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 | 348.16 | ||
Character | \(\chi\) | \(=\) | 349.348 |
Dual form | 349.2.b.b.348.11 |
$q$-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 | \(0.112743\pi\) | ||||
−0.937926 | + | 0.346835i | \(0.887257\pi\) | |||||||
\(3\) | −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 | \(0.229433\pi\) | ||||
−0.751289 | + | 0.659974i | \(0.770567\pi\) | |||||||
\(8\) | 2.97992i | 1.05356i | ||||||||
\(9\) | 2.71933 | 0.906445 | ||||||||
\(10\) | − | 1.56429i | − | 0.494672i | ||||||
\(11\) | − | 5.72888i | − | 1.72732i | −0.504072 | − | 0.863662i | \(-0.668165\pi\) | ||
0.504072 | − | 0.863662i | \(-0.331835\pi\) | |||||||
\(12\) | −2.48154 | −0.716360 | ||||||||
\(13\) | 1.18640i | 0.329047i | 0.986373 | + | 0.164524i | \(0.0526086\pi\) | ||||
−0.986373 | + | 0.164524i | \(0.947391\pi\) | |||||||
\(14\) | −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 | \(0.0786842\pi\) | ||||
−0.969603 | + | 0.244684i | \(0.921316\pi\) | |||||||
\(44\) | − | 5.94456i | − | 0.896175i | ||||||
\(45\) | −4.33623 | −0.646407 | ||||||||
\(46\) | − | 4.65541i | − | 0.686403i | ||||||
\(47\) | − | 9.60778i | − | 1.40144i | −0.713437 | − | 0.700720i | \(-0.752862\pi\) | ||
0.713437 | − | 0.700720i | \(-0.247138\pi\) | |||||||
\(48\) | 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 | \(0.0911779\pi\) | ||||
−0.959255 | + | 0.282543i | \(0.908822\pi\) | |||||||
\(54\) | 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 | \(0.240964\pi\) | ||||
−0.726893 | + | 0.686751i | \(0.759036\pi\) | |||||||
\(60\) | 3.95705 | 0.510853 | ||||||||
\(61\) | 14.5748i | 1.86612i | 0.359726 | + | 0.933058i | \(0.382870\pi\) | ||||
−0.359726 | + | 0.933058i | \(0.617130\pi\) | |||||||
\(62\) | − | 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 | \(-0.943229\pi\) | ||
0.984138 | − | 0.177407i | \(-0.0567709\pi\) | |||||||
\(72\) | 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 | \(0.132127\pi\) | ||||
−0.915080 | + | 0.403273i | \(0.867873\pi\) | |||||||
\(80\) | 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 | \(0.248632\pi\) | ||||
−0.710138 | + | 0.704062i | \(0.751368\pi\) | |||||||
\(90\) | − | 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 | \(-0.992134\pi\) | ||
0.999695 | − | 0.0247087i | \(-0.00786583\pi\) | |||||||
\(98\) | − | 5.09709i | − | 0.514884i | ||||||
\(99\) | − | 15.5787i | − | 1.56572i | ||||||
\(100\) | −2.54978 | −0.254978 | ||||||||
\(101\) | − | 9.78271i | − | 0.973416i | −0.873565 | − | 0.486708i | \(-0.838198\pi\) | ||
0.873565 | − | 0.486708i | \(-0.161802\pi\) | |||||||
\(102\) | 18.7309i | 1.85464i | ||||||||
\(103\) | − | 5.00860i | − | 0.493512i | −0.969078 | − | 0.246756i | \(-0.920635\pi\) | ||
0.969078 | − | 0.246756i | \(-0.0793646\pi\) | |||||||
\(104\) | −3.53537 | −0.346671 | ||||||||
\(105\) | 13.3177i | 1.29967i | ||||||||
\(106\) | −4.03570 | −0.391982 | ||||||||
\(107\) | − | 18.0456i | − | 1.74453i | −0.489033 | − | 0.872266i | \(-0.662650\pi\) | ||
0.489033 | − | 0.872266i | \(-0.337350\pi\) | |||||||
\(108\) | 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 | \(0.0828790\pi\) | ||||
−0.966294 | + | 0.257440i | \(0.917121\pi\) | |||||||
\(114\) | 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 | \(0.0664610\pi\) | ||||
−0.978282 | + | 0.207280i | \(0.933539\pi\) | |||||||
\(128\) | 3.65724i | 0.323257i | ||||||||
\(129\) | − | 7.67436i | − | 0.675690i | ||||||
\(130\) | 1.85587 | 0.162770 | ||||||||
\(131\) | 12.6227i | 1.10285i | 0.834226 | + | 0.551423i | \(0.185915\pi\) | ||||
−0.834226 | + | 0.551423i | \(0.814085\pi\) | |||||||
\(132\) | 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 | \(0.266226\pi\) | ||||
−0.670158 | + | 0.742218i | \(0.733774\pi\) | |||||||
\(138\) | 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 | \(-0.866485\pi\) | ||
