Properties

Label 1008.2.r.h.673.3
Level 1008
Weight 2
Character 1008.673
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: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.3
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.h.337.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.11334 - 1.32683i) q^{3} +(0.439693 + 0.761570i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.520945 - 2.95442i) q^{9} +O(q^{10})\) \(q+(1.11334 - 1.32683i) q^{3} +(0.439693 + 0.761570i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-0.520945 - 2.95442i) q^{9} +(1.93969 - 3.35965i) q^{11} +(2.72668 + 4.72275i) q^{13} +(1.50000 + 0.264490i) q^{15} +1.65270 q^{17} -2.41147 q^{19} +(-0.592396 - 1.62760i) q^{21} +(1.58125 + 2.73881i) q^{23} +(2.11334 - 3.66041i) q^{25} +(-4.50000 - 2.59808i) q^{27} +(3.02481 - 5.23913i) q^{29} +(-2.27719 - 3.94421i) q^{31} +(-2.29813 - 6.31407i) q^{33} +0.879385 q^{35} -4.55438 q^{37} +(9.30200 + 1.64019i) q^{39} +(0.592396 + 1.02606i) q^{41} +(0.0923963 - 0.160035i) q^{43} +(2.02094 - 1.69577i) q^{45} +(-0.511144 + 0.885328i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(1.84002 - 2.19285i) q^{51} +7.29086 q^{53} +3.41147 q^{55} +(-2.68479 + 3.19961i) q^{57} +(3.33022 + 5.76811i) q^{59} +(1.29813 - 2.24843i) q^{61} +(-2.81908 - 1.02606i) q^{63} +(-2.39780 + 4.15312i) q^{65} +(-1.47906 - 2.56180i) q^{67} +(5.39440 + 0.951178i) q^{69} +3.68004 q^{71} -12.7811 q^{73} +(-2.50387 - 6.87933i) q^{75} +(-1.93969 - 3.35965i) q^{77} +(-2.97906 + 5.15988i) q^{79} +(-8.45723 + 3.07818i) q^{81} +(-0.109470 + 0.189608i) q^{83} +(0.726682 + 1.25865i) q^{85} +(-3.58378 - 9.84635i) q^{87} +11.0273 q^{89} +5.45336 q^{91} +(-7.76857 - 1.36981i) q^{93} +(-1.06031 - 1.83651i) q^{95} +(-6.25150 + 10.8279i) q^{97} +(-10.9363 - 3.98048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{5} + 3q^{7} + O(q^{10}) \) \( 6q - 3q^{5} + 3q^{7} + 6q^{11} + 3q^{13} + 9q^{15} + 12q^{17} + 6q^{19} + 12q^{23} + 6q^{25} - 27q^{27} - 9q^{29} - 3q^{31} - 6q^{35} - 6q^{37} + 18q^{39} - 3q^{43} + 9q^{45} + 3q^{47} - 3q^{49} - 9q^{51} + 12q^{53} - 9q^{57} - 3q^{59} - 6q^{61} - 15q^{65} - 12q^{67} - 9q^{69} - 18q^{71} - 42q^{73} + 9q^{75} - 6q^{77} - 21q^{79} - 18q^{83} - 9q^{85} - 9q^{87} + 24q^{89} + 6q^{91} - 27q^{93} - 12q^{95} + 3q^{97} - 18q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 1.11334 1.32683i 0.642788 0.766044i
\(4\) 0 0
\(5\) 0.439693 + 0.761570i 0.196637 + 0.340584i 0.947436 0.319946i \(-0.103665\pi\)
−0.750799 + 0.660530i \(0.770331\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 0 0
\(9\) −0.520945 2.95442i −0.173648 0.984808i
\(10\) 0 0
\(11\) 1.93969 3.35965i 0.584839 1.01297i −0.410056 0.912060i \(-0.634491\pi\)
0.994895 0.100911i \(-0.0321758\pi\)
\(12\) 0 0
\(13\) 2.72668 + 4.72275i 0.756245 + 1.30986i 0.944753 + 0.327784i \(0.106302\pi\)
−0.188507 + 0.982072i \(0.560365\pi\)
\(14\) 0 0
\(15\) 1.50000 + 0.264490i 0.387298 + 0.0682911i
\(16\) 0 0
\(17\) 1.65270 0.400840 0.200420 0.979710i \(-0.435769\pi\)
0.200420 + 0.979710i \(0.435769\pi\)
\(18\) 0 0
\(19\) −2.41147 −0.553230 −0.276615 0.960981i \(-0.589213\pi\)
−0.276615 + 0.960981i \(0.589213\pi\)
\(20\) 0 0
\(21\) −0.592396 1.62760i −0.129271 0.355170i
\(22\) 0 0
\(23\) 1.58125 + 2.73881i 0.329714 + 0.571081i 0.982455 0.186500i \(-0.0597144\pi\)
−0.652741 + 0.757581i \(0.726381\pi\)
\(24\) 0 0
\(25\) 2.11334 3.66041i 0.422668 0.732083i
\(26\) 0 0
\(27\) −4.50000 2.59808i −0.866025 0.500000i
\(28\) 0 0
\(29\) 3.02481 5.23913i 0.561694 0.972883i −0.435655 0.900114i \(-0.643483\pi\)
0.997349 0.0727688i \(-0.0231835\pi\)
\(30\) 0 0
\(31\) −2.27719 3.94421i −0.408995 0.708400i 0.585782 0.810468i \(-0.300787\pi\)
−0.994777 + 0.102068i \(0.967454\pi\)
\(32\) 0 0
\(33\) −2.29813 6.31407i −0.400054 1.09914i
\(34\) 0 0
\(35\) 0.879385 0.148643
\(36\) 0 0
\(37\) −4.55438 −0.748735 −0.374368 0.927280i \(-0.622140\pi\)
−0.374368 + 0.927280i \(0.622140\pi\)
\(38\) 0 0
\(39\) 9.30200 + 1.64019i 1.48951 + 0.262641i
\(40\) 0 0
\(41\) 0.592396 + 1.02606i 0.0925168 + 0.160244i 0.908570 0.417734i \(-0.137175\pi\)
−0.816053 + 0.577977i \(0.803842\pi\)
\(42\) 0 0
\(43\) 0.0923963 0.160035i 0.0140903 0.0244051i −0.858894 0.512153i \(-0.828848\pi\)
0.872985 + 0.487748i \(0.162181\pi\)
\(44\) 0 0
