Properties

Label 684.3.s.a.445.16
Level $684$
Weight $3$
Character 684.445
Analytic conductor $18.638$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 684.s (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.6376500822\)
Analytic rank: \(0\)
Dimension: \(80\)
Relative dimension: \(40\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 445.16
Character \(\chi\) \(=\) 684.445
Dual form 684.3.s.a.601.16

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.719501 + 2.91244i) q^{3} +(-1.98064 - 3.43056i) q^{5} +(2.79341 + 4.83834i) q^{7} +(-7.96464 - 4.19101i) q^{9} +O(q^{10})\) \(q+(-0.719501 + 2.91244i) q^{3} +(-1.98064 - 3.43056i) q^{5} +(2.79341 + 4.83834i) q^{7} +(-7.96464 - 4.19101i) q^{9} +(-6.63076 - 11.4848i) q^{11} +25.1234i q^{13} +(11.4164 - 3.30019i) q^{15} +(5.39015 - 9.33602i) q^{17} +(12.0131 - 14.7202i) q^{19} +(-16.1012 + 4.65447i) q^{21} -43.7153 q^{23} +(4.65417 - 8.06125i) q^{25} +(17.9366 - 20.1811i) q^{27} +(-24.1872 - 13.9645i) q^{29} +(4.29533 + 2.47991i) q^{31} +(38.2197 - 11.0484i) q^{33} +(11.0655 - 19.1660i) q^{35} -25.3930i q^{37} +(-73.1704 - 18.0763i) q^{39} +(28.4041 - 16.3991i) q^{41} -39.9131 q^{43} +(1.39753 + 35.6240i) q^{45} +(9.60811 - 16.6417i) q^{47} +(8.89367 - 15.4043i) q^{49} +(23.3124 + 22.4158i) q^{51} +(73.0025 - 42.1480i) q^{53} +(-26.2662 + 45.4944i) q^{55} +(34.2284 + 45.5787i) q^{57} +(-12.1135 + 6.99374i) q^{59} +(-31.7016 + 54.9088i) q^{61} +(-1.97102 - 50.2428i) q^{63} +(86.1873 - 49.7602i) q^{65} -79.8298i q^{67} +(31.4532 - 127.318i) q^{69} +(-63.5140 - 36.6698i) q^{71} +(49.7782 - 86.2184i) q^{73} +(20.1293 + 19.3551i) q^{75} +(37.0449 - 64.1636i) q^{77} -79.2932i q^{79} +(45.8709 + 66.7597i) q^{81} +(9.92316 + 17.1874i) q^{83} -42.7037 q^{85} +(58.0735 - 60.3964i) q^{87} +(2.17243 - 1.25425i) q^{89} +(-121.555 + 70.1800i) q^{91} +(-10.3131 + 10.7256i) q^{93} +(-74.2922 - 12.0563i) q^{95} -77.4269i q^{97} +(4.67863 + 119.262i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - q^{7} + 4 q^{9} + O(q^{10}) \) \( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(343\) \(533\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.719501 + 2.91244i −0.239834 + 0.970814i
\(4\) 0 0
\(5\) −1.98064 3.43056i −0.396127 0.686112i 0.597117 0.802154i \(-0.296313\pi\)
−0.993244 + 0.116042i \(0.962979\pi\)
\(6\) 0 0
\(7\) 2.79341 + 4.83834i 0.399059 + 0.691191i 0.993610 0.112867i \(-0.0360035\pi\)
−0.594551 + 0.804058i \(0.702670\pi\)
\(8\) 0 0
\(9\) −7.96464 4.19101i −0.884960 0.465668i
\(10\) 0 0
\(11\) −6.63076 11.4848i −0.602796 1.04407i −0.992396 0.123089i \(-0.960720\pi\)
0.389600 0.920984i \(-0.372613\pi\)
\(12\) 0 0
\(13\) 25.1234i 1.93257i 0.257481 + 0.966283i \(0.417108\pi\)
−0.257481 + 0.966283i \(0.582892\pi\)
\(14\) 0 0
\(15\) 11.4164 3.30019i 0.761092 0.220013i
\(16\) 0 0
\(17\) 5.39015 9.33602i 0.317068 0.549178i −0.662807 0.748790i \(-0.730635\pi\)
0.979875 + 0.199613i \(0.0639684\pi\)
\(18\) 0 0
\(19\) 12.0131 14.7202i 0.632269 0.774749i
\(20\) 0 0
\(21\) −16.1012 + 4.65447i −0.766725 + 0.221641i
\(22\) 0 0
\(23\) −43.7153 −1.90067 −0.950333 0.311235i \(-0.899257\pi\)
−0.950333 + 0.311235i \(0.899257\pi\)
\(24\) 0 0
\(25\) 4.65417 8.06125i 0.186167 0.322450i
\(26\) 0 0
\(27\) 17.9366 20.1811i 0.664320 0.747448i
\(28\) 0 0
\(29\) −24.1872 13.9645i −0.834042 0.481534i 0.0211926 0.999775i \(-0.493254\pi\)
−0.855235 + 0.518241i \(0.826587\pi\)
\(30\) 0 0
\(31\) 4.29533 + 2.47991i 0.138559 + 0.0799971i 0.567677 0.823251i \(-0.307842\pi\)
−0.429118 + 0.903248i \(0.641176\pi\)
\(32\) 0 0
\(33\) 38.2197 11.0484i 1.15817 0.334799i
\(34\) 0 0
\(35\) 11.0655 19.1660i 0.316156 0.547599i
\(36\) 0 0
\(37\) 25.3930i 0.686298i −0.939281 0.343149i \(-0.888506\pi\)
0.939281 0.343149i \(-0.111494\pi\)
\(38\) 0 0
\(39\) −73.1704 18.0763i −1.87616 0.463495i
\(40\) 0 0
\(41\) 28.4041 16.3991i 0.692782 0.399978i −0.111871 0.993723i \(-0.535684\pi\)
0.804654 + 0.593745i \(0.202351\pi\)
\(42\) 0 0
\(43\) −39.9131 −0.928212 −0.464106 0.885780i \(-0.653624\pi\)
−0.464106 + 0.885780i \(0.653624\pi\)
\(44\) 0 0
\(45\) 1.39753 + 35.6240i 0.0310562 + 0.791645i
\(46\) 0 0
\(47\) 9.60811 16.6417i 0.204428 0.354080i −0.745522 0.666481i \(-0.767800\pi\)
0.949950 + 0.312401i \(0.101133\pi\)
\(48\) 0 0
