Properties

Label 930.2.bg.h.691.2
Level $930$
Weight $2$
Character 930.691
Analytic conductor $7.426$
Analytic rank $0$
Dimension $24$
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: \(24\)
Relative dimension: \(3\) over \(\Q(\zeta_{15})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label 691.2
Character \(\chi\) \(=\) 930.691
Dual form 930.2.bg.h.751.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.309017 + 0.951057i) q^{2} +(0.978148 + 0.207912i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.21753 + 0.987309i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\) \(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} +(-2.21753 + 0.987309i) q^{7} +(0.809017 - 0.587785i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.978148 - 0.207912i) q^{10} +(0.123923 - 1.17905i) q^{11} +(-0.669131 - 0.743145i) q^{12} +(3.35271 - 3.72356i) q^{13} +(-0.253732 - 2.41409i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-0.409428 - 3.89545i) q^{17} +(-0.669131 + 0.743145i) q^{18} +(-4.85854 - 5.39595i) q^{19} +(-0.104528 + 0.994522i) q^{20} +(-2.37435 + 0.504683i) q^{21} +(1.08305 + 0.482205i) q^{22} +(-1.97960 + 1.43826i) q^{23} +(0.913545 - 0.406737i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.50527 + 4.33926i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.37435 + 0.504683i) q^{28} +(0.450571 - 1.38671i) q^{29} +1.00000 q^{30} +(4.34691 + 3.47913i) q^{31} -1.00000 q^{32} +(0.366354 - 1.12752i) q^{33} +(3.83131 + 0.814370i) q^{34} +(1.96380 + 1.42679i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.71413 - 8.16512i) q^{37} +(6.63323 - 2.95330i) q^{38} +(4.05361 - 2.94512i) q^{39} +(-0.913545 - 0.406737i) q^{40} +(4.38106 - 0.931224i) q^{41} +(0.253732 - 2.41409i) q^{42} +(3.69833 + 4.10741i) q^{43} +(-0.793285 + 0.881033i) q^{44} +(-0.104528 - 0.994522i) q^{45} +(-0.756140 - 2.32716i) q^{46} +(-3.65030 - 11.2345i) q^{47} +(0.104528 + 0.994522i) q^{48} +(-0.741240 + 0.823231i) q^{49} +(-0.669131 - 0.743145i) q^{50} +(0.409428 - 3.89545i) q^{51} +(-4.90105 + 1.04175i) q^{52} +(-2.56744 - 1.14310i) q^{53} +(-0.809017 + 0.587785i) q^{54} +(-1.08305 + 0.482205i) q^{55} +(-1.21370 + 2.10218i) q^{56} +(-3.63049 - 6.28818i) q^{57} +(1.17961 + 0.857037i) q^{58} +(-4.14462 - 0.880967i) q^{59} +(-0.309017 + 0.951057i) q^{60} +15.5255 q^{61} +(-4.65212 + 3.05905i) q^{62} -2.42739 q^{63} +(0.309017 - 0.951057i) q^{64} +(-4.90105 - 1.04175i) q^{65} +(0.959127 + 0.696847i) q^{66} +(5.37596 + 9.31143i) q^{67} +(-1.95845 + 3.39214i) q^{68} +(-2.23537 + 0.995252i) q^{69} +(-1.96380 + 1.42679i) q^{70} +(-11.9451 - 5.31832i) q^{71} +(0.978148 - 0.207912i) q^{72} +(1.34183 - 12.7667i) q^{73} +(6.30874 + 7.00657i) q^{74} +(-0.669131 + 0.743145i) q^{75} +(0.758978 + 7.22119i) q^{76} +(0.889285 + 2.73694i) q^{77} +(1.54834 + 4.76531i) q^{78} +(-0.640131 - 6.09044i) q^{79} +(0.669131 - 0.743145i) q^{80} +(0.669131 + 0.743145i) q^{81} +(-0.468177 + 4.45440i) q^{82} +(4.23749 - 0.900707i) q^{83} +(2.21753 + 0.987309i) q^{84} +(-3.16884 + 2.30230i) q^{85} +(-5.04923 + 2.24806i) q^{86} +(0.729039 - 1.26273i) q^{87} +(-0.592773 - 1.02671i) q^{88} +(2.85803 + 2.07648i) q^{89} +(0.978148 + 0.207912i) q^{90} +(-3.75844 + 11.5673i) q^{91} +2.44692 q^{92} +(3.52857 + 4.30688i) q^{93} +11.8126 q^{94} +(-2.24376 + 6.90559i) q^{95} +(-0.978148 - 0.207912i) q^{96} +(-10.7779 - 7.83059i) q^{97} +(-0.553883 - 0.959354i) q^{98} +(0.592773 - 1.02671i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 6 q^{2} - 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} - 11 q^{7} + 6 q^{8} + 3 q^{9} - 3 q^{10} - 5 q^{11} - 3 q^{12} - 13 q^{13} - 4 q^{14} + 6 q^{15} - 6 q^{16} + 31 q^{17} - 3 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} + 5 q^{22} - 9 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} + 6 q^{27} + 4 q^{28} + 11 q^{29} + 24 q^{30} + 17 q^{31} - 24 q^{32} + 10 q^{33} + 9 q^{34} + 7 q^{35} - 12 q^{36} + 8 q^{37} - 2 q^{38} - q^{39} - 3 q^{40} + 12 q^{41} + 4 q^{42} - 7 q^{43} - 10 q^{44} + 3 q^{45} - 6 q^{46} - 46 q^{47} - 3 q^{48} + 20 q^{49} - 3 q^{50} - 31 q^{51} + 17 q^{52} + 48 q^{53} - 6 q^{54} - 5 q^{55} + q^{56} - 2 q^{57} + 14 q^{58} + 12 q^{59} + 6 q^{60} - 4 q^{61} + 13 q^{62} + 2 q^{63} - 6 q^{64} + 17 q^{65} + 10 q^{66} - 33 q^{67} + q^{68} - 12 q^{69} - 7 q^{70} - 35 q^{71} - 3 q^{72} + 19 q^{73} + 7 q^{74} - 3 q^{75} + 2 q^{76} + 26 q^{77} - 4 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} - 12 q^{82} + 11 q^{84} - 2 q^{85} - 48 q^{86} + 3 q^{87} + 21 q^{89} - 3 q^{90} + 72 q^{91} + 6 q^{92} + 19 q^{93} - 14 q^{94} + 6 q^{95} + 3 q^{96} - 35 q^{97} - 5 q^{98}+O(q^{100}) \) 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
\(7\) −2.21753 + 0.987309i −0.838149 + 0.373168i −0.780490 0.625168i \(-0.785030\pi\)
−0.0576590 + 0.998336i \(0.518364\pi\)
\(8\) 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
\(11\) 0.123923 1.17905i 0.0373643 0.355497i −0.959827 0.280594i \(-0.909469\pi\)
0.997191 0.0749033i \(-0.0238648\pi\)
\(12\) −0.669131 0.743145i −0.193161 0.214527i
\(13\) 3.35271 3.72356i 0.929874 1.03273i −0.0695085 0.997581i \(-0.522143\pi\)
0.999382 0.0351479i \(-0.0111902\pi\)
\(14\) −0.253732 2.41409i −0.0678126 0.645194i
\(15\) −0.309017 0.951057i −0.0797878 0.245562i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) −0.409428 3.89545i −0.0993009 0.944785i −0.924819 0.380408i \(-0.875783\pi\)
0.825518 0.564376i \(-0.190883\pi\)
\(18\) −0.669131 + 0.743145i −0.157716 + 0.175161i
\(19\) −4.85854 5.39595i −1.11462 1.23792i −0.968597 0.248636i \(-0.920018\pi\)
−0.146028 0.989280i \(-0.546649\pi\)
\(20\) −0.104528 + 0.994522i −0.0233733 + 0.222382i
\(21\) −2.37435 + 0.504683i −0.518125 + 0.110131i
\(22\) 1.08305 + 0.482205i 0.230907 + 0.102806i
\(23\) −1.97960 + 1.43826i −0.412775 + 0.299899i −0.774724 0.632299i \(-0.782111\pi\)
0.361949 + 0.932198i \(0.382111\pi\)
\(24\) 0.913545 0.406737i 0.186477 0.0830248i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 2.50527 + 4.33926i 0.491324 + 0.850998i
\(27\) 0.809017 + 0.587785i 0.155695 + 0.113119i
\(28\) 2.37435 + 0.504683i 0.448710 + 0.0953762i
\(29\) 0.450571 1.38671i 0.0836689 0.257506i −0.900467 0.434925i \(-0.856775\pi\)
0.984135 + 0.177419i \(0.0567748\pi\)
\(30\) 1.00000 0.182574
\(31\) 4.34691 + 3.47913i 0.780728 + 0.624871i
\(32\) −1.00000 −0.176777
\(33\) 0.366354 1.12752i 0.0637740 0.196276i
\(34\) 3.83131 + 0.814370i 0.657064 + 0.139663i
\(35\) 1.96380 + 1.42679i 0.331943 + 0.241171i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 4.71413 8.16512i 0.774999 1.34234i −0.159797 0.987150i \(-0.551084\pi\)
0.934795 0.355187i \(-0.115583\pi\)
\(38\) 6.63323 2.95330i 1.07605 0.479089i
\(39\) 4.05361 2.94512i 0.649098 0.471597i
\(40\) −0.913545 0.406737i −0.144444 0.0643107i
\(41\) 4.38106 0.931224i 0.684207 0.145433i 0.147323 0.989088i \(-0.452934\pi\)
0.536884 + 0.843656i \(0.319601\pi\)
\(42\) 0.253732 2.41409i 0.0391516 0.372503i
\(43\) 3.69833 + 4.10741i 0.563990 + 0.626375i 0.955922 0.293619i \(-0.0948598\pi\)
−0.391932 + 0.919994i \(0.628193\pi\)
\(44\) −0.793285 + 0.881033i −0.119592 + 0.132821i
\(45\) −0.104528 0.994522i −0.0155822 0.148255i
\(46\) −0.756140 2.32716i −0.111487 0.343121i
\(47\) −3.65030 11.2345i −0.532451 1.63872i −0.749092 0.662465i \(-0.769510\pi\)
0.216641 0.976251i \(-0.430490\pi\)
\(48\) 0.104528 + 0.994522i 0.0150874 + 0.143547i
\(49\) −0.741240 + 0.823231i −0.105891 + 0.117604i
\(50\) −0.669131 0.743145i −0.0946294 0.105097i
\(51\) 0.409428 3.89545i 0.0573314 0.545472i
\(52\) −4.90105 + 1.04175i −0.679653 + 0.144465i
\(53\) −2.56744 1.14310i −0.352665 0.157017i 0.222755 0.974874i \(-0.428495\pi\)
−0.575420 + 0.817858i \(0.695162\pi\)
\(54\) −0.809017 + 0.587785i −0.110093 + 0.0799874i
\(55\) −1.08305 + 0.482205i −0.146038 + 0.0650205i
\(56\) −1.21370 + 2.10218i −0.162187 + 0.280916i
\(57\) −3.63049 6.28818i −0.480870 0.832890i
\(58\) 1.17961 + 0.857037i 0.154890 + 0.112534i
