Properties

Label 882.2.bk.a.131.14
Level $882$
Weight $2$
Character 882.131
Analytic conductor $7.043$
Analytic rank $0$
Dimension $672$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(5,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([35, 29]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.bk (of order \(42\), degree \(12\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(672\)
Relative dimension: \(56\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 131.14
Character \(\chi\) \(=\) 882.131
Dual form 882.2.bk.a.101.14

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.781831 - 0.623490i) q^{2} +(-0.242548 + 1.71498i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.249299 - 3.32667i) q^{5} +(1.25891 - 1.18960i) q^{6} +(2.64448 - 0.0819252i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-2.88234 - 0.831931i) q^{9} +O(q^{10})\) \(q+(-0.781831 - 0.623490i) q^{2} +(-0.242548 + 1.71498i) q^{3} +(0.222521 + 0.974928i) q^{4} +(-0.249299 - 3.32667i) q^{5} +(1.25891 - 1.18960i) q^{6} +(2.64448 - 0.0819252i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-2.88234 - 0.831931i) q^{9} +(-1.87923 + 2.75633i) q^{10} +(-4.54704 + 1.78458i) q^{11} +(-1.72596 + 0.145153i) q^{12} +(-4.62858 + 1.81658i) q^{13} +(-2.11862 - 1.58476i) q^{14} +(5.76565 + 0.379331i) q^{15} +(-0.900969 + 0.433884i) q^{16} +(-3.86932 + 1.19353i) q^{17} +(1.73480 + 2.44754i) q^{18} +(7.24954 + 4.18553i) q^{19} +(3.18778 - 0.983301i) q^{20} +(-0.500913 + 4.55512i) q^{21} +(4.66768 + 1.43979i) q^{22} +(1.38432 + 1.49194i) q^{23} +(1.43991 + 0.962632i) q^{24} +(-6.06040 + 0.913458i) q^{25} +(4.75139 + 1.46561i) q^{26} +(2.12585 - 4.74139i) q^{27} +(0.668324 + 2.55995i) q^{28} +(1.06734 + 3.46022i) q^{29} +(-4.27125 - 3.89139i) q^{30} +4.94097i q^{31} +(0.974928 + 0.222521i) q^{32} +(-1.95765 - 8.23094i) q^{33} +(3.76931 + 1.47934i) q^{34} +(-0.931805 - 8.77689i) q^{35} +(0.169691 - 2.99520i) q^{36} +(0.886574 + 0.822621i) q^{37} +(-3.05829 - 7.79239i) q^{38} +(-1.99276 - 8.37854i) q^{39} +(-3.10539 - 1.21878i) q^{40} +(-1.77529 + 1.21037i) q^{41} +(3.23170 - 3.24902i) q^{42} +(6.65895 + 4.53999i) q^{43} +(-2.75165 - 4.03593i) q^{44} +(-2.04899 + 9.79598i) q^{45} +(-0.152094 - 2.02956i) q^{46} +(-4.91816 + 6.16718i) q^{47} +(-0.525576 - 1.65038i) q^{48} +(6.98658 - 0.433300i) q^{49} +(5.30774 + 3.06443i) q^{50} +(-1.10839 - 6.92531i) q^{51} +(-2.80099 - 4.10830i) q^{52} +(6.40114 + 6.89879i) q^{53} +(-4.61827 + 2.38152i) q^{54} +(7.07028 + 14.6816i) q^{55} +(1.07359 - 2.41814i) q^{56} +(-8.93647 + 11.4177i) q^{57} +(1.32293 - 3.37078i) q^{58} +(-2.43139 + 1.17090i) q^{59} +(0.913157 + 5.70550i) q^{60} +(-8.51672 - 1.94389i) q^{61} +(3.08064 - 3.86300i) q^{62} +(-7.69046 - 1.96389i) q^{63} +(-0.623490 - 0.781831i) q^{64} +(7.19706 + 14.9448i) q^{65} +(-3.60135 + 7.65579i) q^{66} -16.0140 q^{67} +(-2.02461 - 3.50672i) q^{68} +(-2.89442 + 2.01222i) q^{69} +(-4.74378 + 7.44302i) q^{70} +(1.57169 - 0.358727i) q^{71} +(-2.00014 + 2.23594i) q^{72} +(3.01894 + 1.18485i) q^{73} +(-0.180256 - 1.19592i) q^{74} +(-0.0966307 - 10.6150i) q^{75} +(-2.46741 + 7.99915i) q^{76} +(-11.8784 + 5.09181i) q^{77} +(-3.66593 + 7.79307i) q^{78} -7.87304 q^{79} +(1.66800 + 2.88906i) q^{80} +(7.61578 + 4.79582i) q^{81} +(2.14264 + 0.160568i) q^{82} +(1.41829 - 3.61375i) q^{83} +(-4.55237 + 0.525255i) q^{84} +(4.93509 + 12.5744i) q^{85} +(-2.37554 - 7.70130i) q^{86} +(-6.19310 + 0.991196i) q^{87} +(-0.365034 + 4.87104i) q^{88} +(1.51443 - 0.228264i) q^{89} +(7.70966 - 6.38128i) q^{90} +(-12.0914 + 5.18312i) q^{91} +(-1.14650 + 1.68160i) q^{92} +(-8.47368 - 1.19842i) q^{93} +(7.69035 - 1.75527i) q^{94} +(12.1165 - 25.1603i) q^{95} +(-0.618086 + 1.61801i) q^{96} +(1.11935 - 0.646260i) q^{97} +(-5.73248 - 4.01729i) q^{98} +(14.5908 - 1.36095i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 672 q + 112 q^{4} + 14 q^{6} - 2 q^{7} + 10 q^{9} - 6 q^{13} + 6 q^{14} + 6 q^{15} - 112 q^{16} + 18 q^{17} + 8 q^{18} + 12 q^{21} + 18 q^{23} + 56 q^{25} - 12 q^{26} + 48 q^{27} + 2 q^{28} - 6 q^{29} + 4 q^{30} - 30 q^{35} - 10 q^{36} - 26 q^{37} + 4 q^{39} + 6 q^{41} + 14 q^{42} + 2 q^{43} + 58 q^{45} + 78 q^{46} - 90 q^{47} + 8 q^{49} + 24 q^{50} + 6 q^{51} - 22 q^{52} + 12 q^{53} - 18 q^{54} - 42 q^{55} - 6 q^{56} - 28 q^{57} + 78 q^{58} - 60 q^{59} - 6 q^{60} + 98 q^{61} - 36 q^{62} - 36 q^{63} + 112 q^{64} - 24 q^{66} + 28 q^{67} - 18 q^{68} + 14 q^{69} + 18 q^{70} + 126 q^{71} - 8 q^{72} - 18 q^{74} - 102 q^{75} + 42 q^{77} - 8 q^{78} - 8 q^{79} + 26 q^{81} + 30 q^{84} + 80 q^{87} - 186 q^{89} - 102 q^{90} + 12 q^{91} - 18 q^{92} - 224 q^{93} - 6 q^{97} + 24 q^{98} + 194 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.781831 0.623490i −0.552838 0.440874i
\(3\) −0.242548 + 1.71498i −0.140035 + 0.990147i
\(4\) 0.222521 + 0.974928i 0.111260 + 0.487464i
\(5\) −0.249299 3.32667i −0.111490 1.48773i −0.719884 0.694095i \(-0.755805\pi\)
0.608394 0.793635i \(-0.291814\pi\)
\(6\) 1.25891 1.18960i 0.513946 0.485653i
\(7\) 2.64448 0.0819252i 0.999520 0.0309648i
\(8\) 0.433884 0.900969i 0.153401 0.318541i
\(9\) −2.88234 0.831931i −0.960780 0.277310i
\(10\) −1.87923 + 2.75633i −0.594265 + 0.871627i
\(11\) −4.54704 + 1.78458i −1.37098 + 0.538071i −0.932663 0.360748i \(-0.882522\pi\)
−0.438320 + 0.898819i \(0.644426\pi\)
\(12\) −1.72596 + 0.145153i −0.498241 + 0.0419022i
\(13\) −4.62858 + 1.81658i −1.28374 + 0.503829i −0.906468 0.422275i \(-0.861232\pi\)
−0.377268 + 0.926104i \(0.623136\pi\)
\(14\) −2.11862 1.58476i −0.566225 0.423544i
\(15\) 5.76565 + 0.379331i 1.48868 + 0.0979428i
\(16\) −0.900969 + 0.433884i −0.225242 + 0.108471i
\(17\) −3.86932 + 1.19353i −0.938448 + 0.289473i −0.725996 0.687699i \(-0.758621\pi\)
−0.212452 + 0.977172i \(0.568145\pi\)
\(18\) 1.73480 + 2.44754i 0.408897 + 0.576891i
\(19\) 7.24954 + 4.18553i 1.66316 + 0.960226i 0.971193 + 0.238296i \(0.0765889\pi\)
0.691967 + 0.721929i \(0.256744\pi\)
\(20\) 3.18778 0.983301i 0.712810 0.219873i
\(21\) −0.500913 + 4.55512i −0.109308 + 0.994008i
\(22\) 4.66768 + 1.43979i 0.995154 + 0.306964i
\(23\) 1.38432 + 1.49194i 0.288651 + 0.311092i 0.860685 0.509138i \(-0.170036\pi\)
−0.572034 + 0.820230i \(0.693845\pi\)
\(24\) 1.43991 + 0.962632i 0.293920 + 0.196496i
\(25\) −6.06040 + 0.913458i −1.21208 + 0.182692i
\(26\) 4.75139 + 1.46561i 0.931823 + 0.287429i
\(27\) 2.12585 4.74139i 0.409121 0.912480i
\(28\) 0.668324 + 2.55995i 0.126301 + 0.483785i
\(29\) 1.06734 + 3.46022i 0.198199 + 0.642546i 0.999046 + 0.0436764i \(0.0139071\pi\)
−0.800847 + 0.598870i \(0.795617\pi\)
\(30\) −4.27125 3.89139i −0.779821 0.710468i
\(31\) 4.94097i 0.887424i 0.896170 + 0.443712i \(0.146339\pi\)
−0.896170 + 0.443712i \(0.853661\pi\)
\(32\) 0.974928 + 0.222521i 0.172345 + 0.0393365i
\(33\) −1.95765 8.23094i −0.340784 1.43282i
\(34\) 3.76931 + 1.47934i 0.646431 + 0.253706i
\(35\) −0.931805 8.77689i −0.157504 1.48356i
\(36\) 0.169691 2.99520i 0.0282819 0.499199i
\(37\) 0.886574 + 0.822621i 0.145752 + 0.135238i 0.749679 0.661801i \(-0.230208\pi\)
−0.603927 + 0.797039i \(0.706398\pi\)
\(38\) −3.05829 7.79239i −0.496120 1.26409i
\(39\) −1.99276 8.37854i −0.319097 1.34164i
\(40\) −3.10539 1.21878i −0.491005 0.192705i
\(41\) −1.77529 + 1.21037i −0.277254 + 0.189029i −0.693962 0.720012i \(-0.744136\pi\)
0.416707 + 0.909041i \(0.363184\pi\)
\(42\) 3.23170 3.24902i 0.498662 0.501335i
\(43\) 6.65895 + 4.53999i 1.01548 + 0.692343i 0.952144 0.305650i \(-0.0988736\pi\)
0.0633360 + 0.997992i \(0.479826\pi\)
\(44\) −2.75165 4.03593i −0.414827 0.608439i
\(45\) −2.04899 + 9.79598i −0.305445 + 1.46030i
\(46\) −0.152094 2.02956i −0.0224251 0.299242i
\(47\) −4.91816 + 6.16718i −0.717388 + 0.899576i −0.998187 0.0601906i \(-0.980829\pi\)
0.280799 + 0.959767i \(0.409401\pi\)
\(48\) −0.525576 1.65038i −0.0758603 0.238213i
\(49\) 6.98658 0.433300i 0.998082 0.0619000i
\(50\) 5.30774 + 3.06443i 0.750628 + 0.433375i
\(51\) −1.10839 6.92531i −0.155205 0.969738i
\(52\) −2.80099 4.10830i −0.388428 0.569719i
\(53\) 6.40114 + 6.89879i 0.879265 + 0.947622i 0.998979 0.0451864i \(-0.0143882\pi\)
