Properties

Label 624.2.bv.e.433.2
Level $624$
Weight $2$
Character 624.433
Analytic conductor $4.983$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.bv (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 78)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 433.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 624.433
Dual form 624.2.bv.e.49.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{3} +3.73205i q^{5} +(-2.36603 + 1.36603i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{3} +3.73205i q^{5} +(-2.36603 + 1.36603i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.09808 - 0.633975i) q^{11} +(-2.59808 + 2.50000i) q^{13} +(3.23205 + 1.86603i) q^{15} +(-2.86603 - 4.96410i) q^{17} +(-4.09808 + 2.36603i) q^{19} +2.73205i q^{21} +(-2.09808 + 3.63397i) q^{23} -8.92820 q^{25} -1.00000 q^{27} +(2.23205 - 3.86603i) q^{29} -1.46410i q^{31} +(-1.09808 + 0.633975i) q^{33} +(-5.09808 - 8.83013i) q^{35} +(3.06218 + 1.76795i) q^{37} +(0.866025 + 3.50000i) q^{39} +(8.13397 + 4.69615i) q^{41} +(4.83013 + 8.36603i) q^{43} +(3.23205 - 1.86603i) q^{45} +2.19615i q^{47} +(0.232051 - 0.401924i) q^{49} -5.73205 q^{51} -6.46410 q^{53} +(2.36603 - 4.09808i) q^{55} +4.73205i q^{57} +(6.92820 - 4.00000i) q^{59} +(4.59808 + 7.96410i) q^{61} +(2.36603 + 1.36603i) q^{63} +(-9.33013 - 9.69615i) q^{65} +(11.3660 + 6.56218i) q^{67} +(2.09808 + 3.63397i) q^{69} +(-4.09808 + 2.36603i) q^{71} +6.26795i q^{73} +(-4.46410 + 7.73205i) q^{75} +3.46410 q^{77} +2.53590 q^{79} +(-0.500000 + 0.866025i) q^{81} +0.196152i q^{83} +(18.5263 - 10.6962i) q^{85} +(-2.23205 - 3.86603i) q^{87} +(-8.19615 - 4.73205i) q^{89} +(2.73205 - 9.46410i) q^{91} +(-1.26795 - 0.732051i) q^{93} +(-8.83013 - 15.2942i) q^{95} +(-5.19615 + 3.00000i) q^{97} +1.26795i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{3} - 6 q^{7} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} - 6 q^{7} - 2 q^{9} + 6 q^{11} + 6 q^{15} - 8 q^{17} - 6 q^{19} + 2 q^{23} - 8 q^{25} - 4 q^{27} + 2 q^{29} + 6 q^{33} - 10 q^{35} - 12 q^{37} + 36 q^{41} + 2 q^{43} + 6 q^{45} - 6 q^{49} - 16 q^{51} - 12 q^{53} + 6 q^{55} + 8 q^{61} + 6 q^{63} - 20 q^{65} + 42 q^{67} - 2 q^{69} - 6 q^{71} - 4 q^{75} + 24 q^{79} - 2 q^{81} + 36 q^{85} - 2 q^{87} - 12 q^{89} + 4 q^{91} - 12 q^{93} - 18 q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(1\) \(1\)

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
\(5\) 3.73205i 1.66902i 0.550990 + 0.834512i \(0.314250\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(6\) 0 0
\(7\) −2.36603 + 1.36603i −0.894274 + 0.516309i −0.875338 0.483512i \(-0.839361\pi\)
−0.0189356 + 0.999821i \(0.506028\pi\)
\(8\) 0 0
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 0 0
\(11\) −1.09808 0.633975i −0.331082 0.191151i 0.325239 0.945632i \(-0.394555\pi\)
−0.656322 + 0.754481i \(0.727889\pi\)
\(12\) 0 0
\(13\) −2.59808 + 2.50000i −0.720577 + 0.693375i
\(14\) 0 0
\(15\) 3.23205 + 1.86603i 0.834512 + 0.481806i
\(16\) 0 0
\(17\) −2.86603 4.96410i −0.695113 1.20397i −0.970143 0.242536i \(-0.922021\pi\)
0.275029 0.961436i \(-0.411312\pi\)
\(18\) 0 0
\(19\) −4.09808 + 2.36603i −0.940163 + 0.542803i −0.890011 0.455938i \(-0.849304\pi\)
−0.0501517 + 0.998742i \(0.515970\pi\)
\(20\) 0 0
\(21\) 2.73205i 0.596182i
\(22\) 0 0
\(23\) −2.09808 + 3.63397i −0.437479 + 0.757736i −0.997494 0.0707462i \(-0.977462\pi\)
0.560015 + 0.828482i \(0.310795\pi\)
\(24\) 0 0
\(25\) −8.92820 −1.78564
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.23205 3.86603i 0.414481 0.717903i −0.580892 0.813980i \(-0.697296\pi\)
0.995374 + 0.0960774i \(0.0306296\pi\)
\(30\) 0 0
\(31\) 1.46410i 0.262960i −0.991319 0.131480i \(-0.958027\pi\)
0.991319 0.131480i \(-0.0419730\pi\)
\(32\) 0 0
\(33\) −1.09808 + 0.633975i −0.191151 + 0.110361i
\(34\) 0 0
\(35\) −5.09808 8.83013i −0.861732 1.49256i
\(36\) 0 0
\(37\) 3.06218 + 1.76795i 0.503419 + 0.290649i 0.730124 0.683314i \(-0.239462\pi\)
−0.226705 + 0.973963i \(0.572795\pi\)
\(38\) 0 0
\(39\) 0.866025 + 3.50000i 0.138675 + 0.560449i
\(40\) 0 0
\(41\) 8.13397 + 4.69615i 1.27031 + 0.733416i 0.975047 0.221999i \(-0.0712582\pi\)
0.295267 + 0.955415i \(0.404592\pi\)
\(42\) 0 0
