Properties

Label 1470.2.g.k.589.3
Level $1470$
Weight $2$
Character 1470.589
Analytic conductor $11.738$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.1698758656.6
Defining polynomial: \(x^{8} + 18 x^{6} + 97 x^{4} + 176 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.3
Root \(-3.16053i\) of defining polynomial
Character \(\chi\) \(=\) 1470.589
Dual form 1470.2.g.k.589.7

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.63280 + 1.52773i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(1.63280 + 1.52773i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(1.52773 - 1.63280i) q^{10} +4.46967 q^{11} -1.00000i q^{12} -5.88388i q^{13} +(-1.52773 + 1.63280i) q^{15} +1.00000 q^{16} -7.73528i q^{17} +1.00000i q^{18} -6.61827 q^{19} +(-1.63280 - 1.52773i) q^{20} -4.46967i q^{22} -2.61827i q^{23} -1.00000 q^{24} +(0.332104 + 4.98896i) q^{25} -5.88388 q^{26} -1.00000i q^{27} +8.17246 q^{29} +(1.63280 + 1.52773i) q^{30} +8.46967 q^{31} -1.00000i q^{32} +4.46967i q^{33} -7.73528 q^{34} +1.00000 q^{36} +3.18719i q^{37} +6.61827i q^{38} +5.88388 q^{39} +(-1.52773 + 1.63280i) q^{40} +3.56282 q^{41} -1.43108i q^{43} -4.46967 q^{44} +(-1.63280 - 1.52773i) q^{45} -2.61827 q^{46} +6.79073i q^{47} +1.00000i q^{48} +(4.98896 - 0.332104i) q^{50} +7.73528 q^{51} +5.88388i q^{52} +1.38173i q^{53} -1.00000 q^{54} +(7.29809 + 6.82843i) q^{55} -6.61827i q^{57} -8.17246i q^{58} -4.66421 q^{59} +(1.52773 - 1.63280i) q^{60} +9.79683 q^{61} -8.46967i q^{62} -1.00000 q^{64} +(8.98896 - 9.60723i) q^{65} +4.46967 q^{66} +1.85140i q^{67} +7.73528i q^{68} +2.61827 q^{69} +2.02386 q^{71} -1.00000i q^{72} -4.01687i q^{73} +3.18719 q^{74} +(-4.98896 + 0.332104i) q^{75} +6.61827 q^{76} -5.88388i q^{78} +6.98527 q^{79} +(1.63280 + 1.52773i) q^{80} +1.00000 q^{81} -3.56282i q^{82} -5.35965i q^{83} +(11.8174 - 12.6302i) q^{85} -1.43108 q^{86} +8.17246i q^{87} +4.46967i q^{88} -14.3912 q^{89} +(-1.52773 + 1.63280i) q^{90} +2.61827i q^{92} +8.46967i q^{93} +6.79073 q^{94} +(-10.8063 - 10.1109i) q^{95} +1.00000 q^{96} -7.71966i q^{97} -4.46967 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 4q^{5} + 8q^{6} - 8q^{9} + 8q^{16} - 24q^{19} - 4q^{20} - 8q^{24} + 4q^{25} + 16q^{29} + 4q^{30} + 32q^{31} - 8q^{34} + 8q^{36} + 24q^{41} - 4q^{45} + 8q^{46} - 4q^{50} + 8q^{51} - 8q^{54} - 40q^{59} + 24q^{61} - 8q^{64} + 28q^{65} - 8q^{69} - 40q^{71} + 16q^{74} + 4q^{75} + 24q^{76} + 16q^{79} + 4q^{80} + 8q^{81} + 28q^{85} + 8q^{86} - 88q^{89} - 24q^{94} + 24q^{95} + 8q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 1.63280 + 1.52773i 0.730213 + 0.683220i
\(6\) 1.00000 0.408248
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 1.52773 1.63280i 0.483109 0.516338i
\(11\) 4.46967 1.34766 0.673828 0.738889i \(-0.264649\pi\)
0.673828 + 0.738889i \(0.264649\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 5.88388i 1.63189i −0.578126 0.815947i \(-0.696216\pi\)
0.578126 0.815947i \(-0.303784\pi\)
\(14\) 0 0
\(15\) −1.52773 + 1.63280i −0.394457 + 0.421588i
\(16\) 1.00000 0.250000
\(17\) 7.73528i 1.87608i −0.346527 0.938040i \(-0.612639\pi\)
0.346527 0.938040i \(-0.387361\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −6.61827 −1.51834 −0.759168 0.650895i \(-0.774394\pi\)
−0.759168 + 0.650895i \(0.774394\pi\)
\(20\) −1.63280 1.52773i −0.365106 0.341610i
\(21\) 0 0
\(22\) 4.46967i 0.952936i
\(23\) 2.61827i 0.545947i −0.962022 0.272974i \(-0.911993\pi\)
0.962022 0.272974i \(-0.0880071\pi\)
\(24\) −1.00000 −0.204124
\(25\) 0.332104 + 4.98896i 0.0664208 + 0.997792i
\(26\) −5.88388 −1.15392
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 8.17246 1.51759 0.758794 0.651331i \(-0.225789\pi\)
0.758794 + 0.651331i \(0.225789\pi\)
\(30\) 1.63280 + 1.52773i 0.298108 + 0.278923i
\(31\) 8.46967 1.52120 0.760598 0.649223i \(-0.224906\pi\)
0.760598 + 0.649223i \(0.224906\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.46967i 0.778069i
\(34\) −7.73528 −1.32659
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.18719i 0.523970i 0.965072 + 0.261985i \(0.0843772\pi\)
−0.965072 + 0.261985i \(0.915623\pi\)
\(38\) 6.61827i 1.07363i
\(39\) 5.88388 0.942175
\(40\) −1.52773 + 1.63280i −0.241555 + 0.258169i
\(41\) 3.56282 0.556419 0.278209 0.960520i \(-0.410259\pi\)
0.278209 + 0.960520i \(0.410259\pi\)
\(42\) 0 0
\(43\) 1.43108i 0.218238i −0.994029 0.109119i \(-0.965197\pi\)
