Properties

Label 336.3.bh.e.241.1
Level $336$
Weight $3$
Character 336.241
Analytic conductor $9.155$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 336.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.15533688251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 336.241
Dual form 336.3.bh.e.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{3} +(-1.24264 + 0.717439i) q^{5} +(-1.74264 + 6.77962i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{3} +(-1.24264 + 0.717439i) q^{5} +(-1.74264 + 6.77962i) q^{7} +(1.50000 + 2.59808i) q^{9} +(3.00000 - 5.19615i) q^{11} -21.3280i q^{13} +2.48528 q^{15} +(-7.75736 - 4.47871i) q^{17} +(6.25736 - 3.61269i) q^{19} +(8.48528 - 8.66025i) q^{21} +(-18.7279 - 32.4377i) q^{23} +(-11.4706 + 19.8676i) q^{25} -5.19615i q^{27} -33.9411 q^{29} +(-38.2279 - 22.0709i) q^{31} +(-9.00000 + 5.19615i) q^{33} +(-2.69848 - 9.67487i) q^{35} +(13.9853 + 24.2232i) q^{37} +(-18.4706 + 31.9920i) q^{39} -54.8313i q^{41} +1.48528 q^{43} +(-3.72792 - 2.15232i) q^{45} +(37.2426 - 21.5020i) q^{47} +(-42.9264 - 23.6289i) q^{49} +(7.75736 + 13.4361i) q^{51} +(42.7279 - 74.0069i) q^{53} +8.60927i q^{55} -12.5147 q^{57} +(35.6985 + 20.6105i) q^{59} +(-1.02944 + 0.594346i) q^{61} +(-20.2279 + 5.64191i) q^{63} +(15.3015 + 26.5030i) q^{65} +(2.19848 - 3.80789i) q^{67} +64.8754i q^{69} -137.397 q^{71} +(68.3528 + 39.4635i) q^{73} +(34.4117 - 19.8676i) q^{75} +(30.0000 + 29.3939i) q^{77} +(49.1690 + 85.1633i) q^{79} +(-4.50000 + 7.79423i) q^{81} -110.401i q^{83} +12.8528 q^{85} +(50.9117 + 29.3939i) q^{87} +(-18.0000 + 10.3923i) q^{89} +(144.595 + 37.1670i) q^{91} +(38.2279 + 66.2127i) q^{93} +(-5.18377 + 8.97855i) q^{95} -10.9867i q^{97} +18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 6 q^{3} + 12 q^{5} + 10 q^{7} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 6 q^{3} + 12 q^{5} + 10 q^{7} + 6 q^{9} + 12 q^{11} - 24 q^{15} - 48 q^{17} + 42 q^{19} - 24 q^{23} + 22 q^{25} - 102 q^{31} - 36 q^{33} + 108 q^{35} + 22 q^{37} - 6 q^{39} - 28 q^{43} + 36 q^{45} + 132 q^{47} - 2 q^{49} + 48 q^{51} + 120 q^{53} - 84 q^{57} + 24 q^{59} - 72 q^{61} - 30 q^{63} + 180 q^{65} - 110 q^{67} - 312 q^{71} - 66 q^{73} - 66 q^{75} + 120 q^{77} + 10 q^{79} - 18 q^{81} - 288 q^{85} - 72 q^{89} + 222 q^{91} + 102 q^{93} + 132 q^{95} + 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.50000 0.866025i −0.500000 0.288675i
\(4\) 0 0
\(5\) −1.24264 + 0.717439i −0.248528 + 0.143488i −0.619090 0.785320i \(-0.712498\pi\)
0.370562 + 0.928808i \(0.379165\pi\)
\(6\) 0 0
\(7\) −1.74264 + 6.77962i −0.248949 + 0.968517i
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 3.00000 5.19615i 0.272727 0.472377i −0.696832 0.717234i \(-0.745408\pi\)
0.969559 + 0.244857i \(0.0787410\pi\)
\(12\) 0 0
\(13\) 21.3280i 1.64061i −0.571924 0.820306i \(-0.693803\pi\)
0.571924 0.820306i \(-0.306197\pi\)
\(14\) 0 0
\(15\) 2.48528 0.165685
\(16\) 0 0
\(17\) −7.75736 4.47871i −0.456315 0.263454i 0.254178 0.967157i \(-0.418195\pi\)
−0.710494 + 0.703704i \(0.751528\pi\)
\(18\) 0 0
\(19\) 6.25736 3.61269i 0.329335 0.190141i −0.326211 0.945297i \(-0.605772\pi\)
0.655546 + 0.755156i \(0.272439\pi\)
\(20\) 0 0
\(21\) 8.48528 8.66025i 0.404061 0.412393i
\(22\) 0 0
\(23\) −18.7279 32.4377i −0.814257 1.41034i −0.909860 0.414916i \(-0.863811\pi\)
0.0956024 0.995420i \(-0.469522\pi\)
\(24\) 0 0
\(25\) −11.4706 + 19.8676i −0.458823 + 0.794704i
\(26\) 0 0
\(27\) 5.19615i 0.192450i
\(28\) 0 0
\(29\) −33.9411 −1.17038 −0.585192 0.810895i \(-0.698981\pi\)
−0.585192 + 0.810895i \(0.698981\pi\)
\(30\) 0 0
\(31\) −38.2279 22.0709i −1.23316 0.711965i −0.265472 0.964119i \(-0.585528\pi\)
−0.967687 + 0.252154i \(0.918861\pi\)
\(32\) 0 0
\(33\) −9.00000 + 5.19615i −0.272727 + 0.157459i
\(34\) 0 0
\(35\) −2.69848 9.67487i −0.0770996 0.276425i
\(36\) 0 0
\(37\) 13.9853 + 24.2232i 0.377981 + 0.654682i 0.990768 0.135566i \(-0.0432853\pi\)
−0.612788 + 0.790248i \(0.709952\pi\)
\(38\) 0 0
\(39\) −18.4706 + 31.9920i −0.473604 + 0.820306i
\(40\) 0 0
\(41\) 54.8313i 1.33735i −0.743556 0.668674i \(-0.766862\pi\)
0.743556 0.668674i \(-0.233138\pi\)
\(42\) 0 0
\(43\) 1.48528 0.0345414 0.0172707 0.999851i \(-0.494502\pi\)
