Properties

Label 1152.2.p.f.959.11
Level $1152$
Weight $2$
Character 1152.959
Analytic conductor $9.199$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.p (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 959.11
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.f.191.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.54472 - 0.783472i) q^{3} +(-1.07112 + 1.85524i) q^{5} +(-1.13037 + 0.652621i) q^{7} +(1.77234 - 2.42050i) q^{9} +O(q^{10})\) \(q+(1.54472 - 0.783472i) q^{3} +(-1.07112 + 1.85524i) q^{5} +(-1.13037 + 0.652621i) q^{7} +(1.77234 - 2.42050i) q^{9} +(2.36103 - 1.36314i) q^{11} +(1.16603 + 0.673209i) q^{13} +(-0.201060 + 3.70502i) q^{15} +4.27575i q^{17} +2.16174 q^{19} +(-1.23480 + 1.89374i) q^{21} +(1.01947 - 1.76577i) q^{23} +(0.205398 + 0.355759i) q^{25} +(0.841387 - 5.12758i) q^{27} +(2.72776 + 4.72461i) q^{29} +(6.09216 + 3.51731i) q^{31} +(2.57915 - 3.95547i) q^{33} -2.79615i q^{35} -10.3381i q^{37} +(2.32864 + 0.126368i) q^{39} +(0.596355 + 0.344306i) q^{41} +(1.22839 + 2.12763i) q^{43} +(2.59220 + 5.88076i) q^{45} +(6.56713 + 11.3746i) q^{47} +(-2.64817 + 4.58677i) q^{49} +(3.34993 + 6.60485i) q^{51} -9.56171 q^{53} +5.84035i q^{55} +(3.33929 - 1.69366i) q^{57} +(8.97985 + 5.18452i) q^{59} +(7.68757 - 4.43842i) q^{61} +(-0.423741 + 3.89273i) q^{63} +(-2.49793 + 1.44218i) q^{65} +(6.23532 - 10.7999i) q^{67} +(0.191364 - 3.52635i) q^{69} -4.94992 q^{71} -12.8268 q^{73} +(0.596010 + 0.388627i) q^{75} +(-1.77923 + 3.08171i) q^{77} +(-0.680856 + 0.393093i) q^{79} +(-2.71761 - 8.57990i) q^{81} +(-1.82152 + 1.05165i) q^{83} +(-7.93253 - 4.57985i) q^{85} +(7.91523 + 5.16110i) q^{87} +12.1722i q^{89} -1.75740 q^{91} +(12.1664 + 0.660234i) q^{93} +(-2.31548 + 4.01053i) q^{95} +(-8.05440 - 13.9506i) q^{97} +(0.885074 - 8.13081i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{7} - 4q^{9} + O(q^{10}) \) \( 24q - 12q^{7} - 4q^{9} - 20q^{15} + 12q^{23} - 12q^{25} + 36q^{31} + 4q^{33} - 20q^{39} - 12q^{41} - 12q^{47} + 12q^{49} + 4q^{57} + 92q^{63} - 48q^{65} + 24q^{73} - 84q^{79} - 20q^{81} - 68q^{87} - 24q^{95} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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
\(3\) 1.54472 0.783472i 0.891847 0.452338i
\(4\) 0 0
\(5\) −1.07112 + 1.85524i −0.479020 + 0.829687i −0.999711 0.0240584i \(-0.992341\pi\)
0.520690 + 0.853746i \(0.325675\pi\)
\(6\) 0 0
\(7\) −1.13037 + 0.652621i −0.427241 + 0.246668i −0.698170 0.715932i \(-0.746002\pi\)
0.270930 + 0.962599i \(0.412669\pi\)
\(8\) 0 0
\(9\) 1.77234 2.42050i 0.590781 0.806832i
\(10\) 0 0
\(11\) 2.36103 1.36314i 0.711876 0.411002i −0.0998790 0.995000i \(-0.531846\pi\)
0.811755 + 0.583998i \(0.198512\pi\)
\(12\) 0 0
\(13\) 1.16603 + 0.673209i 0.323399 + 0.186715i 0.652907 0.757438i \(-0.273549\pi\)
−0.329507 + 0.944153i \(0.606883\pi\)
\(14\) 0 0
\(15\) −0.201060 + 3.70502i −0.0519135 + 0.956633i
\(16\) 0 0
\(17\) 4.27575i 1.03702i 0.855071 + 0.518511i \(0.173513\pi\)
−0.855071 + 0.518511i \(0.826487\pi\)
\(18\) 0 0
\(19\) 2.16174 0.495937 0.247968 0.968768i \(-0.420237\pi\)
0.247968 + 0.968768i \(0.420237\pi\)
\(20\) 0 0
\(21\) −1.23480 + 1.89374i −0.269456 + 0.413247i
\(22\) 0 0
\(23\) 1.01947 1.76577i 0.212573 0.368188i −0.739946 0.672666i \(-0.765149\pi\)
0.952519 + 0.304479i \(0.0984822\pi\)
\(24\) 0 0
\(25\) 0.205398 + 0.355759i 0.0410796 + 0.0711519i
\(26\) 0 0
\(27\) 0.841387 5.12758i 0.161925 0.986803i
\(28\) 0 0
\(29\) 2.72776 + 4.72461i 0.506531 + 0.877338i 0.999971 + 0.00755840i \(0.00240594\pi\)
−0.493440 + 0.869780i \(0.664261\pi\)
\(30\) 0 0
\(31\) 6.09216 + 3.51731i 1.09418 + 0.631728i 0.934688 0.355470i \(-0.115679\pi\)
0.159497 + 0.987198i \(0.449013\pi\)
\(32\) 0 0
\(33\) 2.57915 3.95547i 0.448973 0.688559i
\(34\) 0 0
\(35\) 2.79615i 0.472635i
\(36\) 0 0
\(37\) 10.3381i 1.69957i −0.527126 0.849787i \(-0.676731\pi\)
0.527126 0.849787i \(-0.323269\pi\)
\(38\) 0 0
\(39\) 2.32864 + 0.126368i 0.372881 + 0.0202351i
\(40\) 0 0
\(41\) 0.596355 + 0.344306i 0.0931350 + 0.0537715i 0.545844 0.837887i \(-0.316209\pi\)
−0.452709 + 0.891658i \(0.649542\pi\)
\(42\) 0 0
\(43\) 1.22839 + 2.12763i 0.187327 + 0.324460i 0.944358 0.328919i \(-0.106684\pi\)
−0.757031 + 0.653379i \(0.773351\pi\)
\(44\) 0 0
\(45\) 2.59220 + 5.88076i 0.386422 + 0.876652i
\(46\) 0 0
