Properties

Label 819.2.n.d.172.1
Level $819$
Weight $2$
Character 819.172
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.n (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 172.1
Root \(-0.181721 - 0.314749i\) of defining polynomial
Character \(\chi\) \(=\) 819.172
Dual form 819.2.n.d.100.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19402 + 2.06810i) q^{2} +(-1.85136 - 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} +(2.60682 - 0.452230i) q^{7} +4.06616 q^{8} +O(q^{10})\) \(q+(-1.19402 + 2.06810i) q^{2} +(-1.85136 - 3.20665i) q^{4} +(0.491140 + 0.850679i) q^{5} +(2.60682 - 0.452230i) q^{7} +4.06616 q^{8} -2.34572 q^{10} +0.587802 q^{11} +(2.39227 - 2.69760i) q^{13} +(-2.17733 + 5.93113i) q^{14} +(-1.15235 + 1.99593i) q^{16} +(-3.22710 - 5.58950i) q^{17} -3.82689 q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} +(4.13001 - 7.15338i) q^{23} +(2.01756 - 3.49452i) q^{25} +(2.72249 + 8.16844i) q^{26} +(-6.27630 - 7.52191i) q^{28} +(-1.98009 - 3.42962i) q^{29} +(1.49436 - 2.58831i) q^{31} +(1.31430 + 2.27644i) q^{32} +15.4129 q^{34} +(1.66501 + 1.99546i) q^{35} +(-0.877941 + 1.52064i) q^{37} +(4.56938 - 7.91440i) q^{38} +(1.99705 + 3.45900i) q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} +(-1.08823 - 1.88488i) q^{44} +(9.86261 + 17.0825i) q^{46} +(-2.17030 - 3.75906i) q^{47} +(6.59098 - 2.35776i) q^{49} +(4.81802 + 8.34505i) q^{50} +(-13.0792 - 2.67695i) q^{52} +(0.212770 - 0.368529i) q^{53} +(0.288693 + 0.500031i) q^{55} +(10.5997 - 1.83884i) q^{56} +9.45706 q^{58} +(3.00431 + 5.20362i) q^{59} +2.20674 q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(3.46973 + 0.710156i) q^{65} +7.01303 q^{67} +(-11.9491 + 20.6964i) q^{68} +(-6.11486 + 1.06080i) q^{70} +(1.80127 - 3.11988i) q^{71} +(-2.46714 + 4.27321i) q^{73} +(-2.09656 - 3.63134i) q^{74} +(7.08496 + 12.2715i) q^{76} +(1.53229 - 0.265822i) q^{77} +(-1.39270 - 2.41223i) q^{79} -2.26386 q^{80} -8.76812 q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} +(-7.61885 - 13.1962i) q^{86} +2.39010 q^{88} +(-1.04656 + 1.81269i) q^{89} +(5.01627 - 8.11400i) q^{91} -30.5845 q^{92} +10.3655 q^{94} +(-1.87954 - 3.25546i) q^{95} +(-3.84852 + 6.66584i) q^{97} +(-2.99367 + 16.4460i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} + O(q^{10}) \) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} - 8q^{10} + 8q^{11} - 2q^{13} + 2q^{14} + 8q^{16} - 5q^{17} + 2q^{19} + q^{20} - 5q^{22} + q^{23} + 7q^{25} - 5q^{26} - 7q^{28} - 3q^{29} + 16q^{31} - 8q^{32} + 32q^{34} - 8q^{35} - 13q^{37} + 17q^{38} - 5q^{40} + 8q^{41} - 11q^{43} - 21q^{44} + 16q^{46} + q^{47} - 3q^{49} - 6q^{50} - 25q^{52} + 2q^{53} + 9q^{55} + 18q^{56} + 16q^{58} - 13q^{59} + 10q^{61} - 5q^{62} - 30q^{64} - 19q^{65} + 22q^{67} - 29q^{68} - 39q^{70} - 6q^{71} - 30q^{73} + 3q^{74} - 9q^{76} - 11q^{77} + 7q^{79} - 14q^{80} - 2q^{82} + 54q^{83} - q^{85} + 7q^{86} - 4q^{89} - 20q^{91} - 54q^{92} - 90q^{94} + 6q^{95} - 35q^{97} - 62q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19402 + 2.06810i −0.844299 + 1.46237i 0.0419302 + 0.999121i \(0.486649\pi\)
−0.886229 + 0.463248i \(0.846684\pi\)
\(3\) 0 0
\(4\) −1.85136 3.20665i −0.925680 1.60333i
\(5\) 0.491140 + 0.850679i 0.219644 + 0.380435i 0.954699 0.297572i \(-0.0961769\pi\)
−0.735055 + 0.678008i \(0.762844\pi\)
\(6\) 0 0
\(7\) 2.60682 0.452230i 0.985284 0.170927i
\(8\) 4.06616 1.43761
\(9\) 0 0
\(10\) −2.34572 −0.741782
\(11\) 0.587802 0.177229 0.0886146 0.996066i \(-0.471756\pi\)
0.0886146 + 0.996066i \(0.471756\pi\)
\(12\) 0 0
\(13\) 2.39227 2.69760i 0.663496 0.748179i
\(14\) −2.17733 + 5.93113i −0.581916 + 1.58516i
\(15\) 0 0
\(16\) −1.15235 + 1.99593i −0.288088 + 0.498983i
\(17\) −3.22710 5.58950i −0.782687 1.35565i −0.930371 0.366619i \(-0.880515\pi\)
0.147685 0.989035i \(-0.452818\pi\)
\(18\) 0 0
\(19\) −3.82689 −0.877950 −0.438975 0.898499i \(-0.644658\pi\)
−0.438975 + 0.898499i \(0.644658\pi\)
\(20\) 1.81855 3.14983i 0.406641 0.704323i
\(21\) 0 0
\(22\) −0.701847 + 1.21563i −0.149634 + 0.259174i
\(23\) 4.13001 7.15338i 0.861166 1.49158i −0.00963902 0.999954i \(-0.503068\pi\)
0.870805 0.491629i \(-0.163598\pi\)
\(24\) 0 0
\(25\) 2.01756 3.49452i 0.403513 0.698904i
\(26\) 2.72249 + 8.16844i 0.533925 + 1.60196i
\(27\) 0 0
\(28\) −6.27630 7.52191i −1.18611 1.42151i
\(29\) −1.98009 3.42962i −0.367694 0.636864i 0.621511 0.783406i \(-0.286519\pi\)
−0.989205 + 0.146541i \(0.953186\pi\)
\(30\) 0 0
\(31\) 1.49436 2.58831i 0.268395 0.464874i −0.700053 0.714091i \(-0.746840\pi\)
0.968448 + 0.249218i \(0.0801734\pi\)
\(32\) 1.31430 + 2.27644i 0.232338 + 0.402421i
\(33\) 0 0
\(34\) 15.4129 2.64329
\(35\) 1.66501 + 1.99546i 0.281439 + 0.337294i
\(36\) 0 0
\(37\) −0.877941 + 1.52064i −0.144333 + 0.249991i −0.929124 0.369769i \(-0.879437\pi\)