\(59\) −4.14462 0.880967i −0.539584 0.114692i −0.0699453 0.997551i \(-0.522282\pi\)
−0.469639 + 0.882859i \(0.655616\pi\)
\(60\) −0.309017 + 0.951057i −0.0398939 + 0.122781i
\(61\) 15.5255 1.98784 0.993921 0.110094i \(-0.0351152\pi\)
0.993921 + 0.110094i \(0.0351152\pi\)
\(62\) −4.65212 + 3.05905i −0.590820 + 0.388499i
\(63\) −2.42739 −0.305823
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −4.90105 1.04175i −0.607900 0.129213i
\(66\) 0.959127 + 0.696847i 0.118060 + 0.0857759i
\(67\) 5.37596 + 9.31143i 0.656778 + 1.13757i 0.981445 + 0.191744i \(0.0614144\pi\)
−0.324667 + 0.945828i \(0.605252\pi\)
\(68\) −1.95845 + 3.39214i −0.237497 + 0.411357i
\(69\) −2.23537 + 0.995252i −0.269107 + 0.119814i
\(70\) −1.96380 + 1.42679i −0.234719 + 0.170533i
\(71\) −11.9451 5.31832i −1.41763 0.631168i −0.452218 0.891907i \(-0.649367\pi\)
−0.965409 + 0.260739i \(0.916034\pi\)
\(72\) 0.978148 0.207912i 0.115276 0.0245026i
\(73\) 1.34183 12.7667i 0.157050 1.49423i −0.577900 0.816107i \(-0.696128\pi\)
0.734950 0.678121i \(-0.237206\pi\)
\(74\) 6.30874 + 7.00657i 0.733376 + 0.814497i
\(75\) −0.669131 + 0.743145i −0.0772645 + 0.0858110i
\(76\) 0.758978 + 7.22119i 0.0870608 + 0.828328i
\(77\) 0.889285 + 2.73694i 0.101343 + 0.311903i
\(78\) 1.54834 + 4.76531i 0.175315 + 0.539565i
\(79\) −0.640131 6.09044i −0.0720204 0.685228i −0.969653 0.244484i \(-0.921381\pi\)
0.897633 0.440744i \(-0.145285\pi\)
\(80\) 0.669131 0.743145i 0.0748111 0.0830861i
\(81\) 0.669131 + 0.743145i 0.0743478 + 0.0825716i
\(82\) −0.468177 + 4.45440i −0.0517014 + 0.491906i
\(83\) 4.23749 0.900707i 0.465125 0.0988655i 0.0306130 0.999531i \(-0.490254\pi\)
0.434512 + 0.900666i \(0.356921\pi\)
\(84\) 2.21753 + 0.987309i 0.241953 + 0.107724i
\(85\) −3.16884 + 2.30230i −0.343709 + 0.249719i
\(86\) −5.04923 + 2.24806i −0.544473 + 0.242415i
\(87\) 0.729039 1.26273i 0.0781612 0.135379i
\(88\) −0.592773 1.02671i −0.0631898 0.109448i
\(89\) 2.85803 + 2.07648i 0.302951 + 0.220107i 0.728866 0.684657i \(-0.240048\pi\)
−0.425915 + 0.904763i \(0.640048\pi\)
\(90\) 0.978148 + 0.207912i 0.103106 + 0.0219158i
\(91\) −3.75844 + 11.5673i −0.393991 + 1.21258i
\(92\) 2.44692 0.255109
\(93\) 3.52857 + 4.30688i 0.365895 + 0.446603i
\(94\) 11.8126 1.21838
\(95\) −2.24376 + 6.90559i −0.230205 + 0.708499i
\(96\) −0.978148 0.207912i −0.0998318 0.0212199i
\(97\) −10.7779 7.83059i −1.09433 0.795076i −0.114204 0.993457i \(-0.536432\pi\)
−0.980125 + 0.198381i \(0.936432\pi\)
\(98\) −0.553883 0.959354i −0.0559506 0.0969093i
\(99\) 0.592773 1.02671i 0.0595759 0.103189i
\(100\) 0.913545 0.406737i 0.0913545 0.0406737i
\(101\) −14.6330 + 10.6315i −1.45604 + 1.05787i −0.471662 + 0.881780i \(0.656346\pi\)
−0.984374 + 0.176092i \(0.943654\pi\)
\(102\) 3.57827 + 1.59315i 0.354301 + 0.157745i
\(103\) 11.2491 2.39107i 1.10841 0.235600i 0.382885 0.923796i \(-0.374931\pi\)
0.725524 + 0.688197i \(0.241597\pi\)
\(104\) 0.523744 4.98309i 0.0513573 0.488633i
\(105\) 1.62424 + 1.80390i 0.158510 + 0.176043i
\(106\) 1.88053 2.08854i 0.182653 0.202857i
\(107\) −1.70231 16.1964i −0.164568 1.56576i −0.695612 0.718418i \(-0.744867\pi\)
0.531043 0.847345i \(-0.321800\pi\)
\(108\) −0.309017 0.951057i −0.0297352 0.0915155i
\(109\) 4.78415 + 14.7241i 0.458239 + 1.41031i 0.867291 + 0.497802i \(0.165859\pi\)
−0.409052 + 0.912511i \(0.634141\pi\)
\(110\) −0.123923 1.17905i −0.0118156 0.112418i
\(111\) 6.30874 7.00657i 0.598799 0.665034i
\(112\) −1.62424 1.80390i −0.153476 0.170453i
\(113\) −0.249769 + 2.37640i −0.0234963 + 0.223553i 0.976472 + 0.215642i \(0.0691846\pi\)
−0.999969 + 0.00791013i \(0.997482\pi\)
\(114\) 7.10230 1.50964i 0.665191 0.141391i
\(115\) 2.23537 + 0.995252i 0.208450 + 0.0928078i
\(116\) −1.17961 + 0.857037i −0.109524 + 0.0795739i
\(117\) 4.57736 2.03797i 0.423177 0.188410i
\(118\) 2.11861 3.66954i 0.195034 0.337808i
\(119\) 4.75393 + 8.23405i 0.435792 + 0.754814i
\(120\) −0.809017 0.587785i −0.0738528 0.0536572i
\(121\) 9.38482 + 1.99480i 0.853165 + 0.181346i
\(122\) −4.79766 + 14.7657i −0.434359 + 1.33682i
\(123\) 4.47894 0.403852
\(124\) −1.47174 5.36973i −0.132166 0.482216i
\(125\) 1.00000 0.0894427
\(126\) 0.750106 2.30859i 0.0668247 0.205665i
\(127\) −11.2437 2.38991i −0.997713 0.212070i −0.320016 0.947412i \(-0.603688\pi\)
−0.677697 + 0.735342i \(0.737022\pi\)
\(128\) 0.809017 + 0.587785i 0.0715077 + 0.0519534i
\(129\) 2.76354 + 4.78658i 0.243316 + 0.421435i
\(130\) 2.50527 4.33926i 0.219727 0.380578i
\(131\) −14.4424 + 6.43019i −1.26184 + 0.561808i −0.925077 0.379780i \(-0.876000\pi\)
−0.336765 + 0.941589i \(0.609333\pi\)
\(132\) −0.959127 + 0.696847i −0.0834813 + 0.0606527i
\(133\) 16.1014 + 7.16882i 1.39617 + 0.621616i
\(134\) −10.5170 + 2.23545i −0.908527 + 0.193113i
\(135\) 0.104528 0.994522i 0.00899638 0.0855948i
\(136\) −2.62092 2.91083i −0.224742 0.249601i
\(137\) −14.3993 + 15.9920i −1.23021 + 1.36629i −0.322568 + 0.946546i \(0.604546\pi\)
−0.907643 + 0.419742i \(0.862121\pi\)
\(138\) −0.255773 2.43352i −0.0217728 0.207155i
\(139\) 3.97898 + 12.2460i 0.337493 + 1.03870i 0.965481 + 0.260473i \(0.0838784\pi\)
−0.627989 + 0.778223i \(0.716122\pi\)
\(140\) −0.750106 2.30859i −0.0633955 0.195111i
\(141\) −1.23476 11.7479i −0.103985 0.989353i
\(142\) 8.74927 9.71705i 0.734223 0.815437i
\(143\) −3.97479 4.41445i −0.332389 0.369155i
\(144\) −0.104528 + 0.994522i −0.00871071 + 0.0828768i
\(145\) −1.42622 + 0.303151i −0.118441 + 0.0251754i
\(146\) 11.7272 + 5.22129i 0.970550 + 0.432117i
\(147\) −0.896202 + 0.651129i −0.0739175 + 0.0537042i
\(148\) −8.61315 + 3.83482i −0.707996 + 0.315220i
\(149\) −2.07963 + 3.60202i −0.170370 + 0.295089i −0.938549 0.345146i \(-0.887830\pi\)
0.768179 + 0.640235i \(0.221163\pi\)
\(150\) −0.500000 0.866025i −0.0408248 0.0707107i
\(151\) 0.462719 + 0.336185i 0.0376555 + 0.0273583i 0.606454 0.795119i \(-0.292591\pi\)
−0.568798 + 0.822477i \(0.692591\pi\)
\(152\) −7.10230 1.50964i −0.576073 0.122448i
\(153\) 1.21039 3.72520i 0.0978542 0.301164i
\(154\) −2.87779 −0.231899
\(155\) 0.839564 5.50410i 0.0674354 0.442100i
\(156\) −5.01054 −0.401164
\(157\) 2.58846 7.96645i 0.206581 0.635792i −0.793063 0.609139i \(-0.791515\pi\)
0.999645 0.0266530i \(-0.00848493\pi\)
\(158\) 5.99017 + 1.27325i 0.476552 + 0.101294i
\(159\) −2.27367 1.65192i −0.180314 0.131006i
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 2.96982 5.14388i 0.234055 0.405394i
\(162\) −0.913545 + 0.406737i −0.0717749 + 0.0319562i
\(163\) −14.6567 + 10.6487i −1.14800 + 0.834074i −0.988214 0.153077i \(-0.951082\pi\)
−0.159790 + 0.987151i \(0.551082\pi\)
\(164\) −4.09171 1.82175i −0.319509 0.142255i
\(165\) −1.15964 + 0.246489i −0.0902778 + 0.0191891i
\(166\) −0.452834 + 4.30843i −0.0351468 + 0.334399i
\(167\) 12.7335 + 14.1420i 0.985349 + 1.09434i 0.995535 + 0.0943925i \(0.0300909\pi\)
−0.0101864 + 0.999948i \(0.503242\pi\)
\(168\) −1.62424 + 1.80390i −0.125313 + 0.139174i
\(169\) −1.26537 12.0392i −0.0973363 0.926093i
\(170\) −1.21039 3.72520i −0.0928327 0.285710i
\(171\) −2.24376 6.90559i −0.171585 0.528084i
\(172\) −0.577736 5.49679i −0.0440520 0.419127i
\(173\) 10.7945 11.9885i 0.820687 0.911465i −0.176659 0.984272i \(-0.556529\pi\)
0.997346 + 0.0728067i \(0.0231956\pi\)
\(174\) 0.975644 + 1.08356i 0.0739634 + 0.0821447i
\(175\) 0.253732 2.41409i 0.0191803 0.182488i
\(176\) 1.15964 0.246489i 0.0874111 0.0185798i
\(177\) −3.87089 1.72343i −0.290954 0.129541i
\(178\) −2.85803 + 2.07648i −0.214219 + 0.155639i
\(179\) 3.08971 1.37563i 0.230936 0.102819i −0.288007 0.957628i \(-0.592993\pi\)
0.518942 + 0.854809i \(0.326326\pi\)
\(180\) −0.500000 + 0.866025i −0.0372678 + 0.0645497i
\(181\) 1.50501 + 2.60675i 0.111866 + 0.193758i 0.916523 0.399982i \(-0.130984\pi\)
−0.804656 + 0.593741i \(0.797650\pi\)
\(182\) −9.83971 7.14897i −0.729368 0.529917i
\(183\) 15.1863 + 3.22794i 1.12260 + 0.238616i
\(184\) −0.756140 + 2.32716i −0.0557434 + 0.171561i
\(185\) −9.42826 −0.693180
\(186\) −5.18647 + 2.02497i −0.380291 + 0.148478i
\(187\) −4.64367 −0.339579
\(188\) −3.65030 + 11.2345i −0.266226 + 0.819358i
