Properties

Label 1152.2.p.f.959.1
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 959.1
Character \(\chi\) \(=\) 1152.959
Dual form 1152.2.p.f.191.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.68783 - 0.388876i) q^{3} +(0.538609 - 0.932899i) q^{5} +(4.07105 - 2.35042i) q^{7} +(2.69755 + 1.31271i) q^{9} +O(q^{10})\) \(q+(-1.68783 - 0.388876i) q^{3} +(0.538609 - 0.932899i) q^{5} +(4.07105 - 2.35042i) q^{7} +(2.69755 + 1.31271i) q^{9} +(4.28563 - 2.47431i) q^{11} +(-1.05002 - 0.606232i) q^{13} +(-1.27186 + 1.36512i) q^{15} +3.12017i q^{17} -2.05903 q^{19} +(-7.78527 + 2.38398i) q^{21} +(1.71835 - 2.97627i) q^{23} +(1.91980 + 3.32519i) q^{25} +(-4.04253 - 3.26465i) q^{27} +(0.723042 + 1.25234i) q^{29} +(6.45450 + 3.72651i) q^{31} +(-8.19561 + 2.50964i) q^{33} -5.06384i q^{35} +9.04031i q^{37} +(1.53652 + 1.43155i) q^{39} +(-8.75630 - 5.05545i) q^{41} +(-0.0592540 - 0.102631i) q^{43} +(2.67756 - 1.80950i) q^{45} +(-1.98823 - 3.44372i) q^{47} +(7.54897 - 13.0752i) q^{49} +(1.21336 - 5.26632i) q^{51} +0.401027 q^{53} -5.33074i q^{55} +(3.47530 + 0.800709i) q^{57} +(-8.97357 - 5.18089i) q^{59} +(11.7417 - 6.77909i) q^{61} +(14.0673 - 0.996260i) q^{63} +(-1.13111 + 0.653045i) q^{65} +(4.94046 - 8.55712i) q^{67} +(-4.05769 + 4.35522i) q^{69} +12.8855 q^{71} +0.327300 q^{73} +(-1.94721 - 6.35893i) q^{75} +(11.6313 - 20.1461i) q^{77} +(-8.98705 + 5.18867i) q^{79} +(5.55357 + 7.08223i) q^{81} +(-8.21751 + 4.74438i) q^{83} +(2.91081 + 1.68055i) q^{85} +(-0.733366 - 2.39492i) q^{87} -9.80272i q^{89} -5.69961 q^{91} +(-9.44496 - 8.79972i) q^{93} +(-1.10902 + 1.92087i) q^{95} +(2.79591 + 4.84266i) q^{97} +(14.8088 - 1.04877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 12q^{7} - 4q^{9} + O(q^{10}) \) \( 24q - 12q^{7} - 4q^{9} - 20q^{15} + 12q^{23} - 12q^{25} + 36q^{31} + 4q^{33} - 20q^{39} - 12q^{41} - 12q^{47} + 12q^{49} + 4q^{57} + 92q^{63} - 48q^{65} + 24q^{73} - 84q^{79} - 20q^{81} - 68q^{87} - 24q^{95} - 12q^{97} + O(q^{100}) \)

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
\(3\) −1.68783 0.388876i −0.974470 0.224518i
\(4\) 0 0
\(5\) 0.538609 0.932899i 0.240873 0.417205i −0.720090 0.693881i \(-0.755899\pi\)
0.960963 + 0.276676i \(0.0892328\pi\)
\(6\) 0 0
\(7\) 4.07105 2.35042i 1.53871 0.888376i 0.539798 0.841795i \(-0.318501\pi\)
0.998914 0.0465815i \(-0.0148327\pi\)
\(8\) 0 0
\(9\) 2.69755 + 1.31271i 0.899184 + 0.437571i
\(10\) 0 0
\(11\) 4.28563 2.47431i 1.29216 0.746032i 0.313127 0.949711i \(-0.398623\pi\)
0.979038 + 0.203679i \(0.0652900\pi\)
\(12\) 0 0
\(13\) −1.05002 0.606232i −0.291225 0.168139i 0.347269 0.937765i \(-0.387109\pi\)
−0.638494 + 0.769627i \(0.720442\pi\)
\(14\) 0 0
\(15\) −1.27186 + 1.36512i −0.328394 + 0.352474i
\(16\) 0 0
\(17\) 3.12017i 0.756753i 0.925652 + 0.378376i \(0.123518\pi\)
−0.925652 + 0.378376i \(0.876482\pi\)
\(18\) 0 0
\(19\) −2.05903 −0.472375 −0.236187 0.971708i \(-0.575898\pi\)
−0.236187 + 0.971708i \(0.575898\pi\)
\(20\) 0 0
\(21\) −7.78527 + 2.38398i −1.69889 + 0.520228i
\(22\) 0 0
\(23\) 1.71835 2.97627i 0.358301 0.620596i −0.629376 0.777101i \(-0.716689\pi\)
0.987677 + 0.156505i \(0.0500228\pi\)
\(24\) 0 0
\(25\) 1.91980 + 3.32519i 0.383960 + 0.665038i
\(26\) 0 0
\(27\) −4.04253 3.26465i −0.777985 0.628283i
\(28\) 0 0
\(29\) 0.723042 + 1.25234i 0.134265 + 0.232555i 0.925317 0.379195i \(-0.123799\pi\)
−0.791051 + 0.611750i \(0.790466\pi\)
\(30\) 0 0
\(31\) 6.45450 + 3.72651i 1.15926 + 0.669301i 0.951127 0.308799i \(-0.0999271\pi\)
0.208136 + 0.978100i \(0.433260\pi\)
\(32\) 0 0
\(33\) −8.19561 + 2.50964i −1.42667 + 0.436872i
\(34\) 0 0
\(35\) 5.06384i 0.855945i
\(36\) 0 0
\(37\) 9.04031i 1.48622i 0.669171 + 0.743109i \(0.266649\pi\)
−0.669171 + 0.743109i \(0.733351\pi\)
\(38\) 0 0
\(39\) 1.53652 + 1.43155i 0.246040 + 0.229231i
\(40\) 0 0
\(41\) −8.75630 5.05545i −1.36750 0.789529i −0.376896 0.926256i \(-0.623009\pi\)
−0.990609 + 0.136726i \(0.956342\pi\)
\(42\) 0 0
\(43\) −0.0592540 0.102631i −0.00903614 0.0156511i 0.861472 0.507805i \(-0.169543\pi\)
−0.870508 + 0.492154i \(0.836210\pi\)
\(44\) 0 0
\(45\) 2.67756 1.80950i 0.399146 0.269745i
\(46\) 0 0
\(47\) −1.98823 3.44372i −0.290014 0.502319i 0.683799 0.729671i \(-0.260327\pi\)
−0.973813 + 0.227352i \(0.926993\pi\)
\(48\) 0 0