0.0172707 + 0.999851i \(0.494502\pi\)
\(44\) 0 0
\(45\) −3.72792 2.15232i −0.0828427 0.0478293i
\(46\) 0 0
\(47\) 37.2426 21.5020i 0.792397 0.457490i −0.0484090 0.998828i \(-0.515415\pi\)
0.840806 + 0.541337i \(0.182082\pi\)
\(48\) 0 0
\(49\) −42.9264 23.6289i −0.876049 0.482222i
\(50\) 0 0
\(51\) 7.75736 + 13.4361i 0.152105 + 0.263454i
\(52\) 0 0
\(53\) 42.7279 74.0069i 0.806187 1.39636i −0.109299 0.994009i \(-0.534861\pi\)
0.915487 0.402348i \(-0.131806\pi\)
\(54\) 0 0
\(55\) 8.60927i 0.156532i
\(56\) 0 0
\(57\) −12.5147 −0.219556
\(58\) 0 0
\(59\) 35.6985 + 20.6105i 0.605059 + 0.349331i 0.771029 0.636800i \(-0.219742\pi\)
−0.165970 + 0.986131i \(0.553076\pi\)
\(60\) 0 0
\(61\) −1.02944 + 0.594346i −0.0168760 + 0.00974337i −0.508414 0.861113i \(-0.669768\pi\)
0.491538 + 0.870856i \(0.336435\pi\)
\(62\) 0 0
\(63\) −20.2279 + 5.64191i −0.321078 + 0.0895542i
\(64\) 0 0
\(65\) 15.3015 + 26.5030i 0.235408 + 0.407738i
\(66\) 0 0
\(67\) 2.19848 3.80789i 0.0328132 0.0568341i −0.849152 0.528148i \(-0.822887\pi\)
0.881966 + 0.471314i \(0.156220\pi\)
\(68\) 0 0
\(69\) 64.8754i 0.940224i
\(70\) 0 0
\(71\) −137.397 −1.93517 −0.967584 0.252548i \(-0.918731\pi\)
−0.967584 + 0.252548i \(0.918731\pi\)
\(72\) 0 0
\(73\) 68.3528 + 39.4635i 0.936340 + 0.540596i 0.888811 0.458274i \(-0.151532\pi\)
0.0475288 + 0.998870i \(0.484865\pi\)
\(74\) 0 0
\(75\) 34.4117 19.8676i 0.458823 0.264901i
\(76\) 0 0
\(77\) 30.0000 + 29.3939i 0.389610 + 0.381739i
\(78\) 0 0
\(79\) 49.1690 + 85.1633i 0.622393 + 1.07802i 0.989039 + 0.147656i \(0.0471728\pi\)
−0.366646 + 0.930361i \(0.619494\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 110.401i 1.33013i −0.746784 0.665067i \(-0.768403\pi\)
0.746784 0.665067i \(-0.231597\pi\)
\(84\) 0 0
\(85\) 12.8528 0.151210
\(86\) 0 0
\(87\) 50.9117 + 29.3939i 0.585192 + 0.337861i
\(88\) 0 0
\(89\) −18.0000 + 10.3923i −0.202247 + 0.116767i −0.597703 0.801717i \(-0.703920\pi\)
0.395456 + 0.918485i \(0.370587\pi\)
\(90\) 0 0
\(91\) 144.595 + 37.1670i 1.58896 + 0.408428i
\(92\) 0 0
\(93\) 38.2279 + 66.2127i 0.411053 + 0.711965i
\(94\) 0 0
\(95\) −5.18377 + 8.97855i −0.0545660 + 0.0945110i
\(96\) 0 0
\(97\) 10.9867i 0.113264i −0.998395 0.0566322i \(-0.981964\pi\)
0.998395 0.0566322i \(-0.0180362\pi\)
\(98\) 0 0
\(99\) 18.0000 0.181818
\(100\) 0 0
\(101\) −92.8234 53.5916i −0.919043 0.530610i −0.0357136 0.999362i \(-0.511370\pi\)
−0.883330 + 0.468752i \(0.844704\pi\)
\(102\) 0 0
\(103\) −91.1102 + 52.6025i −0.884565 + 0.510704i −0.872161 0.489219i \(-0.837282\pi\)
−0.0124040 + 0.999923i \(0.503948\pi\)
\(104\) 0 0
\(105\) −4.33095 + 16.8493i −0.0412472 + 0.160469i
\(106\) 0 0
\(107\) 59.2721 + 102.662i 0.553945 + 0.959460i 0.997985 + 0.0634534i \(0.0202114\pi\)
−0.444040 + 0.896007i \(0.646455\pi\)
\(108\) 0 0
\(109\) −55.5294 + 96.1798i −0.509444 + 0.882384i 0.490496 + 0.871444i \(0.336816\pi\)
−0.999940 + 0.0109400i \(0.996518\pi\)
\(110\) 0 0
\(111\) 48.4464i 0.436454i
\(112\) 0 0
\(113\) 101.397 0.897318 0.448659 0.893703i \(-0.351902\pi\)
0.448659 + 0.893703i \(0.351902\pi\)
\(114\) 0 0
\(115\) 46.5442 + 26.8723i 0.404732 + 0.233672i
\(116\) 0 0
\(117\) 55.4117 31.9920i 0.473604 0.273435i
\(118\) 0 0
\(119\) 43.8823 44.7871i 0.368758 0.376362i
\(120\) 0 0
\(121\) 42.5000 + 73.6122i 0.351240 + 0.608365i
\(122\) 0 0
\(123\) −47.4853 + 82.2469i −0.386059 + 0.668674i
\(124\) 0 0
\(125\) 68.7897i 0.550317i
\(126\) 0 0
\(127\) −82.5736 −0.650186 −0.325093 0.945682i \(-0.605396\pi\)
−0.325093 + 0.945682i \(0.605396\pi\)
\(128\) 0 0
\(129\) −2.22792 1.28629i −0.0172707 0.00997125i
\(130\) 0 0
\(131\) 52.4558 30.2854i 0.400426 0.231186i −0.286242 0.958157i \(-0.592406\pi\)
0.686668 + 0.726971i \(0.259073\pi\)
\(132\) 0 0
\(133\) 13.5883 + 48.7181i 0.102168 + 0.366302i
\(134\) 0 0
\(135\) 3.72792 + 6.45695i 0.0276142 + 0.0478293i
\(136\) 0 0
\(137\) −33.5147 + 58.0492i −0.244633 + 0.423717i −0.962028 0.272949i \(-0.912001\pi\)
0.717395 + 0.696666i \(0.245334\pi\)
\(138\) 0 0
\(139\) 91.5525i 0.658651i −0.944216 0.329326i \(-0.893179\pi\)
0.944216 0.329326i \(-0.106821\pi\)
\(140\) 0 0
\(141\) −74.4853 −0.528264
\(142\) 0 0
\(143\) −110.823 63.9839i −0.774989 0.447440i
\(144\) 0 0
