Properties

Label 441.2.g.f.67.4
Level $441$
Weight $2$
Character 441.67
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.4
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.f.79.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.920620 - 1.59456i) q^{2} +(1.58800 + 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} -1.33475 q^{5} +(2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +O(q^{10})\) \(q+(0.920620 - 1.59456i) q^{2} +(1.58800 + 0.691567i) q^{3} +(-0.695084 - 1.20392i) q^{4} -1.33475 q^{5} +(2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(2.04347 + 2.19641i) q^{9} +(-1.22880 + 2.12835i) q^{10} +1.51302 q^{11} +(-0.271199 - 2.39252i) q^{12} +(2.58800 - 4.48254i) q^{13} +(-2.11958 - 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} +(-0.774463 + 1.34141i) q^{17} +(5.38358 - 1.23637i) q^{18} +(1.25211 + 2.16872i) q^{19} +(0.927765 + 1.60694i) q^{20} +(1.39291 - 2.41260i) q^{22} -7.36079 q^{23} +(1.78308 + 0.776526i) q^{24} -3.21843 q^{25} +(-4.76513 - 8.25344i) q^{26} +(1.72605 + 4.90110i) q^{27} +(-0.0309713 - 0.0536439i) q^{29} +(-3.42323 + 2.53001i) q^{30} +(-1.92388 - 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(2.40267 + 1.04635i) q^{33} +(1.42597 + 2.46986i) q^{34} +(1.22392 - 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} +4.61087 q^{38} +(7.20971 - 5.32849i) q^{39} -1.49873 q^{40} +(-4.51188 + 7.81481i) q^{41} +(5.09988 + 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(-2.72753 - 2.93167i) q^{45} +(-6.77649 + 11.7372i) q^{46} +(-4.75925 + 8.24327i) q^{47} +(6.75252 - 4.99060i) q^{48} +(-2.96296 + 5.13199i) q^{50} +(-2.15752 + 1.59456i) q^{51} -7.19550 q^{52} +(0.755374 - 1.30835i) q^{53} +(9.40414 + 1.75975i) q^{54} -2.01950 q^{55} +(0.488532 + 4.30983i) q^{57} -0.114051 q^{58} +(-4.22166 - 7.31212i) q^{59} +(0.361984 + 3.19342i) q^{60} +(1.61958 - 2.80520i) q^{61} -7.08467 q^{62} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(3.88042 - 2.86790i) q^{66} +(-3.46670 - 6.00449i) q^{67} +2.15327 q^{68} +(-11.6889 - 5.09048i) q^{69} -12.3304 q^{71} +(2.29451 + 2.46624i) q^{72} +(1.37936 - 2.38912i) q^{73} -1.03702 q^{74} +(-5.11086 - 2.22576i) q^{75} +(1.74064 - 3.01488i) q^{76} +(-1.85920 - 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} +(-3.23529 + 5.60368i) q^{80} +(-0.648467 + 8.97661i) q^{81} +(8.30746 + 14.3889i) q^{82} +(-2.80111 - 4.85167i) q^{83} +(1.03372 - 1.79045i) q^{85} +18.7802 q^{86} +(-0.0120840 - 0.106605i) q^{87} +1.69889 q^{88} +(-0.703287 - 1.21813i) q^{89} +(-7.18575 + 1.65025i) q^{90} +(5.11636 + 8.86180i) q^{92} +(-0.750637 - 6.62212i) q^{93} +(8.76293 + 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(-1.30320 - 11.4968i) q^{96} +(6.09713 + 10.5605i) q^{97} +(3.09180 + 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + O(q^{10}) \) \( 10q + 2q^{2} - 2q^{3} - 4q^{4} + 8q^{5} + 2q^{6} - 6q^{8} - 4q^{9} + 7q^{10} - 8q^{11} - 22q^{12} + 8q^{13} - 19q^{15} + 2q^{16} - 12q^{17} - 2q^{18} - q^{19} - 5q^{20} - q^{22} - 6q^{23} - 3q^{24} + 2q^{25} - 11q^{26} + 7q^{27} + 7q^{29} - 26q^{30} + 3q^{31} - 2q^{32} + q^{33} - 3q^{34} + 34q^{36} + 40q^{38} + 20q^{39} - 6q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + q^{45} + 3q^{46} - 27q^{47} + 5q^{48} + 19q^{50} + 24q^{51} - 20q^{52} - 21q^{53} + 53q^{54} - 4q^{55} - 4q^{57} + 20q^{58} - 30q^{59} - 41q^{60} + 14q^{61} + 12q^{62} - 50q^{64} - 11q^{65} + 41q^{66} - 2q^{67} + 54q^{68} - 15q^{69} - 6q^{71} + 48q^{72} - 15q^{73} + 72q^{74} - 31q^{75} - 5q^{76} - 20q^{78} - 4q^{79} - 20q^{80} + 8q^{81} + 5q^{82} - 9q^{83} - 6q^{85} + 16q^{86} - 32q^{87} + 36q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 12q^{93} + 3q^{94} - 14q^{95} + q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.920620 1.59456i 0.650977 1.12753i −0.331909 0.943311i \(-0.607693\pi\)
0.982886 0.184214i \(-0.0589739\pi\)
\(3\) 1.58800 + 0.691567i 0.916831 + 0.399277i
\(4\) −0.695084 1.20392i −0.347542 0.601960i
\(5\) −1.33475 −0.596920 −0.298460 0.954422i \(-0.596473\pi\)
−0.298460 + 0.954422i \(0.596473\pi\)
\(6\) 2.56469 1.89549i 1.04703 0.773830i
\(7\) 0 0
\(8\) 1.12285 0.396987
\(9\) 2.04347 + 2.19641i 0.681156 + 0.732138i
\(10\) −1.22880 + 2.12835i −0.388581 + 0.673042i
\(11\) 1.51302 0.456192 0.228096 0.973639i \(-0.426750\pi\)
0.228096 + 0.973639i \(0.426750\pi\)
\(12\) −0.271199 2.39252i −0.0782884 0.690661i
\(13\) 2.58800 4.48254i 0.717781 1.24323i −0.244096 0.969751i \(-0.578491\pi\)
0.961877 0.273482i \(-0.0881755\pi\)
\(14\) 0 0
\(15\) −2.11958 0.923072i −0.547274 0.238336i
\(16\) 2.42388 4.19829i 0.605971 1.04957i
\(17\) −0.774463 + 1.34141i −0.187835 + 0.325340i −0.944528 0.328430i \(-0.893480\pi\)
0.756693 + 0.653770i \(0.226814\pi\)
\(18\) 5.38358 1.23637i 1.26892 0.291416i
\(19\) 1.25211 + 2.16872i 0.287254 + 0.497538i 0.973153 0.230158i \(-0.0739244\pi\)
−0.685900 + 0.727696i \(0.740591\pi\)
\(20\) 0.927765 + 1.60694i 0.207455 + 0.359322i
\(21\) 0 0
\(22\) 1.39291 2.41260i 0.296970 0.514367i
\(23\) −7.36079 −1.53483 −0.767415 0.641151i \(-0.778457\pi\)
−0.767415 + 0.641151i \(0.778457\pi\)
\(24\) 1.78308 + 0.776526i 0.363970 + 0.158508i
\(25\) −3.21843 −0.643687
\(26\) −4.76513 8.25344i −0.934518 1.61863i
\(27\) 1.72605 + 4.90110i 0.332179 + 0.943216i
\(28\) 0 0
\(29\) −0.0309713 0.0536439i −0.00575123 0.00996143i 0.863135 0.504972i \(-0.168497\pi\)
−0.868887 + 0.495011i \(0.835164\pi\)
\(30\) −3.42323 + 2.53001i −0.624993 + 0.461914i
