Properties

Label 2646.2.h.k.667.2
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
Defining polynomial: \(x^{4} - x^{3} - 2 x^{2} - 3 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.2
Root \(1.68614 - 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.k.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.37228 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +1.37228 q^{5} +1.00000 q^{8} +(-0.686141 - 1.18843i) q^{10} -4.37228 q^{11} +(-1.00000 - 1.73205i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-2.18614 - 3.78651i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(-0.686141 + 1.18843i) q^{20} +(2.18614 + 3.78651i) q^{22} +7.37228 q^{23} -3.11684 q^{25} +(-1.00000 + 1.73205i) q^{26} +(1.37228 - 2.37686i) q^{29} +(-1.00000 + 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-2.18614 + 3.78651i) q^{34} +(-1.00000 + 1.73205i) q^{37} +5.00000 q^{38} +1.37228 q^{40} +(5.18614 + 8.98266i) q^{41} +(-4.55842 + 7.89542i) q^{43} +(2.18614 - 3.78651i) q^{44} +(-3.68614 - 6.38458i) q^{46} +(1.55842 + 2.69927i) q^{50} +2.00000 q^{52} +(1.37228 + 2.37686i) q^{53} -6.00000 q^{55} -2.74456 q^{58} +(3.55842 - 6.16337i) q^{59} +(7.05842 + 12.2255i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-1.37228 - 2.37686i) q^{65} +(-7.55842 + 13.0916i) q^{67} +4.37228 q^{68} -10.1168 q^{71} +(2.55842 + 4.43132i) q^{73} +2.00000 q^{74} +(-2.50000 - 4.33013i) q^{76} +(-6.05842 - 10.4935i) q^{79} +(-0.686141 - 1.18843i) q^{80} +(5.18614 - 8.98266i) q^{82} +(-2.74456 + 4.75372i) q^{83} +(-3.00000 - 5.19615i) q^{85} +9.11684 q^{86} -4.37228 q^{88} +(1.62772 - 2.81929i) q^{89} +(-3.68614 + 6.38458i) q^{92} +(-3.43070 + 5.94215i) q^{95} +(-4.55842 + 7.89542i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 4 q^{8} + O(q^{10}) \) \( 4 q - 2 q^{2} - 2 q^{4} - 6 q^{5} + 4 q^{8} + 3 q^{10} - 6 q^{11} - 4 q^{13} - 2 q^{16} - 3 q^{17} - 10 q^{19} + 3 q^{20} + 3 q^{22} + 18 q^{23} + 22 q^{25} - 4 q^{26} - 6 q^{29} - 4 q^{31} - 2 q^{32} - 3 q^{34} - 4 q^{37} + 20 q^{38} - 6 q^{40} + 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} + 8 q^{52} - 6 q^{53} - 24 q^{55} + 12 q^{58} - 3 q^{59} + 11 q^{61} + 8 q^{62} + 4 q^{64} + 6 q^{65} - 13 q^{67} + 6 q^{68} - 6 q^{71} - 7 q^{73} + 8 q^{74} - 10 q^{76} - 7 q^{79} + 3 q^{80} + 15 q^{82} + 12 q^{83} - 12 q^{85} + 2 q^{86} - 6 q^{88} + 18 q^{89} - 9 q^{92} + 15 q^{95} - q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 1.37228 0.613703 0.306851 0.951757i \(-0.400725\pi\)
0.306851 + 0.951757i \(0.400725\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.686141 1.18843i −0.216977 0.375815i
\(11\) −4.37228 −1.31829 −0.659146 0.752015i \(-0.729082\pi\)
−0.659146 + 0.752015i \(0.729082\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.18614 3.78651i −0.530217 0.918363i −0.999379 0.0352504i \(-0.988777\pi\)
0.469162 0.883112i \(-0.344556\pi\)
\(18\) 0 0
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) −0.686141 + 1.18843i −0.153426 + 0.265741i
\(21\) 0 0
\(22\) 2.18614 + 3.78651i 0.466087 + 0.807286i
\(23\) 7.37228 1.53723 0.768613 0.639713i \(-0.220947\pi\)
0.768613 + 0.639713i \(0.220947\pi\)
\(24\) 0 0
\(25\) −3.11684 −0.623369
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.37228 2.37686i 0.254826 0.441372i −0.710022 0.704179i \(-0.751315\pi\)
0.964848 + 0.262807i \(0.0846484\pi\)
\(30\) 0 0
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.18614 + 3.78651i −0.374920 + 0.649381i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 5.00000 0.811107
\(39\) 0 0
\(40\) 1.37228 0.216977
\(41\) 5.18614 + 8.98266i 0.809939 + 1.40286i 0.912906 + 0.408171i \(0.133833\pi\)
−0.102966 + 0.994685i \(0.532833\pi\)
\(42\) 0 0
\(43\) −4.55842 + 7.89542i −0.695153 + 1.20404i 0.274976 + 0.961451i \(0.411330\pi\)
−0.970129 + 0.242589i \(0.922003\pi\)
\(44\) 2.18614 3.78651i 0.329573 0.570837i
\(45\) 0 0
\(46\) −3.68614 6.38458i −0.543492 0.941355i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.55842 + 2.69927i 0.220394 + 0.381734i
\(51\) 0 0
\(52\) 2.00000 0.277350
\(53\) 1.37228 + 2.37686i 0.188497 + 0.326487i 0.944749 0.327793i \(-0.106305\pi\)
−0.756252 + 0.654280i \(0.772972\pi\)
\(54\) 0 0
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) 0 0
