Properties

Label 1456.2.cc.c.673.5
Level $1456$
Weight $2$
Character 1456.673
Analytic conductor $11.626$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1456 = 2^{4} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1456.cc (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.6262185343\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 673.5
Root \(-1.30089 + 0.554694i\) of defining polynomial
Character \(\chi\) \(=\) 1456.673
Dual form 1456.2.cc.c.225.5

$q$-expansion

\(f(q)\) \(=\) \(q+(1.13082 + 1.95864i) q^{3} +3.60178i q^{5} +(0.866025 + 0.500000i) q^{7} +(-1.05753 + 1.83169i) q^{9} +O(q^{10})\) \(q+(1.13082 + 1.95864i) q^{3} +3.60178i q^{5} +(0.866025 + 0.500000i) q^{7} +(-1.05753 + 1.83169i) q^{9} +(-0.767631 + 0.443192i) q^{11} +(-1.17349 - 3.40924i) q^{13} +(-7.05461 + 4.07298i) q^{15} +(-2.48008 + 4.29563i) q^{17} +(-2.06008 - 1.18939i) q^{19} +2.26165i q^{21} +(1.92926 + 3.34157i) q^{23} -7.97282 q^{25} +2.00144 q^{27} +(-0.640986 - 1.11022i) q^{29} +8.46921i q^{31} +(-1.73611 - 1.00234i) q^{33} +(-1.80089 + 3.11923i) q^{35} +(-8.34686 + 4.81906i) q^{37} +(5.35049 - 6.15370i) q^{39} +(10.4652 - 6.04207i) q^{41} +(1.82125 - 3.15450i) q^{43} +(-6.59734 - 3.80898i) q^{45} -2.98229i q^{47} +(0.500000 + 0.866025i) q^{49} -11.2181 q^{51} +4.92032 q^{53} +(-1.59628 - 2.76484i) q^{55} -5.37995i q^{57} +(-6.34577 - 3.66373i) q^{59} +(0.769632 - 1.33304i) q^{61} +(-1.83169 + 1.05753i) q^{63} +(12.2793 - 4.22664i) q^{65} +(-7.29756 + 4.21325i) q^{67} +(-4.36330 + 7.55745i) q^{69} +(5.58490 + 3.22444i) q^{71} -7.14859i q^{73} +(-9.01585 - 15.6159i) q^{75} -0.886384 q^{77} -0.757551 q^{79} +(5.43585 + 9.41518i) q^{81} -4.76766i q^{83} +(-15.4719 - 8.93270i) q^{85} +(1.44969 - 2.51093i) q^{87} +(3.13400 - 1.80942i) q^{89} +(0.688351 - 3.53923i) q^{91} +(-16.5882 + 9.57719i) q^{93} +(4.28391 - 7.41995i) q^{95} +(-0.401229 - 0.231650i) q^{97} -1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 4 q^{9} - 6 q^{11} + 4 q^{13} - 6 q^{15} - 4 q^{17} + 12 q^{23} - 20 q^{25} - 12 q^{27} + 8 q^{29} - 30 q^{33} - 6 q^{35} - 42 q^{37} + 4 q^{39} + 30 q^{41} - 2 q^{43} + 6 q^{49} - 52 q^{51} - 44 q^{53} + 6 q^{55} - 18 q^{59} + 14 q^{61} - 12 q^{63} + 60 q^{65} + 24 q^{67} + 4 q^{69} + 24 q^{71} - 46 q^{75} + 8 q^{77} + 56 q^{79} + 2 q^{81} - 48 q^{85} + 2 q^{87} - 12 q^{89} - 14 q^{91} - 18 q^{93} + 22 q^{95} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

\(n\) \(561\) \(911\) \(1093\) \(1249\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(1\)

Coefficient data

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

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
\(3\) 1.13082 + 1.95864i 0.652882 + 1.13082i 0.982420 + 0.186682i \(0.0597734\pi\)
−0.329539 + 0.944142i \(0.606893\pi\)
\(4\) 0 0
\(5\) 3.60178i 1.61076i 0.592756 + 0.805382i \(0.298040\pi\)
−0.592756 + 0.805382i \(0.701960\pi\)
\(6\) 0 0
\(7\) 0.866025 + 0.500000i 0.327327 + 0.188982i
\(8\) 0 0
\(9\) −1.05753 + 1.83169i −0.352509 + 0.610563i
\(10\) 0 0
\(11\) −0.767631 + 0.443192i −0.231450 + 0.133627i −0.611241 0.791445i \(-0.709329\pi\)
0.379791 + 0.925072i \(0.375996\pi\)
\(12\) 0 0
\(13\) −1.17349 3.40924i −0.325467 0.945553i
\(14\) 0 0
\(15\) −7.05461 + 4.07298i −1.82149 + 1.05164i
\(16\) 0 0
\(17\) −2.48008 + 4.29563i −0.601508 + 1.04184i 0.391085 + 0.920355i \(0.372100\pi\)
−0.992593 + 0.121488i \(0.961233\pi\)
\(18\) 0 0
\(19\) −2.06008 1.18939i −0.472615 0.272864i 0.244719 0.969594i \(-0.421304\pi\)
−0.717334 + 0.696730i \(0.754638\pi\)
\(20\) 0 0
\(21\) 2.26165i 0.493532i
\(22\) 0 0
\(23\) 1.92926 + 3.34157i 0.402278 + 0.696765i 0.994000 0.109376i \(-0.0348853\pi\)
−0.591723 + 0.806142i \(0.701552\pi\)
\(24\) 0 0
\(25\) −7.97282 −1.59456
\(26\) 0 0
\(27\) 2.00144 0.385177
\(28\) 0 0
\(29\) −0.640986 1.11022i −0.119028 0.206163i 0.800355 0.599527i \(-0.204645\pi\)
−0.919383 + 0.393364i \(0.871311\pi\)
\(30\) 0 0
\(31\) 8.46921i 1.52111i 0.649271 + 0.760557i \(0.275074\pi\)
−0.649271 + 0.760557i \(0.724926\pi\)
\(32\) 0 0
\(33\) −1.73611 1.00234i −0.302218 0.174486i
\(34\) 0 0
\(35\) −1.80089 + 3.11923i −0.304406 + 0.527247i
\(36\) 0 0
\(37\) −8.34686 + 4.81906i −1.37222 + 0.792249i −0.991207 0.132323i \(-0.957757\pi\)
