Properties

Label 930.2.bg.c.751.2
Level $930$
Weight $2$
Character 930.751
Analytic conductor $7.426$
Analytic rank $0$
Dimension $16$
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] = [930,2,Mod(121,930)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(930, base_ring=CyclotomicField(30))
 
chi = DirichletCharacter(H, H._module([0, 0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("930.121");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 930.bg (of order \(15\), degree \(8\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.42608738798\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(2\) over \(\Q(\zeta_{15})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 40x^{14} + 654x^{12} + 5650x^{10} + 27831x^{8} + 78445x^{6} + 119819x^{4} + 87030x^{2} + 22801 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 751.2
Root \(1.00725i\) of defining polynomial
Character \(\chi\) \(=\) 930.751
Dual form 930.2.bg.c.691.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 + 0.951057i) q^{2} +(0.978148 - 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.19037 + 1.42044i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\) \(q+(0.309017 + 0.951057i) q^{2} +(0.978148 - 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(3.19037 + 1.42044i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.978148 + 0.207912i) q^{10} +(0.412071 + 3.92059i) q^{11} +(-0.669131 + 0.743145i) q^{12} +(1.98047 + 2.19953i) q^{13} +(-0.365044 + 3.47316i) q^{14} +(0.309017 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.838261 - 7.97552i) q^{17} +(0.669131 + 0.743145i) q^{18} +(-2.35264 + 2.61287i) q^{19} +(0.104528 + 0.994522i) q^{20} +(3.41598 + 0.726089i) q^{21} +(-3.60137 + 1.60343i) q^{22} +(-4.87954 - 3.54519i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-1.47988 + 2.56323i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.41598 + 0.726089i) q^{28} +(1.43570 + 4.41862i) q^{29} +1.00000 q^{30} +(2.58958 - 4.92890i) q^{31} +1.00000 q^{32} +(1.21820 + 3.74925i) q^{33} +(7.84421 - 1.66734i) q^{34} +(2.82533 - 2.05272i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.86873 + 8.43289i) q^{37} +(-3.21200 - 1.43007i) q^{38} +(2.39450 + 1.73970i) q^{39} +(-0.913545 + 0.406737i) q^{40} +(10.0697 + 2.14038i) q^{41} +(0.365044 + 3.47316i) q^{42} +(-4.77909 + 5.30772i) q^{43} +(-2.63784 - 2.92962i) q^{44} +(0.104528 - 0.994522i) q^{45} +(1.86382 - 5.73624i) q^{46} +(-1.34327 + 4.13417i) q^{47} +(0.104528 - 0.994522i) q^{48} +(3.47688 + 3.86147i) q^{49} +(0.669131 - 0.743145i) q^{50} +(-0.838261 - 7.97552i) q^{51} +(-2.89508 - 0.615369i) q^{52} +(8.36017 - 3.72219i) q^{53} +(0.809017 + 0.587785i) q^{54} +(3.60137 + 1.60343i) q^{55} +(-1.74615 - 3.02442i) q^{56} +(-1.75798 + 3.04492i) q^{57} +(-3.75870 + 2.73086i) q^{58} +(-13.3203 + 2.83133i) q^{59} +(0.309017 + 0.951057i) q^{60} -10.3475 q^{61} +(5.48789 + 0.939726i) q^{62} +3.49229 q^{63} +(0.309017 + 0.951057i) q^{64} +(2.89508 - 0.615369i) q^{65} +(-3.18930 + 2.31716i) q^{66} +(3.28687 - 5.69302i) q^{67} +(4.00973 + 6.94505i) q^{68} +(-5.51000 - 2.45321i) q^{69} +(2.82533 + 2.05272i) q^{70} +(11.9280 - 5.31067i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(0.00255919 + 0.0243491i) q^{73} +(-6.51564 + 7.23635i) q^{74} +(-0.669131 - 0.743145i) q^{75} +(0.367519 - 3.49671i) q^{76} +(-4.25433 + 13.0935i) q^{77} +(-0.914616 + 2.81490i) q^{78} +(-0.200527 + 1.90789i) q^{79} +(-0.669131 - 0.743145i) q^{80} +(0.669131 - 0.743145i) q^{81} +(1.07608 + 10.2383i) q^{82} +(-10.3149 - 2.19249i) q^{83} +(-3.19037 + 1.42044i) q^{84} +(-6.48787 - 4.71372i) q^{85} +(-6.52476 - 2.90501i) q^{86} +(2.32301 + 4.02357i) q^{87} +(1.97110 - 3.41404i) q^{88} +(2.70979 - 1.96878i) q^{89} +(0.978148 - 0.207912i) q^{90} +(3.19411 + 9.83045i) q^{91} +6.03144 q^{92} +(1.50822 - 5.35960i) q^{93} -4.34692 q^{94} +(1.08649 + 3.34389i) q^{95} +(0.978148 - 0.207912i) q^{96} +(-1.10581 + 0.803415i) q^{97} +(-2.59806 + 4.49997i) q^{98} +(1.97110 + 3.41404i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{2} - 2 q^{3} - 4 q^{4} + 8 q^{5} + 8 q^{6} + 11 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 2 q^{11} - 2 q^{12} + 14 q^{13} - 4 q^{14} - 4 q^{15} - 4 q^{16} - 4 q^{17} + 2 q^{18} + q^{19} - 2 q^{20} - 16 q^{21} - 13 q^{22} + 3 q^{23} - 2 q^{24} - 8 q^{25} + 9 q^{26} + 4 q^{27} + 16 q^{28} + 13 q^{29} + 16 q^{30} + 9 q^{31} + 16 q^{32} + 14 q^{33} + 26 q^{34} + 7 q^{35} - 8 q^{36} - 11 q^{37} - 14 q^{38} - 7 q^{39} - 2 q^{40} + 42 q^{41} + 4 q^{42} - 18 q^{43} + 7 q^{44} - 2 q^{45} - 7 q^{46} - 37 q^{47} - 2 q^{48} + 11 q^{49} + 2 q^{50} + 4 q^{51} - 16 q^{52} + 14 q^{53} + 4 q^{54} + 13 q^{55} - 9 q^{56} + 4 q^{57} - 12 q^{58} + 2 q^{59} - 4 q^{60} - 16 q^{61} + 9 q^{62} + 18 q^{63} - 4 q^{64} + 16 q^{65} - 11 q^{66} + 41 q^{67} + 16 q^{68} + 9 q^{69} + 7 q^{70} + q^{71} + 2 q^{72} - 53 q^{73} + 44 q^{74} - 2 q^{75} + 16 q^{76} - 16 q^{77} - 2 q^{78} + 30 q^{79} - 2 q^{80} + 2 q^{81} - 8 q^{82} - 11 q^{84} - 38 q^{85} + 7 q^{86} - q^{87} - 3 q^{88} - 49 q^{89} - 2 q^{90} + 2 q^{91} + 8 q^{92} + 6 q^{93} + 48 q^{94} + 2 q^{95} - 2 q^{96} + 21 q^{97} - 19 q^{98} - 3 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

\(n\) \(187\) \(311\) \(871\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{14}{15}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 + 0.951057i 0.218508 + 0.672499i
\(3\) 0.978148 0.207912i 0.564734 0.120038i
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0.500000 + 0.866025i 0.204124 + 0.353553i
\(7\) 3.19037 + 1.42044i 1.20585 + 0.536877i 0.908497 0.417891i \(-0.137231\pi\)
0.297349 + 0.954769i \(0.403897\pi\)
\(8\) −0.809017 0.587785i −0.286031 0.207813i
\(9\) 0.913545 0.406737i 0.304515 0.135579i
\(10\) 0.978148 + 0.207912i 0.309317 + 0.0657474i
\(11\) 0.412071 + 3.92059i 0.124244 + 1.18210i 0.861954 + 0.506986i \(0.169240\pi\)
−0.737710 + 0.675118i \(0.764093\pi\)
\(12\) −0.669131 + 0.743145i −0.193161 + 0.214527i
\(13\) 1.98047 + 2.19953i 0.549282 + 0.610040i 0.952304 0.305151i \(-0.0987068\pi\)
−0.403022 + 0.915190i \(0.632040\pi\)
\(14\) −0.365044 + 3.47316i −0.0975621 + 0.928242i
\(15\) 0.309017 0.951057i 0.0797878 0.245562i
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 0.838261 7.97552i 0.203308 1.93435i −0.129966 0.991518i \(-0.541487\pi\)
0.333274 0.942830i \(-0.391847\pi\)
\(18\) 0.669131 + 0.743145i 0.157716 + 0.175161i
\(19\) −2.35264 + 2.61287i −0.539733 + 0.599435i −0.949891 0.312580i \(-0.898807\pi\)
0.410158 + 0.912014i \(0.365473\pi\)
\(20\) 0.104528 + 0.994522i 0.0233733 + 0.222382i
\(21\) 3.41598 + 0.726089i 0.745428 + 0.158446i
\(22\) −3.60137 + 1.60343i −0.767815 + 0.341853i
\(23\) −4.87954 3.54519i −1.01745 0.739224i −0.0516951 0.998663i \(-0.516462\pi\)
−0.965760 + 0.259439i \(0.916462\pi\)
\(24\) −0.913545 0.406737i −0.186477 0.0830248i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −1.47988 + 2.56323i −0.290228 + 0.502690i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) −3.41598 + 0.726089i −0.645559 + 0.137218i
\(29\) 1.43570 + 4.41862i 0.266602 + 0.820518i 0.991320 + 0.131472i \(0.0419702\pi\)
−0.724718 + 0.689046i \(0.758030\pi\)
\(30\) 1.00000 0.182574
\(31\) 2.58958 4.92890i 0.465103 0.885257i
\(32\) 1.00000 0.176777
\(33\) 1.21820 + 3.74925i 0.212062 + 0.652660i
\(34\) 7.84421 1.66734i 1.34527 0.285946i
\(35\) 2.82533 2.05272i 0.477567 0.346973i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) 4.86873 + 8.43289i 0.800415 + 1.38636i 0.919343 + 0.393456i \(0.128721\pi\)
−0.118929 + 0.992903i \(0.537946\pi\)
\(38\) −3.21200 1.43007i −0.521055 0.231989i
\(39\) 2.39450 + 1.73970i 0.383426 + 0.278575i
\(40\) −0.913545 + 0.406737i −0.144444 + 0.0643107i
\(41\) 10.0697 + 2.14038i 1.57262 + 0.334271i 0.909976 0.414662i \(-0.136100\pi\)
0.662646 + 0.748933i \(0.269434\pi\)
\(42\) 0.365044 + 3.47316i 0.0563275 + 0.535921i
\(43\) −4.77909 + 5.30772i −0.728805 + 0.809419i −0.987679 0.156491i \(-0.949982\pi\)
0.258875 + 0.965911i \(0.416648\pi\)
\(44\) −2.63784 2.92962i −0.397669 0.441657i
