Properties

Label 1512.2.j.c.323.20
Level 1512
Weight 2
Character 1512.323
Analytic conductor 12.073
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.j (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 323.20
Character \(\chi\) = 1512.323
Dual form 1512.2.j.c.323.19

$q$-expansion

\(f(q)\) \(=\) \(q+(0.481042 + 1.32989i) q^{2} +(-1.53720 + 1.27946i) q^{4} +0.436221 q^{5} +1.00000i q^{7} +(-2.44100 - 1.42882i) q^{8} +O(q^{10})\) \(q+(0.481042 + 1.32989i) q^{2} +(-1.53720 + 1.27946i) q^{4} +0.436221 q^{5} +1.00000i q^{7} +(-2.44100 - 1.42882i) q^{8} +(0.209841 + 0.580125i) q^{10} -2.73863i q^{11} -1.64657i q^{13} +(-1.32989 + 0.481042i) q^{14} +(0.725955 - 3.93357i) q^{16} +5.22231i q^{17} -5.99963 q^{19} +(-0.670559 + 0.558129i) q^{20} +(3.64206 - 1.31739i) q^{22} -7.68296 q^{23} -4.80971 q^{25} +(2.18975 - 0.792068i) q^{26} +(-1.27946 - 1.53720i) q^{28} -4.94791 q^{29} +9.77950i q^{31} +(5.58042 - 0.926774i) q^{32} +(-6.94508 + 2.51215i) q^{34} +0.436221i q^{35} +3.81676i q^{37} +(-2.88607 - 7.97883i) q^{38} +(-1.06481 - 0.623284i) q^{40} -9.74668i q^{41} -8.84195 q^{43} +(3.50397 + 4.20981i) q^{44} +(-3.69582 - 10.2175i) q^{46} +4.54668 q^{47} -1.00000 q^{49} +(-2.31367 - 6.39637i) q^{50} +(2.10672 + 2.53110i) q^{52} +9.94845 q^{53} -1.19465i q^{55} +(1.42882 - 2.44100i) q^{56} +(-2.38015 - 6.58016i) q^{58} -13.2892i q^{59} +6.26145i q^{61} +(-13.0056 + 4.70435i) q^{62} +(3.91692 + 6.97551i) q^{64} -0.718269i q^{65} +9.42171 q^{67} +(-6.68175 - 8.02773i) q^{68} +(-0.580125 + 0.209841i) q^{70} -9.76751 q^{71} -9.14079 q^{73} +(-5.07586 + 1.83602i) q^{74} +(9.22262 - 7.67629i) q^{76} +2.73863 q^{77} -5.19984i q^{79} +(0.316677 - 1.71591i) q^{80} +(12.9620 - 4.68856i) q^{82} +0.227071i q^{83} +2.27808i q^{85} +(-4.25335 - 11.7588i) q^{86} +(-3.91302 + 6.68497i) q^{88} -2.46567i q^{89} +1.64657 q^{91} +(11.8102 - 9.83005i) q^{92} +(2.18714 + 6.04657i) q^{94} -2.61717 q^{95} -3.37287 q^{97} +(-0.481042 - 1.32989i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 8q^{4} + O(q^{10}) \) \( 32q + 8q^{4} - 8q^{10} - 8q^{16} - 64q^{19} + 24q^{22} - 16q^{25} - 8q^{28} + 8q^{34} - 24q^{40} - 48q^{43} - 8q^{46} - 32q^{49} - 24q^{52} - 96q^{58} - 40q^{64} + 16q^{67} - 16q^{70} - 16q^{73} + 16q^{76} + 24q^{82} + 72q^{88} + 16q^{91} - 56q^{94} + 64q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(-1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.481042 + 1.32989i 0.340148 + 0.940372i
\(3\) 0 0
\(4\) −1.53720 + 1.27946i −0.768599 + 0.639731i
\(5\) 0.436221 0.195084 0.0975421 0.995231i \(-0.468902\pi\)
0.0975421 + 0.995231i \(0.468902\pi\)
\(6\) 0 0
\(7\) 1.00000i 0.377964i
\(8\) −2.44100 1.42882i −0.863022 0.505166i
\(9\) 0 0
\(10\) 0.209841 + 0.580125i 0.0663575 + 0.183452i
\(11\) 2.73863i 0.825727i −0.910793 0.412863i \(-0.864529\pi\)
0.910793 0.412863i \(-0.135471\pi\)
\(12\) 0 0
\(13\) 1.64657i 0.456676i −0.973582 0.228338i \(-0.926671\pi\)
0.973582 0.228338i \(-0.0733291\pi\)
\(14\) −1.32989 + 0.481042i −0.355427 + 0.128564i
\(15\) 0 0
\(16\) 0.725955 3.93357i 0.181489 0.983393i
\(17\) 5.22231i 1.26660i 0.773908 + 0.633298i \(0.218299\pi\)
−0.773908 + 0.633298i \(0.781701\pi\)
\(18\) 0 0
\(19\) −5.99963 −1.37641 −0.688204 0.725517i \(-0.741601\pi\)
−0.688204 + 0.725517i \(0.741601\pi\)
\(20\) −0.670559 + 0.558129i −0.149942 + 0.124801i
\(21\) 0 0
\(22\) 3.64206 1.31739i 0.776490 0.280869i
\(23\) −7.68296 −1.60201 −0.801004 0.598659i \(-0.795700\pi\)
−0.801004 + 0.598659i \(0.795700\pi\)
\(24\) 0 0
\(25\) −4.80971 −0.961942
\(26\) 2.18975 0.792068i 0.429445 0.155337i
\(27\) 0 0
\(28\) −1.27946 1.53720i −0.241796 0.290503i
\(29\) −4.94791 −0.918804 −0.459402 0.888228i \(-0.651936\pi\)
−0.459402 + 0.888228i \(0.651936\pi\)
\(30\) 0 0
\(31\) 9.77950i 1.75645i 0.478248 + 0.878225i \(0.341272\pi\)
−0.478248 + 0.878225i \(0.658728\pi\)
\(32\) 5.58042 0.926774i 0.986488 0.163832i
\(33\) 0 0
\(34\) −6.94508 + 2.51215i −1.19107 + 0.430830i
\(35\) 0.436221i 0.0737349i
\(36\) 0 0
\(37\) 3.81676i 0.627472i 0.949510 + 0.313736i \(0.101581\pi\)
−0.949510 + 0.313736i \(0.898419\pi\)
\(38\) −2.88607 7.97883i −0.468182 1.29434i
\(39\) 0 0
\(40\) −1.06481 0.623284i −0.168362 0.0985499i
\(41\) 9.74668i 1.52218i −0.648649 0.761088i \(-0.724666\pi\)
0.648649 0.761088i \(-0.275334\pi\)
\(42\) 0 0
\(43\) −8.84195 −1.34838 −0.674192 0.738556i \(-0.735508\pi\)
