Properties

Label 252.2.bj.b.103.10
Level $252$
Weight $2$
Character 252.103
Analytic conductor $2.012$
Analytic rank $0$
Dimension $84$
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] = [252,2,Mod(103,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 2, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.103");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 252.bj (of order \(6\), degree \(2\), 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: \(2.01223013094\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 103.10
Character \(\chi\) \(=\) 252.103
Dual form 252.2.bj.b.115.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15944 + 0.809751i) q^{2} +(0.630196 - 1.61334i) q^{3} +(0.688607 - 1.87772i) q^{4} +(2.22429 - 1.28420i) q^{5} +(0.575725 + 2.38087i) q^{6} +(2.01495 + 1.71464i) q^{7} +(0.722083 + 2.73470i) q^{8} +(-2.20571 - 2.03344i) q^{9} +O(q^{10})\) \(q+(-1.15944 + 0.809751i) q^{2} +(0.630196 - 1.61334i) q^{3} +(0.688607 - 1.87772i) q^{4} +(2.22429 - 1.28420i) q^{5} +(0.575725 + 2.38087i) q^{6} +(2.01495 + 1.71464i) q^{7} +(0.722083 + 2.73470i) q^{8} +(-2.20571 - 2.03344i) q^{9} +(-1.53906 + 3.29008i) q^{10} +(-4.82437 - 2.78535i) q^{11} +(-2.59543 - 2.29428i) q^{12} +(3.36591 + 1.94331i) q^{13} +(-3.72464 - 0.356415i) q^{14} +(-0.670100 - 4.39783i) q^{15} +(-3.05164 - 2.58602i) q^{16} +(2.65106 - 1.53059i) q^{17} +(4.20396 + 0.571576i) q^{18} +(1.51774 - 2.62880i) q^{19} +(-0.879693 - 5.06090i) q^{20} +(4.03610 - 2.17023i) q^{21} +(7.84902 - 0.677087i) q^{22} +(-3.90063 + 2.25203i) q^{23} +(4.86705 + 0.558435i) q^{24} +(0.798325 - 1.38274i) q^{25} +(-5.47616 + 0.472395i) q^{26} +(-4.67064 + 2.27708i) q^{27} +(4.60711 - 2.60279i) q^{28} +(2.91327 + 5.04593i) q^{29} +(4.33809 + 4.55641i) q^{30} +0.712343 q^{31} +(5.63223 + 0.527268i) q^{32} +(-7.53401 + 6.02802i) q^{33} +(-1.83435 + 3.92132i) q^{34} +(6.68377 + 1.22627i) q^{35} +(-5.33708 + 2.74145i) q^{36} +(3.16687 - 5.48519i) q^{37} +(0.368945 + 4.27693i) q^{38} +(5.25639 - 4.20567i) q^{39} +(5.11802 + 5.15549i) q^{40} +(-5.66744 - 3.27210i) q^{41} +(-2.92227 + 5.78449i) q^{42} +(0.877494 - 0.506621i) q^{43} +(-8.55220 + 7.14079i) q^{44} +(-7.51747 - 1.69040i) q^{45} +(2.69896 - 5.76963i) q^{46} -0.374318 q^{47} +(-6.09525 + 3.29362i) q^{48} +(1.12004 + 6.90981i) q^{49} +(0.194064 + 2.24965i) q^{50} +(-0.798668 - 5.24161i) q^{51} +(5.96677 - 4.98204i) q^{52} +(-2.00394 - 3.47093i) q^{53} +(3.57146 - 6.42220i) q^{54} -14.3078 q^{55} +(-3.23406 + 6.74840i) q^{56} +(-3.28467 - 4.10529i) q^{57} +(-7.46370 - 3.49143i) q^{58} +6.31292 q^{59} +(-8.71932 - 1.77012i) q^{60} +9.20740i q^{61} +(-0.825920 + 0.576821i) q^{62} +(-0.957781 - 7.87925i) q^{63} +(-6.95719 + 3.94936i) q^{64} +9.98236 q^{65} +(3.85405 - 13.0898i) q^{66} +6.34532i q^{67} +(-1.04847 - 6.03190i) q^{68} +(1.17512 + 7.71224i) q^{69} +(-8.74241 + 3.99041i) q^{70} +12.0334i q^{71} +(3.96814 - 7.50026i) q^{72} +(-13.8670 + 8.00612i) q^{73} +(0.769831 + 8.92413i) q^{74} +(-1.72772 - 2.15936i) q^{75} +(-3.89102 - 4.66010i) q^{76} +(-4.94500 - 13.8844i) q^{77} +(-2.68892 + 9.13259i) q^{78} +6.94093i q^{79} +(-10.1087 - 1.83316i) q^{80} +(0.730282 + 8.97032i) q^{81} +(9.22065 - 0.795409i) q^{82} +(4.89941 + 8.48603i) q^{83} +(-1.29579 - 9.07309i) q^{84} +(3.93115 - 6.80896i) q^{85} +(-0.607165 + 1.29795i) q^{86} +(9.97670 - 1.52016i) q^{87} +(4.13351 - 15.2045i) q^{88} +(2.02208 + 1.16745i) q^{89} +(10.0849 - 4.12736i) q^{90} +(3.45006 + 9.68697i) q^{91} +(1.54267 + 8.87503i) q^{92} +(0.448916 - 1.14925i) q^{93} +(0.434000 - 0.303104i) q^{94} -7.79631i q^{95} +(4.40007 - 8.75439i) q^{96} +(-3.10755 + 1.79414i) q^{97} +(-6.89384 - 7.10457i) q^{98} +(4.97732 + 15.9537i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q + 2 q^{2} - 2 q^{4} + 6 q^{5} - 16 q^{8} + 4 q^{9} - 18 q^{10} - 6 q^{12} + 18 q^{13} + 14 q^{14} + 14 q^{16} + 6 q^{17} - 10 q^{18} - 24 q^{20} + 4 q^{21} + 6 q^{22} - 6 q^{24} + 16 q^{25} - 30 q^{26} - 4 q^{28} + 10 q^{29} + 11 q^{30} - 18 q^{32} - 18 q^{33} - 24 q^{34} - 38 q^{36} + 2 q^{37} + 33 q^{38} + 6 q^{40} + 6 q^{41} - 38 q^{42} - 13 q^{44} - 54 q^{45} + 10 q^{46} + 9 q^{48} - 28 q^{49} - 17 q^{50} - 27 q^{52} - 2 q^{53} - 39 q^{54} + 58 q^{56} + 6 q^{57} - 13 q^{58} - 31 q^{60} - 8 q^{64} - 100 q^{65} + 30 q^{66} - 18 q^{68} - 18 q^{69} - 19 q^{70} + 26 q^{72} + 30 q^{73} - 23 q^{74} - 2 q^{77} + 15 q^{78} + 3 q^{80} - 32 q^{81} - 18 q^{82} + 23 q^{84} - 50 q^{85} - 9 q^{86} + q^{88} - 102 q^{89} - 39 q^{90} + 28 q^{92} - 36 q^{93} + 63 q^{96} + 6 q^{97} + 21 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15944 + 0.809751i −0.819849 + 0.572580i
\(3\) 0.630196 1.61334i 0.363844 0.931460i
\(4\) 0.688607 1.87772i 0.344304 0.938858i
\(5\) 2.22429 1.28420i 0.994735 0.574310i 0.0880487 0.996116i \(-0.471937\pi\)
0.906686 + 0.421806i \(0.138604\pi\)
\(6\) 0.575725 + 2.38087i 0.235039 + 0.971986i
\(7\) 2.01495 + 1.71464i 0.761579 + 0.648072i
\(8\) 0.722083 + 2.73470i 0.255295 + 0.966863i
\(9\) −2.20571 2.03344i −0.735235 0.677812i
\(10\) −1.53906 + 3.29008i −0.486693 + 1.04041i
\(11\) −4.82437 2.78535i −1.45460 0.839816i −0.455866 0.890048i \(-0.650670\pi\)
−0.998738 + 0.0502327i \(0.984004\pi\)
\(12\) −2.59543 2.29428i −0.749236 0.662303i
\(13\) 3.36591 + 1.94331i 0.933534 + 0.538976i 0.887928 0.459983i \(-0.152145\pi\)
0.0456066 + 0.998959i \(0.485478\pi\)
\(14\) −3.72464 0.356415i −0.995453 0.0952558i
\(15\) −0.670100 4.39783i −0.173019 1.13552i
\(16\) −3.05164 2.58602i −0.762910 0.646505i
\(17\) 2.65106 1.53059i 0.642975 0.371222i −0.142784 0.989754i \(-0.545606\pi\)
0.785760 + 0.618532i \(0.212272\pi\)
\(18\) 4.20396 + 0.571576i 0.990883 + 0.134722i
\(19\) 1.51774 2.62880i 0.348193 0.603089i −0.637735 0.770256i \(-0.720129\pi\)
0.985929 + 0.167167i \(0.0534619\pi\)
\(20\) −0.879693 5.06090i −0.196705 1.13165i
\(21\) 4.03610 2.17023i 0.880749 0.473583i
\(22\) 7.84902 0.677087i 1.67342 0.144356i
\(23\) −3.90063 + 2.25203i −0.813337 + 0.469580i −0.848113 0.529815i \(-0.822261\pi\)
0.0347766 + 0.999395i \(0.488928\pi\)
\(24\) 4.86705 + 0.558435i 0.993482 + 0.113990i
\(25\) 0.798325 1.38274i 0.159665 0.276548i
\(26\) −5.47616 + 0.472395i −1.07396 + 0.0926444i
\(27\) −4.67064 + 2.27708i −0.898865 + 0.438225i
\(28\) 4.60711 2.60279i 0.870662 0.491881i
\(29\) 2.91327 + 5.04593i 0.540980 + 0.937005i 0.998848 + 0.0479847i \(0.0152799\pi\)
−0.457868 + 0.889020i \(0.651387\pi\)
\(30\) 4.33809 + 4.55641i 0.792023 + 0.831883i
\(31\) 0.712343 0.127941 0.0639703 0.997952i \(-0.479624\pi\)
0.0639703 + 0.997952i \(0.479624\pi\)
\(32\) 5.63223 + 0.527268i 0.995647 + 0.0932087i
\(33\) −7.53401 + 6.02802i −1.31150 + 1.04934i
\(34\) −1.83435 + 3.92132i −0.314588 + 0.672501i
\(35\) 6.68377 + 1.22627i 1.12976 + 0.207277i
\(36\) −5.33708 + 2.74145i −0.889513 + 0.456909i
\(37\) 3.16687 5.48519i 0.520631 0.901759i −0.479081 0.877771i \(-0.659030\pi\)
0.999712 0.0239888i \(-0.00763660\pi\)
\(38\) 0.368945 + 4.27693i 0.0598508 + 0.693810i
\(39\) 5.25639 4.20567i 0.841695 0.673447i
\(40\) 5.11802 + 5.15549i 0.809230 + 0.815154i
\(41\) −5.66744 3.27210i −0.885105 0.511016i −0.0127671 0.999918i \(-0.504064\pi\)
−0.872338 + 0.488903i \(0.837397\pi\)
\(42\) −2.92227 + 5.78449i −0.450916 + 0.892566i
\(43\) 0.877494 0.506621i 0.133817 0.0772590i −0.431597 0.902066i \(-0.642050\pi\)
0.565414 + 0.824807i \(0.308716\pi\)
\(44\) −8.55220 + 7.14079i −1.28929 + 1.07652i
\(45\) −7.51747 1.69040i −1.12064 0.251990i
\(46\) 2.69896 5.76963i 0.397941 0.850685i
\(47\) −0.374318 −0.0545999 −0.0272999 0.999627i \(-0.508691\pi\)
−0.0272999 + 0.999627i \(0.508691\pi\)
\(48\) −6.09525 + 3.29362i −0.879773 + 0.475394i
\(49\) 1.12004 + 6.90981i 0.160005 + 0.987116i
\(50\) 0.194064 + 2.24965i 0.0274447 + 0.318149i
\(51\) −0.798668 5.24161i −0.111836 0.733973i
\(52\) 5.96677 4.98204i 0.827442 0.690885i
\(53\) −2.00394 3.47093i −0.275263 0.476769i 0.694939 0.719069i \(-0.255431\pi\)
−0.970201 + 0.242300i \(0.922098\pi\)