0.994029 0.109119i \(-0.0348029\pi\)
\(44\) −4.46967 −0.673828
\(45\) −1.63280 1.52773i −0.243404 0.227740i
\(46\) −2.61827 −0.386043
\(47\) 6.79073i 0.990530i 0.868742 + 0.495265i \(0.164929\pi\)
−0.868742 + 0.495265i \(0.835071\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.98896 0.332104i 0.705545 0.0469666i
\(51\) 7.73528 1.08316
\(52\) 5.88388i 0.815947i
\(53\) 1.38173i 0.189795i 0.995487 + 0.0948976i \(0.0302524\pi\)
−0.995487 + 0.0948976i \(0.969748\pi\)
\(54\) −1.00000 −0.136083
\(55\) 7.29809 + 6.82843i 0.984075 + 0.920745i
\(56\) 0 0
\(57\) 6.61827i 0.876611i
\(58\) 8.17246i 1.07310i
\(59\) −4.66421 −0.607228 −0.303614 0.952795i \(-0.598193\pi\)
−0.303614 + 0.952795i \(0.598193\pi\)
\(60\) 1.52773 1.63280i 0.197229 0.210794i
\(61\) 9.79683 1.25436 0.627178 0.778876i \(-0.284210\pi\)
0.627178 + 0.778876i \(0.284210\pi\)
\(62\) 8.46967i 1.07565i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 8.98896 9.60723i 1.11494 1.19163i
\(66\) 4.46967 0.550178
\(67\) 1.85140i 0.226184i 0.993585 + 0.113092i \(0.0360755\pi\)
−0.993585 + 0.113092i \(0.963925\pi\)
\(68\) 7.73528i 0.938040i
\(69\) 2.61827 0.315203
\(70\) 0 0
\(71\) 2.02386 0.240187 0.120094 0.992763i \(-0.461680\pi\)
0.120094 + 0.992763i \(0.461680\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 4.01687i 0.470139i −0.971979 0.235069i \(-0.924468\pi\)
0.971979 0.235069i \(-0.0755318\pi\)
\(74\) 3.18719 0.370503
\(75\) −4.98896 + 0.332104i −0.576075 + 0.0383481i
\(76\) 6.61827 0.759168
\(77\) 0 0
\(78\) 5.88388i 0.666218i
\(79\) 6.98527 0.785904 0.392952 0.919559i \(-0.371454\pi\)
0.392952 + 0.919559i \(0.371454\pi\)
\(80\) 1.63280 + 1.52773i 0.182553 + 0.170805i
\(81\) 1.00000 0.111111
\(82\) 3.56282i 0.393447i
\(83\) 5.35965i 0.588298i −0.955760 0.294149i \(-0.904964\pi\)
0.955760 0.294149i \(-0.0950361\pi\)
\(84\) 0 0
\(85\) 11.8174 12.6302i 1.28178 1.36994i
\(86\) −1.43108 −0.154318
\(87\) 8.17246i 0.876180i
\(88\) 4.46967i 0.476468i
\(89\) −14.3912 −1.52547 −0.762734 0.646712i \(-0.776144\pi\)
−0.762734 + 0.646712i \(0.776144\pi\)
\(90\) −1.52773 + 1.63280i −0.161036 + 0.172113i
\(91\) 0 0
\(92\) 2.61827i 0.272974i
\(93\) 8.46967i 0.878263i
\(94\) 6.79073 0.700410
\(95\) −10.8063 10.1109i −1.10871 1.03736i
\(96\) 1.00000 0.102062
\(97\) 7.71966i 0.783813i −0.920005 0.391906i \(-0.871816\pi\)
0.920005 0.391906i \(-0.128184\pi\)
\(98\) 0 0
\(99\) −4.46967 −0.449218
\(100\) −0.332104 4.98896i −0.0332104 0.498896i
\(101\) −13.3544 −1.32882 −0.664408 0.747370i \(-0.731316\pi\)
−0.664408 + 0.747370i \(0.731316\pi\)
\(102\) 7.73528i 0.765906i
\(103\) 9.35965i 0.922233i 0.887339 + 0.461117i \(0.152551\pi\)
−0.887339 + 0.461117i \(0.847449\pi\)
\(104\) 5.88388 0.576962
\(105\) 0 0
\(106\) 1.38173 0.134205
\(107\) 11.0165i 1.06501i 0.846428 + 0.532503i \(0.178748\pi\)
−0.846428 + 0.532503i \(0.821252\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 4.69544 0.449741 0.224871 0.974389i \(-0.427804\pi\)
0.224871 + 0.974389i \(0.427804\pi\)
\(110\) 6.82843 7.29809i 0.651065 0.695846i
\(111\) −3.18719 −0.302514
\(112\) 0 0
\(113\) 12.5723i 1.18271i 0.806413 + 0.591353i \(0.201406\pi\)
−0.806413 + 0.591353i \(0.798594\pi\)
\(114\) −6.61827 −0.619858
\(115\) 4.00000 4.27512i 0.373002 0.398657i
\(116\) −8.17246 −0.758794
\(117\) 5.88388i 0.543965i
\(118\) 4.66421i 0.429375i
\(119\) 0 0
\(120\) −1.63280 1.52773i −0.149054 0.139462i
\(121\) 8.97792 0.816174
\(122\) 9.79683i 0.886963i
\(123\) 3.56282i 0.321248i
\(124\) −8.46967 −0.760598
\(125\) −7.07950 + 8.65336i −0.633210 + 0.773980i
\(126\) 0 0
\(127\) 6.59619i 0.585317i −0.956217 0.292658i \(-0.905460\pi\)
0.956217 0.292658i \(-0.0945399\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 1.43108 0.126000
\(130\) −9.60723 8.98896i −0.842610 0.788384i
\(131\) −2.32106 −0.202792 −0.101396 0.994846i \(-0.532331\pi\)
−0.101396 + 0.994846i \(0.532331\pi\)
\(132\) 4.46967i 0.389035i
\(133\) 0 0
\(134\) 1.85140 0.159936
\(135\) 1.52773 1.63280i 0.131486 0.140529i
\(136\) 7.73528 0.663294
\(137\) 14.2751i 1.21961i −0.792553 0.609803i \(-0.791249\pi\)
0.792553 0.609803i \(-0.208751\pi\)
\(138\) 2.61827i 0.222882i
\(139\) 14.9632 1.26916 0.634581 0.772857i \(-0.281173\pi\)
0.634581 + 0.772857i \(0.281173\pi\)
\(140\) 0 0
\(141\) −6.79073 −0.571883
\(142\) 2.02386i 0.169838i
\(143\) 26.2990i 2.19923i
\(144\) −1.00000 −0.0833333