−0.674192 + 0.738556i \(0.735508\pi\)
\(44\) 3.50397 + 4.20981i 0.528243 + 0.634653i
\(45\) 0 0
\(46\) −3.69582 10.2175i −0.544919 1.50648i
\(47\) 4.54668 0.663202 0.331601 0.943420i \(-0.392411\pi\)
0.331601 + 0.943420i \(0.392411\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) −2.31367 6.39637i −0.327202 0.904583i
\(51\) 0 0
\(52\) 2.10672 + 2.53110i 0.292150 + 0.351001i
\(53\) 9.94845 1.36652 0.683262 0.730173i \(-0.260561\pi\)
0.683262 + 0.730173i \(0.260561\pi\)
\(54\) 0 0
\(55\) 1.19465i 0.161086i
\(56\) 1.42882 2.44100i 0.190935 0.326192i
\(57\) 0 0
\(58\) −2.38015 6.58016i −0.312529 0.864018i
\(59\) 13.2892i 1.73011i −0.501681 0.865053i \(-0.667285\pi\)
0.501681 0.865053i \(-0.332715\pi\)
\(60\) 0 0
\(61\) 6.26145i 0.801696i 0.916145 + 0.400848i \(0.131284\pi\)
−0.916145 + 0.400848i \(0.868716\pi\)
\(62\) −13.0056 + 4.70435i −1.65172 + 0.597453i
\(63\) 0 0
\(64\) 3.91692 + 6.97551i 0.489615 + 0.871939i
\(65\) 0.718269i 0.0890903i
\(66\) 0 0
\(67\) 9.42171 1.15104 0.575522 0.817786i \(-0.304799\pi\)
0.575522 + 0.817786i \(0.304799\pi\)
\(68\) −6.68175 8.02773i −0.810281 0.973505i
\(69\) 0 0
\(70\) −0.580125 + 0.209841i −0.0693382 + 0.0250808i
\(71\) −9.76751 −1.15919 −0.579595 0.814905i \(-0.696789\pi\)
−0.579595 + 0.814905i \(0.696789\pi\)
\(72\) 0 0
\(73\) −9.14079 −1.06985 −0.534924 0.844900i \(-0.679660\pi\)
−0.534924 + 0.844900i \(0.679660\pi\)
\(74\) −5.07586 + 1.83602i −0.590057 + 0.213433i
\(75\) 0 0
\(76\) 9.22262 7.67629i 1.05791 0.880531i
\(77\) 2.73863 0.312095
\(78\) 0 0
\(79\) 5.19984i 0.585028i −0.956261 0.292514i \(-0.905508\pi\)
0.956261 0.292514i \(-0.0944917\pi\)
\(80\) 0.316677 1.71591i 0.0354056 0.191844i
\(81\) 0 0
\(82\) 12.9620 4.68856i 1.43141 0.517764i
\(83\) 0.227071i 0.0249243i 0.999922 + 0.0124622i \(0.00396693\pi\)
−0.999922 + 0.0124622i \(0.996033\pi\)
\(84\) 0 0
\(85\) 2.27808i 0.247093i
\(86\) −4.25335 11.7588i −0.458650 1.26798i
\(87\) 0 0
\(88\) −3.91302 + 6.68497i −0.417129 + 0.712621i
\(89\) 2.46567i 0.261360i −0.991425 0.130680i \(-0.958284\pi\)
0.991425 0.130680i \(-0.0417161\pi\)
\(90\) 0 0
\(91\) 1.64657 0.172607
\(92\) 11.8102 9.83005i 1.23130 1.02485i
\(93\) 0 0
\(94\) 2.18714 + 6.04657i 0.225587 + 0.623657i
\(95\) −2.61717 −0.268516
\(96\) 0 0
\(97\) −3.37287 −0.342463 −0.171232 0.985231i \(-0.554775\pi\)
−0.171232 + 0.985231i \(0.554775\pi\)
\(98\) −0.481042 1.32989i −0.0485925 0.134339i
\(99\) 0 0
\(100\) 7.39348 6.15384i 0.739348 0.615384i
\(101\) −1.20021 −0.119425 −0.0597125 0.998216i \(-0.519018\pi\)
−0.0597125 + 0.998216i \(0.519018\pi\)
\(102\) 0 0
\(103\) 10.7004i 1.05434i −0.849761 0.527169i \(-0.823254\pi\)
0.849761 0.527169i \(-0.176746\pi\)
\(104\) −2.35266 + 4.01927i −0.230697 + 0.394122i
\(105\) 0 0
\(106\) 4.78562 + 13.2303i 0.464820 + 1.28504i
\(107\) 1.49655i 0.144676i −0.997380 0.0723382i \(-0.976954\pi\)
0.997380 0.0723382i \(-0.0230461\pi\)
\(108\) 0 0
\(109\) 18.4352i 1.76578i 0.469583 + 0.882888i \(0.344404\pi\)
−0.469583 + 0.882888i \(0.655596\pi\)
\(110\) 1.58875 0.574675i 0.151481 0.0547931i
\(111\) 0 0
\(112\) 3.93357 + 0.725955i 0.371688 + 0.0685963i
\(113\) 5.25692i 0.494529i 0.968948 + 0.247265i \(0.0795317\pi\)
−0.968948 + 0.247265i \(0.920468\pi\)
\(114\) 0 0
\(115\) −3.35147 −0.312526
\(116\) 7.60592 6.33066i 0.706192 0.587787i
\(117\) 0 0
\(118\) 17.6731 6.39266i 1.62694 0.588492i
\(119\) −5.22231 −0.478729
\(120\) 0 0
\(121\) 3.49993 0.318175
\(122\) −8.32702 + 3.01202i −0.753893 + 0.272695i
\(123\) 0 0
\(124\) −12.5125 15.0330i −1.12366 1.35001i
\(125\) −4.27921 −0.382744
\(126\) 0 0
\(127\) 19.7677i 1.75410i 0.480396 + 0.877051i \(0.340493\pi\)
−0.480396 + 0.877051i \(0.659507\pi\)
\(128\) −7.39244 + 8.56457i −0.653405 + 0.757008i
\(129\) 0 0
\(130\) 0.955216 0.345517i 0.0837780 0.0303039i
\(131\) 9.25252i 0.808397i −0.914671 0.404198i \(-0.867551\pi\)
0.914671 0.404198i \(-0.132449\pi\)
\(132\) 0 0
\(133\) 5.99963i 0.520234i
\(134\) 4.53223 + 12.5298i 0.391525 + 1.08241i
\(135\) 0 0
\(136\) 7.46177 12.7476i 0.639842 1.09310i
\(137\) 2.53255i 0.216370i −0.994131 0.108185i \(-0.965496\pi\)
0.994131 0.108185i \(-0.0345039\pi\)
\(138\) 0 0
\(139\) −19.7831 −1.67798 −0.838991 0.544146i \(-0.816854\pi\)
−0.838991 + 0.544146i \(0.816854\pi\)
\(140\) −0.558129 0.670559i −0.0471705 0.0566726i
\(141\) 0 0
\(142\) −4.69858 12.9897i −0.394296 1.09007i