\(47\) 6.56713 + 11.3746i 0.957914 + 1.65916i 0.727555 + 0.686049i \(0.240657\pi\)
0.230359 + 0.973106i \(0.426010\pi\)
\(48\) 0 0
\(49\) −2.64817 + 4.58677i −0.378310 + 0.655252i
\(50\) 0 0
\(51\) 3.34993 + 6.60485i 0.469084 + 0.924864i
\(52\) 0 0
\(53\) −9.56171 −1.31340 −0.656701 0.754151i \(-0.728049\pi\)
−0.656701 + 0.754151i \(0.728049\pi\)
\(54\) 0 0
\(55\) 5.84035i 0.787513i
\(56\) 0 0
\(57\) 3.33929 1.69366i 0.442299 0.224331i
\(58\) 0 0
\(59\) 8.97985 + 5.18452i 1.16908 + 0.674967i 0.953463 0.301512i \(-0.0974912\pi\)
0.215615 + 0.976479i \(0.430825\pi\)
\(60\) 0 0
\(61\) 7.68757 4.43842i 0.984292 0.568281i 0.0807290 0.996736i \(-0.474275\pi\)
0.903563 + 0.428455i \(0.140942\pi\)
\(62\) 0 0
\(63\) −0.423741 + 3.89273i −0.0533863 + 0.490438i
\(64\) 0 0
\(65\) −2.49793 + 1.44218i −0.309829 + 0.178880i
\(66\) 0 0
\(67\) 6.23532 10.7999i 0.761766 1.31942i −0.180174 0.983635i \(-0.557666\pi\)
0.941940 0.335782i \(-0.109001\pi\)
\(68\) 0 0
\(69\) 0.191364 3.52635i 0.0230375 0.424522i
\(70\) 0 0
\(71\) −4.94992 −0.587448 −0.293724 0.955890i \(-0.594895\pi\)
−0.293724 + 0.955890i \(0.594895\pi\)
\(72\) 0 0
\(73\) −12.8268 −1.50126 −0.750630 0.660723i \(-0.770250\pi\)
−0.750630 + 0.660723i \(0.770250\pi\)
\(74\) 0 0
\(75\) 0.596010 + 0.388627i 0.0688214 + 0.0448747i
\(76\) 0 0
\(77\) −1.77923 + 3.08171i −0.202762 + 0.351194i
\(78\) 0 0
\(79\) −0.680856 + 0.393093i −0.0766023 + 0.0442264i −0.537812 0.843065i \(-0.680749\pi\)
0.461210 + 0.887291i \(0.347416\pi\)
\(80\) 0 0
\(81\) −2.71761 8.57990i −0.301956 0.953322i
\(82\) 0 0
\(83\) −1.82152 + 1.05165i −0.199938 + 0.115434i −0.596626 0.802519i \(-0.703493\pi\)
0.396689 + 0.917953i \(0.370159\pi\)
\(84\) 0 0
\(85\) −7.93253 4.57985i −0.860404 0.496754i
\(86\) 0 0
\(87\) 7.91523 + 5.16110i 0.848602 + 0.553328i
\(88\) 0 0
\(89\) 12.1722i 1.29025i 0.764077 + 0.645125i \(0.223195\pi\)
−0.764077 + 0.645125i \(0.776805\pi\)
\(90\) 0 0
\(91\) −1.75740 −0.184226
\(92\) 0 0
\(93\) 12.1664 + 0.660234i 1.26160 + 0.0684631i
\(94\) 0 0
\(95\) −2.31548 + 4.01053i −0.237564 + 0.411472i
\(96\) 0 0
\(97\) −8.05440 13.9506i −0.817801 1.41647i −0.907299 0.420485i \(-0.861860\pi\)
0.0894986 0.995987i \(-0.471474\pi\)
\(98\) 0 0
\(99\) 0.885074 8.13081i 0.0889533 0.817177i
\(100\) 0 0
\(101\) −7.26875 12.5898i −0.723267 1.25274i −0.959683 0.281084i \(-0.909306\pi\)
0.236416 0.971652i \(-0.424027\pi\)
\(102\) 0 0
\(103\) 3.14001 + 1.81289i 0.309395 + 0.178629i 0.646656 0.762782i \(-0.276167\pi\)
−0.337261 + 0.941411i \(0.609500\pi\)
\(104\) 0 0
\(105\) −2.19070 4.31927i −0.213791 0.421518i
\(106\) 0 0
\(107\) 11.6508i 1.12632i −0.826347 0.563161i \(-0.809585\pi\)
0.826347 0.563161i \(-0.190415\pi\)
\(108\) 0 0
\(109\) 6.96341i 0.666974i −0.942755 0.333487i \(-0.891775\pi\)
0.942755 0.333487i \(-0.108225\pi\)
\(110\) 0 0
\(111\) −8.09962 15.9695i −0.768782 1.51576i
\(112\) 0 0
\(113\) 11.7540 + 6.78616i 1.10572 + 0.638388i 0.937718 0.347398i \(-0.112935\pi\)
0.168003 + 0.985786i \(0.446268\pi\)
\(114\) 0 0
\(115\) 2.18394 + 3.78270i 0.203654 + 0.352739i
\(116\) 0 0
\(117\) 3.69611 1.62922i 0.341705 0.150621i
\(118\) 0 0
\(119\) −2.79045 4.83319i −0.255800 0.443058i
\(120\) 0 0
\(121\) −1.78370 + 3.08946i −0.162155 + 0.280860i
\(122\) 0 0
\(123\) 1.19096 + 0.0646296i 0.107385 + 0.00582745i
\(124\) 0 0
\(125\) −11.5912 −1.03675
\(126\) 0 0
\(127\) 22.0340i 1.95520i −0.210465 0.977601i \(-0.567498\pi\)
0.210465 0.977601i \(-0.432502\pi\)
\(128\) 0 0
\(129\) 3.56446 + 2.32419i 0.313833 + 0.204634i
\(130\) 0 0
\(131\) −1.64258 0.948346i −0.143513 0.0828573i 0.426524 0.904476i \(-0.359738\pi\)
−0.570037 + 0.821619i \(0.693071\pi\)
\(132\) 0 0
\(133\) −2.44357 + 1.41080i −0.211884 + 0.122331i
\(134\) 0 0
\(135\) 8.61165 + 7.05323i 0.741172 + 0.607046i
\(136\) 0 0
\(137\) 2.63976 1.52407i 0.225530 0.130210i −0.382978 0.923757i \(-0.625102\pi\)
0.608508 + 0.793548i \(0.291768\pi\)
\(138\) 0 0
\(139\) 1.82552 3.16190i 0.154839 0.268189i −0.778161 0.628064i \(-0.783848\pi\)
0.933000 + 0.359875i \(0.117181\pi\)
\(140\) 0 0
\(141\) 19.0561 + 12.4254i 1.60481 + 1.04641i
\(142\) 0 0
\(143\) 3.67071 0.306960
\(144\) 0 0
\(145\) −11.6870 −0.970555
\(146\) 0 0
\(147\) −0.497088 + 9.16006i −0.0409991 + 0.755509i
\(148\) 0 0
\(149\) −6.98401 + 12.0967i −0.572153 + 0.990997i 0.424192 + 0.905572i \(0.360558\pi\)