−0.119714 + 0.992808i \(0.538198\pi\)
\(54\) −4.61827 + 2.38152i −0.628466 + 0.324084i
\(55\) 7.07028 + 14.6816i 0.953356 + 1.97966i
\(56\) 1.07359 2.41814i 0.143464 0.323138i
\(57\) −8.93647 + 11.4177i −1.18366 + 1.51231i
\(58\) 1.32293 3.37078i 0.173710 0.442605i
\(59\) −2.43139 + 1.17090i −0.316540 + 0.152438i −0.585407 0.810740i \(-0.699065\pi\)
0.268867 + 0.963177i \(0.413351\pi\)
\(60\) 0.913157 + 5.70550i 0.117888 + 0.736577i
\(61\) −8.51672 1.94389i −1.09045 0.248889i −0.360758 0.932660i \(-0.617482\pi\)
−0.729697 + 0.683770i \(0.760339\pi\)
\(62\) 3.08064 3.86300i 0.391242 0.490602i
\(63\) −7.69046 1.96389i −0.968907 0.247427i
\(64\) −0.623490 0.781831i −0.0779362 0.0977289i
\(65\) 7.19706 + 14.9448i 0.892685 + 1.85368i
\(66\) −3.60135 + 7.65579i −0.443296 + 0.942362i
\(67\) −16.0140 −1.95642 −0.978211 0.207614i \(-0.933430\pi\)
−0.978211 + 0.207614i \(0.933430\pi\)
\(68\) −2.02461 3.50672i −0.245520 0.425253i
\(69\) −2.89442 + 2.01222i −0.348448 + 0.242243i
\(70\) −4.74378 + 7.44302i −0.566991 + 0.889611i
\(71\) 1.57169 0.358727i 0.186525 0.0425731i −0.128238 0.991743i \(-0.540932\pi\)
0.314763 + 0.949170i \(0.398075\pi\)
\(72\) −2.00014 + 2.23594i −0.235719 + 0.263508i
\(73\) 3.01894 + 1.18485i 0.353340 + 0.138676i 0.535371 0.844617i \(-0.320172\pi\)
−0.182031 + 0.983293i \(0.558267\pi\)
\(74\) −0.180256 1.19592i −0.0209543 0.139023i
\(75\) −0.0966307 10.6150i −0.0111580 1.22572i
\(76\) −2.46741 + 7.99915i −0.283031 + 0.917565i
\(77\) −11.8784 + 5.09181i −1.35366 + 0.580266i
\(78\) −3.66593 + 7.79307i −0.415085 + 0.882392i
\(79\) −7.87304 −0.885786 −0.442893 0.896575i \(-0.646048\pi\)
−0.442893 + 0.896575i \(0.646048\pi\)
\(80\) 1.66800 + 2.88906i 0.186488 + 0.323006i
\(81\) 7.61578 + 4.79582i 0.846198 + 0.532869i
\(82\) 2.14264 + 0.160568i 0.236615 + 0.0177318i
\(83\) 1.41829 3.61375i 0.155678 0.396661i −0.831661 0.555283i \(-0.812610\pi\)
0.987339 + 0.158622i \(0.0507052\pi\)
\(84\) −4.55237 + 0.525255i −0.496705 + 0.0573100i
\(85\) 4.93509 + 12.5744i 0.535285 + 1.36388i
\(86\) −2.37554 7.70130i −0.256161 0.830452i
\(87\) −6.19310 + 0.991196i −0.663970 + 0.106267i
\(88\) −0.365034 + 4.87104i −0.0389128 + 0.519255i
\(89\) 1.51443 0.228264i 0.160529 0.0241959i −0.0682857 0.997666i \(-0.521753\pi\)
0.228815 + 0.973470i \(0.426515\pi\)
\(90\) 7.70966 6.38128i 0.812670 0.672646i
\(91\) −12.0914 + 5.18312i −1.26752 + 0.543338i
\(92\) −1.14650 + 1.68160i −0.119531 + 0.175319i
\(93\) −8.47368 1.19842i −0.878679 0.124270i
\(94\) 7.69035 1.75527i 0.793199 0.181043i
\(95\) 12.1165 25.1603i 1.24313 2.58139i
\(96\) −0.618086 + 1.61801i −0.0630832 + 0.165138i
\(97\) 1.11935 0.646260i 0.113653 0.0656177i −0.442096 0.896968i \(-0.645765\pi\)
0.555749 + 0.831350i \(0.312432\pi\)
\(98\) −5.73248 4.01729i −0.579068 0.405808i
\(99\) 14.5908 1.36095i 1.46643 0.136781i
\(100\) −2.23912 5.70519i −0.223912 0.570519i
\(101\) −2.13708 + 1.45704i −0.212647 + 0.144981i −0.664960 0.746879i \(-0.731551\pi\)
0.452313 + 0.891859i \(0.350599\pi\)
\(102\) −3.45129 + 6.10549i −0.341729 + 0.604534i
\(103\) −0.176088 + 0.0131960i −0.0173505 + 0.00130024i −0.0834025 0.996516i \(-0.526579\pi\)
0.0660520 + 0.997816i \(0.478960\pi\)
\(104\) −0.371580 + 4.95839i −0.0364364 + 0.486210i
\(105\) 15.2782 + 0.530782i 1.49100 + 0.0517990i
\(106\) −0.703289 9.38474i −0.0683095 0.911527i
\(107\) 0.714793 + 4.74234i 0.0691016 + 0.458459i 0.996445 + 0.0842475i \(0.0268486\pi\)
−0.927343 + 0.374212i \(0.877913\pi\)
\(108\) 5.09556 + 1.01750i 0.490320 + 0.0979086i
\(109\) −17.0061 2.56325i −1.62889 0.245515i −0.729919 0.683533i \(-0.760442\pi\)
−0.898966 + 0.438018i \(0.855680\pi\)
\(110\) 3.62605 15.8868i 0.345730 1.51474i
\(111\) −1.62582 + 1.32094i −0.154316 + 0.125378i
\(112\) −2.34705 + 1.22121i −0.221775 + 0.115394i
\(113\) −1.83430 12.1698i −0.172557 1.14484i −0.892580 0.450890i \(-0.851107\pi\)
0.720023 0.693950i \(-0.244131\pi\)
\(114\) 14.1056 3.35489i 1.32111 0.314214i
\(115\) 4.61809 4.97711i 0.430639 0.464118i
\(116\) −3.13596 + 1.81055i −0.291166 + 0.168105i
\(117\) 14.8524 1.38535i 1.37311 0.128076i
\(118\) 2.63098 + 0.600504i 0.242201 + 0.0552809i
\(119\) −10.1346 + 3.47326i −0.929035 + 0.318393i
\(120\) 2.84339 5.03008i 0.259564 0.459182i
\(121\) 9.42725 8.74721i 0.857023 0.795201i
\(122\) 5.44665 + 6.82988i 0.493116 + 0.618349i
\(123\) −1.64518 3.33817i −0.148341 0.300993i
\(124\) −4.81708 + 1.09947i −0.432587 + 0.0987352i
\(125\) 0.837980 + 3.67143i 0.0749512 + 0.328383i
\(126\) 4.78818 + 6.33035i 0.426565 + 0.563953i
\(127\) 0.583680 2.55727i 0.0517932 0.226921i −0.942407 0.334469i \(-0.891443\pi\)
0.994200 + 0.107548i \(0.0343001\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −9.40113 + 10.3188i −0.827723 + 0.908522i
\(130\) 3.69107 16.1716i 0.323728 1.41835i
\(131\) 5.13740 + 3.50262i 0.448856 + 0.306025i 0.766569 0.642162i \(-0.221962\pi\)
−0.317713 + 0.948187i \(0.602915\pi\)
\(132\) 7.58896 3.74013i 0.660534 0.325536i
\(133\) 19.5142 + 10.4746i 1.69210 + 0.908266i
\(134\) 12.5203 + 9.98457i 1.08158 + 0.862535i
\(135\) −16.3030 5.88998i −1.40314 0.506929i
\(136\) −0.603504 + 4.00399i −0.0517501 + 0.343339i
\(137\) 8.21414 + 0.615564i 0.701781 + 0.0525912i 0.420841 0.907134i \(-0.361735\pi\)
0.280940 + 0.959725i \(0.409354\pi\)
\(138\) 3.51755 + 0.231425i 0.299434 + 0.0197002i
\(139\) −9.12929 13.3902i −0.774337 1.13574i −0.987329 0.158689i \(-0.949273\pi\)
0.212992 0.977054i \(-0.431679\pi\)
\(140\) 8.34948 2.86148i 0.705660 0.241839i
\(141\) −9.38373 9.93041i −0.790253 0.836291i
\(142\) −1.45246 0.699466i −0.121887 0.0586979i
\(143\) 17.8045 16.5201i 1.48888 1.38148i
\(144\) 2.95786 0.501057i 0.246488 0.0417548i
\(145\) 11.2449 4.41330i 0.933838 0.366504i
\(146\) −1.62156 2.80863i −0.134201 0.232444i
\(147\) −0.951476 + 12.0870i −0.0784764 + 0.996916i
\(148\) −0.604714 + 1.04740i −0.0497072 + 0.0860954i
\(149\) −1.81981 + 12.0737i −0.149085 + 0.989114i 0.781728 + 0.623619i \(0.214338\pi\)
−0.930813 + 0.365495i \(0.880900\pi\)
\(150\) −6.54282 + 8.35942i −0.534219 + 0.682544i
\(151\) 8.64864 + 2.66775i 0.703816 + 0.217099i 0.625948 0.779865i \(-0.284712\pi\)
0.0778686 + 0.996964i \(0.475189\pi\)
\(152\) 6.91649 4.71558i 0.561001 0.382484i
\(153\) 12.1456 0.221146i 0.981917 0.0178786i
\(154\) 12.4616 + 3.42510i 1.00418 + 0.276002i
\(155\) 16.4369 1.23178i 1.32025 0.0989388i
\(156\) 7.72504 3.80720i 0.618498 0.304820i
\(157\) −7.22710 15.0072i −0.576785 1.19771i −0.961534 0.274686i \(-0.911426\pi\)
0.384749 0.923021i \(-0.374288\pi\)
\(158\) 6.15539 + 4.90876i 0.489696 + 0.390520i
\(159\) −13.3839 + 9.30457i −1.06141 + 0.737901i
\(160\) 0.497204 3.29873i 0.0393074 0.260788i
\(161\) 3.78304 + 3.83201i 0.298145 + 0.302004i
\(162\) −2.96412 8.49788i −0.232883 0.667657i
\(163\) −1.19830 + 15.9902i −0.0938579 + 1.25245i 0.729125 + 0.684380i \(0.239927\pi\)
−0.822983 + 0.568066i \(0.807692\pi\)
\(164\) −1.57507 1.46145i −0.122992 0.114120i
\(165\) −26.8936 + 8.56443i −2.09366 + 0.666740i
\(166\) −3.36200 + 1.94105i −0.260942 + 0.150655i
\(167\) −16.2358 15.0646i −1.25636 1.16574i −0.978753 0.205042i \(-0.934267\pi\)
−0.277611 0.960694i \(-0.589543\pi\)
\(168\) 3.88668 + 2.42770i 0.299864 + 0.187301i
\(169\) 8.59406 7.97413i 0.661082 0.613394i
\(170\) 3.98160 12.9080i 0.305375 0.990001i
\(171\) −17.4136 18.0952i −1.33165 1.38378i
\(172\) −2.94441 + 7.50224i −0.224509 + 0.572040i
\(173\) −1.75325 7.68148i −0.133297 0.584012i −0.996819 0.0797009i \(-0.974603\pi\)
0.863522 0.504311i \(-0.168254\pi\)
\(174\) 5.45996 + 3.08638i 0.413918 + 0.233978i
\(175\) −15.9518 + 2.91212i −1.20584 + 0.220136i
\(176\) 3.32244 3.58074i 0.250438 0.269908i
\(177\) −1.41834 4.45379i −0.106609 0.334768i
\(178\) −1.32635 0.765769i −0.0994142 0.0573968i
\(179\) 7.37543 + 23.9105i 0.551265 + 1.78716i 0.614211 + 0.789141i \(0.289474\pi\)
−0.0629461 + 0.998017i \(0.520050\pi\)
\(180\) −10.0063 + 0.182194i −0.745827 + 0.0135799i
\(181\) −19.0046 + 15.1557i −1.41260 + 1.12651i −0.438943 + 0.898515i \(0.644647\pi\)
−0.973661 + 0.227999i \(0.926782\pi\)
\(182\) 12.6850 + 3.48652i 0.940277 + 0.258438i