\(49\) 7.54897 13.0752i 1.07842 1.86789i
\(50\) 0 0
\(51\) 1.21336 5.26632i 0.169904 0.737433i
\(52\) 0 0
\(53\) 0.401027 0.0550853 0.0275426 0.999621i \(-0.491232\pi\)
0.0275426 + 0.999621i \(0.491232\pi\)
\(54\) 0 0
\(55\) 5.33074i 0.718797i
\(56\) 0 0
\(57\) 3.47530 + 0.800709i 0.460315 + 0.106056i
\(58\) 0 0
\(59\) −8.97357 5.18089i −1.16826 0.674495i −0.214990 0.976616i \(-0.568972\pi\)
−0.953269 + 0.302121i \(0.902305\pi\)
\(60\) 0 0
\(61\) 11.7417 6.77909i 1.50337 0.867973i 0.503381 0.864065i \(-0.332089\pi\)
0.999992 0.00390851i \(-0.00124412\pi\)
\(62\) 0 0
\(63\) 14.0673 0.996260i 1.77231 0.125517i
\(64\) 0 0
\(65\) −1.13111 + 0.653045i −0.140297 + 0.0810002i
\(66\) 0 0
\(67\) 4.94046 8.55712i 0.603573 1.04542i −0.388702 0.921363i \(-0.627077\pi\)
0.992275 0.124056i \(-0.0395901\pi\)
\(68\) 0 0
\(69\) −4.05769 + 4.35522i −0.488488 + 0.524307i
\(70\) 0 0
\(71\) 12.8855 1.52922 0.764612 0.644491i \(-0.222931\pi\)
0.764612 + 0.644491i \(0.222931\pi\)
\(72\) 0 0
\(73\) 0.327300 0.0383076 0.0191538 0.999817i \(-0.493903\pi\)
0.0191538 + 0.999817i \(0.493903\pi\)
\(74\) 0 0
\(75\) −1.94721 6.35893i −0.224845 0.734265i
\(76\) 0 0
\(77\) 11.6313 20.1461i 1.32551 2.29586i
\(78\) 0 0
\(79\) −8.98705 + 5.18867i −1.01112 + 0.583771i −0.911520 0.411256i \(-0.865090\pi\)
−0.0996017 + 0.995027i \(0.531757\pi\)
\(80\) 0 0
\(81\) 5.55357 + 7.08223i 0.617063 + 0.786914i
\(82\) 0 0
\(83\) −8.21751 + 4.74438i −0.901989 + 0.520764i −0.877845 0.478945i \(-0.841019\pi\)
−0.0241442 + 0.999708i \(0.507686\pi\)
\(84\) 0 0
\(85\) 2.91081 + 1.68055i 0.315721 + 0.182282i
\(86\) 0 0
\(87\) −0.733366 2.39492i −0.0786251 0.256762i
\(88\) 0 0
\(89\) 9.80272i 1.03909i −0.854444 0.519543i \(-0.826102\pi\)
0.854444 0.519543i \(-0.173898\pi\)
\(90\) 0 0
\(91\) −5.69961 −0.597481
\(92\) 0 0
\(93\) −9.44496 8.79972i −0.979397 0.912488i
\(94\) 0 0
\(95\) −1.10902 + 1.92087i −0.113783 + 0.197077i
\(96\) 0 0
\(97\) 2.79591 + 4.84266i 0.283882 + 0.491698i 0.972337 0.233581i \(-0.0750443\pi\)
−0.688455 + 0.725279i \(0.741711\pi\)
\(98\) 0 0
\(99\) 14.8088 1.04877i 1.48834 0.105405i
\(100\) 0 0
\(101\) −3.29078 5.69980i −0.327445 0.567152i 0.654559 0.756011i \(-0.272854\pi\)
−0.982004 + 0.188859i \(0.939521\pi\)
\(102\) 0 0
\(103\) −5.27010 3.04270i −0.519279 0.299806i 0.217361 0.976091i \(-0.430255\pi\)
−0.736639 + 0.676286i \(0.763589\pi\)
\(104\) 0 0
\(105\) −1.96920 + 8.54691i −0.192175 + 0.834093i
\(106\) 0 0
\(107\) 8.55222i 0.826774i 0.910555 + 0.413387i \(0.135654\pi\)
−0.910555 + 0.413387i \(0.864346\pi\)
\(108\) 0 0
\(109\) 14.0641i 1.34710i 0.739142 + 0.673550i \(0.235231\pi\)
−0.739142 + 0.673550i \(0.764769\pi\)
\(110\) 0 0
\(111\) 3.51556 15.2585i 0.333682 1.44827i
\(112\) 0 0
\(113\) −11.4863 6.63162i −1.08054 0.623850i −0.149498 0.988762i \(-0.547766\pi\)
−0.931042 + 0.364911i \(0.881099\pi\)
\(114\) 0 0
\(115\) −1.85104 3.20610i −0.172610 0.298970i
\(116\) 0 0
\(117\) −2.03669 3.01372i −0.188292 0.278619i
\(118\) 0 0
\(119\) 7.33372 + 12.7024i 0.672281 + 1.16443i
\(120\) 0 0
\(121\) 6.74439 11.6816i 0.613127 1.06197i
\(122\) 0 0
\(123\) 12.8132 + 11.9379i 1.15533 + 1.07640i
\(124\) 0 0
\(125\) 9.52218 0.851690
\(126\) 0 0
\(127\) 1.69445i 0.150358i −0.997170 0.0751791i \(-0.976047\pi\)
0.997170 0.0751791i \(-0.0239529\pi\)
\(128\) 0 0
\(129\) 0.0601000 + 0.196266i 0.00529151 + 0.0172803i
\(130\) 0 0
\(131\) 4.75341 + 2.74438i 0.415308 + 0.239778i 0.693068 0.720873i \(-0.256259\pi\)
−0.277760 + 0.960650i \(0.589592\pi\)
\(132\) 0 0
\(133\) −8.38243 + 4.83960i −0.726849 + 0.419646i
\(134\) 0 0
\(135\) −5.22294 + 2.01290i −0.449519 + 0.173243i
\(136\) 0 0
\(137\) −11.6559 + 6.72954i −0.995832 + 0.574944i −0.907012 0.421104i \(-0.861643\pi\)
−0.0888193 + 0.996048i \(0.528309\pi\)
\(138\) 0 0
\(139\) 6.33263 10.9684i 0.537126 0.930330i −0.461931 0.886916i \(-0.652843\pi\)
0.999057 0.0434141i \(-0.0138235\pi\)
\(140\) 0 0
\(141\) 2.01662 + 6.58560i 0.169830 + 0.554608i
\(142\) 0 0
\(143\) −6.00002 −0.501747
\(144\) 0 0
\(145\) 1.55775 0.129364
\(146\) 0 0
\(147\) −17.8260 + 19.1331i −1.47026 + 1.57807i
\(148\) 0 0
\(149\) −4.82503 + 8.35719i −0.395282 + 0.684648i −0.993137 0.116956i \(-0.962686\pi\)
0.597855 + 0.801604i \(0.296020\pi\)
\(150\) 0 0