\(189\) −2.37435 0.504683i −0.172708 0.0367103i
\(190\) −5.87425 4.26789i −0.426163 0.309625i
\(191\) 1.49938 + 2.59700i 0.108491 + 0.187912i 0.915159 0.403093i \(-0.132065\pi\)
−0.806668 + 0.591005i \(0.798731\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) −21.1806 + 9.43019i −1.52461 + 0.678800i −0.986453 0.164045i \(-0.947546\pi\)
−0.538157 + 0.842845i \(0.680879\pi\)
\(194\) 10.7779 7.83059i 0.773807 0.562204i
\(195\) −4.57736 2.03797i −0.327791 0.145942i
\(196\) 1.08356 0.230318i 0.0773970 0.0164513i
\(197\) 0.775256 7.37607i 0.0552347 0.525523i −0.931565 0.363576i \(-0.881556\pi\)
0.986799 0.161947i \(-0.0517775\pi\)
\(198\) 0.793285 + 0.881033i 0.0563763 + 0.0626123i
\(199\) −1.91055 + 2.12188i −0.135436 + 0.150416i −0.807047 0.590487i \(-0.798936\pi\)
0.671612 + 0.740903i \(0.265602\pi\)
\(200\) 0.104528 + 0.994522i 0.00739128 + 0.0703233i
\(201\) 3.32252 + 10.2257i 0.234353 + 0.721264i
\(202\) −5.58930 17.2021i −0.393262 1.21034i
\(203\) 0.369960 + 3.51994i 0.0259661 + 0.247051i
\(204\) −2.62092 + 2.91083i −0.183501 + 0.203799i
\(205\) −2.99699 3.32850i −0.209319 0.232473i
\(206\) −1.20212 + 11.4374i −0.0837559 + 0.796884i
\(207\) −2.39345 + 0.508744i −0.166356 + 0.0353601i
\(208\) 4.57736 + 2.03797i 0.317383 + 0.141308i
\(209\) −6.96419 + 5.05978i −0.481723 + 0.349993i
\(210\) −2.21753 + 0.987309i −0.153024 + 0.0681308i
\(211\) 0.621186 1.07593i 0.0427642 0.0740698i −0.843851 0.536578i \(-0.819717\pi\)
0.886615 + 0.462508i \(0.153050\pi\)
\(212\) 1.40521 + 2.43389i 0.0965099 + 0.167160i
\(213\) −10.5784 7.68563i −0.724818 0.526611i
\(214\) 15.9297 + 3.38596i 1.08893 + 0.231460i
\(215\) 1.70796 5.25656i 0.116482 0.358494i
\(216\) 1.00000 0.0680414
\(217\) −13.0744 3.42335i −0.887548 0.232392i
\(218\) −15.4818 −1.04856
\(219\) 3.96686 12.2087i 0.268055 0.824990i
\(220\) 1.15964 + 0.246489i 0.0781829 + 0.0166183i
\(221\) −15.8776 11.5358i −1.06804 0.775979i
\(222\) 4.71413 + 8.16512i 0.316392 + 0.548007i
\(223\) −4.85770 + 8.41378i −0.325296 + 0.563428i −0.981572 0.191092i \(-0.938797\pi\)
0.656277 + 0.754520i \(0.272130\pi\)
\(224\) 2.21753 0.987309i 0.148165 0.0659674i
\(225\) −0.809017 + 0.587785i −0.0539345 + 0.0391857i
\(226\) −2.18290 0.971892i −0.145205 0.0646493i
\(227\) −14.3286 + 3.04565i −0.951026 + 0.202147i −0.657203 0.753713i \(-0.728261\pi\)
−0.293822 + 0.955860i \(0.594927\pi\)
\(228\) −0.758978 + 7.22119i −0.0502646 + 0.478235i
\(229\) 4.22905 + 4.69683i 0.279463 + 0.310376i 0.866492 0.499190i \(-0.166369\pi\)
−0.587029 + 0.809566i \(0.699703\pi\)
\(230\) −1.63731 + 1.81842i −0.107961 + 0.119903i
\(231\) 0.300811 + 2.86202i 0.0197919 + 0.188307i
\(232\) −0.450571 1.38671i −0.0295814 0.0910423i
\(233\) −0.0653714 0.201193i −0.00428262 0.0131806i 0.948892 0.315600i \(-0.102206\pi\)
−0.953175 + 0.302419i \(0.902206\pi\)
\(234\) 0.523744 + 4.98309i 0.0342382 + 0.325755i
\(235\) −7.90419 + 8.77849i −0.515613 + 0.572646i
\(236\) 2.83525 + 3.14887i 0.184559 + 0.204974i
\(237\) 0.640131 6.09044i 0.0415810 0.395617i
\(238\) −9.30009 + 1.97680i −0.602835 + 0.128137i
\(239\) 11.0928 + 4.93884i 0.717535 + 0.319467i 0.732826 0.680416i \(-0.238201\pi\)
−0.0152911 + 0.999883i \(0.504868\pi\)
\(240\) 0.809017 0.587785i 0.0522218 0.0379414i
\(241\) 9.68139 4.31043i 0.623633 0.277659i −0.0704935 0.997512i \(-0.522457\pi\)
0.694127 + 0.719853i \(0.255791\pi\)
\(242\) −4.79724 + 8.30906i −0.308378 + 0.534127i
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −12.5604 9.12569i −0.804099 0.584212i
\(245\) 1.08356 + 0.230318i 0.0692260 + 0.0147144i
\(246\) −1.38407 + 4.25972i −0.0882450 + 0.271590i
\(247\) −36.3814 −2.31489
\(248\) 5.56171 + 0.259629i 0.353169 + 0.0164865i
\(249\) 4.33216 0.274540
\(250\) −0.309017 + 0.951057i −0.0195440 + 0.0601501i
\(251\) 21.1020 + 4.48537i 1.33195 + 0.283114i 0.818252 0.574859i \(-0.194943\pi\)
0.513695 + 0.857973i \(0.328276\pi\)
\(252\) 1.96380 + 1.42679i 0.123708 + 0.0898790i
\(253\) 1.45047 + 2.51229i 0.0911902 + 0.157946i
\(254\) 5.74742 9.95483i 0.360625 0.624621i
\(255\) −3.57827 + 1.59315i −0.224080 + 0.0997668i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) −0.776845 0.345874i −0.0484583 0.0215750i 0.382364 0.924012i \(-0.375110\pi\)
−0.430823 + 0.902437i \(0.641777\pi\)
\(258\) −5.40629 + 1.14914i −0.336581 + 0.0715425i
\(259\) −2.39225 + 22.7607i −0.148647 + 1.41428i
\(260\) 3.35271 + 3.72356i 0.207926 + 0.230925i
\(261\) 0.975644 1.08356i 0.0603909 0.0670709i
\(262\) −1.65251 15.7226i −0.102093 0.971346i
\(263\) −2.33772 7.19476i −0.144150 0.443648i 0.852751 0.522318i \(-0.174933\pi\)
−0.996901 + 0.0786701i \(0.974933\pi\)
\(264\) −0.366354 1.12752i −0.0225475 0.0693942i
\(265\) 0.293768 + 2.79502i 0.0180460 + 0.171696i
\(266\) −11.7936 + 13.0981i −0.723111 + 0.803096i
\(267\) 2.36385 + 2.62532i 0.144665 + 0.160667i
\(268\) 1.12388 10.6930i 0.0686520 0.653180i
\(269\) −0.141034 + 0.0299777i −0.00859899 + 0.00182777i −0.212209 0.977224i \(-0.568066\pi\)
0.203610 + 0.979052i \(0.434732\pi\)
\(270\) 0.913545 + 0.406737i 0.0555966 + 0.0247532i
\(271\) 14.9729 10.8784i 0.909539 0.660818i −0.0313596 0.999508i \(-0.509984\pi\)
0.940898 + 0.338690i \(0.109984\pi\)
\(272\) 3.57827 1.59315i 0.216964 0.0965988i
\(273\) −6.08128 + 10.5331i −0.368056 + 0.637491i
\(274\) −10.7597 18.6363i −0.650016 1.12586i
\(275\) 0.959127 + 0.696847i 0.0578375 + 0.0420214i
\(276\) 2.39345 + 0.508744i 0.144069 + 0.0306228i
\(277\) 7.95939 24.4965i 0.478234 1.47185i −0.363313 0.931667i \(-0.618354\pi\)
0.841547 0.540184i \(-0.181646\pi\)
\(278\) −12.8762 −0.772266
\(279\) 2.55601 + 4.94639i 0.153024 + 0.296133i
\(280\) 2.42739 0.145064
\(281\) −7.50466 + 23.0970i −0.447690 + 1.37785i 0.431816 + 0.901962i \(0.357873\pi\)
−0.879506 + 0.475887i \(0.842127\pi\)
\(282\) 11.5545 + 2.45598i 0.688060 + 0.146252i
\(283\) 8.54142 + 6.20570i 0.507735 + 0.368891i 0.811964 0.583708i \(-0.198399\pi\)
−0.304229 + 0.952599i \(0.598399\pi\)
\(284\) 6.53779 + 11.3238i 0.387947 + 0.671943i
\(285\) −3.63049 + 6.28818i −0.215051 + 0.372480i
\(286\) 5.42667 2.41611i 0.320886 0.142868i
\(287\) −8.79575 + 6.39048i −0.519197 + 0.377218i
\(288\) −0.913545 0.406737i −0.0538312 0.0239672i
\(289\) 1.62164 0.344690i 0.0953905 0.0202759i
\(290\) 0.152411 1.45009i 0.00894986 0.0851522i
\(291\) −8.91429 9.90032i −0.522565 0.580367i
\(292\) −8.58964 + 9.53976i −0.502671 + 0.558272i
\(293\) −1.84247 17.5299i −0.107638 1.02411i −0.906388 0.422447i \(-0.861171\pi\)
0.798749 0.601664i \(-0.205495\pi\)
\(294\) −0.342319 1.05355i −0.0199644 0.0614442i
\(295\) 1.30937 + 4.02983i 0.0762346 + 0.234626i
\(296\) −0.985522 9.37662i −0.0572823 0.545005i
\(297\) 0.793285 0.881033i 0.0460311 0.0511227i
\(298\) −2.78309 3.09093i −0.161220 0.179053i
\(299\) −1.28156 + 12.1932i −0.0741146 + 0.705153i
\(300\) 0.978148 0.207912i 0.0564734 0.0120038i
\(301\) −12.2565 5.45693i −0.706451 0.314532i
\(302\) −0.462719 + 0.336185i −0.0266265 + 0.0193453i
\(303\) −16.5236 + 7.35679i −0.949257 + 0.422636i
\(304\) 3.63049 6.28818i 0.208223 0.360652i
\(305\) −7.76277 13.4455i −0.444495 0.769888i
\(306\) 3.16884 + 2.30230i 0.181151 + 0.131614i
\(307\) −15.3553 3.26388i −0.876375 0.186279i −0.252305 0.967648i \(-0.581189\pi\)
−0.624070 + 0.781369i \(0.714522\pi\)
\(308\) 0.889285 2.73694i 0.0506717 0.155951i
\(309\) 11.5004 0.654237
\(310\) 4.97527 + 2.49933i 0.282576 + 0.141953i
\(311\) −8.78604 −0.498210 −0.249105 0.968476i \(-0.580137\pi\)
−0.249105 + 0.968476i \(0.580137\pi\)
\(312\) 1.54834 4.76531i 0.0876576 0.269782i
\(313\) 8.84317 + 1.87967i 0.499845 + 0.106245i 0.450933 0.892558i \(-0.351091\pi\)
0.0489121 + 0.998803i \(0.484425\pi\)
\(314\) 6.77667 + 4.92354i 0.382430 + 0.277851i
\(315\) 1.21370 + 2.10218i 0.0683840 + 0.118445i
\(316\) −3.06199 + 5.30353i −0.172251 + 0.298347i
\(317\) 24.5039 10.9098i 1.37627 0.612757i 0.420617 0.907238i \(-0.361814\pi\)
0.955657 + 0.294482i \(0.0951470\pi\)
\(318\) 2.27367 1.65192i 0.127501 0.0926350i
\(319\) −1.57917 0.703093i −0.0884166 0.0393656i
