Properties

Label 1152.2.i.k.385.4
Level $1152$
Weight $2$
Character 1152.385
Analytic conductor $9.199$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 3 x^{10} - 8 x^{9} + 22 x^{8} - 42 x^{7} + 51 x^{6} - 126 x^{5} + 198 x^{4} - 216 x^{3} + 243 x^{2} - 486 x + 729\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 385.4
Root \(1.73202 - 0.0102491i\) of defining polynomial
Character \(\chi\) \(=\) 1152.385
Dual form 1152.2.i.k.769.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.857134 + 1.50510i) q^{3} +(0.551563 + 0.955334i) q^{5} +(-1.62490 + 2.81442i) q^{7} +(-1.53064 + 2.58014i) q^{9} +O(q^{10})\) \(q+(0.857134 + 1.50510i) q^{3} +(0.551563 + 0.955334i) q^{5} +(-1.62490 + 2.81442i) q^{7} +(-1.53064 + 2.58014i) q^{9} +(1.28869 - 2.23208i) q^{11} +(1.58731 + 2.74930i) q^{13} +(-0.965109 + 1.64901i) q^{15} +4.71601 q^{17} -5.75569 q^{19} +(-5.62873 - 0.0333075i) q^{21} +(2.35397 + 4.07719i) q^{23} +(1.89156 - 3.27627i) q^{25} +(-5.19533 - 0.0922374i) q^{27} +(-3.66250 + 6.34363i) q^{29} +(-2.93135 - 5.07724i) q^{31} +(4.46408 + 0.0264158i) q^{33} -3.58494 q^{35} -0.0714979 q^{37} +(-2.77743 + 4.74558i) q^{39} +(-1.63887 - 2.83861i) q^{41} +(-2.12088 + 3.67347i) q^{43} +(-3.30914 - 0.0391645i) q^{45} +(-4.72803 + 8.18919i) q^{47} +(-1.78062 - 3.08413i) q^{49} +(4.04225 + 7.09806i) q^{51} -6.42812 q^{53} +2.84317 q^{55} +(-4.93340 - 8.66288i) q^{57} +(-4.19606 - 7.26779i) q^{59} +(4.66250 - 8.07568i) q^{61} +(-4.77445 - 8.50035i) q^{63} +(-1.75100 + 3.03283i) q^{65} +(6.09975 + 10.5651i) q^{67} +(-4.11890 + 7.03765i) q^{69} -0.335627 q^{71} +14.8664 q^{73} +(6.55243 + 0.0387734i) q^{75} +(4.18800 + 7.25382i) q^{77} +(4.85985 - 8.41750i) q^{79} +(-4.31427 - 7.89855i) q^{81} +(-3.07022 + 5.31778i) q^{83} +(2.60117 + 4.50537i) q^{85} +(-12.6870 - 0.0750744i) q^{87} +4.42812 q^{89} -10.3169 q^{91} +(5.12919 - 8.76384i) q^{93} +(-3.17462 - 5.49861i) q^{95} +(6.39456 - 11.0757i) q^{97} +(3.78655 + 6.74151i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{3} - 2q^{5} + 6q^{7} - 2q^{9} + O(q^{10}) \) \( 12q + 4q^{3} - 2q^{5} + 6q^{7} - 2q^{9} + 4q^{11} + 10q^{13} + 4q^{15} + 4q^{17} + 4q^{19} + 2q^{21} + 8q^{23} - 14q^{25} - 14q^{27} - 2q^{29} + 8q^{31} - 10q^{33} + 8q^{35} + 22q^{39} - 2q^{41} - 2q^{43} + 10q^{45} - 14q^{47} - 18q^{49} - 38q^{51} + 24q^{53} - 16q^{55} - 38q^{57} + 6q^{59} + 14q^{61} - 16q^{63} - 8q^{65} + 4q^{67} - 50q^{69} - 28q^{71} + 60q^{73} + 50q^{75} + 2q^{77} + 16q^{79} + 22q^{81} + 24q^{83} + 16q^{85} - 36q^{87} - 48q^{89} - 52q^{91} + 42q^{93} - 20q^{95} - 14q^{97} + 68q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.857134 + 1.50510i 0.494867 + 0.868969i
\(4\) 0 0
\(5\) 0.551563 + 0.955334i 0.246666 + 0.427238i 0.962599 0.270931i \(-0.0873315\pi\)
−0.715933 + 0.698169i \(0.753998\pi\)
\(6\) 0 0
\(7\) −1.62490 + 2.81442i −0.614156 + 1.06375i 0.376376 + 0.926467i \(0.377170\pi\)
−0.990532 + 0.137282i \(0.956163\pi\)
\(8\) 0 0
\(9\) −1.53064 + 2.58014i −0.510214 + 0.860048i
\(10\) 0 0
\(11\) 1.28869 2.23208i 0.388555 0.672997i −0.603701 0.797211i \(-0.706308\pi\)
0.992255 + 0.124215i \(0.0396411\pi\)
\(12\) 0 0
\(13\) 1.58731 + 2.74930i 0.440241 + 0.762520i 0.997707 0.0676799i \(-0.0215597\pi\)
−0.557466 + 0.830200i \(0.688226\pi\)
\(14\) 0 0
\(15\) −0.965109 + 1.64901i −0.249190 + 0.425771i
\(16\) 0 0
\(17\) 4.71601 1.14380 0.571900 0.820323i \(-0.306206\pi\)
0.571900 + 0.820323i \(0.306206\pi\)
\(18\) 0 0
\(19\) −5.75569 −1.32045 −0.660223 0.751070i \(-0.729538\pi\)
−0.660223 + 0.751070i \(0.729538\pi\)
\(20\) 0 0
\(21\) −5.62873 0.0333075i −1.22829 0.00726830i
\(22\) 0 0
\(23\) 2.35397 + 4.07719i 0.490836 + 0.850152i 0.999944 0.0105499i \(-0.00335820\pi\)
−0.509109 + 0.860702i \(0.670025\pi\)
\(24\) 0 0
\(25\) 1.89156 3.27627i 0.378312 0.655255i
\(26\) 0 0
\(27\) −5.19533 0.0922374i −0.999842 0.0177511i
\(28\) 0 0
\(29\) −3.66250 + 6.34363i −0.680108 + 1.17798i 0.294839 + 0.955547i \(0.404734\pi\)
−0.974947 + 0.222435i \(0.928599\pi\)
\(30\) 0 0
\(31\) −2.93135 5.07724i −0.526485 0.911899i −0.999524 0.0308575i \(-0.990176\pi\)
0.473039 0.881042i \(-0.343157\pi\)
\(32\) 0 0
\(33\) 4.46408 + 0.0264158i 0.777096 + 0.00459840i
\(34\) 0 0
\(35\) −3.58494 −0.605966
\(36\) 0 0
\(37\) −0.0714979 −0.0117542 −0.00587709 0.999983i \(-0.501871\pi\)
−0.00587709 + 0.999983i \(0.501871\pi\)