\(145\) 13.3440 + 12.4853i 1.10816 + 1.03685i
\(146\) −4.01687 −0.332438
\(147\) 0 0
\(148\) 3.18719i 0.261985i
\(149\) −11.1651 −0.914681 −0.457341 0.889292i \(-0.651198\pi\)
−0.457341 + 0.889292i \(0.651198\pi\)
\(150\) 0.332104 + 4.98896i 0.0271162 + 0.407347i
\(151\) 0.664208 0.0540525 0.0270263 0.999635i \(-0.491396\pi\)
0.0270263 + 0.999635i \(0.491396\pi\)
\(152\) 6.61827i 0.536813i
\(153\) 7.73528i 0.625360i
\(154\) 0 0
\(155\) 13.8293 + 12.9393i 1.11080 + 1.03931i
\(156\) −5.88388 −0.471087
\(157\) 8.08184i 0.645001i −0.946569 0.322500i \(-0.895477\pi\)
0.946569 0.322500i \(-0.104523\pi\)
\(158\) 6.98527i 0.555718i
\(159\) −1.38173 −0.109578
\(160\) 1.52773 1.63280i 0.120777 0.129085i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 0.836668i 0.0655329i 0.999463 + 0.0327664i \(0.0104317\pi\)
−0.999463 + 0.0327664i \(0.989568\pi\)
\(164\) −3.56282 −0.278209
\(165\) −6.82843 + 7.29809i −0.531592 + 0.568156i
\(166\) −5.35965 −0.415989
\(167\) 2.66762i 0.206427i 0.994659 + 0.103213i \(0.0329125\pi\)
−0.994659 + 0.103213i \(0.967088\pi\)
\(168\) 0 0
\(169\) −21.6200 −1.66308
\(170\) −12.6302 11.8174i −0.968692 0.906352i
\(171\) 6.61827 0.506112
\(172\) 1.43108i 0.109119i
\(173\) 0.647340i 0.0492164i −0.999697 0.0246082i \(-0.992166\pi\)
0.999697 0.0246082i \(-0.00783382\pi\)
\(174\) 8.17246 0.619553
\(175\) 0 0
\(176\) 4.46967 0.336914
\(177\) 4.66421i 0.350583i
\(178\) 14.3912i 1.07867i
\(179\) 25.7374 1.92371 0.961853 0.273566i \(-0.0882033\pi\)
0.961853 + 0.273566i \(0.0882033\pi\)
\(180\) 1.63280 + 1.52773i 0.121702 + 0.113870i
\(181\) 7.42245 0.551707 0.275853 0.961200i \(-0.411040\pi\)
0.275853 + 0.961200i \(0.411040\pi\)
\(182\) 0 0
\(183\) 9.79683i 0.724203i
\(184\) 2.61827 0.193021
\(185\) −4.86915 + 5.20406i −0.357987 + 0.382610i
\(186\) 8.46967 0.621026
\(187\) 34.5741i 2.52831i
\(188\) 6.79073i 0.495265i
\(189\) 0 0
\(190\) −10.1109 + 10.8063i −0.733522 + 0.783975i
\(191\) −1.08452 −0.0784733 −0.0392367 0.999230i \(-0.512493\pi\)
−0.0392367 + 0.999230i \(0.512493\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 8.93933i 0.643467i 0.946830 + 0.321734i \(0.104266\pi\)
−0.946830 + 0.321734i \(0.895734\pi\)
\(194\) −7.71966 −0.554239
\(195\) 9.60723 + 8.98896i 0.687988 + 0.643713i
\(196\) 0 0
\(197\) 7.45890i 0.531425i −0.964052 0.265712i \(-0.914393\pi\)
0.964052 0.265712i \(-0.0856071\pi\)
\(198\) 4.46967i 0.317645i
\(199\) −25.8293 −1.83099 −0.915496 0.402328i \(-0.868201\pi\)
−0.915496 + 0.402328i \(0.868201\pi\)
\(200\) −4.98896 + 0.332104i −0.352773 + 0.0234833i
\(201\) −1.85140 −0.130587
\(202\) 13.3544i 0.939615i
\(203\) 0 0
\(204\) −7.73528 −0.541578
\(205\) 5.81739 + 5.44301i 0.406304 + 0.380156i
\(206\) 9.35965 0.652118
\(207\) 2.61827i 0.181982i
\(208\) 5.88388i 0.407974i
\(209\) −29.5815 −2.04619
\(210\) 0 0
\(211\) 5.53375 0.380959 0.190479 0.981691i \(-0.438996\pi\)
0.190479 + 0.981691i \(0.438996\pi\)
\(212\) 1.38173i 0.0948976i
\(213\) 2.02386i 0.138672i
\(214\) 11.0165 0.753073
\(215\) 2.18630 2.33668i 0.149105 0.159360i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 4.69544i 0.318015i
\(219\) 4.01687 0.271435
\(220\) −7.29809 6.82843i −0.492037 0.460372i
\(221\) −45.5134 −3.06157
\(222\) 3.18719i 0.213910i
\(223\) 3.28248i 0.219811i 0.993942 + 0.109906i \(0.0350548\pi\)
−0.993942 + 0.109906i \(0.964945\pi\)
\(224\) 0 0
\(225\) −0.332104 4.98896i −0.0221403 0.332597i
\(226\) 12.5723 0.836299
\(227\) 4.42031i 0.293387i −0.989182 0.146693i \(-0.953137\pi\)
0.989182 0.146693i \(-0.0468630\pi\)
\(228\) 6.61827i 0.438306i
\(229\) 7.97270 0.526851 0.263426 0.964680i \(-0.415148\pi\)
0.263426 + 0.964680i \(0.415148\pi\)
\(230\) −4.27512 4.00000i −0.281893 0.263752i
\(231\) 0 0
\(232\) 8.17246i 0.536548i
\(233\) 17.9558i 1.17633i −0.808742 0.588163i \(-0.799851\pi\)
0.808742 0.588163i \(-0.200149\pi\)
\(234\) 5.88388 0.384641
\(235\) −10.3744 + 11.0879i −0.676750 + 0.723297i
\(236\) 4.66421 0.303614
\(237\) 6.98527i 0.453742i
\(238\) 0 0
\(239\) −5.41296 −0.350135 −0.175068 0.984556i \(-0.556014\pi\)
−0.175068 + 0.984556i \(0.556014\pi\)
\(240\) −1.52773 + 1.63280i −0.0986143 + 0.105397i
\(241\) −4.69669 −0.302541 −0.151270 0.988492i \(-0.548336\pi\)
−0.151270 + 0.988492i \(0.548336\pi\)
\(242\) 8.97792i 0.577122i
\(243\) 1.00000i 0.0641500i
\(244\) −9.79683 −0.627178
\(245\) 0 0
\(246\) 3.56282 0.227157
\(247\) 38.9411i 2.47776i