\(151\) −3.55145 + 2.05043i −0.289013 + 0.166862i −0.637497 0.770453i \(-0.720030\pi\)
0.348484 + 0.937315i \(0.386697\pi\)
\(152\) 0 0
\(153\) −4.09589 + 8.41682i −0.331133 + 0.680460i
\(154\) 0 0
\(155\) 6.95291 4.01427i 0.558471 0.322434i
\(156\) 0 0
\(157\) 19.0033 + 10.9716i 1.51663 + 0.875625i 0.999809 + 0.0195297i \(0.00621691\pi\)
0.516818 + 0.856095i \(0.327116\pi\)
\(158\) 0 0
\(159\) −0.676866 0.155950i −0.0536789 0.0123676i
\(160\) 0 0
\(161\) 16.1554i 1.27322i
\(162\) 0 0
\(163\) −8.42867 −0.660185 −0.330092 0.943949i \(-0.607080\pi\)
−0.330092 + 0.943949i \(0.607080\pi\)
\(164\) 0 0
\(165\) −2.07300 + 8.99739i −0.161383 + 0.700446i
\(166\) 0 0
\(167\) −8.04030 + 13.9262i −0.622177 + 1.07764i 0.366903 + 0.930259i \(0.380418\pi\)
−0.989080 + 0.147383i \(0.952915\pi\)
\(168\) 0 0
\(169\) −5.76497 9.98521i −0.443459 0.768093i
\(170\) 0 0
\(171\) −5.55435 2.70292i −0.424752 0.206698i
\(172\) 0 0
\(173\) −9.55535 16.5504i −0.726480 1.25830i −0.958362 0.285556i \(-0.907822\pi\)
0.231882 0.972744i \(-0.425512\pi\)
\(174\) 0 0
\(175\) 15.6312 + 9.02468i 1.18161 + 0.682202i
\(176\) 0 0
\(177\) 13.1312 + 12.2341i 0.986998 + 0.919570i
\(178\) 0 0
\(179\) 0.424929i 0.0317607i −0.999874 0.0158803i \(-0.994945\pi\)
0.999874 0.0158803i \(-0.00505508\pi\)
\(180\) 0 0
\(181\) 13.0403i 0.969278i 0.874714 + 0.484639i \(0.161049\pi\)
−0.874714 + 0.484639i \(0.838951\pi\)
\(182\) 0 0
\(183\) −22.4543 + 6.87588i −1.65987 + 0.508280i
\(184\) 0 0
\(185\) 8.43369 + 4.86920i 0.620057 + 0.357990i
\(186\) 0 0
\(187\) 7.72026 + 13.3719i 0.564562 + 0.977849i
\(188\) 0 0
\(189\) −24.1307 3.78891i −1.75525 0.275603i
\(190\) 0 0
\(191\) −10.3515 17.9294i −0.749010 1.29732i −0.948298 0.317382i \(-0.897196\pi\)
0.199288 0.979941i \(-0.436137\pi\)
\(192\) 0 0
\(193\) −3.46861 + 6.00782i −0.249676 + 0.432452i −0.963436 0.267939i \(-0.913658\pi\)
0.713760 + 0.700391i \(0.246991\pi\)
\(194\) 0 0
\(195\) 2.16307 0.662370i 0.154901 0.0474333i
\(196\) 0 0
\(197\) 6.30640 0.449312 0.224656 0.974438i \(-0.427874\pi\)
0.224656 + 0.974438i \(0.427874\pi\)
\(198\) 0 0
\(199\) 22.7691i 1.61406i −0.590510 0.807031i \(-0.701073\pi\)
0.590510 0.807031i \(-0.298927\pi\)
\(200\) 0 0
\(201\) −11.6663 + 12.5218i −0.822879 + 0.883217i
\(202\) 0 0
\(203\) 5.88708 + 3.39891i 0.413192 + 0.238556i
\(204\) 0 0
\(205\) −9.43246 + 5.44583i −0.658791 + 0.380353i
\(206\) 0 0
\(207\) 8.54234 5.77294i 0.593733 0.401247i
\(208\) 0 0
\(209\) −8.82425 + 5.09468i −0.610386 + 0.352407i
\(210\) 0 0
\(211\) −5.45859 + 9.45455i −0.375785 + 0.650878i −0.990444 0.137915i \(-0.955960\pi\)
0.614660 + 0.788792i \(0.289293\pi\)
\(212\) 0 0
\(213\) −21.7485 5.01085i −1.49018 0.343338i
\(214\) 0 0
\(215\) −0.127659 −0.00870627
\(216\) 0 0
\(217\) 35.0355 2.37836
\(218\) 0 0
\(219\) −0.552427 0.127279i −0.0373296 0.00860072i
\(220\) 0 0
\(221\) 1.89155 3.27626i 0.127239 0.220385i
\(222\) 0 0
\(223\) −15.8367 + 9.14333i −1.06050 + 0.612283i −0.925572 0.378572i \(-0.876415\pi\)
−0.134933 + 0.990855i \(0.543082\pi\)
\(224\) 0 0
\(225\) 0.813735 + 11.4900i 0.0542490 + 0.766001i
\(226\) 0 0
\(227\) 3.01058 1.73816i 0.199819 0.115366i −0.396752 0.917926i \(-0.629863\pi\)
0.596571 + 0.802560i \(0.296529\pi\)
\(228\) 0 0
\(229\) 6.77911 + 3.91392i 0.447976 + 0.258639i 0.706975 0.707238i \(-0.250059\pi\)
−0.258999 + 0.965878i \(0.583393\pi\)
\(230\) 0 0
\(231\) −27.4660 + 29.4800i −1.80713 + 1.93964i
\(232\) 0 0
\(233\) 11.9622i 0.783669i 0.920036 + 0.391835i \(0.128159\pi\)
−0.920036 + 0.391835i \(0.871841\pi\)
\(234\) 0 0
\(235\) −4.28353 −0.279426
\(236\) 0 0
\(237\) 17.1864 5.26276i 1.11637 0.341853i
\(238\) 0 0
\(239\) 1.26987 2.19948i 0.0821412 0.142273i −0.822028 0.569447i \(-0.807157\pi\)
0.904169 + 0.427174i \(0.140491\pi\)
\(240\) 0 0
\(241\) 2.01191 + 3.48473i 0.129599 + 0.224471i 0.923521 0.383548i \(-0.125298\pi\)
−0.793923 + 0.608019i \(0.791964\pi\)
\(242\) 0 0
\(243\) −6.61938 14.1133i −0.424633 0.905365i
\(244\) 0 0
\(245\) −8.13189 14.0849i −0.519528 0.899848i
\(246\) 0 0
\(247\) 2.16204 + 1.24825i 0.137567 + 0.0794244i
\(248\) 0 0
\(249\) 15.7148 4.81213i 0.995882 0.304956i
\(250\) 0 0
\(251\) 8.64335i 0.545563i 0.962076 + 0.272782i \(0.0879437\pi\)
−0.962076 + 0.272782i \(0.912056\pi\)
\(252\) 0 0
\(253\) 17.0069i 1.06922i
