Properties

Label 1008.2.r.j.337.3
Level 1008
Weight 2
Character 1008.337
Analytic conductor 8.049
Analytic rank 0
Dimension 6
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.309123.1
Defining polynomial: \(x^{6} - 3 x^{5} + 10 x^{4} - 15 x^{3} + 19 x^{2} - 12 x + 3\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 252)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 337.3
Root \(0.500000 - 1.41036i\) of defining polynomial
Character \(\chi\) \(=\) 1008.337
Dual form 1008.2.r.j.673.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.71053 + 0.272169i) q^{3} +(-0.119562 + 0.207087i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.85185 + 0.931107i) q^{9} +O(q^{10})\) \(q+(1.71053 + 0.272169i) q^{3} +(-0.119562 + 0.207087i) q^{5} +(-0.500000 - 0.866025i) q^{7} +(2.85185 + 0.931107i) q^{9} +(-2.56238 - 4.43818i) q^{11} +(2.44282 - 4.23109i) q^{13} +(-0.260877 + 0.321688i) q^{15} +3.70370 q^{17} -3.66019 q^{19} +(-0.619562 - 1.61745i) q^{21} +(3.71053 - 6.42683i) q^{23} +(2.47141 + 4.28061i) q^{25} +(4.62476 + 2.36887i) q^{27} +(-1.73229 - 3.00041i) q^{29} +(-0.358685 + 0.621261i) q^{31} +(-3.17511 - 8.28905i) q^{33} +0.239123 q^{35} +4.60301 q^{37} +(5.33009 - 6.57256i) q^{39} +(-2.80150 + 4.85235i) q^{41} +(6.24433 + 10.8155i) q^{43} +(-0.533792 + 0.479256i) q^{45} +(2.16991 + 3.75839i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(6.33530 + 1.00803i) q^{51} -0.942820 q^{53} +1.22545 q^{55} +(-6.26088 - 0.996189i) q^{57} +(3.78947 - 6.56355i) q^{59} +(-2.75404 - 4.77014i) q^{61} +(-0.619562 - 2.93533i) q^{63} +(0.584135 + 1.01175i) q^{65} +(-0.330095 + 0.571741i) q^{67} +(8.09617 - 9.98342i) q^{69} -13.7414 q^{71} -3.66019 q^{73} +(3.06238 + 7.99476i) q^{75} +(-2.56238 + 4.43818i) q^{77} +(-3.11273 - 5.39140i) q^{79} +(7.26608 + 5.31075i) q^{81} +(4.85185 + 8.40365i) q^{83} +(-0.442820 + 0.766987i) q^{85} +(-2.14652 - 5.60377i) q^{87} -7.48865 q^{89} -4.88564 q^{91} +(-0.782630 + 0.965064i) q^{93} +(0.437618 - 0.757977i) q^{95} +(8.57442 + 14.8513i) q^{97} +(-3.17511 - 15.0429i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{3} - q^{5} - 3q^{7} + 8q^{9} + O(q^{10}) \) \( 6q + 2q^{3} - q^{5} - 3q^{7} + 8q^{9} + 2q^{11} - 3q^{13} - q^{15} + 4q^{17} - 6q^{19} - 4q^{21} + 14q^{23} + 6q^{25} - 7q^{27} - q^{29} - 3q^{31} + 8q^{33} + 2q^{35} - 6q^{37} + 24q^{39} + 3q^{43} + 23q^{45} + 21q^{47} - 3q^{49} - 5q^{51} + 12q^{53} - 12q^{55} - 37q^{57} + 31q^{59} - 6q^{61} - 4q^{63} - 15q^{65} + 6q^{67} + 5q^{69} - 34q^{71} - 6q^{73} + q^{75} + 2q^{77} - 9q^{79} + 8q^{81} + 20q^{83} + 15q^{85} + 23q^{87} + 24q^{89} + 6q^{91} - 3q^{93} + 20q^{95} + 9q^{97} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) 1.71053 + 0.272169i 0.987577 + 0.157137i
\(4\) 0 0
\(5\) −0.119562 + 0.207087i −0.0534696 + 0.0926120i −0.891521 0.452979i \(-0.850361\pi\)
0.838052 + 0.545591i \(0.183695\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) 0 0
\(9\) 2.85185 + 0.931107i 0.950616 + 0.310369i
\(10\) 0 0
\(11\) −2.56238 4.43818i −0.772587 1.33816i −0.936141 0.351626i \(-0.885629\pi\)
0.163554 0.986534i \(-0.447704\pi\)
\(12\) 0 0
\(13\) 2.44282 4.23109i 0.677516 1.17349i −0.298210 0.954500i \(-0.596390\pi\)
0.975727 0.218993i \(-0.0702770\pi\)
\(14\) 0 0
\(15\) −0.260877 + 0.321688i −0.0673581 + 0.0830595i
\(16\) 0 0
\(17\) 3.70370 0.898278 0.449139 0.893462i \(-0.351731\pi\)
0.449139 + 0.893462i \(0.351731\pi\)
\(18\) 0 0
\(19\) −3.66019 −0.839705 −0.419853 0.907592i \(-0.637918\pi\)
−0.419853 + 0.907592i \(0.637918\pi\)
\(20\) 0 0
\(21\) −0.619562 1.61745i −0.135199 0.352956i
\(22\) 0 0
\(23\) 3.71053 6.42683i 0.773700 1.34009i −0.161823 0.986820i \(-0.551737\pi\)
0.935522 0.353267i \(-0.114929\pi\)
\(24\) 0 0
\(25\) 2.47141 + 4.28061i 0.494282 + 0.856122i
\(26\) 0 0
\(27\) 4.62476 + 2.36887i 0.890036 + 0.455890i
\(28\) 0 0
\(29\) −1.73229 3.00041i −0.321678 0.557162i 0.659157 0.752006i \(-0.270913\pi\)
−0.980834 + 0.194844i \(0.937580\pi\)
\(30\) 0 0
\(31\) −0.358685 + 0.621261i −0.0644217 + 0.111582i −0.896437 0.443171i \(-0.853854\pi\)
0.832016 + 0.554752i \(0.187187\pi\)
\(32\) 0 0
\(33\) −3.17511 8.28905i −0.552715 1.44294i
\(34\) 0 0
\(35\) 0.239123 0.0404192
\(36\) 0 0
\(37\) 4.60301 0.756730 0.378365 0.925656i \(-0.376486\pi\)
0.378365 + 0.925656i \(0.376486\pi\)
\(38\) 0 0
\(39\) 5.33009 6.57256i 0.853498 1.05245i
\(40\) 0 0
