Properties

Label 576.2.bm.a.517.57
Level $576$
Weight $2$
Character 576.517
Analytic conductor $4.599$
Analytic rank $0$
Dimension $1504$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,2,Mod(13,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(48))
 
chi = DirichletCharacter(H, H._module([0, 45, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bm (of order \(48\), degree \(16\), 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: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(1504\)
Relative dimension: \(94\) over \(\Q(\zeta_{48})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label 517.57
Character \(\chi\) \(=\) 576.517
Dual form 576.2.bm.a.205.57

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.359606 + 1.36773i) q^{2} +(0.298442 + 1.70615i) q^{3} +(-1.74137 + 0.983687i) q^{4} +(0.924132 - 1.05377i) q^{5} +(-2.22622 + 1.02173i) q^{6} +(4.48276 - 0.590167i) q^{7} +(-1.97162 - 2.02798i) q^{8} +(-2.82187 + 1.01837i) q^{9} +O(q^{10})\) \(q+(0.359606 + 1.36773i) q^{2} +(0.298442 + 1.70615i) q^{3} +(-1.74137 + 0.983687i) q^{4} +(0.924132 - 1.05377i) q^{5} +(-2.22622 + 1.02173i) q^{6} +(4.48276 - 0.590167i) q^{7} +(-1.97162 - 2.02798i) q^{8} +(-2.82187 + 1.01837i) q^{9} +(1.77360 + 0.885021i) q^{10} +(-1.71336 + 3.47435i) q^{11} +(-2.19801 - 2.67745i) q^{12} +(-0.777400 + 2.29015i) q^{13} +(2.41921 + 5.91897i) q^{14} +(2.07369 + 1.26221i) q^{15} +(2.06472 - 3.42592i) q^{16} +(-4.38076 + 4.38076i) q^{17} +(-2.40761 - 3.49334i) q^{18} +(0.960595 + 4.82924i) q^{19} +(-0.572673 + 2.74406i) q^{20} +(2.34475 + 7.47211i) q^{21} +(-5.36810 - 1.09402i) q^{22} +(1.02233 - 7.76534i) q^{23} +(2.87161 - 3.96911i) q^{24} +(0.396218 + 3.00958i) q^{25} +(-3.41186 - 0.239723i) q^{26} +(-2.57965 - 4.51059i) q^{27} +(-7.22559 + 5.43733i) q^{28} +(7.06050 + 0.462769i) q^{29} +(-0.980659 + 3.29014i) q^{30} +(-0.129689 - 0.0748762i) q^{31} +(5.42822 + 1.59200i) q^{32} +(-6.43908 - 1.88635i) q^{33} +(-7.56703 - 4.41634i) q^{34} +(3.52076 - 5.26919i) q^{35} +(3.91215 - 4.54919i) q^{36} +(0.836186 - 4.20379i) q^{37} +(-6.25966 + 3.05046i) q^{38} +(-4.13933 - 0.642883i) q^{39} +(-3.95907 + 0.203517i) q^{40} +(0.688328 - 5.22837i) q^{41} +(-9.37664 + 5.89400i) q^{42} +(-0.680767 - 0.335717i) q^{43} +(-0.434082 - 7.73552i) q^{44} +(-1.53465 + 3.91471i) q^{45} +(10.9885 - 1.39419i) q^{46} +(-6.96522 - 1.86633i) q^{47} +(6.46132 + 2.50028i) q^{48} +(12.9854 - 3.47942i) q^{49} +(-3.97380 + 1.62418i) q^{50} +(-8.78161 - 6.16681i) q^{51} +(-0.899048 - 4.75271i) q^{52} +(2.43350 + 3.64199i) q^{53} +(5.24161 - 5.15030i) q^{54} +(2.07780 + 5.01624i) q^{55} +(-10.0352 - 7.92736i) q^{56} +(-7.95270 + 3.08016i) q^{57} +(1.90605 + 9.82326i) q^{58} +(-3.61828 + 4.12586i) q^{59} +(-4.85267 - 0.158122i) q^{60} +(0.273068 - 4.16621i) q^{61} +(0.0557733 - 0.204306i) q^{62} +(-12.0487 + 6.23048i) q^{63} +(-0.225406 + 7.99682i) q^{64} +(1.69487 + 2.93560i) q^{65} +(0.264484 - 9.48526i) q^{66} +(14.0532 - 6.93027i) q^{67} +(3.31921 - 11.9378i) q^{68} +(13.5539 - 0.573264i) q^{69} +(8.47292 + 2.92062i) q^{70} +(4.52696 - 10.9290i) q^{71} +(7.62889 + 3.71484i) q^{72} +(2.67255 + 6.45210i) q^{73} +(6.05034 - 0.368031i) q^{74} +(-5.01653 + 1.57419i) q^{75} +(-6.42321 - 7.46455i) q^{76} +(-5.63013 + 16.5858i) q^{77} +(-0.609239 - 5.89267i) q^{78} +(0.189066 - 0.705603i) q^{79} +(-1.70206 - 5.34175i) q^{80} +(6.92584 - 5.74741i) q^{81} +(7.39853 - 0.938706i) q^{82} +(3.58112 - 3.14055i) q^{83} +(-11.4333 - 10.7052i) q^{84} +(0.567915 + 8.66471i) q^{85} +(0.214362 - 1.05183i) q^{86} +(1.31760 + 12.1843i) q^{87} +(10.4240 - 3.37544i) q^{88} +(-3.19080 - 1.32167i) q^{89} +(-5.90613 - 0.691231i) q^{90} +(-2.13333 + 10.7250i) q^{91} +(5.85841 + 14.5280i) q^{92} +(0.0890449 - 0.243615i) q^{93} +(0.0478946 - 10.1977i) q^{94} +(5.97663 + 3.45061i) q^{95} +(-1.09618 + 9.73645i) q^{96} +(10.7249 - 6.19202i) q^{97} +(9.42851 + 16.5092i) q^{98} +(1.29669 - 11.5490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1504 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{5} - 16 q^{6} - 8 q^{7} - 32 q^{8} - 16 q^{9} - 32 q^{10} - 8 q^{11} - 16 q^{12} - 8 q^{13} - 8 q^{14} - 16 q^{15} - 8 q^{16} - 32 q^{17} - 16 q^{18} - 32 q^{19} - 8 q^{20} - 16 q^{21} - 8 q^{22} - 8 q^{23} + 64 q^{24} - 8 q^{25} - 32 q^{26} - 16 q^{27} - 32 q^{28} - 8 q^{29} - 96 q^{30} - 8 q^{32} - 8 q^{34} - 32 q^{35} - 96 q^{36} - 32 q^{37} - 8 q^{38} - 16 q^{39} - 8 q^{40} - 8 q^{41} + 64 q^{42} - 8 q^{43} - 32 q^{44} - 16 q^{45} - 32 q^{46} - 8 q^{47} - 16 q^{48} - 8 q^{49} - 8 q^{50} - 16 q^{51} - 8 q^{52} - 32 q^{53} - 16 q^{54} - 32 q^{55} - 8 q^{56} - 16 q^{57} - 80 q^{58} - 8 q^{59} - 16 q^{60} - 8 q^{61} - 64 q^{62} - 32 q^{63} - 32 q^{64} - 16 q^{65} - 32 q^{66} - 8 q^{67} - 8 q^{68} - 16 q^{69} - 8 q^{70} - 32 q^{71} - 16 q^{72} - 32 q^{73} - 8 q^{74} - 16 q^{75} + 40 q^{76} - 8 q^{77} - 40 q^{78} - 8 q^{79} - 160 q^{80} - 16 q^{81} - 32 q^{82} - 8 q^{83} - 128 q^{84} - 8 q^{85} - 216 q^{86} - 16 q^{87} - 8 q^{88} - 32 q^{89} - 160 q^{90} - 32 q^{91} + 144 q^{92} - 40 q^{93} - 8 q^{94} - 152 q^{96} - 304 q^{98} - 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{16}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.359606 + 1.36773i 0.254280 + 0.967131i
\(3\) 0.298442 + 1.70615i 0.172305 + 0.985044i
\(4\) −1.74137 + 0.983687i −0.870684 + 0.491843i
\(5\) 0.924132 1.05377i 0.413285 0.471261i −0.507320 0.861758i \(-0.669364\pi\)
0.920604 + 0.390497i \(0.127697\pi\)
\(6\) −2.22622 + 1.02173i −0.908852 + 0.417118i
\(7\) 4.48276 0.590167i 1.69432 0.223062i 0.779354 0.626584i \(-0.215547\pi\)
0.914970 + 0.403522i \(0.132214\pi\)
\(8\) −1.97162 2.02798i −0.697074 0.716999i
\(9\) −2.82187 + 1.01837i −0.940622 + 0.339457i
\(10\) 1.77360 + 0.885021i 0.560861 + 0.279868i
\(11\) −1.71336 + 3.47435i −0.516597 + 1.04755i 0.469739 + 0.882806i \(0.344348\pi\)
−0.986335 + 0.164749i \(0.947319\pi\)
\(12\) −2.19801 2.67745i −0.634511 0.772914i
\(13\) −0.777400 + 2.29015i −0.215612 + 0.635173i 0.784279 + 0.620408i \(0.213033\pi\)
−0.999891 + 0.0147643i \(0.995300\pi\)
\(14\) 2.41921 + 5.91897i 0.646562 + 1.58191i
\(15\) 2.07369 + 1.26221i 0.535423 + 0.325903i
\(16\) 2.06472 3.42592i 0.516180 0.856480i
\(17\) −4.38076 + 4.38076i −1.06249 + 1.06249i −0.0645764 + 0.997913i \(0.520570\pi\)
−0.997913 + 0.0645764i \(0.979430\pi\)
\(18\) −2.40761 3.49334i −0.567480 0.823387i
\(19\) 0.960595 + 4.82924i 0.220376 + 1.10790i 0.919556 + 0.392958i \(0.128548\pi\)
−0.699181 + 0.714945i \(0.746452\pi\)
\(20\) −0.572673 + 2.74406i −0.128054 + 0.613590i
\(21\) 2.34475 + 7.47211i 0.511667 + 1.63055i
\(22\) −5.36810 1.09402i −1.14448 0.233245i
\(23\) 1.02233 7.76534i 0.213170 1.61918i −0.465712 0.884936i \(-0.654202\pi\)
0.678881 0.734248i \(-0.262465\pi\)
\(24\) 2.87161 3.96911i 0.586166 0.810191i
\(25\) 0.396218 + 3.00958i 0.0792437 + 0.601915i
\(26\) −3.41186 0.239723i −0.669121 0.0470136i
\(27\) −2.57965 4.51059i −0.496454 0.868063i
\(28\) −7.22559 + 5.43733i −1.36551 + 1.02756i
\(29\) 7.06050 + 0.462769i 1.31110 + 0.0859341i 0.704860 0.709347i \(-0.251010\pi\)
0.606241 + 0.795281i \(0.292677\pi\)
\(30\) −0.980659 + 3.29014i −0.179043 + 0.600695i
\(31\) −0.129689 0.0748762i −0.0232929 0.0134482i 0.488308 0.872671i \(-0.337614\pi\)
−0.511601 + 0.859223i \(0.670947\pi\)
\(32\) 5.42822 + 1.59200i 0.959582 + 0.281428i
\(33\) −6.43908 1.88635i −1.12090 0.328371i
\(34\) −7.56703 4.41634i −1.29774 0.757397i
\(35\) 3.52076 5.26919i 0.595118 0.890656i
\(36\) 3.91215 4.54919i 0.652024 0.758198i
\(37\) 0.836186 4.20379i 0.137468 0.691099i −0.849163 0.528130i \(-0.822893\pi\)
0.986631 0.162968i \(-0.0521068\pi\)
\(38\) −6.25966 + 3.05046i −1.01545 + 0.494849i
\(39\) −4.13933 0.642883i −0.662824 0.102944i
\(40\) −3.95907 + 0.203517i −0.625983 + 0.0321789i
\(41\) 0.688328 5.22837i 0.107499 0.816535i −0.849733 0.527213i \(-0.823237\pi\)
0.957232 0.289322i \(-0.0934297\pi\)
\(42\) −9.37664 + 5.89400i −1.44685 + 0.909464i
\(43\) −0.680767 0.335717i −0.103816 0.0511964i 0.389639 0.920968i \(-0.372600\pi\)
−0.493455 + 0.869771i \(0.664266\pi\)
\(44\) −0.434082 7.73552i −0.0654404 1.16617i
\(45\) −1.53465 + 3.91471i −0.228772 + 0.583570i