0.784791 + 0.619760i \(0.212770\pi\)
\(38\) 4.56938 7.91440i 0.741252 1.28389i
\(39\) 0 0
\(40\) 1.99705 + 3.45900i 0.315762 + 0.546916i
\(41\) 1.83584 + 3.17977i 0.286710 + 0.496597i 0.973023 0.230710i \(-0.0741049\pi\)
−0.686312 + 0.727307i \(0.740772\pi\)
\(42\) 0 0
\(43\) −3.19042 + 5.52598i −0.486535 + 0.842703i −0.999880 0.0154788i \(-0.995073\pi\)
0.513345 + 0.858182i \(0.328406\pi\)
\(44\) −1.08823 1.88488i −0.164058 0.284156i
\(45\) 0 0
\(46\) 9.86261 + 17.0825i 1.45416 + 2.51868i
\(47\) −2.17030 3.75906i −0.316570 0.548316i 0.663200 0.748442i \(-0.269198\pi\)
−0.979770 + 0.200127i \(0.935865\pi\)
\(48\) 0 0
\(49\) 6.59098 2.35776i 0.941568 0.336823i
\(50\) 4.81802 + 8.34505i 0.681370 + 1.18017i
\(51\) 0 0
\(52\) −13.0792 2.67695i −1.81376 0.371226i
\(53\) 0.212770 0.368529i 0.0292263 0.0506214i −0.851042 0.525097i \(-0.824029\pi\)
0.880269 + 0.474476i \(0.157362\pi\)
\(54\) 0 0
\(55\) 0.288693 + 0.500031i 0.0389274 + 0.0674242i
\(56\) 10.5997 1.83884i 1.41645 0.245725i
\(57\) 0 0
\(58\) 9.45706 1.24177
\(59\) 3.00431 + 5.20362i 0.391128 + 0.677454i 0.992599 0.121441i \(-0.0387516\pi\)
−0.601470 + 0.798895i \(0.705418\pi\)
\(60\) 0 0
\(61\) 2.20674 0.282544 0.141272 0.989971i \(-0.454881\pi\)
0.141272 + 0.989971i \(0.454881\pi\)
\(62\) 3.56859 + 6.18097i 0.453211 + 0.784985i
\(63\) 0 0
\(64\) −10.8866 −1.36083
\(65\) 3.46973 + 0.710156i 0.430367 + 0.0880841i
\(66\) 0 0
\(67\) 7.01303 0.856778 0.428389 0.903594i \(-0.359081\pi\)
0.428389 + 0.903594i \(0.359081\pi\)
\(68\) −11.9491 + 20.6964i −1.44904 + 2.50980i
\(69\) 0 0
\(70\) −6.11486 + 1.06080i −0.730866 + 0.126790i
\(71\) 1.80127 3.11988i 0.213771 0.370262i −0.739121 0.673573i \(-0.764759\pi\)
0.952892 + 0.303311i \(0.0980920\pi\)
\(72\) 0 0
\(73\) −2.46714 + 4.27321i −0.288756 + 0.500141i −0.973513 0.228631i \(-0.926575\pi\)
0.684757 + 0.728772i \(0.259908\pi\)
\(74\) −2.09656 3.63134i −0.243720 0.422135i
\(75\) 0 0
\(76\) 7.08496 + 12.2715i 0.812701 + 1.40764i
\(77\) 1.53229 0.265822i 0.174621 0.0302932i
\(78\) 0 0
\(79\) −1.39270 2.41223i −0.156691 0.271397i 0.776982 0.629522i \(-0.216749\pi\)
−0.933674 + 0.358125i \(0.883416\pi\)
\(80\) −2.26386 −0.253108
\(81\) 0 0
\(82\) −8.76812 −0.968277
\(83\) 2.86819 0.314825 0.157412 0.987533i \(-0.449685\pi\)
0.157412 + 0.987533i \(0.449685\pi\)
\(84\) 0 0
\(85\) 3.16992 5.49045i 0.343826 0.595523i
\(86\) −7.61885 13.1962i −0.821562 1.42299i
\(87\) 0 0
\(88\) 2.39010 0.254786
\(89\) −1.04656 + 1.81269i −0.110935 + 0.192145i −0.916147 0.400842i \(-0.868718\pi\)
0.805213 + 0.592986i \(0.202051\pi\)
\(90\) 0 0
\(91\) 5.01627 8.11400i 0.525848 0.850578i
\(92\) −30.5845 −3.18866
\(93\) 0 0
\(94\) 10.3655 1.06912
\(95\) −1.87954 3.25546i −0.192837 0.334003i
\(96\) 0 0
\(97\) −3.84852 + 6.66584i −0.390758 + 0.676813i −0.992550 0.121840i \(-0.961120\pi\)
0.601791 + 0.798653i \(0.294454\pi\)
\(98\) −2.99367 + 16.4460i −0.302406 + 1.66130i
\(99\) 0 0
\(100\) −14.9409 −1.49409
\(101\) 2.63732 0.262423 0.131212 0.991354i \(-0.458113\pi\)
0.131212 + 0.991354i \(0.458113\pi\)
\(102\) 0 0
\(103\) 5.43095 + 9.40669i 0.535128 + 0.926868i 0.999157 + 0.0410486i \(0.0130699\pi\)
−0.464029 + 0.885820i \(0.653597\pi\)
\(104\) 9.72736 10.9689i 0.953846 1.07559i
\(105\) 0 0
\(106\) 0.508103 + 0.880061i 0.0493514 + 0.0854791i
\(107\) −7.99024 + 13.8395i −0.772446 + 1.33792i 0.163773 + 0.986498i \(0.447634\pi\)
−0.936219 + 0.351418i \(0.885700\pi\)
\(108\) 0 0
\(109\) −4.61738 + 7.99754i −0.442265 + 0.766026i −0.997857 0.0654294i \(-0.979158\pi\)
0.555592 + 0.831455i \(0.312492\pi\)
\(110\) −1.37882 −0.131465
\(111\) 0 0
\(112\) −2.10135 + 5.72416i −0.198559 + 0.540882i
\(113\) 5.09012 8.81635i 0.478838 0.829372i −0.520867 0.853638i \(-0.674391\pi\)
0.999706 + 0.0242655i \(0.00772470\pi\)
\(114\) 0 0
\(115\) 8.11364 0.756601
\(116\) −7.33173 + 12.6989i −0.680734 + 1.17907i
\(117\) 0 0
\(118\) −14.3488 −1.32092
\(119\) −10.9402 13.1114i −1.00289 1.20192i
\(120\) 0 0
\(121\) −10.6545 −0.968590
\(122\) −2.63489 + 4.56376i −0.238552 + 0.413184i
\(123\) 0 0
\(124\) −11.0664 −0.993792
\(125\) 8.87502 0.793806
\(126\) 0 0
\(127\) −2.12513 3.68083i −0.188575 0.326621i 0.756201 0.654340i \(-0.227053\pi\)
−0.944775 + 0.327719i \(0.893720\pi\)
\(128\) 10.3702 17.9617i 0.916606 1.58761i
\(129\) 0 0
\(130\) −5.61160 + 6.32781i −0.492170 + 0.554986i
\(131\) −1.08478 1.87890i −0.0947779 0.164160i 0.814738 0.579829i \(-0.196881\pi\)
−0.909516 + 0.415669i \(0.863547\pi\)
\(132\) 0 0
\(133\) −9.97601 + 1.73063i −0.865030 + 0.150065i
\(134\) −8.37369 + 14.5037i −0.723376 + 1.25292i
\(135\) 0 0
\(136\) −13.1219 22.7278i −1.12519 1.94889i
\(137\) 4.18158 + 7.24271i 0.357257 + 0.618787i 0.987501 0.157610i \(-0.0503788\pi\)
−0.630245 + 0.776396i \(0.717045\pi\)
\(138\) 0 0
