Properties

Label 378.2.z.a.209.16
Level $378$
Weight $2$
Character 378.209
Analytic conductor $3.018$
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] = [378,2,Mod(41,378)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(378, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([17, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("378.41");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 378.z (of order \(18\), degree \(6\), 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: \(3.01834519640\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 209.16
Character \(\chi\) \(=\) 378.209
Dual form 378.2.z.a.293.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.342020 + 0.939693i) q^{2} +(-1.29192 + 1.15367i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.588971 - 3.34022i) q^{5} +(-1.52595 - 0.819431i) q^{6} +(-2.60253 + 0.476291i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.338113 - 2.98089i) q^{9} +O(q^{10})\) \(q+(0.342020 + 0.939693i) q^{2} +(-1.29192 + 1.15367i) q^{3} +(-0.766044 + 0.642788i) q^{4} +(-0.588971 - 3.34022i) q^{5} +(-1.52595 - 0.819431i) q^{6} +(-2.60253 + 0.476291i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.338113 - 2.98089i) q^{9} +(2.93734 - 1.69587i) q^{10} +(5.82199 + 1.02657i) q^{11} +(0.248106 - 1.71419i) q^{12} +(1.71844 - 4.72138i) q^{13} +(-1.33768 - 2.28267i) q^{14} +(4.61440 + 3.63582i) q^{15} +(0.173648 - 0.984808i) q^{16} +(-0.893547 - 1.54767i) q^{17} +(2.91676 - 0.701801i) q^{18} +(1.39029 + 0.802683i) q^{19} +(2.59823 + 2.18017i) q^{20} +(2.81278 - 3.61777i) q^{21} +(1.02657 + 5.82199i) q^{22} +(-2.97175 - 3.54159i) q^{23} +(1.69567 - 0.353144i) q^{24} +(-6.11171 + 2.22448i) q^{25} +5.02439 q^{26} +(3.00213 + 4.24113i) q^{27} +(1.68750 - 2.03773i) q^{28} +(-0.134460 - 0.369425i) q^{29} +(-1.83834 + 5.57964i) q^{30} +(-5.48946 - 6.54208i) q^{31} +(0.984808 - 0.173648i) q^{32} +(-8.70587 + 5.39038i) q^{33} +(1.14872 - 1.36899i) q^{34} +(3.12373 + 8.41249i) q^{35} +(1.65707 + 2.50083i) q^{36} +(-3.02735 - 5.24352i) q^{37} +(-0.278769 + 1.58098i) q^{38} +(3.22680 + 8.08215i) q^{39} +(-1.16005 + 3.18720i) q^{40} +(4.59052 + 1.67081i) q^{41} +(4.36162 + 1.40579i) q^{42} +(1.47068 - 8.34064i) q^{43} +(-5.11977 + 2.95590i) q^{44} +(-10.1559 + 0.626284i) q^{45} +(2.31161 - 4.00383i) q^{46} +(4.18245 + 3.50949i) q^{47} +(0.911799 + 1.47262i) q^{48} +(6.54629 - 2.47912i) q^{49} +(-4.18066 - 4.98231i) q^{50} +(2.93988 + 0.968610i) q^{51} +(1.71844 + 4.72138i) q^{52} +3.16613i q^{53} +(-2.95857 + 4.27163i) q^{54} -20.0514i q^{55} +(2.49200 + 0.888783i) q^{56} +(-2.72217 + 0.566925i) q^{57} +(0.301158 - 0.252702i) q^{58} +(0.911701 + 5.17051i) q^{59} +(-5.87189 + 0.180878i) q^{60} +(-2.75704 + 3.28571i) q^{61} +(4.27004 - 7.39593i) q^{62} +(0.539822 + 7.91888i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-16.7825 - 2.95922i) q^{65} +(-8.04288 - 6.33722i) q^{66} +(-10.1189 - 3.68299i) q^{67} +(1.67932 + 0.611222i) q^{68} +(7.92508 + 1.14705i) q^{69} +(-6.83677 + 5.81258i) q^{70} +(8.84053 - 5.10408i) q^{71} +(-1.78326 + 2.41247i) q^{72} +(-1.36302 - 0.786939i) q^{73} +(3.89188 - 4.63816i) q^{74} +(5.32953 - 9.92472i) q^{75} +(-1.58098 + 0.278769i) q^{76} +(-15.6408 + 0.101275i) q^{77} +(-6.49110 + 5.79646i) q^{78} +(-12.3072 + 4.47946i) q^{79} -3.39175 q^{80} +(-8.77136 - 2.01575i) q^{81} +4.88513i q^{82} +(-4.62440 + 1.68314i) q^{83} +(0.170750 + 4.57939i) q^{84} +(-4.64328 + 3.89617i) q^{85} +(8.34064 - 1.47068i) q^{86} +(0.599904 + 0.322146i) q^{87} +(-4.52871 - 3.80004i) q^{88} +(-0.381819 + 0.661330i) q^{89} +(-4.06205 - 9.32927i) q^{90} +(-2.22354 + 13.1060i) q^{91} +(4.55299 + 0.802814i) q^{92} +(14.6393 + 2.11885i) q^{93} +(-1.86736 + 5.13053i) q^{94} +(1.86230 - 5.11662i) q^{95} +(-1.07196 + 1.36048i) q^{96} +(6.77329 + 1.19431i) q^{97} +(4.56858 + 5.30359i) q^{98} +(5.02859 - 17.0076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(325\)
\(\chi(n)\) \(e\left(\frac{7}{18}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.342020 + 0.939693i 0.241845 + 0.664463i
\(3\) −1.29192 + 1.15367i −0.745890 + 0.666069i
\(4\) −0.766044 + 0.642788i −0.383022 + 0.321394i
\(5\) −0.588971 3.34022i −0.263396 1.49379i −0.773565 0.633717i \(-0.781528\pi\)
0.510169 0.860074i \(-0.329583\pi\)
\(6\) −1.52595 0.819431i −0.622968 0.334531i
\(7\) −2.60253 + 0.476291i −0.983663 + 0.180021i
\(8\) −0.866025 0.500000i −0.306186 0.176777i
\(9\) 0.338113 2.98089i 0.112704 0.993629i
\(10\) 2.93734 1.69587i 0.928868 0.536282i
\(11\) 5.82199 + 1.02657i 1.75540 + 0.309524i 0.956454 0.291883i \(-0.0942818\pi\)
0.798943 + 0.601407i \(0.205393\pi\)
\(12\) 0.248106 1.71419i 0.0716220 0.494844i
\(13\) 1.71844 4.72138i 0.476610 1.30947i −0.435744 0.900071i \(-0.643515\pi\)
0.912353 0.409404i \(-0.134263\pi\)
\(14\) −1.33768 2.28267i −0.357511 0.610070i
\(15\) 4.61440 + 3.63582i 1.19143 + 0.938764i
\(16\) 0.173648 0.984808i 0.0434120 0.246202i
\(17\) −0.893547 1.54767i −0.216717 0.375365i 0.737085 0.675800i \(-0.236202\pi\)
−0.953802 + 0.300435i \(0.902868\pi\)
\(18\) 2.91676 0.701801i 0.687486 0.165416i
\(19\) 1.39029 + 0.802683i 0.318954 + 0.184148i 0.650926 0.759141i \(-0.274381\pi\)
−0.331972 + 0.943289i \(0.607714\pi\)
\(20\) 2.59823 + 2.18017i 0.580982 + 0.487501i
\(21\) 2.81278 3.61777i 0.613798 0.789463i
\(22\) 1.02657 + 5.82199i 0.218866 + 1.24125i
\(23\) −2.97175 3.54159i −0.619653 0.738474i 0.361358 0.932427i \(-0.382313\pi\)
−0.981011 + 0.193954i \(0.937869\pi\)
\(24\) 1.69567 0.353144i 0.346127 0.0720852i
\(25\) −6.11171 + 2.22448i −1.22234 + 0.444896i
\(26\) 5.02439 0.985363
\(27\) 3.00213 + 4.24113i 0.577760 + 0.816207i
\(28\) 1.68750 2.03773i 0.318907 0.385095i
\(29\) −0.134460 0.369425i −0.0249686 0.0686005i 0.926582 0.376092i \(-0.122733\pi\)
−0.951551 + 0.307492i \(0.900510\pi\)
\(30\) −1.83834 + 5.57964i −0.335633 + 1.01870i
\(31\) −5.48946 6.54208i −0.985936 1.17499i −0.984570 0.174994i \(-0.944009\pi\)
−0.00136659 0.999999i \(-0.500435\pi\)
\(32\) 0.984808 0.173648i 0.174091 0.0306970i
\(33\) −8.70587 + 5.39038i −1.51550 + 0.938345i
\(34\) 1.14872 1.36899i 0.197004 0.234781i
\(35\) 3.12373 + 8.41249i 0.528006 + 1.42197i
\(36\) 1.65707 + 2.50083i 0.276178 + 0.416804i
\(37\) −3.02735 5.24352i −0.497693 0.862029i 0.502304 0.864691i \(-0.332486\pi\)
−0.999996 + 0.00266226i \(0.999153\pi\)
\(38\) −0.278769 + 1.58098i −0.0452223 + 0.256468i
\(39\) 3.22680 + 8.08215i 0.516702 + 1.29418i
\(40\) −1.16005 + 3.18720i −0.183419 + 0.503940i
\(41\) 4.59052 + 1.67081i 0.716919 + 0.260937i 0.674617 0.738168i \(-0.264309\pi\)
0.0423018 + 0.999105i \(0.486531\pi\)
\(42\) 4.36162 + 1.40579i 0.673013 + 0.216918i
\(43\) 1.47068 8.34064i 0.224277 1.27194i −0.639787 0.768552i \(-0.720977\pi\)
0.864063 0.503383i \(-0.167911\pi\)
\(44\) −5.11977 + 2.95590i −0.771835 + 0.445619i
\(45\) −10.1559 + 0.626284i −1.51396 + 0.0933610i
\(46\) 2.31161 4.00383i 0.340829 0.590332i
\(47\) 4.18245 + 3.50949i 0.610072 + 0.511912i 0.894665 0.446737i \(-0.147414\pi\)
−0.284593 + 0.958648i \(0.591858\pi\)
\(48\) 0.911799 + 1.47262i 0.131607 + 0.212555i
\(49\) 6.54629 2.47912i 0.935185 0.354160i
\(50\) −4.18066 4.98231i −0.591234 0.704605i
\(51\) 2.93988 + 0.968610i 0.411666 + 0.135632i
\(52\) 1.71844 + 4.72138i 0.238305 + 0.654737i
\(53\) 3.16613i 0.434902i 0.976071 + 0.217451i \(0.0697742\pi\)
−0.976071 + 0.217451i \(0.930226\pi\)
\(54\) −2.95857 + 4.27163i −0.402611 + 0.581296i
\(55\) 20.0514i 2.70372i
\(56\) 2.49200 + 0.888783i 0.333008 + 0.118769i
\(57\) −2.72217 + 0.566925i −0.360560 + 0.0750911i
\(58\) 0.301158 0.252702i 0.0395440 0.0331814i
\(59\) 0.911701 + 5.17051i 0.118693 + 0.673143i 0.984855 + 0.173380i \(0.0554687\pi\)
−0.866162 + 0.499764i \(0.833420\pi\)
\(60\) −5.87189 + 0.180878i −0.758058 + 0.0233513i
\(61\) −2.75704 + 3.28571i −0.353002 + 0.420692i −0.913101 0.407734i \(-0.866319\pi\)
0.560098 + 0.828426i \(0.310763\pi\)