\(54\) 3.57146 6.42220i 0.486015 0.873951i
\(55\) −14.3078 −1.92926
\(56\) −3.23406 + 6.74840i −0.432170 + 0.901792i
\(57\) −3.28467 4.10529i −0.435065 0.543758i
\(58\) −7.46370 3.49143i −0.980032 0.458448i
\(59\) 6.31292 0.821872 0.410936 0.911664i \(-0.365202\pi\)
0.410936 + 0.911664i \(0.365202\pi\)
\(60\) −8.71932 1.77012i −1.12566 0.228521i
\(61\) 9.20740i 1.17889i 0.807810 + 0.589443i \(0.200653\pi\)
−0.807810 + 0.589443i \(0.799347\pi\)
\(62\) −0.825920 + 0.576821i −0.104892 + 0.0732563i
\(63\) −0.957781 7.87925i −0.120669 0.992693i
\(64\) −6.95719 + 3.94936i −0.869649 + 0.493671i
\(65\) 9.98236 1.23816
\(66\) 3.85405 13.0898i 0.474401 1.61124i
\(67\) 6.34532i 0.775205i 0.921827 + 0.387602i \(0.126697\pi\)
−0.921827 + 0.387602i \(0.873303\pi\)
\(68\) −1.04847 6.03190i −0.127146 0.731476i
\(69\) 1.17512 + 7.71224i 0.141468 + 0.928444i
\(70\) −8.74241 + 3.99041i −1.04492 + 0.476945i
\(71\) 12.0334i 1.42810i 0.700092 + 0.714052i \(0.253142\pi\)
−0.700092 + 0.714052i \(0.746858\pi\)
\(72\) 3.96814 7.50026i 0.467649 0.883914i
\(73\) −13.8670 + 8.00612i −1.62301 + 0.937046i −0.636902 + 0.770944i \(0.719785\pi\)
−0.986109 + 0.166101i \(0.946882\pi\)
\(74\) 0.769831 + 8.92413i 0.0894910 + 1.03741i
\(75\) −1.72772 2.15936i −0.199500 0.249342i
\(76\) −3.89102 4.66010i −0.446331 0.534550i
\(77\) −4.94500 13.8844i −0.563534 1.58227i
\(78\) −2.68892 + 9.13259i −0.304461 + 1.03406i
\(79\) 6.94093i 0.780916i 0.920621 + 0.390458i \(0.127683\pi\)
−0.920621 + 0.390458i \(0.872317\pi\)
\(80\) −10.1087 1.83316i −1.13019 0.204954i
\(81\) 0.730282 + 8.97032i 0.0811424 + 0.996703i
\(82\) 9.22065 0.795409i 1.01825 0.0878383i
\(83\) 4.89941 + 8.48603i 0.537780 + 0.931463i 0.999023 + 0.0441890i \(0.0140704\pi\)
−0.461243 + 0.887274i \(0.652596\pi\)
\(84\) −1.29579 9.07309i −0.141383 0.989955i
\(85\) 3.93115 6.80896i 0.426393 0.738535i
\(86\) −0.607165 + 1.29795i −0.0654723 + 0.139961i
\(87\) 9.97670 1.52016i 1.06961 0.162978i
\(88\) 4.13351 15.2045i 0.440634 1.62080i
\(89\) 2.02208 + 1.16745i 0.214340 + 0.123749i 0.603327 0.797494i \(-0.293841\pi\)
−0.388987 + 0.921243i \(0.627175\pi\)
\(90\) 10.0849 4.12736i 1.06304 0.435062i
\(91\) 3.45006 + 9.68697i 0.361665 + 1.01547i
\(92\) 1.54267 + 8.87503i 0.160834 + 0.925286i
\(93\) 0.448916 1.14925i 0.0465504 0.119172i
\(94\) 0.434000 0.303104i 0.0447636 0.0312628i
\(95\) 7.79631i 0.799885i
\(96\) 4.40007 8.75439i 0.449080 0.893492i
\(97\) −3.10755 + 1.79414i −0.315524 + 0.182168i −0.649396 0.760451i \(-0.724978\pi\)
0.333872 + 0.942618i \(0.391645\pi\)
\(98\) −6.89384 7.10457i −0.696383 0.717670i
\(99\) 4.97732 + 15.9537i 0.500239 + 1.60341i
\(100\) −2.04666 2.45119i −0.204666 0.245119i
\(101\) −4.14074 2.39066i −0.412019 0.237879i 0.279638 0.960106i \(-0.409786\pi\)
−0.691657 + 0.722226i \(0.743119\pi\)
\(102\) 5.17041 + 5.43062i 0.511947 + 0.537711i
\(103\) −3.99131 6.91315i −0.393275 0.681173i 0.599604 0.800297i \(-0.295325\pi\)
−0.992879 + 0.119124i \(0.961991\pi\)
\(104\) −2.88390 + 10.6080i −0.282790 + 1.04020i
\(105\) 6.19047 10.0104i 0.604128 0.976913i
\(106\) 5.13404 + 2.40164i 0.498662 + 0.233268i
\(107\) 8.26726 + 4.77310i 0.799226 + 0.461433i 0.843201 0.537599i \(-0.180669\pi\)
−0.0439743 + 0.999033i \(0.514002\pi\)
\(108\) 1.05948 + 10.3382i 0.101949 + 0.994790i
\(109\) −6.07838 10.5281i −0.582203 1.00841i −0.995218 0.0976814i \(-0.968857\pi\)
0.413014 0.910725i \(-0.364476\pi\)
\(110\) 16.5890 11.5857i 1.58170 1.10466i
\(111\) −6.85370 8.56598i −0.650524 0.813046i
\(112\) −1.71481 10.4432i −0.162035 0.986785i
\(113\) 2.22557 3.85479i 0.209364 0.362628i −0.742151 0.670233i \(-0.766194\pi\)
0.951514 + 0.307605i \(0.0995274\pi\)
\(114\) 7.13264 + 2.10007i 0.668033 + 0.196690i
\(115\) −5.78409 + 10.0183i −0.539370 + 0.934215i
\(116\) 11.4809 1.99563i 1.06598 0.185289i
\(117\) −3.47261 11.1307i −0.321043 1.02903i
\(118\) −7.31945 + 5.11189i −0.673810 + 0.470588i
\(119\) 7.96614 + 1.46154i 0.730255 + 0.133979i
\(120\) 11.5429 5.00812i 1.05372 0.457177i
\(121\) 10.0164 + 17.3489i 0.910581 + 1.57717i
\(122\) −7.45570 10.6754i −0.675007 0.966508i
\(123\) −8.85059 + 7.08142i −0.798031 + 0.638510i
\(124\) 0.490525 1.33758i 0.0440504 0.120118i
\(125\) 8.74114i 0.781832i
\(126\) 7.49072 + 8.35997i 0.667327 + 0.744765i
\(127\) 11.0210i 0.977951i −0.872297 0.488976i \(-0.837371\pi\)
0.872297 0.488976i \(-0.162629\pi\)
\(128\) 4.86845 10.2126i 0.430315 0.902679i
\(129\) −0.264357 1.73496i −0.0232754 0.152755i
\(130\) −11.5740 + 8.08322i −1.01510 + 0.708945i
\(131\) 1.13765 + 1.97046i 0.0993966 + 0.172160i 0.911435 0.411444i \(-0.134975\pi\)
−0.812038 + 0.583604i \(0.801642\pi\)
\(132\) 6.13094 + 18.2977i 0.533629 + 1.59261i
\(133\) 7.56561 2.69453i 0.656022 0.233645i
\(134\) −5.13813 7.35703i −0.443867 0.635550i
\(135\) −7.46466 + 11.0629i −0.642456 + 0.952145i
\(136\) 6.09998 + 6.14464i 0.523069 + 0.526898i
\(137\) 4.55094 7.88247i 0.388813 0.673445i −0.603477 0.797381i \(-0.706218\pi\)
0.992290 + 0.123936i \(0.0395517\pi\)
\(138\) −7.60747 7.99033i −0.647591 0.680182i
\(139\) 5.95136 10.3081i 0.504788 0.874318i −0.495197 0.868781i \(-0.664904\pi\)
0.999985 0.00553705i \(-0.00176251\pi\)
\(140\) 6.90508 11.7058i 0.583586 0.989322i
\(141\) −0.235894 + 0.603901i −0.0198658 + 0.0508576i
\(142\) −9.74408 13.9520i −0.817705 1.17083i
\(143\) −10.8256 18.7505i −0.905281 1.56799i
\(144\) 1.47252 + 11.9093i 0.122710 + 0.992443i
\(145\) 12.9599 + 7.48242i 1.07626 + 0.621381i
\(146\) 9.59502 20.5115i 0.794089 1.69754i
\(147\) 11.8537 + 2.54754i 0.977676 + 0.210117i
\(148\) −8.11890 9.72363i −0.667369 0.799278i
\(149\) 11.2762 + 19.5309i 0.923778 + 1.60003i 0.793514 + 0.608552i \(0.208249\pi\)
0.130264 + 0.991479i \(0.458417\pi\)
\(150\) 3.75174 + 1.10463i 0.306328 + 0.0901927i
\(151\) 5.17264 + 2.98642i 0.420943 + 0.243032i 0.695481 0.718545i \(-0.255191\pi\)
−0.274538 + 0.961576i \(0.588525\pi\)
\(152\) 8.28493 + 2.25235i 0.671996 + 0.182690i
\(153\) −8.95980 2.01472i −0.724357 0.162881i
\(154\) 16.9763 + 12.0939i 1.36799 + 0.974556i
\(155\) 1.58446 0.914789i 0.127267 0.0734777i
\(156\) −4.27748 12.7661i −0.342472 1.02210i
\(157\) 1.14569i 0.0914364i −0.998954 0.0457182i \(-0.985442\pi\)
0.998954 0.0457182i \(-0.0145576\pi\)
\(158\) −5.62043 8.04760i −0.447137 0.640233i
\(159\) −6.86265 + 1.04567i −0.544243 + 0.0829267i
\(160\) 13.2049 6.06009i 1.04394 0.479092i
\(161\) −11.7210 2.15044i −0.923742 0.169478i
\(162\) −8.11044 9.80921i −0.637217 0.770685i
\(163\) 2.38087 + 1.37460i 0.186484 + 0.107667i 0.590336 0.807158i \(-0.298995\pi\)
−0.403852 + 0.914825i \(0.632329\pi\)
\(164\) −10.0467 + 8.38866i −0.784516 + 0.655044i
\(165\) −9.01670 + 23.0832i −0.701949 + 1.79703i
\(166\) −12.5522 5.87175i −0.974236 0.455736i
\(167\) 4.44178 7.69338i 0.343715 0.595332i −0.641404 0.767203i \(-0.721648\pi\)
0.985119 + 0.171871i \(0.0549812\pi\)
\(168\) 8.84934 + 9.47044i 0.682741 + 0.730660i
\(169\) 1.05288 + 1.82364i 0.0809908 + 0.140280i
\(170\) 0.955618 + 11.0778i 0.0732925 + 0.849631i
\(171\) −8.69319 + 2.71214i −0.664785 + 0.207403i
\(172\) −0.347043 1.99655i −0.0264618 0.152235i
\(173\) 10.9273i 0.830788i 0.909642 + 0.415394i \(0.136356\pi\)
−0.909642 + 0.415394i \(0.863644\pi\)
\(174\) −10.3364 + 9.84117i −0.783604 + 0.746057i
\(175\) 3.97948 1.41731i 0.300821 0.107139i
\(176\) 7.51928 + 20.9758i 0.566787 + 1.58111i
\(177\) 3.97837 10.1849i 0.299033 0.765541i
\(178\) −3.28982 + 0.283793i −0.246583 + 0.0212712i
\(179\) −10.2820 + 5.93630i −0.768511 + 0.443700i −0.832343 0.554261i \(-0.813001\pi\)
0.0638324 + 0.997961i \(0.479668\pi\)
\(180\) −8.35067 + 12.9517i −0.622423 + 0.965360i
\(181\) 19.2790i 1.43300i −0.697589 0.716498i \(-0.745744\pi\)
0.697589 0.716498i \(-0.254256\pi\)
\(182\) −11.8442 8.43778i −0.877949 0.625450i
\(183\) 14.8546 + 5.80246i 1.09809 + 0.428930i
\(184\) −8.97520 9.04090i −0.661660 0.666504i
\(185\) 16.2676i 1.19602i
\(186\) 0.410114 + 1.69600i 0.0300710 + 0.124357i
\(187\) −17.0529 −1.24703
