Properties

Label 418.2.q.b.109.1
Level $418$
Weight $2$
Character 418.109
Analytic conductor $3.338$
Analytic rank $0$
Dimension $60$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [418,2,Mod(21,418)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(418, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("418.21");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 418 = 2 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 418.q (of order \(18\), degree \(6\), 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: \(3.33774680449\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(10\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 109.1
Character \(\chi\) \(=\) 418.109
Dual form 418.2.q.b.395.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.939693 + 0.342020i) q^{2} +(-3.24219 - 0.571685i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.49158 - 2.09069i) q^{5} +(3.24219 - 0.571685i) q^{6} +(3.04403 - 1.75747i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(7.36587 + 2.68096i) q^{9} +O(q^{10})\) \(q+(-0.939693 + 0.342020i) q^{2} +(-3.24219 - 0.571685i) q^{3} +(0.766044 - 0.642788i) q^{4} +(-2.49158 - 2.09069i) q^{5} +(3.24219 - 0.571685i) q^{6} +(3.04403 - 1.75747i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(7.36587 + 2.68096i) q^{9} +(3.05638 + 1.11243i) q^{10} +(-1.06895 - 3.13964i) q^{11} +(-2.85113 + 1.64610i) q^{12} +(-0.777184 - 4.40763i) q^{13} +(-2.25937 + 2.69261i) q^{14} +(6.88296 + 8.20279i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-1.65951 - 4.55945i) q^{17} -7.83860 q^{18} +(1.49510 + 4.09447i) q^{19} -3.25253 q^{20} +(-10.8740 + 3.95783i) q^{21} +(2.07831 + 2.58469i) q^{22} +(-2.81159 + 2.35920i) q^{23} +(2.11619 - 2.52197i) q^{24} +(0.968774 + 5.49419i) q^{25} +(2.23781 + 3.87600i) q^{26} +(-13.7955 - 7.96482i) q^{27} +(1.20218 - 3.30297i) q^{28} +(-0.773042 - 0.281364i) q^{29} +(-9.27339 - 5.35399i) q^{30} +(-6.08322 + 3.51215i) q^{31} +(0.173648 + 0.984808i) q^{32} +(1.67086 + 10.7904i) q^{33} +(3.11885 + 3.71690i) q^{34} +(-11.2588 - 1.98523i) q^{35} +(7.36587 - 2.68096i) q^{36} -0.457611i q^{37} +(-2.80533 - 3.33619i) q^{38} +14.7347i q^{39} +(3.05638 - 1.11243i) q^{40} +(0.954338 - 5.41232i) q^{41} +(8.86461 - 7.43829i) q^{42} +(3.56993 - 4.25448i) q^{43} +(-2.83699 - 1.71800i) q^{44} +(-12.7476 - 22.0795i) q^{45} +(1.83513 - 3.17854i) q^{46} +(3.68045 + 1.33957i) q^{47} +(-1.12600 + 3.09366i) q^{48} +(2.67743 - 4.63745i) q^{49} +(-2.78947 - 4.83151i) q^{50} +(2.77386 + 15.7313i) q^{51} +(-3.42853 - 2.87687i) q^{52} +(0.795178 + 0.947656i) q^{53} +(15.6876 + 2.76615i) q^{54} +(-3.90062 + 10.0575i) q^{55} +3.51495i q^{56} +(-2.50666 - 14.1298i) q^{57} +0.822654 q^{58} +(2.71657 + 7.46371i) q^{59} +(10.5453 + 1.85942i) q^{60} +(-1.37415 - 1.63764i) q^{61} +(4.51513 - 5.38092i) q^{62} +(27.1337 - 4.78440i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-7.27855 + 12.6068i) q^{65} +(-5.26063 - 9.56820i) q^{66} +(-2.24793 + 6.17614i) q^{67} +(-4.20202 - 2.42604i) q^{68} +(10.4644 - 6.04163i) q^{69} +(11.2588 - 1.98523i) q^{70} +(-6.42680 + 7.65916i) q^{71} +(-6.00471 + 5.03855i) q^{72} +(-2.79393 - 0.492645i) q^{73} +(0.156512 + 0.430014i) q^{74} -18.3670i q^{75} +(3.77719 + 2.17551i) q^{76} +(-8.77176 - 7.67852i) q^{77} +(-5.03955 - 13.8460i) q^{78} +(-0.646397 + 3.66590i) q^{79} +(-2.49158 + 2.09069i) q^{80} +(22.1600 + 18.5944i) q^{81} +(0.954338 + 5.41232i) q^{82} +(-6.89565 + 3.98121i) q^{83} +(-5.78596 + 10.0216i) q^{84} +(-5.39759 + 14.8298i) q^{85} +(-1.89952 + 5.21889i) q^{86} +(2.34550 + 1.35417i) q^{87} +(3.25348 + 0.644081i) q^{88} +(0.164120 - 0.0289389i) q^{89} +(19.5305 + 16.3880i) q^{90} +(-10.1121 - 12.0511i) q^{91} +(-0.637335 + 3.61450i) q^{92} +(21.7308 - 7.90935i) q^{93} -3.91665 q^{94} +(4.83507 - 13.3275i) q^{95} -3.29220i q^{96} +(-4.96306 - 13.6359i) q^{97} +(-0.929862 + 5.27351i) q^{98} +(0.543482 - 25.9920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 60 q - 3 q^{3} + 3 q^{6} + 18 q^{7} - 30 q^{8} - 3 q^{9} + 3 q^{11} - 6 q^{13} - 12 q^{14} + 24 q^{15} + 6 q^{17} - 60 q^{18} + 30 q^{19} - 12 q^{20} - 12 q^{21} + 12 q^{22} - 3 q^{24} - 12 q^{25} + 6 q^{26} + 9 q^{27} - 6 q^{28} + 3 q^{29} - 9 q^{31} + 9 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} + 6 q^{38} - 15 q^{41} + 6 q^{42} + 3 q^{43} - 12 q^{44} - 48 q^{45} - 3 q^{46} + 54 q^{47} - 6 q^{48} + 6 q^{49} - 36 q^{50} + 45 q^{51} + 3 q^{52} + 24 q^{53} + 27 q^{54} - 48 q^{55} - 30 q^{57} + 24 q^{58} - 39 q^{59} + 12 q^{60} - 54 q^{61} + 66 q^{63} - 30 q^{64} - 30 q^{66} + 9 q^{67} + 27 q^{68} + 54 q^{69} - 24 q^{70} - 33 q^{71} + 6 q^{72} - 12 q^{74} + 18 q^{77} - 36 q^{79} - 93 q^{81} - 15 q^{82} + 36 q^{83} - 24 q^{84} + 60 q^{85} - 3 q^{86} - 54 q^{87} + 3 q^{88} - 3 q^{89} + 24 q^{90} - 12 q^{91} - 102 q^{93} + 12 q^{94} - 24 q^{95} - 6 q^{97} + 18 q^{98} + 75 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/418\mathbb{Z}\right)^\times\).

\(n\) \(287\) \(343\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.939693 + 0.342020i −0.664463 + 0.241845i
\(3\) −3.24219 0.571685i −1.87188 0.330062i −0.881916 0.471406i \(-0.843747\pi\)
−0.989961 + 0.141343i \(0.954858\pi\)
\(4\) 0.766044 0.642788i 0.383022 0.321394i
\(5\) −2.49158 2.09069i −1.11427 0.934983i −0.115968 0.993253i \(-0.536997\pi\)
−0.998301 + 0.0582700i \(0.981442\pi\)
\(6\) 3.24219 0.571685i 1.32362 0.233389i
\(7\) 3.04403 1.75747i 1.15054 0.664263i 0.201519 0.979485i \(-0.435412\pi\)
0.949018 + 0.315222i \(0.102079\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 7.36587 + 2.68096i 2.45529 + 0.893653i
\(10\) 3.05638 + 1.11243i 0.966511 + 0.351781i
\(11\) −1.06895 3.13964i −0.322301 0.946637i
\(12\) −2.85113 + 1.64610i −0.823051 + 0.475188i
\(13\) −0.777184 4.40763i −0.215552 1.22246i −0.879946 0.475074i \(-0.842421\pi\)
0.664394 0.747382i \(-0.268690\pi\)
\(14\) −2.25937 + 2.69261i −0.603841 + 0.719629i
\(15\) 6.88296 + 8.20279i 1.77717 + 2.11795i
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) −1.65951 4.55945i −0.402489 1.10583i −0.961052 0.276368i \(-0.910869\pi\)
0.558563 0.829462i \(-0.311353\pi\)
\(18\) −7.83860 −1.84757
\(19\) 1.49510 + 4.09447i 0.343000 + 0.939335i
\(20\) −3.25253 −0.727288
\(21\) −10.8740 + 3.95783i −2.37291 + 0.863669i
\(22\) 2.07831 + 2.58469i 0.443096 + 0.551059i
\(23\) −2.81159 + 2.35920i −0.586256 + 0.491927i −0.886995 0.461779i \(-0.847211\pi\)
0.300739 + 0.953707i \(0.402767\pi\)
\(24\) 2.11619 2.52197i 0.431965 0.514796i
\(25\) 0.968774 + 5.49419i 0.193755 + 1.09884i
\(26\) 2.23781 + 3.87600i 0.438871 + 0.760147i
\(27\) −13.7955 7.96482i −2.65494 1.53283i
\(28\) 1.20218 3.30297i 0.227191 0.624203i
\(29\) −0.773042 0.281364i −0.143550 0.0522481i 0.269246 0.963071i \(-0.413226\pi\)
−0.412796 + 0.910823i \(0.635448\pi\)
\(30\) −9.27339 5.35399i −1.69308 0.977501i
\(31\) −6.08322 + 3.51215i −1.09258 + 0.630800i −0.934262 0.356588i \(-0.883940\pi\)
−0.158316 + 0.987388i \(0.550607\pi\)
\(32\) 0.173648 + 0.984808i 0.0306970 + 0.174091i
\(33\) 1.67086 + 10.7904i 0.290859 + 1.87837i
\(34\) 3.11885 + 3.71690i 0.534878 + 0.637443i
\(35\) −11.2588 1.98523i −1.90308 0.335565i
\(36\) 7.36587 2.68096i 1.22765 0.446826i
\(37\) 0.457611i 0.0752309i −0.999292 0.0376154i \(-0.988024\pi\)
0.999292 0.0376154i \(-0.0119762\pi\)
\(38\) −2.80533 3.33619i −0.455084 0.541201i
\(39\) 14.7347i 2.35943i
\(40\) 3.05638 1.11243i 0.483256 0.175891i
\(41\) 0.954338 5.41232i 0.149043 0.845262i −0.814989 0.579476i \(-0.803257\pi\)
0.964032 0.265787i \(-0.0856316\pi\)
\(42\) 8.86461 7.43829i 1.36784 1.14775i
\(43\) 3.56993 4.25448i 0.544409 0.648802i −0.421761 0.906707i \(-0.638588\pi\)
0.966170 + 0.257906i \(0.0830323\pi\)
\(44\) −2.83699 1.71800i −0.427692 0.258998i
\(45\) −12.7476 22.0795i −1.90030 3.29142i
\(46\) 1.83513 3.17854i 0.270575 0.468650i
\(47\) 3.68045 + 1.33957i 0.536848 + 0.195397i 0.596194 0.802841i \(-0.296679\pi\)