\(49\) 8.89367 15.4043i 0.181504 0.314373i
\(50\) 0 0
\(51\) 23.3124 + 22.4158i 0.457106 + 0.439525i
\(52\) 0 0
\(53\) 73.0025 42.1480i 1.37741 0.795246i 0.385559 0.922683i \(-0.374009\pi\)
0.991847 + 0.127438i \(0.0406753\pi\)
\(54\) 0 0
\(55\) −26.2662 + 45.4944i −0.477568 + 0.827171i
\(56\) 0 0
\(57\) 34.2284 + 45.5787i 0.600498 + 0.799627i
\(58\) 0 0
\(59\) −12.1135 + 6.99374i −0.205314 + 0.118538i −0.599132 0.800651i \(-0.704487\pi\)
0.393818 + 0.919188i \(0.371154\pi\)
\(60\) 0 0
\(61\) −31.7016 + 54.9088i −0.519699 + 0.900144i 0.480039 + 0.877247i \(0.340622\pi\)
−0.999738 + 0.0228974i \(0.992711\pi\)
\(62\) 0 0
\(63\) −1.97102 50.2428i −0.0312860 0.797505i
\(64\) 0 0
\(65\) 86.1873 49.7602i 1.32596 0.765542i
\(66\) 0 0
\(67\) 79.8298i 1.19149i −0.803174 0.595745i \(-0.796857\pi\)
0.803174 0.595745i \(-0.203143\pi\)
\(68\) 0 0
\(69\) 31.4532 127.318i 0.455844 1.84519i
\(70\) 0 0
\(71\) −63.5140 36.6698i −0.894564 0.516476i −0.0191311 0.999817i \(-0.506090\pi\)
−0.875432 + 0.483341i \(0.839423\pi\)
\(72\) 0 0
\(73\) 49.7782 86.2184i 0.681893 1.18107i −0.292509 0.956263i \(-0.594490\pi\)
0.974402 0.224811i \(-0.0721764\pi\)
\(74\) 0 0
\(75\) 20.1293 + 19.3551i 0.268390 + 0.258068i
\(76\) 0 0
\(77\) 37.0449 64.1636i 0.481102 0.833294i
\(78\) 0 0
\(79\) 79.2932i 1.00371i −0.864951 0.501856i \(-0.832651\pi\)
0.864951 0.501856i \(-0.167349\pi\)
\(80\) 0 0
\(81\) 45.8709 + 66.7597i 0.566307 + 0.824194i
\(82\) 0 0
\(83\) 9.92316 + 17.1874i 0.119556 + 0.207077i 0.919592 0.392875i \(-0.128520\pi\)
−0.800036 + 0.599952i \(0.795186\pi\)
\(84\) 0 0
\(85\) −42.7037 −0.502397
\(86\) 0 0
\(87\) 58.0735 60.3964i 0.667512 0.694211i
\(88\) 0 0
\(89\) 2.17243 1.25425i 0.0244093 0.0140927i −0.487746 0.872986i \(-0.662181\pi\)
0.512155 + 0.858893i \(0.328847\pi\)
\(90\) 0 0
\(91\) −121.555 + 70.1800i −1.33577 + 0.771209i
\(92\) 0 0
\(93\) −10.3131 + 10.7256i −0.110893 + 0.115329i
\(94\) 0 0
\(95\) −74.2922 12.0563i −0.782024 0.126909i
\(96\) 0 0
\(97\) 77.4269i 0.798215i −0.916904 0.399108i \(-0.869320\pi\)
0.916904 0.399108i \(-0.130680\pi\)
\(98\) 0 0
\(99\) 4.67863 + 119.262i 0.0472589 + 1.20467i
\(100\) 0 0
\(101\) −29.9666 + 51.9036i −0.296699 + 0.513897i −0.975379 0.220537i \(-0.929219\pi\)
0.678680 + 0.734434i \(0.262552\pi\)
\(102\) 0 0
\(103\) 96.2690 + 55.5809i 0.934651 + 0.539621i 0.888279 0.459303i \(-0.151901\pi\)
0.0463713 + 0.998924i \(0.485234\pi\)
\(104\) 0 0
\(105\) 47.8581 + 46.0175i 0.455792 + 0.438262i
\(106\) 0 0
\(107\) 39.3147i 0.367427i −0.982980 0.183713i \(-0.941188\pi\)
0.982980 0.183713i \(-0.0588118\pi\)
\(108\) 0 0
\(109\) 9.98429 + 5.76443i 0.0915990 + 0.0528847i 0.545100 0.838371i \(-0.316492\pi\)
−0.453501 + 0.891256i \(0.649825\pi\)
\(110\) 0 0
\(111\) 73.9557 + 18.2703i 0.666267 + 0.164597i
\(112\) 0 0
\(113\) −56.0972 32.3877i −0.496436 0.286617i 0.230805 0.973000i \(-0.425864\pi\)
−0.727240 + 0.686383i \(0.759197\pi\)
\(114\) 0 0
\(115\) 86.5841 + 149.968i 0.752905 + 1.30407i
\(116\) 0 0
\(117\) 105.292 200.099i 0.899934 1.71024i
\(118\) 0 0
\(119\) 60.2277 0.506115
\(120\) 0 0
\(121\) −27.4338 + 47.5168i −0.226726 + 0.392701i
\(122\) 0 0
\(123\) 27.3247 + 94.5244i 0.222152 + 0.768491i
\(124\) 0 0
\(125\) −135.905 −1.08724
\(126\) 0 0
\(127\) −114.338 + 66.0128i −0.900296 + 0.519786i −0.877296 0.479949i \(-0.840655\pi\)
−0.0229998 + 0.999735i \(0.507322\pi\)
\(128\) 0 0
\(129\) 28.7175 116.245i 0.222617 0.901122i
\(130\) 0 0
\(131\) 49.7841 + 86.2286i 0.380031 + 0.658233i 0.991066 0.133370i \(-0.0425799\pi\)
−0.611035 + 0.791604i \(0.709247\pi\)
\(132\) 0 0
\(133\) 104.779 + 17.0038i 0.787812 + 0.127848i
\(134\) 0 0
\(135\) −104.758 21.5613i −0.775989 0.159713i
\(136\) 0 0
\(137\) −54.5400 + 94.4660i −0.398102 + 0.689533i −0.993492 0.113904i \(-0.963664\pi\)
0.595390 + 0.803437i \(0.296998\pi\)
\(138\) 0 0
\(139\) 4.21609 0.0303316 0.0151658 0.999885i \(-0.495172\pi\)
0.0151658 + 0.999885i \(0.495172\pi\)
\(140\) 0 0
\(141\) 41.5551 + 39.9568i 0.294717 + 0.283382i
\(142\) 0 0
\(143\) 288.537 166.587i 2.01774 1.16494i
\(144\) 0 0
\(145\) 110.634i 0.762995i
\(146\) 0 0
\(147\) 38.4651 + 36.9857i 0.261667 + 0.251604i
\(148\) 0 0
\(149\) −133.072 230.487i −0.893100 1.54690i −0.836138 0.548519i \(-0.815192\pi\)
−0.0569625 0.998376i \(-0.518142\pi\)
\(150\) 0 0