\(31\) −1.92388 3.33227i −0.345540 0.598493i 0.639912 0.768448i \(-0.278971\pi\)
−0.985452 + 0.169956i \(0.945638\pi\)
\(32\) −3.34011 5.78523i −0.590453 1.02269i
\(33\) 2.40267 + 1.04635i 0.418250 + 0.182147i
\(34\) 1.42597 + 2.46986i 0.244552 + 0.423577i
\(35\) 0 0
\(36\) 1.22392 3.98687i 0.203987 0.664478i
\(37\) −0.281608 0.487760i −0.0462961 0.0801872i 0.841949 0.539557i \(-0.181408\pi\)
−0.888245 + 0.459370i \(0.848075\pi\)
\(38\) 4.61087 0.747982
\(39\) 7.20971 5.32849i 1.15448 0.853241i
\(40\) −1.49873 −0.236969
\(41\) −4.51188 + 7.81481i −0.704638 + 1.22047i 0.262185 + 0.965018i \(0.415557\pi\)
−0.966822 + 0.255450i \(0.917776\pi\)
\(42\) 0 0
\(43\) 5.09988 + 8.83325i 0.777724 + 1.34706i 0.933251 + 0.359226i \(0.116959\pi\)
−0.155526 + 0.987832i \(0.549707\pi\)
\(44\) −1.05167 1.82155i −0.158546 0.274609i
\(45\) −2.72753 2.93167i −0.406596 0.437028i
\(46\) −6.77649 + 11.7372i −0.999139 + 1.73056i
\(47\) −4.75925 + 8.24327i −0.694209 + 1.20240i 0.276238 + 0.961089i \(0.410912\pi\)
−0.970447 + 0.241315i \(0.922421\pi\)
\(48\) 6.75252 4.99060i 0.974643 0.720330i
\(49\) 0 0
\(50\) −2.96296 + 5.13199i −0.419025 + 0.725773i
\(51\) −2.15752 + 1.59456i −0.302113 + 0.223283i
\(52\) −7.19550 −0.997836
\(53\) 0.755374 1.30835i 0.103759 0.179715i −0.809472 0.587159i \(-0.800246\pi\)
0.913230 + 0.407444i \(0.133580\pi\)
\(54\) 9.40414 + 1.75975i 1.27974 + 0.239471i
\(55\) −2.01950 −0.272310
\(56\) 0 0
\(57\) 0.488532 + 4.30983i 0.0647077 + 0.570851i
\(58\) −0.114051 −0.0149757
\(59\) −4.22166 7.31212i −0.549613 0.951957i −0.998301 0.0582689i \(-0.981442\pi\)
0.448688 0.893688i \(-0.351891\pi\)
\(60\) 0.361984 + 3.19342i 0.0467319 + 0.412269i
\(61\) 1.61958 2.80520i 0.207367 0.359169i −0.743518 0.668716i \(-0.766844\pi\)
0.950884 + 0.309547i \(0.100177\pi\)
\(62\) −7.08467 −0.899754
\(63\) 0 0
\(64\) −2.60434 −0.325543
\(65\) −3.45434 + 5.98309i −0.428458 + 0.742111i
\(66\) 3.88042 2.86790i 0.477646 0.353014i
\(67\) −3.46670 6.00449i −0.423524 0.733566i 0.572757 0.819725i \(-0.305874\pi\)
−0.996281 + 0.0861595i \(0.972541\pi\)
\(68\) 2.15327 0.261122
\(69\) −11.6889 5.09048i −1.40718 0.612822i
\(70\) 0 0
\(71\) −12.3304 −1.46335 −0.731673 0.681656i \(-0.761260\pi\)
−0.731673 + 0.681656i \(0.761260\pi\)
\(72\) 2.29451 + 2.46624i 0.270410 + 0.290649i
\(73\) 1.37936 2.38912i 0.161442 0.279625i −0.773944 0.633254i \(-0.781719\pi\)
0.935386 + 0.353629i \(0.115052\pi\)
\(74\) −1.03702 −0.120551
\(75\) −5.11086 2.22576i −0.590152 0.257009i
\(76\) 1.74064 3.01488i 0.199665 0.345830i
\(77\) 0 0
\(78\) −1.85920 16.4018i −0.210512 1.85714i
\(79\) 2.95969 5.12633i 0.332991 0.576758i −0.650106 0.759844i \(-0.725275\pi\)
0.983097 + 0.183086i \(0.0586087\pi\)
\(80\) −3.23529 + 5.60368i −0.361716 + 0.626511i
\(81\) −0.648467 + 8.97661i −0.0720519 + 0.997401i
\(82\) 8.30746 + 14.3889i 0.917406 + 1.58899i
\(83\) −2.80111 4.85167i −0.307462 0.532540i 0.670344 0.742050i \(-0.266146\pi\)
−0.977806 + 0.209510i \(0.932813\pi\)
\(84\) 0 0
\(85\) 1.03372 1.79045i 0.112122 0.194202i
\(86\) 18.7802 2.02512
\(87\) −0.0120840 0.106605i −0.00129554 0.0114293i
\(88\) 1.69889 0.181102
\(89\) −0.703287 1.21813i −0.0745483 0.129121i 0.826341 0.563169i \(-0.190418\pi\)
−0.900890 + 0.434048i \(0.857085\pi\)
\(90\) −7.18575 + 1.65025i −0.757444 + 0.173952i
\(91\) 0 0
\(92\) 5.11636 + 8.86180i 0.533418 + 0.923906i
\(93\) −0.750637 6.62212i −0.0778374 0.686682i
\(94\) 8.76293 + 15.1778i 0.903827 + 1.56548i
\(95\) −1.67126 2.89470i −0.171467 0.296990i
\(96\) −1.30320 11.4968i −0.133007 1.17339i
\(97\) 6.09713 + 10.5605i 0.619070 + 1.07226i 0.989656 + 0.143462i \(0.0458236\pi\)
−0.370586 + 0.928798i \(0.620843\pi\)
\(98\) 0 0
\(99\) 3.09180 + 3.32321i 0.310738 + 0.333995i
\(100\) 2.23708 + 3.87474i 0.223708 + 0.387474i
\(101\) −1.11867 −0.111312 −0.0556560 0.998450i \(-0.517725\pi\)
−0.0556560 + 0.998450i \(0.517725\pi\)
\(102\) 0.556368 + 4.90828i 0.0550886 + 0.485993i
\(103\) −1.93045 −0.190213 −0.0951063 0.995467i \(-0.530319\pi\)
−0.0951063 + 0.995467i \(0.530319\pi\)
\(104\) 2.90593 5.03322i 0.284950 0.493548i
\(105\) 0 0
\(106\) −1.39082 2.40898i −0.135089 0.233981i
\(107\) 2.88969 + 5.00509i 0.279357 + 0.483860i 0.971225 0.238163i \(-0.0765454\pi\)
−0.691868 + 0.722024i \(0.743212\pi\)
\(108\) 4.70077 5.48470i 0.452332 0.527766i
\(109\) −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i \(-0.962494\pi\)
0.598340 + 0.801242i \(0.295827\pi\)
\(110\) −1.85920 + 3.22022i −0.177267 + 0.307036i
\(111\) −0.109874 0.969312i −0.0104288 0.0920030i
\(112\) 0 0
\(113\) 7.25105 12.5592i 0.682121 1.18147i −0.292211 0.956354i \(-0.594391\pi\)
0.974332 0.225115i \(-0.0722758\pi\)
\(114\) 7.32205 + 3.18873i 0.685773 + 0.298652i
\(115\) 9.82483 0.916170
\(116\) −0.0430553 + 0.0745740i −0.00399759 + 0.00692403i
\(117\) 15.1340 3.47562i 1.39914 0.321322i
\(118\) −15.5462 −1.43114
\(119\) 0 0
\(120\) −2.37997 1.03647i −0.217261 0.0946164i
\(121\) −8.71078 −0.791889
\(122\) −2.98204 5.16505i −0.269982 0.467622i
\(123\) −12.5693 + 9.28962i −1.13334 + 0.837617i
\(124\) −2.67452 + 4.63241i −0.240179 + 0.416002i
\(125\) 10.9696 0.981149
\(126\) 0 0
\(127\) 8.50004 0.754257 0.377128 0.926161i \(-0.376912\pi\)
0.377128 + 0.926161i \(0.376912\pi\)
\(128\) 4.28260 7.41769i 0.378532 0.655637i
\(129\) 1.98981 + 17.5541i 0.175193 + 1.54555i
\(130\) 6.36027 + 11.0163i 0.557832 + 0.966194i
\(131\) 2.01346 0.175917 0.0879585 0.996124i \(-0.471966\pi\)
0.0879585 + 0.996124i \(0.471966\pi\)
\(132\) −0.410328 3.61992i −0.0357145 0.315074i
