Properties

Label 441.2.z.a.142.13
Level $441$
Weight $2$
Character 441.142
Analytic conductor $3.521$
Analytic rank $0$
Dimension $648$
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] = [441,2,Mod(4,441)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(441, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([14, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("441.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.z (of order \(21\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label 142.13
Character \(\chi\) \(=\) 441.142
Dual form 441.2.z.a.382.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.682865 + 1.73991i) q^{2} +(0.970846 + 1.43438i) q^{3} +(-1.09488 - 1.01590i) q^{4} +(-0.565392 + 0.272278i) q^{5} +(-3.15866 + 0.709696i) q^{6} +(-2.38327 - 1.14891i) q^{7} +(-0.852795 + 0.410684i) q^{8} +(-1.11491 + 2.78513i) q^{9} +O(q^{10})\) \(q+(-0.682865 + 1.73991i) q^{2} +(0.970846 + 1.43438i) q^{3} +(-1.09488 - 1.01590i) q^{4} +(-0.565392 + 0.272278i) q^{5} +(-3.15866 + 0.709696i) q^{6} +(-2.38327 - 1.14891i) q^{7} +(-0.852795 + 0.410684i) q^{8} +(-1.11491 + 2.78513i) q^{9} +(-0.0876540 - 1.16966i) q^{10} +(-1.43447 - 1.79877i) q^{11} +(0.394231 - 2.55677i) q^{12} +(-0.0553948 + 0.141144i) q^{13} +(3.62646 - 3.36213i) q^{14} +(-0.939461 - 0.546649i) q^{15} +(-0.355444 - 4.74306i) q^{16} +(-4.56665 + 4.23723i) q^{17} +(-4.08455 - 3.84172i) q^{18} +(1.98955 - 3.44601i) q^{19} +(0.895646 + 0.276270i) q^{20} +(-0.665808 - 4.53395i) q^{21} +(4.10926 - 1.26754i) q^{22} +(-1.14358 + 5.01037i) q^{23} +(-1.41701 - 0.824524i) q^{24} +(-2.87192 + 3.60127i) q^{25} +(-0.207750 - 0.192764i) q^{26} +(-5.07736 + 1.10472i) q^{27} +(1.44222 + 3.67910i) q^{28} +(4.55246 + 1.40425i) q^{29} +(1.59264 - 1.26129i) q^{30} +(-2.14880 + 3.72183i) q^{31} +(6.68627 + 2.06244i) q^{32} +(1.18748 - 3.80392i) q^{33} +(-4.25400 - 10.8390i) q^{34} +(1.66031 + 0.000673016i) q^{35} +(4.05012 - 1.91675i) q^{36} +(-2.69261 - 0.830560i) q^{37} +(4.63715 + 5.81481i) q^{38} +(-0.256234 + 0.0575714i) q^{39} +(0.370343 - 0.464395i) q^{40} +(7.50721 + 5.11833i) q^{41} +(8.34333 + 1.93763i) q^{42} +(6.56247 - 4.47422i) q^{43} +(-0.256798 + 3.42673i) q^{44} +(-0.127968 - 1.87826i) q^{45} +(-7.93668 - 5.41114i) q^{46} +(-1.56481 + 3.98706i) q^{47} +(6.45830 - 5.11463i) q^{48} +(4.35999 + 5.47636i) q^{49} +(-4.30476 - 7.45606i) q^{50} +(-10.5113 - 2.43663i) q^{51} +(0.204039 - 0.0982600i) q^{52} +(-7.82609 + 2.41403i) q^{53} +(1.54504 - 9.58853i) q^{54} +(1.30081 + 0.626436i) q^{55} +(2.50428 + 0.00101513i) q^{56} +(6.87445 - 0.491761i) q^{57} +(-5.55198 + 6.96196i) q^{58} +(8.62434 - 5.87998i) q^{59} +(0.473257 + 1.55292i) q^{60} +(2.24401 - 2.08214i) q^{61} +(-5.00832 - 6.28023i) q^{62} +(5.85703 - 5.35679i) q^{63} +(-2.22320 + 2.78780i) q^{64} +(-0.00711060 - 0.0948843i) q^{65} +(5.80760 + 4.66367i) q^{66} +(-0.672978 + 1.16563i) q^{67} +9.30456 q^{68} +(-8.29704 + 3.22396i) q^{69} +(-1.13494 + 2.88833i) q^{70} +(-0.851336 + 3.72995i) q^{71} +(-0.193017 - 2.83302i) q^{72} +(-8.10834 - 1.22214i) q^{73} +(3.28379 - 4.11774i) q^{74} +(-7.95379 - 0.623152i) q^{75} +(-5.67914 + 1.75178i) q^{76} +(1.35211 + 5.93506i) q^{77} +(0.0748041 - 0.485138i) q^{78} +(6.42322 + 11.1253i) q^{79} +(1.49240 + 2.58491i) q^{80} +(-6.51393 - 6.21037i) q^{81} +(-14.0319 + 9.56675i) q^{82} +(-2.57811 - 6.56892i) q^{83} +(-3.87707 + 5.64054i) q^{84} +(1.42824 - 3.63910i) q^{85} +(3.30346 + 14.4734i) q^{86} +(2.40551 + 7.89329i) q^{87} +(1.96204 + 0.944869i) q^{88} +(3.57244 + 9.10244i) q^{89} +(3.35539 + 1.05994i) q^{90} +(0.294183 - 0.272740i) q^{91} +(6.34213 - 4.32399i) q^{92} +(-7.42470 + 0.531122i) q^{93} +(-5.86858 - 5.44525i) q^{94} +(-0.186604 + 2.49006i) q^{95} +(3.53301 + 11.5930i) q^{96} +(6.19120 - 10.7235i) q^{97} +(-12.5057 + 3.84638i) q^{98} +(6.60914 - 1.98972i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 8 q^{2} - 13 q^{3} + 44 q^{4} + 3 q^{5} + 2 q^{6} - 7 q^{7} - 16 q^{8} - 39 q^{9} - 22 q^{10} - 5 q^{11} + 2 q^{12} - 4 q^{13} + 52 q^{14} - 4 q^{15} + 38 q^{16} - 37 q^{17} - 16 q^{18} - 14 q^{19} - 11 q^{20} - 6 q^{21} - q^{22} - 20 q^{23} - 26 q^{24} - 97 q^{25} - 44 q^{26} + 14 q^{27} - 22 q^{28} - 53 q^{29} - 9 q^{30} + 10 q^{31} - 10 q^{32} + 2 q^{33} - 7 q^{34} - 32 q^{35} - 22 q^{36} - 39 q^{37} + 59 q^{38} - 26 q^{39} - 19 q^{40} - 17 q^{41} - 83 q^{42} - q^{43} - 31 q^{44} + 81 q^{45} + 56 q^{46} + 50 q^{47} - 23 q^{48} - 19 q^{49} - 21 q^{50} - 30 q^{51} - 9 q^{52} + 50 q^{53} + 48 q^{54} + 20 q^{55} - 239 q^{56} + 33 q^{57} + 17 q^{58} - 37 q^{59} - 152 q^{60} - 105 q^{61} - 30 q^{62} + 6 q^{63} - 88 q^{64} - 5 q^{65} - 99 q^{66} + 13 q^{67} - 290 q^{68} + 64 q^{69} + 17 q^{70} - 19 q^{71} + 11 q^{72} - 40 q^{73} - 57 q^{74} + 69 q^{75} - 41 q^{76} + 19 q^{77} + 81 q^{78} + 13 q^{79} + 163 q^{80} - 179 q^{81} - 28 q^{82} + 73 q^{83} - 341 q^{84} - 10 q^{85} + 15 q^{86} + 13 q^{87} - 13 q^{88} - 104 q^{89} + 171 q^{90} - 49 q^{91} - 91 q^{92} - 275 q^{93} - 4 q^{94} - 29 q^{95} + 231 q^{96} - 11 q^{97} - 33 q^{98} + 62 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{4}{21}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.682865 + 1.73991i −0.482858 + 1.23030i 0.457223 + 0.889352i \(0.348844\pi\)
−0.940081 + 0.340951i \(0.889251\pi\)
\(3\) 0.970846 + 1.43438i 0.560518 + 0.828142i
\(4\) −1.09488 1.01590i −0.547441 0.507951i
\(5\) −0.565392 + 0.272278i −0.252851 + 0.121767i −0.556016 0.831171i \(-0.687671\pi\)
0.303165 + 0.952938i \(0.401957\pi\)
\(6\) −3.15866 + 0.709696i −1.28952 + 0.289732i
\(7\) −2.38327 1.14891i −0.900793 0.434249i
\(8\) −0.852795 + 0.410684i −0.301508 + 0.145199i
\(9\) −1.11491 + 2.78513i −0.371638 + 0.928378i
\(10\) −0.0876540 1.16966i −0.0277186 0.369879i
\(11\) −1.43447 1.79877i −0.432510 0.542351i 0.517042 0.855960i \(-0.327033\pi\)
−0.949552 + 0.313609i \(0.898462\pi\)
\(12\) 0.394231 2.55677i 0.113805 0.738075i
\(13\) −0.0553948 + 0.141144i −0.0153638 + 0.0391462i −0.938350 0.345687i \(-0.887646\pi\)
0.922986 + 0.384833i \(0.125741\pi\)
\(14\) 3.62646 3.36213i 0.969213 0.898567i
\(15\) −0.939461 0.546649i −0.242568 0.141144i
\(16\) −0.355444 4.74306i −0.0888609 1.18577i
\(17\) −4.56665 + 4.23723i −1.10758 + 1.02768i −0.108138 + 0.994136i \(0.534489\pi\)
−0.999437 + 0.0335440i \(0.989321\pi\)
\(18\) −4.08455 3.84172i −0.962737 0.905502i
\(19\) 1.98955 3.44601i 0.456435 0.790569i −0.542334 0.840163i \(-0.682459\pi\)
0.998769 + 0.0495939i \(0.0157927\pi\)
\(20\) 0.895646 + 0.276270i 0.200273 + 0.0617759i
\(21\) −0.665808 4.53395i −0.145291 0.989389i
\(22\) 4.10926 1.26754i 0.876097 0.270240i
\(23\) −1.14358 + 5.01037i −0.238454 + 1.04473i 0.703948 + 0.710251i \(0.251419\pi\)
−0.942402 + 0.334483i \(0.891438\pi\)
\(24\) −1.41701 0.824524i −0.289246 0.168305i
\(25\) −2.87192 + 3.60127i −0.574383 + 0.720254i
\(26\) −0.207750 0.192764i −0.0407432 0.0378041i
\(27\) −5.07736 + 1.10472i −0.977139 + 0.212603i
\(28\) 1.44222 + 3.67910i 0.272554 + 0.695284i
\(29\) 4.55246 + 1.40425i 0.845371 + 0.260762i 0.687036 0.726623i \(-0.258911\pi\)
0.158335 + 0.987386i \(0.449388\pi\)
\(30\) 1.59264 1.26129i 0.290776 0.230279i
\(31\) −2.14880 + 3.72183i −0.385936 + 0.668461i −0.991899 0.127032i \(-0.959455\pi\)
0.605962 + 0.795493i \(0.292788\pi\)
\(32\) 6.68627 + 2.06244i 1.18198 + 0.364592i
\(33\) 1.18748 3.80392i 0.206713 0.662178i
\(34\) −4.25400 10.8390i −0.729555 1.85888i
\(35\) 1.66031 0.000673016i 0.280643 0.000113760i
\(36\) 4.05012 1.91675i 0.675020 0.319458i
\(37\) −2.69261 0.830560i −0.442662 0.136543i 0.0654085 0.997859i \(-0.479165\pi\)
−0.508071 + 0.861315i \(0.669641\pi\)
\(38\) 4.63715 + 5.81481i 0.752246 + 0.943286i
\(39\) −0.256234 + 0.0575714i −0.0410303 + 0.00921880i
\(40\) 0.370343 0.464395i 0.0585564 0.0734273i
\(41\) 7.50721 + 5.11833i 1.17243 + 0.799349i 0.983191 0.182582i \(-0.0584455\pi\)
0.189239 + 0.981931i \(0.439398\pi\)
\(42\) 8.34333 + 1.93763i 1.28740 + 0.298982i
\(43\) 6.56247 4.47422i 1.00077 0.682311i 0.0521177 0.998641i \(-0.483403\pi\)
0.948649 + 0.316330i \(0.102451\pi\)
\(44\) −0.256798 + 3.42673i −0.0387138 + 0.516599i
\(45\) −0.127968 1.87826i −0.0190763 0.279994i
\(46\) −7.93668 5.41114i −1.17020 0.797829i
