Properties

Label 175.2.s.a.13.6
Level $175$
Weight $2$
Character 175.13
Analytic conductor $1.397$
Analytic rank $0$
Dimension $144$
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] = [175,2,Mod(13,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([19, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("175.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 175.s (of order \(20\), degree \(8\), 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: \(1.39738203537\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(18\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) \(=\) 175.13
Dual form 175.2.s.a.27.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23441 + 0.195511i) q^{2} +(0.157781 + 0.0803936i) q^{3} +(-0.416571 + 0.135352i) q^{4} +(-0.231923 + 2.22401i) q^{5} +(-0.210485 - 0.0683906i) q^{6} +(-2.64293 - 0.122096i) q^{7} +(2.71491 - 1.38332i) q^{8} +(-1.74492 - 2.40168i) q^{9} +O(q^{10})\) \(q+(-1.23441 + 0.195511i) q^{2} +(0.157781 + 0.0803936i) q^{3} +(-0.416571 + 0.135352i) q^{4} +(-0.231923 + 2.22401i) q^{5} +(-0.210485 - 0.0683906i) q^{6} +(-2.64293 - 0.122096i) q^{7} +(2.71491 - 1.38332i) q^{8} +(-1.74492 - 2.40168i) q^{9} +(-0.148530 - 2.79068i) q^{10} +(-3.51525 - 2.55398i) q^{11} +(-0.0766087 - 0.0121336i) q^{12} +(-0.920768 + 5.81350i) q^{13} +(3.28633 - 0.366007i) q^{14} +(-0.215389 + 0.332262i) q^{15} +(-2.37214 + 1.72346i) q^{16} +(-4.71092 + 2.40034i) q^{17} +(2.62351 + 2.62351i) q^{18} +(0.103086 - 0.317266i) q^{19} +(-0.204412 - 0.957849i) q^{20} +(-0.407190 - 0.231739i) q^{21} +(4.83859 + 2.46538i) q^{22} +(-0.153926 - 0.971852i) q^{23} +0.539572 q^{24} +(-4.89242 - 1.03160i) q^{25} -7.35626i q^{26} +(-0.165342 - 1.04393i) q^{27} +(1.11750 - 0.306865i) q^{28} +(2.47743 - 0.804965i) q^{29} +(0.200918 - 0.452258i) q^{30} +(6.20740 + 2.01691i) q^{31} +(-1.71789 + 1.71789i) q^{32} +(-0.349317 - 0.685574i) q^{33} +(5.34592 - 3.88404i) q^{34} +(0.884501 - 5.84959i) q^{35} +(1.05196 + 0.764293i) q^{36} +(-1.08273 + 6.83606i) q^{37} +(-0.0652212 + 0.411790i) q^{38} +(-0.612649 + 0.843238i) q^{39} +(2.44685 + 6.35881i) q^{40} +(-2.38618 - 3.28430i) q^{41} +(0.547947 + 0.206451i) q^{42} +(5.61888 + 5.61888i) q^{43} +(1.81004 + 0.588117i) q^{44} +(5.74605 - 3.32372i) q^{45} +(0.380016 + 1.16957i) q^{46} +(1.52215 - 2.98738i) q^{47} +(-0.512835 + 0.0812251i) q^{48} +(6.97019 + 0.645383i) q^{49} +(6.24094 + 0.316892i) q^{50} -0.936268 q^{51} +(-0.403305 - 2.54637i) q^{52} +(1.70178 - 3.33992i) q^{53} +(0.408199 + 1.25631i) q^{54} +(6.49534 - 7.22562i) q^{55} +(-7.34422 + 3.32453i) q^{56} +(0.0417712 - 0.0417712i) q^{57} +(-2.90078 + 1.47802i) q^{58} +(-9.49701 + 6.89998i) q^{59} +(0.0447526 - 0.167564i) q^{60} +(-3.64737 + 5.02017i) q^{61} +(-8.05680 - 1.27607i) q^{62} +(4.31848 + 6.56053i) q^{63} +(5.23164 - 7.20073i) q^{64} +(-12.7157 - 3.39608i) q^{65} +(0.565238 + 0.777983i) q^{66} +(0.434079 + 0.851927i) q^{67} +(1.63755 - 1.63755i) q^{68} +(0.0538440 - 0.165715i) q^{69} +(0.0518240 + 7.39371i) q^{70} +(-0.933657 - 2.87350i) q^{71} +(-8.05960 - 4.10657i) q^{72} +(2.02522 - 0.320764i) q^{73} -8.65018i q^{74} +(-0.688999 - 0.556087i) q^{75} +0.146117i q^{76} +(8.97874 + 7.17919i) q^{77} +(0.591396 - 1.16068i) q^{78} +(-5.09315 + 1.65486i) q^{79} +(-3.28284 - 5.67538i) q^{80} +(-2.69425 + 8.29203i) q^{81} +(3.58764 + 3.58764i) q^{82} +(1.06861 + 2.09726i) q^{83} +(0.200990 + 0.0414220i) q^{84} +(-4.24579 - 11.0338i) q^{85} +(-8.03455 - 5.83744i) q^{86} +(0.455606 + 0.0721609i) q^{87} +(-13.0765 - 2.07112i) q^{88} +(-5.91955 - 4.30080i) q^{89} +(-6.44315 + 5.22625i) q^{90} +(3.14333 - 15.2523i) q^{91} +(0.195664 + 0.384012i) q^{92} +(0.817266 + 0.817266i) q^{93} +(-1.29489 + 3.98525i) q^{94} +(0.681693 + 0.302845i) q^{95} +(-0.409159 + 0.132944i) q^{96} +(-5.99925 + 11.7742i) q^{97} +(-8.73024 + 0.566082i) q^{98} +12.8990i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 16 q^{2} - 20 q^{4} - 14 q^{7} - 12 q^{8} - 20 q^{9} - 12 q^{11} - 10 q^{14} - 20 q^{15} + 12 q^{16} - 28 q^{18} - 6 q^{21} + 16 q^{22} - 8 q^{23} - 20 q^{25} - 70 q^{28} + 40 q^{30} - 20 q^{32} - 40 q^{35} - 28 q^{36} + 4 q^{37} - 60 q^{39} - 30 q^{42} + 72 q^{43} - 20 q^{44} - 12 q^{46} + 140 q^{50} - 32 q^{51} - 104 q^{53} - 22 q^{56} + 120 q^{57} - 32 q^{58} - 120 q^{60} + 48 q^{63} + 40 q^{64} - 20 q^{65} - 16 q^{67} + 90 q^{70} - 12 q^{71} - 64 q^{72} + 74 q^{77} + 60 q^{78} - 20 q^{79} - 8 q^{81} + 190 q^{84} - 12 q^{86} + 92 q^{88} - 6 q^{91} - 20 q^{92} - 160 q^{93} + 80 q^{95} + 162 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{19}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23441 + 0.195511i −0.872859 + 0.138247i −0.576764 0.816911i \(-0.695685\pi\)
−0.296095 + 0.955158i \(0.595685\pi\)
\(3\) 0.157781 + 0.0803936i 0.0910951 + 0.0464153i 0.498944 0.866634i \(-0.333721\pi\)
−0.407849 + 0.913049i \(0.633721\pi\)
\(4\) −0.416571 + 0.135352i −0.208286 + 0.0676761i
\(5\) −0.231923 + 2.22401i −0.103719 + 0.994607i
\(6\) −0.210485 0.0683906i −0.0859300 0.0279204i
\(7\) −2.64293 0.122096i −0.998935 0.0461480i
\(8\) 2.71491 1.38332i 0.959866 0.489076i
\(9\) −1.74492 2.40168i −0.581641 0.800561i
\(10\) −0.148530 2.79068i −0.0469693 0.882490i
\(11\) −3.51525 2.55398i −1.05989 0.770053i −0.0858201 0.996311i \(-0.527351\pi\)
−0.974068 + 0.226257i \(0.927351\pi\)
\(12\) −0.0766087 0.0121336i −0.0221150 0.00350267i
\(13\) −0.920768 + 5.81350i −0.255375 + 1.61238i 0.442917 + 0.896562i \(0.353944\pi\)
−0.698292 + 0.715813i \(0.746056\pi\)
\(14\) 3.28633 0.366007i 0.878309 0.0978194i
\(15\) −0.215389 + 0.332262i −0.0556133 + 0.0857897i
\(16\) −2.37214 + 1.72346i −0.593036 + 0.430866i
\(17\) −4.71092 + 2.40034i −1.14257 + 0.582167i −0.919677 0.392677i \(-0.871549\pi\)
−0.222890 + 0.974844i \(0.571549\pi\)
\(18\) 2.62351 + 2.62351i 0.618366 + 0.618366i
\(19\) 0.103086 0.317266i 0.0236495 0.0727857i −0.938535 0.345184i \(-0.887817\pi\)
0.962185 + 0.272398i \(0.0878167\pi\)
\(20\) −0.204412 0.957849i −0.0457079 0.214182i
\(21\) −0.407190 0.231739i −0.0888561 0.0505697i
\(22\) 4.83859 + 2.46538i 1.03159 + 0.525622i
\(23\) −0.153926 0.971852i −0.0320958 0.202645i 0.966430 0.256932i \(-0.0827116\pi\)
−0.998525 + 0.0542866i \(0.982712\pi\)
\(24\) 0.539572 0.110140
\(25\) −4.89242 1.03160i −0.978485 0.206320i
\(26\) 7.35626i 1.44268i
\(27\) −0.165342 1.04393i −0.0318201 0.200904i
\(28\) 1.11750 0.306865i 0.211187 0.0579921i
\(29\) 2.47743 0.804965i 0.460047 0.149478i −0.0698191 0.997560i \(-0.522242\pi\)
0.529866 + 0.848081i \(0.322242\pi\)
\(30\) 0.200918 0.452258i 0.0366824 0.0825707i
\(31\) 6.20740 + 2.01691i 1.11488 + 0.362247i 0.807812 0.589440i \(-0.200651\pi\)
0.307070 + 0.951687i \(0.400651\pi\)
\(32\) −1.71789 + 1.71789i −0.303683 + 0.303683i
\(33\) −0.349317 0.685574i −0.0608083 0.119343i
\(34\) 5.34592 3.88404i 0.916817 0.666107i
\(35\) 0.884501 5.84959i 0.149508 0.988761i
\(36\) 1.05196 + 0.764293i 0.175326 + 0.127382i
\(37\) −1.08273 + 6.83606i −0.177999 + 1.12384i 0.723265 + 0.690571i \(0.242641\pi\)
−0.901264 + 0.433271i \(0.857359\pi\)
\(38\) −0.0652212 + 0.411790i −0.0105803 + 0.0668012i
\(39\) −0.612649 + 0.843238i −0.0981023 + 0.135026i
\(40\) 2.44685 + 6.35881i 0.386882 + 1.00542i
\(41\) −2.38618 3.28430i −0.372659 0.512921i 0.580962 0.813930i \(-0.302676\pi\)
−0.953621 + 0.301010i \(0.902676\pi\)
\(42\) 0.547947 + 0.206451i 0.0845500 + 0.0318561i
\(43\) 5.61888 + 5.61888i 0.856871 + 0.856871i 0.990968 0.134097i \(-0.0428134\pi\)
−0.134097 + 0.990968i \(0.542813\pi\)
\(44\) 1.81004 + 0.588117i 0.272874 + 0.0886620i
\(45\) 5.74605 3.32372i 0.856570 0.495471i
\(46\) 0.380016 + 1.16957i 0.0560303 + 0.172444i
\(47\) 1.52215 2.98738i 0.222028 0.435754i −0.752943 0.658085i \(-0.771367\pi\)
0.974971 + 0.222331i \(0.0713666\pi\)
\(48\) −0.512835 + 0.0812251i −0.0740214 + 0.0117238i
\(49\) 6.97019 + 0.645383i 0.995741 + 0.0921976i
\(50\) 6.24094 + 0.316892i 0.882602 + 0.0448153i
\(51\) −0.936268 −0.131104
\(52\) −0.403305 2.54637i −0.0559283 0.353117i
\(53\) 1.70178 3.33992i 0.233757 0.458774i −0.744094 0.668075i \(-0.767119\pi\)
0.977851 + 0.209301i \(0.0671187\pi\)
\(54\) 0.408199 + 1.25631i 0.0555489 + 0.170962i
