Properties

Label 930.2.bg.c.691.2
Level $930$
Weight $2$
Character 930.691
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 691.2
Root \(-1.00725i\) of defining polynomial
Character \(\chi\) \(=\) 930.691
Dual form 930.2.bg.c.751.2

$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).

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

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 0.297349 0.954769i \(-0.403897\pi\)
0.908497 + 0.417891i \(0.137231\pi\)
\(8\) −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 −0.737710 0.675118i \(-0.764093\pi\)
0.861954 0.506986i \(-0.169240\pi\)
\(12\) −0.669131 0.743145i −0.193161 0.214527i
\(13\) 1.98047 2.19953i 0.549282 0.610040i −0.403022 0.915190i \(-0.632040\pi\)
0.952304 + 0.305151i \(0.0987068\pi\)
\(14\) −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 0.333274 + 0.942830i \(0.391847\pi\)
−0.129966 + 0.991518i \(0.541487\pi\)
\(18\) 0.669131 0.743145i 0.157716 0.175161i
\(19\) −2.35264 2.61287i −0.539733 0.599435i 0.410158 0.912014i \(-0.365473\pi\)
−0.949891 + 0.312580i \(0.898807\pi\)
\(20\) 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 −0.965760 0.259439i \(-0.916462\pi\)
−0.0516951 + 0.998663i \(0.516462\pi\)
\(24\) −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 −0.724718 0.689046i \(-0.758030\pi\)
0.991320 0.131472i \(-0.0419702\pi\)
\(30\) 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 −0.118929 0.992903i \(-0.537946\pi\)
0.919343 0.393456i \(-0.128721\pi\)
\(38\) −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 0.662646 0.748933i \(-0.269434\pi\)
0.909976 + 0.414662i \(0.136100\pi\)
\(42\) 0.365044 3.47316i 0.0563275 0.535921i
\(43\) −4.77909 5.30772i −0.728805 0.809419i 0.258875 0.965911i \(-0.416648\pi\)
−0.987679 + 0.156491i \(0.949982\pi\)
\(44\) −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 −0.999964 0.00843901i \(-0.997314\pi\)
0.804028 0.594592i \(-0.202686\pi\)
\(48\) 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 0.890537 0.454911i \(-0.150329\pi\)
0.257821 + 0.966193i \(0.416996\pi\)
\(54\) 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 −0.770855 0.637011i \(-0.780171\pi\)
−0.963307 + 0.268403i \(0.913504\pi\)
\(60\) 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 0.993914 0.110161i \(-0.0351367\pi\)
−0.592359 + 0.805674i \(0.701803\pi\)
\(68\) 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 0.964947 0.262444i \(-0.0845284\pi\)
0.450642 + 0.892705i \(0.351195\pi\)
\(72\) −0.978148 + 0.207912i −0.115276 + 0.0245026i
\(73\) 0.00255919 0.0243491i 0.000299530 0.00284984i −0.994371 0.105953i \(-0.966211\pi\)
0.994671 + 0.103103i \(0.0328773\pi\)
\(74\) −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 −0.999994 0.00340917i \(-0.998915\pi\)
0.977433 0.211245i \(-0.0677518\pi\)
\(80\) −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 −0.735655 0.677357i \(-0.763125\pi\)
−0.396548 + 0.918014i \(0.629792\pi\)
\(84\) −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 0.722068 0.691822i \(-0.243192\pi\)
−0.434831 + 0.900512i \(0.643192\pi\)
\(90\) 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 0.530230 0.847854i \(-0.322106\pi\)
−0.642507 + 0.766280i \(0.722106\pi\)
\(98\) −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 −0.999880 0.0155113i \(-0.995062\pi\)
−0.294228 + 0.955735i \(0.595062\pi\)
\(102\) 7.32614 + 3.26181i 0.725396 + 0.322967i
\(103\) −14.9776 + 3.18359i −1.47579 + 0.313689i −0.874376 0.485249i \(-0.838729\pi\)
−0.601413 + 0.798938i \(0.705396\pi\)
\(104\) −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 0.795312 + 0.606201i \(0.207307\pi\)
−0.651896 + 0.758309i \(0.726026\pi\)
\(108\) −0.309017 0.951057i −0.0297352 0.0915155i
\(109\) 2.49092 + 7.66625i 0.238586 + 0.734293i 0.996625 + 0.0820842i \(0.0261577\pi\)
