Properties

Label 69.2.g.a.11.4
Level $69$
Weight $2$
Character 69.11
Analytic conductor $0.551$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,2,Mod(5,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 69.g (of order \(22\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.550967773947\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 11.4
Character \(\chi\) \(=\) 69.11
Dual form 69.2.g.a.44.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0493131 + 0.0767326i) q^{2} +(-1.63918 - 0.559548i) q^{3} +(0.827374 - 1.81170i) q^{4} +(2.86859 - 0.842294i) q^{5} +(-0.0378973 - 0.153371i) q^{6} +(-1.75762 + 1.52299i) q^{7} +(0.360384 - 0.0518154i) q^{8} +(2.37381 + 1.83440i) q^{9} +O(q^{10})\) \(q+(0.0493131 + 0.0767326i) q^{2} +(-1.63918 - 0.559548i) q^{3} +(0.827374 - 1.81170i) q^{4} +(2.86859 - 0.842294i) q^{5} +(-0.0378973 - 0.153371i) q^{6} +(-1.75762 + 1.52299i) q^{7} +(0.360384 - 0.0518154i) q^{8} +(2.37381 + 1.83440i) q^{9} +(0.206090 + 0.178578i) q^{10} +(-1.83549 - 1.17959i) q^{11} +(-2.36995 + 2.50674i) q^{12} +(-2.74970 + 3.17332i) q^{13} +(-0.203536 - 0.0597637i) q^{14} +(-5.17344 - 0.224445i) q^{15} +(-2.58680 - 2.98533i) q^{16} +(1.67699 + 3.67210i) q^{17} +(-0.0236984 + 0.272609i) q^{18} +(2.40861 + 1.09998i) q^{19} +(0.847416 - 5.89391i) q^{20} +(3.73324 - 1.51297i) q^{21} -0.199011i q^{22} +(3.72801 + 3.01694i) q^{23} +(-0.619727 - 0.116718i) q^{24} +(3.31309 - 2.12919i) q^{25} +(-0.379093 - 0.0545053i) q^{26} +(-2.86466 - 4.33517i) q^{27} +(1.30498 + 4.44435i) q^{28} +(-5.44962 + 2.48876i) q^{29} +(-0.237896 - 0.408039i) q^{30} +(-0.113954 - 0.792566i) q^{31} +(0.306661 - 1.04439i) q^{32} +(2.34865 + 2.96061i) q^{33} +(-0.199072 + 0.309763i) q^{34} +(-3.75909 + 5.84926i) q^{35} +(5.28740 - 2.78289i) q^{36} +(2.32136 - 7.90582i) q^{37} +(0.0343720 + 0.239062i) q^{38} +(6.28287 - 3.66305i) q^{39} +(0.990151 - 0.452187i) q^{40} +(-2.47018 - 8.41266i) q^{41} +(0.300192 + 0.211852i) q^{42} +(-2.82529 - 0.406215i) q^{43} +(-3.65570 + 2.34938i) q^{44} +(8.35460 + 3.26269i) q^{45} +(-0.0476583 + 0.434835i) q^{46} +1.51008i q^{47} +(2.56979 + 6.34092i) q^{48} +(-0.226463 + 1.57508i) q^{49} +(0.326757 + 0.149225i) q^{50} +(-0.694172 - 6.95759i) q^{51} +(3.47406 + 7.60714i) q^{52} +(-8.87718 - 10.2448i) q^{53} +(0.191384 - 0.433594i) q^{54} +(-6.25882 - 1.83776i) q^{55} +(-0.554504 + 0.639932i) q^{56} +(-3.33266 - 3.15080i) q^{57} +(-0.459706 - 0.295435i) q^{58} +(8.68772 + 7.52796i) q^{59} +(-4.68699 + 9.18700i) q^{60} +(7.58399 - 1.09041i) q^{61} +(0.0551963 - 0.0478278i) q^{62} +(-6.96603 + 0.391106i) q^{63} +(-7.48502 + 2.19780i) q^{64} +(-5.21489 + 11.4190i) q^{65} +(-0.111356 + 0.326215i) q^{66} +(-3.16308 - 4.92185i) q^{67} +8.04024 q^{68} +(-4.42275 - 7.03131i) q^{69} -0.634201 q^{70} +(-0.646263 - 1.00561i) q^{71} +(0.950534 + 0.538088i) q^{72} +(-4.99950 + 10.9474i) q^{73} +(0.721107 - 0.211736i) q^{74} +(-6.62213 + 1.63629i) q^{75} +(3.98565 - 3.45358i) q^{76} +(5.02260 - 0.722140i) q^{77} +(0.590903 + 0.301465i) q^{78} +(-3.43555 - 2.97692i) q^{79} +(-9.93499 - 6.38483i) q^{80} +(2.26996 + 8.70903i) q^{81} +(0.523713 - 0.604397i) q^{82} +(4.90673 + 1.44075i) q^{83} +(0.347736 - 8.01529i) q^{84} +(7.90360 + 9.12124i) q^{85} +(-0.108154 - 0.236824i) q^{86} +(10.3255 - 1.03019i) q^{87} +(-0.722601 - 0.330001i) q^{88} +(0.192932 - 1.34187i) q^{89} +(0.161636 + 0.801963i) q^{90} -9.76524i q^{91} +(8.55024 - 4.25788i) q^{92} +(-0.256689 + 1.36292i) q^{93} +(-0.115873 + 0.0744668i) q^{94} +(7.83583 + 1.12662i) q^{95} +(-1.08706 + 1.54035i) q^{96} +(-0.909010 - 3.09580i) q^{97} +(-0.132028 + 0.0602950i) q^{98} +(-2.19325 - 6.16715i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 11 q^{3} - 10 q^{4} - 14 q^{6} - 22 q^{7} - 11 q^{9} - 22 q^{10} + 4 q^{12} - 22 q^{13} - 46 q^{16} + 12 q^{18} - 22 q^{19} + 22 q^{21} + 50 q^{24} + 8 q^{25} + 10 q^{27} - 22 q^{28} + 33 q^{30} - 22 q^{31} + 22 q^{36} + 22 q^{37} + 13 q^{39} + 132 q^{40} - 11 q^{42} + 22 q^{43} + 66 q^{46} - 58 q^{48} + 68 q^{49} - 11 q^{51} + 94 q^{52} - 33 q^{54} - 44 q^{57} - 8 q^{58} - 121 q^{60} - 66 q^{61} - 66 q^{63} - 20 q^{64} - 66 q^{66} - 44 q^{67} - 66 q^{69} - 132 q^{70} - 101 q^{72} - 44 q^{73} - 44 q^{75} - 110 q^{76} + 84 q^{78} - 66 q^{79} + 77 q^{81} - 132 q^{82} + 77 q^{84} - 44 q^{85} + 73 q^{87} + 66 q^{88} + 176 q^{90} + 116 q^{93} + 100 q^{94} + 85 q^{96} + 44 q^{97} + 121 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{9}{22}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0493131 + 0.0767326i 0.0348696 + 0.0542581i 0.858251 0.513231i \(-0.171551\pi\)
−0.823381 + 0.567489i \(0.807915\pi\)
\(3\) −1.63918 0.559548i −0.946380 0.323055i
\(4\) 0.827374 1.81170i 0.413687 0.905848i
\(5\) 2.86859 0.842294i 1.28287 0.376685i 0.431913 0.901915i \(-0.357839\pi\)
0.850960 + 0.525230i \(0.176021\pi\)
\(6\) −0.0378973 0.153371i −0.0154715 0.0626136i
\(7\) −1.75762 + 1.52299i −0.664318 + 0.575635i −0.920380 0.391025i \(-0.872120\pi\)
0.256062 + 0.966660i \(0.417575\pi\)
\(8\) 0.360384 0.0518154i 0.127415 0.0183195i
\(9\) 2.37381 + 1.83440i 0.791270 + 0.611466i
\(10\) 0.206090 + 0.178578i 0.0651715 + 0.0564714i
\(11\) −1.83549 1.17959i −0.553420 0.355661i 0.233847 0.972273i \(-0.424868\pi\)
−0.787267 + 0.616612i \(0.788505\pi\)
\(12\) −2.36995 + 2.50674i −0.684144 + 0.723633i
\(13\) −2.74970 + 3.17332i −0.762629 + 0.880120i −0.995728 0.0923325i \(-0.970568\pi\)
0.233100 + 0.972453i \(0.425113\pi\)
\(14\) −0.203536 0.0597637i −0.0543974 0.0159725i
\(15\) −5.17344 0.224445i −1.33578 0.0579514i
\(16\) −2.58680 2.98533i −0.646700 0.746331i
\(17\) 1.67699 + 3.67210i 0.406731 + 0.890616i 0.996543 + 0.0830757i \(0.0264743\pi\)
−0.589813 + 0.807540i \(0.700798\pi\)
\(18\) −0.0236984 + 0.272609i −0.00558576 + 0.0642544i
\(19\) 2.40861 + 1.09998i 0.552574 + 0.252352i 0.672076 0.740482i \(-0.265403\pi\)
−0.119502 + 0.992834i \(0.538130\pi\)
\(20\) 0.847416 5.89391i 0.189488 1.31792i
\(21\) 3.73324 1.51297i 0.814660 0.330158i
\(22\) 0.199011i 0.0424293i
\(23\) 3.72801 + 3.01694i 0.777344 + 0.629076i
\(24\) −0.619727 0.116718i −0.126501 0.0238249i
\(25\) 3.31309 2.12919i 0.662618 0.425838i
\(26\) −0.379093 0.0545053i −0.0743462 0.0106894i
\(27\) −2.86466 4.33517i −0.551305 0.834304i
\(28\) 1.30498 + 4.44435i 0.246618 + 0.839904i
\(29\) −5.44962 + 2.48876i −1.01197 + 0.462151i −0.851200 0.524841i \(-0.824125\pi\)
−0.160769 + 0.986992i \(0.551397\pi\)
\(30\) −0.237896 0.408039i −0.0434336 0.0744975i
\(31\) −0.113954 0.792566i −0.0204667 0.142349i 0.977026 0.213121i \(-0.0683629\pi\)
−0.997493 + 0.0707719i \(0.977454\pi\)
\(32\) 0.306661 1.04439i 0.0542105 0.184624i
\(33\) 2.34865 + 2.96061i 0.408847 + 0.515376i
\(34\) −0.199072 + 0.309763i −0.0341406 + 0.0531239i
\(35\) −3.75909 + 5.84926i −0.635403 + 0.988706i
\(36\) 5.28740 2.78289i 0.881234 0.463815i
\(37\) 2.32136 7.90582i 0.381629 1.29971i −0.515101 0.857130i \(-0.672245\pi\)
0.896729 0.442579i \(-0.145936\pi\)
\(38\) 0.0343720 + 0.239062i 0.00557587 + 0.0387811i
\(39\) 6.28287 3.66305i 1.00606 0.586557i
\(40\) 0.990151 0.452187i 0.156557 0.0714970i
\(41\) −2.47018 8.41266i −0.385777 1.31384i −0.892235 0.451572i \(-0.850864\pi\)
0.506458 0.862265i \(-0.330955\pi\)
\(42\) 0.300192 + 0.211852i 0.0463206 + 0.0326894i
\(43\) −2.82529 0.406215i −0.430853 0.0619473i −0.0765230 0.997068i \(-0.524382\pi\)
−0.354330 + 0.935121i \(0.615291\pi\)
\(44\) −3.65570 + 2.34938i −0.551118 + 0.354182i
\(45\) 8.35460 + 3.26269i 1.24543 + 0.486374i
\(46\) −0.0476583 + 0.434835i −0.00702684 + 0.0641129i
\(47\) 1.51008i 0.220268i 0.993917 + 0.110134i \(0.0351280\pi\)
−0.993917 + 0.110134i \(0.964872\pi\)
\(48\) 2.56979 + 6.34092i 0.370917 + 0.915233i
\(49\) −0.226463 + 1.57508i −0.0323518 + 0.225012i
\(50\) 0.326757 + 0.149225i 0.0462104 + 0.0211036i
\(51\) −0.694172 6.95759i −0.0972035 0.974258i
\(52\) 3.47406 + 7.60714i 0.481766 + 1.05492i
\(53\) −8.87718 10.2448i −1.21937 1.40723i −0.885516 0.464610i \(-0.846195\pi\)
−0.333858 0.942623i \(-0.608351\pi\)
\(54\) 0.191384 0.433594i 0.0260440 0.0590046i
\(55\) −6.25882 1.83776i −0.843940 0.247803i
