Properties

Label 684.3.s.a.445.3
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 445.3
Character \(\chi\) \(=\) 684.445
Dual form 684.3.s.a.601.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.96123 - 0.480768i) q^{3} +(-0.920304 - 1.59401i) q^{5} +(3.31490 + 5.74157i) q^{7} +(8.53772 + 2.84733i) q^{9} +O(q^{10})\) \(q+(-2.96123 - 0.480768i) q^{3} +(-0.920304 - 1.59401i) q^{5} +(3.31490 + 5.74157i) q^{7} +(8.53772 + 2.84733i) q^{9} +(-7.65648 - 13.2614i) q^{11} +2.53444i q^{13} +(1.95888 + 5.16269i) q^{15} +(-12.9506 + 22.4311i) q^{17} +(7.42625 - 17.4886i) q^{19} +(-7.05580 - 18.5958i) q^{21} +5.08329 q^{23} +(10.8061 - 18.7167i) q^{25} +(-23.9132 - 12.5362i) q^{27} +(-12.8830 - 7.43798i) q^{29} +(34.8501 + 20.1207i) q^{31} +(16.2969 + 42.9510i) q^{33} +(6.10143 - 10.5680i) q^{35} +17.0230i q^{37} +(1.21848 - 7.50505i) q^{39} +(-46.5938 + 26.9009i) q^{41} -50.4200 q^{43} +(-3.31862 - 16.2297i) q^{45} +(-32.3041 + 55.9524i) q^{47} +(2.52290 - 4.36980i) q^{49} +(49.1338 - 60.1974i) q^{51} +(-88.6168 + 51.1629i) q^{53} +(-14.0926 + 24.4091i) q^{55} +(-30.3988 + 48.2174i) q^{57} +(47.8066 - 27.6012i) q^{59} +(-41.5863 + 72.0295i) q^{61} +(11.9535 + 58.4586i) q^{63} +(4.03993 - 2.33245i) q^{65} +111.101i q^{67} +(-15.0528 - 2.44388i) q^{69} +(83.8226 + 48.3950i) q^{71} +(-66.6462 + 115.435i) q^{73} +(-40.9976 + 50.2291i) q^{75} +(50.7609 - 87.9205i) q^{77} +33.4509i q^{79} +(64.7855 + 48.6194i) q^{81} +(-45.0486 - 78.0264i) q^{83} +47.6740 q^{85} +(34.5734 + 28.2193i) q^{87} +(-26.4870 + 15.2923i) q^{89} +(-14.5517 + 8.40140i) q^{91} +(-93.5256 - 76.3368i) q^{93} +(-34.7115 + 4.25727i) q^{95} -79.5927i q^{97} +(-27.6093 - 135.023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80 q - q^{7} + 4 q^{9} + O(q^{10}) \) \( 80 q - q^{7} + 4 q^{9} - 6 q^{11} + 33 q^{15} - 21 q^{17} - 20 q^{19} - 48 q^{23} - 200 q^{25} - 63 q^{27} - 27 q^{29} - 24 q^{31} + 27 q^{33} - 54 q^{35} - 81 q^{39} - 18 q^{41} - 152 q^{43} + 188 q^{45} - 12 q^{47} - 267 q^{49} - 126 q^{51} - 36 q^{53} + 126 q^{57} - 135 q^{59} - 7 q^{61} - 190 q^{63} - 288 q^{65} + 48 q^{69} - 81 q^{71} + 55 q^{73} + 165 q^{75} + 30 q^{77} + 28 q^{81} - 93 q^{83} + 306 q^{87} + 216 q^{89} + 96 q^{91} + 24 q^{93} + 288 q^{95} - 241 q^{99} + O(q^{100}) \)

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
\(3\) −2.96123 0.480768i −0.987075 0.160256i
\(4\) 0 0
\(5\) −0.920304 1.59401i −0.184061 0.318803i 0.759199 0.650859i \(-0.225591\pi\)
−0.943260 + 0.332056i \(0.892258\pi\)
\(6\) 0 0
\(7\) 3.31490 + 5.74157i 0.473557 + 0.820225i 0.999542 0.0302694i \(-0.00963651\pi\)
−0.525985 + 0.850494i \(0.676303\pi\)
\(8\) 0 0
\(9\) 8.53772 + 2.84733i 0.948636 + 0.316370i
\(10\) 0 0
\(11\) −7.65648 13.2614i −0.696044 1.20558i −0.969828 0.243792i \(-0.921609\pi\)
0.273784 0.961791i \(-0.411725\pi\)
\(12\) 0 0
\(13\) 2.53444i 0.194957i 0.995238 + 0.0974784i \(0.0310777\pi\)
−0.995238 + 0.0974784i \(0.968922\pi\)
\(14\) 0 0
\(15\) 1.95888 + 5.16269i 0.130592 + 0.344179i
\(16\) 0 0
\(17\) −12.9506 + 22.4311i −0.761800 + 1.31948i 0.180121 + 0.983644i \(0.442351\pi\)
−0.941922 + 0.335833i \(0.890982\pi\)
\(18\) 0 0
\(19\) 7.42625 17.4886i 0.390856 0.920452i
\(20\) 0 0
\(21\) −7.05580 18.5958i −0.335990 0.885514i
\(22\) 0 0
\(23\) 5.08329 0.221013 0.110506 0.993875i \(-0.464753\pi\)
0.110506 + 0.993875i \(0.464753\pi\)
\(24\) 0 0
\(25\) 10.8061 18.7167i 0.432243 0.748667i
\(26\) 0 0
\(27\) −23.9132 12.5362i −0.885675 0.464305i
\(28\) 0 0
\(29\) −12.8830 7.43798i −0.444240 0.256482i 0.261155 0.965297i \(-0.415897\pi\)
−0.705394 + 0.708815i \(0.749230\pi\)
\(30\) 0 0
\(31\) 34.8501 + 20.1207i 1.12420 + 0.649055i 0.942469 0.334294i \(-0.108498\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(32\) 0 0
\(33\) 16.2969 + 42.9510i 0.493846 + 1.30155i
\(34\) 0 0
\(35\) 6.10143 10.5680i 0.174326 0.301942i
\(36\) 0 0
\(37\) 17.0230i 0.460082i 0.973181 + 0.230041i \(0.0738861\pi\)
−0.973181 + 0.230041i \(0.926114\pi\)
\(38\) 0 0
\(39\) 1.21848 7.50505i 0.0312430 0.192437i
\(40\) 0 0
\(41\) −46.5938 + 26.9009i −1.13643 + 0.656121i −0.945545 0.325491i \(-0.894470\pi\)
−0.190889 + 0.981612i \(0.561137\pi\)
\(42\) 0 0
\(43\) −50.4200 −1.17256 −0.586279 0.810109i \(-0.699408\pi\)
−0.586279 + 0.810109i \(0.699408\pi\)
\(44\) 0 0
