514880i | −0.966294 | − | 0.257440i | \(-0.917121\pi\) | ||
0.966294 | − | 0.257440i | \(-0.0828790\pi\) | |||||||
\(114\) | − | 10.1627i | − | 0.951821i | ||||||
\(115\) | 7.56729 | 0.705654 | ||||||||
\(116\) | 4.04573 | 0.375637 | ||||||||
\(117\) | − | 3.22621i | − | 0.298263i | ||||||
\(118\) | −10.3496 | −0.952755 | ||||||||
\(119\) | 27.8821i | 2.55595i | ||||||||
\(120\) | − | 11.3639i | − | 1.03738i | ||||||
\(121\) | −21.8201 | −1.98365 | ||||||||
\(122\) | −14.2979 | −1.29447 | ||||||||
\(123\) | −16.5715 | −1.49420 | ||||||||
\(124\) | −7.30671 | −0.656162 | ||||||||
\(125\) | 11.8913 | 1.06359 | ||||||||
\(126\) | −9.31613 | −0.829947 | ||||||||
\(127\) | − | 4.67185i | − | 0.414559i | −0.978282 | − | 0.207280i | \(-0.933539\pi\) | ||
0.978282 | − | 0.207280i | \(-0.0664610\pi\) | |||||||
\(128\) | − | 3.65724i | − | 0.323257i | ||||||
\(129\) | 7.67436i | 0.675690i | ||||||||
\(130\) | 1.85587 | 0.162770 | ||||||||
\(131\) | − | 12.6227i | − | 1.10285i | −0.834226 | − | 0.551423i | \(-0.814085\pi\) | ||
0.834226 | − | 0.551423i | \(-0.185915\pi\) | |||||||
\(132\) | − | 14.2165i | − | 1.23739i | ||||||
\(133\) | 15.1277i | 1.31174i | ||||||||
\(134\) | 2.27137i | 0.196216i | ||||||||
\(135\) | −1.07032 | −0.0921183 | ||||||||
\(136\) | 23.7916i | 2.04012i | ||||||||
\(137\) | − | 17.3749i | − | 1.48444i | −0.670158 | − | 0.742218i | \(-0.733774\pi\) | ||
0.670158 | − | 0.742218i | \(-0.266226\pi\) | |||||||
\(138\) | − | 11.1335i | − | 0.947745i | ||||||
\(139\) | 9.56374 | 0.811185 | 0.405593 | − | 0.914054i | \(-0.367065\pi\) | ||||
0.405593 | + | 0.914054i | \(0.367065\pi\) | |||||||
\(140\) | 5.77836i | 0.488361i | ||||||||
\(141\) | − | 22.9771i | − | 1.93502i | ||||||
\(142\) | 2.93290 | 0.246124 | ||||||||
\(143\) | 6.79673 | 0.568371 | ||||||||
\(144\) | −2.30599 | −0.192166 | ||||||||
\(145\) | −6.21724 | −0.516314 | ||||||||
\(146\) | − | 5.86441i | − | 0.485342i | ||||||
\(147\) | 12.4259 | 1.02487 | ||||||||
\(148\) | 4.73937 | 0.389573 | ||||||||
\(149\) | 9.94243i | 0.814515i | 0.913313 | + | 0.407258i | \(0.133515\pi\) | ||||
−0.913313 | + | 0.407258i | \(0.866485\pi\) | |||||||
\(150\) | − | 5.76492i | − | 0.470704i | ||||||
\(151\) | −2.12122 | −0.172622 | −0.0863112 | − | 0.996268i | \(-0.527508\pi\) | ||||
−0.0863112 | + | 0.996268i | \(0.527508\pi\) | |||||||
\(152\) | 12.9084i | 1.04701i | ||||||||
\(153\) | −21.7111 | −1.75524 | ||||||||
\(154\) | − | 19.6265i | − | 1.58155i | ||||||
\(155\) | 11.2285 | 0.901896 | ||||||||
\(156\) | 2.94409i | 0.235716i | ||||||||
\(157\) | 5.66729 | 0.452299 | 0.226149 | − | 0.974093i | \(-0.427386\pi\) | ||||
0.226149 | + | 0.974093i | \(0.427386\pi\) | |||||||
\(158\) | −7.03250 | −0.559476 | ||||||||
\(159\) | 9.83841i | 0.780236i | ||||||||
\(160\) | 8.17700i | 0.646449i | ||||||||
\(161\) | 16.5728i | 1.30612i | ||||||||
\(162\) | 9.57769i | 0.752494i | ||||||||
\(163\) | 2.89238i | 0.226549i | 0.993564 | + | 0.113274i | \(0.0361339\pi\) | ||||
−0.993564 | + | 0.113274i | \(0.963866\pi\) | |||||||
\(164\) | 7.19014 | 0.561456 | ||||||||
\(165\) | 21.8470i | 1.70079i | ||||||||
\(166\) | 15.3073i | 1.18808i | ||||||||
\(167\) | 5.61638i | 0.434609i | 0.976104 | + | 0.217304i | \(0.0697264\pi\) | ||||
−0.976104 | + | 0.217304i | \(0.930274\pi\) | |||||||
\(168\) | 24.8876 | 1.92012 | ||||||||
\(169\) | 11.5925 | 0.891728 | ||||||||
\(170\) | − | 12.4893i | − | 0.957883i | ||||||
\(171\) | −11.7796 | −0.900807 | ||||||||
\(172\) | − | 3.32981i | − | 0.253895i | ||||||
\(173\) | − | 4.86677i | − | 0.370014i | −0.982737 | − | 0.185007i | \(-0.940769\pi\) | ||
0.982737 | − | 0.185007i | \(-0.0592307\pi\) | |||||||
\(174\) | 9.14719i | 0.693447i | ||||||||
\(175\) | 8.58142i | 0.648694i | ||||||||
\(176\) | − | 4.85808i | − | 0.366192i | ||||||
\(177\) | 25.2306i | 1.89645i | ||||||||
\(178\) | −13.0318 | −0.976772 | ||||||||
\(179\) | − | 13.8165i | − | 1.03269i | −0.856381 | − | 0.516345i | \(-0.827292\pi\) | ||
0.856381 | − | 0.516345i | \(-0.172708\pi\) | |||||||
\(180\) | −4.49947 | −0.335371 | ||||||||
\(181\) | −2.22392 | −0.165303 | −0.0826513 | − | 0.996579i | \(-0.526339\pi\) | ||||
−0.0826513 | + | 0.996579i | \(0.526339\pi\) | |||||||
\(182\) | 4.06446i | 0.301278i | ||||||||
\(183\) | 34.8559i | 2.57662i | ||||||||
\(184\) | 14.1415i | 1.04252i | ||||||||
\(185\) | −7.28317 | −0.535470 | ||||||||
\(186\) | − | 16.5201i | − | 1.21131i | ||||||
\(187\) | − | 45.7393i | − | 3.34479i | ||||||
\(188\) | 9.96948i | 0.727099i | ||||||||
\(189\) | − | 2.34406i | − | 0.170505i | ||||||
\(190\) | − | 6.77618i | − | 0.491595i | ||||||
\(191\) | −10.5192 | −0.761140 | −0.380570 | − | 0.924752i | \(-0.624272\pi\) | ||||
−0.380570 | + | 0.924752i | \(0.624272\pi\) | |||||||
\(192\) | 16.0865 | 1.16094 | ||||||||
\(193\) | 0.641023i | 0.0461418i | 0.999734 | + | 0.0230709i | \(0.00734435\pi\) | ||||
−0.999734 | + | 0.0230709i | \(0.992656\pi\) | |||||||
\(194\) | 0.477456 | 0.0342794 | ||||||||
\(195\) | − | 4.52431i | − | 0.323993i | ||||||
\(196\) | −5.39143 | −0.385102 | ||||||||
\(197\) | − | 15.4721i | − | 1.10234i | −0.834391 | − | 0.551172i | \(-0.814181\pi\) | ||
0.834391 | − | 0.551172i | \(-0.185819\pi\) | |||||||
\(198\) | 15.2827 | 1.08609 | ||||||||
\(199\) | − | 1.38720i | − | 0.0983358i | −0.998791 | − | 0.0491679i | \(-0.984343\pi\) | ||
0.998791 | − | 0.0491679i | \(-0.0156569\pi\) | |||||||
\(200\) | 7.32248i | 0.517777i | ||||||||
\(201\) | 5.53723 | 0.390566 | ||||||||
\(202\) | 9.59680 | 0.675229 | ||||||||
\(203\) | − | 13.6161i | − | 0.955664i | ||||||
\(204\) | 19.8126 | 1.38716 | ||||||||
\(205\) | −11.0494 | −0.771722 | ||||||||
\(206\) | 4.91342 | 0.342334 | ||||||||
\(207\) | −12.9049 | −0.896950 | ||||||||
\(208\) | 1.00606i | 0.0697578i | ||||||||
\(209\) | − | 24.8163i | − | 1.71658i | ||||||
\(210\) | −13.0646 | −0.901542 | ||||||||
\(211\) | 0.541778i | 0.0372975i | 0.999826 | + | 0.0186488i | \(0.00593643\pi\) | ||||
−0.999826 | + | 0.0186488i | \(0.994064\pi\) | |||||||
\(212\) | − | 4.26876i | − | 0.293179i | ||||||
\(213\) | − | 7.14995i | − | 0.489907i | ||||||
\(214\) | 17.7026 | 1.21013 | ||||||||
\(215\) | 5.11705i | 0.348980i | ||||||||
\(216\) | − | 2.00017i | − | 0.136095i | ||||||
\(217\) | 24.5911i | 1.66935i | ||||||||
\(218\) | − | 4.40819i | − | 0.298560i | ||||||
\(219\) | −14.2965 | −0.966068 | ||||||||
\(220\) | − | 9.47915i | − | 0.639084i | ||||||
\(221\) | 9.47217i | 0.637167i | ||||||||
\(222\) | 10.7155i | 0.719175i | ||||||||
