Properties

Label 504.2.y.a.173.20
Level $504$
Weight $2$
Character 504.173
Analytic conductor $4.024$
Analytic rank $0$
Dimension $184$
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] = [504,2,Mod(173,504)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(504, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 1, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("504.173");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 504.y (of order \(6\), degree \(2\), 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: \(4.02446026187\)
Analytic rank: \(0\)
Dimension: \(184\)
Relative dimension: \(92\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 173.20
Character \(\chi\) \(=\) 504.173
Dual form 504.2.y.a.437.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.12327 + 0.859225i) q^{2} +(0.944647 + 1.45177i) q^{3} +(0.523464 - 1.93028i) q^{4} -3.97106i q^{5} +(-2.30849 - 0.819065i) q^{6} +(-2.57827 - 0.593742i) q^{7} +(1.07056 + 2.61800i) q^{8} +(-1.21528 + 2.74282i) q^{9} +O(q^{10})\) \(q+(-1.12327 + 0.859225i) q^{2} +(0.944647 + 1.45177i) q^{3} +(0.523464 - 1.93028i) q^{4} -3.97106i q^{5} +(-2.30849 - 0.819065i) q^{6} +(-2.57827 - 0.593742i) q^{7} +(1.07056 + 2.61800i) q^{8} +(-1.21528 + 2.74282i) q^{9} +(3.41204 + 4.46057i) q^{10} -2.29171 q^{11} +(3.29682 - 1.06349i) q^{12} +(0.364860 + 0.631957i) q^{13} +(3.40625 - 1.54838i) q^{14} +(5.76508 - 3.75125i) q^{15} +(-3.45197 - 2.02086i) q^{16} +(-3.53491 - 6.12264i) q^{17} +(-0.991615 - 4.12513i) q^{18} +(-1.20692 + 2.09045i) q^{19} +(-7.66527 - 2.07871i) q^{20} +(-1.57358 - 4.30393i) q^{21} +(2.57421 - 1.96910i) q^{22} -1.38400i q^{23} +(-2.78944 + 4.02729i) q^{24} -10.7693 q^{25} +(-0.952829 - 0.396360i) q^{26} +(-5.12997 + 0.826688i) q^{27} +(-2.49572 + 4.66598i) q^{28} +(3.75443 - 6.50286i) q^{29} +(-3.25256 + 9.16716i) q^{30} +(-5.08798 - 2.93755i) q^{31} +(5.61387 - 0.696048i) q^{32} +(-2.16486 - 3.32705i) q^{33} +(9.23137 + 3.84008i) q^{34} +(-2.35778 + 10.2385i) q^{35} +(4.65827 + 3.78161i) q^{36} +(-1.62245 - 0.936723i) q^{37} +(-0.440470 - 3.38515i) q^{38} +(-0.572792 + 1.12667i) q^{39} +(10.3962 - 4.25125i) q^{40} +(-4.35544 - 7.54384i) q^{41} +(5.46560 + 3.48242i) q^{42} +(10.4290 + 6.02121i) q^{43} +(-1.19963 + 4.42365i) q^{44} +(10.8919 + 4.82596i) q^{45} +(1.18917 + 1.55461i) q^{46} +(-1.73952 - 3.01293i) q^{47} +(-0.327061 - 6.92048i) q^{48} +(6.29494 + 3.06165i) q^{49} +(12.0969 - 9.25328i) q^{50} +(5.54943 - 10.9156i) q^{51} +(1.41085 - 0.373477i) q^{52} +(1.80951 + 3.13416i) q^{53} +(5.05202 - 5.33639i) q^{54} +9.10054i q^{55} +(-1.20577 - 7.38553i) q^{56} +(-4.17497 + 0.222563i) q^{57} +(1.37019 + 10.5304i) q^{58} +(-5.72312 - 3.30424i) q^{59} +(-4.22317 - 13.0919i) q^{60} +(1.14171 + 1.97750i) q^{61} +(8.23918 - 1.07207i) q^{62} +(4.76186 - 6.35018i) q^{63} +(-5.70782 + 5.60543i) q^{64} +(2.50954 - 1.44888i) q^{65} +(5.29040 + 1.87706i) q^{66} +(1.46604 + 0.846418i) q^{67} +(-13.6688 + 3.61838i) q^{68} +(2.00926 - 1.30740i) q^{69} +(-6.14872 - 13.5264i) q^{70} +7.40857i q^{71} +(-8.48174 - 0.245259i) q^{72} +(0.925740 - 0.534476i) q^{73} +(2.62730 - 0.341860i) q^{74} +(-10.1732 - 15.6346i) q^{75} +(3.40338 + 3.42397i) q^{76} +(5.90865 + 1.36069i) q^{77} +(-0.324664 - 1.75771i) q^{78} +(-1.89917 - 3.28947i) q^{79} +(-8.02498 + 13.7080i) q^{80} +(-6.04617 - 6.66662i) q^{81} +(11.3742 + 4.73145i) q^{82} +(11.0110 + 6.35720i) q^{83} +(-9.13152 + 0.784493i) q^{84} +(-24.3134 + 14.0373i) q^{85} +(-16.8882 + 2.19746i) q^{86} +(12.9873 - 0.692336i) q^{87} +(-2.45341 - 5.99970i) q^{88} +(-2.05246 + 3.55496i) q^{89} +(-16.3811 + 3.93777i) q^{90} +(-0.565489 - 1.84599i) q^{91} +(-2.67152 - 0.724476i) q^{92} +(-0.541699 - 10.1615i) q^{93} +(4.54273 + 1.88969i) q^{94} +(8.30131 + 4.79276i) q^{95} +(6.31363 + 7.49254i) q^{96} +(8.60686 + 4.96917i) q^{97} +(-9.70156 + 1.96972i) q^{98} +(2.78508 - 6.28577i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 184 q - 3 q^{2} + q^{4} + 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 3 q^{12} - 3 q^{14} - 2 q^{15} + q^{16} - 15 q^{18} - 6 q^{22} - 12 q^{24} - 156 q^{25} + 6 q^{26} - 8 q^{28} - 14 q^{30} - 6 q^{31} - 33 q^{32} - 6 q^{33} - 6 q^{34} + 22 q^{36} - 66 q^{38} + 10 q^{39} - 15 q^{42} + 9 q^{44} + 2 q^{46} - 6 q^{47} - 9 q^{48} - 2 q^{49} + 9 q^{50} + 24 q^{54} + 60 q^{56} + 4 q^{57} + 6 q^{58} + 34 q^{60} - 12 q^{62} - 30 q^{63} - 8 q^{64} - 6 q^{65} - 21 q^{66} - 36 q^{68} + 30 q^{70} + 9 q^{72} - 12 q^{73} - 12 q^{76} + 19 q^{78} + 2 q^{79} + 57 q^{80} + 6 q^{81} + 9 q^{84} + 12 q^{87} - 18 q^{88} + 24 q^{89} + 75 q^{90} - 36 q^{92} - 3 q^{94} + 54 q^{95} - 54 q^{96} + 45 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).

\(n\) \(73\) \(127\) \(253\) \(281\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.12327 + 0.859225i −0.794271 + 0.607564i
\(3\) 0.944647 + 1.45177i 0.545392 + 0.838181i
\(4\) 0.523464 1.93028i 0.261732 0.965141i
\(5\) 3.97106i 1.77591i −0.459928 0.887956i \(-0.652125\pi\)
0.459928 0.887956i \(-0.347875\pi\)
\(6\) −2.30849 0.819065i −0.942438 0.334382i
\(7\) −2.57827 0.593742i −0.974494 0.224413i
\(8\) 1.07056 + 2.61800i 0.378499 + 0.925602i
\(9\) −1.21528 + 2.74282i −0.405094 + 0.914275i
\(10\) 3.41204 + 4.46057i 1.07898 + 1.41056i
\(11\) −2.29171 −0.690978 −0.345489 0.938423i \(-0.612287\pi\)
−0.345489 + 0.938423i \(0.612287\pi\)
\(12\) 3.29682 1.06349i 0.951709 0.307002i
\(13\) 0.364860 + 0.631957i 0.101194 + 0.175273i 0.912177 0.409797i \(-0.134400\pi\)
−0.810983 + 0.585070i \(0.801067\pi\)
\(14\) 3.40625 1.54838i 0.910357 0.413823i
\(15\) 5.76508 3.75125i 1.48854 0.968569i
\(16\) −3.45197 2.02086i −0.862993 0.505216i
\(17\) −3.53491 6.12264i −0.857340 1.48496i −0.874457 0.485104i \(-0.838782\pi\)
0.0171162 0.999854i \(-0.494551\pi\)
\(18\) −0.991615 4.12513i −0.233726 0.972303i
\(19\) −1.20692 + 2.09045i −0.276887 + 0.479582i −0.970609 0.240660i \(-0.922636\pi\)
0.693723 + 0.720242i \(0.255969\pi\)
\(20\) −7.66527 2.07871i −1.71401 0.464813i
\(21\) −1.57358 4.30393i −0.343383 0.939196i
\(22\) 2.57421 1.96910i 0.548823 0.419813i
\(23\) 1.38400i 0.288585i −0.989535 0.144292i \(-0.953909\pi\)
0.989535 0.144292i \(-0.0460906\pi\)
\(24\) −2.78944 + 4.02729i −0.569391 + 0.822067i
\(25\) −10.7693 −2.15387
\(26\) −0.952829 0.396360i −0.186865 0.0777325i
\(27\) −5.12997 + 0.826688i −0.987263 + 0.159096i
\(28\) −2.49572 + 4.66598i −0.471646 + 0.881788i
\(29\) 3.75443 6.50286i 0.697180 1.20755i −0.272260 0.962224i \(-0.587771\pi\)
0.969440 0.245327i \(-0.0788955\pi\)
\(30\) −3.25256 + 9.16716i −0.593833 + 1.67369i
\(31\) −5.08798 2.93755i −0.913829 0.527599i −0.0321675 0.999482i \(-0.510241\pi\)