\(38\) 0 0
\(39\) −2.77743 + 4.74558i −0.444745 + 0.759901i
\(40\) 0 0
\(41\) −1.63887 2.83861i −0.255949 0.443317i 0.709204 0.705004i \(-0.249055\pi\)
−0.965153 + 0.261687i \(0.915721\pi\)
\(42\) 0 0
\(43\) −2.12088 + 3.67347i −0.323431 + 0.560198i −0.981193 0.193027i \(-0.938170\pi\)
0.657763 + 0.753225i \(0.271503\pi\)
\(44\) 0 0
\(45\) −3.30914 0.0391645i −0.493298 0.00583830i
\(46\) 0 0
\(47\) −4.72803 + 8.18919i −0.689654 + 1.19452i 0.282296 + 0.959327i \(0.408904\pi\)
−0.971950 + 0.235188i \(0.924429\pi\)
\(48\) 0 0
\(49\) −1.78062 3.08413i −0.254375 0.440590i
\(50\) 0 0
\(51\) 4.04225 + 7.09806i 0.566029 + 0.993927i
\(52\) 0 0
\(53\) −6.42812 −0.882970 −0.441485 0.897269i \(-0.645548\pi\)
−0.441485 + 0.897269i \(0.645548\pi\)
\(54\) 0 0
\(55\) 2.84317 0.383373
\(56\) 0 0
\(57\) −4.93340 8.66288i −0.653445 1.14743i
\(58\) 0 0
\(59\) −4.19606 7.26779i −0.546281 0.946186i −0.998525 0.0542918i \(-0.982710\pi\)
0.452244 0.891894i \(-0.350623\pi\)
\(60\) 0 0
\(61\) 4.66250 8.07568i 0.596971 1.03398i −0.396294 0.918124i \(-0.629704\pi\)
0.993265 0.115861i \(-0.0369628\pi\)
\(62\) 0 0
\(63\) −4.77445 8.50035i −0.601524 1.07094i
\(64\) 0 0
\(65\) −1.75100 + 3.03283i −0.217185 + 0.376176i
\(66\) 0 0
\(67\) 6.09975 + 10.5651i 0.745203 + 1.29073i 0.950100 + 0.311945i \(0.100981\pi\)
−0.204897 + 0.978783i \(0.565686\pi\)
\(68\) 0 0
\(69\) −4.11890 + 7.03765i −0.495858 + 0.847233i
\(70\) 0 0
\(71\) −0.335627 −0.0398316 −0.0199158 0.999802i \(-0.506340\pi\)
−0.0199158 + 0.999802i \(0.506340\pi\)
\(72\) 0 0
\(73\) 14.8664 1.73998 0.869989 0.493071i \(-0.164126\pi\)
0.869989 + 0.493071i \(0.164126\pi\)
\(74\) 0 0
\(75\) 6.55243 + 0.0387734i 0.756610 + 0.00447717i
\(76\) 0 0
\(77\) 4.18800 + 7.25382i 0.477266 + 0.826650i
\(78\) 0 0
\(79\) 4.85985 8.41750i 0.546776 0.947043i −0.451717 0.892161i \(-0.649188\pi\)
0.998493 0.0548820i \(-0.0174783\pi\)
\(80\) 0 0
\(81\) −4.31427 7.89855i −0.479364 0.877616i
\(82\) 0 0
\(83\) −3.07022 + 5.31778i −0.337000 + 0.583702i −0.983867 0.178901i \(-0.942746\pi\)
0.646867 + 0.762603i \(0.276079\pi\)
\(84\) 0 0
\(85\) 2.60117 + 4.50537i 0.282137 + 0.488676i
\(86\) 0 0
\(87\) −12.6870 0.0750744i −1.36019 0.00804882i
\(88\) 0 0
\(89\) 4.42812 0.469379 0.234690 0.972070i \(-0.424593\pi\)
0.234690 + 0.972070i \(0.424593\pi\)
\(90\) 0 0
\(91\) −10.3169 −1.08151
\(92\) 0 0
\(93\) 5.12919 8.76384i 0.531872 0.908768i
\(94\) 0 0
\(95\) −3.17462 5.49861i −0.325709 0.564145i
\(96\) 0 0
\(97\) 6.39456 11.0757i 0.649270 1.12457i −0.334028 0.942563i \(-0.608408\pi\)
0.983298 0.182005i \(-0.0582586\pi\)
\(98\) 0 0
\(99\) 3.78655 + 6.74151i 0.380563 + 0.677548i
\(100\) 0 0
\(101\) 3.80137 6.58417i 0.378250 0.655149i −0.612557 0.790426i \(-0.709859\pi\)
0.990808 + 0.135277i \(0.0431925\pi\)
\(102\) 0 0
\(103\) 5.62490 + 9.74262i 0.554238 + 0.959969i 0.997962 + 0.0638053i \(0.0203237\pi\)
−0.443724 + 0.896163i \(0.646343\pi\)
\(104\) 0 0
\(105\) −3.07278 5.39569i −0.299872 0.526566i
\(106\) 0 0
\(107\) −2.81493 −0.272130 −0.136065 0.990700i \(-0.543446\pi\)
−0.136065 + 0.990700i \(0.543446\pi\)
\(108\) 0 0
\(109\) −15.6539 −1.49937 −0.749685 0.661795i \(-0.769795\pi\)
−0.749685 + 0.661795i \(0.769795\pi\)
\(110\) 0 0
\(111\) −0.0612833 0.107611i −0.00581675 0.0102140i
\(112\) 0 0
\(113\) 10.1828 + 17.6370i 0.957913 + 1.65915i 0.727557 + 0.686047i \(0.240656\pi\)
0.230355 + 0.973107i \(0.426011\pi\)
\(114\) 0 0
\(115\) −2.59672 + 4.49765i −0.242145 + 0.419408i
\(116\) 0 0
\(117\) −9.52320 0.112709i −0.880420 0.0104200i
\(118\) 0 0
\(119\) −7.66306 + 13.2728i −0.702472 + 1.21672i
\(120\) 0 0
\(121\) 2.17855 + 3.77337i 0.198050 + 0.343033i
\(122\) 0 0
\(123\) 2.86766 4.89974i 0.258568 0.441795i
\(124\) 0 0
\(125\) 9.68887 0.866599
\(126\) 0 0
\(127\) 3.09888 0.274981 0.137491 0.990503i \(-0.456096\pi\)
0.137491 + 0.990503i \(0.456096\pi\)
\(128\) 0 0
\(129\) −7.34680 0.0434741i −0.646850 0.00382768i
\(130\) 0 0
\(131\) 0.251085 + 0.434893i 0.0219374 + 0.0379968i 0.876786 0.480881i \(-0.159683\pi\)
−0.854848 + 0.518878i \(0.826350\pi\)
\(132\) 0 0
\(133\) 9.35244 16.1989i 0.810960 1.40462i
\(134\) 0 0
\(135\) −2.77743 5.01416i −0.239043 0.431550i
\(136\) 0 0
\(137\) −4.88868 + 8.46744i −0.417668 + 0.723423i −0.995704 0.0925885i \(-0.970486\pi\)
0.578036 + 0.816011i \(0.303819\pi\)
\(138\) 0 0