\(248\) 8.46967i 0.537824i
\(249\) 5.35965 0.339654
\(250\) 8.65336 + 7.07950i 0.547287 + 0.447747i
\(251\) 7.73402 0.488167 0.244084 0.969754i \(-0.421513\pi\)
0.244084 + 0.969754i \(0.421513\pi\)
\(252\) 0 0
\(253\) 11.7028i 0.735748i
\(254\) −6.59619 −0.413882
\(255\) 12.6302 + 11.8174i 0.790934 + 0.740033i
\(256\) 1.00000 0.0625000
\(257\) 1.34442i 0.0838626i 0.999120 + 0.0419313i \(0.0133511\pi\)
−0.999120 + 0.0419313i \(0.986649\pi\)
\(258\) 1.43108i 0.0890953i
\(259\) 0 0
\(260\) −8.98896 + 9.60723i −0.557472 + 0.595815i
\(261\) −8.17246 −0.505863
\(262\) 2.32106i 0.143396i
\(263\) 4.36700i 0.269281i 0.990895 + 0.134640i \(0.0429879\pi\)
−0.990895 + 0.134640i \(0.957012\pi\)
\(264\) −4.46967 −0.275089
\(265\) −2.11091 + 2.25610i −0.129672 + 0.138591i
\(266\) 0 0
\(267\) 14.3912i 0.880730i
\(268\) 1.85140i 0.113092i
\(269\) −23.0671 −1.40643 −0.703213 0.710979i \(-0.748252\pi\)
−0.703213 + 0.710979i \(0.748252\pi\)
\(270\) −1.63280 1.52773i −0.0993693 0.0929745i
\(271\) 14.7209 0.894233 0.447117 0.894476i \(-0.352451\pi\)
0.447117 + 0.894476i \(0.352451\pi\)
\(272\) 7.73528i 0.469020i
\(273\) 0 0
\(274\) −14.2751 −0.862392
\(275\) 1.48440 + 22.2990i 0.0895124 + 1.34468i
\(276\) −2.61827 −0.157601
\(277\) 3.21104i 0.192933i −0.995336 0.0964665i \(-0.969246\pi\)
0.995336 0.0964665i \(-0.0307541\pi\)
\(278\) 14.9632i 0.897432i
\(279\) −8.46967 −0.507066
\(280\) 0 0
\(281\) −7.72488 −0.460827 −0.230414 0.973093i \(-0.574008\pi\)
−0.230414 + 0.973093i \(0.574008\pi\)
\(282\) 6.79073i 0.404382i
\(283\) 29.5594i 1.75712i 0.477630 + 0.878561i \(0.341496\pi\)
−0.477630 + 0.878561i \(0.658504\pi\)
\(284\) −2.02386 −0.120094
\(285\) 10.1109 10.8063i 0.598918 0.640113i
\(286\) −26.2990 −1.55509
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −42.8345 −2.51968
\(290\) 12.4853 13.3440i 0.733161 0.783589i
\(291\) 7.71966 0.452535
\(292\) 4.01687i 0.235069i
\(293\) 1.17679i 0.0687487i −0.999409 0.0343743i \(-0.989056\pi\)
0.999409 0.0343743i \(-0.0109438\pi\)
\(294\) 0 0
\(295\) −7.61574 7.12563i −0.443406 0.414870i
\(296\) −3.18719 −0.185252
\(297\) 4.46967i 0.259356i
\(298\) 11.1651i 0.646777i
\(299\) −15.4056 −0.890928
\(300\) 4.98896 0.332104i 0.288038 0.0191740i
\(301\) 0 0
\(302\) 0.664208i 0.0382209i
\(303\) 13.3544i 0.767192i
\(304\) −6.61827 −0.379584
\(305\) 15.9963 + 14.9669i 0.915946 + 0.857001i
\(306\) 7.73528 0.442196
\(307\) 20.3761i 1.16293i 0.813572 + 0.581464i \(0.197520\pi\)
−0.813572 + 0.581464i \(0.802480\pi\)
\(308\) 0 0
\(309\) −9.35965 −0.532452
\(310\) 12.9393 13.8293i 0.734905 0.785452i
\(311\) −18.8934 −1.07135 −0.535673 0.844425i \(-0.679942\pi\)
−0.535673 + 0.844425i \(0.679942\pi\)
\(312\) 5.88388i 0.333109i
\(313\) 16.4849i 0.931781i −0.884842 0.465891i \(-0.845734\pi\)
0.884842 0.465891i \(-0.154266\pi\)
\(314\) −8.08184 −0.456084
\(315\) 0 0
\(316\) −6.98527 −0.392952
\(317\) 10.3211i 0.579689i −0.957074 0.289844i \(-0.906396\pi\)
0.957074 0.289844i \(-0.0936035\pi\)
\(318\) 1.38173i 0.0774836i
\(319\) 36.5282 2.04518
\(320\) −1.63280 1.52773i −0.0912766 0.0854025i
\(321\) −11.0165 −0.614881
\(322\) 0 0
\(323\) 51.1941i 2.84852i
\(324\) −1.00000 −0.0555556
\(325\) 29.3544 1.95406i 1.62829 0.108392i
\(326\) 0.836668 0.0463387
\(327\) 4.69544i 0.259658i
\(328\) 3.56282i 0.196724i
\(329\) 0 0
\(330\) 7.29809 + 6.82843i 0.401747 + 0.375893i
\(331\) −19.1906 −1.05481 −0.527405 0.849614i \(-0.676835\pi\)
−0.527405 + 0.849614i \(0.676835\pi\)
\(332\) 5.35965i 0.294149i
\(333\) 3.18719i 0.174657i
\(334\) 2.66762 0.145966
\(335\) −2.82843 + 3.02297i −0.154533 + 0.165162i
\(336\) 0 0
\(337\) 27.6035i 1.50366i 0.659357 + 0.751830i \(0.270829\pi\)
−0.659357 + 0.751830i \(0.729171\pi\)
\(338\) 21.6200i 1.17598i
\(339\) −12.5723 −0.682835
\(340\) −11.8174 + 12.6302i −0.640888 + 0.684969i
\(341\) 37.8566 2.05005
\(342\) 6.61827i 0.357875i
\(343\) 0 0
\(344\) 1.43108 0.0771588
\(345\) 4.27512 + 4.00000i 0.230165 + 0.215353i
\(346\) −0.647340 −0.0348012
\(347\) 20.3761i 1.09385i 0.837182 + 0.546924i \(0.184202\pi\)
−0.837182 + 0.546924i \(0.815798\pi\)
\(348\) 8.17246i 0.438090i
\(349\) 17.8281 0.954314 0.477157 0.878818i \(-0.341667\pi\)
0.477157 + 0.878818i \(0.341667\pi\)
\(350\) 0 0
\(351\) −5.88388 −0.314058
\(352\) 4.46967i 0.238234i
\(353\) 3.51347i 0.187003i −0.995619 0.0935014i \(-0.970194\pi\)
0.995619 0.0935014i \(-0.0298060\pi\)
