Properties

Label 1456.2.cc.c.225.5
Level $1456$
Weight $2$
Character 1456.225
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 225.5
Root \(-1.30089 - 0.554694i\) of defining polynomial
Character \(\chi\) \(=\) 1456.225
Dual form 1456.2.cc.c.673.5

$q$-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 \(\left(\mathbb{Z}/1456\mathbb{Z}\right)^\times\).

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

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 −0.329539 0.944142i \(-0.606893\pi\)
0.982420 0.186682i \(-0.0597734\pi\)
\(4\) 0 0
\(5\) 3.60178i 1.61076i −0.592756 0.805382i \(-0.701960\pi\)
0.592756 0.805382i \(-0.298040\pi\)
\(6\) 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 0.379791 0.925072i \(-0.375996\pi\)
−0.611241 + 0.791445i \(0.709329\pi\)
\(12\) 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 −0.992593 0.121488i \(-0.961233\pi\)
0.391085 0.920355i \(-0.372100\pi\)
\(18\) 0 0
\(19\) −2.06008 + 1.18939i −0.472615 + 0.272864i −0.717334 0.696730i \(-0.754638\pi\)
0.244719 + 0.969594i \(0.421304\pi\)
\(20\) 0 0
\(21\) 2.26165i 0.493532i
\(22\) 0 0
\(23\) 1.92926 3.34157i 0.402278 0.696765i −0.591723 0.806142i \(-0.701552\pi\)
0.994000 + 0.109376i \(0.0348853\pi\)
\(24\) 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 −0.919383 0.393364i \(-0.871311\pi\)
0.800355 + 0.599527i \(0.204645\pi\)
\(30\) 0 0
\(31\) 8.46921i 1.52111i −0.649271 0.760557i \(-0.724926\pi\)
0.649271 0.760557i \(-0.275074\pi\)
\(32\) 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 −0.381009 0.924571i \(-0.624423\pi\)
−0.991207 + 0.132323i \(0.957757\pi\)
\(38\) 0 0
\(39\) 5.35049 + 6.15370i 0.856763 + 0.985380i
\(40\) 0 0
\(41\) 10.4652 + 6.04207i 1.63438 + 0.943612i 0.982719 + 0.185106i \(0.0592628\pi\)
0.651666 + 0.758506i \(0.274071\pi\)
\(42\) 0 0
\(43\) 1.82125 + 3.15450i 0.277738 + 0.481056i 0.970822 0.239800i \(-0.0770820\pi\)
−0.693084 + 0.720856i \(0.743749\pi\)
\(44\) 0 0
\(45\) −6.59734 + 3.80898i −0.983474 + 0.567809i
\(46\) 0 0
\(47\) 2.98229i 0.435012i 0.976059 + 0.217506i \(0.0697922\pi\)
−0.976059 + 0.217506i \(0.930208\pi\)
\(48\) 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 −0.852532 0.522675i \(-0.824934\pi\)
0.0263837 + 0.999652i \(0.491601\pi\)
\(60\) 0 0
\(61\) 0.769632 + 1.33304i 0.0985412 + 0.170678i 0.911081 0.412227i \(-0.135249\pi\)
−0.812540 + 0.582906i \(0.801916\pi\)
\(62\) 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 −0.0170931 0.999854i \(-0.505441\pi\)
−0.874445 + 0.485124i \(0.838775\pi\)
\(68\) 0 0
\(69\) −4.36330 7.55745i −0.525279 0.909811i
\(70\) 0 0
\(71\) 5.58490 3.22444i 0.662805 0.382671i −0.130540 0.991443i \(-0.541671\pi\)
0.793345 + 0.608772i \(0.208338\pi\)
\(72\) 0 0
\(73\) 7.14859i 0.836679i 0.908291 + 0.418340i \(0.137388\pi\)
−0.908291 + 0.418340i \(0.862612\pi\)
\(74\) 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 \(0.0842697\pi\)
−0.965160 + 0.261659i \(0.915730\pi\)
\(84\) 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 0.656819 0.754048i \(-0.271902\pi\)
−0.324615 + 0.945846i \(0.605235\pi\)
\(90\) 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 −0.520231 0.854026i \(-0.674154\pi\)
0.479492 + 0.877546i \(0.340821\pi\)
\(98\) 0 0
\(99\) 1.87475i 0.188419i
\(100\) 0 0
\(101\) 2.91152 5.04289i 0.289707 0.501787i −0.684033 0.729451i \(-0.739776\pi\)
0.973740 + 0.227664i \(0.0731089\pi\)
