Properties

Label 819.2.et.c.136.4
Level $819$
Weight $2$
Character 819.136
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
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.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 136.4
Character \(\chi\) \(=\) 819.136
Dual form 819.2.et.c.271.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.556084 + 0.556084i) q^{2} +1.38154i q^{4} +(-0.542987 + 2.02645i) q^{5} +(-0.405927 - 2.61443i) q^{7} +(-1.88042 - 1.88042i) q^{8} +O(q^{10})\) \(q+(-0.556084 + 0.556084i) q^{2} +1.38154i q^{4} +(-0.542987 + 2.02645i) q^{5} +(-0.405927 - 2.61443i) q^{7} +(-1.88042 - 1.88042i) q^{8} +(-0.824932 - 1.42882i) q^{10} +(0.632763 - 2.36150i) q^{11} +(1.96880 - 3.02057i) q^{13} +(1.67957 + 1.22811i) q^{14} -0.671737 q^{16} -6.55339 q^{17} +(-7.74006 + 2.07394i) q^{19} +(-2.79963 - 0.750158i) q^{20} +(0.961326 + 1.66506i) q^{22} -3.84618i q^{23} +(0.518448 + 0.299326i) q^{25} +(0.584868 + 2.77451i) q^{26} +(3.61194 - 0.560804i) q^{28} +(1.25425 - 2.17242i) q^{29} +(-0.457027 + 0.122460i) q^{31} +(4.13438 - 4.13438i) q^{32} +(3.64424 - 3.64424i) q^{34} +(5.51843 + 0.597007i) q^{35} +(-5.00037 - 5.00037i) q^{37} +(3.15084 - 5.45741i) q^{38} +(4.83163 - 2.78954i) q^{40} +(11.0034 - 2.94834i) q^{41} +(0.810492 - 0.467938i) q^{43} +(3.26252 + 0.874188i) q^{44} +(2.13880 + 2.13880i) q^{46} +(-7.03848 - 1.88596i) q^{47} +(-6.67045 + 2.12253i) q^{49} +(-0.454751 + 0.121850i) q^{50} +(4.17303 + 2.71998i) q^{52} +(1.08341 - 1.87652i) q^{53} +(4.44190 + 2.56453i) q^{55} +(-4.15291 + 5.67954i) q^{56} +(0.510581 + 1.90552i) q^{58} +(3.92820 - 3.92820i) q^{59} +(8.13407 + 4.69621i) q^{61} +(0.186047 - 0.322243i) q^{62} +3.25466i q^{64} +(5.05200 + 5.62981i) q^{65} +(-11.1395 - 2.98482i) q^{67} -9.05378i q^{68} +(-3.40069 + 2.73672i) q^{70} +(-9.44098 - 2.52970i) q^{71} +(2.62580 + 9.79963i) q^{73} +5.56125 q^{74} +(-2.86524 - 10.6932i) q^{76} +(-6.43083 - 0.695715i) q^{77} +(1.07540 + 1.86264i) q^{79} +(0.364744 - 1.36124i) q^{80} +(-4.47927 + 7.75833i) q^{82} +(-1.52436 - 1.52436i) q^{83} +(3.55840 - 13.2801i) q^{85} +(-0.190489 + 0.710914i) q^{86} +(-5.63048 + 3.25076i) q^{88} +(-4.45304 + 4.45304i) q^{89} +(-8.69623 - 3.92116i) q^{91} +5.31366 q^{92} +(4.96274 - 2.86524i) q^{94} -16.8110i q^{95} +(4.17950 - 15.5981i) q^{97} +(2.52902 - 4.88964i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{12}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.556084 + 0.556084i −0.393211 + 0.393211i −0.875830 0.482619i \(-0.839685\pi\)
0.482619 + 0.875830i \(0.339685\pi\)
\(3\) 0 0
\(4\) 1.38154i 0.690770i
\(5\) −0.542987 + 2.02645i −0.242831 + 0.906258i 0.731630 + 0.681702i \(0.238760\pi\)
−0.974461 + 0.224556i \(0.927907\pi\)
\(6\) 0 0
\(7\) −0.405927 2.61443i −0.153426 0.988160i
\(8\) −1.88042 1.88042i −0.664829 0.664829i
\(9\) 0 0
\(10\) −0.824932 1.42882i −0.260867 0.451834i
\(11\) 0.632763 2.36150i 0.190785 0.712020i −0.802532 0.596608i \(-0.796515\pi\)
0.993318 0.115412i \(-0.0368188\pi\)
\(12\) 0 0
\(13\) 1.96880 3.02057i 0.546048 0.837754i
\(14\) 1.67957 + 1.22811i 0.448884 + 0.328227i
\(15\) 0 0
\(16\) −0.671737 −0.167934
\(17\) −6.55339 −1.58943 −0.794715 0.606983i \(-0.792380\pi\)
−0.794715 + 0.606983i \(0.792380\pi\)
\(18\) 0 0
\(19\) −7.74006 + 2.07394i −1.77569 + 0.475795i −0.989787 0.142552i \(-0.954469\pi\)
−0.785905 + 0.618347i \(0.787803\pi\)
\(20\) −2.79963 0.750158i −0.626016 0.167740i
\(21\) 0 0
\(22\) 0.961326 + 1.66506i 0.204955 + 0.354993i
\(23\) 3.84618i 0.801984i −0.916082 0.400992i \(-0.868665\pi\)
0.916082 0.400992i \(-0.131335\pi\)
\(24\) 0 0
\(25\) 0.518448 + 0.299326i 0.103690 + 0.0598652i
\(26\) 0.584868 + 2.77451i 0.114702 + 0.544126i
\(27\) 0 0
\(28\) 3.61194 0.560804i 0.682592 0.105982i
\(29\) 1.25425 2.17242i 0.232908 0.403408i −0.725755 0.687954i \(-0.758509\pi\)
0.958663 + 0.284545i \(0.0918426\pi\)
\(30\) 0 0
\(31\) −0.457027 + 0.122460i −0.0820844 + 0.0219945i −0.299628 0.954056i \(-0.596862\pi\)
0.217543 + 0.976051i \(0.430196\pi\)
\(32\) 4.13438 4.13438i 0.730863 0.730863i
\(33\) 0 0
\(34\) 3.64424 3.64424i 0.624981 0.624981i
\(35\) 5.51843 + 0.597007i 0.932784 + 0.100913i
\(36\) 0 0
\(37\) −5.00037 5.00037i −0.822055 0.822055i 0.164347 0.986403i \(-0.447448\pi\)
−0.986403 + 0.164347i \(0.947448\pi\)
\(38\) 3.15084 5.45741i 0.511134 0.885309i
\(39\) 0 0
\(40\) 4.83163 2.78954i 0.763948 0.441065i
\(41\) 11.0034 2.94834i 1.71844 0.460454i 0.740970 0.671538i \(-0.234366\pi\)
0.977468 + 0.211084i \(0.0676993\pi\)
\(42\) 0 0
\(43\) 0.810492 0.467938i 0.123599 0.0713598i −0.436926 0.899497i \(-0.643933\pi\)
0.560525 + 0.828138i \(0.310599\pi\)
\(44\) 3.26252 + 0.874188i 0.491843 + 0.131789i
\(45\) 0 0
\(46\) 2.13880 + 2.13880i 0.315349 + 0.315349i
\(47\) −7.03848 1.88596i −1.02667 0.275095i −0.294090 0.955778i \(-0.595017\pi\)
−0.732578 + 0.680683i \(0.761683\pi\)
\(48\) 0 0
\(49\) −6.67045 + 2.12253i −0.952921 + 0.303219i