\(145\) 42.1766 24.3507i 0.290873 0.167936i
\(146\) 0 0
\(147\) 43.9264 + 72.6187i 0.298819 + 0.494005i
\(148\) 0 0
\(149\) −40.5442 70.2245i −0.272108 0.471306i 0.697293 0.716786i \(-0.254388\pi\)
−0.969402 + 0.245480i \(0.921054\pi\)
\(150\) 0 0
\(151\) −25.6030 + 44.3457i −0.169556 + 0.293680i −0.938264 0.345920i \(-0.887567\pi\)
0.768708 + 0.639600i \(0.220900\pi\)
\(152\) 0 0
\(153\) 26.8723i 0.175636i
\(154\) 0 0
\(155\) 63.3381 0.408633
\(156\) 0 0
\(157\) 162.000 + 93.5307i 1.03185 + 0.595737i 0.917513 0.397705i \(-0.130193\pi\)
0.114334 + 0.993442i \(0.463527\pi\)
\(158\) 0 0
\(159\) −128.184 + 74.0069i −0.806187 + 0.465452i
\(160\) 0 0
\(161\) 252.551 70.4409i 1.56864 0.437521i
\(162\) 0 0
\(163\) 41.9706 + 72.6951i 0.257488 + 0.445982i 0.965568 0.260149i \(-0.0837718\pi\)
−0.708080 + 0.706132i \(0.750439\pi\)
\(164\) 0 0
\(165\) 7.45584 12.9139i 0.0451869 0.0782661i
\(166\) 0 0
\(167\) 127.620i 0.764190i 0.924123 + 0.382095i \(0.124797\pi\)
−0.924123 + 0.382095i \(0.875203\pi\)
\(168\) 0 0
\(169\) −285.882 −1.69161
\(170\) 0 0
\(171\) 18.7721 + 10.8381i 0.109778 + 0.0633805i
\(172\) 0 0
\(173\) −123.816 + 71.4853i −0.715701 + 0.413210i −0.813168 0.582029i \(-0.802259\pi\)
0.0974675 + 0.995239i \(0.468926\pi\)
\(174\) 0 0
\(175\) −114.706 112.388i −0.655461 0.642218i
\(176\) 0 0
\(177\) −35.6985 61.8316i −0.201686 0.349331i
\(178\) 0 0
\(179\) 84.6396 146.600i 0.472847 0.818995i −0.526670 0.850070i \(-0.676560\pi\)
0.999517 + 0.0310748i \(0.00989300\pi\)
\(180\) 0 0
\(181\) 209.969i 1.16005i −0.814600 0.580024i \(-0.803043\pi\)
0.814600 0.580024i \(-0.196957\pi\)
\(182\) 0 0
\(183\) 2.05887 0.0112507
\(184\) 0 0
\(185\) −34.7574 20.0672i −0.187878 0.108471i
\(186\) 0 0
\(187\) −46.5442 + 26.8723i −0.248899 + 0.143702i
\(188\) 0 0
\(189\) 35.2279 + 9.05503i 0.186391 + 0.0479102i
\(190\) 0 0
\(191\) 33.3015 + 57.6799i 0.174353 + 0.301989i 0.939937 0.341347i \(-0.110883\pi\)
−0.765584 + 0.643336i \(0.777550\pi\)
\(192\) 0 0
\(193\) 4.89697 8.48180i 0.0253729 0.0439472i −0.853060 0.521813i \(-0.825256\pi\)
0.878433 + 0.477865i \(0.158589\pi\)
\(194\) 0 0
\(195\) 53.0060i 0.271826i
\(196\) 0 0
\(197\) −267.161 −1.35615 −0.678075 0.734993i \(-0.737185\pi\)
−0.678075 + 0.734993i \(0.737185\pi\)
\(198\) 0 0
\(199\) 113.397 + 65.4698i 0.569834 + 0.328994i 0.757083 0.653319i \(-0.226624\pi\)
−0.187249 + 0.982312i \(0.559957\pi\)
\(200\) 0 0
\(201\) −6.59545 + 3.80789i −0.0328132 + 0.0189447i
\(202\) 0 0
\(203\) 59.1472 230.108i 0.291365 1.13354i
\(204\) 0 0
\(205\) 39.3381 + 68.1356i 0.191893 + 0.332369i
\(206\) 0 0
\(207\) 56.1838 97.3131i 0.271419 0.470112i
\(208\) 0 0
\(209\) 43.3523i 0.207427i
\(210\) 0 0
\(211\) 23.0883 0.109423 0.0547116 0.998502i \(-0.482576\pi\)
0.0547116 + 0.998502i \(0.482576\pi\)
\(212\) 0 0
\(213\) 206.095 + 118.989i 0.967584 + 0.558635i
\(214\) 0 0
\(215\) −1.84567 + 1.06560i −0.00858452 + 0.00495627i
\(216\) 0 0
\(217\) 216.250 220.709i 0.996543 1.01709i
\(218\) 0 0
\(219\) −68.3528 118.391i −0.312113 0.540596i
\(220\) 0 0
\(221\) −95.5219 + 165.449i −0.432226 + 0.748637i
\(222\) 0 0
\(223\) 228.631i 1.02525i −0.858613 0.512625i \(-0.828673\pi\)
0.858613 0.512625i \(-0.171327\pi\)
\(224\) 0 0
\(225\) −68.8234 −0.305882
\(226\) 0 0
\(227\) −56.8234 32.8070i −0.250323 0.144524i 0.369589 0.929195i \(-0.379498\pi\)
−0.619912 + 0.784671i \(0.712832\pi\)
\(228\) 0 0
\(229\) 80.9558 46.7399i 0.353519 0.204104i −0.312715 0.949847i \(-0.601239\pi\)
0.666234 + 0.745743i \(0.267905\pi\)
\(230\) 0 0
\(231\) −19.5442 70.0716i −0.0846067 0.303340i
\(232\) 0 0
\(233\) 118.757 + 205.694i 0.509688 + 0.882806i 0.999937 + 0.0112234i \(0.00357259\pi\)
−0.490249 + 0.871583i \(0.663094\pi\)
\(234\) 0 0
\(235\) −30.8528 + 53.4386i −0.131289 + 0.227398i
\(236\) 0 0
\(237\) 170.327i 0.718678i
\(238\) 0 0
\(239\) −366.853 −1.53495 −0.767475 0.641079i \(-0.778487\pi\)
−0.767475 + 0.641079i \(0.778487\pi\)
\(240\) 0 0
\(241\) −364.617 210.512i −1.51293 0.873493i −0.999885 0.0151343i \(-0.995182\pi\)
−0.513049 0.858359i \(-0.671484\pi\)
\(242\) 0 0
\(243\) 13.5000 7.79423i 0.0555556 0.0320750i
\(244\) 0 0
\(245\) 70.2944 1.43488i 0.286916 0.00585664i
\(246\) 0 0
\(247\) −77.0513 133.457i −0.311949 0.540311i
