Properties

Label 2646.2.e.n.2125.1
Level $2646$
Weight $2$
Character 2646.2125
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.e (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: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 2125.1
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 2646.2125
Dual form 2646.2.e.n.1549.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-0.686141 + 1.18843i) q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{4} +(-0.686141 + 1.18843i) q^{5} +1.00000 q^{8} +(-0.686141 + 1.18843i) q^{10} +(2.18614 + 3.78651i) q^{11} +(-1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(-2.18614 + 3.78651i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(-0.686141 + 1.18843i) q^{20} +(2.18614 + 3.78651i) q^{22} +(-3.68614 + 6.38458i) q^{23} +(1.55842 + 2.69927i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(1.37228 - 2.37686i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(-2.18614 + 3.78651i) q^{34} +(-1.00000 - 1.73205i) q^{37} +(-2.50000 - 4.33013i) q^{38} +(-0.686141 + 1.18843i) q^{40} +(5.18614 + 8.98266i) q^{41} +(-4.55842 + 7.89542i) q^{43} +(2.18614 + 3.78651i) q^{44} +(-3.68614 + 6.38458i) q^{46} +(1.55842 + 2.69927i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(1.37228 - 2.37686i) q^{53} -6.00000 q^{55} +(1.37228 - 2.37686i) q^{58} -7.11684 q^{59} -14.1168 q^{61} +2.00000 q^{62} +1.00000 q^{64} +2.74456 q^{65} +15.1168 q^{67} +(-2.18614 + 3.78651i) q^{68} -10.1168 q^{71} +(2.55842 - 4.43132i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-2.50000 - 4.33013i) q^{76} +12.1168 q^{79} +(-0.686141 + 1.18843i) q^{80} +(5.18614 + 8.98266i) q^{82} +(-2.74456 + 4.75372i) q^{83} +(-3.00000 - 5.19615i) q^{85} +(-4.55842 + 7.89542i) q^{86} +(2.18614 + 3.78651i) q^{88} +(1.62772 + 2.81929i) q^{89} +(-3.68614 + 6.38458i) q^{92} +6.86141 q^{95} +(-4.55842 + 7.89542i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8} + O(q^{10}) \) \( 4 q + 4 q^{2} + 4 q^{4} + 3 q^{5} + 4 q^{8} + 3 q^{10} + 3 q^{11} - 4 q^{13} + 4 q^{16} - 3 q^{17} - 10 q^{19} + 3 q^{20} + 3 q^{22} - 9 q^{23} - 11 q^{25} - 4 q^{26} - 6 q^{29} + 8 q^{31} + 4 q^{32} - 3 q^{34} - 4 q^{37} - 10 q^{38} + 3 q^{40} + 15 q^{41} - q^{43} + 3 q^{44} - 9 q^{46} - 11 q^{50} - 4 q^{52} - 6 q^{53} - 24 q^{55} - 6 q^{58} + 6 q^{59} - 22 q^{61} + 8 q^{62} + 4 q^{64} - 12 q^{65} + 26 q^{67} - 3 q^{68} - 6 q^{71} - 7 q^{73} - 4 q^{74} - 10 q^{76} + 14 q^{79} + 3 q^{80} + 15 q^{82} + 12 q^{83} - 12 q^{85} - q^{86} + 3 q^{88} + 18 q^{89} - 9 q^{92} - 30 q^{95} - q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −0.686141 + 1.18843i −0.306851 + 0.531482i −0.977672 0.210138i \(-0.932609\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −0.686141 + 1.18843i −0.216977 + 0.375815i
\(11\) 2.18614 + 3.78651i 0.659146 + 1.14167i 0.980837 + 0.194830i \(0.0624155\pi\)
−0.321691 + 0.946845i \(0.604251\pi\)
\(12\) 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
\(16\) 1.00000 0.250000
\(17\) −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
\(23\) −3.68614 + 6.38458i −0.768613 + 1.33128i 0.169701 + 0.985496i \(0.445720\pi\)
−0.938315 + 0.345782i \(0.887614\pi\)
\(24\) 0 0
\(25\) 1.55842 + 2.69927i 0.311684 + 0.539853i
\(26\) −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