\(62\) 4.27004 7.39593i 0.542296 0.939284i
\(63\) 0.539822 + 7.91888i 0.0680112 + 0.997685i
\(64\) 0.500000 + 0.866025i 0.0625000 + 0.108253i
\(65\) −16.7825 2.95922i −2.08162 0.367046i
\(66\) −8.04288 6.33722i −0.990011 0.780058i
\(67\) −10.1189 3.68299i −1.23623 0.449949i −0.360500 0.932759i \(-0.617394\pi\)
−0.875725 + 0.482810i \(0.839616\pi\)
\(68\) 1.67932 + 0.611222i 0.203647 + 0.0741216i
\(69\) 7.92508 + 1.14705i 0.954067 + 0.138089i
\(70\) −6.83677 + 5.81258i −0.817151 + 0.694737i
\(71\) 8.84053 5.10408i 1.04918 0.605743i 0.126759 0.991934i \(-0.459543\pi\)
0.922419 + 0.386190i \(0.126209\pi\)
\(72\) −1.78326 + 2.41247i −0.210159 + 0.284312i
\(73\) −1.36302 0.786939i −0.159529 0.0921042i 0.418110 0.908396i \(-0.362693\pi\)
−0.577639 + 0.816292i \(0.696026\pi\)
\(74\) 3.89188 4.63816i 0.452422 0.539176i
\(75\) 5.32953 9.92472i 0.615401 1.14601i
\(76\) −1.58098 + 0.278769i −0.181351 + 0.0319770i
\(77\) −15.6408 + 0.101275i −1.78244 + 0.0115414i
\(78\) −6.49110 + 5.79646i −0.734973 + 0.656320i
\(79\) −12.3072 + 4.47946i −1.38467 + 0.503979i −0.923591 0.383379i \(-0.874760\pi\)
−0.461080 + 0.887358i \(0.652538\pi\)
\(80\) −3.39175 −0.379209
\(81\) −8.77136 2.01575i −0.974596 0.223972i
\(82\) 4.88513i 0.539472i
\(83\) −4.62440 + 1.68314i −0.507594 + 0.184749i −0.583106 0.812396i \(-0.698163\pi\)
0.0755126 + 0.997145i \(0.475941\pi\)
\(84\) 0.170750 + 4.57939i 0.0186304 + 0.499653i
\(85\) −4.64328 + 3.89617i −0.503634 + 0.422599i
\(86\) 8.34064 1.47068i 0.899394 0.158587i
\(87\) 0.599904 + 0.322146i 0.0643165 + 0.0345377i
\(88\) −4.52871 3.80004i −0.482762 0.405085i
\(89\) −0.381819 + 0.661330i −0.0404728 + 0.0701009i −0.885552 0.464540i \(-0.846220\pi\)
0.845079 + 0.534641i \(0.179553\pi\)
\(90\) −4.06205 9.32927i −0.428178 0.983391i
\(91\) −2.22354 + 13.1060i −0.233090 + 1.37388i
\(92\) 4.55299 + 0.802814i 0.474682 + 0.0836992i
\(93\) 14.6393 + 2.11885i 1.51803 + 0.219714i
\(94\) −1.86736 + 5.13053i −0.192603 + 0.529174i
\(95\) 1.86230 5.11662i 0.191068 0.524955i
\(96\) −1.07196 + 1.36048i −0.109407 + 0.138853i
\(97\) 6.77329 + 1.19431i 0.687724 + 0.121264i 0.506581 0.862193i \(-0.330909\pi\)
0.181143 + 0.983457i \(0.442020\pi\)
\(98\) 4.56858 + 5.30359i 0.461496 + 0.535744i
\(99\) 5.02859 17.0076i 0.505392 1.70933i
\(100\) 3.25197 5.63258i 0.325197 0.563258i
\(101\) 1.25817 + 1.05573i 0.125193 + 0.105049i 0.703234 0.710958i \(-0.251738\pi\)
−0.578042 + 0.816007i \(0.696183\pi\)
\(102\) 0.0953040 + 3.09387i 0.00943650 + 0.306339i
\(103\) 11.8869 2.09598i 1.17125 0.206523i 0.446015 0.895025i \(-0.352843\pi\)
0.725234 + 0.688502i \(0.241732\pi\)
\(104\) −3.84890 + 3.22961i −0.377416 + 0.316690i
\(105\) −13.7408 7.26452i −1.34096 0.708945i
\(106\) −2.97519 + 1.08288i −0.288976 + 0.105179i
\(107\) 6.36147i 0.614986i 0.951550 + 0.307493i \(0.0994901\pi\)
−0.951550 + 0.307493i \(0.900510\pi\)
\(108\) −5.02591 1.31916i −0.483619 0.126937i
\(109\) 4.54397 0.435234 0.217617 0.976034i \(-0.430172\pi\)
0.217617 + 0.976034i \(0.430172\pi\)
\(110\) 18.8421 6.85797i 1.79652 0.653881i
\(111\) 9.96035 + 3.28166i 0.945395 + 0.311481i
\(112\) 0.0171310 + 2.64570i 0.00161873 + 0.249995i
\(113\) 13.8518 2.44245i 1.30307 0.229766i 0.521321 0.853361i \(-0.325440\pi\)
0.781748 + 0.623595i \(0.214328\pi\)
\(114\) −1.46377 2.36410i −0.137095 0.221418i
\(115\) −10.0794 + 12.0122i −0.939911 + 1.12014i
\(116\) 0.340464 + 0.196567i 0.0316113 + 0.0182508i
\(117\) −13.4929 6.71883i −1.24742 0.621156i
\(118\) −4.54687 + 2.62514i −0.418573 + 0.241664i
\(119\) 3.06262 + 3.60226i 0.280750 + 0.330219i
\(120\) −2.17828 5.45591i −0.198848 0.498054i
\(121\) 22.5051 + 8.19120i 2.04592 + 0.744654i
\(122\) −4.03052 1.46699i −0.364906 0.132815i
\(123\) −7.85814 + 3.13737i −0.708545 + 0.282887i
\(124\) 8.41034 + 1.48297i 0.755271 + 0.133175i
\(125\) 2.55050 + 4.41760i 0.228124 + 0.395122i
\(126\) −7.25668 + 3.21568i −0.646476 + 0.286476i
\(127\) −10.3565 + 17.9380i −0.918993 + 1.59174i −0.118047 + 0.993008i \(0.537663\pi\)
−0.800947 + 0.598735i \(0.795670\pi\)
\(128\) −0.642788 + 0.766044i −0.0568149 + 0.0677094i
\(129\) 7.72230 + 12.4721i 0.679911 + 1.09811i
\(130\) −2.95922 16.7825i −0.259540 1.47193i
\(131\) −4.24237 + 3.55977i −0.370657 + 0.311018i −0.809021 0.587779i \(-0.800002\pi\)
0.438364 + 0.898797i \(0.355558\pi\)
\(132\) 3.20421 9.72530i 0.278891 0.846478i
\(133\) −4.00057 1.42682i −0.346894 0.123721i
\(134\) 10.7684i 0.930244i
\(135\) 12.3981 12.5257i 1.06706 1.07804i
\(136\) 1.78709i 0.153242i
\(137\) 0.439665 + 1.20797i 0.0375631 + 0.103204i 0.957056 0.289902i \(-0.0936228\pi\)
−0.919493 + 0.393106i \(0.871401\pi\)
\(138\) 1.63266 + 7.83945i 0.138981 + 0.667338i
\(139\) 7.76148 + 9.24977i 0.658320 + 0.784555i 0.987144 0.159836i \(-0.0510966\pi\)
−0.328824 + 0.944391i \(0.606652\pi\)
\(140\) −7.80036 4.43645i −0.659251 0.374948i
\(141\) −9.45216 + 0.291165i −0.796015 + 0.0245206i
\(142\) 7.81991 + 6.56168i 0.656232 + 0.550644i
\(143\) 14.8516 25.7237i 1.24195 2.15113i
\(144\) −2.87689 0.850601i −0.239741 0.0708834i
\(145\) −1.15477 + 0.666706i −0.0958983 + 0.0553669i
\(146\) 0.273301 1.54997i 0.0226185 0.128276i
\(147\) −5.59721 + 10.7551i −0.461650 + 0.887062i
\(148\) 5.68955 + 2.07083i 0.467678 + 0.170221i
\(149\) −3.11442 + 8.55680i −0.255143 + 0.701000i 0.744307 + 0.667838i \(0.232780\pi\)
−0.999450 + 0.0331623i \(0.989442\pi\)
\(150\) 11.1490 + 1.61367i 0.910311 + 0.131755i
\(151\) 2.04684 11.6082i 0.166569 0.944662i −0.780862 0.624703i \(-0.785220\pi\)
0.947432 0.319958i \(-0.103669\pi\)
\(152\) −0.802683 1.39029i −0.0651062 0.112767i
\(153\) −4.91554 + 2.14028i −0.397398 + 0.173031i
\(154\) −5.44465 14.6629i −0.438742 1.18157i
\(155\) −18.6189 + 22.1891i −1.49550 + 1.78227i
\(156\) −7.66698 4.11713i −0.613849 0.329635i
\(157\) −9.79853 + 1.72775i −0.782008 + 0.137889i −0.550379 0.834915i \(-0.685517\pi\)
−0.231629 + 0.972804i \(0.574406\pi\)
\(158\) −8.41864 10.0329i −0.669751 0.798178i
\(159\) −3.65266 4.09039i −0.289675 0.324389i
\(160\) −1.16005 3.18720i −0.0917097 0.251970i
\(161\) 9.42089 + 7.80168i 0.742470 + 0.614858i
\(162\) −1.10580 8.93181i −0.0868796 0.701749i
\(163\) 2.03725 0.159570 0.0797848 0.996812i \(-0.474577\pi\)
0.0797848 + 0.996812i \(0.474577\pi\)
\(164\) −4.59052 + 1.67081i −0.358460 + 0.130469i
\(165\) 23.1325 + 25.9047i 1.80087 + 2.01668i
\(166\) −3.16328 3.76984i −0.245518 0.292597i
\(167\) −2.52761 14.3348i −0.195592 1.10926i −0.911573 0.411139i \(-0.865131\pi\)
0.715980 0.698120i \(-0.245980\pi\)
\(168\) −4.24482 + 1.72670i −0.327495 + 0.133218i
\(169\) −9.37979 7.87058i −0.721522 0.605429i
\(170\) −5.24930 3.03069i −0.402603 0.232443i
\(171\) 2.86278 3.87289i 0.218922 0.296168i
\(172\) 4.23465 + 7.33463i 0.322889 + 0.559261i
\(173\) 2.50773 14.2220i 0.190659 1.08128i −0.727807 0.685782i \(-0.759460\pi\)
0.918466 0.395500i \(-0.129429\pi\)
\(174\) −0.0975389 + 0.673906i −0.00739441 + 0.0510887i
\(175\) 14.8464 8.70022i 1.12228 0.657675i
\(176\) 2.02196 5.55528i 0.152411 0.418745i
\(177\) −7.14288 5.62809i −0.536892 0.423033i
\(178\) −0.752037 0.132604i −0.0563676 0.00993912i
\(179\) 21.3104 12.3036i 1.59282 0.919612i 0.599994 0.800005i \(-0.295170\pi\)
0.992821 0.119608i \(-0.0381637\pi\)
\(180\) 7.37734 7.00788i 0.549874 0.522336i
\(181\) 6.64468 + 3.83631i 0.493895 + 0.285150i 0.726189 0.687495i \(-0.241290\pi\)
−0.232294 + 0.972646i \(0.574623\pi\)
\(182\) −13.0761 + 2.39307i −0.969265 + 0.177386i
\(183\) −0.228738 7.42557i −0.0169088 0.548914i
\(184\) 0.802814 + 4.55299i 0.0591843 + 0.335651i
\(185\) −15.7315 + 13.2003i −1.15660 + 0.970504i
\(186\) 3.01588 + 14.4811i 0.221135 + 1.06181i
\(187\) −3.61343 9.92781i −0.264240 0.725994i
\(188\) −5.45980 −0.398197
\(189\) −9.83314 9.60778i −0.715256 0.698863i
\(190\) 5.44500 0.395022
\(191\) 9.16428 + 25.1787i 0.663104 + 1.82186i 0.562258 + 0.826962i \(0.309933\pi\)
0.100846 + 0.994902i \(0.467845\pi\)