\(46\) 10.9885 1.39419i 1.62017 0.205563i
\(47\) −6.96522 1.86633i −1.01598 0.272232i −0.287855 0.957674i \(-0.592942\pi\)
−0.728127 + 0.685442i \(0.759609\pi\)
\(48\) 6.46132 + 2.50028i 0.932611 + 0.360884i
\(49\) 12.9854 3.47942i 1.85505 0.497059i
\(50\) −3.97380 + 1.62418i −0.561981 + 0.229694i
\(51\) −8.78161 6.16681i −1.22967 0.863525i
\(52\) −0.899048 4.75271i −0.124676 0.659082i
\(53\) 2.43350 + 3.64199i 0.334267 + 0.500266i 0.960087 0.279702i \(-0.0902355\pi\)
−0.625820 + 0.779968i \(0.715236\pi\)
\(54\) 5.24161 5.15030i 0.713292 0.700867i
\(55\) 2.07780 + 5.01624i 0.280170 + 0.676390i
\(56\) −10.0352 7.92736i −1.34100 1.05934i
\(57\) −7.95270 + 3.08016i −1.05336 + 0.407977i
\(58\) 1.90605 + 9.82326i 0.250277 + 1.28986i
\(59\) −3.61828 + 4.12586i −0.471060 + 0.537141i −0.937764 0.347272i \(-0.887108\pi\)
0.466704 + 0.884414i \(0.345441\pi\)
\(60\) −4.85267 0.158122i −0.626477 0.0204135i
\(61\) 0.273068 4.16621i 0.0349628 0.533429i −0.944073 0.329738i \(-0.893040\pi\)
0.979035 0.203691i \(-0.0652937\pi\)
\(62\) 0.0557733 0.204306i 0.00708322 0.0259469i
\(63\) −12.0487 + 6.23048i −1.51800 + 0.784967i
\(64\) −0.225406 + 7.99682i −0.0281758 + 0.999603i
\(65\) 1.69487 + 2.93560i 0.210223 + 0.364117i
\(66\) 0.264484 9.48526i 0.0325558 1.16755i
\(67\) 14.0532 6.93027i 1.71687 0.846668i 0.730343 0.683080i \(-0.239360\pi\)
0.986529 0.163587i \(-0.0523065\pi\)
\(68\) 3.31921 11.9378i 0.402514 1.44767i
\(69\) 13.5539 0.573264i 1.63170 0.0690128i
\(70\) 8.47292 + 2.92062i 1.01271 + 0.349081i
\(71\) 4.52696 10.9290i 0.537251 1.29704i −0.389384 0.921076i \(-0.627312\pi\)
0.926635 0.375963i \(-0.122688\pi\)
\(72\) 7.62889 + 3.71484i 0.899073 + 0.437799i
\(73\) 2.67255 + 6.45210i 0.312798 + 0.755161i 0.999599 + 0.0283156i \(0.00901432\pi\)
−0.686801 + 0.726845i \(0.740986\pi\)
\(74\) 6.05034 0.368031i 0.703338 0.0427827i
\(75\) −5.01653 + 1.57419i −0.579259 + 0.181772i
\(76\) −6.42321 7.46455i −0.736792 0.856243i
\(77\) −5.63013 + 16.5858i −0.641613 + 1.89013i
\(78\) −0.609239 5.89267i −0.0689827 0.667214i
\(79\) 0.189066 0.705603i 0.0212715 0.0793865i −0.954474 0.298294i \(-0.903583\pi\)
0.975746 + 0.218907i \(0.0702492\pi\)
\(80\) −1.70206 5.34175i −0.190296 0.597225i
\(81\) 6.92584 5.74741i 0.769538 0.638601i
\(82\) 7.39853 0.938706i 0.817031 0.103663i
\(83\) 3.58112 3.14055i 0.393078 0.344721i −0.439880 0.898057i \(-0.644979\pi\)
0.832958 + 0.553336i \(0.186646\pi\)
\(84\) −11.4333 10.7052i −1.24747 1.16803i
\(85\) 0.567915 + 8.66471i 0.0615990 + 0.939820i
\(86\) 0.214362 1.05183i 0.0231153 0.113422i
\(87\) 1.31760 + 12.1843i 0.141261 + 1.30630i
\(88\) 10.4240 3.37544i 1.11120 0.359824i
\(89\) −3.19080 1.32167i −0.338224 0.140097i 0.207106 0.978319i \(-0.433596\pi\)
−0.545330 + 0.838222i \(0.683596\pi\)
\(90\) −5.90613 0.691231i −0.622561 0.0728622i
\(91\) −2.13333 + 10.7250i −0.223634 + 1.12428i
\(92\) 5.85841 + 14.5280i 0.610782 + 1.51464i
\(93\) 0.0890449 0.243615i 0.00923353 0.0252617i
\(94\) 0.0478946 10.1977i 0.00493995 1.05181i
\(95\) 5.97663 + 3.45061i 0.613189 + 0.354025i
\(96\) −1.09618 + 9.73645i −0.111878 + 0.993722i
\(97\) 10.7249 6.19202i 1.08895 0.628704i 0.155651 0.987812i \(-0.450252\pi\)
0.933296 + 0.359108i \(0.116919\pi\)
\(98\) 9.42851 + 16.5092i 0.952423 + 1.66768i
\(99\) 1.29669 11.5490i 0.130323 1.16071i
\(100\) −3.65044 4.85102i −0.365044 0.485102i
\(101\) −4.42694 + 1.50274i −0.440497 + 0.149529i −0.532872 0.846196i \(-0.678887\pi\)
0.0923751 + 0.995724i \(0.470554\pi\)
\(102\) 5.27661 14.2285i 0.522462 1.40883i
\(103\) 10.7790 8.27101i 1.06208 0.814966i 0.0787727 0.996893i \(-0.474900\pi\)
0.983312 + 0.181926i \(0.0582332\pi\)
\(104\) 6.17711 2.93876i 0.605716 0.288169i
\(105\) 10.0408 + 4.43439i 0.979877 + 0.432752i
\(106\) −4.10616 + 4.63805i −0.398825 + 0.450487i
\(107\) −8.64801 + 5.77842i −0.836035 + 0.558620i −0.898271 0.439441i \(-0.855177\pi\)
0.0622369 + 0.998061i \(0.480177\pi\)
\(108\) 8.92912 + 5.31702i 0.859205 + 0.511631i
\(109\) 1.73740 + 8.73449i 0.166413 + 0.836612i 0.970314 + 0.241849i \(0.0777540\pi\)
−0.803901 + 0.594763i \(0.797246\pi\)
\(110\) −6.11367 + 4.64573i −0.582916 + 0.442953i
\(111\) 7.42183 + 0.172068i 0.704449 + 0.0163320i
\(112\) 7.23378 16.5761i 0.683528 1.56629i
\(113\) −16.8939 + 4.52670i −1.58924 + 0.425836i −0.941771 0.336254i \(-0.890840\pi\)
−0.647471 + 0.762090i \(0.724173\pi\)
\(114\) −7.07266 9.76950i −0.662416 0.914998i
\(115\) −7.23812 8.25349i −0.674958 0.769642i
\(116\) −12.7501 + 6.13947i −1.18382 + 0.570035i
\(117\) −0.138499 7.25417i −0.0128042 0.670648i
\(118\) −6.94422 3.46515i −0.639267 0.318993i
\(119\) −17.0525 + 22.2232i −1.56320 + 2.03720i
\(120\) −1.52878 6.69401i −0.139558 0.611076i
\(121\) −2.43911 3.17871i −0.221737 0.288974i
\(122\) 5.79645 1.12471i 0.524785 0.101826i
\(123\) 9.12579 0.385977i 0.822845 0.0348023i
\(124\) 0.299492 + 0.00281326i 0.0268951 + 0.000252638i
\(125\) 9.36446 + 6.25713i 0.837583 + 0.559655i
\(126\) −12.8544 14.2389i −1.14516 1.26850i
\(127\) −14.1391 −1.25464 −0.627320 0.778761i \(-0.715848\pi\)
−0.627320 + 0.778761i \(0.715848\pi\)
\(128\) −11.0185 + 2.56741i −0.973911 + 0.226929i
\(129\) 0.369613 1.26168i 0.0325426 0.111085i
\(130\) −3.40562 + 3.37378i −0.298693 + 0.295900i
\(131\) 4.55043 2.24403i 0.397573 0.196061i −0.232501 0.972596i \(-0.574691\pi\)
0.630075 + 0.776535i \(0.283024\pi\)
\(132\) 13.0684 3.04921i 1.13746 0.265400i
\(133\) 7.15617 + 21.0814i 0.620519 + 1.82799i
\(134\) 14.5324 + 16.7288i 1.25540 + 1.44515i
\(135\) −7.13706 1.45002i −0.614261 0.124798i
\(136\) 17.5213 + 0.246887i 1.50244 + 0.0211704i
\(137\) 7.58765 9.88842i 0.648257 0.844825i −0.347420 0.937710i \(-0.612942\pi\)
0.995677 + 0.0928849i \(0.0296089\pi\)
\(138\) 5.65813 + 18.3319i 0.481652 + 1.56052i
\(139\) −8.13816 + 0.533403i −0.690270 + 0.0452427i −0.406501 0.913650i \(-0.633251\pi\)
−0.283768 + 0.958893i \(0.591585\pi\)
\(140\) −0.947706 + 12.6389i −0.0800958 + 1.06818i
\(141\) 1.10551 12.4407i 0.0931008 1.04769i
\(142\) 16.5759 + 2.26151i 1.39102 + 0.189781i
\(143\) −6.62480 6.62480i −0.553994 0.553994i
\(144\) −2.33751 + 11.7701i −0.194792 + 0.980844i
\(145\) 7.01249 7.01249i 0.582355 0.582355i
\(146\) −7.86366 + 5.97553i −0.650801 + 0.494539i
\(147\) 9.81176 + 21.1165i 0.809261 + 1.74166i
\(148\) 2.67910 + 8.14289i 0.220221 + 0.669341i
\(149\) 0.168774 + 2.57500i 0.0138265 + 0.210952i 0.999182 + 0.0404392i \(0.0128757\pi\)
−0.985355 + 0.170513i \(0.945458\pi\)
\(150\) −3.95704 6.29516i −0.323091 0.513998i
\(151\) −6.49156 4.98115i −0.528275 0.405360i 0.309893 0.950771i \(-0.399707\pi\)
−0.838168 + 0.545411i \(0.816373\pi\)
\(152\) 7.89967 11.4695i 0.640748 0.930300i
\(153\) 7.90067 16.8231i 0.638731 1.36007i
\(154\) −24.7095 1.73614i −1.99115 0.139902i
\(155\) −0.198752 + 0.0674674i −0.0159642 + 0.00541911i
\(156\) 7.84050 2.95231i 0.627742 0.236374i
\(157\) 2.80903 + 5.69615i 0.224185 + 0.454602i 0.979684 0.200548i \(-0.0642722\pi\)
−0.755499 + 0.655150i \(0.772606\pi\)
\(158\) 1.03306 + 0.00485190i 0.0821860 + 0.000385996i
\(159\) −5.48751 + 5.23883i −0.435188 + 0.415466i
\(160\) 6.69399 4.24888i 0.529207 0.335903i
\(161\) 35.4135i 2.79097i
\(162\) 10.3515 + 7.40588i 0.813288 + 0.581861i
\(163\) 6.16104 9.22065i 0.482570 0.722217i −0.507676 0.861548i \(-0.669495\pi\)
0.990246 + 0.139331i \(0.0444952\pi\)
\(164\) 3.94445 + 9.78162i 0.308010 + 0.763816i
\(165\) −7.93834 + 5.04208i −0.617999 + 0.392525i
\(166\) 5.58322 + 3.76864i 0.433342 + 0.292503i
\(167\) 0.307343 0.235833i 0.0237829 0.0182493i −0.596802 0.802389i \(-0.703562\pi\)
0.620585 + 0.784140i \(0.286895\pi\)
\(168\) 10.5303 19.4873i 0.812432 1.50348i
\(169\) 5.67317 + 4.35317i 0.436397 + 0.334860i
\(170\) −11.6468 + 3.89263i −0.893265 + 0.298551i
\(171\) −7.62862 12.6492i −0.583375 0.967310i
\(172\) 1.51571 0.0850545i 0.115571 0.00648534i
\(173\) 5.62202 4.93038i 0.427434 0.374850i −0.418429 0.908250i \(-0.637419\pi\)
0.845863 + 0.533400i \(0.179086\pi\)
\(174\) −16.1911 + 6.18367i −1.22744 + 0.468783i
\(175\) 3.55230 + 13.2574i 0.268529 + 1.00216i
\(176\) 8.36523 + 13.0434i 0.630553 + 0.983182i
\(177\) −8.11917 4.94199i −0.610274 0.371463i
