Properties

Label 336.2.q.c.289.1
Level $336$
Weight $2$
Character 336.289
Analytic conductor $2.683$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.2.q.c.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} -3.00000 q^{13} -2.00000 q^{15} +(-4.00000 - 6.92820i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +4.00000 q^{29} +(1.50000 + 2.59808i) q^{31} +(1.00000 - 1.73205i) q^{33} +(-5.00000 - 1.73205i) q^{35} +(0.500000 - 0.866025i) q^{37} +(1.50000 + 2.59808i) q^{39} +6.00000 q^{41} -11.0000 q^{43} +(1.00000 + 1.73205i) q^{45} +(3.00000 - 5.19615i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-4.00000 + 6.92820i) q^{51} +(6.00000 + 10.3923i) q^{53} +4.00000 q^{55} +1.00000 q^{57} +(2.00000 + 3.46410i) q^{59} +(3.00000 - 5.19615i) q^{61} +(2.50000 + 0.866025i) q^{63} +(-3.00000 + 5.19615i) q^{65} +(6.50000 + 11.2583i) q^{67} -8.00000 q^{69} +10.0000 q^{71} +(5.50000 + 9.52628i) q^{73} +(0.500000 - 0.866025i) q^{75} +(4.00000 - 3.46410i) q^{77} +(-1.50000 + 2.59808i) q^{79} +(-0.500000 - 0.866025i) q^{81} -2.00000 q^{83} -16.0000 q^{85} +(-2.00000 - 3.46410i) q^{87} +(1.50000 + 7.79423i) q^{91} +(1.50000 - 2.59808i) q^{93} +(1.00000 + 1.73205i) q^{95} +10.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} + 2q^{5} - q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} + 2q^{5} - q^{7} - q^{9} + 2q^{11} - 6q^{13} - 4q^{15} - 8q^{17} - q^{19} - 4q^{21} + 8q^{23} + q^{25} + 2q^{27} + 8q^{29} + 3q^{31} + 2q^{33} - 10q^{35} + q^{37} + 3q^{39} + 12q^{41} - 22q^{43} + 2q^{45} + 6q^{47} - 13q^{49} - 8q^{51} + 12q^{53} + 8q^{55} + 2q^{57} + 4q^{59} + 6q^{61} + 5q^{63} - 6q^{65} + 13q^{67} - 16q^{69} + 20q^{71} + 11q^{73} + q^{75} + 8q^{77} - 3q^{79} - q^{81} - 4q^{83} - 32q^{85} - 4q^{87} + 3q^{91} + 3q^{93} + 2q^{95} + 20q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 0
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) 1.00000 1.73205i 0.447214 0.774597i −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 0 0
\(7\) −0.500000 2.59808i −0.188982 0.981981i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 1.00000 + 1.73205i 0.301511 + 0.522233i 0.976478 0.215615i \(-0.0691756\pi\)
−0.674967 + 0.737848i \(0.735842\pi\)
\(12\) 0 0
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 0 0
\(17\) −4.00000 6.92820i −0.970143 1.68034i −0.695113 0.718900i \(-0.744646\pi\)
−0.275029 0.961436i \(-0.588688\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) −2.00000 + 1.73205i −0.436436 + 0.377964i
\(22\) 0 0
\(23\) 4.00000 6.92820i 0.834058 1.44463i −0.0607377 0.998154i \(-0.519345\pi\)
0.894795 0.446476i \(-0.147321\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 1.50000 + 2.59808i 0.269408 + 0.466628i 0.968709 0.248199i \(-0.0798387\pi\)
−0.699301 + 0.714827i \(0.746505\pi\)
\(32\) 0 0
\(33\) 1.00000 1.73205i 0.174078 0.301511i
\(34\) 0 0
\(35\) −5.00000 1.73205i −0.845154 0.292770i
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 0 0
\(39\) 1.50000 + 2.59808i 0.240192 + 0.416025i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 0 0
\(45\) 1.00000 + 1.73205i 0.149071 + 0.258199i
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −6.50000 + 2.59808i −0.928571 + 0.371154i
\(50\) 0 0
\(51\) −4.00000 + 6.92820i −0.560112 + 0.970143i
\(52\) 0 0
\(53\) 6.00000 + 10.3923i 0.824163 + 1.42749i 0.902557 + 0.430570i \(0.141688\pi\)
−0.0783936 + 0.996922i \(0.524979\pi\)
\(54\) 0 0
\(55\) 4.00000 0.539360
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) 0 0
\(59\) 2.00000 + 3.46410i 0.260378 + 0.450988i 0.966342 0.257260i \(-0.0828195\pi\)
−0.705965 + 0.708247i \(0.749486\pi\)
\(60\) 0 0
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) 0 0
