Properties

Label 1512.2.c.f.757.22
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.22
Character \(\chi\) = 1512.757
Dual form 1512.2.c.f.757.21

$q$-expansion

\(f(q)\) \(=\) \(q+(1.29659 + 0.564669i) q^{2} +(1.36230 + 1.46429i) q^{4} -1.53368i q^{5} +1.00000 q^{7} +(0.939505 + 2.66783i) q^{8} +O(q^{10})\) \(q+(1.29659 + 0.564669i) q^{2} +(1.36230 + 1.46429i) q^{4} -1.53368i q^{5} +1.00000 q^{7} +(0.939505 + 2.66783i) q^{8} +(0.866019 - 1.98855i) q^{10} +2.28335i q^{11} -7.10447i q^{13} +(1.29659 + 0.564669i) q^{14} +(-0.288288 + 3.98960i) q^{16} +6.81307 q^{17} +1.60676i q^{19} +(2.24575 - 2.08932i) q^{20} +(-1.28934 + 2.96057i) q^{22} +1.16757 q^{23} +2.64784 q^{25} +(4.01168 - 9.21160i) q^{26} +(1.36230 + 1.46429i) q^{28} -4.07059i q^{29} -7.90568 q^{31} +(-2.62659 + 5.01009i) q^{32} +(8.83376 + 3.84713i) q^{34} -1.53368i q^{35} +7.04836i q^{37} +(-0.907287 + 2.08331i) q^{38} +(4.09159 - 1.44090i) q^{40} +10.1710 q^{41} -0.344719i q^{43} +(-3.34348 + 3.11060i) q^{44} +(1.51386 + 0.659289i) q^{46} +3.10859 q^{47} +1.00000 q^{49} +(3.43317 + 1.49515i) q^{50} +(10.4030 - 9.67841i) q^{52} +5.66835i q^{53} +3.50191 q^{55} +(0.939505 + 2.66783i) q^{56} +(2.29853 - 5.27789i) q^{58} +1.38165i q^{59} -5.50516i q^{61} +(-10.2504 - 4.46409i) q^{62} +(-6.23466 + 5.01288i) q^{64} -10.8960 q^{65} -8.35907i q^{67} +(9.28143 + 9.97630i) q^{68} +(0.866019 - 1.98855i) q^{70} +12.2819 q^{71} -5.95132 q^{73} +(-3.97999 + 9.13885i) q^{74} +(-2.35276 + 2.18889i) q^{76} +2.28335i q^{77} -15.0027 q^{79} +(6.11875 + 0.442140i) q^{80} +(13.1876 + 5.74322i) q^{82} +14.7419i q^{83} -10.4490i q^{85} +(0.194652 - 0.446959i) q^{86} +(-6.09159 + 2.14522i) q^{88} -11.8923 q^{89} -7.10447i q^{91} +(1.59058 + 1.70966i) q^{92} +(4.03057 + 1.75532i) q^{94} +2.46425 q^{95} -2.60256 q^{97} +(1.29659 + 0.564669i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 24q^{7} + O(q^{10}) \) \( 24q + 24q^{7} + 20q^{10} - 4q^{16} + 4q^{22} - 24q^{25} - 16q^{31} + 4q^{34} + 12q^{40} - 52q^{46} + 24q^{49} + 12q^{52} - 8q^{55} - 28q^{58} + 24q^{64} + 20q^{70} - 24q^{76} + 32q^{79} + 44q^{82} - 60q^{88} + 12q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.29659 + 0.564669i 0.916829 + 0.399281i
\(3\) 0 0
\(4\) 1.36230 + 1.46429i 0.681149 + 0.732145i
\(5\) 1.53368i 0.685881i −0.939357 0.342940i \(-0.888577\pi\)
0.939357 0.342940i \(-0.111423\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0.939505 + 2.66783i 0.332165 + 0.943221i
\(9\) 0 0
\(10\) 0.866019 1.98855i 0.273859 0.628835i
\(11\) 2.28335i 0.688455i 0.938886 + 0.344228i \(0.111859\pi\)
−0.938886 + 0.344228i \(0.888141\pi\)
\(12\) 0 0
\(13\) 7.10447i 1.97043i −0.171333 0.985213i \(-0.554807\pi\)
0.171333 0.985213i \(-0.445193\pi\)
\(14\) 1.29659 + 0.564669i 0.346529 + 0.150914i
\(15\) 0 0
\(16\) −0.288288 + 3.98960i −0.0720720 + 0.997399i
\(17\) 6.81307 1.65241 0.826206 0.563368i \(-0.190495\pi\)
0.826206 + 0.563368i \(0.190495\pi\)
\(18\) 0 0
\(19\) 1.60676i 0.368616i 0.982869 + 0.184308i \(0.0590044\pi\)
−0.982869 + 0.184308i \(0.940996\pi\)
\(20\) 2.24575 2.08932i 0.502164 0.467187i
\(21\) 0 0
\(22\) −1.28934 + 2.96057i −0.274887 + 0.631195i
\(23\) 1.16757 0.243455 0.121727 0.992564i \(-0.461157\pi\)
0.121727 + 0.992564i \(0.461157\pi\)
\(24\) 0 0
\(25\) 2.64784 0.529568
\(26\) 4.01168 9.21160i 0.786754 1.80654i
\(27\) 0 0
\(28\) 1.36230 + 1.46429i 0.257450 + 0.276725i
\(29\) 4.07059i 0.755889i −0.925828 0.377944i \(-0.876631\pi\)
0.925828 0.377944i \(-0.123369\pi\)
\(30\) 0 0
\(31\) −7.90568 −1.41990 −0.709951 0.704251i \(-0.751283\pi\)
−0.709951 + 0.704251i \(0.751283\pi\)
\(32\) −2.62659 + 5.01009i −0.464321 + 0.885667i
\(33\) 0 0
\(34\) 8.83376 + 3.84713i 1.51498 + 0.659777i
\(35\) 1.53368i 0.259238i
\(36\) 0 0
\(37\) 7.04836i 1.15874i 0.815063 + 0.579372i \(0.196702\pi\)
−0.815063 + 0.579372i \(0.803298\pi\)
\(38\) −0.907287 + 2.08331i −0.147181 + 0.337958i
\(39\) 0 0
\(40\) 4.09159 1.44090i 0.646937 0.227826i
\(41\) 10.1710 1.58844 0.794218 0.607633i \(-0.207881\pi\)
0.794218 + 0.607633i \(0.207881\pi\)
\(42\) 0 0
\(43\) 0.344719i 0.0525691i −0.999655 0.0262846i \(-0.991632\pi\)
0.999655 0.0262846i \(-0.00836760\pi\)
\(44\) −3.34348 + 3.11060i −0.504049 + 0.468941i
\(45\) 0 0
\(46\) 1.51386 + 0.659289i 0.223206 + 0.0972069i
\(47\) 3.10859 0.453434 0.226717 0.973961i \(-0.427201\pi\)