\(178\) 0.660260 4.83943i 0.0494886 0.362731i
\(179\) 23.7424 4.72266i 1.77459 0.352988i 0.804168 0.594402i \(-0.202611\pi\)
0.970422 + 0.241414i \(0.0776110\pi\)
\(180\) −1.17846 8.32656i −0.0878373 0.620625i
\(181\) −6.95642 10.4110i −0.517067 0.773845i 0.477424 0.878673i \(-0.341571\pi\)
−0.994490 + 0.104828i \(0.966571\pi\)
\(182\) −15.4360 + 0.938944i −1.14419 + 0.0695992i
\(183\) 7.18966 0.777478i 0.531475 0.0574728i
\(184\) −17.7636 + 13.2371i −1.30955 + 0.975849i
\(185\) −3.65708 4.76601i −0.268874 0.350404i
\(186\) 0.365221 + 0.0341840i 0.0267793 + 0.00250649i
\(187\) −7.71446 22.7261i −0.564137 1.66189i
\(188\) 13.9649 3.60164i 1.01849 0.262676i
\(189\) −14.2259 18.6975i −1.03479 1.36004i
\(190\) −2.57027 + 9.41527i −0.186467 + 0.683055i
\(191\) −3.33521 5.77676i −0.241328 0.417992i 0.719765 0.694218i \(-0.244250\pi\)
−0.961093 + 0.276226i \(0.910916\pi\)
\(192\) −13.7110 + 2.00201i −0.989507 + 0.144483i
\(193\) −3.43176 + 5.94398i −0.247023 + 0.427857i −0.962699 0.270576i \(-0.912786\pi\)
0.715675 + 0.698433i \(0.246119\pi\)
\(194\) 12.3257 + 12.4421i 0.884936 + 0.893288i
\(195\) −4.50274 + 3.76780i −0.322448 + 0.269818i
\(196\) −19.1896 + 18.8325i −1.37069 + 1.34518i
\(197\) −11.8187 2.35088i −0.842044 0.167493i −0.244821 0.969568i \(-0.578729\pi\)
−0.597223 + 0.802075i \(0.703729\pi\)
\(198\) 16.2622 2.37955i 1.15570 0.169107i
\(199\) 7.82868 18.9001i 0.554960 1.33979i −0.358753 0.933433i \(-0.616798\pi\)
0.913713 0.406360i \(-0.133202\pi\)
\(200\) 5.32217 6.73727i 0.376334 0.476397i
\(201\) 16.0181 + 21.9085i 1.12983 + 1.54531i
\(202\) −3.64730 5.51446i −0.256623 0.387996i
\(203\) 31.9236 2.09238i 2.24060 0.146857i
\(204\) 21.3582 + 2.10033i 1.49537 + 0.147052i
\(205\) −4.87340 5.55705i −0.340373 0.388121i
\(206\) 15.1887 + 11.7684i 1.05825 + 0.819946i
\(207\) 5.02312 + 22.9538i 0.349131 + 1.59540i
\(208\) 6.24075 + 7.39183i 0.432718 + 0.512531i
\(209\) −18.4243 4.93677i −1.27443 0.341484i
\(210\) −2.45433 + 15.3277i −0.169365 + 1.05771i
\(211\) −13.6722 4.64108i −0.941231 0.319505i −0.191685 0.981457i \(-0.561395\pi\)
−0.749546 + 0.661952i \(0.769728\pi\)
\(212\) −7.82020 3.94824i −0.537093 0.271166i
\(213\) 19.9976 + 4.46196i 1.37021 + 0.305729i
\(214\) −11.0132 9.75019i −0.752846 0.666509i
\(215\) −0.982887 + 0.407125i −0.0670323 + 0.0277657i
\(216\) −4.06129 + 14.1247i −0.276336 + 0.961061i
\(217\) −0.625556 0.259114i −0.0424655 0.0175898i
\(218\) −11.3216 + 5.51726i −0.766798 + 0.373676i
\(219\) −10.2106 + 6.48533i −0.689970 + 0.438238i
\(220\) −8.55262 6.69122i −0.576617 0.451122i
\(221\) −6.62698 13.4382i −0.445779 0.903950i
\(222\) 2.43359 + 10.2129i 0.163332 + 0.685447i
\(223\) −1.24110 + 0.716552i −0.0831105 + 0.0479839i −0.540979 0.841036i \(-0.681946\pi\)
0.457869 + 0.889020i \(0.348613\pi\)
\(224\) 25.2729 + 3.93300i 1.68862 + 0.262784i
\(225\) −4.18294 8.08912i −0.278863 0.539275i
\(226\) −12.2664 21.4784i −0.815951 1.42872i
\(227\) −3.60298 0.236152i −0.239138 0.0156739i −0.0546372 0.998506i \(-0.517400\pi\)
−0.184501 + 0.982832i \(0.559067\pi\)
\(228\) 10.8187 13.1867i 0.716483 0.873308i
\(229\) 19.5667 + 17.1595i 1.29300 + 1.13393i 0.983081 + 0.183173i \(0.0586369\pi\)
0.309924 + 0.950761i \(0.399696\pi\)
\(230\) 8.68568 12.8678i 0.572717 0.848477i
\(231\) −29.9781 4.65592i −1.97241 0.306337i
\(232\) −12.9822 15.2310i −0.852320 0.999961i
\(233\) −1.29149 + 0.534954i −0.0846086 + 0.0350460i −0.424586 0.905387i \(-0.639580\pi\)
0.339978 + 0.940433i \(0.389580\pi\)
\(234\) 9.87194 2.79807i 0.645349 0.182916i
\(235\) −8.40347 + 5.61502i −0.548182 + 0.366283i
\(236\) 2.24221 10.7439i 0.145955 0.699368i
\(237\) 1.26029 + 0.111992i 0.0818644 + 0.00727468i
\(238\) −36.5276 15.3316i −2.36773 0.993800i
\(239\) −2.08587 7.78456i −0.134923 0.503541i −0.999998 0.00189816i \(-0.999396\pi\)
0.865075 0.501643i \(-0.167271\pi\)
\(240\) 8.60583 4.49816i 0.555504 0.290355i
\(241\) −1.96556 + 7.33556i −0.126613 + 0.472525i −0.999892 0.0146949i \(-0.995322\pi\)
0.873279 + 0.487220i \(0.161989\pi\)
\(242\) 3.47050 4.47913i 0.223092 0.287929i
\(243\) 11.8729 + 10.1012i 0.761645 + 0.647994i
\(244\) 3.62273 + 7.52352i 0.231922 + 0.481644i
\(245\) 8.33368 16.8990i 0.532419 1.07964i
\(246\) 3.80960 + 12.3428i 0.242891 + 0.786949i
\(247\) −11.8064 1.55435i −0.751226 0.0989007i
\(248\) 0.103851 + 0.410635i 0.00659455 + 0.0260754i
\(249\) 6.42700 + 5.17263i 0.407294 + 0.327802i
\(250\) −5.19055 + 15.0581i −0.328279 + 0.952361i
\(251\) 3.89677 + 0.775115i 0.245962 + 0.0489248i 0.316531 0.948582i \(-0.397482\pi\)
−0.0705697 + 0.997507i \(0.522482\pi\)
\(252\) 14.8524 22.7017i 0.935615 1.43007i
\(253\) 25.2279 + 16.8567i 1.58606 + 1.05977i
\(254\) −5.08450 19.3384i −0.319030 1.21340i
\(255\) −14.6138 + 3.55486i −0.915150 + 0.222614i
\(256\) −7.47385 14.1471i −0.467116 0.884196i
\(257\) −5.07621 + 8.79225i −0.316645 + 0.548445i −0.979786 0.200049i \(-0.935890\pi\)
0.663141 + 0.748495i \(0.269223\pi\)
\(258\) 1.85855 + 0.0518233i 0.115708 + 0.00322638i
\(259\) 1.26748 19.3381i 0.0787576 1.20161i
\(260\) −5.83910 3.44474i −0.362126 0.213634i
\(261\) −20.3950 + 5.88433i −1.26242 + 0.364231i
\(262\) 4.70558 + 5.41680i 0.290712 + 0.334651i
\(263\) 6.30260 0.829753i 0.388635 0.0511648i 0.0663229 0.997798i \(-0.478873\pi\)
0.322312 + 0.946633i \(0.395540\pi\)
\(264\) 8.86996 + 16.7775i 0.545908 + 1.03258i
\(265\) 6.08670 + 0.801329i 0.373903 + 0.0492253i
\(266\) −26.2603 + 17.3687i −1.61012 + 1.06494i
\(267\) 1.30270 5.83841i 0.0797238 0.357305i
\(268\) −17.6546 + 25.8921i −1.07842 + 1.58161i
\(269\) −18.8028 + 3.74010i −1.14643 + 0.228038i −0.731516 0.681825i \(-0.761187\pi\)
−0.414909 + 0.909863i \(0.636187\pi\)
\(270\) −0.583294 10.2830i −0.0354982 0.625804i
\(271\) −18.5076 18.5076i −1.12426 1.12426i −0.991094 0.133166i \(-0.957486\pi\)
−0.133166 0.991094i \(-0.542514\pi\)
\(272\) 5.96308 + 24.0532i 0.361565 + 1.45844i
\(273\) −18.9350 0.438991i −1.14600 0.0265690i
\(274\) 16.2532 + 6.82192i 0.981894 + 0.412127i
\(275\) −11.1352 3.77988i −0.671476 0.227935i
\(276\) −23.0384 + 14.3311i −1.38675 + 0.862628i
\(277\) 4.08741 + 2.01569i 0.245589 + 0.121111i 0.560918 0.827871i \(-0.310448\pi\)
−0.315329 + 0.948982i \(0.602115\pi\)
\(278\) −3.65608 10.9390i −0.219277 0.656077i
\(279\) 0.442218 + 0.0792187i 0.0264749 + 0.00474270i
\(280\) −17.6274 + 3.24883i −1.05344 + 0.194155i
\(281\) 3.18431 + 24.1872i 0.189960 + 1.44289i 0.775040 + 0.631912i \(0.217730\pi\)
−0.585080 + 0.810975i \(0.698937\pi\)
\(282\) 17.4130 2.96170i 1.03693 0.176367i
\(283\) 17.9483 + 15.7402i 1.06691 + 0.935659i 0.998078 0.0619687i \(-0.0197379\pi\)
0.0688368 + 0.997628i \(0.478071\pi\)
\(284\) 2.86766 + 23.4846i 0.170164 + 1.39355i
\(285\) −4.10356 + 11.2268i −0.243074 + 0.665018i
\(286\) 6.67862 11.4433i 0.394915 0.676654i
\(287\) 23.8438i 1.40745i
\(288\) −16.9389 + 1.03553i −0.998137 + 0.0610190i
\(289\) 21.3820i 1.25777i
\(290\) 12.1129 + 7.06945i 0.711295 + 0.415133i
\(291\) 13.7652 + 16.4503i 0.806933 + 0.964332i
\(292\) −11.0007 8.60652i −0.643769 0.503659i
\(293\) 9.61162 + 8.42917i 0.561517 + 0.492437i 0.892407 0.451232i \(-0.149015\pi\)
−0.330889 + 0.943670i \(0.607349\pi\)
\(294\) −25.3533 + 21.0135i −1.47863 + 1.22553i
\(295\) 1.00394 + 7.62568i 0.0584517 + 0.443984i
\(296\) −10.1738 + 6.59252i −0.591343 + 0.383182i
\(297\) 20.0912 1.23435i 1.16581 0.0716240i
\(298\) −3.46121 + 1.15682i −0.200502 + 0.0670128i
\(299\) 16.9890 + 8.37805i 0.982500 + 0.484515i
\(300\) 7.18711 7.67593i 0.414948 0.443170i
\(301\) −3.24984 1.10317i −0.187318 0.0635858i
\(302\) 4.47846 10.6699i 0.257706 0.613986i
\(303\) −3.88509 7.10453i −0.223192 0.408144i
\(304\) 18.5279 + 6.68011i 1.06265 + 0.383130i
\(305\) −4.13788 4.13788i −0.236934 0.236934i
\(306\) 25.8506 + 4.75628i 1.47778 + 0.271899i
\(307\) −11.3211 + 2.25190i −0.646127 + 0.128523i −0.507266 0.861789i \(-0.669344\pi\)
−0.138860 + 0.990312i \(0.544344\pi\)
\(308\) −6.51113 34.4203i −0.371006 1.96128i
\(309\) 17.3284 + 15.9221i 0.985780 + 0.905777i
\(310\) −0.163750 0.247578i −0.00930035 0.0140615i
\(311\) −4.07662 0.536698i −0.231164 0.0304333i 0.0140541 0.999901i \(-0.495526\pi\)
−0.245218 + 0.969468i \(0.578860\pi\)