−0.881661 + 0.471883i \(0.843574\pi\)
\(32\) 5.61387 0.696048i 0.992401 0.123045i
\(33\) −2.16486 3.32705i −0.376854 0.579164i
\(34\) 9.23137 + 3.84008i 1.58317 + 0.658569i
\(35\) −2.35778 + 10.2385i −0.398538 + 1.73062i
\(36\) 4.65827 + 3.78161i 0.776378 + 0.630268i
\(37\) −1.62245 0.936723i −0.266729 0.153996i 0.360671 0.932693i \(-0.382548\pi\)
−0.627400 + 0.778697i \(0.715881\pi\)
\(38\) −0.440470 3.38515i −0.0714537 0.549145i
\(39\) −0.572792 + 1.12667i −0.0917202 + 0.180412i
\(40\) 10.3962 4.25125i 1.64379 0.672181i
\(41\) −4.35544 7.54384i −0.680205 1.17815i −0.974918 0.222564i \(-0.928557\pi\)
0.294713 0.955586i \(-0.404776\pi\)
\(42\) 5.46560 + 3.48242i 0.843360 + 0.537348i
\(43\) 10.4290 + 6.02121i 1.59041 + 0.918226i 0.993235 + 0.116119i \(0.0370453\pi\)
0.597179 + 0.802108i \(0.296288\pi\)
\(44\) −1.19963 + 4.42365i −0.180851 + 0.666891i
\(45\) 10.8919 + 4.82596i 1.62367 + 0.719412i
\(46\) 1.18917 + 1.55461i 0.175334 + 0.229215i
\(47\) −1.73952 3.01293i −0.253734 0.439481i 0.710817 0.703377i \(-0.248326\pi\)
−0.964551 + 0.263896i \(0.914992\pi\)
\(48\) −0.327061 6.92048i −0.0472073 0.998885i
\(49\) 6.29494 + 3.06165i 0.899277 + 0.437379i
\(50\) 12.0969 9.25328i 1.71075 1.30861i
\(51\) 5.54943 10.9156i 0.777076 1.52849i
\(52\) 1.41085 0.373477i 0.195649 0.0517919i
\(53\) 1.80951 + 3.13416i 0.248555 + 0.430509i 0.963125 0.269054i \(-0.0867111\pi\)
−0.714570 + 0.699564i \(0.753378\pi\)
\(54\) 5.05202 5.33639i 0.687493 0.726191i
\(55\) 9.10054i 1.22712i
\(56\) −1.20577 7.38553i −0.161128 0.986934i
\(57\) −4.17497 + 0.222563i −0.552989 + 0.0294792i
\(58\) 1.37019 + 10.5304i 0.179915 + 1.38270i
\(59\) −5.72312 3.30424i −0.745087 0.430176i 0.0788292 0.996888i \(-0.474882\pi\)
−0.823916 + 0.566712i \(0.808215\pi\)
\(60\) −4.22317 13.0919i −0.545208 1.69015i
\(61\) 1.14171 + 1.97750i 0.146181 + 0.253193i 0.929813 0.368032i \(-0.119968\pi\)
−0.783632 + 0.621225i \(0.786635\pi\)
\(62\) 8.23918 1.07207i 1.04638 0.136153i
\(63\) 4.76186 6.35018i 0.599937 0.800047i
\(64\) −5.70782 + 5.60543i −0.713477 + 0.700678i
\(65\) 2.50954 1.44888i 0.311270 0.179712i
\(66\) 5.29040 + 1.87706i 0.651203 + 0.231050i
\(67\) 1.46604 + 0.846418i 0.179105 + 0.103406i 0.586872 0.809680i \(-0.300359\pi\)
−0.407767 + 0.913086i \(0.633692\pi\)
\(68\) −13.6688 + 3.61838i −1.65759 + 0.438793i
\(69\) 2.00926 1.30740i 0.241886 0.157392i
\(70\) −6.14872 13.5264i −0.734913 1.61672i
\(71\) 7.40857i 0.879235i 0.898185 + 0.439618i \(0.144886\pi\)
−0.898185 + 0.439618i \(0.855114\pi\)
\(72\) −8.48174 0.245259i −0.999582 0.0289041i
\(73\) 0.925740 0.534476i 0.108350 0.0625557i −0.444846 0.895607i \(-0.646742\pi\)
0.553196 + 0.833051i \(0.313408\pi\)
\(74\) 2.62730 0.341860i 0.305418 0.0397404i
\(75\) −10.1732 15.6346i −1.17470 1.80533i
\(76\) 3.40338 + 3.42397i 0.390394 + 0.392757i
\(77\) 5.90865 + 1.36069i 0.673354 + 0.155065i
\(78\) −0.324664 1.75771i −0.0367609 0.199022i
\(79\) −1.89917 3.28947i −0.213674 0.370094i 0.739188 0.673500i \(-0.235210\pi\)
−0.952862 + 0.303406i \(0.901876\pi\)
\(80\) −8.02498 + 13.7080i −0.897220 + 1.53260i
\(81\) −6.04617 6.66662i −0.671797 0.740735i
\(82\) 11.3742 + 4.73145i 1.25607 + 0.522502i
\(83\) 11.0110 + 6.35720i 1.20861 + 0.697794i 0.962456 0.271436i \(-0.0874985\pi\)
0.246158 + 0.969230i \(0.420832\pi\)
\(84\) −9.13152 + 0.784493i −0.996330 + 0.0855953i