\(63\) 2.50000 + 0.866025i 0.314970 + 0.109109i
\(64\) 0 0
\(65\) −3.00000 + 5.19615i −0.372104 + 0.644503i
\(66\) 0 0
\(67\) 6.50000 + 11.2583i 0.794101 + 1.37542i 0.923408 + 0.383819i \(0.125391\pi\)
−0.129307 + 0.991605i \(0.541275\pi\)
\(68\) 0 0
\(69\) −8.00000 −0.963087
\(70\) 0 0
\(71\) 10.0000 1.18678 0.593391 0.804914i \(-0.297789\pi\)
0.593391 + 0.804914i \(0.297789\pi\)
\(72\) 0 0
\(73\) 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i \(0.0559458\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) 4.00000 3.46410i 0.455842 0.394771i
\(78\) 0 0
\(79\) −1.50000 + 2.59808i −0.168763 + 0.292306i −0.937985 0.346675i \(-0.887311\pi\)
0.769222 + 0.638982i \(0.220644\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) −16.0000 −1.73544
\(86\) 0 0
\(87\) −2.00000 3.46410i −0.214423 0.371391i
\(88\) 0 0
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) 1.50000 + 7.79423i 0.157243 + 0.817057i
\(92\) 0 0
\(93\) 1.50000 2.59808i 0.155543 0.269408i
\(94\) 0 0
\(95\) 1.00000 + 1.73205i 0.102598 + 0.177705i
\(96\) 0 0
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) −5.00000 8.66025i −0.497519 0.861727i 0.502477 0.864590i \(-0.332422\pi\)
−0.999996 + 0.00286291i \(0.999089\pi\)
\(102\) 0 0
\(103\) 5.50000 9.52628i 0.541931 0.938652i −0.456862 0.889538i \(-0.651027\pi\)
0.998793 0.0491146i \(-0.0156400\pi\)
\(104\) 0 0
\(105\) 1.00000 + 5.19615i 0.0975900 + 0.507093i
\(106\) 0 0
\(107\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(108\) 0 0
\(109\) 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i \(0.00994332\pi\)
−0.472708 + 0.881219i \(0.656723\pi\)
\(110\) 0 0
\(111\) −1.00000 −0.0949158
\(112\) 0 0
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) −8.00000 13.8564i −0.746004 1.29212i
\(116\) 0 0
\(117\) 1.50000 2.59808i 0.138675 0.240192i
\(118\) 0 0
\(119\) −16.0000 + 13.8564i −1.46672 + 1.27021i
\(120\) 0 0
\(121\) 3.50000 6.06218i 0.318182 0.551107i
\(122\) 0 0
\(123\) −3.00000 5.19615i −0.270501 0.468521i
\(124\) 0 0
\(125\) 12.0000 1.07331
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 0 0
\(129\) 5.50000 + 9.52628i 0.484248 + 0.838742i
\(130\) 0 0
\(131\) −1.00000 + 1.73205i −0.0873704 + 0.151330i −0.906399 0.422423i \(-0.861180\pi\)
0.819028 + 0.573753i \(0.194513\pi\)
\(132\) 0 0
\(133\) 2.50000 + 0.866025i 0.216777 + 0.0750939i
\(134\) 0 0
\(135\) 1.00000 1.73205i 0.0860663 0.149071i
\(136\) 0 0
\(137\) −2.00000 3.46410i −0.170872 0.295958i 0.767853 0.640626i \(-0.221325\pi\)
−0.938725 + 0.344668i \(0.887992\pi\)
\(138\) 0 0
\(139\) 5.00000 0.424094 0.212047 0.977259i \(-0.431987\pi\)
0.212047 + 0.977259i \(0.431987\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) −3.00000 5.19615i −0.250873 0.434524i
\(144\) 0 0
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) 0 0
\(147\) 5.50000 + 4.33013i 0.453632 + 0.357143i
\(148\) 0 0
\(149\) 6.00000 10.3923i 0.491539 0.851371i −0.508413 0.861113i \(-0.669768\pi\)
0.999953 + 0.00974235i \(0.00310113\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) 8.00000 0.646762
\(154\) 0 0
\(155\) 6.00000 0.481932
\(156\) 0 0
\(157\) −1.00000 1.73205i −0.0798087 0.138233i 0.823359 0.567521i \(-0.192098\pi\)
−0.903167 + 0.429289i \(0.858764\pi\)
\(158\) 0 0
\(159\) 6.00000 10.3923i 0.475831 0.824163i
\(160\) 0 0
\(161\) −20.0000 6.92820i −1.57622 0.546019i
\(162\) 0 0
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 0 0
\(165\) −2.00000 3.46410i −0.155700 0.269680i
\(166\) 0 0
\(167\) 2.00000 0.154765 0.0773823 0.997001i \(-0.475344\pi\)
0.0773823 + 0.997001i \(0.475344\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) −0.500000 0.866025i −0.0382360 0.0662266i