\(183\) 5.39945 14.1346i 0.399139 1.04486i
\(184\) 1.94483 0.599900i 0.143375 0.0442252i
\(185\) 2.51556 3.15441i 0.184948 0.231917i
\(186\) 5.87779 + 6.22021i 0.430980 + 0.456088i
\(187\) 15.4640 12.3321i 1.13084 0.901815i
\(188\) −7.10695 3.42253i −0.518328 0.249614i
\(189\) 5.23334 12.7127i 0.380670 0.924711i
\(190\) −25.1603 + 12.1165i −1.82532 + 0.879026i
\(191\) 3.79644 7.88338i 0.274700 0.570421i −0.717284 0.696781i \(-0.754615\pi\)
0.991985 + 0.126359i \(0.0403293\pi\)
\(192\) 1.49205 0.879644i 0.107680 0.0634828i
\(193\) 14.4737 + 6.97019i 1.04184 + 0.501725i 0.874932 0.484247i \(-0.160906\pi\)
0.166912 + 0.985972i \(0.446621\pi\)
\(194\) −1.27808 0.192640i −0.0917610 0.0138308i
\(195\) −27.3758 + 8.71801i −1.96042 + 0.624309i
\(196\) 1.97710 + 6.71499i 0.141221 + 0.479642i
\(197\) 8.36687i 0.596115i 0.954548 + 0.298058i \(0.0963387\pi\)
−0.954548 + 0.298058i \(0.903661\pi\)
\(198\) −12.2561 8.03316i −0.871000 0.570892i
\(199\) 15.3682 1.15169i 1.08943 0.0816411i 0.482116 0.876107i \(-0.339868\pi\)
0.607309 + 0.794466i \(0.292249\pi\)
\(200\) −1.80651 + 5.85657i −0.127740 + 0.414122i
\(201\) 3.88416 27.4638i 0.273967 1.93714i
\(202\) 2.57928 + 0.193291i 0.181478 + 0.0135999i
\(203\) 3.10603 + 9.06304i 0.218000 + 0.636101i
\(204\) 6.50504 2.62162i 0.455444 0.183550i
\(205\) 4.46909 + 5.60406i 0.312135 + 0.391405i
\(206\) 0.145899 + 0.0994722i 0.0101653 + 0.00693056i
\(207\) −2.74889 5.45195i −0.191061 0.378937i
\(208\) 3.38202 3.64495i 0.234501 0.252732i
\(209\) −40.4334 6.09435i −2.79683 0.421555i
\(210\) −11.6141 9.94080i −0.801446 0.685980i
\(211\) 23.8955 3.60167i 1.64504 0.247949i 0.739790 0.672837i \(-0.234925\pi\)
0.905246 + 0.424888i \(0.139687\pi\)
\(212\) −5.30144 + 7.77578i −0.364104 + 0.534043i
\(213\) 0.234003 + 2.78243i 0.0160336 + 0.190649i
\(214\) 2.39795 4.15338i 0.163921 0.283919i
\(215\) 13.4430 23.2839i 0.916803 1.58795i
\(216\) −3.34947 3.97254i −0.227902 0.270297i
\(217\) 0.404790 + 13.0663i 0.0274789 + 0.886998i
\(218\) 11.6977 + 12.6071i 0.792269 + 0.853863i
\(219\) −2.76423 + 4.89005i −0.186789 + 0.330439i
\(220\) −12.7402 + 10.1600i −0.858944 + 0.684985i
\(221\) 15.7413 12.5533i 1.05887 0.844424i
\(222\) 2.09471 0.0190685i 0.140587 0.00127979i
\(223\) −1.32490 1.42791i −0.0887221 0.0956196i 0.687130 0.726534i \(-0.258870\pi\)
−0.775852 + 0.630915i \(0.782680\pi\)
\(224\) 2.59641 + 0.508582i 0.173480 + 0.0339810i
\(225\) 18.2281 + 2.40893i 1.21520 + 0.160596i
\(226\) −6.15364 + 10.6584i −0.409334 + 0.708987i
\(227\) 5.09244 8.82036i 0.337997 0.585428i −0.646059 0.763288i \(-0.723584\pi\)
0.984056 + 0.177860i \(0.0569173\pi\)
\(228\) −13.1199 6.17175i −0.868890 0.408734i
\(229\) −7.75833 + 11.3794i −0.512685 + 0.751970i −0.992077 0.125630i \(-0.959905\pi\)
0.479392 + 0.877601i \(0.340857\pi\)
\(230\) −6.71374 + 1.01193i −0.442691 + 0.0667249i
\(231\) −5.85130 21.6062i −0.384988 1.42158i
\(232\) 3.58065 + 0.539696i 0.235081 + 0.0354328i
\(233\) 13.2724 14.3042i 0.869502 0.937100i −0.129010 0.991643i \(-0.541180\pi\)
0.998511 + 0.0545435i \(0.0173703\pi\)
\(234\) −12.4758 8.17721i −0.815571 0.534561i
\(235\) 21.7422 + 14.8236i 1.41831 + 0.966986i
\(236\) −1.68257 2.10988i −0.109526 0.137342i
\(237\) 1.90959 13.5021i 0.124041 0.877058i
\(238\) 10.0891 + 3.60330i 0.653977 + 0.233567i
\(239\) −16.7019 1.25163i −1.08036 0.0809615i −0.477362 0.878707i \(-0.658407\pi\)
−0.602995 + 0.797745i \(0.706026\pi\)
\(240\) −5.35925 + 2.15985i −0.345938 + 0.139418i
\(241\) 6.24237 20.2373i 0.402106 1.30360i −0.497716 0.867340i \(-0.665828\pi\)
0.899822 0.436257i \(-0.143696\pi\)
\(242\) −12.8243 + 0.961050i −0.824378 + 0.0617786i
\(243\) −10.0719 + 11.8977i −0.646115 + 0.763240i
\(244\) 8.73575i 0.559249i
\(245\) −3.18319 23.1340i −0.203367 1.47798i
\(246\) −0.795064 + 3.63564i −0.0506914 + 0.231800i
\(247\) −41.1584 6.20363i −2.61885 0.394728i
\(248\) 4.45166 + 2.14380i 0.282680 + 0.136132i
\(249\) 5.85352 + 3.30886i 0.370952 + 0.209690i
\(250\) 1.63394 3.39291i 0.103339 0.214587i
\(251\) −13.5581 + 6.52922i −0.855777 + 0.412121i −0.809719 0.586818i \(-0.800380\pi\)
−0.0460584 + 0.998939i \(0.514666\pi\)
\(252\) 0.203363 7.93465i 0.0128107 0.499836i
\(253\) −8.95705 4.31349i −0.563125 0.271187i
\(254\) −2.05077 + 1.63544i −0.128677 + 0.102616i
\(255\) −22.7619 + 5.41370i −1.42540 + 0.339019i
\(256\) 0.623490 0.781831i 0.0389681 0.0488645i
\(257\) 6.16512 1.90169i 0.384570 0.118624i −0.0964411 0.995339i \(-0.530746\pi\)
0.481011 + 0.876715i \(0.340270\pi\)
\(258\) 13.7838 2.20607i 0.858141 0.137344i
\(259\) 2.41192 + 2.10277i 0.149870 + 0.130660i
\(260\) −12.9687 + 10.3422i −0.804282 + 0.641393i
\(261\) −0.197764 10.8615i −0.0122413 0.672308i
\(262\) −1.83273 5.94157i −0.113227 0.367072i
\(263\) 5.48751 + 3.16822i 0.338375 + 0.195361i 0.659553 0.751658i \(-0.270746\pi\)
−0.321178 + 0.947019i \(0.604079\pi\)
\(264\) −8.26522 1.80749i −0.508689 0.111243i
\(265\) 21.3542 23.0143i 1.31178 1.41376i
\(266\) −8.72598 20.3563i −0.535024 1.24812i
\(267\) 0.0241470 + 2.65259i 0.00147777 + 0.162336i
\(268\) −3.56345 15.6125i −0.217672 0.953685i
\(269\) −9.63915 + 24.5602i −0.587709 + 1.49746i 0.259255 + 0.965809i \(0.416523\pi\)
−0.846964 + 0.531650i \(0.821572\pi\)
\(270\) 9.07384 + 14.7697i 0.552216 + 0.898856i
\(271\) 2.18619 7.08745i 0.132801 0.430532i −0.864609 0.502444i \(-0.832434\pi\)
0.997411 + 0.0719128i \(0.0229103\pi\)
\(272\) 2.96829 2.75417i 0.179979 0.166996i
\(273\) −5.95623 21.9936i −0.360487 1.33112i
\(274\) −6.03827 5.60270i −0.364785 0.338471i
\(275\) 25.9267 14.9688i 1.56344 0.902653i
\(276\) −2.60584 2.37409i −0.156853 0.142904i
\(277\) 7.07983 + 6.56913i 0.425386 + 0.394700i 0.863606 0.504167i \(-0.168200\pi\)
−0.438220 + 0.898868i \(0.644391\pi\)
\(278\) −1.21109 + 16.1609i −0.0726365 + 0.969267i
\(279\) 4.11054 14.2415i 0.246092 0.852619i
\(280\) −8.31200 2.96862i −0.496737 0.177409i
\(281\) −0.455254 + 3.02041i −0.0271582 + 0.180183i −0.998297 0.0583311i \(-0.981422\pi\)
0.971139 + 0.238514i \(0.0766602\pi\)
\(282\) 1.14499 + 13.6146i 0.0681830 + 0.810736i
\(283\) −20.9283 16.6897i −1.24406 0.992102i −0.999749 0.0224043i \(-0.992868\pi\)
−0.244308 0.969698i \(-0.578561\pi\)
\(284\) 0.699466 + 1.45246i 0.0415057 + 0.0861874i
\(285\) 40.2106 + 26.8822i 2.38187 + 1.59237i
\(286\) −24.2202 + 1.81506i −1.43217 + 0.107326i
\(287\) −4.59557 + 3.34626i −0.271268 + 0.197523i
\(288\) −2.62495 1.45245i −0.154677 0.0855867i
\(289\) −0.498920 + 0.340158i −0.0293482 + 0.0200093i
\(290\) −11.5433 3.56062i −0.677844 0.209087i
\(291\) 0.836829 + 2.07642i 0.0490558 + 0.121722i
\(292\) −0.483362 + 3.20690i −0.0282866 + 0.187670i
\(293\) −1.33023 + 2.30403i −0.0777128 + 0.134603i −0.902263 0.431187i \(-0.858095\pi\)
0.824550 + 0.565789i \(0.191428\pi\)
\(294\) 8.27999 8.85673i 0.482899 0.516535i
\(295\) 4.50132 + 7.79652i 0.262077 + 0.453931i
\(296\) 1.12583 0.441854i 0.0654373 0.0256822i
\(297\) −1.20495 + 25.3530i −0.0699181 + 1.47113i
\(298\) 8.95060 8.30495i 0.518494 0.481093i
\(299\) −9.11767 4.39084i −0.527288 0.253929i
\(300\) 10.3274 2.45628i 0.596253 0.141813i
\(301\) 17.9814 + 11.4604i 1.03643 + 0.660566i
\(302\) −5.09846 7.47807i −0.293384 0.430315i
\(303\) −1.98045 4.01846i −0.113774 0.230855i
\(304\) −8.34764 0.625569i −0.478770 0.0358789i
\(305\) −4.34345 + 28.8169i −0.248705 + 1.65005i
\(306\) −9.63372 7.39978i −0.550723 0.423017i
\(307\) −1.68554 1.34417i −0.0961987 0.0767159i 0.574209 0.818708i \(-0.305310\pi\)
−0.670408 + 0.741993i \(0.733881\pi\)
\(308\) −7.60733 10.4475i −0.433468 0.595302i
\(309\) 0.0200789 0.305189i 0.00114225 0.0173616i
\(310\) −13.6189 9.28522i −0.773503 0.527365i
\(311\) −2.36944 + 10.3812i −0.134359 + 0.588665i 0.862257 + 0.506470i \(0.169050\pi\)
−0.996616 + 0.0821944i \(0.973807\pi\)
\(312\) −8.41343 1.83990i −0.476317 0.104164i
\(313\) 19.3291i 1.09254i −0.837608 0.546272i \(-0.816046\pi\)
0.837608 0.546272i \(-0.183954\pi\)
\(314\) −3.70648 + 16.2391i −0.209169 + 0.916428i
\(315\) −4.61598 + 26.0732i −0.260081 + 1.46906i
\(316\) −1.75192 7.67564i −0.0985529 0.431789i