\(43\) 4.83013 + 8.36603i 0.736587 + 1.27581i 0.954023 + 0.299732i \(0.0968974\pi\)
−0.217436 + 0.976075i \(0.569769\pi\)
\(44\) 0 0
\(45\) 3.23205 1.86603i 0.481806 0.278171i
\(46\) 0 0
\(47\) 2.19615i 0.320342i 0.987089 + 0.160171i \(0.0512045\pi\)
−0.987089 + 0.160171i \(0.948795\pi\)
\(48\) 0 0
\(49\) 0.232051 0.401924i 0.0331501 0.0574177i
\(50\) 0 0
\(51\) −5.73205 −0.802648
\(52\) 0 0
\(53\) −6.46410 −0.887913 −0.443956 0.896048i \(-0.646425\pi\)
−0.443956 + 0.896048i \(0.646425\pi\)
\(54\) 0 0
\(55\) 2.36603 4.09808i 0.319035 0.552584i
\(56\) 0 0
\(57\) 4.73205i 0.626775i
\(58\) 0 0
\(59\) 6.92820 4.00000i 0.901975 0.520756i 0.0241347 0.999709i \(-0.492317\pi\)
0.877841 + 0.478953i \(0.158984\pi\)
\(60\) 0 0
\(61\) 4.59808 + 7.96410i 0.588723 + 1.01970i 0.994400 + 0.105682i \(0.0337026\pi\)
−0.405677 + 0.914017i \(0.632964\pi\)
\(62\) 0 0
\(63\) 2.36603 + 1.36603i 0.298091 + 0.172103i
\(64\) 0 0
\(65\) −9.33013 9.69615i −1.15726 1.20266i
\(66\) 0 0
\(67\) 11.3660 + 6.56218i 1.38858 + 0.801698i 0.993155 0.116800i \(-0.0372638\pi\)
0.395426 + 0.918498i \(0.370597\pi\)
\(68\) 0 0
\(69\) 2.09808 + 3.63397i 0.252579 + 0.437479i
\(70\) 0 0
\(71\) −4.09808 + 2.36603i −0.486352 + 0.280796i −0.723060 0.690785i \(-0.757265\pi\)
0.236708 + 0.971581i \(0.423932\pi\)
\(72\) 0 0
\(73\) 6.26795i 0.733608i 0.930298 + 0.366804i \(0.119548\pi\)
−0.930298 + 0.366804i \(0.880452\pi\)
\(74\) 0 0
\(75\) −4.46410 + 7.73205i −0.515470 + 0.892820i
\(76\) 0 0
\(77\) 3.46410 0.394771
\(78\) 0 0
\(79\) 2.53590 0.285311 0.142655 0.989772i \(-0.454436\pi\)
0.142655 + 0.989772i \(0.454436\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 0.196152i 0.0215305i 0.999942 + 0.0107653i \(0.00342676\pi\)
−0.999942 + 0.0107653i \(0.996573\pi\)
\(84\) 0 0
\(85\) 18.5263 10.6962i 2.00946 1.16016i
\(86\) 0 0
\(87\) −2.23205 3.86603i −0.239301 0.414481i
\(88\) 0 0
\(89\) −8.19615 4.73205i −0.868790 0.501596i −0.00184433 0.999998i \(-0.500587\pi\)
−0.866946 + 0.498402i \(0.833920\pi\)
\(90\) 0 0
\(91\) 2.73205 9.46410i 0.286397 0.992107i
\(92\) 0 0
\(93\) −1.26795 0.732051i −0.131480 0.0759101i
\(94\) 0 0
\(95\) −8.83013 15.2942i −0.905952 1.56915i
\(96\) 0 0
\(97\) −5.19615 + 3.00000i −0.527589 + 0.304604i −0.740034 0.672569i \(-0.765191\pi\)
0.212445 + 0.977173i \(0.431857\pi\)
\(98\) 0 0
\(99\) 1.26795i 0.127434i
\(100\) 0 0
\(101\) 0.964102 1.66987i 0.0959317 0.166159i −0.814065 0.580773i \(-0.802750\pi\)
0.909997 + 0.414615i \(0.136084\pi\)
\(102\) 0 0
\(103\) −15.2679 −1.50440 −0.752198 0.658937i \(-0.771006\pi\)
−0.752198 + 0.658937i \(0.771006\pi\)
\(104\) 0 0
\(105\) −10.1962 −0.995043
\(106\) 0 0
\(107\) 5.09808 8.83013i 0.492850 0.853641i −0.507116 0.861878i \(-0.669289\pi\)
0.999966 + 0.00823695i \(0.00262193\pi\)
\(108\) 0 0
\(109\) 1.46410i 0.140236i 0.997539 + 0.0701178i \(0.0223375\pi\)
−0.997539 + 0.0701178i \(0.977662\pi\)
\(110\) 0 0
\(111\) 3.06218 1.76795i 0.290649 0.167806i
\(112\) 0 0
\(113\) 0.669873 + 1.16025i 0.0630163 + 0.109148i 0.895812 0.444432i \(-0.146595\pi\)
−0.832796 + 0.553580i \(0.813261\pi\)
\(114\) 0 0
\(115\) −13.5622 7.83013i −1.26468 0.730163i
\(116\) 0 0
\(117\) 3.46410 + 1.00000i 0.320256 + 0.0924500i
\(118\) 0 0
\(119\) 13.5622 + 7.83013i 1.24324 + 0.717787i
\(120\) 0 0
\(121\) −4.69615 8.13397i −0.426923 0.739452i
\(122\) 0 0
\(123\) 8.13397 4.69615i 0.733416 0.423438i
\(124\) 0 0
\(125\) 14.6603i 1.31125i
\(126\) 0 0
\(127\) 4.92820 8.53590i 0.437307 0.757438i −0.560173 0.828375i \(-0.689266\pi\)
0.997481 + 0.0709368i \(0.0225989\pi\)
\(128\) 0 0
\(129\) 9.66025 0.850538
\(130\) 0 0
\(131\) −6.53590 −0.571044 −0.285522 0.958372i \(-0.592167\pi\)
−0.285522 + 0.958372i \(0.592167\pi\)
\(132\) 0 0
\(133\) 6.46410 11.1962i 0.560509 0.970830i
\(134\) 0 0
\(135\) 3.73205i 0.321204i
\(136\) 0 0
\(137\) −10.3301 + 5.96410i −0.882562 + 0.509548i −0.871502 0.490391i \(-0.836854\pi\)
−0.0110599 + 0.999939i \(0.503521\pi\)
\(138\) 0 0
\(139\) 8.92820 + 15.4641i 0.757280 + 1.31165i 0.944233 + 0.329279i \(0.106806\pi\)
−0.186952 + 0.982369i \(0.559861\pi\)
\(140\) 0 0
\(141\) 1.90192 + 1.09808i 0.160171 + 0.0924747i
\(142\) 0 0
\(143\) 4.43782 1.09808i 0.371109 0.0918257i
\(144\) 0 0