−0.996345 + 0.0854250i \(0.972775\pi\)
\(150\) 0 0
\(151\) −19.4354 + 11.2211i −1.58163 + 0.913156i −0.587012 + 0.809578i \(0.699696\pi\)
−0.994621 + 0.103578i \(0.966971\pi\)
\(152\) 0 0
\(153\) 10.3494 + 7.57809i 0.836702 + 0.612653i
\(154\) 0 0
\(155\) −13.0509 + 7.53494i −1.04827 + 0.605221i
\(156\) 0 0
\(157\) 2.67761 + 1.54592i 0.213697 + 0.123378i 0.603028 0.797720i \(-0.293961\pi\)
−0.389332 + 0.921098i \(0.627294\pi\)
\(158\) 0 0
\(159\) −14.7702 + 7.49133i −1.17135 + 0.594101i
\(160\) 0 0
\(161\) 2.66130i 0.209740i
\(162\) 0 0
\(163\) −10.4313 −0.817042 −0.408521 0.912749i \(-0.633955\pi\)
−0.408521 + 0.912749i \(0.633955\pi\)
\(164\) 0 0
\(165\) 4.57575 + 9.02173i 0.356222 + 0.702341i
\(166\) 0 0
\(167\) 6.50275 11.2631i 0.503198 0.871564i −0.496795 0.867868i \(-0.665490\pi\)
0.999993 0.00369641i \(-0.00117661\pi\)
\(168\) 0 0
\(169\) −5.59358 9.68836i −0.430275 0.745259i
\(170\) 0 0
\(171\) 3.83134 5.23248i 0.292990 0.400138i
\(172\) 0 0
\(173\) 2.69963 + 4.67590i 0.205249 + 0.355502i 0.950212 0.311604i \(-0.100866\pi\)
−0.744963 + 0.667106i \(0.767533\pi\)
\(174\) 0 0
\(175\) −0.464352 0.268094i −0.0351017 0.0202660i
\(176\) 0 0
\(177\) 17.9333 + 0.973185i 1.34795 + 0.0731491i
\(178\) 0 0
\(179\) 4.69284i 0.350759i 0.984501 + 0.175380i \(0.0561153\pi\)
−0.984501 + 0.175380i \(0.943885\pi\)
\(180\) 0 0
\(181\) 6.33810i 0.471108i −0.971861 0.235554i \(-0.924310\pi\)
0.971861 0.235554i \(-0.0756904\pi\)
\(182\) 0 0
\(183\) 8.39779 12.8791i 0.620783 0.952053i
\(184\) 0 0
\(185\) 19.1796 + 11.0734i 1.41011 + 0.814130i
\(186\) 0 0
\(187\) 5.82844 + 10.0952i 0.426218 + 0.738231i
\(188\) 0 0
\(189\) 2.39529 + 6.34518i 0.174231 + 0.461544i
\(190\) 0 0
\(191\) −1.26279 2.18721i −0.0913720 0.158261i 0.816717 0.577039i \(-0.195792\pi\)
−0.908089 + 0.418778i \(0.862459\pi\)
\(192\) 0 0
\(193\) −5.77236 + 9.99802i −0.415504 + 0.719673i −0.995481 0.0949590i \(-0.969728\pi\)
0.579978 + 0.814632i \(0.303061\pi\)
\(194\) 0 0
\(195\) −2.72870 + 4.18482i −0.195406 + 0.299681i
\(196\) 0 0
\(197\) −2.44368 −0.174105 −0.0870526 0.996204i \(-0.527745\pi\)
−0.0870526 + 0.996204i \(0.527745\pi\)
\(198\) 0 0
\(199\) 5.28327i 0.374521i 0.982310 + 0.187261i \(0.0599609\pi\)
−0.982310 + 0.187261i \(0.940039\pi\)
\(200\) 0 0
\(201\) 1.17043 21.5680i 0.0825558 1.52129i
\(202\) 0 0
\(203\) −6.16676 3.56038i −0.432822 0.249890i
\(204\) 0 0
\(205\) −1.27754 + 0.737586i −0.0892270 + 0.0515153i
\(206\) 0 0
\(207\) −2.46719 5.59716i −0.171482 0.389029i
\(208\) 0 0
\(209\) 5.10392 2.94675i 0.353046 0.203831i
\(210\) 0 0
\(211\) −7.23279 + 12.5276i −0.497926 + 0.862432i −0.999997 0.00239362i \(-0.999238\pi\)
0.502072 + 0.864826i \(0.332571\pi\)
\(212\) 0 0
\(213\) −7.64626 + 3.87813i −0.523913 + 0.265725i
\(214\) 0 0
\(215\) −5.26300 −0.358934
\(216\) 0 0
\(217\) −9.18189 −0.623307
\(218\) 0 0
\(219\) −19.8138 + 10.0494i −1.33889 + 0.679076i
\(220\) 0 0
\(221\) −2.87847 + 4.98566i −0.193627 + 0.335372i
\(222\) 0 0
\(223\) 16.6575 9.61719i 1.11547 0.644015i 0.175227 0.984528i \(-0.443934\pi\)
0.940240 + 0.340513i \(0.110601\pi\)
\(224\) 0 0
\(225\) 1.22515 + 0.133363i 0.0816766 + 0.00889086i
\(226\) 0 0
\(227\) 0.503060 0.290442i 0.0333893 0.0192773i −0.483212 0.875503i \(-0.660530\pi\)
0.516602 + 0.856226i \(0.327197\pi\)
\(228\) 0 0
\(229\) −7.78703 4.49584i −0.514581 0.297094i 0.220134 0.975470i \(-0.429351\pi\)
−0.734715 + 0.678376i \(0.762684\pi\)
\(230\) 0 0
\(231\) −0.333978 + 6.15437i −0.0219742 + 0.404928i
\(232\) 0 0
\(233\) 1.68699i 0.110518i −0.998472 0.0552592i \(-0.982401\pi\)
0.998472 0.0552592i \(-0.0175985\pi\)
\(234\) 0 0
\(235\) −28.1368 −1.83544
\(236\) 0 0
\(237\) −0.743758 + 1.14065i −0.0483122 + 0.0740933i
\(238\) 0 0
\(239\) −1.75123 + 3.03323i −0.113278 + 0.196203i −0.917090 0.398680i \(-0.869468\pi\)
0.803812 + 0.594883i \(0.202802\pi\)
\(240\) 0 0
\(241\) 1.18735 + 2.05655i 0.0764837 + 0.132474i 0.901731 0.432299i \(-0.142297\pi\)
−0.825247 + 0.564772i \(0.808964\pi\)
\(242\) 0 0
\(243\) −10.9201 11.1244i −0.700522 0.713631i
\(244\) 0 0
\(245\) −5.67303 9.82597i −0.362436 0.627758i
\(246\) 0 0
\(247\) 2.52066 + 1.45530i 0.160386 + 0.0925986i
\(248\) 0 0
\(249\) −1.98980 + 3.05163i −0.126099 + 0.193389i
\(250\) 0 0