\(55\) 6.49534 7.22562i 0.875831 0.974302i
\(56\) −7.34422 + 3.32453i −0.981413 + 0.444259i
\(57\) 0.0417712 0.0417712i 0.00553273 0.00553273i
\(58\) −2.90078 + 1.47802i −0.380891 + 0.194074i
\(59\) −9.49701 + 6.89998i −1.23641 + 0.898301i −0.997353 0.0727060i \(-0.976837\pi\)
−0.239052 + 0.971007i \(0.576837\pi\)
\(60\) 0.0447526 0.167564i 0.00577754 0.0216324i
\(61\) −3.64737 + 5.02017i −0.466998 + 0.642767i −0.975941 0.218033i \(-0.930036\pi\)
0.508944 + 0.860800i \(0.330036\pi\)
\(62\) −8.05680 1.27607i −1.02322 0.162061i
\(63\) 4.31848 + 6.56053i 0.544077 + 0.826549i
\(64\) 5.23164 7.20073i 0.653955 0.900092i
\(65\) −12.7157 3.39608i −1.57719 0.421232i
\(66\) 0.565238 + 0.777983i 0.0695760 + 0.0957631i
\(67\) 0.434079 + 0.851927i 0.0530311 + 0.104079i 0.916001 0.401176i \(-0.131398\pi\)
−0.862970 + 0.505255i \(0.831398\pi\)
\(68\) 1.63755 1.63755i 0.198582 0.198582i
\(69\) 0.0538440 0.165715i 0.00648206 0.0199497i
\(70\) 0.0518240 + 7.39371i 0.00619416 + 0.883718i
\(71\) −0.933657 2.87350i −0.110805 0.341022i 0.880244 0.474521i \(-0.157379\pi\)
−0.991049 + 0.133499i \(0.957379\pi\)
\(72\) −8.05960 4.10657i −0.949832 0.483964i
\(73\) 2.02522 0.320764i 0.237034 0.0375426i −0.0367870 0.999323i \(-0.511712\pi\)
0.273821 + 0.961781i \(0.411712\pi\)
\(74\) 8.65018i 1.00556i
\(75\) −0.688999 0.556087i −0.0795588 0.0642114i
\(76\) 0.146117i 0.0167607i
\(77\) 8.97874 + 7.17919i 1.02322 + 0.818145i
\(78\) 0.591396 1.16068i 0.0669625 0.131421i
\(79\) −5.09315 + 1.65486i −0.573024 + 0.186187i −0.581173 0.813780i \(-0.697406\pi\)
0.00814898 + 0.999967i \(0.497406\pi\)
\(80\) −3.28284 5.67538i −0.367033 0.634526i
\(81\) −2.69425 + 8.29203i −0.299361 + 0.921337i
\(82\) 3.58764 + 3.58764i 0.396189 + 0.396189i
\(83\) 1.06861 + 2.09726i 0.117295 + 0.230204i 0.942188 0.335085i \(-0.108765\pi\)
−0.824893 + 0.565288i \(0.808765\pi\)
\(84\) 0.200990 + 0.0414220i 0.0219298 + 0.00451951i
\(85\) −4.24579 11.0338i −0.460521 1.19679i
\(86\) −8.03455 5.83744i −0.866388 0.629468i
\(87\) 0.455606 + 0.0721609i 0.0488461 + 0.00773646i
\(88\) −13.0765 2.07112i −1.39396 0.220782i
\(89\) −5.91955 4.30080i −0.627471 0.455884i 0.228052 0.973649i \(-0.426764\pi\)
−0.855523 + 0.517765i \(0.826764\pi\)
\(90\) −6.44315 + 5.22625i −0.679168 + 0.550895i
\(91\) 3.14333 15.2523i 0.329511 1.59887i
\(92\) 0.195664 + 0.384012i 0.0203993 + 0.0400360i
\(93\) 0.817266 + 0.817266i 0.0847465 + 0.0847465i
\(94\) −1.29489 + 3.98525i −0.133557 + 0.411047i
\(95\) 0.681693 + 0.302845i 0.0699403 + 0.0310713i
\(96\) −0.409159 + 0.132944i −0.0417596 + 0.0135685i
\(97\) −5.99925 + 11.7742i −0.609132 + 1.19549i 0.356187 + 0.934415i \(0.384077\pi\)
−0.965319 + 0.261074i \(0.915923\pi\)
\(98\) −8.73024 + 0.566082i −0.881887 + 0.0571830i
\(99\) 12.8990i 1.29640i
\(100\) 2.17767 0.232466i 0.217767 0.0232466i
\(101\) 4.19859i 0.417775i 0.977940 + 0.208888i \(0.0669843\pi\)
−0.977940 + 0.208888i \(0.933016\pi\)
\(102\) 1.15574 0.183051i 0.114435 0.0181247i
\(103\) −15.4605 7.87752i −1.52337 0.776196i −0.526127 0.850406i \(-0.676356\pi\)
−0.997243 + 0.0742105i \(0.976356\pi\)
\(104\) 5.54211 + 17.0568i 0.543448 + 1.67256i
\(105\) 0.609827 0.851848i 0.0595130 0.0831318i
\(106\) −1.44770 + 4.45555i −0.140613 + 0.432761i
\(107\) 10.4565 10.4565i 1.01087 1.01087i 0.0109250 0.999940i \(-0.496522\pi\)
0.999940 0.0109250i \(-0.00347759\pi\)
\(108\) 0.210175 + 0.412491i 0.0202241 + 0.0396920i
\(109\) 2.07269 + 2.85281i 0.198528 + 0.273250i 0.896661 0.442718i \(-0.145986\pi\)
−0.698133 + 0.715968i \(0.745986\pi\)
\(110\) −6.60522 + 10.1893i −0.629783 + 0.971510i
\(111\) −0.720410 + 0.991559i −0.0683783 + 0.0941146i
\(112\) 6.47984 4.26537i 0.612287 0.403039i
\(113\) −14.1723 2.24467i −1.33322 0.211161i −0.551177 0.834389i \(-0.685821\pi\)
−0.782040 + 0.623228i \(0.785821\pi\)
\(114\) −0.0433960 + 0.0597295i −0.00406441 + 0.00559418i
\(115\) 2.19711 0.116938i 0.204881 0.0109045i
\(116\) −0.923072 + 0.670651i −0.0857051 + 0.0622684i
\(117\) 15.5689 7.93273i 1.43934 0.733381i
\(118\) 10.3742 10.3742i 0.955020 0.955020i
\(119\) 12.7437 5.76874i 1.16822 0.528820i
\(120\) −0.125139 + 1.20001i −0.0114236 + 0.109546i
\(121\) 2.43499 + 7.49412i 0.221363 + 0.681284i
\(122\) 3.52085 6.91005i 0.318762 0.625606i
\(123\) −0.112458 0.710035i −0.0101400 0.0640217i
\(124\) −2.85882 −0.256730
\(125\) 3.42895 10.6415i 0.306695 0.951808i
\(126\) −6.61343 7.25407i −0.589171 0.646244i
\(127\) −9.69898 + 1.53617i −0.860645 + 0.136313i −0.571129 0.820860i \(-0.693494\pi\)
−0.289516 + 0.957173i \(0.593494\pi\)
\(128\) −2.84425 + 5.58216i −0.251399 + 0.493398i
\(129\) 0.434833 + 1.33828i 0.0382849 + 0.117829i
\(130\) 16.3604 + 1.70609i 1.43490 + 0.149634i
\(131\) 21.0453 + 6.83804i 1.83874 + 0.597443i 0.998471 + 0.0552719i \(0.0176026\pi\)
0.840268 + 0.542171i \(0.182397\pi\)
\(132\) 0.238310 + 0.238310i 0.0207422 + 0.0207422i
\(133\) −0.311186 + 0.825926i −0.0269832 + 0.0716168i
\(134\) −0.702392 0.966759i −0.0606774 0.0835153i
\(135\) 2.36005 0.125610i 0.203121 0.0108108i
\(136\) −9.46931 + 13.0334i −0.811987 + 1.11760i
\(137\) 0.478131 3.01880i 0.0408495 0.257914i −0.958809 0.284052i \(-0.908321\pi\)
0.999658 + 0.0261385i \(0.00832108\pi\)
\(138\) −0.0340664 + 0.215087i −0.00289993 + 0.0183094i
\(139\) −10.5193 7.64275i −0.892239 0.648250i 0.0442216 0.999022i \(-0.485919\pi\)
−0.936461 + 0.350772i \(0.885919\pi\)
\(140\) 0.423297 + 2.55649i 0.0357751 + 0.216063i
\(141\) 0.480333 0.348982i 0.0404513 0.0293896i
\(142\) 1.71432 + 3.36454i 0.143862 + 0.282346i
\(143\) 18.0843 18.0843i 1.51228 1.51228i
\(144\) 8.27842 + 2.68982i 0.689868 + 0.224152i
\(145\) 1.21568 + 5.69651i 0.100956 + 0.473069i
\(146\) −2.43724 + 0.791908i −0.201707 + 0.0655387i
\(147\) 1.04788 + 0.662188i 0.0864277 + 0.0546163i
\(148\) −0.474244 2.99426i −0.0389826 0.246126i
\(149\) 7.52417i 0.616404i 0.951321 + 0.308202i \(0.0997272\pi\)
−0.951321 + 0.308202i \(0.900273\pi\)
\(150\) 0.959228 + 0.551732i 0.0783207 + 0.0450487i
\(151\) 20.8915 1.70012 0.850062 0.526683i \(-0.176564\pi\)
0.850062 + 0.526683i \(0.176564\pi\)
\(152\) −0.159010 1.00395i −0.0128974 0.0814310i
\(153\) 13.9850 + 7.12574i 1.13062 + 0.576082i
\(154\) −12.4870 7.10662i −1.00624 0.572667i
\(155\) −5.92526 + 13.3375i −0.475928 + 1.07130i
\(156\) 0.141078 0.434192i 0.0112953 0.0347632i
\(157\) −13.5717 13.5717i −1.08314 1.08314i −0.996215 0.0869256i \(-0.972296\pi\)
−0.0869256 0.996215i \(-0.527704\pi\)
\(158\) 5.96349 3.03855i 0.474430 0.241734i
\(159\) 0.537017 0.390166i 0.0425882 0.0309422i
\(160\) −3.42218 4.21902i −0.270547 0.333543i
\(161\) 0.288157 + 2.58733i 0.0227100 + 0.203910i
\(162\) 1.70462 10.7625i 0.133927 0.845583i
\(163\) 2.15388 + 0.341141i 0.168705 + 0.0267203i 0.240215 0.970720i \(-0.422782\pi\)
−0.0715104 + 0.997440i \(0.522782\pi\)
\(164\) 1.43855 + 1.04517i 0.112332 + 0.0816140i
\(165\) 1.60574 0.617884i 0.125006 0.0481022i
\(166\) −1.72913 2.37995i −0.134207 0.184720i
\(167\) −2.88263 + 1.46877i −0.223065 + 0.113657i −0.561952 0.827170i \(-0.689949\pi\)
0.338887 + 0.940827i \(0.389949\pi\)
\(168\) −1.42605 0.0658796i −0.110022 0.00508272i
\(169\) −20.5852 6.68855i −1.58348 0.514504i
\(170\) 7.39828 + 12.7902i 0.567422 + 0.980960i
\(171\) −0.941848 + 0.306025i −0.0720249 + 0.0234023i
\(172\) −3.10119 1.58014i −0.236464 0.120484i
\(173\) −20.6542 + 3.27130i −1.57031 + 0.248712i −0.880060 0.474862i \(-0.842498\pi\)
−0.690247 + 0.723574i \(0.742498\pi\)
\(174\) −0.576513 −0.0437053
\(175\) 12.8044 + 3.32379i 0.967921 + 0.251255i
\(176\) 12.7404 0.960341
\(177\) −2.05317 + 0.325189i −0.154325 + 0.0244427i
\(178\) 8.14800 + 4.15161i 0.610718 + 0.311177i
\(179\) −2.81593 + 0.914950i −0.210472 + 0.0683866i −0.412356 0.911023i \(-0.635294\pi\)
0.201883 + 0.979410i \(0.435294\pi\)
\(180\) −1.94377 + 2.16231i −0.144880 + 0.161169i
\(181\) 7.12519 + 2.31511i 0.529611 + 0.172081i 0.561603 0.827407i \(-0.310185\pi\)
−0.0319916 + 0.999488i \(0.510185\pi\)
\(182\) −0.898170 + 19.4421i −0.0665768 + 1.44114i
\(183\) −0.979077 + 0.498865i −0.0723754 + 0.0368771i
\(184\) −1.76227 2.42556i −0.129917 0.178815i
\(185\) −14.9523 3.99343i −1.09932 0.293603i
\(186\) −1.16863 0.849056i −0.0856878 0.0622558i
