Properties

Label 349.2.e.a.123.9
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.9
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.06897 + 0.617172i) q^{2} +(0.625735 - 1.08381i) q^{3} +(-0.238198 + 0.412572i) q^{4} +(0.733047 - 1.26968i) q^{5} +1.54474i q^{6} +(-0.833145 + 0.481016i) q^{7} -3.05672i q^{8} +(0.716910 + 1.24172i) q^{9} +O(q^{10})\) \(q+(-1.06897 + 0.617172i) q^{2} +(0.625735 - 1.08381i) q^{3} +(-0.238198 + 0.412572i) q^{4} +(0.733047 - 1.26968i) q^{5} +1.54474i q^{6} +(-0.833145 + 0.481016i) q^{7} -3.05672i q^{8} +(0.716910 + 1.24172i) q^{9} +1.80966i q^{10} +0.842874i q^{11} +(0.298098 + 0.516321i) q^{12} +(5.14146 - 2.96842i) q^{13} +(0.593739 - 1.02839i) q^{14} +(-0.917388 - 1.58896i) q^{15} +(1.41013 + 2.44241i) q^{16} -2.44219 q^{17} +(-1.53271 - 0.884913i) q^{18} +(3.80272 - 6.58650i) q^{19} +(0.349221 + 0.604869i) q^{20} +1.20396i q^{21} +(-0.520198 - 0.901009i) q^{22} +(0.0324754 + 0.0562491i) q^{23} +(-3.31289 - 1.91270i) q^{24} +(1.42528 + 2.46866i) q^{25} +(-3.66405 + 6.34632i) q^{26} +5.54880 q^{27} -0.458309i q^{28} +(3.19627 - 5.53610i) q^{29} +(1.96132 + 1.13237i) q^{30} -6.39813 q^{31} +(2.27963 + 1.31614i) q^{32} +(0.913511 + 0.527416i) q^{33} +(2.61063 - 1.50725i) q^{34} +1.41043i q^{35} -0.683067 q^{36} +8.13346 q^{37} +9.38771i q^{38} -7.42979i q^{39} +(-3.88105 - 2.24072i) q^{40} -2.84700 q^{41} +(-0.743048 - 1.28700i) q^{42} +(6.80445 + 3.92855i) q^{43} +(-0.347746 - 0.200771i) q^{44} +2.10212 q^{45} +(-0.0694306 - 0.0400858i) q^{46} -10.6006i q^{47} +3.52946 q^{48} +(-3.03725 + 5.26067i) q^{49} +(-3.04718 - 1.75929i) q^{50} +(-1.52816 + 2.64686i) q^{51} +2.82829i q^{52} +3.35841i q^{53} +(-5.93151 + 3.42456i) q^{54} +(1.07018 + 0.617866i) q^{55} +(1.47033 + 2.54669i) q^{56} +(-4.75899 - 8.24281i) q^{57} +7.89058i q^{58} +(1.47326 + 0.850588i) q^{59} +0.874081 q^{60} +10.6426i q^{61} +(6.83943 - 3.94875i) q^{62} +(-1.19458 - 0.689691i) q^{63} -8.88965 q^{64} -8.70398i q^{65} -1.30202 q^{66} -13.7641 q^{67} +(0.581725 - 1.00758i) q^{68} +0.0812841 q^{69} +(-0.870478 - 1.50771i) q^{70} +(-10.5955 + 6.11732i) q^{71} +(3.79561 - 2.19140i) q^{72} +(-0.676506 + 1.17174i) q^{73} +(-8.69444 + 5.01974i) q^{74} +3.56740 q^{75} +(1.81160 + 3.13778i) q^{76} +(-0.405436 - 0.702236i) q^{77} +(4.58545 + 7.94224i) q^{78} -3.87581i q^{79} +4.13476 q^{80} +(1.32135 - 2.28864i) q^{81} +(3.04337 - 1.75709i) q^{82} +(-0.686933 - 1.18980i) q^{83} +(-0.496718 - 0.286780i) q^{84} +(-1.79024 + 3.10079i) q^{85} -9.69837 q^{86} +(-4.00004 - 6.92827i) q^{87} +2.57643 q^{88} +(-10.7719 - 6.21914i) q^{89} +(-2.24711 + 1.29737i) q^{90} +(-2.85572 + 4.94625i) q^{91} -0.0309423 q^{92} +(-4.00354 + 6.93433i) q^{93} +(6.54239 + 11.3318i) q^{94} +(-5.57514 - 9.65643i) q^{95} +(2.85289 - 1.64712i) q^{96} +(0.538617 - 0.310971i) q^{97} -7.49801i q^{98} +(-1.04662 + 0.604265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.06897 + 0.617172i −0.755878 + 0.436406i −0.827814 0.561003i \(-0.810416\pi\)
0.0719360 + 0.997409i \(0.477082\pi\)
\(3\) 0.625735 1.08381i 0.361269 0.625735i −0.626901 0.779099i \(-0.715677\pi\)
0.988170 + 0.153363i \(0.0490104\pi\)
\(4\) −0.238198 + 0.412572i −0.119099 + 0.206286i
\(5\) 0.733047 1.26968i 0.327829 0.567816i −0.654252 0.756277i \(-0.727016\pi\)
0.982081 + 0.188461i \(0.0603497\pi\)
\(6\) 1.54474i 0.630639i
\(7\) −0.833145 + 0.481016i −0.314899 + 0.181807i −0.649117 0.760689i \(-0.724861\pi\)
0.334218 + 0.942496i \(0.391528\pi\)
\(8\) 3.05672i 1.08071i
\(9\) 0.716910 + 1.24172i 0.238970 + 0.413908i
\(10\) 1.80966i 0.572266i
\(11\) 0.842874i 0.254136i 0.991894 + 0.127068i \(0.0405566\pi\)
−0.991894 + 0.127068i \(0.959443\pi\)
\(12\) 0.298098 + 0.516321i 0.0860536 + 0.149049i
\(13\) 5.14146 2.96842i 1.42598 0.823292i 0.429183 0.903218i \(-0.358802\pi\)
0.996801 + 0.0799257i \(0.0254683\pi\)
\(14\) 0.593739 1.02839i 0.158684 0.274848i
\(15\) −0.917388 1.58896i −0.236868 0.410268i
\(16\) 1.41013 + 2.44241i 0.352532 + 0.610603i
\(17\) −2.44219 −0.592318 −0.296159 0.955139i \(-0.595706\pi\)
−0.296159 + 0.955139i \(0.595706\pi\)
\(18\) −1.53271 0.884913i −0.361264 0.208576i
\(19\) 3.80272 6.58650i 0.872403 1.51105i 0.0128987 0.999917i \(-0.495894\pi\)
0.859504 0.511129i \(-0.170773\pi\)
\(20\) 0.349221 + 0.604869i 0.0780883 + 0.135253i
\(21\) 1.20396i 0.262725i
\(22\) −0.520198 0.901009i −0.110907 0.192096i
\(23\) 0.0324754 + 0.0562491i 0.00677159 + 0.0117287i 0.869391 0.494124i \(-0.164511\pi\)
−0.862620 + 0.505853i \(0.831178\pi\)
\(24\) −3.31289 1.91270i −0.676242 0.390428i
\(25\) 1.42528 + 2.46866i 0.285057 + 0.493732i
\(26\) −3.66405 + 6.34632i −0.718580 + 1.24462i
\(27\) 5.54880 1.06787
\(28\) 0.458309i 0.0866123i
\(29\) 3.19627 5.53610i 0.593532 1.02803i −0.400220 0.916419i \(-0.631066\pi\)
0.993752 0.111609i \(-0.0356003\pi\)
\(30\) 1.96132 + 1.13237i 0.358087 + 0.206742i
\(31\) −6.39813 −1.14914 −0.574569 0.818456i \(-0.694830\pi\)
−0.574569 + 0.818456i \(0.694830\pi\)
\(32\) 2.27963 + 1.31614i 0.402985 + 0.232663i
\(33\) 0.913511 + 0.527416i 0.159022 + 0.0918113i
\(34\) 2.61063 1.50725i 0.447720 0.258491i
\(35\) 1.41043i 0.238406i
\(36\) −0.683067 −0.113845
\(37\) 8.13346 1.33713 0.668566 0.743653i \(-0.266908\pi\)
0.668566 + 0.743653i \(0.266908\pi\)
\(38\) 9.38771i 1.52289i
\(39\) 7.42979i 1.18972i
\(40\) −3.88105 2.24072i −0.613647 0.354289i
\(41\) −2.84700 −0.444627 −0.222314 0.974975i \(-0.571361\pi\)
−0.222314 + 0.974975i \(0.571361\pi\)
\(42\) −0.743048 1.28700i −0.114655 0.198588i