\(192\) −1.64506 0.542003i −0.118722 0.0391157i
\(193\) −1.68733 + 1.41584i −0.121457 + 0.101914i −0.701493 0.712676i \(-0.747483\pi\)
0.580036 + 0.814591i \(0.303038\pi\)
\(194\) 1.19431 + 6.77329i 0.0857467 + 0.486294i
\(195\) 25.0956 15.5384i 1.79714 1.11273i
\(196\) −3.42120 + 6.10699i −0.244372 + 0.436214i
\(197\) −7.23110 4.17488i −0.515195 0.297448i 0.219772 0.975551i \(-0.429469\pi\)
−0.734966 + 0.678103i \(0.762802\pi\)
\(198\) 17.7018 1.09161i 1.25801 0.0775775i
\(199\) 13.2610 7.65623i 0.940046 0.542736i 0.0500710 0.998746i \(-0.484055\pi\)
0.889975 + 0.456010i \(0.150722\pi\)
\(200\) 6.40514 + 1.12940i 0.452912 + 0.0798605i
\(201\) 17.3218 6.91574i 1.22179 0.487799i
\(202\) −0.561742 + 1.54337i −0.0395240 + 0.108591i
\(203\) 0.525889 + 0.897397i 0.0369102 + 0.0629849i
\(204\) −2.87469 + 1.14772i −0.201269 + 0.0803567i
\(205\) 2.87720 16.3174i 0.200952 1.13966i
\(206\) 6.03513 + 10.4531i 0.420487 + 0.728305i
\(207\) −11.5619 + 7.66099i −0.803606 + 0.532476i
\(208\) −4.35125 2.51219i −0.301705 0.174189i
\(209\) 7.27024 + 6.10045i 0.502893 + 0.421977i
\(210\) 2.12679 15.3967i 0.146762 1.06248i
\(211\) 3.76549 + 21.3551i 0.259227 + 1.47015i 0.784985 + 0.619514i \(0.212670\pi\)
−0.525759 + 0.850634i \(0.676218\pi\)
\(212\) −2.03515 2.42540i −0.139775 0.166577i
\(213\) −5.53285 + 16.7931i −0.379105 + 1.15064i
\(214\) −5.97783 + 2.17575i −0.408636 + 0.148731i
\(215\) −28.7257 −1.95908
\(216\) −0.479354 5.17399i −0.0326159 0.352046i
\(217\) 17.4024 + 14.4114i 1.18135 + 0.978307i
\(218\) 1.55413 + 4.26994i 0.105259 + 0.289197i
\(219\) 2.66877 0.555805i 0.180339 0.0375578i
\(220\) 12.8888 + 15.3602i 0.868960 + 1.03559i
\(221\) −8.84264 + 1.55920i −0.594820 + 0.104883i
\(222\) 0.322891 + 10.4821i 0.0216710 + 0.703510i
\(223\) −12.6316 + 15.0537i −0.845874 + 1.00807i 0.153927 + 0.988082i \(0.450808\pi\)
−0.999800 + 0.0199906i \(0.993636\pi\)
\(224\) −2.48028 + 0.920979i −0.165721 + 0.0615355i
\(225\) 4.56448 + 18.9704i 0.304298 + 1.26470i
\(226\) 7.03275 + 12.1811i 0.467811 + 0.810273i
\(227\) −1.95774 + 11.1029i −0.129940 + 0.736924i 0.848311 + 0.529498i \(0.177620\pi\)
−0.978251 + 0.207426i \(0.933491\pi\)
\(228\) 1.72089 2.18407i 0.113969 0.144643i
\(229\) −4.81100 + 13.2181i −0.317920 + 0.873478i 0.673074 + 0.739575i \(0.264973\pi\)
−0.990994 + 0.133903i \(0.957249\pi\)
\(230\) −14.7351 5.36315i −0.971606 0.353636i
\(231\) 20.0899 18.1751i 1.32182 1.19584i
\(232\) −0.0682670 + 0.387162i −0.00448195 + 0.0254184i
\(233\) 5.82309 3.36196i 0.381483 0.220250i −0.296980 0.954884i \(-0.595980\pi\)
0.678463 + 0.734634i \(0.262646\pi\)
\(234\) 1.69881 14.9771i 0.111055 0.979085i
\(235\) 9.25912 16.0373i 0.603999 1.04616i
\(236\) −4.02194 3.37481i −0.261806 0.219682i
\(237\) 10.7321 19.9855i 0.697128 1.29820i
\(238\) −2.33754 + 4.10997i −0.151520 + 0.266410i
\(239\) 13.2190 + 15.7538i 0.855064 + 1.01903i 0.999564 + 0.0295212i \(0.00939824\pi\)
−0.144500 + 0.989505i \(0.546157\pi\)
\(240\) 4.38186 3.91294i 0.282848 0.252579i
\(241\) −7.91792 21.7543i −0.510038 1.40132i −0.881197 0.472749i \(-0.843262\pi\)
0.371159 0.928569i \(-0.378961\pi\)
\(242\) 23.9495i 1.53953i
\(243\) 13.6574 7.51503i 0.876122 0.482089i
\(244\) 4.28919i 0.274587i
\(245\) −12.1364 20.4059i −0.775365 1.30369i
\(246\) −5.63581 6.31120i −0.359326 0.402387i
\(247\) 6.17890 5.18471i 0.393154 0.329895i
\(248\) 1.48297 + 8.41034i 0.0941687 + 0.534057i
\(249\) 4.03257 7.50950i 0.255554 0.475895i
\(250\) −3.27886 + 3.90760i −0.207373 + 0.247138i
\(251\) 10.9424 18.9528i 0.690679 1.19629i −0.280937 0.959726i \(-0.590645\pi\)
0.971616 0.236564i \(-0.0760214\pi\)
\(252\) −5.50368 5.71922i −0.346699 0.360277i
\(253\) −13.6658 23.6699i −0.859162 1.48811i
\(254\) −20.3984 3.59679i −1.27991 0.225682i
\(255\) 1.50386 10.3903i 0.0941756 0.650668i
\(256\) −0.939693 0.342020i −0.0587308 0.0213763i
\(257\) 9.38249 + 3.41495i 0.585264 + 0.213019i 0.617645 0.786457i \(-0.288087\pi\)
−0.0323813 + 0.999476i \(0.510309\pi\)
\(258\) −9.07876 + 11.5223i −0.565219 + 0.717347i
\(259\) 10.3762 + 12.2045i 0.644745 + 0.758351i
\(260\) 14.7583 8.52072i 0.915272 0.528433i
\(261\) −1.14668 + 0.275902i −0.0709775 + 0.0170779i
\(262\) −4.79606 2.76901i −0.296302 0.171070i
\(263\) 11.3621 13.5408i 0.700616 0.834961i −0.291980 0.956424i \(-0.594314\pi\)
0.992596 + 0.121463i \(0.0387586\pi\)
\(264\) 10.2347 0.315271i 0.629902 0.0194036i
\(265\) 10.5756 1.86476i 0.649653 0.114551i
\(266\) −0.0275015 4.24731i −0.00168623 0.260419i
\(267\) −0.269674 1.29488i −0.0165038 0.0792452i
\(268\) 10.1189 3.68299i 0.618113 0.224975i
\(269\) −23.7183 −1.44613 −0.723065 0.690780i \(-0.757267\pi\)
−0.723065 + 0.690780i \(0.757267\pi\)
\(270\) 16.0107 + 7.36641i 0.974380 + 0.448306i
\(271\) 7.59459i 0.461339i −0.973032 0.230669i \(-0.925908\pi\)
0.973032 0.230669i \(-0.0740915\pi\)
\(272\) −1.67932 + 0.611222i −0.101824 + 0.0370608i
\(273\) −12.2473 19.4971i −0.741240 1.18002i
\(274\) −0.984746 + 0.826300i −0.0594907 + 0.0499186i
\(275\) −37.8659 + 6.67679i −2.28340 + 0.402625i
\(276\) −6.80827 + 4.21545i −0.409810 + 0.253740i
\(277\) −0.314131 0.263587i −0.0188743 0.0158374i 0.633302 0.773905i \(-0.281699\pi\)
−0.652176 + 0.758068i \(0.726144\pi\)
\(278\) −6.03736 + 10.4570i −0.362097 + 0.627170i
\(279\) −21.3573 + 14.1515i −1.27863 + 0.847228i
\(280\) 1.50102 8.84729i 0.0897029 0.528727i
\(281\) −0.919047 0.162053i −0.0548257 0.00966726i 0.146168 0.989260i \(-0.453306\pi\)
−0.200994 + 0.979593i \(0.564417\pi\)
\(282\) −3.50644 8.78254i −0.208805 0.522993i
\(283\) 1.62474 4.46394i 0.0965808 0.265354i −0.881989 0.471271i \(-0.843795\pi\)
0.978569 + 0.205917i \(0.0660177\pi\)
\(284\) −3.49140 + 9.59254i −0.207176 + 0.569212i
\(285\) 3.49693 + 8.75874i 0.207140 + 0.518823i
\(286\) 29.2519 + 5.15791i 1.72970 + 0.304993i
\(287\) −12.7428 2.16191i −0.752181 0.127614i
\(288\) −0.184650 2.99431i −0.0108806 0.176442i
\(289\) 6.90315 11.9566i 0.406067 0.703329i
\(290\) −1.02145 0.857100i −0.0599817 0.0503307i
\(291\) −10.1284 + 6.27115i −0.593737 + 0.367622i
\(292\) 1.54997 0.273301i 0.0907049 0.0159937i
\(293\) 19.8636 16.6675i 1.16044 0.973727i 0.160531 0.987031i \(-0.448679\pi\)
0.999911 + 0.0133043i \(0.00423502\pi\)
\(294\) −12.0208 1.58121i −0.701068 0.0922181i
\(295\) 16.7337 6.09056i 0.974272 0.354606i
\(296\) 6.05469i 0.351922i
\(297\) 13.1245 + 27.7738i 0.761563 + 1.61160i
\(298\) −9.10595 −0.527494
\(299\) −21.8280 + 7.94474i −1.26234 + 0.459456i
\(300\) 2.29683 + 11.0285i 0.132607 + 0.636733i
\(301\) 0.145088 + 22.4072i 0.00836271 + 1.29153i
\(302\) 11.6082 2.04684i 0.667977 0.117782i
\(303\) −2.84341 + 0.0875888i −0.163350 + 0.00503185i
\(304\) 1.03191 1.22978i 0.0591841 0.0705329i
\(305\) 12.5988 + 7.27392i 0.721405 + 0.416503i
\(306\) −3.69242 3.88708i −0.211081 0.222210i
\(307\) −11.3241 + 6.53797i −0.646300 + 0.373142i −0.787037 0.616905i \(-0.788386\pi\)
0.140737 + 0.990047i \(0.455053\pi\)
\(308\) 11.9165 10.1313i 0.679005 0.577286i
\(309\) −12.9388 + 16.4213i −0.736065 + 0.934176i
\(310\) −27.2189 9.90689i −1.54593 0.562673i
\(311\) −15.8107 5.75464i −0.896545 0.326316i −0.147677 0.989036i \(-0.547180\pi\)
−0.748867 + 0.662720i \(0.769402\pi\)
\(312\) 1.24658 8.61275i 0.0705737 0.487601i
\(313\) −3.78665 0.667688i −0.214034 0.0377400i 0.0656029 0.997846i \(-0.479103\pi\)
−0.279637 + 0.960106i \(0.590214\pi\)
\(314\) −4.97485 8.61669i −0.280747 0.486268i
\(315\) 26.1328 6.46711i 1.47242 0.364380i
\(316\) 6.54854 11.3424i 0.368384 0.638060i
\(317\) −4.08949 + 4.87367i −0.229689 + 0.273732i −0.868563 0.495579i \(-0.834956\pi\)
0.638874 + 0.769311i \(0.279400\pi\)
\(318\) 2.59443 4.83137i 0.145488 0.270930i
\(319\) −0.403581 2.28882i −0.0225962 0.128150i
\(320\) 2.59823 2.18017i 0.145245 0.121875i
\(321\) −7.33901 8.21851i −0.409623 0.458712i
\(322\) −4.10904 + 11.5211i −0.228988 + 0.642044i
\(323\) 2.86894i 0.159632i
\(324\) 8.01495 4.09397i 0.445275 0.227443i