\(320\) −0.978148 + 0.207912i −0.0546801 + 0.0116226i
\(321\) 1.70231 16.1964i 0.0950135 0.903994i
\(322\) 3.97439 + 4.41401i 0.221484 + 0.245983i
\(323\) −19.0304 + 21.1354i −1.05888 + 1.17601i
\(324\) −0.104528 0.994522i −0.00580714 0.0552512i
\(325\) 1.54834 + 4.76531i 0.0858866 + 0.264332i
\(326\) −5.59838 17.2300i −0.310065 0.954283i
\(327\) 1.61829 + 15.3970i 0.0894918 + 0.851457i
\(328\) 2.99699 3.32850i 0.165481 0.183786i
\(329\) 19.1866 + 21.3088i 1.05779 + 1.17479i
\(330\) 0.123923 1.17905i 0.00682176 0.0649047i
\(331\) 26.8999 5.71776i 1.47855 0.314276i 0.603134 0.797640i \(-0.293918\pi\)
0.875420 + 0.483364i \(0.160585\pi\)
\(332\) −3.95763 1.76205i −0.217203 0.0967050i
\(333\) 7.62763 5.54179i 0.417991 0.303688i
\(334\) −17.3847 + 7.74017i −0.951249 + 0.423523i
\(335\) 5.37596 9.31143i 0.293720 0.508738i
\(336\) −1.21370 2.10218i −0.0662126 0.114684i
\(337\) 4.21180 + 3.06005i 0.229431 + 0.166691i 0.696562 0.717497i \(-0.254712\pi\)
−0.467131 + 0.884188i \(0.654712\pi\)
\(338\) 11.8410 + 2.51688i 0.644065 + 0.136900i
\(339\) −0.738392 + 2.27254i −0.0401039 + 0.123427i
\(340\) 3.91690 0.212424
\(341\) 4.64076 4.69409i 0.251311 0.254199i
\(342\) 7.26097 0.392628
\(343\) 6.08168 18.7175i 0.328380 1.01065i
\(344\) 5.40629 + 1.14914i 0.291488 + 0.0619576i
\(345\) 1.97960 + 1.43826i 0.106578 + 0.0774335i
\(346\) 8.06603 + 13.9708i 0.433632 + 0.751073i
\(347\) −8.99975 + 15.5880i −0.483132 + 0.836809i −0.999812 0.0193693i \(-0.993834\pi\)
0.516681 + 0.856178i \(0.327167\pi\)
\(348\) −1.33202 + 0.593054i −0.0714038 + 0.0317910i
\(349\) 3.05998 2.22321i 0.163797 0.119006i −0.502867 0.864364i \(-0.667721\pi\)
0.666664 + 0.745358i \(0.267721\pi\)
\(350\) 2.21753 + 0.987309i 0.118532 + 0.0527739i
\(351\) 4.90105 1.04175i 0.261599 0.0556045i
\(352\) −0.123923 + 1.17905i −0.00660514 + 0.0628437i
\(353\) 4.61807 + 5.12888i 0.245795 + 0.272983i 0.853400 0.521256i \(-0.174536\pi\)
−0.607605 + 0.794239i \(0.707870\pi\)
\(354\) 2.83525 3.14887i 0.150692 0.167360i
\(355\) 1.36677 + 13.0040i 0.0725406 + 0.690178i
\(356\) −1.09167 3.35982i −0.0578585 0.178070i
\(357\) 2.93809 + 9.04251i 0.155500 + 0.478581i
\(358\) 0.353527 + 3.36358i 0.0186845 + 0.177771i
\(359\) −4.31348 + 4.79061i −0.227657 + 0.252839i −0.846141 0.532958i \(-0.821080\pi\)
0.618485 + 0.785797i \(0.287747\pi\)
\(360\) −0.669131 0.743145i −0.0352663 0.0391672i
\(361\) −3.52488 + 33.5370i −0.185520 + 1.76510i
\(362\) −2.94424 + 0.625818i −0.154746 + 0.0328923i
\(363\) 8.76499 + 3.90243i 0.460043 + 0.204824i
\(364\) 9.83971 7.14897i 0.515741 0.374708i
\(365\) −11.7272 + 5.22129i −0.613830 + 0.273295i
\(366\) −7.76277 + 13.4455i −0.405767 + 0.702808i
\(367\) 1.94467 + 3.36826i 0.101511 + 0.175822i 0.912307 0.409506i \(-0.134299\pi\)
−0.810797 + 0.585328i \(0.800966\pi\)
\(368\) −1.97960 1.43826i −0.103194 0.0749747i
\(369\) 4.38106 + 0.931224i 0.228069 + 0.0484776i
\(370\) 2.91349 8.96681i 0.151465 0.466162i
\(371\) 6.82197 0.354179
\(372\) −0.323150 5.55838i −0.0167545 0.288189i
\(373\) −4.20129 −0.217535 −0.108767 0.994067i \(-0.534690\pi\)
−0.108767 + 0.994067i \(0.534690\pi\)
\(374\) 1.43497 4.41639i 0.0742007 0.228366i
\(375\) 0.978148 + 0.207912i 0.0505113 + 0.0107365i
\(376\) −9.55662 6.94329i −0.492845 0.358073i
\(377\) −3.65288 6.32697i −0.188133 0.325856i
\(378\) 1.21370 2.10218i 0.0624258 0.108125i
\(379\) −24.3300 + 10.8324i −1.24975 + 0.556424i −0.921578 0.388194i \(-0.873099\pi\)
−0.328171 + 0.944618i \(0.606432\pi\)
\(380\) 5.87425 4.26789i 0.301343 0.218938i
\(381\) −10.5011 4.67537i −0.537986 0.239527i
\(382\) −2.93323 + 0.623476i −0.150077 + 0.0318998i
\(383\) 3.86897 36.8108i 0.197695 1.88094i −0.224553 0.974462i \(-0.572092\pi\)
0.422248 0.906480i \(-0.361241\pi\)
\(384\) 0.669131 + 0.743145i 0.0341464 + 0.0379235i
\(385\) 1.92561 2.13861i 0.0981384 0.108994i
\(386\) −2.42349 23.0580i −0.123353 1.17362i
\(387\) 1.70796 + 5.25656i 0.0868204 + 0.267206i
\(388\) 4.11679 + 12.6702i 0.208998 + 0.643230i
\(389\) −1.12028 10.6587i −0.0568004 0.540420i −0.985511 0.169614i \(-0.945748\pi\)
0.928710 0.370806i \(-0.120919\pi\)
\(390\) 3.35271 3.72356i 0.169771 0.188550i
\(391\) 6.41318 + 7.12256i 0.324329 + 0.360203i
\(392\) −0.115793 + 1.10170i −0.00584843 + 0.0556441i
\(393\) −15.4637 + 3.28692i −0.780043 + 0.165803i
\(394\) 6.77549 + 3.01664i 0.341344 + 0.151976i
\(395\) −4.95441 + 3.59959i −0.249284 + 0.181115i
\(396\) −1.08305 + 0.482205i −0.0544253 + 0.0242317i
\(397\) −4.59606 + 7.96061i −0.230670 + 0.399532i −0.958005 0.286750i \(-0.907425\pi\)
0.727336 + 0.686282i \(0.240758\pi\)
\(398\) −1.42764 2.47274i −0.0715611 0.123947i
\(399\) 14.2591 + 10.3598i 0.713848 + 0.518641i
\(400\) −0.978148 0.207912i −0.0489074 0.0103956i
\(401\) 7.73412 23.8032i 0.386223 1.18867i −0.549366 0.835582i \(-0.685131\pi\)
0.935589 0.353091i \(-0.114869\pi\)
\(402\) −10.7519 −0.536257
\(403\) 27.5287 4.52146i 1.37130 0.225230i
\(404\) 18.0874 0.899879
\(405\) 0.309017 0.951057i 0.0153552 0.0472584i
\(406\) −3.46198 0.735867i −0.171815 0.0365205i
\(407\) −9.04290 6.57005i −0.448240 0.325666i
\(408\) −1.95845 3.39214i −0.0969578 0.167936i
\(409\) 15.3682 26.6185i 0.759909 1.31620i −0.182987 0.983115i \(-0.558577\pi\)
0.942896 0.333086i \(-0.108090\pi\)
\(410\) 4.09171 1.82175i 0.202075 0.0899697i
\(411\) −17.4095 + 12.6488i −0.858748 + 0.623917i
\(412\) −10.5062 4.67765i −0.517602 0.230451i
\(413\) 10.0606 2.13845i 0.495051 0.105226i
\(414\) 0.255773 2.43352i 0.0125706 0.119601i
\(415\) −2.89878 3.21942i −0.142296 0.158035i
\(416\) −3.35271 + 3.72356i −0.164380 + 0.182562i
\(417\) 1.34593 + 12.8057i 0.0659107 + 0.627098i
\(418\) −2.66009 8.18690i −0.130109 0.400434i
\(419\) 4.37702 + 13.4711i 0.213831 + 0.658105i 0.999235 + 0.0391205i \(0.0124556\pi\)
−0.785403 + 0.618984i \(0.787544\pi\)
\(420\) −0.253732 2.41409i −0.0123808 0.117796i
\(421\) 11.6123 12.8968i 0.565948 0.628549i −0.390447 0.920625i \(-0.627679\pi\)
0.956395 + 0.292076i \(0.0943461\pi\)
\(422\) 0.831310 + 0.923263i 0.0404675 + 0.0449437i
\(423\) 1.23476 11.7479i 0.0600359 0.571203i
\(424\) −2.74900 + 0.584317i −0.133503 + 0.0283770i
\(425\) 3.57827 + 1.59315i 0.173572 + 0.0772790i
\(426\) 10.5784 7.68563i 0.512524 0.372370i
\(427\) −34.4284 + 15.3285i −1.66611 + 0.741799i
\(428\) −8.14279 + 14.1037i −0.393597 + 0.681730i
\(429\) −2.97011 5.14439i −0.143398 0.248373i
\(430\) 4.47150 + 3.24873i 0.215635 + 0.156668i
\(431\) 30.7556 + 6.53730i 1.48144 + 0.314891i 0.876510 0.481384i \(-0.159866\pi\)
0.604935 + 0.796275i \(0.293199\pi\)
\(432\) −0.309017 + 0.951057i −0.0148676 + 0.0457577i
\(433\) −17.1822 −0.825723 −0.412861 0.910794i \(-0.635471\pi\)
−0.412861 + 0.910794i \(0.635471\pi\)
\(434\) 7.29601 11.3766i 0.350220 0.546095i
\(435\) −1.45808 −0.0699095
\(436\) 4.78415 14.7241i 0.229119 0.705157i
\(437\) 17.3788 + 3.69397i 0.831339 + 0.176707i
\(438\) 10.3854 + 7.54541i 0.496232 + 0.360534i
\(439\) 13.5481 + 23.4660i 0.646614 + 1.11997i 0.983926 + 0.178576i \(0.0571490\pi\)
−0.337312 + 0.941393i \(0.609518\pi\)
\(440\) −0.592773 + 1.02671i −0.0282594 + 0.0489466i
\(441\) −1.01199 + 0.450569i −0.0481902 + 0.0214557i
\(442\) 15.8776 11.5358i 0.755221 0.548700i
\(443\) 19.7707 + 8.80250i 0.939336 + 0.418219i 0.818535 0.574457i \(-0.194787\pi\)
0.120802 + 0.992677i \(0.461454\pi\)
\(444\) −9.22223 + 1.96025i −0.437668 + 0.0930292i
\(445\) 0.369270 3.51337i 0.0175051 0.166550i
\(446\) −6.50087 7.21995i −0.307825 0.341874i
\(447\) −2.78309 + 3.09093i −0.131635 + 0.146196i
\(448\) 0.253732 + 2.41409i 0.0119877 + 0.114055i
\(449\) −4.32649 13.3156i −0.204180 0.628401i −0.999746 0.0225344i \(-0.992826\pi\)
0.795566 0.605867i \(-0.207174\pi\)
\(450\) −0.309017 0.951057i −0.0145672 0.0448332i
\(451\) −0.555045 5.28090i −0.0261360 0.248668i
\(452\) 1.59888 1.77573i 0.0752049 0.0835235i
\(453\) 0.382710 + 0.425043i 0.0179813 + 0.0199703i
\(454\) 1.53121 14.5685i 0.0718634 0.683734i
\(455\) 11.8968 2.52874i 0.557729 0.118549i