\(312\) 6.85745 + 9.66201i 0.388227 + 0.547004i
\(313\) −15.5018 + 2.04086i −0.876216 + 0.115356i −0.555199 0.831717i \(-0.687358\pi\)
−0.321017 + 0.947073i \(0.604025\pi\)
\(314\) −6.78064 + 5.89036i −0.382654 + 0.332412i
\(315\) −4.56913 + 18.4544i −0.257441 + 1.03979i
\(316\) 0.364859 + 1.41469i 0.0205249 + 0.0795828i
\(317\) 0.960020 14.6471i 0.0539201 0.822661i −0.882177 0.470919i \(-0.843923\pi\)
0.936097 0.351743i \(-0.114411\pi\)
\(318\) −9.13864 5.62151i −0.512470 0.315239i
\(319\) −13.7050 + 23.7377i −0.767332 + 1.32906i
\(320\) 8.21852 + 7.62765i 0.459429 + 0.426399i
\(321\) −12.4397 13.0302i −0.694319 0.727277i
\(322\) 48.4361 12.7349i 2.69924 0.709688i
\(323\) −25.3638 16.9476i −1.41128 0.942988i
\(324\) −6.40679 + 16.8212i −0.355933 + 0.934511i
\(325\) −7.20040 1.43225i −0.399406 0.0794468i
\(326\) 14.8269 + 5.11084i 0.821186 + 0.283063i
\(327\) −14.3838 + 5.57099i −0.795426 + 0.308076i
\(328\) −11.9602 + 8.91246i −0.660389 + 0.492109i
\(329\) −32.3249 4.25565i −1.78213 0.234622i
\(330\) −9.75087 9.04434i −0.536768 0.497874i
\(331\) 4.89364 9.92332i 0.268979 0.545435i −0.719915 0.694063i \(-0.755819\pi\)
0.988893 + 0.148628i \(0.0474857\pi\)
\(332\) −3.14672 + 8.99155i −0.172699 + 0.493476i
\(333\) 1.92141 + 12.7141i 0.105293 + 0.696727i
\(334\) 0.433078 + 0.335555i 0.0236970 + 0.0183608i
\(335\) 5.68410 21.2133i 0.310556 1.15901i
\(336\) 30.4401 + 7.39489i 1.66064 + 0.403424i
\(337\) −3.82808 14.2866i −0.208529 0.778240i −0.988345 0.152231i \(-0.951354\pi\)
0.779816 0.626009i \(-0.215313\pi\)
\(338\) −3.91386 + 9.32478i −0.212886 + 0.507201i
\(339\) −12.7650 27.4725i −0.693302 1.49210i
\(340\) −9.51231 14.5298i −0.515877 0.787989i
\(341\) 0.482350 0.322296i 0.0261207 0.0174533i
\(342\) 14.5574 14.9826i 0.787175 0.810167i
\(343\) 26.9159 11.1489i 1.45332 0.601986i
\(344\) 0.661388 + 2.04249i 0.0356596 + 0.110124i
\(345\) 11.9215 14.8125i 0.641832 0.797477i
\(346\) 8.76514 + 5.91641i 0.471217 + 0.318068i
\(347\) −8.06366 7.07164i −0.432880 0.379625i 0.414993 0.909824i \(-0.363784\pi\)
−0.847873 + 0.530199i \(0.822117\pi\)
\(348\) −14.2800 19.9213i −0.765488 1.06789i
\(349\) 0.0299433 + 0.00196259i 0.00160283 + 0.000105055i 0.0662045 0.997806i \(-0.478911\pi\)
−0.0646017 + 0.997911i \(0.520578\pi\)
\(350\) −16.8551 + 9.62602i −0.900942 + 0.514532i
\(351\) 12.3353 2.40125i 0.658411 0.128169i
\(352\) −14.8316 + 16.1318i −0.790529 + 0.859830i
\(353\) −24.2568 + 14.0047i −1.29106 + 0.745393i −0.978842 0.204618i \(-0.934405\pi\)
−0.312216 + 0.950011i \(0.601071\pi\)
\(354\) 3.83960 12.8820i 0.204073 0.684670i
\(355\) −7.33320 14.8703i −0.389206 0.789231i
\(356\) 6.85646 0.837229i 0.363392 0.0443731i
\(357\) −43.0053 22.4617i −2.27608 1.18880i
\(358\) 14.9972 + 30.7749i 0.792628 + 1.62650i
\(359\) 3.76459 + 1.55934i 0.198688 + 0.0822991i 0.479808 0.877373i \(-0.340706\pi\)
−0.281121 + 0.959672i \(0.590706\pi\)
\(360\) 10.9647 4.60609i 0.577890 0.242762i
\(361\) −4.84509 + 2.00690i −0.255005 + 0.105626i
\(362\) 11.7379 13.2584i 0.616930 0.696844i
\(363\) 4.69541 5.11014i 0.246445 0.268213i
\(364\) −6.83511 20.7747i −0.358257 1.08889i
\(365\) 9.26882 + 3.14634i 0.485152 + 0.164687i
\(366\) 3.64882 + 9.55392i 0.190727 + 0.499391i
\(367\) −28.4655 7.62732i −1.48589 0.398143i −0.577542 0.816361i \(-0.695988\pi\)
−0.908347 + 0.418218i \(0.862655\pi\)
\(368\) −24.4926 19.5357i −1.27677 1.01837i
\(369\) 3.38205 + 15.4547i 0.176062 + 0.804541i
\(370\) 5.20350 6.71578i 0.270517 0.349137i
\(371\) 13.0582 + 14.8900i 0.677947 + 0.773050i
\(372\) 0.0845810 + 0.511816i 0.00438532 + 0.0265364i
\(373\) −24.0882 + 1.57882i −1.24724 + 0.0817484i −0.674677 0.738113i \(-0.735717\pi\)
−0.572562 + 0.819861i \(0.694051\pi\)
\(374\) 28.3089 18.7237i 1.46382 0.968180i
\(375\) −7.88083 + 17.8445i −0.406964 + 0.921487i
\(376\) 9.94792 + 17.8050i 0.513025 + 0.918224i
\(377\) −6.54864 + 15.8098i −0.337272 + 0.814247i
\(378\) 20.4573 26.1810i 1.05221 1.34660i
\(379\) 7.39320 + 1.47060i 0.379763 + 0.0755396i 0.381281 0.924459i \(-0.375483\pi\)
−0.00151760 + 0.999999i \(0.500483\pi\)
\(380\) −13.8018 0.129647i −0.708019 0.00665073i
\(381\) −4.21969 24.1233i −0.216181 1.23588i
\(382\) 6.70168 6.63903i 0.342888 0.339682i
\(383\) 7.83439 13.5696i 0.400319 0.693372i −0.593446 0.804874i \(-0.702233\pi\)
0.993764 + 0.111502i \(0.0355661\pi\)
\(384\) −7.66877 18.0330i −0.391345 0.920244i
\(385\) 12.2747 + 21.2604i 0.625575 + 1.08353i
\(386\) −9.36384 2.55623i −0.476607 0.130109i
\(387\) 2.26292 + 0.254076i 0.115030 + 0.0129154i
\(388\) −12.5850 + 21.3325i −0.638905 + 1.08299i
\(389\) −8.19254 24.1345i −0.415378 1.22367i −0.930418 0.366499i \(-0.880556\pi\)
0.515040 0.857166i \(-0.327777\pi\)
\(390\) −6.77255 4.80361i −0.342941 0.243240i
\(391\) 29.5395 + 38.4966i 1.49388 + 1.94686i
\(392\) −32.6584 19.4739i −1.64950 0.983583i
\(393\) 5.18667 + 7.09399i 0.261633 + 0.357844i
\(394\) −1.03469 17.0101i −0.0521271 0.856957i
\(395\) −0.568822 0.851302i −0.0286205 0.0428337i
\(396\) 9.10254 + 21.3865i 0.457420 + 1.07471i
\(397\) −4.15862 + 0.827201i −0.208715 + 0.0415160i −0.298340 0.954460i \(-0.596433\pi\)
0.0896253 + 0.995976i \(0.471433\pi\)
\(398\) 28.6655 + 3.91093i 1.43687 + 0.196037i
\(399\) −33.8322 + 18.5010i −1.69373 + 0.926211i
\(400\) 11.1286 + 4.85652i 0.556432 + 0.242826i
\(401\) 7.89460 + 29.4631i 0.394238 + 1.47132i 0.823075 + 0.567933i \(0.192257\pi\)
−0.428837 + 0.903382i \(0.641077\pi\)
\(402\) −24.2047 + 29.7869i −1.20722 + 1.48563i
\(403\) 0.272298 0.238799i 0.0135641 0.0118954i
\(404\) 6.23070 6.97155i 0.309989 0.346848i
\(405\) 0.343947 12.6096i 0.0170909 0.626577i
\(406\) 14.3417 + 42.9104i 0.711768 + 2.12961i
\(407\) 13.1727 + 10.1078i 0.652948 + 0.501025i
\(408\) 4.80786 + 29.9675i 0.238024 + 1.48361i
\(409\) −22.9248 + 17.5908i −1.13356 + 0.869811i −0.992747 0.120226i \(-0.961638\pi\)
−0.140813 + 0.990036i \(0.544972\pi\)
\(410\) 5.84804 8.66384i 0.288814 0.427877i
\(411\) 19.1356 + 9.99452i 0.943887 + 0.492993i
\(412\) −10.6341 + 25.0060i −0.523904 + 1.23196i
\(413\) −13.7849 + 20.6306i −0.678313 + 1.01517i
\(414\) −29.5883 + 15.1246i −1.45419 + 0.743334i
\(415\) 6.67596i 0.327710i
\(416\) −7.86581 + 11.1938i −0.385653 + 0.548821i
\(417\) −3.33883 13.7257i −0.163503 0.672150i
\(418\) 0.126690 26.9747i 0.00619661 1.31938i
\(419\) 15.9948 + 32.4343i 0.781398 + 1.58452i 0.811063 + 0.584959i \(0.198889\pi\)
−0.0296652 + 0.999560i \(0.509444\pi\)
\(420\) −21.8467 + 2.15506i −1.06601 + 0.105156i
\(421\) −21.3465 + 7.24615i −1.04036 + 0.353156i −0.788777 0.614679i \(-0.789286\pi\)
−0.251586 + 0.967835i \(0.580952\pi\)
\(422\) 1.43115 20.3688i 0.0696671 0.991537i
\(423\) 21.5555 1.82666i 1.04807 0.0888150i
\(424\) 2.58794 12.1157i 0.125681 0.588392i
\(425\) −14.9200 11.4485i −0.723724 0.555333i
\(426\) 1.08848 + 28.9558i 0.0527370 + 1.40291i
\(427\) −1.23466 18.8373i −0.0597494 0.911600i
\(428\) 9.37521 18.5693i 0.453168 0.897580i
\(429\) 9.32576 13.2800i 0.450252 0.641164i
\(430\) −0.910289 1.19792i −0.0438980 0.0577688i
\(431\) 13.8387 13.8387i 0.666585 0.666585i −0.290339 0.956924i \(-0.593768\pi\)
0.956924 + 0.290339i \(0.0937680\pi\)
\(432\) −20.7792 0.475432i −0.999738 0.0228742i
\(433\) −12.8784 12.8784i −0.618895 0.618895i 0.326353 0.945248i \(-0.394180\pi\)
−0.945248 + 0.326353i \(0.894180\pi\)
\(434\) 0.129444 0.948770i 0.00621351 0.0455424i
\(435\) 14.0571 + 9.87150i 0.673988 + 0.473302i
\(436\) −11.6174 13.5009i −0.556375 0.646576i
\(437\) 38.4827 2.52229i 1.84088 0.120657i
\(438\) −12.5420 11.6332i −0.599279 0.555856i
\(439\) −18.6907 + 24.3582i −0.892059 + 1.16255i 0.0939030 + 0.995581i \(0.470066\pi\)
−0.985962 + 0.166972i \(0.946601\pi\)
\(440\) 6.07621 14.1039i 0.289672 0.672375i
\(441\) −33.0996 + 23.0423i −1.57617 + 1.09725i
\(442\) 15.9967 13.8964i 0.760885 0.660982i
\(443\) 6.62208 + 19.5080i 0.314624 + 0.926853i 0.983092 + 0.183112i \(0.0586172\pi\)
−0.668468 + 0.743741i \(0.733050\pi\)
\(444\) −13.0934 + 7.00112i −0.621385 + 0.332258i
\(445\) −4.34146 + 2.14097i −0.205805 + 0.101492i
\(446\) −1.42636 1.43982i −0.0675400 0.0681774i
\(447\) −4.34295 + 1.05644i −0.205414 + 0.0499679i
\(448\) 3.70902 + 35.9809i 0.175235 + 1.69994i