\(139\) 0.288457 0.499622i 0.0244666 0.0423774i −0.853533 0.521039i \(-0.825545\pi\)
0.877999 + 0.478662i \(0.158878\pi\)
\(140\) 3.31619 9.03343i 0.280269 0.763464i
\(141\) 0 0
\(142\) 4.30149 + 7.45040i 0.360973 + 0.625224i
\(143\) 1.40618 1.58566i 0.117591 0.132599i
\(144\) 0 0
\(145\) 1.94500 3.36885i 0.161524 0.279767i
\(146\) −5.89161 10.2046i −0.487593 0.844537i
\(147\) 0 0
\(148\) 6.50154 0.534423
\(149\) −2.80662 −0.229928 −0.114964 0.993370i \(-0.536675\pi\)
−0.114964 + 0.993370i \(0.536675\pi\)
\(150\) 0 0
\(151\) 11.5054 19.9280i 0.936300 1.62172i 0.164000 0.986460i \(-0.447560\pi\)
0.772300 0.635258i \(-0.219106\pi\)
\(152\) −15.5608 −1.26215
\(153\) 0 0
\(154\) −1.27984 + 3.48633i −0.103132 + 0.280937i
\(155\) 2.93576 0.235806
\(156\) 0 0
\(157\) −11.2880 + 19.5513i −0.900879 + 1.56037i −0.0745227 + 0.997219i \(0.523743\pi\)
−0.826356 + 0.563148i \(0.809590\pi\)
\(158\) 6.65165 0.529177
\(159\) 0 0
\(160\) −1.29101 + 2.23610i −0.102064 + 0.176779i
\(161\) 7.53119 20.5153i 0.593541 1.61683i
\(162\) 0 0
\(163\) 8.17714 0.640483 0.320242 0.947336i \(-0.396236\pi\)
0.320242 + 0.947336i \(0.396236\pi\)
\(164\) 6.79761 11.7738i 0.530804 0.919380i
\(165\) 0 0
\(166\) −3.42467 + 5.93170i −0.265806 + 0.460389i
\(167\) −1.16386 2.01586i −0.0900619 0.155992i 0.817475 0.575964i \(-0.195373\pi\)
−0.907537 + 0.419972i \(0.862040\pi\)
\(168\) 0 0
\(169\) −1.55408 12.9068i −0.119545 0.992829i
\(170\) 7.56988 + 13.1114i 0.580583 + 1.00560i
\(171\) 0 0
\(172\) 23.6265 1.80150
\(173\) 8.13372 0.618396 0.309198 0.950998i \(-0.399939\pi\)
0.309198 + 0.950998i \(0.399939\pi\)
\(174\) 0 0
\(175\) 3.67909 10.0220i 0.278113 0.757590i
\(176\) −0.677355 + 1.17321i −0.0510576 + 0.0884343i
\(177\) 0 0
\(178\) −2.49922 4.32877i −0.187324 0.324455i
\(179\) 20.9925 1.56906 0.784528 0.620093i \(-0.212905\pi\)
0.784528 + 0.620093i \(0.212905\pi\)
\(180\) 0 0
\(181\) −1.60807 −0.119527 −0.0597635 0.998213i \(-0.519035\pi\)
−0.0597635 + 0.998213i \(0.519035\pi\)
\(182\) 10.7910 + 20.0624i 0.799885 + 1.48713i
\(183\) 0 0
\(184\) 16.7933 29.0868i 1.23802 2.14431i
\(185\) −1.72477 −0.126807
\(186\) 0 0
\(187\) −1.89690 3.28552i −0.138715 0.240261i
\(188\) −8.03601 + 13.9188i −0.586086 + 1.01513i
\(189\) 0 0
\(190\) 8.97683 0.651247
\(191\) 11.5622 0.836614 0.418307 0.908306i \(-0.362624\pi\)
0.418307 + 0.908306i \(0.362624\pi\)
\(192\) 0 0
\(193\) 23.5788 1.69724 0.848621 0.529001i \(-0.177433\pi\)
0.848621 + 0.529001i \(0.177433\pi\)
\(194\) −9.19041 15.9183i −0.659833 1.14286i
\(195\) 0 0
\(196\) −19.7628 16.7699i −1.41163 1.19785i
\(197\) −0.735472 1.27387i −0.0524002 0.0907598i 0.838636 0.544693i \(-0.183354\pi\)
−0.891036 + 0.453933i \(0.850020\pi\)
\(198\) 0 0
\(199\) −4.69700 8.13543i −0.332961 0.576706i 0.650130 0.759823i \(-0.274714\pi\)
−0.983091 + 0.183117i \(0.941381\pi\)
\(200\) 8.20374 14.2093i 0.580092 1.00475i
\(201\) 0 0
\(202\) −3.14901 + 5.45425i −0.221564 + 0.383760i
\(203\) −6.71271 8.04493i −0.471140 0.564643i
\(204\) 0 0
\(205\) −1.80331 + 3.12343i −0.125949 + 0.218150i
\(206\) −25.9386 −1.80723
\(207\) 0 0
\(208\) 2.62749 + 7.88340i 0.182183 + 0.546615i
\(209\) −2.24946 −0.155598
\(210\) 0 0
\(211\) 4.47109 + 7.74416i 0.307803 + 0.533130i 0.977881 0.209160i \(-0.0670730\pi\)
−0.670079 + 0.742290i \(0.733740\pi\)
\(212\) −1.57566 −0.108217
\(213\) 0 0
\(214\) −19.0810 33.0493i −1.30435 2.25920i
\(215\) −6.26778 −0.427459
\(216\) 0 0
\(217\) 2.72501 7.42303i 0.184986 0.503908i
\(218\) −11.0265 19.0984i −0.746808 1.29351i
\(219\) 0 0
\(220\) 1.06895 1.85148i 0.0720686 0.124827i
\(221\) −22.7983 4.66618i −1.53358 0.313881i
\(222\) 0 0
\(223\) −10.9098 18.8963i −0.730574 1.26539i −0.956638 0.291279i \(-0.905919\pi\)
0.226064 0.974112i \(-0.427414\pi\)
\(224\) 4.45562 + 5.33989i 0.297704 + 0.356786i
\(225\) 0 0
\(226\) 12.1554 + 21.0538i 0.808565 + 1.40048i
\(227\) −9.27627 16.0670i −0.615687 1.06640i −0.990263 0.139206i \(-0.955545\pi\)
0.374576 0.927196i \(-0.377788\pi\)
\(228\) 0 0
\(229\) −9.67525 16.7580i −0.639359 1.10740i −0.985574 0.169247i \(-0.945867\pi\)
0.346215 0.938155i \(-0.387467\pi\)
\(230\) −9.68784 + 16.7798i −0.638797 + 1.10643i
\(231\) 0 0
\(232\) −8.05137 13.9454i −0.528599 0.915560i
\(233\) 8.08170 + 13.9979i 0.529450 + 0.917034i 0.999410 + 0.0343462i \(0.0109349\pi\)
−0.469960 + 0.882688i \(0.655732\pi\)
\(234\) 0 0
\(235\) 2.13184 3.69245i 0.139066 0.240869i
\(236\) 11.1241 19.2676i 0.724119 1.25421i
\(237\) 0 0
\(238\) 40.1785 6.97016i 2.60439 0.451808i
\(239\) −16.1037 −1.04166 −0.520831 0.853660i \(-0.674378\pi\)
−0.520831 + 0.853660i \(0.674378\pi\)
\(240\) 0 0
\(241\) 2.00300 + 3.46930i 0.129025 + 0.223477i 0.923299 0.384082i \(-0.125482\pi\)
−0.794274 + 0.607559i \(0.792149\pi\)
\(242\) 12.7217 22.0346i 0.817779 1.41643i
\(243\) 0 0