\(102\) 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 −0.943663 0.330909i \(-0.892645\pi\)
0.758407 + 0.651781i \(0.225978\pi\)
\(108\) 0 0
\(109\) 10.4180i 0.997867i −0.866640 0.498934i \(-0.833725\pi\)
0.866640 0.498934i \(-0.166275\pi\)
\(110\) 0 0
\(111\) −18.8777 + 10.8990i −1.79179 + 1.03449i
\(112\) 0 0
\(113\) 2.45505 + 4.25228i 0.230952 + 0.400021i 0.958089 0.286472i \(-0.0924826\pi\)
−0.727136 + 0.686493i \(0.759149\pi\)
\(114\) 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 −0.452357 0.891837i \(-0.649417\pi\)
0.998532 0.0541658i \(-0.0172500\pi\)
\(128\) 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 −0.198147 0.980172i \(-0.563492\pi\)
0.749780 + 0.661687i \(0.230159\pi\)
\(138\) 0 0
\(139\) 8.34028 + 14.4458i 0.707413 + 1.22528i 0.965813 + 0.259238i \(0.0834714\pi\)
−0.258400 + 0.966038i \(0.583195\pi\)
\(140\) 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 −0.586777 0.809748i \(-0.699604\pi\)
0.407874 + 0.913038i \(0.366270\pi\)
\(150\) 0 0
\(151\) 15.8972i 1.29370i −0.762618 0.646849i \(-0.776086\pi\)
0.762618 0.646849i \(-0.223914\pi\)
\(152\) 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 −0.419265 0.907864i \(-0.637712\pi\)
0.576601 + 0.817026i \(0.304379\pi\)
\(164\) 0 0
\(165\) 3.61023 + 6.25309i 0.281056 + 0.486803i
\(166\) 0 0
\(167\) 11.9441 + 6.89591i 0.924260 + 0.533622i 0.884992 0.465607i \(-0.154164\pi\)
0.0392682 + 0.999229i \(0.487497\pi\)
\(168\) 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 0.787461 0.616364i \(-0.211395\pi\)
−0.927518 + 0.373779i \(0.878062\pi\)
\(174\) 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 −0.734653 0.678443i \(-0.762655\pi\)
0.954876 + 0.297006i \(0.0959882\pi\)
\(180\) 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 0.583794 0.811902i \(-0.301568\pi\)
−0.995025 + 0.0996290i \(0.968234\pi\)
\(192\) 0 0
\(193\) 12.2017 + 7.04468i 0.878301 + 0.507087i 0.870098 0.492879i \(-0.164055\pi\)
0.00820314 + 0.999966i \(0.497389\pi\)
\(194\) 0 0
\(195\) 22.1643 19.2713i 1.58722 1.38004i
\(196\) 0 0
\(197\) −19.8815 11.4786i −1.41650 0.817814i −0.420507 0.907289i \(-0.638148\pi\)
−0.995989 + 0.0894753i \(0.971481\pi\)
\(198\) 0 0
\(199\) 1.57492 + 2.72785i 0.111643 + 0.193372i 0.916433 0.400188i \(-0.131055\pi\)
−0.804790 + 0.593560i \(0.797722\pi\)
\(200\) 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 0.488275 + 0.872690i \(0.337626\pi\)
−0.999909 + 0.0134864i \(0.995707\pi\)
\(212\) 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 0.367561 0.930000i \(-0.380193\pi\)
−0.621623 + 0.783317i \(0.713526\pi\)
\(224\) 0 0
\(225\) 8.43147 + 14.6037i 0.562098 + 0.973582i
\(226\) 0 0
\(227\) −11.7488 + 6.78316i −0.779793 + 0.450214i −0.836357 0.548185i \(-0.815319\pi\)
0.0565636 + 0.998399i \(0.481986\pi\)
\(228\) 0 0
\(229\) 16.5180i 1.09154i −0.837935 0.545770i \(-0.816237\pi\)
0.837935 0.545770i \(-0.183763\pi\)
\(230\) 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 \(-0.557220\pi\)
0.178796 0.983886i \(-0.442780\pi\)
\(240\) 0 0
\(241\) −25.5602 + 14.7572i −1.64648 + 0.950593i −0.668018 + 0.744145i \(0.732857\pi\)
−0.978458 + 0.206448i \(0.933810\pi\)
\(242\) 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 0.994859 0.101267i \(-0.0322897\pi\)
−0.585130 + 0.810940i \(0.698956\pi\)
\(252\) 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 −0.928628 0.371011i \(-0.879011\pi\)