\(45\) −3.31862 16.2297i −0.0737472 0.360659i
\(46\) 0 0
\(47\) −32.3041 + 55.9524i −0.687322 + 1.19048i 0.285380 + 0.958415i \(0.407880\pi\)
−0.972701 + 0.232061i \(0.925453\pi\)
\(48\) 0 0
\(49\) 2.52290 4.36980i 0.0514878 0.0891795i
\(50\) 0 0
\(51\) 49.1338 60.1974i 0.963409 1.18034i
\(52\) 0 0
\(53\) −88.6168 + 51.1629i −1.67201 + 0.965338i −0.705506 + 0.708704i \(0.749280\pi\)
−0.966509 + 0.256634i \(0.917387\pi\)
\(54\) 0 0
\(55\) −14.0926 + 24.4091i −0.256229 + 0.443801i
\(56\) 0 0
\(57\) −30.3988 + 48.2174i −0.533312 + 0.845919i
\(58\) 0 0
\(59\) 47.8066 27.6012i 0.810281 0.467816i −0.0367722 0.999324i \(-0.511708\pi\)
0.847054 + 0.531508i \(0.178374\pi\)
\(60\) 0 0
\(61\) −41.5863 + 72.0295i −0.681742 + 1.18081i 0.292707 + 0.956202i \(0.405444\pi\)
−0.974449 + 0.224609i \(0.927889\pi\)
\(62\) 0 0
\(63\) 11.9535 + 58.4586i 0.189739 + 0.927914i
\(64\) 0 0
\(65\) 4.03993 2.33245i 0.0621527 0.0358839i
\(66\) 0 0
\(67\) 111.101i 1.65822i 0.559086 + 0.829110i \(0.311152\pi\)
−0.559086 + 0.829110i \(0.688848\pi\)
\(68\) 0 0
\(69\) −15.0528 2.44388i −0.218156 0.0354186i
\(70\) 0 0
\(71\) 83.8226 + 48.3950i 1.18060 + 0.681620i 0.956153 0.292866i \(-0.0946091\pi\)
0.224447 + 0.974486i \(0.427942\pi\)
\(72\) 0 0
\(73\) −66.6462 + 115.435i −0.912961 + 1.58130i −0.103102 + 0.994671i \(0.532877\pi\)
−0.809859 + 0.586624i \(0.800456\pi\)
\(74\) 0 0
\(75\) −40.9976 + 50.2291i −0.546635 + 0.669721i
\(76\) 0 0
\(77\) 50.7609 87.9205i 0.659232 1.14182i
\(78\) 0 0
\(79\) 33.4509i 0.423429i 0.977332 + 0.211715i \(0.0679048\pi\)
−0.977332 + 0.211715i \(0.932095\pi\)
\(80\) 0 0
\(81\) 64.7855 + 48.6194i 0.799820 + 0.600239i
\(82\) 0 0
\(83\) −45.0486 78.0264i −0.542754 0.940077i −0.998745 0.0500924i \(-0.984048\pi\)
0.455991 0.889984i \(-0.349285\pi\)
\(84\) 0 0
\(85\) 47.6740 0.560870
\(86\) 0 0
\(87\) 34.5734 + 28.2193i 0.397396 + 0.324359i
\(88\) 0 0
\(89\) −26.4870 + 15.2923i −0.297606 + 0.171823i −0.641367 0.767234i \(-0.721632\pi\)
0.343761 + 0.939057i \(0.388299\pi\)
\(90\) 0 0
\(91\) −14.5517 + 8.40140i −0.159908 + 0.0923231i
\(92\) 0 0
\(93\) −93.5256 76.3368i −1.00565 0.820826i
\(94\) 0 0
\(95\) −34.7115 + 4.25727i −0.365384 + 0.0448134i
\(96\) 0 0
\(97\) 79.5927i 0.820544i −0.911963 0.410272i \(-0.865434\pi\)
0.911963 0.410272i \(-0.134566\pi\)
\(98\) 0 0
\(99\) −27.6093 135.023i −0.278882 1.36387i
\(100\) 0 0
\(101\) −61.3987 + 106.346i −0.607908 + 1.05293i 0.383677 + 0.923467i \(0.374658\pi\)
−0.991585 + 0.129460i \(0.958676\pi\)
\(102\) 0 0
\(103\) −57.5120 33.2045i −0.558369 0.322374i 0.194122 0.980977i \(-0.437814\pi\)
−0.752490 + 0.658603i \(0.771148\pi\)
\(104\) 0 0
\(105\) −23.1485 + 28.3608i −0.220462 + 0.270103i
\(106\) 0 0
\(107\) 14.3363i 0.133984i −0.997753 0.0669922i \(-0.978660\pi\)
0.997753 0.0669922i \(-0.0213403\pi\)
\(108\) 0 0
\(109\) 20.7750 + 11.9944i 0.190596 + 0.110041i 0.592262 0.805746i \(-0.298235\pi\)
−0.401665 + 0.915786i \(0.631569\pi\)
\(110\) 0 0
\(111\) 8.18414 50.4091i 0.0737310 0.454136i
\(112\) 0 0
\(113\) −41.1529 23.7596i −0.364185 0.210262i 0.306730 0.951797i \(-0.400765\pi\)
−0.670915 + 0.741534i \(0.734098\pi\)
\(114\) 0 0
\(115\) −4.67817 8.10283i −0.0406797 0.0704594i
\(116\) 0 0
\(117\) −7.21638 + 21.6383i −0.0616784 + 0.184943i
\(118\) 0 0
\(119\) −171.720 −1.44302
\(120\) 0 0
\(121\) −56.7434 + 98.2824i −0.468954 + 0.812251i
\(122\) 0 0
\(123\) 150.908 57.2590i 1.22689 0.465520i
\(124\) 0 0
\(125\) −85.7947 −0.686358
\(126\) 0 0
\(127\) 145.228 83.8477i 1.14353 0.660218i 0.196228 0.980558i \(-0.437131\pi\)
0.947302 + 0.320341i \(0.103797\pi\)
\(128\) 0 0
\(129\) 149.305 + 24.2403i 1.15740 + 0.187910i
\(130\) 0 0
\(131\) −118.141 204.627i −0.901842 1.56204i −0.825102 0.564984i \(-0.808882\pi\)
−0.0767398 0.997051i \(-0.524451\pi\)
\(132\) 0 0
\(133\) 125.029 15.3345i 0.940070 0.115297i
\(134\) 0 0
\(135\) 2.02449 + 49.6552i 0.0149962 + 0.367816i
\(136\) 0 0
\(137\) 15.6168 27.0491i 0.113991 0.197439i −0.803385 0.595460i \(-0.796970\pi\)
0.917376 + 0.398021i \(0.130303\pi\)
\(138\) 0 0
\(139\) 34.3740 0.247295 0.123648 0.992326i \(-0.460541\pi\)
0.123648 + 0.992326i \(0.460541\pi\)
\(140\) 0 0
\(141\) 122.560 150.157i 0.869219 1.06494i
\(142\) 0 0
\(143\) 33.6102 19.4049i 0.235037 0.135698i
\(144\) 0 0
\(145\) 27.3808i 0.188833i
\(146\) 0 0
