Properties

Label 216.2.d.b.109.2
Level 216
Weight 2
Character 216.109
Analytic conductor 1.725
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 216.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{7})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.2
Root \(-1.32288 + 0.500000i\)
Character \(\chi\) = 216.109
Dual form 216.2.d.b.109.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.32288 + 0.500000i) q^{2} +(1.50000 - 1.32288i) q^{4} -1.00000i q^{5} +1.00000 q^{7} +(-1.32288 + 2.50000i) q^{8} +O(q^{10})\) \(q+(-1.32288 + 0.500000i) q^{2} +(1.50000 - 1.32288i) q^{4} -1.00000i q^{5} +1.00000 q^{7} +(-1.32288 + 2.50000i) q^{8} +(0.500000 + 1.32288i) q^{10} -3.00000i q^{11} -5.29150i q^{13} +(-1.32288 + 0.500000i) q^{14} +(0.500000 - 3.96863i) q^{16} +5.29150 q^{17} +5.29150i q^{19} +(-1.32288 - 1.50000i) q^{20} +(1.50000 + 3.96863i) q^{22} +5.29150 q^{23} +4.00000 q^{25} +(2.64575 + 7.00000i) q^{26} +(1.50000 - 1.32288i) q^{28} -6.00000i q^{29} -7.00000 q^{31} +(1.32288 + 5.50000i) q^{32} +(-7.00000 + 2.64575i) q^{34} -1.00000i q^{35} -5.29150i q^{37} +(-2.64575 - 7.00000i) q^{38} +(2.50000 + 1.32288i) q^{40} -5.29150 q^{41} +10.5830i q^{43} +(-3.96863 - 4.50000i) q^{44} +(-7.00000 + 2.64575i) q^{46} -6.00000 q^{49} +(-5.29150 + 2.00000i) q^{50} +(-7.00000 - 7.93725i) q^{52} +9.00000i q^{53} -3.00000 q^{55} +(-1.32288 + 2.50000i) q^{56} +(3.00000 + 7.93725i) q^{58} +4.00000i q^{59} +(9.26013 - 3.50000i) q^{62} +(-4.50000 - 6.61438i) q^{64} -5.29150 q^{65} +(7.93725 - 7.00000i) q^{68} +(0.500000 + 1.32288i) q^{70} -15.8745 q^{71} +3.00000 q^{73} +(2.64575 + 7.00000i) q^{74} +(7.00000 + 7.93725i) q^{76} -3.00000i q^{77} +4.00000 q^{79} +(-3.96863 - 0.500000i) q^{80} +(7.00000 - 2.64575i) q^{82} +7.00000i q^{83} -5.29150i q^{85} +(-5.29150 - 14.0000i) q^{86} +(7.50000 + 3.96863i) q^{88} +10.5830 q^{89} -5.29150i q^{91} +(7.93725 - 7.00000i) q^{92} +5.29150 q^{95} +7.00000 q^{97} +(7.93725 - 3.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{4} + 4q^{7} + O(q^{10}) \) \( 4q + 6q^{4} + 4q^{7} + 2q^{10} + 2q^{16} + 6q^{22} + 16q^{25} + 6q^{28} - 28q^{31} - 28q^{34} + 10q^{40} - 28q^{46} - 24q^{49} - 28q^{52} - 12q^{55} + 12q^{58} - 18q^{64} + 2q^{70} + 12q^{73} + 28q^{76} + 16q^{79} + 28q^{82} + 30q^{88} + 28q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.32288 + 0.500000i −0.935414 + 0.353553i
\(3\) 0 0
\(4\) 1.50000 1.32288i 0.750000 0.661438i
\(5\) 1.00000i 0.447214i −0.974679 0.223607i \(-0.928217\pi\)
0.974679 0.223607i \(-0.0717831\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) −1.32288 + 2.50000i −0.467707 + 0.883883i
\(9\) 0 0
\(10\) 0.500000 + 1.32288i 0.158114 + 0.418330i
\(11\) 3.00000i 0.904534i −0.891883 0.452267i \(-0.850615\pi\)
0.891883 0.452267i \(-0.149385\pi\)
\(12\) 0 0
\(13\) 5.29150i 1.46760i −0.679366 0.733799i \(-0.737745\pi\)
0.679366 0.733799i \(-0.262255\pi\)
\(14\) −1.32288 + 0.500000i −0.353553 + 0.133631i
\(15\) 0 0
\(16\) 0.500000 3.96863i 0.125000 0.992157i
\(17\) 5.29150 1.28338 0.641689 0.766965i \(-0.278234\pi\)
0.641689 + 0.766965i \(0.278234\pi\)
\(18\) 0 0
\(19\) 5.29150i 1.21395i 0.794719 + 0.606977i \(0.207618\pi\)
−0.794719 + 0.606977i \(0.792382\pi\)
\(20\) −1.32288 1.50000i −0.295804 0.335410i
\(21\) 0 0
\(22\) 1.50000 + 3.96863i 0.319801 + 0.846114i
\(23\) 5.29150 1.10335 0.551677 0.834058i \(-0.313988\pi\)
0.551677 + 0.834058i \(0.313988\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) 2.64575 + 7.00000i 0.518875 + 1.37281i
\(27\) 0 0
\(28\) 1.50000 1.32288i 0.283473 0.250000i
\(29\) 6.00000i 1.11417i −0.830455 0.557086i \(-0.811919\pi\)
0.830455 0.557086i \(-0.188081\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 1.32288 + 5.50000i 0.233854 + 0.972272i
\(33\) 0 0
\(34\) −7.00000 + 2.64575i −1.20049 + 0.453743i
\(35\) 1.00000i 0.169031i
\(36\) 0 0
\(37\) 5.29150i 0.869918i −0.900450 0.434959i \(-0.856763\pi\)
0.900450 0.434959i \(-0.143237\pi\)
\(38\) −2.64575 7.00000i −0.429198 1.13555i
\(39\) 0 0
\(40\) 2.50000 + 1.32288i 0.395285 + 0.209165i
\(41\) −5.29150 −0.826394 −0.413197 0.910642i \(-0.635588\pi\)
−0.413197 + 0.910642i \(0.635588\pi\)
\(42\) 0 0