\(47\) −1.56481 + 3.98706i −0.228250 + 0.581573i −0.998415 0.0562720i \(-0.982079\pi\)
0.770165 + 0.637845i \(0.220174\pi\)
\(48\) 6.45830 5.11463i 0.932175 0.738233i
\(49\) 4.35999 + 5.47636i 0.622856 + 0.782337i
\(50\) −4.30476 7.45606i −0.608785 1.05445i
\(51\) −10.5113 2.43663i −1.47188 0.341196i
\(52\) 0.204039 0.0982600i 0.0282951 0.0136262i
\(53\) −7.82609 + 2.41403i −1.07500 + 0.331592i −0.781203 0.624277i \(-0.785394\pi\)
−0.293792 + 0.955869i \(0.594917\pi\)
\(54\) 1.54504 9.58853i 0.210253 1.30483i
\(55\) 1.30081 + 0.626436i 0.175401 + 0.0844686i
\(56\) 2.50428 + 0.00101513i 0.334649 + 0.000135652i
\(57\) 6.87445 0.491761i 0.910544 0.0651353i
\(58\) −5.55198 + 6.96196i −0.729011 + 0.914151i
\(59\) 8.62434 5.87998i 1.12279 0.765508i 0.148083 0.988975i \(-0.452690\pi\)
0.974711 + 0.223467i \(0.0717375\pi\)
\(60\) 0.473257 + 1.55292i 0.0610972 + 0.200481i
\(61\) 2.24401 2.08214i 0.287316 0.266591i −0.523326 0.852133i \(-0.675309\pi\)
0.810642 + 0.585542i \(0.199118\pi\)
\(62\) −5.00832 6.28023i −0.636057 0.797590i
\(63\) 5.85703 5.35679i 0.737916 0.674892i
\(64\) −2.22320 + 2.78780i −0.277899 + 0.348475i
\(65\) −0.00711060 0.0948843i −0.000881961 0.0117690i
\(66\) 5.80760 + 4.66367i 0.714866 + 0.574058i
\(67\) −0.672978 + 1.16563i −0.0822173 + 0.142405i −0.904202 0.427105i \(-0.859534\pi\)
0.821985 + 0.569510i \(0.192867\pi\)
\(68\) 9.30456 1.12834
\(69\) −8.29704 + 3.22396i −0.998846 + 0.388119i
\(70\) −1.13494 + 2.88833i −0.135651 + 0.345222i
\(71\) −0.851336 + 3.72995i −0.101035 + 0.442663i 0.898954 + 0.438042i \(0.144328\pi\)
−0.999989 + 0.00462099i \(0.998529\pi\)
\(72\) −0.193017 2.83302i −0.0227473 0.333875i
\(73\) −8.10834 1.22214i −0.949009 0.143040i −0.343744 0.939064i \(-0.611695\pi\)
−0.605266 + 0.796023i \(0.706933\pi\)
\(74\) 3.28379 4.11774i 0.381733 0.478677i
\(75\) −7.95379 0.623152i −0.918425 0.0719554i
\(76\) −5.67914 + 1.75178i −0.651442 + 0.200943i
\(77\) 1.35211 + 5.93506i 0.154087 + 0.676363i
\(78\) 0.0748041 0.485138i 0.00846990 0.0549310i
\(79\) 6.42322 + 11.1253i 0.722669 + 1.25170i 0.959926 + 0.280252i \(0.0904180\pi\)
−0.237258 + 0.971447i \(0.576249\pi\)
\(80\) 1.49240 + 2.58491i 0.166855 + 0.289002i
\(81\) −6.51393 6.21037i −0.723770 0.690041i
\(82\) −14.0319 + 9.56675i −1.54956 + 1.05647i
\(83\) −2.57811 6.56892i −0.282985 0.721033i −0.999719 0.0236871i \(-0.992459\pi\)
0.716735 0.697346i \(-0.245636\pi\)
\(84\) −3.87707 + 5.64054i −0.423023 + 0.615433i
\(85\) 1.42824 3.63910i 0.154914 0.394716i
\(86\) 3.30346 + 14.4734i 0.356221 + 1.56071i
\(87\) 2.40551 + 7.89329i 0.257898 + 0.846249i
\(88\) 1.96204 + 0.944869i 0.209154 + 0.100723i
\(89\) 3.57244 + 9.10244i 0.378678 + 0.964856i 0.985448 + 0.169978i \(0.0543698\pi\)
−0.606770 + 0.794878i \(0.707535\pi\)
\(90\) 3.35539 + 1.05994i 0.353689 + 0.111728i
\(91\) 0.294183 0.272740i 0.0308388 0.0285909i
\(92\) 6.34213 4.32399i 0.661213 0.450808i
\(93\) −7.42470 + 0.531122i −0.769905 + 0.0550748i
\(94\) −5.86858 5.44525i −0.605298 0.561634i
\(95\) −0.186604 + 2.49006i −0.0191452 + 0.255475i
\(96\) 3.53301 + 11.5930i 0.360586 + 1.18321i
\(97\) 6.19120 10.7235i 0.628621 1.08880i −0.359208 0.933258i \(-0.616953\pi\)
0.987829 0.155546i \(-0.0497136\pi\)
\(98\) −12.5057 + 3.84638i −1.26326 + 0.388543i
\(99\) 6.60914 1.98972i 0.664244 0.199975i
\(100\) 6.80295 1.02538i 0.680295 0.102538i
\(101\) −8.57506 + 4.12953i −0.853251 + 0.410904i −0.808783 0.588107i \(-0.799873\pi\)
−0.0444675 + 0.999011i \(0.514159\pi\)
\(102\) 11.4173 16.6249i 1.13048 1.64611i
\(103\) −4.21692 + 2.03076i −0.415506 + 0.200097i −0.629944 0.776640i \(-0.716922\pi\)
0.214438 + 0.976738i \(0.431208\pi\)
\(104\) −0.0107251 0.143116i −0.00105168 0.0140337i
\(105\) 1.61094 + 2.38217i 0.157212 + 0.232476i
\(106\) 1.14396 15.2651i 0.111112 1.48268i
\(107\) 2.83433 + 7.22177i 0.274005 + 0.698154i 0.999946 + 0.0103969i \(0.00330951\pi\)
−0.725941 + 0.687757i \(0.758595\pi\)
\(108\) 6.68140 + 3.94856i 0.642918 + 0.379951i
\(109\) −4.43982 + 11.3125i −0.425257 + 1.08354i 0.544347 + 0.838860i \(0.316777\pi\)
−0.969604 + 0.244678i \(0.921318\pi\)
\(110\) −1.97822 + 1.83552i −0.188616 + 0.175010i
\(111\) −1.42277 4.66858i −0.135043 0.443122i
\(112\) −4.60226 + 11.7124i −0.434872 + 1.10672i
\(113\) −17.8700 2.69347i −1.68107 0.253380i −0.762028 0.647544i \(-0.775796\pi\)
−0.919040 + 0.394163i \(0.871034\pi\)
\(114\) −3.83870 + 12.2967i −0.359527 + 1.15170i
\(115\) −0.717642 3.14420i −0.0669205 0.293198i
\(116\) −3.55783 6.16234i −0.330336 0.572159i
\(117\) −0.331343 0.311645i −0.0306327 0.0288116i
\(118\) 4.34138 + 19.0208i 0.399656 + 1.75101i
\(119\) 15.7518 4.85179i 1.44397 0.444763i
\(120\) 1.02567 + 0.0803574i 0.0936302 + 0.00733560i
\(121\) 1.26986 5.56362i 0.115442 0.505783i
\(122\) 2.09038 + 5.32620i 0.189254 + 0.482212i
\(123\) −0.0533020 + 15.7373i −0.00480608 + 1.41899i
\(124\) 6.13370 1.89200i 0.550823 0.169906i
\(125\) 1.34141 5.87711i 0.119980 0.525665i
\(126\) 5.32079 + 13.8487i 0.474013 + 1.23374i
\(127\) 4.28174 + 18.7595i 0.379943 + 1.66464i 0.697642 + 0.716446i \(0.254233\pi\)
−0.317699 + 0.948191i \(0.602910\pi\)
\(128\) 3.66476 + 6.34754i 0.323922 + 0.561049i
\(129\) 12.7889 + 5.06932i 1.12600 + 0.446329i
\(130\) 0.169946 + 0.0524214i 0.0149052 + 0.00459766i
\(131\) 0.556386 + 0.267941i 0.0486117 + 0.0234101i 0.458032 0.888936i \(-0.348555\pi\)
−0.409420 + 0.912346i \(0.634269\pi\)
\(132\) −5.16456 + 2.95848i −0.449517 + 0.257503i
\(133\) −8.70082 + 5.92696i −0.754457 + 0.513932i
\(134\) −1.56854 1.96689i −0.135501 0.169913i
\(135\) 2.56991 2.00706i 0.221182 0.172740i
\(136\) 2.15425 5.48894i 0.184725 0.470673i
\(137\) −13.1083 6.31261i −1.11992 0.539323i −0.220049 0.975489i \(-0.570622\pi\)
−0.899866 + 0.436166i \(0.856336\pi\)
\(138\) 0.0563513 16.6376i 0.00479694 1.41629i
\(139\) −0.355721 0.242526i −0.0301718 0.0205708i 0.548140 0.836386i \(-0.315336\pi\)
−0.578312 + 0.815816i \(0.696288\pi\)
\(140\) −1.81716 1.68745i −0.153578 0.142615i
\(141\) −7.23816 + 1.62629i −0.609563 + 0.136958i
\(142\) −5.90843 4.02830i −0.495825 0.338047i
\(143\) 0.333348 0.102824i 0.0278760 0.00859859i
\(144\) 13.6064 + 4.29816i 1.13386 + 0.358180i
\(145\) −2.95627 + 0.445586i −0.245505 + 0.0370039i
\(146\) 7.66331 13.2732i 0.634220 1.09850i
\(147\) −3.62232 + 11.5706i −0.298764 + 0.954327i
\(148\) 2.10432 + 3.64479i 0.172974 + 0.299600i
\(149\) −6.49081 8.13922i −0.531748 0.666791i 0.441309 0.897355i \(-0.354514\pi\)
−0.973057 + 0.230564i \(0.925943\pi\)
\(150\) 6.51559 13.4134i 0.531996 1.09520i
\(151\) −4.29892 + 18.8348i −0.349841 + 1.53275i 0.427699 + 0.903921i \(0.359324\pi\)
−0.777540 + 0.628833i \(0.783533\pi\)
\(152\) −0.281460 + 3.75582i −0.0228294 + 0.304637i
\(153\) −6.70983 17.4429i −0.542458 1.41017i
\(154\) −11.2498 1.70030i −0.906533 0.137014i
\(155\) 0.201540 2.68937i 0.0161881 0.216015i
\(156\) 0.339033 + 0.197275i 0.0271444 + 0.0157946i
\(157\) 10.0571 6.85678i 0.802640 0.547231i −0.0910863 0.995843i \(-0.529034\pi\)
0.893727 + 0.448612i \(0.148082\pi\)
\(158\) −23.7433 + 3.57873i −1.88891 + 0.284708i
\(159\) −11.0606 8.88196i −0.877160 0.704385i
\(160\) −4.34192 + 0.654440i −0.343259 + 0.0517380i
\(161\) 8.48196 10.6272i 0.668472 0.837541i
\(162\) 15.2536 7.09281i 1.19844 0.557264i
\(163\) −0.353131 + 0.240761i −0.0276594 + 0.0188578i −0.577071 0.816694i \(-0.695804\pi\)
0.549411 + 0.835552i \(0.314852\pi\)
\(164\) −3.01979 13.2306i −0.235806 1.03313i
\(165\) 0.364335 + 2.47403i 0.0283634 + 0.192603i
\(166\) 13.1898 1.02373
\(167\) 18.1959 16.8833i 1.40804 1.30647i 0.514502 0.857489i \(-0.327977\pi\)
0.893540 0.448983i \(-0.148213\pi\)
\(168\) 2.42982 + 3.59309i 0.187465 + 0.277213i
\(169\) 9.51282 + 8.82661i 0.731755 + 0.678970i
\(170\) 5.35641 + 4.97002i 0.410818 + 0.381183i
\(171\) 7.37941 + 9.38318i 0.564318 + 0.717550i
\(172\) −11.7305 1.76809i −0.894442 0.134815i
\(173\) 3.76407 1.16106i 0.286177 0.0882740i −0.148343 0.988936i \(-0.547394\pi\)
0.434520 + 0.900662i \(0.356918\pi\)
\(174\) −15.3763 1.20468i −1.16567 0.0913262i
\(175\) 10.9821 5.28322i 0.830170 0.399374i
\(176\) −8.02183 + 7.44317i −0.604668 + 0.561050i
\(177\) 16.8071 + 6.66207i 1.26330 + 0.500752i