\(172\) 0 0
\(173\) −8.00000 + 13.8564i −0.608229 + 1.05348i 0.383304 + 0.923622i \(0.374786\pi\)
−0.991532 + 0.129861i \(0.958547\pi\)
\(174\) 0 0
\(175\) 2.00000 1.73205i 0.151186 0.130931i
\(176\) 0 0
\(177\) 2.00000 3.46410i 0.150329 0.260378i
\(178\) 0 0
\(179\) 3.00000 + 5.19615i 0.224231 + 0.388379i 0.956088 0.293079i \(-0.0946798\pi\)
−0.731858 + 0.681457i \(0.761346\pi\)
\(180\) 0 0
\(181\) −15.0000 −1.11494 −0.557471 0.830197i \(-0.688228\pi\)
−0.557471 + 0.830197i \(0.688228\pi\)
\(182\) 0 0
\(183\) −6.00000 −0.443533
\(184\) 0 0
\(185\) −1.00000 1.73205i −0.0735215 0.127343i
\(186\) 0 0
\(187\) 8.00000 13.8564i 0.585018 1.01328i
\(188\) 0 0
\(189\) −0.500000 2.59808i −0.0363696 0.188982i
\(190\) 0 0
\(191\) 3.00000 5.19615i 0.217072 0.375980i −0.736839 0.676068i \(-0.763683\pi\)
0.953912 + 0.300088i \(0.0970159\pi\)
\(192\) 0 0
\(193\) −5.50000 9.52628i −0.395899 0.685717i 0.597317 0.802005i \(-0.296234\pi\)
−0.993215 + 0.116289i \(0.962900\pi\)
\(194\) 0 0
\(195\) 6.00000 0.429669
\(196\) 0 0
\(197\) 8.00000 0.569976 0.284988 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) 0 0
\(199\) 4.00000 + 6.92820i 0.283552 + 0.491127i 0.972257 0.233915i \(-0.0751537\pi\)
−0.688705 + 0.725042i \(0.741820\pi\)
\(200\) 0 0
\(201\) 6.50000 11.2583i 0.458475 0.794101i
\(202\) 0 0
\(203\) −2.00000 10.3923i −0.140372 0.729397i
\(204\) 0 0
\(205\) 6.00000 10.3923i 0.419058 0.725830i
\(206\) 0 0
\(207\) 4.00000 + 6.92820i 0.278019 + 0.481543i
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) −5.00000 8.66025i −0.342594 0.593391i
\(214\) 0 0
\(215\) −11.0000 + 19.0526i −0.750194 + 1.29937i
\(216\) 0 0
\(217\) 6.00000 5.19615i 0.407307 0.352738i
\(218\) 0 0
\(219\) 5.50000 9.52628i 0.371656 0.643726i
\(220\) 0 0
\(221\) 12.0000 + 20.7846i 0.807207 + 1.39812i
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 0 0
\(227\) −9.00000 15.5885i −0.597351 1.03464i −0.993210 0.116331i \(-0.962887\pi\)
0.395860 0.918311i \(-0.370447\pi\)
\(228\) 0 0
\(229\) −0.500000 + 0.866025i −0.0330409 + 0.0572286i −0.882073 0.471113i \(-0.843853\pi\)
0.849032 + 0.528341i \(0.177186\pi\)
\(230\) 0 0
\(231\) −5.00000 1.73205i −0.328976 0.113961i
\(232\) 0 0
\(233\) −7.00000 + 12.1244i −0.458585 + 0.794293i −0.998886 0.0471787i \(-0.984977\pi\)
0.540301 + 0.841472i \(0.318310\pi\)
\(234\) 0 0
\(235\) −6.00000 10.3923i −0.391397 0.677919i
\(236\) 0 0
\(237\) 3.00000 0.194871
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) −7.00000 12.1244i −0.450910 0.780998i 0.547533 0.836784i \(-0.315567\pi\)
−0.998443 + 0.0557856i \(0.982234\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −2.00000 + 13.8564i −0.127775 + 0.885253i
\(246\) 0 0
\(247\) 1.50000 2.59808i 0.0954427 0.165312i
\(248\) 0 0
\(249\) 1.00000 + 1.73205i 0.0633724 + 0.109764i
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 16.0000 1.00591
\(254\) 0 0
\(255\) 8.00000 + 13.8564i 0.500979 + 0.867722i
\(256\) 0 0
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) −2.50000 0.866025i −0.155342 0.0538122i
\(260\) 0 0
\(261\) −2.00000 + 3.46410i −0.123797 + 0.214423i
\(262\) 0 0
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 0 0
\(265\) 24.0000 1.47431
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.00000 + 1.73205i 0.0609711 + 0.105605i 0.894900 0.446267i \(-0.147247\pi\)
−0.833929 + 0.551872i \(0.813914\pi\)
\(270\) 0 0
\(271\) −12.0000 + 20.7846i −0.728948 + 1.26258i 0.228380 + 0.973572i \(0.426657\pi\)
−0.957328 + 0.289003i \(0.906676\pi\)
\(272\) 0 0
\(273\) 6.00000 5.19615i 0.363137 0.314485i
\(274\) 0 0
\(275\) −1.00000 + 1.73205i −0.0603023 + 0.104447i