\(45\) 0.104528 0.994522i 0.0155822 0.148255i
\(46\) 1.86382 5.73624i 0.274805 0.845763i
\(47\) −1.34327 + 4.13417i −0.195937 + 0.603031i 0.804028 + 0.594592i \(0.202686\pi\)
−0.999964 + 0.00843901i \(0.997314\pi\)
\(48\) 0.104528 0.994522i 0.0150874 0.143547i
\(49\) 3.47688 + 3.86147i 0.496697 + 0.551638i
\(50\) 0.669131 0.743145i 0.0946294 0.105097i
\(51\) −0.838261 7.97552i −0.117380 1.11680i
\(52\) −2.89508 0.615369i −0.401476 0.0853363i
\(53\) 8.36017 3.72219i 1.14836 0.511282i 0.257821 0.966193i \(-0.416996\pi\)
0.890537 + 0.454911i \(0.150329\pi\)
\(54\) 0.809017 + 0.587785i 0.110093 + 0.0799874i
\(55\) 3.60137 + 1.60343i 0.485609 + 0.216207i
\(56\) −1.74615 3.02442i −0.233339 0.404155i
\(57\) −1.75798 + 3.04492i −0.232851 + 0.403309i
\(58\) −3.75870 + 2.73086i −0.493542 + 0.358579i
\(59\) −13.3203 + 2.83133i −1.73416 + 0.368607i −0.963307 0.268403i \(-0.913504\pi\)
−0.770855 + 0.637011i \(0.780171\pi\)
\(60\) 0.309017 + 0.951057i 0.0398939 + 0.122781i
\(61\) −10.3475 −1.32486 −0.662430 0.749123i \(-0.730475\pi\)
−0.662430 + 0.749123i \(0.730475\pi\)
\(62\) 5.48789 + 0.939726i 0.696962 + 0.119345i
\(63\) 3.49229 0.439988
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 2.89508 0.615369i 0.359091 0.0763271i
\(66\) −3.18930 + 2.31716i −0.392576 + 0.285223i
\(67\) 3.28687 5.69302i 0.401554 0.695513i −0.592359 0.805674i \(-0.701803\pi\)
0.993914 + 0.110161i \(0.0351367\pi\)
\(68\) 4.00973 + 6.94505i 0.486251 + 0.842211i
\(69\) −5.51000 2.45321i −0.663326 0.295332i
\(70\) 2.82533 + 2.05272i 0.337691 + 0.245347i
\(71\) 11.9280 5.31067i 1.41559 0.630261i 0.450642 0.892705i \(-0.351195\pi\)
0.964947 + 0.262444i \(0.0845284\pi\)
\(72\) −0.978148 0.207912i −0.115276 0.0245026i
\(73\) 0.00255919 + 0.0243491i 0.000299530 + 0.00284984i 0.994671 0.103103i \(-0.0328773\pi\)
−0.994371 + 0.105953i \(0.966211\pi\)
\(74\) −6.51564 + 7.23635i −0.757427 + 0.841208i
\(75\) −0.669131 0.743145i −0.0772645 0.0858110i
\(76\) 0.367519 3.49671i 0.0421573 0.401100i
\(77\) −4.25433 + 13.0935i −0.484825 + 1.49214i
\(78\) −0.914616 + 2.81490i −0.103560 + 0.318725i
\(79\) −0.200527 + 1.90789i −0.0225611 + 0.214654i 0.977433 + 0.211245i \(0.0677518\pi\)
−0.999994 + 0.00340917i \(0.998915\pi\)
\(80\) −0.669131 0.743145i −0.0748111 0.0830861i
\(81\) 0.669131 0.743145i 0.0743478 0.0825716i
\(82\) 1.07608 + 10.2383i 0.118834 + 1.13063i
\(83\) −10.3149 2.19249i −1.13220 0.240657i −0.396548 0.918014i \(-0.629792\pi\)
−0.735655 + 0.677357i \(0.763125\pi\)
\(84\) −3.19037 + 1.42044i −0.348098 + 0.154983i
\(85\) −6.48787 4.71372i −0.703709 0.511274i
\(86\) −6.52476 2.90501i −0.703583 0.313255i
\(87\) 2.32301 + 4.02357i 0.249053 + 0.431372i
\(88\) 1.97110 3.41404i 0.210119 0.363938i
\(89\) 2.70979 1.96878i 0.287237 0.208690i −0.434831 0.900512i \(-0.643192\pi\)
0.722068 + 0.691822i \(0.243192\pi\)
\(90\) 0.978148 0.207912i 0.103106 0.0219158i
\(91\) 3.19411 + 9.83045i 0.334834 + 1.03051i
\(92\) 6.03144 0.628822
\(93\) 1.50822 5.35960i 0.156395 0.555764i
\(94\) −4.34692 −0.448351
\(95\) 1.08649 + 3.34389i 0.111472 + 0.343075i
\(96\) 0.978148 0.207912i 0.0998318 0.0212199i
\(97\) −1.10581 + 0.803415i −0.112278 + 0.0815745i −0.642507 0.766280i \(-0.722106\pi\)
0.530230 + 0.847854i \(0.322106\pi\)
\(98\) −2.59806 + 4.49997i −0.262444 + 0.454566i
\(99\) 1.97110 + 3.41404i 0.198103 + 0.343124i
\(100\) 0.913545 + 0.406737i 0.0913545 + 0.0406737i
\(101\) −13.0056 9.44913i −1.29411 0.940224i −0.294228 0.955735i \(-0.595062\pi\)
−0.999880 + 0.0155113i \(0.995062\pi\)
\(102\) 7.32614 3.26181i 0.725396 0.322967i
\(103\) −14.9776 3.18359i −1.47579 0.313689i −0.601413 0.798938i \(-0.705396\pi\)
−0.874376 + 0.485249i \(0.838729\pi\)
\(104\) −0.309379 2.94355i −0.0303371 0.288638i
\(105\) 2.33680 2.59528i 0.228048 0.253273i
\(106\) 6.12344 + 6.80077i 0.594761 + 0.660550i
\(107\) 1.48350 14.1146i 0.143416 1.36451i −0.651896 0.758309i \(-0.726026\pi\)
0.795312 0.606201i \(-0.207307\pi\)
\(108\) −0.309017 + 0.951057i −0.0297352 + 0.0915155i
\(109\) 2.49092 7.66625i 0.238586 0.734293i −0.758039 0.652209i \(-0.773842\pi\)
0.996625 0.0820842i \(-0.0261577\pi\)
\(110\) −0.412071 + 3.92059i −0.0392894 + 0.373814i
\(111\) 6.51564 + 7.23635i 0.618437 + 0.686844i
\(112\) 2.33680 2.59528i 0.220807 0.245231i
\(113\) −1.37972 13.1272i −0.129793 1.23490i −0.844531 0.535507i \(-0.820121\pi\)
0.714738 0.699393i \(-0.246546\pi\)
\(114\) −3.43914 0.731011i −0.322105 0.0684655i
\(115\) −5.51000 + 2.45321i −0.513810 + 0.228763i
\(116\) −3.75870 2.73086i −0.348987 0.253554i
\(117\) 2.70387 + 1.20384i 0.249973 + 0.111295i
\(118\) −6.80897 11.7935i −0.626816 1.08568i
\(119\) 14.0031 24.2542i 1.28367 2.22338i
\(120\) −0.809017 + 0.587785i −0.0738528 + 0.0536572i
\(121\) −4.44163 + 0.944099i −0.403785 + 0.0858271i
\(122\) −3.19755 9.84105i −0.289493 0.890967i
\(123\) 10.2947 0.928238
\(124\) 0.802118 + 5.50968i 0.0720323 + 0.494784i
\(125\) −1.00000 −0.0894427
\(126\) 1.07918 + 3.32137i 0.0961408 + 0.295891i
\(127\) 9.38612 1.99508i 0.832884 0.177035i 0.228314 0.973587i \(-0.426679\pi\)
0.604569 + 0.796553i \(0.293345\pi\)
\(128\) −0.809017 + 0.587785i −0.0715077 + 0.0519534i
\(129\) −3.57112 + 6.18536i −0.314420 + 0.544591i
\(130\) 1.47988 + 2.56323i 0.129794 + 0.224810i
\(131\) −5.77756 2.57234i −0.504788 0.224746i 0.138511 0.990361i \(-0.455768\pi\)
−0.643299 + 0.765615i \(0.722435\pi\)
\(132\) −3.18930 2.31716i −0.277593 0.201683i
\(133\) −11.2172 + 4.99424i −0.972658 + 0.433055i
\(134\) 6.43008 + 1.36676i 0.555474 + 0.118070i
\(135\) −0.104528 0.994522i −0.00899638 0.0855948i
\(136\) −5.36606 + 5.95962i −0.460136 + 0.511033i
\(137\) 0.611466 + 0.679102i 0.0522411 + 0.0580196i 0.768699 0.639611i \(-0.220904\pi\)
−0.716458 + 0.697630i \(0.754238\pi\)
\(138\) 0.630458 5.99840i 0.0536681 0.510618i
\(139\) −3.90400 + 12.0153i −0.331133 + 1.01912i 0.637463 + 0.770481i \(0.279984\pi\)
−0.968596 + 0.248641i \(0.920016\pi\)
\(140\) −1.07918 + 3.32137i −0.0912072 + 0.280707i
\(141\) −0.454377 + 4.32311i −0.0382655 + 0.364072i
\(142\) 8.73670 + 9.70308i 0.733167 + 0.814265i
\(143\) −7.80737 + 8.67097i −0.652885 + 0.725103i
\(144\) −0.104528 0.994522i −0.00871071 0.0828768i
\(145\) 4.54449 + 0.965961i 0.377399 + 0.0802187i
\(146\) −0.0223665 + 0.00995820i −0.00185106 + 0.000824147i
\(147\) 4.20375 + 3.05420i 0.346719 + 0.251906i
\(148\) −8.89562 3.96058i −0.731215 0.325558i
\(149\) −10.2541 17.7607i −0.840052 1.45501i −0.889850 0.456253i \(-0.849191\pi\)
0.0497978 0.998759i \(-0.484142\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) −2.98570 + 2.16924i −0.242973 + 0.176530i −0.702607 0.711578i \(-0.747981\pi\)
0.459634 + 0.888109i \(0.347981\pi\)
\(152\) 3.43914 0.731011i 0.278951 0.0592928i
\(153\) −2.47815 7.62695i −0.200346 0.616603i
\(154\) −13.7673 −1.10940
\(155\) −2.97376 4.70710i −0.238858 0.378083i
\(156\) −2.95976 −0.236970
\(157\) 3.80048 + 11.6967i 0.303312 + 0.933497i 0.980302 + 0.197505i \(0.0632839\pi\)
−0.676990 + 0.735992i \(0.736716\pi\)
\(158\) −1.87648 + 0.398857i −0.149284 + 0.0317314i
\(159\) 7.40359 5.37902i 0.587143 0.426584i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) −10.5318 18.2416i −0.830021 1.43764i
\(162\) 0.913545 + 0.406737i 0.0717749 + 0.0319562i
\(163\) 6.71673 + 4.87999i 0.526095 + 0.382230i 0.818895 0.573943i \(-0.194587\pi\)
−0.292800 + 0.956174i \(0.594587\pi\)
\(164\) −9.40463 + 4.18721i −0.734378 + 0.326966i
\(165\) 3.85604 + 0.819627i 0.300193 + 0.0638079i
\(166\) −1.10228 10.4875i −0.0855538 0.813990i
\(167\) 1.35504 1.50493i 0.104857 0.116455i −0.688432 0.725301i \(-0.741701\pi\)
0.793288 + 0.608846i \(0.208367\pi\)
\(168\) −2.33680 2.59528i −0.180288 0.200230i
\(169\) 0.443182 4.21660i 0.0340909 0.324354i
\(170\) 2.47815 7.62695i 0.190065 0.584961i
\(171\) −1.08649 + 3.34389i −0.0830863 + 0.255713i
\(172\) 0.746567 7.10311i 0.0569252 0.541607i
\(173\) 7.97598 + 8.85822i 0.606402 + 0.673478i 0.965675 0.259755i \(-0.0836418\pi\)
−0.359272 + 0.933233i \(0.616975\pi\)
\(174\) −3.10879 + 3.45266i −0.235677 + 0.261746i
\(175\) −0.365044 3.47316i −0.0275947 0.262546i