−0.0593454 + 0.998238i \(0.518901\pi\)
\(48\) −1.12600 + 3.09366i −0.162524 + 0.446531i
\(49\) 2.67743 4.63745i 0.382490 0.662493i
\(50\) −2.78947 4.83151i −0.394491 0.683278i
\(51\) 2.77386 + 15.7313i 0.388417 + 2.20282i
\(52\) −3.42853 2.87687i −0.475451 0.398951i
\(53\) 0.795178 + 0.947656i 0.109226 + 0.130171i 0.817888 0.575378i \(-0.195145\pi\)
−0.708661 + 0.705549i \(0.750701\pi\)
\(54\) 15.6876 + 2.76615i 2.13482 + 0.376426i
\(55\) −3.90062 + 10.0575i −0.525959 + 1.35615i
\(56\) 3.51495i 0.469705i
\(57\) −2.50666 14.1298i −0.332015 1.87153i
\(58\) 0.822654 0.108020
\(59\) 2.71657 + 7.46371i 0.353667 + 0.971692i 0.981182 + 0.193087i \(0.0618500\pi\)
−0.627515 + 0.778605i \(0.715928\pi\)
\(60\) 10.5453 + 1.85942i 1.36139 + 0.240050i
\(61\) −1.37415 1.63764i −0.175941 0.209679i 0.670866 0.741579i \(-0.265923\pi\)
−0.846807 + 0.531900i \(0.821478\pi\)
\(62\) 4.51513 5.38092i 0.573422 0.683378i
\(63\) 27.1337 4.78440i 3.41852 0.602778i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −7.27855 + 12.6068i −0.902792 + 1.56368i
\(66\) −5.26063 9.56820i −0.647538 1.17776i
\(67\) −2.24793 + 6.17614i −0.274629 + 0.754536i 0.723320 + 0.690513i \(0.242615\pi\)
−0.997948 + 0.0640228i \(0.979607\pi\)
\(68\) −4.20202 2.42604i −0.509569 0.294200i
\(69\) 10.4644 6.04163i 1.25977 0.727326i
\(70\) 11.2588 1.98523i 1.34568 0.237280i
\(71\) −6.42680 + 7.65916i −0.762721 + 0.908975i −0.998017 0.0629485i \(-0.979950\pi\)
0.235296 + 0.971924i \(0.424394\pi\)
\(72\) −6.00471 + 5.03855i −0.707662 + 0.593799i
\(73\) −2.79393 0.492645i −0.327005 0.0576598i 0.00773583 0.999970i \(-0.497538\pi\)
−0.334741 + 0.942310i \(0.608649\pi\)
\(74\) 0.156512 + 0.430014i 0.0181942 + 0.0499881i
\(75\) 18.3670i 2.12084i
\(76\) 3.77719 + 2.17551i 0.433273 + 0.249548i
\(77\) −8.77176 7.67852i −0.999635 0.875049i
\(78\) −5.03955 13.8460i −0.570616 1.56776i
\(79\) −0.646397 + 3.66590i −0.0727253 + 0.412446i 0.926611 + 0.376021i \(0.122708\pi\)
−0.999336 + 0.0364247i \(0.988403\pi\)
\(80\) −2.49158 + 2.09069i −0.278567 + 0.233746i
\(81\) 22.1600 + 18.5944i 2.46222 + 2.06605i
\(82\) 0.954338 + 5.41232i 0.105389 + 0.597691i
\(83\) −6.89565 + 3.98121i −0.756896 + 0.436994i −0.828180 0.560462i \(-0.810624\pi\)
0.0712840 + 0.997456i \(0.477290\pi\)
\(84\) −5.78596 + 10.0216i −0.631300 + 1.09344i
\(85\) −5.39759 + 14.8298i −0.585451 + 1.60851i
\(86\) −1.89952 + 5.21889i −0.204830 + 0.562767i
\(87\) 2.34550 + 1.35417i 0.251464 + 0.145183i
\(88\) 3.25348 + 0.644081i 0.346823 + 0.0686592i
\(89\) 0.164120 0.0289389i 0.0173967 0.00306751i −0.164943 0.986303i \(-0.552744\pi\)
0.182340 + 0.983236i \(0.441633\pi\)
\(90\) 19.5305 + 16.3880i 2.05870 + 1.72745i
\(91\) −10.1121 12.0511i −1.06003 1.26330i
\(92\) −0.637335 + 3.61450i −0.0664467 + 0.376838i
\(93\) 21.7308 7.90935i 2.25338 0.820161i
\(94\) −3.91665 −0.403971
\(95\) 4.83507 13.3275i 0.496068 1.36737i
\(96\) 3.29220i 0.336009i
\(97\) −4.96306 13.6359i −0.503922 1.38451i −0.887415 0.460971i \(-0.847501\pi\)
0.383493 0.923544i \(-0.374721\pi\)
\(98\) −0.929862 + 5.27351i −0.0939303 + 0.532705i
\(99\) 0.543482 25.9920i 0.0546220 2.61229i
\(100\) 4.27372 + 3.58608i 0.427372 + 0.358608i
\(101\) 15.0674 2.65679i 1.49926 0.264360i 0.637016 0.770851i \(-0.280169\pi\)
0.862246 + 0.506490i \(0.169057\pi\)
\(102\) −7.98700 13.8339i −0.790831 1.36976i
\(103\) −1.79815 1.03816i −0.177177 0.102293i 0.408789 0.912629i \(-0.365951\pi\)
−0.585966 + 0.810336i \(0.699285\pi\)
\(104\) 4.20571 + 1.53075i 0.412404 + 0.150103i
\(105\) 35.3682 + 12.8730i 3.45158 + 1.25627i
\(106\) −1.07134 0.618539i −0.104058 0.0600778i
\(107\) 2.14244 + 3.71082i 0.207118 + 0.358738i 0.950805 0.309789i \(-0.100258\pi\)
−0.743688 + 0.668527i \(0.766925\pi\)
\(108\) −15.6876 + 2.76615i −1.50954 + 0.266173i
\(109\) 5.12069 + 4.29677i 0.490473 + 0.411556i 0.854196 0.519951i \(-0.174050\pi\)
−0.363722 + 0.931507i \(0.618494\pi\)
\(110\) 0.225511 10.7851i 0.0215017 1.02832i
\(111\) −0.261610 + 1.48366i −0.0248309 + 0.140823i
\(112\) −1.20218 3.30297i −0.113596 0.312101i
\(113\) 0.557845i 0.0524777i −0.999656 0.0262388i \(-0.991647\pi\)
0.999656 0.0262388i \(-0.00835304\pi\)
\(114\) 7.18815 + 12.4203i 0.673232 + 1.16327i
\(115\) 11.9376 1.11319
\(116\) −0.773042 + 0.281364i −0.0717752 + 0.0261240i
\(117\) 6.09203 34.5496i 0.563208 3.19411i
\(118\) −5.10547 6.08447i −0.469997 0.560121i
\(119\) −13.0647 10.9626i −1.19764 1.00494i
\(120\) −10.5453 + 1.85942i −0.962650 + 0.169741i
\(121\) −8.71468 + 6.71225i −0.792244 + 0.610204i
\(122\) 1.85138 + 1.06890i 0.167616 + 0.0967733i
\(123\) −6.18828 + 17.0022i −0.557979 + 1.53303i
\(124\) −2.40245 + 6.60068i −0.215746 + 0.592758i
\(125\) 0.941517 1.63076i 0.0842119 0.145859i
\(126\) −23.8610 + 13.7761i −2.12570 + 1.22728i
\(127\) −1.79490 10.1794i −0.159271 0.903273i −0.954776 0.297325i \(-0.903905\pi\)
0.795505 0.605947i \(-0.207206\pi\)
\(128\) 0.766044 + 0.642788i 0.0677094 + 0.0568149i
\(129\) −14.0066 + 11.7529i −1.23321 + 1.03479i
\(130\) 2.52781 14.3359i 0.221704 1.25734i
\(131\) −3.99844 10.9856i −0.349345 0.959817i −0.982577 0.185856i \(-0.940494\pi\)
0.633232 0.773962i \(-0.281728\pi\)
\(132\) 8.21589 + 7.19192i 0.715101 + 0.625977i
\(133\) 11.7471 + 9.83610i 1.01860 + 0.852898i
\(134\) 6.57251i 0.567779i
\(135\) 17.7206 + 48.6870i 1.52515 + 4.19031i
\(136\) 4.77836 + 0.842553i 0.409741 + 0.0722483i
\(137\) −4.88367 + 4.09788i −0.417240 + 0.350106i −0.827112 0.562037i \(-0.810018\pi\)
0.409872 + 0.912143i \(0.365573\pi\)
\(138\) −7.76697 + 9.25631i −0.661168 + 0.787949i
\(139\) −17.7850 + 3.13598i −1.50851 + 0.265990i −0.865904 0.500210i \(-0.833256\pi\)
−0.642601 + 0.766201i \(0.722145\pi\)
\(140\) −9.90081 + 5.71624i −0.836771 + 0.483110i
\(141\) −11.1669 6.44720i −0.940421 0.542952i
\(142\) 3.41963 9.39535i 0.286969 0.788441i
\(143\) −13.0076 + 7.15162i −1.08775 + 0.598048i
\(144\) 3.91930 6.78842i 0.326608 0.565702i
\(145\) 1.33785 + 2.31723i 0.111103 + 0.192436i
\(146\) 2.79393 0.492645i 0.231227 0.0407716i
\(147\) −11.3319 + 13.5048i −0.934639 + 1.11386i
\(148\) −0.294147 0.350551i −0.0241787 0.0288151i
\(149\) −6.66692 1.17556i −0.546176 0.0963055i −0.106250 0.994339i \(-0.533884\pi\)
−0.439926 + 0.898034i \(0.644995\pi\)
\(150\) 6.28189 + 17.2593i 0.512914 + 1.40922i
\(151\) 23.3289 1.89848 0.949240 0.314554i \(-0.101855\pi\)
0.949240 + 0.314554i \(0.101855\pi\)
\(152\) −4.29346 0.752437i −0.348246 0.0610307i
\(153\) 38.0334i 3.07482i
\(154\) 10.8690 + 4.21533i 0.875847 + 0.339681i
\(155\) 22.4996 + 3.96729i 1.80721 + 0.318660i
\(156\) 9.47125 + 11.2874i 0.758307 + 0.903715i
\(157\) −9.77262 8.20020i −0.779940 0.654447i 0.163293 0.986578i \(-0.447788\pi\)
−0.943234 + 0.332130i \(0.892233\pi\)
\(158\) −0.646397 3.66590i −0.0514246 0.291643i
\(159\) −2.03635 3.52707i −0.161493 0.279715i
\(160\) 1.62626 2.81677i 0.128567 0.222685i
\(161\) −4.41233 + 12.1228i −0.347740 + 0.955409i
\(162\) −27.1832 9.89389i −2.13572 0.777337i
\(163\) −6.19564 + 10.7312i −0.485280 + 0.840530i −0.999857 0.0169144i \(-0.994616\pi\)
0.514577 + 0.857444i \(0.327949\pi\)
\(164\) −2.74791 4.75951i −0.214576 0.371656i
\(165\) 18.3963 30.3784i 1.43215 2.36496i
\(166\) 5.11814 6.09956i 0.397245 0.473418i
\(167\) 11.1664 9.36972i 0.864082 0.725051i −0.0987613 0.995111i \(-0.531488\pi\)
0.962843 + 0.270060i \(0.0870436\pi\)
\(168\) 2.00944 11.3961i 0.155032 0.879230i
\(169\) −6.60716 + 2.40481i −0.508243 + 0.184985i
\(170\) 15.7815i 1.21039i
\(171\) 0.0356421 + 34.1676i 0.00272562 + 2.61286i
\(172\) 5.55382i 0.423475i
\(173\) −3.06221 + 1.11455i −0.232815 + 0.0847378i −0.455793 0.890086i \(-0.650644\pi\)
0.222978 + 0.974823i \(0.428422\pi\)
\(174\) −2.66720 0.470299i −0.202200 0.0356533i
\(175\) 12.6049 + 15.0219i 0.952839 + 1.13555i
\(176\) −3.27756 + 0.507519i −0.247056 + 0.0382557i
\(177\) −4.54073 25.7517i −0.341302 1.93562i
\(178\) −0.144325 + 0.0833262i −0.0108176 + 0.00624556i