\(56\) −0.554504 + 0.639932i −0.0740988 + 0.0855145i
\(57\) −3.33266 3.15080i −0.441421 0.417333i
\(58\) −0.459706 0.295435i −0.0603624 0.0387925i
\(59\) 8.68772 + 7.52796i 1.13105 + 0.980056i 0.999936 0.0113115i \(-0.00360064\pi\)
0.131109 + 0.991368i \(0.458146\pi\)
\(60\) −4.68699 + 9.18700i −0.605088 + 1.18604i
\(61\) 7.58399 1.09041i 0.971030 0.139613i 0.361497 0.932373i \(-0.382266\pi\)
0.609534 + 0.792760i \(0.291357\pi\)
\(62\) 0.0551963 0.0478278i 0.00700993 0.00607414i
\(63\) −6.96603 + 0.391106i −0.877637 + 0.0492747i
\(64\) −7.48502 + 2.19780i −0.935628 + 0.274725i
\(65\) −5.21489 + 11.4190i −0.646827 + 1.41635i
\(66\) −0.111356 + 0.326215i −0.0137070 + 0.0401542i
\(67\) −3.16308 4.92185i −0.386432 0.601300i 0.592479 0.805586i \(-0.298149\pi\)
−0.978911 + 0.204286i \(0.934513\pi\)
\(68\) 8.04024 0.975022
\(69\) −4.42275 7.03131i −0.532436 0.846470i
\(70\) −0.634201 −0.0758016
\(71\) −0.646263 1.00561i −0.0766973 0.119343i 0.800786 0.598951i \(-0.204415\pi\)
−0.877483 + 0.479607i \(0.840779\pi\)
\(72\) 0.950534 + 0.538088i 0.112022 + 0.0634143i
\(73\) −4.99950 + 10.9474i −0.585147 + 1.28129i 0.353184 + 0.935554i \(0.385099\pi\)
−0.938331 + 0.345739i \(0.887628\pi\)
\(74\) 0.721107 0.211736i 0.0838270 0.0246138i
\(75\) −6.62213 + 1.63629i −0.764657 + 0.188943i
\(76\) 3.98565 3.45358i 0.457185 0.396153i
\(77\) 5.02260 0.722140i 0.572378 0.0822955i
\(78\) 0.590903 + 0.301465i 0.0669065 + 0.0341342i
\(79\) −3.43555 2.97692i −0.386530 0.334930i 0.439821 0.898085i \(-0.355042\pi\)
−0.826351 + 0.563155i \(0.809587\pi\)
\(80\) −9.93499 6.38483i −1.11077 0.713846i
\(81\) 2.26996 + 8.70903i 0.252218 + 0.967671i
\(82\) 0.523713 0.604397i 0.0578344 0.0667445i
\(83\) 4.90673 + 1.44075i 0.538584 + 0.158143i 0.539701 0.841857i \(-0.318537\pi\)
−0.00111693 + 0.999999i \(0.500356\pi\)
\(84\) 0.347736 8.01529i 0.0379411 0.874540i
\(85\) 7.90360 + 9.12124i 0.857266 + 0.989337i
\(86\) −0.108154 0.236824i −0.0116625 0.0255373i
\(87\) 10.3255 1.03019i 1.10701 0.110448i
\(88\) −0.722601 0.330001i −0.0770295 0.0351782i
\(89\) 0.192932 1.34187i 0.0204508 0.142238i −0.977038 0.213066i \(-0.931655\pi\)
0.997489 + 0.0708278i \(0.0225641\pi\)
\(90\) 0.161636 + 0.801963i 0.0170379 + 0.0845344i
\(91\) 9.76524i 1.02368i
\(92\) 8.55024 4.25788i 0.891424 0.443915i
\(93\) −0.256689 + 1.36292i −0.0266174 + 0.141328i
\(94\) −0.115873 + 0.0744668i −0.0119513 + 0.00768066i
\(95\) 7.83583 + 1.12662i 0.803940 + 0.115589i
\(96\) −1.08706 + 1.54035i −0.110948 + 0.157211i
\(97\) −0.909010 3.09580i −0.0922960 0.314331i 0.900386 0.435093i \(-0.143284\pi\)
−0.992682 + 0.120762i \(0.961466\pi\)
\(98\) −0.132028 + 0.0602950i −0.0133368 + 0.00609072i
\(99\) −2.19325 6.16715i −0.220430 0.619822i
\(100\) −1.11629 7.76395i −0.111629 0.776395i
\(101\) 0.00740668 0.0252248i 0.000736992 0.00250997i −0.959124 0.282987i \(-0.908675\pi\)
0.959861 + 0.280477i \(0.0904928\pi\)
\(102\) 0.499642 0.396366i 0.0494720 0.0392460i
\(103\) −3.92526 + 6.10783i −0.386768 + 0.601822i −0.978979 0.203960i \(-0.934619\pi\)
0.592211 + 0.805783i \(0.298255\pi\)
\(104\) −0.826520 + 1.28609i −0.0810470 + 0.126112i
\(105\) 9.43477 7.48459i 0.920739 0.730421i
\(106\) 0.348350 1.18637i 0.0338348 0.115231i
\(107\) −1.79487 12.4836i −0.173517 1.20684i −0.871382 0.490606i \(-0.836775\pi\)
0.697865 0.716229i \(-0.254134\pi\)
\(108\) −10.2242 + 1.60310i −0.983820 + 0.154258i
\(109\) 6.78010 3.09637i 0.649416 0.296578i −0.0633385 0.997992i \(-0.520175\pi\)
0.712754 + 0.701414i \(0.247448\pi\)
\(110\) −0.167626 0.570881i −0.0159825 0.0544314i
\(111\) −8.22881 + 11.6601i −0.781044 + 1.10673i
\(112\) 9.09322 + 1.30741i 0.859229 + 0.123538i
\(113\) 6.35973 4.08715i 0.598273 0.384486i −0.206171 0.978516i \(-0.566100\pi\)
0.804443 + 0.594030i \(0.202464\pi\)
\(114\) 0.0774252 0.411099i 0.00725153 0.0385029i
\(115\) 13.2353 + 5.51429i 1.23420 + 0.514210i
\(116\) 11.9322i 1.10788i
\(117\) −12.3484 + 2.48882i −1.14161 + 0.230091i
\(118\) −0.149221 + 1.03786i −0.0137370 + 0.0955426i
\(119\) −8.54008 3.90013i −0.782868 0.357524i
\(120\) −1.87605 + 0.187177i −0.171260 + 0.0170869i
\(121\) −2.59200 5.67569i −0.235637 0.515972i
\(122\) 0.457660 + 0.528168i 0.0414346 + 0.0478181i
\(123\) −0.658225 + 15.1720i −0.0593502 + 1.36802i
\(124\) −1.53017 0.449299i −0.137413 0.0403482i
\(125\) −2.07868 + 2.39893i −0.185923 + 0.214566i
\(126\) −0.373527 0.515235i −0.0332764 0.0459008i
\(127\) 2.86462 + 1.84098i 0.254194 + 0.163360i 0.661532 0.749917i \(-0.269907\pi\)
−0.407338 + 0.913277i \(0.633543\pi\)
\(128\) −2.18299 1.89157i −0.192951 0.167193i
\(129\) 4.40386 + 2.24675i 0.387738 + 0.197815i
\(130\) −1.13337 + 0.162954i −0.0994033 + 0.0142920i
\(131\) 7.58982 6.57662i 0.663126 0.574602i −0.256910 0.966435i \(-0.582705\pi\)
0.920036 + 0.391834i \(0.128159\pi\)
\(132\) 7.30693 1.80550i 0.635987 0.157149i
\(133\) −5.90868 + 1.73495i −0.512348 + 0.150439i
\(134\) 0.221685 0.485423i 0.0191507 0.0419342i
\(135\) −11.8690 10.0229i −1.02152 0.862637i
\(136\) 0.794633 + 1.23647i 0.0681392 + 0.106027i
\(137\) 0.176109 0.0150460 0.00752300 0.999972i \(-0.497605\pi\)
0.00752300 + 0.999972i \(0.497605\pi\)
\(138\) 0.321431 0.686104i 0.0273621 0.0584051i
\(139\) 0.0267888 0.00227220 0.00113610 0.999999i \(-0.499638\pi\)
0.00113610 + 0.999999i \(0.499638\pi\)
\(140\) 7.48691 + 11.6499i 0.632759 + 0.984593i
\(141\) 0.844965 2.47530i 0.0711589 0.208457i
\(142\) 0.0452935 0.0991789i 0.00380095 0.00832291i
\(143\) 8.79026 2.58105i 0.735078 0.215839i
\(144\) −0.664294 11.8318i −0.0553578 0.985985i
\(145\) −13.5365 + 11.7294i −1.12414 + 0.974075i
\(146\) −1.08656 + 0.156224i −0.0899244 + 0.0129292i
\(147\) 1.25255 2.45512i 0.103308 0.202495i
\(148\) −12.4023 10.7467i −1.01946 0.883370i
\(149\) 6.93332 + 4.45577i 0.568000 + 0.365031i 0.792901 0.609350i \(-0.208570\pi\)
−0.224901 + 0.974382i \(0.572206\pi\)
\(150\) −0.452114 0.427442i −0.0369150 0.0349005i
\(151\) −10.0638 + 11.6142i −0.818979 + 0.945153i −0.999260 0.0384627i \(-0.987754\pi\)
0.180281 + 0.983615i \(0.442299\pi\)
\(152\) 0.925022 + 0.271611i 0.0750292 + 0.0220306i
\(153\) −2.75524 + 11.7932i −0.222748 + 0.953420i
\(154\) 0.303091 + 0.349786i 0.0244238 + 0.0281866i
\(155\) −0.994461 2.17757i −0.0798770 0.174906i
\(156\) −1.43805 14.4134i −0.115136 1.15399i
\(157\) −6.74721 3.08135i −0.538486 0.245918i 0.127557 0.991831i \(-0.459286\pi\)
−0.666044 + 0.745913i \(0.732014\pi\)
\(158\) 0.0590095 0.410420i 0.00469455 0.0326513i
\(159\) 8.81881 + 21.7603i 0.699377 + 1.72570i
\(160\) 3.25423i 0.257269i
\(161\) −11.1472 + 0.375070i −0.878522 + 0.0295596i
\(162\) −0.556328 + 0.603649i −0.0437093 + 0.0474271i
\(163\) 7.41896 4.76787i 0.581098 0.373449i −0.216823 0.976211i \(-0.569570\pi\)
0.797921 + 0.602762i \(0.205933\pi\)
\(164\) −17.2849 2.48520i −1.34973 0.194061i
\(165\) 9.23101 + 6.51453i 0.718633 + 0.507155i
\(166\) 0.131414 + 0.447554i 0.0101997 + 0.0347369i
\(167\) −12.9651 + 5.92096i −1.00327 + 0.458178i −0.848172 0.529722i \(-0.822296\pi\)
−0.155097 + 0.987899i \(0.549569\pi\)
\(168\) 1.26700 0.738691i 0.0977515 0.0569912i
\(169\) −0.659030 4.58365i −0.0506946 0.352589i
\(170\) −0.310146 + 1.05626i −0.0237871 + 0.0810114i
\(171\) 3.69980 + 7.02950i 0.282931 + 0.537559i
\(172\) −3.07351 + 4.78248i −0.234353 + 0.364660i
\(173\) −3.74820 + 5.83232i −0.284971 + 0.443423i −0.953997 0.299816i \(-0.903075\pi\)
0.669027 + 0.743238i \(0.266711\pi\)
\(174\) 0.588230 + 0.741499i 0.0445936 + 0.0562129i
\(175\) −2.58042 + 8.78810i −0.195061 + 0.664318i
\(176\) 1.22656 + 8.53090i 0.0924553 + 0.643040i
\(177\) −10.0285 17.2009i −0.753786 1.29290i
\(178\) 0.112480 0.0513677i 0.00843070 0.00385017i
\(179\) 3.67930 + 12.5305i 0.275003 + 0.936576i 0.974958 + 0.222388i \(0.0713853\pi\)
−0.699955 + 0.714187i \(0.746796\pi\)
\(180\) 12.8234 12.4365i 0.955799 0.926964i
\(181\) 17.4433 + 2.50797i 1.29655 + 0.186416i 0.755821 0.654779i \(-0.227238\pi\)
0.540732 + 0.841195i \(0.318147\pi\)
\(182\) 0.749313 0.481554i 0.0555427 0.0356952i
\(183\) −13.0417 2.45623i −0.964067 0.181570i
\(184\) 1.49984 + 0.894090i 0.110570 + 0.0659132i
\(185\) 24.6338i 1.81112i
