Properties

Label 2646.2.h.k.361.2
Level $2646$
Weight $2$
Character 2646.361
Analytic conductor $21.128$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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 361.2
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 2646.361
Dual form 2646.2.h.k.667.2

$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

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

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 −0.970725 0.240192i \(-0.922790\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −2.18614 + 3.78651i −0.530217 + 0.918363i 0.469162 + 0.883112i \(0.344556\pi\)
−0.999379 + 0.0352504i \(0.988777\pi\)
\(18\) 0 0
\(19\) −2.50000 4.33013i −0.573539 0.993399i −0.996199 0.0871106i \(-0.972237\pi\)
0.422659 0.906289i \(-0.361097\pi\)
\(20\) −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 0.964848 0.262807i \(-0.0846484\pi\)
−0.710022 + 0.704179i \(0.751315\pi\)
\(30\) 0 0
\(31\) −1.00000 1.73205i −0.179605 0.311086i 0.762140 0.647412i \(-0.224149\pi\)
−0.941745 + 0.336327i \(0.890815\pi\)
\(32\) −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 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 5.00000 0.811107
\(39\) 0 0
\(40\) 1.37228 0.216977
\(41\) 5.18614 8.98266i 0.809939 1.40286i −0.102966 0.994685i \(-0.532833\pi\)
0.912906 0.408171i \(-0.133833\pi\)
\(42\) 0 0
\(43\) −4.55842 7.89542i −0.695153 1.20404i −0.970129 0.242589i \(-0.922003\pi\)
0.274976 0.961451i \(-0.411330\pi\)
\(44\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 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 −0.756252 0.654280i \(-0.772972\pi\)
0.944749 + 0.327793i \(0.106305\pi\)
\(54\) 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 0.999121 0.0419083i \(-0.0133437\pi\)
−0.535854 + 0.844310i \(0.680010\pi\)
\(60\) 0 0
\(61\) 7.05842 12.2255i 0.903738 1.56532i 0.0811364 0.996703i \(-0.474145\pi\)
0.822602 0.568618i \(-0.192522\pi\)
\(62\) 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 −0.794101 0.607785i \(-0.792058\pi\)
−0.129307 0.991605i \(-0.541275\pi\)
\(68\) 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 −0.676567 0.736381i \(-0.736533\pi\)
0.976008 + 0.217734i \(0.0698666\pi\)
\(74\) 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 0.292859 + 0.956156i \(0.405393\pi\)
−0.974485 + 0.224455i \(0.927940\pi\)
\(80\) −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 0.675166 0.737666i \(-0.264072\pi\)
−0.976420 + 0.215877i \(0.930739\pi\)
\(84\) 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 0.939306 0.343079i \(-0.111470\pi\)
−0.766769 + 0.641924i \(0.778137\pi\)
\(90\) 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 0.536263 0.844051i \(-0.319835\pi\)
−0.999101 + 0.0423924i \(0.986502\pi\)
\(98\) 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 0.824001 0.566588i \(-0.191737\pi\)
−0.902680 + 0.430312i \(0.858403\pi\)
\(108\) 0 0
\(109\) −7.00000 + 12.1244i −0.670478 + 1.16130i 0.307290 + 0.951616i \(0.400578\pi\)
−0.977769 + 0.209687i \(0.932756\pi\)
\(110\) 3.00000 5.19615i 0.286039 0.495434i
\(111\) 0 0
\(112\) 0 0
\(113\) 0.686141 1.18843i 0.0645467 0.111798i −0.831946 0.554856i \(-0.812773\pi\)
0.896493 + 0.443058i \(0.146107\pi\)
\(114\) 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 0.0736742 0.997282i \(-0.476528\pi\)
0.826835 0.562445i \(-0.190139\pi\)
\(140\) 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 0.981289 0.192543i \(-0.0616734\pi\)
−0.657391 + 0.753549i \(0.728340\pi\)
\(158\) −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 −0.986354 0.164641i \(-0.947353\pi\)
0.350593 0.936528i \(-0.385980\pi\)
\(164\) −10.3723 −0.809939
\(165\) 0 0
\(166\) 5.48913 0.426039
\(167\) 8.74456 15.1460i 0.676675 1.17203i −0.299302 0.954158i \(-0.596754\pi\)
0.975976 0.217876i \(-0.0699129\pi\)
\(168\) 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 −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) 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 −0.447170 0.894449i \(-0.647568\pi\)
0.998201 0.0599635i \(-0.0190984\pi\)
\(180\) 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 −0.898078 0.439836i \(-0.855037\pi\)
0.829948 + 0.557841i \(0.188370\pi\)
\(192\) 0 0
\(193\) 3.50000 + 6.06218i 0.251936 + 0.436365i 0.964059 0.265689i \(-0.0855996\pi\)
−0.712123 + 0.702055i \(0.752266\pi\)
\(194\) 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 −0.632581 0.774494i \(-0.718005\pi\)
