Properties

Label 804.2.ba.b.41.13
Level 804
Weight 2
Character 804.41
Analytic conductor 6.420
Analytic rank 0
Dimension 440
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.ba (of order \(66\), degree \(20\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(440\)
Relative dimension: \(22\) over \(\Q(\zeta_{66})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label 41.13
Character \(\chi\) = 804.41
Dual form 804.2.ba.b.353.13

$q$-expansion

\(f(q)\) \(=\) \(q+(0.354927 - 1.69530i) q^{3} +(-0.606307 + 4.21696i) q^{5} +(-0.295017 - 3.08956i) q^{7} +(-2.74805 - 1.20341i) q^{9} +O(q^{10})\) \(q+(0.354927 - 1.69530i) q^{3} +(-0.606307 + 4.21696i) q^{5} +(-0.295017 - 3.08956i) q^{7} +(-2.74805 - 1.20341i) q^{9} +(-5.34850 + 2.14122i) q^{11} +(1.06287 + 1.11471i) q^{13} +(6.93379 + 2.52458i) q^{15} +(-3.13592 + 1.08535i) q^{17} +(0.373168 + 0.0356332i) q^{19} +(-5.34242 - 0.596426i) q^{21} +(3.36039 - 0.160075i) q^{23} +(-12.6176 - 3.70487i) q^{25} +(-3.01550 + 4.23164i) q^{27} +(-5.55526 + 3.20733i) q^{29} +(-5.06664 + 5.31374i) q^{31} +(1.73167 + 9.82726i) q^{33} +(13.2074 + 0.629146i) q^{35} +(2.92489 - 5.06605i) q^{37} +(2.26700 - 1.40624i) q^{39} +(-10.4018 - 2.00479i) q^{41} +(0.118743 + 0.102891i) q^{43} +(6.74090 - 10.8588i) q^{45} +(2.91118 - 5.64690i) q^{47} +(-2.58483 + 0.498185i) q^{49} +(0.726970 + 5.70153i) q^{51} +(1.39615 + 1.61125i) q^{53} +(-5.78658 - 23.8526i) q^{55} +(0.192856 - 0.619982i) q^{57} +(0.864195 + 2.94318i) q^{59} +(-5.18649 + 12.9552i) q^{61} +(-2.90729 + 8.84530i) q^{63} +(-5.34509 + 3.80622i) q^{65} +(1.49951 + 8.04683i) q^{67} +(0.921319 - 5.75367i) q^{69} +(4.54395 + 1.57268i) q^{71} +(2.76888 + 1.10849i) q^{73} +(-10.7592 + 20.0757i) q^{75} +(8.19331 + 15.8928i) q^{77} +(0.363719 - 0.0882373i) q^{79} +(6.10360 + 6.61408i) q^{81} +(6.94036 - 8.82538i) q^{83} +(-2.67555 - 13.8821i) q^{85} +(3.46566 + 10.5562i) q^{87} +(-1.23838 + 1.92696i) q^{89} +(3.13038 - 3.61265i) q^{91} +(7.21007 + 10.4754i) q^{93} +(-0.376518 + 1.55203i) q^{95} +(-0.393962 - 0.227454i) q^{97} +(17.2747 + 0.552271i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 440q - 12q^{7} + 4q^{9} + O(q^{10}) \) \( 440q - 12q^{7} + 4q^{9} - 2q^{15} - 10q^{19} + 22q^{21} - 68q^{25} + 50q^{31} + 11q^{33} - 22q^{37} - 45q^{39} + 22q^{43} + 22q^{45} - 18q^{49} - 6q^{51} + 126q^{55} - 183q^{57} - 56q^{61} - 141q^{63} - 12q^{67} + 33q^{69} + 356q^{73} + 165q^{75} + 228q^{79} + 24q^{81} - 6q^{85} + 75q^{87} - 4q^{91} - 75q^{93} + 12q^{97} + 88q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(-1\) \(e\left(\frac{53}{66}\right)\) \(1\)

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
\(3\) 0.354927 1.69530i 0.204917 0.978779i
\(4\) 0 0
\(5\) −0.606307 + 4.21696i −0.271149 + 1.88588i 0.165442 + 0.986220i \(0.447095\pi\)
−0.436590 + 0.899660i \(0.643814\pi\)
\(6\) 0 0
\(7\) −0.295017 3.08956i −0.111506 1.16774i −0.862015 0.506883i \(-0.830798\pi\)
0.750509 0.660860i \(-0.229808\pi\)
\(8\) 0 0
\(9\) −2.74805 1.20341i −0.916018 0.401137i
\(10\) 0 0
\(11\) −5.34850 + 2.14122i −1.61263 + 0.645601i −0.990525 0.137330i \(-0.956148\pi\)
−0.622108 + 0.782931i \(0.713724\pi\)
\(12\) 0 0
\(13\) 1.06287 + 1.11471i 0.294787 + 0.309164i 0.854426 0.519573i \(-0.173909\pi\)
−0.559639 + 0.828736i \(0.689060\pi\)
\(14\) 0 0
\(15\) 6.93379 + 2.52458i 1.79030 + 0.651844i
\(16\) 0 0
\(17\) −3.13592 + 1.08535i −0.760572 + 0.263236i −0.679702 0.733488i \(-0.737891\pi\)
−0.0808697 + 0.996725i \(0.525770\pi\)
\(18\) 0 0
\(19\) 0.373168 + 0.0356332i 0.0856105 + 0.00817481i 0.137773 0.990464i \(-0.456005\pi\)
−0.0521629 + 0.998639i \(0.516611\pi\)
\(20\) 0 0
\(21\) −5.34242 0.596426i −1.16581 0.130151i
\(22\) 0 0
\(23\) 3.36039 0.160075i 0.700690 0.0333780i 0.305786 0.952100i \(-0.401081\pi\)
0.394904 + 0.918722i \(0.370778\pi\)
\(24\) 0 0
\(25\) −12.6176 3.70487i −2.52353 0.740975i
\(26\) 0 0
\(27\) −3.01550 + 4.23164i −0.580333 + 0.814380i
\(28\) 0 0
\(29\) −5.55526 + 3.20733i −1.03159 + 0.595586i −0.917438 0.397878i \(-0.869747\pi\)
−0.114147 + 0.993464i \(0.536414\pi\)
\(30\) 0 0
\(31\) −5.06664 + 5.31374i −0.909996 + 0.954376i −0.999133 0.0416434i \(-0.986741\pi\)
0.0891369 + 0.996019i \(0.471589\pi\)
\(32\) 0 0
\(33\) 1.73167 + 9.82726i 0.301445 + 1.71071i
\(34\) 0 0
\(35\) 13.2074 + 0.629146i 2.23246 + 0.106345i
\(36\) 0 0
\(37\) 2.92489 5.06605i 0.480848 0.832854i −0.518910 0.854829i \(-0.673662\pi\)
0.999759 + 0.0219750i \(0.00699543\pi\)
