Properties

Label 930.2.bg.c.751.1
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 751.1
Root \(-2.23655i\) of defining polynomial
Character \(\chi\) \(=\) 930.751
Dual form 930.2.bg.c.691.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 + 0.951057i) q^{2} +(0.978148 - 0.207912i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.70387 - 1.20384i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +O(q^{10})\) \(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} +(-2.70387 - 1.20384i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(0.913545 - 0.406737i) q^{9} +(0.978148 + 0.207912i) q^{10} +(-0.0918838 - 0.874216i) q^{11} +(-0.669131 + 0.743145i) q^{12} +(-2.33680 - 2.59528i) q^{13} +(0.309379 - 2.94355i) 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} +(1.65932 - 1.84287i) q^{19} +(0.104528 + 0.994522i) q^{20} +(-2.89508 - 0.615369i) q^{21} +(0.803035 - 0.357534i) q^{22} +(1.80064 + 1.30824i) q^{23} +(-0.913545 - 0.406737i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.74615 - 3.02442i) q^{26} +(0.809017 - 0.587785i) q^{27} +(2.89508 - 0.615369i) q^{28} +(0.877888 + 2.70186i) q^{29} +1.00000 q^{30} +(3.49214 + 4.33647i) q^{31} +1.00000 q^{32} +(-0.271636 - 0.836008i) q^{33} +(7.84421 - 1.66734i) q^{34} +(-2.39450 + 1.73970i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.48588 - 4.30566i) q^{37} +(2.26543 + 1.00863i) q^{38} +(-2.82533 - 2.05272i) q^{39} +(-0.913545 + 0.406737i) q^{40} +(-3.87180 - 0.822977i) q^{41} +(-0.309379 - 2.94355i) q^{42} +(2.45890 - 2.73089i) q^{43} +(0.588187 + 0.653248i) q^{44} +(0.104528 - 0.994522i) q^{45} +(-0.687785 + 2.11678i) q^{46} +(2.05322 - 6.31917i) q^{47} +(0.104528 - 0.994522i) q^{48} +(1.17779 + 1.30807i) q^{49} +(0.669131 - 0.743145i) q^{50} +(-0.838261 - 7.97552i) q^{51} +(3.41598 + 0.726089i) q^{52} +(-9.06496 + 4.03598i) q^{53} +(0.809017 + 0.587785i) q^{54} +(-0.803035 - 0.357534i) q^{55} +(1.47988 + 2.56323i) q^{56} +(1.23991 - 2.14759i) q^{57} +(-2.29834 + 1.66984i) q^{58} +(3.74182 - 0.795347i) q^{59} +(0.309017 + 0.951057i) q^{60} +3.90546 q^{61} +(-3.04510 + 4.66126i) q^{62} -2.95976 q^{63} +(0.309017 + 0.951057i) q^{64} +(-3.41598 + 0.726089i) q^{65} +(0.711151 - 0.516682i) q^{66} +(3.84467 - 6.65917i) q^{67} +(4.00973 + 6.94505i) q^{68} +(2.03329 + 0.905281i) q^{69} +(-2.39450 - 1.73970i) q^{70} +(-8.88239 + 3.95470i) q^{71} +(-0.978148 - 0.207912i) q^{72} +(1.59395 + 15.1654i) q^{73} +(3.32675 - 3.69473i) q^{74} +(-0.669131 - 0.743145i) q^{75} +(-0.259212 + 2.46624i) q^{76} +(-0.803976 + 2.47438i) q^{77} +(1.07918 - 3.32137i) q^{78} +(0.930158 - 8.84987i) q^{79} +(-0.669131 - 0.743145i) q^{80} +(0.669131 - 0.743145i) q^{81} +(-0.413755 - 3.93662i) q^{82} +(16.4192 + 3.49001i) q^{83} +(2.70387 - 1.20384i) q^{84} +(-6.48787 - 4.71372i) q^{85} +(3.35707 + 1.49467i) q^{86} +(1.42045 + 2.46030i) q^{87} +(-0.439516 + 0.761263i) q^{88} +(-11.8190 + 8.58700i) q^{89} +(0.978148 - 0.207912i) q^{90} +(3.19411 + 9.83045i) q^{91} -2.22572 q^{92} +(4.31743 + 3.51565i) q^{93} +6.64437 q^{94} +(-0.766307 - 2.35845i) q^{95} +(0.978148 - 0.207912i) q^{96} +(5.43339 - 3.94759i) q^{97} +(-0.880088 + 1.52436i) q^{98} +(-0.439516 - 0.761263i) 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
\(7\) −2.70387 1.20384i −1.02197 0.455010i −0.173825 0.984777i \(-0.555613\pi\)
−0.848143 + 0.529767i \(0.822279\pi\)
\(8\) −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
\(11\) −0.0918838 0.874216i −0.0277040 0.263586i −0.999603 0.0281864i \(-0.991027\pi\)
0.971899 0.235400i \(-0.0756399\pi\)
\(12\) −0.669131 + 0.743145i −0.193161 + 0.214527i
\(13\) −2.33680 2.59528i −0.648112 0.719801i 0.326125 0.945327i \(-0.394257\pi\)
−0.974237 + 0.225525i \(0.927590\pi\)
\(14\) 0.309379 2.94355i 0.0826850 0.786696i
\(15\) 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
\(19\) 1.65932 1.84287i 0.380675 0.422783i −0.522107 0.852880i \(-0.674854\pi\)
0.902783 + 0.430097i \(0.141521\pi\)
\(20\) 0.104528 + 0.994522i 0.0233733 + 0.222382i
\(21\) −2.89508 0.615369i −0.631759 0.134284i
\(22\) 0.803035 0.357534i 0.171208 0.0762266i
\(23\) 1.80064 + 1.30824i 0.375460 + 0.272788i 0.759471 0.650541i \(-0.225458\pi\)
−0.384011 + 0.923328i \(0.625458\pi\)
\(24\) −0.913545 0.406737i −0.186477 0.0830248i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 1.74615 3.02442i 0.342448 0.593137i
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) 2.89508 0.615369i 0.547119 0.116294i
\(29\) 0.877888 + 2.70186i 0.163020 + 0.501723i 0.998885 0.0472117i \(-0.0150335\pi\)
−0.835865 + 0.548935i \(0.815034\pi\)
\(30\) 1.00000 0.182574
\(31\) 3.49214 + 4.33647i 0.627206 + 0.778853i
\(32\) 1.00000 0.176777
\(33\) −0.271636 0.836008i −0.0472857 0.145530i
\(34\) 7.84421 1.66734i 1.34527 0.285946i
\(35\) −2.39450 + 1.73970i −0.404744 + 0.294063i
\(36\) −0.500000 + 0.866025i −0.0833333 + 0.144338i
\(37\) −2.48588 4.30566i −0.408675 0.707846i 0.586066 0.810263i \(-0.300676\pi\)
−0.994742 + 0.102417i \(0.967342\pi\)
\(38\) 2.26543 + 1.00863i 0.367501 + 0.163622i
\(39\) −2.82533 2.05272i −0.452414 0.328698i
\(40\) −0.913545 + 0.406737i −0.144444 + 0.0643107i
\(41\) −3.87180 0.822977i −0.604674 0.128527i −0.104606 0.994514i \(-0.533358\pi\)
−0.500068 + 0.865986i \(0.666692\pi\)
\(42\) −0.309379 2.94355i −0.0477382 0.454199i
\(43\) 2.45890 2.73089i 0.374979 0.416457i −0.525886 0.850555i \(-0.676266\pi\)
0.900866 + 0.434098i \(0.142933\pi\)
\(44\) 0.588187 + 0.653248i 0.0886725 + 0.0984808i
\(45\) 0.104528 0.994522i 0.0155822 0.148255i
\(46\) −0.687785 + 2.11678i −0.101408 + 0.312103i
\(47\) 2.05322 6.31917i 0.299493 0.921745i −0.682182 0.731183i \(-0.738969\pi\)
0.981675 0.190563i \(-0.0610313\pi\)
\(48\) 0.104528 0.994522i 0.0150874 0.143547i
\(49\) 1.17779 + 1.30807i 0.168255 + 0.186867i
\(50\) 0.669131 0.743145i 0.0946294 0.105097i
\(51\) −0.838261 7.97552i −0.117380 1.11680i
\(52\) 3.41598 + 0.726089i 0.473711 + 0.100690i
\(53\) −9.06496 + 4.03598i −1.24517 + 0.554384i −0.920240 0.391354i \(-0.872007\pi\)
−0.324928 + 0.945739i \(0.605340\pi\)
\(54\) 0.809017 + 0.587785i 0.110093 + 0.0799874i
\(55\) −0.803035 0.357534i −0.108281 0.0482099i
\(56\) 1.47988 + 2.56323i 0.197757 + 0.342526i
\(57\) 1.23991 2.14759i 0.164230 0.284455i
\(58\) −2.29834 + 1.66984i −0.301787 + 0.219261i
\(59\) 3.74182 0.795347i 0.487143 0.103545i 0.0422090 0.999109i \(-0.486560\pi\)
0.444934 + 0.895563i \(0.353227\pi\)
\(60\) 0.309017 + 0.951057i 0.0398939 + 0.122781i
\(61\) 3.90546 0.500043 0.250021 0.968240i \(-0.419562\pi\)
0.250021 + 0.968240i \(0.419562\pi\)
\(62\) −3.04510 + 4.66126i −0.386728 + 0.591981i
\(63\) −2.95976 −0.372895
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) −3.41598 + 0.726089i −0.423700 + 0.0900602i
\(66\) 0.711151 0.516682i 0.0875367 0.0635991i
\(67\) 3.84467 6.65917i 0.469702 0.813547i −0.529698 0.848186i \(-0.677695\pi\)
0.999400 + 0.0346389i \(0.0110281\pi\)
\(68\) 4.00973 + 6.94505i 0.486251 + 0.842211i
\(69\) 2.03329 + 0.905281i 0.244780 + 0.108983i
\(70\) −2.39450 1.73970i −0.286197 0.207934i
\(71\) −8.88239 + 3.95470i −1.05415 + 0.469336i −0.859286 0.511495i \(-0.829092\pi\)
−0.194860 + 0.980831i \(0.562425\pi\)
\(72\) −0.978148 0.207912i −0.115276 0.0245026i
\(73\) 1.59395 + 15.1654i 0.186557 + 1.77497i 0.542101 + 0.840314i \(0.317629\pi\)
−0.355544 + 0.934660i \(0.615704\pi\)
\(74\) 3.32675 3.69473i 0.386727 0.429504i
\(75\) −0.669131 0.743145i −0.0772645 0.0858110i
\(76\) −0.259212 + 2.46624i −0.0297337 + 0.282897i
\(77\) −0.803976 + 2.47438i −0.0916216 + 0.281982i
\(78\) 1.07918 3.32137i 0.122193 0.376071i
\(79\) 0.930158 8.84987i 0.104651 0.995688i −0.808619 0.588333i \(-0.799785\pi\)
0.913270 0.407355i \(-0.133549\pi\)
\(80\) −0.669131 0.743145i −0.0748111 0.0830861i
