Properties

Label 336.2.q.c.193.1
Level $336$
Weight $2$
Character 336.193
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 193.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 336.193
Dual form 336.2.q.c.289.1

$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 0
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) 1.00000 + 1.73205i 0.447214 + 0.774597i 0.998203 0.0599153i \(-0.0190830\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 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 −0.674967 0.737848i \(-0.735842\pi\)
0.976478 + 0.215615i \(0.0691756\pi\)
\(12\) 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 −0.275029 + 0.961436i \(0.588688\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 0 0
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) 0 0
\(21\) −2.00000 1.73205i −0.436436 0.377964i
\(22\) 0 0
\(23\) 4.00000 + 6.92820i 0.834058 + 1.44463i 0.894795 + 0.446476i \(0.147321\pi\)
−0.0607377 + 0.998154i \(0.519345\pi\)
\(24\) 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 −0.699301 0.714827i \(-0.746505\pi\)
0.968709 + 0.248199i \(0.0798387\pi\)
\(32\) 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 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 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 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 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 −0.0783936 0.996922i \(-0.524979\pi\)
0.902557 0.430570i \(-0.141688\pi\)
\(54\) 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 −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) 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 −0.129307 0.991605i \(-0.541275\pi\)
0.923408 0.383819i \(-0.125391\pi\)
\(68\) 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 −0.340868 0.940111i \(-0.610721\pi\)
0.984594 0.174855i \(-0.0559458\pi\)
\(74\) 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 0.769222 0.638982i \(-0.220644\pi\)
−0.937985 + 0.346675i \(0.887311\pi\)
\(80\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) 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 −0.999996 0.00286291i \(-0.999089\pi\)
0.502477 + 0.864590i \(0.332422\pi\)
\(102\) 0 0
\(103\) 5.50000 + 9.52628i 0.541931 + 0.938652i 0.998793 + 0.0491146i \(0.0156400\pi\)
−0.456862 + 0.889538i \(0.651027\pi\)
\(104\) 0 0
\(105\) 1.00000 5.19615i 0.0975900 0.507093i
\(106\) 0 0
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) 0 0
\(109\) 5.50000 9.52628i 0.526804 0.912452i −0.472708 0.881219i \(-0.656723\pi\)
0.999512 0.0312328i \(-0.00994332\pi\)
\(110\) 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 0.819028 0.573753i \(-0.194513\pi\)
−0.906399 + 0.422423i \(0.861180\pi\)
\(132\) 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 −0.938725 0.344668i \(-0.887992\pi\)
0.767853 + 0.640626i \(0.221325\pi\)
\(138\) 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 0.999953 0.00974235i \(-0.00310113\pi\)
−0.508413 + 0.861113i \(0.669768\pi\)
\(150\) 0 0
\(151\) −4.00000 + 6.92820i −0.325515 + 0.563809i −0.981617 0.190864i \(-0.938871\pi\)
0.656101 + 0.754673i \(0.272204\pi\)
\(152\) 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 −0.903167 0.429289i \(-0.858764\pi\)
0.823359 + 0.567521i \(0.192098\pi\)
\(158\) 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 0.777007 0.629492i \(-0.216737\pi\)
−0.933659 + 0.358162i \(0.883403\pi\)
\(164\) 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 −0.991532 0.129861i \(-0.958547\pi\)
0.383304 0.923622i \(-0.374786\pi\)
\(174\) 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 −0.731858 0.681457i \(-0.761346\pi\)
0.956088 + 0.293079i \(0.0946798\pi\)
\(180\) 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 0.953912 0.300088i \(-0.0970159\pi\)
−0.736839 + 0.676068i \(0.763683\pi\)
\(192\) 0 0
\(193\) −5.50000 + 9.52628i −0.395899 + 0.685717i −0.993215 0.116289i \(-0.962900\pi\)
0.597317 + 0.802005i \(0.296234\pi\)
\(194\) 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 −0.688705 0.725042i \(-0.741820\pi\)
0.972257 + 0.233915i \(0.0751537\pi\)
\(200\) 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 0.395860 + 0.918311i \(0.370447\pi\)
−0.993210 + 0.116331i \(0.962887\pi\)