\(45\) 2.02094 1.69577i 0.301265 0.252791i
\(46\) 0 0
\(47\) −0.511144 + 0.885328i −0.0745581 + 0.129138i −0.900894 0.434039i \(-0.857088\pi\)
0.826336 + 0.563178i \(0.190421\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) 1.84002 2.19285i 0.257655 0.307061i
\(52\) 0 0
\(53\) 7.29086 1.00148 0.500738 0.865599i \(-0.333062\pi\)
0.500738 + 0.865599i \(0.333062\pi\)
\(54\) 0 0
\(55\) 3.41147 0.460003
\(56\) 0 0
\(57\) −2.68479 + 3.19961i −0.355609 + 0.423799i
\(58\) 0 0
\(59\) 3.33022 + 5.76811i 0.433558 + 0.750944i 0.997177 0.0750906i \(-0.0239246\pi\)
−0.563619 + 0.826035i \(0.690591\pi\)
\(60\) 0 0
\(61\) 1.29813 2.24843i 0.166209 0.287882i −0.770875 0.636986i \(-0.780181\pi\)
0.937084 + 0.349104i \(0.113514\pi\)
\(62\) 0 0
\(63\) −2.81908 1.02606i −0.355170 0.129271i
\(64\) 0 0
\(65\) −2.39780 + 4.15312i −0.297411 + 0.515131i
\(66\) 0 0
\(67\) −1.47906 2.56180i −0.180695 0.312974i 0.761422 0.648256i \(-0.224501\pi\)
−0.942118 + 0.335283i \(0.891168\pi\)
\(68\) 0 0
\(69\) 5.39440 + 0.951178i 0.649409 + 0.114508i
\(70\) 0 0
\(71\) 3.68004 0.436741 0.218370 0.975866i \(-0.429926\pi\)
0.218370 + 0.975866i \(0.429926\pi\)
\(72\) 0 0
\(73\) −12.7811 −1.49591 −0.747955 0.663750i \(-0.768964\pi\)
−0.747955 + 0.663750i \(0.768964\pi\)
\(74\) 0 0
\(75\) −2.50387 6.87933i −0.289122 0.794356i
\(76\) 0 0
\(77\) −1.93969 3.35965i −0.221048 0.382867i
\(78\) 0 0
\(79\) −2.97906 + 5.15988i −0.335170 + 0.580531i −0.983517 0.180813i \(-0.942127\pi\)
0.648348 + 0.761345i \(0.275460\pi\)
\(80\) 0 0
\(81\) −8.45723 + 3.07818i −0.939693 + 0.342020i
\(82\) 0 0
\(83\) −0.109470 + 0.189608i −0.0120159 + 0.0208122i −0.871971 0.489558i \(-0.837158\pi\)
0.859955 + 0.510370i \(0.170492\pi\)
\(84\) 0 0
\(85\) 0.726682 + 1.25865i 0.0788197 + 0.136520i
\(86\) 0 0
\(87\) −3.58378 9.84635i −0.384221 1.05564i
\(88\) 0 0
\(89\) 11.0273 1.16890 0.584448 0.811431i \(-0.301311\pi\)
0.584448 + 0.811431i \(0.301311\pi\)
\(90\) 0 0
\(91\) 5.45336 0.571668
\(92\) 0 0
\(93\) −7.76857 1.36981i −0.805563 0.142043i
\(94\) 0 0
\(95\) −1.06031 1.83651i −0.108785 0.188422i
\(96\) 0 0
\(97\) −6.25150 + 10.8279i −0.634743 + 1.09941i 0.351826 + 0.936065i \(0.385561\pi\)
−0.986569 + 0.163342i \(0.947773\pi\)
\(98\) 0 0
\(99\) −10.9363 3.98048i −1.09914 0.400054i
\(100\) 0 0
\(101\) 4.85844 8.41507i 0.483433 0.837330i −0.516386 0.856356i \(-0.672723\pi\)
0.999819 + 0.0190255i \(0.00605638\pi\)
\(102\) 0 0
\(103\) 3.29813 + 5.71253i 0.324975 + 0.562873i 0.981507 0.191425i \(-0.0613109\pi\)
−0.656533 + 0.754298i \(0.727978\pi\)
\(104\) 0 0
\(105\) 0.979055 1.16679i 0.0955460 0.113867i
\(106\) 0 0
\(107\) −2.38919 −0.230971 −0.115486 0.993309i \(-0.536842\pi\)
−0.115486 + 0.993309i \(0.536842\pi\)
\(108\) 0 0
\(109\) 3.95811 0.379118 0.189559 0.981869i \(-0.439294\pi\)
0.189559 + 0.981869i \(0.439294\pi\)
\(110\) 0 0
\(111\) −5.07057 + 6.04288i −0.481278 + 0.573564i
\(112\) 0 0
\(113\) −8.22668 14.2490i −0.773901 1.34044i −0.935410 0.353565i \(-0.884969\pi\)
0.161509 0.986871i \(-0.448364\pi\)
\(114\) 0 0
\(115\) −1.39053 + 2.40847i −0.129668 + 0.224591i
\(116\) 0 0
\(117\) 12.5326 10.5161i 1.15864 0.972210i
\(118\) 0 0
\(119\) 0.826352 1.43128i 0.0757515 0.131206i
\(120\) 0 0
\(121\) −2.02481 3.50708i −0.184074 0.318826i
\(122\) 0 0
\(123\) 2.02094 + 0.356347i 0.182222 + 0.0321307i
\(124\) 0 0
\(125\) 8.11381 0.725721
\(126\) 0 0
\(127\) −17.6536 −1.56651 −0.783253 0.621702i \(-0.786441\pi\)
−0.783253 + 0.621702i \(0.786441\pi\)
\(128\) 0 0
\(129\) −0.109470 0.300767i −0.00963833 0.0264811i
\(130\) 0 0
\(131\) −9.59879 16.6256i −0.838650 1.45259i −0.891023 0.453958i \(-0.850012\pi\)
0.0523729 0.998628i \(-0.483322\pi\)
\(132\) 0 0
\(133\) −1.20574 + 2.08840i −0.104551 + 0.181087i
\(134\) 0 0
\(135\) 4.56942i 0.393273i
\(136\) 0 0
\(137\) −9.07785 + 15.7233i −0.775573 + 1.34333i 0.158899 + 0.987295i \(0.449206\pi\)
−0.934472 + 0.356037i \(0.884128\pi\)
\(138\) 0 0
\(139\) 11.0287 + 19.1022i 0.935441 + 1.62023i 0.773846 + 0.633374i \(0.218330\pi\)
0.161595 + 0.986857i \(0.448336\pi\)
\(140\) 0 0
\(141\) 0.605600 + 1.66387i 0.0510007 + 0.140123i
\(142\) 0 0
\(143\) 21.1557 1.76913
\(144\) 0 0
\(145\) 5.31996 0.441798
\(146\) 0 0
\(147\) −1.70574 0.300767i −0.140687 0.0248069i
\(148\) 0 0
\(149\) 7.57785 + 13.1252i 0.620802 + 1.07526i 0.989337 + 0.145646i \(0.0465261\pi\)