\(43\) 10.5830i 1.61389i 0.590624 + 0.806947i \(0.298881\pi\)
−0.590624 + 0.806947i \(0.701119\pi\)
\(44\) −3.96863 4.50000i −0.598293 0.678401i
\(45\) 0 0
\(46\) −7.00000 + 2.64575i −1.03209 + 0.390095i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) −5.29150 + 2.00000i −0.748331 + 0.282843i
\(51\) 0 0
\(52\) −7.00000 7.93725i −0.970725 1.10070i
\(53\) 9.00000i 1.23625i 0.786082 + 0.618123i \(0.212106\pi\)
−0.786082 + 0.618123i \(0.787894\pi\)
\(54\) 0 0
\(55\) −3.00000 −0.404520
\(56\) −1.32288 + 2.50000i −0.176777 + 0.334077i
\(57\) 0 0
\(58\) 3.00000 + 7.93725i 0.393919 + 1.04221i
\(59\) 4.00000i 0.520756i 0.965507 + 0.260378i \(0.0838471\pi\)
−0.965507 + 0.260378i \(0.916153\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 9.26013 3.50000i 1.17604 0.444500i
\(63\) 0 0
\(64\) −4.50000 6.61438i −0.562500 0.826797i
\(65\) −5.29150 −0.656330
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 7.93725 7.00000i 0.962533 0.848875i
\(69\) 0 0
\(70\) 0.500000 + 1.32288i 0.0597614 + 0.158114i
\(71\) −15.8745 −1.88396 −0.941979 0.335673i \(-0.891036\pi\)
−0.941979 + 0.335673i \(0.891036\pi\)
\(72\) 0 0
\(73\) 3.00000 0.351123 0.175562 0.984468i \(-0.443826\pi\)
0.175562 + 0.984468i \(0.443826\pi\)
\(74\) 2.64575 + 7.00000i 0.307562 + 0.813733i
\(75\) 0 0
\(76\) 7.00000 + 7.93725i 0.802955 + 0.910465i
\(77\) 3.00000i 0.341882i
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) −3.96863 0.500000i −0.443706 0.0559017i
\(81\) 0 0
\(82\) 7.00000 2.64575i 0.773021 0.292174i
\(83\) 7.00000i 0.768350i 0.923260 + 0.384175i \(0.125514\pi\)
−0.923260 + 0.384175i \(0.874486\pi\)
\(84\) 0 0
\(85\) 5.29150i 0.573944i
\(86\) −5.29150 14.0000i −0.570597 1.50966i
\(87\) 0 0
\(88\) 7.50000 + 3.96863i 0.799503 + 0.423057i
\(89\) 10.5830 1.12180 0.560898 0.827885i \(-0.310456\pi\)
0.560898 + 0.827885i \(0.310456\pi\)
\(90\) 0 0
\(91\) 5.29150i 0.554700i
\(92\) 7.93725 7.00000i 0.827516 0.729800i
\(93\) 0 0
\(94\) 0 0
\(95\) 5.29150 0.542897
\(96\) 0 0
\(97\) 7.00000 0.710742 0.355371 0.934725i \(-0.384354\pi\)
0.355371 + 0.934725i \(0.384354\pi\)
\(98\) 7.93725 3.00000i 0.801784 0.303046i
\(99\) 0 0
\(100\) 6.00000 5.29150i 0.600000 0.529150i
\(101\) 17.0000i 1.69156i 0.533529 + 0.845782i \(0.320865\pi\)
−0.533529 + 0.845782i \(0.679135\pi\)
\(102\) 0 0
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 13.2288 + 7.00000i 1.29719 + 0.686406i
\(105\) 0 0
\(106\) −4.50000 11.9059i −0.437079 1.15640i
\(107\) 3.00000i 0.290021i −0.989430 0.145010i \(-0.953678\pi\)
0.989430 0.145010i \(-0.0463216\pi\)
\(108\) 0 0
\(109\) 5.29150i 0.506834i 0.967357 + 0.253417i \(0.0815545\pi\)
−0.967357 + 0.253417i \(0.918446\pi\)
\(110\) 3.96863 1.50000i 0.378394 0.143019i
\(111\) 0 0
\(112\) 0.500000 3.96863i 0.0472456 0.375000i
\(113\) −15.8745 −1.49335 −0.746674 0.665190i \(-0.768350\pi\)
−0.746674 + 0.665190i \(0.768350\pi\)
\(114\) 0 0
\(115\) 5.29150i 0.493435i
\(116\) −7.93725 9.00000i −0.736956 0.835629i
\(117\) 0 0
\(118\) −2.00000 5.29150i −0.184115 0.487122i
\(119\) 5.29150 0.485071
\(120\) 0 0
\(121\) 2.00000 0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) −10.5000 + 9.26013i −0.942928 + 0.831584i
\(125\) 9.00000i 0.804984i
\(126\) 0 0
\(127\) 13.0000 1.15356 0.576782 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) 9.26013 + 6.50000i 0.818488 + 0.574524i
\(129\) 0 0
\(130\) 7.00000 2.64575i 0.613941 0.232048i
\(131\) 7.00000i 0.611593i 0.952097 + 0.305796i \(0.0989227\pi\)
−0.952097 + 0.305796i \(0.901077\pi\)
\(132\) 0 0
\(133\) 5.29150i 0.458831i
\(134\) 0 0
\(135\) 0 0
\(136\) −7.00000 + 13.2288i −0.600245 + 1.13436i
\(137\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 10.5830i 0.897639i −0.893622 0.448819i \(-0.851845\pi\)
0.893622 0.448819i \(-0.148155\pi\)
\(140\) −1.32288 1.50000i −0.111803 0.126773i
\(141\) 0 0
\(142\) 21.0000 7.93725i 1.76228 0.666080i
\(143\) −15.8745 −1.32749
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) −3.96863 + 1.50000i −0.328446 + 0.124141i
\(147\) 0 0
\(148\) −7.00000 7.93725i −0.575396 0.652438i
\(149\) 3.00000i 0.245770i 0.992421 + 0.122885i \(0.0392146\pi\)
−0.992421 + 0.122885i \(0.960785\pi\)
\(150\) 0 0
\(151\) 3.00000 0.244137 0.122068 0.992522i \(-0.461047\pi\)