\(50\) −0.454751 + 0.121850i −0.0643115 + 0.0172322i
\(51\) 0 0
\(52\) 4.17303 + 2.71998i 0.578696 + 0.377194i
\(53\) 1.08341 1.87652i 0.148818 0.257760i −0.781973 0.623312i \(-0.785787\pi\)
0.930791 + 0.365552i \(0.119120\pi\)
\(54\) 0 0
\(55\) 4.44190 + 2.56453i 0.598945 + 0.345801i
\(56\) −4.15291 + 5.67954i −0.554956 + 0.758960i
\(57\) 0 0
\(58\) 0.510581 + 1.90552i 0.0670426 + 0.250206i
\(59\) 3.92820 3.92820i 0.511408 0.511408i −0.403550 0.914958i \(-0.632224\pi\)
0.914958 + 0.403550i \(0.132224\pi\)
\(60\) 0 0
\(61\) 8.13407 + 4.69621i 1.04146 + 0.601288i 0.920247 0.391339i \(-0.127988\pi\)
0.121214 + 0.992626i \(0.461321\pi\)
\(62\) 0.186047 0.322243i 0.0236280 0.0409249i
\(63\) 0 0
\(64\) 3.25466i 0.406832i
\(65\) 5.05200 + 5.62981i 0.626624 + 0.698293i
\(66\) 0 0
\(67\) −11.1395 2.98482i −1.36091 0.364653i −0.496756 0.867890i \(-0.665476\pi\)
−0.864149 + 0.503237i \(0.832142\pi\)
\(68\) 9.05378i 1.09793i
\(69\) 0 0
\(70\) −3.40069 + 2.73672i −0.406461 + 0.327101i
\(71\) −9.44098 2.52970i −1.12044 0.300221i −0.349377 0.936982i \(-0.613607\pi\)
−0.771061 + 0.636762i \(0.780274\pi\)
\(72\) 0 0
\(73\) 2.62580 + 9.79963i 0.307327 + 1.14696i 0.930924 + 0.365214i \(0.119004\pi\)
−0.623597 + 0.781746i \(0.714329\pi\)
\(74\) 5.56125 0.646482
\(75\) 0 0
\(76\) −2.86524 10.6932i −0.328665 1.22660i
\(77\) −6.43083 0.695715i −0.732862 0.0792841i
\(78\) 0 0
\(79\) 1.07540 + 1.86264i 0.120992 + 0.209564i 0.920159 0.391545i \(-0.128059\pi\)
−0.799167 + 0.601109i \(0.794726\pi\)
\(80\) 0.364744 1.36124i 0.0407796 0.152192i
\(81\) 0 0
\(82\) −4.47927 + 7.75833i −0.494653 + 0.856764i
\(83\) −1.52436 1.52436i −0.167320 0.167320i 0.618480 0.785801i \(-0.287749\pi\)
−0.785801 + 0.618480i \(0.787749\pi\)
\(84\) 0 0
\(85\) 3.55840 13.2801i 0.385963 1.44043i
\(86\) −0.190489 + 0.710914i −0.0205409 + 0.0766598i
\(87\) 0 0
\(88\) −5.63048 + 3.25076i −0.600212 + 0.346532i
\(89\) −4.45304 + 4.45304i −0.472021 + 0.472021i −0.902568 0.430547i \(-0.858321\pi\)
0.430547 + 0.902568i \(0.358321\pi\)
\(90\) 0 0
\(91\) −8.69623 3.92116i −0.911613 0.411050i
\(92\) 5.31366 0.553987
\(93\) 0 0
\(94\) 4.96274 2.86524i 0.511867 0.295527i
\(95\) 16.8110i 1.72477i
\(96\) 0 0
\(97\) 4.17950 15.5981i 0.424363 1.58375i −0.340946 0.940083i \(-0.610747\pi\)
0.765309 0.643663i \(-0.222586\pi\)
\(98\) 2.52902 4.88964i 0.255470 0.493928i
\(99\) 0 0
\(100\) −0.413531 + 0.716257i −0.0413531 + 0.0716257i
\(101\) 1.76991 + 3.06558i 0.176113 + 0.305037i 0.940546 0.339667i \(-0.110314\pi\)
−0.764433 + 0.644703i \(0.776981\pi\)
\(102\) 0 0
\(103\) −4.58234 7.93684i −0.451511 0.782041i 0.546969 0.837153i \(-0.315782\pi\)
−0.998480 + 0.0551124i \(0.982448\pi\)
\(104\) −9.38211 + 1.97776i −0.919992 + 0.193935i
\(105\) 0 0
\(106\) 0.441036 + 1.64597i 0.0428372 + 0.159871i
\(107\) 2.01759 0.195048 0.0975240 0.995233i \(-0.468908\pi\)
0.0975240 + 0.995233i \(0.468908\pi\)
\(108\) 0 0
\(109\) −1.45769 5.44016i −0.139621 0.521073i −0.999936 0.0113102i \(-0.996400\pi\)
0.860315 0.509763i \(-0.170267\pi\)
\(110\) −3.89616 + 1.04397i −0.371485 + 0.0995390i
\(111\) 0 0
\(112\) 0.272676 + 1.75621i 0.0257655 + 0.165946i
\(113\) 6.20648 + 10.7499i 0.583857 + 1.01127i 0.995017 + 0.0997064i \(0.0317904\pi\)
−0.411160 + 0.911563i \(0.634876\pi\)
\(114\) 0 0
\(115\) 7.79411 + 2.08842i 0.726804 + 0.194747i
\(116\) 3.00129 + 1.73279i 0.278663 + 0.160886i
\(117\) 0 0
\(118\) 4.36881i 0.402182i
\(119\) 2.66020 + 17.1334i 0.243860 + 1.57061i
\(120\) 0 0
\(121\) 4.34997 + 2.51145i 0.395451 + 0.228314i
\(122\) −7.13471 + 1.91174i −0.645947 + 0.173081i
\(123\) 0 0
\(124\) −0.169183 0.631401i −0.0151931 0.0567015i
\(125\) −8.30541 + 8.30541i −0.742859 + 0.742859i
\(126\) 0 0
\(127\) −9.05461 5.22768i −0.803467 0.463882i 0.0412153 0.999150i \(-0.486877\pi\)
−0.844682 + 0.535269i \(0.820210\pi\)
\(128\) 6.45891 + 6.45891i 0.570892 + 0.570892i
\(129\) 0 0
\(130\) −5.93999 0.321313i −0.520971 0.0281810i
\(131\) −18.0680 + 10.4315i −1.57860 + 0.911408i −0.583550 + 0.812077i \(0.698337\pi\)
−0.995055 + 0.0993303i \(0.968330\pi\)
\(132\) 0 0
\(133\) 8.56407 + 19.3940i 0.742599 + 1.68167i
\(134\) 7.85430 4.53468i 0.678508 0.391737i
\(135\) 0 0
\(136\) 12.3231 + 12.3231i 1.05670 + 1.05670i
\(137\) −7.97181 7.97181i −0.681078 0.681078i 0.279165 0.960243i \(-0.409942\pi\)
−0.960243 + 0.279165i \(0.909942\pi\)
\(138\) 0 0
\(139\) −8.83314 + 5.09981i −0.749217 + 0.432561i −0.825411 0.564532i \(-0.809057\pi\)
0.0761940 + 0.997093i \(0.475723\pi\)
\(140\) −0.824789 + 7.62393i −0.0697074 + 0.644340i
\(141\) 0 0
\(142\) 6.65671 3.84325i 0.558618 0.322518i
\(143\) −5.88729 6.56064i −0.492320 0.548628i
\(144\) 0 0
\(145\) 3.72127 + 3.72127i 0.309035 + 0.309035i
\(146\) −6.90958 3.98925i −0.571841 0.330153i
\(147\) 0 0
\(148\) 6.90821 6.90821i 0.567852 0.567852i
\(149\) 1.21789 + 4.54523i 0.0997734 + 0.372359i 0.997700 0.0677861i \(-0.0215935\pi\)
−0.897926 + 0.440145i \(0.854927\pi\)