\(147\) −9.57175 + 11.7270i −0.0651139 + 0.0797757i
\(148\) 0 0
\(149\) 112.018 + 194.021i 0.751799 + 1.30215i 0.946950 + 0.321381i \(0.104147\pi\)
−0.195151 + 0.980773i \(0.562520\pi\)
\(150\) 0 0
\(151\) −10.4885 + 6.05557i −0.0694606 + 0.0401031i −0.534328 0.845277i \(-0.679435\pi\)
0.464867 + 0.885380i \(0.346102\pi\)
\(152\) 0 0
\(153\) −174.437 + 154.636i −1.14011 + 1.01069i
\(154\) 0 0
\(155\) 74.0687i 0.477863i
\(156\) 0 0
\(157\) 97.9548 + 169.663i 0.623916 + 1.08065i 0.988749 + 0.149582i \(0.0477927\pi\)
−0.364833 + 0.931073i \(0.618874\pi\)
\(158\) 0 0
\(159\) 287.012 108.901i 1.80511 0.684911i
\(160\) 0 0
\(161\) 16.8506 + 29.1861i 0.104662 + 0.181280i
\(162\) 0 0
\(163\) −314.591 −1.93001 −0.965003 0.262239i \(-0.915539\pi\)
−0.965003 + 0.262239i \(0.915539\pi\)
\(164\) 0 0
\(165\) 53.4664 65.5055i 0.324039 0.397003i
\(166\) 0 0
\(167\) 103.021i 0.616890i 0.951242 + 0.308445i \(0.0998085\pi\)
−0.951242 + 0.308445i \(0.900191\pi\)
\(168\) 0 0
\(169\) 162.577 0.961992
\(170\) 0 0
\(171\) 113.199 128.168i 0.661983 0.749519i
\(172\) 0 0
\(173\) 40.6365i 0.234893i −0.993079 0.117447i \(-0.962529\pi\)
0.993079 0.117447i \(-0.0374709\pi\)
\(174\) 0 0
\(175\) 143.284 0.818767
\(176\) 0 0
\(177\) −154.836 + 58.7494i −0.874779 + 0.331917i
\(178\) 0 0
\(179\) 74.3147i 0.415166i −0.978217 0.207583i \(-0.933440\pi\)
0.978217 0.207583i \(-0.0665597\pi\)
\(180\) 0 0
\(181\) −85.8009 + 49.5372i −0.474038 + 0.273686i −0.717929 0.696117i \(-0.754910\pi\)
0.243890 + 0.969803i \(0.421576\pi\)
\(182\) 0 0
\(183\) 157.776 193.302i 0.862163 1.05630i
\(184\) 0 0
\(185\) 27.1349 15.6664i 0.146675 0.0846831i
\(186\) 0 0
\(187\) 396.624 2.12099
\(188\) 0 0
\(189\) −7.29214 178.856i −0.0385828 0.946327i
\(190\) 0 0
\(191\) −166.239 287.934i −0.870359 1.50751i −0.861626 0.507544i \(-0.830553\pi\)
−0.00873349 0.999962i \(-0.502780\pi\)
\(192\) 0 0
\(193\) −229.030 + 132.231i −1.18669 + 0.685133i −0.957552 0.288262i \(-0.906923\pi\)
−0.229134 + 0.973395i \(0.573589\pi\)
\(194\) 0 0
\(195\) −13.0845 + 4.96465i −0.0671001 + 0.0254598i
\(196\) 0 0
\(197\) 36.4851 0.185203 0.0926017 0.995703i \(-0.470482\pi\)
0.0926017 + 0.995703i \(0.470482\pi\)
\(198\) 0 0
\(199\) −151.188 261.866i −0.759740 1.31591i −0.942983 0.332841i \(-0.891993\pi\)
0.183243 0.983068i \(-0.441341\pi\)
\(200\) 0 0
\(201\) 53.4137 328.994i 0.265740 1.63679i
\(202\) 0 0
\(203\) 98.6246i 0.485835i
\(204\) 0 0
\(205\) 85.7609 + 49.5141i 0.418346 + 0.241532i
\(206\) 0 0
\(207\) 43.3997 + 14.4738i 0.209660 + 0.0699217i
\(208\) 0 0
\(209\) −288.782 + 35.4184i −1.38173 + 0.169466i
\(210\) 0 0
\(211\) 249.001 143.761i 1.18010 0.681330i 0.224061 0.974575i \(-0.428068\pi\)
0.956037 + 0.293245i \(0.0947351\pi\)
\(212\) 0 0
\(213\) −224.951 183.608i −1.05611 0.862009i
\(214\) 0 0
\(215\) 46.4017 + 80.3702i 0.215822 + 0.373815i
\(216\) 0 0
\(217\) 266.792i 1.22946i
\(218\) 0 0
\(219\) 252.852 309.786i 1.15457 1.41455i
\(220\) 0 0
\(221\) −56.8503 32.8225i −0.257241 0.148518i
\(222\) 0 0
\(223\) 414.250i 1.85762i 0.370552 + 0.928812i \(0.379169\pi\)
−0.370552 + 0.928812i \(0.620831\pi\)
\(224\) 0 0
\(225\) 145.552 129.029i 0.646897 0.573464i
\(226\) 0 0
\(227\) 235.073 135.719i 1.03556 0.597882i 0.116989 0.993133i \(-0.462676\pi\)
0.918573 + 0.395251i \(0.129343\pi\)
\(228\) 0 0
\(229\) −23.6064 + 40.8875i −0.103085 + 0.178548i −0.912954 0.408062i \(-0.866205\pi\)
0.809869 + 0.586610i \(0.199538\pi\)
\(230\) 0 0
\(231\) −192.584 + 235.948i −0.833696 + 1.02142i
\(232\) 0 0
\(233\) 140.000 242.488i 0.600860 1.04072i −0.391832 0.920037i \(-0.628158\pi\)
0.992691 0.120682i \(-0.0385083\pi\)
\(234\) 0 0
\(235\) 118.918 0.506036
\(236\) 0 0
\(237\) 16.0821 99.0558i 0.0678572 0.417957i
\(238\) 0 0
\(239\) −116.760 + 202.234i −0.488534 + 0.846166i −0.999913 0.0131891i \(-0.995802\pi\)
0.511379 + 0.859356i \(0.329135\pi\)
\(240\) 0 0
\(241\) 88.3112 + 50.9865i 0.366436 + 0.211562i 0.671900 0.740641i \(-0.265478\pi\)
−0.305464 + 0.952204i \(0.598812\pi\)
\(242\) 0 0
\(243\) −168.470 175.120i −0.693291 0.720658i
\(244\) 0 0
\(245\) −9.28735 −0.0379076
\(246\) 0 0
\(247\) 44.3237 + 18.8214i 0.179448 + 0.0761999i
\(248\) 0 0
\(249\) 95.8863 + 252.712i 0.385086 + 1.01491i
\(250\) 0 0
\(251\) −32.2790 55.9089i −0.128602 0.222745i 0.794533 0.607220i \(-0.207716\pi\)