\(43\) 6.80445 + 3.92855i 1.03767 + 0.599099i 0.919172 0.393856i \(-0.128859\pi\)
0.118497 + 0.992954i \(0.462192\pi\)
\(44\) −0.347746 0.200771i −0.0524246 0.0302674i
\(45\) 2.10212 0.313365
\(46\) −0.0694306 0.0400858i −0.0102370 0.00591033i
\(47\) 10.6006i 1.54626i −0.634250 0.773128i \(-0.718691\pi\)
0.634250 0.773128i \(-0.281309\pi\)
\(48\) 3.52946 0.509434
\(49\) −3.03725 + 5.26067i −0.433892 + 0.751524i
\(50\) −3.04718 1.75929i −0.430936 0.248801i
\(51\) −1.52816 + 2.64686i −0.213986 + 0.370634i
\(52\) 2.82829i 0.392213i
\(53\) 3.35841i 0.461313i 0.973035 + 0.230657i \(0.0740874\pi\)
−0.973035 + 0.230657i \(0.925913\pi\)
\(54\) −5.93151 + 3.42456i −0.807177 + 0.466024i
\(55\) 1.07018 + 0.617866i 0.144302 + 0.0833131i
\(56\) 1.47033 + 2.54669i 0.196482 + 0.340316i
\(57\) −4.75899 8.24281i −0.630343 1.09179i
\(58\) 7.89058i 1.03608i
\(59\) 1.47326 + 0.850588i 0.191802 + 0.110737i 0.592826 0.805331i \(-0.298012\pi\)
−0.401024 + 0.916068i \(0.631346\pi\)
\(60\) 0.874081 0.112843
\(61\) 10.6426i 1.36265i 0.731981 + 0.681325i \(0.238596\pi\)
−0.731981 + 0.681325i \(0.761404\pi\)
\(62\) 6.83943 3.94875i 0.868608 0.501491i
\(63\) −1.19458 0.689691i −0.150503 0.0868929i
\(64\) −8.88965 −1.11121
\(65\) 8.70398i 1.07960i
\(66\) −1.30202 −0.160268
\(67\) −13.7641 −1.68155 −0.840776 0.541384i \(-0.817901\pi\)
−0.840776 + 0.541384i \(0.817901\pi\)
\(68\) 0.581725 1.00758i 0.0705446 0.122187i
\(69\) 0.0812841 0.00978545
\(70\) −0.870478 1.50771i −0.104042 0.180206i
\(71\) −10.5955 + 6.11732i −1.25746 + 0.725993i −0.972579 0.232571i \(-0.925286\pi\)
−0.284877 + 0.958564i \(0.591953\pi\)
\(72\) 3.79561 2.19140i 0.447317 0.258259i
\(73\) −0.676506 + 1.17174i −0.0791790 + 0.137142i −0.902896 0.429859i \(-0.858563\pi\)
0.823717 + 0.567001i \(0.191897\pi\)
\(74\) −8.69444 + 5.01974i −1.01071 + 0.583533i
\(75\) 3.56740 0.411928
\(76\) 1.81160 + 3.13778i 0.207805 + 0.359929i
\(77\) −0.405436 0.702236i −0.0462037 0.0800272i
\(78\) 4.58545 + 7.94224i 0.519200 + 0.899281i
\(79\) 3.87581i 0.436062i −0.975942 0.218031i \(-0.930037\pi\)
0.975942 0.218031i \(-0.0699634\pi\)
\(80\) 4.13476 0.462280
\(81\) 1.32135 2.28864i 0.146817 0.254294i
\(82\) 3.04337 1.75709i 0.336084 0.194038i
\(83\) −0.686933 1.18980i −0.0754007 0.130598i 0.825860 0.563876i \(-0.190690\pi\)
−0.901260 + 0.433278i \(0.857357\pi\)
\(84\) −0.496718 0.286780i −0.0541964 0.0312903i
\(85\) −1.79024 + 3.10079i −0.194179 + 0.336328i
\(86\) −9.69837 −1.04580
\(87\) −4.00004 6.92827i −0.428849 0.742788i
\(88\) 2.57643 0.274649
\(89\) −10.7719 6.21914i −1.14182 0.659228i −0.194936 0.980816i \(-0.562450\pi\)
−0.946880 + 0.321588i \(0.895783\pi\)
\(90\) −2.24711 + 1.29737i −0.236866 + 0.136754i
\(91\) −2.85572 + 4.94625i −0.299361 + 0.518508i
\(92\) −0.0309423 −0.00322596
\(93\) −4.00354 + 6.93433i −0.415148 + 0.719057i
\(94\) 6.54239 + 11.3318i 0.674796 + 1.16878i
\(95\) −5.57514 9.65643i −0.571997 0.990729i
\(96\) 2.85289 1.64712i 0.291172 0.168108i
\(97\) 0.538617 0.310971i 0.0546883 0.0315743i −0.472407 0.881381i \(-0.656615\pi\)
0.527095 + 0.849806i \(0.323281\pi\)
\(98\) 7.49801i 0.757413i
\(99\) −1.04662 + 0.604265i −0.105189 + 0.0607309i
\(100\) −1.35800 −0.135800
\(101\) 19.3988i 1.93025i −0.261790 0.965125i \(-0.584313\pi\)
0.261790 0.965125i \(-0.415687\pi\)
\(102\) 3.77256i 0.373539i
\(103\) 2.36276i 0.232809i 0.993202 + 0.116405i \(0.0371370\pi\)
−0.993202 + 0.116405i \(0.962863\pi\)
\(104\) −9.07364 15.7160i −0.889744 1.54108i
\(105\) 1.52863 + 0.882557i 0.149179 + 0.0861287i
\(106\) −2.07272 3.59005i −0.201320 0.348696i
\(107\) −8.25942 + 4.76858i −0.798468 + 0.460996i −0.842935 0.538015i \(-0.819174\pi\)
0.0444672 + 0.999011i \(0.485841\pi\)
\(108\) −1.32171 + 2.28928i −0.127182 + 0.220286i
\(109\) −7.67129 + 13.2871i −0.734776 + 1.27267i 0.220045 + 0.975490i \(0.429379\pi\)
−0.954822 + 0.297180i \(0.903954\pi\)
\(110\) −1.52532 −0.145433
\(111\) 5.08939 8.81509i 0.483064 0.836691i
\(112\) −2.34968 1.35659i −0.222024 0.128186i
\(113\) −13.2419 + 7.64522i −1.24569 + 0.719201i −0.970248 0.242115i \(-0.922159\pi\)
−0.275446 + 0.961317i \(0.588825\pi\)
\(114\) 10.1745 + 5.87422i 0.952925 + 0.550172i
\(115\) 0.0952241 0.00887969
\(116\) 1.52269 + 2.63738i 0.141378 + 0.244874i
\(117\) 7.37193 + 4.25618i 0.681535 + 0.393484i
\(118\) −2.09983 −0.193305
\(119\) 2.03470 1.17473i 0.186520 0.107688i
\(120\) −4.85702 + 2.80420i −0.443383 + 0.255987i
\(121\) 10.2896 0.935415
\(122\) −6.56834 11.3767i −0.594669 1.03000i
\(123\) −1.78147 + 3.08560i −0.160630 + 0.278219i
\(124\) 1.52402 2.63969i 0.136861 0.237051i
\(125\) 11.5097 1.02946
\(126\) 1.70263 0.151682
\(127\) 21.1281i 1.87481i 0.348238 + 0.937406i \(0.386780\pi\)
−0.348238 + 0.937406i \(0.613220\pi\)
\(128\) 4.94354 2.85415i 0.436951 0.252274i
\(129\) 8.51558 4.91647i 0.749755 0.432871i
\(130\) 5.37185 + 9.30431i 0.471142 + 0.816042i
\(131\) 3.82737i 0.334399i 0.985923 + 0.167200i \(0.0534724\pi\)
−0.985923 + 0.167200i \(0.946528\pi\)
\(132\) −0.435194 + 0.251259i −0.0378787 + 0.0218693i
\(133\) 7.31667i 0.634436i
\(134\) 14.7134 8.49481i 1.27105 0.733839i
\(135\) 4.06753 7.04517i 0.350077 0.606352i
\(136\) 7.46510i 0.640127i
\(137\) 14.2169 + 8.20813i 1.21463 + 0.701268i 0.963765 0.266753i \(-0.0859509\pi\)
0.250867 + 0.968021i \(0.419284\pi\)
\(138\) −0.0868904 + 0.0501662i −0.00739661 + 0.00427043i
\(139\) 1.00015 0.0848319 0.0424159 0.999100i \(-0.486495\pi\)
0.0424159 + 0.999100i \(0.486495\pi\)
\(140\) −0.581904 0.335962i −0.0491799 0.0283940i
\(141\) −11.4890 6.63317i −0.967547 0.558614i
\(142\) 7.55088 13.0785i 0.633656 1.09752i