\(244\) −4.08548 7.07625i −0.261546 0.453011i
\(245\) 5.24279 + 4.44882i 0.334949 + 0.284225i
\(246\) 0 0
\(247\) −9.15497 + 10.3234i −0.582517 + 0.656864i
\(248\) 6.07631 10.5245i 0.385846 0.668305i
\(249\) 0 0
\(250\) −10.5969 + 18.3544i −0.670209 + 1.16084i
\(251\) 1.62344 2.81188i 0.102471 0.177484i −0.810231 0.586110i \(-0.800659\pi\)
0.912702 + 0.408626i \(0.133992\pi\)
\(252\) 0 0
\(253\) 2.42763 4.20477i 0.152624 0.264352i
\(254\) 10.1498 0.636853
\(255\) 0 0
\(256\) 13.8778 + 24.0371i 0.867365 + 1.50232i
\(257\) −13.4462 + 23.2895i −0.838751 + 1.45276i 0.0521891 + 0.998637i \(0.483380\pi\)
−0.890940 + 0.454122i \(0.849953\pi\)
\(258\) 0 0
\(259\) −1.60095 + 4.36106i −0.0994784 + 0.270983i
\(260\) −4.14650 12.4410i −0.257155 0.771556i
\(261\) 0 0
\(262\) 5.18100 0.320084
\(263\) 3.80706 0.234753 0.117377 0.993087i \(-0.462552\pi\)
0.117377 + 0.993087i \(0.462552\pi\)
\(264\) 0 0
\(265\) 0.418000 0.0256775
\(266\) 8.33241 22.6978i 0.510893 1.39169i
\(267\) 0 0
\(268\) −12.9836 22.4883i −0.793102 1.37369i
\(269\) −11.9190 20.6444i −0.726716 1.25871i −0.958264 0.285886i \(-0.907712\pi\)
0.231548 0.972824i \(-0.425621\pi\)
\(270\) 0 0
\(271\) −4.95068 + 8.57482i −0.300732 + 0.520883i −0.976302 0.216413i \(-0.930564\pi\)
0.675570 + 0.737296i \(0.263898\pi\)
\(272\) 14.8750 0.901931
\(273\) 0 0
\(274\) −19.9715 −1.20653
\(275\) 1.18593 2.05409i 0.0715142 0.123866i
\(276\) 0 0
\(277\) −5.89289 10.2068i −0.354069 0.613266i 0.632889 0.774243i \(-0.281869\pi\)
−0.986958 + 0.160977i \(0.948536\pi\)
\(278\) 0.688846 + 1.19312i 0.0413142 + 0.0715584i
\(279\) 0 0
\(280\) 6.77022 + 8.11385i 0.404598 + 0.484895i
\(281\) −12.9976 −0.775372 −0.387686 0.921791i \(-0.626726\pi\)
−0.387686 + 0.921791i \(0.626726\pi\)
\(282\) 0 0
\(283\) −16.8050 −0.998952 −0.499476 0.866328i \(-0.666474\pi\)
−0.499476 + 0.866328i \(0.666474\pi\)
\(284\) −13.3392 −0.791534
\(285\) 0 0
\(286\) 1.60029 + 4.80143i 0.0946270 + 0.283914i
\(287\) 6.22369 + 7.45886i 0.367373 + 0.440283i
\(288\) 0 0
\(289\) −12.3283 + 21.3533i −0.725197 + 1.25608i
\(290\) 4.64474 + 8.04493i 0.272749 + 0.472414i
\(291\) 0 0
\(292\) 18.2702 1.06918
\(293\) −7.04782 + 12.2072i −0.411738 + 0.713151i −0.995080 0.0990757i \(-0.968411\pi\)
0.583342 + 0.812227i \(0.301745\pi\)
\(294\) 0 0
\(295\) −2.95108 + 5.11141i −0.171818 + 0.297598i
\(296\) −3.56985 + 6.18316i −0.207493 + 0.359389i
\(297\) 0 0
\(298\) 3.35116 5.80438i 0.194128 0.336239i
\(299\) −9.41686 28.2539i −0.544591 1.63397i
\(300\) 0 0
\(301\) −5.81784 + 15.8480i −0.335335 + 0.913464i
\(302\) 27.4754 + 47.5888i 1.58103 + 2.73843i
\(303\) 0 0
\(304\) 4.40993 7.63822i 0.252927 0.438082i
\(305\) 1.08382 + 1.87723i 0.0620593 + 0.107490i
\(306\) 0 0
\(307\) 15.8786 0.906240 0.453120 0.891450i \(-0.350311\pi\)
0.453120 + 0.891450i \(0.350311\pi\)
\(308\) −3.68922 4.42140i −0.210213 0.251932i
\(309\) 0 0
\(310\) −3.50535 + 6.07145i −0.199091 + 0.344835i
\(311\) −14.3017 + 24.7713i −0.810975 + 1.40465i 0.101208 + 0.994865i \(0.467729\pi\)
−0.912183 + 0.409784i \(0.865604\pi\)
\(312\) 0 0
\(313\) 9.28962 + 16.0901i 0.525080 + 0.909465i 0.999573 + 0.0292063i \(0.00929798\pi\)
−0.474493 + 0.880259i \(0.657369\pi\)
\(314\) −26.9561 46.6893i −1.52122 2.63483i
\(315\) 0 0
\(316\) −5.15679 + 8.93182i −0.290092 + 0.502454i
\(317\) 15.3223 + 26.5389i 0.860584 + 1.49057i 0.871366 + 0.490633i \(0.163234\pi\)
−0.0107826 + 0.999942i \(0.503432\pi\)
\(318\) 0 0
\(319\) −1.16390 2.01594i −0.0651660 0.112871i
\(320\) −5.34685 9.26102i −0.298898 0.517707i
\(321\) 0 0
\(322\) 33.4352 + 40.0709i 1.86327 + 2.23306i
\(323\) 12.3498 + 21.3904i 0.687160 + 1.19020i
\(324\) 0 0
\(325\) −4.60026 13.8024i −0.255177 0.765620i
\(326\) −9.76366 + 16.9112i −0.540759 + 0.936622i
\(327\) 0 0
\(328\) 7.46483 + 12.9295i 0.412177 + 0.713911i
\(329\) −7.35752 8.81772i −0.405633 0.486136i
\(330\) 0 0
\(331\) 27.2277 1.49657 0.748284 0.663378i \(-0.230878\pi\)
0.748284 + 0.663378i \(0.230878\pi\)
\(332\) −5.31005 9.19728i −0.291427 0.504766i
\(333\) 0 0
\(334\) 5.55867 0.304157
\(335\) 3.44438 + 5.96584i 0.188187 + 0.325949i
\(336\) 0 0
\(337\) −12.3160 −0.670898 −0.335449 0.942058i \(-0.608888\pi\)
−0.335449 + 0.942058i \(0.608888\pi\)
\(338\) 28.5481 + 12.1969i 1.55281 + 0.663426i
\(339\) 0 0
\(340\) −23.4746 −1.27309
\(341\) 0.878389 1.52141i 0.0475674 0.0823892i
\(342\) 0 0
\(343\) 16.1152 9.12688i 0.870140 0.492805i
\(344\) −12.9728 + 22.4695i −0.699445 + 1.21148i
\(345\) 0 0
\(346\) −9.71182 + 16.8214i −0.522111 + 0.904322i
\(347\) 3.07253 + 5.32177i 0.164942 + 0.285688i 0.936635 0.350308i \(-0.113923\pi\)
−0.771693 + 0.635996i \(0.780590\pi\)
\(348\) 0 0
\(349\) −6.51563 11.2854i −0.348774 0.604094i 0.637258 0.770650i \(-0.280068\pi\)
−0.986032 + 0.166557i \(0.946735\pi\)