\(41\) −2.80150 + 4.85235i −0.437522 + 0.757810i −0.997498 0.0706992i \(-0.977477\pi\)
0.559976 + 0.828509i \(0.310810\pi\)
\(42\) 0 0
\(43\) 6.24433 + 10.8155i 0.952251 + 1.64935i 0.740538 + 0.672015i \(0.234571\pi\)
0.211713 + 0.977332i \(0.432096\pi\)
\(44\) 0 0
\(45\) −0.533792 + 0.479256i −0.0795730 + 0.0714432i
\(46\) 0 0
\(47\) 2.16991 + 3.75839i 0.316513 + 0.548217i 0.979758 0.200186i \(-0.0641545\pi\)
−0.663245 + 0.748403i \(0.730821\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) 0 0
\(51\) 6.33530 + 1.00803i 0.887119 + 0.141152i
\(52\) 0 0
\(53\) −0.942820 −0.129506 −0.0647531 0.997901i \(-0.520626\pi\)
−0.0647531 + 0.997901i \(0.520626\pi\)
\(54\) 0 0
\(55\) 1.22545 0.165240
\(56\) 0 0
\(57\) −6.26088 0.996189i −0.829273 0.131948i
\(58\) 0 0
\(59\) 3.78947 6.56355i 0.493347 0.854501i −0.506624 0.862167i \(-0.669107\pi\)
0.999971 + 0.00766579i \(0.00244012\pi\)
\(60\) 0 0
\(61\) −2.75404 4.77014i −0.352619 0.610754i 0.634089 0.773260i \(-0.281375\pi\)
−0.986707 + 0.162507i \(0.948042\pi\)
\(62\) 0 0
\(63\) −0.619562 2.93533i −0.0780574 0.369816i
\(64\) 0 0
\(65\) 0.584135 + 1.01175i 0.0724530 + 0.125492i
\(66\) 0 0
\(67\) −0.330095 + 0.571741i −0.0403275 + 0.0698493i −0.885485 0.464669i \(-0.846173\pi\)
0.845157 + 0.534518i \(0.179507\pi\)
\(68\) 0 0
\(69\) 8.09617 9.98342i 0.974665 1.20186i
\(70\) 0 0
\(71\) −13.7414 −1.63081 −0.815405 0.578891i \(-0.803486\pi\)
−0.815405 + 0.578891i \(0.803486\pi\)
\(72\) 0 0
\(73\) −3.66019 −0.428393 −0.214196 0.976791i \(-0.568713\pi\)
−0.214196 + 0.976791i \(0.568713\pi\)
\(74\) 0 0
\(75\) 3.06238 + 7.99476i 0.353613 + 0.923156i
\(76\) 0 0
\(77\) −2.56238 + 4.43818i −0.292010 + 0.505777i
\(78\) 0 0
\(79\) −3.11273 5.39140i −0.350209 0.606580i 0.636077 0.771626i \(-0.280556\pi\)
−0.986286 + 0.165046i \(0.947223\pi\)
\(80\) 0 0
\(81\) 7.26608 + 5.31075i 0.807342 + 0.590084i
\(82\) 0 0
\(83\) 4.85185 + 8.40365i 0.532560 + 0.922420i 0.999277 + 0.0380138i \(0.0121031\pi\)
−0.466718 + 0.884406i \(0.654564\pi\)
\(84\) 0 0
\(85\) −0.442820 + 0.766987i −0.0480306 + 0.0831914i
\(86\) 0 0
\(87\) −2.14652 5.60377i −0.230131 0.600788i
\(88\) 0 0
\(89\) −7.48865 −0.793795 −0.396898 0.917863i \(-0.629913\pi\)
−0.396898 + 0.917863i \(0.629913\pi\)
\(90\) 0 0
\(91\) −4.88564 −0.512154
\(92\) 0 0
\(93\) −0.782630 + 0.965064i −0.0811550 + 0.100072i
\(94\) 0 0
\(95\) 0.437618 0.757977i 0.0448987 0.0777668i
\(96\) 0 0
\(97\) 8.57442 + 14.8513i 0.870600 + 1.50792i 0.861377 + 0.507967i \(0.169603\pi\)
0.00922376 + 0.999957i \(0.497064\pi\)
\(98\) 0 0
\(99\) −3.17511 15.0429i −0.319110 1.51186i
\(100\) 0 0
\(101\) −3.59097 6.21975i −0.357315 0.618888i 0.630196 0.776436i \(-0.282974\pi\)
−0.987511 + 0.157548i \(0.949641\pi\)
\(102\) 0 0
\(103\) −6.41423 + 11.1098i −0.632013 + 1.09468i 0.355127 + 0.934818i \(0.384438\pi\)
−0.987140 + 0.159860i \(0.948896\pi\)
\(104\) 0 0
\(105\) 0.409028 + 0.0650819i 0.0399171 + 0.00635134i
\(106\) 0 0
\(107\) −7.56526 −0.731361 −0.365681 0.930740i \(-0.619164\pi\)
−0.365681 + 0.930740i \(0.619164\pi\)
\(108\) 0 0
\(109\) −6.98057 −0.668617 −0.334309 0.942464i \(-0.608503\pi\)
−0.334309 + 0.942464i \(0.608503\pi\)
\(110\) 0 0
\(111\) 7.87360 + 1.25280i 0.747329 + 0.118910i
\(112\) 0 0
\(113\) 9.78495 16.9480i 0.920491 1.59434i 0.121834 0.992550i \(-0.461122\pi\)
0.798657 0.601787i \(-0.205544\pi\)
\(114\) 0 0
\(115\) 0.887275 + 1.53681i 0.0827388 + 0.143308i
\(116\) 0 0
\(117\) 10.9061 9.79190i 1.00827 0.905261i
\(118\) 0 0
\(119\) −1.85185 3.20750i −0.169759 0.294031i
\(120\) 0 0
\(121\) −7.63160 + 13.2183i −0.693782 + 1.20167i
\(122\) 0 0
\(123\) −6.11273 + 7.53762i −0.551166 + 0.679645i
\(124\) 0 0
\(125\) −2.37756 −0.212655
\(126\) 0 0
\(127\) 16.8090 1.49156 0.745780 0.666192i \(-0.232077\pi\)
0.745780 + 0.666192i \(0.232077\pi\)
\(128\) 0 0
\(129\) 7.73749 + 20.1998i 0.681248 + 1.77849i
\(130\) 0 0
\(131\) 2.44966 4.24293i 0.214027 0.370706i −0.738944 0.673767i \(-0.764675\pi\)
0.952971 + 0.303061i \(0.0980085\pi\)
\(132\) 0 0
\(133\) 1.83009 + 3.16982i 0.158689 + 0.274858i
\(134\) 0 0
\(135\) −1.04351 + 0.674501i −0.0898108 + 0.0580518i
\(136\) 0 0
\(137\) −2.72257 4.71563i −0.232605 0.402884i 0.725969 0.687727i \(-0.241392\pi\)
−0.958574 + 0.284844i \(0.908058\pi\)
\(138\) 0 0
\(139\) 2.83009 4.90187i 0.240046 0.415771i −0.720681 0.693266i \(-0.756171\pi\)