\(178\) −18.2769 −1.36991
\(179\) 2.94976 2.73698i 0.220475 0.204571i −0.562200 0.827001i \(-0.690045\pi\)
0.782675 + 0.622430i \(0.213854\pi\)
\(180\) −1.76802 + 2.18648i −0.131780 + 0.162970i
\(181\) 9.06723 11.3699i 0.673962 0.845122i −0.320821 0.947140i \(-0.603959\pi\)
0.994783 + 0.102018i \(0.0325301\pi\)
\(182\) 0.273656 + 0.698097i 0.0202848 + 0.0517464i
\(183\) 5.16518 + 1.19734i 0.381821 + 0.0885098i
\(184\) −1.08244 4.74247i −0.0797983 0.349619i
\(185\) 1.74852 0.263547i 0.128554 0.0193764i
\(186\) 4.14596 13.2810i 0.303996 0.973810i
\(187\) 14.1726 + 2.13617i 1.03640 + 0.156212i
\(188\) 5.76374 2.77567i 0.420364 0.202437i
\(189\) 13.3700 + 3.20060i 0.972522 + 0.232810i
\(190\) −4.20506 2.02505i −0.305067 0.146912i
\(191\) −18.1484 12.3734i −1.31317 0.895305i −0.314625 0.949216i \(-0.601879\pi\)
−0.998546 + 0.0539115i \(0.982831\pi\)
\(192\) −6.15715 0.482392i −0.444354 0.0348136i
\(193\) −0.597072 + 7.96738i −0.0429782 + 0.573504i 0.933597 + 0.358326i \(0.116652\pi\)
−0.976575 + 0.215178i \(0.930967\pi\)
\(194\) 14.4301 + 18.0948i 1.03602 + 1.29913i
\(195\) 0.129197 0.102317i 0.00925201 0.00732710i
\(196\) 0.789767 10.4253i 0.0564120 0.744664i
\(197\) −6.05865 −0.431661 −0.215830 0.976431i \(-0.569246\pi\)
−0.215830 + 0.976431i \(0.569246\pi\)
\(198\) −1.05121 + 12.8580i −0.0747063 + 0.913780i
\(199\) −6.21506 4.23736i −0.440574 0.300378i 0.322643 0.946521i \(-0.395429\pi\)
−0.763217 + 0.646143i \(0.776381\pi\)
\(200\) 0.970170 4.25059i 0.0686014 0.300562i
\(201\) −2.32532 + 0.166341i −0.164016 + 0.0117328i
\(202\) −1.32941 17.7398i −0.0935370 1.24817i
\(203\) −9.23640 8.57710i −0.648268 0.601994i
\(204\) 9.03330 + 13.3463i 0.632457 + 0.934429i
\(205\) −5.63813 0.849811i −0.393784 0.0593534i
\(206\) −0.653759 8.72381i −0.0455496 0.607817i
\(207\) −12.6795 8.77117i −0.881289 0.609638i
\(208\) 0.689143 + 0.212573i 0.0477835 + 0.0147393i
\(209\) −9.05256 + 1.36445i −0.626179 + 0.0943812i
\(210\) −5.24482 + 1.17619i −0.361927 + 0.0811647i
\(211\) 13.4830 + 2.03224i 0.928210 + 0.139905i 0.595711 0.803199i \(-0.296870\pi\)
0.332499 + 0.943104i \(0.392108\pi\)
\(212\) 11.0211 + 5.30746i 0.756929 + 0.364518i
\(213\) −6.17670 + 2.40006i −0.423220 + 0.164450i
\(214\) −14.5007 −0.991247
\(215\) −2.49214 + 4.31651i −0.169962 + 0.294383i
\(216\) 3.87626 3.02729i 0.263746 0.205981i
\(217\) 9.39725 6.40136i 0.637927 0.434553i
\(218\) −16.6509 15.4498i −1.12774 1.04639i
\(219\) −6.11894 12.8170i −0.413480 0.866091i
\(220\) −0.787834 2.00737i −0.0531157 0.135337i
\(221\) −0.345090 0.879274i −0.0232133 0.0591464i
\(222\) 9.09447 + 0.712520i 0.610381 + 0.0478212i
\(223\) 4.26391 + 3.95633i 0.285533 + 0.264935i 0.809915 0.586547i \(-0.199513\pi\)
−0.524382 + 0.851483i \(0.675704\pi\)
\(224\) −13.5656 12.5973i −0.906393 0.841694i
\(225\) −6.82807 12.0138i −0.455205 0.800918i
\(226\) 16.8892 29.2529i 1.12345 1.94588i
\(227\) 25.3619 1.68333 0.841665 0.539999i \(-0.181576\pi\)
0.841665 + 0.539999i \(0.181576\pi\)
\(228\) −8.02630 6.44535i −0.531554 0.426854i
\(229\) −4.30817 2.07471i −0.284692 0.137101i 0.286088 0.958203i \(-0.407645\pi\)
−0.570780 + 0.821103i \(0.693359\pi\)
\(230\) 5.96067 + 0.898427i 0.393035 + 0.0592405i
\(231\) −7.20047 + 7.70147i −0.473756 + 0.506720i
\(232\) −4.45902 + 0.672089i −0.292749 + 0.0441248i
\(233\) −1.54306 0.475972i −0.101089 0.0311819i 0.243798 0.969826i \(-0.421607\pi\)
−0.344887 + 0.938644i \(0.612083\pi\)
\(234\) 0.768497 0.363697i 0.0502382 0.0237756i
\(235\) −0.200862 2.68032i −0.0131028 0.174845i
\(236\) −15.4161 2.32361i −1.00350 0.151254i
\(237\) −9.72205 + 20.0144i −0.631515 + 1.30007i
\(238\) −2.31466 + 30.7198i −0.150037 + 1.99127i
\(239\) 0.138619 + 1.84974i 0.00896650 + 0.119650i 0.999891 0.0147707i \(-0.00470182\pi\)
−0.990924 + 0.134420i \(0.957083\pi\)
\(240\) −2.25887 + 4.65023i −0.145809 + 0.300171i
\(241\) 5.71438 25.0363i 0.368095 1.61273i −0.363911 0.931434i \(-0.618559\pi\)
0.732006 0.681298i \(-0.238584\pi\)
\(242\) 8.81305 + 6.00864i 0.566525 + 0.386250i
\(243\) 2.58403 15.3728i 0.165766 0.986165i
\(244\) −4.57218 −0.292704
\(245\) −3.95620 1.90916i −0.252752 0.121972i
\(246\) −27.3452 10.8392i −1.74346 0.691083i
\(247\) 0.376171 + 0.471704i 0.0239352 + 0.0300138i
\(248\) 0.303988 4.05644i 0.0193033 0.257584i
\(249\) 6.91941 10.0754i 0.438500 0.638504i
\(250\) 9.30965 + 6.34721i 0.588794 + 0.401433i
\(251\) −19.1591 9.22652i −1.20931 0.582373i −0.282994 0.959122i \(-0.591328\pi\)
−0.926315 + 0.376749i \(0.877042\pi\)
\(252\) −11.8547 0.0851099i −0.746778 0.00536142i
\(253\) 10.6530 5.13020i 0.669746 0.322533i
\(254\) −35.5637 5.36037i −2.23147 0.336340i
\(255\) 6.60647 1.48436i 0.413713 0.0929542i
\(256\) −20.5985 + 3.10472i −1.28741 + 0.194045i
\(257\) 2.61787 + 11.4697i 0.163299 + 0.715457i 0.988575 + 0.150729i \(0.0481620\pi\)
−0.825277 + 0.564729i \(0.808981\pi\)
\(258\) −17.5533 + 18.7899i −1.09282 + 1.16981i
\(259\) 5.46298 + 5.07303i 0.339453 + 0.315223i
\(260\) −0.0886079 + 0.111111i −0.00549523 + 0.00689080i
\(261\) −8.98662 + 11.1136i −0.556258 + 0.687914i
\(262\) −0.846131 + 0.785094i −0.0522741 + 0.0485033i
\(263\) 3.55951 0.219489 0.109744 0.993960i \(-0.464997\pi\)
0.109744 + 0.993960i \(0.464997\pi\)
\(264\) 0.549535 + 3.73164i 0.0338215 + 0.229667i
\(265\) 3.76752 3.49575i 0.231437 0.214742i
\(266\) −4.37089 19.1860i −0.267997 1.17637i
\(267\) −9.58809 + 13.9613i −0.586782 + 0.854419i
\(268\) 1.92100 0.592550i 0.117344 0.0361957i
\(269\) 0.974529 + 0.146887i 0.0594181 + 0.00895583i 0.178684 0.983907i \(-0.442816\pi\)
−0.119266 + 0.992862i \(0.538054\pi\)
\(270\) 1.73720 + 5.84196i 0.105723 + 0.355530i
\(271\) −5.53089 5.13192i −0.335978 0.311742i 0.494083 0.869415i \(-0.335504\pi\)
−0.830061 + 0.557673i \(0.811694\pi\)
\(272\) 21.7207 + 20.1538i 1.31701 + 1.22201i
\(273\) 0.676821 + 0.157183i 0.0409630 + 0.00951313i
\(274\) 19.9346 18.4966i 1.20429 1.11742i
\(275\) 10.5976 0.639057
\(276\) 12.3595 + 4.89912i 0.743955 + 0.294892i
\(277\) 4.78324 + 20.9568i 0.287397 + 1.25917i 0.888083 + 0.459684i \(0.152037\pi\)
−0.600685 + 0.799486i \(0.705106\pi\)
\(278\) 0.664883 0.453310i 0.0398771 0.0271877i
\(279\) −7.97007 10.1342i −0.477156 0.606720i
\(280\) −1.41618 + 0.681289i −0.0846329 + 0.0407148i
\(281\) −7.31402 + 1.10241i −0.436318 + 0.0657643i −0.363529 0.931583i \(-0.618428\pi\)
−0.0727892 + 0.997347i \(0.523190\pi\)
\(282\) 2.11309 13.7043i 0.125832 0.816079i
\(283\) 23.2510 3.50453i 1.38213 0.208323i 0.584463 0.811420i \(-0.301305\pi\)
0.797667 + 0.603098i \(0.206067\pi\)
\(284\) 4.72138 3.21898i 0.280162 0.191011i
\(285\) −3.75287 + 2.14980i −0.222301 + 0.127343i
\(286\) −0.0487266 + 0.650211i −0.00288126 + 0.0384478i
\(287\) −12.0112 20.8235i −0.709000 1.22917i
\(288\) −13.1988 + 16.3227i −0.777747 + 0.961825i
\(289\) 1.62975 21.7475i 0.0958675 1.27926i
\(290\) 1.24345 5.44793i 0.0730181 0.319913i
\(291\) 21.3923 1.53029i 1.25404 0.0897069i
\(292\) 7.63611 + 9.57538i 0.446869 + 0.560356i
\(293\) 9.03184 + 15.6436i 0.527646 + 0.913910i 0.999481 + 0.0322226i \(0.0102586\pi\)
−0.471835 + 0.881687i \(0.656408\pi\)
\(294\) −17.6583 14.2037i −1.02985 0.828375i
\(295\) −3.27514 + 5.67272i −0.190686 + 0.330278i
\(296\) 2.63734 0.397515i 0.153292 0.0231051i
\(297\) 9.27049 + 7.54833i 0.537928 + 0.437999i
\(298\) 18.5939 5.73545i 1.07711 0.332246i
\(299\) −0.643833 0.438958i −0.0372338 0.0253856i
\(300\) 8.07540 + 8.76255i 0.466234 + 0.505906i
\(301\) −20.7807 + 3.12356i −1.19778 + 0.180039i
\(302\) −29.8353 20.3414i −1.71683 1.17051i
\(303\) −14.2484 8.29079i −0.818549 0.476294i
\(304\) −17.0518 8.21172i −0.977989 0.470975i
\(305\) −0.701825 + 1.78822i −0.0401864 + 0.102393i
\(306\) 34.9310 + 0.236623i 1.99687 + 0.0135269i
\(307\) 17.9175 + 22.4679i 1.02261 + 1.28231i 0.958720 + 0.284351i \(0.0917781\pi\)
0.0638863 + 0.997957i \(0.479650\pi\)
\(308\) 4.54904 7.87180i 0.259206 0.448538i
\(309\) −7.00688 4.07713i −0.398607 0.231940i
\(310\) 4.54164 + 2.18714i 0.257948 + 0.124221i
\(311\) 19.4146 + 5.98861i 1.10090 + 0.339583i 0.791389 0.611313i \(-0.209358\pi\)
0.309511 + 0.950896i \(0.399835\pi\)
\(312\) 0.194871 0.154328i 0.0110324 0.00873709i