\(449\) 14.6180 0.689864 0.344932 0.938628i \(-0.387902\pi\)
0.344932 + 0.938628i \(0.387902\pi\)
\(450\) 9.55952 8.63002i 0.450640 0.406823i
\(451\) 16.9858 + 11.3496i 0.799831 + 0.534430i
\(452\) 24.9656 24.5009i 1.17428 1.15243i
\(453\) 6.56121 12.5621i 0.308273 0.590220i
\(454\) −0.972661 5.01282i −0.0456492 0.235263i
\(455\) 9.33019 + 12.1593i 0.437406 + 0.570039i
\(456\) 21.9262 + 10.0550i 1.02679 + 0.470869i
\(457\) 21.2974 27.7554i 0.996252 1.29834i 0.0420704 0.999115i \(-0.486605\pi\)
0.954182 0.299227i \(-0.0967287\pi\)
\(458\) −16.4333 + 32.9326i −0.767878 + 1.53884i
\(459\) 31.0606 + 8.45897i 1.44978 + 0.394831i
\(460\) 20.7231 + 7.25232i 0.966219 + 0.338141i
\(461\) −1.62085 1.84823i −0.0754906 0.0860806i 0.712862 0.701305i \(-0.247399\pi\)
−0.788352 + 0.615224i \(0.789065\pi\)
\(462\) −4.41226 42.6762i −0.205277 1.98548i
\(463\) 30.0621 8.05511i 1.39710 0.374353i 0.519800 0.854288i \(-0.326007\pi\)
0.877304 + 0.479936i \(0.159340\pi\)
\(464\) 16.1634 23.2332i 0.750365 1.07857i
\(465\) −0.174425 0.318966i −0.00808877 0.0147917i
\(466\) −1.19610 1.57404i −0.0554083 0.0729160i
\(467\) 0.798122 + 4.01243i 0.0369327 + 0.185673i 0.994848 0.101378i \(-0.0323251\pi\)
−0.957915 + 0.287051i \(0.907325\pi\)
\(468\) 7.37701 + 12.4959i 0.341002 + 0.577625i
\(469\) 58.9071 39.3605i 2.72008 1.81750i
\(470\) −10.7018 9.47448i −0.493635 0.437025i
\(471\) −8.88012 + 6.49258i −0.409174 + 0.299162i
\(472\) 15.5011 0.796836i 0.713494 0.0366774i
\(473\) 2.33279 1.79002i 0.107262 0.0823050i
\(474\) 0.300031 + 1.76400i 0.0137809 + 0.0810233i
\(475\) −14.1534 + 4.80442i −0.649401 + 0.220442i
\(476\) 7.83395 55.4732i 0.359069 2.54261i
\(477\) −10.5759 7.79900i −0.484237 0.357092i
\(478\) 9.89708 5.65227i 0.452682 0.258529i
\(479\) −6.37515 + 3.68070i −0.291288 + 0.168175i −0.638523 0.769603i \(-0.720454\pi\)
0.347234 + 0.937778i \(0.387121\pi\)
\(480\) 9.24697 + 10.1529i 0.422065 + 0.463414i
\(481\) 8.97725 + 5.18302i 0.409327 + 0.236325i
\(482\) −10.7399 0.0504411i −0.489188 0.00229753i
\(483\) 60.4205 10.5689i 2.74923 0.480900i
\(484\) 7.37424 + 3.13598i 0.335193 + 0.142545i
\(485\) 3.38625 17.0238i 0.153762 0.773012i
\(486\) −9.54620 + 19.8713i −0.433024 + 0.901382i
\(487\) 7.47462 + 3.09609i 0.338707 + 0.140297i 0.545553 0.838076i \(-0.316320\pi\)
−0.206845 + 0.978374i \(0.566320\pi\)
\(488\) −8.98738 + 7.66042i −0.406839 + 0.346771i
\(489\) 17.5705 + 7.75981i 0.794565 + 0.350911i
\(490\) 26.1101 + 5.32123i 1.17954 + 0.240389i
\(491\) −0.352333 5.37557i −0.0159006 0.242596i −0.998409 0.0563798i \(-0.982044\pi\)
0.982509 0.186216i \(-0.0596224\pi\)
\(492\) −15.5117 + 9.64905i −0.699320 + 0.435013i
\(493\) −32.9576 + 28.9030i −1.48434 + 1.30173i
\(494\) −2.11974 16.7070i −0.0953715 0.751682i
\(495\) −10.9717 12.0392i −0.493139 0.541122i
\(496\) −0.524292 + 0.289707i −0.0235414 + 0.0130082i
\(497\) 13.8433 51.6639i 0.620957 2.31744i
\(498\) −4.76358 + 10.6505i −0.213461 + 0.477260i
\(499\) 1.84480 5.43460i 0.0825846 0.243286i −0.897792 0.440419i \(-0.854830\pi\)
0.980377 + 0.197133i \(0.0631631\pi\)
\(500\) −22.4620 1.68427i −1.00453 0.0753229i
\(501\) 0.494089 + 0.453990i 0.0220743 + 0.0202828i
\(502\) 0.341152 + 5.60846i 0.0152264 + 0.250318i
\(503\) 8.12202 + 19.6083i 0.362143 + 0.874291i 0.994986 + 0.100011i \(0.0318877\pi\)
−0.632843 + 0.774280i \(0.718112\pi\)
\(504\) 36.3908 + 12.1504i 1.62098 + 0.541224i
\(505\) −2.50753 + 6.05372i −0.111584 + 0.269387i
\(506\) −13.9833 + 40.5666i −0.621635 + 1.80341i
\(507\) −5.73404 + 10.9784i −0.254658 + 0.487569i
\(508\) 24.6213 13.9084i 1.09240 0.617087i
\(509\) −7.70740 + 3.80087i −0.341625 + 0.168471i −0.605005 0.796221i \(-0.706829\pi\)
0.263381 + 0.964692i \(0.415162\pi\)
\(510\) −10.1173 18.7093i −0.448001 0.828463i
\(511\) 15.7882 + 27.3460i 0.698429 + 1.20971i
\(512\) 16.6618 15.3096i 0.736355 0.676595i
\(513\) 19.3047 16.7906i 0.852324 0.741323i
\(514\) −13.8508 3.78113i −0.610935 0.166779i
\(515\) 1.24546 19.0021i 0.0548816 0.837332i
\(516\) 0.597465 + 2.56063i 0.0263019 + 0.112725i
\(517\) 18.4182 21.0019i 0.810031 0.923663i
\(518\) 26.9050 5.22050i 1.18214 0.229376i
\(519\) 10.0898 + 8.12056i 0.442893 + 0.356453i
\(520\) 2.61170 9.22506i 0.114530 0.404546i
\(521\) 0.555320 + 1.34066i 0.0243290 + 0.0587354i 0.935577 0.353122i \(-0.114880\pi\)
−0.911248 + 0.411858i \(0.864880\pi\)
\(522\) −15.3823 25.7789i −0.673267 1.12831i
\(523\) −12.6473 18.9280i −0.553028 0.827665i 0.444655 0.895702i \(-0.353326\pi\)
−0.997683 + 0.0680374i \(0.978326\pi\)
\(524\) −5.71656 + 8.38387i −0.249729 + 0.366251i
\(525\) −21.5589 + 10.0173i −0.940906 + 0.437191i
\(526\) 3.40133 + 8.32187i 0.148305 + 0.362851i
\(527\) 0.896152 0.240123i 0.0390370 0.0104599i
\(528\) −19.7574 + 18.1650i −0.859829 + 0.790529i
\(529\) −37.0390 9.92457i −1.61039 0.431503i
\(530\) 1.09281 + 8.61312i 0.0474687 + 0.374130i
\(531\) 6.00865 15.3274i 0.260753 0.665151i
\(532\) −33.1990 29.6710i −1.43936 1.28640i
\(533\) 11.4386 + 5.64091i 0.495463 + 0.244335i
\(534\) 8.45382 0.317788i 0.365833 0.0137520i
\(535\) −1.90278 + 14.4530i −0.0822643 + 0.624859i
\(536\) −41.7621 14.8357i −1.80385 0.640806i
\(537\) 15.1433 + 39.0986i 0.653480 + 1.68723i
\(538\) −11.8770 24.3721i −0.512055 1.05076i
\(539\) −10.1599 + 51.0771i −0.437617 + 2.20005i
\(540\) 13.8546 4.49562i 0.596208 0.193461i
\(541\) −22.0082 + 32.9377i −0.946208 + 1.41610i −0.0372069 + 0.999308i \(0.511846\pi\)
−0.909001 + 0.416793i \(0.863154\pi\)
\(542\) 18.6580 31.9689i 0.801430 1.37318i
\(543\) 15.6866 14.9757i 0.673178 0.642671i
\(544\) −30.7538 + 16.8055i −1.31856 + 0.720531i
\(545\) 10.8097 + 6.24100i 0.463038 + 0.267335i
\(546\) −6.20873 26.0559i −0.265709 1.11509i
\(547\) −2.43168 0.159381i −0.103971 0.00681463i 0.0133288 0.999911i \(-0.495757\pi\)
−0.117300 + 0.993097i \(0.537424\pi\)
\(548\) −3.48578 + 24.6832i −0.148905 + 1.05442i
\(549\) 3.47218 + 12.0346i 0.148189 + 0.513623i
\(550\) 1.16558 16.5892i 0.0497007 0.707365i
\(551\) 4.54746 + 34.5414i 0.193728 + 1.47151i
\(552\) −27.8857 26.3568i −1.18690 1.12182i
\(553\) 0.431113 3.27463i 0.0183328 0.139251i
\(554\) −1.28706 + 6.31532i −0.0546819 + 0.268312i
\(555\) 7.04007 7.66189i 0.298834 0.325229i
\(556\) 13.6468 8.93425i 0.578754 0.378897i
\(557\) −3.62169 18.2075i −0.153456 0.771476i −0.978474 0.206369i \(-0.933835\pi\)
0.825018 0.565106i \(-0.191165\pi\)
\(558\) 0.0506742 + 0.633321i 0.00214521 + 0.0268106i
\(559\) 1.29807 1.29807i 0.0549025 0.0549025i
\(560\) −10.7824 22.9413i −0.455641 0.969445i
\(561\) 36.4717 19.9444i 1.53983 0.842053i
\(562\) −31.9365 + 13.0531i −1.34716 + 0.550613i
\(563\) 9.46658 27.8876i 0.398969 1.17532i −0.543032 0.839712i \(-0.682724\pi\)
0.942000 0.335612i \(-0.108943\pi\)
\(564\) 10.3126 + 22.7513i 0.434240 + 0.958001i
\(565\) −10.8421 + 21.9855i −0.456129 + 0.924939i
\(566\) −15.0741 + 30.2087i −0.633610 + 1.26977i
\(567\) 27.6550 29.8516i 1.16140 1.25365i
\(568\) −31.0893 + 12.3674i −1.30448 + 0.518923i
\(569\) −19.7045 + 2.59415i −0.826056 + 0.108752i −0.531688 0.846940i \(-0.678442\pi\)
−0.294367 + 0.955692i \(0.595109\pi\)
\(570\) −16.8309 1.57534i −0.704969 0.0659838i
\(571\) 4.45736 5.08265i 0.186535 0.212702i −0.651012 0.759067i \(-0.725655\pi\)
0.837547 + 0.546365i \(0.183989\pi\)
\(572\) 18.0529 + 5.01948i 0.754831 + 0.209875i
\(573\) 8.86063 7.41439i 0.370158 0.309741i
\(574\) 32.6118 8.57436i 1.36119 0.357887i
\(575\) 23.7754 0.991504
\(576\) −7.50766 22.7955i −0.312819 0.949813i
\(577\) −13.8066 −0.574775 −0.287387 0.957814i \(-0.592787\pi\)
−0.287387 + 0.957814i \(0.592787\pi\)
\(578\) 29.2448 7.68910i 1.21642 0.319824i
\(579\) −11.1655 4.08115i −0.464021 0.169607i
\(580\) −5.31323 + 19.1094i −0.220620 + 0.793475i
\(581\) 14.1998 16.1918i 0.589108 0.671749i
\(582\) −17.5495 + 24.7427i −0.727448 + 1.02562i
\(583\) −16.8230 + 2.21479i −0.696737 + 0.0917272i
\(584\) 7.81547 18.1410i 0.323407 0.750679i
\(585\) −7.77222 6.55787i −0.321342 0.271134i
\(586\) −8.07243 + 16.1773i −0.333469 + 0.668277i
\(587\) 4.64181 9.41267i 0.191588 0.388502i −0.779790 0.626041i \(-0.784674\pi\)
0.971378 + 0.237539i \(0.0763408\pi\)
\(588\) −37.8579 27.1199i −1.56123 1.11841i