−0.923135 + 0.384476i \(0.874382\pi\)
\(252\) 0 0
\(253\) −38.9201 67.4116i −0.153834 0.266449i
\(254\) 0 0
\(255\) −141.173 22.9201i −0.553621 0.0898829i
\(256\) 0 0
\(257\) 135.701i 0.528018i 0.964520 + 0.264009i \(0.0850449\pi\)
−0.964520 + 0.264009i \(0.914955\pi\)
\(258\) 0 0
\(259\) −97.7390 + 56.4296i −0.377371 + 0.217875i
\(260\) 0 0
\(261\) −88.8128 100.185i −0.340279 0.383852i
\(262\) 0 0
\(263\) −343.580 −1.30639 −0.653195 0.757190i \(-0.726572\pi\)
−0.653195 + 0.757190i \(0.726572\pi\)
\(264\) 0 0
\(265\) 163.109 + 94.1709i 0.615505 + 0.355362i
\(266\) 0 0
\(267\) 85.7859 32.5497i 0.321296 0.121909i
\(268\) 0 0
\(269\) 406.540 + 234.716i 1.51130 + 0.872550i 0.999913 + 0.0132004i \(0.00420193\pi\)
0.511388 + 0.859350i \(0.329131\pi\)
\(270\) 0 0
\(271\) −5.21532 + 9.03320i −0.0192447 + 0.0333328i −0.875487 0.483241i \(-0.839459\pi\)
0.856243 + 0.516574i \(0.172793\pi\)
\(272\) 0 0
\(273\) 47.1299 17.8825i 0.172637 0.0655036i
\(274\) 0 0
\(275\) −330.946 −1.20344
\(276\) 0 0
\(277\) −239.373 414.607i −0.864163 1.49677i −0.867875 0.496782i \(-0.834515\pi\)
0.00371208 0.999993i \(-0.498818\pi\)
\(278\) 0 0
\(279\) 240.250 + 271.015i 0.861112 + 0.971379i
\(280\) 0 0
\(281\) −225.326 130.092i −0.801873 0.462962i 0.0422526 0.999107i \(-0.486547\pi\)
−0.844126 + 0.536145i \(0.819880\pi\)
\(282\) 0 0
\(283\) 135.474 + 234.648i 0.478707 + 0.829145i 0.999702 0.0244150i \(-0.00777232\pi\)
−0.520995 + 0.853560i \(0.674439\pi\)
\(284\) 0 0
\(285\) 104.835 + 4.08143i 0.367843 + 0.0143208i
\(286\) 0 0
\(287\) −308.907 178.348i −1.07633 0.621421i
\(288\) 0 0
\(289\) −190.936 330.712i −0.660680 1.14433i
\(290\) 0 0
\(291\) −38.2657 + 235.692i −0.131497 + 0.809938i
\(292\) 0 0
\(293\) 196.791 + 113.617i 0.671641 + 0.387772i 0.796698 0.604377i \(-0.206578\pi\)
−0.125057 + 0.992150i \(0.539911\pi\)
\(294\) 0 0
\(295\) −87.9932 50.8029i −0.298282 0.172213i
\(296\) 0 0
\(297\) 16.8428 + 413.107i 0.0567097 + 1.39093i
\(298\) 0 0
\(299\) 12.8833i 0.0430879i
\(300\) 0 0
\(301\) −167.137 289.490i −0.555273 0.961761i
\(302\) 0 0
\(303\) 232.943 285.395i 0.768789 0.941898i
\(304\) 0 0
\(305\) 153.088 0.501928
\(306\) 0 0
\(307\) 429.650 + 248.058i 1.39951 + 0.808008i 0.994341 0.106233i \(-0.0338790\pi\)
0.405170 + 0.914241i \(0.367212\pi\)
\(308\) 0 0
\(309\) 154.342 + 125.976i 0.499489 + 0.407690i
\(310\) 0 0
\(311\) −86.7171 + 150.198i −0.278833 + 0.482953i −0.971095 0.238693i \(-0.923281\pi\)
0.692262 + 0.721646i \(0.256614\pi\)
\(312\) 0 0
\(313\) 105.550 182.818i 0.337221 0.584084i −0.646688 0.762755i \(-0.723846\pi\)
0.983909 + 0.178671i \(0.0571797\pi\)
\(314\) 0 0
\(315\) 82.1828 72.8537i 0.260898 0.231282i
\(316\) 0 0
\(317\) −143.794 83.0192i −0.453607 0.261890i 0.255745 0.966744i \(-0.417679\pi\)
−0.709352 + 0.704854i \(0.751013\pi\)
\(318\) 0 0
\(319\) 227.795i 0.714091i
\(320\) 0 0
\(321\) −6.89246 + 42.4531i −0.0214718 + 0.132253i
\(322\) 0 0
\(323\) 296.114 + 393.067i 0.916761 + 1.21693i
\(324\) 0 0
\(325\) 47.4363 + 27.3873i 0.145958 + 0.0842688i
\(326\) 0 0
\(327\) −55.7529 45.5062i −0.170498 0.139163i
\(328\) 0 0
\(329\) −428.339 −1.30194
\(330\) 0 0
\(331\) −182.184 + 105.184i −0.550404 + 0.317776i −0.749285 0.662248i \(-0.769603\pi\)
0.198881 + 0.980024i \(0.436269\pi\)
\(332\) 0 0
\(333\) −48.4702 + 145.338i −0.145556 + 0.436450i
\(334\) 0 0
\(335\) 177.096 102.246i 0.528645 0.305213i
\(336\) 0 0
\(337\) −178.809 + 103.235i −0.530590 + 0.306336i −0.741257 0.671222i \(-0.765770\pi\)
0.210667 + 0.977558i \(0.432437\pi\)
\(338\) 0 0
\(339\) 110.440 + 90.1427i 0.325782 + 0.265908i
\(340\) 0 0
\(341\) 616.215i 1.80708i
\(342\) 0 0
\(343\) 358.313 1.04464
\(344\) 0 0
\(345\) 9.95754 + 26.2434i 0.0288624 + 0.0760679i
\(346\) 0 0
\(347\) 76.2543 + 132.076i 0.219753 + 0.380624i 0.954732 0.297466i \(-0.0961415\pi\)
−0.734979 + 0.678090i \(0.762808\pi\)
\(348\) 0 0
\(349\) 22.5332 + 39.0287i 0.0645651 + 0.111830i 0.896501 0.443042i \(-0.146101\pi\)
−0.831936 + 0.554872i \(0.812767\pi\)
\(350\) 0 0
\(351\) 31.7723 60.6066i 0.0905195 0.172668i
\(352\) 0 0
\(353\) −87.1767 150.995i −0.246960 0.427747i 0.715721 0.698386i \(-0.246098\pi\)
−0.962681 + 0.270640i \(0.912765\pi\)
\(354\) 0 0
\(355\) 178.153i 0.501838i
\(356\) 0 0
\(357\) 508.501 + 82.5574i 1.42437 + 0.231253i
\(358\) 0 0
