Properties

Label 441.2.g.f.79.4
Level $441$
Weight $2$
Character 441.79
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 79.4
Root \(0.920620 + 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.f.67.4

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.920620 + 1.59456i 0.650977 + 1.12753i 0.982886 + 0.184214i \(0.0589739\pi\)
−0.331909 + 0.943311i \(0.607693\pi\)
\(3\) 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 0.961877 + 0.273482i \(0.0881755\pi\)
−0.244096 + 0.969751i \(0.578491\pi\)
\(14\) 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 0.756693 0.653770i \(-0.226814\pi\)
−0.944528 + 0.328430i \(0.893480\pi\)
\(18\) 5.38358 + 1.23637i 1.26892 + 0.291416i
\(19\) 1.25211 2.16872i 0.287254 0.497538i −0.685900 0.727696i \(-0.740591\pi\)
0.973153 + 0.230158i \(0.0739244\pi\)
\(20\) 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 −0.868887 0.495011i \(-0.835164\pi\)
0.863135 + 0.504972i \(0.168497\pi\)
\(30\) −3.42323 2.53001i −0.624993 0.461914i
\(31\) −1.92388 + 3.33227i −0.345540 + 0.598493i −0.985452 0.169956i \(-0.945638\pi\)
0.639912 + 0.768448i \(0.278971\pi\)
\(32\) −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 −0.888245 0.459370i \(-0.848075\pi\)
0.841949 + 0.539557i \(0.181408\pi\)
\(38\) 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 −0.966822 0.255450i \(-0.917776\pi\)
0.262185 0.965018i \(-0.415557\pi\)
\(42\) 0 0
\(43\) 5.09988 8.83325i 0.777724 1.34706i −0.155526 0.987832i \(-0.549707\pi\)
0.933251 0.359226i \(-0.116959\pi\)
\(44\) −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 −0.970447 0.241315i \(-0.922421\pi\)
0.276238 0.961089i \(-0.410912\pi\)
\(48\) 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 0.913230 0.407444i \(-0.133580\pi\)
−0.809472 + 0.587159i \(0.800246\pi\)
\(54\) 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 0.448688 + 0.893688i \(0.351891\pi\)
−0.998301 + 0.0582689i \(0.981442\pi\)
\(60\) 0.361984 3.19342i 0.0467319 0.412269i
\(61\) 1.61958 + 2.80520i 0.207367 + 0.359169i 0.950884 0.309547i \(-0.100177\pi\)
−0.743518 + 0.668716i \(0.766844\pi\)
\(62\) −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 −0.996281 0.0861595i \(-0.972541\pi\)
0.572757 + 0.819725i \(0.305874\pi\)
\(68\) 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 0.935386 0.353629i \(-0.115052\pi\)
−0.773944 + 0.633254i \(0.781719\pi\)
\(74\) −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 0.983097 0.183086i \(-0.0586087\pi\)
−0.650106 + 0.759844i \(0.725275\pi\)
\(80\) −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 −0.977806 0.209510i \(-0.932813\pi\)
0.670344 + 0.742050i \(0.266146\pi\)
\(84\) 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 −0.900890 0.434048i \(-0.857085\pi\)
0.826341 + 0.563169i \(0.190418\pi\)
\(90\) −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 −0.370586 0.928798i \(-0.620843\pi\)
0.989656 0.143462i \(-0.0458236\pi\)
\(98\) 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 −0.691868 0.722024i \(-0.743212\pi\)
0.971225 + 0.238163i \(0.0765454\pi\)
\(108\) 4.70077 + 5.48470i 0.452332 + 0.527766i
\(109\) −4.12106 7.13788i −0.394726 0.683685i 0.598340 0.801242i \(-0.295827\pi\)
−0.993066 + 0.117557i \(0.962494\pi\)
\(110\) −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 0.974332 + 0.225115i \(0.0722758\pi\)