\(85\) −24.3134 + 14.0373i −2.63715 + 1.52256i
\(86\) −16.8882 + 2.19746i −1.82110 + 0.236959i
\(87\) 12.9873 0.692336i 1.39238 0.0742263i
\(88\) −2.45341 5.99970i −0.261534 0.639570i
\(89\) −2.05246 + 3.55496i −0.217560 + 0.376825i −0.954062 0.299611i \(-0.903143\pi\)
0.736501 + 0.676436i \(0.236476\pi\)
\(90\) −16.3811 + 3.93777i −1.72672 + 0.415077i
\(91\) −0.565489 1.84599i −0.0592794 0.193512i
\(92\) −2.67152 0.724476i −0.278525 0.0755319i
\(93\) −0.541699 10.1615i −0.0561716 1.05370i
\(94\) 4.54273 + 1.88969i 0.468547 + 0.194907i
\(95\) 8.30131 + 4.79276i 0.851696 + 0.491727i
\(96\) 6.31363 + 7.49254i 0.644382 + 0.764704i
\(97\) 8.60686 + 4.96917i 0.873894 + 0.504543i 0.868640 0.495443i \(-0.164994\pi\)
0.00525356 + 0.999986i \(0.498328\pi\)
\(98\) −9.70156 + 1.96972i −0.980005 + 0.198972i
\(99\) 2.78508 6.28577i 0.279911 0.631743i
\(100\) −5.63736 + 20.7878i −0.563736 + 2.07878i
\(101\) 4.52304i 0.450059i −0.974352 0.225030i \(-0.927752\pi\)
0.974352 0.225030i \(-0.0722479\pi\)
\(102\) 3.14547 + 17.0294i 0.311447 + 1.68616i
\(103\) 14.6007i 1.43864i −0.694676 0.719322i \(-0.744452\pi\)
0.694676 0.719322i \(-0.255548\pi\)
\(104\) −1.26386 + 1.63175i −0.123931 + 0.160006i
\(105\) −17.0912 + 6.24877i −1.66793 + 0.609818i
\(106\) −4.72551 1.96573i −0.458982 0.190928i
\(107\) 7.10349 12.3036i 0.686721 1.18943i −0.286172 0.958178i \(-0.592383\pi\)
0.972893 0.231257i \(-0.0742837\pi\)
\(108\) −1.08961 + 10.3350i −0.104848 + 0.994488i
\(109\) −4.48809 + 2.59120i −0.429881 + 0.248192i −0.699296 0.714832i \(-0.746503\pi\)
0.269415 + 0.963024i \(0.413170\pi\)
\(110\) −7.81941 10.2223i −0.745552 0.974662i
\(111\) −0.172737 3.24030i −0.0163954 0.307556i
\(112\) 7.70024 + 7.25991i 0.727604 + 0.685997i
\(113\) −2.37957 + 1.37385i −0.223852 + 0.129241i −0.607732 0.794142i \(-0.707921\pi\)
0.383881 + 0.923383i \(0.374587\pi\)
\(114\) 4.49838 3.83724i 0.421312 0.359390i
\(115\) −5.49597 −0.512502
\(116\) −10.5870 10.6511i −0.982982 0.988931i
\(117\) −2.17675 + 0.232742i −0.201241 + 0.0215170i
\(118\) 9.26769 1.20590i 0.853160 0.111012i
\(119\) 5.47867 + 17.8846i 0.502229 + 1.63948i
\(120\) 15.9926 + 11.0770i 1.45992 + 1.01119i
\(121\) −5.74805 −0.522550
\(122\) −2.98157 1.24028i −0.269938 0.112289i
\(123\) 6.83758 13.4494i 0.616524 1.21269i
\(124\) −8.33367 + 8.28354i −0.748385 + 0.743884i
\(125\) 22.9104i 2.04917i
\(126\) 0.107390 + 11.2245i 0.00956706 + 0.999954i
\(127\) 11.1350 0.988074 0.494037 0.869441i \(-0.335521\pi\)
0.494037 + 0.869441i \(0.335521\pi\)
\(128\) 1.59509 11.2007i 0.140987 0.990011i
\(129\) 1.11034 + 20.8285i 0.0977603 + 1.83385i
\(130\) −1.57397 + 3.78374i −0.138046 + 0.331856i
\(131\) 6.70139i 0.585503i 0.956189 + 0.292752i \(0.0945709\pi\)
−0.956189 + 0.292752i \(0.905429\pi\)
\(132\) −7.55536 + 2.43720i −0.657610 + 0.212131i
\(133\) 4.35296 4.67314i 0.377449 0.405213i
\(134\) −2.37402 + 0.308903i −0.205084 + 0.0266852i
\(135\) 3.28283 + 20.3714i 0.282541 + 1.75329i
\(136\) 12.2447 15.8090i 1.04998 1.35561i
\(137\) 16.5869i 1.41712i 0.705652 + 0.708558i \(0.250654\pi\)
−0.705652 + 0.708558i \(0.749346\pi\)
\(138\) −1.13359 + 3.19496i −0.0964975 + 0.271973i
\(139\) 1.93078 + 3.34421i 0.163767 + 0.283652i 0.936217 0.351423i \(-0.114302\pi\)
−0.772450 + 0.635076i \(0.780969\pi\)
\(140\) 18.5289 + 9.91065i 1.56598 + 0.837603i