\(179\) −14.2959 8.25375i −1.06853 0.616914i −0.140748 0.990045i \(-0.544951\pi\)
−0.927778 + 0.373132i \(0.878284\pi\)
\(180\) −23.9577 8.71989i −1.78570 0.649942i
\(181\) −1.53732 + 4.22374i −0.114268 + 0.313948i −0.983623 0.180240i \(-0.942313\pi\)
0.869355 + 0.494188i \(0.164535\pi\)
\(182\) 13.6239 + 7.86579i 1.00987 + 0.583051i
\(183\) 3.51902 + 6.09513i 0.260134 + 0.450565i
\(184\) −0.637335 3.61450i −0.0469849 0.266465i
\(185\) −0.956722 + 1.14018i −0.0703396 + 0.0838274i
\(186\) −17.7151 + 14.8647i −1.29893 + 1.08993i
\(187\) −12.5411 + 10.0841i −0.917097 + 0.737422i
\(188\) 3.68045 1.33957i 0.268424 0.0976984i
\(189\) −55.9918 −4.07281
\(190\) 0.0147893 + 14.1774i 0.00107293 + 1.02854i
\(191\) 18.2790 1.32262 0.661310 0.750113i \(-0.270001\pi\)
0.661310 + 0.750113i \(0.270001\pi\)
\(192\) 1.12600 + 3.09366i 0.0812620 + 0.223266i
\(193\) 2.70281 15.3284i 0.194552 1.10336i −0.718502 0.695525i \(-0.755172\pi\)
0.913055 0.407837i \(-0.133717\pi\)
\(194\) 9.32750 + 11.1161i 0.669675 + 0.798088i
\(195\) 30.8055 36.7126i 2.20603 2.62904i
\(196\) −0.929862 5.27351i −0.0664187 0.376679i
\(197\) 3.94211 2.27598i 0.280864 0.162157i −0.352951 0.935642i \(-0.614822\pi\)
0.633814 + 0.773485i \(0.281488\pi\)
\(198\) 8.37908 + 24.6104i 0.595475 + 1.74898i
\(199\) −7.56876 2.75480i −0.536535 0.195283i 0.0595190 0.998227i \(-0.481043\pi\)
−0.596054 + 0.802944i \(0.703266\pi\)
\(200\) −5.24249 1.90811i −0.370700 0.134924i
\(201\) 10.8190 18.7391i 0.763115 1.32175i
\(202\) −13.2500 + 7.64991i −0.932270 + 0.538246i
\(203\) −2.84766 + 0.502119i −0.199866 + 0.0352418i
\(204\) 12.2368 + 10.2679i 0.856747 + 0.718896i
\(205\) −13.6933 + 11.4900i −0.956380 + 0.802498i
\(206\) 2.04478 + 0.360550i 0.142466 + 0.0251207i
\(207\) −27.0347 + 9.83982i −1.87904 + 0.683915i
\(208\) −4.47562 −0.310329
\(209\) 11.2570 9.07088i 0.778660 0.627446i
\(210\) −37.6380 −2.59727
\(211\) 4.52047 1.64532i 0.311202 0.113268i −0.181698 0.983354i \(-0.558159\pi\)
0.492900 + 0.870086i \(0.335937\pi\)
\(212\) 1.21828 + 0.214816i 0.0836721 + 0.0147536i
\(213\) 25.2155 21.1583i 1.72774 1.44974i
\(214\) −3.28241 2.75427i −0.224381 0.188278i
\(215\) −17.7895 + 3.13678i −1.21324 + 0.213926i
\(216\) 13.7955 7.96482i 0.938663 0.541937i
\(217\) −12.3450 + 21.3822i −0.838034 + 1.45152i
\(218\) −6.28146 2.28626i −0.425434 0.154845i
\(219\) 8.77680 + 3.19450i 0.593081 + 0.215864i
\(220\) 3.47680 + 10.2118i 0.234406 + 0.688477i
\(221\) −18.8066 + 10.8580i −1.26507 + 0.730389i
\(222\) −0.261610 1.48366i −0.0175581 0.0995768i
\(223\) 13.0818 15.5903i 0.876022 1.04400i −0.122648 0.992450i \(-0.539139\pi\)
0.998670 0.0515523i \(-0.0164169\pi\)
\(224\) 2.25937 + 2.69261i 0.150960 + 0.179907i
\(225\) −7.59382 + 43.0667i −0.506255 + 2.87111i
\(226\) 0.190794 + 0.524203i 0.0126915 + 0.0348695i
\(227\) −0.498408 −0.0330805 −0.0165403 0.999863i \(-0.505265\pi\)
−0.0165403 + 0.999863i \(0.505265\pi\)
\(228\) −11.0026 9.21277i −0.728668 0.610131i
\(229\) 12.3981 0.819292 0.409646 0.912245i \(-0.365652\pi\)
0.409646 + 0.912245i \(0.365652\pi\)
\(230\) −11.2177 + 4.08291i −0.739674 + 0.269219i
\(231\) 24.0500 + 29.9099i 1.58237 + 1.96793i
\(232\) 0.630190 0.528792i 0.0413740 0.0347169i
\(233\) −10.9766 + 13.0815i −0.719104 + 0.856995i −0.994543 0.104324i \(-0.966732\pi\)
0.275439 + 0.961318i \(0.411177\pi\)
\(234\) 6.09203 + 34.5496i 0.398248 + 2.25858i
\(235\) −6.36951 11.0323i −0.415501 0.719668i
\(236\) 6.87859 + 3.97135i 0.447758 + 0.258513i
\(237\) 4.19148 11.5160i 0.272266 0.748044i
\(238\) 16.0262 + 5.83308i 1.03883 + 0.378102i
\(239\) −5.33949 3.08275i −0.345383 0.199407i 0.317267 0.948336i \(-0.397235\pi\)
−0.662650 + 0.748929i \(0.730568\pi\)
\(240\) 9.27339 5.35399i 0.598594 0.345599i
\(241\) −2.26900 12.8681i −0.146159 0.828909i −0.966429 0.256933i \(-0.917288\pi\)
0.820270 0.571976i \(-0.193823\pi\)
\(242\) 5.89340 9.28805i 0.378842 0.597058i
\(243\) −30.4985 36.3467i −1.95648 2.33164i
\(244\) −2.10531 0.371224i −0.134779 0.0237652i
\(245\) −16.3665 + 5.95691i −1.04562 + 0.380573i
\(246\) 18.0933i 1.15359i
\(247\) 16.8849 9.77201i 1.07436 0.621778i
\(248\) 7.02429i 0.446043i
\(249\) 24.6330 8.96568i 1.56105 0.568177i
\(250\) −0.326986 + 1.85443i −0.0206804 + 0.117284i
\(251\) 18.9645 15.9131i 1.19703 1.00443i 0.197318 0.980340i \(-0.436777\pi\)
0.999710 0.0240859i \(-0.00766751\pi\)
\(252\) 17.7103 21.1063i 1.11564 1.32957i
\(253\) 10.4125 + 6.30550i 0.654628 + 0.396423i
\(254\) 5.16820 + 8.95158i 0.324282 + 0.561672i
\(255\) 25.9779 44.9951i 1.62680 2.81770i
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) −9.41992 + 25.8810i −0.587599 + 1.61441i 0.187282 + 0.982306i \(0.440032\pi\)
−0.774881 + 0.632108i \(0.782190\pi\)
\(258\) 9.14216 15.8347i 0.569166 0.985824i
\(259\) −0.804240 1.39299i −0.0499731 0.0865559i
\(260\) 2.52781 + 14.3359i 0.156768 + 0.889077i
\(261\) −4.93980 4.14499i −0.305766 0.256568i
\(262\) 7.51460 + 8.95555i 0.464254 + 0.553276i
\(263\) −7.41931 1.30822i −0.457494 0.0806686i −0.0598483 0.998207i \(-0.519062\pi\)
−0.397646 + 0.917539i \(0.630173\pi\)
\(264\) −10.1802 3.94820i −0.626547 0.242995i
\(265\) 4.02363i 0.247170i
\(266\) −14.4028 5.22517i −0.883091 0.320376i
\(267\) −0.548653 −0.0335770
\(268\) 2.24793 + 6.17614i 0.137314 + 0.377268i
\(269\) −17.0100 2.99931i −1.03712 0.182871i −0.370933 0.928660i \(-0.620962\pi\)
−0.666183 + 0.745788i \(0.732073\pi\)
\(270\) −33.3039 39.6900i −2.02681 2.41546i
\(271\) −7.84890 + 9.35395i −0.476787 + 0.568212i −0.949806 0.312840i \(-0.898720\pi\)
0.473019 + 0.881052i \(0.343164\pi\)
\(272\) −4.77836 + 0.842553i −0.289730 + 0.0510873i
\(273\) 25.8958 + 44.8528i 1.56728 + 2.71461i
\(274\) 3.18759 5.52106i 0.192569 0.333540i
\(275\) 16.2142 8.91462i 0.977753 0.537572i
\(276\) 4.13272 11.3545i 0.248760 0.683463i
\(277\) 20.8666 + 12.0473i 1.25375 + 0.723853i 0.971852 0.235591i \(-0.0757025\pi\)
0.281899 + 0.959444i \(0.409036\pi\)
\(278\) 15.6399 9.02969i 0.938018 0.541565i
\(279\) −54.2241 + 9.56117i −3.24631 + 0.572412i
\(280\) 7.34865 8.75778i 0.439166 0.523378i
\(281\) 17.4051 14.6046i 1.03830 0.871236i 0.0464837 0.998919i \(-0.485198\pi\)
0.991815 + 0.127683i \(0.0407540\pi\)
\(282\) 12.6985 + 2.23909i 0.756185 + 0.133336i
\(283\) 8.63619 + 23.7277i 0.513368 + 1.41047i 0.877705 + 0.479201i \(0.159073\pi\)
−0.364337 + 0.931267i \(0.618704\pi\)
\(284\) 9.99833i 0.593291i
\(285\) −23.2953 + 40.4461i −1.37990 + 2.39582i
\(286\) 9.77714 11.1692i 0.578135 0.660448i
\(287\) −6.60698 18.1525i −0.389997 1.07151i
\(288\) −1.36116 + 7.71951i −0.0802070 + 0.454876i
\(289\) −5.01191 + 4.20549i −0.294818 + 0.247382i
\(290\) −2.04971 1.71991i −0.120363 0.100997i
\(291\) 8.29572 + 47.0474i 0.486304 + 2.75797i
\(292\) −2.45694 + 1.41852i −0.143782 + 0.0830123i
\(293\) −9.72207 + 16.8391i −0.567969 + 0.983752i 0.428797 + 0.903401i \(0.358937\pi\)
−0.996767 + 0.0803511i \(0.974396\pi\)
\(294\) 6.02957 16.5661i 0.351652 0.966156i
\(295\) 8.83571 24.2759i 0.514435 1.41340i
\(296\) 0.396303 + 0.228806i 0.0230347 + 0.0132991i
\(297\) −10.2600 + 51.8268i −0.595344 + 3.00730i
\(298\) 6.66692 1.17556i 0.386204 0.0680983i
\(299\) 12.5836 + 10.5589i 0.727728 + 0.610636i
\(300\) −11.8061 14.0699i −0.681625 0.812329i
\(301\) 3.38986 19.2248i 0.195388 1.10810i
\(302\) −21.9220 + 7.97895i −1.26147 + 0.459137i
\(303\) −50.3701 −2.89369
\(304\) 4.29189 0.761392i 0.246157 0.0436688i
\(305\) 6.95323i 0.398141i
\(306\) 13.0082 + 35.7397i 0.743629 + 2.04310i
\(307\) 2.21174 12.5434i 0.126231 0.715889i −0.854339 0.519716i \(-0.826038\pi\)
0.980569 0.196173i \(-0.0628513\pi\)
\(308\) −11.6552 0.243706i −0.664118 0.0138864i
\(309\) 5.23643 + 4.39388i 0.297890 + 0.249959i
\(310\) −22.4996 + 3.96729i −1.27789 + 0.225327i
\(311\) 7.30151 + 12.6466i 0.414030 + 0.717122i 0.995326 0.0965707i \(-0.0307874\pi\)
−0.581296 + 0.813692i \(0.697454\pi\)
\(312\) −12.7606 7.36733i −0.722426 0.417093i