\(313\) 11.6206 + 20.1274i 0.656833 + 1.13767i 0.981431 + 0.191816i \(0.0614376\pi\)
−0.324598 + 0.945852i \(0.605229\pi\)
\(314\) 5.06258 + 22.1806i 0.285698 + 1.25173i
\(315\) −1.85298 + 4.62343i −0.104403 + 0.260501i
\(316\) 4.26959 18.7063i 0.240183 1.05231i
\(317\) 3.05518 0.942398i 0.171596 0.0529303i −0.207767 0.978178i \(-0.566619\pi\)
0.379363 + 0.925248i \(0.376143\pi\)
\(318\) 23.0067 13.1792i 1.29015 0.739054i
\(319\) −4.00446 10.2032i −0.224207 0.571270i
\(320\) 0.497919 2.18153i 0.0278345 0.121951i
\(321\) −7.60708 + 11.0767i −0.424586 + 0.618244i
\(322\) 12.6984 + 22.0148i 0.707652 + 1.22684i
\(323\) 5.51594 + 24.1669i 0.306915 + 1.34468i
\(324\) 0.822856 + 13.4171i 0.0457142 + 0.745397i
\(325\) −0.349207 0.604844i −0.0193705 0.0335507i
\(326\) −0.177762 0.778824i −0.00984530 0.0431351i
\(327\) −20.5368 + 4.61427i −1.13569 + 0.255169i
\(328\) −8.50413 1.28179i −0.469562 0.0707751i
\(329\) 8.31016 7.70443i 0.458154 0.424759i
\(330\) −4.55339 1.05552i −0.250656 0.0581044i
\(331\) 22.6285 20.9961i 1.24377 1.15405i 0.261781 0.965127i \(-0.415690\pi\)
0.981992 0.188925i \(-0.0605003\pi\)
\(332\) −3.85065 + 9.81131i −0.211332 + 0.538465i
\(333\) 5.31525 6.57327i 0.291274 0.360213i
\(334\) 16.9502 + 43.1883i 0.927472 + 2.36316i
\(335\) 0.0631199 0.842277i 0.00344861 0.0460185i
\(336\) −21.2682 + 4.76953i −1.16027 + 0.260199i
\(337\) −0.0525174 0.700795i −0.00286080 0.0381748i 0.995591 0.0938038i \(-0.0299026\pi\)
−0.998452 + 0.0556290i \(0.982284\pi\)
\(338\) −21.8535 + 10.5241i −1.18867 + 0.572435i
\(339\) −13.4856 28.2474i −0.732435 1.53419i
\(340\) −5.26072 + 2.53343i −0.285303 + 0.137395i
\(341\) 9.77714 1.47367i 0.529462 0.0798035i
\(342\) −21.3650 + 6.43207i −1.15529 + 0.347807i
\(343\) −4.09919 18.0609i −0.221335 0.975198i
\(344\) −3.75895 + 6.51069i −0.202669 + 0.351033i
\(345\) 3.81326 4.08191i 0.205299 0.219762i
\(346\) −0.550207 + 7.34200i −0.0295793 + 0.394708i
\(347\) 13.5548 + 12.5770i 0.727661 + 0.675171i 0.954314 0.298805i \(-0.0965880\pi\)
−0.226653 + 0.973975i \(0.572778\pi\)
\(348\) 5.38506 11.0860i 0.288669 0.594271i
\(349\) −17.4578 + 11.9025i −0.934496 + 0.637128i −0.931841 0.362868i \(-0.881798\pi\)
−0.00265528 + 0.999996i \(0.500845\pi\)
\(350\) 1.69304 + 22.7156i 0.0904969 + 1.21420i
\(351\) 0.125335 0.777833i 0.00668990 0.0415177i
\(352\) −5.88142 14.9856i −0.313481 0.798736i
\(353\) −8.70130 4.19033i −0.463123 0.223028i 0.187747 0.982217i \(-0.439882\pi\)
−0.650870 + 0.759189i \(0.725596\pi\)
\(354\) −23.0684 + 24.6935i −1.22607 + 1.31244i
\(355\) −0.534246 2.34068i −0.0283548 0.124231i
\(356\) 5.33578 13.5953i 0.282796 0.720552i
\(357\) 22.2519 + 17.8838i 1.17770 + 0.946510i
\(358\) 2.74781 + 7.00130i 0.145226 + 0.370030i
\(359\) 16.5860 11.3081i 0.875375 0.596821i −0.0400998 0.999196i \(-0.512768\pi\)
0.915475 + 0.402375i \(0.131815\pi\)
\(360\) 0.880502 + 1.54922i 0.0464065 + 0.0816508i
\(361\) 1.58334 + 2.74243i 0.0833339 + 0.144339i
\(362\) 13.5910 + 23.5403i 0.714327 + 1.23725i
\(363\) 9.21320 3.57995i 0.483568 0.187899i
\(364\) −0.599173 0.000242878i −0.0314052 1.27303e-5i
\(365\) 4.91715 1.51674i 0.257376 0.0793898i
\(366\) −5.61038 + 8.16933i −0.293259 + 0.427018i
\(367\) −2.37496 + 2.97810i −0.123972 + 0.155456i −0.839944 0.542673i \(-0.817412\pi\)
0.715972 + 0.698129i \(0.245984\pi\)
\(368\) 24.1710 + 3.64319i 1.26000 + 0.189914i
\(369\) −22.6251 + 15.2021i −1.17782 + 0.791389i
\(370\) −0.735456 + 3.22224i −0.0382345 + 0.167516i
\(371\) 21.4252 + 3.23821i 1.11234 + 0.168120i
\(372\) 8.66873 + 6.96125i 0.449453 + 0.360924i
\(373\) −26.9487 −1.39535 −0.697675 0.716414i \(-0.745782\pi\)
−0.697675 + 0.716414i \(0.745782\pi\)
\(374\) −13.3947 + 23.2003i −0.692623 + 1.19966i
\(375\) 9.73234 3.78167i 0.502576 0.195285i
\(376\) −0.302965 4.04279i −0.0156242 0.208491i
\(377\) −0.450383 + 0.564763i −0.0231959 + 0.0290868i
\(378\) −14.6986 + 21.0770i −0.756017 + 1.08408i
\(379\) 8.03763 + 10.0789i 0.412865 + 0.517717i 0.944168 0.329466i \(-0.106869\pi\)
−0.531302 + 0.847182i \(0.678297\pi\)
\(380\) 2.73397 2.53675i 0.140250 0.130133i
\(381\) −22.7514 + 24.3543i −1.16559 + 1.24771i
\(382\) 33.9214 23.1272i 1.73557 1.18329i
\(383\) 10.0572 12.6113i 0.513899 0.644409i −0.455402 0.890286i \(-0.650505\pi\)
0.969301 + 0.245877i \(0.0790760\pi\)
\(384\) −5.54690 + 11.4192i −0.283064 + 0.582731i
\(385\) −2.38046 2.98749i −0.121320 0.152256i
\(386\) −13.4548 6.47949i −0.684832 0.329798i
\(387\) 5.14469 + 23.2657i 0.261519 + 1.18266i
\(388\) −17.6726 + 5.45128i −0.897192 + 0.276747i
\(389\) −21.2663 + 10.2413i −1.07825 + 0.519256i −0.886756 0.462238i \(-0.847047\pi\)
−0.191491 + 0.981494i \(0.561332\pi\)
\(390\) 0.0897990 + 0.294661i 0.00454715 + 0.0149207i
\(391\) −16.0077 27.7262i −0.809547 1.40218i
\(392\) −5.96723 2.87963i −0.301391 0.145443i
\(393\) 0.155835 + 1.05820i 0.00786081 + 0.0533792i
\(394\) 4.13724 10.5415i 0.208431 0.531073i
\(395\) −6.66083 4.54128i −0.335143 0.228496i
\(396\) −9.25760 4.53573i −0.465212 0.227929i
\(397\) 0.853863 11.3940i 0.0428542 0.571849i −0.933907 0.357517i \(-0.883623\pi\)
0.976761 0.214332i \(-0.0687575\pi\)
\(398\) 11.6167 7.92011i 0.582291 0.396999i
\(399\) −16.9487 6.72616i −0.848496 0.336729i
\(400\) 18.1019 + 12.3416i 0.905093 + 0.617082i
\(401\) −15.1963 + 19.0555i −0.758866 + 0.951588i −0.999820 0.0189485i \(-0.993968\pi\)
0.240954 + 0.970536i \(0.422540\pi\)
\(402\) 1.29846 4.15944i 0.0647614 0.207454i
\(403\) −0.406281 0.509460i −0.0202383 0.0253780i
\(404\) 13.5839 + 4.19007i 0.675824 + 0.208464i
\(405\) 5.37388 + 1.73769i 0.267030 + 0.0863466i
\(406\) 21.2306 10.2135i 1.05366 0.506888i
\(407\) 2.36849 + 6.03481i 0.117402 + 0.299135i
\(408\) 9.96470 2.23890i 0.493326 0.110842i
\(409\) 14.9913 + 4.62421i 0.741273 + 0.228652i 0.642316 0.766440i \(-0.277973\pi\)
0.0989560 + 0.995092i \(0.468450\pi\)
\(410\) 5.32868 9.22954i 0.263165 0.455814i
\(411\) −3.67141 24.9309i −0.181097 1.22975i
\(412\) 6.68009 + 2.06054i 0.329104 + 0.101515i
\(413\) −27.3098 + 4.10496i −1.34383 + 0.201992i
\(414\) 23.9195 16.0718i 1.17558 0.789884i
\(415\) 3.24622 + 3.01205i 0.159351 + 0.147856i
\(416\) −0.661485 + 0.829476i −0.0324320 + 0.0406684i
\(417\) 0.00252565 0.745696i 0.000123682 0.0365169i
\(418\) 3.80765 16.6824i 0.186238 0.815962i
\(419\) −11.0919 + 3.42139i −0.541874 + 0.167146i −0.553596 0.832785i \(-0.686745\pi\)
0.0117223 + 0.999931i \(0.496269\pi\)
\(420\) 0.656267 4.24476i 0.0320225 0.207123i
\(421\) −32.4913 10.0222i −1.58353 0.488453i −0.626737 0.779231i \(-0.715610\pi\)
−0.956791 + 0.290778i \(0.906086\pi\)
\(422\) −12.7430 + 22.0715i −0.620320 + 1.07443i
\(423\) −9.35987 8.80343i −0.455092 0.428037i
\(424\) 5.68264 5.27272i 0.275973 0.256066i
\(425\) −2.14438 28.6147i −0.104018 1.38802i
\(426\) 0.0419505 12.3858i 0.00203251 0.600095i
\(427\) −7.74030 + 2.38413i −0.374579 + 0.115376i
\(428\) 4.23335 10.7864i 0.204626 0.521380i
\(429\) 0.471119 + 0.378322i 0.0227458 + 0.0182656i
\(430\) −5.80854 7.28368i −0.280113 0.351250i
\(431\) 0.814313 + 10.8663i 0.0392241 + 0.523409i 0.981863 + 0.189594i \(0.0607171\pi\)
−0.942639 + 0.333815i \(0.891664\pi\)
\(432\) 7.04447 + 23.6896i 0.338927 + 1.13977i
\(433\) 8.63886 4.16026i 0.415157 0.199929i −0.214633 0.976695i \(-0.568855\pi\)
0.629790 + 0.776766i \(0.283141\pi\)
\(434\) 4.72074 + 20.7216i 0.226603 + 0.994671i
\(435\) −3.50923 3.80783i −0.168255 0.182572i
\(436\) 16.3534 7.87540i 0.783188 0.377163i
\(437\) 14.9906 + 13.9092i 0.717096 + 0.665367i
\(438\) 26.4788 1.89415i 1.26521 0.0905059i
\(439\) −5.99388 + 15.2722i −0.286072 + 0.728901i 0.713528 + 0.700627i \(0.247096\pi\)
−0.999600 + 0.0282737i \(0.990999\pi\)
\(440\) −1.36659 −0.0651496
\(441\) −20.1134 + 6.03748i −0.957781 + 0.287499i
\(442\) 1.76551 0.0839767
\(443\) 3.43650 8.75607i 0.163273 0.416013i −0.825700 0.564110i \(-0.809219\pi\)
0.988973 + 0.148097i \(0.0473146\pi\)
\(444\) −3.18506 + 6.55694i −0.151156 + 0.311179i
\(445\) −4.49823 4.17375i −0.213236 0.197855i
\(446\) −9.79534 + 4.71719i −0.463823 + 0.223365i
\(447\) 5.37319 17.2122i 0.254143 0.814111i
\(448\) 8.50143 4.08983i 0.401655 0.193226i
\(449\) 23.9538 11.5356i 1.13045 0.544397i 0.227345 0.973814i \(-0.426995\pi\)