0.785620 + 0.618710i \(0.212344\pi\)
\(258\) 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 −0.904180 0.427152i \(-0.859517\pi\)
0.822015 + 0.569466i \(0.192850\pi\)
\(264\) 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 0.624984 0.780637i \(-0.285105\pi\)
−0.988544 + 0.150934i \(0.951772\pi\)
\(270\) 0 0
\(271\) 11.2828 + 6.51416i 0.685384 + 0.395707i 0.801881 0.597484i \(-0.203833\pi\)
−0.116496 + 0.993191i \(0.537166\pi\)
\(272\) 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 0.985020 + 0.172438i \(0.0551646\pi\)
−0.343174 + 0.939272i \(0.611502\pi\)
\(278\) 0 0
\(279\) −15.5130 + 8.95641i −0.928737 + 0.536206i
\(280\) 0 0
\(281\) 17.2678i 1.03011i −0.857158 0.515054i \(-0.827772\pi\)
0.857158 0.515054i \(-0.172228\pi\)
\(282\) 0 0
\(283\) 10.6201 18.3946i 0.631299 1.09344i −0.355987 0.934491i \(-0.615855\pi\)
0.987286 0.158952i \(-0.0508114\pi\)
\(284\) 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 −0.510589 0.859825i \(-0.670572\pi\)
0.489336 + 0.872095i \(0.337239\pi\)
\(294\) 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 \(-0.868380\pi\)
0.915721 0.401814i \(-0.131620\pi\)
\(308\) 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 \(-0.993731\pi\)
0.999806 0.0196930i \(-0.00626889\pi\)
\(318\) 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 −0.596590 0.802546i \(-0.703478\pi\)
0.396730 + 0.917935i \(0.370145\pi\)
\(332\) 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 0.952940 0.303160i \(-0.0980415\pi\)
−0.739014 + 0.673690i \(0.764708\pi\)
\(348\) 0 0
\(349\) 18.7038 + 10.7986i 1.00119 + 0.578037i 0.908600 0.417668i \(-0.137152\pi\)
0.0925892 + 0.995704i \(0.470486\pi\)
\(350\) 0 0
\(351\) −2.34866 + 6.82338i −0.125362 + 0.364205i
\(352\) 0 0
\(353\) 18.7214 + 10.8088i 0.996439 + 0.575295i 0.907193 0.420715i \(-0.138221\pi\)
0.0892465 + 0.996010i \(0.471554\pi\)
\(354\) 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 \(0.117595\pi\)
−0.932531 + 0.361090i \(0.882405\pi\)
\(360\) 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 −0.975649 0.219339i \(-0.929610\pi\)
0.677778 + 0.735267i \(0.262943\pi\)
\(368\) 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 0.912981 + 0.408002i \(0.133774\pi\)
−0.103151 + 0.994666i \(0.532892\pi\)
\(374\) 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 −0.254729 0.967012i \(-0.581986\pi\)
−0.964822 + 0.262904i \(0.915320\pi\)
\(380\) 0 0
\(381\) −13.9206 24.1112i −0.713175 1.23526i
\(382\) 0 0
\(383\) −13.9436 + 8.05032i −0.712483 + 0.411352i −0.811980 0.583686i \(-0.801610\pi\)
0.0994967 + 0.995038i \(0.468277\pi\)
\(384\) 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 −0.187560 0.982253i \(-0.560058\pi\)
0.756876 + 0.653558i \(0.226724\pi\)
\(398\) 0 0
\(399\) 2.68998 + 4.65918i 0.134667 + 0.233251i
\(400\) 0 0
\(401\) 16.8396 + 9.72236i 0.840930 + 0.485511i 0.857580 0.514350i \(-0.171967\pi\)
−0.0166501 + 0.999861i \(0.505300\pi\)
\(402\) 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 0.113105 0.993583i \(-0.463921\pi\)
0.917020 + 0.398840i \(0.130587\pi\)
\(410\) 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 0.214825 0.976653i \(-0.431082\pi\)
0.738394 0.674370i \(-0.235585\pi\)
\(420\) 0 0
\(421\) 22.0284i 1.07360i 0.843710 + 0.536799i \(0.180367\pi\)
−0.843710 + 0.536799i \(0.819633\pi\)