0.913313 | − | 0.407258i | \(-0.133515\pi\) | |||||||
\(150\) | 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 | \(-0.963866\pi\) | ||
0.993564 | − | 0.113274i | \(-0.0361339\pi\) | |||||||
\(164\) | 7.19014 | 0.561456 | ||||||||
\(165\) | − | 21.8470i | − | 1.70079i | ||||||
\(166\) | − | 15.3073i | − | 1.18808i | ||||||
\(167\) | − | 5.61638i | − | 0.434609i | −0.976104 | − | 0.217304i | \(-0.930274\pi\) | ||
0.976104 | − | 0.217304i | \(-0.0697264\pi\) | |||||||
\(168\) | 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 | \(0.0592307\pi\) | ||||
−0.982737 | + | 0.185007i | \(0.940769\pi\) | |||||||
\(174\) | − | 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 | \(0.172708\pi\) | ||||
−0.856381 | + | 0.516345i | \(0.827292\pi\) | |||||||
\(180\) | −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 | \(-0.992656\pi\) | ||
0.999734 | − | 0.0230709i | \(-0.00734435\pi\) | |||||||
\(194\) | 0.477456 | 0.0342794 | ||||||||
\(195\) | 4.52431i | 0.323993i | ||||||||
\(196\) | −5.39143 | −0.385102 | ||||||||
\(197\) | 15.4721i | 1.10234i | 0.834391 | + | 0.551172i | \(0.185819\pi\) | ||||
−0.834391 | + | 0.551172i | \(0.814181\pi\) | |||||||
\(198\) | 15.2827 | 1.08609 | ||||||||
\(199\) | 1.38720i | 0.0983358i | 0.998791 | + | 0.0491679i | \(0.0156569\pi\) | ||||
−0.998791 | + | 0.0491679i | \(0.984343\pi\) | |||||||
\(200\) | − | 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 | \(-0.994064\pi\) | ||
0.999826 | − | 0.0186488i | \(-0.00593643\pi\) | |||||||
\(212\) | 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 | \(-0.846963\pi\) | ||
0.886635 | − | 0.462470i | \(-0.153037\pi\) | |||||||
\(230\) | 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 | \(0.0199286\pi\) | ||||
−0.998041 | + | 0.0625667i | \(0.980071\pi\) | |||||||
\(252\) | 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 | \(-0.616848\pi\) | ||
0.358901 | − | 0.933376i | \(-0.383152\pi\) | |||||||
\(278\) | 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 | \(-0.760004\pi\) | ||
0.728977 | − | 0.684538i | \(-0.239996\pi\) | |||||||
\(312\) | 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 | \(0.0422451\pi\) | ||||
−0.991206 | + | 0.132328i | \(0.957755\pi\) | |||||||
\(318\) | 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 | \(-0.879189\pi\) | ||
0.928835 | − | 0.370493i | \(-0.120811\pi\) | |||||||
\(332\) | −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 | \(-0.958564\pi\) | ||
0.991539 | − | 0.129809i | \(-0.0414363\pi\) | |||||||
\(348\) | −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 | \(0.227406\pi\) | ||||
−0.755475 | + | 0.655177i | \(0.772594\pi\) | |||||||
\(360\) | − | 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 | \(0.196054\pi\) | ||||
−0.816242 | + | 0.577710i | \(0.803946\pi\) | |||||||
\(368\) | 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 | \(-0.758364\pi\) | ||
0.725441 | − | 0.688284i | \(-0.241636\pi\) | |||||||
\(374\) | −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 | \(-0.902793\pi\) | ||
0.953731 | − | 0.300662i | \(-0.0972075\pi\) | |||||||
\(380\) | 7.16748 | 0.367684 | ||||||||
\(381\) | − | 11.1728i | − | 0.572399i | ||||||
\(382\) | − | 10.3193i | − | 0.527979i | ||||||
\(383\) | − | 5.62366i | − | 0.287356i | −0.989625 | − | 0.143678i | \(-0.954107\pi\) | ||
0.989625 | − | 0.143678i | \(-0.0458929\pi\) | |||||||
\(384\) | − | 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 | \(0.189256\pi\) | ||||
−0.828392 | + | 0.560149i | \(0.810744\pi\) | |||||||
\(390\) | −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 | \(-0.947448\pi\) | ||
0.986402 | − | 0.164349i | \(-0.0525524\pi\) | |||||||
\(402\) | 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 | \(0.117158\pi\) | ||||
−0.933026 | + | 0.359810i | \(0.882842\pi\) | |||||||
\(422\) | 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 | \(-0.914382\pi\) | ||