\(139\) −0.188498 0.326488i −0.0159882 0.0276924i 0.857921 0.513782i \(-0.171756\pi\)
−0.873909 + 0.486090i \(0.838423\pi\)
\(140\) 0 0
\(141\) −16.3781 0.0969159i −1.37928 0.00816179i
\(142\) 0 0
\(143\) 8.18221 0.684231
\(144\) 0 0
\(145\) −8.08038 −0.671039
\(146\) 0 0
\(147\) 3.11569 5.32353i 0.256978 0.439077i
\(148\) 0 0
\(149\) 4.83712 + 8.37814i 0.396272 + 0.686364i 0.993263 0.115885i \(-0.0369703\pi\)
−0.596990 + 0.802248i \(0.703637\pi\)
\(150\) 0 0
\(151\) 8.42915 14.5997i 0.685954 1.18811i −0.287181 0.957876i \(-0.592718\pi\)
0.973136 0.230232i \(-0.0739484\pi\)
\(152\) 0 0
\(153\) −7.21852 + 12.1680i −0.583583 + 0.983723i
\(154\) 0 0
\(155\) 3.23364 5.60083i 0.259732 0.449870i
\(156\) 0 0
\(157\) −4.36262 7.55628i −0.348175 0.603057i 0.637750 0.770243i \(-0.279865\pi\)
−0.985925 + 0.167187i \(0.946532\pi\)
\(158\) 0 0
\(159\) −5.50976 9.67495i −0.436952 0.767273i
\(160\) 0 0
\(161\) −15.2999 −1.20580
\(162\) 0 0
\(163\) −12.2063 −0.956067 −0.478034 0.878342i \(-0.658650\pi\)
−0.478034 + 0.878342i \(0.658650\pi\)
\(164\) 0 0
\(165\) 2.43698 + 4.27925i 0.189719 + 0.333140i
\(166\) 0 0
\(167\) 11.3806 + 19.7118i 0.880657 + 1.52534i 0.850612 + 0.525794i \(0.176232\pi\)
0.0300447 + 0.999549i \(0.490435\pi\)
\(168\) 0 0
\(169\) 1.46088 2.53033i 0.112376 0.194640i
\(170\) 0 0
\(171\) 8.80990 14.8505i 0.673710 1.13565i
\(172\) 0 0
\(173\) −11.9797 + 20.7494i −0.910798 + 1.57755i −0.0978588 + 0.995200i \(0.531199\pi\)
−0.812939 + 0.582348i \(0.802134\pi\)
\(174\) 0 0
\(175\) 6.14720 + 10.6473i 0.464684 + 0.804857i
\(176\) 0 0
\(177\) 7.34215 12.5450i 0.551870 0.942937i
\(178\) 0 0
\(179\) 10.9992 0.822121 0.411061 0.911608i \(-0.365158\pi\)
0.411061 + 0.911608i \(0.365158\pi\)
\(180\) 0 0
\(181\) 22.2168 1.65136 0.825679 0.564140i \(-0.190792\pi\)
0.825679 + 0.564140i \(0.190792\pi\)
\(182\) 0 0
\(183\) 16.1511 + 0.0955726i 1.19392 + 0.00706493i
\(184\) 0 0
\(185\) −0.0394356 0.0683044i −0.00289936 0.00502184i
\(186\) 0 0
\(187\) 6.07748 10.5265i 0.444429 0.769774i
\(188\) 0 0
\(189\) 8.70151 14.4720i 0.632942 1.05268i
\(190\) 0 0
\(191\) 5.48760 9.50479i 0.397068 0.687743i −0.596294 0.802766i \(-0.703361\pi\)
0.993363 + 0.115023i \(0.0366942\pi\)
\(192\) 0 0
\(193\) −7.11682 12.3267i −0.512280 0.887294i −0.999899 0.0142378i \(-0.995468\pi\)
0.487619 0.873057i \(-0.337866\pi\)
\(194\) 0 0
\(195\) −6.06555 0.0358923i −0.434363 0.00257030i
\(196\) 0 0
\(197\) 8.15037 0.580690 0.290345 0.956922i \(-0.406230\pi\)
0.290345 + 0.956922i \(0.406230\pi\)
\(198\) 0 0
\(199\) 6.09200 0.431850 0.215925 0.976410i \(-0.430723\pi\)
0.215925 + 0.976410i \(0.430723\pi\)
\(200\) 0 0
\(201\) −10.6732 + 18.2364i −0.752827 + 1.28630i
\(202\) 0 0
\(203\) −11.9024 20.6156i −0.835385 1.44693i
\(204\) 0 0
\(205\) 1.80788 3.13135i 0.126268 0.218703i
\(206\) 0 0
\(207\) −14.1228 0.167147i −0.981603 0.0116175i
\(208\) 0 0
\(209\) −7.41730 + 12.8471i −0.513066 + 0.888656i
\(210\) 0 0
\(211\) 3.01985 + 5.23054i 0.207895 + 0.360085i 0.951051 0.309033i \(-0.100005\pi\)
−0.743156 + 0.669118i \(0.766672\pi\)
\(212\) 0 0
\(213\) −0.287677 0.505151i −0.0197113 0.0346124i
\(214\) 0 0
\(215\) −4.67918 −0.319118
\(216\) 0 0
\(217\) 19.0526 1.29338
\(218\) 0 0
\(219\) 12.7425 + 22.3754i 0.861057 + 1.51199i
\(220\) 0 0
\(221\) 7.48578 + 12.9657i 0.503548 + 0.872170i
\(222\) 0 0
\(223\) 10.5391 18.2542i 0.705749 1.22239i −0.260671 0.965428i \(-0.583944\pi\)
0.966420 0.256966i \(-0.0827228\pi\)
\(224\) 0 0
\(225\) 5.55796 + 9.89529i 0.370530 + 0.659686i
\(226\) 0 0
\(227\) 14.9946 25.9713i 0.995224 1.72378i 0.413069 0.910700i \(-0.364457\pi\)
0.582155 0.813078i \(-0.302210\pi\)
\(228\) 0 0
\(229\) 9.53170 + 16.5094i 0.629873 + 1.09097i 0.987577 + 0.157136i \(0.0502262\pi\)
−0.357704 + 0.933835i \(0.616440\pi\)
\(230\) 0 0
\(231\) −7.32804 + 12.5208i −0.482150 + 0.823811i
\(232\) 0 0
\(233\) 7.91098 0.518266 0.259133 0.965842i \(-0.416563\pi\)
0.259133 + 0.965842i \(0.416563\pi\)
\(234\) 0 0
\(235\) −10.4312 −0.680457
\(236\) 0 0
\(237\) 16.8347 + 0.0996179i 1.09353 + 0.00647088i
\(238\) 0 0
\(239\) 2.96685 + 5.13873i 0.191910 + 0.332397i 0.945883 0.324508i \(-0.105199\pi\)
−0.753973 + 0.656905i \(0.771865\pi\)
\(240\) 0 0
\(241\) −14.2494 + 24.6808i −0.917888 + 1.58983i −0.115270 + 0.993334i \(0.536773\pi\)
−0.802618 + 0.596494i \(0.796560\pi\)
\(242\) 0 0