\(81\) 0.669131 0.743145i 0.0743478 0.0825716i
\(82\) −0.413755 3.93662i −0.0456916 0.434727i
\(83\) 16.4192 + 3.49001i 1.80224 + 0.383079i 0.981992 0.188923i \(-0.0604998\pi\)
0.820252 + 0.572002i \(0.193833\pi\)
\(84\) 2.70387 1.20384i 0.295017 0.131350i
\(85\) −6.48787 4.71372i −0.703709 0.511274i
\(86\) 3.35707 + 1.49467i 0.362002 + 0.161174i
\(87\) 1.42045 + 2.46030i 0.152289 + 0.263771i
\(88\) −0.439516 + 0.761263i −0.0468525 + 0.0811510i
\(89\) −11.8190 + 8.58700i −1.25281 + 0.910220i −0.998382 0.0568716i \(-0.981887\pi\)
−0.254429 + 0.967092i \(0.581887\pi\)
\(90\) 0.978148 0.207912i 0.103106 0.0219158i
\(91\) 3.19411 + 9.83045i 0.334834 + 1.03051i
\(92\) −2.22572 −0.232047
\(93\) 4.31743 + 3.51565i 0.447697 + 0.364556i
\(94\) 6.64437 0.685314
\(95\) −0.766307 2.35845i −0.0786214 0.241972i
\(96\) 0.978148 0.207912i 0.0998318 0.0212199i
\(97\) 5.43339 3.94759i 0.551677 0.400817i −0.276727 0.960949i \(-0.589250\pi\)
0.828403 + 0.560132i \(0.189250\pi\)
\(98\) −0.880088 + 1.52436i −0.0889024 + 0.153983i
\(99\) −0.439516 0.761263i −0.0441730 0.0765099i
\(100\) 0.913545 + 0.406737i 0.0913545 + 0.0406737i
\(101\) −2.42498 1.76185i −0.241295 0.175311i 0.460565 0.887626i \(-0.347647\pi\)
−0.701860 + 0.712315i \(0.747647\pi\)
\(102\) 7.32614 3.26181i 0.725396 0.322967i
\(103\) −2.29784 0.488421i −0.226413 0.0481255i 0.0933081 0.995637i \(-0.470256\pi\)
−0.319721 + 0.947512i \(0.603589\pi\)
\(104\) 0.365044 + 3.47316i 0.0357955 + 0.340572i
\(105\) −1.98047 + 2.19953i −0.193274 + 0.214652i
\(106\) −6.63967 7.37410i −0.644902 0.716236i
\(107\) −0.727163 + 6.91850i −0.0702975 + 0.668836i 0.901461 + 0.432860i \(0.142495\pi\)
−0.971759 + 0.235976i \(0.924171\pi\)
\(108\) −0.309017 + 0.951057i −0.0297352 + 0.0915155i
\(109\) −2.07270 + 6.37911i −0.198529 + 0.611008i 0.801389 + 0.598144i \(0.204095\pi\)
−0.999917 + 0.0128642i \(0.995905\pi\)
\(110\) 0.0918838 0.874216i 0.00876078 0.0833532i
\(111\) −3.32675 3.69473i −0.315761 0.350688i
\(112\) −1.98047 + 2.19953i −0.187136 + 0.207836i
\(113\) −0.225721 2.14759i −0.0212341 0.202029i 0.978762 0.205002i \(-0.0657202\pi\)
−0.999996 + 0.00297352i \(0.999053\pi\)
\(114\) 2.42563 + 0.515584i 0.227181 + 0.0482889i
\(115\) 2.03329 0.905281i 0.189606 0.0844179i
\(116\) −2.29834 1.66984i −0.213396 0.155041i
\(117\) −3.19037 1.42044i −0.294950 0.131320i
\(118\) 1.91271 + 3.31290i 0.176079 + 0.304977i
\(119\) −11.8678 + 20.5557i −1.08792 + 1.88434i
\(120\) −0.809017 + 0.587785i −0.0738528 + 0.0536572i
\(121\) 10.0038 2.12638i 0.909438 0.193307i
\(122\) 1.20685 + 3.71431i 0.109263 + 0.336278i
\(123\) −3.95830 −0.356908
\(124\) −5.37411 1.45565i −0.482610 0.130721i
\(125\) −1.00000 −0.0894427
\(126\) −0.914616 2.81490i −0.0814805 0.250771i
\(127\) 15.9730 3.39517i 1.41738 0.301272i 0.565384 0.824828i \(-0.308728\pi\)
0.851991 + 0.523556i \(0.175395\pi\)
\(128\) −0.809017 + 0.587785i −0.0715077 + 0.0519534i
\(129\) 1.83739 3.18245i 0.161773 0.280199i
\(130\) −1.74615 3.02442i −0.153147 0.265259i
\(131\) −13.3747 5.95480i −1.16855 0.520274i −0.271605 0.962409i \(-0.587555\pi\)
−0.896948 + 0.442135i \(0.854221\pi\)
\(132\) 0.711151 + 0.516682i 0.0618978 + 0.0449714i
\(133\) −6.70513 + 2.98532i −0.581408 + 0.258860i
\(134\) 7.52132 + 1.59871i 0.649743 + 0.138107i
\(135\) −0.104528 0.994522i −0.00899638 0.0855948i
\(136\) −5.36606 + 5.95962i −0.460136 + 0.511033i
\(137\) −6.74314 7.48902i −0.576106 0.639830i 0.382707 0.923870i \(-0.374992\pi\)
−0.958812 + 0.284040i \(0.908325\pi\)
\(138\) −0.232651 + 2.21353i −0.0198046 + 0.188428i
\(139\) 3.28014 10.0952i 0.278218 0.856267i −0.710132 0.704068i \(-0.751365\pi\)
0.988350 0.152198i \(-0.0486352\pi\)
\(140\) 0.914616 2.81490i 0.0772992 0.237902i
\(141\) 0.694525 6.60797i 0.0584896 0.556491i
\(142\) −6.50595 7.22559i −0.545967 0.606358i
\(143\) −2.05412 + 2.28133i −0.171774 + 0.190775i
\(144\) −0.104528 0.994522i −0.00871071 0.0828768i
\(145\) 2.77882 + 0.590657i 0.230769 + 0.0490514i
\(146\) −13.9306 + 6.20229i −1.15290 + 0.513305i
\(147\) 1.42401 + 1.03461i 0.117451 + 0.0853329i
\(148\) 4.54192 + 2.02219i 0.373344 + 0.166223i
\(149\) 9.07764 + 15.7229i 0.743669 + 1.28807i 0.950814 + 0.309763i \(0.100250\pi\)
−0.207145 + 0.978310i \(0.566417\pi\)
\(150\) 0.500000 0.866025i 0.0408248 0.0707107i
\(151\) 16.3461 11.8761i 1.33022 0.966465i 0.330482 0.943812i \(-0.392789\pi\)
0.999743 0.0226526i \(-0.00721115\pi\)
\(152\) −2.42563 + 0.515584i −0.196745 + 0.0418194i
\(153\) −2.47815 7.62695i −0.200346 0.616603i
\(154\) −2.60172 −0.209653
\(155\) 5.50156 0.856045i 0.441896 0.0687592i
\(156\) 3.49229 0.279607
\(157\) 1.46194 + 4.49940i 0.116676 + 0.359091i 0.992293 0.123915i \(-0.0395450\pi\)
−0.875617 + 0.483006i \(0.839545\pi\)
\(158\) 8.70416 1.85013i 0.692466 0.147188i
\(159\) −8.02774 + 5.83249i −0.636641 + 0.462547i
\(160\) 0.500000 0.866025i 0.0395285 0.0684653i
\(161\) −3.29380 5.70502i −0.259587 0.449619i
\(162\) 0.913545 + 0.406737i 0.0717749 + 0.0319562i
\(163\) 2.03034 + 1.47513i 0.159029 + 0.115541i 0.664454 0.747329i \(-0.268664\pi\)
−0.505425 + 0.862870i \(0.668664\pi\)
\(164\) 3.61609 1.60999i 0.282369 0.125719i
\(165\) −0.859822 0.182761i −0.0669371 0.0142279i
\(166\) 1.75462 + 16.6941i 0.136185 + 1.29571i
\(167\) −7.13025 + 7.91894i −0.551755 + 0.612786i −0.952921 0.303219i \(-0.901939\pi\)
0.401166 + 0.916006i \(0.368605\pi\)
\(168\) 1.98047 + 2.19953i 0.152796 + 0.169697i
\(169\) 0.0840285 0.799478i 0.00646373 0.0614983i
\(170\) 2.47815 7.62695i 0.190065 0.584961i
\(171\) 0.766307 2.35845i 0.0586010 0.180355i
\(172\) −0.384118 + 3.65464i −0.0292888 + 0.278664i
\(173\) 8.35844 + 9.28299i 0.635481 + 0.705773i 0.971755 0.235991i \(-0.0758337\pi\)
−0.336275 + 0.941764i \(0.609167\pi\)
\(174\) −1.90094 + 2.11120i −0.144110 + 0.160050i
\(175\) 0.309379 + 2.94355i 0.0233869 + 0.222511i
\(176\) −0.859822 0.182761i −0.0648115 0.0137761i
\(177\) 3.49469 1.55593i 0.262677 0.116951i
\(178\) −11.8190 8.58700i −0.885871 0.643623i
\(179\) −3.76389 1.67579i −0.281326 0.125255i 0.261223 0.965278i \(-0.415874\pi\)
−0.542549 + 0.840024i \(0.682541\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −7.64407 + 13.2399i −0.568179 + 0.984115i 0.428567 + 0.903510i \(0.359019\pi\)
−0.996746 + 0.0806051i \(0.974315\pi\)
\(182\) −8.36228 + 6.07555i −0.619854 + 0.450350i
\(183\) 3.82012 0.811991i 0.282391 0.0600241i
\(184\) −0.687785 2.11678i −0.0507042 0.156051i
\(185\) −4.97175 −0.365530
\(186\) −2.00942 + 5.19252i −0.147338 + 0.380734i
\(187\) −7.04935 −0.515500
\(188\) 2.05322 + 6.31917i 0.149747 + 0.460873i
\(189\) −2.89508 + 0.615369i −0.210586 + 0.0447615i
\(190\) 2.00622 1.45760i 0.145546 0.105746i
\(191\) −12.0392 + 20.8524i −0.871123 + 1.50883i −0.0102861 + 0.999947i \(0.503274\pi\)
−0.860837 + 0.508882i \(0.830059\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −1.14108 0.508043i −0.0821370 0.0365697i 0.365257 0.930907i \(-0.380981\pi\)
−0.447394 + 0.894337i \(0.647648\pi\)
\(194\) 5.43339 + 3.94759i 0.390094 + 0.283420i
\(195\) −3.19037 + 1.42044i −0.228467 + 0.101720i
\(196\) −1.72171 0.365961i −0.122979 0.0261401i
\(197\) −0.761479 7.24499i −0.0542531 0.516184i −0.987576 0.157145i \(-0.949771\pi\)
0.933322 0.359039i \(-0.116896\pi\)
\(198\) 0.588187 0.653248i 0.0418006 0.0464243i
\(199\) 15.8452 + 17.5979i 1.12323 + 1.24748i 0.965614 + 0.259979i \(0.0837156\pi\)
0.157621 + 0.987500i \(0.449618\pi\)
\(200\) −0.104528 + 0.994522i −0.00739128 + 0.0703233i
\(201\) 2.37614 7.31301i 0.167600 0.515820i
\(202\) 0.926261 2.85074i 0.0651715 0.200577i
\(203\) 0.878917 8.36233i 0.0616879 0.586921i
\(204\) 5.36606 + 5.95962i 0.375700 + 0.417257i
\(205\) −2.64862 + 2.94159i −0.184988 + 0.205450i
\(206\) −0.245556 2.33631i −0.0171087 0.162778i
\(207\) 2.17708 + 0.462753i 0.151318 + 0.0321635i