0.960727 + 0.277495i \(0.0895043\pi\)
\(140\) 0 0
\(141\) 2.68878 + 7.01942i 0.226436 + 0.591142i
\(142\) 0 0
\(143\) −25.0377 −2.09376
\(144\) 0 0
\(145\) 0.828460 0.0687999
\(146\) 0 0
\(147\) −1.09097 + 1.34528i −0.0899818 + 0.110957i
\(148\) 0 0
\(149\) −1.14132 + 1.97682i −0.0935002 + 0.161947i −0.908982 0.416836i \(-0.863139\pi\)
0.815481 + 0.578783i \(0.196472\pi\)
\(150\) 0 0
\(151\) 5.63160 + 9.75422i 0.458293 + 0.793787i 0.998871 0.0475071i \(-0.0151277\pi\)
−0.540578 + 0.841294i \(0.681794\pi\)
\(152\) 0 0
\(153\) 10.5624 + 3.44854i 0.853918 + 0.278798i
\(154\) 0 0
\(155\) −0.0857699 0.148558i −0.00688921 0.0119325i
\(156\) 0 0
\(157\) −2.77292 + 4.80283i −0.221303 + 0.383308i −0.955204 0.295949i \(-0.904364\pi\)
0.733901 + 0.679256i \(0.237698\pi\)
\(158\) 0 0
\(159\) −1.61273 0.256606i −0.127897 0.0203502i
\(160\) 0 0
\(161\) −7.42107 −0.584862
\(162\) 0 0
\(163\) −6.66019 −0.521666 −0.260833 0.965384i \(-0.583997\pi\)
−0.260833 + 0.965384i \(0.583997\pi\)
\(164\) 0 0
\(165\) 2.09617 + 0.333529i 0.163187 + 0.0259652i
\(166\) 0 0
\(167\) 2.20370 3.81691i 0.170527 0.295362i −0.768077 0.640357i \(-0.778786\pi\)
0.938604 + 0.344996i \(0.112120\pi\)
\(168\) 0 0
\(169\) −5.43474 9.41325i −0.418057 0.724096i
\(170\) 0 0
\(171\) −10.4383 3.40803i −0.798237 0.260619i
\(172\) 0 0
\(173\) −12.6654 21.9371i −0.962932 1.66785i −0.715072 0.699051i \(-0.753606\pi\)
−0.247860 0.968796i \(-0.579727\pi\)
\(174\) 0 0
\(175\) 2.47141 4.28061i 0.186821 0.323584i
\(176\) 0 0
\(177\) 8.26840 10.1958i 0.621491 0.766363i
\(178\) 0 0
\(179\) −9.54583 −0.713489 −0.356744 0.934202i \(-0.616113\pi\)
−0.356744 + 0.934202i \(0.616113\pi\)
\(180\) 0 0
\(181\) 12.3743 0.919774 0.459887 0.887978i \(-0.347890\pi\)
0.459887 + 0.887978i \(0.347890\pi\)
\(182\) 0 0
\(183\) −3.41260 8.90904i −0.252266 0.658575i
\(184\) 0 0
\(185\) −0.550343 + 0.953223i −0.0404621 + 0.0700823i
\(186\) 0 0
\(187\) −9.49028 16.4377i −0.693998 1.20204i
\(188\) 0 0
\(189\) −0.260877 5.18960i −0.0189760 0.377488i
\(190\) 0 0
\(191\) 6.58414 + 11.4041i 0.476411 + 0.825169i 0.999635 0.0270270i \(-0.00860400\pi\)
−0.523223 + 0.852196i \(0.675271\pi\)
\(192\) 0 0
\(193\) −5.57442 + 9.65518i −0.401256 + 0.694995i −0.993878 0.110486i \(-0.964759\pi\)
0.592622 + 0.805481i \(0.298093\pi\)
\(194\) 0 0
\(195\) 0.723815 + 1.88962i 0.0518335 + 0.135318i
\(196\) 0 0
\(197\) −0.144194 −0.0102734 −0.00513669 0.999987i \(-0.501635\pi\)
−0.00513669 + 0.999987i \(0.501635\pi\)
\(198\) 0 0
\(199\) 19.4692 1.38014 0.690068 0.723744i \(-0.257581\pi\)
0.690068 + 0.723744i \(0.257581\pi\)
\(200\) 0 0
\(201\) −0.720248 + 0.888141i −0.0508024 + 0.0626446i
\(202\) 0 0
\(203\) −1.73229 + 3.00041i −0.121583 + 0.210587i
\(204\) 0 0
\(205\) −0.669905 1.16031i −0.0467882 0.0810395i
\(206\) 0 0
\(207\) 16.5659 14.8734i 1.15141 1.03378i
\(208\) 0 0
\(209\) 9.37880 + 16.2446i 0.648745 + 1.12366i
\(210\) 0 0
\(211\) −1.61436 + 2.79615i −0.111137 + 0.192495i −0.916229 0.400655i \(-0.868783\pi\)
0.805092 + 0.593150i \(0.202116\pi\)
\(212\) 0 0
\(213\) −23.5052 3.73999i −1.61055 0.256260i
\(214\) 0 0
\(215\) −2.98633 −0.203666
\(216\) 0 0
\(217\) 0.717370 0.0486982
\(218\) 0 0
\(219\) −6.26088 0.996189i −0.423071 0.0673162i
\(220\) 0 0
\(221\) 9.04746 15.6707i 0.608598 1.05412i
\(222\) 0 0
\(223\) 10.3856 + 17.9885i 0.695474 + 1.20460i 0.970021 + 0.243022i \(0.0781389\pi\)
−0.274547 + 0.961574i \(0.588528\pi\)
\(224\) 0 0
\(225\) 3.06238 + 14.5088i 0.204159 + 0.967253i
\(226\) 0 0
\(227\) 10.9714 + 19.0030i 0.728198 + 1.26128i 0.957644 + 0.287955i \(0.0929752\pi\)
−0.229446 + 0.973321i \(0.573691\pi\)
\(228\) 0 0
\(229\) −11.3856 + 19.7205i −0.752384 + 1.30317i 0.194280 + 0.980946i \(0.437763\pi\)
−0.946664 + 0.322222i \(0.895570\pi\)
\(230\) 0 0
\(231\) −5.59097 + 6.89425i −0.367859 + 0.453608i
\(232\) 0 0
\(233\) −25.7817 −1.68901 −0.844507 0.535544i \(-0.820106\pi\)
−0.844507 + 0.535544i \(0.820106\pi\)
\(234\) 0 0
\(235\) −1.03775 −0.0676953
\(236\) 0 0
\(237\) −3.85705 10.0694i −0.250542 0.654075i
\(238\) 0 0
\(239\) −13.6488 + 23.6405i −0.882870 + 1.52918i −0.0347345 + 0.999397i \(0.511059\pi\)
−0.848136 + 0.529779i \(0.822275\pi\)
\(240\) 0 0
\(241\) −5.01724 8.69011i −0.323189 0.559779i 0.657955 0.753057i \(-0.271422\pi\)
−0.981144 + 0.193277i \(0.938088\pi\)
\(242\) 0 0
\(243\) 10.9834 + 11.0618i 0.704589 + 0.709616i