\(143\) −4.50934 −0.377090
\(144\) 0 0
\(145\) −2.15839 −0.179244
\(146\) −4.39710 12.1562i −0.363906 1.00606i
\(147\) 0 0
\(148\) −4.88340 5.86712i −0.401413 0.482274i
\(149\) 8.16461 0.668871 0.334435 0.942419i \(-0.391454\pi\)
0.334435 + 0.942419i \(0.391454\pi\)
\(150\) 0 0
\(151\) 14.8741i 1.21044i 0.796058 + 0.605220i \(0.206915\pi\)
−0.796058 + 0.605220i \(0.793085\pi\)
\(152\) 14.6451 + 8.57242i 1.18787 + 0.695315i
\(153\) 0 0
\(154\) 1.31739 + 3.64206i 0.106159 + 0.293486i
\(155\) 4.26603i 0.342656i
\(156\) 0 0
\(157\) 4.92207i 0.392824i 0.980521 + 0.196412i \(0.0629290\pi\)
−0.980521 + 0.196412i \(0.937071\pi\)
\(158\) 6.91520 2.50134i 0.550144 0.198996i
\(159\) 0 0
\(160\) 2.43430 0.404279i 0.192448 0.0319610i
\(161\) 7.68296i 0.605502i
\(162\) 0 0
\(163\) −5.87250 −0.459970 −0.229985 0.973194i \(-0.573868\pi\)
−0.229985 + 0.973194i \(0.573868\pi\)
\(164\) 12.4705 + 14.9826i 0.973782 + 1.16994i
\(165\) 0 0
\(166\) −0.301979 + 0.109231i −0.0234381 + 0.00847795i
\(167\) −22.1181 −1.71155 −0.855777 0.517345i \(-0.826920\pi\)
−0.855777 + 0.517345i \(0.826920\pi\)
\(168\) 0 0
\(169\) 10.2888 0.791447
\(170\) −3.02960 + 1.09585i −0.232359 + 0.0840481i
\(171\) 0 0
\(172\) 13.5918 11.3129i 1.03637 0.862603i
\(173\) 24.1920 1.83928 0.919642 0.392758i \(-0.128479\pi\)
0.919642 + 0.392758i \(0.128479\pi\)
\(174\) 0 0
\(175\) 4.80971i 0.363580i
\(176\) −10.7726 1.98812i −0.812014 0.149860i
\(177\) 0 0
\(178\) 3.27906 1.18609i 0.245776 0.0889010i
\(179\) 5.41287i 0.404577i 0.979326 + 0.202288i \(0.0648378\pi\)
−0.979326 + 0.202288i \(0.935162\pi\)
\(180\) 0 0
\(181\) 6.19672i 0.460598i −0.973120 0.230299i \(-0.926030\pi\)
0.973120 0.230299i \(-0.0739705\pi\)
\(182\) 0.792068 + 2.18975i 0.0587120 + 0.162315i
\(183\) 0 0
\(184\) 18.7541 + 10.9776i 1.38257 + 0.809280i
\(185\) 1.66495i 0.122410i
\(186\) 0 0
\(187\) 14.3020 1.04586
\(188\) −6.98915 + 5.81731i −0.509736 + 0.424271i
\(189\) 0 0
\(190\) −1.25897 3.48054i −0.0913350 0.252505i
\(191\) −13.6191 −0.985444 −0.492722 0.870187i \(-0.663998\pi\)
−0.492722 + 0.870187i \(0.663998\pi\)
\(192\) 0 0
\(193\) 5.89278 0.424172 0.212086 0.977251i \(-0.431974\pi\)
0.212086 + 0.977251i \(0.431974\pi\)
\(194\) −1.62249 4.48554i −0.116488 0.322043i
\(195\) 0 0
\(196\) 1.53720 1.27946i 0.109800 0.0913901i
\(197\) 19.0323 1.35600 0.677998 0.735064i \(-0.262848\pi\)
0.677998 + 0.735064i \(0.262848\pi\)
\(198\) 0 0
\(199\) 5.91398i 0.419231i −0.977784 0.209616i \(-0.932779\pi\)
0.977784 0.209616i \(-0.0672212\pi\)
\(200\) 11.7405 + 6.87223i 0.830177 + 0.485940i
\(201\) 0 0
\(202\) −0.577349 1.59614i −0.0406221 0.112304i
\(203\) 4.94791i 0.347275i
\(204\) 0 0
\(205\) 4.25171i 0.296952i
\(206\) 14.2303 5.14732i 0.991469 0.358631i
\(207\) 0 0
\(208\) −6.47690 1.19534i −0.449092 0.0828816i
\(209\) 16.4307i 1.13654i
\(210\) 0 0
\(211\) 12.9334 0.890369 0.445185 0.895439i \(-0.353138\pi\)
0.445185 + 0.895439i \(0.353138\pi\)
\(212\) −15.2927 + 12.7287i −1.05031 + 0.874208i
\(213\) 0 0
\(214\) 1.99024 0.719901i 0.136050 0.0492114i
\(215\) −3.85705 −0.263049
\(216\) 0 0
\(217\) −9.77950 −0.663876
\(218\) −24.5168 + 8.86812i −1.66049 + 0.600625i
\(219\) 0 0
\(220\) 1.52851 + 1.83641i 0.103052 + 0.123811i
\(221\) 8.59890 0.578424
\(222\) 0 0
\(223\) 0.758557i 0.0507967i −0.999677 0.0253984i \(-0.991915\pi\)
0.999677 0.0253984i \(-0.00808542\pi\)
\(224\) 0.926774 + 5.58042i 0.0619227 + 0.372858i
\(225\) 0 0
\(226\) −6.99111 + 2.52880i −0.465042 + 0.168213i
\(227\) 3.60986i 0.239595i −0.992798 0.119797i \(-0.961776\pi\)
0.992798 0.119797i \(-0.0382245\pi\)
\(228\) 0 0
\(229\) 3.47625i 0.229717i −0.993382 0.114859i \(-0.963358\pi\)
0.993382 0.114859i \(-0.0366415\pi\)
\(230\) −1.61220 4.45708i −0.106305 0.293891i
\(231\) 0 0
\(232\) 12.0778 + 7.06970i 0.792949 + 0.464149i
\(233\) 22.9786i 1.50538i 0.658376 + 0.752689i \(0.271244\pi\)
−0.658376 + 0.752689i \(0.728756\pi\)
\(234\) 0 0
\(235\) 1.98336 0.129380
\(236\) 17.0030 + 20.4281i 1.10680 + 1.32976i
\(237\) 0 0
\(238\) −2.51215 6.94508i −0.162838 0.450183i
\(239\) −10.4478 −0.675813 −0.337906 0.941180i \(-0.609719\pi\)
−0.337906 + 0.941180i \(0.609719\pi\)
\(240\) 0 0
\(241\) −10.0939 −0.650208 −0.325104 0.945678i \(-0.605399\pi\)
−0.325104 + 0.945678i \(0.605399\pi\)
\(242\) 1.68361 + 4.65450i 0.108227 + 0.299203i
\(243\) 0 0
\(244\) −8.01128 9.62508i −0.512870 0.616183i