\(151\) −199.036 + 114.913i −1.31812 + 0.761016i −0.983426 0.181311i \(-0.941966\pi\)
−0.334693 + 0.942327i \(0.608633\pi\)
\(152\) 0 0
\(153\) −82.0580 + 51.7678i −0.536327 + 0.338352i
\(154\) 0 0
\(155\) 19.6472i 0.126756i
\(156\) 0 0
\(157\) −66.7469 115.609i −0.425139 0.736363i 0.571294 0.820745i \(-0.306442\pi\)
−0.996433 + 0.0843824i \(0.973108\pi\)
\(158\) 0 0
\(159\) 70.2283 + 242.941i 0.441687 + 1.52793i
\(160\) 0 0
\(161\) −122.115 211.509i −0.758478 1.31372i
\(162\) 0 0
\(163\) −215.134 −1.31984 −0.659921 0.751335i \(-0.729410\pi\)
−0.659921 + 0.751335i \(0.729410\pi\)
\(164\) 0 0
\(165\) −113.601 109.232i −0.688493 0.662013i
\(166\) 0 0
\(167\) 104.289i 0.624487i −0.950002 0.312243i \(-0.898920\pi\)
0.950002 0.312243i \(-0.101080\pi\)
\(168\) 0 0
\(169\) −462.184 −2.73481
\(170\) 0 0
\(171\) −157.373 + 66.8942i −0.920308 + 0.391194i
\(172\) 0 0
\(173\) 334.413i 1.93302i 0.256623 + 0.966512i \(0.417390\pi\)
−0.256623 + 0.966512i \(0.582610\pi\)
\(174\) 0 0
\(175\) 52.0041 0.297166
\(176\) 0 0
\(177\) −11.6532 40.3119i −0.0658372 0.227751i
\(178\) 0 0
\(179\) 147.280i 0.822793i 0.911456 + 0.411397i \(0.134959\pi\)
−0.911456 + 0.411397i \(0.865041\pi\)
\(180\) 0 0
\(181\) −181.475 + 104.775i −1.00263 + 0.578867i −0.909024 0.416743i \(-0.863172\pi\)
−0.0936021 + 0.995610i \(0.529838\pi\)
\(182\) 0 0
\(183\) −137.109 131.836i −0.749232 0.720416i
\(184\) 0 0
\(185\) −87.1123 + 50.2943i −0.470877 + 0.271861i
\(186\) 0 0
\(187\) −142.963 −0.764509
\(188\) 0 0
\(189\) 147.747 + 30.4093i 0.781732 + 0.160896i
\(190\) 0 0
\(191\) −130.504 226.039i −0.683266 1.18345i −0.973978 0.226641i \(-0.927225\pi\)
0.290712 0.956811i \(-0.406108\pi\)
\(192\) 0 0
\(193\) 274.813 158.663i 1.42390 0.822090i 0.427272 0.904123i \(-0.359475\pi\)
0.996630 + 0.0820329i \(0.0261413\pi\)
\(194\) 0 0
\(195\) 82.9120 + 286.818i 0.425190 + 1.47086i
\(196\) 0 0
\(197\) 117.271 0.595286 0.297643 0.954677i \(-0.403800\pi\)
0.297643 + 0.954677i \(0.403800\pi\)
\(198\) 0 0
\(199\) 113.149 + 195.981i 0.568590 + 0.984827i 0.996706 + 0.0811029i \(0.0258442\pi\)
−0.428116 + 0.903724i \(0.640822\pi\)
\(200\) 0 0
\(201\) 232.500 + 57.4376i 1.15671 + 0.285759i
\(202\) 0 0
\(203\) 156.034i 0.768643i
\(204\) 0 0
\(205\) −112.516 64.9613i −0.548860 0.316884i
\(206\) 0 0
\(207\) 348.177 + 183.211i 1.68201 + 0.885079i
\(208\) 0 0
\(209\) −248.715 40.3621i −1.19002 0.193120i
\(210\) 0 0
\(211\) −104.403 + 60.2773i −0.494803 + 0.285674i −0.726565 0.687098i \(-0.758884\pi\)
0.231762 + 0.972773i \(0.425551\pi\)
\(212\) 0 0
\(213\) 152.497 158.597i 0.715949 0.744586i
\(214\) 0 0
\(215\) 79.0534 + 136.924i 0.367690 + 0.636858i
\(216\) 0 0
\(217\) 27.7097i 0.127694i
\(218\) 0 0
\(219\) 215.291 + 207.010i 0.983062 + 0.945253i
\(220\) 0 0
\(221\) 234.552 + 135.419i 1.06132 + 0.612755i
\(222\) 0 0
\(223\) 68.1444i 0.305580i 0.988259 + 0.152790i \(0.0488259\pi\)
−0.988259 + 0.152790i \(0.951174\pi\)
\(224\) 0 0
\(225\) −70.8535 + 44.6993i −0.314905 + 0.198664i
\(226\) 0 0
\(227\) 54.7779 31.6260i 0.241312 0.139322i −0.374467 0.927240i \(-0.622174\pi\)
0.615780 + 0.787918i \(0.288841\pi\)
\(228\) 0 0
\(229\) −53.9886 + 93.5111i −0.235758 + 0.408345i −0.959493 0.281733i \(-0.909091\pi\)
0.723735 + 0.690079i \(0.242424\pi\)
\(230\) 0 0
\(231\) 160.219 + 154.057i 0.693589 + 0.666913i
\(232\) 0 0
\(233\) 201.984 349.846i 0.866884 1.50149i 0.00171917 0.999999i \(-0.499453\pi\)
0.865165 0.501488i \(-0.167214\pi\)
\(234\) 0 0
\(235\) −76.1207 −0.323918
\(236\) 0 0
\(237\) 230.937 + 57.0515i 0.974417 + 0.240724i
\(238\) 0 0
\(239\) −117.285 + 203.144i −0.490734 + 0.849977i −0.999943 0.0106663i \(-0.996605\pi\)
0.509209 + 0.860643i \(0.329938\pi\)
\(240\) 0 0
\(241\) 86.4868 + 49.9332i 0.358866 + 0.207192i 0.668583 0.743637i \(-0.266901\pi\)
−0.309717 + 0.950829i \(0.600234\pi\)
\(242\) 0 0
\(243\) −227.438 + 85.5626i −0.935959 + 0.352109i
\(244\) 0 0
\(245\) −70.4605 −0.287594
\(246\) 0 0
\(247\) 369.822 + 301.810i 1.49725 + 1.22190i
\(248\) 0 0
\(249\) −57.1971 + 16.5343i −0.229707 + 0.0664027i
\(250\) 0 0
\(251\) 54.7583 + 94.8441i 0.218160 + 0.377865i 0.954246 0.299024i \(-0.0966610\pi\)
−0.736085 + 0.676889i \(0.763328\pi\)
\(252\) 0 0
\(253\) 289.866 + 502.062i 1.14571 + 1.98443i
\(254\) 0 0