\(176\) 3.85604 + 0.819627i 0.290660 + 0.0617817i
\(177\) −12.4406 + 5.53891i −0.935093 + 0.416330i
\(178\) 2.70979 + 1.96878i 0.203107 + 0.147566i
\(179\) −7.09527 3.15902i −0.530325 0.236116i 0.124063 0.992274i \(-0.460407\pi\)
−0.654389 + 0.756158i \(0.727074\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −6.27701 + 10.8721i −0.466566 + 0.808116i −0.999271 0.0381850i \(-0.987842\pi\)
0.532705 + 0.846301i \(0.321176\pi\)
\(182\) −8.36228 + 6.07555i −0.619854 + 0.450350i
\(183\) −10.1214 + 2.15137i −0.748194 + 0.159033i
\(184\) 1.86382 + 5.73624i 0.137403 + 0.422882i
\(185\) 9.73747 0.715913
\(186\) 5.56334 0.221805i 0.407924 0.0162636i
\(187\) 31.6142 2.31186
\(188\) −1.34327 4.13417i −0.0979683 0.301515i
\(189\) 3.41598 0.726089i 0.248476 0.0528152i
\(190\) −2.84448 + 2.06664i −0.206360 + 0.149929i
\(191\) −10.2917 + 17.8258i −0.744682 + 1.28983i 0.205661 + 0.978623i \(0.434065\pi\)
−0.950343 + 0.311204i \(0.899268\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 5.43690 + 2.42066i 0.391356 + 0.174243i 0.592975 0.805221i \(-0.297953\pi\)
−0.201618 + 0.979464i \(0.564620\pi\)
\(194\) −1.10581 0.803415i −0.0793923 0.0576819i
\(195\) 2.70387 1.20384i 0.193629 0.0862090i
\(196\) −5.08257 1.08033i −0.363041 0.0771667i
\(197\) −1.35257 12.8689i −0.0963668 0.916869i −0.930743 0.365674i \(-0.880839\pi\)
0.834376 0.551195i \(-0.185828\pi\)
\(198\) −2.63784 + 2.92962i −0.187463 + 0.208199i
\(199\) −6.57164 7.29854i −0.465851 0.517380i 0.463741 0.885971i \(-0.346507\pi\)
−0.929592 + 0.368591i \(0.879840\pi\)
\(200\) −0.104528 + 0.994522i −0.00739128 + 0.0703233i
\(201\) 2.03139 6.25199i 0.143284 0.440981i
\(202\) 4.96770 15.2890i 0.349526 1.07573i
\(203\) −1.69600 + 16.1364i −0.119036 + 1.13255i
\(204\) 5.36606 + 5.95962i 0.375700 + 0.417257i
\(205\) 6.88847 7.65042i 0.481111 0.534328i
\(206\) −1.60056 15.2284i −0.111517 1.06101i
\(207\) −5.89964 1.25401i −0.410054 0.0871596i
\(208\) 2.70387 1.20384i 0.187480 0.0834715i
\(209\) −11.2135 8.14707i −0.775652 0.563545i
\(210\) 3.19037 + 1.42044i 0.220156 + 0.0980199i
\(211\) −0.977516 1.69311i −0.0672950 0.116558i 0.830415 0.557146i \(-0.188104\pi\)
−0.897710 + 0.440587i \(0.854770\pi\)
\(212\) −4.57567 + 7.92530i −0.314258 + 0.544312i
\(213\) 10.5632 7.67459i 0.723776 0.525854i
\(214\) 13.8822 2.95075i 0.948968 0.201709i
\(215\) 2.20707 + 6.79267i 0.150521 + 0.463256i
\(216\) −1.00000 −0.0680414
\(217\) 15.2630 12.0467i 1.03612 0.817780i
\(218\) 8.06077 0.545944
\(219\) 0.00756572 + 0.0232849i 0.000511244 + 0.00157345i
\(220\) −3.85604 + 0.819627i −0.259974 + 0.0552593i
\(221\) 19.2025 13.9515i 1.29170 0.938477i
\(222\) −4.86873 + 8.43289i −0.326768 + 0.565979i
\(223\) −1.44258 2.49863i −0.0966025 0.167320i 0.813674 0.581322i \(-0.197464\pi\)
−0.910276 + 0.414001i \(0.864131\pi\)
\(224\) 3.19037 + 1.42044i 0.213166 + 0.0949074i
\(225\) −0.809017 0.587785i −0.0539345 0.0391857i
\(226\) 12.0583 5.36871i 0.802107 0.357121i
\(227\) −6.39246 1.35876i −0.424282 0.0901840i −0.00917810 0.999958i \(-0.502922\pi\)
−0.415104 + 0.909774i \(0.636255\pi\)
\(228\) −0.367519 3.49671i −0.0243395 0.231575i
\(229\) 18.7459 20.8194i 1.23876 1.37578i 0.338188 0.941079i \(-0.390186\pi\)
0.900573 0.434705i \(-0.143147\pi\)
\(230\) −4.03582 4.48224i −0.266114 0.295550i
\(231\) −1.43907 + 13.6919i −0.0946841 + 0.900859i
\(232\) 1.43570 4.41862i 0.0942582 0.290097i
\(233\) −3.49734 + 10.7637i −0.229118 + 0.705153i 0.768729 + 0.639574i \(0.220889\pi\)
−0.997847 + 0.0655789i \(0.979111\pi\)
\(234\) −0.309379 + 2.94355i −0.0202247 + 0.192426i
\(235\) 2.90866 + 3.23039i 0.189740 + 0.210728i
\(236\) 9.11218 10.1201i 0.593152 0.658762i
\(237\) 0.200527 + 1.90789i 0.0130256 + 0.123931i
\(238\) 27.3943 + 5.82284i 1.77571 + 0.377438i
\(239\) −25.0952 + 11.1731i −1.62328 + 0.722729i −0.998321 0.0579317i \(-0.981549\pi\)
−0.624955 + 0.780661i \(0.714883\pi\)
\(240\) −0.809017 0.587785i −0.0522218 0.0379414i
\(241\) −3.36085 1.49635i −0.216491 0.0963882i 0.295626 0.955304i \(-0.404472\pi\)
−0.512117 + 0.858916i \(0.671139\pi\)
\(242\) −2.27043 3.93250i −0.145949 0.252791i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 8.37130 6.08210i 0.535917 0.389367i
\(245\) 5.08257 1.08033i 0.324714 0.0690200i
\(246\) 3.18122 + 9.79080i 0.202827 + 0.624238i
\(247\) −10.4064 −0.662145
\(248\) −4.99215 + 2.46545i −0.317002 + 0.156556i
\(249\) −10.5453 −0.668281
\(250\) −0.309017 0.951057i −0.0195440 0.0601501i
\(251\) −3.67537 + 0.781223i −0.231987 + 0.0493104i −0.322438 0.946591i \(-0.604502\pi\)
0.0904511 + 0.995901i \(0.471169\pi\)
\(252\) −2.82533 + 2.05272i −0.177979 + 0.129309i
\(253\) 11.8886 20.5916i 0.747427 1.29458i
\(254\) 4.79791 + 8.31022i 0.301047 + 0.521430i
\(255\) −7.32614 3.26181i −0.458780 0.204262i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 9.14120 4.06992i 0.570212 0.253875i −0.101315 0.994854i \(-0.532305\pi\)
0.671528 + 0.740980i \(0.265638\pi\)
\(258\) −6.98616 1.48496i −0.434940 0.0924493i
\(259\) 3.55460 + 33.8198i 0.220872 + 2.10146i
\(260\) −1.98047 + 2.19953i −0.122823 + 0.136409i
\(261\) 3.10879 + 3.45266i 0.192429 + 0.213714i
\(262\) 0.661072 6.28968i 0.0408412 0.388578i
\(263\) 6.27414 19.3098i 0.386880 1.19069i −0.548227 0.836329i \(-0.684697\pi\)
0.935107 0.354365i \(-0.115303\pi\)
\(264\) 1.21820 3.74925i 0.0749753 0.230750i
\(265\) 0.956576 9.10121i 0.0587620 0.559083i
\(266\) −8.21612 9.12493i −0.503763 0.559485i
\(267\) 2.24124 2.48915i 0.137162 0.152334i
\(268\) 0.687142 + 6.53772i 0.0419739 + 0.399355i
\(269\) −14.0201 2.98007i −0.854821 0.181698i −0.240398 0.970674i \(-0.577278\pi\)
−0.614423 + 0.788977i \(0.710611\pi\)
\(270\) 0.913545 0.406737i 0.0555966 0.0247532i
\(271\) −20.3135 14.7586i −1.23396 0.896524i −0.236779 0.971564i \(-0.576092\pi\)
−0.997181 + 0.0750397i \(0.976092\pi\)
\(272\) −7.32614 3.26181i −0.444212 0.197776i
\(273\) 5.16818 + 8.95154i 0.312792 + 0.541772i
\(274\) −0.456911 + 0.791393i −0.0276030 + 0.0478098i
\(275\) 3.18930 2.31716i 0.192322 0.139730i
\(276\) 5.89964 1.25401i 0.355117 0.0754824i
\(277\) 2.81423 + 8.66130i 0.169090 + 0.520407i 0.999314 0.0370230i \(-0.0117875\pi\)
−0.830224 + 0.557430i \(0.811787\pi\)
\(278\) −12.6336 −0.757713
\(279\) 0.360938 5.55605i 0.0216088 0.332632i
\(280\) −3.49229 −0.208704
\(281\) −9.45482 29.0989i −0.564027 1.73590i −0.670824 0.741616i \(-0.734059\pi\)
0.106797 0.994281i \(-0.465941\pi\)
\(282\) −4.25193 + 0.903776i −0.253199 + 0.0538191i
\(283\) −8.60711 + 6.25343i −0.511640 + 0.371728i −0.813445 0.581641i \(-0.802411\pi\)
0.301805 + 0.953370i \(0.402411\pi\)
\(284\) −6.52839 + 11.3075i −0.387389 + 0.670977i
\(285\) 1.75798 + 3.04492i 0.104134 + 0.180365i
\(286\) −10.6592 4.74578i −0.630291 0.280624i
\(287\) 29.0857 + 21.1320i 1.71688 + 1.24738i
\(288\) 0.913545 0.406737i 0.0538312 0.0239672i
\(289\) −46.2778 9.83664i −2.72222 0.578626i
\(290\) 0.485641 + 4.62056i 0.0285178 + 0.271329i
\(291\) −0.914603 + 1.01577i −0.0536149 + 0.0595454i
\(292\) −0.0163824 0.0181945i −0.000958710 0.00106476i
\(293\) −2.45530 + 23.3606i −0.143440 + 1.36474i 0.651774 + 0.758414i \(0.274025\pi\)
−0.795214 + 0.606329i \(0.792641\pi\)
\(294\) −1.60569 + 4.94180i −0.0936457 + 0.288212i
\(295\) −4.20817 + 12.9514i −0.245009 + 0.754061i
\(296\) 1.01784 9.68412i 0.0591609 0.562878i
\(297\) 2.63784 + 2.92962i 0.153063 + 0.169994i
\(298\) 13.7227 15.2406i 0.794936 0.882866i
\(299\) −1.86600 17.7538i −0.107914 1.02673i
\(300\) 0.978148 + 0.207912i 0.0564734 + 0.0120038i
\(301\) −22.7864 + 10.1452i −1.31339 + 0.584757i
\(302\) −2.98570 2.16924i −0.171808 0.124826i
\(303\) −14.6860 6.53863i −0.843689 0.375634i
\(304\) 1.75798 + 3.04492i 0.100827 + 0.174638i
\(305\) −5.17375 + 8.96119i −0.296248 + 0.513116i
\(306\) 6.48787 4.71372i 0.370887 0.269465i
\(307\) −1.96771 + 0.418251i −0.112303 + 0.0238708i −0.263721 0.964599i \(-0.584950\pi\)
0.151417 + 0.988470i \(0.451616\pi\)
\(308\) −4.25433 13.0935i −0.242413 0.746070i
\(309\) −15.3122 −0.871083
\(310\) 3.55777 4.28279i 0.202068 0.243246i
\(311\) 30.8324 1.74834 0.874172 0.485616i \(-0.161405\pi\)