\(325\) 32.6783i 1.81267i
\(326\) 0.696780 + 1.91439i 0.0385911 + 0.106028i
\(327\) −5.87045 + 5.24222i −0.324636 + 0.289896i
\(328\) −3.14010 3.74223i −0.173383 0.206630i
\(329\) −12.5565 7.14148i −0.692260 0.393722i
\(330\) −16.4307 + 30.5974i −0.904480 + 1.68433i
\(331\) −1.60830 1.34953i −0.0884004 0.0741767i 0.597517 0.801857i \(-0.296154\pi\)
−0.685917 + 0.727680i \(0.740599\pi\)
\(332\) 2.46059 4.26187i 0.135042 0.233900i
\(333\) −16.6539 + 7.25127i −0.912629 + 0.397367i
\(334\) 12.6058 7.27796i 0.689759 0.398232i
\(335\) −6.34224 + 35.9687i −0.346514 + 1.96518i
\(336\) −3.07438 3.39826i −0.167721 0.185390i
\(337\) −4.75287 1.72990i −0.258905 0.0942338i 0.209307 0.977850i \(-0.432879\pi\)
−0.468212 + 0.883616i \(0.655102\pi\)
\(338\) 4.18785 11.5060i 0.227789 0.625845i
\(339\) −15.0777 + 19.1358i −0.818906 + 1.03931i
\(340\) 1.05255 5.96929i 0.0570823 0.323730i
\(341\) −25.2437 43.7233i −1.36702 2.36775i
\(342\) 4.61846 + 1.36553i 0.249738 + 0.0738392i
\(343\) −15.8561 + 9.56992i −0.856150 + 0.516727i
\(344\) −5.44396 + 6.48786i −0.293519 + 0.349802i
\(345\) −0.836242 27.1471i −0.0450217 1.46155i
\(346\) 14.2220 2.50773i 0.764582 0.134816i
\(347\) 9.92985 + 11.8339i 0.533062 + 0.635279i 0.963617 0.267285i \(-0.0861266\pi\)
−0.430555 + 0.902564i \(0.641682\pi\)
\(348\) −0.666625 + 0.138833i −0.0357348 + 0.00744222i
\(349\) 7.10042 + 19.5083i 0.380077 + 1.04425i 0.971323 + 0.237762i \(0.0764139\pi\)
−0.591246 + 0.806491i \(0.701364\pi\)
\(350\) 13.2533 + 10.9754i 0.708419 + 0.586659i
\(351\) 25.1830 6.88605i 1.34417 0.367550i
\(352\) 5.91181 0.315100
\(353\) 29.0492 10.5731i 1.54614 0.562747i 0.578628 0.815591i \(-0.303588\pi\)
0.967507 + 0.252844i \(0.0813660\pi\)
\(354\) 2.84566 8.63704i 0.151245 0.459053i
\(355\) −22.2556 26.5231i −1.18120 1.40770i
\(356\) −0.132604 0.752037i −0.00702802 0.0398579i
\(357\) −8.11247 1.12059i −0.429357 0.0593081i
\(358\) 18.8502 + 15.8172i 0.996262 + 0.835963i
\(359\) 0.0115214 + 0.00665186i 0.000608074 + 0.000351072i 0.500304 0.865850i \(-0.333222\pi\)
−0.499696 + 0.866201i \(0.666555\pi\)
\(360\) 9.10845 + 4.53560i 0.480058 + 0.239047i
\(361\) −8.21140 14.2226i −0.432179 0.748556i
\(362\) −1.33234 + 7.55605i −0.0700260 + 0.397137i
\(363\) −38.5247 + 15.3810i −2.02202 + 0.807294i
\(364\) −6.72104 11.4690i −0.352278 0.601141i
\(365\) −1.82577 + 5.01626i −0.0955651 + 0.262563i
\(366\) 6.89952 2.75464i 0.360644 0.143987i
\(367\) 3.00138 + 0.529224i 0.156671 + 0.0276253i 0.251433 0.967875i \(-0.419098\pi\)
−0.0947626 + 0.995500i \(0.530209\pi\)
\(368\) −4.00383 + 2.31161i −0.208714 + 0.120501i
\(369\) 6.53262 13.1189i 0.340074 0.682943i
\(370\) −17.7847 10.2680i −0.924582 0.533807i
\(371\) −1.50800 8.23995i −0.0782915 0.427797i
\(372\) −12.5763 + 7.78684i −0.652053 + 0.403729i
\(373\) 4.45776 + 25.2812i 0.230814 + 1.30901i 0.851253 + 0.524756i \(0.175843\pi\)
−0.620439 + 0.784255i \(0.713046\pi\)
\(374\) 8.09323 6.79102i 0.418491 0.351155i
\(375\) −8.39148 2.76476i −0.433334 0.142771i
\(376\) −1.86736 5.13053i −0.0963017 0.264587i
\(377\) −1.97526 −0.101731
\(378\) 5.66523 12.5262i 0.291388 0.644277i
\(379\) −24.4008 −1.25338 −0.626692 0.779267i \(-0.715591\pi\)
−0.626692 + 0.779267i \(0.715591\pi\)
\(380\) 1.86230 + 5.11662i 0.0955339 + 0.262477i
\(381\) −7.31469 35.1225i −0.374743 1.79938i
\(382\) −20.5258 + 17.2232i −1.05019 + 0.881216i
\(383\) 5.57597 + 31.6229i 0.284919 + 1.61586i 0.705575 + 0.708635i \(0.250689\pi\)
−0.420656 + 0.907220i \(0.638200\pi\)
\(384\) −0.0533290 1.73123i −0.00272143 0.0883464i
\(385\) 9.55028 + 52.1842i 0.486727 + 2.65955i
\(386\) −1.90755 1.10133i −0.0970919 0.0560560i
\(387\) −24.3652 7.20400i −1.23855 0.366200i
\(388\) −5.95633 + 3.43889i −0.302387 + 0.174583i
\(389\) 7.82218 + 1.37926i 0.396600 + 0.0699313i 0.368392 0.929671i \(-0.379909\pi\)
0.0282088 + 0.999602i \(0.491020\pi\)
\(390\) 23.1845 + 18.2678i 1.17399 + 0.925024i
\(391\) −2.82582 + 7.76387i −0.142908 + 0.392636i
\(392\) −6.90882 1.12617i −0.348948 0.0568800i
\(393\) 1.37402 9.49320i 0.0693099 0.478869i
\(394\) 1.44992 8.22291i 0.0730459 0.414264i
\(395\) 22.2110 + 38.4706i 1.11756 + 1.93566i
\(396\) 7.08015 + 16.2609i 0.355791 + 0.817141i
\(397\) 11.0476 + 6.37836i 0.554465 + 0.320121i 0.750921 0.660392i \(-0.229610\pi\)
−0.196456 + 0.980513i \(0.562943\pi\)
\(398\) 11.7300 + 9.84266i 0.587973 + 0.493368i
\(399\) 6.81450 2.77198i 0.341152 0.138773i
\(400\) 1.12940 + 6.40514i 0.0564699 + 0.320257i
\(401\) 0.333197 + 0.397088i 0.0166390 + 0.0198296i 0.774300 0.632819i \(-0.218102\pi\)
−0.757661 + 0.652649i \(0.773658\pi\)
\(402\) 12.4231 + 13.9118i 0.619607 + 0.693860i
\(403\) −40.3210 + 14.6756i −2.00853 + 0.731045i
\(404\) −1.64242 −0.0817136
\(405\) −1.56697 + 30.4855i −0.0778634 + 1.51484i
\(406\) −0.663413 + 0.801102i −0.0329246 + 0.0397580i
\(407\) −12.2423 33.6355i −0.606830 1.66725i
\(408\) −2.06171 2.30878i −0.102070 0.114302i
\(409\) −4.06920 4.84948i −0.201209 0.239791i 0.655999 0.754761i \(-0.272247\pi\)
−0.857208 + 0.514970i \(0.827803\pi\)
\(410\) 16.3174 2.87720i 0.805859 0.142095i
\(411\) −1.96160 1.05337i −0.0967588 0.0519591i
\(412\) −7.75861 + 9.24635i −0.382239 + 0.455535i
\(413\) −4.83539 13.0222i −0.237934 0.640779i
\(414\) −11.1534 8.24440i −0.548158 0.405190i
\(415\) 8.34570 + 14.4552i 0.409674 + 0.709577i
\(416\) 0.872475 4.94805i 0.0427766 0.242598i
\(417\) −20.6983 2.99581i −1.01360 0.146705i
\(418\) −3.24598 + 8.91826i −0.158766 + 0.436207i
\(419\) 14.7613 + 5.37267i 0.721136 + 0.262472i 0.676408 0.736527i \(-0.263536\pi\)
0.0447282 + 0.998999i \(0.485758\pi\)
\(420\) 15.1956 3.26747i 0.741470 0.159436i
\(421\) 5.62674 31.9108i 0.274230 1.55524i −0.467166 0.884170i \(-0.654725\pi\)
0.741396 0.671068i \(-0.234164\pi\)
\(422\) −18.7794 + 10.8423i −0.914166 + 0.527794i
\(423\) 11.8755 11.2808i 0.577408 0.548491i
\(424\) 1.58307 2.74195i 0.0768805 0.133161i
\(425\) 8.90386 + 7.47123i 0.431901 + 0.362408i
\(426\) −17.6727 + 0.544391i −0.856244 + 0.0263758i
\(427\) 5.61031 9.86429i 0.271502 0.477367i
\(428\) −4.08907 4.87317i −0.197653 0.235553i
\(429\) 10.4895 + 50.3668i 0.506438 + 2.43173i
\(430\) −9.82478 26.9934i −0.473793 1.30174i
\(431\) 19.0894i 0.919506i −0.888047 0.459753i \(-0.847938\pi\)
0.888047 0.459753i \(-0.152062\pi\)
\(432\) 4.69802 2.22006i 0.226033 0.106813i
\(433\) 6.39156i 0.307159i −0.988136 0.153579i \(-0.950920\pi\)
0.988136 0.153579i \(-0.0490800\pi\)
\(434\) −7.59028 + 21.2819i −0.364345 + 1.02156i
\(435\) 0.722712 2.19355i 0.0346514 0.105172i
\(436\) −3.48088 + 2.92081i −0.166704 + 0.139881i
\(437\) −1.28881 7.30921i −0.0616522 0.349647i
\(438\) 1.43506 + 2.31773i 0.0685698 + 0.110745i
\(439\) 12.7631 15.2105i 0.609150 0.725957i −0.370014 0.929026i \(-0.620647\pi\)
0.979164 + 0.203069i \(0.0650917\pi\)
\(440\) −10.0257 + 17.3650i −0.477955 + 0.827843i
\(441\) −5.17659 20.3520i −0.246504 0.969142i
\(442\) −4.48953 7.77609i −0.213545 0.369871i
\(443\) −29.6889 5.23496i −1.41056 0.248721i −0.584087 0.811691i \(-0.698547\pi\)
−0.826477 + 0.562970i \(0.809659\pi\)
\(444\) −9.73948 + 3.88849i −0.462215 + 0.184540i
\(445\) 2.43387 + 0.885856i 0.115376 + 0.0419936i
\(446\) −18.4661 6.72113i −0.874397 0.318255i
\(447\) −5.84810 14.6477i −0.276606 0.692812i
\(448\) −1.71374 2.01571i −0.0809668 0.0952333i
\(449\) −15.0790 + 8.70584i −0.711620 + 0.410854i −0.811661 0.584129i \(-0.801436\pi\)
0.100040 + 0.994983i \(0.468103\pi\)
\(450\) −16.2652 + 10.7775i −0.766751 + 0.508055i
\(451\) 25.0108 + 14.4400i 1.17771 + 0.679952i
\(452\) −9.04113 + 10.7748i −0.425259 + 0.506804i
\(453\) 10.7476 + 17.3582i 0.504967 + 0.815560i
\(454\) −11.1029 + 1.95774i −0.521084 + 0.0918812i
\(455\) 45.0865 0.291937i 2.11369 0.0136862i
\(456\) 2.64093 + 0.870113i 0.123673 + 0.0407468i
\(457\) 19.7002 7.17030i 0.921538 0.335412i 0.162688 0.986678i \(-0.447984\pi\)
0.758850 + 0.651265i \(0.225761\pi\)
\(458\) −14.0664 −0.657281