0.226717 + 0.973961i \(0.427201\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 3.43317 + 1.49515i 0.485523 + 0.211447i
\(51\) 0 0
\(52\) 10.4030 9.67841i 1.44264 1.34215i
\(53\) 5.66835i 0.778608i 0.921109 + 0.389304i \(0.127284\pi\)
−0.921109 + 0.389304i \(0.872716\pi\)
\(54\) 0 0
\(55\) 3.50191 0.472198
\(56\) 0.939505 + 2.66783i 0.125547 + 0.356504i
\(57\) 0 0
\(58\) 2.29853 5.27789i 0.301812 0.693020i
\(59\) 1.38165i 0.179875i 0.995947 + 0.0899374i \(0.0286667\pi\)
−0.995947 + 0.0899374i \(0.971333\pi\)
\(60\) 0 0
\(61\) 5.50516i 0.704863i −0.935838 0.352431i \(-0.885355\pi\)
0.935838 0.352431i \(-0.114645\pi\)
\(62\) −10.2504 4.46409i −1.30181 0.566940i
\(63\) 0 0
\(64\) −6.23466 + 5.01288i −0.779333 + 0.626611i
\(65\) −10.8960 −1.35148
\(66\) 0 0
\(67\) 8.35907i 1.02122i −0.859811 0.510612i \(-0.829419\pi\)
0.859811 0.510612i \(-0.170581\pi\)
\(68\) 9.28143 + 9.97630i 1.12554 + 1.20980i
\(69\) 0 0
\(70\) 0.866019 1.98855i 0.103509 0.237677i
\(71\) 12.2819 1.45759 0.728795 0.684732i \(-0.240081\pi\)
0.728795 + 0.684732i \(0.240081\pi\)
\(72\) 0 0
\(73\) −5.95132 −0.696549 −0.348275 0.937393i \(-0.613232\pi\)
−0.348275 + 0.937393i \(0.613232\pi\)
\(74\) −3.97999 + 9.13885i −0.462665 + 1.06237i
\(75\) 0 0
\(76\) −2.35276 + 2.18889i −0.269880 + 0.251082i
\(77\) 2.28335i 0.260212i
\(78\) 0 0
\(79\) −15.0027 −1.68794 −0.843968 0.536393i \(-0.819787\pi\)
−0.843968 + 0.536393i \(0.819787\pi\)
\(80\) 6.11875 + 0.442140i 0.684097 + 0.0494328i
\(81\) 0 0
\(82\) 13.1876 + 5.74322i 1.45632 + 0.634233i
\(83\) 14.7419i 1.61814i 0.587715 + 0.809068i \(0.300027\pi\)
−0.587715 + 0.809068i \(0.699973\pi\)
\(84\) 0 0
\(85\) 10.4490i 1.13336i
\(86\) 0.194652 0.446959i 0.0209899 0.0481969i
\(87\) 0 0
\(88\) −6.09159 + 2.14522i −0.649366 + 0.228681i
\(89\) −11.8923 −1.26058 −0.630290 0.776360i \(-0.717064\pi\)
−0.630290 + 0.776360i \(0.717064\pi\)
\(90\) 0 0
\(91\) 7.10447i 0.744751i
\(92\) 1.59058 + 1.70966i 0.165829 + 0.178244i
\(93\) 0 0
\(94\) 4.03057 + 1.75532i 0.415722 + 0.181048i
\(95\) 2.46425 0.252827
\(96\) 0 0
\(97\) −2.60256 −0.264250 −0.132125 0.991233i \(-0.542180\pi\)
−0.132125 + 0.991233i \(0.542180\pi\)
\(98\) 1.29659 + 0.564669i 0.130976 + 0.0570402i
\(99\) 0 0
\(100\) 3.60715 + 3.87720i 0.360715 + 0.387720i
\(101\) 9.58182i 0.953427i −0.879059 0.476713i \(-0.841828\pi\)
0.879059 0.476713i \(-0.158172\pi\)
\(102\) 0 0
\(103\) 9.44175 0.930323 0.465162 0.885226i \(-0.345996\pi\)
0.465162 + 0.885226i \(0.345996\pi\)
\(104\) 18.9535 6.67469i 1.85855 0.654507i
\(105\) 0 0
\(106\) −3.20074 + 7.34954i −0.310884 + 0.713850i
\(107\) 5.04240i 0.487467i −0.969842 0.243733i \(-0.921628\pi\)
0.969842 0.243733i \(-0.0783722\pi\)
\(108\) 0 0
\(109\) 2.35923i 0.225973i 0.993597 + 0.112987i \(0.0360417\pi\)
−0.993597 + 0.112987i \(0.963958\pi\)
\(110\) 4.54055 + 1.97742i 0.432925 + 0.188540i
\(111\) 0 0
\(112\) −0.288288 + 3.98960i −0.0272407 + 0.376982i
\(113\) −14.0317 −1.31999 −0.659994 0.751271i \(-0.729441\pi\)
−0.659994 + 0.751271i \(0.729441\pi\)
\(114\) 0 0
\(115\) 1.79067i 0.166981i
\(116\) 5.96052 5.54535i 0.553420 0.514873i
\(117\) 0 0
\(118\) −0.780172 + 1.79143i −0.0718207 + 0.164914i
\(119\) 6.81307 0.624553
\(120\) 0 0
\(121\) 5.78632 0.526029
\(122\) 3.10859 7.13794i 0.281439 0.646238i
\(123\) 0 0
\(124\) −10.7699 11.5762i −0.967165 1.03957i
\(125\) 11.7293i 1.04910i
\(126\) 0 0
\(127\) −17.0218 −1.51044 −0.755220 0.655472i \(-0.772470\pi\)
−0.755220 + 0.655472i \(0.772470\pi\)
\(128\) −10.9144 + 2.97914i −0.964708 + 0.263322i
\(129\) 0 0
\(130\) −14.1276 6.15261i −1.23907 0.539619i
\(131\) 17.8861i 1.56272i 0.624082 + 0.781359i \(0.285473\pi\)
−0.624082 + 0.781359i \(0.714527\pi\)
\(132\) 0 0
\(133\) 1.60676i 0.139324i
\(134\) 4.72011 10.8383i 0.407755 0.936287i
\(135\) 0 0
\(136\) 6.40091 + 18.1761i 0.548874 + 1.55859i
\(137\) 9.18009 0.784308 0.392154 0.919900i \(-0.371730\pi\)
0.392154 + 0.919900i \(0.371730\pi\)
\(138\) 0 0
\(139\) 12.0518i 1.02222i −0.859516 0.511108i \(-0.829235\pi\)
0.859516 0.511108i \(-0.170765\pi\)
\(140\) 2.24575 2.08932i 0.189800 0.176580i
\(141\) 0 0
\(142\) 15.9246 + 6.93519i 1.33636 + 0.581988i
\(143\) 16.2220 1.35655
\(144\) 0 0
\(145\) −6.24296 −0.518449
\(146\) −7.71643 3.36053i −0.638616 0.278119i
\(147\) 0 0
\(148\) −10.3208 + 9.60197i −0.848368 + 0.789277i