\(313\) −3.91322 1.42430i −0.221188 0.0805059i 0.229049 0.973415i \(-0.426438\pi\)
−0.450237 + 0.892909i \(0.648661\pi\)
\(314\) 11.9879 + 4.36324i 0.676516 + 0.246232i
\(315\) −77.6085 44.8073i −4.37274 2.52460i
\(316\) 1.86123 + 3.22374i 0.104702 + 0.181349i
\(317\) −10.3025 + 1.81662i −0.578648 + 0.102031i −0.455309 0.890333i \(-0.650471\pi\)
−0.123339 + 0.992365i \(0.539360\pi\)
\(318\) 3.11988 + 2.61789i 0.174954 + 0.146804i
\(319\) −0.0570380 + 2.72784i −0.00319352 + 0.152730i
\(320\) −0.564796 + 3.20312i −0.0315730 + 0.179060i
\(321\) −4.82478 13.2560i −0.269293 0.739876i
\(322\) 12.9008i 0.718933i
\(323\) 16.1874 13.6116i 0.900691 0.757372i
\(324\) 28.9278 1.60710
\(325\) 23.4634 8.53999i 1.30152 0.473713i
\(326\) 2.15172 12.2030i 0.119173 0.675864i
\(327\) −14.1458 16.8584i −0.782267 0.932269i
\(328\) 4.21004 + 3.53264i 0.232460 + 0.195057i
\(329\) 13.5577 2.39058i 0.747458 0.131797i
\(330\) −6.89681 + 34.8383i −0.379657 + 1.91778i
\(331\) −14.9079 8.60708i −0.819412 0.473088i 0.0308017 0.999526i \(-0.490194\pi\)
−0.850214 + 0.526438i \(0.823527\pi\)
\(332\) −2.72331 + 7.48222i −0.149461 + 0.410640i
\(333\) 1.22684 3.37071i 0.0672302 0.184714i
\(334\) −7.28835 + 12.6238i −0.398801 + 0.690743i
\(335\) 18.5133 10.6886i 1.01149 0.583983i
\(336\) 2.00944 + 11.3961i 0.109624 + 0.621709i
\(337\) −17.3294 14.5411i −0.943992 0.792104i 0.0342832 0.999412i \(-0.489085\pi\)
−0.978276 + 0.207309i \(0.933530\pi\)
\(338\) 5.38621 4.51956i 0.292971 0.245832i
\(339\) −0.318912 + 1.80864i −0.0173209 + 0.0982318i
\(340\) 5.39759 + 14.8298i 0.292725 + 0.804257i
\(341\) 17.5295 + 15.3448i 0.949278 + 0.830967i
\(342\) −11.7195 32.0949i −0.633718 1.73549i
\(343\) 5.78257i 0.312229i
\(344\) 1.89952 + 5.21889i 0.102415 + 0.281384i
\(345\) −38.7041 6.82457i −2.08376 0.367422i
\(346\) 2.49633 2.09467i 0.134204 0.112610i
\(347\) −8.36054 + 9.96370i −0.448817 + 0.534880i −0.942253 0.334903i \(-0.891297\pi\)
0.493435 + 0.869782i \(0.335741\pi\)
\(348\) 2.66720 0.470299i 0.142977 0.0252107i
\(349\) 21.1025 12.1836i 1.12959 0.652171i 0.185760 0.982595i \(-0.440525\pi\)
0.943832 + 0.330424i \(0.107192\pi\)
\(350\) −16.9825 9.80485i −0.907753 0.524091i
\(351\) −24.3843 + 66.9954i −1.30154 + 3.57595i
\(352\) 2.90632 1.59790i 0.154907 0.0851686i
\(353\) −0.376492 + 0.652102i −0.0200386 + 0.0347079i −0.875871 0.482546i \(-0.839712\pi\)
0.855832 + 0.517254i \(0.173046\pi\)
\(354\) 13.0745 + 22.6457i 0.694902 + 1.20361i
\(355\) 32.0258 5.64701i 1.69975 0.299712i
\(356\) 0.107122 0.127663i 0.00567746 0.00676613i
\(357\) 36.0911 + 43.0117i 1.91014 + 2.27642i
\(358\) 16.2567 + 2.86650i 0.859194 + 0.151499i
\(359\) −10.2840 28.2552i −0.542771 1.49125i −0.843281 0.537473i \(-0.819379\pi\)
0.300510 0.953779i \(-0.402843\pi\)
\(360\) 25.4953 1.34372
\(361\) −14.5293 + 12.2433i −0.764702 + 0.644384i
\(362\) 4.49481i 0.236242i
\(363\) 32.0919 16.7803i 1.68439 0.880738i
\(364\) −15.4926 2.73176i −0.812032 0.143183i
\(365\) 5.93134 + 7.06869i 0.310460 + 0.369992i
\(366\) −5.39146 4.52397i −0.281816 0.236472i
\(367\) −3.64926 20.6960i −0.190490 1.08032i −0.918697 0.394964i \(-0.870757\pi\)
0.728207 0.685358i \(-0.240354\pi\)
\(368\) 1.83513 + 3.17854i 0.0956629 + 0.165693i
\(369\) 21.5397 37.3079i 1.12131 1.94217i
\(370\) 0.509061 1.39863i 0.0264648 0.0727115i
\(371\) 4.08603 + 1.48719i 0.212136 + 0.0772113i
\(372\) 11.5627 20.0272i 0.599498 1.03836i
\(373\) −3.93628 6.81784i −0.203813 0.353014i 0.745941 0.666012i \(-0.232000\pi\)
−0.949754 + 0.312998i \(0.898667\pi\)
\(374\) 8.33583 13.7653i 0.431036 0.711785i
\(375\) −3.98485 + 4.74896i −0.205777 + 0.245235i
\(376\) −3.00033 + 2.51757i −0.154730 + 0.129834i
\(377\) −0.639354 + 3.62595i −0.0329284 + 0.186746i
\(378\) 52.6151 19.1503i 2.70623 0.984987i
\(379\) 19.5962i 1.00659i −0.864115 0.503294i \(-0.832121\pi\)
0.864115 0.503294i \(-0.167879\pi\)
\(380\) −4.86287 13.3174i −0.249460 0.683167i
\(381\) 34.0295i 1.74339i
\(382\) −17.1766 + 6.25177i −0.878832 + 0.319869i
\(383\) −1.88152 0.331764i −0.0961414 0.0169523i 0.125370 0.992110i \(-0.459988\pi\)
−0.221512 + 0.975158i \(0.571099\pi\)
\(384\) −2.11619 2.52197i −0.107991 0.128699i
\(385\) 5.80220 + 37.4707i 0.295707 + 1.90968i
\(386\) 2.70281 + 15.3284i 0.137569 + 0.780195i
\(387\) 37.7017 21.7671i 1.91649 1.10648i
\(388\) −12.5669 7.25550i −0.637988 0.368342i
\(389\) 27.4666 + 9.99702i 1.39261 + 0.506869i 0.925977 0.377581i \(-0.123244\pi\)
0.466635 + 0.884450i \(0.345466\pi\)
\(390\) −16.3913 + 45.0347i −0.830005 + 2.28042i
\(391\) 15.4225 + 8.90419i 0.779950 + 0.450304i
\(392\) 2.67743 + 4.63745i 0.135231 + 0.234227i
\(393\) 6.68337 + 37.9032i 0.337131 + 1.91197i
\(394\) −2.92594 + 3.48700i −0.147407 + 0.175673i
\(395\) 9.27479 7.78247i 0.466665 0.391579i
\(396\) −16.2910 20.2604i −0.818654 1.01812i
\(397\) 6.98132 2.54099i 0.350382 0.127529i −0.160832 0.986982i \(-0.551418\pi\)
0.511215 + 0.859453i \(0.329196\pi\)
\(398\) 8.05450 0.403736
\(399\) −32.4630 38.6061i −1.62518 1.93272i
\(400\) 5.57894 0.278947
\(401\) −5.35803 14.7211i −0.267567 0.735135i −0.998605 0.0527981i \(-0.983186\pi\)
0.731038 0.682337i \(-0.239036\pi\)
\(402\) −3.75741 + 21.3093i −0.187402 + 1.06281i
\(403\) 20.2080 + 24.0830i 1.00663 + 1.19966i
\(404\) 9.83454 11.7203i 0.489287 0.583109i
\(405\) −16.3383 92.6591i −0.811856 4.60427i
\(406\) 2.50419 1.44579i 0.124281 0.0717536i
\(407\) −1.43674 + 0.489165i −0.0712163 + 0.0242470i
\(408\) −15.0106 5.46343i −0.743138 0.270480i
\(409\) −3.26449 1.18818i −0.161419 0.0587516i 0.260047 0.965596i \(-0.416262\pi\)
−0.421466 + 0.906844i \(0.638484\pi\)
\(410\) 8.93765 15.4805i 0.441399 0.764525i
\(411\) 18.1765 10.4942i 0.896579 0.517640i
\(412\) −2.04478 + 0.360550i −0.100739 + 0.0177630i
\(413\) 21.3866 + 17.9455i 1.05237 + 0.883039i
\(414\) 22.0389 18.4928i 1.08315 0.908872i
\(415\) 25.5045 + 4.49714i 1.25197 + 0.220756i
\(416\) 4.20571 1.53075i 0.206202 0.0750513i
\(417\) 59.4551 2.91153
\(418\) −7.47566 + 12.3739i −0.365647 + 0.605229i
\(419\) 26.1361 1.27683 0.638415 0.769692i \(-0.279590\pi\)
0.638415 + 0.769692i \(0.279590\pi\)
\(420\) 35.3682 12.8730i 1.72579 0.628136i
\(421\) −36.8997 6.50642i −1.79838 0.317104i −0.828375 0.560174i \(-0.810734\pi\)
−0.970009 + 0.243071i \(0.921845\pi\)
\(422\) −3.68512 + 3.09218i −0.179389 + 0.150525i
\(423\) 23.5183 + 19.7342i 1.14350 + 0.959511i
\(424\) −1.21828 + 0.214816i −0.0591651 + 0.0104324i
\(425\) 23.4428 13.5347i 1.13714 0.656530i
\(426\) −16.4583 + 28.5065i −0.797405 + 1.38115i
\(427\) −7.06107 2.57002i −0.341709 0.124372i
\(428\) 4.02647 + 1.46552i 0.194627 + 0.0708384i
\(429\) 46.2615 15.7506i 2.23353 0.760448i
\(430\) 15.6439 9.03199i 0.754414 0.435561i
\(431\) −3.99357 22.6487i −0.192364 1.09095i −0.916123 0.400897i \(-0.868699\pi\)
0.723760 0.690052i \(-0.242412\pi\)
\(432\) −10.2394 + 12.2028i −0.492642 + 0.587108i
\(433\) −12.7943 15.2476i −0.614853 0.732754i 0.365323 0.930881i \(-0.380959\pi\)
−0.980176 + 0.198127i \(0.936514\pi\)
\(434\) 4.28738 24.3149i 0.205801 1.16715i
\(435\) −3.01285 8.27772i −0.144455 0.396886i
\(436\) 6.68459 0.320134
\(437\) −13.8633 7.98470i −0.663171 0.381960i
\(438\) −9.34008 −0.446286
\(439\) −13.2981 + 4.84010i −0.634682 + 0.231005i −0.639268 0.768984i \(-0.720762\pi\)
0.00458595 + 0.999989i \(0.498540\pi\)
\(440\) −6.75975 8.40679i −0.322259 0.400778i
\(441\) 32.1544 26.9808i 1.53116 1.28480i
\(442\) 13.9588 16.6354i 0.663952 0.791268i
\(443\) −6.50369 36.8842i −0.308999 1.75242i −0.604055 0.796943i \(-0.706449\pi\)
0.295055 0.955480i \(-0.404662\pi\)
\(444\) 0.753275 + 1.30471i 0.0357488 + 0.0619188i
\(445\) −0.469422 0.271021i −0.0222527 0.0128476i
\(446\) −6.96068 + 19.1243i −0.329598 + 0.905562i
\(447\) 20.9434 + 7.62276i 0.990587 + 0.360544i
\(448\) −3.04403 1.75747i −0.143817 0.0830329i
\(449\) 23.6829 13.6733i 1.11766 0.645284i 0.176861 0.984236i \(-0.443406\pi\)
0.940804 + 0.338952i \(0.110072\pi\)