−0.292211 + 0.956354i \(0.594391\pi\)
\(114\) 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 0.849564 0.527485i \(-0.176865\pi\)
−0.881598 + 0.472002i \(0.843532\pi\)
\(140\) 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 0.280986 + 0.959712i \(0.409338\pi\)
−0.971628 + 0.236515i \(0.923995\pi\)
\(158\) −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 −0.521154 0.853463i \(-0.674498\pi\)
0.999697 + 0.0246014i \(0.00783167\pi\)
\(164\) 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 0.789741 0.613440i \(-0.210215\pi\)
−0.926126 + 0.377215i \(0.876882\pi\)
\(168\) 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 0.991838 0.127502i \(-0.0406958\pi\)
−0.606339 + 0.795206i \(0.707362\pi\)
\(174\) −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 0.896061 0.443931i \(-0.146416\pi\)
−0.832486 + 0.554046i \(0.813083\pi\)
\(180\) −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 −0.904910 0.425603i \(-0.860062\pi\)
0.0838717 0.996477i \(-0.473271\pi\)
\(192\) −4.13568 + 1.80108i −0.298467 + 0.129982i
\(193\) −3.09349 + 5.35808i −0.222674 + 0.385683i −0.955619 0.294605i \(-0.904812\pi\)
0.732945 + 0.680288i \(0.238145\pi\)
\(194\) 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 0.977845 0.209332i \(-0.0671289\pi\)
−0.670209 + 0.742172i \(0.733796\pi\)
\(200\) −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 0.751453 0.659786i \(-0.229353\pi\)
−0.947118 + 0.320885i \(0.896020\pi\)
\(212\) −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 −0.992779 0.119957i \(-0.961724\pi\)
0.600276 + 0.799793i \(0.295058\pi\)
\(224\) 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 0.355311 + 0.934748i \(0.384375\pi\)
−0.987171 + 0.159666i \(0.948958\pi\)
\(234\) 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 0.859662 0.510864i \(-0.170674\pi\)
−0.872252 + 0.489057i \(0.837341\pi\)
\(240\) −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 0.519079 0.854726i \(-0.326275\pi\)
−0.999754 + 0.0221730i \(0.992942\pi\)
\(270\) −12.5522 + 2.34883i −0.763903 + 0.142945i
\(271\) −7.39882 + 12.8151i −0.449446 + 0.778464i −0.998350 0.0574218i \(-0.981712\pi\)
0.548904 + 0.835886i \(0.315045\pi\)
\(272\) 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 0.159566 + 0.987187i \(0.448991\pi\)
−0.934712 + 0.355406i \(0.884343\pi\)
\(282\) 3.41901 30.1625i 0.203599 1.79615i
\(283\) 9.37768 16.2426i 0.557445 0.965524i −0.440263 0.897869i \(-0.645115\pi\)
0.997709 0.0676550i \(-0.0215517\pi\)
\(284\) 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 0.899738 0.436430i \(-0.143757\pi\)
−0.827829 + 0.560981i \(0.810424\pi\)
\(294\) 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 −0.153231 0.988190i \(-0.548968\pi\)
0.932413 0.361393i \(-0.117699\pi\)
\(312\) 8.09542 + 5.98309i 0.458313 + 0.338726i
\(313\) 2.74666 + 4.75735i 0.155250 + 0.268901i 0.933150 0.359487i \(-0.117048\pi\)
−0.777900 + 0.628388i \(0.783715\pi\)
\(314\) −31.8671 −1.79837
\(315\) 0 0
\(316\) −8.22893 −0.462914
\(317\) −4.93879 8.55424i −0.277390 0.480454i 0.693345 0.720606i \(-0.256136\pi\)
−0.970735 + 0.240152i \(0.922803\pi\)
\(318\) −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 0.996692 + 0.0812710i \(0.0258979\pi\)
−0.427963 + 0.903796i \(0.640769\pi\)
\(332\) −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 0.885698 0.464261i \(-0.153680\pi\)