\(359\) −85.1783 + 147.533i −0.237265 + 0.410956i −0.959929 0.280244i \(-0.909584\pi\)
0.722663 + 0.691200i \(0.242918\pi\)
\(360\) 0 0
\(361\) −250.701 259.749i −0.694464 0.719528i
\(362\) 0 0
\(363\) 215.281 263.756i 0.593061 0.726601i
\(364\) 0 0
\(365\) 245.339 0.672161
\(366\) 0 0
\(367\) 206.861 358.293i 0.563653 0.976276i −0.433520 0.901144i \(-0.642729\pi\)
0.997174 0.0751323i \(-0.0239379\pi\)
\(368\) 0 0
\(369\) −474.401 + 97.0050i −1.28564 + 0.262886i
\(370\) 0 0
\(371\) −587.511 339.200i −1.58359 0.914285i
\(372\) 0 0
\(373\) −37.5725 21.6925i −0.100731 0.0581568i 0.448788 0.893638i \(-0.351856\pi\)
−0.549519 + 0.835481i \(0.685189\pi\)
\(374\) 0 0
\(375\) 254.058 + 41.2474i 0.677487 + 0.109993i
\(376\) 0 0
\(377\) 18.8511 32.6511i 0.0500029 0.0866076i
\(378\) 0 0
\(379\) 151.050i 0.398548i 0.979944 + 0.199274i \(0.0638583\pi\)
−0.979944 + 0.199274i \(0.936142\pi\)
\(380\) 0 0
\(381\) −470.365 + 178.471i −1.23455 + 0.468427i
\(382\) 0 0
\(383\) 150.175 86.7033i 0.392101 0.226379i −0.290969 0.956732i \(-0.593978\pi\)
0.683070 + 0.730353i \(0.260644\pi\)
\(384\) 0 0
\(385\) −186.862 −0.485355
\(386\) 0 0
\(387\) −430.472 143.562i −1.11233 0.370962i
\(388\) 0 0
\(389\) −42.1929 + 73.0802i −0.108465 + 0.187867i −0.915149 0.403117i \(-0.867927\pi\)
0.806684 + 0.590984i \(0.201260\pi\)
\(390\) 0 0
\(391\) −65.8317 + 114.024i −0.168367 + 0.291621i
\(392\) 0 0
\(393\) 251.465 + 662.744i 0.639860 + 1.68637i
\(394\) 0 0
\(395\) 53.3212 30.7850i 0.134990 0.0779368i
\(396\) 0 0
\(397\) −277.537 + 480.708i −0.699085 + 1.21085i 0.269699 + 0.962945i \(0.413076\pi\)
−0.968784 + 0.247906i \(0.920258\pi\)
\(398\) 0 0
\(399\) −377.612 14.7011i −0.946397 0.0368450i
\(400\) 0 0
\(401\) 271.836 156.944i 0.677894 0.391382i −0.121167 0.992632i \(-0.538664\pi\)
0.799061 + 0.601250i \(0.205330\pi\)
\(402\) 0 0
\(403\) −50.9947 + 88.3254i −0.126538 + 0.219170i
\(404\) 0 0
\(405\) 17.8776 148.013i 0.0441423 0.365465i
\(406\) 0 0
\(407\) 225.750 130.337i 0.554667 0.320237i
\(408\) 0 0
\(409\) 100.493i 0.245705i 0.992425 + 0.122852i \(0.0392042\pi\)
−0.992425 + 0.122852i \(0.960796\pi\)
\(410\) 0 0
\(411\) −59.2493 + 72.5905i −0.144159 + 0.176619i
\(412\) 0 0
\(413\) 316.948 + 182.990i 0.767429 + 0.443075i
\(414\) 0 0
\(415\) −82.9167 + 143.616i −0.199799 + 0.346063i
\(416\) 0 0
\(417\) −101.789 16.5259i −0.244099 0.0396305i
\(418\) 0 0
\(419\) −229.603 + 397.685i −0.547980 + 0.949129i 0.450433 + 0.892810i \(0.351270\pi\)
−0.998413 + 0.0563185i \(0.982064\pi\)
\(420\) 0 0
\(421\) 77.2913i 0.183590i −0.995778 0.0917949i \(-0.970740\pi\)
0.995778 0.0917949i \(-0.0292604\pi\)
\(422\) 0 0
\(423\) −435.118 + 385.725i −1.02865 + 0.911880i
\(424\) 0 0
\(425\) 279.891 + 484.785i 0.658566 + 1.14067i
\(426\) 0 0
\(427\) −551.417 −1.29137
\(428\) 0 0
\(429\) −108.857 + 41.3035i −0.253745 + 0.0962785i
\(430\) 0 0
\(431\) 353.010 203.810i 0.819049 0.472878i −0.0310396 0.999518i \(-0.509882\pi\)
0.850088 + 0.526640i \(0.176548\pi\)
\(432\) 0 0
\(433\) 539.985 311.760i 1.24708 0.720001i 0.276553 0.960999i \(-0.410808\pi\)
0.970526 + 0.240998i \(0.0774746\pi\)
\(434\) 0 0
\(435\) 13.1638 81.0808i 0.0302617 0.186393i
\(436\) 0 0
\(437\) 37.7498 88.8995i 0.0863840 0.203431i
\(438\) 0 0
\(439\) 463.843i 1.05659i 0.849061 + 0.528294i \(0.177168\pi\)
−0.849061 + 0.528294i \(0.822832\pi\)
\(440\) 0 0
\(441\) 33.9821 30.1246i 0.0770569 0.0683097i
\(442\) 0 0
\(443\) 39.5266 68.4622i 0.0892249 0.154542i −0.817959 0.575277i \(-0.804894\pi\)
0.907184 + 0.420735i \(0.138228\pi\)
\(444\) 0 0
\(445\) 48.7521 + 28.1470i 0.109555 + 0.0632518i
\(446\) 0 0
\(447\) −238.432 628.395i −0.533404 1.40581i
\(448\) 0 0
\(449\) 368.400i 0.820491i −0.911975 0.410245i \(-0.865443\pi\)
0.911975 0.410245i \(-0.134557\pi\)
\(450\) 0 0
\(451\) 713.489 + 411.933i 1.58202 + 0.913377i
\(452\) 0 0
\(453\) 33.9703 12.8893i 0.0749896 0.0284533i
\(454\) 0 0
\(455\) 26.7839 + 15.4637i 0.0588657 + 0.0339861i
\(456\) 0 0
\(457\) −333.410 577.483i −0.729562 1.26364i −0.957068 0.289862i \(-0.906390\pi\)
0.227506 0.973777i \(-0.426943\pi\)
\(458\) 0 0
\(459\) 590.893 374.048i 1.28735 0.814920i
\(460\) 0 0
\(461\) −634.642 −1.37666 −0.688332 0.725396i \(-0.741657\pi\)
−0.688332 + 0.725396i \(0.741657\pi\)
\(462\) 0 0