\(354\) −4.66421 −0.247900
\(355\) 3.30456 + 3.09190i 0.175388 + 0.164101i
\(356\) 14.3912 0.762734
\(357\) 0 0
\(358\) 25.7374i 1.36027i
\(359\) 2.19796 0.116004 0.0580018 0.998316i \(-0.481527\pi\)
0.0580018 + 0.998316i \(0.481527\pi\)
\(360\) 1.52773 1.63280i 0.0805182 0.0860564i
\(361\) 24.8015 1.30534
\(362\) 7.42245i 0.390116i
\(363\) 8.97792i 0.471218i
\(364\) 0 0
\(365\) 6.13668 6.55876i 0.321208 0.343301i
\(366\) 9.79683 0.512089
\(367\) 28.7721i 1.50189i 0.660365 + 0.750945i \(0.270402\pi\)
−0.660365 + 0.750945i \(0.729598\pi\)
\(368\) 2.61827i 0.136487i
\(369\) −3.56282 −0.185473
\(370\) 5.20406 + 4.86915i 0.270546 + 0.253135i
\(371\) 0 0
\(372\) 8.46967i 0.439132i
\(373\) 14.5689i 0.754350i −0.926142 0.377175i \(-0.876896\pi\)
0.926142 0.377175i \(-0.123104\pi\)
\(374\) −34.5741 −1.78778
\(375\) −8.65336 7.07950i −0.446858 0.365584i
\(376\) −6.79073 −0.350205
\(377\) 48.0858i 2.47654i
\(378\) 0 0
\(379\) 30.7868 1.58141 0.790705 0.612197i \(-0.209714\pi\)
0.790705 + 0.612197i \(0.209714\pi\)
\(380\) 10.8063 + 10.1109i 0.554354 + 0.518679i
\(381\) 6.59619 0.337933
\(382\) 1.08452i 0.0554890i
\(383\) 23.3410i 1.19267i −0.802736 0.596334i \(-0.796623\pi\)
0.802736 0.596334i \(-0.203377\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 8.93933 0.455000
\(387\) 1.43108i 0.0727460i
\(388\) 7.71966i 0.391906i
\(389\) 1.21842 0.0617762 0.0308881 0.999523i \(-0.490166\pi\)
0.0308881 + 0.999523i \(0.490166\pi\)
\(390\) 8.98896 9.60723i 0.455174 0.486481i
\(391\) −20.2530 −1.02424
\(392\) 0 0
\(393\) 2.32106i 0.117082i
\(394\) −7.45890 −0.375774
\(395\) 11.4056 + 10.6716i 0.573877 + 0.536946i
\(396\) 4.46967 0.224609
\(397\) 8.40595i 0.421883i 0.977499 + 0.210941i \(0.0676529\pi\)
−0.977499 + 0.210941i \(0.932347\pi\)
\(398\) 25.8293i 1.29471i
\(399\) 0 0
\(400\) 0.332104 + 4.98896i 0.0166052 + 0.249448i
\(401\) −0.664208 −0.0331690 −0.0165845 0.999862i \(-0.505279\pi\)
−0.0165845 + 0.999862i \(0.505279\pi\)
\(402\) 1.85140i 0.0923393i
\(403\) 49.8345i 2.48243i
\(404\) 13.3544 0.664408
\(405\) 1.63280 + 1.52773i 0.0811347 + 0.0759133i
\(406\) 0 0
\(407\) 14.2457i 0.706131i
\(408\) 7.73528i 0.382953i
\(409\) 7.38476 0.365153 0.182576 0.983192i \(-0.441556\pi\)
0.182576 + 0.983192i \(0.441556\pi\)
\(410\) 5.44301 5.81739i 0.268811 0.287300i
\(411\) 14.2751 0.704140
\(412\) 9.35965i 0.461117i
\(413\) 0 0
\(414\) 2.61827 0.128681
\(415\) 8.18807 8.75126i 0.401937 0.429582i
\(416\) −5.88388 −0.288481
\(417\) 14.9632i 0.732750i
\(418\) 29.5815i 1.44688i
\(419\) −18.6274 −0.910009 −0.455004 0.890489i \(-0.650362\pi\)
−0.455004 + 0.890489i \(0.650362\pi\)
\(420\) 0 0
\(421\) −13.5043 −0.658159 −0.329079 0.944302i \(-0.606738\pi\)
−0.329079 + 0.944302i \(0.606738\pi\)
\(422\) 5.53375i 0.269379i
\(423\) 6.79073i 0.330177i
\(424\) −1.38173 −0.0671027
\(425\) 38.5910 2.56892i 1.87194 0.124611i
\(426\) 2.02386 0.0980561
\(427\) 0 0
\(428\) 11.0165i 0.532503i
\(429\) 26.2990 1.26973
\(430\) −2.33668 2.18630i −0.112685 0.105433i
\(431\) −31.6807 −1.52601 −0.763003 0.646395i \(-0.776276\pi\)
−0.763003 + 0.646395i \(0.776276\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 25.3184i 1.21672i −0.793660 0.608362i \(-0.791827\pi\)
0.793660 0.608362i \(-0.208173\pi\)
\(434\) 0 0
\(435\) −12.4853 + 13.3440i −0.598623 + 0.639797i
\(436\) −4.69544 −0.224871
\(437\) 17.3284i 0.828931i
\(438\) 4.01687i 0.191933i
\(439\) −32.8146 −1.56615 −0.783077 0.621924i \(-0.786351\pi\)
−0.783077 + 0.621924i \(0.786351\pi\)
\(440\) −6.82843 + 7.29809i −0.325532 + 0.347923i
\(441\) 0 0
\(442\) 45.5134i 2.16485i
\(443\) 16.6421i 0.790691i 0.918532 + 0.395346i \(0.129375\pi\)
−0.918532 + 0.395346i \(0.870625\pi\)
\(444\) 3.18719 0.151257
\(445\) −23.4981 21.9859i −1.11392 1.04223i
\(446\) 3.28248 0.155430
\(447\) 11.1651i 0.528091i
\(448\) 0 0
\(449\) −20.1759 −0.952158 −0.476079 0.879402i \(-0.657942\pi\)
−0.476079 + 0.879402i \(0.657942\pi\)
\(450\) −4.98896 + 0.332104i −0.235182 + 0.0156555i
\(451\) 15.9246 0.749860
\(452\) 12.5723i 0.591353i
\(453\) 0.664208i 0.0312072i
\(454\) −4.42031 −0.207456
\(455\) 0 0
\(456\) 6.61827 0.309929
\(457\) 35.4124i 1.65652i 0.560342 + 0.828261i \(0.310670\pi\)
−0.560342 + 0.828261i \(0.689330\pi\)
\(458\) 7.97270i 0.372540i
\(459\) −7.73528 −0.361052
\(460\) −4.00000 + 4.27512i −0.186501 + 0.199329i
