Properties

Label 1680.2.bg.o.961.1
Level $1680$
Weight $2$
Character 1680.961
Analytic conductor $13.415$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{11} +2.26795 q^{13} +1.00000 q^{15} +(-1.63397 - 2.83013i) q^{17} +(2.23205 - 3.86603i) q^{19} +(-1.73205 + 2.00000i) q^{21} +(-2.36603 + 4.09808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -4.19615 q^{29} +(-0.232051 - 0.401924i) q^{31} +(0.366025 - 0.633975i) q^{33} +(2.59808 + 0.500000i) q^{35} +(1.59808 - 2.76795i) q^{37} +(-1.13397 - 1.96410i) q^{39} -0.732051 q^{41} -3.19615 q^{43} +(-0.500000 - 0.866025i) q^{45} +(1.00000 - 1.73205i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(-1.63397 + 2.83013i) q^{51} +(-6.19615 - 10.7321i) q^{53} -0.732051 q^{55} -4.46410 q^{57} +(-0.0980762 - 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(2.59808 + 0.500000i) q^{63} +(-1.13397 + 1.96410i) q^{65} +(-7.33013 - 12.6962i) q^{67} +4.73205 q^{69} -6.19615 q^{71} +(-6.33013 - 10.9641i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(1.26795 - 1.46410i) q^{77} +(-3.69615 + 6.40192i) q^{79} +(-0.500000 - 0.866025i) q^{81} -15.1244 q^{83} +3.26795 q^{85} +(2.09808 + 3.63397i) q^{87} +(-7.56218 + 13.0981i) q^{89} +(-1.96410 - 5.66987i) q^{91} +(-0.232051 + 0.401924i) q^{93} +(2.23205 + 3.86603i) q^{95} +14.9282 q^{97} -0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{3} - 2q^{5} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{3} - 2q^{5} - 2q^{9} - 2q^{11} + 16q^{13} + 4q^{15} - 10q^{17} + 2q^{19} - 6q^{23} - 2q^{25} + 4q^{27} + 4q^{29} + 6q^{31} - 2q^{33} - 4q^{37} - 8q^{39} + 4q^{41} + 8q^{43} - 2q^{45} + 4q^{47} - 22q^{49} - 10q^{51} - 4q^{53} + 4q^{55} - 4q^{57} + 10q^{59} - 8q^{61} - 8q^{65} - 12q^{67} + 12q^{69} - 4q^{71} - 8q^{73} - 2q^{75} + 12q^{77} + 6q^{79} - 2q^{81} - 12q^{83} + 20q^{85} - 2q^{87} - 6q^{89} + 6q^{91} + 6q^{93} + 2q^{95} + 32q^{97} + 4q^{99} + O(q^{100}) \)

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
\(7\) −0.866025 2.50000i −0.327327 0.944911i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0.366025 + 0.633975i 0.110361 + 0.191151i 0.915916 0.401371i \(-0.131466\pi\)
−0.805555 + 0.592521i \(0.798133\pi\)
\(12\) 0 0
\(13\) 2.26795 0.629016 0.314508 0.949255i \(-0.398160\pi\)
0.314508 + 0.949255i \(0.398160\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) −1.63397 2.83013i −0.396297 0.686407i 0.596969 0.802264i \(-0.296372\pi\)
−0.993266 + 0.115858i \(0.963038\pi\)
\(18\) 0 0
\(19\) 2.23205 3.86603i 0.512068 0.886927i −0.487835 0.872936i \(-0.662213\pi\)
0.999902 0.0139909i \(-0.00445360\pi\)
\(20\) 0 0
\(21\) −1.73205 + 2.00000i −0.377964 + 0.436436i
\(22\) 0 0
\(23\) −2.36603 + 4.09808i −0.493350 + 0.854508i −0.999971 0.00766135i \(-0.997561\pi\)
0.506620 + 0.862169i \(0.330895\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.19615 −0.779206 −0.389603 0.920983i \(-0.627388\pi\)
−0.389603 + 0.920983i \(0.627388\pi\)
\(30\) 0 0
\(31\) −0.232051 0.401924i −0.0416776 0.0721876i 0.844434 0.535659i \(-0.179937\pi\)
−0.886112 + 0.463472i \(0.846604\pi\)
\(32\) 0 0
\(33\) 0.366025 0.633975i 0.0637168 0.110361i
\(34\) 0 0
\(35\) 2.59808 + 0.500000i 0.439155 + 0.0845154i
\(36\) 0 0
\(37\) 1.59808 2.76795i 0.262722 0.455048i −0.704242 0.709960i \(-0.748713\pi\)
0.966964 + 0.254912i \(0.0820464\pi\)
\(38\) 0 0
\(39\) −1.13397 1.96410i −0.181581 0.314508i
\(40\) 0 0
\(41\) −0.732051 −0.114327 −0.0571636 0.998365i \(-0.518206\pi\)
−0.0571636 + 0.998365i \(0.518206\pi\)
\(42\) 0 0
\(43\) −3.19615 −0.487409 −0.243704 0.969850i \(-0.578363\pi\)
−0.243704 + 0.969850i \(0.578363\pi\)
\(44\) 0 0
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) 0 0
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 0 0
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 0 0
\(51\) −1.63397 + 2.83013i −0.228802 + 0.396297i
\(52\) 0 0
\(53\) −6.19615 10.7321i −0.851107 1.47416i −0.880210 0.474584i \(-0.842598\pi\)
0.0291032 0.999576i \(-0.490735\pi\)
\(54\) 0 0
\(55\) −0.732051 −0.0987097
\(56\) 0 0
\(57\) −4.46410 −0.591285
\(58\) 0 0
\(59\) −0.0980762 0.169873i −0.0127684 0.0221156i 0.859571 0.511017i \(-0.170731\pi\)