0.874172 + 0.485616i \(0.161405\pi\)
\(312\) −0.914616 2.81490i −0.0517799 0.159362i
\(313\) −9.51265 + 2.02198i −0.537687 + 0.114289i −0.468748 0.883332i \(-0.655295\pi\)
−0.0689389 + 0.997621i \(0.521961\pi\)
\(314\) −9.94979 + 7.22895i −0.561499 + 0.407953i
\(315\) 1.74615 3.02442i 0.0983842 0.170407i
\(316\) −0.959199 1.66138i −0.0539592 0.0934600i
\(317\) 1.34852 + 0.600399i 0.0757403 + 0.0337218i 0.444257 0.895899i \(-0.353468\pi\)
−0.368517 + 0.929621i \(0.620134\pi\)
\(318\) 7.40359 + 5.37902i 0.415173 + 0.301641i
\(319\) −16.7320 + 7.44957i −0.936813 + 0.417096i
\(320\) 0.978148 + 0.207912i 0.0546801 + 0.0116226i
\(321\) −1.48350 14.1146i −0.0828011 0.787800i
\(322\) 14.0943 15.6533i 0.785444 0.872324i
\(323\) 18.8669 + 20.9538i 1.04978 + 1.16590i
\(324\) −0.104528 + 0.994522i −0.00580714 + 0.0552512i
\(325\) 0.914616 2.81490i 0.0507338 0.156142i
\(326\) −2.56556 + 7.89599i −0.142093 + 0.437319i
\(327\) 0.842580 8.01661i 0.0465948 0.443320i
\(328\) −6.88847 7.65042i −0.380352 0.422424i
\(329\) −10.1579 + 11.2815i −0.560023 + 0.621968i
\(330\) 0.412071 + 3.92059i 0.0226838 + 0.215822i
\(331\) 30.1049 + 6.39900i 1.65472 + 0.351721i 0.938266 0.345916i \(-0.112432\pi\)
0.716452 + 0.697637i \(0.245765\pi\)
\(332\) 9.63361 4.28916i 0.528713 0.235398i
\(333\) 7.87778 + 5.72354i 0.431699 + 0.313648i
\(334\) 1.85001 + 0.823675i 0.101228 + 0.0450695i
\(335\) −3.28687 5.69302i −0.179581 0.311043i
\(336\) 1.74615 3.02442i 0.0952601 0.164995i
\(337\) 16.8165 12.2179i 0.916055 0.665553i −0.0264839 0.999649i \(-0.508431\pi\)
0.942539 + 0.334096i \(0.108431\pi\)
\(338\) 4.14717 0.881509i 0.225576 0.0479478i
\(339\) −4.07886 12.5534i −0.221533 0.681809i
\(340\) 8.01945 0.434916
\(341\) 20.3913 + 8.12165i 1.10425 + 0.439812i
\(342\) −3.51597 −0.190122
\(343\) −1.94671 5.99136i −0.105112 0.323503i
\(344\) 6.98616 1.48496i 0.376669 0.0800634i
\(345\) −4.87954 + 3.54519i −0.262706 + 0.190867i
\(346\) −5.95995 + 10.3229i −0.320409 + 0.554965i
\(347\) −1.32012 2.28651i −0.0708676 0.122746i 0.828414 0.560116i \(-0.189243\pi\)
−0.899282 + 0.437370i \(0.855910\pi\)
\(348\) −4.24435 1.88970i −0.227521 0.101299i
\(349\) −7.06145 5.13044i −0.377991 0.274626i 0.382526 0.923945i \(-0.375054\pi\)
−0.760517 + 0.649318i \(0.775054\pi\)
\(350\) 3.19037 1.42044i 0.170532 0.0759259i
\(351\) 2.89508 + 0.615369i 0.154528 + 0.0328459i
\(352\) 0.412071 + 3.92059i 0.0219635 + 0.208968i
\(353\) −5.14815 + 5.71760i −0.274008 + 0.304317i −0.864405 0.502796i \(-0.832305\pi\)
0.590397 + 0.807113i \(0.298971\pi\)
\(354\) −9.11218 10.1201i −0.484307 0.537877i
\(355\) 1.36481 12.9853i 0.0724364 0.689186i
\(356\) −1.03505 + 3.18555i −0.0548574 + 0.168834i
\(357\) 8.65442 26.6356i 0.458040 1.40970i
\(358\) 0.811845 7.72419i 0.0429074 0.408236i
\(359\) −14.4370 16.0339i −0.761956 0.846238i 0.229951 0.973202i \(-0.426143\pi\)
−0.991907 + 0.126964i \(0.959477\pi\)
\(360\) −0.669131 + 0.743145i −0.0352663 + 0.0391672i
\(361\) 0.693856 + 6.60159i 0.0365187 + 0.347452i
\(362\) −12.2797 2.61013i −0.645405 0.137185i
\(363\) −4.14829 + 1.84694i −0.217729 + 0.0969390i
\(364\) −8.36228 6.07555i −0.438303 0.318446i
\(365\) 0.0223665 + 0.00995820i 0.00117072 + 0.000521236i
\(366\) −5.17375 8.96119i −0.270436 0.468409i
\(367\) −3.54058 + 6.13246i −0.184817 + 0.320112i −0.943515 0.331331i \(-0.892502\pi\)
0.758698 + 0.651442i \(0.225836\pi\)
\(368\) −4.87954 + 3.54519i −0.254364 + 0.184806i
\(369\) 10.0697 2.14038i 0.524207 0.111424i
\(370\) 3.00904 + 9.26088i 0.156433 + 0.481450i
\(371\) 31.9592 1.65924
\(372\) 1.93012 + 5.22251i 0.100072 + 0.270775i
\(373\) 18.2472 0.944803 0.472401 0.881384i \(-0.343387\pi\)
0.472401 + 0.881384i \(0.343387\pi\)
\(374\) 9.76933 + 30.0669i 0.505160 + 1.55472i
\(375\) −0.978148 + 0.207912i −0.0505113 + 0.0107365i
\(376\) 3.51673 2.55506i 0.181362 0.131767i
\(377\) −6.87554 + 11.9088i −0.354108 + 0.613334i
\(378\) 1.74615 + 3.02442i 0.0898121 + 0.155559i
\(379\) 23.7635 + 10.5802i 1.22065 + 0.543468i 0.912972 0.408023i \(-0.133782\pi\)
0.307677 + 0.951491i \(0.400448\pi\)
\(380\) −2.84448 2.06664i −0.145919 0.106016i
\(381\) 8.76621 3.90297i 0.449107 0.199955i
\(382\) −20.1336 4.27953i −1.03013 0.218960i
\(383\) 1.27309 + 12.1126i 0.0650517 + 0.618926i 0.977675 + 0.210124i \(0.0673866\pi\)
−0.912623 + 0.408802i \(0.865947\pi\)
\(384\) −0.669131 + 0.743145i −0.0341464 + 0.0379235i
\(385\) 9.21211 + 10.2311i 0.469493 + 0.521425i
\(386\) −0.622093 + 5.91882i −0.0316637 + 0.301260i
\(387\) −2.20707 + 6.79267i −0.112192 + 0.345291i
\(388\) 0.422380 1.29995i 0.0214431 0.0659951i
\(389\) 1.52822 14.5400i 0.0774836 0.737208i −0.884949 0.465688i \(-0.845807\pi\)
0.962433 0.271520i \(-0.0875263\pi\)
\(390\) 1.98047 + 2.19953i 0.100285 + 0.111378i
\(391\) −32.3651 + 35.9451i −1.63677 + 1.81782i
\(392\) −0.543142 5.16765i −0.0274328 0.261006i
\(393\) −6.18613 1.31490i −0.312049 0.0663280i
\(394\) 11.8211 5.26307i 0.595536 0.265150i
\(395\) 1.55202 + 1.12761i 0.0780905 + 0.0567360i
\(396\) −3.60137 1.60343i −0.180976 0.0805756i
\(397\) 8.50496 + 14.7310i 0.426852 + 0.739329i 0.996591 0.0824963i \(-0.0262893\pi\)
−0.569740 + 0.821825i \(0.692956\pi\)
\(398\) 4.91058 8.50537i 0.246145 0.426336i
\(399\) −9.93376 + 7.21730i −0.497310 + 0.361317i
\(400\) −0.978148 + 0.207912i −0.0489074 + 0.0103956i
\(401\) 11.1483 + 34.3108i 0.556717 + 1.71340i 0.691364 + 0.722507i \(0.257010\pi\)
−0.134647 + 0.990894i \(0.542990\pi\)
\(402\) 6.57373 0.327868
\(403\) 15.9698 4.06565i 0.795515 0.202525i
\(404\) 16.0758 0.799802
\(405\) −0.309017 0.951057i −0.0153552 0.0472584i
\(406\) −15.8707 + 3.37342i −0.787649 + 0.167420i
\(407\) −31.0557 + 22.5633i −1.53937 + 1.11842i
\(408\) −4.00973 + 6.94505i −0.198511 + 0.343831i
\(409\) −4.39322 7.60928i −0.217231 0.376255i 0.736730 0.676187i \(-0.236369\pi\)
−0.953960 + 0.299933i \(0.903036\pi\)
\(410\) 9.40463 + 4.18721i 0.464462 + 0.206792i
\(411\) 0.739297 + 0.537131i 0.0364668 + 0.0264947i
\(412\) 13.9884 6.22805i 0.689160 0.306834i
\(413\) −46.5186 9.88783i −2.28903 0.486548i
\(414\) −0.630458 5.99840i −0.0309853 0.294805i
\(415\) −7.05618 + 7.83669i −0.346374 + 0.384688i
\(416\) 1.98047 + 2.19953i 0.0971003 + 0.107841i
\(417\) −1.32057 + 12.5644i −0.0646687 + 0.615281i
\(418\) 4.28317 13.1822i 0.209497 0.644764i
\(419\) −2.26594 + 6.97385i −0.110698 + 0.340695i −0.991026 0.133672i \(-0.957323\pi\)
0.880327 + 0.474367i \(0.157323\pi\)
\(420\) −0.365044 + 3.47316i −0.0178123 + 0.169473i
\(421\) −25.2705 28.0658i −1.23161 1.36784i −0.906522 0.422159i \(-0.861273\pi\)
−0.325089 0.945684i \(-0.605394\pi\)
\(422\) 1.30817 1.45287i 0.0636808 0.0707247i
\(423\) 0.454377 + 4.32311i 0.0220926 + 0.210197i
\(424\) −8.95136 1.90267i −0.434717 0.0924019i
\(425\) −7.32614 + 3.26181i −0.355370 + 0.158221i
\(426\) 10.5632 + 7.67459i 0.511787 + 0.371835i
\(427\) −33.0123 14.6980i −1.59758 0.711288i
\(428\) 7.09617 + 12.2909i 0.343006 + 0.594104i
\(429\) −5.83397 + 10.1047i −0.281667 + 0.487861i
\(430\) −5.77819 + 4.19810i −0.278649 + 0.202450i
\(431\) 30.2994 6.44035i 1.45947 0.310221i 0.591288 0.806461i \(-0.298620\pi\)
0.868185 + 0.496240i \(0.165286\pi\)
\(432\) −0.309017 0.951057i −0.0148676 0.0457577i
\(433\) −0.0384231 −0.00184649 −0.000923247 1.00000i \(-0.500294\pi\)
−0.000923247 1.00000i \(0.500294\pi\)
\(434\) 16.1736 + 10.7933i 0.776356 + 0.518095i
\(435\) 4.64601 0.222759
\(436\) 2.49092 + 7.66625i 0.119293 + 0.367147i
\(437\) 20.7430 4.40905i 0.992271 0.210914i
\(438\) −0.0198073 + 0.0143908i −0.000946430 + 0.000687621i
\(439\) 6.64782 11.5144i 0.317283 0.549550i −0.662637 0.748941i \(-0.730563\pi\)
0.979920 + 0.199390i \(0.0638961\pi\)
\(440\) −1.97110 3.41404i −0.0939683 0.162758i
\(441\) 4.74689 + 2.11345i 0.226042 + 0.100641i
\(442\) 19.2025 + 13.9515i 0.913372 + 0.663604i
\(443\) 13.8586 6.17024i 0.658441 0.293157i −0.0501862 0.998740i \(-0.515981\pi\)
0.708627 + 0.705583i \(0.249315\pi\)
\(444\) −9.52468 2.02453i −0.452021 0.0960801i
\(445\) −0.350116 3.33114i −0.0165971 0.157911i
\(446\) 1.93055 2.14410i 0.0914143 0.101526i