\(255\) 30.7254 124.372i 0.120492 0.487734i
\(256\) 0 0
\(257\) 248.204i 0.965775i 0.875682 + 0.482888i \(0.160412\pi\)
−0.875682 + 0.482888i \(0.839588\pi\)
\(258\) 0 0
\(259\) 122.860 70.9332i 0.474363 0.273873i
\(260\) 0 0
\(261\) 134.117 + 212.591i 0.513858 + 0.814525i
\(262\) 0 0
\(263\) −463.434 −1.76210 −0.881052 0.473019i \(-0.843164\pi\)
−0.881052 + 0.473019i \(0.843164\pi\)
\(264\) 0 0
\(265\) −289.183 166.960i −1.09126 0.630037i
\(266\) 0 0
\(267\) 2.08987 + 7.22952i 0.00782725 + 0.0270768i
\(268\) 0 0
\(269\) 208.925 + 120.623i 0.776673 + 0.448412i 0.835250 0.549871i \(-0.185323\pi\)
−0.0585770 + 0.998283i \(0.518656\pi\)
\(270\) 0 0
\(271\) −49.7374 + 86.1478i −0.183533 + 0.317888i −0.943081 0.332563i \(-0.892087\pi\)
0.759548 + 0.650451i \(0.225420\pi\)
\(272\) 0 0
\(273\) −116.936 404.517i −0.428337 1.48175i
\(274\) 0 0
\(275\) −123.443 −0.448882
\(276\) 0 0
\(277\) 235.476 + 407.856i 0.850093 + 1.47240i 0.881124 + 0.472886i \(0.156788\pi\)
−0.0310310 + 0.999518i \(0.509879\pi\)
\(278\) 0 0
\(279\) −23.8174 37.7533i −0.0853671 0.135317i
\(280\) 0 0
\(281\) −225.286 130.069i −0.801729 0.462878i 0.0423465 0.999103i \(-0.486517\pi\)
−0.844075 + 0.536225i \(0.819850\pi\)
\(282\) 0 0
\(283\) −79.5473 137.780i −0.281086 0.486855i 0.690567 0.723269i \(-0.257361\pi\)
−0.971652 + 0.236414i \(0.924028\pi\)
\(284\) 0 0
\(285\) 88.5667 207.697i 0.310760 0.728762i
\(286\) 0 0
\(287\) 158.689 + 91.6190i 0.552922 + 0.319230i
\(288\) 0 0
\(289\) 86.3925 + 149.636i 0.298936 + 0.517772i
\(290\) 0 0
\(291\) 225.501 + 55.7087i 0.774918 + 0.191439i
\(292\) 0 0
\(293\) 36.6938 + 21.1852i 0.125235 + 0.0723043i 0.561309 0.827607i \(-0.310298\pi\)
−0.436074 + 0.899911i \(0.643631\pi\)
\(294\) 0 0
\(295\) 47.9849 + 27.7041i 0.162661 + 0.0939122i
\(296\) 0 0
\(297\) −350.710 72.1828i −1.18084 0.243040i
\(298\) 0 0
\(299\) 1098.28i 3.67316i
\(300\) 0 0
\(301\) −111.494 193.113i −0.370412 0.641572i
\(302\) 0 0
\(303\) −129.605 124.621i −0.427740 0.411289i
\(304\) 0 0
\(305\) 251.157 0.823467
\(306\) 0 0
\(307\) −136.415 78.7594i −0.444349 0.256545i 0.261092 0.965314i \(-0.415918\pi\)
−0.705441 + 0.708769i \(0.749251\pi\)
\(308\) 0 0
\(309\) −231.142 + 240.387i −0.748032 + 0.777953i
\(310\) 0 0
\(311\) −25.7344 + 44.5733i −0.0827474 + 0.143323i −0.904429 0.426624i \(-0.859703\pi\)
0.821682 + 0.569947i \(0.193036\pi\)
\(312\) 0 0
\(313\) 205.217 355.446i 0.655646 1.13561i −0.326086 0.945340i \(-0.605730\pi\)
0.981732 0.190271i \(-0.0609368\pi\)
\(314\) 0 0
\(315\) −168.457 + 106.274i −0.534785 + 0.337379i
\(316\) 0 0
\(317\) 70.9840 + 40.9826i 0.223924 + 0.129283i 0.607766 0.794116i \(-0.292066\pi\)
−0.383842 + 0.923399i \(0.625399\pi\)
\(318\) 0 0
\(319\) 370.381i 1.16107i
\(320\) 0 0
\(321\) 114.502 + 28.2869i 0.356703 + 0.0881213i
\(322\) 0 0
\(323\) −72.6758 191.499i −0.225002 0.592876i
\(324\) 0 0
\(325\) 202.526 + 116.928i 0.623156 + 0.359780i
\(326\) 0 0
\(327\) −23.9723 + 24.9312i −0.0733098 + 0.0762421i
\(328\) 0 0
\(329\) 107.358 0.326315
\(330\) 0 0
\(331\) −409.814 + 236.606i −1.23811 + 0.714822i −0.968707 0.248207i \(-0.920159\pi\)
−0.269400 + 0.963028i \(0.586825\pi\)
\(332\) 0 0
\(333\) −106.422 + 202.246i −0.319587 + 0.607346i
\(334\) 0 0
\(335\) −273.861 + 158.114i −0.817496 + 0.471981i
\(336\) 0 0
\(337\) −21.5323 + 12.4317i −0.0638942 + 0.0368893i −0.531607 0.846991i \(-0.678412\pi\)
0.467713 + 0.883881i \(0.345078\pi\)
\(338\) 0 0
\(339\) 134.689 140.077i 0.397314 0.413206i
\(340\) 0 0
\(341\) 65.7747i 0.192888i
\(342\) 0 0
\(343\) 373.129 1.08784
\(344\) 0 0
\(345\) −499.071 + 144.269i −1.44658 + 0.418171i
\(346\) 0 0
\(347\) 118.491 + 205.232i 0.341473 + 0.591448i 0.984706 0.174222i \(-0.0557410\pi\)
−0.643234 + 0.765670i \(0.722408\pi\)
\(348\) 0 0
\(349\) −316.275 547.805i −0.906233 1.56964i −0.819254 0.573431i \(-0.805612\pi\)
−0.0869793 0.996210i \(-0.527721\pi\)
\(350\) 0 0
\(351\) 507.017 + 450.629i 1.44449 + 1.28384i
\(352\) 0 0
\(353\) 18.7051 + 32.3982i 0.0529891 + 0.0917797i 0.891303 0.453408i \(-0.149792\pi\)
−0.838314 + 0.545187i \(0.816458\pi\)
\(354\) 0 0
\(355\) 290.518i 0.818361i
\(356\) 0 0
\(357\) −43.3339 + 175.410i −0.121383 + 0.491344i
\(358\) 0 0
\(359\) 311.259 539.116i 0.867017 1.50172i 0.00198589 0.999998i \(-0.499368\pi\)
0.865031 0.501719i \(-0.167299\pi\)