−0.368535 + 0.929614i \(0.620141\pi\)
\(150\) 0 0
\(151\) −9.47818 + 16.4167i −0.771323 + 1.33597i 0.165515 + 0.986207i \(0.447071\pi\)
−0.936838 + 0.349764i \(0.886262\pi\)
\(152\) 0 0
\(153\) −0.860967 4.88279i −0.0696051 0.394750i
\(154\) 0 0
\(155\) 2.00253 3.46848i 0.160847 0.278595i
\(156\) 0 0
\(157\) 9.02869 + 15.6381i 0.720568 + 1.24806i 0.960773 + 0.277337i \(0.0894520\pi\)
−0.240205 + 0.970722i \(0.577215\pi\)
\(158\) 0 0
\(159\) 8.11721 9.67372i 0.643737 0.767176i
\(160\) 0 0
\(161\) 3.16250 0.249240
\(162\) 0 0
\(163\) −0.958111 −0.0750450 −0.0375225 0.999296i \(-0.511947\pi\)
−0.0375225 + 0.999296i \(0.511947\pi\)
\(164\) 0 0
\(165\) 3.79813 4.52644i 0.295684 0.352383i
\(166\) 0 0
\(167\) 9.91921 + 17.1806i 0.767572 + 1.32947i 0.938876 + 0.344255i \(0.111869\pi\)
−0.171304 + 0.985218i \(0.554798\pi\)
\(168\) 0 0
\(169\) −8.36959 + 14.4965i −0.643814 + 1.11512i
\(170\) 0 0
\(171\) 1.25624 + 7.12452i 0.0960674 + 0.544825i
\(172\) 0 0
\(173\) −11.3414 + 19.6438i −0.862268 + 1.49349i 0.00746626 + 0.999972i \(0.497623\pi\)
−0.869734 + 0.493520i \(0.835710\pi\)
\(174\) 0 0
\(175\) −2.11334 3.66041i −0.159754 0.276701i
\(176\) 0 0
\(177\) 11.3610 + 2.00324i 0.853943 + 0.150573i
\(178\) 0 0
\(179\) 7.34730 0.549163 0.274581 0.961564i \(-0.411461\pi\)
0.274581 + 0.961564i \(0.411461\pi\)
\(180\) 0 0
\(181\) −3.44562 −0.256111 −0.128056 0.991767i \(-0.540874\pi\)
−0.128056 + 0.991767i \(0.540874\pi\)
\(182\) 0 0
\(183\) −1.53802 4.22567i −0.113694 0.312371i
\(184\) 0 0
\(185\) −2.00253 3.46848i −0.147229 0.255008i
\(186\) 0 0
\(187\) 3.20574 5.55250i 0.234427 0.406039i
\(188\) 0 0
\(189\) −4.50000 + 2.59808i −0.327327 + 0.188982i
\(190\) 0 0
\(191\) 2.82888 4.89976i 0.204690 0.354534i −0.745344 0.666680i \(-0.767715\pi\)
0.950034 + 0.312146i \(0.101048\pi\)
\(192\) 0 0
\(193\) −4.79813 8.31061i −0.345377 0.598211i 0.640045 0.768337i \(-0.278916\pi\)
−0.985422 + 0.170127i \(0.945582\pi\)
\(194\) 0 0
\(195\) 2.84090 + 7.80531i 0.203441 + 0.558950i
\(196\) 0 0
\(197\) 8.31996 0.592772 0.296386 0.955068i \(-0.404218\pi\)
0.296386 + 0.955068i \(0.404218\pi\)
\(198\) 0 0
\(199\) −6.59627 −0.467597 −0.233798 0.972285i \(-0.575116\pi\)
−0.233798 + 0.972285i \(0.575116\pi\)
\(200\) 0 0
\(201\) −5.04576 0.889704i −0.355900 0.0627548i
\(202\) 0 0
\(203\) −3.02481 5.23913i −0.212300 0.367715i
\(204\) 0 0
\(205\) −0.520945 + 0.902302i −0.0363843 + 0.0630195i
\(206\) 0 0
\(207\) 7.26786 6.09845i 0.505151 0.423872i
\(208\) 0 0
\(209\) −4.67752 + 8.10170i −0.323551 + 0.560406i
\(210\) 0 0
\(211\) −1.68479 2.91815i −0.115986 0.200893i 0.802188 0.597072i \(-0.203669\pi\)
−0.918173 + 0.396179i \(0.870336\pi\)
\(212\) 0 0
\(213\) 4.09714 4.88279i 0.280732 0.334563i
\(214\) 0 0
\(215\) 0.162504 0.0110827
\(216\) 0 0
\(217\) −4.55438 −0.309171
\(218\) 0 0
\(219\) −14.2297 + 16.9583i −0.961552 + 1.14593i
\(220\) 0 0
\(221\) 4.50640 + 7.80531i 0.303133 + 0.525042i
\(222\) 0 0
\(223\) −3.13816 + 5.43545i −0.210146 + 0.363984i −0.951760 0.306843i \(-0.900727\pi\)
0.741614 + 0.670827i \(0.234061\pi\)
\(224\) 0 0
\(225\) −11.9153 4.33683i −0.794356 0.289122i
\(226\) 0 0
\(227\) −3.08125 + 5.33688i −0.204510 + 0.354221i −0.949976 0.312322i \(-0.898893\pi\)
0.745467 + 0.666543i \(0.232227\pi\)
\(228\) 0 0
\(229\) −11.6925 20.2521i −0.772664 1.33829i −0.936098 0.351740i \(-0.885590\pi\)
0.163434 0.986554i \(-0.447743\pi\)
\(230\) 0 0
\(231\) −6.61721 1.16679i −0.435381 0.0767693i
\(232\) 0 0
\(233\) −8.52528 −0.558510 −0.279255 0.960217i \(-0.590087\pi\)
−0.279255 + 0.960217i \(0.590087\pi\)
\(234\) 0 0
\(235\) −0.898986 −0.0586434
\(236\) 0 0
\(237\) 3.52956 + 9.69739i 0.229270 + 0.629913i
\(238\) 0 0
\(239\) 7.28106 + 12.6112i 0.470973 + 0.815748i 0.999449 0.0331997i \(-0.0105697\pi\)
−0.528476 + 0.848948i \(0.677236\pi\)
\(240\) 0 0
\(241\) 2.70187 4.67977i 0.174043 0.301451i −0.765787 0.643094i \(-0.777650\pi\)
0.939830 + 0.341644i \(0.110984\pi\)
\(242\) 0 0
\(243\) −5.33157 + 14.6484i −0.342020 + 0.939693i
\(244\) 0 0
\(245\) 0.439693 0.761570i 0.0280909 0.0486549i
\(246\) 0 0
\(247\) −6.57532 11.3888i −0.418378 0.724651i
\(248\) 0 0
\(249\) 0.129700 + 0.356347i 0.00821939 + 0.0225826i
\(250\) 0 0
\(251\) 12.0669 0.761654 0.380827 0.924646i \(-0.375639\pi\)