\(38\) 0 0
\(39\) 2.26700 1.40624i 0.363010 0.225178i
\(40\) 0 0
\(41\) −10.4018 2.00479i −1.62449 0.313095i −0.705903 0.708308i \(-0.749459\pi\)
−0.918590 + 0.395213i \(0.870671\pi\)
\(42\) 0 0
\(43\) 0.118743 + 0.102891i 0.0181081 + 0.0156908i 0.663868 0.747850i \(-0.268914\pi\)
−0.645760 + 0.763541i \(0.723459\pi\)
\(44\) 0 0
\(45\) 6.74090 10.8588i 1.00487 1.61873i
\(46\) 0 0
\(47\) 2.91118 5.64690i 0.424639 0.823685i −0.575344 0.817911i \(-0.695132\pi\)
0.999983 0.00577368i \(-0.00183783\pi\)
\(48\) 0 0
\(49\) −2.58483 + 0.498185i −0.369261 + 0.0711692i
\(50\) 0 0
\(51\) 0.726970 + 5.70153i 0.101796 + 0.798374i
\(52\) 0 0
\(53\) 1.39615 + 1.61125i 0.191776 + 0.221322i 0.843492 0.537142i \(-0.180496\pi\)
−0.651716 + 0.758463i \(0.725950\pi\)
\(54\) 0 0
\(55\) −5.78658 23.8526i −0.780263 3.21629i
\(56\) 0 0
\(57\) 0.192856 0.619982i 0.0255444 0.0821186i
\(58\) 0 0
\(59\) 0.864195 + 2.94318i 0.112509 + 0.383169i 0.996426 0.0844747i \(-0.0269212\pi\)
−0.883917 + 0.467644i \(0.845103\pi\)
\(60\) 0 0
\(61\) −5.18649 + 12.9552i −0.664062 + 1.65875i 0.0851109 + 0.996371i \(0.472876\pi\)
−0.749173 + 0.662375i \(0.769549\pi\)
\(62\) 0 0
\(63\) −2.90729 + 8.84530i −0.366284 + 1.11440i
\(64\) 0 0
\(65\) −5.34509 + 3.80622i −0.662977 + 0.472104i
\(66\) 0 0
\(67\) 1.49951 + 8.04683i 0.183194 + 0.983077i
\(68\) 0 0
\(69\) 0.921319 5.75367i 0.110914 0.692661i
\(70\) 0 0
\(71\) 4.54395 + 1.57268i 0.539268 + 0.186642i 0.583106 0.812396i \(-0.301837\pi\)
−0.0438379 + 0.999039i \(0.513959\pi\)
\(72\) 0 0
\(73\) 2.76888 + 1.10849i 0.324073 + 0.129739i 0.527994 0.849248i \(-0.322944\pi\)
−0.203921 + 0.978987i \(0.565369\pi\)
\(74\) 0 0
\(75\) −10.7592 + 20.0757i −1.24237 + 2.31814i
\(76\) 0 0
\(77\) 8.19331 + 15.8928i 0.933714 + 1.81115i
\(78\) 0 0
\(79\) 0.363719 0.0882373i 0.0409216 0.00992748i −0.215246 0.976560i \(-0.569055\pi\)
0.256167 + 0.966632i \(0.417540\pi\)
\(80\) 0 0
\(81\) 6.10360 + 6.61408i 0.678178 + 0.734898i
\(82\) 0 0
\(83\) 6.94036 8.82538i 0.761803 0.968712i −0.238194 0.971218i \(-0.576555\pi\)
0.999997 + 0.00250596i \(0.000797672\pi\)
\(84\) 0 0
\(85\) −2.67555 13.8821i −0.290204 1.50572i
\(86\) 0 0
\(87\) 3.46566 + 10.5562i 0.371558 + 1.13174i
\(88\) 0 0
\(89\) −1.23838 + 1.92696i −0.131268 + 0.204258i −0.900665 0.434513i \(-0.856920\pi\)
0.769397 + 0.638771i \(0.220557\pi\)
\(90\) 0 0
\(91\) 3.13038 3.61265i 0.328153 0.378709i
\(92\) 0 0
\(93\) 7.21007 + 10.4754i 0.747650 + 1.08625i
\(94\) 0 0
\(95\) −0.376518 + 1.55203i −0.0386299 + 0.159235i
\(96\) 0 0
\(97\) −0.393962 0.227454i −0.0400008 0.0230945i 0.479866 0.877342i \(-0.340685\pi\)
−0.519867 + 0.854247i \(0.674019\pi\)
\(98\) 0 0
\(99\) 17.2747 + 0.552271i 1.73618 + 0.0555053i
\(100\) 0 0
\(101\) 7.12702 10.0085i 0.709165 0.995882i −0.290079 0.957003i \(-0.593682\pi\)
0.999244 0.0388797i \(-0.0123789\pi\)
\(102\) 0 0
\(103\) −13.1880 12.5747i −1.29945 1.23902i −0.953723 0.300686i \(-0.902784\pi\)
−0.345726 0.938336i \(-0.612367\pi\)
\(104\) 0 0
\(105\) 5.75425 22.1671i 0.561557 2.16329i
\(106\) 0 0
\(107\) −1.02067 + 0.146751i −0.0986721 + 0.0141869i −0.191474 0.981498i \(-0.561327\pi\)
0.0928019 + 0.995685i \(0.470418\pi\)
\(108\) 0 0
\(109\) −3.29791 + 11.2316i −0.315882 + 1.07580i 0.636598 + 0.771196i \(0.280341\pi\)
−0.952480 + 0.304601i \(0.901477\pi\)
\(110\) 0 0
\(111\) −7.55033 6.75662i −0.716646 0.641310i
\(112\) 0 0
\(113\) −7.84294 + 6.16776i −0.737802 + 0.580214i −0.914757 0.404005i \(-0.867618\pi\)
0.176955 + 0.984219i \(0.443375\pi\)
\(114\) 0 0
\(115\) −1.36240 + 14.2677i −0.127044 + 1.33047i
\(116\) 0 0
\(117\) −1.57937 4.34234i −0.146013 0.401450i
\(118\) 0 0
\(119\) 4.27841 + 9.36840i 0.392201 + 0.858800i
\(120\) 0 0
\(121\) 16.0606 15.3137i 1.46005 1.39216i
\(122\) 0 0
\(123\) −7.09060 + 16.9226i −0.639338 + 1.52586i
\(124\) 0 0
\(125\) 14.4244 31.5851i 1.29016 2.82506i
\(126\) 0 0
\(127\) 6.65841 0.635801i 0.590839 0.0564183i 0.204645 0.978836i \(-0.434396\pi\)
0.386193 + 0.922418i \(0.373790\pi\)
\(128\) 0 0
\(129\) 0.216576 0.164785i 0.0190685 0.0145085i
\(130\) 0 0
\(131\) −2.72329 4.23752i −0.237935 0.370234i 0.701666 0.712506i \(-0.252440\pi\)
−0.939601 + 0.342272i \(0.888803\pi\)
\(132\) 0 0
\(133\) 1.16343i 0.100883i
\(134\) 0 0
\(135\) −16.0163 15.2819i −1.37847 1.31526i
\(136\) 0 0
\(137\) 14.7333 9.46850i 1.25875 0.808948i 0.270636 0.962682i \(-0.412766\pi\)
0.988112 + 0.153734i \(0.0491298\pi\)
\(138\) 0 0