−0.872339 + 0.488901i \(0.837398\pi\)
\(60\) 0 0
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) 0 0
\(63\) 2.59808 + 0.500000i 0.327327 + 0.0629941i
\(64\) 0 0
\(65\) −1.13397 + 1.96410i −0.140652 + 0.243617i
\(66\) 0 0
\(67\) −7.33013 12.6962i −0.895518 1.55108i −0.833163 0.553028i \(-0.813472\pi\)
−0.0623548 0.998054i \(-0.519861\pi\)
\(68\) 0 0
\(69\) 4.73205 0.569672
\(70\) 0 0
\(71\) −6.19615 −0.735348 −0.367674 0.929955i \(-0.619846\pi\)
−0.367674 + 0.929955i \(0.619846\pi\)
\(72\) 0 0
\(73\) −6.33013 10.9641i −0.740885 1.28325i −0.952093 0.305810i \(-0.901073\pi\)
0.211207 0.977441i \(-0.432260\pi\)
\(74\) 0 0
\(75\) −0.500000 + 0.866025i −0.0577350 + 0.100000i
\(76\) 0 0
\(77\) 1.26795 1.46410i 0.144496 0.166850i
\(78\) 0 0
\(79\) −3.69615 + 6.40192i −0.415850 + 0.720273i −0.995517 0.0945803i \(-0.969849\pi\)
0.579668 + 0.814853i \(0.303182\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −15.1244 −1.66011 −0.830057 0.557679i \(-0.811692\pi\)
−0.830057 + 0.557679i \(0.811692\pi\)
\(84\) 0 0
\(85\) 3.26795 0.354459
\(86\) 0 0
\(87\) 2.09808 + 3.63397i 0.224937 + 0.389603i
\(88\) 0 0
\(89\) −7.56218 + 13.0981i −0.801589 + 1.38839i 0.116980 + 0.993134i \(0.462679\pi\)
−0.918570 + 0.395259i \(0.870655\pi\)
\(90\) 0 0
\(91\) −1.96410 5.66987i −0.205894 0.594364i
\(92\) 0 0
\(93\) −0.232051 + 0.401924i −0.0240625 + 0.0416776i
\(94\) 0 0
\(95\) 2.23205 + 3.86603i 0.229004 + 0.396646i
\(96\) 0 0
\(97\) 14.9282 1.51573 0.757865 0.652412i \(-0.226243\pi\)
0.757865 + 0.652412i \(0.226243\pi\)
\(98\) 0 0
\(99\) −0.732051 −0.0735739
\(100\) 0 0
\(101\) 3.63397 + 6.29423i 0.361594 + 0.626299i 0.988223 0.153018i \(-0.0488993\pi\)
−0.626629 + 0.779317i \(0.715566\pi\)
\(102\) 0 0
\(103\) −4.59808 + 7.96410i −0.453062 + 0.784726i −0.998574 0.0533764i \(-0.983002\pi\)
0.545513 + 0.838103i \(0.316335\pi\)
\(104\) 0 0
\(105\) −0.866025 2.50000i −0.0845154 0.243975i
\(106\) 0 0
\(107\) 1.09808 1.90192i 0.106155 0.183866i −0.808054 0.589108i \(-0.799479\pi\)
0.914210 + 0.405242i \(0.132813\pi\)
\(108\) 0 0
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 0 0
\(111\) −3.19615 −0.303365
\(112\) 0 0
\(113\) 8.92820 0.839895 0.419947 0.907548i \(-0.362049\pi\)
0.419947 + 0.907548i \(0.362049\pi\)
\(114\) 0 0
\(115\) −2.36603 4.09808i −0.220633 0.382148i
\(116\) 0 0
\(117\) −1.13397 + 1.96410i −0.104836 + 0.181581i
\(118\) 0 0
\(119\) −5.66025 + 6.53590i −0.518875 + 0.599145i
\(120\) 0 0
\(121\) 5.23205 9.06218i 0.475641 0.823834i
\(122\) 0 0
\(123\) 0.366025 + 0.633975i 0.0330034 + 0.0571636i
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −4.80385 −0.426273 −0.213136 0.977022i \(-0.568368\pi\)
−0.213136 + 0.977022i \(0.568368\pi\)
\(128\) 0 0
\(129\) 1.59808 + 2.76795i 0.140703 + 0.243704i
\(130\) 0 0
\(131\) 7.73205 13.3923i 0.675552 1.17009i −0.300755 0.953702i \(-0.597239\pi\)
0.976307 0.216390i \(-0.0694281\pi\)
\(132\) 0 0
\(133\) −11.5981 2.23205i −1.00568 0.193543i
\(134\) 0 0
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 0 0
\(137\) −1.09808 1.90192i −0.0938150 0.162492i 0.815298 0.579041i \(-0.196573\pi\)
−0.909113 + 0.416549i \(0.863240\pi\)
\(138\) 0 0
\(139\) −5.92820 −0.502824 −0.251412 0.967880i \(-0.580895\pi\)
−0.251412 + 0.967880i \(0.580895\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 0 0
\(143\) 0.830127 + 1.43782i 0.0694187 + 0.120237i
\(144\) 0 0
\(145\) 2.09808 3.63397i 0.174236 0.301785i
\(146\) 0 0
\(147\) 6.50000 + 2.59808i 0.536111 + 0.214286i
\(148\) 0 0
\(149\) −2.92820 + 5.07180i −0.239888 + 0.415498i −0.960682 0.277651i \(-0.910444\pi\)
0.720794 + 0.693149i \(0.243777\pi\)
\(150\) 0 0
\(151\) −4.46410 7.73205i −0.363283 0.629225i 0.625216 0.780452i \(-0.285011\pi\)
−0.988499 + 0.151227i \(0.951678\pi\)
\(152\) 0 0
\(153\) 3.26795 0.264198
\(154\) 0 0
\(155\) 0.464102 0.0372775
\(156\) 0 0
\(157\) −3.19615 5.53590i −0.255081 0.441813i 0.709837 0.704366i \(-0.248769\pi\)
−0.964917 + 0.262553i \(0.915435\pi\)
\(158\) 0 0
\(159\) −6.19615 + 10.7321i −0.491387 + 0.851107i
\(160\) 0 0
\(161\) 12.2942 + 2.36603i 0.968921 + 0.186469i