\(187\) 22.6905 + 3.59382i 1.65929 + 0.262806i
\(188\) −0.229734 + 1.45048i −0.0167551 + 0.105787i
\(189\) 0.309528 + 2.77922i 0.0225149 + 0.202158i
\(190\) −0.900698 0.240556i −0.0653435 0.0174518i
\(191\) 13.4621 9.78076i 0.974081 0.707711i 0.0177028 0.999843i \(-0.494365\pi\)
0.956378 + 0.292132i \(0.0943647\pi\)
\(192\) 1.40435 0.715551i 0.101350 0.0516405i
\(193\) 12.8852 + 12.8852i 0.927494 + 0.927494i 0.997543 0.0700499i \(-0.0223158\pi\)
−0.0700499 + 0.997543i \(0.522316\pi\)
\(194\) 5.10354 15.7071i 0.366413 1.12770i
\(195\) −1.73328 1.55810i −0.124123 0.111578i
\(196\) −2.99093 + 0.674582i −0.213638 + 0.0481844i
\(197\) 4.14736 + 2.11319i 0.295487 + 0.150558i 0.595449 0.803393i \(-0.296974\pi\)
−0.299962 + 0.953951i \(0.596974\pi\)
\(198\) −2.52190 15.9227i −0.179224 1.13157i
\(199\) −6.23169 −0.441753 −0.220877 0.975302i \(-0.570892\pi\)
−0.220877 + 0.975302i \(0.570892\pi\)
\(200\) −14.7095 + 3.96707i −1.04012 + 0.280514i
\(201\) 0.169315i 0.0119426i
\(202\) −0.820871 5.18277i −0.0577563 0.364659i
\(203\) −6.64596 + 1.82498i −0.466455 + 0.128089i
\(204\) 0.390022 0.126726i 0.0273070 0.00887259i
\(205\) 7.85771 4.54518i 0.548806 0.317449i
\(206\) 20.6247 + 6.70139i 1.43699 + 0.466908i
\(207\) −2.06549 + 2.06549i −0.143561 + 0.143561i
\(208\) −7.83516 15.3774i −0.543271 1.06623i
\(209\) −1.17266 + 0.851989i −0.0811148 + 0.0589333i
\(210\) −0.586231 + 1.17076i −0.0404538 + 0.0807899i
\(211\) −13.8588 10.0690i −0.954080 0.693180i −0.00231176 0.999997i \(-0.500736\pi\)
−0.951768 + 0.306818i \(0.900736\pi\)
\(212\) −0.256845 + 1.62166i −0.0176402 + 0.111376i
\(213\) 0.0836975 0.528445i 0.00573486 0.0362085i
\(214\) −10.8632 + 14.9519i −0.742594 + 1.02209i
\(215\) −13.7996 + 11.1933i −0.941124 + 0.763376i
\(216\) −1.89297 2.60545i −0.128800 0.177278i
\(217\) −16.1595 6.08845i −1.09698 0.413311i
\(218\) −3.11631 3.11631i −0.211063 0.211063i
\(219\) 0.345330 + 0.112204i 0.0233352 + 0.00758207i
\(220\) −1.72777 + 3.88914i −0.116486 + 0.262206i
\(221\) −9.61669 29.5971i −0.646888 1.99092i
\(222\) 0.695420 1.36484i 0.0466735 0.0916019i
\(223\) −2.26574 + 0.358858i −0.151725 + 0.0240309i −0.231835 0.972755i \(-0.574473\pi\)
0.0801098 + 0.996786i \(0.474473\pi\)
\(224\) 4.75002 4.33052i 0.317374 0.289345i
\(225\) 6.05933 + 13.5501i 0.403956 + 0.903340i
\(226\) 17.9333 1.19290
\(227\) −0.533605 3.36905i −0.0354166 0.223612i 0.963631 0.267235i \(-0.0861099\pi\)
−0.999048 + 0.0436231i \(0.986110\pi\)
\(228\) −0.0117469 + 0.0230545i −0.000777954 + 0.00152682i
\(229\) −3.99883 12.3071i −0.264250 0.813279i −0.991865 0.127293i \(-0.959371\pi\)
0.727615 0.685986i \(-0.240629\pi\)
\(230\) −2.68927 + 0.573908i −0.177325 + 0.0378424i
\(231\) 0.839516 + 1.85458i 0.0552361 + 0.122022i
\(232\) 5.61247 5.61247i 0.368477 0.368477i
\(233\) 1.49427 0.761371i 0.0978932 0.0498791i −0.404358 0.914601i \(-0.632505\pi\)
0.502252 + 0.864722i \(0.332505\pi\)
\(234\) −17.6674 + 12.8361i −1.15495 + 0.839123i
\(235\) 6.29094 + 4.07811i 0.410375 + 0.266027i
\(236\) 3.02225 4.15978i 0.196732 0.270778i
\(237\) −0.936645 0.148350i −0.0608416 0.00963637i
\(238\) −14.6031 + 9.61253i −0.946580 + 0.623088i
\(239\) −5.86889 + 8.07784i −0.379627 + 0.522512i −0.955486 0.295037i \(-0.904668\pi\)
0.575859 + 0.817549i \(0.304668\pi\)
\(240\) −0.0617068 1.15939i −0.00398316 0.0748382i
\(241\) 15.6102 + 21.4856i 1.00554 + 1.38401i 0.921864 + 0.387514i \(0.126666\pi\)
0.0836757 + 0.996493i \(0.473334\pi\)
\(242\) −4.47096 8.77475i −0.287404 0.564062i
\(243\) −3.33384 + 3.33384i −0.213866 + 0.213866i
\(244\) 0.839898 2.58494i 0.0537689 0.165484i
\(245\) −3.05189 + 15.3521i −0.194978 + 0.980808i
\(246\) 0.277639 + 0.854486i 0.0177016 + 0.0544801i
\(247\) 1.74951 + 0.891418i 0.111318 + 0.0567196i
\(248\) 19.6426 3.11108i 1.24730 0.197554i
\(249\) 0.416817i 0.0264147i
\(250\) −2.15219 + 13.8064i −0.136117 + 0.873194i
\(251\) 9.42659i 0.595001i −0.954722 0.297501i \(-0.903847\pi\)
0.954722 0.297501i \(-0.0961530\pi\)
\(252\) −2.68694 2.14841i −0.169261 0.135337i
\(253\) −1.94100 + 3.80943i −0.122030 + 0.239497i
\(254\) 11.6722 3.79252i 0.732377 0.237964i
\(255\) 0.217142 2.08227i 0.0135980 0.130397i
\(256\) −3.08127 + 9.48319i −0.192580 + 0.592699i
\(257\) 9.00174 + 9.00174i 0.561513 + 0.561513i 0.929737 0.368224i \(-0.120034\pi\)
−0.368224 + 0.929737i \(0.620034\pi\)
\(258\) −0.798409 1.56697i −0.0497068 0.0975551i
\(259\) 3.69623 17.9351i 0.229672 1.11443i
\(260\) 5.75668 0.306391i 0.357014 0.0190016i
\(261\) −6.25619 4.54539i −0.387249 0.281353i
\(262\) −27.3155 4.32635i −1.68756 0.267283i
\(263\) −16.3861 2.59530i −1.01041 0.160033i −0.370783 0.928720i \(-0.620911\pi\)
−0.639626 + 0.768686i \(0.720911\pi\)
\(264\) −1.89673 1.37806i −0.116736 0.0848134i
\(265\) 7.03334 + 4.55937i 0.432054 + 0.280080i
\(266\) 0.222653 1.08037i 0.0136517 0.0662418i
\(267\) −0.588237 1.15448i −0.0359995 0.0706531i
\(268\) −0.296135 0.296135i −0.0180893 0.0180893i
\(269\) −6.11636 + 18.8242i −0.372921 + 1.14773i 0.571949 + 0.820289i \(0.306187\pi\)
−0.944870 + 0.327445i \(0.893813\pi\)
\(270\) −2.88871 + 0.616471i −0.175801 + 0.0375172i
\(271\) −1.30082 + 0.422662i −0.0790191 + 0.0256749i −0.348260 0.937398i \(-0.613227\pi\)
0.269241 + 0.963073i \(0.413227\pi\)
\(272\) 7.03810 13.8130i 0.426747 0.837539i
\(273\) 1.72214 2.15382i 0.104229 0.130355i
\(274\) 3.81992i 0.230770i
\(275\) 14.5634 + 16.1215i 0.878206 + 0.972161i
\(276\) 0.0763200i 0.00459392i
\(277\) 24.9752 3.95568i 1.50061 0.237674i 0.648573 0.761152i \(-0.275366\pi\)
0.852039 + 0.523479i \(0.175366\pi\)
\(278\) 14.4794 + 7.37763i 0.868418 + 0.442481i
\(279\) −5.98748 18.4276i −0.358461 1.10323i
\(280\) −5.69049 17.1046i −0.340072 1.02220i
\(281\) −1.70772 + 5.25582i −0.101874 + 0.313536i −0.988984 0.148022i \(-0.952709\pi\)
0.887110 + 0.461558i \(0.152709\pi\)
\(282\) −0.524697 + 0.524697i −0.0312453 + 0.0312453i
\(283\) −4.79207 9.40496i −0.284859 0.559067i 0.703593 0.710603i \(-0.251578\pi\)
−0.988452 + 0.151536i \(0.951578\pi\)
\(284\) 0.777870 + 1.07065i 0.0461581 + 0.0635312i
\(285\) 0.0832117 + 0.102587i 0.00492904 + 0.00607674i
\(286\) −18.7877 + 25.8591i −1.11094 + 1.52908i
\(287\) 5.90552 + 8.97152i 0.348592 + 0.529572i
\(288\) 7.12342 + 1.12824i 0.419751 + 0.0664821i
\(289\) 6.43885 8.86231i 0.378756 0.521312i
\(290\) −2.61437 6.79415i −0.153521 0.398966i
\(291\) −1.89314 + 1.37545i −0.110978 + 0.0806301i
\(292\) −0.800234 + 0.407739i −0.0468301 + 0.0238611i
\(293\) −9.97473 + 9.97473i −0.582730 + 0.582730i −0.935653 0.352922i \(-0.885188\pi\)
0.352922 + 0.935653i \(0.385188\pi\)
\(294\) −1.42298 0.612538i −0.0829898 0.0357240i
\(295\) −13.1430 22.7217i −0.765217 1.32291i
\(296\) 6.51693 + 20.0570i 0.378789 + 1.16579i
\(297\) −2.08495 + 4.09195i −0.120981 + 0.237439i
\(298\) −1.47106 9.28790i −0.0852162 0.538034i
\(299\) 5.79159 0.334937
\(300\) 0.362285 + 0.138392i 0.0209165 + 0.00799008i
\(301\) −14.1643 15.5364i −0.816415 0.895501i
\(302\) −25.7886 + 4.08452i −1.48397 + 0.235038i
\(303\) −0.337540 + 0.662459i −0.0193911 + 0.0380573i
\(304\) 0.302261 + 0.930264i 0.0173359 + 0.0533543i
\(305\) −10.3190 9.27607i −0.590864 0.531146i
\(306\) −18.6564 6.06184i −1.06652 0.346532i
\(307\) 1.28906 + 1.28906i 0.0735708 + 0.0735708i 0.742935 0.669364i \(-0.233433\pi\)
−0.669364 + 0.742935i \(0.733433\pi\)
\(308\) −4.71200 1.77535i −0.268491 0.101160i
\(309\) −1.80608 2.48585i −0.102744 0.141415i
\(310\) 4.70656 17.6224i 0.267314 1.00089i
\(311\) −4.39371 + 6.04742i −0.249144 + 0.342918i −0.915211 0.402974i \(-0.867976\pi\)
0.666067 + 0.745892i \(0.267976\pi\)
\(312\) −0.496821 + 3.13680i −0.0281269 + 0.177586i
\(313\) −1.00496 + 6.34509i −0.0568039 + 0.358646i 0.942871 + 0.333157i \(0.108114\pi\)
−0.999675 + 0.0254883i \(0.991886\pi\)
\(314\) 19.4065 + 14.0996i 1.09517 + 0.795688i
\(315\) −15.5922 + 8.08279i −0.878523 + 0.455414i
\(316\) 1.89767 1.37874i 0.106752 0.0775601i
\(317\) 3.79057 + 7.43940i 0.212899 + 0.417839i 0.972617 0.232415i \(-0.0746627\pi\)
−0.759717 + 0.650253i \(0.774663\pi\)
\(318\) −0.586617 + 0.586617i −0.0328959 + 0.0328959i
\(319\) −10.7646 3.49764i −0.602704 0.195830i