\(450\) −7.59382 43.0667i −0.357976 2.03018i
\(451\) −18.0129 + 2.78923i −0.848193 + 0.131340i
\(452\) −0.358576 0.427334i −0.0168660 0.0201001i
\(453\) −75.6366 13.3368i −3.55372 0.626617i
\(454\) 0.468351 0.170466i 0.0219808 0.00800035i
\(455\) 51.1674i 2.39877i
\(456\) 13.4901 + 4.89405i 0.631730 + 0.229185i
\(457\) 7.92199i 0.370575i −0.982684 0.185287i \(-0.940678\pi\)
0.982684 0.185287i \(-0.0593216\pi\)
\(458\) −11.6504 + 4.24041i −0.544389 + 0.198141i
\(459\) −13.4216 + 76.1175i −0.626465 + 3.55286i
\(460\) 9.14476 7.67337i 0.426377 0.357773i
\(461\) −9.98853 + 11.9039i −0.465212 + 0.554418i −0.946734 0.322016i \(-0.895640\pi\)
0.481522 + 0.876434i \(0.340084\pi\)
\(462\) −32.8294 19.8805i −1.52736 0.924925i
\(463\) 4.98719 + 8.63806i 0.231774 + 0.401445i 0.958330 0.285662i \(-0.0922136\pi\)
−0.726556 + 0.687107i \(0.758880\pi\)
\(464\) −0.411327 + 0.712440i −0.0190954 + 0.0330742i
\(465\) −70.6799 25.7254i −3.27770 1.19299i
\(466\) 5.84055 16.0468i 0.270558 0.743353i
\(467\) −14.5874 + 25.2662i −0.675026 + 1.16918i 0.301436 + 0.953487i \(0.402534\pi\)
−0.976461 + 0.215692i \(0.930799\pi\)
\(468\) −17.5413 30.3824i −0.810847 1.40443i
\(469\) 4.01163 + 22.7511i 0.185240 + 1.05055i
\(470\) 9.75865 + 8.18848i 0.450133 + 0.377706i
\(471\) 26.9967 + 32.1734i 1.24394 + 1.48247i
\(472\) −7.82204 1.37924i −0.360039 0.0634845i
\(473\) −17.1736 6.66046i −0.789643 0.306248i
\(474\) 12.2551i 0.562894i
\(475\) −21.0474 + 12.1810i −0.965719 + 0.558902i
\(476\) −17.0548 −0.781705
\(477\) 3.31655 + 9.11215i 0.151854 + 0.417217i
\(478\) 6.07184 + 1.07063i 0.277720 + 0.0489694i
\(479\) −24.5847 29.2989i −1.12330 1.33870i −0.934203 0.356743i \(-0.883887\pi\)
−0.189100 0.981958i \(-0.560557\pi\)
\(480\) −6.88296 + 8.20279i −0.314163 + 0.374404i
\(481\) −2.01698 + 0.355648i −0.0919664 + 0.0162162i
\(482\) 6.53332 + 11.3160i 0.297585 + 0.515432i
\(483\) 21.2360 36.7818i 0.966272 1.67363i
\(484\) −2.36128 + 10.7436i −0.107331 + 0.488344i
\(485\) −16.1425 + 44.3511i −0.732992 + 2.01388i
\(486\) 41.0905 + 23.7236i 1.86390 + 1.07613i
\(487\) −2.29305 + 1.32389i −0.103908 + 0.0599913i −0.551053 0.834470i \(-0.685774\pi\)
0.447145 + 0.894461i \(0.352441\pi\)
\(488\) 2.10531 0.371224i 0.0953031 0.0168045i
\(489\) 26.2223 31.2505i 1.18581 1.41320i
\(490\) 13.3421 11.1953i 0.602734 0.505754i
\(491\) −4.24422 0.748370i −0.191539 0.0337735i 0.0770558 0.997027i \(-0.475448\pi\)
−0.268595 + 0.963253i \(0.586559\pi\)
\(492\) 6.18828 + 17.0022i 0.278989 + 0.766517i
\(493\) 3.99158i 0.179772i
\(494\) −12.5244 + 14.9577i −0.563500 + 0.672977i
\(495\) −55.6952 + 63.6249i −2.50331 + 2.85973i
\(496\) 2.40245 + 6.60068i 0.107873 + 0.296379i
\(497\) −6.10262 + 34.6097i −0.273740 + 1.55246i
\(498\) −20.0810 + 16.8500i −0.899851 + 0.755065i
\(499\) −12.3107 10.3299i −0.551105 0.462432i 0.324210 0.945985i \(-0.394901\pi\)
−0.875315 + 0.483553i \(0.839346\pi\)
\(500\) −0.326986 1.85443i −0.0146232 0.0829325i
\(501\) −41.5601 + 23.9947i −1.85677 + 1.07201i
\(502\) −12.3782 + 21.4397i −0.552466 + 0.956898i
\(503\) 5.43018 14.9193i 0.242120 0.665219i −0.757799 0.652488i \(-0.773725\pi\)
0.999919 0.0127309i \(-0.00405249\pi\)
\(504\) −9.42343 + 25.8907i −0.419753 + 1.15326i
\(505\) −43.0961 24.8816i −1.91775 1.10722i
\(506\) −11.9411 2.36395i −0.530849 0.105090i
\(507\) 22.7964 4.01963i 1.01243 0.178518i
\(508\) −7.91814 6.64411i −0.351311 0.294785i
\(509\) 4.79284 + 5.71189i 0.212439 + 0.253175i 0.861732 0.507363i \(-0.169380\pi\)
−0.649293 + 0.760538i \(0.724935\pi\)
\(510\) −9.02205 + 51.1666i −0.399503 + 2.26569i
\(511\) −9.37063 + 3.41063i −0.414532 + 0.150877i
\(512\) 1.00000 0.0441942
\(513\) 11.9860 68.3933i 0.529197 3.01964i
\(514\) 27.5420i 1.21483i
\(515\) 2.30976 + 6.34602i 0.101780 + 0.279639i
\(516\) −3.17504 + 18.0065i −0.139773 + 0.792693i
\(517\) 0.271557 12.9872i 0.0119431 0.571177i
\(518\) 1.23217 + 1.03391i 0.0541383 + 0.0454275i
\(519\) 10.5654 1.86297i 0.463770 0.0817752i
\(520\) −7.27855 12.6068i −0.319185 0.552845i
\(521\) 21.7251 + 12.5430i 0.951796 + 0.549520i 0.893638 0.448788i \(-0.148144\pi\)
0.0581574 + 0.998307i \(0.481477\pi\)
\(522\) 6.05957 + 2.20550i 0.265220 + 0.0965322i
\(523\) −34.6437 12.6093i −1.51486 0.551365i −0.555004 0.831848i \(-0.687283\pi\)
−0.959859 + 0.280483i \(0.909506\pi\)
\(524\) −10.1244 5.84532i −0.442286 0.255354i
\(525\) −32.2796 55.9098i −1.40880 2.44011i
\(526\) 7.41931 1.30822i 0.323497 0.0570413i
\(527\) 26.1086 + 21.9077i 1.13731 + 0.954315i
\(528\) 10.9166 + 0.228262i 0.475085 + 0.00993383i
\(529\) −1.65472 + 9.38439i −0.0719444 + 0.408017i
\(530\) 1.37616 + 3.78098i 0.0597767 + 0.164235i
\(531\) 62.2597i 2.70184i
\(532\) 15.3213 0.0159825i 0.664263 0.000692929i
\(533\) −24.5972 −1.06542
\(534\) 0.515565 0.187650i 0.0223107 0.00812043i
\(535\) 2.42008 13.7250i 0.104629 0.593383i
\(536\) −4.22473 5.03484i −0.182481 0.217472i
\(537\) 41.6315 + 34.9329i 1.79653 + 1.50747i
\(538\) 17.0100 2.99931i 0.733351 0.129310i
\(539\) −17.4220 3.44897i −0.750417 0.148557i
\(540\) 44.8702 + 25.9058i 1.93090 + 1.11481i
\(541\) 2.21533 6.08657i 0.0952444 0.261682i −0.882917 0.469529i \(-0.844424\pi\)
0.978161 + 0.207848i \(0.0666458\pi\)
\(542\) 4.17631 11.4743i 0.179388 0.492864i
\(543\) 7.39892 12.8153i 0.317518 0.549957i
\(544\) 4.20202 2.42604i 0.180160 0.104015i
\(545\) −3.77543 21.4115i −0.161722 0.917169i
\(546\) −39.6746 33.2910i −1.69792 1.42472i
\(547\) −5.36643 + 4.50297i −0.229452 + 0.192533i −0.750264 0.661138i \(-0.770074\pi\)
0.520812 + 0.853671i \(0.325629\pi\)
\(548\) −1.10704 + 6.27832i −0.0472903 + 0.268197i
\(549\) −5.73133 15.7467i −0.244607 0.672053i
\(550\) −12.1874 + 13.9226i −0.519672 + 0.593661i
\(551\) −0.00374061 3.58587i −0.000159356 0.152763i
\(552\) 12.0833i 0.514297i
\(553\) 4.47507 + 12.2951i 0.190299 + 0.522843i
\(554\) −23.7286 4.18399i −1.00813 0.177761i
\(555\) 3.75369 3.14972i 0.159335 0.133698i
\(556\) −11.6083 + 13.8343i −0.492303 + 0.586704i
\(557\) 3.31374 0.584302i 0.140408 0.0247577i −0.103003 0.994681i \(-0.532845\pi\)
0.243410 + 0.969923i \(0.421734\pi\)
\(558\) 47.6839 27.5303i 2.01862 1.16545i
\(559\) −21.5266 12.4284i −0.910480 0.525666i
\(560\) −3.91014 + 10.7430i −0.165233 + 0.453975i
\(561\) 46.4256 25.5249i 1.96009 1.07766i
\(562\) −11.3603 + 19.6767i −0.479207 + 0.830011i
\(563\) −7.60351 13.1697i −0.320450 0.555036i 0.660131 0.751151i \(-0.270501\pi\)
−0.980581 + 0.196115i \(0.937167\pi\)
\(564\) −12.6985 + 2.23909i −0.534703 + 0.0942826i
\(565\) −1.16628 + 1.38992i −0.0490657 + 0.0584743i
\(566\) −16.2307 19.3430i −0.682229 0.813048i
\(567\) 100.135 + 17.6565i 4.20527 + 0.741503i
\(568\) −3.41963 9.39535i −0.143484 0.394220i
\(569\) −12.6748 −0.531353 −0.265677 0.964062i \(-0.585595\pi\)
−0.265677 + 0.964062i \(0.585595\pi\)
\(570\) 8.05708 45.9743i 0.337474 1.92565i
\(571\) 31.2387i 1.30730i −0.756797 0.653650i \(-0.773237\pi\)
0.756797 0.653650i \(-0.226763\pi\)
\(572\) −5.36742 + 13.8396i −0.224423 + 0.578662i
\(573\) −59.2638 10.4498i −2.47578 0.436547i
\(574\) 12.4171 + 14.7981i 0.518278 + 0.617659i
\(575\) −15.6857 13.1618i −0.654138 0.548887i
\(576\) −1.36116 7.71951i −0.0567149 0.321646i
\(577\) −19.2938 33.4178i −0.803209 1.39120i −0.917493 0.397751i \(-0.869791\pi\)
0.114284 0.993448i \(-0.463543\pi\)
\(578\) 3.27129 5.66605i 0.136068 0.235677i
\(579\) −17.5260 + 48.1523i −0.728357 + 2.00114i
\(580\) 2.51434 + 0.915146i 0.104402 + 0.0379994i
\(581\) −13.9937 + 24.2379i −0.580558 + 1.00556i
\(582\) −23.8866 41.3728i −0.990131 1.71496i
\(583\) 2.12529 3.50957i 0.0880206 0.145352i
\(584\) 1.82361 2.17329i 0.0754615 0.0899315i
\(585\) −87.4111 + 73.3467i −3.61401 + 3.03251i
\(586\) 3.37644 19.1487i 0.139479 0.791027i
\(587\) −2.65130 + 0.964995i −0.109431 + 0.0398296i −0.396155 0.918183i \(-0.629656\pi\)
0.286724 + 0.958013i \(0.407434\pi\)
\(588\) 17.6293i 0.727020i
\(589\) −23.4754 19.6565i −0.967287 0.809933i