\(133\) 0 0
\(134\) −12.7660 −1.10282
\(135\) −2.30386 6.54175i −0.198285 0.563024i
\(136\) −0.869605 + 1.50620i −0.0745680 + 0.129156i
\(137\) 2.21740 0.189445 0.0947225 0.995504i \(-0.469804\pi\)
0.0947225 + 0.995504i \(0.469804\pi\)
\(138\) −18.8781 + 13.9523i −1.60701 + 1.18770i
\(139\) −0.377669 + 0.654143i −0.0320335 + 0.0554836i −0.881598 0.472002i \(-0.843532\pi\)
0.849564 + 0.527485i \(0.176865\pi\)
\(140\) 0 0
\(141\) −13.2585 + 9.79894i −1.11656 + 0.825220i
\(142\) −11.3516 + 19.6615i −0.952604 + 1.64996i
\(143\) 3.91568 6.78216i 0.327446 0.567153i
\(144\) 14.1743 3.25523i 1.18119 0.271269i
\(145\) 0.0413391 + 0.0716014i 0.00343303 + 0.00594618i
\(146\) −2.53973 4.39894i −0.210189 0.364059i
\(147\) 0 0
\(148\) −0.391482 + 0.678068i −0.0321797 + 0.0557368i
\(149\) 6.58499 0.539463 0.269732 0.962936i \(-0.413065\pi\)
0.269732 + 0.962936i \(0.413065\pi\)
\(150\) −8.25428 + 6.10050i −0.673959 + 0.498104i
\(151\) 12.6671 1.03083 0.515417 0.856939i \(-0.327637\pi\)
0.515417 + 0.856939i \(0.327637\pi\)
\(152\) 1.40593 + 2.43514i 0.114036 + 0.197516i
\(153\) −4.52888 + 1.04009i −0.366138 + 0.0840861i
\(154\) 0 0
\(155\) 2.56791 + 4.44775i 0.206260 + 0.357252i
\(156\) −11.4264 4.97617i −0.914846 0.398413i
\(157\) −8.65372 14.9887i −0.690642 1.19623i −0.971628 0.236515i \(-0.923995\pi\)
0.280986 0.959712i \(-0.409338\pi\)
\(158\) −5.44950 9.43882i −0.433539 0.750912i
\(159\) 2.10434 1.55526i 0.166885 0.123340i
\(160\) 4.45822 + 7.72186i 0.352453 + 0.610467i
\(161\) 0 0
\(162\) 13.7168 + 9.29807i 1.07769 + 0.730525i
\(163\) 6.10963 + 10.5822i 0.478543 + 0.828861i 0.999697 0.0246014i \(-0.00783167\pi\)
−0.521154 + 0.853463i \(0.674498\pi\)
\(164\) 12.5445 0.979564
\(165\) −3.20697 1.39662i −0.249662 0.108727i
\(166\) −10.3150 −0.800602
\(167\) −1.76248 + 3.05270i −0.136385 + 0.236225i −0.926126 0.377215i \(-0.876882\pi\)
0.789741 + 0.613440i \(0.210215\pi\)
\(168\) 0 0
\(169\) −6.89546 11.9433i −0.530420 0.918714i
\(170\) −1.90332 3.29665i −0.145978 0.252842i
\(171\) −2.20475 + 7.18186i −0.168602 + 0.549210i
\(172\) 7.08968 12.2797i 0.540583 0.936318i
\(173\) 5.07046 8.78229i 0.385500 0.667705i −0.606339 0.795206i \(-0.707362\pi\)
0.991838 + 0.127502i \(0.0406958\pi\)
\(174\) −0.181113 0.0788742i −0.0137302 0.00597944i
\(175\) 0 0
\(176\) 3.66738 6.35208i 0.276439 0.478806i
\(177\) −1.64715 14.5312i −0.123808 1.09223i
\(178\) −2.58984 −0.194117
\(179\) 0.850579 1.47325i 0.0635752 0.110116i −0.832486 0.554046i \(-0.813083\pi\)
0.896061 + 0.443931i \(0.146416\pi\)
\(180\) −1.63364 + 5.32148i −0.121764 + 0.396640i
\(181\) 16.9941 1.26316 0.631581 0.775310i \(-0.282406\pi\)
0.631581 + 0.775310i \(0.282406\pi\)
\(182\) 0 0
\(183\) 4.51188 3.33460i 0.333528 0.246501i
\(184\) −8.26505 −0.609308
\(185\) 0.375877 + 0.651039i 0.0276351 + 0.0478653i
\(186\) −11.2504 4.89953i −0.824922 0.359251i
\(187\) −1.17178 + 2.02957i −0.0856887 + 0.148417i
\(188\) 13.2323 0.965066
\(189\) 0 0
\(190\) −6.15437 −0.446485
\(191\) −11.3470 + 19.6535i −0.821038 + 1.42208i 0.0838717 + 0.996477i \(0.473271\pi\)
−0.904910 + 0.425603i \(0.860062\pi\)
\(192\) −4.13568 1.80108i −0.298467 0.129982i
\(193\) −3.09349 5.35808i −0.222674 0.385683i 0.732945 0.680288i \(-0.238145\pi\)
−0.955619 + 0.294605i \(0.904812\pi\)
\(194\) 22.4526 1.61200
\(195\) −9.62319 + 7.11222i −0.689131 + 0.509317i
\(196\) 0 0
\(197\) 9.77010 0.696091 0.348045 0.937478i \(-0.386846\pi\)
0.348045 + 0.937478i \(0.386846\pi\)
\(198\) 8.14544 1.87065i 0.578871 0.132942i
\(199\) 4.33973 7.51664i 0.307636 0.532840i −0.670209 0.742172i \(-0.733796\pi\)
0.977845 + 0.209332i \(0.0671289\pi\)
\(200\) −3.61381 −0.255535
\(201\) −1.35259 11.9326i −0.0954044 0.841659i
\(202\) −1.02987 + 1.78379i −0.0724615 + 0.125507i
\(203\) 0 0
\(204\) 3.41938 + 1.48913i 0.239405 + 0.104260i
\(205\) 6.02225 10.4308i 0.420612 0.728522i
\(206\) −1.77721 + 3.07822i −0.123824 + 0.214470i
\(207\) −15.0415 16.1673i −1.04546 1.12371i
\(208\) −12.5460 21.7303i −0.869909 1.50673i
\(209\) 1.89446 + 3.28130i 0.131043 + 0.226973i
\(210\) 0 0
\(211\) −2.84219 + 4.92283i −0.195665 + 0.338901i −0.947118 0.320885i \(-0.896020\pi\)
0.751453 + 0.659786i \(0.229353\pi\)
\(212\) −2.10019 −0.144242
\(213\) −19.5806 8.52728i −1.34164 0.584280i
\(214\) 10.6412 0.727420
\(215\) −6.80708 11.7902i −0.464239 0.804086i
\(216\) 1.93810 + 5.50319i 0.131871 + 0.374445i
\(217\) 0 0
\(218\) 7.58786 + 13.1426i 0.513915 + 0.890126i
\(219\) 3.84265 2.83999i 0.259662 0.191909i
\(220\) 1.40372 + 2.43132i 0.0946390 + 0.163920i
\(221\) 4.00862 + 6.94313i 0.269649 + 0.467045i
\(222\) −1.64678 0.717167i −0.110525 0.0481331i
\(223\) −5.86133 10.1521i −0.392503 0.679836i 0.600276 0.799793i \(-0.295058\pi\)
−0.992779 + 0.119957i \(0.961724\pi\)
\(224\) 0 0
\(225\) −6.57677 7.06901i −0.438451 0.471267i
\(226\) −13.3509 23.1245i −0.888091 1.53822i
\(227\) −11.1831 −0.742247 −0.371123 0.928584i \(-0.621027\pi\)
−0.371123 + 0.928584i \(0.621027\pi\)
\(228\) 4.84913 3.58385i 0.321141 0.237346i
\(229\) 9.65647 0.638118 0.319059 0.947735i \(-0.396633\pi\)
0.319059 + 0.947735i \(0.396633\pi\)
\(230\) 9.04494 15.6663i 0.596406 1.03301i
\(231\) 0 0
\(232\) −0.0347761 0.0602340i −0.00228317 0.00395456i
\(233\) −9.64492 16.7055i −0.631860 1.09441i −0.987171 0.159666i \(-0.948958\pi\)
0.355311 0.934748i \(-0.384375\pi\)
\(234\) 8.39058 27.3318i 0.548509 1.78674i
\(235\) 6.35243 11.0027i 0.414387 0.717739i
\(236\) −5.86881 + 10.1651i −0.382027 + 0.661690i
