Properties

Label 1680.2.bg.k.961.1
Level $1680$
Weight $2$
Character 1680.961
Analytic conductor $13.415$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1680.bg (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.4148675396\)
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 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1680.961
Dual form 1680.2.bg.k.1201.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.00000 - 1.73205i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} +7.00000 q^{13} -1.00000 q^{15} +(2.00000 + 3.46410i) q^{17} +(0.500000 - 0.866025i) q^{19} +(0.500000 - 2.59808i) q^{21} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{25} -1.00000 q^{27} -8.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(0.500000 - 0.866025i) q^{33} +(2.50000 - 0.866025i) q^{35} +(1.50000 - 2.59808i) q^{37} +(3.50000 + 6.06218i) q^{39} +9.00000 q^{41} +4.00000 q^{43} +(-0.500000 - 0.866025i) q^{45} +(-1.50000 + 2.59808i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(0.500000 + 0.866025i) q^{53} +1.00000 q^{55} +1.00000 q^{57} +(6.00000 + 10.3923i) q^{59} +(2.00000 - 3.46410i) q^{61} +(2.50000 - 0.866025i) q^{63} +(-3.50000 + 6.06218i) q^{65} +(6.00000 + 10.3923i) q^{67} +1.00000 q^{69} +14.0000 q^{71} +(7.00000 + 12.1244i) q^{73} +(0.500000 - 0.866025i) q^{75} +(-0.500000 + 2.59808i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-0.500000 - 0.866025i) q^{81} -12.0000 q^{83} -4.00000 q^{85} +(-4.00000 - 6.92820i) q^{87} +(1.00000 - 1.73205i) q^{89} +(-14.0000 - 12.1244i) q^{91} +(-3.00000 + 5.19615i) q^{93} +(0.500000 + 0.866025i) q^{95} -16.0000 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{3} - q^{5} - 4q^{7} - q^{9} + O(q^{10}) \) \( 2q + q^{3} - q^{5} - 4q^{7} - q^{9} - q^{11} + 14q^{13} - 2q^{15} + 4q^{17} + q^{19} + q^{21} + q^{23} - q^{25} - 2q^{27} - 16q^{29} + 6q^{31} + q^{33} + 5q^{35} + 3q^{37} + 7q^{39} + 18q^{41} + 8q^{43} - q^{45} - 3q^{47} + 2q^{49} - 4q^{51} + q^{53} + 2q^{55} + 2q^{57} + 12q^{59} + 4q^{61} + 5q^{63} - 7q^{65} + 12q^{67} + 2q^{69} + 28q^{71} + 14q^{73} + q^{75} - q^{77} + 4q^{79} - q^{81} - 24q^{83} - 8q^{85} - 8q^{87} + 2q^{89} - 28q^{91} - 6q^{93} + q^{95} - 32q^{97} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times\).

\(n\) \(241\) \(337\) \(421\) \(1121\) \(1471\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(1\) \(1\) \(1\)

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
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 0 0
\(13\) 7.00000 1.94145 0.970725 0.240192i \(-0.0772105\pi\)
0.970725 + 0.240192i \(0.0772105\pi\)
\(14\) 0 0
\(15\) −1.00000 −0.258199
\(16\) 0 0
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 0 0
\(19\) 0.500000 0.866025i 0.114708 0.198680i −0.802955 0.596040i \(-0.796740\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(20\) 0 0
\(21\) 0.500000 2.59808i 0.109109 0.566947i
\(22\) 0 0
\(23\) 0.500000 0.866025i 0.104257 0.180579i −0.809177 0.587565i \(-0.800087\pi\)
0.913434 + 0.406986i \(0.133420\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) 3.00000 + 5.19615i 0.538816 + 0.933257i 0.998968 + 0.0454165i \(0.0144615\pi\)
−0.460152 + 0.887840i \(0.652205\pi\)
\(32\) 0 0
\(33\) 0.500000 0.866025i 0.0870388 0.150756i
\(34\) 0 0
\(35\) 2.50000 0.866025i 0.422577 0.146385i
\(36\) 0 0
\(37\) 1.50000 2.59808i 0.246598 0.427121i −0.715981 0.698119i \(-0.754020\pi\)
0.962580 + 0.270998i \(0.0873538\pi\)
\(38\) 0 0
\(39\) 3.50000 + 6.06218i 0.560449 + 0.970725i
\(40\) 0 0
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) 0 0
\(47\) −1.50000 + 2.59808i −0.218797 + 0.378968i −0.954441 0.298401i \(-0.903547\pi\)
0.735643 + 0.677369i \(0.236880\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) 0 0
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) 0 0