\(188\) −0.257758 + 0.702863i −0.0187989 + 0.0512616i
\(189\) −13.3155 3.42025i −0.968558 0.248787i
\(190\) 6.31307 + 9.03936i 0.457998 + 0.655784i
\(191\) 19.2424i 1.39233i −0.717882 0.696164i \(-0.754888\pi\)
0.717882 0.696164i \(-0.245112\pi\)
\(192\) 1.98726 + 13.7132i 0.143418 + 0.989662i
\(193\) −10.5865 −0.762035 −0.381017 0.924568i \(-0.624426\pi\)
−0.381017 + 0.924568i \(0.624426\pi\)
\(194\) 2.15021 4.59655i 0.154376 0.330013i
\(195\) 6.29084 16.1049i 0.450496 1.15330i
\(196\) 13.7459 + 2.65503i 0.981853 + 0.189645i
\(197\) −20.7335 −1.47720 −0.738600 0.674144i \(-0.764513\pi\)
−0.738600 + 0.674144i \(0.764513\pi\)
\(198\) −18.6894 14.4670i −1.32820 1.02813i
\(199\) −8.54532 14.8009i −0.605762 1.04921i −0.991931 0.126782i \(-0.959535\pi\)
0.386169 0.922428i \(-0.373798\pi\)
\(200\) 4.35784 + 1.18473i 0.308146 + 0.0837730i
\(201\) 10.2371 + 3.99880i 0.722072 + 0.282053i
\(202\) 6.73678 0.581142i 0.473998 0.0408890i
\(203\) −2.78185 + 15.1625i −0.195248 + 1.06420i
\(204\) −10.3922 2.10974i −0.727602 0.147711i
\(205\) −16.8081 −1.17393
\(206\) 10.2256 + 4.78342i 0.712452 + 0.333277i
\(207\) 13.1830 + 2.96436i 0.916281 + 0.206037i
\(208\) −5.24611 14.6346i −0.363752 1.01472i
\(209\) −14.6443 + 8.45489i −1.01297 + 0.584837i
\(210\) 0.928434 + 16.6192i 0.0640680 + 1.14683i
\(211\) −15.2397 8.79863i −1.04914 0.605723i −0.126734 0.991937i \(-0.540449\pi\)
−0.922409 + 0.386214i \(0.873783\pi\)
\(212\) −7.89735 + 1.37273i −0.542392 + 0.0942793i
\(213\) 19.4140 + 7.58341i 1.33022 + 0.519607i
\(214\) −13.4504 + 1.16029i −0.919452 + 0.0793156i
\(215\) 1.30120 2.25375i 0.0887413 0.153704i
\(216\) −9.59974 11.1286i −0.653179 0.757203i
\(217\) 1.43534 + 1.22141i 0.0974369 + 0.0829148i
\(218\) 15.5726 + 7.28470i 1.05471 + 0.493382i
\(219\) 4.17763 + 27.4176i 0.282298 + 1.85271i
\(220\) −9.85244 + 26.8659i −0.664251 + 1.81130i
\(221\) 11.8976 0.800319
\(222\) 14.8828 + 4.38195i 0.998866 + 0.294098i
\(223\) 6.65202 + 11.5216i 0.445452 + 0.771546i 0.998084 0.0618796i \(-0.0197095\pi\)
−0.552631 + 0.833426i \(0.686376\pi\)
\(224\) 10.4446 + 10.7196i 0.697858 + 0.716237i
\(225\) −4.57258 + 1.42658i −0.304839 + 0.0951050i
\(226\) 0.541009 + 6.27156i 0.0359874 + 0.417178i
\(227\) 0.464516 0.804566i 0.0308310 0.0534009i −0.850198 0.526463i \(-0.823518\pi\)
0.881029 + 0.473062i \(0.156851\pi\)
\(228\) −9.97041 + 3.34075i −0.660307 + 0.221247i
\(229\) −3.43576 + 1.98364i −0.227042 + 0.131083i −0.609207 0.793012i \(-0.708512\pi\)
0.382165 + 0.924094i \(0.375179\pi\)
\(230\) −1.40605 16.2994i −0.0927120 1.07475i
\(231\) −25.5165 0.771950i −1.67886 0.0507906i
\(232\) −11.6955 + 11.6105i −0.767846 + 0.762266i
\(233\) 11.9029 20.6164i 0.779785 1.35063i −0.152280 0.988337i \(-0.548662\pi\)
0.932065 0.362290i \(-0.118005\pi\)
\(234\) 13.0394 + 10.0935i 0.852412 + 0.659830i
\(235\) −0.832593 + 0.480698i −0.0543124 + 0.0313573i
\(236\) 4.34712 11.8539i 0.282973 0.771621i
\(237\) 11.1981 + 4.37415i 0.727392 + 0.284131i
\(238\) −10.4198 + 4.75602i −0.675413 + 0.308287i
\(239\) −6.99639 4.03937i −0.452559 0.261285i 0.256351 0.966584i \(-0.417480\pi\)
−0.708910 + 0.705299i \(0.750813\pi\)
\(240\) −9.32797 + 15.1535i −0.602118 + 0.978154i
\(241\) −17.5457 10.1300i −1.13022 0.652531i −0.186227 0.982507i \(-0.559626\pi\)
−0.943989 + 0.329976i \(0.892959\pi\)
\(242\) −25.6617 12.0042i −1.64960 0.771662i
\(243\) 14.9324 + 4.47487i 0.957912 + 0.287063i
\(244\) 17.2889 + 6.34028i 1.10681 + 0.405895i
\(245\) 11.3649 + 13.9311i 0.726074 + 0.890026i
\(246\) 4.52755 15.3773i 0.288666 0.980419i
\(247\) 10.2171 5.89887i 0.650101 0.375336i
\(248\) 0.514371 + 1.94805i 0.0326626 + 0.123701i
\(249\) 16.7784 2.55654i 1.06329 0.162014i
\(250\) −7.07815 10.1348i −0.447661 0.640984i
\(251\) 1.78038 0.112376 0.0561881 0.998420i \(-0.482105\pi\)
0.0561881 + 0.998420i \(0.482105\pi\)
\(252\) −15.4545 3.62727i −0.973545 0.228497i
\(253\) 25.0908 1.57744
\(254\) 8.92422 + 12.7781i 0.559956 + 0.801772i
\(255\) −8.50774 10.6332i −0.532775 0.665880i
\(256\) 2.62501 + 15.7832i 0.164063 + 0.986450i
\(257\) −9.99678 + 5.77165i −0.623582 + 0.360025i −0.778262 0.627939i \(-0.783899\pi\)
0.154680 + 0.987965i \(0.450565\pi\)
\(258\) 1.71139 + 1.79752i 0.106547 + 0.111909i
\(259\) 15.7862 5.62233i 0.980907 0.349355i
\(260\) 6.87392 18.7440i 0.426303 1.16246i
\(261\) 3.83475 17.0538i 0.237365 1.05560i
\(262\) −2.91462 1.36342i −0.180066 0.0842326i
\(263\) 11.8720 + 6.85430i 0.732059 + 0.422654i 0.819175 0.573544i \(-0.194432\pi\)
−0.0871162 + 0.996198i \(0.527765\pi\)
\(264\) −21.9250 16.2505i −1.34939 1.00015i
\(265\) −8.91471 5.14691i −0.547626 0.316172i
\(266\) −6.58998 + 9.25041i −0.404058 + 0.567179i
\(267\) 3.15779 2.52657i 0.193254 0.154624i
\(268\) 11.9147 + 4.36943i 0.727807 + 0.266906i
\(269\) 0.384540 0.222014i 0.0234458 0.0135364i −0.488231 0.872714i \(-0.662358\pi\)
0.511677 + 0.859178i \(0.329024\pi\)
\(270\) −0.303383 18.8713i −0.0184633 1.14847i
\(271\) −1.81389 + 3.14175i −0.110186 + 0.190848i −0.915845 0.401532i \(-0.868478\pi\)
0.805659 + 0.592379i \(0.201811\pi\)
\(272\) −12.0482 2.18488i −0.730529 0.132478i
\(273\) 17.8026 + 0.538580i 1.07746 + 0.0325963i
\(274\) 1.10628 + 12.8244i 0.0668330 + 0.774750i
\(275\) −7.70284 + 4.44724i −0.464499 + 0.268178i
\(276\) 15.2906 + 3.10416i 0.920386 + 0.186849i
\(277\) 1.82235 3.15639i 0.109494 0.189649i −0.806071 0.591818i \(-0.798410\pi\)
0.915565 + 0.402169i \(0.131744\pi\)
\(278\) 1.44671 + 16.7707i 0.0867677 + 1.00584i
\(279\) −1.57122 1.44850i −0.0940665 0.0867197i
\(280\) 1.47276 + 19.1636i 0.0880144 + 1.14524i
\(281\) −9.22049 15.9704i −0.550049 0.952712i −0.998270 0.0587897i \(-0.981276\pi\)
0.448222 0.893922i \(-0.352057\pi\)
\(282\) −0.215504 0.891202i −0.0128331 0.0530703i
\(283\) 32.2782 1.91874 0.959369 0.282153i \(-0.0910487\pi\)
0.959369 + 0.282153i \(0.0910487\pi\)
\(284\) 22.5954 + 8.28630i 1.34079 + 0.491702i
\(285\) −12.5781 4.91320i −0.745061 0.291033i
\(286\) 27.7348 + 12.9740i 1.64000 + 0.767171i
\(287\) −5.80914 16.3107i −0.342903 0.962791i
\(288\) −11.3509 12.6158i −0.668857 0.743391i
\(289\) −3.81460 + 6.60709i −0.224388 + 0.388652i
\(290\) −21.0852 + 1.81889i −1.23816 + 0.106809i
\(291\) 0.936193 + 6.14418i 0.0548806 + 0.360178i
\(292\) 5.48431 + 31.5514i 0.320945 + 1.84641i
\(293\) 8.82787 + 5.09677i 0.515730 + 0.297757i 0.735186 0.677866i \(-0.237095\pi\)
−0.219456 + 0.975622i \(0.570428\pi\)
\(294\) −15.8065 + 6.64482i −0.921856 + 0.387534i
\(295\) 14.0418 8.10703i 0.817544 0.472010i
\(296\) 17.2871 + 4.69970i 1.00479 + 0.273164i
\(297\) 28.8754 + 2.02389i 1.67552 + 0.117438i
\(298\) −28.8892 13.5140i −1.67350 0.782846i
\(299\) −17.5055 −1.01237
\(300\) −5.24440 + 1.75722i −0.302785 + 0.101453i
\(301\) 2.63678 + 0.483768i 0.151981 + 0.0278839i
\(302\) −8.41563 + 0.725965i −0.484265 + 0.0417746i
\(303\) −6.46641 + 5.17383i −0.371486 + 0.297229i
\(304\) −11.4297 + 4.09726i −0.655540 + 0.234994i
\(305\) 11.8241 + 20.4800i 0.677047 + 1.17268i
\(306\) 12.0198 4.91925i 0.687125 0.281215i
\(307\) −25.7276 −1.46835 −0.734175 0.678960i \(-0.762431\pi\)
−0.734175 + 0.678960i \(0.762431\pi\)
\(308\) −29.4761 0.275596i −1.67956 0.0157036i
\(309\) −13.6685 + 2.08268i −0.777576 + 0.118480i
\(310\) −1.09634 + 2.34366i −0.0622678 + 0.133111i
\(311\) −5.20808 −0.295323 −0.147661 0.989038i \(-0.547175\pi\)
−0.147661 + 0.989038i \(0.547175\pi\)
\(312\) 15.2968 + 11.3378i 0.866011 + 0.641877i
\(313\) 4.08044i 0.230640i 0.993328 + 0.115320i \(0.0367894\pi\)
−0.993328 + 0.115320i \(0.963211\pi\)
\(314\) 0.927727 + 1.32837i 0.0523547 + 0.0749640i
\(315\) −12.2489 16.2958i −0.690148 0.918165i
\(316\) 13.0331 + 4.77958i 0.733170 + 0.268872i
\(317\) 0.637548 0.0358083 0.0179041 0.999840i \(-0.494301\pi\)
0.0179041 + 0.999840i \(0.494301\pi\)
\(318\) 7.11011 6.76942i 0.398715 0.379610i
\(319\) 32.4579i 1.81729i
\(320\) −10.4031 + 17.7190i −0.581550 + 0.990520i
\(321\) 12.9106 10.3299i 0.720600 0.576558i
\(322\) 15.3311 6.99776i 0.854368 0.389970i