\(237\) 8.24519 6.09378i 0.535582 0.395833i
\(238\) 0 0
\(239\) −0.194641 + 0.337128i −0.0125903 + 0.0218070i −0.872252 0.489057i \(-0.837341\pi\)
0.859662 + 0.510864i \(0.170674\pi\)
\(240\) −9.01295 + 6.66121i −0.581784 + 0.429979i
\(241\) −10.6361 −0.685134 −0.342567 0.939493i \(-0.611296\pi\)
−0.342567 + 0.939493i \(0.611296\pi\)
\(242\) −8.01932 + 13.8899i −0.515502 + 0.892875i
\(243\) −7.23769 + 13.8064i −0.464298 + 0.885679i
\(244\) −4.50299 −0.288274
\(245\) 0 0
\(246\) 3.24130 + 28.5948i 0.206658 + 1.82314i
\(247\) 12.9618 0.824741
\(248\) −2.16023 3.74163i −0.137175 0.237594i
\(249\) −1.09290 9.64159i −0.0692599 0.611011i
\(250\) 10.0988 17.4917i 0.638705 1.10627i
\(251\) 3.26628 0.206166 0.103083 0.994673i \(-0.467129\pi\)
0.103083 + 0.994673i \(0.467129\pi\)
\(252\) 0 0
\(253\) −11.1370 −0.700176
\(254\) 7.82531 13.5538i 0.491004 0.850443i
\(255\) 2.87976 2.12835i 0.180337 0.133282i
\(256\) −10.4896 18.1686i −0.655603 1.13554i
\(257\) 4.69573 0.292912 0.146456 0.989217i \(-0.453213\pi\)
0.146456 + 0.989217i \(0.453213\pi\)
\(258\) 29.8229 + 12.9878i 1.85669 + 0.808584i
\(259\) 0 0
\(260\) 9.60421 0.595628
\(261\) 0.0545353 0.177646i 0.00337565 0.0109960i
\(262\) 1.85363 3.21059i 0.114518 0.198351i
\(263\) 19.5498 1.20549 0.602747 0.797932i \(-0.294073\pi\)
0.602747 + 0.797932i \(0.294073\pi\)
\(264\) 2.69783 + 1.17490i 0.166040 + 0.0723098i
\(265\) −1.00824 + 1.74632i −0.0619355 + 0.107276i
\(266\) 0 0
\(267\) −0.274400 2.42076i −0.0167930 0.148148i
\(268\) −4.81929 + 8.34725i −0.294385 + 0.509890i
\(269\) −7.88365 + 13.6549i −0.480675 + 0.832553i −0.999754 0.0221730i \(-0.992942\pi\)
0.519079 + 0.854726i \(0.326275\pi\)
\(270\) −12.5522 2.34883i −0.763903 0.142945i
\(271\) −7.39882 12.8151i −0.449446 0.778464i 0.548904 0.835886i \(-0.315045\pi\)
−0.998350 + 0.0574218i \(0.981712\pi\)
\(272\) 3.75442 + 6.50285i 0.227645 + 0.394293i
\(273\) 0 0
\(274\) 2.04138 3.53578i 0.123324 0.213604i
\(275\) −4.86954 −0.293644
\(276\) 1.99624 + 17.6108i 0.120159 + 1.06005i
\(277\) −7.45122 −0.447701 −0.223850 0.974624i \(-0.571863\pi\)
−0.223850 + 0.974624i \(0.571863\pi\)
\(278\) 0.695380 + 1.20443i 0.0417061 + 0.0722371i
\(279\) 3.38764 11.0350i 0.202812 0.660650i
\(280\) 0 0
\(281\) −12.9938 22.5060i −0.775146 1.34259i −0.934712 0.355406i \(-0.884343\pi\)
0.159566 0.987187i \(-0.448991\pi\)
\(282\) 3.41901 + 30.1625i 0.203599 + 1.79615i
\(283\) 9.37768 + 16.2426i 0.557445 + 0.965524i 0.997709 + 0.0676550i \(0.0215517\pi\)
−0.440263 + 0.897869i \(0.645115\pi\)
\(284\) 8.57064 + 14.8448i 0.508574 + 0.880876i
\(285\) −0.652070 5.75257i −0.0386253 0.340753i
\(286\) −7.20971 12.4876i −0.426319 0.738406i
\(287\) 0 0
\(288\) 5.88136 19.1582i 0.346563 1.12891i
\(289\) 7.30041 + 12.6447i 0.429436 + 0.743805i
\(290\) 0.152230 0.00893928
\(291\) 2.37890 + 20.9867i 0.139454 + 1.23026i
\(292\) −3.83507 −0.224431
\(293\) 1.23089 2.13196i 0.0719093 0.124551i −0.827829 0.560981i \(-0.810424\pi\)
0.899738 + 0.436430i \(0.143757\pi\)
\(294\) 0 0
\(295\) 5.63487 + 9.75988i 0.328075 + 0.568242i
\(296\) −0.316203 0.547680i −0.0183790 0.0318333i
\(297\) 2.61155 + 7.41544i 0.151537 + 0.430287i
\(298\) 6.06227 10.5002i 0.351178 0.608258i
\(299\) −19.0497 + 32.9950i −1.10167 + 1.90815i
\(300\) 0.872835 + 7.70016i 0.0503932 + 0.444569i
\(301\) 0 0
\(302\) 11.6616 20.1985i 0.671050 1.16229i
\(303\) −1.77645 0.773637i −0.102054 0.0444443i
\(304\) 12.1399 0.696270
\(305\) −2.16175 + 3.74425i −0.123781 + 0.214395i
\(306\) −2.51090 + 8.17911i −0.143538 + 0.467568i
\(307\) 4.66277 0.266118 0.133059 0.991108i \(-0.457520\pi\)
0.133059 + 0.991108i \(0.457520\pi\)
\(308\) 0 0
\(309\) −3.06555 1.33503i −0.174393 0.0759475i
\(310\) 9.45629 0.537081
\(311\) 13.7410 + 23.8002i 0.779183 + 1.34958i 0.932413 + 0.361393i \(0.117699\pi\)
−0.153231 + 0.988190i \(0.548968\pi\)
\(312\) 8.09542 5.98309i 0.458313 0.338726i
\(313\) 2.74666 4.75735i 0.155250 0.268901i −0.777900 0.628388i \(-0.783715\pi\)
0.933150 + 0.359487i \(0.117048\pi\)
\(314\) −31.8671 −1.79837
\(315\) 0 0
\(316\) −8.22893 −0.462914
\(317\) −4.93879 + 8.55424i −0.277390 + 0.480454i −0.970735 0.240152i \(-0.922803\pi\)
0.693345 + 0.720606i \(0.256136\pi\)
\(318\) −0.542654 4.78730i −0.0304305 0.268459i
\(319\) −0.0468601 0.0811641i −0.00262366 0.00454432i
\(320\) 3.47615 0.194323
\(321\) 1.12746 + 9.94649i 0.0629288 + 0.555159i
\(322\) 0 0
\(323\) −3.87885 −0.215825
\(324\) 11.2579 5.45879i 0.625437 0.303266i
\(325\) −8.32930 + 14.4268i −0.462026 + 0.800253i
\(326\) 22.4986 1.24608
\(327\) −11.4806 + 8.48494i −0.634876 + 0.469218i
\(328\) −5.06616 + 8.77485i −0.279732 + 0.484510i
\(329\) 0 0
\(330\) −5.17940 + 3.82794i −0.285116 + 0.210721i
\(331\) 10.3471 17.9217i 0.568729 0.985067i −0.427963 0.903796i \(-0.640769\pi\)
0.996692 0.0812710i \(-0.0258979\pi\)
\(332\) −3.89401 + 6.74463i −0.213712 + 0.370160i
\(333\) 0.495864 1.61525i 0.0271732 0.0885152i
\(334\) 3.24514 + 5.62076i 0.177566 + 0.307554i
\(335\) 4.62718 + 8.01452i 0.252810 + 0.437880i
\(336\) 0 0
\(337\) 0.748747 1.29687i 0.0407869 0.0706449i −0.844911 0.534906i \(-0.820347\pi\)
0.885698 + 0.464261i \(0.153680\pi\)
\(338\) −25.3924 −1.38116
\(339\) 20.2002 14.9294i 1.09712 0.810852i
\(340\) −2.87408 −0.155869
\(341\) −2.91087 5.04177i −0.157632 0.273027i
\(342\) 9.42217 + 10.1274i 0.509493 + 0.547626i
\(343\) 0 0
\(344\) 5.72639 + 9.91840i 0.308746 + 0.534764i
\(345\) 15.6018 + 6.79453i 0.839973 + 0.365805i