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 1.00000 0.176777
\(33\) 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 \(0.885902\pi\)
\(38\) −2.50000 4.33013i −0.405554 0.702439i
\(39\) 0 0
\(40\) −0.686141 + 1.18843i −0.108488 + 0.187907i
\(41\) 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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 1.55842 + 2.69927i 0.220394 + 0.381734i
\(51\) 0 0
\(52\) −1.00000 1.73205i −0.138675 0.240192i
\(53\) 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
\(58\) 1.37228 2.37686i 0.180189 0.312097i
\(59\) −7.11684 −0.926534 −0.463267 0.886219i \(-0.653323\pi\)
−0.463267 + 0.886219i \(0.653323\pi\)
\(60\) 0 0
\(61\) −14.1168 −1.80748 −0.903738 0.428085i \(-0.859188\pi\)
−0.903738 + 0.428085i \(0.859188\pi\)
\(62\) 2.00000 0.254000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.74456 0.340421
\(66\) 0 0
\(67\) 15.1168 1.84682 0.923408 0.383819i \(-0.125391\pi\)
0.923408 + 0.383819i \(0.125391\pi\)
\(68\) −2.18614 + 3.78651i −0.265108 + 0.459181i
\(69\) 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 \(0.0698666\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) 0 0
\(76\) −2.50000 4.33013i −0.286770 0.496700i
\(77\) 0 0
\(78\) 0 0
\(79\) 12.1168 1.36325 0.681626 0.731701i \(-0.261273\pi\)
0.681626 + 0.731701i \(0.261273\pi\)
\(80\) −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
\(86\) −4.55842 + 7.89542i −0.491547 + 0.851385i
\(87\) 0 0
\(88\) 2.18614 + 3.78651i 0.233043 + 0.403643i
\(89\) 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
\(95\) 6.86141 0.703965
\(96\) 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
\(101\) 3.68614 + 6.38458i 0.366785 + 0.635290i 0.989061 0.147508i \(-0.0471252\pi\)
−0.622276 + 0.782798i \(0.713792\pi\)
\(102\) 0 0
\(103\) 5.00000 8.66025i 0.492665 0.853320i −0.507300 0.861770i \(-0.669356\pi\)
0.999964 + 0.00844953i \(0.00268960\pi\)
\(104\) −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 \(0.932756\pi\)
\(110\) −6.00000 −0.572078
\(111\) 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
\(115\) −5.05842 8.76144i −0.471700 0.817009i
\(116\) 1.37228 2.37686i 0.127413 0.220686i
\(117\) 0 0
\(118\) −7.11684 −0.655159
\(119\) 0 0
\(120\) 0 0
\(121\) −4.05842 + 7.02939i −0.368947 + 0.639036i
\(122\) −14.1168 −1.27808
\(123\) 0 0
\(124\) 2.00000 0.179605
\(125\) −11.1386 −0.996266
\(126\) 0 0
\(127\) −14.1168 −1.25267 −0.626334 0.779555i \(-0.715445\pi\)
−0.626334 + 0.779555i \(0.715445\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 2.74456 0.240714
\(131\) −3.68614 + 6.38458i −0.322060 + 0.557824i −0.980913 0.194448i \(-0.937708\pi\)
0.658853 + 0.752271i \(0.271042\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 15.1168 1.30590
\(135\) 0 0
\(136\) −2.18614 + 3.78651i −0.187460 + 0.324690i
\(137\) 8.18614 + 14.1788i 0.699389 + 1.21138i 0.968678 + 0.248318i \(0.0798779\pi\)
−0.269289 + 0.963059i \(0.586789\pi\)
\(138\) 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
\(142\) −10.1168 −0.848987
\(143\) 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
\(149\) 7.37228 12.7692i 0.603961 1.04609i −0.388254 0.921552i \(-0.626922\pi\)
0.992215 0.124538i \(-0.0397450\pi\)
\(150\) 0 0
\(151\) 4.05842 + 7.02939i 0.330270 + 0.572044i 0.982565 0.185921i \(-0.0595270\pi\)
