Properties

Label 1512.2.c.f.757.3
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 757.3
Character \(\chi\) = 1512.757
Dual form 1512.2.c.f.757.4

$q$-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 \(0.111423\pi\)
−0.939357 + 0.342940i \(0.888577\pi\)
\(6\) 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 \(-0.888141\pi\)
0.938886 0.344228i \(-0.111859\pi\)
\(12\) 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 \(-0.809505\pi\)
−0.826206 + 0.563368i \(0.809505\pi\)
\(18\) 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 \(-0.538843\pi\)
−0.121727 + 0.992564i \(0.538843\pi\)
\(24\) 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 \(0.123369\pi\)
−0.925828 + 0.377944i \(0.876631\pi\)
\(30\) 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 \(-0.792119\pi\)
−0.794218 + 0.607633i \(0.792119\pi\)
\(42\) 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 \(-0.572799\pi\)
−0.226717 + 0.973961i \(0.572799\pi\)
\(48\) 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 \(-0.872716\pi\)
0.921109 0.389304i \(-0.127284\pi\)
\(54\) 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 \(-0.971333\pi\)
0.995947 0.0899374i \(-0.0286667\pi\)
\(60\) 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 \(-0.759919\pi\)
−0.728795 + 0.684732i \(0.759919\pi\)
\(72\) 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 \(-0.699973\pi\)
0.587715 0.809068i \(-0.300027\pi\)
\(84\) 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 \(-0.282936\pi\)
0.630290 + 0.776360i \(0.282936\pi\)
\(90\) 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 \(0.158172\pi\)
−0.879059 + 0.476713i \(0.841828\pi\)
\(102\) 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 \(0.0783722\pi\)
−0.969842 + 0.243733i \(0.921628\pi\)
\(108\) 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 \(-0.270559\pi\)
0.659994 + 0.751271i \(0.270559\pi\)
\(114\) 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 \(-0.714527\pi\)
0.624082 0.781359i \(-0.285473\pi\)
\(132\) 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 \(-0.628270\pi\)
−0.392154 + 0.919900i \(0.628270\pi\)
\(138\) 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 \(0.102290\pi\)
−0.948809 + 0.315851i \(0.897710\pi\)
\(150\) 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 \(-0.158980\pi\)
0.877845 + 0.478944i \(0.158980\pi\)
\(168\) 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 \(-0.627255\pi\)
0.389218 0.921145i \(-0.372745\pi\)
\(174\) 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 \(-0.893048\pi\)
0.944082 0.329712i \(-0.106952\pi\)
\(180\) 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 \(-0.497411\pi\)
0.00813476 + 0.999967i \(0.497411\pi\)
\(192\) 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 \(0.176766\pi\)
−0.849729 + 0.527220i \(0.823234\pi\)
\(198\) 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 \(-0.779551\pi\)
0.769613 0.638510i \(-0.220449\pi\)
\(228\) 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 \(-0.292087\pi\)
0.607712 + 0.794157i \(0.292087\pi\)
\(234\) 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 \(-0.539905\pi\)
−0.125039 + 0.992152i \(0.539905\pi\)
\(240\) 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 \(0.140823\pi\)
−0.903723 + 0.428117i \(0.859177\pi\)
\(252\) 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 \(-0.613129\pi\)
−0.347969 + 0.937506i \(0.613129\pi\)
\(258\) 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 \(-0.358361\pi\)
0.430432 + 0.902623i \(0.358361\pi\)
\(264\) 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 \(0.163507\pi\)
−0.870945 + 0.491380i \(0.836493\pi\)
\(270\) 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 \(-0.392900\pi\)
0.330153 + 0.943927i \(0.392900\pi\)
\(282\) 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 \(0.0827548\pi\)
−0.966395 + 0.257063i \(0.917245\pi\)
\(294\) 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 \(-0.504005\pi\)
−0.0125832 + 0.999921i \(0.504005\pi\)
\(312\) 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 \(0.101980\pi\)
−0.949116 + 0.314927i \(0.898020\pi\)