\(139\) 8.55641 + 1.23023i 0.725746 + 0.104346i 0.495279 0.868734i \(-0.335066\pi\)
0.230466 + 0.973080i \(0.425975\pi\)
\(140\) 0 0
\(141\) −8.53991 6.93955i −0.719190 0.584415i
\(142\) 0 0
\(143\) −8.07158 3.68617i −0.674980 0.308253i
\(144\) 0 0
\(145\) −10.1570 25.3709i −0.843491 2.10694i
\(146\) 0 0
\(147\) −0.0728546 + 4.55886i −0.00600894 + 0.376009i
\(148\) 0 0
\(149\) −9.94457 + 4.54153i −0.814691 + 0.372057i −0.778779 0.627298i \(-0.784161\pi\)
−0.0359117 + 0.999355i \(0.511433\pi\)
\(150\) 0 0
\(151\) 3.03650 + 8.77339i 0.247107 + 0.713968i 0.998533 + 0.0541507i \(0.0172452\pi\)
−0.751426 + 0.659817i \(0.770634\pi\)
\(152\) 0 0
\(153\) 9.92380 + 0.791196i 0.802291 + 0.0639644i
\(154\) 0 0
\(155\) −19.3359 24.5876i −1.55309 1.97492i
\(156\) 0 0
\(157\) −0.126031 2.64571i −0.0100584 0.211151i −0.998301 0.0582601i \(-0.981445\pi\)
0.988243 0.152891i \(-0.0488583\pi\)
\(158\) 0 0
\(159\) 3.22707 1.79502i 0.255924 0.142354i
\(160\) 0 0
\(161\) −1.48593 10.3349i −0.117108 0.814504i
\(162\) 0 0
\(163\) 7.59768 + 13.1596i 0.595096 + 1.03074i 0.993533 + 0.113541i \(0.0362194\pi\)
−0.398437 + 0.917196i \(0.630447\pi\)
\(164\) 0 0
\(165\) −42.4911 + 1.34403i −3.30792 + 0.104633i
\(166\) 0 0
\(167\) −9.89558 7.04661i −0.765743 0.545283i 0.129117 0.991629i \(-0.458786\pi\)
−0.894860 + 0.446346i \(0.852725\pi\)
\(168\) 0 0
\(169\) 0.505688 10.6157i 0.0388991 0.816592i
\(170\) 0 0
\(171\) −0.982603 0.546996i −0.0751415 0.0418298i
\(172\) 0 0
\(173\) −6.27092 1.52131i −0.476769 0.115663i −0.00982875 0.999952i \(-0.503129\pi\)
−0.466941 + 0.884289i \(0.654644\pi\)
\(174\) 0 0
\(175\) −7.72400 + 40.0759i −0.583880 + 3.02946i
\(176\) 0 0
\(177\) 5.29628 0.420453i 0.398093 0.0316032i
\(178\) 0 0
\(179\) −19.2913 12.3978i −1.44190 0.926653i −0.999556 0.0298077i \(-0.990511\pi\)
−0.442344 0.896845i \(-0.645853\pi\)
\(180\) 0 0
\(181\) −11.7407 6.05273i −0.872677 0.449896i −0.0371268 0.999311i \(-0.511821\pi\)
−0.835550 + 0.549414i \(0.814851\pi\)
\(182\) 0 0
\(183\) 20.1221 + 13.3908i 1.48747 + 0.989875i
\(184\) 0 0
\(185\) 19.5899 + 15.4057i 1.44028 + 1.13265i
\(186\) 0 0
\(187\) 14.4485 12.5197i 1.05658 0.915530i
\(188\) 0 0
\(189\) 13.9635 + 8.06814i 1.01570 + 0.586871i
\(190\) 0 0
\(191\) 2.68091 1.38211i 0.193984 0.100006i −0.358498 0.933530i \(-0.616711\pi\)
0.552482 + 0.833525i \(0.313681\pi\)
\(192\) 0 0
\(193\) 6.64319 1.95062i 0.478187 0.140408i −0.0337517 0.999430i \(-0.510746\pi\)
0.511939 + 0.859022i \(0.328927\pi\)
\(194\) 0 0
\(195\) 4.55555 + 10.4124i 0.326230 + 0.745650i
\(196\) 0 0
\(197\) 3.87942 11.2088i 0.276397 0.798596i −0.718299 0.695735i \(-0.755079\pi\)
0.994696 0.102862i \(-0.0327999\pi\)
\(198\) 0 0
\(199\) −11.6192 16.3169i −0.823663 1.15667i −0.985470 0.169850i \(-0.945672\pi\)
0.161807 0.986822i \(-0.448268\pi\)
\(200\) 0 0
\(201\) 14.1740 + 0.313924i 0.999755 + 0.0221425i
\(202\) 0 0
\(203\) 11.5481 + 16.2171i 0.810519 + 1.13822i
\(204\) 0 0
\(205\) 14.7608 42.6485i 1.03094 2.97870i
\(206\) 0 0
\(207\) −9.42717 3.60404i −0.655234 0.250498i
\(208\) 0 0
\(209\) −2.07219 + 0.608449i −0.143336 + 0.0420873i
\(210\) 0 0
\(211\) 22.8993 11.8054i 1.57645 0.812718i 0.576463 0.817123i \(-0.304433\pi\)
0.999990 + 0.00440540i \(0.00140229\pi\)
\(212\) 0 0
\(213\) 4.27892 7.14516i 0.293187 0.489578i
\(214\) 0 0
\(215\) −0.505882 + 0.438350i −0.0345009 + 0.0298952i
\(216\) 0 0
\(217\) 17.9118 + 14.0860i 1.21594 + 0.956222i
\(218\) 0 0
\(219\) 2.86197 4.30063i 0.193394 0.290610i
\(220\) 0 0
\(221\) −4.54292 2.34204i −0.305590 0.157543i
\(222\) 0 0
\(223\) −11.7753 7.56750i −0.788530 0.506757i 0.0833246 0.996522i \(-0.473446\pi\)
−0.871854 + 0.489765i \(0.837083\pi\)
\(224\) 0 0
\(225\) 30.2155 + 25.3654i 2.01436 + 1.69103i
\(226\) 0 0
\(227\) −4.97463 + 25.8108i −0.330178 + 1.71312i 0.314999 + 0.949092i \(0.397996\pi\)
−0.645177 + 0.764033i \(0.723216\pi\)
\(228\) 0 0
\(229\) 6.42665 + 1.55909i 0.424685 + 0.103027i 0.442405 0.896816i \(-0.354126\pi\)
−0.0177199 + 0.999843i \(0.505641\pi\)
\(230\) 0 0
\(231\) 29.8510 8.24930i 1.96405 0.542764i
\(232\) 0 0
\(233\) −0.980955 + 20.5928i −0.0642645 + 1.34908i 0.704572 + 0.709632i \(0.251139\pi\)
−0.768837 + 0.639445i \(0.779164\pi\)
\(234\) 0 0
\(235\) 22.0477 + 15.7001i 1.43823 + 1.02416i
\(236\) 0 0
\(237\) −0.0204946 0.647929i −0.00133127 0.0420875i
\(238\) 0 0
\(239\) 3.37469 + 5.84513i 0.218290 + 0.378090i 0.954285 0.298897i \(-0.0966186\pi\)
−0.735995 + 0.676987i \(0.763285\pi\)