\(320\) 14.8011 + 13.3052i 0.827409 + 0.743785i
\(321\) 2.49047 0.809203i 0.139004 0.0451653i
\(322\) −0.861557 3.13749i −0.0480127 0.174846i
\(323\) 0.275914 + 1.74206i 0.0153523 + 0.0969306i
\(324\) 3.81890i 0.212161i
\(325\) 10.5020 27.4922i 0.582546 1.52500i
\(326\) −2.72547 −0.150950
\(327\) 0.0976839 + 0.616752i 0.00540193 + 0.0341065i
\(328\) −11.0215 5.61573i −0.608560 0.310077i
\(329\) −4.38768 + 7.70960i −0.241900 + 0.425044i
\(330\) −1.86133 + 1.07666i −0.102463 + 0.0592683i
\(331\) 1.30276 4.00948i 0.0716062 0.220381i −0.908848 0.417126i \(-0.863037\pi\)
0.980455 + 0.196745i \(0.0630372\pi\)
\(332\) −0.729019 0.729019i −0.0400101 0.0400101i
\(333\) 18.3073 9.32804i 1.00323 0.511174i
\(334\) 3.27119 2.37666i 0.178991 0.130045i
\(335\) −1.99537 + 0.767812i −0.109018 + 0.0419501i
\(336\) 1.36531 0.152057i 0.0744836 0.00829541i
\(337\) −2.48550 + 15.6928i −0.135394 + 0.854844i 0.822718 + 0.568450i \(0.192457\pi\)
−0.958112 + 0.286394i \(0.907543\pi\)
\(338\) 26.7183 + 4.23176i 1.45328 + 0.230178i
\(339\) −2.05567 1.49353i −0.111648 0.0811174i
\(340\) 3.26213 + 4.02170i 0.176914 + 0.218107i
\(341\) −16.6694 22.9435i −0.902700 1.24246i
\(342\) 1.10279 0.561902i 0.0596323 0.0303842i
\(343\) −18.3429 2.55674i −0.990425 0.138051i
\(344\) 23.0274 + 7.48207i 1.24156 + 0.403406i
\(345\) 0.356063 + 0.158183i 0.0191698 + 0.00851627i
\(346\) 24.8561 8.07624i 1.33627 0.434182i
\(347\) −7.38490 3.76280i −0.396442 0.201997i 0.244392 0.969676i \(-0.421412\pi\)
−0.640835 + 0.767679i \(0.721412\pi\)
\(348\) −0.199560 + 0.0316071i −0.0106975 + 0.00169432i
\(349\) 4.16930 0.223177 0.111589 0.993754i \(-0.464406\pi\)
0.111589 + 0.993754i \(0.464406\pi\)
\(350\) −16.4557 1.59952i −0.879594 0.0854979i
\(351\) 6.22112 0.332059
\(352\) 10.4263 1.65136i 0.555722 0.0880177i
\(353\) 21.3205 + 10.8634i 1.13478 + 0.578198i 0.917430 0.397896i \(-0.130260\pi\)
0.217347 + 0.976094i \(0.430260\pi\)
\(354\) 2.47087 0.802834i 0.131325 0.0426701i
\(355\) 6.60723 1.41003i 0.350675 0.0748366i
\(356\) 3.04804 + 0.990368i 0.161546 + 0.0524894i
\(357\) 2.47449 + 0.114315i 0.130964 + 0.00605017i
\(358\) 3.29712 1.67997i 0.174258 0.0887891i
\(359\) 10.4712 + 14.4123i 0.552648 + 0.760654i 0.990368 0.138457i \(-0.0442142\pi\)
−0.437721 + 0.899111i \(0.644214\pi\)
\(360\) 11.0023 16.9722i 0.579870 0.894513i
\(361\) 15.2813 + 11.1025i 0.804279 + 0.584343i
\(362\) −9.24803 1.46474i −0.486066 0.0769852i
\(363\) −0.218284 + 1.37819i −0.0114569 + 0.0723362i
\(364\) 0.755006 + 6.77912i 0.0395731 + 0.355322i
\(365\) 0.243685 + 4.57850i 0.0127550 + 0.239650i
\(366\) 1.11105 0.807223i 0.0580754 0.0421942i
\(367\) −12.8889 + 6.56720i −0.672793 + 0.342805i −0.756787 0.653661i \(-0.773232\pi\)
0.0839946 + 0.996466i \(0.473232\pi\)
\(368\) 2.04009 + 2.04009i 0.106347 + 0.106347i
\(369\) −3.72413 + 11.4617i −0.193870 + 0.596672i
\(370\) 19.2381 + 2.00618i 1.00014 + 0.104296i
\(371\) −4.90547 + 8.61941i −0.254679 + 0.447498i
\(372\) −0.451069 0.229831i −0.0233868 0.0119162i
\(373\) 3.68715 + 23.2798i 0.190913 + 1.20538i 0.877948 + 0.478756i \(0.158912\pi\)
−0.687035 + 0.726625i \(0.741088\pi\)
\(374\) −28.7120 −1.48466
\(375\) 1.39654 1.40337i 0.0721168 0.0724697i
\(376\) 10.2161i 0.526854i
\(377\) 2.39853 + 15.1437i 0.123531 + 0.779941i
\(378\) −0.925452 3.37018i −0.0476001 0.173343i
\(379\) 14.3686 4.66864i 0.738066 0.239812i 0.0842276 0.996447i \(-0.473158\pi\)
0.653838 + 0.756634i \(0.273158\pi\)
\(380\) −0.324965 0.0338879i −0.0166703 0.00173841i
\(381\) −1.65382 0.537357i −0.0847276 0.0275297i
\(382\) −14.7054 + 14.7054i −0.752396 + 0.752396i
\(383\) −4.24204 8.32548i −0.216758 0.425412i 0.756866 0.653570i \(-0.226730\pi\)
−0.973624 + 0.228158i \(0.926730\pi\)
\(384\) −0.897540 + 0.652101i −0.0458024 + 0.0332774i
\(385\) −18.0490 + 18.3038i −0.919860 + 0.932846i
\(386\) −18.4247 13.3864i −0.937795 0.681348i
\(387\) 3.69024 23.2993i 0.187586 1.18437i
\(388\) 0.905453 5.71680i 0.0459674 0.290227i
\(389\) 13.8549 19.0696i 0.702471 0.966869i −0.297455 0.954736i \(-0.596138\pi\)
0.999926 0.0121331i \(-0.00386217\pi\)
\(390\) 2.44420 + 1.58446i 0.123767 + 0.0802322i
\(391\) 3.05791 + 4.20885i 0.154645 + 0.212851i
\(392\) 19.8162 7.88981i 1.00087 0.398496i
\(393\) 2.77083 + 2.77083i 0.139770 + 0.139770i
\(394\) −5.53270 1.79768i −0.278733 0.0905659i
\(395\) −2.49921 11.7110i −0.125749 0.589245i
\(396\) −1.74591 5.37336i −0.0877353 0.270021i
\(397\) −0.760728 + 1.49301i −0.0381798 + 0.0749322i −0.909308 0.416123i \(-0.863389\pi\)
0.871129 + 0.491055i \(0.163389\pi\)
\(398\) 7.69246 1.21837i 0.385588 0.0610712i
\(399\) −0.115498 + 0.105298i −0.00578216 + 0.00527151i
\(400\) 13.3834 5.98481i 0.669172 0.299240i
\(401\) −29.0431 −1.45034 −0.725171 0.688568i \(-0.758239\pi\)
−0.725171 + 0.688568i \(0.758239\pi\)
\(402\) −0.0331031 0.209004i −0.00165103 0.0104242i
\(403\) −17.4409 + 34.2296i −0.868792 + 1.70510i
\(404\) −0.568288 1.74901i −0.0282734 0.0870166i
\(405\) −17.8167 7.91514i −0.885318 0.393306i
\(406\) 7.84703 3.55214i 0.389441 0.176290i
\(407\) 21.2652 21.2652i 1.05408 1.05408i
\(408\) −2.54188 + 1.29515i −0.125842 + 0.0641197i
\(409\) 20.4231 14.8382i 1.00986 0.733703i 0.0456772 0.998956i \(-0.485455\pi\)
0.964179 + 0.265253i \(0.0854554\pi\)
\(410\) −8.81100 + 7.14688i −0.435144 + 0.352959i
\(411\) 0.318133 0.437872i 0.0156923 0.0215986i
\(412\) 7.50665 + 1.18894i 0.369826 + 0.0585747i
\(413\) 25.9424 17.0766i 1.27654 0.840286i
\(414\) 2.14583 2.95349i 0.105462 0.145156i
\(415\) −4.91215 + 1.89018i −0.241128 + 0.0927855i
\(416\) −8.40518 11.5687i −0.412098 0.567204i
\(417\) −1.04533 2.05157i −0.0511900 0.100466i
\(418\) 1.28097 1.28097i 0.0626544 0.0626544i
\(419\) −7.17191 + 22.0729i −0.350371 + 1.07833i 0.608274 + 0.793727i \(0.291862\pi\)
−0.958645 + 0.284604i \(0.908138\pi\)
\(420\) −0.138737 + 0.437397i −0.00676968 + 0.0213428i
\(421\) 7.00904 + 21.5716i 0.341600 + 1.05134i 0.963379 + 0.268144i \(0.0864101\pi\)
−0.621779 + 0.783193i \(0.713590\pi\)
\(422\) 19.0761 + 9.71974i 0.928608 + 0.473149i
\(423\) −9.83077 + 1.55704i −0.477988 + 0.0757059i
\(424\) 11.4217i 0.554686i
\(425\) 25.5240 6.88367i 1.23810 0.333907i
\(426\) 0.668681i 0.0323977i
\(427\) 10.2527 12.8226i 0.496163 0.620531i
\(428\) −2.94056 + 5.77117i −0.142137 + 0.278960i
\(429\) 4.30723 1.39950i 0.207955 0.0675686i
\(430\) 14.8459 16.5151i 0.715934 0.796427i
\(431\) −11.0978 + 34.1556i −0.534564 + 1.64522i 0.210025 + 0.977696i \(0.432645\pi\)
−0.744589 + 0.667523i \(0.767355\pi\)
\(432\) 2.19138 + 2.19138i 0.105433 + 0.105433i
\(433\) −2.85277 5.59888i −0.137096 0.269065i 0.812244 0.583318i \(-0.198246\pi\)
−0.949339 + 0.314253i \(0.898246\pi\)
\(434\) 21.1378 + 4.35628i 1.01465 + 0.209108i
\(435\) −0.266152 + 0.996536i −0.0127610 + 0.0477802i
\(436\) −1.24956 0.907857i −0.0598430 0.0434785i
\(437\) −0.324203 0.0513487i −0.0155087 0.00245634i
\(438\) −0.448216 0.0709904i −0.0214166 0.00339205i
\(439\) 28.7166 + 20.8638i 1.37057 + 0.995777i 0.997692 + 0.0678955i \(0.0216285\pi\)
0.372876 + 0.927881i \(0.378372\pi\)
\(440\) 7.63895 28.6020i 0.364173 1.36355i
\(441\) −10.6124 17.8663i −0.505354 0.850777i
\(442\) 17.6575 + 34.6548i 0.839881 + 1.64836i
\(443\) −13.5005 13.5005i −0.641429 0.641429i 0.309478 0.950907i \(-0.399846\pi\)
−0.950907 + 0.309478i \(0.899846\pi\)
\(444\) 0.165892 0.510564i 0.00787290 0.0242303i
\(445\) 10.9379 12.1677i 0.518506 0.576803i
\(446\) 2.72669 0.885955i 0.129112 0.0419512i
\(447\) −0.604895 + 1.18717i −0.0286106 + 0.0561514i
\(448\) −14.7060 + 18.3923i −0.694796 + 0.868954i
\(449\) 23.4517i 1.10675i −0.832931 0.553377i \(-0.813339\pi\)
0.832931 0.553377i \(-0.186661\pi\)
\(450\) −10.1289 15.5417i −0.477481 0.732643i
\(451\) 17.6394i 0.830606i
\(452\) 6.20759 0.983186i 0.291981 0.0462452i
\(453\) 3.29629 + 1.67954i 0.154873 + 0.0789117i
\(454\) 1.31737 + 4.05446i 0.0618274 + 0.190285i
\(455\) 33.1922 + 10.5282i 1.55607 + 0.493568i
\(456\) 0.0556223 0.171188i 0.00260475 0.00801660i
\(457\) −14.2402 + 14.2402i −0.666130 + 0.666130i −0.956818 0.290688i \(-0.906116\pi\)
0.290688 + 0.956818i \(0.406116\pi\)
\(458\) 7.34238 + 14.4102i 0.343087 + 0.673346i
\(459\) 3.28469 + 4.52099i 0.153316 + 0.211022i