\(254\) 0 0
\(255\) −4.25942 3.96843i −0.266735 0.248513i
\(256\) 0 0
\(257\) −11.1468 6.43561i −0.695319 0.401443i 0.110283 0.993900i \(-0.464824\pi\)
−0.805602 + 0.592458i \(0.798158\pi\)
\(258\) 0 0
\(259\) 21.2485 + 36.8035i 1.32032 + 2.28686i
\(260\) 0 0
\(261\) 0.306472 + 4.32741i 0.0189701 + 0.267860i
\(262\) 0 0
\(263\) −2.90296 5.02808i −0.179004 0.310045i 0.762535 0.646946i \(-0.223954\pi\)
−0.941540 + 0.336902i \(0.890621\pi\)
\(264\) 0 0
\(265\) 0.215997 0.374117i 0.0132686 0.0229819i
\(266\) 0 0
\(267\) −3.81204 + 16.5453i −0.233293 + 1.01256i
\(268\) 0 0
\(269\) −3.75093 −0.228699 −0.114349 0.993441i \(-0.536478\pi\)
−0.114349 + 0.993441i \(0.536478\pi\)
\(270\) 0 0
\(271\) 22.3745i 1.35916i 0.733603 + 0.679578i \(0.237837\pi\)
−0.733603 + 0.679578i \(0.762163\pi\)
\(272\) 0 0
\(273\) 9.61998 + 2.21644i 0.582227 + 0.134145i
\(274\) 0 0
\(275\) 16.4551 + 9.50035i 0.992279 + 0.572893i
\(276\) 0 0
\(277\) 7.37669 4.25893i 0.443222 0.255894i −0.261741 0.965138i \(-0.584297\pi\)
0.704963 + 0.709244i \(0.250963\pi\)
\(278\) 0 0
\(279\) 12.5195 + 18.5254i 0.749524 + 1.10908i
\(280\) 0 0
\(281\) 10.7826 6.22534i 0.643236 0.371373i −0.142624 0.989777i \(-0.545554\pi\)
0.785860 + 0.618404i \(0.212221\pi\)
\(282\) 0 0
\(283\) −8.15797 + 14.1300i −0.484941 + 0.839942i −0.999850 0.0173026i \(-0.994492\pi\)
0.514910 + 0.857244i \(0.327825\pi\)
\(284\) 0 0
\(285\) 2.61881 2.81084i 0.155125 0.166500i
\(286\) 0 0
\(287\) −47.5298 −2.80560
\(288\) 0 0
\(289\) 7.26453 0.427325
\(290\) 0 0
\(291\) −2.83584 9.26087i −0.166240 0.542882i
\(292\) 0 0
\(293\) 6.80318 11.7835i 0.397446 0.688397i −0.595964 0.803011i \(-0.703230\pi\)
0.993410 + 0.114614i \(0.0365633\pi\)
\(294\) 0 0
\(295\) −9.66650 + 5.58096i −0.562805 + 0.324936i
\(296\) 0 0
\(297\) −25.4025 3.98862i −1.47400 0.231443i
\(298\) 0 0
\(299\) −3.60862 + 2.08344i −0.208692 + 0.120488i
\(300\) 0 0
\(301\) −0.482452 0.278544i −0.0278081 0.0160550i
\(302\) 0 0
\(303\) 3.33777 + 10.9000i 0.191750 + 0.626189i
\(304\) 0 0
\(305\) 14.6051i 0.836287i
\(306\) 0 0
\(307\) 7.53173 0.429859 0.214929 0.976630i \(-0.431048\pi\)
0.214929 + 0.976630i \(0.431048\pi\)
\(308\) 0 0
\(309\) 7.71182 + 7.18497i 0.438710 + 0.408739i
\(310\) 0 0
\(311\) 10.7246 18.5755i 0.608136 1.05332i −0.383411 0.923578i \(-0.625251\pi\)
0.991547 0.129745i \(-0.0414158\pi\)
\(312\) 0 0
\(313\) −7.12564 12.3420i −0.402765 0.697609i 0.591294 0.806456i \(-0.298617\pi\)
−0.994058 + 0.108847i \(0.965284\pi\)
\(314\) 0 0
\(315\) 6.64737 13.6600i 0.374537 0.769652i
\(316\) 0 0
\(317\) 17.3799 + 30.1029i 0.976153 + 1.69075i 0.676075 + 0.736833i \(0.263679\pi\)
0.300078 + 0.953915i \(0.402987\pi\)
\(318\) 0 0
\(319\) 6.19737 + 3.57805i 0.346986 + 0.200333i
\(320\) 0 0
\(321\) 3.32575 14.4347i 0.185625 0.805667i
\(322\) 0 0
\(323\) 6.42454i 0.357471i
\(324\) 0 0
\(325\) 4.65538i 0.258234i
\(326\) 0 0
\(327\) 5.46920 23.7379i 0.302447 1.31271i
\(328\) 0 0
\(329\) −16.1884 9.34638i −0.892496 0.515283i
\(330\) 0 0
\(331\) 6.85837 + 11.8791i 0.376970 + 0.652932i 0.990620 0.136647i \(-0.0436325\pi\)
−0.613650 + 0.789579i \(0.710299\pi\)
\(332\) 0 0
\(333\) −11.8673 + 24.3867i −0.650326 + 1.33638i
\(334\) 0 0
\(335\) −5.32195 9.21790i −0.290769 0.503627i
\(336\) 0 0
\(337\) −2.12713 + 3.68431i −0.115872 + 0.200697i −0.918128 0.396284i \(-0.870300\pi\)
0.802256 + 0.596981i \(0.203633\pi\)
\(338\) 0 0
\(339\) 16.8081 + 15.6598i 0.912889 + 0.850524i
\(340\) 0 0
\(341\) 36.8821 1.99728
\(342\) 0 0
\(343\) 38.0671i 2.05543i
\(344\) 0 0
\(345\) 1.87747 + 6.13118i 0.101080 + 0.330092i
\(346\) 0 0
\(347\) −12.9663 7.48608i −0.696066 0.401874i 0.109814 0.993952i \(-0.464974\pi\)
−0.805881 + 0.592078i \(0.798308\pi\)
\(348\) 0 0
\(349\) −14.1751 + 8.18402i −0.758777 + 0.438080i −0.828857 0.559461i \(-0.811008\pi\)
0.0700793 + 0.997541i \(0.477675\pi\)
\(350\) 0 0
\(351\) 2.26562 + 5.87868i 0.120930 + 0.313781i
\(352\) 0 0
\(353\) −14.6621 + 8.46517i −0.780385 + 0.450555i −0.836567 0.547865i \(-0.815441\pi\)
0.0561818 + 0.998421i \(0.482107\pi\)
\(354\) 0 0
\(355\) 6.94024 12.0208i 0.368350 0.638000i
\(356\) 0 0
\(357\) −7.43844 24.2914i −0.393684 1.28564i
\(358\) 0 0
\(359\) 20.9540 1.10591 0.552955 0.833211i \(-0.313500\pi\)
0.552955 + 0.833211i \(0.313500\pi\)