−0.381009 + 0.924571i \(0.624423\pi\)
\(38\) 0 0
\(39\) 5.35049 6.15370i 0.856763 0.985380i
\(40\) 0 0
\(41\) 10.4652 6.04207i 1.63438 0.943612i 0.651666 0.758506i \(-0.274071\pi\)
0.982719 0.185106i \(-0.0592628\pi\)
\(42\) 0 0
\(43\) 1.82125 3.15450i 0.277738 0.481056i −0.693084 0.720856i \(-0.743749\pi\)
0.970822 + 0.239800i \(0.0770820\pi\)
\(44\) 0 0
\(45\) −6.59734 3.80898i −0.983474 0.567809i
\(46\) 0 0
\(47\) 2.98229i 0.435012i −0.976059 0.217506i \(-0.930208\pi\)
0.976059 0.217506i \(-0.0697922\pi\)
\(48\) 0 0
\(49\) 0.500000 + 0.866025i 0.0714286 + 0.123718i
\(50\) 0 0
\(51\) −11.2181 −1.57085
\(52\) 0 0
\(53\) 4.92032 0.675858 0.337929 0.941172i \(-0.390274\pi\)
0.337929 + 0.941172i \(0.390274\pi\)
\(54\) 0 0
\(55\) −1.59628 2.76484i −0.215242 0.372811i
\(56\) 0 0
\(57\) 5.37995i 0.712592i
\(58\) 0 0
\(59\) −6.34577 3.66373i −0.826148 0.476977i 0.0263837 0.999652i \(-0.491601\pi\)
−0.852532 + 0.522675i \(0.824934\pi\)
\(60\) 0 0
\(61\) 0.769632 1.33304i 0.0985412 0.170678i −0.812540 0.582906i \(-0.801916\pi\)
0.911081 + 0.412227i \(0.135249\pi\)
\(62\) 0 0
\(63\) −1.83169 + 1.05753i −0.230771 + 0.133236i
\(64\) 0 0
\(65\) 12.2793 4.22664i 1.52306 0.524250i
\(66\) 0 0
\(67\) −7.29756 + 4.21325i −0.891539 + 0.514730i −0.874445 0.485124i \(-0.838775\pi\)
−0.0170931 + 0.999854i \(0.505441\pi\)
\(68\) 0 0
\(69\) −4.36330 + 7.55745i −0.525279 + 0.909811i
\(70\) 0 0
\(71\) 5.58490 + 3.22444i 0.662805 + 0.382671i 0.793345 0.608772i \(-0.208338\pi\)
−0.130540 + 0.991443i \(0.541671\pi\)
\(72\) 0 0
\(73\) 7.14859i 0.836679i −0.908291 0.418340i \(-0.862612\pi\)
0.908291 0.418340i \(-0.137388\pi\)
\(74\) 0 0
\(75\) −9.01585 15.6159i −1.04106 1.80317i
\(76\) 0 0
\(77\) −0.886384 −0.101013
\(78\) 0 0
\(79\) −0.757551 −0.0852311 −0.0426156 0.999092i \(-0.513569\pi\)
−0.0426156 + 0.999092i \(0.513569\pi\)
\(80\) 0 0
\(81\) 5.43585 + 9.41518i 0.603984 + 1.04613i
\(82\) 0 0
\(83\) 4.76766i 0.523319i −0.965160 0.261659i \(-0.915730\pi\)
0.965160 0.261659i \(-0.0842697\pi\)
\(84\) 0 0
\(85\) −15.4719 8.93270i −1.67816 0.968888i
\(86\) 0 0
\(87\) 1.44969 2.51093i 0.155423 0.269200i
\(88\) 0 0
\(89\) 3.13400 1.80942i 0.332204 0.191798i −0.324615 0.945846i \(-0.605235\pi\)
0.656819 + 0.754048i \(0.271902\pi\)
\(90\) 0 0
\(91\) 0.688351 3.53923i 0.0721588 0.371012i
\(92\) 0 0
\(93\) −16.5882 + 9.57719i −1.72011 + 0.993108i
\(94\) 0 0
\(95\) 4.28391 7.41995i 0.439520 0.761271i
\(96\) 0 0
\(97\) −0.401229 0.231650i −0.0407386 0.0235205i 0.479492 0.877546i \(-0.340821\pi\)
−0.520231 + 0.854026i \(0.674154\pi\)
\(98\) 0 0
\(99\) 1.87475i 0.188419i
\(100\) 0 0
\(101\) 2.91152 + 5.04289i 0.289707 + 0.501787i 0.973740 0.227664i \(-0.0731089\pi\)
−0.684033 + 0.729451i \(0.739776\pi\)
\(102\) 0 0
\(103\) 8.23888 0.811801 0.405901 0.913917i \(-0.366958\pi\)
0.405901 + 0.913917i \(0.366958\pi\)
\(104\) 0 0
\(105\) −8.14596 −0.794964
\(106\) 0 0
\(107\) −1.91630 3.31913i −0.185256 0.320872i 0.758407 0.651781i \(-0.225978\pi\)
−0.943663 + 0.330909i \(0.892645\pi\)
\(108\) 0 0
\(109\) 10.4180i 0.997867i 0.866640 + 0.498934i \(0.166275\pi\)
−0.866640 + 0.498934i \(0.833725\pi\)
\(110\) 0 0
\(111\) −18.8777 10.8990i −1.79179 1.03449i
\(112\) 0 0
\(113\) 2.45505 4.25228i 0.230952 0.400021i −0.727136 0.686493i \(-0.759149\pi\)
0.958089 + 0.286472i \(0.0924826\pi\)
\(114\) 0 0
\(115\) −12.0356 + 6.94875i −1.12233 + 0.647975i
\(116\) 0 0
\(117\) 7.48567 + 1.45590i 0.692050 + 0.134598i
\(118\) 0 0
\(119\) −4.29563 + 2.48008i −0.393779 + 0.227349i
\(120\) 0 0
\(121\) −5.10716 + 8.84586i −0.464287 + 0.804169i
\(122\) 0 0
\(123\) 23.6685 + 13.6650i 2.13412 + 1.23213i
\(124\) 0 0
\(125\) 10.7074i 0.957702i
\(126\) 0 0
\(127\) 6.15508 + 10.6609i 0.546175 + 0.946003i 0.998532 + 0.0541658i \(0.0172500\pi\)
−0.452357 + 0.891837i \(0.649417\pi\)
\(128\) 0 0
\(129\) 8.23805 0.725320
\(130\) 0 0
\(131\) 8.20265 0.716669 0.358335 0.933593i \(-0.383345\pi\)
0.358335 + 0.933593i \(0.383345\pi\)
\(132\) 0 0
\(133\) −1.18939 2.06008i −0.103133 0.178632i
\(134\) 0 0
\(135\) 7.20874i 0.620429i
\(136\) 0 0
\(137\) 6.45670 + 3.72778i 0.551633 + 0.318485i 0.749780 0.661687i \(-0.230159\pi\)
−0.198147 + 0.980172i \(0.563492\pi\)
\(138\) 0 0