\(149\) 7.71091i 0.631702i −0.948809 0.315851i \(-0.897710\pi\)
0.948809 0.315851i \(-0.102290\pi\)
\(150\) 0 0
\(151\) 5.91312 0.481203 0.240601 0.970624i \(-0.422655\pi\)
0.240601 + 0.970624i \(0.422655\pi\)
\(152\) −4.28657 + 1.50956i −0.347686 + 0.122441i
\(153\) 0 0
\(154\) −1.28934 + 2.96057i −0.103898 + 0.238569i
\(155\) 12.1247i 0.973883i
\(156\) 0 0
\(157\) 0.906198i 0.0723225i −0.999346 0.0361612i \(-0.988487\pi\)
0.999346 0.0361612i \(-0.0115130\pi\)
\(158\) −19.4524 8.47156i −1.54755 0.673961i
\(159\) 0 0
\(160\) 7.68385 + 4.02834i 0.607462 + 0.318468i
\(161\) 1.16757 0.0920172
\(162\) 0 0
\(163\) 4.46083i 0.349400i 0.984622 + 0.174700i \(0.0558955\pi\)
−0.984622 + 0.174700i \(0.944105\pi\)
\(164\) 13.8559 + 14.8932i 1.08196 + 1.16297i
\(165\) 0 0
\(166\) −8.32430 + 19.1142i −0.646091 + 1.48355i
\(167\) −22.6885 −1.75569 −0.877845 0.478944i \(-0.841020\pi\)
−0.877845 + 0.478944i \(0.841020\pi\)
\(168\) 0 0
\(169\) −37.4735 −2.88258
\(170\) 5.90025 13.5481i 0.452528 1.03909i
\(171\) 0 0
\(172\) 0.504768 0.469610i 0.0384882 0.0358074i
\(173\) 24.2316i 1.84229i 0.389218 + 0.921145i \(0.372745\pi\)
−0.389218 + 0.921145i \(0.627255\pi\)
\(174\) 0 0
\(175\) 2.64784 0.200158
\(176\) −9.10964 0.658262i −0.686665 0.0496183i
\(177\) 0 0
\(178\) −15.4194 6.71520i −1.15574 0.503326i
\(179\) 8.82249i 0.659424i 0.944082 + 0.329712i \(0.106952\pi\)
−0.944082 + 0.329712i \(0.893048\pi\)
\(180\) 0 0
\(181\) 4.29583i 0.319306i −0.987173 0.159653i \(-0.948962\pi\)
0.987173 0.159653i \(-0.0510376\pi\)
\(182\) 4.01168 9.21160i 0.297365 0.682809i
\(183\) 0 0
\(184\) 1.09694 + 3.11488i 0.0808672 + 0.229632i
\(185\) 10.8099 0.794760
\(186\) 0 0
\(187\) 15.5566i 1.13761i
\(188\) 4.23483 + 4.55188i 0.308856 + 0.331980i
\(189\) 0 0
\(190\) 3.19512 + 1.39148i 0.231799 + 0.100949i
\(191\) −0.224849 −0.0162695 −0.00813476 0.999967i \(-0.502589\pi\)
−0.00813476 + 0.999967i \(0.502589\pi\)
\(192\) 0 0
\(193\) −11.7447 −0.845404 −0.422702 0.906269i \(-0.638918\pi\)
−0.422702 + 0.906269i \(0.638918\pi\)
\(194\) −3.37446 1.46958i −0.242272 0.105510i
\(195\) 0 0
\(196\) 1.36230 + 1.46429i 0.0973070 + 0.104592i
\(197\) 14.7998i 1.05444i −0.849729 0.527220i \(-0.823234\pi\)
0.849729 0.527220i \(-0.176766\pi\)
\(198\) 0 0
\(199\) −19.6242 −1.39112 −0.695561 0.718467i \(-0.744844\pi\)
−0.695561 + 0.718467i \(0.744844\pi\)
\(200\) 2.48766 + 7.06399i 0.175904 + 0.499500i
\(201\) 0 0
\(202\) 5.41056 12.4237i 0.380685 0.874129i
\(203\) 4.07059i 0.285699i
\(204\) 0 0
\(205\) 15.5989i 1.08948i
\(206\) 12.2421 + 5.33146i 0.852947 + 0.371461i
\(207\) 0 0
\(208\) 28.3440 + 2.04813i 1.96530 + 0.142013i
\(209\) −3.66879 −0.253776
\(210\) 0 0
\(211\) 0.913482i 0.0628867i −0.999506 0.0314434i \(-0.989990\pi\)
0.999506 0.0314434i \(-0.0100104\pi\)
\(212\) −8.30011 + 7.72199i −0.570054 + 0.530348i
\(213\) 0 0
\(214\) 2.84728 6.53793i 0.194636 0.446924i
\(215\) −0.528687 −0.0360561
\(216\) 0 0
\(217\) −7.90568 −0.536673
\(218\) −1.33218 + 3.05896i −0.0902269 + 0.207179i
\(219\) 0 0
\(220\) 4.77065 + 5.12782i 0.321637 + 0.345717i
\(221\) 48.4033i 3.25596i
\(222\) 0 0
\(223\) −11.8646 −0.794512 −0.397256 0.917708i \(-0.630037\pi\)
−0.397256 + 0.917708i \(0.630037\pi\)
\(224\) −2.62659 + 5.01009i −0.175497 + 0.334751i
\(225\) 0 0
\(226\) −18.1933 7.92324i −1.21020 0.527046i
\(227\) 19.2403i 1.27702i 0.769613 + 0.638510i \(0.220449\pi\)
−0.769613 + 0.638510i \(0.779551\pi\)
\(228\) 0 0
\(229\) 7.11176i 0.469958i −0.972000 0.234979i \(-0.924498\pi\)
0.972000 0.234979i \(-0.0755022\pi\)
\(230\) 1.01114 2.32177i 0.0666723 0.153093i
\(231\) 0 0
\(232\) 10.8596 3.82434i 0.712970 0.251080i
\(233\) −18.5527 −1.21542 −0.607712 0.794157i \(-0.707913\pi\)
−0.607712 + 0.794157i \(0.707913\pi\)
\(234\) 0 0
\(235\) 4.76757i 0.311002i
\(236\) −2.02313 + 1.88221i −0.131694 + 0.122522i
\(237\) 0 0
\(238\) 8.83376 + 3.84713i 0.572608 + 0.249372i
\(239\) 3.86610 0.250077 0.125039 0.992152i \(-0.460095\pi\)
0.125039 + 0.992152i \(0.460095\pi\)
\(240\) 0 0
\(241\) −11.5687 −0.745205 −0.372603 0.927991i \(-0.621535\pi\)
−0.372603 + 0.927991i \(0.621535\pi\)
\(242\) 7.50250 + 3.26736i 0.482279 + 0.210034i
\(243\) 0 0
\(244\) 8.06114 7.49966i 0.516062 0.480117i
\(245\) 1.53368i 0.0979829i
\(246\) 0 0
\(247\) 11.4152 0.726331
\(248\) −7.42743 21.0910i −0.471642 1.33928i
\(249\) 0 0
\(250\) 6.62317 15.2081i 0.418886 0.961846i