−0.844911 + 0.534906i \(0.820347\pi\)
\(338\) −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 −0.131326 0.991339i \(-0.541923\pi\)
0.924188 0.381938i \(-0.124743\pi\)
\(348\) −0.119945 0.0886477i −0.00642971 0.00475202i
\(349\) −18.0006 + 31.1780i −0.963551 + 1.66892i −0.250094 + 0.968222i \(0.580461\pi\)
−0.713458 + 0.700698i \(0.752872\pi\)
\(350\) 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 −0.785761 0.618531i \(-0.787728\pi\)
0.928544 + 0.371224i \(0.121062\pi\)
\(360\) −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 −0.971549 0.236838i \(-0.923889\pi\)
0.690882 + 0.722968i \(0.257222\pi\)
\(398\) −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 0.461685 + 0.887044i \(0.347245\pi\)
−0.999045 + 0.0436908i \(0.986088\pi\)
\(410\) −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 −0.990369 0.138455i \(-0.955787\pi\)
0.375279 0.926912i \(-0.377547\pi\)
\(420\) 0 0
\(421\) −14.8304 + 25.6869i −0.722788 + 1.25191i 0.237090 + 0.971488i \(0.423806\pi\)
−0.959878 + 0.280418i \(0.909527\pi\)
\(422\) 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 0.918887 0.394520i \(-0.129089\pi\)
−0.801108 + 0.598520i \(0.795756\pi\)
\(432\) 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 0.633158 0.774022i \(-0.281758\pi\)
−0.986902 + 0.161320i \(0.948425\pi\)
\(440\) −2.26760 −0.108103
\(441\) 0 0
\(442\) 14.7617 0.702141
\(443\) 10.9510 + 18.9676i 0.520297 + 0.901180i 0.999722 + 0.0235972i \(0.00751192\pi\)
−0.479425 + 0.877583i \(0.659155\pi\)
\(444\) −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 −0.745009 0.667054i \(-0.767555\pi\)
−0.205181 0.978724i \(-0.565778\pi\)
\(458\) 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 −0.897103 0.441822i \(-0.854332\pi\)
0.831181 + 0.556003i \(0.187666\pi\)
\(462\) 0 0
\(463\) −13.9324 24.1317i −0.647494 1.12149i −0.983719 0.179711i \(-0.942484\pi\)
0.336225 0.941782i \(-0.390850\pi\)
\(464\) −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 −0.373661 0.927565i \(-0.621898\pi\)
0.990126 0.140182i \(-0.0447689\pi\)
\(468\) −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 0.862536 0.505996i \(-0.168875\pi\)
−0.869473 + 0.493980i \(0.835541\pi\)
\(488\) 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 0.585498 0.810674i \(-0.300899\pi\)
−0.994813 + 0.101720i \(0.967566\pi\)
\(492\) 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 0.995890 0.0905758i \(-0.0288707\pi\)
−0.576386 + 0.817178i \(0.695537\pi\)
\(522\) −0.233061 + 0.250504i −0.0102008 + 0.0109643i
\(523\) 20.9715 36.3236i 0.917018 1.58832i 0.113097 0.993584i \(-0.463923\pi\)
0.803920 0.594737i \(-0.202744\pi\)
\(524\) −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 −0.895371 0.445320i \(-0.853090\pi\)
0.833344 + 0.552754i \(0.186423\pi\)
\(542\) −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 −0.834840 0.550492i \(-0.814440\pi\)
0.894160 + 0.447747i \(0.147773\pi\)
\(548\) −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 0.981078 + 0.193614i \(0.0620211\pi\)
−0.322864 + 0.946445i \(0.604646\pi\)
\(558\) −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 −0.862975 0.505247i \(-0.831401\pi\)
0.869044 + 0.494734i \(0.164735\pi\)
\(564\) 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 0.983878 0.178843i \(-0.0572354\pi\)
−0.646821 + 0.762641i \(0.723902\pi\)
\(570\) −9.77313 + 4.25616i −0.409351 + 0.178271i