\(244\) 0 0
\(245\) −0.119562 0.207087i −0.00763851 0.0132303i
\(246\) 0 0
\(247\) −8.94119 + 15.4866i −0.568914 + 0.985388i
\(248\) 0 0
\(249\) 6.01204 + 15.6952i 0.380997 + 0.994645i
\(250\) 0 0
\(251\) 28.3171 1.78736 0.893680 0.448705i \(-0.148115\pi\)
0.893680 + 0.448705i \(0.148115\pi\)
\(252\) 0 0
\(253\) −38.0312 −2.39100
\(254\) 0 0
\(255\) −0.966208 + 1.19143i −0.0605063 + 0.0746105i
\(256\) 0 0
\(257\) −14.4315 + 24.9960i −0.900210 + 1.55921i −0.0729899 + 0.997333i \(0.523254\pi\)
−0.827221 + 0.561877i \(0.810079\pi\)
\(258\) 0 0
\(259\) −2.30150 3.98632i −0.143009 0.247698i
\(260\) 0 0
\(261\) −2.14652 10.1697i −0.132866 0.629486i
\(262\) 0 0
\(263\) −0.604645 1.04728i −0.0372840 0.0645778i 0.846781 0.531941i \(-0.178537\pi\)
−0.884065 + 0.467363i \(0.845204\pi\)
\(264\) 0 0
\(265\) 0.112725 0.195246i 0.00692465 0.0119938i
\(266\) 0 0
\(267\) −12.8096 2.03818i −0.783934 0.124734i
\(268\) 0 0
\(269\) 9.01367 0.549573 0.274787 0.961505i \(-0.411393\pi\)
0.274787 + 0.961505i \(0.411393\pi\)
\(270\) 0 0
\(271\) −17.6030 −1.06931 −0.534653 0.845071i \(-0.679558\pi\)
−0.534653 + 0.845071i \(0.679558\pi\)
\(272\) 0 0
\(273\) −8.35705 1.32972i −0.505792 0.0804782i
\(274\) 0 0
\(275\) 12.6654 21.9371i 0.763752 1.32286i
\(276\) 0 0
\(277\) −0.727085 1.25935i −0.0436863 0.0756669i 0.843355 0.537356i \(-0.180577\pi\)
−0.887042 + 0.461689i \(0.847244\pi\)
\(278\) 0 0
\(279\) −1.60138 + 1.43777i −0.0958718 + 0.0860768i
\(280\) 0 0
\(281\) 10.1482 + 17.5771i 0.605388 + 1.04856i 0.991990 + 0.126316i \(0.0403154\pi\)
−0.386602 + 0.922247i \(0.626351\pi\)
\(282\) 0 0
\(283\) −2.30150 + 3.98632i −0.136810 + 0.236962i −0.926288 0.376817i \(-0.877018\pi\)
0.789477 + 0.613780i \(0.210352\pi\)
\(284\) 0 0
\(285\) 0.954858 1.17744i 0.0565609 0.0697455i
\(286\) 0 0
\(287\) 5.60301 0.330735
\(288\) 0 0
\(289\) −3.28263 −0.193096
\(290\) 0 0
\(291\) 10.6248 + 27.7374i 0.622835 + 1.62599i
\(292\) 0 0
\(293\) 3.53667 6.12569i 0.206614 0.357867i −0.744031 0.668145i \(-0.767089\pi\)
0.950646 + 0.310278i \(0.100422\pi\)
\(294\) 0 0
\(295\) 0.906150 + 1.56950i 0.0527581 + 0.0913797i
\(296\) 0 0
\(297\) −1.33693 26.5955i −0.0775766 1.54323i
\(298\) 0 0
\(299\) −18.1283 31.3992i −1.04839 1.81586i
\(300\) 0 0
\(301\) 6.24433 10.8155i 0.359917 0.623394i
\(302\) 0 0
\(303\) −4.44966 11.6164i −0.255626 0.667347i
\(304\) 0 0
\(305\) 1.31711 0.0754175
\(306\) 0 0
\(307\) −15.7518 −0.899006 −0.449503 0.893279i \(-0.648399\pi\)
−0.449503 + 0.893279i \(0.648399\pi\)
\(308\) 0 0
\(309\) −13.9955 + 17.2579i −0.796175 + 0.981767i
\(310\) 0 0
\(311\) −9.81191 + 16.9947i −0.556382 + 0.963682i 0.441412 + 0.897304i \(0.354478\pi\)
−0.997795 + 0.0663780i \(0.978856\pi\)
\(312\) 0 0
\(313\) 12.7427 + 22.0710i 0.720259 + 1.24753i 0.960896 + 0.276911i \(0.0893106\pi\)
−0.240636 + 0.970615i \(0.577356\pi\)
\(314\) 0 0
\(315\) 0.681943 + 0.222649i 0.0384232 + 0.0125449i
\(316\) 0 0
\(317\) −4.14132 7.17297i −0.232599 0.402874i 0.725973 0.687723i \(-0.241390\pi\)
−0.958572 + 0.284849i \(0.908056\pi\)
\(318\) 0 0
\(319\) −8.87756 + 15.3764i −0.497048 + 0.860912i
\(320\) 0 0
\(321\) −12.9406 2.05903i −0.722276 0.114924i
\(322\) 0 0
\(323\) −13.5562 −0.754289
\(324\) 0 0
\(325\) 24.1488 1.33954
\(326\) 0 0
\(327\) −11.9405 1.89989i −0.660311 0.105064i
\(328\) 0 0
\(329\) 2.16991 3.75839i 0.119631 0.207207i
\(330\) 0 0
\(331\) −5.99028 10.3755i −0.329256 0.570288i 0.653109 0.757264i \(-0.273465\pi\)
−0.982364 + 0.186976i \(0.940131\pi\)
\(332\) 0 0
\(333\) 13.1271 + 4.28590i 0.719360 + 0.234866i
\(334\) 0 0
\(335\) −0.0789334 0.136717i −0.00431259 0.00746963i
\(336\) 0 0
\(337\) 6.46006 11.1892i 0.351902 0.609512i −0.634681 0.772774i \(-0.718868\pi\)
0.986583 + 0.163262i \(0.0522017\pi\)
\(338\) 0 0
\(339\) 21.3502 26.3270i 1.15958 1.42989i
\(340\) 0 0
\(341\) 3.67635 0.199086
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 1.09944 + 2.87024i 0.0591920 + 0.154529i
\(346\) 0 0
\(347\) 8.09329 14.0180i 0.434471 0.752526i −0.562781 0.826606i \(-0.690269\pi\)
0.997252 + 0.0740802i \(0.0236021\pi\)
\(348\) 0 0
\(349\) 9.05718 + 15.6875i 0.484820 + 0.839732i 0.999848 0.0174409i \(-0.00555188\pi\)
−0.515028 + 0.857173i \(0.672219\pi\)
\(350\) 0 0
\(351\) 21.3204 13.7811i 1.13800 0.735578i
\(352\) 0 0
\(353\) 5.84897 + 10.1307i 0.311309 + 0.539203i 0.978646 0.205553i \(-0.0658992\pi\)