0.380827 + 0.924646i \(0.375639\pi\)
\(252\) 0 0
\(253\) 12.2686 0.771318
\(254\) 0 0
\(255\) 2.47906 + 0.437124i 0.155244 + 0.0273738i
\(256\) 0 0
\(257\) −5.28312 9.15063i −0.329552 0.570801i 0.652871 0.757469i \(-0.273564\pi\)
−0.982423 + 0.186668i \(0.940231\pi\)
\(258\) 0 0
\(259\) −2.27719 + 3.94421i −0.141498 + 0.245081i
\(260\) 0 0
\(261\) −17.0544 6.20729i −1.05564 0.384221i
\(262\) 0 0
\(263\) −14.1766 + 24.5547i −0.874169 + 1.51411i −0.0165240 + 0.999863i \(0.505260\pi\)
−0.857645 + 0.514242i \(0.828073\pi\)
\(264\) 0 0
\(265\) 3.20574 + 5.55250i 0.196927 + 0.341087i
\(266\) 0 0
\(267\) 12.2772 14.6314i 0.751352 0.895426i
\(268\) 0 0
\(269\) 7.48339 0.456271 0.228135 0.973629i \(-0.426737\pi\)
0.228135 + 0.973629i \(0.426737\pi\)
\(270\) 0 0
\(271\) −13.6382 −0.828459 −0.414229 0.910172i \(-0.635949\pi\)
−0.414229 + 0.910172i \(0.635949\pi\)
\(272\) 0 0
\(273\) 6.07145 7.23567i 0.367461 0.437923i
\(274\) 0 0
\(275\) −8.19846 14.2002i −0.494386 0.856302i
\(276\) 0 0
\(277\) 3.07532 5.32661i 0.184778 0.320045i −0.758724 0.651413i \(-0.774177\pi\)
0.943502 + 0.331368i \(0.107510\pi\)
\(278\) 0 0
\(279\) −10.4666 + 8.78249i −0.626617 + 0.525794i
\(280\) 0 0
\(281\) −1.65611 + 2.86846i −0.0987951 + 0.171118i −0.911186 0.411995i \(-0.864832\pi\)
0.812391 + 0.583113i \(0.198165\pi\)
\(282\) 0 0
\(283\) 14.5116 + 25.1348i 0.862626 + 1.49411i 0.869385 + 0.494134i \(0.164515\pi\)
−0.00675974 + 0.999977i \(0.502152\pi\)
\(284\) 0 0
\(285\) −3.61721 0.637812i −0.214265 0.0377807i
\(286\) 0 0
\(287\) 1.18479 0.0699361
\(288\) 0 0
\(289\) −14.2686 −0.839328
\(290\) 0 0
\(291\) 7.40673 + 20.3498i 0.434190 + 1.19293i
\(292\) 0 0
\(293\) 4.20961 + 7.29125i 0.245928 + 0.425960i 0.962392 0.271664i \(-0.0875740\pi\)
−0.716464 + 0.697624i \(0.754241\pi\)
\(294\) 0 0
\(295\) −2.92855 + 5.07239i −0.170507 + 0.295326i
\(296\) 0 0
\(297\) −17.4572 + 10.0789i −1.01297 + 0.584839i
\(298\) 0 0
\(299\) −8.62314 + 14.9357i −0.498689 + 0.863755i
\(300\) 0 0
\(301\) −0.0923963 0.160035i −0.00532563 0.00922427i
\(302\) 0 0
\(303\) −5.75624 15.8152i −0.330688 0.908557i
\(304\) 0 0
\(305\) 2.28312 0.130731
\(306\) 0 0
\(307\) 12.6878 0.724130 0.362065 0.932153i \(-0.382072\pi\)
0.362065 + 0.932153i \(0.382072\pi\)
\(308\) 0 0
\(309\) 11.2515 + 1.98394i 0.640075 + 0.112863i
\(310\) 0 0
\(311\) −8.24510 14.2809i −0.467537 0.809797i 0.531775 0.846886i \(-0.321525\pi\)
−0.999312 + 0.0370881i \(0.988192\pi\)
\(312\) 0 0
\(313\) −14.2592 + 24.6977i −0.805980 + 1.39600i 0.109648 + 0.993970i \(0.465028\pi\)
−0.915628 + 0.402027i \(0.868306\pi\)
\(314\) 0 0
\(315\) −0.458111 2.59808i −0.0258116 0.146385i
\(316\) 0 0
\(317\) 12.9474 22.4256i 0.727200 1.25955i −0.230862 0.972987i \(-0.574154\pi\)
0.958062 0.286561i \(-0.0925122\pi\)
\(318\) 0 0
\(319\) −11.7344 20.3246i −0.657002 1.13796i
\(320\) 0 0
\(321\) −2.65998 + 3.17004i −0.148465 + 0.176934i
\(322\) 0 0
\(323\) −3.98545 −0.221756
\(324\) 0 0
\(325\) 23.0496 1.27856
\(326\) 0 0
\(327\) 4.40673 5.25173i 0.243693 0.290421i
\(328\) 0 0
\(329\) 0.511144 + 0.885328i 0.0281803 + 0.0488097i
\(330\) 0 0
\(331\) 4.10947 7.11781i 0.225877 0.391230i −0.730705 0.682693i \(-0.760809\pi\)
0.956582 + 0.291463i \(0.0941419\pi\)
\(332\) 0 0
\(333\) 2.37258 + 13.4556i 0.130016 + 0.737360i
\(334\) 0 0
\(335\) 1.30066 2.25281i 0.0710626 0.123084i
\(336\) 0 0
\(337\) −2.28564 3.95885i −0.124507 0.215652i 0.797033 0.603936i \(-0.206402\pi\)
−0.921540 + 0.388283i \(0.873068\pi\)
\(338\) 0 0
\(339\) −28.0651 4.94864i −1.52429 0.268773i
\(340\) 0 0
\(341\) −17.6682 −0.956786
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 1.64749 + 4.52644i 0.0886978 + 0.243695i
\(346\) 0 0
\(347\) 11.2331 + 19.4563i 0.603023 + 1.04447i 0.992361 + 0.123372i \(0.0393707\pi\)
−0.389337 + 0.921095i \(0.627296\pi\)
\(348\) 0 0
\(349\) −13.0496 + 22.6026i −0.698531 + 1.20989i 0.270445 + 0.962735i \(0.412829\pi\)
−0.968976 + 0.247155i \(0.920504\pi\)
\(350\) 0 0
\(351\) 28.3365i 1.51249i
\(352\) 0 0
\(353\) 0.177519 0.307471i 0.00944836 0.0163650i −0.861263 0.508160i \(-0.830326\pi\)
0.870711 + 0.491795i \(0.163659\pi\)
\(354\) 0 0
\(355\) 1.61809 + 2.80261i 0.0858792 + 0.148747i
\(356\) 0 0
\(357\) −0.979055 2.68993i −0.0518171 0.142366i
\(358\) 0 0
\(359\) −5.45605 −0.287959 −0.143980 0.989581i \(-0.545990\pi\)