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 0 0
\(61\) 2.00000 3.46410i 0.256074 0.443533i −0.709113 0.705095i \(-0.750904\pi\)
0.965187 + 0.261562i \(0.0842377\pi\)
\(62\) 0 0
\(63\) 2.50000 0.866025i 0.314970 0.109109i
\(64\) 0 0
\(65\) −3.50000 + 6.06218i −0.434122 + 0.751921i
\(66\) 0 0
\(67\) 6.00000 + 10.3923i 0.733017 + 1.26962i 0.955588 + 0.294706i \(0.0952216\pi\)
−0.222571 + 0.974916i \(0.571445\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 14.0000 1.66149 0.830747 0.556650i \(-0.187914\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(72\) 0 0
\(73\) 7.00000 + 12.1244i 0.819288 + 1.41905i 0.906208 + 0.422833i \(0.138964\pi\)
−0.0869195 + 0.996215i \(0.527702\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) −0.500000 + 2.59808i −0.0569803 + 0.296078i
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) −4.00000 6.92820i −0.428845 0.742781i
\(88\) 0 0
\(89\) 1.00000 1.73205i 0.106000 0.183597i −0.808146 0.588982i \(-0.799529\pi\)
0.914146 + 0.405385i \(0.132862\pi\)
\(90\) 0 0
\(91\) −14.0000 12.1244i −1.46760 1.27098i
\(92\) 0 0
\(93\) −3.00000 + 5.19615i −0.311086 + 0.538816i
\(94\) 0 0
\(95\) 0.500000 + 0.866025i 0.0512989 + 0.0888523i
\(96\) 0 0
\(97\) −16.0000 −1.62455 −0.812277 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) 0 0
\(99\) 1.00000 0.100504
\(100\) 0 0
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 0 0
\(103\) 8.00000 13.8564i 0.788263 1.36531i −0.138767 0.990325i \(-0.544314\pi\)
0.927030 0.374987i \(-0.122353\pi\)
\(104\) 0 0
\(105\) 2.00000 + 1.73205i 0.195180 + 0.169031i
\(106\) 0 0
\(107\) −9.00000 + 15.5885i −0.870063 + 1.50699i −0.00813215 + 0.999967i \(0.502589\pi\)
−0.861931 + 0.507026i \(0.830745\pi\)
\(108\) 0 0
\(109\) 5.00000 + 8.66025i 0.478913 + 0.829502i 0.999708 0.0241802i \(-0.00769755\pi\)
−0.520794 + 0.853682i \(0.674364\pi\)
\(110\) 0 0
\(111\) 3.00000 0.284747
\(112\) 0 0
\(113\) −6.00000 −0.564433 −0.282216 0.959351i \(-0.591070\pi\)
−0.282216 + 0.959351i \(0.591070\pi\)
\(114\) 0 0
\(115\) 0.500000 + 0.866025i 0.0466252 + 0.0807573i
\(116\) 0 0
\(117\) −3.50000 + 6.06218i −0.323575 + 0.560449i
\(118\) 0 0
\(119\) 2.00000 10.3923i 0.183340 0.952661i
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 0 0
\(123\) 4.50000 + 7.79423i 0.405751 + 0.702782i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.00000 −0.443678 −0.221839 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 0 0
\(129\) 2.00000 + 3.46410i 0.176090 + 0.304997i
\(130\) 0 0
\(131\) −6.50000 + 11.2583i −0.567908 + 0.983645i 0.428865 + 0.903369i \(0.358914\pi\)
−0.996773 + 0.0802763i \(0.974420\pi\)
\(132\) 0 0
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) 0 0
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 0 0
\(137\) 1.00000 + 1.73205i 0.0854358 + 0.147979i 0.905577 0.424182i \(-0.139438\pi\)
−0.820141 + 0.572161i \(0.806105\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −3.00000 −0.252646
\(142\) 0 0
\(143\) −3.50000 6.06218i −0.292685 0.506945i
\(144\) 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
\(149\) 2.00000 3.46410i 0.163846 0.283790i −0.772399 0.635138i \(-0.780943\pi\)
0.936245 + 0.351348i \(0.114277\pi\)
\(150\) 0 0
\(151\) −1.00000 1.73205i −0.0813788 0.140952i 0.822464 0.568818i \(-0.192599\pi\)
−0.903842 + 0.427865i \(0.859266\pi\)
\(152\) 0 0
\(153\) −4.00000 −0.323381
\(154\) 0 0
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) −7.50000 12.9904i −0.598565 1.03675i −0.993033 0.117836i \(-0.962404\pi\)
0.394468 0.918910i \(-0.370929\pi\)
\(158\) 0 0
\(159\) −0.500000 + 0.866025i −0.0396526 + 0.0686803i
\(160\) 0 0
\(161\) −2.50000 + 0.866025i −0.197028 + 0.0682524i
\(162\) 0 0
\(163\) 4.00000 6.92820i 0.313304 0.542659i −0.665771 0.746156i \(-0.731897\pi\)
0.979076 + 0.203497i \(0.0652307\pi\)
\(164\) 0 0