\(245\) −0.436221 −0.0278692
\(246\) 0 0
\(247\) 9.87880i 0.628573i
\(248\) 13.9732 23.8717i 0.887299 1.51586i
\(249\) 0 0
\(250\) −2.05848 5.69086i −0.130189 0.359922i
\(251\) 18.0568i 1.13974i 0.821736 + 0.569868i \(0.193006\pi\)
−0.821736 + 0.569868i \(0.806994\pi\)
\(252\) 0 0
\(253\) 21.0408i 1.32282i
\(254\) −26.2889 + 9.50910i −1.64951 + 0.596654i
\(255\) 0 0
\(256\) −14.9460 5.71119i −0.934124 0.356950i
\(257\) 3.77643i 0.235567i 0.993039 + 0.117784i \(0.0375789\pi\)
−0.993039 + 0.117784i \(0.962421\pi\)
\(258\) 0 0
\(259\) −3.81676 −0.237162
\(260\) 0.918997 + 1.10412i 0.0569938 + 0.0684747i
\(261\) 0 0
\(262\) 12.3048 4.45085i 0.760194 0.274974i
\(263\) 19.1460 1.18060 0.590298 0.807185i \(-0.299010\pi\)
0.590298 + 0.807185i \(0.299010\pi\)
\(264\) 0 0
\(265\) 4.33973 0.266587
\(266\) 7.97883 2.88607i 0.489213 0.176956i
\(267\) 0 0
\(268\) −14.4830 + 12.0547i −0.884692 + 0.736359i
\(269\) 11.9031 0.725747 0.362873 0.931838i \(-0.381796\pi\)
0.362873 + 0.931838i \(0.381796\pi\)
\(270\) 0 0
\(271\) 26.4765i 1.60833i 0.594403 + 0.804167i \(0.297388\pi\)
−0.594403 + 0.804167i \(0.702612\pi\)
\(272\) 20.5423 + 3.79116i 1.24556 + 0.229873i
\(273\) 0 0
\(274\) 3.36800 1.21826i 0.203469 0.0735979i
\(275\) 13.1720i 0.794302i
\(276\) 0 0
\(277\) 9.49587i 0.570552i −0.958445 0.285276i \(-0.907915\pi\)
0.958445 0.285276i \(-0.0920852\pi\)
\(278\) −9.51650 26.3093i −0.570762 1.57793i
\(279\) 0 0
\(280\) 0.623284 1.06481i 0.0372484 0.0636349i
\(281\) 16.7754i 1.00073i 0.865813 + 0.500367i \(0.166802\pi\)
−0.865813 + 0.500367i \(0.833198\pi\)
\(282\) 0 0
\(283\) 13.6841 0.813437 0.406719 0.913554i \(-0.366673\pi\)
0.406719 + 0.913554i \(0.366673\pi\)
\(284\) 15.0146 12.4972i 0.890952 0.741569i
\(285\) 0 0
\(286\) −2.16918 5.99691i −0.128266 0.354605i
\(287\) 9.74668 0.575328
\(288\) 0 0
\(289\) −10.2725 −0.604268
\(290\) −1.03827 2.87041i −0.0609695 0.168556i
\(291\) 0 0
\(292\) 14.0512 11.6953i 0.822284 0.684415i
\(293\) 9.46088 0.552710 0.276355 0.961056i \(-0.410873\pi\)
0.276355 + 0.961056i \(0.410873\pi\)
\(294\) 0 0
\(295\) 5.79703i 0.337516i
\(296\) 5.45348 9.31670i 0.316977 0.541522i
\(297\) 0 0
\(298\) 3.92752 + 10.8580i 0.227515 + 0.628987i
\(299\) 12.6505i 0.731599i
\(300\) 0 0
\(301\) 8.84195i 0.509641i
\(302\) −19.7809 + 7.15508i −1.13826 + 0.411728i
\(303\) 0 0
\(304\) −4.35546 + 23.6000i −0.249803 + 1.35355i
\(305\) 2.73138i 0.156398i
\(306\) 0 0
\(307\) −12.4055 −0.708019 −0.354009 0.935242i \(-0.615182\pi\)
−0.354009 + 0.935242i \(0.615182\pi\)
\(308\) −4.20981 + 3.50397i −0.239876 + 0.199657i
\(309\) 0 0
\(310\) −5.67333 + 2.05214i −0.322224 + 0.116554i
\(311\) 1.70862 0.0968870 0.0484435 0.998826i \(-0.484574\pi\)
0.0484435 + 0.998826i \(0.484574\pi\)
\(312\) 0 0
\(313\) 11.9889 0.677652 0.338826 0.940849i \(-0.389970\pi\)
0.338826 + 0.940849i \(0.389970\pi\)
\(314\) −6.54580 + 2.36772i −0.369401 + 0.133618i
\(315\) 0 0
\(316\) 6.65300 + 7.99318i 0.374260 + 0.449652i
\(317\) −24.6470 −1.38431 −0.692155 0.721748i \(-0.743339\pi\)
−0.692155 + 0.721748i \(0.743339\pi\)
\(318\) 0 0
\(319\) 13.5505i 0.758681i
\(320\) 1.70864 + 3.04287i 0.0955161 + 0.170101i
\(321\) 0 0
\(322\) 10.2175 3.69582i 0.569397 0.205960i
\(323\) 31.3319i 1.74336i
\(324\) 0 0
\(325\) 7.91952i 0.439296i
\(326\) −2.82492 7.80976i −0.156458 0.432543i
\(327\) 0 0
\(328\) −13.9263 + 23.7916i −0.768951 + 1.31367i
\(329\) 4.54668i 0.250667i
\(330\) 0 0
\(331\) −5.66221 −0.311223 −0.155612 0.987818i \(-0.549735\pi\)
−0.155612 + 0.987818i \(0.549735\pi\)
\(332\) −0.290529 0.349054i −0.0159449 0.0191568i
\(333\) 0 0
\(334\) −10.6397 29.4146i −0.582181 1.60950i
\(335\) 4.10995 0.224551
\(336\) 0 0
\(337\) −32.2480 −1.75666 −0.878331 0.478053i \(-0.841343\pi\)
−0.878331 + 0.478053i \(0.841343\pi\)
\(338\) 4.94935 + 13.6830i 0.269209 + 0.744255i
\(339\) 0 0
\(340\) −2.91472 3.50187i −0.158073 0.189915i
\(341\) 26.7824 1.45035
\(342\) 0 0
\(343\) 1.00000i 0.0539949i
\(344\) 21.5832 + 12.6336i 1.16369 + 0.681158i
\(345\) 0 0
\(346\) 11.6374 + 32.1726i 0.625628 + 1.72961i
\(347\) 20.3357i 1.09168i −0.837889 0.545840i \(-0.816211\pi\)
0.837889 0.545840i \(-0.183789\pi\)
\(348\) 0 0
\(349\) 8.27539i 0.442971i −0.975164 0.221486i \(-0.928909\pi\)
0.975164 0.221486i \(-0.0710906\pi\)
\(350\) 6.39637 2.31367i 0.341900 0.123671i
\(351\) 0 0
\(352\) −2.53809 15.2827i −0.135280 0.814570i