\(276\) 0 0
\(277\) −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i \(-0.996047\pi\)
0.489207 0.872167i \(-0.337286\pi\)
\(278\) 0 0
\(279\) −3.00000 −0.179605
\(280\) 0 0
\(281\) 20.0000 1.19310 0.596550 0.802576i \(-0.296538\pi\)
0.596550 + 0.802576i \(0.296538\pi\)
\(282\) 0 0
\(283\) 9.50000 + 16.4545i 0.564716 + 0.978117i 0.997076 + 0.0764162i \(0.0243478\pi\)
−0.432360 + 0.901701i \(0.642319\pi\)
\(284\) 0 0
\(285\) 1.00000 1.73205i 0.0592349 0.102598i
\(286\) 0 0
\(287\) −3.00000 15.5885i −0.177084 0.920158i
\(288\) 0 0
\(289\) −23.5000 + 40.7032i −1.38235 + 2.39431i
\(290\) 0 0
\(291\) −5.00000 8.66025i −0.293105 0.507673i
\(292\) 0 0
\(293\) −24.0000 −1.40209 −0.701047 0.713115i \(-0.747284\pi\)
−0.701047 + 0.713115i \(0.747284\pi\)
\(294\) 0 0
\(295\) 8.00000 0.465778
\(296\) 0 0
\(297\) 1.00000 + 1.73205i 0.0580259 + 0.100504i
\(298\) 0 0
\(299\) −12.0000 + 20.7846i −0.693978 + 1.20201i
\(300\) 0 0
\(301\) 5.50000 + 28.5788i 0.317015 + 1.64726i
\(302\) 0 0
\(303\) −5.00000 + 8.66025i −0.287242 + 0.497519i
\(304\) 0 0
\(305\) −6.00000 10.3923i −0.343559 0.595062i
\(306\) 0 0
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) 0 0
\(309\) −11.0000 −0.625768
\(310\) 0 0
\(311\) −1.00000 1.73205i −0.0567048 0.0982156i 0.836280 0.548303i \(-0.184726\pi\)
−0.892984 + 0.450088i \(0.851393\pi\)
\(312\) 0 0
\(313\) 8.50000 14.7224i 0.480448 0.832161i −0.519300 0.854592i \(-0.673807\pi\)
0.999748 + 0.0224310i \(0.00714060\pi\)
\(314\) 0 0
\(315\) 4.00000 3.46410i 0.225374 0.195180i
\(316\) 0 0
\(317\) 12.0000 20.7846i 0.673987 1.16738i −0.302777 0.953062i \(-0.597914\pi\)
0.976764 0.214318i \(-0.0687530\pi\)
\(318\) 0 0
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) −1.50000 2.59808i −0.0832050 0.144115i
\(326\) 0 0
\(327\) 5.50000 9.52628i 0.304151 0.526804i
\(328\) 0 0
\(329\) −15.0000 5.19615i −0.826977 0.286473i
\(330\) 0 0
\(331\) 8.50000 14.7224i 0.467202 0.809218i −0.532096 0.846684i \(-0.678595\pi\)
0.999298 + 0.0374662i \(0.0119287\pi\)
\(332\) 0 0
\(333\) 0.500000 + 0.866025i 0.0273998 + 0.0474579i
\(334\) 0 0
\(335\) 26.0000 1.42053
\(336\) 0 0
\(337\) 21.0000 1.14394 0.571971 0.820274i \(-0.306179\pi\)
0.571971 + 0.820274i \(0.306179\pi\)
\(338\) 0 0
\(339\) 7.00000 + 12.1244i 0.380188 + 0.658505i
\(340\) 0 0
\(341\) −3.00000 + 5.19615i −0.162459 + 0.281387i
\(342\) 0 0
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 0 0
\(345\) −8.00000 + 13.8564i −0.430706 + 0.746004i
\(346\) 0 0
\(347\) 12.0000 + 20.7846i 0.644194 + 1.11578i 0.984487 + 0.175457i \(0.0561403\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) −3.00000 −0.160128
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) 10.0000 17.3205i 0.530745 0.919277i
\(356\) 0 0
\(357\) 20.0000 + 6.92820i 1.05851 + 0.366679i
\(358\) 0 0
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 22.0000 1.15153
\(366\) 0 0
\(367\) 2.50000 + 4.33013i 0.130499 + 0.226031i 0.923869 0.382709i \(-0.125009\pi\)
−0.793370 + 0.608740i \(0.791675\pi\)
\(368\) 0 0
\(369\) −3.00000 + 5.19615i −0.156174 + 0.270501i
\(370\) 0 0
\(371\) 24.0000 20.7846i 1.24602 1.07908i
\(372\) 0 0
\(373\) 2.50000 4.33013i 0.129445 0.224205i −0.794017 0.607896i \(-0.792014\pi\)
0.923462 + 0.383691i \(0.125347\pi\)
\(374\) 0 0
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) 0 0
\(377\) −12.0000 −0.618031
\(378\) 0 0
\(379\) −13.0000 −0.667765 −0.333883 0.942615i \(-0.608359\pi\)
−0.333883 + 0.942615i \(0.608359\pi\)
\(380\) 0 0
\(381\) 1.50000 + 2.59808i 0.0768473 + 0.133103i
\(382\) 0 0
\(383\) −14.0000 + 24.2487i −0.715367 + 1.23905i 0.247451 + 0.968900i \(0.420407\pi\)
−0.962818 + 0.270151i \(0.912926\pi\)