\(456\) −6.63323 2.95330i −0.310629 0.138301i
\(457\) 20.6340 14.9915i 0.965219 0.701273i 0.0108624 0.999941i \(-0.496542\pi\)
0.954357 + 0.298668i \(0.0965423\pi\)
\(458\) −5.77380 + 2.57066i −0.269792 + 0.120119i
\(459\) 1.95845 3.39214i 0.0914127 0.158331i
\(460\) −1.22346 2.11910i −0.0570441 0.0988034i
\(461\) 8.06073 + 5.85646i 0.375426 + 0.272763i 0.759457 0.650557i \(-0.225465\pi\)
−0.384032 + 0.923320i \(0.625465\pi\)
\(462\) −2.81490 0.598325i −0.130961 0.0278366i
\(463\) 3.50133 10.7760i 0.162721 0.500803i −0.836140 0.548516i \(-0.815193\pi\)
0.998861 + 0.0477125i \(0.0151931\pi\)
\(464\) 1.45808 0.0676896
\(465\) 1.96558 5.20927i 0.0911518 0.241574i
\(466\) 0.211546 0.00979970
\(467\) 0.670171 2.06257i 0.0310118 0.0954446i −0.934353 0.356350i \(-0.884021\pi\)
0.965364 + 0.260905i \(0.0840211\pi\)
\(468\) −4.90105 1.04175i −0.226551 0.0481549i
\(469\) −21.1146 15.3407i −0.974983 0.708367i
\(470\) −5.90631 10.2300i −0.272438 0.471876i
\(471\) 4.18821 7.25420i 0.192983 0.334256i
\(472\) −3.87089 + 1.72343i −0.178172 + 0.0793273i
\(473\) 5.30116 3.85152i 0.243748 0.177093i
\(474\) 5.59454 + 2.49085i 0.256966 + 0.114409i
\(475\) 7.10230 1.50964i 0.325876 0.0692671i
\(476\) 0.993842 9.45578i 0.0455527 0.433405i
\(477\) −1.88053 2.08854i −0.0861037 0.0956278i
\(478\) −8.12499 + 9.02371i −0.371628 + 0.412735i
\(479\) 0.138884 + 1.32140i 0.00634579 + 0.0603761i 0.997237 0.0742922i \(-0.0236698\pi\)
−0.990891 + 0.134668i \(0.957003\pi\)
\(480\) 0.309017 + 0.951057i 0.0141046 + 0.0434096i
\(481\) −14.5982 44.9286i −0.665620 2.04857i
\(482\) 1.10775 + 10.5395i 0.0504567 + 0.480063i
\(483\) 3.97439 4.41401i 0.180841 0.200844i
\(484\) −6.41996 7.13009i −0.291816 0.324095i
\(485\) −1.39255 + 13.2492i −0.0632324 + 0.601616i
\(486\) −0.978148 + 0.207912i −0.0443697 + 0.00943107i
\(487\) 25.5622 + 11.3810i 1.15833 + 0.515723i 0.893717 0.448631i \(-0.148088\pi\)
0.264615 + 0.964354i \(0.414755\pi\)
\(488\) 12.5604 9.12569i 0.568584 0.413100i
\(489\) −16.5505 + 7.36874i −0.748438 + 0.333226i
\(490\) −0.553883 + 0.959354i −0.0250219 + 0.0433392i
\(491\) 9.35582 + 16.2048i 0.422222 + 0.731310i 0.996157 0.0875911i \(-0.0279169\pi\)
−0.573934 + 0.818901i \(0.694584\pi\)
\(492\) −3.62354 2.63265i −0.163362 0.118689i
\(493\) −5.58635 1.18741i −0.251596 0.0534785i
\(494\) 11.2425 34.6008i 0.505823 1.55676i
\(495\) −1.18555 −0.0532863
\(496\) −1.96558 + 5.20927i −0.0882573 + 0.233903i
\(497\) 31.7396 1.42371
\(498\) −1.33871 + 4.12013i −0.0599891 + 0.184627i
\(499\) 5.04830 + 1.07305i 0.225993 + 0.0480363i 0.319516 0.947581i \(-0.396480\pi\)
−0.0935233 + 0.995617i \(0.529813\pi\)
\(500\) −0.809017 0.587785i −0.0361803 0.0262866i
\(501\) 9.51497 + 16.4804i 0.425097 + 0.736290i
\(502\) −10.7867 + 18.6831i −0.481435 + 0.833870i
\(503\) 32.1645 14.3206i 1.43414 0.638522i 0.465067 0.885276i \(-0.346030\pi\)
0.969078 + 0.246753i \(0.0793637\pi\)
\(504\) −1.96380 + 1.42679i −0.0874747 + 0.0635541i
\(505\) 16.5236 + 7.35679i 0.735291 + 0.327373i
\(506\) −2.83755 + 0.603139i −0.126144 + 0.0268128i
\(507\) 1.26537 12.0392i 0.0561972 0.534680i
\(508\) 7.69155 + 8.54233i 0.341257 + 0.379005i
\(509\) 3.68439 4.09193i 0.163308 0.181372i −0.655937 0.754816i \(-0.727726\pi\)
0.819245 + 0.573444i \(0.194393\pi\)
\(510\) −0.409428 3.89545i −0.0181298 0.172493i
\(511\) 9.62912 + 29.6354i 0.425967 + 1.31099i
\(512\) −0.309017 0.951057i −0.0136568 0.0420312i
\(513\) −0.758978 7.22119i −0.0335097 0.318824i
\(514\) 0.569004 0.631943i 0.0250977 0.0278738i
\(515\) −7.69529 8.54649i −0.339095 0.376603i
\(516\) 0.577736 5.49679i 0.0254334 0.241983i
\(517\) −13.6984 + 2.91168i −0.602454 + 0.128056i
\(518\) −20.9075 9.30861i −0.918622 0.408997i
\(519\) 13.0511 9.48219i 0.572880 0.416222i
\(520\) −4.57736 + 2.03797i −0.200730 + 0.0893709i
\(521\) 8.97805 15.5504i 0.393336 0.681277i −0.599551 0.800336i \(-0.704654\pi\)
0.992887 + 0.119059i \(0.0379877\pi\)
\(522\) 0.729039 + 1.26273i 0.0319092 + 0.0552683i
\(523\) 24.2729 + 17.6353i 1.06138 + 0.771136i 0.974343 0.225069i \(-0.0722607\pi\)
0.0870353 + 0.996205i \(0.472261\pi\)
\(524\) 15.4637 + 3.28692i 0.675537 + 0.143590i
\(525\) 0.750106 2.30859i 0.0327373 0.100755i
\(526\) 7.56502 0.329851
\(527\) 11.7730 18.3576i 0.512841 0.799670i
\(528\) 1.18555 0.0515943
\(529\) −5.25718 + 16.1799i −0.228573 + 0.703475i
\(530\) −2.74900 0.584317i −0.119409 0.0253811i
\(531\) −3.42798 2.49057i −0.148762 0.108082i
\(532\) −8.81261 15.2639i −0.382075 0.661774i
\(533\) 11.2210 19.4353i 0.486033 0.841835i
\(534\) −3.22730 + 1.43689i −0.139659 + 0.0621802i
\(535\) −13.1753 + 9.57243i −0.569619 + 0.413852i
\(536\) 9.82236 + 4.37320i 0.424261 + 0.188893i
\(537\) 3.30820 0.703180i 0.142759 0.0303445i
\(538\) 0.0150714 0.143395i 0.000649774 0.00618219i
\(539\) 0.878775 + 0.975978i 0.0378515 + 0.0420383i
\(540\) −0.669131 + 0.743145i −0.0287948 + 0.0319799i
\(541\) −2.29419 21.8278i −0.0986350 0.938450i −0.926188 0.377062i \(-0.876934\pi\)
0.827553 0.561388i \(-0.189732\pi\)
\(542\) 5.71914 + 17.6017i 0.245658 + 0.756057i
\(543\) 0.930147 + 2.86270i 0.0399164 + 0.122850i
\(544\) 0.409428 + 3.89545i 0.0175541 + 0.167016i
\(545\) 10.3594 11.5052i 0.443747 0.492831i
\(546\) −8.13834 9.03854i −0.348289 0.386814i
\(547\) −3.08289 + 29.3318i −0.131815 + 1.25414i 0.706012 + 0.708200i \(0.250492\pi\)
−0.837827 + 0.545936i \(0.816174\pi\)
\(548\) 21.0491 4.47412i 0.899173 0.191125i
\(549\) 14.1833 + 6.31481i 0.605328 + 0.269509i
\(550\) −0.959127 + 0.696847i −0.0408973 + 0.0297136i
\(551\) −9.67176 + 4.30614i −0.412031 + 0.183448i
\(552\) −1.22346 + 2.11910i −0.0520739 + 0.0901947i
\(553\) 7.43266 + 12.8738i 0.316069 + 0.547448i
\(554\) 20.8380 + 15.1397i 0.885320 + 0.643223i
\(555\) −9.22223 1.96025i −0.391462 0.0832078i
\(556\) 3.97898 12.2460i 0.168746 0.519348i
\(557\) 42.1476 1.78585 0.892926 0.450204i \(-0.148649\pi\)
0.892926 + 0.450204i \(0.148649\pi\)
\(558\) −5.49415 + 0.902388i −0.232586 + 0.0382011i
\(559\) 27.6936 1.17132
\(560\) −0.750106 + 2.30859i −0.0316977 + 0.0975556i
\(561\) −4.54220 0.965473i −0.191772 0.0407623i
\(562\) −19.6474 14.2747i −0.828777 0.602142i
\(563\) 3.16639 + 5.48434i 0.133447 + 0.231138i 0.925003 0.379959i \(-0.124062\pi\)
−0.791556 + 0.611097i \(0.790729\pi\)
\(564\) −5.90631 + 10.2300i −0.248701 + 0.430762i
\(565\) 2.18290 0.971892i 0.0918355 0.0408878i
\(566\) −8.54142 + 6.20570i −0.359023 + 0.260845i
\(567\) −2.21753 0.987309i −0.0931276 0.0414631i
\(568\) −12.7898 + 2.71857i −0.536650 + 0.114069i
\(569\) −3.28945 + 31.2970i −0.137901 + 1.31204i 0.678520 + 0.734582i \(0.262622\pi\)
−0.816421 + 0.577457i \(0.804045\pi\)
\(570\) −4.85854 5.39595i −0.203502 0.226012i
\(571\) −0.195657 + 0.217299i −0.00818798 + 0.00909367i −0.747225 0.664571i \(-0.768614\pi\)
0.739037 + 0.673665i \(0.235281\pi\)
\(572\) 0.620923 + 5.90769i 0.0259621 + 0.247013i
\(573\) 0.926667 + 2.85199i 0.0387121 + 0.119143i
\(574\) −3.35968 10.3400i −0.140230 0.431584i
\(575\) −0.255773 2.43352i −0.0106665 0.101485i
\(576\) 0.669131 0.743145i 0.0278804 0.0309644i
\(577\) −4.07722 4.52821i −0.169737 0.188512i 0.652275 0.757983i \(-0.273815\pi\)
−0.822012 + 0.569471i \(0.807148\pi\)
\(578\) −0.173294 + 1.64878i −0.00720809 + 0.0685804i
\(579\) −22.6784 + 4.82043i −0.942480 + 0.200330i
\(580\) 1.33202 + 0.593054i 0.0553091 + 0.0246252i
\(581\) −8.50751 + 6.18107i −0.352951 + 0.256434i
\(582\) 12.1704 5.41863i 0.504481 0.224609i
\(583\) −1.66594 + 2.88549i −0.0689960 + 0.119505i
\(584\) −6.41851 11.1172i −0.265600 0.460032i
\(585\) −4.05361 2.94512i −0.167596 0.121766i
\(586\) 17.2413 + 3.66476i 0.712233 + 0.151390i
\(587\) 2.17355 6.68950i 0.0897121 0.276105i −0.896127 0.443797i \(-0.853631\pi\)
0.985840 + 0.167691i \(0.0536312\pi\)
\(588\) 1.10777 0.0456835
\(589\) −2.34638 40.3592i −0.0966810 1.66297i
\(590\) −4.23722 −0.174443
\(591\) 2.29189 7.05370i 0.0942756 0.290150i
\(592\) 9.22223 + 1.96025i 0.379031 + 0.0805656i
\(593\) −4.55098 3.30648i −0.186887 0.135781i 0.490408 0.871493i \(-0.336848\pi\)