\(223\) | −13.5560 | −0.907775 | −0.453887 | − | 0.891059i | \(-0.649963\pi\) | ||||
−0.453887 | + | 0.891059i | \(0.649963\pi\) | |||||||
\(224\) | −17.9081 | −1.19654 | ||||||||
\(225\) | −6.68215 | −0.445476 | ||||||||
\(226\) | −5.36924 | −0.357156 | ||||||||
\(227\) | −16.5742 | −1.10007 | −0.550033 | − | 0.835143i | \(-0.685385\pi\) | ||||
−0.550033 | + | 0.835143i | \(0.685385\pi\) | |||||||
\(228\) | 10.7495 | 0.711905 | ||||||||
\(229\) | 13.9969i | 0.924940i | 0.886635 | + | 0.462470i | \(0.153037\pi\) | ||||
−0.886635 | + | 0.462470i | \(0.846963\pi\) | |||||||
\(230\) | − | 7.42349i | − | 0.489490i | ||||||
\(231\) | −47.8463 | −3.14806 | ||||||||
\(232\) | − | 11.6186i | − | 0.762796i | ||||||
\(233\) | 15.3066 | 1.00277 | 0.501386 | − | 0.865224i | \(-0.332824\pi\) | ||||
0.501386 | + | 0.865224i | \(0.332824\pi\) | |||||||
\(234\) | −3.16490 | −0.206896 | ||||||||
\(235\) | − | 15.3205i | − | 0.999400i | ||||||
\(236\) | − | 10.9472i | − | 0.712604i | ||||||
\(237\) | 17.1441i | 1.11363i | ||||||||
\(238\) | 27.3522 | 1.77298 | ||||||||
\(239\) | −18.7774 | −1.21461 | −0.607304 | − | 0.794469i | \(-0.707749\pi\) | ||||
−0.607304 | + | 0.794469i | \(0.707749\pi\) | |||||||
\(240\) | −3.23383 | −0.208743 | ||||||||
\(241\) | −5.02258 | −0.323533 | −0.161766 | − | 0.986829i | \(-0.551719\pi\) | ||||
−0.161766 | + | 0.986829i | \(0.551719\pi\) | |||||||
\(242\) | 21.4055i | 1.37599i | ||||||||
\(243\) | 21.3352 | 1.36866 | ||||||||
\(244\) | − | 15.1235i | − | 0.968184i | ||||||
\(245\) | 8.28523 | 0.529324 | ||||||||
\(246\) | 16.2565i | 1.03648i | ||||||||
\(247\) | 5.13922i | 0.327001i | ||||||||
\(248\) | 20.9834i | 1.33245i | ||||||||
\(249\) | 37.3169 | 2.36486 | ||||||||
\(250\) | − | 11.6653i | − | 0.737781i | ||||||
\(251\) | − | 1.98249i | − | 0.125133i | −0.998041 | − | 0.0625667i | \(-0.980071\pi\) | ||
0.998041 | − | 0.0625667i | \(-0.0199286\pi\) | |||||||
\(252\) | − | 9.85411i | − | 0.620751i | ||||||
\(253\) | − | 27.1870i | − | 1.70923i | ||||||
\(254\) | −4.58306 | −0.287567 | ||||||||
\(255\) | −30.4468 | −1.90666 | ||||||||
\(256\) | −17.0407 | −1.06505 | ||||||||
\(257\) | −28.8615 | −1.80033 | −0.900166 | − | 0.435547i | \(-0.856555\pi\) | ||||
−0.900166 | + | 0.435547i | \(0.856555\pi\) | |||||||
\(258\) | 7.52852 | 0.468705 | ||||||||
\(259\) | − | 15.9506i | − | 0.991121i | ||||||
\(260\) | 1.96304i | 0.121742i | ||||||||
\(261\) | 10.6025 | 0.656281 | ||||||||
\(262\) | −12.3828 | −0.765011 | ||||||||
\(263\) | 0.463991 | 0.0286109 | 0.0143054 | − | 0.999898i | \(-0.495446\pi\) | ||||
0.0143054 | + | 0.999898i | \(0.495446\pi\) | |||||||
\(264\) | −40.8270 | −2.51273 | ||||||||
\(265\) | 6.55997i | 0.402976i | ||||||||
\(266\) | 14.8402 | 0.909913 | ||||||||
\(267\) | 31.7694i | 1.94425i | ||||||||
\(268\) | −2.40253 | −0.146758 | ||||||||
\(269\) | 0.424473 | 0.0258806 | 0.0129403 | − | 0.999916i | \(-0.495881\pi\) | ||||
0.0129403 | + | 0.999916i | \(0.495881\pi\) | |||||||
\(270\) | 1.04998i | 0.0638996i | ||||||||
\(271\) | 22.0294 | 1.33819 | 0.669097 | − | 0.743176i | \(-0.266681\pi\) | ||||
0.669097 | + | 0.743176i | \(0.266681\pi\) | |||||||
\(272\) | 6.77040 | 0.410516 | ||||||||
\(273\) | 9.90850 | 0.599690 | ||||||||
\(274\) | −17.0447 | −1.02971 | ||||||||
\(275\) | − | 14.0774i | − | 0.848901i | ||||||
\(276\) | 11.7764 | 0.708856 | ||||||||
\(277\) | 31.0689i | 1.86675i | 0.358901 | + | 0.933376i | \(0.383152\pi\) | ||||
−0.358901 | + | 0.933376i | \(0.616848\pi\) | |||||||
\(278\) | − | 9.38199i | − | 0.562694i | ||||||
\(279\) | −19.1485 | −1.14639 | ||||||||
\(280\) | 16.5943 | 0.991702 | ||||||||
\(281\) | −16.5425 | −0.986842 | −0.493421 | − | 0.869791i | \(-0.664254\pi\) | ||||
−0.493421 | + | 0.869791i | \(0.664254\pi\) | |||||||
\(282\) | −22.5405 | −1.34227 | ||||||||
\(283\) | 12.7168 | 0.755936 | 0.377968 | − | 0.925819i | \(-0.376623\pi\) | ||||
0.377968 | + | 0.925819i | \(0.376623\pi\) | |||||||
\(284\) | 3.10227i | 0.184086i | ||||||||
\(285\) | −16.5192 | −0.978515 | ||||||||
\(286\) | − | 6.66756i | − | 0.394261i | ||||||
\(287\) | − | 24.1988i | − | 1.42841i | ||||||
\(288\) | − | 13.9446i | − | 0.821695i | ||||||
\(289\) | 46.7440 | 2.74965 | ||||||||
\(290\) | 6.09909i | 0.358151i | ||||||||
\(291\) | − | 1.16396i | − | 0.0682327i | ||||||
\(292\) | 6.20307 | 0.363007 | ||||||||
\(293\) | 15.0794 | 0.880947 | 0.440473 | − | 0.897766i | \(-0.354811\pi\) | ||||
0.440473 | + | 0.897766i | \(0.354811\pi\) | |||||||
\(294\) | − | 12.1898i | − | 0.710921i | ||||||
\(295\) | 16.8231i | 0.979476i | ||||||||
\(296\) | − | 13.6105i | − | 0.791097i | ||||||
\(297\) | 3.84532i | 0.223128i | ||||||||
\(298\) | 9.75348 | 0.565004 | ||||||||
\(299\) | 5.63016i | 0.325600i | ||||||||
\(300\) | 6.09783 | 0.352059 | ||||||||
\(301\) | −11.2066 | −0.645940 | ||||||||
\(302\) | 2.08091i | 0.119743i | ||||||||
\(303\) | − | 23.3955i | − | 1.34404i | ||||||
\(304\) | 3.67335 | 0.210681 | ||||||||
\(305\) | 23.2409i | 1.33077i | ||||||||
\(306\) | 21.2985i | 1.21756i | ||||||||
\(307\) | −2.64152 | −0.150759 | −0.0753797 | − | 0.997155i | \(-0.524017\pi\) | ||||
−0.0753797 | + | 0.997155i | \(0.524017\pi\) | |||||||
\(308\) | 20.7599 | 1.18290 | ||||||||
\(309\) | − | 11.9781i | − | 0.681412i | ||||||
\(310\) | − | 11.0151i | − | 0.625617i | ||||||
\(311\) | 24.1439i | 1.36908i | 0.728977 | + | 0.684538i | \(0.239996\pi\) | ||||
−0.728977 | + | 0.684538i | \(0.760004\pi\) | |||||||
\(312\) | 8.45487 | 0.478663 | ||||||||
\(313\) | −13.0338 | −0.736712 | −0.368356 | − | 0.929685i | \(-0.620079\pi\) | ||||
−0.368356 | + | 0.929685i | \(0.620079\pi\) | |||||||
\(314\) | − | 5.55959i | − | 0.313746i | ||||||
\(315\) | 15.1432i | 0.853223i | ||||||||
\(316\) | − | 7.43861i | − | 0.418455i | ||||||
\(317\) | − | 4.71205i | − | 0.264655i | −0.991206 | − | 0.132328i | \(-0.957755\pi\) | ||
0.991206 | − | 0.132328i | \(-0.0422451\pi\) | |||||||
\(318\) | 9.65144 | 0.541226 | ||||||||
\(319\) | 22.3366i | 1.25061i | ||||||||
\(320\) | 10.7260 | 0.599603 | ||||||||
\(321\) | − | 43.1562i | − | 2.40874i | ||||||
\(322\) | 16.2579 | 0.906016 | ||||||||
\(323\) | 34.5849 | 1.92436 | ||||||||
\(324\) | −10.1308 | −0.562821 | ||||||||
\(325\) | 2.91530i | 0.161712i | ||||||||
\(326\) | 2.83741 | 0.157150 | ||||||||
\(327\) | −10.7465 | −0.594281 | ||||||||
\(328\) | − | 20.6487i | − | 1.14013i | ||||||
\(329\) | 33.5528 | 1.84983 | ||||||||
\(330\) | 21.4319 | 1.17979 | ||||||||