\(350\) 16.3336 + 19.5752i 0.873065 + 1.04634i
\(351\) 0 0
\(352\) 0.772550 + 1.33810i 0.0411771 + 0.0713208i
\(353\) −31.6665 −1.68544 −0.842718 0.538356i \(-0.819046\pi\)
−0.842718 + 0.538356i \(0.819046\pi\)
\(354\) 0 0
\(355\) 3.53870 0.187814
\(356\) 7.75021 0.410761
\(357\) 0 0
\(358\) −25.0655 + 43.4147i −1.32475 + 2.29454i
\(359\) 9.96610 + 17.2618i 0.525991 + 0.911043i 0.999542 + 0.0302764i \(0.00963874\pi\)
−0.473551 + 0.880767i \(0.657028\pi\)
\(360\) 0 0
\(361\) −4.35488 −0.229204
\(362\) 1.92007 3.32566i 0.100917 0.174793i
\(363\) 0 0
\(364\) −35.3057 1.06350i −1.85052 0.0557426i
\(365\) −4.84684 −0.253695
\(366\) 0 0
\(367\) 19.7190 1.02932 0.514662 0.857393i \(-0.327918\pi\)
0.514662 + 0.857393i \(0.327918\pi\)
\(368\) 9.51844 + 16.4864i 0.496183 + 0.859414i
\(369\) 0 0
\(370\) 2.05940 3.56699i 0.107063 0.185439i
\(371\) 0.387993 1.05691i 0.0201436 0.0548719i
\(372\) 0 0
\(373\) 17.5469 0.908544 0.454272 0.890863i \(-0.349899\pi\)
0.454272 + 0.890863i \(0.349899\pi\)
\(374\) 9.05972 0.468467
\(375\) 0 0
\(376\) −8.82478 15.2850i −0.455103 0.788262i
\(377\) −13.9887 2.86308i −0.720452 0.147456i
\(378\) 0 0
\(379\) 5.85068 + 10.1337i 0.300529 + 0.520532i 0.976256 0.216620i \(-0.0695034\pi\)
−0.675727 + 0.737152i \(0.736170\pi\)
\(380\) −6.95942 + 12.0541i −0.357010 + 0.618360i
\(381\) 0 0
\(382\) −13.8055 + 23.9119i −0.706352 + 1.22344i
\(383\) 21.5288 1.10007 0.550036 0.835141i \(-0.314614\pi\)
0.550036 + 0.835141i \(0.314614\pi\)
\(384\) 0 0
\(385\) 0.978699 + 1.17293i 0.0498791 + 0.0597783i
\(386\) −28.1536 + 48.7634i −1.43298 + 2.48199i
\(387\) 0 0
\(388\) 28.5000 1.44687
\(389\) 13.2455 22.9419i 0.671574 1.16320i −0.305884 0.952069i \(-0.598952\pi\)
0.977458 0.211131i \(-0.0677147\pi\)
\(390\) 0 0
\(391\) −53.3118 −2.69609
\(392\) 26.8000 9.58703i 1.35360 0.484218i
\(393\) 0 0
\(394\) 3.51267 0.176966
\(395\) 1.36802 2.36949i 0.0688327 0.119222i
\(396\) 0 0
\(397\) −33.7989 −1.69632 −0.848160 0.529740i \(-0.822289\pi\)
−0.848160 + 0.529740i \(0.822289\pi\)
\(398\) 22.4332 1.12447
\(399\) 0 0
\(400\) 4.64989 + 8.05384i 0.232494 + 0.402692i
\(401\) 10.8059 18.7164i 0.539623 0.934655i −0.459301 0.888281i \(-0.651900\pi\)
0.998924 0.0463741i \(-0.0147666\pi\)
\(402\) 0 0
\(403\) −3.40730 10.2231i −0.169730 0.509250i
\(404\) −4.88264 8.45697i −0.242920 0.420750i
\(405\) 0 0
\(406\) 24.6528 4.27676i 1.22350 0.212252i
\(407\) −0.516056 + 0.893835i −0.0255799 + 0.0443058i
\(408\) 0 0
\(409\) −3.87109 6.70492i −0.191413 0.331537i 0.754306 0.656523i \(-0.227974\pi\)
−0.945719 + 0.324986i \(0.894640\pi\)
\(410\) −4.30637 7.45886i −0.212677 0.368367i
\(411\) 0 0
\(412\) 20.1093 34.8303i 0.990714 1.71597i
\(413\) 10.1849 + 12.2062i 0.501167 + 0.600630i
\(414\) 0 0
\(415\) 1.40868 + 2.43991i 0.0691495 + 0.119770i
\(416\) 9.28509 + 1.90040i 0.455239 + 0.0931746i
\(417\) 0 0
\(418\) 2.68589 4.65211i 0.131371 0.227542i
\(419\) −4.05097 7.01649i −0.197903 0.342778i 0.749945 0.661500i \(-0.230080\pi\)
−0.947848 + 0.318722i \(0.896746\pi\)
\(420\) 0 0
\(421\) −32.1124 −1.56506 −0.782530 0.622612i \(-0.786071\pi\)
−0.782530 + 0.622612i \(0.786071\pi\)
\(422\) −21.3543 −1.03951
\(423\) 0 0
\(424\) 0.865159 1.49850i 0.0420158 0.0727735i
\(425\) −26.0435 −1.26330
\(426\) 0 0
\(427\) 5.75257 0.997954i 0.278386 0.0482944i
\(428\) 59.1713 2.86015
\(429\) 0 0
\(430\) 7.48384 12.9624i 0.360903 0.625102i
\(431\) 29.5281 1.42232 0.711159 0.703031i \(-0.248171\pi\)
0.711159 + 0.703031i \(0.248171\pi\)
\(432\) 0 0
\(433\) −11.0455 + 19.1314i −0.530813 + 0.919395i 0.468540 + 0.883442i \(0.344780\pi\)
−0.999353 + 0.0359531i \(0.988553\pi\)
\(434\) 12.0979 + 14.4988i 0.580716 + 0.695967i
\(435\) 0 0
\(436\) 34.1938 1.63758
\(437\) −15.8051 + 27.3752i −0.756060 + 1.30953i
\(438\) 0 0
\(439\) 3.17790 5.50428i 0.151673 0.262705i −0.780170 0.625568i \(-0.784867\pi\)
0.931843 + 0.362863i \(0.118201\pi\)
\(440\) 1.17387 + 2.03321i 0.0559622 + 0.0969294i
\(441\) 0 0
\(442\) 36.8718 41.5777i 1.75381 1.97765i
\(443\) −6.78135 11.7456i −0.322192 0.558052i 0.658748 0.752363i \(-0.271086\pi\)
−0.980940 + 0.194311i \(0.937753\pi\)
\(444\) 0 0
\(445\) −2.05602 −0.0974648
\(446\) 52.1060 2.46729
\(447\) 0 0
\(448\) −28.3794 + 4.92325i −1.34080 + 0.232602i
\(449\) 10.9559 18.9762i 0.517041 0.895541i −0.482763 0.875751i \(-0.660367\pi\)
0.999804 0.0197900i \(-0.00629977\pi\)
\(450\) 0 0
\(451\) 1.07911 + 1.86908i 0.0508134 + 0.0880115i
\(452\) −37.6946 −1.77300
\(453\) 0 0
\(454\) 44.3041 2.07930
\(455\) 9.36610 + 0.282132i 0.439090 + 0.0132265i
\(456\) 0 0
\(457\) −7.60732 + 13.1763i −0.355855 + 0.616359i −0.987264 0.159091i \(-0.949144\pi\)
0.631409 + 0.775450i \(0.282477\pi\)
\(458\) 46.2097 2.15924
\(459\) 0 0
\(460\) −15.0213 26.0176i −0.700371 1.21308i