\(360\) 0 0
\(361\) −14.7604 −0.776862
\(362\) 0 0
\(363\) −15.9261 + 17.0939i −0.835904 + 0.897197i
\(364\) 0 0
\(365\) 0.176287 0.305338i 0.00922728 0.0159821i
\(366\) 0 0
\(367\) −15.1275 + 8.73384i −0.789647 + 0.455903i −0.839838 0.542837i \(-0.817350\pi\)
0.0501914 + 0.998740i \(0.484017\pi\)
\(368\) 0 0
\(369\) −16.9842 25.1319i −0.884163 1.30831i
\(370\) 0 0
\(371\) 1.63260 0.942582i 0.0847604 0.0489364i
\(372\) 0 0
\(373\) 17.5467 + 10.1306i 0.908534 + 0.524542i 0.879959 0.475049i \(-0.157570\pi\)
0.0285749 + 0.999592i \(0.490903\pi\)
\(374\) 0 0
\(375\) −16.0718 3.70295i −0.829946 0.191219i
\(376\) 0 0
\(377\) 1.75332i 0.0903008i
\(378\) 0 0
\(379\) −20.0937 −1.03214 −0.516072 0.856545i \(-0.672606\pi\)
−0.516072 + 0.856545i \(0.672606\pi\)
\(380\) 0 0
\(381\) −0.658931 + 2.85995i −0.0337581 + 0.146520i
\(382\) 0 0
\(383\) −1.82133 + 3.15464i −0.0930659 + 0.161195i −0.908800 0.417233i \(-0.863000\pi\)
0.815734 + 0.578427i \(0.196333\pi\)
\(384\) 0 0
\(385\) −12.5295 21.7017i −0.638562 1.10602i
\(386\) 0 0
\(387\) −0.0251156 0.354636i −0.00127670 0.0180271i
\(388\) 0 0
\(389\) −9.87792 17.1091i −0.500831 0.867464i −1.00000 0.000959266i \(-0.999695\pi\)
0.499169 0.866505i \(-0.333639\pi\)
\(390\) 0 0
\(391\) 9.28648 + 5.36155i 0.469638 + 0.271145i
\(392\) 0 0
\(393\) −6.95573 6.48054i −0.350870 0.326900i
\(394\) 0 0
\(395\) 11.1787i 0.562460i
\(396\) 0 0
\(397\) 4.63889i 0.232819i −0.993201 0.116410i \(-0.962861\pi\)
0.993201 0.116410i \(-0.0371385\pi\)
\(398\) 0 0
\(399\) 16.0301 4.90870i 0.802511 0.245743i
\(400\) 0 0
\(401\) 21.4727 + 12.3972i 1.07229 + 0.619089i 0.928807 0.370564i \(-0.120835\pi\)
0.143486 + 0.989652i \(0.454169\pi\)
\(402\) 0 0
\(403\) −4.51826 7.82585i −0.225070 0.389834i
\(404\) 0 0
\(405\) 9.59820 1.36636i 0.476939 0.0678951i
\(406\) 0 0
\(407\) 22.3685 + 38.7434i 1.10877 + 1.92044i
\(408\) 0 0
\(409\) −6.97230 + 12.0764i −0.344758 + 0.597138i −0.985310 0.170777i \(-0.945372\pi\)
0.640552 + 0.767915i \(0.278706\pi\)
\(410\) 0 0
\(411\) 22.2902 6.82563i 1.09949 0.336684i
\(412\) 0 0
\(413\) −48.7091 −2.39682
\(414\) 0 0
\(415\) 10.2215i 0.501753i
\(416\) 0 0
\(417\) −14.9538 + 16.0503i −0.732289 + 0.785984i
\(418\) 0 0
\(419\) −15.0259 8.67521i −0.734063 0.423812i 0.0858435 0.996309i \(-0.472642\pi\)
−0.819907 + 0.572497i \(0.805975\pi\)
\(420\) 0 0
\(421\) 7.33241 4.23337i 0.357360 0.206322i −0.310562 0.950553i \(-0.600517\pi\)
0.667922 + 0.744231i \(0.267184\pi\)
\(422\) 0 0
\(423\) −0.842741 11.8996i −0.0409755 0.578578i
\(424\) 0 0
\(425\) −10.3752 + 5.99010i −0.503269 + 0.290563i
\(426\) 0 0
\(427\) 31.8674 55.1960i 1.54217 2.67112i
\(428\) 0 0
\(429\) 10.1270 + 2.33326i 0.488937 + 0.112651i
\(430\) 0 0
\(431\) 12.1512 0.585302 0.292651 0.956219i \(-0.405463\pi\)
0.292651 + 0.956219i \(0.405463\pi\)
\(432\) 0 0
\(433\) 19.4672 0.935532 0.467766 0.883852i \(-0.345059\pi\)
0.467766 + 0.883852i \(0.345059\pi\)
\(434\) 0 0
\(435\) −2.62922 0.605771i −0.126061 0.0290445i
\(436\) 0 0
\(437\) −3.53815 + 6.12825i −0.169252 + 0.293154i
\(438\) 0 0
\(439\) −7.44979 + 4.30114i −0.355559 + 0.205282i −0.667131 0.744940i \(-0.732478\pi\)
0.311572 + 0.950223i \(0.399145\pi\)
\(440\) 0 0
\(441\) 37.5277 25.3614i 1.78703 1.20768i
\(442\) 0 0
\(443\) −14.6579 + 8.46276i −0.696419 + 0.402078i −0.806012 0.591899i \(-0.798379\pi\)
0.109593 + 0.993977i \(0.465045\pi\)
\(444\) 0 0
\(445\) −9.14494 5.27984i −0.433512 0.250288i
\(446\) 0 0
\(447\) 11.3937 12.2292i 0.538906 0.578421i
\(448\) 0 0
\(449\) 40.9499i 1.93255i 0.257522 + 0.966273i \(0.417094\pi\)
−0.257522 + 0.966273i \(0.582906\pi\)
\(450\) 0 0
\(451\) −50.0350 −2.35606
\(452\) 0 0
\(453\) 6.79162 2.07971i 0.319098 0.0977133i
\(454\) 0 0
\(455\) −3.06986 + 5.31716i −0.143917 + 0.249272i
\(456\) 0 0
\(457\) 7.34163 + 12.7161i 0.343427 + 0.594833i 0.985067 0.172173i \(-0.0550788\pi\)
−0.641640 + 0.767006i \(0.721745\pi\)
\(458\) 0 0
\(459\) 10.1863 12.6134i 0.475455 0.588742i
\(460\) 0 0
\(461\) 18.6860 + 32.3651i 0.870294 + 1.50739i 0.861693 + 0.507431i \(0.169405\pi\)
0.00860141 + 0.999963i \(0.497262\pi\)
\(462\) 0 0
\(463\) 1.24136 + 0.716699i 0.0576909 + 0.0333078i 0.528568 0.848891i \(-0.322729\pi\)
−0.470877 + 0.882199i \(0.656062\pi\)
\(464\) 0 0