\(422\) 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 0.999993 0.00377645i \(-0.00120209\pi\)
0.496726 + 0.867907i \(0.334535\pi\)
\(432\) 0 0
\(433\) 6.10678 + 10.5773i 0.293473 + 0.508310i 0.974629 0.223828i \(-0.0718555\pi\)
−0.681155 + 0.732139i \(0.738522\pi\)
\(434\) 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 −0.614493 0.788922i \(-0.710639\pi\)
0.990473 + 0.137706i \(0.0439728\pi\)
\(440\) 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 0.285388 0.958412i \(-0.407877\pi\)
0.972703 + 0.232052i \(0.0745441\pi\)
\(450\) 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 0.334603 0.942359i \(-0.391398\pi\)
−0.648805 + 0.760955i \(0.724731\pi\)
\(458\) 0 0
\(459\) −4.96373 8.59743i −0.231687 0.401294i
\(460\) 0 0
\(461\) 1.27498 0.736110i 0.0593817 0.0342840i −0.470015 0.882658i \(-0.655752\pi\)
0.529397 + 0.848374i \(0.322418\pi\)
\(462\) 0 0
\(463\) 14.0366i 0.652335i −0.945312 0.326168i \(-0.894243\pi\)
0.945312 0.326168i \(-0.105757\pi\)
\(464\) 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 −0.984068 0.177795i \(-0.943104\pi\)
−0.646009 0.763330i \(-0.723563\pi\)
\(480\) 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 −0.939250 0.343234i \(-0.888478\pi\)
−0.172376 + 0.985031i \(0.555144\pi\)
\(488\) 0 0
\(489\) 5.24584i 0.237225i
\(490\) 0 0
\(491\) −17.3931 + 30.1258i −0.784941 + 1.35956i 0.144094 + 0.989564i \(0.453973\pi\)
−0.929034 + 0.369993i \(0.879360\pi\)
\(492\) 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 \(-0.999505\pi\)
0.999999 0.00155537i \(-0.000495089\pi\)
\(500\) 0 0
\(501\) 27.0133 15.5961i 1.20686 0.696783i
\(502\) 0 0
\(503\) 12.8686 + 22.2891i 0.573782 + 0.993820i 0.996173 + 0.0874060i \(0.0278578\pi\)
−0.422391 + 0.906414i \(0.638809\pi\)
\(504\) 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 0.358759 0.933430i \(-0.383200\pi\)
−0.628995 + 0.777409i \(0.716533\pi\)
\(510\) 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 −0.933059 0.359723i \(-0.882871\pi\)
0.778059 + 0.628191i \(0.216204\pi\)
\(524\) 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 \(0.184806\pi\)
−0.836141 + 0.548515i \(0.815194\pi\)
\(542\) 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 0.154383 0.988011i \(-0.450661\pi\)
−0.778451 + 0.627705i \(0.783994\pi\)
\(558\) 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 0.999572 + 0.0292428i \(0.00930961\pi\)
−0.474461 + 0.880276i \(0.657357\pi\)
\(564\) 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 −0.797780 0.602948i \(-0.793993\pi\)
0.921059 + 0.389424i \(0.127326\pi\)
\(570\) 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 \(-0.728425\pi\)
0.657592 0.753374i \(-0.271575\pi\)
\(578\) 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 −0.323166 0.946342i \(-0.604747\pi\)
−0.981139 + 0.193301i \(0.938080\pi\)
\(588\) 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 \(0.255168\pi\)
−0.695533 + 0.718495i \(0.744832\pi\)
\(594\) 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 −0.994834 0.101518i \(-0.967630\pi\)
0.585334 + 0.810792i \(0.300963\pi\)
\(602\) 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 0.947613 0.319420i \(-0.103488\pi\)
−0.750433 + 0.660947i \(0.770155\pi\)
\(608\) 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 0.277593 0.960699i \(-0.410463\pi\)
−0.693193 + 0.720752i \(0.743797\pi\)
\(614\) 0 0
\(615\) −49.2184 85.2488i −1.98468 3.43756i