\(331\) | 13.4811i | 0.740986i | 0.928835 | + | 0.370493i | \(0.120811\pi\) | ||||
−0.928835 | + | 0.370493i | \(0.879189\pi\) | |||||||
\(332\) | −16.1913 | −0.888613 | ||||||||
\(333\) | 12.4203 | 0.680630 | ||||||||
\(334\) | 5.50965 | 0.301475 | ||||||||
\(335\) | 3.69207 | 0.201719 | ||||||||
\(336\) | − | 7.08228i | − | 0.386370i | ||||||
\(337\) | −0.532975 | −0.0290330 | −0.0145165 | − | 0.999895i | \(-0.504621\pi\) | ||||
−0.0145165 | + | 0.999895i | \(0.504621\pi\) | |||||||
\(338\) | − | 11.3722i | − | 0.618564i | ||||||
\(339\) | 13.0894i | 0.710916i | ||||||||
\(340\) | 13.2105 | 0.716439 | ||||||||
\(341\) | − | 40.3406i | − | 2.18457i | ||||||
\(342\) | 11.5557i | 0.624862i | ||||||||
\(343\) | − | 6.30062i | − | 0.340201i | ||||||
\(344\) | −9.56256 | −0.515579 | ||||||||
\(345\) | −18.0973 | −0.974325 | ||||||||
\(346\) | −4.77428 | −0.256667 | ||||||||
\(347\) | 4.83614i | 0.259617i | 0.991539 | + | 0.129809i | \(0.0414363\pi\) | ||||
−0.991539 | + | 0.129809i | \(0.958564\pi\) | |||||||
\(348\) | −9.67542 | −0.518657 | ||||||||
\(349\) | 16.2907 | + | 9.14396i | 0.872023 | + | 0.489465i | ||||
\(350\) | 8.41834 | 0.449979 | ||||||||
\(351\) | − | 0.796329i | − | 0.0425049i | ||||||
\(352\) | 29.3775 | 1.56582 | ||||||||
\(353\) | −24.0371 | −1.27936 | −0.639682 | − | 0.768640i | \(-0.720934\pi\) | ||||
−0.639682 | + | 0.768640i | \(0.720934\pi\) | |||||||
\(354\) | 24.7511 | 1.31551 | ||||||||
\(355\) | − | 4.76738i | − | 0.253026i | ||||||
\(356\) | − | 13.7843i | − | 0.730568i | ||||||
\(357\) | − | 66.6804i | − | 3.52910i | ||||||
\(358\) | −13.5539 | −0.716345 | ||||||||
\(359\) | − | 24.8277i | − | 1.31035i | −0.755475 | − | 0.655177i | \(-0.772594\pi\) | ||
0.755475 | − | 0.655177i | \(-0.227406\pi\) | |||||||
\(360\) | 12.9216i | 0.681029i | ||||||||
\(361\) | −0.235592 | −0.0123996 | ||||||||
\(362\) | 2.18166i | 0.114665i | ||||||||
\(363\) | 52.1831 | 2.73890 | ||||||||
\(364\) | −4.29917 | −0.225338 | ||||||||
\(365\) | −9.53250 | −0.498954 | ||||||||
\(366\) | 34.1935 | 1.78732 | ||||||||
\(367\) | − | 22.1347i | − | 1.15542i | −0.816242 | − | 0.577710i | \(-0.803946\pi\) | ||
0.816242 | − | 0.577710i | \(-0.196054\pi\) | |||||||
\(368\) | 4.02425 | 0.209779 | ||||||||
\(369\) | 18.8430 | 0.980929 | ||||||||
\(370\) | 7.14477i | 0.371439i | ||||||||
\(371\) | −14.3667 | −0.745883 | ||||||||
\(372\) | 17.4741 | 0.905989 | ||||||||
\(373\) | 26.5860i | 1.37657i | 0.725441 | + | 0.688284i | \(0.241636\pi\) | ||||
−0.725441 | + | 0.688284i | \(0.758364\pi\) | |||||||
\(374\) | −44.8701 | −2.32018 | ||||||||
\(375\) | −28.4382 | −1.46854 | ||||||||
\(376\) | 28.6304 | 1.47650 | ||||||||
\(377\) | − | 4.62570i | − | 0.238236i | ||||||
\(378\) | −2.29951 | −0.118274 | ||||||||
\(379\) | 11.7065i | 0.601323i | 0.953731 | + | 0.300662i | \(0.0972075\pi\) | ||||
−0.953731 | + | 0.300662i | \(0.902793\pi\) | |||||||
\(380\) | 7.16748 | 0.367684 | ||||||||
\(381\) | 11.1728i | 0.572399i | ||||||||
\(382\) | 10.3193i | 0.527979i | ||||||||
\(383\) | 5.62366i | 0.287356i | 0.989625 | + | 0.143678i | \(0.0458929\pi\) | ||||
−0.989625 | + | 0.143678i | \(0.954107\pi\) | |||||||
\(384\) | 8.74634i | 0.446335i | ||||||||
\(385\) | −31.9026 | −1.62591 | ||||||||
\(386\) | 0.628841 | 0.0320072 | ||||||||
\(387\) | − | 8.72634i | − | 0.443585i | ||||||
\(388\) | 0.505028i | 0.0256389i | ||||||||
\(389\) | − | 22.0957i | − | 1.12030i | −0.828392 | − | 0.560149i | \(-0.810744\pi\) | ||
0.828392 | − | 0.560149i | \(-0.189256\pi\) | |||||||
\(390\) | −4.43833 | −0.224744 | ||||||||
\(391\) | 37.8888 | 1.91612 | ||||||||
\(392\) | 15.4832i | 0.782017i | ||||||||
\(393\) | 30.1873i | 1.52275i | ||||||||
\(394\) | −15.1781 | −0.764663 | ||||||||
\(395\) | 11.4312i | 0.575167i | ||||||||
\(396\) | 16.1652i | 0.812333i | ||||||||
\(397\) | −0.306913 | −0.0154035 | −0.00770176 | − | 0.999970i | \(-0.502452\pi\) | ||||
−0.00770176 | + | 0.999970i | \(0.502452\pi\) | |||||||
\(398\) | −1.36084 | −0.0682125 | ||||||||
\(399\) | − | 36.1781i | − | 1.81117i | ||||||
\(400\) | 2.08376 | 0.104188 | ||||||||
\(401\) | 6.58218i | 0.328698i | 0.986402 | + | 0.164349i | \(0.0525524\pi\) | ||||
−0.986402 | + | 0.164349i | \(0.947448\pi\) | |||||||
\(402\) | − | 5.43200i | − | 0.270924i | ||||||
\(403\) | 8.35415i | 0.416150i | ||||||||
\(404\) | 10.1510i | 0.505031i | ||||||||
\(405\) | 15.5684 | 0.773599 | ||||||||
\(406\) | −13.3574 | −0.662915 | ||||||||
\(407\) | 26.1662i | 1.29701i | ||||||||
\(408\) | − | 56.8980i | − | 2.81687i | ||||||
\(409\) | −5.44638 | −0.269306 | −0.134653 | − | 0.990893i | \(-0.542992\pi\) | ||||
−0.134653 | + | 0.990893i | \(0.542992\pi\) | |||||||
\(410\) | 10.8394i | 0.535320i | ||||||||
\(411\) | 41.5523i | 2.04962i | ||||||||
\(412\) | 5.19715i | 0.256045i | ||||||||
\(413\) | −36.8435 | −1.81295 | ||||||||
\(414\) | 12.6596i | 0.622186i | ||||||||
\(415\) | 24.8818 | 1.22140 | ||||||||
\(416\) | −6.08379 | −0.298282 | ||||||||
\(417\) | −22.8718 | −1.12004 | ||||||||
\(418\) | −24.3447 | −1.19074 | ||||||||
\(419\) | −30.1276 | −1.47183 | −0.735915 | − | 0.677074i | \(-0.763248\pi\) | ||||
−0.735915 | + | 0.677074i | \(0.763248\pi\) | |||||||
\(420\) | − | 13.8190i | − | 0.674300i | ||||||
\(421\) | − | 14.7654i | − | 0.719619i | −0.933026 | − | 0.359810i | \(-0.882842\pi\) | ||
0.933026 | − | 0.359810i | \(-0.117158\pi\) | |||||||
\(422\) | 0.531482 | 0.0258721 | ||||||||
\(423\) | 26.1268i | 1.27033i | ||||||||
\(424\) | −12.2590 | −0.595352 | ||||||||
\(425\) | 19.6188 | 0.951653 | ||||||||
\(426\) | −7.01408 | −0.339833 | ||||||||
\(427\) | −50.8990 | −2.46318 | ||||||||
\(428\) | 18.7249i | 0.905103i | ||||||||
\(429\) | −16.2545 | −0.784773 | ||||||||
\(430\) | 5.01980 | 0.242076 | ||||||||
\(431\) | 11.0341i | 0.531492i | 0.964043 | + | 0.265746i | \(0.0856183\pi\) | ||||
−0.964043 | + | 0.265746i | \(0.914382\pi\) | |||||||
\(432\) | −0.569190 | −0.0273852 | ||||||||
\(433\) | − | 30.0172i | − | 1.44254i | −0.692657 | − | 0.721268i | \(-0.743560\pi\) | ||
0.692657 | − | 0.721268i | \(-0.256440\pi\) | |||||||
\(434\) | 24.1238 | 1.15798 | ||||||||
\(435\) | 14.8686 | 0.712895 | ||||||||
\(436\) | 4.66275 | 0.223305 | ||||||||
\(437\) | 20.5569 | 0.983371 | ||||||||
\(438\) | 14.0248i | 0.670132i | ||||||||
\(439\) | 39.5031i | 1.88538i | 0.333669 | + | 0.942690i | \(0.391713\pi\) | ||||
−0.333669 | + | 0.942690i | \(0.608287\pi\) | |||||||
\(440\) | −27.2223 | −1.29777 | ||||||||
\(441\) | −14.1292 | −0.672819 | ||||||||
