Properties

Label 315.2.bs.e.52.17
Level $315$
Weight $2$
Character 315.52
Analytic conductor $2.515$
Analytic rank $0$
Dimension $160$
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] = [315,2,Mod(52,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([8, 3, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.52");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 315.bs (of order \(12\), degree \(4\), 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: \(2.51528766367\)
Analytic rank: \(0\)
Dimension: \(160\)
Relative dimension: \(40\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 52.17
Character \(\chi\) \(=\) 315.52
Dual form 315.2.bs.e.103.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.333535 - 0.333535i) q^{2} +(0.667654 - 1.59820i) q^{3} -1.77751i q^{4} +(1.47915 - 1.67694i) q^{5} +(-0.755740 + 0.310369i) q^{6} +(2.25720 - 1.38023i) q^{7} +(-1.25993 + 1.25993i) q^{8} +(-2.10848 - 2.13409i) q^{9} +O(q^{10})\) \(q+(-0.333535 - 0.333535i) q^{2} +(0.667654 - 1.59820i) q^{3} -1.77751i q^{4} +(1.47915 - 1.67694i) q^{5} +(-0.755740 + 0.310369i) q^{6} +(2.25720 - 1.38023i) q^{7} +(-1.25993 + 1.25993i) q^{8} +(-2.10848 - 2.13409i) q^{9} +(-1.05266 + 0.0659706i) q^{10} +(2.19142 + 3.79566i) q^{11} +(-2.84081 - 1.18676i) q^{12} +(-0.658316 + 2.45687i) q^{13} +(-1.21321 - 0.292499i) q^{14} +(-1.69252 - 3.48359i) q^{15} -2.71456 q^{16} +(1.24657 + 4.65226i) q^{17} +(-0.00854215 + 1.41504i) q^{18} +(0.572230 + 0.991131i) q^{19} +(-2.98077 - 2.62920i) q^{20} +(-0.698856 - 4.52897i) q^{21} +(0.535068 - 1.99690i) q^{22} +(0.794370 + 2.96463i) q^{23} +(1.17242 + 2.85482i) q^{24} +(-0.624250 - 4.96088i) q^{25} +(1.03902 - 0.599880i) q^{26} +(-4.81843 + 1.94493i) q^{27} +(-2.45338 - 4.01220i) q^{28} +(-2.79231 - 1.61214i) q^{29} +(-0.597381 + 1.72641i) q^{30} -0.183484i q^{31} +(3.42526 + 3.42526i) q^{32} +(7.52933 - 0.968144i) q^{33} +(1.13592 - 1.96746i) q^{34} +(1.02417 - 5.82676i) q^{35} +(-3.79336 + 3.74784i) q^{36} +(-0.855220 + 3.19173i) q^{37} +(0.139718 - 0.521435i) q^{38} +(3.48704 + 2.69246i) q^{39} +(0.249205 + 3.97645i) q^{40} +(4.26796 - 2.46411i) q^{41} +(-1.27748 + 1.74366i) q^{42} +(-2.74125 - 10.2305i) q^{43} +(6.74681 - 3.89528i) q^{44} +(-6.69748 + 0.379158i) q^{45} +(0.723857 - 1.25376i) q^{46} +(-5.98299 + 5.98299i) q^{47} +(-1.81239 + 4.33840i) q^{48} +(3.18992 - 6.23093i) q^{49} +(-1.44642 + 1.86283i) q^{50} +(8.26751 + 1.11383i) q^{51} +(4.36711 + 1.17016i) q^{52} +(2.39192 + 8.92678i) q^{53} +(2.25581 + 0.958411i) q^{54} +(9.60652 + 1.93945i) q^{55} +(-1.10492 + 4.58291i) q^{56} +(1.96608 - 0.252804i) q^{57} +(0.393627 + 1.46904i) q^{58} -4.65449 q^{59} +(-6.19210 + 3.00848i) q^{60} -8.65893i q^{61} +(-0.0611983 + 0.0611983i) q^{62} +(-7.70479 - 1.90688i) q^{63} +3.14423i q^{64} +(3.14627 + 4.73803i) q^{65} +(-2.83420 - 2.18838i) q^{66} +(6.82613 + 6.82613i) q^{67} +(8.26943 - 2.21579i) q^{68} +(5.26843 + 0.709786i) q^{69} +(-2.28502 + 1.60183i) q^{70} +3.16867 q^{71} +(5.34533 + 0.0322680i) q^{72} +(-12.9431 + 3.46809i) q^{73} +(1.34980 - 0.779306i) q^{74} +(-8.34525 - 2.31448i) q^{75} +(1.76174 - 1.01714i) q^{76} +(10.1854 + 5.54289i) q^{77} +(-0.265020 - 2.06108i) q^{78} -11.6692i q^{79} +(-4.01523 + 4.55215i) q^{80} +(-0.108656 + 8.99934i) q^{81} +(-2.24538 - 0.601647i) q^{82} +(-9.05156 + 2.42536i) q^{83} +(-8.05029 + 1.24222i) q^{84} +(9.64541 + 4.79095i) q^{85} +(-2.49792 + 4.32653i) q^{86} +(-4.44082 + 3.38631i) q^{87} +(-7.54330 - 2.02122i) q^{88} +(-2.18123 - 3.77800i) q^{89} +(2.36030 + 2.10738i) q^{90} +(1.90510 + 6.45428i) q^{91} +(5.26965 - 1.41200i) q^{92} +(-0.293244 - 0.122504i) q^{93} +3.99107 q^{94} +(2.50848 + 0.506434i) q^{95} +(7.76113 - 3.18736i) q^{96} +(4.14520 + 15.4701i) q^{97} +(-3.14218 + 1.01428i) q^{98} +(3.47970 - 12.6797i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 160 q + 4 q^{2} - 18 q^{3} - 6 q^{5} + 24 q^{6} - 16 q^{8} - 24 q^{10} - 16 q^{11} - 30 q^{12} + 16 q^{15} - 152 q^{16} - 6 q^{17} + 58 q^{18} + 60 q^{20} - 36 q^{21} + 8 q^{22} + 8 q^{23} + 2 q^{25} - 36 q^{26} - 36 q^{27} + 22 q^{28} - 26 q^{30} + 12 q^{32} - 6 q^{33} - 36 q^{35} - 32 q^{36} - 4 q^{37} - 18 q^{38} - 6 q^{40} - 12 q^{41} - 28 q^{42} - 4 q^{43} - 54 q^{45} - 16 q^{46} - 18 q^{48} - 44 q^{50} + 80 q^{51} + 54 q^{52} + 8 q^{53} + 148 q^{56} - 4 q^{57} + 28 q^{58} + 104 q^{60} - 60 q^{63} - 124 q^{65} + 36 q^{66} - 24 q^{67} + 42 q^{68} - 34 q^{70} - 40 q^{71} + 70 q^{72} + 36 q^{73} - 60 q^{75} + 96 q^{76} + 58 q^{77} - 62 q^{78} + 36 q^{80} + 8 q^{81} - 66 q^{82} - 138 q^{83} - 20 q^{85} - 16 q^{86} + 102 q^{87} + 46 q^{88} + 18 q^{90} - 48 q^{91} - 26 q^{92} + 82 q^{93} + 188 q^{95} - 48 q^{96} + 48 q^{97} + 102 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(136\) \(281\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.333535 0.333535i −0.235845 0.235845i 0.579282 0.815127i \(-0.303333\pi\)
−0.815127 + 0.579282i \(0.803333\pi\)
\(3\) 0.667654 1.59820i 0.385470 0.922720i
\(4\) 1.77751i 0.888755i
\(5\) 1.47915 1.67694i 0.661495 0.749950i
\(6\) −0.755740 + 0.310369i −0.308530 + 0.126708i
\(7\) 2.25720 1.38023i 0.853142 0.521679i
\(8\) −1.25993 + 1.25993i −0.445453 + 0.445453i
\(9\) −2.10848 2.13409i −0.702825 0.711362i
\(10\) −1.05266 + 0.0659706i −0.332882 + 0.0208617i
\(11\) 2.19142 + 3.79566i 0.660739 + 1.14443i 0.980422 + 0.196909i \(0.0630903\pi\)
−0.319683 + 0.947525i \(0.603576\pi\)
\(12\) −2.84081 1.18676i −0.820072 0.342588i
\(13\) −0.658316 + 2.45687i −0.182584 + 0.681413i 0.812551 + 0.582890i \(0.198078\pi\)
−0.995135 + 0.0985225i \(0.968588\pi\)
\(14\) −1.21321 0.292499i −0.324244 0.0781738i
\(15\) −1.69252 3.48359i −0.437008 0.899458i
\(16\) −2.71456 −0.678639
\(17\) 1.24657 + 4.65226i 0.302337 + 1.12834i 0.935213 + 0.354085i \(0.115208\pi\)
−0.632876 + 0.774253i \(0.718126\pi\)
\(18\) −0.00854215 + 1.41504i −0.00201340 + 0.333529i
\(19\) 0.572230 + 0.991131i 0.131279 + 0.227381i 0.924170 0.381982i \(-0.124758\pi\)
−0.792891 + 0.609363i \(0.791425\pi\)
\(20\) −2.98077 2.62920i −0.666521 0.587906i
\(21\) −0.698856 4.52897i −0.152503 0.988303i
\(22\) 0.535068 1.99690i 0.114077 0.425740i
\(23\) 0.794370 + 2.96463i 0.165638 + 0.618168i 0.997958 + 0.0638731i \(0.0203453\pi\)
−0.832320 + 0.554295i \(0.812988\pi\)
\(24\) 1.17242 + 2.85482i 0.239319 + 0.582737i
\(25\) −0.624250 4.96088i −0.124850 0.992176i
\(26\) 1.03902 0.599880i 0.203769 0.117646i
\(27\) −4.81843 + 1.94493i −0.927307 + 0.374302i
\(28\) −2.45338 4.01220i −0.463645 0.758234i
\(29\) −2.79231 1.61214i −0.518519 0.299367i 0.217810 0.975991i \(-0.430109\pi\)
−0.736328 + 0.676624i \(0.763442\pi\)
\(30\) −0.597381 + 1.72641i −0.109066 + 0.315198i
\(31\) 0.183484i 0.0329547i −0.999864 0.0164773i \(-0.994755\pi\)
0.999864 0.0164773i \(-0.00524514\pi\)
\(32\) 3.42526 + 3.42526i 0.605506 + 0.605506i
\(33\) 7.52933 0.968144i 1.31069 0.168532i
\(34\) 1.13592 1.96746i 0.194808 0.337417i
\(35\) 1.02417 5.82676i 0.173116 0.984902i
\(36\) −3.79336 + 3.74784i −0.632227 + 0.624639i
\(37\) −0.855220 + 3.19173i −0.140597 + 0.524716i 0.859315 + 0.511447i \(0.170890\pi\)
−0.999912 + 0.0132691i \(0.995776\pi\)
\(38\) 0.139718 0.521435i 0.0226653 0.0845879i
\(39\) 3.48704 + 2.69246i 0.558373 + 0.431138i
\(40\) 0.249205 + 3.97645i 0.0394027 + 0.628732i
\(41\) 4.26796 2.46411i 0.666543 0.384829i −0.128223 0.991745i \(-0.540927\pi\)
0.794765 + 0.606917i \(0.207594\pi\)
\(42\) −1.27748 + 1.74366i −0.197119 + 0.269053i
\(43\) −2.74125 10.2305i −0.418037 1.56014i −0.778673 0.627430i \(-0.784107\pi\)
0.360635 0.932707i \(-0.382560\pi\)
\(44\) 6.74681 3.89528i 1.01712 0.587235i
\(45\) −6.69748 + 0.379158i −0.998401 + 0.0565215i
\(46\) 0.723857 1.25376i 0.106727 0.184856i
\(47\) −5.98299 + 5.98299i −0.872709 + 0.872709i −0.992767 0.120058i \(-0.961692\pi\)
0.120058 + 0.992767i \(0.461692\pi\)
\(48\) −1.81239 + 4.33840i −0.261595 + 0.626194i
\(49\) 3.18992 6.23093i 0.455702 0.890132i
\(50\) −1.44642 + 1.86283i −0.204554 + 0.263445i
\(51\) 8.26751 + 1.11383i 1.15768 + 0.155968i
\(52\) 4.36711 + 1.17016i 0.605609 + 0.162272i