\(208\) −3.19037 + 1.42044i −0.221212 + 0.0984901i
\(209\) −1.76353 1.28128i −0.121986 0.0886279i
\(210\) −2.70387 1.20384i −0.186585 0.0830730i
\(211\) −5.71160 9.89278i −0.393203 0.681047i 0.599667 0.800249i \(-0.295300\pi\)
−0.992870 + 0.119202i \(0.961966\pi\)
\(212\) 4.96142 8.59342i 0.340751 0.590199i
\(213\) −7.86607 + 5.71503i −0.538974 + 0.391587i
\(214\) −6.80459 + 1.44636i −0.465152 + 0.0988711i
\(215\) −1.13557 3.49492i −0.0774451 0.238351i
\(216\) −1.00000 −0.0680414
\(217\) −4.22188 15.9293i −0.286600 1.08135i
\(218\) −6.70740 −0.454282
\(219\) 4.71217 + 14.5026i 0.318419 + 0.979993i
\(220\) 0.859822 0.182761i 0.0579692 0.0123217i
\(221\) −22.6576 + 16.4617i −1.52411 + 1.10733i
\(222\) 2.48588 4.30566i 0.166841 0.288977i
\(223\) −6.17667 10.6983i −0.413620 0.716411i 0.581662 0.813430i \(-0.302403\pi\)
−0.995283 + 0.0970192i \(0.969069\pi\)
\(224\) −2.70387 1.20384i −0.180660 0.0804351i
\(225\) −0.809017 0.587785i −0.0539345 0.0391857i
\(226\) 1.97273 0.878317i 0.131224 0.0584248i
\(227\) −12.4277 2.64159i −0.824855 0.175328i −0.223901 0.974612i \(-0.571879\pi\)
−0.600954 + 0.799284i \(0.705213\pi\)
\(228\) 0.259212 + 2.46624i 0.0171667 + 0.163331i
\(229\) −6.22257 + 6.91086i −0.411199 + 0.456682i −0.912794 0.408420i \(-0.866080\pi\)
0.501595 + 0.865102i \(0.332747\pi\)
\(230\) 1.48930 + 1.65403i 0.0982013 + 0.109064i
\(231\) −0.271954 + 2.58747i −0.0178933 + 0.170243i
\(232\) 0.877888 2.70186i 0.0576362 0.177386i
\(233\) 1.29441 3.98378i 0.0847995 0.260986i −0.899662 0.436587i \(-0.856187\pi\)
0.984461 + 0.175601i \(0.0561870\pi\)
\(234\) 0.365044 3.47316i 0.0238637 0.227048i
\(235\) −4.44595 4.93773i −0.290022 0.322102i
\(236\) −2.55970 + 2.84283i −0.166622 + 0.185053i
\(237\) −0.930158 8.84987i −0.0604203 0.574861i
\(238\) −23.2170 4.93492i −1.50493 0.319883i
\(239\) −2.19268 + 0.976244i −0.141833 + 0.0631480i −0.476426 0.879215i \(-0.658068\pi\)
0.334593 + 0.942363i \(0.391401\pi\)
\(240\) −0.809017 0.587785i −0.0522218 0.0379414i
\(241\) 13.9051 + 6.19093i 0.895704 + 0.398793i 0.802360 0.596841i \(-0.203578\pi\)
0.0933443 + 0.995634i \(0.470244\pi\)
\(242\) 5.11365 + 8.85711i 0.328718 + 0.569356i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −3.15958 + 2.29557i −0.202272 + 0.146959i
\(245\) 1.72171 0.365961i 0.109996 0.0233804i
\(246\) −1.22318 3.76457i −0.0779873 0.240020i
\(247\) −8.66027 −0.551040
\(248\) −0.276286 5.56091i −0.0175441 0.353118i
\(249\) 16.7860 1.06377
\(250\) −0.309017 0.951057i −0.0195440 0.0601501i
\(251\) −2.64179 + 0.561530i −0.166748 + 0.0354434i −0.290529 0.956866i \(-0.593831\pi\)
0.123781 + 0.992310i \(0.460498\pi\)
\(252\) 2.39450 1.73970i 0.150839 0.109591i
\(253\) 0.978238 1.69436i 0.0615013 0.106523i
\(254\) 8.16493 + 14.1421i 0.512313 + 0.887352i
\(255\) −7.32614 3.26181i −0.458780 0.204262i
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 18.2684 8.13363i 1.13955 0.507362i 0.251845 0.967768i \(-0.418963\pi\)
0.887708 + 0.460406i \(0.152296\pi\)
\(258\) 3.59447 + 0.764028i 0.223782 + 0.0475663i
\(259\) 1.53816 + 14.6346i 0.0955763 + 0.909348i
\(260\) 2.33680 2.59528i 0.144922 0.160952i
\(261\) 1.90094 + 2.11120i 0.117665 + 0.130680i
\(262\) 1.53034 14.5602i 0.0945449 0.899535i
\(263\) 2.80872 8.64436i 0.173193 0.533034i −0.826353 0.563152i \(-0.809588\pi\)
0.999546 + 0.0301183i \(0.00958840\pi\)
\(264\) −0.271636 + 0.836008i −0.0167180 + 0.0514528i
\(265\) −1.03722 + 9.86847i −0.0637158 + 0.606216i
\(266\) −4.91120 5.45444i −0.301125 0.334433i
\(267\) −9.77538 + 10.8567i −0.598243 + 0.664417i
\(268\) 0.803756 + 7.64723i 0.0490972 + 0.467129i
\(269\) 14.8011 + 3.14607i 0.902437 + 0.191819i 0.635687 0.771947i \(-0.280717\pi\)
0.266750 + 0.963766i \(0.414050\pi\)
\(270\) 0.913545 0.406737i 0.0555966 0.0247532i
\(271\) 3.96433 + 2.88025i 0.240816 + 0.174963i 0.701647 0.712525i \(-0.252449\pi\)
−0.460831 + 0.887488i \(0.652449\pi\)
\(272\) −7.32614 3.26181i −0.444212 0.197776i
\(273\) 5.16818 + 8.95154i 0.312792 + 0.541772i
\(274\) 5.03873 8.72734i 0.304401 0.527238i
\(275\) −0.711151 + 0.516682i −0.0428840 + 0.0311571i
\(276\) −2.17708 + 0.462753i −0.131045 + 0.0278544i
\(277\) −8.52416 26.2347i −0.512167 1.57629i −0.788378 0.615192i \(-0.789079\pi\)
0.276210 0.961097i \(-0.410921\pi\)
\(278\) 10.6148 0.636631
\(279\) 4.95403 + 2.54118i 0.296590 + 0.152137i
\(280\) 2.95976 0.176879
\(281\) −3.92589 12.0826i −0.234199 0.720790i −0.997227 0.0744245i \(-0.976288\pi\)
0.763028 0.646366i \(-0.223712\pi\)
\(282\) 6.49917 1.38144i 0.387020 0.0822636i
\(283\) 9.68112 7.03375i 0.575483 0.418113i −0.261610 0.965174i \(-0.584253\pi\)
0.837093 + 0.547061i \(0.184253\pi\)
\(284\) 4.86150 8.42036i 0.288477 0.499656i
\(285\) −1.23991 2.14759i −0.0734460 0.127212i
\(286\) −2.80443 1.24861i −0.165830 0.0738321i
\(287\) 9.47814 + 6.88627i 0.559477 + 0.406484i
\(288\) 0.913545 0.406737i 0.0538312 0.0239672i
\(289\) −46.2778 9.83664i −2.72222 0.578626i
\(290\) 0.296955 + 2.82534i 0.0174378 + 0.165910i
\(291\) 4.49390 4.99099i 0.263437 0.292577i
\(292\) −10.2035 11.3322i −0.597116 0.663164i
\(293\) −1.32462 + 12.6029i −0.0773849 + 0.736268i 0.885186 + 0.465237i \(0.154031\pi\)
−0.962571 + 0.271030i \(0.912636\pi\)
\(294\) −0.543925 + 1.67403i −0.0317223 + 0.0976313i
\(295\) 1.18212 3.63818i 0.0688255 0.211823i
\(296\) −0.519689 + 4.94451i −0.0302063 + 0.287394i
\(297\) −0.588187 0.653248i −0.0341301 0.0379053i
\(298\) −12.1483 + 13.4920i −0.703729 + 0.781571i
\(299\) −0.812485 7.73028i −0.0469872 0.447054i
\(300\) 0.978148 + 0.207912i 0.0564734 + 0.0120038i
\(301\) −9.93613 + 4.42385i −0.572709 + 0.254986i
\(302\) 16.3461 + 11.8761i 0.940611 + 0.683394i
\(303\) −2.73830 1.21917i −0.157311 0.0700395i
\(304\) −1.23991 2.14759i −0.0711138 0.123173i
\(305\) 1.95273 3.38223i 0.111813 0.193666i
\(306\) 6.48787 4.71372i 0.370887 0.269465i
\(307\) 9.01152 1.91546i 0.514315 0.109321i 0.0565595 0.998399i \(-0.481987\pi\)
0.457755 + 0.889078i \(0.348654\pi\)
\(308\) −0.803976 2.47438i −0.0458108 0.140991i
\(309\) −2.34917 −0.133640
\(310\) 2.51422 + 4.96776i 0.142798 + 0.282150i
\(311\) 31.2399 1.77145 0.885726 0.464208i \(-0.153661\pi\)
0.885726 + 0.464208i \(0.153661\pi\)
\(312\) 1.07918 + 3.32137i 0.0610964 + 0.188035i
\(313\) 7.49437 1.59298i 0.423607 0.0900405i 0.00882459 0.999961i \(-0.497191\pi\)
0.414782 + 0.909921i \(0.363858\pi\)
\(314\) −3.82742 + 2.78078i −0.215994 + 0.156929i
\(315\) −1.47988 + 2.56323i −0.0833818 + 0.144421i
\(316\) 4.44931 + 7.70643i 0.250293 + 0.433520i
\(317\) −18.4334 8.20706i −1.03532 0.460955i −0.182526 0.983201i \(-0.558427\pi\)
−0.852795 + 0.522246i \(0.825094\pi\)
\(318\) −8.02774 5.83249i −0.450173 0.327070i
\(319\) 2.28135 1.01572i 0.127731 0.0568695i
\(320\) 0.978148 + 0.207912i 0.0546801 + 0.0116226i
\(321\) 0.727163 + 6.91850i 0.0405863 + 0.386153i
\(322\) 4.40796 4.89553i 0.245646 0.272817i
\(323\) −13.3069 14.7788i −0.740414 0.822314i
\(324\) −0.104528 + 0.994522i −0.00580714 + 0.0552512i
\(325\) −1.07918 + 3.32137i −0.0598620 + 0.184236i
\(326\) −0.775521 + 2.38681i −0.0429522 + 0.132193i
\(327\) −0.701114 + 6.67065i −0.0387717 + 0.368888i
\(328\) 2.64862 + 2.94159i 0.146246 + 0.162422i
\(329\) −13.1589 + 14.6145i −0.725476 + 0.805723i
\(330\) −0.0918838 0.874216i −0.00505804 0.0481240i
\(331\) 13.4094 + 2.85025i 0.737046 + 0.156664i 0.561114 0.827738i \(-0.310373\pi\)
0.175932 + 0.984402i \(0.443706\pi\)
\(332\) −15.3348 + 6.82750i −0.841607 + 0.374708i
\(333\) −4.02223 2.92232i −0.220417 0.160142i
\(334\) −9.73473 4.33418i −0.532661 0.237156i
\(335\) −3.84467 6.65917i −0.210057 0.363829i
\(336\) −1.47988 + 2.56323i −0.0807341 + 0.139835i
\(337\) −23.7342 + 17.2439i −1.29288 + 0.939335i −0.999859 0.0167705i \(-0.994662\pi\)
−0.293024 + 0.956105i \(0.594662\pi\)