\(248\) 0 0
\(249\) −95.6102 + 165.602i −0.383977 + 0.665067i
\(250\) 0 0
\(251\) 146.621i 0.584148i 0.956396 + 0.292074i \(0.0943454\pi\)
−0.956396 + 0.292074i \(0.905655\pi\)
\(252\) 0 0
\(253\) −224.735 −0.888281
\(254\) 0 0
\(255\) −19.2792 11.1309i −0.0756048 0.0436504i
\(256\) 0 0
\(257\) 21.7279 12.5446i 0.0845444 0.0488118i −0.457132 0.889399i \(-0.651123\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(258\) 0 0
\(259\) −188.595 + 52.6025i −0.728168 + 0.203098i
\(260\) 0 0
\(261\) −50.9117 88.1816i −0.195064 0.337861i
\(262\) 0 0
\(263\) −45.3381 + 78.5279i −0.172388 + 0.298585i −0.939254 0.343222i \(-0.888482\pi\)
0.766866 + 0.641807i \(0.221815\pi\)
\(264\) 0 0
\(265\) 122.619i 0.462712i
\(266\) 0 0
\(267\) 36.0000 0.134831
\(268\) 0 0
\(269\) −59.2355 34.1996i −0.220206 0.127136i 0.385839 0.922566i \(-0.373912\pi\)
−0.606046 + 0.795430i \(0.707245\pi\)
\(270\) 0 0
\(271\) 106.971 61.7595i 0.394725 0.227895i −0.289480 0.957184i \(-0.593482\pi\)
0.684206 + 0.729289i \(0.260149\pi\)
\(272\) 0 0
\(273\) −184.706 180.974i −0.676577 0.662908i
\(274\) 0 0
\(275\) 68.8234 + 119.206i 0.250267 + 0.433475i
\(276\) 0 0
\(277\) 136.441 236.323i 0.492567 0.853151i −0.507396 0.861713i \(-0.669392\pi\)
0.999963 + 0.00856145i \(0.00272523\pi\)
\(278\) 0 0
\(279\) 132.425i 0.474643i
\(280\) 0 0
\(281\) 133.103 0.473675 0.236837 0.971549i \(-0.423889\pi\)
0.236837 + 0.971549i \(0.423889\pi\)
\(282\) 0 0
\(283\) 111.507 + 64.3787i 0.394018 + 0.227486i 0.683900 0.729576i \(-0.260283\pi\)
−0.289882 + 0.957063i \(0.593616\pi\)
\(284\) 0 0
\(285\) 15.5513 8.97855i 0.0545660 0.0315037i
\(286\) 0 0
\(287\) 371.735 + 95.5512i 1.29524 + 0.332931i
\(288\) 0 0
\(289\) −104.382 180.795i −0.361184 0.625589i
\(290\) 0 0
\(291\) −9.51472 + 16.4800i −0.0326966 + 0.0566322i
\(292\) 0 0
\(293\) 308.984i 1.05455i −0.849694 0.527276i \(-0.823213\pi\)
0.849694 0.527276i \(-0.176787\pi\)
\(294\) 0 0
\(295\) −59.1472 −0.200499
\(296\) 0 0
\(297\) −27.0000 15.5885i −0.0909091 0.0524864i
\(298\) 0 0
\(299\) −691.831 + 399.429i −2.31381 + 1.33588i
\(300\) 0 0
\(301\) −2.58831 + 10.0696i −0.00859904 + 0.0334539i
\(302\) 0 0
\(303\) 92.8234 + 160.775i 0.306348 + 0.530610i
\(304\) 0 0
\(305\) 0.852814 1.47712i 0.00279611 0.00484301i
\(306\) 0 0
\(307\) 606.090i 1.97423i −0.160003 0.987117i \(-0.551150\pi\)
0.160003 0.987117i \(-0.448850\pi\)
\(308\) 0 0
\(309\) 182.220 0.589710
\(310\) 0 0
\(311\) 176.044 + 101.639i 0.566057 + 0.326813i 0.755573 0.655064i \(-0.227359\pi\)
−0.189516 + 0.981878i \(0.560692\pi\)
\(312\) 0 0
\(313\) −351.294 + 202.820i −1.12234 + 0.647986i −0.941999 0.335617i \(-0.891055\pi\)
−0.180346 + 0.983603i \(0.557722\pi\)
\(314\) 0 0
\(315\) 21.0883 21.5232i 0.0669470 0.0683275i
\(316\) 0 0
\(317\) 13.0294 + 22.5676i 0.0411023 + 0.0711913i 0.885845 0.463982i \(-0.153580\pi\)
−0.844742 + 0.535173i \(0.820246\pi\)
\(318\) 0 0
\(319\) −101.823 + 176.363i −0.319196 + 0.552863i
\(320\) 0 0
\(321\) 205.325i 0.639640i
\(322\) 0 0
\(323\) −64.7208 −0.200374
\(324\) 0 0
\(325\) 423.735 + 244.644i 1.30380 + 0.752750i
\(326\) 0 0
\(327\) 166.588 96.1798i 0.509444 0.294128i
\(328\) 0 0
\(329\) 80.8751 + 289.961i 0.245821 + 0.881341i
\(330\) 0 0
\(331\) −54.3162 94.0785i −0.164097 0.284225i 0.772237 0.635335i \(-0.219138\pi\)
−0.936334 + 0.351110i \(0.885804\pi\)
\(332\) 0 0
\(333\) −41.9558 + 72.6697i −0.125994 + 0.218227i
\(334\) 0 0
\(335\) 6.30911i 0.0188332i
\(336\) 0 0
\(337\) 441.735 1.31079 0.655393 0.755288i \(-0.272503\pi\)
0.655393 + 0.755288i \(0.272503\pi\)
\(338\) 0 0
\(339\) −152.095 87.8124i −0.448659 0.259033i
\(340\) 0 0
\(341\) −229.368 + 132.425i −0.672632 + 0.388344i
\(342\) 0 0
\(343\) 235.000 249.848i 0.685131 0.728420i
\(344\) 0 0
\(345\) −46.5442 80.6168i −0.134911 0.233672i
\(346\) 0 0
\(347\) 17.0955 29.6102i 0.0492664 0.0853320i −0.840341 0.542059i \(-0.817645\pi\)
0.889607 + 0.456727i \(0.150978\pi\)
\(348\) 0 0
\(349\) 221.787i 0.635493i 0.948176 + 0.317746i \(0.102926\pi\)
−0.948176 + 0.317746i \(0.897074\pi\)
\(350\) 0 0
\(351\) −110.823 −0.315736
\(352\) 0 0
\(353\) 387.448 + 223.693i 1.09759 + 0.633692i 0.935586 0.353099i \(-0.114872\pi\)
0.162000 + 0.986791i \(0.448206\pi\)