\(384\) 0 0
\(385\) −2.00000 10.3923i −0.101929 0.529641i
\(386\) 0 0
\(387\) 5.50000 9.52628i 0.279581 0.484248i
\(388\) 0 0
\(389\) −5.00000 8.66025i −0.253510 0.439092i 0.710980 0.703213i \(-0.248252\pi\)
−0.964490 + 0.264120i \(0.914918\pi\)
\(390\) 0 0
\(391\) −64.0000 −3.23662
\(392\) 0 0
\(393\) 2.00000 0.100887
\(394\) 0 0
\(395\) 3.00000 + 5.19615i 0.150946 + 0.261447i
\(396\) 0 0
\(397\) −1.50000 + 2.59808i −0.0752828 + 0.130394i −0.901209 0.433384i \(-0.857319\pi\)
0.825926 + 0.563778i \(0.190653\pi\)
\(398\) 0 0
\(399\) −0.500000 2.59808i −0.0250313 0.130066i
\(400\) 0 0
\(401\) 6.00000 10.3923i 0.299626 0.518967i −0.676425 0.736512i \(-0.736472\pi\)
0.976050 + 0.217545i \(0.0698049\pi\)
\(402\) 0 0
\(403\) −4.50000 7.79423i −0.224161 0.388258i
\(404\) 0 0
\(405\) −2.00000 −0.0993808
\(406\) 0 0
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) 9.50000 + 16.4545i 0.469745 + 0.813622i 0.999402 0.0345902i \(-0.0110126\pi\)
−0.529657 + 0.848212i \(0.677679\pi\)
\(410\) 0 0
\(411\) −2.00000 + 3.46410i −0.0986527 + 0.170872i
\(412\) 0 0
\(413\) 8.00000 6.92820i 0.393654 0.340915i
\(414\) 0 0
\(415\) −2.00000 + 3.46410i −0.0981761 + 0.170046i
\(416\) 0 0
\(417\) −2.50000 4.33013i −0.122426 0.212047i
\(418\) 0 0
\(419\) −18.0000 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(420\) 0 0
\(421\) −27.0000 −1.31590 −0.657950 0.753062i \(-0.728576\pi\)
−0.657950 + 0.753062i \(0.728576\pi\)
\(422\) 0 0
\(423\) 3.00000 + 5.19615i 0.145865 + 0.252646i
\(424\) 0 0
\(425\) 4.00000 6.92820i 0.194029 0.336067i
\(426\) 0 0
\(427\) −15.0000 5.19615i −0.725901 0.251459i
\(428\) 0 0
\(429\) −3.00000 + 5.19615i −0.144841 + 0.250873i
\(430\) 0 0
\(431\) −15.0000 25.9808i −0.722525 1.25145i −0.959985 0.280052i \(-0.909648\pi\)
0.237460 0.971397i \(-0.423685\pi\)
\(432\) 0 0
\(433\) −25.0000 −1.20142 −0.600712 0.799466i \(-0.705116\pi\)
−0.600712 + 0.799466i \(0.705116\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) 0 0
\(437\) 4.00000 + 6.92820i 0.191346 + 0.331421i
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 1.00000 6.92820i 0.0476190 0.329914i
\(442\) 0 0
\(443\) −2.00000 + 3.46410i −0.0950229 + 0.164584i −0.909618 0.415445i \(-0.863626\pi\)
0.814595 + 0.580030i \(0.196959\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) 22.0000 1.03824 0.519122 0.854700i \(-0.326259\pi\)
0.519122 + 0.854700i \(0.326259\pi\)
\(450\) 0 0
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) 0 0
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) 0 0
\(455\) 15.0000 + 5.19615i 0.703211 + 0.243599i
\(456\) 0 0
\(457\) −6.50000 + 11.2583i −0.304057 + 0.526642i −0.977051 0.213006i \(-0.931675\pi\)
0.672994 + 0.739648i \(0.265008\pi\)
\(458\) 0 0
\(459\) −4.00000 6.92820i −0.186704 0.323381i
\(460\) 0 0
\(461\) 4.00000 0.186299 0.0931493 0.995652i \(-0.470307\pi\)
0.0931493 + 0.995652i \(0.470307\pi\)
\(462\) 0 0
\(463\) 11.0000 0.511213 0.255607 0.966781i \(-0.417725\pi\)
0.255607 + 0.966781i \(0.417725\pi\)
\(464\) 0 0
\(465\) −3.00000 5.19615i −0.139122 0.240966i
\(466\) 0 0
\(467\) 17.0000 29.4449i 0.786666 1.36255i −0.141332 0.989962i \(-0.545139\pi\)
0.927999 0.372584i \(-0.121528\pi\)
\(468\) 0 0
\(469\) 26.0000 22.5167i 1.20057 1.03972i
\(470\) 0 0
\(471\) −1.00000 + 1.73205i −0.0460776 + 0.0798087i
\(472\) 0 0
\(473\) −11.0000 19.0526i −0.505781 0.876038i
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) −12.0000 −0.549442
\(478\) 0 0
\(479\) −14.0000 24.2487i −0.639676 1.10795i −0.985504 0.169654i \(-0.945735\pi\)
0.345827 0.938298i \(-0.387598\pi\)
\(480\) 0 0
\(481\) −1.50000 + 2.59808i −0.0683941 + 0.118462i
\(482\) 0 0