−0.667337 + 0.744756i \(0.732566\pi\)
\(354\) 0 0
\(355\) 1.64295 2.84567i 0.0871987 0.151033i
\(356\) 0 0
\(357\) −2.29467 5.99054i −0.121447 0.317053i
\(358\) 0 0
\(359\) −35.7245 −1.88547 −0.942734 0.333547i \(-0.891755\pi\)
−0.942734 + 0.333547i \(0.891755\pi\)
\(360\) 0 0
\(361\) −5.60301 −0.294895
\(362\) 0 0
\(363\) −16.6517 + 20.5333i −0.873989 + 1.07772i
\(364\) 0 0
\(365\) 0.437618 0.757977i 0.0229060 0.0396743i
\(366\) 0 0
\(367\) 8.52696 + 14.7691i 0.445103 + 0.770942i 0.998059 0.0622687i \(-0.0198336\pi\)
−0.552956 + 0.833210i \(0.686500\pi\)
\(368\) 0 0
\(369\) −12.5075 + 11.2297i −0.651116 + 0.584593i
\(370\) 0 0
\(371\) 0.471410 + 0.816506i 0.0244744 + 0.0423909i
\(372\) 0 0
\(373\) 12.9617 22.4503i 0.671131 1.16243i −0.306453 0.951886i \(-0.599142\pi\)
0.977584 0.210547i \(-0.0675246\pi\)
\(374\) 0 0
\(375\) −4.06690 0.647097i −0.210014 0.0334160i
\(376\) 0 0
\(377\) −16.9267 −0.871767
\(378\) 0 0
\(379\) −26.8446 −1.37892 −0.689458 0.724326i \(-0.742151\pi\)
−0.689458 + 0.724326i \(0.742151\pi\)
\(380\) 0 0
\(381\) 28.7524 + 4.57489i 1.47303 + 0.234379i
\(382\) 0 0
\(383\) 12.4263 21.5229i 0.634953 1.09977i −0.351573 0.936161i \(-0.614353\pi\)
0.986525 0.163610i \(-0.0523137\pi\)
\(384\) 0 0
\(385\) −0.612725 1.06127i −0.0312274 0.0540874i
\(386\) 0 0
\(387\) 7.73749 + 36.6583i 0.393319 + 1.86344i
\(388\) 0 0
\(389\) 9.12640 + 15.8074i 0.462727 + 0.801466i 0.999096 0.0425174i \(-0.0135378\pi\)
−0.536369 + 0.843984i \(0.680204\pi\)
\(390\) 0 0
\(391\) 13.7427 23.8030i 0.694998 1.20377i
\(392\) 0 0
\(393\) 5.34501 6.59095i 0.269620 0.332470i
\(394\) 0 0
\(395\) 1.48865 0.0749021
\(396\) 0 0
\(397\) 12.3743 0.621048 0.310524 0.950566i \(-0.399496\pi\)
0.310524 + 0.950566i \(0.399496\pi\)
\(398\) 0 0
\(399\) 2.26771 + 5.92017i 0.113528 + 0.296379i
\(400\) 0 0
\(401\) 5.48113 9.49359i 0.273714 0.474087i −0.696096 0.717949i \(-0.745081\pi\)
0.969810 + 0.243862i \(0.0784144\pi\)
\(402\) 0 0
\(403\) 1.75241 + 3.03526i 0.0872935 + 0.151197i
\(404\) 0 0
\(405\) −1.96853 + 0.869747i −0.0978171 + 0.0432181i
\(406\) 0 0
\(407\) −11.7947 20.4290i −0.584640 1.01263i
\(408\) 0 0
\(409\) 6.66019 11.5358i 0.329325 0.570408i −0.653053 0.757312i \(-0.726512\pi\)
0.982378 + 0.186904i \(0.0598454\pi\)
\(410\) 0 0
\(411\) −3.37360 8.80724i −0.166408 0.434429i
\(412\) 0 0
\(413\) −7.57893 −0.372935
\(414\) 0 0
\(415\) −2.32038 −0.113903
\(416\) 0 0
\(417\) 6.17511 7.61455i 0.302396 0.372886i
\(418\) 0 0
\(419\) 2.35705 4.08253i 0.115149 0.199445i −0.802690 0.596396i \(-0.796599\pi\)
0.917839 + 0.396952i \(0.129932\pi\)
\(420\) 0 0
\(421\) −9.65856 16.7291i −0.470729 0.815327i 0.528710 0.848802i \(-0.322676\pi\)
−0.999440 + 0.0334755i \(0.989342\pi\)
\(422\) 0 0
\(423\) 2.68878 + 12.7388i 0.130733 + 0.619380i
\(424\) 0 0
\(425\) 9.15335 + 15.8541i 0.444003 + 0.769036i
\(426\) 0 0
\(427\) −2.75404 + 4.77014i −0.133277 + 0.230843i
\(428\) 0 0
\(429\) −42.8279 6.81449i −2.06775 0.329007i
\(430\) 0 0
\(431\) 30.2794 1.45851 0.729253 0.684244i \(-0.239868\pi\)
0.729253 + 0.684244i \(0.239868\pi\)
\(432\) 0 0
\(433\) 34.2060 1.64384 0.821918 0.569606i \(-0.192904\pi\)
0.821918 + 0.569606i \(0.192904\pi\)
\(434\) 0 0
\(435\) 1.41711 + 0.225481i 0.0679452 + 0.0108110i
\(436\) 0 0
\(437\) −13.5813 + 23.5234i −0.649680 + 1.12528i
\(438\) 0 0
\(439\) −0.311220 0.539049i −0.0148537 0.0257274i 0.858503 0.512809i \(-0.171395\pi\)
−0.873357 + 0.487081i \(0.838062\pi\)
\(440\) 0 0
\(441\) −2.23229 + 2.00422i −0.106299 + 0.0954390i
\(442\) 0 0
\(443\) −2.58934 4.48486i −0.123023 0.213082i 0.797935 0.602743i \(-0.205926\pi\)
−0.920958 + 0.389661i \(0.872592\pi\)
\(444\) 0 0
\(445\) 0.895355 1.55080i 0.0424439 0.0735150i
\(446\) 0 0
\(447\) −2.49028 + 3.07078i −0.117786 + 0.145243i
\(448\) 0 0
\(449\) −10.4977 −0.495416 −0.247708 0.968835i \(-0.579677\pi\)
−0.247708 + 0.968835i \(0.579677\pi\)
\(450\) 0 0
\(451\) 28.7141 1.35209
\(452\) 0 0
\(453\) 6.97825 + 18.2177i 0.327867 + 0.855940i
\(454\) 0 0
\(455\) 0.584135 1.01175i 0.0273847 0.0474317i
\(456\) 0 0
\(457\) 1.60464 + 2.77933i 0.0750621 + 0.130011i 0.901113 0.433584i \(-0.142751\pi\)
−0.826051 + 0.563595i \(0.809418\pi\)
\(458\) 0 0
\(459\) 17.1287 + 8.77359i 0.799500 + 0.409516i
\(460\) 0 0
\(461\) 18.1150 + 31.3762i 0.843702 + 1.46133i 0.886744 + 0.462261i \(0.152962\pi\)
−0.0430418 + 0.999073i \(0.513705\pi\)