\(150\) 0 0
\(151\) 0.563961 0.151113i 0.0458945 0.0122974i −0.235799 0.971802i \(-0.575771\pi\)
0.281693 + 0.959505i \(0.409104\pi\)
\(152\) 18.4545 + 10.6547i 1.49685 + 0.864210i
\(153\) 0 0
\(154\) 3.96296 3.18921i 0.319344 0.256994i
\(155\) 0.992638i 0.0797306i
\(156\) 0 0
\(157\) −9.61395 5.55061i −0.767276 0.442987i 0.0646257 0.997910i \(-0.479415\pi\)
−0.831902 + 0.554922i \(0.812748\pi\)
\(158\) −1.63380 0.437774i −0.129978 0.0348275i
\(159\) 0 0
\(160\) 6.13322 + 10.6231i 0.484874 + 0.839826i
\(161\) −10.0556 + 1.56127i −0.792489 + 0.123045i
\(162\) 0 0
\(163\) 15.9158 4.26463i 1.24662 0.334031i 0.425592 0.904915i \(-0.360066\pi\)
0.821031 + 0.570884i \(0.193399\pi\)
\(164\) 4.07326 + 15.2016i 0.318068 + 1.18705i
\(165\) 0 0
\(166\) 1.69535 0.131584
\(167\) −0.00245012 0.00914399i −0.000189596 0.000707583i 0.965831 0.259173i \(-0.0834499\pi\)
−0.966021 + 0.258465i \(0.916783\pi\)
\(168\) 0 0
\(169\) −5.24763 11.8938i −0.403664 0.914907i
\(170\) 5.40610 + 9.36364i 0.414629 + 0.718159i
\(171\) 0 0
\(172\) 0.646475 + 1.11973i 0.0492933 + 0.0853784i
\(173\) −10.4806 + 18.1529i −0.796823 + 1.38014i 0.124852 + 0.992175i \(0.460154\pi\)
−0.921675 + 0.387963i \(0.873179\pi\)
\(174\) 0 0
\(175\) 0.572114 1.47695i 0.0432478 0.111647i
\(176\) −0.425051 + 1.58631i −0.0320394 + 0.119573i
\(177\) 0 0
\(178\) 4.95253i 0.371208i
\(179\) 8.35625 4.82448i 0.624576 0.360599i −0.154073 0.988060i \(-0.549239\pi\)
0.778648 + 0.627461i \(0.215906\pi\)
\(180\) 0 0
\(181\) 1.25766 0.0934813 0.0467407 0.998907i \(-0.485117\pi\)
0.0467407 + 0.998907i \(0.485117\pi\)
\(182\) 7.01633 2.65534i 0.520085 0.196827i
\(183\) 0 0
\(184\) −7.23244 + 7.23244i −0.533183 + 0.533183i
\(185\) 12.8481 7.41788i 0.944614 0.545373i
\(186\) 0 0
\(187\) −4.14674 + 15.4759i −0.303240 + 1.13171i
\(188\) 2.60552 9.72395i 0.190027 0.709192i
\(189\) 0 0
\(190\) 9.34833 + 9.34833i 0.678199 + 0.678199i
\(191\) 1.22251 2.11745i 0.0884578 0.153213i −0.818402 0.574647i \(-0.805139\pi\)
0.906859 + 0.421433i \(0.138473\pi\)
\(192\) 0 0
\(193\) 4.45444 16.6242i 0.320638 1.19664i −0.597987 0.801506i \(-0.704033\pi\)
0.918625 0.395131i \(-0.129301\pi\)
\(194\) 6.34970 + 10.9980i 0.455882 + 0.789610i
\(195\) 0 0
\(196\) −2.93236 9.21550i −0.209454 0.658250i
\(197\) −6.05858 22.6109i −0.431656 1.61096i −0.748944 0.662634i \(-0.769439\pi\)
0.317287 0.948329i \(-0.397228\pi\)
\(198\) 0 0
\(199\) −18.6415 −1.32146 −0.660732 0.750622i \(-0.729754\pi\)
−0.660732 + 0.750622i \(0.729754\pi\)
\(200\) −0.412042 1.53776i −0.0291357 0.108736i
\(201\) 0 0
\(202\) −2.68894 0.720500i −0.189193 0.0506942i
\(203\) −6.18877 2.39729i −0.434366 0.168257i
\(204\) 0 0
\(205\) 23.8987i 1.66916i
\(206\) 6.96172 + 1.86539i 0.485046 + 0.129968i
\(207\) 0 0
\(208\) −1.32252 + 2.02903i −0.0917002 + 0.140688i
\(209\) 19.5905i 1.35510i
\(210\) 0 0
\(211\) −5.61294 + 9.72190i −0.386411 + 0.669283i −0.991964 0.126522i \(-0.959619\pi\)
0.605553 + 0.795805i \(0.292952\pi\)
\(212\) 2.59249 + 1.49677i 0.178053 + 0.102799i
\(213\) 0 0
\(214\) −1.12195 + 1.12195i −0.0766950 + 0.0766950i
\(215\) 0.508168 + 1.89651i 0.0346567 + 0.129341i
\(216\) 0 0
\(217\) 0.505682 + 1.14515i 0.0343279 + 0.0777381i
\(218\) 3.83579 + 2.21459i 0.259792 + 0.149991i
\(219\) 0 0
\(220\) −3.54300 + 6.13666i −0.238869 + 0.413734i
\(221\) −12.9023 + 19.7949i −0.867905 + 1.33155i
\(222\) 0 0
\(223\) 9.81982 2.63121i 0.657584 0.176199i 0.0854284 0.996344i \(-0.472774\pi\)
0.572155 + 0.820145i \(0.306107\pi\)
\(224\) −12.4873 9.13079i −0.834343 0.610076i
\(225\) 0 0
\(226\) −9.42920 2.52655i −0.627221 0.168063i
\(227\) 4.65548 + 4.65548i 0.308995 + 0.308995i 0.844520 0.535524i \(-0.179886\pi\)
−0.535524 + 0.844520i \(0.679886\pi\)
\(228\) 0 0
\(229\) 1.20056 + 0.321690i 0.0793354 + 0.0212578i 0.298268 0.954482i \(-0.403591\pi\)
−0.218933 + 0.975740i \(0.570258\pi\)
\(230\) −5.49552 + 3.17284i −0.362364 + 0.209211i
\(231\) 0 0
\(232\) −6.44358 + 1.72655i −0.423042 + 0.113354i
\(233\) −12.6928 + 7.32822i −0.831536 + 0.480088i −0.854378 0.519652i \(-0.826062\pi\)
0.0228423 + 0.999739i \(0.492728\pi\)
\(234\) 0 0
\(235\) 7.64360 13.2391i 0.498614 0.863624i
\(236\) 5.42696 + 5.42696i 0.353265 + 0.353265i
\(237\) 0 0
\(238\) −11.0069 8.04829i −0.713470 0.521693i
\(239\) 4.85743 4.85743i 0.314201 0.314201i −0.532334 0.846535i \(-0.678685\pi\)
0.846535 + 0.532334i \(0.178685\pi\)
\(240\) 0 0
\(241\) −13.5158 + 13.5158i −0.870627 + 0.870627i −0.992541 0.121914i \(-0.961097\pi\)
0.121914 + 0.992541i \(0.461097\pi\)
\(242\) −3.81553 + 1.02237i −0.245271 + 0.0657202i
\(243\) 0 0
\(244\) −6.48800 + 11.2375i −0.415352 + 0.719410i
\(245\) −0.679246 14.6699i −0.0433955 0.937223i
\(246\) 0 0
\(247\) −8.97418 + 27.4626i −0.571013 + 1.74740i
\(248\) 1.08968 + 0.629127i 0.0691947 + 0.0399496i
\(249\) 0 0
\(250\) 9.23702i 0.584200i
\(251\) 1.37023 + 2.37330i 0.0864880 + 0.149802i 0.906024 0.423226i \(-0.139102\pi\)