\(483\) 4.00000 + 20.7846i 0.182006 + 0.945732i
\(484\) 0 0
\(485\) 10.0000 17.3205i 0.454077 0.786484i
\(486\) 0 0
\(487\) −9.50000 16.4545i −0.430486 0.745624i 0.566429 0.824110i \(-0.308325\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) −16.0000 27.7128i −0.720604 1.24812i
\(494\) 0 0
\(495\) −2.00000 + 3.46410i −0.0898933 + 0.155700i
\(496\) 0 0
\(497\) −5.00000 25.9808i −0.224281 1.16540i
\(498\) 0 0
\(499\) −14.5000 + 25.1147i −0.649109 + 1.12429i 0.334227 + 0.942493i \(0.391525\pi\)
−0.983336 + 0.181797i \(0.941809\pi\)
\(500\) 0 0
\(501\) −1.00000 1.73205i −0.0446767 0.0773823i
\(502\) 0 0
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 0 0
\(505\) −20.0000 −0.889988
\(506\) 0 0
\(507\) 2.00000 + 3.46410i 0.0888231 + 0.153846i
\(508\) 0 0
\(509\) −9.00000 + 15.5885i −0.398918 + 0.690946i −0.993593 0.113020i \(-0.963948\pi\)
0.594675 + 0.803966i \(0.297281\pi\)
\(510\) 0 0
\(511\) 22.0000 19.0526i 0.973223 0.842836i
\(512\) 0 0
\(513\) −0.500000 + 0.866025i −0.0220755 + 0.0382360i
\(514\) 0 0
\(515\) −11.0000 19.0526i −0.484718 0.839556i
\(516\) 0 0
\(517\) 12.0000 0.527759
\(518\) 0 0
\(519\) 16.0000 0.702322
\(520\) 0 0
\(521\) 18.0000 + 31.1769i 0.788594 + 1.36589i 0.926828 + 0.375486i \(0.122524\pi\)
−0.138234 + 0.990400i \(0.544143\pi\)
\(522\) 0 0
\(523\) −15.5000 + 26.8468i −0.677768 + 1.17393i 0.297884 + 0.954602i \(0.403719\pi\)
−0.975652 + 0.219326i \(0.929614\pi\)
\(524\) 0 0
\(525\) −2.50000 0.866025i −0.109109 0.0377964i
\(526\) 0 0
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) 0 0
\(529\) −20.5000 35.5070i −0.891304 1.54378i
\(530\) 0 0
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) −18.0000 −0.779667
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 3.00000 5.19615i 0.129460 0.224231i
\(538\) 0 0
\(539\) −11.0000 8.66025i −0.473804 0.373024i
\(540\) 0 0
\(541\) 7.50000 12.9904i 0.322450 0.558500i −0.658543 0.752543i \(-0.728827\pi\)
0.980993 + 0.194043i \(0.0621602\pi\)
\(542\) 0 0
\(543\) 7.50000 + 12.9904i 0.321856 + 0.557471i
\(544\) 0 0
\(545\) 22.0000 0.942376
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 0 0
\(549\) 3.00000 + 5.19615i 0.128037 + 0.221766i
\(550\) 0 0
\(551\) −2.00000 + 3.46410i −0.0852029 + 0.147576i
\(552\) 0 0
\(553\) 7.50000 + 2.59808i 0.318932 + 0.110481i
\(554\) 0 0
\(555\) −1.00000 + 1.73205i −0.0424476 + 0.0735215i
\(556\) 0 0
\(557\) −11.0000 19.0526i −0.466085 0.807283i 0.533165 0.846011i \(-0.321003\pi\)
−0.999250 + 0.0387286i \(0.987669\pi\)
\(558\) 0 0
\(559\) 33.0000 1.39575
\(560\) 0 0
\(561\) −16.0000 −0.675521
\(562\) 0 0
\(563\) −23.0000 39.8372i −0.969334 1.67894i −0.697489 0.716596i \(-0.745699\pi\)
−0.271846 0.962341i \(-0.587634\pi\)
\(564\) 0 0
\(565\) −14.0000 + 24.2487i −0.588984 + 1.02015i
\(566\) 0 0
\(567\) −2.00000 + 1.73205i −0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −10.5000 18.1865i −0.439411 0.761083i 0.558233 0.829684i \(-0.311480\pi\)
−0.997644 + 0.0686016i \(0.978146\pi\)
\(572\) 0 0
\(573\) −6.00000 −0.250654
\(574\) 0 0
\(575\) 8.00000 0.333623
\(576\) 0 0
\(577\) 20.5000 + 35.5070i 0.853426 + 1.47818i 0.878097 + 0.478482i \(0.158813\pi\)
−0.0246713 + 0.999696i \(0.507854\pi\)
\(578\) 0 0
\(579\) −5.50000 + 9.52628i −0.228572 + 0.395899i
\(580\) 0 0
\(581\) 1.00000 + 5.19615i 0.0414870 + 0.215573i
\(582\) 0 0
\(583\) −12.0000 + 20.7846i −0.496989 + 0.860811i
\(584\) 0 0
\(585\) −3.00000 5.19615i −0.124035 0.214834i
\(586\) 0 0
\(587\) −32.0000 −1.32078 −0.660391 0.750922i \(-0.729609\pi\)
−0.660391 + 0.750922i \(0.729609\pi\)
\(588\) 0 0
\(589\) −3.00000 −0.123613
\(590\) 0 0
\(591\) −4.00000 6.92820i −0.164538 0.284988i
\(592\) 0 0