\(353\) 8.23298i 0.438197i −0.975703 0.219099i \(-0.929688\pi\)
0.975703 0.219099i \(-0.0703117\pi\)
\(354\) 0 0
\(355\) −4.26080 −0.226140
\(356\) 3.15473 + 3.79022i 0.167200 + 0.200881i
\(357\) 0 0
\(358\) −7.19850 + 2.60381i −0.380453 + 0.137616i
\(359\) −10.5802 −0.558403 −0.279202 0.960232i \(-0.590070\pi\)
−0.279202 + 0.960232i \(0.590070\pi\)
\(360\) 0 0
\(361\) 16.9955 0.894502
\(362\) 8.24093 2.98088i 0.433134 0.156672i
\(363\) 0 0
\(364\) −2.53110 + 2.10672i −0.132666 + 0.110422i
\(365\) −3.98741 −0.208710
\(366\) 0 0
\(367\) 23.7595i 1.24023i −0.784509 0.620117i \(-0.787085\pi\)
0.784509 0.620117i \(-0.212915\pi\)
\(368\) −5.57748 + 30.2215i −0.290746 + 1.57540i
\(369\) 0 0
\(370\) −2.21420 + 0.800912i −0.115111 + 0.0416374i
\(371\) 9.94845i 0.516498i
\(372\) 0 0
\(373\) 12.1442i 0.628802i 0.949290 + 0.314401i \(0.101804\pi\)
−0.949290 + 0.314401i \(0.898196\pi\)
\(374\) 6.87984 + 19.0200i 0.355748 + 0.983500i
\(375\) 0 0
\(376\) −11.0984 6.49642i −0.572358 0.335027i
\(377\) 8.14708i 0.419596i
\(378\) 0 0
\(379\) −32.1386 −1.65085 −0.825426 0.564511i \(-0.809065\pi\)
−0.825426 + 0.564511i \(0.809065\pi\)
\(380\) 4.02310 3.34856i 0.206381 0.171778i
\(381\) 0 0
\(382\) −6.55136 18.1119i −0.335197 0.926684i
\(383\) −30.0530 −1.53564 −0.767819 0.640667i \(-0.778658\pi\)
−0.767819 + 0.640667i \(0.778658\pi\)
\(384\) 0 0
\(385\) 1.19465 0.0608849
\(386\) 2.83467 + 7.83673i 0.144281 + 0.398879i
\(387\) 0 0
\(388\) 5.18477 4.31546i 0.263217 0.219084i
\(389\) −12.8723 −0.652652 −0.326326 0.945257i \(-0.605811\pi\)
−0.326326 + 0.945257i \(0.605811\pi\)
\(390\) 0 0
\(391\) 40.1228i 2.02910i
\(392\) 2.44100 + 1.42882i 0.123289 + 0.0721666i
\(393\) 0 0
\(394\) 9.15533 + 25.3108i 0.461239 + 1.27514i
\(395\) 2.26828i 0.114130i
\(396\) 0 0
\(397\) 20.8323i 1.04554i −0.852473 0.522771i \(-0.824898\pi\)
0.852473 0.522771i \(-0.175102\pi\)
\(398\) 7.86493 2.84487i 0.394233 0.142601i
\(399\) 0 0
\(400\) −3.49163 + 18.9193i −0.174582 + 0.945967i
\(401\) 15.8270i 0.790361i −0.918604 0.395180i \(-0.870682\pi\)
0.918604 0.395180i \(-0.129318\pi\)
\(402\) 0 0
\(403\) 16.1026 0.802129
\(404\) 1.84495 1.53562i 0.0917899 0.0763998i
\(405\) 0 0
\(406\) 6.58016 2.38015i 0.326568 0.118125i
\(407\) 10.4527 0.518120
\(408\) 0 0
\(409\) −3.95136 −0.195382 −0.0976910 0.995217i \(-0.531146\pi\)
−0.0976910 + 0.995217i \(0.531146\pi\)
\(410\) 5.65429 2.04525i 0.279246 0.101008i
\(411\) 0 0
\(412\) 13.6907 + 16.4486i 0.674492 + 0.810363i
\(413\) 13.2892 0.653919
\(414\) 0 0
\(415\) 0.0990534i 0.00486234i
\(416\) −1.52600 9.18855i −0.0748181 0.450506i
\(417\) 0 0
\(418\) −21.8510 + 7.90387i −1.06877 + 0.386591i
\(419\) 3.56977i 0.174395i 0.996191 + 0.0871974i \(0.0277911\pi\)
−0.996191 + 0.0871974i \(0.972209\pi\)
\(420\) 0 0
\(421\) 16.3767i 0.798152i 0.916918 + 0.399076i \(0.130669\pi\)
−0.916918 + 0.399076i \(0.869331\pi\)
\(422\) 6.22148 + 17.1999i 0.302857 + 0.837278i
\(423\) 0 0
\(424\) −24.2841 14.2146i −1.17934 0.690321i
\(425\) 25.1178i 1.21839i
\(426\) 0 0
\(427\) −6.26145 −0.303013
\(428\) 1.91477 + 2.30049i 0.0925540 + 0.111198i
\(429\) 0 0
\(430\) −1.85540 5.12944i −0.0894754 0.247363i
\(431\) −28.7503 −1.38485 −0.692426 0.721489i \(-0.743458\pi\)
−0.692426 + 0.721489i \(0.743458\pi\)
\(432\) 0 0
\(433\) −23.6276 −1.13547 −0.567735 0.823212i \(-0.692180\pi\)
−0.567735 + 0.823212i \(0.692180\pi\)
\(434\) −4.70435 13.0056i −0.225816 0.624290i
\(435\) 0 0
\(436\) −23.5872 28.3386i −1.12962 1.35717i
\(437\) 46.0949 2.20502
\(438\) 0 0
\(439\) 15.4891i 0.739255i −0.929180 0.369628i \(-0.879485\pi\)
0.929180 0.369628i \(-0.120515\pi\)
\(440\) −1.70694 + 2.91613i −0.0813753 + 0.139021i
\(441\) 0 0
\(442\) 4.13643 + 11.4356i 0.196750 + 0.543934i
\(443\) 21.7640i 1.03404i 0.855974 + 0.517019i \(0.172958\pi\)
−0.855974 + 0.517019i \(0.827042\pi\)
\(444\) 0 0
\(445\) 1.07558i 0.0509872i
\(446\) 1.00879 0.364897i 0.0477678 0.0172784i
\(447\) 0 0
\(448\) −6.97551 + 3.91692i −0.329562 + 0.185057i
\(449\) 28.9358i 1.36557i 0.730621 + 0.682783i \(0.239231\pi\)
−0.730621 + 0.682783i \(0.760769\pi\)
\(450\) 0 0
\(451\) −26.6925 −1.25690
\(452\) −6.72603 8.08093i −0.316366 0.380095i
\(453\) 0 0
\(454\) 4.80070 1.73649i 0.225308 0.0814976i
\(455\) 0.718269 0.0336730
\(456\) 0 0
\(457\) 26.2466 1.22776 0.613882 0.789397i \(-0.289607\pi\)
0.613882 + 0.789397i \(0.289607\pi\)