0.122068 + 0.992522i \(0.461047\pi\)
\(152\) −13.2288 7.00000i −1.07299 0.567775i
\(153\) 0 0
\(154\) 1.50000 + 3.96863i 0.120873 + 0.319801i
\(155\) 7.00000i 0.562254i
\(156\) 0 0
\(157\) 10.5830i 0.844616i 0.906452 + 0.422308i \(0.138780\pi\)
−0.906452 + 0.422308i \(0.861220\pi\)
\(158\) −5.29150 + 2.00000i −0.420969 + 0.159111i
\(159\) 0 0
\(160\) 5.50000 1.32288i 0.434813 0.104583i
\(161\) 5.29150 0.417029
\(162\) 0 0
\(163\) 5.29150i 0.414462i −0.978292 0.207231i \(-0.933555\pi\)
0.978292 0.207231i \(-0.0664452\pi\)
\(164\) −7.93725 + 7.00000i −0.619795 + 0.546608i
\(165\) 0 0
\(166\) −3.50000 9.26013i −0.271653 0.718725i
\(167\) 10.5830 0.818938 0.409469 0.912324i \(-0.365714\pi\)
0.409469 + 0.912324i \(0.365714\pi\)
\(168\) 0 0
\(169\) −15.0000 −1.15385
\(170\) 2.64575 + 7.00000i 0.202920 + 0.536875i
\(171\) 0 0
\(172\) 14.0000 + 15.8745i 1.06749 + 1.21042i
\(173\) 15.0000i 1.14043i −0.821496 0.570214i \(-0.806860\pi\)
0.821496 0.570214i \(-0.193140\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) −11.9059 1.50000i −0.897440 0.113067i
\(177\) 0 0
\(178\) −14.0000 + 5.29150i −1.04934 + 0.396615i
\(179\) 23.0000i 1.71910i −0.511051 0.859550i \(-0.670744\pi\)
0.511051 0.859550i \(-0.329256\pi\)
\(180\) 0 0
\(181\) 21.1660i 1.57326i 0.617426 + 0.786629i \(0.288175\pi\)
−0.617426 + 0.786629i \(0.711825\pi\)
\(182\) 2.64575 + 7.00000i 0.196116 + 0.518875i
\(183\) 0 0
\(184\) −7.00000 + 13.2288i −0.516047 + 0.975237i
\(185\) −5.29150 −0.389039
\(186\) 0 0
\(187\) 15.8745i 1.16086i
\(188\) 0 0
\(189\) 0 0
\(190\) −7.00000 + 2.64575i −0.507833 + 0.191943i
\(191\) 5.29150 0.382880 0.191440 0.981504i \(-0.438684\pi\)
0.191440 + 0.981504i \(0.438684\pi\)
\(192\) 0 0
\(193\) −3.00000 −0.215945 −0.107972 0.994154i \(-0.534436\pi\)
−0.107972 + 0.994154i \(0.534436\pi\)
\(194\) −9.26013 + 3.50000i −0.664839 + 0.251285i
\(195\) 0 0
\(196\) −9.00000 + 7.93725i −0.642857 + 0.566947i
\(197\) 13.0000i 0.926212i 0.886303 + 0.463106i \(0.153265\pi\)
−0.886303 + 0.463106i \(0.846735\pi\)
\(198\) 0 0
\(199\) −17.0000 −1.20510 −0.602549 0.798082i \(-0.705848\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) −5.29150 + 10.0000i −0.374166 + 0.707107i
\(201\) 0 0
\(202\) −8.50000 22.4889i −0.598058 1.58231i
\(203\) 6.00000i 0.421117i
\(204\) 0 0
\(205\) 5.29150i 0.369575i
\(206\) 0 0
\(207\) 0 0
\(208\) −21.0000 2.64575i −1.45609 0.183450i
\(209\) 15.8745 1.09806
\(210\) 0 0
\(211\) 5.29150i 0.364282i −0.983272 0.182141i \(-0.941697\pi\)
0.983272 0.182141i \(-0.0583027\pi\)
\(212\) 11.9059 + 13.5000i 0.817699 + 0.927184i
\(213\) 0 0
\(214\) 1.50000 + 3.96863i 0.102538 + 0.271290i
\(215\) 10.5830 0.721755
\(216\) 0 0
\(217\) −7.00000 −0.475191
\(218\) −2.64575 7.00000i −0.179193 0.474100i
\(219\) 0 0
\(220\) −4.50000 + 3.96863i −0.303390 + 0.267565i
\(221\) 28.0000i 1.88348i
\(222\) 0 0
\(223\) −16.0000 −1.07144 −0.535720 0.844396i \(-0.679960\pi\)
−0.535720 + 0.844396i \(0.679960\pi\)
\(224\) 1.32288 + 5.50000i 0.0883883 + 0.367484i
\(225\) 0 0
\(226\) 21.0000 7.93725i 1.39690 0.527978i
\(227\) 4.00000i 0.265489i −0.991150 0.132745i \(-0.957621\pi\)
0.991150 0.132745i \(-0.0423790\pi\)
\(228\) 0 0
\(229\) 21.1660i 1.39869i 0.714785 + 0.699345i \(0.246525\pi\)
−0.714785 + 0.699345i \(0.753475\pi\)
\(230\) 2.64575 + 7.00000i 0.174456 + 0.461566i
\(231\) 0 0
\(232\) 15.0000 + 7.93725i 0.984798 + 0.521106i
\(233\) 10.5830 0.693316 0.346658 0.937992i \(-0.387316\pi\)
0.346658 + 0.937992i \(0.387316\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 5.29150 + 6.00000i 0.344447 + 0.390567i
\(237\) 0 0
\(238\) −7.00000 + 2.64575i −0.453743 + 0.171499i
\(239\) 15.8745 1.02684 0.513418 0.858138i \(-0.328379\pi\)
0.513418 + 0.858138i \(0.328379\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −2.64575 + 1.00000i −0.170075 + 0.0642824i
\(243\) 0 0
\(244\) 0 0
\(245\) 6.00000i 0.383326i
\(246\) 0 0
\(247\) 28.0000 1.78160
\(248\) 9.26013 17.5000i 0.588019 1.11125i
\(249\) 0 0
\(250\) 4.50000 + 11.9059i 0.284605 + 0.752994i
\(251\) 12.0000i 0.757433i 0.925513 + 0.378717i \(0.123635\pi\)
−0.925513 + 0.378717i \(0.876365\pi\)
\(252\) 0 0
\(253\) 15.8745i 0.998022i