\(139\) 8.34028 14.4458i 0.707413 1.22528i −0.258400 0.966038i \(-0.583195\pi\)
0.965813 0.259238i \(-0.0834714\pi\)
\(140\) 0 0
\(141\) 5.84125 3.37245i 0.491922 0.284011i
\(142\) 0 0
\(143\) 2.41175 + 2.09696i 0.201681 + 0.175357i
\(144\) 0 0
\(145\) 3.99877 2.30869i 0.332080 0.191726i
\(146\) 0 0
\(147\) −1.13082 + 1.95864i −0.0932688 + 0.161546i
\(148\) 0 0
\(149\) −2.18380 1.26082i −0.178904 0.103290i 0.407874 0.913038i \(-0.366270\pi\)
−0.586777 + 0.809748i \(0.699604\pi\)
\(150\) 0 0
\(151\) 15.8972i 1.29370i 0.762618 + 0.646849i \(0.223914\pi\)
−0.762618 + 0.646849i \(0.776086\pi\)
\(152\) 0 0
\(153\) −5.24550 9.08548i −0.424074 0.734517i
\(154\) 0 0
\(155\) −30.5042 −2.45016
\(156\) 0 0
\(157\) 12.9831 1.03616 0.518082 0.855331i \(-0.326646\pi\)
0.518082 + 0.855331i \(0.326646\pi\)
\(158\) 0 0
\(159\) 5.56402 + 9.63717i 0.441256 + 0.764277i
\(160\) 0 0
\(161\) 3.85851i 0.304093i
\(162\) 0 0
\(163\) 2.00873 + 1.15974i 0.157336 + 0.0908378i 0.576601 0.817026i \(-0.304379\pi\)
−0.419265 + 0.907864i \(0.637712\pi\)
\(164\) 0 0
\(165\) 3.61023 6.25309i 0.281056 0.486803i
\(166\) 0 0
\(167\) 11.9441 6.89591i 0.924260 0.533622i 0.0392682 0.999229i \(-0.487497\pi\)
0.884992 + 0.465607i \(0.154164\pi\)
\(168\) 0 0
\(169\) −10.2459 + 8.00140i −0.788143 + 0.615493i
\(170\) 0 0
\(171\) 4.35718 2.51562i 0.333202 0.192374i
\(172\) 0 0
\(173\) −1.84216 + 3.19071i −0.140057 + 0.242585i −0.927518 0.373779i \(-0.878062\pi\)
0.787461 + 0.616364i \(0.211395\pi\)
\(174\) 0 0
\(175\) −6.90466 3.98641i −0.521943 0.301344i
\(176\) 0 0
\(177\) 16.5721i 1.24564i
\(178\) 0 0
\(179\) 2.94638 + 5.10328i 0.220223 + 0.381437i 0.954876 0.297006i \(-0.0959882\pi\)
−0.734653 + 0.678443i \(0.762655\pi\)
\(180\) 0 0
\(181\) −2.11543 −0.157239 −0.0786193 0.996905i \(-0.525051\pi\)
−0.0786193 + 0.996905i \(0.525051\pi\)
\(182\) 0 0
\(183\) 3.48127 0.257343
\(184\) 0 0
\(185\) −17.3572 30.0635i −1.27613 2.21032i
\(186\) 0 0
\(187\) 4.39661i 0.321512i
\(188\) 0 0
\(189\) 1.73330 + 1.00072i 0.126079 + 0.0727916i
\(190\) 0 0
\(191\) −5.68333 + 9.84381i −0.411231 + 0.712273i −0.995025 0.0996290i \(-0.968234\pi\)
0.583794 + 0.811902i \(0.301568\pi\)
\(192\) 0 0
\(193\) 12.2017 7.04468i 0.878301 0.507087i 0.00820314 0.999966i \(-0.497389\pi\)
0.870098 + 0.492879i \(0.164055\pi\)
\(194\) 0 0
\(195\) 22.1643 + 19.2713i 1.58722 + 1.38004i
\(196\) 0 0
\(197\) −19.8815 + 11.4786i −1.41650 + 0.817814i −0.995989 0.0894753i \(-0.971481\pi\)
−0.420507 + 0.907289i \(0.638148\pi\)
\(198\) 0 0
\(199\) 1.57492 2.72785i 0.111643 0.193372i −0.804790 0.593560i \(-0.797722\pi\)
0.916433 + 0.400188i \(0.131055\pi\)
\(200\) 0 0
\(201\) −16.5045 9.52888i −1.16414 0.672116i
\(202\) 0 0
\(203\) 1.28197i 0.0899768i
\(204\) 0 0
\(205\) 21.7622 + 37.6932i 1.51994 + 2.63261i
\(206\) 0 0
\(207\) −8.16096 −0.567226
\(208\) 0 0
\(209\) 2.10851 0.145849
\(210\) 0 0
\(211\) −7.43191 12.8725i −0.511634 0.886176i −0.999909 0.0134864i \(-0.995707\pi\)
0.488275 0.872690i \(-0.337626\pi\)
\(212\) 0 0
\(213\) 14.5851i 0.999355i
\(214\) 0 0
\(215\) 11.3618 + 6.55974i 0.774868 + 0.447370i
\(216\) 0 0
\(217\) −4.23460 + 7.33455i −0.287464 + 0.497902i
\(218\) 0 0
\(219\) 14.0016 8.08380i 0.946137 0.546253i
\(220\) 0 0
\(221\) 17.5552 + 3.41433i 1.18089 + 0.229673i
\(222\) 0 0
\(223\) −3.79396 + 2.19044i −0.254062 + 0.146683i −0.621623 0.783317i \(-0.713526\pi\)
0.367561 + 0.930000i \(0.380193\pi\)
\(224\) 0 0
\(225\) 8.43147 14.6037i 0.562098 0.973582i
\(226\) 0 0
\(227\) −11.7488 6.78316i −0.779793 0.450214i 0.0565636 0.998399i \(-0.481986\pi\)
−0.836357 + 0.548185i \(0.815319\pi\)
\(228\) 0 0
\(229\) 16.5180i 1.09154i 0.837935 + 0.545770i \(0.183763\pi\)
−0.837935 + 0.545770i \(0.816237\pi\)
\(230\) 0 0
\(231\) −1.00234 1.73611i −0.0659494 0.114228i
\(232\) 0 0
\(233\) 16.5026 1.08112 0.540561 0.841305i \(-0.318212\pi\)
0.540561 + 0.841305i \(0.318212\pi\)
\(234\) 0 0
\(235\) 10.7416 0.700702
\(236\) 0 0
\(237\) −0.856657 1.48377i −0.0556458 0.0963814i
\(238\) 0 0
\(239\) 30.4210i 1.96777i 0.178796 + 0.983886i \(0.442780\pi\)
−0.178796 + 0.983886i \(0.557220\pi\)
\(240\) 0 0
\(241\) −25.5602 14.7572i −1.64648 0.950593i −0.978458 0.206448i \(-0.933810\pi\)
−0.668018 0.744145i \(-0.732857\pi\)