\(354\) 0 0
\(355\) 170.735 98.5739i 0.480944 0.277673i
\(356\) 0 0
\(357\) −104.610 + 29.1776i −0.293026 + 0.0817299i
\(358\) 0 0
\(359\) 145.882 + 252.675i 0.406357 + 0.703831i 0.994478 0.104941i \(-0.0334655\pi\)
−0.588121 + 0.808773i \(0.700132\pi\)
\(360\) 0 0
\(361\) −154.397 + 267.423i −0.427692 + 0.740785i
\(362\) 0 0
\(363\) 147.224i 0.405577i
\(364\) 0 0
\(365\) −113.251 −0.310276
\(366\) 0 0
\(367\) 363.169 + 209.676i 0.989561 + 0.571324i 0.905143 0.425107i \(-0.139763\pi\)
0.0844183 + 0.996430i \(0.473097\pi\)
\(368\) 0 0
\(369\) 142.456 82.2469i 0.386059 0.222891i
\(370\) 0 0
\(371\) 427.279 + 418.646i 1.15170 + 1.12843i
\(372\) 0 0
\(373\) −15.6909 27.1775i −0.0420668 0.0728618i 0.844225 0.535988i \(-0.180061\pi\)
−0.886292 + 0.463127i \(0.846728\pi\)
\(374\) 0 0
\(375\) −59.5736 + 103.184i −0.158863 + 0.275159i
\(376\) 0 0
\(377\) 723.895i 1.92015i
\(378\) 0 0
\(379\) −206.779 −0.545590 −0.272795 0.962072i \(-0.587948\pi\)
−0.272795 + 0.962072i \(0.587948\pi\)
\(380\) 0 0
\(381\) 123.860 + 71.5108i 0.325093 + 0.187692i
\(382\) 0 0
\(383\) 431.772 249.283i 1.12734 0.650871i 0.184076 0.982912i \(-0.441071\pi\)
0.943265 + 0.332041i \(0.107737\pi\)
\(384\) 0 0
\(385\) −58.3675 15.0029i −0.151604 0.0389685i
\(386\) 0 0
\(387\) 2.22792 + 3.85887i 0.00575690 + 0.00997125i
\(388\) 0 0
\(389\) 324.213 561.554i 0.833453 1.44358i −0.0618308 0.998087i \(-0.519694\pi\)
0.895284 0.445496i \(-0.146973\pi\)
\(390\) 0 0
\(391\) 335.508i 0.858077i
\(392\) 0 0
\(393\) −104.912 −0.266951
\(394\) 0 0
\(395\) −122.199 70.5516i −0.309364 0.178612i
\(396\) 0 0
\(397\) 65.6026 37.8757i 0.165246 0.0954047i −0.415096 0.909777i \(-0.636252\pi\)
0.580342 + 0.814373i \(0.302919\pi\)
\(398\) 0 0
\(399\) 21.8087 84.8450i 0.0546583 0.212644i
\(400\) 0 0
\(401\) 282.125 + 488.655i 0.703553 + 1.21859i 0.967211 + 0.253974i \(0.0817377\pi\)
−0.263658 + 0.964616i \(0.584929\pi\)
\(402\) 0 0
\(403\) −470.727 + 815.324i −1.16806 + 2.02314i
\(404\) 0 0
\(405\) 12.9139i 0.0318862i
\(406\) 0 0
\(407\) 167.823 0.412342
\(408\) 0 0
\(409\) −309.559 178.724i −0.756868 0.436978i 0.0713023 0.997455i \(-0.477284\pi\)
−0.828170 + 0.560477i \(0.810618\pi\)
\(410\) 0 0
\(411\) 100.544 58.0492i 0.244633 0.141239i
\(412\) 0 0
\(413\) −201.941 + 206.105i −0.488962 + 0.499044i
\(414\) 0 0
\(415\) 79.2061 + 137.189i 0.190858 + 0.330576i
\(416\) 0 0
\(417\) −79.2868 + 137.329i −0.190136 + 0.329326i
\(418\) 0 0
\(419\) 502.175i 1.19851i 0.800559 + 0.599254i \(0.204536\pi\)
−0.800559 + 0.599254i \(0.795464\pi\)
\(420\) 0 0
\(421\) 33.7939 0.0802706 0.0401353 0.999194i \(-0.487221\pi\)
0.0401353 + 0.999194i \(0.487221\pi\)
\(422\) 0 0
\(423\) 111.728 + 64.5061i 0.264132 + 0.152497i
\(424\) 0 0
\(425\) 177.963 102.747i 0.418735 0.241757i
\(426\) 0 0
\(427\) −2.23550 8.01492i −0.00523536 0.0187703i
\(428\) 0 0
\(429\) 110.823 + 191.952i 0.258330 + 0.447440i
\(430\) 0 0
\(431\) 251.860 436.234i 0.584362 1.01214i −0.410593 0.911819i \(-0.634678\pi\)
0.994955 0.100326i \(-0.0319884\pi\)
\(432\) 0 0
\(433\) 837.548i 1.93429i −0.254224 0.967145i \(-0.581820\pi\)
0.254224 0.967145i \(-0.418180\pi\)
\(434\) 0 0
\(435\) −84.3532 −0.193916
\(436\) 0 0
\(437\) −234.375 135.316i −0.536326 0.309648i
\(438\) 0 0
\(439\) 164.558 95.0079i 0.374848 0.216419i −0.300726 0.953711i \(-0.597229\pi\)
0.675575 + 0.737292i \(0.263896\pi\)
\(440\) 0 0
\(441\) −3.00000 146.969i −0.00680272 0.333264i
\(442\) 0 0
\(443\) −84.7279 146.753i −0.191259 0.331271i 0.754408 0.656405i \(-0.227924\pi\)
−0.945668 + 0.325134i \(0.894591\pi\)
\(444\) 0 0
\(445\) 14.9117 25.8278i 0.0335094 0.0580400i
\(446\) 0 0
\(447\) 140.449i 0.314204i
\(448\) 0 0
\(449\) 18.1035 0.0403195 0.0201598 0.999797i \(-0.493583\pi\)
0.0201598 + 0.999797i \(0.493583\pi\)
\(450\) 0 0
\(451\) −284.912 164.494i −0.631733 0.364731i
\(452\) 0 0
\(453\) 76.8091 44.3457i 0.169556 0.0978935i
\(454\) 0 0
\(455\) −206.345 + 57.5532i −0.453506 + 0.126491i
\(456\) 0 0
\(457\) 164.412 + 284.769i 0.359763 + 0.623128i 0.987921 0.154958i \(-0.0495242\pi\)
−0.628158 + 0.778086i \(0.716191\pi\)
\(458\) 0 0
\(459\) −23.2721 + 40.3084i −0.0507017 + 0.0878179i
\(460\) 0 0