\(240\) 0 0
\(241\) 3.90362 + 27.1503i 0.251454 + 1.74890i 0.589496 + 0.807771i \(0.299326\pi\)
−0.338042 + 0.941131i \(0.609765\pi\)
\(242\) 0 0
\(243\) 13.3792 7.99989i 0.858273 0.513193i
\(244\) 0 0
\(245\) −0.533624 11.2022i −0.0340920 0.715679i
\(246\) 0 0
\(247\) 0.356908 + 0.453845i 0.0227095 + 0.0288775i
\(248\) 0 0
\(249\) −12.4983 14.8983i −0.792048 0.944143i
\(250\) 0 0
\(251\) −3.62965 10.4872i −0.229101 0.661945i −0.999697 0.0246205i \(-0.992162\pi\)
0.770595 0.637325i \(-0.219959\pi\)
\(252\) 0 0
\(253\) −17.6303 + 8.05149i −1.10841 + 0.506193i
\(254\) 0 0
\(255\) −24.4839 0.391273i −1.53324 0.0245025i
\(256\) 0 0
\(257\) 7.02930 + 17.5583i 0.438475 + 1.09526i 0.968884 + 0.247516i \(0.0796144\pi\)
−0.530408 + 0.847742i \(0.677961\pi\)
\(258\) 0 0
\(259\) −16.5147 7.54203i −1.02618 0.468639i
\(260\) 0 0
\(261\) 19.1259 2.12865i 1.18386 0.131760i
\(262\) 0 0
\(263\) −13.9779 2.00973i −0.861917 0.123925i −0.302841 0.953041i \(-0.597935\pi\)
−0.559076 + 0.829116i \(0.688844\pi\)
\(264\) 0 0
\(265\) −7.64106 + 4.91061i −0.469386 + 0.301656i
\(266\) 0 0
\(267\) 2.82724 + 2.78336i 0.173024 + 0.170339i
\(268\) 0 0
\(269\) 16.1978i 0.987597i 0.869576 + 0.493799i \(0.164392\pi\)
−0.869576 + 0.493799i \(0.835608\pi\)
\(270\) 0 0
\(271\) 2.88664 + 4.49170i 0.175351 + 0.272851i 0.917793 0.397059i \(-0.129969\pi\)
−0.742442 + 0.669910i \(0.766333\pi\)
\(272\) 0 0
\(273\) −5.01346 6.58915i −0.303428 0.398794i
\(274\) 0 0
\(275\) 75.4184 7.20158i 4.54790 0.434272i
\(276\) 0 0
\(277\) −10.0366 + 21.9772i −0.603043 + 1.32048i 0.324189 + 0.945992i \(0.394909\pi\)
−0.927232 + 0.374487i \(0.877819\pi\)
\(278\) 0 0
\(279\) 20.3180 8.50519i 1.21641 0.509192i
\(280\) 0 0
\(281\) −13.0301 + 12.4242i −0.777312 + 0.741166i −0.970788 0.239939i \(-0.922872\pi\)
0.193476 + 0.981105i \(0.438024\pi\)
\(282\) 0 0
\(283\) 1.76612 + 3.86727i 0.104985 + 0.229885i 0.954833 0.297142i \(-0.0960336\pi\)
−0.849848 + 0.527028i \(0.823306\pi\)
\(284\) 0 0
\(285\) 2.49751 + 1.18916i 0.147940 + 0.0704400i
\(286\) 0 0
\(287\) −3.12519 + 32.7285i −0.184474 + 1.93190i
\(288\) 0 0
\(289\) −4.70691 + 3.70155i −0.276877 + 0.217738i
\(290\) 0 0
\(291\) −0.525430 + 0.587153i −0.0308012 + 0.0344195i
\(292\) 0 0
\(293\) −2.18836 + 7.45288i −0.127845 + 0.435402i −0.998392 0.0566841i \(-0.981947\pi\)
0.870547 + 0.492086i \(0.163765\pi\)
\(294\) 0 0
\(295\) −12.9352 + 1.85980i −0.753117 + 0.108282i
\(296\) 0 0
\(297\) 7.06753 29.0898i 0.410100 1.68796i
\(298\) 0 0
\(299\) 3.75010 + 3.57571i 0.216874 + 0.206789i
\(300\) 0 0
\(301\) 0.282857 0.397217i 0.0163036 0.0228952i
\(302\) 0 0
\(303\) −14.4378 15.6347i −0.829429 0.898189i
\(304\) 0 0
\(305\) −51.4870 29.7260i −2.94814 1.70211i
\(306\) 0 0
\(307\) 1.30583 5.38272i 0.0745279 0.307208i −0.922332 0.386399i \(-0.873719\pi\)
0.996859 + 0.0791913i \(0.0252338\pi\)
\(308\) 0 0
\(309\) −25.9986 + 17.8944i −1.47901 + 1.01798i
\(310\) 0 0
\(311\) −7.91488 + 9.13426i −0.448812 + 0.517956i −0.934397 0.356233i \(-0.884061\pi\)
0.485586 + 0.874189i \(0.338606\pi\)
\(312\) 0 0
\(313\) −15.9193 + 24.7709i −0.899813 + 1.40014i 0.0165828 + 0.999862i \(0.494721\pi\)
−0.916396 + 0.400274i \(0.868915\pi\)
\(314\) 0 0
\(315\) −35.5375 17.6229i −2.00231 0.992936i
\(316\) 0 0
\(317\) −2.77787 14.4130i −0.156021 0.809514i −0.972637 0.232332i \(-0.925364\pi\)
0.816616 0.577182i \(-0.195848\pi\)
\(318\) 0 0
\(319\) 22.8447 29.0494i 1.27906 1.62646i
\(320\) 0 0
\(321\) −0.113479 + 1.78243i −0.00633376 + 0.0994854i
\(322\) 0 0
\(323\) −1.20890 + 0.293275i −0.0672649 + 0.0163183i
\(324\) 0 0
\(325\) −9.28107 18.0028i −0.514821 0.998613i
\(326\) 0 0
\(327\) 17.8704 + 9.57734i 0.988238 + 0.529628i
\(328\) 0 0
\(329\) −18.3053 7.32832i −1.00920 0.404024i
\(330\) 0 0
\(331\) 4.93615 + 1.70842i 0.271315 + 0.0939031i 0.459338 0.888262i \(-0.348087\pi\)
−0.188023 + 0.982165i \(0.560208\pi\)
\(332\) 0 0
\(333\) −14.1343 + 10.4019i −0.774554 + 0.570023i
\(334\) 0 0
\(335\) −34.8423 + 1.44452i −1.90364 + 0.0789226i
\(336\) 0 0
\(337\) 15.9342 11.3467i 0.867990 0.618093i −0.0568779 0.998381i \(-0.518115\pi\)
0.924868 + 0.380288i \(0.124175\pi\)
\(338\) 0 0
\(339\) 7.67250 + 15.4852i 0.416713 + 0.841041i
\(340\) 0 0
\(341\) 15.7211 39.2693i 0.851343 2.12655i
\(342\) 0 0
\(343\) −3.81898 13.0062i −0.206206 0.702271i
\(344\) 0 0
\(345\) 23.7044 + 7.37365i 1.27620 + 0.396984i
\(346\) 0 0
\(347\) 1.90110 + 7.83645i 0.102056 + 0.420683i 0.999803 0.0198291i \(-0.00631220\pi\)