\(590\) 25.8339i 1.06356i
\(591\) −14.0822 + 5.12550i −0.579264 + 0.210835i
\(592\) −0.450659 0.0794634i −0.0185220 0.00326593i
\(593\) 18.2824 + 21.7881i 0.750768 + 0.894731i 0.997227 0.0744225i \(-0.0237114\pi\)
−0.246459 + 0.969153i \(0.579267\pi\)
\(594\) −8.08460 52.2104i −0.331715 2.14222i
\(595\) 9.63247 + 54.6284i 0.394893 + 2.23955i
\(596\) −5.86279 + 3.38489i −0.240149 + 0.138650i
\(597\) 22.9644 + 13.2585i 0.939872 + 0.542635i
\(598\) −15.4361 5.61827i −0.631228 0.229748i
\(599\) 5.33123 14.6474i 0.217828 0.598478i −0.781860 0.623454i \(-0.785729\pi\)
0.999688 + 0.0249763i \(0.00795103\pi\)
\(600\) 15.9063 + 9.18351i 0.649372 + 0.374915i
\(601\) 4.63664 + 8.03089i 0.189132 + 0.327587i 0.944961 0.327182i \(-0.106099\pi\)
−0.755829 + 0.654769i \(0.772766\pi\)
\(602\) 3.38986 + 19.2248i 0.138160 + 0.783546i
\(603\) −33.1160 + 39.4661i −1.34859 + 1.60718i
\(604\) 17.8710 14.9955i 0.727160 0.610159i
\(605\) 35.7465 + 1.49555i 1.45330 + 0.0608026i
\(606\) 47.3324 17.2276i 1.92275 0.699823i
\(607\) −39.7452 −1.61321 −0.806604 0.591092i \(-0.798697\pi\)
−0.806604 + 0.591092i \(0.798697\pi\)
\(608\) −3.77264 + 2.18339i −0.153001 + 0.0885480i
\(609\) 9.51969 0.385757
\(610\) −2.37815 6.53390i −0.0962883 0.264550i
\(611\) 3.04395 17.2631i 0.123145 0.698391i
\(612\) −24.4474 29.1353i −0.988228 1.17772i
\(613\) 5.88538 7.01392i 0.237708 0.283290i −0.633981 0.773349i \(-0.718580\pi\)
0.871689 + 0.490059i \(0.163025\pi\)
\(614\) 2.21174 + 12.5434i 0.0892585 + 0.506210i
\(615\) 50.9648 29.4245i 2.05510 1.18651i
\(616\) 11.0357 3.75731i 0.444640 0.151386i
\(617\) −9.75250 3.54962i −0.392621 0.142902i 0.138163 0.990409i \(-0.455880\pi\)
−0.530784 + 0.847507i \(0.678102\pi\)
\(618\) −6.42343 2.33794i −0.258388 0.0940456i
\(619\) −22.0565 + 38.2030i −0.886525 + 1.53551i −0.0425698 + 0.999093i \(0.513554\pi\)
−0.843955 + 0.536413i \(0.819779\pi\)
\(620\) 19.7858 11.4234i 0.794618 0.458773i
\(621\) 57.5777 10.1525i 2.31052 0.407406i
\(622\) −11.1866 9.38664i −0.448540 0.376370i
\(623\) 0.448729 0.376528i 0.0179780 0.0150853i
\(624\) 14.5108 + 2.55865i 0.580897 + 0.102428i
\(625\) 20.4572 7.44581i 0.818288 0.297832i
\(626\) 4.16436 0.166441
\(627\) −41.6829 + 22.9740i −1.66465 + 0.917494i
\(628\) −12.7573 −0.509070
\(629\) −2.08646 + 0.759409i −0.0831926 + 0.0302796i
\(630\) 88.2531 + 15.5614i 3.51609 + 0.619981i
\(631\) −20.7105 + 17.3782i −0.824472 + 0.691814i −0.954015 0.299760i \(-0.903093\pi\)
0.129543 + 0.991574i \(0.458649\pi\)
\(632\) −2.85156 2.39275i −0.113429 0.0951783i
\(633\) −15.5968 + 2.75014i −0.619917 + 0.109308i
\(634\) 9.05990 5.23074i 0.359815 0.207739i
\(635\) −16.8097 + 29.1153i −0.667073 + 1.15541i
\(636\) −3.82709 1.39295i −0.151754 0.0552340i
\(637\) −22.5210 8.19697i −0.892315 0.324776i
\(638\) −0.879378 2.58284i −0.0348149 0.102256i
\(639\) −67.8729 + 39.1864i −2.68501 + 1.55019i
\(640\) −0.564796 3.20312i −0.0223255 0.126614i
\(641\) 25.8444 30.8001i 1.02079 1.21653i 0.0447389 0.998999i \(-0.485754\pi\)
0.976053 0.217533i \(-0.0698011\pi\)
\(642\) 9.06761 + 10.8064i 0.357870 + 0.426493i
\(643\) −4.80334 + 27.2411i −0.189425 + 1.07428i 0.730711 + 0.682687i \(0.239189\pi\)
−0.920136 + 0.391598i \(0.871922\pi\)
\(644\) 4.41233 + 12.1228i 0.173870 + 0.477704i
\(645\) 59.4703 2.34164
\(646\) −10.5557 + 18.3272i −0.415310 + 0.721073i
\(647\) 7.16076 0.281519 0.140759 0.990044i \(-0.455046\pi\)
0.140759 + 0.990044i \(0.455046\pi\)
\(648\) −27.1832 + 9.89389i −1.06786 + 0.388669i
\(649\) 20.5295 16.5074i 0.805852 0.647971i
\(650\) −19.1276 + 16.0499i −0.750244 + 0.629530i
\(651\) 52.2487 62.2676i 2.04779 2.44046i
\(652\) 2.15172 + 12.2030i 0.0842680 + 0.477908i
\(653\) 22.1487 + 38.3627i 0.866747 + 1.50125i 0.865302 + 0.501250i \(0.167126\pi\)
0.00144449 + 0.999999i \(0.499540\pi\)
\(654\) 19.0586 + 11.0035i 0.745252 + 0.430271i
\(655\) −13.0050 + 35.7310i −0.508149 + 1.39613i
\(656\) −5.16438 1.87968i −0.201635 0.0733891i
\(657\) −19.2590 11.1192i −0.751364 0.433800i
\(658\) −11.9224 + 6.88341i −0.464784 + 0.268343i
\(659\) 2.44110 + 13.8442i 0.0950918 + 0.539292i 0.994719 + 0.102634i \(0.0327271\pi\)
−0.899627 + 0.436658i \(0.856162\pi\)
\(660\) −5.43451 35.0961i −0.211538 1.36611i
\(661\) −0.924952 1.10231i −0.0359765 0.0428751i 0.747756 0.663973i \(-0.231131\pi\)
−0.783733 + 0.621098i \(0.786687\pi\)
\(662\) 16.9526 + 2.98921i 0.658883 + 0.116179i
\(663\) 67.1820 24.4522i 2.60913 0.949646i
\(664\) 7.96242i 0.309002i
\(665\) −8.70460 49.0669i −0.337550 1.90273i
\(666\) 3.58703i 0.138995i
\(667\) 2.83727 1.03268i 0.109860 0.0399856i
\(668\) 2.53122 14.3553i 0.0979358 0.555421i
\(669\) −51.3264 + 43.0679i −1.98439 + 1.66510i
\(670\) −13.7411 + 16.3760i −0.530863 + 0.632658i
\(671\) −3.67272 + 6.06489i −0.141784 + 0.234132i
\(672\) −5.78596 10.0216i −0.223198 0.386591i
\(673\) −10.8985 + 18.8768i −0.420108 + 0.727648i −0.995950 0.0899130i \(-0.971341\pi\)
0.575842 + 0.817561i \(0.304674\pi\)
\(674\) 21.2577 + 7.73715i 0.818814 + 0.298024i
\(675\) 30.3955 83.5110i 1.16992 3.21434i
\(676\) −3.51560 + 6.08919i −0.135215 + 0.234200i
\(677\) 10.1291 + 17.5442i 0.389294 + 0.674277i 0.992355 0.123418i \(-0.0393856\pi\)
−0.603061 + 0.797695i \(0.706052\pi\)
\(678\) −0.318912 1.80864i −0.0122477 0.0694604i
\(679\) −39.0724 32.7857i −1.49946 1.25820i
\(680\) −10.1442 12.0893i −0.389010 0.463605i
\(681\) 1.61593 + 0.284933i 0.0619227 + 0.0109186i
\(682\) −21.7206 8.42394i −0.831725 0.322569i
\(683\) 39.4841i 1.51082i −0.655254 0.755409i \(-0.727438\pi\)
0.655254 0.755409i \(-0.272562\pi\)
\(684\) 21.9898 + 26.1510i 0.840802 + 0.999909i
\(685\) 20.7354 0.792261
\(686\) −1.97775 5.43384i −0.0755110 0.207465i
\(687\) −40.1971 7.08783i −1.53361 0.270417i
\(688\) −3.56993 4.25448i −0.136102 0.162200i
\(689\) 3.55892 4.24135i 0.135584 0.161583i
\(690\) 38.7041 6.82457i 1.47344 0.259807i
\(691\) −3.67395 6.36348i −0.139764 0.242078i 0.787643 0.616131i \(-0.211301\pi\)
−0.927407 + 0.374053i \(0.877968\pi\)
\(692\) −1.62937 + 2.82215i −0.0619392 + 0.107282i
\(693\) −44.0259 80.0757i −1.67241 3.04182i
\(694\) 4.44855 12.2223i 0.168865 0.463952i
\(695\) 50.8692 + 29.3693i 1.92958 + 1.11404i
\(696\) −2.34550 + 1.35417i −0.0889058 + 0.0513298i
\(697\) −26.2610 + 4.63052i −0.994705 + 0.175393i
\(698\) −15.6629 + 18.6663i −0.592849 + 0.706529i
\(699\) 43.0668 36.1373i 1.62894 1.36684i
\(700\) 19.3118 + 3.40519i 0.729917 + 0.128704i
\(701\) −1.45744 4.00428i −0.0550467 0.151240i 0.909122 0.416531i \(-0.136754\pi\)
−0.964168 + 0.265291i \(0.914532\pi\)
\(702\) 71.2950i 2.69086i
\(703\) 1.87368 0.684176i 0.0706670 0.0258042i
\(704\) −2.18453 + 2.49556i −0.0823327 + 0.0940549i
\(705\) 14.3441 + 39.4101i 0.540231 + 1.48427i
\(706\) 0.130754 0.741544i 0.00492100 0.0279084i
\(707\) 41.1964 34.5679i 1.54935 1.30006i
\(708\) −20.0313 16.8083i −0.752822 0.631693i
\(709\) −5.73801 32.5418i −0.215495 1.22213i −0.880045 0.474891i \(-0.842488\pi\)
0.664550 0.747244i \(-0.268623\pi\)
\(710\) −28.1630 + 16.2599i −1.05694 + 0.610224i
\(711\) −14.5894 + 25.2696i −0.547145 + 0.947683i
\(712\) −0.0569984 + 0.156602i −0.00213611 + 0.00586891i
\(713\) 8.81763 24.2262i 0.330223 0.907279i
\(714\) −48.6254 28.0739i −1.81976 1.05064i
\(715\) 47.3613 + 9.37594i 1.77121 + 0.350640i
\(716\) −16.2567 + 2.86650i −0.607542 + 0.107126i
\(717\) 15.5492 + 13.0474i 0.580697 + 0.487263i
\(718\) 19.3277 + 23.0338i 0.721303 + 0.859615i
\(719\) 1.23365 6.99635i 0.0460072 0.260920i −0.953125 0.302578i \(-0.902153\pi\)
0.999132 + 0.0416579i \(0.0132640\pi\)
\(720\) −23.9577 + 8.71989i −0.892851 + 0.324971i
\(721\) −7.29816 −0.271798
\(722\) 9.46565 16.4743i 0.352275 0.613109i
\(723\) 43.0180i 1.59986i
\(724\) 1.53732 + 4.22374i 0.0571339 + 0.156974i
\(725\) 0.796966 4.51982i 0.0295986 0.167862i
\(726\) −24.4173 + 26.7444i −0.906212 + 0.992578i
\(727\) 18.9807 + 15.9267i 0.703957 + 0.590690i 0.922896 0.385049i \(-0.125815\pi\)