\(186\) −0.117238 + 0.0475134i −0.00859634 + 0.00348385i
\(187\) 1.25350 8.71826i 0.0916648 0.637543i
\(188\) 2.73581 + 1.24940i 0.199530 + 0.0911221i
\(189\) 11.6374 + 3.25674i 0.846496 + 0.236893i
\(190\) 0.299960 + 0.656821i 0.0217614 + 0.0476508i
\(191\) 5.26648 + 6.07784i 0.381069 + 0.439777i 0.913588 0.406641i \(-0.133300\pi\)
−0.532519 + 0.846418i \(0.678755\pi\)
\(192\) 13.4991 + 0.585645i 0.974211 + 0.0422653i
\(193\) 14.7495 + 4.33084i 1.06169 + 0.311740i 0.765532 0.643398i \(-0.222476\pi\)
0.296159 + 0.955139i \(0.404294\pi\)
\(194\) 0.192723 0.222414i 0.0138367 0.0159684i
\(195\) 14.9376 15.7998i 1.06971 1.13145i
\(196\) 2.66620 + 1.71346i 0.190443 + 0.122390i
\(197\) −7.54187 6.53507i −0.537336 0.465604i 0.343415 0.939184i \(-0.388416\pi\)
−0.880751 + 0.473579i \(0.842962\pi\)
\(198\) 0.365066 0.472415i 0.0259441 0.0335730i
\(199\) 3.33749 0.479858i 0.236588 0.0340162i −0.0230008 0.999735i \(-0.507322\pi\)
0.259589 + 0.965719i \(0.416413\pi\)
\(200\) 1.08366 0.938996i 0.0766263 0.0663970i
\(201\) 2.43084 + 9.83769i 0.171458 + 0.693897i
\(202\) 0.00230081 0.000675580i 0.000161885 4.75336e-5i
\(203\) 5.78802 12.6740i 0.406239 0.889540i
\(204\) −13.1794 4.49890i −0.922741 0.314986i
\(205\) −14.1719 22.0519i −0.989806 1.54017i
\(206\) −0.662236 −0.0461402
\(207\) 3.31531 + 14.0003i 0.230430 + 0.973089i
\(208\) 16.5863 1.15005
\(209\) −3.12345 4.86018i −0.216053 0.336186i
\(210\) 1.03957 + 0.354866i 0.0717371 + 0.0244881i
\(211\) 9.21238 20.1723i 0.634206 1.38872i −0.270516 0.962715i \(-0.587194\pi\)
0.904722 0.426002i \(-0.140078\pi\)
\(212\) −25.9052 + 7.60646i −1.77918 + 0.522414i
\(213\) 0.496656 + 2.00998i 0.0340303 + 0.137722i
\(214\) 0.869389 0.753330i 0.0594302 0.0514966i
\(215\) −8.44675 + 1.21446i −0.576064 + 0.0828255i
\(216\) −1.25701 1.41389i −0.0855286 0.0962032i
\(217\) 1.40736 + 1.21948i 0.0955375 + 0.0827837i
\(218\) 0.571940 + 0.367563i 0.0387366 + 0.0248945i
\(219\) 14.3207 15.1472i 0.967700 1.02356i
\(220\) −8.50784 + 9.81857i −0.573599 + 0.661968i
\(221\) −16.2640 4.77553i −1.09403 0.321237i
\(222\) −1.30050 0.0564210i −0.0872839 0.00378673i
\(223\) 5.94109 + 6.85638i 0.397845 + 0.459137i 0.918961 0.394348i \(-0.129030\pi\)
−0.521116 + 0.853486i \(0.674484\pi\)
\(224\) 1.05160 + 2.30268i 0.0702630 + 0.153855i
\(225\) 11.7704 + 1.02323i 0.784696 + 0.0682150i
\(226\) 0.627235 + 0.286449i 0.0417230 + 0.0190543i
\(227\) −1.48093 + 10.3001i −0.0982930 + 0.683643i 0.879780 + 0.475381i \(0.157690\pi\)
−0.978073 + 0.208262i \(0.933219\pi\)
\(228\) −8.46564 + 3.43088i −0.560651 + 0.227215i
\(229\) 8.08087i 0.533999i 0.963697 + 0.266999i \(0.0860322\pi\)
−0.963697 + 0.266999i \(0.913968\pi\)
\(230\) 0.229546 + 1.28750i 0.0151358 + 0.0848956i
\(231\) −8.63700 1.62667i −0.568273 0.107027i
\(232\) −1.83500 + 1.17928i −0.120474 + 0.0774237i
\(233\) 1.22435 + 0.176036i 0.0802101 + 0.0115325i 0.182303 0.983242i \(-0.441645\pi\)
−0.102093 + 0.994775i \(0.532554\pi\)
\(234\) −0.799911 0.824793i −0.0522918 0.0539184i
\(235\) 1.27193 + 4.33181i 0.0829718 + 0.282576i
\(236\) 20.8264 9.51108i 1.35568 0.619119i
\(237\) 3.96575 + 6.80207i 0.257603 + 0.441842i
\(238\) −0.121871 0.847630i −0.00789971 0.0549437i
\(239\) −4.83072 + 16.4519i −0.312474 + 1.06419i 0.642201 + 0.766536i \(0.278021\pi\)
−0.954675 + 0.297651i \(0.903797\pi\)
\(240\) 12.7126 + 16.0250i 0.820595 + 1.03441i
\(241\) −7.72335 + 12.0178i −0.497505 + 0.774132i −0.995671 0.0929492i \(-0.970371\pi\)
0.498166 + 0.867082i \(0.334007\pi\)
\(242\) 0.307691 0.478777i 0.0197791 0.0307769i
\(243\) 1.15226 15.5458i 0.0739175 0.997264i
\(244\) 4.29930 14.6421i 0.275234 0.937362i
\(245\) 0.677054 + 4.70902i 0.0432554 + 0.300848i
\(246\) −1.19665 + 0.697672i −0.0762955 + 0.0444819i
\(247\) −10.1135 + 4.61870i −0.643509 + 0.293881i
\(248\) −0.0821343 0.279724i −0.00521553 0.0177625i
\(249\) −7.23684 5.10720i −0.458616 0.323655i
\(250\) −0.286582 0.0412043i −0.0181250 0.00260599i
\(251\) 17.2979 11.1167i 1.09184 0.701681i 0.134575 0.990903i \(-0.457033\pi\)
0.957262 + 0.289223i \(0.0933969\pi\)
\(252\) −5.05494 + 12.9439i −0.318432 + 0.815390i
\(253\) −3.28394 9.93510i −0.206459 0.624614i
\(254\) 0.310594i 0.0194884i
\(255\) −7.85163 19.3738i −0.491688 1.21323i
\(256\) −2.18291 + 15.1824i −0.136432 + 0.948903i
\(257\) 6.32741 + 2.88963i 0.394693 + 0.180250i 0.602867 0.797842i \(-0.294025\pi\)
−0.208174 + 0.978092i \(0.566752\pi\)
\(258\) 0.0447690 + 0.448713i 0.00278719 + 0.0279357i
\(259\) 7.96039 + 17.4308i 0.494635 + 1.08310i
\(260\) 16.3731 + 18.8956i 1.01542 + 1.17185i
\(261\) −17.5017 4.08894i −1.08333 0.253099i
\(262\) 0.878918 + 0.258074i 0.0542997 + 0.0159438i
\(263\) 7.02743 8.11008i 0.433330 0.500089i −0.496522 0.868024i \(-0.665390\pi\)
0.929851 + 0.367935i \(0.119935\pi\)
\(264\) 0.999821 + 0.945260i 0.0615347 + 0.0581768i
\(265\) −34.0941 21.9110i −2.09439 1.34598i
\(266\) −0.424502 0.367833i −0.0260279 0.0225533i
\(267\) −1.06709 + 2.09162i −0.0653051 + 0.128005i
\(268\) −11.5340 + 1.65833i −0.704548 + 0.101299i
\(269\) −10.3530 + 8.97091i −0.631232 + 0.546966i −0.910637 0.413207i \(-0.864408\pi\)
0.279404 + 0.960173i \(0.409863\pi\)
\(270\) 0.183788 1.40500i 0.0111850 0.0855058i
\(271\) −24.5704 + 7.21453i −1.49255 + 0.438251i −0.923353 0.383952i \(-0.874563\pi\)
−0.569194 + 0.822203i \(0.692745\pi\)
\(272\) 6.62438 14.5054i 0.401662 0.879517i
\(273\) −5.46413 + 16.0070i −0.330704 + 0.968786i
\(274\) 0.00868447 + 0.0135133i 0.000524648 + 0.000816368i
\(275\) −8.59271 −0.518160
\(276\) −16.3979 + 2.19515i −0.987035 + 0.132133i
\(277\) −17.2093 −1.03401 −0.517003 0.855984i \(-0.672952\pi\)
−0.517003 + 0.855984i \(0.672952\pi\)
\(278\) 0.00132104 + 0.00205557i 7.92305e−5 + 0.000123285i
\(279\) 1.18338 2.09044i 0.0708470 0.125151i
\(280\) −1.05164 + 2.30276i −0.0628472 + 0.137616i
\(281\) 11.6031 3.40697i 0.692182 0.203243i 0.0833244 0.996522i \(-0.473446\pi\)
0.608858 + 0.793279i \(0.291628\pi\)
\(282\) 0.231604 0.0572280i 0.0137918 0.00340788i
\(283\) 23.6748 20.5143i 1.40732 1.21945i 0.464749 0.885443i \(-0.346145\pi\)
0.942571 0.334007i \(-0.108401\pi\)
\(284\) −2.35655 + 0.338821i −0.139836 + 0.0201053i
\(285\) −12.2139 6.23126i −0.723491 0.369108i
\(286\) 0.631525 + 0.547220i 0.0373429 + 0.0323578i
\(287\) 17.1540 + 11.0242i 1.01257 + 0.650739i
\(288\) 2.64378 1.91665i 0.155787 0.112940i
\(289\) 0.460599 0.531559i 0.0270940 0.0312682i
\(290\) −1.56755 0.460275i −0.0920499 0.0270283i
\(291\) −0.242223 + 5.58321i −0.0141993 + 0.327293i
\(292\) 15.6969 + 18.1151i 0.918589 + 1.06011i
\(293\) −8.08610 17.7061i −0.472395 1.03440i −0.984485 0.175469i \(-0.943856\pi\)
0.512090 0.858932i \(-0.328871\pi\)
\(294\) 0.250155 0.0249584i 0.0145893 0.00145560i
\(295\) 31.2623 + 14.2770i 1.82016 + 0.831239i
\(296\) 0.426937 2.96941i 0.0248152 0.172594i
\(297\) 0.144306 + 11.3363i 0.00837350 + 0.657798i
\(298\) 0.751740i 0.0435471i
\(299\) −19.8246 + 3.53449i −1.14649 + 0.204405i
\(300\) −2.51451 + 13.3511i −0.145175 + 0.770827i
\(301\) 5.58445 3.58891i 0.321882 0.206861i
\(302\) −1.38747 0.199487i −0.0798397 0.0114792i
\(303\) −0.0262554 + 0.0372036i −0.00150833 + 0.00213729i
\(304\) −2.94681 10.0359i −0.169011 0.575599i
\(305\) 20.8369 9.51590i 1.19312 0.544879i
\(306\) −1.04079 + 0.370140i −0.0594979 + 0.0211595i
\(307\) −0.450480 3.13316i −0.0257103 0.178819i 0.972920 0.231142i \(-0.0742464\pi\)
−0.998630 + 0.0523236i \(0.983337\pi\)
\(308\) 2.84727 9.69690i 0.162238 0.552532i
\(309\) 9.85183 7.81545i 0.560451 0.444605i
\(310\) 0.118050 0.183690i 0.00670481 0.0104329i
\(311\) 15.8730 24.6989i 0.900075 1.40054i −0.0161457 0.999870i \(-0.505140\pi\)
0.916221 0.400674i \(-0.131224\pi\)
\(312\) 2.07444 1.64565i 0.117442 0.0931668i
\(313\) 4.62093 15.7374i 0.261190 0.889532i −0.719587 0.694402i \(-0.755669\pi\)
0.980777 0.195130i \(-0.0625129\pi\)
\(314\) −0.0962857 0.669682i −0.00543372 0.0377923i
\(315\) −19.6533 + 6.98937i −1.10734 + 0.393806i
\(316\) −8.23577 + 3.76115i −0.463298 + 0.211581i
\(317\) 7.10249 + 24.1889i 0.398916 + 1.35858i 0.877094 + 0.480319i \(0.159479\pi\)
−0.478178 + 0.878263i \(0.658703\pi\)