\(162\) 0 0
\(163\) 10.9282 18.9282i 0.855963 1.48257i −0.0197859 0.999804i \(-0.506298\pi\)
0.875749 0.482767i \(-0.160368\pi\)
\(164\) 0 0
\(165\) 0.366025 + 0.633975i 0.0284950 + 0.0493549i
\(166\) 0 0
\(167\) 17.6603 1.36659 0.683296 0.730142i \(-0.260546\pi\)
0.683296 + 0.730142i \(0.260546\pi\)
\(168\) 0 0
\(169\) −7.85641 −0.604339
\(170\) 0 0
\(171\) 2.23205 + 3.86603i 0.170689 + 0.295642i
\(172\) 0 0
\(173\) −7.26795 + 12.5885i −0.552572 + 0.957083i 0.445516 + 0.895274i \(0.353020\pi\)
−0.998088 + 0.0618087i \(0.980313\pi\)
\(174\) 0 0
\(175\) −1.73205 + 2.00000i −0.130931 + 0.151186i
\(176\) 0 0
\(177\) −0.0980762 + 0.169873i −0.00737186 + 0.0127684i
\(178\) 0 0
\(179\) −5.00000 8.66025i −0.373718 0.647298i 0.616417 0.787420i \(-0.288584\pi\)
−0.990134 + 0.140122i \(0.955250\pi\)
\(180\) 0 0
\(181\) −24.3205 −1.80773 −0.903865 0.427819i \(-0.859282\pi\)
−0.903865 + 0.427819i \(0.859282\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 0 0
\(185\) 1.59808 + 2.76795i 0.117493 + 0.203504i
\(186\) 0 0
\(187\) 1.19615 2.07180i 0.0874713 0.151505i
\(188\) 0 0
\(189\) −0.866025 2.50000i −0.0629941 0.181848i
\(190\) 0 0
\(191\) −4.46410 + 7.73205i −0.323011 + 0.559472i −0.981108 0.193462i \(-0.938028\pi\)
0.658097 + 0.752933i \(0.271362\pi\)
\(192\) 0 0
\(193\) −0.598076 1.03590i −0.0430505 0.0745656i 0.843697 0.536819i \(-0.180374\pi\)
−0.886748 + 0.462254i \(0.847041\pi\)
\(194\) 0 0
\(195\) 2.26795 0.162411
\(196\) 0 0
\(197\) −0.339746 −0.0242059 −0.0121029 0.999927i \(-0.503853\pi\)
−0.0121029 + 0.999927i \(0.503853\pi\)
\(198\) 0 0
\(199\) 11.0000 + 19.0526i 0.779769 + 1.35060i 0.932075 + 0.362267i \(0.117997\pi\)
−0.152305 + 0.988334i \(0.548670\pi\)
\(200\) 0 0
\(201\) −7.33013 + 12.6962i −0.517027 + 0.895518i
\(202\) 0 0
\(203\) 3.63397 + 10.4904i 0.255055 + 0.736280i
\(204\) 0 0
\(205\) 0.366025 0.633975i 0.0255643 0.0442787i
\(206\) 0 0
\(207\) −2.36603 4.09808i −0.164450 0.284836i
\(208\) 0 0
\(209\) 3.26795 0.226049
\(210\) 0 0
\(211\) −7.07180 −0.486843 −0.243421 0.969921i \(-0.578270\pi\)
−0.243421 + 0.969921i \(0.578270\pi\)
\(212\) 0 0
\(213\) 3.09808 + 5.36603i 0.212277 + 0.367674i
\(214\) 0 0
\(215\) 1.59808 2.76795i 0.108988 0.188773i
\(216\) 0 0
\(217\) −0.803848 + 0.928203i −0.0545687 + 0.0630105i
\(218\) 0 0
\(219\) −6.33013 + 10.9641i −0.427750 + 0.740885i
\(220\) 0 0
\(221\) −3.70577 6.41858i −0.249277 0.431761i
\(222\) 0 0
\(223\) 20.3923 1.36557 0.682785 0.730619i \(-0.260769\pi\)
0.682785 + 0.730619i \(0.260769\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −0.830127 1.43782i −0.0550975 0.0954316i 0.837161 0.546956i \(-0.184214\pi\)
−0.892259 + 0.451525i \(0.850880\pi\)
\(228\) 0 0
\(229\) 1.50000 2.59808i 0.0991228 0.171686i −0.812199 0.583380i \(-0.801730\pi\)
0.911322 + 0.411695i \(0.135063\pi\)
\(230\) 0 0
\(231\) −1.90192 0.366025i −0.125137 0.0240827i
\(232\) 0 0
\(233\) −8.66025 + 15.0000i −0.567352 + 0.982683i 0.429474 + 0.903079i \(0.358699\pi\)
−0.996827 + 0.0796037i \(0.974635\pi\)
\(234\) 0 0
\(235\) 1.00000 + 1.73205i 0.0652328 + 0.112987i
\(236\) 0 0
\(237\) 7.39230 0.480182
\(238\) 0 0
\(239\) −7.07180 −0.457437 −0.228718 0.973493i \(-0.573453\pi\)
−0.228718 + 0.973493i \(0.573453\pi\)
\(240\) 0 0
\(241\) −6.73205 11.6603i −0.433650 0.751103i 0.563535 0.826092i \(-0.309441\pi\)
−0.997184 + 0.0749893i \(0.976108\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) −1.00000 6.92820i −0.0638877 0.442627i
\(246\) 0 0
\(247\) 5.06218 8.76795i 0.322099 0.557891i
\(248\) 0 0
\(249\) 7.56218 + 13.0981i 0.479234 + 0.830057i
\(250\) 0 0
\(251\) 24.5885 1.55201 0.776005 0.630727i \(-0.217243\pi\)
0.776005 + 0.630727i \(0.217243\pi\)
\(252\) 0 0
\(253\) −3.46410 −0.217786
\(254\) 0 0
\(255\) −1.63397 2.83013i −0.102323 0.177229i
\(256\) 0 0
\(257\) 2.83013 4.90192i 0.176538 0.305774i −0.764154 0.645034i \(-0.776843\pi\)
0.940693 + 0.339260i \(0.110177\pi\)
\(258\) 0 0
\(259\) −8.30385 1.59808i −0.515976 0.0992996i
\(260\) 0 0
\(261\) 2.09808 3.63397i 0.129868 0.224937i
\(262\) 0 0
\(263\) 4.19615 + 7.26795i 0.258746 + 0.448161i 0.965906 0.258892i \(-0.0833575\pi\)