−0.652295 + 0.757965i \(0.726194\pi\)
\(152\) −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
\(157\) −8.11684 −0.647795 −0.323897 0.946092i \(-0.604993\pi\)
−0.323897 + 0.946092i \(0.604993\pi\)
\(158\) 12.1168 0.963964
\(159\) 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 \(-0.385980\pi\)
\(164\) 5.18614 + 8.98266i 0.404970 + 0.701428i
\(165\) 0 0
\(166\) −2.74456 + 4.75372i −0.213019 + 0.368960i
\(167\) 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
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.18614 + 3.78651i 0.164787 + 0.285419i
\(177\) 0 0
\(178\) 1.62772 + 2.81929i 0.122003 + 0.211315i
\(179\) 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
\(184\) −3.68614 + 6.38458i −0.271746 + 0.470678i
\(185\) 2.74456 0.201784
\(186\) 0 0
\(187\) −19.1168 −1.39796
\(188\) 0 0
\(189\) 0 0
\(190\) 6.86141 0.497779
\(191\) 1.88316 0.136260 0.0681302 0.997676i \(-0.478297\pi\)
0.0681302 + 0.997676i \(0.478297\pi\)
\(192\) 0 0
\(193\) −7.00000 −0.503871 −0.251936 0.967744i \(-0.581067\pi\)
−0.251936 + 0.967744i \(0.581067\pi\)
\(194\) −4.55842 + 7.89542i −0.327276 + 0.566858i
\(195\) 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 \(0.0513380\pi\)
\(200\) 1.55842 + 2.69927i 0.110197 + 0.190867i
\(201\) 0 0
\(202\) 3.68614 + 6.38458i 0.259356 + 0.449218i
\(203\) 0 0
\(204\) 0 0
\(205\) −14.2337 −0.994124
\(206\) 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 \(0.647678\pi\)
\(212\) 1.37228 2.37686i 0.0942487 0.163243i
\(213\) 0 0
\(214\) −0.813859 1.40965i −0.0556343 0.0963614i
\(215\) −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
\(220\) −6.00000 −0.404520
\(221\) 8.74456 0.588223
\(222\) 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
\(227\) −11.8723 20.5634i −0.787991 1.36484i −0.927196 0.374577i \(-0.877788\pi\)
0.139205 0.990264i \(-0.455545\pi\)
\(228\) 0 0
\(229\) 10.0584 17.4217i 0.664679 1.15126i −0.314693 0.949194i \(-0.601902\pi\)
0.979372 0.202065i \(-0.0647651\pi\)
\(230\) −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
\(236\) −7.11684 −0.463267
\(237\) 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
\(241\) −0.441578 0.764836i −0.0284445 0.0492674i 0.851453 0.524431i \(-0.175722\pi\)
−0.879897 + 0.475164i \(0.842389\pi\)
\(242\) −4.05842 + 7.02939i −0.260885 + 0.451867i
\(243\) 0 0
\(244\) −14.1168 −0.903738
\(245\) 0 0
\(246\) 0 0
\(247\) −5.00000 + 8.66025i −0.318142 + 0.551039i
\(248\) 2.00000 0.127000
\(249\) 0 0
\(250\) −11.1386 −0.704467
\(251\) 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
\(254\) −14.1168 −0.885770
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 10.9307 18.9325i 0.681839 1.18098i −0.292581 0.956241i \(-0.594514\pi\)
0.974419 0.224738i \(-0.0721527\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 2.74456 0.170211
\(261\) 0 0
\(262\) −3.68614 + 6.38458i −0.227731 + 0.394441i
\(263\) 6.68614 + 11.5807i 0.412285 + 0.714099i 0.995139 0.0984781i \(-0.0313974\pi\)
−0.582854 + 0.812577i \(0.698064\pi\)
\(264\) 0 0
\(265\) 1.88316 + 3.26172i 0.115681 + 0.200366i
\(266\) 0 0
\(267\) 0 0
\(268\) 15.1168 0.923408
\(269\) −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
\(275\) −6.81386 + 11.8020i −0.410891 + 0.711684i
\(276\) 0 0
\(277\) −11.1168 19.2549i −0.667946 1.15692i −0.978477 0.206354i \(-0.933840\pi\)