\(461\) −8.10813 + 14.0437i −0.377633 + 0.654080i −0.990717 0.135937i \(-0.956595\pi\)
0.613084 + 0.790018i \(0.289929\pi\)
\(462\) 0 0
\(463\) −1.44769 −0.0672799 −0.0336400 0.999434i \(-0.510710\pi\)
−0.0336400 + 0.999434i \(0.510710\pi\)
\(464\) 9.12705 0.423713
\(465\) 0 0
\(466\) −38.5988 −1.78805
\(467\) 7.00337 + 12.1302i 0.324078 + 0.561319i 0.981325 0.192356i \(-0.0616128\pi\)
−0.657248 + 0.753675i \(0.728279\pi\)
\(468\) 0 0
\(469\) 18.2817 3.17150i 0.844169 0.146446i
\(470\) 5.09091 + 8.81772i 0.234826 + 0.406731i
\(471\) 0 0
\(472\) 12.2160 + 21.1588i 0.562288 + 0.973912i
\(473\) −1.87534 + 3.24818i −0.0862282 + 0.149352i
\(474\) 0 0
\(475\) −7.72100 + 13.3732i −0.354264 + 0.613603i
\(476\) −21.7895 + 59.3553i −0.998719 + 2.72055i
\(477\) 0 0
\(478\) 19.2281 33.3041i 0.879474 1.52329i
\(479\) 30.0243 1.37185 0.685923 0.727674i \(-0.259399\pi\)
0.685923 + 0.727674i \(0.259399\pi\)
\(480\) 0 0
\(481\) 2.00180 + 6.00611i 0.0912742 + 0.273855i
\(482\) −9.56649 −0.435742
\(483\) 0 0
\(484\) 19.7253 + 34.1652i 0.896605 + 1.55296i
\(485\) −7.56065 −0.343312
\(486\) 0 0
\(487\) 14.2452 + 24.6733i 0.645510 + 1.11806i 0.984184 + 0.177152i \(0.0566884\pi\)
−0.338674 + 0.940904i \(0.609978\pi\)
\(488\) 8.97297 0.406187
\(489\) 0 0
\(490\) −15.4606 + 5.53064i −0.698438 + 0.249849i
\(491\) −14.2339 24.6538i −0.642365 1.11261i −0.984903 0.173105i \(-0.944620\pi\)
0.342539 0.939504i \(-0.388713\pi\)
\(492\) 0 0
\(493\) −12.7799 + 22.1354i −0.575578 + 0.996930i
\(494\) −10.4187 31.2598i −0.468759 1.40644i
\(495\) 0 0
\(496\) 3.44406 + 5.96528i 0.154643 + 0.267849i
\(497\) 3.28467 8.94755i 0.147337 0.401353i
\(498\) 0 0
\(499\) 13.1164 + 22.7183i 0.587172 + 1.01701i 0.994601 + 0.103775i \(0.0330921\pi\)
−0.407429 + 0.913237i \(0.633575\pi\)
\(500\) −16.4309 28.4591i −0.734811 1.27273i
\(501\) 0 0
\(502\) 3.87684 + 6.71488i 0.173032 + 0.299700i
\(503\) 4.26588 7.38872i 0.190206 0.329447i −0.755112 0.655595i \(-0.772418\pi\)
0.945318 + 0.326149i \(0.105751\pi\)
\(504\) 0 0
\(505\) 1.29529 + 2.24352i 0.0576398 + 0.0998351i
\(506\) 5.79726 + 10.0412i 0.257720 + 0.446384i
\(507\) 0 0
\(508\) −7.86876 + 13.6291i −0.349120 + 0.604693i
\(509\) −6.51298 + 11.2808i −0.288683 + 0.500014i −0.973496 0.228706i \(-0.926551\pi\)
0.684813 + 0.728719i \(0.259884\pi\)
\(510\) 0 0
\(511\) −4.49890 + 12.2552i −0.199020 + 0.542137i
\(512\) −24.8008 −1.09605
\(513\) 0 0
\(514\) −32.1100 55.6162i −1.41631 2.45312i
\(515\) −5.33472 + 9.24000i −0.235076 + 0.407163i
\(516\) 0 0
\(517\) −1.27571 2.20959i −0.0561055 0.0971775i
\(518\) −7.10753 8.51811i −0.312287 0.374264i
\(519\) 0 0
\(520\) 14.1085 + 2.88761i 0.618698 + 0.126630i
\(521\) 2.23285 3.86741i 0.0978230 0.169434i −0.812960 0.582319i \(-0.802145\pi\)
0.910783 + 0.412885i \(0.135479\pi\)
\(522\) 0 0
\(523\) 1.45406 2.51850i 0.0635815 0.110126i −0.832482 0.554051i \(-0.813081\pi\)
0.896064 + 0.443925i \(0.146414\pi\)
\(524\) −4.01665 + 6.95704i −0.175468 + 0.303920i
\(525\) 0 0
\(526\) −4.54570 + 7.87339i −0.198202 + 0.343296i
\(527\) −19.2898 −0.840277
\(528\) 0 0
\(529\) −22.6139 39.1684i −0.983213 1.70297i
\(530\) −0.499100 + 0.864466i −0.0216795 + 0.0375500i
\(531\) 0 0
\(532\) 24.0187 + 28.7855i 1.04134 + 1.24801i
\(533\) 12.9696 + 2.65451i 0.561775 + 0.114980i
\(534\) 0 0
\(535\) −15.6973 −0.678654
\(536\) 28.5161 1.23171
\(537\) 0 0
\(538\) 56.9262 2.45426
\(539\) 3.87419 1.38590i 0.166873 0.0596948i
\(540\) 0 0
\(541\) 9.23193 + 15.9902i 0.396912 + 0.687471i 0.993343 0.115193i \(-0.0367486\pi\)
−0.596431 + 0.802664i \(0.703415\pi\)
\(542\) −11.8224 20.4770i −0.507815 0.879562i
\(543\) 0 0
\(544\) 8.48277 14.6926i 0.363696 0.629940i
\(545\) −9.07112 −0.388564
\(546\) 0 0
\(547\) 34.9817 1.49571 0.747856 0.663861i \(-0.231083\pi\)
0.747856 + 0.663861i \(0.231083\pi\)
\(548\) 15.4832 26.8177i 0.661411 1.14560i
\(549\) 0 0
\(550\) 2.83204 + 4.90524i 0.120759 + 0.209160i
\(551\) 7.57760 + 13.1248i 0.322817 + 0.559135i
\(552\) 0 0
\(553\) −4.72140 5.65842i −0.200774 0.240621i
\(554\) 28.1449 1.19576
\(555\) 0 0
\(556\) −2.13615 −0.0905930
\(557\) −0.0531413 −0.00225167 −0.00112583 0.999999i \(-0.500358\pi\)
−0.00112583 + 0.999999i \(0.500358\pi\)
\(558\) 0 0
\(559\) 7.27451 + 21.8261i 0.307679 + 0.923146i
\(560\) −5.90148 + 1.02379i −0.249383 + 0.0432629i
\(561\) 0 0
\(562\) 15.5194 26.8804i 0.654646 1.13388i
\(563\) 3.99253 + 6.91527i 0.168265 + 0.291444i 0.937810 0.347149i \(-0.112850\pi\)
−0.769545 + 0.638593i \(0.779517\pi\)
\(564\) 0 0
\(565\) 9.99985 0.420697
\(566\) 20.0655 34.7544i 0.843414 1.46084i
\(567\) 0 0
\(568\) 7.32424 12.6860i 0.307318 0.532291i
\(569\) −13.3621 + 23.1438i −0.560167 + 0.970237i 0.437315 + 0.899308i \(0.355930\pi\)
−0.997481 + 0.0709285i \(0.977404\pi\)
\(570\) 0 0
\(571\) −6.74647 + 11.6852i −0.282331 + 0.489012i −0.971958 0.235153i \(-0.924441\pi\)