\(317\) −7.36533 + 1.68109i −0.413678 + 0.0944193i −0.424294 0.905524i \(-0.639478\pi\)
0.0106163 + 0.999944i \(0.496621\pi\)
\(318\) 16.2653 + 1.07012i 0.912111 + 0.0600092i
\(319\) −11.0282 13.8290i −0.617463 0.774275i
\(320\) −2.44546 + 2.26905i −0.136705 + 0.126844i
\(321\) −8.30641 + 0.0756148i −0.463619 + 0.00422041i
\(322\) −0.568483 5.35467i −0.0316803 0.298404i
\(323\) −33.0464 7.54261i −1.83875 0.419682i
\(324\) −2.98090 + 8.49201i −0.165606 + 0.471778i
\(325\) 26.3916 15.2372i 1.46394 0.845209i
\(326\) 10.9066 11.7545i 0.604059 0.651021i
\(327\) 8.52072 28.5434i 0.471197 1.57845i
\(328\) 0.320239 + 2.12465i 0.0176822 + 0.117314i
\(329\) −12.5008 + 16.7119i −0.689189 + 0.921358i
\(330\) 26.3661 + 10.0719i 1.45140 + 0.554441i
\(331\) −1.36867 + 5.99652i −0.0752287 + 0.329598i −0.998513 0.0545195i \(-0.982637\pi\)
0.923284 + 0.384118i \(0.125494\pi\)
\(332\) 3.83875 + 0.578598i 0.210679 + 0.0317547i
\(333\) −1.87105 3.10864i −0.102533 0.170352i
\(334\) 3.30102 + 21.9009i 0.180624 + 1.19836i
\(335\) 3.99228 + 53.2732i 0.218121 + 2.91063i
\(336\) −1.52508 4.32136i −0.0832002 0.235749i
\(337\) −1.53127 + 20.4334i −0.0834138 + 1.11308i 0.785746 + 0.618549i \(0.212279\pi\)
−0.869160 + 0.494531i \(0.835340\pi\)
\(338\) −11.6909 + 0.876111i −0.635901 + 0.0476542i
\(339\) 21.3160 0.194043i 1.15772 0.0105390i
\(340\) −11.1610 + 7.60942i −0.605288 + 0.412679i
\(341\) −8.81755 22.4668i −0.477497 1.21664i
\(342\) 2.33230 + 25.0046i 0.126116 + 1.35209i
\(343\) 18.4404 1.71823i 0.995687 0.0927757i
\(344\) 6.97960 4.02968i 0.376315 0.217266i
\(345\) 7.41556 + 9.12713i 0.399240 + 0.491388i
\(346\) −3.41858 + 7.09876i −0.183784 + 0.381632i
\(347\) −16.7048 + 3.81275i −0.896758 + 0.204679i −0.645970 0.763363i \(-0.723547\pi\)
−0.250788 + 0.968042i \(0.580690\pi\)
\(348\) −2.34444 5.81726i −0.125675 0.311838i
\(349\) 4.55458 6.68034i 0.243801 0.357591i −0.684761 0.728768i \(-0.740093\pi\)
0.928562 + 0.371177i \(0.121046\pi\)
\(350\) 14.2873 + 7.66898i 0.763688 + 0.409924i
\(351\) −1.22655 + 25.8077i −0.0654686 + 1.37751i
\(352\) −4.83014 + 0.728027i −0.257447 + 0.0388039i
\(353\) 1.27468 17.0094i 0.0678444 0.905321i −0.854624 0.519248i \(-0.826212\pi\)
0.922468 0.386073i \(-0.126169\pi\)
\(354\) −1.66799 + 4.36644i −0.0886528 + 0.232073i
\(355\) −1.58519 5.13904i −0.0841329 0.272752i
\(356\) 0.559534 + 1.42567i 0.0296552 + 0.0755603i
\(357\) −3.49847 18.2231i −0.185158 0.964467i
\(358\) 9.14164 23.2925i 0.483151 1.23105i
\(359\) 12.0678 + 0.904358i 0.636915 + 0.0477302i 0.389275 0.921122i \(-0.372726\pi\)
0.247641 + 0.968852i \(0.420345\pi\)
\(360\) 7.93685 + 6.09639i 0.418309 + 0.321308i
\(361\) 25.5373 + 44.2318i 1.34407 + 2.32799i
\(362\) 24.3079 1.27759
\(363\) 12.7148 + 18.2892i 0.667352 + 0.959934i
\(364\) −7.74375 10.6349i −0.405883 0.557418i
\(365\) 3.18897 10.3384i 0.166918 0.541135i
\(366\) −13.0342 + 7.68435i −0.681309 + 0.401667i
\(367\) −1.15932 7.69158i −0.0605159 0.401497i −0.998497 0.0548100i \(-0.982545\pi\)
0.937981 0.346687i \(-0.112693\pi\)
\(368\) −1.89456 0.743560i −0.0987608 0.0387607i
\(369\) 6.12395 2.01179i 0.318800 0.104730i
\(370\) −3.93349 + 0.897793i −0.204492 + 0.0466741i
\(371\) 17.4929 + 17.7193i 0.908186 + 0.919941i
\(372\) −0.717198 8.52790i −0.0371850 0.442151i
\(373\) 7.89525 + 13.6750i 0.408801 + 0.708063i 0.994756 0.102280i \(-0.0326138\pi\)
−0.585955 + 0.810344i \(0.699280\pi\)
\(374\) −19.7792 −1.02276
\(375\) −6.49969 + 0.546625i −0.335643 + 0.0282276i
\(376\) 3.42253 + 7.10695i 0.176503 + 0.366513i
\(377\) −11.2260 14.0770i −0.578169 0.725001i
\(378\) −12.0178 + 6.67623i −0.618130 + 0.343388i
\(379\) 18.6291 23.3601i 0.956911 1.19993i −0.0228458 0.999739i \(-0.507273\pi\)
0.979757 0.200190i \(-0.0641559\pi\)
\(380\) 27.2256 + 6.21407i 1.39664 + 0.318775i
\(381\) 4.24411 + 1.62126i 0.217432 + 0.0830598i
\(382\) −7.88338 + 3.79644i −0.403349 + 0.194243i
\(383\) 2.87409 7.32307i 0.146859 0.374191i −0.838448 0.544981i \(-0.816537\pi\)
0.985307 + 0.170790i \(0.0546320\pi\)
\(384\) −1.71498 0.242548i −0.0875174 0.0123775i
\(385\) 19.9000 + 38.2459i 1.01420 + 1.94919i
\(386\) −6.97019 14.4737i −0.354773 0.736694i
\(387\) −15.4164 18.6256i −0.783660 0.946792i
\(388\) 0.879137 + 0.947484i 0.0446314 + 0.0481012i
\(389\) 19.8046 + 29.0480i 1.00413 + 1.47279i 0.876755 + 0.480938i \(0.159704\pi\)
0.127378 + 0.991854i \(0.459344\pi\)
\(390\) 26.8389 + 10.2525i 1.35904 + 0.519157i
\(391\) −7.13706 4.12058i −0.360936 0.208387i
\(392\) 2.64097 6.48269i 0.133389 0.327425i
\(393\) −7.25300 + 7.96100i −0.365865 + 0.401579i
\(394\) 5.21666 6.54148i 0.262812 0.329555i
\(395\) 1.96274 + 26.1910i 0.0987562 + 1.31781i
\(396\) 4.57358 + 13.9221i 0.229831 + 0.699612i
\(397\) −4.34256 6.36937i −0.217947 0.319670i 0.701658 0.712514i \(-0.252443\pi\)
−0.919605 + 0.392844i \(0.871491\pi\)
\(398\) −12.7334 8.68151i −0.638269 0.435165i
\(399\) −22.6969 + 30.9259i −1.13627 + 1.54823i
\(400\) 5.06390 3.45251i 0.253195 0.172625i
\(401\) 14.0139 + 5.50004i 0.699819 + 0.274659i 0.688457 0.725277i \(-0.258288\pi\)
0.0113616 + 0.999935i \(0.496383\pi\)
\(402\) −20.1601 + 19.0503i −1.00550 + 0.950142i
\(403\) −8.97567 22.8696i −0.447110 1.13922i
\(404\) −1.89605 1.75928i −0.0943321 0.0875274i
\(405\) 14.0555 26.5308i 0.698422 1.31832i
\(406\) 3.22232 9.02235i 0.159921 0.447772i
\(407\) −5.49932 2.15832i −0.272591 0.106984i
\(408\) −6.72040 2.00616i −0.332709 0.0993197i
\(409\) 20.1867 + 4.60747i 0.998166 + 0.227825i 0.690236 0.723584i \(-0.257507\pi\)
0.307930 + 0.951409i \(0.400364\pi\)
\(410\) 7.16787i 0.353996i
\(411\) −3.04800 + 13.9378i −0.150347 + 0.687502i
\(412\) −0.0520485 0.168737i −0.00256425 0.00831308i
\(413\) −6.33384 + 3.29561i −0.311668 + 0.162166i
\(414\) −1.25006 + 5.97641i −0.0614373 + 0.293725i
\(415\) −12.3753 3.81728i −0.607481 0.187383i
\(416\) −4.91675 + 0.741082i −0.241064 + 0.0363345i
\(417\) 25.1783 12.4088i 1.23299 0.607663i
\(418\) 27.8123 + 29.9745i 1.36034 + 1.46610i
\(419\) 17.8642 + 5.51038i 0.872723 + 0.269199i 0.698590 0.715523i \(-0.253811\pi\)
0.174134 + 0.984722i \(0.444288\pi\)
\(420\) 2.88225 + 15.0133i 0.140639 + 0.732573i
\(421\) 1.90367 0.587205i 0.0927793 0.0286186i −0.248018 0.968755i \(-0.579779\pi\)
0.340797 + 0.940137i \(0.389303\pi\)
\(422\) −20.9279 12.0827i −1.01875 0.588178i
\(423\) 19.3065 13.6844i 0.938714 0.665356i
\(424\) 8.99295 2.77396i 0.436736 0.134715i
\(425\) 22.3594 10.7677i 1.08459 0.522311i
\(426\) 1.55186 2.32129i 0.0751880 0.112467i
\(427\) −22.6816 4.44284i −1.09764 0.215004i
\(428\) −4.46438 + 1.75214i −0.215794 + 0.0846929i
\(429\) 24.0133 + 34.5413i 1.15937 + 1.66767i
\(430\) −25.0274 + 9.82254i −1.20693 + 0.473685i
\(431\) −5.76397 + 8.45419i −0.277641 + 0.407224i −0.939578 0.342335i \(-0.888782\pi\)
0.661937 + 0.749559i \(0.269735\pi\)
\(432\) 0.141883 + 5.19421i 0.00682635 + 0.249907i
\(433\) −1.09543 + 2.27469i −0.0526431 + 0.109314i −0.925631 0.378427i \(-0.876465\pi\)
0.872988 + 0.487742i \(0.162179\pi\)
\(434\) 7.83023 10.4680i 0.375863 0.502481i
\(435\) 4.84131 + 20.3553i 0.232123 + 0.975960i
\(436\) −1.28522 17.1501i −0.0615508 0.821339i
\(437\) 3.79113 + 16.6100i 0.181354 + 0.794565i
\(438\) 5.21006 2.09973i 0.248946 0.100329i
\(439\) 28.9734 + 23.1055i 1.38283 + 1.10277i 0.982473 + 0.186406i \(0.0596838\pi\)
0.400353 + 0.916361i \(0.368888\pi\)
\(440\) 16.2953 0.776849
\(441\) −20.4982 4.56343i −0.976103 0.217306i
\(442\) −20.1339 −0.957671
\(443\) 19.3881 + 15.4615i 0.921157 + 0.734598i 0.964395 0.264466i \(-0.0851958\pi\)
−0.0432376 + 0.999065i \(0.513767\pi\)
\(444\) −1.64960 1.29112i −0.0782863 0.0612738i
\(445\) −1.13690 4.98110i −0.0538944 0.236127i
\(446\) 0.145566 + 1.94245i 0.00689276 + 0.0919775i
\(447\) −20.2648 6.04939i −0.958491 0.286127i
\(448\) −1.71286 2.01646i −0.0809250 0.0952688i
\(449\) −9.36345 + 19.4434i −0.441888 + 0.917591i 0.554460 + 0.832210i \(0.312925\pi\)
−0.996348 + 0.0853804i \(0.972789\pi\)
\(450\) −12.7493 13.2484i −0.601009 0.624535i
\(451\) 5.91232 8.67177i 0.278400 0.408338i
\(452\) 11.4565 4.49635i 0.538870 0.211491i