−0.758039 + 0.652209i \(0.773842\pi\)
\(110\) −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 0.714738 + 0.699393i \(0.246546\pi\)
−0.844531 + 0.535507i \(0.820121\pi\)
\(114\) −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 0.604569 0.796553i \(-0.293345\pi\)
0.228314 + 0.973587i \(0.426679\pi\)
\(128\) −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 −0.643299 0.765615i \(-0.722435\pi\)
0.138511 + 0.990361i \(0.455768\pi\)
\(132\) −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 −0.716458 0.697630i \(-0.754238\pi\)
0.768699 + 0.639611i \(0.220904\pi\)
\(138\) 0.630458 + 5.99840i 0.0536681 + 0.510618i
\(139\) −3.90400 12.0153i −0.331133 1.01912i −0.968596 0.248641i \(-0.920016\pi\)
0.637463 0.770481i \(-0.279984\pi\)
\(140\) −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 0.0497978 + 0.998759i \(0.484142\pi\)
−0.889850 + 0.456253i \(0.849191\pi\)
\(150\) 0.500000 + 0.866025i 0.0408248 + 0.0707107i
\(151\) −2.98570 2.16924i −0.242973 0.176530i 0.459634 0.888109i \(-0.347981\pi\)
−0.702607 + 0.711578i \(0.747981\pi\)
\(152\) 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 −0.676990 0.735992i \(-0.736716\pi\)
0.980302 0.197505i \(-0.0632839\pi\)
\(158\) −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 −0.292800 0.956174i \(-0.594587\pi\)
0.818895 + 0.573943i \(0.194587\pi\)
\(164\) −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 0.793288 0.608846i \(-0.208367\pi\)
−0.688432 + 0.725301i \(0.741701\pi\)
\(168\) −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 −0.359272 0.933233i \(-0.616975\pi\)
0.965675 + 0.259755i \(0.0836418\pi\)
\(174\) −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 −0.654389 0.756158i \(-0.727074\pi\)
0.124063 + 0.992274i \(0.460407\pi\)
\(180\) 0.500000 0.866025i 0.0372678 0.0645497i
\(181\) −6.27701 10.8721i −0.466566 0.808116i 0.532705 0.846301i \(-0.321176\pi\)
−0.999271 + 0.0381850i \(0.987842\pi\)
\(182\) −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 −0.950343 0.311204i \(-0.899268\pi\)
0.205661 0.978623i \(-0.434065\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 5.43690 2.42066i 0.391356 0.174243i −0.201618 0.979464i \(-0.564620\pi\)
0.592975 + 0.805221i \(0.297953\pi\)
\(194\) −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 0.834376 + 0.551195i \(0.185828\pi\)
−0.930743 + 0.365674i \(0.880839\pi\)
\(198\) −2.63784 2.92962i −0.187463 0.208199i
\(199\) −6.57164 + 7.29854i −0.465851 + 0.517380i −0.929592 0.368591i \(-0.879840\pi\)
0.463741 + 0.885971i \(0.346507\pi\)
\(200\) −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 −0.897710 0.440587i \(-0.854770\pi\)
0.830415 + 0.557146i \(0.188104\pi\)
\(212\) −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 −0.910276 0.414001i \(-0.864131\pi\)
0.813674 + 0.581322i \(0.197464\pi\)
\(224\) 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 −0.415104 0.909774i \(-0.636255\pi\)
−0.00917810 + 0.999958i \(0.502922\pi\)
\(228\) −0.367519 + 3.49671i −0.0243395 + 0.231575i
\(229\) 18.7459 + 20.8194i 1.23876 + 1.37578i 0.900573 + 0.434705i \(0.143147\pi\)
0.338188 + 0.941079i \(0.390186\pi\)
\(230\) −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 −0.997847 0.0655789i \(-0.979111\pi\)
0.768729 0.639574i \(-0.220889\pi\)
\(234\) −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 −0.624955 0.780661i \(-0.714883\pi\)
−0.998321 + 0.0579317i \(0.981549\pi\)
\(240\) −0.809017 + 0.587785i −0.0522218 + 0.0379414i
\(241\) −3.36085 + 1.49635i −0.216491 + 0.0963882i −0.512117 0.858916i \(-0.671139\pi\)
0.295626 + 0.955304i \(0.404472\pi\)
\(242\) −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 0.0904511 0.995901i \(-0.471169\pi\)
−0.322438 + 0.946591i \(0.604502\pi\)
\(252\) −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 0.671528 0.740980i \(-0.265638\pi\)