0.903106 + 0.429418i \(0.141281\pi\)
\(450\) 25.5656 3.67645i 1.20517 0.173310i
\(451\) −1.56218 20.8459i −0.0735604 0.981595i
\(452\) 16.8293 + 21.1032i 0.791581 + 0.992612i
\(453\) −31.1899 + 12.1194i −1.46543 + 0.569419i
\(454\) −17.3188 + 44.1275i −0.812810 + 2.07101i
\(455\) −0.0920675 + 0.234305i −0.00431619 + 0.0109844i
\(456\) −5.66054 + 3.24260i −0.265079 + 0.151849i
\(457\) 1.90964 + 25.4823i 0.0893290 + 1.19201i 0.844159 + 0.536093i \(0.180100\pi\)
−0.754830 + 0.655920i \(0.772281\pi\)
\(458\) 6.55171 6.07909i 0.306141 0.284057i
\(459\) 18.5056 26.5588i 0.863766 1.23966i
\(460\) −2.40846 + 4.17158i −0.112295 + 0.194501i
\(461\) −6.40150 1.97460i −0.298148 0.0919663i 0.142073 0.989856i \(-0.454623\pi\)
−0.440220 + 0.897890i \(0.645100\pi\)
\(462\) −8.48293 17.7872i −0.394662 0.827537i
\(463\) −13.8859 + 4.28325i −0.645335 + 0.199059i −0.600110 0.799917i \(-0.704877\pi\)
−0.0452247 + 0.998977i \(0.514400\pi\)
\(464\) 5.04230 22.0917i 0.234083 1.02558i
\(465\) 4.05325 2.32188i 0.187965 0.107674i
\(466\) 1.88185 2.35977i 0.0871751 0.109314i
\(467\) −17.5503 16.2843i −0.812132 0.753548i 0.160217 0.987082i \(-0.448781\pi\)
−0.972349 + 0.233534i \(0.924971\pi\)
\(468\) 0.0461810 + 0.677827i 0.00213472 + 0.0313326i
\(469\) 2.94310 2.00483i 0.135900 0.0925743i
\(470\) 4.80067 + 1.48081i 0.221439 + 0.0683047i
\(471\) 19.5991 + 7.76879i 0.903079 + 0.357967i
\(472\) −4.93998 + 8.55630i −0.227381 + 0.393836i
\(473\) −17.4618 5.38625i −0.802894 0.247660i
\(474\) −28.1844 30.5826i −1.29455 1.40471i
\(475\) 6.69617 + 17.0616i 0.307242 + 0.782839i
\(476\) −22.1753 10.6901i −1.01640 0.489982i
\(477\) 2.00203 24.4881i 0.0916667 1.12123i
\(478\) −3.31304 1.02194i −0.151535 0.0467423i
\(479\) −25.5668 32.0598i −1.16818 1.46485i −0.857613 0.514295i \(-0.828054\pi\)
−0.310564 0.950553i \(-0.600518\pi\)
\(480\) −5.15406 5.59263i −0.235250 0.255267i
\(481\) 0.266385 0.334036i 0.0121461 0.0152307i
\(482\) 39.6588 + 27.0389i 1.80641 + 1.23159i
\(483\) 23.4782 + 1.84901i 1.06829 + 0.0841328i
\(484\) −7.04244 + 4.80145i −0.320111 + 0.218248i
\(485\) −0.580684 + 7.74870i −0.0263675 + 0.351850i
\(486\) 24.9827 + 14.9935i 1.13324 + 0.680120i
\(487\) 5.11962 + 3.49050i 0.231992 + 0.158169i 0.673737 0.738971i \(-0.264688\pi\)
−0.441745 + 0.897141i \(0.645640\pi\)
\(488\) −1.05858 + 2.69722i −0.0479197 + 0.122097i
\(489\) −0.688180 0.272784i −0.0311206 0.0123357i
\(490\) 6.02331 5.57974i 0.272106 0.252067i
\(491\) −0.480040 0.831454i −0.0216639 0.0375230i 0.854990 0.518644i \(-0.173563\pi\)
−0.876654 + 0.481121i \(0.840230\pi\)
\(492\) 16.0460 17.1764i 0.723408 0.774371i
\(493\) −26.7396 + 12.8771i −1.20429 + 0.579957i
\(494\) −1.07760 + 0.332395i −0.0484834 + 0.0149551i
\(495\) −3.19500 + 2.92450i −0.143604 + 0.131447i
\(496\) 18.4167 + 8.86900i 0.826933 + 0.398230i
\(497\) 6.31436 7.91138i 0.283238 0.354874i
\(498\) 12.8053 + 18.9193i 0.573820 + 0.847794i
\(499\) −10.2855 + 12.8977i −0.460444 + 0.577379i −0.956802 0.290739i \(-0.906099\pi\)
0.496358 + 0.868118i \(0.334670\pi\)
\(500\) −7.43926 + 5.07200i −0.332694 + 0.226827i
\(501\) 41.8826 + 9.70880i 1.87118 + 0.433757i
\(502\) 29.1364 27.0346i 1.30042 1.20661i
\(503\) −19.8733 24.9203i −0.886104 1.11114i −0.993145 0.116885i \(-0.962709\pi\)
0.107041 0.994255i \(-0.465862\pi\)
\(504\) −2.79489 + 6.97363i −0.124494 + 0.310630i
\(505\) 3.72389 4.66961i 0.165711 0.207795i
\(506\) 1.65155 + 22.0384i 0.0734205 + 0.979728i
\(507\) −3.42526 + 22.2143i −0.152121 + 0.986573i
\(508\) 14.3698 24.8893i 0.637558 1.10428i
\(509\) 22.6788 1.00522 0.502611 0.864513i \(-0.332373\pi\)
0.502611 + 0.864513i \(0.332373\pi\)
\(510\) −1.92867 + 12.5083i −0.0854029 + 0.553876i
\(511\) 17.9203 + 12.2285i 0.792746 + 0.540956i
\(512\) 5.40210 23.6682i 0.238742 1.04600i
\(513\) −6.29481 + 19.6945i −0.277923 + 0.869535i
\(514\) −21.7438 3.27736i −0.959079 0.144558i
\(515\) 1.83128 2.29636i 0.0806959 0.101190i
\(516\) −8.85239 18.5426i −0.389705 0.816291i
\(517\) 9.41650 2.90461i 0.414137 0.127744i
\(518\) −12.5571 + 6.04091i −0.551727 + 0.265422i
\(519\) 5.31975 + 4.27191i 0.233511 + 0.187516i
\(520\) 0.0450314 + 0.0779966i 0.00197476 + 0.00342038i
\(521\) 3.84035 + 6.65168i 0.168249 + 0.291415i 0.937804 0.347165i \(-0.112856\pi\)
−0.769556 + 0.638580i \(0.779522\pi\)
\(522\) −13.2000 23.2250i −0.577749 1.01653i
\(523\) −21.3455 + 14.5531i −0.933374 + 0.636363i −0.931542 0.363635i \(-0.881536\pi\)
−0.00183207 + 0.999998i \(0.500583\pi\)
\(524\) −0.336975 0.858598i −0.0147208 0.0375080i
\(525\) 18.2401 + 10.6234i 0.796064 + 0.463642i
\(526\) −2.43066 + 6.19322i −0.105982 + 0.270037i
\(527\) −5.95745 26.1013i −0.259511 1.13699i
\(528\) −18.4643 4.28021i −0.803557 0.186272i
\(529\) −3.07372 1.48023i −0.133640 0.0643577i
\(530\) 3.50958 + 8.94227i 0.152447 + 0.388427i
\(531\) 6.76111 + 30.5756i 0.293407 + 1.32687i
\(532\) 15.5476 + 2.34987i 0.674073 + 0.101880i
\(533\) −1.13828 + 0.776066i −0.0493044 + 0.0336152i
\(534\) −17.7441 26.2161i −0.767862 1.13448i
\(535\) −3.56884 3.31140i −0.154294 0.143164i
\(536\) 0.0952053 1.27043i 0.00411224 0.0548741i
\(537\) 6.78964 + 1.57390i 0.292994 + 0.0679189i
\(538\) −0.921041 + 1.59529i −0.0397089 + 0.0687778i
\(539\) 3.59643 15.6983i 0.154909 0.676175i
\(540\) −4.85272 0.413285i −0.208828 0.0177850i
\(541\) 22.4540 3.38440i 0.965374 0.145507i 0.352608 0.935771i \(-0.385295\pi\)
0.612766 + 0.790264i \(0.290057\pi\)
\(542\) 12.7059 6.11885i 0.545766 0.262827i
\(543\) 25.1118 + 1.96742i 1.07765 + 0.0844300i
\(544\) −39.2729 + 18.9128i −1.68381 + 0.810881i
\(545\) −0.569904 7.60485i −0.0244120 0.325756i
\(546\) −0.735661 + 1.07027i −0.0314834 + 0.0458035i
\(547\) 2.25984 30.1554i 0.0966236 1.28935i −0.712482 0.701690i \(-0.752429\pi\)
0.809106 0.587663i \(-0.199952\pi\)
\(548\) 7.93902 + 20.2283i 0.339138 + 0.864109i
\(549\) 3.29715 + 8.57128i 0.140719 + 0.365813i
\(550\) −7.23670 + 18.4388i −0.308574 + 0.786234i
\(551\) 13.8964 12.8940i 0.592007 0.549303i
\(552\) 5.75164 6.15684i 0.244806 0.262052i
\(553\) −2.52622 33.8945i −0.107426 1.44134i
\(554\) −39.7292 5.98821i −1.68793 0.254415i
\(555\) 2.07558 + 2.25219i 0.0881033 + 0.0956001i
\(556\) 0.143089 + 0.626915i 0.00606834 + 0.0265871i
\(557\) 0.398432 + 0.690104i 0.0168821 + 0.0292406i 0.874343 0.485308i \(-0.161293\pi\)
−0.857461 + 0.514549i \(0.827959\pi\)
\(558\) 23.0751 6.94691i 0.976848 0.294086i
\(559\) 0.267980 + 1.17410i 0.0113344 + 0.0496591i
\(560\) −0.586954 7.87519i −0.0248033 0.332788i
\(561\) 10.6953 + 22.4028i 0.451556 + 0.945847i
\(562\) 3.07639 13.4785i 0.129770 0.568558i
\(563\) 7.78815 + 19.8439i 0.328231 + 0.836319i 0.995782 + 0.0917549i \(0.0292476\pi\)
−0.667550 + 0.744565i \(0.732657\pi\)
\(564\) 9.57709 + 5.57267i 0.403268 + 0.234652i
\(565\) 10.8369 3.34275i 0.455913 0.140631i
\(566\) −9.77974 + 42.8479i −0.411073 + 1.80103i
\(567\) 8.38929 + 22.2850i 0.352317 + 0.935881i
\(568\) −0.805816 3.53051i −0.0338113 0.148137i
\(569\) 5.17585 + 8.96484i 0.216983 + 0.375826i 0.953884 0.300175i \(-0.0970450\pi\)
−0.736901 + 0.676000i \(0.763712\pi\)
\(570\) −1.17777 7.99768i −0.0493312 0.334986i
\(571\) −39.5115 12.1877i −1.65351 0.510039i −0.678951 0.734184i \(-0.737565\pi\)
−0.974556 + 0.224144i \(0.928041\pi\)
\(572\) −0.469436 0.226069i −0.0196281 0.00945240i
\(573\) 0.128855 38.0444i 0.00538301 1.58933i
\(574\) 44.4331 6.67880i 1.85460 0.278768i
\(575\) −14.7594 18.5077i −0.615510 0.771825i
\(576\) −5.28572 9.30005i −0.220238 0.387502i
\(577\) −1.89758 + 4.83495i −0.0789972 + 0.201282i −0.964916 0.262559i \(-0.915434\pi\)
0.885919 + 0.463840i \(0.153529\pi\)
\(578\) 36.7257 + 17.6862i 1.52759 + 0.735648i
\(579\) −12.0079 + 6.87867i −0.499033 + 0.285868i
\(580\) 3.68944 + 2.51542i 0.153196 + 0.104447i
\(581\) −1.40278 + 18.6176i −0.0581973 + 0.772387i
\(582\) −11.9455 + 38.2656i −0.495156 + 1.58616i
\(583\) 15.5686 + 10.6145i 0.644786 + 0.439608i
\(584\) 7.41666 2.28774i 0.306904 0.0946672i
\(585\) 0.272193 + 0.0859840i 0.0112538 + 0.00355500i
\(586\) −33.3860 + 5.03213i −1.37916 + 0.207875i
\(587\) 12.8310 22.2240i 0.529593 0.917281i −0.469812 0.882767i \(-0.655678\pi\)
0.999404 0.0345146i \(-0.0109885\pi\)
\(588\) 15.7206 8.98852i 0.648307 0.370681i