−0.143980 + 0.989581i \(0.545990\pi\)
\(360\) 0 0
\(361\) −13.1848 −0.693936
\(362\) 0 0
\(363\) −6.90760 1.21800i −0.362555 0.0639283i
\(364\) 0 0
\(365\) −5.61974 9.73367i −0.294150 0.509484i
\(366\) 0 0
\(367\) 5.46198 9.46043i 0.285113 0.493830i −0.687523 0.726162i \(-0.741302\pi\)
0.972637 + 0.232332i \(0.0746355\pi\)
\(368\) 0 0
\(369\) 2.72281 2.28471i 0.141744 0.118937i
\(370\) 0 0
\(371\) 3.64543 6.31407i 0.189261 0.327810i
\(372\) 0 0
\(373\) −0.865715 1.49946i −0.0448250 0.0776392i 0.842742 0.538317i \(-0.180940\pi\)
−0.887567 + 0.460678i \(0.847606\pi\)
\(374\) 0 0
\(375\) 9.03343 10.7656i 0.466484 0.555935i
\(376\) 0 0
\(377\) 32.9908 1.69911
\(378\) 0 0
\(379\) 12.1334 0.623251 0.311626 0.950205i \(-0.399127\pi\)
0.311626 + 0.950205i \(0.399127\pi\)
\(380\) 0 0
\(381\) −19.6545 + 23.4233i −1.00693 + 1.20001i
\(382\) 0 0
\(383\) −4.35591 7.54467i −0.222577 0.385514i 0.733013 0.680215i \(-0.238113\pi\)
−0.955590 + 0.294700i \(0.904780\pi\)
\(384\) 0 0
\(385\) 1.70574 2.95442i 0.0869324 0.150571i
\(386\) 0 0
\(387\) −0.520945 0.189608i −0.0264811 0.00963833i
\(388\) 0 0
\(389\) −1.82160 + 3.15511i −0.0923590 + 0.159970i −0.908503 0.417878i \(-0.862774\pi\)
0.816144 + 0.577848i \(0.196107\pi\)
\(390\) 0 0
\(391\) 2.61334 + 4.52644i 0.132162 + 0.228912i
\(392\) 0 0
\(393\) −32.7460 5.77401i −1.65182 0.291260i
\(394\) 0 0
\(395\) −5.23947 −0.263627
\(396\) 0 0
\(397\) −15.4456 −0.775194 −0.387597 0.921829i \(-0.626695\pi\)
−0.387597 + 0.921829i \(0.626695\pi\)
\(398\) 0 0
\(399\) 1.42855 + 3.92490i 0.0715169 + 0.196491i
\(400\) 0 0
\(401\) −9.21095 15.9538i −0.459973 0.796697i 0.538986 0.842315i \(-0.318808\pi\)
−0.998959 + 0.0456182i \(0.985474\pi\)
\(402\) 0 0
\(403\) 12.4183 21.5092i 0.618601 1.07145i
\(404\) 0 0
\(405\) −6.06283 5.08732i −0.301265 0.252791i
\(406\) 0 0
\(407\) −8.83409 + 15.3011i −0.437890 + 0.758447i
\(408\) 0 0
\(409\) 14.3182 + 24.7999i 0.707989 + 1.22627i 0.965602 + 0.260025i \(0.0837309\pi\)
−0.257612 + 0.966248i \(0.582936\pi\)
\(410\) 0 0
\(411\) 10.7554 + 29.5501i 0.530523 + 1.45760i
\(412\) 0 0
\(413\) 6.66044 0.327739
\(414\) 0 0
\(415\) −0.192533 −0.00945109
\(416\) 0 0
\(417\) 37.6241 + 6.63414i 1.84246 + 0.324875i
\(418\) 0 0
\(419\) −17.3478 30.0472i −0.847494 1.46790i −0.883438 0.468548i \(-0.844777\pi\)
0.0359442 0.999354i \(-0.488556\pi\)
\(420\) 0 0
\(421\) 13.7010 23.7308i 0.667745 1.15657i −0.310788 0.950479i \(-0.600593\pi\)
0.978533 0.206090i \(-0.0660738\pi\)
\(422\) 0 0
\(423\) 2.88191 + 1.04893i 0.140123 + 0.0510007i
\(424\) 0 0
\(425\) 3.49273 6.04958i 0.169422 0.293448i
\(426\) 0 0
\(427\) −1.29813 2.24843i −0.0628211 0.108809i
\(428\) 0 0
\(429\) 23.5535 28.0700i 1.13717 1.35523i
\(430\) 0 0
\(431\) −26.5921 −1.28090 −0.640449 0.768000i \(-0.721252\pi\)
−0.640449 + 0.768000i \(0.721252\pi\)
\(432\) 0 0
\(433\) 37.1830 1.78690 0.893451 0.449160i \(-0.148277\pi\)
0.893451 + 0.449160i \(0.148277\pi\)
\(434\) 0 0
\(435\) 5.92292 7.05866i 0.283982 0.338437i
\(436\) 0 0
\(437\) −3.81315 6.60457i −0.182408 0.315939i
\(438\) 0 0
\(439\) 12.5373 21.7152i 0.598373 1.03641i −0.394689 0.918815i \(-0.629147\pi\)
0.993061 0.117597i \(-0.0375192\pi\)
\(440\) 0 0
\(441\) −2.29813 + 1.92836i −0.109435 + 0.0918268i
\(442\) 0 0
\(443\) 1.02229 1.77066i 0.0485704 0.0841264i −0.840718 0.541473i \(-0.817867\pi\)
0.889288 + 0.457347i \(0.151200\pi\)
\(444\) 0 0
\(445\) 4.84864 + 8.39809i 0.229848 + 0.398108i
\(446\) 0 0
\(447\) 25.8516 + 4.55834i 1.22274 + 0.215602i
\(448\) 0 0
\(449\) −10.2344 −0.482992 −0.241496 0.970402i \(-0.577638\pi\)
−0.241496 + 0.970402i \(0.577638\pi\)
\(450\) 0 0
\(451\) 4.59627 0.216430
\(452\) 0 0
\(453\) 11.2297 + 30.8533i 0.527616 + 1.44961i
\(454\) 0 0
\(455\) 2.39780 + 4.15312i 0.112411 + 0.194701i
\(456\) 0 0
\(457\) 21.2973 36.8879i 0.996244 1.72554i 0.423129 0.906070i \(-0.360932\pi\)
0.573115 0.819475i \(-0.305735\pi\)
\(458\) 0 0
\(459\) −7.43717 4.29385i −0.347137 0.200420i
\(460\) 0 0
\(461\) −0.252374 + 0.437124i −0.0117542 + 0.0203589i −0.871843 0.489786i \(-0.837075\pi\)
0.860088 + 0.510145i \(0.170408\pi\)
\(462\) 0 0
\(463\) 1.34002 + 2.32099i 0.0622761 + 0.107865i 0.895482 0.445097i \(-0.146831\pi\)
−0.833206 + 0.552962i \(0.813497\pi\)
\(464\) 0 0
\(465\) −2.37258 6.51860i −0.110026 0.302293i