\(447\) −13.7227 15.2406i −0.649062 0.720857i
\(448\) −0.365044 + 3.47316i −0.0172467 + 0.164092i
\(449\) 2.24576 6.91173i 0.105984 0.326185i −0.883976 0.467532i \(-0.845143\pi\)
0.989960 + 0.141347i \(0.0451433\pi\)
\(450\) 0.309017 0.951057i 0.0145672 0.0448332i
\(451\) −4.24213 + 40.3612i −0.199754 + 1.90053i
\(452\) 8.83217 + 9.80912i 0.415430 + 0.461382i
\(453\) −2.46945 + 2.74260i −0.116025 + 0.128859i
\(454\) −0.683121 6.49947i −0.0320605 0.305035i
\(455\) 10.1105 + 2.14905i 0.473986 + 0.100749i
\(456\) 3.21200 1.43007i 0.150416 0.0669693i
\(457\) 15.8135 + 11.4892i 0.739726 + 0.537443i 0.892625 0.450799i \(-0.148861\pi\)
−0.152899 + 0.988242i \(0.548861\pi\)
\(458\) 25.5932 + 11.3948i 1.19589 + 0.532445i
\(459\) −4.00973 6.94505i −0.187158 0.324167i
\(460\) 3.01572 5.22338i 0.140609 0.243542i
\(461\) −20.5384 + 14.9221i −0.956571 + 0.694989i −0.952352 0.305002i \(-0.901343\pi\)
−0.00421894 + 0.999991i \(0.501343\pi\)
\(462\) −13.4664 + 2.86238i −0.626515 + 0.133170i
\(463\) 5.37341 + 16.5377i 0.249724 + 0.768570i 0.994824 + 0.101617i \(0.0324018\pi\)
−0.745100 + 0.666953i \(0.767598\pi\)
\(464\) 4.64601 0.215686
\(465\) −3.88744 3.98595i −0.180276 0.184844i
\(466\) −11.3176 −0.524279
\(467\) 10.4566 + 32.1822i 0.483875 + 1.48921i 0.833604 + 0.552362i \(0.186274\pi\)
−0.349729 + 0.936851i \(0.613726\pi\)
\(468\) −2.89508 + 0.615369i −0.133825 + 0.0284454i
\(469\) 18.5729 13.4940i 0.857618 0.623096i
\(470\) −2.17346 + 3.76455i −0.100254 + 0.173646i
\(471\) 6.14931 + 10.6509i 0.283345 + 0.490768i
\(472\) 12.4406 + 5.53891i 0.572625 + 0.254949i
\(473\) −22.7787 16.5497i −1.04737 0.760957i
\(474\) −1.75254 + 0.780283i −0.0804970 + 0.0358396i
\(475\) 3.43914 + 0.731011i 0.157798 + 0.0335411i
\(476\) 2.92745 + 27.8529i 0.134180 + 1.27663i
\(477\) 6.12344 6.80077i 0.280373 0.311386i
\(478\) −18.3811 20.4143i −0.840733 0.933728i
\(479\) 1.51370 14.4019i 0.0691629 0.658041i −0.903938 0.427663i \(-0.859337\pi\)
0.973101 0.230378i \(-0.0739962\pi\)
\(480\) 0.309017 0.951057i 0.0141046 0.0434096i
\(481\) −8.90604 + 27.4100i −0.406081 + 1.24979i
\(482\) 0.384551 3.65876i 0.0175158 0.166652i
\(483\) −14.0943 15.6533i −0.641312 0.712249i
\(484\) 3.03843 3.37452i 0.138110 0.153387i
\(485\) 0.142875 + 1.35936i 0.00648762 + 0.0617256i
\(486\) 0.978148 + 0.207912i 0.0443697 + 0.00943107i
\(487\) −7.41986 + 3.30353i −0.336226 + 0.149697i −0.567903 0.823095i \(-0.692245\pi\)
0.231677 + 0.972793i \(0.425579\pi\)
\(488\) 8.37130 + 6.08210i 0.378951 + 0.275324i
\(489\) 7.58456 + 3.37686i 0.342986 + 0.152707i
\(490\) 2.59806 + 4.49997i 0.117368 + 0.203288i
\(491\) −21.7682 + 37.7035i −0.982383 + 1.70154i −0.329350 + 0.944208i \(0.606830\pi\)
−0.653033 + 0.757329i \(0.726504\pi\)
\(492\) −8.32855 + 6.05104i −0.375480 + 0.272802i
\(493\) 36.4443 7.74648i 1.64137 0.348884i
\(494\) −3.21576 9.89710i −0.144684 0.445291i
\(495\) 3.94219 0.177188
\(496\) −3.88744 3.98595i −0.174551 0.178975i
\(497\) 45.5981 2.04536
\(498\) −3.25868 10.0292i −0.146025 0.449418i
\(499\) 16.8048 3.57197i 0.752286 0.159903i 0.184218 0.982885i \(-0.441025\pi\)
0.568067 + 0.822982i \(0.307691\pi\)
\(500\) 0.809017 0.587785i 0.0361803 0.0262866i
\(501\) 1.01254 1.75377i 0.0452370 0.0783528i
\(502\) −1.87874 3.25407i −0.0838522 0.145236i
\(503\) 11.3827 + 5.06793i 0.507532 + 0.225968i 0.644495 0.764608i \(-0.277068\pi\)
−0.136963 + 0.990576i \(0.543734\pi\)
\(504\) −2.82533 2.05272i −0.125850 0.0914354i
\(505\) −14.6860 + 6.53863i −0.653518 + 0.290965i
\(506\) 23.2575 + 4.94354i 1.03392 + 0.219767i
\(507\) −0.443182 4.21660i −0.0196824 0.187266i
\(508\) −6.42085 + 7.13108i −0.284879 + 0.316391i
\(509\) 3.42208 + 3.80060i 0.151681 + 0.168459i 0.814196 0.580589i \(-0.197178\pi\)
−0.662516 + 0.749048i \(0.730511\pi\)
\(510\) 0.838261 7.97552i 0.0371188 0.353162i
\(511\) −0.0264217 + 0.0813177i −0.00116883 + 0.00359728i
\(512\) 0.309017 0.951057i 0.0136568 0.0420312i
\(513\) −0.367519 + 3.49671i −0.0162264 + 0.154383i
\(514\) 6.69551 + 7.43612i 0.295326 + 0.327993i
\(515\) −10.2459 + 11.3792i −0.451488 + 0.501428i
\(516\) −0.746567 7.10311i −0.0328658 0.312697i
\(517\) −16.7619 3.56286i −0.737189 0.156694i
\(518\) −31.0661 + 13.8315i −1.36497 + 0.607722i
\(519\) 9.64341 + 7.00635i 0.423299 + 0.307544i
\(520\) −2.70387 1.20384i −0.118573 0.0527920i
\(521\) 1.54470 + 2.67551i 0.0676747 + 0.117216i 0.897877 0.440246i \(-0.145109\pi\)
−0.830203 + 0.557462i \(0.811775\pi\)
\(522\) −2.32301 + 4.02357i −0.101675 + 0.176107i
\(523\) −36.1153 + 26.2393i −1.57921 + 1.14736i −0.661617 + 0.749842i \(0.730129\pi\)
−0.917593 + 0.397521i \(0.869871\pi\)
\(524\) 6.18613 1.31490i 0.270242 0.0574418i
\(525\) −1.07918 3.32137i −0.0470992 0.144956i
\(526\) 20.3035 0.885277
\(527\) −37.1398 24.7850i −1.61784 1.07965i
\(528\) 3.94219 0.171562
\(529\) 4.13413 + 12.7235i 0.179745 + 0.553198i
\(530\) 8.95136 1.90267i 0.388822 0.0826468i
\(531\) −11.0171 + 8.00442i −0.478103 + 0.347362i
\(532\) 6.13940 10.6338i 0.266177 0.461032i
\(533\) 15.2348 + 26.3875i 0.659895 + 1.14297i
\(534\) 3.05991 + 1.36236i 0.132415 + 0.0589550i
\(535\) −11.4818 8.34205i −0.496403 0.360658i
\(536\) −6.00540 + 2.67378i −0.259394 + 0.115490i
\(537\) −7.59702 1.61480i −0.327836 0.0696836i
\(538\) −1.49824 14.2548i −0.0645937 0.614568i
\(539\) −13.7065 + 15.2226i −0.590382 + 0.655686i
\(540\) 0.669131 + 0.743145i 0.0287948 + 0.0319799i
\(541\) 2.52972 24.0687i 0.108761 1.03479i −0.794957 0.606666i \(-0.792506\pi\)
0.903718 0.428129i \(-0.140827\pi\)
\(542\) 7.75908 23.8800i 0.333281 1.02573i
\(543\) −3.87940 + 11.9396i −0.166481 + 0.512376i
\(544\) 0.838261 7.97552i 0.0359402 0.341948i
\(545\) −5.39371 5.99032i −0.231041 0.256597i
\(546\) −6.91637 + 7.68141i −0.295993 + 0.328734i
\(547\) 2.16199 + 20.5700i 0.0924400 + 0.879508i 0.938235 + 0.345999i \(0.112460\pi\)
−0.845795 + 0.533508i \(0.820873\pi\)
\(548\) −0.893852 0.189994i −0.0381835 0.00811615i
\(549\) −9.45291 + 4.20871i −0.403440 + 0.179623i
\(550\) 3.18930 + 2.31716i 0.135992 + 0.0988041i
\(551\) −14.9230 6.64414i −0.635741 0.283050i
\(552\) 3.01572 + 5.22338i 0.128358 + 0.222322i
\(553\) −3.34981 + 5.80203i −0.142448 + 0.246728i
\(554\) −7.36774 + 5.35298i −0.313025 + 0.227426i
\(555\) 9.52468 2.02453i 0.404300 0.0859366i
\(556\) −3.90400 12.0153i −0.165566 0.509561i
\(557\) −21.2011 −0.898319 −0.449160 0.893451i \(-0.648277\pi\)
−0.449160 + 0.893451i \(0.648277\pi\)
\(558\) 5.39566 1.37364i 0.228416 0.0581509i
\(559\) −21.1393 −0.894098
\(560\) −1.07918 3.32137i −0.0456036 0.140353i
\(561\) 30.9234 6.57296i 1.30559 0.277511i
\(562\) 24.7530 17.9841i 1.04414 0.758615i
\(563\) −0.325891 + 0.564459i −0.0137347 + 0.0237891i −0.872811 0.488058i \(-0.837705\pi\)
0.859076 + 0.511847i \(0.171039\pi\)
\(564\) −2.17346 3.76455i −0.0915192 0.158516i
\(565\) −12.0583 5.36871i −0.507297 0.225863i
\(566\) −8.60711 6.25343i −0.361784 0.262851i
\(567\) 3.19037 1.42044i 0.133983 0.0596530i
\(568\) −12.7715 2.71466i −0.535879 0.113905i
\(569\) 4.72231 + 44.9298i 0.197970 + 1.88356i 0.418560 + 0.908189i \(0.362535\pi\)
−0.220590 + 0.975367i \(0.570798\pi\)
\(570\) −2.35264 + 2.61287i −0.0985414 + 0.109441i
\(571\) 5.25514 + 5.83642i 0.219921 + 0.244247i 0.843002 0.537910i \(-0.180786\pi\)
−0.623081 + 0.782157i \(0.714119\pi\)
\(572\) 1.21963 11.6040i 0.0509953 0.485188i
\(573\) −6.36063 + 19.5760i −0.265719 + 0.817799i
\(574\) −11.1098 + 34.1923i −0.463713 + 1.42716i
\(575\) −0.630458 + 5.99840i −0.0262919 + 0.250151i
\(576\) 0.669131 + 0.743145i 0.0278804 + 0.0309644i
\(577\) −2.28034 + 2.53257i −0.0949317 + 0.105432i −0.788739 0.614729i \(-0.789265\pi\)
0.693807 + 0.720161i \(0.255932\pi\)
\(578\) −4.94541 47.0525i −0.205702 1.95712i
\(579\) 5.82137 + 1.23737i 0.241928 + 0.0514234i
\(580\) −4.24435 + 1.88970i −0.176237 + 0.0784657i
\(581\) −29.7939 21.6465i −1.23606 0.898050i
\(582\) −1.24868 0.555949i −0.0517595 0.0230448i
\(583\) 18.0382 + 31.2430i 0.747065 + 1.29395i
\(584\) 0.0122416 0.0212031i 0.000506560 0.000877389i
\(585\) 2.39450 1.73970i 0.0990002 0.0719279i
\(586\) −22.9760 + 4.88370i −0.949130 + 0.201744i