\(462\) 0 0
\(463\) 14.5253 25.1586i 0.675049 1.16922i −0.301406 0.953496i \(-0.597456\pi\)
0.976455 0.215723i \(-0.0692108\pi\)
\(464\) 0 0
\(465\) −0.106279 0.277457i −0.00492859 0.0128668i
\(466\) 0 0
\(467\) 37.4933 1.73498 0.867491 0.497452i \(-0.165731\pi\)
0.867491 + 0.497452i \(0.165731\pi\)
\(468\) 0 0
\(469\) 0.660190 0.0304847
\(470\) 0 0
\(471\) −6.05034 + 7.46070i −0.278785 + 0.343771i
\(472\) 0 0
\(473\) 32.0007 55.4268i 1.47139 2.54853i
\(474\) 0 0
\(475\) −9.04583 15.6678i −0.415051 0.718890i
\(476\) 0 0
\(477\) −2.68878 0.877867i −0.123111 0.0401948i
\(478\) 0 0
\(479\) 14.9549 + 25.9026i 0.683305 + 1.18352i 0.973966 + 0.226693i \(0.0727914\pi\)
−0.290661 + 0.956826i \(0.593875\pi\)
\(480\) 0 0
\(481\) 11.2443 19.4757i 0.512697 0.888017i
\(482\) 0 0
\(483\) −12.6940 2.01978i −0.577596 0.0919033i
\(484\) 0 0
\(485\) −4.10069 −0.186203
\(486\) 0 0
\(487\) −21.2632 −0.963528 −0.481764 0.876301i \(-0.660004\pi\)
−0.481764 + 0.876301i \(0.660004\pi\)
\(488\) 0 0
\(489\) −11.3925 1.81270i −0.515186 0.0819729i
\(490\) 0 0
\(491\) −10.6985 + 18.5303i −0.482816 + 0.836262i −0.999805 0.0197296i \(-0.993719\pi\)
0.516989 + 0.855992i \(0.327053\pi\)
\(492\) 0 0
\(493\) −6.41586 11.1126i −0.288956 0.500487i
\(494\) 0 0
\(495\) 3.49480 + 1.14103i 0.157079 + 0.0512853i
\(496\) 0 0
\(497\) 6.87072 + 11.9004i 0.308194 + 0.533808i
\(498\) 0 0
\(499\) 7.28263 12.6139i 0.326015 0.564675i −0.655702 0.755020i \(-0.727627\pi\)
0.981717 + 0.190345i \(0.0609606\pi\)
\(500\) 0 0
\(501\) 4.80834 5.92918i 0.214821 0.264896i
\(502\) 0 0
\(503\) −2.92339 −0.130348 −0.0651738 0.997874i \(-0.520760\pi\)
−0.0651738 + 0.997874i \(0.520760\pi\)
\(504\) 0 0
\(505\) 1.71737 0.0764220
\(506\) 0 0
\(507\) −6.73431 17.5808i −0.299081 0.780792i
\(508\) 0 0
\(509\) 9.62025 16.6628i 0.426410 0.738564i −0.570141 0.821547i \(-0.693111\pi\)
0.996551 + 0.0829830i \(0.0264447\pi\)
\(510\) 0 0
\(511\) 1.83009 + 3.16982i 0.0809586 + 0.140224i
\(512\) 0 0
\(513\) −16.9275 8.67053i −0.747368 0.382813i
\(514\) 0 0
\(515\) −1.53379 2.65661i −0.0675869 0.117064i
\(516\) 0 0
\(517\) 11.1202 19.2608i 0.489068 0.847091i
\(518\) 0 0
\(519\) −15.6940 40.9713i −0.688889 1.79844i
\(520\) 0 0
\(521\) 27.7486 1.21569 0.607844 0.794057i \(-0.292035\pi\)
0.607844 + 0.794057i \(0.292035\pi\)
\(522\) 0 0
\(523\) 2.73680 0.119672 0.0598360 0.998208i \(-0.480942\pi\)
0.0598360 + 0.998208i \(0.480942\pi\)
\(524\) 0 0
\(525\) 5.39248 6.64948i 0.235347 0.290207i
\(526\) 0 0
\(527\) −1.32846 + 2.30096i −0.0578686 + 0.100231i
\(528\) 0 0
\(529\) −16.0361 27.7754i −0.697222 1.20762i
\(530\) 0 0
\(531\) 16.9184 15.1898i 0.734194 0.659183i
\(532\) 0 0
\(533\) 13.6871 + 23.7068i 0.592856 + 1.02686i
\(534\) 0 0
\(535\) 0.904515 1.56667i 0.0391056 0.0677329i
\(536\) 0 0
\(537\) −16.3285 2.59808i −0.704625 0.112115i
\(538\) 0 0
\(539\) 5.12476 0.220739
\(540\) 0 0
\(541\) −11.9773 −0.514944 −0.257472 0.966286i \(-0.582890\pi\)
−0.257472 + 0.966286i \(0.582890\pi\)
\(542\) 0 0
\(543\) 21.1666 + 3.36789i 0.908347 + 0.144530i
\(544\) 0 0
\(545\) 0.834608 1.44558i 0.0357507 0.0619220i
\(546\) 0 0
\(547\) −10.7346 18.5929i −0.458979 0.794975i 0.539928 0.841711i \(-0.318451\pi\)
−0.998907 + 0.0467363i \(0.985118\pi\)
\(548\) 0 0
\(549\) −3.41260 16.1680i −0.145646 0.690034i
\(550\) 0 0
\(551\) 6.34050 + 10.9821i 0.270114 + 0.467852i
\(552\) 0 0
\(553\) −3.11273 + 5.39140i −0.132367 + 0.229266i
\(554\) 0 0
\(555\) −1.20082 + 1.48073i −0.0509719 + 0.0628536i
\(556\) 0 0
\(557\) −31.8493 −1.34950 −0.674748 0.738048i \(-0.735748\pi\)
−0.674748 + 0.738048i \(0.735748\pi\)
\(558\) 0 0
\(559\) 61.0150 2.58066
\(560\) 0 0
\(561\) −11.7596 30.7001i −0.496492 1.29616i
\(562\) 0 0
\(563\) 17.7742 30.7857i 0.749091 1.29746i −0.199167 0.979966i \(-0.563824\pi\)
0.948259 0.317499i \(-0.102843\pi\)
\(564\) 0 0
\(565\) 2.33981 + 4.05267i 0.0984366 + 0.170497i
\(566\) 0 0
\(567\) 0.966208 8.94799i 0.0405769 0.375780i
\(568\) 0 0
\(569\) −10.8743 18.8348i −0.455874 0.789597i 0.542864 0.839821i \(-0.317340\pi\)
−0.998738 + 0.0502237i \(0.984007\pi\)
\(570\) 0 0
\(571\) −4.79987 + 8.31362i −0.200868 + 0.347914i −0.948808 0.315852i \(-0.897710\pi\)
0.747940 + 0.663766i \(0.231043\pi\)
\(572\) 0 0
\(573\) 8.15856 + 21.2990i 0.340829 + 0.889779i
\(574\) 0 0
\(575\) 36.6810 1.52970
\(576\) 0 0
\(577\) 13.0183 0.541960 0.270980 0.962585i \(-0.412652\pi\)