\(616\) 0 0
\(617\) −17.3105 + 9.99422i −0.696895 + 0.402352i −0.806190 0.591657i \(-0.798474\pi\)
0.109295 + 0.994009i \(0.465141\pi\)
\(618\) 0 0
\(619\) 41.7176i 1.67677i −0.545078 0.838386i \(-0.683500\pi\)
0.545078 0.838386i \(-0.316500\pi\)
\(620\) 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 −0.772263 0.635303i \(-0.780875\pi\)
0.164057 + 0.986451i \(0.447542\pi\)
\(632\) 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 0.737815 0.675003i \(-0.235858\pi\)
−0.953477 + 0.301465i \(0.902524\pi\)
\(642\) 0 0
\(643\) −15.2725 + 8.81757i −0.602288 + 0.347731i −0.769941 0.638115i \(-0.779714\pi\)
0.167653 + 0.985846i \(0.446381\pi\)
\(644\) 0 0
\(645\) 29.6716i 1.16832i
\(646\) 0 0
\(647\) −8.33632 + 14.4389i −0.327735 + 0.567653i −0.982062 0.188558i \(-0.939619\pi\)
0.654327 + 0.756211i \(0.272952\pi\)
\(648\) 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 −0.792121 0.610364i \(-0.791023\pi\)
0.924651 + 0.380816i \(0.124357\pi\)
\(654\) 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 0.982344 + 0.187082i \(0.0599031\pi\)
−0.329154 + 0.944276i \(0.606764\pi\)
\(660\) 0 0
\(661\) −21.7945 12.5830i −0.847707 0.489424i 0.0121696 0.999926i \(-0.496126\pi\)
−0.859876 + 0.510502i \(0.829460\pi\)
\(662\) 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 −0.883345 0.468723i \(-0.844714\pi\)
0.847599 + 0.530638i \(0.178048\pi\)
\(674\) 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 −0.625807 0.779978i \(-0.715230\pi\)
0.362578 + 0.931954i \(0.381897\pi\)
\(684\) 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 0.321916 0.946768i \(-0.395673\pi\)
−0.658967 + 0.752172i \(0.729006\pi\)
\(692\) 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 0.559242 0.829004i \(-0.311092\pi\)
0.997560 0.0698158i \(-0.0222412\pi\)
\(710\) 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 0.964744 + 0.263188i \(0.0847741\pi\)
−0.254444 + 0.967087i \(0.581893\pi\)
\(720\) 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 \(0.0689029\pi\)
−0.976663 + 0.214778i \(0.931097\pi\)
\(734\) 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 0.456556 0.889695i \(-0.349083\pi\)
−0.542220 + 0.840236i \(0.682416\pi\)
\(740\) 0 0
\(741\) −18.3416 6.31331i −0.673794 0.231925i
\(742\) 0 0
\(743\) 2.13665 + 1.23360i 0.0783862 + 0.0452563i 0.538681 0.842510i \(-0.318923\pi\)
−0.460295 + 0.887766i \(0.652256\pi\)
\(744\) 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 −0.279405 0.960173i \(-0.590137\pi\)
0.971237 0.238115i \(-0.0765295\pi\)
\(752\) 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 0.358034 + 0.933709i \(0.383447\pi\)
−0.987632 + 0.156788i \(0.949886\pi\)
\(758\) 0 0
\(759\) 7.73512i 0.280767i
\(760\) 0 0
\(761\) 19.7969 11.4297i 0.717636 0.414328i −0.0962458 0.995358i \(-0.530683\pi\)
0.813882 + 0.581030i \(0.197350\pi\)
\(762\) 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 −0.987294 0.158902i \(-0.949205\pi\)
−0.631260 0.775571i \(-0.717462\pi\)
\(770\) 0 0
\(771\) 5.18507 + 8.98080i 0.186736 + 0.323436i
\(772\) 0 0
\(773\) −4.93605 + 2.84983i −0.177538 + 0.102501i −0.586135 0.810213i \(-0.699351\pi\)
0.408598 + 0.912715i \(0.366018\pi\)
\(774\) 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 −0.217490 0.976062i \(-0.569787\pi\)
0.736550 + 0.676384i \(0.236454\pi\)
\(788\) 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