−0.677295 + 0.735712i \(0.736848\pi\)
\(594\) 0.592773 + 1.02671i 0.0243218 + 0.0421266i
\(595\) 4.75393 8.23405i 0.194892 0.337563i
\(596\) 3.79967 1.69172i 0.155641 0.0692956i
\(597\) −2.30997 + 1.67829i −0.0945407 + 0.0686878i
\(598\) −11.2004 4.98675i −0.458020 0.203924i
\(599\) −20.7452 + 4.40954i −0.847628 + 0.180169i −0.611196 0.791479i \(-0.709311\pi\)
−0.236432 + 0.971648i \(0.575978\pi\)
\(600\) −0.104528 + 0.994522i −0.00426736 + 0.0406012i
\(601\) 11.5582 + 12.8367i 0.471470 + 0.523621i 0.931235 0.364420i \(-0.118733\pi\)
−0.459764 + 0.888041i \(0.652066\pi\)
\(602\) 8.97731 9.97031i 0.365888 0.406359i
\(603\) 1.12388 + 10.6930i 0.0457680 + 0.435453i
\(604\) −0.176743 0.543959i −0.00719156 0.0221334i
\(605\) −2.96486 9.12489i −0.120539 0.370980i
\(606\) −1.89064 17.9883i −0.0768021 0.730723i
\(607\) −23.8001 + 26.4327i −0.966018 + 1.07287i 0.0312874 + 0.999510i \(0.490039\pi\)
−0.997305 + 0.0733613i \(0.976627\pi\)
\(608\) 4.85854 + 5.39595i 0.197040 + 0.218835i
\(609\) −0.369960 + 3.51994i −0.0149916 + 0.142635i
\(610\) 15.1863 3.22794i 0.614874 0.130696i
\(611\) −54.0706 24.0738i −2.18746 0.973921i
\(612\) −3.16884 + 2.30230i −0.128093 + 0.0930649i
\(613\) 16.5332 7.36105i 0.667769 0.297310i −0.0447133 0.999000i \(-0.514237\pi\)
0.712483 + 0.701690i \(0.247571\pi\)
\(614\) 7.84919 13.5952i 0.316767 0.548657i
\(615\) −2.23947 3.87887i −0.0903041 0.156411i
\(616\) 2.32818 + 1.69152i 0.0938050 + 0.0681533i
\(617\) 14.8934 + 3.16570i 0.599587 + 0.127446i 0.497699 0.867350i \(-0.334178\pi\)
0.101888 + 0.994796i \(0.467512\pi\)
\(618\) −3.55383 + 10.9376i −0.142956 + 0.439973i
\(619\) −35.2811 −1.41807 −0.709034 0.705175i \(-0.750869\pi\)
−0.709034 + 0.705175i \(0.750869\pi\)
\(620\) −3.91445 + 3.95943i −0.157208 + 0.159014i
\(621\) −2.44692 −0.0981916
\(622\) 2.71503 8.35602i 0.108863 0.335046i
\(623\) −8.38791 1.78291i −0.336055 0.0714306i
\(624\) 4.05361 + 2.94512i 0.162274 + 0.117899i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −4.52036 + 7.82950i −0.180670 + 0.312930i
\(627\) −7.86400 + 3.50128i −0.314058 + 0.139828i
\(628\) −6.77667 + 4.92354i −0.270419 + 0.196471i
\(629\) −33.7369 15.0206i −1.34518 0.598911i
\(630\) −2.37435 + 0.504683i −0.0945963 + 0.0201071i
\(631\) −1.84070 + 17.5131i −0.0732771 + 0.697185i 0.894789 + 0.446489i \(0.147326\pi\)
−0.968066 + 0.250695i \(0.919341\pi\)
\(632\) −4.09775 4.55101i −0.163000 0.181030i
\(633\) 0.831310 0.923263i 0.0330416 0.0366964i
\(634\) 2.80375 + 26.6759i 0.111351 + 1.05943i
\(635\) 3.55210 + 10.9322i 0.140961 + 0.433833i
\(636\) 0.868465 + 2.67286i 0.0344369 + 0.105986i
\(637\) 0.580186 + 5.52010i 0.0229878 + 0.218714i
\(638\) 1.15667 1.28461i 0.0457931 0.0508584i
\(639\) −8.74927 9.71705i −0.346116 0.384401i
\(640\) 0.104528 0.994522i 0.00413185 0.0393119i
\(641\) −16.2218 + 3.44805i −0.640722 + 0.136190i −0.516805 0.856103i \(-0.672879\pi\)
−0.123917 + 0.992293i \(0.539546\pi\)
\(642\) 14.8776 + 6.62395i 0.587173 + 0.261426i
\(643\) −13.6294 + 9.90237i −0.537493 + 0.390511i −0.823153 0.567820i \(-0.807787\pi\)
0.285660 + 0.958331i \(0.407787\pi\)
\(644\) −5.42613 + 2.41587i −0.213819 + 0.0951985i
\(645\) 2.76354 4.78658i 0.108814 0.188472i
\(646\) −14.2203 24.6302i −0.559489 0.969063i
\(647\) 8.38997 + 6.09567i 0.329844 + 0.239645i 0.740364 0.672206i \(-0.234653\pi\)
−0.410521 + 0.911851i \(0.634653\pi\)
\(648\) 0.978148 + 0.207912i 0.0384253 + 0.00816754i
\(649\) −1.55232 + 4.77755i −0.0609339 + 0.187535i
\(650\) −5.01054 −0.196530
\(651\) −12.0769 6.06686i −0.473333 0.237779i
\(652\) 18.1167 0.709506
\(653\) 0.685937 2.11110i 0.0268428 0.0826136i −0.936738 0.350032i \(-0.886171\pi\)
0.963580 + 0.267419i \(0.0861706\pi\)
\(654\) −15.1435 3.21885i −0.592159 0.125867i
\(655\) 12.7899 + 9.29243i 0.499744 + 0.363085i
\(656\) 2.23947 + 3.87887i 0.0874366 + 0.151445i
\(657\) 6.41851 11.1172i 0.250410 0.433723i
\(658\) −26.1949 + 11.6627i −1.02118 + 0.454660i
\(659\) −28.3776 + 20.6175i −1.10543 + 0.803145i −0.981939 0.189200i \(-0.939410\pi\)
−0.123495 + 0.992345i \(0.539410\pi\)
\(660\) 1.08305 + 0.482205i 0.0421577 + 0.0187698i
\(661\) −8.46187 + 1.79863i −0.329129 + 0.0699584i −0.369512 0.929226i \(-0.620475\pi\)
0.0403838 + 0.999184i \(0.487142\pi\)
\(662\) −2.87463 + 27.3502i −0.111725 + 1.06300i
\(663\) −13.1322 14.5848i −0.510014 0.566427i
\(664\) 2.89878 3.21942i 0.112495 0.124938i
\(665\) −1.84234 17.5287i −0.0714428 0.679733i
\(666\) 2.91349 + 8.96681i 0.112896 + 0.347457i
\(667\) 1.10251 + 3.39318i 0.0426894 + 0.131384i
\(668\) −1.98917 18.9257i −0.0769633 0.732257i
\(669\) −6.50087 + 7.21995i −0.251338 + 0.279139i
\(670\) 7.19444 + 7.99023i 0.277945 + 0.308690i
\(671\) 1.92398 18.3054i 0.0742743 0.706673i
\(672\) 2.37435 0.504683i 0.0915925 0.0194686i
\(673\) −6.35397 2.82897i −0.244928 0.109049i 0.280602 0.959824i \(-0.409466\pi\)
−0.525529 + 0.850775i \(0.676133\pi\)
\(674\) −4.21180 + 3.06005i −0.162232 + 0.117869i
\(675\) −0.913545 + 0.406737i −0.0351624 + 0.0156553i
\(676\) −6.05277 + 10.4837i −0.232799 + 0.403219i
\(677\) 23.1353 + 40.0716i 0.889163 + 1.54008i 0.840867 + 0.541242i \(0.182046\pi\)
0.0482963 + 0.998833i \(0.484621\pi\)
\(678\) −1.93314 1.40450i −0.0742416 0.0539397i
\(679\) 31.6315 + 6.72349i 1.21391 + 0.258024i
\(680\) −1.21039 + 3.72520i −0.0464163 + 0.142855i
\(681\) −14.6488 −0.561342
\(682\) 3.03027 + 5.86418i 0.116035 + 0.224551i
\(683\) 15.9513 0.610358 0.305179 0.952295i \(-0.401284\pi\)
0.305179 + 0.952295i \(0.401284\pi\)
\(684\) −2.24376 + 6.90559i −0.0857924 + 0.264042i
\(685\) 21.0491 + 4.47412i 0.804245 + 0.170948i
\(686\) 15.9220 + 11.5680i 0.607906 + 0.441670i
\(687\) 3.16011 + 5.47347i 0.120566 + 0.208826i
\(688\) −2.76354 + 4.78658i −0.105359 + 0.182487i
\(689\) −12.8643 + 5.72754i −0.490089 + 0.218202i
\(690\) −1.97960 + 1.43826i −0.0753621 + 0.0547538i
\(691\) 20.4609 + 9.10977i 0.778368 + 0.346552i 0.757165 0.653223i \(-0.226584\pi\)
0.0212031 + 0.999775i \(0.493250\pi\)
\(692\) −15.7795 + 3.35404i −0.599848 + 0.127502i
\(693\) −0.300811 + 2.86202i −0.0114268 + 0.108719i
\(694\) −12.0440 13.3762i −0.457185 0.507755i
\(695\) 8.61589 9.56891i 0.326819 0.362970i
\(696\) −0.152411 1.45009i −0.00577711 0.0549655i
\(697\) −5.42126 16.6849i −0.205345 0.631987i
\(698\) 1.16881 + 3.59723i 0.0442401 + 0.136157i
\(699\) −0.0221126 0.210388i −0.000836376 0.00795759i
\(700\) −1.62424 + 1.80390i −0.0613906 + 0.0681812i
\(701\) −13.1894 14.6483i −0.498155 0.553258i 0.440662 0.897673i \(-0.354744\pi\)
−0.938817 + 0.344416i \(0.888077\pi\)
\(702\) −0.523744 + 4.98309i −0.0197675 + 0.188075i
\(703\) −66.9624 + 14.2333i −2.52553 + 0.536819i
\(704\) −1.08305 0.482205i −0.0408190 0.0181738i
\(705\) −9.55662 + 6.94329i −0.359923 + 0.261499i
\(706\) −6.30492 + 2.80713i −0.237289 + 0.105648i
\(707\) 21.9525 38.0229i 0.825611 1.43000i
\(708\) 2.11861 + 3.66954i 0.0796222 + 0.137910i
\(709\) −4.61290 3.35147i −0.173241 0.125867i 0.497786 0.867300i \(-0.334147\pi\)
−0.671027 + 0.741433i \(0.734147\pi\)
\(710\) −12.7898 2.71857i −0.479995 0.102026i
\(711\) 1.89242 5.82426i 0.0709712 0.218427i
\(712\) 3.53272 0.132394
\(713\) −13.6091 0.635292i −0.509663 0.0237919i
\(714\) −9.50786 −0.355823
\(715\) −1.83563 + 5.64949i −0.0686487 + 0.211279i
\(716\) −3.30820 0.703180i −0.123633 0.0262791i
\(717\) 9.82357 + 7.13724i 0.366868 + 0.266545i
\(718\) −3.22320 5.58274i −0.120289 0.208346i
\(719\) −9.74751 + 16.8832i −0.363521 + 0.629637i −0.988538 0.150975i \(-0.951759\pi\)
0.625017 + 0.780611i \(0.285092\pi\)
\(720\) 0.913545 0.406737i 0.0340458 0.0151582i
\(721\) −22.5846 + 16.4087i −0.841093 + 0.611090i
\(722\) −30.8063 13.7158i −1.14649 0.510451i
\(723\) 10.3660 2.20337i 0.385516 0.0819440i
\(724\) 0.314633 2.99353i 0.0116932 0.111254i
\(725\) 0.975644 + 1.08356i 0.0362345 + 0.0402425i
\(726\) −6.41996 + 7.13009i −0.238267 + 0.264622i
\(727\) −3.41047 32.4484i −0.126487 1.20345i −0.855079 0.518498i \(-0.826492\pi\)
0.728592 0.684948i \(-0.240175\pi\)