\(141\) 2.73086 5.37154i 0.229980 0.452365i
\(142\) −6.36563 8.32181i −0.534192 0.698351i
\(143\) −0.836155 1.44826i −0.0699228 0.121110i
\(144\) 9.73800 7.01223i 0.811500 0.584353i
\(145\) −25.8233 14.9091i −2.14451 1.23813i
\(146\) −0.580619 + 1.39578i −0.0480524 + 0.115516i
\(147\) 1.50168 + 12.0310i 0.123857 + 0.992300i
\(148\) −2.65743 + 2.64145i −0.218440 + 0.217126i
\(149\) −5.97768 −0.489710 −0.244855 0.969560i \(-0.578740\pi\)
−0.244855 + 0.969560i \(0.578740\pi\)
\(150\) 24.8609 + 8.82078i 2.02989 + 0.720214i
\(151\) 2.52587 0.205552 0.102776 0.994705i \(-0.467228\pi\)
0.102776 + 0.994705i \(0.467228\pi\)
\(152\) −6.76487 0.921774i −0.548703 0.0747657i
\(153\) 21.0892 2.25489i 1.70496 0.182297i
\(154\) −7.80614 + 3.54845i −0.629037 + 0.285942i
\(155\) −11.6652 + 20.2047i −0.936970 + 1.62288i
\(156\) 1.87495 + 1.69542i 0.150116 + 0.135742i
\(157\) 5.22202 9.04480i 0.416763 0.721854i −0.578849 0.815435i \(-0.696498\pi\)
0.995612 + 0.0935808i \(0.0298313\pi\)
\(158\) 4.95968 + 2.06314i 0.394571 + 0.164134i
\(159\) −2.84073 + 5.58766i −0.225285 + 0.443130i
\(160\) −2.76405 22.2930i −0.218517 1.76242i
\(161\) −0.821741 + 3.56834i −0.0647623 + 0.281224i
\(162\) 12.5196 + 2.29337i 0.983633 + 0.180184i
\(163\) −11.1724 6.45037i −0.875087 0.505232i −0.00605184 0.999982i \(-0.501926\pi\)
−0.869035 + 0.494750i \(0.835260\pi\)
\(164\) −16.8416 + 4.45829i −1.31511 + 0.348134i
\(165\) −13.2119 + 8.59680i −1.02855 + 0.669260i
\(166\) −17.8306 + 2.32008i −1.38392 + 0.180073i
\(167\) −6.23486 10.7991i −0.482468 0.835659i 0.517329 0.855786i \(-0.326926\pi\)
−0.999797 + 0.0201270i \(0.993593\pi\)
\(168\) 9.58309 8.72723i 0.739351 0.673320i
\(169\) 6.23375 10.7972i 0.479520 0.830552i
\(170\) 15.2492 36.6583i 1.16956 2.81157i
\(171\) −4.26699 5.85086i −0.326305 0.447427i
\(172\) 17.0819 16.9791i 1.30248 1.29464i
\(173\) 15.0773 8.70488i 1.14631 0.661820i 0.198321 0.980137i \(-0.436451\pi\)
0.947984 + 0.318317i \(0.103118\pi\)
\(174\) −13.9933 + 11.9367i −1.06083 + 0.904917i
\(175\) 27.7662 + 6.39420i 2.09893 + 0.483356i
\(176\) 7.91093 + 4.63124i 0.596309 + 0.349093i
\(177\) −0.609320 11.4300i −0.0457993 0.859132i
\(178\) −0.749052 5.75670i −0.0561438 0.431483i
\(179\) −1.10901 1.92086i −0.0828914 0.143572i 0.821599 0.570065i \(-0.193082\pi\)
−0.904491 + 0.426493i \(0.859749\pi\)
\(180\) 15.0170 18.4983i 1.11930 1.37878i
\(181\) −6.08899 −0.452591 −0.226295 0.974059i \(-0.572661\pi\)
−0.226295 + 0.974059i \(0.572661\pi\)
\(182\) 2.22131 + 1.58766i 0.164655 + 0.117685i
\(183\) −1.79237 + 3.52555i −0.132496 + 0.260616i
\(184\) 3.62332 1.48166i 0.267115 0.109229i
\(185\) −3.71978 + 6.44285i −0.273484 + 0.473688i
\(186\) 9.33952 + 10.9487i 0.684807 + 0.802797i
\(187\) 8.10099 + 14.0313i 0.592403 + 1.02607i
\(188\) −6.72638 + 1.78060i −0.490571 + 0.129863i
\(189\) 13.7173 + 0.914451i 0.997785 + 0.0665166i
\(190\) −13.4427 + 1.74914i −0.975233 + 0.126896i
\(191\) −10.2673 + 5.92784i −0.742918 + 0.428924i −0.823129 0.567854i \(-0.807774\pi\)
0.0802116 + 0.996778i \(0.474440\pi\)
\(192\) −13.5297 2.99130i −0.976420 0.215878i
\(193\) 1.41644 2.45335i 0.101958 0.176596i −0.810534 0.585692i \(-0.800823\pi\)
0.912491 + 0.409096i \(0.134156\pi\)
\(194\) −13.9374 + 1.81352i −1.00065 + 0.130203i
\(195\) 4.47408 + 2.27459i 0.320395 + 0.162887i