\(442\) | 9.29216 | 0.441983 | ||||||||
\(443\) | 17.4133 | 0.827331 | 0.413666 | − | 0.910429i | \(-0.364248\pi\) | ||||
0.413666 | + | 0.910429i | \(0.364248\pi\) | |||||||
\(444\) | −11.3343 | −0.537900 | ||||||||
\(445\) | 21.1829i | 1.00417i | ||||||||
\(446\) | 13.2984i | 0.629695i | ||||||||
\(447\) | − | 23.7774i | − | 1.12463i | ||||||
\(448\) | 23.4906i | 1.10983i | ||||||||
\(449\) | −4.08923 | −0.192983 | −0.0964913 | − | 0.995334i | \(-0.530762\pi\) | ||||
−0.0964913 | + | 0.995334i | \(0.530762\pi\) | |||||||
\(450\) | 6.55516i | 0.309013i | ||||||||
\(451\) | 39.6971i | 1.86926i | ||||||||
\(452\) | − | 5.67930i | − | 0.267132i | ||||||
\(453\) | 5.07292 | 0.238347 | ||||||||
\(454\) | 16.2592i | 0.763082i | ||||||||
\(455\) | 6.60671 | 0.309727 | ||||||||
\(456\) | − | 30.8706i | − | 1.44565i | ||||||
\(457\) | −1.43677 | −0.0672094 | −0.0336047 | − | 0.999435i | \(-0.510699\pi\) | ||||
−0.0336047 | + | 0.999435i | \(0.510699\pi\) | |||||||
\(458\) | 13.7309 | 0.641603 | ||||||||
\(459\) | −5.35898 | −0.250136 | ||||||||
\(460\) | 7.85217 | 0.366110 | ||||||||
\(461\) | − | 16.9247i | − | 0.788263i | −0.919054 | − | 0.394131i | \(-0.871045\pi\) | ||
0.919054 | − | 0.394131i | \(-0.128955\pi\) | |||||||
\(462\) | 46.9371i | 2.18371i | ||||||||
\(463\) | − | 16.7577i | − | 0.778797i | −0.921069 | − | 0.389399i | \(-0.872683\pi\) | ||
0.921069 | − | 0.389399i | \(-0.127317\pi\) | |||||||
\(464\) | −3.30630 | −0.153491 | ||||||||
\(465\) | −26.8531 | −1.24528 | ||||||||
\(466\) | − | 15.0158i | − | 0.695591i | ||||||
\(467\) | 8.98624 | 0.415834 | 0.207917 | − | 0.978147i | \(-0.433332\pi\) | ||||
0.207917 | + | 0.978147i | \(0.433332\pi\) | |||||||
\(468\) | − | 3.34766i | − | 0.154746i | ||||||
\(469\) | 8.08584i | 0.373370i | ||||||||
\(470\) | −15.0294 | −0.693253 | ||||||||
\(471\) | −13.5534 | −0.624507 | ||||||||
\(472\) | −31.4383 | −1.44707 | ||||||||
\(473\) | 18.3840 | 0.845296 | ||||||||
\(474\) | 16.8183 | 0.772491 | ||||||||
\(475\) | 10.6444 | 0.488398 | ||||||||
\(476\) | 28.9317i | 1.32608i | ||||||||
\(477\) | − | 11.1870i | − | 0.512219i | ||||||
\(478\) | 18.4206i | 0.842537i | ||||||||
\(479\) | 8.78802 | 0.401535 | 0.200767 | − | 0.979639i | \(-0.435656\pi\) | ||||
0.200767 | + | 0.979639i | \(0.435656\pi\) | |||||||
\(480\) | − | 19.5554i | − | 0.892578i | ||||||
\(481\) | − | 5.41877i | − | 0.247075i | ||||||
\(482\) | 4.92713i | 0.224425i | ||||||||
\(483\) | − | 39.6341i | − | 1.80341i | ||||||
\(484\) | −22.6416 | −1.02916 | ||||||||
\(485\) | − | 0.776097i | − | 0.0352407i | ||||||
\(486\) | − | 20.9298i | − | 0.949394i | ||||||
\(487\) | − | 10.7584i | − | 0.487508i | −0.969837 | − | 0.243754i | \(-0.921621\pi\) | ||
0.969837 | − | 0.243754i | \(-0.0783790\pi\) | |||||||
\(488\) | −43.4318 | −1.96607 | ||||||||
\(489\) | − | 6.91716i | − | 0.312805i | ||||||
\(490\) | − | 8.12778i | − | 0.367176i | ||||||
\(491\) | 25.6701 | 1.15847 | 0.579237 | − | 0.815159i | \(-0.303350\pi\) | ||||
0.579237 | + | 0.815159i | \(0.303350\pi\) | |||||||
\(492\) | −17.1953 | −0.775225 | ||||||||
\(493\) | −31.1292 | −1.40199 | ||||||||
\(494\) | 5.04155 | 0.226830 | ||||||||
\(495\) | − | 24.8418i | − | 1.11655i | ||||||
\(496\) | 5.97127 | 0.268118 | ||||||||
\(497\) | 10.4409 | 0.468336 | ||||||||
\(498\) | − | 36.6077i | − | 1.64043i | ||||||
\(499\) | − | 28.5206i | − | 1.27676i | −0.769723 | − | 0.638378i | \(-0.779606\pi\) | ||
0.769723 | − | 0.638378i | \(-0.220394\pi\) | |||||||
\(500\) | 12.3390 | 0.551816 | ||||||||
\(501\) | − | 13.4317i | − | 0.600082i | ||||||
\(502\) | −1.94481 | −0.0868012 | ||||||||
\(503\) | − | 9.51645i | − | 0.424318i | −0.977235 | − | 0.212159i | \(-0.931951\pi\) | ||
0.977235 | − | 0.212159i | \(-0.0680494\pi\) | |||||||
\(504\) | −28.2991 | −1.26054 | ||||||||
\(505\) | − | 15.5994i | − | 0.694166i | ||||||
\(506\) | −26.6703 | −1.18564 | ||||||||
\(507\) | −27.7235 | −1.23125 | ||||||||
\(508\) | − | 4.84772i | − | 0.215083i | ||||||
\(509\) | 29.6614i | 1.31472i | 0.753577 | + | 0.657360i | \(0.228327\pi\) | ||||
−0.753577 | + | 0.657360i | \(0.771673\pi\) | |||||||
\(510\) | 29.8682i | 1.32259i | ||||||||
\(511\) | − | 20.8767i | − | 0.923533i | ||||||
\(512\) | 9.40242i | 0.415532i | ||||||||
\(513\) | −2.90757 | −0.128372 | ||||||||
\(514\) | 28.3130i | 1.24883i | ||||||||
\(515\) | − | 7.98667i | − | 0.351935i | ||||||
\(516\) | 7.96327i | 0.350564i | ||||||||
\(517\) | −55.0419 | −2.42074 | ||||||||
\(518\) | −15.6475 | −0.687510 | ||||||||
\(519\) | 11.6389i | 0.510893i | ||||||||
\(520\) | 5.63747 | 0.247219 | ||||||||
\(521\) | 32.5969i | 1.42810i | 0.700096 | + | 0.714049i | \(0.253141\pi\) | ||||
−0.700096 | + | 0.714049i | \(0.746859\pi\) | |||||||
\(522\) | − | 10.4011i | − | 0.455242i | ||||||
\(523\) | 34.8552i | 1.52411i | 0.647510 | + | 0.762057i | \(0.275810\pi\) | ||||
−0.647510 | + | 0.762057i | \(0.724190\pi\) | |||||||
\(524\) | − | 13.0979i | − | 0.572182i | ||||||
\(525\) | − | 20.5226i | − | 0.895679i | ||||||
\(526\) | − | 0.455173i | − | 0.0198465i | ||||||
\(527\) | 56.2201 | 2.44899 | ||||||||
\(528\) | 11.6182i | 0.505616i | ||||||||
\(529\) | −0.479320 | −0.0208400 | ||||||||
\(530\) | 6.43531 | 0.279532 | ||||||||
\(531\) | − | 28.6891i | − | 1.24500i | ||||||
\(532\) | 15.6972i | 0.680560i | ||||||||
\(533\) | − | 8.22087i | − | 0.356085i | ||||||
\(534\) | 31.1656 | 1.34867 | ||||||||
\(535\) | − | 28.7753i | − | 1.24407i | ||||||
\(536\) | 6.89961i | 0.298018i | ||||||||
\(537\) | 33.0422i | 1.42588i | ||||||||
\(538\) | − | 0.416407i | − | 0.0179526i | ||||||
\(539\) | − | 29.7663i | − | 1.28213i | ||||||
\(540\) | −1.11061 | −0.0477931 | ||||||||
\(541\) | −2.51302 | −0.108043 | −0.0540215 | − | 0.998540i | \(-0.517204\pi\) | ||||
−0.0540215 | + | 0.998540i | \(0.517204\pi\) | |||||||
\(542\) | − | 21.6108i | − | 0.928263i | ||||||
\(543\) | 5.31853 | 0.228240 | ||||||||
\(544\) | 40.9415i | 1.75535i | ||||||||
\(545\) | −7.16543 | −0.306933 | ||||||||
\(546\) | − | 9.72021i | − | 0.415986i | ||||||
\(547\) | 11.3367 | 0.484724 | 0.242362 | − | 0.970186i | \(-0.422078\pi\) | ||||
0.242362 | + | 0.970186i | \(0.422078\pi\) | |||||||
\(548\) | − | 18.0290i | − | 0.770160i | ||||||
\(549\) | − | 39.6338i | − | 1.69153i | ||||||
\(550\) | −13.8099 | −0.588857 | ||||||||
\(551\) | −16.8894 | −0.719514 | ||||||||
\(552\) | − | 33.8196i | − | 1.43946i | ||||||
\(553\) | −25.0350 | −1.06460 | ||||||||
\(554\) | 30.4785 | 1.29491 | ||||||||