\(251\) 13.5653i 0.856235i −0.903723 0.428117i \(-0.859177\pi\)
0.903723 0.428117i \(-0.140823\pi\)
\(252\) 0 0
\(253\) 2.66596i 0.167608i
\(254\) −22.0703 9.61167i −1.38481 0.603090i
\(255\) 0 0
\(256\) −15.8338 2.30031i −0.989611 0.143769i
\(257\) 11.1567 0.695938 0.347969 0.937506i \(-0.386871\pi\)
0.347969 + 0.937506i \(0.386871\pi\)
\(258\) 0 0
\(259\) 7.04836i 0.437964i
\(260\) −14.8435 15.9548i −0.920557 0.989477i
\(261\) 0 0
\(262\) −10.0997 + 23.1910i −0.623964 + 1.43274i
\(263\) −13.9609 −0.860864 −0.430432 0.902623i \(-0.641639\pi\)
−0.430432 + 0.902623i \(0.641639\pi\)
\(264\) 0 0
\(265\) 8.69341 0.534032
\(266\) −0.907287 + 2.08331i −0.0556294 + 0.127736i
\(267\) 0 0
\(268\) 12.2401 11.3875i 0.747683 0.695605i
\(269\) 16.1185i 0.982761i −0.870945 0.491380i \(-0.836493\pi\)
0.870945 0.491380i \(-0.163507\pi\)
\(270\) 0 0
\(271\) 8.91716 0.541679 0.270840 0.962624i \(-0.412699\pi\)
0.270840 + 0.962624i \(0.412699\pi\)
\(272\) −1.96413 + 27.1814i −0.119093 + 1.64811i
\(273\) 0 0
\(274\) 11.9028 + 5.18371i 0.719076 + 0.313159i
\(275\) 6.04594i 0.364584i
\(276\) 0 0
\(277\) 26.8189i 1.61139i 0.592328 + 0.805697i \(0.298209\pi\)
−0.592328 + 0.805697i \(0.701791\pi\)
\(278\) 6.80525 15.6262i 0.408152 0.937197i
\(279\) 0 0
\(280\) 4.09159 1.44090i 0.244519 0.0861100i
\(281\) −11.0688 −0.660306 −0.330153 0.943927i \(-0.607100\pi\)
−0.330153 + 0.943927i \(0.607100\pi\)
\(282\) 0 0
\(283\) 21.7405i 1.29234i −0.763194 0.646170i \(-0.776370\pi\)
0.763194 0.646170i \(-0.223630\pi\)
\(284\) 16.7316 + 17.9842i 0.992836 + 1.06717i
\(285\) 0 0
\(286\) 21.0333 + 9.16005i 1.24372 + 0.541645i
\(287\) 10.1710 0.600373
\(288\) 0 0
\(289\) 29.4179 1.73046
\(290\) −8.09456 3.52520i −0.475329 0.207007i
\(291\) 0 0
\(292\) −8.10747 8.71446i −0.474454 0.509975i
\(293\) 8.80042i 0.514126i −0.966395 0.257063i \(-0.917245\pi\)
0.966395 0.257063i \(-0.0827548\pi\)
\(294\) 0 0
\(295\) 2.11900 0.123373
\(296\) −18.8039 + 6.62197i −1.09295 + 0.384894i
\(297\) 0 0
\(298\) 4.35411 9.99789i 0.252227 0.579162i
\(299\) 8.29496i 0.479710i
\(300\) 0 0
\(301\) 0.344719i 0.0198693i
\(302\) 7.66690 + 3.33896i 0.441181 + 0.192135i
\(303\) 0 0
\(304\) −6.41033 0.463210i −0.367657 0.0265669i
\(305\) −8.44312 −0.483452
\(306\) 0 0
\(307\) 3.11170i 0.177594i −0.996050 0.0887971i \(-0.971698\pi\)
0.996050 0.0887971i \(-0.0283023\pi\)
\(308\) −3.34348 + 3.11060i −0.190513 + 0.177243i
\(309\) 0 0
\(310\) −6.84647 + 15.7208i −0.388853 + 0.892884i
\(311\) 0.443815 0.0251664 0.0125832 0.999921i \(-0.495995\pi\)
0.0125832 + 0.999921i \(0.495995\pi\)
\(312\) 0 0
\(313\) 19.1601 1.08299 0.541497 0.840703i \(-0.317858\pi\)
0.541497 + 0.840703i \(0.317858\pi\)
\(314\) 0.511702 1.17497i 0.0288770 0.0663073i
\(315\) 0 0
\(316\) −20.4382 21.9683i −1.14974 1.23581i
\(317\) 11.2142i 0.629854i −0.949116 0.314927i \(-0.898020\pi\)
0.949116 0.314927i \(-0.101980\pi\)
\(318\) 0 0
\(319\) 9.29456 0.520396
\(320\) 7.68814 + 9.56195i 0.429780 + 0.534529i
\(321\) 0 0
\(322\) 1.51386 + 0.659289i 0.0843640 + 0.0367408i
\(323\) 10.9470i 0.609105i
\(324\) 0 0
\(325\) 18.8115i 1.04347i
\(326\) −2.51889 + 5.78388i −0.139509 + 0.320339i
\(327\) 0 0
\(328\) 9.55566 + 27.1344i 0.527623 + 1.49825i
\(329\) 3.10859 0.171382
\(330\) 0 0
\(331\) 17.8007i 0.978414i −0.872168 0.489207i \(-0.837286\pi\)
0.872168 0.489207i \(-0.162714\pi\)
\(332\) −21.5864 + 20.0829i −1.18471 + 1.10219i
\(333\) 0 0
\(334\) −29.4177 12.8115i −1.60967 0.701014i
\(335\) −12.8201 −0.700437
\(336\) 0 0
\(337\) −3.46393 −0.188692 −0.0943461 0.995539i \(-0.530076\pi\)
−0.0943461 + 0.995539i \(0.530076\pi\)
\(338\) −48.5879 21.1601i −2.64283 1.15096i
\(339\) 0 0
\(340\) 15.3004 14.2347i 0.829781 0.771985i
\(341\) 18.0514i 0.977539i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0.919652 0.323865i 0.0495843 0.0174616i
\(345\) 0 0
\(346\) −13.6828 + 31.4184i −0.735592 + 1.68906i
\(347\) 27.3962i 1.47070i 0.677686 + 0.735352i \(0.262983\pi\)
−0.677686 + 0.735352i \(0.737017\pi\)
\(348\) 0 0
\(349\) 1.62149i 0.0867961i 0.999058 + 0.0433981i \(0.0138184\pi\)
−0.999058 + 0.0433981i \(0.986182\pi\)
\(350\) 3.43317 + 1.49515i 0.183510 + 0.0799193i
\(351\) 0 0
\(352\) −11.4398 5.99743i −0.609742 0.319664i
\(353\) −16.5882 −0.882903 −0.441452 0.897285i \(-0.645536\pi\)
−0.441452 + 0.897285i \(0.645536\pi\)
\(354\) 0 0