\(465\) −13.2964 + 4.07159i −0.616606 + 0.188815i
\(466\) 0 0
\(467\) 14.7591i 0.682970i 0.939887 + 0.341485i \(0.110930\pi\)
−0.939887 + 0.341485i \(0.889070\pi\)
\(468\) 0 0
\(469\) 46.4486i 2.14480i
\(470\) 0 0
\(471\) −27.8078 25.9080i −1.28131 1.19378i
\(472\) 0 0
\(473\) −0.507881 0.293225i −0.0233524 0.0134825i
\(474\) 0 0
\(475\) −3.95293 6.84668i −0.181373 0.314147i
\(476\) 0 0
\(477\) 1.08179 + 0.526433i 0.0495318 + 0.0241037i
\(478\) 0 0
\(479\) 12.3517 + 21.3938i 0.564365 + 0.977509i 0.997108 + 0.0759917i \(0.0242123\pi\)
−0.432743 + 0.901517i \(0.642454\pi\)
\(480\) 0 0
\(481\) 5.48052 9.49255i 0.249890 0.432823i
\(482\) 0 0
\(483\) −6.28245 + 27.2676i −0.285861 + 1.24072i
\(484\) 0 0
\(485\) 6.02362 0.273519
\(486\) 0 0
\(487\) 34.5414i 1.56522i −0.622513 0.782610i \(-0.713888\pi\)
0.622513 0.782610i \(-0.286112\pi\)
\(488\) 0 0
\(489\) 14.2262 + 3.27771i 0.643330 + 0.148223i
\(490\) 0 0
\(491\) 31.8995 + 18.4172i 1.43961 + 0.831156i 0.997822 0.0659653i \(-0.0210127\pi\)
0.441783 + 0.897122i \(0.354346\pi\)
\(492\) 0 0
\(493\) −3.90753 + 2.25601i −0.175986 + 0.101606i
\(494\) 0 0
\(495\) 6.99774 14.3799i 0.314525 0.646331i
\(496\) 0 0
\(497\) 52.4574 30.2863i 2.35304 1.35853i
\(498\) 0 0
\(499\) 20.9375 36.2648i 0.937291 1.62344i 0.166793 0.985992i \(-0.446659\pi\)
0.770497 0.637443i \(-0.220008\pi\)
\(500\) 0 0
\(501\) 18.9862 20.3784i 0.848242 0.910440i
\(502\) 0 0
\(503\) 10.4048 0.463929 0.231964 0.972724i \(-0.425485\pi\)
0.231964 + 0.972724i \(0.425485\pi\)
\(504\) 0 0
\(505\) −7.08979 −0.315491
\(506\) 0 0
\(507\) 5.84728 + 19.0952i 0.259687 + 0.848048i
\(508\) 0 0
\(509\) 7.73328 13.3944i 0.342771 0.593698i −0.642175 0.766558i \(-0.721968\pi\)
0.984946 + 0.172861i \(0.0553010\pi\)
\(510\) 0 0
\(511\) 1.33245 0.769293i 0.0589443 0.0340315i
\(512\) 0 0
\(513\) 8.32371 + 6.72203i 0.367501 + 0.296785i
\(514\) 0 0
\(515\) −5.67706 + 3.27765i −0.250161 + 0.144430i
\(516\) 0 0
\(517\) −17.0417 9.83900i −0.749491 0.432719i
\(518\) 0 0
\(519\) 9.69179 + 31.6501i 0.425423 + 1.38928i
\(520\) 0 0
\(521\) 14.2431i 0.624002i −0.950082 0.312001i \(-0.899001\pi\)
0.950082 0.312001i \(-0.100999\pi\)
\(522\) 0 0
\(523\) −2.33839 −0.102251 −0.0511254 0.998692i \(-0.516281\pi\)
−0.0511254 + 0.998692i \(0.516281\pi\)
\(524\) 0 0
\(525\) −22.8734 21.3107i −0.998275 0.930077i
\(526\) 0 0
\(527\) −11.6273 + 20.1392i −0.506495 + 0.877275i
\(528\) 0 0
\(529\) 5.59453 + 9.69002i 0.243241 + 0.421305i
\(530\) 0 0
\(531\) −17.4056 25.7555i −0.755340 1.11769i
\(532\) 0 0
\(533\) 6.12956 + 10.6167i 0.265501 + 0.459861i
\(534\) 0 0
\(535\) 7.97836 + 4.60631i 0.344934 + 0.199148i
\(536\) 0 0
\(537\) −0.165244 + 0.717208i −0.00713082 + 0.0309498i
\(538\) 0 0
\(539\) 74.7139i 3.21815i
\(540\) 0 0
\(541\) 25.7952i 1.10902i 0.832176 + 0.554512i \(0.187095\pi\)
−0.832176 + 0.554512i \(0.812905\pi\)
\(542\) 0 0
\(543\) 5.07106 22.0098i 0.217620 0.944533i
\(544\) 0 0
\(545\) 13.1204 + 7.57507i 0.562017 + 0.324480i
\(546\) 0 0
\(547\) −7.47104 12.9402i −0.319439 0.553284i 0.660932 0.750445i \(-0.270161\pi\)
−0.980371 + 0.197162i \(0.936828\pi\)
\(548\) 0 0
\(549\) 40.5729 2.87341i 1.73161 0.122634i
\(550\) 0 0
\(551\) −1.48877 2.57862i −0.0634236 0.109853i
\(552\) 0 0
\(553\) −24.3911 + 42.2467i −1.03722 + 1.79651i
\(554\) 0 0
\(555\) −12.3411 11.4980i −0.523852 0.488065i
\(556\) 0 0
\(557\) −25.4302 −1.07751 −0.538756 0.842462i \(-0.681105\pi\)
−0.538756 + 0.842462i \(0.681105\pi\)
\(558\) 0 0
\(559\) 0.143687i 0.00607730i
\(560\) 0 0
\(561\) −7.83050 25.5717i −0.330604 1.07964i
\(562\) 0 0
\(563\) −21.5279 12.4291i −0.907292 0.523825i −0.0277333 0.999615i \(-0.508829\pi\)
−0.879559 + 0.475790i \(0.842162\pi\)
\(564\) 0 0
\(565\) −12.3733 + 7.14371i −0.520547 + 0.300538i
\(566\) 0 0
\(567\) 39.2551 + 15.7789i 1.64856 + 0.662650i
\(568\) 0 0
\(569\) 18.6202 10.7504i 0.780600 0.450680i −0.0560427 0.998428i \(-0.517848\pi\)
0.836643 + 0.547749i \(0.184515\pi\)
\(570\) 0 0
\(571\) −14.5882 + 25.2675i −0.610498 + 1.05741i 0.380658 + 0.924716i \(0.375697\pi\)
−0.991157 + 0.132698i \(0.957636\pi\)
\(572\) 0 0
\(573\) 10.4993 + 34.2872i 0.438616 + 1.43237i
\(574\) 0 0
\(575\) 13.1956 0.550293
\(576\) 0 0
\(577\) −34.8813 −1.45213 −0.726063 0.687628i \(-0.758652\pi\)