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 8.00000 + 41.5692i 0.327968 + 1.70417i
\(596\) 0 0
\(597\) 4.00000 6.92820i 0.163709 0.283552i
\(598\) 0 0
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) −1.00000 −0.0407909 −0.0203954 0.999792i \(-0.506493\pi\)
−0.0203954 + 0.999792i \(0.506493\pi\)
\(602\) 0 0
\(603\) −13.0000 −0.529401
\(604\) 0 0
\(605\) −7.00000 12.1244i −0.284590 0.492925i
\(606\) 0 0
\(607\) −1.50000 + 2.59808i −0.0608831 + 0.105453i −0.894860 0.446346i \(-0.852725\pi\)
0.833977 + 0.551799i \(0.186058\pi\)
\(608\) 0 0
\(609\) −8.00000 + 6.92820i −0.324176 + 0.280745i
\(610\) 0 0
\(611\) −9.00000 + 15.5885i −0.364101 + 0.630641i
\(612\) 0 0
\(613\) 15.0000 + 25.9808i 0.605844 + 1.04935i 0.991917 + 0.126885i \(0.0404979\pi\)
−0.386073 + 0.922468i \(0.626169\pi\)
\(614\) 0 0
\(615\) −12.0000 −0.483887
\(616\) 0 0
\(617\) 26.0000 1.04672 0.523360 0.852111i \(-0.324678\pi\)
0.523360 + 0.852111i \(0.324678\pi\)
\(618\) 0 0
\(619\) −5.50000 9.52628i −0.221064 0.382893i 0.734068 0.679076i \(-0.237620\pi\)
−0.955131 + 0.296183i \(0.904286\pi\)
\(620\) 0 0
\(621\) 4.00000 6.92820i 0.160514 0.278019i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) 1.00000 + 1.73205i 0.0399362 + 0.0691714i
\(628\) 0 0
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) 16.0000 0.636950 0.318475 0.947931i \(-0.396829\pi\)
0.318475 + 0.947931i \(0.396829\pi\)
\(632\) 0 0
\(633\) −2.00000 3.46410i −0.0794929 0.137686i
\(634\) 0 0
\(635\) −3.00000 + 5.19615i −0.119051 + 0.206203i
\(636\) 0 0
\(637\) 19.5000 7.79423i 0.772618 0.308819i
\(638\) 0 0
\(639\) −5.00000 + 8.66025i −0.197797 + 0.342594i
\(640\) 0 0
\(641\) 20.0000 + 34.6410i 0.789953 + 1.36824i 0.925995 + 0.377535i \(0.123228\pi\)
−0.136043 + 0.990703i \(0.543438\pi\)
\(642\) 0 0
\(643\) −35.0000 −1.38027 −0.690133 0.723683i \(-0.742448\pi\)
−0.690133 + 0.723683i \(0.742448\pi\)
\(644\) 0 0
\(645\) 22.0000 0.866249
\(646\) 0 0
\(647\) 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i \(-0.129037\pi\)
−0.801010 + 0.598651i \(0.795704\pi\)
\(648\) 0 0
\(649\) −4.00000 + 6.92820i −0.157014 + 0.271956i
\(650\) 0 0
\(651\) −7.50000 2.59808i −0.293948 0.101827i
\(652\) 0 0
\(653\) 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 0 0
\(655\) 2.00000 + 3.46410i 0.0781465 + 0.135354i
\(656\) 0 0
\(657\) −11.0000 −0.429151
\(658\) 0 0
\(659\) 28.0000 1.09073 0.545363 0.838200i \(-0.316392\pi\)
0.545363 + 0.838200i \(0.316392\pi\)
\(660\) 0 0
\(661\) 14.5000 + 25.1147i 0.563985 + 0.976850i 0.997143 + 0.0755324i \(0.0240656\pi\)
−0.433159 + 0.901318i \(0.642601\pi\)
\(662\) 0 0
\(663\) 12.0000 20.7846i 0.466041 0.807207i
\(664\) 0 0
\(665\) 4.00000 3.46410i 0.155113 0.134332i
\(666\) 0 0
\(667\) 16.0000 27.7128i 0.619522 1.07304i
\(668\) 0 0
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 0 0
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) −1.00000 −0.0385472 −0.0192736 0.999814i \(-0.506135\pi\)
−0.0192736 + 0.999814i \(0.506135\pi\)
\(674\) 0 0
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 0 0
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 0 0
\(679\) −5.00000 25.9808i −0.191882 0.997050i
\(680\) 0 0
\(681\) −9.00000 + 15.5885i −0.344881 + 0.597351i
\(682\) 0 0
\(683\) 18.0000 + 31.1769i 0.688751 + 1.19295i 0.972242 + 0.233977i \(0.0751739\pi\)
−0.283491 + 0.958975i \(0.591493\pi\)
\(684\) 0 0
\(685\) −8.00000 −0.305664
\(686\) 0 0
\(687\) 1.00000 0.0381524
\(688\) 0 0
\(689\) −18.0000 31.1769i −0.685745 1.18775i
\(690\) 0 0
\(691\) −21.5000 + 37.2391i −0.817899 + 1.41664i 0.0893292 + 0.996002i \(0.471528\pi\)
−0.907228 + 0.420640i \(0.861806\pi\)
\(692\) 0 0