\(466\) 0 0
\(467\) 31.4165 1.45378 0.726892 0.686752i \(-0.240964\pi\)
0.726892 + 0.686752i \(0.240964\pi\)
\(468\) 0 0
\(469\) −2.95811 −0.136593
\(470\) 0 0
\(471\) 30.8011 + 5.43107i 1.41924 + 0.250250i
\(472\) 0 0
\(473\) −0.358441 0.620838i −0.0164811 0.0285461i
\(474\) 0 0
\(475\) −5.09627 + 8.82699i −0.233833 + 0.405010i
\(476\) 0 0
\(477\) −3.79813 21.5403i −0.173905 0.986262i
\(478\) 0 0
\(479\) −8.22028 + 14.2380i −0.375594 + 0.650549i −0.990416 0.138118i \(-0.955895\pi\)
0.614821 + 0.788666i \(0.289228\pi\)
\(480\) 0 0
\(481\) −12.4183 21.5092i −0.566227 0.980735i
\(482\) 0 0
\(483\) 3.52094 4.19610i 0.160209 0.190929i
\(484\) 0 0
\(485\) −10.9949 −0.499255
\(486\) 0 0
\(487\) 2.97535 0.134826 0.0674129 0.997725i \(-0.478526\pi\)
0.0674129 + 0.997725i \(0.478526\pi\)
\(488\) 0 0
\(489\) −1.06670 + 1.27125i −0.0482380 + 0.0574878i
\(490\) 0 0
\(491\) −13.2430 22.9376i −0.597650 1.03516i −0.993167 0.116702i \(-0.962768\pi\)
0.395517 0.918459i \(-0.370565\pi\)
\(492\) 0 0
\(493\) 4.99912 8.65873i 0.225149 0.389970i
\(494\) 0 0
\(495\) −1.77719 10.0789i −0.0798787 0.453015i
\(496\) 0 0
\(497\) 1.84002 3.18701i 0.0825363 0.142957i
\(498\) 0 0
\(499\) −6.72193 11.6427i −0.300915 0.521200i 0.675428 0.737426i \(-0.263959\pi\)
−0.976343 + 0.216225i \(0.930625\pi\)
\(500\) 0 0
\(501\) 33.8391 + 5.96675i 1.51182 + 0.266575i
\(502\) 0 0
\(503\) 22.6631 1.01050 0.505250 0.862973i \(-0.331400\pi\)
0.505250 + 0.862973i \(0.331400\pi\)
\(504\) 0 0
\(505\) 8.54488 0.380242
\(506\) 0 0
\(507\) 9.91622 + 27.2446i 0.440395 + 1.20997i
\(508\) 0 0
\(509\) −4.77379 8.26844i −0.211594 0.366492i 0.740619 0.671925i \(-0.234532\pi\)
−0.952214 + 0.305433i \(0.901199\pi\)
\(510\) 0 0
\(511\) −6.39053 + 11.0687i −0.282700 + 0.489651i
\(512\) 0 0
\(513\) 10.8516 + 6.26519i 0.479111 + 0.276615i
\(514\) 0 0
\(515\) −2.90033 + 5.02352i −0.127804 + 0.221363i
\(516\) 0 0
\(517\) 1.98293 + 3.43453i 0.0872090 + 0.151050i
\(518\) 0 0
\(519\) 13.4372 + 36.9183i 0.589826 + 1.62053i
\(520\) 0 0
\(521\) −3.11287 −0.136377 −0.0681887 0.997672i \(-0.521722\pi\)
−0.0681887 + 0.997672i \(0.521722\pi\)
\(522\) 0 0
\(523\) 16.1489 0.706142 0.353071 0.935597i \(-0.385137\pi\)
0.353071 + 0.935597i \(0.385137\pi\)
\(524\) 0 0
\(525\) −7.20961 1.27125i −0.314653 0.0554818i
\(526\) 0 0
\(527\) −3.76352 6.51860i −0.163941 0.283955i
\(528\) 0 0
\(529\) 6.49928 11.2571i 0.282578 0.489439i
\(530\) 0 0
\(531\) 15.3066 12.8438i 0.664249 0.557371i
\(532\) 0 0
\(533\) −3.23055 + 5.59548i −0.139931 + 0.242367i
\(534\) 0 0
\(535\) −1.05051 1.81953i −0.0454174 0.0786652i
\(536\) 0 0
\(537\) 8.18004 9.74860i 0.352995 0.420683i
\(538\) 0 0
\(539\) −3.87939 −0.167097
\(540\) 0 0
\(541\) −5.01548 −0.215632 −0.107816 0.994171i \(-0.534386\pi\)
−0.107816 + 0.994171i \(0.534386\pi\)
\(542\) 0 0
\(543\) −3.83615 + 4.57175i −0.164625 + 0.196192i
\(544\) 0 0
\(545\) 1.74035 + 3.01438i 0.0745485 + 0.129122i
\(546\) 0 0
\(547\) 8.23901 14.2704i 0.352275 0.610157i −0.634373 0.773027i \(-0.718742\pi\)
0.986648 + 0.162870i \(0.0520750\pi\)
\(548\) 0 0
\(549\) −7.31908 2.66393i −0.312371 0.113694i
\(550\) 0 0
\(551\) −7.29426 + 12.6340i −0.310746 + 0.538228i
\(552\) 0 0
\(553\) 2.97906 + 5.15988i 0.126682 + 0.219420i
\(554\) 0 0
\(555\) −6.83157 1.20459i −0.289984 0.0511320i
\(556\) 0 0
\(557\) −34.5631 −1.46448 −0.732242 0.681045i \(-0.761526\pi\)
−0.732242 + 0.681045i \(0.761526\pi\)
\(558\) 0 0
\(559\) 1.00774 0.0426229
\(560\) 0 0
\(561\) −3.79813 10.4353i −0.160357 0.440578i
\(562\) 0 0
\(563\) −18.6052 32.2251i −0.784115 1.35813i −0.929526 0.368756i \(-0.879784\pi\)
0.145411 0.989371i \(-0.453550\pi\)
\(564\) 0 0
\(565\) 7.23442 12.5304i 0.304354 0.527157i
\(566\) 0 0
\(567\) −1.56283 + 8.86327i −0.0656328 + 0.372222i
\(568\) 0 0
\(569\) −0.202333 + 0.350452i −0.00848226 + 0.0146917i −0.870235 0.492636i \(-0.836033\pi\)
0.861753 + 0.507328i \(0.169367\pi\)
\(570\) 0 0
\(571\) −18.8897 32.7178i −0.790507 1.36920i −0.925653 0.378373i \(-0.876484\pi\)
0.135146 0.990826i \(-0.456850\pi\)
\(572\) 0 0
\(573\) −3.35163 9.20854i −0.140017 0.384692i
\(574\) 0 0
\(575\) 13.3669 0.557438
\(576\) 0 0
\(577\) −2.21120 −0.0920535 −0.0460267 0.998940i \(-0.514656\pi\)
−0.0460267 + 0.998940i \(0.514656\pi\)
\(578\) 0 0