\(459\) 3.88133 8.43596i 0.181165 0.393757i
\(460\) 15.6808i 0.731121i
\(461\) −10.2920 + 3.74598i −0.479346 + 0.174468i −0.570381 0.821380i \(-0.693205\pi\)
0.0910353 + 0.995848i \(0.470982\pi\)
\(462\) 23.9502 + 12.6620i 1.11426 + 0.589092i
\(463\) 28.5593 23.9641i 1.32726 1.11371i 0.342555 0.939498i \(-0.388708\pi\)
0.984709 0.174209i \(-0.0557367\pi\)
\(464\) −0.387162 + 0.0682670i −0.0179735 + 0.00316922i
\(465\) −1.54472 50.1465i −0.0716346 2.32549i
\(466\) 5.15083 + 4.32206i 0.238607 + 0.200215i
\(467\) −12.5094 + 21.6670i −0.578867 + 1.00263i 0.416743 + 0.909025i \(0.363172\pi\)
−0.995610 + 0.0936026i \(0.970162\pi\)
\(468\) 14.6549 3.52612i 0.677424 0.162995i
\(469\) 28.0890 + 4.76553i 1.29703 + 0.220052i
\(470\) 18.2369 + 3.21566i 0.841206 + 0.148327i
\(471\) 10.6657 13.5363i 0.491448 0.623722i
\(472\) 1.79570 4.93365i 0.0826538 0.227089i
\(473\) 17.1246 47.0494i 0.787389 2.16333i
\(474\) 22.4509 + 3.24946i 1.03120 + 0.149253i
\(475\) −10.2826 1.81310i −0.471798 0.0831907i
\(476\) −4.66159 0.790878i −0.213664 0.0362498i
\(477\) 9.43789 + 1.07051i 0.432131 + 0.0490153i
\(478\) −10.2825 + 17.8099i −0.470312 + 0.814605i
\(479\) −2.42248 2.03270i −0.110686 0.0928765i 0.585765 0.810481i \(-0.300794\pi\)
−0.696451 + 0.717604i \(0.745239\pi\)
\(480\) 5.17565 + 2.77930i 0.236235 + 0.126857i
\(481\) −29.9589 + 5.28257i −1.36601 + 0.240864i
\(482\) 17.7343 14.8808i 0.807774 0.677803i
\(483\) −21.1716 + 0.789415i −0.963339 + 0.0359196i
\(484\) −22.5051 + 8.19120i −1.02296 + 0.372327i
\(485\) 23.3277i 1.05926i
\(486\) 11.7329 + 10.2635i 0.532216 + 0.465560i
\(487\) −12.2791 −0.556418 −0.278209 0.960521i \(-0.589741\pi\)
−0.278209 + 0.960521i \(0.589741\pi\)
\(488\) 4.03052 1.46699i 0.182453 0.0664074i
\(489\) −2.63196 + 2.35030i −0.119021 + 0.106284i
\(490\) 15.0244 18.3837i 0.678734 0.830491i
\(491\) 6.68367 1.17851i 0.301630 0.0531855i −0.0207850 0.999784i \(-0.506617\pi\)
0.322415 + 0.946599i \(0.395505\pi\)
\(492\) 4.00303 7.45448i 0.180470 0.336074i
\(493\) −0.451602 + 0.538198i −0.0203391 + 0.0242392i
\(494\) 6.98535 + 4.03299i 0.314286 + 0.181453i
\(495\) −59.7708 6.77961i −2.68650 0.304721i
\(496\) −7.39593 + 4.27004i −0.332087 + 0.191731i
\(497\) −20.5767 + 17.4942i −0.922991 + 0.784721i
\(498\) 8.43584 + 1.22098i 0.378019 + 0.0547132i
\(499\) −4.24722 1.54586i −0.190132 0.0692022i 0.245200 0.969473i \(-0.421147\pi\)
−0.435331 + 0.900270i \(0.643369\pi\)
\(500\) −4.79338 1.74465i −0.214366 0.0780230i
\(501\) 19.8030 + 15.6034i 0.884734 + 0.697107i
\(502\) 21.5523 + 3.80026i 0.961928 + 0.169614i
\(503\) 8.26199 + 14.3102i 0.368384 + 0.638060i 0.989313 0.145807i \(-0.0465778\pi\)
−0.620929 + 0.783867i \(0.713245\pi\)
\(504\) 3.49194 7.12786i 0.155543 0.317500i
\(505\) 2.78534 4.82435i 0.123946 0.214681i
\(506\) 17.5684 20.9372i 0.781011 0.930773i
\(507\) 21.1980 0.652984i 0.941434 0.0290001i
\(508\) −3.59679 20.3984i −0.159582 0.905032i
\(509\) 12.0018 10.0707i 0.531969 0.446375i −0.336811 0.941572i \(-0.609348\pi\)
0.868781 + 0.495197i \(0.164904\pi\)
\(510\) 10.2781 2.14054i 0.455121 0.0947845i
\(511\) 3.92210 + 1.39884i 0.173504 + 0.0618809i
\(512\) 1.00000i 0.0441942i
\(513\) 0.769540 + 8.30616i 0.0339760 + 0.366726i
\(514\) 9.98464i 0.440404i
\(515\) −14.0021 38.4703i −0.617004 1.69520i
\(516\) −13.9325 4.59038i −0.613346 0.202080i
\(517\) 20.7474 + 24.7258i 0.912470 + 1.08744i
\(518\) −7.91961 + 13.9246i −0.347968 + 0.611812i
\(519\) 13.1677 + 21.2668i 0.577998 + 0.933510i
\(520\) 13.0545 + 10.9540i 0.572478 + 0.480366i
\(521\) 0.635723 1.10110i 0.0278515 0.0482403i −0.851764 0.523926i \(-0.824467\pi\)
0.879615 + 0.475686i \(0.157800\pi\)
\(522\) −0.651450 0.983160i −0.0285132 0.0430317i
\(523\) −12.9025 + 7.44924i −0.564186 + 0.325733i −0.754824 0.655928i \(-0.772278\pi\)
0.190638 + 0.981660i \(0.438944\pi\)
\(524\) 0.961666 5.45388i 0.0420106 0.238254i
\(525\) −9.14320 + 28.3678i −0.399042 + 1.23807i
\(526\) 16.6102 + 6.04564i 0.724241 + 0.263602i
\(527\) −5.21989 + 14.3415i −0.227382 + 0.624727i
\(528\) 3.79673 + 9.50964i 0.165231 + 0.413854i
\(529\) 0.282318 1.60110i 0.0122747 0.0696132i
\(530\) 5.36936 + 9.30001i 0.233230 + 0.403967i
\(531\) 15.7210 0.969461i 0.682232 0.0420710i
\(532\) 3.98176 1.47851i 0.172631 0.0641015i
\(533\) 15.7771 18.8024i 0.683381 0.814422i
\(534\) 1.12455 0.696285i 0.0486642 0.0301312i
\(535\) 21.2487 3.74672i 0.918661 0.161985i
\(536\) 6.92176 + 8.24904i 0.298975 + 0.356304i
\(537\) −13.3371 + 40.4803i −0.575540 + 1.74685i
\(538\) −8.11214 22.2879i −0.349739 0.960900i
\(539\) 40.6575 7.71316i 1.75124 0.332229i
\(540\) −1.44618 + 17.5646i −0.0622338 + 0.755860i
\(541\) −15.6445 −0.672609 −0.336304 0.941753i \(-0.609177\pi\)
−0.336304 + 0.941753i \(0.609177\pi\)
\(542\) 7.13658 2.59750i 0.306542 0.111572i
\(543\) −13.0102 + 2.70953i −0.558321 + 0.116277i
\(544\) −1.14872 1.36899i −0.0492511 0.0586951i
\(545\) −2.67627 15.1779i −0.114639 0.650148i
\(546\) 14.1325 18.1771i 0.604814 0.777908i
\(547\) 2.90719 + 2.43942i 0.124302 + 0.104302i 0.702820 0.711368i \(-0.251924\pi\)
−0.578517 + 0.815670i \(0.696369\pi\)
\(548\) −1.11327 0.642747i −0.0475566 0.0274568i
\(549\) 8.86213 + 9.32935i 0.378227 + 0.398167i
\(550\) −19.2250 33.2987i −0.819758 1.41986i
\(551\) 0.109594 0.621536i 0.00466884 0.0264783i
\(552\) −6.28979 4.95591i −0.267711 0.210938i
\(553\) 29.8964 17.5197i 1.27132 0.745015i
\(554\) 0.140252 0.385338i 0.00595872 0.0163715i
\(555\) 5.09510 35.2026i 0.216275 1.49427i
\(556\) −11.8913 2.09675i −0.504302 0.0889221i
\(557\) 12.9923 7.50110i 0.550500 0.317832i −0.198823 0.980035i \(-0.563712\pi\)
0.749324 + 0.662204i \(0.230379\pi\)
\(558\) −20.6027 15.2292i −0.872180 0.644702i
\(559\) −36.8520 21.2765i −1.55867 0.899901i
\(560\) 8.82711 1.61546i 0.373014 0.0682656i
\(561\) 16.1216 + 8.65725i 0.680656 + 0.365509i
\(562\) −0.162053 0.919047i −0.00683578 0.0387677i
\(563\) −12.1730 + 10.2144i −0.513032 + 0.430485i −0.862195 0.506577i \(-0.830911\pi\)
0.349163 + 0.937062i \(0.386466\pi\)
\(564\) 7.05362 6.29878i 0.297011 0.265226i
\(565\) −16.3166 44.8295i −0.686445 1.88599i
\(566\) 4.75042 0.199675
\(567\) 23.7878 + 1.06832i 0.998993 + 0.0448654i
\(568\) −10.2082 −0.428325
\(569\) 10.8568 + 29.8287i 0.455139 + 1.25048i 0.929064 + 0.369919i \(0.120615\pi\)
−0.473925 + 0.880565i \(0.657163\pi\)
\(570\) −7.03450 + 6.28171i −0.294643 + 0.263112i
\(571\) 15.9869 13.4146i 0.669031 0.561383i −0.243748 0.969839i \(-0.578377\pi\)
0.912778 + 0.408455i \(0.133932\pi\)
\(572\) 5.15791 + 29.2519i 0.215663 + 1.22308i
\(573\) −40.8873 21.9563i −1.70809 0.917237i
\(574\) −2.32674 12.7137i −0.0971164 0.530659i
\(575\) 26.0407 + 15.0346i 1.08597 + 0.626986i
\(576\) 2.75058 1.19763i 0.114607 0.0499012i
\(577\) −10.9520 + 6.32314i −0.455938 + 0.263236i −0.710335 0.703864i \(-0.751456\pi\)
0.254397 + 0.967100i \(0.418123\pi\)
\(578\) 13.5965 + 2.39744i 0.565542 + 0.0997203i
\(579\) 0.546491 3.77576i 0.0227114 0.156915i
\(580\) 0.456054 1.25300i 0.0189366 0.0520279i
\(581\) 11.2335 6.58299i 0.466042 0.273108i
\(582\) −9.35707 7.37271i −0.387863 0.305609i
\(583\) −3.25027 + 18.4332i −0.134613 + 0.763426i
\(584\) 0.786939 + 1.36302i 0.0325638 + 0.0564021i
\(585\) −14.4955 + 49.0263i −0.599314 + 2.02699i
\(586\) 22.4561 + 12.9650i 0.927652 + 0.535580i
\(587\) −22.8987 19.2143i −0.945131 0.793059i 0.0333397 0.999444i \(-0.489386\pi\)
−0.978471 + 0.206385i \(0.933830\pi\)
\(588\) −2.62551 11.8367i −0.108274 0.488136i
\(589\) −2.38071 13.5017i −0.0980955 0.556327i
\(590\) 11.4465 + 13.6414i 0.471245 + 0.561608i
\(591\) 14.1584 2.94867i 0.582400 0.121292i
\(592\) −5.68955 + 2.07083i −0.233839 + 0.0851105i
\(593\) 41.8483 1.71850 0.859252 0.511552i \(-0.170929\pi\)
0.859252 + 0.511552i \(0.170929\pi\)
\(594\) −21.6099 + 21.8322i −0.886667 + 0.895787i
\(595\) 10.2285 12.3515i 0.419330 0.506360i
\(596\) −3.11442 8.55680i −0.127572 0.350500i