\(53\) 2.39192 + 8.92678i 0.328556 + 1.22619i 0.910689 + 0.413093i \(0.135552\pi\)
−0.582133 + 0.813094i \(0.697782\pi\)
\(54\) 2.25581 + 0.958411i 0.306978 + 0.130423i
\(55\) 9.60652 + 1.93945i 1.29534 + 0.261515i
\(56\) −1.10492 + 4.58291i −0.147651 + 0.612418i
\(57\) 1.96608 0.252804i 0.260413 0.0334847i
\(58\) 0.393627 + 1.46904i 0.0516858 + 0.192894i
\(59\) −4.65449 −0.605963 −0.302982 0.952996i \(-0.597982\pi\)
−0.302982 + 0.952996i \(0.597982\pi\)
\(60\) −6.19210 + 3.00848i −0.799397 + 0.388392i
\(61\) 8.65893i 1.10866i −0.832296 0.554331i \(-0.812974\pi\)
0.832296 0.554331i \(-0.187026\pi\)
\(62\) −0.0611983 + 0.0611983i −0.00777219 + 0.00777219i
\(63\) −7.70479 1.90688i −0.970713 0.240244i
\(64\) 3.14423i 0.393029i
\(65\) 3.14627 + 4.73803i 0.390247 + 0.587680i
\(66\) −2.83420 2.18838i −0.348866 0.269371i
\(67\) 6.82613 + 6.82613i 0.833945 + 0.833945i 0.988054 0.154109i \(-0.0492508\pi\)
−0.154109 + 0.988054i \(0.549251\pi\)
\(68\) 8.26943 2.21579i 1.00282 0.268704i
\(69\) 5.26843 + 0.709786i 0.634244 + 0.0854481i
\(70\) −2.28502 + 1.60183i −0.273112 + 0.191455i
\(71\) 3.16867 0.376052 0.188026 0.982164i \(-0.439791\pi\)
0.188026 + 0.982164i \(0.439791\pi\)
\(72\) 5.34533 + 0.0322680i 0.629954 + 0.00380283i
\(73\) −12.9431 + 3.46809i −1.51487 + 0.405909i −0.918051 0.396463i \(-0.870237\pi\)
−0.596824 + 0.802372i \(0.703571\pi\)
\(74\) 1.34980 0.779306i 0.156911 0.0905924i
\(75\) −8.34525 2.31448i −0.963626 0.267253i
\(76\) 1.76174 1.01714i 0.202086 0.116674i
\(77\) 10.1854 + 5.54289i 1.16073 + 0.631671i
\(78\) −0.265020 2.06108i −0.0300076 0.233371i
\(79\) 11.6692i 1.31289i −0.754376 0.656443i \(-0.772060\pi\)
0.754376 0.656443i \(-0.227940\pi\)
\(80\) −4.01523 + 4.55215i −0.448916 + 0.508946i
\(81\) −0.108656 + 8.99934i −0.0120729 + 0.999927i
\(82\) −2.24538 0.601647i −0.247960 0.0664408i
\(83\) −9.05156 + 2.42536i −0.993538 + 0.266218i −0.718736 0.695283i \(-0.755279\pi\)
−0.274802 + 0.961501i \(0.588612\pi\)
\(84\) −8.05029 + 1.24222i −0.878359 + 0.135538i
\(85\) 9.64541 + 4.79095i 1.04619 + 0.519652i
\(86\) −2.49792 + 4.32653i −0.269358 + 0.466542i
\(87\) −4.44082 + 3.38631i −0.476105 + 0.363051i
\(88\) −7.54330 2.02122i −0.804119 0.215463i
\(89\) −2.18123 3.77800i −0.231210 0.400467i 0.726955 0.686685i \(-0.240935\pi\)
−0.958164 + 0.286218i \(0.907602\pi\)
\(90\) 2.36030 + 2.10738i 0.248798 + 0.222137i
\(91\) 1.90510 + 6.45428i 0.199709 + 0.676592i
\(92\) 5.26965 1.41200i 0.549399 0.147211i
\(93\) −0.293244 0.122504i −0.0304080 0.0127030i
\(94\) 3.99107 0.411648
\(95\) 2.50848 + 0.506434i 0.257364 + 0.0519590i
\(96\) 7.76113 3.18736i 0.792117 0.325308i
\(97\) 4.14520 + 15.4701i 0.420882 + 1.57075i 0.772755 + 0.634704i \(0.218878\pi\)
−0.351874 + 0.936047i \(0.614455\pi\)
\(98\) −3.14218 + 1.01428i −0.317408 + 0.102458i
\(99\) 3.47970 12.6797i 0.349723 1.27436i
\(100\) −8.81801 + 1.10961i −0.881801 + 0.110961i
\(101\) 3.23368 1.86696i 0.321763 0.185770i −0.330415 0.943836i \(-0.607189\pi\)
0.652178 + 0.758066i \(0.273855\pi\)
\(102\) −2.38600 3.12900i −0.236249 0.309817i
\(103\) −0.663063 + 0.177667i −0.0653335 + 0.0175061i −0.291338 0.956620i \(-0.594100\pi\)
0.226004 + 0.974126i \(0.427434\pi\)
\(104\) −2.26605 3.92492i −0.222205 0.384870i
\(105\) −8.62852 5.52708i −0.842058 0.539388i
\(106\) 2.17960 3.77518i 0.211702 0.366678i
\(107\) 3.71766 13.8745i 0.359399 1.34130i −0.515457 0.856915i \(-0.672378\pi\)
0.874857 0.484382i \(-0.160955\pi\)
\(108\) 3.45713 + 8.56480i 0.332663 + 0.824148i
\(109\) 15.7341 + 9.08408i 1.50705 + 0.870097i 0.999966 + 0.00820196i \(0.00261079\pi\)
0.507086 + 0.861895i \(0.330723\pi\)
\(110\) −2.55723 3.85098i −0.243823 0.367177i
\(111\) 4.53002 + 3.49778i 0.429970 + 0.331995i
\(112\) −6.12730 + 3.74672i −0.578976 + 0.354032i
\(113\) 5.19080 + 1.39087i 0.488310 + 0.130842i 0.494569 0.869138i \(-0.335326\pi\)
−0.00625951 + 0.999980i \(0.501992\pi\)
\(114\) −0.740073 0.571435i −0.0693142 0.0535198i
\(115\) 6.14649 + 3.05301i 0.573163 + 0.284695i
\(116\) −2.86559 + 4.96335i −0.266064 + 0.460836i
\(117\) 6.63122 3.77535i 0.613056 0.349031i
\(118\) 1.55243 + 1.55243i 0.142913 + 0.142913i
\(119\) 9.23495 + 8.78053i 0.846567 + 0.804910i
\(120\) 6.52154 + 2.25661i 0.595332 + 0.206000i
\(121\) −4.10467 + 7.10950i −0.373152 + 0.646319i
\(122\) −2.88805 + 2.88805i −0.261472 + 0.261472i
\(123\) −1.08861 8.46621i −0.0981568 0.763373i
\(124\) −0.326144 −0.0292886
\(125\) −9.24245 6.29104i −0.826670 0.562688i
\(126\) 1.93381 + 3.20583i 0.172277 + 0.285598i
\(127\) −10.5696 10.5696i −0.937904 0.937904i 0.0602778 0.998182i \(-0.480801\pi\)
−0.998182 + 0.0602778i \(0.980801\pi\)
\(128\) 7.89923 7.89923i 0.698200 0.698200i
\(129\) −18.1806 2.44937i −1.60071 0.215655i
\(130\) 0.530905 2.62969i 0.0465634 0.230639i
\(131\) −19.5185 11.2690i −1.70534 0.984577i −0.940145 0.340775i \(-0.889311\pi\)
−0.765192 0.643802i \(-0.777356\pi\)
\(132\) −1.72088 13.3834i −0.149784 1.16488i
\(133\) 2.65963 + 1.44737i 0.230619 + 0.125503i
\(134\) 4.55350i 0.393363i
\(135\) −3.86563 + 10.9570i −0.332700 + 0.943033i
\(136\) −7.43211 4.29093i −0.637298 0.367944i
\(137\) 3.94806 14.7343i 0.337305 1.25884i −0.564043 0.825745i \(-0.690755\pi\)
0.901348 0.433095i \(-0.142579\pi\)
\(138\) −1.52047 1.99394i −0.129431 0.169736i
\(139\) −3.11124 5.38882i −0.263892 0.457074i 0.703381 0.710813i \(-0.251673\pi\)
−0.967273 + 0.253739i \(0.918339\pi\)
\(140\) −10.3571 1.82046i −0.875336 0.153857i
\(141\) 5.56744 + 13.5566i 0.468863 + 1.14167i
\(142\) −1.05686 1.05686i −0.0886899 0.0886899i
\(143\) −10.7681 + 2.88530i −0.900472 + 0.241281i
\(144\) 5.72358 + 5.79310i 0.476965 + 0.482758i
\(145\) −6.83370 + 2.29794i −0.567508 + 0.190834i
\(146\) 5.47370 + 3.16024i 0.453007 + 0.261543i
\(147\) −7.82850 9.25822i −0.645683 0.763605i
\(148\) 5.67332 + 1.52016i 0.466344 + 0.124957i
\(149\) −4.15088 2.39651i −0.340053 0.196330i 0.320242 0.947336i \(-0.396236\pi\)
−0.660295 + 0.751006i \(0.729569\pi\)
\(150\) 2.01147 + 3.55539i 0.164236 + 0.290296i
\(151\) 1.65388 + 2.86460i 0.134590 + 0.233118i 0.925441 0.378892i \(-0.123695\pi\)
−0.790850 + 0.612009i \(0.790361\pi\)
\(152\) −1.96973 0.527786i −0.159766 0.0428091i
\(153\) 7.29996 12.4695i 0.590167 1.00810i
\(154\) −1.54843 5.24592i −0.124776 0.422728i
\(155\) −0.307691 0.271400i −0.0247144 0.0217993i
\(156\) 4.78587 6.19824i 0.383176 0.496256i
\(157\) 2.11334 2.11334i 0.168663 0.168663i −0.617728 0.786392i \(-0.711947\pi\)
0.786392 + 0.617728i \(0.211947\pi\)
\(158\) −3.89208 + 3.89208i −0.309637 + 0.309637i
\(159\) 15.8637 + 2.13723i 1.25808 + 0.169493i
\(160\) 10.8104 0.677490i 0.854638 0.0535603i
\(161\) 5.88493 + 5.59535i 0.463797 + 0.440975i
\(162\) 3.03783 2.96535i 0.238675 0.232980i
\(163\) 6.23321 + 1.67018i 0.488222 + 0.130819i 0.494529 0.869161i \(-0.335341\pi\)
−0.00630629 + 0.999980i \(0.502007\pi\)
\(164\) −4.37997 7.58633i −0.342018 0.592393i
\(165\) 9.51346 14.0582i 0.740622 1.09443i
\(166\) 3.82795 + 2.21007i 0.297107 + 0.171535i
\(167\) −9.32441 2.49847i −0.721545 0.193337i −0.120684 0.992691i \(-0.538509\pi\)
−0.600861 + 0.799354i \(0.705175\pi\)
\(168\) 6.58670 + 4.82568i 0.508175 + 0.372309i
\(169\) 5.65551 + 3.26521i 0.435039 + 0.251170i
\(170\) −1.61913 4.81503i −0.124182 0.369296i
\(171\) 0.908627 3.31096i 0.0694845 0.253196i
\(172\) −18.1848 + 4.87261i −1.38658 + 0.371533i
\(173\) −1.94670 1.94670i −0.148005 0.148005i 0.629221 0.777226i \(-0.283374\pi\)
−0.777226 + 0.629221i \(0.783374\pi\)
\(174\) 2.61062 + 0.351714i 0.197911 + 0.0266634i
\(175\) −8.25622 10.3361i −0.624112 0.781335i
\(176\) −5.94874 10.3035i −0.448403 0.776658i
\(177\) −3.10759 + 7.43880i −0.233581 + 0.559135i
\(178\) −0.532578 + 1.98761i −0.0399184 + 0.148978i
\(179\) −10.9309 6.31098i −0.817016 0.471705i 0.0323701 0.999476i \(-0.489694\pi\)
−0.849387 + 0.527771i \(0.823028\pi\)
\(180\) 0.673957 + 11.9048i 0.0502338 + 0.887334i
\(181\) 9.38149i 0.697320i −0.937249 0.348660i \(-0.886637\pi\)
0.937249 0.348660i \(-0.113363\pi\)
\(182\) 1.51731 2.78814i 0.112470 0.206671i
\(183\) −13.8387 5.78117i −1.02298 0.427356i
\(184\) −4.73608 2.73438i −0.349148 0.201581i