\(728\) 3.75844 + 11.5673i 0.139297 + 0.428712i
\(729\) 0.309017 + 0.951057i 0.0114451 + 0.0352243i
\(730\) −1.34183 12.7667i −0.0496635 0.472517i
\(731\) 14.4860 16.0883i 0.535785 0.595049i
\(732\) −10.3886 11.5377i −0.383974 0.426447i
\(733\) −2.12434 + 20.2118i −0.0784644 + 0.746539i 0.882583 + 0.470156i \(0.155802\pi\)
−0.961048 + 0.276383i \(0.910864\pi\)
\(734\) −3.80434 + 0.808637i −0.140421 + 0.0298474i
\(735\) 1.01199 + 0.450569i 0.0373280 + 0.0166195i
\(736\) 1.97960 1.43826i 0.0729691 0.0530151i
\(737\) 11.6449 5.18463i 0.428944 0.190978i
\(738\) −2.23947 + 3.87887i −0.0824360 + 0.142783i
\(739\) 0.529226 + 0.916646i 0.0194679 + 0.0337194i 0.875595 0.483046i \(-0.160469\pi\)
−0.856127 + 0.516765i \(0.827136\pi\)
\(740\) 7.62763 + 5.54179i 0.280397 + 0.203720i
\(741\) −35.5864 7.56412i −1.30730 0.277875i
\(742\) −2.10811 + 6.48808i −0.0773910 + 0.238185i
\(743\) 52.8036 1.93718 0.968588 0.248669i \(-0.0799932\pi\)
0.968588 + 0.248669i \(0.0799932\pi\)
\(744\) 5.38619 + 1.41030i 0.197467 + 0.0517041i
\(745\) 4.15926 0.152383
\(746\) 1.29827 3.99566i 0.0475330 0.146292i
\(747\) 4.23749 + 0.900707i 0.155042 + 0.0329552i
\(748\) 3.75681 + 2.72948i 0.137363 + 0.0997997i
\(749\) 19.7658 + 34.2353i 0.722225 + 1.25093i
\(750\) −0.500000 + 0.866025i −0.0182574 + 0.0316228i
\(751\) −2.60198 + 1.15848i −0.0949477 + 0.0422734i −0.453661 0.891174i \(-0.649882\pi\)
0.358713 + 0.933448i \(0.383216\pi\)
\(752\) 9.55662 6.94329i 0.348494 0.253196i
\(753\) 19.7083 + 8.77471i 0.718211 + 0.319768i
\(754\) 7.14611 1.51895i 0.260246 0.0553170i
\(755\) 0.0597852 0.568819i 0.00217581 0.0207014i
\(756\) 1.62424 + 1.80390i 0.0590731 + 0.0656074i
\(757\) −28.2341 + 31.3571i −1.02619 + 1.13969i −0.0360828 + 0.999349i \(0.511488\pi\)
−0.990103 + 0.140345i \(0.955179\pi\)
\(758\) −2.78386 26.4866i −0.101114 0.962037i
\(759\) 0.896439 + 2.75896i 0.0325387 + 0.100144i
\(760\) 2.24376 + 6.90559i 0.0813898 + 0.250492i
\(761\) −5.11313 48.6482i −0.185351 1.76350i −0.552670 0.833400i \(-0.686391\pi\)
0.367319 0.930095i \(-0.380276\pi\)
\(762\) 7.69155 8.54233i 0.278636 0.309456i
\(763\) −25.1463 27.9277i −0.910356 1.01105i
\(764\) 0.313455 2.98233i 0.0113404 0.107897i
\(765\) −3.83131 + 0.814370i −0.138521 + 0.0294436i
\(766\) 33.8135 + 15.0548i 1.22173 + 0.543950i
\(767\) −17.1760 + 12.4791i −0.620191 + 0.450595i
\(768\) −0.913545 + 0.406737i −0.0329647 + 0.0146768i
\(769\) −18.3535 + 31.7892i −0.661844 + 1.14635i 0.318287 + 0.947995i \(0.396893\pi\)
−0.980131 + 0.198353i \(0.936441\pi\)
\(770\) 1.43889 + 2.49224i 0.0518541 + 0.0898140i
\(771\) −0.687958 0.499831i −0.0247762 0.0180010i
\(772\) 22.6784 + 4.82043i 0.816212 + 0.173491i
\(773\) 6.14591 18.9152i 0.221053 0.680331i −0.777615 0.628740i \(-0.783571\pi\)
0.998668 0.0515908i \(-0.0164291\pi\)
\(774\) −5.52707 −0.198666
\(775\) −5.18647 + 2.02497i −0.186304 + 0.0727390i
\(776\) −13.3222 −0.478239
\(777\) −7.07219 + 21.7660i −0.253714 + 0.780850i
\(778\) 10.4833 + 2.22828i 0.375843 + 0.0798879i
\(779\) −26.3104 19.1156i −0.942668 0.684888i
\(780\) 2.50527 + 4.33926i 0.0897031 + 0.155370i
\(781\) −7.75085 + 13.4249i −0.277347 + 0.480380i
\(782\) −8.75574 + 3.89831i −0.313105 + 0.139403i
\(783\) 1.17961 0.857037i 0.0421558 0.0306280i
\(784\) −1.01199 0.450569i −0.0361427 0.0160918i
\(785\) −8.19338 + 1.74156i −0.292434 + 0.0621588i
\(786\) 1.65251 15.7226i 0.0589432 0.560807i
\(787\) −7.81102 8.67502i −0.278433 0.309231i 0.587666 0.809104i \(-0.300047\pi\)
−0.866099 + 0.499872i \(0.833380\pi\)
\(788\) −4.96274 + 5.51168i −0.176790 + 0.196345i
\(789\) −0.790760 7.52358i −0.0281518 0.267846i
\(790\) −1.89242 5.82426i −0.0673292 0.207218i
\(791\) −1.79237 5.51634i −0.0637292 0.196138i
\(792\) −0.123923 1.17905i −0.00440342 0.0418958i
\(793\) 52.0526 57.8103i 1.84844 2.05290i
\(794\) −6.15073 6.83108i −0.218281 0.242426i
\(795\) −0.293768 + 2.79502i −0.0104189 + 0.0991290i
\(796\) 2.79288 0.593646i 0.0989911 0.0210412i
\(797\) −9.35467 4.16497i −0.331360 0.147531i 0.234312 0.972161i \(-0.424716\pi\)
−0.565671 + 0.824631i \(0.691383\pi\)
\(798\) −14.2591 + 10.3598i −0.504767 + 0.366735i
\(799\) −42.2688 + 18.8193i −1.49536 + 0.665778i
\(800\) 0.500000 0.866025i 0.0176777 0.0306186i
\(801\) 1.76636 + 3.05943i 0.0624113 + 0.108100i
\(802\) 20.2482 + 14.7112i 0.714988 + 0.519469i
\(803\) −14.8863 3.16418i −0.525327 0.111662i
\(804\) 3.32252 10.2257i 0.117176 0.360632i
\(805\) −5.93964 −0.209345
\(806\) −4.20667 + 27.5785i −0.148174 + 0.971412i
\(807\) −0.144185 −0.00507554
\(808\) −5.58930 + 17.2021i −0.196631 + 0.605168i
\(809\) −13.9694 2.96928i −0.491137 0.104394i −0.0443155 0.999018i \(-0.514111\pi\)
−0.446821 + 0.894623i \(0.647444\pi\)
\(810\) 0.809017 + 0.587785i 0.0284260 + 0.0206527i
\(811\) −4.21289 7.29694i −0.147935 0.256230i 0.782529 0.622614i \(-0.213929\pi\)
−0.930464 + 0.366383i \(0.880596\pi\)
\(812\) 1.76966 3.06515i 0.0621030 0.107566i
\(813\) 16.9075 7.52768i 0.592970 0.264007i
\(814\) 9.04290 6.57005i 0.316954 0.230280i
\(815\) 16.5505 + 7.36874i 0.579737 + 0.258116i
\(816\) 3.83131 0.814370i 0.134123 0.0285087i
\(817\) 4.19493 39.9121i 0.146762 1.39635i
\(818\) 20.5667 + 22.8416i 0.719097 + 0.798638i
\(819\) −8.13834 + 9.03854i −0.284376 + 0.315832i
\(820\) 0.468177 + 4.45440i 0.0163494 + 0.155554i
\(821\) 4.40303 + 13.5511i 0.153667 + 0.472938i 0.998023 0.0628437i \(-0.0200170\pi\)
−0.844356 + 0.535782i \(0.820017\pi\)
\(822\) −6.64985 20.4661i −0.231940 0.713838i
\(823\) −1.95994 18.6476i −0.0683193 0.650014i −0.974077 0.226218i \(-0.927364\pi\)
0.905757 0.423797i \(-0.139303\pi\)
\(824\) 7.69529 8.54649i 0.268078 0.297731i
\(825\) 0.793285 + 0.881033i 0.0276187 + 0.0306736i
\(826\) −1.07512 + 10.2290i −0.0374081 + 0.355914i
\(827\) −48.6359 + 10.3379i −1.69123 + 0.359483i −0.950117 0.311892i \(-0.899037\pi\)
−0.741117 + 0.671375i \(0.765704\pi\)
\(828\) 2.23537 + 0.995252i 0.0776846 + 0.0345874i
\(829\) 8.80867 6.39987i 0.305938 0.222277i −0.424214 0.905562i \(-0.639449\pi\)
0.730152 + 0.683285i \(0.239449\pi\)
\(830\) 3.95763 1.76205i 0.137371 0.0611616i
\(831\) 12.8786 22.3063i 0.446753 0.773798i
\(832\) −2.50527 4.33926i −0.0868546 0.150437i
\(833\) 3.51033 + 2.55041i 0.121626 + 0.0883664i
\(834\) −12.5949 2.67712i −0.436125 0.0927011i
\(835\) 5.88057 18.0985i 0.203506 0.626326i
\(836\) 8.60822 0.297721
\(837\) 1.47174 + 5.36973i 0.0508708 + 0.185605i
\(838\) −14.1643 −0.489298
\(839\) 4.52885 13.9384i 0.156353 0.481205i −0.841942 0.539567i \(-0.818588\pi\)
0.998295 + 0.0583621i \(0.0185878\pi\)
\(840\) 2.37435 + 0.504683i 0.0819228 + 0.0174132i
\(841\) 21.7415 + 15.7961i 0.749708 + 0.544695i
\(842\) 8.67715 + 15.0293i 0.299034 + 0.517942i
\(843\) −12.1428 + 21.0319i −0.418220 + 0.724378i
\(844\) −1.13496 + 0.505319i −0.0390671 + 0.0173938i
\(845\) −9.79358 + 7.11545i −0.336909 + 0.244779i
\(846\) 10.7914 + 4.80463i 0.371015 + 0.165187i
\(847\) −22.7806 + 4.84217i −0.782752 + 0.166379i
\(848\) 0.293768 2.79502i 0.0100880 0.0959812i
\(849\) 7.06453 + 7.84596i 0.242454 + 0.269272i
\(850\) −2.62092 + 2.91083i −0.0898968 + 0.0998405i
\(851\) 2.41149 + 22.9438i 0.0826650 + 0.786505i
\(852\) 4.04058 + 12.4356i 0.138428 + 0.426037i
\(853\) −4.99111 15.3610i −0.170892 0.525952i 0.828530 0.559945i \(-0.189178\pi\)
−0.999422 + 0.0339927i \(0.989178\pi\)
\(854\) −3.93932 37.4801i −0.134801 1.28254i
\(855\) −4.85854 + 5.39595i −0.166158 + 0.184538i
\(856\) −10.8972 12.1026i −0.372458 0.413657i
\(857\) −0.895623 + 8.52128i −0.0305939 + 0.291081i 0.968518 + 0.248944i \(0.0800835\pi\)
−0.999112 + 0.0421376i \(0.986583\pi\)
\(858\) 5.81042 1.23504i 0.198365 0.0421637i
\(859\) −37.9451 16.8942i −1.29467 0.576424i −0.360336 0.932823i \(-0.617338\pi\)
−0.934334 + 0.356398i \(0.884005\pi\)
\(860\) −4.47150 + 3.24873i −0.152477 + 0.110781i
\(861\) −9.93219 + 4.42210i −0.338488 + 0.150705i
\(862\) −15.7213 + 27.2302i −0.535471 + 0.927463i
\(863\) 0.799072 + 1.38403i 0.0272007 + 0.0471130i 0.879305 0.476258i \(-0.158007\pi\)