\(589\) 8.55032 + 14.8096i 0.352310 + 0.610218i
\(590\) −7.63354 9.57216i −0.314268 0.394080i
\(591\) −5.88202 8.69043i −0.241954 0.357476i
\(592\) −2.98233 + 13.0664i −0.122573 + 0.537027i
\(593\) −0.192758 + 2.57218i −0.00791563 + 0.105627i −0.999762 0.0218118i \(-0.993057\pi\)
0.991846 + 0.127439i \(0.0406756\pi\)
\(594\) −19.4639 + 10.9753i −0.798614 + 0.450323i
\(595\) −7.58490 + 7.03204i −0.310951 + 0.288286i
\(596\) −1.16198 + 15.5055i −0.0475965 + 0.635131i
\(597\) 0.0441276 13.0286i 0.00180602 0.533225i
\(598\) 1.20340 0.820463i 0.0492106 0.0335512i
\(599\) 18.3985 2.77312i 0.751741 0.113307i 0.238016 0.971261i \(-0.423503\pi\)
0.513726 + 0.857955i \(0.328265\pi\)
\(600\) 7.03887 2.73508i 0.287361 0.111659i
\(601\) −44.7682 + 6.74772i −1.82613 + 0.275245i −0.970282 0.241977i \(-0.922204\pi\)
−0.855851 + 0.517222i \(0.826966\pi\)
\(602\) 8.75565 38.2895i 0.356854 1.56056i
\(603\) −2.49613 3.17391i −0.101650 0.129252i
\(604\) 23.8411 16.2546i 0.970082 0.661391i
\(605\) 0.796885 + 3.49138i 0.0323980 + 0.141945i
\(606\) 24.1550 19.1295i 0.981229 0.777081i
\(607\) −38.5931 −1.56645 −0.783223 0.621741i \(-0.786426\pi\)
−0.783223 + 0.621741i \(0.786426\pi\)
\(608\) 20.4099 18.9376i 0.827731 0.768022i
\(609\) 3.33573 21.5756i 0.135170 0.874287i
\(610\) −2.63210 2.44223i −0.106570 0.0988829i
\(611\) −0.476066 0.441725i −0.0192596 0.0178703i
\(612\) −10.3738 + 25.9144i −0.419336 + 1.04753i
\(613\) −11.1469 1.68013i −0.450220 0.0678598i −0.0799814 0.996796i \(-0.525486\pi\)
−0.370239 + 0.928937i \(0.620724\pi\)
\(614\) −51.3273 + 15.8324i −2.07140 + 0.638943i
\(615\) −4.25480 8.91228i −0.171570 0.359378i
\(616\) −3.59051 4.50610i −0.144666 0.181556i
\(617\) −3.47494 + 3.22428i −0.139896 + 0.129804i −0.747017 0.664805i \(-0.768515\pi\)
0.607121 + 0.794609i \(0.292324\pi\)
\(618\) 11.8786 9.40722i 0.477827 0.378414i
\(619\) 17.3987 0.699312 0.349656 0.936878i \(-0.386298\pi\)
0.349656 + 0.936878i \(0.386298\pi\)
\(620\) −2.95280 + 2.73980i −0.118587 + 0.110033i
\(621\) 0.271333 26.7028i 0.0108882 1.07155i
\(622\) −23.6772 + 29.6902i −0.949368 + 1.19047i
\(623\) 1.94381 25.7980i 0.0778772 1.03358i
\(624\) 0.364142 + 1.19487i 0.0145773 + 0.0478331i
\(625\) −4.28309 18.7654i −0.171324 0.750617i
\(626\) −42.9552 + 6.47445i −1.71683 + 0.258771i
\(627\) −10.7458 11.6602i −0.429146 0.465662i
\(628\) −17.9771 2.70961i −0.717365 0.108125i
\(629\) 15.8155 7.61633i 0.630604 0.303683i
\(630\) −6.77903 6.38119i −0.270083 0.254233i
\(631\) 29.8226 + 14.3618i 1.18722 + 0.571735i 0.920007 0.391903i \(-0.128183\pi\)
0.267213 + 0.963638i \(0.413897\pi\)
\(632\) −10.0467 6.84972i −0.399636 0.272467i
\(633\) 10.1749 + 21.3128i 0.404418 + 0.847109i
\(634\) −0.446586 + 5.95927i −0.0177362 + 0.236673i
\(635\) −7.52867 9.44066i −0.298766 0.374641i
\(636\) 3.08682 + 20.9612i 0.122400 + 0.831164i
\(637\) −1.01447 + 0.312023i −0.0401949 + 0.0123628i
\(638\) 20.4872 0.811095
\(639\) −9.43923 6.52966i −0.373410 0.258309i
\(640\) −3.80032 2.59102i −0.150221 0.102419i
\(641\) −7.94367 + 34.8035i −0.313756 + 1.37466i 0.534544 + 0.845140i \(0.320483\pi\)
−0.848300 + 0.529515i \(0.822374\pi\)
\(642\) −14.0779 20.7996i −0.555612 0.820893i
\(643\) 0.645320 + 8.61120i 0.0254490 + 0.339593i 0.995366 + 0.0961575i \(0.0306553\pi\)
−0.969917 + 0.243435i \(0.921726\pi\)
\(644\) −20.0829 + 3.01869i −0.791379 + 0.118953i
\(645\) −8.61101 + 0.615984i −0.339058 + 0.0242543i
\(646\) −45.8149 6.90549i −1.80257 0.271693i
\(647\) 0.799031 + 10.6623i 0.0314131 + 0.419179i 0.990636 + 0.136529i \(0.0435946\pi\)
−0.959223 + 0.282650i \(0.908786\pi\)
\(648\) 8.10555 + 2.62100i 0.318416 + 0.102963i
\(649\) −22.9482 7.07857i −0.900794 0.277858i
\(650\) 1.29084 0.194562i 0.0506308 0.00763136i
\(651\) 18.3053 + 7.26453i 0.717441 + 0.284719i
\(652\) 0.631227 + 0.0951421i 0.0247207 + 0.00372605i
\(653\) −35.6086 17.1482i −1.39347 0.671062i −0.421647 0.906760i \(-0.638548\pi\)
−0.971826 + 0.235698i \(0.924262\pi\)
\(654\) 5.99544 38.8831i 0.234440 1.52045i
\(655\) −0.387531 −0.0151421
\(656\) 21.6082 37.4265i 0.843658 1.46126i
\(657\) 12.4439 21.2202i 0.485484 0.827880i
\(658\) 7.73031 + 19.7200i 0.301359 + 0.768766i
\(659\) 15.3865 + 14.2765i 0.599371 + 0.556135i 0.920422 0.390927i \(-0.127846\pi\)
−0.321051 + 0.947062i \(0.604036\pi\)
\(660\) 2.11447 3.07890i 0.0823057 0.119846i
\(661\) 4.03752 + 10.2874i 0.157041 + 0.400135i 0.987641 0.156736i \(-0.0500971\pi\)
−0.830599 + 0.556871i \(0.812002\pi\)
\(662\) 21.0792 + 53.7090i 0.819268 + 2.08746i
\(663\) 0.926188 1.34863i 0.0359702 0.0523765i
\(664\) 4.89635 + 4.54315i 0.190015 + 0.176308i
\(665\) 3.30559 5.72010i 0.128185 0.221816i
\(666\) 7.80731 + 13.7367i 0.302527 + 0.532287i
\(667\) −12.2419 + 21.2036i −0.474009 + 0.821008i
\(668\) −37.0742 −1.43444
\(669\) −1.53530 + 9.95707i −0.0593580 + 0.384963i
\(670\) 1.42238 + 0.684984i 0.0549515 + 0.0264632i
\(671\) −6.96428 1.04970i −0.268853 0.0405231i
\(672\) 4.89923 31.6884i 0.188992 1.22241i
\(673\) −6.33819 + 0.955329i −0.244319 + 0.0368252i −0.270060 0.962843i \(-0.587044\pi\)
0.0257409 + 0.999669i \(0.491806\pi\)
\(674\) 1.25518 + 0.387173i 0.0483479 + 0.0149133i
\(675\) 10.6034 21.4576i 0.408124 0.825904i
\(676\) −1.44845 19.3282i −0.0557095 0.743392i
\(677\) 0.753981 + 0.113644i 0.0289778 + 0.00436771i 0.163515 0.986541i \(-0.447717\pi\)
−0.134537 + 0.990909i \(0.542955\pi\)
\(678\) 58.3568 4.17452i 2.24118 0.160322i
\(679\) −27.0757 + 18.4438i −1.03907 + 0.707808i
\(680\) 0.276524 + 3.68996i 0.0106042 + 0.141504i
\(681\) 24.6225 + 36.3788i 0.943538 + 1.39404i
\(682\) −4.11242 + 18.0177i −0.157473 + 0.689932i
\(683\) −30.7727 20.9805i −1.17748 0.802796i −0.193509 0.981098i \(-0.561987\pi\)
−0.983976 + 0.178303i \(0.942939\pi\)
\(684\) 1.45281 17.7702i 0.0555495 0.679462i
\(685\) 9.13010 0.348843
\(686\) 34.2236 + 5.20095i 1.30666 + 0.198573i
\(687\) −1.20665 8.19380i −0.0460365 0.312613i
\(688\) −23.5541 29.5359i −0.897991 1.12604i
\(689\) 0.0927998 1.23833i 0.00353539 0.0471765i
\(690\) 4.49821 + 9.42213i 0.171244 + 0.358694i
\(691\) −32.0907 21.8791i −1.22079 0.832320i −0.230736 0.973016i \(-0.574113\pi\)
−0.990053 + 0.140697i \(0.955066\pi\)
\(692\) −5.30074 2.55270i −0.201504 0.0970392i
\(693\) −18.0374 2.85129i −0.685185 0.108311i
\(694\) −31.1390 + 14.9958i −1.18202 + 0.569231i
\(695\) 0.267156 + 0.0402673i 0.0101338 + 0.00152743i
\(696\) −5.29305 5.74345i −0.200633 0.217705i
\(697\) −55.9704 + 8.43618i −2.12003 + 0.319543i
\(698\) −8.78803 38.5029i −0.332632 1.45736i
\(699\) −0.815350 2.67544i −0.0308394 0.101194i
\(700\) −17.3914 5.37225i −0.657332 0.203052i
\(701\) −16.9120 + 21.2070i −0.638758 + 0.800978i −0.990847 0.134989i \(-0.956900\pi\)
0.352089 + 0.935967i \(0.385472\pi\)
\(702\) 1.26777 + 0.749227i 0.0478490 + 0.0282777i
\(703\) −8.21921 + 7.62631i −0.309993 + 0.287632i
\(704\) 8.20374 0.309190
\(705\) 3.64960 2.89029i 0.137452 0.108855i
\(706\) 13.2326 12.2781i 0.498016 0.462091i
\(707\) 25.1812 + 0.0102073i 0.947037 + 0.000383887i
\(708\) −11.6337 24.3685i −0.437223 0.915825i
\(709\) −7.28039 + 2.24570i −0.273421 + 0.0843391i −0.428433 0.903573i \(-0.640934\pi\)
0.155013 + 0.987912i \(0.450458\pi\)
\(710\) 4.43740 + 0.668830i 0.166533 + 0.0251008i
\(711\) −38.1469 + 5.48571i −1.43062 + 0.205730i
\(712\) −6.78479 6.29536i −0.254271 0.235929i
\(713\) −16.1904 15.0225i −0.606336 0.562598i
\(714\) −46.3112 + 26.5041i −1.73315 + 0.991893i
\(715\) −0.160475 + 0.148899i −0.00600144 + 0.00556853i
\(716\) −6.01014 −0.224609
\(717\) −2.51866 + 1.99464i −0.0940610 + 0.0744914i
\(718\) 8.34916 + 36.5801i 0.311588 + 1.36516i
\(719\) −10.3103 + 7.02945i −0.384509 + 0.262154i −0.740113 0.672483i \(-0.765228\pi\)
0.355603 + 0.934637i \(0.384275\pi\)
\(720\) −8.86322 + 1.27457i −0.330313 + 0.0475006i
\(721\) 12.3833 + 0.00501963i 0.461177 + 0.000186941i
\(722\) −5.85280 + 0.882168i −0.217819 + 0.0328309i
\(723\) 41.4595 16.1098i 1.54189 0.599130i
\(724\) −21.4783 + 3.23733i −0.798235 + 0.120315i
\(725\) −18.1314 + 12.3618i −0.673382 + 0.459104i
\(726\) −0.0625736 + 18.4748i −0.00232232 + 0.685663i
\(727\) −0.398294 + 5.31486i −0.0147719 + 0.197117i 0.984935 + 0.172923i \(0.0553211\pi\)