\(323\) 9.29214i 0.517028i
\(324\) 17.3466 + 4.80577i 0.963700 + 0.266987i
\(325\) 5.37418 3.10278i 0.298106 0.172111i
\(326\) −3.87356 + 0.334148i −0.214536 + 0.0185068i
\(327\) −20.8159 + 3.17173i −1.15112 + 0.175397i
\(328\) 4.85585 17.8615i 0.268120 0.986236i
\(329\) −0.754231 0.641819i −0.0415821 0.0353847i
\(330\) −8.23735 34.0649i −0.453451 1.87521i
\(331\) 0.792614i 0.0435660i −0.999763 0.0217830i \(-0.993066\pi\)
0.999763 0.0217830i \(-0.00693429\pi\)
\(332\) 19.3081 3.35617i 1.05967 0.184194i
\(333\) −18.1390 + 5.65908i −0.994009 + 0.310116i
\(334\) 1.07974 + 12.5168i 0.0590810 + 0.684887i
\(335\) 8.14865 + 14.1139i 0.445208 + 0.771123i
\(336\) −17.9290 3.81466i −0.978106 0.208107i
\(337\) 10.3481 17.9234i 0.563697 0.976351i −0.433473 0.901167i \(-0.642712\pi\)
0.997170 0.0751846i \(-0.0239546\pi\)
\(338\) −2.69745 1.26184i −0.146722 0.0686348i
\(339\) −4.81653 6.01986i −0.261598 0.326954i
\(340\) −10.0783 12.0703i −0.546571 0.654603i
\(341\) −3.43661 1.98413i −0.186103 0.107447i
\(342\) 7.88308 10.1839i 0.426268 0.550681i
\(343\) −9.59101 + 15.8434i −0.517866 + 0.855462i
\(344\) 2.01908 + 2.03386i 0.108862 + 0.109658i
\(345\) 12.5178 + 15.6452i 0.673938 + 0.842310i
\(346\) −8.84839 12.6696i −0.475693 0.681120i
\(347\) 25.5636i 1.37233i −0.727448 0.686163i \(-0.759294\pi\)
0.727448 0.686163i \(-0.240706\pi\)
\(348\) 4.01561 19.7802i 0.215259 1.06033i
\(349\) −1.57229 + 0.907760i −0.0841626 + 0.0485913i −0.541491 0.840707i \(-0.682140\pi\)
0.457328 + 0.889298i \(0.348807\pi\)
\(350\) −3.46631 + 4.86568i −0.185282 + 0.260081i
\(351\) −20.1460 1.41204i −1.07531 0.0753691i
\(352\) −25.7033 18.2315i −1.36999 0.971741i
\(353\) −22.4290 12.9494i −1.19377 0.689226i −0.234614 0.972089i \(-0.575383\pi\)
−0.959160 + 0.282863i \(0.908716\pi\)
\(354\) 3.63451 + 15.0302i 0.193172 + 0.798848i
\(355\) 15.4533 + 26.7659i 0.820176 + 1.42059i
\(356\) 3.58456 2.99298i 0.189981 0.158628i
\(357\) 7.37819 11.9310i 0.390495 0.631456i
\(358\) 7.11442 15.2086i 0.376009 0.803801i
\(359\) −2.34262 1.35251i −0.123639 0.0713828i 0.436905 0.899508i \(-0.356075\pi\)
−0.560544 + 0.828125i \(0.689408\pi\)
\(360\) −0.805507 21.7787i −0.0424539 1.14784i
\(361\) 4.89293 + 8.47480i 0.257523 + 0.446042i
\(362\) 15.6112 + 22.3529i 0.820506 + 1.17484i
\(363\) 34.3019 5.22660i 1.80038 0.274325i
\(364\) 20.5651 + 0.192280i 1.07791 + 0.0100782i
\(365\) −20.5629 + 35.6160i −1.07631 + 1.86422i
\(366\) −21.9216 + 5.30093i −1.14586 + 0.277084i
\(367\) 3.40486 5.89740i 0.177732 0.307842i −0.763371 0.645960i \(-0.776457\pi\)
0.941104 + 0.338119i \(0.109791\pi\)
\(368\) 17.7271 + 3.21471i 0.924088 + 0.167579i
\(369\) 5.84711 + 18.7417i 0.304388 + 0.975652i
\(370\) 13.1727 + 18.8613i 0.684815 + 0.980552i
\(371\) 1.91354 10.4298i 0.0993463 0.541487i
\(372\) −1.84884 1.63432i −0.0958578 0.0847354i
\(373\) −16.7574 29.0246i −0.867663 1.50284i −0.864378 0.502843i \(-0.832288\pi\)
−0.00328544 0.999995i \(-0.501046\pi\)
\(374\) 19.7718 13.8086i 1.02238 0.714026i
\(375\) 14.1024 + 5.50863i 0.728245 + 0.284465i
\(376\) −0.270289 1.02365i −0.0139391 0.0527906i
\(377\) 22.6455i 1.16630i
\(378\) 18.2081 6.81664i 0.936522 0.350610i
\(379\) 9.31826i 0.478647i −0.970940 0.239323i \(-0.923074\pi\)
0.970940 0.239323i \(-0.0769256\pi\)
\(380\) −14.6393 5.36860i −0.750978 0.275403i
\(381\) −17.7805 6.94536i −0.910922 0.355821i
\(382\) 15.5815 + 22.3104i 0.797220 + 1.14150i
\(383\) −0.928250 1.60778i −0.0474314 0.0821535i 0.841335 0.540514i \(-0.181770\pi\)
−0.888766 + 0.458360i \(0.848437\pi\)
\(384\) −13.4084 14.2904i −0.684242 0.729255i
\(385\) −28.8294 24.5326i −1.46928 1.25030i
\(386\) 12.2744 8.57245i 0.624753 0.436326i
\(387\) −2.96567 0.666869i −0.150754 0.0338989i
\(388\) 1.22901 + 7.07056i 0.0623937 + 0.358953i
\(389\) 6.66174 11.5385i 0.337764 0.585024i −0.646248 0.763127i \(-0.723663\pi\)
0.984012 + 0.178104i \(0.0569962\pi\)
\(390\) 5.74709 + 23.7667i 0.291015 + 1.20347i
\(391\) −6.89385 + 11.9405i −0.348637 + 0.603857i
\(392\) −18.0875 + 8.05243i −0.913558 + 0.406709i
\(393\) 3.89596 0.593629i 0.196525 0.0299446i
\(394\) 24.0393 16.7890i 1.21108 0.845816i
\(395\) 8.91353 + 15.4387i 0.448488 + 0.776804i
\(396\) 33.3840 + 1.63986i 1.67761 + 0.0824061i
\(397\) −8.02033 4.63054i −0.402529 0.232400i 0.285046 0.958514i \(-0.407991\pi\)
−0.687575 + 0.726114i \(0.741325\pi\)
\(398\) 21.8929 + 10.2412i 1.09739 + 0.513346i
\(399\) 0.420636 13.9040i 0.0210581 0.696068i
\(400\) −6.01199 + 2.15514i −0.300600 + 0.107757i
\(401\) 4.92359 + 8.52790i 0.245872 + 0.425863i 0.962376 0.271720i \(-0.0875923\pi\)
−0.716504 + 0.697583i \(0.754259\pi\)
\(402\) −15.1074 + 3.65316i −0.753488 + 0.182203i
\(403\) 2.39768 + 1.38430i 0.119437 + 0.0689570i
\(404\) −7.34032 + 6.12892i −0.365195 + 0.304925i
\(405\) 13.1440 + 19.0148i 0.653132 + 0.944854i
\(406\) −9.05244 19.8326i −0.449265 0.984276i
\(407\) −30.5564 + 17.6417i −1.51462 + 0.874468i
\(408\) 13.7575 5.96900i 0.681100 0.295510i
\(409\) 20.0274i 0.990292i 0.868810 + 0.495146i \(0.164885\pi\)
−0.868810 + 0.495146i \(0.835115\pi\)
\(410\) 19.4880 13.6104i 0.962442 0.672167i
\(411\) −9.84908 12.3097i −0.485819 0.607193i
\(412\) −15.7294 + 2.73410i −0.774931 + 0.134700i
\(413\) 12.7202 + 10.8244i 0.625920 + 0.532632i
\(414\) −17.6853 + 7.23793i −0.869184 + 0.355725i
\(415\) 21.7955 + 12.5836i 1.06990 + 0.617706i
\(416\) 17.9329 + 12.7199i 0.879233 + 0.623643i
\(417\) −12.8798 16.0976i −0.630728 0.788304i
\(418\) 10.1328 21.6612i 0.495614 1.05948i
\(419\) −15.0233 + 26.0211i −0.733935 + 1.27121i 0.221255 + 0.975216i \(0.428985\pi\)
−0.955189 + 0.295996i \(0.904349\pi\)
\(420\) −14.5339 18.5172i −0.709180 0.903545i
\(421\) 4.68787 + 8.11963i 0.228473 + 0.395727i 0.957356 0.288912i \(-0.0932934\pi\)
−0.728883 + 0.684639i \(0.759960\pi\)
\(422\) 24.7942 2.13885i 1.20696 0.104117i
\(423\) 0.825635 + 0.761151i 0.0401438 + 0.0370084i
\(424\) 8.04494 7.98648i 0.390697 0.387858i
\(425\) 4.88763i 0.237085i
\(426\) −28.6500 + 6.92795i −1.38810 + 0.335660i
\(427\) −15.7873 + 18.5524i −0.764003 + 0.897815i
\(428\) 14.6554 12.2368i 0.708397 0.591487i
\(429\) −37.0731 + 5.64885i −1.78990 + 0.272729i
\(430\) 0.316307 + 3.66674i 0.0152537 + 0.176826i
\(431\) −11.7434 + 6.78007i −0.565661 + 0.326584i −0.755414 0.655247i \(-0.772564\pi\)
0.189754 + 0.981832i \(0.439231\pi\)
\(432\) 20.1417 + 5.12953i 0.969068 + 0.246794i
\(433\) 28.8432i 1.38611i −0.720882 0.693057i \(-0.756263\pi\)
0.720882 0.693057i \(-0.243737\pi\)
\(434\) −2.65323 0.253890i −0.127359 0.0121871i
\(435\) 20.2389 16.1933i 0.970383 0.776411i
\(436\) −23.9543 + 4.16378i −1.14721 + 0.199409i
\(437\) 13.6720i 0.654019i
\(438\) −27.0451 28.4062i −1.29227 1.35730i
\(439\) 14.4978 0.691944 0.345972 0.938245i \(-0.387549\pi\)
0.345972 + 0.938245i \(0.387549\pi\)
\(440\) −10.3314 39.1275i −0.492530 1.86533i
\(441\) 11.5802 17.5185i 0.551437 0.834216i
\(442\) −13.7946 + 9.63409i −0.656141 + 0.458247i
\(443\) 27.6886i 1.31552i −0.753226 0.657762i \(-0.771503\pi\)
0.753226 0.657762i \(-0.228497\pi\)
\(444\) −20.8040 + 6.97071i −0.987313 + 0.330815i
\(445\) 5.99694 0.284282
\(446\) −17.0423 7.97218i −0.806976 0.377494i
\(447\) 38.6160 5.88395i 1.82648 0.278301i
\(448\) −20.7901 3.97129i −0.982241 0.187626i
\(449\) 5.91384 0.279091 0.139546 0.990216i \(-0.455436\pi\)
0.139546 + 0.990216i \(0.455436\pi\)
\(450\) 4.14647 5.35668i 0.195466 0.252517i
\(451\) 18.2279 + 31.5716i 0.858318 + 1.48665i
\(452\) −5.70567 6.83342i −0.268372 0.321417i
\(453\) 8.07788 6.46317i 0.379532 0.303666i
\(454\) 0.112919 + 1.30899i 0.00529953 + 0.0614339i
\(455\) 20.1139 + 17.1161i 0.942956 + 0.802416i
\(456\) 8.85493 11.9469i 0.414670 0.559467i
\(457\) 28.1559 1.31708 0.658539 0.752547i \(-0.271175\pi\)
0.658539 + 0.752547i \(0.271175\pi\)
\(458\) 2.37731 5.08203i 0.111085 0.237467i
\(459\) −8.89685 + 13.1855i −0.415270 + 0.615446i
\(460\) 14.8286 + 17.7596i 0.691389 + 0.828045i
\(461\) 17.0229 9.82816i 0.792835 0.457743i −0.0481250 0.998841i \(-0.515325\pi\)
