Properties

Label 624.2.ch.a.19.52
Level $624$
Weight $2$
Character 624.19
Analytic conductor $4.983$
Analytic rank $0$
Dimension $224$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [624,2,Mod(19,624)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(624, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 9, 0, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("624.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 624.ch (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.98266508613\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(56\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 19.52
Character \(\chi\) \(=\) 624.19
Dual form 624.2.ch.a.427.52

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.37030 + 0.349682i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.75545 + 0.958338i) q^{4} +0.533822i q^{5} +(-0.0168930 - 1.41411i) q^{6} +(-0.607709 + 2.26800i) q^{7} +(2.07037 + 1.92706i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(1.37030 + 0.349682i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(1.75545 + 0.958338i) q^{4} +0.533822i q^{5} +(-0.0168930 - 1.41411i) q^{6} +(-0.607709 + 2.26800i) q^{7} +(2.07037 + 1.92706i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.186668 + 0.731496i) q^{10} +(3.37391 + 1.94793i) q^{11} +(0.471341 - 1.94367i) q^{12} +(-2.94803 + 2.07584i) q^{13} +(-1.62582 + 2.89534i) q^{14} +(0.515632 - 0.138163i) q^{15} +(2.16318 + 3.36462i) q^{16} +(3.15055 - 1.81897i) q^{17} +(-1.36156 + 0.382317i) q^{18} +(1.70786 - 0.986032i) q^{19} +(-0.511582 + 0.937095i) q^{20} +2.34801 q^{21} +(3.94211 + 3.84904i) q^{22} +(-1.31196 - 0.757460i) q^{23} +(1.32554 - 2.49859i) q^{24} +4.71503 q^{25} +(-4.76557 + 1.81366i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-3.24031 + 3.39896i) q^{28} +(-1.79742 + 0.481619i) q^{29} +(0.754884 - 0.00901784i) q^{30} +(-6.22485 - 6.22485i) q^{31} +(1.78765 + 5.36696i) q^{32} +(1.00832 - 3.76310i) q^{33} +(4.95326 - 1.39085i) q^{34} +(-1.21071 - 0.324408i) q^{35} +(-1.99943 + 0.0477771i) q^{36} +(5.28586 - 9.15537i) q^{37} +(2.68508 - 0.753953i) q^{38} +(2.76812 + 2.31031i) q^{39} +(-1.02871 + 1.10521i) q^{40} +(-2.24090 + 0.600446i) q^{41} +(3.21747 + 0.821055i) q^{42} +(0.913123 + 0.244670i) q^{43} +(4.05593 + 6.65282i) q^{44} +(-0.266911 - 0.462303i) q^{45} +(-1.53291 - 1.49672i) q^{46} +(-8.16284 + 8.16284i) q^{47} +(2.69010 - 2.96029i) q^{48} +(1.28766 + 0.743432i) q^{49} +(6.46101 + 1.64876i) q^{50} +(-2.57241 - 2.57241i) q^{51} +(-7.16446 + 0.818823i) q^{52} +(6.50758 - 6.50758i) q^{53} +(0.721686 + 1.21621i) q^{54} +(-1.03985 + 1.80106i) q^{55} +(-5.62875 + 3.52452i) q^{56} +(-1.39446 - 1.39446i) q^{57} +(-2.63142 + 0.0314350i) q^{58} +(-5.15044 + 2.97361i) q^{59} +(1.03757 + 0.251612i) q^{60} +(2.62650 - 9.80222i) q^{61} +(-6.35319 - 10.7066i) q^{62} +(-0.607709 - 2.26800i) q^{63} +(0.572890 + 7.97946i) q^{64} +(-1.10813 - 1.57372i) q^{65} +(2.69759 - 4.80399i) q^{66} +(2.24423 + 1.29571i) q^{67} +(7.27380 - 0.173810i) q^{68} +(-0.392090 + 1.46330i) q^{69} +(-1.54559 - 0.867900i) q^{70} +(-15.2954 - 4.09840i) q^{71} +(-2.75653 - 0.633695i) q^{72} +(-3.70208 + 3.70208i) q^{73} +(10.4447 - 10.6972i) q^{74} +(-1.22034 - 4.55437i) q^{75} +(3.94300 - 0.0942196i) q^{76} +(-6.46825 + 6.46825i) q^{77} +(2.98528 + 4.13378i) q^{78} +0.388573i q^{79} +(-1.79611 + 1.15475i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-3.28067 + 0.0391908i) q^{82} +12.6374i q^{83} +(4.12180 + 2.25018i) q^{84} +(0.971006 + 1.68183i) q^{85} +(1.16570 + 0.654574i) q^{86} +(0.930416 + 1.61153i) q^{87} +(3.23148 + 10.5346i) q^{88} +(-3.89942 - 14.5528i) q^{89} +(-0.204089 - 0.726828i) q^{90} +(-2.91647 - 7.94764i) q^{91} +(-1.57717 - 2.58698i) q^{92} +(-4.40163 + 7.62385i) q^{93} +(-14.0399 + 8.33114i) q^{94} +(0.526366 + 0.911692i) q^{95} +(4.72141 - 3.11581i) q^{96} +(2.20489 + 0.590799i) q^{97} +(1.50452 + 1.46900i) q^{98} -3.89585 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 224 q+O(q^{10}) \) Copy content Toggle raw display \( 224 q - 8 q^{10} - 32 q^{14} - 48 q^{16} - 12 q^{20} + 8 q^{22} + 12 q^{24} - 224 q^{25} - 16 q^{26} - 52 q^{28} + 40 q^{32} + 64 q^{34} - 40 q^{38} - 40 q^{40} - 16 q^{43} + 24 q^{44} + 16 q^{46} - 16 q^{50} - 16 q^{52} - 32 q^{55} - 20 q^{56} - 32 q^{58} + 96 q^{59} - 64 q^{60} - 24 q^{68} - 48 q^{70} + 64 q^{71} - 16 q^{73} + 96 q^{74} - 16 q^{75} + 76 q^{76} - 24 q^{78} + 100 q^{80} + 112 q^{81} + 48 q^{82} - 64 q^{86} - 60 q^{88} - 16 q^{89} + 40 q^{91} - 48 q^{92} + 64 q^{94} - 56 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).

\(n\) \(79\) \(145\) \(209\) \(469\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{12}\right)\) \(1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37030 + 0.349682i 0.968949 + 0.247262i
\(3\) −0.258819 0.965926i −0.149429 0.557678i
\(4\) 1.75545 + 0.958338i 0.877723 + 0.479169i
\(5\) 0.533822i 0.238732i 0.992850 + 0.119366i \(0.0380863\pi\)
−0.992850 + 0.119366i \(0.961914\pi\)
\(6\) −0.0168930 1.41411i −0.00689653 0.577309i
\(7\) −0.607709 + 2.26800i −0.229692 + 0.857224i 0.750778 + 0.660555i \(0.229679\pi\)
−0.980470 + 0.196669i \(0.936988\pi\)
\(8\) 2.07037 + 1.92706i 0.731987 + 0.681318i
\(9\) −0.866025 + 0.500000i −0.288675 + 0.166667i
\(10\) −0.186668 + 0.731496i −0.0590296 + 0.231319i
\(11\) 3.37391 + 1.94793i 1.01727 + 0.587322i 0.913312 0.407260i \(-0.133516\pi\)
0.103959 + 0.994582i \(0.466849\pi\)
\(12\) 0.471341 1.94367i 0.136064 0.561088i
\(13\) −2.94803 + 2.07584i −0.817636 + 0.575736i
\(14\) −1.62582 + 2.89534i −0.434519 + 0.773811i
\(15\) 0.515632 0.138163i 0.133136 0.0356736i
\(16\) 2.16318 + 3.36462i 0.540794 + 0.841155i
\(17\) 3.15055 1.81897i 0.764120 0.441165i −0.0666528 0.997776i \(-0.521232\pi\)
0.830773 + 0.556611i \(0.187899\pi\)
\(18\) −1.36156 + 0.382317i −0.320922 + 0.0901129i
\(19\) 1.70786 0.986032i 0.391810 0.226211i −0.291134 0.956682i \(-0.594033\pi\)
0.682944 + 0.730471i \(0.260699\pi\)
\(20\) −0.511582 + 0.937095i −0.114393 + 0.209541i
\(21\) 2.34801 0.512377
\(22\) 3.94211 + 3.84904i 0.840460 + 0.820617i
\(23\) −1.31196 0.757460i −0.273562 0.157941i 0.356943 0.934126i \(-0.383819\pi\)
−0.630505 + 0.776185i \(0.717152\pi\)
\(24\) 1.32554 2.49859i 0.270575 0.510022i
\(25\) 4.71503 0.943007
\(26\) −4.76557 + 1.81366i −0.934605 + 0.355688i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −3.24031 + 3.39896i −0.612361 + 0.642343i
\(29\) −1.79742 + 0.481619i −0.333773 + 0.0894343i −0.421814 0.906683i \(-0.638606\pi\)
0.0880401 + 0.996117i \(0.471940\pi\)
\(30\) 0.754884 0.00901784i 0.137822 0.00164643i
\(31\) −6.22485 6.22485i −1.11802 1.11802i −0.992032 0.125983i \(-0.959792\pi\)
−0.125983 0.992032i \(-0.540208\pi\)
\(32\) 1.78765 + 5.36696i 0.316015 + 0.948754i
\(33\) 1.00832 3.76310i 0.175526 0.655072i
\(34\) 4.95326 1.39085i 0.849477 0.238528i
\(35\) −1.21071 0.324408i −0.204647 0.0548350i
\(36\) −1.99943 + 0.0477771i −0.333238 + 0.00796286i
\(37\) 5.28586 9.15537i 0.868990 1.50513i 0.00595919 0.999982i \(-0.498103\pi\)
0.863030 0.505152i \(-0.168564\pi\)
\(38\) 2.68508 0.753953i 0.435577 0.122307i
\(39\) 2.76812 + 2.31031i 0.443254 + 0.369945i
\(40\) −1.02871 + 1.10521i −0.162653 + 0.174749i
\(41\) −2.24090 + 0.600446i −0.349969 + 0.0937740i −0.429521 0.903057i \(-0.641318\pi\)
0.0795521 + 0.996831i \(0.474651\pi\)
\(42\) 3.21747 + 0.821055i 0.496467 + 0.126692i
\(43\) 0.913123 + 0.244670i 0.139250 + 0.0373119i 0.327771 0.944757i \(-0.393703\pi\)
−0.188521 + 0.982069i \(0.560369\pi\)
\(44\) 4.05593 + 6.65282i 0.611455 + 1.00295i
\(45\) −0.266911 0.462303i −0.0397887 0.0689161i
\(46\) −1.53291 1.49672i −0.226015 0.220679i
\(47\) −8.16284 + 8.16284i −1.19067 + 1.19067i −0.213793 + 0.976879i \(0.568582\pi\)
−0.976879 + 0.213793i \(0.931418\pi\)
\(48\) 2.69010 2.96029i 0.388283 0.427282i
\(49\) 1.28766 + 0.743432i 0.183952 + 0.106205i
\(50\) 6.46101 + 1.64876i 0.913725 + 0.233170i
\(51\) −2.57241 2.57241i −0.360210 0.360210i
\(52\) −7.16446 + 0.818823i −0.993532 + 0.113550i