−0.707160 + 0.707053i \(0.750024\pi\)
\(264\) 0 0
\(265\) 12.3923 0.761253
\(266\) 0 0
\(267\) 15.1244 0.925596
\(268\) 0 0
\(269\) 6.26795 + 10.8564i 0.382164 + 0.661927i 0.991371 0.131084i \(-0.0418457\pi\)
−0.609208 + 0.793011i \(0.708512\pi\)
\(270\) 0 0
\(271\) 1.53590 2.66025i 0.0932992 0.161599i −0.815598 0.578619i \(-0.803592\pi\)
0.908897 + 0.417020i \(0.136925\pi\)
\(272\) 0 0
\(273\) −3.92820 + 4.53590i −0.237746 + 0.274525i
\(274\) 0 0
\(275\) 0.366025 0.633975i 0.0220722 0.0382301i
\(276\) 0 0
\(277\) 7.33013 + 12.6962i 0.440425 + 0.762838i 0.997721 0.0674759i \(-0.0214946\pi\)
−0.557296 + 0.830314i \(0.688161\pi\)
\(278\) 0 0
\(279\) 0.464102 0.0277850
\(280\) 0 0
\(281\) 13.8564 0.826604 0.413302 0.910594i \(-0.364375\pi\)
0.413302 + 0.910594i \(0.364375\pi\)
\(282\) 0 0
\(283\) −12.0622 20.8923i −0.717022 1.24192i −0.962174 0.272434i \(-0.912171\pi\)
0.245152 0.969485i \(-0.421162\pi\)
\(284\) 0 0
\(285\) 2.23205 3.86603i 0.132215 0.229004i
\(286\) 0 0
\(287\) 0.633975 + 1.83013i 0.0374223 + 0.108029i
\(288\) 0 0
\(289\) 3.16025 5.47372i 0.185897 0.321984i
\(290\) 0 0
\(291\) −7.46410 12.9282i −0.437553 0.757865i
\(292\) 0 0
\(293\) 18.9282 1.10580 0.552899 0.833248i \(-0.313522\pi\)
0.552899 + 0.833248i \(0.313522\pi\)
\(294\) 0 0
\(295\) 0.196152 0.0114204
\(296\) 0 0
\(297\) 0.366025 + 0.633975i 0.0212389 + 0.0367869i
\(298\) 0 0
\(299\) −5.36603 + 9.29423i −0.310325 + 0.537499i
\(300\) 0 0
\(301\) 2.76795 + 7.99038i 0.159542 + 0.460558i
\(302\) 0 0
\(303\) 3.63397 6.29423i 0.208766 0.361594i
\(304\) 0 0
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) 0 0
\(307\) 32.1244 1.83343 0.916717 0.399537i \(-0.130829\pi\)
0.916717 + 0.399537i \(0.130829\pi\)
\(308\) 0 0
\(309\) 9.19615 0.523151
\(310\) 0 0
\(311\) 4.56218 + 7.90192i 0.258697 + 0.448077i 0.965893 0.258941i \(-0.0833734\pi\)
−0.707196 + 0.707018i \(0.750040\pi\)
\(312\) 0 0
\(313\) 6.33013 10.9641i 0.357800 0.619728i −0.629793 0.776763i \(-0.716860\pi\)
0.987593 + 0.157035i \(0.0501936\pi\)
\(314\) 0 0
\(315\) −1.73205 + 2.00000i −0.0975900 + 0.112687i
\(316\) 0 0
\(317\) 14.2224 24.6340i 0.798811 1.38358i −0.121579 0.992582i \(-0.538796\pi\)
0.920391 0.391000i \(-0.127871\pi\)
\(318\) 0 0
\(319\) −1.53590 2.66025i −0.0859938 0.148946i
\(320\) 0 0
\(321\) −2.19615 −0.122577
\(322\) 0 0
\(323\) −14.5885 −0.811723
\(324\) 0 0
\(325\) −1.13397 1.96410i −0.0629016 0.108949i
\(326\) 0 0
\(327\) −5.50000 + 9.52628i −0.304151 + 0.526804i
\(328\) 0 0
\(329\) −5.19615 1.00000i −0.286473 0.0551318i
\(330\) 0 0
\(331\) 4.03590 6.99038i 0.221833 0.384226i −0.733532 0.679655i \(-0.762129\pi\)
0.955365 + 0.295429i \(0.0954627\pi\)
\(332\) 0 0
\(333\) 1.59808 + 2.76795i 0.0875740 + 0.151683i
\(334\) 0 0
\(335\) 14.6603 0.800975
\(336\) 0 0
\(337\) 17.9808 0.979475 0.489737 0.871870i \(-0.337093\pi\)
0.489737 + 0.871870i \(0.337093\pi\)
\(338\) 0 0
\(339\) −4.46410 7.73205i −0.242457 0.419947i
\(340\) 0 0
\(341\) 0.169873 0.294229i 0.00919914 0.0159334i
\(342\) 0 0
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) 0 0
\(345\) −2.36603 + 4.09808i −0.127383 + 0.220633i
\(346\) 0 0
\(347\) −10.5359 18.2487i −0.565597 0.979642i −0.996994 0.0774801i \(-0.975313\pi\)
0.431397 0.902162i \(-0.358021\pi\)
\(348\) 0 0
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 0 0
\(351\) 2.26795 0.121054
\(352\) 0 0
\(353\) 1.56218 + 2.70577i 0.0831463 + 0.144014i 0.904600 0.426262i \(-0.140170\pi\)
−0.821453 + 0.570276i \(0.806836\pi\)
\(354\) 0 0
\(355\) 3.09808 5.36603i 0.164429 0.284799i
\(356\) 0 0
\(357\) 8.49038 + 1.63397i 0.449359 + 0.0864791i
\(358\) 0 0
\(359\) −0.633975 + 1.09808i −0.0334599 + 0.0579542i −0.882270 0.470743i \(-0.843986\pi\)
0.848811 + 0.528697i \(0.177319\pi\)
\(360\) 0 0
\(361\) −0.464102 0.803848i −0.0244264 0.0423078i
\(362\) 0 0
\(363\) −10.4641 −0.549223
\(364\) 0 0
\(365\) 12.6603 0.662668
\(366\) 0 0
\(367\) 5.59808 + 9.69615i 0.292217 + 0.506135i 0.974334 0.225108i \(-0.0722736\pi\)
−0.682117 + 0.731244i \(0.738940\pi\)
\(368\) 0 0
\(369\) 0.366025 0.633975i 0.0190545 0.0330034i