\(360\) 0 0
\(361\) −72.3702 353.672i −0.200471 0.979700i
\(362\) 0 0
\(363\) −118.651 114.088i −0.326863 0.314292i
\(364\) 0 0
\(365\) −394.370 −1.08047
\(366\) 0 0
\(367\) 280.673 486.140i 0.764776 1.32463i −0.175589 0.984464i \(-0.556183\pi\)
0.940365 0.340167i \(-0.110484\pi\)
\(368\) 0 0
\(369\) −294.957 + 11.5711i −0.799341 + 0.0313581i
\(370\) 0 0
\(371\) 407.852 + 235.474i 1.09933 + 0.634700i
\(372\) 0 0
\(373\) −165.463 95.5303i −0.443601 0.256113i 0.261523 0.965197i \(-0.415775\pi\)
−0.705124 + 0.709084i \(0.749109\pi\)
\(374\) 0 0
\(375\) 97.7835 395.814i 0.260756 1.05550i
\(376\) 0 0
\(377\) 350.835 607.664i 0.930597 1.61184i
\(378\) 0 0
\(379\) 284.754i 0.751329i −0.926756 0.375665i \(-0.877414\pi\)
0.926756 0.375665i \(-0.122586\pi\)
\(380\) 0 0
\(381\) −109.993 380.498i −0.288694 0.998682i
\(382\) 0 0
\(383\) −224.972 + 129.887i −0.587393 + 0.339132i −0.764066 0.645138i \(-0.776800\pi\)
0.176673 + 0.984270i \(0.443466\pi\)
\(384\) 0 0
\(385\) −293.490 −0.762311
\(386\) 0 0
\(387\) 317.894 + 167.276i 0.821430 + 0.432239i
\(388\) 0 0
\(389\) −184.925 + 320.300i −0.475386 + 0.823393i −0.999603 0.0281922i \(-0.991025\pi\)
0.524216 + 0.851585i \(0.324358\pi\)
\(390\) 0 0
\(391\) −235.632 + 408.127i −0.602640 + 1.04380i
\(392\) 0 0
\(393\) −286.955 + 82.9517i −0.730166 + 0.211073i
\(394\) 0 0
\(395\) −272.020 + 157.051i −0.688659 + 0.397597i
\(396\) 0 0
\(397\) 279.296 483.754i 0.703515 1.21852i −0.263709 0.964602i \(-0.584946\pi\)
0.967225 0.253922i \(-0.0817207\pi\)
\(398\) 0 0
\(399\) −124.911 + 292.929i −0.313060 + 0.734157i
\(400\) 0 0
\(401\) 661.224 381.758i 1.64894 0.952015i 0.671444 0.741055i \(-0.265674\pi\)
0.977495 0.210960i \(-0.0676590\pi\)
\(402\) 0 0
\(403\) −62.3037 + 107.913i −0.154600 + 0.267775i
\(404\) 0 0
\(405\) 138.170 289.590i 0.341160 0.715036i
\(406\) 0 0
\(407\) −291.634 + 168.375i −0.716545 + 0.413697i
\(408\) 0 0
\(409\) 675.395i 1.65133i −0.564159 0.825666i \(-0.690800\pi\)
0.564159 0.825666i \(-0.309200\pi\)
\(410\) 0 0
\(411\) −235.885 226.813i −0.573930 0.551856i
\(412\) 0 0
\(413\) −67.6761 39.0728i −0.163865 0.0946073i
\(414\) 0 0
\(415\) 39.3083 68.0840i 0.0947188 0.164058i
\(416\) 0 0
\(417\) −3.03348 + 12.2791i −0.00727454 + 0.0294464i
\(418\) 0 0
\(419\) −280.195 + 485.312i −0.668724 + 1.15826i 0.309538 + 0.950887i \(0.399826\pi\)
−0.978261 + 0.207376i \(0.933508\pi\)
\(420\) 0 0
\(421\) 379.086i 0.900443i −0.892917 0.450221i \(-0.851345\pi\)
0.892917 0.450221i \(-0.148655\pi\)
\(422\) 0 0
\(423\) −146.271 + 92.2777i −0.345794 + 0.218151i
\(424\) 0 0
\(425\) −50.1733 86.9028i −0.118055 0.204477i
\(426\) 0 0
\(427\) −354.223 −0.829562
\(428\) 0 0
\(429\) 277.572 + 960.207i 0.647021 + 2.23824i
\(430\) 0 0
\(431\) 406.143 234.487i 0.942328 0.544053i 0.0516388 0.998666i \(-0.483556\pi\)
0.890689 + 0.454612i \(0.150222\pi\)
\(432\) 0 0
\(433\) −190.975 + 110.259i −0.441050 + 0.254640i −0.704043 0.710157i \(-0.748624\pi\)
0.262993 + 0.964798i \(0.415290\pi\)
\(434\) 0 0
\(435\) −322.216 79.6015i −0.740726 0.182992i
\(436\) 0 0
\(437\) −525.157 + 643.499i −1.20173 + 1.47254i
\(438\) 0 0
\(439\) 527.944i 1.20261i 0.799021 + 0.601303i \(0.205352\pi\)
−0.799021 + 0.601303i \(0.794648\pi\)
\(440\) 0 0
\(441\) −135.394 + 85.4162i −0.307017 + 0.193687i
\(442\) 0 0
\(443\) 2.16032 3.74178i 0.00487657 0.00844646i −0.863577 0.504217i \(-0.831781\pi\)
0.868453 + 0.495771i \(0.165114\pi\)
\(444\) 0 0
\(445\) −8.60559 4.96844i −0.0193384 0.0111650i
\(446\) 0 0
\(447\) 767.027 221.728i 1.71594 0.496037i
\(448\) 0 0
\(449\) 139.442i 0.310561i 0.987870 + 0.155281i \(0.0496281\pi\)
−0.987870 + 0.155281i \(0.950372\pi\)
\(450\) 0 0
\(451\) −376.681 217.477i −0.835213 0.482210i
\(452\) 0 0
\(453\) −191.472 662.361i −0.422676 1.46217i
\(454\) 0 0
\(455\) 481.513 + 278.002i 1.05827 + 0.610993i
\(456\) 0 0
\(457\) −23.1575 40.1100i −0.0506729 0.0877680i 0.839576 0.543242i \(-0.182803\pi\)
−0.890249 + 0.455474i \(0.849470\pi\)
\(458\) 0 0
\(459\) −91.7300 276.236i −0.199847 0.601821i
\(460\) 0 0
\(461\) 239.445 0.519404 0.259702 0.965689i \(-0.416376\pi\)
0.259702 + 0.965689i \(0.416376\pi\)
\(462\) 0 0
\(463\) −24.8923 + 43.1147i −0.0537631 + 0.0931204i −0.891654 0.452717i \(-0.850455\pi\)
0.837891 + 0.545837i \(0.183788\pi\)