\(143\) 2.50200 + 4.33360i 0.209228 + 0.362394i
\(144\) −2.02187 + 3.50198i −0.168489 + 0.291832i
\(145\) −4.68603 8.11644i −0.389154 0.674034i
\(146\) 1.67008i 0.138217i
\(147\) 3.80103 + 6.58357i 0.313503 + 0.543004i
\(148\) −1.93738 + 3.35563i −0.159251 + 0.275831i
\(149\) 1.04595 0.603880i 0.0856876 0.0494718i −0.456544 0.889701i \(-0.650913\pi\)
0.542232 + 0.840229i \(0.317580\pi\)
\(150\) −3.81345 + 2.20170i −0.311367 + 0.179768i
\(151\) 1.70940 2.96076i 0.139109 0.240943i −0.788051 0.615610i \(-0.788910\pi\)
0.927159 + 0.374667i \(0.122243\pi\)
\(152\) −20.1331 11.6238i −1.63301 0.942819i
\(153\) −1.75083 3.03253i −0.141546 0.245165i
\(154\) 0.866800 + 0.500447i 0.0698487 + 0.0403272i
\(155\) −4.69013 + 8.12355i −0.376721 + 0.652499i
\(156\) 3.06532 + 1.76976i 0.245422 + 0.141694i
\(157\) 3.88559 6.73005i 0.310104 0.537116i −0.668280 0.743909i \(-0.732969\pi\)
0.978385 + 0.206793i \(0.0663027\pi\)
\(158\) 2.39204 + 4.14313i 0.190300 + 0.329610i
\(159\) 3.63986 + 2.10148i 0.288660 + 0.166658i
\(160\) 3.34215 1.92959i 0.264220 0.152548i
\(161\) −0.0541134 0.0312424i −0.00426474 0.00246225i
\(162\) 3.26200i 0.256287i
\(163\) 23.6852i 1.85517i −0.373615 0.927584i \(-0.621882\pi\)
0.373615 0.927584i \(-0.378118\pi\)
\(164\) 0.678152 1.17459i 0.0529547 0.0917203i
\(165\) 1.33929 0.773242i 0.104264 0.0601968i
\(166\) 1.46863 + 0.847911i 0.113987 + 0.0658107i
\(167\) 18.7982i 1.45465i 0.686295 + 0.727323i \(0.259236\pi\)
−0.686295 + 0.727323i \(0.740764\pi\)
\(168\) 3.68016 0.283931
\(169\) 11.1231 19.2657i 0.855619 1.48198i
\(170\) 4.41954i 0.338963i
\(171\) 10.9048 0.833913
\(172\) −3.24162 + 1.87155i −0.247171 + 0.142704i
\(173\) 7.20482 4.15970i 0.547772 0.316256i −0.200451 0.979704i \(-0.564241\pi\)
0.748223 + 0.663447i \(0.230907\pi\)
\(174\) 8.55186 + 4.93742i 0.648315 + 0.374305i
\(175\) −2.37493 1.37117i −0.179528 0.103651i
\(176\) −2.05864 + 1.18856i −0.155176 + 0.0895910i
\(177\) 1.84374 1.06449i 0.138584 0.0800117i
\(178\) 15.3531 1.15076
\(179\) 0.240673i 0.0179888i −0.999960 0.00899438i \(-0.997137\pi\)
0.999960 0.00899438i \(-0.00286304\pi\)
\(180\) −0.500721 + 0.867274i −0.0373215 + 0.0646428i
\(181\) 5.62535 0.418129 0.209064 0.977902i \(-0.432958\pi\)
0.209064 + 0.977902i \(0.432958\pi\)
\(182\) 7.04987i 0.522571i
\(183\) 11.5346 + 6.65948i 0.852659 + 0.492283i
\(184\) 0.171938 0.0992683i 0.0126754 0.00731816i
\(185\) 5.96221 10.3269i 0.438350 0.759245i
\(186\) 9.88348i 0.724692i
\(187\) 2.05846i 0.150529i
\(188\) 4.37351 + 2.52504i 0.318971 + 0.184158i
\(189\) −4.62295 + 2.66906i −0.336270 + 0.194146i
\(190\) 11.9193 + 6.88164i 0.864720 + 0.499247i
\(191\) 2.12638 + 3.68301i 0.153860 + 0.266493i 0.932643 0.360800i \(-0.117496\pi\)
−0.778783 + 0.627293i \(0.784163\pi\)
\(192\) −5.56257 + 9.63465i −0.401444 + 0.695321i
\(193\) 8.79642 + 5.07862i 0.633180 + 0.365567i 0.781983 0.623300i \(-0.214209\pi\)
−0.148803 + 0.988867i \(0.547542\pi\)
\(194\) −0.383844 + 0.664838i −0.0275584 + 0.0477326i
\(195\) −9.43342 5.44639i −0.675541 0.390024i
\(196\) −1.44693 2.50616i −0.103352 0.179012i
\(197\) 14.7347 + 8.50706i 1.04980 + 0.606103i 0.922594 0.385773i \(-0.126065\pi\)
0.127208 + 0.991876i \(0.459398\pi\)
\(198\) 0.745870 1.29188i 0.0530067 0.0918103i
\(199\) 1.59463 0.920661i 0.113040 0.0652639i −0.442414 0.896811i \(-0.645878\pi\)
0.555454 + 0.831547i \(0.312544\pi\)
\(200\) 7.54602 4.35670i 0.533584 0.308065i
\(201\) −8.61268 + 14.9176i −0.607491 + 1.05221i
\(202\) 11.9724 + 20.7368i 0.842373 + 1.45903i
\(203\) 6.14983i 0.431633i
\(204\) −0.728012 1.26095i −0.0509711 0.0882845i
\(205\) −2.08699 + 3.61477i −0.145762 + 0.252467i
\(206\) −1.45823 2.52572i −0.101600 0.175976i
\(207\) −0.0465639 + 0.0806510i −0.00323642 + 0.00560564i
\(208\) 14.5002 + 8.37170i 1.00541 + 0.580473i
\(209\) 5.55158 + 3.20521i 0.384011 + 0.221709i
\(210\) −2.17876 −0.150348
\(211\) −16.2790 + 9.39866i −1.12069 + 0.647031i −0.941577 0.336798i \(-0.890656\pi\)
−0.179113 + 0.983829i \(0.557323\pi\)
\(212\) −1.38558 0.799968i −0.0951623 0.0549420i
\(213\) 15.3113i 1.04911i
\(214\) 5.88606 10.1950i 0.402363 0.696913i
\(215\) 9.97598 5.75963i 0.680356 0.392804i
\(216\) 16.9611i 1.15406i
\(217\) 5.33057 3.07761i 0.361863 0.208922i
\(218\) 18.9380i 1.28264i
\(219\) 0.846627 + 1.46640i 0.0572098 + 0.0990903i
\(220\) −0.509828 + 0.294349i −0.0343726 + 0.0198450i
\(221\) −12.5564 + 7.24945i −0.844636 + 0.487651i
\(222\) 12.5641i 0.843248i
\(223\) −9.72361 −0.651141 −0.325570 0.945518i \(-0.605556\pi\)
−0.325570 + 0.945518i \(0.605556\pi\)
\(224\) −2.53235 −0.169199
\(225\) −2.04360 + 3.53962i −0.136240 + 0.235975i
\(226\) 9.43682 16.3451i 0.627728 1.08726i
\(227\) −9.18654 15.9115i −0.609732 1.05609i −0.991284 0.131739i \(-0.957944\pi\)
0.381553 0.924347i \(-0.375390\pi\)
\(228\) 4.53433 0.300293
\(229\) 8.07058 4.65955i 0.533319 0.307912i −0.209048 0.977905i \(-0.567036\pi\)
0.742367 + 0.669994i \(0.233703\pi\)
\(230\) −0.101792 + 0.0587696i −0.00671196 + 0.00387515i
\(231\) −1.01478 −0.0667678
\(232\) −16.9223 9.77011i −1.11100 0.641439i
\(233\) 11.5447 + 19.9961i 0.756321 + 1.30999i 0.944715 + 0.327892i \(0.106338\pi\)
−0.188395 + 0.982093i \(0.560328\pi\)
\(234\) −10.5072 −0.686876
\(235\) −13.4593 7.77074i −0.877989 0.506907i
\(236\) −0.701857 + 0.405217i −0.0456870 + 0.0263774i
\(237\) −4.20062 2.42523i −0.272860 0.157536i
\(238\) −1.45002 + 2.51151i −0.0939911 + 0.162797i
\(239\) −25.9495 −1.67854 −0.839268 0.543718i \(-0.817016\pi\)
−0.839268 + 0.543718i \(0.817016\pi\)