\(461\) −12.5940 −0.586562 −0.293281 0.956026i \(-0.594747\pi\)
−0.293281 + 0.956026i \(0.594747\pi\)
\(462\) 0 0
\(463\) 32.5061i 1.51069i 0.655330 + 0.755343i \(0.272530\pi\)
−0.655330 + 0.755343i \(0.727470\pi\)
\(464\) 8.17246 0.379397
\(465\) −12.9393 + 13.8293i −0.600047 + 0.641319i
\(466\) −17.9558 −0.831788
\(467\) 9.20531i 0.425971i −0.977055 0.212985i \(-0.931681\pi\)
0.977055 0.212985i \(-0.0683187\pi\)
\(468\) 5.88388i 0.271982i
\(469\) 0 0
\(470\) 11.0879 + 10.3744i 0.511448 + 0.478534i
\(471\) 8.08184 0.372391
\(472\) 4.66421i 0.214688i
\(473\) 6.39646i 0.294109i
\(474\) 6.98527 0.320844
\(475\) −2.19796 33.0183i −0.100849 1.51498i
\(476\) 0 0
\(477\) 1.38173i 0.0632651i
\(478\) 5.41296i 0.247583i
\(479\) 39.4914 1.80441 0.902203 0.431312i \(-0.141949\pi\)
0.902203 + 0.431312i \(0.141949\pi\)
\(480\) 1.63280 + 1.52773i 0.0745270 + 0.0697308i
\(481\) 18.7530 0.855065
\(482\) 4.69669i 0.213928i
\(483\) 0 0
\(484\) −8.97792 −0.408087
\(485\) 11.7935 12.6047i 0.535517 0.572350i
\(486\) 1.00000 0.0453609
\(487\) 29.2678i 1.32625i 0.748509 + 0.663125i \(0.230770\pi\)
−0.748509 + 0.663125i \(0.769230\pi\)
\(488\) 9.79683i 0.443482i
\(489\) −0.836668 −0.0378354
\(490\) 0 0
\(491\) 15.3631 0.693325 0.346663 0.937990i \(-0.387315\pi\)
0.346663 + 0.937990i \(0.387315\pi\)
\(492\) 3.56282i 0.160624i
\(493\) 63.2162i 2.84712i
\(494\) 38.9411 1.75204
\(495\) −7.29809 6.82843i −0.328025 0.306915i
\(496\) 8.46967 0.380299
\(497\) 0 0
\(498\) 5.35965i 0.240172i
\(499\) −20.5502 −0.919955 −0.459978 0.887930i \(-0.652143\pi\)
−0.459978 + 0.887930i \(0.652143\pi\)
\(500\) 7.07950 8.65336i 0.316605 0.386990i
\(501\) −2.66762 −0.119181
\(502\) 7.73402i 0.345186i
\(503\) 20.4788i 0.913105i 0.889696 + 0.456553i \(0.150916\pi\)
−0.889696 + 0.456553i \(0.849084\pi\)
\(504\) 0 0
\(505\) −21.8052 20.4019i −0.970318 0.907873i
\(506\) −11.7028 −0.520253
\(507\) 21.6200i 0.960180i
\(508\) 6.59619i 0.292658i
\(509\) −12.0702 −0.535001 −0.267501 0.963558i \(-0.586198\pi\)
−0.267501 + 0.963558i \(0.586198\pi\)
\(510\) 11.8174 12.6302i 0.523283 0.559275i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 6.61827i 0.292204i
\(514\) 1.34442 0.0592998
\(515\) −14.2990 + 15.2825i −0.630088 + 0.673426i
\(516\) −1.43108 −0.0629999
\(517\) 30.3523i 1.33489i
\(518\) 0 0
\(519\) 0.647340 0.0284151
\(520\) 9.60723 + 8.98896i 0.421305 + 0.394192i
\(521\) 14.7049 0.644235 0.322117 0.946700i \(-0.395605\pi\)
0.322117 + 0.946700i \(0.395605\pi\)
\(522\) 8.17246i 0.357699i
\(523\) 6.44417i 0.281784i 0.990025 + 0.140892i \(0.0449970\pi\)
−0.990025 + 0.140892i \(0.955003\pi\)
\(524\) 2.32106 0.101396
\(525\) 0 0
\(526\) 4.36700 0.190410
\(527\) 65.5152i 2.85389i
\(528\) 4.46967i 0.194517i
\(529\) 16.1447 0.701942
\(530\) 2.25610 + 2.11091i 0.0979985 + 0.0916919i
\(531\) 4.66421 0.202409
\(532\) 0 0
\(533\) 20.9632i 0.908016i
\(534\) −14.3912 −0.622770
\(535\) −16.8302 + 17.9878i −0.727633 + 0.777680i
\(536\) −1.85140 −0.0799681
\(537\) 25.7374i 1.11065i
\(538\) 23.0671i 0.994494i
\(539\) 0 0
\(540\) −1.52773 + 1.63280i −0.0657429 + 0.0702647i
\(541\) −11.5815 −0.497926 −0.248963 0.968513i \(-0.580090\pi\)
−0.248963 + 0.968513i \(0.580090\pi\)
\(542\) 14.7209i 0.632318i
\(543\) 7.42245i 0.318528i
\(544\) −7.73528 −0.331647
\(545\) 7.66674 + 7.17335i 0.328407 + 0.307272i
\(546\) 0 0
\(547\) 19.2656i 0.823737i −0.911243 0.411868i \(-0.864876\pi\)
0.911243 0.411868i \(-0.135124\pi\)
\(548\) 14.2751i 0.609803i
\(549\) −9.79683 −0.418119
\(550\) 22.2990 1.48440i 0.950832 0.0632948i
\(551\) −54.0875 −2.30421
\(552\) 2.61827i 0.111441i
\(553\) 0 0
\(554\) −3.21104 −0.136424
\(555\) −5.20406 4.86915i −0.220900 0.206684i
\(556\) −14.9632 −0.634581
\(557\) 21.0404i 0.891509i −0.895155 0.445754i \(-0.852936\pi\)
0.895155 0.445754i \(-0.147064\pi\)
\(558\) 8.46967i 0.358550i
\(559\) −8.42031 −0.356141
\(560\) 0 0
\(561\) 34.5741 1.45972
\(562\) 7.72488i 0.325854i
\(563\) 3.61092i 0.152182i 0.997101 + 0.0760910i \(0.0242439\pi\)
−0.997101 + 0.0760910i \(0.975756\pi\)
\(564\) 6.79073 0.285941
\(565\) −19.2071 + 20.5282i −0.808048 + 0.863626i
\(566\) 29.5594 1.24247
\(567\) 0 0
\(568\) 2.02386i 0.0849191i
\(569\) −33.2145 −1.39242 −0.696211 0.717837i \(-0.745132\pi\)
−0.696211 + 0.717837i \(0.745132\pi\)
\(570\) −10.8063 10.1109i −0.452628 0.423499i
\(571\) −32.1776 −1.34659 −0.673296 0.739373i \(-0.735122\pi\)