\(165\) 0.500000 + 0.866025i 0.0389249 + 0.0674200i
\(166\) 0 0
\(167\) 5.00000 0.386912 0.193456 0.981109i \(-0.438030\pi\)
0.193456 + 0.981109i \(0.438030\pi\)
\(168\) 0 0
\(169\) 36.0000 2.76923
\(170\) 0 0
\(171\) 0.500000 + 0.866025i 0.0382360 + 0.0662266i
\(172\) 0 0
\(173\) 10.5000 18.1865i 0.798300 1.38270i −0.122422 0.992478i \(-0.539066\pi\)
0.920722 0.390218i \(-0.127601\pi\)
\(174\) 0 0
\(175\) −0.500000 + 2.59808i −0.0377964 + 0.196396i
\(176\) 0 0
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) 0 0
\(179\) 6.50000 + 11.2583i 0.485833 + 0.841487i 0.999867 0.0162823i \(-0.00518305\pi\)
−0.514035 + 0.857769i \(0.671850\pi\)
\(180\) 0 0
\(181\) −12.0000 −0.891953 −0.445976 0.895045i \(-0.647144\pi\)
−0.445976 + 0.895045i \(0.647144\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 0 0
\(185\) 1.50000 + 2.59808i 0.110282 + 0.191014i
\(186\) 0 0
\(187\) 2.00000 3.46410i 0.146254 0.253320i
\(188\) 0 0
\(189\) 2.00000 + 1.73205i 0.145479 + 0.125988i
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) 0 0
\(193\) −13.0000 22.5167i −0.935760 1.62078i −0.773272 0.634074i \(-0.781381\pi\)
−0.162488 0.986710i \(-0.551952\pi\)
\(194\) 0 0
\(195\) −7.00000 −0.501280
\(196\) 0 0
\(197\) −3.00000 −0.213741 −0.106871 0.994273i \(-0.534083\pi\)
−0.106871 + 0.994273i \(0.534083\pi\)
\(198\) 0 0
\(199\) −6.00000 10.3923i −0.425329 0.736691i 0.571122 0.820865i \(-0.306508\pi\)
−0.996451 + 0.0841740i \(0.973175\pi\)
\(200\) 0 0
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) 0 0
\(203\) 16.0000 + 13.8564i 1.12298 + 0.972529i
\(204\) 0 0
\(205\) −4.50000 + 7.79423i −0.314294 + 0.544373i
\(206\) 0 0
\(207\) 0.500000 + 0.866025i 0.0347524 + 0.0601929i
\(208\) 0 0
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) 15.0000 1.03264 0.516321 0.856395i \(-0.327301\pi\)
0.516321 + 0.856395i \(0.327301\pi\)
\(212\) 0 0
\(213\) 7.00000 + 12.1244i 0.479632 + 0.830747i
\(214\) 0 0
\(215\) −2.00000 + 3.46410i −0.136399 + 0.236250i
\(216\) 0 0
\(217\) 3.00000 15.5885i 0.203653 1.05821i
\(218\) 0 0
\(219\) −7.00000 + 12.1244i −0.473016 + 0.819288i
\(220\) 0 0
\(221\) 14.0000 + 24.2487i 0.941742 + 1.63114i
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −10.0000 17.3205i −0.663723 1.14960i −0.979630 0.200812i \(-0.935642\pi\)
0.315906 0.948790i \(-0.397691\pi\)
\(228\) 0 0
\(229\) 11.0000 19.0526i 0.726900 1.25903i −0.231287 0.972886i \(-0.574293\pi\)
0.958187 0.286143i \(-0.0923732\pi\)
\(230\) 0 0
\(231\) −2.50000 + 0.866025i −0.164488 + 0.0569803i
\(232\) 0 0
\(233\) −13.0000 + 22.5167i −0.851658 + 1.47512i 0.0280525 + 0.999606i \(0.491069\pi\)
−0.879711 + 0.475509i \(0.842264\pi\)
\(234\) 0 0
\(235\) −1.50000 2.59808i −0.0978492 0.169480i
\(236\) 0 0
\(237\) 4.00000 0.259828
\(238\) 0 0
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) 0 0
\(241\) −3.50000 6.06218i −0.225455 0.390499i 0.731001 0.682376i \(-0.239053\pi\)
−0.956456 + 0.291877i \(0.905720\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) −6.50000 2.59808i −0.415270 0.165985i
\(246\) 0 0
\(247\) 3.50000 6.06218i 0.222700 0.385727i
\(248\) 0 0
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) −1.00000 −0.0628695
\(254\) 0 0
\(255\) −2.00000 3.46410i −0.125245 0.216930i
\(256\) 0 0
\(257\) 4.00000 6.92820i 0.249513 0.432169i −0.713878 0.700270i \(-0.753063\pi\)
0.963391 + 0.268101i \(0.0863961\pi\)
\(258\) 0 0
\(259\) −7.50000 + 2.59808i −0.466027 + 0.161437i
\(260\) 0 0
\(261\) 4.00000 6.92820i 0.247594 0.428845i
\(262\) 0 0
\(263\) −8.00000 13.8564i −0.493301 0.854423i 0.506669 0.862141i \(-0.330877\pi\)
−0.999970 + 0.00771799i \(0.997543\pi\)
\(264\) 0 0
\(265\) −1.00000 −0.0614295
\(266\) 0 0
\(267\) 2.00000 0.122398
\(268\) 0 0
\(269\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 0 0
\(273\) 3.50000 18.1865i 0.211830 1.10070i