−0.218940 + 0.975738i \(0.570260\pi\)
\(728\) 15.4926 2.73176i 0.574193 0.101246i
\(729\) 34.7113 + 60.1217i 1.28560 + 2.22673i
\(730\) −7.99127 4.61376i −0.295770 0.170763i
\(731\) −25.3224 9.21660i −0.936583 0.340888i
\(732\) 6.61360 + 2.40715i 0.244446 + 0.0889709i
\(733\) 26.5839 + 15.3482i 0.981899 + 0.566900i 0.902843 0.429970i \(-0.141476\pi\)
0.0790562 + 0.996870i \(0.474809\pi\)
\(734\) 10.5076 + 18.1997i 0.387844 + 0.671765i
\(735\) 56.4687 9.95695i 2.08288 0.367268i
\(736\) −2.81159 2.35920i −0.103636 0.0869613i
\(737\) 21.7938 + 0.455699i 0.802785 + 0.0167859i
\(738\) −7.48067 + 42.4250i −0.275367 + 1.56169i
\(739\) 0.907765 + 2.49406i 0.0333927 + 0.0917456i 0.955269 0.295740i \(-0.0955661\pi\)
−0.921876 + 0.387485i \(0.873344\pi\)
\(740\) 1.48839i 0.0547145i
\(741\) −60.3306 + 22.0298i −2.21630 + 0.809286i
\(742\) −4.34826 −0.159630
\(743\) 36.7899 13.3904i 1.34969 0.491247i 0.436839 0.899540i \(-0.356098\pi\)
0.912851 + 0.408293i \(0.133876\pi\)
\(744\) −4.01568 + 22.7741i −0.147222 + 0.834938i
\(745\) 14.1535 + 16.8674i 0.518543 + 0.617975i
\(746\) 6.03074 + 5.06039i 0.220801 + 0.185274i
\(747\) −61.4659 + 10.8381i −2.24892 + 0.396545i
\(748\) −3.12513 + 15.7861i −0.114266 + 0.577198i
\(749\) 13.0433 + 7.53057i 0.476593 + 0.275161i
\(750\) 2.12030 5.82547i 0.0774223 0.212716i
\(751\) −14.3818 + 39.5135i −0.524798 + 1.44187i 0.340324 + 0.940308i \(0.389463\pi\)
−0.865122 + 0.501562i \(0.832759\pi\)
\(752\) 1.95832 3.39192i 0.0714127 0.123690i
\(753\) −70.5837 + 40.7515i −2.57221 + 1.48507i
\(754\) −0.639354 3.62595i −0.0232839 0.132049i
\(755\) −58.1259 48.7734i −2.11542 1.77505i
\(756\) −42.8922 + 35.9909i −1.55998 + 1.30898i
\(757\) −5.70939 + 32.3796i −0.207511 + 1.17685i 0.685928 + 0.727670i \(0.259397\pi\)
−0.893439 + 0.449185i \(0.851714\pi\)
\(758\) 6.70229 + 18.4144i 0.243438 + 0.668841i
\(759\) −30.1545 26.3963i −1.09454 0.958123i
\(760\) 9.12441 + 10.8510i 0.330977 + 0.393609i
\(761\) 8.59812i 0.311682i −0.987782 0.155841i \(-0.950191\pi\)
0.987782 0.155841i \(-0.0498087\pi\)
\(762\) −11.6388 31.9773i −0.421629 1.15841i
\(763\) 23.1390 + 4.08004i 0.837689 + 0.147707i
\(764\) 14.0025 11.7495i 0.506593 0.425082i
\(765\) −79.5159 + 94.7634i −2.87490 + 3.42618i
\(766\) 1.88152 0.331764i 0.0679823 0.0119871i
\(767\) 30.7860 17.7743i 1.11162 0.641792i
\(768\) 2.85113 + 1.64610i 0.102881 + 0.0593986i
\(769\) −0.888438 + 2.44096i −0.0320379 + 0.0880234i −0.954680 0.297633i \(-0.903803\pi\)
0.922642 + 0.385656i \(0.126025\pi\)
\(770\) −18.2680 33.2264i −0.658333 1.19740i
\(771\) 45.3369 78.5259i 1.63277 2.82804i
\(772\) −7.78243 13.4796i −0.280096 0.485140i
\(773\) 22.8360 4.02660i 0.821353 0.144827i 0.252847 0.967506i \(-0.418633\pi\)
0.568505 + 0.822679i \(0.307522\pi\)
\(774\) −27.9832 + 33.3491i −1.00584 + 1.19871i
\(775\) −25.1897 30.0199i −0.904839 1.07835i
\(776\) 14.2906 + 2.51981i 0.513001 + 0.0904559i
\(777\) 1.81115 + 4.97609i 0.0649746 + 0.178516i
\(778\) −29.2293 −1.04792
\(779\) 23.5874 4.18447i 0.845107 0.149924i
\(780\) 47.9249i 1.71599i
\(781\) 30.9170 + 11.9906i 1.10630 + 0.429056i
\(782\) −17.5378 3.09239i −0.627152 0.110584i
\(783\) 8.42346 + 10.0387i 0.301030 + 0.358754i
\(784\) −4.10206 3.44204i −0.146502 0.122930i
\(785\) 7.20524 + 40.8630i 0.257166 + 1.45846i
\(786\) −19.2440 33.3316i −0.686410 1.18890i
\(787\) 19.5316 33.8297i 0.696226 1.20590i −0.273540 0.961861i \(-0.588194\pi\)
0.969766 0.244038i \(-0.0784722\pi\)
\(788\) 1.55686 4.27744i 0.0554609 0.152378i
\(789\) 23.3069 + 8.48302i 0.829748 + 0.302003i
\(790\) −6.05369 + 10.4853i −0.215381 + 0.373050i
\(791\) −0.980399 1.69810i −0.0348590 0.0603775i
\(792\) 22.2380 + 13.4667i 0.790193 + 0.478517i
\(793\) −6.15016 + 7.32948i −0.218399 + 0.260277i
\(794\) −5.69122 + 4.77550i −0.201974 + 0.169476i
\(795\) −2.30025 + 13.0454i −0.0815814 + 0.462671i
\(796\) −7.56876 + 2.75480i −0.268267 + 0.0976414i
\(797\) 25.4569i 0.901729i −0.892592 0.450865i \(-0.851116\pi\)
0.892592 0.450865i \(-0.148884\pi\)
\(798\) 43.7093 + 25.1748i 1.54729 + 0.891180i
\(799\) 19.0039i 0.672308i
\(800\) −5.24249 + 1.90811i −0.185350 + 0.0674619i
\(801\) 1.28647 + 0.226840i 0.0454553 + 0.00801500i
\(802\) 10.0698 + 12.0007i 0.355577 + 0.423760i
\(803\) 1.43985 + 9.29855i 0.0508111 + 0.328139i
\(804\) −3.75741 21.3093i −0.132514 0.751522i
\(805\) 36.3386 20.9801i 1.28077 0.739451i
\(806\) −27.2262 15.7190i −0.959001 0.553680i
\(807\) 53.4348 + 19.4487i 1.88099 + 0.684626i
\(808\) −5.23285 + 14.3771i −0.184091 + 0.505786i
\(809\) −46.8523 27.0502i −1.64724 0.951033i −0.978163 0.207837i \(-0.933358\pi\)
−0.669074 0.743196i \(-0.733309\pi\)
\(810\) 47.0442 + 81.4830i 1.65297 + 2.86302i
\(811\) −8.14999 46.2209i −0.286185 1.62303i −0.701022 0.713139i \(-0.747273\pi\)
0.414837 0.909896i \(-0.363838\pi\)
\(812\) −1.85868 + 2.21509i −0.0652268 + 0.0777342i
\(813\) 30.7951 25.8402i 1.08003 0.906254i
\(814\) 1.18279 0.951057i 0.0414566 0.0333345i
\(815\) 37.8724 13.7844i 1.32661 0.482848i
\(816\) 15.9740 0.559202
\(817\) 22.7572 + 8.25608i 0.796175 + 0.288844i
\(818\) 3.47400 0.121466
\(819\) −42.1757 115.877i −1.47374 4.04906i
\(820\) −3.10401 + 17.6037i −0.108397 + 0.614749i
\(821\) −3.96687 4.72753i −0.138445 0.164992i 0.692367 0.721545i \(-0.256568\pi\)
−0.830812 + 0.556554i \(0.812123\pi\)
\(822\) −13.4911 + 16.0780i −0.470555 + 0.560785i
\(823\) 4.39757 + 24.9398i 0.153290 + 0.869348i 0.960333 + 0.278856i \(0.0899553\pi\)
−0.807043 + 0.590492i \(0.798934\pi\)
\(824\) 1.79815 1.03816i 0.0626414 0.0361660i
\(825\) −57.6658 + 19.6335i −2.00767 + 0.683549i
\(826\) −26.2345 9.54859i −0.912816 0.332238i
\(827\) −16.1905 5.89286i −0.562999 0.204915i 0.0448135 0.998995i \(-0.485731\pi\)
−0.607813 + 0.794080i \(0.707953\pi\)
\(828\) −14.3849 + 24.9153i −0.499908 + 0.865867i
\(829\) 18.4059 10.6267i 0.639264 0.369079i −0.145067 0.989422i \(-0.546340\pi\)
0.784331 + 0.620343i \(0.213006\pi\)
\(830\) −25.5045 + 4.49714i −0.885275 + 0.156098i
\(831\) −60.7660 50.9888i −2.10795 1.76878i
\(832\) −3.42853 + 2.87687i −0.118863 + 0.0997377i
\(833\) −25.5875 4.51176i −0.886553 0.156323i
\(834\) −55.8695 + 20.3348i −1.93460 + 0.704138i
\(835\) −47.4112 −1.64073
\(836\) 2.79269 14.1845i 0.0965871 0.490582i
\(837\) 111.894 3.86764
\(838\) −24.5599 + 8.93906i −0.848406 + 0.308795i
\(839\) 15.2655 + 2.69172i 0.527023 + 0.0929284i 0.430828 0.902434i \(-0.358222\pi\)
0.0961952 + 0.995362i \(0.469333\pi\)
\(840\) −28.8324 + 24.1932i −0.994812 + 0.834746i
\(841\) −21.6969 18.2058i −0.748168 0.627787i
\(842\) 36.8997 6.50642i 1.27165 0.224226i
\(843\) −64.7797 + 37.4006i −2.23113 + 1.28814i
\(844\) 2.40529 4.16609i 0.0827936 0.143403i
\(845\) 21.4900 + 7.82171i 0.739278 + 0.269075i
\(846\) −28.8495 10.5004i −0.991867 0.361010i
\(847\) −14.7312 + 35.7482i −0.506170 + 1.22832i
\(848\) 1.07134 0.618539i 0.0367900 0.0212407i
\(849\) −14.4354 81.8669i −0.495420 2.80967i
\(850\) −17.3999 + 20.7364i −0.596812 + 0.711252i
\(851\) 1.07960 + 1.28661i 0.0370081 + 0.0441046i
\(852\) 5.71589 32.4164i 0.195823 1.11057i
\(853\) 12.5524 + 34.4874i 0.429786 + 1.18083i 0.945943 + 0.324333i \(0.105140\pi\)
−0.516157 + 0.856494i \(0.672638\pi\)
\(854\) 7.51423 0.257132
\(855\) 71.3450 85.2060i 2.43995 2.91398i
\(856\) −4.28488 −0.146454
\(857\) −30.1515 + 10.9742i −1.02995 + 0.374873i −0.801064 0.598579i \(-0.795732\pi\)
−0.228891 + 0.973452i \(0.573510\pi\)
\(858\) −38.0846 + 30.6231i −1.30019 + 1.04546i
\(859\) −23.0097 + 19.3075i −0.785083 + 0.658762i −0.944523 0.328445i \(-0.893475\pi\)
0.159441 + 0.987208i \(0.449031\pi\)
\(860\) −11.6113 + 13.8378i −0.395942 + 0.471865i
\(861\) 11.0435 + 62.6310i 0.376362 + 2.13446i
\(862\) 11.4990 + 19.9169i 0.391659 + 0.678373i
\(863\) 11.7651 + 6.79258i 0.400489 + 0.231222i 0.686695 0.726946i \(-0.259061\pi\)
−0.286206 + 0.958168i \(0.592394\pi\)
\(864\) 5.44826 14.9690i 0.185353 0.509254i