−0.897747 + 0.440512i \(0.854797\pi\)
\(348\) 0 0
\(349\) 3.25401 + 3.75533i 0.174183 + 0.201018i 0.836128 0.548535i \(-0.184814\pi\)
−0.661945 + 0.749553i \(0.730269\pi\)
\(350\) 0 0
\(351\) −7.92211 + 1.13629i −0.422851 + 0.0606507i
\(352\) 0 0
\(353\) 26.5842 5.12369i 1.41493 0.272706i 0.576228 0.817289i \(-0.304524\pi\)
0.838707 + 0.544583i \(0.183312\pi\)
\(354\) 0 0
\(355\) −9.38694 + 18.2081i −0.498207 + 0.966387i
\(356\) 0 0
\(357\) 17.4007 3.92806i 0.920944 0.207895i
\(358\) 0 0
\(359\) 15.4265 + 13.3671i 0.814177 + 0.705489i 0.958826 0.283995i \(-0.0916597\pi\)
−0.144649 + 0.989483i \(0.546205\pi\)
\(360\) 0 0
\(361\) −18.5187 3.56918i −0.974666 0.187852i
\(362\) 0 0
\(363\) −20.2610 32.6627i −1.06342 1.71435i
\(364\) 0 0
\(365\) −6.35325 + 11.0041i −0.332544 + 0.575984i
\(366\) 0 0
\(367\) −17.2173 0.820159i −0.898734 0.0428120i −0.406872 0.913485i \(-0.633381\pi\)
−0.491862 + 0.870673i \(0.663684\pi\)
\(368\) 0 0
\(369\) 26.1722 + 18.0270i 1.36247 + 0.938446i
\(370\) 0 0
\(371\) 4.56615 4.78884i 0.237063 0.248624i
\(372\) 0 0
\(373\) −6.10626 + 3.52545i −0.316170 + 0.182541i −0.649684 0.760204i \(-0.725099\pi\)
0.333514 + 0.942745i \(0.391765\pi\)
\(374\) 0 0
\(375\) −48.4265 35.6641i −2.50073 1.84169i
\(376\) 0 0
\(377\) −9.47974 2.78350i −0.488232 0.143358i
\(378\) 0 0
\(379\) −0.768266 + 0.0365970i −0.0394632 + 0.00187986i −0.0673042 0.997732i \(-0.521440\pi\)
0.0278410 + 0.999612i \(0.491137\pi\)
\(380\) 0 0
\(381\) 1.28538 11.5136i 0.0658520 0.589862i
\(382\) 0 0
\(383\) −7.47379 0.713661i −0.381893 0.0364663i −0.0976555 0.995220i \(-0.531134\pi\)
−0.284237 + 0.958754i \(0.591740\pi\)
\(384\) 0 0
\(385\) −71.9869 + 24.9149i −3.66879 + 1.26978i
\(386\) 0 0
\(387\) −0.202491 0.425647i −0.0102932 0.0216369i
\(388\) 0 0
\(389\) 11.1481 + 11.6917i 0.565229 + 0.592795i 0.942872 0.333156i \(-0.108114\pi\)
−0.377643 + 0.925951i \(0.623265\pi\)
\(390\) 0 0
\(391\) −10.3642 + 4.14919i −0.524139 + 0.209834i
\(392\) 0 0
\(393\) −8.15041 + 3.11277i −0.411134 + 0.157018i
\(394\) 0 0
\(395\) 0.151568 + 1.58729i 0.00762619 + 0.0798651i
\(396\) 0 0
\(397\) 3.11736 21.6817i 0.156456 1.08818i −0.748643 0.662974i \(-0.769294\pi\)
0.905099 0.425202i \(-0.139797\pi\)
\(398\) 0 0
\(399\) −1.97237 0.412934i −0.0987418 0.0206726i
\(400\) 0 0
\(401\) −27.5475 −1.37566 −0.687829 0.725873i \(-0.741436\pi\)
−0.687829 + 0.725873i \(0.741436\pi\)
\(402\) 0 0
\(403\) −11.3084 −0.563313
\(404\) 0 0
\(405\) −31.5919 + 21.7284i −1.56982 + 1.07970i
\(406\) 0 0
\(407\) −4.79624 + 33.3586i −0.237741 + 1.65352i
\(408\) 0 0
\(409\) 2.08694 + 21.8554i 0.103193 + 1.08068i 0.887656 + 0.460507i \(0.152332\pi\)
−0.784464 + 0.620175i \(0.787062\pi\)
\(410\) 0 0
\(411\) −10.8227 28.3379i −0.533843 1.39780i
\(412\) 0 0
\(413\) 8.83816 3.53827i 0.434897 0.174107i
\(414\) 0 0
\(415\) 33.0083 + 34.6181i 1.62031 + 1.69933i
\(416\) 0 0
\(417\) 5.12250 14.0690i 0.250850 0.688962i
\(418\) 0 0
\(419\) 20.6175 7.13577i 1.00723 0.348605i 0.226862 0.973927i \(-0.427153\pi\)
0.780367 + 0.625322i \(0.215032\pi\)
\(420\) 0 0
\(421\) 9.37835 + 0.895524i 0.457073 + 0.0436452i 0.321054 0.947061i \(-0.395963\pi\)
0.136019 + 0.990706i \(0.456569\pi\)
\(422\) 0 0
\(423\) −14.7956 + 12.0146i −0.719388 + 0.584172i
\(424\) 0 0
\(425\) 43.5890 2.07640i 2.11438 0.100720i
\(426\) 0 0
\(427\) 41.5560 + 12.2019i 2.01104 + 0.590493i
\(428\) 0 0
\(429\) −9.11397 + 12.3754i −0.440027 + 0.597490i
\(430\) 0 0
\(431\) 23.2702 13.4351i 1.12089 0.647144i 0.179260 0.983802i \(-0.442630\pi\)
0.941627 + 0.336657i \(0.109296\pi\)
\(432\) 0 0
\(433\) −23.0976 + 24.2241i −1.11000 + 1.16414i −0.124899 + 0.992169i \(0.539861\pi\)
−0.985103 + 0.171967i \(0.944988\pi\)
\(434\) 0 0
\(435\) −46.6162 + 8.21426i −2.23507 + 0.393844i
\(436\) 0 0
\(437\) 1.25969 + 0.0600066i 0.0602593 + 0.00287050i
\(438\) 0 0
\(439\) −7.23239 + 12.5269i −0.345183 + 0.597875i −0.985387 0.170330i \(-0.945517\pi\)
0.640204 + 0.768205i \(0.278850\pi\)
\(440\) 0 0
\(441\) 7.70276 + 1.74157i 0.366798 + 0.0829321i
\(442\) 0 0
\(443\) −36.6488 7.06347i −1.74124 0.335596i −0.783097 0.621900i \(-0.786361\pi\)
−0.958139 + 0.286304i \(0.907573\pi\)
\(444\) 0 0
\(445\) −7.37508 6.39054i −0.349612 0.302941i
\(446\) 0 0
\(447\) 4.16964 + 18.4709i 0.197217 + 0.873643i
\(448\) 0 0
\(449\) −2.78293 + 5.39814i −0.131335 + 0.254754i −0.945328 0.326120i \(-0.894259\pi\)
0.813994 + 0.580874i \(0.197289\pi\)
\(450\) 0 0