0.270980 + 0.962585i \(0.412652\pi\)
\(578\) 0 0
\(579\) −12.1631 + 14.9983i −0.505480 + 0.623309i
\(580\) 0 0
\(581\) 4.85185 8.40365i 0.201289 0.348642i
\(582\) 0 0
\(583\) 2.41586 + 4.18440i 0.100055 + 0.173300i
\(584\) 0 0
\(585\) 0.723815 + 3.42926i 0.0299261 + 0.141782i
\(586\) 0 0
\(587\) 8.64364 + 14.9712i 0.356761 + 0.617928i 0.987418 0.158134i \(-0.0505477\pi\)
−0.630657 + 0.776062i \(0.717214\pi\)
\(588\) 0 0
\(589\) 1.31285 2.27393i 0.0540952 0.0936957i
\(590\) 0 0
\(591\) −0.246648 0.0392450i −0.0101457 0.00161432i
\(592\) 0 0
\(593\) 12.4153 0.509836 0.254918 0.966963i \(-0.417952\pi\)
0.254918 + 0.966963i \(0.417952\pi\)
\(594\) 0 0
\(595\) 0.885640 0.0363077
\(596\) 0 0
\(597\) 33.3027 + 5.29891i 1.36299 + 0.216870i
\(598\) 0 0
\(599\) −3.94282 + 6.82916i −0.161099 + 0.279032i −0.935263 0.353953i \(-0.884837\pi\)
0.774164 + 0.632985i \(0.218171\pi\)
\(600\) 0 0
\(601\) −11.1413 19.2973i −0.454464 0.787154i 0.544193 0.838960i \(-0.316836\pi\)
−0.998657 + 0.0518055i \(0.983502\pi\)
\(602\) 0 0
\(603\) −1.47373 + 1.32317i −0.0600151 + 0.0538835i
\(604\) 0 0
\(605\) −1.82489 3.16081i −0.0741925 0.128505i
\(606\) 0 0
\(607\) 11.0458 19.1319i 0.448336 0.776541i −0.549942 0.835203i \(-0.685350\pi\)
0.998278 + 0.0586617i \(0.0186833\pi\)
\(608\) 0 0
\(609\) −3.77975 + 4.66082i −0.153163 + 0.188866i
\(610\) 0 0
\(611\) 21.2028 0.857771
\(612\) 0 0
\(613\) −29.5264 −1.19256 −0.596280 0.802777i \(-0.703355\pi\)
−0.596280 + 0.802777i \(0.703355\pi\)
\(614\) 0 0
\(615\) −0.830095 2.16708i −0.0334727 0.0873849i
\(616\) 0 0
\(617\) 5.01655 8.68892i 0.201959 0.349803i −0.747201 0.664598i \(-0.768603\pi\)
0.949159 + 0.314796i \(0.101936\pi\)
\(618\) 0 0
\(619\) −19.1283 33.1312i −0.768833 1.33166i −0.938196 0.346103i \(-0.887505\pi\)
0.169364 0.985554i \(-0.445829\pi\)
\(620\) 0 0
\(621\) 32.3847 20.9328i 1.29955 0.840004i
\(622\) 0 0
\(623\) 3.74433 + 6.48536i 0.150013 + 0.259831i
\(624\) 0 0
\(625\) −12.0728 + 20.9107i −0.482911 + 0.836427i
\(626\) 0 0
\(627\) 11.6215 + 30.3395i 0.464118 + 1.21164i
\(628\) 0 0
\(629\) 17.0482 0.679754
\(630\) 0 0
\(631\) 23.0377 0.917118 0.458559 0.888664i \(-0.348366\pi\)
0.458559 + 0.888664i \(0.348366\pi\)
\(632\) 0 0
\(633\) −3.52244 + 4.34354i −0.140004 + 0.172640i
\(634\) 0 0
\(635\) −2.00972 + 3.48093i −0.0797531 + 0.138136i
\(636\) 0 0
\(637\) 2.44282 + 4.23109i 0.0967881 + 0.167642i
\(638\) 0 0
\(639\) −39.1885 12.7948i −1.55027 0.506153i
\(640\) 0 0
\(641\) 8.68646 + 15.0454i 0.343094 + 0.594257i 0.985006 0.172522i \(-0.0551916\pi\)
−0.641911 + 0.766779i \(0.721858\pi\)
\(642\) 0 0
\(643\) −9.47949 + 16.4190i −0.373835 + 0.647501i −0.990152 0.139997i \(-0.955291\pi\)
0.616317 + 0.787498i \(0.288624\pi\)
\(644\) 0 0
\(645\) −5.10821 0.812785i −0.201136 0.0320034i
\(646\) 0 0
\(647\) −19.0194 −0.747731 −0.373865 0.927483i \(-0.621968\pi\)
−0.373865 + 0.927483i \(0.621968\pi\)
\(648\) 0 0
\(649\) −38.8402 −1.52461
\(650\) 0 0
\(651\) 1.22708 + 0.195246i 0.0480933 + 0.00765228i
\(652\) 0 0
\(653\) 3.59329 6.22377i 0.140616 0.243555i −0.787112 0.616810i \(-0.788425\pi\)
0.927729 + 0.373255i \(0.121758\pi\)
\(654\) 0 0
\(655\) 0.585770 + 1.01458i 0.0228879 + 0.0396430i
\(656\) 0 0
\(657\) −10.4383 3.40803i −0.407237 0.132960i
\(658\) 0 0
\(659\) 12.7261 + 22.0423i 0.495740 + 0.858647i 0.999988 0.00491209i \(-0.00156357\pi\)
−0.504248 + 0.863559i \(0.668230\pi\)
\(660\) 0 0
\(661\) −4.14295 + 7.17580i −0.161142 + 0.279106i −0.935279 0.353912i \(-0.884851\pi\)
0.774136 + 0.633019i \(0.218184\pi\)
\(662\) 0 0
\(663\) 19.7411 24.3428i 0.766679 0.945395i
\(664\) 0 0
\(665\) −0.875237 −0.0339402
\(666\) 0 0
\(667\) −25.7108 −0.995527
\(668\) 0 0
\(669\) 12.8691 + 33.5965i 0.497548 + 1.29892i
\(670\) 0 0
\(671\) −14.1138 + 24.4458i −0.544857 + 0.943721i
\(672\) 0 0
\(673\) 5.91586 + 10.2466i 0.228040 + 0.394977i 0.957227 0.289338i \(-0.0934350\pi\)
−0.729187 + 0.684314i \(0.760102\pi\)
\(674\) 0 0
\(675\) 1.28947 + 25.6513i 0.0496316 + 0.987317i
\(676\) 0 0
\(677\) −6.80314 11.7834i −0.261466 0.452872i 0.705166 0.709042i \(-0.250873\pi\)
−0.966632 + 0.256170i \(0.917539\pi\)
\(678\) 0 0
\(679\) 8.57442 14.8513i 0.329056 0.569942i
\(680\) 0 0
\(681\) 13.5949 + 35.4914i 0.520959 + 1.36003i
\(682\) 0 0
\(683\) −3.58142 −0.137039 −0.0685196 0.997650i \(-0.521828\pi\)
−0.0685196 + 0.997650i \(0.521828\pi\)