−0.819536 + 0.573027i \(0.805769\pi\)
\(252\) 0 0
\(253\) −9.08277 2.43372i −0.571029 0.153007i
\(254\) 7.94215 2.12809i 0.498335 0.133528i
\(255\) 0 0
\(256\) −13.6927 −0.855794
\(257\) 10.9615 0.683758 0.341879 0.939744i \(-0.388937\pi\)
0.341879 + 0.939744i \(0.388937\pi\)
\(258\) 0 0
\(259\) −11.0433 + 15.1029i −0.686198 + 0.938447i
\(260\) −7.77782 + 6.97955i −0.482360 + 0.432853i
\(261\) 0 0
\(262\) 4.24649 15.8481i 0.262349 0.979100i
\(263\) −11.0595 19.1556i −0.681958 1.18119i −0.974383 0.224897i \(-0.927795\pi\)
0.292425 0.956289i \(-0.405538\pi\)
\(264\) 0 0
\(265\) 3.21440 + 3.21440i 0.197459 + 0.197459i
\(266\) −15.5470 6.02233i −0.953249 0.369252i
\(267\) 0 0
\(268\) 4.12365 15.3897i 0.251892 0.940073i
\(269\) 9.12867i 0.556585i −0.960496 0.278292i \(-0.910232\pi\)
0.960496 0.278292i \(-0.0897684\pi\)
\(270\) 0 0
\(271\) 13.7284 13.7284i 0.833942 0.833942i −0.154112 0.988053i \(-0.549252\pi\)
0.988053 + 0.154112i \(0.0492516\pi\)
\(272\) 4.40216 0.266920
\(273\) 0 0
\(274\) 8.86600 0.535614
\(275\) 1.03491 1.03491i 0.0624077 0.0624077i
\(276\) 0 0
\(277\) 28.0822i 1.68730i 0.536896 + 0.843649i \(0.319597\pi\)
−0.536896 + 0.843649i \(0.680403\pi\)
\(278\) 2.07604 7.74789i 0.124513 0.464688i
\(279\) 0 0
\(280\) −9.25434 11.4996i −0.553053 0.687232i
\(281\) −3.79779 3.79779i −0.226557 0.226557i 0.584695 0.811253i \(-0.301214\pi\)
−0.811253 + 0.584695i \(0.801214\pi\)
\(282\) 0 0
\(283\) 0.692540 + 1.19951i 0.0411672 + 0.0713037i 0.885875 0.463924i \(-0.153559\pi\)
−0.844708 + 0.535228i \(0.820226\pi\)
\(284\) 3.49489 13.0431i 0.207383 0.773966i
\(285\) 0 0
\(286\) 6.92210 + 0.374439i 0.409312 + 0.0221410i
\(287\) −12.1748 27.5707i −0.718655 1.62745i
\(288\) 0 0
\(289\) 25.9469 1.52629
\(290\) −4.13868 −0.243032
\(291\) 0 0
\(292\) −13.5386 + 3.62765i −0.792286 + 0.212292i
\(293\) 17.3288 + 4.64324i 1.01236 + 0.271261i 0.726615 0.687045i \(-0.241092\pi\)
0.285745 + 0.958306i \(0.407759\pi\)
\(294\) 0 0
\(295\) 5.82735 + 10.0933i 0.339281 + 0.587653i
\(296\) 18.8056i 1.09305i
\(297\) 0 0
\(298\) −3.20478 1.85028i −0.185648 0.107184i
\(299\) −11.6176 7.57237i −0.671866 0.437922i
\(300\) 0 0
\(301\) −1.55239 1.92902i −0.0894782 0.111187i
\(302\) −0.229578 + 0.397641i −0.0132107 + 0.0228817i
\(303\) 0 0
\(304\) 5.19929 1.39315i 0.298200 0.0799024i
\(305\) −13.9333 + 13.9333i −0.797820 + 0.797820i
\(306\) 0 0
\(307\) −5.47242 + 5.47242i −0.312327 + 0.312327i −0.845811 0.533483i \(-0.820883\pi\)
0.533483 + 0.845811i \(0.320883\pi\)
\(308\) 0.961159 8.88446i 0.0547671 0.506239i
\(309\) 0 0
\(310\) 0.551990 + 0.551990i 0.0313509 + 0.0313509i
\(311\) −3.27357 + 5.66998i −0.185627 + 0.321515i −0.943788 0.330553i \(-0.892765\pi\)
0.758161 + 0.652068i \(0.226098\pi\)
\(312\) 0 0
\(313\) −14.8538 + 8.57583i −0.839585 + 0.484735i −0.857123 0.515111i \(-0.827751\pi\)
0.0175379 + 0.999846i \(0.494417\pi\)
\(314\) 8.43277 2.25955i 0.475889 0.127514i
\(315\) 0 0
\(316\) −2.57332 + 1.48570i −0.144760 + 0.0835774i
\(317\) 15.5081 + 4.15537i 0.871019 + 0.233389i 0.666528 0.745480i \(-0.267780\pi\)
0.204491 + 0.978869i \(0.434446\pi\)
\(318\) 0 0
\(319\) −4.33654 4.33654i −0.242800 0.242800i
\(320\) −6.59541 1.76723i −0.368695 0.0987914i
\(321\) 0 0
\(322\) 4.72354 6.45993i 0.263233 0.359998i
\(323\) 50.7236 13.5914i 2.82234 0.756243i
\(324\) 0 0
\(325\) 1.92486 0.976692i 0.106772 0.0541771i
\(326\) −6.47904 + 11.2220i −0.358841 + 0.621530i
\(327\) 0 0
\(328\) −26.2351 15.1468i −1.44859 0.836345i
\(329\) −2.07358 + 19.1672i −0.114320 + 1.05672i
\(330\) 0 0
\(331\) −1.47690 5.51186i −0.0811776 0.302959i 0.913385 0.407096i \(-0.133459\pi\)
−0.994563 + 0.104137i \(0.966792\pi\)
\(332\) 2.10597 2.10597i 0.115580 0.115580i
\(333\) 0 0
\(334\) 0.00644730 + 0.00372235i 0.000352781 + 0.000203678i
\(335\) 12.0972 20.9529i 0.660940 1.14478i
\(336\) 0 0
\(337\) 6.54996i 0.356799i −0.983958 0.178399i \(-0.942908\pi\)
0.983958 0.178399i \(-0.0570919\pi\)
\(338\) 9.53207 + 3.69583i 0.518476 + 0.201027i
\(339\) 0 0
\(340\) 18.3471 + 4.91608i 0.995009 + 0.266612i
\(341\) 1.15676i 0.0626420i
\(342\) 0 0
\(343\) 8.25691 + 16.5778i 0.445831 + 0.895117i
\(344\) −2.40399 0.644146i −0.129614 0.0347300i
\(345\) 0 0
\(346\) −4.26645 15.9226i −0.229366 0.856005i
\(347\) 22.8051 1.22424 0.612120 0.790765i \(-0.290317\pi\)
0.612120 + 0.790765i \(0.290317\pi\)
\(348\) 0 0
\(349\) −0.529316 1.97543i −0.0283336 0.105743i 0.950311 0.311302i \(-0.100765\pi\)
−0.978645 + 0.205560i \(0.934099\pi\)
\(350\) 0.503164 + 1.13945i 0.0268953 + 0.0609062i
\(351\) 0 0
\(352\) −7.14728 12.3795i −0.380951 0.659827i
\(353\) −6.69454 + 24.9843i −0.356314 + 1.32978i 0.522508 + 0.852634i \(0.324996\pi\)
−0.878823 + 0.477149i \(0.841670\pi\)
\(354\) 0 0
\(355\) 10.2527 17.7581i 0.544154 0.942503i
\(356\) −6.15206 6.15206i −0.326058 0.326058i
\(357\) 0 0
\(358\) −1.96396 + 7.32960i −0.103798 + 0.387381i
\(359\) 3.89528 14.5374i 0.205585 0.767255i −0.783685 0.621158i \(-0.786662\pi\)