\(451\) 59.9269 11.5500i 2.82185 0.543866i
\(452\) 0 0
\(453\) 15.9512 2.03385i 0.749454 0.0955587i
\(454\) 0 0
\(455\) 13.3364 + 15.3911i 0.625221 + 0.721544i
\(456\) 0 0
\(457\) −2.94610 12.1440i −0.137813 0.568073i −0.998283 0.0585720i \(-0.981345\pi\)
0.860470 0.509501i \(-0.170170\pi\)
\(458\) 0 0
\(459\) 4.86353 16.5430i 0.227010 0.772159i
\(460\) 0 0
\(461\) −3.50252 11.9285i −0.163129 0.555566i −0.999967 0.00811540i \(-0.997417\pi\)
0.836838 0.547450i \(-0.184401\pi\)
\(462\) 0 0
\(463\) 7.60634 18.9997i 0.353497 0.882992i −0.639921 0.768441i \(-0.721033\pi\)
0.993417 0.114551i \(-0.0365429\pi\)
\(464\) 0 0
\(465\) −48.5460 + 24.0532i −2.25127 + 1.11544i
\(466\) 0 0
\(467\) −7.51464 + 5.35115i −0.347736 + 0.247622i −0.740557 0.671993i \(-0.765438\pi\)
0.392821 + 0.919615i \(0.371499\pi\)
\(468\) 0 0
\(469\) 24.4188 7.00677i 1.12755 0.323543i
\(470\) 0 0
\(471\) −4.53000 0.725375i −0.208731 0.0334235i
\(472\) 0 0
\(473\) −0.855409 0.296060i −0.0393317 0.0136128i
\(474\) 0 0
\(475\) −4.57648 1.83215i −0.209983 0.0840646i
\(476\) 0 0
\(477\) −1.89771 6.10794i −0.0868902 0.279663i
\(478\) 0 0
\(479\) 8.80975 + 17.0885i 0.402528 + 0.780795i 0.999774 0.0212630i \(-0.00676873\pi\)
−0.597246 + 0.802058i \(0.703738\pi\)
\(480\) 0 0
\(481\) 8.75593 2.12417i 0.399236 0.0968536i
\(482\) 0 0
\(483\) −18.0481 1.14904i −0.821217 0.0522829i
\(484\) 0 0
\(485\) 1.19803 1.52341i 0.0543995 0.0691747i
\(486\) 0 0
\(487\) 0.0504807 + 0.261919i 0.00228750 + 0.0118687i 0.983055 0.183313i \(-0.0586823\pi\)
−0.980767 + 0.195182i \(0.937470\pi\)
\(488\) 0 0
\(489\) 25.0060 8.20963i 1.13081 0.371252i
\(490\) 0 0
\(491\) −4.10090 + 6.38112i −0.185071 + 0.287976i −0.921375 0.388675i \(-0.872933\pi\)
0.736304 + 0.676651i \(0.236569\pi\)
\(492\) 0 0
\(493\) 13.9398 16.0873i 0.627815 0.724537i
\(494\) 0 0
\(495\) −12.8027 + 72.5119i −0.575438 + 3.25917i
\(496\) 0 0
\(497\) 3.51833 14.5028i 0.157819 0.650538i
\(498\) 0 0
\(499\) −28.5894 16.5061i −1.27984 0.738915i −0.303019 0.952984i \(-0.597995\pi\)
−0.976818 + 0.214070i \(0.931328\pi\)
\(500\) 0 0
\(501\) −15.4583 + 14.2749i −0.690626 + 0.637756i
\(502\) 0 0
\(503\) −12.8092 + 17.9880i −0.571133 + 0.802045i −0.994591 0.103871i \(-0.966877\pi\)
0.423457 + 0.905916i \(0.360816\pi\)
\(504\) 0 0
\(505\) 37.8842 + 36.1225i 1.68583 + 1.60743i
\(506\) 0 0
\(507\) −17.8173 4.62509i −0.791293 0.205407i
\(508\) 0 0
\(509\) −11.2173 + 1.61280i −0.497197 + 0.0714861i −0.386352 0.922352i \(-0.626265\pi\)
−0.110845 + 0.993838i \(0.535356\pi\)
\(510\) 0 0
\(511\) 2.60788 8.88163i 0.115366 0.392900i
\(512\) 0 0
\(513\) −1.27607 + 1.47166i −0.0563400 + 0.0649753i
\(514\) 0 0
\(515\) 61.0229 47.9889i 2.68899 2.11465i
\(516\) 0 0
\(517\) −3.47921 + 36.4359i −0.153015 + 1.60245i
\(518\) 0 0
\(519\) −4.80479 + 10.0911i −0.210907 + 0.442951i
\(520\) 0 0
\(521\) 11.8525 + 25.9534i 0.519269 + 1.13704i 0.969715 + 0.244238i \(0.0785377\pi\)
−0.450446 + 0.892804i \(0.648735\pi\)
\(522\) 0 0
\(523\) −9.57913 + 9.13368i −0.418866 + 0.399388i −0.869987 0.493075i \(-0.835873\pi\)
0.451121 + 0.892463i \(0.351024\pi\)
\(524\) 0 0
\(525\) 65.1991 + 27.3185i 2.84552 + 1.19228i
\(526\) 0 0
\(527\) 10.1213 22.1625i 0.440890 0.965416i
\(528\) 0 0
\(529\) −11.6292 + 1.11046i −0.505619 + 0.0482808i
\(530\) 0 0
\(531\) 1.16700 9.12799i 0.0506435 0.396121i
\(532\) 0 0
\(533\) −8.82104 13.7258i −0.382082 0.594531i
\(534\) 0 0
\(535\) 4.39311i 0.189931i
\(536\) 0 0
\(537\) −27.8649 + 28.3042i −1.20246 + 1.22141i
\(538\) 0 0
\(539\) 12.7582 8.19921i 0.549536 0.353165i
\(540\) 0 0
\(541\) 29.6342 + 4.26075i 1.27407 + 0.183184i 0.745960 0.665991i \(-0.231991\pi\)
0.528112 + 0.849175i \(0.322900\pi\)
\(542\) 0 0
\(543\) −14.4283 + 17.7556i −0.619176 + 0.761967i
\(544\) 0 0
\(545\) −45.3638 20.7170i −1.94317 0.887417i
\(546\) 0 0
\(547\) 12.9717 + 32.4018i 0.554631 + 1.38540i 0.895404 + 0.445255i \(0.146887\pi\)
−0.340773 + 0.940146i \(0.610689\pi\)
\(548\) 0 0
\(549\) 29.8432 29.3602i 1.27368 1.25306i
\(550\) 0 0
\(551\) −2.18733 + 0.998920i −0.0931834 + 0.0425554i
\(552\) 0 0
\(553\) −0.379918 1.09770i −0.0161557 0.0466789i
\(554\) 0 0
\(555\) 33.0702 27.7428i 1.40375 1.17762i
\(556\) 0 0
\(557\) 13.7885 + 17.5335i 0.584238 + 0.742919i 0.984865 0.173322i \(-0.0554502\pi\)
−0.400627 + 0.916241i \(0.631208\pi\)
\(558\) 0 0
\(559\) 0.0115147 + 0.241723i 0.000487020 + 0.0102238i
\(560\) 0 0
\(561\) −16.0964 28.9380i −0.679591 1.22176i
\(562\) 0 0