−0.101315 + 0.994854i \(0.532305\pi\)
\(258\) −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 0.935107 + 0.354365i \(0.115303\pi\)
−0.548227 + 0.836329i \(0.684697\pi\)
\(264\) 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 −0.614423 0.788977i \(-0.710611\pi\)
−0.240398 + 0.970674i \(0.577278\pi\)
\(270\) 0.913545 + 0.406737i 0.0555966 + 0.0247532i
\(271\) −20.3135 + 14.7586i −1.23396 + 0.896524i −0.997181 0.0750397i \(-0.976092\pi\)
−0.236779 + 0.971564i \(0.576092\pi\)
\(272\) −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 −0.830224 0.557430i \(-0.811787\pi\)
0.999314 + 0.0370230i \(0.0117875\pi\)
\(278\) −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 0.106797 + 0.994281i \(0.465941\pi\)
−0.670824 + 0.741616i \(0.734059\pi\)
\(282\) −4.25193 0.903776i −0.253199 0.0538191i
\(283\) −8.60711 6.25343i −0.511640 0.371728i 0.301805 0.953370i \(-0.402411\pi\)
−0.813445 + 0.581641i \(0.802411\pi\)
\(284\) −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 −0.795214 0.606329i \(-0.792641\pi\)
0.651774 0.758414i \(-0.274025\pi\)
\(294\) −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 0.151417 0.988470i \(-0.451616\pi\)
−0.263721 + 0.964599i \(0.584950\pi\)
\(308\) −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 −0.0689389 0.997621i \(-0.521961\pi\)
−0.468748 + 0.883332i \(0.655295\pi\)
\(314\) −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 −0.368517 0.929621i \(-0.620134\pi\)
0.444257 + 0.895899i \(0.353468\pi\)
\(318\) 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 0.716452 0.697637i \(-0.245765\pi\)
0.938266 + 0.345916i \(0.112432\pi\)
\(332\) 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 0.942539 0.334096i \(-0.108431\pi\)
−0.0264839 + 0.999649i \(0.508431\pi\)
\(338\) 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 −0.899282 0.437370i \(-0.855910\pi\)
0.828414 + 0.560116i \(0.189243\pi\)
\(348\) −4.24435 + 1.88970i −0.227521 + 0.101299i
\(349\) −7.06145 + 5.13044i −0.377991 + 0.274626i −0.760517 0.649318i \(-0.775054\pi\)
0.382526 + 0.923945i \(0.375054\pi\)
\(350\) 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 0.590397 0.807113i \(-0.298971\pi\)
−0.864405 + 0.502796i \(0.832305\pi\)
\(354\) −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 −0.991907 0.126964i \(-0.959477\pi\)
0.229951 + 0.973202i \(0.426143\pi\)
\(360\) −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 0.758698 0.651442i \(-0.225836\pi\)
−0.943515 + 0.331331i \(0.892502\pi\)
\(368\) −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 0.307677 0.951491i \(-0.400448\pi\)
0.912972 + 0.408023i \(0.133782\pi\)
\(380\) −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 −0.912623 0.408802i \(-0.865947\pi\)
0.977675 0.210124i \(-0.0673866\pi\)
\(384\) −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 0.962433 + 0.271520i \(0.0875263\pi\)
−0.884949 + 0.465688i \(0.845807\pi\)
\(390\) 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 −0.569740 0.821825i \(-0.692956\pi\)
0.996591 + 0.0824963i \(0.0262893\pi\)
\(398\) 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 −0.134647 0.990894i \(-0.542990\pi\)
0.691364 0.722507i \(-0.257010\pi\)
\(402\) 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 −0.953960 0.299933i \(-0.903036\pi\)
0.736730 + 0.676187i \(0.236369\pi\)
\(410\) 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 0.880327 0.474367i \(-0.157323\pi\)
−0.991026 + 0.133672i \(0.957323\pi\)
\(420\) −0.365044 3.47316i −0.0178123 0.169473i
\(421\) −25.2705 + 28.0658i −1.23161 + 1.36784i −0.325089 + 0.945684i \(0.605394\pi\)
−0.906522 + 0.422159i \(0.861273\pi\)
\(422\) 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 0.868185 0.496240i \(-0.165286\pi\)