\(587\) 4.82195 + 14.8404i 0.199023 + 0.612530i 0.999906 + 0.0137092i \(0.00436391\pi\)
−0.800883 + 0.598821i \(0.795636\pi\)
\(588\) −5.19612 −0.214284
\(589\) 6.78623 + 18.3622i 0.279622 + 0.756601i
\(590\) −13.6179 −0.560641
\(591\) −3.99860 12.3064i −0.164481 0.506219i
\(592\) 9.52468 2.02453i 0.391462 0.0832078i
\(593\) −4.55033 + 3.30601i −0.186860 + 0.135761i −0.677282 0.735723i \(-0.736842\pi\)
0.490423 + 0.871485i \(0.336842\pi\)
\(594\) −1.97110 + 3.41404i −0.0808750 + 0.140080i
\(595\) −14.0031 24.2542i −0.574073 0.994324i
\(596\) 18.7352 + 8.34147i 0.767426 + 0.341680i
\(597\) −7.94548 5.77273i −0.325187 0.236262i
\(598\) 16.3083 7.26091i 0.666895 0.296921i
\(599\) −3.41120 0.725073i −0.139378 0.0296257i 0.137694 0.990475i \(-0.456031\pi\)
−0.277072 + 0.960849i \(0.589364\pi\)
\(600\) 0.104528 + 0.994522i 0.00426736 + 0.0406012i
\(601\) 5.90974 6.56343i 0.241063 0.267728i −0.610457 0.792049i \(-0.709014\pi\)
0.851520 + 0.524321i \(0.175681\pi\)
\(602\) −16.6900 18.5361i −0.680233 0.755476i
\(603\) 0.687142 6.53772i 0.0279826 0.266236i
\(604\) 1.14044 3.50991i 0.0464037 0.142816i
\(605\) −1.40320 + 4.31862i −0.0570484 + 0.175577i
\(606\) 1.68038 15.9878i 0.0682608 0.649458i
\(607\) 6.93539 + 7.70253i 0.281499 + 0.312636i 0.867268 0.497842i \(-0.165874\pi\)
−0.585769 + 0.810478i \(0.699207\pi\)
\(608\) −2.35264 + 2.61287i −0.0954123 + 0.105966i
\(609\) 1.69600 + 16.1364i 0.0687254 + 0.653878i
\(610\) −10.1214 2.15137i −0.409803 0.0871062i
\(611\) −11.7535 + 5.23301i −0.475497 + 0.211705i
\(612\) 6.48787 + 4.71372i 0.262257 + 0.190541i
\(613\) 28.9110 + 12.8720i 1.16770 + 0.519895i 0.896681 0.442678i \(-0.145972\pi\)
0.271022 + 0.962573i \(0.412638\pi\)
\(614\) −1.00584 1.74216i −0.0405923 0.0703079i
\(615\) 5.14733 8.91543i 0.207560 0.359505i
\(616\) 11.1380 8.09221i 0.448762 0.326044i
\(617\) 40.1353 8.53102i 1.61579 0.343446i 0.690682 0.723159i \(-0.257311\pi\)
0.925104 + 0.379713i \(0.123977\pi\)
\(618\) −4.73174 14.5628i −0.190339 0.585802i
\(619\) 17.1577 0.689627 0.344813 0.938671i \(-0.387942\pi\)
0.344813 + 0.938671i \(0.387942\pi\)
\(620\) 5.17258 + 2.06019i 0.207736 + 0.0827391i
\(621\) −6.03144 −0.242034
\(622\) 9.52773 + 29.3233i 0.382027 + 1.17576i
\(623\) 11.4418 2.43202i 0.458405 0.0974369i
\(624\) 2.39450 1.73970i 0.0958565 0.0696439i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −4.86258 8.42224i −0.194348 0.336620i
\(627\) −12.6623 5.63762i −0.505684 0.225145i
\(628\) −9.94979 7.22895i −0.397040 0.288466i
\(629\) 71.3380 31.7617i 2.84443 1.26642i
\(630\) 3.41598 + 0.726089i 0.136096 + 0.0289281i
\(631\) 2.35090 + 22.3673i 0.0935879 + 0.890429i 0.936096 + 0.351745i \(0.114412\pi\)
−0.842508 + 0.538684i \(0.818922\pi\)
\(632\) 1.28366 1.42565i 0.0510612 0.0567092i
\(633\) −1.30817 1.45287i −0.0519951 0.0577465i
\(634\) −0.154298 + 1.46805i −0.00612797 + 0.0583037i
\(635\) 2.96527 9.12616i 0.117673 0.362161i
\(636\) −2.82792 + 8.70344i −0.112134 + 0.345114i
\(637\) −1.60757 + 15.2950i −0.0636943 + 0.606010i
\(638\) −12.2554 13.6110i −0.485198 0.538867i
\(639\) 8.73670 9.70308i 0.345618 0.383848i
\(640\) 0.104528 + 0.994522i 0.00413185 + 0.0393119i
\(641\) 13.1819 + 2.80191i 0.520656 + 0.110669i 0.460741 0.887535i \(-0.347584\pi\)
0.0599148 + 0.998203i \(0.480917\pi\)
\(642\) 12.9653 5.77255i 0.511702 0.227824i
\(643\) 17.8623 + 12.9777i 0.704420 + 0.511791i 0.881369 0.472429i \(-0.156623\pi\)
−0.176949 + 0.984220i \(0.556623\pi\)
\(644\) 19.2425 + 8.56733i 0.758262 + 0.337600i
\(645\) 3.57112 + 6.18536i 0.140613 + 0.243548i
\(646\) −14.0981 + 24.4186i −0.554681 + 0.960736i
\(647\) 5.68429 4.12988i 0.223472 0.162362i −0.470416 0.882445i \(-0.655896\pi\)
0.693888 + 0.720083i \(0.255896\pi\)
\(648\) −0.978148 + 0.207912i −0.0384253 + 0.00816754i
\(649\) −16.5894 51.0570i −0.651192 2.00416i
\(650\) 2.95976 0.116091
\(651\) 12.4248 14.9568i 0.486966 0.586201i
\(652\) −8.30234 −0.325145
\(653\) −0.947713 2.91676i −0.0370869 0.114142i 0.930799 0.365531i \(-0.119113\pi\)
−0.967886 + 0.251389i \(0.919113\pi\)
\(654\) 7.88462 1.67593i 0.308313 0.0655340i
\(655\) −5.11649 + 3.71735i −0.199918 + 0.145249i
\(656\) 5.14733 8.91543i 0.200969 0.348089i
\(657\) 0.0122416 + 0.0212031i 0.000477590 + 0.000827210i
\(658\) −13.8683 6.17456i −0.540642 0.240709i
\(659\) 4.06509 + 2.95346i 0.158354 + 0.115051i 0.664140 0.747608i \(-0.268798\pi\)
−0.505787 + 0.862659i \(0.668798\pi\)
\(660\) −3.60137 + 1.60343i −0.140183 + 0.0624136i
\(661\) −37.3597 7.94105i −1.45312 0.308871i −0.587361 0.809325i \(-0.699833\pi\)
−0.865763 + 0.500454i \(0.833167\pi\)
\(662\) 3.21713 + 30.6089i 0.125037 + 1.18965i
\(663\) 15.8823 17.6390i 0.616816 0.685043i
\(664\) 7.05618 + 7.83669i 0.273833 + 0.304122i
\(665\) −1.28348 + 12.2115i −0.0497714 + 0.473543i
\(666\) −3.00904 + 9.26088i −0.116598 + 0.358852i
\(667\) 8.65933 26.6507i 0.335291 1.03192i
\(668\) −0.211679 + 2.01399i −0.00819010 + 0.0779236i
\(669\) −1.93055 2.14410i −0.0746395 0.0828955i
\(670\) 4.39868 4.88523i 0.169936 0.188733i
\(671\) −4.26390 40.5683i −0.164606 1.56612i
\(672\) 3.41598 + 0.726089i 0.131774 + 0.0280095i
\(673\) 4.18763 1.86445i 0.161421 0.0718694i −0.324435 0.945908i \(-0.605174\pi\)
0.485857 + 0.874038i \(0.338508\pi\)
\(674\) 16.8165 + 12.2179i 0.647749 + 0.470617i
\(675\) −0.913545 0.406737i −0.0351624 0.0156553i
\(676\) 2.11991 + 3.67179i 0.0815351 + 0.141223i
\(677\) −7.92702 + 13.7300i −0.304660 + 0.527687i −0.977186 0.212387i \(-0.931876\pi\)
0.672525 + 0.740074i \(0.265210\pi\)
\(678\) 10.6786 7.75845i 0.410109 0.297962i
\(679\) −4.66914 + 0.992456i −0.179185 + 0.0380870i
\(680\) 2.47815 + 7.62695i 0.0950326 + 0.292480i
\(681\) −6.53527 −0.250432
\(682\) −1.42288 + 21.9030i −0.0544851 + 0.838710i
\(683\) 25.9303 0.992196 0.496098 0.868266i \(-0.334766\pi\)
0.496098 + 0.868266i \(0.334766\pi\)
\(684\) −1.08649 3.34389i −0.0415431 0.127857i
\(685\) 0.893852 0.189994i 0.0341523 0.00725931i
\(686\) 5.09655 3.70286i 0.194587 0.141376i
\(687\) 14.0076 24.2619i 0.534424 0.925650i
\(688\) 3.57112 + 6.18536i 0.136148 + 0.235815i
\(689\) 24.7441 + 11.0168i 0.942675 + 0.419706i
\(690\) −4.87954 3.54519i −0.185761 0.134963i
\(691\) −19.5312 + 8.69584i −0.743001 + 0.330805i −0.743087 0.669195i \(-0.766639\pi\)
8.62619e−5 1.00000i \(0.499973\pi\)
\(692\) −11.6594 2.47829i −0.443225 0.0942104i
\(693\) 1.43907 + 13.6919i 0.0546659 + 0.520111i
\(694\) 1.76666 1.96208i 0.0670616 0.0744795i
\(695\) 8.45353 + 9.38860i 0.320661 + 0.356130i
\(696\) 0.485641 4.62056i 0.0184082 0.175142i
\(697\) 25.5117 78.5168i 0.966323 2.97404i
\(698\) 2.69723 8.30123i 0.102092 0.314206i
\(699\) −1.18301 + 11.2556i −0.0447457 + 0.425727i
\(700\) 2.33680 + 2.59528i 0.0883228 + 0.0980924i
\(701\) 19.4633 21.6162i 0.735118 0.816431i −0.253428 0.967354i \(-0.581558\pi\)
0.988545 + 0.150923i \(0.0482246\pi\)
\(702\) 0.309379 + 2.94355i 0.0116768 + 0.111097i
\(703\) −33.4885 7.11820i −1.26304 0.268468i
\(704\) −3.60137 + 1.60343i −0.135732 + 0.0604317i
\(705\) 3.51673 + 2.55506i 0.132448 + 0.0962290i
\(706\) −7.02862 3.12935i −0.264526 0.117774i
\(707\) −28.0708 48.6200i −1.05571 1.82854i
\(708\) 6.80897 11.7935i 0.255897 0.443226i
\(709\) 14.0019 10.1730i 0.525853 0.382055i −0.292951 0.956127i \(-0.594637\pi\)
0.818804 + 0.574073i \(0.194637\pi\)
\(710\) 12.7715 2.71466i 0.479305 0.101879i
\(711\) 0.592818 + 1.82451i 0.0222324 + 0.0684243i
\(712\) −3.34948 −0.125527
\(713\) −30.1099 + 14.8702i −1.12762 + 0.556893i
\(714\) 28.0063 1.04811
\(715\) 3.60559 + 11.0969i 0.134841 + 0.414999i
\(716\) 7.59702 1.61480i 0.283914 0.0603478i
\(717\) −22.2238 + 16.1466i −0.829964 + 0.603004i
\(718\) 10.7879 18.6852i 0.402600 0.697324i
\(719\) 0.547833 + 0.948875i 0.0204307 + 0.0353871i 0.876060 0.482202i \(-0.160163\pi\)
−0.855629 + 0.517589i \(0.826830\pi\)
\(720\) −0.913545 0.406737i −0.0340458 0.0151582i
\(721\) −43.2620 31.4317i −1.61116 1.17058i
\(722\) −6.06408 + 2.69990i −0.225682 + 0.100480i
\(723\) −3.59852 0.764888i −0.133830 0.0284465i
\(724\) −1.31225 12.4852i −0.0487694 0.464010i