\(185\) 4.08733 + 6.15518i 0.300507 + 0.452538i
\(186\) 0.0569477 + 0.138666i 0.00417561 + 0.0101675i
\(187\) −14.9266 + 14.9266i −1.09154 + 1.09154i
\(188\) 10.6348 + 10.6348i 0.775624 + 0.775624i
\(189\) −8.19170 + 11.0407i −0.595859 + 0.803089i
\(190\) −0.667751 1.00558i −0.0484438 0.0729523i
\(191\) −18.1657 −1.31442 −0.657211 0.753707i \(-0.728264\pi\)
−0.657211 + 0.753707i \(0.728264\pi\)
\(192\) 5.02510 + 2.09926i 0.362655 + 0.151501i
\(193\) 3.51448 3.51448i 0.252978 0.252978i −0.569213 0.822190i \(-0.692752\pi\)
0.822190 + 0.569213i \(0.192752\pi\)
\(194\) 3.77725 6.54239i 0.271191 0.469716i
\(195\) 9.67293 1.86501i 0.692693 0.133556i
\(196\) −11.0755 5.67010i −0.791109 0.405007i
\(197\) 11.6177 + 11.6177i 0.827724 + 0.827724i 0.987202 0.159478i \(-0.0509810\pi\)
−0.159478 + 0.987202i \(0.550981\pi\)
\(198\) −5.38973 + 3.06853i −0.383032 + 0.218071i
\(199\) 4.00776 6.94165i 0.284103 0.492080i −0.688288 0.725437i \(-0.741638\pi\)
0.972391 + 0.233357i \(0.0749710\pi\)
\(200\) 7.03687 + 5.46385i 0.497582 + 0.386353i
\(201\) 15.4670 6.35202i 1.09096 0.448037i
\(202\) −1.70124 0.455846i −0.119699 0.0320732i
\(203\) −8.52793 + 0.215111i −0.598544 + 0.0150978i
\(204\) 1.97985 14.6956i 0.138617 1.02890i
\(205\) 2.18078 10.8019i 0.152312 0.754436i
\(206\) 0.280413 + 0.161896i 0.0195373 + 0.0112799i
\(207\) 4.65187 7.94610i 0.323327 0.552292i
\(208\) 1.78704 6.66931i 0.123909 0.462434i
\(209\) −2.50800 + 4.34398i −0.173482 + 0.300479i
\(210\) 1.03444 + 4.72138i 0.0713831 + 0.325806i
\(211\) 10.7899 + 18.6886i 0.742807 + 1.28658i 0.951212 + 0.308537i \(0.0998392\pi\)
−0.208406 + 0.978042i \(0.566827\pi\)
\(212\) 15.8674 4.25166i 1.08978 0.292006i
\(213\) 2.11558 5.06417i 0.144957 0.346991i
\(214\) −5.86759 + 3.38765i −0.401100 + 0.231575i
\(215\) −21.2106 10.5355i −1.44655 0.718515i
\(216\) 3.62041 8.52136i 0.246337 0.579805i
\(217\) −0.253250 0.414160i −0.0171918 0.0281150i
\(218\) −2.21801 8.27772i −0.150223 0.560638i
\(219\) −3.09881 + 23.0011i −0.209398 + 1.55427i
\(220\) 3.44739 17.0757i 0.232423 1.15124i
\(221\) −12.2506 −0.824066
\(222\) −0.344288 2.67755i −0.0231071 0.179705i
\(223\) −17.7714 + 4.76182i −1.19006 + 0.318875i −0.798909 0.601452i \(-0.794589\pi\)
−0.391149 + 0.920327i \(0.627922\pi\)
\(224\) 12.4592 + 3.00385i 0.832462 + 0.200703i
\(225\) −9.27073 + 11.7921i −0.618049 + 0.786140i
\(226\) −1.26741 2.19522i −0.0843068 0.146024i
\(227\) 12.2817 + 3.29086i 0.815162 + 0.218422i 0.642230 0.766512i \(-0.278009\pi\)
0.172932 + 0.984934i \(0.444676\pi\)
\(228\) −0.449362 3.49472i −0.0297597 0.231443i
\(229\) −13.5544 + 23.4769i −0.895701 + 1.55140i −0.0627668 + 0.998028i \(0.519992\pi\)
−0.832934 + 0.553372i \(0.813341\pi\)
\(230\) −1.03178 3.06835i −0.0680338 0.202321i
\(231\) 15.6589 12.5775i 1.03028 0.827540i
\(232\) 5.54930 1.48693i 0.364329 0.0976218i
\(233\) 17.2072 + 4.61065i 1.12728 + 0.302054i 0.773826 0.633398i \(-0.218340\pi\)
0.353454 + 0.935452i \(0.385007\pi\)
\(234\) −3.47095 0.952532i −0.226903 0.0622690i
\(235\) 1.18339 + 18.8828i 0.0771958 + 1.23178i
\(236\) 8.27340i 0.538553i
\(237\) −18.6497 7.79098i −1.21143 0.506078i
\(238\) −0.151567 6.00879i −0.00982465 0.389492i
\(239\) 13.1142 7.57150i 0.848289 0.489760i −0.0117841 0.999931i \(-0.503751\pi\)
0.860073 + 0.510171i \(0.170418\pi\)
\(240\) 4.59445 + 9.45639i 0.296571 + 0.610407i
\(241\) 6.06381 3.50094i 0.390604 0.225515i −0.291818 0.956474i \(-0.594260\pi\)
0.682422 + 0.730959i \(0.260927\pi\)
\(242\) 3.74032 1.00222i 0.240437 0.0644248i
\(243\) 14.3102 + 6.18210i 0.917999 + 0.396582i
\(244\) −15.3913 −0.985328
\(245\) −5.73053 14.5657i −0.366110 0.930572i
\(246\) −2.46069 + 3.18687i −0.156888 + 0.203187i
\(247\) −2.81179 + 0.753416i −0.178910 + 0.0479387i
\(248\) 0.231177 + 0.231177i 0.0146798 + 0.0146798i
\(249\) −2.16711 + 16.0855i −0.137335 + 1.01938i
\(250\) 0.984397 + 5.18096i 0.0622587 + 0.327672i
\(251\) 6.97675i 0.440369i 0.975458 + 0.220184i \(0.0706659\pi\)
−0.975458 + 0.220184i \(0.929334\pi\)
\(252\) −3.38949 + 13.6953i −0.213518 + 0.862725i
\(253\) −9.51191 + 9.51191i −0.598009 + 0.598009i
\(254\) 7.05068i 0.442399i
\(255\) 14.0967 12.2166i 0.882769 0.765032i
\(256\) 1.01912 0.0636951
\(257\) −0.592855 2.21257i −0.0369813 0.138016i 0.944967 0.327166i \(-0.106094\pi\)
−0.981948 + 0.189150i \(0.939427\pi\)
\(258\) 5.24691 + 6.88080i 0.326658 + 0.428380i
\(259\) 2.47492 + 8.38477i 0.153784 + 0.521004i
\(260\) 8.42188 5.59253i 0.522303 0.346834i
\(261\) 2.44707 + 9.35819i 0.151470 + 0.579257i
\(262\) 2.75149 + 10.2687i 0.169987 + 0.634402i
\(263\) −4.06739 1.08985i −0.250806 0.0672033i 0.131225 0.991353i \(-0.458109\pi\)
−0.382032 + 0.924149i \(0.624775\pi\)
\(264\) −8.26663 + 10.7062i −0.508776 + 0.658922i
\(265\) 18.5077 + 9.19290i 1.13692 + 0.564716i
\(266\) −0.404330 1.36983i −0.0247911 0.0839895i
\(267\) −7.49430 + 0.963640i −0.458644 + 0.0589738i
\(268\) 12.1335 12.1335i 0.741172 0.741172i
\(269\) −11.9594 + 20.7143i −0.729177 + 1.26297i 0.228054 + 0.973649i \(0.426764\pi\)
−0.957231 + 0.289324i \(0.906570\pi\)
\(270\) 4.94388 2.36523i 0.300875 0.143944i
\(271\) −3.41746 + 1.97307i −0.207596 + 0.119855i −0.600193 0.799855i \(-0.704910\pi\)
0.392598 + 0.919710i \(0.371576\pi\)
\(272\) −3.38388 12.6288i −0.205178 0.765735i
\(273\) 11.5872 + 1.26450i 0.701287 + 0.0765309i
\(274\) −6.23123 + 3.59760i −0.376442 + 0.217339i
\(275\) 17.4618 13.2408i 1.05299 0.798452i
\(276\) 1.26165 9.36468i 0.0759424 0.563688i
\(277\) −4.32841 + 16.1538i −0.260069 + 0.970590i 0.705131 + 0.709077i \(0.250888\pi\)
−0.965200 + 0.261513i \(0.915778\pi\)
\(278\) −0.759653 + 2.83506i −0.0455610 + 0.170036i
\(279\) −0.391571 + 0.386871i −0.0234427 + 0.0231614i
\(280\) 6.05093 + 8.63169i 0.361612 + 0.515842i
\(281\) −4.53249 + 7.85050i −0.270385 + 0.468321i −0.968961 0.247215i \(-0.920484\pi\)
0.698575 + 0.715537i \(0.253818\pi\)
\(282\) 2.66465 6.37852i 0.158678 0.379836i
\(283\) 13.4963 + 13.4963i 0.802269 + 0.802269i 0.983450 0.181181i \(-0.0579919\pi\)
−0.181181 + 0.983450i \(0.557992\pi\)
\(284\) 5.63234i 0.334218i
\(285\) 2.48418 3.67092i 0.147150 0.217447i
\(286\) 4.55388 + 2.62918i 0.269276 + 0.155467i
\(287\) 6.23260 11.4528i 0.367899 0.676035i
\(288\) 0.0877242 14.5319i 0.00516920 0.856299i
\(289\) −5.36714 + 3.09872i −0.315714 + 0.182277i
\(290\) 3.04572 + 1.51283i 0.178851 + 0.0888366i
\(291\) 27.4919 + 3.70382i 1.61160 + 0.217122i
\(292\) 6.16456 + 23.0065i 0.360754 + 1.34635i
\(293\) −4.73297 + 17.6637i −0.276503 + 1.03192i 0.678324 + 0.734763i \(0.262706\pi\)
−0.954827 + 0.297161i \(0.903960\pi\)
\(294\) −0.476863 + 5.69901i −0.0278112 + 0.332373i
\(295\) −6.88468 + 7.80530i −0.400841 + 0.454442i
\(296\) −2.94383 5.09887i −0.171107 0.296366i
\(297\) −17.9415 14.0269i −1.04107 0.813925i
\(298\) 0.585142 + 2.18378i 0.0338964 + 0.126503i
\(299\) −7.80665 −0.451470
\(300\) −4.11400 + 14.8338i −0.237522 + 0.856427i
\(301\) −20.3080 19.3087i −1.17054 1.11294i
\(302\) 0.403817 1.50707i 0.0232371 0.0867220i
\(303\) −0.824802 6.41454i −0.0473836 0.368506i
\(304\) −1.55335 2.69048i −0.0890908 0.154310i
\(305\) −14.5205 12.8078i −0.831441 0.733374i
\(306\) −6.59379 + 1.72421i −0.376942 + 0.0985664i
\(307\) 17.8602 17.8602i 1.01934 1.01934i 0.0195279 0.999809i \(-0.493784\pi\)
0.999809 0.0195279i \(-0.00621633\pi\)
\(308\) 9.85253 18.1046i 0.561400 1.03161i
\(309\) −0.158749 + 1.17833i −0.00903093 + 0.0670326i
\(310\) 0.0121045 + 0.193147i 0.000687492 + 0.0109700i
\(311\) 5.21765i 0.295866i 0.988997 + 0.147933i \(0.0472620\pi\)
−0.988997 + 0.147933i \(0.952738\pi\)
\(312\) −7.78573 + 1.00111i −0.440780 + 0.0566769i
\(313\) 4.91025 + 4.91025i 0.277543 + 0.277543i 0.832128 0.554584i \(-0.187123\pi\)
−0.554584 + 0.832128i \(0.687123\pi\)
\(314\) −1.40975 −0.0795567
\(315\) −14.5942 + 10.0999i −0.822292 + 0.569066i
\(316\) −20.7421 −1.16683
\(317\) −8.62273 8.62273i −0.484301 0.484301i 0.422201 0.906502i \(-0.361258\pi\)
−0.906502 + 0.422201i \(0.861258\pi\)
\(318\) −4.57827 6.00395i −0.256736 0.336685i
\(319\) 14.1315i 0.791214i
\(320\) 5.27268 + 4.65078i 0.294752 + 0.259986i