\(355\) 18.8364i 0.999732i
\(356\) −16.2008 17.4137i −0.858642 0.922927i
\(357\) 0 0
\(358\) −4.98178 + 11.4392i −0.263296 + 0.604578i
\(359\) −7.84388 −0.413984 −0.206992 0.978343i \(-0.566367\pi\)
−0.206992 + 0.978343i \(0.566367\pi\)
\(360\) 0 0
\(361\) 16.4183 0.864122
\(362\) 2.42572 5.56993i 0.127493 0.292749i
\(363\) 0 0
\(364\) 10.4030 9.67841i 0.545266 0.507287i
\(365\) 9.12740i 0.477750i
\(366\) 0 0
\(367\) 0.761448 0.0397472 0.0198736 0.999803i \(-0.493674\pi\)
0.0198736 + 0.999803i \(0.493674\pi\)
\(368\) −0.336596 + 4.65813i −0.0175463 + 0.242822i
\(369\) 0 0
\(370\) 14.0160 + 6.10402i 0.728659 + 0.317333i
\(371\) 5.66835i 0.294286i
\(372\) 0 0
\(373\) 13.3240i 0.689888i −0.938623 0.344944i \(-0.887898\pi\)
0.938623 0.344944i \(-0.112102\pi\)
\(374\) −8.78433 + 20.1706i −0.454227 + 1.04299i
\(375\) 0 0
\(376\) 2.92054 + 8.29320i 0.150615 + 0.427689i
\(377\) −28.9194 −1.48942
\(378\) 0 0
\(379\) 13.6595i 0.701640i −0.936443 0.350820i \(-0.885903\pi\)
0.936443 0.350820i \(-0.114097\pi\)
\(380\) 3.35704 + 3.60837i 0.172213 + 0.185106i
\(381\) 0 0
\(382\) −0.291538 0.126965i −0.0149164 0.00649612i
\(383\) 9.70332 0.495816 0.247908 0.968784i \(-0.420257\pi\)
0.247908 + 0.968784i \(0.420257\pi\)
\(384\) 0 0
\(385\) 3.50191 0.178474
\(386\) −15.2281 6.63188i −0.775090 0.337554i
\(387\) 0 0
\(388\) −3.54546 3.81090i −0.179994 0.193469i
\(389\) 24.7223i 1.25347i 0.779233 + 0.626734i \(0.215609\pi\)
−0.779233 + 0.626734i \(0.784391\pi\)
\(390\) 0 0
\(391\) 7.95472 0.402287
\(392\) 0.939505 + 2.66783i 0.0474522 + 0.134746i
\(393\) 0 0
\(394\) 8.35697 19.1892i 0.421018 0.966740i
\(395\) 23.0093i 1.15772i
\(396\) 0 0
\(397\) 29.1070i 1.46084i 0.682999 + 0.730420i \(0.260675\pi\)
−0.682999 + 0.730420i \(0.739325\pi\)
\(398\) −25.4446 11.0812i −1.27542 0.555449i
\(399\) 0 0
\(400\) −0.763340 + 10.5638i −0.0381670 + 0.528191i
\(401\) −13.7247 −0.685380 −0.342690 0.939449i \(-0.611338\pi\)
−0.342690 + 0.939449i \(0.611338\pi\)
\(402\) 0 0
\(403\) 56.1657i 2.79781i
\(404\) 14.0306 13.0533i 0.698046 0.649426i
\(405\) 0 0
\(406\) 2.29853 5.27789i 0.114074 0.261937i
\(407\) −16.0939 −0.797743
\(408\) 0 0
\(409\) 18.1707 0.898486 0.449243 0.893410i \(-0.351694\pi\)
0.449243 + 0.893410i \(0.351694\pi\)
\(410\) 8.80824 20.2255i 0.435008 0.998864i
\(411\) 0 0
\(412\) 12.8625 + 13.8255i 0.633689 + 0.681131i
\(413\) 1.38165i 0.0679863i
\(414\) 0 0
\(415\) 22.6093 1.10985
\(416\) 35.5941 + 18.6606i 1.74514 + 0.914909i
\(417\) 0 0
\(418\) −4.75692 2.07165i −0.232669 0.101328i
\(419\) 32.9489i 1.60966i −0.593507 0.804829i \(-0.702257\pi\)
0.593507 0.804829i \(-0.297743\pi\)
\(420\) 0 0
\(421\) 27.5222i 1.34135i 0.741751 + 0.670675i \(0.233996\pi\)
−0.741751 + 0.670675i \(0.766004\pi\)
\(422\) 0.515815 1.18441i 0.0251095 0.0576563i
\(423\) 0 0
\(424\) −15.1222 + 5.32545i −0.734400 + 0.258626i
\(425\) 18.0399 0.875064
\(426\) 0 0
\(427\) 5.50516i 0.266413i
\(428\) 7.38353 6.86925i 0.356896 0.332038i
\(429\) 0 0
\(430\) −0.685491 0.298533i −0.0330573 0.0143965i
\(431\) 40.3524 1.94371 0.971855 0.235582i \(-0.0756996\pi\)
0.971855 + 0.235582i \(0.0756996\pi\)
\(432\) 0 0
\(433\) −38.5928 −1.85465 −0.927327 0.374253i \(-0.877899\pi\)
−0.927327 + 0.374253i \(0.877899\pi\)
\(434\) −10.2504 4.46409i −0.492037 0.214283i
\(435\) 0 0
\(436\) −3.45460 + 3.21397i −0.165445 + 0.153921i
\(437\) 1.87600i 0.0897413i
\(438\) 0 0
\(439\) −1.68908 −0.0806152 −0.0403076 0.999187i \(-0.512834\pi\)
−0.0403076 + 0.999187i \(0.512834\pi\)
\(440\) 3.29007 + 9.34252i 0.156848 + 0.445387i
\(441\) 0 0
\(442\) 27.3318 62.7592i 1.30004 2.98515i
\(443\) 18.3190i 0.870361i −0.900343 0.435180i \(-0.856685\pi\)
0.900343 0.435180i \(-0.143315\pi\)
\(444\) 0 0
\(445\) 18.2389i 0.864607i
\(446\) −15.3835 6.69956i −0.728431 0.317234i
\(447\) 0 0
\(448\) −6.23466 + 5.01288i −0.294560 + 0.236837i
\(449\) −34.2644 −1.61704 −0.808518 0.588471i \(-0.799730\pi\)
−0.808518 + 0.588471i \(0.799730\pi\)
\(450\) 0 0
\(451\) 23.2238i 1.09357i
\(452\) −19.1153 20.5464i −0.899108 0.966422i
\(453\) 0 0
\(454\) −10.8644 + 24.9467i −0.509890 + 1.17081i
\(455\) −10.8960 −0.510810
\(456\) 0 0
\(457\) 3.08541 0.144330 0.0721648 0.997393i \(-0.477009\pi\)
0.0721648 + 0.997393i \(0.477009\pi\)
\(458\) 4.01579 9.22104i 0.187645 0.430871i
\(459\) 0 0
\(460\) 2.62206 2.43943i 0.122254 0.113739i