\(251\) 16.4883i 1.04073i 0.853942 + 0.520367i \(0.174205\pi\)
−0.853942 + 0.520367i \(0.825795\pi\)
\(252\) 0 0
\(253\) 5.55870i 0.349472i
\(254\) 0 0
\(255\) −15.8417 0.859683i −0.992049 0.0538354i
\(256\) 0 0
\(257\) 1.98224 + 1.14444i 0.123649 + 0.0713885i 0.560549 0.828122i \(-0.310590\pi\)
−0.436900 + 0.899510i \(0.643924\pi\)
\(258\) 0 0
\(259\) 6.74687 + 11.6859i 0.419230 + 0.726127i
\(260\) 0 0
\(261\) 16.2704 + 1.77111i 1.00711 + 0.109629i
\(262\) 0 0
\(263\) −14.5336 25.1729i −0.896179 1.55223i −0.832339 0.554267i \(-0.812999\pi\)
−0.0638398 0.997960i \(-0.520335\pi\)
\(264\) 0 0
\(265\) 10.2417 17.7392i 0.629146 1.08971i
\(266\) 0 0
\(267\) 9.53658 + 18.8027i 0.583629 + 1.15070i
\(268\) 0 0
\(269\) −11.4025 −0.695223 −0.347612 0.937639i \(-0.613007\pi\)
−0.347612 + 0.937639i \(0.613007\pi\)
\(270\) 0 0
\(271\) 28.9854i 1.76074i −0.474287 0.880370i \(-0.657294\pi\)
0.474287 0.880370i \(-0.342706\pi\)
\(272\) 0 0
\(273\) −2.71470 + 1.37688i −0.164301 + 0.0833323i
\(274\) 0 0
\(275\) 0.969899 + 0.559972i 0.0584871 + 0.0337676i
\(276\) 0 0
\(277\) 20.1047 11.6075i 1.20798 0.697425i 0.245659 0.969356i \(-0.420996\pi\)
0.962317 + 0.271931i \(0.0876622\pi\)
\(278\) 0 0
\(279\) 19.3110 8.51218i 1.15612 0.509611i
\(280\) 0 0
\(281\) −12.7582 + 7.36593i −0.761088 + 0.439415i −0.829686 0.558230i \(-0.811481\pi\)
0.0685980 + 0.997644i \(0.478147\pi\)
\(282\) 0 0
\(283\) 12.4785 21.6134i 0.741770 1.28478i −0.209919 0.977719i \(-0.567320\pi\)
0.951689 0.307065i \(-0.0993468\pi\)
\(284\) 0 0
\(285\) −0.434639 + 8.00928i −0.0257458 + 0.474429i
\(286\) 0 0
\(287\) −0.898805 −0.0530548
\(288\) 0 0
\(289\) −1.28204 −0.0754142
\(290\) 0 0
\(291\) −23.3718 15.2395i −1.37008 0.893354i
\(292\) 0 0
\(293\) −11.0395 + 19.1210i −0.644934 + 1.11706i 0.339382 + 0.940648i \(0.389782\pi\)
−0.984317 + 0.176410i \(0.943551\pi\)
\(294\) 0 0
\(295\) −19.2370 + 11.1065i −1.12002 + 0.646645i
\(296\) 0 0
\(297\) −5.00307 13.2533i −0.290307 0.769033i
\(298\) 0 0
\(299\) 2.37746 1.37263i 0.137492 0.0793811i
\(300\) 0 0
\(301\) −2.77707 1.60334i −0.160068 0.0924151i
\(302\) 0 0
\(303\) −21.0920 13.7530i −1.21170 0.790087i
\(304\) 0 0
\(305\) 19.0163i 1.08887i
\(306\) 0 0
\(307\) −28.0180 −1.59907 −0.799535 0.600619i \(-0.794921\pi\)
−0.799535 + 0.600619i \(0.794921\pi\)
\(308\) 0 0
\(309\) 6.27080 + 0.340297i 0.356733 + 0.0193588i
\(310\) 0 0
\(311\) 6.78751 11.7563i 0.384884 0.666639i −0.606869 0.794802i \(-0.707575\pi\)
0.991753 + 0.128163i \(0.0409080\pi\)
\(312\) 0 0
\(313\) 13.9417 + 24.1478i 0.788034 + 1.36491i 0.927170 + 0.374641i \(0.122234\pi\)
−0.139136 + 0.990273i \(0.544433\pi\)
\(314\) 0 0
\(315\) −6.76806 4.95573i −0.381337 0.279224i
\(316\) 0 0
\(317\) 3.15169 + 5.45888i 0.177016 + 0.306601i 0.940857 0.338803i \(-0.110022\pi\)
−0.763841 + 0.645405i \(0.776689\pi\)
\(318\) 0 0
\(319\) 12.8806 + 7.43662i 0.721176 + 0.416371i
\(320\) 0 0
\(321\) −9.12805 17.9972i −0.509478 1.00451i
\(322\) 0 0
\(323\) 9.24305i 0.514297i
\(324\) 0 0
\(325\) 0.553103i 0.0306806i
\(326\) 0 0
\(327\) −5.45564 10.7565i −0.301698 0.594838i
\(328\) 0 0
\(329\) −14.8466 8.57169i −0.818520 0.472573i
\(330\) 0 0
\(331\) 0.733725 + 1.27085i 0.0403292 + 0.0698522i 0.885485 0.464667i \(-0.153826\pi\)
−0.845156 + 0.534519i \(0.820493\pi\)
\(332\) 0 0
\(333\) −25.0233 18.3227i −1.37127 1.00408i
\(334\) 0 0
\(335\) 13.3576 + 23.1360i 0.729802 + 1.26405i
\(336\) 0 0
\(337\) −1.25721 + 2.17756i −0.0684848 + 0.118619i −0.898235 0.439516i \(-0.855150\pi\)
0.829750 + 0.558136i \(0.188483\pi\)
\(338\) 0 0
\(339\) 23.4734 + 1.27383i 1.27490 + 0.0691849i
\(340\) 0 0
\(341\) 19.1783 1.03857
\(342\) 0 0
\(343\) 16.0497i 0.866603i
\(344\) 0 0
\(345\) 6.33723 + 4.13217i 0.341185 + 0.222468i
\(346\) 0 0
\(347\) −17.4849 10.0949i −0.938638 0.541923i −0.0491051 0.998794i \(-0.515637\pi\)
−0.889533 + 0.456871i \(0.848970\pi\)
\(348\) 0 0
\(349\) 6.58266 3.80050i 0.352362 0.203436i −0.313363 0.949633i \(-0.601456\pi\)
0.665725 + 0.746197i \(0.268122\pi\)
\(350\) 0 0
\(351\) 4.43302 5.41250i 0.236617 0.288898i
\(352\) 0 0
\(353\) −8.78534 + 5.07222i −0.467596 + 0.269967i −0.715233 0.698886i \(-0.753679\pi\)
0.247637 + 0.968853i \(0.420346\pi\)
\(354\) 0 0
\(355\) 5.30197 9.18328i 0.281399 0.487398i
\(356\) 0 0
\(357\) −8.09714 5.27971i −0.428546 0.279432i
\(358\) 0 0