\(254\) −17.1974 + 6.50000i −1.07906 + 0.407846i
\(255\) 0 0
\(256\) −15.5000 3.96863i −0.968750 0.248039i
\(257\) 15.8745 0.990225 0.495112 0.868829i \(-0.335127\pi\)
0.495112 + 0.868829i \(0.335127\pi\)
\(258\) 0 0
\(259\) 5.29150i 0.328798i
\(260\) −7.93725 + 7.00000i −0.492248 + 0.434122i
\(261\) 0 0
\(262\) −3.50000 9.26013i −0.216231 0.572093i
\(263\) −5.29150 −0.326288 −0.163144 0.986602i \(-0.552164\pi\)
−0.163144 + 0.986602i \(0.552164\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) −2.64575 7.00000i −0.162221 0.429198i
\(267\) 0 0
\(268\) 0 0
\(269\) 18.0000i 1.09748i −0.835993 0.548740i \(-0.815108\pi\)
0.835993 0.548740i \(-0.184892\pi\)
\(270\) 0 0
\(271\) 15.0000 0.911185 0.455593 0.890188i \(-0.349427\pi\)
0.455593 + 0.890188i \(0.349427\pi\)
\(272\) 2.64575 21.0000i 0.160422 1.27331i
\(273\) 0 0
\(274\) 0 0
\(275\) 12.0000i 0.723627i
\(276\) 0 0
\(277\) 10.5830i 0.635871i −0.948112 0.317936i \(-0.897010\pi\)
0.948112 0.317936i \(-0.102990\pi\)
\(278\) 5.29150 + 14.0000i 0.317363 + 0.839664i
\(279\) 0 0
\(280\) 2.50000 + 1.32288i 0.149404 + 0.0790569i
\(281\) −15.8745 −0.946994 −0.473497 0.880795i \(-0.657008\pi\)
−0.473497 + 0.880795i \(0.657008\pi\)
\(282\) 0 0
\(283\) 26.4575i 1.57274i 0.617758 + 0.786368i \(0.288041\pi\)
−0.617758 + 0.786368i \(0.711959\pi\)
\(284\) −23.8118 + 21.0000i −1.41297 + 1.24612i
\(285\) 0 0
\(286\) 21.0000 7.93725i 1.24176 0.469340i
\(287\) −5.29150 −0.312348
\(288\) 0 0
\(289\) 11.0000 0.647059
\(290\) 7.93725 3.00000i 0.466092 0.176166i
\(291\) 0 0
\(292\) 4.50000 3.96863i 0.263343 0.232246i
\(293\) 30.0000i 1.75262i 0.481749 + 0.876309i \(0.340002\pi\)
−0.481749 + 0.876309i \(0.659998\pi\)
\(294\) 0 0
\(295\) 4.00000 0.232889
\(296\) 13.2288 + 7.00000i 0.768906 + 0.406867i
\(297\) 0 0
\(298\) −1.50000 3.96863i −0.0868927 0.229896i
\(299\) 28.0000i 1.61928i
\(300\) 0 0
\(301\) 10.5830i 0.609994i
\(302\) −3.96863 + 1.50000i −0.228369 + 0.0863153i
\(303\) 0 0
\(304\) 21.0000 + 2.64575i 1.20443 + 0.151744i
\(305\) 0 0
\(306\) 0 0
\(307\) 15.8745i 0.906006i −0.891509 0.453003i \(-0.850353\pi\)
0.891509 0.453003i \(-0.149647\pi\)
\(308\) −3.96863 4.50000i −0.226134 0.256411i
\(309\) 0 0
\(310\) −3.50000 9.26013i −0.198787 0.525940i
\(311\) −26.4575 −1.50027 −0.750134 0.661286i \(-0.770011\pi\)
−0.750134 + 0.661286i \(0.770011\pi\)
\(312\) 0 0
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) −5.29150 14.0000i −0.298617 0.790066i
\(315\) 0 0
\(316\) 6.00000 5.29150i 0.337526 0.297670i
\(317\) 13.0000i 0.730153i −0.930978 0.365076i \(-0.881043\pi\)
0.930978 0.365076i \(-0.118957\pi\)
\(318\) 0 0
\(319\) −18.0000 −1.00781
\(320\) −6.61438 + 4.50000i −0.369755 + 0.251558i
\(321\) 0 0
\(322\) −7.00000 + 2.64575i −0.390095 + 0.147442i
\(323\) 28.0000i 1.55796i
\(324\) 0 0
\(325\) 21.1660i 1.17408i
\(326\) 2.64575 + 7.00000i 0.146535 + 0.387694i
\(327\) 0 0
\(328\) 7.00000 13.2288i 0.386510 0.730436i
\(329\) 0 0
\(330\) 0 0
\(331\) 21.1660i 1.16339i −0.813407 0.581695i \(-0.802390\pi\)
0.813407 0.581695i \(-0.197610\pi\)
\(332\) 9.26013 + 10.5000i 0.508216 + 0.576262i
\(333\) 0 0
\(334\) −14.0000 + 5.29150i −0.766046 + 0.289538i
\(335\) 0 0
\(336\) 0 0
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) 19.8431 7.50000i 1.07932 0.407946i
\(339\) 0 0
\(340\) −7.00000 7.93725i −0.379628 0.430458i
\(341\) 21.0000i 1.13721i
\(342\) 0 0
\(343\) −13.0000 −0.701934
\(344\) −26.4575 14.0000i −1.42649 0.754829i
\(345\) 0 0
\(346\) 7.50000 + 19.8431i 0.403202 + 1.06677i
\(347\) 23.0000i 1.23470i 0.786687 + 0.617352i \(0.211795\pi\)
−0.786687 + 0.617352i \(0.788205\pi\)
\(348\) 0 0
\(349\) 5.29150i 0.283248i −0.989921 0.141624i \(-0.954768\pi\)
0.989921 0.141624i \(-0.0452323\pi\)
\(350\) −5.29150 + 2.00000i −0.282843 + 0.106904i
\(351\) 0 0
\(352\) 16.5000 3.96863i 0.879453 0.211529i
\(353\) −15.8745 −0.844915 −0.422457 0.906383i \(-0.638832\pi\)
−0.422457 + 0.906383i \(0.638832\pi\)
\(354\) 0 0
\(355\) 15.8745i 0.842531i
\(356\) 15.8745 14.0000i 0.841347 0.741999i
\(357\) 0 0
\(358\) 11.5000 + 30.4261i 0.607794 + 1.60807i
\(359\) 21.1660 1.11710 0.558550 0.829471i \(-0.311358\pi\)
0.558550 + 0.829471i \(0.311358\pi\)
\(360\) 0 0