\(321\) −19.6921 15.2049i −1.09910 0.848655i
\(322\) −0.0965855 3.82907i −0.00538250 0.213386i
\(323\) −3.89767 + 3.89767i −0.216872 + 0.216872i
\(324\) 15.9964 + 0.193137i 0.888690 + 0.0107299i
\(325\) 12.5992 + 1.73213i 0.698877 + 0.0960811i
\(326\) −1.52193 2.63605i −0.0842917 0.145998i
\(327\) 25.0231 19.0812i 1.38378 1.05519i
\(328\) −2.27273 + 8.48193i −0.125490 + 0.468336i
\(329\) −5.24690 + 21.7627i −0.289271 + 1.19982i
\(330\) −7.86198 + 1.51584i −0.432788 + 0.0834445i
\(331\) −23.7736 −1.30671 −0.653356 0.757051i \(-0.726640\pi\)
−0.653356 + 0.757051i \(0.726640\pi\)
\(332\) 4.31110 + 16.0892i 0.236602 + 0.883011i
\(333\) 8.61463 4.90456i 0.472079 0.268768i
\(334\) 2.27669 + 3.94334i 0.124575 + 0.215770i
\(335\) 21.5439 1.35016i 1.17707 0.0737669i
\(336\) 1.89708 + 12.2942i 0.103494 + 0.670701i
\(337\) 4.41431 16.4744i 0.240463 0.897420i −0.735147 0.677908i \(-0.762887\pi\)
0.975610 0.219512i \(-0.0704465\pi\)
\(338\) −0.797247 2.97537i −0.0433645 0.161839i
\(339\) 5.68855 7.36731i 0.308960 0.400138i
\(340\) 8.51596 17.1448i 0.461843 0.929808i
\(341\) 0.696442 0.402091i 0.0377144 0.0217744i
\(342\) −1.40738 + 0.801263i −0.0761024 + 0.0433273i
\(343\) −1.39985 18.4673i −0.0755846 0.997139i
\(344\) 16.3435 + 9.43593i 0.881183 + 0.508751i
\(345\) 8.98305 7.78496i 0.483631 0.419128i
\(346\) 1.29859i 0.0698124i
\(347\) 6.11801 + 6.11801i 0.328432 + 0.328432i 0.851990 0.523558i \(-0.175396\pi\)
−0.523558 + 0.851990i \(0.675396\pi\)
\(348\) 6.01920 + 7.89359i 0.322663 + 0.423141i
\(349\) −8.10283 + 14.0345i −0.433735 + 0.751250i −0.997191 0.0748953i \(-0.976138\pi\)
0.563457 + 0.826145i \(0.309471\pi\)
\(350\) −0.693708 + 6.20118i −0.0370803 + 0.331467i
\(351\) −1.60639 13.1186i −0.0857429 0.700220i
\(352\) −5.49492 + 20.5073i −0.292880 + 1.09304i
\(353\) −2.12963 + 7.94789i −0.113349 + 0.423024i −0.999158 0.0410260i \(-0.986937\pi\)
0.885809 + 0.464049i \(0.153604\pi\)
\(354\) 3.51759 1.44461i 0.186958 0.0767801i
\(355\) 4.68693 5.31367i 0.248757 0.282020i
\(356\) −6.71543 + 3.87715i −0.355917 + 0.205489i
\(357\) 20.1988 8.89693i 1.06903 0.470876i
\(358\) 1.54092 + 5.75078i 0.0814399 + 0.303938i
\(359\) −5.59954 + 3.23290i −0.295533 + 0.170626i −0.640434 0.768013i \(-0.721246\pi\)
0.344902 + 0.938639i \(0.387912\pi\)
\(360\) 7.96065 8.91607i 0.419563 0.469918i
\(361\) 8.84511 15.3202i 0.465532 0.806325i
\(362\) −3.12905 + 3.12905i −0.164459 + 0.164459i
\(363\) 8.62190 + 11.3068i 0.452532 + 0.593452i
\(364\) 11.4725 3.38633i 0.601324 0.177492i
\(365\) −13.3290 + 26.8346i −0.697669 + 1.40459i
\(366\) 2.68746 + 6.54390i 0.140476 + 0.342055i
\(367\) −16.5797 4.44253i −0.865455 0.231898i −0.201334 0.979523i \(-0.564528\pi\)
−0.664121 + 0.747625i \(0.731194\pi\)
\(368\) −2.15636 8.04765i −0.112408 0.419513i
\(369\) −14.2575 3.91268i −0.742216 0.203686i
\(370\) 0.689700 3.41623i 0.0358558 0.177602i
\(371\) 17.7201 + 16.8481i 0.919981 + 0.874711i
\(372\) −0.217752 + 0.521243i −0.0112899 + 0.0270252i
\(373\) −0.582516 2.17398i −0.0301615 0.112564i 0.949204 0.314661i \(-0.101891\pi\)
−0.979365 + 0.202097i \(0.935224\pi\)
\(374\) 9.95709 0.514869
\(375\) −16.2251 + 10.5710i −0.837860 + 0.545885i
\(376\) 15.0763i 0.777501i
\(377\) 5.79904 5.79904i 0.298666 0.298666i
\(378\) 6.41466 0.950224i 0.329934 0.0488742i
\(379\) 1.63972i 0.0842266i −0.999113 0.0421133i \(-0.986591\pi\)
0.999113 0.0421133i \(-0.0134090\pi\)
\(380\) 0.900191 4.45884i 0.0461788 0.228734i
\(381\) −23.9492 + 9.83552i −1.22696 + 0.503889i
\(382\) 6.05888 + 6.05888i 0.309999 + 0.309999i
\(383\) 13.8954 3.72327i 0.710023 0.190250i 0.114308 0.993445i \(-0.463535\pi\)
0.595716 + 0.803195i \(0.296868\pi\)
\(384\) −7.35058 17.8985i −0.375108 0.913378i
\(385\) 24.3607 8.88151i 1.24154 0.452644i
\(386\) −2.34440 −0.119327
\(387\) −16.0529 + 27.4208i −0.816015 + 1.39388i
\(388\) 27.4983 7.36814i 1.39601 0.374060i
\(389\) −28.9749 + 16.7286i −1.46908 + 0.848176i −0.999399 0.0346585i \(-0.988966\pi\)
−0.469684 + 0.882834i \(0.655632\pi\)
\(390\) −3.84830 2.60421i −0.194866 0.131869i
\(391\) −12.8020 + 7.39123i −0.647424 + 0.373790i
\(392\) 3.83146 + 11.8696i 0.193518 + 0.599506i
\(393\) −31.0417 + 23.6706i −1.56585 + 1.19402i
\(394\) 7.74979i 0.390429i
\(395\) −19.5685 17.2604i −0.984599 0.868467i
\(396\) −22.5384 6.18520i −1.13259 0.310818i
\(397\) 17.2664 + 4.62651i 0.866575 + 0.232198i 0.664606 0.747194i \(-0.268599\pi\)
0.201969 + 0.979392i \(0.435266\pi\)
\(398\) −3.65201 + 0.978553i −0.183059 + 0.0490504i
\(399\) 4.08890 3.28427i 0.204701 0.164419i
\(400\) 1.69456 + 13.4666i 0.0847281 + 0.673329i
\(401\) 0.704740 1.22065i 0.0351930 0.0609561i −0.847892 0.530168i \(-0.822129\pi\)
0.883085 + 0.469212i \(0.155462\pi\)
\(402\) −7.27740 3.04016i −0.362964 0.151630i
\(403\) 0.450796 + 0.120790i 0.0224557 + 0.00601700i
\(404\) −3.31855 5.74789i −0.165104 0.285968i
\(405\) 14.9306 + 13.4936i 0.741909 + 0.670500i
\(406\) 2.91611 + 2.77261i 0.144724 + 0.137603i
\(407\) −13.9888 + 3.74830i −0.693401 + 0.185796i
\(408\) −11.8198 + 9.01313i −0.585169 + 0.446216i
\(409\) 39.6926 1.96267 0.981336 0.192303i \(-0.0615957\pi\)
0.981336 + 0.192303i \(0.0615957\pi\)
\(410\) −4.33017 + 2.87544i −0.213852 + 0.142008i
\(411\) −20.9125 16.1472i −1.03154 0.796484i
\(412\) 0.315805 + 1.17860i 0.0155586 + 0.0580655i
\(413\) −10.5061 + 6.42428i −0.516973 + 0.316118i
\(414\) −4.20186 + 1.09874i −0.206510 + 0.0540002i
\(415\) −9.32141 + 18.7664i −0.457570 + 0.921205i
\(416\) −10.6703 + 6.16051i −0.523155 + 0.302044i
\(417\) −10.6896 + 1.37451i −0.523474 + 0.0673099i
\(418\) 2.28537 0.612363i 0.111781 0.0299517i
\(419\) −12.9847 22.4901i −0.634343 1.09871i −0.986654 0.162831i \(-0.947938\pi\)
0.352312 0.935883i \(-0.385396\pi\)
\(420\) −9.82443 + 15.3373i −0.479383 + 0.748383i
\(421\) 16.4814 28.5467i 0.803255 1.39128i −0.114208 0.993457i \(-0.536433\pi\)
0.917463 0.397822i \(-0.130234\pi\)
\(422\) 2.63451 9.83211i 0.128246 0.478620i
\(423\) 25.3832 + 0.153230i 1.23417 + 0.00745031i
\(424\) −14.2608 8.23346i −0.692564 0.399852i
\(425\) 22.3011 9.08824i 1.08176 0.440845i
\(426\) −2.39469 + 0.983457i −0.116023 + 0.0476487i
\(427\) −11.9513 19.5449i −0.578366 0.945846i
\(428\) −24.6620 6.60817i −1.19208 0.319418i
\(429\) −2.57807 + 19.1359i −0.124471 + 0.923890i
\(430\) 3.56053 + 10.5884i 0.171704 + 0.510620i
\(431\) 9.59692 16.6224i 0.462267 0.800670i −0.536806 0.843706i \(-0.680369\pi\)
0.999074 + 0.0430351i \(0.0137027\pi\)
\(432\) 13.0799 5.27963i 0.629307 0.254016i
\(433\) −15.9138 15.9138i −0.764768 0.764768i 0.212412 0.977180i \(-0.431868\pi\)
−0.977180 + 0.212412i \(0.931868\pi\)
\(434\) −0.0536689 + 0.222605i −0.00257619 + 0.0106854i
\(435\) −0.889981 + 12.4558i −0.0426713 + 0.597211i
\(436\) 16.1470 27.9675i 0.773303 1.33940i
\(437\) −2.48377 + 2.48377i −0.118815 + 0.118815i
\(438\) 8.70523 6.63811i 0.415952 0.317181i
\(439\) −0.126419 −0.00603366 −0.00301683 0.999995i \(-0.500960\pi\)
−0.00301683 + 0.999995i \(0.500960\pi\)
\(440\) −14.5471 + 9.65998i −0.693507 + 0.460521i
\(441\) −20.0232 + 6.33020i −0.953486 + 0.301438i
\(442\) 4.08601 + 4.08601i 0.194352 + 0.194352i
\(443\) −9.13798 + 9.13798i −0.434158 + 0.434158i −0.890040 0.455882i \(-0.849324\pi\)
0.455882 + 0.890040i \(0.349324\pi\)
\(444\) 6.21734 8.05215i 0.295062 0.382138i
\(445\) −9.56183 1.93043i −0.453274 0.0915110i
\(446\) 7.51560 + 4.33913i 0.355874 + 0.205464i
\(447\) −6.60145 + 5.03388i −0.312238 + 0.238095i
\(448\) 4.33977 + 7.09716i 0.205035 + 0.335309i
\(449\) 23.8726i 1.12662i 0.826246 + 0.563310i \(0.190472\pi\)
−0.826246 + 0.563310i \(0.809528\pi\)
\(450\) 7.02518 0.840963i 0.331170 0.0396434i
\(451\) 18.7058 + 10.7998i 0.880822 + 0.508543i
\(452\) 2.47229 9.22670i 0.116287 0.433988i
\(453\) 5.68241 0.730662i 0.266983 0.0343295i
\(454\) −2.99874 5.19397i −0.140738 0.243765i
\(455\) 13.6414 + 6.35209i 0.639516 + 0.297790i
\(456\) −2.15860 + 2.79563i −0.101086 + 0.130918i
\(457\) −15.1501 15.1501i −0.708691 0.708691i 0.257569 0.966260i \(-0.417079\pi\)
−0.966260 + 0.257569i \(0.917079\pi\)
\(458\) 12.3512 3.30951i 0.577136 0.154643i
\(459\) −15.0548 19.9921i −0.702699 0.933150i