\(461\) 8.62369i 0.401645i 0.979628 + 0.200823i \(0.0643615\pi\)
−0.979628 + 0.200823i \(0.935639\pi\)
\(462\) 0 0
\(463\) 3.29178 0.152982 0.0764910 0.997070i \(-0.475628\pi\)
0.0764910 + 0.997070i \(0.475628\pi\)
\(464\) 16.2400 + 1.17350i 0.753923 + 0.0544784i
\(465\) 0 0
\(466\) −24.0552 10.4761i −1.11434 0.485296i
\(467\) 31.3473i 1.45058i −0.688443 0.725290i \(-0.741706\pi\)
0.688443 0.725290i \(-0.258294\pi\)
\(468\) 0 0
\(469\) 8.35907i 0.385986i
\(470\) 2.69210 6.18159i 0.124177 0.285135i
\(471\) 0 0
\(472\) −3.68600 + 1.29806i −0.169662 + 0.0597482i
\(473\) 0.787113 0.0361915
\(474\) 0 0
\(475\) 4.25444i 0.195207i
\(476\) 9.28143 + 9.97630i 0.425414 + 0.457263i
\(477\) 0 0
\(478\) 5.01275 + 2.18307i 0.229278 + 0.0998512i
\(479\) 23.7139 1.08351 0.541757 0.840535i \(-0.317759\pi\)
0.541757 + 0.840535i \(0.317759\pi\)
\(480\) 0 0
\(481\) 50.0749 2.28322
\(482\) −14.9999 6.53248i −0.683225 0.297546i
\(483\) 0 0
\(484\) 7.88270 + 8.47285i 0.358304 + 0.385130i
\(485\) 3.99148i 0.181244i
\(486\) 0 0
\(487\) 35.7317 1.61916 0.809580 0.587010i \(-0.199695\pi\)
0.809580 + 0.587010i \(0.199695\pi\)
\(488\) 14.6868 5.17212i 0.664842 0.234131i
\(489\) 0 0
\(490\) 0.866019 1.98855i 0.0391227 0.0898335i
\(491\) 40.3543i 1.82116i 0.413330 + 0.910581i \(0.364366\pi\)
−0.413330 + 0.910581i \(0.635634\pi\)
\(492\) 0 0
\(493\) 27.7332i 1.24904i
\(494\) 14.8008 + 6.44580i 0.665921 + 0.290010i
\(495\) 0 0
\(496\) 2.27911 31.5405i 0.102335 1.41621i
\(497\) 12.2819 0.550917
\(498\) 0 0
\(499\) 41.0646i 1.83831i 0.393902 + 0.919153i \(0.371125\pi\)
−0.393902 + 0.919153i \(0.628875\pi\)
\(500\) 17.1751 15.9788i 0.768094 0.714594i
\(501\) 0 0
\(502\) 7.65991 17.5887i 0.341879 0.785021i
\(503\) 13.5744 0.605252 0.302626 0.953109i \(-0.402137\pi\)
0.302626 + 0.953109i \(0.402137\pi\)
\(504\) 0 0
\(505\) −14.6954 −0.653937
\(506\) −1.50539 + 3.45667i −0.0669226 + 0.153668i
\(507\) 0 0
\(508\) −23.1887 24.9248i −1.02883 1.10586i
\(509\) 13.3591i 0.592132i 0.955167 + 0.296066i \(0.0956749\pi\)
−0.955167 + 0.296066i \(0.904325\pi\)
\(510\) 0 0
\(511\) −5.95132 −0.263271
\(512\) −19.2310 11.9234i −0.849899 0.526945i
\(513\) 0 0
\(514\) 14.4657 + 6.29986i 0.638056 + 0.277875i
\(515\) 14.4806i 0.638091i
\(516\) 0 0
\(517\) 7.09799i 0.312169i
\(518\) −3.97999 + 9.13885i −0.174871 + 0.401538i
\(519\) 0 0
\(520\) −10.2368 29.0686i −0.448914 1.27474i
\(521\) −20.5338 −0.899600 −0.449800 0.893129i \(-0.648505\pi\)
−0.449800 + 0.893129i \(0.648505\pi\)
\(522\) 0 0
\(523\) 4.37298i 0.191217i 0.995419 + 0.0956086i \(0.0304797\pi\)
−0.995419 + 0.0956086i \(0.969520\pi\)
\(524\) −26.1905 + 24.3662i −1.14414 + 1.06444i
\(525\) 0 0
\(526\) −18.1015 7.88327i −0.789264 0.343727i
\(527\) −53.8619 −2.34626
\(528\) 0 0
\(529\) −21.6368 −0.940730
\(530\) 11.2718 + 4.90890i 0.489616 + 0.213229i
\(531\) 0 0
\(532\) −2.35276 + 2.18889i −0.102005 + 0.0949002i
\(533\) 72.2593i 3.12990i
\(534\) 0 0
\(535\) −7.73340 −0.334344
\(536\) 22.3006 7.85339i 0.963239 0.339215i
\(537\) 0 0
\(538\) 9.10160 20.8991i 0.392398 0.901023i
\(539\) 2.28335i 0.0983507i
\(540\) 0 0
\(541\) 11.8762i 0.510598i 0.966862 + 0.255299i \(0.0821740\pi\)
−0.966862 + 0.255299i \(0.917826\pi\)
\(542\) 11.5619 + 5.03525i 0.496627 + 0.216282i
\(543\) 0 0
\(544\) −17.8952 + 34.1341i −0.767249 + 1.46349i
\(545\) 3.61829 0.154991
\(546\) 0 0
\(547\) 5.50044i 0.235182i −0.993062 0.117591i \(-0.962483\pi\)
0.993062 0.117591i \(-0.0375171\pi\)
\(548\) 12.5060 + 13.4423i 0.534231 + 0.574227i
\(549\) 0 0
\(550\) −3.41395 + 7.83911i −0.145571 + 0.334261i
\(551\) 6.54045 0.278633
\(552\) 0 0
\(553\) −15.0027 −0.637980
\(554\) −15.1438 + 34.7732i −0.643399 + 1.47737i
\(555\) 0 0
\(556\) 17.6473 16.4181i 0.748410 0.696282i
\(557\) 8.19596i 0.347274i 0.984810 + 0.173637i \(0.0555519\pi\)
−0.984810 + 0.173637i \(0.944448\pi\)
\(558\) 0 0
\(559\) −2.44905 −0.103584
\(560\) 6.11875 + 0.442140i 0.258564 + 0.0186838i
\(561\) 0 0
\(562\) −14.3516 6.25018i −0.605388 0.263648i
\(563\) 0.145215i 0.00612008i 0.999995 + 0.00306004i \(0.000974043\pi\)
−0.999995 + 0.00306004i \(0.999026\pi\)
\(564\) 0 0
\(565\) 21.5200i 0.905354i
\(566\) 12.2762 28.1886i 0.516007 1.18485i
\(567\) 0 0
\(568\) 11.5389 + 32.7660i 0.484160 + 1.37483i
\(569\) 5.09548 0.213613 0.106807 0.994280i \(-0.465937\pi\)
0.106807 + 0.994280i \(0.465937\pi\)
\(570\) 0 0