−0.726063 + 0.687628i \(0.758652\pi\)
\(578\) 0 0
\(579\) 8.19073 8.79132i 0.340395 0.365355i
\(580\) 0 0
\(581\) −22.3026 + 38.6293i −0.925268 + 1.60261i
\(582\) 0 0
\(583\) 1.71865 0.992263i 0.0711792 0.0410954i
\(584\) 0 0
\(585\) −3.90848 + 0.276802i −0.161596 + 0.0114444i
\(586\) 0 0
\(587\) −20.5905 + 11.8879i −0.849862 + 0.490668i −0.860604 0.509274i \(-0.829914\pi\)
0.0107423 + 0.999942i \(0.496581\pi\)
\(588\) 0 0
\(589\) −13.2900 7.67301i −0.547607 0.316161i
\(590\) 0 0
\(591\) −10.6441 2.45241i −0.437841 0.100879i
\(592\) 0 0
\(593\) 33.9535i 1.39430i 0.716923 + 0.697152i \(0.245550\pi\)
−0.716923 + 0.697152i \(0.754450\pi\)
\(594\) 0 0
\(595\) 15.8000 0.647739
\(596\) 0 0
\(597\) −8.85437 + 38.4305i −0.362385 + 1.57285i
\(598\) 0 0
\(599\) 8.46524 14.6622i 0.345881 0.599083i −0.639633 0.768681i \(-0.720914\pi\)
0.985513 + 0.169598i \(0.0542469\pi\)
\(600\) 0 0
\(601\) 10.5145 + 18.2116i 0.428895 + 0.742868i 0.996775 0.0802433i \(-0.0255697\pi\)
−0.567880 + 0.823111i \(0.692236\pi\)
\(602\) 0 0
\(603\) 24.5602 16.5979i 1.00017 0.675918i
\(604\) 0 0
\(605\) −7.26519 12.5837i −0.295372 0.511599i
\(606\) 0 0
\(607\) 24.0727 + 13.8984i 0.977082 + 0.564119i 0.901388 0.433012i \(-0.142549\pi\)
0.0756944 + 0.997131i \(0.475883\pi\)
\(608\) 0 0
\(609\) −8.61464 8.02612i −0.349083 0.325235i
\(610\) 0 0
\(611\) 4.82133i 0.195050i
\(612\) 0 0
\(613\) 13.4417i 0.542906i −0.962452 0.271453i \(-0.912496\pi\)
0.962452 0.271453i \(-0.0875042\pi\)
\(614\) 0 0
\(615\) 18.0382 5.52359i 0.727368 0.222733i
\(616\) 0 0
\(617\) 11.1656 + 6.44644i 0.449509 + 0.259524i 0.707623 0.706591i \(-0.249768\pi\)
−0.258114 + 0.966114i \(0.583101\pi\)
\(618\) 0 0
\(619\) −6.59418 11.4215i −0.265043 0.459067i 0.702532 0.711652i \(-0.252053\pi\)
−0.967575 + 0.252585i \(0.918719\pi\)
\(620\) 0 0
\(621\) −16.6630 + 6.42185i −0.668663 + 0.257700i
\(622\) 0 0
\(623\) −23.0405 39.9073i −0.923099 1.59885i
\(624\) 0 0
\(625\) −4.47026 + 7.74272i −0.178810 + 0.309709i
\(626\) 0 0
\(627\) 16.8750 5.16743i 0.673924 0.206367i
\(628\) 0 0
\(629\) −28.2073 −1.12470
\(630\) 0 0
\(631\) 6.49548i 0.258581i −0.991607 0.129290i \(-0.958730\pi\)
0.991607 0.129290i \(-0.0412699\pi\)
\(632\) 0 0
\(633\) 12.8898 13.8350i 0.512324 0.549891i
\(634\) 0 0
\(635\) −1.58075 0.912648i −0.0627302 0.0362173i
\(636\) 0 0
\(637\) −15.8532 + 9.15285i −0.628127 + 0.362649i
\(638\) 0 0
\(639\) 34.7592 + 16.9149i 1.37505 + 0.669145i
\(640\) 0 0
\(641\) −27.0483 + 15.6164i −1.06835 + 0.616809i −0.927729 0.373255i \(-0.878242\pi\)
−0.140616 + 0.990064i \(0.544908\pi\)
\(642\) 0 0
\(643\) −8.12404 + 14.0713i −0.320381 + 0.554916i −0.980567 0.196186i \(-0.937144\pi\)
0.660186 + 0.751102i \(0.270478\pi\)
\(644\) 0 0
\(645\) 0.215467 + 0.0496435i 0.00848400 + 0.00195471i
\(646\) 0 0
\(647\) 22.1277 0.869929 0.434964 0.900448i \(-0.356761\pi\)
0.434964 + 0.900448i \(0.356761\pi\)
\(648\) 0 0
\(649\) −51.2765 −2.01278
\(650\) 0 0
\(651\) −59.1340 13.6244i −2.31764 0.533984i
\(652\) 0 0
\(653\) −18.5882 + 32.1957i −0.727412 + 1.25991i 0.230562 + 0.973058i \(0.425944\pi\)
−0.957974 + 0.286856i \(0.907390\pi\)
\(654\) 0 0
\(655\) 5.12047 2.95630i 0.200073 0.115512i
\(656\) 0 0
\(657\) 0.882908 + 0.429651i 0.0344455 + 0.0167623i
\(658\) 0 0
\(659\) 40.8491 23.5842i 1.59125 0.918711i 0.598161 0.801376i \(-0.295898\pi\)
0.993092 0.117334i \(-0.0374349\pi\)
\(660\) 0 0
\(661\) −33.1291 19.1271i −1.28857 0.743957i −0.310172 0.950680i \(-0.600387\pi\)
−0.978399 + 0.206723i \(0.933720\pi\)
\(662\) 0 0
\(663\) −4.46667 + 4.79419i −0.173471 + 0.186191i
\(664\) 0 0
\(665\) 10.4266i 0.404327i
\(666\) 0 0
\(667\) 4.96976 0.192430
\(668\) 0 0
\(669\) 30.2853 9.27389i 1.17090 0.358549i
\(670\) 0 0
\(671\) 33.5471 58.1053i 1.29507 2.24313i
\(672\) 0 0
\(673\) 2.66960 + 4.62389i 0.102906 + 0.178238i 0.912881 0.408227i \(-0.133853\pi\)
−0.809975 + 0.586465i \(0.800519\pi\)
\(674\) 0 0
\(675\) 3.09474 19.7097i 0.119117 0.758625i
\(676\) 0 0
\(677\) 2.31625 + 4.01186i 0.0890206 + 0.154188i 0.907097 0.420921i \(-0.138293\pi\)
−0.818077 + 0.575109i \(0.804960\pi\)
\(678\) 0 0
\(679\) 22.7646 + 13.1432i 0.873626 + 0.504388i
\(680\) 0 0
\(681\) −5.75727 + 1.76298i −0.220619 + 0.0675574i
\(682\) 0 0
\(683\) 6.06774i 0.232175i 0.993239 + 0.116088i \(0.0370354\pi\)