\(361\) −9.00000 −0.473684
\(362\) −10.5830 28.0000i −0.556230 1.47165i
\(363\) 0 0
\(364\) −7.00000 7.93725i −0.366900 0.416025i
\(365\) 3.00000i 0.157027i
\(366\) 0 0
\(367\) −3.00000 −0.156599 −0.0782994 0.996930i \(-0.524949\pi\)
−0.0782994 + 0.996930i \(0.524949\pi\)
\(368\) 2.64575 21.0000i 0.137919 1.09470i
\(369\) 0 0
\(370\) 7.00000 2.64575i 0.363913 0.137546i
\(371\) 9.00000i 0.467257i
\(372\) 0 0
\(373\) 26.4575i 1.36992i −0.728582 0.684959i \(-0.759820\pi\)
0.728582 0.684959i \(-0.240180\pi\)
\(374\) 7.93725 + 21.0000i 0.410426 + 1.08588i
\(375\) 0 0
\(376\) 0 0
\(377\) −31.7490 −1.63516
\(378\) 0 0
\(379\) 21.1660i 1.08722i 0.839336 + 0.543612i \(0.182944\pi\)
−0.839336 + 0.543612i \(0.817056\pi\)
\(380\) 7.93725 7.00000i 0.407173 0.359092i
\(381\) 0 0
\(382\) −7.00000 + 2.64575i −0.358151 + 0.135368i
\(383\) −15.8745 −0.811149 −0.405575 0.914062i \(-0.632929\pi\)
−0.405575 + 0.914062i \(0.632929\pi\)
\(384\) 0 0
\(385\) −3.00000 −0.152894
\(386\) 3.96863 1.50000i 0.201998 0.0763480i
\(387\) 0 0
\(388\) 10.5000 9.26013i 0.533057 0.470112i
\(389\) 5.00000i 0.253510i −0.991934 0.126755i \(-0.959544\pi\)
0.991934 0.126755i \(-0.0404562\pi\)
\(390\) 0 0
\(391\) 28.0000 1.41602
\(392\) 7.93725 15.0000i 0.400892 0.757614i
\(393\) 0 0
\(394\) −6.50000 17.1974i −0.327465 0.866392i
\(395\) 4.00000i 0.201262i
\(396\) 0 0
\(397\) 5.29150i 0.265573i 0.991145 + 0.132786i \(0.0423924\pi\)
−0.991145 + 0.132786i \(0.957608\pi\)
\(398\) 22.4889 8.50000i 1.12727 0.426067i
\(399\) 0 0
\(400\) 2.00000 15.8745i 0.100000 0.793725i
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 37.0405i 1.84512i
\(404\) 22.4889 + 25.5000i 1.11886 + 1.26867i
\(405\) 0 0
\(406\) 3.00000 + 7.93725i 0.148888 + 0.393919i
\(407\) −15.8745 −0.786870
\(408\) 0 0
\(409\) −11.0000 −0.543915 −0.271957 0.962309i \(-0.587671\pi\)
−0.271957 + 0.962309i \(0.587671\pi\)
\(410\) −2.64575 7.00000i −0.130664 0.345705i
\(411\) 0 0
\(412\) 0 0
\(413\) 4.00000i 0.196827i
\(414\) 0 0
\(415\) 7.00000 0.343616
\(416\) 29.1033 7.00000i 1.42690 0.343203i
\(417\) 0 0
\(418\) −21.0000 + 7.93725i −1.02714 + 0.388224i
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 10.5830i 0.515784i −0.966174 0.257892i \(-0.916972\pi\)
0.966174 0.257892i \(-0.0830279\pi\)
\(422\) 2.64575 + 7.00000i 0.128793 + 0.340755i
\(423\) 0 0
\(424\) −22.5000 11.9059i −1.09270 0.578201i
\(425\) 21.1660 1.02670
\(426\) 0 0
\(427\) 0 0
\(428\) −3.96863 4.50000i −0.191831 0.217516i
\(429\) 0 0
\(430\) −14.0000 + 5.29150i −0.675140 + 0.255179i
\(431\) 31.7490 1.52930 0.764648 0.644448i \(-0.222913\pi\)
0.764648 + 0.644448i \(0.222913\pi\)
\(432\) 0 0
\(433\) 5.00000 0.240285 0.120142 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) 9.26013 3.50000i 0.444500 0.168005i
\(435\) 0 0
\(436\) 7.00000 + 7.93725i 0.335239 + 0.380126i
\(437\) 28.0000i 1.33942i
\(438\) 0 0
\(439\) −21.0000 −1.00228 −0.501138 0.865368i \(-0.667085\pi\)
−0.501138 + 0.865368i \(0.667085\pi\)
\(440\) 3.96863 7.50000i 0.189197 0.357548i
\(441\) 0 0
\(442\) 14.0000 + 37.0405i 0.665912 + 1.76184i
\(443\) 24.0000i 1.14027i 0.821549 + 0.570137i \(0.193110\pi\)
−0.821549 + 0.570137i \(0.806890\pi\)
\(444\) 0 0
\(445\) 10.5830i 0.501683i
\(446\) 21.1660 8.00000i 1.00224 0.378811i
\(447\) 0 0
\(448\) −4.50000 6.61438i −0.212605 0.312500i
\(449\) −15.8745 −0.749164 −0.374582 0.927194i \(-0.622214\pi\)
−0.374582 + 0.927194i \(0.622214\pi\)
\(450\) 0 0
\(451\) 15.8745i 0.747501i
\(452\) −23.8118 + 21.0000i −1.12001 + 0.987757i
\(453\) 0 0
\(454\) 2.00000 + 5.29150i 0.0938647 + 0.248343i
\(455\) −5.29150 −0.248069
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) −10.5830 28.0000i −0.494511 1.30835i
\(459\) 0 0
\(460\) −7.00000 7.93725i −0.326377 0.370076i
\(461\) 9.00000i 0.419172i 0.977790 + 0.209586i \(0.0672116\pi\)
−0.977790 + 0.209586i \(0.932788\pi\)
\(462\) 0 0
\(463\) −41.0000 −1.90543 −0.952716 0.303863i \(-0.901724\pi\)
−0.952716 + 0.303863i \(0.901724\pi\)
\(464\) −23.8118 3.00000i −1.10543 0.139272i
\(465\) 0 0
\(466\) −14.0000 + 5.29150i −0.648537 + 0.245124i
\(467\) 1.00000i 0.0462745i −0.999732 0.0231372i \(-0.992635\pi\)