\(460\) 5.42676 10.9254i 0.253024 0.509401i
\(461\) 13.3585 + 7.71252i 0.622166 + 0.359208i 0.777712 0.628621i \(-0.216380\pi\)
−0.155546 + 0.987829i \(0.549714\pi\)
\(462\) −9.41784 1.02776i −0.438157 0.0478158i
\(463\) −30.1174 8.06993i −1.39967 0.375042i −0.521446 0.853284i \(-0.674607\pi\)
−0.878228 + 0.478242i \(0.841274\pi\)
\(464\) 7.57988 + 4.37625i 0.351887 + 0.203162i
\(465\) −0.639182 + 0.310551i −0.0296413 + 0.0144014i
\(466\) −4.20138 7.27701i −0.194625 0.337101i
\(467\) −12.1387 3.25256i −0.561713 0.150511i −0.0332200 0.999448i \(-0.510576\pi\)
−0.528493 + 0.848937i \(0.677243\pi\)
\(468\) −6.71071 11.7870i −0.310203 0.544856i
\(469\) 24.8296 + 5.98630i 1.14652 + 0.276422i
\(470\) 5.90338 6.69278i 0.272303 0.308715i
\(471\) −1.96656 4.78853i −0.0906143 0.220644i
\(472\) 5.86434 5.86434i 0.269928 0.269928i
\(473\) 32.8242 32.8242i 1.50926 1.50926i
\(474\) 3.62175 + 8.81887i 0.166353 + 0.405064i
\(475\) 4.55967 3.45748i 0.209212 0.158640i
\(476\) 15.6075 16.4152i 0.715367 0.752390i
\(477\) 14.0072 23.9265i 0.641346 1.09552i
\(478\) −6.89941 1.84869i −0.315572 0.0845572i
\(479\) −18.9242 32.7777i −0.864670 1.49765i −0.867375 0.497656i \(-0.834194\pi\)
0.00270469 0.999996i \(-0.499139\pi\)
\(480\) 6.13485 17.7295i 0.280016 0.809238i
\(481\) −7.27865 4.20233i −0.331878 0.191610i
\(482\) −3.19018 0.854805i −0.145308 0.0389353i
\(483\) 12.8716 5.66953i 0.585677 0.257972i
\(484\) 12.6372 + 7.29610i 0.574419 + 0.331641i
\(485\) 32.0738 + 15.9313i 1.45640 + 0.723403i
\(486\) −2.71100 6.83489i −0.122973 0.310037i
\(487\) 3.06565 0.821437i 0.138918 0.0372229i −0.188690 0.982037i \(-0.560424\pi\)
0.327608 + 0.944814i \(0.393758\pi\)
\(488\) 10.9096 + 10.9096i 0.493856 + 0.493856i
\(489\) 6.83091 8.84680i 0.308904 0.400066i
\(490\) −2.94685 + 6.76951i −0.133125 + 0.305815i
\(491\) 2.47604 + 4.28862i 0.111742 + 0.193543i 0.916473 0.400097i \(-0.131024\pi\)
−0.804731 + 0.593640i \(0.797690\pi\)
\(492\) −15.0488 + 1.93502i −0.678451 + 0.0872373i
\(493\) 4.01929 15.0002i 0.181020 0.675574i
\(494\) 1.18912 + 0.686538i 0.0535010 + 0.0308888i
\(495\) −16.1162 24.5904i −0.724368 1.10526i
\(496\) 0.498078i 0.0223643i
\(497\) 7.15233 4.37351i 0.320826 0.196179i
\(498\) 6.08787 4.64226i 0.272804 0.208025i
\(499\) −29.8401 17.2282i −1.33583 0.771241i −0.349642 0.936883i \(-0.613697\pi\)
−0.986186 + 0.165643i \(0.947030\pi\)
\(500\) −11.1824 + 16.4285i −0.500091 + 0.734706i
\(501\) −10.2185 + 13.2341i −0.456530 + 0.591258i
\(502\) 2.32699 2.32699i 0.103859 0.103859i
\(503\) 3.79506 + 3.79506i 0.169213 + 0.169213i 0.786634 0.617420i \(-0.211822\pi\)
−0.617420 + 0.786634i \(0.711822\pi\)
\(504\) 12.1100 7.30497i 0.539424 0.325389i
\(505\) 1.65230 8.18419i 0.0735263 0.364192i
\(506\) 6.34511 0.282074
\(507\) 8.99437 6.85859i 0.399454 0.304601i
\(508\) −18.7876 + 18.7876i −0.833566 + 0.833566i
\(509\) 4.68893 8.12146i 0.207833 0.359977i −0.743199 0.669071i \(-0.766692\pi\)
0.951032 + 0.309093i \(0.100026\pi\)
\(510\) −8.77639 0.627081i −0.388625 0.0277676i
\(511\) −24.4284 + 25.6927i −1.08065 + 1.13658i
\(512\) −16.1384 16.1384i −0.713222 0.713222i
\(513\) −4.68493 3.66275i −0.206845 0.161714i
\(514\) −0.540230 + 0.935705i −0.0238285 + 0.0412722i
\(515\) −0.682830 + 1.37471i −0.0300891 + 0.0605770i
\(516\) −4.35377 + 32.3162i −0.191664 + 1.42264i
\(517\) −35.8207 9.59812i −1.57539 0.422125i
\(518\) 1.97114 3.62208i 0.0866069 0.159145i
\(519\) −4.41094 + 1.81149i −0.193619 + 0.0795157i
\(520\) −9.93367 2.00550i −0.435620 0.0879469i
\(521\) 28.7122 + 16.5770i 1.25791 + 0.726252i 0.972667 0.232205i \(-0.0745940\pi\)
0.285238 + 0.958457i \(0.407927\pi\)
\(522\) 2.30510 3.93746i 0.100891 0.172338i
\(523\) −1.35899 + 5.07183i −0.0594247 + 0.221776i −0.989252 0.146220i \(-0.953289\pi\)
0.929827 + 0.367996i \(0.119956\pi\)
\(524\) −20.0307 + 34.6943i −0.875047 + 1.51563i
\(525\) −22.0314 + 6.29415i −0.961530 + 0.274699i
\(526\) 0.993112 + 1.72012i 0.0433018 + 0.0750008i
\(527\) 0.853614 0.228725i 0.0371840 0.00996343i
\(528\) −20.4388 + 2.62808i −0.889484 + 0.114373i
\(529\) 11.7606 6.78998i 0.511330 0.295216i
\(530\) −3.10680 9.23910i −0.134951 0.401321i
\(531\) 9.81389 + 9.93309i 0.425886 + 0.431059i
\(532\) 2.57272 4.72752i 0.111541 0.204964i
\(533\) 3.24432 + 12.1080i 0.140527 + 0.524454i
\(534\) 2.82102 + 2.17820i 0.122077 + 0.0942600i
\(535\) −17.7677 26.7567i −0.768165 1.15679i
\(536\) −17.2009 −0.742966
\(537\) −17.3843 + 13.2563i −0.750187 + 0.572050i
\(538\) 10.8978 2.92006i 0.469838 0.125893i
\(539\) 30.6409 1.54677i 1.31980 0.0666242i
\(540\) 19.4763 + 6.87119i 0.838125 + 0.295689i
\(541\) 5.00106 + 8.66209i 0.215012 + 0.372412i 0.953276 0.302100i \(-0.0976875\pi\)
−0.738264 + 0.674512i \(0.764354\pi\)
\(542\) 1.79793 + 0.481753i 0.0772276 + 0.0206931i
\(543\) −14.9935 6.26359i −0.643432 0.268796i
\(544\) −11.6654 + 20.2050i −0.500149 + 0.866283i
\(545\) 38.5065 12.9484i 1.64944 0.554649i
\(546\) −3.44297 4.28647i −0.147345 0.183444i
\(547\) 35.9383 9.62964i 1.53661 0.411734i 0.611442 0.791289i \(-0.290590\pi\)
0.925169 + 0.379556i \(0.123923\pi\)
\(548\) −26.1904 7.01771i −1.11880 0.299782i
\(549\) −18.4789 + 18.2571i −0.788660 + 0.779196i
\(550\) −10.2404 1.40784i −0.436652 0.0600306i
\(551\) 3.69006i 0.157202i
\(552\) −7.53213 + 5.74357i −0.320589 + 0.244463i
\(553\) −16.1062 26.3397i −0.684905 1.12008i
\(554\) 6.83154 3.94419i 0.290244 0.167573i
\(555\) 12.5661 2.42284i 0.533402 0.102844i
\(556\) −9.57868 + 5.53025i −0.406227 + 0.234535i
\(557\) 0.477858 0.128042i 0.0202475 0.00542530i −0.248681 0.968585i \(-0.579997\pi\)
0.268929 + 0.963160i \(0.413330\pi\)
\(558\) 0.259637 + 0.00156735i 0.0109913 + 6.63511e-5i
\(559\) 26.9396 1.13942
\(560\) −2.78016 + 15.8171i −0.117483 + 0.668393i
\(561\) 13.8899 + 33.8215i 0.586431 + 1.42794i
\(562\) 4.13015 1.10667i 0.174220 0.0466821i
\(563\) 1.11218 + 1.11218i 0.0468726 + 0.0468726i 0.730155 0.683282i \(-0.239448\pi\)
−0.683282 + 0.730155i \(0.739448\pi\)
\(564\) 24.0969 9.89618i 1.01466 0.416704i
\(565\) 10.0104 6.64736i 0.421139 0.279657i
\(566\) 9.00294i 0.378422i
\(567\) 12.1759 + 20.4633i 0.511341 + 0.859378i
\(568\) −3.99231 + 3.99231i −0.167513 + 0.167513i
\(569\) 32.9279i 1.38041i −0.723614 0.690205i \(-0.757521\pi\)
0.723614 0.690205i \(-0.242479\pi\)
\(570\) −2.05294 + 0.395821i −0.0859882 + 0.0165791i
\(571\) 24.8485 1.03988 0.519939 0.854203i \(-0.325955\pi\)
0.519939 + 0.854203i \(0.325955\pi\)
\(572\) 5.12864 + 19.1404i 0.214439 + 0.800299i
\(573\) −12.1284 + 29.0324i −0.506671 + 1.21284i
\(574\) −5.89868 + 1.74110i −0.246206 + 0.0726723i
\(575\) 14.2113 5.79144i 0.592651 0.241520i
\(576\) 6.71006 6.62953i 0.279586 0.276230i
\(577\) −2.95088 11.0128i −0.122847 0.458470i 0.876907 0.480660i \(-0.159603\pi\)
−0.999754 + 0.0221899i \(0.992936\pi\)
\(578\) 2.82366 + 0.756596i 0.117449 + 0.0314703i
\(579\) −3.27038 7.96329i −0.135912 0.330943i
\(580\) 4.08461 + 12.1470i 0.169604 + 0.504375i
\(581\) −17.0836 + 17.9678i −0.708748 + 0.745429i
\(582\) −7.93414 10.4048i −0.328881 0.431295i
\(583\) −28.6413 + 28.6413i −1.18620 + 1.18620i
\(584\) 11.9378 20.6769i 0.493991 0.855618i
\(585\) 3.47752 16.7044i 0.143778 0.690643i
\(586\) 7.47006 4.31284i 0.308585 0.178162i
\(587\) 2.45406 + 9.15866i 0.101290 + 0.378018i 0.997898 0.0648065i \(-0.0206430\pi\)
−0.896608 + 0.442825i \(0.853976\pi\)
\(588\) −16.4566 + 13.9152i −0.678658 + 0.573854i
\(589\) 0.181857 0.104995i 0.00749327 0.00432624i
\(590\) 4.89962 0.307060i 0.201714 0.0126414i
\(591\) 26.3239 10.8107i 1.08282 0.444695i
\(592\) 2.32154 8.66412i 0.0954149 0.356093i
\(593\) 0.403868 1.50726i 0.0165849 0.0618956i −0.957137 0.289634i \(-0.906466\pi\)
0.973722 + 0.227738i \(0.0731331\pi\)
\(594\) 1.30565 + 10.6626i 0.0535714 + 0.437491i
\(595\) 28.3843 2.49877i 1.16364 0.102439i
\(596\) −4.25982 + 7.37822i −0.174489 + 0.302224i
\(597\) −8.41833 11.0398i −0.344539 0.451830i
\(598\) 2.60379 + 2.60379i 0.106477 + 0.106477i
\(599\) 3.37770i 0.138009i −0.997616 0.0690046i \(-0.978018\pi\)
0.997616 0.0690046i \(-0.0219823\pi\)
\(600\) 13.4305 7.59836i 0.548298 0.310202i