\(359\) −20.5983 −1.08714 −0.543570 0.839364i \(-0.682928\pi\)
−0.543570 + 0.839364i \(0.682928\pi\)
\(360\) 0 0
\(361\) −14.3269 −0.754047
\(362\) 0 0
\(363\) −0.334818 + 6.16985i −0.0175734 + 0.323833i
\(364\) 0 0
\(365\) 13.7390 23.7967i 0.719133 1.24558i
\(366\) 0 0
\(367\) −11.1457 + 6.43498i −0.581802 + 0.335903i −0.761849 0.647755i \(-0.775708\pi\)
0.180047 + 0.983658i \(0.442375\pi\)
\(368\) 0 0
\(369\) 1.89034 0.833247i 0.0984069 0.0433771i
\(370\) 0 0
\(371\) 10.8083 6.24017i 0.561139 0.323974i
\(372\) 0 0
\(373\) 6.12551 + 3.53656i 0.317167 + 0.183116i 0.650129 0.759824i \(-0.274715\pi\)
−0.332962 + 0.942940i \(0.608048\pi\)
\(374\) 0 0
\(375\) −17.9053 + 9.08141i −0.924624 + 0.468962i
\(376\) 0 0
\(377\) 7.34540i 0.378307i
\(378\) 0 0
\(379\) 26.0887 1.34009 0.670043 0.742322i \(-0.266276\pi\)
0.670043 + 0.742322i \(0.266276\pi\)
\(380\) 0 0
\(381\) −17.2630 34.0365i −0.884412 1.74374i
\(382\) 0 0
\(383\) −9.84884 + 17.0587i −0.503252 + 0.871659i 0.496741 + 0.867899i \(0.334530\pi\)
−0.999993 + 0.00375959i \(0.998803\pi\)
\(384\) 0 0
\(385\) −3.81154 6.60178i −0.194254 0.336458i
\(386\) 0 0
\(387\) 7.32704 + 0.797580i 0.372454 + 0.0405433i
\(388\) 0 0
\(389\) 7.05645 + 12.2221i 0.357776 + 0.619687i 0.987589 0.157060i \(-0.0502017\pi\)
−0.629813 + 0.776747i \(0.716868\pi\)
\(390\) 0 0
\(391\) 7.54998 + 4.35898i 0.381819 + 0.220443i
\(392\) 0 0
\(393\) −3.28034 0.178014i −0.165471 0.00897961i
\(394\) 0 0
\(395\) 1.68420i 0.0847413i
\(396\) 0 0
\(397\) 17.1597i 0.861220i −0.902538 0.430610i \(-0.858298\pi\)
0.902538 0.430610i \(-0.141702\pi\)
\(398\) 0 0
\(399\) −2.66932 + 4.09376i −0.133633 + 0.204944i
\(400\) 0 0
\(401\) −21.5726 12.4549i −1.07728 0.621969i −0.147120 0.989119i \(-0.547000\pi\)
−0.930162 + 0.367149i \(0.880334\pi\)
\(402\) 0 0
\(403\) 4.73577 + 8.20260i 0.235906 + 0.408601i
\(404\) 0 0
\(405\) 18.8286 + 4.14831i 0.935602 + 0.206131i
\(406\) 0 0
\(407\) −14.0923 24.4085i −0.698528 1.20989i
\(408\) 0 0
\(409\) −7.64539 + 13.2422i −0.378040 + 0.654785i −0.990777 0.135502i \(-0.956735\pi\)
0.612737 + 0.790287i \(0.290069\pi\)
\(410\) 0 0
\(411\) 2.88364 4.42244i 0.142239 0.218143i
\(412\) 0 0
\(413\) −13.5341 −0.665970
\(414\) 0 0
\(415\) 4.50580i 0.221181i
\(416\) 0 0
\(417\) 0.342669 6.31451i 0.0167806 0.309223i
\(418\) 0 0
\(419\) 5.38781 + 3.11065i 0.263212 + 0.151965i 0.625799 0.779985i \(-0.284773\pi\)
−0.362587 + 0.931950i \(0.618106\pi\)
\(420\) 0 0
\(421\) 3.60960 2.08400i 0.175921 0.101568i −0.409454 0.912331i \(-0.634281\pi\)
0.585375 + 0.810763i \(0.300947\pi\)
\(422\) 0 0
\(423\) 39.1714 + 4.26397i 1.90458 + 0.207321i
\(424\) 0 0
\(425\) −1.52114 + 0.878230i −0.0737861 + 0.0426004i
\(426\) 0 0
\(427\) −5.79321 + 10.0341i −0.280353 + 0.485586i
\(428\) 0 0
\(429\) 5.67024 2.87590i 0.273762 0.138850i
\(430\) 0 0
\(431\) 34.3973 1.65686 0.828429 0.560094i \(-0.189235\pi\)
0.828429 + 0.560094i \(0.189235\pi\)
\(432\) 0 0
\(433\) 23.7319 1.14048 0.570241 0.821478i \(-0.306850\pi\)
0.570241 + 0.821478i \(0.306850\pi\)
\(434\) 0 0
\(435\) −18.0532 + 9.15646i −0.865586 + 0.439019i
\(436\) 0 0
\(437\) 2.20382 3.81712i 0.105423 0.182598i
\(438\) 0 0
\(439\) −28.5367 + 16.4757i −1.36198 + 0.786342i −0.989888 0.141852i \(-0.954694\pi\)
−0.372096 + 0.928194i \(0.621361\pi\)
\(440\) 0 0
\(441\) 6.40879 + 14.5392i 0.305180 + 0.692343i
\(442\) 0 0
\(443\) 3.04392 1.75741i 0.144621 0.0834969i −0.425944 0.904750i \(-0.640058\pi\)
0.570564 + 0.821253i \(0.306724\pi\)
\(444\) 0 0
\(445\) −22.5823 13.0379i −1.07050 0.618056i
\(446\) 0 0
\(447\) −1.31097 + 24.1578i −0.0620066 + 1.14262i
\(448\) 0 0
\(449\) 27.5711i 1.30116i −0.759437 0.650581i \(-0.774525\pi\)
0.759437 0.650581i \(-0.225475\pi\)
\(450\) 0 0
\(451\) 1.87735 0.0884008
\(452\) 0 0
\(453\) −21.2310 + 32.5606i −0.997519 + 1.52983i
\(454\) 0 0
\(455\) 1.88239 3.26040i 0.0882479 0.152850i
\(456\) 0 0
\(457\) −3.69999 6.40857i −0.173078 0.299780i 0.766416 0.642344i \(-0.222038\pi\)
−0.939494 + 0.342564i \(0.888705\pi\)
\(458\) 0 0
\(459\) 21.9242 + 3.59756i 1.02334 + 0.167920i
\(460\) 0 0
\(461\) 6.03604 + 10.4547i 0.281126 + 0.486925i 0.971662 0.236373i \(-0.0759586\pi\)
−0.690536 + 0.723298i \(0.742625\pi\)
\(462\) 0 0
\(463\) 11.6479 + 6.72493i 0.541325 + 0.312534i 0.745616 0.666376i \(-0.232155\pi\)