0.989270 0.146096i \(-0.0466709\pi\)
\(360\) 0 0
\(361\) 39.1529 22.6049i 2.06068 1.18973i
\(362\) −0.699366 + 0.699366i −0.0367579 + 0.0367579i
\(363\) 0 0
\(364\) 5.41725 12.0142i 0.283941 0.629715i
\(365\) −21.2843 −1.11407
\(366\) 0 0
\(367\) 13.2477 7.64858i 0.691526 0.399253i −0.112657 0.993634i \(-0.535936\pi\)
0.804184 + 0.594381i \(0.202603\pi\)
\(368\) 2.58362i 0.134681i
\(369\) 0 0
\(370\) −3.01968 + 11.2696i −0.156986 + 0.585879i
\(371\) −5.34581 2.07076i −0.277540 0.107509i
\(372\) 0 0
\(373\) 10.2210 17.7032i 0.529221 0.916638i −0.470198 0.882561i \(-0.655817\pi\)
0.999419 0.0340771i \(-0.0108492\pi\)
\(374\) −6.29994 10.9118i −0.325762 0.564237i
\(375\) 0 0
\(376\) 9.68892 + 16.7817i 0.499668 + 0.865450i
\(377\) −4.09257 8.06561i −0.210778 0.415400i
\(378\) 0 0
\(379\) −1.64237 6.12940i −0.0843628 0.314846i 0.910830 0.412782i \(-0.135443\pi\)
−0.995193 + 0.0979355i \(0.968776\pi\)
\(380\) 23.2251 1.19142
\(381\) 0 0
\(382\) 0.497662 + 1.85730i 0.0254626 + 0.0950277i
\(383\) 6.04679 1.62023i 0.308976 0.0827899i −0.100999 0.994887i \(-0.532204\pi\)
0.409975 + 0.912097i \(0.365537\pi\)
\(384\) 0 0
\(385\) 4.90169 12.6540i 0.249813 0.644909i
\(386\) 6.76741 + 11.7215i 0.344452 + 0.596609i
\(387\) 0 0
\(388\) 21.5494 + 5.77414i 1.09400 + 0.293138i
\(389\) −4.72095 2.72564i −0.239362 0.138196i 0.375522 0.926814i \(-0.377464\pi\)
−0.614883 + 0.788618i \(0.710797\pi\)
\(390\) 0 0
\(391\) 25.2055i 1.27470i
\(392\) 16.5345 + 8.55200i 0.835118 + 0.431941i
\(393\) 0 0
\(394\) 15.9427 + 9.20450i 0.803180 + 0.463716i
\(395\) −4.35848 + 1.16785i −0.219299 + 0.0587610i
\(396\) 0 0
\(397\) 2.48129 + 9.26032i 0.124533 + 0.464762i 0.999823 0.0188365i \(-0.00599620\pi\)
−0.875290 + 0.483598i \(0.839330\pi\)
\(398\) 10.3663 10.3663i 0.519614 0.519614i
\(399\) 0 0
\(400\) −0.348261 0.201069i −0.0174130 0.0100534i
\(401\) −26.5226 26.5226i −1.32447 1.32447i −0.910112 0.414362i \(-0.864005\pi\)
−0.414362 0.910112i \(-0.635995\pi\)
\(402\) 0 0
\(403\) −0.529898 + 1.62158i −0.0263961 + 0.0807766i
\(404\) −4.23523 + 2.44521i −0.210710 + 0.121654i
\(405\) 0 0
\(406\) 4.77457 2.10838i 0.236958 0.104637i
\(407\) −14.9724 + 8.64434i −0.742156 + 0.428484i
\(408\) 0 0
\(409\) −21.7339 21.7339i −1.07467 1.07467i −0.996977 0.0776962i \(-0.975244\pi\)
−0.0776962 0.996977i \(-0.524756\pi\)
\(410\) −13.2897 13.2897i −0.656332 0.656332i
\(411\) 0 0
\(412\) 10.9651 6.33069i 0.540210 0.311891i
\(413\) −11.8645 8.67542i −0.583816 0.426889i
\(414\) 0 0
\(415\) 3.91676 2.26134i 0.192266 0.111005i
\(416\) −4.34839 20.6280i −0.213197 1.01137i
\(417\) 0 0
\(418\) −10.8940 10.8940i −0.532842 0.532842i
\(419\) −20.2493 11.6909i −0.989241 0.571138i −0.0841936 0.996449i \(-0.526831\pi\)
−0.905047 + 0.425311i \(0.860165\pi\)
\(420\) 0 0
\(421\) 14.1492 14.1492i 0.689589 0.689589i −0.272552 0.962141i \(-0.587868\pi\)
0.962141 + 0.272552i \(0.0878676\pi\)
\(422\) −2.28493 8.52747i −0.111229 0.415111i
\(423\) 0 0
\(424\) −5.56591 + 1.49138i −0.270305 + 0.0724279i
\(425\) −3.39759 1.96160i −0.164807 0.0951516i
\(426\) 0 0
\(427\) 8.97605 23.1722i 0.434382 1.12138i
\(428\) 2.78739i 0.134733i
\(429\) 0 0
\(430\) −1.33720 0.772034i −0.0644856 0.0372308i
\(431\) 12.7388 + 3.41335i 0.613606 + 0.164415i 0.552220 0.833699i \(-0.313781\pi\)
0.0613869 + 0.998114i \(0.480448\pi\)
\(432\) 0 0
\(433\) −5.53868 9.59327i −0.266172 0.461023i 0.701698 0.712474i \(-0.252426\pi\)
−0.967870 + 0.251451i \(0.919092\pi\)
\(434\) −0.918003 0.355600i −0.0440656 0.0170693i
\(435\) 0 0
\(436\) 7.51581 2.01385i 0.359942 0.0964462i
\(437\) 7.97676 + 29.7697i 0.381580 + 1.42408i
\(438\) 0 0
\(439\) 13.2330 0.631578 0.315789 0.948829i \(-0.397731\pi\)
0.315789 + 0.948829i \(0.397731\pi\)
\(440\) −3.53024 13.1750i −0.168298 0.628095i
\(441\) 0 0
\(442\) −3.83287 18.1824i −0.182311 0.864850i
\(443\) −2.45582 4.25360i −0.116679 0.202095i 0.801770 0.597632i \(-0.203892\pi\)
−0.918450 + 0.395537i \(0.870558\pi\)
\(444\) 0 0
\(445\) −6.60594 11.4418i −0.313151 0.542394i
\(446\) −3.99747 + 6.92382i −0.189286 + 0.327852i
\(447\) 0 0
\(448\) 8.50906 1.32115i 0.402015 0.0624186i
\(449\) −0.246197 + 0.918821i −0.0116188 + 0.0433618i −0.971492 0.237073i \(-0.923812\pi\)
0.959873 + 0.280435i \(0.0904786\pi\)
\(450\) 0 0
\(451\) 27.8501i 1.31141i
\(452\) −14.8515 + 8.57451i −0.698555 + 0.403311i
\(453\) 0 0
\(454\) −5.17768 −0.243001
\(455\) 12.6680 15.4934i 0.593885 0.726341i
\(456\) 0 0
\(457\) −13.6046 + 13.6046i −0.636394 + 0.636394i −0.949664 0.313270i \(-0.898576\pi\)
0.313270 + 0.949664i \(0.398576\pi\)
\(458\) −0.846500 + 0.488727i −0.0395543 + 0.0228367i
\(459\) 0 0
\(460\) −2.88524 + 10.7679i −0.134525 + 0.502055i
\(461\) −1.66867 + 6.22758i −0.0777179 + 0.290047i −0.993836 0.110862i \(-0.964639\pi\)
0.916118 + 0.400909i \(0.131306\pi\)
\(462\) 0 0
\(463\) 7.67988 + 7.67988i 0.356914 + 0.356914i 0.862674 0.505760i \(-0.168788\pi\)