0.987022 + 0.160585i \(0.0513380\pi\)
\(200\) −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 −0.447478 0.894295i \(-0.647678\pi\)
0.998221 0.0596196i \(-0.0189888\pi\)
\(212\) −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 0.925188 0.379509i \(-0.123907\pi\)
−0.791258 + 0.611482i \(0.790574\pi\)
\(224\) 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 0.607022 0.794685i \(-0.292364\pi\)
−0.991728 + 0.128354i \(0.959030\pi\)
\(234\) 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 0.381215 + 0.924487i \(0.375506\pi\)
−0.991236 + 0.132102i \(0.957827\pi\)
\(240\) 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 −0.956244 0.292571i \(-0.905489\pi\)
0.731496 + 0.681846i \(0.238823\pi\)
\(270\) 0 0
\(271\) 9.11684 + 15.7908i 0.553809 + 0.959225i 0.997995 + 0.0632906i \(0.0201595\pi\)
−0.444186 + 0.895934i \(0.646507\pi\)
\(272\) −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 0.979860 0.199685i \(-0.0639917\pi\)
−0.662862 + 0.748742i \(0.730658\pi\)
\(282\) 0 0
\(283\) −4.94158 8.55906i −0.293746 0.508784i 0.680946 0.732333i \(-0.261569\pi\)
−0.974692 + 0.223550i \(0.928235\pi\)
\(284\) 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 −0.925665 0.378344i \(-0.876494\pi\)
0.790488 + 0.612478i \(0.209827\pi\)
\(294\) 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 −0.950759 0.309931i \(-0.899694\pi\)
0.206971 0.978347i \(-0.433639\pi\)
\(312\) 0 0
\(313\) 1.44158 2.49689i 0.0814828 0.141132i −0.822404 0.568904i \(-0.807368\pi\)
0.903887 + 0.427771i \(0.140701\pi\)
\(314\) −8.11684 −0.458060
\(315\) 0 0
\(316\) 12.1168 0.681626
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 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 −0.647505 0.762061i \(-0.724187\pi\)
0.983717 + 0.179725i \(0.0575207\pi\)
\(332\) −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 −0.963058 0.269294i \(-0.913210\pi\)
0.714745 + 0.699385i \(0.246543\pi\)
\(338\) −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 0.945591 0.325359i \(-0.105485\pi\)
−0.754564 + 0.656226i \(0.772152\pi\)
\(348\) 0 0
\(349\) 11.0000 + 19.0526i 0.588817 + 1.01986i 0.994388 + 0.105797i \(0.0337393\pi\)
−0.405571 + 0.914063i \(0.632927\pi\)
\(350\) 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 0.761178 0.648543i \(-0.224621\pi\)
−0.942244 + 0.334928i \(0.891288\pi\)
\(360\) 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 0.998125 + 0.0612128i \(0.0194968\pi\)
−0.446051 + 0.895008i \(0.647170\pi\)
\(398\) 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 −0.958708 0.284393i \(-0.908208\pi\)
0.233063 0.972462i \(-0.425125\pi\)
\(410\) 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 −0.302347 0.953198i \(-0.597770\pi\)
0.976667 0.214759i \(-0.0688964\pi\)
\(420\) 0 0
\(421\) 0.116844 + 0.202380i 0.00569463 + 0.00986338i 0.868859 0.495060i \(-0.164854\pi\)
−0.863164 + 0.504924i \(0.831521\pi\)
\(422\) 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 0.254554 + 0.967059i \(0.418071\pi\)
−0.964774 + 0.263079i \(0.915262\pi\)
\(432\) 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 −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) 8.74456 0.415936
\(443\) −11.4416 + 19.8174i −0.543606 + 0.941553i 0.455087 + 0.890447i \(0.349608\pi\)
−0.998693 + 0.0511061i \(0.983725\pi\)
\(444\) 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 0.147554 + 0.989054i \(0.452860\pi\)
−0.930323 + 0.366742i \(0.880473\pi\)
\(458\) 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 0.961523 + 0.274724i \(0.0885865\pi\)
−0.242844 + 0.970065i \(0.578080\pi\)
\(462\) 0 0
\(463\) 2.94158 5.09496i 0.136707 0.236783i −0.789541 0.613697i \(-0.789682\pi\)
0.926248 + 0.376914i \(0.123015\pi\)
\(464\) −2.74456 −0.127413
\(465\) 0 0
\(466\) 11.7446 0.544056
\(467\) −15.0475 26.0631i −0.696317 1.20606i −0.969735 0.244162i \(-0.921487\pi\)
0.273417 0.961896i \(-0.411846\pi\)
\(468\) 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 −0.619179 0.785250i \(-0.712535\pi\)
0.989636 + 0.143600i \(0.0458679\pi\)
\(488\) 7.05842 12.2255i 0.319520 0.553424i
\(489\) 0 0
\(490\) 0 0
\(491\) −9.81386 + 16.9981i −0.442893 + 0.767114i −0.997903 0.0647303i \(-0.979381\pi\)
0.555010 + 0.831844i \(0.312715\pi\)
\(492\) 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 −0.820629 0.571461i \(-0.806377\pi\)
0.905215 + 0.424955i \(0.139710\pi\)