\(53\) 6.50758 6.50758i 0.893885 0.893885i −0.101001 0.994886i \(-0.532205\pi\)
0.994886 + 0.101001i \(0.0322046\pi\)
\(54\) 0.721686 + 1.21621i 0.0982090 + 0.165505i
\(55\) −1.03985 + 1.80106i −0.140213 + 0.242856i
\(56\) −5.62875 + 3.52452i −0.752174 + 0.470983i
\(57\) −1.39446 1.39446i −0.184701 0.184701i
\(58\) −2.63142 + 0.0314350i −0.345523 + 0.00412762i
\(59\) −5.15044 + 2.97361i −0.670530 + 0.387131i −0.796277 0.604932i \(-0.793200\pi\)
0.125748 + 0.992062i \(0.459867\pi\)
\(60\) 1.03757 + 0.251612i 0.133950 + 0.0324830i
\(61\) 2.62650 9.80222i 0.336289 1.25505i −0.566177 0.824284i \(-0.691578\pi\)
0.902465 0.430762i \(-0.141755\pi\)
\(62\) −6.35319 10.7066i −0.806856 1.35974i
\(63\) −0.607709 2.26800i −0.0765641 0.285741i
\(64\) 0.572890 + 7.97946i 0.0716112 + 0.997433i
\(65\) −1.10813 1.57372i −0.137447 0.195196i
\(66\) 2.69759 4.80399i 0.332050 0.591330i
\(67\) 2.24423 + 1.29571i 0.274176 + 0.158296i 0.630784 0.775958i \(-0.282733\pi\)
−0.356608 + 0.934254i \(0.616067\pi\)
\(68\) 7.27380 0.173810i 0.882078 0.0210776i
\(69\) −0.392090 + 1.46330i −0.0472021 + 0.176161i
\(70\) −1.54559 0.867900i −0.184734 0.103734i
\(71\) −15.2954 4.09840i −1.81524 0.486391i −0.819055 0.573714i \(-0.805502\pi\)
−0.996180 + 0.0873236i \(0.972169\pi\)
\(72\) −2.75653 0.633695i −0.324860 0.0746817i
\(73\) −3.70208 + 3.70208i −0.433296 + 0.433296i −0.889748 0.456452i \(-0.849120\pi\)
0.456452 + 0.889748i \(0.349120\pi\)
\(74\) 10.4447 10.6972i 1.21417 1.24353i
\(75\) −1.22034 4.55437i −0.140913 0.525894i
\(76\) 3.94300 0.0942196i 0.452294 0.0108077i
\(77\) −6.46825 + 6.46825i −0.737125 + 0.737125i
\(78\) 2.98528 + 4.13378i 0.338016 + 0.468058i
\(79\) 0.388573i 0.0437178i 0.999761 + 0.0218589i \(0.00695846\pi\)
−0.999761 + 0.0218589i \(0.993042\pi\)
\(80\) −1.79611 + 1.15475i −0.200811 + 0.129105i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) −3.28067 + 0.0391908i −0.362289 + 0.00432790i
\(83\) 12.6374i 1.38714i 0.720391 + 0.693568i \(0.243962\pi\)
−0.720391 + 0.693568i \(0.756038\pi\)
\(84\) 4.12180 + 2.25018i 0.449725 + 0.245515i
\(85\) 0.971006 + 1.68183i 0.105320 + 0.182420i
\(86\) 1.16570 + 0.654574i 0.125700 + 0.0705846i
\(87\) 0.930416 + 1.61153i 0.0997510 + 0.172774i
\(88\) 3.23148 + 10.5346i 0.344477 + 1.12300i
\(89\) −3.89942 14.5528i −0.413338 1.54260i −0.788141 0.615494i \(-0.788956\pi\)
0.374803 0.927104i \(-0.377710\pi\)
\(90\) −0.204089 0.726828i −0.0215129 0.0766144i
\(91\) −2.91647 7.94764i −0.305730 0.833139i
\(92\) −1.57717 2.58698i −0.164431 0.269711i
\(93\) −4.40163 + 7.62385i −0.456428 + 0.790556i
\(94\) −14.0399 + 8.33114i −1.44811 + 0.859291i
\(95\) 0.526366 + 0.911692i 0.0540040 + 0.0935377i
\(96\) 4.72141 3.11581i 0.481877 0.318006i
\(97\) 2.20489 + 0.590799i 0.223873 + 0.0599865i 0.369012 0.929425i \(-0.379696\pi\)
−0.145139 + 0.989411i \(0.546363\pi\)
\(98\) 1.50452 + 1.46900i 0.151979 + 0.148391i
\(99\) −3.89585 −0.391548
\(100\) 8.27698 + 4.51860i 0.827698 + 0.451860i
\(101\) −0.854187 + 0.228879i −0.0849948 + 0.0227743i −0.301066 0.953603i \(-0.597342\pi\)
0.216071 + 0.976378i \(0.430676\pi\)
\(102\) −2.62545 4.42450i −0.259958 0.438091i
\(103\) 12.8601i 1.26714i −0.773685 0.633571i \(-0.781589\pi\)
0.773685 0.633571i \(-0.218411\pi\)
\(104\) −10.1038 1.38325i −0.990758 0.135639i
\(105\) 1.25342i 0.122321i
\(106\) 11.1929 6.64176i 1.08715 0.645104i
\(107\) 15.6617 4.19653i 1.51407 0.405694i 0.596285 0.802773i \(-0.296643\pi\)
0.917785 + 0.397079i \(0.129976\pi\)
\(108\) 0.563640 + 1.91893i 0.0542362 + 0.184650i
\(109\) 2.46001 0.235626 0.117813 0.993036i \(-0.462412\pi\)
0.117813 + 0.993036i \(0.462412\pi\)
\(110\) −2.05470 + 2.10438i −0.195908 + 0.200645i
\(111\) −10.2115 2.73616i −0.969232 0.259705i
\(112\) −8.94554 + 2.86137i −0.845274 + 0.270374i
\(113\) −5.49465 9.51702i −0.516893 0.895286i −0.999808 0.0196179i \(-0.993755\pi\)
0.482914 0.875668i \(-0.339578\pi\)
\(114\) −1.42321 2.39845i −0.133296 0.224635i
\(115\) 0.404349 0.700353i 0.0377057 0.0653082i
\(116\) −3.61683 0.877086i −0.335815 0.0814354i
\(117\) 1.51514 3.27175i 0.140075 0.302473i
\(118\) −8.09746 + 2.27372i −0.745432 + 0.209313i
\(119\) 2.21081 + 8.25085i 0.202664 + 0.756354i
\(120\) 1.33380 + 0.707604i 0.121759 + 0.0645952i
\(121\) 2.08883 + 3.61795i 0.189893 + 0.328905i
\(122\) 7.02675 12.5135i 0.636172 1.13292i
\(123\) 1.15997 + 2.00913i 0.104591 + 0.181157i
\(124\) −4.96187 16.8929i −0.445589 1.51703i
\(125\) 5.18610i 0.463859i
\(126\) −0.0396648 3.32035i −0.00353362 0.295800i
\(127\) −1.21311 + 2.10117i −0.107646 + 0.186449i −0.914816 0.403870i \(-0.867665\pi\)
0.807170 + 0.590319i \(0.200998\pi\)
\(128\) −2.00524 + 11.1346i −0.177240 + 0.984168i
\(129\) 0.945334i 0.0832320i
\(130\) −0.968171 2.54397i −0.0849142 0.223121i
\(131\) −11.1029 + 11.1029i −0.970065 + 0.970065i −0.999565 0.0294997i \(-0.990609\pi\)
0.0294997 + 0.999565i \(0.490609\pi\)
\(132\) 5.37638 5.63961i 0.467954 0.490865i
\(133\) 1.19844 + 4.47264i 0.103918 + 0.387827i
\(134\) 2.62218 + 2.56027i 0.226522 + 0.221174i
\(135\) −0.377469 + 0.377469i −0.0324874 + 0.0324874i
\(136\) 10.0281 + 2.30535i 0.859900 + 0.197682i
\(137\) −1.40135 0.375491i −0.119726 0.0320804i 0.198459 0.980109i \(-0.436406\pi\)
−0.318184 + 0.948029i \(0.603073\pi\)
\(138\) −1.04897 + 1.86805i −0.0892944 + 0.159019i
\(139\) 3.57867 13.3558i 0.303539 1.13282i −0.630657 0.776062i \(-0.717214\pi\)
0.934196 0.356761i \(-0.116119\pi\)
\(140\) −1.81444 1.72975i −0.153348 0.146191i
\(141\) 9.99739 + 5.77200i 0.841932 + 0.486090i
\(142\) −19.5262 10.9646i −1.63860 0.920127i
\(143\) −13.9900 + 1.26117i −1.16990 + 0.105464i
\(144\) −3.55567 1.83226i −0.296306 0.152688i
\(145\) −0.257099 0.959505i −0.0213509 0.0796825i
\(146\) −6.36751 + 3.77841i −0.526979 + 0.312704i
\(147\) 0.384829 1.43620i 0.0317402 0.118456i
\(148\) 18.0530 11.0061i 1.48395 0.904697i
\(149\) −3.62712 + 2.09412i −0.297145 + 0.171557i −0.641160 0.767407i \(-0.721546\pi\)
0.344014 + 0.938964i \(0.388213\pi\)
\(150\) −0.0796510 6.66759i −0.00650347 0.544406i
\(151\) −12.2722 12.2722i −0.998698 0.998698i 0.00130076 0.999999i \(-0.499586\pi\)
−0.999999 + 0.00130076i \(0.999586\pi\)
\(152\) 5.43605 + 1.24969i 0.440922 + 0.101363i
\(153\) −1.81897 + 3.15055i −0.147055 + 0.254707i
\(154\) −11.1253 + 6.60161i −0.896500 + 0.531973i
\(155\) 3.32296 3.32296i 0.266907 0.266907i
\(156\) 2.64522 + 6.70841i 0.211787 + 0.537103i
\(157\) −3.38489 3.38489i −0.270144 0.270144i 0.559014 0.829158i \(-0.311180\pi\)
−0.829158 + 0.559014i \(0.811180\pi\)
\(158\) −0.135877 + 0.532461i −0.0108098 + 0.0423603i
\(159\) −7.97013 4.60156i −0.632072 0.364927i
\(160\) −2.86500 + 0.954288i −0.226498 + 0.0754431i
\(161\) 2.51521 2.51521i 0.198226 0.198226i
\(162\) 0.987984 1.01187i 0.0776233 0.0795003i
\(163\) 6.49279 + 11.2458i 0.508554 + 0.880842i 0.999951 + 0.00990589i \(0.00315320\pi\)
−0.491397 + 0.870936i \(0.663513\pi\)
\(164\) −4.50920 1.09349i −0.352109 0.0853869i
\(165\) 2.00883 + 0.538264i 0.156387 + 0.0419038i
\(166\) −4.41908 + 17.3171i −0.342987 + 1.34406i
\(167\) 10.1056 2.70778i 0.781994 0.209535i 0.154330 0.988019i \(-0.450678\pi\)
0.627663 + 0.778485i \(0.284011\pi\)
\(168\) 4.86125 + 4.52475i 0.375054 + 0.349092i
\(169\) 4.38174 12.2393i 0.337057 0.941484i
\(170\) 0.742464 + 2.64416i 0.0569444 + 0.202798i
\(171\) −0.986032 + 1.70786i −0.0754038 + 0.130603i
\(172\) 1.36846 + 1.30459i 0.104344 + 0.0994737i
\(173\) −0.699941 0.187549i −0.0532155 0.0142591i 0.232113 0.972689i \(-0.425436\pi\)
−0.285329 + 0.958430i \(0.592103\pi\)
\(174\) 0.711427 + 2.53363i 0.0539331 + 0.192074i
\(175\) −2.86537 + 10.6937i −0.216601 + 0.808368i
\(176\) 0.744318 + 15.5656i 0.0561051 + 1.17330i
\(177\) 4.20531 + 4.20531i 0.316091 + 0.316091i
\(178\) −0.254513 21.3053i −0.0190766 1.59690i
\(179\) −6.18050 + 1.65606i −0.461952 + 0.123780i −0.482286 0.876014i \(-0.660194\pi\)
0.0203345 + 0.999793i \(0.493527\pi\)
\(180\) −0.0255045 1.06734i −0.00190099 0.0795548i
\(181\) 9.45013 + 9.45013i 0.702423 + 0.702423i 0.964930 0.262507i \(-0.0845494\pi\)