\(58\) −2.74456 −0.360379
\(59\) 3.55842 6.16337i 0.463267 0.802402i −0.535854 0.844310i \(-0.680010\pi\)
0.999121 + 0.0419083i \(0.0133437\pi\)
\(60\) 0 0
\(61\) 7.05842 + 12.2255i 0.903738 + 1.56532i 0.822602 + 0.568618i \(0.192522\pi\)
0.0811364 + 0.996703i \(0.474145\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.37228 2.37686i −0.170211 0.294813i
\(66\) 0 0
\(67\) −7.55842 + 13.0916i −0.923408 + 1.59939i −0.129307 + 0.991605i \(0.541275\pi\)
−0.794101 + 0.607785i \(0.792058\pi\)
\(68\) 4.37228 0.530217
\(69\) 0 0
\(70\) 0 0
\(71\) −10.1168 −1.20065 −0.600324 0.799757i \(-0.704962\pi\)
−0.600324 + 0.799757i \(0.704962\pi\)
\(72\) 0 0
\(73\) 2.55842 + 4.43132i 0.299441 + 0.518646i 0.976008 0.217734i \(-0.0698666\pi\)
−0.676567 + 0.736381i \(0.736533\pi\)
\(74\) 2.00000 0.232495
\(75\) 0 0
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) 0 0
\(78\) 0 0
\(79\) −6.05842 10.4935i −0.681626 1.18061i −0.974485 0.224455i \(-0.927940\pi\)
0.292859 0.956156i \(-0.405393\pi\)
\(80\) −0.686141 1.18843i −0.0767129 0.132871i
\(81\) 0 0
\(82\) 5.18614 8.98266i 0.572713 0.991969i
\(83\) −2.74456 + 4.75372i −0.301255 + 0.521789i −0.976420 0.215877i \(-0.930739\pi\)
0.675166 + 0.737666i \(0.264072\pi\)
\(84\) 0 0
\(85\) −3.00000 5.19615i −0.325396 0.563602i
\(86\) 9.11684 0.983095
\(87\) 0 0
\(88\) −4.37228 −0.466087
\(89\) 1.62772 2.81929i 0.172538 0.298844i −0.766769 0.641924i \(-0.778137\pi\)
0.939306 + 0.343079i \(0.111470\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −3.68614 + 6.38458i −0.384307 + 0.665639i
\(93\) 0 0
\(94\) 0 0
\(95\) −3.43070 + 5.94215i −0.351983 + 0.609652i
\(96\) 0 0
\(97\) −4.55842 + 7.89542i −0.462838 + 0.801658i −0.999101 0.0423924i \(-0.986502\pi\)
0.536263 + 0.844051i \(0.319835\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 1.55842 2.69927i 0.155842 0.269927i
\(101\) −7.37228 −0.733569 −0.366785 0.930306i \(-0.619541\pi\)
−0.366785 + 0.930306i \(0.619541\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) −1.00000 1.73205i −0.0980581 0.169842i
\(105\) 0 0
\(106\) 1.37228 2.37686i 0.133288 0.230861i
\(107\) −0.813859 + 1.40965i −0.0786788 + 0.136276i −0.902680 0.430312i \(-0.858403\pi\)
0.824001 + 0.566588i \(0.191737\pi\)
\(108\) 0 0
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) 3.00000 + 5.19615i 0.286039 + 0.495434i
\(111\) 0 0
\(112\) 0 0
\(113\) 0.686141 + 1.18843i 0.0645467 + 0.111798i 0.896493 0.443058i \(-0.146107\pi\)
−0.831946 + 0.554856i \(0.812773\pi\)
\(114\) 0 0
\(115\) 10.1168 0.943401
\(116\) 1.37228 + 2.37686i 0.127413 + 0.220686i
\(117\) 0 0
\(118\) −7.11684 −0.655159
\(119\) 0 0
\(120\) 0 0
\(121\) 8.11684 0.737895
\(122\) 7.05842 12.2255i 0.639040 1.10685i
\(123\) 0 0
\(124\) −1.00000 1.73205i −0.0898027 0.155543i
\(125\) −11.1386 −0.996266
\(126\) 0 0
\(127\) −14.1168 −1.25267 −0.626334 0.779555i \(-0.715445\pi\)
−0.626334 + 0.779555i \(0.715445\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −1.37228 + 2.37686i −0.120357 + 0.208464i
\(131\) 7.37228 0.644119 0.322060 0.946719i \(-0.395625\pi\)
0.322060 + 0.946719i \(0.395625\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 15.1168 1.30590
\(135\) 0 0
\(136\) −2.18614 3.78651i −0.187460 0.324690i
\(137\) −16.3723 −1.39878 −0.699389 0.714741i \(-0.746545\pi\)
−0.699389 + 0.714741i \(0.746545\pi\)
\(138\) 0 0
\(139\) 10.6168 + 18.3889i 0.900509 + 1.55973i 0.826835 + 0.562445i \(0.190139\pi\)
0.0736742 + 0.997282i \(0.476528\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 5.05842 + 8.76144i 0.424493 + 0.735244i
\(143\) 4.37228 + 7.57301i 0.365629 + 0.633287i
\(144\) 0 0
\(145\) 1.88316 3.26172i 0.156388 0.270871i
\(146\) 2.55842 4.43132i 0.211737 0.366738i
\(147\) 0 0
\(148\) −1.00000 1.73205i −0.0821995 0.142374i
\(149\) −14.7446 −1.20792 −0.603961 0.797014i \(-0.706412\pi\)
−0.603961 + 0.797014i \(0.706412\pi\)
\(150\) 0 0
\(151\) −8.11684 −0.660539 −0.330270 0.943887i \(-0.607140\pi\)
−0.330270 + 0.943887i \(0.607140\pi\)
\(152\) −2.50000 + 4.33013i −0.202777 + 0.351220i
\(153\) 0 0
\(154\) 0 0
\(155\) −1.37228 + 2.37686i −0.110224 + 0.190914i
\(156\) 0 0
\(157\) 4.05842 7.02939i 0.323897 0.561007i −0.657391 0.753549i \(-0.728340\pi\)