−0.505760 + 0.862674i \(0.668788\pi\)
\(464\) −0.842525 + 1.45930i −0.0391132 + 0.0677461i
\(465\) 0 0
\(466\) 2.98318 11.1334i 0.138193 0.515745i
\(467\) 10.7238 + 18.5741i 0.496236 + 0.859507i 0.999991 0.00434034i \(-0.00138158\pi\)
−0.503754 + 0.863847i \(0.668048\pi\)
\(468\) 0 0
\(469\) −3.28177 + 30.3350i −0.151538 + 1.40074i
\(470\) 3.11157 + 11.6125i 0.143526 + 0.535647i
\(471\) 0 0
\(472\) −14.7733 −0.679997
\(473\) −0.592187 2.21007i −0.0272288 0.101619i
\(474\) 0 0
\(475\) −4.63361 1.24157i −0.212604 0.0569672i
\(476\) −23.6704 + 3.67517i −1.08493 + 0.168451i
\(477\) 0 0
\(478\) 5.40228i 0.247095i
\(479\) 17.4860 + 4.68536i 0.798956 + 0.214080i 0.635126 0.772409i \(-0.280948\pi\)
0.163831 + 0.986489i \(0.447615\pi\)
\(480\) 0 0
\(481\) −24.9487 + 5.25920i −1.13756 + 0.239799i
\(482\) 15.0318i 0.684680i
\(483\) 0 0
\(484\) −3.46968 + 6.00966i −0.157713 + 0.273166i
\(485\) 29.3394 + 16.9391i 1.33223 + 0.769165i
\(486\) 0 0
\(487\) 5.09200 5.09200i 0.230740 0.230740i −0.582261 0.813002i \(-0.697832\pi\)
0.813002 + 0.582261i \(0.197832\pi\)
\(488\) −6.46463 24.1263i −0.292640 1.09215i
\(489\) 0 0
\(490\) 8.53539 + 7.77996i 0.385590 + 0.351463i
\(491\) 24.3966 + 14.0854i 1.10101 + 0.635666i 0.936485 0.350708i \(-0.114059\pi\)
0.164520 + 0.986374i \(0.447392\pi\)
\(492\) 0 0
\(493\) −8.21957 + 14.2367i −0.370191 + 0.641190i
\(494\) −10.2811 20.2619i −0.462568 0.911625i
\(495\) 0 0
\(496\) 0.307002 0.0822609i 0.0137848 0.00369362i
\(497\) −2.78138 + 25.7096i −0.124762 + 1.15323i
\(498\) 0 0
\(499\) −20.3207 5.44491i −0.909678 0.243748i −0.226510 0.974009i \(-0.572732\pi\)
−0.683168 + 0.730261i \(0.739398\pi\)
\(500\) −11.4743 11.4743i −0.513145 0.513145i
\(501\) 0 0
\(502\) −2.08172 0.557794i −0.0929116 0.0248956i
\(503\) 18.9822 10.9594i 0.846374 0.488655i −0.0130514 0.999915i \(-0.504155\pi\)
0.859426 + 0.511260i \(0.170821\pi\)
\(504\) 0 0
\(505\) −7.17330 + 1.92208i −0.319208 + 0.0855314i
\(506\) 6.40414 3.69743i 0.284699 0.164371i
\(507\) 0 0
\(508\) 7.22226 12.5093i 0.320436 0.555011i
\(509\) 2.12967 + 2.12967i 0.0943961 + 0.0943961i 0.752728 0.658332i \(-0.228738\pi\)
−0.658332 + 0.752728i \(0.728738\pi\)
\(510\) 0 0
\(511\) 24.5545 10.8429i 1.08623 0.479661i
\(512\) −5.30352 + 5.30352i −0.234385 + 0.234385i
\(513\) 0 0
\(514\) −6.09550 + 6.09550i −0.268861 + 0.268861i
\(515\) 18.5718 4.97630i 0.818371 0.219282i
\(516\) 0 0
\(517\) −8.90738 + 15.4280i −0.391746 + 0.678525i
\(518\) −2.25746 14.5395i −0.0991871 0.638828i
\(519\) 0 0
\(520\) 1.08653 20.0863i 0.0476476 0.880843i
\(521\) −20.7786 11.9965i −0.910328 0.525578i −0.0297912 0.999556i \(-0.509484\pi\)
−0.880537 + 0.473978i \(0.842818\pi\)
\(522\) 0 0
\(523\) 9.58298i 0.419034i −0.977805 0.209517i \(-0.932811\pi\)
0.977805 0.209517i \(-0.0671892\pi\)
\(524\) −14.4116 24.9616i −0.629573 1.09045i
\(525\) 0 0
\(526\) 16.8021 + 4.50212i 0.732608 + 0.196302i
\(527\) 2.99507 0.802528i 0.130467 0.0349587i
\(528\) 0 0
\(529\) 8.20689 0.356821
\(530\) −3.57496 −0.155286
\(531\) 0 0
\(532\) −26.7935 + 11.8316i −1.16165 + 0.512966i
\(533\) 12.7578 39.0411i 0.552602 1.69106i
\(534\) 0 0
\(535\) −1.09553 + 4.08856i −0.0473637 + 0.176764i
\(536\) 15.3342 + 26.5596i 0.662337 + 1.14720i
\(537\) 0 0
\(538\) 5.07631 + 5.07631i 0.218855 + 0.218855i
\(539\) 0.791552 + 17.0953i 0.0340946 + 0.736349i
\(540\) 0 0
\(541\) −5.61424 + 20.9526i −0.241375 + 0.900823i 0.733796 + 0.679370i \(0.237747\pi\)
−0.975171 + 0.221454i \(0.928920\pi\)
\(542\) 15.2683i 0.655830i
\(543\) 0 0
\(544\) −27.0942 + 27.0942i −1.16166 + 1.16166i
\(545\) 11.8157 0.506131
\(546\) 0 0
\(547\) −24.6132 −1.05238 −0.526191 0.850366i \(-0.676380\pi\)
−0.526191 + 0.850366i \(0.676380\pi\)
\(548\) 11.0134 11.0134i 0.470468 0.470468i
\(549\) 0 0
\(550\) 1.15100i 0.0490788i
\(551\) −5.20248 + 19.4159i −0.221633 + 0.827146i
\(552\) 0 0
\(553\) 4.43321 3.56764i 0.188519 0.151712i
\(554\) −15.6161 15.6161i −0.663464 0.663464i
\(555\) 0 0
\(556\) −7.04560 12.2033i −0.298800 0.517537i
\(557\) −0.132844 + 0.495782i −0.00562880 + 0.0210070i −0.968683 0.248300i \(-0.920128\pi\)
0.963054 + 0.269307i \(0.0867947\pi\)
\(558\) 0 0
\(559\) 0.182263 3.36942i 0.00770889 0.142511i
\(560\) −3.70693 0.401032i −0.156646 0.0169467i
\(561\) 0 0
\(562\) 4.22379 0.178170
\(563\) 43.2008 1.82070 0.910349 0.413842i \(-0.135813\pi\)
0.910349 + 0.413842i \(0.135813\pi\)
\(564\) 0 0
\(565\) −25.1543 + 6.74007i −1.05825 + 0.283557i
\(566\) −1.05214 0.281920i −0.0442248 0.0118500i
\(567\) 0 0
\(568\) 12.9961 + 22.5099i 0.545305 + 0.944496i
\(569\) 30.7249i 1.28805i −0.765003 0.644027i \(-0.777263\pi\)
0.765003 0.644027i \(-0.222737\pi\)
\(570\) 0 0
\(571\) 18.1885 + 10.5012i 0.761167 + 0.439460i 0.829715 0.558188i \(-0.188503\pi\)
−0.0685475 + 0.997648i \(0.521836\pi\)
\(572\) 9.06379 8.13353i 0.378976 0.340080i
\(573\) 0 0
\(574\) 22.1018 + 8.56142i 0.922513 + 0.357347i
\(575\) 1.15126 1.99405i 0.0480110 0.0831574i
\(576\) 0 0