\(242\) 0 0
\(243\) −9.29184 + 16.0939i −0.596072 + 1.03243i
\(244\) 0 0
\(245\) −3.11923 + 1.80089i −0.199280 + 0.115055i
\(246\) 0 0
\(247\) −1.63743 + 8.41904i −0.104187 + 0.535691i
\(248\) 0 0
\(249\) 9.33816 5.39139i 0.591782 0.341665i
\(250\) 0 0
\(251\) 6.49134 11.2433i 0.409730 0.709673i −0.585130 0.810940i \(-0.698956\pi\)
0.994859 + 0.101267i \(0.0322897\pi\)
\(252\) 0 0
\(253\) −2.96191 1.71006i −0.186214 0.107511i
\(254\) 0 0
\(255\) 40.4053i 2.53028i
\(256\) 0 0
\(257\) −2.29261 3.97091i −0.143009 0.247698i 0.785620 0.618710i \(-0.212344\pi\)
−0.928628 + 0.371011i \(0.879011\pi\)
\(258\) 0 0
\(259\) −9.63812 −0.598884
\(260\) 0 0
\(261\) 2.71144 0.167834
\(262\) 0 0
\(263\) −1.33250 2.30795i −0.0821652 0.142314i 0.822015 0.569466i \(-0.192850\pi\)
−0.904180 + 0.427152i \(0.859517\pi\)
\(264\) 0 0
\(265\) 17.7219i 1.08865i
\(266\) 0 0
\(267\) 7.08801 + 4.09227i 0.433779 + 0.250443i
\(268\) 0 0
\(269\) −5.96282 + 10.3279i −0.363559 + 0.629703i −0.988544 0.150934i \(-0.951772\pi\)
0.624984 + 0.780637i \(0.285105\pi\)
\(270\) 0 0
\(271\) 11.2828 6.51416i 0.685384 0.395707i −0.116496 0.993191i \(-0.537166\pi\)
0.801881 + 0.597484i \(0.203833\pi\)
\(272\) 0 0
\(273\) 7.71051 2.65402i 0.466661 0.160628i
\(274\) 0 0
\(275\) 6.12018 3.53349i 0.369061 0.213077i
\(276\) 0 0
\(277\) 10.6824 18.5025i 0.641846 1.11171i −0.343174 0.939272i \(-0.611502\pi\)
0.985020 0.172438i \(-0.0551646\pi\)
\(278\) 0 0
\(279\) −15.5130 8.95641i −0.928737 0.536206i
\(280\) 0 0
\(281\) 17.2678i 1.03011i 0.857158 + 0.515054i \(0.172228\pi\)
−0.857158 + 0.515054i \(0.827772\pi\)
\(282\) 0 0
\(283\) 10.6201 + 18.3946i 0.631299 + 1.09344i 0.987286 + 0.158952i \(0.0508114\pi\)
−0.355987 + 0.934491i \(0.615855\pi\)
\(284\) 0 0
\(285\) 19.3774 1.14782
\(286\) 0 0
\(287\) 12.0841 0.713304
\(288\) 0 0
\(289\) −3.80160 6.58457i −0.223624 0.387327i
\(290\) 0 0
\(291\) 1.04782i 0.0614243i
\(292\) 0 0
\(293\) −0.363782 0.210030i −0.0212524 0.0122701i 0.489336 0.872095i \(-0.337239\pi\)
−0.510589 + 0.859825i \(0.670572\pi\)
\(294\) 0 0
\(295\) 13.1959 22.8561i 0.768298 1.33073i
\(296\) 0 0
\(297\) −1.53637 + 0.887022i −0.0891490 + 0.0514702i
\(298\) 0 0
\(299\) 9.12826 10.4986i 0.527901 0.607149i
\(300\) 0 0
\(301\) 3.15450 1.82125i 0.181822 0.104975i
\(302\) 0 0
\(303\) −6.58482 + 11.4053i −0.378288 + 0.655215i
\(304\) 0 0
\(305\) 4.80132 + 2.77204i 0.274923 + 0.158727i
\(306\) 0 0
\(307\) 14.0807i 0.803628i 0.915721 + 0.401814i \(0.131620\pi\)
−0.915721 + 0.401814i \(0.868380\pi\)
\(308\) 0 0
\(309\) 9.31673 + 16.1370i 0.530010 + 0.918004i
\(310\) 0 0
\(311\) 10.3848 0.588867 0.294434 0.955672i \(-0.404869\pi\)
0.294434 + 0.955672i \(0.404869\pi\)
\(312\) 0 0
\(313\) 6.84759 0.387048 0.193524 0.981096i \(-0.438008\pi\)
0.193524 + 0.981096i \(0.438008\pi\)
\(314\) 0 0
\(315\) −3.80898 6.59734i −0.214612 0.371718i
\(316\) 0 0
\(317\) 0.701249i 0.0393861i 0.999806 + 0.0196930i \(0.00626889\pi\)
−0.999806 + 0.0196930i \(0.993731\pi\)
\(318\) 0 0
\(319\) 0.984082 + 0.568160i 0.0550980 + 0.0318109i
\(320\) 0 0
\(321\) 4.33400 7.50670i 0.241900 0.418983i
\(322\) 0 0
\(323\) 10.2183 5.89956i 0.568563 0.328260i
\(324\) 0 0
\(325\) 9.35600 + 27.1813i 0.518977 + 1.50774i
\(326\) 0 0
\(327\) −20.4052 + 11.7810i −1.12841 + 0.651489i
\(328\) 0 0
\(329\) 1.49115 2.58274i 0.0822095 0.142391i
\(330\) 0 0
\(331\) −3.63613 2.09932i −0.199860 0.115389i 0.396730 0.917935i \(-0.370145\pi\)
−0.596590 + 0.802546i \(0.703478\pi\)
\(332\) 0 0
\(333\) 20.3851i 1.11710i
\(334\) 0 0
\(335\) −15.1752 26.2842i −0.829109 1.43606i
\(336\) 0 0
\(337\) −20.4278 −1.11278 −0.556388 0.830923i \(-0.687813\pi\)
−0.556388 + 0.830923i \(0.687813\pi\)
\(338\) 0 0
\(339\) 11.1049 0.603138
\(340\) 0 0
\(341\) −3.75349 6.50123i −0.203263 0.352061i
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 0 0
\(345\) −27.2203 15.7156i −1.46549 0.846102i
\(346\) 0 0
\(347\) 3.98500 6.90222i 0.213926 0.370531i −0.739014 0.673690i \(-0.764708\pi\)
0.952940 + 0.303160i \(0.0980415\pi\)
\(348\) 0 0
\(349\) 18.7038 10.7986i 1.00119 0.578037i 0.0925892 0.995704i \(-0.470486\pi\)
0.908600 + 0.417668i \(0.137152\pi\)
\(350\) 0 0
\(351\) −2.34866 6.82338i −0.125362 0.364205i
\(352\) 0 0