0.310531 0.950563i \(-0.399493\pi\)
\(278\) 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
\(283\) 9.88316 0.587493 0.293746 0.955883i \(-0.405098\pi\)
0.293746 + 0.955883i \(0.405098\pi\)
\(284\) −10.1168 −0.600324
\(285\) 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
\(290\) 1.88316 + 3.26172i 0.110583 + 0.191535i
\(291\) 0 0
\(292\) 2.55842 4.43132i 0.149720 0.259323i
\(293\) −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
\(299\) 14.7446 0.852700
\(300\) 0 0
\(301\) 0 0
\(302\) 4.05842 + 7.02939i 0.233536 + 0.404496i
\(303\) 0 0
\(304\) −2.50000 4.33013i −0.143385 0.248350i
\(305\) 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
\(310\) −1.37228 + 2.37686i −0.0779403 + 0.134997i
\(311\) 26.2337 1.48758 0.743788 0.668416i \(-0.233027\pi\)
0.743788 + 0.668416i \(0.233027\pi\)
\(312\) 0 0
\(313\) −2.88316 −0.162966 −0.0814828 0.996675i \(-0.525966\pi\)
−0.0814828 + 0.996675i \(0.525966\pi\)
\(314\) −8.11684 −0.458060
\(315\) 0 0
\(316\) 12.1168 0.681626
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) −0.686141 + 1.18843i −0.0383564 + 0.0664353i
\(321\) 0 0
\(322\) 0 0
\(323\) 21.8614 1.21640
\(324\) 0 0
\(325\) 3.11684 5.39853i 0.172891 0.299457i
\(326\) −8.11684 14.0588i −0.449550 0.778644i
\(327\) 0 0
\(328\) 5.18614 + 8.98266i 0.286357 + 0.495984i
\(329\) 0 0
\(330\) 0 0
\(331\) −12.2337 −0.672424 −0.336212 0.941786i \(-0.609146\pi\)
−0.336212 + 0.941786i \(0.609146\pi\)
\(332\) −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 \(0.913210\pi\)
\(338\) 4.50000 7.79423i 0.244768 0.423950i
\(339\) 0 0
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) 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
\(346\) 6.00000 0.322562
\(347\) −7.11684 −0.382052 −0.191026 0.981585i \(-0.561182\pi\)
−0.191026 + 0.981585i \(0.561182\pi\)
\(348\) 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
\(353\) −3.81386 6.60580i −0.202991 0.351591i 0.746500 0.665386i \(-0.231733\pi\)
−0.949491 + 0.313795i \(0.898400\pi\)
\(354\) 0 0
\(355\) 6.94158 12.0232i 0.368421 0.638123i
\(356\) 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
\(362\) 18.1168 0.952200
\(363\) 0 0
\(364\) 0 0
\(365\) 3.51087 + 6.08101i 0.183768 + 0.318295i
\(366\) 0 0
\(367\) −11.1168 19.2549i −0.580295 1.00510i −0.995444 0.0953465i \(-0.969604\pi\)
0.415150 0.909753i \(-0.363729\pi\)
\(368\) −3.68614 + 6.38458i −0.192153 + 0.332819i
\(369\) 0 0
\(370\) 2.74456 0.142683
\(371\) 0 0
\(372\) 0 0
\(373\) 5.00000 8.66025i 0.258890 0.448411i −0.707055 0.707159i \(-0.749977\pi\)
0.965945 + 0.258748i \(0.0833099\pi\)
\(374\) −19.1168 −0.988508
\(375\) 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 \(0.424769\pi\)
\(380\) 6.86141 0.351983
\(381\) 0 0
\(382\) 1.88316 0.0963506
\(383\) −10.6277 + 18.4077i −0.543051 + 0.940592i 0.455676 + 0.890146i \(0.349398\pi\)
−0.998727 + 0.0504462i \(0.983936\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −7.00000 −0.356291
\(387\) 0 0
\(388\) −4.55842 + 7.89542i −0.231419 + 0.400829i
\(389\) −17.4891 30.2921i −0.886734 1.53587i −0.843713 0.536794i \(-0.819635\pi\)
−0.0430204 0.999074i \(-0.513698\pi\)
\(390\) 0 0
\(391\) −16.1168 27.9152i −0.815064 1.41173i
\(392\) 0 0
\(393\) 0 0
\(394\) 6.00000 0.302276
\(395\) −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