0.591288 + 0.806461i \(0.298620\pi\)
\(432\) −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 0.979920 0.199390i \(-0.0638961\pi\)
−0.662637 + 0.748941i \(0.730563\pi\)
\(440\) −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 0.708627 0.705583i \(-0.249315\pi\)
−0.0501862 + 0.998740i \(0.515981\pi\)
\(444\) −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 0.989960 0.141347i \(-0.0451433\pi\)
−0.883976 + 0.467532i \(0.845143\pi\)
\(450\) 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 −0.152899 0.988242i \(-0.548861\pi\)
0.892625 + 0.450799i \(0.148861\pi\)
\(458\) 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 −0.00421894 0.999991i \(-0.501343\pi\)
−0.952352 + 0.305002i \(0.901343\pi\)
\(462\) −13.4664 2.86238i −0.626515 0.133170i
\(463\) 5.37341 16.5377i 0.249724 0.768570i −0.745100 0.666953i \(-0.767598\pi\)
0.994824 0.101617i \(-0.0324018\pi\)
\(464\) 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 −0.349729 0.936851i \(-0.613726\pi\)
0.833604 0.552362i \(-0.186274\pi\)
\(468\) −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 0.973101 + 0.230378i \(0.0739962\pi\)
−0.903938 + 0.427663i \(0.859337\pi\)
\(480\) 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 0.231677 0.972793i \(-0.425579\pi\)
−0.567903 + 0.823095i \(0.692245\pi\)
\(488\) 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 −0.653033 0.757329i \(-0.726504\pi\)
−0.329350 0.944208i \(-0.606830\pi\)
\(492\) −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 0.568067 0.822982i \(-0.307691\pi\)
0.184218 + 0.982885i \(0.441025\pi\)
\(500\) 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 −0.136963 0.990576i \(-0.543734\pi\)
0.644495 + 0.764608i \(0.277068\pi\)
\(504\) −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 −0.662516 0.749048i \(-0.730511\pi\)
0.814196 + 0.580589i \(0.197178\pi\)
\(510\) 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 −0.830203 0.557462i \(-0.811775\pi\)
0.897877 + 0.440246i \(0.145109\pi\)
\(522\) −2.32301 4.02357i −0.101675 0.176107i
\(523\) −36.1153 26.2393i −1.57921 1.14736i −0.917593 0.397521i \(-0.869871\pi\)
−0.661617 0.749842i \(-0.730129\pi\)
\(524\) 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 0.903718 + 0.428129i \(0.140827\pi\)
−0.794957 + 0.606666i \(0.792506\pi\)
\(542\) 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 −0.845795 0.533508i \(-0.820873\pi\)
0.938235 0.345999i \(-0.112460\pi\)
\(548\) −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 0.859076 0.511847i \(-0.171039\pi\)
−0.872811 + 0.488058i \(0.837705\pi\)
\(564\) −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 −0.220590 0.975367i \(-0.570798\pi\)
0.418560 0.908189i \(-0.362535\pi\)
\(570\) −2.35264 2.61287i −0.0985414 0.109441i
\(571\) 5.25514 5.83642i 0.219921 0.244247i −0.623081 0.782157i \(-0.714119\pi\)
0.843002 + 0.537910i \(0.180786\pi\)
\(572\) 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 0.693807 0.720161i \(-0.255932\pi\)
−0.788739 + 0.614729i \(0.789265\pi\)
\(578\) −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 −0.800883 0.598821i \(-0.795636\pi\)
0.999906 0.0137092i \(-0.00436391\pi\)
\(588\) −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 0.490423 0.871485i \(-0.336842\pi\)
−0.677282 + 0.735723i \(0.736842\pi\)
\(594\) −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 −0.277072 0.960849i \(-0.589364\pi\)
0.137694 + 0.990475i \(0.456031\pi\)
\(600\) 0.104528 0.994522i 0.00426736 0.0406012i
\(601\) 5.90974 + 6.56343i 0.241063 + 0.267728i 0.851520 0.524321i \(-0.175681\pi\)
−0.610457 + 0.792049i \(0.709014\pi\)
\(602\) −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 −0.585769 0.810478i \(-0.699207\pi\)
0.867268 + 0.497842i \(0.165874\pi\)
\(608\) −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 0.271022 0.962573i \(-0.412638\pi\)