\(597\) −8.29939 + 25.1900i −0.339671 + 1.03096i
\(598\) −14.9312 17.7943i −0.610583 0.727665i
\(599\) −2.11789 + 0.373441i −0.0865347 + 0.0152584i −0.216748 0.976228i \(-0.569545\pi\)
0.130213 + 0.991486i \(0.458434\pi\)
\(600\) −9.57787 + 5.93029i −0.391015 + 0.242103i
\(601\) 11.7749 14.0328i 0.480308 0.572409i −0.470417 0.882444i \(-0.655896\pi\)
0.950725 + 0.310035i \(0.100341\pi\)
\(602\) −21.0063 + 7.80005i −0.856151 + 0.317906i
\(603\) −14.3999 + 28.9181i −0.586410 + 1.17764i
\(604\) 5.89364 + 10.2081i 0.239809 + 0.415361i
\(605\) 14.1055 79.9964i 0.573471 3.25232i
\(606\) −1.05481 2.64198i −0.0428488 0.107323i
\(607\) −8.05702 + 22.1365i −0.327024 + 0.898492i 0.661836 + 0.749648i \(0.269777\pi\)
−0.988861 + 0.148844i \(0.952445\pi\)
\(608\) 1.50855 + 0.549068i 0.0611798 + 0.0222676i
\(609\) −1.71470 0.552665i −0.0694832 0.0223951i
\(610\) −2.52621 + 14.3268i −0.102283 + 0.580076i
\(611\) 23.7569 13.7161i 0.961102 0.554892i
\(612\) 2.38978 4.79920i 0.0966012 0.193996i
\(613\) −19.6552 + 34.0438i −0.793866 + 1.37502i 0.129690 + 0.991555i \(0.458602\pi\)
−0.923556 + 0.383462i \(0.874732\pi\)
\(614\) −10.0168 8.40505i −0.404243 0.339200i
\(615\) 15.1077 + 24.4001i 0.609202 + 0.983907i
\(616\) 13.5960 + 7.73271i 0.547799 + 0.311560i
\(617\) 19.5415 + 23.2886i 0.786711 + 0.937565i 0.999216 0.0395946i \(-0.0126066\pi\)
−0.212505 + 0.977160i \(0.568162\pi\)
\(618\) −19.8563 6.54211i −0.798739 0.263162i
\(619\) −11.0590 30.3844i −0.444499 1.22125i −0.936503 0.350659i \(-0.885958\pi\)
0.492004 0.870593i \(-0.336265\pi\)
\(620\) 28.9658i 1.16329i
\(621\) 6.09879 23.2359i 0.244736 0.932425i
\(622\) 16.8254i 0.674638i
\(623\) 0.678709 1.90299i 0.0271919 0.0762416i
\(624\) 8.51969 1.77433i 0.341061 0.0710300i
\(625\) −11.6580 + 9.78221i −0.466319 + 0.391288i
\(626\) −0.667688 3.78665i −0.0266862 0.151345i
\(627\) −16.4304 + 0.506125i −0.656169 + 0.0202127i
\(628\) 6.39554 7.62191i 0.255210 0.304147i
\(629\) −5.41015 + 9.37066i −0.215717 + 0.373633i
\(630\) 15.0151 + 22.3450i 0.598214 + 0.890244i
\(631\) 10.4957 + 18.1790i 0.417826 + 0.723695i 0.995720 0.0924158i \(-0.0294589\pi\)
−0.577895 + 0.816111i \(0.696126\pi\)
\(632\) 12.8981 + 2.27428i 0.513059 + 0.0904661i
\(633\) −29.5014 23.2450i −1.17257 0.923906i
\(634\) −5.97844 2.17597i −0.237434 0.0864189i
\(635\) 66.0167 + 24.0281i 2.61979 + 0.953526i
\(636\) 5.42735 + 0.785537i 0.215209 + 0.0311486i
\(637\) −0.455444 35.1677i −0.0180454 1.39340i
\(638\) 2.01276 1.16207i 0.0796859 0.0460066i
\(639\) −12.2256 28.0784i −0.483637 1.11076i
\(640\) 2.93734 + 1.69587i 0.116109 + 0.0670353i
\(641\) −9.44214 + 11.2527i −0.372942 + 0.444455i −0.919573 0.392918i \(-0.871466\pi\)
0.546631 + 0.837373i \(0.315910\pi\)
\(642\) 5.21278 9.70730i 0.205732 0.383117i
\(643\) −38.0576 + 6.71058i −1.50084 + 0.264639i −0.862873 0.505421i \(-0.831337\pi\)
−0.637971 + 0.770060i \(0.720226\pi\)
\(644\) −12.2316 + 0.0792004i −0.481994 + 0.00312093i
\(645\) 37.1113 33.1399i 1.46126 1.30488i
\(646\) 2.69592 0.981236i 0.106070 0.0386062i
\(647\) 9.26330 0.364178 0.182089 0.983282i \(-0.441714\pi\)
0.182089 + 0.983282i \(0.441714\pi\)
\(648\) 6.58835 + 6.13137i 0.258815 + 0.240863i
\(649\) 31.0386i 1.21837i
\(650\) −30.7076 + 11.1766i −1.20445 + 0.438384i
\(651\) −39.1084 + 1.45822i −1.53278 + 0.0571521i
\(652\) −1.56062 + 1.30952i −0.0611187 + 0.0512847i
\(653\) 11.8096 2.08235i 0.462145 0.0814887i 0.0622722 0.998059i \(-0.480165\pi\)
0.399873 + 0.916571i \(0.369054\pi\)
\(654\) −6.93389 3.72347i −0.271136 0.145599i
\(655\) 14.3890 + 12.0738i 0.562226 + 0.471764i
\(656\) 2.44257 4.23065i 0.0953662 0.165179i
\(657\) −2.80663 + 3.79693i −0.109497 + 0.148132i
\(658\) 2.41623 14.2417i 0.0941945 0.555201i
\(659\) 10.9123 + 1.92413i 0.425083 + 0.0749536i 0.382097 0.924122i \(-0.375202\pi\)
0.0429856 + 0.999076i \(0.486313\pi\)
\(660\) −34.3718 4.97486i −1.33792 0.193646i
\(661\) 4.59265 12.6182i 0.178633 0.490791i −0.817768 0.575547i \(-0.804789\pi\)
0.996402 + 0.0847566i \(0.0270113\pi\)
\(662\) 0.718069 1.97288i 0.0279085 0.0766780i
\(663\) 9.62519 12.2158i 0.373811 0.474422i
\(664\) 4.84642 + 0.854554i 0.188078 + 0.0331631i
\(665\) −2.40968 + 14.2031i −0.0934434 + 0.550775i
\(666\) −12.5099 13.1695i −0.484750 0.510307i
\(667\) −0.908773 + 1.57404i −0.0351878 + 0.0609471i
\(668\) 11.1505 + 9.35637i 0.431425 + 0.362009i
\(669\) −1.04798 34.0208i −0.0405173 1.31532i
\(670\) −35.9687 + 6.34224i −1.38959 + 0.245022i
\(671\) −19.4245 + 16.2991i −0.749873 + 0.629218i
\(672\) 2.14182 4.05125i 0.0826226 0.156280i
\(673\) −44.5338 + 16.2090i −1.71665 + 0.624810i −0.997541 0.0700856i \(-0.977673\pi\)
−0.719111 + 0.694896i \(0.755451\pi\)
\(674\) 5.05790i 0.194823i
\(675\) −27.7825 19.2424i −1.06935 0.740640i
\(676\) 12.2444 0.470940
\(677\) 36.7206 13.3652i 1.41129 0.513666i 0.479779 0.877389i \(-0.340717\pi\)
0.931507 + 0.363723i \(0.118494\pi\)
\(678\) −23.1386 7.62353i −0.888634 0.292780i
\(679\) −18.1965 + 0.117823i −0.698318 + 0.00452164i
\(680\) 5.96929 1.05255i 0.228912 0.0403633i
\(681\) −10.2798 16.6026i −0.393922 0.636213i
\(682\) 32.4526 38.6755i 1.24268 1.48096i
\(683\) 5.14546 + 2.97073i 0.196886 + 0.113672i 0.595202 0.803576i \(-0.297072\pi\)
−0.398316 + 0.917248i \(0.630405\pi\)
\(684\) 0.296430 + 4.80697i 0.0113343 + 0.183799i
\(685\) 3.77593 2.18004i 0.144271 0.0832949i
\(686\) −14.4159 11.6268i −0.550401 0.443912i
\(687\) −9.03386 22.6270i −0.344663 0.863275i
\(688\) −7.95854 2.89667i −0.303417 0.110435i
\(689\) 14.9485 + 5.44082i 0.569493 + 0.207279i
\(690\) 25.2239 10.0707i 0.960257 0.383383i
\(691\) 35.2625 + 6.21772i 1.34145 + 0.236533i 0.797872 0.602827i \(-0.205959\pi\)
0.543576 + 0.839360i \(0.317070\pi\)
\(692\) 7.22072 + 12.5067i 0.274491 + 0.475432i
\(693\) −4.98648 + 46.6578i −0.189421 + 1.77238i
\(694\) −7.72405 + 13.3785i −0.293201 + 0.507839i
\(695\) 26.3250 31.3729i 0.998563 1.19004i
\(696\) −0.358459 0.578939i −0.0135874 0.0219446i
\(697\) −1.51598 8.59756i −0.0574219 0.325656i
\(698\) −15.9033 + 13.3444i −0.601948 + 0.505094i
\(699\) −3.64438 + 11.0613i −0.137843 + 0.418376i
\(700\) −5.78060 + 16.2078i −0.218486 + 0.612599i
\(701\) 23.7517i 0.897089i 0.893761 + 0.448544i \(0.148057\pi\)
−0.893761 + 0.448544i \(0.851943\pi\)
\(702\) 15.0839 + 21.3091i 0.569304 + 0.804260i
\(703\) 9.72000i 0.366597i
\(704\) 2.02196 + 5.55528i 0.0762054 + 0.209373i
\(705\) 6.53960 + 31.4008i 0.246296 + 1.18262i
\(706\) 19.8709 + 23.6812i 0.747849 + 0.891252i
\(707\) −3.77725 2.14831i −0.142058 0.0807955i
\(708\) 9.08943 0.279992i 0.341602 0.0105227i
\(709\) 17.4693 + 14.6585i 0.656073 + 0.550511i 0.908907 0.416999i \(-0.136918\pi\)
−0.252834 + 0.967510i \(0.581363\pi\)
\(710\) 17.3118 29.9848i 0.649699 1.12531i
\(711\) 9.19154 + 38.2010i 0.344710 + 1.43265i
\(712\) 0.661330 0.381819i 0.0247844 0.0143093i
\(713\) −6.85610 + 38.8829i −0.256763 + 1.45618i
\(714\) −1.72161 8.00649i −0.0644298 0.299635i
\(715\) −94.6700 34.4571i −3.54046 1.28862i
\(716\) −8.41614 + 23.1232i −0.314526 + 0.864153i
\(717\) −35.2524 5.10232i −1.31653 0.190550i
\(718\) −0.00231017 + 0.0131016i −8.62147e−5 + 0.000488948i
\(719\) −22.5456 39.0501i −0.840808 1.45632i −0.889212 0.457495i \(-0.848747\pi\)
0.0484037 0.998828i \(-0.484587\pi\)
\(720\) −1.14679 + 10.1104i −0.0427384 + 0.376793i
\(721\) −29.9376 + 11.1165i −1.11494 + 0.413998i
\(722\) 10.5564 12.5806i 0.392867 0.468201i
\(723\) 35.3265 + 18.9702i 1.31381 + 0.705509i
\(724\) −7.55605 + 1.33234i −0.280818 + 0.0495158i
\(725\) 1.64356 + 1.95872i 0.0610402 + 0.0727449i
\(726\) −27.6297 30.9408i −1.02543 1.14832i
\(727\) 11.2011 + 30.7749i 0.415428 + 1.14138i 0.954263 + 0.298967i \(0.0966421\pi\)
−0.538836 + 0.842411i \(0.681136\pi\)
\(728\) 8.47864 10.2384i 0.314239 0.379459i
\(729\) −8.97443 + 25.4649i −0.332386 + 0.943143i
\(730\) −5.33819 −0.197575
\(731\) −14.2227 + 5.17663i −0.526044 + 0.191465i