\(555\) | 17.4178 | 0.739345 | ||||||||
\(556\) | 9.92378 | 0.420862 | ||||||||
\(557\) | − | 31.2893i | − | 1.32577i | −0.748721 | − | 0.662885i | \(-0.769332\pi\) | ||
0.748721 | − | 0.662885i | \(-0.230668\pi\) | |||||||
\(558\) | 18.7846i | 0.795216i | ||||||||
\(559\) | −3.80714 | −0.161025 | ||||||||
\(560\) | − | 4.72226i | − | 0.199552i | ||||||
\(561\) | 109.386i | 4.61829i | ||||||||
\(562\) | 16.2281i | 0.684542i | ||||||||
\(563\) | 22.0702 | 0.930148 | 0.465074 | − | 0.885272i | \(-0.346028\pi\) | ||||
0.465074 | + | 0.885272i | \(0.346028\pi\) | |||||||
\(564\) | − | 23.8421i | − | 1.00394i | ||||||
\(565\) | 8.72761i | 0.367173i | ||||||||
\(566\) | − | 12.4752i | − | 0.524370i | ||||||
\(567\) | 34.0957i | 1.43188i | ||||||||
\(568\) | 8.90912 | 0.373818 | ||||||||
\(569\) | − | 8.99663i | − | 0.377158i | −0.982058 | − | 0.188579i | \(-0.939612\pi\) | ||
0.982058 | − | 0.188579i | \(-0.0603882\pi\) | |||||||
\(570\) | 16.2053i | 0.678766i | ||||||||
\(571\) | − | 17.9832i | − | 0.752574i | −0.926503 | − | 0.376287i | \(-0.877201\pi\) | ||
0.926503 | − | 0.376287i | \(-0.122799\pi\) | |||||||
\(572\) | 7.05260 | 0.294884 | ||||||||
\(573\) | 25.1567 | 1.05094 | ||||||||
\(574\) | −23.7389 | −0.990844 | ||||||||
\(575\) | 11.6612 | 0.486307 | ||||||||
\(576\) | −18.2916 | −0.762150 | ||||||||
\(577\) | −12.7766 | −0.531897 | −0.265949 | − | 0.963987i | \(-0.585685\pi\) | ||||
−0.265949 | + | 0.963987i | \(0.585685\pi\) | |||||||
\(578\) | − | 45.8557i | − | 1.90735i | ||||||
\(579\) | − | 1.53301i | − | 0.0637099i | ||||||
\(580\) | −6.45129 | −0.267875 | ||||||||
\(581\) | 54.4927i | 2.26074i | ||||||||
\(582\) | −1.14184 | −0.0473309 | ||||||||
\(583\) | 23.5680 | 0.976085 | ||||||||
\(584\) | − | 17.8140i | − | 0.737149i | ||||||
\(585\) | 5.14449i | 0.212698i | ||||||||
\(586\) | − | 14.7928i | − | 0.611085i | ||||||
\(587\) | 27.0706 | 1.11732 | 0.558662 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558662 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(588\) | 12.8937 | 0.531727 | ||||||||
\(589\) | 30.5028 | 1.25685 | ||||||||
\(590\) | 16.5034 | 0.679432 | ||||||||
\(591\) | 37.0018i | 1.52205i | ||||||||
\(592\) | −3.87316 | −0.159186 | ||||||||
\(593\) | − | 12.3372i | − | 0.506628i | −0.967384 | − | 0.253314i | \(-0.918479\pi\) | ||
0.967384 | − | 0.253314i | \(-0.0815205\pi\) | |||||||
\(594\) | 3.77225 | 0.154777 | ||||||||
\(595\) | − | 44.4606i | − | 1.82271i | ||||||
\(596\) | 10.3167i | 0.422589i | ||||||||
\(597\) | 3.31750i | 0.135776i | ||||||||
\(598\) | 5.52316 | 0.225859 | ||||||||
\(599\) | 11.2676i | 0.460382i | 0.973145 | + | 0.230191i | \(0.0739352\pi\) | ||||
−0.973145 | + | 0.230191i | \(0.926065\pi\) | |||||||
\(600\) | − | 17.5118i | − | 0.714916i | ||||||
\(601\) | 8.67363i | 0.353805i | 0.984228 | + | 0.176902i | \(0.0566077\pi\) | ||||
−0.984228 | + | 0.176902i | \(0.943392\pi\) | |||||||
\(602\) | 10.9937i | 0.448068i | ||||||||
\(603\) | −6.29625 | −0.256403 | ||||||||
\(604\) | −2.20108 | −0.0895605 | ||||||||
\(605\) | 34.7942 | 1.41459 | ||||||||
\(606\) | −22.9509 | −0.932316 | ||||||||
\(607\) | −19.8405 | −0.805299 | −0.402650 | − | 0.915354i | \(-0.631911\pi\) | ||||
−0.402650 | + | 0.915354i | \(0.631911\pi\) | |||||||
\(608\) | 22.2132i | 0.900866i | ||||||||
\(609\) | 32.5631i | 1.31952i | ||||||||
\(610\) | 22.7993 | 0.923115 | ||||||||
\(611\) | 11.3986 | 0.461139 | ||||||||
\(612\) | −22.5285 | −0.910659 | ||||||||
\(613\) | −45.1114 | −1.82203 | −0.911017 | − | 0.412369i | \(-0.864701\pi\) | ||||
−0.911017 | + | 0.412369i | \(0.864701\pi\) | |||||||
\(614\) | 2.59132i | 0.104577i | ||||||||
\(615\) | 26.4247 | 1.06555 | ||||||||
\(616\) | − | 59.6184i | − | 2.40209i | ||||||
\(617\) | −18.6381 | −0.750340 | −0.375170 | − | 0.926956i | \(-0.622416\pi\) | ||||
−0.375170 | + | 0.926956i | \(0.622416\pi\) | |||||||
\(618\) | −11.7505 | −0.472674 | ||||||||
\(619\) | − | 11.8408i | − | 0.475923i | −0.971275 | − | 0.237961i | \(-0.923521\pi\) | ||
0.971275 | − | 0.237961i | \(-0.0764792\pi\) | |||||||
\(620\) | 11.6512 | 0.467924 | ||||||||
\(621\) | −3.18532 | −0.127823 | ||||||||
\(622\) | 23.6851 | 0.949685 | ||||||||
\(623\) | −46.3919 | −1.85865 | ||||||||
\(624\) | − | 2.40601i | − | 0.0963174i | ||||||
\(625\) | −6.67544 | −0.267018 | ||||||||
\(626\) | 12.7861i | 0.511035i | ||||||||
\(627\) | 59.3486i | 2.37015i | ||||||||
\(628\) | 5.88064 | 0.234663 | ||||||||
\(629\) | −36.4662 | −1.45400 | ||||||||
\(630\) | 14.8554 | 0.591855 | ||||||||
\(631\) | −36.4135 | −1.44960 | −0.724800 | − | 0.688960i | \(-0.758068\pi\) | ||||
−0.724800 | + | 0.688960i | \(0.758068\pi\) | |||||||
\(632\) | −21.3623 | −0.849745 | ||||||||
\(633\) | − | 1.29567i | − | 0.0514982i | ||||||
\(634\) | −4.62251 | −0.183583 | ||||||||
\(635\) | 7.44969i | 0.295632i | ||||||||
\(636\) | 10.2088i | 0.404805i | ||||||||
\(637\) | 6.16431i | 0.244239i | ||||||||
\(638\) | 21.9122 | 0.867511 | ||||||||
\(639\) | 8.13004i | 0.321620i | ||||||||
\(640\) | 5.83181i | 0.230523i | ||||||||
\(641\) | −20.0689 | −0.792674 | −0.396337 | − | 0.918105i | \(-0.629719\pi\) | ||||
−0.396337 | + | 0.918105i | \(0.629719\pi\) | |||||||
\(642\) | −42.3361 | −1.67087 | ||||||||
\(643\) | 1.91957i | 0.0757005i | 0.999283 | + | 0.0378502i | \(0.0120510\pi\) | ||||
−0.999283 | + | 0.0378502i | \(0.987949\pi\) | |||||||
\(644\) | 17.1967i | 0.677646i | ||||||||
\(645\) | − | 12.2375i | − | 0.481850i | ||||||
\(646\) | − | 33.9277i | − | 1.33487i | ||||||
\(647\) | −5.25465 | −0.206582 | −0.103291 | − | 0.994651i | \(-0.532937\pi\) | ||||
−0.103291 | + | 0.994651i | \(0.532937\pi\) | |||||||
\(648\) | 29.0936i | 1.14291i | ||||||||
\(649\) | 60.4401 | 2.37248 | ||||||||
\(650\) | 2.85990 | 0.112174 | ||||||||
\(651\) | − | 58.8099i | − | 2.30494i | ||||||
\(652\) | 3.00127i | 0.117539i | ||||||||
\(653\) | −47.0966 | −1.84303 | −0.921516 | − | 0.388339i | \(-0.873049\pi\) | ||||
−0.921516 | + | 0.388339i | \(0.873049\pi\) | |||||||
\(654\) | 10.5422i | 0.412234i | ||||||||
\(655\) | 20.1280i | 0.786466i | ||||||||
\(656\) | −5.87601 | −0.229420 | ||||||||
\(657\) | 16.2562 | 0.634216 | ||||||||
\(658\) | − | 32.9152i | − | 1.28317i | ||||||
\(659\) | 30.4873i | 1.18762i | 0.804607 | + | 0.593808i | \(0.202376\pi\) | ||||
−0.804607 | + | 0.593808i | \(0.797624\pi\) | |||||||
\(660\) | 22.6695i | 0.882409i | ||||||||