\(370\) 0 0
\(371\) −21.4641 + 24.7846i −1.11436 + 1.28675i
\(372\) 0 0
\(373\) −13.2583 + 22.9641i −0.686490 + 1.18904i 0.286476 + 0.958088i \(0.407516\pi\)
−0.972966 + 0.230949i \(0.925817\pi\)
\(374\) 0 0
\(375\) −0.500000 0.866025i −0.0258199 0.0447214i
\(376\) 0 0
\(377\) −9.51666 −0.490133
\(378\) 0 0
\(379\) −6.32051 −0.324663 −0.162331 0.986736i \(-0.551901\pi\)
−0.162331 + 0.986736i \(0.551901\pi\)
\(380\) 0 0
\(381\) 2.40192 + 4.16025i 0.123054 + 0.213136i
\(382\) 0 0
\(383\) −11.6603 + 20.1962i −0.595811 + 1.03198i 0.397621 + 0.917550i \(0.369836\pi\)
−0.993432 + 0.114425i \(0.963497\pi\)
\(384\) 0 0
\(385\) 0.633975 + 1.83013i 0.0323103 + 0.0932719i
\(386\) 0 0
\(387\) 1.59808 2.76795i 0.0812348 0.140703i
\(388\) 0 0
\(389\) −2.70577 4.68653i −0.137188 0.237617i 0.789243 0.614081i \(-0.210473\pi\)
−0.926431 + 0.376464i \(0.877140\pi\)
\(390\) 0 0
\(391\) 15.4641 0.782053
\(392\) 0 0
\(393\) −15.4641 −0.780061
\(394\) 0 0
\(395\) −3.69615 6.40192i −0.185974 0.322116i
\(396\) 0 0
\(397\) 15.5981 27.0167i 0.782845 1.35593i −0.147433 0.989072i \(-0.547101\pi\)
0.930278 0.366855i \(-0.119566\pi\)
\(398\) 0 0
\(399\) 3.86603 + 11.1603i 0.193543 + 0.558712i
\(400\) 0 0
\(401\) 8.19615 14.1962i 0.409296 0.708922i −0.585515 0.810662i \(-0.699108\pi\)
0.994811 + 0.101740i \(0.0324409\pi\)
\(402\) 0 0
\(403\) −0.526279 0.911543i −0.0262158 0.0454072i
\(404\) 0 0
\(405\) 1.00000 0.0496904
\(406\) 0 0
\(407\) 2.33975 0.115977
\(408\) 0 0
\(409\) −1.57180 2.72243i −0.0777203 0.134616i 0.824546 0.565795i \(-0.191431\pi\)
−0.902266 + 0.431180i \(0.858097\pi\)
\(410\) 0 0
\(411\) −1.09808 + 1.90192i −0.0541641 + 0.0938150i
\(412\) 0 0
\(413\) −0.339746 + 0.392305i −0.0167178 + 0.0193041i
\(414\) 0 0
\(415\) 7.56218 13.0981i 0.371213 0.642959i
\(416\) 0 0
\(417\) 2.96410 + 5.13397i 0.145153 + 0.251412i
\(418\) 0 0
\(419\) 35.4641 1.73253 0.866267 0.499581i \(-0.166513\pi\)
0.866267 + 0.499581i \(0.166513\pi\)
\(420\) 0 0
\(421\) 0.0717968 0.00349916 0.00174958 0.999998i \(-0.499443\pi\)
0.00174958 + 0.999998i \(0.499443\pi\)
\(422\) 0 0
\(423\) 1.00000 + 1.73205i 0.0486217 + 0.0842152i
\(424\) 0 0
\(425\) −1.63397 + 2.83013i −0.0792594 + 0.137281i
\(426\) 0 0
\(427\) 10.3923 + 2.00000i 0.502919 + 0.0967868i
\(428\) 0 0
\(429\) 0.830127 1.43782i 0.0400789 0.0694187i
\(430\) 0 0
\(431\) 8.66025 + 15.0000i 0.417150 + 0.722525i 0.995651 0.0931566i \(-0.0296957\pi\)
−0.578502 + 0.815681i \(0.696362\pi\)
\(432\) 0 0
\(433\) 15.1962 0.730280 0.365140 0.930953i \(-0.381021\pi\)
0.365140 + 0.930953i \(0.381021\pi\)
\(434\) 0 0
\(435\) −4.19615 −0.201190
\(436\) 0 0
\(437\) 10.5622 + 18.2942i 0.505257 + 0.875132i
\(438\) 0 0
\(439\) 0.267949 0.464102i 0.0127885 0.0221504i −0.859560 0.511034i \(-0.829263\pi\)
0.872349 + 0.488884i \(0.162596\pi\)
\(440\) 0 0
\(441\) −1.00000 6.92820i −0.0476190 0.329914i
\(442\) 0 0
\(443\) 4.73205 8.19615i 0.224827 0.389411i −0.731441 0.681905i \(-0.761152\pi\)
0.956267 + 0.292494i \(0.0944851\pi\)
\(444\) 0 0
\(445\) −7.56218 13.0981i −0.358482 0.620908i
\(446\) 0 0
\(447\) 5.85641 0.276999
\(448\) 0 0
\(449\) −35.8564 −1.69217 −0.846084 0.533049i \(-0.821046\pi\)
−0.846084 + 0.533049i \(0.821046\pi\)
\(450\) 0 0
\(451\) −0.267949 0.464102i −0.0126172 0.0218537i
\(452\) 0 0
\(453\) −4.46410 + 7.73205i −0.209742 + 0.363283i
\(454\) 0 0
\(455\) 5.89230 + 1.13397i 0.276236 + 0.0531615i
\(456\) 0 0
\(457\) 8.33013 14.4282i 0.389667 0.674923i −0.602738 0.797939i \(-0.705923\pi\)
0.992405 + 0.123016i \(0.0392568\pi\)
\(458\) 0 0
\(459\) −1.63397 2.83013i −0.0762674 0.132099i
\(460\) 0 0
\(461\) 16.9808 0.790873 0.395436 0.918493i \(-0.370593\pi\)
0.395436 + 0.918493i \(0.370593\pi\)
\(462\) 0 0
\(463\) −25.7321 −1.19587 −0.597935 0.801545i \(-0.704012\pi\)
−0.597935 + 0.801545i \(0.704012\pi\)
\(464\) 0 0
\(465\) −0.232051 0.401924i −0.0107611 0.0186388i
\(466\) 0 0
\(467\) −0.0717968 + 0.124356i −0.00332236 + 0.00575449i −0.867682 0.497120i \(-0.834391\pi\)
0.864359 + 0.502874i \(0.167724\pi\)
\(468\) 0 0
\(469\) −25.3923 + 29.3205i −1.17251 + 1.35390i
\(470\) 0 0