\(463\) −187.291 + 324.397i −0.404516 + 0.700642i −0.994265 0.106944i \(-0.965893\pi\)
0.589749 + 0.807587i \(0.299227\pi\)
\(464\) 0 0
\(465\) −35.6099 + 219.334i −0.0765804 + 0.471686i
\(466\) 0 0
\(467\) 246.992 0.528890 0.264445 0.964401i \(-0.414811\pi\)
0.264445 + 0.964401i \(0.414811\pi\)
\(468\) 0 0
\(469\) −637.893 + 368.287i −1.36011 + 0.785261i
\(470\) 0 0
\(471\) −208.498 549.503i −0.442671 1.16667i
\(472\) 0 0
\(473\) 386.040 + 668.641i 0.816152 + 1.41362i
\(474\) 0 0
\(475\) −247.080 327.978i −0.520168 0.690480i
\(476\) 0 0
\(477\) −902.263 + 184.494i −1.89154 + 0.386780i
\(478\) 0 0
\(479\) 254.438 440.699i 0.531185 0.920040i −0.468152 0.883648i \(-0.655080\pi\)
0.999338 0.0363920i \(-0.0115865\pi\)
\(480\) 0 0
\(481\) −43.1438 −0.0896961
\(482\) 0 0
\(483\) −35.8667 94.5278i −0.0742581 0.195710i
\(484\) 0 0
\(485\) −126.872 + 73.2495i −0.261591 + 0.151030i
\(486\) 0 0
\(487\) 358.976i 0.737118i −0.929604 0.368559i \(-0.879851\pi\)
0.929604 0.368559i \(-0.120149\pi\)
\(488\) 0 0
\(489\) 931.575 + 151.245i 1.90506 + 0.309295i
\(490\) 0 0
\(491\) 248.985 + 431.254i 0.507097 + 0.878318i 0.999966 + 0.00821480i \(0.00261488\pi\)
−0.492869 + 0.870104i \(0.664052\pi\)
\(492\) 0 0
\(493\) 333.684 192.653i 0.676844 0.390776i
\(494\) 0 0
\(495\) −189.819 + 168.272i −0.383473 + 0.339943i
\(496\) 0 0
\(497\) 641.698i 1.29114i
\(498\) 0 0
\(499\) −377.629 654.073i −0.756772 1.31077i −0.944489 0.328544i \(-0.893442\pi\)
0.187717 0.982223i \(-0.439891\pi\)
\(500\) 0 0
\(501\) 49.5290 305.067i 0.0988603 0.608917i
\(502\) 0 0
\(503\) 34.5273 + 59.8030i 0.0686427 + 0.118893i 0.898304 0.439374i \(-0.144800\pi\)
−0.829661 + 0.558267i \(0.811466\pi\)
\(504\) 0 0
\(505\) 226.022 0.447568
\(506\) 0 0
\(507\) −481.426 78.1617i −0.949559 0.154165i
\(508\) 0 0
\(509\) 414.128i 0.813611i 0.913515 + 0.406806i \(0.133357\pi\)
−0.913515 + 0.406806i \(0.866643\pi\)
\(510\) 0 0
\(511\) −883.701 −1.72936
\(512\) 0 0
\(513\) −396.827 + 325.111i −0.773542 + 0.633745i
\(514\) 0 0
\(515\) 122.233i 0.237346i
\(516\) 0 0
\(517\) 989.343 1.91362
\(518\) 0 0
\(519\) −19.5368 + 120.334i −0.0376431 + 0.231857i
\(520\) 0 0
\(521\) 395.573i 0.759258i 0.925139 + 0.379629i \(0.123948\pi\)
−0.925139 + 0.379629i \(0.876052\pi\)
\(522\) 0 0
\(523\) −430.932 + 248.799i −0.823962 + 0.475715i −0.851781 0.523898i \(-0.824477\pi\)
0.0278188 + 0.999613i \(0.491144\pi\)
\(524\) 0 0
\(525\) −424.297 68.8865i −0.808185 0.131212i
\(526\) 0 0
\(527\) −902.660 + 521.151i −1.71283 + 0.988901i
\(528\) 0 0
\(529\) −503.160 −0.951153
\(530\) 0 0
\(531\) 486.749 99.5300i 0.916665 0.187439i
\(532\) 0 0
\(533\) −68.1788 118.089i −0.127915 0.221556i
\(534\) 0 0
\(535\) −22.8523 + 13.1938i −0.0427146 + 0.0246613i
\(536\) 0 0
\(537\) −35.7282 + 220.063i −0.0665329 + 0.409800i
\(538\) 0 0
\(539\) −77.2662 −0.143351
\(540\) 0 0
\(541\) −116.908 202.490i −0.216095 0.374288i 0.737515 0.675330i \(-0.235999\pi\)
−0.953611 + 0.301042i \(0.902666\pi\)
\(542\) 0 0
\(543\) 277.892 105.440i 0.511772 0.194181i
\(544\) 0 0
\(545\) 44.1541i 0.0810168i
\(546\) 0 0
\(547\) 331.612 + 191.456i 0.606238 + 0.350012i 0.771492 0.636239i \(-0.219511\pi\)
−0.165254 + 0.986251i \(0.552844\pi\)
\(548\) 0 0
\(549\) −560.144 + 496.558i −1.02030 + 0.904478i
\(550\) 0 0
\(551\) −225.752 + 170.068i −0.409713 + 0.308654i
\(552\) 0 0
\(553\) −192.061 + 110.886i −0.347307 + 0.200518i
\(554\) 0 0
\(555\) −87.8846 + 33.3460i −0.158351 + 0.0600830i
\(556\) 0 0
\(557\) 440.741 + 763.386i 0.791277 + 1.37053i 0.925177 + 0.379537i \(0.123917\pi\)
−0.133900 + 0.990995i \(0.542750\pi\)
\(558\) 0 0
\(559\) 127.786i 0.228598i
\(560\) 0 0
\(561\) −1174.49 190.684i −2.09357 0.339901i
\(562\) 0 0
\(563\) −51.5358 29.7542i −0.0915379 0.0528494i 0.453532 0.891240i \(-0.350164\pi\)
−0.545070 + 0.838390i \(0.683497\pi\)
\(564\) 0 0
\(565\) 87.4644i 0.154804i
\(566\) 0 0
\(567\) −64.3946 + 533.139i −0.113571 + 0.940280i
\(568\) 0 0
\(569\) 791.507 456.977i 1.39105 0.803123i 0.397618 0.917551i \(-0.369837\pi\)
0.993432 + 0.114428i \(0.0365034\pi\)
\(570\) 0 0
\(571\) 14.0632 24.3582i 0.0246291 0.0426588i −0.853448 0.521178i \(-0.825493\pi\)
0.878077 + 0.478519i \(0.158826\pi\)
\(572\) 0 0
\(573\) 353.841 + 932.559i 0.617523 + 1.62750i
\(574\) 0 0
\(575\) 54.9304 95.1423i 0.0955312 0.165465i
\(576\) 0 0