−0.204291 + 0.978910i \(0.565489\pi\)
\(464\) 0 0
\(465\) −14.2566 + 21.8644i −0.661134 + 1.01394i
\(466\) 0 0
\(467\) 12.9746i 0.600391i −0.953878 0.300196i \(-0.902948\pi\)
0.953878 0.300196i \(-0.0970519\pi\)
\(468\) 0 0
\(469\) 16.2772i 0.751612i
\(470\) 0 0
\(471\) 5.34735 + 0.290184i 0.246393 + 0.0133710i
\(472\) 0 0
\(473\) 5.80051 + 3.34892i 0.266708 + 0.153984i
\(474\) 0 0
\(475\) 0.444016 + 0.769058i 0.0203729 + 0.0352868i
\(476\) 0 0
\(477\) −16.9466 + 23.1441i −0.775932 + 1.05969i
\(478\) 0 0
\(479\) 7.54472 + 13.0678i 0.344727 + 0.597085i 0.985304 0.170809i \(-0.0546381\pi\)
−0.640577 + 0.767894i \(0.721305\pi\)
\(480\) 0 0
\(481\) 6.95971 12.0546i 0.317335 0.549641i
\(482\) 0 0
\(483\) 2.08505 + 4.11097i 0.0948733 + 0.187056i
\(484\) 0 0
\(485\) 34.5090 1.56697
\(486\) 0 0
\(487\) 8.93710i 0.404979i −0.979284 0.202489i \(-0.935097\pi\)
0.979284 0.202489i \(-0.0649032\pi\)
\(488\) 0 0
\(489\) −16.1135 + 8.17263i −0.728676 + 0.369579i
\(490\) 0 0
\(491\) −10.0926 5.82696i −0.455472 0.262967i 0.254666 0.967029i \(-0.418034\pi\)
−0.710138 + 0.704062i \(0.751368\pi\)
\(492\) 0 0
\(493\) −20.2013 + 11.6632i −0.909819 + 0.525284i
\(494\) 0 0
\(495\) 14.1365 + 10.3511i 0.635391 + 0.465247i
\(496\) 0 0
\(497\) 5.59526 3.23043i 0.250982 0.144904i
\(498\) 0 0
\(499\) 12.6569 21.9224i 0.566601 0.981381i −0.430298 0.902687i \(-0.641592\pi\)
0.996899 0.0786941i \(-0.0250750\pi\)
\(500\) 0 0
\(501\) 1.22063 22.4931i 0.0545337 1.00492i
\(502\) 0 0
\(503\) 27.4640 1.22456 0.612279 0.790642i \(-0.290253\pi\)
0.612279 + 0.790642i \(0.290253\pi\)
\(504\) 0 0
\(505\) 31.1428 1.38584
\(506\) 0 0
\(507\) −16.2311 10.5834i −0.720848 0.470027i
\(508\) 0 0
\(509\) 9.31530 16.1346i 0.412894 0.715153i −0.582311 0.812966i \(-0.697851\pi\)
0.995205 + 0.0978134i \(0.0311848\pi\)
\(510\) 0 0
\(511\) 14.4990 8.37102i 0.641399 0.370312i
\(512\) 0 0
\(513\) 1.81886 11.0845i 0.0803046 0.489392i
\(514\) 0 0
\(515\) −6.72667 + 3.88364i −0.296412 + 0.171134i
\(516\) 0 0
\(517\) 31.0103 + 17.9038i 1.36383 + 0.787409i
\(518\) 0 0
\(519\) 7.83362 + 5.10788i 0.343858 + 0.224211i
\(520\) 0 0
\(521\) 24.1019i 1.05593i −0.849268 0.527963i \(-0.822956\pi\)
0.849268 0.527963i \(-0.177044\pi\)
\(522\) 0 0
\(523\) −33.9903 −1.48629 −0.743146 0.669129i \(-0.766667\pi\)
−0.743146 + 0.669129i \(0.766667\pi\)
\(524\) 0 0
\(525\) −0.927340 0.0503239i −0.0404724 0.00219631i
\(526\) 0 0
\(527\) −15.0391 + 26.0486i −0.655116 + 1.13469i
\(528\) 0 0
\(529\) 9.42138 + 16.3183i 0.409625 + 0.709492i
\(530\) 0 0
\(531\) 28.4645 12.5470i 1.23525 0.544491i
\(532\) 0 0
\(533\) 0.463580 + 0.802943i 0.0200799 + 0.0347793i
\(534\) 0 0
\(535\) 21.6149 + 12.4794i 0.934494 + 0.539530i
\(536\) 0 0
\(537\) 3.67671 + 7.24914i 0.158662 + 0.312823i
\(538\) 0 0
\(539\) 14.4393i 0.621945i
\(540\) 0 0
\(541\) 38.0055i 1.63399i 0.576648 + 0.816993i \(0.304361\pi\)
−0.576648 + 0.816993i \(0.695639\pi\)
\(542\) 0 0
\(543\) −4.96573 9.79062i −0.213100 0.420156i
\(544\) 0 0
\(545\) 12.9188 + 7.45866i 0.553380 + 0.319494i
\(546\) 0 0
\(547\) 12.0534 + 20.8771i 0.515367 + 0.892642i 0.999841 + 0.0178365i \(0.00567782\pi\)
−0.484474 + 0.874806i \(0.660989\pi\)
\(548\) 0 0
\(549\) 2.88182 26.4741i 0.122993 1.12989i
\(550\) 0 0
\(551\) 5.89669 + 10.2134i 0.251207 + 0.435104i
\(552\) 0 0
\(553\) 0.513081 0.888682i 0.0218184 0.0377906i
\(554\) 0 0
\(555\) 38.3029 + 2.07858i 1.62587 + 0.0882308i
\(556\) 0 0
\(557\) −36.9729 −1.56659 −0.783295 0.621650i \(-0.786463\pi\)
−0.783295 + 0.621650i \(0.786463\pi\)
\(558\) 0 0
\(559\) 3.30784i 0.139907i
\(560\) 0 0
\(561\) 16.9126 + 11.0278i 0.714051 + 0.465594i
\(562\) 0 0
\(563\) −13.5859 7.84380i −0.572576 0.330577i 0.185602 0.982625i \(-0.440577\pi\)
−0.758177 + 0.652048i \(0.773910\pi\)
\(564\) 0 0
\(565\) −25.1799 + 14.5376i −1.05933 + 0.611602i
\(566\) 0 0
\(567\) 8.67133 + 7.92492i 0.364162 + 0.332815i
\(568\) 0 0
\(569\) 28.9567 16.7181i 1.21393 0.700861i 0.250314 0.968165i \(-0.419466\pi\)
0.963612 + 0.267304i \(0.0861327\pi\)
\(570\) 0 0
\(571\) 18.1141 31.3746i 0.758053 1.31299i −0.185788 0.982590i \(-0.559484\pi\)
0.943842 0.330397i \(-0.107183\pi\)
\(572\) 0 0
\(573\) −3.66427 2.38928i −0.153077 0.0998135i
\(574\) 0 0
\(575\) 0.837584 0.0349297
\(576\) 0 0
\(577\) 4.34600 0.180926 0.0904631 0.995900i \(-0.471165\pi\)