−0.262507 + 0.964930i \(0.584549\pi\)
\(182\) −1.21730 11.9105i −0.0902323 0.882864i
\(183\) −10.1480 −0.750162
\(184\) −1.25658 4.09645i −0.0926360 0.301994i
\(185\) 4.88734 + 2.82171i 0.359324 + 0.207456i
\(186\) −8.69748 + 8.90779i −0.637730 + 0.653151i
\(187\) 14.1729 1.03642
\(188\) −22.1522 + 6.50665i −1.61561 + 0.474546i
\(189\) −2.03343 + 1.17400i −0.147911 + 0.0853962i
\(190\) 0.402477 + 1.43335i 0.0291987 + 0.103986i
\(191\) 8.42783 4.86581i 0.609816 0.352078i −0.163077 0.986613i \(-0.552142\pi\)
0.772894 + 0.634536i \(0.218809\pi\)
\(192\) 7.55929 2.61861i 0.545545 0.188982i
\(193\) 8.95490 2.39946i 0.644588 0.172717i 0.0783073 0.996929i \(-0.475048\pi\)
0.566281 + 0.824212i \(0.308382\pi\)
\(194\) 2.81477 + 1.58058i 0.202089 + 0.113479i
\(195\) −1.23329 + 1.47768i −0.0883180 + 0.105819i
\(196\) 1.54796 + 2.53907i 0.110569 + 0.181362i
\(197\) 21.8453 + 12.6124i 1.55641 + 0.898595i 0.997596 + 0.0693043i \(0.0220779\pi\)
0.558817 + 0.829291i \(0.311255\pi\)
\(198\) −5.33848 1.36231i −0.379390 0.0968150i
\(199\) 3.43544 1.98345i 0.243532 0.140603i −0.373267 0.927724i \(-0.621762\pi\)
0.616799 + 0.787121i \(0.288429\pi\)
\(200\) 9.76188 + 9.08615i 0.690269 + 0.642488i
\(201\) 0.670707 2.50311i 0.0473080 0.176556i
\(202\) −1.25053 + 0.0149388i −0.0879868 + 0.00105109i
\(203\) 4.36924i 0.306661i
\(204\) −2.05049 6.98097i −0.143563 0.488766i
\(205\) −0.320531 1.19624i −0.0223869 0.0835490i
\(206\) 4.49694 17.6222i 0.313317 1.22780i
\(207\) 1.51492 0.105294
\(208\) −13.3615 5.42858i −0.926455 0.376404i
\(209\) 7.68287 0.531435
\(210\) −0.438297 + 1.71756i −0.0302454 + 0.118523i
\(211\) −6.12337 22.8527i −0.421550 1.57325i −0.771343 0.636420i \(-0.780415\pi\)
0.349792 0.936827i \(-0.386252\pi\)
\(212\) 17.6602 5.18724i 1.21291 0.356261i
\(213\) 15.8350i 1.08500i
\(214\) 22.9286 0.273905i 1.56737 0.0187238i
\(215\) −0.130610 + 0.487445i −0.00890756 + 0.0332435i
\(216\) 0.101339 + 2.82661i 0.00689522 + 0.192327i
\(217\) 17.9008 10.3351i 1.21519 0.701589i
\(218\) 3.37095 + 0.860219i 0.228309 + 0.0582614i
\(219\) 4.53410 + 2.61777i 0.306386 + 0.176892i
\(220\) −3.55142 + 2.16515i −0.239437 + 0.145974i
\(221\) −5.51201 + 11.9024i −0.370778 + 0.800644i
\(222\) −13.0360 7.32014i −0.874921 0.491295i
\(223\) −6.20919 + 1.66375i −0.415798 + 0.111413i −0.460652 0.887581i \(-0.652384\pi\)
0.0448539 + 0.998994i \(0.485718\pi\)
\(224\) −13.2586 + 0.792844i −0.885881 + 0.0529741i
\(225\) −4.08334 + 2.35752i −0.272223 + 0.157168i
\(226\) −4.20139 14.9625i −0.279473 0.995294i
\(227\) −6.82677 + 3.94144i −0.453109 + 0.261602i −0.709142 0.705065i \(-0.750918\pi\)
0.256034 + 0.966668i \(0.417584\pi\)
\(228\) −1.11153 3.78426i −0.0736131 0.250619i
\(229\) 13.8327 0.914090 0.457045 0.889444i \(-0.348908\pi\)
0.457045 + 0.889444i \(0.348908\pi\)
\(230\) 0.798980 0.818300i 0.0526832 0.0539571i
\(231\) 7.92195 + 4.57374i 0.521226 + 0.300930i
\(232\) −4.64945 2.46661i −0.305251 0.161941i
\(233\) −14.2035 −0.930504 −0.465252 0.885178i \(-0.654036\pi\)
−0.465252 + 0.885178i \(0.654036\pi\)
\(234\) 3.22027 3.95346i 0.210516 0.258446i
\(235\) −4.35750 4.35750i −0.284252 0.284252i
\(236\) −11.8910 + 0.284141i −0.774040 + 0.0184960i
\(237\) 0.375332 0.100570i 0.0243805 0.00653272i
\(238\) 0.144298 + 12.0792i 0.00935347 + 0.782980i
\(239\) 15.5667 + 15.5667i 1.00693 + 1.00693i 0.999976 + 0.00694960i \(0.00221214\pi\)
0.00694960 + 0.999976i \(0.497788\pi\)
\(240\) 1.58027 + 1.43604i 0.102006 + 0.0926957i
\(241\) 7.84894 29.2926i 0.505594 1.88690i 0.0456479 0.998958i \(-0.485465\pi\)
0.459947 0.887947i \(-0.347869\pi\)
\(242\) 1.59719 + 5.68810i 0.102671 + 0.365645i
\(243\) −0.965926 0.258819i −0.0619642 0.0166032i
\(244\) 14.0045 14.6902i 0.896547 0.940443i
\(245\) −0.396861 + 0.687383i −0.0253545 + 0.0439153i
\(246\) 0.886954 + 3.15874i 0.0565501 + 0.201394i
\(247\) −2.98796 + 6.45210i −0.190120 + 0.410537i
\(248\) −0.892110 24.8834i −0.0566490 1.58010i
\(249\) 12.2068 3.27080i 0.773575 0.207279i
\(250\) −1.81349 + 7.10651i −0.114695 + 0.449455i
\(251\) 4.72846 + 1.26699i 0.298458 + 0.0799715i 0.404940 0.914343i \(-0.367292\pi\)
−0.106483 + 0.994315i \(0.533959\pi\)
\(252\) 1.10671 4.56374i 0.0697163 0.287489i
\(253\) −2.95095 5.11120i −0.185525 0.321338i
\(254\) −2.39707 + 2.45503i −0.150406 + 0.154043i
\(255\) 1.37321 1.37321i 0.0859938 0.0859938i
\(256\) −6.64135 + 14.5565i −0.415084 + 0.909783i
\(257\) −3.28896 1.89888i −0.205160 0.118449i 0.393900 0.919153i \(-0.371126\pi\)
−0.599060 + 0.800704i \(0.704459\pi\)
\(258\) 0.330566 1.29539i 0.0205802 0.0806475i
\(259\) 17.5521 + 17.5521i 1.09064 + 1.09064i
\(260\) −0.437106 3.82455i −0.0271082 0.237188i
\(261\) 1.31581 1.31581i 0.0814464 0.0814464i
\(262\) −19.0968 + 11.3318i −1.17980 + 0.700082i
\(263\) −5.84694 + 10.1272i −0.360538 + 0.624470i −0.988049 0.154137i \(-0.950740\pi\)
0.627511 + 0.778607i \(0.284074\pi\)
\(264\) 9.33932 5.84793i 0.574795 0.359915i
\(265\) 3.47389 + 3.47389i 0.213399 + 0.213399i
\(266\) 0.0782216 + 6.54794i 0.00479607 + 0.401480i
\(267\) −13.0477 + 7.53311i −0.798508 + 0.461019i
\(268\) 2.69790 + 4.42527i 0.164800 + 0.270317i
\(269\) −3.97866 + 14.8486i −0.242583 + 0.905334i 0.731999 + 0.681305i \(0.238587\pi\)
−0.974583 + 0.224028i \(0.928079\pi\)
\(270\) −0.649240 + 0.385252i −0.0395115 + 0.0234457i
\(271\) 2.10230 + 7.84587i 0.127705 + 0.476603i 0.999922 0.0125175i \(-0.00398455\pi\)
−0.872216 + 0.489120i \(0.837318\pi\)
\(272\) 12.9353 + 6.66565i 0.784320 + 0.404164i
\(273\) −6.92199 + 4.87410i −0.418938 + 0.294994i
\(274\) −1.78897 1.00456i −0.108076 0.0606879i
\(275\) 15.9081 + 9.18453i 0.959293 + 0.553848i
\(276\) −2.09063 + 2.19299i −0.125841 + 0.132002i
\(277\) −4.91337 + 18.3370i −0.295216 + 1.10176i 0.645830 + 0.763481i \(0.276512\pi\)
−0.941046 + 0.338279i \(0.890155\pi\)
\(278\) 9.57413 17.0500i 0.574218 1.02259i
\(279\) 8.50330 + 2.27845i 0.509079 + 0.136407i
\(280\) −1.88146 3.00475i −0.112439 0.179568i
\(281\) −14.5744 + 14.5744i −0.869438 + 0.869438i −0.992410 0.122972i \(-0.960757\pi\)
0.122972 + 0.992410i \(0.460757\pi\)
\(282\) 11.6811 + 11.4053i 0.695597 + 0.679174i
\(283\) 1.35643 + 5.06227i 0.0806314 + 0.300920i 0.994451 0.105200i \(-0.0335481\pi\)
−0.913820 + 0.406120i \(0.866881\pi\)
\(284\) −22.9227 21.8527i −1.36021 1.29672i
\(285\) 0.744394 0.744394i 0.0440941 0.0440941i
\(286\) −19.6114 3.16386i −1.15965 0.187083i
\(287\) 5.44725i 0.321541i
\(288\) −4.23163 3.75410i −0.249351 0.221213i
\(289\) −1.88270 + 3.26092i −0.110747 + 0.191819i
\(290\) −0.0167807 1.40471i −0.000985396 0.0824876i
\(291\) 2.28267i 0.133813i
\(292\) −10.0466 + 2.95095i −0.587935 + 0.172691i
\(293\) −0.793311 1.37406i −0.0463458 0.0802732i 0.841922 0.539599i \(-0.181424\pi\)
−0.888268 + 0.459326i \(0.848091\pi\)
\(294\) 1.02954 1.83346i 0.0600443 0.106929i
\(295\) −1.58738 2.74942i −0.0924206 0.160077i
\(296\) 28.5866 8.76888i 1.66156 0.509681i
\(297\) 1.00832 + 3.76310i 0.0585087 + 0.218357i
\(298\) −5.70252 + 1.60123i −0.330338 + 0.0927569i
\(299\) 5.44006 0.490411i 0.314607 0.0283612i
\(300\) 2.22239 9.16445i 0.128310 0.529110i
\(301\) −1.10983 + 1.92227i −0.0639693 + 0.110798i
\(302\) −12.5252 21.1080i −0.720747 1.21463i
\(303\) 0.442160 + 0.765843i 0.0254014 + 0.0439966i
\(304\) 7.01202 + 3.61333i 0.402167 + 0.207239i
\(305\) 5.23264 + 1.40208i 0.299620 + 0.0802830i
\(306\) −3.59423 + 3.68114i −0.205468 + 0.210437i
\(307\) 20.4026 1.16444 0.582220 0.813031i \(-0.302184\pi\)
0.582220 + 0.813031i \(0.302184\pi\)
\(308\) −17.5534 + 5.15588i −1.00020 + 0.293784i
\(309\) −12.4219 + 3.32843i −0.706656 + 0.189348i
\(310\) 5.71543 3.39147i 0.324615 0.192623i
\(311\) 13.8416i 0.784884i 0.919777 + 0.392442i \(0.128370\pi\)
−0.919777 + 0.392442i \(0.871630\pi\)
\(312\) 1.27894 + 10.1175i 0.0724056 + 0.572792i
\(313\) 22.6851i 1.28224i 0.767442 + 0.641119i \(0.221529\pi\)
−0.767442 + 0.641119i \(0.778471\pi\)
\(314\) −3.45468 5.82196i −0.194959 0.328552i
\(315\) 1.21071 0.324408i 0.0682157 0.0182783i