\(318\) −1.23484 + 1.74976i −0.0692464 + 0.0981214i
\(319\) 12.9384 + 1.86026i 0.724413 + 0.104155i
\(320\) −19.6203 + 12.6092i −1.09681 + 0.704875i
\(321\) −4.04307 + 21.4672i −0.225662 + 1.19818i
\(322\) −0.578482 0.836857i −0.0322376 0.0466362i
\(323\) 10.6893i 0.594770i
\(324\) 17.6562 + 3.09315i 0.980902 + 0.171842i
\(325\) −2.35338 + 16.3681i −0.130542 + 0.907940i
\(326\) 0.731703 + 0.334157i 0.0405253 + 0.0185073i
\(327\) −12.8464 + 1.28170i −0.710405 + 0.0708784i
\(328\) −1.32612 2.90380i −0.0732227 0.160335i
\(329\) −2.29984 2.65415i −0.126794 0.146328i
\(330\) −0.0446670 + 1.02957i −0.00245884 + 0.0566760i
\(331\) 1.08617 + 0.318927i 0.0597011 + 0.0175298i 0.311447 0.950264i \(-0.399186\pi\)
−0.251746 + 0.967793i \(0.581005\pi\)
\(332\) 6.66990 7.69747i 0.366058 0.422454i
\(333\) 20.0129 14.5086i 1.09670 0.795068i
\(334\) −1.09368 0.702865i −0.0598434 0.0384590i
\(335\) −13.2192 11.4545i −0.722244 0.625828i
\(336\) −14.1739 7.23117i −0.773247 0.394493i
\(337\) 17.4933 2.51516i 0.952922 0.137010i 0.351719 0.936106i \(-0.385597\pi\)
0.601203 + 0.799096i \(0.294688\pi\)
\(338\) 0.319217 0.276603i 0.0173631 0.0150452i
\(339\) −12.7117 + 3.14099i −0.690404 + 0.170595i
\(340\) 23.0641 6.77224i 1.25083 0.367277i
\(341\) −0.725747 + 1.58916i −0.0393014 + 0.0860580i
\(342\) −0.356943 + 0.630541i −0.0193013 + 0.0340958i
\(343\) −10.8022 16.8086i −0.583266 0.907580i
\(344\) −1.03924 −0.0560320
\(345\) −18.6095 16.4447i −1.00190 0.885353i
\(346\) −0.632364 −0.0339961
\(347\) −13.1106 20.4004i −0.703812 1.09515i −0.990551 0.137144i \(-0.956208\pi\)
0.286740 0.958009i \(-0.407429\pi\)
\(348\) 6.67664 19.5590i 0.357905 1.04847i
\(349\) −0.385372 + 0.843847i −0.0206285 + 0.0451701i −0.919666 0.392702i \(-0.871540\pi\)
0.899037 + 0.437872i \(0.144268\pi\)
\(350\) −0.801582 + 0.235366i −0.0428464 + 0.0125808i
\(351\) 21.6338 + 2.82991i 1.15473 + 0.151049i
\(352\) −1.79483 + 1.55523i −0.0956648 + 0.0828940i
\(353\) 6.49232 0.933455i 0.345552 0.0496828i 0.0326458 0.999467i \(-0.489607\pi\)
0.312906 + 0.949784i \(0.398698\pi\)
\(354\) 0.825333 1.61774i 0.0438659 0.0859818i
\(355\) −2.70088 2.34033i −0.143348 0.124212i
\(356\) −2.27144 1.45977i −0.120386 0.0773674i
\(357\) 11.8164 + 11.1716i 0.625391 + 0.591263i
\(358\) −0.780063 + 0.900241i −0.0412276 + 0.0475792i
\(359\) 28.3588 + 8.32689i 1.49672 + 0.439476i 0.924678 0.380749i \(-0.124334\pi\)
0.572040 + 0.820225i \(0.306152\pi\)
\(360\) 3.17992 + 0.742926i 0.167597 + 0.0391556i
\(361\) −7.85088 9.06040i −0.413204 0.476863i
\(362\) 0.667741 + 1.46215i 0.0350957 + 0.0768488i
\(363\) 1.07293 + 10.7538i 0.0563142 + 0.564429i
\(364\) −17.6917 8.07951i −0.927295 0.423481i
\(365\) −5.12060 + 35.6146i −0.268025 + 1.86415i
\(366\) −0.454651 1.12184i −0.0237650 0.0586397i
\(367\) 10.1557i 0.530121i −0.964232 0.265061i \(-0.914608\pi\)
0.964232 0.265061i \(-0.0853919\pi\)
\(368\) −0.637058 18.9335i −0.0332089 0.986979i
\(369\) 9.56844 24.5014i 0.498113 1.27549i
\(370\) 1.89022 1.21477i 0.0982678 0.0631529i
\(371\) 31.2054 + 4.48666i 1.62010 + 0.232936i
\(372\) 2.25682 + 1.59269i 0.117011 + 0.0825769i
\(373\) 6.89101 + 23.4686i 0.356803 + 1.21516i 0.921014 + 0.389528i \(0.127362\pi\)
−0.564212 + 0.825630i \(0.690820\pi\)
\(374\) 0.730789 0.333740i 0.0377882 0.0172573i
\(375\) 4.74964 2.76915i 0.245271 0.142998i
\(376\) 0.0782456 + 0.544210i 0.00403521 + 0.0280655i
\(377\) 7.08718 24.1367i 0.365008 1.24310i
\(378\) 0.323978 + 1.05357i 0.0166636 + 0.0541897i
\(379\) −8.22194 + 12.7936i −0.422333 + 0.657163i −0.985596 0.169115i \(-0.945909\pi\)
0.563264 + 0.826277i \(0.309546\pi\)
\(380\) 8.52426 13.2640i 0.437285 0.680429i
\(381\) −3.66550 4.62058i −0.187789 0.236720i
\(382\) −0.206662 + 0.703828i −0.0105738 + 0.0360109i
\(383\) 3.16581 + 22.0187i 0.161765 + 1.12510i 0.895304 + 0.445455i \(0.146958\pi\)
−0.733539 + 0.679647i \(0.762133\pi\)
\(384\) 2.51989 + 4.32212i 0.128592 + 0.220562i
\(385\) 13.7995 6.30203i 0.703289 0.321181i
\(386\) 0.395025 + 1.34533i 0.0201063 + 0.0684756i
\(387\) −5.96154 6.14699i −0.303042 0.312469i
\(388\) −6.36075 0.914537i −0.322918 0.0464286i
\(389\) −18.0396 + 11.5933i −0.914644 + 0.587806i −0.911099 0.412188i \(-0.864765\pi\)
−0.00354508 + 0.999994i \(0.501128\pi\)
\(390\) 1.94898 + 0.367065i 0.0986904 + 0.0185871i
\(391\) −4.82668 + 18.7490i −0.244096 + 0.948179i
\(392\) 0.579369i 0.0292625i
\(393\) −16.1210 + 6.53338i −0.813197 + 0.329565i
\(394\) 0.129540 0.900971i 0.00652614 0.0453903i
\(395\) −12.3626 5.64583i −0.622032 0.284073i
\(396\) −12.9876 1.12904i −0.652653 0.0567363i
\(397\) −3.52795 7.72512i −0.177062 0.387713i 0.800204 0.599728i \(-0.204725\pi\)
−0.977266 + 0.212015i \(0.931997\pi\)
\(398\) 0.201402 + 0.232431i 0.0100954 + 0.0116507i
\(399\) 10.6562 + 0.462308i 0.533476 + 0.0231444i
\(400\) −14.9266 4.38285i −0.746331 0.219143i
\(401\) −13.7779 + 15.9006i −0.688038 + 0.794038i −0.987084 0.160201i \(-0.948786\pi\)
0.299047 + 0.954238i \(0.403331\pi\)
\(402\) −0.634999 + 0.671651i −0.0316709 + 0.0334989i
\(403\) 2.82840 + 1.81770i 0.140893 + 0.0905463i
\(404\) −0.0395716 0.0342890i −0.00196876 0.00170594i
\(405\) 13.8472 + 23.0707i 0.688071 + 1.14639i
\(406\) 1.25793 0.180863i 0.0624302 0.00897610i
\(407\) −13.5865 + 11.7728i −0.673457 + 0.583554i
\(408\) −0.610679 2.47144i −0.0302331 0.122354i
\(409\) 4.43640 1.30264i 0.219366 0.0644116i −0.170203 0.985409i \(-0.554442\pi\)
0.389569 + 0.920997i \(0.372624\pi\)
\(410\) 0.993239 2.17489i 0.0490526 0.107410i
\(411\) −0.288674 0.0985415i −0.0142392 0.00486069i
\(412\) 7.81787 + 12.1648i 0.385159 + 0.599319i
\(413\) −26.7347 −1.31553
\(414\) −0.910792 + 0.944791i −0.0447630 + 0.0464339i
\(415\) 15.2889 0.750505
\(416\) 2.47096 + 3.84489i 0.121149 + 0.188511i
\(417\) −0.0439116 0.0149896i −0.00215036 0.000734045i
\(418\) 0.218908 0.479341i 0.0107071 0.0234453i
\(419\) −27.2100 + 7.98957i −1.32929 + 0.390316i −0.867838 0.496847i \(-0.834491\pi\)
−0.461456 + 0.887163i \(0.652673\pi\)
\(420\) −5.75372 23.2855i −0.280753 1.13622i
\(421\) −20.9582 + 18.1604i −1.02144 + 0.885082i −0.993420 0.114526i \(-0.963465\pi\)
−0.0280186 + 0.999607i \(0.508920\pi\)
\(422\) 2.00216 0.287868i 0.0974637 0.0140132i
\(423\) −2.77010 + 3.58465i −0.134687 + 0.174292i
\(424\) −3.73003 3.23209i −0.181146 0.156964i
\(425\) 13.3746 + 8.59536i 0.648765 + 0.416936i
\(426\) −0.129740 + 0.137228i −0.00628590 + 0.00664872i
\(427\) −11.6691 + 13.4669i −0.564707 + 0.651707i
\(428\) −24.1015 7.07685i −1.16499 0.342072i
\(429\) −15.8530 0.687769i −0.765391 0.0332058i
\(430\) −0.509724 0.588253i −0.0245811 0.0283681i
\(431\) 1.32102 + 2.89263i 0.0636313 + 0.139333i 0.938776 0.344528i \(-0.111961\pi\)
−0.875145 + 0.483861i \(0.839234\pi\)
\(432\) −5.53158 + 19.7662i −0.266138 + 0.951000i
\(433\) −9.75228 4.45372i −0.468665 0.214032i 0.167062 0.985946i \(-0.446572\pi\)
−0.635726 + 0.771914i \(0.719299\pi\)
\(434\) −0.0241729 + 0.168126i −0.00116034 + 0.00807032i
\(435\) 28.7518 11.6523i 1.37855 0.558685i
\(436\) 14.8453i 0.710962i
\(437\) 5.66077 + 11.3674i 0.270791 + 0.543775i
\(438\) 1.86848 + 0.351905i 0.0892795 + 0.0168147i
\(439\) −24.2784 + 15.6028i −1.15875 + 0.744681i −0.971362 0.237606i \(-0.923637\pi\)
−0.187384 + 0.982287i \(0.560001\pi\)
\(440\) −2.35080 0.337995i −0.112070 0.0161133i
\(441\) −3.42691 + 3.32352i −0.163186 + 0.158263i
\(442\) −0.435587 1.48347i −0.0207188 0.0705616i
\(443\) −0.857521 + 0.391617i −0.0407420 + 0.0186063i −0.435682 0.900101i \(-0.643493\pi\)
0.394940 + 0.918707i \(0.370765\pi\)
\(444\) 14.3163 + 24.5554i 0.679423 + 1.16535i
\(445\) −0.576809 4.01179i −0.0273434 0.190177i
\(446\) −0.233135 + 0.793984i −0.0110393 + 0.0375962i
\(447\) −8.87173 11.1833i −0.419618 0.528954i
\(448\) 9.80861 15.2625i 0.463413 0.721085i
\(449\) 14.0428 21.8511i 0.662723 1.03122i −0.333361 0.942799i \(-0.608183\pi\)
0.996084 0.0884175i \(-0.0281810\pi\)
\(450\) 0.501921 + 0.953634i 0.0236608 + 0.0449548i
\(451\) −5.38955 + 18.3551i −0.253784 + 0.864309i
\(452\) −2.14280 14.9035i −0.100789 0.701001i
\(453\) 22.9951 13.4066i 1.08040 0.629898i