0.0904631 + 0.995900i \(0.471165\pi\)
\(578\) 0 0
\(579\) −1.08353 + 19.9667i −0.0450299 + 0.829786i
\(580\) 0 0
\(581\) 1.37266 2.37752i 0.0569477 0.0986363i
\(582\) 0 0
\(583\) −22.5754 + 13.0339i −0.934979 + 0.539811i
\(584\) 0 0
\(585\) −0.936393 + 8.60225i −0.0387151 + 0.355659i
\(586\) 0 0
\(587\) 35.0281 20.2235i 1.44576 0.834711i 0.447538 0.894265i \(-0.352301\pi\)
0.998225 + 0.0595537i \(0.0189678\pi\)
\(588\) 0 0
\(589\) 13.1697 + 7.60351i 0.542646 + 0.313297i
\(590\) 0 0
\(591\) −3.77481 + 1.91456i −0.155275 + 0.0787543i
\(592\) 0 0
\(593\) 9.69635i 0.398181i 0.979981 + 0.199091i \(0.0637988\pi\)
−0.979981 + 0.199091i \(0.936201\pi\)
\(594\) 0 0
\(595\) 11.9556 0.490133
\(596\) 0 0
\(597\) 4.13930 + 8.16119i 0.169410 + 0.334015i
\(598\) 0 0
\(599\) −20.8663 + 36.1415i −0.852574 + 1.47670i 0.0263039 + 0.999654i \(0.491626\pi\)
−0.878878 + 0.477047i \(0.841707\pi\)
\(600\) 0 0
\(601\) −1.58836 2.75112i −0.0647905 0.112220i 0.831811 0.555060i \(-0.187305\pi\)
−0.896601 + 0.442839i \(0.853971\pi\)
\(602\) 0 0
\(603\) −15.0900 34.2337i −0.614511 1.39410i
\(604\) 0 0
\(605\) −3.82112 6.61838i −0.155351 0.269075i
\(606\) 0 0
\(607\) 4.14402 + 2.39255i 0.168201 + 0.0971107i 0.581737 0.813377i \(-0.302373\pi\)
−0.413536 + 0.910488i \(0.635707\pi\)
\(608\) 0 0
\(609\) −12.3154 0.668319i −0.499045 0.0270816i
\(610\) 0 0
\(611\) 17.6842i 0.715426i
\(612\) 0 0
\(613\) 37.8359i 1.52818i 0.645111 + 0.764089i \(0.276811\pi\)
−0.645111 + 0.764089i \(0.723189\pi\)
\(614\) 0 0
\(615\) −1.39556 + 2.14028i −0.0562745 + 0.0863045i
\(616\) 0 0
\(617\) −34.4083 19.8657i −1.38523 0.799761i −0.392454 0.919772i \(-0.628374\pi\)
−0.992773 + 0.120011i \(0.961707\pi\)
\(618\) 0 0
\(619\) 18.1582 + 31.4510i 0.729840 + 1.26412i 0.956950 + 0.290252i \(0.0937390\pi\)
−0.227110 + 0.973869i \(0.572928\pi\)
\(620\) 0 0
\(621\) −8.19634 6.71309i −0.328908 0.269387i
\(622\) 0 0
\(623\) −7.94383 13.7591i −0.318263 0.551247i
\(624\) 0 0
\(625\) 11.3886 19.7257i 0.455545 0.789028i
\(626\) 0 0
\(627\) 5.57545 8.55069i 0.222662 0.341482i
\(628\) 0 0
\(629\) 44.2032 1.76250
\(630\) 0 0
\(631\) 30.0129i 1.19480i 0.801945 + 0.597398i \(0.203799\pi\)
−0.801945 + 0.597398i \(0.796201\pi\)
\(632\) 0 0
\(633\) −1.35767 + 25.0183i −0.0539624 + 0.994388i
\(634\) 0 0
\(635\) 40.8783 + 23.6011i 1.62221 + 0.936581i
\(636\) 0 0
\(637\) −6.17571 + 3.56555i −0.244690 + 0.141272i
\(638\) 0 0
\(639\) −8.77296 + 11.9813i −0.347053 + 0.473972i
\(640\) 0 0
\(641\) 12.8537 7.42111i 0.507692 0.293116i −0.224192 0.974545i \(-0.571974\pi\)
0.731885 + 0.681429i \(0.238641\pi\)
\(642\) 0 0
\(643\) 16.9226 29.3107i 0.667361 1.15590i −0.311279 0.950319i \(-0.600757\pi\)
0.978639 0.205584i \(-0.0659093\pi\)
\(644\) 0 0
\(645\) −8.12989 + 4.12342i −0.320114 + 0.162359i
\(646\) 0 0
\(647\) 17.5923 0.691624 0.345812 0.938304i \(-0.387603\pi\)
0.345812 + 0.938304i \(0.387603\pi\)
\(648\) 0 0
\(649\) 28.2689 1.10965
\(650\) 0 0
\(651\) −14.1835 + 7.19376i −0.555894 + 0.281946i
\(652\) 0 0
\(653\) 12.9079 22.3571i 0.505124 0.874900i −0.494859 0.868974i \(-0.664780\pi\)
0.999982 0.00592671i \(-0.00188654\pi\)
\(654\) 0 0
\(655\) 3.51881 2.03159i 0.137491 0.0793807i
\(656\) 0 0
\(657\) −22.7334 + 31.0471i −0.886915 + 1.21126i
\(658\) 0 0
\(659\) 19.1802 11.0737i 0.747153 0.431369i −0.0775113 0.996991i \(-0.524697\pi\)
0.824664 + 0.565622i \(0.191364\pi\)
\(660\) 0 0
\(661\) 16.8395 + 9.72232i 0.654983 + 0.378154i 0.790363 0.612639i \(-0.209892\pi\)
−0.135380 + 0.990794i \(0.543226\pi\)
\(662\) 0 0
\(663\) −0.540318 + 9.95668i −0.0209842 + 0.386685i
\(664\) 0 0
\(665\) 6.04453i 0.234397i
\(666\) 0 0
\(667\) 11.1234 0.430700
\(668\) 0 0
\(669\) 18.1964 27.9066i 0.703513 1.07893i
\(670\) 0 0
\(671\) 12.1004 20.9585i 0.467130 0.809092i
\(672\) 0 0
\(673\) 11.6142 + 20.1164i 0.447695 + 0.775431i 0.998236 0.0593778i \(-0.0189117\pi\)
−0.550540 + 0.834808i \(0.685578\pi\)
\(674\) 0 0
\(675\) 1.99700 0.753862i 0.0768647 0.0290162i
\(676\) 0 0
\(677\) −14.3138 24.7922i −0.550123 0.952841i −0.998265 0.0588787i \(-0.981247\pi\)
0.448142 0.893962i \(-0.352086\pi\)
\(678\) 0 0
\(679\) 18.2090 + 10.5129i 0.698796 + 0.403450i
\(680\) 0 0
\(681\) 0.549536 0.842786i 0.0210583 0.0322956i
\(682\) 0 0
\(683\) 36.7625i 1.40668i −0.710855 0.703339i \(-0.751692\pi\)