\(460\) −0.899424 + 0.346096i −0.0419358 + 0.0161368i
\(461\) 18.7781 25.8458i 0.874582 1.20376i −0.103310 0.994649i \(-0.532943\pi\)
0.977892 0.209110i \(-0.0670567\pi\)
\(462\) −1.39890 2.12517i −0.0650826 0.0988719i
\(463\) −7.84420 1.24240i −0.364551 0.0577392i −0.0285280 0.999593i \(-0.509082\pi\)
−0.336023 + 0.941854i \(0.609082\pi\)
\(464\) −4.48949 + 6.17925i −0.208419 + 0.286864i
\(465\) −2.00715 + 1.62806i −0.0930793 + 0.0754996i
\(466\) −1.69569 + 1.23199i −0.0785513 + 0.0570709i
\(467\) −13.1500 + 6.70025i −0.608508 + 0.310050i −0.730956 0.682425i \(-0.760926\pi\)
0.122448 + 0.992475i \(0.460926\pi\)
\(468\) −5.41183 + 5.41183i −0.250162 + 0.250162i
\(469\) −1.04322 2.30458i −0.0481716 0.106416i
\(470\) −8.56291 3.80411i −0.394977 0.175470i
\(471\) −1.05028 3.23244i −0.0483945 0.148943i
\(472\) −16.2387 + 31.8702i −0.747445 + 1.46694i
\(473\) −5.40127 34.1023i −0.248351 1.56802i
\(474\) 1.18521 0.0544384
\(475\) −0.831631 + 1.44585i −0.0381578 + 0.0663404i
\(476\) −4.52786 + 4.12798i −0.207534 + 0.189206i
\(477\) −10.9909 + 1.74079i −0.503239 + 0.0797052i
\(478\) 5.66531 11.1188i 0.259125 0.508562i
\(479\) 8.26880 + 25.4488i 0.377811 + 1.16278i 0.941562 + 0.336839i \(0.109358\pi\)
−0.563751 + 0.825945i \(0.690642\pi\)
\(480\) −0.200774 0.940805i −0.00916406 0.0429417i
\(481\) −38.7445 12.5889i −1.76660 0.574002i
\(482\) −23.4700 23.4700i −1.06903 1.06903i
\(483\) −0.162539 + 0.431399i −0.00739579 + 0.0196293i
\(484\) −2.02869 2.79226i −0.0922133 0.126921i
\(485\) −24.7945 16.0731i −1.12586 0.729842i
\(486\) 3.46352 4.76712i 0.157108 0.216241i
\(487\) −4.70106 + 29.6813i −0.213025 + 1.34499i 0.616867 + 0.787067i \(0.288401\pi\)
−0.829893 + 0.557923i \(0.811599\pi\)
\(488\) −2.95779 + 18.6748i −0.133893 + 0.845367i
\(489\) 0.312417 + 0.226984i 0.0141280 + 0.0102646i
\(490\) 0.765776 19.5474i 0.0345942 0.883062i
\(491\) −28.9714 + 21.0489i −1.30746 + 0.949925i −0.999999 0.00163542i \(-0.999479\pi\)
−0.307461 + 0.951561i \(0.599479\pi\)
\(492\) 0.142952 + 0.280559i 0.00644476 + 0.0126486i
\(493\) −9.73879 + 9.73879i −0.438613 + 0.438613i
\(494\) −2.33389 0.758327i −0.105007 0.0341187i
\(495\) −28.6875 2.99158i −1.28941 0.134462i
\(496\) −18.2009 + 5.91383i −0.817245 + 0.265539i
\(497\) 2.11675 + 7.70847i 0.0949492 + 0.345772i
\(498\) −0.0814924 0.514523i −0.00365176 0.0230563i
\(499\) 4.46251i 0.199770i −0.994999 0.0998848i \(-0.968153\pi\)
0.994999 0.0998848i \(-0.0318474\pi\)
\(500\) 0.0119523 + 4.89708i 0.000534524 + 0.219004i
\(501\) −0.572906 −0.0255955
\(502\) 1.84300 + 11.6363i 0.0822573 + 0.519352i
\(503\) 5.84493 + 2.97814i 0.260613 + 0.132789i 0.579416 0.815032i \(-0.303281\pi\)
−0.318803 + 0.947821i \(0.603281\pi\)
\(504\) 20.7996 + 11.8374i 0.926487 + 0.527281i
\(505\) −9.33769 0.973751i −0.415522 0.0433313i
\(506\) 1.65120 5.08188i 0.0734049 0.225917i
\(507\) −2.71025 2.71025i −0.120367 0.120367i
\(508\) 3.83239 1.95270i 0.170035 0.0866371i
\(509\) 19.3515 14.0597i 0.857740 0.623185i −0.0695290 0.997580i \(-0.522150\pi\)
0.927269 + 0.374395i \(0.122150\pi\)
\(510\) 0.139064 + 2.61282i 0.00615785 + 0.115698i
\(511\) −5.39169 + 0.600485i −0.238514 + 0.0265639i
\(512\) 3.90961 24.6843i 0.172782 1.09090i
\(513\) −0.348247 0.0551569i −0.0153755 0.00243524i
\(514\) −12.8718 9.35189i −0.567750 0.412494i
\(515\) 21.1053 32.5573i 0.930012 1.43465i
\(516\) −0.362278 0.498632i −0.0159484 0.0219511i
\(517\) −12.9804 + 6.61386i −0.570879 + 0.290877i
\(518\) −1.05615 + 22.8619i −0.0464047 + 1.00449i
\(519\) −3.52183 1.14431i −0.154591 0.0502298i
\(520\) −39.2199 + 8.36980i −1.71991 + 0.367040i
\(521\) −28.8783 + 9.38314i −1.26518 + 0.411083i −0.863338 0.504625i \(-0.831631\pi\)
−0.401844 + 0.915708i \(0.631631\pi\)
\(522\) 8.61138 + 4.38772i 0.376910 + 0.192045i
\(523\) −5.35328 + 0.847876i −0.234082 + 0.0370750i −0.272373 0.962192i \(-0.587809\pi\)
0.0382910 + 0.999267i \(0.487809\pi\)
\(524\) −9.69243 −0.423416
\(525\) 1.75308 + 1.55382i 0.0765108 + 0.0678144i
\(526\) 20.7345 0.904069
\(527\) −34.0839 + 5.39835i −1.48472 + 0.235156i
\(528\) 2.01019 + 1.02424i 0.0874824 + 0.0445745i
\(529\) 20.9535 6.80820i 0.911022 0.296009i
\(530\) −9.57342 4.25303i −0.415843 0.184740i
\(531\) 33.1431 + 10.7688i 1.43829 + 0.467328i
\(532\) 0.0178403 0.386177i 0.000773474 0.0167429i
\(533\) 21.2904 10.8480i 0.922189 0.469879i
\(534\) 0.951840 + 1.31009i 0.0411901 + 0.0566933i
\(535\) 20.8302 + 25.6804i 0.900567 + 1.11026i
\(536\) 2.35697 + 1.71244i 0.101806 + 0.0739660i
\(537\) −0.517857 0.0820205i −0.0223472 0.00353944i
\(538\) 3.86975 24.4326i 0.166837 1.05337i
\(539\) −22.8536 20.0704i −0.984376 0.864493i
\(540\) −0.966128 + 0.371764i −0.0415755 + 0.0159982i
\(541\) −1.61027 + 1.16993i −0.0692308 + 0.0502991i −0.621862 0.783127i \(-0.713624\pi\)
0.552632 + 0.833426i \(0.313624\pi\)
\(542\) 1.52311 0.776062i 0.0654231 0.0333347i
\(543\) 0.938102 + 0.938102i 0.0402578 + 0.0402578i
\(544\) 3.96934 12.2164i 0.170184 0.523772i
\(545\) −6.82539 + 3.94805i −0.292367 + 0.169116i
\(546\) −1.70474 + 2.99539i −0.0729559 + 0.128191i
\(547\) −22.6516 11.5416i −0.968514 0.493483i −0.103172 0.994664i \(-0.532899\pi\)
−0.865343 + 0.501181i \(0.832899\pi\)
\(548\) 0.209426 + 1.32226i 0.00894623 + 0.0564843i
\(549\) 18.4212 0.786199
\(550\) −21.1291 17.0532i −0.900949 0.727150i
\(551\) 0.868984i 0.0370199i
\(552\) −0.0830543 0.524384i −0.00353503 0.0223193i
\(553\) 13.6629 3.75184i 0.581006 0.159545i
\(554\) −30.0562 + 9.76585i −1.27697 + 0.414911i
\(555\) −2.03816 1.83216i −0.0865149 0.0777710i
\(556\) 5.41652 + 1.75993i 0.229712 + 0.0746379i
\(557\) 3.74492 3.74492i 0.158678 0.158678i −0.623303 0.781980i \(-0.714210\pi\)
0.781980 + 0.623303i \(0.214210\pi\)
\(558\) 10.9938 + 21.5765i 0.465404 + 0.913407i
\(559\) −37.8391 + 27.4917i −1.60042 + 1.16277i
\(560\) 7.98338 + 15.4005i 0.337359 + 0.650788i
\(561\) 3.29122 + 2.39121i 0.138955 + 0.100957i
\(562\) 1.08045 6.82171i 0.0455761 0.287756i
\(563\) −0.296988 + 1.87511i −0.0125166 + 0.0790264i −0.993156 0.116796i \(-0.962738\pi\)
0.980639 + 0.195822i \(0.0627376\pi\)
\(564\) −0.152857 + 0.210390i −0.00643646 + 0.00885902i
\(565\) 8.27905 30.9987i 0.348302 1.30412i
\(566\) 7.75415 + 10.6727i 0.325931 + 0.448606i
\(567\) 8.13313 21.5863i 0.341559 0.906541i
\(568\) −6.50976 6.50976i −0.273143 0.273143i
\(569\) −23.6607 7.68782i −0.991908 0.322290i −0.232280 0.972649i \(-0.574619\pi\)
−0.759627 + 0.650359i \(0.774619\pi\)
\(570\) −0.122774 0.110366i −0.00514245 0.00462271i
\(571\) −13.9665 42.9845i −0.584480 1.79884i −0.601350 0.798986i \(-0.705370\pi\)
0.0168702 0.999858i \(-0.494630\pi\)
\(572\) −5.08565 + 9.98115i −0.212642 + 0.417333i
\(573\) 2.91037 0.460958i 0.121583 0.0192568i
\(574\) −9.04386 9.91993i −0.377483 0.414050i
\(575\) −0.249490 + 4.91350i −0.0104044 + 0.204907i
\(576\) −26.4227 −1.10095
\(577\) −5.85129 36.9436i −0.243592 1.53798i −0.741620 0.670820i \(-0.765942\pi\)
0.498028 0.867161i \(-0.334058\pi\)
\(578\) −6.21549 + 12.1986i −0.258530 + 0.507394i
\(579\) 0.997153 + 3.06892i 0.0414403 + 0.127540i
\(580\) −1.27745 2.20846i −0.0530433 0.0917013i
\(581\) −2.56819 5.67338i −0.106546 0.235371i
\(582\) 2.06799 2.06799i 0.0857211 0.0857211i
\(583\) −14.5123 + 7.39437i −0.601037 + 0.306243i
\(584\) 5.05458 3.67237i 0.209160 0.151964i
\(585\) 14.0317 + 36.4650i 0.580138 + 1.50764i
\(586\) 10.3627 14.2631i 0.428080 0.589202i
\(587\) 13.6195 + 2.15712i 0.562138 + 0.0890338i 0.431035 0.902335i \(-0.358148\pi\)
0.131102 + 0.991369i \(0.458148\pi\)
\(588\) −0.526146 0.134016i −0.0216979 0.00552671i
\(589\) 1.27979 1.76148i 0.0527329 0.0725806i
\(590\) 20.6662 + 25.4783i 0.850815 + 1.04892i
\(591\) 0.484490 + 0.666843i 0.0199293 + 0.0274303i
\(592\) −9.21332 18.0822i −0.378665 0.743172i
\(593\) −21.1417 + 21.1417i −0.868184 + 0.868184i −0.992271 0.124087i \(-0.960400\pi\)
0.124087 + 0.992271i \(0.460400\pi\)
\(594\) 1.77366 5.45877i 0.0727742 0.223976i
\(595\) 9.87416 + 29.6801i 0.404801 + 1.21676i
\(596\) −1.01841 3.13435i −0.0417158 0.128388i
\(597\) −0.983245 0.500989i −0.0402416 0.0205041i
\(598\) −7.14920 + 1.13232i −0.292352 + 0.0463041i
\(599\) 17.4403i 0.712593i 0.934373 + 0.356296i \(0.115961\pi\)