\(240\) 2.58727 4.48128i 0.167007 0.289265i
\(241\) −10.3768 + 17.9732i −0.668429 + 1.15775i 0.309914 + 0.950765i \(0.399700\pi\)
−0.978343 + 0.206989i \(0.933634\pi\)
\(242\) −10.9993 + 6.35043i −0.707059 + 0.408221i
\(243\) 6.66957 + 11.5520i 0.427853 + 0.741063i
\(244\) −4.39085 2.53506i −0.281095 0.162291i
\(245\) 4.45289 + 7.71263i 0.284485 + 0.492742i
\(246\) 4.39789i 0.280400i
\(247\) 45.1522i 2.87297i
\(248\) 19.5573i 1.24189i
\(249\) −1.71935 −0.108960
\(250\) −12.3035 + 7.10344i −0.778143 + 0.449261i
\(251\) 25.5351i 1.61176i −0.592078 0.805881i \(-0.701692\pi\)
0.592078 0.805881i \(-0.298308\pi\)
\(252\) 0.569094 0.328567i 0.0358495 0.0206977i
\(253\) −0.0474108 + 0.0273727i −0.00298069 + 0.00172090i
\(254\) −13.0396 22.5853i −0.818180 1.41713i
\(255\) 2.24043 + 3.88055i 0.140301 + 0.243009i
\(256\) 5.36665 9.29530i 0.335415 0.580956i
\(257\) −9.25996 −0.577621 −0.288810 0.957386i \(-0.593260\pi\)
−0.288810 + 0.957386i \(0.593260\pi\)
\(258\) −6.06861 + 10.5111i −0.377815 + 0.654395i
\(259\) −6.77635 + 3.91233i −0.421062 + 0.243100i
\(260\) 3.59101 + 2.07327i 0.222705 + 0.128579i
\(261\) 9.16575 0.567346
\(262\) −2.36215 4.09136i −0.145934 0.252765i
\(263\) 12.5771 0.775539 0.387769 0.921756i \(-0.373246\pi\)
0.387769 + 0.921756i \(0.373246\pi\)
\(264\) 1.61216 2.79235i 0.0992219 0.171857i
\(265\) 4.26409 + 2.46187i 0.261941 + 0.151232i
\(266\) −4.51564 7.82132i −0.276872 0.479556i
\(267\) −13.4807 + 7.78308i −0.825004 + 0.476317i
\(268\) 3.27858 5.67867i 0.200271 0.346880i
\(269\) −6.12762 −0.373607 −0.186804 0.982397i \(-0.559813\pi\)
−0.186804 + 0.982397i \(0.559813\pi\)
\(270\) 10.0415i 0.611104i
\(271\) −4.55958 7.89743i −0.276975 0.479735i 0.693657 0.720306i \(-0.255999\pi\)
−0.970631 + 0.240571i \(0.922665\pi\)
\(272\) −3.44380 5.96483i −0.208811 0.361671i
\(273\) 3.57385 + 6.19009i 0.216299 + 0.374641i
\(274\) −20.2633 −1.22415
\(275\) −2.08077 + 1.20133i −0.125475 + 0.0724431i
\(276\) −0.0193617 + 0.0335355i −0.00116544 + 0.00201860i
\(277\) −8.98195 + 5.18573i −0.539673 + 0.311580i −0.744946 0.667124i \(-0.767525\pi\)
0.205273 + 0.978705i \(0.434192\pi\)
\(278\) −1.06914 + 0.617266i −0.0641225 + 0.0370212i
\(279\) −4.58689 7.94472i −0.274610 0.475638i
\(280\) 4.31130 0.257649
\(281\) −5.55107 + 9.61473i −0.331149 + 0.573567i −0.982737 0.185006i \(-0.940770\pi\)
0.651588 + 0.758573i \(0.274103\pi\)
\(282\) 16.3752 0.975130
\(283\) 7.52811 0.447500 0.223750 0.974647i \(-0.428170\pi\)
0.223750 + 0.974647i \(0.428170\pi\)
\(284\) 5.82855i 0.345861i
\(285\) −13.9543 −0.826579
\(286\) −5.34915 3.08833i −0.316302 0.182617i
\(287\) 2.37197 1.36946i 0.140013 0.0808364i
\(288\) 3.77423i 0.222398i
\(289\) −11.0357 −0.649160
\(290\) 10.0185 + 5.78417i 0.588305 + 0.339658i
\(291\) 0.778341i 0.0456272i
\(292\) −0.322285 0.558214i −0.0188603 0.0326670i
\(293\) −9.69447 16.7913i −0.566357 0.980959i −0.996922 0.0783997i \(-0.975019\pi\)
0.430565 0.902560i \(-0.358314\pi\)
\(294\) −8.12639 4.69177i −0.473940 0.273630i
\(295\) 2.15994 1.24704i 0.125757 0.0726056i
\(296\) 24.8617i 1.44506i
\(297\) 4.67694i 0.271383i
\(298\) −0.745395 + 1.29106i −0.0431796 + 0.0747892i
\(299\) 0.333942 + 0.192801i 0.0193124 + 0.0111500i
\(300\) −0.849749 + 1.47181i −0.0490603 + 0.0849749i
\(301\) −7.55879 −0.435682
\(302\) 4.21996i 0.242832i
\(303\) −21.0245 12.1385i −1.20783 0.697339i
\(304\) 21.4492 1.23020
\(305\) 13.5127 + 7.80156i 0.773735 + 0.446716i
\(306\) 3.74318 + 2.16113i 0.213983 + 0.123543i
\(307\) −9.96689 17.2632i −0.568840 0.985260i −0.996681 0.0814062i \(-0.974059\pi\)
0.427841 0.903854i \(-0.359274\pi\)
\(308\) 0.386297 0.0220113
\(309\) 2.56077 + 1.47846i 0.145677 + 0.0841067i
\(310\) 11.5785i 0.657613i
\(311\) 5.76116i 0.326686i 0.986569 + 0.163343i \(0.0522277\pi\)
−0.986569 + 0.163343i \(0.947772\pi\)
\(312\) −22.7108 −1.28575
\(313\) −2.05179 −0.115974 −0.0579871 0.998317i \(-0.518468\pi\)
−0.0579871 + 0.998317i \(0.518468\pi\)
\(314\) 9.59231i 0.541326i
\(315\) −1.75137 + 1.01115i −0.0986784 + 0.0569720i
\(316\) 1.59905 + 0.923210i 0.0899534 + 0.0519346i
\(317\) −0.402890 0.232609i −0.0226285 0.0130646i 0.488643 0.872484i \(-0.337492\pi\)
−0.511272 + 0.859419i \(0.670825\pi\)
\(318\) −5.18789 −0.290922
\(319\) 4.66623 + 2.69405i 0.261259 + 0.150838i
\(320\) −6.51654 + 11.2870i −0.364285 + 0.630961i
\(321\) 11.9355i 0.666173i
\(322\) 0.0771277 0.00429816
\(323\) −9.28695 + 16.0855i −0.516740 + 0.895019i
\(324\) 0.629486 + 1.09030i 0.0349714 + 0.0605723i
\(325\) 14.6561 + 8.46168i 0.812972 + 0.469370i
\(326\) 14.6178 + 25.3188i 0.809607 + 1.40228i
\(327\) 9.60039 + 16.6284i 0.530903 + 0.919551i
\(328\) 8.70250i 0.480515i
\(329\) 5.09906 + 8.83183i 0.281120 + 0.486915i
\(330\) −0.954446 + 1.65315i −0.0525405 + 0.0910028i
\(331\) 19.1538 + 11.0584i 1.05279 + 0.607827i 0.923428 0.383771i \(-0.125375\pi\)
0.129359 + 0.991598i \(0.458708\pi\)
\(332\) 0.654505 0.0359206
\(333\) 5.83096 + 10.0995i 0.319535 + 0.553450i
\(334\) −11.6017 20.0947i −0.634817 1.09954i
\(335\) −10.0897 + 17.4759i −0.551261 + 0.954812i
\(336\) −2.94056 + 1.69773i −0.160420 + 0.0926188i
\(337\) 8.42704 + 14.5961i 0.459050 + 0.795098i 0.998911 0.0466563i \(-0.0148566\pi\)
−0.539861 + 0.841754i \(0.681523\pi\)
\(338\) 27.4593i 1.49359i
\(339\) 19.1355i 1.03930i
\(340\) −0.852865 1.47720i −0.0462531 0.0801127i
\(341\) 5.39282i 0.292037i
\(342\) −11.6570 + 6.73015i −0.630336 + 0.363925i
\(343\) 12.5781i 0.679153i
\(344\) 12.0085 20.7993i 0.647455 1.12142i
\(345\) 0.0595851 0.103204i 0.00320795 0.00555634i