\(401\) −0.127719 + 0.221215i −0.00637797 + 0.0110470i −0.869197 0.494466i \(-0.835364\pi\)
0.862819 + 0.505513i \(0.168697\pi\)
\(402\) 0 0
\(403\) −2.00000 3.46410i −0.0996271 0.172559i
\(404\) 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
\(409\) 29.3505 1.45129 0.725645 0.688069i \(-0.241541\pi\)
0.725645 + 0.688069i \(0.241541\pi\)
\(410\) −14.2337 −0.702952
\(411\) 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
\(416\) −1.00000 1.73205i −0.0490290 0.0849208i
\(417\) 0 0
\(418\) 10.9307 18.9325i 0.534638 0.926020i
\(419\) 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
\(425\) −13.6277 −0.661041
\(426\) 0 0
\(427\) 0 0
\(428\) −0.813859 1.40965i −0.0393394 0.0681378i
\(429\) 0 0
\(430\) −6.25544 10.8347i −0.301664 0.522497i
\(431\) −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
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 36.8614 1.76332
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) 8.74456 0.415936
\(443\) 22.8832 1.08721 0.543606 0.839341i \(-0.317059\pi\)
0.543606 + 0.839341i \(0.317059\pi\)
\(444\) 0 0
\(445\) −4.46738 −0.211774
\(446\) 2.00000 3.46410i 0.0947027 0.164030i
\(447\) 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
\(452\) 0.686141 + 1.18843i 0.0322733 + 0.0558991i
\(453\) 0 0
\(454\) −11.8723 20.5634i −0.557194 0.965088i
\(455\) 0 0
\(456\) 0 0
\(457\) 33.4674 1.56554 0.782769 0.622312i \(-0.213807\pi\)
0.782769 + 0.622312i \(0.213807\pi\)
\(458\) 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 \(0.789682\pi\)
\(464\) 1.37228 2.37686i 0.0637066 0.110343i
\(465\) 0 0
\(466\) −5.87228 10.1711i −0.272028 0.471167i
\(467\) −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
\(472\) −7.11684 −0.327579
\(473\) −39.8614 −1.83283
\(474\) 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
\(479\) 10.6277 + 18.4077i 0.485593 + 0.841072i 0.999863 0.0165568i \(-0.00527043\pi\)
−0.514270 + 0.857628i \(0.671937\pi\)
\(480\) 0 0
\(481\) −2.00000 + 3.46410i −0.0911922 + 0.157949i
\(482\) −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 \(0.0458679\pi\)
\(488\) −14.1168 −0.639040
\(489\) 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
\(493\) 6.00000 + 10.3923i 0.270226 + 0.468046i
\(494\) −5.00000 + 8.66025i −0.224961 + 0.389643i
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 0 0
\(499\) −0.441578 + 0.764836i −0.0197677 + 0.0342387i −0.875740 0.482783i \(-0.839626\pi\)
0.855972 + 0.517022i \(0.172959\pi\)
\(500\) −11.1386 −0.498133
\(501\) 0 0
\(502\) 9.00000 0.401690
\(503\) −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
\(506\) −32.2337 −1.43296
\(507\) 0 0
\(508\) −14.1168 −0.626334
\(509\) 8.48913 14.7036i 0.376274 0.651725i −0.614243 0.789117i \(-0.710539\pi\)
0.990517 + 0.137392i \(0.0438718\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 10.9307 18.9325i 0.482133 0.835078i
\(515\) 6.86141 + 11.8843i 0.302350 + 0.523685i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 2.74456 0.120357
\(521\) 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
\(527\) −4.37228 + 7.57301i −0.190460 + 0.329886i
\(528\) 0 0
\(529\) −15.6753 27.1504i −0.681533 1.18045i
\(530\) 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
\(535\) 2.23369 0.0965708
\(536\) 15.1168 0.652948