\(338\) 0.786315 0.167136i 0.0427699 0.00909102i
\(339\) −0.667299 2.05373i −0.0362427 0.111544i
\(340\) 8.01945 0.434916
\(341\) 3.47014 3.45133i 0.187919 0.186900i
\(342\) 2.47982 0.134093
\(343\) 4.79243 + 14.7496i 0.258767 + 0.796402i
\(344\) −3.59447 + 0.764028i −0.193801 + 0.0411937i
\(345\) 1.80064 1.30824i 0.0969434 0.0704335i
\(346\) −6.24575 + 10.8180i −0.335774 + 0.581577i
\(347\) −4.62123 8.00420i −0.248081 0.429688i 0.714913 0.699214i \(-0.246466\pi\)
−0.962993 + 0.269526i \(0.913133\pi\)
\(348\) −2.59530 1.15550i −0.139122 0.0619413i
\(349\) −0.458431 0.333070i −0.0245393 0.0178288i 0.575448 0.817838i \(-0.304828\pi\)
−0.599987 + 0.800010i \(0.704828\pi\)
\(350\) −2.70387 + 1.20384i −0.144528 + 0.0643481i
\(351\) −3.41598 0.726089i −0.182331 0.0387558i
\(352\) −0.0918838 0.874216i −0.00489742 0.0465959i
\(353\) 18.2501 20.2688i 0.971356 1.07880i −0.0255091 0.999675i \(-0.508121\pi\)
0.996865 0.0791250i \(-0.0252126\pi\)
\(354\) 2.55970 + 2.84283i 0.136046 + 0.151095i
\(355\) −1.01633 + 9.66973i −0.0539412 + 0.513216i
\(356\) 4.51445 13.8941i 0.239265 0.736383i
\(357\) −7.33472 + 22.5740i −0.388195 + 1.19474i
\(358\) 0.430667 4.09752i 0.0227614 0.216561i
\(359\) 3.91505 + 4.34811i 0.206629 + 0.229484i 0.837548 0.546364i \(-0.183989\pi\)
−0.630919 + 0.775849i \(0.717322\pi\)
\(360\) −0.669131 + 0.743145i −0.0352663 + 0.0391672i
\(361\) 1.34324 + 12.7801i 0.0706969 + 0.672636i
\(362\) −14.9541 3.17858i −0.785968 0.167063i
\(363\) 9.34311 4.15982i 0.490386 0.218334i
\(364\) −8.36228 6.07555i −0.438303 0.318446i
\(365\) 13.9306 + 6.20229i 0.729160 + 0.324643i
\(366\) 1.95273 + 3.38223i 0.102071 + 0.176792i
\(367\) −6.34598 + 10.9916i −0.331257 + 0.573755i −0.982759 0.184893i \(-0.940806\pi\)
0.651501 + 0.758648i \(0.274140\pi\)
\(368\) 1.80064 1.30824i 0.0938650 0.0681969i
\(369\) −3.87180 + 0.822977i −0.201558 + 0.0428425i
\(370\) −1.53636 4.72842i −0.0798713 0.245819i
\(371\) 29.3692 1.52477
\(372\) −5.55932 0.306501i −0.288237 0.0158913i
\(373\) 22.1559 1.14719 0.573594 0.819140i \(-0.305549\pi\)
0.573594 + 0.819140i \(0.305549\pi\)
\(374\) −2.17837 6.70433i −0.112641 0.346673i
\(375\) −0.978148 + 0.207912i −0.0505113 + 0.0107365i
\(376\) −5.37541 + 3.90546i −0.277215 + 0.201409i
\(377\) 4.96064 8.59208i 0.255486 0.442515i
\(378\) −1.47988 2.56323i −0.0761168 0.131838i
\(379\) 30.8993 + 13.7572i 1.58719 + 0.706662i 0.995069 0.0991874i \(-0.0316243\pi\)
0.592120 + 0.805850i \(0.298291\pi\)
\(380\) 2.00622 + 1.45760i 0.102917 + 0.0747734i
\(381\) 14.9181 6.64195i 0.764276 0.340277i
\(382\) −23.5521 5.00616i −1.20503 0.256138i
\(383\) 1.77704 + 16.9074i 0.0908026 + 0.863929i 0.941214 + 0.337811i \(0.109686\pi\)
−0.850411 + 0.526118i \(0.823647\pi\)
\(384\) −0.669131 + 0.743145i −0.0341464 + 0.0379235i
\(385\) 1.74089 + 1.93346i 0.0887240 + 0.0985380i
\(386\) 0.130563 1.24223i 0.00664551 0.0632278i
\(387\) 1.13557 3.49492i 0.0577241 0.177657i
\(388\) −2.07537 + 6.38733i −0.105361 + 0.324267i
\(389\) −3.27860 + 31.1938i −0.166231 + 1.58159i 0.519976 + 0.854181i \(0.325941\pi\)
−0.686208 + 0.727406i \(0.740726\pi\)
\(390\) −2.33680 2.59528i −0.118329 0.131417i
\(391\) 11.9433 13.2644i 0.604001 0.670811i
\(392\) −0.183989 1.75053i −0.00929283 0.0884153i
\(393\) −14.3205 3.04392i −0.722374 0.153545i
\(394\) 6.65508 2.96303i 0.335278 0.149276i
\(395\) −7.19913 5.23047i −0.362228 0.263174i
\(396\) 0.803035 + 0.357534i 0.0403540 + 0.0179668i
\(397\) −11.3308 19.6255i −0.568675 0.984975i −0.996697 0.0812062i \(-0.974123\pi\)
0.428022 0.903768i \(-0.359211\pi\)
\(398\) −11.8401 + 20.5077i −0.593492 + 1.02796i
\(399\) −5.93792 + 4.31415i −0.297268 + 0.215978i
\(400\) −0.978148 + 0.207912i −0.0489074 + 0.0103956i
\(401\) 7.35316 + 22.6307i 0.367199 + 1.13012i 0.948592 + 0.316501i \(0.102508\pi\)
−0.581393 + 0.813623i \(0.697492\pi\)
\(402\) 7.68935 0.383510
\(403\) 3.09393 19.1965i 0.154119 0.956248i
\(404\) 2.99744 0.149128
\(405\) −0.309017 0.951057i −0.0153552 0.0472584i
\(406\) 8.22465 1.74820i 0.408183 0.0867619i
\(407\) −3.53567 + 2.56881i −0.175256 + 0.127331i
\(408\) −4.00973 + 6.94505i −0.198511 + 0.343831i
\(409\) 1.86634 + 3.23260i 0.0922846 + 0.159842i 0.908472 0.417946i \(-0.137250\pi\)
−0.816188 + 0.577787i \(0.803916\pi\)
\(410\) −3.61609 1.60999i −0.178586 0.0795116i
\(411\) −8.15284 5.92339i −0.402150 0.292179i
\(412\) 2.14608 0.955496i 0.105730 0.0470739i
\(413\) −11.0749 2.35404i −0.544959 0.115835i
\(414\) 0.232651 + 2.21353i 0.0114342 + 0.108789i
\(415\) 11.2321 12.4745i 0.551360 0.612347i
\(416\) −2.33680 2.59528i −0.114571 0.127244i
\(417\) 1.10954 10.5566i 0.0543346 0.516959i
\(418\) 0.673608 2.07315i 0.0329472 0.101401i
\(419\) −0.160630 + 0.494367i −0.00784727 + 0.0241514i −0.954903 0.296916i \(-0.904042\pi\)
0.947056 + 0.321068i \(0.104042\pi\)
\(420\) 0.309379 2.94355i 0.0150962 0.143630i
\(421\) 7.96329 + 8.84413i 0.388107 + 0.431037i 0.905261 0.424856i \(-0.139675\pi\)
−0.517154 + 0.855892i \(0.673009\pi\)
\(422\) 7.64361 8.48909i 0.372085 0.413242i
\(423\) −0.694525 6.60797i −0.0337690 0.321290i
\(424\) 9.70599 + 2.06307i 0.471365 + 0.100192i
\(425\) −7.32614 + 3.26181i −0.355370 + 0.158221i
\(426\) −7.86607 5.71503i −0.381112 0.276894i
\(427\) −10.5599 4.70156i −0.511028 0.227524i
\(428\) −3.47830 6.02460i −0.168130 0.291210i
\(429\) −1.53492 + 2.65856i −0.0741065 + 0.128356i
\(430\) 2.97295 2.15998i 0.143369 0.104163i
\(431\) 15.2788 3.24760i 0.735952 0.156432i 0.175338 0.984508i \(-0.443898\pi\)
0.560615 + 0.828077i \(0.310565\pi\)
\(432\) −0.309017 0.951057i −0.0148676 0.0457577i
\(433\) 25.7677 1.23831 0.619157 0.785267i \(-0.287474\pi\)
0.619157 + 0.785267i \(0.287474\pi\)
\(434\) 13.8450 8.93765i 0.664581 0.429021i
\(435\) 2.84091 0.136211
\(436\) −2.07270 6.37911i −0.0992643 0.305504i
\(437\) 5.39877 1.14754i 0.258258 0.0548945i
\(438\) −12.3366 + 8.96309i −0.589467 + 0.428273i
\(439\) 6.12565 10.6099i 0.292361 0.506384i −0.682006 0.731346i \(-0.738892\pi\)
0.974368 + 0.224962i \(0.0722257\pi\)
\(440\) 0.439516 + 0.761263i 0.0209531 + 0.0362918i
\(441\) 1.60800 + 0.715928i 0.0765715 + 0.0340918i
\(442\) −22.6576 16.4617i −1.07771 0.783003i
\(443\) 23.6602 10.5342i 1.12413 0.500496i 0.241425 0.970420i \(-0.422385\pi\)
0.882707 + 0.469924i \(0.155719\pi\)
\(444\) 4.86311 + 1.03368i 0.230793 + 0.0490565i
\(445\) 1.52706 + 14.5290i 0.0723898 + 0.688743i
\(446\) 8.26599 9.18031i 0.391406 0.434701i
\(447\) 12.1483 + 13.4920i 0.574593 + 0.638150i
\(448\) 0.309379 2.94355i 0.0146168 0.139069i
\(449\) −2.63548 + 8.11117i −0.124376 + 0.382790i −0.993787 0.111300i \(-0.964499\pi\)
0.869411 + 0.494090i \(0.164499\pi\)
\(450\) 0.309017 0.951057i 0.0145672 0.0448332i
\(451\) −0.363704 + 3.46041i −0.0171261 + 0.162944i
\(452\) 1.44494 + 1.60476i 0.0679641 + 0.0754818i
\(453\) 13.5197 15.0151i 0.635211 0.705473i
\(454\) −1.32807 12.6357i −0.0623294 0.593024i
\(455\) 10.1105 + 2.14905i 0.473986 + 0.100749i
\(456\) −2.26543 + 1.00863i −0.106088 + 0.0472336i
\(457\) 1.14377 + 0.830998i 0.0535033 + 0.0388724i 0.614215 0.789138i \(-0.289473\pi\)
−0.560712 + 0.828011i \(0.689473\pi\)
\(458\) −8.49550 3.78244i −0.396968 0.176742i
\(459\) −4.00973 6.94505i −0.187158 0.324167i
\(460\) −1.11286 + 1.92753i −0.0518873 + 0.0898715i
\(461\) 22.9563 16.6787i 1.06918 0.776806i 0.0934170 0.995627i \(-0.470221\pi\)
0.975765 + 0.218821i \(0.0702210\pi\)
\(462\) −2.54487 + 0.540928i −0.118398 + 0.0251663i
\(463\) −7.75266 23.8602i −0.360297 1.10888i −0.952874 0.303366i \(-0.901889\pi\)
0.592577 0.805514i \(-0.298111\pi\)
\(464\) 2.84091 0.131886
\(465\) 5.20336 1.98118i 0.241300 0.0918749i
\(466\) 4.18879 0.194042
\(467\) 0.164134 + 0.505153i 0.00759522 + 0.0233757i 0.954782 0.297306i \(-0.0960881\pi\)
−0.947187 + 0.320681i \(0.896088\pi\)