\(346\) −5.13450 + 8.89322i −0.276033 + 0.478102i
\(347\) −11.4347 + 6.60180i −0.613844 + 0.354403i −0.774469 0.632612i \(-0.781983\pi\)
0.160624 + 0.987016i \(0.448649\pi\)
\(348\) 3.81121 0.204302
\(349\) 12.1493 14.1913i 0.650339 0.759644i
\(350\) 3.38499 0.180935
\(351\) 28.5289 16.4712i 1.52276 0.879166i
\(352\) −1.10934 + 1.92144i −0.0591282 + 0.102413i
\(353\) −7.62920 + 13.2142i −0.406061 + 0.703319i −0.994444 0.105264i \(-0.966431\pi\)
0.588383 + 0.808582i \(0.299765\pi\)
\(354\) −1.31394 + 2.27581i −0.0698352 + 0.120958i
\(355\) 17.9372i 0.952006i
\(356\) 5.13168 2.96278i 0.271979 0.157027i
\(357\) 2.94029i 0.155617i
\(358\) 0.148537 + 0.257273i 0.00785041 + 0.0135973i
\(359\) 3.90675i 0.206190i 0.994671 + 0.103095i \(0.0328746\pi\)
−0.994671 + 0.103095i \(0.967125\pi\)
\(360\) 6.42559i 0.338658i
\(361\) −19.4213 33.6387i −1.02217 1.77046i
\(362\) −6.01334 + 3.47181i −0.316054 + 0.182474i
\(363\) 6.43855 11.1519i 0.337936 0.585322i
\(364\) −1.36045 2.35638i −0.0713072 0.123508i
\(365\) 0.991822 + 1.71789i 0.0519143 + 0.0899183i
\(366\) −16.4402 −0.859341
\(367\) 6.02468 + 3.47835i 0.314486 + 0.181568i 0.648932 0.760846i \(-0.275216\pi\)
−0.334446 + 0.942415i \(0.608549\pi\)
\(368\) −0.0915889 + 0.158637i −0.00477440 + 0.00826950i
\(369\) −2.04105 3.53520i −0.106253 0.184035i
\(370\) 14.7188i 0.765195i
\(371\) −1.61545 2.79804i −0.0838700 0.145267i
\(372\) −1.90727 3.30349i −0.0988874 0.171278i
\(373\) 25.1389 + 14.5140i 1.30164 + 0.751505i 0.980686 0.195588i \(-0.0626616\pi\)
0.320959 + 0.947093i \(0.395995\pi\)
\(374\) 1.27042 + 2.20043i 0.0656919 + 0.113782i
\(375\) 7.20201 12.4743i 0.371910 0.644168i
\(376\) −32.4031 −1.67106
\(377\) 37.9515i 1.95460i
\(378\) 3.29454 5.70631i 0.169453 0.293501i
\(379\) −0.775888 0.447959i −0.0398547 0.0230101i 0.479940 0.877301i \(-0.340658\pi\)
−0.519795 + 0.854291i \(0.673992\pi\)
\(380\) 5.31196 0.272498
\(381\) 22.8987 + 13.2206i 1.17314 + 0.677311i
\(382\) −4.54609 2.62469i −0.232598 0.134291i
\(383\) 7.78065 4.49216i 0.397573 0.229539i −0.287863 0.957671i \(-0.592945\pi\)
0.685436 + 0.728133i \(0.259612\pi\)
\(384\) 7.14378i 0.364555i
\(385\) −1.18882 −0.0605876
\(386\) −12.5375 −0.638142
\(387\) 11.2657i 0.572667i
\(388\) 0.296291i 0.0150419i
\(389\) −6.50833 3.75758i −0.329985 0.190517i 0.325849 0.945422i \(-0.394350\pi\)
−0.655835 + 0.754905i \(0.727683\pi\)
\(390\) 13.4454 0.680835
\(391\) −0.0793111 0.137371i −0.00401093 0.00694714i
\(392\) 16.0804 + 9.28402i 0.812183 + 0.468914i
\(393\) 4.14813 + 2.39492i 0.209245 + 0.120808i
\(394\) −21.0013 −1.05803
\(395\) −4.92102 2.84115i −0.247603 0.142954i
\(396\) 0.575739i 0.0289320i
\(397\) 22.4977 1.12913 0.564564 0.825390i \(-0.309044\pi\)
0.564564 + 0.825390i \(0.309044\pi\)
\(398\) −1.13641 + 1.96832i −0.0569631 + 0.0986631i
\(399\) 7.92985 + 4.57830i 0.396989 + 0.229202i
\(400\) −4.01966 + 6.96225i −0.200983 + 0.348113i
\(401\) 4.24255i 0.211863i 0.994373 + 0.105931i \(0.0337824\pi\)
−0.994373 + 0.105931i \(0.966218\pi\)
\(402\) 21.2620i 1.06045i
\(403\) −32.8957 + 18.9924i −1.63865 + 0.946077i
\(404\) 8.00338 + 4.62075i 0.398183 + 0.229891i
\(405\) −1.93722 3.35537i −0.0962614 0.166730i
\(406\) −3.79550 6.57400i −0.188367 0.326262i
\(407\) 6.85548i 0.339813i
\(408\) 8.09071 + 4.67118i 0.400550 + 0.231258i
\(409\) 8.07159 0.399114 0.199557 0.979886i \(-0.436050\pi\)
0.199557 + 0.979886i \(0.436050\pi\)
\(410\) 5.15212i 0.254445i
\(411\) 17.7920 10.2722i 0.877617 0.506692i
\(412\) −0.974807 0.562805i −0.0480253 0.0277274i
\(413\) −1.63659 −0.0805312
\(414\) 0.114952i 0.00564957i
\(415\) −2.01422 −0.0988741
\(416\) 15.6275 0.766200
\(417\) 0.625831 1.08397i 0.0306471 0.0530823i
\(418\) −7.91266 −0.387021
\(419\) −2.82441 4.89202i −0.137981 0.238991i 0.788751 0.614713i \(-0.210728\pi\)
−0.926732 + 0.375722i \(0.877395\pi\)
\(420\) −0.728236 + 0.420447i −0.0355343 + 0.0205157i
\(421\) −17.6899 + 10.2132i −0.862151 + 0.497763i −0.864732 0.502234i \(-0.832512\pi\)
0.00258107 + 0.999997i \(0.499178\pi\)
\(422\) 11.6012 20.0938i 0.564736 0.978152i
\(423\) 13.1630 7.59968i 0.640008 0.369509i
\(424\) 10.2657 0.498548
\(425\) −3.48081 6.02894i −0.168844 0.292447i
\(426\) −9.44971 16.3674i −0.457840 0.793002i
\(427\) −5.11929 8.86686i −0.247740 0.429098i
\(428\) 4.54347i 0.219617i
\(429\) 6.26237 0.302350
\(430\) −7.10936 + 12.3138i −0.342844 + 0.593823i
\(431\) −14.6922 + 8.48254i −0.707698 + 0.408590i −0.810208 0.586142i \(-0.800646\pi\)
0.102510 + 0.994732i \(0.467313\pi\)
\(432\) 7.82451 + 13.5524i 0.376457 + 0.652042i
\(433\) −20.7558 11.9834i −0.997460 0.575884i −0.0899639 0.995945i \(-0.528675\pi\)
−0.907496 + 0.420062i \(0.862008\pi\)
\(434\) −3.79882 + 6.57975i −0.182349 + 0.315838i
\(435\) −11.7289 −0.562356
\(436\) −3.65458 6.32991i −0.175022 0.303148i
\(437\) 0.493979 0.0236302
\(438\) −1.81004 1.04503i −0.0864872 0.0499334i
\(439\) 8.13833 4.69867i 0.388421 0.224255i −0.293055 0.956096i \(-0.594672\pi\)
0.681476 + 0.731841i \(0.261338\pi\)
\(440\) 1.88865 3.27123i 0.0900377 0.155950i
\(441\) −8.70973 −0.414749
\(442\) 8.94831 15.4989i 0.425628 0.737208i
\(443\) −12.1743 21.0865i −0.578419 1.00185i −0.995661 0.0930552i \(-0.970337\pi\)
0.417242 0.908795i \(-0.362997\pi\)
\(444\) 2.42457 + 4.19948i 0.115065 + 0.199298i
\(445\) −15.7926 + 9.11785i −0.748640 + 0.432228i
\(446\) 10.3943 6.00114i 0.492183 0.284162i
\(447\) 1.51148i 0.0714904i
\(448\) 7.40637 4.27607i 0.349918 0.202025i
\(449\) −17.0365 −0.804003 −0.402001 0.915639i \(-0.631685\pi\)
−0.402001 + 0.915639i \(0.631685\pi\)