\(589\) 0.237016 0.698227i 0.00976607 0.0287699i
\(590\) −10.0688 + 4.11536i −0.414528 + 0.169427i
\(591\) 0.483757 20.8659i 0.0198991 0.858310i
\(592\) −12.6754 11.5444i −0.520954 0.474470i
\(593\) 11.8263 11.8263i 0.485649 0.485649i −0.421281 0.906930i \(-0.638419\pi\)
0.906930 + 0.421281i \(0.138419\pi\)
\(594\) 8.91316 + 27.0355i 0.365712 + 1.10928i
\(595\) 7.65945 + 38.5066i 0.314007 + 1.57862i
\(596\) −2.82689 4.31799i −0.115794 0.176872i
\(597\) 34.5827 + 7.71628i 1.41538 + 0.315806i
\(598\) −5.34956 + 26.2492i −0.218760 + 1.07341i
\(599\) 2.15789 16.3908i 0.0881692 0.669711i −0.889101 0.457712i \(-0.848669\pi\)
0.977270 0.212000i \(-0.0679975\pi\)
\(600\) 13.0831 + 7.06971i 0.534116 + 0.288620i
\(601\) −3.27537 24.8789i −0.133605 1.01483i −0.918561 0.395279i \(-0.870648\pi\)
0.784956 0.619552i \(-0.212686\pi\)
\(602\) 0.340180 4.84161i 0.0138647 0.197329i
\(603\) −32.5987 + 33.8677i −1.32752 + 1.37920i
\(604\) 16.2041 + 2.28835i 0.659334 + 0.0931116i
\(605\) −5.60369 0.367285i −0.227823 0.0149323i
\(606\) 8.31997 7.86857i 0.337976 0.319639i
\(607\) −22.3011 12.8755i −0.905173 0.522602i −0.0262980 0.999654i \(-0.508372\pi\)
−0.878875 + 0.477052i \(0.841705\pi\)
\(608\) −2.47382 + 27.7434i −0.100327 + 1.12514i
\(609\) 13.0973 + 53.8419i 0.530728 + 2.18178i
\(610\) 4.17150 7.14751i 0.168899 0.289394i
\(611\) 9.68893 14.5005i 0.391972 0.586628i
\(612\) 2.79072 + 37.0670i 0.112808 + 1.49835i
\(613\) −7.92580 + 39.8457i −0.320120 + 1.60935i 0.400685 + 0.916216i \(0.368772\pi\)
−0.720806 + 0.693137i \(0.756228\pi\)
\(614\) −7.15110 14.6743i −0.288595 0.592208i
\(615\) 8.02671 9.97319i 0.323668 0.402158i
\(616\) 44.7362 21.2832i 1.80247 0.857525i
\(617\) 0.896334 6.80833i 0.0360851 0.274093i −0.963885 0.266320i \(-0.914192\pi\)
0.999970 0.00777343i \(-0.00247439\pi\)
\(618\) −15.5457 + 29.4263i −0.625341 + 1.18370i
\(619\) −27.1942 13.4107i −1.09303 0.539021i −0.195823 0.980639i \(-0.562738\pi\)
−0.897203 + 0.441619i \(0.854404\pi\)
\(620\) 0.279734 0.312996i 0.0112344 0.0125702i
\(621\) −37.6635 + 15.4206i −1.51138 + 0.618806i
\(622\) −0.731920 5.76872i −0.0293473 0.231305i
\(623\) −15.0836 4.04164i −0.604311 0.161925i
\(624\) −10.7490 + 12.8537i −0.430306 + 0.514558i
\(625\) 0.587020 0.157292i 0.0234808 0.00629166i
\(626\) −8.36589 20.4684i −0.334368 0.818083i
\(627\) 2.92428 32.9079i 0.116784 1.31421i
\(628\) −10.4948 7.15588i −0.418787 0.285551i
\(629\) 14.7526 + 22.0789i 0.588226 + 0.880343i
\(630\) −26.8837 + 0.386975i −1.07107 + 0.0154175i
\(631\) −9.60750 23.1946i −0.382469 0.923361i −0.991487 0.130205i \(-0.958436\pi\)
0.609019 0.793156i \(-0.291564\pi\)
\(632\) −1.80371 + 1.00776i −0.0717479 + 0.0400866i
\(633\) 3.83801 24.7118i 0.152547 0.982206i
\(634\) 20.3785 3.95412i 0.809332 0.157038i
\(635\) −13.0664 + 14.8994i −0.518524 + 0.591263i
\(636\) 4.40240 14.5207i 0.174567 0.575784i
\(637\) −2.12645 + 32.4433i −0.0842528 + 1.28545i
\(638\) −37.3952 10.2085i −1.48049 0.404158i
\(639\) −1.64465 + 35.4504i −0.0650615 + 1.40240i
\(640\) −7.47714 + 13.9837i −0.295560 + 0.552752i
\(641\) 4.93155 + 8.54169i 0.194784 + 0.337377i 0.946830 0.321735i \(-0.104266\pi\)
−0.752045 + 0.659111i \(0.770933\pi\)
\(642\) 13.3484 21.7000i 0.526821 0.856429i
\(643\) −28.6792 + 14.1430i −1.13100 + 0.557745i −0.908790 0.417254i \(-0.862992\pi\)
−0.222206 + 0.975000i \(0.571326\pi\)
\(644\) 34.8358 + 61.6679i 1.37272 + 2.43005i
\(645\) −0.987949 1.55545i −0.0389005 0.0612456i
\(646\) 14.0587 40.7853i 0.553133 1.60468i
\(647\) 15.7055 37.9163i 0.617446 1.49065i −0.237214 0.971457i \(-0.576234\pi\)
0.854660 0.519188i \(-0.173766\pi\)
\(648\) −25.3108 2.71376i −0.994301 0.106606i
\(649\) −8.13526 19.6402i −0.319337 0.770947i
\(650\) −0.630376 10.3632i −0.0247254 0.406480i
\(651\) 0.255394 1.14462i 0.0100097 0.0448612i
\(652\) −1.65841 + 22.1171i −0.0649482 + 0.866172i
\(653\) −2.13610 + 6.29274i −0.0835919 + 0.246254i −0.980687 0.195584i \(-0.937340\pi\)
0.897095 + 0.441837i \(0.145673\pi\)
\(654\) −12.7921 17.6698i −0.500211 0.690943i
\(655\) 1.84051 6.86889i 0.0719148 0.268390i
\(656\) −16.4908 13.1533i −0.643857 0.513550i
\(657\) −14.1122 15.4853i −0.550569 0.604139i
\(658\) −5.80363 45.7420i −0.226249 1.78321i
\(659\) −32.7667 + 28.7356i −1.27641 + 1.11938i −0.289661 + 0.957129i \(0.593543\pi\)
−0.986749 + 0.162252i \(0.948124\pi\)
\(660\) 8.86374 16.5889i 0.345021 0.645724i
\(661\) −1.15549 17.6294i −0.0449435 0.685705i −0.959581 0.281431i \(-0.909191\pi\)
0.914638 0.404274i \(-0.132476\pi\)
\(662\) 15.3322 + 3.12469i 0.595903 + 0.121445i
\(663\) 20.9497 15.3171i 0.813620 0.594867i
\(664\) −13.4296 1.07044i −0.521169 0.0415412i
\(665\) 28.8282 + 11.9410i 1.11791 + 0.463054i
\(666\) −16.6985 + 7.20002i −0.647052 + 0.278995i
\(667\) 10.8117 54.3540i 0.418630 2.10460i
\(668\) −0.303212 + 0.713001i −0.0117316 + 0.0275868i
\(669\) −1.59294 1.90366i −0.0615866 0.0735996i
\(670\) 31.0582 + 0.145868i 1.19988 + 0.00563538i
\(671\) 14.0070 + 8.08694i 0.540734 + 0.312193i
\(672\) 0.832232 + 44.2931i 0.0321041 + 1.70864i
\(673\) 35.0637 20.2440i 1.35160 0.780349i 0.363130 0.931738i \(-0.381708\pi\)
0.988474 + 0.151389i \(0.0483746\pi\)
\(674\) 18.1636 10.3733i 0.699635 0.399565i
\(675\) 12.5529 9.55083i 0.483160 0.367612i
\(676\) −14.1612 1.99986i −0.544663 0.0769176i
\(677\) 1.36311 0.462714i 0.0523887 0.0177836i −0.295122 0.955460i \(-0.595360\pi\)
0.347511 + 0.937676i \(0.387027\pi\)
\(678\) 32.9845 27.3384i 1.26676 1.04992i
\(679\) 44.4228 34.0868i 1.70479 1.30813i
\(680\) 16.4521 18.2353i 0.630911 0.699290i
\(681\) −0.672370 6.21769i −0.0257653 0.238262i
\(682\) 0.614270 + 0.543825i 0.0235216 + 0.0208241i
\(683\) −9.30311 + 6.21614i −0.355974 + 0.237854i −0.720679 0.693269i \(-0.756170\pi\)
0.364705 + 0.931123i \(0.381170\pi\)
\(684\) 25.7271 + 14.5228i 0.983700 + 0.555292i
\(685\) −3.40814 17.1339i −0.130218 0.654651i
\(686\) 24.9279 + 32.8045i 0.951750 + 1.25248i
\(687\) −23.4372 + 38.5048i −0.894183 + 1.46905i
\(688\) −2.55573 + 1.63909i −0.0974364 + 0.0624897i
\(689\) −10.2325 + 2.74179i −0.389827 + 0.104454i
\(690\) 24.5465 + 10.9787i 0.934469 + 0.417954i
\(691\) 10.5438 + 12.0229i 0.401106 + 0.457373i 0.916769 0.399418i \(-0.130788\pi\)
−0.515663 + 0.856791i \(0.672454\pi\)
\(692\) −4.94006 + 14.1159i −0.187793 + 0.536606i
\(693\) −1.00304 52.5365i −0.0381025 1.99570i
\(694\) 6.77235 13.5719i 0.257075 0.515182i
\(695\) −6.95865 + 9.06869i −0.263957 + 0.343995i
\(696\) 22.1118 26.6950i 0.838146 1.01187i
\(697\) 19.8888 + 25.9196i 0.753343 + 0.981776i
\(698\) 0.00808348 + 0.0416600i 0.000305964 + 0.00157686i
\(699\) −1.29815 2.04382i −0.0491004 0.0773045i
\(700\) −19.2270 19.5916i −0.726711 0.740493i
\(701\) −11.4618 7.65852i −0.432905 0.289258i 0.319962 0.947430i \(-0.396330\pi\)
−0.752867 + 0.658172i \(0.771330\pi\)
\(702\) 7.72011 + 16.0079i 0.291377 + 0.604179i
\(703\) 21.1043 0.795965
\(704\) −27.3975 14.4846i −1.03258 0.545907i
\(705\) −12.0880 12.6618i −0.455260 0.476870i
\(706\) −27.8775 28.1406i −1.04918 1.05908i
\(707\) −18.9580 + 9.34908i −0.712991 + 0.351608i
\(708\) 18.9998 + 0.619102i 0.714057 + 0.0232673i
\(709\) −2.20388 6.49242i −0.0827685 0.243828i 0.897665 0.440678i \(-0.145262\pi\)
−0.980434 + 0.196850i \(0.936929\pi\)
\(710\) 17.7014 15.3773i 0.664323 0.577098i
\(711\) 0.185047 + 2.18365i 0.00693980 + 0.0818934i
\(712\) 3.61073 + 9.07672i 0.135318 + 0.340164i
\(713\) −0.714023 + 0.930534i −0.0267404 + 0.0348488i
\(714\) 15.2566 66.8969i 0.570963 2.50355i
\(715\) −13.1032 + 0.858830i −0.490033 + 0.0321184i
\(716\) −36.6986 + 31.5790i −1.37149 + 1.18016i
\(717\) 12.6591 5.88203i 0.472762 0.219668i
\(718\) −0.778993 + 5.70969i −0.0290718 + 0.213084i
\(719\) 30.3132 + 30.3132i 1.13049 + 1.13049i 0.990096 + 0.140395i \(0.0448371\pi\)
0.140395 + 0.990096i \(0.455163\pi\)
\(720\) 10.2429 + 13.3404i 0.381729 + 0.497166i
\(721\) 43.4383 43.4383i 1.61773 1.61773i
\(722\) −4.48722 5.90508i −0.166997 0.219764i
\(723\) −13.1021 1.16429i −0.487274 0.0433004i
\(724\) 22.3549 + 11.2865i 0.830812 + 0.419458i
\(725\) 1.40476 + 21.4325i 0.0521714 + 0.795982i
\(726\) 8.67778 + 4.58442i 0.322063 + 0.170144i
\(727\) 23.4117 + 17.9644i 0.868293 + 0.666264i 0.943669 0.330891i \(-0.107349\pi\)