\(458\) 4.62302 1.67222i 0.216020 0.0781378i
\(459\) 0 0
\(460\) 5.15188 4.28808i 0.240207 0.199933i
\(461\) 7.47471 0.348132 0.174066 0.984734i \(-0.444309\pi\)
0.174066 + 0.984734i \(0.444309\pi\)
\(462\) 0 0
\(463\) 8.09410i 0.376165i −0.982153 0.188082i \(-0.939773\pi\)
0.982153 0.188082i \(-0.0602272\pi\)
\(464\) −3.59196 + 19.4630i −0.166753 + 0.903546i
\(465\) 0 0
\(466\) −30.5590 + 11.0537i −1.41562 + 0.512051i
\(467\) 16.0617i 0.743246i 0.928384 + 0.371623i \(0.121199\pi\)
−0.928384 + 0.371623i \(0.878801\pi\)
\(468\) 0 0
\(469\) 9.42171i 0.435054i
\(470\) 0.954079 + 2.63765i 0.0440084 + 0.121666i
\(471\) 0 0
\(472\) −18.9879 + 32.4389i −0.873991 + 1.49312i
\(473\) 24.2148i 1.11340i
\(474\) 0 0
\(475\) 28.8565 1.32403
\(476\) 8.02773 6.68175i 0.367950 0.306257i
\(477\) 0 0
\(478\) −5.02583 13.8944i −0.229876 0.635515i
\(479\) 31.6989 1.44836 0.724181 0.689610i \(-0.242218\pi\)
0.724181 + 0.689610i \(0.242218\pi\)
\(480\) 0 0
\(481\) 6.28456 0.286551
\(482\) −4.85561 13.4238i −0.221167 0.611437i
\(483\) 0 0
\(484\) −5.38008 + 4.47802i −0.244549 + 0.203546i
\(485\) −1.47132 −0.0668092
\(486\) 0 0
\(487\) 30.5363i 1.38373i 0.722025 + 0.691867i \(0.243211\pi\)
−0.722025 + 0.691867i \(0.756789\pi\)
\(488\) 8.94651 15.2842i 0.404990 0.691882i
\(489\) 0 0
\(490\) −0.209841 0.580125i −0.00947964 0.0262074i
\(491\) 41.2201i 1.86024i −0.367259 0.930119i \(-0.619704\pi\)
0.367259 0.930119i \(-0.380296\pi\)
\(492\) 0 0
\(493\) 25.8395i 1.16375i
\(494\) −13.1377 + 4.75211i −0.591092 + 0.213808i
\(495\) 0 0
\(496\) 38.4684 + 7.09948i 1.72728 + 0.318776i
\(497\) 9.76751i 0.438133i
\(498\) 0 0
\(499\) 4.03676 0.180710 0.0903552 0.995910i \(-0.471200\pi\)
0.0903552 + 0.995910i \(0.471200\pi\)
\(500\) 6.57799 5.47508i 0.294177 0.244853i
\(501\) 0 0
\(502\) −24.0135 + 8.68608i −1.07178 + 0.387679i
\(503\) −40.2393 −1.79418 −0.897092 0.441845i \(-0.854324\pi\)
−0.897092 + 0.441845i \(0.854324\pi\)
\(504\) 0 0
\(505\) −0.523556 −0.0232979
\(506\) −27.9818 + 10.1215i −1.24394 + 0.449955i
\(507\) 0 0
\(508\) −25.2921 30.3869i −1.12215 1.34820i
\(509\) 9.68050 0.429081 0.214540 0.976715i \(-0.431175\pi\)
0.214540 + 0.976715i \(0.431175\pi\)
\(510\) 0 0
\(511\) 9.14079i 0.404365i
\(512\) 0.405604 22.6238i 0.0179253 0.999839i
\(513\) 0 0
\(514\) −5.02222 + 1.81662i −0.221521 + 0.0801276i
\(515\) 4.66773i 0.205685i
\(516\) 0 0
\(517\) 12.4517i 0.547624i
\(518\) −1.83602 5.07586i −0.0806701 0.223020i
\(519\) 0 0
\(520\) −1.02628 + 1.75329i −0.0450054 + 0.0768869i
\(521\) 3.92629i 0.172014i 0.996295 + 0.0860069i \(0.0274107\pi\)
−0.996295 + 0.0860069i \(0.972589\pi\)
\(522\) 0 0
\(523\) 20.8709 0.912623 0.456311 0.889820i \(-0.349170\pi\)
0.456311 + 0.889820i \(0.349170\pi\)
\(524\) 11.8382 + 14.2230i 0.517156 + 0.621333i
\(525\) 0 0
\(526\) 9.21005 + 25.4621i 0.401577 + 1.11020i
\(527\) −51.0716 −2.22471
\(528\) 0 0
\(529\) 36.0279 1.56643
\(530\) 2.08759 + 5.77134i 0.0906791 + 0.250691i
\(531\) 0 0
\(532\) 7.67629 + 9.22262i 0.332810 + 0.399851i
\(533\) −16.0486 −0.695141
\(534\) 0 0
\(535\) 0.652825i 0.0282241i
\(536\) −22.9983 13.4620i −0.993377 0.581469i
\(537\) 0 0
\(538\) 5.72590 + 15.8298i 0.246861 + 0.682472i
\(539\) 2.73863i 0.117961i
\(540\) 0 0
\(541\) 3.18975i 0.137138i −0.997646 0.0685691i \(-0.978157\pi\)
0.997646 0.0685691i \(-0.0218434\pi\)
\(542\) −35.2108 + 12.7363i −1.51243 + 0.547071i
\(543\) 0 0
\(544\) 4.83990 + 29.1427i 0.207509 + 1.24948i
\(545\) 8.04185i 0.344475i
\(546\) 0 0
\(547\) 27.9137 1.19350 0.596751 0.802426i \(-0.296458\pi\)
0.596751 + 0.802426i \(0.296458\pi\)
\(548\) 3.24030 + 3.89303i 0.138419 + 0.166302i
\(549\) 0 0
\(550\) −17.5173 + 6.33628i −0.746939 + 0.270180i
\(551\) 29.6856 1.26465
\(552\) 0 0
\(553\) 5.19984 0.221120
\(554\) 12.6284 4.56791i 0.536531 0.194072i
\(555\) 0 0
\(556\) 30.4106 25.3117i 1.28970 1.07346i
\(557\) 14.0025 0.593304 0.296652 0.954986i \(-0.404130\pi\)
0.296652 + 0.954986i \(0.404130\pi\)
\(558\) 0 0
\(559\) 14.5589i 0.615775i
\(560\) 1.71591 + 0.316677i 0.0725104 + 0.0133821i
\(561\) 0 0
\(562\) −22.3093 + 8.06965i −0.941063 + 0.340398i
\(563\) 13.8839i 0.585137i 0.956245 + 0.292569i \(0.0945100\pi\)
−0.956245 + 0.292569i \(0.905490\pi\)
\(564\) 0 0
\(565\) 2.29318i 0.0964749i
\(566\) 6.58264 + 18.1983i 0.276689 + 0.764933i
\(567\) 0 0
\(568\) 23.8424 + 13.9561i 1.00041 + 0.585583i
\(569\) 14.7512i 0.618401i 0.950997 + 0.309200i \(0.100061\pi\)