\(571\) 7.64289 13.2379i 0.319845 0.553988i −0.660610 0.750729i \(-0.729702\pi\)
0.980456 + 0.196741i \(0.0630358\pi\)
\(572\) −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 −0.999994 0.00340833i \(-0.998915\pi\)
0.497045 0.867725i \(-0.334418\pi\)
\(578\) 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 0.207339 + 0.978269i \(0.433520\pi\)
−0.950875 + 0.309574i \(0.899814\pi\)
\(588\) 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 0.487953 + 0.872870i \(0.337744\pi\)
−0.999904 + 0.0138558i \(0.995589\pi\)
\(594\) 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 0.107019 + 0.994257i \(0.465869\pi\)
−0.914561 + 0.404447i \(0.867464\pi\)
\(600\) −5.73873 + 2.49920i −0.234283 + 0.102029i
\(601\) −1.86447 + 3.22936i −0.0760534 + 0.131728i −0.901544 0.432688i \(-0.857565\pi\)
0.825490 + 0.564416i \(0.190899\pi\)
\(602\) 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 0.901833 0.432084i \(-0.142222\pi\)
−0.825113 + 0.564968i \(0.808888\pi\)
\(614\) 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 −0.965965 0.258672i \(-0.916715\pi\)
0.258966 0.965886i \(-0.416618\pi\)
\(618\) −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 −0.865448 0.501000i \(-0.832966\pi\)
−0.00115462 0.999999i \(-0.500368\pi\)
\(644\) 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 −0.859381 0.511336i \(-0.829151\pi\)
−0.0131398 0.999914i \(-0.504183\pi\)
\(648\) −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 0.175356 + 0.984505i \(0.443892\pi\)
−0.940284 + 0.340390i \(0.889441\pi\)
\(660\) 0.547687 4.83170i 0.0213187 0.188074i
\(661\) −0.0933694 + 0.161721i −0.00363165 + 0.00629020i −0.867836 0.496852i \(-0.834489\pi\)
0.864204 + 0.503142i \(0.167823\pi\)
\(662\) −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 −0.951544 0.307512i \(-0.900503\pi\)
0.742086 + 0.670305i \(0.233837\pi\)
\(674\) −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 0.998571 + 0.0534326i \(0.0170162\pi\)
−0.453012 + 0.891505i \(0.649650\pi\)
\(678\) −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 0.956779 0.290816i \(-0.0939267\pi\)
−0.730243 + 0.683187i \(0.760593\pi\)
\(684\) 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 0.956770 0.290844i \(-0.0939361\pi\)
−0.730264 + 0.683165i \(0.760603\pi\)
\(692\) −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 0.860096 0.510133i \(-0.170404\pi\)
−0.871836 + 0.489798i \(0.837070\pi\)
\(710\) 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 −0.998681 0.0513506i \(-0.983647\pi\)
0.543811 + 0.839208i \(0.316981\pi\)
\(720\) −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 −0.265899 0.964001i \(-0.585669\pi\)
0.967799 0.251726i \(-0.0809980\pi\)
\(728\) 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 −0.997587 0.0694277i \(-0.977883\pi\)
0.438667 0.898650i \(-0.355451\pi\)
\(740\) 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 0.815498 0.578760i \(-0.196463\pi\)
−0.908970 + 0.416862i \(0.863130\pi\)
\(744\) −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 0.990507 0.137462i \(-0.0438943\pi\)
−0.614299 + 0.789074i \(0.710561\pi\)
\(770\) 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 0.622561 + 0.782572i \(0.286092\pi\)
0.366447 + 0.930439i \(0.380574\pi\)
\(774\) 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
\(781\) −18.6560 −0.667566