\(577\) 696.198 1.20658 0.603291 0.797521i \(-0.293856\pi\)
0.603291 + 0.797521i \(0.293856\pi\)
\(578\) 0 0
\(579\) 741.783 281.455i 1.28115 0.486105i
\(580\) 0 0
\(581\) 298.663 517.299i 0.514049 0.890360i
\(582\) 0 0
\(583\) 1356.99 + 783.456i 2.32759 + 1.34383i
\(584\) 0 0
\(585\) 41.1330 8.41085i 0.0703129 0.0143775i
\(586\) 0 0
\(587\) −249.452 −0.424961 −0.212481 0.977165i \(-0.568154\pi\)
−0.212481 + 0.977165i \(0.568154\pi\)
\(588\) 0 0
\(589\) 610.689 460.058i 1.03682 0.781082i
\(590\) 0 0
\(591\) −108.041 17.5409i −0.182810 0.0296800i
\(592\) 0 0
\(593\) 98.5298 + 170.659i 0.166155 + 0.287789i 0.937065 0.349156i \(-0.113532\pi\)
−0.770910 + 0.636944i \(0.780198\pi\)
\(594\) 0 0
\(595\) 158.034 + 273.724i 0.265604 + 0.460040i
\(596\) 0 0
\(597\) 321.806 + 848.131i 0.539039 + 1.42065i
\(598\) 0 0
\(599\) 350.250i 0.584724i 0.956308 + 0.292362i \(0.0944412\pi\)
−0.956308 + 0.292362i \(0.905559\pi\)
\(600\) 0 0
\(601\) −718.814 + 415.008i −1.19603 + 0.690528i −0.959668 0.281137i \(-0.909289\pi\)
−0.236362 + 0.971665i \(0.575955\pi\)
\(602\) 0 0
\(603\) −316.340 + 948.547i −0.524610 + 1.57305i
\(604\) 0 0
\(605\) 208.885 0.345264
\(606\) 0 0
\(607\) −812.587 469.147i −1.33869 0.772895i −0.352080 0.935970i \(-0.614525\pi\)
−0.986614 + 0.163075i \(0.947859\pi\)
\(608\) 0 0
\(609\) −47.4156 + 292.050i −0.0778581 + 0.479556i
\(610\) 0 0
\(611\) −141.808 81.8728i −0.232091 0.133998i
\(612\) 0 0
\(613\) 89.8809 155.678i 0.146625 0.253961i −0.783353 0.621577i \(-0.786492\pi\)
0.929978 + 0.367615i \(0.119826\pi\)
\(614\) 0 0
\(615\) −230.153 187.854i −0.374232 0.305453i
\(616\) 0 0
\(617\) −121.557 −0.197013 −0.0985067 0.995136i \(-0.531407\pi\)
−0.0985067 + 0.995136i \(0.531407\pi\)
\(618\) 0 0
\(619\) 156.050 + 270.287i 0.252101 + 0.436651i 0.964104 0.265525i \(-0.0855452\pi\)
−0.712003 + 0.702176i \(0.752212\pi\)
\(620\) 0 0
\(621\) −121.558 63.7254i −0.195745 0.102617i
\(622\) 0 0
\(623\) −175.603 101.385i −0.281867 0.162736i
\(624\) 0 0
\(625\) −191.195 331.159i −0.305912 0.529855i
\(626\) 0 0
\(627\) 872.178 + 33.9555i 1.39103 + 0.0541555i
\(628\) 0 0
\(629\) −381.846 220.459i −0.607068 0.350491i
\(630\) 0 0
\(631\) −445.955 772.417i −0.706744 1.22412i −0.966059 0.258323i \(-0.916830\pi\)
0.259315 0.965793i \(-0.416503\pi\)
\(632\) 0 0
\(633\) −806.463 + 305.996i −1.27403 + 0.483406i
\(634\) 0 0
\(635\) −267.309 154.331i −0.420958 0.243040i
\(636\) 0 0
\(637\) 11.0750 + 6.39414i 0.0173862 + 0.0100379i
\(638\) 0 0
\(639\) 577.858 + 651.854i 0.904316 + 1.02012i
\(640\) 0 0
\(641\) 483.178i 0.753788i 0.926256 + 0.376894i \(0.123008\pi\)
−0.926256 + 0.376894i \(0.876992\pi\)
\(642\) 0 0
\(643\) −168.993 292.705i −0.262820 0.455217i 0.704170 0.710031i \(-0.251319\pi\)
−0.966990 + 0.254814i \(0.917986\pi\)
\(644\) 0 0
\(645\) −98.7666 260.303i −0.153127 0.403570i
\(646\) 0 0
\(647\) 556.371 0.859924 0.429962 0.902847i \(-0.358527\pi\)
0.429962 + 0.902847i \(0.358527\pi\)
\(648\) 0 0
\(649\) −732.061 422.655i −1.12798 0.651241i
\(650\) 0 0
\(651\) 128.265 790.033i 0.197028 1.21357i
\(652\) 0 0
\(653\) 11.4095 19.7619i 0.0174725 0.0302632i −0.857157 0.515055i \(-0.827771\pi\)
0.874629 + 0.484792i \(0.161105\pi\)
\(654\) 0 0
\(655\) −217.452 + 376.637i −0.331987 + 0.575019i
\(656\) 0 0
\(657\) −897.687 + 795.785i −1.36634 + 1.21124i
\(658\) 0 0
\(659\) 215.748 + 124.562i 0.327387 + 0.189017i 0.654680 0.755906i \(-0.272803\pi\)
−0.327294 + 0.944923i \(0.606137\pi\)
\(660\) 0 0
\(661\) 948.636i 1.43515i −0.696480 0.717577i \(-0.745251\pi\)
0.696480 0.717577i \(-0.254749\pi\)
\(662\) 0 0
\(663\) 152.566 + 124.527i 0.230115 + 0.187823i
\(664\) 0 0
\(665\) −139.508 185.186i −0.209787 0.278475i
\(666\) 0 0
\(667\) −65.4878 37.8094i −0.0981826 0.0566858i
\(668\) 0 0
\(669\) 199.158 1226.69i 0.297695 1.83361i
\(670\) 0 0
\(671\) 1273.62 1.89809
\(672\) 0 0
\(673\) −498.486 + 287.801i −0.740692 + 0.427639i −0.822321 0.569024i \(-0.807321\pi\)
0.0816286 + 0.996663i \(0.473988\pi\)
\(674\) 0 0
\(675\) −493.045 + 312.109i −0.730437 + 0.462383i
\(676\) 0 0
\(677\) 773.523 446.594i 1.14257 0.659666i 0.195508 0.980702i \(-0.437364\pi\)
0.947067 + 0.321036i \(0.104031\pi\)
\(678\) 0 0
\(679\) 456.987 263.842i 0.673030 0.388574i
\(680\) 0 0
\(681\) −761.352 + 288.880i −1.11799 + 0.424199i
\(682\) 0 0