\(346\) −9.33593 16.1703i −0.501903 0.869321i
\(347\) 14.7694 + 25.5813i 0.792862 + 1.37328i 0.924188 + 0.381938i \(0.124743\pi\)
−0.131326 + 0.991339i \(0.541923\pi\)
\(348\) −0.119945 + 0.0886477i −0.00642971 + 0.00475202i
\(349\) −18.0006 31.1780i −0.963551 1.66892i −0.713458 0.700698i \(-0.752872\pi\)
−0.250094 0.968222i \(-0.580461\pi\)
\(350\) 0 0
\(351\) 26.4364 + 4.94691i 1.41107 + 0.264046i
\(352\) −5.05363 8.75315i −0.269360 0.466545i
\(353\) 29.4930 1.56975 0.784877 0.619652i \(-0.212726\pi\)
0.784877 + 0.619652i \(0.212726\pi\)
\(354\) −24.6873 10.7512i −1.31211 0.571421i
\(355\) 16.4580 0.873500
\(356\) −0.977687 + 1.69340i −0.0518173 + 0.0897502i
\(357\) 0 0
\(358\) −1.56612 2.71260i −0.0827720 0.143365i
\(359\) 2.70535 + 4.68580i 0.142783 + 0.247307i 0.928544 0.371224i \(-0.121062\pi\)
−0.785761 + 0.618531i \(0.787728\pi\)
\(360\) −3.06260 3.29182i −0.161413 0.173494i
\(361\) 6.36444 11.0235i 0.334971 0.580186i
\(362\) 15.6451 27.0981i 0.822289 1.42425i
\(363\) −13.8327 6.02409i −0.726028 0.316183i
\(364\) 0 0
\(365\) −1.84110 + 3.18888i −0.0963676 + 0.166914i
\(366\) −1.16350 10.2644i −0.0608169 0.536527i
\(367\) 23.0843 1.20499 0.602496 0.798122i \(-0.294173\pi\)
0.602496 + 0.798122i \(0.294173\pi\)
\(368\) −17.8417 + 30.9027i −0.930063 + 1.61092i
\(369\) −26.3844 + 6.05936i −1.37352 + 0.315438i
\(370\) 1.38416 0.0719591
\(371\) 0 0
\(372\) −7.45075 + 5.50664i −0.386304 + 0.285506i
\(373\) 21.5030 1.11338 0.556692 0.830719i \(-0.312070\pi\)
0.556692 + 0.830719i \(0.312070\pi\)
\(374\) 2.15752 + 3.73694i 0.111563 + 0.193232i
\(375\) 17.4197 + 7.58620i 0.899548 + 0.391750i
\(376\) −5.34392 + 9.25595i −0.275592 + 0.477339i
\(377\) −0.320615 −0.0165125
\(378\) 0 0
\(379\) 5.72168 0.293903 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(380\) −2.32333 + 4.02412i −0.119184 + 0.206433i
\(381\) 13.4980 + 5.87835i 0.691526 + 0.301157i
\(382\) 20.8925 + 36.1869i 1.06895 + 1.85148i
\(383\) 34.9209 1.78437 0.892187 0.451666i \(-0.149170\pi\)
0.892187 + 0.451666i \(0.149170\pi\)
\(384\) 11.9306 8.81756i 0.608831 0.449969i
\(385\) 0 0
\(386\) −11.3917 −0.579823
\(387\) −8.98003 + 29.2519i −0.456480 + 1.48696i
\(388\) 8.47603 14.6809i 0.430305 0.745311i
\(389\) −28.8822 −1.46438 −0.732192 0.681098i \(-0.761503\pi\)
−0.732192 + 0.681098i \(0.761503\pi\)
\(390\) 2.48157 + 21.8924i 0.125659 + 1.10857i
\(391\) 5.70066 9.87383i 0.288295 0.499341i
\(392\) 0 0
\(393\) 3.19737 + 1.39244i 0.161286 + 0.0702395i
\(394\) 8.99455 15.5790i 0.453139 0.784860i
\(395\) −3.95046 + 6.84239i −0.198769 + 0.344278i
\(396\) 1.85182 6.03219i 0.0930574 0.303129i
\(397\) −5.59226 9.68607i −0.280667 0.486130i 0.690882 0.722968i \(-0.257222\pi\)
−0.971549 + 0.236838i \(0.923889\pi\)
\(398\) −7.99049 13.8399i −0.400527 0.693734i
\(399\) 0 0
\(400\) −7.80111 + 13.5119i −0.390056 + 0.675596i
\(401\) −1.08212 −0.0540386 −0.0270193 0.999635i \(-0.508602\pi\)
−0.0270193 + 0.999635i \(0.508602\pi\)
\(402\) −20.2724 8.82858i −1.01110 0.440330i
\(403\) −19.9160 −0.992088
\(404\) 0.777570 + 1.34679i 0.0386856 + 0.0670054i
\(405\) 0.865544 11.9816i 0.0430092 0.595368i
\(406\) 0 0
\(407\) −0.426078 0.737988i −0.0211199 0.0365807i
\(408\) −2.42257 + 1.79045i −0.119935 + 0.0886405i
\(409\) −10.8674 18.8229i −0.537360 0.930735i −0.999045 0.0436908i \(-0.986088\pi\)
0.461685 0.887044i \(-0.347245\pi\)
\(410\) −11.0884 19.2057i −0.547618 0.948501i
\(411\) 3.52122 + 1.53348i 0.173689 + 0.0756410i
\(412\) 1.34182 + 2.32410i 0.0661069 + 0.114500i
\(413\) 0 0
\(414\) −39.6273 + 9.10068i −1.94758 + 0.447274i
\(415\) 3.73879 + 6.47578i 0.183530 + 0.317884i
\(416\) −34.5767 −1.69526
\(417\) −1.05212 + 0.777593i −0.0515226 + 0.0380789i
\(418\) 6.97632 0.341223
\(419\) −12.5906 + 21.8075i −0.615090 + 1.06537i 0.375279 + 0.926912i \(0.377547\pi\)
−0.990369 + 0.138455i \(0.955787\pi\)
\(420\) 0 0
\(421\) −14.8304 25.6869i −0.722788 1.25191i −0.959878 0.280418i \(-0.909527\pi\)
0.237090 0.971488i \(-0.423806\pi\)
\(422\) 5.23316 + 9.06411i 0.254746 + 0.441234i
\(423\) −27.8310 + 6.39158i −1.35319 + 0.310769i
\(424\) 0.848171 1.46907i 0.0411908 0.0713446i
\(425\) 2.49256 4.31724i 0.120907 0.209417i
\(426\) −31.6236 + 23.3721i −1.53217 + 1.13238i
\(427\) 0 0
\(428\) 4.01715 6.95791i 0.194176 0.336323i
\(429\) 10.9084 8.06209i 0.526663 0.389241i
\(430\) −25.0669 −1.20884
\(431\) 2.44517 4.23516i 0.117780 0.204000i −0.801108 0.598520i \(-0.795756\pi\)
0.918887 + 0.394520i \(0.129089\pi\)
\(432\) 24.7600 + 4.63321i 1.19127 + 0.222915i
\(433\) −9.71430 −0.466839 −0.233420 0.972376i \(-0.574992\pi\)
−0.233420 + 0.972376i \(0.574992\pi\)
\(434\) 0 0
\(435\) 0.0161292 + 0.142292i 0.000773334 + 0.00682236i
\(436\) 11.4579 0.548735
\(437\) −9.21651 15.9635i −0.440885 0.763636i
\(438\) −0.990919 8.74189i −0.0473479 0.417704i
\(439\) −7.41176 + 12.8375i −0.353744 + 0.612703i −0.986902 0.161320i \(-0.948425\pi\)
0.633158 + 0.774022i \(0.281758\pi\)
\(440\) −2.26760 −0.108103
\(441\) 0 0
\(442\) 14.7617 0.702141
\(443\) 10.9510 18.9676i 0.520297 0.901180i −0.479425 0.877583i \(-0.659155\pi\)
0.999722 0.0235972i \(-0.00751192\pi\)
\(444\) −1.09060 + 0.806033i −0.0517577 + 0.0382526i
\(445\) 0.938715 + 1.62590i 0.0444994 + 0.0770751i
\(446\) −21.5842 −1.02204
\(447\) 10.4569 + 4.55396i 0.494596 + 0.215395i
\(448\) 0 0
\(449\) 21.4952 1.01442 0.507212 0.861822i \(-0.330676\pi\)
0.507212 + 0.861822i \(0.330676\pi\)
\(450\) −17.3267 + 3.97919i −0.816787 + 0.187581i
\(451\) −6.82655 + 11.8239i −0.321450 + 0.556767i