\(454\) −0.863384 + 0.394294i −0.0405206 + 0.0185052i
\(455\) −8.22521 28.0125i −0.385604 1.31325i
\(456\) −1.36430 0.962814i −0.0638890 0.0450879i
\(457\) 10.1520 + 1.45964i 0.474892 + 0.0682792i 0.375605 0.926780i \(-0.377435\pi\)
0.0992868 + 0.995059i \(0.468344\pi\)
\(458\) −0.620066 + 0.398492i −0.0289738 + 0.0186203i
\(459\) 11.1152 17.7894i 0.518812 0.830338i
\(460\) 20.9408 19.4159i 0.976368 0.905273i
\(461\) 0.980298i 0.0456570i −0.999739 0.0228285i \(-0.992733\pi\)
0.999739 0.0228285i \(-0.00726717\pi\)
\(462\) −0.301098 0.742956i −0.0140084 0.0345654i
\(463\) 3.35764 23.3529i 0.156043 1.08530i −0.749793 0.661673i \(-0.769847\pi\)
0.905836 0.423629i \(-0.139244\pi\)
\(464\) 21.5268 + 9.83097i 0.999357 + 0.456391i
\(465\) 0.411645 + 4.12587i 0.0190896 + 0.191333i
\(466\) 0.0468690 + 0.102629i 0.00217116 + 0.00475418i
\(467\) 6.29319 + 7.26272i 0.291214 + 0.336079i 0.882438 0.470428i \(-0.155901\pi\)
−0.591224 + 0.806507i \(0.701355\pi\)
\(468\) −5.70776 + 24.4307i −0.263841 + 1.12931i
\(469\) 13.0554 + 3.83342i 0.602843 + 0.177011i
\(470\) −0.269668 + 0.311214i −0.0124389 + 0.0143552i
\(471\) 9.33572 + 8.82627i 0.430167 + 0.406693i
\(472\) 3.52098 + 2.26280i 0.162066 + 0.104154i
\(473\) 4.70661 + 4.07830i 0.216410 + 0.187520i
\(474\) −0.326377 + 0.639733i −0.0149910 + 0.0293839i
\(475\) 10.3220 1.48408i 0.473606 0.0680943i
\(476\) −14.1317 + 12.2452i −0.647725 + 0.561257i
\(477\) −2.27967 40.6035i −0.104379 1.85911i
\(478\) −1.50062 + 0.440621i −0.0686366 + 0.0201535i
\(479\) −2.18987 + 4.79516i −0.100058 + 0.219096i −0.953040 0.302843i \(-0.902064\pi\)
0.852982 + 0.521940i \(0.174791\pi\)
\(480\) −1.82090 + 5.33426i −0.0831123 + 0.243475i
\(481\) 18.7047 + 29.1050i 0.852859 + 1.32707i
\(482\) −1.30302 −0.0593508
\(483\) 18.4821 + 5.62259i 0.840965 + 0.255837i
\(484\) −12.4272 −0.564872
\(485\) −5.21516 8.11494i −0.236808 0.368480i
\(486\) 1.24969 0.678196i 0.0566872 0.0307636i
\(487\) −3.61513 + 7.91602i −0.163817 + 0.358709i −0.973683 0.227905i \(-0.926812\pi\)
0.809866 + 0.586615i \(0.199540\pi\)
\(488\) 2.67665 0.785935i 0.121166 0.0355776i
\(489\) −14.8288 + 3.66413i −0.670584 + 0.165698i
\(490\) −0.327947 + 0.284168i −0.0148152 + 0.0128374i
\(491\) −34.5744 + 4.97106i −1.56032 + 0.224341i −0.867748 0.497005i \(-0.834433\pi\)
−0.692575 + 0.721346i \(0.743524\pi\)
\(492\) 26.9425 + 13.7454i 1.21466 + 0.619693i
\(493\) −18.2779 15.8379i −0.823197 0.713305i
\(494\) −0.853134 0.548276i −0.0383843 0.0246681i
\(495\) −11.4861 15.8437i −0.516261 0.712120i
\(496\) −2.07129 + 2.39040i −0.0930038 + 0.107332i
\(497\) 2.66741 + 0.783222i 0.119650 + 0.0351323i
\(498\) 0.0350176 0.807153i 0.00156918 0.0361694i
\(499\) −7.27888 8.40028i −0.325848 0.376048i 0.569063 0.822294i \(-0.307306\pi\)
−0.894910 + 0.446246i \(0.852761\pi\)
\(500\) 2.62628 + 5.75075i 0.117451 + 0.257181i
\(501\) 24.5652 2.45091i 1.09749 0.109499i
\(502\) 1.70603 + 0.779117i 0.0761438 + 0.0347737i
\(503\) 2.11528 14.7121i 0.0943156 0.655979i −0.886742 0.462264i \(-0.847037\pi\)
0.981058 0.193715i \(-0.0620537\pi\)
\(504\) −2.49018 + 0.501896i −0.110921 + 0.0223562i
\(505\) 0.0785984i 0.00349758i
\(506\) 0.600405 0.741915i 0.0266912 0.0329821i
\(507\) −1.48451 + 7.88218i −0.0659293 + 0.350060i
\(508\) 5.70540 3.66664i 0.253136 0.162681i
\(509\) −21.5714 3.10149i −0.956134 0.137471i −0.353452 0.935453i \(-0.614992\pi\)
−0.602682 + 0.797982i \(0.705901\pi\)
\(510\) 1.09941 1.55786i 0.0486828 0.0689831i
\(511\) −7.88549 26.8555i −0.348833 1.18802i
\(512\) −6.52760 + 2.98106i −0.288482 + 0.131745i
\(513\) −2.13128 13.5928i −0.0940985 0.600138i
\(514\) 0.0902949 + 0.628015i 0.00398274 + 0.0277006i
\(515\) −6.11539 + 20.8271i −0.269476 + 0.917751i
\(516\) 7.71406 6.11955i 0.339592 0.269398i
\(517\) 1.78129 2.77174i 0.0783409 0.121901i
\(518\) −0.944962 + 1.47039i −0.0415192 + 0.0646052i
\(519\) 9.40744 7.46291i 0.412941 0.327585i
\(520\) −1.28768 + 4.38544i −0.0564686 + 0.192314i
\(521\) 2.73831 + 19.0454i 0.119968 + 0.834393i 0.957588 + 0.288141i \(0.0930371\pi\)
−0.837620 + 0.546253i \(0.816054\pi\)
\(522\) −0.549310 1.54459i −0.0240426 0.0676050i
\(523\) 25.4900 11.6409i 1.11460 0.509021i 0.228980 0.973431i \(-0.426461\pi\)
0.885620 + 0.464410i \(0.153734\pi\)
\(524\) −5.63521 19.1918i −0.246175 0.838396i
\(525\) 9.14714 12.9614i 0.399214 0.565682i
\(526\) 0.968852 + 0.139300i 0.0422439 + 0.00607376i
\(527\) 2.71928 1.74758i 0.118454 0.0761257i
\(528\) 2.76290 14.6700i 0.120240 0.638429i
\(529\) 4.79612 + 22.4944i 0.208527 + 0.978017i
\(530\) 3.69663i 0.160571i
\(531\) 6.81374 + 33.8067i 0.295691 + 1.46709i
\(532\) −1.74550 + 12.1402i −0.0756768 + 0.526344i
\(533\) 33.4883 + 15.2936i 1.45054 + 0.662439i
\(534\) −0.213117 + 0.0212630i −0.00922246 + 0.000920142i
\(535\) −15.6636 34.2985i −0.677197 1.48286i
\(536\) −1.39495 1.60986i −0.0602528 0.0695354i
\(537\) 0.980416 22.5985i 0.0423081 0.975198i
\(538\) −1.19890 0.352028i −0.0516882 0.0151770i
\(539\) 2.27363 2.62391i 0.0979321 0.113020i
\(540\) −27.9787 + 13.2104i −1.20401 + 0.568484i
\(541\) 31.8524 + 20.4703i 1.36944 + 0.880085i 0.998814 0.0486969i \(-0.0155068\pi\)
0.370626 + 0.928782i \(0.379143\pi\)
\(542\) −1.76523 1.52958i −0.0758232 0.0657012i
\(543\) −27.1894 13.8714i −1.16681 0.595279i
\(544\) 4.34938 0.625346i 0.186478 0.0268115i
\(545\) 16.8413 14.5930i 0.721401 0.625098i
\(546\) −1.49771 + 0.370076i −0.0640961 + 0.0158378i
\(547\) −11.8390 + 3.47626i −0.506201 + 0.148634i −0.524854 0.851192i \(-0.675880\pi\)
0.0186536 + 0.999826i \(0.494062\pi\)
\(548\) 0.145708 0.319056i 0.00622433 0.0136294i
\(549\) 20.0032 + 11.3236i 0.853716 + 0.483281i
\(550\) −0.423733 0.659341i −0.0180680 0.0281144i
\(551\) −15.8636 −0.675812
\(552\) −1.95822 2.30481i −0.0833473 0.0980990i
\(553\) 10.5722 0.449577
\(554\) −0.848643 1.32051i −0.0360554 0.0561033i
\(555\) −13.7838 + 40.3792i −0.585091 + 1.71400i
\(556\) 0.0221643 0.0485332i 0.000939978 0.00205826i
\(557\) 36.7098 10.7790i 1.55545 0.456720i 0.612723 0.790298i \(-0.290074\pi\)
0.942723 + 0.333577i \(0.108256\pi\)
\(558\) 0.218761 0.0122823i 0.00926088 0.000519950i
\(559\) 9.05774 7.84858i 0.383102 0.331959i
\(560\) 27.1860 3.90875i 1.14882 0.165175i
\(561\) −6.93300 + 13.5894i −0.292711 + 0.573745i
\(562\) 0.833609 + 0.722327i 0.0351637 + 0.0304695i
\(563\) −3.79582 2.43943i −0.159975 0.102810i 0.458204 0.888847i \(-0.348493\pi\)
−0.618179 + 0.786037i \(0.712129\pi\)
\(564\) −3.78538 3.57881i −0.159393 0.150695i
\(565\) 14.8009 17.0811i 0.622677 0.718608i
\(566\) 2.74159 + 0.805004i 0.115238 + 0.0338368i
\(567\) −17.2535 11.8501i −0.724578 0.497656i
\(568\) −0.285009 0.328918i −0.0119587 0.0138011i
\(569\) 6.71978 + 14.7143i 0.281708 + 0.616854i 0.996601 0.0823795i \(-0.0262520\pi\)
−0.714893 + 0.699234i \(0.753525\pi\)
\(570\) −0.124165 1.24449i −0.00520070 0.0521259i
\(571\) −23.7301 10.8372i −0.993074 0.453522i −0.148472 0.988917i \(-0.547436\pi\)
−0.844602 + 0.535395i \(0.820163\pi\)
\(572\) 2.59675 18.0608i 0.108575 0.755159i
\(573\) −5.23185 12.9095i −0.218564 0.539303i
\(574\) 1.85991i 0.0776311i
\(575\) 18.7749 + 2.05775i 0.782966 + 0.0858139i
\(576\) −21.7997 8.51336i −0.908320 0.354723i
\(577\) 11.8301 7.60273i 0.492493 0.316506i −0.270715 0.962660i \(-0.587260\pi\)
0.763207 + 0.646154i \(0.223624\pi\)
\(578\) 0.0635014 + 0.00913013i 0.00264131 + 0.000379763i
\(579\) −21.7537 15.3521i −0.904053 0.638010i
\(580\) 10.0504 + 34.2286i 0.417321 + 1.42126i
\(581\) −10.8184 + 4.94060i −0.448823 + 0.204971i
\(582\) −0.440359 + 0.256739i −0.0182535 + 0.0106422i
\(583\) 4.20921 + 29.2757i 0.174328 + 1.21247i
\(584\) −1.23450 + 4.20431i −0.0510838 + 0.173976i
\(585\) −33.3262 + 17.5404i −1.37787 + 0.725206i
\(586\) 0.959884 1.49361i 0.0396524 0.0617004i
\(587\) −10.0631 + 15.6584i −0.415347 + 0.646293i −0.984387 0.176017i \(-0.943679\pi\)
0.569040 + 0.822310i \(0.307315\pi\)
\(588\) −3.41161 4.30054i −0.140693 0.177351i
\(589\) 0.597334 2.03433i 0.0246127 0.0838232i
\(590\) 0.446127 + 3.10288i 0.0183667 + 0.127744i
\(591\) 8.70578 + 14.9322i 0.358108 + 0.614228i
\(592\) −29.6063 + 13.5208i −1.21681 + 0.555700i