\(461\) 794.331i 1.72306i 0.507706 + 0.861530i \(0.330494\pi\)
−0.507706 + 0.861530i \(0.669506\pi\)
\(462\) 0 0
\(463\) 403.396 0.871266 0.435633 0.900124i \(-0.356525\pi\)
0.435633 + 0.900124i \(0.356525\pi\)
\(464\) 0 0
\(465\) −95.0071 54.8524i −0.204316 0.117962i
\(466\) 0 0
\(467\) 2.44870 1.41376i 0.00524347 0.00302732i −0.497376 0.867535i \(-0.665703\pi\)
0.502619 + 0.864508i \(0.332370\pi\)
\(468\) 0 0
\(469\) 21.9848 + 21.5407i 0.0468760 + 0.0459289i
\(470\) 0 0
\(471\) −162.000 280.592i −0.343949 0.595737i
\(472\) 0 0
\(473\) 4.45584 7.71775i 0.00942039 0.0163166i
\(474\) 0 0
\(475\) 165.758i 0.348965i
\(476\) 0 0
\(477\) 256.368 0.537458
\(478\) 0 0
\(479\) −328.669 189.757i −0.686157 0.396153i 0.116014 0.993248i \(-0.462988\pi\)
−0.802171 + 0.597095i \(0.796322\pi\)
\(480\) 0 0
\(481\) 516.632 298.278i 1.07408 0.620120i
\(482\) 0 0
\(483\) −439.831 113.055i −0.910622 0.234067i
\(484\) 0 0
\(485\) 7.88225 + 13.6525i 0.0162521 + 0.0281494i
\(486\) 0 0
\(487\) 287.757 498.410i 0.590877 1.02343i −0.403238 0.915095i \(-0.632115\pi\)
0.994115 0.108333i \(-0.0345513\pi\)
\(488\) 0 0
\(489\) 145.390i 0.297322i
\(490\) 0 0
\(491\) −238.441 −0.485623 −0.242811 0.970074i \(-0.578070\pi\)
−0.242811 + 0.970074i \(0.578070\pi\)
\(492\) 0 0
\(493\) 263.294 + 152.013i 0.534064 + 0.308342i
\(494\) 0 0
\(495\) −22.3675 + 12.9139i −0.0451869 + 0.0260887i
\(496\) 0 0
\(497\) 239.434 931.499i 0.481758 1.87424i
\(498\) 0 0
\(499\) −143.287 248.180i −0.287148 0.497355i 0.685980 0.727620i \(-0.259374\pi\)
−0.973128 + 0.230266i \(0.926040\pi\)
\(500\) 0 0
\(501\) 110.522 191.429i 0.220603 0.382095i
\(502\) 0 0
\(503\) 25.4374i 0.0505714i 0.999680 + 0.0252857i \(0.00804954\pi\)
−0.999680 + 0.0252857i \(0.991950\pi\)
\(504\) 0 0
\(505\) 153.795 0.304544
\(506\) 0 0
\(507\) 428.823 + 247.581i 0.845805 + 0.488326i
\(508\) 0 0
\(509\) −697.889 + 402.926i −1.37110 + 0.791603i −0.991066 0.133370i \(-0.957420\pi\)
−0.380031 + 0.924974i \(0.624087\pi\)
\(510\) 0 0
\(511\) −386.662 + 394.635i −0.756677 + 0.772280i
\(512\) 0 0
\(513\) −18.7721 32.5142i −0.0365927 0.0633805i
\(514\) 0 0
\(515\) 75.4781 130.732i 0.146559 0.253848i
\(516\) 0 0
\(517\) 258.025i 0.499080i
\(518\) 0 0
\(519\) 247.632 0.477134
\(520\) 0 0
\(521\) −661.706 382.036i −1.27007 0.733274i −0.295068 0.955476i \(-0.595342\pi\)
−0.975001 + 0.222202i \(0.928676\pi\)
\(522\) 0 0
\(523\) 153.096 88.3900i 0.292726 0.169006i −0.346444 0.938071i \(-0.612611\pi\)
0.639171 + 0.769065i \(0.279278\pi\)
\(524\) 0 0
\(525\) 74.7275 + 267.920i 0.142338 + 0.510324i
\(526\) 0 0
\(527\) 197.698 + 342.424i 0.375139 + 0.649761i
\(528\) 0 0
\(529\) −436.970 + 756.854i −0.826030 + 1.43073i
\(530\) 0 0
\(531\) 123.663i 0.232887i
\(532\) 0 0
\(533\) −1169.44 −2.19407
\(534\) 0 0
\(535\) −147.308 85.0482i −0.275342 0.158969i
\(536\) 0 0
\(537\) −253.919 + 146.600i −0.472847 + 0.272998i
\(538\) 0 0
\(539\) −251.558 + 152.166i −0.466713 + 0.282311i
\(540\) 0 0
\(541\) −8.58831 14.8754i −0.0158749 0.0274961i 0.857979 0.513685i \(-0.171720\pi\)
−0.873854 + 0.486189i \(0.838387\pi\)
\(542\) 0 0
\(543\) −181.838 + 314.953i −0.334877 + 0.580024i
\(544\) 0 0
\(545\) 159.356i 0.292396i
\(546\) 0 0
\(547\) −212.676 −0.388805 −0.194402 0.980922i \(-0.562277\pi\)
−0.194402 + 0.980922i \(0.562277\pi\)
\(548\) 0 0
\(549\) −3.08831 1.78304i −0.00562534 0.00324779i
\(550\) 0 0
\(551\) −212.382 + 122.619i −0.385448 + 0.222538i
\(552\) 0 0
\(553\) −663.058 + 184.938i −1.19902 + 0.334427i
\(554\) 0 0
\(555\) 34.7574 + 60.2015i 0.0626259 + 0.108471i
\(556\) 0 0
\(557\) 440.823 763.528i 0.791424 1.37079i −0.133661 0.991027i \(-0.542673\pi\)
0.925085 0.379760i \(-0.123993\pi\)
\(558\) 0 0
\(559\) 31.6780i 0.0566691i
\(560\) 0 0
\(561\) 93.0883 0.165933
\(562\) 0 0
\(563\) −664.301 383.534i −1.17993 0.681233i −0.223932 0.974605i \(-0.571889\pi\)
−0.955998 + 0.293372i \(0.905223\pi\)
\(564\) 0 0
\(565\) −126.000 + 72.7461i −0.223009 + 0.128754i
\(566\) 0 0
\(567\) −45.0000 44.0908i −0.0793651 0.0777616i
\(568\) 0 0
\(569\) 14.6468 + 25.3689i 0.0257412 + 0.0445851i 0.878609 0.477542i \(-0.158472\pi\)
−0.852868 + 0.522127i \(0.825139\pi\)
\(570\) 0 0
\(571\) 482.521 835.752i 0.845046 1.46366i −0.0405347 0.999178i \(-0.512906\pi\)