\(274\) 0 0
\(275\) −0.500000 + 0.866025i −0.0301511 + 0.0522233i
\(276\) 0 0
\(277\) 1.00000 + 1.73205i 0.0600842 + 0.104069i 0.894503 0.447062i \(-0.147530\pi\)
−0.834419 + 0.551131i \(0.814196\pi\)
\(278\) 0 0
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) 0 0
\(283\) −1.00000 1.73205i −0.0594438 0.102960i 0.834772 0.550596i \(-0.185599\pi\)
−0.894216 + 0.447636i \(0.852266\pi\)
\(284\) 0 0
\(285\) −0.500000 + 0.866025i −0.0296174 + 0.0512989i
\(286\) 0 0
\(287\) −18.0000 15.5885i −1.06251 0.920158i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) −8.00000 13.8564i −0.468968 0.812277i
\(292\) 0 0
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) −12.0000 −0.698667
\(296\) 0 0
\(297\) 0.500000 + 0.866025i 0.0290129 + 0.0502519i
\(298\) 0 0
\(299\) 3.50000 6.06218i 0.202410 0.350585i
\(300\) 0 0
\(301\) −8.00000 6.92820i −0.461112 0.399335i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.00000 + 3.46410i 0.114520 + 0.198354i
\(306\) 0 0
\(307\) −8.00000 −0.456584 −0.228292 0.973593i \(-0.573314\pi\)
−0.228292 + 0.973593i \(0.573314\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 0 0
\(311\) 8.00000 + 13.8564i 0.453638 + 0.785725i 0.998609 0.0527306i \(-0.0167924\pi\)
−0.544970 + 0.838455i \(0.683459\pi\)
\(312\) 0 0
\(313\) 12.0000 20.7846i 0.678280 1.17482i −0.297218 0.954810i \(-0.596059\pi\)
0.975499 0.220006i \(-0.0706077\pi\)
\(314\) 0 0
\(315\) −0.500000 + 2.59808i −0.0281718 + 0.146385i
\(316\) 0 0
\(317\) −5.00000 + 8.66025i −0.280828 + 0.486408i −0.971589 0.236675i \(-0.923942\pi\)
0.690761 + 0.723083i \(0.257276\pi\)
\(318\) 0 0
\(319\) 4.00000 + 6.92820i 0.223957 + 0.387905i
\(320\) 0 0
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) 4.00000 0.222566
\(324\) 0 0
\(325\) −3.50000 6.06218i −0.194145 0.336269i
\(326\) 0 0
\(327\) −5.00000 + 8.66025i −0.276501 + 0.478913i
\(328\) 0 0
\(329\) 7.50000 2.59808i 0.413488 0.143237i
\(330\) 0 0
\(331\) −4.50000 + 7.79423i −0.247342 + 0.428410i −0.962788 0.270259i \(-0.912891\pi\)
0.715445 + 0.698669i \(0.246224\pi\)
\(332\) 0 0
\(333\) 1.50000 + 2.59808i 0.0821995 + 0.142374i
\(334\) 0 0
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) −3.00000 5.19615i −0.162938 0.282216i
\(340\) 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
\(345\) −0.500000 + 0.866025i −0.0269191 + 0.0466252i
\(346\) 0 0
\(347\) −17.0000 29.4449i −0.912608 1.58068i −0.810366 0.585923i \(-0.800732\pi\)
−0.102241 0.994760i \(-0.532601\pi\)
\(348\) 0 0
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) −7.00000 −0.373632
\(352\) 0 0
\(353\) 4.00000 + 6.92820i 0.212899 + 0.368751i 0.952620 0.304162i \(-0.0983763\pi\)
−0.739722 + 0.672913i \(0.765043\pi\)
\(354\) 0 0
\(355\) −7.00000 + 12.1244i −0.371521 + 0.643494i
\(356\) 0 0
\(357\) 10.0000 3.46410i 0.529256 0.183340i
\(358\) 0 0
\(359\) 18.0000 31.1769i 0.950004 1.64545i 0.204595 0.978847i \(-0.434412\pi\)
0.745409 0.666608i \(-0.232254\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 0 0
\(363\) 10.0000 0.524864
\(364\) 0 0
\(365\) −14.0000 −0.732793
\(366\) 0 0
\(367\) 9.50000 + 16.4545i 0.495896 + 0.858917i 0.999989 0.00473247i \(-0.00150640\pi\)
−0.504093 + 0.863649i \(0.668173\pi\)
\(368\) 0 0
\(369\) −4.50000 + 7.79423i −0.234261 + 0.405751i
\(370\) 0 0
\(371\) 0.500000 2.59808i 0.0259587 0.134885i
\(372\) 0 0
\(373\) −13.0000 + 22.5167i −0.673114 + 1.16587i 0.303902 + 0.952703i \(0.401711\pi\)
−0.977016 + 0.213165i \(0.931623\pi\)
\(374\) 0 0
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 0 0
\(377\) −56.0000 −2.88415
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) −2.50000 4.33013i −0.128079 0.221839i
\(382\) 0 0
\(383\) 6.50000 11.2583i 0.332134 0.575274i −0.650796 0.759253i \(-0.725565\pi\)
0.982930 + 0.183979i \(0.0588979\pi\)
\(384\) 0 0