\(593\) 4.80543 + 16.3658i 0.197336 + 0.672063i 0.997394 + 0.0721416i \(0.0229833\pi\)
−0.800059 + 0.599921i \(0.795198\pi\)
\(594\) −0.862747 + 0.570100i −0.0353989 + 0.0233915i
\(595\) −27.7831 3.99460i −1.13899 0.163763i
\(596\) 13.8090 8.87448i 0.565637 0.363513i
\(597\) −5.73924 1.08091i −0.234891 0.0442388i
\(598\) −1.24882 1.34690i −0.0510682 0.0550788i
\(599\) 16.9822i 0.693873i −0.937889 0.346936i \(-0.887222\pi\)
0.937889 0.346936i \(-0.112778\pi\)
\(600\) −2.30172 + 0.932822i −0.0939675 + 0.0380823i
\(601\) 3.82091 26.5750i 0.155858 1.08402i −0.750305 0.661092i \(-0.770093\pi\)
0.906164 0.422927i \(-0.138997\pi\)
\(602\) 0.550772 + 0.251529i 0.0224478 + 0.0102516i
\(603\) 1.52008 17.4859i 0.0619025 0.712081i
\(604\) 12.7149 + 27.8418i 0.517364 + 1.13287i
\(605\) −12.2160 14.0980i −0.496651 0.573166i
\(606\) −0.00414946 0.000180021i −0.000168560 7.31284e-6i
\(607\) −36.3363 10.6693i −1.47485 0.433054i −0.557175 0.830395i \(-0.688115\pi\)
−0.917671 + 0.397341i \(0.869933\pi\)
\(608\) 1.88743 2.17821i 0.0765456 0.0883383i
\(609\) −16.5793 + 17.5363i −0.671827 + 0.710605i
\(610\) 1.75771 + 1.12961i 0.0711677 + 0.0457367i
\(611\) −4.79198 4.15227i −0.193863 0.167983i
\(612\) 19.0860 + 14.7490i 0.771506 + 0.596193i
\(613\) −9.56357 + 1.37503i −0.386269 + 0.0555371i −0.332714 0.943028i \(-0.607964\pi\)
−0.0535550 + 0.998565i \(0.517055\pi\)
\(614\) 0.218201 0.189072i 0.00880587 0.00763033i
\(615\) 10.8911 + 44.0768i 0.439173 + 1.77735i
\(616\) 1.77265 0.520496i 0.0714219 0.0209714i
\(617\) 0.0412945 0.0904223i 0.00166245 0.00364026i −0.908799 0.417234i \(-0.862999\pi\)
0.910461 + 0.413594i \(0.135727\pi\)
\(618\) 1.08552 + 0.370553i 0.0436662 + 0.0149058i
\(619\) −18.8279 29.2969i −0.756759 1.17754i −0.979260 0.202607i \(-0.935058\pi\)
0.222501 0.974932i \(-0.428578\pi\)
\(620\) −4.76788 −0.191483
\(621\) 2.39946 24.8041i 0.0962870 0.995354i
\(622\) 2.67795 0.107376
\(623\) 1.70455 + 2.65234i 0.0682915 + 0.106264i
\(624\) −27.1879 9.28084i −1.08839 0.371531i
\(625\) −12.1224 + 26.5443i −0.484895 + 1.06177i
\(626\) 1.43545 0.421485i 0.0573720 0.0168459i
\(627\) 2.40038 + 9.71443i 0.0958621 + 0.387957i
\(628\) −11.1649 + 9.67447i −0.445529 + 0.386053i
\(629\) 32.9239 4.73374i 1.31276 0.188747i
\(630\) −1.50547 1.16338i −0.0599795 0.0463501i
\(631\) 22.8246 + 19.7776i 0.908631 + 0.787334i 0.977641 0.210282i \(-0.0674383\pi\)
−0.0690092 + 0.997616i \(0.521984\pi\)
\(632\) −1.39237 0.894822i −0.0553855 0.0355941i
\(633\) −26.3881 + 27.9112i −1.04883 + 1.10937i
\(634\) −1.50583 + 1.73782i −0.0598041 + 0.0690176i
\(635\) 9.76806 + 2.86816i 0.387634 + 0.113819i
\(636\) 46.7195 + 2.02688i 1.85255 + 0.0803711i
\(637\) −4.37554 5.04964i −0.173365 0.200074i
\(638\) 0.495290 + 1.08453i 0.0196087 + 0.0429371i
\(639\) 0.310575 3.57262i 0.0122861 0.141331i
\(640\) −7.85537 3.58743i −0.310511 0.141806i
\(641\) 4.21724 29.3316i 0.166571 1.15853i −0.719335 0.694663i \(-0.755554\pi\)
0.885906 0.463864i \(-0.153537\pi\)
\(642\) −1.84661 + 0.748376i −0.0728798 + 0.0295361i
\(643\) 45.2646i 1.78506i 0.450988 + 0.892530i \(0.351072\pi\)
−0.450988 + 0.892530i \(0.648928\pi\)
\(644\) −8.54338 + 20.5056i −0.336656 + 0.808036i
\(645\) 14.5253 + 2.73565i 0.571933 + 0.107716i
\(646\) −0.820220 + 0.527124i −0.0322711 + 0.0207394i
\(647\) −5.31305 0.763901i −0.208877 0.0300320i 0.0370817 0.999312i \(-0.488194\pi\)
−0.245959 + 0.969280i \(0.579103\pi\)
\(648\) 1.26932 + 3.02098i 0.0498636 + 0.118675i
\(649\) −7.06625 24.0655i −0.277375 0.944652i
\(650\) −1.37202 + 0.626581i −0.0538151 + 0.0245765i
\(651\) −1.62455 2.78643i −0.0636711 0.109209i
\(652\) −2.49969 17.3857i −0.0978953 0.680877i
\(653\) 6.26288 21.3294i 0.245085 0.834684i −0.741432 0.671028i \(-0.765853\pi\)
0.986517 0.163656i \(-0.0523288\pi\)
\(654\) −0.731842 0.922530i −0.0286173 0.0360738i
\(655\) 16.2326 25.2585i 0.634262 0.986931i
\(656\) −18.7247 + 29.1361i −0.731075 + 1.13758i
\(657\) −31.9497 + 16.8159i −1.24648 + 0.656052i
\(658\) 0.0902481 0.307357i 0.00351824 0.0119820i
\(659\) −5.74790 39.9775i −0.223906 1.55730i −0.723057 0.690788i \(-0.757264\pi\)
0.499151 0.866515i \(-0.333645\pi\)
\(660\) 19.4398 11.3338i 0.756695 0.441169i
\(661\) 12.1235 5.53663i 0.471551 0.215350i −0.165442 0.986219i \(-0.552905\pi\)
0.636993 + 0.770869i \(0.280178\pi\)
\(662\) 0.0290900 + 0.0990716i 0.00113062 + 0.00385053i
\(663\) 23.9874 + 16.9284i 0.931594 + 0.657446i
\(664\) 1.84296 + 0.264978i 0.0715208 + 0.0102831i
\(665\) −15.4883 + 9.95370i −0.600609 + 0.385988i
\(666\) 2.10018 + 0.820177i 0.0813804 + 0.0317812i
\(667\) −27.8247 7.16307i −1.07738 0.277355i
\(668\) 28.3877i 1.09835i
\(669\) −5.90203 14.5632i −0.228186 0.563044i
\(670\) 0.227055 1.57920i 0.00877191 0.0610100i
\(671\) −15.2065 6.94460i −0.587042 0.268093i
\(672\) −0.435298 4.36293i −0.0167920 0.168304i
\(673\) 12.0122 + 26.3031i 0.463037 + 1.01391i 0.986785 + 0.162036i \(0.0518061\pi\)
−0.523748 + 0.851873i \(0.675467\pi\)
\(674\) 1.05564 + 1.21828i 0.0406619 + 0.0469263i
\(675\) −18.7213 8.26338i −0.720583 0.318057i
\(676\) −8.84945 2.59843i −0.340363 0.0999397i
\(677\) −4.15973 + 4.80059i −0.159872 + 0.184502i −0.830034 0.557713i \(-0.811679\pi\)
0.670162 + 0.742215i \(0.266224\pi\)
\(678\) −0.867868 0.820509i −0.0333303 0.0315114i
\(679\) 6.31256 + 4.05684i 0.242254 + 0.155687i
\(680\) 3.32095 + 2.87762i 0.127353 + 0.110352i
\(681\) 8.19093 16.0551i 0.313877 0.615232i
\(682\) −0.157729 + 0.0226781i −0.00603977 + 0.000868388i
\(683\) 14.9179 12.9265i 0.570818 0.494617i −0.320958 0.947093i \(-0.604005\pi\)
0.891776 + 0.452477i \(0.149459\pi\)
\(684\) 15.7964 0.886886i 0.603992 0.0339109i
\(685\) 0.505184 0.148336i 0.0193021 0.00566761i
\(686\) 0.757078 1.65777i 0.0289054 0.0632939i
\(687\) 4.52164 13.2460i 0.172511 0.505366i
\(688\) 6.09577 + 9.48521i 0.232399 + 0.361620i
\(689\) 56.9196 2.16846
\(690\) 0.344154 2.23889i 0.0131017 0.0852332i
\(691\) −15.8325 −0.602295 −0.301147 0.953578i \(-0.597370\pi\)
−0.301147 + 0.953578i \(0.597370\pi\)
\(692\) 7.46522 + 11.6161i 0.283785 + 0.441578i
\(693\) 13.2474 + 7.49922i 0.503227 + 0.284872i
\(694\) 0.918856 2.01201i 0.0348793 0.0763750i
\(695\) 0.0768461 0.0225641i 0.00291494 0.000855903i
\(696\) 3.66776 0.906284i 0.139026 0.0343526i
\(697\) 26.7497 23.1787i 1.01322 0.877957i
\(698\) −0.0837544 + 0.0120421i −0.00317015 + 0.000455799i
\(699\) −1.90843 0.973639i −0.0721836 0.0368264i
\(700\) 13.7864 + 11.9460i 0.521077 + 0.451516i
\(701\) −33.2792 21.3872i −1.25694 0.807785i −0.269076 0.963119i \(-0.586718\pi\)
−0.987862 + 0.155334i \(0.950355\pi\)
\(702\) 0.849684 + 1.79957i 0.0320693 + 0.0679205i
\(703\) 14.2875 16.4886i 0.538862 0.621880i
\(704\) 16.3312 + 4.79526i 0.615504 + 0.180728i
\(705\) 0.338930 7.81232i 0.0127649 0.294229i
\(706\) 0.391783 + 0.452141i 0.0147449 + 0.0170166i
\(707\) 0.0253990 + 0.0556160i 0.000955226 + 0.00209165i
\(708\) −39.4600 + 3.93700i −1.48300 + 0.147962i
\(709\) 37.4007 + 17.0803i 1.40461 + 0.641465i 0.966315 0.257364i \(-0.0828539\pi\)
0.438299 + 0.898829i \(0.355581\pi\)
\(710\) 0.0463907 0.322654i 0.00174101 0.0121090i
\(711\) −2.69449 13.3688i −0.101051 0.501371i
\(712\) 0.493587i 0.0184979i
\(713\) 1.96631 3.29849i 0.0736387 0.123529i
\(714\) −0.274522 + 1.45761i −0.0102737 + 0.0545497i
\(715\) 23.0417 14.8080i 0.861709 0.553787i
\(716\) 25.7457 + 3.70167i 0.962161 + 0.138338i
\(717\) 17.1241 24.2646i 0.639510 0.906179i
\(718\) 0.759514 + 2.58667i 0.0283448 + 0.0965335i
\(719\) −5.56254 + 2.54033i −0.207448 + 0.0947381i −0.516429 0.856330i \(-0.672739\pi\)
0.308982 + 0.951068i \(0.400012\pi\)
\(720\) −11.8715 33.3811i −0.442423 1.24404i
\(721\) −2.40302 16.7134i −0.0894932 0.622439i
\(722\) 0.308077 1.04921i 0.0114654 0.0390477i
\(723\) 19.3845 15.3777i 0.720916 0.571902i
\(724\) 18.9758 29.5270i 0.705232 1.09736i
\(725\) −12.7560 + 19.8488i −0.473747 + 0.737164i
\(726\) −0.772260 + 0.612632i −0.0286612 + 0.0227369i
\(727\) 4.50469 15.3416i 0.167070 0.568987i −0.832811 0.553557i \(-0.813270\pi\)
0.999881 0.0154301i \(-0.00491173\pi\)
\(728\) −0.505990 3.51924i −0.0187532 0.130432i
\(729\) −10.5874 + 24.8376i −0.392126 + 0.919912i