\(579\) −16.3687 2.88624i −0.680260 0.119948i
\(580\) 0 0
\(581\) 0.109470 + 0.189608i 0.00454160 + 0.00786628i
\(582\) 0 0
\(583\) 14.1420 24.4947i 0.585703 1.01447i
\(584\) 0 0
\(585\) 13.5192 + 4.92058i 0.558950 + 0.203441i
\(586\) 0 0
\(587\) 12.1049 20.9663i 0.499622 0.865371i −0.500378 0.865807i \(-0.666806\pi\)
1.00000 0.000436347i \(0.000138894\pi\)
\(588\) 0 0
\(589\) 5.49138 + 9.51135i 0.226268 + 0.391908i
\(590\) 0 0
\(591\) 9.26295 11.0391i 0.381027 0.454090i
\(592\) 0 0
\(593\) 12.2385 0.502577 0.251288 0.967912i \(-0.419146\pi\)
0.251288 + 0.967912i \(0.419146\pi\)
\(594\) 0 0
\(595\) 1.45336 0.0595821
\(596\) 0 0
\(597\) −7.34389 + 8.75211i −0.300566 + 0.358200i
\(598\) 0 0
\(599\) 19.8084 + 34.3092i 0.809349 + 1.40183i 0.913315 + 0.407253i \(0.133513\pi\)
−0.103966 + 0.994581i \(0.533153\pi\)
\(600\) 0 0
\(601\) 15.0039 25.9875i 0.612021 1.06005i −0.378879 0.925446i \(-0.623690\pi\)
0.990899 0.134605i \(-0.0429764\pi\)
\(602\) 0 0
\(603\) −6.79813 + 5.70431i −0.276841 + 0.232298i
\(604\) 0 0
\(605\) 1.78059 3.08408i 0.0723914 0.125386i
\(606\) 0 0
\(607\) −9.74216 16.8739i −0.395422 0.684891i 0.597733 0.801695i \(-0.296068\pi\)
−0.993155 + 0.116804i \(0.962735\pi\)
\(608\) 0 0
\(609\) −10.3191 1.81953i −0.418150 0.0737312i
\(610\) 0 0
\(611\) −5.57491 −0.225537
\(612\) 0 0
\(613\) −18.5276 −0.748325 −0.374162 0.927363i \(-0.622070\pi\)
−0.374162 + 0.927363i \(0.622070\pi\)
\(614\) 0 0
\(615\) 0.617211 + 1.69577i 0.0248884 + 0.0683802i
\(616\) 0 0
\(617\) −13.9201 24.1103i −0.560402 0.970644i −0.997461 0.0712118i \(-0.977313\pi\)
0.437059 0.899433i \(-0.356020\pi\)
\(618\) 0 0
\(619\) −22.4907 + 38.9550i −0.903976 + 1.56573i −0.0816906 + 0.996658i \(0.526032\pi\)
−0.822286 + 0.569075i \(0.807301\pi\)
\(620\) 0 0
\(621\) 16.4329i 0.659428i
\(622\) 0 0
\(623\) 5.51367 9.54996i 0.220901 0.382611i
\(624\) 0 0
\(625\) −6.99912 12.1228i −0.279965 0.484913i
\(626\) 0 0
\(627\) 5.54189 + 15.2262i 0.221322 + 0.608076i
\(628\) 0 0
\(629\) −7.52704 −0.300123
\(630\) 0 0
\(631\) −9.43613 −0.375646 −0.187823 0.982203i \(-0.560143\pi\)
−0.187823 + 0.982203i \(0.560143\pi\)
\(632\) 0 0
\(633\) −5.74763 1.01346i −0.228448 0.0402815i
\(634\) 0 0
\(635\) −7.76217 13.4445i −0.308032 0.533528i
\(636\) 0 0
\(637\) 2.72668 4.72275i 0.108035 0.187122i
\(638\) 0 0
\(639\) −1.91710 10.8724i −0.0758393 0.430106i
\(640\) 0 0
\(641\) −18.6951 + 32.3808i −0.738410 + 1.27896i 0.214800 + 0.976658i \(0.431090\pi\)
−0.953211 + 0.302306i \(0.902243\pi\)
\(642\) 0 0
\(643\) 0.805874 + 1.39581i 0.0317806 + 0.0550456i 0.881478 0.472225i \(-0.156549\pi\)
−0.849698 + 0.527270i \(0.823216\pi\)
\(644\) 0 0
\(645\) 0.180922 0.215615i 0.00712380 0.00848982i
\(646\) 0 0
\(647\) 41.1762 1.61880 0.809402 0.587255i \(-0.199791\pi\)
0.809402 + 0.587255i \(0.199791\pi\)
\(648\) 0 0
\(649\) 25.8384 1.01425
\(650\) 0 0
\(651\) −5.07057 + 6.04288i −0.198731 + 0.236839i
\(652\) 0 0
\(653\) −1.52600 2.64310i −0.0597169 0.103433i 0.834621 0.550824i \(-0.185686\pi\)
−0.894338 + 0.447391i \(0.852353\pi\)
\(654\) 0 0
\(655\) 8.44104 14.6203i 0.329819 0.571263i
\(656\) 0 0
\(657\) 6.65822 + 37.7607i 0.259762 + 1.47318i
\(658\) 0 0
\(659\) 20.8175 36.0569i 0.810934 1.40458i −0.101277 0.994858i \(-0.532293\pi\)
0.912211 0.409721i \(-0.134374\pi\)
\(660\) 0 0
\(661\) −10.1505 17.5812i −0.394808 0.683828i 0.598269 0.801296i \(-0.295856\pi\)
−0.993077 + 0.117468i \(0.962522\pi\)
\(662\) 0 0
\(663\) 15.3735 + 2.71075i 0.597056 + 0.105277i
\(664\) 0 0
\(665\) −2.12061 −0.0822339
\(666\) 0 0
\(667\) 19.1320 0.740793
\(668\) 0 0
\(669\) 3.71806 + 10.2153i 0.143749 + 0.394946i
\(670\) 0 0
\(671\) −5.03596 8.72254i −0.194411 0.336730i
\(672\) 0 0
\(673\) 0.415345 0.719398i 0.0160104 0.0277307i −0.857909 0.513801i \(-0.828237\pi\)
0.873920 + 0.486071i \(0.161570\pi\)
\(674\) 0 0
\(675\) −19.0201 + 10.9812i −0.732083 + 0.422668i
\(676\) 0 0
\(677\) −5.43360 + 9.41127i −0.208830 + 0.361705i −0.951346 0.308124i \(-0.900299\pi\)
0.742516 + 0.669828i \(0.233632\pi\)
\(678\) 0 0
\(679\) 6.25150 + 10.8279i 0.239910 + 0.415537i
\(680\) 0 0
\(681\) 3.65064 + 10.0301i 0.139893 + 0.384353i
\(682\) 0 0
\(683\) −32.6946 −1.25102 −0.625512 0.780215i \(-0.715110\pi\)
−0.625512 + 0.780215i \(0.715110\pi\)
\(684\) 0 0
\(685\) −15.9659 −0.610024
\(686\) 0 0