0.981289 + 0.192543i \(0.0616734\pi\)
\(158\) −6.05842 + 10.4935i −0.481982 + 0.834818i
\(159\) 0 0
\(160\) −0.686141 + 1.18843i −0.0542442 + 0.0939537i
\(161\) 0 0
\(162\) 0 0
\(163\) −8.11684 + 14.0588i −0.635760 + 1.10117i 0.350593 + 0.936528i \(0.385980\pi\)
−0.986354 + 0.164641i \(0.947353\pi\)
\(164\) −10.3723 −0.809939
\(165\) 0 0
\(166\) 5.48913 0.426039
\(167\) 8.74456 + 15.1460i 0.676675 + 1.17203i 0.975976 + 0.217876i \(0.0699129\pi\)
−0.299302 + 0.954158i \(0.596754\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) −3.00000 + 5.19615i −0.230089 + 0.398527i
\(171\) 0 0
\(172\) −4.55842 7.89542i −0.347576 0.602020i
\(173\) −3.00000 5.19615i −0.228086 0.395056i 0.729155 0.684349i \(-0.239913\pi\)
−0.957241 + 0.289292i \(0.906580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.18614 + 3.78651i 0.164787 + 0.285419i
\(177\) 0 0
\(178\) −3.25544 −0.244005
\(179\) 7.37228 + 12.7692i 0.551030 + 0.954412i 0.998201 + 0.0599635i \(0.0190984\pi\)
−0.447170 + 0.894449i \(0.647568\pi\)
\(180\) 0 0
\(181\) 18.1168 1.34661 0.673307 0.739363i \(-0.264873\pi\)
0.673307 + 0.739363i \(0.264873\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 7.37228 0.543492
\(185\) −1.37228 + 2.37686i −0.100892 + 0.174750i
\(186\) 0 0
\(187\) 9.55842 + 16.5557i 0.698981 + 1.21067i
\(188\) 0 0
\(189\) 0 0
\(190\) 6.86141 0.497779
\(191\) −0.941578 1.63086i −0.0681302 0.118005i 0.829948 0.557841i \(-0.188370\pi\)
−0.898078 + 0.439836i \(0.855037\pi\)
\(192\) 0 0
\(193\) 3.50000 6.06218i 0.251936 0.436365i −0.712123 0.702055i \(-0.752266\pi\)
0.964059 + 0.265689i \(0.0855996\pi\)
\(194\) 9.11684 0.654551
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 5.00000 + 8.66025i 0.354441 + 0.613909i 0.987022 0.160585i \(-0.0513380\pi\)
−0.632581 + 0.774494i \(0.718005\pi\)
\(200\) −3.11684 −0.220394
\(201\) 0 0
\(202\) 3.68614 + 6.38458i 0.259356 + 0.449218i
\(203\) 0 0
\(204\) 0 0
\(205\) 7.11684 + 12.3267i 0.497062 + 0.860937i
\(206\) 5.00000 + 8.66025i 0.348367 + 0.603388i
\(207\) 0 0
\(208\) −1.00000 + 1.73205i −0.0693375 + 0.120096i
\(209\) 10.9307 18.9325i 0.756093 1.30959i
\(210\) 0 0
\(211\) 8.00000 + 13.8564i 0.550743 + 0.953914i 0.998221 + 0.0596196i \(0.0189888\pi\)
−0.447478 + 0.894295i \(0.647678\pi\)
\(212\) −2.74456 −0.188497
\(213\) 0 0
\(214\) 1.62772 0.111269
\(215\) −6.25544 + 10.8347i −0.426617 + 0.738923i
\(216\) 0 0
\(217\) 0 0
\(218\) −7.00000 + 12.1244i −0.474100 + 0.821165i
\(219\) 0 0
\(220\) 3.00000 5.19615i 0.202260 0.350325i
\(221\) −4.37228 + 7.57301i −0.294111 + 0.509416i
\(222\) 0 0
\(223\) 2.00000 3.46410i 0.133930 0.231973i −0.791258 0.611482i \(-0.790574\pi\)
0.925188 + 0.379509i \(0.123907\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0.686141 1.18843i 0.0456414 0.0790532i
\(227\) 23.7446 1.57598 0.787991 0.615687i \(-0.211121\pi\)
0.787991 + 0.615687i \(0.211121\pi\)
\(228\) 0 0
\(229\) −20.1168 −1.32936 −0.664679 0.747129i \(-0.731432\pi\)
−0.664679 + 0.747129i \(0.731432\pi\)
\(230\) −5.05842 8.76144i −0.333542 0.577713i
\(231\) 0 0
\(232\) 1.37228 2.37686i 0.0900947 0.156049i
\(233\) −5.87228 + 10.1711i −0.384706 + 0.666330i −0.991728 0.128354i \(-0.959030\pi\)
0.607022 + 0.794685i \(0.292364\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 3.55842 + 6.16337i 0.231634 + 0.401201i
\(237\) 0 0
\(238\) 0 0
\(239\) −9.43070 16.3345i −0.610021 1.05659i −0.991236 0.132102i \(-0.957827\pi\)
0.381215 0.924487i \(-0.375506\pi\)
\(240\) 0 0
\(241\) 0.883156 0.0568891 0.0284445 0.999595i \(-0.490945\pi\)
0.0284445 + 0.999595i \(0.490945\pi\)
\(242\) −4.05842 7.02939i −0.260885 0.451867i
\(243\) 0 0
\(244\) −14.1168 −0.903738
\(245\) 0 0
\(246\) 0 0
\(247\) 10.0000 0.636285
\(248\) −1.00000 + 1.73205i −0.0635001 + 0.109985i
\(249\) 0 0
\(250\) 5.56930 + 9.64630i 0.352233 + 0.610086i
\(251\) 9.00000 0.568075 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(252\) 0 0
\(253\) −32.2337 −2.02651
\(254\) 7.05842 + 12.2255i 0.442885 + 0.767099i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −21.8614 −1.36368 −0.681839 0.731503i \(-0.738819\pi\)
−0.681839 + 0.731503i \(0.738819\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.74456 0.170211
\(261\) 0 0