\(468\) 3.41598 0.726089i 0.157904 0.0335635i
\(469\) −18.4121 + 13.3772i −0.850192 + 0.617701i
\(470\) 3.32218 5.75419i 0.153241 0.265421i
\(471\) 2.36547 + 4.09712i 0.108995 + 0.188785i
\(472\) −3.49469 1.55593i −0.160856 0.0716177i
\(473\) −2.61332 1.89869i −0.120161 0.0873018i
\(474\) 8.12929 3.61939i 0.373391 0.166244i
\(475\) −2.42563 0.515584i −0.111296 0.0236566i
\(476\) −2.48105 23.6056i −0.113719 1.08196i
\(477\) −6.63967 + 7.37410i −0.304010 + 0.337637i
\(478\) −1.60604 1.78369i −0.0734585 0.0815839i
\(479\) 1.09768 10.4438i 0.0501544 0.477187i −0.940400 0.340069i \(-0.889549\pi\)
0.990555 0.137118i \(-0.0437839\pi\)
\(480\) 0.309017 0.951057i 0.0141046 0.0434096i
\(481\) −5.36540 + 16.5130i −0.244641 + 0.752929i
\(482\) −1.59103 + 15.1376i −0.0724693 + 0.689499i
\(483\) −4.40796 4.89553i −0.200569 0.222754i
\(484\) −6.84340 + 7.60037i −0.311064 + 0.345471i
\(485\) −0.702017 6.67924i −0.0318769 0.303289i
\(486\) 0.978148 + 0.207912i 0.0443697 + 0.00943107i
\(487\) 12.8257 5.71038i 0.581189 0.258762i −0.0950154 0.995476i \(-0.530290\pi\)
0.676205 + 0.736714i \(0.263623\pi\)
\(488\) −3.15958 2.29557i −0.143028 0.103916i
\(489\) 2.29267 + 1.02076i 0.103678 + 0.0461605i
\(490\) 0.880088 + 1.52436i 0.0397583 + 0.0688635i
\(491\) 16.0982 27.8829i 0.726502 1.25834i −0.231851 0.972751i \(-0.574478\pi\)
0.958353 0.285587i \(-0.0921886\pi\)
\(492\) 3.20233 2.32663i 0.144372 0.104893i
\(493\) 22.2847 4.73675i 1.00365 0.213332i
\(494\) −2.67617 8.23640i −0.120407 0.370573i
\(495\) −0.879031 −0.0395095
\(496\) 5.20336 1.98118i 0.233638 0.0889575i
\(497\) 28.7777 1.29086
\(498\) 5.18717 + 15.9645i 0.232443 + 0.715385i
\(499\) 32.5696 6.92288i 1.45802 0.309911i 0.590386 0.807121i \(-0.298976\pi\)
0.867630 + 0.497210i \(0.165642\pi\)
\(500\) 0.809017 0.587785i 0.0361803 0.0262866i
\(501\) −5.32800 + 9.22836i −0.238037 + 0.412293i
\(502\) −1.35040 2.33897i −0.0602715 0.104393i
\(503\) 25.2371 + 11.2363i 1.12527 + 0.501001i 0.883077 0.469228i \(-0.155468\pi\)
0.242190 + 0.970229i \(0.422134\pi\)
\(504\) 2.39450 + 1.73970i 0.106659 + 0.0774925i
\(505\) −2.73830 + 1.21917i −0.121853 + 0.0542524i
\(506\) 1.91372 + 0.406774i 0.0850753 + 0.0180833i
\(507\) −0.0840285 0.799478i −0.00373184 0.0355061i
\(508\) −10.9268 + 12.1354i −0.484799 + 0.538423i
\(509\) −7.20625 8.00335i −0.319411 0.354742i 0.561962 0.827163i \(-0.310047\pi\)
−0.881373 + 0.472421i \(0.843380\pi\)
\(510\) 0.838261 7.97552i 0.0371188 0.353162i
\(511\) 13.9469 42.9241i 0.616975 1.89885i
\(512\) 0.309017 0.951057i 0.0136568 0.0420312i
\(513\) 0.259212 2.46624i 0.0114445 0.108887i
\(514\) 13.3808 + 14.8609i 0.590202 + 0.655485i
\(515\) −1.57190 + 1.74578i −0.0692664 + 0.0769281i
\(516\) 0.384118 + 3.65464i 0.0169099 + 0.160887i
\(517\) −5.71297 1.21433i −0.251256 0.0534062i
\(518\) −13.4430 + 5.98521i −0.590651 + 0.262975i
\(519\) 10.1058 + 7.34232i 0.443597 + 0.322292i
\(520\) 3.19037 + 1.42044i 0.139907 + 0.0622906i
\(521\) −19.2375 33.3203i −0.842809 1.45979i −0.887511 0.460787i \(-0.847567\pi\)
0.0447016 0.999000i \(-0.485766\pi\)
\(522\) −1.42045 + 2.46030i −0.0621715 + 0.107684i
\(523\) −7.15308 + 5.19702i −0.312783 + 0.227250i −0.733090 0.680132i \(-0.761922\pi\)
0.420307 + 0.907382i \(0.361922\pi\)
\(524\) 14.3205 3.04392i 0.625595 0.132974i
\(525\) 0.914616 + 2.81490i 0.0399171 + 0.122852i
\(526\) 9.08922 0.396309
\(527\) 37.5129 24.2165i 1.63409 1.05489i
\(528\) −0.879031 −0.0382549
\(529\) −5.57658 17.1629i −0.242460 0.746215i
\(530\) −9.70599 + 2.06307i −0.421601 + 0.0896142i
\(531\) 3.09482 2.24852i 0.134304 0.0975774i
\(532\) 3.66984 6.35635i 0.159108 0.275583i
\(533\) 6.91178 + 11.9715i 0.299382 + 0.518545i
\(534\) −13.3461 5.94205i −0.577540 0.257137i
\(535\) 5.62801 + 4.08899i 0.243320 + 0.176782i
\(536\) −7.02457 + 3.12754i −0.303415 + 0.135089i
\(537\) −4.03005 0.856615i −0.173910 0.0369656i
\(538\) 1.58170 + 15.0488i 0.0681918 + 0.648802i
\(539\) 1.03531 1.14983i 0.0445941 0.0495267i
\(540\) 0.669131 + 0.743145i 0.0287948 + 0.0319799i
\(541\) −0.972127 + 9.24917i −0.0417950 + 0.397653i 0.953547 + 0.301245i \(0.0974021\pi\)
−0.995342 + 0.0964081i \(0.969265\pi\)
\(542\) −1.51424 + 4.66035i −0.0650422 + 0.200179i
\(543\) −4.72429 + 14.5399i −0.202739 + 0.623966i
\(544\) 0.838261 7.97552i 0.0359402 0.341948i
\(545\) 4.48812 + 4.98457i 0.192250 + 0.213515i
\(546\) −6.91637 + 7.68141i −0.295993 + 0.328734i
\(547\) −2.92128 27.7941i −0.124905 1.18839i −0.859952 0.510374i \(-0.829507\pi\)
0.735048 0.678015i \(-0.237160\pi\)
\(548\) 9.85725 + 2.09522i 0.421081 + 0.0895035i
\(549\) 3.56782 1.58849i 0.152271 0.0677953i
\(550\) −0.711151 0.516682i −0.0303236 0.0220314i
\(551\) 6.43587 + 2.86543i 0.274177 + 0.122072i
\(552\) −1.11286 1.92753i −0.0473664 0.0820411i
\(553\) −13.1689 + 22.8092i −0.559998 + 0.969945i
\(554\) 22.3165 16.2139i 0.948139 0.688863i
\(555\) −4.86311 + 1.03368i −0.206427 + 0.0438775i
\(556\) 3.28014 + 10.0952i 0.139109 + 0.428133i
\(557\) −14.8342 −0.628547 −0.314273 0.949333i \(-0.601761\pi\)
−0.314273 + 0.949333i \(0.601761\pi\)
\(558\) −0.885929 + 5.49683i −0.0375044 + 0.232699i
\(559\) −12.8334 −0.542795
\(560\) 0.914616 + 2.81490i 0.0386496 + 0.118951i
\(561\) −6.89531 + 1.46564i −0.291120 + 0.0618795i
\(562\) 10.2781 7.46749i 0.433556 0.314997i
\(563\) −0.742707 + 1.28641i −0.0313014 + 0.0542156i −0.881252 0.472647i \(-0.843298\pi\)
0.849950 + 0.526863i \(0.176632\pi\)
\(564\) 3.32218 + 5.75419i 0.139889 + 0.242295i
\(565\) −1.97273 0.878317i −0.0829935 0.0369511i
\(566\) 9.68112 + 7.03375i 0.406928 + 0.295650i
\(567\) −2.70387 + 1.20384i −0.113552 + 0.0505566i
\(568\) 9.51052 + 2.02152i 0.399053 + 0.0848212i
\(569\) −3.92520 37.3458i −0.164553 1.56562i −0.695697 0.718336i \(-0.744904\pi\)
0.531144 0.847282i \(-0.321762\pi\)
\(570\) 1.65932 1.84287i 0.0695015 0.0771892i
\(571\) 20.6621 + 22.9476i 0.864682 + 0.960326i 0.999534 0.0305396i \(-0.00972257\pi\)
−0.134852 + 0.990866i \(0.543056\pi\)
\(572\) 0.320885 3.05302i 0.0134169 0.127653i
\(573\) −7.44061 + 22.8998i −0.310836 + 0.956654i
\(574\) −3.62033 + 11.1422i −0.151109 + 0.465067i
\(575\) 0.232651 2.21353i 0.00970221 0.0923104i
\(576\) 0.669131 + 0.743145i 0.0278804 + 0.0309644i
\(577\) −2.63440 + 2.92579i −0.109671 + 0.121802i −0.795481 0.605979i \(-0.792782\pi\)
0.685810 + 0.727781i \(0.259448\pi\)
\(578\) −4.94541 47.0525i −0.205702 1.95712i
\(579\) −1.22178 0.259696i −0.0507753 0.0107926i
\(580\) −2.59530 + 1.15550i −0.107764 + 0.0479795i
\(581\) −40.1941 29.2027i −1.66753 1.21153i
\(582\) 6.13540 + 2.73166i 0.254321 + 0.113231i
\(583\) 4.36124 + 7.55389i 0.180624 + 0.312850i
\(584\) 7.62446 13.2059i 0.315502 0.546466i
\(585\) −2.82533 + 2.05272i −0.116813 + 0.0848695i
\(586\) −12.3954 + 2.63472i −0.512048 + 0.108839i
\(587\) 8.50043 + 26.1616i 0.350850 + 1.07981i 0.958377 + 0.285507i \(0.0921619\pi\)
−0.607526 + 0.794299i \(0.707838\pi\)
\(588\) −1.76018 −0.0725885
\(589\) 13.7861 + 0.760067i 0.568047 + 0.0313180i
\(590\) 3.82541 0.157490
\(591\) −2.25116 6.92835i −0.0926002 0.284994i
\(592\) −4.86311 + 1.03368i −0.199872 + 0.0424842i
\(593\) −6.48030 + 4.70821i −0.266114 + 0.193343i −0.712838 0.701329i \(-0.752591\pi\)
0.446724 + 0.894672i \(0.352591\pi\)
\(594\) 0.439516 0.761263i 0.0180335 0.0312350i
\(595\) 11.8678 + 20.5557i 0.486534 + 0.842701i
\(596\) −16.5857 7.38442i −0.679376 0.302478i
\(597\) 19.1577 + 13.9189i 0.784073 + 0.569663i
\(598\) 7.10086 3.16151i 0.290376 0.129284i
\(599\) −44.3982 9.43714i −1.81406 0.385591i −0.829203 0.558947i \(-0.811206\pi\)
−0.984859 + 0.173356i \(0.944539\pi\)
\(600\) 0.104528 + 0.994522i 0.00426736 + 0.0406012i
\(601\) −10.2423 + 11.3752i −0.417792 + 0.464005i −0.914898 0.403685i \(-0.867729\pi\)
0.497106 + 0.867690i \(0.334396\pi\)