\(453\) −6.67286 + 14.1852i −0.313518 + 0.666480i
\(454\) −9.48084 + 3.72095i −0.444958 + 0.174633i
\(455\) 20.2569 + 38.9318i 0.949656 + 1.82515i
\(456\) 6.40957 + 13.0054i 0.300156 + 0.609035i
\(457\) 20.9952 10.1107i 0.982112 0.472960i 0.127281 0.991867i \(-0.459375\pi\)
0.854831 + 0.518906i \(0.173661\pi\)
\(458\) 13.1606 4.05952i 0.614956 0.189689i
\(459\) −2.56663 + 20.8832i −0.119800 + 0.974745i
\(460\) 5.87995 + 3.39479i 0.274154 + 0.158283i
\(461\) 3.79312 1.17002i 0.176663 0.0544933i −0.205162 0.978728i \(-0.565772\pi\)
0.381825 + 0.924235i \(0.375296\pi\)
\(462\) −8.89651 + 20.5406i −0.413903 + 0.955637i
\(463\) −5.99874 1.85037i −0.278785 0.0859939i 0.152210 0.988348i \(-0.451361\pi\)
−0.430995 + 0.902354i \(0.641837\pi\)
\(464\) −2.46297 2.65445i −0.114340 0.123230i
\(465\) −1.87426 + 28.4879i −0.0869168 + 1.32109i
\(466\) −19.2953 + 2.90830i −0.893837 + 0.134724i
\(467\) −28.2061 8.70042i −1.30522 0.402608i −0.437303 0.899314i \(-0.644066\pi\)
−0.867919 + 0.496706i \(0.834543\pi\)
\(468\) 4.65559 + 14.1718i 0.215205 + 0.655089i
\(469\) −42.3487 + 1.31195i −1.95548 + 0.0605803i
\(470\) −7.75640 25.1456i −0.357776 1.15988i
\(471\) 27.4901 8.75439i 1.26668 0.403381i
\(472\) 2.69864i 0.124215i
\(473\) −38.3805 8.76009i −1.76474 0.402789i
\(474\) −9.91142 + 9.36578i −0.455246 + 0.430185i
\(475\) −47.7584 18.7438i −2.19131 0.860025i
\(476\) −5.64133 9.10761i −0.258570 0.417446i
\(477\) −12.7110 25.2100i −0.581995 1.15429i
\(478\) 12.2777 + 11.3920i 0.561569 + 0.521060i
\(479\) 6.59168 + 16.7953i 0.301182 + 0.767398i 0.998707 + 0.0508381i \(0.0161892\pi\)
−0.697525 + 0.716560i \(0.745716\pi\)
\(480\) 5.53668 + 1.65280i 0.252714 + 0.0754395i
\(481\) −5.59793 2.19703i −0.255244 0.100176i
\(482\) −17.4982 + 11.9301i −0.797022 + 0.543400i
\(483\) −7.48940 + 5.55841i −0.340779 + 0.252916i
\(484\) 10.6257 + 7.24445i 0.482985 + 0.329293i
\(485\) −2.42894 3.56261i −0.110293 0.161770i
\(486\) 15.2927 3.02227i 0.693690 0.137093i
\(487\) −1.92894 25.7399i −0.0874086 1.16639i −0.852593 0.522576i \(-0.824971\pi\)
0.765184 0.643811i \(-0.222648\pi\)
\(488\) −5.44665 + 6.82988i −0.246558 + 0.309174i
\(489\) −27.1322 5.93344i −1.22696 0.268319i
\(490\) −11.9351 + 20.0716i −0.539172 + 0.906741i
\(491\) −18.5427 10.7056i −0.836820 0.483138i 0.0193620 0.999813i \(-0.493836\pi\)
−0.856182 + 0.516674i \(0.827170\pi\)
\(492\) 2.88839 2.34675i 0.130219 0.105799i
\(493\) −8.25973 12.1148i −0.371999 0.545623i
\(494\) 28.3110 + 30.5120i 1.27377 + 1.37280i
\(495\) −8.16489 48.1993i −0.366985 2.16640i
\(496\) −2.14380 4.45166i −0.0962597 0.199885i
\(497\) 4.12691 1.07741i 0.185117 0.0483284i
\(498\) −2.51343 6.23658i −0.112629 0.279468i
\(499\) 2.89465 7.37546i 0.129582 0.330171i −0.851327 0.524635i \(-0.824202\pi\)
0.980910 + 0.194465i \(0.0622969\pi\)
\(500\) −3.39291 + 1.63394i −0.151736 + 0.0730720i
\(501\) 29.7735 24.1903i 1.33018 1.08074i
\(502\) 14.6710 + 3.34856i 0.654800 + 0.149454i
\(503\) 11.5524 14.4862i 0.515095 0.645908i −0.454465 0.890765i \(-0.650169\pi\)
0.969559 + 0.244857i \(0.0787409\pi\)
\(504\) −5.10617 + 6.07676i −0.227447 + 0.270681i
\(505\) 5.37985 + 6.74612i 0.239400 + 0.300198i
\(506\) 4.31349 + 8.95705i 0.191758 + 0.398190i
\(507\) 11.5910 + 16.6728i 0.514776 + 0.740465i
\(508\) 2.62303 0.116378
\(509\) −4.23057 7.32757i −0.187517 0.324789i 0.756905 0.653525i \(-0.226711\pi\)
−0.944422 + 0.328736i \(0.893377\pi\)
\(510\) 21.1713 + 9.95919i 0.937483 + 0.441001i
\(511\) 8.08060 + 2.88598i 0.357465 + 0.127668i
\(512\) −0.974928 + 0.222521i −0.0430861 + 0.00983413i
\(513\) 35.2567 25.4751i 1.55662 1.12475i
\(514\) −6.00577 2.35709i −0.264903 0.103967i
\(515\) 0.0877973 + 0.582497i 0.00386881 + 0.0256679i
\(516\) −12.1521 6.86927i −0.534965 0.302403i
\(517\) 11.3572 36.8193i 0.499491 1.61931i
\(518\) −0.574660 3.14782i −0.0252491 0.138307i
\(519\) 13.5989 1.14367i 0.596924 0.0502014i
\(520\) 16.5875 0.727411
\(521\) −9.91985 17.1817i −0.434597 0.752744i 0.562666 0.826684i \(-0.309776\pi\)
−0.997263 + 0.0739408i \(0.976442\pi\)
\(522\) −6.61740 + 8.61515i −0.289636 + 0.377075i
\(523\) 7.49955 + 0.562013i 0.327932 + 0.0245751i 0.237679 0.971344i \(-0.423613\pi\)
0.0902531 + 0.995919i \(0.471232\pi\)
\(524\) −2.27162 + 5.78800i −0.0992363 + 0.252850i
\(525\) −1.12518 28.0634i −0.0491068 1.22479i
\(526\) −2.31496 5.89842i −0.100937 0.257183i
\(527\) −5.89718 19.1182i −0.256885 0.832801i
\(528\) 5.33506 + 6.56643i 0.232179 + 0.285767i
\(529\) 1.40924 18.8050i 0.0612714 0.817610i
\(530\) −31.0446 + 4.67922i −1.34849 + 0.203252i
\(531\) 7.98220 1.35217i 0.346398 0.0586793i
\(532\) −5.86969 + 21.3558i −0.254483 + 0.925889i
\(533\) 6.01834 8.82728i 0.260683 0.382352i
\(534\) 1.63498 2.08893i 0.0707527 0.0903971i
\(535\) 15.5980 3.56014i 0.674360 0.153918i
\(536\) −6.94821 + 14.4281i −0.300117 + 0.623200i
\(537\) −42.7951 + 6.84929i −1.84675 + 0.295569i
\(538\) 22.8492 13.1920i 0.985099 0.568747i
\(539\) −30.9950 + 14.4383i −1.33505 + 0.621903i
\(540\) 2.11455 17.2049i 0.0909958 0.740380i
\(541\) −14.7057 37.4695i −0.632248 1.61094i −0.782753 0.622332i \(-0.786185\pi\)
0.150505 0.988609i \(-0.451910\pi\)
\(542\) −6.12818 + 4.17812i −0.263228 + 0.179466i
\(543\) −21.3823 36.2686i −0.917600 1.55644i
\(544\) −4.03789 + 0.302598i −0.173123 + 0.0129738i
\(545\) −4.28748 + 57.2125i −0.183656 + 2.45071i
\(546\) −9.05605 + 20.9090i −0.387563 + 0.894822i
\(547\) −0.290455 3.87586i −0.0124190 0.165720i −0.999965 0.00838818i \(-0.997330\pi\)
0.987546 0.157332i \(-0.0502891\pi\)
\(548\) 1.22769 + 8.14517i 0.0524442 + 0.347944i
\(549\) 22.9309 + 12.6883i 0.978668 + 0.541522i
\(550\) −29.6032 4.46197i −1.26229 0.190259i
\(551\) −6.74513 + 29.5523i −0.287352 + 1.25897i
\(552\) 0.557106 + 3.48085i 0.0237120 + 0.148155i
\(553\) −20.8201 + 0.645000i −0.885361 + 0.0274282i
\(554\) −1.43945 9.55015i −0.0611565 0.405747i
\(555\) 4.79963 + 5.07924i 0.203733 + 0.215602i
\(556\) 11.0230 11.8800i 0.467481 0.503825i
\(557\) 22.3930 12.9286i 0.948822 0.547803i 0.0561073 0.998425i \(-0.482131\pi\)
0.892715 + 0.450622i \(0.148798\pi\)
\(558\) −12.0932 + 8.57161i −0.511946 + 0.362865i
\(559\) −39.0687 8.91718i −1.65243 0.377156i
\(560\) 4.64767 + 7.50341i 0.196400 + 0.317077i
\(561\) 17.3987 + 29.5116i 0.734572 + 1.24598i
\(562\) 2.23913 2.07761i 0.0944519 0.0876386i
\(563\) 20.0105 + 25.0924i 0.843342 + 1.05752i 0.997583 + 0.0694840i \(0.0221353\pi\)
−0.154241 + 0.988033i \(0.549293\pi\)
\(564\) 7.59336 11.3582i 0.319738 0.478266i
\(565\) −40.0276 + 9.13604i −1.68397 + 0.384356i
\(566\) 5.95650 + 26.0971i 0.250370 + 1.09694i
\(567\) 20.5327 + 12.0585i 0.862292 + 0.506411i
\(568\) 0.358727 1.57169i 0.0150519 0.0659465i
\(569\) 20.8748i 0.875118i −0.899190 0.437559i \(-0.855843\pi\)
0.899190 0.437559i \(-0.144157\pi\)
\(570\) −14.6771 46.0883i −0.614757 1.93043i
\(571\) −8.53293 + 37.3852i −0.357092 + 1.56452i 0.403306 + 0.915065i \(0.367861\pi\)
−0.760398 + 0.649458i \(0.774996\pi\)
\(572\) 20.0678 + 13.6820i 0.839077 + 0.572073i
\(573\) 12.5991 + 8.42292i 0.526333 + 0.351873i
\(574\) 5.67932 + 0.249084i 0.237050 + 0.0103966i
\(575\) −9.75236 7.77725i −0.406702 0.324334i
\(576\) 1.14668 + 2.77221i 0.0477784 + 0.115509i
\(577\) 4.18829 27.7875i 0.174361 1.15681i −0.714838 0.699290i \(-0.753500\pi\)
0.889199 0.457520i \(-0.151262\pi\)
\(578\) 0.602156 + 0.0451253i 0.0250464 + 0.00187697i
\(579\) −15.4643 + 23.1316i −0.642676 + 0.961318i
\(580\) 6.80487 + 9.98091i 0.282557 + 0.414435i
\(581\) 3.45459 9.67270i 0.143321 0.401291i
\(582\) 0.640371 2.14517i 0.0265442 0.0889201i
\(583\) −41.4177 19.9457i −1.71535 0.826067i
\(584\) 2.37738 2.20588i 0.0983766 0.0912801i
\(585\) −8.31130 49.0636i −0.343630 2.02853i
\(586\) 2.47655 0.971975i 0.102305 0.0401519i
\(587\) −12.2897 21.2863i −0.507249 0.878581i −0.999965 0.00839101i \(-0.997329\pi\)
0.492716 0.870190i \(-0.336004\pi\)
\(588\) −11.9956 + 1.76198i −0.494692 + 0.0726629i
\(589\) −20.6805 + 35.8197i −0.852127 + 1.47593i
\(590\) 1.34177 8.90209i 0.0552400 0.366493i
\(591\) −14.3491 2.02937i −0.590241 0.0834769i