\(262\) −3.68614 6.38458i −0.227731 0.394441i
\(263\) −13.3723 −0.824570 −0.412285 0.911055i \(-0.635269\pi\)
−0.412285 + 0.911055i \(0.635269\pi\)
\(264\) 0 0
\(265\) 1.88316 + 3.26172i 0.115681 + 0.200366i
\(266\) 0 0
\(267\) 0 0
\(268\) −7.55842 13.0916i −0.461704 0.799695i
\(269\) −3.68614 6.38458i −0.224748 0.389275i 0.731496 0.681846i \(-0.238823\pi\)
−0.956244 + 0.292571i \(0.905489\pi\)
\(270\) 0 0
\(271\) 9.11684 15.7908i 0.553809 0.959225i −0.444186 0.895934i \(-0.646507\pi\)
0.997995 0.0632906i \(-0.0201595\pi\)
\(272\) −2.18614 + 3.78651i −0.132554 + 0.229591i
\(273\) 0 0
\(274\) 8.18614 + 14.1788i 0.494543 + 0.856573i
\(275\) 13.6277 0.821782
\(276\) 0 0
\(277\) 22.2337 1.33589 0.667946 0.744209i \(-0.267174\pi\)
0.667946 + 0.744209i \(0.267174\pi\)
\(278\) 10.6168 18.3889i 0.636756 1.10289i
\(279\) 0 0
\(280\) 0 0
\(281\) 5.31386 9.20387i 0.316998 0.549057i −0.662862 0.748742i \(-0.730658\pi\)
0.979860 + 0.199685i \(0.0639917\pi\)
\(282\) 0 0
\(283\) −4.94158 + 8.55906i −0.293746 + 0.508784i −0.974692 0.223550i \(-0.928235\pi\)
0.680946 + 0.732333i \(0.261569\pi\)
\(284\) 5.05842 8.76144i 0.300162 0.519896i
\(285\) 0 0
\(286\) 4.37228 7.57301i 0.258538 0.447802i
\(287\) 0 0
\(288\) 0 0
\(289\) −1.05842 + 1.83324i −0.0622601 + 0.107838i
\(290\) −3.76631 −0.221165
\(291\) 0 0
\(292\) −5.11684 −0.299441
\(293\) −2.31386 4.00772i −0.135177 0.234134i 0.790488 0.612478i \(-0.209827\pi\)
−0.925665 + 0.378344i \(0.876494\pi\)
\(294\) 0 0
\(295\) 4.88316 8.45787i 0.284308 0.492436i
\(296\) −1.00000 + 1.73205i −0.0581238 + 0.100673i
\(297\) 0 0
\(298\) 7.37228 + 12.7692i 0.427065 + 0.739698i
\(299\) −7.37228 12.7692i −0.426350 0.738460i
\(300\) 0 0
\(301\) 0 0
\(302\) 4.05842 + 7.02939i 0.233536 + 0.404496i
\(303\) 0 0
\(304\) 5.00000 0.286770
\(305\) 9.68614 + 16.7769i 0.554627 + 0.960642i
\(306\) 0 0
\(307\) −13.0000 −0.741949 −0.370975 0.928643i \(-0.620976\pi\)
−0.370975 + 0.928643i \(0.620976\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 2.74456 0.155881
\(311\) −13.1168 + 22.7190i −0.743788 + 1.28828i 0.206971 + 0.978347i \(0.433639\pi\)
−0.950759 + 0.309931i \(0.899694\pi\)
\(312\) 0 0
\(313\) 1.44158 + 2.49689i 0.0814828 + 0.141132i 0.903887 0.427771i \(-0.140701\pi\)
−0.822404 + 0.568904i \(0.807368\pi\)
\(314\) −8.11684 −0.458060
\(315\) 0 0
\(316\) 12.1168 0.681626
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 0 0
\(319\) −6.00000 + 10.3923i −0.335936 + 0.581857i
\(320\) 1.37228 0.0767129
\(321\) 0 0
\(322\) 0 0
\(323\) 21.8614 1.21640
\(324\) 0 0
\(325\) 3.11684 + 5.39853i 0.172891 + 0.299457i
\(326\) 16.2337 0.899101
\(327\) 0 0
\(328\) 5.18614 + 8.98266i 0.286357 + 0.495984i
\(329\) 0 0
\(330\) 0 0
\(331\) 6.11684 + 10.5947i 0.336212 + 0.582337i 0.983717 0.179725i \(-0.0575207\pi\)
−0.647505 + 0.762061i \(0.724187\pi\)
\(332\) −2.74456 4.75372i −0.150627 0.260894i
\(333\) 0 0
\(334\) 8.74456 15.1460i 0.478481 0.828754i
\(335\) −10.3723 + 17.9653i −0.566698 + 0.981550i
\(336\) 0 0
\(337\) −4.55842 7.89542i −0.248313 0.430091i 0.714745 0.699385i \(-0.246543\pi\)
−0.963058 + 0.269294i \(0.913210\pi\)
\(338\) −9.00000 −0.489535
\(339\) 0 0
\(340\) 6.00000 0.325396
\(341\) 4.37228 7.57301i 0.236772 0.410102i
\(342\) 0 0
\(343\) 0 0
\(344\) −4.55842 + 7.89542i −0.245774 + 0.425692i
\(345\) 0 0
\(346\) −3.00000 + 5.19615i −0.161281 + 0.279347i
\(347\) 3.55842 6.16337i 0.191026 0.330867i −0.754564 0.656226i \(-0.772152\pi\)
0.945591 + 0.325359i \(0.105485\pi\)
\(348\) 0 0
\(349\) 11.0000 19.0526i 0.588817 1.01986i −0.405571 0.914063i \(-0.632927\pi\)
0.994388 0.105797i \(-0.0337393\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 2.18614 3.78651i 0.116522 0.201821i
\(353\) 7.62772 0.405983 0.202991 0.979181i \(-0.434934\pi\)
0.202991 + 0.979181i \(0.434934\pi\)
\(354\) 0 0
\(355\) −13.8832 −0.736841
\(356\) 1.62772 + 2.81929i 0.0862689 + 0.149422i
\(357\) 0 0
\(358\) 7.37228 12.7692i 0.389637 0.674871i
\(359\) −3.43070 + 5.94215i −0.181066 + 0.313615i −0.942244 0.334928i \(-0.891288\pi\)
0.761178 + 0.648543i \(0.224621\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) −9.05842 15.6896i −0.476100 0.824630i
\(363\) 0 0
\(364\) 0 0
\(365\) 3.51087 + 6.08101i 0.183768 + 0.318295i