\(471\) −3.19615 + 5.53590i −0.147271 + 0.255081i
\(472\) 0 0
\(473\) −1.16987 2.02628i −0.0537908 0.0931684i
\(474\) 0 0
\(475\) −4.46410 −0.204827
\(476\) 0 0
\(477\) 12.3923 0.567405
\(478\) 0 0
\(479\) 4.39230 + 7.60770i 0.200690 + 0.347604i 0.948751 0.316025i \(-0.102348\pi\)
−0.748061 + 0.663630i \(0.769015\pi\)
\(480\) 0 0
\(481\) 3.62436 6.27757i 0.165256 0.286232i
\(482\) 0 0
\(483\) −4.09808 11.8301i −0.186469 0.538289i
\(484\) 0 0
\(485\) −7.46410 + 12.9282i −0.338927 + 0.587039i
\(486\) 0 0
\(487\) −0.205771 0.356406i −0.00932439 0.0161503i 0.861326 0.508053i \(-0.169635\pi\)
−0.870650 + 0.491903i \(0.836301\pi\)
\(488\) 0 0
\(489\) −21.8564 −0.988381
\(490\) 0 0
\(491\) 38.2487 1.72614 0.863070 0.505084i \(-0.168539\pi\)
0.863070 + 0.505084i \(0.168539\pi\)
\(492\) 0 0
\(493\) 6.85641 + 11.8756i 0.308797 + 0.534852i
\(494\) 0 0
\(495\) 0.366025 0.633975i 0.0164516 0.0284950i
\(496\) 0 0
\(497\) 5.36603 + 15.4904i 0.240699 + 0.694839i
\(498\) 0 0
\(499\) −6.76795 + 11.7224i −0.302975 + 0.524768i −0.976808 0.214115i \(-0.931313\pi\)
0.673833 + 0.738883i \(0.264647\pi\)
\(500\) 0 0
\(501\) −8.83013 15.2942i −0.394501 0.683296i
\(502\) 0 0
\(503\) −14.3923 −0.641721 −0.320861 0.947126i \(-0.603972\pi\)
−0.320861 + 0.947126i \(0.603972\pi\)
\(504\) 0 0
\(505\) −7.26795 −0.323419
\(506\) 0 0
\(507\) 3.92820 + 6.80385i 0.174458 + 0.302169i
\(508\) 0 0
\(509\) −2.26795 + 3.92820i −0.100525 + 0.174115i −0.911901 0.410410i \(-0.865386\pi\)
0.811376 + 0.584525i \(0.198719\pi\)
\(510\) 0 0
\(511\) −21.9282 + 25.3205i −0.970047 + 1.12011i
\(512\) 0 0
\(513\) 2.23205 3.86603i 0.0985475 0.170689i
\(514\) 0 0
\(515\) −4.59808 7.96410i −0.202615 0.350940i
\(516\) 0 0
\(517\) 1.46410 0.0643911
\(518\) 0 0
\(519\) 14.5359 0.638055
\(520\) 0 0
\(521\) 2.73205 + 4.73205i 0.119693 + 0.207315i 0.919646 0.392748i \(-0.128476\pi\)
−0.799953 + 0.600063i \(0.795142\pi\)
\(522\) 0 0
\(523\) −13.8660 + 24.0167i −0.606319 + 1.05018i 0.385523 + 0.922698i \(0.374021\pi\)
−0.991842 + 0.127477i \(0.959312\pi\)
\(524\) 0 0
\(525\) 2.59808 + 0.500000i 0.113389 + 0.0218218i
\(526\) 0 0
\(527\) −0.758330 + 1.31347i −0.0330334 + 0.0572155i
\(528\) 0 0
\(529\) 0.303848 + 0.526279i 0.0132108 + 0.0228817i
\(530\) 0 0
\(531\) 0.196152 0.00851229
\(532\) 0 0
\(533\) −1.66025 −0.0719136
\(534\) 0 0
\(535\) 1.09808 + 1.90192i 0.0474740 + 0.0822273i
\(536\) 0 0
\(537\) −5.00000 + 8.66025i −0.215766 + 0.373718i
\(538\) 0 0
\(539\) −4.75833 1.90192i −0.204956 0.0819217i
\(540\) 0 0
\(541\) −2.89230 + 5.00962i −0.124350 + 0.215380i −0.921479 0.388429i \(-0.873018\pi\)
0.797129 + 0.603809i \(0.206351\pi\)
\(542\) 0 0
\(543\) 12.1603 + 21.0622i 0.521846 + 0.903865i
\(544\) 0 0
\(545\) 11.0000 0.471188
\(546\) 0 0
\(547\) 26.2487 1.12231 0.561157 0.827709i \(-0.310356\pi\)
0.561157 + 0.827709i \(0.310356\pi\)
\(548\) 0 0
\(549\) −2.00000 3.46410i −0.0853579 0.147844i
\(550\) 0 0
\(551\) −9.36603 + 16.2224i −0.399006 + 0.691099i
\(552\) 0 0
\(553\) 19.2058 + 3.69615i 0.816712 + 0.157176i
\(554\) 0 0
\(555\) 1.59808 2.76795i 0.0678346 0.117493i
\(556\) 0 0
\(557\) −7.39230 12.8038i −0.313222 0.542516i 0.665836 0.746098i \(-0.268075\pi\)
−0.979058 + 0.203582i \(0.934742\pi\)
\(558\) 0 0
\(559\) −7.24871 −0.306588
\(560\) 0 0
\(561\) −2.39230 −0.101003
\(562\) 0 0
\(563\) −9.00000 15.5885i −0.379305 0.656975i 0.611656 0.791123i \(-0.290503\pi\)
−0.990961 + 0.134148i \(0.957170\pi\)
\(564\) 0 0
\(565\) −4.46410 + 7.73205i −0.187806 + 0.325290i
\(566\) 0 0
\(567\) −1.73205 + 2.00000i −0.0727393 + 0.0839921i
\(568\) 0 0
\(569\) −16.2224 + 28.0981i −0.680080 + 1.17793i 0.294876 + 0.955535i \(0.404722\pi\)
−0.974956 + 0.222397i \(0.928612\pi\)
\(570\) 0 0
\(571\) 9.30385 + 16.1147i 0.389354 + 0.674381i 0.992363 0.123354i \(-0.0393650\pi\)
−0.603009 + 0.797734i \(0.706032\pi\)
\(572\) 0 0
\(573\) 8.92820 0.372981
\(574\) 0 0
\(575\) 4.73205 0.197340
\(576\) 0 0
\(577\) −14.3301 24.8205i −0.596571 1.03329i −0.993323 0.115365i \(-0.963196\pi\)
0.396752 0.917926i \(-0.370137\pi\)
\(578\) 0 0
\(579\) −0.598076 + 1.03590i −0.0248552 + 0.0430505i
\(580\) 0 0