\(243\) 8.19018 13.2635i 0.525400 0.850855i
\(244\) 0 0
\(245\) 1.96425 3.40218i 0.125491 0.217357i
\(246\) 0 0
\(247\) −9.13607 15.8241i −0.581314 1.00687i
\(248\) 0 0
\(249\) −10.6354 0.0629338i −0.673989 0.00398827i
\(250\) 0 0
\(251\) 15.6924 0.990498 0.495249 0.868751i \(-0.335077\pi\)
0.495249 + 0.868751i \(0.335077\pi\)
\(252\) 0 0
\(253\) 12.1341 0.762866
\(254\) 0 0
\(255\) −4.55146 + 7.77673i −0.285024 + 0.486997i
\(256\) 0 0
\(257\) 11.5645 + 20.0304i 0.721377 + 1.24946i 0.960448 + 0.278459i \(0.0898237\pi\)
−0.239071 + 0.971002i \(0.576843\pi\)
\(258\) 0 0
\(259\) 0.116177 0.201225i 0.00721890 0.0125035i
\(260\) 0 0
\(261\) −10.7615 19.1596i −0.666120 1.18595i
\(262\) 0 0
\(263\) 12.0737 20.9122i 0.744494 1.28950i −0.205937 0.978565i \(-0.566024\pi\)
0.950431 0.310936i \(-0.100642\pi\)
\(264\) 0 0
\(265\) −3.54551 6.14100i −0.217799 0.377239i
\(266\) 0 0
\(267\) 3.79549 + 6.66475i 0.232280 + 0.407876i
\(268\) 0 0
\(269\) −9.45599 −0.576542 −0.288271 0.957549i \(-0.593080\pi\)
−0.288271 + 0.957549i \(0.593080\pi\)
\(270\) 0 0
\(271\) −15.5750 −0.946115 −0.473057 0.881032i \(-0.656850\pi\)
−0.473057 + 0.881032i \(0.656850\pi\)
\(272\) 0 0
\(273\) −8.84298 15.5280i −0.535201 0.939795i
\(274\) 0 0
\(275\) −4.87526 8.44420i −0.293989 0.509205i
\(276\) 0 0
\(277\) 2.87862 4.98592i 0.172960 0.299575i −0.766494 0.642252i \(-0.778000\pi\)
0.939453 + 0.342677i \(0.111334\pi\)
\(278\) 0 0
\(279\) 17.5868 + 0.208144i 1.05290 + 0.0124613i
\(280\) 0 0
\(281\) 5.99712 10.3873i 0.357758 0.619656i −0.629828 0.776735i \(-0.716874\pi\)
0.987586 + 0.157079i \(0.0502078\pi\)
\(282\) 0 0
\(283\) −0.604018 1.04619i −0.0359051 0.0621895i 0.847514 0.530772i \(-0.178098\pi\)
−0.883420 + 0.468583i \(0.844765\pi\)
\(284\) 0 0
\(285\) 5.55487 9.49117i 0.329042 0.562208i
\(286\) 0 0
\(287\) 10.6520 0.628771
\(288\) 0 0
\(289\) 5.24075 0.308279
\(290\) 0 0
\(291\) 22.1510 + 0.131077i 1.29852 + 0.00768386i
\(292\) 0 0
\(293\) −10.4657 18.1272i −0.611415 1.05900i −0.991002 0.133846i \(-0.957267\pi\)
0.379587 0.925156i \(-0.376066\pi\)
\(294\) 0 0
\(295\) 4.62878 8.01728i 0.269498 0.466784i
\(296\) 0 0
\(297\) −6.90106 + 11.4775i −0.400440 + 0.665993i
\(298\) 0 0
\(299\) −7.47295 + 12.9435i −0.432172 + 0.748544i
\(300\) 0 0
\(301\) −6.89244 11.9381i −0.397274 0.688098i
\(302\) 0 0
\(303\) 13.1681 + 0.0779211i 0.756488 + 0.00447645i
\(304\) 0 0
\(305\) 10.2866 0.589011
\(306\) 0 0
\(307\) 5.12445 0.292468 0.146234 0.989250i \(-0.453285\pi\)
0.146234 + 0.989250i \(0.453285\pi\)
\(308\) 0 0
\(309\) −9.84230 + 16.8168i −0.559909 + 0.956672i
\(310\) 0 0
\(311\) −4.70739 8.15344i −0.266931 0.462339i 0.701136 0.713027i \(-0.252676\pi\)
−0.968068 + 0.250688i \(0.919343\pi\)
\(312\) 0 0
\(313\) −9.48986 + 16.4369i −0.536398 + 0.929069i 0.462696 + 0.886517i \(0.346882\pi\)
−0.999094 + 0.0425521i \(0.986451\pi\)
\(314\) 0 0
\(315\) 5.48726 9.24967i 0.309172 0.521160i
\(316\) 0 0
\(317\) 14.2294 24.6461i 0.799205 1.38426i −0.120930 0.992661i \(-0.538588\pi\)
0.920135 0.391602i \(-0.128079\pi\)
\(318\) 0 0
\(319\) 9.43965 + 16.3499i 0.528519 + 0.915421i
\(320\) 0 0
\(321\) −2.41278 4.23675i −0.134668 0.236472i
\(322\) 0 0
\(323\) −27.1439 −1.51033
\(324\) 0 0
\(325\) 12.0100 0.666193
\(326\) 0 0
\(327\) −13.4175 23.5606i −0.741988 1.30291i
\(328\) 0 0
\(329\) −15.3652 26.6133i −0.847110 1.46724i
\(330\) 0 0
\(331\) 0.837151 1.44999i 0.0460140 0.0796986i −0.842101 0.539320i \(-0.818681\pi\)
0.888115 + 0.459621i \(0.152015\pi\)
\(332\) 0 0
\(333\) 0.109438 0.184475i 0.00599715 0.0101092i
\(334\) 0 0
\(335\) −6.72878 + 11.6546i −0.367633 + 0.636758i
\(336\) 0 0
\(337\) −15.1064 26.1651i −0.822899 1.42530i −0.903514 0.428558i \(-0.859022\pi\)
0.0806146 0.996745i \(-0.474312\pi\)
\(338\) 0 0
\(339\) −17.8175 + 30.4434i −0.967714 + 1.65346i
\(340\) 0 0
\(341\) −15.1104 −0.818273
\(342\) 0 0
\(343\) −11.1753 −0.603408
\(344\) 0 0
\(345\) −8.99514 0.0532279i −0.484282 0.00286570i
\(346\) 0 0
\(347\) 8.46076 + 14.6545i 0.454197 + 0.786693i 0.998642 0.0521042i \(-0.0165928\pi\)
−0.544444 + 0.838797i \(0.683259\pi\)
\(348\) 0 0
\(349\) 8.92436 15.4574i 0.477710 0.827418i −0.521964 0.852968i \(-0.674800\pi\)
0.999674 + 0.0255500i \(0.00813369\pi\)
\(350\) 0 0
\(351\) −7.99302 14.4300i −0.426636 0.770214i
\(352\) 0 0
\(353\) −6.93593 + 12.0134i −0.369162 + 0.639407i −0.989435 0.144979i \(-0.953689\pi\)