\(316\) −0.372384 + 0.682118i −0.0209482 + 0.0383721i
\(317\) −0.613334 −0.0344483 −0.0172241 0.999852i \(-0.505483\pi\)
−0.0172241 + 0.999852i \(0.505483\pi\)
\(318\) −9.31239 9.09252i −0.522213 0.509883i
\(319\) −7.00250 1.87631i −0.392065 0.105053i
\(320\) −4.25961 + 0.305821i −0.238120 + 0.0170959i
\(321\) −8.10707 14.0419i −0.452493 0.783740i
\(322\) 4.32612 2.56707i 0.241085 0.143057i
\(323\) 3.58713 6.21309i 0.199593 0.345705i
\(324\) 1.70767 1.04109i 0.0948704 0.0578384i
\(325\) −13.9001 + 9.78768i −0.771036 + 0.542923i
\(326\) 4.96460 + 17.6806i 0.274964 + 0.979237i
\(327\) −0.636696 2.37618i −0.0352094 0.131403i
\(328\) −5.79659 3.07519i −0.320063 0.169799i
\(329\) −13.5527 23.4739i −0.747184 1.29416i
\(330\) 2.56447 + 1.44003i 0.141170 + 0.0792712i
\(331\) −16.4049 28.4141i −0.901695 1.56178i −0.825293 0.564704i \(-0.808990\pi\)
−0.0764018 0.997077i \(-0.524343\pi\)
\(332\) −12.1109 + 22.1843i −0.664673 + 1.21752i
\(333\) 10.5717i 0.579326i
\(334\) 14.7945 0.176736i 0.809522 0.00967054i
\(335\) −0.691677 + 1.19802i −0.0377903 + 0.0654548i
\(336\) 5.07915 + 7.90015i 0.277090 + 0.430989i
\(337\) 14.1269i 0.769543i 0.923012 + 0.384771i \(0.125720\pi\)
−0.923012 + 0.384771i \(0.874280\pi\)
\(338\) 10.2842 15.2393i 0.559384 0.828908i
\(339\) −7.77061 + 7.77061i −0.422042 + 0.422042i
\(340\) 0.0927838 + 3.88292i 0.00503191 + 0.210581i
\(341\) −8.87651 33.1276i −0.480690 1.79396i
\(342\) −1.94837 + 1.99548i −0.105356 + 0.107903i
\(343\) −14.0907 + 14.0907i −0.760825 + 0.760825i
\(344\) 1.41901 + 2.26620i 0.0765079 + 0.122185i
\(345\) −0.781142 0.209306i −0.0420553 0.0112687i
\(346\) −0.893546 0.501754i −0.0480374 0.0269745i
\(347\) 2.78260 10.3848i 0.149378 0.557485i −0.850144 0.526551i \(-0.823485\pi\)
0.999521 0.0309342i \(-0.00984824\pi\)
\(348\) 0.0889052 + 3.72060i 0.00476582 + 0.199445i
\(349\) −24.3032 14.0315i −1.30092 0.751087i −0.320359 0.947296i \(-0.603803\pi\)
−0.980562 + 0.196209i \(0.937137\pi\)
\(350\) −7.66581 + 13.6516i −0.409755 + 0.729709i
\(351\) −3.55241 0.616727i −0.189614 0.0329184i
\(352\) −4.42308 + 21.5898i −0.235751 + 1.15074i
\(353\) −1.47342 5.49889i −0.0784224 0.292677i 0.915565 0.402170i \(-0.131744\pi\)
−0.993988 + 0.109493i \(0.965077\pi\)
\(354\) 4.29202 + 7.23306i 0.228118 + 0.384433i
\(355\) 2.18782 8.16504i 0.116117 0.433356i
\(356\) 7.10133 29.2837i 0.376370 1.55203i
\(357\) 7.39751 4.27095i 0.391518 0.226043i
\(358\) −9.04823 + 0.108090i −0.478214 + 0.00571274i
\(359\) 22.2817 + 22.2817i 1.17598 + 1.17598i 0.980759 + 0.195223i \(0.0625430\pi\)
0.195223 + 0.980759i \(0.437457\pi\)
\(360\) 0.338280 1.47149i 0.0178289 0.0775545i
\(361\) −7.55548 + 13.0865i −0.397657 + 0.688762i
\(362\) 9.64498 + 16.2541i 0.506929 + 0.854294i
\(363\) 2.95405 2.95405i 0.155047 0.155047i
\(364\) 2.49682 16.7466i 0.130869 0.877761i
\(365\) −1.97625 1.97625i −0.103442 0.103442i
\(366\) −13.9058 3.54857i −0.726869 0.185487i
\(367\) −11.3072 6.52823i −0.590232 0.340771i 0.174957 0.984576i \(-0.444021\pi\)
−0.765189 + 0.643805i \(0.777355\pi\)
\(368\) −0.289432 6.05277i −0.0150877 0.315522i
\(369\) 1.64045 1.64045i 0.0853984 0.0853984i
\(370\) 5.71042 + 5.57560i 0.296871 + 0.289862i
\(371\) 10.8045 + 18.7139i 0.560941 + 0.971578i
\(372\) −15.0330 + 9.16500i −0.779427 + 0.475183i
\(373\) 14.2057 + 3.80642i 0.735546 + 0.197089i 0.607098 0.794627i \(-0.292334\pi\)
0.128448 + 0.991716i \(0.459000\pi\)
\(374\) 19.4211 + 4.95600i 1.00424 + 0.256269i
\(375\) 5.00939 1.34226i 0.258684 0.0693141i
\(376\) −32.6304 + 1.16985i −1.68278 + 0.0603305i
\(377\) 4.29909 5.15100i 0.221415 0.265290i
\(378\) −3.19694 + 0.897682i −0.164433 + 0.0461718i
\(379\) −10.5370 + 18.2507i −0.541251 + 0.937474i 0.457582 + 0.889168i \(0.348716\pi\)
−0.998833 + 0.0483063i \(0.984618\pi\)
\(380\) 0.0502965 + 2.10486i 0.00258016 + 0.107977i
\(381\) 2.34355 + 0.627953i 0.120064 + 0.0321710i
\(382\) 13.2501 3.72056i 0.677936 0.190360i
\(383\) 1.86734 6.96900i 0.0954166 0.356099i −0.901666 0.432434i \(-0.857655\pi\)
0.997082 + 0.0763343i \(0.0243216\pi\)
\(384\) 11.2742 0.944927i 0.575333 0.0482206i
\(385\) −3.45289 3.45289i −0.175976 0.175976i
\(386\) 13.1100 0.156611i 0.667279 0.00797131i
\(387\) −0.913123 + 0.244670i −0.0464166 + 0.0124373i
\(388\) 3.30438 + 3.15015i 0.167754 + 0.159924i
\(389\) 11.1696 + 11.1696i 0.566320 + 0.566320i 0.931096 0.364775i \(-0.118854\pi\)
−0.364775 + 0.931096i \(0.618854\pi\)
\(390\) −2.20670 + 1.59361i −0.111741 + 0.0806955i
\(391\) −5.51119 −0.278713
\(392\) 1.23330 + 4.02058i 0.0622913 + 0.203070i
\(393\) 13.5982 + 7.85094i 0.685940 + 0.396027i
\(394\) 25.5243 + 24.9217i 1.28589 + 1.25553i
\(395\) −0.207429 −0.0104369
\(396\) −6.83895 3.73354i −0.343670 0.187618i
\(397\) 32.3156 18.6574i 1.62187 0.936389i 0.635455 0.772138i \(-0.280813\pi\)
0.986419 0.164251i \(-0.0525207\pi\)
\(398\) 5.40117 1.51661i 0.270736 0.0760210i
\(399\) 4.01006 2.31521i 0.200754 0.115906i
\(400\) 10.1994 + 15.8643i 0.509972 + 0.793215i
\(401\) −25.7203 + 6.89174i −1.28441 + 0.344157i −0.835535 0.549437i \(-0.814842\pi\)
−0.448876 + 0.893594i \(0.648175\pi\)
\(402\) 1.79436 3.19548i 0.0894947 0.159376i
\(403\) 31.2728 + 5.42920i 1.55781 + 0.270448i
\(404\) −1.71882 0.416816i −0.0855146 0.0207374i
\(405\) 0.462303 + 0.266911i 0.0229720 + 0.0132629i
\(406\) 1.52785 5.98718i 0.0758257 0.297139i
\(407\) 35.6680 20.5929i 1.76800 1.02075i
\(408\) −0.368664 10.2830i −0.0182516 0.509086i
\(409\) −7.10682 + 26.5230i −0.351410 + 1.31148i 0.533533 + 0.845779i \(0.320864\pi\)
−0.884943 + 0.465699i \(0.845803\pi\)
\(410\) −0.0209209 1.75129i −0.00103321 0.0864901i
\(411\) 1.45079i 0.0715620i
\(412\) 12.3243 22.5752i 0.607175 1.11220i
\(413\) −3.61417 13.4883i −0.177842 0.663715i
\(414\) 2.07590 + 0.529740i 0.102025 + 0.0260353i
\(415\) −6.74613 −0.331154
\(416\) −16.4110 12.1111i −0.804617 0.593794i
\(417\) −13.8269 −0.677108
\(418\) 10.5278 + 2.68656i 0.514933 + 0.131404i
\(419\) 1.27861 + 4.77184i 0.0624643 + 0.233120i 0.990099 0.140368i \(-0.0448285\pi\)
−0.927635 + 0.373488i \(0.878162\pi\)
\(420\) −1.20120 + 2.20031i −0.0586125 + 0.107364i
\(421\) 22.5927i 1.10110i 0.834802 + 0.550550i \(0.185582\pi\)
−0.834802 + 0.550550i \(0.814418\pi\)
\(422\) −0.399669 33.4563i −0.0194556 1.62863i
\(423\) 2.98781 11.1506i 0.145272 0.542163i
\(424\) 26.0136 0.932630i 1.26333 0.0452925i
\(425\) 14.8549 8.57651i 0.720571 0.416022i
\(426\) −5.53722 + 21.6987i −0.268279 + 1.05131i
\(427\) 20.6353 + 11.9138i 0.998612 + 0.576549i
\(428\) 31.5149 + 7.64239i 1.52333 + 0.369409i
\(429\) 4.83906 + 13.1868i 0.233632 + 0.636667i
\(430\) −0.349426 + 0.622274i −0.0168508 + 0.0300087i
\(431\) 11.2716 3.02022i 0.542934 0.145479i 0.0230797 0.999734i \(-0.492653\pi\)
0.519854 + 0.854255i \(0.325986\pi\)
\(432\) −0.849551 + 3.90874i −0.0408740 + 0.188059i
\(433\) 24.2127 13.9792i 1.16359 0.671797i 0.211425 0.977394i \(-0.432190\pi\)
0.952161 + 0.305598i \(0.0988562\pi\)
\(434\) 28.1435 7.90253i 1.35093 0.379334i
\(435\) −0.860269 + 0.496676i −0.0412467 + 0.0238138i
\(436\) 4.31840 + 2.35752i 0.206814 + 0.112905i
\(437\) −2.98752 −0.142913
\(438\) 5.29770 + 5.17262i 0.253134 + 0.247157i
\(439\) 1.47017 + 0.848802i 0.0701673 + 0.0405111i 0.534673 0.845059i \(-0.320435\pi\)
−0.464506 + 0.885570i \(0.653768\pi\)
\(440\) −5.62363 + 1.72503i −0.268096 + 0.0822377i
\(441\) −1.48686 −0.0708031
\(442\) −11.7152 + 14.3824i −0.557234 + 0.684103i
\(443\) 9.20791 + 9.20791i 0.437481 + 0.437481i 0.891163 0.453683i \(-0.149890\pi\)
−0.453683 + 0.891163i \(0.649890\pi\)
\(444\) −15.3035 14.5892i −0.726274 0.692375i
\(445\) 7.76863 2.08160i 0.368268 0.0986772i
\(446\) −9.09024 + 0.108592i −0.430435 + 0.00514198i
\(447\) 2.96153 + 2.96153i 0.140076 + 0.140076i
\(448\) −18.4456 3.54988i −0.871471 0.167716i
\(449\) 5.48227 20.4601i 0.258724 0.965572i −0.707256 0.706957i \(-0.750067\pi\)
0.965980 0.258615i \(-0.0832661\pi\)
\(450\) −6.41978 + 1.80264i −0.302631 + 0.0849771i
\(451\) −8.73020 2.33925i −0.411089 0.110151i
\(452\) −0.525038 21.9723i −0.0246957 1.03349i