−0.950997 + 0.309200i \(0.899939\pi\)
\(570\) 0 0
\(571\) 4.28135 0.179169 0.0895845 0.995979i \(-0.471446\pi\)
0.0895845 + 0.995979i \(0.471446\pi\)
\(572\) 6.93174 5.76952i 0.289831 0.241236i
\(573\) 0 0
\(574\) 4.68856 + 12.9620i 0.195697 + 0.541022i
\(575\) 36.9528 1.54104
\(576\) 0 0
\(577\) 11.1951 0.466059 0.233030 0.972470i \(-0.425136\pi\)
0.233030 + 0.972470i \(0.425136\pi\)
\(578\) −4.94152 13.6613i −0.205540 0.568236i
\(579\) 0 0
\(580\) 3.31787 2.76157i 0.137767 0.114668i
\(581\) −0.227071 −0.00942051
\(582\) 0 0
\(583\) 27.2451i 1.12838i
\(584\) 22.3126 + 13.0606i 0.923303 + 0.540451i
\(585\) 0 0
\(586\) 4.55107 + 12.5819i 0.188003 + 0.519753i
\(587\) 1.45377i 0.0600035i 0.999550 + 0.0300018i \(0.00955129\pi\)
−0.999550 + 0.0300018i \(0.990449\pi\)
\(588\) 0 0
\(589\) 58.6733i 2.41759i
\(590\) 7.70940 2.78861i 0.317391 0.114805i
\(591\) 0 0
\(592\) 15.0135 + 2.77080i 0.617051 + 0.113879i
\(593\) 13.1827i 0.541347i −0.962671 0.270674i \(-0.912754\pi\)
0.962671 0.270674i \(-0.0872464\pi\)
\(594\) 0 0
\(595\) −2.27808 −0.0933924
\(596\) −12.5506 + 10.4463i −0.514093 + 0.427897i
\(597\) 0 0
\(598\) −16.8238 + 6.08543i −0.687975 + 0.248852i
\(599\) 14.4852 0.591848 0.295924 0.955211i \(-0.404372\pi\)
0.295924 + 0.955211i \(0.404372\pi\)
\(600\) 0 0
\(601\) −27.7364 −1.13139 −0.565695 0.824614i \(-0.691392\pi\)
−0.565695 + 0.824614i \(0.691392\pi\)
\(602\) 11.7588 4.25335i 0.479253 0.173353i
\(603\) 0 0
\(604\) −19.0309 22.8645i −0.774356 0.930343i
\(605\) 1.52674 0.0620709
\(606\) 0 0
\(607\) 18.5137i 0.751447i 0.926732 + 0.375723i \(0.122606\pi\)
−0.926732 + 0.375723i \(0.877394\pi\)
\(608\) −33.4804 + 5.56030i −1.35781 + 0.225500i
\(609\) 0 0
\(610\) −3.63242 + 1.31391i −0.147073 + 0.0531985i
\(611\) 7.48643i 0.302868i
\(612\) 0 0
\(613\) 25.3069i 1.02213i 0.859541 + 0.511067i \(0.170750\pi\)
−0.859541 + 0.511067i \(0.829250\pi\)
\(614\) −5.96756 16.4979i −0.240831 0.665801i
\(615\) 0 0
\(616\) −6.68497 3.91302i −0.269345 0.157660i
\(617\) 47.8249i 1.92536i 0.270647 + 0.962679i \(0.412762\pi\)
−0.270647 + 0.962679i \(0.587238\pi\)
\(618\) 0 0
\(619\) 3.22411 0.129588 0.0647939 0.997899i \(-0.479361\pi\)
0.0647939 + 0.997899i \(0.479361\pi\)
\(620\) −5.45822 6.55773i −0.219207 0.263365i
\(621\) 0 0
\(622\) 0.821918 + 2.27227i 0.0329559 + 0.0911098i
\(623\) 2.46567 0.0987848
\(624\) 0 0
\(625\) 22.1819 0.887275
\(626\) 5.76715 + 15.9439i 0.230502 + 0.637245i
\(627\) 0 0
\(628\) −6.29760 7.56620i −0.251302 0.301924i
\(629\) −19.9323 −0.794754
\(630\) 0 0
\(631\) 22.6025i 0.899791i −0.893081 0.449896i \(-0.851461\pi\)
0.893081 0.449896i \(-0.148539\pi\)
\(632\) −7.42966 + 12.6928i −0.295536 + 0.504892i
\(633\) 0 0
\(634\) −11.8562 32.7777i −0.470870 1.30177i
\(635\) 8.62311i 0.342198i
\(636\) 0 0
\(637\) 1.64657i 0.0652394i
\(638\) −18.0206 + 6.51835i −0.713443 + 0.258064i
\(639\) 0 0
\(640\) −3.22474 + 3.73605i −0.127469 + 0.147680i
\(641\) 15.4383i 0.609775i −0.952388 0.304888i \(-0.901381\pi\)
0.952388 0.304888i \(-0.0986189\pi\)
\(642\) 0 0
\(643\) 1.41036 0.0556191 0.0278095 0.999613i \(-0.491147\pi\)
0.0278095 + 0.999613i \(0.491147\pi\)
\(644\) 9.83005 + 11.8102i 0.387358 + 0.465388i
\(645\) 0 0
\(646\) 41.6679 15.0720i 1.63940 0.592998i
\(647\) 0.811574 0.0319063 0.0159531 0.999873i \(-0.494922\pi\)
0.0159531 + 0.999873i \(0.494922\pi\)
\(648\) 0 0
\(649\) −36.3941 −1.42860
\(650\) −10.5321 + 3.80962i −0.413102 + 0.149426i
\(651\) 0 0
\(652\) 9.02719 7.51364i 0.353532 0.294257i
\(653\) −9.82168 −0.384352 −0.192176 0.981360i \(-0.561554\pi\)
−0.192176 + 0.981360i \(0.561554\pi\)
\(654\) 0 0
\(655\) 4.03615i 0.157705i
\(656\) −38.3393 7.07565i −1.49690 0.276258i
\(657\) 0 0
\(658\) −6.04657 + 2.18714i −0.235720 + 0.0852637i
\(659\) 11.1456i 0.434170i −0.976153 0.217085i \(-0.930345\pi\)
0.976153 0.217085i \(-0.0696548\pi\)
\(660\) 0 0
\(661\) 15.3989i 0.598947i 0.954105 + 0.299474i \(0.0968111\pi\)
−0.954105 + 0.299474i \(0.903189\pi\)
\(662\) −2.72376 7.53010i −0.105862 0.292666i
\(663\) 0 0
\(664\) 0.324445 0.554280i 0.0125909 0.0215102i
\(665\) 2.61717i 0.101489i
\(666\) 0 0
\(667\) 38.0146 1.47193
\(668\) 34.0000 28.2993i 1.31550 1.09493i
\(669\) 0 0
\(670\) 1.97706 + 5.46577i 0.0763804 + 0.211161i
\(671\) 17.1478 0.661982
\(672\) 0 0
\(673\) 20.4112 0.786795 0.393398 0.919368i \(-0.371300\pi\)