\(571\) 25.3061i 1.05903i 0.848301 + 0.529514i \(0.177626\pi\)
−0.848301 + 0.529514i \(0.822374\pi\)
\(572\) 22.0992 + 23.7537i 0.924013 + 0.993191i
\(573\) 0 0
\(574\) 13.1876 + 5.74322i 0.550439 + 0.239717i
\(575\) 3.09153 0.128926
\(576\) 0 0
\(577\) 19.5004 0.811814 0.405907 0.913914i \(-0.366956\pi\)
0.405907 + 0.913914i \(0.366956\pi\)
\(578\) 38.1430 + 16.6114i 1.58654 + 0.690942i
\(579\) 0 0
\(580\) −8.50477 9.14150i −0.353141 0.379580i
\(581\) 14.7419i 0.611598i
\(582\) 0 0
\(583\) −12.9428 −0.536037
\(584\) −5.59130 15.8771i −0.231369 0.657000i
\(585\) 0 0
\(586\) 4.96932 11.4105i 0.205281 0.471365i
\(587\) 36.0783i 1.48911i 0.667561 + 0.744555i \(0.267338\pi\)
−0.667561 + 0.744555i \(0.732662\pi\)
\(588\) 0 0
\(589\) 12.7025i 0.523399i
\(590\) 2.74747 + 1.19653i 0.113112 + 0.0492604i
\(591\) 0 0
\(592\) −28.1201 2.03196i −1.15573 0.0835130i
\(593\) 16.7669 0.688535 0.344268 0.938872i \(-0.388127\pi\)
0.344268 + 0.938872i \(0.388127\pi\)
\(594\) 0 0
\(595\) 10.4490i 0.428369i
\(596\) 11.2910 10.5046i 0.462497 0.430283i
\(597\) 0 0
\(598\) 4.68390 10.7552i 0.191539 0.439811i
\(599\) 31.1008 1.27074 0.635372 0.772206i \(-0.280847\pi\)
0.635372 + 0.772206i \(0.280847\pi\)
\(600\) 0 0
\(601\) 17.1858 0.701022 0.350511 0.936559i \(-0.386008\pi\)
0.350511 + 0.936559i \(0.386008\pi\)
\(602\) 0.194652 0.446959i 0.00793342 0.0182167i
\(603\) 0 0
\(604\) 8.05543 + 8.65852i 0.327771 + 0.352310i
\(605\) 8.87434i 0.360793i
\(606\) 0 0
\(607\) 12.9692 0.526404 0.263202 0.964741i \(-0.415221\pi\)
0.263202 + 0.964741i \(0.415221\pi\)
\(608\) −8.05001 4.22030i −0.326471 0.171156i
\(609\) 0 0
\(610\) −10.9473 4.76757i −0.443242 0.193033i
\(611\) 22.0849i 0.893459i
\(612\) 0 0
\(613\) 26.5265i 1.07139i −0.844410 0.535697i \(-0.820049\pi\)
0.844410 0.535697i \(-0.179951\pi\)
\(614\) 1.75708 4.03460i 0.0709100 0.162823i
\(615\) 0 0
\(616\) −6.09159 + 2.14522i −0.245437 + 0.0864332i
\(617\) 37.3263 1.50270 0.751350 0.659904i \(-0.229403\pi\)
0.751350 + 0.659904i \(0.229403\pi\)
\(618\) 0 0
\(619\) 10.8774i 0.437200i −0.975815 0.218600i \(-0.929851\pi\)
0.975815 0.218600i \(-0.0701489\pi\)
\(620\) −17.7541 + 16.5175i −0.713023 + 0.663360i
\(621\) 0 0
\(622\) 0.575446 + 0.250608i 0.0230733 + 0.0100485i
\(623\) −11.8923 −0.476454
\(624\) 0 0
\(625\) −4.74975 −0.189990
\(626\) 24.8428 + 10.8191i 0.992920 + 0.432419i
\(627\) 0 0
\(628\) 1.32694 1.23451i 0.0529505 0.0492624i
\(629\) 48.0210i 1.91472i
\(630\) 0 0
\(631\) −24.2943 −0.967140 −0.483570 0.875306i \(-0.660660\pi\)
−0.483570 + 0.875306i \(0.660660\pi\)
\(632\) −14.0951 40.0247i −0.560674 1.59210i
\(633\) 0 0
\(634\) 6.33233 14.5403i 0.251489 0.577468i
\(635\) 26.1059i 1.03598i
\(636\) 0 0
\(637\) 7.10447i 0.281489i
\(638\) 12.0512 + 5.24835i 0.477113 + 0.207784i
\(639\) 0 0
\(640\) 4.56904 + 16.7392i 0.180607 + 0.661675i
\(641\) 16.5765 0.654731 0.327365 0.944898i \(-0.393839\pi\)
0.327365 + 0.944898i \(0.393839\pi\)
\(642\) 0 0
\(643\) 7.15319i 0.282094i −0.990003 0.141047i \(-0.954953\pi\)
0.990003 0.141047i \(-0.0450469\pi\)
\(644\) 1.59058 + 1.70966i 0.0626775 + 0.0673699i
\(645\) 0 0
\(646\) −6.18141 + 14.1937i −0.243204 + 0.558445i
\(647\) 7.94968 0.312534 0.156267 0.987715i \(-0.450054\pi\)
0.156267 + 0.987715i \(0.450054\pi\)
\(648\) 0 0
\(649\) −3.15478 −0.123836
\(650\) 10.6223 24.3908i 0.416640 0.956687i
\(651\) 0 0
\(652\) −6.53195 + 6.07699i −0.255811 + 0.237993i
\(653\) 7.45217i 0.291626i −0.989312 0.145813i \(-0.953420\pi\)
0.989312 0.145813i \(-0.0465798\pi\)
\(654\) 0 0
\(655\) 27.4315 1.07184
\(656\) −2.93216 + 40.5780i −0.114482 + 1.58431i
\(657\) 0 0
\(658\) 4.03057 + 1.75532i 0.157128 + 0.0684297i
\(659\) 26.2741i 1.02349i 0.859136 + 0.511747i \(0.171001\pi\)
−0.859136 + 0.511747i \(0.828999\pi\)
\(660\) 0 0
\(661\) 3.98821i 0.155123i 0.996988 + 0.0775617i \(0.0247135\pi\)
−0.996988 + 0.0775617i \(0.975287\pi\)
\(662\) 10.0515 23.0802i 0.390662 0.897038i
\(663\) 0 0
\(664\) −39.3290 + 13.8501i −1.52626 + 0.537488i
\(665\) 2.46425 0.0955594
\(666\) 0 0
\(667\) 4.75268i 0.184025i
\(668\) −30.9085 33.2226i −1.19589 1.28542i
\(669\) 0 0
\(670\) −16.6224 7.23911i −0.642181 0.279671i
\(671\) 12.5702 0.485267
\(672\) 0 0
\(673\) 30.5709 1.17842 0.589211 0.807979i \(-0.299439\pi\)
0.589211 + 0.807979i \(0.299439\pi\)
\(674\) −4.49130 1.95597i −0.172998 0.0753413i
\(675\) 0 0