\(732\) 4.94829 + 5.54128i 0.182894 + 0.204812i
\(733\) 20.5348 + 24.4724i 0.758470 + 0.903909i 0.997750 0.0670416i \(-0.0213560\pi\)
−0.239281 + 0.970950i \(0.576912\pi\)
\(734\) 0.529224 + 3.00138i 0.0195340 + 0.110783i
\(735\) 39.2208 + 12.3615i 1.44668 + 0.455961i
\(736\) −3.54159 2.97175i −0.130545 0.109540i
\(737\) −55.1315 31.8302i −2.03080 1.17248i
\(738\) 14.5620 + 1.65172i 0.536035 + 0.0608008i
\(739\) 12.5266 + 21.6967i 0.460799 + 0.798127i 0.999001 0.0446889i \(-0.0142297\pi\)
−0.538202 + 0.842816i \(0.680896\pi\)
\(740\) 3.56604 20.2240i 0.131090 0.743449i
\(741\) −2.00122 + 13.8266i −0.0735166 + 0.507933i
\(742\) 7.22725 4.23529i 0.265321 0.155482i
\(743\) −3.24557 + 8.91713i −0.119068 + 0.327138i −0.984881 0.173230i \(-0.944580\pi\)
0.865813 + 0.500368i \(0.166802\pi\)
\(744\) −11.6186 9.15463i −0.425958 0.335625i
\(745\) 30.4159 + 5.36314i 1.11435 + 0.196490i
\(746\) −22.2319 + 12.8356i −0.813968 + 0.469945i
\(747\) 3.45369 + 14.3539i 0.126364 + 0.525182i
\(748\) 9.14952 + 5.28248i 0.334540 + 0.193147i
\(749\) −3.02991 16.5559i −0.110711 0.604939i
\(750\) −0.272032 8.83101i −0.00993319 0.322463i
\(751\) −5.68100 32.2186i −0.207303 1.17567i −0.893775 0.448516i \(-0.851953\pi\)
0.686472 0.727156i \(-0.259158\pi\)
\(752\) 4.18245 3.50949i 0.152518 0.127978i
\(753\) 7.72849 + 37.1094i 0.281642 + 1.35234i
\(754\) −0.675578 1.85613i −0.0246031 0.0675964i
\(755\) −39.9794 −1.45500
\(756\) 13.7084 + 1.03936i 0.498569 + 0.0378013i
\(757\) 10.1663 0.369500 0.184750 0.982786i \(-0.440852\pi\)
0.184750 + 0.982786i \(0.440852\pi\)
\(758\) −8.34555 22.9292i −0.303124 0.832827i
\(759\) 44.9622 + 14.8138i 1.63203 + 0.537707i
\(760\) −4.17111 + 3.49998i −0.151302 + 0.126958i
\(761\) −0.948028 5.37653i −0.0343660 0.194899i 0.962791 0.270245i \(-0.0871049\pi\)
−0.997157 + 0.0753464i \(0.975994\pi\)
\(762\) 30.5026 18.8862i 1.10499 0.684173i
\(763\) −11.8258 + 2.16425i −0.428123 + 0.0783512i
\(764\) −23.2048 13.3973i −0.839519 0.484697i
\(765\) 10.0441 + 15.1584i 0.363145 + 0.548054i
\(766\) −27.8087 + 16.0554i −1.00477 + 0.580104i
\(767\) 25.9786 + 4.58074i 0.938035 + 0.165401i
\(768\) 1.60858 0.642228i 0.0580448 0.0231744i
\(769\) 11.5799 31.8156i 0.417583 1.14730i −0.535486 0.844544i \(-0.679871\pi\)
0.953068 0.302755i \(-0.0979064\pi\)
\(770\) −45.7707 + 26.8224i −1.64946 + 0.966611i
\(771\) −16.0611 + 6.41242i −0.578428 + 0.230938i
\(772\) 0.382486 2.16919i 0.0137660 0.0780708i
\(773\) 26.3939 + 45.7155i 0.949322 + 1.64427i 0.746858 + 0.664984i \(0.231562\pi\)
0.202464 + 0.979290i \(0.435105\pi\)
\(774\) −1.56385 25.3597i −0.0562115 0.911537i
\(775\) 48.1027 + 27.7721i 1.72790 + 0.997604i
\(776\) −5.26869 4.42095i −0.189135 0.158703i
\(777\) −27.4851 3.79658i −0.986023 0.136202i
\(778\) 1.37926 + 7.82218i 0.0494489 + 0.280439i
\(779\) 5.04102 + 6.00765i 0.180613 + 0.215246i
\(780\) −9.23651 + 28.0343i −0.330720 + 1.00379i
\(781\) 56.7092 20.6405i 2.02922 0.738574i
\(782\) −8.26214 −0.295453
\(783\) 1.16312 1.67932i 0.0415664 0.0600142i
\(784\) −1.30470 6.87734i −0.0465966 0.245619i
\(785\) 11.5421 + 31.7117i 0.411955 + 1.13184i
\(786\) 9.39063 1.95572i 0.334953 0.0697580i
\(787\) −3.95690 4.71565i −0.141048 0.168095i 0.690896 0.722954i \(-0.257216\pi\)
−0.831944 + 0.554860i \(0.812772\pi\)
\(788\) 8.22291 1.44992i 0.292929 0.0516513i
\(789\) 0.942657 + 30.6017i 0.0335595 + 1.08945i
\(790\) −28.5539 + 34.0292i −1.01590 + 1.21070i
\(791\) −34.8864 + 12.9540i −1.24042 + 0.460592i
\(792\) −12.8587 + 12.2147i −0.456914 + 0.434031i
\(793\) 10.7753 + 18.6633i 0.382641 + 0.662753i
\(794\) −2.21518 + 12.5629i −0.0786138 + 0.445841i
\(795\) −11.5115 + 14.6098i −0.408271 + 0.518156i
\(796\) −5.23717 + 14.3890i −0.185626 + 0.510005i
\(797\) −13.3197 4.84797i −0.471807 0.171724i 0.0951636 0.995462i \(-0.469663\pi\)
−0.566971 + 0.823738i \(0.691885\pi\)
\(798\) 4.93551 + 5.45546i 0.174715 + 0.193121i
\(799\) 1.69431 9.60894i 0.0599406 0.339940i
\(800\) −5.63258 + 3.25197i −0.199142 + 0.114975i
\(801\) 1.84225 + 1.36176i 0.0650928 + 0.0481156i
\(802\) −0.259181 + 0.448915i −0.00915200 + 0.0158517i
\(803\) −7.12763 5.98079i −0.251529 0.211058i
\(804\) −8.82392 + 16.4320i −0.311196 + 0.579512i
\(805\) 20.5107 36.0628i 0.722906 1.27105i
\(806\) −27.5812 32.8699i −0.971505 1.15779i
\(807\) 30.6421 27.3630i 1.07865 0.963223i
\(808\) −0.561742 1.54337i −0.0197620 0.0542957i
\(809\) 0.0409937i 0.00144126i 1.00000 0.000720631i \(0.000229384\pi\)
−1.00000 0.000720631i \(0.999771\pi\)
\(810\) −29.1829 + 8.95418i −1.02538 + 0.314618i
\(811\) 2.77830i 0.0975593i 0.998810 + 0.0487797i \(0.0155332\pi\)
−0.998810 + 0.0487797i \(0.984467\pi\)
\(812\) −0.979690 0.349411i −0.0343804 0.0122619i
\(813\) 8.76162 + 9.81160i 0.307283 + 0.344108i
\(814\) 27.4199 23.0080i 0.961068 0.806432i
\(815\) −1.19988 6.80485i −0.0420299 0.238364i
\(816\) 1.46440 2.72702i 0.0512642 0.0954649i
\(817\) 8.73956 10.4154i 0.305759 0.364389i
\(818\) 3.16527 5.48241i 0.110671 0.191688i
\(819\) 38.3157 + 11.0594i 1.33886 + 0.386447i
\(820\) 8.28456 + 14.3493i 0.289310 + 0.501099i
\(821\) 31.5365 + 5.56073i 1.10063 + 0.194071i 0.694321 0.719665i \(-0.255705\pi\)
0.406309 + 0.913736i \(0.366816\pi\)
\(822\) 0.318939 2.20358i 0.0111243 0.0768587i
\(823\) 36.6406 + 13.3361i 1.27721 + 0.464867i 0.889509 0.456918i \(-0.151047\pi\)
0.387702 + 0.921785i \(0.373269\pi\)
\(824\) −11.3423 4.12827i −0.395129 0.143815i
\(825\) 41.2170 52.3105i 1.43499 1.82122i
\(826\) 10.5830 8.99763i 0.368231 0.313067i
\(827\) −31.2739 + 18.0560i −1.08750 + 0.627869i −0.932910 0.360110i \(-0.882739\pi\)
−0.154591 + 0.987979i \(0.549406\pi\)
\(828\) 3.93252 13.3005i 0.136665 0.462224i
\(829\) 23.9244 + 13.8128i 0.830930 + 0.479738i 0.854171 0.519992i \(-0.174065\pi\)
−0.0232407 + 0.999730i \(0.507398\pi\)
\(830\) −10.7290 + 12.7864i −0.372410 + 0.443821i
\(831\) 0.709922 0.0218685i 0.0246269 0.000758611i
\(832\) 4.94805 0.872475i 0.171543 0.0302476i
\(833\) −9.68628 7.91629i −0.335610 0.274283i
\(834\) −4.26411 20.4747i −0.147654 0.708981i
\(835\) −46.3926 + 16.8855i −1.60548 + 0.584348i
\(836\) −9.49062 −0.328240
\(837\) 11.2658 42.9217i 0.389402 1.48359i
\(838\) 15.7086i 0.542646i
\(839\) −12.4498 + 4.53134i −0.429814 + 0.156439i −0.547862 0.836568i \(-0.684558\pi\)
0.118049 + 0.993008i \(0.462336\pi\)
\(840\) 8.26762 + 13.1617i 0.285260 + 0.454120i
\(841\) 22.0969 18.5415i 0.761962 0.639362i
\(842\) 31.9108 5.62674i 1.09972 0.193910i
\(843\) 1.37429 0.850914i 0.0473330 0.0293070i
\(844\) −16.6113 13.9386i −0.571786 0.479785i
\(845\) −20.7650 + 35.9661i −0.714339 + 1.23727i
\(846\) 14.6621 + 7.30108i 0.504095 + 0.251016i
\(847\) −62.4716 10.5988i −2.14655 0.364180i
\(848\) 3.11803 + 0.549793i 0.107074 + 0.0188800i
\(849\) 3.05086 + 7.64146i 0.104705 + 0.262254i
\(850\) −3.97536 + 10.9222i −0.136354 + 0.374628i
\(851\) −9.57389 + 26.3041i −0.328189 + 0.901692i
\(852\) −6.55597 16.4207i −0.224604 0.562564i
\(853\) 34.9167 + 6.15675i 1.19552 + 0.210803i 0.735763 0.677239i \(-0.236824\pi\)
0.459761 + 0.888043i \(0.347935\pi\)
\(854\) 11.1882 + 1.89818i 0.382854 + 0.0649543i
\(855\) −14.6224 7.28130i −0.500076 0.249015i
\(856\) 3.18073 5.50919i 0.108715 0.188300i
\(857\) −15.8927 13.3356i −0.542884 0.455534i 0.329639 0.944107i \(-0.393073\pi\)
−0.872523 + 0.488573i \(0.837518\pi\)
\(858\) −43.7416 + 27.0833i −1.49332 + 0.924610i
\(859\) −42.1444 + 7.43120i −1.43795 + 0.253549i −0.837642 0.546220i \(-0.816066\pi\)
−0.600308 + 0.799769i \(0.704955\pi\)
\(860\) 22.0052 18.4645i 0.750371 0.629636i
\(861\) 18.9567 11.9079i 0.646044 0.405819i
\(862\) 17.9382 6.52897i 0.610978 0.222378i
\(863\) 36.6851i 1.24877i 0.781115 + 0.624387i \(0.214651\pi\)
−0.781115 + 0.624387i \(0.785349\pi\)
\(864\) 3.69299 + 3.65539i 0.125638 + 0.124359i
\(865\) −48.9817 −1.66543
\(866\) 6.00610 2.18604i 0.204096 0.0742847i
\(867\) 4.87561 + 23.4109i 0.165584 + 0.795075i
\(868\) −22.5945 + 0.146300i −0.766906 + 0.00496575i