\(464\) 0 0
\(465\) 57.2213 + 14.1362i 0.123057 + 0.0304004i
\(466\) 0 0
\(467\) −412.789 −0.883917 −0.441958 0.897036i \(-0.645716\pi\)
−0.441958 + 0.897036i \(0.645716\pi\)
\(468\) 0 0
\(469\) 386.243 222.998i 0.823547 0.475475i
\(470\) 0 0
\(471\) 384.729 111.216i 0.816834 0.236127i
\(472\) 0 0
\(473\) 264.654 + 458.395i 0.559523 + 0.969122i
\(474\) 0 0
\(475\) −62.7524 165.351i −0.132110 0.348108i
\(476\) 0 0
\(477\) −758.081 + 29.7394i −1.58927 + 0.0623468i
\(478\) 0 0
\(479\) 216.233 374.527i 0.451426 0.781893i −0.547049 0.837101i \(-0.684249\pi\)
0.998475 + 0.0552080i \(0.0175822\pi\)
\(480\) 0 0
\(481\) 637.958 1.32632
\(482\) 0 0
\(483\) 703.870 203.472i 1.45729 0.421266i
\(484\) 0 0
\(485\) −265.618 + 153.354i −0.547665 + 0.316195i
\(486\) 0 0
\(487\) 566.439i 1.16312i −0.813504 0.581559i \(-0.802443\pi\)
0.813504 0.581559i \(-0.197557\pi\)
\(488\) 0 0
\(489\) 154.789 626.566i 0.316542 1.28132i
\(490\) 0 0
\(491\) 114.618 + 198.523i 0.233437 + 0.404325i 0.958817 0.284024i \(-0.0916694\pi\)
−0.725380 + 0.688348i \(0.758336\pi\)
\(492\) 0 0
\(493\) −260.746 + 150.542i −0.528896 + 0.305358i
\(494\) 0 0
\(495\) 399.868 252.265i 0.807815 0.509625i
\(496\) 0 0
\(497\) 409.736i 0.824419i
\(498\) 0 0
\(499\) 273.965 + 474.521i 0.549028 + 0.950945i 0.998341 + 0.0575705i \(0.0183354\pi\)
−0.449313 + 0.893374i \(0.648331\pi\)
\(500\) 0 0
\(501\) 303.737 + 75.0363i 0.606261 + 0.149773i
\(502\) 0 0
\(503\) 37.9593 + 65.7474i 0.0754658 + 0.130711i 0.901289 0.433219i \(-0.142622\pi\)
−0.825823 + 0.563929i \(0.809289\pi\)
\(504\) 0 0
\(505\) 237.411 0.470121
\(506\) 0 0
\(507\) 332.542 1346.08i 0.655901 2.65500i
\(508\) 0 0
\(509\) 102.887i 0.202135i −0.994880 0.101067i \(-0.967774\pi\)
0.994880 0.101067i \(-0.0322258\pi\)
\(510\) 0 0
\(511\) 556.205 1.08846
\(512\) 0 0
\(513\) −81.5956 506.469i −0.159056 0.987270i
\(514\) 0 0
\(515\) 440.342i 0.855034i
\(516\) 0 0
\(517\) −254.836 −0.492913
\(518\) 0 0
\(519\) −973.958 240.610i −1.87661 0.463604i
\(520\) 0 0
\(521\) 478.933i 0.919258i 0.888111 + 0.459629i \(0.152018\pi\)
−0.888111 + 0.459629i \(0.847982\pi\)
\(522\) 0 0
\(523\) −863.569 + 498.582i −1.65118 + 0.953311i −0.674597 + 0.738187i \(0.735682\pi\)
−0.976587 + 0.215125i \(0.930984\pi\)
\(524\) 0 0
\(525\) −37.4170 + 151.459i −0.0712704 + 0.288493i
\(526\) 0 0
\(527\) 46.3050 26.7342i 0.0878652 0.0507290i
\(528\) 0 0
\(529\) 1382.03 2.61253
\(530\) 0 0
\(531\) 125.791 4.93475i 0.236894 0.00929331i
\(532\) 0 0
\(533\) 412.001 + 713.606i 0.772985 + 1.33885i
\(534\) 0 0
\(535\) −134.871 + 77.8680i −0.252096 + 0.145548i
\(536\) 0 0
\(537\) −428.944 105.968i −0.798779 0.197333i
\(538\) 0 0
\(539\) −235.887 −0.437638
\(540\) 0 0
\(541\) 99.7528 + 172.777i 0.184386 + 0.319366i 0.943369 0.331744i \(-0.107637\pi\)
−0.758983 + 0.651110i \(0.774304\pi\)
\(542\) 0 0
\(543\) −174.579 603.922i −0.321508 1.11220i
\(544\) 0 0
\(545\) 45.6690i 0.0837963i
\(546\) 0 0
\(547\) 378.396 + 218.467i 0.691765 + 0.399391i 0.804273 0.594260i \(-0.202555\pi\)
−0.112508 + 0.993651i \(0.535888\pi\)
\(548\) 0 0
\(549\) 482.615 304.467i 0.879080 0.554585i
\(550\) 0 0
\(551\) −496.124 + 188.284i −0.900407 + 0.341714i
\(552\) 0 0
\(553\) 383.647 221.499i 0.693756 0.400540i
\(554\) 0 0
\(555\) −83.8019 289.896i −0.150994 0.522336i
\(556\) 0 0
\(557\) −288.865 500.329i −0.518609 0.898257i −0.999766 0.0216224i \(-0.993117\pi\)
0.481158 0.876634i \(-0.340216\pi\)
\(558\) 0 0
\(559\) 1002.75i 1.79383i
\(560\) 0 0
\(561\) 102.862 416.372i 0.183355 0.742196i
\(562\) 0 0
\(563\) −48.9658 28.2704i −0.0869730 0.0502139i 0.455883 0.890040i \(-0.349324\pi\)
−0.542856 + 0.839826i \(0.682657\pi\)
\(564\) 0 0
\(565\) 256.593i 0.454147i
\(566\) 0 0
\(567\) −194.870 + 408.426i −0.343685 + 0.720329i
\(568\) 0 0
\(569\) −133.057 + 76.8207i −0.233844 + 0.135010i −0.612344 0.790591i \(-0.709773\pi\)
0.378500 + 0.925601i \(0.376440\pi\)
\(570\) 0 0
\(571\) −112.166 + 194.277i −0.196438 + 0.340241i −0.947371 0.320138i \(-0.896271\pi\)
0.750933 + 0.660378i \(0.229604\pi\)
\(572\) 0 0
\(573\) 752.224 217.449i 1.31278 0.379493i
\(574\) 0 0
\(575\) −203.458 + 352.400i −0.353841 + 0.612870i
\(576\) 0 0
\(577\) 149.144 0.258483 0.129241 0.991613i \(-0.458746\pi\)
0.129241 + 0.991613i \(0.458746\pi\)
\(578\) 0 0