−0.934373 + 0.356296i \(0.884039\pi\)
\(600\) −2.63981 0.556622i −0.107770 0.0227240i
\(601\) 1.64343i 0.0670368i 0.999438 + 0.0335184i \(0.0106712\pi\)
−0.999438 + 0.0335184i \(0.989329\pi\)
\(602\) 20.5221 + 16.4090i 0.836416 + 0.668779i
\(603\) 1.28862 2.52907i 0.0524768 0.102992i
\(604\) −8.70279 + 2.82771i −0.354111 + 0.115058i
\(605\) −17.2317 + 3.67737i −0.700569 + 0.149506i
\(606\) 0.287144 0.883738i 0.0116644 0.0358994i
\(607\) −8.01541 8.01541i −0.325335 0.325335i 0.525474 0.850810i \(-0.323888\pi\)
−0.850810 + 0.525474i \(0.823888\pi\)
\(608\) 0.367938 + 0.722118i 0.0149218 + 0.0292858i
\(609\) −1.19533 0.246344i −0.0484370 0.00998237i
\(610\) 14.5514 + 9.43299i 0.589170 + 0.381931i
\(611\) 15.9656 + 11.5997i 0.645899 + 0.469273i
\(612\) −6.79026 1.07547i −0.274480 0.0434733i
\(613\) 38.2131 + 6.05236i 1.54341 + 0.244452i 0.869340 0.494214i \(-0.164544\pi\)
0.674071 + 0.738666i \(0.264544\pi\)
\(614\) −1.84326 1.33921i −0.0743879 0.0540460i
\(615\) 1.60520 0.0854348i 0.0647281 0.00344506i
\(616\) 34.3076 + 7.07043i 1.38229 + 0.284876i
\(617\) 16.3170 + 32.0240i 0.656899 + 1.28924i 0.943559 + 0.331204i \(0.107455\pi\)
−0.286660 + 0.958032i \(0.592545\pi\)
\(618\) 2.71545 + 2.71545i 0.109231 + 0.109231i
\(619\) 0.158585 0.488075i 0.00637408 0.0196174i −0.947819 0.318809i \(-0.896717\pi\)
0.954193 + 0.299192i \(0.0967171\pi\)
\(620\) 0.663027 6.35804i 0.0266278 0.255345i
\(621\) −0.989093 + 0.321376i −0.0396909 + 0.0128964i
\(622\) 4.24130 8.32401i 0.170060 0.333762i
\(623\) 15.1199 + 12.0895i 0.605764 + 0.484355i
\(624\) 3.05616i 0.122344i
\(625\) 22.8716 + 10.0940i 0.914864 + 0.403762i
\(626\) 8.02892i 0.320900i
\(627\) −0.253519 + 0.0401534i −0.0101246 + 0.00160357i
\(628\) 7.49055 + 3.81663i 0.298905 + 0.152300i
\(629\) −11.3082 34.8031i −0.450888 1.38769i
\(630\) 17.6669 13.0259i 0.703867 0.518966i
\(631\) 14.3375 44.1262i 0.570766 1.75664i −0.0793991 0.996843i \(-0.525300\pi\)
0.650165 0.759793i \(-0.274700\pi\)
\(632\) −11.5382 + 11.5382i −0.458967 + 0.458967i
\(633\) −1.37718 2.70286i −0.0547379 0.107429i
\(634\) −6.13360 8.44217i −0.243596 0.335281i
\(635\) −1.16703 21.9269i −0.0463121 0.870142i
\(636\) −0.170896 + 0.235218i −0.00677648 + 0.00932702i
\(637\) −10.1699 + 39.9269i −0.402945 + 1.58196i
\(638\) 13.9718 + 2.21292i 0.553149 + 0.0876102i
\(639\) −5.27208 + 7.25639i −0.208560 + 0.287058i
\(640\) −11.7551 7.62027i −0.464662 0.301218i
\(641\) 0.291011 0.211432i 0.0114942 0.00835104i −0.582023 0.813172i \(-0.697739\pi\)
0.593518 + 0.804821i \(0.297739\pi\)
\(642\) −2.91605 + 1.48580i −0.115087 + 0.0586399i
\(643\) 20.7122 20.7122i 0.816810 0.816810i −0.168834 0.985644i \(-0.554000\pi\)
0.985644 + 0.168834i \(0.0540002\pi\)
\(644\) −0.470240 1.03881i −0.0185300 0.0409347i
\(645\) −3.07719 + 0.656693i −0.121164 + 0.0258573i
\(646\) −0.681183 2.09647i −0.0268008 0.0824843i
\(647\) 18.5916 36.4880i 0.730910 1.43449i −0.163176 0.986597i \(-0.552174\pi\)
0.894086 0.447895i \(-0.147826\pi\)
\(648\) 4.15587 + 26.2391i 0.163258 + 1.03077i
\(649\) 51.0068 2.00219
\(650\) −7.58871 + 35.9899i −0.297654 + 1.41164i
\(651\) −2.06019 2.25976i −0.0807454 0.0885671i
\(652\) −0.943420 + 0.149423i −0.0369472 + 0.00585186i
\(653\) 4.11669 8.07947i 0.161099 0.316174i −0.796321 0.604875i \(-0.793223\pi\)
0.957419 + 0.288701i \(0.0932232\pi\)
\(654\) −0.241164 0.742226i −0.00943026 0.0290233i
\(655\) −20.0888 + 45.2191i −0.784933 + 1.76686i
\(656\) 11.3207 + 3.67833i 0.442000 + 0.143615i
\(657\) −4.30423 4.30423i −0.167924 0.167924i
\(658\) 3.90888 10.3746i 0.152384 0.404445i
\(659\) 8.09879 + 11.1470i 0.315484 + 0.434227i 0.937082 0.349110i \(-0.113516\pi\)
−0.621598 + 0.783337i \(0.713516\pi\)
\(660\) −0.585272 + 0.474733i −0.0227817 + 0.0184790i
\(661\) 13.6373 18.7701i 0.530428 0.730071i −0.456768 0.889586i \(-0.650993\pi\)
0.987196 + 0.159515i \(0.0509929\pi\)
\(662\) −0.824240 + 5.20405i −0.0320350 + 0.202261i
\(663\) 0.862086 5.44299i 0.0334806 0.211388i
\(664\) 5.80233 + 4.21564i 0.225174 + 0.163599i
\(665\) −1.76469 0.883631i −0.0684319 0.0342658i
\(666\) −20.7750 + 15.0939i −0.805014 + 0.584877i
\(667\) −1.16365 2.28379i −0.0450566 0.0884287i
\(668\) 1.00202 1.00202i 0.0387693 0.0387693i
\(669\) −0.386341 0.125530i −0.0149368 0.00485327i
\(670\) 2.31298 1.33791i 0.0893583 0.0516880i
\(671\) 25.6428 8.33186i 0.989930 0.321648i
\(672\) 1.09761 0.301405i 0.0423413 0.0116269i
\(673\) −1.46242 9.23334i −0.0563721 0.355919i −0.999710 0.0240854i \(-0.992333\pi\)
0.943338 0.331834i \(-0.107667\pi\)
\(674\) 19.8573i 0.764876i
\(675\) −0.267992 + 5.27790i −0.0103150 + 0.203147i
\(676\) 9.48054 0.364636
\(677\) 2.25056 + 14.2095i 0.0864961 + 0.546115i 0.992441 + 0.122720i \(0.0391617\pi\)
−0.905945 + 0.423395i \(0.860838\pi\)
\(678\) 2.82954 + 1.44172i 0.108668 + 0.0553689i
\(679\) 17.2932 30.3859i 0.663652 1.16610i
\(680\) −26.7902 24.0826i −1.02736 0.923525i
\(681\) 0.186657 0.574472i 0.00715272 0.0220138i
\(682\) 25.0626 + 25.0626i 0.959697 + 0.959697i
\(683\) −4.40939 + 2.24670i −0.168721 + 0.0859675i −0.536311 0.844020i \(-0.680183\pi\)
0.367591 + 0.929988i \(0.380183\pi\)
\(684\) 0.350926 0.254963i 0.0134180 0.00974874i
\(685\) 6.60295 + 1.76350i 0.252286 + 0.0673799i
\(686\) 23.1426 0.430190i 0.883587 0.0164247i
\(687\) 0.358474 2.26332i 0.0136766 0.0863510i
\(688\) −23.0127 3.64486i −0.877352 0.138959i
\(689\) 17.8497 + 12.9686i 0.680020 + 0.494063i
\(690\) −0.470455 0.125648i −0.0179099 0.00478333i
\(691\) 11.7388 + 16.1571i 0.446565 + 0.614644i 0.971655 0.236403i \(-0.0759685\pi\)
−0.525090 + 0.851046i \(0.675969\pi\)
\(692\) 8.16116 4.15832i 0.310241 0.158076i
\(693\) 1.57492 34.0912i 0.0598262 1.29502i
\(694\) 9.85166 + 3.20100i 0.373964 + 0.121508i
\(695\) 19.4372 21.6226i 0.737296 0.820191i
\(696\) 1.33675 0.434337i 0.0506694 0.0164635i
\(697\) 19.1245 + 9.74444i 0.724393 + 0.369097i
\(698\) −5.14662 + 0.815145i −0.194803 + 0.0308537i
\(699\) 0.296978 0.0112327
\(700\) −5.78383 + 0.348506i −0.218608 + 0.0131723i
\(701\) 28.9617 1.09387 0.546935 0.837175i \(-0.315795\pi\)
0.546935 + 0.837175i \(0.315795\pi\)
\(702\) −7.67940 + 1.21630i −0.289840 + 0.0459062i
\(703\) 2.05723 + 1.04821i 0.0775901 + 0.0395341i
\(704\) −36.7810 + 11.9509i −1.38624 + 0.450416i
\(705\) 0.664739 + 1.14920i 0.0250355 + 0.0432814i
\(706\) −28.4422 9.24142i −1.07044 0.347805i
\(707\) 0.512631 11.0966i 0.0192795 0.417330i
\(708\) 0.811275 0.413365i 0.0304896 0.0155352i
\(709\) −8.64868 11.9039i −0.324808 0.447060i 0.615119 0.788434i \(-0.289108\pi\)
−0.939928 + 0.341374i \(0.889108\pi\)
\(710\) −7.88035 + 3.03234i −0.295744 + 0.113802i
\(711\) 12.8616 + 9.34451i 0.482348 + 0.350447i
\(712\) −22.0204 3.48769i −0.825250 0.130707i
\(713\) 1.00465 6.34313i 0.0376246 0.237552i
\(714\) −3.07689 + 0.342680i −0.115150 + 0.0128245i
\(715\) 36.0254 + 44.4138i 1.34727 + 1.66098i
\(716\) 1.04919 0.762284i 0.0392102 0.0284879i
\(717\) −1.57541 + 0.802711i −0.0588347 + 0.0299778i
\(718\) −15.7435 15.7435i −0.587542 0.587542i
\(719\) 3.65557 11.2507i 0.136330 0.419580i −0.859465 0.511195i \(-0.829203\pi\)
0.995794 + 0.0916151i \(0.0292029\pi\)
\(720\) −7.90214 + 17.7874i −0.294495 + 0.662899i
\(721\) 39.8993 + 22.7074i 1.48593 + 0.845669i
\(722\) −21.0340 10.7174i −0.782806 0.398859i
\(723\) 0.735693 + 4.64498i 0.0273607 + 0.172749i
\(724\) −3.28151 −0.121956
\(725\) −12.9510 + 1.38252i −0.480989 + 0.0513454i
\(726\) 1.74393i 0.0647232i
\(727\) −0.162394 1.02532i −0.00602288 0.0380270i 0.984494 0.175419i \(-0.0561280\pi\)
−0.990517 + 0.137392i \(0.956128\pi\)
\(728\) −12.5648 45.7568i −0.465684 1.69586i
\(729\) 24.0821 7.82474i 0.891928 0.289805i
\(730\) −1.19596 5.60411i −0.0442643 0.207417i
\(731\) −39.9573 12.9829i −1.47787 0.480191i
\(732\) 0.340333 0.340333i 0.0125791 0.0125791i
\(733\) 13.0537 + 25.6193i 0.482149 + 0.946270i 0.996082 + 0.0884397i \(0.0281881\pi\)
−0.513933 + 0.857830i \(0.671812\pi\)
\(734\) 14.6262 10.6265i 0.539861 0.392232i
\(735\) −1.71574 + 2.17692i −0.0632860 + 0.0802968i
\(736\) 1.93396 + 1.40511i 0.0712869 + 0.0517929i
\(737\) 0.649909 4.10336i 0.0239397 0.151149i
\(738\) 2.35621 14.8765i 0.0867333 0.547613i