\(581\) 13.0981 + 37.8109i 0.543400 + 1.56866i
\(582\) 0 0
\(583\) 4.53590 7.85641i 0.187858 0.325379i
\(584\) 0 0
\(585\) −1.13397 1.96410i −0.0468841 0.0812056i
\(586\) 0 0
\(587\) −40.7321 −1.68119 −0.840596 0.541663i \(-0.817795\pi\)
−0.840596 + 0.541663i \(0.817795\pi\)
\(588\) 0 0
\(589\) −2.07180 −0.0853669
\(590\) 0 0
\(591\) 0.169873 + 0.294229i 0.00698764 + 0.0121029i
\(592\) 0 0
\(593\) −13.9545 + 24.1699i −0.573042 + 0.992538i 0.423209 + 0.906032i \(0.360903\pi\)
−0.996251 + 0.0865058i \(0.972430\pi\)
\(594\) 0 0
\(595\) −2.83013 8.16987i −0.116024 0.334932i
\(596\) 0 0
\(597\) 11.0000 19.0526i 0.450200 0.779769i
\(598\) 0 0
\(599\) −19.1244 33.1244i −0.781400 1.35342i −0.931126 0.364697i \(-0.881173\pi\)
0.149726 0.988727i \(-0.452161\pi\)
\(600\) 0 0
\(601\) −0.0717968 −0.00292865 −0.00146433 0.999999i \(-0.500466\pi\)
−0.00146433 + 0.999999i \(0.500466\pi\)
\(602\) 0 0
\(603\) 14.6603 0.597012
\(604\) 0 0
\(605\) 5.23205 + 9.06218i 0.212713 + 0.368430i
\(606\) 0 0
\(607\) 1.59808 2.76795i 0.0648639 0.112348i −0.831770 0.555121i \(-0.812672\pi\)
0.896634 + 0.442773i \(0.146005\pi\)
\(608\) 0 0
\(609\) 7.26795 8.39230i 0.294512 0.340073i
\(610\) 0 0
\(611\) 2.26795 3.92820i 0.0917514 0.158918i
\(612\) 0 0
\(613\) 13.4641 + 23.3205i 0.543810 + 0.941906i 0.998681 + 0.0513490i \(0.0163521\pi\)
−0.454871 + 0.890557i \(0.650315\pi\)
\(614\) 0 0
\(615\) −0.732051 −0.0295191
\(616\) 0 0
\(617\) −36.2487 −1.45932 −0.729659 0.683811i \(-0.760321\pi\)
−0.729659 + 0.683811i \(0.760321\pi\)
\(618\) 0 0
\(619\) −15.0359 26.0429i −0.604344 1.04675i −0.992155 0.125015i \(-0.960102\pi\)
0.387811 0.921739i \(-0.373231\pi\)
\(620\) 0 0
\(621\) −2.36603 + 4.09808i −0.0949453 + 0.164450i
\(622\) 0 0
\(623\) 39.2942 + 7.56218i 1.57429 + 0.302972i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 0 0
\(627\) −1.63397 2.83013i −0.0652547 0.113024i
\(628\) 0 0
\(629\) −10.4449 −0.416464
\(630\) 0 0
\(631\) −48.7846 −1.94208 −0.971042 0.238908i \(-0.923211\pi\)
−0.971042 + 0.238908i \(0.923211\pi\)
\(632\) 0 0
\(633\) 3.53590 + 6.12436i 0.140539 + 0.243421i
\(634\) 0 0
\(635\) 2.40192 4.16025i 0.0953174 0.165095i
\(636\) 0 0
\(637\) −12.4737 + 9.82051i −0.494227 + 0.389103i
\(638\) 0 0
\(639\) 3.09808 5.36603i 0.122558 0.212277i
\(640\) 0 0
\(641\) −1.90192 3.29423i −0.0751215 0.130114i 0.826018 0.563644i \(-0.190601\pi\)
−0.901139 + 0.433530i \(0.857268\pi\)
\(642\) 0 0
\(643\) −4.51666 −0.178120 −0.0890599 0.996026i \(-0.528386\pi\)
−0.0890599 + 0.996026i \(0.528386\pi\)
\(644\) 0 0
\(645\) −3.19615 −0.125848
\(646\) 0 0
\(647\) −13.9545 24.1699i −0.548607 0.950216i −0.998370 0.0570678i \(-0.981825\pi\)
0.449763 0.893148i \(-0.351508\pi\)
\(648\) 0 0
\(649\) 0.0717968 0.124356i 0.00281827 0.00488139i
\(650\) 0 0
\(651\) 1.20577 + 0.232051i 0.0472579 + 0.00909479i
\(652\) 0 0
\(653\) 22.2942 38.6147i 0.872441 1.51111i 0.0129762 0.999916i \(-0.495869\pi\)
0.859464 0.511196i \(-0.170797\pi\)
\(654\) 0 0
\(655\) 7.73205 + 13.3923i 0.302116 + 0.523281i
\(656\) 0 0
\(657\) 12.6603 0.493924
\(658\) 0 0
\(659\) −2.92820 −0.114067 −0.0570333 0.998372i \(-0.518164\pi\)
−0.0570333 + 0.998372i \(0.518164\pi\)
\(660\) 0 0
\(661\) −5.23205 9.06218i −0.203503 0.352478i 0.746152 0.665776i \(-0.231899\pi\)
−0.949655 + 0.313298i \(0.898566\pi\)
\(662\) 0 0
\(663\) −3.70577 + 6.41858i −0.143920 + 0.249277i
\(664\) 0 0
\(665\) 7.73205 8.92820i 0.299836 0.346221i
\(666\) 0 0
\(667\) 9.92820 17.1962i 0.384422 0.665838i
\(668\) 0 0
\(669\) −10.1962 17.6603i −0.394206 0.682785i
\(670\) 0 0
\(671\) −2.92820 −0.113042
\(672\) 0 0
\(673\) −27.3397 −1.05387 −0.526935 0.849906i \(-0.676659\pi\)
−0.526935 + 0.849906i \(0.676659\pi\)
\(674\) 0 0
\(675\) −0.500000 0.866025i −0.0192450 0.0333333i
\(676\) 0 0
\(677\) 16.5622 28.6865i 0.636536 1.10251i −0.349651 0.936880i \(-0.613700\pi\)
0.986187 0.165633i \(-0.0529668\pi\)
\(678\) 0 0
\(679\) −12.9282 37.3205i −0.496139 1.43223i
\(680\) 0 0
\(681\) −0.830127 + 1.43782i −0.0318105 + 0.0550975i
\(682\) 0 0
\(683\) −14.0263 24.2942i −0.536701 0.929593i −0.999079 0.0429101i \(-0.986337\pi\)