0.689627 + 0.724164i \(0.257774\pi\)
\(572\) −7.68799 1.57352i −0.321451 0.0657920i
\(573\) 0 0
\(574\) −22.8569 + 3.96520i −0.954028 + 0.165504i
\(575\) −16.6651 28.8648i −0.694982 1.20374i
\(576\) 0 0
\(577\) −6.00662 + 10.4038i −0.250059 + 0.433115i −0.963542 0.267558i \(-0.913783\pi\)
0.713483 + 0.700673i \(0.247117\pi\)
\(578\) −29.4406 50.9925i −1.22457 2.12101i
\(579\) 0 0
\(580\) −14.4036 −0.598078
\(581\) 7.47684 1.29708i 0.310192 0.0538119i
\(582\) 0 0
\(583\) 0.125067 0.216622i 0.00517974 0.00897158i
\(584\) −10.0318 + 17.3756i −0.415118 + 0.719005i
\(585\) 0 0
\(586\) −16.8305 29.1512i −0.695260 1.20422i
\(587\) 5.21177 + 9.02705i 0.215113 + 0.372586i 0.953307 0.302002i \(-0.0976548\pi\)
−0.738195 + 0.674588i \(0.764321\pi\)
\(588\) 0 0
\(589\) −5.71876 + 9.90518i −0.235637 + 0.408136i
\(590\) −7.04728 12.2062i −0.290132 0.502523i
\(591\) 0 0
\(592\) −2.02339 3.50462i −0.0831610 0.144039i
\(593\) −11.1751 19.3558i −0.458905 0.794847i 0.539998 0.841666i \(-0.318425\pi\)
−0.998903 + 0.0468194i \(0.985091\pi\)
\(594\) 0 0
\(595\) 5.78044 15.7461i 0.236975 0.645528i
\(596\) 5.19607 + 8.99986i 0.212839 + 0.368649i
\(597\) 0 0
\(598\) 69.6759 + 14.2607i 2.84926 + 0.583163i
\(599\) 0.579463 1.00366i 0.0236762 0.0410084i −0.853945 0.520364i \(-0.825796\pi\)
0.877621 + 0.479356i \(0.159130\pi\)
\(600\) 0 0
\(601\) −21.0907 36.5301i −0.860306 1.49009i −0.871633 0.490158i \(-0.836939\pi\)
0.0113271 0.999936i \(-0.496394\pi\)
\(602\) −25.8287 30.9547i −1.05270 1.26162i
\(603\) 0 0
\(604\) −85.2029 −3.46686
\(605\) −5.23284 9.06355i −0.212745 0.368486i
\(606\) 0 0
\(607\) −18.1569 −0.736965 −0.368482 0.929635i \(-0.620123\pi\)
−0.368482 + 0.929635i \(0.620123\pi\)
\(608\) −5.02970 8.71169i −0.203981 0.353306i
\(609\) 0 0
\(610\) −5.17640 −0.209586
\(611\) −15.3324 3.13811i −0.620282 0.126954i
\(612\) 0 0
\(613\) −0.902645 −0.0364575 −0.0182288 0.999834i \(-0.505803\pi\)
−0.0182288 + 0.999834i \(0.505803\pi\)
\(614\) −18.9594 + 32.8386i −0.765137 + 1.32526i
\(615\) 0 0
\(616\) 6.23055 1.08087i 0.251036 0.0435497i
\(617\) −13.0218 + 22.5544i −0.524238 + 0.908008i 0.475363 + 0.879790i \(0.342317\pi\)
−0.999602 + 0.0282180i \(0.991017\pi\)
\(618\) 0 0
\(619\) −13.4171 + 23.2390i −0.539277 + 0.934056i 0.459666 + 0.888092i \(0.347969\pi\)
−0.998943 + 0.0459638i \(0.985364\pi\)
\(620\) −5.43515 9.41396i −0.218281 0.378074i
\(621\) 0 0
\(622\) −34.1530 59.1547i −1.36941 2.37189i
\(623\) −1.90843 + 5.19863i −0.0764596 + 0.208279i
\(624\) 0 0
\(625\) −5.72894 9.92281i −0.229158 0.396912i
\(626\) −44.3679 −1.77330
\(627\) 0 0
\(628\) 83.5925 3.33570
\(629\) 11.3328 0.451869
\(630\) 0 0
\(631\) 16.8061 29.1089i 0.669039 1.15881i −0.309135 0.951018i \(-0.600039\pi\)
0.978173 0.207791i \(-0.0666273\pi\)
\(632\) −5.66296 9.80853i −0.225260 0.390162i
\(633\) 0 0
\(634\) −73.1802 −2.90636
\(635\) 2.08747 3.61561i 0.0828388 0.143481i
\(636\) 0 0
\(637\) 9.40711 23.4202i 0.372723 0.927942i
\(638\) 5.55889 0.220078
\(639\) 0 0
\(640\) 20.3729 0.805310
\(641\) 10.5921 + 18.3460i 0.418361 + 0.724622i 0.995775 0.0918294i \(-0.0292714\pi\)
−0.577414 + 0.816452i \(0.695938\pi\)
\(642\) 0 0
\(643\) −0.330770 + 0.572910i −0.0130443 + 0.0225933i −0.872474 0.488661i \(-0.837486\pi\)
0.859430 + 0.511254i \(0.170819\pi\)
\(644\) −79.7282 + 13.8312i −3.14173 + 0.545027i
\(645\) 0 0
\(646\) −58.9834 −2.32067
\(647\) 40.0323 1.57383 0.786916 0.617060i \(-0.211676\pi\)
0.786916 + 0.617060i \(0.211676\pi\)
\(648\) 0 0
\(649\) 1.76594 + 3.05870i 0.0693193 + 0.120065i
\(650\) 34.0376 + 6.96654i 1.33506 + 0.273250i
\(651\) 0 0
\(652\) −15.1388 26.2212i −0.592883 1.02690i
\(653\) 6.35602 11.0089i 0.248730 0.430813i −0.714444 0.699693i \(-0.753320\pi\)
0.963174 + 0.268880i \(0.0866534\pi\)
\(654\) 0 0
\(655\) 1.06556 1.84560i 0.0416349 0.0721138i
\(656\) −8.46215 −0.330391
\(657\) 0 0
\(658\) 27.0209 4.68759i 1.05339 0.182741i
\(659\) −7.09522 + 12.2893i −0.276391 + 0.478723i −0.970485 0.241161i \(-0.922472\pi\)
0.694094 + 0.719884i \(0.255805\pi\)
\(660\) 0 0
\(661\) 50.1780 1.95170 0.975848 0.218449i \(-0.0700996\pi\)
0.975848 + 0.218449i \(0.0700996\pi\)
\(662\) −32.5104 + 56.3096i −1.26355 + 2.18853i
\(663\) 0 0
\(664\) 11.6625 0.452594
\(665\) −6.37183 7.63640i −0.247089 0.296127i
\(666\) 0 0
\(667\) −32.7112 −1.26658
\(668\) −4.30944 + 7.46417i −0.166737 + 0.288797i
\(669\) 0 0
\(670\) −16.4506 −0.635542
\(671\) 1.29713 0.0500751
\(672\) 0 0
\(673\) 0.937137 + 1.62317i 0.0361240 + 0.0625685i 0.883522 0.468389i \(-0.155166\pi\)
−0.847398 + 0.530958i \(0.821832\pi\)
\(674\) 14.7056 25.4708i 0.566438 0.981100i
\(675\) 0 0
\(676\) −38.5104 + 28.8785i −1.48117 + 1.11071i
\(677\) −1.00439 1.73966i −0.0386020 0.0668607i 0.846079 0.533058i \(-0.178957\pi\)