\(693\) 1.00000 + 5.19615i 0.0379869 + 0.197386i
\(694\) 0 0
\(695\) 5.00000 8.66025i 0.189661 0.328502i
\(696\) 0 0
\(697\) −24.0000 41.5692i −0.909065 1.57455i
\(698\) 0 0
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) −8.00000 −0.302156 −0.151078 0.988522i \(-0.548274\pi\)
−0.151078 + 0.988522i \(0.548274\pi\)
\(702\) 0 0
\(703\) 0.500000 + 0.866025i 0.0188579 + 0.0326628i
\(704\) 0 0
\(705\) −6.00000 + 10.3923i −0.225973 + 0.391397i
\(706\) 0 0
\(707\) −20.0000 + 17.3205i −0.752177 + 0.651405i
\(708\) 0 0
\(709\) −7.00000 + 12.1244i −0.262891 + 0.455340i −0.967009 0.254743i \(-0.918009\pi\)
0.704118 + 0.710083i \(0.251342\pi\)
\(710\) 0 0
\(711\) −1.50000 2.59808i −0.0562544 0.0974355i
\(712\) 0 0
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) −12.0000 −0.448775
\(716\) 0 0
\(717\) 9.00000 + 15.5885i 0.336111 + 0.582162i
\(718\) 0 0
\(719\) −3.00000 + 5.19615i −0.111881 + 0.193784i −0.916529 0.399969i \(-0.869021\pi\)
0.804648 + 0.593753i \(0.202354\pi\)
\(720\) 0 0
\(721\) −27.5000 9.52628i −1.02415 0.354777i
\(722\) 0 0
\(723\) −7.00000 + 12.1244i −0.260333 + 0.450910i
\(724\) 0 0
\(725\) 2.00000 + 3.46410i 0.0742781 + 0.128654i
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 44.0000 + 76.2102i 1.62740 + 2.81874i
\(732\) 0 0
\(733\) −22.5000 + 38.9711i −0.831056 + 1.43943i 0.0661448 + 0.997810i \(0.478930\pi\)
−0.897201 + 0.441622i \(0.854403\pi\)
\(734\) 0 0
\(735\) 13.0000 5.19615i 0.479512 0.191663i
\(736\) 0 0
\(737\) −13.0000 + 22.5167i −0.478861 + 0.829412i
\(738\) 0 0
\(739\) −4.50000 7.79423i −0.165535 0.286715i 0.771310 0.636460i \(-0.219602\pi\)
−0.936845 + 0.349744i \(0.886268\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) 0 0
\(743\) 18.0000 0.660356 0.330178 0.943919i \(-0.392891\pi\)
0.330178 + 0.943919i \(0.392891\pi\)
\(744\) 0 0
\(745\) −12.0000 20.7846i −0.439646 0.761489i
\(746\) 0 0
\(747\) 1.00000 1.73205i 0.0365881 0.0633724i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 7.50000 12.9904i 0.273679 0.474026i −0.696122 0.717923i \(-0.745093\pi\)
0.969801 + 0.243898i \(0.0784261\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −16.0000 −0.582300
\(756\) 0 0
\(757\) 42.0000 1.52652 0.763258 0.646094i \(-0.223599\pi\)
0.763258 + 0.646094i \(0.223599\pi\)
\(758\) 0 0
\(759\) −8.00000 13.8564i −0.290382 0.502956i
\(760\) 0 0
\(761\) −4.00000 + 6.92820i −0.145000 + 0.251147i −0.929373 0.369142i \(-0.879652\pi\)
0.784373 + 0.620289i \(0.212985\pi\)
\(762\) 0 0
\(763\) 22.0000 19.0526i 0.796453 0.689749i
\(764\) 0 0
\(765\) 8.00000 13.8564i 0.289241 0.500979i
\(766\) 0 0
\(767\) −6.00000 10.3923i −0.216647 0.375244i
\(768\) 0 0
\(769\) 31.0000 1.11789 0.558944 0.829205i \(-0.311207\pi\)
0.558944 + 0.829205i \(0.311207\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 0 0
\(773\) −11.0000 19.0526i −0.395643 0.685273i 0.597540 0.801839i \(-0.296145\pi\)
−0.993183 + 0.116566i \(0.962811\pi\)
\(774\) 0 0
\(775\) −1.50000 + 2.59808i −0.0538816 + 0.0933257i
\(776\) 0 0
\(777\) 0.500000 + 2.59808i 0.0179374 + 0.0932055i
\(778\) 0 0
\(779\) −3.00000 + 5.19615i −0.107486 + 0.186171i
\(780\) 0 0
\(781\) 10.0000 + 17.3205i 0.357828 + 0.619777i
\(782\) 0 0
\(783\) 4.00000 0.142948
\(784\) 0 0
\(785\) −4.00000 −0.142766
\(786\) 0 0
\(787\) 12.0000 + 20.7846i 0.427754 + 0.740891i 0.996673 0.0815020i \(-0.0259717\pi\)
−0.568919 + 0.822393i \(0.692638\pi\)
\(788\) 0 0
\(789\) 6.00000 10.3923i 0.213606 0.369976i
\(790\) 0 0
\(791\) 7.00000 + 36.3731i 0.248891 + 1.29328i
\(792\) 0 0
\(793\) −9.00000 + 15.5885i −0.319599 + 0.553562i
\(794\) 0 0
\(795\) −12.0000 20.7846i −0.425596 0.737154i
\(796\) 0 0
\(797\) −48.0000