\(684\) 0 0
\(685\) 1.30206 0.0497492
\(686\) 0 0
\(687\) −24.8428 + 30.6338i −0.947813 + 1.16875i
\(688\) 0 0
\(689\) −2.30314 + 3.98916i −0.0877426 + 0.151975i
\(690\) 0 0
\(691\) 5.85868 + 10.1475i 0.222875 + 0.386031i 0.955680 0.294408i \(-0.0951225\pi\)
−0.732805 + 0.680439i \(0.761789\pi\)
\(692\) 0 0
\(693\) −11.4399 + 10.2712i −0.434567 + 0.390169i
\(694\) 0 0
\(695\) 0.676742 + 1.17215i 0.0256703 + 0.0444622i
\(696\) 0 0
\(697\) −10.3759 + 17.9716i −0.393016 + 0.680724i
\(698\) 0 0
\(699\) −44.1004 7.01697i −1.66803 0.265406i
\(700\) 0 0
\(701\) −10.5926 −0.400077 −0.200039 0.979788i \(-0.564107\pi\)
−0.200039 + 0.979788i \(0.564107\pi\)
\(702\) 0 0
\(703\) −16.8479 −0.635430
\(704\) 0 0
\(705\) −1.77511 0.282443i −0.0668543 0.0106374i
\(706\) 0 0
\(707\) −3.59097 + 6.21975i −0.135052 + 0.233918i
\(708\) 0 0
\(709\) −19.1488 33.1668i −0.719150 1.24560i −0.961337 0.275374i \(-0.911198\pi\)
0.242187 0.970230i \(-0.422135\pi\)
\(710\) 0 0
\(711\) −3.85705 18.2737i −0.144651 0.685318i
\(712\) 0 0
\(713\) 2.66182 + 4.61042i 0.0996861 + 0.172661i
\(714\) 0 0
\(715\) 2.99355 5.18499i 0.111953 0.193908i
\(716\) 0 0
\(717\) −29.7810 + 36.7230i −1.11219 + 1.37145i
\(718\) 0 0
\(719\) −41.6752 −1.55422 −0.777112 0.629362i \(-0.783316\pi\)
−0.777112 + 0.629362i \(0.783316\pi\)
\(720\) 0 0
\(721\) 12.8285 0.477757
\(722\) 0 0
\(723\) −6.21698 16.2303i −0.231212 0.603610i
\(724\) 0 0
\(725\) 8.56238 14.8305i 0.317999 0.550790i
\(726\) 0 0
\(727\) −16.4126 28.4274i −0.608709 1.05432i −0.991453 0.130461i \(-0.958354\pi\)
0.382744 0.923854i \(-0.374979\pi\)
\(728\) 0 0
\(729\) 15.7769 + 21.9110i 0.584329 + 0.811517i
\(730\) 0 0
\(731\) 23.1271 + 40.0573i 0.855386 + 1.48157i
\(732\) 0 0
\(733\) −4.64884 + 8.05203i −0.171709 + 0.297408i −0.939017 0.343870i \(-0.888262\pi\)
0.767309 + 0.641278i \(0.221595\pi\)
\(734\) 0 0
\(735\) −0.148152 0.386770i −0.00546465 0.0142662i
\(736\) 0 0
\(737\) 3.38332 0.124626
\(738\) 0 0
\(739\) −11.3776 −0.418530 −0.209265 0.977859i \(-0.567107\pi\)
−0.209265 + 0.977859i \(0.567107\pi\)
\(740\) 0 0
\(741\) −19.5092 + 24.0568i −0.716687 + 0.883749i
\(742\) 0 0
\(743\) −1.16182 + 2.01234i −0.0426232 + 0.0738256i −0.886550 0.462633i \(-0.846905\pi\)
0.843927 + 0.536458i \(0.180238\pi\)
\(744\) 0 0
\(745\) −0.272915 0.472703i −0.00999883 0.0173185i
\(746\) 0 0
\(747\) 6.01204 + 28.4835i 0.219969 + 1.04216i
\(748\) 0 0
\(749\) 3.78263 + 6.55171i 0.138214 + 0.239394i
\(750\) 0 0
\(751\) −5.56690 + 9.64215i −0.203139 + 0.351847i −0.949538 0.313652i \(-0.898448\pi\)
0.746399 + 0.665498i \(0.231781\pi\)
\(752\) 0 0
\(753\) 48.4374 + 7.70703i 1.76516 + 0.280860i
\(754\) 0 0
\(755\) −2.69329 −0.0980190
\(756\) 0 0
\(757\) 52.1639 1.89593 0.947964 0.318376i \(-0.103138\pi\)
0.947964 + 0.318376i \(0.103138\pi\)
\(758\) 0 0
\(759\) −65.0537 10.3509i −2.36130 0.375714i
\(760\) 0 0
\(761\) 23.5127 40.7252i 0.852336 1.47629i −0.0267592 0.999642i \(-0.508519\pi\)
0.879095 0.476647i \(-0.158148\pi\)
\(762\) 0 0
\(763\) 3.49028 + 6.04535i 0.126357 + 0.218856i
\(764\) 0 0
\(765\) −1.97700 + 1.77502i −0.0714787 + 0.0641759i
\(766\) 0 0
\(767\) −18.5140 32.0671i −0.668501 1.15788i
\(768\) 0 0
\(769\) 3.30314 5.72121i 0.119114 0.206312i −0.800303 0.599596i \(-0.795328\pi\)
0.919417 + 0.393284i \(0.128661\pi\)
\(770\) 0 0
\(771\) −31.4887 + 38.8288i −1.13404 + 1.39838i
\(772\) 0 0
\(773\) 19.0870 0.686512 0.343256 0.939242i \(-0.388470\pi\)
0.343256 + 0.939242i \(0.388470\pi\)
\(774\) 0 0
\(775\) −3.54583 −0.127370
\(776\) 0 0
\(777\) −2.85185 7.44514i −0.102309 0.267093i
\(778\) 0 0
\(779\) 10.2540 17.7605i 0.367389 0.636337i
\(780\) 0 0
\(781\) 35.2108 + 60.9869i 1.25994 + 2.18228i
\(782\) 0 0
\(783\) −0.903827 17.9797i −0.0323001 0.642544i
\(784\) 0 0
\(785\) −0.663069 1.14847i −0.0236659 0.0409906i
\(786\) 0 0
\(787\) 25.4503 44.0813i 0.907207 1.57133i 0.0892796 0.996007i \(-0.471544\pi\)
0.817927 0.575322i \(-0.195123\pi\)
\(788\) 0 0
\(789\) −0.749229 1.95596i −0.0266733 0.0696342i
\(790\) 0 0
\(791\) −19.5699 −0.695826
\(792\) 0 0
\(793\) −26.9105 −0.955620
\(794\) 0 0
\(795\) 0.245960 0.303294i 0.00872330 0.0107567i
\(796\) 0 0
\(797\) −4.38727 + 7.59898i −0.155405 + 0.269170i −0.933207 0.359341i \(-0.883002\pi\)
0.777801 + 0.628510i \(0.216335\pi\)
\(798\) 0 0
\(799\) 8.03667 + 13.9199i 0.284317 + 0.492451i
\(800\)