\(145\) 14.4282 + 8.33013i 1.19820 + 0.691779i
\(146\) 0 0
\(147\) −0.232051 0.401924i −0.0191392 0.0331501i
\(148\) 0 0
\(149\) 11.4282 6.59808i 0.936235 0.540535i 0.0474568 0.998873i \(-0.484888\pi\)
0.888778 + 0.458338i \(0.151555\pi\)
\(150\) 0 0
\(151\) 6.73205i 0.547847i 0.961752 + 0.273923i \(0.0883214\pi\)
−0.961752 + 0.273923i \(0.911679\pi\)
\(152\) 0 0
\(153\) −2.86603 + 4.96410i −0.231704 + 0.401324i
\(154\) 0 0
\(155\) 5.46410 0.438887
\(156\) 0 0
\(157\) 7.58846 0.605625 0.302812 0.953050i \(-0.402074\pi\)
0.302812 + 0.953050i \(0.402074\pi\)
\(158\) 0 0
\(159\) −3.23205 + 5.59808i −0.256318 + 0.443956i
\(160\) 0 0
\(161\) 11.4641i 0.903498i
\(162\) 0 0
\(163\) −11.6603 + 6.73205i −0.913302 + 0.527295i −0.881492 0.472199i \(-0.843460\pi\)
−0.0318096 + 0.999494i \(0.510127\pi\)
\(164\) 0 0
\(165\) −2.36603 4.09808i −0.184195 0.319035i
\(166\) 0 0
\(167\) 8.19615 + 4.73205i 0.634237 + 0.366177i 0.782391 0.622787i \(-0.214000\pi\)
−0.148154 + 0.988964i \(0.547333\pi\)
\(168\) 0 0
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) 0 0
\(171\) 4.09808 + 2.36603i 0.313388 + 0.180934i
\(172\) 0 0
\(173\) 2.19615 + 3.80385i 0.166970 + 0.289201i 0.937353 0.348380i \(-0.113268\pi\)
−0.770383 + 0.637582i \(0.779935\pi\)
\(174\) 0 0
\(175\) 21.1244 12.1962i 1.59685 0.921942i
\(176\) 0 0
\(177\) 8.00000i 0.601317i
\(178\) 0 0
\(179\) 8.02628 13.9019i 0.599912 1.03908i −0.392921 0.919572i \(-0.628535\pi\)
0.992833 0.119506i \(-0.0381312\pi\)
\(180\) 0 0
\(181\) −19.1962 −1.42684 −0.713419 0.700737i \(-0.752855\pi\)
−0.713419 + 0.700737i \(0.752855\pi\)
\(182\) 0 0
\(183\) 9.19615 0.679799
\(184\) 0 0
\(185\) −6.59808 + 11.4282i −0.485100 + 0.840218i
\(186\) 0 0
\(187\) 7.26795i 0.531485i
\(188\) 0 0
\(189\) 2.36603 1.36603i 0.172103 0.0993637i
\(190\) 0 0
\(191\) −3.46410 6.00000i −0.250654 0.434145i 0.713052 0.701111i \(-0.247312\pi\)
−0.963706 + 0.266966i \(0.913979\pi\)
\(192\) 0 0
\(193\) −10.1603 5.86603i −0.731351 0.422246i 0.0875652 0.996159i \(-0.472091\pi\)
−0.818916 + 0.573913i \(0.805425\pi\)
\(194\) 0 0
\(195\) −13.0622 + 3.23205i −0.935402 + 0.231452i
\(196\) 0 0
\(197\) 15.4641 + 8.92820i 1.10177 + 0.636108i 0.936686 0.350171i \(-0.113877\pi\)
0.165086 + 0.986279i \(0.447210\pi\)
\(198\) 0 0
\(199\) 7.09808 + 12.2942i 0.503169 + 0.871515i 0.999993 + 0.00366345i \(0.00116611\pi\)
−0.496824 + 0.867851i \(0.665501\pi\)
\(200\) 0 0
\(201\) 11.3660 6.56218i 0.801698 0.462860i
\(202\) 0 0
\(203\) 12.1962i 0.856002i
\(204\) 0 0
\(205\) −17.5263 + 30.3564i −1.22409 + 2.12018i
\(206\) 0 0
\(207\) 4.19615 0.291653
\(208\) 0 0
\(209\) 6.00000 0.415029
\(210\) 0 0
\(211\) 8.19615 14.1962i 0.564246 0.977303i −0.432873 0.901455i \(-0.642500\pi\)
0.997119 0.0758485i \(-0.0241665\pi\)
\(212\) 0 0
\(213\) 4.73205i 0.324235i
\(214\) 0 0
\(215\) −31.2224 + 18.0263i −2.12935 + 1.22938i
\(216\) 0 0
\(217\) 2.00000 + 3.46410i 0.135769 + 0.235159i
\(218\) 0 0
\(219\) 5.42820 + 3.13397i 0.366804 + 0.211774i
\(220\) 0 0
\(221\) 19.8564 + 5.73205i 1.33569 + 0.385579i
\(222\) 0 0
\(223\) −23.3205 13.4641i −1.56166 0.901623i −0.997090 0.0762356i \(-0.975710\pi\)
−0.564567 0.825387i \(-0.690957\pi\)
\(224\) 0 0
\(225\) 4.46410 + 7.73205i 0.297607 + 0.515470i
\(226\) 0 0
\(227\) 10.5622 6.09808i 0.701036 0.404744i −0.106697 0.994292i \(-0.534027\pi\)
0.807733 + 0.589548i \(0.200694\pi\)
\(228\) 0 0
\(229\) 11.8564i 0.783493i 0.920073 + 0.391747i \(0.128129\pi\)
−0.920073 + 0.391747i \(0.871871\pi\)
\(230\) 0 0
\(231\) 1.73205 3.00000i 0.113961 0.197386i
\(232\) 0 0
\(233\) 7.85641 0.514690 0.257345 0.966320i \(-0.417152\pi\)
0.257345 + 0.966320i \(0.417152\pi\)
\(234\) 0 0
\(235\) −8.19615 −0.534658
\(236\) 0 0
\(237\) 1.26795 2.19615i 0.0823622 0.142655i
\(238\) 0 0
\(239\) 7.66025i 0.495501i −0.968824 0.247750i \(-0.920309\pi\)
0.968824 0.247750i \(-0.0796913\pi\)
\(240\) 0 0
\(241\) −11.7679 + 6.79423i −0.758040 + 0.437655i −0.828592 0.559853i \(-0.810857\pi\)
0.0705514 + 0.997508i \(0.477524\pi\)
\(242\) 0 0
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 1.50000 + 0.866025i 0.0958315 + 0.0553283i
\(246\) 0 0
\(247\) 4.73205 16.3923i 0.301093 1.04302i
\(248\) 0 0