0.620273 + 0.784386i \(0.287022\pi\)
\(354\) 0 0
\(355\) −0.185119 0.320636i −0.00982510 0.0170176i
\(356\) 0 0
\(357\) −26.5452 0.157079i −1.40492 0.00831348i
\(358\) 0 0
\(359\) −0.333139 −0.0175824 −0.00879120 0.999961i \(-0.502798\pi\)
−0.00879120 + 0.999961i \(0.502798\pi\)
\(360\) 0 0
\(361\) 14.1280 0.743577
\(362\) 0 0
\(363\) −3.81197 + 6.51322i −0.200077 + 0.341855i
\(364\) 0 0
\(365\) 8.19974 + 14.2024i 0.429194 + 0.743386i
\(366\) 0 0
\(367\) 10.5763 18.3188i 0.552081 0.956232i −0.446043 0.895011i \(-0.647167\pi\)
0.998124 0.0612208i \(-0.0194994\pi\)
\(368\) 0 0
\(369\) 9.83256 + 0.116371i 0.511862 + 0.00605801i
\(370\) 0 0
\(371\) 10.4451 18.0914i 0.542281 0.939258i
\(372\) 0 0
\(373\) 4.33750 + 7.51278i 0.224587 + 0.388997i 0.956196 0.292729i \(-0.0945632\pi\)
−0.731608 + 0.681725i \(0.761230\pi\)
\(374\) 0 0
\(375\) 8.30467 + 14.5827i 0.428851 + 0.753048i
\(376\) 0 0
\(377\) −23.2541 −1.19765
\(378\) 0 0
\(379\) 14.2538 0.732168 0.366084 0.930582i \(-0.380698\pi\)
0.366084 + 0.930582i \(0.380698\pi\)
\(380\) 0 0
\(381\) 2.65616 + 4.66412i 0.136079 + 0.238950i
\(382\) 0 0
\(383\) 5.11696 + 8.86283i 0.261464 + 0.452869i 0.966631 0.256172i \(-0.0824613\pi\)
−0.705167 + 0.709041i \(0.749128\pi\)
\(384\) 0 0
\(385\) −4.61988 + 8.00187i −0.235451 + 0.407813i
\(386\) 0 0
\(387\) −6.23177 11.0949i −0.316778 0.563987i
\(388\) 0 0
\(389\) 1.62675 2.81761i 0.0824793 0.142858i −0.821835 0.569726i \(-0.807049\pi\)
0.904314 + 0.426867i \(0.140383\pi\)
\(390\) 0 0
\(391\) 11.1013 + 19.2281i 0.561418 + 0.972405i
\(392\) 0 0
\(393\) −0.439342 + 0.750670i −0.0221619 + 0.0378663i
\(394\) 0 0
\(395\) 10.7220 0.539484
\(396\) 0 0
\(397\) −30.8709 −1.54936 −0.774682 0.632351i \(-0.782090\pi\)
−0.774682 + 0.632351i \(0.782090\pi\)
\(398\) 0 0
\(399\) 32.3972 + 0.191708i 1.62189 + 0.00959739i
\(400\) 0 0
\(401\) −2.01000 3.48143i −0.100375 0.173854i 0.811464 0.584402i \(-0.198671\pi\)
−0.911839 + 0.410548i \(0.865338\pi\)
\(402\) 0 0
\(403\) 9.30592 16.1183i 0.463561 0.802911i
\(404\) 0 0
\(405\) 5.16616 8.47812i 0.256709 0.421281i
\(406\) 0 0
\(407\) −0.0921386 + 0.159589i −0.00456714 + 0.00791052i
\(408\) 0 0
\(409\) −3.33949 5.78416i −0.165127 0.286008i 0.771573 0.636140i \(-0.219470\pi\)
−0.936700 + 0.350132i \(0.886137\pi\)
\(410\) 0 0
\(411\) −16.9346 0.100209i −0.835322 0.00494294i
\(412\) 0 0
\(413\) 27.2728 1.34201
\(414\) 0 0
\(415\) −6.77367 −0.332507
\(416\) 0 0
\(417\) 0.329829 0.563553i 0.0161518 0.0275973i
\(418\) 0 0
\(419\) 17.0507 + 29.5327i 0.832982 + 1.44277i 0.895663 + 0.444733i \(0.146701\pi\)
−0.0626815 + 0.998034i \(0.519965\pi\)
\(420\) 0 0
\(421\) 9.34688 16.1893i 0.455539 0.789017i −0.543180 0.839616i \(-0.682780\pi\)
0.998719 + 0.0505996i \(0.0161132\pi\)
\(422\) 0 0
\(423\) −13.8924 24.7337i −0.675469 1.20259i
\(424\) 0 0
\(425\) 8.92060 15.4509i 0.432713 0.749481i
\(426\) 0 0
\(427\) 15.1522 + 26.2444i 0.733267 + 1.27006i
\(428\) 0 0
\(429\) 7.01325 + 12.3150i 0.338603 + 0.594575i
\(430\) 0 0
\(431\) −6.49967 −0.313078 −0.156539 0.987672i \(-0.550034\pi\)
−0.156539 + 0.987672i \(0.550034\pi\)
\(432\) 0 0
\(433\) 28.3266 1.36129 0.680645 0.732613i \(-0.261700\pi\)
0.680645 + 0.732613i \(0.261700\pi\)
\(434\) 0 0
\(435\) −6.92597 12.1618i −0.332075 0.583112i
\(436\) 0 0
\(437\) −13.5487 23.4670i −0.648122 1.12258i
\(438\) 0 0
\(439\) 3.82047 6.61724i 0.182341 0.315824i −0.760336 0.649530i \(-0.774966\pi\)
0.942677 + 0.333706i \(0.108299\pi\)
\(440\) 0 0
\(441\) 10.6830 + 0.126436i 0.508714 + 0.00602075i
\(442\) 0 0
\(443\) −6.94625 + 12.0313i −0.330026 + 0.571623i −0.982517 0.186175i \(-0.940391\pi\)
0.652490 + 0.757797i \(0.273724\pi\)
\(444\) 0 0
\(445\) 2.44238 + 4.23033i 0.115780 + 0.200537i
\(446\) 0 0
\(447\) −8.46386 + 14.4615i −0.400327 + 0.684007i
\(448\) 0 0
\(449\) 11.8869 0.560976 0.280488 0.959857i \(-0.409504\pi\)
0.280488 + 0.959857i \(0.409504\pi\)
\(450\) 0 0
\(451\) −8.44800 −0.397801
\(452\) 0 0
\(453\) 29.1989 + 0.172782i 1.37188 + 0.00811801i
\(454\) 0 0
\(455\) −5.69042 9.85610i −0.266771 0.462061i
\(456\) 0 0
\(457\) 0.860741 1.49085i 0.0402638 0.0697389i −0.845191 0.534464i \(-0.820514\pi\)
0.885455 + 0.464725i \(0.153847\pi\)
\(458\) 0 0
\(459\) −24.5012 0.434992i −1.14362 0.0203037i
\(460\) 0 0
\(461\) −15.8265 + 27.4123i −0.737113 + 1.27672i 0.216677 + 0.976243i \(0.430478\pi\)