\(366\) 0 0
\(367\) 22.2337 1.16059 0.580295 0.814407i \(-0.302937\pi\)
0.580295 + 0.814407i \(0.302937\pi\)
\(368\) −3.68614 6.38458i −0.192153 0.332819i
\(369\) 0 0
\(370\) 2.74456 0.142683
\(371\) 0 0
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 9.55842 16.5557i 0.494254 0.856073i
\(375\) 0 0
\(376\) 0 0
\(377\) −5.48913 −0.282704
\(378\) 0 0
\(379\) 9.11684 0.468301 0.234150 0.972200i \(-0.424769\pi\)
0.234150 + 0.972200i \(0.424769\pi\)
\(380\) −3.43070 5.94215i −0.175991 0.304826i
\(381\) 0 0
\(382\) −0.941578 + 1.63086i −0.0481753 + 0.0834421i
\(383\) 21.2554 1.08610 0.543051 0.839700i \(-0.317269\pi\)
0.543051 + 0.839700i \(0.317269\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −7.00000 −0.356291
\(387\) 0 0
\(388\) −4.55842 7.89542i −0.231419 0.400829i
\(389\) 34.9783 1.77347 0.886734 0.462280i \(-0.152969\pi\)
0.886734 + 0.462280i \(0.152969\pi\)
\(390\) 0 0
\(391\) −16.1168 27.9152i −0.815064 1.41173i
\(392\) 0 0
\(393\) 0 0
\(394\) −3.00000 5.19615i −0.151138 0.261778i
\(395\) −8.31386 14.4000i −0.418316 0.724544i
\(396\) 0 0
\(397\) 11.0000 19.0526i 0.552074 0.956221i −0.446051 0.895008i \(-0.647170\pi\)
0.998125 0.0612128i \(-0.0194968\pi\)
\(398\) 5.00000 8.66025i 0.250627 0.434099i
\(399\) 0 0
\(400\) 1.55842 + 2.69927i 0.0779211 + 0.134963i
\(401\) 0.255437 0.0127559 0.00637797 0.999980i \(-0.497970\pi\)
0.00637797 + 0.999980i \(0.497970\pi\)
\(402\) 0 0
\(403\) 4.00000 0.199254
\(404\) 3.68614 6.38458i 0.183392 0.317645i
\(405\) 0 0
\(406\) 0 0
\(407\) 4.37228 7.57301i 0.216726 0.375380i
\(408\) 0 0
\(409\) −14.6753 + 25.4183i −0.725645 + 1.25685i 0.233063 + 0.972462i \(0.425125\pi\)
−0.958708 + 0.284393i \(0.908208\pi\)
\(410\) 7.11684 12.3267i 0.351476 0.608774i
\(411\) 0 0
\(412\) 5.00000 8.66025i 0.246332 0.426660i
\(413\) 0 0
\(414\) 0 0
\(415\) −3.76631 + 6.52344i −0.184881 + 0.320223i
\(416\) 2.00000 0.0980581
\(417\) 0 0
\(418\) −21.8614 −1.06928
\(419\) 13.8030 + 23.9075i 0.674320 + 1.16796i 0.976667 + 0.214759i \(0.0688964\pi\)
−0.302347 + 0.953198i \(0.597770\pi\)
\(420\) 0 0
\(421\) 0.116844 0.202380i 0.00569463 0.00986338i −0.863164 0.504924i \(-0.831521\pi\)
0.868859 + 0.495060i \(0.164854\pi\)
\(422\) 8.00000 13.8564i 0.389434 0.674519i
\(423\) 0 0
\(424\) 1.37228 + 2.37686i 0.0666439 + 0.115431i
\(425\) 6.81386 + 11.8020i 0.330521 + 0.572479i
\(426\) 0 0
\(427\) 0 0
\(428\) −0.813859 1.40965i −0.0393394 0.0681378i
\(429\) 0 0
\(430\) 12.5109 0.603328
\(431\) −14.7446 25.5383i −0.710221 1.23014i −0.964774 0.263079i \(-0.915262\pi\)
0.254554 0.967059i \(-0.418071\pi\)
\(432\) 0 0
\(433\) −2.88316 −0.138556 −0.0692778 0.997597i \(-0.522069\pi\)
−0.0692778 + 0.997597i \(0.522069\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 14.0000 0.670478
\(437\) −18.4307 + 31.9229i −0.881660 + 1.52708i
\(438\) 0 0
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) 8.74456 0.415936
\(443\) −11.4416 19.8174i −0.543606 0.941553i −0.998693 0.0511061i \(-0.983725\pi\)
0.455087 0.890447i \(-0.349608\pi\)
\(444\) 0 0
\(445\) 2.23369 3.86886i 0.105887 0.183402i
\(446\) −4.00000 −0.189405
\(447\) 0 0
\(448\) 0 0
\(449\) −33.0000 −1.55737 −0.778683 0.627417i \(-0.784112\pi\)
−0.778683 + 0.627417i \(0.784112\pi\)
\(450\) 0 0
\(451\) −22.6753 39.2747i −1.06774 1.84937i
\(452\) −1.37228 −0.0645467
\(453\) 0 0
\(454\) −11.8723 20.5634i −0.557194 0.965088i
\(455\) 0 0
\(456\) 0 0
\(457\) −16.7337 28.9836i −0.782769 1.35580i −0.930323 0.366742i \(-0.880473\pi\)
0.147554 0.989054i \(-0.452860\pi\)
\(458\) 10.0584 + 17.4217i 0.469999 + 0.814062i
\(459\) 0 0
\(460\) −5.05842 + 8.76144i −0.235850 + 0.408504i
\(461\) 15.4307 26.7268i 0.718680 1.24479i −0.242844 0.970065i \(-0.578080\pi\)
0.961523 0.274724i \(-0.0885865\pi\)
\(462\) 0 0
\(463\) 2.94158 + 5.09496i 0.136707 + 0.236783i 0.926248 0.376914i \(-0.123015\pi\)
−0.789541 + 0.613697i \(0.789682\pi\)
\(464\) −2.74456 −0.127413
\(465\) 0 0
\(466\) 11.7446 0.544056
\(467\) −15.0475 + 26.0631i −0.696317 + 1.20606i 0.273417 + 0.961896i \(0.411846\pi\)
−0.969735 + 0.244162i \(0.921487\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 3.55842 6.16337i 0.163790 0.283692i
\(473\) 19.9307 34.5210i 0.916415 1.58728i