0.999732 0.0231372i \(-0.00736547\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −10.0000 5.29150i −0.460287 0.243561i
\(473\) 31.7490 1.45982
\(474\) 0 0
\(475\) 21.1660i 0.971163i
\(476\) 7.93725 7.00000i 0.363803 0.320844i
\(477\) 0 0
\(478\) −21.0000 + 7.93725i −0.960518 + 0.363042i
\(479\) −21.1660 −0.967100 −0.483550 0.875317i \(-0.660653\pi\)
−0.483550 + 0.875317i \(0.660653\pi\)
\(480\) 0 0
\(481\) −28.0000 −1.27669
\(482\) 13.2288 5.00000i 0.602553 0.227744i
\(483\) 0 0
\(484\) 3.00000 2.64575i 0.136364 0.120261i
\(485\) 7.00000i 0.317854i
\(486\) 0 0
\(487\) −40.0000 −1.81257 −0.906287 0.422664i \(-0.861095\pi\)
−0.906287 + 0.422664i \(0.861095\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −3.00000 7.93725i −0.135526 0.358569i
\(491\) 29.0000i 1.30875i −0.756169 0.654376i \(-0.772931\pi\)
0.756169 0.654376i \(-0.227069\pi\)
\(492\) 0 0
\(493\) 31.7490i 1.42990i
\(494\) −37.0405 + 14.0000i −1.66653 + 0.629890i
\(495\) 0 0
\(496\) −3.50000 + 27.7804i −0.157155 + 1.24738i
\(497\) −15.8745 −0.712069
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −11.9059 13.5000i −0.532447 0.603738i
\(501\) 0 0
\(502\) −6.00000 15.8745i −0.267793 0.708514i
\(503\) −15.8745 −0.707809 −0.353905 0.935282i \(-0.615146\pi\)
−0.353905 + 0.935282i \(0.615146\pi\)
\(504\) 0 0
\(505\) 17.0000 0.756490
\(506\) 7.93725 + 21.0000i 0.352854 + 0.933564i
\(507\) 0 0
\(508\) 19.5000 17.1974i 0.865173 0.763011i
\(509\) 21.0000i 0.930809i −0.885098 0.465404i \(-0.845909\pi\)
0.885098 0.465404i \(-0.154091\pi\)
\(510\) 0 0
\(511\) 3.00000 0.132712
\(512\) 22.4889 2.50000i 0.993878 0.110485i
\(513\) 0 0
\(514\) −21.0000 + 7.93725i −0.926270 + 0.350097i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 2.64575 + 7.00000i 0.116248 + 0.307562i
\(519\) 0 0
\(520\) 7.00000 13.2288i 0.306970 0.580119i
\(521\) −15.8745 −0.695475 −0.347737 0.937592i \(-0.613050\pi\)
−0.347737 + 0.937592i \(0.613050\pi\)
\(522\) 0 0
\(523\) 15.8745i 0.694144i 0.937839 + 0.347072i \(0.112824\pi\)
−0.937839 + 0.347072i \(0.887176\pi\)
\(524\) 9.26013 + 10.5000i 0.404531 + 0.458695i
\(525\) 0 0
\(526\) 7.00000 2.64575i 0.305215 0.115360i
\(527\) −37.0405 −1.61351
\(528\) 0 0
\(529\) 5.00000 0.217391
\(530\) −11.9059 + 4.50000i −0.517158 + 0.195468i
\(531\) 0 0
\(532\) 7.00000 + 7.93725i 0.303488 + 0.344124i
\(533\) 28.0000i 1.21281i
\(534\) 0 0
\(535\) −3.00000 −0.129701
\(536\) 0 0
\(537\) 0 0
\(538\) 9.00000 + 23.8118i 0.388018 + 1.02660i
\(539\) 18.0000i 0.775315i
\(540\) 0 0
\(541\) 10.5830i 0.454999i 0.973778 + 0.227499i \(0.0730550\pi\)
−0.973778 + 0.227499i \(0.926945\pi\)
\(542\) −19.8431 + 7.50000i −0.852336 + 0.322153i
\(543\) 0 0
\(544\) 7.00000 + 29.1033i 0.300123 + 1.24779i
\(545\) 5.29150 0.226663
\(546\) 0 0
\(547\) 5.29150i 0.226248i 0.993581 + 0.113124i \(0.0360858\pi\)
−0.993581 + 0.113124i \(0.963914\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 6.00000 + 15.8745i 0.255841 + 0.676891i
\(551\) 31.7490 1.35255
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) 5.29150 + 14.0000i 0.224814 + 0.594803i
\(555\) 0 0
\(556\) −14.0000 15.8745i −0.593732 0.673229i
\(557\) 39.0000i 1.65248i −0.563316 0.826242i \(-0.690475\pi\)
0.563316 0.826242i \(-0.309525\pi\)
\(558\) 0 0
\(559\) 56.0000 2.36855
\(560\) −3.96863 0.500000i −0.167705 0.0211289i
\(561\) 0 0
\(562\) 21.0000 7.93725i 0.885832 0.334813i
\(563\) 3.00000i 0.126435i −0.998000 0.0632175i \(-0.979864\pi\)
0.998000 0.0632175i \(-0.0201362\pi\)
\(564\) 0 0
\(565\) 15.8745i 0.667846i
\(566\) −13.2288 35.0000i −0.556046 1.47116i
\(567\) 0 0
\(568\) 21.0000 39.6863i 0.881140 1.66520i
\(569\) 31.7490 1.33099 0.665494 0.746403i \(-0.268221\pi\)
0.665494 + 0.746403i \(0.268221\pi\)
\(570\) 0 0
\(571\) 26.4575i 1.10721i −0.832779 0.553606i \(-0.813251\pi\)
0.832779 0.553606i \(-0.186749\pi\)
\(572\) −23.8118 + 21.0000i −0.995620 + 0.878054i
\(573\) 0 0
\(574\) 7.00000 2.64575i 0.292174 0.110432i
\(575\) 21.1660 0.882684
\(576\) 0 0
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) −14.5516 + 5.50000i −0.605268 + 0.228770i
\(579\) 0 0
\(580\) −9.00000 + 7.93725i −0.373705 + 0.329577i
\(581\) 7.00000i 0.290409i
\(582\) 0 0
\(583\) 27.0000 1.11823
\(584\) −3.96863 + 7.50000i −0.164223 + 0.310352i