\(601\) 23.4692 + 13.5499i 0.957327 + 0.552713i 0.895349 0.445365i \(-0.146926\pi\)
0.0619776 + 0.998078i \(0.480259\pi\)
\(602\) 0.333302 + 13.2136i 0.0135844 + 0.538545i
\(603\) 0.174824 28.9603i 0.00711938 1.17935i
\(604\) 5.09185 2.93978i 0.207184 0.119618i
\(605\) 5.85079 + 17.3993i 0.237868 + 0.707382i
\(606\) −1.86437 + 2.41457i −0.0757350 + 0.0980853i
\(607\) −0.893061 3.33295i −0.0362482 0.135280i 0.945431 0.325824i \(-0.105642\pi\)
−0.981679 + 0.190544i \(0.938975\pi\)
\(608\) −1.43485 + 5.35492i −0.0581907 + 0.217171i
\(609\) −5.34992 + 13.7729i −0.216790 + 0.558108i
\(610\) 0.571235 + 9.11494i 0.0231286 + 0.369053i
\(611\) −10.7607 18.6381i −0.435332 0.754018i
\(612\) −22.1646 12.9758i −0.895950 0.524514i
\(613\) −1.32900 4.95989i −0.0536777 0.200328i 0.933880 0.357588i \(-0.116401\pi\)
−0.987557 + 0.157260i \(0.949734\pi\)
\(614\) −11.9140 −0.480810
\(615\) −15.8075 10.6972i −0.637422 0.431354i
\(616\) −19.8165 + 5.84921i −0.798430 + 0.235671i
\(617\) −5.94379 + 22.1825i −0.239288 + 0.893035i 0.736881 + 0.676023i \(0.236298\pi\)
−0.976169 + 0.217012i \(0.930369\pi\)
\(618\) 0.445961 0.340064i 0.0179392 0.0136794i
\(619\) 15.1235 + 26.1947i 0.607867 + 1.05286i 0.991591 + 0.129408i \(0.0413078\pi\)
−0.383725 + 0.923448i \(0.625359\pi\)
\(620\) −0.482415 + 0.546924i −0.0193743 + 0.0219650i
\(621\) −9.59361 12.7399i −0.384978 0.511233i
\(622\) 1.74027 1.74027i 0.0697784 0.0697784i
\(623\) −10.1380 5.51710i −0.406170 0.221038i
\(624\) −9.46576 7.30883i −0.378934 0.292587i
\(625\) −24.2206 + 6.19365i −0.968825 + 0.247746i
\(626\) 3.27547i 0.130914i
\(627\) 5.26806 + 6.90855i 0.210386 + 0.275901i
\(628\) −3.75649 3.75649i −0.149900 0.149900i
\(629\) −15.9148 −0.634565
\(630\) 8.23636 + 1.49901i 0.328144 + 0.0597220i
\(631\) 42.5624 1.69438 0.847191 0.531288i \(-0.178292\pi\)
0.847191 + 0.531288i \(0.178292\pi\)
\(632\) 14.7024 + 14.7024i 0.584828 + 0.584828i
\(633\) 37.0721 4.76684i 1.47348 0.189465i
\(634\) 5.75196i 0.228440i
\(635\) −33.3587 + 2.09059i −1.32380 + 0.0829627i
\(636\) 3.79895 28.1979i 0.150638 1.11812i
\(637\) 13.2086 + 11.9391i 0.523344 + 0.473045i
\(638\) −4.71336 + 4.71336i −0.186604 + 0.186604i
\(639\) −6.68107 6.76222i −0.264299 0.267509i
\(640\) −1.56241 24.9306i −0.0617596 0.985470i
\(641\) 1.77150 + 3.06833i 0.0699701 + 0.121192i 0.898888 0.438179i \(-0.144376\pi\)
−0.828918 + 0.559370i \(0.811043\pi\)
\(642\) 1.49662 + 11.6394i 0.0590670 + 0.459369i
\(643\) −0.201747 + 0.752929i −0.00795611 + 0.0296926i −0.969790 0.243942i \(-0.921559\pi\)
0.961834 + 0.273635i \(0.0882260\pi\)
\(644\) 9.94578 10.4605i 0.391919 0.412202i
\(645\) −30.9992 + 26.8648i −1.22059 + 1.05780i
\(646\) 2.60002 0.102296
\(647\) −3.86364 14.4193i −0.151895 0.566881i −0.999351 0.0360153i \(-0.988534\pi\)
0.847456 0.530866i \(-0.178133\pi\)
\(648\) −11.2016 11.4754i −0.440042 0.450798i
\(649\) −10.2000 17.6669i −0.400384 0.693485i
\(650\) −3.62454 4.77999i −0.142166 0.187487i
\(651\) −0.830994 + 0.128229i −0.0325692 + 0.00502568i
\(652\) 2.96876 11.0796i 0.116266 0.433910i
\(653\) 2.76606 + 10.3231i 0.108244 + 0.403974i 0.998693 0.0511101i \(-0.0162759\pi\)
−0.890449 + 0.455084i \(0.849609\pi\)
\(654\) −14.7103 1.98184i −0.575218 0.0774959i
\(655\) −47.7681 + 16.0628i −1.86645 + 0.627625i
\(656\) −11.5856 + 6.68896i −0.452342 + 0.261160i
\(657\) 34.6914 + 20.3093i 1.35344 + 0.792341i
\(658\) 9.00865 5.50861i 0.351194 0.214748i
\(659\) 18.6085 + 10.7436i 0.724884 + 0.418512i 0.816547 0.577278i \(-0.195885\pi\)
−0.0916639 + 0.995790i \(0.529219\pi\)
\(660\) −24.9887 16.9103i −0.972682 0.658231i
\(661\) 7.77963i 0.302593i −0.988488 0.151296i \(-0.951655\pi\)
0.988488 0.151296i \(-0.0483448\pi\)
\(662\) 7.92930 + 7.92930i 0.308181 + 0.308181i
\(663\) −8.17918 + 19.5789i −0.317653 + 0.760382i
\(664\) 8.34855 14.4601i 0.323987 0.561161i
\(665\) 6.36114 2.31916i 0.246674 0.0899332i
\(666\) −4.50912 1.23744i −0.174725 0.0479497i
\(667\) 2.56127 9.55879i 0.0991728 0.370118i
\(668\) −4.44105 + 16.5742i −0.171829 + 0.641276i
\(669\) −4.25478 + 31.5814i −0.164499 + 1.22101i
\(670\) −7.63595 6.73530i −0.295002 0.260207i
\(671\) 32.8663 18.9754i 1.26879 0.732536i
\(672\) 13.1191 17.9067i 0.506082 0.690765i
\(673\) −0.246995 0.921796i −0.00952094 0.0355326i 0.961002 0.276542i \(-0.0891884\pi\)
−0.970523 + 0.241009i \(0.922522\pi\)
\(674\) −6.96712 + 4.02247i −0.268364 + 0.154940i
\(675\) 12.6565 + 22.6895i 0.487148 + 0.873320i
\(676\) 5.80394 10.0527i 0.223228 0.386643i
\(677\) −9.42246 + 9.42246i −0.362135 + 0.362135i −0.864598 0.502464i \(-0.832427\pi\)
0.502464 + 0.864598i \(0.332427\pi\)
\(678\) −4.35458 + 0.559926i −0.167237 + 0.0215038i
\(679\) 30.7089 + 29.1978i 1.17850 + 1.12051i
\(680\) −18.1888 + 6.11628i −0.697509 + 0.234549i
\(681\) 13.4593 17.4314i 0.515763 0.667971i
\(682\) −0.366399 0.0981763i −0.0140301 0.00375936i
\(683\) 12.5338 + 46.7767i 0.479591 + 1.78986i 0.603271 + 0.797537i \(0.293864\pi\)
−0.123679 + 0.992322i \(0.539469\pi\)
\(684\) −5.88527 1.61509i −0.225029 0.0617546i
\(685\) −18.8688 28.4149i −0.720942 1.08568i
\(686\) −5.69258 + 6.62638i −0.217344 + 0.252996i
\(687\) 28.4711 + 37.3371i 1.08624 + 1.42450i
\(688\) 7.44129 + 27.7713i 0.283697 + 1.05877i
\(689\) −23.5066 −0.895529
\(690\) −5.59271 0.399604i −0.212911 0.0152127i
\(691\) 48.0951i 1.82962i 0.403879 + 0.914812i \(0.367662\pi\)
−0.403879 + 0.914812i \(0.632338\pi\)
\(692\) −3.46028 + 3.46028i −0.131540 + 0.131540i
\(693\) −9.64661 33.4235i −0.366445 1.26965i
\(694\) 4.08114i 0.154918i
\(695\) −13.6387 2.75350i −0.517345 0.104446i
\(696\) 1.32860 9.86164i 0.0503606 0.373804i
\(697\) 16.7840 + 16.7840i 0.635738 + 0.635738i
\(698\) 7.38357 1.97842i 0.279472 0.0748844i
\(699\) 18.8572 24.4222i 0.713245 0.923732i
\(700\) −18.3725 + 14.6755i −0.694415 + 0.554682i
\(701\) −7.85185 −0.296560 −0.148280 0.988945i \(-0.547374\pi\)
−0.148280 + 0.988945i \(0.547374\pi\)
\(702\) −3.83973 + 4.91130i −0.144921 + 0.185365i
\(703\) −3.65280 + 0.978765i −0.137768 + 0.0369148i
\(704\) −11.9344 + 6.89034i −0.449795 + 0.259689i
\(705\) 30.9686 + 10.7159i 1.16635 + 0.403585i
\(706\) 3.36120 1.94059i 0.126501 0.0730351i
\(707\) 4.72221 8.67734i 0.177597 0.326345i
\(708\) 13.2225 + 5.52377i 0.496933 + 0.207596i
\(709\) 11.8510i 0.445074i 0.974924 + 0.222537i \(0.0714337\pi\)
−0.974924 + 0.222537i \(0.928566\pi\)
\(710\) −3.33555 + 0.209039i −0.125181 + 0.00784510i
\(711\) −24.9031 + 24.6042i −0.933938 + 0.922729i
\(712\) 7.50821 + 2.01182i 0.281382 + 0.0753961i
\(713\) 0.543962 0.145754i 0.0203715 0.00545853i
\(714\) −9.70443 3.76956i −0.363179 0.141072i
\(715\) −11.0891 + 22.3252i −0.414709 + 0.834915i
\(716\) −11.2178 + 19.4298i −0.419230 + 0.726127i
\(717\) −3.34500 26.0143i −0.124921 0.971521i
\(718\) 2.94593 + 0.789358i 0.109941 + 0.0294586i
\(719\) 16.9071 + 29.2840i 0.630529 + 1.09211i 0.987444 + 0.157972i \(0.0504955\pi\)
−0.356914 + 0.934137i \(0.616171\pi\)
\(720\) 18.1807 1.02925i 0.677554 0.0383577i
\(721\) −1.25144 + 1.31621i −0.0466062 + 0.0490183i
\(722\) −8.05996 + 2.15966i −0.299961 + 0.0803742i
\(723\) −1.54667 12.0286i −0.0575214 0.447348i
\(724\) −16.6757 −0.619747
\(725\) −6.25453 + 14.8587i −0.232288 + 0.551838i
\(726\) 0.895500 6.64690i 0.0332351 0.246690i
\(727\) 6.01324 + 22.4417i 0.223019 + 0.832318i 0.983189 + 0.182593i \(0.0584491\pi\)
−0.760170 + 0.649725i \(0.774884\pi\)
\(728\) −10.5322 5.73165i −0.390350 0.212429i
\(729\) 19.4345 18.7430i 0.719796 0.694186i
\(730\) 13.3959 4.50460i 0.495806 0.166723i
\(731\) 44.1778 25.5060i 1.63397 0.943375i
\(732\) −10.2761 + 24.5984i −0.379815 + 0.909183i
\(733\) −0.181271 + 0.0485713i −0.00669538 + 0.00179402i −0.262165 0.965023i \(-0.584437\pi\)
0.255470 + 0.966817i \(0.417770\pi\)
\(734\) 4.04818 + 7.01165i 0.149421 + 0.258805i
\(735\) −27.1050 0.566357i −0.999782 0.0208904i
\(736\) −7.43370 + 12.8755i −0.274010 + 0.474599i
\(737\) −10.9507 + 40.8686i −0.403374 + 1.50541i
\(738\) 3.45036 + 6.06039i 0.127009 + 0.223086i
\(739\) −20.2871 11.7127i −0.746272 0.430860i 0.0780736 0.996948i \(-0.475123\pi\)
−0.824345 + 0.566087i \(0.808456\pi\)