\(577\) −8.56673 + 2.29545i −0.356638 + 0.0955608i −0.432689 0.901543i \(-0.642435\pi\)
0.0760516 + 0.997104i \(0.475769\pi\)
\(578\) −14.4287 + 14.4287i −0.600153 + 0.600153i
\(579\) 0 0
\(580\) −5.14109 + 5.14109i −0.213472 + 0.213472i
\(581\) −3.36655 + 4.60411i −0.139668 + 0.191011i
\(582\) 0 0
\(583\) −3.74587 3.74587i −0.155138 0.155138i
\(584\) 13.4898 23.3650i 0.558212 0.966852i
\(585\) 0 0
\(586\) −12.2183 + 7.05424i −0.504734 + 0.291408i
\(587\) −30.5954 + 8.19801i −1.26281 + 0.338368i −0.827271 0.561803i \(-0.810108\pi\)
−0.435536 + 0.900171i \(0.643441\pi\)
\(588\) 0 0
\(589\) 3.28344 1.89570i 0.135292 0.0781108i
\(590\) −8.85320 2.37221i −0.364480 0.0976622i
\(591\) 0 0
\(592\) 3.35893 + 3.35893i 0.138051 + 0.138051i
\(593\) 5.48978 + 1.47098i 0.225438 + 0.0604060i 0.369770 0.929123i \(-0.379437\pi\)
−0.144332 + 0.989529i \(0.546103\pi\)
\(594\) 0 0
\(595\) −36.1644 3.91242i −1.48260 0.160393i
\(596\) −6.27941 + 1.68256i −0.257215 + 0.0689205i
\(597\) 0 0
\(598\) 10.6713 2.24951i 0.436380 0.0919892i
\(599\) −5.44521 + 9.43138i −0.222485 + 0.385356i −0.955562 0.294790i \(-0.904750\pi\)
0.733077 + 0.680146i \(0.238084\pi\)
\(600\) 0 0
\(601\) −1.42936 0.825243i −0.0583049 0.0336624i 0.470564 0.882366i \(-0.344050\pi\)
−0.528869 + 0.848703i \(0.677384\pi\)
\(602\) 1.93596 + 0.209440i 0.0789037 + 0.00853614i
\(603\) 0 0
\(604\) 0.208769 + 0.779135i 0.00849468 + 0.0317026i
\(605\) −7.45132 + 7.45132i −0.302939 + 0.302939i
\(606\) 0 0
\(607\) 22.6877 + 13.0987i 0.920865 + 0.531662i 0.883911 0.467655i \(-0.154901\pi\)
0.0369540 + 0.999317i \(0.488234\pi\)
\(608\) −23.4259 + 40.5749i −0.950046 + 1.64553i
\(609\) 0 0
\(610\) 15.4962i 0.627423i
\(611\) −19.5540 + 17.5471i −0.791072 + 0.709880i
\(612\) 0 0
\(613\) 22.6882 + 6.07928i 0.916367 + 0.245540i 0.686032 0.727571i \(-0.259351\pi\)
0.230335 + 0.973111i \(0.426018\pi\)
\(614\) 6.08625i 0.245621i
\(615\) 0 0
\(616\) 10.7844 + 13.4009i 0.434517 + 0.539938i
\(617\) 7.41451 + 1.98671i 0.298497 + 0.0799820i 0.404959 0.914335i \(-0.367286\pi\)
−0.106462 + 0.994317i \(0.533952\pi\)
\(618\) 0 0
\(619\) −7.36942 27.5031i −0.296202 1.10544i −0.940258 0.340463i \(-0.889416\pi\)
0.644056 0.764978i \(-0.277250\pi\)
\(620\) 1.37137 0.0550755
\(621\) 0 0
\(622\) −1.33261 4.97337i −0.0534328 0.199414i
\(623\) 13.4498 + 9.83454i 0.538853 + 0.394012i
\(624\) 0 0
\(625\) −10.8242 18.7480i −0.432967 0.749921i
\(626\) 3.49107 13.0288i 0.139531 0.520737i
\(627\) 0 0
\(628\) 7.66840 13.2821i 0.306003 0.530012i
\(629\) 32.7694 + 32.7694i 1.30660 + 1.30660i
\(630\) 0 0
\(631\) −2.62809 + 9.80818i −0.104623 + 0.390458i −0.998302 0.0582487i \(-0.981448\pi\)
0.893679 + 0.448706i \(0.148115\pi\)
\(632\) 1.48035 5.52475i 0.0588852 0.219763i
\(633\) 0 0
\(634\) −10.9345 + 6.31305i −0.434265 + 0.250723i
\(635\) 15.5102 15.5102i 0.615503 0.615503i
\(636\) 0 0
\(637\) −6.72156 + 24.3274i −0.266318 + 0.963885i
\(638\) 4.82296 0.190943
\(639\) 0 0
\(640\) −16.5958 + 9.58157i −0.656005 + 0.378745i
\(641\) 23.1705i 0.915180i −0.889163 0.457590i \(-0.848713\pi\)
0.889163 0.457590i \(-0.151287\pi\)
\(642\) 0 0
\(643\) 6.46488 24.1273i 0.254950 0.951486i −0.713168 0.700993i \(-0.752741\pi\)
0.968118 0.250493i \(-0.0805928\pi\)
\(644\) −2.15696 13.8922i −0.0849959 0.547428i
\(645\) 0 0
\(646\) −20.6487 + 35.7646i −0.812411 + 1.40714i
\(647\) −2.29221 3.97022i −0.0901160 0.156085i 0.817444 0.576008i \(-0.195390\pi\)
−0.907560 + 0.419923i \(0.862057\pi\)
\(648\) 0 0
\(649\) −6.79083 11.7621i −0.266564 0.461702i
\(650\) −0.527259 + 1.61350i −0.0206808 + 0.0632869i
\(651\) 0 0
\(652\) 5.89176 + 21.9883i 0.230739 + 0.861130i
\(653\) 25.4566 0.996192 0.498096 0.867122i \(-0.334033\pi\)
0.498096 + 0.867122i \(0.334033\pi\)
\(654\) 0 0
\(655\) −11.3284 42.2780i −0.442636 1.65194i
\(656\) −7.39138 + 1.98051i −0.288585 + 0.0773260i
\(657\) 0 0
\(658\) −9.50546 11.8116i −0.370561 0.460465i
\(659\) 6.21741 + 10.7689i 0.242196 + 0.419496i 0.961339 0.275366i \(-0.0887990\pi\)
−0.719144 + 0.694861i \(0.755466\pi\)
\(660\) 0 0
\(661\) 36.4077 + 9.75540i 1.41609 + 0.379441i 0.884096 0.467305i \(-0.154775\pi\)
0.531998 + 0.846746i \(0.321442\pi\)
\(662\) 3.88634 + 2.24378i 0.151047 + 0.0872069i
\(663\) 0 0
\(664\) 5.73288i 0.222479i
\(665\) −43.9511 + 6.82403i −1.70435 + 0.264625i
\(666\) 0 0
\(667\) −8.35552 4.82406i −0.323527 0.186788i
\(668\) 0.0126328 0.00338495i 0.000488778 0.000130968i
\(669\) 0 0
\(670\) 4.92454 + 18.3786i 0.190252 + 0.710029i
\(671\) 16.2371 16.2371i 0.626825 0.626825i
\(672\) 0 0
\(673\) 21.1591 + 12.2162i 0.815624 + 0.470901i 0.848905 0.528545i \(-0.177262\pi\)
−0.0332811 + 0.999446i \(0.510596\pi\)
\(674\) 3.64233 + 3.64233i 0.140297 + 0.140297i
\(675\) 0 0
\(676\) 16.4318 7.24981i 0.631991 0.278839i
\(677\) 3.00229 1.73338i 0.115388 0.0666190i −0.441195 0.897411i \(-0.645445\pi\)
0.556583 + 0.830792i \(0.312112\pi\)
\(678\) 0 0
\(679\) −42.4766 4.59530i −1.63010 0.176351i