\(563\) 1.75169 + 12.1833i 0.0738250 + 0.513464i 0.992860 + 0.119288i \(0.0380610\pi\)
−0.919035 + 0.394176i \(0.871030\pi\)
\(564\) 0 0
\(565\) −21.2539 36.8129i −0.894159 1.54873i
\(566\) 0 0
\(567\) 18.6339 20.8087i 0.782551 0.873883i
\(568\) 0 0
\(569\) 26.8976 + 19.1537i 1.12761 + 0.802965i 0.982465 0.186446i \(-0.0596969\pi\)
0.145141 + 0.989411i \(0.453636\pi\)
\(570\) 0 0
\(571\) 0.0868183 1.82254i 0.00363323 0.0762710i −0.996322 0.0856827i \(-0.972693\pi\)
0.999956 + 0.00941174i \(0.00299589\pi\)
\(572\) 0 0
\(573\) −1.39155 5.03549i −0.0581329 0.210360i
\(574\) 0 0
\(575\) −42.9933 10.4301i −1.79294 0.434963i
\(576\) 0 0
\(577\) −0.209927 + 1.08920i −0.00873936 + 0.0453441i −0.986037 0.166529i \(-0.946744\pi\)
0.977297 + 0.211873i \(0.0679563\pi\)
\(578\) 0 0
\(579\) −0.949025 11.9545i −0.0394401 0.496812i
\(580\) 0 0
\(581\) −29.3141 18.8390i −1.21615 0.781573i
\(582\) 0 0
\(583\) −10.9174 5.62829i −0.452151 0.233100i
\(584\) 0 0
\(585\) 19.2690 4.02736i 0.796677 0.166511i
\(586\) 0 0
\(587\) −14.1258 11.1087i −0.583036 0.458505i 0.282559 0.959250i \(-0.408817\pi\)
−0.865595 + 0.500746i \(0.833059\pi\)
\(588\) 0 0
\(589\) −2.08005 + 1.80238i −0.0857070 + 0.0742656i
\(590\) 0 0
\(591\) −17.6254 10.5551i −0.725011 0.434178i
\(592\) 0 0
\(593\) −9.58828 + 4.94310i −0.393744 + 0.202989i −0.643717 0.765264i \(-0.722608\pi\)
0.249973 + 0.968253i \(0.419578\pi\)
\(594\) 0 0
\(595\) −42.1002 + 12.3617i −1.72594 + 0.506781i
\(596\) 0 0
\(597\) −31.7859 + 13.9067i −1.30091 + 0.569162i
\(598\) 0 0
\(599\) 1.04442 3.01765i 0.0426738 0.123298i −0.921651 0.388020i \(-0.873159\pi\)
0.964325 + 0.264722i \(0.0852803\pi\)
\(600\) 0 0
\(601\) −3.69220 5.18497i −0.150608 0.211499i 0.732379 0.680898i \(-0.238410\pi\)
−0.882986 + 0.469399i \(0.844471\pi\)
\(602\) 0 0
\(603\) 5.56292 23.9176i 0.226539 0.974002i
\(604\) 0 0
\(605\) 54.8397 + 77.0115i 2.22955 + 3.13096i
\(606\) 0 0
\(607\) 4.49809 12.9964i 0.182572 0.527506i −0.816162 0.577824i \(-0.803902\pi\)
0.998733 + 0.0503174i \(0.0160233\pi\)
\(608\) 0 0
\(609\) 31.5915 13.8216i 1.28015 0.560080i
\(610\) 0 0
\(611\) 9.38884 2.75681i 0.379832 0.111529i
\(612\) 0 0
\(613\) −23.7393 + 12.2385i −0.958823 + 0.494308i −0.865270 0.501307i \(-0.832853\pi\)
−0.0935533 + 0.995614i \(0.529823\pi\)
\(614\) 0 0
\(615\) −67.0629 40.1610i −2.70424 1.61945i
\(616\) 0 0
\(617\) 4.81268 4.17021i 0.193751 0.167886i −0.552583 0.833458i \(-0.686358\pi\)
0.746334 + 0.665572i \(0.231812\pi\)
\(618\) 0 0
\(619\) −12.7834 10.0530i −0.513809 0.404064i 0.327308 0.944918i \(-0.393859\pi\)
−0.841116 + 0.540854i \(0.818101\pi\)
\(620\) 0 0
\(621\) −9.45587 + 14.7027i −0.379451 + 0.589998i
\(622\) 0 0
\(623\) 6.31881 + 3.25757i 0.253158 + 0.130512i
\(624\) 0 0
\(625\) 69.1337 + 44.4295i 2.76535 + 1.77718i
\(626\) 0 0
\(627\) 0.296026 + 3.72892i 0.0118221 + 0.148919i
\(628\) 0 0
\(629\) −3.67376 + 19.0613i −0.146482 + 0.760022i
\(630\) 0 0
\(631\) 34.7069 + 8.41980i 1.38166 + 0.335187i 0.856645 0.515906i \(-0.172545\pi\)
0.525014 + 0.851093i \(0.324060\pi\)
\(632\) 0 0
\(633\) −11.8861 43.0111i −0.472429 1.70954i
\(634\) 0 0
\(635\) −1.35589 + 28.4637i −0.0538070 + 1.12955i
\(636\) 0 0
\(637\) −3.30266 2.35182i −0.130856 0.0931823i
\(638\) 0 0
\(639\) −10.5944 9.79005i −0.419110 0.387288i
\(640\) 0 0
\(641\) 1.91537 + 3.31751i 0.0756524 + 0.131034i 0.901370 0.433050i \(-0.142563\pi\)
−0.825717 + 0.564084i \(0.809229\pi\)
\(642\) 0 0
\(643\) −4.05839 28.2267i −0.160047 1.11315i −0.898540 0.438892i \(-0.855371\pi\)
0.738492 0.674262i \(-0.235538\pi\)
\(644\) 0 0
\(645\) 0.563581 + 1.01320i 0.0221910 + 0.0398948i
\(646\) 0 0
\(647\) −1.47317 30.9257i −0.0579164 1.21581i −0.821539 0.570152i \(-0.806884\pi\)
0.763623 0.645663i \(-0.223419\pi\)
\(648\) 0 0
\(649\) −10.9241 13.8912i −0.428809 0.545275i
\(650\) 0 0
\(651\) 30.2374 25.3664i 1.18510 0.994186i
\(652\) 0 0
\(653\) 4.31635 + 12.4713i 0.168912 + 0.488038i 0.997408 0.0719565i \(-0.0229243\pi\)
−0.828496 + 0.559995i \(0.810803\pi\)
\(654\) 0 0
\(655\) 19.5206 8.91475i 0.762732 0.348328i
\(656\) 0 0
\(657\) −6.27505 6.37830i −0.244813 0.248841i
\(658\) 0 0
\(659\) −4.60925 11.5134i −0.179551 0.448497i 0.811102 0.584905i \(-0.198868\pi\)
−0.990653 + 0.136408i \(0.956444\pi\)
\(660\) 0 0
\(661\) −38.1537 17.4242i −1.48401 0.677723i −0.501707 0.865038i \(-0.667294\pi\)
−0.982300 + 0.187314i \(0.940022\pi\)
\(662\) 0 0
\(663\) −5.58285 + 6.87034i −0.216820 + 0.266822i