\(318\) 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 \(-0.737017\pi\)
0.677686 0.735352i \(-0.262983\pi\)
\(348\) 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 \(-0.354464\pi\)
0.441452 + 0.897285i \(0.354464\pi\)
\(354\) 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 \(-0.433633\pi\)
0.206992 + 0.978343i \(0.433633\pi\)
\(360\) 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 \(-0.579743\pi\)
−0.247908 + 0.968784i \(0.579743\pi\)
\(384\) 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 \(-0.784391\pi\)
0.779233 0.626734i \(-0.215609\pi\)
\(390\) 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 \(-0.388662\pi\)
0.342690 + 0.939449i \(0.388662\pi\)
\(402\) 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 \(0.297743\pi\)
−0.593507 + 0.804829i \(0.702257\pi\)
\(420\) 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 \(-0.924300\pi\)
−0.971855 + 0.235582i \(0.924300\pi\)
\(432\) 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 \(0.143315\pi\)
−0.900343 + 0.435180i \(0.856685\pi\)
\(444\) 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 \(-0.200270\pi\)
0.808518 + 0.588471i \(0.200270\pi\)
\(450\) 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 \(-0.935639\pi\)
0.979628 0.200823i \(-0.0643615\pi\)
\(462\) 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 \(0.258294\pi\)
−0.688443 + 0.725290i \(0.741706\pi\)
\(468\) 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 \(-0.682241\pi\)
−0.541757 + 0.840535i \(0.682241\pi\)
\(480\) 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 \(-0.635634\pi\)
0.413330 0.910581i \(-0.364366\pi\)
\(492\) 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 \(-0.597863\pi\)
−0.302626 + 0.953109i \(0.597863\pi\)
\(504\) 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 \(-0.904325\pi\)
0.955167 0.296066i \(-0.0956749\pi\)
\(510\) 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 \(-0.351495\pi\)
0.449800 + 0.893129i \(0.351495\pi\)
\(522\) 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 \(-0.944448\pi\)
0.984810 0.173637i \(-0.0555519\pi\)
\(558\) 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 \(-0.999026\pi\)
0.999995 0.00306004i \(-0.000974043\pi\)
\(564\) 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 \(-0.534063\pi\)
−0.106807 + 0.994280i \(0.534063\pi\)
\(570\) 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 \(-0.732662\pi\)
0.667561 0.744555i \(-0.267338\pi\)
\(588\) 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 \(-0.611873\pi\)
−0.344268 + 0.938872i \(0.611873\pi\)
\(594\) 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 \(-0.719153\pi\)
−0.635372 + 0.772206i \(0.719153\pi\)
\(600\) 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 \(-0.770597\pi\)
−0.751350 + 0.659904i \(0.770597\pi\)
\(618\) 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 \(-0.606161\pi\)
−0.327365 + 0.944898i \(0.606161\pi\)
\(642\) 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 \(-0.549946\pi\)
−0.156267 + 0.987715i \(0.549946\pi\)
\(648\) 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 \(0.0465798\pi\)
−0.989312 + 0.145813i \(0.953420\pi\)
\(654\) 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 \(-0.828999\pi\)
0.859136 0.511747i \(-0.171001\pi\)
\(660\) 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 \(0.138287\pi\)
−0.907105 + 0.420904i \(0.861713\pi\)
\(678\) 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 \(0.0802746\pi\)
−0.968368 + 0.249525i \(0.919725\pi\)
\(684\) 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 \(0.0162616\pi\)
−0.998695 + 0.0510650i \(0.983738\pi\)
\(702\) 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 \(-0.630199\pi\)
−0.397721 + 0.917506i \(0.630199\pi\)
\(720\) 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 \(-0.272036\pi\)
0.656501 + 0.754326i \(0.272036\pi\)
\(744\) 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 \(-0.631494\pi\)
−0.401451 + 0.915880i \(0.631494\pi\)
\(762\) 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 \(-0.744692\pi\)
0.695219 0.718798i \(-0.255308\pi\)
\(774\) 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 </