\(452\) −20.1603 −0.948263
\(453\) 20.1153 + 8.76016i 0.945101 + 0.411588i
\(454\) −10.2954 + 17.8321i −0.483185 + 0.836902i
\(455\) 0 0
\(456\) 0.548548 + 4.83929i 0.0256881 + 0.226621i
\(457\) −20.3128 + 35.1827i −0.950190 + 1.64578i −0.205181 + 0.978724i \(0.565778\pi\)
−0.745009 + 0.667054i \(0.767555\pi\)
\(458\) 8.88995 15.3978i 0.415400 0.719494i
\(459\) −7.91114 1.48037i −0.369261 0.0690978i
\(460\) −6.82908 11.8283i −0.318408 0.551498i
\(461\) −1.41541 2.45155i −0.0659220 0.114180i 0.831181 0.556003i \(-0.187666\pi\)
−0.897103 + 0.441822i \(0.854332\pi\)
\(462\) 0 0
\(463\) −13.9324 + 24.1317i −0.647494 + 1.12149i 0.336225 + 0.941782i \(0.390850\pi\)
−0.983719 + 0.179711i \(0.942484\pi\)
\(464\) −0.300284 −0.0139403
\(465\) 1.00192 + 8.83890i 0.0464627 + 0.409894i
\(466\) −35.5173 −1.64531
\(467\) 13.3219 + 23.0742i 0.616464 + 1.06775i 0.990126 + 0.140182i \(0.0447689\pi\)
−0.373661 + 0.927565i \(0.621898\pi\)
\(468\) −14.7038 15.8043i −0.679682 0.730554i
\(469\) 0 0
\(470\) −11.6964 20.2587i −0.539513 0.934463i
\(471\) −3.37640 29.7866i −0.155576 1.37249i
\(472\) −4.74028 8.21041i −0.218189 0.377915i
\(473\) 7.71620 + 13.3648i 0.354791 + 0.614516i
\(474\) −2.12622 18.7575i −0.0976604 0.861561i
\(475\) −4.02983 6.97987i −0.184901 0.320258i
\(476\) 0 0
\(477\) 4.41725 1.01445i 0.202252 0.0464485i
\(478\) 0.358381 + 0.620734i 0.0163920 + 0.0283917i
\(479\) 31.5791 1.44289 0.721443 0.692474i \(-0.243479\pi\)
0.721443 + 0.692474i \(0.243479\pi\)
\(480\) 1.73945 + 15.3455i 0.0793947 + 0.700421i
\(481\) −2.91520 −0.132922
\(482\) −9.79185 + 16.9600i −0.446007 + 0.772506i
\(483\) 0 0
\(484\) 6.05472 + 10.4871i 0.275215 + 0.476686i
\(485\) −8.13817 14.0957i −0.369535 0.640054i
\(486\) 15.3519 + 24.2514i 0.696378 + 1.10006i
\(487\) −0.153087 + 0.265154i −0.00693703 + 0.0120153i −0.869473 0.493980i \(-0.835541\pi\)
0.862536 + 0.505996i \(0.168875\pi\)
\(488\) 1.81855 3.14982i 0.0823218 0.142586i
\(489\) 2.38378 + 21.0297i 0.107798 + 0.950996i
\(490\) 0 0
\(491\) −9.06981 + 15.7094i −0.409315 + 0.708954i −0.994813 0.101720i \(-0.967566\pi\)
0.585498 + 0.810674i \(0.300899\pi\)
\(492\) 19.9207 + 8.67539i 0.898094 + 0.391117i
\(493\) 0.0959447 0.00432113
\(494\) 11.9329 20.6684i 0.536887 0.929916i
\(495\) −4.12679 4.43567i −0.185486 0.199368i
\(496\) −18.6531 −0.837549
\(497\) 0 0
\(498\) −16.3803 7.13355i −0.734017 0.319662i
\(499\) −21.3091 −0.953928 −0.476964 0.878923i \(-0.658263\pi\)
−0.476964 + 0.878923i \(0.658263\pi\)
\(500\) −7.62478 13.2065i −0.340990 0.590613i
\(501\) −4.90996 + 3.62881i −0.219361 + 0.162123i
\(502\) 3.00701 5.20829i 0.134209 0.232457i
\(503\) 17.0738 0.761285 0.380642 0.924722i \(-0.375703\pi\)
0.380642 + 0.924722i \(0.375703\pi\)
\(504\) 0 0
\(505\) 1.49315 0.0664443
\(506\) −10.2529 + 17.7586i −0.455799 + 0.789466i
\(507\) −2.69038 23.7346i −0.119484 1.05409i
\(508\) −5.90824 10.2334i −0.262136 0.454032i
\(509\) −36.7735 −1.62996 −0.814979 0.579490i \(-0.803252\pi\)
−0.814979 + 0.579490i \(0.803252\pi\)
\(510\) −0.742614 6.55135i −0.0328835 0.290099i
\(511\) 0 0
\(512\) −21.4975 −0.950065
\(513\) −8.46788 + 9.88003i −0.373866 + 0.436214i
\(514\) 4.32299 7.48764i 0.190679 0.330265i
\(515\) 2.57667 0.113542
\(516\) 19.7506 14.5971i 0.869473 0.642603i
\(517\) −7.20083 + 12.4722i −0.316692 + 0.548527i
\(518\) 0 0
\(519\) 14.1254 10.4397i 0.620037 0.458251i
\(520\) −3.87870 + 6.71810i −0.170092 + 0.294608i
\(521\) 9.57535 16.5850i 0.419504 0.726602i −0.576386 0.817178i \(-0.695537\pi\)
0.995890 + 0.0905758i \(0.0288707\pi\)
\(522\) −0.233061 0.250504i −0.0102008 0.0109643i
\(523\) 20.9715 + 36.3236i 0.917018 + 1.58832i 0.803920 + 0.594737i \(0.202744\pi\)
0.113097 + 0.993584i \(0.463923\pi\)
\(524\) −1.39952 2.42405i −0.0611385 0.105895i
\(525\) 0 0
\(526\) 17.9980 31.1734i 0.784749 1.35922i
\(527\) 5.95991 0.259618
\(528\) 10.2167 7.55085i 0.444624 0.328609i
\(529\) 31.1812 1.35570
\(530\) 1.85641 + 3.21539i 0.0806372 + 0.139668i
\(531\) 7.43362 24.2146i 0.322592 1.05082i
\(532\) 0 0
\(533\) 23.3535 + 40.4494i 1.01155 + 1.75206i
\(534\) −4.11266 1.79105i −0.177972 0.0775063i
\(535\) −3.85702 6.68056i −0.166754 0.288826i
\(536\) −3.89258 6.74214i −0.168134 0.291216i
\(537\) 2.36956 1.75128i 0.102254 0.0755732i
\(538\) 14.5157 + 25.1419i 0.625816 + 1.08395i
\(539\) 0 0
\(540\) −6.27438 + 7.32073i −0.270006 + 0.315034i
\(541\) −1.44272 2.49886i −0.0620273 0.107434i 0.833344 0.552754i \(-0.186423\pi\)
−0.895371 + 0.445320i \(0.853090\pi\)
\(542\) −27.2460 −1.17032
\(543\) 26.9866 + 11.7526i 1.15811 + 0.504351i
\(544\) 10.3472 0.443631
\(545\) 5.50059 9.52731i 0.235620 0.408105i
\(546\) 0 0
\(547\) 1.38738 + 2.40301i 0.0593201 + 0.102745i 0.894160 0.447747i \(-0.147773\pi\)
−0.834840 + 0.550492i \(0.814440\pi\)
\(548\) −1.54128 2.66957i −0.0658401 0.114038i
\(549\) 9.47096 2.17507i 0.404211 0.0928296i
\(550\) −4.48300 + 7.76478i −0.191156 + 0.331091i
\(551\) 0.0775590 0.134336i 0.00330413 0.00572291i
\(552\) −13.1249 5.71584i −0.558632 0.243282i
\(553\) 0 0
\(554\) −6.85975 + 11.8814i −0.291443 + 0.504794i
\(555\) 0.146655 + 1.29379i 0.00622516 + 0.0549184i
\(556\) 1.05005 0.0445319
\(557\) 15.5344 26.9064i 0.658214 1.14006i −0.322864 0.946445i \(-0.604646\pi\)
0.981078 0.193614i \(-0.0620211\pi\)
\(558\) −14.4773 15.5609i −0.612873 0.658744i
\(559\) 52.7939 2.23294
\(560\) 0 0
\(561\) −3.26436 + 2.41260i −0.137822 + 0.101860i
\(562\) −47.8495 −2.01841