\(228\) 0 0
\(229\) −0.500000 0.866025i −0.0330409 0.0572286i 0.849032 0.528341i \(-0.177186\pi\)
−0.882073 + 0.471113i \(0.843853\pi\)
\(230\) 0 0
\(231\) −5.00000 + 1.73205i −0.328976 + 0.113961i
\(232\) 0 0
\(233\) −7.00000 12.1244i −0.458585 0.794293i 0.540301 0.841472i \(-0.318310\pi\)
−0.998886 + 0.0471787i \(0.984977\pi\)
\(234\) 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 −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) 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 −0.997374 0.0724199i \(-0.976928\pi\)
0.435970 0.899961i \(-0.356405\pi\)
\(258\) 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 −0.619586 0.784929i \(-0.712699\pi\)
0.989561 + 0.144112i \(0.0460326\pi\)
\(264\) 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 −0.833929 0.551872i \(-0.813914\pi\)
0.894900 + 0.446267i \(0.147247\pi\)
\(270\) 0 0
\(271\) −12.0000 20.7846i −0.728948 1.26258i −0.957328 0.289003i \(-0.906676\pi\)
0.228380 0.973572i \(-0.426657\pi\)
\(272\) 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 0.489207 + 0.872167i \(0.337286\pi\)
−0.999923 + 0.0124177i \(0.996047\pi\)
\(278\) 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 −0.432360 0.901701i \(-0.642319\pi\)
0.997076 0.0764162i \(-0.0243478\pi\)
\(284\) 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 −0.892984 0.450088i \(-0.851393\pi\)
0.836280 + 0.548303i \(0.184726\pi\)
\(312\) 0 0
\(313\) 8.50000 + 14.7224i 0.480448 + 0.832161i 0.999748 0.0224310i \(-0.00714060\pi\)
−0.519300 + 0.854592i \(0.673807\pi\)
\(314\) 0 0
\(315\) 4.00000 + 3.46410i 0.225374 + 0.195180i
\(316\) 0 0
\(317\) 12.0000 + 20.7846i 0.673987 + 1.16738i 0.976764 + 0.214318i \(0.0687530\pi\)
−0.302777 + 0.953062i \(0.597914\pi\)
\(318\) 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 0.999298 0.0374662i \(-0.0119287\pi\)
−0.532096 + 0.846684i \(0.678595\pi\)
\(332\) 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 −0.340293 0.940319i \(-0.610526\pi\)
0.984487 0.175457i \(-0.0561403\pi\)
\(348\) 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 −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) 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 −0.999476 0.0323801i \(-0.989691\pi\)
0.471696 0.881761i \(-0.343642\pi\)
\(360\) 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 −0.793370 0.608740i \(-0.791675\pi\)
0.923869 + 0.382709i \(0.125009\pi\)
\(368\) 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 0.923462 0.383691i \(-0.125347\pi\)
−0.794017 + 0.607896i \(0.792014\pi\)
\(374\) 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 −0.962818 0.270151i \(-0.912926\pi\)
0.247451 0.968900i \(-0.420407\pi\)
\(384\) 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 −0.964490 0.264120i \(-0.914918\pi\)
0.710980 + 0.703213i \(0.248252\pi\)
\(390\) 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 0.825926 0.563778i \(-0.190653\pi\)
−0.901209 + 0.433384i \(0.857319\pi\)
\(398\) 0 0
\(399\) −0.500000 + 2.59808i −0.0250313 + 0.130066i
\(400\) 0 0
\(401\) 6.00000 + 10.3923i 0.299626 + 0.518967i 0.976050 0.217545i \(-0.0698049\pi\)
−0.676425 + 0.736512i \(0.736472\pi\)
\(402\) 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 −0.529657 0.848212i \(-0.677679\pi\)
0.999402 + 0.0345902i \(0.0110126\pi\)
\(410\) 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 0.237460 + 0.971397i \(0.423685\pi\)
−0.959985 + 0.280052i \(0.909648\pi\)
\(432\) 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 0.996284 + 0.0861252i \(0.0274485\pi\)
−0.423556 + 0.905870i \(0.639218\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) −2.00000 3.46410i −0.0950229 0.164584i 0.814595 0.580030i \(-0.196959\pi\)
−0.909618 + 0.415445i \(0.863626\pi\)
\(444\) 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 0.672994 0.739648i \(-0.265008\pi\)
−0.977051 + 0.213006i \(0.931675\pi\)
\(458\) 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 0.927999 + 0.372584i \(0.121528\pi\)
−0.141332 + 0.989962i \(0.545139\pi\)
\(468\) 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 0.345827 + 0.938298i \(0.387598\pi\)
−0.985504 + 0.169654i \(0.945735\pi\)
\(480\) 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 −0.996915 0.0784867i \(-0.974991\pi\)