0.840959 + 0.541098i \(0.181991\pi\)
\(462\) 30.2100 19.7670i 1.40550 0.919643i
\(463\) −2.94753 1.70176i −0.136983 0.0790873i 0.429942 0.902856i \(-0.358534\pi\)
−0.566925 + 0.823769i \(0.691867\pi\)
\(464\) 4.15862 22.9321i 0.193059 1.06460i
\(465\) −0.477342 3.13277i −0.0221362 0.145279i
\(466\) 2.89346 + 33.5419i 0.134037 + 1.55380i
\(467\) −13.9746 + 24.2047i −0.646666 + 1.12006i 0.337248 + 0.941416i \(0.390504\pi\)
−0.983914 + 0.178643i \(0.942829\pi\)
\(468\) −23.2916 1.14411i −1.07665 0.0528865i
\(469\) −10.8799 + 12.7855i −0.502388 + 0.590380i
\(470\) 0.576097 1.23153i 0.0265734 0.0568064i
\(471\) −1.84839 0.722012i −0.0851693 0.0332686i
\(472\) 4.55845 + 17.2639i 0.209820 + 0.794638i
\(473\) −5.64448 −0.259533
\(474\) −16.5255 + 3.99607i −0.759039 + 0.183546i
\(475\) −2.42330 4.19728i −0.111189 0.192584i
\(476\) 8.22991 13.9517i 0.377217 0.639477i
\(477\) −2.63780 + 11.7307i −0.120777 + 0.537113i
\(478\) 11.3828 0.981924i 0.520636 0.0449121i
\(479\) −11.7187 + 20.2975i −0.535443 + 0.927415i 0.463699 + 0.885993i \(0.346522\pi\)
−0.999142 + 0.0414216i \(0.986811\pi\)
\(480\) −1.45532 25.1229i −0.0664260 1.14670i
\(481\) 21.3188 12.3084i 0.972054 0.561216i
\(482\) 28.5460 2.46249i 1.30023 0.112163i
\(483\) −10.8559 + 17.5547i −0.493960 + 0.798765i
\(484\) 39.4737 6.86137i 1.79426 0.311880i
\(485\) −4.60807 + 7.98141i −0.209242 + 0.362417i
\(486\) −20.9367 + 6.90315i −0.949709 + 0.313133i
\(487\) −17.8385 + 10.2991i −0.808340 + 0.466695i −0.846379 0.532581i \(-0.821222\pi\)
0.0380392 + 0.999276i \(0.487889\pi\)
\(488\) −25.1795 + 6.64851i −1.13982 + 0.300964i
\(489\) 3.71810 2.97488i 0.168138 0.134529i
\(490\) −24.4576 6.94960i −1.10488 0.313951i
\(491\) 3.12221 + 1.80261i 0.140903 + 0.0813506i 0.568794 0.822480i \(-0.307410\pi\)
−0.427891 + 0.903830i \(0.640743\pi\)
\(492\) 7.20232 + 21.4952i 0.324706 + 0.969079i
\(493\) 15.4465 + 8.91802i 0.695674 + 0.401647i
\(494\) −7.06956 + 15.1127i −0.318074 + 0.679954i
\(495\) 31.5588 + 29.0939i 1.41846 + 1.30768i
\(496\) −2.17382 1.84213i −0.0976072 0.0827142i
\(497\) −20.6330 + 24.2467i −0.925515 + 1.08761i
\(498\) −17.3834 + 16.5505i −0.778970 + 0.741645i
\(499\) 18.2668 10.5464i 0.817735 0.472120i −0.0318996 0.999491i \(-0.510156\pi\)
0.849635 + 0.527371i \(0.176822\pi\)
\(500\) 16.4134 + 6.01922i 0.734029 + 0.269187i
\(501\) −9.61282 12.0144i −0.429469 0.536765i
\(502\) −2.06424 + 1.44166i −0.0921315 + 0.0643444i
\(503\) 14.3184 0.638426 0.319213 0.947683i \(-0.396581\pi\)
0.319213 + 0.947683i \(0.396581\pi\)
\(504\) 20.8558 8.30872i 0.928992 0.370100i
\(505\) −12.2803 −0.546467
\(506\) −29.0913 + 20.3173i −1.29326 + 0.903213i
\(507\) 3.60567 0.549398i 0.160133 0.0243996i
\(508\) −20.6942 7.58911i −0.918158 0.336712i
\(509\) 9.28348 5.35982i 0.411483 0.237570i −0.279944 0.960016i \(-0.590316\pi\)
0.691427 + 0.722447i \(0.256982\pi\)
\(510\) 18.4745 + 5.43947i 0.818065 + 0.240864i
\(511\) −41.6689 7.64497i −1.84332 0.338194i
\(512\) −15.8240 16.1741i −0.699329 0.714800i
\(513\) −1.10282 + 15.7342i −0.0486905 + 0.694683i
\(514\) 6.91709 14.7868i 0.305100 0.652217i
\(515\) −17.7557 10.2513i −0.782409 0.451724i
\(516\) −3.43981 0.698320i −0.151429 0.0307418i
\(517\) 1.80585 + 1.04261i 0.0794212 + 0.0458538i
\(518\) −13.7505 + 19.3016i −0.604161 + 0.848066i
\(519\) 17.6294 + 6.88634i 0.773845 + 0.302277i
\(520\) 7.20809 + 27.2988i 0.316096 + 1.19713i
\(521\) 4.42878 2.55696i 0.194028 0.112022i −0.399839 0.916586i \(-0.630934\pi\)
0.593867 + 0.804563i \(0.297600\pi\)
\(522\) 9.36313 + 22.8780i 0.409813 + 1.00134i
\(523\) 21.0669 36.4890i 0.921193 1.59555i 0.123620 0.992330i \(-0.460550\pi\)
0.797573 0.603223i \(-0.206117\pi\)
\(524\) 4.48336 0.779304i 0.195856 0.0340440i
\(525\) 0.221253 7.31343i 0.00965626 0.319184i
\(526\) −19.3152 + 1.66620i −0.842181 + 0.0726498i
\(527\) 1.88846 1.09030i 0.0822627 0.0474944i
\(528\) 38.5797 + 1.08775i 1.67896 + 0.0473383i
\(529\) −1.35675 + 2.34996i −0.0589890 + 0.102172i
\(530\) 14.5038 1.25115i 0.630005 0.0543467i
\(531\) −13.9244 12.8369i −0.604269 0.557074i
\(532\) 0.150173 16.0615i 0.00651080 0.696357i
\(533\) −12.7174 22.0271i −0.550851 0.954102i
\(534\) −1.61538 + 5.48644i −0.0699043 + 0.237421i
\(535\) 24.5184 1.06002
\(536\) −17.3526 + 4.58185i −0.749517 + 0.197906i
\(537\) 3.09759 + 20.3293i 0.133671 + 0.877274i
\(538\) −0.266075 + 0.568794i −0.0114713 + 0.0245225i
\(539\) 13.8428 36.4552i 0.596251 1.57024i
\(540\) 15.6328 + 21.6345i 0.672730 + 0.931002i
\(541\) 7.93311 13.7406i 0.341071 0.590753i −0.643561 0.765395i \(-0.722544\pi\)
0.984632 + 0.174642i \(0.0558769\pi\)
\(542\) −0.440936 5.11148i −0.0189398 0.219557i
\(543\) −31.1035 12.1495i −1.33478 0.521387i
\(544\) 15.7384 7.22280i 0.674777 0.309675i
\(545\) −27.0402 15.6117i −1.15828 0.668731i
\(546\) −21.0771 + 13.7912i −0.902018 + 0.590208i
\(547\) 11.3942 6.57845i 0.487182 0.281274i −0.236223 0.971699i \(-0.575910\pi\)
0.723404 + 0.690424i \(0.242576\pi\)
\(548\) −11.6672 13.9733i −0.498399 0.596910i
\(549\) 18.7226 20.3088i 0.799063 0.866759i
\(550\) 5.32984 11.3937i 0.227265 0.485829i
\(551\) 17.6863 0.753463
\(552\) −20.2421 + 8.78248i −0.861563 + 0.373807i
\(553\) −11.9012 + 13.9856i −0.506090 + 0.594729i
\(554\) 0.442991 + 5.13530i 0.0188209 + 0.218178i
\(555\) −26.2451 10.2518i −1.11404 0.435163i
\(556\) −15.2575 18.2732i −0.647060 0.774955i
\(557\) −8.64104 14.9667i −0.366133 0.634160i 0.622825 0.782361i \(-0.285985\pi\)
−0.988957 + 0.148201i \(0.952652\pi\)
\(558\) 2.99466 + 0.407158i 0.126774 + 0.0172364i
\(559\) 3.93808 0.166563
\(560\) −17.2253 21.0265i −0.727903 0.888531i
\(561\) −10.7467 + 27.5121i −0.453725 + 1.16156i
\(562\) 23.6226 + 11.0504i 0.996461 + 0.466133i
\(563\) 16.7902 0.707621 0.353811 0.935317i \(-0.384886\pi\)
0.353811 + 0.935317i \(0.384886\pi\)
\(564\) 0.971516 + 0.858792i 0.0409082 + 0.0361617i
\(565\) 11.4323i 0.480959i
\(566\) −37.4246 + 26.1373i −1.57308 + 1.09863i
\(567\) −13.9094 + 19.3269i −0.584139 + 0.811654i
\(568\) −32.9078 + 8.68913i −1.38078 + 0.364588i
\(569\) −21.4440 −0.898978 −0.449489 0.893286i \(-0.648394\pi\)
−0.449489 + 0.893286i \(0.648394\pi\)
\(570\) 18.5620 4.48853i 0.777477 0.188004i
\(571\) 6.51241i 0.272536i −0.990672 0.136268i \(-0.956489\pi\)
0.990672 0.136268i \(-0.0435108\pi\)
\(572\) −42.6627 + 7.41568i −1.78382 + 0.310065i
\(573\) −31.0444 12.1265i −1.29690 0.506590i
\(574\) 19.9430 + 14.2074i 0.832403 + 0.593004i
\(575\) 7.19140i 0.299902i
\(576\) 23.3763 + 5.43586i 0.974013 + 0.226494i
\(577\) −32.2941 + 18.6450i −1.34442 + 0.776201i −0.987453 0.157916i \(-0.949523\pi\)
−0.356967 + 0.934117i \(0.616189\pi\)
\(578\) −0.927286 10.7494i −0.0385700 0.447116i
\(579\) −6.67158 + 17.0796i −0.277262 + 0.709805i
\(580\) 22.9742 19.1826i 0.953950 0.796515i
\(581\) −4.67840 + 25.4996i −0.194093 + 1.05790i
\(582\) −6.06072 6.36574i −0.251225 0.263868i
\(583\) 22.3267i 0.924679i
\(584\) −31.9075 32.1411i −1.32034 1.33001i
\(585\) −22.0181 20.2985i −0.910338 0.839239i
\(586\) −14.3625 + 1.23897i −0.593310 + 0.0511812i
\(587\) 3.71458 + 6.43385i 0.153317 + 0.265553i 0.932445 0.361312i \(-0.117671\pi\)
−0.779128 + 0.626865i \(0.784338\pi\)
\(588\) 12.9461 20.5036i 0.533888 0.845555i
\(589\) 1.08115 1.87261i 0.0445481 0.0771596i
\(590\) −9.71595 + 20.7700i −0.399999 + 0.855086i
\(591\) −13.0662 + 33.4501i −0.537470 + 1.37595i
\(592\) −23.8490 + 8.54922i −0.980186 + 0.351371i
\(593\) −13.4550 7.76825i −0.552531 0.319004i 0.197611 0.980280i \(-0.436682\pi\)
−0.750142 + 0.661277i \(0.770015\pi\)
\(594\) −35.1182 + 21.0353i −1.44092 + 0.863089i
\(595\) 19.5960 6.97920i 0.803356 0.286119i
\(596\) 44.4383 7.72432i 1.82026 0.316401i
\(597\) −29.2641 + 4.45899i −1.19770 + 0.182494i
\(598\) 20.2966 14.1751i 0.829990 0.579663i
\(599\) 26.1634i 1.06901i 0.845167 + 0.534503i \(0.179501\pi\)
−0.845167 + 0.534503i \(0.820499\pi\)
\(600\) 4.65766 6.28405i 0.190148 0.256545i