0.710855 0.703339i \(-0.248308\pi\)
\(684\) 0 0
\(685\) 6.52984i 0.249492i
\(686\) 0 0
\(687\) −15.5512 0.843914i −0.593314 0.0321973i
\(688\) 0 0
\(689\) −11.1493 6.43703i −0.424753 0.245231i
\(690\) 0 0
\(691\) −18.7269 32.4360i −0.712407 1.23392i −0.963951 0.266079i \(-0.914272\pi\)
0.251545 0.967846i \(-0.419061\pi\)
\(692\) 0 0
\(693\) 4.30587 + 9.76846i 0.163567 + 0.371073i
\(694\) 0 0
\(695\) 3.91071 + 6.77355i 0.148342 + 0.256936i
\(696\) 0 0
\(697\) −1.47216 + 2.54986i −0.0557622 + 0.0965830i
\(698\) 0 0
\(699\) −1.32171 2.60594i −0.0499917 0.0985655i
\(700\) 0 0
\(701\) 13.9693 0.527615 0.263807 0.964575i \(-0.415022\pi\)
0.263807 + 0.964575i \(0.415022\pi\)
\(702\) 0 0
\(703\) 22.3483i 0.842881i
\(704\) 0 0
\(705\) −43.4635 + 22.0444i −1.63693 + 0.830239i
\(706\) 0 0
\(707\) 16.4328 + 9.48747i 0.618019 + 0.356813i
\(708\) 0 0
\(709\) −21.0480 + 12.1521i −0.790476 + 0.456381i −0.840130 0.542385i \(-0.817521\pi\)
0.0496543 + 0.998766i \(0.484188\pi\)
\(710\) 0 0
\(711\) −0.255231 + 2.34470i −0.00957192 + 0.0879333i
\(712\) 0 0
\(713\) 12.4215 7.17156i 0.465189 0.268577i
\(714\) 0 0
\(715\) −3.93178 + 6.81004i −0.147040 + 0.254681i
\(716\) 0 0
\(717\) −0.328724 + 6.05754i −0.0122764 + 0.226223i
\(718\) 0 0
\(719\) −34.8725 −1.30052 −0.650262 0.759710i \(-0.725341\pi\)
−0.650262 + 0.759710i \(0.725341\pi\)
\(720\) 0 0
\(721\) −4.73251 −0.176248
\(722\) 0 0
\(723\) 3.44537 + 2.24654i 0.128135 + 0.0835497i
\(724\) 0 0
\(725\) −1.12055 + 1.94085i −0.0416162 + 0.0720813i
\(726\) 0 0
\(727\) 24.1521 13.9443i 0.895754 0.517164i 0.0199335 0.999801i \(-0.493655\pi\)
0.875820 + 0.482638i \(0.160321\pi\)
\(728\) 0 0
\(729\) −25.5841 8.62856i −0.947561 0.319576i
\(730\) 0 0
\(731\) −9.09721 + 5.25227i −0.336472 + 0.194262i
\(732\) 0 0
\(733\) −27.4750 15.8627i −1.01481 0.585902i −0.102215 0.994762i \(-0.532593\pi\)
−0.912597 + 0.408860i \(0.865926\pi\)
\(734\) 0 0
\(735\) −16.4616 10.7337i −0.607196 0.395920i
\(736\) 0 0
\(737\) 33.9984i 1.25235i
\(738\) 0 0
\(739\) 1.80482 0.0663913 0.0331957 0.999449i \(-0.489432\pi\)
0.0331957 + 0.999449i \(0.489432\pi\)
\(740\) 0 0
\(741\) 5.03391 + 0.273174i 0.184925 + 0.0100353i
\(742\) 0 0
\(743\) 6.84368 11.8536i 0.251070 0.434866i −0.712751 0.701418i \(-0.752551\pi\)
0.963821 + 0.266551i \(0.0858842\pi\)
\(744\) 0 0
\(745\) −14.9614 25.9140i −0.548145 0.949415i
\(746\) 0 0
\(747\) −0.682829 + 6.27287i −0.0249834 + 0.229512i
\(748\) 0 0
\(749\) 7.60353 + 13.1697i 0.277827 + 0.481210i
\(750\) 0 0
\(751\) 20.8511 + 12.0384i 0.760868 + 0.439287i 0.829607 0.558348i \(-0.188564\pi\)
−0.0687396 + 0.997635i \(0.521898\pi\)
\(752\) 0 0
\(753\) 12.9182 + 25.4699i 0.470764 + 0.928176i
\(754\) 0 0
\(755\) 48.0764i 1.74968i
\(756\) 0 0
\(757\) 11.0608i 0.402013i 0.979590 + 0.201007i \(0.0644213\pi\)
−0.979590 + 0.201007i \(0.935579\pi\)
\(758\) 0 0
\(759\) −4.35508 8.58665i −0.158080 0.311676i
\(760\) 0 0
\(761\) −0.392113 0.226386i −0.0142141 0.00820650i 0.492876 0.870099i \(-0.335946\pi\)
−0.507090 + 0.861893i \(0.669279\pi\)
\(762\) 0 0
\(763\) 4.54447 + 7.87125i 0.164521 + 0.284958i
\(764\) 0 0
\(765\) −25.1447 + 11.0836i −0.909107 + 0.400728i
\(766\) 0 0
\(767\) 6.98053 + 12.0906i 0.252052 + 0.436568i
\(768\) 0 0
\(769\) 1.71970 2.97861i 0.0620139 0.107411i −0.833352 0.552743i \(-0.813581\pi\)
0.895366 + 0.445332i \(0.146914\pi\)
\(770\) 0 0
\(771\) 3.95865 + 0.214824i 0.142567 + 0.00773668i
\(772\) 0 0
\(773\) 27.5126 0.989558 0.494779 0.869019i \(-0.335249\pi\)
0.494779 + 0.869019i \(0.335249\pi\)
\(774\) 0 0
\(775\) 2.88979i 0.103804i
\(776\) 0 0
\(777\) 19.5776 + 12.7655i 0.702344 + 0.457961i
\(778\) 0 0
\(779\) 1.28916 + 0.744298i 0.0461890 + 0.0266673i
\(780\) 0 0
\(781\) −11.6869 + 6.74744i −0.418190 + 0.241442i
\(782\) 0 0
\(783\) 26.5209 10.0116i 0.947780 0.357784i
\(784\) 0 0
\(785\) −5.73609 + 3.31173i −0.204730 + 0.118201i
\(786\) 0 0
\(787\) −3.03995 + 5.26534i −0.108362 + 0.187689i −0.915107 0.403211i \(-0.867894\pi\)
0.806745 + 0.590900i \(0.201227\pi\)
\(788\) 0 0
\(789\) −42.1726 27.4985i −1.50139 0.978973i
\(790\) 0 0
\(791\) −17.7152 −0.629879
\(792\) 0 0
\(793\) 11.9519 0.424426
\(794\) 0 0
\(795\) 1.92248 35.4263i 0.0681832 1.25644i
\(796\) 0 0
\(797\) 24.0930 41.7303i 0.853418 1.47816i −0.0246874 0.999695i \(-0.507859\pi\)