\(579\) 264.370 + 914.536i 0.456597 + 1.57951i
\(580\) 0 0
\(581\) −55.4390 + 96.0231i −0.0954199 + 0.165272i
\(582\) 0 0
\(583\) −968.123 558.946i −1.66059 0.958742i
\(584\) 0 0
\(585\) −894.996 + 35.1106i −1.52991 + 0.0600181i
\(586\) 0 0
\(587\) −860.561 −1.46603 −0.733016 0.680211i \(-0.761888\pi\)
−0.733016 + 0.680211i \(0.761888\pi\)
\(588\) 0 0
\(589\) 88.1051 33.4368i 0.149584 0.0567687i
\(590\) 0 0
\(591\) −84.3768 + 341.546i −0.142770 + 0.577912i
\(592\) 0 0
\(593\) 258.516 + 447.763i 0.435946 + 0.755081i 0.997372 0.0724456i \(-0.0230804\pi\)
−0.561426 + 0.827527i \(0.689747\pi\)
\(594\) 0 0
\(595\) −119.289 206.615i −0.200486 0.347252i
\(596\) 0 0
\(597\) −652.193 + 188.533i −1.09245 + 0.315801i
\(598\) 0 0
\(599\) 995.005i 1.66111i −0.556936 0.830555i \(-0.688023\pi\)
0.556936 0.830555i \(-0.311977\pi\)
\(600\) 0 0
\(601\) 1005.66 580.617i 1.67331 0.966085i 0.707542 0.706672i \(-0.249804\pi\)
0.965766 0.259413i \(-0.0835292\pi\)
\(602\) 0 0
\(603\) −334.567 + 635.815i −0.554838 + 1.05442i
\(604\) 0 0
\(605\) 217.346 0.359249
\(606\) 0 0
\(607\) −272.695 157.440i −0.449250 0.259375i 0.258263 0.966075i \(-0.416850\pi\)
−0.707513 + 0.706700i \(0.750183\pi\)
\(608\) 0 0
\(609\) 454.441 + 112.267i 0.746209 + 0.184346i
\(610\) 0 0
\(611\) 418.097 + 241.388i 0.684283 + 0.395071i
\(612\) 0 0
\(613\) 1.68671 2.92147i 0.00275157 0.00476586i −0.864646 0.502381i \(-0.832457\pi\)
0.867398 + 0.497615i \(0.165791\pi\)
\(614\) 0 0
\(615\) 270.152 280.957i 0.439271 0.456841i
\(616\) 0 0
\(617\) 85.9129 0.139243 0.0696215 0.997573i \(-0.477821\pi\)
0.0696215 + 0.997573i \(0.477821\pi\)
\(618\) 0 0
\(619\) −174.074 301.505i −0.281218 0.487084i 0.690467 0.723364i \(-0.257405\pi\)
−0.971685 + 0.236280i \(0.924072\pi\)
\(620\) 0 0
\(621\) −784.106 + 882.223i −1.26265 + 1.42065i
\(622\) 0 0
\(623\) 12.1370 + 7.00730i 0.0194815 + 0.0112477i
\(624\) 0 0
\(625\) 152.823 + 264.698i 0.244517 + 0.423516i
\(626\) 0 0
\(627\) 296.503 695.327i 0.472891 1.10898i
\(628\) 0 0
\(629\) −237.070 136.872i −0.376899 0.217603i
\(630\) 0 0
\(631\) 178.654 + 309.437i 0.283128 + 0.490391i 0.972153 0.234345i \(-0.0752947\pi\)
−0.689026 + 0.724737i \(0.741961\pi\)
\(632\) 0 0
\(633\) −100.436 347.438i −0.158666 0.548876i
\(634\) 0 0
\(635\) 452.922 + 261.495i 0.713263 + 0.411803i
\(636\) 0 0
\(637\) 387.008 + 223.439i 0.607548 + 0.350768i
\(638\) 0 0
\(639\) 352.182 + 558.250i 0.551146 + 0.873630i
\(640\) 0 0
\(641\) 142.047i 0.221603i −0.993843 0.110801i \(-0.964658\pi\)
0.993843 0.110801i \(-0.0353417\pi\)
\(642\) 0 0
\(643\) −435.578 754.443i −0.677415 1.17332i −0.975757 0.218858i \(-0.929767\pi\)
0.298342 0.954459i \(-0.403566\pi\)
\(644\) 0 0
\(645\) −455.663 + 131.721i −0.706455 + 0.204219i
\(646\) 0 0
\(647\) 594.022 0.918117 0.459058 0.888406i \(-0.348187\pi\)
0.459058 + 0.888406i \(0.348187\pi\)
\(648\) 0 0
\(649\) 160.643 + 92.7475i 0.247525 + 0.142908i
\(650\) 0 0
\(651\) −80.7028 19.9371i −0.123967 0.0306254i
\(652\) 0 0
\(653\) −391.470 + 678.046i −0.599495 + 1.03836i 0.393401 + 0.919367i \(0.371298\pi\)
−0.992896 + 0.118988i \(0.962035\pi\)
\(654\) 0 0
\(655\) 197.208 341.575i 0.301081 0.521488i
\(656\) 0 0
\(657\) −757.807 + 478.077i −1.15344 + 0.727667i
\(658\) 0 0
\(659\) −184.847 106.722i −0.280497 0.161945i 0.353152 0.935566i \(-0.385110\pi\)
−0.633648 + 0.773621i \(0.718443\pi\)
\(660\) 0 0
\(661\) 476.262i 0.720517i 0.932852 + 0.360259i \(0.117312\pi\)
−0.932852 + 0.360259i \(0.882688\pi\)
\(662\) 0 0
\(663\) −563.160 + 585.686i −0.849412 + 0.883387i
\(664\) 0 0
\(665\) −149.196 393.129i −0.224356 0.591172i
\(666\) 0 0
\(667\) 1057.35 + 610.462i 1.58523 + 0.915236i
\(668\) 0 0
\(669\) −198.467 49.0300i −0.296662 0.0732884i
\(670\) 0 0
\(671\) 840.823 1.25309
\(672\) 0 0
\(673\) 1023.15 590.714i 1.52028 0.877732i 0.520563 0.853823i \(-0.325722\pi\)
0.999714 0.0239093i \(-0.00761130\pi\)
\(674\) 0 0
\(675\) −79.2049 238.518i −0.117341 0.353360i
\(676\) 0 0
\(677\) 1014.38 585.651i 1.49834 0.865067i 0.498342 0.866980i \(-0.333942\pi\)
0.999998 + 0.00191292i \(0.000608900\pi\)
\(678\) 0 0
\(679\) 374.617 216.285i 0.551719 0.318535i
\(680\) 0 0
\(681\) 52.6962 + 182.292i 0.0773806 + 0.267683i
\(682\) 0 0
\(683\) 795.560i 1.16480i 0.812902 + 0.582401i \(0.197887\pi\)