\(601\) −34.2829 + 19.7932i −1.39843 + 0.807383i −0.994228 0.107288i \(-0.965783\pi\)
−0.404200 + 0.914671i \(0.632450\pi\)
\(602\) −3.44892 + 1.57423i −0.140567 + 0.0641609i
\(603\) 12.9028 13.9959i 0.525443 0.569958i
\(604\) 9.16957 7.65628i 0.373105 0.311529i
\(605\) 44.5588 + 25.7260i 1.81157 + 1.04591i
\(606\) 3.30792 11.2349i 0.134375 0.456388i
\(607\) −2.76834 4.79490i −0.112363 0.194619i 0.804359 0.594143i \(-0.202509\pi\)
−0.916723 + 0.399524i \(0.869175\pi\)
\(608\) 9.93434 14.0058i 0.402891 0.568009i
\(609\) 22.7091 + 14.0434i 0.920218 + 0.569067i
\(610\) −30.2930 14.1707i −1.22653 0.573756i
\(611\) −1.25992 0.727414i −0.0509709 0.0294280i
\(612\) −9.95286 + 15.4366i −0.402321 + 0.623988i
\(613\) 24.0237 + 41.6103i 0.970308 + 1.68062i 0.694622 + 0.719375i \(0.255572\pi\)
0.275686 + 0.961248i \(0.411095\pi\)
\(614\) 29.8296 20.8329i 1.20382 0.840748i
\(615\) −10.5924 + 27.1171i −0.427126 + 1.09347i
\(616\) 34.3990 23.5488i 1.38597 0.948807i
\(617\) 16.8217 29.1360i 0.677215 1.17297i −0.298601 0.954378i \(-0.596520\pi\)
0.975816 0.218593i \(-0.0701466\pi\)
\(618\) 14.1614 13.4829i 0.569655 0.542360i
\(619\) −15.4670 + 26.7897i −0.621673 + 1.07677i 0.367502 + 0.930023i \(0.380213\pi\)
−0.989174 + 0.146746i \(0.953120\pi\)
\(620\) −0.626644 3.60510i −0.0251666 0.144784i
\(621\) 13.0904 19.4005i 0.525298 0.778514i
\(622\) 6.03846 4.21724i 0.242120 0.169096i
\(623\) 2.07264 + 5.81948i 0.0830384 + 0.233153i
\(624\) −26.9165 0.758911i −1.07752 0.0303808i
\(625\) 15.2170 + 26.3566i 0.608679 + 1.05426i
\(626\) −3.30414 4.73104i −0.132060 0.189090i
\(627\) 4.41180 + 28.9544i 0.176190 + 1.15633i
\(628\) −2.15129 0.788934i −0.0858458 0.0314819i
\(629\) 19.3887i 0.773079i
\(630\) 27.3974 + 8.97547i 1.09154 + 0.357591i
\(631\) 17.8791i 0.711757i −0.934532 0.355878i \(-0.884182\pi\)
0.934532 0.355878i \(-0.115818\pi\)
\(632\) −18.9814 + 5.01193i −0.755039 + 0.199364i
\(633\) −23.7991 + 19.0419i −0.945931 + 0.756846i
\(634\) −0.739199 + 0.516255i −0.0293574 + 0.0205031i
\(635\) −14.1531 24.5138i −0.561648 0.972802i
\(636\) −2.76220 + 13.6062i −0.109529 + 0.539519i
\(637\) −9.65794 + 25.4344i −0.382662 + 1.00775i
\(638\) 26.2828 + 37.6330i 1.04055 + 1.48991i
\(639\) 24.4692 26.5422i 0.967986 1.04999i
\(640\) −2.28618 28.9680i −0.0903691 1.14506i
\(641\) 4.93534 8.54827i 0.194934 0.337636i −0.751945 0.659226i \(-0.770884\pi\)
0.946879 + 0.321590i \(0.104217\pi\)
\(642\) −6.60447 + 22.4313i −0.260658 + 0.885291i
\(643\) −19.6415 + 34.0201i −0.774585 + 1.34162i 0.160442 + 0.987045i \(0.448708\pi\)
−0.935027 + 0.354576i \(0.884625\pi\)
\(644\) −12.1091 + 20.5279i −0.477164 + 0.808911i
\(645\) −2.81604 3.51958i −0.110882 0.138583i
\(646\) 7.52432 + 10.7737i 0.296040 + 0.423885i
\(647\) −12.5252 21.6942i −0.492415 0.852888i 0.507546 0.861624i \(-0.330553\pi\)
−0.999962 + 0.00873594i \(0.997219\pi\)
\(648\) −24.0038 + 8.47442i −0.942960 + 0.332907i
\(649\) −30.4559 17.5837i −1.19550 0.690221i
\(650\) −3.71856 + 7.94924i −0.145854 + 0.311795i
\(651\) 2.87509 1.54595i 0.112684 0.0605906i
\(652\) 4.22058 3.52404i 0.165291 0.138012i
\(653\) −4.50694 7.80625i −0.176370 0.305482i 0.764264 0.644903i \(-0.223102\pi\)
−0.940635 + 0.339421i \(0.889769\pi\)
\(654\) 21.5665 20.5331i 0.843316 0.802908i
\(655\) 5.06092 + 2.92192i 0.197747 + 0.114169i
\(656\) 8.83328 + 24.6414i 0.344882 + 0.962084i
\(657\) 46.8665 + 10.5385i 1.82844 + 0.411147i
\(658\) 1.39420 + 0.133412i 0.0543516 + 0.00520096i
\(659\) −11.1541 + 6.43982i −0.434502 + 0.250860i −0.701263 0.712903i \(-0.747380\pi\)
0.266761 + 0.963763i \(0.414047\pi\)
\(660\) 37.1348 + 32.8261i 1.44547 + 1.27775i
\(661\) 6.31666i 0.245690i −0.992426 0.122845i \(-0.960798\pi\)
0.992426 0.122845i \(-0.0392017\pi\)
\(662\) 0.641820 + 0.918989i 0.0249450 + 0.0357175i
\(663\) 7.49782 19.1948i 0.291191 0.745466i
\(664\) −19.6690 + 19.5261i −0.763305 + 0.757758i
\(665\) 13.3678 15.7092i 0.518383 0.609175i
\(666\) 16.4486 21.2494i 0.637371 0.823398i
\(667\) −22.7271 13.1215i −0.879998 0.508067i
\(668\) −11.3874 13.6381i −0.440590 0.527675i
\(669\) 22.7804 3.47106i 0.880740 0.134199i
\(670\) −20.8766 9.76583i −0.806533 0.377287i
\(671\) 25.6459 44.4199i 0.990047 1.71481i
\(672\) 23.8765 10.0951i 0.921057 0.389428i
\(673\) 17.4382 + 30.2039i 0.672195 + 1.16428i 0.977280 + 0.211951i \(0.0679817\pi\)
−0.305085 + 0.952325i \(0.598685\pi\)
\(674\) 2.51550 + 29.1605i 0.0968935 + 1.12322i
\(675\) −0.580077 + 8.27614i −0.0223272 + 0.318549i
\(676\) 4.14930 0.721238i 0.159589 0.0277399i
\(677\) 40.7999i 1.56807i −0.620718 0.784034i \(-0.713159\pi\)
0.620718 0.784034i \(-0.286841\pi\)
\(678\) 10.4591 + 3.07948i 0.401678 + 0.118267i
\(679\) −9.33786 1.71321i −0.358354 0.0657470i
\(680\) 21.4591 + 5.83390i 0.822918 + 0.223720i
\(681\) −1.00530 1.25645i −0.0385231 0.0481474i
\(682\) 5.59120 0.482319i 0.214098 0.0184689i
\(683\) 25.0149 14.4424i 0.957168 0.552621i 0.0618679 0.998084i \(-0.480294\pi\)
0.895300 + 0.445463i \(0.146961\pi\)
\(684\) −0.893560 + 18.1909i −0.0341661 + 0.695548i
\(685\) 23.3772i 0.893199i
\(686\) −1.70898 26.1358i −0.0652492 0.997869i
\(687\) 1.03507 + 6.79312i 0.0394905 + 0.259174i
\(688\) −3.98793 0.723189i −0.152038 0.0275713i
\(689\) 15.5771i 0.593440i
\(690\) −27.1824 8.00336i −1.03482 0.304683i
\(691\) −15.2927 −0.581762 −0.290881 0.956759i \(-0.593948\pi\)
−0.290881 + 0.956759i \(0.593948\pi\)
\(692\) 20.5184 + 7.52462i 0.779992 + 0.286043i
\(693\) −17.3258 + 40.6802i −0.658153 + 1.54531i
\(694\) 20.7001 + 29.6395i 0.785766 + 1.12510i
\(695\) 30.5709i 1.15962i
\(696\) 11.3612 + 26.1856i 0.430645 + 0.992564i
\(697\) −20.0329 −0.758801
\(698\) 1.08791 2.32565i 0.0411782 0.0880273i
\(699\) −25.7601 32.1958i −0.974335 1.21776i
\(700\) 0.0789902 8.44831i 0.00298555 0.319316i
\(701\) 47.8578 1.80756 0.903782 0.427993i \(-0.140779\pi\)
0.903782 + 0.427993i \(0.140779\pi\)
\(702\) 24.5015 14.6761i 0.924750 0.553913i
\(703\) −9.61299 16.6502i −0.362561 0.627973i
\(704\) 44.5645 + 0.325028i 1.67959 + 0.0122500i
\(705\) 0.250831 + 1.64619i 0.00944683 + 0.0619990i
\(706\) 36.4908 3.14784i 1.37335 0.118471i
\(707\) −4.24427 11.9169i −0.159622 0.448182i
\(708\) −16.3847 14.4836i −0.615776 0.544328i
\(709\) −13.4988 −0.506958 −0.253479 0.967341i \(-0.581575\pi\)
−0.253479 + 0.967341i \(0.581575\pi\)
\(710\) −39.5909 18.5202i −1.48582 0.695049i
\(711\) 14.1139 15.3097i 0.529314 0.574157i
\(712\) −1.73251 + 6.37278i −0.0649287 + 0.238830i
\(713\) −2.77858 + 1.60422i −0.104059 + 0.0600784i
\(714\) 1.10657 + 19.8078i 0.0414122 + 0.741288i
\(715\) −48.1586 27.8044i −1.80103 1.03983i
\(716\) 4.06645 + 23.3944i 0.151970 + 0.874290i
\(717\) −10.9260 + 8.74194i −0.408037 + 0.326474i
\(718\) 3.81132 0.328780i 0.142237 0.0122700i
\(719\) −13.5701 + 23.5041i −0.506078 + 0.876554i 0.493897 + 0.869521i \(0.335572\pi\)
−0.999975 + 0.00703306i \(0.997761\pi\)
\(720\) 18.5692 + 24.5988i 0.692034 + 0.916744i
\(721\) 3.81126 20.7733i 0.141939 0.773638i
\(722\) −12.5355 5.86398i −0.466525 0.218235i
\(723\) −27.4003 + 21.9232i −1.01903 + 0.815332i
\(724\) −36.2005 13.2757i −1.34538 0.493386i
\(725\) 9.30294 0.345502
\(726\) −35.5388 + 33.8359i −1.31897 + 1.25577i
\(727\) −19.5557 33.8715i −0.725282 1.25622i −0.958858 0.283886i \(-0.908376\pi\)
0.233576 0.972338i \(-0.424957\pi\)
\(728\) −23.9997 + 16.4297i −0.889490 + 0.608925i
\(729\) 16.6298 21.2709i 0.615918 0.787810i
\(730\) −4.99860 57.9454i −0.185006 2.14466i
\(731\) 1.55086 2.68616i 0.0573605 0.0993513i
\(732\) 21.1244 23.8972i 0.780780 0.883264i
\(733\) 22.5472 13.0176i 0.832800 0.480817i −0.0220104 0.999758i \(-0.507007\pi\)
0.854810 + 0.518940i \(0.173673\pi\)
\(734\) 0.827683 + 9.59478i 0.0305503 + 0.354150i
\(735\) 29.6377 9.55600i 1.09320 0.352478i
\(736\) −23.1566 + 10.6273i −0.853565 + 0.391726i
\(737\) 17.6740 30.6122i 0.651029 1.12762i
\(738\) −21.9555 16.9951i −0.808191 0.625600i
\(739\) 21.3801 12.3438i 0.786480 0.454074i −0.0522420 0.998634i \(-0.516637\pi\)
0.838722 + 0.544560i \(0.183303\pi\)