\(680\) −31.6635 + 18.2810i −1.21424 + 0.701043i
\(681\) 0 0
\(682\) −0.643255 0.643255i −0.0246315 0.0246315i
\(683\) −26.9394 26.9394i −1.03081 1.03081i −0.999510 0.0312978i \(-0.990036\pi\)
−0.0312978 0.999510i \(-0.509964\pi\)
\(684\) 0 0
\(685\) 20.4831 11.8259i 0.782619 0.451845i
\(686\) −13.8102 4.62711i −0.527275 0.176664i
\(687\) 0 0
\(688\) −0.544437 + 0.314331i −0.0207565 + 0.0119838i
\(689\) −3.53513 6.96700i −0.134678 0.265422i
\(690\) 0 0
\(691\) 15.8802 + 15.8802i 0.604110 + 0.604110i 0.941401 0.337290i \(-0.109510\pi\)
−0.337290 + 0.941401i \(0.609510\pi\)
\(692\) −25.0789 14.4793i −0.953359 0.550422i
\(693\) 0 0
\(694\) −12.6815 + 12.6815i −0.481384 + 0.481384i
\(695\) −5.53826 20.6691i −0.210078 0.784023i
\(696\) 0 0
\(697\) −72.1094 + 19.3217i −2.73134 + 0.731860i
\(698\) 1.39285 + 0.804163i 0.0527202 + 0.0304380i
\(699\) 0 0
\(700\) 2.04047 + 0.790399i 0.0771223 + 0.0298743i
\(701\) 43.0296i 1.62520i 0.582819 + 0.812602i \(0.301950\pi\)
−0.582819 + 0.812602i \(0.698050\pi\)
\(702\) 0 0
\(703\) 49.0736 + 28.3327i 1.85085 + 1.06859i
\(704\) 7.68589 + 2.05943i 0.289673 + 0.0776176i
\(705\) 0 0
\(706\) −10.1707 17.6161i −0.382778 0.662992i
\(707\) 7.29628 5.87171i 0.274405 0.220829i
\(708\) 0 0
\(709\) 19.1430 5.12936i 0.718932 0.192637i 0.119237 0.992866i \(-0.461955\pi\)
0.599695 + 0.800228i \(0.295288\pi\)
\(710\) 4.17367 + 15.5763i 0.156635 + 0.584570i
\(711\) 0 0
\(712\) 16.7472 0.627627
\(713\) 0.471003 + 1.75781i 0.0176392 + 0.0658304i
\(714\) 0 0
\(715\) 16.4916 8.36798i 0.616749 0.312945i
\(716\) 6.66522 + 11.5445i 0.249091 + 0.431438i
\(717\) 0 0
\(718\) 5.91791 + 10.2501i 0.220854 + 0.382531i
\(719\) −23.2898 + 40.3391i −0.868563 + 1.50440i −0.00509796 + 0.999987i \(0.501623\pi\)
−0.863465 + 0.504408i \(0.831711\pi\)
\(720\) 0 0
\(721\) −18.8902 + 15.2020i −0.703508 + 0.566151i
\(722\) −9.20205 + 34.3425i −0.342465 + 1.27810i
\(723\) 0 0
\(724\) 1.73751i 0.0645742i
\(725\) 1.30052 0.750858i 0.0483003 0.0278862i
\(726\) 0 0
\(727\) 38.0896 1.41266 0.706332 0.707880i \(-0.250348\pi\)
0.706332 + 0.707880i \(0.250348\pi\)
\(728\) 8.97914 + 23.7260i 0.332789 + 0.879345i
\(729\) 0 0
\(730\) 11.8358 11.8358i 0.438064 0.438064i
\(731\) −5.31147 + 3.06658i −0.196452 + 0.113421i
\(732\) 0 0
\(733\) 8.16549 30.4740i 0.301599 1.12558i −0.634234 0.773141i \(-0.718684\pi\)
0.935833 0.352443i \(-0.114649\pi\)
\(734\) −3.11360 + 11.6201i −0.114925 + 0.428906i
\(735\) 0 0
\(736\) −15.9016 15.9016i −0.586140 0.586140i
\(737\) −14.0973 + 24.4173i −0.519281 + 0.899422i
\(738\) 0 0
\(739\) −7.67265 + 28.6347i −0.282243 + 1.05335i 0.668587 + 0.743634i \(0.266899\pi\)
−0.950830 + 0.309712i \(0.899767\pi\)
\(740\) 10.2481 + 17.7502i 0.376728 + 0.652512i
\(741\) 0 0
\(742\) 4.12424 1.82120i 0.151405 0.0668583i
\(743\) −6.49849 24.2527i −0.238406 0.889745i −0.976584 0.215138i \(-0.930980\pi\)
0.738177 0.674607i \(-0.235687\pi\)
\(744\) 0 0
\(745\) −9.87198 −0.361682
\(746\) 4.16077 + 15.5282i 0.152337 + 0.568528i
\(747\) 0 0
\(748\) −21.3805 5.72890i −0.781750 0.209469i
\(749\) −0.818995 5.27485i −0.0299254 0.192739i
\(750\) 0 0
\(751\) 31.1328i 1.13605i −0.823011 0.568025i \(-0.807707\pi\)
0.823011 0.568025i \(-0.192293\pi\)
\(752\) 4.72801 + 1.26687i 0.172413 + 0.0461979i
\(753\) 0 0
\(754\) 6.76097 + 2.20934i 0.246220 + 0.0804595i
\(755\) 1.22489i 0.0445784i
\(756\) 0 0
\(757\) 1.51455 2.62328i 0.0550472 0.0953446i −0.837189 0.546914i \(-0.815802\pi\)
0.892236 + 0.451570i \(0.149136\pi\)
\(758\) 4.32176 + 2.49517i 0.156973 + 0.0906286i
\(759\) 0 0
\(760\) −31.6118 + 31.6118i −1.14668 + 1.14668i
\(761\) −7.59236 28.3351i −0.275223 1.02715i −0.955692 0.294369i \(-0.904890\pi\)
0.680469 0.732777i \(-0.261776\pi\)
\(762\) 0 0
\(763\) −13.6312 + 6.01932i −0.493482 + 0.217914i
\(764\) 2.92535 + 1.68895i 0.105835 + 0.0611040i
\(765\) 0 0
\(766\) −2.46154 + 4.26351i −0.0889389 + 0.154047i
\(767\) −4.13153 19.5992i −0.149181 0.707687i
\(768\) 0 0
\(769\) −30.9694 + 8.29823i −1.11679 + 0.299242i −0.769582 0.638548i \(-0.779535\pi\)
−0.347203 + 0.937790i \(0.612869\pi\)
\(770\) 4.31095 + 9.76245i 0.155356 + 0.351814i
\(771\) 0 0
\(772\) 22.9670 + 6.15399i 0.826601 + 0.221487i
\(773\) 31.5168 + 31.5168i 1.13358 + 1.13358i 0.989577 + 0.144005i \(0.0459983\pi\)
0.144005 + 0.989577i \(0.454002\pi\)
\(774\) 0 0
\(775\) −0.273600 0.0733109i −0.00982801 0.00263341i
\(776\) −37.1902 + 21.4718i −1.33505 + 0.770791i
\(777\) 0 0
\(778\) 4.14094 1.10956i 0.148460 0.0397797i
\(779\) −79.0521 + 45.6408i −2.83234 + 1.63525i
\(780\) 0 0
\(781\) −11.9478 + 20.6942i −0.427526 + 0.740497i
\(782\) −14.0164 14.0164i −0.501225 0.501225i
\(783\) 0 0
\(784\) 4.48079 1.42578i 0.160028 0.0509208i
\(785\) 16.4683 16.4683i 0.587779 0.587779i
\(786\) 0 0
\(787\) 13.0345 13.0345i 0.464631 0.464631i −0.435539 0.900170i \(-0.643442\pi\)
0.900170 + 0.435539i \(0.143442\pi\)
\(788\) 31.2379 8.37018i 1.11281 0.298175<