\(740\) 10.9409 7.26527i 0.402195 0.267077i
\(741\) −0.673193 + 4.99681i −0.0247303 + 0.183563i
\(742\) −0.290828 11.5297i −0.0106766 0.423268i
\(743\) −6.49618 1.74065i −0.238322 0.0638581i 0.137681 0.990477i \(-0.456035\pi\)
−0.376003 + 0.926618i \(0.622702\pi\)
\(744\) 0.523813 0.215120i 0.0192039 0.00788670i
\(745\) −10.1586 + 3.41598i −0.372181 + 0.125152i
\(746\) −0.530808 + 0.919386i −0.0194343 + 0.0336611i
\(747\) 24.2609 + 14.2030i 0.887661 + 0.519661i
\(748\) 26.5322 + 26.5322i 0.970113 + 0.970113i
\(749\) −10.7585 36.4487i −0.393108 1.33181i
\(750\) 8.93743 + 1.88582i 0.326349 + 0.0688606i
\(751\) 14.1908 24.5791i 0.517829 0.896905i −0.481957 0.876195i \(-0.660074\pi\)
0.999786 0.0207105i \(-0.00659284\pi\)
\(752\) 16.2412 16.2412i 0.592255 0.592255i
\(753\) 11.1502 + 4.65806i 0.406337 + 0.169749i
\(754\) −3.86836 −0.140877
\(755\) 7.25008 + 1.46371i 0.263857 + 0.0532699i
\(756\) 19.6249 + 14.5608i 0.713749 + 0.529572i
\(757\) −29.2331 29.2331i −1.06249 1.06249i −0.997912 0.0645808i \(-0.979429\pi\)
−0.0645808 0.997912i \(-0.520571\pi\)
\(758\) −0.546903 + 0.546903i −0.0198644 + 0.0198644i
\(759\) 8.85126 + 21.5526i 0.321280 + 0.782309i
\(760\) −3.79858 + 2.52244i −0.137789 + 0.0914984i
\(761\) −25.6949 14.8350i −0.931439 0.537767i −0.0441729 0.999024i \(-0.514065\pi\)
−0.887267 + 0.461257i \(0.847399\pi\)
\(762\) 11.2684 + 4.70742i 0.408211 + 0.170532i
\(763\) 48.0532 1.21211i 1.73964 0.0438812i
\(764\) 32.2897i 1.16820i
\(765\) −10.1128 30.6858i −0.365629 1.10945i
\(766\) −5.87645 3.39277i −0.212325 0.122586i
\(767\) 3.06413 11.4355i 0.110639 0.412911i
\(768\) 0.680421 1.62876i 0.0245526 0.0587728i
\(769\) −13.2591 22.9654i −0.478135 0.828154i 0.521551 0.853220i \(-0.325354\pi\)
−0.999686 + 0.0250661i \(0.992020\pi\)
\(770\) −11.0874 5.16286i −0.399564 0.186057i
\(771\) −3.93194 0.529728i −0.141605 0.0190777i
\(772\) −6.24702 6.24702i −0.224835 0.224835i
\(773\) 14.0750 3.77140i 0.506244 0.135648i 0.00334779 0.999994i \(-0.498934\pi\)
0.502896 + 0.864347i \(0.332268\pi\)
\(774\) 14.5000 3.79160i 0.521192 0.136286i
\(775\) −0.910241 + 0.114540i −0.0326968 + 0.00411439i
\(776\) −24.7139 14.2686i −0.887178 0.512213i
\(777\) 15.0529 + 1.64271i 0.540020 + 0.0589320i
\(778\) 15.2437 + 4.08454i 0.546513 + 0.146438i
\(779\) 4.88450 + 2.82007i 0.175006 + 0.101039i
\(780\) −3.31507 17.1937i −0.118698 0.615634i
\(781\) 6.94390 + 12.0272i 0.248472 + 0.430367i
\(782\) 6.73513 + 1.80467i 0.240848 + 0.0645350i
\(783\) 16.5900 + 2.33713i 0.592880 + 0.0835223i
\(784\) −8.65921 + 16.9142i −0.309257 + 0.604079i
\(785\) −0.418003 6.66990i −0.0149192 0.238059i
\(786\) 18.2484 + 2.45851i 0.650900 + 0.0876921i
\(787\) −20.1337 + 20.1337i −0.717690 + 0.717690i −0.968132 0.250442i \(-0.919424\pi\)
0.250442 + 0.968132i \(0.419424\pi\)
\(788\) 20.6505 20.6505i 0.735644 0.735644i
\(789\) −4.45742 + 5.77285i −0.158688 + 0.205519i
\(790\) 0.769823 + 12.2837i 0.0273891 + 0.437036i
\(791\) 13.6364 4.02504i 0.484855 0.143114i
\(792\) 11.5914 + 20.3598i 0.411883 + 0.723453i
\(793\) 21.2738 + 5.70031i 0.755456 + 0.202424i
\(794\) −4.21584 7.30204i −0.149614 0.259140i
\(795\) 27.0488 23.4412i 0.959322 0.831375i
\(796\) −12.3388 7.12383i −0.437339 0.252498i
\(797\) −45.0757 12.0780i −1.59666 0.427824i −0.652630 0.757677i \(-0.726334\pi\)
−0.944032 + 0.329853i \(0.893001\pi\)
\(798\) −2.45921 0.268372i −0.0870550 0.00950025i
\(799\) −35.2926 20.3762i −1.24856 0.720859i
\(800\) 14.8541 19.1305i 0.525171 0.676366i
\(801\) −3.46351 + 12.6208i −0.122377 + 0.445932i
\(802\) −0.642183 + 0.172072i −0.0226763 + 0.00607608i
\(803\) −41.5275 41.5275i −1.46547 1.46547i
\(804\) −11.2908 27.4927i −0.398195 0.969594i
\(805\) 18.0877 1.59233i 0.637509 0.0561222i
\(806\) −0.110068 0.190644i −0.00387699 0.00671514i
\(807\) 25.1208 + 32.9435i 0.884294 + 1.15967i
\(808\) −1.72196 + 6.42645i −0.0605784 + 0.226082i
\(809\) 1.73589 + 1.00221i 0.0610305 + 0.0352360i 0.530205 0.847870i \(-0.322115\pi\)
−0.469174 + 0.883106i \(0.655448\pi\)
\(810\) −0.479314 9.48046i −0.0168414 0.333109i
\(811\) 3.78401i 0.132874i −0.997791 0.0664372i \(-0.978837\pi\)
0.997791 0.0664372i \(-0.0211632\pi\)
\(812\) 0.382361 + 15.1585i 0.0134183 + 0.531958i
\(813\) 0.871677 + 6.77910i 0.0305711 + 0.237753i
\(814\) 5.91595 + 3.41558i 0.207354 + 0.119716i
\(815\) 12.0206 7.98226i 0.421064 0.279606i
\(816\) −22.4426 3.02357i −0.785649 0.105846i
\(817\) 8.57114 8.57114i 0.299866 0.299866i
\(818\) −13.2388 13.2388i −0.462886 0.462886i
\(819\) 9.75713 17.6743i 0.340942 0.617591i
\(820\) −19.2004 3.87635i −0.670508 0.135368i
\(821\) 31.2903 1.09204 0.546019 0.837773i \(-0.316143\pi\)
0.546019 + 0.837773i \(0.316143\pi\)
\(822\) 1.58938 + 12.3607i 0.0554359 + 0.431129i
\(823\) 12.9297 12.9297i 0.450702 0.450702i −0.444885 0.895588i \(-0.646756\pi\)
0.895588 + 0.444885i \(0.146756\pi\)
\(824\) 0.611565 1.05926i 0.0213049 0.0369011i
\(825\) −9.50302 36.7477i −0.330853 1.27939i
\(826\) 5.64688 + 1.36144i 0.196480 + 0.0473704i
\(827\) −35.2752 35.2752i −1.22664 1.22664i −0.965228 0.261410i \(-0.915812\pi\)
−0.261410 0.965228i \(-0.584188\pi\)
\(828\) −14.1243 8.26873i −0.490852 0.287358i
\(829\) −6.23516 + 10.7996i −0.216556 + 0.375086i −0.953753 0.300592i \(-0.902816\pi\)
0.737197 + 0.675678i \(0.236149\pi\)
\(830\) 9.36825 3.15022i 0.325177 0.109346i
\(831\) 22.9272 + 17.7028i 0.795335 + 0.614105i
\(832\) −7.72496 2.06990i −0.267815 0.0717607i
\(833\) 32.9643 + 7.07303i 1.14215 + 0.245066i
\(834\) 4.02381 + 3.10692i 0.139333 + 0.107584i
\(835\) −17.9820 + 11.9409i −0.622291 + 0.413231i
\(836\) 7.72146 + 4.45798i 0.267052 + 0.154183i
\(837\) 0.356864 + 0.884104i 0.0123350 + 0.0305591i
\(838\) −3.17039 + 11.8321i −0.109519 + 0.408732i
\(839\) 22.1258 38.3230i 0.763868 1.32306i −0.176975 0.984215i \(-0.556631\pi\)
0.940843 0.338843i \(-0.110035\pi\)
\(840\) 17.8351 3.90761i 0.615368 0.134825i
\(841\) −9.30201 16.1115i −0.320759 0.555571i
\(842\) −15.0184 + 4.02417i −0.517569 + 0.138682i
\(843\) 9.52052 + 12.4852i 0.327904 + 0.430014i
\(844\) 33.2192 19.1791i 1.14345 0.660173i
\(845\) 13.8409 4.65422i 0.476141 0.160110i
\(846\) −8.41508 8.51729i −0.289316 0.292831i
\(847\) 0.547694 + 21.7130i 0.0188190 + 0.746067i
\(848\) −6.49301 24.2322i −0.222971 0.832139i
\(849\) 30.5805 12.5589i 1.04952 0.431019i
\(850\) −10.4694 4.40695i −0.359099 0.151157i
\(851\) −10.1416 −0.347651
\(852\) −9.00160 3.76046i −0.308390 0.128831i
\(853\) −21.4401 + 5.74486i −0.734095 + 0.196700i −0.606452 0.795120i \(-0.707408\pi\)
−0.127643 + 0.991820i \(0.540741\pi\)
\(854\) −2.53273 + 10.5051i −0.0866683 + 0.359477i
\(855\) −4.20829 6.42111i −0.143921 0.219597i
\(856\) 12.7969 + 22.1649i 0.437389 + 0.757580i
\(857\) 39.9154 + 10.6953i 1.36348 + 0.365344i 0.865095 0.501609i \(-0.167258\pi\)
0.498389 + 0.866953i \(0.333925\pi\)
\(858\) 7.24237 5.52261i 0.247250 0.188539i
\(859\) 3.15889 5.47136i 0.107780 0.186680i −0.807091 0.590428i \(-0.798959\pi\)
0.914871 + 0.403747i \(0.132292\pi\)
\(860\) −18.7269 + 37.7021i −0.638583 + 1.28563i
\(861\) −14.1426 17.6074i −0.481977 0.600059i
\(862\) −8.74504 + 2.34323i −0.297857 + 0.0798106i
\(863\) −11.8562 3.17685i −0.403589 0.108141i 0.0513135 0.998683i \(-0.483659\pi\)
−0.454903 + 0.890541i \(0.650326\pi\)
\(864\) −23.1663 9.84247i −0.788132 0.334848i
\(865\) −6.14396 + 0.385043i −0.208901 + 0.0130918i
\(866\) 10.6156i 0.360733i
\(867\) 1.36897 + 10.6466i 0.0464928 + 0.361578i
\(868\) −0.736173 + 0.450155i −0.0249874 + 0.0152793i
\(869\) 44.2922 25.5721i 1.50251 0.867475i
\(870\) 4.45129 3.85761i 0.150913 0.130785i
\(871\) −21.2647 + 12.2772i −0.720526 + 0.415996i
\(872\) −31.2692 + 8.37855i −1.05891 + 0.283733i
\(873\) 24.2745 41.4646i 0.821567 1.40336i
\(874\) 1.65685 0.0560438
\(875\) −29.5452 1.44341i −0.998809 0.0487963i
\(876\) 40.8847 + 5.50816i 1.38137 + 0.186104i
\(877\) 38.9915 10.4477i 1.31665 0.352795i 0.468928 0.883237i \(-0.344641\pi\)
0.847721 + 0.530442i \(0.177974\pi\)
\(878\) 0.0421652 + 0.0421652i 0.00142301 + 0.00142301i
\(879\) 25.0701 + 19.3575i 0.845593 + 0.652911i