\(385\) −2.00000 1.73205i −0.101929 0.0882735i
\(386\) 0 0
\(387\) −2.00000 + 3.46410i −0.101666 + 0.176090i
\(388\) 0 0
\(389\) 7.00000 + 12.1244i 0.354914 + 0.614729i 0.987103 0.160085i \(-0.0511768\pi\)
−0.632189 + 0.774814i \(0.717843\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 0 0
\(393\) −13.0000 −0.655763
\(394\) 0 0
\(395\) 2.00000 + 3.46410i 0.100631 + 0.174298i
\(396\) 0 0
\(397\) −9.00000 + 15.5885i −0.451697 + 0.782362i −0.998492 0.0549046i \(-0.982515\pi\)
0.546795 + 0.837267i \(0.315848\pi\)
\(398\) 0 0
\(399\) −2.00000 1.73205i −0.100125 0.0867110i
\(400\) 0 0
\(401\) 8.50000 14.7224i 0.424470 0.735203i −0.571901 0.820323i \(-0.693794\pi\)
0.996371 + 0.0851195i \(0.0271272\pi\)
\(402\) 0 0
\(403\) 21.0000 + 36.3731i 1.04608 + 1.81187i
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) −3.00000 −0.148704
\(408\) 0 0
\(409\) −5.00000 8.66025i −0.247234 0.428222i 0.715523 0.698589i \(-0.246188\pi\)
−0.962757 + 0.270367i \(0.912855\pi\)
\(410\) 0 0
\(411\) −1.00000 + 1.73205i −0.0493264 + 0.0854358i
\(412\) 0 0
\(413\) 6.00000 31.1769i 0.295241 1.53412i
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 0 0
\(417\) 2.00000 + 3.46410i 0.0979404 + 0.169638i
\(418\) 0 0
\(419\) −11.0000 −0.537385 −0.268693 0.963226i \(-0.586592\pi\)
−0.268693 + 0.963226i \(0.586592\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) 0 0
\(423\) −1.50000 2.59808i −0.0729325 0.126323i
\(424\) 0 0
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) −10.0000 + 3.46410i −0.483934 + 0.167640i
\(428\) 0 0
\(429\) 3.50000 6.06218i 0.168982 0.292685i
\(430\) 0 0
\(431\) −6.00000 10.3923i −0.289010 0.500580i 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 0 0
\(433\) 40.0000 1.92228 0.961139 0.276066i \(-0.0890309\pi\)
0.961139 + 0.276066i \(0.0890309\pi\)
\(434\) 0 0
\(435\) 8.00000 0.383571
\(436\) 0 0
\(437\) −0.500000 0.866025i −0.0239182 0.0414276i
\(438\) 0 0
\(439\) 8.00000 13.8564i 0.381819 0.661330i −0.609503 0.792784i \(-0.708631\pi\)
0.991322 + 0.131453i \(0.0419644\pi\)
\(440\) 0 0
\(441\) −6.50000 2.59808i −0.309524 0.123718i
\(442\) 0 0
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 0 0
\(445\) 1.00000 + 1.73205i 0.0474045 + 0.0821071i
\(446\) 0 0
\(447\) 4.00000 0.189194
\(448\) 0 0
\(449\) −25.0000 −1.17982 −0.589911 0.807468i \(-0.700837\pi\)
−0.589911 + 0.807468i \(0.700837\pi\)
\(450\) 0 0
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) 0 0
\(453\) 1.00000 1.73205i 0.0469841 0.0813788i
\(454\) 0 0
\(455\) 17.5000 6.06218i 0.820413 0.284199i
\(456\) 0 0
\(457\) −5.00000 + 8.66025i −0.233890 + 0.405110i −0.958950 0.283577i \(-0.908479\pi\)
0.725059 + 0.688686i \(0.241812\pi\)
\(458\) 0 0
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) 0 0
\(463\) −33.0000 −1.53364 −0.766820 0.641862i \(-0.778162\pi\)
−0.766820 + 0.641862i \(0.778162\pi\)
\(464\) 0 0
\(465\) −3.00000 5.19615i −0.139122 0.240966i
\(466\) 0 0
\(467\) 6.00000 10.3923i 0.277647 0.480899i −0.693153 0.720791i \(-0.743779\pi\)
0.970799 + 0.239892i \(0.0771121\pi\)
\(468\) 0 0
\(469\) 6.00000 31.1769i 0.277054 1.43962i
\(470\) 0 0
\(471\) 7.50000 12.9904i 0.345582 0.598565i
\(472\) 0 0
\(473\) −2.00000 3.46410i −0.0919601 0.159280i
\(474\) 0 0
\(475\) −1.00000 −0.0458831
\(476\) 0 0
\(477\) −1.00000 −0.0457869
\(478\) 0 0
\(479\) 13.0000 + 22.5167i 0.593985 + 1.02881i 0.993689 + 0.112168i \(0.0357796\pi\)
−0.399704 + 0.916644i \(0.630887\pi\)
\(480\) 0 0
\(481\) 10.5000 18.1865i 0.478759 0.829235i
\(482\) 0 0
\(483\) −2.00000 1.73205i −0.0910032 0.0788110i
\(484\) 0 0
\(485\) 8.00000 13.8564i 0.363261 0.629187i
\(486\) 0 0
\(487\) −4.00000 6.92820i −0.181257 0.313947i 0.761052 0.648691i \(-0.224683\pi\)
−0.942309 + 0.334744i \(0.891350\pi\)
\(488\) 0 0
\(489\) 8.00000 0.361773
\(490\) 0 0