\(865\) 9.95992 + 3.62511i 0.338647 + 0.123258i
\(866\) 17.2377 + 9.95217i 0.585760 + 0.338189i
\(867\) 18.6538 10.7698i 0.633515 0.365760i
\(868\) 4.28738 + 24.3149i 0.145523 + 0.825303i
\(869\) 12.2006 1.88922i 0.413876 0.0640872i
\(870\) 5.66230 + 6.74806i 0.191970 + 0.228781i
\(871\) 28.9692 + 5.10805i 0.981584 + 0.173080i
\(872\) −6.28146 + 2.28626i −0.212717 + 0.0774227i
\(873\) 113.746i 3.84972i
\(874\) 15.7582 + 2.76164i 0.533027 + 0.0934139i
\(875\) 6.61877i 0.223755i
\(876\) 8.77680 3.19450i 0.296541 0.107932i
\(877\) 4.49462 25.4903i 0.151773 0.860745i −0.809905 0.586562i \(-0.800481\pi\)
0.961677 0.274184i \(-0.0884077\pi\)
\(878\) 10.8407 9.09641i 0.365855 0.306989i
\(879\) 41.1474 49.0376i 1.38787 1.65400i
\(880\) 9.22738 + 5.58783i 0.311055 + 0.188366i
\(881\) −19.9344 34.5274i −0.671607 1.16326i −0.977448 0.211174i \(-0.932271\pi\)
0.305842 0.952082i \(-0.401062\pi\)
\(882\) −20.9873 + 36.3511i −0.706679 + 1.22400i
\(883\) −46.4653 16.9120i −1.56368 0.569133i −0.592104 0.805861i \(-0.701703\pi\)
−0.971576 + 0.236728i \(0.923925\pi\)
\(884\) −7.42732 + 20.4064i −0.249808 + 0.686341i
\(885\) −42.5252 + 73.6558i −1.42947 + 2.47591i
\(886\) 18.7266 + 32.4355i 0.629133 + 1.08969i
\(887\) 4.69979 + 26.6538i 0.157804 + 0.894948i 0.956178 + 0.292787i \(0.0945826\pi\)
−0.798374 + 0.602162i \(0.794306\pi\)
\(888\) −1.15408 0.968391i −0.0387285 0.0324971i
\(889\) −23.3537 27.8319i −0.783258 0.933451i
\(890\) 0.533807 + 0.0941245i 0.0178932 + 0.00315506i
\(891\) 34.6919 89.4509i 1.16222 2.99672i
\(892\) 20.3517i 0.681424i
\(893\) 0.0178090 + 17.0723i 0.000595956 + 0.571302i
\(894\) −22.2875 −0.745404
\(895\) 18.3634 + 50.4531i 0.613822 + 1.68646i
\(896\) 3.46155 + 0.610364i 0.115642 + 0.0203908i
\(897\) −34.7620 41.4277i −1.16067 1.38323i
\(898\) −17.5781 + 20.9487i −0.586588 + 0.699068i
\(899\) 5.69078 1.00344i 0.189798 0.0334665i
\(900\) 21.8655 + 37.8722i 0.728852 + 1.26241i
\(901\) 3.00119 5.19822i 0.0999842 0.173178i
\(902\) 15.9726 8.78179i 0.531829 0.292402i
\(903\) −21.9811 + 60.3926i −0.731485 + 2.00974i
\(904\) 0.483108 + 0.278923i 0.0160679 + 0.00927683i
\(905\) 12.6609 7.30975i 0.420861 0.242984i
\(906\) 75.6366 13.3368i 2.51286 0.443085i
\(907\) 25.7825 30.7264i 0.856094 1.02025i −0.143438 0.989659i \(-0.545816\pi\)
0.999532 0.0305938i \(-0.00973983\pi\)
\(908\) −0.381803 + 0.320371i −0.0126706 + 0.0106319i
\(909\) 118.107 + 20.8255i 3.91737 + 0.690738i
\(910\) −17.5003 48.0817i −0.580129 1.59389i
\(911\) 47.1893i 1.56345i 0.623623 + 0.781725i \(0.285660\pi\)
−0.623623 + 0.781725i \(0.714340\pi\)
\(912\) −14.3504 + 0.0149697i −0.475188 + 0.000495695i
\(913\) 19.8707 + 17.3942i 0.657624 + 0.575662i
\(914\) 2.70948 + 7.44423i 0.0896216 + 0.246233i
\(915\) 3.97506 22.5437i 0.131411 0.745271i
\(916\) 9.49752 7.96937i 0.313807 0.263315i
\(917\) −31.4783 26.4134i −1.03951 0.872249i
\(918\) −13.4216 76.1175i −0.442978 2.51225i
\(919\) −35.3197 + 20.3918i −1.16509 + 0.672665i −0.952518 0.304481i \(-0.901517\pi\)
−0.212571 + 0.977146i \(0.568184\pi\)
\(920\) −5.96882 + 10.3383i −0.196786 + 0.340844i
\(921\) −14.3417 + 39.4036i −0.472576 + 1.29839i
\(922\) 5.31479 14.6023i 0.175033 0.480900i
\(923\) 38.7535 + 22.3744i 1.27559 + 0.736461i
\(924\) 37.6491 + 7.45325i 1.23856 + 0.245194i
\(925\) 2.51420 0.443322i 0.0826665 0.0145763i
\(926\) −7.64081 6.41140i −0.251093 0.210692i
\(927\) −10.4617 12.4677i −0.343606 0.409494i
\(928\) 0.142852 0.810156i 0.00468936 0.0265947i
\(929\) 21.4527 7.80814i 0.703840 0.256177i 0.0347904 0.999395i \(-0.488924\pi\)
0.669049 + 0.743218i \(0.266701\pi\)
\(930\) 75.2160 2.46643
\(931\) 22.9909 + 4.02920i 0.753497 + 0.132052i
\(932\) 17.0766i 0.559364i
\(933\) −16.4430 45.1767i −0.538319 1.47902i
\(934\) 5.06616 28.7316i 0.165770 0.940128i
\(935\) 52.3299 + 1.09420i 1.71137 + 0.0357840i
\(936\) 26.8748 + 22.5507i 0.878431 + 0.737091i
\(937\) −11.8657 + 2.09224i −0.387636 + 0.0683506i −0.364070 0.931372i \(-0.618613\pi\)
−0.0235659 + 0.999722i \(0.507502\pi\)
\(938\) −11.5510 20.0070i −0.377154 0.653250i
\(939\) 11.8731 + 6.85496i 0.387465 + 0.223703i
\(940\) −11.9708 4.35700i −0.390443 0.142110i
\(941\) 1.93595 + 0.704628i 0.0631101 + 0.0229702i 0.373382 0.927678i \(-0.378198\pi\)
−0.310272 + 0.950648i \(0.600420\pi\)
\(942\) −36.3726 20.9997i −1.18508 0.684208i
\(943\) 10.0855 + 17.4687i 0.328431 + 0.568858i
\(944\) 7.82204 1.37924i 0.254586 0.0448903i
\(945\) 139.508 + 117.061i 4.53820 + 3.80801i
\(946\) 18.4159 + 0.385069i 0.598753 + 0.0125197i
\(947\) 1.80074 10.2125i 0.0585161 0.331861i −0.941470 0.337096i \(-0.890555\pi\)
0.999986 + 0.00523504i \(0.00166637\pi\)
\(948\) −4.19148 11.5160i −0.136133 0.374022i
\(949\) 12.6975i 0.412178i
\(950\) 15.6119 18.6450i 0.506517 0.604924i
\(951\) 34.4413 1.11684
\(952\) 16.0262 5.83308i 0.519414 0.189051i
\(953\) 0.235521 1.33571i 0.00762929 0.0432678i −0.980755 0.195240i \(-0.937451\pi\)
0.988385 + 0.151972i \(0.0485625\pi\)
\(954\) −6.23308 7.42829i −0.201803 0.240500i
\(955\) −45.5435 38.2156i −1.47375 1.23663i
\(956\) −6.07184 + 1.07063i −0.196377 + 0.0346266i
\(957\) 1.74439 8.81156i 0.0563882 0.284837i
\(958\) 33.1229 + 19.1235i 1.07015 + 0.617852i
\(959\) −7.66413 + 21.0570i −0.247488 + 0.679967i
\(960\) 3.66235 10.0622i 0.118202 0.324757i
\(961\) 9.17035 15.8835i 0.295818 0.512371i
\(962\) 1.77370 1.02405i 0.0571865 0.0330166i
\(963\) 5.83240 + 33.0772i 0.187947 + 1.06590i
\(964\) −10.0096 8.39908i −0.322388 0.270516i
\(965\) −38.7811 + 32.5412i −1.24841 + 1.04754i
\(966\) −7.37519 + 41.8268i −0.237293 + 1.34575i
\(967\) 13.0097 + 35.7439i 0.418365 + 1.14945i 0.952630 + 0.304131i \(0.0983660\pi\)
−0.534265 + 0.845317i \(0.679412\pi\)
\(968\) −1.45564 10.9033i −0.0467859 0.350444i
\(969\) −60.2642 + 34.8774i −1.93596 + 1.12042i
\(970\) 47.1975i 1.51542i
\(971\) −5.47322 15.0375i −0.175644 0.482578i 0.820364 0.571842i \(-0.193771\pi\)
−0.996008 + 0.0892639i \(0.971549\pi\)
\(972\) −46.7264 8.23913i −1.49875 0.264270i
\(973\) −48.6268 + 40.8027i −1.55890 + 1.30808i
\(974\) 1.70196 2.02832i 0.0545345 0.0649916i
\(975\) −80.9550 + 14.2745i −2.59263 + 0.457151i
\(976\) −1.85138 + 1.06890i −0.0592613 + 0.0342145i
\(977\) −30.3259 17.5086i −0.970210 0.560151i −0.0709098 0.997483i \(-0.522590\pi\)
−0.899300 + 0.437332i \(0.855924\pi\)
\(978\) −13.9526 + 38.3344i −0.446154 + 1.22580i
\(979\) −0.266295 0.484345i −0.00851081 0.0154797i
\(980\) −8.70843 + 15.0834i −0.278180 + 0.481823i
\(981\) 26.1989 + 45.3778i 0.836466 + 1.44880i
\(982\) 4.24422 0.748370i 0.135438 0.0238814i
\(983\) −6.21020 + 7.40103i −0.198075 + 0.236056i −0.855935 0.517084i \(-0.827017\pi\)
0.657860 + 0.753140i \(0.271462\pi\)
\(984\) −11.6302 13.8603i −0.370756 0.441850i
\(985\) −14.5805 2.57093i −0.464572 0.0819165i
\(986\) −1.36520 3.75086i −0.0434768 0.119452i
\(987\) −45.3231 −1.44265
\(988\) 6.65327 18.3392i 0.211669 0.583448i
\(989\) 20.3840i 0.648174i
\(990\) 30.5754 78.8368i 0.971749 2.50560i
\(991\) 50.3287 + 8.87430i 1.59874 + 0.281901i 0.900794 0.434246i \(-0.142985\pi\)
0.697949 + 0.716148i \(0.254096\pi\)
\(992\) −4.51513 5.38092i −0.143355 0.170844i
\(993\) 43.4136 + 36.4284i 1.37769 + 1.15602i
\(994\) −6.10262 34.6097i −0.193563 1.09775i
\(995\) 13.0987 + 22.6877i 0.415258 + 0.719248i
\(996\) 13.1069 22.7019i 0.415309 0.719337i
\(997\) 19.2430 52.8697i 0.609432 1.67440i −0.122035 0.992526i \(-0.538942\pi\)
0.731468 0.681876i \(-0.238836\pi\)
\(998\) 15.1014 + 5.49645i 0.478025 + 0.173987i
\(999\) −3.64479 + 6.31296i −0.115316 + 0.199733i
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 418.2.q.b.109.1 yes 60
11.10 odd 2 418.2.q.a.109.1 60
19.15 odd 18 418.2.q.a.395.1 yes 60
209.186 even 18 inner 418.2.q.b.395.1 yes 60
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.q.a.109.1 60 11.10 odd 2
418.2.q.a.395.1 yes 60 19.15 odd 18
418.2.q.b.109.1 yes 60 1.1 even 1 trivial
418.2.q.b.395.1 yes 60 209.186 even 18 inner