\(474\) 0 0
\(475\) 7.79211 13.4963i 0.357527 0.619254i
\(476\) 0 0
\(477\) 0 0
\(478\) −9.43070 + 16.3345i −0.431350 + 0.747121i
\(479\) −21.2554 −0.971186 −0.485593 0.874185i \(-0.661396\pi\)
−0.485593 + 0.874185i \(0.661396\pi\)
\(480\) 0 0
\(481\) 4.00000 0.182384
\(482\) −0.441578 0.764836i −0.0201133 0.0348373i
\(483\) 0 0
\(484\) −4.05842 + 7.02939i −0.184474 + 0.319518i
\(485\) −6.25544 + 10.8347i −0.284045 + 0.491980i
\(486\) 0 0
\(487\) 8.17527 + 14.1600i 0.370457 + 0.641650i 0.989636 0.143600i \(-0.0458679\pi\)
−0.619179 + 0.785250i \(0.712535\pi\)
\(488\) 7.05842 + 12.2255i 0.319520 + 0.553424i
\(489\) 0 0
\(490\) 0 0
\(491\) −9.81386 16.9981i −0.442893 0.767114i 0.555010 0.831844i \(-0.312715\pi\)
−0.997903 + 0.0647303i \(0.979381\pi\)
\(492\) 0 0
\(493\) −12.0000 −0.540453
\(494\) −5.00000 8.66025i −0.224961 0.389643i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) 0.883156 0.0395355 0.0197677 0.999805i \(-0.493707\pi\)
0.0197677 + 0.999805i \(0.493707\pi\)
\(500\) 5.56930 9.64630i 0.249067 0.431396i
\(501\) 0 0
\(502\) −4.50000 7.79423i −0.200845 0.347873i
\(503\) −2.23369 −0.0995952 −0.0497976 0.998759i \(-0.515858\pi\)
−0.0497976 + 0.998759i \(0.515858\pi\)
\(504\) 0 0
\(505\) −10.1168 −0.450194
\(506\) 16.1168 + 27.9152i 0.716481 + 1.24098i
\(507\) 0 0
\(508\) 7.05842 12.2255i 0.313167 0.542421i
\(509\) −16.9783 −0.752548 −0.376274 0.926508i \(-0.622795\pi\)
−0.376274 + 0.926508i \(0.622795\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 10.9307 + 18.9325i 0.482133 + 0.835078i
\(515\) −13.7228 −0.604699
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −1.37228 2.37686i −0.0601785 0.104232i
\(521\) 1.93070 + 3.34408i 0.0845856 + 0.146507i 0.905215 0.424955i \(-0.139710\pi\)
−0.820629 + 0.571461i \(0.806377\pi\)
\(522\) 0 0
\(523\) 8.94158 15.4873i 0.390988 0.677211i −0.601592 0.798803i \(-0.705467\pi\)
0.992580 + 0.121592i \(0.0388001\pi\)
\(524\) −3.68614 + 6.38458i −0.161030 + 0.278912i
\(525\) 0 0
\(526\) 6.68614 + 11.5807i 0.291530 + 0.504944i
\(527\) 8.74456 0.380919
\(528\) 0 0
\(529\) 31.3505 1.36307
\(530\) 1.88316 3.26172i 0.0817991 0.141680i
\(531\) 0 0
\(532\) 0 0
\(533\) 10.3723 17.9653i 0.449273 0.778164i
\(534\) 0 0
\(535\) −1.11684 + 1.93443i −0.0482854 + 0.0836327i
\(536\) −7.55842 + 13.0916i −0.326474 + 0.565470i
\(537\) 0 0
\(538\) −3.68614 + 6.38458i −0.158921 + 0.275259i
\(539\) 0 0
\(540\) 0 0
\(541\) −14.1168 + 24.4511i −0.606931 + 1.05123i 0.384813 + 0.922995i \(0.374266\pi\)
−0.991743 + 0.128240i \(0.959067\pi\)
\(542\) −18.2337 −0.783204
\(543\) 0 0
\(544\) 4.37228 0.187460
\(545\) −9.60597 16.6380i −0.411475 0.712695i
\(546\) 0 0
\(547\) −0.441578 + 0.764836i −0.0188805 + 0.0327020i −0.875311 0.483560i \(-0.839344\pi\)
0.856431 + 0.516262i \(0.172677\pi\)
\(548\) 8.18614 14.1788i 0.349695 0.605689i
\(549\) 0 0
\(550\) −6.81386 11.8020i −0.290544 0.503237i
\(551\) 6.86141 + 11.8843i 0.292306 + 0.506288i
\(552\) 0 0
\(553\) 0 0
\(554\) −11.1168 19.2549i −0.472309 0.818064i
\(555\) 0 0
\(556\) −21.2337 −0.900509
\(557\) 3.25544 + 5.63858i 0.137937 + 0.238914i 0.926716 0.375763i \(-0.122619\pi\)
−0.788778 + 0.614678i \(0.789286\pi\)
\(558\) 0 0
\(559\) 18.2337 0.771203
\(560\) 0 0
\(561\) 0 0
\(562\) −10.6277 −0.448303
\(563\) 1.50000 2.59808i 0.0632175 0.109496i −0.832684 0.553748i \(-0.813197\pi\)
0.895902 + 0.444252i \(0.146530\pi\)
\(564\) 0 0
\(565\) 0.941578 + 1.63086i 0.0396125 + 0.0686108i
\(566\) 9.88316 0.415420
\(567\) 0 0
\(568\) −10.1168 −0.424493
\(569\) −0.558422 0.967215i −0.0234103 0.0405478i 0.854083 0.520137i \(-0.174119\pi\)
−0.877493 + 0.479589i \(0.840786\pi\)
\(570\) 0 0
\(571\) −14.6753 + 25.4183i −0.614141 + 1.06372i 0.376394 + 0.926460i \(0.377164\pi\)
−0.990535 + 0.137263i \(0.956169\pi\)
\(572\) −8.74456 −0.365629
\(573\) 0 0
\(574\) 0 0
\(575\) −22.9783 −0.958259
\(576\) 0 0
\(577\) −13.5584 23.4839i −0.564444 0.977647i −0.997101 0.0760878i \(-0.975757\pi\)
0.432657 0.901559i \(-0.357576\pi\)
\(578\) 2.11684 0.0880491
\(579\) 0 0
\(580\) 1.88316 + 3.26172i 0.0781938 + 0.135436i
\(581\) 0 0
\(582\) 0 0
\(583\) −6.00000 10.3923i −0.248495 0.430405i
\(584\) 2.55842 + 4.43132i 0.105868 + 0.183369i
\(585\) 0 0