\(740\) −30.5459 11.2020i −1.12289 0.411792i
\(741\) −3.07806 20.2011i −0.113075 0.742107i
\(742\) 6.22688 + 13.6422i 0.228596 + 0.500821i
\(743\) 32.6332 + 18.8408i 1.19720 + 0.691202i 0.959929 0.280242i \(-0.0904146\pi\)
0.237268 + 0.971444i \(0.423748\pi\)
\(744\) 3.46701 + 0.397798i 0.127107 + 0.0145840i
\(745\) 50.1630 + 28.9616i 1.83783 + 1.06107i
\(746\) 42.9319 + 20.0830i 1.57185 + 0.735292i
\(747\) 6.44913 28.6803i 0.235961 1.04936i
\(748\) −11.7428 + 32.0205i −0.429358 + 1.17079i
\(749\) 8.47396 + 23.7929i 0.309632 + 0.869374i
\(750\) −20.8115 + 5.03250i −0.759929 + 0.183761i
\(751\) −29.7813 + 17.1942i −1.08673 + 0.627426i −0.932705 0.360640i \(-0.882558\pi\)
−0.154029 + 0.988066i \(0.549225\pi\)
\(752\) 1.14228 + 0.967993i 0.0416548 + 0.0352991i
\(753\) 1.12198 2.87234i 0.0408874 0.104674i
\(754\) −18.3372 26.2561i −0.667801 0.956191i
\(755\) 15.3406 0.558303
\(756\) −15.5914 + 22.6475i −0.567054 + 0.823681i
\(757\) 25.0283 0.909668 0.454834 0.890576i \(-0.349699\pi\)
0.454834 + 0.890576i \(0.349699\pi\)
\(758\) 7.54547 + 10.8040i 0.274064 + 0.392418i
\(759\) 15.8121 40.4798i 0.573943 1.46933i
\(760\) 21.3206 5.62958i 0.773379 0.204206i
\(761\) −6.45607 + 3.72741i −0.234032 + 0.135119i −0.612431 0.790524i \(-0.709808\pi\)
0.378399 + 0.925643i \(0.376475\pi\)
\(762\) 26.2394 6.34504i 0.950555 0.229857i
\(763\) 5.80419 31.6357i 0.210126 1.14529i
\(764\) −36.1317 13.2504i −1.30720 0.479384i
\(765\) −22.5165 + 7.02481i −0.814087 + 0.253983i
\(766\) 2.37815 + 1.11247i 0.0859260 + 0.0401952i
\(767\) 21.2487 + 12.2679i 0.767245 + 0.442969i
\(768\) 27.1179 + 5.71147i 0.978532 + 0.206095i
\(769\) 31.9762 + 18.4615i 1.15309 + 0.665737i 0.949639 0.313347i \(-0.101450\pi\)
0.203452 + 0.979085i \(0.434784\pi\)
\(770\) 53.2914 + 5.09950i 1.92049 + 0.183773i
\(771\) 3.01167 + 19.7654i 0.108463 + 0.711835i
\(772\) −7.28996 + 19.8785i −0.262371 + 0.715443i
\(773\) −3.26165 + 1.88311i −0.117313 + 0.0677309i −0.557509 0.830171i \(-0.688243\pi\)
0.440195 + 0.897902i \(0.354909\pi\)
\(774\) 3.97852 1.62826i 0.143005 0.0585267i
\(775\) 0.568682 0.984986i 0.0204277 0.0353817i
\(776\) −7.15036 7.20270i −0.256683 0.258562i
\(777\) 0.877687 29.0116i 0.0314869 1.04079i
\(778\) 1.61939 + 18.7725i 0.0580580 + 0.673028i
\(779\) −17.2034 + 9.93239i −0.616376 + 0.355865i
\(780\) −25.9085 22.9024i −0.927674 0.820036i
\(781\) 33.5173 58.0537i 1.19934 2.07733i
\(782\) −1.67582 19.4266i −0.0599270 0.694694i
\(783\) −25.0968 16.9340i −0.896887 0.605170i
\(784\) 14.4510 23.9827i 0.516106 0.856525i
\(785\) −1.47130 2.54836i −0.0525129 0.0909550i
\(786\) −4.03644 + 3.84303i −0.143975 + 0.137076i
\(787\) −50.5644 −1.80242 −0.901212 0.433377i \(-0.857322\pi\)
−0.901212 + 0.433377i \(0.857322\pi\)
\(788\) −14.2772 + 38.9316i −0.508605 + 1.38688i
\(789\) 18.5400 14.8340i 0.660040 0.528103i
\(790\) −22.8362 10.6825i −0.812475 0.380067i
\(791\) 11.0940 3.95117i 0.394456 0.140488i
\(792\) −40.0346 + 25.1314i −1.42257 + 0.893005i
\(793\) −17.8928 + 30.9912i −0.635392 + 1.10053i
\(794\) 13.0487 1.12563i 0.463081 0.0399472i
\(795\) −13.9217 + 11.1389i −0.493752 + 0.395055i
\(796\) −33.6763 + 5.85366i −1.19363 + 0.207478i
\(797\) 14.2897 + 8.25016i 0.506167 + 0.292236i 0.731257 0.682102i \(-0.238934\pi\)
−0.225090 + 0.974338i \(0.572268\pi\)
\(798\) 10.7710 + 16.4614i 0.381291 + 0.582728i
\(799\) −0.992338 + 0.572926i −0.0351064 + 0.0202687i
\(800\) 5.22542 7.36698i 0.184747 0.260462i
\(801\) −2.08618 6.68682i −0.0737117 0.236267i
\(802\) −12.6141 5.90072i −0.445419 0.208362i
\(803\) 89.1995 3.14778
\(804\) 14.5580 16.4688i 0.513420 0.580811i
\(805\) −28.8325 + 10.2688i −1.01621 + 0.361929i
\(806\) −3.90091 + 0.336508i −0.137404 + 0.0118530i
\(807\) −0.115848 0.760305i −0.00407805 0.0267640i
\(808\) 3.54778 13.0500i 0.124810 0.459096i
\(809\) 1.63374 + 2.82972i 0.0574392 + 0.0994876i 0.893315 0.449431i \(-0.148373\pi\)
−0.835876 + 0.548918i \(0.815040\pi\)
\(810\) −30.6370 11.4032i −1.07647 0.400667i
\(811\) −0.801585 −0.0281475 −0.0140737 0.999901i \(-0.504480\pi\)
−0.0140737 + 0.999901i \(0.504480\pi\)
\(812\) 26.5552 + 15.6645i 0.931906 + 0.549717i
\(813\) 3.92560 + 4.90634i 0.137677 + 0.172073i
\(814\) 21.1429 45.1976i 0.741059 1.58418i
\(815\) 7.06101 0.247336
\(816\) −11.1177 + 18.0609i −0.389196 + 0.632258i
\(817\) 3.07568i 0.107604i
\(818\) −16.2172 23.2206i −0.567022 0.811890i
\(819\) 12.0880 28.3821i 0.422389 0.991751i
\(820\) −11.5742 + 31.5608i −0.404187 + 1.10215i
\(821\) −25.3988 −0.886426 −0.443213 0.896416i \(-0.646161\pi\)
−0.443213 + 0.896416i \(0.646161\pi\)
\(822\) 21.3872 + 6.29707i 0.745965 + 0.219636i
\(823\) 10.7849i 0.375938i 0.982175 + 0.187969i \(0.0601905\pi\)
−0.982175 + 0.187969i \(0.939809\pi\)
\(824\) 16.0233 15.9069i 0.558200 0.554143i
\(825\) 2.32059 + 15.2299i 0.0807926 + 0.530237i
\(826\) −23.5134 2.25002i −0.818134 0.0782881i
\(827\) 3.34832i 0.116432i 0.998304 + 0.0582162i \(0.0185413\pi\)
−0.998304 + 0.0582162i \(0.981459\pi\)
\(828\) 14.6441 22.7126i 0.508919 0.789319i
\(829\) 8.23383 4.75381i 0.285973 0.165106i −0.350151 0.936693i \(-0.613870\pi\)
0.636124 + 0.771587i \(0.280537\pi\)
\(830\) −35.4602 + 3.05893i −1.23084 + 0.106177i
\(831\) −3.94389 4.92920i −0.136812 0.170992i
\(832\) −31.0921 0.226768i −1.07792 0.00786178i
\(833\) 13.5454 + 16.6040i 0.469319 + 0.575294i
\(834\) 27.9685 + 8.23480i 0.968469 + 0.285148i
\(835\) 22.8165i 0.789597i
\(836\) 5.79172 + 33.3199i 0.200311 + 1.15239i
\(837\) −3.32710 + 1.62207i −0.115001 + 0.0560668i
\(838\) −3.65198 42.3350i −0.126156 1.46244i
\(839\) 17.7731 + 30.7839i 0.613596 + 1.06278i 0.990629 + 0.136579i \(0.0436108\pi\)
−0.377034 + 0.926200i \(0.623056\pi\)
\(840\) 31.8454 + 9.70076i 1.09877 + 0.334708i
\(841\) −2.47424 + 4.28551i −0.0853186 + 0.147776i
\(842\) −12.0102 5.61823i −0.413899 0.193617i
\(843\) −31.5763 + 4.81130i −1.08754 + 0.165710i
\(844\) −27.0155 + 22.5570i −0.929912 + 0.776444i
\(845\) 4.68383 + 2.70421i 0.161129 + 0.0930277i
\(846\) −1.57362 0.213951i −0.0541021 0.00735579i
\(847\) −9.56455 + 52.1316i −0.328642 + 1.79126i
\(848\) −2.86058 + 15.7743i −0.0982326 + 0.541690i
\(849\) 20.3416 52.0755i 0.698121 1.78723i
\(850\) 3.95776 + 5.66692i 0.135750 + 0.194374i
\(851\) 28.5276i 0.977912i
\(852\) 27.6081 31.2319i 0.945838 1.06999i
\(853\) 29.1774 16.8456i 0.999017 0.576783i 0.0910594 0.995845i \(-0.470975\pi\)
0.907957 + 0.419063i \(0.137641\pi\)
\(854\) 3.28165 34.2943i 0.112296 1.17353i
\(855\) −15.8533 + 17.1964i −0.542171 + 0.588104i
\(856\) −7.08337 + 26.0551i −0.242105 + 0.890544i
\(857\) 4.71098 + 2.71988i 0.160924 + 0.0929095i 0.578299 0.815825i \(-0.303717\pi\)
−0.417375 + 0.908734i \(0.637050\pi\)
\(858\) 38.4099 36.5694i 1.31129 1.24846i
\(859\) −7.53547 13.0518i −0.257107 0.445322i 0.708359 0.705853i \(-0.249436\pi\)
−0.965466 + 0.260530i \(0.916103\pi\)
\(860\) −3.33589 3.99524i −0.113753 0.136237i
\(861\) −29.9756 0.906849i −1.02156 0.0309053i
\(862\) 8.12564 17.3703i 0.276760 0.591636i
\(863\) 6.63530 + 3.83089i 0.225868 + 0.130405i 0.608665 0.793428i \(-0.291706\pi\)
−0.382796 + 0.923833i \(0.625039\pi\)
\(864\) −27.5067 + 10.3624i −0.935799 + 0.352535i
\(865\) 14.0328 + 24.3055i 0.477130 + 0.826413i
\(866\) 23.3558 + 33.4420i 0.793662 + 1.13640i
\(867\) 8.25550 + 10.3180i 0.280372 + 0.350418i
\(868\) 3.28185 1.85408i 0.111393 0.0629316i
\(869\) 19.3330 33.4857i 0.655826 1.13592i
\(870\) −10.3533 + 35.1637i −0.351010 + 1.19216i
\(871\) −12.3309 + 21.3578i −0.417817 + 0.723680i
\(872\) 24.4020 24.2247i 0.826357 0.820352i
\(873\) 10.5026 + 2.36164i 0.355460 + 0.0799296i
\(874\) −11.0709 15.8518i −0.374478 0.536197i
\(875\) −14.9879 + 17.6130i −0.506683 + 0.595427i
\(876\) 54.3592 + 11.0355i 1.83663 + 0.372856i
\(877\) 20.1930 + 34.9752i 0.681868 + 1.18103i 0.974410 + 0.224777i \(0.0721654\pi\)
−0.292542 + 0.956253i \(0.594501\pi\)
\(878\) −16.8094 + 11.7396i −0.567289 + 0.396193i
\(879\) 13.7861 11.0304i 0.464993 0.372045i
\(880\) 43.6622 + 37.0002i 1.47185 + 1.24728i