\(537\) 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 \(-0.374266\pi\)
\(542\) 9.11684 + 15.7908i 0.391602 + 0.678275i
\(543\) 0 0
\(544\) −2.18614 + 3.78651i −0.0937300 + 0.162345i
\(545\) −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
\(551\) −13.7228 −0.584611
\(552\) 0 0
\(553\) 0 0
\(554\) −11.1168 19.2549i −0.472309 0.818064i
\(555\) 0 0
\(556\) 10.6168 + 18.3889i 0.450254 + 0.779864i
\(557\) 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
\(562\) 5.31386 9.20387i 0.224152 0.388242i
\(563\) −3.00000 −0.126435 −0.0632175 0.998000i \(-0.520136\pi\)
−0.0632175 + 0.998000i \(0.520136\pi\)
\(564\) 0 0
\(565\) −1.88316 −0.0792250
\(566\) 9.88316 0.415420
\(567\) 0 0
\(568\) −10.1168 −0.424493
\(569\) 1.11684 0.0468205 0.0234103 0.999726i \(-0.492548\pi\)
0.0234103 + 0.999726i \(0.492548\pi\)
\(570\) 0 0
\(571\) 29.3505 1.22828 0.614141 0.789197i \(-0.289503\pi\)
0.614141 + 0.789197i \(0.289503\pi\)
\(572\) 4.37228 7.57301i 0.182814 0.316644i
\(573\) 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 \(0.975757\pi\)
\(578\) −1.05842 1.83324i −0.0440246 0.0762528i
\(579\) 0 0
\(580\) 1.88316 + 3.26172i 0.0781938 + 0.135436i
\(581\) 0 0
\(582\) 0 0
\(583\) 12.0000 0.496989
\(584\) 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
\(590\) 4.88316 8.45787i 0.201036 0.348205i
\(591\) 0 0
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 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
\(598\) 14.7446 0.602950
\(599\) −24.0000 −0.980613 −0.490307 0.871550i \(-0.663115\pi\)
−0.490307 + 0.871550i \(0.663115\pi\)
\(600\) 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
\(605\) −5.56930 9.64630i −0.226424 0.392178i
\(606\) 0 0
\(607\) 6.11684 10.5947i 0.248275 0.430025i −0.714772 0.699357i \(-0.753470\pi\)
0.963047 + 0.269332i \(0.0868030\pi\)
\(608\) −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 \(0.155310\pi\)
\(614\) −13.0000 −0.524637
\(615\) 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
\(619\) 11.7337 + 20.3233i 0.471617 + 0.816864i 0.999473 0.0324697i \(-0.0103373\pi\)
−0.527856 + 0.849334i \(0.677004\pi\)
\(620\) −1.37228 + 2.37686i −0.0551121 + 0.0954570i
\(621\) 0 0
\(622\) 26.2337 1.05188
\(623\) 0 0
\(624\) 0 0
\(625\) −0.149468 + 0.258886i −0.00597872 + 0.0103555i
\(626\) −2.88316 −0.115234
\(627\) 0 0
\(628\) −8.11684 −0.323897
\(629\) 8.74456 0.348669
\(630\) 0 0
\(631\) 14.3505 0.571286 0.285643 0.958336i \(-0.407793\pi\)
0.285643 + 0.958336i \(0.407793\pi\)
\(632\) 12.1168 0.481982
\(633\) 0 0
\(634\) 6.00000 0.238290
\(635\) 9.68614 16.7769i 0.384383 0.665770i
\(636\) 0 0
\(637\) 0 0
\(638\) 12.0000 0.475085
\(639\) 0 0
\(640\) −0.686141 + 1.18843i −0.0271221 + 0.0469768i
\(641\) −23.1060 40.0207i −0.912631 1.58072i −0.810333 0.585969i \(-0.800714\pi\)
−0.102298 0.994754i \(-0.532619\pi\)
\(642\) 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
\(646\) 21.8614 0.860126
\(647\) −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
\(653\) −7.62772 + 13.2116i −0.298496 + 0.517010i −0.975792 0.218701i \(-0.929818\pi\)
0.677296 + 0.735710i \(0.263152\pi\)
\(654\) 0 0
\(655\) −5.05842 8.76144i −0.197649 0.342338i
\(656\) 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
\(661\) 9.88316 0.384410 0.192205 0.981355i \(-0.438436\pi\)
0.192205 + 0.981355i \(0.438436\pi\)