0.964043 | − | 0.265746i | \(-0.0856183\pi\) | |||||||
\(432\) | −0.569190 | −0.0273852 | ||||||||
\(433\) | 30.0172i | 1.44254i | 0.692657 | + | 0.721268i | \(0.256440\pi\) | ||||
−0.692657 | + | 0.721268i | \(0.743560\pi\) | |||||||
\(434\) | 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 | \(-0.608287\pi\) | ||
0.333669 | − | 0.942690i | \(-0.391713\pi\) | |||||||
\(440\) | −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 | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394131i | \(0.871045\pi\) | |||||||
\(462\) | − | 46.9371i | − | 2.18371i | ||||||
\(463\) | 16.7577i | 0.778797i | 0.921069 | + | 0.389399i | \(0.127317\pi\) | ||||
−0.921069 | + | 0.389399i | \(0.872683\pi\) | |||||||
\(464\) | −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 | \(0.0783790\pi\) | ||||
−0.969837 | + | 0.243754i | \(0.921621\pi\) | |||||||
\(488\) | −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 | \(0.220394\pi\) | ||||
−0.769723 | + | 0.638378i | \(0.779606\pi\) | |||||||
\(500\) | 12.3390 | 0.551816 | ||||||||
\(501\) | 13.4317i | 0.600082i | ||||||||
\(502\) | −1.94481 | −0.0868012 | ||||||||
\(503\) | 9.51645i | 0.424318i | 0.977235 | + | 0.212159i | \(0.0680494\pi\) | ||||
−0.977235 | + | 0.212159i | \(0.931951\pi\) | |||||||
\(504\) | −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 | \(-0.771673\pi\) | ||
0.753577 | − | 0.657360i | \(-0.228327\pi\) | |||||||
\(510\) | − | 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 | \(-0.746859\pi\) | ||
0.700096 | − | 0.714049i | \(-0.253141\pi\) | |||||||
\(522\) | 10.4011i | 0.455242i | ||||||||
\(523\) | − | 34.8552i | − | 1.52411i | −0.647510 | − | 0.762057i | \(-0.724190\pi\) | ||
0.647510 | − | 0.762057i | \(-0.275810\pi\) | |||||||
\(524\) | 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 | \(0.230668\pi\) | ||||
−0.748721 | + | 0.662885i | \(0.769332\pi\) | |||||||
\(558\) | − | 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 | \(0.0603882\pi\) | ||||
−0.982058 | + | 0.188579i | \(0.939612\pi\) | |||||||
\(570\) | − | 16.2053i | − | 0.678766i | ||||||
\(571\) | 17.9832i | 0.752574i | 0.926503 | + | 0.376287i | \(0.122799\pi\) | ||||
−0.926503 | + | 0.376287i | \(0.877201\pi\) | |||||||
\(572\) | 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 | \(0.0815205\pi\) | ||||
−0.967384 | + | 0.253314i | \(0.918479\pi\) | |||||||
\(594\) | 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 | \(-0.926065\pi\) | ||
0.973145 | − | 0.230191i | \(-0.0739352\pi\) | |||||||
\(600\) | 17.5118i | 0.714916i | ||||||||
\(601\) | − | 8.67363i | − | 0.353805i | −0.984228 | − | 0.176902i | \(-0.943392\pi\) | ||
0.984228 | − | 0.176902i | \(-0.0566077\pi\) | |||||||
\(602\) | − | 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 | \(0.0764792\pi\) | ||||
−0.971275 | + | 0.237961i | \(0.923521\pi\) | |||||||
\(620\) | 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 | \(-0.987949\pi\) | ||
0.999283 | − | 0.0378502i | \(-0.0120510\pi\) | |||||||
\(644\) | − | 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 | \(-0.797624\pi\) | ||
0.804607 | − | 0.593808i | \(-0.202376\pi\) | |||||||
\(660\) | − | 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 | \(0.151311\pi\) | ||||
−0.889129 | + | 0.457656i | \(0.848689\pi\) | |||||||
\(678\) | 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 | \(-0.952306\pi\) | ||
0.988796 | − | 0.149275i | \(-0.0476940\pi\) | |||||||
\(692\) | 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 | \(0.195258\pi\) | ||||
−0.817683 | + | 0.575669i | \(0.804742\pi\) | |||||||
\(710\) | −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 | \(0.111986\pi\) | ||||
−0.938749 | + | 0.344600i | \(0.888014\pi\) | |||||||
\(720\) | 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 | \(-0.819329\pi\) | ||