\(450\) 5.04501i 0.237824i
\(451\) 2.39966i 0.112996i
\(452\) 7.28431i 0.342625i
\(453\) −2.13926 3.70531i −0.100511 0.174090i
\(454\) 19.6403 + 11.3393i 0.921766 + 0.532182i
\(455\) 4.18676 + 7.25167i 0.196278 + 0.339964i
\(456\) −25.1960 + 14.5469i −1.17991 + 0.681221i
\(457\) −12.7803 + 22.1362i −0.597839 + 1.03549i 0.395300 + 0.918552i \(0.370640\pi\)
−0.993139 + 0.116936i \(0.962693\pi\)
\(458\) −5.75149 + 9.96187i −0.268749 + 0.465487i
\(459\) −13.5512 −0.632516
\(460\) −0.0226822 + 0.0392867i −0.00105756 + 0.00183175i
\(461\) 33.8789 + 19.5600i 1.57790 + 0.911001i 0.995152 + 0.0983471i \(0.0313555\pi\)
0.582747 + 0.812654i \(0.301978\pi\)
\(462\) 1.08478 0.626295i 0.0504683 0.0291379i
\(463\) −1.95147 1.12668i −0.0906924 0.0523613i 0.453968 0.891018i \(-0.350008\pi\)
−0.544660 + 0.838657i \(0.683341\pi\)
\(464\) 18.0286 0.836955
\(465\) 5.86957 + 10.1664i 0.272195 + 0.471455i
\(466\) −24.6820 14.2502i −1.14337 0.660126i
\(467\) −18.0535 −0.835419 −0.417709 0.908581i \(-0.637167\pi\)
−0.417709 + 0.908581i \(0.637167\pi\)
\(468\) −3.51196 + 2.02763i −0.162340 + 0.0937273i
\(469\) 11.4675 6.62075i 0.529519 0.305718i
\(470\) 19.1835 0.884870
\(471\) −4.86271 8.42246i −0.224062 0.388086i
\(472\) 2.60001 4.50335i 0.119675 0.207284i
\(473\) −3.31127 + 5.73529i −0.152253 + 0.263709i
\(474\) 5.98713 0.274998
\(475\) 21.6798 0.994736
\(476\) 1.11928i 0.0513020i
\(477\) −4.17022 + 2.40768i −0.190941 + 0.110240i
\(478\) 27.7394 16.0153i 1.26877 0.732524i
\(479\) −0.512067 0.886926i −0.0233969 0.0405247i 0.854090 0.520125i \(-0.174115\pi\)
−0.877487 + 0.479601i \(0.840781\pi\)
\(480\) 4.82965i 0.220443i
\(481\) 41.8178 24.1435i 1.90673 1.10085i
\(482\) 25.6171i 1.16683i
\(483\) −0.0677214 + 0.0390990i −0.00308143 + 0.00177906i
\(484\) −2.45096 + 4.24518i −0.111407 + 0.192963i
\(485\) 0.911825i 0.0414038i
\(486\) −14.2592 8.23254i −0.646809 0.373435i
\(487\) 18.5686 10.7206i 0.841424 0.485796i −0.0163243 0.999867i \(-0.505196\pi\)
0.857748 + 0.514071i \(0.171863\pi\)
\(488\) 32.5316 1.47264
\(489\) −25.6702 14.8207i −1.16084 0.670214i
\(490\) −9.52004 5.49640i −0.430072 0.248302i
\(491\) −4.68515 + 8.11491i −0.211438 + 0.366221i −0.952165 0.305585i \(-0.901148\pi\)
0.740727 + 0.671806i \(0.234481\pi\)
\(492\) −0.848687 1.46997i −0.0382618 0.0662713i
\(493\) −7.80589 + 13.5202i −0.351560 + 0.608919i
\(494\) 27.8667 + 48.2665i 1.25378 + 2.17161i
\(495\) 1.77182i 0.0796373i
\(496\) −9.02218 15.6269i −0.405108 0.701667i
\(497\) 5.88507 10.1932i 0.263981 0.457229i
\(498\) 1.83794 1.06114i 0.0823601 0.0475506i
\(499\) −18.9325 + 10.9307i −0.847537 + 0.489326i −0.859819 0.510599i \(-0.829424\pi\)
0.0122822 + 0.999925i \(0.496090\pi\)
\(500\) −2.74158 + 4.74856i −0.122607 + 0.212362i
\(501\) 20.3736 + 11.7627i 0.910224 + 0.525518i
\(502\) 15.7595 + 27.2963i 0.703383 + 1.21829i
\(503\) 32.5528 + 18.7944i 1.45146 + 0.837999i 0.998564 0.0535653i \(-0.0170585\pi\)
0.452893 + 0.891565i \(0.350392\pi\)
\(504\) −2.10820 + 3.65150i −0.0939065 + 0.162651i
\(505\) −24.6301 14.2202i −1.09603 0.632792i
\(506\) 0.0337873 0.0585213i 0.00150203 0.00260159i
\(507\) −13.9202 24.1105i −0.618217 1.07078i
\(508\) −8.71684 5.03267i −0.386747 0.223289i
\(509\) −23.8929 + 13.7946i −1.05904 + 0.611435i −0.925165 0.379564i \(-0.876074\pi\)
−0.133870 + 0.990999i \(0.542741\pi\)
\(510\) −4.78993 2.76546i −0.212101 0.122457i
\(511\) 1.30164i 0.0575812i
\(512\) 24.6652i 1.09006i
\(513\) 21.1005 36.5471i 0.931610 1.61360i
\(514\) 9.89865 5.71499i 0.436611 0.252077i
\(515\) 2.99994 + 1.73201i 0.132193 + 0.0763217i
\(516\) 4.68438i 0.206218i
\(517\) 8.93497 0.392959
\(518\) 4.82915 8.36434i 0.212181 0.367508i
\(519\) 10.4115i 0.457014i
\(520\) −26.6056 −1.16673
\(521\) −8.05389 + 4.64992i −0.352847 + 0.203716i −0.665939 0.746007i \(-0.731969\pi\)
0.313091 + 0.949723i \(0.398635\pi\)
\(522\) −9.79793 + 5.65684i −0.428844 + 0.247593i
\(523\) −7.99156 4.61393i −0.349447 0.201753i 0.314995 0.949093i \(-0.397997\pi\)
−0.664441 + 0.747340i \(0.731331\pi\)
\(524\) −1.57906 0.911673i −0.0689818 0.0398266i
\(525\) −2.97216 + 1.71598i −0.129716 + 0.0748914i
\(526\) −13.4446 + 7.76225i −0.586213 + 0.338450i
\(527\) 15.6254 0.680655
\(528\) 2.97489i 0.129466i
\(529\) 11.4979 19.9149i 0.499908 0.865867i
\(530\) −6.07760 −0.263994
\(531\) 2.43918i 0.105851i
\(532\) −3.01865 1.74282i −0.130875 0.0755608i
\(533\) −14.6377 + 8.45111i −0.634031 + 0.366058i
\(534\) 9.60699 16.6398i 0.415735 0.720074i
\(535\) 13.9824i 0.604511i
\(536\) 42.0730i 1.81728i
\(537\) −0.260843 0.150598i −0.0112562 0.00649877i
\(538\) 6.55026 3.78179i 0.282402 0.163045i
\(539\) −4.43408 2.56001i −0.190989 0.110268i
\(540\) 1.93776 + 3.35630i 0.0833878 + 0.144432i
\(541\) 10.7204 18.5683i 0.460905 0.798311i −0.538101 0.842880i \(-0.680858\pi\)
0.999006 + 0.0445689i \(0.0141914\pi\)
\(542\) 9.74814 + 5.62809i 0.418718 + 0.241747i
\(543\) 3.51998 6.09679i 0.151057 0.261638i
\(544\) −5.56728 3.21427i −0.238695 0.137811i
\(545\) 11.2468 + 19.4801i 0.481762 + 0.834435i
\(546\) −7.64069 4.41136i −0.326992 0.188789i
\(547\) 16.9764 29.4041i 0.725861 1.25723i −0.232758 0.972535i \(-0.574775\pi\)
0.958619 0.284693i \(-0.0918916\pi\)
\(548\) −6.77289 + 3.91033i −0.289323 + 0.167041i
\(549\) −13.2152 + 7.62982i −0.564013 + 0.325633i
\(550\) 1.48286 2.56838i 0.0632293 0.109516i
\(551\) −24.3090 42.1044i −1.03560 1.79371i
\(552\) 0.248463i 0.0105753i
\(553\) 1.86433 + 3.22911i 0.0792792 + 0.137316i
\(554\) 6.40097 11.0868i 0.271951 0.471033i
\(555\) −7.46153 12.9238i −0.316724 0.548583i