\(880\) −26.0775 5.26475i −0.879071 0.177475i
\(881\) 27.8168i 0.937172i −0.883418 0.468586i \(-0.844764\pi\)
0.883418 0.468586i \(-0.155236\pi\)
\(882\) 8.78977 + 4.56709i 0.295967 + 0.153782i
\(883\) −6.46292 + 6.46292i −0.217494 + 0.217494i −0.807442 0.589947i \(-0.799149\pi\)
0.589947 + 0.807442i \(0.299149\pi\)
\(884\) 21.7756i 0.732392i
\(885\) 7.87784 + 16.2143i 0.264811 + 0.545038i
\(886\) 6.09566 0.204788
\(887\) −6.59151 24.5999i −0.221321 0.825982i −0.983845 0.179022i \(-0.942707\pi\)
0.762524 0.646960i \(-0.223960\pi\)
\(888\) −10.1145 + 1.30055i −0.339419 + 0.0436436i
\(889\) −38.4464 9.26924i −1.28945 0.310880i
\(890\) 2.54534 + 3.83307i 0.0853199 + 0.128485i
\(891\) −34.3965 + 19.3090i −1.15233 + 0.646874i
\(892\) 8.46418 + 31.5888i 0.283402 + 1.05767i
\(893\) −9.35358 2.50628i −0.313005 0.0838696i
\(894\) 3.88079 + 0.522836i 0.129793 + 0.0174863i
\(895\) −26.7516 + 8.99565i −0.894207 + 0.300691i
\(896\) 6.92738 28.7329i 0.231427 0.959900i
\(897\) −5.21214 + 12.4766i −0.174028 + 0.416581i
\(898\) 7.96236 7.96236i 0.265707 0.265707i
\(899\) −0.295802 + 0.512344i −0.00986554 + 0.0170876i
\(900\) 20.9606 + 16.4788i 0.698685 + 0.549294i
\(901\) −38.5480 + 22.2557i −1.28422 + 0.741444i
\(902\) −2.63693 9.84114i −0.0878000 0.327674i
\(903\) −44.4179 + 19.5647i −1.47814 + 0.651073i
\(904\) −8.29245 + 4.78765i −0.275803 + 0.159235i
\(905\) −15.7322 13.8766i −0.522955 0.461274i
\(906\) −2.13898 1.65158i −0.0710629 0.0548701i
\(907\) 5.94724 22.1954i 0.197475 0.736986i −0.794137 0.607738i \(-0.792077\pi\)
0.991612 0.129248i \(-0.0412563\pi\)
\(908\) 5.84953 21.8308i 0.194124 0.724479i
\(909\) −10.8024 2.96450i −0.358293 0.0983262i
\(910\) −2.43122 6.66851i −0.0805942 0.221059i
\(911\) −23.6040 + 40.8832i −0.782034 + 1.35452i 0.148721 + 0.988879i \(0.452484\pi\)
−0.930755 + 0.365643i \(0.880849\pi\)
\(912\) −5.33702 + 0.686251i −0.176727 + 0.0227240i
\(913\) −29.0416 29.0416i −0.961137 0.961137i
\(914\) 10.1062i 0.334282i
\(915\) −30.1641 + 14.6554i −0.997195 + 0.484494i
\(916\) 41.7305 + 24.0931i 1.37881 + 0.796059i
\(917\) −59.6110 + 1.50364i −1.96853 + 0.0496546i
\(918\) −1.64674 + 11.6894i −0.0543507 + 0.385806i
\(919\) −12.0321 + 6.94671i −0.396901 + 0.229151i −0.685146 0.728406i \(-0.740262\pi\)
0.288245 + 0.957557i \(0.406928\pi\)
\(920\) −11.5907 + 3.89757i −0.382135 + 0.128499i
\(921\) −16.6197 40.4686i −0.547639 1.33349i
\(922\) −1.88312 7.02791i −0.0620173 0.231452i
\(923\) −2.08599 + 7.78501i −0.0686611 + 0.256247i
\(924\) −22.3567 27.8339i −0.735480 0.915668i
\(925\) 16.3676 + 2.25021i 0.538164 + 0.0739865i
\(926\) 7.35360 + 12.7368i 0.241654 + 0.418557i
\(927\) 1.77721 + 1.04043i 0.0583712 + 0.0341721i
\(928\) −4.04238 15.0864i −0.132698 0.495235i
\(929\) 35.8214 1.17526 0.587632 0.809129i \(-0.300060\pi\)
0.587632 + 0.809129i \(0.300060\pi\)
\(930\) 0.316769 + 0.109610i 0.0103873 + 0.00359425i
\(931\) 8.00103 0.403897i 0.262223 0.0132372i
\(932\) 8.19548 30.5859i 0.268452 1.00188i
\(933\) 8.33884 + 3.48359i 0.273001 + 0.114047i
\(934\) 2.96385 + 5.13353i 0.0969800 + 0.167974i
\(935\) 2.95237 + 47.1097i 0.0965528 + 1.54065i
\(936\) −3.59820 + 13.1115i −0.117611 + 0.428564i
\(937\) −1.45460 + 1.45460i −0.0475197 + 0.0475197i −0.730467 0.682948i \(-0.760698\pi\)
0.682948 + 0.730467i \(0.260698\pi\)
\(938\) −6.28489 10.2782i −0.205209 0.335594i
\(939\) 11.1259 4.56920i 0.363080 0.149110i
\(940\) 33.5644 2.10349i 1.09475 0.0686082i
\(941\) 34.0264i 1.10923i −0.832107 0.554615i \(-0.812866\pi\)
0.832107 0.554615i \(-0.187134\pi\)
\(942\) −0.941224 + 2.25306i −0.0306667 + 0.0734085i
\(943\) 10.6955 + 10.6955i 0.348293 + 0.348293i
\(944\) 12.6349 0.411231
\(945\) 6.39777 + 30.0677i 0.208120 + 0.978103i
\(946\) −21.8960 −0.711902
\(947\) −13.5530 13.5530i −0.440413 0.440413i 0.451738 0.892151i \(-0.350804\pi\)
−0.892151 + 0.451738i \(0.850804\pi\)
\(948\) −13.8485 + 33.1500i −0.449779 + 1.07666i
\(949\) 34.0826i 1.10637i
\(950\) −2.67399 0.367619i −0.0867559 0.0119271i
\(951\) −19.5378 + 8.02383i −0.633558 + 0.260191i
\(952\) −22.6983 + 0.572547i −0.735655 + 0.0185563i
\(953\) 23.2988 23.2988i 0.754721 0.754721i −0.220635 0.975356i \(-0.570813\pi\)
0.975356 + 0.220635i \(0.0708131\pi\)
\(954\) −12.6522 + 3.30842i −0.409630 + 0.107114i
\(955\) −26.8697 + 30.4627i −0.869483 + 0.985751i
\(956\) −13.4584 23.3107i −0.435276 0.753921i
\(957\) −22.5850 9.43497i −0.730069 0.304989i
\(958\) −4.62062 + 17.2444i −0.149285 + 0.557141i
\(959\) −11.4253 38.7076i −0.368941 1.24993i
\(960\) 10.9532 5.32168i 0.353513 0.171756i
\(961\) 30.9663 0.998914
\(962\) 1.02606 + 3.82930i 0.0330815 + 0.123462i
\(963\) −37.4480 + 21.3202i −1.20674 + 0.687034i
\(964\) −6.22295 10.7785i −0.200428 0.347151i
\(965\) −0.695137 11.0920i −0.0223773 0.357064i
\(966\) −6.18410 2.40213i −0.198970 0.0772873i
\(967\) −9.20097 + 34.3385i −0.295883 + 1.10425i 0.644630 + 0.764495i \(0.277011\pi\)
−0.940513 + 0.339757i \(0.889655\pi\)
\(968\) −3.78588 14.1291i −0.121683 0.454126i
\(969\) 3.62696 + 8.83155i 0.116515 + 0.283710i
\(970\) −5.38408 16.0114i −0.172872 0.514094i
\(971\) 26.5026 15.3013i 0.850510 0.491042i −0.0103128 0.999947i \(-0.503283\pi\)
0.860823 + 0.508905i \(0.169949\pi\)
\(972\) 10.9887 25.4365i 0.352464 0.815876i
\(973\) −14.4605 7.86942i −0.463583 0.252282i
\(974\) −1.29648 0.748521i −0.0415418 0.0239842i
\(975\) 11.1802 18.9795i 0.358052 0.607831i
\(976\) 23.5052i 0.752382i
\(977\) −17.4169 17.4169i −0.557217 0.557217i 0.371297 0.928514i \(-0.378913\pi\)
−0.928514 + 0.371297i \(0.878913\pi\)
\(978\) −5.22906 + 0.672368i −0.167207 + 0.0215000i
\(979\) 9.55999 16.5584i 0.305539 0.529208i
\(980\) −25.8908 + 10.1861i −0.827050 + 0.325382i
\(981\) −13.7887 52.7315i −0.440240 1.68359i
\(982\) 0.604560 2.25625i 0.0192923 0.0719998i
\(983\) −10.5661 + 39.4332i −0.337006 + 1.25772i 0.564671 + 0.825316i \(0.309003\pi\)
−0.901678 + 0.432409i \(0.857664\pi\)
\(984\) 12.0384 + 9.29526i 0.383771 + 0.296322i
\(985\) 36.6663 2.29788i 1.16829 0.0732167i
\(986\) −6.34365 + 3.66251i −0.202023 + 0.116638i
\(987\) 31.2781 + 22.9156i 0.995592 + 0.729410i
\(988\) 1.33920 + 4.99798i 0.0426058 + 0.159007i
\(989\) 28.1521 16.2536i 0.895184 0.516835i
\(990\) −2.82646 + 13.5771i −0.0898309 + 0.431508i
\(991\) −21.2713 + 36.8430i −0.675705 + 1.17036i 0.300557 + 0.953764i \(0.402827\pi\)
−0.976262 + 0.216592i \(0.930506\pi\)
\(992\) 0.628480 0.628480i 0.0199543 0.0199543i
\(993\) −15.8725 + 37.9949i −0.503699 + 1.20573i
\(994\) −3.84427 0.926835i −0.121933 0.0293974i
\(995\) −5.71265 16.9885i −0.181103 0.538571i
\(996\) 28.5921 + 3.85205i 0.905975 + 0.122057i
\(997\) −55.8729 14.9711i −1.76951 0.474140i −0.780905 0.624650i \(-0.785242\pi\)
−0.988608 + 0.150510i \(0.951908\pi\)
\(998\) 4.20651 + 15.6989i 0.133155 + 0.496941i
\(999\) −2.08687 17.0424i −0.0660257 0.539199i
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 315.2.bs.e.52.17 160
3.2 odd 2 945.2.bv.e.262.24 160
5.3 odd 4 inner 315.2.bs.e.178.17 yes 160
7.5 odd 6 315.2.cg.e.187.17 yes 160
9.4 even 3 315.2.cg.e.157.24 yes 160
9.5 odd 6 945.2.cj.e.577.17 160
15.8 even 4 945.2.bv.e.73.24 160
21.5 even 6 945.2.cj.e.397.24 160
35.33 even 12 315.2.cg.e.313.24 yes 160
45.13 odd 12 315.2.cg.e.283.17 yes 160
45.23 even 12 945.2.cj.e.388.24 160
63.5 even 6 945.2.bv.e.712.24 160
63.40 odd 6 inner 315.2.bs.e.292.17 yes 160
105.68 odd 12 945.2.cj.e.208.17 160
315.68 odd 12 945.2.bv.e.523.24 160
315.103 even 12 inner 315.2.bs.e.103.17 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.2.bs.e.52.17 160 1.1 even 1 trivial
315.2.bs.e.103.17 yes 160 315.103 even 12 inner
315.2.bs.e.178.17 yes 160 5.3 odd 4 inner
315.2.bs.e.292.17 yes 160 63.40 odd 6 inner
315.2.cg.e.157.24 yes 160 9.4 even 3
315.2.cg.e.187.17 yes 160 7.5 odd 6
315.2.cg.e.283.17 yes 160 45.13 odd 12
315.2.cg.e.313.24 yes 160 35.33 even 12
945.2.bv.e.73.24 160 15.8 even 4
945.2.bv.e.262.24 160 3.2 odd 2
945.2.bv.e.523.24 160 315.68 odd 12
945.2.bv.e.712.24 160 63.5 even 6
945.2.cj.e.208.17 160 105.68 odd 12
945.2.cj.e.388.24 160 45.23 even 12
945.2.cj.e.397.24 160 21.5 even 6
945.2.cj.e.577.17 160 9.5 odd 6