Properties

Label 1512.2.j.c.323.13
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 323.13
Character \(\chi\) = 1512.323
Dual form 1512.2.j.c.323.14

$q$-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 \(-0.531098\pi\)
−0.0975421 + 0.995231i \(0.531098\pi\)
\(6\) 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 \(0.135471\pi\)
−0.910793 + 0.412863i \(0.864529\pi\)
\(12\) 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 \(-0.781701\pi\)
0.773908 0.633298i \(-0.218299\pi\)
\(18\) 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 \(-0.204300\pi\)
0.801004 + 0.598659i \(0.204300\pi\)
\(24\) 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 \(-0.348064\pi\)
0.459402 + 0.888228i \(0.348064\pi\)
\(30\) 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 \(0.275334\pi\)
−0.648649 + 0.761088i \(0.724666\pi\)
\(42\) 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 \(-0.607589\pi\)
−0.331601 + 0.943420i \(0.607589\pi\)
\(48\) 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 \(-0.739439\pi\)
−0.683262 + 0.730173i \(0.739439\pi\)
\(54\) 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 \(0.332715\pi\)
−0.501681 + 0.865053i \(0.667285\pi\)
\(60\) 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 \(-0.303211\pi\)
0.579595 + 0.814905i \(0.303211\pi\)
\(72\) 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 \(-0.996033\pi\)
0.999922 0.0124622i \(-0.00396693\pi\)
\(84\) 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 \(0.0417161\pi\)
−0.991425 + 0.130680i \(0.958284\pi\)
\(90\) 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 \(-0.480982\pi\)
0.0597125 + 0.998216i \(0.480982\pi\)
\(102\) 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 \(0.0230461\pi\)
−0.997380 + 0.0723382i \(0.976954\pi\)
\(108\) 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 \(-0.920468\pi\)
0.968948 0.247265i \(-0.0795317\pi\)
\(114\) 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 \(0.132449\pi\)
−0.914671 + 0.404198i \(0.867551\pi\)
\(132\) 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 \(0.0345039\pi\)
−0.994131 + 0.108185i \(0.965496\pi\)
\(138\) 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 \(-0.608546\pi\)
−0.334435 + 0.942419i \(0.608546\pi\)
\(150\) 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 \(-0.173080\pi\)
0.855777 + 0.517345i \(0.173080\pi\)
\(168\) 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 \(-0.871521\pi\)
−0.919642 + 0.392758i \(0.871521\pi\)
\(174\) 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 \(-0.935162\pi\)
0.979326 0.202288i \(-0.0648378\pi\)
\(180\) 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 \(-0.336002\pi\)
0.492722 + 0.870187i \(0.336002\pi\)
\(192\) 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 \(-0.737152\pi\)
−0.677998 + 0.735064i \(0.737152\pi\)
\(198\) 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 \(0.0382245\pi\)
−0.992798 + 0.119797i \(0.961776\pi\)
\(228\) 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 \(-0.728756\pi\)
0.658376 0.752689i \(-0.271244\pi\)
\(234\) 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 \(-0.390281\pi\)
0.337906 + 0.941180i \(0.390281\pi\)
\(240\) 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 \(-0.806994\pi\)
0.821736 0.569868i \(-0.193006\pi\)
\(252\) 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 \(-0.962421\pi\)
0.993039 0.117784i \(-0.0375789\pi\)
\(258\) 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 \(-0.700990\pi\)
−0.590298 + 0.807185i \(0.700990\pi\)
\(264\) 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 \(-0.618204\pi\)
−0.362873 + 0.931838i \(0.618204\pi\)
\(270\) 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 \(-0.833198\pi\)
0.865813 0.500367i \(-0.166802\pi\)
\(282\) 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 \(-0.589127\pi\)
−0.276355 + 0.961056i \(0.589127\pi\)
\(294\) 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 \(-0.515426\pi\)
−0.0484435 + 0.998826i \(0.515426\pi\)
\(312\) 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 \(-0.256661\pi\)
0.692155 + 0.721748i \(0.256661\pi\)