\(453\) −8.67776 + 15.0303i −0.407717 + 0.706186i
\(454\) −10.7330 + 3.01375i −0.503723 + 0.141443i
\(455\) 4.24262 1.55688i 0.198897 0.0729876i
\(456\) −0.199846 5.57426i −0.00935866 0.261039i
\(457\) −23.3623 + 6.25990i −1.09284 + 0.292826i −0.759846 0.650103i \(-0.774726\pi\)
−0.332995 + 0.942929i \(0.608059\pi\)
\(458\) 18.9549 + 4.83704i 0.885706 + 0.226020i
\(459\) 3.51398 + 0.941568i 0.164019 + 0.0439486i
\(460\) 1.38099 0.841928i 0.0643889 0.0392551i
\(461\) −14.9547 25.9023i −0.696511 1.20639i −0.969669 0.244423i \(-0.921401\pi\)
0.273158 0.961969i \(-0.411932\pi\)
\(462\) 9.25610 + 9.03756i 0.430633 + 0.420465i
\(463\) −14.2329 + 14.2329i −0.661460 + 0.661460i −0.955724 0.294264i \(-0.904926\pi\)
0.294264 + 0.955724i \(0.404926\pi\)
\(464\) −5.50861 5.00583i −0.255731 0.232390i
\(465\) −4.06978 2.34969i −0.188731 0.108964i
\(466\) −19.4631 4.96672i −0.901611 0.230079i
\(467\) −12.3341 12.3341i −0.570753 0.570753i 0.361586 0.932339i \(-0.382235\pi\)
−0.932339 + 0.361586i \(0.882235\pi\)
\(468\) 5.79520 4.29135i 0.267883 0.198368i
\(469\) −4.30250 + 4.30250i −0.198671 + 0.198671i
\(470\) −4.44735 7.49482i −0.205141 0.345710i
\(471\) −2.39348 + 4.14563i −0.110286 + 0.191021i
\(472\) −16.3936 3.76872i −0.754578 0.173469i
\(473\) 2.60419 + 2.60419i 0.119741 + 0.119741i
\(474\) 0.549485 0.00656415i 0.0252387 0.000301501i
\(475\) 8.05261 4.64918i 0.369479 0.213319i
\(476\) −4.02615 + 16.6026i −0.184538 + 0.760980i
\(477\) −2.38194 + 8.88952i −0.109062 + 0.407023i
\(478\) 15.8876 + 26.7744i 0.726684 + 1.22463i
\(479\) 2.10903 + 7.87103i 0.0963643 + 0.359636i 0.997223 0.0744765i \(-0.0237286\pi\)
−0.900859 + 0.434113i \(0.857062\pi\)
\(480\) 1.66329 + 2.52039i 0.0759184 + 0.115040i
\(481\) 3.42228 + 37.9629i 0.156043 + 1.73096i
\(482\) 20.9985 37.3951i 0.956456 1.70330i
\(483\) −3.08049 1.77852i −0.140167 0.0809255i
\(484\) 0.199596 + 8.35292i 0.00907256 + 0.379678i
\(485\) −0.315381 + 1.17702i −0.0143207 + 0.0534457i
\(486\) −1.23310 0.692427i −0.0559347 0.0314091i
\(487\) −6.85958 1.83802i −0.310837 0.0832886i 0.100028 0.994985i \(-0.468107\pi\)
−0.410865 + 0.911696i \(0.634773\pi\)
\(488\) 24.3273 15.2328i 1.10124 0.689558i
\(489\) 9.18219 9.18219i 0.415233 0.415233i
\(490\) −0.784183 + 0.803146i −0.0354258 + 0.0362824i
\(491\) −2.81287 10.4978i −0.126943 0.473758i 0.872958 0.487795i \(-0.162199\pi\)
−0.999901 + 0.0140366i \(0.995532\pi\)
\(492\) 0.110840 + 4.63857i 0.00499707 + 0.209123i
\(493\) −4.78682 + 4.78682i −0.215588 + 0.215588i
\(494\) −6.35059 + 7.79648i −0.285727 + 0.350780i
\(495\) 2.07969i 0.0934751i
\(496\) 7.47882 34.4097i 0.335809 1.54504i
\(497\) 18.5904 32.1994i 0.833891 1.44434i
\(498\) 17.8707 0.213484i 0.800806 0.00956643i
\(499\) 2.67017i 0.119533i 0.998212 + 0.0597665i \(0.0190356\pi\)
−0.998212 + 0.0597665i \(0.980964\pi\)
\(500\) −4.97004 + 9.10391i −0.222267 + 0.407139i
\(501\) −5.23104 9.06042i −0.233705 0.404790i
\(502\) 6.03637 + 3.38961i 0.269416 + 0.151286i
\(503\) −18.1620 31.4575i −0.809804 1.40262i −0.912999 0.407961i \(-0.866240\pi\)
0.103195 0.994661i \(-0.467093\pi\)
\(504\) 3.11239 5.86670i 0.138637 0.261323i
\(505\) −0.122181 0.455984i −0.00543696 0.0202910i
\(506\) −2.25640 8.03577i −0.100309 0.357234i
\(507\) −12.9563 1.06467i −0.575411 0.0472836i
\(508\) −4.14319 + 2.52592i −0.183824 + 0.112070i
\(509\) −12.0932 + 20.9460i −0.536022 + 0.928417i 0.463091 + 0.886311i \(0.346740\pi\)
−0.999113 + 0.0421063i \(0.986593\pi\)
\(510\) 2.36190 1.40152i 0.104587 0.0620605i
\(511\) −6.14653 10.6461i −0.271907 0.470956i
\(512\) −14.1908 + 17.6245i −0.627150 + 0.778898i
\(513\) 1.90487 + 0.510408i 0.0841020 + 0.0225351i
\(514\) −3.84286 3.75213i −0.169501 0.165499i
\(515\) 6.86500 0.302508
\(516\) 0.905950 1.65948i 0.0398822 0.0730546i
\(517\) −43.4412 + 11.6400i −1.91054 + 0.511928i
\(518\) 17.9140 + 30.1893i 0.787097 + 1.32644i
\(519\) 0.724632i 0.0318078i
\(520\) 0.738409 5.39363i 0.0323814 0.236526i
\(521\) 23.6753i 1.03723i −0.855007 0.518617i \(-0.826447\pi\)
0.855007 0.518617i \(-0.173553\pi\)
\(522\) 2.26316 1.34294i 0.0990560 0.0587787i
\(523\) 3.67223 0.983972i 0.160576 0.0430261i −0.177636 0.984096i \(-0.556845\pi\)
0.338211 + 0.941070i \(0.390178\pi\)
\(524\) −30.1309 + 8.85020i −1.31627 + 0.386623i
\(525\) 11.0709 0.483175
\(526\) −11.5534 + 11.8327i −0.503751 + 0.515932i
\(527\) −30.9345 8.28887i −1.34753 0.361069i
\(528\) 14.8426 4.74763i 0.645941 0.206614i
\(529\) −10.3525 17.9311i −0.450109 0.779612i
\(530\) 3.54552 + 5.97503i 0.154007 + 0.259539i
\(531\) 2.97361 5.15044i 0.129044 0.223510i
\(532\) −2.18251 + 8.99999i −0.0946237 + 0.390199i
\(533\) 5.35979 6.42189i 0.232158 0.278163i
\(534\) −20.5135 + 5.76007i −0.887706 + 0.249262i
\(535\) 2.24020 + 8.36054i 0.0968523 + 0.361458i
\(536\) 2.14949 + 7.00736i 0.0928439 + 0.302672i
\(537\) 3.19926 + 5.54128i 0.138058 + 0.239124i
\(538\) −10.6442 + 18.9557i −0.458906 + 0.817240i
\(539\) 2.89630 + 5.01654i 0.124753 + 0.216078i
\(540\) −1.02437 + 0.300883i −0.0440818 + 0.0129480i
\(541\) 1.42522i 0.0612750i 0.999531 + 0.0306375i \(0.00975374\pi\)
−0.999531 + 0.0306375i \(0.990246\pi\)
\(542\) 0.137216 + 11.4863i 0.00589392 + 0.493380i
\(543\) 6.68225 11.5740i 0.286763 0.496688i
\(544\) 15.3944 + 13.6572i 0.660031 + 0.585547i
\(545\) 1.31320i 0.0562515i
\(546\) −11.1896 + 4.25848i −0.478870 + 0.182246i
\(547\) 19.1963 19.1963i 0.820777 0.820777i −0.165443 0.986219i \(-0.552905\pi\)
0.986219 + 0.165443i \(0.0529053\pi\)
\(548\) −2.10015 2.00212i −0.0897139 0.0855265i
\(549\) 2.62650 + 9.80222i 0.112096 + 0.418349i
\(550\) 18.5872 + 18.1483i 0.792560 + 0.773848i
\(551\) −2.59486 + 2.59486i −0.110545 + 0.110545i
\(552\) −3.63164 + 2.27400i −0.154573 + 0.0967878i
\(553\) −0.881283 0.236139i −0.0374760 0.0100417i
\(554\) −13.1449 + 23.4090i −0.558473 + 0.994554i
\(555\) 1.46062 5.45112i 0.0620000 0.231387i
\(556\) 19.0815 20.0158i 0.809237 0.848858i
\(557\) 13.2980 + 7.67760i 0.563454 + 0.325311i 0.754531 0.656265i \(-0.227864\pi\)
−0.191076 + 0.981575i \(0.561198\pi\)
\(558\) 10.8553 + 6.09561i 0.459543 + 0.258048i
\(559\) −3.19981 + 1.17421i −0.135337 + 0.0496636i
\(560\) −1.52746 4.77533i −0.0645471 0.201794i
\(561\) −3.66821 13.6899i −0.154872 0.577990i
\(562\) −25.0678 + 14.8749i −1.05742 + 0.627461i
\(563\) −3.82358 + 14.2698i −0.161145 + 0.601400i 0.837356 + 0.546658i \(0.184100\pi\)
−0.998501 + 0.0547417i \(0.982566\pi\)
\(564\) 12.0183 + 19.7133i 0.506064 + 0.830080i
\(565\) 5.08039 2.93317i 0.213734 0.123399i
\(566\) 0.0885334 + 7.41114i 0.00372134 + 0.311514i
\(567\) 1.66029 + 1.66029i 0.0697257 + 0.0697257i
\(568\) −23.7694 37.9604i −0.997343 1.59278i
\(569\) −1.72345 + 2.98511i −0.0722509 + 0.125142i −0.899887 0.436122i \(-0.856352\pi\)
0.827637 + 0.561264i \(0.189685\pi\)
\(570\) 1.28034 0.759742i 0.0536277 0.0318221i
\(571\) −9.88364 + 9.88364i −0.413618 + 0.413618i −0.882997 0.469379i \(-0.844478\pi\)
0.469379 + 0.882997i \(0.344478\pi\)
\(572\) −25.7672 11.1932i −1.07738 0.468011i
\(573\) −6.88129 6.88129i −0.287470 0.287470i
\(574\) 1.90480 7.46437i 0.0795050 0.311557i
\(575\) −6.18593 3.57145i −0.257971 0.148940i
\(576\) −4.48587 6.62397i −0.186911 0.275999i
\(577\) −21.1231 + 21.1231i −0.879364 + 0.879364i −0.993469 0.114104i \(-0.963600\pi\)
0.114104 + 0.993469i \(0.463600\pi\)
\(578\) −3.72014 + 3.81010i −0.154738 + 0.158479i
\(579\) −4.63540 8.02875i −0.192641 0.333663i
\(580\) 0.468208 1.93075i 0.0194413 0.0801699i
\(581\) −28.6617 7.67987i −1.18909 0.318615i
\(582\) 0.798209 3.12794i 0.0330868 0.129657i
\(583\) 34.6322 9.27968i 1.43432 0.384325i
\(584\) −14.7988 + 0.530561i −0.612379 + 0.0219548i
\(585\) 1.74653 + 0.808817i 0.0722102 + 0.0334405i
\(586\) −0.606592 2.16028i −0.0250581 0.0892402i
\(587\) −13.6443 + 23.6326i −0.563159 + 0.975420i 0.434059 + 0.900884i \(0.357081\pi\)
−0.997218 + 0.0745356i \(0.976253\pi\)
\(588\) 2.05191 2.15238i 0.0846194 0.0887625i
\(589\) −16.7691 4.49325i −0.690957 0.185141i
\(590\) −1.21376 4.32260i −0.0499697 0.177959i
\(591\) 6.52865 24.3653i 0.268553 1.00225i