0.462378 0.886683i \(-0.346996\pi\)
\(684\) 0 0
\(685\) 2.19615 0.0839107
\(686\) 0 0
\(687\) −3.00000 −0.114457
\(688\) 0 0
\(689\) −14.0526 24.3397i −0.535360 0.927270i
\(690\) 0 0
\(691\) 4.42820 7.66987i 0.168457 0.291776i −0.769421 0.638742i \(-0.779455\pi\)
0.937877 + 0.346967i \(0.112788\pi\)
\(692\) 0 0
\(693\) 0.633975 + 1.83013i 0.0240827 + 0.0695208i
\(694\) 0 0
\(695\) 2.96410 5.13397i 0.112435 0.194743i
\(696\) 0 0
\(697\) 1.19615 + 2.07180i 0.0453075 + 0.0784749i
\(698\) 0 0
\(699\) 17.3205 0.655122
\(700\) 0 0
\(701\) −8.58846 −0.324382 −0.162191 0.986759i \(-0.551856\pi\)
−0.162191 + 0.986759i \(0.551856\pi\)
\(702\) 0 0
\(703\) −7.13397 12.3564i −0.269063 0.466031i
\(704\) 0 0
\(705\) 1.00000 1.73205i 0.0376622 0.0652328i
\(706\) 0 0
\(707\) 12.5885 14.5359i 0.473438 0.546679i
\(708\) 0 0
\(709\) 0.535898 0.928203i 0.0201261 0.0348594i −0.855787 0.517328i \(-0.826927\pi\)
0.875913 + 0.482469i \(0.160260\pi\)
\(710\) 0 0
\(711\) −3.69615 6.40192i −0.138617 0.240091i
\(712\) 0 0
\(713\) 2.19615 0.0822466
\(714\) 0 0
\(715\) −1.66025 −0.0620900
\(716\) 0 0
\(717\) 3.53590 + 6.12436i 0.132051 + 0.228718i
\(718\) 0 0
\(719\) −10.2679 + 17.7846i −0.382930 + 0.663254i −0.991480 0.130262i \(-0.958418\pi\)
0.608550 + 0.793516i \(0.291752\pi\)
\(720\) 0 0
\(721\) 23.8923 + 4.59808i 0.889796 + 0.171241i
\(722\) 0 0
\(723\) −6.73205 + 11.6603i −0.250368 + 0.433650i
\(724\) 0 0
\(725\) 2.09808 + 3.63397i 0.0779206 + 0.134962i
\(726\) 0 0
\(727\) 13.3397 0.494744 0.247372 0.968921i \(-0.420433\pi\)
0.247372 + 0.968921i \(0.420433\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 5.22243 + 9.04552i 0.193159 + 0.334561i
\(732\) 0 0
\(733\) 0.669873 1.16025i 0.0247423 0.0428550i −0.853389 0.521274i \(-0.825457\pi\)
0.878131 + 0.478419i \(0.158790\pi\)
\(734\) 0 0
\(735\) −5.50000 + 4.33013i −0.202871 + 0.159719i
\(736\) 0 0
\(737\) 5.36603 9.29423i 0.197660 0.342357i
\(738\) 0 0
\(739\) 13.8923 + 24.0622i 0.511037 + 0.885142i 0.999918 + 0.0127913i \(0.00407171\pi\)
−0.488881 + 0.872350i \(0.662595\pi\)
\(740\) 0 0
\(741\) −10.1244 −0.371927
\(742\) 0 0
\(743\) 15.9090 0.583643 0.291822 0.956473i \(-0.405739\pi\)
0.291822 + 0.956473i \(0.405739\pi\)
\(744\) 0 0
\(745\) −2.92820 5.07180i −0.107281 0.185816i
\(746\) 0 0
\(747\) 7.56218 13.0981i 0.276686 0.479234i
\(748\) 0 0
\(749\) −5.70577 1.09808i −0.208484 0.0401228i
\(750\) 0 0
\(751\) 9.03590 15.6506i 0.329725 0.571100i −0.652732 0.757588i \(-0.726377\pi\)
0.982457 + 0.186489i \(0.0597108\pi\)
\(752\) 0 0
\(753\) −12.2942 21.2942i −0.448027 0.776005i
\(754\) 0 0
\(755\) 8.92820 0.324931
\(756\) 0 0
\(757\) −27.8564 −1.01246 −0.506229 0.862399i \(-0.668961\pi\)
−0.506229 + 0.862399i \(0.668961\pi\)
\(758\) 0 0
\(759\) 1.73205 + 3.00000i 0.0628695 + 0.108893i
\(760\) 0 0
\(761\) −23.3660 + 40.4711i −0.847018 + 1.46708i 0.0368396 + 0.999321i \(0.488271\pi\)
−0.883857 + 0.467757i \(0.845062\pi\)
\(762\) 0 0
\(763\) −19.0526 + 22.0000i −0.689749 + 0.796453i
\(764\) 0 0
\(765\) −1.63397 + 2.83013i −0.0590765 + 0.102323i
\(766\) 0 0
\(767\) −0.222432 0.385263i −0.00803155 0.0139111i
\(768\) 0 0
\(769\) 52.3205 1.88673 0.943363 0.331763i \(-0.107643\pi\)
0.943363 + 0.331763i \(0.107643\pi\)
\(770\) 0 0
\(771\) −5.66025 −0.203849
\(772\) 0 0
\(773\) −21.7583 37.6865i −0.782593 1.35549i −0.930427 0.366478i \(-0.880563\pi\)
0.147834 0.989012i \(-0.452770\pi\)
\(774\) 0 0
\(775\) −0.232051 + 0.401924i −0.00833551 + 0.0144375i
\(776\) 0 0
\(777\) 2.76795 + 7.99038i 0.0992996 + 0.286653i
\(778\) 0 0
\(779\) −1.63397 + 2.83013i −0.0585432 + 0.101400i
\(780\) 0 0
\(781\) −2.26795 3.92820i −0.0811536 0.140562i
\(782\) 0 0
\(783\) −4.19615 −0.149958
\(784\) 0 0
\(785\) 6.39230 0.228151
\(786\) 0 0
\(787\) 6.73205 + 11.6603i 0.239972 + 0.415643i 0.960706 0.277568i \(-0.0895285\pi\)
−0.720734 + 0.693212i \(0.756195\pi\)
\(788\) 0 0
\(789\) 4.19615 7.26795i 0.149387 0.258746i
\(790\) 0 0
\(791\) −7.73205 22.3205i −0.274920 0.793626i
\(792\) 0 0
\(793\) −4.53590 + 7.85641i −0.161074 + 0.278989i
\(794\) 0 0
\(795\) −6.19615 10.7321i −0.219755 0.380627i