\(586\) −2.31386 + 4.00772i −0.0955846 + 0.165557i
\(587\) −4.24456 + 7.35180i −0.175192 + 0.303441i −0.940228 0.340547i \(-0.889388\pi\)
0.765036 + 0.643988i \(0.222721\pi\)
\(588\) 0 0
\(589\) −5.00000 8.66025i −0.206021 0.356840i
\(590\) −9.76631 −0.402073
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) 1.62772 2.81929i 0.0668424 0.115774i −0.830667 0.556769i \(-0.812041\pi\)
0.897510 + 0.440995i \(0.145374\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 7.37228 12.7692i 0.301980 0.523045i
\(597\) 0 0
\(598\) −7.37228 + 12.7692i −0.301475 + 0.522170i
\(599\) 12.0000 20.7846i 0.490307 0.849236i −0.509631 0.860393i \(-0.670218\pi\)
0.999938 + 0.0111569i \(0.00355143\pi\)
\(600\) 0 0
\(601\) −3.44158 + 5.96099i −0.140385 + 0.243154i −0.927642 0.373472i \(-0.878167\pi\)
0.787257 + 0.616625i \(0.211501\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4.05842 7.02939i 0.165135 0.286022i
\(605\) 11.1386 0.452848
\(606\) 0 0
\(607\) −12.2337 −0.496550 −0.248275 0.968690i \(-0.579864\pi\)
−0.248275 + 0.968690i \(0.579864\pi\)
\(608\) −2.50000 4.33013i −0.101388 0.175610i
\(609\) 0 0
\(610\) 9.68614 16.7769i 0.392180 0.679276i
\(611\) 0 0
\(612\) 0 0
\(613\) 0.883156 + 1.52967i 0.0356703 + 0.0617828i 0.883309 0.468790i \(-0.155310\pi\)
−0.847639 + 0.530573i \(0.821977\pi\)
\(614\) 6.50000 + 11.2583i 0.262319 + 0.454349i
\(615\) 0 0
\(616\) 0 0
\(617\) −4.93070 8.54023i −0.198503 0.343817i 0.749540 0.661959i \(-0.230275\pi\)
−0.948043 + 0.318142i \(0.896941\pi\)
\(618\) 0 0
\(619\) −23.4674 −0.943233 −0.471617 0.881804i \(-0.656329\pi\)
−0.471617 + 0.881804i \(0.656329\pi\)
\(620\) −1.37228 2.37686i −0.0551121 0.0954570i
\(621\) 0 0
\(622\) 26.2337 1.05188
\(623\) 0 0
\(624\) 0 0
\(625\) 0.298936 0.0119574
\(626\) 1.44158 2.49689i 0.0576170 0.0997956i
\(627\) 0 0
\(628\) 4.05842 + 7.02939i 0.161949 + 0.280503i
\(629\) 8.74456 0.348669
\(630\) 0 0
\(631\) 14.3505 0.571286 0.285643 0.958336i \(-0.407793\pi\)
0.285643 + 0.958336i \(0.407793\pi\)
\(632\) −6.05842 10.4935i −0.240991 0.417409i
\(633\) 0 0
\(634\) −3.00000 + 5.19615i −0.119145 + 0.206366i
\(635\) −19.3723 −0.768766
\(636\) 0 0
\(637\) 0 0
\(638\) 12.0000 0.475085
\(639\) 0 0
\(640\) −0.686141 1.18843i −0.0271221 0.0469768i
\(641\) 46.2119 1.82526 0.912631 0.408785i \(-0.134047\pi\)
0.912631 + 0.408785i \(0.134047\pi\)
\(642\) 0 0
\(643\) 12.6753 + 21.9542i 0.499864 + 0.865789i 1.00000 0.000157386i \(-5.00974e-5\pi\)
−0.500136 + 0.865947i \(0.666717\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −10.9307 18.9325i −0.430063 0.744891i
\(647\) −8.74456 15.1460i −0.343784 0.595452i 0.641348 0.767250i \(-0.278376\pi\)
−0.985132 + 0.171798i \(0.945042\pi\)
\(648\) 0 0
\(649\) −15.5584 + 26.9480i −0.610721 + 1.05780i
\(650\) 3.11684 5.39853i 0.122253 0.211748i
\(651\) 0 0
\(652\) −8.11684 14.0588i −0.317880 0.550585i
\(653\) 15.2554 0.596991 0.298496 0.954411i \(-0.403515\pi\)
0.298496 + 0.954411i \(0.403515\pi\)
\(654\) 0 0
\(655\) 10.1168 0.395298
\(656\) 5.18614 8.98266i 0.202485 0.350714i
\(657\) 0 0
\(658\) 0 0
\(659\) −4.62772 + 8.01544i −0.180270 + 0.312237i −0.941973 0.335690i \(-0.891031\pi\)
0.761702 + 0.647927i \(0.224364\pi\)
\(660\) 0 0
\(661\) −4.94158 + 8.55906i −0.192205 + 0.332909i −0.945981 0.324223i \(-0.894897\pi\)
0.753776 + 0.657132i \(0.228231\pi\)
\(662\) 6.11684 10.5947i 0.237738 0.411774i
\(663\) 0 0
\(664\) −2.74456 + 4.75372i −0.106510 + 0.184480i
\(665\) 0 0
\(666\) 0 0
\(667\) 10.1168 17.5229i 0.391726 0.678489i
\(668\) −17.4891 −0.676675
\(669\) 0 0
\(670\) 20.7446 0.801432
\(671\) −30.8614 53.4535i −1.19139 2.06355i
\(672\) 0 0
\(673\) 10.0584 17.4217i 0.387724 0.671557i −0.604419 0.796666i \(-0.706595\pi\)
0.992143 + 0.125109i \(0.0399281\pi\)
\(674\) −4.55842 + 7.89542i −0.175584 + 0.304120i
\(675\) 0 0
\(676\) 4.50000 + 7.79423i 0.173077 + 0.299778i
\(677\) −17.2337 29.8496i −0.662344 1.14721i −0.979998 0.199007i \(-0.936228\pi\)
0.317654 0.948207i \(-0.397105\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.00000 5.19615i −0.115045 0.199263i
\(681\) 0 0
\(682\) −8.74456 −0.334847
\(683\) −22.4198 38.8323i −0.857871 1.48588i −0.873956 0.486005i \(-0.838454\pi\)
0.0160849 0.999871i \(-0.494880\pi\)