−0.812902 + 0.582401i \(0.802113\pi\)
\(684\) 0 0
\(685\) 432.095 0.630796
\(686\) 0 0
\(687\) −233.501 224.520i −0.339885 0.326812i
\(688\) 0 0
\(689\) 1058.90 + 1834.07i 1.53687 + 2.66193i
\(690\) 0 0
\(691\) 278.681 + 482.690i 0.403302 + 0.698539i 0.994122 0.108264i \(-0.0345292\pi\)
−0.590820 + 0.806803i \(0.701196\pi\)
\(692\) 0 0
\(693\) −563.960 + 355.785i −0.813794 + 0.513398i
\(694\) 0 0
\(695\) −8.35055 14.4636i −0.0120152 0.0208109i
\(696\) 0 0
\(697\) 353.575i 0.507281i
\(698\) 0 0
\(699\) 873.580 + 839.981i 1.24976 + 1.20169i
\(700\) 0 0
\(701\) 394.685 683.614i 0.563031 0.975198i −0.434199 0.900817i \(-0.642968\pi\)
0.997230 0.0743813i \(-0.0236982\pi\)
\(702\) 0 0
\(703\) −373.791 305.049i −0.531708 0.433925i
\(704\) 0 0
\(705\) 54.7689 221.697i 0.0776864 0.314464i
\(706\) 0 0
\(707\) −334.836 −0.473601
\(708\) 0 0
\(709\) −596.941 + 1033.93i −0.841948 + 1.45830i 0.0462968 + 0.998928i \(0.485258\pi\)
−0.888245 + 0.459370i \(0.848075\pi\)
\(710\) 0 0
\(711\) −332.319 + 631.542i −0.467396 + 0.888244i
\(712\) 0 0
\(713\) −187.772 108.410i −0.263354 0.152048i
\(714\) 0 0
\(715\) −1142.97 659.896i −1.59856 0.922931i
\(716\) 0 0
\(717\) −507.259 487.750i −0.707475 0.680265i
\(718\) 0 0
\(719\) −171.089 + 296.335i −0.237954 + 0.412148i −0.960127 0.279564i \(-0.909810\pi\)
0.722173 + 0.691712i \(0.243143\pi\)
\(720\) 0 0
\(721\) 621.042i 0.861363i
\(722\) 0 0
\(723\) −207.655 + 215.961i −0.287213 + 0.298701i
\(724\) 0 0
\(725\) −225.143 + 129.986i −0.310542 + 0.179291i
\(726\) 0 0
\(727\) 541.308 0.744577 0.372289 0.928117i \(-0.378573\pi\)
0.372289 + 0.928117i \(0.378573\pi\)
\(728\) 0 0
\(729\) −85.5542 723.962i −0.117358 0.993090i
\(730\) 0 0
\(731\) −215.138 + 372.630i −0.294306 + 0.509753i
\(732\) 0 0
\(733\) 642.502 1112.85i 0.876538 1.51821i 0.0214218 0.999771i \(-0.493181\pi\)
0.855116 0.518437i \(-0.173486\pi\)
\(734\) 0 0
\(735\) 50.6964 205.212i 0.0689747 0.279200i
\(736\) 0 0
\(737\) −916.830 + 529.332i −1.24400 + 0.718225i
\(738\) 0 0
\(739\) 371.062 642.698i 0.502113 0.869686i −0.497884 0.867244i \(-0.665889\pi\)
0.999997 0.00244211i \(-0.000777349\pi\)
\(740\) 0 0
\(741\) −1145.09 + 859.932i −1.54533 + 1.16050i
\(742\) 0 0
\(743\) 455.142 262.776i 0.612573 0.353669i −0.161399 0.986889i \(-0.551600\pi\)
0.773972 + 0.633220i \(0.218267\pi\)
\(744\) 0 0
\(745\) −527.134 + 913.023i −0.707563 + 1.22553i
\(746\) 0 0
\(747\) −7.00173 178.480i −0.00937314 0.238928i
\(748\) 0 0
\(749\) 190.218 109.822i 0.253962 0.146625i
\(750\) 0 0
\(751\) 168.525i 0.224401i 0.993686 + 0.112200i \(0.0357898\pi\)
−0.993686 + 0.112200i \(0.964210\pi\)
\(752\) 0 0
\(753\) −315.627 + 91.2399i −0.419159 + 0.121168i
\(754\) 0 0
\(755\) 788.435 + 455.203i 1.04429 + 0.602918i
\(756\) 0 0
\(757\) 510.495 884.204i 0.674366 1.16804i −0.302287 0.953217i \(-0.597750\pi\)
0.976654 0.214820i \(-0.0689164\pi\)
\(758\) 0 0
\(759\) −1670.78 + 482.983i −2.20130 + 0.636341i
\(760\) 0 0
\(761\) −505.546 + 875.632i −0.664318 + 1.15063i 0.315151 + 0.949041i \(0.397945\pi\)
−0.979470 + 0.201592i \(0.935389\pi\)
\(762\) 0 0
\(763\) 64.4098i 0.0844165i
\(764\) 0 0
\(765\) 340.120 + 178.972i 0.444601 + 0.233950i
\(766\) 0 0
\(767\) −175.706 304.332i −0.229083 0.396783i
\(768\) 0 0
\(769\) −56.6415 −0.0736560 −0.0368280 0.999322i \(-0.511725\pi\)
−0.0368280 + 0.999322i \(0.511725\pi\)
\(770\) 0 0
\(771\) −722.880 178.583i −0.937588 0.231625i
\(772\) 0 0
\(773\) −1027.30 + 593.110i −1.32897 + 0.767283i −0.985141 0.171749i \(-0.945058\pi\)
−0.343832 + 0.939031i \(0.611725\pi\)
\(774\) 0 0
\(775\) 39.9824 23.0838i 0.0515901 0.0297856i
\(776\) 0 0
\(777\) 118.191 + 408.859i 0.152112 + 0.526202i
\(778\) 0 0
\(779\) 99.8229 615.119i 0.128142 0.789626i
\(780\) 0 0
\(781\) 972.595i 1.24532i
\(782\) 0 0
\(783\) −715.656 + 237.649i −0.913993 + 0.303511i
\(784\) 0 0
\(785\) −264.403 + 457.959i −0.336818 + 0.583387i
\(786\) 0 0
\(787\) 574.530 + 331.705i 0.730026 + 0.421481i 0.818432 0.574604i \(-0.194844\pi\)
−0.0884057 + 0.996085i \(0.528177\pi\)
\(788\) 0 0
\(789\) 333.441 1349.72i 0.422612 1.71068i
\(790\) 0 0
\(791\) 361.890i 0.457509i
\(792\) 0 0
\(793\) −1379.49 796.451i −1.73959 1.00435i
\(794\) 0 0
\(795\) 694.328 722.100i 0.873368 0.908302i
\(796\) 0 0
\(797\) 31.4026 + 18.1303i 0.0394010 +