\(592\) −1.15570 0.356485i −0.0474989 0.0146515i
\(593\) −23.2197 + 15.8309i −0.953518 + 0.650098i −0.936838 0.349763i \(-0.886262\pi\)
−0.0166799 + 0.999861i \(0.505310\pi\)
\(594\) 16.7494 19.0705i 0.687237 0.782473i
\(595\) 14.0809 + 32.8485i 0.577261 + 1.34666i
\(596\) −12.1759 + 0.912458i −0.498745 + 0.0373758i
\(597\) −1.75240 + 26.6356i −0.0717209 + 1.09012i
\(598\) 4.39084 + 9.11767i 0.179555 + 0.372849i
\(599\) 30.9143 + 24.6533i 1.26312 + 1.00731i 0.999084 + 0.0427940i \(0.0136259\pi\)
0.264038 + 0.964512i \(0.414946\pi\)
\(600\) −9.60575 4.51863i −0.392153 0.184472i
\(601\) −4.49636 + 29.8314i −0.183410 + 1.21685i 0.687786 + 0.725914i \(0.258583\pi\)
−0.871196 + 0.490935i \(0.836655\pi\)
\(602\) −6.91299 20.1713i −0.281753 0.822122i
\(603\) 46.1578 + 13.3225i 1.87969 + 0.542536i
\(604\) −0.676363 + 9.02543i −0.0275208 + 0.367240i
\(605\) −31.4493 29.1806i −1.27859 1.18636i
\(606\) −0.957090 + 4.37655i −0.0388791 + 0.177785i
\(607\) 8.18998 4.72849i 0.332421 0.191923i −0.324494 0.945888i \(-0.605194\pi\)
0.656916 + 0.753964i \(0.271861\pi\)
\(608\) 6.13642 + 5.69376i 0.248865 + 0.230913i
\(609\) −16.2963 + 3.12857i −0.660361 + 0.126776i
\(610\) 21.3629 19.8219i 0.864958 0.802564i
\(611\) 11.5609 37.4795i 0.467704 1.51626i
\(612\) 2.91826 + 11.7919i 0.117964 + 0.476660i
\(613\) 0.623773 1.58935i 0.0251940 0.0641932i −0.917723 0.397220i \(-0.869975\pi\)
0.942917 + 0.333027i \(0.108070\pi\)
\(614\) 0.479729 + 2.10183i 0.0193603 + 0.0848230i
\(615\) −10.6948 + 6.30517i −0.431258 + 0.254249i
\(616\) −0.566265 + 12.9113i −0.0228155 + 0.520211i
\(617\) 12.6787 13.6643i 0.510423 0.550105i −0.424282 0.905530i \(-0.639473\pi\)
0.934705 + 0.355425i \(0.115664\pi\)
\(618\) −0.205981 + 0.226088i −0.00828576 + 0.00909458i
\(619\) 16.1836 + 9.34359i 0.650473 + 0.375551i 0.788637 0.614859i \(-0.210787\pi\)
−0.138165 + 0.990409i \(0.544120\pi\)
\(620\) 4.85846 + 15.7507i 0.195120 + 0.632565i
\(621\) 10.0167 3.39195i 0.401958 0.136114i
\(622\) 8.32509 6.63904i 0.333806 0.266201i
\(623\) 3.98619 0.727710i 0.159703 0.0291551i
\(624\) 5.43073 + 6.68418i 0.217403 + 0.267581i
\(625\) −17.2781 + 5.32959i −0.691125 + 0.213184i
\(626\) −12.0515 + 15.1121i −0.481674 + 0.604000i
\(627\) 20.2587 67.8644i 0.809056 2.71024i
\(628\) 13.0228 10.3853i 0.519666 0.414419i
\(629\) −4.41226 2.12483i −0.175928 0.0847226i
\(630\) 19.8653 17.5068i 0.791452 0.697488i
\(631\) −4.04182 + 1.94644i −0.160902 + 0.0774865i −0.512602 0.858627i \(-0.671318\pi\)
0.351699 + 0.936113i \(0.385604\pi\)
\(632\) −3.41598 + 7.09336i −0.135880 + 0.282159i
\(633\) 0.381005 + 41.8540i 0.0151436 + 1.66355i
\(634\) 6.80659 + 3.27788i 0.270324 + 0.130181i
\(635\) −8.65269 1.30418i −0.343372 0.0517549i
\(636\) −12.0495 10.9779i −0.477793 0.435301i
\(637\) −31.5508 + 14.6972i −1.25009 + 0.582326i
\(638\) 17.6879i 0.700272i
\(639\) −4.82857 0.273560i −0.191015 0.0108219i
\(640\) 3.32667 0.249299i 0.131498 0.00985441i
\(641\) −13.1738 + 42.7083i −0.520332 + 1.68687i 0.188981 + 0.981981i \(0.439482\pi\)
−0.709313 + 0.704894i \(0.750995\pi\)
\(642\) 6.54136 + 5.11984i 0.258167 + 0.202064i
\(643\) 23.5276 + 1.76315i 0.927837 + 0.0695318i 0.530069 0.847954i \(-0.322166\pi\)
0.397768 + 0.917486i \(0.369785\pi\)
\(644\) −2.89412 + 4.54089i −0.114044 + 0.178936i
\(645\) 36.6710 + 28.7019i 1.44392 + 1.13014i
\(646\) 21.1339 + 26.5011i 0.831504 + 1.04267i
\(647\) −32.8387 22.3891i −1.29102 0.880205i −0.293888 0.955840i \(-0.594949\pi\)
−0.997136 + 0.0756353i \(0.975902\pi\)
\(648\) 7.62525 4.78076i 0.299548 0.187806i
\(649\) 8.96606 9.66312i 0.351949 0.379311i
\(650\) −30.1341 4.54198i −1.18196 0.178151i
\(651\) −22.5067 2.47499i −0.882106 0.0970026i
\(652\) −15.8559 + 2.38989i −0.620965 + 0.0935954i
\(653\) 1.17740 1.72692i 0.0460751 0.0675797i −0.802510 0.596639i \(-0.796503\pi\)
0.848585 + 0.529059i \(0.177455\pi\)
\(654\) −24.4583 + 17.0036i −0.956395 + 0.664892i
\(655\) 10.3713 17.9636i 0.405240 0.701896i
\(656\) 1.07432 1.86078i 0.0419452 0.0726513i
\(657\) −7.71590 5.92668i −0.301026 0.231222i
\(658\) 20.1932 5.27182i 0.787213 0.205517i
\(659\) −5.04019 5.43204i −0.196338 0.211602i 0.627208 0.778852i \(-0.284198\pi\)
−0.823546 + 0.567250i \(0.808007\pi\)
\(660\) −14.3341 24.3135i −0.557953 0.946402i
\(661\) −26.5687 + 21.1879i −1.03340 + 0.824112i −0.984622 0.174698i \(-0.944105\pi\)
−0.0487815 + 0.998809i \(0.515534\pi\)
\(662\) 4.80883 3.83492i 0.186901 0.149048i
\(663\) 17.7106 + 30.0409i 0.687824 + 1.16669i
\(664\) −2.64050 2.84579i −0.102471 0.110438i
\(665\) 29.9807 67.5285i 1.16260 2.61864i
\(666\) −0.475364 + 3.59701i −0.0184200 + 0.139381i
\(667\) −3.68491 + 6.38245i −0.142680 + 0.247130i
\(668\) 11.0741 19.1809i 0.428470 0.742133i
\(669\) 2.77019 1.92585i 0.107102 0.0744578i
\(670\) 30.0940 44.1398i 1.16263 1.70527i
\(671\) 42.1949 6.35986i 1.62892 0.245520i
\(672\) −1.50196 + 4.32945i −0.0579395 + 0.167012i
\(673\) −6.55245 0.987623i −0.252578 0.0380701i 0.0215326 0.999768i \(-0.493145\pi\)
−0.274111 + 0.961698i \(0.588384\pi\)
\(674\) 13.9372 15.0208i 0.536842 0.578578i
\(675\) −8.55246 + 30.6766i −0.329184 + 1.18074i
\(676\) 9.68656 + 6.60418i 0.372560 + 0.254007i
\(677\) 3.16345 + 3.96684i 0.121581 + 0.152458i 0.838897 0.544290i \(-0.183201\pi\)
−0.717316 + 0.696748i \(0.754629\pi\)
\(678\) −16.7865 13.1386i −0.644680 0.504584i
\(679\) 2.90717 1.80073i 0.111567 0.0691055i
\(680\) 13.4704 + 1.00947i 0.516566 + 0.0387113i
\(681\) 13.8916 + 10.8728i 0.532328 + 0.416647i
\(682\) −7.11395 + 23.0629i −0.272407 + 0.883123i
\(683\) 44.9730 3.37026i 1.72084 0.128959i 0.822647 0.568553i \(-0.192497\pi\)
0.898197 + 0.439593i \(0.144877\pi\)
\(684\) 13.7667 21.0036i 0.526381 0.803091i
\(685\) 27.4791i 1.04992i
\(686\) −15.4886 10.1540i −0.591356 0.387682i
\(687\) −17.6337 16.0654i −0.672767 0.612935i
\(688\) −7.96933 1.20118i −0.303828 0.0457947i
\(689\) −42.1604 20.3034i −1.60618 0.773497i
\(690\) −0.107048 11.7594i −0.00407525 0.447673i
\(691\) 15.3785 31.9338i 0.585026 1.21482i −0.372918 0.927864i \(-0.621643\pi\)
0.957944 0.286955i \(-0.0926430\pi\)
\(692\) 7.09876 3.41858i 0.269854 0.129955i
\(693\) 38.4735 4.79436i 1.46149 0.182123i
\(694\) 15.4375 + 7.43431i 0.586000 + 0.282203i
\(695\) −42.2688 + 33.7083i −1.60335 + 1.27863i
\(696\) −1.79405 + 6.00985i −0.0680032 + 0.227803i
\(697\) 5.42457 6.80219i 0.205470 0.257651i
\(698\) −7.72604 + 2.38317i −0.292435 + 0.0902042i
\(699\) 21.3123 + 26.2313i 0.806106 + 0.992161i
\(700\) −6.38872 14.9038i −0.241471 0.563312i
\(701\) −14.1349 + 11.2722i −0.533868 + 0.425746i −0.852959 0.521978i \(-0.825194\pi\)
0.319090 + 0.947724i \(0.396623\pi\)
\(702\) 17.0498 19.4125i 0.643502 0.732677i
\(703\) 2.98416 + 9.67440i 0.112550 + 0.364877i
\(704\) 4.23027 + 2.44235i 0.159434 + 0.0920495i
\(705\) −30.6958 + 33.6922i −1.15607 + 1.26892i
\(706\) −11.6018 + 12.5038i −0.436639 + 0.470585i
\(707\) −5.53211 + 4.02819i −0.208056 + 0.151496i
\(708\) 4.02652 2.37384i 0.151326 0.0892144i
\(709\) 5.43040 + 23.7922i 0.203943 + 0.893533i 0.968507 + 0.248986i \(0.0800972\pi\)
−0.764564 + 0.644548i \(0.777046\pi\)
\(710\) −1.96479 + 5.00621i −0.0737374 + 0.187880i
\(711\) 22.6928 + 6.54982i 0.851046 + 0.245637i
\(712\) 0.451429 1.46350i 0.0169180 0.0548468i
\(713\) −7.37164 + 6.83988i −0.276070 + 0.256156i
\(714\) −8.62668 + 16.4286i −0.322846 + 0.614826i
\(715\) −59.3956 55.1111i −2.22127 2.06104i
\(716\) −21.6699 + 12.5111i −0.809841 + 0.467562i
\(717\) 6.19754 28.3399i 0.231451 1.05837i
\(718\) −8.87115 8.23122i −0.331068 0.307186i
\(719\) −3.25449 + 43.4282i −0.121372 + 1.61960i 0.521242 + 0.853409i \(0.325469\pi\)
−0.642614 + 0.766190i \(0.722150\pi\)
\(720\) −2.40424 9.71490i −0.0896008 0.362053i
\(721\) −0.464581 + 0.0493227i −0.0173019 + 0.00183687i
\(722\) 7.61226 50.5040i 0.283299 1.87957i
\(723\) 33.1925 + 15.6141i 1.23444 + 0.580693i
\(724\) −19.0046 15.1557i −0.706302 0.563257i
\(725\) −9.62924 19.9953i −0.357621 0.742608i
\(726\) 1.46232 22.2266i 0.0542719 0.824907i
\(727\) 22.2928 1.67062i 0.826795 0.0619597i 0.345391 0.938459i \(-0.387746\pi\)
0.481404 + 0.876499i \(0.340127\pi\)