\(249\) 0.169873 + 0.0980762i 0.0107653 + 0.00621533i
\(250\) 0 0
\(251\) −6.73205 11.6603i −0.424923 0.735989i 0.571490 0.820609i \(-0.306366\pi\)
−0.996413 + 0.0846203i \(0.973032\pi\)
\(252\) 0 0
\(253\) 4.60770 2.66025i 0.289683 0.167249i
\(254\) 0 0
\(255\) 21.3923i 1.33964i
\(256\) 0 0
\(257\) 4.66987 8.08846i 0.291299 0.504544i −0.682818 0.730588i \(-0.739246\pi\)
0.974117 + 0.226044i \(0.0725793\pi\)
\(258\) 0 0
\(259\) −9.66025 −0.600259
\(260\) 0 0
\(261\) −4.46410 −0.276321
\(262\) 0 0
\(263\) −5.02628 + 8.70577i −0.309934 + 0.536821i −0.978348 0.206969i \(-0.933640\pi\)
0.668414 + 0.743790i \(0.266974\pi\)
\(264\) 0 0
\(265\) 24.1244i 1.48195i
\(266\) 0 0
\(267\) −8.19615 + 4.73205i −0.501596 + 0.289597i
\(268\) 0 0
\(269\) −2.73205 4.73205i −0.166576 0.288518i 0.770638 0.637273i \(-0.219938\pi\)
−0.937214 + 0.348755i \(0.886604\pi\)
\(270\) 0 0
\(271\) 18.9282 + 10.9282i 1.14981 + 0.663841i 0.948840 0.315757i \(-0.102258\pi\)
0.200966 + 0.979598i \(0.435592\pi\)
\(272\) 0 0
\(273\) −6.83013 7.09808i −0.413378 0.429595i
\(274\) 0 0
\(275\) 9.80385 + 5.66025i 0.591194 + 0.341326i
\(276\) 0 0
\(277\) −2.86603 4.96410i −0.172203 0.298264i 0.766987 0.641663i \(-0.221755\pi\)
−0.939190 + 0.343399i \(0.888422\pi\)
\(278\) 0 0
\(279\) −1.26795 + 0.732051i −0.0759101 + 0.0438267i
\(280\) 0 0
\(281\) 12.3205i 0.734980i −0.930027 0.367490i \(-0.880217\pi\)
0.930027 0.367490i \(-0.119783\pi\)
\(282\) 0 0
\(283\) −12.8301 + 22.2224i −0.762672 + 1.32099i 0.178797 + 0.983886i \(0.442780\pi\)
−0.941469 + 0.337100i \(0.890554\pi\)
\(284\) 0 0
\(285\) −17.6603 −1.04610
\(286\) 0 0
\(287\) −25.6603 −1.51468
\(288\) 0 0
\(289\) −7.92820 + 13.7321i −0.466365 + 0.807768i
\(290\) 0 0
\(291\) 6.00000i 0.351726i
\(292\) 0 0
\(293\) −26.4282 + 15.2583i −1.54395 + 0.891401i −0.545368 + 0.838196i \(0.683610\pi\)
−0.998584 + 0.0532048i \(0.983056\pi\)
\(294\) 0 0
\(295\) 14.9282 + 25.8564i 0.869154 + 1.50542i
\(296\) 0 0
\(297\) 1.09808 + 0.633975i 0.0637168 + 0.0367869i
\(298\) 0 0
\(299\) −3.63397 14.6865i −0.210158 0.849344i
\(300\) 0 0
\(301\) −22.8564 13.1962i −1.31742 0.760614i
\(302\) 0 0
\(303\) −0.964102 1.66987i −0.0553862 0.0959317i
\(304\) 0 0
\(305\) −29.7224 + 17.1603i −1.70190 + 0.982593i
\(306\) 0 0
\(307\) 22.5885i 1.28919i −0.764524 0.644596i \(-0.777026\pi\)
0.764524 0.644596i \(-0.222974\pi\)
\(308\) 0 0
\(309\) −7.63397 + 13.2224i −0.434282 + 0.752198i
\(310\) 0 0
\(311\) −1.66025 −0.0941444 −0.0470722 0.998891i \(-0.514989\pi\)
−0.0470722 + 0.998891i \(0.514989\pi\)
\(312\) 0 0
\(313\) 6.53590 0.369431 0.184715 0.982792i \(-0.440864\pi\)
0.184715 + 0.982792i \(0.440864\pi\)
\(314\) 0 0
\(315\) −5.09808 + 8.83013i −0.287244 + 0.497521i
\(316\) 0 0
\(317\) 20.6603i 1.16040i 0.814476 + 0.580198i \(0.197025\pi\)
−0.814476 + 0.580198i \(0.802975\pi\)
\(318\) 0 0
\(319\) −4.90192 + 2.83013i −0.274455 + 0.158457i
\(320\) 0 0
\(321\) −5.09808 8.83013i −0.284547 0.492850i
\(322\) 0 0
\(323\) 23.4904 + 13.5622i 1.30704 + 0.754620i
\(324\) 0 0
\(325\) 23.1962 22.3205i 1.28669 1.23812i
\(326\) 0 0
\(327\) 1.26795 + 0.732051i 0.0701178 + 0.0404825i
\(328\) 0 0
\(329\) −3.00000 5.19615i −0.165395 0.286473i
\(330\) 0 0
\(331\) −17.3205 + 10.0000i −0.952021 + 0.549650i −0.893708 0.448649i \(-0.851905\pi\)
−0.0583130 + 0.998298i \(0.518572\pi\)
\(332\) 0 0
\(333\) 3.53590i 0.193766i
\(334\) 0 0
\(335\) −24.4904 + 42.4186i −1.33805 + 2.31757i
\(336\) 0 0
\(337\) 20.8564 1.13612 0.568060 0.822987i \(-0.307694\pi\)
0.568060 + 0.822987i \(0.307694\pi\)
\(338\) 0 0
\(339\) 1.33975 0.0727650
\(340\) 0 0
\(341\) −0.928203 + 1.60770i −0.0502650 + 0.0870616i
\(342\) 0 0
\(343\) 17.8564i 0.964155i
\(344\) 0 0
\(345\) −13.5622 + 7.83013i −0.730163 + 0.421560i
\(346\) 0 0
\(347\) 16.5622 + 28.6865i 0.889104 + 1.53997i 0.840936 + 0.541135i \(0.182005\pi\)
0.0481683 + 0.998839i \(0.484662\pi\)
\(348\) 0 0
\(349\) 13.2679 + 7.66025i 0.710217 + 0.410044i 0.811141 0.584850i \(-0.198847\pi\)
−0.100924 + 0.994894i \(0.532180\pi\)
\(350\) 0 0
\(351\) 2.59808 2.50000i 0.138675 0.133440i
\(352\) 0 0
\(353\) 18.8660 + 10.8923i 1.00414 + 0.579739i 0.909470 0.415770i \(-0.136488\pi\)
0.0946674 + 0.995509i \(0.469821\pi\)
\(354\) 0 0