0.393398 + 0.919368i \(0.371300\pi\)
\(674\) −15.5126 42.8862i −0.597525 1.65192i
\(675\) 0 0
\(676\) −15.8159 + 13.1641i −0.608305 + 0.506313i
\(677\) −50.5124 −1.94135 −0.970674 0.240401i \(-0.922721\pi\)
−0.970674 + 0.240401i \(0.922721\pi\)
\(678\) 0 0
\(679\) 3.37287i 0.129439i
\(680\) 3.25498 5.56080i 0.124823 0.213247i
\(681\) 0 0
\(682\) 12.8834 + 35.6176i 0.493333 + 1.36387i
\(683\) 33.3625i 1.27658i −0.769796 0.638291i \(-0.779642\pi\)
0.769796 0.638291i \(-0.220358\pi\)
\(684\) 0 0
\(685\) 1.10475i 0.0422104i
\(686\) 1.32989 0.481042i 0.0507753 0.0183663i
\(687\) 0 0
\(688\) −6.41886 + 34.7804i −0.244717 + 1.32599i
\(689\) 16.3808i 0.624059i
\(690\) 0 0
\(691\) 24.3714 0.927133 0.463567 0.886062i \(-0.346569\pi\)
0.463567 + 0.886062i \(0.346569\pi\)
\(692\) −37.1879 + 30.9527i −1.41367 + 1.17665i
\(693\) 0 0
\(694\) 27.0442 9.78234i 1.02659 0.371333i
\(695\) −8.62982 −0.327348
\(696\) 0 0
\(697\) 50.9002 1.92798
\(698\) 11.0053 3.98081i 0.416558 0.150676i
\(699\) 0 0
\(700\) 6.15384 + 7.39348i 0.232593 + 0.279447i
\(701\) −34.1271 −1.28896 −0.644481 0.764620i \(-0.722927\pi\)
−0.644481 + 0.764620i \(0.722927\pi\)
\(702\) 0 0
\(703\) 22.8991i 0.863658i
\(704\) 19.1033 10.7270i 0.719983 0.404288i
\(705\) 0 0
\(706\) 10.9489 3.96041i 0.412069 0.149052i
\(707\) 1.20021i 0.0451384i
\(708\) 0 0
\(709\) 22.8145i 0.856818i −0.903585 0.428409i \(-0.859074\pi\)
0.903585 0.428409i \(-0.140926\pi\)
\(710\) −2.04962 5.66638i −0.0769209 0.212655i
\(711\) 0 0
\(712\) −3.52300 + 6.01868i −0.132030 + 0.225560i
\(713\) 75.1355i 2.81385i
\(714\) 0 0
\(715\) −1.96707 −0.0735642
\(716\) −6.92556 8.32065i −0.258820 0.310957i
\(717\) 0 0
\(718\) −5.08953 14.0705i −0.189940 0.525107i
\(719\) −2.18175 −0.0813654 −0.0406827 0.999172i \(-0.512953\pi\)
−0.0406827 + 0.999172i \(0.512953\pi\)
\(720\) 0 0
\(721\) 10.7004 0.398502
\(722\) 8.17556 + 22.6021i 0.304263 + 0.841164i
\(723\) 0 0
\(724\) 7.92846 + 9.52558i 0.294659 + 0.354015i
\(725\) 23.7980 0.883837
\(726\) 0 0
\(727\) 15.3017i 0.567507i −0.958897 0.283754i \(-0.908420\pi\)
0.958897 0.283754i \(-0.0915798\pi\)
\(728\) −4.01927 2.35266i −0.148964 0.0871953i
\(729\) 0 0
\(730\) −1.91811 5.30280i −0.0709924 0.196265i
\(731\) 46.1754i 1.70786i
\(732\) 0 0
\(733\) 15.8711i 0.586213i 0.956080 + 0.293106i \(0.0946890\pi\)
−0.956080 + 0.293106i \(0.905311\pi\)
\(734\) 31.5974 11.4293i 1.16628 0.421863i
\(735\) 0 0
\(736\) −42.8741 + 7.12036i −1.58036 + 0.262460i
\(737\) 25.8025i 0.950449i
\(738\) 0 0
\(739\) 31.1319 1.14521 0.572603 0.819833i \(-0.305934\pi\)
0.572603 + 0.819833i \(0.305934\pi\)
\(740\) −2.13024 2.55936i −0.0783093 0.0940840i
\(741\) 0 0
\(742\) −13.2303 + 4.78562i −0.485700 + 0.175686i
\(743\) −14.6629 −0.537930 −0.268965 0.963150i \(-0.586682\pi\)
−0.268965 + 0.963150i \(0.586682\pi\)
\(744\) 0 0
\(745\) 3.56158 0.130486
\(746\) −16.1504 + 5.84186i −0.591308 + 0.213886i
\(747\) 0 0
\(748\) −21.9849 + 18.2988i −0.803849 + 0.669071i
\(749\) 1.49655 0.0546826
\(750\) 0 0
\(751\) 8.46100i 0.308746i 0.988013 + 0.154373i \(0.0493358\pi\)
−0.988013 + 0.154373i \(0.950664\pi\)
\(752\) 3.30069 17.8847i 0.120364 0.652188i
\(753\) 0 0
\(754\) −10.8347 + 3.91908i −0.394576 + 0.142725i
\(755\) 6.48842i 0.236138i
\(756\) 0 0
\(757\) 39.6473i 1.44101i −0.693451 0.720504i \(-0.743911\pi\)
0.693451 0.720504i \(-0.256089\pi\)
\(758\) −15.4600 42.7408i −0.561533 1.55241i
\(759\) 0 0
\(760\) 6.38849 + 3.73947i 0.231735 + 0.135645i
\(761\) 49.7301i 1.80271i −0.433076 0.901357i \(-0.642572\pi\)
0.433076 0.901357i \(-0.357428\pi\)
\(762\) 0 0
\(763\) −18.4352 −0.667401
\(764\) 20.9353 17.4251i 0.757411 0.630419i
\(765\) 0 0
\(766\) −14.4568 39.9671i −0.522344 1.44407i
\(767\) −21.8816 −0.790098
\(768\) 0 0
\(769\) 5.62877 0.202979 0.101489 0.994837i \(-0.467639\pi\)
0.101489 + 0.994837i \(0.467639\pi\)
\(770\) 0.574675 + 1.58875i 0.0207099 + 0.0572544i
\(771\) 0 0
\(772\) −9.05837 + 7.53959i −0.326018 + 0.271356i
\(773\) −25.3999 −0.913570 −0.456785 0.889577i \(-0.650999\pi\)
−0.456785 + 0.889577i \(0.650999\pi\)
\(774\) 0 0
\(775\) 47.0366i 1.68960i
\(776\) 8.23317 + 4.81924i 0.295553 + 0.173001i
\(777\) 0 0
\(778\) −6.19211 17.1187i −0.221998 0.613736i
\(779\) 58.4764i 2.09514i
\(780\) 0 0
\(781\) 26.7495i 0.957174i
\(782\) 53.3588 19.3007i 1.90811 0.690193i
\(783\) 0 0
\(784\) −0.725955 + 3.93357i −0.0259270 + 0.140485i