−0.673296 + 0.739373i \(0.735122\pi\)
\(572\) 26.2990i 1.09962i
\(573\) 1.08452i 0.0453066i
\(574\) 0 0
\(575\) 13.0624 0.869539i 0.544741 0.0362623i
\(576\) 1.00000 0.0416667
\(577\) 34.1902i 1.42336i 0.702505 + 0.711679i \(0.252065\pi\)
−0.702505 + 0.711679i \(0.747935\pi\)
\(578\) 42.8345i 1.78168i
\(579\) −8.93933 −0.371506
\(580\) −13.3440 12.4853i −0.554081 0.518423i
\(581\) 0 0
\(582\) 7.71966i 0.319990i
\(583\) 6.17587i 0.255779i
\(584\) 4.01687 0.166219
\(585\) −8.98896 + 9.60723i −0.371648 + 0.397210i
\(586\) −1.17679 −0.0486126
\(587\) 34.5962i 1.42794i 0.700178 + 0.713969i \(0.253104\pi\)
−0.700178 + 0.713969i \(0.746896\pi\)
\(588\) 0 0
\(589\) −56.0545 −2.30969
\(590\) −7.12563 + 7.61574i −0.293358 + 0.313535i
\(591\) 7.45890 0.306818
\(592\) 3.18719i 0.130993i
\(593\) 33.0845i 1.35862i 0.733853 + 0.679309i \(0.237720\pi\)
−0.733853 + 0.679309i \(0.762280\pi\)
\(594\) −4.46967 −0.183393
\(595\) 0 0
\(596\) 11.1651 0.457341
\(597\) 25.8293i 1.05712i
\(598\) 15.4056i 0.629981i
\(599\) −6.07485 −0.248212 −0.124106 0.992269i \(-0.539606\pi\)
−0.124106 + 0.992269i \(0.539606\pi\)
\(600\) −0.332104 4.98896i −0.0135581 0.203673i
\(601\) −11.7469 −0.479167 −0.239584 0.970876i \(-0.577011\pi\)
−0.239584 + 0.970876i \(0.577011\pi\)
\(602\) 0 0
\(603\) 1.85140i 0.0753947i
\(604\) −0.664208 −0.0270263
\(605\) 14.6592 + 13.7158i 0.595981 + 0.557627i
\(606\) −13.3544 −0.542487
\(607\) 45.8180i 1.85970i −0.367944 0.929848i \(-0.619938\pi\)
0.367944 0.929848i \(-0.380062\pi\)
\(608\) 6.61827i 0.268406i
\(609\) 0 0
\(610\) 14.9669 15.9963i 0.605991 0.647672i
\(611\) 39.9558 1.61644
\(612\) 7.73528i 0.312680i
\(613\) 34.2514i 1.38340i −0.722184 0.691701i \(-0.756862\pi\)
0.722184 0.691701i \(-0.243138\pi\)
\(614\) 20.3761 0.822314
\(615\) −5.44301 + 5.81739i −0.219483 + 0.234580i
\(616\) 0 0
\(617\) 38.8106i 1.56246i −0.624245 0.781228i \(-0.714593\pi\)
0.624245 0.781228i \(-0.285407\pi\)
\(618\) 9.35965i 0.376500i
\(619\) 4.27512 0.171832 0.0859159 0.996302i \(-0.472618\pi\)
0.0859159 + 0.996302i \(0.472618\pi\)
\(620\) −13.8293 12.9393i −0.555399 0.519656i
\(621\) −2.61827 −0.105068
\(622\) 18.8934i 0.757556i
\(623\) 0 0
\(624\) 5.88388 0.235544
\(625\) −24.7794 + 3.31371i −0.991177 + 0.132548i
\(626\) −16.4849 −0.658869
\(627\) 29.5815i 1.18137i
\(628\) 8.08184i 0.322500i
\(629\) 24.6538 0.983011
\(630\) 0 0
\(631\) 36.8419 1.46665 0.733326 0.679878i \(-0.237967\pi\)
0.733326 + 0.679878i \(0.237967\pi\)
\(632\) 6.98527i 0.277859i
\(633\) 5.53375i 0.219947i
\(634\) −10.3211 −0.409902
\(635\) 10.0772 10.7703i 0.399900 0.427406i
\(636\) 1.38173 0.0547892
\(637\) 0 0
\(638\) 36.5282i 1.44616i
\(639\) −2.02386 −0.0800625
\(640\) −1.52773 + 1.63280i −0.0603887 + 0.0645423i
\(641\) 49.9043 1.97110 0.985551 0.169382i \(-0.0541770\pi\)
0.985551 + 0.169382i \(0.0541770\pi\)
\(642\) 11.0165i 0.434787i
\(643\) 29.0091i 1.14401i −0.820251 0.572004i \(-0.806166\pi\)
0.820251 0.572004i \(-0.193834\pi\)
\(644\) 0 0
\(645\) 2.33668 + 2.18630i 0.0920066 + 0.0860855i
\(646\) 51.1941 2.01421
\(647\) 4.94329i 0.194341i 0.995268 + 0.0971705i \(0.0309792\pi\)
−0.995268 + 0.0971705i \(0.969021\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −20.8475 −0.818334
\(650\) −1.95406 29.3544i −0.0766446 1.15138i
\(651\) 0 0
\(652\) 0.836668i 0.0327664i
\(653\) 9.40559i 0.368069i −0.982920 0.184035i \(-0.941084\pi\)
0.982920 0.184035i \(-0.0589158\pi\)
\(654\) 4.69544 0.183606
\(655\) −3.78984 3.54595i −0.148081 0.138552i
\(656\) 3.56282 0.139105
\(657\) 4.01687i 0.156713i
\(658\) 0 0
\(659\) −13.4090 −0.522340 −0.261170 0.965293i \(-0.584108\pi\)
−0.261170 + 0.965293i \(0.584108\pi\)
\(660\) 6.82843 7.29809i 0.265796 0.284078i
\(661\) 13.2509 0.515400 0.257700 0.966225i \(-0.417035\pi\)
0.257700 + 0.966225i \(0.417035\pi\)
\(662\) 19.1906i 0.745864i
\(663\) 45.5134i 1.76760i
\(664\) 5.35965 0.207995
\(665\) 0 0
\(666\) −3.18719 −0.123501
\(667\) 21.3977i 0.828522i
\(668\) 2.66762i 0.103213i
\(669\) −3.28248 −0.126908
\(670\) 3.02297 + 2.82843i 0.116787 + 0.109272i
\(671\) 43.7886 1.69044
\(672\) 0 0
\(673\) 21.8236i 0.841237i −0.907238 0.420619i \(-0.861813\pi\)
0.907238 0.420619i \(-0.138187\pi\)
\(674\) 27.6035 1.06325
\(675\) 4.98896 0.332104i 0.192025 0.0127827i
\(676\) 21.6200 0.831540
\(677\) 41.0572i 1.57796i 0.614421 + 0.788979i \(0.289390\pi\)
−0.614421 + 0.788979i \(0.710610\pi\)