\(353\) 18.7214 10.8088i 0.996439 0.575295i 0.0892465 0.996010i \(-0.471554\pi\)
0.907193 + 0.420715i \(0.138221\pi\)
\(354\) 0 0
\(355\) −11.6137 + 20.1156i −0.616393 + 1.06762i
\(356\) 0 0
\(357\) −9.71520 5.60907i −0.514183 0.296863i
\(358\) 0 0
\(359\) 13.6834i 0.722180i −0.932531 0.361090i \(-0.882405\pi\)
0.932531 0.361090i \(-0.117595\pi\)
\(360\) 0 0
\(361\) −6.67071 11.5540i −0.351090 0.608106i
\(362\) 0 0
\(363\) −23.1012 −1.21250
\(364\) 0 0
\(365\) 25.7477 1.34769
\(366\) 0 0
\(367\) −5.70638 9.88374i −0.297871 0.515927i 0.677778 0.735267i \(-0.262943\pi\)
−0.975649 + 0.219339i \(0.929610\pi\)
\(368\) 0 0
\(369\) 25.5586i 1.33053i
\(370\) 0 0
\(371\) 4.26112 + 2.46016i 0.221227 + 0.127725i
\(372\) 0 0
\(373\) 15.6404 27.0900i 0.809830 1.40267i −0.103151 0.994666i \(-0.532892\pi\)
0.912981 0.408002i \(-0.133774\pi\)
\(374\) 0 0
\(375\) 20.9721 12.1082i 1.08299 0.625266i
\(376\) 0 0
\(377\) −3.03282 + 3.48811i −0.156198 + 0.179647i
\(378\) 0 0
\(379\) −23.7421 + 13.7075i −1.21955 + 0.704108i −0.964822 0.262904i \(-0.915320\pi\)
−0.254729 + 0.967012i \(0.581986\pi\)
\(380\) 0 0
\(381\) −13.9206 + 24.1112i −0.713175 + 1.23526i
\(382\) 0 0
\(383\) −13.9436 8.05032i −0.712483 0.411352i 0.0994967 0.995038i \(-0.468277\pi\)
−0.811980 + 0.583686i \(0.801610\pi\)
\(384\) 0 0
\(385\) 3.19256i 0.162708i
\(386\) 0 0
\(387\) 3.85204 + 6.67193i 0.195810 + 0.339153i
\(388\) 0 0
\(389\) −21.1380 −1.07174 −0.535870 0.844301i \(-0.680016\pi\)
−0.535870 + 0.844301i \(0.680016\pi\)
\(390\) 0 0
\(391\) −19.1388 −0.967893
\(392\) 0 0
\(393\) 9.27576 + 16.0661i 0.467900 + 0.810427i
\(394\) 0 0
\(395\) 2.72853i 0.137287i
\(396\) 0 0
\(397\) 11.3436 + 6.54921i 0.569317 + 0.328695i 0.756876 0.653558i \(-0.226724\pi\)
−0.187560 + 0.982253i \(0.560058\pi\)
\(398\) 0 0
\(399\) 2.68998 4.65918i 0.134667 0.233251i
\(400\) 0 0
\(401\) 16.8396 9.72236i 0.840930 0.485511i −0.0166501 0.999861i \(-0.505300\pi\)
0.857580 + 0.514350i \(0.171967\pi\)
\(402\) 0 0
\(403\) 28.8736 9.93851i 1.43830 0.495072i
\(404\) 0 0
\(405\) −33.9114 + 19.5788i −1.68507 + 0.972876i
\(406\) 0 0
\(407\) 4.27154 7.39853i 0.211732 0.366731i
\(408\) 0 0
\(409\) 20.8330 + 12.0279i 1.03013 + 0.594743i 0.917020 0.398840i \(-0.130587\pi\)
0.113105 + 0.993583i \(0.463921\pi\)
\(410\) 0 0
\(411\) 16.8618i 0.831733i
\(412\) 0 0
\(413\) −3.66373 6.34577i −0.180280 0.312255i
\(414\) 0 0
\(415\) 17.1721 0.842944
\(416\) 0 0
\(417\) 37.7256 1.84743
\(418\) 0 0
\(419\) 19.5119 + 33.7956i 0.953218 + 1.65102i 0.738394 + 0.674370i \(0.235585\pi\)
0.214825 + 0.976653i \(0.431082\pi\)
\(420\) 0 0
\(421\) 22.0284i 1.07360i −0.843710 0.536799i \(-0.819633\pi\)
0.843710 0.536799i \(-0.180367\pi\)
\(422\) 0 0
\(423\) 5.46263 + 3.15385i 0.265602 + 0.153346i
\(424\) 0 0
\(425\) 19.7732 34.2482i 0.959142 1.66128i
\(426\) 0 0
\(427\) 1.33304 0.769632i 0.0645104 0.0372451i
\(428\) 0 0
\(429\) −1.37993 + 7.09506i −0.0666237 + 0.342553i
\(430\) 0 0
\(431\) 31.0727 17.9398i 1.49672 0.864131i 0.496726 0.867907i \(-0.334535\pi\)
0.999993 + 0.00377645i \(0.00120209\pi\)
\(432\) 0 0
\(433\) 6.10678 10.5773i 0.293473 0.508310i −0.681155 0.732139i \(-0.738522\pi\)
0.974629 + 0.223828i \(0.0718555\pi\)
\(434\) 0 0
\(435\) 9.04381 + 5.22145i 0.433618 + 0.250349i
\(436\) 0 0
\(437\) 9.17853i 0.439069i
\(438\) 0 0
\(439\) 7.87765 + 13.6445i 0.375980 + 0.651216i 0.990473 0.137706i \(-0.0439728\pi\)
−0.614493 + 0.788922i \(0.710639\pi\)
\(440\) 0 0
\(441\) −2.11505 −0.100717
\(442\) 0 0
\(443\) 15.0706 0.716028 0.358014 0.933716i \(-0.383454\pi\)
0.358014 + 0.933716i \(0.383454\pi\)
\(444\) 0 0
\(445\) 6.51712 + 11.2880i 0.308941 + 0.535102i
\(446\) 0 0
\(447\) 5.70305i 0.269745i
\(448\) 0 0
\(449\) 26.6585 + 15.3913i 1.25809 + 0.726360i 0.972703 0.232052i \(-0.0745441\pi\)
0.285388 + 0.958412i \(0.407877\pi\)
\(450\) 0 0
\(451\) −5.35559 + 9.27616i −0.252185 + 0.436797i
\(452\) 0 0
\(453\) −31.1370 + 17.9770i −1.46295 + 0.844632i
\(454\) 0 0
\(455\) 12.7475 + 2.47929i 0.597614 + 0.116231i
\(456\) 0 0
\(457\) −6.71687 + 3.87799i −0.314202 + 0.181405i −0.648805 0.760955i \(-0.724731\pi\)
0.334603 + 0.942359i \(0.391398\pi\)
\(458\) 0 0
\(459\) −4.96373 + 8.59743i −0.231687 + 0.401294i
\(460\) 0 0