\(556\) −0.238235 + 0.412635i −0.0101034 + 0.0174996i
\(557\) 10.0891 + 5.82492i 0.427487 + 0.246810i 0.698276 0.715829i \(-0.253951\pi\)
−0.270788 + 0.962639i \(0.587284\pi\)
\(558\) 9.80651 + 5.66179i 0.415143 + 0.239683i
\(559\) 46.6464 1.97293
\(560\) −3.44485 + 1.98889i −0.145572 + 0.0840458i
\(561\) −2.23097 1.28805i −0.0941915 0.0543815i
\(562\) 13.7038i 0.578062i
\(563\) −9.89526 + 17.1391i −0.417035 + 0.722327i −0.995640 0.0932818i \(-0.970264\pi\)
0.578604 + 0.815608i \(0.303598\pi\)
\(564\) 5.47332 3.16002i 0.230468 0.133061i
\(565\) 22.4172i 0.943100i
\(566\) −8.04735 + 4.64614i −0.338255 + 0.195292i
\(567\) 2.54236i 0.106769i
\(568\) 18.6990 + 32.3876i 0.784591 + 1.35895i
\(569\) −19.6115 + 11.3227i −0.822158 + 0.474673i −0.851160 0.524906i \(-0.824100\pi\)
0.0290024 + 0.999579i \(0.490767\pi\)
\(570\) 14.9167 8.61217i 0.624793 0.360724i
\(571\) 12.5713i 0.526094i −0.964783 0.263047i \(-0.915273\pi\)
0.964783 0.263047i \(-0.0847274\pi\)
\(572\) −2.38389 −0.0996756
\(573\) 5.32222 0.222339
\(574\) −1.69038 + 2.92782i −0.0705550 + 0.122205i
\(575\) −0.0925733 + 0.160342i −0.00386057 + 0.00668671i
\(576\) −6.37308 11.0385i −0.265545 0.459938i
\(577\) −22.7575 −0.947409 −0.473704 0.880684i \(-0.657083\pi\)
−0.473704 + 0.880684i \(0.657083\pi\)
\(578\) 11.7969 6.81093i 0.490685 0.283297i
\(579\) 11.0085 6.35574i 0.457496 0.264136i
\(580\) 4.46482 0.185392
\(581\) 1.14463 + 0.660852i 0.0474872 + 0.0274168i
\(582\) 0.480370 + 0.832026i 0.0199120 + 0.0344886i
\(583\) −2.83072 −0.117236
\(584\) 3.58169 + 2.06789i 0.148212 + 0.0855700i
\(585\) 10.8079 6.23997i 0.446853 0.257991i
\(586\) 20.7263 + 11.9663i 0.856194 + 0.494324i
\(587\) 0.360249 0.623969i 0.0148691 0.0257540i −0.858495 0.512822i \(-0.828600\pi\)
0.873364 + 0.487068i \(0.161934\pi\)
\(588\) −3.62159 −0.149352
\(589\) −24.3303 + 42.1413i −1.00251 + 1.73640i
\(590\) −1.53928 + 2.66611i −0.0633711 + 0.109762i
\(591\) 18.4400 10.6463i 0.758521 0.437932i
\(592\) 11.4692 + 19.8652i 0.471381 + 0.816456i
\(593\) 23.4324 + 13.5287i 0.962252 + 0.555557i 0.896865 0.442303i \(-0.145839\pi\)
0.0653868 + 0.997860i \(0.479172\pi\)
\(594\) −2.88647 4.99952i −0.118433 0.205133i
\(595\) 3.44454i 0.141212i
\(596\) 0.575372i 0.0235682i
\(597\) 2.30436i 0.0943112i
\(598\) −0.475966 −0.0194637
\(599\) −3.73378 + 2.15570i −0.152558 + 0.0880795i −0.574336 0.818620i \(-0.694740\pi\)
0.421778 + 0.906699i \(0.361406\pi\)
\(600\) 10.9046i 0.445177i
\(601\) −5.01034 + 2.89272i −0.204376 + 0.117996i −0.598695 0.800977i \(-0.704314\pi\)
0.394319 + 0.918974i \(0.370980\pi\)
\(602\) 8.08014 4.66507i 0.329322 0.190134i
\(603\) −9.86762 17.0912i −0.401840 0.696008i
\(604\) 0.814350 + 1.41050i 0.0331354 + 0.0573923i
\(605\) 7.54274 13.0644i 0.306656 0.531144i
\(606\) 29.9662 1.21729
\(607\) −15.2716 + 26.4512i −0.619856 + 1.07362i 0.369656 + 0.929169i \(0.379476\pi\)
−0.989512 + 0.144453i \(0.953858\pi\)
\(608\) 17.3375 10.0098i 0.703130 0.405952i
\(609\) 6.66522 + 3.84817i 0.270088 + 0.155936i
\(610\) −19.2596 −0.779799
\(611\) −31.4670 54.5025i −1.27302 2.20494i
\(612\) 1.66818 0.0674321
\(613\) −1.64132 + 2.84285i −0.0662924 + 0.114822i −0.897267 0.441489i \(-0.854450\pi\)
0.830974 + 0.556311i \(0.187784\pi\)
\(614\) 21.3087 + 12.3026i 0.859948 + 0.496491i
\(615\) 2.61181 + 4.52378i 0.105318 + 0.182416i
\(616\) −2.14654 + 1.23931i −0.0864866 + 0.0499331i
\(617\) 7.68951 13.3186i 0.309568 0.536188i −0.668700 0.743532i \(-0.733149\pi\)
0.978268 + 0.207345i \(0.0664822\pi\)
\(618\) −3.64986 −0.146819
\(619\) 17.4857i 0.702810i 0.936224 + 0.351405i \(0.114296\pi\)
−0.936224 + 0.351405i \(0.885704\pi\)
\(620\) −2.23436 3.87003i −0.0897342 0.155424i
\(621\) 0.180199 + 0.312115i 0.00723116 + 0.0125247i
\(622\) −3.55563 6.15853i −0.142568 0.246934i
\(623\) 11.9660 0.479409
\(624\) 18.1466 10.4769i 0.726445 0.419413i
\(625\) 1.31072 2.27024i 0.0524290 0.0908096i
\(626\) 2.19331 1.26631i 0.0876623 0.0506118i
\(627\) 6.94765 4.01123i 0.277462 0.160193i
\(628\) 1.85108 + 3.20617i 0.0738663 + 0.127940i
\(629\) −19.8634 −0.792007
\(630\) 1.24811 2.16179i 0.0497259 0.0861277i
\(631\) 12.2502 0.487674 0.243837 0.969816i \(-0.421594\pi\)
0.243837 + 0.969816i \(0.421594\pi\)
\(632\) −11.8473 −0.471259
\(633\) 23.5243i 0.935007i
\(634\) 0.574238 0.0228059
\(635\) 26.8258 + 15.4879i 1.06455 + 0.614618i
\(636\) −1.73402 + 1.00114i −0.0687583 + 0.0396976i
\(637\) 36.0633i 1.42888i
\(638\) −6.65076 −0.263306
\(639\) −15.1921 8.77115i −0.600989 0.346981i
\(640\) 8.36892i 0.330811i
\(641\) 12.3137 + 21.3280i 0.486363 + 0.842406i 0.999877 0.0156753i \(-0.00498981\pi\)
−0.513514 + 0.858081i \(0.671656\pi\)
\(642\) −7.36623 12.7587i −0.290722 0.503545i
\(643\) −8.68833 5.01621i −0.342634 0.197820i 0.318802 0.947821i \(-0.396719\pi\)
−0.661436 + 0.750001i \(0.730053\pi\)
\(644\) 0.0257795 0.0148838i 0.00101585 0.000586503i
\(645\) 14.4160i 0.567630i
\(646\) 22.9266i 0.902034i
\(647\) −19.0351 + 32.9697i −0.748347 + 1.29617i 0.200268 + 0.979741i \(0.435819\pi\)
−0.948615 + 0.316433i \(0.897515\pi\)
\(648\) −6.99575 4.03900i −0.274819 0.158667i
\(649\) −0.716938 + 1.24177i −0.0281423 + 0.0487439i
\(650\) −20.8892 −0.819343
\(651\) 7.70307i 0.301907i
\(652\) 9.77184 + 5.64177i 0.382695 + 0.220949i
\(653\) 11.4965 0.449894 0.224947 0.974371i \(-0.427779\pi\)
0.224947 + 0.974371i \(0.427779\pi\)
\(654\) −20.5251 11.8502i −0.802596 0.463379i
\(655\) 4.85952 + 2.80565i 0.189877 + 0.109626i
\(656\) −4.01464 6.95355i −0.156745 0.271491i
\(657\) −1.93998 −0.0756857