0.843196 | − | 0.537606i | \(-0.180671\pi\) | |||||||
\(734\) | −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 | \(-0.784645\pi\) | ||
0.779734 | − | 0.626112i | \(-0.215355\pi\) | |||||||
\(752\) | 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 | \(-0.957073\pi\) | ||
0.990920 | − | 0.134449i | \(-0.0429265\pi\) | |||||||
\(758\) | 11.4840 | 0.417119 | ||||||||
\(759\) | − | 65.0180i | − | 2.36000i | ||||||
\(760\) | 20.5836i | 0.746647i | ||||||||
\(761\) | 18.4892i | 0.670235i | 0.942176 | + | 0.335117i | \(0.108776\pi\) | ||||
−0.942176 | + | 0.335117i | \(0.891224\pi\) | |||||||
\(762\) | 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 | \(-0.985651\pi\) | ||
0.998984 | − | 0.0450644i | \(-0.0143493\pi\) | |||||||
\(770\) | − | 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 | \(0.0758302\pi\) | ||||
−0.971758 | + | 0.235981i | \(0.924170\pi\) | |||||||
\(788\) | 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 | \(0.168713\pi\) | ||||
−0.862794 | + | 0.505556i | \(0.831287\pi\) | |||||||
\(798\) | −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 | \(0.00496421\pi\) | ||||
−0.999878 | + | 0.0155949i | \(0.995036\pi\) | |||||||
\(812\) | 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 | \(0.128125\pi\) | ||||
−0.920078 | + | 0.391736i | \(0.871875\pi\) | |||||||
\(828\) | −13.3907 | −0.465358 | ||||||||
\(829\) | − | 2.34189i | − | 0.0813372i | −0.999173 | − | 0.0406686i | \(-0.987051\pi\) | ||
0.999173 | − | 0.0406686i | \(-0.0129488\pi\) | |||||||
\(830\) | 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 | \(0.378698\pi\) | ||||
−0.371925 | + | 0.928263i | \(0.621302\pi\) | |||||||
\(840\) | −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 | \(-0.735572\pi\) | ||
0.674340 | − | 0.738421i | \(-0.264428\pi\) | |||||||
\(858\) | − | 15.9456i | − | 0.544373i | ||||||
\(859\) | − | 35.0119i | − | 1.19459i | −0.802021 | − | 0.597295i | \(-0.796242\pi\) | ||
0.802021 | − | 0.597295i | \(-0.203758\pi\) | |||||||
\(860\) | − | 5.30969i | − | 0.181059i | ||||||
\(861\) | − | 57.8717i | − | 1.97226i | ||||||
\(862\) | 10.8244 | 0.368680 | ||||||||
\(863\) | 2.88320i | 0.0981454i | 0.998795 | + | 0.0490727i | \(0.0156266\pi\) | ||||
−0.998795 | + | 0.0490727i | \(0.984373\pi\) | |||||||
\(864\) | 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 | \(0.184960\pi\) | ||||
−0.835877 | + | 0.548917i | \(0.815040\pi\) | |||||||
\(878\) | 38.7524 | 1.30783 | ||||||||
\(879\) | −36.0625 | −1.21636 | ||||||||
\(880\) | − | 7.74666i | − | 0.261140i | ||||||
\(881\) | − | 16.7339i | − | 0.563780i | −0.959447 | − | 0.281890i | \(-0.909039\pi\) | ||
0.959447 | − | 0.281890i | \(-0.0909613\pi\) | |||||||
\(882\) | − | 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 | \(-0.978029\pi\) | ||
0.997619 | − | 0.0689705i | \(-0.0219714\pi\) | |||||||
\(888\) | − | 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 | \(-0.946270\pi\) | ||
0.985788 | − | 0.167997i | \(-0.0537298\pi\) | |||||||
\(908\) | −17.1981 | −0.570740 | ||||||||
\(909\) | − | 26.6025i | − | 0.882348i | ||||||
\(910\) | 6.48116i | 0.214848i | ||||||||
\(911\) | 15.1869i | 0.503164i | 0.967836 | + | 0.251582i | \(0.0809507\pi\) | ||||
−0.967836 | + | 0.251582i | \(0.919049\pi\) | |||||||
\(912\) | −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 | \(0.238004\pi\) | ||||
−0.733247 | + | 0.679962i | \(0.761996\pi\) | |||||||
\(920\) | 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 | \(-0.930893\pi\) | ||
0.976525 | − | 0.215403i | \(-0.0691065\pi\) | |||||||
\(998\) | −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.348.16 | yes | 26 | |
349.348 | even | 2 | inner | 349.2.b.b.348.11 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
349.2.b.b.348.11 | ✓ | 26 | 349.348 | even | 2 | inner | |
349.2.b.b.348.16 | yes | 26 | 1.1 | even | 1 | trivial |