\(602\) −7.27776 8.08278i −0.296619 0.329429i
\(603\) 0.803756 7.64723i 0.0327315 0.311419i
\(604\) −6.24365 + 19.2160i −0.254050 + 0.781887i
\(605\) 3.16041 9.72674i 0.128489 0.395448i
\(606\) 0.313318 2.98102i 0.0127277 0.121096i
\(607\) 10.1807 + 11.3068i 0.413222 + 0.458929i 0.913442 0.406969i \(-0.133414\pi\)
−0.500220 + 0.865898i \(0.666748\pi\)
\(608\) 1.65932 1.84287i 0.0672945 0.0747381i
\(609\) −0.878917 8.36233i −0.0356155 0.338859i
\(610\) 3.82012 + 0.811991i 0.154672 + 0.0328765i
\(611\) −21.1980 + 9.43795i −0.857579 + 0.381819i
\(612\) 6.48787 + 4.71372i 0.262257 + 0.190541i
\(613\) −18.9062 8.41756i −0.763612 0.339982i −0.0122961 0.999924i \(-0.503914\pi\)
−0.751316 + 0.659942i \(0.770581\pi\)
\(614\) 4.60642 + 7.97856i 0.185900 + 0.321988i
\(615\) −1.97915 + 3.42799i −0.0798071 + 0.138230i
\(616\) 2.10484 1.52925i 0.0848063 0.0616154i
\(617\) 44.9540 9.55527i 1.80978 0.384681i 0.825944 0.563753i \(-0.190643\pi\)
0.983836 + 0.179072i \(0.0573096\pi\)
\(618\) −0.725935 2.23420i −0.0292014 0.0898726i
\(619\) 4.82990 0.194130 0.0970650 0.995278i \(-0.469055\pi\)
0.0970650 + 0.995278i \(0.469055\pi\)
\(620\) −3.94769 + 3.92629i −0.158543 + 0.157684i
\(621\) 2.22572 0.0893150
\(622\) 9.65366 + 29.7109i 0.387076 + 1.19130i
\(623\) 42.2945 8.98997i 1.69449 0.360175i
\(624\) −2.82533 + 2.05272i −0.113104 + 0.0821745i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 3.83090 + 6.63532i 0.153114 + 0.265201i
\(627\) −1.99138 0.886621i −0.0795282 0.0354082i
\(628\) −3.82742 2.78078i −0.152731 0.110965i
\(629\) −36.4237 + 16.2169i −1.45231 + 0.646610i
\(630\) −2.89508 0.615369i −0.115343 0.0245169i
\(631\) 4.25756 + 40.5079i 0.169491 + 1.61260i 0.666946 + 0.745106i \(0.267601\pi\)
−0.497455 + 0.867490i \(0.665732\pi\)
\(632\) −5.95434 + 6.61296i −0.236851 + 0.263049i
\(633\) −7.64361 8.48909i −0.303806 0.337411i
\(634\) 2.10916 20.0673i 0.0837653 0.796974i
\(635\) 5.04620 15.5306i 0.200252 0.616314i
\(636\) 3.06632 9.43717i 0.121588 0.374208i
\(637\) 0.642542 6.11338i 0.0254585 0.242221i
\(638\) 1.67098 + 1.85581i 0.0661548 + 0.0734724i
\(639\) −6.50595 + 7.22559i −0.257371 + 0.285840i
\(640\) 0.104528 + 0.994522i 0.00413185 + 0.0393119i
\(641\) −27.5011 5.84553i −1.08623 0.230885i −0.370196 0.928953i \(-0.620710\pi\)
−0.716031 + 0.698069i \(0.754043\pi\)
\(642\) −6.35517 + 2.82951i −0.250819 + 0.111672i
\(643\) 16.9577 + 12.3205i 0.668745 + 0.485871i 0.869605 0.493748i \(-0.164374\pi\)
−0.200860 + 0.979620i \(0.564374\pi\)
\(644\) 6.01806 + 2.67941i 0.237145 + 0.105584i
\(645\) −1.83739 3.18245i −0.0723470 0.125309i
\(646\) 9.94341 17.2225i 0.391218 0.677610i
\(647\) −32.2298 + 23.4163i −1.26708 + 0.920590i −0.999082 0.0428291i \(-0.986363\pi\)
−0.268001 + 0.963419i \(0.586363\pi\)
\(648\) −0.978148 + 0.207912i −0.0384253 + 0.00816754i
\(649\) −1.03912 3.19808i −0.0407889 0.125535i
\(650\) −3.49229 −0.136979
\(651\) −7.44150 14.7034i −0.291655 0.576271i
\(652\) −2.50964 −0.0982851
\(653\) −12.3217 37.9224i −0.482187 1.48402i −0.836014 0.548708i \(-0.815120\pi\)
0.353827 0.935311i \(-0.384880\pi\)
\(654\) −6.56082 + 1.39455i −0.256549 + 0.0545311i
\(655\) −11.8444 + 8.60544i −0.462798 + 0.336242i
\(656\) −1.97915 + 3.42799i −0.0772729 + 0.133841i
\(657\) 7.62446 + 13.2059i 0.297458 + 0.515213i
\(658\) −17.9655 7.99877i −0.700369 0.311825i
\(659\) 10.0842 + 7.32660i 0.392825 + 0.285404i 0.766612 0.642111i \(-0.221941\pi\)
−0.373787 + 0.927514i \(0.621941\pi\)
\(660\) 0.803035 0.357534i 0.0312581 0.0139170i
\(661\) −20.3432 4.32407i −0.791257 0.168187i −0.205482 0.978661i \(-0.565876\pi\)
−0.585775 + 0.810474i \(0.699210\pi\)
\(662\) 1.43298 + 13.6339i 0.0556942 + 0.529895i
\(663\) −18.7399 + 20.8127i −0.727796 + 0.808300i
\(664\) −11.2321 12.4745i −0.435888 0.484103i
\(665\) −0.767205 + 7.29947i −0.0297509 + 0.283061i
\(666\) 1.53636 4.72842i 0.0595326 0.183222i
\(667\) −1.95393 + 6.01358i −0.0756565 + 0.232847i
\(668\) 1.11385 10.5976i 0.0430963 0.410034i
\(669\) −8.26599 9.18031i −0.319582 0.354931i
\(670\) 5.14518 5.71430i 0.198776 0.220763i
\(671\) −0.358848 3.41422i −0.0138532 0.131804i
\(672\) −2.89508 0.615369i −0.111680 0.0237384i
\(673\) −22.8823 + 10.1879i −0.882048 + 0.392713i −0.797224 0.603683i \(-0.793699\pi\)
−0.0848232 + 0.996396i \(0.527033\pi\)
\(674\) −23.7342 17.2439i −0.914206 0.664210i
\(675\) −0.913545 0.406737i −0.0351624 0.0156553i
\(676\) 0.401941 + 0.696182i 0.0154593 + 0.0267762i
\(677\) 7.93110 13.7371i 0.304817 0.527958i −0.672404 0.740185i \(-0.734738\pi\)
0.977221 + 0.212226i \(0.0680714\pi\)
\(678\) 1.74701 1.26928i 0.0670935 0.0487463i
\(679\) −19.4435 + 4.13284i −0.746172 + 0.158604i
\(680\) 2.47815 + 7.62695i 0.0950326 + 0.292480i
\(681\) −12.7053 −0.486870
\(682\) 4.35475 + 2.23378i 0.166752 + 0.0855358i
\(683\) −5.88130 −0.225042 −0.112521 0.993649i \(-0.535892\pi\)
−0.112521 + 0.993649i \(0.535892\pi\)
\(684\) 0.766307 + 2.35845i 0.0293005 + 0.0901776i
\(685\) −9.85725 + 2.09522i −0.376626 + 0.0800544i
\(686\) −12.5467 + 9.11574i −0.479037 + 0.348040i
\(687\) −4.64974 + 8.05358i −0.177399 + 0.307263i
\(688\) −1.83739 3.18245i −0.0700497 0.121330i
\(689\) 31.6575 + 14.0948i 1.20605 + 0.536970i
\(690\) 1.80064 + 1.30824i 0.0685493 + 0.0498040i
\(691\) 26.2828 11.7019i 0.999846 0.445160i 0.159493 0.987199i \(-0.449014\pi\)
0.840353 + 0.542039i \(0.182347\pi\)
\(692\) −12.2185 2.59713i −0.464479 0.0987280i
\(693\) 0.271954 + 2.58747i 0.0103307 + 0.0982898i
\(694\) 6.18441 6.86848i 0.234757 0.260724i
\(695\) −7.10266 7.88830i −0.269419 0.299220i
\(696\) 0.296955 2.82534i 0.0112561 0.107094i
\(697\) −9.80926 + 30.1898i −0.371552 + 1.14352i
\(698\) 0.175105 0.538918i 0.00662783 0.0203983i
\(699\) 0.437848 4.16585i 0.0165609 0.157567i
\(700\) −1.98047 2.19953i −0.0748546 0.0831344i
\(701\) 23.9082 26.5527i 0.903000 1.00288i −0.0969712 0.995287i \(-0.530915\pi\)
0.999971 0.00759590i \(-0.00241787\pi\)
\(702\) −0.365044 3.47316i −0.0137777 0.131086i
\(703\) −12.0596 2.56335i −0.454838 0.0966787i
\(704\) 0.803035 0.357534i 0.0302655 0.0134751i
\(705\) −5.37541 3.90546i −0.202449 0.147088i
\(706\) 24.9164 + 11.0935i 0.937740 + 0.417509i
\(707\) 4.43586 + 7.68313i 0.166828 + 0.288954i
\(708\) −1.91271 + 3.31290i −0.0718839 + 0.124506i
\(709\) −16.4340 + 11.9400i −0.617190 + 0.448415i −0.851939 0.523641i \(-0.824573\pi\)
0.234749 + 0.972056i \(0.424573\pi\)
\(710\) −9.51052 + 2.02152i −0.356923 + 0.0758664i
\(711\) −2.74982 8.46309i −0.103126 0.317390i
\(712\) 14.6091 0.547498
\(713\) 0.614934 + 12.3770i 0.0230294 + 0.463523i
\(714\) −23.7357 −0.888285
\(715\) 0.948631 + 2.91959i 0.0354768 + 0.109186i
\(716\) 4.03005 0.856615i 0.150610 0.0320132i
\(717\) −1.94179 + 1.41079i −0.0725175 + 0.0526871i
\(718\) −2.92548 + 5.06708i −0.109178 + 0.189102i
\(719\) −10.6201 18.3945i −0.396062 0.686000i 0.597174 0.802112i \(-0.296290\pi\)
−0.993236 + 0.116112i \(0.962957\pi\)
\(720\) −0.913545 0.406737i −0.0340458 0.0151582i
\(721\) 5.62509 + 4.08687i 0.209489 + 0.152203i
\(722\) −11.7395 + 5.22676i −0.436899 + 0.194520i
\(723\) 14.8884 + 3.16462i 0.553705 + 0.117694i
\(724\) −1.59805 15.2044i −0.0593909 0.565067i
\(725\) 1.90094 2.11120i 0.0705990 0.0784082i
\(726\) 6.84340 + 7.60037i 0.253982 + 0.282076i
\(727\) 1.03045 9.80412i 0.0382174 0.363615i −0.958654 0.284574i \(-0.908148\pi\)
0.996871 0.0790404i \(-0.0251856\pi\)
\(728\) 3.19411 9.83045i 0.118382 0.364341i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) −1.59395 + 15.1654i −0.0589946 + 0.561296i
\(731\) −19.7191 21.9002i −0.729336 0.810010i
\(732\) −2.61326 + 2.90232i −0.0965890 + 0.107273i
\(733\) 0.378284 + 3.59913i 0.0139722 + 0.132937i 0.999284 0.0378263i \(-0.0120434\pi\)
−0.985312 + 0.170763i \(0.945377\pi\)