\(728\) −0.576419 + 13.1428i −0.0213635 + 0.487105i
\(729\) −17.9615 20.1590i −0.665241 0.746629i
\(730\) −8.93911 + 6.09458i −0.330851 + 0.225571i
\(731\) −31.1842 9.61906i −1.15339 0.355774i
\(732\) 14.9817 + 2.11884i 0.553738 + 0.0783144i
\(733\) −3.75125 + 24.8879i −0.138556 + 0.919257i 0.806238 + 0.591591i \(0.201500\pi\)
−0.944794 + 0.327666i \(0.893738\pi\)
\(734\) −3.88923 + 6.73634i −0.143554 + 0.248643i
\(735\) 40.4465 + 0.151972i 1.49189 + 0.00560556i
\(736\) 1.01762 + 1.76258i 0.0375101 + 0.0649695i
\(737\) 72.8163 28.5783i 2.68222 1.05269i
\(738\) −6.04223 2.24534i −0.222418 0.0826521i
\(739\) 22.3909 20.7757i 0.823663 0.764248i −0.150855 0.988556i \(-0.548203\pi\)
0.974518 + 0.224308i \(0.0720123\pi\)
\(740\) 3.63509 + 1.75057i 0.133629 + 0.0643521i
\(741\) 20.6220 69.0813i 0.757568 2.53777i
\(742\) −2.62868 24.7602i −0.0965020 0.908974i
\(743\) −0.978719 1.43552i −0.0359057 0.0526640i 0.807866 0.589366i \(-0.200622\pi\)
−0.843772 + 0.536702i \(0.819670\pi\)
\(744\) −4.75633 + 7.11454i −0.174375 + 0.260832i
\(745\) 40.6188 + 3.04396i 1.48816 + 0.111522i
\(746\) 2.35345 15.6141i 0.0861660 0.571674i
\(747\) −7.09440 + 9.23614i −0.259570 + 0.337933i
\(748\) 15.4640 + 12.3321i 0.565420 + 0.450907i
\(749\) 2.27877 + 12.4825i 0.0832646 + 0.456100i
\(750\) 5.42248 + 3.62512i 0.198001 + 0.132371i
\(751\) −43.5774 29.7106i −1.59016 1.08415i −0.948320 0.317317i \(-0.897218\pi\)
−0.641842 0.766837i \(-0.721829\pi\)
\(752\) 1.75527 7.69035i 0.0640082 0.280438i
\(753\) −7.90903 24.8355i −0.288221 0.905056i
\(754\) 18.0051i 0.655708i
\(755\) 6.71862 29.4362i 0.244516 1.07129i
\(756\) 13.5585 + 2.27330i 0.493117 + 0.0826789i
\(757\) 3.19261 + 13.9877i 0.116037 + 0.508393i 0.999225 + 0.0393724i \(0.0125359\pi\)
−0.883187 + 0.469021i \(0.844607\pi\)
\(758\) −29.1296 + 6.64864i −1.05803 + 0.241489i
\(759\) 9.57008 14.3150i 0.347372 0.519601i
\(760\) −17.4114 21.8333i −0.631579 0.791975i
\(761\) −27.6473 + 25.6530i −1.00222 + 0.929920i −0.997542 0.0700691i \(-0.977678\pi\)
−0.00467327 + 0.999989i \(0.501488\pi\)
\(762\) −2.30734 3.91371i −0.0835860 0.141779i
\(763\) −45.1822 5.38525i −1.63571 0.194959i
\(764\) 8.53051 + 1.94703i 0.308623 + 0.0704412i
\(765\) −3.76358 40.3493i −0.136072 1.45883i
\(766\) −6.81292 + 3.93344i −0.246161 + 0.142121i
\(767\) 9.12684 9.83640i 0.329551 0.355172i
\(768\) 1.18960 + 1.25891i 0.0429261 + 0.0454269i
\(769\) 4.11861 + 27.3252i 0.148521 + 0.985371i 0.931609 + 0.363461i \(0.118405\pi\)
−0.783089 + 0.621910i \(0.786357\pi\)
\(770\) 8.28750 42.3093i 0.298661 1.52472i
\(771\) 1.76603 + 11.0343i 0.0636020 + 0.397392i
\(772\) −3.57472 + 15.6619i −0.128657 + 0.563683i
\(773\) −24.1764 3.64401i −0.869565 0.131066i −0.300920 0.953649i \(-0.597294\pi\)
−0.568644 + 0.822584i \(0.692532\pi\)
\(774\) 0.440158 + 24.1740i 0.0158212 + 0.868918i
\(775\) −4.51336 29.9442i −0.162125 1.07563i
\(776\) −0.0965901 1.28891i −0.00346738 0.0462690i
\(777\) −4.19123 + 3.62639i −0.150359 + 0.130096i
\(778\) 2.62728 35.0586i 0.0941925 1.25691i
\(779\) −17.9361 + 1.34413i −0.642628 + 0.0481583i
\(780\) −14.5911 24.7495i −0.522446 0.886174i
\(781\) −6.50634 + 4.43595i −0.232815 + 0.158731i
\(782\) 3.01084 + 7.67148i 0.107667 + 0.274332i
\(783\) 18.6752 + 2.29526i 0.667398 + 0.0820260i
\(784\) −6.10669 + 3.42175i −0.218096 + 0.122205i
\(785\) −48.1223 + 27.7834i −1.71756 + 0.991633i
\(786\) 10.6342 1.70199i 0.379310 0.0607081i
\(787\) −22.8479 + 47.4442i −0.814441 + 1.69120i −0.0962514 + 0.995357i \(0.530685\pi\)
−0.718190 + 0.695847i \(0.755029\pi\)
\(788\) −8.15710 + 1.86180i −0.290585 + 0.0663240i
\(789\) −6.76443 + 8.64256i −0.240820 + 0.307683i
\(790\) 14.7953 21.7007i 0.526392 0.772075i
\(791\) −5.84780 32.0326i −0.207924 1.13895i
\(792\) 5.10452 13.7363i 0.181381 0.488099i
\(793\) 42.9515 6.47390i 1.52525 0.229895i
\(794\) −0.576085 + 7.68732i −0.0204445 + 0.272813i
\(795\) 34.2898 + 42.2041i 1.21613 + 1.49683i
\(796\) 4.54257 + 14.7266i 0.161007 + 0.521972i
\(797\) 11.3663 + 28.9608i 0.402614 + 1.02584i 0.978119 + 0.208046i \(0.0667103\pi\)
−0.575505 + 0.817798i \(0.695194\pi\)
\(798\) 37.0272 10.0276i 1.31075 0.354972i
\(799\) 11.6693 29.7328i 0.412829 1.05187i
\(800\) −6.11172 0.458010i −0.216082 0.0161931i
\(801\) −4.55501 0.601968i −0.160943 0.0212695i
\(802\) −7.52727 13.0376i −0.265797 0.460374i
\(803\) −15.8417 −0.559041
\(804\) 27.6395 2.32449i 0.974770 0.0819783i
\(805\) 11.8047 13.5402i 0.416061 0.477230i
\(806\) −7.24152 + 23.4764i −0.255072 + 0.826922i
\(807\) −39.7823 22.4880i −1.40040 0.791615i
\(808\) 0.385500 + 2.55763i 0.0135619 + 0.0899770i
\(809\) −35.6673 13.9984i −1.25400 0.492158i −0.356963 0.934119i \(-0.616188\pi\)
−0.897034 + 0.441961i \(0.854283\pi\)
\(810\) −27.5307 + 11.9791i −0.967329 + 0.420904i
\(811\) −27.4663 + 6.26899i −0.964471 + 0.220134i −0.675628 0.737243i \(-0.736128\pi\)
−0.288842 + 0.957377i \(0.593270\pi\)
\(812\) −8.14465 + 5.04487i −0.285821 + 0.177040i
\(813\) 11.6246 + 5.46832i 0.407693 + 0.191782i
\(814\) 2.95385 + 5.11621i 0.103532 + 0.179323i
\(815\) 53.4927 1.87377
\(816\) 4.00340 + 5.75858i 0.140147 + 0.201591i
\(817\) 29.2721 + 60.7841i 1.02410 + 2.12657i
\(818\) −12.9099 16.1884i −0.451383 0.566016i
\(819\) 39.1634 4.88033i 1.36848 0.170533i
\(820\) −4.46909 + 5.60406i −0.156067 + 0.195702i
\(821\) −10.3892 2.37127i −0.362586 0.0827579i 0.0373467 0.999302i \(-0.488109\pi\)
−0.399933 + 0.916544i \(0.630967\pi\)
\(822\) 11.0731 8.99662i 0.386219 0.313793i
\(823\) 7.90785 3.80822i 0.275650 0.132746i −0.290952 0.956738i \(-0.593972\pi\)
0.566602 + 0.823992i \(0.308258\pi\)
\(824\) −0.0645127 + 0.164376i −0.00224741 + 0.00572630i
\(825\) 19.3828 + 48.0946i 0.674822 + 1.67444i
\(826\) 7.00677 + 1.37248i 0.243797 + 0.0477546i
\(827\) 8.06881 + 16.7551i 0.280580 + 0.582631i 0.992863 0.119262i \(-0.0380529\pi\)
−0.712283 + 0.701893i \(0.752339\pi\)
\(828\) 4.70357 3.89314i 0.163460 0.135296i
\(829\) 19.3871 + 20.8943i 0.673341 + 0.725689i 0.973623 0.228161i \(-0.0732714\pi\)
−0.300282 + 0.953850i \(0.597081\pi\)
\(830\) 7.29538 + 10.7004i 0.253226 + 0.371415i
\(831\) −12.9831 + 10.5485i −0.450380 + 0.365923i
\(832\) 4.30613 + 2.48615i 0.149288 + 0.0861916i
\(833\) −26.5162 + 10.0152i −0.918730 + 0.347008i
\(834\) −27.4220 5.99680i −0.949545 0.207652i
\(835\) −46.0674 + 57.7667i −1.59423 + 1.99910i
\(836\) −3.05572 40.7757i −0.105684 1.41026i
\(837\) 23.4270 + 10.5038i 0.809757 + 0.363063i
\(838\) −10.5311 15.4463i −0.363792 0.533585i
\(839\) −29.1272 19.8586i −1.00558 0.685594i −0.0557787 0.998443i \(-0.517764\pi\)
−0.949803 + 0.312849i \(0.898717\pi\)
\(840\) 7.10719 13.5349i 0.245221 0.466999i
\(841\) 13.1270 8.94986i 0.452656 0.308616i
\(842\) −1.85447 0.727825i −0.0639092 0.0250825i
\(843\) −5.06954 1.51335i −0.174604 0.0521224i
\(844\) 8.82863 + 22.4950i 0.303894 + 0.774309i
\(845\) −28.6697 26.6016i −0.986269 0.915124i
\(846\) −23.6265 1.33855i −0.812295 0.0460201i
\(847\) 24.2136 23.9042i 0.831989 0.821357i
\(848\) −8.76050 3.43824i −0.300837 0.118070i
\(849\) 33.6987 31.8436i 1.15654 1.09287i
\(850\) −24.1948 5.52231i −0.829876 0.189414i
\(851\) 2.46149i 0.0843787i
\(852\) −2.66059 + 0.847284i −0.0911504 + 0.0290275i
\(853\) −8.50711 27.5794i −0.291278 0.944299i −0.976418 0.215888i \(-0.930735\pi\)
0.685140 0.728411i \(-0.259741\pi\)
\(854\) 14.9631 + 17.6153i 0.512027 + 0.602783i
\(855\) −55.8556 + 62.4403i −1.91022 + 2.13541i
\(856\) 4.58284 + 1.41362i 0.156638 + 0.0483165i
\(857\) 0.886952 0.133686i 0.0302977 0.00456664i −0.133876 0.990998i \(-0.542742\pi\)
0.164174 + 0.986431i \(0.447504\pi\)
\(858\) 2.76177 41.9775i 0.0942852 1.43309i
\(859\) 23.7038 + 25.5466i 0.808762 + 0.871638i 0.993810 0.111091i \(-0.0354346\pi\)
−0.185048 + 0.982729i \(0.559244\pi\)
\(860\) 25.6915 + 7.92477i 0.876072 + 0.270232i
\(861\) −4.62413 8.69296i −0.157590 0.296255i
\(862\) 9.77756 3.01598i 0.333025 0.102725i
\(863\) 18.9817 + 10.9591i 0.646143 + 0.373051i 0.786977 0.616982i \(-0.211645\pi\)
−0.140834 + 0.990033i \(0.544978\pi\)
\(864\) 3.12761 4.14946i 0.106404 0.141168i