0.885581 0.464485i \(-0.153761\pi\)
\(572\) 0 0
\(573\) 115.360i 0.201326i
\(574\) 0 0
\(575\) 859.279 1.49440
\(576\) 0 0
\(577\) 227.883 + 131.568i 0.394944 + 0.228021i 0.684300 0.729201i \(-0.260108\pi\)
−0.289356 + 0.957222i \(0.593441\pi\)
\(578\) 0 0
\(579\) −14.6909 + 8.48180i −0.0253729 + 0.0146491i
\(580\) 0 0
\(581\) 748.477 + 192.389i 1.28826 + 0.331135i
\(582\) 0 0
\(583\) −256.368 444.042i −0.439738 0.761649i
\(584\) 0 0
\(585\) −45.9045 + 79.5090i −0.0784693 + 0.135913i
\(586\) 0 0
\(587\) 436.477i 0.743572i −0.928318 0.371786i \(-0.878746\pi\)
0.928318 0.371786i \(-0.121254\pi\)
\(588\) 0 0
\(589\) −318.941 −0.541496
\(590\) 0 0
\(591\) 400.742 + 231.369i 0.678075 + 0.391487i
\(592\) 0 0
\(593\) 603.603 348.490i 1.01788 0.587673i 0.104391 0.994536i \(-0.466711\pi\)
0.913489 + 0.406863i \(0.133377\pi\)
\(594\) 0 0
\(595\) −22.3978 + 87.1372i −0.0376434 + 0.146449i
\(596\) 0 0
\(597\) −113.397 196.409i −0.189945 0.328994i
\(598\) 0 0
\(599\) 199.206 345.035i 0.332564 0.576018i −0.650450 0.759549i \(-0.725419\pi\)
0.983014 + 0.183531i \(0.0587528\pi\)
\(600\) 0 0
\(601\) 36.1691i 0.0601816i 0.999547 + 0.0300908i \(0.00957964\pi\)
−0.999547 + 0.0300908i \(0.990420\pi\)
\(602\) 0 0
\(603\) 13.1909 0.0218755
\(604\) 0 0
\(605\) −105.624 60.9823i −0.174586 0.100797i
\(606\) 0 0
\(607\) −27.3457 + 15.7880i −0.0450505 + 0.0260099i −0.522356 0.852727i \(-0.674947\pi\)
0.477306 + 0.878737i \(0.341613\pi\)
\(608\) 0 0
\(609\) −288.000 + 293.939i −0.472906 + 0.482658i
\(610\) 0 0
\(611\) −458.595 794.310i −0.750565 1.30002i
\(612\) 0 0
\(613\) 204.632 354.434i 0.333821 0.578195i −0.649436 0.760416i \(-0.724995\pi\)
0.983258 + 0.182220i \(0.0583285\pi\)
\(614\) 0 0
\(615\) 136.271i 0.221579i
\(616\) 0 0
\(617\) 1227.38 1.98927 0.994636 0.103436i \(-0.0329837\pi\)
0.994636 + 0.103436i \(0.0329837\pi\)
\(618\) 0 0
\(619\) −412.022 237.881i −0.665625 0.384299i 0.128792 0.991672i \(-0.458890\pi\)
−0.794417 + 0.607373i \(0.792223\pi\)
\(620\) 0 0
\(621\) −168.551 + 97.3131i −0.271419 + 0.156704i
\(622\) 0 0
\(623\) −39.0883 140.143i −0.0627421 0.224949i
\(624\) 0 0
\(625\) −237.412 411.209i −0.379859 0.657935i
\(626\) 0 0
\(627\) −37.5442 + 65.0284i −0.0598790 + 0.103714i
\(628\) 0 0
\(629\) 250.544i 0.398322i
\(630\) 0 0
\(631\) 54.9420 0.0870713 0.0435357 0.999052i \(-0.486138\pi\)
0.0435357 + 0.999052i \(0.486138\pi\)
\(632\) 0 0
\(633\) −34.6325 19.9951i −0.0547116 0.0315878i
\(634\) 0 0
\(635\) 102.609 59.2415i 0.161589 0.0932937i
\(636\) 0 0
\(637\) −503.956 + 915.533i −0.791139 + 1.43726i
\(638\) 0 0
\(639\) −206.095 356.968i −0.322528 0.558635i
\(640\) 0 0
\(641\) 114.551 198.409i 0.178707 0.309530i −0.762731 0.646716i \(-0.776142\pi\)
0.941438 + 0.337186i \(0.109475\pi\)
\(642\) 0 0
\(643\) 854.640i 1.32914i 0.747224 + 0.664572i \(0.231386\pi\)
−0.747224 + 0.664572i \(0.768614\pi\)
\(644\) 0 0
\(645\) 3.69134 0.00572301
\(646\) 0 0
\(647\) −868.632 501.505i −1.34255 0.775124i −0.355372 0.934725i \(-0.615646\pi\)
−0.987182 + 0.159601i \(0.948979\pi\)
\(648\) 0 0
\(649\) 214.191 123.663i 0.330032 0.190544i
\(650\) 0 0
\(651\) −515.514 + 143.786i −0.791881 + 0.220869i
\(652\) 0 0
\(653\) −635.382 1100.51i −0.973020 1.68532i −0.686321 0.727299i \(-0.740776\pi\)
−0.286698 0.958021i \(-0.592558\pi\)
\(654\) 0 0
\(655\) −43.4558 + 75.2677i −0.0663448 + 0.114913i
\(656\) 0 0
\(657\) 236.781i 0.360397i
\(658\) 0 0
\(659\) 783.308 1.18863 0.594315 0.804232i \(-0.297423\pi\)
0.594315 + 0.804232i \(0.297423\pi\)
\(660\) 0 0
\(661\) 72.5589 + 41.8919i 0.109771 + 0.0633765i 0.553881 0.832596i \(-0.313146\pi\)
−0.444109 + 0.895973i \(0.646480\pi\)
\(662\) 0 0
\(663\) 286.566 165.449i 0.432226 0.249546i
\(664\) 0 0
\(665\) −51.8377 50.7903i −0.0779514 0.0763764i
\(666\) 0 0
\(667\) 635.647 + 1100.97i 0.952994 + 1.65063i
\(668\) 0 0
\(669\) −198.000 + 342.946i −0.295964 + 0.512625i
\(670\) 0 0
\(671\) 7.13215i 0.0106291i
\(672\) 0 0
\(673\) 415.676 0.617647 0.308823 0.951119i \(-0.400065\pi\)
0.308823 + 0.951119i \(0.400065\pi\)
\(674\) 0 0
\(675\) 103.235 + 59.6028i 0.152941 + 0.0883004i
\(676\) 0 0
\(677\) 685.279 395.646i 1.01223 0.584411i 0.100386 0.994949i \(-0.467992\pi\)