\(461\) 1.27498 + 0.736110i 0.0593817 + 0.0342840i 0.529397 0.848374i \(-0.322418\pi\)
−0.470015 + 0.882658i \(0.655752\pi\)
\(462\) 0 0
\(463\) 14.0366i 0.652335i 0.945312 + 0.326168i \(0.105757\pi\)
−0.945312 + 0.326168i \(0.894243\pi\)
\(464\) 0 0
\(465\) −34.4949 59.7469i −1.59966 2.77070i
\(466\) 0 0
\(467\) 31.3806 1.45212 0.726060 0.687631i \(-0.241349\pi\)
0.726060 + 0.687631i \(0.241349\pi\)
\(468\) 0 0
\(469\) −8.42649 −0.389099
\(470\) 0 0
\(471\) 14.6816 + 25.4293i 0.676492 + 1.17172i
\(472\) 0 0
\(473\) 3.22865i 0.148454i
\(474\) 0 0
\(475\) 16.4246 + 9.48277i 0.753614 + 0.435099i
\(476\) 0 0
\(477\) −5.20337 + 9.01251i −0.238246 + 0.412654i
\(478\) 0 0
\(479\) −35.6760 + 20.5975i −1.63008 + 0.941125i −0.646009 + 0.763330i \(0.723563\pi\)
−0.984068 + 0.177795i \(0.943104\pi\)
\(480\) 0 0
\(481\) 26.2243 + 22.8014i 1.19572 + 1.03965i
\(482\) 0 0
\(483\) −7.55745 + 4.36330i −0.343876 + 0.198537i
\(484\) 0 0
\(485\) 0.834351 1.44514i 0.0378859 0.0656204i
\(486\) 0 0
\(487\) −24.5314 14.1632i −1.11163 0.641798i −0.172376 0.985031i \(-0.555144\pi\)
−0.939250 + 0.343234i \(0.888478\pi\)
\(488\) 0 0
\(489\) 5.24584i 0.237225i
\(490\) 0 0
\(491\) −17.3931 30.1258i −0.784941 1.35956i −0.929034 0.369993i \(-0.879360\pi\)
0.144094 0.989564i \(-0.453973\pi\)
\(492\) 0 0
\(493\) 6.35879 0.286386
\(494\) 0 0
\(495\) 6.75244 0.303499
\(496\) 0 0
\(497\) 3.22444 + 5.58490i 0.144636 + 0.250517i
\(498\) 0 0
\(499\) 0.0694885i 0.00311073i 0.999999 + 0.00155537i \(0.000495089\pi\)
−0.999999 + 0.00155537i \(0.999505\pi\)
\(500\) 0 0
\(501\) 27.0133 + 15.5961i 1.20686 + 0.696783i
\(502\) 0 0
\(503\) 12.8686 22.2891i 0.573782 0.993820i −0.422391 0.906414i \(-0.638809\pi\)
0.996173 0.0874060i \(-0.0278578\pi\)
\(504\) 0 0
\(505\) −18.1634 + 10.4866i −0.808260 + 0.466649i
\(506\) 0 0
\(507\) −27.2582 11.0198i −1.21058 0.489407i
\(508\) 0 0
\(509\) −6.09682 + 3.52000i −0.270237 + 0.156021i −0.628995 0.777409i \(-0.716533\pi\)
0.358759 + 0.933430i \(0.383200\pi\)
\(510\) 0 0
\(511\) 3.57430 6.19086i 0.158118 0.273868i
\(512\) 0 0
\(513\) −4.12312 2.38049i −0.182040 0.105101i
\(514\) 0 0
\(515\) 29.6746i 1.30762i
\(516\) 0 0
\(517\) 1.32173 + 2.28930i 0.0581295 + 0.100683i
\(518\) 0 0
\(519\) −8.33263 −0.365762
\(520\) 0 0
\(521\) 16.3253 0.715225 0.357613 0.933870i \(-0.383591\pi\)
0.357613 + 0.933870i \(0.383591\pi\)
\(522\) 0 0
\(523\) −3.54473 6.13965i −0.155000 0.268468i 0.778059 0.628191i \(-0.216204\pi\)
−0.933059 + 0.359723i \(0.882871\pi\)
\(524\) 0 0
\(525\) 18.0317i 0.786968i
\(526\) 0 0
\(527\) −36.3805 21.0043i −1.58476 0.914963i
\(528\) 0 0
\(529\) 4.05594 7.02510i 0.176345 0.305439i
\(530\) 0 0
\(531\) 13.4216 7.74899i 0.582449 0.336277i
\(532\) 0 0
\(533\) −32.8796 28.5880i −1.42417 1.23828i
\(534\) 0 0
\(535\) 11.9548 6.90209i 0.516850 0.298403i
\(536\) 0 0
\(537\) −6.66368 + 11.5418i −0.287559 + 0.498067i
\(538\) 0 0
\(539\) −0.767631 0.443192i −0.0330642 0.0190896i
\(540\) 0 0
\(541\) 25.5162i 1.09703i −0.836141 0.548515i \(-0.815194\pi\)
0.836141 0.548515i \(-0.184806\pi\)
\(542\) 0 0
\(543\) −2.39218 4.14338i −0.102658 0.177809i
\(544\) 0 0
\(545\) −37.5235 −1.60733
\(546\) 0 0
\(547\) 13.3073 0.568978 0.284489 0.958679i \(-0.408176\pi\)
0.284489 + 0.958679i \(0.408176\pi\)
\(548\) 0 0
\(549\) 1.62781 + 2.81945i 0.0694733 + 0.120331i
\(550\) 0 0
\(551\) 3.04952i 0.129914i
\(552\) 0 0
\(553\) −0.656058 0.378775i −0.0278984 0.0161072i
\(554\) 0 0
\(555\) 39.2559 67.9932i 1.66632 2.88615i
\(556\) 0 0
\(557\) −14.7285 + 8.50353i −0.624069 + 0.360306i −0.778451 0.627705i \(-0.783994\pi\)
0.154383 + 0.988011i \(0.450661\pi\)
\(558\) 0 0
\(559\) −12.8916 2.50732i −0.545259 0.106048i
\(560\) 0 0
\(561\) 8.61140 4.97179i 0.363573 0.209909i
\(562\) 0 0
\(563\) 12.4596 21.5807i 0.525111 0.909519i −0.474461 0.880276i \(-0.657357\pi\)
0.999572 0.0292428i \(-0.00930961\pi\)
\(564\) 0 0
\(565\) 15.3158 + 8.84257i 0.644340 + 0.372010i
\(566\) 0 0
\(567\) 10.8717i 0.456569i
\(568\) 0 0
\(569\) 2.94065 + 5.09335i 0.123278 + 0.213524i 0.921059 0.389424i \(-0.127326\pi\)
−0.797780 + 0.602948i \(0.793993\pi\)
\(570\) 0 0
\(571\) 8.92622 0.373551 0.186775 0.982403i \(-0.440196\pi\)
0.186775 + 0.982403i \(0.440196\pi\)