−0.993239 + 0.116088i \(0.962965\pi\)
\(684\) 0 0
\(685\) 14.4984i 0.553955i
\(686\) 0 0
\(687\) −9.91997 9.24227i −0.378470 0.352615i
\(688\) 0 0
\(689\) −0.421088 0.243115i −0.0160422 0.00926196i
\(690\) 0 0
\(691\) 11.0823 + 19.1951i 0.421590 + 0.730216i 0.996095 0.0882853i \(-0.0281387\pi\)
−0.574505 + 0.818501i \(0.694805\pi\)
\(692\) 0 0
\(693\) 57.8221 39.0764i 2.19648 1.48439i
\(694\) 0 0
\(695\) −6.82162 11.8154i −0.258759 0.448184i
\(696\) 0 0
\(697\) 15.7739 27.3212i 0.597479 1.03486i
\(698\) 0 0
\(699\) 4.65181 20.1902i 0.175947 0.763662i
\(700\) 0 0
\(701\) −7.47732 −0.282414 −0.141207 0.989980i \(-0.545098\pi\)
−0.141207 + 0.989980i \(0.545098\pi\)
\(702\) 0 0
\(703\) 18.6143i 0.702052i
\(704\) 0 0
\(705\) 7.22987 + 1.66576i 0.272293 + 0.0627362i
\(706\) 0 0
\(707\) −26.7939 15.4695i −1.00769 0.581789i
\(708\) 0 0
\(709\) 38.8031 22.4030i 1.45728 0.841362i 0.458404 0.888744i \(-0.348421\pi\)
0.998877 + 0.0473824i \(0.0150879\pi\)
\(710\) 0 0
\(711\) −31.0543 + 2.19929i −1.16463 + 0.0824799i
\(712\) 0 0
\(713\) 22.1822 12.8069i 0.830730 0.479622i
\(714\) 0 0
\(715\) −3.23167 + 5.59741i −0.120857 + 0.209331i
\(716\) 0 0
\(717\) −2.99866 + 3.21854i −0.111987 + 0.120198i
\(718\) 0 0
\(719\) −4.62241 −0.172387 −0.0861933 0.996278i \(-0.527470\pi\)
−0.0861933 + 0.996278i \(0.527470\pi\)
\(720\) 0 0
\(721\) −28.6065 −1.06536
\(722\) 0 0
\(723\) −2.04064 6.66402i −0.0758922 0.247838i
\(724\) 0 0
\(725\) −2.77619 + 4.80850i −0.103105 + 0.178583i
\(726\) 0 0
\(727\) 1.19976 0.692682i 0.0444967 0.0256902i −0.477587 0.878585i \(-0.658488\pi\)
0.522083 + 0.852894i \(0.325155\pi\)
\(728\) 0 0
\(729\) 5.68409 + 26.3949i 0.210522 + 0.977589i
\(730\) 0 0
\(731\) 0.320226 0.184883i 0.0118440 0.00683813i
\(732\) 0 0
\(733\) −31.9391 18.4400i −1.17970 0.681098i −0.223752 0.974646i \(-0.571831\pi\)
−0.955944 + 0.293548i \(0.905164\pi\)
\(734\) 0 0
\(735\) 8.24801 + 26.9352i 0.304232 + 0.993518i
\(736\) 0 0
\(737\) 48.8968i 1.80114i
\(738\) 0 0
\(739\) 6.13367 0.225631 0.112815 0.993616i \(-0.464013\pi\)
0.112815 + 0.993616i \(0.464013\pi\)
\(740\) 0 0
\(741\) −3.16374 2.94760i −0.116223 0.108283i
\(742\) 0 0
\(743\) −4.31592 + 7.47540i −0.158336 + 0.274246i −0.934269 0.356570i \(-0.883946\pi\)
0.775933 + 0.630816i \(0.217280\pi\)
\(744\) 0 0
\(745\) 5.19761 + 9.00253i 0.190426 + 0.329827i
\(746\) 0 0
\(747\) −28.3952 + 2.01097i −1.03893 + 0.0735777i
\(748\) 0 0
\(749\) 20.1013 + 34.8165i 0.734486 + 1.27217i
\(750\) 0 0
\(751\) 18.0911 + 10.4449i 0.660153 + 0.381140i 0.792335 0.610086i \(-0.208865\pi\)
−0.132182 + 0.991225i \(0.542198\pi\)
\(752\) 0 0
\(753\) 3.36119 14.5885i 0.122489 0.531635i
\(754\) 0 0
\(755\) 4.41753i 0.160770i
\(756\) 0 0
\(757\) 25.5413i 0.928313i 0.885753 + 0.464157i \(0.153643\pi\)
−0.885753 + 0.464157i \(0.846357\pi\)
\(758\) 0 0
\(759\) −6.61358 + 28.7048i −0.240058 + 1.04192i
\(760\) 0 0
\(761\) 35.8817 + 20.7163i 1.30071 + 0.750965i 0.980526 0.196390i \(-0.0629218\pi\)
0.320184 + 0.947355i \(0.396255\pi\)
\(762\) 0 0
\(763\) 33.0566 + 57.2558i 1.19673 + 2.07280i
\(764\) 0 0
\(765\) 5.64596 + 8.35444i 0.204130 + 0.302055i
\(766\) 0 0
\(767\) 6.28165 + 10.8801i 0.226817 + 0.392859i
\(768\) 0 0
\(769\) −8.41361 + 14.5728i −0.303403 + 0.525509i −0.976904 0.213677i \(-0.931456\pi\)
0.673502 + 0.739186i \(0.264789\pi\)
\(770\) 0 0
\(771\) 16.3113 + 15.1970i 0.587437 + 0.547305i
\(772\) 0 0
\(773\) 45.3934 1.63269 0.816344 0.577566i \(-0.195998\pi\)
0.816344 + 0.577566i \(0.195998\pi\)
\(774\) 0 0
\(775\) 28.6166i 1.02794i
\(776\) 0 0
\(777\) −21.5519 70.3812i −0.773172 2.52491i
\(778\) 0 0
\(779\) 18.0295 + 10.4094i 0.645975 + 0.372954i
\(780\) 0 0
\(781\) 55.2223 31.8826i 1.97601 1.14085i
\(782\) 0 0
\(783\) 1.16555 7.42312i 0.0416535 0.265281i
\(784\) 0 0
\(785\) 20.4707 11.8188i 0.730631 0.421830i
\(786\) 0 0
\(787\) 12.6788 21.9603i 0.451950 0.782800i −0.546557 0.837422i \(-0.684062\pi\)
0.998507 + 0.0546214i \(0.0173952\pi\)
\(788\) 0 0
\(789\) 2.94441 + 9.61544i 0.104824 + 0.342319i
\(790\) 0 0
\(791\) −62.3484 −2.21686
\(792\) 0 0
\(793\) −16.4388 −0.583759
\(794\) 0 0
\(795\) −0.510052 + 0.547451i −0.0180897 + 0.0194161i
\(796\) 0 0
\(797\) 3.96853 6.87370i 0.140573 0.243479i −0.787140 0.616775i \(-0.788439\