0.911844 + 0.410538i \(0.134659\pi\)
\(678\) 0 0
\(679\) 74.4853 + 19.1458i 0.109698 + 0.0281970i
\(680\) 0 0
\(681\) 56.8234 + 98.4210i 0.0834411 + 0.144524i
\(682\) 0 0
\(683\) −164.080 + 284.195i −0.240235 + 0.416099i −0.960781 0.277308i \(-0.910558\pi\)
0.720546 + 0.693407i \(0.243891\pi\)
\(684\) 0 0
\(685\) 96.1791i 0.140407i
\(686\) 0 0
\(687\) −161.912 −0.235679
\(688\) 0 0
\(689\) −1578.42 911.300i −2.29088 1.32264i
\(690\) 0 0
\(691\) −875.182 + 505.287i −1.26654 + 0.731240i −0.974333 0.225113i \(-0.927725\pi\)
−0.292212 + 0.956353i \(0.594391\pi\)
\(692\) 0 0
\(693\) −31.3675 + 122.033i −0.0452634 + 0.176094i
\(694\) 0 0
\(695\) 65.6833 + 113.767i 0.0945084 + 0.163693i
\(696\) 0 0
\(697\) −245.574 + 425.346i −0.352329 + 0.610252i
\(698\) 0 0
\(699\) 411.388i 0.588537i
\(700\) 0 0
\(701\) −0.103464 −0.000147594 −7.37972e−5 1.00000i \(-0.500023\pi\)
−7.37972e−5 1.00000i \(0.500023\pi\)
\(702\) 0 0
\(703\) 175.022 + 101.049i 0.248964 + 0.143740i
\(704\) 0 0
\(705\) 92.5584 53.4386i 0.131289 0.0757995i
\(706\) 0 0
\(707\) 525.088 535.916i 0.742699 0.758014i
\(708\) 0 0
\(709\) −602.588 1043.71i −0.849912 1.47209i −0.881286 0.472584i \(-0.843321\pi\)
0.0313734 0.999508i \(-0.490012\pi\)
\(710\) 0 0
\(711\) −147.507 + 255.490i −0.207464 + 0.359339i
\(712\) 0 0
\(713\) 1653.37i 2.31889i
\(714\) 0 0
\(715\) 183.618 0.256809
\(716\) 0 0
\(717\) 550.279 + 317.704i 0.767475 + 0.443102i
\(718\) 0 0
\(719\) −850.925 + 491.282i −1.18348 + 0.683285i −0.956818 0.290688i \(-0.906116\pi\)
−0.226666 + 0.973973i \(0.572783\pi\)
\(720\) 0 0
\(721\) −197.852 709.359i −0.274414 0.983855i
\(722\) 0 0
\(723\) 364.617 + 631.536i 0.504312 + 0.873493i
\(724\) 0 0
\(725\) 389.324 674.329i 0.536998 0.930108i
\(726\) 0 0
\(727\) 630.440i 0.867181i 0.901110 + 0.433590i \(0.142753\pi\)
−0.901110 + 0.433590i \(0.857247\pi\)
\(728\) 0 0
\(729\) −27.0000 −0.0370370
\(730\) 0 0
\(731\) −11.5219 6.65215i −0.0157618 0.00910007i
\(732\) 0 0
\(733\) 258.486 149.237i 0.352641 0.203597i −0.313207 0.949685i \(-0.601403\pi\)
0.665848 + 0.746088i \(0.268070\pi\)
\(734\) 0 0
\(735\) −106.684 58.7244i −0.145149 0.0798971i
\(736\) 0 0
\(737\) −13.1909 22.8473i −0.0178981 0.0310004i
\(738\) 0 0
\(739\) 172.684 299.097i 0.233672 0.404732i −0.725214 0.688524i \(-0.758259\pi\)
0.958886 + 0.283792i \(0.0915924\pi\)
\(740\) 0 0
\(741\) 266.914i 0.360207i
\(742\) 0 0
\(743\) −683.616 −0.920076 −0.460038 0.887899i \(-0.652164\pi\)
−0.460038 + 0.887899i \(0.652164\pi\)
\(744\) 0 0
\(745\) 100.764 + 58.1759i 0.135253 + 0.0780885i
\(746\) 0 0
\(747\) 286.831 165.602i 0.383977 0.221689i
\(748\) 0 0
\(749\) −799.301 + 222.939i −1.06716 + 0.297648i
\(750\) 0 0
\(751\) −289.169 500.855i −0.385045 0.666918i 0.606730 0.794908i \(-0.292481\pi\)
−0.991775 + 0.127990i \(0.959148\pi\)
\(752\) 0 0
\(753\) 126.978 219.932i 0.168629 0.292074i
\(754\) 0 0
\(755\) 73.4744i 0.0973171i
\(756\) 0 0
\(757\) 1204.82 1.59158 0.795788 0.605576i \(-0.207057\pi\)
0.795788 + 0.605576i \(0.207057\pi\)
\(758\) 0 0
\(759\) 337.103 + 194.626i 0.444140 + 0.256425i
\(760\) 0 0
\(761\) −202.669 + 117.011i −0.266319 + 0.153760i −0.627214 0.778847i \(-0.715805\pi\)
0.360894 + 0.932607i \(0.382471\pi\)
\(762\) 0 0
\(763\) −555.294 544.075i −0.727778 0.713074i
\(764\) 0 0
\(765\) 19.2792 + 33.3926i 0.0252016 + 0.0436504i
\(766\) 0 0
\(767\) 439.581 761.376i 0.573117 0.992668i
\(768\) 0 0
\(769\) 1290.16i 1.67771i 0.544358 + 0.838853i \(0.316774\pi\)
−0.544358 + 0.838853i \(0.683226\pi\)
\(770\) 0 0
\(771\) −43.4558 −0.0563630
\(772\) 0 0
\(773\) 345.646 + 199.559i 0.447149 + 0.258161i 0.706625 0.707588i \(-0.250217\pi\)
−0.259477 + 0.965749i \(0.583550\pi\)
\(774\) 0 0
\(775\) 876.992 506.331i 1.13160 0.653331i
\(776\) 0 0
\(777\) 328.448 + 84.4247i 0.422713 + 0.108655i
\(778\) 0 0
\(779\) −198.088 343.099i −0.254285 0.440435i
\(780\) 0 0
\(781\) −412.191 + 713.936i −0.527773 + 0.914130i
\(782\) 0 0
\(783\) 176.363i 0.225240i
\(784\) 0 0
\(785\) −268.410 −0.341924
\(786\) 0 0
\(787\) 1348.16 + 778.361i 1.71304 + 0.989023i 0.930401 + 0.366544i \(0.119459\pi\)
0.782637 + 0.622478i \(0.213874\pi\)
\(788\) 0 0
\(789\) 136.014 78.5279i 0.172388 0.0995284i
\(790\) 0 0
\(791\)