\(687\) −39.8888 7.03347i −1.52185 0.268344i
\(688\) 0 0
\(689\) 19.8799 + 34.4329i 0.757362 + 1.31179i
\(690\) 0 0
\(691\) 7.49912 12.9889i 0.285280 0.494120i −0.687397 0.726282i \(-0.741247\pi\)
0.972677 + 0.232162i \(0.0745801\pi\)
\(692\) 0 0
\(693\) −8.91534 + 7.48086i −0.338666 + 0.284174i
\(694\) 0 0
\(695\) −9.69846 + 16.7982i −0.367884 + 0.637193i
\(696\) 0 0
\(697\) 0.979055 + 1.69577i 0.0370844 + 0.0642320i
\(698\) 0 0
\(699\) −9.49154 + 11.3116i −0.359003 + 0.427843i
\(700\) 0 0
\(701\) 26.4688 0.999714 0.499857 0.866108i \(-0.333386\pi\)
0.499857 + 0.866108i \(0.333386\pi\)
\(702\) 0 0
\(703\) 10.9828 0.414223
\(704\) 0 0
\(705\) −1.00088 + 1.19280i −0.0376952 + 0.0449234i
\(706\) 0 0
\(707\) −4.85844 8.41507i −0.182720 0.316481i
\(708\) 0 0
\(709\) −7.68004 + 13.3022i −0.288430 + 0.499576i −0.973435 0.228963i \(-0.926467\pi\)
0.685005 + 0.728538i \(0.259800\pi\)
\(710\) 0 0
\(711\) 16.7964 + 6.11338i 0.629913 + 0.229270i
\(712\) 0 0
\(713\) 7.20162 12.4736i 0.269703 0.467139i
\(714\) 0 0
\(715\) 9.30200 + 16.1115i 0.347875 + 0.602538i
\(716\) 0 0
\(717\) 24.8391 + 4.37981i 0.927635 + 0.163567i
\(718\) 0 0
\(719\) −26.7306 −0.996883 −0.498442 0.866923i \(-0.666094\pi\)
−0.498442 + 0.866923i \(0.666094\pi\)
\(720\) 0 0
\(721\) 6.59627 0.245658
\(722\) 0 0
\(723\) −3.20115 8.79509i −0.119052 0.327093i
\(724\) 0 0
\(725\) −12.7849 22.1441i −0.474820 0.822413i
\(726\) 0 0
\(727\) −22.8221 + 39.5290i −0.846424 + 1.46605i 0.0379552 + 0.999279i \(0.487916\pi\)
−0.884379 + 0.466770i \(0.845418\pi\)
\(728\) 0 0
\(729\) 13.5000 + 23.3827i 0.500000 + 0.866025i
\(730\) 0 0
\(731\) 0.152704 0.264490i 0.00564795 0.00978253i
\(732\) 0 0
\(733\) −2.98751 5.17452i −0.110346 0.191125i 0.805564 0.592509i \(-0.201863\pi\)
−0.915910 + 0.401384i \(0.868529\pi\)
\(734\) 0 0
\(735\) −0.520945 1.43128i −0.0192153 0.0527937i
\(736\) 0 0
\(737\) −11.4757 −0.422711
\(738\) 0 0
\(739\) 35.5963 1.30943 0.654715 0.755876i \(-0.272789\pi\)
0.654715 + 0.755876i \(0.272789\pi\)
\(740\) 0 0
\(741\) −22.4315 3.95529i −0.824043 0.145301i
\(742\) 0 0
\(743\) −14.6544 25.3821i −0.537616 0.931178i −0.999032 0.0439943i \(-0.985992\pi\)
0.461416 0.887184i \(-0.347342\pi\)
\(744\) 0 0
\(745\) −6.66385 + 11.5421i −0.244145 + 0.422871i
\(746\) 0 0
\(747\) 0.617211 + 0.224647i 0.0225826 + 0.00821939i
\(748\) 0 0
\(749\) −1.19459 + 2.06910i −0.0436495 + 0.0756031i
\(750\) 0 0
\(751\) −8.66684 15.0114i −0.316258 0.547774i 0.663446 0.748224i \(-0.269093\pi\)
−0.979704 + 0.200450i \(0.935760\pi\)
\(752\) 0 0
\(753\) 13.4345 16.0107i 0.489582 0.583461i
\(754\) 0 0
\(755\) −16.6699 −0.606681
\(756\) 0 0
\(757\) −2.77156 −0.100734 −0.0503671 0.998731i \(-0.516039\pi\)
−0.0503671 + 0.998731i \(0.516039\pi\)
\(758\) 0 0
\(759\) 13.6591 16.2783i 0.495794 0.590864i
\(760\) 0 0
\(761\) −3.75372 6.50163i −0.136072 0.235684i 0.789934 0.613191i \(-0.210115\pi\)
−0.926007 + 0.377508i \(0.876781\pi\)
\(762\) 0 0
\(763\) 1.97906 3.42782i 0.0716466 0.124096i
\(764\) 0 0
\(765\) 3.34002 2.80261i 0.120759 0.101329i
\(766\) 0 0
\(767\) −18.1609 + 31.4556i −0.655752 + 1.13580i
\(768\) 0 0
\(769\) −1.02182 1.76985i −0.0368478 0.0638223i 0.847013 0.531572i \(-0.178398\pi\)
−0.883861 + 0.467749i \(0.845065\pi\)
\(770\) 0 0
\(771\) −18.0232 3.17798i −0.649090 0.114452i
\(772\) 0 0
\(773\) −24.9418 −0.897094 −0.448547 0.893759i \(-0.648058\pi\)
−0.448547 + 0.893759i \(0.648058\pi\)
\(774\) 0 0
\(775\) −19.2499 −0.691477
\(776\) 0 0
\(777\) 2.69800 + 7.41268i 0.0967901 + 0.265929i
\(778\) 0 0
\(779\) −1.42855 2.47432i −0.0511831 0.0886516i
\(780\) 0 0
\(781\) 7.13816 12.3636i 0.255423 0.442406i
\(782\) 0 0
\(783\) −27.2233 + 15.7174i −0.972883 + 0.561694i
\(784\) 0 0
\(785\) −7.93969 + 13.7520i −0.283380 + 0.490828i
\(786\) 0 0
\(787\) 3.55350 + 6.15484i 0.126669 + 0.219396i 0.922384 0.386274i \(-0.126238\pi\)
−0.795715 + 0.605671i \(0.792905\pi\)
\(788\) 0 0
\(789\) 16.7964 + 46.1477i 0.597967 + 1.64290i
\(790\) 0 0
\(791\) −16.4534 −0.585014
\(792\) 0 0
\(793\) 14.1584 0.502779
\(794\) 0 0
\(795\) 10.9363 + 1.92836i 0.387870 + 0.0683920i
\(796\) 0 0
\(797\) −16.8314 29.1528i −0.596199 1.03265i −0.993376 0.114905i \(-0.963344\pi\)
0.397178 0.917742i \(-0.369990\pi\)
\(798\) 0 0
\(799\) −0.844770 + 1.46318i −0.0298858 + 0.0517638i
\(800\)