\(491\) 12.0000 0.541552 0.270776 0.962642i \(-0.412720\pi\)
0.270776 + 0.962642i \(0.412720\pi\)
\(492\) 0 0
\(493\) −16.0000 27.7128i −0.720604 1.24812i
\(494\) 0 0
\(495\) −0.500000 + 0.866025i −0.0224733 + 0.0389249i
\(496\) 0 0
\(497\) −28.0000 24.2487i −1.25597 1.08770i
\(498\) 0 0
\(499\) 12.0000 20.7846i 0.537194 0.930447i −0.461860 0.886953i \(-0.652818\pi\)
0.999054 0.0434940i \(-0.0138489\pi\)
\(500\) 0 0
\(501\) 2.50000 + 4.33013i 0.111692 + 0.193456i
\(502\) 0 0
\(503\) −28.0000 −1.24846 −0.624229 0.781241i \(-0.714587\pi\)
−0.624229 + 0.781241i \(0.714587\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 18.0000 + 31.1769i 0.799408 + 1.38462i
\(508\) 0 0
\(509\) −15.0000 + 25.9808i −0.664863 + 1.15158i 0.314459 + 0.949271i \(0.398177\pi\)
−0.979322 + 0.202306i \(0.935156\pi\)
\(510\) 0 0
\(511\) 7.00000 36.3731i 0.309662 1.60905i
\(512\) 0 0
\(513\) −0.500000 + 0.866025i −0.0220755 + 0.0382360i
\(514\) 0 0
\(515\) 8.00000 + 13.8564i 0.352522 + 0.610586i
\(516\) 0 0
\(517\) 3.00000 0.131940
\(518\) 0 0
\(519\) 21.0000 0.921798
\(520\) 0 0
\(521\) 10.5000 + 18.1865i 0.460013 + 0.796766i 0.998961 0.0455727i \(-0.0145113\pi\)
−0.538948 + 0.842339i \(0.681178\pi\)
\(522\) 0 0
\(523\) −7.00000 + 12.1244i −0.306089 + 0.530161i −0.977503 0.210921i \(-0.932354\pi\)
0.671414 + 0.741082i \(0.265687\pi\)
\(524\) 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
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 0 0
\(531\) −12.0000 −0.520756
\(532\) 0 0
\(533\) 63.0000 2.72883
\(534\) 0 0
\(535\) −9.00000 15.5885i −0.389104 0.673948i
\(536\) 0 0
\(537\) −6.50000 + 11.2583i −0.280496 + 0.485833i
\(538\) 0 0
\(539\) 5.50000 4.33013i 0.236902 0.186512i
\(540\) 0 0
\(541\) −1.00000 + 1.73205i −0.0429934 + 0.0744667i −0.886721 0.462304i \(-0.847023\pi\)
0.843728 + 0.536771i \(0.180356\pi\)
\(542\) 0 0
\(543\) −6.00000 10.3923i −0.257485 0.445976i
\(544\) 0 0
\(545\) −10.0000 −0.428353
\(546\) 0 0
\(547\) −36.0000 −1.53925 −0.769624 0.638497i \(-0.779557\pi\)
−0.769624 + 0.638497i \(0.779557\pi\)
\(548\) 0 0
\(549\) 2.00000 + 3.46410i 0.0853579 + 0.147844i
\(550\) 0 0
\(551\) −4.00000 + 6.92820i −0.170406 + 0.295151i
\(552\) 0 0
\(553\) −10.0000 + 3.46410i −0.425243 + 0.147309i
\(554\) 0 0
\(555\) −1.50000 + 2.59808i −0.0636715 + 0.110282i
\(556\) 0 0
\(557\) −22.5000 38.9711i −0.953356 1.65126i −0.738087 0.674705i \(-0.764271\pi\)
−0.215268 0.976555i \(-0.569063\pi\)
\(558\) 0 0
\(559\) 28.0000 1.18427
\(560\) 0 0
\(561\) 4.00000 0.168880
\(562\) 0 0
\(563\) 7.00000 + 12.1244i 0.295015 + 0.510981i 0.974988 0.222256i \(-0.0713421\pi\)
−0.679974 + 0.733237i \(0.738009\pi\)
\(564\) 0 0
\(565\) 3.00000 5.19615i 0.126211 0.218604i
\(566\) 0 0
\(567\) −0.500000 + 2.59808i −0.0209980 + 0.109109i
\(568\) 0 0
\(569\) 18.5000 32.0429i 0.775560 1.34331i −0.158919 0.987292i \(-0.550801\pi\)
0.934479 0.356018i \(-0.115866\pi\)
\(570\) 0 0
\(571\) −4.00000 6.92820i −0.167395 0.289936i 0.770108 0.637913i \(-0.220202\pi\)
−0.937503 + 0.347977i \(0.886869\pi\)
\(572\) 0 0
\(573\) −10.0000 −0.417756
\(574\) 0 0
\(575\) −1.00000 −0.0417029
\(576\) 0 0
\(577\) 7.00000 + 12.1244i 0.291414 + 0.504744i 0.974144 0.225927i \(-0.0725410\pi\)
−0.682730 + 0.730670i \(0.739208\pi\)
\(578\) 0 0
\(579\) 13.0000 22.5167i 0.540262 0.935760i
\(580\) 0 0
\(581\) 24.0000 + 20.7846i 0.995688 + 0.862291i
\(582\) 0 0
\(583\) 0.500000 0.866025i 0.0207079 0.0358671i
\(584\) 0 0
\(585\) −3.50000 6.06218i −0.144707 0.250640i
\(586\) 0 0
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) 6.00000 0.247226
\(590\) 0 0
\(591\) −1.50000 2.59808i −0.0617018 0.106871i
\(592\) 0 0
\(593\) −6.00000 + 10.3923i −0.246390 + 0.426761i −0.962522 0.271205i \(-0.912578\pi\)
0.716131 + 0.697966i \(0.245911\pi\)
\(594\) 0 0
\(595\) 8.00000 + 6.92820i 0.327968 + 0.284029i
\(596\) 0 0