\(563\) 0.144020 + 0.249451i 0.00606973 + 0.0105131i 0.869044 0.494734i \(-0.164735\pi\)
−0.862975 + 0.505247i \(0.831401\pi\)
\(564\) 21.0129 + 9.15104i 0.884802 + 0.385328i
\(565\) −9.67836 + 16.7634i −0.407172 + 0.705242i
\(566\) 34.5331 1.45154
\(567\) 0 0
\(568\) −13.8451 −0.580929
\(569\) 8.04004 13.9258i 0.337056 0.583798i −0.646821 0.762641i \(-0.723902\pi\)
0.983878 + 0.178843i \(0.0572354\pi\)
\(570\) −9.77313 4.25616i −0.409351 0.178271i
\(571\) 7.64289 + 13.2379i 0.319845 + 0.553988i 0.980456 0.196741i \(-0.0630358\pi\)
−0.660610 + 0.750729i \(0.729702\pi\)
\(572\) −10.8869 −0.455204
\(573\) −31.6107 + 23.3626i −1.32056 + 0.975985i
\(574\) 0 0
\(575\) 23.6902 0.987950
\(576\) −5.32189 5.72021i −0.221745 0.238342i
\(577\) −12.0812 + 20.9253i −0.502949 + 0.871133i 0.497045 + 0.867725i \(0.334418\pi\)
−0.999994 + 0.00340833i \(0.998915\pi\)
\(578\) 26.8836 1.11821
\(579\) −1.20698 10.6480i −0.0501603 0.442515i
\(580\) 0.0574683 0.0995380i 0.00238624 0.00413309i
\(581\) 0 0
\(582\) 35.6546 + 15.5275i 1.47793 + 0.643634i
\(583\) 1.14289 1.97955i 0.0473338 0.0819845i
\(584\) 1.54881 2.68262i 0.0640902 0.111007i
\(585\) −20.2002 + 4.63910i −0.835174 + 0.191803i
\(586\) −2.26636 3.92546i −0.0936226 0.162159i
\(587\) −18.0145 31.2020i −0.743537 1.28784i −0.950875 0.309574i \(-0.899814\pi\)
0.207339 0.978269i \(-0.433520\pi\)
\(588\) 0 0
\(589\) 4.81783 8.34472i 0.198515 0.343838i
\(590\) 20.7503 0.854276
\(591\) 15.5149 + 6.75668i 0.638197 + 0.277933i
\(592\) −2.73034 −0.112216
\(593\) −12.4668 21.5932i −0.511951 0.886726i −0.999904 0.0138558i \(-0.995589\pi\)
0.487953 0.872870i \(-0.337744\pi\)
\(594\) 14.2286 + 2.66253i 0.583807 + 0.109245i
\(595\) 0 0
\(596\) −4.57712 7.92780i −0.187486 0.324735i
\(597\) 12.0897 8.93518i 0.494800 0.365693i
\(598\) 35.0751 + 60.7518i 1.43433 + 2.48433i
\(599\) −19.7642 34.2325i −0.807542 1.39870i −0.914561 0.404447i \(-0.867464\pi\)
0.107019 0.994257i \(-0.465869\pi\)
\(600\) −5.73873 2.49920i −0.234283 0.102029i
\(601\) −1.86447 3.22936i −0.0760534 0.131728i 0.825490 0.564416i \(-0.190899\pi\)
−0.901544 + 0.432688i \(0.857565\pi\)
\(602\) 0 0
\(603\) 6.10427 19.8843i 0.248585 0.809751i
\(604\) −8.80470 15.2502i −0.358258 0.620521i
\(605\) 11.6267 0.472694
\(606\) −2.86904 + 2.12043i −0.116547 + 0.0861365i
\(607\) −23.6528 −0.960036 −0.480018 0.877259i \(-0.659370\pi\)
−0.480018 + 0.877259i \(0.659370\pi\)
\(608\) 8.36436 14.4875i 0.339219 0.587545i
\(609\) 0 0
\(610\) 3.98029 + 6.89407i 0.161157 + 0.279133i
\(611\) 24.6339 + 42.6671i 0.996580 + 1.72613i
\(612\) 4.40013 + 4.72947i 0.177865 + 0.191177i
\(613\) 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i \(-0.808888\pi\)
0.901833 + 0.432084i \(0.142222\pi\)
\(614\) 4.29264 7.43507i 0.173237 0.300055i
\(615\) 16.7769 12.3994i 0.676512 0.499990i
\(616\) 0 0
\(617\) −17.5615 + 30.4174i −0.706999 + 1.22456i 0.258966 + 0.965886i \(0.416618\pi\)
−0.965965 + 0.258672i \(0.916715\pi\)
\(618\) −4.95100 + 3.65914i −0.199158 + 0.147192i
\(619\) 21.1632 0.850622 0.425311 0.905047i \(-0.360165\pi\)
0.425311 + 0.905047i \(0.360165\pi\)
\(620\) 3.56983 6.18312i 0.143368 0.248320i
\(621\) −12.7051 36.0759i −0.509839 1.44768i
\(622\) 50.6011 2.02892
\(623\) 0 0
\(624\) −4.89504 43.1841i −0.195959 1.72875i
\(625\) 1.45048 0.0580192
\(626\) −5.05726 8.75943i −0.202129 0.350097i
\(627\) 0.739157 + 6.52085i 0.0295191 + 0.260418i
\(628\) −12.0301 + 20.8368i −0.480054 + 0.831477i
\(629\) 0.872381 0.0347841
\(630\) 0 0
\(631\) 4.74845 0.189033 0.0945164 0.995523i \(-0.469870\pi\)
0.0945164 + 0.995523i \(0.469870\pi\)
\(632\) 3.32329 5.75610i 0.132193 0.228965i
\(633\) −7.91786 + 5.85186i −0.314707 + 0.232591i
\(634\) 9.09350 + 15.7504i 0.361149 + 0.625529i
\(635\) −11.3455 −0.450231
\(636\) −3.33510 1.45242i −0.132245 0.0575924i
\(637\) 0 0
\(638\) −0.172562 −0.00683178
\(639\) −25.1967 27.0826i −0.996767 1.07137i
\(640\) −5.71622 + 9.90078i −0.225953 + 0.391363i
\(641\) −9.87469 −0.390027 −0.195013 0.980801i \(-0.562475\pi\)
−0.195013 + 0.980801i \(0.562475\pi\)
\(642\) 16.8982 + 7.35913i 0.666921 + 0.290442i
\(643\) −21.9748 + 38.0615i −0.866602 + 1.50100i −0.00115462 + 0.999999i \(0.500368\pi\)
−0.865448 + 0.501000i \(0.832966\pi\)
\(644\) 0 0
\(645\) −2.65590 23.4304i −0.104576 0.922570i
\(646\) −3.57095 + 6.18507i −0.140497 + 0.243348i
\(647\) −22.1936 + 38.4404i −0.872521 + 1.51125i −0.0131398 + 0.999914i \(0.504183\pi\)
−0.859381 + 0.511336i \(0.829151\pi\)
\(648\) −0.728131 + 10.0794i −0.0286037 + 0.395955i
\(649\) −6.38743 11.0634i −0.250729 0.434275i
\(650\) 15.3362 + 26.5631i 0.601537 + 1.04189i
\(651\) 0 0
\(652\) 8.49341 14.7110i 0.332628 0.576128i
\(653\) 41.9912 1.64324 0.821622 0.570033i \(-0.193070\pi\)
0.821622 + 0.570033i \(0.193070\pi\)
\(654\) 2.96053 + 26.1179i 0.115766 + 1.02129i
\(655\) −2.68748 −0.105008
\(656\) 21.8726 + 37.8844i 0.853980 + 1.47914i
\(657\) 8.06616 1.85245i 0.314691 0.0722708i
\(658\) 0 0
\(659\) −19.6365 34.0114i −0.764928 1.32489i −0.940284 0.340390i \(-0.889441\pi\)
0.175356 0.984505i \(-0.443892\pi\)
\(660\) 0.547687 + 4.83170i 0.0213187 + 0.188074i
\(661\) −0.0933694 0.161721i −0.00363165 0.00629020i 0.864204 0.503142i \(-0.167823\pi\)
−0.867836 + 0.496852i \(0.834489\pi\)
\(662\) −19.0515 32.9982i −0.740459 1.28251i
\(663\) 1.56403 + 13.7979i 0.0607419 + 0.535866i
\(664\) −3.14522 5.44769i −0.122058 0.211411i
\(665\) 0 0
\(666\) −2.11911 2.27772i −0.0821139 0.0882598i
\(667\) 0.227973 + 0.394862i 0.00882717 + 0.0152891i