−0.999707 + 0.0241945i \(0.992298\pi\)
\(728\) −0.138868 + 0.353408i −0.00514678 + 0.0130982i
\(729\) 24.5592 11.2181i 0.909600 0.415486i
\(730\) −0.718756 + 9.59114i −0.0266024 + 0.354984i
\(731\) −11.0102 + 48.2389i −0.407227 + 1.78418i
\(732\) −4.43888 6.55826i −0.164066 0.242400i
\(733\) 25.4037 + 31.8553i 0.938308 + 1.17660i 0.984094 + 0.177649i \(0.0568493\pi\)
−0.0457862 + 0.998951i \(0.514579\pi\)
\(734\) −3.55986 6.16586i −0.131397 0.227586i
\(735\) −1.10240 7.52821i −0.0406625 0.277682i
\(736\) −17.9799 + 31.1421i −0.662748 + 1.14791i
\(737\) 3.06208 0.461534i 0.112793 0.0170008i
\(738\) −11.0004 49.7467i −0.404929 1.83120i
\(739\) 1.68372 0.519358i 0.0619365 0.0191049i −0.263632 0.964623i \(-0.584920\pi\)
0.325569 + 0.945518i \(0.394444\pi\)
\(740\) −2.18217 1.48778i −0.0802180 0.0546917i
\(741\) −0.311400 + 0.997526i −0.0114396 + 0.0366450i
\(742\) −20.2647 + 35.0667i −0.743942 + 1.28734i
\(743\) 24.5405 + 16.7314i 0.900303 + 0.613816i 0.922525 0.385937i \(-0.126122\pi\)
−0.0222220 + 0.999753i \(0.507074\pi\)
\(744\) 6.11362 3.50214i 0.224136 0.128395i
\(745\) 5.88599 + 2.83454i 0.215646 + 0.103850i
\(746\) 18.4023 46.8883i 0.673757 1.71670i
\(747\) 21.1697 + 0.143404i 0.774559 + 0.00524688i
\(748\) −13.3472 16.7368i −0.488020 0.611958i
\(749\) 1.54220 20.4679i 0.0563507 0.747879i
\(750\) −0.0660995 + 19.5158i −0.00241361 + 0.712615i
\(751\) 13.7228 + 6.60857i 0.500753 + 0.241150i 0.667170 0.744905i \(-0.267505\pi\)
−0.166417 + 0.986055i \(0.553220\pi\)
\(752\) 19.4671 + 6.00480i 0.709892 + 0.218973i
\(753\) −5.36614 36.4390i −0.195553 1.32791i
\(754\) −0.675086 1.16928i −0.0245852 0.0425828i
\(755\) −2.69774 11.8196i −0.0981807 0.430158i
\(756\) −11.3870 17.0869i −0.414143 0.621443i
\(757\) −8.87208 + 38.8711i −0.322461 + 1.41279i 0.510698 + 0.859760i \(0.329387\pi\)
−0.833159 + 0.553034i \(0.813470\pi\)
\(758\) −23.0249 + 7.10225i −0.836304 + 0.257965i
\(759\) 17.7011 + 10.2998i 0.642508 + 0.373859i
\(760\) −0.863493 2.20015i −0.0313222 0.0798077i
\(761\) 7.25537 31.7878i 0.263007 1.15231i −0.654964 0.755660i \(-0.727316\pi\)
0.917971 0.396648i \(-0.129827\pi\)
\(762\) −26.8381 56.2162i −0.972242 2.03650i
\(763\) 23.5784 21.8597i 0.853594 0.791376i
\(764\) 7.30022 + 31.9843i 0.264113 + 1.15715i
\(765\) 8.54301 + 8.03513i 0.308873 + 0.290511i
\(766\) 15.0749 + 26.1105i 0.544678 + 0.943409i
\(767\) 0.352178 + 1.54299i 0.0127164 + 0.0557142i
\(768\) −24.4513 26.5319i −0.882312 0.957389i
\(769\) 28.1192 + 4.23829i 1.01400 + 0.152837i 0.634962 0.772543i \(-0.281016\pi\)
0.379042 + 0.925380i \(0.376254\pi\)
\(770\) 6.82349 2.10174i 0.245902 0.0757415i
\(771\) −13.9103 + 14.8903i −0.500969 + 0.536261i
\(772\) 8.74780 8.11677i 0.314840 0.292129i
\(773\) −7.13525 + 18.1803i −0.256637 + 0.653901i −0.999886 0.0151145i \(-0.995189\pi\)
0.743249 + 0.669015i \(0.233284\pi\)
\(774\) −43.9934 6.93603i −1.58131 0.249311i
\(775\) −7.23215 18.4272i −0.259786 0.661925i
\(776\) −0.875860 + 11.6875i −0.0314416 + 0.419558i
\(777\) −1.97296 + 12.7611i −0.0707794 + 0.457804i
\(778\) −3.29697 43.9950i −0.118202 1.57730i
\(779\) 32.5738 15.6867i 1.16708 0.562035i
\(780\) −0.245400 0.0192263i −0.00878674 0.000688410i
\(781\) 7.93056 3.81915i 0.283778 0.136660i
\(782\) 59.1723 8.91879i 2.11600 0.318935i
\(783\) −24.6658 2.10068i −0.881483 0.0750722i
\(784\) 24.4250 22.6263i 0.872321 0.808080i
\(785\) −3.81922 + 6.61509i −0.136314 + 0.236103i
\(786\) −1.94759 0.451470i −0.0694682 0.0161034i
\(787\) 2.49559 33.3013i 0.0889580 1.18706i −0.756855 0.653583i \(-0.773265\pi\)
0.845813 0.533479i \(-0.179116\pi\)
\(788\) 6.63351 + 6.15499i 0.236309 + 0.219263i
\(789\) 3.45573 + 5.10570i 0.123027 + 0.181768i
\(790\) 12.4499 8.48817i 0.442946 0.301996i
\(791\) 39.4946 + 26.9504i 1.40426 + 0.958246i
\(792\) −4.81909 + 4.41110i −0.171239 + 0.156741i
\(793\) 0.169574 + 0.432068i 0.00602175 + 0.0153432i
\(794\) 19.2415 + 9.26621i 0.682855 + 0.328846i
\(795\) 8.67193 + 2.01024i 0.307562 + 0.0712957i
\(796\) 2.50002 + 10.9533i 0.0886108 + 0.388229i
\(797\) −6.07601 + 15.4814i −0.215223 + 0.548380i −0.997188 0.0749430i \(-0.976123\pi\)
0.781965 + 0.623323i \(0.214218\pi\)
\(798\) 23.2766 24.8962i 0.823982 0.881315i
\(799\) −9.74818 24.8380i −0.344866 0.878704i
\(800\) −26.6298 + 18.1559i −0.941506 + 0.641908i
\(801\) −29.3345 0.198713i −1.03648 0.00702116i
\(802\) −22.7779 39.4525i −0.804317 1.39312i
\(803\) 9.43286 + 16.3382i 0.332878 + 0.576562i
\(804\) 2.71494 + 2.18018i 0.0957485 + 0.0768889i
\(805\) −1.90207 + 8.31799i −0.0670393 + 0.293171i
\(806\) 1.16385 0.359000i 0.0409949 0.0126452i
\(807\) 0.735426 + 1.54045i 0.0258882 + 0.0542265i
\(808\) 5.61683 7.04329i 0.197600 0.247782i
\(809\) 50.4846 + 7.60933i 1.77494 + 0.267530i 0.953203 0.302332i \(-0.0977652\pi\)
0.821741 + 0.569862i \(0.193003\pi\)
\(810\) −6.69306 + 8.16346i −0.235170 + 0.286835i
\(811\) −4.75960 + 20.8532i −0.167132 + 0.732254i 0.820002 + 0.572361i \(0.193972\pi\)
−0.987134 + 0.159894i \(0.948885\pi\)
\(812\) 1.39928 + 18.7742i 0.0491050 + 0.658845i
\(813\) 1.99149 12.9157i 0.0698448 0.452974i
\(814\) −12.1174 −0.424714
\(815\) 0.134104 0.232274i 0.00469745 0.00813622i
\(816\) −7.82090 + 50.7220i −0.273786 + 1.77563i
\(817\) −2.36180 31.5160i −0.0826289 1.10261i
\(818\) −18.2827 + 22.9258i −0.639241 + 0.801583i
\(819\) 0.431628 + 1.12342i 0.0150823 + 0.0392555i
\(820\) 5.30976 + 6.65823i 0.185425 + 0.232516i
\(821\) 33.7919 31.3543i 1.17934 1.09427i 0.185596 0.982626i \(-0.440579\pi\)
0.993748 0.111645i \(-0.0356119\pi\)
\(822\) 45.8846 + 10.6365i 1.60041 + 0.370990i
\(823\) 34.2081 23.3227i 1.19242 0.812978i 0.206215 0.978507i \(-0.433885\pi\)
0.986205 + 0.165528i \(0.0529329\pi\)
\(824\) 2.76217 3.46365i 0.0962247 0.120662i
\(825\) 10.2886 + 15.2010i 0.358203 + 0.529230i
\(826\) 11.5066 50.3197i 0.400366 1.75085i
\(827\) 41.0705 + 19.7785i 1.42816 + 0.687767i 0.978655 0.205510i \(-0.0658853\pi\)
0.449507 + 0.893277i \(0.351600\pi\)
\(828\) 4.97196 + 22.4846i 0.172787 + 0.781393i
\(829\) −32.5729 + 10.0474i −1.13130 + 0.348961i −0.803217 0.595687i \(-0.796880\pi\)
−0.328087 + 0.944648i \(0.606404\pi\)
\(830\) −7.45743 + 3.59131i −0.258851 + 0.124656i
\(831\) −25.4162 + 27.2068i −0.881680 + 0.943793i
\(832\) −0.270327 0.468219i −0.00937189 0.0162326i
\(833\) −43.1152 6.53432i −1.49385 0.226401i
\(834\) 1.29572 + 0.513604i 0.0448671 + 0.0177846i
\(835\) −5.69086 + 14.5001i −0.196940 + 0.501795i
\(836\) 11.2976 + 7.70260i 0.390737 + 0.266400i
\(837\) 6.79866 21.2709i 0.234996 0.735230i
\(838\) 1.62134 21.6352i 0.0560081 0.747376i
\(839\) −33.5671 + 22.8857i −1.15887 + 0.790101i −0.981010 0.193956i \(-0.937868\pi\)
−0.177855 + 0.984057i \(0.556916\pi\)
\(840\) −2.35212 1.36992i −0.0811559 0.0472667i
\(841\) −5.20794 3.55071i −0.179584 0.122438i
\(842\) 39.6249 49.6881i 1.36556 1.71236i
\(843\) −8.68207 9.42084i −0.299026 0.324471i
\(844\) −12.6978 15.9225i −0.437075 0.548075i
\(845\) −7.78177 2.40036i −0.267701 0.0825748i
\(846\) 21.7087 10.2738i 0.746361 0.353220i
\(847\) −9.41854 + 11.8007i −0.323625 + 0.405476i
\(848\) 14.2316 + 36.2616i 0.488716 + 1.24523i
\(849\) 27.6000 + 29.9486i 0.947230 + 1.02783i
\(850\) 51.2514 + 15.8090i 1.75791 + 0.542243i
\(851\) 7.24063 12.5411i 0.248206 0.429905i
\(852\) 9.20098 + 3.64713i 0.315221 + 0.124949i
\(853\) 25.7570 + 7.94497i 0.881901 + 0.272031i 0.702447 0.711736i \(-0.252091\pi\)
0.179454 + 0.983766i \(0.442567\pi\)
\(854\) 1.13740 15.0955i 0.0389211 0.516556i
\(855\) −6.72710 3.29592i −0.230062 0.112718i
\(856\) −5.38297 4.99467i −0.183986 0.170714i
\(857\) −20.3325 + 25.4961i −0.694545 + 0.870932i −0.996603 0.0823578i \(-0.973755\pi\)
0.302058 + 0.953290i \(0.402326\pi\)
\(858\) −0.979958 + 0.561362i −0.0334552 + 0.0191646i
\(859\) −6.28674 + 27.5440i −0.214501 + 0.939789i 0.746965 + 0.664864i \(0.231510\pi\)
−0.961465 + 0.274926i \(0.911347\pi\)
\(860\) 7.11374 2.19430i 0.242577 0.0748250i
\(861\) 18.2079 37.4451i 0.620523 1.27613i
\(862\) −19.4624 6.00335i −0.662891 0.204475i
\(863\) −18.0190 + 31.2099i −0.613375 + 1.06240i 0.377292 + 0.926094i \(0.376855\pi\)
−0.990667 + 0.136303i \(0.956478\pi\)
\(864\) −36.2270 3.08530i −1.23247 0.104964i