\(597\) 6.00000 10.3923i 0.245564 0.425329i
\(598\) 0 0
\(599\) 3.00000 + 5.19615i 0.122577 + 0.212309i 0.920783 0.390075i \(-0.127551\pi\)
−0.798206 + 0.602384i \(0.794218\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 0 0
\(605\) 5.00000 + 8.66025i 0.203279 + 0.352089i
\(606\) 0 0
\(607\) 12.5000 21.6506i 0.507359 0.878772i −0.492604 0.870253i \(-0.663955\pi\)
0.999964 0.00851879i \(-0.00271165\pi\)
\(608\) 0 0
\(609\) −4.00000 + 20.7846i −0.162088 + 0.842235i
\(610\) 0 0
\(611\) −10.5000 + 18.1865i −0.424785 + 0.735748i
\(612\) 0 0
\(613\) 7.50000 + 12.9904i 0.302922 + 0.524677i 0.976797 0.214169i \(-0.0687045\pi\)
−0.673874 + 0.738846i \(0.735371\pi\)
\(614\) 0 0
\(615\) −9.00000 −0.362915
\(616\) 0 0
\(617\) 8.00000 0.322068 0.161034 0.986949i \(-0.448517\pi\)
0.161034 + 0.986949i \(0.448517\pi\)
\(618\) 0 0
\(619\) −3.50000 6.06218i −0.140677 0.243659i 0.787075 0.616858i \(-0.211595\pi\)
−0.927752 + 0.373198i \(0.878261\pi\)
\(620\) 0 0
\(621\) −0.500000 + 0.866025i −0.0200643 + 0.0347524i
\(622\) 0 0
\(623\) −5.00000 + 1.73205i −0.200321 + 0.0693932i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −0.500000 0.866025i −0.0199681 0.0345857i
\(628\) 0 0
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −14.0000 −0.557331 −0.278666 0.960388i \(-0.589892\pi\)
−0.278666 + 0.960388i \(0.589892\pi\)
\(632\) 0 0
\(633\) 7.50000 + 12.9904i 0.298098 + 0.516321i
\(634\) 0 0
\(635\) 2.50000 4.33013i 0.0992095 0.171836i
\(636\) 0 0
\(637\) 7.00000 + 48.4974i 0.277350 + 1.92154i
\(638\) 0 0
\(639\) −7.00000 + 12.1244i −0.276916 + 0.479632i
\(640\) 0 0
\(641\) 11.5000 + 19.9186i 0.454223 + 0.786737i 0.998643 0.0520757i \(-0.0165837\pi\)
−0.544420 + 0.838812i \(0.683250\pi\)
\(642\) 0 0
\(643\) −26.0000 −1.02534 −0.512670 0.858586i \(-0.671344\pi\)
−0.512670 + 0.858586i \(0.671344\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 0 0
\(647\) −7.50000 12.9904i −0.294855 0.510705i 0.680096 0.733123i \(-0.261938\pi\)
−0.974951 + 0.222419i \(0.928605\pi\)
\(648\) 0 0
\(649\) 6.00000 10.3923i 0.235521 0.407934i
\(650\) 0 0
\(651\) 15.0000 5.19615i 0.587896 0.203653i
\(652\) 0 0
\(653\) −14.5000 + 25.1147i −0.567429 + 0.982816i 0.429390 + 0.903119i \(0.358728\pi\)
−0.996819 + 0.0796966i \(0.974605\pi\)
\(654\) 0 0
\(655\) −6.50000 11.2583i −0.253976 0.439899i
\(656\) 0 0
\(657\) −14.0000 −0.546192
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) −4.00000 6.92820i −0.155582 0.269476i 0.777689 0.628649i \(-0.216392\pi\)
−0.933271 + 0.359174i \(0.883059\pi\)
\(662\) 0 0
\(663\) −14.0000 + 24.2487i −0.543715 + 0.941742i
\(664\) 0 0
\(665\) 0.500000 2.59808i 0.0193892 0.100749i
\(666\) 0 0
\(667\) −4.00000 + 6.92820i −0.154881 + 0.268261i
\(668\) 0 0
\(669\) 2.00000 + 3.46410i 0.0773245 + 0.133930i
\(670\) 0 0
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) −12.0000 −0.462566 −0.231283 0.972887i \(-0.574292\pi\)
−0.231283 + 0.972887i \(0.574292\pi\)
\(674\) 0 0
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 0 0
\(677\) −0.500000 + 0.866025i −0.0192166 + 0.0332841i −0.875474 0.483266i \(-0.839451\pi\)
0.856257 + 0.516550i \(0.172784\pi\)
\(678\) 0 0
\(679\) 32.0000 + 27.7128i 1.22805 + 1.06352i
\(680\) 0 0
\(681\) 10.0000 17.3205i 0.383201 0.663723i
\(682\) 0 0
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) 0 0
\(685\) −2.00000 −0.0764161
\(686\) 0 0
\(687\) 22.0000 0.839352
\(688\) 0 0
\(689\) 3.50000 + 6.06218i 0.133339 + 0.230951i
\(690\) 0 0
\(691\) 6.00000 10.3923i 0.228251 0.395342i −0.729039 0.684472i \(-0.760033\pi\)
0.957290 + 0.289130i \(0.0933661\pi\)
\(692\) 0 0
\(693\) −2.00000 1.73205i −0.0759737 0.0657952i
\(694\) 0 0
\(695\) −2.00000 + 3.46410i −0.0758643 + 0.131401i
\(696\) 0 0
\(697\) 18.0000 + 31.1769i 0.681799 + 1.18091i
\(698\) 0 0
\(699\) −26.0000 −0.983410