\(572\) 0 0
\(573\) −25.7074 −1.07394
\(574\) 0 0
\(575\) −15.3816 26.6417i −0.641457 1.11104i
\(576\) 0 0
\(577\) 36.1933i 1.50675i 0.657592 + 0.753374i \(0.271575\pi\)
−0.657592 + 0.753374i \(0.728425\pi\)
\(578\) 0 0
\(579\) 27.5961 + 15.9326i 1.14685 + 0.662136i
\(580\) 0 0
\(581\) 2.38383 4.12892i 0.0988980 0.171296i
\(582\) 0 0
\(583\) −3.77699 + 2.18065i −0.156427 + 0.0903132i
\(584\) 0 0
\(585\) −5.24383 + 26.9617i −0.216806 + 1.11473i
\(586\) 0 0
\(587\) −31.6008 + 18.2447i −1.30431 + 0.753041i −0.981139 0.193301i \(-0.938080\pi\)
−0.323166 + 0.946342i \(0.604747\pi\)
\(588\) 0 0
\(589\) 10.0732 17.4472i 0.415058 0.718901i
\(590\) 0 0
\(591\) −44.9649 25.9605i −1.84961 1.06787i
\(592\) 0 0
\(593\) 34.9930i 1.43699i −0.695533 0.718495i \(-0.744832\pi\)
0.695533 0.718495i \(-0.255168\pi\)
\(594\) 0 0
\(595\) −8.93270 15.4719i −0.366205 0.634286i
\(596\) 0 0
\(597\) 7.12385 0.291560
\(598\) 0 0
\(599\) 32.5052 1.32812 0.664062 0.747677i \(-0.268831\pi\)
0.664062 + 0.747677i \(0.268831\pi\)
\(600\) 0 0
\(601\) −10.0390 17.3881i −0.409500 0.709275i 0.585334 0.810792i \(-0.300963\pi\)
−0.994834 + 0.101518i \(0.967630\pi\)
\(602\) 0 0
\(603\) 17.8225i 0.725788i
\(604\) 0 0
\(605\) −31.8608 18.3949i −1.29533 0.747858i
\(606\) 0 0
\(607\) 4.85800 8.41431i 0.197180 0.341526i −0.750433 0.660947i \(-0.770155\pi\)
0.947613 + 0.319420i \(0.103488\pi\)
\(608\) 0 0
\(609\) 2.51093 1.44969i 0.101748 0.0587442i
\(610\) 0 0
\(611\) −10.1674 + 3.49968i −0.411327 + 0.141582i
\(612\) 0 0
\(613\) −10.2898 + 5.94080i −0.415600 + 0.239947i −0.693193 0.720752i \(-0.743797\pi\)
0.277593 + 0.960699i \(0.410463\pi\)
\(614\) 0 0
\(615\) −49.2184 + 85.2488i −1.98468 + 3.43756i
\(616\) 0 0
\(617\) −17.3105 9.99422i −0.696895 0.402352i 0.109295 0.994009i \(-0.465141\pi\)
−0.806190 + 0.591657i \(0.798474\pi\)
\(618\) 0 0
\(619\) 41.7176i 1.67677i 0.545078 + 0.838386i \(0.316500\pi\)
−0.545078 + 0.838386i \(0.683500\pi\)
\(620\) 0 0
\(621\) 3.86129 + 6.68794i 0.154948 + 0.268378i
\(622\) 0 0
\(623\) 3.61884 0.144986
\(624\) 0 0
\(625\) −1.29828 −0.0519312
\(626\) 0 0
\(627\) 2.38435 + 4.12982i 0.0952219 + 0.164929i
\(628\) 0 0
\(629\) 47.8066i 1.90618i
\(630\) 0 0
\(631\) −15.2780 8.82074i −0.608206 0.351148i 0.164057 0.986451i \(-0.447542\pi\)
−0.772263 + 0.635303i \(0.780875\pi\)
\(632\) 0 0
\(633\) 16.8084 29.1130i 0.668073 1.15714i
\(634\) 0 0
\(635\) −38.3982 + 22.1692i −1.52379 + 0.879759i
\(636\) 0 0
\(637\) 2.36575 2.72089i 0.0937343 0.107806i
\(638\) 0 0
\(639\) −11.8124 + 6.81987i −0.467290 + 0.269790i
\(640\) 0 0
\(641\) −5.46012 + 9.45721i −0.215662 + 0.373537i −0.953477 0.301465i \(-0.902524\pi\)
0.737815 + 0.675003i \(0.235858\pi\)
\(642\) 0 0
\(643\) −15.2725 8.81757i −0.602288 0.347731i 0.167653 0.985846i \(-0.446381\pi\)
−0.769941 + 0.638115i \(0.779714\pi\)
\(644\) 0 0
\(645\) 29.6716i 1.16832i
\(646\) 0 0
\(647\) −8.33632 14.4389i −0.327735 0.567653i 0.654327 0.756211i \(-0.272952\pi\)
−0.982062 + 0.188558i \(0.939619\pi\)
\(648\) 0 0
\(649\) 6.49495 0.254949
\(650\) 0 0
\(651\) −19.1544 −0.750719
\(652\) 0 0
\(653\) 3.38664 + 5.86584i 0.132530 + 0.229548i 0.924651 0.380816i \(-0.124357\pi\)
−0.792121 + 0.610364i \(0.791023\pi\)
\(654\) 0 0
\(655\) 29.5441i 1.15439i
\(656\) 0 0
\(657\) 13.0940 + 7.55983i 0.510846 + 0.294937i
\(658\) 0 0
\(659\) 16.7680 29.0431i 0.653190 1.13136i −0.329154 0.944276i \(-0.606764\pi\)
0.982344 0.187082i \(-0.0599031\pi\)
\(660\) 0 0
\(661\) −21.7945 + 12.5830i −0.847707 + 0.489424i −0.859876 0.510502i \(-0.829460\pi\)
0.0121696 + 0.999926i \(0.496126\pi\)
\(662\) 0 0
\(663\) 13.1643 + 38.2454i 0.511261 + 1.48533i
\(664\) 0 0
\(665\) 7.41995 4.28391i 0.287733 0.166123i
\(666\) 0 0
\(667\) 2.47325 4.28380i 0.0957647 0.165869i
\(668\) 0 0
\(669\) −8.58060 4.95401i −0.331745 0.191533i
\(670\) 0 0
\(671\) 1.36438i 0.0526713i
\(672\) 0 0
\(673\) −0.927341 1.60620i −0.0357464 0.0619145i 0.847599 0.530638i \(-0.178048\pi\)
−0.883345 + 0.468723i \(0.844714\pi\)
\(674\) 0 0
\(675\) −15.9571 −0.614189
\(676\) 0 0
\(677\) −14.7209 −0.565770 −0.282885 0.959154i \(-0.591291\pi\)
−0.282885 + 0.959154i \(0.591291\pi\)
\(678\) 0 0
\(679\) −0.231650 0.401229i −0.00888990 0.0153978i
\(680\) 0 0