\(730\) −2.98531 + 1.36335i −0.110491 + 0.0504597i
\(731\) −3.24633 11.0560i −0.120070 0.408920i
\(732\) −15.2403 + 21.5953i −0.563296 + 0.798185i
\(733\) −53.4614 7.68658i −1.97464 0.283910i −0.997431 0.0716318i \(-0.977179\pi\)
−0.977209 0.212279i \(-0.931912\pi\)
\(734\) 0.779270 0.500807i 0.0287634 0.0184851i
\(735\) 1.52511 8.09776i 0.0562545 0.298690i
\(736\) 4.29410 2.96832i 0.158283 0.109414i
\(737\) 12.7651i 0.470210i
\(738\) 2.35190 0.474026i 0.0865747 0.0174491i
\(739\) −1.27077 + 8.83843i −0.0467462 + 0.325127i 0.953008 + 0.302946i \(0.0979701\pi\)
−0.999754 + 0.0221810i \(0.992939\pi\)
\(740\) −44.6290 20.3814i −1.64060 0.749235i
\(741\) 19.1623 1.91186i 0.703944 0.0702338i
\(742\) 1.19456 + 2.61572i 0.0438537 + 0.0960263i
\(743\) −2.35436 2.71707i −0.0863730 0.0996798i 0.710918 0.703275i \(-0.248280\pi\)
−0.797291 + 0.603595i \(0.793734\pi\)
\(744\) −0.0218862 + 0.504475i −0.000802387 + 0.0184950i
\(745\) 23.6419 + 6.94190i 0.866173 + 0.254331i
\(746\) −1.46099 + 1.68607i −0.0534907 + 0.0617315i
\(747\) 9.00475 + 12.4210i 0.329467 + 0.454459i
\(748\) −14.7577 9.48422i −0.539596 0.346777i
\(749\) 22.1671 + 19.2079i 0.809967 + 0.701840i
\(750\) 0.446703 + 0.227898i 0.0163113 + 0.00832164i
\(751\) −4.07465 + 0.585846i −0.148686 + 0.0213778i −0.216256 0.976337i \(-0.569385\pi\)
0.0675699 + 0.997715i \(0.478475\pi\)
\(752\) 4.50809 3.90628i 0.164393 0.142447i
\(753\) −34.5747 + 8.54324i −1.25997 + 0.311333i
\(754\) 2.20156 0.646437i 0.0801762 0.0235419i
\(755\) −19.0863 + 41.7931i −0.694621 + 1.52101i
\(756\) 15.5287 18.3889i 0.564773 0.668798i
\(757\) 16.7170 + 26.0122i 0.607591 + 0.945429i 0.999675 + 0.0255001i \(0.00811781\pi\)
−0.392084 + 0.919929i \(0.628246\pi\)
\(758\) −1.38713 −0.0503830
\(759\) −0.176207 + 18.1229i −0.00639591 + 0.657820i
\(760\) 2.88229 0.104552
\(761\) 13.5631 + 21.1046i 0.491661 + 0.765040i 0.995088 0.0989983i \(-0.0315639\pi\)
−0.503426 + 0.864038i \(0.667927\pi\)
\(762\) 0.173792 0.509118i 0.00629583 0.0184434i
\(763\) −7.20111 + 15.7682i −0.260698 + 0.570849i
\(764\) 15.3685 4.51261i 0.556015 0.163261i
\(765\) 2.02966 + 36.1505i 0.0733824 + 1.30702i
\(766\) −1.53344 + 1.32873i −0.0554053 + 0.0480089i
\(767\) −47.7772 + 6.86933i −1.72514 + 0.248037i
\(768\) 12.0735 23.6653i 0.435664 0.853948i
\(769\) 27.1639 + 23.5377i 0.979556 + 0.848790i 0.988508 0.151170i \(-0.0483041\pi\)
−0.00895217 + 0.999960i \(0.502850\pi\)
\(770\) 1.16407 + 0.748101i 0.0419501 + 0.0269597i
\(771\) −8.75486 8.27711i −0.315299 0.298093i
\(772\) 20.0495 23.1384i 0.721597 0.832767i
\(773\) −35.5723 10.4450i −1.27945 0.375679i −0.429748 0.902949i \(-0.641398\pi\)
−0.849698 + 0.527270i \(0.823216\pi\)
\(774\) 0.177693 0.760572i 0.00638703 0.0273382i
\(775\) −2.06506 2.38321i −0.0741793 0.0856075i
\(776\) −0.488003 1.06858i −0.0175183 0.0383597i
\(777\) −3.29511 33.0265i −0.118211 1.18482i
\(778\) −1.77918 0.812522i −0.0637865 0.0291303i
\(779\) 3.30402 22.9800i 0.118379 0.823344i
\(780\) −16.2655 40.1348i −0.582397 1.43706i
\(781\) 2.60810i 0.0933252i
\(782\) −1.67668 + 0.554208i −0.0599580 + 0.0198184i
\(783\) 26.4005 + 16.4956i 0.943477 + 0.589503i
\(784\) 5.28795 3.39836i 0.188855 0.121370i
\(785\) −21.9504 3.15599i −0.783443 0.112642i
\(786\) −1.29630 0.914826i −0.0462375 0.0326308i
\(787\) 5.27661 + 17.9705i 0.188091 + 0.640579i 0.998502 + 0.0547170i \(0.0174257\pi\)
−0.810411 + 0.585862i \(0.800756\pi\)
\(788\) −18.0795 + 8.25663i −0.644056 + 0.294130i
\(789\) −16.0572 + 9.36169i −0.571651 + 0.333285i
\(790\) −0.176420 1.22703i −0.00627676 0.0436558i
\(791\) −4.95331 + 16.8694i −0.176120 + 0.599808i
\(792\) −1.10997 2.10890i −0.0394409 0.0749364i
\(793\) −17.3934 + 27.0647i −0.617659 + 0.961097i
\(794\) 0.418795 0.651658i 0.0148625 0.0231265i
\(795\) 43.6261 + 54.9933i 1.54726 + 1.95041i
\(796\) 1.89199 6.44353i 0.0670599 0.228385i
\(797\) 1.32524 + 9.21725i 0.0469424 + 0.326492i 0.999738 + 0.0228799i \(0.00728352\pi\)
−0.952796 + 0.303612i \(0.901807\pi\)
\(798\) 0.490014 + 0.840473i 0.0173463 + 0.0297524i
\(799\) −5.54518 + 2.53240i −0.196174 + 0.0895898i
\(800\) −1.20771 4.11310i −0.0426992 0.145420i
\(801\) 2.91952 2.83144i 0.103156 0.100044i
\(802\) −1.89953 0.273111i −0.0670746 0.00964387i
\(803\) 22.0900 14.1964i 0.779538 0.500979i
\(804\) 19.8341 + 3.73550i 0.699496 + 0.131741i
\(805\) −31.6608 + 10.4651i −1.11590 + 0.368848i
\(806\) 0.306667i 0.0108019i
\(807\) 21.9900 8.91193i 0.774086 0.313715i
\(808\) 0.00136221 0.00947441i 4.79225e−5 0.000333309i
\(809\) −20.5731 9.39543i −0.723312 0.330326i 0.0195143 0.999810i \(-0.493788\pi\)
−0.742827 + 0.669484i \(0.766515\pi\)
\(810\) −1.08743 + 2.20021i −0.0382083 + 0.0773076i
\(811\) −15.1076 33.0810i −0.530499 1.16163i −0.965310 0.261108i \(-0.915912\pi\)
0.434811 0.900522i \(-0.356815\pi\)
\(812\) −18.1726 20.9723i −0.637732 0.735982i
\(813\) 44.3122 + 1.92244i 1.55410 + 0.0674231i
\(814\) −1.57335 0.461976i −0.0551457 0.0161922i
\(815\) 17.2660 19.9260i 0.604802 0.697978i
\(816\) −18.9750 + 20.0702i −0.664257 + 0.702598i
\(817\) −6.35821 4.08617i −0.222445 0.142957i
\(818\) 0.318728 + 0.276179i 0.0111441 + 0.00965638i
\(819\) 17.9134 23.1808i 0.625943 0.810004i
\(820\) −51.6767 + 7.42999i −1.80463 + 0.259466i
\(821\) 7.97182 6.90762i 0.278218 0.241078i −0.504562 0.863375i \(-0.668346\pi\)
0.782781 + 0.622298i \(0.213801\pi\)
\(822\) −0.00667405 0.0270101i −0.000232784 0.000942085i
\(823\) 6.88377 2.02126i 0.239953 0.0704566i −0.159545 0.987191i \(-0.551003\pi\)
0.399498 + 0.916734i \(0.369184\pi\)
\(824\) −1.09812 + 2.40455i −0.0382549 + 0.0837666i
\(825\) 14.0850 + 4.80804i 0.490376 + 0.167394i
\(826\) −1.31837 2.05142i −0.0458720 0.0713782i
\(827\) 48.5964 1.68986 0.844931 0.534875i \(-0.179641\pi\)
0.844931 + 0.534875i \(0.179641\pi\)
\(828\) 28.1073 + 5.57715i 0.976797 + 0.193819i
\(829\) −38.9457 −1.35264 −0.676319 0.736608i \(-0.736426\pi\)
−0.676319 + 0.736608i \(0.736426\pi\)
\(830\) 0.753944 + 1.17316i 0.0261698 + 0.0407210i
\(831\) 28.2091 + 9.62943i 0.978563 + 0.334041i
\(832\) 13.6072 29.7957i 0.471745 1.03298i
\(833\) −6.16364 + 1.80981i −0.213557 + 0.0627061i
\(834\) −0.00101522 0.00410864i −3.51543e−5 0.000142270i
\(835\) −32.2044 + 27.9052i −1.11448 + 0.965700i
\(836\) −11.3894 + 1.63755i −0.393912 + 0.0566360i
\(837\) −3.10947 + 2.76445i −0.107479 + 0.0955532i
\(838\) −1.95487 1.69390i −0.0675298 0.0585149i
\(839\) −31.4475 20.2101i −1.08569 0.697729i −0.129823 0.991537i \(-0.541441\pi\)
−0.955864 + 0.293808i \(0.905077\pi\)
\(840\) 3.01232 3.18619i 0.103935 0.109934i
\(841\) 4.51347 5.20882i 0.155637 0.179615i
\(842\) −2.42700 0.712632i −0.0836401 0.0245589i
\(843\) −20.9259 0.907851i −0.720726 0.0312681i
\(844\) −28.9240 33.3800i −0.995604 1.14899i
\(845\) −5.75127 12.5935i −0.197850 0.433230i
\(846\) −0.411662 0.0357865i −0.0141532 0.00123036i
\(847\) 13.1998 + 6.02813i 0.453549 + 0.207129i
\(848\) −7.62061 + 53.0025i −0.261693 + 1.82011i
\(849\) −50.2859 + 20.3794i −1.72581 + 0.699420i
\(850\) 1.45013i 0.0497392i
\(851\) 32.5055 22.4696i 1.11427 0.770247i
\(852\) 4.05240 + 0.763217i 0.138833 + 0.0261474i
\(853\) −32.3001 + 20.7580i −1.10593 + 0.710740i −0.960403 0.278614i \(-0.910125\pi\)
−0.145530 + 0.989354i \(0.546489\pi\)
\(854\) −1.60879 0.231308i −0.0550515 0.00791521i
\(855\) 16.5341 + 17.0484i 0.565455 + 0.583044i
\(856\) −1.29369 4.40589i −0.0442173 0.150590i
\(857\) −20.4018 + 9.31720i −0.696913 + 0.318269i −0.732183 0.681108i \(-0.761498\pi\)
0.0352698 + 0.999378i \(0.488771\pi\)
\(858\) −0.728987 1.25036i −0.0248872 0.0426866i
\(859\) 3.18215 + 22.1324i 0.108574 + 0.755146i 0.969265 + 0.246019i \(0.0791226\pi\)
−0.860691 + 0.509127i \(0.829968\pi\)
\(860\) −4.78839 + 16.3078i −0.163283 + 0.556090i
\(861\) −21.9499 27.6691i −0.748051 0.942962i
\(862\) −0.156816 + 0.244010i −0.00534116 + 0.00831101i
\(863\) −25.4789 + 39.6460i −0.867312 + 1.34956i 0.0687149 + 0.997636i \(0.478110\pi\)
−0.936027 + 0.351928i \(0.885526\pi\)
\(864\) −5.40609 + 1.66240i −0.183919 + 0.0565561i
\(865\) −5.83953 + 19.8876i −0.198550 + 0.676199i
\(866\) −0.139169 0.967944i −0.00472917 0.0328921i