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) −1.50000 2.59808i −0.0565736 0.0979883i
\(704\) 0 0
\(705\) 1.50000 2.59808i 0.0564933 0.0978492i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −2.00000 + 3.46410i −0.0751116 + 0.130097i −0.901135 0.433539i \(-0.857265\pi\)
0.826023 + 0.563636i \(0.190598\pi\)
\(710\) 0 0
\(711\) 2.00000 + 3.46410i 0.0750059 + 0.129914i
\(712\) 0 0
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 7.00000 0.261785
\(716\) 0 0
\(717\) 3.00000 + 5.19615i 0.112037 + 0.194054i
\(718\) 0 0
\(719\) 13.0000 22.5167i 0.484818 0.839730i −0.515030 0.857172i \(-0.672219\pi\)
0.999848 + 0.0174426i \(0.00555244\pi\)
\(720\) 0 0
\(721\) −40.0000 + 13.8564i −1.48968 + 0.516040i
\(722\) 0 0
\(723\) 3.50000 6.06218i 0.130166 0.225455i
\(724\) 0 0
\(725\) 4.00000 + 6.92820i 0.148556 + 0.257307i
\(726\) 0 0
\(727\) −17.0000 −0.630495 −0.315248 0.949009i \(-0.602088\pi\)
−0.315248 + 0.949009i \(0.602088\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 8.00000 + 13.8564i 0.295891 + 0.512498i
\(732\) 0 0
\(733\) −18.5000 + 32.0429i −0.683313 + 1.18353i 0.290651 + 0.956829i \(0.406128\pi\)
−0.973964 + 0.226704i \(0.927205\pi\)
\(734\) 0 0
\(735\) −1.00000 6.92820i −0.0368856 0.255551i
\(736\) 0 0
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) 20.5000 + 35.5070i 0.754105 + 1.30615i 0.945818 + 0.324697i \(0.105262\pi\)
−0.191714 + 0.981451i \(0.561404\pi\)
\(740\) 0 0
\(741\) 7.00000 0.257151
\(742\) 0 0
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) 0 0
\(745\) 2.00000 + 3.46410i 0.0732743 + 0.126915i
\(746\) 0 0
\(747\) 6.00000 10.3923i 0.219529 0.380235i
\(748\) 0 0
\(749\) 45.0000 15.5885i 1.64426 0.569590i
\(750\) 0 0
\(751\) −13.0000 + 22.5167i −0.474377 + 0.821645i −0.999570 0.0293387i \(-0.990660\pi\)
0.525193 + 0.850983i \(0.323993\pi\)
\(752\) 0 0
\(753\) 1.50000 + 2.59808i 0.0546630 + 0.0946792i
\(754\) 0 0
\(755\) 2.00000 0.0727875
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 0 0
\(759\) −0.500000 0.866025i −0.0181489 0.0314347i
\(760\) 0 0
\(761\) 8.50000 14.7224i 0.308125 0.533688i −0.669827 0.742517i \(-0.733632\pi\)
0.977952 + 0.208829i \(0.0669652\pi\)
\(762\) 0 0
\(763\) 5.00000 25.9808i 0.181012 0.940567i
\(764\) 0 0
\(765\) 2.00000 3.46410i 0.0723102 0.125245i
\(766\) 0 0
\(767\) 42.0000 + 72.7461i 1.51653 + 2.62671i
\(768\) 0 0
\(769\) −29.0000 −1.04577 −0.522883 0.852404i \(-0.675144\pi\)
−0.522883 + 0.852404i \(0.675144\pi\)
\(770\) 0 0
\(771\) 8.00000 0.288113
\(772\) 0 0
\(773\) −21.5000 37.2391i −0.773301 1.33940i −0.935744 0.352679i \(-0.885271\pi\)
0.162443 0.986718i \(-0.448063\pi\)
\(774\) 0 0
\(775\) 3.00000 5.19615i 0.107763 0.186651i
\(776\) 0 0
\(777\) −6.00000 5.19615i −0.215249 0.186411i
\(778\) 0 0
\(779\) 4.50000 7.79423i 0.161229 0.279257i
\(780\) 0 0
\(781\) −7.00000 12.1244i −0.250480 0.433844i
\(782\) 0 0
\(783\) 8.00000 0.285897
\(784\) 0 0
\(785\) 15.0000 0.535373
\(786\) 0 0
\(787\) −11.0000 19.0526i −0.392108 0.679150i 0.600620 0.799535i \(-0.294921\pi\)
−0.992727 + 0.120384i \(0.961587\pi\)
\(788\) 0 0
\(789\) 8.00000 13.8564i 0.284808 0.493301i
\(790\) 0 0
\(791\) 12.0000 + 10.3923i 0.426671 + 0.369508i
\(792\) 0 0
\(793\) 14.0000 24.2487i 0.497155 0.861097i
\(794\) 0 0
\(795\) −0.500000 0.866025i −0.0177332 0.0307148i
\(796\) 0 0
\(797\) −6.00000 −0.212531 −0.106265 0.994338i \(-0.533889\pi\)
−0.106265 + 0.994338i \(0.533889\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 0 0
\(801\) 1.00000 + 1.73205i 0.0353333 + 0.0611990i
\(802\) 0 0
\(803\) 7.00000 12.1244i 0.247025 0.427859i
\(804\) 0 0
\(805\) 0.500000 2.59808i 0.0176227 0.0915702i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −26.5000 45.8993i −0.931690 1.61374i −0.780432 0.625241i \(-0.785001\pi\)
−0.151259 0.988494i \(-0.548333\pi\)
\(810\) 0