\(196\) 9.20502 10.5483i 0.657502 0.753453i
\(197\) −14.0278 −0.999438 −0.499719 0.866188i \(-0.666563\pi\)
−0.499719 + 0.866188i \(0.666563\pi\)
\(198\) 2.27250 + 9.45362i 0.161499 + 0.671839i
\(199\) −4.83204 + 2.78978i −0.342535 + 0.197762i −0.661392 0.750040i \(-0.730034\pi\)
0.318858 + 0.947803i \(0.396701\pi\)
\(200\) −11.5292 28.1941i −0.815236 1.99362i
\(201\) 0.156084 + 2.92792i 0.0110093 + 0.206520i
\(202\) 3.88631 + 5.08059i 0.273440 + 0.357469i
\(203\) −13.5409 + 14.5370i −0.950388 + 1.02029i
\(204\) −18.1653 16.4259i −1.27182 1.15004i
\(205\) −29.9571 + 17.2957i −2.09229 + 1.20799i
\(206\) 12.5452 + 16.4004i 0.874069 + 1.14267i
\(207\) 3.79608 + 1.68196i 0.263846 + 0.116904i
\(208\) 0.0176112 2.91883i 0.00122112 0.202384i
\(209\) 2.76592 4.79071i 0.191323 0.331381i
\(210\) 13.8289 21.7042i 0.954284 1.49773i
\(211\) 2.70924 1.56418i 0.186511 0.107682i −0.403837 0.914831i \(-0.632324\pi\)
0.590348 + 0.807149i \(0.298990\pi\)
\(212\) 6.99701 1.85224i 0.480557 0.127212i
\(213\) −10.7556 + 6.99848i −0.736958 + 0.479528i
\(214\) 2.59244 + 19.9238i 0.177216 + 1.36196i
\(215\) 23.9106 41.4144i 1.63069 2.82444i
\(216\) −7.65619 12.5452i −0.520938 0.853595i
\(217\) 11.3740 + 10.5947i 0.772120 + 0.719217i
\(218\) 2.81490 6.76689i 0.190649 0.458312i
\(219\) 1.65044 + 0.839072i 0.111526 + 0.0566992i
\(220\) 17.5666 + 4.76380i 1.18434 + 0.321175i
\(221\) 2.57949 4.46781i 0.173515 0.300538i
\(222\) 2.97818 + 3.49131i 0.199882 + 0.234321i
\(223\) −6.50445 3.75534i −0.435570 0.251476i 0.266147 0.963933i \(-0.414249\pi\)
−0.701717 + 0.712456i \(0.747583\pi\)
\(224\) −14.8873 1.53859i −0.994702 0.102801i
\(225\) 13.0878 29.5384i 0.872519 1.96923i
\(226\) 1.49246 3.58779i 0.0992767 0.238656i
\(227\) 15.6848i 1.04104i 0.853850 + 0.520519i \(0.174261\pi\)
−0.853850 + 0.520519i \(0.825739\pi\)
\(228\) −1.75584 + 8.17537i −0.116283 + 0.541427i
\(229\) 5.62226 0.371529 0.185765 0.982594i \(-0.440524\pi\)
0.185765 + 0.982594i \(0.440524\pi\)
\(230\) 6.17345 4.72228i 0.407065 0.311378i
\(231\) 3.60619 + 9.86339i 0.237270 + 0.648963i
\(232\) 21.0438 + 2.86740i 1.38159 + 0.188254i
\(233\) 20.3295 + 11.7372i 1.33183 + 0.768932i 0.985580 0.169210i \(-0.0541217\pi\)
0.346250 + 0.938142i \(0.387455\pi\)
\(234\) 2.24510 2.13175i 0.146767 0.139357i
\(235\) −11.9645 + 6.90773i −0.780480 + 0.450610i
\(236\) −9.37397 + 9.31758i −0.610193 + 0.606523i
\(237\) 2.98151 5.86455i 0.193670 0.380944i
\(238\) −21.5209 15.3818i −1.39500 0.997055i
\(239\) −19.7345 + 11.3937i −1.27652 + 0.737000i −0.976207 0.216840i \(-0.930425\pi\)
−0.300315 + 0.953840i \(0.597092\pi\)
\(240\) −27.4817 + 1.29878i −1.77393 + 0.0838360i
\(241\) 21.3577i 1.37577i −0.725821 0.687884i \(-0.758540\pi\)
0.725821 0.687884i \(-0.241460\pi\)
\(242\) 6.45660 4.93887i 0.415046 0.317483i
\(243\) 3.96690 15.0753i 0.254477 0.967079i
\(244\) 4.41478 1.16867i 0.282627 0.0748166i
\(245\) 12.1580 24.9976i 0.776747 1.59704i
\(246\) 3.87560 + 20.9823i 0.247099 + 1.33778i
\(247\) −1.76143 −0.112077
\(248\) 2.24352 16.4651i 0.142464 1.04554i
\(249\) 1.17230 + 21.9908i 0.0742916 + 1.39361i
\(250\) −19.6852 25.7345i −1.24500 1.62759i
\(251\) 3.53437i 0.223087i −0.993760 0.111544i \(-0.964421\pi\)
0.993760 0.111544i \(-0.0355795\pi\)
\(252\) −9.76497 12.5158i −0.615135 0.788422i
\(253\) 3.17174i 0.199406i