−0.884681 + 0.466197i \(0.845624\pi\)
\(678\) 0 0
\(679\) −7.01790 + 19.1170i −0.269322 + 0.733644i
\(680\) 12.8894 22.3251i 0.494286 0.856128i
\(681\) 0 0
\(682\) 2.09762 + 3.63319i 0.0803222 + 0.139122i
\(683\) −7.05061 12.2120i −0.269784 0.467280i 0.699022 0.715100i \(-0.253619\pi\)
−0.968806 + 0.247820i \(0.920286\pi\)
\(684\) 0 0
\(685\) −4.10748 + 7.11437i −0.156939 + 0.271826i
\(686\) −0.366563 + 44.2255i −0.0139955 + 1.68854i
\(687\) 0 0
\(688\) −7.35298 12.7357i −0.280330 0.485546i
\(689\) −0.485139 1.45559i −0.0184823 0.0554536i
\(690\) 0 0
\(691\) 17.8460 30.9102i 0.678895 1.17588i −0.296419 0.955058i \(-0.595793\pi\)
0.975314 0.220822i \(-0.0708741\pi\)
\(692\) −15.0585 26.0820i −0.572437 0.991489i
\(693\) 0 0
\(694\) −14.6746 −0.557041
\(695\) 0.566691 0.0214958
\(696\) 0 0
\(697\) 11.8489 20.5229i 0.448809 0.777360i
\(698\) 31.1191 1.17788
\(699\) 0 0
\(700\) −38.9483 + 6.75674i −1.47211 + 0.255381i
\(701\) 6.15865 0.232609 0.116305 0.993214i \(-0.462895\pi\)
0.116305 + 0.993214i \(0.462895\pi\)
\(702\) 0 0
\(703\) 3.35979 5.81932i 0.126717 0.219480i
\(704\) −6.39918 −0.241178
\(705\) 0 0
\(706\) 37.8103 65.4894i 1.42301 2.46473i
\(707\) 6.87501 1.19268i 0.258561 0.0448552i
\(708\) 0 0
\(709\) 34.0371 1.27829 0.639144 0.769087i \(-0.279289\pi\)
0.639144 + 0.769087i \(0.279289\pi\)
\(710\) −4.22527 + 7.31838i −0.158571 + 0.274654i
\(711\) 0 0
\(712\) −4.25547 + 7.37069i −0.159480 + 0.276228i
\(713\) −12.3434 21.3794i −0.462265 0.800667i
\(714\) 0 0
\(715\) 2.03952 + 0.417432i 0.0762736 + 0.0156111i
\(716\) −38.8648 67.3158i −1.45244 2.51571i
\(717\) 0 0
\(718\) −47.5989 −1.77637
\(719\) 22.9648 0.856444 0.428222 0.903674i \(-0.359140\pi\)
0.428222 + 0.903674i \(0.359140\pi\)
\(720\) 0 0
\(721\) 18.4115 + 22.0655i 0.685679 + 0.821761i
\(722\) 5.19981 9.00633i 0.193517 0.335181i
\(723\) 0 0
\(724\) 2.97712 + 5.15653i 0.110644 + 0.191641i
\(725\) −15.9798 −0.593476
\(726\) 0 0
\(727\) 1.06558 0.0395203 0.0197601 0.999805i \(-0.493710\pi\)
0.0197601 + 0.999805i \(0.493710\pi\)
\(728\) 20.3970 32.9928i 0.755963 1.22280i
\(729\) 0 0
\(730\) 5.78721 10.0237i 0.214194 0.370996i
\(731\) 41.1833 1.52322
\(732\) 0 0
\(733\) 13.1689 + 22.8092i 0.486404 + 0.842476i 0.999878 0.0156289i \(-0.00497504\pi\)
−0.513474 + 0.858105i \(0.671642\pi\)
\(734\) −23.5448 + 40.7809i −0.869056 + 1.50525i
\(735\) 0 0
\(736\) 21.7123 0.800326
\(737\) 4.12228 0.151846
\(738\) 0 0
\(739\) 34.2149 1.25862 0.629308 0.777156i \(-0.283338\pi\)
0.629308 + 0.777156i \(0.283338\pi\)
\(740\) 3.19317 + 5.53073i 0.117383 + 0.203314i
\(741\) 0 0
\(742\) 1.72252 + 2.06438i 0.0632358 + 0.0757857i
\(743\) 11.2391 + 19.4667i 0.412322 + 0.714163i 0.995143 0.0984379i \(-0.0313846\pi\)
−0.582821 + 0.812600i \(0.698051\pi\)
\(744\) 0 0
\(745\) −1.37845 2.38754i −0.0505023 0.0874726i
\(746\) −20.9513 + 36.2888i −0.767083 + 1.32863i
\(747\) 0 0
\(748\) −7.02368 + 12.1654i −0.256811 + 0.444810i
\(749\) −14.5705 + 39.6905i −0.532393 + 1.45026i
\(750\) 0 0
\(751\) 21.2712 36.8428i 0.776197 1.34441i −0.157923 0.987451i \(-0.550480\pi\)
0.934119 0.356961i \(-0.116187\pi\)
\(752\) 10.0038 0.364801
\(753\) 0 0
\(754\) 22.6239 25.5114i 0.823912 0.929069i
\(755\) 22.6031 0.822612
\(756\) 0 0
\(757\) 5.61902 + 9.73243i 0.204227 + 0.353731i 0.949886 0.312596i \(-0.101199\pi\)
−0.745659 + 0.666327i \(0.767865\pi\)
\(758\) −27.9433 −1.01495
\(759\) 0 0
\(760\) −7.64252 13.2372i −0.277223 0.480165i
\(761\) −12.8084 −0.464306 −0.232153 0.972679i \(-0.574577\pi\)
−0.232153 + 0.972679i \(0.574577\pi\)
\(762\) 0 0
\(763\) −8.41994 + 22.9362i −0.304822 + 0.830347i
\(764\) −21.4059 37.0760i −0.774437 1.34136i
\(765\) 0 0
\(766\) −25.7058 + 44.5238i −0.928789 + 1.60871i
\(767\) 21.2244 + 4.34404i 0.766369 + 0.156854i
\(768\) 0 0
\(769\) 25.6759 + 44.4719i 0.925895 + 1.60370i 0.790115 + 0.612958i \(0.210021\pi\)
0.135780 + 0.990739i \(0.456646\pi\)
\(770\) −3.59433 + 0.623543i −0.129531 + 0.0224709i
\(771\) 0 0
\(772\) −43.6529 75.6091i −1.57110 2.72123i
\(773\) 10.0023 + 17.3245i 0.359759 + 0.623120i 0.987920 0.154963i \(-0.0495257\pi\)
−0.628162 + 0.778083i \(0.716192\pi\)
\(774\) 0 0
\(775\) −6.02993 10.4441i −0.216602 0.375165i
\(776\) −15.6487 + 27.1044i −0.561756 + 0.972990i
\(777\) 0 0
\(778\) 31.6308 + 54.7861i 1.13402 + 1.96418i
\(779\) −7.02558 12.1687i −0.251717 0.435987i
\(780\) 0 0
\(781\) 1.05879 1.83388i 0.0378864 0.0656212i
\(782\) 63.6552 110.254i 2.27631 3.94268i
\(783\) 0 0
\(784\) −2.88920 + 15.8721i −0.103186 + 0.566861i
\(785\) −22.1759 −0.791492
\(786\) 0 0
\(787\) −14.6596 25.3911i −0.522558 0.905096i −0.999656 0.0262462i \(-0.991645\pi\)
0.477098 0.878850i \(-0.341689\pi\)
\(788\) −2.72325 + 4.71680i −0.0970117 + 0.168029i
\(789\) 0 0
\(790\) 3.26689 + 5.65842i 0.116231 +