\(662\) −12.2337 −0.475476
\(663\) 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
\(668\) 8.74456 + 15.1460i 0.338337 + 0.586017i
\(669\) 0 0
\(670\) −10.3723 + 17.9653i −0.400716 + 0.694061i
\(671\) −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
\(677\) 34.4674 1.32469 0.662344 0.749199i \(-0.269562\pi\)
0.662344 + 0.749199i \(0.269562\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −3.00000 5.19615i −0.115045 0.199263i
\(681\) 0 0
\(682\) 4.37228 + 7.57301i 0.167423 + 0.289986i
\(683\) −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
\(688\) −4.55842 + 7.89542i −0.173788 + 0.301010i
\(689\) −5.48913 −0.209119
\(690\) 0 0
\(691\) −5.88316 −0.223806 −0.111903 0.993719i \(-0.535695\pi\)
−0.111903 + 0.993719i \(0.535695\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −7.11684 −0.270152
\(695\) −29.1386 −1.10529
\(696\) 0 0
\(697\) −45.3505 −1.71777
\(698\) 11.0000 19.0526i 0.416356 0.721150i
\(699\) 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
\(704\) 2.18614 + 3.78651i 0.0823933 + 0.142709i
\(705\) 0 0
\(706\) −3.81386 6.60580i −0.143536 0.248612i
\(707\) 0 0
\(708\) 0 0
\(709\) 44.0000 1.65245 0.826227 0.563337i \(-0.190483\pi\)
0.826227 + 0.563337i \(0.190483\pi\)
\(710\) 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
\(716\) 7.37228 12.7692i 0.275515 0.477206i
\(717\) 0 0
\(718\) −3.43070 5.94215i −0.128033 0.221759i
\(719\) −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
\(724\) 18.1168 0.673307
\(725\) 8.55437 0.317701
\(726\) 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
\(731\) −19.9307 34.5210i −0.737164 1.27680i
\(732\) 0 0
\(733\) 11.9416 20.6834i 0.441072 0.763960i −0.556697 0.830716i \(-0.687932\pi\)
0.997769 + 0.0667560i \(0.0212649\pi\)
\(734\) −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 \(0.220296\pi\)
\(740\) 2.74456 0.100892
\(741\) 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
\(745\) 10.1168 + 17.5229i 0.370652 + 0.641989i
\(746\) 5.00000 8.66025i 0.183063 0.317074i
\(747\) 0 0
\(748\) −19.1168 −0.698981
\(749\) 0 0
\(750\) 0 0
\(751\) −0.0584220 + 0.101190i −0.00213185 + 0.00369247i −0.867089 0.498153i \(-0.834012\pi\)
0.864958 + 0.501845i \(0.167345\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −5.48913 −0.199902
\(755\) −11.1386 −0.405375
\(756\) 0 0
\(757\) 11.7663 0.427654 0.213827 0.976872i \(-0.431407\pi\)
0.213827 + 0.976872i \(0.431407\pi\)
\(758\) 9.11684 0.331139
\(759\) 0 0
\(760\) 6.86141 0.248889
\(761\) 6.25544 10.8347i 0.226759 0.392759i −0.730086 0.683355i \(-0.760520\pi\)
0.956846 + 0.290596i \(0.0938536\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1.88316 0.0681302
\(765\) 0 0
\(766\) −10.6277 + 18.4077i −0.383995 + 0.665099i
\(767\) 7.11684 + 12.3267i 0.256974 + 0.445093i
\(768\) 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
\(772\) −7.00000 −0.251936
\(773\) −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
\(779\) 25.9307 44.9133i 0.929064 1.60919i
\(780\) 0 0
\(781\) −22.1168 38.3075i −0.791403 1.37075i
\(782\) −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
\(787\) −4.00000 −0.142585 −0.0712923 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 6.00000 0.213741
\(789\) 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
\(794\) 11.0000 + 19.0526i 0.390375 + 0.676150i