\(585\) 0 0
\(586\) −15.0000 39.6863i −0.619644 1.63942i
\(587\) 23.0000i 0.949312i −0.880172 0.474656i \(-0.842573\pi\)
0.880172 0.474656i \(-0.157427\pi\)
\(588\) 0 0
\(589\) 37.0405i 1.52623i
\(590\) −5.29150 + 2.00000i −0.217848 + 0.0823387i
\(591\) 0 0
\(592\) −21.0000 2.64575i −0.863095 0.108740i
\(593\) −31.7490 −1.30378 −0.651888 0.758315i \(-0.726023\pi\)
−0.651888 + 0.758315i \(0.726023\pi\)
\(594\) 0 0
\(595\) 5.29150i 0.216930i
\(596\) 3.96863 + 4.50000i 0.162561 + 0.184327i
\(597\) 0 0
\(598\) 14.0000 + 37.0405i 0.572503 + 1.51470i
\(599\) 21.1660 0.864820 0.432410 0.901677i \(-0.357663\pi\)
0.432410 + 0.901677i \(0.357663\pi\)
\(600\) 0 0
\(601\) 5.00000 0.203954 0.101977 0.994787i \(-0.467483\pi\)
0.101977 + 0.994787i \(0.467483\pi\)
\(602\) −5.29150 14.0000i −0.215666 0.570597i
\(603\) 0 0
\(604\) 4.50000 3.96863i 0.183102 0.161481i
\(605\) 2.00000i 0.0813116i
\(606\) 0 0
\(607\) −8.00000 −0.324710 −0.162355 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) −29.1033 + 7.00000i −1.18029 + 0.283887i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 10.5830i 0.427444i −0.976895 0.213722i \(-0.931441\pi\)
0.976895 0.213722i \(-0.0685586\pi\)
\(614\) 7.93725 + 21.0000i 0.320321 + 0.847491i
\(615\) 0 0
\(616\) 7.50000 + 3.96863i 0.302184 + 0.159901i
\(617\) 5.29150 0.213028 0.106514 0.994311i \(-0.466031\pi\)
0.106514 + 0.994311i \(0.466031\pi\)
\(618\) 0 0
\(619\) 15.8745i 0.638050i 0.947746 + 0.319025i \(0.103355\pi\)
−0.947746 + 0.319025i \(0.896645\pi\)
\(620\) 9.26013 + 10.5000i 0.371896 + 0.421690i
\(621\) 0 0
\(622\) 35.0000 13.2288i 1.40337 0.530425i
\(623\) 10.5830 0.423999
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 1.32288 0.500000i 0.0528727 0.0199840i
\(627\) 0 0
\(628\) 14.0000 + 15.8745i 0.558661 + 0.633462i
\(629\) 28.0000i 1.11643i
\(630\) 0 0
\(631\) −23.0000 −0.915616 −0.457808 0.889051i \(-0.651365\pi\)
−0.457808 + 0.889051i \(0.651365\pi\)
\(632\) −5.29150 + 10.0000i −0.210485 + 0.397779i
\(633\) 0 0
\(634\) 6.50000 + 17.1974i 0.258148 + 0.682995i
\(635\) 13.0000i 0.515889i
\(636\) 0 0
\(637\) 31.7490i 1.25794i
\(638\) 23.8118 9.00000i 0.942717 0.356313i
\(639\) 0 0
\(640\) 6.50000 9.26013i 0.256935 0.366039i
\(641\) 37.0405 1.46301 0.731506 0.681835i \(-0.238818\pi\)
0.731506 + 0.681835i \(0.238818\pi\)
\(642\) 0 0
\(643\) 21.1660i 0.834706i −0.908744 0.417353i \(-0.862958\pi\)
0.908744 0.417353i \(-0.137042\pi\)
\(644\) 7.93725 7.00000i 0.312772 0.275839i
\(645\) 0 0
\(646\) −14.0000 37.0405i −0.550823 1.45734i
\(647\) 31.7490 1.24818 0.624091 0.781351i \(-0.285469\pi\)
0.624091 + 0.781351i \(0.285469\pi\)
\(648\) 0 0
\(649\) 12.0000 0.471041
\(650\) 10.5830 + 28.0000i 0.415100 + 1.09825i
\(651\) 0 0
\(652\) −7.00000 7.93725i −0.274141 0.310847i
\(653\) 3.00000i 0.117399i −0.998276 0.0586995i \(-0.981305\pi\)
0.998276 0.0586995i \(-0.0186954\pi\)
\(654\) 0 0
\(655\) 7.00000 0.273513
\(656\) −2.64575 + 21.0000i −0.103299 + 0.819912i
\(657\) 0 0
\(658\) 0 0
\(659\) 15.0000i 0.584317i −0.956370 0.292159i \(-0.905627\pi\)
0.956370 0.292159i \(-0.0943735\pi\)
\(660\) 0 0
\(661\) 26.4575i 1.02908i 0.857467 + 0.514539i \(0.172037\pi\)
−0.857467 + 0.514539i \(0.827963\pi\)
\(662\) 10.5830 + 28.0000i 0.411320 + 1.08825i
\(663\) 0 0
\(664\) −17.5000 9.26013i −0.679132 0.359363i
\(665\) 5.29150 0.205196
\(666\) 0 0
\(667\) 31.7490i 1.22933i
\(668\) 15.8745 14.0000i 0.614203 0.541676i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 29.0000 1.11787 0.558934 0.829212i \(-0.311211\pi\)
0.558934 + 0.829212i \(0.311211\pi\)
\(674\) −44.9778 + 17.0000i −1.73248 + 0.654816i
\(675\) 0 0
\(676\) −22.5000 + 19.8431i −0.865385 + 0.763197i
\(677\) 6.00000i 0.230599i −0.993331 0.115299i \(-0.963217\pi\)
0.993331 0.115299i \(-0.0367827\pi\)
\(678\) 0 0
\(679\) 7.00000 0.268635
\(680\) 13.2288 + 7.00000i 0.507300 + 0.268438i
\(681\) 0 0
\(682\) −10.5000 27.7804i −0.402066 1.06377i
\(683\) 44.0000i 1.68361i −0.539779 0.841807i \(-0.681492\pi\)
0.539779 0.841807i \(-0.318508\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 17.1974 6.50000i 0.656599 0.248171i
\(687\) 0 0
\(688\) 42.0000 + 5.29150i 1.60123 + 0.201737i
\(689\) 47.6235 1.81431