−0.953790 + 0.300474i \(0.902855\pi\)
\(462\) 0 0
\(463\) 1.71702 + 2.97396i 0.0797966 + 0.138212i 0.903162 0.429300i \(-0.141240\pi\)
−0.823366 + 0.567511i \(0.807906\pi\)
\(464\) 0 0
\(465\) 11.2015 + 0.0662837i 0.519456 + 0.00307383i
\(466\) 0 0
\(467\) −15.5333 −0.718797 −0.359398 0.933184i \(-0.617018\pi\)
−0.359398 + 0.933184i \(0.617018\pi\)
\(468\) 0 0
\(469\) −39.6460 −1.83068
\(470\) 0 0
\(471\) 7.63359 13.0429i 0.351737 0.600986i
\(472\) 0 0
\(473\) 5.46631 + 9.46792i 0.251341 + 0.435335i
\(474\) 0 0
\(475\) −10.8872 + 18.8572i −0.499540 + 0.865228i
\(476\) 0 0
\(477\) 9.83914 16.5855i 0.450503 0.759396i
\(478\) 0 0
\(479\) −16.6927 + 28.9126i −0.762710 + 1.32105i 0.178739 + 0.983897i \(0.442798\pi\)
−0.941449 + 0.337156i \(0.890535\pi\)
\(480\) 0 0
\(481\) −0.113489 0.196569i −0.00517467 0.00896280i
\(482\) 0 0
\(483\) −13.1140 23.0278i −0.596710 1.04780i
\(484\) 0 0
\(485\) 14.1080 0.640612
\(486\) 0 0
\(487\) −20.0794 −0.909883 −0.454941 0.890521i \(-0.650340\pi\)
−0.454941 + 0.890521i \(0.650340\pi\)
\(488\) 0 0
\(489\) −10.4624 18.3716i −0.473126 0.830793i
\(490\) 0 0
\(491\) −2.10538 3.64663i −0.0950146 0.164570i 0.814600 0.580023i \(-0.196956\pi\)
−0.909615 + 0.415453i \(0.863623\pi\)
\(492\) 0 0
\(493\) −17.2724 + 29.9166i −0.777908 + 1.34738i
\(494\) 0 0
\(495\) −4.35188 + 7.33579i −0.195602 + 0.329719i
\(496\) 0 0
\(497\) 0.545361 0.944593i 0.0244628 0.0423708i
\(498\) 0 0
\(499\) −5.24770 9.08928i −0.234919 0.406892i 0.724330 0.689453i \(-0.242149\pi\)
−0.959249 + 0.282561i \(0.908816\pi\)
\(500\) 0 0
\(501\) −19.9134 + 34.0245i −0.889667 + 1.52010i
\(502\) 0 0
\(503\) −34.5118 −1.53881 −0.769403 0.638764i \(-0.779446\pi\)
−0.769403 + 0.638764i \(0.779446\pi\)
\(504\) 0 0
\(505\) 8.38677 0.373206
\(506\) 0 0
\(507\) 5.06056 + 0.0299454i 0.224748 + 0.00132992i
\(508\) 0 0
\(509\) −2.62702 4.55013i −0.116440 0.201681i 0.801914 0.597439i \(-0.203815\pi\)
−0.918355 + 0.395758i \(0.870482\pi\)
\(510\) 0 0
\(511\) −24.1564 + 41.8402i −1.06862 + 1.85090i
\(512\) 0 0
\(513\) 29.9027 + 0.530890i 1.32024 + 0.0234394i
\(514\) 0 0
\(515\) −6.20497 + 10.7473i −0.273424 + 0.473584i
\(516\) 0 0
\(517\) 12.1859 + 21.1066i 0.535937 + 0.928269i
\(518\) 0 0
\(519\) −41.4981 0.245561i −1.82156 0.0107789i
\(520\) 0 0
\(521\) −12.9218 −0.566113 −0.283056 0.959103i \(-0.591348\pi\)
−0.283056 + 0.959103i \(0.591348\pi\)
\(522\) 0 0
\(523\) 5.10475 0.223215 0.111607 0.993752i \(-0.464400\pi\)
0.111607 + 0.993752i \(0.464400\pi\)
\(524\) 0 0
\(525\) −10.7562 + 18.3783i −0.469439 + 0.802093i
\(526\) 0 0
\(527\) −13.8243 23.9443i −0.602194 1.04303i
\(528\) 0 0
\(529\) 0.417694 0.723468i 0.0181606 0.0314551i
\(530\) 0 0
\(531\) 25.1746 + 0.297947i 1.09248 + 0.0129298i
\(532\) 0 0
\(533\) 5.20281 9.01153i 0.225359 0.390333i
\(534\) 0 0
\(535\) −1.55261 2.68920i −0.0671252 0.116264i
\(536\) 0 0
\(537\) 9.42782 + 16.5549i 0.406840 + 0.714398i
\(538\) 0 0
\(539\) −9.17869 −0.395354
\(540\) 0 0
\(541\) −37.9746 −1.63266 −0.816328 0.577589i \(-0.803994\pi\)
−0.816328 + 0.577589i \(0.803994\pi\)
\(542\) 0 0
\(543\) 19.0427 + 33.4384i 0.817202 + 1.43498i
\(544\) 0 0
\(545\) −8.63410 14.9547i −0.369844 0.640589i
\(546\) 0 0
\(547\) 15.9350 27.6003i 0.681332 1.18010i −0.293243 0.956038i \(-0.594734\pi\)
0.974575 0.224063i \(-0.0719323\pi\)
\(548\) 0 0
\(549\) 13.6998 + 24.3909i 0.584693 + 1.04098i
\(550\) 0 0
\(551\) 21.0802 36.5120i 0.898046 1.55546i
\(552\) 0 0
\(553\) 15.7936 + 27.3553i 0.671611 + 1.16326i
\(554\) 0 0
\(555\) 0.0690032 0.117900i 0.00292902 0.00500459i
\(556\) 0 0
\(557\) −11.5906 −0.491111 −0.245555 0.969383i \(-0.578970\pi\)
−0.245555 + 0.969383i \(0.578970\pi\)
\(558\) 0 0
\(559\) −13.4660 −0.569550
\(560\) 0 0
\(561\) 21.0526 + 0.124577i 0.888843 + 0.00525965i
\(562\) 0 0
\(563\) 1.25138 + 2.16745i 0.0527392 + 0.0913470i 0.891190 0.453631i \(-0.149871\pi\)
−0.838451 + 0.544978i \(0.816538\pi\)
\(564\) 0 0
\(565\) −11.2328 + 19.4559i −0.472569 + 0.818514i
\(566\) 0 0
\(567\) 29.2401 + 0.692223i 1.22797 + 0.0290706i
\(568\) 0 0
\(569\) 12.9597 22.4469i 0.543301 0.941024i −0.455411 0.890281i \(-0.650508\pi\)
0.998712 0.0507432i \(-0.0161590\pi\)
\(570\) 0 0
\(571\) 5.03679 + 8.72398i 0.210783 + 0.365087i 0.951960 0.306223i \(-0.0990653\pi\)
−0.741177 + 0.671310i \(0.765732\pi\)
\(572\) 0 0