\(592\) 42.2386 2.01977i 1.73600 0.0830120i
\(593\) −17.0037 17.0037i −0.698259 0.698259i 0.265776 0.964035i \(-0.414372\pi\)
−0.964035 + 0.265776i \(0.914372\pi\)
\(594\) 0.0658125 + 5.50917i 0.00270032 + 0.226044i
\(595\) −4.40448 + 1.18018i −0.180566 + 0.0483826i
\(596\) −8.37408 + 0.200102i −0.343016 + 0.00819650i
\(597\) −2.80503 2.80503i −0.114802 0.114802i
\(598\) 7.62601 + 1.23028i 0.311851 + 0.0503100i
\(599\) −3.28310 −0.134144 −0.0670719 0.997748i \(-0.521366\pi\)
−0.0670719 + 0.997748i \(0.521366\pi\)
\(600\) 6.24998 11.7809i 0.255155 0.480954i
\(601\) −21.4370 12.3767i −0.874433 0.504854i −0.00561426 0.999984i \(-0.501787\pi\)
−0.868819 + 0.495130i \(0.835120\pi\)
\(602\) −2.19298 + 2.24601i −0.0893791 + 0.0915404i
\(603\) −2.59141 −0.105531
\(604\) −9.78226 33.3041i −0.398035 1.35513i
\(605\) −1.93134 + 1.11506i −0.0785202 + 0.0453337i
\(606\) 0.338090 + 1.20405i 0.0137340 + 0.0489112i
\(607\) −9.39899 + 5.42651i −0.381493 + 0.220255i −0.678468 0.734630i \(-0.737356\pi\)
0.296975 + 0.954885i \(0.404022\pi\)
\(608\) 8.34506 + 7.40333i 0.338437 + 0.300245i
\(609\) −4.22037 + 1.13084i −0.171018 + 0.0458241i
\(610\) 6.68001 + 3.75103i 0.270466 + 0.151875i
\(611\) 7.11949 41.0090i 0.288024 1.65905i
\(612\) −6.21239 + 3.78743i −0.251121 + 0.153098i
\(613\) −15.6438 9.03197i −0.631849 0.364798i 0.149619 0.988744i \(-0.452195\pi\)
−0.781468 + 0.623946i \(0.785529\pi\)
\(614\) 27.9577 + 7.13443i 1.12828 + 0.287922i
\(615\) −1.07252 + 0.619219i −0.0432481 + 0.0249693i
\(616\) −25.8564 + 0.926993i −1.04178 + 0.0373496i
\(617\) 7.72467 28.8289i 0.310984 1.16061i −0.616687 0.787208i \(-0.711526\pi\)
0.927671 0.373399i \(-0.121808\pi\)
\(618\) −18.1856 + 0.217245i −0.731532 + 0.00873888i
\(619\) 7.86671i 0.316190i −0.987424 0.158095i \(-0.949465\pi\)
0.987424 0.158095i \(-0.0505352\pi\)
\(620\) 9.01779 2.64875i 0.362163 0.106376i
\(621\) −0.392090 1.46330i −0.0157340 0.0587202i
\(622\) −4.84015 + 18.9671i −0.194072 + 0.760512i
\(623\) 35.3756 1.41729
\(624\) −1.78539 + 14.3113i −0.0714727 + 0.572909i
\(625\) 20.8067 0.832269
\(626\) −7.93257 + 31.0854i −0.317049 + 1.24242i
\(627\) −1.98847 7.42108i −0.0794120 0.296369i
\(628\) −2.69812 9.18587i −0.107667 0.366556i
\(629\) 38.4593i 1.53347i
\(630\) 1.77247 0.0211740i 0.0706170 0.000843591i
\(631\) 1.87195 6.98622i 0.0745213 0.278117i −0.918603 0.395182i \(-0.870682\pi\)
0.993124 + 0.117064i \(0.0373484\pi\)
\(632\) −0.748802 + 0.804490i −0.0297858 + 0.0320009i
\(633\) −20.4892 + 11.8294i −0.814373 + 0.470178i
\(634\) −0.840452 0.214472i −0.0333786 0.00851777i
\(635\) −1.12165 0.647586i −0.0445114 0.0256987i
\(636\) −9.58127 15.7159i −0.379922 0.623174i
\(637\) −5.33932 + 0.481329i −0.211551 + 0.0190709i
\(638\) −8.93941 5.01976i −0.353915 0.198734i
\(639\) 15.2954 4.09840i 0.605078 0.162130i
\(640\) −5.94389 1.07044i −0.234953 0.0423130i
\(641\) −26.8343 + 15.4928i −1.05989 + 0.611929i −0.925402 0.378986i \(-0.876273\pi\)
−0.134490 + 0.990915i \(0.542940\pi\)
\(642\) −6.19894 22.0765i −0.244653 0.871288i
\(643\) 20.3386 11.7425i 0.802076 0.463079i −0.0421203 0.999113i \(-0.513411\pi\)
0.844197 + 0.536034i \(0.180078\pi\)
\(644\) 6.82573 2.00489i 0.268972 0.0790037i
\(645\) 0.504640 0.0198702
\(646\) 7.08804 7.25944i 0.278875 0.285619i
\(647\) −11.3945 6.57864i −0.447966 0.258633i 0.259005 0.965876i \(-0.416605\pi\)
−0.706971 + 0.707243i \(0.749939\pi\)
\(648\) 2.70407 0.829466i 0.106226 0.0325845i
\(649\) −23.1694 −0.909480
\(650\) −22.4698 + 8.55146i −0.881339 + 0.335416i
\(651\) −14.6160 14.6160i −0.572845 0.572845i
\(652\) 0.620414 + 25.9637i 0.0242973 + 1.01682i
\(653\) 25.2364 6.76207i 0.987576 0.264620i 0.271344 0.962482i \(-0.412532\pi\)
0.716232 + 0.697862i \(0.245865\pi\)
\(654\) −0.0415568 3.47872i −0.00162500 0.136029i
\(655\) −5.92697 5.92697i −0.231586 0.231586i
\(656\) −6.86772 6.24090i −0.268140 0.243666i
\(657\) 1.35506 5.05714i 0.0528658 0.197298i
\(658\) −10.3628 36.9055i −0.403985 1.43873i
\(659\) −26.3727 7.06653i −1.02733 0.275273i −0.294478 0.955658i \(-0.595146\pi\)
−0.732855 + 0.680385i \(0.761813\pi\)
\(660\) 3.01055 + 2.87003i 0.117185 + 0.111716i
\(661\) 2.95627 5.12042i 0.114986 0.199161i −0.802788 0.596264i \(-0.796651\pi\)
0.917774 + 0.397103i \(0.129984\pi\)
\(662\) −12.5437 44.6724i −0.487526 1.73624i
\(663\) 12.9235 + 2.24361i 0.501906 + 0.0871348i
\(664\) −24.3530 + 26.1642i −0.945081 + 1.01537i
\(665\) −2.38760 + 0.639754i −0.0925870 + 0.0248086i
\(666\) −3.69674 + 14.4864i −0.143246 + 0.561337i
\(667\) 2.72296 + 0.729614i 0.105433 + 0.0282508i
\(668\) 20.3348 + 4.93120i 0.786776 + 0.190794i
\(669\) 3.21411 + 5.56701i 0.124265 + 0.215233i
\(670\) −1.36673 + 1.39978i −0.0528014 + 0.0540782i
\(671\) 27.9556 27.9556i 1.07921 1.07921i
\(672\) 4.19742 + 12.6017i 0.161919 + 0.486120i
\(673\) −21.3547 12.3292i −0.823165 0.475254i 0.0283417 0.999598i \(-0.490977\pi\)
−0.851507 + 0.524344i \(0.824311\pi\)
\(674\) −4.93993 + 19.3581i −0.190279 + 0.745647i
\(675\) 3.33403 + 3.33403i 0.128327 + 0.128327i
\(676\) 19.4213 17.2862i 0.746973 0.664855i
\(677\) −19.7288 + 19.7288i −0.758240 + 0.758240i −0.976002 0.217762i \(-0.930124\pi\)
0.217762 + 0.976002i \(0.430124\pi\)
\(678\) −13.3653 + 7.93083i −0.513292 + 0.304582i
\(679\) −2.67986 + 4.64166i −0.102844 + 0.178131i
\(680\) −1.23064 + 5.35321i −0.0471930 + 0.205286i
\(681\) 5.57403 + 5.57403i 0.213597 + 0.213597i
\(682\) −0.579365 48.4987i −0.0221850 1.85711i
\(683\) −9.92922 + 5.73264i −0.379931 + 0.219353i −0.677788 0.735257i \(-0.737061\pi\)
0.297857 + 0.954610i \(0.403728\pi\)
\(684\) −3.36763 + 2.05310i −0.128765 + 0.0785022i
\(685\) 0.200445 0.748072i 0.00765862 0.0285824i
\(686\) −24.2357 + 14.3812i −0.925323 + 0.549077i
\(687\) −3.58017 13.3614i −0.136592 0.509768i
\(688\) 1.15202 + 3.60158i 0.0439204 + 0.137309i
\(689\) −5.67580 + 32.6933i −0.216231 + 1.24551i
\(690\) −0.997209 0.559964i −0.0379631 0.0213175i
\(691\) −32.4338 18.7256i −1.23384 0.712357i −0.266011 0.963970i \(-0.585706\pi\)
−0.967828 + 0.251613i \(0.919039\pi\)
\(692\) −1.04897 1.00001i −0.0398759 0.0380147i
\(693\) 2.36754 8.83579i 0.0899355 0.335644i
\(694\) 7.44437 13.2573i 0.282584 0.503239i
\(695\) 7.12961 + 1.91037i 0.270442 + 0.0724646i
\(696\) −1.17920 + 5.12943i −0.0446975 + 0.194430i
\(697\) −5.96786 + 5.96786i −0.226049 + 0.226049i
\(698\) −28.3961 27.7257i −1.07481 1.04943i
\(699\) 3.67614 + 13.7196i 0.139045 + 0.518921i
\(700\) −15.2782 + 16.0262i −0.577461 + 0.605734i
\(701\) −6.36427 + 6.36427i −0.240375 + 0.240375i −0.817005 0.576630i \(-0.804367\pi\)
0.576630 + 0.817005i \(0.304367\pi\)
\(702\) −4.65222 2.08732i −0.175587 0.0787806i
\(703\) 20.8481i 0.786301i
\(704\) −13.6105 + 28.0379i −0.512966 + 1.05672i
\(705\) −3.08122 + 5.33683i −0.116045 + 0.200997i
\(706\) −0.0961696 8.05036i −0.00361939 0.302979i
\(707\) 2.07639i 0.0780906i
\(708\) 3.35208 + 11.4123i 0.125979 + 0.428901i
\(709\) −1.68250 2.91418i −0.0631876 0.109444i 0.832701 0.553723i \(-0.186793\pi\)
−0.895889 + 0.444279i \(0.853460\pi\)
\(710\) 5.85313 10.4235i 0.219664 0.391188i
\(711\) −0.194286 0.336514i −0.00728631 0.0126203i
\(712\) 19.9709 37.6442i 0.748442 1.41078i
\(713\) 3.45167 + 12.8818i 0.129266 + 0.482428i
\(714\) 11.6303 3.26571i 0.435252 0.122216i
\(715\) −0.673238 7.46815i −0.0251777 0.279293i
\(716\) −12.4366 3.01589i −0.464777 0.112709i
\(717\) 11.0073 19.0652i 0.411076 0.712004i
\(718\) 22.7411 + 38.3241i 0.848690 + 1.43024i
\(719\) 9.54172 + 16.5267i 0.355846 + 0.616344i 0.987262 0.159100i \(-0.0508594\pi\)
−0.631416 + 0.775444i \(0.717526\pi\)
\(720\) 0.978101 1.89810i 0.0364517 0.0707379i
\(721\) 29.1667 + 7.81519i 1.08622 + 0.291053i
\(722\) −14.9294 + 15.2904i −0.555614 + 0.569049i
\(723\) −30.3260 −1.12783
\(724\) 7.53276 + 25.6456i 0.279953 + 0.953112i
\(725\) −8.47492 + 2.27085i −0.314751 + 0.0843372i
\(726\) 5.08090 3.01495i 0.188570 0.111895i
\(727\) 24.7097i 0.916433i 0.888841 + 0.458216i \(0.151512\pi\)
−0.888841 + 0.458216i \(0.848488\pi\)
\(728\) 9.27737 22.0748i 0.343842 0.818146i