\(658\) −10.9015 6.29399i −0.424985 0.245365i
\(659\) 2.51778i 0.0980789i 0.998797 + 0.0490394i \(0.0156160\pi\)
−0.998797 + 0.0490394i \(0.984384\pi\)
\(660\) 0.736740i 0.0286775i
\(661\) −31.1042 −1.20981 −0.604906 0.796297i \(-0.706789\pi\)
−0.604906 + 0.796297i \(0.706789\pi\)
\(662\) −27.2998 −1.06104
\(663\) 18.1449i 0.704691i
\(664\) −3.63690 + 2.09976i −0.141139 + 0.0814867i
\(665\) 9.28980 + 5.36347i 0.360243 + 0.207986i
\(666\) −12.4663 7.19740i −0.483058 0.278894i
\(667\) 0.415200 0.0160766
\(668\) −7.75559 4.47769i −0.300073 0.173247i
\(669\) −6.08441 + 10.5385i −0.235237 + 0.407442i
\(670\) 24.9084i 0.962295i
\(671\) −8.97040 −0.346299
\(672\) −1.58458 + 2.74457i −0.0611265 + 0.105874i
\(673\) −17.8380 30.8962i −0.687603 1.19096i −0.972611 0.232438i \(-0.925330\pi\)
0.285009 0.958525i \(-0.408004\pi\)
\(674\) −18.0165 10.4019i −0.693971 0.400665i
\(675\) 7.90861 + 13.6981i 0.304402 + 0.527240i
\(676\) 5.29898 + 9.17811i 0.203807 + 0.353004i
\(677\) 30.6902i 1.17952i −0.807579 0.589760i \(-0.799223\pi\)
0.807579 0.589760i \(-0.200777\pi\)
\(678\) −11.8099 20.4554i −0.453557 0.785583i
\(679\) −0.299164 + 0.518167i −0.0114809 + 0.0198854i
\(680\) 9.47825 + 5.47227i 0.363474 + 0.209852i
\(681\) −22.9934 −0.881108
\(682\) 3.32829 + 5.76477i 0.127447 + 0.220745i
\(683\) 16.3156 + 28.2594i 0.624298 + 1.08132i 0.988676 + 0.150065i \(0.0479484\pi\)
−0.364378 + 0.931251i \(0.618718\pi\)
\(684\) −2.59751 + 4.49902i −0.0993183 + 0.172024i
\(685\) 20.8433 12.0339i 0.796383 0.459792i
\(686\) 7.76284 + 13.4456i 0.296387 + 0.513357i
\(687\) 11.6626i 0.444955i
\(688\) 22.1590i 0.844805i
\(689\) 9.96918 + 17.2671i 0.379795 + 0.657825i
\(690\) 0.147097i 0.00559988i
\(691\) 5.04342 2.91182i 0.191861 0.110771i −0.400993 0.916081i \(-0.631335\pi\)
0.592853 + 0.805310i \(0.298001\pi\)
\(692\) 3.96334i 0.150663i
\(693\) 0.581322 1.00688i 0.0220826 0.0382482i
\(694\) 8.14889 14.1143i 0.309328 0.535771i
\(695\) 0.733160 1.26987i 0.0278103 0.0481689i
\(696\) −21.1778 + 12.2270i −0.802742 + 0.463463i
\(697\) 6.95292 0.263361
\(698\) −4.22882 + 22.6684i −0.160063 + 0.858010i
\(699\) 28.8958 1.09294
\(700\) 1.13141 0.653220i 0.0427633 0.0246894i
\(701\) 23.8789 41.3594i 0.901892 1.56212i 0.0768559 0.997042i \(-0.475512\pi\)
0.825036 0.565080i \(-0.191155\pi\)
\(702\) −20.3311 + 35.2145i −0.767347 + 1.32908i
\(703\) 30.9292 53.5710i 1.16652 2.02047i
\(704\) 7.49285i 0.282398i
\(705\) −16.8439 + 9.72486i −0.634380 + 0.366259i
\(706\) 18.8341i 0.708831i
\(707\) 9.33113 + 16.1620i 0.350933 + 0.607834i
\(708\) 1.01424i 0.0381173i
\(709\) 42.4671i 1.59489i −0.603394 0.797443i \(-0.706186\pi\)
0.603394 0.797443i \(-0.293814\pi\)
\(710\) −11.0703 19.1743i −0.415461 0.719600i
\(711\) 4.81268 2.77860i 0.180490 0.104206i
\(712\) −19.0102 + 32.9266i −0.712437 + 1.23398i
\(713\) −0.207782 0.359889i −0.00778150 0.0134779i
\(714\) 1.81466 + 3.14309i 0.0679120 + 0.117627i
\(715\) 7.33635 0.274364
\(716\) 0.0992949 + 0.0573279i 0.00371082 + 0.00214245i
\(717\) −16.2375 + 28.1243i −0.606402 + 1.05032i
\(718\) −2.41114 4.17621i −0.0899828 0.155855i
\(719\) 21.5445i 0.803474i −0.915755 0.401737i \(-0.868407\pi\)
0.915755 0.401737i \(-0.131593\pi\)
\(720\) 2.96425 + 5.13423i 0.110471 + 0.191342i
\(721\) −1.13653 1.96852i −0.0423264 0.0733115i
\(722\) 41.5217 + 23.9725i 1.54528 + 0.892165i
\(723\) 12.9863 + 22.4929i 0.482965 + 0.836520i
\(724\) −1.33995 + 2.32086i −0.0497988 + 0.0862541i
\(725\) 18.2223 0.676761
\(726\) 15.8948i 0.589910i
\(727\) −16.9750 + 29.4016i −0.629568 + 1.09044i 0.358070 + 0.933695i \(0.383435\pi\)
−0.987638 + 0.156749i \(0.949899\pi\)
\(728\) 15.1193 + 8.72914i 0.560359 + 0.323524i
\(729\) 24.6216 0.911912
\(730\) −2.12046 1.22425i −0.0784818 0.0453115i
\(731\) −16.6178 9.59427i −0.614630 0.354857i
\(732\) −5.49502 + 3.17255i −0.203102 + 0.117261i
\(733\) 6.54608i 0.241785i 0.992666 + 0.120892i \(0.0385756\pi\)
−0.992666 + 0.120892i \(0.961424\pi\)
\(734\) −8.58695 −0.316950
\(735\) 11.1453 0.411102
\(736\) 0.170969i 0.00630201i
\(737\) 11.6014i 0.427343i
\(738\) 4.36365 + 2.51935i 0.160628 + 0.0927386i
\(739\) −50.2199 −1.84737 −0.923684 0.383155i \(-0.874837\pi\)
−0.923684 + 0.383155i \(0.874837\pi\)
\(740\) 2.84038 + 4.91968i 0.104414 + 0.180851i
\(741\) −48.9363 28.2534i −1.79772 1.03791i
\(742\) 3.45374 + 1.99402i 0.126791 + 0.0732028i
\(743\) 1.45396 0.0533408 0.0266704 0.999644i \(-0.491510\pi\)
0.0266704 + 0.999644i \(0.491510\pi\)
\(744\) 21.1963 + 12.2377i 0.777095 + 0.448656i
\(745\) 1.77069i 0.0648731i
\(746\) −35.8305 −1.31185
\(747\) 0.984939 1.70596i 0.0360370 0.0624179i
\(748\) 0.849261 + 0.490321i 0.0310520 + 0.0179279i
\(749\) 4.58753 7.94583i 0.167625 0.290334i
\(750\) 17.7795i 0.649216i
\(751\) 33.8963i 1.23689i 0.785826 + 0.618447i \(0.212238\pi\)
−0.785826 + 0.618447i \(0.787762\pi\)
\(752\) 25.8910 14.9482i 0.944148 0.545104i
\(753\) −27.6751 15.9782i −1.00854 0.582279i
\(754\) 23.4226 + 40.5691i 0.853000 + 1.47744i
\(755\) −2.50614 4.34076i −0.0912076 0.157976i
\(756\) 2.54306i 0.0924904i
\(757\) 16.8547 + 9.73104i 0.612593 + 0.353681i 0.773980 0.633210i \(-0.218263\pi\)
−0.161386 + 0.986891i \(0.551597\pi\)
\(758\) 1.10587 0.0401671
\(759\) 0.0685122i 0.00248683i
\(760\) −29.5170 + 17.0417i −1.07070 + 0.618166i
\(761\) 15.5150 + 8.95760i 0.562419 + 0.324713i 0.754116 0.656742i \(-0.228066\pi\)
−0.191697 + 0.981454i \(0.561399\pi\)
\(762\) −32.6375 −1.18233
\(763\) 14.7601i 0.534350i
\(764\) −2.02600 −0.0732983
\(765\) −5.13377 −0.185612
\(766\) −5.54487 + 9.60400i −0.200344 + 0.347007i