\(676\) −51.0501 54.8721i −1.96347 2.11047i
\(677\) 21.9032i 0.841808i −0.907105 0.420904i \(-0.861713\pi\)
0.907105 0.420904i \(-0.138287\pi\)
\(678\) 0 0
\(679\) −2.60256 −0.0998770
\(680\) 27.8763 9.81692i 1.06901 0.376462i
\(681\) 0 0
\(682\) 10.1931 23.4053i 0.390313 0.896236i
\(683\) 13.0423i 0.499051i −0.968368 0.249525i \(-0.919725\pi\)
0.968368 0.249525i \(-0.0802746\pi\)
\(684\) 0 0
\(685\) 14.0793i 0.537942i
\(686\) 1.29659 + 0.564669i 0.0495041 + 0.0215592i
\(687\) 0 0
\(688\) 1.37529 + 0.0993783i 0.0524324 + 0.00378876i
\(689\) 40.2707 1.53419
\(690\) 0 0
\(691\) 3.25399i 0.123788i −0.998083 0.0618938i \(-0.980286\pi\)
0.998083 0.0618938i \(-0.0197140\pi\)
\(692\) −35.4820 + 33.0106i −1.34882 + 1.25487i
\(693\) 0 0
\(694\) −15.4698 + 35.5216i −0.587224 + 1.34838i
\(695\) −18.4835 −0.701118
\(696\) 0 0
\(697\) 69.2954 2.62475
\(698\) −0.915603 + 2.10240i −0.0346561 + 0.0795772i
\(699\) 0 0
\(700\) 3.60715 + 3.87720i 0.136337 + 0.146545i
\(701\) 2.70404i 0.102130i −0.998695 0.0510650i \(-0.983738\pi\)
0.998695 0.0510650i \(-0.0162616\pi\)
\(702\) 0 0
\(703\) −11.3250 −0.427132
\(704\) −11.4462 14.2359i −0.431393 0.536536i
\(705\) 0 0
\(706\) −21.5082 9.36687i −0.809471 0.352527i
\(707\) 9.58182i 0.360361i
\(708\) 0 0
\(709\) 49.0447i 1.84191i 0.389668 + 0.920955i \(0.372590\pi\)
−0.389668 + 0.920955i \(0.627410\pi\)
\(710\) 10.6363 24.4231i 0.399174 0.916583i
\(711\) 0 0
\(712\) −11.1729 31.7266i −0.418721 1.18901i
\(713\) −9.23042 −0.345682
\(714\) 0 0
\(715\) 24.8793i 0.930431i
\(716\) −12.9187 + 12.0189i −0.482794 + 0.449166i
\(717\) 0 0
\(718\) −10.1703 4.42920i −0.379553 0.165296i
\(719\) 21.3291 0.795442 0.397721 0.917506i \(-0.369801\pi\)
0.397721 + 0.917506i \(0.369801\pi\)
\(720\) 0 0
\(721\) 9.44175 0.351629
\(722\) 21.2879 + 9.27092i 0.792252 + 0.345028i
\(723\) 0 0
\(724\) 6.29033 5.85219i 0.233778 0.217495i
\(725\) 10.7783i 0.400294i
\(726\) 0 0
\(727\) −23.5713 −0.874210 −0.437105 0.899411i \(-0.643996\pi\)
−0.437105 + 0.899411i \(0.643996\pi\)
\(728\) 18.9535 6.67469i 0.702465 0.247380i
\(729\) 0 0
\(730\) −5.15396 + 11.8345i −0.190756 + 0.438015i
\(731\) 2.34859i 0.0868658i
\(732\) 0 0
\(733\) 2.28803i 0.0845105i 0.999107 + 0.0422552i \(0.0134543\pi\)
−0.999107 + 0.0422552i \(0.986546\pi\)
\(734\) 0.987286 + 0.429966i 0.0364414 + 0.0158703i
\(735\) 0 0
\(736\) −3.06673 + 5.84962i −0.113041 + 0.215620i
\(737\) 19.0867 0.703067
\(738\) 0 0
\(739\) 33.6953i 1.23950i 0.784798 + 0.619751i \(0.212766\pi\)
−0.784798 + 0.619751i \(0.787234\pi\)
\(740\) 14.7263 + 15.8288i 0.541350 + 0.581879i
\(741\) 0 0
\(742\) −3.20074 + 7.34954i −0.117503 + 0.269810i
\(743\) −35.7898 −1.31300 −0.656501 0.754326i \(-0.727964\pi\)
−0.656501 + 0.754326i \(0.727964\pi\)
\(744\) 0 0
\(745\) −11.8260 −0.433272
\(746\) 7.52362 17.2757i 0.275459 0.632509i
\(747\) 0 0
\(748\) −22.7794 + 21.1927i −0.832896 + 0.774883i
\(749\) 5.04240i 0.184245i
\(750\) 0 0
\(751\) 7.35858 0.268518 0.134259 0.990946i \(-0.457135\pi\)
0.134259 + 0.990946i \(0.457135\pi\)
\(752\) −0.896169 + 12.4020i −0.0326799 + 0.452255i
\(753\) 0 0
\(754\) −37.4966 16.3299i −1.36555 0.594699i
\(755\) 9.06881i 0.330048i
\(756\) 0 0
\(757\) 23.2086i 0.843530i −0.906705 0.421765i \(-0.861411\pi\)
0.906705 0.421765i \(-0.138589\pi\)
\(758\) 7.71308 17.7108i 0.280152 0.643283i
\(759\) 0 0
\(760\) 2.31517 + 6.57420i 0.0839802 + 0.238471i
\(761\) 22.1491 0.802902 0.401451 0.915880i \(-0.368506\pi\)
0.401451 + 0.915880i \(0.368506\pi\)
\(762\) 0 0
\(763\) 2.35923i 0.0854099i
\(764\) −0.306312 0.329245i −0.0110820 0.0119117i
\(765\) 0 0
\(766\) 12.5812 + 5.47916i 0.454579 + 0.197970i
\(767\) 9.81586 0.354430
\(768\) 0 0
\(769\) −27.4818 −0.991020 −0.495510 0.868602i \(-0.665019\pi\)
−0.495510 + 0.868602i \(0.665019\pi\)
\(770\) 4.54055 + 1.97742i 0.163630 + 0.0712613i
\(771\) 0 0
\(772\) −15.9998 17.1977i −0.575846 0.618958i
\(773\) 39.9693i 1.43760i 0.695219 + 0.718798i \(0.255308\pi\)
−0.695219 + 0.718798i \(0.744692\pi\)
\(774\) 0 0
\(775\) −20.9330 −0.751935
\(776\) −2.44512 6.94319i −0.0877746 0.249246i
\(777\) 0 0
\(778\) −13.9599 + 32.0547i −0.500487 + 1.14922i
\(779\) 16.3423i 0.585523i
\(780\) 0 0
\(781\) 28.0438i 1.00348i
\(782\) 10.3140 + 4.49178i 0.368829 + 0.160626i
\(783\) 0 0
\(784\) −0.288288 + 3.98960i −0.0102960 + 0.142486i
\(785\) −1.38981 −0.0496046
\(786\) 0 0