\(725\) 3.10879 3.45266i 0.115458 0.128229i
\(726\) −3.03843 3.37452i −0.112767 0.125240i
\(727\) 0.00131578 0.0125188i 4.87994e−5 0.000464295i −0.994497 0.104761i \(-0.966592\pi\)
0.994546 + 0.104296i \(0.0332590\pi\)
\(728\) 3.19411 9.83045i 0.118382 0.364341i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −0.00255919 + 0.0243491i −9.47198e−5 + 0.000901199i
\(731\) 38.3257 + 42.5650i 1.41753 + 1.57432i
\(732\) 6.92383 7.68969i 0.255912 0.284219i
\(733\) −2.43580 23.1751i −0.0899683 0.855992i −0.942700 0.333642i \(-0.891722\pi\)
0.852731 0.522350i \(-0.174944\pi\)
\(734\) −6.92641 1.47225i −0.255659 0.0543419i
\(735\) 4.74689 2.11345i 0.175092 0.0779558i
\(736\) −4.87954 3.54519i −0.179862 0.130678i
\(737\) 23.6744 + 10.5405i 0.872059 + 0.388266i
\(738\) 5.14733 + 8.91543i 0.189476 + 0.328182i
\(739\) 11.0617 19.1594i 0.406911 0.704791i −0.587630 0.809129i \(-0.699939\pi\)
0.994542 + 0.104338i \(0.0332724\pi\)
\(740\) −7.87778 + 5.72354i −0.289593 + 0.210401i
\(741\) −10.1790 + 2.16362i −0.373936 + 0.0794825i
\(742\) 9.87593 + 30.3950i 0.362557 + 1.11584i
\(743\) 16.0359 0.588300 0.294150 0.955759i \(-0.404964\pi\)
0.294150 + 0.955759i \(0.404964\pi\)
\(744\) −4.37047 + 3.44950i −0.160229 + 0.126465i
\(745\) −20.5083 −0.751365
\(746\) 5.63869 + 17.3541i 0.206447 + 0.635378i
\(747\) −10.3149 + 2.19249i −0.377401 + 0.0802191i
\(748\) −25.5764 + 18.5824i −0.935167 + 0.679439i
\(749\) 24.7819 42.9235i 0.905512 1.56839i
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 7.67236 + 3.41595i 0.279968 + 0.124650i 0.541917 0.840432i \(-0.317699\pi\)
−0.261949 + 0.965082i \(0.584365\pi\)
\(752\) 3.51673 + 2.55506i 0.128242 + 0.0931734i
\(753\) −3.43263 + 1.52830i −0.125092 + 0.0556945i
\(754\) −13.4506 2.85901i −0.489842 0.104119i
\(755\) 0.385766 + 3.67032i 0.0140395 + 0.133576i
\(756\) −2.33680 + 2.59528i −0.0849886 + 0.0943894i
\(757\) −30.0656 33.3912i −1.09275 1.21362i −0.975379 0.220535i \(-0.929220\pi\)
−0.117372 0.993088i \(-0.537447\pi\)
\(758\) −2.71903 + 25.8699i −0.0987597 + 0.939636i
\(759\) 7.34753 22.6134i 0.266698 0.820813i
\(760\) 1.08649 3.34389i 0.0394113 0.121295i
\(761\) −5.34643 + 50.8679i −0.193808 + 1.84396i 0.275960 + 0.961169i \(0.411004\pi\)
−0.469768 + 0.882790i \(0.655662\pi\)
\(762\) 6.42085 + 7.13108i 0.232603 + 0.258332i
\(763\) 18.8364 20.9200i 0.681924 0.757353i
\(764\) −2.15155 20.4707i −0.0778405 0.740602i
\(765\) −7.84421 1.66734i −0.283608 0.0602827i
\(766\) −11.1264 + 4.95378i −0.402012 + 0.178987i
\(767\) −32.6081 23.6912i −1.17741 0.855438i
\(768\) −0.913545 0.406737i −0.0329647 0.0146768i
\(769\) 2.67482 + 4.63292i 0.0964564 + 0.167067i 0.910216 0.414135i \(-0.135916\pi\)
−0.813759 + 0.581202i \(0.802582\pi\)
\(770\) −6.88364 + 11.9228i −0.248069 + 0.429669i
\(771\) 8.09526 5.88155i 0.291543 0.211819i
\(772\) −5.82137 + 1.23737i −0.209516 + 0.0445339i
\(773\) 3.81174 + 11.7313i 0.137099 + 0.421946i 0.995911 0.0903448i \(-0.0287969\pi\)
−0.858812 + 0.512291i \(0.828797\pi\)
\(774\) −7.14224 −0.256722
\(775\) −5.56334 + 0.221805i −0.199841 + 0.00796748i
\(776\) 1.36685 0.0490671
\(777\) 10.5085 + 32.3417i 0.376989 + 1.16025i
\(778\) 14.3006 3.03969i 0.512702 0.108978i
\(779\) −29.2829 + 21.2753i −1.04917 + 0.762266i
\(780\) −1.47988 + 2.56323i −0.0529882 + 0.0917782i
\(781\) 25.7362 + 44.5764i 0.920912 + 1.59507i
\(782\) −44.1872 19.6734i −1.58013 0.703519i
\(783\) 3.75870 + 2.73086i 0.134325 + 0.0975929i
\(784\) 4.74689 2.11345i 0.169532 0.0754804i
\(785\) 12.0299 + 2.55703i 0.429364 + 0.0912642i
\(786\) −0.661072 6.28968i −0.0235797 0.224346i
\(787\) −6.18574 + 6.86996i −0.220498 + 0.244888i −0.843237 0.537542i \(-0.819353\pi\)
0.622739 + 0.782429i \(0.286020\pi\)
\(788\) 8.65838 + 9.61611i 0.308442 + 0.342560i
\(789\) 2.12230 20.1923i 0.0755558 0.718866i
\(790\) −0.592818 + 1.82451i −0.0210915 + 0.0649130i
\(791\) 14.2446 43.8403i 0.506479 1.55878i
\(792\) 0.412071 3.92059i 0.0146423 0.139312i
\(793\) −20.4929 22.7596i −0.727723 0.808218i
\(794\) −11.3819 + 12.6408i −0.403927 + 0.448607i
\(795\) −0.956576 9.10121i −0.0339262 0.322787i
\(796\) 9.60654 + 2.04193i 0.340495 + 0.0723744i
\(797\) −11.7422 + 5.22796i −0.415929 + 0.185184i −0.604022 0.796968i \(-0.706436\pi\)
0.188093 + 0.982151i \(0.439769\pi\)
\(798\) −9.93376 7.21730i −0.351651 0.255490i
\(799\) 31.8462 + 14.1788i 1.12664 + 0.501611i
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) 1.67474 2.90074i 0.0591741 0.102493i
\(802\) −29.1865 + 21.2052i −1.03061 + 0.748783i
\(803\) −0.0944082 + 0.0200671i −0.00333159 + 0.000708152i
\(804\) 2.03139 + 6.25199i 0.0716418 + 0.220491i
\(805\) −21.0636 −0.742394
\(806\) 8.80162 + 13.9319i 0.310024 + 0.490729i
\(807\) −14.3333 −0.504557
\(808\) 4.96770 + 15.2890i 0.174763 + 0.537866i
\(809\) −6.41066 + 1.36263i −0.225387 + 0.0479075i −0.319221 0.947680i \(-0.603421\pi\)
0.0938338 + 0.995588i \(0.470088\pi\)
\(810\) 0.809017 0.587785i 0.0284260 0.0206527i
\(811\) −6.82380 + 11.8192i −0.239616 + 0.415027i −0.960604 0.277920i \(-0.910355\pi\)
0.720988 + 0.692948i \(0.243688\pi\)
\(812\) −8.11262 14.0515i −0.284697 0.493110i
\(813\) −22.9381 10.2127i −0.804475 0.358175i
\(814\) −31.0557 22.5633i −1.08850 0.790843i
\(815\) 7.58456 3.37686i 0.265676 0.118286i
\(816\) −7.84421 1.66734i −0.274602 0.0583685i
\(817\) −2.62491 24.9743i −0.0918339 0.873741i
\(818\) 5.87928 6.52960i 0.205564 0.228302i
\(819\) 6.91637 + 7.68141i 0.241677 + 0.268410i
\(820\) −1.07608 + 10.2383i −0.0375785 + 0.357535i
\(821\) −4.09885 + 12.6150i −0.143051 + 0.440265i −0.996755 0.0804928i \(-0.974351\pi\)
0.853704 + 0.520758i \(0.174351\pi\)
\(822\) −0.282386 + 0.869096i −0.00984936 + 0.0303132i
\(823\) 2.50534 23.8367i 0.0873307 0.830896i −0.859926 0.510419i \(-0.829490\pi\)
0.947256 0.320477i \(-0.103843\pi\)
\(824\) 10.2459 + 11.3792i 0.356932 + 0.396413i
\(825\) 2.63784 2.92962i 0.0918378 0.101996i
\(826\) −4.97115 47.2973i −0.172968 1.64568i
\(827\) −18.9394 4.02569i −0.658587 0.139987i −0.133518 0.991046i \(-0.542627\pi\)
−0.525070 + 0.851059i \(0.675961\pi\)
\(828\) 5.51000 2.45321i 0.191486 0.0852549i
\(829\) −22.4895 16.3395i −0.781091 0.567496i 0.124215 0.992255i \(-0.460359\pi\)
−0.905306 + 0.424760i \(0.860359\pi\)
\(830\) −9.63361 4.28916i −0.334388 0.148879i
\(831\) 4.55351 + 7.88692i 0.157960 + 0.273594i
\(832\) −1.47988 + 2.56323i −0.0513056 + 0.0888639i
\(833\) 33.7118 24.4930i 1.16804 0.848633i
\(834\) −12.3575 + 2.62667i −0.427906 + 0.0909543i
\(835\) −0.625785 1.92597i −0.0216562 0.0666509i
\(836\) 13.8606 0.479380
\(837\) −0.802118 5.50968i −0.0277253 0.190443i
\(838\) −7.33274 −0.253305
\(839\) −7.18099 22.1008i −0.247915 0.763005i −0.995143 0.0984370i \(-0.968616\pi\)
0.747228 0.664568i \(-0.231384\pi\)
\(840\) −3.41598 + 0.726089i −0.117862 + 0.0250524i
\(841\) 5.99850 4.35816i 0.206845 0.150282i
\(842\) 18.8831 32.7065i 0.650755 1.12714i
\(843\) −15.2982 26.4973i −0.526899 0.912615i
\(844\) 1.78601 + 0.795183i 0.0614770 + 0.0273713i
\(845\) −3.43009 2.49211i −0.117999 0.0857310i
\(846\) −3.97111 + 1.76805i −0.136530 + 0.0607869i
\(847\) −15.5115 3.29707i −0.532981 0.113289i
\(848\) −0.956576 9.10121i −0.0328489 0.312537i
\(849\) −7.11887 + 7.90630i −0.244319 + 0.271344i
\(850\) −5.36606 5.95962i −0.184054 0.204413i
\(851\) 6.13906 58.4093i 0.210444 2.00224i
\(852\) −4.03477 + 12.4177i −0.138229 + 0.425425i
\(853\) 5.63913 17.3555i 0.193080 0.594240i −0.806913 0.590670i \(-0.798864\pi\)
0.999994 0.00357018i \(-0.00113642\pi\)
\(854\) 3.77729 35.9385i 0.129256 1.22979i
\(855\) 2.35264 + 2.61287i 0.0804587 + 0.0893584i
\(856\) −9.49653 + 10.5470i −0.324585 + 0.360488i
\(857\) 5.65960 + 53.8475i 0.193328 + 1.83940i 0.475121 + 0.879921i \(0.342404\pi\)
−0.281792 + 0.959475i \(0.590929\pi\)
\(858\) −11.4130 2.42590i −0.389632 0.0828189i
\(859\) 41.1437 18.3183i 1.40380 0.625014i 0.441567 0.897228i \(-0.354423\pi\)
0.962237 + 0.272214i \(0.0877560\pi\)
\(860\) −5.77819 4.19810i −0.197035 0.143154i
\(861\) 32.8437 + 14.6230i 1.11931 + 0.498350i
\(862\) 15.4882 + 26.8263i 0.527529 + 0.913708i