0.896681 + 0.442678i \(0.145972\pi\)
\(614\) −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 0.925104 0.379713i \(-0.123977\pi\)
0.690682 + 0.723159i \(0.257311\pi\)
\(618\) −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 −0.842508 0.538684i \(-0.818922\pi\)
0.936096 0.351745i \(-0.114412\pi\)
\(632\) 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 0.0599148 0.998203i \(-0.480917\pi\)
0.460741 + 0.887535i \(0.347584\pi\)
\(642\) 12.9653 + 5.77255i 0.511702 + 0.227824i
\(643\) 17.8623 12.9777i 0.704420 0.511791i −0.176949 0.984220i \(-0.556623\pi\)
0.881369 + 0.472429i \(0.156623\pi\)
\(644\) 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 0.693888 0.720083i \(-0.255896\pi\)
−0.470416 + 0.882445i \(0.655896\pi\)
\(648\) −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 −0.967886 0.251389i \(-0.919113\pi\)
0.930799 + 0.365531i \(0.119113\pi\)
\(654\) 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 −0.505787 0.862659i \(-0.668798\pi\)
0.664140 + 0.747608i \(0.268798\pi\)
\(660\) −3.60137 1.60343i −0.140183 0.0624136i
\(661\) −37.3597 + 7.94105i −1.45312 + 0.308871i −0.865763 0.500454i \(-0.833167\pi\)
−0.587361 + 0.809325i \(0.699833\pi\)
\(662\) 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 0.485857 0.874038i \(-0.338508\pi\)
−0.324435 + 0.945908i \(0.605174\pi\)
\(674\) 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 0.672525 0.740074i \(-0.265210\pi\)
−0.977186 + 0.212387i \(0.931876\pi\)
\(678\) 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 8.62619e−5 1.00000i \(-0.499973\pi\)
−0.743087 + 0.669195i \(0.766639\pi\)
\(692\) −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 0.988545 0.150923i \(-0.0482246\pi\)
−0.253428 + 0.967354i \(0.581558\pi\)
\(702\) 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 0.818804 0.574073i \(-0.194637\pi\)
−0.292951 + 0.956127i \(0.594637\pi\)
\(710\) 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 −0.855629 0.517589i \(-0.826830\pi\)
0.876060 + 0.482202i \(0.160163\pi\)
\(720\) −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 0.994546 0.104296i \(-0.0332590\pi\)
−0.994497 + 0.104761i \(0.966592\pi\)
\(728\) 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 0.852731 + 0.522350i \(0.174944\pi\)
−0.942700 + 0.333642i \(0.891722\pi\)
\(734\) −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 0.994542 0.104338i \(-0.0332724\pi\)
−0.587630 + 0.809129i \(0.699939\pi\)
\(740\) −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 −0.261949 0.965082i \(-0.584365\pi\)
0.541917 + 0.840432i \(0.317699\pi\)
\(752\) 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 −0.117372 + 0.993088i \(0.537447\pi\)
−0.975379 + 0.220535i \(0.929220\pi\)
\(758\) −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 −0.469768 0.882790i \(-0.655662\pi\)
0.275960 0.961169i \(-0.411004\pi\)
\(762\) 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 −0.813759 0.581202i \(-0.802582\pi\)
0.910216 + 0.414135i \(0.135916\pi\)
\(770\) −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 −0.858812 0.512291i \(-0.828797\pi\)
0.995911 + 0.0903448i \(0.0287969\pi\)
\(774\) −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 0.622739 0.782429i \(-0.286020\pi\)
−0.843237 + 0.537542i \(0.819353\pi\)
\(788\) 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 0.188093 0.982151i \(-0.439769\pi\)
−0.604022 + 0.796968i \(0.706436\pi\)
\(798\) −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 0.0938338 0.995588i \(-0.470088\pi\)
−0.319221 + 0.947680i \(0.603421\pi\)
\(810\) 0.809017 + 0.587785i 0.0284260 + 0.0206527i
\(811\) −6.82380 11.8192i −0.239616 0.415027i 0.720988 0.692948i \(-0.243688\pi\)
−0.960604 + 0.277920i \(0.910355\pi\)