\(881\) 11.4041i 0.384215i −0.981374 0.192107i \(-0.938468\pi\)
0.981374 0.192107i \(-0.0615322\pi\)
\(882\) 0.759113 + 29.6888i 0.0255607 + 0.999673i
\(883\) 31.0063i 1.04345i 0.853115 + 0.521723i \(0.174710\pi\)
−0.853115 + 0.521723i \(0.825290\pi\)
\(884\) 8.19278 22.3403i 0.275553 0.751387i
\(885\) −4.23029 27.7631i −0.142200 0.933248i
\(886\) 22.4208 + 32.1033i 0.753243 + 1.07853i
\(887\) −24.9111 43.1473i −0.836432 1.44874i −0.892859 0.450336i \(-0.851304\pi\)
0.0564269 0.998407i \(-0.482029\pi\)
\(888\) 18.4765 24.9282i 0.620029 0.836535i
\(889\) 18.8969 22.2067i 0.633783 0.744787i
\(890\) −6.95309 + 4.85602i −0.233068 + 0.162774i
\(891\) 21.4624 45.3103i 0.719016 1.51795i
\(892\) 26.2150 4.55673i 0.877744 0.152571i
\(893\) −0.568117 + 0.984008i −0.0190113 + 0.0329286i
\(894\) −40.0085 + 38.0915i −1.33808 + 1.27397i
\(895\) −15.2468 + 26.4082i −0.509643 + 0.882727i
\(896\) 27.3207 12.2303i 0.912720 0.408587i
\(897\) −11.0319 + 28.2423i −0.368345 + 0.942982i
\(898\) −6.85675 + 4.78874i −0.228813 + 0.159802i
\(899\) 2.07525 + 3.59443i 0.0692133 + 0.119881i
\(900\) −0.470009 + 9.56837i −0.0156670 + 0.318946i
\(901\) −10.6251 6.13442i −0.353974 0.204367i
\(902\) −46.6993 21.8454i −1.55492 0.727373i
\(903\) 2.44217 3.94914i 0.0812702 0.131419i
\(904\) 12.1488 + 3.30278i 0.404062 + 0.109849i
\(905\) −24.7580 42.8822i −0.822985 1.42545i
\(906\) −4.13227 + 14.0347i −0.137285 + 0.466273i
\(907\) 9.41097 + 5.43343i 0.312486 + 0.180414i 0.648038 0.761608i \(-0.275590\pi\)
−0.335552 + 0.942022i \(0.608923\pi\)
\(908\) −1.19088 1.42626i −0.0395206 0.0473321i
\(909\) 4.27201 + 13.6930i 0.141694 + 0.454169i
\(910\) −37.1807 3.55786i −1.23253 0.117942i
\(911\) −32.3485 + 18.6764i −1.07175 + 0.618776i −0.928660 0.370933i \(-0.879038\pi\)
−0.143092 + 0.989709i \(0.545705\pi\)
\(912\) −0.592717 + 21.0221i −0.0196268 + 0.696110i
\(913\) 54.5864i 1.80655i
\(914\) −32.6451 + 22.7993i −1.07980 + 0.754132i
\(915\) 40.4926 6.16988i 1.33864 0.203970i
\(916\) 1.35882 + 7.81734i 0.0448967 + 0.258292i
\(917\) −1.08633 + 5.92103i −0.0358737 + 0.195530i
\(918\) −0.361591 22.4920i −0.0119343 0.742348i
\(919\) 37.0569 + 21.3948i 1.22239 + 0.705749i 0.965428 0.260671i \(-0.0839439\pi\)
0.256966 + 0.966420i \(0.417277\pi\)
\(920\) −31.5738 8.58370i −1.04096 0.282996i
\(921\) −16.2134 + 41.5072i −0.534250 + 1.36771i
\(922\) −11.7787 + 25.1795i −0.387910 + 0.829242i
\(923\) −23.3846 + 40.5034i −0.769715 + 1.33318i
\(924\) −19.0204 + 47.3812i −0.625724 + 1.55873i
\(925\) −5.05639 8.75793i −0.166253 0.287959i
\(926\) 4.79548 0.413677i 0.157589 0.0135943i
\(927\) −5.25379 + 23.3644i −0.172557 + 0.767389i
\(928\) 13.7476 + 29.9559i 0.451288 + 0.983350i
\(929\) 55.0800i 1.80712i 0.428464 + 0.903559i \(0.359055\pi\)
−0.428464 + 0.903559i \(0.640945\pi\)
\(930\) 3.09021 + 3.24573i 0.101332 + 0.106432i
\(931\) 19.8645 + 7.54294i 0.651031 + 0.247210i
\(932\) −30.5154 36.5469i −0.999565 1.19713i
\(933\) −3.28211 + 8.40238i −0.107451 + 0.275082i
\(934\) −3.39706 39.3798i −0.111155 1.28855i
\(935\) −37.9307 + 21.8993i −1.24047 + 0.716184i
\(936\) 27.9317 17.5339i 0.912975 0.573112i
\(937\) 48.4798i 1.58377i 0.610672 + 0.791883i \(0.290899\pi\)
−0.610672 + 0.791883i \(0.709101\pi\)
\(938\) 2.26157 23.6341i 0.0738427 0.771680i
\(939\) 6.58313 + 2.57148i 0.214832 + 0.0839170i
\(940\) 0.329285 + 1.89439i 0.0107401 + 0.0617881i
\(941\) 13.9275i 0.454024i 0.973892 + 0.227012i \(0.0728957\pi\)
−0.973892 + 0.227012i \(0.927104\pi\)
\(942\) 2.72775 0.659605i 0.0888749 0.0214911i
\(943\) 29.4754 0.959851
\(944\) −19.2647 16.3253i −0.627014 0.531344i
\(945\) −34.0098 + 9.49205i −1.10634 + 0.308776i
\(946\) 6.54444 4.57062i 0.212778 0.148604i
\(947\) 43.5427i 1.41495i −0.706740 0.707473i \(-0.749835\pi\)
0.706740 0.707473i \(-0.250165\pi\)
\(948\) 15.9245 18.0147i 0.517203 0.585091i
\(949\) −62.2334 −2.02018
\(950\) 6.20843 + 2.90423i 0.201428 + 0.0942256i
\(951\) 0.401780 1.02858i 0.0130286 0.0333540i
\(952\) 1.75533 + 22.8404i 0.0568907 + 0.740261i
\(953\) −44.2712 −1.43409 −0.717043 0.697029i \(-0.754505\pi\)
−0.717043 + 0.697029i \(0.754505\pi\)
\(954\) −6.44060 15.7371i −0.208522 0.509506i
\(955\) −24.7110 42.8007i −0.799629 1.38500i
\(956\) −12.4026 + 10.3557i −0.401127 + 0.334927i
\(957\) −52.3655 20.4548i −1.69274 0.661211i
\(958\) −2.84869 33.0230i −0.0920370 1.06692i
\(959\) 22.6855 8.07955i 0.732553 0.260902i
\(960\) 22.0307 + 27.9501i 0.711036 + 0.902085i
\(961\) −30.4926 −0.983631
\(962\) −14.7511 + 31.5338i −0.475596 + 1.01669i
\(963\) −8.52935 27.3390i −0.274854 0.880987i
\(964\) −31.1034 + 25.9702i −1.00177 + 0.836445i
\(965\) −23.5475 + 13.5952i −0.758022 + 0.437644i
\(966\) −1.62814 29.1442i −0.0523847 0.937698i
\(967\) 42.1020 + 24.3076i 1.35391 + 0.781680i 0.988795 0.149283i \(-0.0476965\pi\)
0.365114 + 0.930963i \(0.381030\pi\)
\(968\) −40.2114 + 39.9192i −1.29244 + 1.28305i
\(969\) −14.9913 5.85587i −0.481591 0.188118i
\(970\) −1.12017 12.9854i −0.0359665 0.416935i
\(971\) 14.2467 24.6760i 0.457198 0.791890i −0.541614 0.840627i \(-0.682186\pi\)
0.998812 + 0.0487375i \(0.0155198\pi\)
\(972\) 18.6851 24.9573i 0.599324 0.800507i
\(973\) 29.6663 10.5658i 0.951056 0.338723i
\(974\) 12.3430 26.3859i 0.395496 0.845459i
\(975\) −1.61905 10.6257i −0.0518510 0.340295i
\(976\) 23.8105 28.0977i 0.762156 0.899384i
\(977\) −26.7252 −0.855014 −0.427507 0.904012i \(-0.640608\pi\)
−0.427507 + 0.904012i \(0.640608\pi\)
\(978\) −1.90201 + 6.45993i −0.0608194 + 0.206566i
\(979\) −6.50351 11.2644i −0.207853 0.360012i
\(980\) 33.9846 11.7469i 1.08560 0.375241i
\(981\) −8.00102 + 35.5818i −0.255453 + 1.13604i
\(982\) −5.07968 + 0.438193i −0.162099 + 0.0139833i
\(983\) 0.109714 0.190029i 0.00349932 0.00606100i −0.864270 0.503027i \(-0.832219\pi\)
0.867770 + 0.496966i \(0.165553\pi\)
\(984\) −25.7564 19.0904i −0.821085 0.608578i
\(985\) −46.1174 + 26.6259i −1.46942 + 0.848372i
\(986\) −25.1306 + 2.16787i −0.800322 + 0.0690390i
\(987\) −1.51078 + 0.812357i −0.0480888 + 0.0258576i
\(988\) −4.04081 23.2469i −0.128555 0.739582i
\(989\) −2.28185 + 3.95228i −0.0725586 + 0.125675i
\(990\) −60.1493 8.17798i −1.91167 0.259913i
\(991\) 21.3172 12.3075i 0.677165 0.390961i −0.121621 0.992577i \(-0.538809\pi\)
0.798786 + 0.601615i \(0.205476\pi\)
\(992\) 4.01208 + 0.375596i 0.127384 + 0.0119252i
\(993\) −1.27875 0.499502i −0.0405800 0.0158512i
\(994\) 4.28889 44.8202i 0.136035 1.42161i
\(995\) −38.0146 21.9478i −1.20514 0.695790i
\(996\) 6.75328 33.2655i 0.213986 1.05406i
\(997\) 38.8835 + 22.4494i 1.23145 + 0.710979i 0.967332 0.253511i \(-0.0815855\pi\)
0.264119 + 0.964490i \(0.414919\pi\)
\(998\) −12.6394 + 27.0194i −0.400093 + 0.855286i
\(999\) −2.30111 + 32.8306i −0.0728038 + 1.03871i
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 252.2.bj.b.103.10 yes 84
3.2 odd 2 756.2.bj.b.523.33 84
4.3 odd 2 inner 252.2.bj.b.103.9 yes 84
7.3 odd 6 252.2.n.b.31.19 84
9.2 odd 6 756.2.n.b.19.6 84
9.7 even 3 252.2.n.b.187.37 yes 84
12.11 even 2 756.2.bj.b.523.34 84
21.17 even 6 756.2.n.b.199.24 84
28.3 even 6 252.2.n.b.31.37 yes 84
36.7 odd 6 252.2.n.b.187.19 yes 84
36.11 even 6 756.2.n.b.19.24 84
63.38 even 6 756.2.bj.b.451.33 84
63.52 odd 6 inner 252.2.bj.b.115.10 yes 84
84.59 odd 6 756.2.n.b.199.6 84
252.115 even 6 inner 252.2.bj.b.115.9 yes 84
252.227 odd 6 756.2.bj.b.451.34 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
252.2.n.b.31.19 84 7.3 odd 6
252.2.n.b.31.37 yes 84 28.3 even 6
252.2.n.b.187.19 yes 84 36.7 odd 6
252.2.n.b.187.37 yes 84 9.7 even 3
252.2.bj.b.103.9 yes 84 4.3 odd 2 inner
252.2.bj.b.103.10 yes 84 1.1 even 1 trivial
252.2.bj.b.115.9 yes 84 252.115 even 6 inner
252.2.bj.b.115.10 yes 84 63.52 odd 6 inner
756.2.n.b.19.6 84 9.2 odd 6
756.2.n.b.19.24 84 36.11 even 6
756.2.n.b.199.6 84 84.59 odd 6
756.2.n.b.199.24 84 21.17 even 6
756.2.bj.b.451.33 84 63.38 even 6
756.2.bj.b.451.34 84 252.227 odd 6
756.2.bj.b.523.33 84 3.2 odd 2
756.2.bj.b.523.34 84 12.11 even 2