\(355\) −8.83013 15.2942i −0.468654 0.811733i
\(356\) 0 0
\(357\) 13.5622 7.83013i 0.717787 0.414414i
\(358\) 0 0
\(359\) 1.12436i 0.0593412i −0.999560 0.0296706i \(-0.990554\pi\)
0.999560 0.0296706i \(-0.00944584\pi\)
\(360\) 0 0
\(361\) 1.69615 2.93782i 0.0892712 0.154622i
\(362\) 0 0
\(363\) −9.39230 −0.492968
\(364\) 0 0
\(365\) −23.3923 −1.22441
\(366\) 0 0
\(367\) −5.63397 + 9.75833i −0.294091 + 0.509381i −0.974773 0.223198i \(-0.928350\pi\)
0.680682 + 0.732579i \(0.261684\pi\)
\(368\) 0 0
\(369\) 9.39230i 0.488944i
\(370\) 0 0
\(371\) 15.2942 8.83013i 0.794037 0.458437i
\(372\) 0 0
\(373\) 6.86603 + 11.8923i 0.355509 + 0.615760i 0.987205 0.159456i \(-0.0509741\pi\)
−0.631696 + 0.775216i \(0.717641\pi\)
\(374\) 0 0
\(375\) −12.6962 7.33013i −0.655626 0.378526i
\(376\) 0 0
\(377\) 3.86603 + 15.6244i 0.199110 + 0.804695i
\(378\) 0 0
\(379\) −4.73205 2.73205i −0.243069 0.140336i 0.373517 0.927623i \(-0.378152\pi\)
−0.616587 + 0.787287i \(0.711485\pi\)
\(380\) 0 0
\(381\) −4.92820 8.53590i −0.252479 0.437307i
\(382\) 0 0
\(383\) 1.26795 0.732051i 0.0647892 0.0374060i −0.467255 0.884122i \(-0.654757\pi\)
0.532045 + 0.846716i \(0.321424\pi\)
\(384\) 0 0
\(385\) 12.9282i 0.658882i
\(386\) 0 0
\(387\) 4.83013 8.36603i 0.245529 0.425269i
\(388\) 0 0
\(389\) −11.7846 −0.597503 −0.298752 0.954331i \(-0.596570\pi\)
−0.298752 + 0.954331i \(0.596570\pi\)
\(390\) 0 0
\(391\) 24.0526 1.21639
\(392\) 0 0
\(393\) −3.26795 + 5.66025i −0.164846 + 0.285522i
\(394\) 0 0
\(395\) 9.46410i 0.476191i
\(396\) 0 0
\(397\) −17.6603 + 10.1962i −0.886343 + 0.511730i −0.872744 0.488177i \(-0.837662\pi\)
−0.0135983 + 0.999908i \(0.504329\pi\)
\(398\) 0 0
\(399\) −6.46410 11.1962i −0.323610 0.560509i
\(400\) 0 0
\(401\) 6.99038 + 4.03590i 0.349083 + 0.201543i 0.664281 0.747483i \(-0.268738\pi\)
−0.315198 + 0.949026i \(0.602071\pi\)
\(402\) 0 0
\(403\) 3.66025 + 3.80385i 0.182330 + 0.189483i
\(404\) 0 0
\(405\) −3.23205 1.86603i −0.160602 0.0927235i
\(406\) 0 0
\(407\) −2.24167 3.88269i −0.111115 0.192458i
\(408\) 0 0
\(409\) 15.3564 8.86603i 0.759325 0.438397i −0.0697281 0.997566i \(-0.522213\pi\)
0.829053 + 0.559169i \(0.188880\pi\)
\(410\) 0 0
\(411\) 11.9282i 0.588375i
\(412\) 0 0
\(413\) −10.9282 + 18.9282i −0.537742 + 0.931396i
\(414\) 0 0
\(415\) −0.732051 −0.0359350
\(416\) 0 0
\(417\) 17.8564 0.874432
\(418\) 0 0
\(419\) −8.73205 + 15.1244i −0.426589 + 0.738873i −0.996567 0.0827863i \(-0.973618\pi\)
0.569979 + 0.821659i \(0.306951\pi\)
\(420\) 0 0
\(421\) 22.7128i 1.10695i −0.832864 0.553477i \(-0.813301\pi\)
0.832864 0.553477i \(-0.186699\pi\)
\(422\) 0 0
\(423\) 1.90192 1.09808i 0.0924747 0.0533903i
\(424\) 0 0
\(425\) 25.5885 + 44.3205i 1.24122 + 2.14986i
\(426\) 0 0
\(427\) −21.7583 12.5622i −1.05296 0.607926i
\(428\) 0 0
\(429\) 1.26795 4.39230i 0.0612172 0.212062i
\(430\) 0 0
\(431\) 11.3660 + 6.56218i 0.547482 + 0.316089i 0.748106 0.663579i \(-0.230964\pi\)
−0.200624 + 0.979668i \(0.564297\pi\)
\(432\) 0 0
\(433\) 6.42820 + 11.1340i 0.308920 + 0.535065i 0.978126 0.208012i \(-0.0666992\pi\)
−0.669207 + 0.743076i \(0.733366\pi\)
\(434\) 0 0
\(435\) 14.4282 8.33013i 0.691779 0.399399i
\(436\) 0 0
\(437\) 19.8564i 0.949861i
\(438\) 0 0
\(439\) 0.169873 0.294229i 0.00810760 0.0140428i −0.861943 0.507005i \(-0.830753\pi\)
0.870051 + 0.492962i \(0.164086\pi\)
\(440\) 0 0
\(441\) −0.464102 −0.0221001
\(442\) 0 0
\(443\) −15.6077 −0.741544 −0.370772 0.928724i \(-0.620907\pi\)
−0.370772 + 0.928724i \(0.620907\pi\)
\(444\) 0 0
\(445\) 17.6603 30.5885i 0.837176 1.45003i
\(446\) 0 0
\(447\) 13.1962i 0.624157i
\(448\) 0 0
\(449\) −9.80385 + 5.66025i −0.462672 + 0.267124i −0.713167 0.700994i \(-0.752740\pi\)
0.250495 + 0.968118i \(0.419407\pi\)
\(450\) 0 0
\(451\) −5.95448 10.3135i −0.280386 0.485642i
\(452\) 0 0
\(453\) 5.83013 + 3.36603i 0.273923 + 0.158150i
\(454\) 0 0
\(455\) 35.3205 + 10.1962i 1.65585 + 0.478003i
\(456\) 0 0
\(457\) −1.16025 0.669873i −0.0542744 0.0313353i 0.472617 0.881268i \(-0.343309\pi\)
−0.526892 + 0.849932i \(0.676643\pi\)
\(458\) 0 0
\(459\) 2.86603 + 4.96410i 0.133775 + 0.231704i
\(460\) 0 0
\(461\) 19.2846 11.1340i 0.898174 0.518561i 0.0215666 0.999767i \(-0.493135\pi\)