\(668\) 4.90028 0.189597
\(669\) −2.28690 20.1750i −0.0884166 0.780012i
\(670\) 17.0395 0.658294
\(671\) 2.45046 4.24432i 0.0945989 0.163850i
\(672\) 0 0
\(673\) −5.43382 9.41166i −0.209458 0.362793i 0.742086 0.670305i \(-0.233837\pi\)
−0.951544 + 0.307512i \(0.900503\pi\)
\(674\) −1.37862 2.38785i −0.0531026 0.0919764i
\(675\) −5.55519 15.7738i −0.213819 0.607136i
\(676\) −9.58584 + 16.6032i −0.368686 + 0.638583i
\(677\) 14.1950 24.5865i 0.545560 0.944937i −0.453012 0.891505i \(-0.649650\pi\)
0.998571 0.0534326i \(-0.0170162\pi\)
\(678\) −5.20910 45.9547i −0.200054 1.76488i
\(679\) 0 0
\(680\) 1.16071 2.01041i 0.0445111 0.0770956i
\(681\) −17.7587 7.73385i −0.680514 0.296362i
\(682\) −10.7192 −0.410460
\(683\) 5.92034 10.2543i 0.226536 0.392371i −0.730243 0.683187i \(-0.760593\pi\)
0.956779 + 0.290816i \(0.0939267\pi\)
\(684\) 10.1789 2.33764i 0.389199 0.0893821i
\(685\) −2.95968 −0.113083
\(686\) 0 0
\(687\) 15.3345 + 6.67810i 0.585046 + 0.254786i
\(688\) 49.4461 1.88511
\(689\) −3.90981 6.77199i −0.148952 0.257992i
\(690\) 25.1976 18.6228i 0.959258 0.708960i
\(691\) 5.95416 10.3129i 0.226507 0.392321i −0.730264 0.683165i \(-0.760603\pi\)
0.956770 + 0.290844i \(0.0939361\pi\)
\(692\) −14.0976 −0.535909
\(693\) 0 0
\(694\) 54.3880 2.06454
\(695\) 0.504096 0.873119i 0.0191214 0.0331193i
\(696\) −0.0135685 0.119702i −0.000514313 0.00453727i
\(697\) −6.98857 12.1046i −0.264711 0.458493i
\(698\) −66.2870 −2.50900
\(699\) −3.76313 33.1984i −0.142335 1.25568i
\(700\) 0 0
\(701\) −31.3902 −1.18559 −0.592795 0.805353i \(-0.701976\pi\)
−0.592795 + 0.805353i \(0.701976\pi\)
\(702\) 32.2260 37.6002i 1.21629 1.41913i
\(703\) 0.705208 1.22146i 0.0265974 0.0460681i
\(704\) −3.94041 −0.148510
\(705\) 17.6968 13.0792i 0.666499 0.492590i
\(706\) 27.1518 47.0284i 1.02187 1.76994i
\(707\) 0 0
\(708\) −16.3495 + 12.0834i −0.614451 + 0.454123i
\(709\) −0.312609 + 0.541455i −0.0117403 + 0.0203348i −0.871836 0.489798i \(-0.837070\pi\)
0.860096 + 0.510133i \(0.170404\pi\)
\(710\) 15.1516 26.2433i 0.568628 0.984893i
\(711\) 17.3076 3.97480i 0.649085 0.149067i
\(712\) −0.789685 1.36777i −0.0295947 0.0512595i
\(713\) 14.1613 + 24.5281i 0.530345 + 0.918584i
\(714\) 0 0
\(715\) −5.22647 + 9.05251i −0.195459 + 0.338545i
\(716\) −2.36489 −0.0883802
\(717\) −0.542236 + 0.400751i −0.0202502 + 0.0149663i
\(718\) 9.96239 0.371793
\(719\) −12.1969 21.1257i −0.454869 0.787857i 0.543811 0.839208i \(-0.316981\pi\)
−0.998681 + 0.0513506i \(0.983647\pi\)
\(720\) −18.9192 + 4.34492i −0.705078 + 0.161926i
\(721\) 0 0
\(722\) −11.7185 20.2970i −0.436116 0.755376i
\(723\) −16.8902 7.35561i −0.628152 0.273558i
\(724\) −11.8123 20.4595i −0.439002 0.760373i
\(725\) 0.0996792 + 0.172649i 0.00370199 + 0.00641204i
\(726\) −22.3404 + 16.5112i −0.829132 + 0.612787i
\(727\) 18.9253 + 32.7796i 0.701900 + 1.21573i 0.967799 + 0.251726i \(0.0809980\pi\)
−0.265899 + 0.964001i \(0.585669\pi\)
\(728\) 0 0
\(729\) −21.0415 + 16.9191i −0.779314 + 0.626634i
\(730\) 3.38991 + 5.87150i 0.125466 + 0.217314i
\(731\) −15.7987 −0.584335
\(732\) −7.15073 3.11412i −0.264299 0.115101i
\(733\) −2.40155 −0.0887033 −0.0443516 0.999016i \(-0.514122\pi\)
−0.0443516 + 0.999016i \(0.514122\pi\)
\(734\) 21.2519 36.8093i 0.784421 1.35866i
\(735\) 0 0
\(736\) 24.5858 + 42.5839i 0.906245 + 1.56966i
\(737\) −5.24517 9.08490i −0.193208 0.334646i
\(738\) −14.6280 + 47.6500i −0.538465 + 1.75402i
\(739\) −15.1940 + 26.3167i −0.558920 + 0.968077i 0.438667 + 0.898650i \(0.355451\pi\)
−0.997587 + 0.0694277i \(0.977883\pi\)
\(740\) 0.522533 0.905053i 0.0192087 0.0332704i
\(741\) 20.5833 + 8.96397i 0.756148 + 0.329300i
\(742\) 0 0
\(743\) −2.54785 + 4.41300i −0.0934715 + 0.161897i −0.908970 0.416862i \(-0.863130\pi\)
0.815498 + 0.578760i \(0.196463\pi\)
\(744\) −0.842852 7.43565i −0.0309004 0.272604i
\(745\) −8.78934 −0.322016
\(746\) 19.7961 34.2879i 0.724787 1.25537i
\(747\) 4.93228 16.0666i 0.180463 0.587847i
\(748\) 3.25793 0.119122
\(749\) 0 0
\(750\) 28.1336 20.7927i 1.02729 0.759242i
\(751\) −0.975011 −0.0355787 −0.0177893 0.999842i \(-0.505663\pi\)
−0.0177893 + 0.999842i \(0.505663\pi\)
\(752\) 23.0718 + 39.9615i 0.841341 + 1.45724i
\(753\) 5.18685 + 2.25885i 0.189019 + 0.0823172i
\(754\) −0.295165 + 0.511240i −0.0107493 + 0.0186183i
\(755\) −16.9075 −0.615326
\(756\) 0 0
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) 5.26750 9.12357i 0.191324 0.331383i
\(759\) −17.6855 7.70198i −0.641943 0.279564i
\(760\) −1.87657 3.25031i −0.0680703 0.117901i
\(761\) 54.1749 1.96384 0.981920 0.189298i \(-0.0606213\pi\)
0.981920 + 0.189298i \(0.0606213\pi\)
\(762\) 21.8000 16.1117i 0.789729 0.583666i
\(763\) 0 0
\(764\) 31.5484 1.14138
\(765\) 6.04494 1.38826i 0.218555 0.0501927i
\(766\) 32.1489 55.6835i 1.16159 2.01193i
\(767\) −43.7025 −1.57801
\(768\) −4.09272 36.1060i −0.147683 1.30286i
\(769\) 10.4326 18.0698i 0.376208 0.651612i −0.614299 0.789074i \(-0.710561\pi\)
0.990507 + 0.137462i \(0.0438943\pi\)
\(770\) 0 0
\(771\) 7.45681 + 3.24742i 0.268551 + 0.116953i
\(772\) −4.30047 + 7.44863i −0.154777 + 0.268082i
\(773\) 27.4972 47.6266i 0.989007 1.71301i 0.366447 0.930439i \(-0.380574\pi\)
0.622561 0.782572i \(-0.286092\pi\)
\(774\) 38.3768 + 41.2491i 1.37942 + 1.48267i
\(775\) 6.19189 + 10.7247i 0.222419 + 0.385242i
\(776\) 6.84616 + 11.8579i 0.245763 + 0.425674i
\(777\) 0 0
\(778\) −26.5895 + 46.0544i −0.953281 + 1.65113i
\(779\) −22.5975 −0.809639
\(780\) 15.2515 + 6.64196i 0.546090 + 0.237820i
\(781\)