\(865\) −25.1166 + 7.74746i −0.853991 + 0.263421i
\(866\) 2.27469 1.09543i 0.0772970 0.0372243i
\(867\) −0.462353 0.938144i −0.0157023 0.0318610i
\(868\) −12.6486 + 3.30217i −0.429322 + 0.112083i
\(869\) 35.7990 14.0501i 1.21440 0.476616i
\(870\) 8.90620 18.9329i 0.301949 0.641885i
\(871\) 74.1220 29.0907i 2.51153 0.985702i
\(872\) −9.68806 + 14.2098i −0.328079 + 0.481204i
\(873\) −3.76401 + 0.931516i −0.127392 + 0.0315270i
\(874\) 7.39215 15.3500i 0.250043 0.519220i
\(875\) 2.51681 + 9.64038i 0.0850836 + 0.325904i
\(876\) −5.38254 1.60678i −0.181859 0.0542882i
\(877\) 0.433546 + 5.78527i 0.0146398 + 0.195355i 0.999728 + 0.0233066i \(0.00741941\pi\)
−0.985089 + 0.172048i \(0.944962\pi\)
\(878\) −8.24627 36.1293i −0.278298 1.21930i
\(879\) −3.62872 2.84016i −0.122394 0.0957962i
\(880\) −12.7402 10.1600i −0.429472 0.342492i
\(881\) 6.36877 0.214569 0.107285 0.994228i \(-0.465784\pi\)
0.107285 + 0.994228i \(0.465784\pi\)
\(882\) 13.1809 + 16.3482i 0.443823 + 0.550474i
\(883\) −39.3192 −1.32320 −0.661598 0.749859i \(-0.730121\pi\)
−0.661598 + 0.749859i \(0.730121\pi\)
\(884\) 15.7413 + 12.5533i 0.529437 + 0.422212i
\(885\) −14.4627 + 5.82867i −0.486158 + 0.195929i
\(886\) −5.51815 24.1766i −0.185386 0.812228i
\(887\) −4.01599 53.5896i −0.134844 1.79936i −0.497525 0.867450i \(-0.665758\pi\)
0.362681 0.931913i \(-0.381861\pi\)
\(888\) 0.484706 + 2.03794i 0.0162657 + 0.0683889i
\(889\) 1.33403 6.81047i 0.0447418 0.228416i
\(890\) −2.21680 + 4.60323i −0.0743073 + 0.154301i
\(891\) −43.1878 8.21578i −1.44684 0.275239i
\(892\) 1.09729 1.60942i 0.0367399 0.0538875i
\(893\) −61.4673 + 24.1242i −2.05693 + 0.807284i
\(894\) 12.0719 + 17.3645i 0.403745 + 0.580755i
\(895\) 77.7037 30.4965i 2.59735 1.01938i
\(896\) 0.0819252 + 2.64448i 0.00273693 + 0.0883460i
\(897\) 9.74169 14.5717i 0.325265 0.486534i
\(898\) 19.4434 9.36345i 0.648835 0.312462i
\(899\) −17.0968 + 5.27367i −0.570210 + 0.175887i
\(900\) 1.70759 + 18.3071i 0.0569197 + 0.610236i
\(901\) −33.0020 19.0537i −1.09946 0.634771i
\(902\) −10.0292 + 3.09360i −0.333936 + 0.103006i
\(903\) −24.0158 + 28.0581i −0.799194 + 0.933717i
\(904\) −11.7605 3.62763i −0.391148 0.120653i
\(905\) 55.1558 + 59.4438i 1.83344 + 1.97598i
\(906\) 14.0614 6.92999i 0.467159 0.230234i
\(907\) 30.8899 4.65590i 1.02568 0.154597i 0.385410 0.922745i \(-0.374060\pi\)
0.640271 + 0.768149i \(0.278822\pi\)
\(908\) 9.73239 + 3.00205i 0.322981 + 0.0996264i
\(909\) 7.37195 2.42177i 0.244512 0.0803252i
\(910\) 8.43611 43.0680i 0.279654 1.42769i
\(911\) 12.2038 + 39.5639i 0.404331 + 1.31081i 0.897553 + 0.440906i \(0.145343\pi\)
−0.493222 + 0.869903i \(0.664181\pi\)
\(912\) 3.09754 14.1643i 0.102570 0.469028i
\(913\) 18.9629i 0.627581i
\(914\) −22.7186 5.18538i −0.751465 0.171517i
\(915\) −48.3670 14.4384i −1.59896 0.477319i
\(916\) −12.8205 5.03166i −0.423600 0.166251i
\(917\) 13.8727 + 8.84173i 0.458117 + 0.291980i
\(918\) 15.0271 14.7269i 0.495970 0.486060i
\(919\) −2.95362 2.74056i −0.0974310 0.0904028i 0.629954 0.776633i \(-0.283074\pi\)
−0.727385 + 0.686230i \(0.759264\pi\)
\(920\) −2.48051 6.32024i −0.0817800 0.208372i
\(921\) 2.71405 2.56464i 0.0894311 0.0845079i
\(922\) −3.69507 1.45021i −0.121691 0.0477601i
\(923\) −6.62301 + 4.51549i −0.217999 + 0.148629i
\(924\) 19.7625 10.5124i 0.650137 0.345834i
\(925\) −6.12442 4.17556i −0.201370 0.137292i
\(926\) 3.53632 + 5.18683i 0.116211 + 0.170450i
\(927\) 0.518525 + 0.108458i 0.0170306 + 0.00356223i
\(928\) 0.270604 + 3.61097i 0.00888303 + 0.118536i
\(929\) 15.0978 18.9320i 0.495343 0.621140i −0.469829 0.882758i \(-0.655684\pi\)
0.965172 + 0.261617i \(0.0842558\pi\)
\(930\) 19.2272 21.1041i 0.630486 0.692031i
\(931\) 52.4631 + 26.1013i 1.71941 + 0.855435i
\(932\) 16.8990 + 9.75661i 0.553544 + 0.319589i
\(933\) −17.2289 6.58150i −0.564049 0.215469i
\(934\) 16.6278 + 24.3885i 0.544078 + 0.798015i
\(935\) −44.8800 48.3692i −1.46773 1.58184i
\(936\) 5.19605 13.9826i 0.169838 0.457037i
\(937\) 16.2329 + 33.7080i 0.530306 + 1.10119i 0.978307 + 0.207159i \(0.0664217\pi\)
−0.448001 + 0.894033i \(0.647864\pi\)
\(938\) 33.9276 + 25.3783i 1.10777 + 0.828630i
\(939\) 33.1491 + 4.68822i 1.08178 + 0.152994i
\(940\) −9.61385 + 24.4957i −0.313569 + 0.798961i
\(941\) −4.21260 + 2.02868i −0.137327 + 0.0661332i −0.501285 0.865282i \(-0.667139\pi\)
0.363958 + 0.931415i \(0.381425\pi\)
\(942\) −26.9509 10.2953i −0.878107 0.335440i
\(943\) −4.26339 0.973090i −0.138835 0.0316882i
\(944\) 1.68257 2.10988i 0.0547631 0.0686708i
\(945\) −43.5955 14.2403i −1.41816 0.463238i
\(946\) 24.5452 + 30.7788i 0.798034 + 1.00070i
\(947\) −15.0724 31.2982i −0.489788 1.01705i −0.988631 0.150362i \(-0.951956\pi\)
0.498843 0.866692i \(-0.333758\pi\)
\(948\) 13.5885 1.14280i 0.441335 0.0371164i
\(949\) −16.1257 −0.523464
\(950\) 25.6525 + 44.4314i 0.832276 + 1.44154i
\(951\) −1.09660 13.0392i −0.0355596 0.422824i
\(952\) −1.26793 + 10.6379i −0.0410938 + 0.344777i
\(953\) 15.4181 3.51907i 0.499440 0.113994i 0.0346225 0.999400i \(-0.488977\pi\)
0.464817 + 0.885407i \(0.346120\pi\)
\(954\) −5.78034 + 27.6351i −0.187145 + 0.894720i
\(955\) −27.1718 10.6642i −0.879259 0.345084i
\(956\) −2.49627 16.5617i −0.0807351 0.535643i
\(957\) 26.3914 15.5591i 0.853112 0.502954i
\(958\) 5.31813 17.2410i 0.171821 0.557030i
\(959\) 21.7726 + 0.954904i 0.703073 + 0.0308355i
\(960\) −3.29825 4.74427i −0.106451 0.153121i
\(961\) 6.58686 0.212479
\(962\) 3.00682 + 5.20796i 0.0969436 + 0.167911i
\(963\) 1.88502 14.2637i 0.0607440 0.459641i
\(964\) 21.1189 + 1.58265i 0.680195 + 0.0509736i
\(965\) 19.5792 49.8870i 0.630277 1.60592i
\(966\) 9.32106 + 0.323824i 0.299900 + 0.0104189i
\(967\) −17.8917 45.5872i −0.575357 1.46599i −0.861480 0.507792i \(-0.830462\pi\)
0.286123 0.958193i \(-0.407633\pi\)
\(968\) −3.79063 12.2889i −0.121836 0.394981i
\(969\) 20.9508 54.8445i 0.673036 1.76186i
\(970\) −0.322224 + 4.29978i −0.0103460 + 0.138058i
\(971\) 27.1341 4.08981i 0.870776 0.131248i 0.301571 0.953444i \(-0.402489\pi\)
0.569205 + 0.822195i \(0.307251\pi\)
\(972\) −13.8406 7.17192i −0.443939 0.230039i
\(973\) −25.2393 34.6623i −0.809133 1.11122i
\(974\) −14.5405 + 21.3270i −0.465907 + 0.683360i
\(975\) 19.7304 + 48.9570i 0.631877 + 1.56788i
\(976\) 8.51672 1.94389i 0.272614 0.0622223i
\(977\) −21.4393 + 44.5191i −0.685903 + 1.42429i 0.208949 + 0.977927i \(0.432996\pi\)
−0.894851 + 0.446365i \(0.852718\pi\)
\(978\) 17.5134 + 21.5556i 0.560017 + 0.689273i
\(979\) −6.47882 + 3.74055i −0.207064 + 0.119549i
\(980\) 21.8456 8.25118i 0.697833 0.263574i
\(981\) 46.8848 + 21.5360i 1.49692 + 0.687593i
\(982\) 7.82241 + 19.9312i 0.249623 + 0.636029i
\(983\) −7.18366 + 4.89774i −0.229123 + 0.156214i −0.672440 0.740151i \(-0.734754\pi\)
0.443317 + 0.896365i \(0.353802\pi\)
\(984\) −3.72141 + 0.0338767i −0.118634 + 0.00107995i
\(985\) 27.8338 2.08585i 0.886858 0.0664608i
\(986\) −1.09574 + 14.6216i −0.0348953 + 0.465646i
\(987\) −25.6287 25.4920i −0.815769 0.811420i
\(988\) −3.11051 41.5069i −0.0989586 1.32051i
\(989\) 2.44471 + 16.2196i 0.0777372 + 0.515753i
\(990\) −23.6682 + 42.7745i −0.752225 + 1.35946i
\(991\) −1.12414 0.169437i −0.0357095 0.00538235i 0.131163 0.991361i \(-0.458129\pi\)
−0.166873 + 0.985978i \(0.553367\pi\)
\(992\) −1.09947 + 4.81708i −0.0349082 + 0.152943i
\(993\) −9.95197 3.80168i −0.315816 0.120643i
\(994\) −3.89830 1.73073i −0.123647 0.0548955i
\(995\) −7.66257 50.8378i −0.242920 1.61167i
\(996\) −1.92337 + 6.44305i −0.0609442 + 0.204156i
\(997\) 2.35397 2.53698i 0.0745511 0.0803470i −0.694675 0.719324i \(-0.744452\pi\)
0.769226 + 0.638977i \(0.220642\pi\)
\(998\) −6.86165 + 3.96158i −0.217202 + 0.125402i
\(999\) 5.78509 2.45482i 0.183032 0.0776671i
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 882.2.bk.a.131.14 yes 672
9.2 odd 6 882.2.bc.a.425.39 672
49.3 odd 42 882.2.bc.a.689.39 yes 672
441.101 even 42 inner 882.2.bk.a.101.14 yes 672
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
882.2.bc.a.425.39 672 9.2 odd 6
882.2.bc.a.689.39 yes 672 49.3 odd 42
882.2.bk.a.101.14 yes 672 441.101 even 42 inner
882.2.bk.a.131.14 yes 672 1.1 even 1 trivial