0.876607 + 0.481207i \(0.159801\pi\)
\(462\) 0 0
\(463\) 10.0526i 0.467182i 0.972335 + 0.233591i \(0.0750477\pi\)
−0.972335 + 0.233591i \(0.924952\pi\)
\(464\) 0 0
\(465\) 2.73205 4.73205i 0.126696 0.219444i
\(466\) 0 0
\(467\) 18.5885 0.860171 0.430086 0.902788i \(-0.358483\pi\)
0.430086 + 0.902788i \(0.358483\pi\)
\(468\) 0 0
\(469\) −35.8564 −1.65570
\(470\) 0 0
\(471\) 3.79423 6.57180i 0.174829 0.302812i
\(472\) 0 0
\(473\) 12.2487i 0.563196i
\(474\) 0 0
\(475\) 36.5885 21.1244i 1.67879 0.969252i
\(476\) 0 0
\(477\) 3.23205 + 5.59808i 0.147985 + 0.256318i
\(478\) 0 0
\(479\) −28.9808 16.7321i −1.32416 0.764507i −0.339775 0.940507i \(-0.610351\pi\)
−0.984390 + 0.176000i \(0.943684\pi\)
\(480\) 0 0
\(481\) −12.3756 + 3.06218i −0.564281 + 0.139623i
\(482\) 0 0
\(483\) −9.92820 5.73205i −0.451749 0.260817i
\(484\) 0 0
\(485\) −11.1962 19.3923i −0.508391 0.880559i
\(486\) 0 0
\(487\) 2.70577 1.56218i 0.122610 0.0707890i −0.437441 0.899247i \(-0.644115\pi\)
0.560051 + 0.828458i \(0.310782\pi\)
\(488\) 0 0
\(489\) 13.4641i 0.608868i
\(490\) 0 0
\(491\) −4.36603 + 7.56218i −0.197036 + 0.341276i −0.947566 0.319560i \(-0.896465\pi\)
0.750530 + 0.660836i \(0.229798\pi\)
\(492\) 0 0
\(493\) −25.5885 −1.15245
\(494\) 0 0
\(495\) −4.73205 −0.212690
\(496\) 0 0
\(497\) 6.46410 11.1962i 0.289955 0.502216i
\(498\) 0 0
\(499\) 32.0000i 1.43252i −0.697835 0.716258i \(-0.745853\pi\)
0.697835 0.716258i \(-0.254147\pi\)
\(500\) 0 0
\(501\) 8.19615 4.73205i 0.366177 0.211412i
\(502\) 0 0
\(503\) 20.4904 + 35.4904i 0.913621 + 1.58244i 0.808908 + 0.587935i \(0.200059\pi\)
0.104713 + 0.994502i \(0.466608\pi\)
\(504\) 0 0
\(505\) 6.23205 + 3.59808i 0.277323 + 0.160112i
\(506\) 0 0
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) 0 0
\(509\) −11.8923 6.86603i −0.527117 0.304331i 0.212725 0.977112i \(-0.431766\pi\)
−0.739842 + 0.672781i \(0.765100\pi\)
\(510\) 0 0
\(511\) −8.56218 14.8301i −0.378768 0.656046i
\(512\) 0 0
\(513\) 4.09808 2.36603i 0.180934 0.104463i
\(514\) 0 0
\(515\) 56.9808i 2.51087i
\(516\) 0 0
\(517\) 1.39230 2.41154i 0.0612335 0.106060i
\(518\) 0 0
\(519\) 4.39230 0.192801
\(520\) 0 0
\(521\) 41.4449 1.81573 0.907866 0.419260i \(-0.137710\pi\)
0.907866 + 0.419260i \(0.137710\pi\)
\(522\) 0 0
\(523\) −11.2224 + 19.4378i −0.490723 + 0.849957i −0.999943 0.0106796i \(-0.996601\pi\)
0.509220 + 0.860636i \(0.329934\pi\)
\(524\) 0 0
\(525\) 24.3923i 1.06457i
\(526\) 0 0
\(527\) −7.26795 + 4.19615i −0.316597 + 0.182787i
\(528\) 0 0
\(529\) 2.69615 + 4.66987i 0.117224 + 0.203038i
\(530\) 0 0
\(531\) −6.92820 4.00000i −0.300658 0.173585i
\(532\) 0 0
\(533\) −32.8731 + 8.13397i −1.42389 + 0.352322i
\(534\) 0 0
\(535\) 32.9545 + 19.0263i 1.42475 + 0.822578i
\(536\) 0 0
\(537\) −8.02628 13.9019i −0.346360 0.599912i
\(538\) 0 0
\(539\) −0.509619 + 0.294229i −0.0219508 + 0.0126733i
\(540\) 0 0
\(541\) 5.67949i 0.244180i −0.992519 0.122090i \(-0.961040\pi\)
0.992519 0.122090i \(-0.0389597\pi\)
\(542\) 0 0
\(543\) −9.59808 + 16.6244i −0.411893 + 0.713419i
\(544\) 0 0
\(545\) −5.46410 −0.234056
\(546\) 0 0
\(547\) 4.19615 0.179415 0.0897073 0.995968i \(-0.471407\pi\)
0.0897073 + 0.995968i \(0.471407\pi\)
\(548\) 0 0
\(549\) 4.59808 7.96410i 0.196241 0.339900i
\(550\) 0 0
\(551\) 21.1244i 0.899928i
\(552\) 0 0
\(553\) −6.00000 + 3.46410i −0.255146 + 0.147309i
\(554\) 0 0
\(555\) 6.59808 + 11.4282i 0.280073 + 0.485100i
\(556\) 0 0
\(557\) 36.6962 + 21.1865i 1.55487 + 0.897702i 0.997734 + 0.0672780i \(0.0214314\pi\)
0.557132 + 0.830424i \(0.311902\pi\)
\(558\) 0 0
\(559\) −33.4641 9.66025i −1.41538 0.408585i
\(560\) 0 0
\(561\) 6.29423 + 3.63397i 0.265743 + 0.153427i
\(562\) 0 0
\(563\) −17.4641 30.2487i −0.736024 1.27483i −0.954273 0.298938i \(-0.903368\pi\)
0.218248 0.975893i \(-0.429966\pi\)
\(564\) 0 0
\(565\) −4.33013 + 2.50000i −0.182170 + 0.105176i
\(566\) 0 0
\(567\) 2.73205i 0.114735i
\(568\) 0 0
\(569\) 15.3205 26.5359i 0.642269 1.11244i −0.342656 0.939461i \(-0.611326\pi\)
0.984925 0.172982i \(-0.0553402\pi\)
\(570\) 0 0
\(571\) 14.0526 0.588081 0.294041 0.955793i \(-0.405000\pi\)
0.294041 + 0.955793i \(0.405000\pi\)
\(572\) 0 0
\(573\) −6.92820 −0.289430
\(574\) 0 0