\(863\) −24.5378 + 42.5007i −0.835276 + 1.44674i 0.0585294 + 0.998286i \(0.481359\pi\)
−0.893805 + 0.448455i \(0.851974\pi\)
\(864\) 0.809017 0.587785i 0.0275233 0.0199969i
\(865\) 11.6594 2.47829i 0.396433 0.0842643i
\(866\) −0.0118734 0.0365425i −0.000403474 0.00124176i
\(867\) −47.3116 −1.60679
\(868\) −5.26714 + 18.7173i −0.178778 + 0.635306i
\(869\) −7.56269 −0.256547
\(870\) 1.43570 + 4.41862i 0.0486747 + 0.149805i
\(871\) 19.0315 4.04527i 0.644857 0.137069i
\(872\) −6.52130 + 4.73800i −0.220839 + 0.160449i
\(873\) −0.683426 + 1.18373i −0.0231305 + 0.0400631i
\(874\) 10.6032 + 18.3653i 0.358658 + 0.621214i
\(875\) −3.19037 1.42044i −0.107854 0.0480198i
\(876\) −0.0198073 0.0143908i −0.000669227 0.000486222i
\(877\) 17.8077 7.92849i 0.601323 0.267726i −0.0834160 0.996515i \(-0.526583\pi\)
0.684739 + 0.728789i \(0.259916\pi\)
\(878\) 13.0051 + 2.76432i 0.438901 + 0.0932912i
\(879\) 2.45530 + 23.3606i 0.0828153 + 0.787934i
\(880\) 2.63784 2.92962i 0.0889216 0.0987574i
\(881\) −1.00442 1.11552i −0.0338399 0.0375830i 0.725987 0.687708i \(-0.241383\pi\)
−0.759827 + 0.650125i \(0.774716\pi\)
\(882\) −0.543142 + 5.16765i −0.0182886 + 0.174004i
\(883\) −7.04514 + 21.6827i −0.237088 + 0.729682i 0.759750 + 0.650216i \(0.225321\pi\)
−0.996838 + 0.0794659i \(0.974679\pi\)
\(884\) −7.33472 + 22.5740i −0.246693 + 0.759244i
\(885\) −1.42346 + 13.5433i −0.0478491 + 0.455254i
\(886\) 10.1508 + 11.2736i 0.341022 + 0.378743i
\(887\) 29.3174 32.5603i 0.984383 1.09327i −0.0112526 0.999937i \(-0.503582\pi\)
0.995635 0.0933309i \(-0.0297514\pi\)
\(888\) −1.01784 9.68412i −0.0341566 0.324978i
\(889\) 32.7791 + 6.96741i 1.09938 + 0.233680i
\(890\) 3.05991 1.36236i 0.102568 0.0456663i
\(891\) 3.18930 + 2.31716i 0.106846 + 0.0776278i
\(892\) 2.63573 + 1.17350i 0.0882508 + 0.0392918i
\(893\) −7.64183 13.2360i −0.255724 0.442927i
\(894\) 10.2541 17.7607i 0.342950 0.594006i
\(895\) −6.28342 + 4.56518i −0.210032 + 0.152597i
\(896\) −3.41598 + 0.726089i −0.114120 + 0.0242569i
\(897\) −5.51646 16.9779i −0.184189 0.566876i
\(898\) 7.26742 0.242517
\(899\) 25.4968 + 4.36598i 0.850366 + 0.145614i
\(900\) 1.00000 0.0333333
\(901\) −22.6784 69.7969i −0.755526 2.32527i
\(902\) −39.6966 + 8.43778i −1.32175 + 0.280947i
\(903\) −20.1791 + 14.6610i −0.671520 + 0.487888i
\(904\) −6.59974 + 11.4311i −0.219504 + 0.380192i
\(905\) 6.27701 + 10.8721i 0.208655 + 0.361401i
\(906\) −3.37147 1.50108i −0.112010 0.0498699i
\(907\) −6.06494 4.40644i −0.201383 0.146313i 0.482523 0.875883i \(-0.339720\pi\)
−0.683906 + 0.729570i \(0.739720\pi\)
\(908\) 5.97026 2.65813i 0.198130 0.0882132i
\(909\) −15.7245 3.34235i −0.521550 0.110859i
\(910\) 1.08044 + 10.2797i 0.0358163 + 0.340770i
\(911\) −20.4501 + 22.7122i −0.677543 + 0.752488i −0.979634 0.200791i \(-0.935649\pi\)
0.302091 + 0.953279i \(0.402315\pi\)
\(912\) 2.35264 + 2.61287i 0.0779038 + 0.0865209i
\(913\) 4.34541 41.3438i 0.143812 1.36828i
\(914\) −6.04024 + 18.5899i −0.199793 + 0.614900i
\(915\) −3.19755 + 9.84105i −0.105708 + 0.325335i
\(916\) −2.92839 + 27.8618i −0.0967567 + 0.920579i
\(917\) −14.7787 16.4134i −0.488036 0.542018i
\(918\) 5.36606 5.95962i 0.177106 0.196697i
\(919\) −0.598664 5.69590i −0.0197481 0.187891i 0.980201 0.198006i \(-0.0634467\pi\)
−0.999949 + 0.0101158i \(0.996780\pi\)
\(920\) 5.89964 + 1.25401i 0.194505 + 0.0413434i
\(921\) −1.83776 + 0.818221i −0.0605561 + 0.0269613i
\(922\) −20.5384 14.9221i −0.676398 0.491432i
\(923\) 35.3039 + 15.7183i 1.16204 + 0.517375i
\(924\) −6.88364 11.9228i −0.226455 0.392232i
\(925\) 4.86873 8.43289i 0.160083 0.277272i
\(926\) −14.0678 + 10.2208i −0.462296 + 0.335878i
\(927\) −14.9776 + 3.18359i −0.491930 + 0.104563i
\(928\) 1.43570 + 4.41862i 0.0471291 + 0.145048i
\(929\) −9.85642 −0.323378 −0.161689 0.986842i \(-0.551694\pi\)
−0.161689 + 0.986842i \(0.551694\pi\)
\(930\) 2.58958 4.92890i 0.0849158 0.161625i
\(931\) −18.2694 −0.598755
\(932\) −3.49734 10.7637i −0.114559 0.352577i
\(933\) 30.1586 6.41041i 0.987349 0.209868i
\(934\) −27.3758 + 19.8897i −0.895763 + 0.650810i
\(935\) 15.8071 27.3787i 0.516948 0.895380i
\(936\) −1.47988 2.56323i −0.0483714 0.0837817i
\(937\) −22.1248 9.85058i −0.722785 0.321805i 0.0121650 0.999926i \(-0.496128\pi\)
−0.734950 + 0.678121i \(0.762794\pi\)
\(938\) 18.5729 + 13.4940i 0.606428 + 0.440595i
\(939\) −8.88438 + 3.95558i −0.289931 + 0.129086i
\(940\) −4.25193 0.903776i −0.138683 0.0294779i
\(941\) −0.870535 8.28259i −0.0283786 0.270005i −0.999506 0.0314414i \(-0.989990\pi\)
0.971127 0.238563i \(-0.0766764\pi\)
\(942\) −8.22938 + 9.13966i −0.268128 + 0.297786i
\(943\) −41.5474 46.1431i −1.35297 1.50263i
\(944\) −1.42346 + 13.5433i −0.0463297 + 0.440798i
\(945\) 1.07918 3.32137i 0.0351057 0.108044i
\(946\) 8.70070 26.7780i 0.282884 0.870628i
\(947\) −4.72835 + 44.9872i −0.153651 + 1.46189i 0.597559 + 0.801825i \(0.296137\pi\)
−0.751209 + 0.660064i \(0.770529\pi\)
\(948\) −1.28366 1.42565i −0.0416913 0.0463029i
\(949\) −0.0484881 + 0.0538515i −0.00157399 + 0.00174809i
\(950\) 0.367519 + 3.49671i 0.0119239 + 0.113448i
\(951\) 1.44388 + 0.306906i 0.0468210 + 0.00995211i
\(952\) −25.5850 + 11.3912i −0.829215 + 0.369190i
\(953\) −10.3449 7.51604i −0.335106 0.243468i 0.407488 0.913210i \(-0.366405\pi\)
−0.742594 + 0.669742i \(0.766405\pi\)
\(954\) 8.36017 + 3.72219i 0.270670 + 0.120510i
\(955\) 10.2917 + 17.8258i 0.333032 + 0.576828i
\(956\) 13.7351 23.7899i 0.444224 0.769419i
\(957\) −14.8175 + 10.7656i −0.478983 + 0.348001i
\(958\) 14.1648 3.01082i 0.457644 0.0972752i
\(959\) 0.986176 + 3.03514i 0.0318453 + 0.0980098i
\(960\) 1.00000 0.0322749
\(961\) −17.5881 25.5276i −0.567359 0.823471i
\(962\) −28.8206 −0.929212
\(963\) −4.38567 13.4977i −0.141326 0.434958i
\(964\) 3.59852 0.764888i 0.115900 0.0246354i
\(965\) 4.81480 3.49816i 0.154994 0.112610i
\(966\) 10.5318 18.2416i 0.338855 0.586914i
\(967\) 8.37126 + 14.4995i 0.269202 + 0.466271i 0.968656 0.248406i \(-0.0799068\pi\)
−0.699454 + 0.714677i \(0.746574\pi\)
\(968\) 4.14829 + 1.84694i 0.133331 + 0.0593628i
\(969\) 22.8112 + 16.5733i 0.732800 + 0.532411i
\(970\) −1.24868 + 0.555949i −0.0400927 + 0.0178504i
\(971\) 16.0211 + 3.40539i 0.514142 + 0.109284i 0.457674 0.889120i \(-0.348683\pi\)
0.0564683 + 0.998404i \(0.482016\pi\)
\(972\) 0.104528 + 0.994522i 0.00335275 + 0.0318993i
\(973\) −29.5222 + 32.7878i −0.946439 + 1.05113i
\(974\) −5.43471 6.03586i −0.174139 0.193401i
\(975\) 0.309379 2.94355i 0.00990806 0.0942689i
\(976\) −3.19755 + 9.84105i −0.102351 + 0.315004i
\(977\) −8.24693 + 25.3814i −0.263843 + 0.812024i 0.728115 + 0.685455i \(0.240397\pi\)
−0.991958 + 0.126569i \(0.959603\pi\)
\(978\) −0.867831 + 8.25686i −0.0277502 + 0.264025i
\(979\) 8.83540 + 9.81271i 0.282381 + 0.313616i
\(980\) −3.47688 + 3.86147i −0.111065 + 0.123350i
\(981\) −0.842580 8.01661i −0.0269015 0.255951i
\(982\) −42.5849 9.05171i −1.35894 0.288852i
\(983\) 8.98638 4.00099i 0.286621 0.127612i −0.258390 0.966041i \(-0.583192\pi\)
0.545011 + 0.838429i \(0.316525\pi\)
\(984\) −8.32855 6.05104i −0.265504 0.192900i
\(985\) −11.8211 5.26307i −0.376650 0.167695i
\(986\) 18.6292 + 32.2668i 0.593276 + 1.02758i
\(987\) −7.59037 + 13.1469i −0.241604 + 0.418470i
\(988\) 8.41897 6.11674i 0.267843 0.194600i
\(989\) 42.1367 8.95642i 1.33987 0.284798i
\(990\) 1.21820 + 3.74925i 0.0387171 + 0.119159i
\(991\) 43.4351 1.37976 0.689880 0.723924i \(-0.257663\pi\)
0.689880 + 0.723924i \(0.257663\pi\)
\(992\) 2.58958 4.92890i 0.0822194 0.156493i
\(993\) 30.7775 0.976695
\(994\) 14.0906 + 43.3664i 0.446927 + 1.37550i
\(995\) −9.60654 + 2.04193i −0.304548 + 0.0647337i
\(996\) 8.53133 6.19837i 0.270325 0.196403i
\(997\) −0.354109 + 0.613335i −0.0112147 + 0.0194245i −0.871578 0.490256i \(-0.836903\pi\)
0.860364 + 0.509681i \(0.170237\pi\)
\(998\) 8.59011 + 14.8785i 0.271915 + 0.470971i
\(999\) 8.89562 + 3.96058i 0.281445 + 0.125307i
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 930.2.bg.c.751.2 yes 16
31.9 even 15 inner 930.2.bg.c.691.2 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.c.691.2 16 31.9 even 15 inner
930.2.bg.c.751.2 yes 16 1.1 even 1 trivial