0.566429 + 0.824110i \(0.308325\pi\)
\(488\) 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 −0.983336 0.181797i \(-0.941809\pi\)
0.334227 0.942493i \(-0.391525\pi\)
\(500\) 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 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 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 −0.138234 0.990400i \(-0.544143\pi\)
0.926828 0.375486i \(-0.122524\pi\)
\(522\) 0 0
\(523\) −15.5000 26.8468i −0.677768 1.17393i −0.975652 0.219326i \(-0.929614\pi\)
0.297884 0.954602i \(-0.403719\pi\)
\(524\) 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 0.980993 0.194043i \(-0.0621602\pi\)
−0.658543 + 0.752543i \(0.728827\pi\)
\(542\) 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 −0.999250 0.0387286i \(-0.987669\pi\)
0.533165 + 0.846011i \(0.321003\pi\)
\(558\) 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 −0.271846 + 0.962341i \(0.587634\pi\)
−0.697489 + 0.716596i \(0.745699\pi\)
\(564\) 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 0.796266 0.604947i \(-0.206806\pi\)
−0.922032 + 0.387113i \(0.873472\pi\)
\(570\) 0 0
\(571\) −10.5000 + 18.1865i −0.439411 + 0.761083i −0.997644 0.0686016i \(-0.978146\pi\)
0.558233 + 0.829684i \(0.311480\pi\)
\(572\) 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 −0.0246713 0.999696i \(-0.507854\pi\)
0.878097 0.478482i \(-0.158813\pi\)
\(578\) 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 0.921026 0.389501i \(-0.127353\pi\)
−0.797831 + 0.602881i \(0.794019\pi\)
\(594\) 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 −0.962175 0.272433i \(-0.912172\pi\)
0.717021 + 0.697051i \(0.245505\pi\)
\(600\) 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 0.833977 0.551799i \(-0.186058\pi\)
−0.894860 + 0.446346i \(0.852725\pi\)
\(608\) 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 −0.386073 0.922468i \(-0.626169\pi\)
0.991917 0.126885i \(-0.0404979\pi\)
\(614\) 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 −0.955131 0.296183i \(-0.904286\pi\)
0.734068 + 0.679076i \(0.237620\pi\)
\(620\) 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 −0.136043 0.990703i \(-0.543438\pi\)
0.925995 0.377535i \(-0.123228\pi\)
\(642\) 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 −0.801010 0.598651i \(-0.795704\pi\)
0.918952 + 0.394369i \(0.129037\pi\)
\(648\) 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 0.918736 0.394872i \(-0.129211\pi\)
−0.801337 + 0.598213i \(0.795878\pi\)
\(654\) 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 −0.433159 0.901318i \(-0.642601\pi\)
0.997143 0.0755324i \(-0.0240656\pi\)
\(662\) 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 0.727386 0.686229i \(-0.240735\pi\)
−0.957984 + 0.286820i \(0.907402\pi\)
\(678\) 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 −0.283491 0.958975i \(-0.591493\pi\)
0.972242 0.233977i \(-0.0751739\pi\)
\(684\) 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 −0.907228 0.420640i \(-0.861806\pi\)
0.0893292 0.996002i \(-0.471528\pi\)
\(692\) 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 0.704118 0.710083i \(-0.251342\pi\)
−0.967009 + 0.254743i \(0.918009\pi\)
\(710\) 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 0.804648 0.593753i \(-0.202354\pi\)
−0.916529 + 0.399969i \(0.869021\pi\)
\(720\) 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 −0.897201 0.441622i \(-0.854403\pi\)
0.0661448 0.997810i \(-0.478930\pi\)
\(734\) 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 −0.936845 0.349744i \(-0.886268\pi\)
0.771310 + 0.636460i \(0.219602\pi\)
\(740\) 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 0.969801 0.243898i \(-0.0784261\pi\)
−0.696122 + 0.717923i \(0.745093\pi\)
\(752\) 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 0.784373 0.620289i \(-0.212985\pi\)
−0.929373 + 0.369142i \(0.879652\pi\)
\(762\) 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 −0.993183 0.116566i \(-0.962811\pi\)
0.597540 + 0.801839i \(0.296145\pi\)
\(774\) 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 −0.568919 0.822393i \(-0.692638\pi\)
0.996673 + 0.0815020i \(0.0259717\pi\)
\(788\) 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
\(797\)