\(575\) 18.7321 32.4449i 0.781181 1.35304i
\(576\) 0 0
\(577\) 3.73205i 0.155367i 0.996978 + 0.0776837i \(0.0247524\pi\)
−0.996978 + 0.0776837i \(0.975248\pi\)
\(578\) 0 0
\(579\) −10.1603 + 5.86603i −0.422246 + 0.243784i
\(580\) 0 0
\(581\) −0.267949 0.464102i −0.0111164 0.0192542i
\(582\) 0 0
\(583\) 7.09808 + 4.09808i 0.293972 + 0.169725i
\(584\) 0 0
\(585\) −3.73205 + 12.9282i −0.154301 + 0.534515i
\(586\) 0 0
\(587\) 13.8564 + 8.00000i 0.571915 + 0.330195i 0.757914 0.652355i \(-0.226219\pi\)
−0.185999 + 0.982550i \(0.559552\pi\)
\(588\) 0 0
\(589\) 3.46410 + 6.00000i 0.142736 + 0.247226i
\(590\) 0 0
\(591\) 15.4641 8.92820i 0.636108 0.367257i
\(592\) 0 0
\(593\) 9.14359i 0.375482i 0.982219 + 0.187741i \(0.0601166\pi\)
−0.982219 + 0.187741i \(0.939883\pi\)
\(594\) 0 0
\(595\) −29.2224 + 50.6147i −1.19800 + 2.07500i
\(596\) 0 0
\(597\) 14.1962 0.581010
\(598\) 0 0
\(599\) 2.53590 0.103614 0.0518070 0.998657i \(-0.483502\pi\)
0.0518070 + 0.998657i \(0.483502\pi\)
\(600\) 0 0
\(601\) −3.96410 + 6.86603i −0.161699 + 0.280071i −0.935478 0.353385i \(-0.885031\pi\)
0.773779 + 0.633456i \(0.218364\pi\)
\(602\) 0 0
\(603\) 13.1244i 0.534465i
\(604\) 0 0
\(605\) 30.3564 17.5263i 1.23416 0.712545i
\(606\) 0 0
\(607\) −20.3923 35.3205i −0.827698 1.43362i −0.899840 0.436221i \(-0.856317\pi\)
0.0721415 0.997394i \(-0.477017\pi\)
\(608\) 0 0
\(609\) 10.5622 + 6.09808i 0.428001 + 0.247107i
\(610\) 0 0
\(611\) −5.49038 5.70577i −0.222117 0.230831i
\(612\) 0 0
\(613\) 8.13397 + 4.69615i 0.328528 + 0.189676i 0.655187 0.755466i \(-0.272590\pi\)
−0.326659 + 0.945142i \(0.605923\pi\)
\(614\) 0 0
\(615\) 17.5263 + 30.3564i 0.706728 + 1.22409i
\(616\) 0 0
\(617\) −11.4737 + 6.62436i −0.461915 + 0.266687i −0.712849 0.701318i \(-0.752596\pi\)
0.250934 + 0.968004i \(0.419262\pi\)
\(618\) 0 0
\(619\) 17.4641i 0.701942i 0.936386 + 0.350971i \(0.114148\pi\)
−0.936386 + 0.350971i \(0.885852\pi\)
\(620\) 0 0
\(621\) 2.09808 3.63397i 0.0841929 0.145826i
\(622\) 0 0
\(623\) 25.8564 1.03592
\(624\) 0 0
\(625\) 10.0718 0.402872
\(626\) 0 0
\(627\) 3.00000 5.19615i 0.119808 0.207514i
\(628\) 0 0
\(629\) 20.2679i 0.808136i
\(630\) 0 0
\(631\) −6.67949 + 3.85641i −0.265906 + 0.153521i −0.627026 0.778998i \(-0.715728\pi\)
0.361119 + 0.932520i \(0.382395\pi\)
\(632\) 0 0
\(633\) −8.19615 14.1962i −0.325768 0.564246i
\(634\) 0 0
\(635\) 31.8564 + 18.3923i 1.26418 + 0.729876i
\(636\) 0 0
\(637\) 0.401924 + 1.62436i 0.0159248 + 0.0643593i
\(638\) 0 0
\(639\) 4.09808 + 2.36603i 0.162117 + 0.0935985i
\(640\) 0 0
\(641\) −12.9904 22.5000i −0.513089 0.888697i −0.999885 0.0151806i \(-0.995168\pi\)
0.486796 0.873516i \(-0.338166\pi\)
\(642\) 0 0
\(643\) 12.0000 6.92820i 0.473234 0.273222i −0.244359 0.969685i \(-0.578577\pi\)
0.717592 + 0.696463i \(0.245244\pi\)
\(644\) 0 0
\(645\) 36.0526i 1.41957i
\(646\) 0 0
\(647\) 11.1244 19.2679i 0.437344 0.757501i −0.560140 0.828398i \(-0.689253\pi\)
0.997484 + 0.0708966i \(0.0225860\pi\)
\(648\) 0 0
\(649\) −10.1436 −0.398171
\(650\) 0 0
\(651\) 4.00000 0.156772
\(652\) 0 0
\(653\) 8.73205 15.1244i 0.341712 0.591862i −0.643039 0.765833i \(-0.722327\pi\)
0.984751 + 0.173972i \(0.0556601\pi\)
\(654\) 0 0
\(655\) 24.3923i 0.953086i
\(656\) 0 0
\(657\) 5.42820 3.13397i 0.211774 0.122268i
\(658\) 0 0
\(659\) −5.12436 8.87564i −0.199617 0.345746i 0.748788 0.662810i \(-0.230636\pi\)
−0.948404 + 0.317064i \(0.897303\pi\)
\(660\) 0 0
\(661\) 9.86603 + 5.69615i 0.383744 + 0.221555i 0.679446 0.733726i \(-0.262220\pi\)
−0.295702 + 0.955280i \(0.595554\pi\)
\(662\) 0 0
\(663\) 14.8923 14.3301i 0.578369 0.556536i
\(664\) 0 0
\(665\) 41.7846 + 24.1244i 1.62034 + 0.935502i
\(666\) 0 0
\(667\) 9.36603 + 16.2224i 0.362654 + 0.628135i
\(668\) 0 0
\(669\) −23.3205 + 13.4641i −0.901623 + 0.520552i
\(670\) 0 0
\(671\) 11.6603i 0.450139i
\(672\) 0 0
\(673\) 13.9641 24.1865i 0.538277 0.932322i −0.460720 0.887545i \(-0.652409\pi\)
0.998997 0.0447770i \(-0.0142577\pi\)
\(674\) 0 0
\(675\) 8.92820 0.343647
\(676\) 0 0
\(677\) −45.4641 −1.74733 −0.873664 0.486530i \(-0.838262\pi\)
−0.873664 + 0.486530i \(0.838262\pi\)
\(678\) 0 0
\(679\) 8.19615 14.1962i 0.314539 0.544798i
\(680\) 0 0
\(681\) 12.1962i 0.467358i
\(682\) 0 0