−0.852105 + 0.523372i \(0.824674\pi\)
\(864\) −0.809017 0.587785i −0.0275233 0.0199969i
\(865\) −15.7795 3.35404i −0.536520 0.114041i
\(866\) 5.30958 16.3412i 0.180427 0.555297i
\(867\) 1.65787 0.0563041
\(868\) 8.56522 + 10.4545i 0.290722 + 0.354848i
\(869\) −7.26027 −0.246288
\(870\) 0.450571 1.38671i 0.0152758 0.0470140i
\(871\) 52.6957 + 11.2008i 1.78552 + 0.379525i
\(872\) 12.5251 + 9.10000i 0.424152 + 0.308165i
\(873\) −6.66110 11.5374i −0.225444 0.390481i
\(874\) −8.88351 + 15.3867i −0.300489 + 0.520463i
\(875\) −2.21753 + 0.987309i −0.0749663 + 0.0333772i
\(876\) −10.3854 + 7.54541i −0.350889 + 0.254936i
\(877\) 38.1797 + 16.9987i 1.28924 + 0.574005i 0.932827 0.360325i \(-0.117334\pi\)
0.356410 + 0.934330i \(0.384001\pi\)
\(878\) −26.5040 + 5.63361i −0.894468 + 0.190125i
\(879\) 1.84247 17.5299i 0.0621450 0.591270i
\(880\) −0.793285 0.881033i −0.0267416 0.0296996i
\(881\) −11.8394 + 13.1490i −0.398881 + 0.443002i −0.908807 0.417216i \(-0.863006\pi\)
0.509927 + 0.860218i \(0.329673\pi\)
\(882\) −0.115793 1.10170i −0.00389896 0.0370961i
\(883\) −2.68730 8.27066i −0.0904348 0.278330i 0.895602 0.444856i \(-0.146745\pi\)
−0.986037 + 0.166526i \(0.946745\pi\)
\(884\) 6.06471 + 18.6653i 0.203978 + 0.627780i
\(885\) 0.442910 + 4.21400i 0.0148882 + 0.141652i
\(886\) −14.4812 + 16.0830i −0.486504 + 0.540318i
\(887\) 33.2360 + 36.9123i 1.11596 + 1.23939i 0.968148 + 0.250378i \(0.0805548\pi\)
0.147807 + 0.989016i \(0.452779\pi\)
\(888\) 0.985522 9.37662i 0.0330720 0.314659i
\(889\) 27.2928 5.80126i 0.915370 0.194568i
\(890\) 3.22730 + 1.43689i 0.108179 + 0.0481646i
\(891\) 0.959127 0.696847i 0.0321320 0.0233452i
\(892\) 8.87546 3.95161i 0.297172 0.132310i
\(893\) −42.8856 + 74.2800i −1.43511 + 2.48568i
\(894\) −2.07963 3.60202i −0.0695532 0.120470i
\(895\) −2.73618 1.98795i −0.0914605 0.0664500i
\(896\) −2.37435 0.504683i −0.0793214 0.0168603i
\(897\) −3.78867 + 11.6603i −0.126500 + 0.389327i
\(898\) 14.0008 0.467214
\(899\) 6.78316 4.46033i 0.226231 0.148760i
\(900\) 1.00000 0.0333333
\(901\) −3.40169 + 10.4693i −0.113327 + 0.348784i
\(902\) 5.19395 + 1.10401i 0.172940 + 0.0367595i
\(903\) −10.8541 7.88595i −0.361201 0.262428i
\(904\) 1.19474 + 2.06936i 0.0397366 + 0.0688258i
\(905\) 1.50501 2.60675i 0.0500282 0.0866514i
\(906\) −0.522504 + 0.232634i −0.0173590 + 0.00772874i
\(907\) 10.9706 7.97058i 0.364272 0.264659i −0.390560 0.920577i \(-0.627719\pi\)
0.754832 + 0.655919i \(0.227719\pi\)
\(908\) 13.3823 + 5.95819i 0.444107 + 0.197729i
\(909\) −17.6921 + 3.76057i −0.586810 + 0.124730i
\(910\) −1.27133 + 12.0959i −0.0421443 + 0.400976i
\(911\) 0.322092 + 0.357720i 0.0106714 + 0.0118518i 0.748457 0.663183i \(-0.230795\pi\)
−0.737786 + 0.675035i \(0.764128\pi\)
\(912\) 4.85854 5.39595i 0.160882 0.178678i
\(913\) −0.536856 5.10784i −0.0177673 0.169045i
\(914\) 7.88150 + 24.2568i 0.260697 + 0.802342i
\(915\) −4.79766 14.7657i −0.158606 0.488138i
\(916\) −0.660642 6.28559i −0.0218282 0.207682i
\(917\) 25.6780 28.5183i 0.847962 0.941758i
\(918\) 2.62092 + 2.91083i 0.0865033 + 0.0960716i
\(919\) −0.182849 + 1.73969i −0.00603162 + 0.0573870i −0.997124 0.0757914i \(-0.975852\pi\)
0.991092 + 0.133178i \(0.0425183\pi\)
\(920\) 2.39345 0.508744i 0.0789097 0.0167728i
\(921\) −14.3412 6.38510i −0.472558 0.210396i
\(922\) −8.06073 + 5.85646i −0.265466 + 0.192872i
\(923\) −59.8516 + 26.6477i −1.97004 + 0.877118i
\(924\) 1.43889 2.49224i 0.0473361 0.0819885i
\(925\) 4.71413 + 8.16512i 0.155000 + 0.268467i
\(926\) 9.16661 + 6.65993i 0.301234 + 0.218859i
\(927\) 11.2491 + 2.39107i 0.369470 + 0.0785332i
\(928\) −0.450571 + 1.38671i −0.0147907 + 0.0455211i
\(929\) −21.6038 −0.708798 −0.354399 0.935094i \(-0.615314\pi\)
−0.354399 + 0.935094i \(0.615314\pi\)
\(930\) 4.34691 + 3.47913i 0.142541 + 0.114085i
\(931\) 8.04346 0.263614
\(932\) −0.0653714 + 0.201193i −0.00214131 + 0.00659028i
\(933\) −8.59404 1.82672i −0.281356 0.0598041i
\(934\) 1.75453 + 1.27474i 0.0574100 + 0.0417108i
\(935\) 2.32184 + 4.02154i 0.0759321 + 0.131518i
\(936\) 2.50527 4.33926i 0.0818873 0.141833i
\(937\) 51.3336 22.8552i 1.67700 0.746647i 0.677053 0.735934i \(-0.263257\pi\)
0.999943 0.0107124i \(-0.00340992\pi\)
\(938\) 21.1146 15.3407i 0.689417 0.500891i
\(939\) 8.25912 + 3.67720i 0.269526 + 0.120001i
\(940\) 11.5545 2.45598i 0.376866 0.0801053i
\(941\) −0.191849 + 1.82532i −0.00625410 + 0.0595038i −0.997204 0.0747298i \(-0.976191\pi\)
0.990950 + 0.134234i \(0.0428572\pi\)
\(942\) 5.60492 + 6.22490i 0.182618 + 0.202818i
\(943\) −7.33341 + 8.14458i −0.238809 + 0.265224i
\(944\) −0.442910 4.21400i −0.0144155 0.137154i
\(945\) 0.750106 + 2.30859i 0.0244009 + 0.0750984i
\(946\) 2.02486 + 6.23189i 0.0658340 + 0.202616i
\(947\) −2.53315 24.1013i −0.0823163 0.783187i −0.955340 0.295509i \(-0.904511\pi\)
0.873024 0.487678i \(-0.162156\pi\)
\(948\) −4.09775 + 4.55101i −0.133089 + 0.147810i
\(949\) −43.0388 47.7994i −1.39710 1.55163i
\(950\) −0.758978 + 7.22119i −0.0246245 + 0.234286i
\(951\) 26.2367 5.57678i 0.850782 0.180839i
\(952\) 8.68586 + 3.86720i 0.281510 + 0.125337i
\(953\) −18.8305 + 13.6811i −0.609979 + 0.443176i −0.849407 0.527738i \(-0.823040\pi\)
0.239428 + 0.970914i \(0.423040\pi\)
\(954\) 2.56744 1.14310i 0.0831239 0.0370091i
\(955\) 1.49938 2.59700i 0.0485187 0.0840369i
\(956\) −6.07130 10.5158i −0.196360 0.340105i
\(957\) −1.39848 1.01606i −0.0452065 0.0328444i
\(958\) −1.29964 0.276247i −0.0419895 0.00892514i
\(959\) 16.1418 49.6793i 0.521245 1.60423i
\(960\) −1.00000 −0.0322749
\(961\) 6.79125 + 30.2470i 0.219073 + 0.975709i
\(962\) 47.2407 1.52310
\(963\) 5.03252 15.4885i 0.162171 0.499110i
\(964\) −10.3660 2.20337i −0.333867 0.0709656i
\(965\) 18.7571 + 13.6278i 0.603811 + 0.438695i
\(966\) 2.96982 + 5.14388i 0.0955524 + 0.165502i
\(967\) 10.3302 17.8925i 0.332198 0.575383i −0.650745 0.759296i \(-0.725543\pi\)
0.982942 + 0.183913i \(0.0588766\pi\)
\(968\) 8.76499 3.90243i 0.281718 0.125429i
\(969\) −23.0089 + 16.7169i −0.739151 + 0.537025i
\(970\) −12.1704 5.41863i −0.390769 0.173982i
\(971\) 33.9090 7.20758i 1.08819 0.231302i 0.371318 0.928506i \(-0.378906\pi\)
0.716873 + 0.697204i \(0.245573\pi\)
\(972\) 0.104528 0.994522i 0.00335275 0.0318993i
\(973\) −20.9141 23.2275i −0.670477 0.744640i
\(974\) −18.7231 + 20.7941i −0.599928 + 0.666287i
\(975\) 0.523744 + 4.98309i 0.0167732 + 0.159587i
\(976\) 4.79766 + 14.7657i 0.153569 + 0.472638i
\(977\) 3.80299 + 11.7044i 0.121669 + 0.374457i 0.993279 0.115741i \(-0.0369243\pi\)
−0.871611 + 0.490198i \(0.836924\pi\)
\(978\) −1.89371 18.0175i −0.0605543 0.576136i
\(979\) 2.80246 3.11244i 0.0895669 0.0994741i
\(980\) −0.741240 0.823231i −0.0236780 0.0262971i
\(981\) −1.61829 + 15.3970i −0.0516681 + 0.491589i
\(982\) −18.3027 + 3.89037i −0.584064 + 0.124147i
\(983\) −14.4529 6.43483i −0.460975 0.205239i 0.163091 0.986611i \(-0.447854\pi\)
−0.624066 + 0.781372i \(0.714520\pi\)
\(984\) 3.62354 2.63265i 0.115514 0.0839259i
\(985\) −6.77549 + 3.01664i −0.215885 + 0.0961182i
\(986\) 2.85557 4.94600i 0.0909400 0.157513i
\(987\) 14.3369 + 24.8323i 0.456350 + 0.790421i
\(988\) 29.4332 + 21.3844i 0.936394 + 0.680330i
\(989\) −13.2288 2.81186i −0.420650 0.0894120i
\(990\) 0.366354 1.12752i 0.0116435 0.0358350i
\(991\) −37.9198 −1.20456 −0.602281 0.798284i \(-0.705741\pi\)
−0.602281 + 0.798284i \(0.705741\pi\)
\(992\) −4.34691 3.47913i −0.138015 0.110463i
\(993\) 27.5009 0.872714
\(994\) −9.80807 + 30.1861i −0.311093 + 0.957446i
\(995\) 2.79288 + 0.593646i 0.0885403 + 0.0188198i
\(996\) −3.50479 2.54638i −0.111054 0.0806852i
\(997\) 0.228319 + 0.395461i 0.00723095 + 0.0125244i 0.869618 0.493725i \(-0.164365\pi\)
−0.862387 + 0.506249i \(0.831032\pi\)
\(998\) −2.58054 + 4.46963i −0.0816856 + 0.141484i
\(999\) 8.61315 3.83482i 0.272508 0.121328i
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.h.691.2 24
31.7 even 15 inner 930.2.bg.h.751.2 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
930.2.bg.h.691.2 24 1.1 even 1 trivial
930.2.bg.h.751.2 yes 24 31.7 even 15 inner