\(522\) 0 0
\(523\) 8.94158 + 15.4873i 0.390988 + 0.677211i 0.992580 0.121592i \(-0.0388001\pi\)
−0.601592 + 0.798803i \(0.705467\pi\)
\(524\) −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 −0.991743 0.128240i \(-0.959067\pi\)
0.384813 0.922995i \(-0.374266\pi\)
\(542\) −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 0.856431 0.516262i \(-0.172677\pi\)
−0.875311 + 0.483560i \(0.839344\pi\)
\(548\) 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 −0.788778 0.614678i \(-0.789286\pi\)
0.926716 + 0.375763i \(0.122619\pi\)
\(558\) 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 0.895902 0.444252i \(-0.146530\pi\)
−0.832684 + 0.553748i \(0.813197\pi\)
\(564\) 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 −0.877493 0.479589i \(-0.840786\pi\)
0.854083 + 0.520137i \(0.174119\pi\)
\(570\) 0 0
\(571\) −14.6753 25.4183i −0.614141 1.06372i −0.990535 0.137263i \(-0.956169\pi\)
0.376394 0.926460i \(-0.377164\pi\)
\(572\) −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 0.432657 + 0.901559i \(0.357576\pi\)
−0.997101 + 0.0760878i \(0.975757\pi\)
\(578\) 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 0.765036 0.643988i \(-0.222721\pi\)
−0.940228 + 0.340547i \(0.889388\pi\)
\(588\) 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 0.897510 0.440995i \(-0.145374\pi\)
−0.830667 + 0.556769i \(0.812041\pi\)
\(594\) 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 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 0 0
\(601\) −3.44158 5.96099i −0.140385 0.243154i 0.787257 0.616625i \(-0.211501\pi\)
−0.927642 + 0.373472i \(0.878167\pi\)
\(602\) 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 −0.847639 0.530573i \(-0.821977\pi\)
0.883309 + 0.468790i \(0.155310\pi\)
\(614\) 6.50000 11.2583i 0.262319 0.454349i
\(615\) 0 0
\(616\) 0 0
\(617\) −4.93070 + 8.54023i −0.198503 + 0.343817i −0.948043 0.318142i \(-0.896941\pi\)
0.749540 + 0.661959i \(0.230275\pi\)
\(618\) 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 −0.500136 0.865947i \(-0.666717\pi\)
1.00000 0.000157386i \(5.00974e-5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −10.9307 + 18.9325i −0.430063 + 0.744891i
\(647\) −8.74456 + 15.1460i −0.343784 + 0.595452i −0.985132 0.171798i \(-0.945042\pi\)
0.641348 + 0.767250i \(0.278376\pi\)
\(648\) 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 0.761702 0.647927i \(-0.224364\pi\)
−0.941973 + 0.335690i \(0.891031\pi\)
\(660\) 0 0
\(661\) −4.94158 8.55906i −0.192205 0.332909i 0.753776 0.657132i \(-0.228231\pi\)
−0.945981 + 0.324223i \(0.894897\pi\)
\(662\) 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 0.992143 0.125109i \(-0.0399281\pi\)
−0.604419 + 0.796666i \(0.706595\pi\)
\(674\) −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 0.317654 + 0.948207i \(0.397105\pi\)
−0.979998 + 0.199007i \(0.936228\pi\)
\(678\) 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 0.0160849 + 0.999871i \(0.494880\pi\)
−0.873956 + 0.486005i \(0.838454\pi\)
\(684\) 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 −0.804635 0.593770i \(-0.797639\pi\)
0.916537 + 0.399949i \(0.130972\pi\)
\(692\) 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 0.0747503 + 0.997202i \(0.476184\pi\)
−0.900978 + 0.433865i \(0.857149\pi\)
\(710\) 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 0.772906 0.634521i \(-0.218803\pi\)
−0.935964 + 0.352095i \(0.885469\pi\)
\(720\) 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 0.881938 0.471366i \(-0.156239\pi\)
−0.849183 + 0.528098i \(0.822905\pi\)
\(728\) 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 −0.937605 0.347702i \(-0.886962\pi\)
0.769921 + 0.638139i \(0.220296\pi\)
\(740\) −1.37228 + 2.37686i −0.0504461 + 0.0873751i
\(741\) 0 0
\(742\) 0 0
\(743\) 21.8614 37.8651i 0.802017 1.38913i −0.116269 0.993218i \(-0.537094\pi\)
0.918286 0.395917i \(-0.129573\pi\)
\(744\) 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 −0.761680 0.647954i \(-0.775625\pi\)
0.941984 + 0.335657i \(0.108958\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 3.50000 6.06218i 0.125968 0.218183i
\(773\) −5.56930 + 9.64630i −0.200314 + 0.346953i −0.948629 0.316389i \(-0.897529\pi\)
0.748316 + 0.663343i \(0.230863\pi\)
\(774\) 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 0.899468 0.436987i \(-0.143954\pi\)
−0.828176 + 0.560469i \(0.810621\pi\)
\(788\) −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