\(683\) −8.78461 + 5.07180i −0.336134 + 0.194067i −0.658561 0.752527i \(-0.728835\pi\)
0.322427 + 0.946594i \(0.395501\pi\)
\(684\) 0 0
\(685\) −22.2583 38.5526i −0.850447 1.47302i
\(686\) 0 0
\(687\) 10.2679 + 5.92820i 0.391747 + 0.226175i
\(688\) 0 0
\(689\) 16.7942 16.1603i 0.639809 0.615657i
\(690\) 0 0
\(691\) 37.8109 + 21.8301i 1.43839 + 0.830457i 0.997738 0.0672190i \(-0.0214126\pi\)
0.440656 + 0.897676i \(0.354746\pi\)
\(692\) 0 0
\(693\) −1.73205 3.00000i −0.0657952 0.113961i
\(694\) 0 0
\(695\) −57.7128 + 33.3205i −2.18917 + 1.26392i
\(696\) 0 0
\(697\) 53.8372i 2.03923i
\(698\) 0 0
\(699\) 3.92820 6.80385i 0.148578 0.257345i
\(700\) 0 0
\(701\) 3.32051 0.125414 0.0627069 0.998032i \(-0.480027\pi\)
0.0627069 + 0.998032i \(0.480027\pi\)
\(702\) 0 0
\(703\) −16.7321 −0.631061
\(704\) 0 0
\(705\) −4.09808 + 7.09808i −0.154342 + 0.267329i
\(706\) 0 0
\(707\) 5.26795i 0.198122i
\(708\) 0 0
\(709\) −11.3827 + 6.57180i −0.427486 + 0.246809i −0.698275 0.715830i \(-0.746049\pi\)
0.270789 + 0.962639i \(0.412715\pi\)
\(710\) 0 0
\(711\) −1.26795 2.19615i −0.0475518 0.0823622i
\(712\) 0 0
\(713\) 5.32051 + 3.07180i 0.199255 + 0.115040i
\(714\) 0 0
\(715\) 4.09808 + 16.5622i 0.153259 + 0.619390i
\(716\) 0 0
\(717\) −6.63397 3.83013i −0.247750 0.143039i
\(718\) 0 0
\(719\) 14.7321 + 25.5167i 0.549413 + 0.951611i 0.998315 + 0.0580299i \(0.0184819\pi\)
−0.448902 + 0.893581i \(0.648185\pi\)
\(720\) 0 0
\(721\) 36.1244 20.8564i 1.34534 0.776733i
\(722\) 0 0
\(723\) 13.5885i 0.505360i
\(724\) 0 0
\(725\) −19.9282 + 34.5167i −0.740115 + 1.28192i
\(726\) 0 0
\(727\) −30.9808 −1.14901 −0.574506 0.818500i \(-0.694806\pi\)
−0.574506 + 0.818500i \(0.694806\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 27.6865 47.9545i 1.02402 1.77366i
\(732\) 0 0
\(733\) 19.0000i 0.701781i 0.936416 + 0.350891i \(0.114121\pi\)
−0.936416 + 0.350891i \(0.885879\pi\)
\(734\) 0 0
\(735\) 1.50000 0.866025i 0.0553283 0.0319438i
\(736\) 0 0
\(737\) −8.32051 14.4115i −0.306490 0.530856i
\(738\) 0 0
\(739\) −2.53590 1.46410i −0.0932845 0.0538578i 0.452632 0.891697i \(-0.350485\pi\)
−0.545917 + 0.837840i \(0.683818\pi\)
\(740\) 0 0
\(741\) −11.8301 12.2942i −0.434591 0.451640i
\(742\) 0 0
\(743\) −41.9090 24.1962i −1.53749 0.887671i −0.998985 0.0450491i \(-0.985656\pi\)
−0.538506 0.842622i \(-0.681011\pi\)
\(744\) 0 0
\(745\) 24.6244 + 42.6506i 0.902167 + 1.56260i
\(746\) 0 0
\(747\) 0.169873 0.0980762i 0.00621533 0.00358842i
\(748\) 0 0
\(749\) 27.8564i 1.01785i
\(750\) 0 0
\(751\) 24.9545 43.2224i 0.910602 1.57721i 0.0973862 0.995247i \(-0.468952\pi\)
0.813216 0.581962i \(-0.197715\pi\)
\(752\) 0 0
\(753\) −13.4641 −0.490659
\(754\) 0 0
\(755\) −25.1244 −0.914369
\(756\) 0 0
\(757\) −10.4641 + 18.1244i −0.380324 + 0.658741i −0.991109 0.133056i \(-0.957521\pi\)
0.610784 + 0.791797i \(0.290854\pi\)
\(758\) 0 0
\(759\) 5.32051i 0.193122i
\(760\) 0 0
\(761\) −9.80385 + 5.66025i −0.355389 + 0.205184i −0.667056 0.745007i \(-0.732446\pi\)
0.311667 + 0.950191i \(0.399113\pi\)
\(762\) 0 0
\(763\) −2.00000 3.46410i −0.0724049 0.125409i
\(764\) 0 0
\(765\) −18.5263 10.6962i −0.669819 0.386720i
\(766\) 0 0
\(767\) −8.00000 + 27.7128i −0.288863 + 1.00065i
\(768\) 0 0
\(769\) 37.9808 + 21.9282i 1.36962 + 0.790751i 0.990879 0.134751i \(-0.0430235\pi\)
0.378742 + 0.925502i \(0.376357\pi\)
\(770\) 0 0
\(771\) −4.66987 8.08846i −0.168181 0.291299i
\(772\) 0 0
\(773\) −42.3731 + 24.4641i −1.52405 + 0.879913i −0.524459 + 0.851436i \(0.675732\pi\)
−0.999594 + 0.0284768i \(0.990934\pi\)
\(774\) 0 0
\(775\) 13.0718i 0.469553i
\(776\) 0 0
\(777\) −4.83013 + 8.36603i −0.173280 + 0.300129i
\(778\) 0 0
\(779\) −44.4449 −1.59240
\(780\) 0 0
\(781\) 6.00000 0.214697
\(782\) 0 0
\(783\) −2.23205 + 3.86603i −0.0797670 + 0.138160i
\(784\) 0 0
\(785\) 28.3205i 1.01080i
\(786\) 0 0
\(787\) 4.05256 2.33975i 0.144458 0.0834029i −0.426029 0.904710i \(-0.640088\pi\)
0.570487 + 0.821307i \(0.306754\pi\)
\(788\) 0 0
\(789\) 5.02628 + 8.70577i 0.178940 + 0.309934i
\(790\) 0 0
\(791\) −3.16987 1.83013i −0.112708 0.0650718i
\(792\) 0 0
\(793\) −31.8564 9.19615i −1.13125 0.326565i
\(794\) 0 0
\(795\) −20.8923 12.0622i −0.740974 0.427801i
\(796\)