\(734\) −12.4146 2.63881i −0.458232 0.0974001i
\(735\) 1.60800 0.715928i 0.0593120 0.0264074i
\(736\) 1.80064 + 1.30824i 0.0663726 + 0.0482225i
\(737\) −6.17482 2.74921i −0.227452 0.101268i
\(738\) −1.97915 3.42799i −0.0728535 0.126186i
\(739\) 1.20425 2.08583i 0.0442991 0.0767283i −0.843026 0.537873i \(-0.819228\pi\)
0.887325 + 0.461145i \(0.152561\pi\)
\(740\) 4.02223 2.92232i 0.147860 0.107427i
\(741\) −8.47102 + 1.80057i −0.311191 + 0.0661456i
\(742\) 9.07558 + 27.9318i 0.333175 + 1.02541i
\(743\) −43.0431 −1.57910 −0.789549 0.613688i \(-0.789685\pi\)
−0.789549 + 0.613688i \(0.789685\pi\)
\(744\) −1.42643 5.38194i −0.0522953 0.197312i
\(745\) 18.1553 0.665158
\(746\) 6.84654 + 21.0715i 0.250670 + 0.771482i
\(747\) 16.4192 3.49001i 0.600748 0.127693i
\(748\) 5.70304 4.14350i 0.208524 0.151502i
\(749\) 10.2949 17.8314i 0.376169 0.651544i
\(750\) −0.500000 0.866025i −0.0182574 0.0316228i
\(751\) 25.1087 + 11.1791i 0.916231 + 0.407932i 0.810014 0.586411i \(-0.199459\pi\)
0.106217 + 0.994343i \(0.466126\pi\)
\(752\) −5.37541 3.90546i −0.196021 0.142417i
\(753\) −2.46731 + 1.09852i −0.0899138 + 0.0400322i
\(754\) 9.70447 + 2.06275i 0.353416 + 0.0751209i
\(755\) −2.11198 20.0942i −0.0768629 0.731302i
\(756\) 1.98047 2.19953i 0.0720288 0.0799961i
\(757\) −20.6794 22.9668i −0.751607 0.834744i 0.239067 0.971003i \(-0.423159\pi\)
−0.990673 + 0.136259i \(0.956492\pi\)
\(758\) −3.53552 + 33.6382i −0.128416 + 1.22179i
\(759\) 0.604584 1.86072i 0.0219450 0.0675398i
\(760\) −0.766307 + 2.35845i −0.0277969 + 0.0855500i
\(761\) −3.48875 + 33.1933i −0.126467 + 1.20326i 0.728674 + 0.684861i \(0.240137\pi\)
−0.855141 + 0.518395i \(0.826530\pi\)
\(762\) 10.9268 + 12.1354i 0.395836 + 0.439621i
\(763\) 13.2838 14.7531i 0.480905 0.534099i
\(764\) −2.51687 23.9464i −0.0910571 0.866351i
\(765\) −7.84421 1.66734i −0.283608 0.0602827i
\(766\) −15.5308 + 6.91475i −0.561150 + 0.249840i
\(767\) −10.8080 7.85249i −0.390255 0.283537i
\(768\) −0.913545 0.406737i −0.0329647 0.0146768i
\(769\) 4.56641 + 7.90925i 0.164669 + 0.285215i 0.936538 0.350567i \(-0.114011\pi\)
−0.771869 + 0.635782i \(0.780678\pi\)
\(770\) −1.30086 + 2.25316i −0.0468798 + 0.0811981i
\(771\) 16.1781 11.7541i 0.582642 0.423314i
\(772\) 1.22178 0.259696i 0.0439727 0.00934668i
\(773\) 1.13355 + 3.48871i 0.0407709 + 0.125480i 0.969370 0.245604i \(-0.0789862\pi\)
−0.928599 + 0.371084i \(0.878986\pi\)
\(774\) 3.67477 0.132087
\(775\) 2.00942 5.19252i 0.0721807 0.186521i
\(776\) −6.71603 −0.241092
\(777\) 4.54724 + 13.9950i 0.163131 + 0.502067i
\(778\) −30.6802 + 6.52127i −1.09994 + 0.233799i
\(779\) −7.94122 + 5.76963i −0.284524 + 0.206718i
\(780\) 1.74615 3.02442i 0.0625221 0.108291i
\(781\) 4.27341 + 7.40176i 0.152915 + 0.264856i
\(782\) 16.3059 + 7.25986i 0.583098 + 0.259612i
\(783\) 2.29834 + 1.66984i 0.0821360 + 0.0596753i
\(784\) 1.60800 0.715928i 0.0574286 0.0255689i
\(785\) 4.62756 + 0.983619i 0.165165 + 0.0351069i
\(786\) −1.53034 14.5602i −0.0545855 0.519347i
\(787\) −36.0275 + 40.0126i −1.28424 + 1.42630i −0.433112 + 0.901340i \(0.642585\pi\)
−0.851130 + 0.524955i \(0.824082\pi\)
\(788\) 4.87455 + 5.41373i 0.173649 + 0.192856i
\(789\) 0.950082 9.03943i 0.0338238 0.321812i
\(790\) 2.74982 8.46309i 0.0978343 0.301103i
\(791\) −1.97504 + 6.07856i −0.0702245 + 0.216129i
\(792\) −0.0918838 + 0.874216i −0.00326495 + 0.0310639i
\(793\) −9.12628 10.1358i −0.324084 0.359931i
\(794\) 15.1635 16.8408i 0.538134 0.597658i
\(795\) 1.03722 + 9.86847i 0.0367863 + 0.349999i
\(796\) −23.1628 4.92340i −0.820983 0.174505i
\(797\) −24.0552 + 10.7101i −0.852079 + 0.379370i −0.785837 0.618434i \(-0.787768\pi\)
−0.0662418 + 0.997804i \(0.521101\pi\)
\(798\) −5.93792 4.31415i −0.210200 0.152719i
\(799\) −48.6775 21.6726i −1.72209 0.766723i
\(800\) −0.500000 0.866025i −0.0176777 0.0306186i
\(801\) −7.30454 + 12.6518i −0.258093 + 0.447030i
\(802\) −19.2508 + 13.9865i −0.679771 + 0.493882i
\(803\) 13.1114 2.78690i 0.462690 0.0983477i
\(804\) 2.37614 + 7.31301i 0.0838000 + 0.257910i
\(805\) −6.58759 −0.232182
\(806\) 19.2131 2.98956i 0.676752 0.105303i
\(807\) 15.1317 0.532662
\(808\) 0.926261 + 2.85074i 0.0325858 + 0.100289i
\(809\) −6.44630 + 1.37020i −0.226640 + 0.0481738i −0.319832 0.947474i \(-0.603626\pi\)
0.0931918 + 0.995648i \(0.470293\pi\)
\(810\) 0.809017 0.587785i 0.0284260 0.0206527i
\(811\) 15.7635 27.3032i 0.553531 0.958743i −0.444486 0.895786i \(-0.646613\pi\)
0.998016 0.0629573i \(-0.0200532\pi\)
\(812\) 4.20420 + 7.28189i 0.147538 + 0.255544i
\(813\) 4.47654 + 1.99308i 0.156999 + 0.0699005i
\(814\) −3.53567 2.56881i −0.123925 0.0900368i
\(815\) 2.29267 1.02076i 0.0803087 0.0357557i
\(816\) −7.84421 1.66734i −0.274602 0.0583685i
\(817\) −0.952545 9.06286i −0.0333253 0.317069i
\(818\) −2.49765 + 2.77392i −0.0873283 + 0.0969879i
\(819\) 6.91637 + 7.68141i 0.241677 + 0.268410i
\(820\) 0.413755 3.93662i 0.0144490 0.137473i
\(821\) −11.4753 + 35.3174i −0.400491 + 1.23259i 0.524110 + 0.851650i \(0.324398\pi\)
−0.924602 + 0.380935i \(0.875602\pi\)
\(822\) 3.11411 9.58424i 0.108617 0.334289i
\(823\) −3.60985 + 34.3455i −0.125832 + 1.19721i 0.731280 + 0.682077i \(0.238923\pi\)
−0.857112 + 0.515130i \(0.827744\pi\)
\(824\) 1.57190 + 1.74578i 0.0547599 + 0.0608170i
\(825\) −0.588187 + 0.653248i −0.0204780 + 0.0227432i
\(826\) −1.18350 11.2603i −0.0411793 0.391795i
\(827\) 47.5200 + 10.1007i 1.65243 + 0.351235i 0.937507 0.347965i \(-0.113127\pi\)
0.714925 + 0.699201i \(0.246461\pi\)
\(828\) −2.03329 + 0.905281i −0.0706619 + 0.0314607i
\(829\) −26.3961 19.1779i −0.916773 0.666075i 0.0259456 0.999663i \(-0.491740\pi\)
−0.942719 + 0.333589i \(0.891740\pi\)
\(830\) 15.3348 + 6.82750i 0.532279 + 0.236986i
\(831\) −13.7924 23.8891i −0.478452 0.828704i
\(832\) 1.74615 3.02442i 0.0605368 0.104853i
\(833\) 11.4198 8.29698i 0.395673 0.287473i
\(834\) 10.3828 2.20693i 0.359527 0.0764198i
\(835\) 3.29288 + 10.1344i 0.113955 + 0.350717i
\(836\) 2.17984 0.0753914
\(837\) 5.37411 + 1.45565i 0.185756 + 0.0503147i
\(838\) −0.519809 −0.0179565
\(839\) 6.24228 + 19.2118i 0.215507 + 0.663264i 0.999117 + 0.0420102i \(0.0133762\pi\)
−0.783610 + 0.621253i \(0.786624\pi\)
\(840\) 2.89508 0.615369i 0.0998898 0.0212322i
\(841\) 16.9321 12.3019i 0.583866 0.424204i
\(842\) −5.95048 + 10.3065i −0.205067 + 0.355186i
\(843\) −6.35222 11.0024i −0.218782 0.378942i
\(844\) 10.4356 + 4.64623i 0.359209 + 0.159930i
\(845\) −0.650354 0.472510i −0.0223729 0.0162548i
\(846\) 6.06993 2.70251i 0.208689 0.0929141i
\(847\) −29.6089 6.29356i −1.01737 0.216249i
\(848\) 1.03722 + 9.86847i 0.0356182 + 0.338885i
\(849\) 8.00717 8.89286i 0.274805 0.305202i
\(850\) −5.36606 5.95962i −0.184054 0.204413i
\(851\) 1.15668 11.0051i 0.0396506 0.377250i
\(852\) 3.00457 9.24711i 0.102935 0.316801i
\(853\) 10.3620 31.8908i 0.354787 1.09192i −0.601346 0.798988i \(-0.705369\pi\)
0.956133 0.292933i \(-0.0946312\pi\)
\(854\) 1.20827 11.4959i 0.0413461 0.393382i
\(855\) −1.65932 1.84287i −0.0567477 0.0630247i
\(856\) 4.65488 5.16976i 0.159100 0.176699i
\(857\) −2.39225 22.7607i −0.0817177 0.777492i −0.956255 0.292534i \(-0.905502\pi\)
0.874537 0.484958i \(-0.161165\pi\)
\(858\) −3.00275 0.638255i −0.102512 0.0217897i
\(859\) −19.7368 + 8.78737i −0.673410 + 0.299821i −0.714807 0.699321i \(-0.753486\pi\)
0.0413977 + 0.999143i \(0.486819\pi\)
\(860\) 2.97295 + 2.15998i 0.101377 + 0.0736546i
\(861\) 10.7028 + 4.76517i 0.364749 + 0.162397i
\(862\) 7.81005 + 13.5274i 0.266011 + 0.460745i
\(863\) −16.5238 + 28.6201i −0.562478 + 0.974240i 0.434802 + 0.900526i \(0.356818\pi\)
−0.997279 + 0.0737136i \(0.976515\pi\)
\(864\) 0.809017 0.587785i 0.0275233 0.0199969i
\(865\) 12.2185 2.59713i 0.415442 0.0883050i
\(866\) 7.96265 + 24.5065i 0.270582 + 0.832765i
\(867\) −47.3116 −1.60679
\(868\) 12.7786 + 10.4055i 0.433732 + 0.353185i