\(683\) 711.769i 1.04212i −0.853519 0.521061i \(-0.825536\pi\)
0.853519 0.521061i \(-0.174464\pi\)
\(684\) 0 0
\(685\) −57.4889 −0.0839253
\(686\) 0 0
\(687\) 89.5613 109.728i 0.130366 0.159720i
\(688\) 0 0
\(689\) −129.669 224.594i −0.188199 0.325971i
\(690\) 0 0
\(691\) −25.8916 44.8455i −0.0374697 0.0648995i 0.846682 0.532099i \(-0.178596\pi\)
−0.884152 + 0.467199i \(0.845263\pi\)
\(692\) 0 0
\(693\) 683.721 606.108i 0.986610 0.874614i
\(694\) 0 0
\(695\) −31.6345 54.7926i −0.0455173 0.0788383i
\(696\) 0 0
\(697\) 1393.53i 1.99933i
\(698\) 0 0
\(699\) −531.153 + 650.753i −0.759875 + 0.930977i
\(700\) 0 0
\(701\) 448.023 775.998i 0.639120 1.10699i −0.346507 0.938048i \(-0.612632\pi\)
0.985626 0.168940i \(-0.0540345\pi\)
\(702\) 0 0
\(703\) 297.709 + 126.417i 0.423484 + 0.179826i
\(704\) 0 0
\(705\) −352.144 57.1722i −0.499495 0.0810953i
\(706\) 0 0
\(707\) −814.122 −1.15152
\(708\) 0 0
\(709\) 305.107 528.460i 0.430334 0.745360i −0.566568 0.824015i \(-0.691729\pi\)
0.996902 + 0.0786550i \(0.0250626\pi\)
\(710\) 0 0
\(711\) −95.2457 + 285.595i −0.133960 + 0.401680i
\(712\) 0 0
\(713\) 177.153 + 102.279i 0.248462 + 0.143449i
\(714\) 0 0
\(715\) −61.8633 35.7168i −0.0865220 0.0499535i
\(716\) 0 0
\(717\) 442.980 542.726i 0.617824 0.756940i
\(718\) 0 0
\(719\) 18.9204 32.7710i 0.0263148 0.0455786i −0.852568 0.522616i \(-0.824956\pi\)
0.878883 + 0.477038i \(0.158289\pi\)
\(720\) 0 0
\(721\) 440.279i 0.610650i
\(722\) 0 0
\(723\) −236.997 193.440i −0.327796 0.267552i
\(724\) 0 0
\(725\) −278.429 + 160.751i −0.384039 + 0.221725i
\(726\) 0 0
\(727\) 178.913 0.246098 0.123049 0.992401i \(-0.460733\pi\)
0.123049 + 0.992401i \(0.460733\pi\)
\(728\) 0 0
\(729\) 414.685 + 599.564i 0.568841 + 0.822448i
\(730\) 0 0
\(731\) 652.970 1130.98i 0.893256 1.54716i
\(732\) 0 0
\(733\) 220.426 381.790i 0.300718 0.520859i −0.675581 0.737286i \(-0.736107\pi\)
0.976299 + 0.216427i \(0.0694403\pi\)
\(734\) 0 0
\(735\) 27.5019 + 4.46506i 0.0374176 + 0.00607492i
\(736\) 0 0
\(737\) 1473.35 850.640i 1.99912 1.15419i
\(738\) 0 0
\(739\) 129.576 224.433i 0.175340 0.303698i −0.764939 0.644103i \(-0.777231\pi\)
0.940279 + 0.340405i \(0.110564\pi\)
\(740\) 0 0
\(741\) −122.204 77.0438i −0.164918 0.103973i
\(742\) 0 0
\(743\) −583.576 + 336.928i −0.785432 + 0.453470i −0.838352 0.545129i \(-0.816481\pi\)
0.0529197 + 0.998599i \(0.483147\pi\)
\(744\) 0 0
\(745\) 206.181 357.117i 0.276754 0.479351i
\(746\) 0 0
\(747\) −162.445 794.436i −0.217464 1.06350i
\(748\) 0 0
\(749\) 82.3131 47.5235i 0.109897 0.0634493i
\(750\) 0 0
\(751\) 1015.51i 1.35220i 0.736808 + 0.676102i \(0.236332\pi\)
−0.736808 + 0.676102i \(0.763668\pi\)
\(752\) 0 0
\(753\) 68.7062 + 181.078i 0.0912434 + 0.240475i
\(754\) 0 0
\(755\) 19.3053 + 11.1459i 0.0255699 + 0.0147628i
\(756\) 0 0
\(757\) 190.298 329.606i 0.251385 0.435411i −0.712523 0.701649i \(-0.752447\pi\)
0.963907 + 0.266238i \(0.0857807\pi\)
\(758\) 0 0
\(759\) 82.8419 + 218.333i 0.109146 + 0.287658i
\(760\) 0 0
\(761\) −246.211 + 426.449i −0.323536 + 0.560380i −0.981215 0.192918i \(-0.938205\pi\)
0.657679 + 0.753298i \(0.271538\pi\)
\(762\) 0 0
\(763\) 159.041i 0.208442i
\(764\) 0 0
\(765\) 407.027 + 135.743i 0.532062 + 0.177442i
\(766\) 0 0
\(767\) 69.9534 + 121.163i 0.0912039 + 0.157970i
\(768\) 0 0
\(769\) 280.145 0.364298 0.182149 0.983271i \(-0.441695\pi\)
0.182149 + 0.983271i \(0.441695\pi\)
\(770\) 0 0
\(771\) 65.2406 401.840i 0.0846181 0.521194i
\(772\) 0 0
\(773\) 765.269 441.828i 0.989999 0.571576i 0.0847249 0.996404i \(-0.472999\pi\)
0.905274 + 0.424828i \(0.139666\pi\)
\(774\) 0 0
\(775\) 753.186 434.852i 0.971853 0.561100i
\(776\) 0 0
\(777\) 316.557 120.111i 0.407409 0.154583i
\(778\) 0 0
\(779\) 124.442 + 1014.63i 0.159746 + 1.30248i
\(780\) 0 0
\(781\) 1482.14i 1.89775i
\(782\) 0 0
\(783\) 214.829 + 339.370i 0.274366 + 0.433423i
\(784\) 0 0
\(785\) 180.296 312.283i 0.229677 0.397812i
\(786\) 0 0
\(787\) 119.325 + 68.8925i 0.151620 + 0.0875381i 0.573891 0.818932i \(-0.305433\pi\)
−0.422270 + 0.906470i \(0.638767\pi\)
\(788\) 0 0
\(789\) 1017.42 + 165.183i 1.28950 + 0.209357i
\(790\) 0 0
\(791\) 315.043i 0.398285i
\(792\) 0 0
\(793\) −182.554 105.398i −0.230207 0.132910i
\(794\) 0 0
\(795\) −437.727 357.279i −0.550601 0.449407i
\(796\) 0 0
\(797\) 658.196 + 380.010i 0.825842 +