\(678\) 12.5723i 0.482837i
\(679\) 0 0
\(680\) 12.6302 + 11.8174i 0.484346 + 0.453176i
\(681\) 4.42031 0.169387
\(682\) 37.8566i 1.44960i
\(683\) 31.0642i 1.18864i −0.804229 0.594320i \(-0.797421\pi\)
0.804229 0.594320i \(-0.202579\pi\)
\(684\) −6.61827 −0.253056
\(685\) 21.8085 23.3085i 0.833259 0.890572i
\(686\) 0 0
\(687\) 7.97270i 0.304178i
\(688\) 1.43108i 0.0545595i
\(689\) 8.12993 0.309726
\(690\) 4.00000 4.27512i 0.152277 0.162751i
\(691\) −32.0012 −1.21738 −0.608692 0.793407i \(-0.708305\pi\)
−0.608692 + 0.793407i \(0.708305\pi\)
\(692\) 0.647340i 0.0246082i
\(693\) 0 0
\(694\) 20.3761 0.773468
\(695\) 24.4320 + 22.8597i 0.926757 + 0.867116i
\(696\) −8.17246 −0.309776
\(697\) 27.5594i 1.04389i
\(698\) 17.8281i 0.674802i
\(699\) 17.9558 0.679152
\(700\) 0 0
\(701\) −45.4635 −1.71713 −0.858567 0.512701i \(-0.828645\pi\)
−0.858567 + 0.512701i \(0.828645\pi\)
\(702\) 5.88388i 0.222073i
\(703\) 21.0937i 0.795563i
\(704\) −4.46967 −0.168457
\(705\) −11.0879 10.3744i −0.417596 0.390722i
\(706\) −3.51347 −0.132231
\(707\) 0 0
\(708\) 4.66421i 0.175292i
\(709\) 47.7597 1.79365 0.896826 0.442384i \(-0.145867\pi\)
0.896826 + 0.442384i \(0.145867\pi\)
\(710\) 3.09190 3.30456i 0.116037 0.124018i
\(711\) −6.98527 −0.261968
\(712\) 14.3912i 0.539335i
\(713\) 22.1759i 0.830493i
\(714\) 0 0
\(715\) 40.1776 42.9411i 1.50256 1.60591i
\(716\) −25.7374 −0.961853
\(717\) 5.41296i 0.202151i
\(718\) 2.19796i 0.0820270i
\(719\) −13.1611 −0.490828 −0.245414 0.969418i \(-0.578924\pi\)
−0.245414 + 0.969418i \(0.578924\pi\)
\(720\) −1.63280 1.52773i −0.0608510 0.0569350i
\(721\) 0 0
\(722\) 24.8015i 0.923016i
\(723\) 4.69669i 0.174672i
\(724\) −7.42245 −0.275853
\(725\) 2.71411 + 40.7721i 0.100799 + 1.51424i
\(726\) 8.97792 0.333202
\(727\) 8.17082i 0.303039i −0.988454 0.151519i \(-0.951583\pi\)
0.988454 0.151519i \(-0.0484166\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −6.55876 6.13668i −0.242751 0.227129i
\(731\) −11.0698 −0.409432
\(732\) 9.79683i 0.362101i
\(733\) 2.01510i 0.0744293i −0.999307 0.0372146i \(-0.988151\pi\)
0.999307 0.0372146i \(-0.0118485\pi\)
\(734\) 28.7721 1.06200
\(735\) 0 0
\(736\) −2.61827 −0.0965107
\(737\) 8.27512i 0.304818i
\(738\) 3.56282i 0.131149i
\(739\) 3.82590 0.140738 0.0703690 0.997521i \(-0.477582\pi\)
0.0703690 + 0.997521i \(0.477582\pi\)
\(740\) 4.86915 5.20406i 0.178994 0.191305i
\(741\) −38.9411 −1.43054
\(742\) 0 0
\(743\) 36.6654i 1.34512i −0.740041 0.672562i \(-0.765194\pi\)
0.740041 0.672562i \(-0.234806\pi\)
\(744\) −8.46967 −0.310513
\(745\) −18.2304 17.0572i −0.667912 0.624928i
\(746\) −14.5689 −0.533406
\(747\) 5.35965i 0.196099i
\(748\) 34.5741i 1.26415i
\(749\) 0 0
\(750\) −7.07950 + 8.65336i −0.258507 + 0.315976i
\(751\) −20.4657 −0.746804 −0.373402 0.927670i \(-0.621809\pi\)
−0.373402 + 0.927670i \(0.621809\pi\)
\(752\) 6.79073i 0.247632i
\(753\) 7.73402i 0.281843i
\(754\) −48.0858 −1.75118
\(755\) 1.08452 + 1.01473i 0.0394698 + 0.0369298i
\(756\) 0 0
\(757\) 37.9575i 1.37959i 0.724006 + 0.689794i \(0.242299\pi\)
−0.724006 + 0.689794i \(0.757701\pi\)
\(758\) 30.7868i 1.11823i
\(759\) 11.7028 0.424784
\(760\) 10.1109 10.8063i 0.366761 0.391987i
\(761\) −34.6131 −1.25472 −0.627361 0.778728i \(-0.715865\pi\)
−0.627361 + 0.778728i \(0.715865\pi\)
\(762\) 6.59619i 0.238955i
\(763\) 0 0
\(764\) 1.08452 0.0392367
\(765\) −11.8174 + 12.6302i −0.427258 + 0.456646i
\(766\) −23.3410 −0.843344
\(767\) 27.4436i 0.990932i
\(768\) 1.00000i 0.0360844i
\(769\) 1.48961 0.0537167 0.0268584 0.999639i \(-0.491450\pi\)
0.0268584 + 0.999639i \(0.491450\pi\)
\(770\) 0 0
\(771\) −1.34442 −0.0484181
\(772\) 8.93933i 0.321734i
\(773\) 0.992258i 0.0356891i 0.999841 + 0.0178445i \(0.00568039\pi\)
−0.999841 + 0.0178445i \(0.994320\pi\)
\(774\) 1.43108 0.0514392
\(775\) 2.81281 + 42.2548i 0.101039 + 1.51784i
\(776\) 7.71966 0.277120
\(777\) 0 0
\(778\) 1.21842i 0.0436824i
\(779\) −23.5797 −0.844830
\(780\) −9.60723 8.98896i −0.343994 0.321856i
\(781\) 9.04596 0.323690
\(782\) 20.2530i 0.724247i
\(783\) 8.17246i 0.292060i
\(784\) 0 0
\(785\) 12.3468 13.1961i 0.440677 0.470988i
\(786\) −2.32106 −0.0827896
\(787\) 10.2513i 0.365418i 0.983167 + 0.182709i \(0.0584867\pi\)
−0.983167 + 0.182709i \(0.941513\pi\)
\(788\) 7.45890i 0.265712i
\(789\) −4.36700 −0.155469
\(790\) 10.6716 11.4056i 0.379678 0.405793i
\(791\) 0 0
\(792\) 4.46967i 0.158823i