\(869\) −7.82216 −0.265349
\(870\) 0.877888 + 2.70186i 0.0297632 + 0.0916017i
\(871\) −26.2667 + 5.58315i −0.890012 + 0.189178i
\(872\) 5.42640 3.94251i 0.183761 0.133510i
\(873\) 3.35802 5.81626i 0.113652 0.196850i
\(874\) 2.75969 + 4.77993i 0.0933480 + 0.161683i
\(875\) 2.70387 + 1.20384i 0.0914077 + 0.0406973i
\(876\) −12.3366 8.96309i −0.416816 0.302835i
\(877\) 35.5570 15.8310i 1.20067 0.534574i 0.293755 0.955881i \(-0.405095\pi\)
0.906919 + 0.421306i \(0.138428\pi\)
\(878\) 11.9836 + 2.54719i 0.404426 + 0.0859634i
\(879\) 1.32462 + 12.6029i 0.0446782 + 0.425084i
\(880\) −0.588187 + 0.653248i −0.0198278 + 0.0220210i
\(881\) −24.5451 27.2601i −0.826946 0.918416i 0.170815 0.985303i \(-0.445360\pi\)
−0.997761 + 0.0668870i \(0.978693\pi\)
\(882\) −0.183989 + 1.75053i −0.00619522 + 0.0589436i
\(883\) 4.02753 12.3955i 0.135537 0.417141i −0.860136 0.510065i \(-0.829621\pi\)
0.995673 + 0.0929242i \(0.0296214\pi\)
\(884\) 8.65442 26.6356i 0.291080 0.895851i
\(885\) 0.399864 3.80445i 0.0134413 0.127885i
\(886\) 17.3300 + 19.2470i 0.582214 + 0.646614i
\(887\) −24.8907 + 27.6439i −0.835749 + 0.928193i −0.998287 0.0585094i \(-0.981365\pi\)
0.162538 + 0.986702i \(0.448032\pi\)
\(888\) 0.519689 + 4.94451i 0.0174396 + 0.165927i
\(889\) −47.2763 10.0489i −1.58559 0.337029i
\(890\) −13.3461 + 5.94205i −0.447361 + 0.199178i
\(891\) −0.711151 0.516682i −0.0238245 0.0173095i
\(892\) 11.2853 + 5.02455i 0.377861 + 0.168234i
\(893\) −8.23842 14.2694i −0.275688 0.477506i
\(894\) −9.07764 + 15.7229i −0.303602 + 0.525854i
\(895\) −3.33322 + 2.42173i −0.111417 + 0.0809494i
\(896\) 2.89508 0.615369i 0.0967179 0.0205580i
\(897\) −2.40195 7.39243i −0.0801987 0.246826i
\(898\) −8.52859 −0.284603
\(899\) −8.65084 + 13.2422i −0.288522 + 0.441652i
\(900\) 1.00000 0.0333333
\(901\) 24.5902 + 75.6810i 0.819220 + 2.52130i
\(902\) −3.40344 + 0.723423i −0.113322 + 0.0240873i
\(903\) −8.79923 + 6.39301i −0.292820 + 0.212746i
\(904\) −1.07971 + 1.87012i −0.0359107 + 0.0621991i
\(905\) 7.64407 + 13.2399i 0.254097 + 0.440110i
\(906\) 18.4581 + 8.21806i 0.613228 + 0.273027i
\(907\) −5.02139 3.64826i −0.166733 0.121138i 0.501290 0.865279i \(-0.332859\pi\)
−0.668023 + 0.744141i \(0.732859\pi\)
\(908\) 11.6069 5.16773i 0.385189 0.171497i
\(909\) −2.93194 0.623204i −0.0972464 0.0206704i
\(910\) 1.08044 + 10.2797i 0.0358163 + 0.340770i
\(911\) 7.51196 8.34288i 0.248882 0.276412i −0.605739 0.795663i \(-0.707122\pi\)
0.854622 + 0.519251i \(0.173789\pi\)
\(912\) −1.65932 1.84287i −0.0549457 0.0610234i
\(913\) 1.54236 14.6746i 0.0510448 0.485659i
\(914\) −0.436881 + 1.34458i −0.0144507 + 0.0444748i
\(915\) 1.20685 3.71431i 0.0398973 0.122791i
\(916\) 0.972060 9.24854i 0.0321178 0.305580i
\(917\) 28.9949 + 32.2021i 0.957496 + 1.06341i
\(918\) 5.36606 5.95962i 0.177106 0.196697i
\(919\) −1.52036 14.4653i −0.0501521 0.477166i −0.990556 0.137107i \(-0.956220\pi\)
0.940404 0.340059i \(-0.110447\pi\)
\(920\) −2.17708 0.462753i −0.0717762 0.0152565i
\(921\) 8.41635 3.74720i 0.277328 0.123474i
\(922\) 22.9563 + 16.6787i 0.756026 + 0.549285i
\(923\) 31.0199 + 13.8110i 1.02103 + 0.454593i
\(924\) −1.30086 2.25316i −0.0427952 0.0741234i
\(925\) −2.48588 + 4.30566i −0.0817351 + 0.141569i
\(926\) 20.2967 14.7464i 0.666992 0.484598i
\(927\) −2.29784 + 0.488421i −0.0754710 + 0.0160418i
\(928\) 0.877888 + 2.70186i 0.0288181 + 0.0886929i
\(929\) 14.6619 0.481041 0.240521 0.970644i \(-0.422682\pi\)
0.240521 + 0.970644i \(0.422682\pi\)
\(930\) 3.49214 + 4.33647i 0.114512 + 0.142198i
\(931\) 4.36493 0.143055
\(932\) 1.29441 + 3.98378i 0.0423997 + 0.130493i
\(933\) 30.5572 6.49514i 1.00040 0.212641i
\(934\) −0.429708 + 0.312201i −0.0140605 + 0.0102155i
\(935\) −3.52468 + 6.10492i −0.115269 + 0.199652i
\(936\) 1.74615 + 3.02442i 0.0570746 + 0.0988561i
\(937\) 19.7067 + 8.77397i 0.643789 + 0.286633i 0.702545 0.711639i \(-0.252047\pi\)
−0.0587566 + 0.998272i \(0.518714\pi\)
\(938\) −18.4121 13.3772i −0.601177 0.436781i
\(939\) 6.99941 3.11634i 0.228417 0.101698i
\(940\) 6.49917 + 1.38144i 0.211980 + 0.0450577i
\(941\) 2.99455 + 28.4912i 0.0976194 + 0.928787i 0.928248 + 0.371961i \(0.121314\pi\)
−0.830629 + 0.556826i \(0.812019\pi\)
\(942\) −3.16562 + 3.51578i −0.103142 + 0.114550i
\(943\) −5.89508 6.54715i −0.191970 0.213205i
\(944\) 0.399864 3.80445i 0.0130145 0.123824i
\(945\) −0.914616 + 2.81490i −0.0297525 + 0.0915687i
\(946\) 0.998199 3.07214i 0.0324543 0.0998839i
\(947\) −0.332191 + 3.16059i −0.0107948 + 0.102705i −0.998593 0.0530364i \(-0.983110\pi\)
0.987798 + 0.155742i \(0.0497767\pi\)
\(948\) 5.95434 + 6.61296i 0.193388 + 0.214779i
\(949\) 35.6337 39.5752i 1.15672 1.28467i
\(950\) −0.259212 2.46624i −0.00840995 0.0800153i
\(951\) −19.7369 4.19521i −0.640013 0.136039i
\(952\) 21.6836 9.65416i 0.702770 0.312893i
\(953\) 20.6426 + 14.9977i 0.668679 + 0.485824i 0.869583 0.493787i \(-0.164388\pi\)
−0.200904 + 0.979611i \(0.564388\pi\)
\(954\) −9.06496 4.03598i −0.293489 0.130670i
\(955\) 12.0392 + 20.8524i 0.389578 + 0.674769i
\(956\) 1.20009 2.07862i 0.0388138 0.0672274i
\(957\) 2.02031 1.46784i 0.0653075 0.0474486i
\(958\) 10.2718 2.18334i 0.331867 0.0705405i
\(959\) 9.21701 + 28.3671i 0.297633 + 0.916020i
\(960\) 1.00000 0.0322749
\(961\) −6.60995 + 30.2871i −0.213224 + 0.977003i
\(962\) −17.3628 −0.559800
\(963\) 2.14971 + 6.61612i 0.0692734 + 0.213202i
\(964\) −14.8884 + 3.16462i −0.479522 + 0.101926i
\(965\) −1.01052 + 0.734186i −0.0325298 + 0.0236343i
\(966\) 3.29380 5.70502i 0.105976 0.183556i
\(967\) 19.8583 + 34.3955i 0.638599 + 1.10609i 0.985740 + 0.168273i \(0.0538189\pi\)
−0.347142 + 0.937813i \(0.612848\pi\)
\(968\) −9.34311 4.15982i −0.300299 0.133702i
\(969\) −16.0888 11.6892i −0.516846 0.375510i
\(970\) 6.13540 2.73166i 0.196996 0.0877082i
\(971\) −33.4915 7.11883i −1.07479 0.228454i −0.363674 0.931526i \(-0.618478\pi\)
−0.711118 + 0.703072i \(0.751811\pi\)
\(972\) 0.104528 + 0.994522i 0.00335275 + 0.0318993i
\(973\) −21.0222 + 23.3475i −0.673940 + 0.748486i
\(974\) 9.39427 + 10.4334i 0.301012 + 0.334307i
\(975\) −0.365044 + 3.47316i −0.0116908 + 0.111230i
\(976\) 1.20685 3.71431i 0.0386304 0.118892i
\(977\) −10.8280 + 33.3252i −0.346419 + 1.06617i 0.614401 + 0.788994i \(0.289398\pi\)
−0.960820 + 0.277173i \(0.910602\pi\)
\(978\) −0.262329 + 2.49589i −0.00838835 + 0.0798098i
\(979\) 8.59286 + 9.54334i 0.274629 + 0.305007i
\(980\) −1.17779 + 1.30807i −0.0376231 + 0.0417846i
\(981\) 0.701114 + 6.67065i 0.0223848 + 0.212978i
\(982\) 31.4929 + 6.69401i 1.00498 + 0.213615i
\(983\) −37.2035 + 16.5641i −1.18661 + 0.528311i −0.902587 0.430507i \(-0.858335\pi\)
−0.284019 + 0.958819i \(0.591668\pi\)
\(984\) 3.20233 + 2.32663i 0.102087 + 0.0741703i
\(985\) −6.65508 2.96303i −0.212049 0.0944101i
\(986\) 11.3913 + 19.7302i 0.362771 + 0.628339i
\(987\) −9.83286 + 17.0310i −0.312983 + 0.542103i
\(988\) 7.00630 5.09038i 0.222900 0.161946i
\(989\) 8.00028 1.70051i 0.254394 0.0540731i
\(990\) −0.271636 0.836008i −0.00863315 0.0265701i
\(991\) −48.7166 −1.54753 −0.773767 0.633470i \(-0.781630\pi\)
−0.773767 + 0.633470i \(0.781630\pi\)
\(992\) 3.49214 + 4.33647i 0.110875 + 0.137683i
\(993\) 13.7090 0.435041
\(994\) 8.89280 + 27.3692i 0.282063 + 0.868099i
\(995\) 23.1628 4.92340i 0.734309 0.156082i
\(996\) −13.5802 + 9.86659i −0.430305 + 0.312635i
\(997\) 15.4584 26.7747i 0.489573 0.847964i −0.510356 0.859964i \(-0.670486\pi\)
0.999928 + 0.0119991i \(0.00381951\pi\)
\(998\) 16.6486 + 28.8362i 0.527003 + 0.912796i
\(999\) −4.54192 2.02219i −0.143700 0.0639794i
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.751.1 yes 16
31.9 even 15 inner 930.2.bg.c.691.1 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.c.691.1 16 31.9 even 15 inner
930.2.bg.c.751.1 yes 16 1.1 even 1 trivial