\(681\) 30.6822i 1.17575i
\(682\) 0 0
\(683\) −6.87930 3.97177i −0.263229 0.151975i 0.362578 0.931954i \(-0.381897\pi\)
−0.625807 + 0.779978i \(0.715230\pi\)
\(684\) 0 0
\(685\) −13.4266 + 23.2556i −0.513005 + 0.888551i
\(686\) 0 0
\(687\) −32.3529 + 18.6790i −1.23434 + 0.712647i
\(688\) 0 0
\(689\) −5.77394 16.7746i −0.219969 0.639060i
\(690\) 0 0
\(691\) −8.86002 + 5.11534i −0.337051 + 0.194597i −0.658967 0.752172i \(-0.729006\pi\)
0.321916 + 0.946768i \(0.395673\pi\)
\(692\) 0 0
\(693\) 0.937375 1.62358i 0.0356079 0.0616748i
\(694\) 0 0
\(695\) 52.0306 + 30.0399i 1.97363 + 1.13948i
\(696\) 0 0
\(697\) 59.9392i 2.27036i
\(698\) 0 0
\(699\) 18.6616 + 32.3228i 0.705845 + 1.22256i
\(700\) 0 0
\(701\) −16.5978 −0.626891 −0.313445 0.949606i \(-0.601483\pi\)
−0.313445 + 0.949606i \(0.601483\pi\)
\(702\) 0 0
\(703\) 22.9269 0.864706
\(704\) 0 0
\(705\) 12.1468 + 21.0389i 0.457475 + 0.792371i
\(706\) 0 0
\(707\) 5.82303i 0.218998i
\(708\) 0 0
\(709\) 41.4531 + 23.9329i 1.55680 + 0.898820i 0.997560 + 0.0698158i \(0.0222412\pi\)
0.559242 + 0.829004i \(0.311092\pi\)
\(710\) 0 0
\(711\) 0.801130 1.38760i 0.0300447 0.0520390i
\(712\) 0 0
\(713\) −28.3004 + 16.3393i −1.05986 + 0.611910i
\(714\) 0 0
\(715\) −7.55279 + 8.68661i −0.282458 + 0.324861i
\(716\) 0 0
\(717\) −59.5840 + 34.4008i −2.22520 + 1.28472i
\(718\) 0 0
\(719\) 19.0461 32.9888i 0.710300 1.23028i −0.254444 0.967087i \(-0.581893\pi\)
0.964744 0.263188i \(-0.0847741\pi\)
\(720\) 0 0
\(721\) 7.13508 + 4.11944i 0.265724 + 0.153416i
\(722\) 0 0
\(723\) 66.7511i 2.48250i
\(724\) 0 0
\(725\) 5.11047 + 8.85159i 0.189798 + 0.328740i
\(726\) 0 0
\(727\) −15.4059 −0.571374 −0.285687 0.958323i \(-0.592222\pi\)
−0.285687 + 0.958323i \(0.592222\pi\)
\(728\) 0 0
\(729\) −9.41460 −0.348689
\(730\) 0 0
\(731\) 9.03369 + 15.6468i 0.334123 + 0.578718i
\(732\) 0 0
\(733\) 11.6298i 0.429557i −0.976663 0.214778i \(-0.931097\pi\)
0.976663 0.214778i \(-0.0689029\pi\)
\(734\) 0 0
\(735\) −7.05461 4.07298i −0.260213 0.150234i
\(736\) 0 0
\(737\) 3.73456 6.46844i 0.137564 0.238268i
\(738\) 0 0
\(739\) −2.32875 + 1.34451i −0.0856645 + 0.0494584i −0.542220 0.840236i \(-0.682416\pi\)
0.456556 + 0.889695i \(0.349083\pi\)
\(740\) 0 0
\(741\) −18.3416 + 6.31331i −0.673794 + 0.231925i
\(742\) 0 0
\(743\) 2.13665 1.23360i 0.0783862 0.0452563i −0.460295 0.887766i \(-0.652256\pi\)
0.538681 + 0.842510i \(0.318923\pi\)
\(744\) 0 0
\(745\) 4.54118 7.86556i 0.166376 0.288172i
\(746\) 0 0
\(747\) 8.73288 + 5.04193i 0.319519 + 0.184475i
\(748\) 0 0
\(749\) 3.83260i 0.140040i
\(750\) 0 0
\(751\) 18.9592 + 32.8383i 0.691832 + 1.19829i 0.971237 + 0.238115i \(0.0765295\pi\)
−0.279405 + 0.960173i \(0.590137\pi\)
\(752\) 0 0
\(753\) 29.3623 1.07002
\(754\) 0 0
\(755\) −57.2583 −2.08384
\(756\) 0 0
\(757\) −17.3225 30.0035i −0.629598 1.09050i −0.987632 0.156788i \(-0.949886\pi\)
0.358034 0.933709i \(-0.383447\pi\)
\(758\) 0 0
\(759\) 7.73512i 0.280767i
\(760\) 0 0
\(761\) 19.7969 + 11.4297i 0.717636 + 0.414328i 0.813882 0.581030i \(-0.197350\pi\)
−0.0962458 + 0.995358i \(0.530683\pi\)
\(762\) 0 0
\(763\) −5.20902 + 9.02229i −0.188579 + 0.326629i
\(764\) 0 0
\(765\) 32.7239 18.8931i 1.18313 0.683083i
\(766\) 0 0
\(767\) −5.04386 + 25.9336i −0.182123 + 0.936408i
\(768\) 0 0
\(769\) −44.8839 + 25.9137i −1.61855 + 0.934473i −0.631260 + 0.775571i \(0.717462\pi\)
−0.987294 + 0.158902i \(0.949205\pi\)
\(770\) 0 0
\(771\) 5.18507 8.98080i 0.186736 0.323436i
\(772\) 0 0
\(773\) −4.93605 2.84983i −0.177538 0.102501i 0.408598 0.912715i \(-0.366018\pi\)
−0.586135 + 0.810213i \(0.699351\pi\)
\(774\) 0 0
\(775\) 67.5234i 2.42551i
\(776\) 0 0
\(777\) −10.8990 18.8777i −0.391000 0.677232i
\(778\) 0 0
\(779\) −28.7454 −1.02991
\(780\) 0 0
\(781\) −5.71619 −0.204541
\(782\) 0 0
\(783\) −1.28289 2.22204i −0.0458469 0.0794092i
\(784\) 0 0
\(785\) 46.7622i 1.66902i
\(786\) 0 0
\(787\) 14.5614 + 8.40705i 0.519059 + 0.299679i 0.736550 0.676384i \(-0.236454\pi\)
−0.217490 + 0.976062i \(0.569787\pi\)
\(788\) 0 0
\(789\) 3.01364 5.21977i 0.107288 0.185829i
\(790\) 0 0
\(791\) 4.25228 2.45505i 0.151194 0.0872917i
\(792\) 0 0
\(793\) −5.44781 1.05955i −0.193457 0.0376258i
\(794\) 0 0
\(795\) −34.7109 + 20.0404i −1.23107 + 0.710759i