\(254\) −12.5076 + 9.56750i −0.784799 + 0.600319i
\(255\) −43.3466 22.0371i −2.71447 1.38002i
\(256\) 7.83221 + 13.9519i 0.489513 + 0.871996i
\(257\) −3.62692 −0.226241 −0.113121 0.993581i \(-0.536085\pi\)
−0.113121 + 0.993581i \(0.536085\pi\)
\(258\) −19.1436 22.4420i −1.19183 1.39718i
\(259\) 3.62694 + 3.37844i 0.225367 + 0.209926i
\(260\) −1.48310 5.60255i −0.0919779 0.347456i
\(261\) 13.2735 + 18.2006i 0.821610 + 1.12659i
\(262\) −5.75801 7.52746i −0.355731 0.465048i
\(263\) 3.46168i 0.213456i −0.994288 0.106728i \(-0.965963\pi\)
0.994288 0.106728i \(-0.0340375\pi\)
\(264\) 6.39259 9.22939i 0.393437 0.568030i
\(265\) 12.4459 7.18566i 0.764547 0.441412i
\(266\) −0.874256 + 8.98936i −0.0536041 + 0.551173i
\(267\) −7.09984 + 0.378484i −0.434503 + 0.0231629i
\(268\) 2.40124 2.38680i 0.146679 0.145797i
\(269\) 11.1391 6.43118i 0.679165 0.392116i −0.120375 0.992728i \(-0.538410\pi\)
0.799540 + 0.600612i \(0.205076\pi\)
\(270\) −21.1911 20.0619i −1.28965 1.22093i
\(271\) 15.4126 + 8.89849i 0.936251 + 0.540545i 0.888783 0.458328i \(-0.151551\pi\)
0.0474680 + 0.998873i \(0.484885\pi\)
\(272\) −0.170624 + 28.2787i −0.0103456 + 1.71465i
\(273\) 2.14576 2.56477i 0.129868 0.155227i
\(274\) −14.2519 18.6316i −0.860989 1.12557i
\(275\) 24.6802 1.48827
\(276\) −1.47187 4.56281i −0.0885961 0.274649i
\(277\) 25.6108i 1.53880i −0.638764 0.769402i \(-0.720554\pi\)
0.638764 0.769402i \(-0.279446\pi\)
\(278\) −5.04222 2.09747i −0.302412 0.125798i
\(279\) 14.2405 10.3855i 0.852557 0.621763i
\(280\) −29.3284 + 4.78818i −1.75271 + 0.286149i
\(281\) −14.9008 8.60300i −0.888909 0.513212i −0.0153234 0.999883i \(-0.504878\pi\)
−0.873585 + 0.486671i \(0.838211\pi\)
\(282\) 1.54787 + 8.38010i 0.0921745 + 0.499028i
\(283\) 14.0317 24.3036i 0.834097 1.44470i −0.0606663 0.998158i \(-0.519323\pi\)
0.894763 0.446541i \(-0.147344\pi\)
\(284\) 14.3006 + 3.87812i 0.848586 + 0.230124i
\(285\) 0.883810 + 16.5791i 0.0523524 + 0.982060i
\(286\) 2.18361 + 0.908343i 0.129120 + 0.0537114i
\(287\) 6.75040 + 22.0361i 0.398463 + 1.30075i
\(288\) −4.91330 + 16.2438i −0.289519 + 0.957172i
\(289\) −16.4911 + 28.5634i −0.970065 + 1.68020i
\(290\) 41.8167 5.44112i 2.45556 0.319513i
\(291\) 0.916341 + 17.1893i 0.0537169 + 1.00765i
\(292\) −0.547098 2.06672i −0.0320165 0.120945i
\(293\) 22.2344 12.8370i 1.29895 0.749947i 0.318724 0.947847i \(-0.396746\pi\)
0.980222 + 0.197900i \(0.0634123\pi\)
\(294\) −12.0241 12.2238i −0.701262 0.712904i
\(295\) −13.1214 + 22.7269i −0.763955 + 1.32321i
\(296\) 0.715412 5.25039i 0.0415825 0.305173i
\(297\) 11.7564 1.89453i 0.682177 0.109932i
\(298\) 6.71453 5.13617i 0.388963 0.297530i
\(299\) 0.874631 0.504968i 0.0505812 0.0292031i
\(300\) −35.5045 + 11.4530i −2.04985 + 0.661241i
\(301\) −23.3138 21.7165i −1.34379 1.25172i
\(302\) −2.83722 + 2.17029i −0.163264 + 0.124886i
\(303\) 6.56642 4.27268i 0.377231 0.245459i
\(304\) 8.39078 4.77715i 0.481244 0.273988i
\(305\) 7.85278 4.53381i 0.449649 0.259605i
\(306\) −21.7514 + 20.6532i −1.24344 + 1.18067i
\(307\) 2.99912 0.171169 0.0855843 0.996331i \(-0.472724\pi\)
0.0855843 + 0.996331i \(0.472724\pi\)
\(308\) 5.71947 10.6931i 0.325897 0.609296i
\(309\) 21.1968 13.7925i 1.20584 0.784626i
\(310\) −4.25725 32.7183i −0.241796 1.85828i
\(311\) 13.8427 23.9763i 0.784949 1.35957i −0.144080 0.989566i \(-0.546022\pi\)