\(573\) 19.0093 + 0.112486i 0.794123 + 0.00469915i
\(574\) 0 0
\(575\) 17.8106 0.742755
\(576\) 0 0
\(577\) −23.4726 −0.977177 −0.488588 0.872514i \(-0.662488\pi\)
−0.488588 + 0.872514i \(0.662488\pi\)
\(578\) 0 0
\(579\) 12.4528 21.2771i 0.517521 0.884248i
\(580\) 0 0
\(581\) −9.97762 17.2818i −0.413942 0.716968i
\(582\) 0 0
\(583\) −8.28385 + 14.3481i −0.343082 + 0.594236i
\(584\) 0 0
\(585\) −5.14497 9.16001i −0.212718 0.378720i
\(586\) 0 0
\(587\) −12.4138 + 21.5012i −0.512370 + 0.887451i 0.487527 + 0.873108i \(0.337899\pi\)
−0.999897 + 0.0143435i \(0.995434\pi\)
\(588\) 0 0
\(589\) 16.8719 + 29.2230i 0.695195 + 1.20411i
\(590\) 0 0
\(591\) 6.98596 + 12.2671i 0.287364 + 0.504601i
\(592\) 0 0
\(593\) −7.70977 −0.316602 −0.158301 0.987391i \(-0.550602\pi\)
−0.158301 + 0.987391i \(0.550602\pi\)
\(594\) 0 0
\(595\) −16.9066 −0.693104
\(596\) 0 0
\(597\) 5.22166 + 9.16906i 0.213708 + 0.375265i
\(598\) 0 0
\(599\) 14.7176 + 25.4916i 0.601344 + 1.04156i 0.992618 + 0.121284i \(0.0387013\pi\)
−0.391274 + 0.920274i \(0.627965\pi\)
\(600\) 0 0
\(601\) −1.76388 + 3.05514i −0.0719503 + 0.124622i −0.899756 0.436393i \(-0.856256\pi\)
0.827806 + 0.561015i \(0.189589\pi\)
\(602\) 0 0
\(603\) −36.5959 0.433121i −1.49030 0.0176381i
\(604\) 0 0
\(605\) −2.40322 + 4.16250i −0.0977047 + 0.169230i
\(606\) 0 0
\(607\) 13.3211 + 23.0728i 0.540687 + 0.936497i 0.998865 + 0.0476362i \(0.0151688\pi\)
−0.458178 + 0.888860i \(0.651498\pi\)
\(608\) 0 0
\(609\) 20.8265 35.5846i 0.843932 1.44196i
\(610\) 0 0
\(611\) −30.0194 −1.21446
\(612\) 0 0
\(613\) 0.706406 0.0285315 0.0142657 0.999898i \(-0.495459\pi\)
0.0142657 + 0.999898i \(0.495459\pi\)
\(614\) 0 0
\(615\) 6.26258 + 0.0370583i 0.252532 + 0.00149433i
\(616\) 0 0
\(617\) 8.58480 + 14.8693i 0.345611 + 0.598616i 0.985465 0.169881i \(-0.0543383\pi\)
−0.639853 + 0.768497i \(0.721005\pi\)
\(618\) 0 0
\(619\) 4.17800 7.23651i 0.167928 0.290860i −0.769763 0.638330i \(-0.779626\pi\)
0.937691 + 0.347470i \(0.112959\pi\)
\(620\) 0 0
\(621\) −11.8536 21.3995i −0.475667 0.858731i
\(622\) 0 0
\(623\) −7.19526 + 12.4626i −0.288272 + 0.499302i
\(624\) 0 0
\(625\) −4.11377 7.12526i −0.164551 0.285010i
\(626\) 0 0
\(627\) −25.6938 0.152041i −1.02611 0.00607193i
\(628\) 0 0
\(629\) −0.337185 −0.0134444
\(630\) 0 0
\(631\) −23.9865 −0.954889 −0.477444 0.878662i \(-0.658437\pi\)
−0.477444 + 0.878662i \(0.658437\pi\)
\(632\) 0 0
\(633\) −5.28406 + 9.02845i −0.210022 + 0.358849i
\(634\) 0 0
\(635\) 1.70923 + 2.96047i 0.0678286 + 0.117483i
\(636\) 0 0
\(637\) 5.65281 9.79095i 0.223972 0.387932i
\(638\) 0 0
\(639\) 0.513724 0.865965i 0.0203226 0.0342570i
\(640\) 0 0
\(641\) 6.58068 11.3981i 0.259921 0.450197i −0.706299 0.707913i \(-0.749637\pi\)
0.966221 + 0.257716i \(0.0829700\pi\)
\(642\) 0 0
\(643\) −7.85931 13.6127i −0.309941 0.536834i 0.668408 0.743795i \(-0.266976\pi\)
−0.978349 + 0.206961i \(0.933643\pi\)
\(644\) 0 0
\(645\) −4.01069 7.04263i −0.157921 0.277303i
\(646\) 0 0
\(647\) 23.5146 0.924455 0.462228 0.886761i \(-0.347050\pi\)
0.462228 + 0.886761i \(0.347050\pi\)
\(648\) 0 0
\(649\) −21.6297 −0.849040
\(650\) 0 0
\(651\) 16.3307 + 28.6761i 0.640049 + 1.12390i
\(652\) 0 0
\(653\) −13.1340 22.7487i −0.513971 0.890224i −0.999869 0.0162084i \(-0.994840\pi\)
0.485897 0.874016i \(-0.338493\pi\)
\(654\) 0 0
\(655\) −0.276979 + 0.479741i −0.0108224 + 0.0187450i
\(656\) 0 0
\(657\) −22.7551 + 38.3574i −0.887761 + 1.49646i
\(658\) 0 0
\(659\) −13.2710 + 22.9860i −0.516963 + 0.895406i 0.482843 + 0.875707i \(0.339604\pi\)
−0.999806 + 0.0196993i \(0.993729\pi\)
\(660\) 0 0
\(661\) 0.981745 + 1.70043i 0.0381855 + 0.0661392i 0.884487 0.466566i \(-0.154509\pi\)
−0.846301 + 0.532705i \(0.821176\pi\)
\(662\) 0 0
\(663\) −13.0984 + 22.3802i −0.508700 + 0.869175i
\(664\) 0 0
\(665\) 20.6338 0.800145
\(666\) 0 0
\(667\) −34.4856 −1.33529
\(668\) 0 0
\(669\) 36.5078 + 0.216032i 1.41147 + 0.00835227i
\(670\) 0 0
\(671\) −12.0170 20.8141i −0.463912 0.803519i
\(672\) 0 0
\(673\) −18.9859 + 32.8846i −0.731854 + 1.26761i 0.224236 + 0.974535i \(0.428011\pi\)
−0.956090 + 0.293073i \(0.905322\pi\)
\(674\) 0 0
\(675\) −10.1295 + 16.8469i −0.389883 + 0.648436i
\(676\) 0 0
\(677\) −13.5894 + 23.5375i −0.522282 + 0.904619i 0.477382 + 0.878696i \(0.341586\pi\)
−0.999664 + 0.0259229i \(0.991748\pi\)
\(678\) 0 0