\(739\) −7.86880 + 10.8305i −0.289458 + 0.398405i −0.928838 0.370486i \(-0.879191\pi\)
0.639380 + 0.768891i \(0.279191\pi\)
\(740\) 6.76924 0.360283i 0.248842 0.0132443i
\(741\) 0.204375 + 0.281298i 0.00750791 + 0.0103338i
\(742\) 4.37017 11.5990i 0.160434 0.425811i
\(743\) 5.16579 + 5.16579i 0.189515 + 0.189515i 0.795486 0.605972i \(-0.207216\pi\)
−0.605972 + 0.795486i \(0.707216\pi\)
\(744\) 3.34934 + 1.08827i 0.122793 + 0.0398978i
\(745\) −16.7338 1.74503i −0.613079 0.0639330i
\(746\) −9.10291 28.0159i −0.333281 1.02573i
\(747\) 3.17231 6.22600i 0.116069 0.227798i
\(748\) −9.93864 + 1.57413i −0.363393 + 0.0575557i
\(749\) −28.9124 + 26.3591i −1.05644 + 0.963139i
\(750\) −1.44952 + 2.00537i −0.0529291 + 0.0732258i
\(751\) −26.2567 −0.958119 −0.479060 0.877782i \(-0.659022\pi\)
−0.479060 + 0.877782i \(0.659022\pi\)
\(752\) 1.53789 + 9.70986i 0.0560811 + 0.354082i
\(753\) 0.757838 1.48734i 0.0276171 0.0542017i
\(754\) −5.92153 18.2246i −0.215650 0.663701i
\(755\) −4.84522 + 46.4628i −0.176336 + 1.69095i
\(756\) −0.505114 1.11585i −0.0183708 0.0405830i
\(757\) 25.7107 25.7107i 0.934472 0.934472i −0.0635094 0.997981i \(-0.520229\pi\)
0.997981 + 0.0635094i \(0.0202293\pi\)
\(758\) −16.8240 + 8.57224i −0.611074 + 0.311358i
\(759\) −0.612507 + 0.445013i −0.0222326 + 0.0161529i
\(760\) 2.26967 0.120800i 0.0823295 0.00438187i
\(761\) −25.6410 + 35.2918i −0.929486 + 1.27933i 0.0305733 + 0.999533i \(0.490267\pi\)
−0.960060 + 0.279796i \(0.909733\pi\)
\(762\) 2.14655 + 0.339979i 0.0777611 + 0.0123162i
\(763\) −5.12966 7.79286i −0.185706 0.282121i
\(764\) −4.28406 + 5.89651i −0.154992 + 0.213328i
\(765\) −19.0912 + 29.4502i −0.690242 + 1.06478i
\(766\) 6.86414 + 9.44768i 0.248012 + 0.341359i
\(767\) −31.3685 61.5641i −1.13265 2.22295i
\(768\) −1.24856 + 1.24856i −0.0450534 + 0.0450534i
\(769\) −0.670773 + 2.06443i −0.0241887 + 0.0744451i −0.962422 0.271558i \(-0.912461\pi\)
0.938233 + 0.346003i \(0.112461\pi\)
\(770\) 18.7012 26.1231i 0.673945 0.941411i
\(771\) 0.696624 + 2.14399i 0.0250883 + 0.0772139i
\(772\) −7.11162 3.62355i −0.255953 0.130414i
\(773\) 34.8685 5.52263i 1.25413 0.198635i 0.506205 0.862413i \(-0.331048\pi\)
0.747930 + 0.663778i \(0.231048\pi\)
\(774\) 29.4823i 1.05972i
\(775\) −28.2886 16.2711i −1.01616 0.584476i
\(776\) 40.2647i 1.44542i
\(777\) 2.02506 2.53266i 0.0726486 0.0908588i
\(778\) −13.3743 + 26.2485i −0.479492 + 0.941055i
\(779\) −1.28798 + 0.418489i −0.0461465 + 0.0149939i
\(780\) 0.932928 + 0.414457i 0.0334042 + 0.0148399i
\(781\) −4.05682 + 12.4856i −0.145165 + 0.446771i
\(782\) −4.59758 4.59758i −0.164409 0.164409i
\(783\) −1.24995 2.45316i −0.0446695 0.0876688i
\(784\) −17.6466 + 10.4819i −0.630235 + 0.374354i
\(785\) 33.3312 27.0360i 1.18964 0.964956i
\(786\) −3.96206 2.87861i −0.141322 0.102677i
\(787\) 2.62740 + 0.416140i 0.0936568 + 0.0148338i 0.203087 0.979161i \(-0.434903\pi\)
−0.109430 + 0.993994i \(0.534903\pi\)
\(788\) −2.01370 0.318938i −0.0717350 0.0113617i
\(789\) −2.37677 1.72683i −0.0846153 0.0614766i
\(790\) 5.37468 + 13.9676i 0.191223 + 0.496943i
\(791\) 37.1823 + 7.66289i 1.32205 + 0.272461i
\(792\) 17.8434 + 35.0197i 0.634038 + 1.24437i
\(793\) −25.8264 25.8264i −0.917122 0.917122i
\(794\) 0.647149 1.99172i 0.0229665 0.0706835i
\(795\) 0.743185 + 1.28482i 0.0263581 + 0.0455678i
\(796\) 2.59595 0.843474i 0.0920109 0.0298961i
\(797\) 11.6782 22.9197i 0.413662 0.811858i −0.586336 0.810068i \(-0.699430\pi\)
0.999998 0.00178998i \(-0.000569767\pi\)
\(798\) 0.121985 0.152562i 0.00431824 0.00540065i
\(799\) 17.7270i 0.627136i
\(800\) 10.1768 6.63247i 0.359805 0.234493i
\(801\) 21.7214i 0.767490i
\(802\) 35.8511 5.67825i 1.26594 0.200506i
\(803\) −7.93839 4.04481i −0.280140 0.142738i
\(804\) −0.0229172 0.0705319i −0.000808228 0.00248747i
\(805\) −5.82108 + 0.0408011i −0.205166 + 0.00143805i
\(806\) 14.8369 45.6633i 0.522607 1.60842i
\(807\) −2.47840 + 2.47840i −0.0872437 + 0.0872437i
\(808\) 5.80797 + 11.3988i 0.204324 + 0.401008i
\(809\) −9.61782 13.2378i −0.338145 0.465416i 0.605754 0.795652i \(-0.292872\pi\)
−0.943898 + 0.330236i \(0.892872\pi\)
\(810\) 23.5406 + 6.28716i 0.827132 + 0.220908i
\(811\) 7.56616 10.4139i 0.265684 0.365683i −0.655243 0.755418i \(-0.727434\pi\)
0.920927 + 0.389736i \(0.127434\pi\)
\(812\) 2.52150 1.65978i 0.0884873 0.0582469i
\(813\) −0.239224 0.0378894i −0.00838996 0.00132884i
\(814\) −22.0924 + 30.4076i −0.774338 + 1.06578i
\(815\) −1.25824 + 4.71113i −0.0440741 + 0.165024i
\(816\) 2.22096 1.61362i 0.0777492 0.0564881i
\(817\) 2.36191 1.20345i 0.0826326 0.0421034i
\(818\) −22.3094 + 22.3094i −0.780030 + 0.780030i
\(819\) −42.1160 + 19.0648i −1.47165 + 0.666177i
\(820\) −2.65810 + 2.95695i −0.0928248 + 0.103261i
\(821\) 14.3042 + 44.0237i 0.499219 + 1.53644i 0.810277 + 0.586048i \(0.199317\pi\)
−0.311057 + 0.950391i \(0.600683\pi\)
\(822\) −0.307097 + 0.602712i −0.0107112 + 0.0210220i
\(823\) −5.75031 36.3060i −0.200443 1.26555i −0.858591 0.512661i \(-0.828660\pi\)
0.658148 0.752889i \(-0.271340\pi\)
\(824\) −52.8710 −1.84185
\(825\) 1.00177 + 3.71447i 0.0348772 + 0.129321i
\(826\) −28.6849 + 26.1516i −0.998075 + 0.909930i
\(827\) −23.7832 + 3.76688i −0.827021 + 0.130987i −0.555575 0.831466i \(-0.687502\pi\)
−0.271446 + 0.962454i \(0.587502\pi\)
\(828\) 0.580855 1.13999i 0.0201861 0.0396175i
\(829\) −5.65439 17.4024i −0.196385 0.604411i −0.999958 0.00920426i \(-0.997070\pi\)
0.803573 0.595207i \(-0.202930\pi\)
\(830\) 5.69405 3.29364i 0.197643 0.114324i
\(831\) 4.25863 + 1.38371i 0.147730 + 0.0480004i
\(832\) 37.0443 + 37.0443i 1.28428 + 1.28428i
\(833\) −34.3851 + 13.6904i −1.19137 + 0.474345i
\(834\) 1.69147 + 2.32811i 0.0585708 + 0.0806157i
\(835\) −2.59802 6.75164i −0.0899081 0.233650i
\(836\) 0.373179 0.513637i 0.0129067 0.0177645i
\(837\) 1.07916 6.81356i 0.0373013 0.235511i
\(838\) 4.53758 28.6492i 0.156748 0.989669i
\(839\) −36.5281 26.5392i −1.26109 0.916235i −0.262279 0.964992i \(-0.584474\pi\)
−0.998811 + 0.0487567i \(0.984474\pi\)
\(840\) 0.477252 3.15627i 0.0164668 0.108902i
\(841\) −17.9718 + 13.0573i −0.619718 + 0.450251i
\(842\) −12.8695 25.2579i −0.443513 0.870443i
\(843\) −0.691980 + 0.691980i −0.0238331 + 0.0238331i
\(844\) 7.13605 + 2.31864i 0.245633 + 0.0798110i
\(845\) 19.6496 44.2305i 0.675967 1.52158i
\(846\) 11.8308 3.84405i 0.406750 0.132161i
\(847\) −5.52051 20.1038i −0.189687 0.690773i
\(848\) 1.71938 + 10.8557i 0.0590437 + 0.372787i
\(849\) 1.86918i 0.0641501i
\(850\) −30.1613 + 13.4875i −1.03452 + 0.462617i
\(851\) 6.81030 0.233454
\(852\) 0.0366603 + 0.231464i 0.00125596 + 0.00792982i
\(853\) −23.9389 12.1975i −0.819652 0.417634i −0.00670974 0.999977i \(-0.502136\pi\)
−0.812943 + 0.582344i \(0.802136\pi\)
\(854\) −10.1490 + 17.8329i −0.347293 + 0.610230i
\(855\) −0.462165 2.16565i −0.0158057 0.0740638i
\(856\) 13.9238 42.8530i 0.475905 1.46468i
\(857\) −11.5482 11.5482i −0.394478 0.394478i 0.481802 0.876280i \(-0.339982\pi\)
−0.876280 + 0.481802i \(0.839982\pi\)
\(858\) −5.04326 + 2.56967i −0.172174 + 0.0877271i
\(859\) −31.0027 + 22.5248i −1.05780 + 0.768536i −0.973680 0.227920i \(-0.926808\pi\)
−0.0841192 + 0.996456i \(0.526808\pi\)
\(860\) 4.23348 6.53061i 0.144360 0.222692i
\(861\) 0.210528 + 1.89030i 0.00717476 + 0.0644214i
\(862\) 7.02146 44.3318i 0.239152 1.50995i
\(863\) 5.35003 + 0.847361i 0.182117 + 0.0288445i 0.246827 0.969060i \(-0.420612\pi\)
−0.0647097 + 0.997904i \(0.520612\pi\)
\(864\) 2.07739 + 1.50931i 0.0706743 + 0.0513479i
\(865\) −2.48521 46.6937i −0.0844996 1.58763i
\(866\) 4.61613 + 6.35356i 0.156863 + 0.215903i
\(867\) 1.72840 0.880665i 0.0586997 0.0299090i
\(868\) 7.55567 + 0.349051i 0.256456 + 0.0118475i
\(869\) 22.1302 + 7.19053i 0.750715 + 0.243922i
\(870\) 0.133707 1.28217i 0.00453309 0.0434696i
\(871\) −5.35236 + 1.73909i −0.181358 + 0.0589268i
\(872\) 9.57351 + 4.87795i 0.324200 + 0.165188i
\(873\) 38.7461 6.13678i 1.31136 0.207699i
\(874\) 0.410238 0.0138765
\(875\) −10.3618 + 27.7062i −0.350292 + 0.936641i
\(876\) −0.159042 −0.00537352
\(877\) 13.5659 2.14862i 0.458087 0.0725539i 0.0768735 0.997041i \(-0.475506\pi\)
0.381214 + 0.924487i \(0.375506\pi\)
\(878\) −39.5272 20.1401i −1.33398 0.679695i