\(865\) −1.81204 + 1.68133i −0.0616114 + 0.0571670i
\(866\) 1.33930 + 17.8717i 0.0455113 + 0.607306i
\(867\) 32.7764 18.7758i 1.11315 0.637658i
\(868\) −16.7920 2.53795i −0.569959 0.0861438i
\(869\) 10.7980 27.5129i 0.366298 0.933312i
\(870\) 9.02162 3.50551i 0.305862 0.118848i
\(871\) −0.127242 0.159557i −0.00431143 0.00540637i
\(872\) −0.859601 11.4706i −0.0291098 0.388443i
\(873\) 22.9636 + 29.1991i 0.777201 + 0.988239i
\(874\) −34.4373 + 16.5841i −1.16486 + 0.560967i
\(875\) −9.94925 + 12.4656i −0.336346 + 0.421414i
\(876\) −6.32128 + 20.2493i −0.213576 + 0.684161i
\(877\) 28.2800 13.6189i 0.954948 0.459879i 0.109530 0.993984i \(-0.465066\pi\)
0.845418 + 0.534105i \(0.179351\pi\)
\(878\) −22.4792 20.8576i −0.758636 0.703911i
\(879\) −13.6704 + 28.1427i −0.461092 + 0.949229i
\(880\) 2.50886 6.39248i 0.0845738 0.215490i
\(881\) 31.9150 1.07524 0.537622 0.843186i \(-0.319323\pi\)
0.537622 + 0.843186i \(0.319323\pi\)
\(882\) 3.23005 39.1183i 0.108761 1.31718i
\(883\) 44.6966 1.50416 0.752080 0.659071i \(-0.229051\pi\)
0.752080 + 0.659071i \(0.229051\pi\)
\(884\) −0.515424 + 1.31328i −0.0173356 + 0.0441704i
\(885\) −11.3165 + 0.809521i −0.380401 + 0.0272118i
\(886\) 12.8881 + 11.9584i 0.432985 + 0.401751i
\(887\) 23.7367 11.4310i 0.797002 0.383816i 0.00936547 0.999956i \(-0.497019\pi\)
0.787636 + 0.616140i \(0.211305\pi\)
\(888\) 3.13064 + 3.39703i 0.105057 + 0.113997i
\(889\) 11.3485 49.6284i 0.380617 1.66448i
\(890\) 10.3336 4.97641i 0.346384 0.166810i
\(891\) −1.82699 + 20.6257i −0.0612064 + 0.690987i
\(892\) −0.649234 8.66343i −0.0217380 0.290073i
\(893\) 10.6262 + 13.3248i 0.355592 + 0.445898i
\(894\) 26.2786 + 21.1025i 0.878889 + 0.705773i
\(895\) −0.922550 + 2.35062i −0.0308375 + 0.0785726i
\(896\) −1.44133 19.3384i −0.0481515 0.646051i
\(897\) 0.00457128 1.34966i 0.000152631 0.0450640i
\(898\) 3.71362 + 49.5548i 0.123925 + 1.65366i
\(899\) −15.0087 + 13.9261i −0.500569 + 0.464460i
\(900\) −4.72889 + 20.0903i −0.157630 + 0.669677i
\(901\) 25.5102 44.1850i 0.849868 1.47201i
\(902\) 37.3368 + 11.5169i 1.24318 + 0.383470i
\(903\) −24.6552 26.7749i −0.820474 0.891014i
\(904\) 16.3456 5.04195i 0.543647 0.167693i
\(905\) −2.03075 + 8.89729i −0.0675044 + 0.295756i
\(906\) 0.211834 62.5436i 0.00703771 2.07787i
\(907\) 13.4721 16.8935i 0.447335 0.560941i −0.506125 0.862460i \(-0.668922\pi\)
0.953460 + 0.301520i \(0.0974939\pi\)
\(908\) −27.7683 25.7652i −0.921525 0.855050i
\(909\) −1.94083 28.4868i −0.0643734 0.944846i
\(910\) −0.344800 0.320188i −0.0114300 0.0106141i
\(911\) 9.32990 + 2.87789i 0.309114 + 0.0953489i 0.445431 0.895316i \(-0.353050\pi\)
−0.136317 + 0.990665i \(0.543527\pi\)
\(912\) −4.77593 32.4312i −0.158147 1.07390i
\(913\) −8.11777 + 14.0604i −0.268659 + 0.465331i
\(914\) −45.6410 14.0784i −1.50967 0.465672i
\(915\) −3.24636 + 0.729402i −0.107321 + 0.0241133i
\(916\) 2.60924 + 6.64824i 0.0862118 + 0.219664i
\(917\) −1.01818 1.27782i −0.0336232 0.0421973i
\(918\) 33.5732 + 50.3341i 1.10808 + 1.66127i
\(919\) −35.8790 11.0672i −1.18354 0.365073i −0.360336 0.932823i \(-0.617338\pi\)
−0.823201 + 0.567750i \(0.807814\pi\)
\(920\) 1.90327 + 2.38663i 0.0627491 + 0.0786848i
\(921\) −14.8324 + 47.5134i −0.488743 + 1.56562i
\(922\) 7.80699 9.78965i 0.257109 0.322405i
\(923\) −0.479299 0.326780i −0.0157763 0.0107561i
\(924\) 15.7076 1.11724i 0.516742 0.0367544i
\(925\) 10.7240 7.31151i 0.352603 0.240401i
\(926\) 2.02975 27.0852i 0.0667019 0.890075i
\(927\) −0.954435 14.0088i −0.0313478 0.460110i
\(928\) 27.5428 + 18.7784i 0.904137 + 0.616430i
\(929\) −6.64059 + 16.9199i −0.217871 + 0.555126i −0.997465 0.0711594i \(-0.977330\pi\)
0.779594 + 0.626285i \(0.215425\pi\)
\(930\) 1.27204 + 8.63782i 0.0417117 + 0.283245i
\(931\) 27.5460 4.12906i 0.902784 0.135324i
\(932\) 1.20593 + 2.08873i 0.0395016 + 0.0684187i
\(933\) 10.2586 + 33.6620i 0.335852 + 1.10204i
\(934\) 40.3177 19.4160i 1.31924 0.635311i
\(935\) −8.59469 + 2.65111i −0.281076 + 0.0867006i
\(936\) 0.410556 + 0.129692i 0.0134194 + 0.00423911i
\(937\) 41.1341 + 19.8092i 1.34379 + 0.647137i 0.960962 0.276681i \(-0.0892345\pi\)
0.382832 + 0.923818i \(0.374949\pi\)
\(938\) 1.47848 + 6.48976i 0.0482740 + 0.211898i
\(939\) −17.5886 + 36.2090i −0.573984 + 1.18163i
\(940\) −2.50302 + 3.13869i −0.0816395 + 0.102373i
\(941\) −37.3247 + 25.4476i −1.21675 + 0.829567i −0.989537 0.144278i \(-0.953914\pi\)
−0.227214 + 0.973845i \(0.572962\pi\)
\(942\) −26.9006 + 28.7957i −0.876467 + 0.938214i
\(943\) −34.2299 + 31.7607i −1.11468 + 1.03427i
\(944\) −30.9546 38.8158i −1.00749 1.26335i
\(945\) −8.43073 + 1.83076i −0.274252 + 0.0595546i
\(946\) 21.2956 26.7039i 0.692381 0.868218i
\(947\) −1.69037 22.5564i −0.0549295 0.732983i −0.954880 0.296991i \(-0.904017\pi\)
0.899951 0.435992i \(-0.143602\pi\)
\(948\) 30.9771 12.0367i 1.00609 0.390934i
\(949\) 0.621657 1.07674i 0.0201798 0.0349525i
\(950\) −34.2582 −1.11148
\(951\) 4.31787 + 3.46738i 0.140017 + 0.112437i
\(952\) −11.4405 + 10.6066i −0.370789 + 0.343762i
\(953\) 6.29993 27.6018i 0.204075 0.894110i −0.764349 0.644802i \(-0.776940\pi\)
0.968424 0.249308i \(-0.0802032\pi\)
\(954\) 41.2400 + 20.2054i 1.33520 + 0.654175i
\(955\) 13.6299 + 2.05438i 0.441055 + 0.0664783i
\(956\) 1.72738 2.16607i 0.0558675 0.0700557i
\(957\) 10.7476 15.6497i 0.347420 0.505882i
\(958\) 73.2398 22.5915i 2.36627 0.729898i
\(959\) 23.9879 + 30.1050i 0.774611 + 0.972140i
\(960\) 3.61255 1.40372i 0.116595 0.0453049i
\(961\) 6.26530 + 10.8518i 0.202107 + 0.350059i
\(962\) 0.399288 + 0.691587i 0.0128736 + 0.0222977i
\(963\) −23.2736 0.157656i −0.749982 0.00508040i
\(964\) −31.6910 + 21.6066i −1.02070 + 0.695901i
\(965\) −1.83177 4.66726i −0.0589666 0.150244i
\(966\) −19.2495 + 39.5873i −0.619343 + 1.27370i
\(967\) −15.1088 + 38.4967i −0.485868 + 1.23797i 0.452324 + 0.891854i \(0.350595\pi\)
−0.938192 + 0.346117i \(0.887500\pi\)
\(968\) 1.20196 + 5.26613i 0.0386325 + 0.169260i
\(969\) −29.3095 + 31.3744i −0.941557 + 1.00789i
\(970\) −13.0855 6.30165i −0.420150 0.202334i
\(971\) 14.4754 + 36.8827i 0.464538 + 1.18362i 0.950799 + 0.309809i \(0.100265\pi\)
−0.486261 + 0.873814i \(0.661640\pi\)
\(972\) −18.4465 + 14.2063i −0.591671 + 0.455666i
\(973\) 0.569138 + 0.986699i 0.0182457 + 0.0316321i
\(974\) −9.56916 + 6.52414i −0.306616 + 0.209047i
\(975\) 0.528553 1.08811i 0.0169272 0.0348473i
\(976\) −10.6733 9.90342i −0.341645 0.317001i
\(977\) 0.457166 6.10046i 0.0146260 0.195171i −0.985104 0.171957i \(-0.944991\pi\)
0.999731 0.0232141i \(-0.00738993\pi\)
\(978\) 0.944554 1.01110i 0.0302035 0.0323313i
\(979\) 11.2486 19.4832i 0.359508 0.622687i
\(980\) 2.39205 + 6.10941i 0.0764114 + 0.195158i
\(981\) −26.5567 24.9779i −0.847890 0.797483i
\(982\) 1.77446 0.267457i 0.0566252 0.00853488i
\(983\) 18.2227 8.77559i 0.581214 0.279898i −0.120087 0.992763i \(-0.538317\pi\)
0.701301 + 0.712865i \(0.252603\pi\)
\(984\) −6.41762 13.4426i −0.204586 0.428535i
\(985\) 3.42551 1.64964i 0.109146 0.0525619i
\(986\) −4.14550 55.3179i −0.132020 1.76168i
\(987\) 19.1190 + 4.44014i 0.608564 + 0.141331i
\(988\) 0.0673418 0.898614i 0.00214243 0.0285887i
\(989\) 14.9127 + 37.9970i 0.474197 + 1.20824i
\(990\) −2.90662 7.55605i −0.0923784 0.240147i
\(991\) −15.1984 + 38.7250i −0.482794 + 1.23014i 0.457327 + 0.889299i \(0.348807\pi\)
−0.940121 + 0.340841i \(0.889288\pi\)
\(992\) −22.0435 + 20.4534i −0.699883 + 0.649397i
\(993\) 52.0853 + 12.0739i 1.65288 + 0.383153i
\(994\) 9.45324 + 16.3888i 0.299838 + 0.519822i
\(995\) 4.66769 + 0.703541i 0.147976 + 0.0223037i
\(996\) −17.8116 + 4.00195i −0.564381 + 0.126807i
\(997\) −3.65555 16.0160i −0.115773 0.507233i −0.999249 0.0387564i \(-0.987660\pi\)
0.883476 0.468476i \(-0.155197\pi\)
\(998\) −15.4172 26.7033i −0.488021 0.845278i
\(999\) 14.5889 + 1.24247i 0.461572 + 0.0393101i
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 441.2.z.a.142.13 yes 648
9.4 even 3 441.2.y.a.436.13 yes 648
49.39 even 21 441.2.y.a.88.13 648
441.382 even 21 inner 441.2.z.a.382.13 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
441.2.y.a.88.13 648 49.39 even 21
441.2.y.a.436.13 yes 648 9.4 even 3
441.2.z.a.142.13 yes 648 1.1 even 1 trivial
441.2.z.a.382.13 yes 648 441.382 even 21 inner