\(664\) 0 0
\(665\) 4.90615 + 0.705398i 0.190252 + 0.0273542i
\(666\) 0 0
\(667\) −18.1544 + 11.6671i −0.702942 + 0.451754i
\(668\) 0 0
\(669\) −17.0085 + 17.2766i −0.657587 + 0.667953i
\(670\) 0 0
\(671\) 80.3964i 3.10367i
\(672\) 0 0
\(673\) −3.70299 5.76197i −0.142740 0.222107i 0.762521 0.646963i \(-0.223961\pi\)
−0.905261 + 0.424856i \(0.860325\pi\)
\(674\) 0 0
\(675\) 53.7262 42.2213i 2.06792 1.62510i
\(676\) 0 0
\(677\) 14.1584 1.35197i 0.544153 0.0519603i 0.180640 0.983549i \(-0.442183\pi\)
0.363513 + 0.931589i \(0.381577\pi\)
\(678\) 0 0
\(679\) −0.586507 + 1.28427i −0.0225081 + 0.0492858i
\(680\) 0 0
\(681\) 41.9914 + 17.5944i 1.60911 + 0.674220i
\(682\) 0 0
\(683\) −25.8052 + 24.6052i −0.987407 + 0.941490i −0.998290 0.0584504i \(-0.981384\pi\)
0.0108837 + 0.999941i \(0.496536\pi\)
\(684\) 0 0
\(685\) 30.9953 + 67.8703i 1.18427 + 2.59319i
\(686\) 0 0
\(687\) 4.92410 10.3417i 0.187866 0.394561i
\(688\) 0 0
\(689\) −0.312137 + 3.26885i −0.0118915 + 0.124533i
\(690\) 0 0
\(691\) −19.2125 + 15.1089i −0.730879 + 0.574770i −0.912733 0.408556i \(-0.866033\pi\)
0.181854 + 0.983325i \(0.441790\pi\)
\(692\) 0 0
\(693\) −3.39007 53.5342i −0.128778 2.03360i
\(694\) 0 0
\(695\) −10.3756 + 35.3361i −0.393570 + 1.34038i
\(696\) 0 0
\(697\) 34.7952 5.00279i 1.31796 0.189494i
\(698\) 0 0
\(699\) 34.5627 + 8.97194i 1.30728 + 0.339350i
\(700\) 0 0
\(701\) −18.2783 17.4283i −0.690361 0.658258i 0.261353 0.965243i \(-0.415831\pi\)
−0.951714 + 0.306986i \(0.900680\pi\)
\(702\) 0 0
\(703\) 1.27199 1.78626i 0.0479741 0.0673702i
\(704\) 0 0
\(705\) 34.4416 31.8049i 1.29714 1.19784i
\(706\) 0 0
\(707\) −33.0244 19.0666i −1.24201 0.717075i
\(708\) 0 0
\(709\) −4.47237 + 18.4354i −0.167964 + 0.692355i 0.824081 + 0.566471i \(0.191692\pi\)
−0.992045 + 0.125884i \(0.959823\pi\)
\(710\) 0 0
\(711\) −1.10571 0.195223i −0.0414672 0.00732144i
\(712\) 0 0
\(713\) −16.1753 + 18.6673i −0.605770 + 0.699096i
\(714\) 0 0
\(715\) 20.4383 31.8026i 0.764348 1.18935i
\(716\) 0 0
\(717\) 11.1070 3.64650i 0.414798 0.136181i
\(718\) 0 0
\(719\) −1.18605 6.15381i −0.0442322 0.229498i 0.953085 0.302704i \(-0.0978892\pi\)
−0.997317 + 0.0732054i \(0.976677\pi\)
\(720\) 0 0
\(721\) −34.9596 + 44.4547i −1.30196 + 1.65558i
\(722\) 0 0
\(723\) 47.4132 + 3.01857i 1.76332 + 0.112262i
\(724\) 0 0
\(725\) 81.9770 19.8874i 3.04455 0.738600i
\(726\) 0 0
\(727\) 21.9554 + 42.5875i 0.814279 + 1.57948i 0.814985 + 0.579482i \(0.196745\pi\)
−0.000705458 1.00000i \(0.500225\pi\)
\(728\) 0 0
\(729\) −8.81355 25.5210i −0.326428 0.945222i
\(730\) 0 0
\(731\) −0.484041 0.193781i −0.0179029 0.00716724i
\(732\) 0 0
\(733\) 22.7614 + 7.87781i 0.840713 + 0.290973i 0.713285 0.700874i \(-0.247207\pi\)
0.127428 + 0.991848i \(0.459328\pi\)
\(734\) 0 0
\(735\) −19.1804 3.07129i −0.707478 0.113286i
\(736\) 0 0
\(737\) −25.2501 39.8277i −0.930101 1.46707i
\(738\) 0 0
\(739\) 14.7241 10.4850i 0.541635 0.385696i −0.276244 0.961088i \(-0.589090\pi\)
0.817878 + 0.575391i \(0.195150\pi\)
\(740\) 0 0
\(741\) 0.896078 0.443983i 0.0329183 0.0163101i
\(742\) 0 0
\(743\) 0.522599 1.30539i 0.0191723 0.0478901i −0.918473 0.395484i \(-0.870577\pi\)
0.937645 + 0.347594i \(0.113001\pi\)
\(744\) 0 0
\(745\) −13.1220 44.6894i −0.480752 1.63729i
\(746\) 0 0
\(747\) −29.6931 + 15.9005i −1.08641 + 0.581770i
\(748\) 0 0
\(749\) 0.754510 + 3.11013i 0.0275692 + 0.113642i
\(750\) 0 0
\(751\) 24.2455 + 27.9808i 0.884732 + 1.02104i 0.999617 + 0.0276568i \(0.00880456\pi\)
−0.114885 + 0.993379i \(0.536650\pi\)
\(752\) 0 0
\(753\) −19.0671 + 2.43114i −0.694845 + 0.0885958i
\(754\) 0 0
\(755\) −38.8380 + 7.48542i −1.41346 + 0.272422i
\(756\) 0 0
\(757\) 3.14182 6.09427i 0.114191 0.221500i −0.824813 0.565406i \(-0.808720\pi\)
0.939004 + 0.343905i \(0.111750\pi\)
\(758\) 0 0
\(759\) 7.39218 + 32.7463i 0.268319 + 1.18861i
\(760\) 0 0
\(761\) −36.1610 31.3337i −1.31084 1.13585i −0.981464 0.191645i \(-0.938618\pi\)
−0.329371 0.944201i \(-0.606837\pi\)
\(762\) 0 0
\(763\) 35.6738 + 6.87555i 1.29148 + 0.248912i
\(764\) 0 0
\(765\) −9.35330 + 41.3685i −0.338169 + 1.49568i
\(766\) 0 0
\(767\) −2.36225 + 4.09154i −0.0852959 + 0.147737i
\(768\) 0 0
\(769\) −20.6084 0.981699i −0.743158 0.0354010i −0.327412 0.944882i \(-0.606176\pi\)
−0.415746 + 0.909481i \(0.636479\pi\)
\(770\) 0 0
\(771\) 32.2614 5.68481i 1.16187 0.204733i
\(772\) 0 0
\(773\) −28.8887 + 30.2976i −1.03905 + 1.08973i −0.0431718 + 0.999068i \(0.513746\pi\)
−0.995882 + 0.0906604i