\(661\) | 7.38284 | 0.287159 | 0.143580 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143580 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(662\) | 13.2249 | 0.513999 | ||||||||
\(663\) | − | 22.6528i | − | 0.879762i | ||||||
\(664\) | 46.4983i | 1.80448i | ||||||||
\(665\) | − | 24.1225i | − | 0.935432i | ||||||
\(666\) | − | 12.1843i | − | 0.472132i | ||||||
\(667\) | −18.5028 | −0.716433 | ||||||||
\(668\) | 5.82782i | 0.225485i | ||||||||
\(669\) | 32.4193 | 1.25340 | ||||||||
\(670\) | − | 3.62190i | − | 0.139926i | ||||||
\(671\) | 83.4975 | 3.22339 | ||||||||
\(672\) | 42.8275 | 1.65211 | ||||||||
\(673\) | 30.5443 | 1.17739 | 0.588697 | − | 0.808353i | \(-0.299641\pi\) | ||||
0.588697 | + | 0.808353i | \(0.299641\pi\) | |||||||
\(674\) | 0.522847i | 0.0201393i | ||||||||
\(675\) | −1.64936 | −0.0634840 | ||||||||
\(676\) | 12.0289 | 0.462649 | ||||||||
\(677\) | − | 23.8157i | − | 0.915311i | −0.889129 | − | 0.457656i | \(-0.848689\pi\) | ||
0.889129 | − | 0.457656i | \(-0.151311\pi\) | |||||||
\(678\) | 12.8406 | 0.493140 | ||||||||
\(679\) | 1.69970 | 0.0652284 | ||||||||
\(680\) | − | 37.9380i | − | 1.45485i | ||||||
\(681\) | 39.6373 | 1.51891 | ||||||||
\(682\) | −39.5740 | −1.51537 | ||||||||
\(683\) | −4.65270 | −0.178031 | −0.0890153 | − | 0.996030i | \(-0.528372\pi\) | ||||
−0.0890153 | + | 0.996030i | \(0.528372\pi\) | |||||||
\(684\) | −12.2230 | −0.467360 | ||||||||
\(685\) | 27.7059i | 1.05859i | ||||||||
\(686\) | −6.18088 | −0.235987 | ||||||||
\(687\) | − | 33.4737i | − | 1.27710i | ||||||
\(688\) | 2.72122i | 0.103746i | ||||||||
\(689\) | −4.88070 | −0.185940 | ||||||||
\(690\) | 17.7534i | 0.675859i | ||||||||
\(691\) | 7.84795i | 0.298550i | 0.988796 | + | 0.149275i | \(0.0476940\pi\) | ||||
−0.988796 | + | 0.149275i | \(0.952306\pi\) | |||||||
\(692\) | − | 5.04998i | − | 0.191972i | ||||||
\(693\) | 54.4049 | 2.06667 | ||||||||
\(694\) | 4.74423 | 0.180089 | ||||||||
\(695\) | −15.2503 | −0.578476 | ||||||||
\(696\) | 27.7859i | 1.05322i | ||||||||
\(697\) | −55.3233 | −2.09552 | ||||||||
\(698\) | 8.97019 | − | 15.9811i | 0.339527 | − | 0.604895i | ||||
\(699\) | −36.6060 | −1.38457 | ||||||||
\(700\) | 8.90448i | 0.336558i | ||||||||
\(701\) | −24.1372 | −0.911649 | −0.455825 | − | 0.890070i | \(-0.650656\pi\) | ||||
−0.455825 | + | 0.890070i | \(0.650656\pi\) | |||||||
\(702\) | −0.781196 | −0.0294843 | ||||||||
\(703\) | −19.7851 | −0.746209 | ||||||||
\(704\) | − | 38.5354i | − | 1.45236i | ||||||
\(705\) | 36.6392i | 1.37991i | ||||||||
\(706\) | 23.5803i | 0.887455i | ||||||||
\(707\) | 34.1637 | 1.28486 | ||||||||
\(708\) | 26.1804i | 0.983921i | ||||||||
\(709\) | − | 30.6567i | − | 1.15134i | −0.817683 | − | 0.575669i | \(-0.804742\pi\) | ||
0.817683 | − | 0.575669i | \(-0.195258\pi\) | |||||||
\(710\) | −4.67679 | −0.175517 | ||||||||
\(711\) | − | 19.4942i | − | 0.731089i | ||||||
\(712\) | −39.5859 | −1.48354 | ||||||||
\(713\) | 33.4167 | 1.25146 | ||||||||
\(714\) | −65.4132 | −2.44803 | ||||||||
\(715\) | −10.8380 | −0.405319 | ||||||||
\(716\) | − | 14.3366i | − | 0.535784i | ||||||
\(717\) | 44.9064 | 1.67706 | ||||||||
\(718\) | −24.3559 | −0.908953 | ||||||||
\(719\) | − | 18.4804i | − | 0.689201i | −0.938749 | − | 0.344600i | \(-0.888014\pi\) | ||
0.938749 | − | 0.344600i | \(-0.111986\pi\) | |||||||
\(720\) | 3.67711 | 0.137038 | ||||||||
\(721\) | 17.4913 | 0.651410 | ||||||||
\(722\) | 0.231115i | 0.00860120i | ||||||||
\(723\) | 12.0116 | 0.446715 | ||||||||
\(724\) | −2.30764 | −0.0857628 | ||||||||
\(725\) | −9.58079 | −0.355821 | ||||||||
\(726\) | − | 51.1914i | − | 1.89989i | ||||||
\(727\) | −1.95848 | −0.0726360 | −0.0363180 | − | 0.999340i | \(-0.511563\pi\) | ||||
−0.0363180 | + | 0.999340i | \(0.511563\pi\) | |||||||
\(728\) | 12.3464i | 0.457588i | ||||||||
\(729\) | −21.7338 | −0.804955 | ||||||||
\(730\) | 9.35135i | 0.346109i | ||||||||
\(731\) | 25.6206i | 0.947612i | ||||||||
\(732\) | 36.1681i | 1.33681i | ||||||||
\(733\) | 29.1103i | 1.07521i | 0.843196 | + | 0.537606i | \(0.180671\pi\) | ||||
−0.843196 | + | 0.537606i | \(0.819329\pi\) | |||||||
\(734\) | −21.7140 | −0.801479 | ||||||||
\(735\) | −19.8142 | −0.730859 | ||||||||
\(736\) | 24.3352i | 0.897008i | ||||||||
\(737\) | − | 13.2645i | − | 0.488603i | ||||||
\(738\) | − | 18.4849i | − | 0.680440i | ||||||
\(739\) | 29.5061 | 1.08540 | 0.542699 | − | 0.839927i | \(-0.317402\pi\) | ||||
0.542699 | + | 0.839927i | \(0.317402\pi\) | |||||||
\(740\) | −7.55736 | −0.277814 | ||||||||
\(741\) | − | 12.2905i | − | 0.451503i | ||||||
\(742\) | 14.0937i | 0.517396i | ||||||||
\(743\) | 1.59648 | 0.0585691 | 0.0292846 | − | 0.999571i | \(-0.490677\pi\) | ||||
0.0292846 | + | 0.999571i | \(0.490677\pi\) | |||||||
\(744\) | − | 50.1822i | − | 1.83977i | ||||||
\(745\) | − | 15.8541i | − | 0.580850i | ||||||
\(746\) | 26.0807 | 0.954883 | ||||||||
\(747\) | −42.4322 | −1.55251 | ||||||||
\(748\) | − | 47.4612i | − | 1.73535i | ||||||
\(749\) | 63.0197 | 2.30269 | ||||||||
\(750\) | 27.8978i | 1.01868i | ||||||||
\(751\) | 34.3164i | 1.25222i | 0.779734 | + | 0.626112i | \(0.215355\pi\) | ||||
−0.779734 | + | 0.626112i | \(0.784645\pi\) | |||||||
\(752\) | − | 8.14738i | − | 0.297104i | ||||||
\(753\) | 4.74114i | 0.172777i | ||||||||
\(754\) | −4.53779 | −0.165257 | ||||||||
\(755\) | 3.38248 | 0.123101 | ||||||||
\(756\) | − | 2.43230i | − | 0.0884621i | ||||||
\(757\) | 7.39838i | 0.268899i | 0.990920 | + | 0.134449i | \(0.0429265\pi\) | ||||
−0.990920 | + | 0.134449i | \(0.957073\pi\) | |||||||
\(758\) | 11.4840 | 0.417119 | ||||||||
\(759\) | 65.0180i | 2.36000i | ||||||||
\(760\) | − | 20.5836i | − | 0.746647i | ||||||
\(761\) | − | 18.4892i | − | 0.670235i | −0.942176 | − | 0.335117i | \(-0.891224\pi\) | ||
0.942176 | − | 0.335117i | \(-0.108776\pi\) | |||||||
\(762\) | 10.9605 | 0.397055 | ||||||||
\(763\) | − | 15.6927i | − | 0.568115i | ||||||
\(764\) | −10.9152 | −0.394897 | ||||||||
\(765\) | 34.6204 | 1.25170 | ||||||||
\(766\) | 5.51679 | 0.199330 | ||||||||
\(767\) | −12.5166 | −0.451946 | ||||||||
\(768\) | 40.7532 | 1.47055 | ||||||||
\(769\) | 2.49935i | 0.0901289i | 0.998984 | + | 0.0450644i | \(0.0143493\pi\) | ||||
−0.998984 | + | 0.0450644i | \(0.985651\pi\) | |||||||
\(770\) | 31.2963i | 1.12784i | ||||||||
\(771\) | 69.0227 | 2.48579 | ||||||||
\(772\) | 0.665155i | 0.0239395i | ||||||||
\(773\) | 47.4026 | 1.70495 | 0.852476 | − | 0.522766i | \(-0.175100\pi\) | ||||
0.852476 | + | 0.522766i | \(0.175100\pi\) | |||||||
\(774\) | −8.56051 | −0.307701 | ||||||||