\(869\) −76.2511 + 13.4451i −2.58664 + 0.456095i
\(870\) 2.30844 0.0711095i 0.0782635 0.00241084i
\(871\) −34.7776 + 41.4463i −1.17839 + 1.40436i
\(872\) −3.93519 2.27199i −0.133262 0.0769391i
\(873\) 5.85025 19.7866i 0.198001 0.669675i
\(874\) 6.42761 3.71098i 0.217417 0.125526i
\(875\) −8.74181 10.2821i −0.295527 0.347600i
\(876\) −1.68713 + 2.14123i −0.0570030 + 0.0723453i
\(877\) 34.5055 + 12.5590i 1.16517 + 0.424086i 0.850941 0.525262i \(-0.176033\pi\)
0.314226 + 0.949348i \(0.398255\pi\)
\(878\) 18.6584 + 6.79111i 0.629691 + 0.229189i
\(879\) −6.43340 + 44.4490i −0.216993 + 1.49923i
\(880\) −19.7467 3.48188i −0.665662 0.117374i
\(881\) 6.77937 + 11.7422i 0.228403 + 0.395605i 0.957335 0.288981i \(-0.0933163\pi\)
−0.728932 + 0.684586i \(0.759983\pi\)
\(882\) 17.3541 11.8252i 0.584343 0.398175i
\(883\) 7.49854 12.9878i 0.252346 0.437076i −0.711825 0.702356i \(-0.752131\pi\)
0.964171 + 0.265281i \(0.0854646\pi\)
\(884\) 5.77162 6.87835i 0.194121 0.231344i
\(885\) −14.5921 + 27.1736i −0.490508 + 0.913430i
\(886\) −5.23496 29.6889i −0.175872 0.997420i
\(887\) −11.1296 + 9.33884i −0.373695 + 0.313568i −0.810221 0.586124i \(-0.800653\pi\)
0.436526 + 0.899692i \(0.356209\pi\)
\(888\) −6.98509 7.82218i −0.234404 0.262495i
\(889\) 18.4094 51.6169i 0.617432 1.73118i
\(890\) 2.59007i 0.0868193i
\(891\) −48.9975 20.7401i −1.64148 0.694821i
\(892\) 19.6513i 0.657973i
\(893\) 2.99780 + 8.23638i 0.100317 + 0.275620i
\(894\) 11.7642 10.5052i 0.393452 0.351347i
\(895\) −53.6478 63.9350i −1.79325 2.13711i
\(896\) 1.30801 2.29981i 0.0436976 0.0768311i
\(897\) 19.0344 35.4462i 0.635541 1.18351i
\(898\) −13.3381 11.1920i −0.445099 0.373482i
\(899\) −1.67870 + 2.90759i −0.0559877 + 0.0969736i
\(900\) −15.6906 11.5982i −0.523018 0.386607i
\(901\) 4.90013 2.82909i 0.163247 0.0942507i
\(902\) −5.01495 + 28.4412i −0.166980 + 0.946988i
\(903\) −26.0379 28.7809i −0.866486 0.957769i
\(904\) −13.2172 4.81068i −0.439599 0.160001i
\(905\) 8.90058 24.4541i 0.295865 0.812883i
\(906\) −12.6355 + 16.0363i −0.419786 + 0.532771i
\(907\) −1.91838 + 10.8797i −0.0636987 + 0.361254i 0.936252 + 0.351329i \(0.114270\pi\)
−0.999951 + 0.00992438i \(0.996841\pi\)
\(908\) −5.63708 9.76371i −0.187073 0.324020i
\(909\) 3.57241 3.39350i 0.118489 0.112555i
\(910\) 15.6948 + 42.2676i 0.520278 + 1.40116i
\(911\) −17.2529 + 20.5612i −0.571614 + 0.681223i −0.971961 0.235141i \(-0.924445\pi\)
0.400348 + 0.916363i \(0.368889\pi\)
\(912\) 0.0856126 + 2.77926i 0.00283492 + 0.0920305i
\(913\) −28.6511 + 5.05196i −0.948213 + 0.167195i
\(914\) 13.4758 + 16.0598i 0.445738 + 0.531210i
\(915\) −24.6683 + 5.13748i −0.815509 + 0.169840i
\(916\) −4.81100 13.2181i −0.158960 0.436739i
\(917\) 9.34539 11.2850i 0.308612 0.372663i
\(918\) 9.25470 + 0.761986i 0.305451 + 0.0251493i
\(919\) −20.6706 −0.681860 −0.340930 0.940089i \(-0.610742\pi\)
−0.340930 + 0.940089i \(0.610742\pi\)
\(920\) 14.7351 5.36315i 0.485803 0.176818i
\(921\) 7.08719 21.5108i 0.233531 0.708803i
\(922\) −7.04014 8.39011i −0.231855 0.276314i
\(923\) −8.90637 50.5105i −0.293157 1.66257i
\(924\) −3.70698 + 26.8365i −0.121951 + 0.882856i
\(925\) 30.1664 + 25.3126i 0.991864 + 0.832273i
\(926\) 32.2868 + 18.6408i 1.06101 + 0.612574i
\(927\) −2.22877 36.1421i −0.0732023 1.18706i
\(928\) −0.196567 0.340464i −0.00645263 0.0111763i
\(929\) 8.28362 46.9787i 0.271777 1.54132i −0.477241 0.878772i \(-0.658363\pi\)
0.749018 0.662550i \(-0.230526\pi\)
\(930\) 46.5939 18.6027i 1.52788 0.610005i
\(931\) 11.0912 + 1.80791i 0.363499 + 0.0592518i
\(932\) −2.29972 + 6.31842i −0.0753298 + 0.206967i
\(933\) 27.0651 10.8058i 0.886072 0.353765i
\(934\) −24.6388 4.34448i −0.806205 0.142156i
\(935\) −31.0329 + 17.9168i −1.01488 + 0.585943i
\(936\) 8.32574 + 12.5651i 0.272135 + 0.410704i
\(937\) −12.5774 7.26158i −0.410887 0.237226i 0.280284 0.959917i \(-0.409571\pi\)
−0.691171 + 0.722692i \(0.742905\pi\)
\(938\) 5.12887 + 28.0249i 0.167464 + 0.915046i
\(939\) 5.66233 3.50592i 0.184783 0.114412i
\(940\) 3.21566 + 18.2369i 0.104883 + 0.594822i
\(941\) −19.0755 + 16.0062i −0.621843 + 0.521789i −0.898382 0.439214i \(-0.855257\pi\)
0.276539 + 0.961003i \(0.410812\pi\)
\(942\) 16.3679 + 5.39276i 0.533294 + 0.175706i
\(943\) −7.72454 21.2230i −0.251546 0.691116i
\(944\) 5.25028 0.170882
\(945\) −26.3006 + 38.5035i −0.855560 + 1.25252i
\(946\) 50.0689 1.62788
\(947\) −11.1659 30.6782i −0.362844 0.996906i −0.978019 0.208515i \(-0.933137\pi\)
0.615175 0.788391i \(-0.289085\pi\)
\(948\) 4.62515 + 22.2083i 0.150218 + 0.721292i
\(949\) −6.05770 + 5.08301i −0.196641 + 0.165002i
\(950\) −1.81310 10.2826i −0.0588247 0.333611i
\(951\) −0.339286 11.0143i −0.0110021 0.357163i
\(952\) −0.851177 4.65096i −0.0275868 0.150739i
\(953\) −17.1700 9.91308i −0.556190 0.321116i 0.195425 0.980719i \(-0.437391\pi\)
−0.751615 + 0.659602i \(0.770725\pi\)
\(954\) 2.22200 + 9.23485i 0.0719398 + 0.298989i
\(955\) 78.7047 45.4402i 2.54683 1.47041i
\(956\) −20.2526 3.57109i −0.655017 0.115497i
\(957\) 3.16193 + 2.49138i 0.102211 + 0.0805348i
\(958\) 1.08158 2.97161i 0.0349442 0.0960084i
\(959\) −1.71959 2.93437i −0.0555283 0.0947556i
\(960\) −0.841513 + 5.81409i −0.0271597 + 0.187649i
\(961\) −7.28159 + 41.2960i −0.234890 + 1.33213i
\(962\) −15.2106 26.3455i −0.490408 0.849411i
\(963\) 18.9628 + 2.15089i 0.611068 + 0.0693115i
\(964\) 20.0489 + 11.5752i 0.645731 + 0.372813i
\(965\) 5.72299 + 4.80216i 0.184230 + 0.154587i
\(966\) −7.98291 19.6248i −0.256846 0.631416i
\(967\) −6.87991 39.0179i −0.221243 1.25473i −0.869738 0.493513i \(-0.835713\pi\)
0.648495 0.761219i \(-0.275399\pi\)
\(968\) −15.3944 18.3463i −0.494795 0.589674i
\(969\) 3.30980 + 3.70644i 0.106326 + 0.119068i
\(970\) 21.9209 7.97854i 0.703836 0.256175i
\(971\) −57.4256 −1.84288 −0.921438 0.388525i \(-0.872985\pi\)
−0.921438 + 0.388525i \(0.872985\pi\)
\(972\) −5.63160 + 14.5356i −0.180634 + 0.466231i
\(973\) −24.6050 20.3761i −0.788801 0.653226i
\(974\) −4.19969 11.5386i −0.134567 0.369719i
\(975\) −37.6999 42.2178i −1.20736 1.35205i
\(976\) 2.75704 + 3.28571i 0.0882506 + 0.105173i
\(977\) 43.8735 7.73609i 1.40364 0.247499i 0.580001 0.814616i \(-0.303052\pi\)
0.823638 + 0.567117i \(0.191941\pi\)
\(978\) −3.10875 1.66938i −0.0994067 0.0533810i
\(979\) −2.90185 + 3.45830i −0.0927437 + 0.110528i
\(980\) 22.4137 + 7.83073i 0.715979 + 0.250143i
\(981\) 1.53637 13.5451i 0.0490526 0.432460i
\(982\) 3.39339 + 5.87752i 0.108287 + 0.187559i
\(983\) −1.07544 + 6.09915i −0.0343013 + 0.194533i −0.997143 0.0755328i \(-0.975934\pi\)
0.962842 + 0.270065i \(0.0870453\pi\)
\(984\) 8.37404 + 1.21203i 0.266955 + 0.0386381i
\(985\) −9.68610 + 26.6124i −0.308625 + 0.847940i
\(986\) −0.660198 0.240292i −0.0210250 0.00765247i
\(987\) 24.4608 5.25974i 0.778597 0.167420i
\(988\) −1.40064 + 7.94344i −0.0445604 + 0.252715i
\(989\) −33.9096 + 19.5777i −1.07826 + 0.622536i
\(990\) −14.0721 58.4849i −0.447239 1.85877i
\(991\) 1.81751 3.14802i 0.0577351 0.100000i −0.835713 0.549166i \(-0.814945\pi\)
0.893448 + 0.449166i \(0.148279\pi\)
\(992\) −6.54208 5.48946i −0.207711 0.174291i
\(993\) 3.63470 0.111964i 0.115344 0.00355306i
\(994\) −23.4768 13.3524i −0.744639 0.423512i
\(995\) −33.3838 39.7853i −1.05834 1.26128i
\(996\) 1.73788 + 8.34469i 0.0550670 + 0.264412i
\(997\) 11.3278 + 31.1227i 0.358754 + 0.985667i 0.979463 + 0.201626i \(0.0646226\pi\)
−0.620709 + 0.784041i \(0.713155\pi\)
\(998\) 4.51980i 0.143072i
\(999\) 13.1500 28.5811i 0.416047 0.904266i
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 378.2.z.a.209.16 144
7.6 odd 2 inner 378.2.z.a.209.21 yes 144
27.23 odd 18 inner 378.2.z.a.293.21 yes 144
189.104 even 18 inner 378.2.z.a.293.16 yes 144
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
378.2.z.a.209.16 144 1.1 even 1 trivial
378.2.z.a.209.21 yes 144 7.6 odd 2 inner
378.2.z.a.293.16 yes 144 189.104 even 18 inner
378.2.z.a.293.21 yes 144 27.23 odd 18 inner