\(679\) 20.7811 + 35.9939i 0.797505 + 1.38132i
\(680\) 0 0
\(681\) 51.9418 + 0.307361i 1.99041 + 0.0117781i
\(682\) 0 0
\(683\) 46.9121 1.79504 0.897520 0.440974i \(-0.145367\pi\)
0.897520 + 0.440974i \(0.145367\pi\)
\(684\) 0 0
\(685\) −10.7857 −0.412099
\(686\) 0 0
\(687\) −16.6783 + 28.4969i −0.636317 + 1.08722i
\(688\) 0 0
\(689\) −10.2034 17.6728i −0.388719 0.673282i
\(690\) 0 0
\(691\) 12.6750 21.9538i 0.482181 0.835161i −0.517610 0.855617i \(-0.673178\pi\)
0.999791 + 0.0204552i \(0.00651153\pi\)
\(692\) 0 0
\(693\) −25.1262 0.297375i −0.954466 0.0112963i
\(694\) 0 0
\(695\) 0.207937 0.360157i 0.00788750 0.0136616i
\(696\) 0 0
\(697\) −7.72895 13.3869i −0.292755 0.507066i
\(698\) 0 0
\(699\) 6.78078 + 11.9068i 0.256472 + 0.450357i
\(700\) 0 0
\(701\) −44.2840 −1.67258 −0.836292 0.548284i \(-0.815281\pi\)
−0.836292 + 0.548284i \(0.815281\pi\)
\(702\) 0 0
\(703\) 0.411520 0.0155208
\(704\) 0 0
\(705\) −8.94095 15.7000i −0.336736 0.591296i
\(706\) 0 0
\(707\) 12.3537 + 21.3973i 0.464609 + 0.804727i
\(708\) 0 0
\(709\) −7.80457 + 13.5179i −0.293107 + 0.507676i −0.974543 0.224202i \(-0.928022\pi\)
0.681436 + 0.731878i \(0.261356\pi\)
\(710\) 0 0
\(711\) 14.2797 + 25.4233i 0.535530 + 0.953448i
\(712\) 0 0
\(713\) 13.8006 23.9033i 0.516836 0.895185i
\(714\) 0 0
\(715\) 4.51300 + 7.81675i 0.168777 + 0.292330i
\(716\) 0 0
\(717\) −5.19131 + 8.86999i −0.193873 + 0.331256i
\(718\) 0 0
\(719\) −21.1560 −0.788985 −0.394493 0.918899i \(-0.629080\pi\)
−0.394493 + 0.918899i \(0.629080\pi\)
\(720\) 0 0
\(721\) −36.5597 −1.36155
\(722\) 0 0
\(723\) −49.3607 0.292087i −1.83574 0.0108628i
\(724\) 0 0
\(725\) 13.8556 + 23.9987i 0.514586 + 0.891289i
\(726\) 0 0
\(727\) 12.9909 22.5009i 0.481805 0.834511i −0.517977 0.855395i \(-0.673315\pi\)
0.999782 + 0.0208834i \(0.00664789\pi\)
\(728\) 0 0
\(729\) 26.9830 + 0.958408i 0.999370 + 0.0354966i
\(730\) 0 0
\(731\) −10.0021 + 17.3241i −0.369940 + 0.640755i
\(732\) 0 0
\(733\) −5.41447 9.37814i −0.199988 0.346390i 0.748536 0.663094i \(-0.230757\pi\)
−0.948524 + 0.316704i \(0.897424\pi\)
\(734\) 0 0
\(735\) 6.80425 + 0.0402635i 0.250978 + 0.00148514i
\(736\) 0 0
\(737\) 31.4427 1.15821
\(738\) 0 0
\(739\) 11.4520 0.421270 0.210635 0.977565i \(-0.432447\pi\)
0.210635 + 0.977565i \(0.432447\pi\)
\(740\) 0 0
\(741\) 15.9860 27.3141i 0.587262 1.00341i
\(742\) 0 0
\(743\) −24.0077 41.5826i −0.880758 1.52552i −0.850500 0.525975i \(-0.823701\pi\)
−0.0302573 0.999542i \(-0.509633\pi\)
\(744\) 0 0
\(745\) −5.33595 + 9.24213i −0.195494 + 0.338605i
\(746\) 0 0
\(747\) −9.02122 16.0612i −0.330069 0.587649i
\(748\) 0 0
\(749\) 4.57399 7.92239i 0.167130 0.289478i
\(750\) 0 0
\(751\) −22.5881 39.1238i −0.824253 1.42765i −0.902489 0.430713i \(-0.858262\pi\)
0.0782360 0.996935i \(-0.475071\pi\)
\(752\) 0 0
\(753\) 13.4505 + 23.6187i 0.490164 + 0.860712i
\(754\) 0 0
\(755\) 18.5968 0.676807
\(756\) 0 0
\(757\) −16.5457 −0.601365 −0.300682 0.953724i \(-0.597214\pi\)
−0.300682 + 0.953724i \(0.597214\pi\)
\(758\) 0 0
\(759\) 10.4006 + 18.2631i 0.377517 + 0.662907i
\(760\) 0 0
\(761\) −20.6826 35.8234i −0.749745 1.29860i −0.947945 0.318435i \(-0.896843\pi\)
0.198200 0.980162i \(-0.436491\pi\)
\(762\) 0 0
\(763\) 25.4361 44.0565i 0.920847 1.59495i
\(764\) 0 0
\(765\) −15.6060 0.184700i −0.564234 0.00667785i
\(766\) 0 0
\(767\) 13.3209 23.0725i 0.480990 0.833100i
\(768\) 0 0
\(769\) −3.22518 5.58617i −0.116303 0.201443i 0.801997 0.597328i \(-0.203771\pi\)
−0.918300 + 0.395886i \(0.870438\pi\)
\(770\) 0 0
\(771\) −20.2353 + 34.5745i −0.728758 + 1.24517i
\(772\) 0 0
\(773\) 0.949001 0.0341332 0.0170666 0.999854i \(-0.494567\pi\)
0.0170666 + 0.999854i \(0.494567\pi\)
\(774\) 0 0
\(775\) −22.1792 −0.796702
\(776\) 0 0
\(777\) 0.402443 + 0.00238142i 0.0144375 + 8.54329e-5i
\(778\) 0 0
\(779\) 9.43285 + 16.3382i 0.337967 + 0.585376i
\(780\) 0 0
\(781\) −0.432519 + 0.749145i −0.0154767 + 0.0268065i
\(782\) 0 0
\(783\) 19.6130 32.6195i 0.700912 1.16572i
\(784\) 0 0
\(785\) 4.81251 8.33552i 0.171766 0.297507i
\(786\) 0 0
\(787\) 17.6992 + 30.6559i 0.630909 + 1.09277i 0.987366 + 0.158454i \(0.0506511\pi\)
−0.356458 + 0.934312i \(0.616016\pi\)
\(788\) 0 0
\(789\) 41.8237 + 0.247488i 1.48896 + 0.00881080i
\(790\) 0 0
\(791\) −66.1840 −2.35323
\(792\) 0 0
\(793\) 29.6033 1.05125
\(794\) 0 0
\(795\) 6.20383 10.6000i 0.220027 0.375943i
\(796\) 0 0