\(775\) | 17.3032 | 0.621548 | ||||||||
\(776\) | 1.45034 | 0.0520643 | ||||||||
\(777\) | 38.1460i | 1.36848i | ||||||||
\(778\) | −21.6758 | −0.777117 | ||||||||
\(779\) | −30.0162 | −1.07544 | ||||||||
\(780\) | − | 4.69463i | − | 0.168095i | ||||||
\(781\) | −17.1278 | −0.612879 | ||||||||
\(782\) | − | 37.1687i | − | 1.32915i | ||||||
\(783\) | 2.61704 | 0.0935254 | ||||||||
\(784\) | 4.40605 | 0.157359 | ||||||||
\(785\) | −9.03701 | −0.322545 | ||||||||
\(786\) | 29.6136 | 1.05628 | ||||||||
\(787\) | − | 13.2402i | − | 0.471961i | −0.971758 | − | 0.235981i | \(-0.924170\pi\) | ||
0.971758 | − | 0.235981i | \(-0.0758302\pi\) | |||||||
\(788\) | − | 16.0546i | − | 0.571922i | ||||||
\(789\) | −1.10964 | −0.0395042 | ||||||||
\(790\) | 11.2140 | 0.398975 | ||||||||
\(791\) | −19.1140 | −0.679615 | ||||||||
\(792\) | 46.4234 | 1.64958 | ||||||||
\(793\) | −17.2915 | −0.614040 | ||||||||
\(794\) | 0.301080i | 0.0106849i | ||||||||
\(795\) | − | 15.6883i | − | 0.556405i | ||||||
\(796\) | − | 1.43942i | − | 0.0510189i | ||||||
\(797\) | − | 28.5449i | − | 1.01111i | −0.862794 | − | 0.505556i | \(-0.831287\pi\) | ||
0.862794 | − | 0.505556i | \(-0.168713\pi\) | |||||||
\(798\) | −35.4906 | −1.25635 | ||||||||
\(799\) | − | 76.7084i | − | 2.71375i | ||||||
\(800\) | 12.6008i | 0.445505i | ||||||||
\(801\) | − | 36.1242i | − | 1.27639i | ||||||
\(802\) | 6.45709 | 0.228008 | ||||||||
\(803\) | 34.2474i | 1.20856i | ||||||||
\(804\) | 5.74568 | 0.202635 | ||||||||
\(805\) | − | 26.4269i | − | 0.931426i | ||||||
\(806\) | 8.19539 | 0.288670 | ||||||||
\(807\) | −1.01513 | −0.0357344 | ||||||||
\(808\) | 29.1517 | 1.02555 | ||||||||
\(809\) | 33.7152 | 1.18536 | 0.592681 | − | 0.805437i | \(-0.298070\pi\) | ||||
0.592681 | + | 0.805437i | \(0.298070\pi\) | |||||||
\(810\) | − | 15.2725i | − | 0.536621i | ||||||
\(811\) | − | 0.888225i | − | 0.0311898i | −0.999878 | − | 0.0155949i | \(-0.995036\pi\) | ||
0.999878 | − | 0.0155949i | \(-0.00496421\pi\) | |||||||
\(812\) | − | 14.1287i | − | 0.495821i | ||||||
\(813\) | −52.6837 | −1.84770 | ||||||||
\(814\) | 25.6690 | 0.899697 | ||||||||
\(815\) | − | 4.61217i | − | 0.161557i | ||||||
\(816\) | −16.1915 | −0.566816 | ||||||||
\(817\) | 13.9007i | 0.486324i | ||||||||
\(818\) | 5.34288i | 0.186809i | ||||||||
\(819\) | −11.2667 | −0.393691 | ||||||||
\(820\) | −11.4654 | −0.400387 | ||||||||
\(821\) | 20.6766 | 0.721619 | 0.360810 | − | 0.932639i | \(-0.382500\pi\) | ||||
0.360810 | + | 0.932639i | \(0.382500\pi\) | |||||||
\(822\) | 40.7626 | 1.42176 | ||||||||
\(823\) | 5.34483 | 0.186309 | 0.0931545 | − | 0.995652i | \(-0.470305\pi\) | ||||
0.0931545 | + | 0.995652i | \(0.470305\pi\) | |||||||
\(824\) | 14.9252 | 0.519945 | ||||||||
\(825\) | 33.6664i | 1.17211i | ||||||||
\(826\) | 36.1433i | 1.25759i | ||||||||
\(827\) | − | 22.5308i | − | 0.783472i | −0.920078 | − | 0.391736i | \(-0.871875\pi\) | ||
0.920078 | − | 0.391736i | \(-0.128125\pi\) | |||||||
\(828\) | −13.3907 | −0.465358 | ||||||||
\(829\) | 2.34189i | 0.0813372i | 0.999173 | + | 0.0406686i | \(0.0129488\pi\) | ||||
−0.999173 | + | 0.0406686i | \(0.987051\pi\) | |||||||
\(830\) | − | 24.4090i | − | 0.847248i | ||||||
\(831\) | − | 74.3017i | − | 2.57750i | ||||||
\(832\) | 7.98030i | 0.276667i | ||||||||
\(833\) | 41.4834 | 1.43732 | ||||||||
\(834\) | 22.4371i | 0.776935i | ||||||||
\(835\) | − | 8.95585i | − | 0.309930i | ||||||
\(836\) | − | 25.7506i | − | 0.890602i | ||||||
\(837\) | −4.72645 | −0.163370 | ||||||||
\(838\) | 29.5551i | 1.02096i | ||||||||
\(839\) | − | 53.7752i | − | 1.85653i | −0.371925 | − | 0.928263i | \(-0.621302\pi\) | ||
0.371925 | − | 0.928263i | \(-0.378698\pi\) | |||||||
\(840\) | −39.6856 | −1.36928 | ||||||||
\(841\) | −13.7982 | −0.475800 | ||||||||
\(842\) | −14.4848 | −0.499178 | ||||||||
\(843\) | 39.5616 | 1.36257 | ||||||||
\(844\) | 0.562174i | 0.0193508i | ||||||||
\(845\) | −18.4853 | −0.635912 | ||||||||
\(846\) | 25.6303 | 0.881187 | ||||||||
\(847\) | 76.2014i | 2.61831i | ||||||||
\(848\) | 3.48856i | 0.119798i | ||||||||
\(849\) | −30.4124 | −1.04375 | ||||||||
\(850\) | − | 19.2460i | − | 0.660132i | ||||||
\(851\) | −21.6751 | −0.743014 | ||||||||
\(852\) | − | 7.41912i | − | 0.254175i | ||||||
\(853\) | 20.4467 | 0.700080 | 0.350040 | − | 0.936735i | \(-0.386168\pi\) | ||||
0.350040 | + | 0.936735i | \(0.386168\pi\) | |||||||
\(854\) | 49.9317i | 1.70863i | ||||||||
\(855\) | 18.7836 | 0.642387 | ||||||||
\(856\) | 53.7744 | 1.83797 | ||||||||
\(857\) | 43.2339i | 1.47684i | 0.674340 | + | 0.738421i | \(0.264428\pi\) | ||||
−0.674340 | + | 0.738421i | \(0.735572\pi\) | |||||||
\(858\) | 15.9456i | 0.544373i | ||||||||
\(859\) | 35.0119i | 1.19459i | 0.802021 | + | 0.597295i | \(0.203758\pi\) | ||||
−0.802021 | + | 0.597295i | \(0.796242\pi\) | |||||||
\(860\) | 5.30969i | 0.181059i | ||||||||
\(861\) | 57.8717i | 1.97226i | ||||||||
\(862\) | 10.8244 | 0.368680 | ||||||||
\(863\) | − | 2.88320i | − | 0.0981454i | −0.998795 | − | 0.0490727i | \(-0.984373\pi\) | ||
0.998795 | − | 0.0490727i | \(-0.0156266\pi\) | |||||||
\(864\) | − | 3.44197i | − | 0.117098i | ||||||
\(865\) | 7.76051i | 0.263865i | ||||||||
\(866\) | −29.4468 | −1.00064 | ||||||||
\(867\) | −111.789 | −3.79655 | ||||||||
\(868\) | 25.5169i | 0.866099i | ||||||||
\(869\) | 41.0689 | 1.39317 | ||||||||
\(870\) | − | 14.5860i | − | 0.494513i | ||||||
\(871\) | 2.74694i | 0.0930766i | ||||||||
\(872\) | − | 13.3905i | − | 0.453460i | ||||||
\(873\) | 1.32351i | 0.0447942i | ||||||||
\(874\) | − | 20.1663i | − | 0.682134i | ||||||
\(875\) | − | 41.5275i | − | 1.40389i | ||||||
\(876\) | −14.8347 | −0.501219 | ||||||||
\(877\) | − | 32.5115i | − | 1.09783i | −0.835877 | − | 0.548917i | \(-0.815040\pi\) | ||
0.835877 | − | 0.548917i | \(-0.184960\pi\) | |||||||
\(878\) | 38.7524 | 1.30783 | ||||||||
\(879\) | −36.0625 | −1.21636 | ||||||||
\(880\) | 7.74666i | 0.261140i | ||||||||
\(881\) | 16.7339i | 0.563780i | 0.959447 | + | 0.281890i | \(0.0909613\pi\) | ||||
−0.959447 | + | 0.281890i | \(0.909039\pi\) | |||||||
\(882\) | 13.8607i | 0.466714i | ||||||||
\(883\) | −42.2003 | −1.42015 | −0.710076 | − | 0.704125i | \(-0.751340\pi\) | ||||
−0.710076 | + | 0.704125i | \(0.751340\pi\) | |||||||
\(884\) | 9.82876i | 0.330577i | ||||||||
\(885\) | − | 40.2326i | − | 1.35240i | ||||||
\(886\) | − | 17.0824i | − | 0.573894i | ||||||
\(887\) | 4.10824i | 0.137941i | 0.997619 | + | 0.0689705i | \(0.0219714\pi\) | ||||