\(729\) 1.00000i 0.0370370i
\(730\) −2.01700 3.39912i −0.0746525 0.125807i
\(731\) 3.32189 0.890096i 0.122864 0.0329214i
\(732\) −17.8143 9.72523i −0.658434 0.359455i
\(733\) 10.5255 0.388767 0.194384 0.980926i \(-0.437729\pi\)
0.194384 + 0.980926i \(0.437729\pi\)
\(734\) −13.2115 12.8996i −0.487645 0.476132i
\(735\) 0.766676 + 0.205430i 0.0282793 + 0.00757740i
\(736\) 1.71993 8.39531i 0.0633976 0.309455i
\(737\) 5.04788 + 8.74319i 0.185941 + 0.322059i
\(738\) 2.82154 1.67427i 0.103862 0.0616308i
\(739\) 21.0102 36.3908i 0.772874 1.33866i −0.163108 0.986608i \(-0.552152\pi\)
0.935982 0.352048i \(-0.114515\pi\)
\(740\) 5.87531 + 9.63708i 0.215981 + 0.354266i
\(741\) 7.00559 + 1.21622i 0.257357 + 0.0446791i
\(742\) 8.26147 + 29.4218i 0.303288 + 1.08011i
\(743\) 8.41627 + 31.4099i 0.308763 + 1.15232i 0.929658 + 0.368425i \(0.120103\pi\)
−0.620895 + 0.783894i \(0.713231\pi\)
\(744\) −23.8046 + 7.30201i −0.872720 + 0.267705i
\(745\) −1.11789 1.93624i −0.0409562 0.0709382i
\(746\) 18.1351 + 10.1834i 0.663973 + 0.372842i
\(747\) −6.31871 10.9443i −0.231189 0.400432i
\(748\) 24.8797 + 13.5824i 0.909692 + 0.496622i
\(749\) 38.0709i 1.39108i
\(750\) 7.33373 0.0876087i 0.267790 0.00319902i
\(751\) −9.63102 + 16.6814i −0.351441 + 0.608713i −0.986502 0.163748i \(-0.947641\pi\)
0.635061 + 0.772462i \(0.280975\pi\)
\(752\) −45.1225 9.80721i −1.64545 0.357632i
\(753\) 4.89526i 0.178393i
\(754\) 7.69226 5.55510i 0.280136 0.202305i
\(755\) 6.55118 6.55118i 0.238422 0.238422i
\(756\) −4.69467 + 0.112181i −0.170744 + 0.00407999i
\(757\) −12.9316 48.2614i −0.470007 1.75409i −0.639730 0.768600i \(-0.720954\pi\)
0.169723 0.985492i \(-0.445713\pi\)
\(758\) −20.8208 + 21.3243i −0.756246 + 0.774533i
\(759\) −4.17328 + 4.17328i −0.151480 + 0.151480i
\(760\) −0.667111 + 2.90188i −0.0241987 + 0.105262i
\(761\) 47.0702 + 12.6124i 1.70629 + 0.457200i 0.974511 0.224339i \(-0.0720222\pi\)
0.731782 + 0.681539i \(0.238689\pi\)
\(762\) 2.99179 + 1.67998i 0.108381 + 0.0608594i
\(763\) −1.49497 + 5.57929i −0.0541214 + 0.201984i
\(764\) 19.4577 0.464949i 0.703954 0.0168213i
\(765\) −1.68183 0.971006i −0.0608068 0.0351068i
\(766\) 4.99575 8.89665i 0.180504 0.321449i
\(767\) 9.01089 19.4578i 0.325364 0.702580i
\(768\) 15.7794 + 2.64754i 0.569391 + 0.0955350i
\(769\) 4.89373 + 18.2636i 0.176472 + 0.658603i 0.996296 + 0.0859877i \(0.0274046\pi\)
−0.819824 + 0.572616i \(0.805929\pi\)
\(770\) −3.52409 5.93891i −0.126999 0.214024i
\(771\) −0.982934 + 3.66836i −0.0353995 + 0.132113i
\(772\) 18.0193 + 4.36971i 0.648530 + 0.157269i
\(773\) −5.66744 + 3.27210i −0.203844 + 0.117689i −0.598447 0.801162i \(-0.704215\pi\)
0.394603 + 0.918852i \(0.370882\pi\)
\(774\) −1.33681 + 0.0159695i −0.0480506 + 0.000574012i
\(775\) −29.3504 29.3504i −1.05430 1.05430i
\(776\) 3.42644 + 5.47213i 0.123002 + 0.196438i
\(777\) 12.4112 21.4969i 0.445250 0.771196i
\(778\) 11.3999 + 19.2115i 0.408706 + 0.688765i
\(779\) −3.23507 + 3.23507i −0.115909 + 0.115909i
\(780\) −3.58110 + 1.41208i −0.128224 + 0.0505605i
\(781\) −43.6220 43.6220i −1.56092 1.56092i
\(782\) −7.55198 1.92716i −0.270058 0.0689152i
\(783\) −1.61153 0.930416i −0.0575913 0.0332503i
\(784\) 0.284072 + 5.94067i 0.0101454 + 0.212167i
\(785\) 1.80693 1.80693i 0.0644921 0.0644921i
\(786\) 15.8883 + 15.5132i 0.566717 + 0.553337i
\(787\) 25.5358 + 44.2293i 0.910253 + 1.57660i 0.813707 + 0.581275i \(0.197446\pi\)
0.0965453 + 0.995329i \(0.469221\pi\)
\(788\) 26.2613 + 43.0755i 0.935519 + 1.53450i
\(789\) 11.2954 + 3.02660i 0.402128 + 0.107750i
\(790\) −0.284239 0.0725340i −0.0101128 0.00258065i
\(791\) 24.9237 6.67830i 0.886186 0.237453i
\(792\) −8.06586 7.50753i −0.286608 0.266769i
\(793\) 12.6049 + 34.3494i 0.447613 + 1.21978i
\(794\) 50.8062 14.2661i 1.80305 0.506284i
\(795\) 2.45641 4.25463i 0.0871199 0.150896i
\(796\) 7.93155 0.189528i 0.281126 0.00671763i
\(797\) −16.1015 4.31438i −0.570343 0.152823i −0.0378893 0.999282i \(-0.512063\pi\)
−0.532454 + 0.846459i \(0.678730\pi\)
\(798\) 6.30458 1.77029i 0.223180 0.0626675i
\(799\) −10.8695 + 40.5654i −0.384534 + 1.43510i
\(800\) 8.42884 + 25.3054i 0.298004 + 0.894682i
\(801\) 10.6534 + 10.6534i 0.376420 + 0.376420i
\(802\) −37.6545 + 0.449820i −1.32963 + 0.0158837i
\(803\) −19.7018 + 5.27909i −0.695263 + 0.186295i
\(804\) 3.57622 3.75131i 0.126124 0.132299i
\(805\) 1.34267 + 1.34267i 0.0473230 + 0.0473230i
\(806\) 40.9547 + 18.3752i 1.44257 + 0.647238i
\(807\) 15.3724 0.541133
\(808\) −2.20955 1.17220i −0.0777317 0.0412380i
\(809\) −22.1429 12.7842i −0.778503 0.449469i 0.0573965 0.998351i \(-0.481720\pi\)
−0.835899 + 0.548883i \(0.815053\pi\)
\(810\) 0.540160 + 0.527407i 0.0189793 + 0.0185312i
\(811\) −47.4647 −1.66671 −0.833356 0.552737i \(-0.813584\pi\)
−0.833356 + 0.552737i \(0.813584\pi\)
\(812\) 4.18721 7.66997i 0.146942 0.269163i
\(813\) 7.03442 4.06132i 0.246708 0.142437i
\(814\) 56.0768 15.7460i 1.96549 0.551898i
\(815\) −6.00327 + 3.46599i −0.210286 + 0.121408i
\(816\) 3.09061 14.2198i 0.108193 0.497792i
\(817\) 1.80074 0.482506i 0.0629998 0.0168807i
\(818\) −19.0131 + 33.8594i −0.664777 + 1.18386i
\(819\) 6.49956 + 5.42462i 0.227113 + 0.189552i
\(820\) 0.583727 2.40711i 0.0203846 0.0840599i
\(821\) 31.2288 + 18.0299i 1.08989 + 0.629249i 0.933547 0.358454i \(-0.116696\pi\)
0.156344 + 0.987703i \(0.450029\pi\)
\(822\) −0.507314 + 1.98801i −0.0176946 + 0.0693399i
\(823\) 36.4257 21.0304i 1.26972 0.733073i 0.294785 0.955564i \(-0.404752\pi\)
0.974935 + 0.222490i \(0.0714186\pi\)
\(824\) 24.7821 26.6252i 0.863327 0.927532i
\(825\) 4.75426 17.7432i 0.165522 0.617737i
\(826\) −0.235895 19.7468i −0.00820784 0.687079i
\(827\) 13.8427i 0.481359i −0.970605 0.240680i \(-0.922630\pi\)
0.970605 0.240680i \(-0.0773703\pi\)
\(828\) 2.65936 + 1.45181i 0.0924191 + 0.0504538i
\(829\) −7.17828 26.7897i −0.249312 0.930445i −0.971167 0.238400i \(-0.923377\pi\)
0.721855 0.692044i \(-0.243290\pi\)
\(830\) −9.24422 2.35900i −0.320872 0.0818821i
\(831\) 18.9838 0.658541
\(832\) −18.2530 22.3344i −0.632810 0.774308i
\(833\) 5.40912 0.187415
\(834\) −18.9470 4.83503i −0.656082 0.167423i
\(835\) 1.44547 + 5.39458i 0.0500227 + 0.186687i
\(836\) 13.4869 + 7.36279i 0.466453 + 0.254647i
\(837\) 8.80326i 0.304285i
\(838\) 0.0834543 + 6.98596i 0.00288288 + 0.241326i
\(839\) −2.06752 + 7.71608i −0.0713786 + 0.266389i −0.992388 0.123152i \(-0.960700\pi\)
0.921009 + 0.389541i \(0.127366\pi\)
\(840\) −2.41541 + 2.59504i −0.0833395 + 0.0895375i
\(841\) −22.1160 + 12.7687i −0.762619 + 0.440298i
\(842\) −7.90026 + 30.9588i −0.272261 + 1.06691i
\(843\) 17.8500 + 10.3057i 0.614785 + 0.354946i
\(844\) 11.1514 45.9850i 0.383847 1.58287i
\(845\) 6.53361 + 2.33907i 0.224763 + 0.0804664i
\(846\) 7.99337 14.2349i 0.274818 0.489407i
\(847\) −9.47491 + 2.53880i −0.325562 + 0.0872340i
\(848\) 35.9726 + 7.81851i 1.23530 + 0.268489i
\(849\) 4.53870 2.62042i 0.155768 0.0899326i
\(850\) 23.3548 6.55788i 0.801062 0.224934i
\(851\) −13.8697 + 8.00765i −0.475446 + 0.274499i
\(852\) −15.1753 + 27.7975i −0.519897 + 0.952326i
\(853\) −1.98737 −0.0680462 −0.0340231 0.999421i \(-0.510832\pi\)
−0.0340231 + 0.999421i \(0.510832\pi\)
\(854\) 24.1105 + 23.5413i 0.825045 + 0.805566i
\(855\) −0.911692 0.526366i −0.0311792 0.0180013i
\(856\) 40.5124 + 21.4926i 1.38469 + 0.734601i
\(857\) −3.92624 −0.134118 −0.0670590 0.997749i \(-0.521362\pi\)
−0.0670590 + 0.997749i \(0.521362\pi\)
\(858\) 2.01976 + 19.7621i 0.0689536 + 0.674666i
\(859\) 12.5948 + 12.5948i 0.429730 + 0.429730i 0.888536 0.458806i \(-0.151723\pi\)
−0.458806 + 0.888536i \(0.651723\pi\)
\(860\) −0.696417 + 0.730514i −0.0237476 + 0.0249103i
\(861\) −5.26164 + 1.40985i −0.179316 + 0.0480476i
\(862\) 16.5016 0.197128i 0.562047 0.00671421i
\(863\) 28.1556 + 28.1556i 0.958428 + 0.958428i 0.999170 0.0407415i \(-0.0129720\pi\)
−0.0407415 + 0.999170i \(0.512972\pi\)
\(864\) −2.53096 + 5.05908i −0.0861049 + 0.172113i
\(865\) 0.100118 0.373644i 0.00340410 0.0127043i
\(866\) 38.0669 10.6889i 1.29356 0.363225i