\(684\) 0 0
\(685\) −22.4674 −0.858434
\(686\) 0 0
\(687\) 0 0
\(688\) 9.11684 0.347576
\(689\) 2.74456 4.75372i 0.104560 0.181102i
\(690\) 0 0
\(691\) 2.94158 + 5.09496i 0.111903 + 0.193822i 0.916537 0.399949i \(-0.130972\pi\)
−0.804635 + 0.593770i \(0.797639\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −7.11684 −0.270152
\(695\) 14.5693 + 25.2348i 0.552645 + 0.957209i
\(696\) 0 0
\(697\) 22.6753 39.2747i 0.858887 1.48764i
\(698\) −22.0000 −0.832712
\(699\) 0 0
\(700\) 0 0
\(701\) 3.76631 0.142252 0.0711258 0.997467i \(-0.477341\pi\)
0.0711258 + 0.997467i \(0.477341\pi\)
\(702\) 0 0
\(703\) −5.00000 8.66025i −0.188579 0.326628i
\(704\) −4.37228 −0.164787
\(705\) 0 0
\(706\) −3.81386 6.60580i −0.143536 0.248612i
\(707\) 0 0
\(708\) 0 0
\(709\) −22.0000 38.1051i −0.826227 1.43107i −0.900978 0.433865i \(-0.857149\pi\)
0.0747503 0.997202i \(-0.476184\pi\)
\(710\) 6.94158 + 12.0232i 0.260513 + 0.451221i
\(711\) 0 0
\(712\) 1.62772 2.81929i 0.0610013 0.105657i
\(713\) −7.37228 + 12.7692i −0.276094 + 0.478209i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) −14.7446 −0.551030
\(717\) 0 0
\(718\) 6.86141 0.256065
\(719\) −4.37228 + 7.57301i −0.163059 + 0.282426i −0.935964 0.352095i \(-0.885469\pi\)
0.772906 + 0.634521i \(0.218803\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −3.00000 + 5.19615i −0.111648 + 0.193381i
\(723\) 0 0
\(724\) −9.05842 + 15.6896i −0.336654 + 0.583101i
\(725\) −4.27719 + 7.40830i −0.158851 + 0.275138i
\(726\) 0 0
\(727\) 0.883156 1.52967i 0.0327544 0.0567324i −0.849183 0.528098i \(-0.822905\pi\)
0.881938 + 0.471366i \(0.156239\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 3.51087 6.08101i 0.129943 0.225068i
\(731\) 39.8614 1.47433
\(732\) 0 0
\(733\) −23.8832 −0.882144 −0.441072 0.897472i \(-0.645402\pi\)
−0.441072 + 0.897472i \(0.645402\pi\)
\(734\) −11.1168 19.2549i −0.410330 0.710713i
\(735\) 0 0
\(736\) −3.68614 + 6.38458i −0.135873 + 0.235339i
\(737\) 33.0475 57.2400i 1.21732 2.10846i
\(738\) 0 0
\(739\) −4.55842 7.89542i −0.167684 0.290438i 0.769921 0.638139i \(-0.220296\pi\)
−0.937605 + 0.347702i \(0.886962\pi\)
\(740\) −1.37228 2.37686i −0.0504461 0.0873751i
\(741\) 0 0
\(742\) 0 0
\(743\) 21.8614 + 37.8651i 0.802017 + 1.38913i 0.918286 + 0.395917i \(0.129573\pi\)
−0.116269 + 0.993218i \(0.537094\pi\)
\(744\) 0 0
\(745\) −20.2337 −0.741305
\(746\) 5.00000 + 8.66025i 0.183063 + 0.317074i
\(747\) 0 0
\(748\) −19.1168 −0.698981
\(749\) 0 0
\(750\) 0 0
\(751\) 0.116844 0.00426370 0.00213185 0.999998i \(-0.499321\pi\)
0.00213185 + 0.999998i \(0.499321\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 2.74456 + 4.75372i 0.0999511 + 0.173120i
\(755\) −11.1386 −0.405375
\(756\) 0 0
\(757\) 11.7663 0.427654 0.213827 0.976872i \(-0.431407\pi\)
0.213827 + 0.976872i \(0.431407\pi\)
\(758\) −4.55842 7.89542i −0.165569 0.286775i
\(759\) 0 0
\(760\) −3.43070 + 5.94215i −0.124445 + 0.215545i
\(761\) −12.5109 −0.453519 −0.226759 0.973951i \(-0.572813\pi\)
−0.226759 + 0.973951i \(0.572813\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.88316 0.0681302
\(765\) 0 0
\(766\) −10.6277 18.4077i −0.383995 0.665099i
\(767\) −14.2337 −0.513949
\(768\) 0 0
\(769\) 5.00000 + 8.66025i 0.180305 + 0.312297i 0.941984 0.335657i \(-0.108958\pi\)
−0.761680 + 0.647954i \(0.775625\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3.50000 + 6.06218i 0.125968 + 0.218183i
\(773\) −5.56930 9.64630i −0.200314 0.346953i 0.748316 0.663343i \(-0.230863\pi\)
−0.948629 + 0.316389i \(0.897529\pi\)
\(774\) 0 0
\(775\) 3.11684 5.39853i 0.111960 0.193921i
\(776\) −4.55842 + 7.89542i −0.163638 + 0.283429i
\(777\) 0 0
\(778\) −17.4891 30.2921i −0.627016 1.08602i
\(779\) −51.8614 −1.85813
\(780\) 0 0
\(781\) 44.2337 1.58281
\(782\) −16.1168 + 27.9152i −0.576337 + 0.998245i
\(783\) 0 0
\(784\) 0 0
\(785\) 5.56930 9.64630i 0.198777 0.344291i
\(786\) 0 0
\(787\) 2.00000 3.46410i 0.0712923 0.123482i −0.828176 0.560469i \(-0.810621\pi\)
0.899468 + 0.436987i \(0.143954\pi\)
\(788\) −3.00000 + 5.19615i −0.106871 + 0.185105i
\(789\) 0 0
\(790\) −8.31386 + 14.4000i −0.295794 + 0.512330i
\(791\) 0 0
\(792\) 0 0
\(793\) 14.1168 24.4511i 0.501304 0.868284i
\(794\) −22.0000 −0.780751