\(879\) −2.37573 + 0.771922i −0.0801315 + 0.0260363i
\(880\) −2.95479 + 28.3347i −0.0996059 + 0.955161i
\(881\) −43.0701 13.9943i −1.45107 0.471481i −0.525740 0.850645i \(-0.676212\pi\)
−0.925330 + 0.379164i \(0.876212\pi\)
\(882\) 16.5932 + 19.9795i 0.558721 + 0.672744i
\(883\) −22.8248 + 11.6298i −0.768117 + 0.391375i −0.793709 0.608297i \(-0.791853\pi\)
0.0255923 + 0.999672i \(0.491853\pi\)
\(884\) 8.01207 + 11.0277i 0.269475 + 0.370901i
\(885\) −0.247047 4.64168i −0.00830439 0.156028i
\(886\) 19.3047 + 14.0257i 0.648553 + 0.471201i
\(887\) 19.1532 + 3.03356i 0.643101 + 0.101857i 0.469463 0.882952i \(-0.344448\pi\)
0.173638 + 0.984810i \(0.444448\pi\)
\(888\) −0.584209 + 3.68855i −0.0196048 + 0.123780i
\(889\) 25.8213 2.87578i 0.866019 0.0964506i
\(890\) −11.1229 + 17.1584i −0.372842 + 0.575150i
\(891\) 30.6486 22.2675i 1.02677 0.745990i
\(892\) 0.895270 0.456163i 0.0299759 0.0152735i
\(893\) −0.790882 0.790882i −0.0264658 0.0264658i
\(894\) 0.514582 1.58372i 0.0172102 0.0529676i
\(895\) −1.38178 6.47484i −0.0461877 0.216430i
\(896\) 8.19872 14.4060i 0.273900 0.481271i
\(897\) 0.913806 + 0.465607i 0.0305111 + 0.0155462i
\(898\) 4.58507 + 28.9490i 0.153006 + 0.966041i
\(899\) 17.0019 0.567046
\(900\) −4.35818 4.82444i −0.145273 0.160815i
\(901\) 19.8190i 0.660265i
\(902\) −3.44870 21.7742i −0.114829 0.725002i
\(903\) −0.985835 3.59007i −0.0328065 0.119470i
\(904\) −41.5816 + 13.5107i −1.38298 + 0.449358i
\(905\) −6.80133 + 15.3095i −0.226084 + 0.508907i
\(906\) −4.39733 1.42878i −0.146092 0.0474681i
\(907\) −31.4892 + 31.4892i −1.04558 + 1.04558i −0.0466719 + 0.998910i \(0.514862\pi\)
−0.998910 + 0.0466719i \(0.985138\pi\)
\(908\) 0.678293 + 1.33123i 0.0225100 + 0.0441783i
\(909\) 10.0837 7.32621i 0.334454 0.242995i
\(910\) −43.0311 6.50662i −1.42647 0.215692i
\(911\) 9.95362 + 7.23173i 0.329778 + 0.239598i 0.740337 0.672236i \(-0.234666\pi\)
−0.410558 + 0.911834i \(0.634666\pi\)
\(912\) −0.0270961 + 0.171078i −0.000897243 + 0.00566497i
\(913\) 1.59993 10.1016i 0.0529500 0.334313i
\(914\) 14.7942 20.3624i 0.489347 0.673529i
\(915\) −0.882408 2.29317i −0.0291715 0.0758100i
\(916\) 3.33160 + 4.58555i 0.110079 + 0.151511i
\(917\) −54.7865 20.6420i −1.80921 0.681660i
\(918\) −4.93855 4.93855i −0.162997 0.162997i
\(919\) 30.0175 + 9.75328i 0.990186 + 0.321731i 0.758937 0.651164i \(-0.225719\pi\)
0.231249 + 0.972895i \(0.425719\pi\)
\(920\) 5.80318 3.35677i 0.191325 0.110669i
\(921\) 0.0997578 + 0.307023i 0.00328713 + 0.0101167i
\(922\) −18.1267 + 35.5756i −0.596971 + 1.17162i
\(923\) 17.5648 2.78199i 0.578152 0.0915703i
\(924\) −0.600740 0.658933i −0.0197629 0.0216773i
\(925\) 12.3492 32.3280i 0.406040 1.06294i
\(926\) 9.92586 0.326184
\(927\) 8.05811 + 50.8769i 0.264663 + 1.67102i
\(928\) −2.87311 + 5.63879i −0.0943144 + 0.185102i
\(929\) 9.92828 + 30.5561i 0.325736 + 1.00251i 0.971107 + 0.238644i \(0.0767028\pi\)
−0.645371 + 0.763869i \(0.723297\pi\)
\(930\) 2.15934 2.40212i 0.0708075 0.0787685i
\(931\) 0.923286 2.14487i 0.0302595 0.0702953i
\(932\) −0.519419 + 0.519419i −0.0170141 + 0.0170141i
\(933\) −1.17942 + 0.600944i −0.0386125 + 0.0196740i
\(934\) 14.9225 10.8418i 0.488278 0.354755i
\(935\) −13.2551 + 49.6303i −0.433489 + 1.62308i
\(936\) 31.2946 43.0733i 1.02289 1.40789i
\(937\) 26.8426 + 4.25145i 0.876910 + 0.138889i 0.578631 0.815590i \(-0.303587\pi\)
0.298280 + 0.954479i \(0.403587\pi\)
\(938\) 1.73834 + 2.64084i 0.0567587 + 0.0862265i
\(939\) −0.668669 + 0.920344i −0.0218212 + 0.0300343i
\(940\) −3.17261 0.847331i −0.103479 0.0276369i
\(941\) −18.1249 24.9468i −0.590855 0.813243i 0.403977 0.914769i \(-0.367627\pi\)
−0.994833 + 0.101526i \(0.967627\pi\)
\(942\) 1.92846 + 3.78481i 0.0628326 + 0.123316i
\(943\) −2.82455 + 2.82455i −0.0919801 + 0.0919801i
\(944\) 10.6364 32.7355i 0.346185 1.06545i
\(945\) −6.25279 + 0.0438271i −0.203403 + 0.00142569i
\(946\) 13.3348 + 41.0401i 0.433550 + 1.33433i
\(947\) 13.3370 + 6.79553i 0.433393 + 0.220825i 0.657056 0.753842i \(-0.271801\pi\)
−0.223663 + 0.974667i \(0.571801\pi\)
\(948\) 0.410259 0.0649786i 0.0133246 0.00211041i
\(949\) 12.0690i 0.391776i
\(950\) 0.743892 1.94737i 0.0241350 0.0631810i
\(951\) 1.47854i 0.0479448i
\(952\) 26.6181 33.2902i 0.862697 1.07894i
\(953\) 20.8237 40.8689i 0.674547 1.32387i −0.259161 0.965834i \(-0.583446\pi\)
0.933707 0.358038i \(-0.116554\pi\)
\(954\) 13.2269 4.29769i 0.428238 0.139143i
\(955\) 18.6303 + 32.2081i 0.602863 + 1.04223i
\(956\) 1.35146 4.15936i 0.0437093 0.134523i
\(957\) −1.41727 1.41727i −0.0458139 0.0458139i
\(958\) −15.1826 29.7975i −0.490528 0.962715i
\(959\) −1.63225 + 7.92012i −0.0527082 + 0.255754i
\(960\) 1.26569 + 3.28923i 0.0408500 + 0.106160i
\(961\) 9.38441 + 6.81817i 0.302723 + 0.219941i
\(962\) 50.2878 + 7.96481i 1.62135 + 0.256796i
\(963\) −43.3589 6.86737i −1.39722 0.221298i
\(964\) −9.41087 6.83740i −0.303104 0.220218i
\(965\) −31.6451 + 25.6683i −1.01869 + 0.826292i
\(966\) 0.116297 0.564301i 0.00374178 0.0181561i
\(967\) 7.21314 + 14.1566i 0.231959 + 0.455245i 0.977420 0.211304i \(-0.0677708\pi\)
−0.745461 + 0.666549i \(0.767771\pi\)
\(968\) 16.9775 + 16.9775i 0.545678 + 0.545678i
\(969\) −0.0965160 + 0.297046i −0.00310054 + 0.00954248i
\(970\) 33.7491 + 14.9932i 1.08362 + 0.481402i
\(971\) −42.9591 + 13.9582i −1.37862 + 0.447942i −0.902216 0.431284i \(-0.858061\pi\)
−0.476406 + 0.879225i \(0.658061\pi\)
\(972\) 0.937539 1.84002i 0.0300716 0.0590188i
\(973\) 26.8688 + 21.4836i 0.861373 + 0.688734i
\(974\) 37.5580i 1.20344i
\(975\) 3.86722 3.49347i 0.123850 0.111881i
\(976\) 18.1947i 0.582397i
\(977\) −28.7282 + 4.55010i −0.919097 + 0.145571i −0.598019 0.801482i \(-0.704045\pi\)
−0.321078 + 0.947053i \(0.604045\pi\)
\(978\) −0.430028 0.219110i −0.0137508 0.00700638i
\(979\) 9.82453 + 30.2368i 0.313993 + 0.966372i
\(980\) −0.806608 6.80831i −0.0257662 0.217484i
\(981\) 3.23486 9.95589i 0.103281 0.317867i
\(982\) 31.6472 31.6472i 1.00990 1.00990i
\(983\) −5.89407 11.5678i −0.187992 0.368954i 0.777704 0.628630i \(-0.216384\pi\)
−0.965696 + 0.259676i \(0.916384\pi\)
\(984\) −1.28752 1.77211i −0.0410445 0.0564929i
\(985\) −5.66162 + 8.73367i −0.180394 + 0.278278i
\(986\) 10.1176 13.9257i 0.322210 0.443484i
\(987\) −1.31210 + 0.863690i −0.0417645 + 0.0274915i
\(988\) −0.849450 0.134540i −0.0270246 0.00428028i
\(989\) 4.59583 6.32561i 0.146139 0.201143i
\(990\) 35.9970 1.91589i 1.14406 0.0608910i
\(991\) −38.6787 + 28.1017i −1.22867 + 0.892681i −0.996790 0.0800630i \(-0.974488\pi\)
−0.231881 + 0.972744i \(0.574488\pi\)
\(992\) −14.1285 + 7.19881i −0.448579 + 0.228563i
\(993\) 0.527888 0.527888i 0.0167520 0.0167520i
\(994\) −4.12003 9.10156i −0.130679 0.288684i
\(995\) 1.44528 13.8593i 0.0458183 0.439371i
\(996\) −0.0564171 0.173634i −0.00178764 0.00550181i
\(997\) −12.3144 + 24.1684i −0.390002 + 0.765422i −0.999628 0.0272669i \(-0.991320\pi\)
0.609626 + 0.792689i \(0.291320\pi\)
\(998\) 0.872472 + 5.50857i 0.0276176 + 0.174371i
\(999\) 7.31537 0.231448
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 175.2.s.a.13.6 yes 144
5.2 odd 4 875.2.s.b.832.6 144
5.3 odd 4 875.2.s.a.832.13 144
5.4 even 2 875.2.s.c.293.13 144
7.6 odd 2 inner 175.2.s.a.13.5 144
25.2 odd 20 inner 175.2.s.a.27.5 yes 144
25.11 even 5 875.2.s.b.468.5 144
25.14 even 10 875.2.s.a.468.14 144
25.23 odd 20 875.2.s.c.657.14 144
35.13 even 4 875.2.s.a.832.14 144
35.27 even 4 875.2.s.b.832.5 144
35.34 odd 2 875.2.s.c.293.14 144
175.27 even 20 inner 175.2.s.a.27.6 yes 144
175.48 even 20 875.2.s.c.657.13 144
175.111 odd 10 875.2.s.b.468.6 144
175.139 odd 10 875.2.s.a.468.13 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
175.2.s.a.13.5 144 7.6 odd 2 inner
175.2.s.a.13.6 yes 144 1.1 even 1 trivial
175.2.s.a.27.5 yes 144 25.2 odd 20 inner
175.2.s.a.27.6 yes 144 175.27 even 20 inner
875.2.s.a.468.13 144 175.139 odd 10
875.2.s.a.468.14 144 25.14 even 10
875.2.s.a.832.13 144 5.3 odd 4
875.2.s.a.832.14 144 35.13 even 4
875.2.s.b.468.5 144 25.11 even 5
875.2.s.b.468.6 144 175.111 odd 10
875.2.s.b.832.5 144 35.27 even 4
875.2.s.b.832.6 144 5.2 odd 4
875.2.s.c.293.13 144 5.4 even 2
875.2.s.c.293.14 144 35.34 odd 2
875.2.s.c.657.13 144 175.48 even 20
875.2.s.c.657.14 144 25.23 odd 20