\(812\) −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 0.853704 0.520758i \(-0.174351\pi\)
−0.996755 + 0.0804928i \(0.974351\pi\)
\(822\) −0.282386 0.869096i −0.00984936 0.0303132i
\(823\) 2.50534 + 23.8367i 0.0873307 + 0.830896i 0.947256 + 0.320477i \(0.103843\pi\)
−0.859926 + 0.510419i \(0.829490\pi\)
\(824\) 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 −0.525070 0.851059i \(-0.675961\pi\)
−0.133518 + 0.991046i \(0.542627\pi\)
\(828\) 5.51000 + 2.45321i 0.191486 + 0.0852549i
\(829\) −22.4895 + 16.3395i −0.781091 + 0.567496i −0.905306 0.424760i \(-0.860359\pi\)
0.124215 + 0.992255i \(0.460359\pi\)
\(830\) −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 0.747228 + 0.664568i \(0.231384\pi\)
−0.995143 + 0.0984370i \(0.968616\pi\)
\(840\) −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 0.999994 + 0.00357018i \(0.00113642\pi\)
−0.806913 + 0.590670i \(0.798864\pi\)
\(854\) 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 −0.281792 0.959475i \(-0.590929\pi\)
0.475121 0.879921i \(-0.342404\pi\)
\(858\) −11.4130 + 2.42590i −0.389632 + 0.0828189i
\(859\) 41.1437 + 18.3183i 1.40380 + 0.625014i 0.962237 0.272214i \(-0.0877560\pi\)
0.441567 + 0.897228i \(0.354423\pi\)
\(860\) −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 −0.893805 0.448455i \(-0.851974\pi\)
0.0585294 0.998286i \(-0.481359\pi\)
\(864\) 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 0.684739 0.728789i \(-0.259916\pi\)
−0.0834160 + 0.996515i \(0.526583\pi\)
\(878\) 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 −0.759827 0.650125i \(-0.774716\pi\)
0.725987 + 0.687708i \(0.241383\pi\)
\(882\) −0.543142 5.16765i −0.0182886 0.174004i
\(883\) −7.04514 21.6827i −0.237088 0.729682i −0.996838 0.0794659i \(-0.974679\pi\)
0.759750 0.650216i \(-0.225321\pi\)
\(884\) −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 0.995635 + 0.0933309i \(0.0297514\pi\)
−0.0112526 + 0.999937i \(0.503582\pi\)
\(888\) −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 −0.683906 0.729570i \(-0.739720\pi\)
0.482523 + 0.875883i \(0.339720\pi\)
\(908\) 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 0.302091 0.953279i \(-0.402315\pi\)
−0.979634 + 0.200791i \(0.935649\pi\)
\(912\) 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 −0.999949 0.0101158i \(-0.996780\pi\)
0.980201 + 0.198006i \(0.0634467\pi\)
\(920\) 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 −0.734950 0.678121i \(-0.762794\pi\)
0.0121650 + 0.999926i \(0.496128\pi\)
\(938\) 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 0.971127 + 0.238563i \(0.0766764\pi\)
−0.999506 + 0.0314414i \(0.989990\pi\)
\(942\) −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 −0.751209 0.660064i \(-0.770529\pi\)
0.597559 0.801825i \(-0.296137\pi\)
\(948\) −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 −0.742594 0.669742i \(-0.766405\pi\)
0.407488 + 0.913210i \(0.366405\pi\)
\(954\) 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 −0.699454 0.714677i \(-0.746574\pi\)
0.968656 + 0.248406i \(0.0799068\pi\)
\(968\) 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 0.0564683 0.998404i \(-0.482016\pi\)
0.457674 + 0.889120i \(0.348683\pi\)
\(972\) 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 −0.991958 0.126569i \(-0.959603\pi\)
0.728115 0.685455i \(-0.240397\pi\)
\(978\) −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 0.545011 0.838429i \(-0.316525\pi\)
−0.258390 + 0.966041i \(0.583192\pi\)
\(984\) −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 0.860364 0.509681i \(-0.170237\pi\)
−0.871578 + 0.490256i \(0.836903\pi\)
\(998\) 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.691.2 16
31.7 even 15 inner 930.2.bg.c.751.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.c.691.2 16 1.1 even 1 trivial
930.2.bg.c.751.2 yes 16 31.7 even 15 inner