\(867\) 3.63709 + 0.974555i 0.123522 + 0.0330976i
\(868\) 41.3284 0.987559i 1.40278 0.0335199i
\(869\) −0.756910 + 1.31101i −0.0256764 + 0.0444729i
\(870\) −1.35250 + 0.379775i −0.0458542 + 0.0128756i
\(871\) −9.30574 + 0.838894i −0.315313 + 0.0284248i
\(872\) 5.09313 + 4.74057i 0.172475 + 0.160536i
\(873\) −2.20489 + 0.590799i −0.0746242 + 0.0199955i
\(874\) −4.09380 1.04468i −0.138475 0.0353369i
\(875\) −11.7621 3.15164i −0.397631 0.106545i
\(876\) 5.45067 + 8.94055i 0.184161 + 0.302073i
\(877\) 20.2294 + 35.0384i 0.683099 + 1.18316i 0.974030 + 0.226418i \(0.0727015\pi\)
−0.290931 + 0.956744i \(0.593965\pi\)
\(878\) 1.71776 + 1.67720i 0.0579716 + 0.0566029i
\(879\) −1.12191 + 1.12191i −0.0378411 + 0.0378411i
\(880\) −8.30927 + 0.397333i −0.280105 + 0.0133941i
\(881\) −47.4692 27.4063i −1.59928 0.923343i −0.991627 0.129138i \(-0.958779\pi\)
−0.607650 0.794205i \(-0.707888\pi\)
\(882\) −2.03745 0.519930i −0.0686045 0.0175069i
\(883\) −23.0875 23.0875i −0.776955 0.776955i 0.202357 0.979312i \(-0.435140\pi\)
−0.979312 + 0.202357i \(0.935140\pi\)
\(884\) −21.0826 + 15.6117i −0.709084 + 0.525078i
\(885\) −2.24489 + 2.24489i −0.0754611 + 0.0754611i
\(886\) 9.39776 + 15.8374i 0.315724 + 0.532069i
\(887\) −13.7684 + 23.8476i −0.462297 + 0.800722i −0.999075 0.0430013i \(-0.986308\pi\)
0.536778 + 0.843724i \(0.319641\pi\)
\(888\) −15.8689 25.3430i −0.532524 0.850456i
\(889\) −4.02824 4.02824i −0.135103 0.135103i
\(890\) 11.3733 0.135865i 0.381232 0.00455420i
\(891\) 3.37391 1.94793i 0.113030 0.0652580i
\(892\) −12.4943 3.02989i −0.418341 0.101448i
\(893\) −5.89215 + 21.9898i −0.197173 + 0.735860i
\(894\) 3.02259 + 5.09378i 0.101091 + 0.170362i
\(895\) −0.884041 3.29928i −0.0295502 0.110283i
\(896\) −24.0346 11.3145i −0.802941 0.377990i
\(897\) −1.88169 5.12777i −0.0628279 0.171211i
\(898\) 14.6669 26.1194i 0.489440 0.871617i
\(899\) 14.1867 + 8.19069i 0.473153 + 0.273175i
\(900\) −9.42738 + 0.225271i −0.314246 + 0.00750903i
\(901\) 8.66536 32.3395i 0.288685 1.07739i
\(902\) −11.1450 6.25827i −0.371088 0.208377i
\(903\) 2.14402 + 0.574488i 0.0713484 + 0.0191178i
\(904\) 6.96387 30.2923i 0.231615 1.00751i
\(905\) −5.04469 + 5.04469i −0.167691 + 0.167691i
\(906\) −17.1470 + 17.5616i −0.569670 + 0.583445i
\(907\) 9.47201 + 35.3500i 0.314513 + 1.17378i 0.924442 + 0.381322i \(0.124531\pi\)
−0.609929 + 0.792456i \(0.708802\pi\)
\(908\) −15.7613 + 0.376621i −0.523055 + 0.0124986i
\(909\) 0.625309 0.625309i 0.0207402 0.0207402i
\(910\) 6.35808 0.649821i 0.210768 0.0215414i
\(911\) 29.5059i 0.977572i −0.872404 0.488786i \(-0.837440\pi\)
0.872404 0.488786i \(-0.162560\pi\)
\(912\) 1.67537 7.70829i 0.0554770 0.255247i
\(913\) −24.6167 + 42.6374i −0.814695 + 1.41109i
\(914\) −34.2023 + 0.408580i −1.13131 + 0.0135146i
\(915\) 5.41723i 0.179088i
\(916\) 24.2825 + 13.2564i 0.802318 + 0.438004i
\(917\) −18.4341 31.9287i −0.608746 1.05438i
\(918\) 4.48596 + 2.51901i 0.148059 + 0.0831396i
\(919\) −26.0843 45.1793i −0.860441 1.49033i −0.871504 0.490389i \(-0.836855\pi\)
0.0110625 0.999939i \(-0.496479\pi\)
\(920\) 2.18677 0.670788i 0.0720958 0.0221152i
\(921\) −5.28059 19.7074i −0.174001 0.649382i
\(922\) −11.4349 40.7234i −0.376588 1.34115i
\(923\) 53.5990 19.6688i 1.76423 0.647405i
\(924\) 9.52336 + 15.6209i 0.313296 + 0.513889i
\(925\) 24.9230 43.1679i 0.819463 1.41935i
\(926\) −24.4804 + 14.5264i −0.804475 + 0.477367i
\(927\) 6.43004 + 11.1372i 0.211190 + 0.365792i
\(928\) −5.79800 8.78575i −0.190329 0.288406i
\(929\) 23.4563 + 6.28511i 0.769578 + 0.206208i 0.622185 0.782870i \(-0.286245\pi\)
0.147393 + 0.989078i \(0.452912\pi\)
\(930\) −4.75517 4.64290i −0.155928 0.152247i
\(931\) 2.93219 0.0960988
\(932\) −24.9335 13.6118i −0.816725 0.445869i
\(933\) 13.3699 3.58246i 0.437712 0.117285i
\(934\) −12.5884 21.2144i −0.411905 0.694156i
\(935\) 7.56579i 0.247428i
\(936\) 9.44177 3.85397i 0.308614 0.125971i
\(937\) 33.2231i 1.08535i 0.839942 + 0.542676i \(0.182589\pi\)
−0.839942 + 0.542676i \(0.817411\pi\)
\(938\) −7.40023 + 4.39121i −0.241626 + 0.143378i
\(939\) 21.9121 5.87134i 0.715075 0.191604i
\(940\) −3.47339 11.8253i −0.113290 0.385699i
\(941\) 55.8728 1.82140 0.910701 0.413066i \(-0.135542\pi\)
0.910701 + 0.413066i \(0.135542\pi\)
\(942\) −4.72944 + 4.84380i −0.154093 + 0.157820i
\(943\) 3.39478 + 0.909628i 0.110549 + 0.0296216i
\(944\) −21.1464 10.8968i −0.688255 0.354662i
\(945\) −0.626709 1.08549i −0.0203868 0.0353110i
\(946\) 2.65788 + 4.47916i 0.0864152 + 0.145630i
\(947\) −24.9573 + 43.2273i −0.811003 + 1.40470i 0.101160 + 0.994870i \(0.467744\pi\)
−0.912163 + 0.409828i \(0.865589\pi\)
\(948\) 0.755255 + 0.183150i 0.0245296 + 0.00594844i
\(949\) 3.22889 18.5988i 0.104814 0.603742i
\(950\) 12.6602 3.55492i 0.410752 0.115337i
\(951\) 0.158743 + 0.592435i 0.00514758 + 0.0192110i
\(952\) −11.3227 + 21.3427i −0.366970 + 0.691721i
\(953\) 29.5801 + 51.2342i 0.958192 + 1.65964i 0.726888 + 0.686756i \(0.240966\pi\)
0.231304 + 0.972882i \(0.425701\pi\)
\(954\) −6.37248 + 11.3484i −0.206317 + 0.367418i
\(955\) 2.59748 + 4.49896i 0.0840524 + 0.145583i
\(956\) 12.4083 + 42.2446i 0.401314 + 1.36629i
\(957\) 7.24952i 0.234344i
\(958\) 0.137656 + 11.5232i 0.00444745 + 0.372296i
\(959\) 1.70323 2.95008i 0.0550001 0.0952630i
\(960\) 1.39787 + 4.03532i 0.0451160 + 0.130239i
\(961\) 46.4974i 1.49992i
\(962\) −8.58539 + 53.2173i −0.276804 + 1.71579i
\(963\) −11.4651 + 11.4651i −0.369459 + 0.369459i
\(964\) 41.8506 43.8997i 1.34792 1.41391i
\(965\) 1.28088 + 4.78032i 0.0412331 + 0.153884i
\(966\) −3.59928 3.51430i −0.115805 0.113071i
\(967\) −37.7368 + 37.7368i −1.21353 + 1.21353i −0.243678 + 0.969856i \(0.578354\pi\)
−0.969856 + 0.243678i \(0.921646\pi\)
\(968\) −2.64736 + 11.5158i −0.0850893 + 0.370132i
\(969\) −6.92980 1.85683i −0.222617 0.0596501i
\(970\) −0.843749 + 1.50259i −0.0270912 + 0.0482451i
\(971\) −9.38772 + 35.0354i −0.301266 + 1.12434i 0.634846 + 0.772639i \(0.281064\pi\)
−0.936112 + 0.351702i \(0.885603\pi\)
\(972\) −1.44759 1.38003i −0.0464316 0.0442644i
\(973\) 28.1161 + 16.2329i 0.901362 + 0.520402i
\(974\) −8.75696 4.91731i −0.280591 0.157561i
\(975\) 13.0518 + 10.8932i 0.417991 + 0.348861i
\(976\) 38.6623 12.3668i 1.23755 0.395850i
\(977\) 14.8071 + 55.2610i 0.473722 + 1.76795i 0.626215 + 0.779650i \(0.284603\pi\)
−0.152493 + 0.988305i \(0.548730\pi\)
\(978\) 15.7932 9.37151i 0.505011 0.299668i
\(979\) 15.1916 56.6957i 0.485525 1.81200i
\(980\) −1.35541 + 0.826336i −0.0432970 + 0.0263963i
\(981\) −2.13043 + 1.23000i −0.0680193 + 0.0392710i
\(982\) −0.183595 15.3687i −0.00585874 0.490435i
\(983\) −30.8831 30.8831i −0.985018 0.985018i 0.0148712 0.999889i \(-0.495266\pi\)
−0.999889 + 0.0148712i \(0.995266\pi\)
\(984\) −1.47014 + 6.39499i −0.0468663 + 0.203865i
\(985\) −6.73277 + 11.6615i −0.214524 + 0.371566i
\(986\) −8.23325 + 4.88552i −0.262200 + 0.155587i
\(987\) −19.1664 + 19.1664i −0.610073 + 0.610073i
\(988\) −11.4285 + 8.46283i −0.363589 + 0.269238i
\(989\) −1.01265 1.01265i −0.0322005 0.0322005i
\(990\) 0.727230 2.84980i 0.0231129 0.0905726i
\(991\) 27.0595 + 15.6228i 0.859574 + 0.496275i 0.863870 0.503716i \(-0.168034\pi\)
−0.00429580 + 0.999991i \(0.501367\pi\)
\(992\) 22.2807 44.5364i 0.707412 1.41403i
\(993\) −23.2000 + 23.2000i −0.736231 + 0.736231i
\(994\) 36.7339 37.6222i 1.16513 1.19330i
\(995\) 1.05881 + 1.83391i 0.0335666 + 0.0581390i
\(996\) 24.5629 + 5.95653i 0.778306 + 0.188740i
\(997\) 9.89613 + 2.65166i 0.313413 + 0.0839789i 0.412097 0.911140i \(-0.364796\pi\)
−0.0986835 + 0.995119i \(0.531463\pi\)
\(998\) −0.933709 + 3.65893i −0.0295560 + 0.115821i
\(999\) 10.2115 2.73616i 0.323077 0.0865683i
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 624.2.ch.a.19.52 224
13.11 odd 12 624.2.cz.a.115.15 yes 224
16.11 odd 4 624.2.cz.a.331.15 yes 224
208.11 even 12 inner 624.2.ch.a.427.52 yes 224
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
624.2.ch.a.19.52 224 1.1 even 1 trivial
624.2.ch.a.427.52 yes 224 208.11 even 12 inner
624.2.cz.a.115.15 yes 224 13.11 odd 12
624.2.cz.a.331.15 yes 224 16.11 odd 4