\(690\) 0 0
\(691\) 42.3320i 1.61039i −0.593013 0.805193i \(-0.702062\pi\)
0.593013 0.805193i \(-0.297938\pi\)
\(692\) −19.8431 22.5000i −0.754323 0.855322i
\(693\) 0 0
\(694\) −11.5000 30.4261i −0.436534 1.15496i
\(695\) −10.5830 −0.401436
\(696\) 0 0
\(697\) −28.0000 −1.06058
\(698\) 2.64575 + 7.00000i 0.100143 + 0.264954i
\(699\) 0 0
\(700\) 6.00000 5.29150i 0.226779 0.200000i
\(701\) 1.00000i 0.0377695i −0.999822 0.0188847i \(-0.993988\pi\)
0.999822 0.0188847i \(-0.00601156\pi\)
\(702\) 0 0
\(703\) 28.0000 1.05604
\(704\) −19.8431 + 13.5000i −0.747866 + 0.508800i
\(705\) 0 0
\(706\) 21.0000 7.93725i 0.790345 0.298722i
\(707\) 17.0000i 0.639351i
\(708\) 0 0
\(709\) 21.1660i 0.794906i 0.917622 + 0.397453i \(0.130106\pi\)
−0.917622 + 0.397453i \(0.869894\pi\)
\(710\) −7.93725 21.0000i −0.297880 0.788116i
\(711\) 0 0
\(712\) −14.0000 + 26.4575i −0.524672 + 0.991537i
\(713\) −37.0405 −1.38718
\(714\) 0 0
\(715\) 15.8745i 0.593673i
\(716\) −30.4261 34.5000i −1.13708 1.28933i
\(717\) 0 0
\(718\) −28.0000 + 10.5830i −1.04495 + 0.394954i
\(719\) 21.1660 0.789359 0.394679 0.918819i \(-0.370856\pi\)
0.394679 + 0.918819i \(0.370856\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 11.9059 4.50000i 0.443091 0.167473i
\(723\) 0 0
\(724\) 28.0000 + 31.7490i 1.04061 + 1.17994i
\(725\) 24.0000i 0.891338i
\(726\) 0 0
\(727\) 33.0000 1.22390 0.611951 0.790896i \(-0.290385\pi\)
0.611951 + 0.790896i \(0.290385\pi\)
\(728\) 13.2288 + 7.00000i 0.490290 + 0.259437i
\(729\) 0 0
\(730\) 1.50000 + 3.96863i 0.0555175 + 0.146885i
\(731\) 56.0000i 2.07123i
\(732\) 0 0
\(733\) 5.29150i 0.195446i −0.995214 0.0977231i \(-0.968844\pi\)
0.995214 0.0977231i \(-0.0311559\pi\)
\(734\) 3.96863 1.50000i 0.146485 0.0553660i
\(735\) 0 0
\(736\) 7.00000 + 29.1033i 0.258023 + 1.07276i
\(737\) 0 0
\(738\) 0 0
\(739\) 5.29150i 0.194651i −0.995253 0.0973255i \(-0.968971\pi\)
0.995253 0.0973255i \(-0.0310288\pi\)
\(740\) −7.93725 + 7.00000i −0.291779 + 0.257325i
\(741\) 0 0
\(742\) −4.50000 11.9059i −0.165200 0.437079i
\(743\) −37.0405 −1.35888 −0.679442 0.733729i \(-0.737778\pi\)
−0.679442 + 0.733729i \(0.737778\pi\)
\(744\) 0 0
\(745\) 3.00000 0.109911
\(746\) 13.2288 + 35.0000i 0.484339 + 1.28144i
\(747\) 0 0
\(748\) −21.0000 23.8118i −0.767836 0.870644i
\(749\) 3.00000i 0.109618i
\(750\) 0 0
\(751\) −31.0000 −1.13121 −0.565603 0.824678i \(-0.691357\pi\)
−0.565603 + 0.824678i \(0.691357\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 42.0000 15.8745i 1.52955 0.578115i
\(755\) 3.00000i 0.109181i
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) −10.5830 28.0000i −0.384392 1.01701i
\(759\) 0 0
\(760\) −7.00000 + 13.2288i −0.253917 + 0.479857i
\(761\) −10.5830 −0.383634 −0.191817 0.981431i \(-0.561438\pi\)
−0.191817 + 0.981431i \(0.561438\pi\)
\(762\) 0 0
\(763\) 5.29150i 0.191565i
\(764\) 7.93725 7.00000i 0.287160 0.253251i
\(765\) 0 0
\(766\) 21.0000 7.93725i 0.758761 0.286785i
\(767\) 21.1660 0.764260
\(768\) 0 0
\(769\) −35.0000 −1.26213 −0.631066 0.775729i \(-0.717382\pi\)
−0.631066 + 0.775729i \(0.717382\pi\)
\(770\) 3.96863 1.50000i 0.143019 0.0540562i
\(771\) 0 0
\(772\) −4.50000 + 3.96863i −0.161959 + 0.142834i
\(773\) 14.0000i 0.503545i 0.967786 + 0.251773i \(0.0810135\pi\)
−0.967786 + 0.251773i \(0.918987\pi\)
\(774\) 0 0
\(775\) −28.0000 −1.00579
\(776\) −9.26013 + 17.5000i −0.332419 + 0.628213i
\(777\) 0 0
\(778\) 2.50000 + 6.61438i 0.0896293 + 0.237137i
\(779\) 28.0000i 1.00320i
\(780\) 0 0
\(781\) 47.6235i 1.70410i
\(782\) −37.0405 + 14.0000i −1.32457 + 0.500639i
\(783\) 0 0
\(784\) −3.00000 + 23.8118i −0.107143 + 0.850420i
\(785\) 10.5830 0.377724
\(786\) 0 0
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 17.1974 + 19.5000i 0.612631 + 0.694659i
\(789\) 0 0
\(790\) 2.00000 + 5.29150i 0.0711568 + 0.188263i
\(791\) −15.8745 −0.564433
\(792\) 0 0
\(793\) 0 0
\(794\) −2.64575 7.00000i −0.0938942 0.248421i
\(795\) 0 0
\(796\) −25.5000 + 22.4889i −0.903824 + 0.797097i
\(797\) 49.0000i 1.73567i 0.496853 + 0.867835i \(0.334489\pi\)
−0.496853 + 0.867835i \(0.665511\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 5.29150 + 22.0000i 0.187083 + 0.777817i
\(801\) 0 0
\(802\)