−0.997619 | + | 0.0689705i | \(0.978029\pi\) | |||||||
\(888\) | 32.5498i | 1.09230i | ||||||||
\(889\) | −16.3153 | −0.547196 | ||||||||
\(890\) | 20.7804 | 0.696560 | ||||||||
\(891\) | − | 55.9324i | − | 1.87381i | ||||||
\(892\) | −14.0663 | −0.470975 | ||||||||
\(893\) | − | 41.6189i | − | 1.39272i | ||||||
\(894\) | −23.3256 | −0.780124 | ||||||||
\(895\) | 22.0316i | 0.736436i | ||||||||
\(896\) | −12.7720 | −0.426683 | ||||||||
\(897\) | − | 13.4646i | − | 0.449570i | ||||||
\(898\) | 4.01152i | 0.133866i | ||||||||
\(899\) | −27.4549 | −0.915672 | ||||||||
\(900\) | −6.93370 | −0.231123 | ||||||||
\(901\) | 32.8452i | 1.09423i | ||||||||
\(902\) | 38.9427 | 1.29665 | ||||||||
\(903\) | 26.8008 | 0.891875 | ||||||||
\(904\) | −16.3098 | −0.542458 | ||||||||
\(905\) | 3.54625 | 0.117881 | ||||||||
\(906\) | − | 4.97652i | − | 0.165334i | ||||||
\(907\) | 10.1189i | 0.335993i | 0.985788 | + | 0.167997i | \(0.0537298\pi\) | ||||
−0.985788 | + | 0.167997i | \(0.946270\pi\) | |||||||
\(908\) | −17.1981 | −0.570740 | ||||||||
\(909\) | 26.6025i | 0.882348i | ||||||||
\(910\) | − | 6.48116i | − | 0.214848i | ||||||
\(911\) | − | 15.1869i | − | 0.503164i | −0.967836 | − | 0.251582i | \(-0.919049\pi\) | ||
0.967836 | − | 0.251582i | \(-0.0809507\pi\) | |||||||
\(912\) | −8.78486 | −0.290896 | ||||||||
\(913\) | − | 89.3928i | − | 2.95847i | ||||||
\(914\) | 1.40947i | 0.0466211i | ||||||||
\(915\) | − | 55.5810i | − | 1.83745i | ||||||
\(916\) | 14.5238i | 0.479880i | ||||||||
\(917\) | −44.0815 | −1.45570 | ||||||||
\(918\) | 5.25714i | 0.173512i | ||||||||
\(919\) | − | 41.2261i | − | 1.35992i | −0.733247 | − | 0.679962i | \(-0.761996\pi\) | ||
0.733247 | − | 0.679962i | \(-0.238004\pi\) | |||||||
\(920\) | − | 22.5499i | − | 0.743449i | ||||||
\(921\) | 6.31722 | 0.208159 | ||||||||
\(922\) | −16.6031 | −0.546794 | ||||||||
\(923\) | 3.54699 | 0.116751 | ||||||||
\(924\) | −49.6475 | −1.63328 | ||||||||
\(925\) | −11.2234 | −0.369023 | ||||||||
\(926\) | −16.4393 | −0.540228 | ||||||||
\(927\) | 13.6200i | 0.447341i | ||||||||
\(928\) | − | 19.9936i | − | 0.656324i | ||||||
\(929\) | 35.9091 | 1.17814 | 0.589070 | − | 0.808082i | \(-0.299494\pi\) | ||||
0.589070 | + | 0.808082i | \(0.299494\pi\) | |||||||
\(930\) | 26.3428i | 0.863815i | ||||||||
\(931\) | 22.5072 | 0.737645 | ||||||||
\(932\) | 15.8829 | 0.520261 | ||||||||
\(933\) | − | 57.7405i | − | 1.89034i | ||||||
\(934\) | − | 8.81547i | − | 0.288451i | ||||||
\(935\) | 72.9356i | 2.38525i | ||||||||
\(936\) | −9.61384 | −0.314238 | ||||||||
\(937\) | 13.4405 | 0.439081 | 0.219541 | − | 0.975603i | \(-0.429544\pi\) | ||||
0.219541 | + | 0.975603i | \(0.429544\pi\) | |||||||
\(938\) | 7.93218 | 0.258995 | ||||||||
\(939\) | 31.1704 | 1.01721 | ||||||||
\(940\) | − | 15.8973i | − | 0.518512i | ||||||
\(941\) | 34.0899 | 1.11130 | 0.555649 | − | 0.831417i | \(-0.312470\pi\) | ||||
0.555649 | + | 0.831417i | \(0.312470\pi\) | |||||||
\(942\) | 13.2958i | 0.433201i | ||||||||
\(943\) | −32.8836 | −1.07084 | ||||||||
\(944\) | 8.94643i | 0.291181i | ||||||||
\(945\) | 3.73782i | 0.121591i | ||||||||
\(946\) | − | 18.0346i | − | 0.586356i | ||||||
\(947\) | 25.4684 | 0.827611 | 0.413805 | − | 0.910365i | \(-0.364199\pi\) | ||||
0.413805 | + | 0.910365i | \(0.364199\pi\) | |||||||
\(948\) | 17.7895i | 0.577777i | ||||||||
\(949\) | − | 7.09230i | − | 0.230226i | ||||||
\(950\) | − | 10.4421i | − | 0.338787i | ||||||
\(951\) | 11.2689i | 0.365420i | ||||||||
\(952\) | 83.0864 | 2.69285 | ||||||||
\(953\) | −12.5906 | −0.407849 | −0.203924 | − | 0.978987i | \(-0.565370\pi\) | ||||
−0.203924 | + | 0.978987i | \(0.565370\pi\) | |||||||
\(954\) | −10.9744 | −0.355310 | ||||||||
\(955\) | 16.7738 | 0.542787 | ||||||||
\(956\) | −19.4843 | −0.630167 | ||||||||
\(957\) | − | 53.4183i | − | 1.72677i | ||||||
\(958\) | − | 8.62101i | − | 0.278532i | ||||||
\(959\) | −60.6775 | −1.95938 | ||||||||
\(960\) | −25.6514 | −0.827897 | ||||||||
\(961\) | 18.5844 | 0.599495 | ||||||||
\(962\) | −5.31579 | −0.171388 | ||||||||
\(963\) | 49.0719i | 1.58132i | ||||||||
\(964\) | −5.21166 | −0.167856 | ||||||||
\(965\) | − | 1.02217i | − | 0.0329048i | ||||||
\(966\) | −38.8809 | −1.25097 | ||||||||
\(967\) | 24.0220 | 0.772496 | 0.386248 | − | 0.922395i | \(-0.373771\pi\) | ||||
0.386248 | + | 0.922395i | \(0.373771\pi\) | |||||||
\(968\) | 65.0222i | 2.08989i | ||||||||
\(969\) | −82.7103 | −2.65704 | ||||||||
\(970\) | −0.761348 | −0.0244454 | ||||||||
\(971\) | 35.4625 | 1.13805 | 0.569024 | − | 0.822321i | \(-0.307321\pi\) | ||||
0.569024 | + | 0.822321i | \(0.307321\pi\) | |||||||
\(972\) | 22.1384 | 0.710090 | ||||||||
\(973\) | − | 33.3990i | − | 1.07072i | ||||||
\(974\) | −10.5539 | −0.338169 | ||||||||
\(975\) | − | 6.97198i | − | 0.223282i | ||||||
\(976\) | 12.3594i | 0.395615i | ||||||||
\(977\) | 35.7682 | 1.14433 | 0.572163 | − | 0.820140i | \(-0.306104\pi\) | ||||
0.572163 | + | 0.820140i | \(0.306104\pi\) | |||||||
\(978\) | −6.78571 | −0.216983 | ||||||||
\(979\) | 76.1038 | 2.43229 | ||||||||
\(980\) | 8.59714 | 0.274626 | ||||||||
\(981\) | 12.2195 | 0.390140 | ||||||||
\(982\) | − | 25.1823i | − | 0.803598i | ||||||
\(983\) | 24.8100 | 0.791316 | 0.395658 | − | 0.918398i | \(-0.370517\pi\) | ||||
0.395658 | + | 0.918398i | \(0.370517\pi\) | |||||||
\(984\) | 49.3816i | 1.57423i | ||||||||
\(985\) | 24.6718i | 0.786108i | ||||||||
\(986\) | 30.5376i | 0.972515i | ||||||||
\(987\) | −80.2420 | −2.55413 | ||||||||
\(988\) | 5.33269i | 0.169656i | ||||||||
\(989\) | 15.2286i | 0.484242i | ||||||||
\(990\) | −24.3697 | −0.774519 | ||||||||
\(991\) | 6.88373 | 0.218669 | 0.109335 | − | 0.994005i | \(-0.465128\pi\) | ||||
0.109335 | + | 0.994005i | \(0.465128\pi\) | |||||||
\(992\) | 36.1091i | 1.14647i | ||||||||
\(993\) | − | 32.2401i | − | 1.02311i | ||||||
\(994\) | − | 10.2424i | − | 0.324870i | ||||||
\(995\) | 2.21202i | 0.0701256i | ||||||||
\(996\) | 38.7217 | 1.22694 | ||||||||
\(997\) | 13.6028i | 0.430806i | 0.976525 | + | 0.215403i | \(0.0691065\pi\) | ||||
−0.976525 | + | 0.215403i | \(0.930893\pi\) | |||||||
\(998\) | −27.9786 | −0.885647 | ||||||||
\(999\) | 3.06573 | 0.0969954 |
(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 | 349.2.b.b.348.11 | ✓ | 26 | |
349.348 | even | 2 | inner | 349.2.b.b.348.16 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.b.b.348.11 | ✓ | 26 | 1.1 | even | 1 | trivial | |
349.2.b.b.348.16 | yes | 26 | 349.348 | even | 2 | inner |