\(318\) 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 \(0.183789\pi\)
−0.837889 + 0.545840i \(0.816211\pi\)
\(348\) 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 \(0.0703117\pi\)
−0.975703 + 0.219099i \(0.929688\pi\)
\(354\) 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 \(-0.409930\pi\)
0.279202 + 0.960232i \(0.409930\pi\)
\(360\) 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 \(-0.221342\pi\)
0.767819 + 0.640667i \(0.221342\pi\)
\(384\) 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 \(-0.394189\pi\)
0.326326 + 0.945257i \(0.394189\pi\)
\(390\) 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 \(0.129318\pi\)
−0.918604 + 0.395180i \(0.870682\pi\)
\(402\) 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 \(-0.972209\pi\)
0.996191 0.0871974i \(-0.0277911\pi\)
\(420\) 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 \(-0.256542\pi\)
0.692426 + 0.721489i \(0.256542\pi\)
\(432\) 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 \(-0.827042\pi\)
0.855974 0.517019i \(-0.172958\pi\)
\(444\) 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 \(-0.760769\pi\)
0.730621 0.682783i \(-0.239231\pi\)
\(450\) 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 \(-0.555691\pi\)
−0.174066 + 0.984734i \(0.555691\pi\)
\(462\) 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 \(-0.878801\pi\)
0.928384 0.371623i \(-0.121199\pi\)
\(468\) 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 \(-0.757782\pi\)
−0.724181 + 0.689610i \(0.757782\pi\)
\(480\) 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 \(0.380296\pi\)
−0.367259 + 0.930119i \(0.619704\pi\)
\(492\) 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 \(-0.145676\pi\)
0.897092 + 0.441845i \(0.145676\pi\)
\(504\) 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 \(-0.568825\pi\)
−0.214540 + 0.976715i \(0.568825\pi\)
\(510\) 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 \(-0.972589\pi\)
0.996295 0.0860069i \(-0.0274107\pi\)
\(522\) 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 \(-0.595870\pi\)
−0.296652 + 0.954986i \(0.595870\pi\)
\(558\) 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 \(-0.905490\pi\)
0.956245 0.292569i \(-0.0945100\pi\)
\(564\) 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 \(-0.899939\pi\)
0.950997 0.309200i \(-0.100061\pi\)
\(570\) 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 \(-0.990449\pi\)
0.999550 0.0300018i \(-0.00955129\pi\)
\(588\) 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 \(0.0872464\pi\)
−0.962671 + 0.270674i \(0.912754\pi\)
\(594\) 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 \(-0.595628\pi\)
−0.295924 + 0.955211i \(0.595628\pi\)
\(600\) 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 \(-0.587238\pi\)
0.270647 0.962679i \(-0.412762\pi\)
\(618\) 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 \(0.0986189\pi\)
−0.952388 + 0.304888i \(0.901381\pi\)
\(642\) 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 \(-0.505078\pi\)
−0.0159531 + 0.999873i \(0.505078\pi\)
\(648\) 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 \(-0.438446\pi\)
0.192176 + 0.981360i \(0.438446\pi\)
\(654\) 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 \(0.0696548\pi\)
−0.976153 + 0.217085i \(0.930345\pi\)
\(660\) 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 \(-0.0772789\pi\)
0.970674 + 0.240401i \(0.0772789\pi\)
\(678\) 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 \(0.220358\pi\)
−0.769796 + 0.638291i \(0.779642\pi\)
\(684\) 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 \(-0.277073\pi\)
0.644481 + 0.764620i \(0.277073\pi\)
\(702\) 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 \(-0.487047\pi\)
0.0406827 + 0.999172i \(0.487047\pi\)
\(720\) 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 \(-0.413318\pi\)
0.268965 + 0.963150i \(0.413318\pi\)
\(744\) 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 \(0.357428\pi\)
−0.433076 + 0.901357i \(0.642572\pi\)
\(762\) 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 \(-0.349001\pi\)
0.456785 + 0.889577i \(0.349001\pi\)
\(774\) 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