−0.0753765 + 0.997155i \(0.524016\pi\)
\(728\) 25.9562 16.8193i 0.962000 0.623363i
\(729\) −13.6908 + 23.2715i −0.507067 + 0.861907i
\(730\) −0.970221 + 13.8087i −0.0359095 + 0.511082i
\(731\) 4.45297 1.51158i 0.164699 0.0559077i
\(732\) −11.7550 + 8.42624i −0.434479 + 0.311443i
\(733\) 3.47794 + 7.05256i 0.128461 + 0.260492i 0.951595 0.307354i \(-0.0994435\pi\)
−0.823135 + 0.567846i \(0.807777\pi\)
\(734\) 0.195736 41.6760i 0.00722475 1.53829i
\(735\) 31.3193 + 9.17509i 1.15523 + 0.338428i
\(736\) 17.9118 40.5244i 0.660238 1.49375i
\(737\) 60.6997i 2.23590i
\(738\) −19.9217 + 10.1833i −0.733328 + 0.374854i
\(739\) −21.4338 + 32.0779i −0.788454 + 1.18000i 0.191639 + 0.981465i \(0.438620\pi\)
−0.980093 + 0.198539i \(0.936380\pi\)
\(740\) 11.0566 + 4.70194i 0.406448 + 0.172847i
\(741\) −0.871592 20.6074i −0.0320187 0.757031i
\(742\) −15.6697 + 23.2146i −0.575253 + 0.852234i
\(743\) 33.7222 25.8759i 1.23715 0.949296i 0.237391 0.971414i \(-0.423708\pi\)
0.999755 + 0.0221187i \(0.00704117\pi\)
\(744\) −0.669610 + 0.299736i −0.0245491 + 0.0109888i
\(745\) 2.86943 + 2.20179i 0.105128 + 0.0806673i
\(746\) −10.8217 32.3784i −0.396209 1.18546i
\(747\) −6.90718 + 12.5091i −0.252720 + 0.457685i
\(748\) 35.7890 + 31.9858i 1.30858 + 1.16952i
\(749\) −35.3567 + 31.0070i −1.29191 + 1.13297i
\(750\) −27.2405 4.36185i −0.994681 0.159272i
\(751\) 9.37729 + 34.9965i 0.342182 + 1.27704i 0.895870 + 0.444317i \(0.146554\pi\)
−0.553688 + 0.832725i \(0.686780\pi\)
\(752\) −20.7751 + 20.0089i −0.757591 + 0.729648i
\(753\) −0.159501 + 6.87978i −0.00581255 + 0.250713i
\(754\) −23.9785 3.27147i −0.873245 0.119140i
\(755\) −11.2480 + 2.23738i −0.409358 + 0.0814264i
\(756\) 43.1650 + 18.5653i 1.56990 + 0.675212i
\(757\) −16.4032 24.5492i −0.596186 0.892255i 0.403557 0.914955i \(-0.367774\pi\)
−0.999742 + 0.0226997i \(0.992774\pi\)
\(758\) 0.647256 + 10.6407i 0.0235094 + 0.386489i
\(759\) −21.2310 + 48.0731i −0.770635 + 1.74494i
\(760\) −4.78589 18.9238i −0.173603 0.686438i
\(761\) −21.0139 27.3858i −0.761753 0.992735i −0.999769 0.0214743i \(-0.993164\pi\)
0.238017 0.971261i \(-0.423503\pi\)
\(762\) 31.4768 14.4463i 1.14028 0.523334i
\(763\) 12.9431 + 38.1293i 0.468573 + 1.38037i
\(764\) 11.4904 + 6.77866i 0.415707 + 0.245243i
\(765\) −10.4265 23.8723i −0.376970 0.863105i
\(766\) 21.3768 + 5.83563i 0.772374 + 0.210850i
\(767\) −6.63598 11.4938i −0.239611 0.415019i
\(768\) 21.9066 16.9736i 0.790485 0.612481i
\(769\) −2.24158 + 3.88253i −0.0808334 + 0.140008i −0.903608 0.428360i \(-0.859092\pi\)
0.822775 + 0.568368i \(0.192425\pi\)
\(770\) −24.6644 + 24.4338i −0.888843 + 0.880532i
\(771\) −16.5158 6.03677i −0.594802 0.217409i
\(772\) 0.128938 13.7264i 0.00464060 0.494025i
\(773\) 42.7651 + 8.50651i 1.53815 + 0.305958i 0.890146 0.455676i \(-0.150602\pi\)
0.648008 + 0.761634i \(0.275602\pi\)
\(774\) 0.466251 + 3.18642i 0.0167590 + 0.114534i
\(775\) 0.173960 0.419977i 0.00624884 0.0150860i
\(776\) −33.7027 9.54154i −1.20986 0.342521i
\(777\) 33.3718 3.60877i 1.19721 0.129464i
\(778\) 30.0633 19.8841i 1.07782 0.712878i
\(779\) 25.9103 1.69825i 0.928332 0.0608461i
\(780\) 4.13459 10.9904i 0.148042 0.393520i
\(781\) 30.2150 + 34.4536i 1.08118 + 1.23285i
\(782\) −42.0304 + 54.2456i −1.50300 + 1.93982i
\(783\) −16.1262 33.0408i −0.576305 1.18078i
\(784\) 14.8909 51.6708i 0.531819 1.84539i
\(785\) 8.59835 + 2.30392i 0.306888 + 0.0822304i
\(786\) −7.83750 + 9.64501i −0.279554 + 0.344026i
\(787\) −11.7891 4.00185i −0.420235 0.142651i 0.103309 0.994649i \(-0.467057\pi\)
−0.523544 + 0.851999i \(0.675390\pi\)
\(788\) 22.8931 7.53211i 0.815535 0.268320i
\(789\) 3.29664 + 10.5055i 0.117363 + 0.374006i
\(790\) 0.959799 1.08413i 0.0341481 0.0385715i
\(791\) −73.0597 + 30.2623i −2.59770 + 1.07600i
\(792\) −25.9777 + 20.1405i −0.923076 + 0.715663i
\(793\) 9.32895 + 3.86418i 0.331281 + 0.137221i
\(794\) −2.62685 5.39040i −0.0932234 0.191298i
\(795\) 0.449341 + 10.6239i 0.0159365 + 0.376793i
\(796\) 4.95917 + 40.6130i 0.175773 + 1.43949i
\(797\) 1.92980 + 3.91325i 0.0683571 + 0.138615i 0.928369 0.371659i \(-0.121211\pi\)
−0.860012 + 0.510273i \(0.829544\pi\)
\(798\) −37.4707 39.6203i −1.32645 1.40254i
\(799\) 38.6889 22.3370i 1.36871 0.790227i
\(800\) −2.64048 + 16.9674i −0.0933552 + 0.599889i
\(801\) 10.3500 + 0.480166i 0.365698 + 0.0169658i
\(802\) −37.4586 + 21.3928i −1.32271 + 0.755405i
\(803\) −26.9958 1.76940i −0.952663 0.0624408i
\(804\) −49.4446 22.3940i −1.74378 0.789775i
\(805\) −37.3177 32.7267i −1.31528 1.15347i
\(806\) 0.424532 + 0.286557i 0.0149535 + 0.0100935i
\(807\) −11.9927 30.9641i −0.422163 1.08999i
\(808\) 11.7758 + 6.01491i 0.414271 + 0.211604i
\(809\) −18.0256 + 7.46643i −0.633745 + 0.262506i −0.676343 0.736587i \(-0.736436\pi\)
0.0425985 + 0.999092i \(0.486436\pi\)
\(810\) 17.3702 4.06406i 0.610328 0.142797i
\(811\) −31.9288 + 21.3341i −1.12117 + 0.749142i −0.970896 0.239502i \(-0.923016\pi\)
−0.150275 + 0.988644i \(0.548016\pi\)
\(812\) −53.5325 + 35.0465i −1.87862 + 1.22989i
\(813\) 26.0533 37.1002i 0.913729 1.30116i
\(814\) −9.08774 + 21.6516i −0.318525 + 0.758887i
\(815\) −4.02284 15.0134i −0.140914 0.525898i
\(816\) −39.2585 + 17.3523i −1.37432 + 0.607454i
\(817\) 0.967316 3.61007i 0.0338421 0.126300i
\(818\) −32.3034 25.0292i −1.12946 0.875125i
\(819\) −4.90203 32.4370i −0.171291 1.13344i
\(820\) 13.9528 + 4.88296i 0.487252 + 0.170521i
\(821\) −16.9788 + 34.4295i −0.592563 + 1.20160i 0.369617 + 0.929184i \(0.379489\pi\)
−0.962180 + 0.272415i \(0.912178\pi\)
\(822\) −6.78854 + 29.7663i −0.236778 + 1.03822i
\(823\) −19.7620 2.60172i −0.688861 0.0906903i −0.222034 0.975039i \(-0.571270\pi\)
−0.466827 + 0.884349i \(0.654603\pi\)
\(824\) −38.0255 5.55226i −1.32468 0.193422i
\(825\) 3.12583 20.1263i 0.108827 0.700708i
\(826\) −33.1743 11.4352i −1.15428 0.397881i
\(827\) −20.8431 4.14594i −0.724784 0.144169i −0.181108 0.983463i \(-0.557968\pi\)
−0.543677 + 0.839295i \(0.682968\pi\)
\(828\) −31.3265 35.0299i −1.08867 1.21737i
\(829\) −5.10075 3.40821i −0.177156 0.118372i 0.463830 0.885924i \(-0.346475\pi\)
−0.640987 + 0.767552i \(0.721475\pi\)
\(830\) 9.13091 2.40071i 0.316939 0.0833300i
\(831\) −2.21920 + 7.57528i −0.0769833 + 0.262784i
\(832\) −18.1387 6.73295i −0.628846 0.233423i
\(833\) −41.6432 + 72.1281i −1.44285 + 2.49909i
\(834\) 17.5724 9.50245i 0.608481 0.329043i
\(835\) 0.0355121 0.541810i 0.00122895 0.0187501i
\(836\) 36.9397 9.52699i 1.27759 0.329498i
\(837\) −0.00318249 + 0.778130i −0.000110003 + 0.0268961i
\(838\) −38.6095 + 33.5401i −1.33374 + 1.15862i
\(839\) 15.3332 2.01866i 0.529362 0.0696918i 0.138892 0.990308i \(-0.455646\pi\)
0.390470 + 0.920616i \(0.372313\pi\)
\(840\) −10.8037 29.1054i −0.372764 1.00423i
\(841\) 20.8846 + 2.74950i 0.720157 + 0.0948105i
\(842\) −17.5871 26.5905i −0.606091 0.916368i
\(843\) −40.3166 + 12.6514i −1.38858 + 0.435736i
\(844\) 28.3736 5.36731i 0.976661 0.184751i
\(845\) 9.83001 1.95531i 0.338162 0.0672647i
\(846\) 10.2499 + 28.8253i 0.352398 + 0.991033i
\(847\) −12.8099 12.8099i −0.440154 0.440154i
\(848\) 17.5017 0.817283i 0.601010 0.0280656i
\(849\) −21.4986 + 35.3199i −0.737830 + 1.21218i
\(850\) 10.2931 24.5234i 0.353051 0.841146i
\(851\) −31.7890 10.7909i −1.08971 0.369907i
\(852\) −39.2123 + 11.9014i −1.34339 + 0.407736i
\(853\) −18.8427 9.29219i −0.645161 0.318158i 0.0901093 0.995932i \(-0.471278\pi\)
−0.735271 + 0.677773i \(0.762945\pi\)
\(854\) 25.3203 8.46267i 0.866443 0.289587i
\(855\) −20.3792 3.65073i −0.696955 0.124852i
\(856\) 28.7691 + 6.14513i 0.983308 + 0.210036i
\(857\) 3.96970 + 30.1529i 0.135602 + 1.03000i 0.914995 + 0.403466i \(0.132195\pi\)
−0.779392 + 0.626536i \(0.784472\pi\)
\(858\) 21.5170 + 7.97955i 0.734579 + 0.272417i
\(859\) −28.8277 25.2812i −0.983588 0.862583i 0.00692891 0.999976i \(-0.497794\pi\)
−0.990517 + 0.137393i \(0.956128\pi\)
\(860\) 1.31108 1.67581i 0.0447076 0.0571446i
\(861\) 40.6809 7.11598i 1.38640 0.242512i
\(862\) 23.9040 + 13.9511i 0.814174 + 0.475176i
\(863\) 20.1654i 0.686437i 0.939256 + 0.343218i \(0.111517\pi\)
−0.939256 + 0.343218i \(0.888483\pi\)
\(864\) −6.82205 28.5913i −0.232091 0.972694i
\(865\) 10.4806i 0.356353i