\(867\) −1.05244 + 0.613593i −0.0357426 + 0.0208387i
\(868\) 3.37374 1.54073i 0.114512 0.0522959i
\(869\) 2.79435 + 9.51667i 0.0947917 + 0.322831i
\(870\) 2.31195 + 1.63159i 0.0783825 + 0.0553162i
\(871\) 24.3161 + 3.49613i 0.823920 + 0.118462i
\(872\) 2.28300 1.46720i 0.0773121 0.0496855i
\(873\) 3.52112 9.01634i 0.119172 0.305157i
\(874\) −0.593099 + 0.994926i −0.0200619 + 0.0336539i
\(875\) 7.38221i 0.249564i
\(876\) −15.5937 38.4771i −0.526861 1.30002i
\(877\) −0.213181 + 1.48271i −0.00719862 + 0.0500675i −0.993104 0.117236i \(-0.962597\pi\)
0.985906 + 0.167303i \(0.0535058\pi\)
\(878\) −2.39449 1.09352i −0.0808100 0.0369047i
\(879\) 3.34715 + 33.5480i 0.112896 + 1.13155i
\(880\) 10.7040 + 23.4385i 0.360832 + 0.790113i
\(881\) −31.1390 35.9364i −1.04910 1.21073i −0.976980 0.213331i \(-0.931569\pi\)
−0.0721212 0.997396i \(-0.522977\pi\)
\(882\) −0.424014 0.0990625i −0.0142773 0.00333561i
\(883\) 31.2489 + 9.17550i 1.05161 + 0.308780i 0.761467 0.648204i \(-0.224479\pi\)
0.290141 + 0.956984i \(0.406298\pi\)
\(884\) −22.1082 + 25.5142i −0.743580 + 0.858136i
\(885\) −43.2558 40.8953i −1.45403 1.37468i
\(886\) −0.0723367 0.0464880i −0.00243020 0.00156179i
\(887\) 29.4790 + 25.5437i 0.989808 + 0.857673i 0.989820 0.142327i \(-0.0454584\pi\)
−1.20318e−5 1.00000i \(0.500004\pi\)
\(888\) −2.36136 + 4.62851i −0.0792420 + 0.155323i
\(889\) −7.83869 + 1.12703i −0.262901 + 0.0377995i
\(890\) 0.279391 0.242094i 0.00936521 0.00811500i
\(891\) 6.10666 18.6629i 0.204581 0.625232i
\(892\) 17.3372 5.09066i 0.580492 0.170448i
\(893\) −1.66106 + 3.63721i −0.0555852 + 0.121715i
\(894\) 0.420635 1.23224i 0.0140681 0.0412121i
\(895\) 21.1088 + 32.8459i 0.705589 + 1.09792i
\(896\) 6.71771 0.224423
\(897\) 34.4738 + 5.29918i 1.15105 + 0.176934i
\(898\) 2.36919 0.0790608
\(899\) 2.59351 + 4.03558i 0.0864984 + 0.134594i
\(900\) 11.5923 20.4779i 0.386411 0.682595i
\(901\) 22.7330 49.7784i 0.757347 1.65836i
\(902\) −1.67421 + 0.491593i −0.0557452 + 0.0163683i
\(903\) −11.1621 + 2.75809i −0.371451 + 0.0917835i
\(904\) 2.08017 1.80247i 0.0691853 0.0599494i
\(905\) 52.1502 7.49807i 1.73353 0.249244i
\(906\) 2.16268 + 1.10335i 0.0718503 + 0.0366563i
\(907\) 27.1104 + 23.4913i 0.900188 + 0.780017i 0.976151 0.217094i \(-0.0696577\pi\)
−0.0759631 + 0.997111i \(0.524203\pi\)
\(908\) 17.4354 + 11.2051i 0.578614 + 0.371853i
\(909\) 0.0638545 0.0462922i 0.00211792 0.00153542i
\(910\) 1.74386 2.01252i 0.0578084 0.0667145i
\(911\) −5.19615 1.52573i −0.172156 0.0505496i 0.194519 0.980899i \(-0.437686\pi\)
−0.366675 + 0.930349i \(0.619504\pi\)
\(912\) −0.785232 + 18.0995i −0.0260016 + 0.599336i
\(913\) −7.30674 8.43243i −0.241818 0.279073i
\(914\) 0.388626 + 0.850972i 0.0128546 + 0.0281476i
\(915\) −39.4800 + 3.93900i −1.30517 + 0.130219i
\(916\) 14.6401 + 6.68590i 0.483722 + 0.220908i
\(917\) −3.32392 + 23.1184i −0.109766 + 0.763437i
\(918\) 1.91315 0.0243536i 0.0631433 0.000803789i
\(919\) 26.4314i 0.871892i −0.899973 0.435946i \(-0.856414\pi\)
0.899973 0.435946i \(-0.143586\pi\)
\(920\) 5.05551 + 1.30147i 0.166675 + 0.0429082i
\(921\) −1.01474 + 5.38787i −0.0334367 + 0.177536i
\(922\) 0.0752208 0.0483415i 0.00247727 0.00159204i
\(923\) 4.96813 + 0.714310i 0.163528 + 0.0235118i
\(924\) −10.0931 + 14.3018i −0.332037 + 0.470493i
\(925\) −9.14215 31.1353i −0.300592 1.02372i
\(926\) 1.95751 0.893963i 0.0643276 0.0293774i
\(927\) −20.5220 + 7.29833i −0.674032 + 0.239709i
\(928\) 0.928051 + 6.45474i 0.0304648 + 0.211887i
\(929\) 7.45067 25.3747i 0.244449 0.832516i −0.742273 0.670097i \(-0.766252\pi\)
0.986722 0.162418i \(-0.0519294\pi\)
\(930\) −0.296289 + 0.235046i −0.00971570 + 0.00770745i
\(931\) −2.27802 + 3.54466i −0.0746590 + 0.116172i
\(932\) 1.33192 2.07251i 0.0436285 0.0678873i
\(933\) −39.8389 + 31.6041i −1.30427 + 1.03467i
\(934\) −0.246951 + 0.841039i −0.00808050 + 0.0275197i
\(935\) −3.74757 26.0649i −0.122559 0.852415i
\(936\) −4.32121 + 1.53677i −0.141243 + 0.0502308i
\(937\) −12.3663 + 5.64751i −0.403990 + 0.184496i −0.607038 0.794673i \(-0.707643\pi\)
0.203048 + 0.979169i \(0.434915\pi\)
\(938\) 0.349654 + 1.19081i 0.0114166 + 0.0388814i
\(939\) −16.3804 + 23.2108i −0.534553 + 0.757457i
\(940\) 8.90029 + 1.27967i 0.290295 + 0.0417382i
\(941\) 27.9736 17.9775i 0.911912 0.586050i 0.00161182 0.999999i \(-0.499487\pi\)
0.910300 + 0.413948i \(0.135851\pi\)
\(942\) −0.216890 + 1.15160i −0.00706666 + 0.0375213i
\(943\) 16.1717 38.8149i 0.526622 1.26399i
\(944\) 45.4090i 1.47794i
\(945\) 36.1261 0.459870i 1.17518 0.0149596i
\(946\) −0.0808413 + 0.562264i −0.00262838 + 0.0182808i
\(947\) −11.0814 5.06070i −0.360097 0.164451i 0.227148 0.973860i \(-0.427060\pi\)
−0.587244 + 0.809410i \(0.699787\pi\)
\(948\) 15.6044 1.55688i 0.506809 0.0505652i
\(949\) −20.9924 45.9670i −0.681442 1.49215i
\(950\) 0.622887 + 0.718850i 0.0202091 + 0.0233226i
\(951\) 1.89259 43.6241i 0.0613715 1.41461i
\(952\) −3.27980 0.963035i −0.106299 0.0312122i
\(953\) −1.29643 + 1.49616i −0.0419954 + 0.0484652i −0.776359 0.630291i \(-0.782935\pi\)
0.734363 + 0.678757i \(0.237481\pi\)
\(954\) 3.00320 2.17721i 0.0972321 0.0704897i
\(955\) 20.2267 + 12.9989i 0.654521 + 0.420635i
\(956\) 25.8091 + 22.3637i 0.834726 + 0.723294i
\(957\) −20.1675 10.2890i −0.651922 0.332595i
\(958\) −0.475934 + 0.0684290i −0.0153767 + 0.00221084i
\(959\) −0.309533 + 0.268212i −0.00999533 + 0.00866100i
\(960\) 39.2166 9.69021i 1.26571 0.312750i
\(961\) 29.1291 8.55308i 0.939649 0.275906i
\(962\) −1.31092 + 2.87051i −0.0422658 + 0.0925491i
\(963\) 18.6392 32.9262i 0.600641 1.06103i
\(964\) 15.3824 + 23.9356i 0.495435 + 0.770912i
\(965\) 45.9581 1.47944
\(966\) 0.479973 + 1.69545i 0.0154429 + 0.0545501i
\(967\) 43.2764 1.39167 0.695837 0.718200i \(-0.255033\pi\)
0.695837 + 0.718200i \(0.255033\pi\)
\(968\) −1.22820 1.91112i −0.0394760 0.0614259i
\(969\) 5.98120 17.5217i 0.192144 0.562879i
\(970\) 0.365505 0.800345i 0.0117357 0.0256975i
\(971\) −48.0056 + 14.0957i −1.54057 + 0.452353i −0.938267 0.345913i \(-0.887569\pi\)
−0.602305 + 0.798266i \(0.705751\pi\)
\(972\) −27.2109 14.9497i −0.872791 0.479513i
\(973\) −0.0470845 + 0.0407990i −0.00150946 + 0.00130796i
\(974\) −0.785690 + 0.112965i −0.0251751 + 0.00361964i
\(975\) 13.0164 25.5134i 0.416857 0.817084i
\(976\) −22.8735 19.8200i −0.732163 0.634423i
\(977\) −5.99830 3.85488i −0.191903 0.123328i 0.441161 0.897428i \(-0.354567\pi\)
−0.633064 + 0.774099i \(0.718203\pi\)
\(978\) −1.01241 0.957167i −0.0323734 0.0306068i
\(979\) −1.93699 + 2.23541i −0.0619065 + 0.0714439i
\(980\) 9.09148 + 2.66950i 0.290417 + 0.0852740i
\(981\) 21.7746 + 5.08722i 0.695211 + 0.162422i
\(982\) −2.08641 2.40785i −0.0665801 0.0768376i
\(983\) −2.46954 5.40753i −0.0787660 0.172474i 0.866152 0.499781i \(-0.166586\pi\)
−0.944918 + 0.327307i \(0.893859\pi\)
\(984\) 0.548931 + 5.50187i 0.0174993 + 0.175393i
\(985\) −27.1390 12.3940i −0.864720 0.394904i
\(986\) 0.313944 2.18353i 0.00999803 0.0695378i
\(987\) 2.28472 + 5.63750i 0.0727233 + 0.179444i
\(988\) 22.1440i 0.704496i
\(989\) −9.30718 10.0381i −0.295951 0.319193i
\(990\) 0.649312 1.66266i 0.0206365 0.0528427i
\(991\) 0.199512 0.128219i 0.00633771 0.00407300i −0.537468 0.843284i \(-0.680619\pi\)
0.543806 + 0.839211i \(0.316983\pi\)
\(992\) −0.862694 0.124037i −0.0273906 0.00393817i
\(993\) −1.60196 1.13054i −0.0508368 0.0358766i
\(994\) 0.0714394 + 0.243300i 0.00226592 + 0.00771702i
\(995\) 9.16970 4.18766i 0.290699 0.132758i
\(996\) −15.2403 + 8.88540i −0.482906 + 0.281545i
\(997\) 5.63024 + 39.1592i 0.178312 + 1.24018i 0.860669 + 0.509165i \(0.170046\pi\)
−0.682357 + 0.731019i \(0.739045\pi\)
\(998\) 0.285631 0.972771i 0.00904150 0.0307925i
\(999\) −40.9230 + 12.5840i −1.29475 + 0.398141i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 69.2.g.a.11.4 yes 60
3.2 odd 2 inner 69.2.g.a.11.3 60
23.21 odd 22 inner 69.2.g.a.44.3 yes 60
69.44 even 22 inner 69.2.g.a.44.4 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.2.g.a.11.3 60 3.2 odd 2 inner
69.2.g.a.11.4 yes 60 1.1 even 1 trivial
69.2.g.a.44.3 yes 60 23.21 odd 22 inner
69.2.g.a.44.4 yes 60 69.44 even 22 inner