\(866\) 12.9830 22.2453i 0.441180 0.755925i
\(867\) 36.4809 6.38129i 1.23895 0.216720i
\(868\) 1.34421 0.164139i 0.0456254 0.00557123i
\(869\) 2.12757 + 1.86583i 0.0721729 + 0.0632939i
\(870\) −8.44652 + 22.7762i −0.286364 + 0.772186i
\(871\) 4.94638 + 37.5715i 0.167602 + 1.27306i
\(872\) 14.2879 20.7445i 0.483849 0.702498i
\(873\) −23.9584 + 28.3949i −0.810870 + 0.961023i
\(874\) 17.2884 + 51.7269i 0.584789 + 1.74969i
\(875\) 45.6714 + 22.5226i 1.54397 + 0.761404i
\(876\) 11.4009 21.3374i 0.385201 0.720924i
\(877\) 28.5138 + 9.67914i 0.962843 + 0.326841i 0.758219 0.652000i \(-0.226070\pi\)
0.204624 + 0.978841i \(0.434403\pi\)
\(878\) −40.0367 16.8045i −1.35117 0.567124i
\(879\) −11.5129 + 18.9144i −0.388320 + 0.637968i
\(880\) 21.4753 + 3.23878i 0.723933 + 0.109179i
\(881\) −8.29369 8.29369i −0.279422 0.279422i 0.553457 0.832878i \(-0.313309\pi\)
−0.832878 + 0.553457i \(0.813309\pi\)
\(882\) −43.4185 36.9851i −1.46198 1.24535i
\(883\) −57.1522 + 11.3683i −1.92332 + 0.382573i −0.999999 0.00144844i \(-0.999539\pi\)
−0.923324 + 0.384021i \(0.874539\pi\)
\(884\) 24.7590 + 16.8819i 0.832734 + 0.567801i
\(885\) −12.7109 + 3.98869i −0.427272 + 0.134078i
\(886\) −24.3003 + 16.0724i −0.816386 + 0.539963i
\(887\) 4.78443 + 0.629882i 0.160645 + 0.0211494i 0.210420 0.977611i \(-0.432517\pi\)
−0.0497744 + 0.998760i \(0.515850\pi\)
\(888\) −14.2841 15.3906i −0.479343 0.516474i
\(889\) −63.3821 + 8.34441i −2.12577 + 0.279863i
\(890\) −4.48948 5.16804i −0.150488 0.173233i
\(891\) 8.10203 + 33.9101i 0.271428 + 1.13603i
\(892\) 1.45636 2.46864i 0.0487624 0.0826561i
\(893\) 2.32217 35.4295i 0.0777085 1.18560i
\(894\) −3.00667 5.56008i −0.100558 0.185957i
\(895\) 16.9645 29.3834i 0.567062 0.982179i
\(896\) −47.8783 + 18.0119i −1.59950 + 0.601734i
\(897\) −9.22395 + 31.4861i −0.307979 + 1.05129i
\(898\) 5.25670 + 19.9934i 0.175418 + 0.667189i
\(899\) −0.881021 0.588679i −0.0293837 0.0196336i
\(900\) 15.2412 + 9.97143i 0.508040 + 0.332381i
\(901\) −26.6152 5.29410i −0.886682 0.176372i
\(902\) −9.41493 + 27.3134i −0.313483 + 0.909436i
\(903\) 0.912285 5.87394i 0.0303589 0.195472i
\(904\) 42.4884 + 25.3355i 1.41314 + 0.842646i
\(905\) −17.3995 2.29069i −0.578378 0.0761450i
\(906\) 19.5410 + 4.45655i 0.649207 + 0.148059i
\(907\) −8.49939 + 17.2351i −0.282218 + 0.572281i −0.991111 0.133035i \(-0.957528\pi\)
0.708894 + 0.705315i \(0.249195\pi\)
\(908\) 6.50641 3.13298i 0.215923 0.103971i
\(909\) 10.9619 8.74881i 0.363583 0.290180i
\(910\) −13.2755 + 17.1337i −0.440078 + 0.567978i
\(911\) −6.56383 + 24.4966i −0.217469 + 0.811607i 0.767813 + 0.640674i \(0.221345\pi\)
−0.985283 + 0.170933i \(0.945322\pi\)
\(912\) −5.86772 + 33.6050i −0.194300 + 1.11277i
\(913\) 4.77564 + 17.8229i 0.158051 + 0.589853i
\(914\) 45.6205 + 19.1482i 1.50899 + 0.633365i
\(915\) 5.82491 8.29474i 0.192566 0.274216i
\(916\) −50.9524 10.6336i −1.68352 0.351343i
\(917\) 19.0742 12.7449i 0.629884 0.420875i
\(918\) −0.400010 + 45.5244i −0.0132023 + 1.50253i
\(919\) 24.6972 10.2299i 0.814684 0.337453i 0.0638628 0.997959i \(-0.479658\pi\)
0.750821 + 0.660506i \(0.229658\pi\)
\(920\) −2.46708 + 30.9515i −0.0813372 + 1.02044i
\(921\) −7.22074 18.6433i −0.237931 0.614318i
\(922\) 1.94501 2.88152i 0.0640554 0.0948978i
\(923\) 21.5099 + 18.8636i 0.708006 + 0.620904i
\(924\) 56.7828 21.3814i 1.86802 0.703396i
\(925\) 12.9829 + 0.850947i 0.426876 + 0.0279790i
\(926\) 21.8277 + 38.2201i 0.717303 + 1.25599i
\(927\) −21.9939 + 34.3167i −0.722374 + 1.12711i
\(928\) 37.5892 + 13.7523i 1.23393 + 0.451442i
\(929\) 24.0591 13.8905i 0.789352 0.455733i −0.0503824 0.998730i \(-0.516044\pi\)
0.839734 + 0.542997i \(0.182711\pi\)
\(930\) 0.373534 0.353268i 0.0122487 0.0115841i
\(931\) 29.2766 + 59.3671i 0.959502 + 1.94568i
\(932\) 1.72274 2.20198i 0.0564301 0.0721281i
\(933\) −0.300950 7.11549i −0.00985268 0.232951i
\(934\) −5.20091 + 2.53451i −0.170179 + 0.0829316i
\(935\) −31.0772 12.8726i −1.01633 0.420980i
\(936\) −14.4382 + 14.5834i −0.471929 + 0.476672i
\(937\) 2.42520 1.00455i 0.0792277 0.0328172i −0.342718 0.939438i \(-0.611347\pi\)
0.421945 + 0.906621i \(0.361347\pi\)
\(938\) 75.0178 + 66.4147i 2.44942 + 2.16852i
\(939\) −8.10840 25.8393i −0.264607 0.843234i
\(940\) 9.11011 18.0442i 0.297139 0.588537i
\(941\) −36.5920 12.4213i −1.19286 0.404923i −0.346767 0.937951i \(-0.612721\pi\)
−0.846097 + 0.533028i \(0.821054\pi\)
\(942\) −12.0734 9.81084i −0.393374 0.319654i
\(943\) −39.8964 10.6902i −1.29920 0.348121i
\(944\) 6.66412 + 20.9147i 0.216899 + 0.680715i
\(945\) −32.8495 2.28804i −1.06859 0.0744298i
\(946\) 3.28714 + 2.54693i 0.106874 + 0.0828079i
\(947\) 17.7934 + 20.2895i 0.578208 + 0.659320i 0.964816 0.262924i \(-0.0846869\pi\)
−0.386609 + 0.922244i \(0.626354\pi\)
\(948\) −2.30479 + 1.04471i −0.0748560 + 0.0339305i
\(949\) −16.8539 + 1.10466i −0.547101 + 0.0358589i
\(950\) −11.6608 17.6303i −0.378325 0.572001i
\(951\) 25.2765 2.73336i 0.819648 0.0886354i
\(952\) 78.6894 9.23374i 2.55034 0.299267i
\(953\) 6.70376 16.1843i 0.217156 0.524261i −0.777334 0.629088i \(-0.783429\pi\)
0.994491 + 0.104826i \(0.0334287\pi\)
\(954\) 6.86377 17.2695i 0.222223 0.559122i
\(955\) −9.16956 1.82394i −0.296720 0.0590213i
\(956\) 11.2898 + 11.5039i 0.365139 + 0.372064i
\(957\) −44.5901 16.2984i −1.44139 0.526851i
\(958\) −7.32674 7.39588i −0.236716 0.238950i
\(959\) 28.1778 48.8054i 0.909909 1.57601i
\(960\) −10.5611 + 16.2984i −0.340859 + 0.526028i
\(961\) −15.4888 26.8274i −0.499638 0.865399i
\(962\) −3.86069 + 14.1423i −0.124474 + 0.455966i
\(963\) 18.5189 25.1128i 0.596765 0.809248i
\(964\) −3.79313 14.7074i −0.122169 0.473693i
\(965\) 3.09219 + 9.10931i 0.0995413 + 0.293239i
\(966\) 36.1829 + 78.8383i 1.16417 + 2.53658i
\(967\) −7.87488 10.2627i −0.253239 0.330027i 0.649383 0.760461i \(-0.275027\pi\)
−0.902622 + 0.430434i \(0.858361\pi\)
\(968\) −1.63736 + 11.2137i −0.0526266 + 0.360421i
\(969\) 21.3454 48.3323i 0.685713 1.55266i
\(970\) 24.5017 1.49039i 0.786702 0.0478536i
\(971\) −2.39507 3.58447i −0.0768613 0.115031i 0.791047 0.611755i \(-0.209536\pi\)
−0.867909 + 0.496724i \(0.834536\pi\)
\(972\) −30.6115 5.91077i −0.981864 0.189588i
\(973\) −36.1666 + 7.19399i −1.15945 + 0.230629i
\(974\) −1.54670 + 11.3366i −0.0495593 + 0.363249i
\(975\) 0.294724 12.7124i 0.00943873 0.407122i
\(976\) −13.7093 9.53757i −0.438824 0.305290i
\(977\) 1.08980 + 4.06720i 0.0348659 + 0.130121i 0.981165 0.193171i \(-0.0618771\pi\)
−0.946299 + 0.323292i \(0.895210\pi\)
\(978\) −4.29487 + 26.8221i −0.137335 + 0.857678i
\(979\) 10.0589 8.82144i 0.321485 0.281935i
\(980\) 2.11135 + 37.6252i 0.0674447 + 1.20189i
\(981\) −13.7976 22.8782i −0.440525 0.730446i
\(982\) 7.22562 2.41498i 0.230579 0.0770651i
\(983\) 24.4368 + 18.7510i 0.779413 + 0.598065i 0.919961 0.392009i \(-0.128220\pi\)
−0.140548 + 0.990074i \(0.544886\pi\)
\(984\) −18.7754 17.7459i −0.598537 0.565719i
\(985\) −13.3993 + 10.2816i −0.426937 + 0.327600i
\(986\) −51.3833 34.6834i −1.63638 1.10454i
\(987\) −2.38633 56.4210i −0.0759578 1.79590i
\(988\) 22.0883 8.90715i 0.702724 0.283374i
\(989\) −3.30292 + 4.94317i −0.105027 + 0.157184i
\(990\) 12.5209 19.3356i 0.397940 0.614526i
\(991\) 62.2941i 1.97884i −0.145084 0.989419i \(-0.546345\pi\)
0.145084 0.989419i \(-0.453655\pi\)
\(992\) −0.584779 0.612910i −0.0185668 0.0194599i
\(993\) 18.3911 + 5.38773i 0.583624 + 0.170974i
\(994\) 75.6404 + 0.355254i 2.39917 + 0.0112680i
\(995\) −12.6816 25.7158i −0.402035 0.815246i
\(996\) −16.2800 2.68530i −0.515852 0.0850870i
\(997\) −2.57533 + 0.874206i −0.0815614 + 0.0276864i −0.361922 0.932208i \(-0.617879\pi\)
0.280361 + 0.959895i \(0.409546\pi\)
\(998\) 8.09647 + 0.568872i 0.256289 + 0.0180073i
\(999\) −21.1186 + 7.07261i −0.668164 + 0.223768i
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 576.2.bm.a.517.57 yes 1504
9.7 even 3 inner 576.2.bm.a.133.72 yes 1504
64.13 even 16 inner 576.2.bm.a.13.72 1504
576.205 even 48 inner 576.2.bm.a.205.57 yes 1504
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.2.bm.a.13.72 1504 64.13 even 16 inner
576.2.bm.a.133.72 yes 1504 9.7 even 3 inner
576.2.bm.a.205.57 yes 1504 576.205 even 48 inner
576.2.bm.a.517.57 yes 1504 1.1 even 1 trivial