0.929029 0.370006i \(-0.120644\pi\)
\(312\) −3.56283 0.293405i −0.201705 0.0166108i
\(313\) −11.5229 + 6.65275i −0.651313 + 0.376036i −0.788959 0.614446i \(-0.789380\pi\)
0.137646 + 0.990482i \(0.456046\pi\)
\(314\) 1.90579 + 14.6466i 0.107550 + 0.826557i
\(315\) −25.2169 18.9096i −1.42081 1.06544i
\(316\) −7.34375 + 1.94402i −0.413118 + 0.109360i
\(317\) 8.98450 + 15.5616i 0.504620 + 0.874027i 0.999986 + 0.00534253i \(0.00170059\pi\)
−0.495366 + 0.868684i \(0.664966\pi\)
\(318\) −1.61015 8.71727i −0.0902929 0.488840i
\(319\) −8.60408 + 14.9027i −0.481736 + 0.834391i
\(320\) 22.2595 + 22.6661i 1.24434 + 1.26707i
\(321\) 24.5723 1.30992i 1.37149 0.0731127i
\(322\) −2.14297 4.71426i −0.119423 0.262715i
\(323\) 17.0654 0.949545
\(324\) −16.0334 + 8.18109i −0.890744 + 0.454505i
\(325\) −3.92930 6.80575i −0.217958 0.377515i
\(326\) 18.0919 2.35408i 1.00202 0.130381i
\(327\) −8.00149 4.06791i −0.442483 0.224956i
\(328\) 15.0870 19.4786i 0.833041 1.07553i
\(329\) 2.69604 + 8.80097i 0.148637 + 0.485213i
\(330\) 7.45393 21.0085i 0.410325 1.15648i
\(331\) −4.73891 + 2.73601i −0.260474 + 0.150385i −0.624551 0.780984i \(-0.714718\pi\)
0.364077 + 0.931369i \(0.381385\pi\)
\(332\) 18.0350 17.9266i 0.989802 0.983848i
\(333\) 4.54100 3.31172i 0.248845 0.181481i
\(334\) 16.2823 + 6.77313i 0.890927 + 0.370609i
\(335\) 3.36118 5.82173i 0.183641 0.318075i
\(336\) −3.26572 + 18.0370i −0.178160 + 0.984002i
\(337\) 2.12429 + 3.67937i 0.115717 + 0.200428i 0.918066 0.396427i \(-0.129750\pi\)
−0.802349 + 0.596855i \(0.796417\pi\)
\(338\) 2.27503 + 17.4843i 0.123745 + 0.951022i
\(339\) −4.24237 2.15680i −0.230414 0.117141i
\(340\) 14.3688 + 54.2797i 0.779259 + 2.94373i
\(341\) 11.6602 + 6.73202i 0.631435 + 0.364559i
\(342\) 9.82018 + 2.90579i 0.531015 + 0.157127i
\(343\) −14.4122 11.6313i −0.778187 0.628033i
\(344\) −4.59864 + 33.7493i −0.247942 + 1.81964i
\(345\) −5.19175 7.97889i −0.279515 0.429569i
\(346\) −9.45639 + 22.7327i −0.508379 + 1.22212i
\(347\) 11.8809 20.5783i 0.637801 1.10470i −0.348113 0.937452i \(-0.613178\pi\)
0.985914 0.167251i \(-0.0534891\pi\)
\(348\) 5.46197 25.4315i 0.292792 1.36327i
\(349\) 16.1703 28.0078i 0.865576 1.49922i −0.000898511 1.00000i \(-0.500286\pi\)
0.866474 0.499222i \(-0.166381\pi\)
\(350\) −36.6830 + 16.6751i −1.96079 + 0.891319i
\(351\) −2.39415 2.94029i −0.127790 0.156941i
\(352\) −12.8654 + 1.59514i −0.685727 + 0.0850214i
\(353\) −6.05240 −0.322137 −0.161068 0.986943i \(-0.551494\pi\)
−0.161068 + 0.986943i \(0.551494\pi\)
\(354\) 10.5054 + 12.3154i 0.558355 + 0.654557i
\(355\) 29.4199 1.56145
\(356\) 5.78769 + 5.82272i 0.306747 + 0.308603i
\(357\) −20.7890 + 24.8484i −1.10027 + 1.31512i
\(358\) 2.89617 + 1.20476i 0.153068 + 0.0636733i
\(359\) −19.7082 11.3785i −1.04016 0.600535i −0.120279 0.992740i \(-0.538379\pi\)
−0.919878 + 0.392205i \(0.871712\pi\)
\(360\) −0.973940 + 33.6815i −0.0513311 + 1.77517i
\(361\) 6.58668 + 11.4085i 0.346667 + 0.600445i
\(362\) 6.83957 5.23181i 0.359480 0.274978i
\(363\) −5.42988 8.34486i −0.284995 0.437991i
\(364\) −3.85929 + 0.125246i −0.202282 + 0.00656467i
\(365\) −2.12244 3.67617i −0.111093 0.192420i
\(366\) −1.01593 5.50018i −0.0531035 0.287499i
\(367\) 23.2510i 1.21369i 0.794819 + 0.606847i \(0.207566\pi\)
−0.794819 + 0.606847i \(0.792434\pi\)
\(368\) −2.79689 + 4.77755i −0.145798 + 0.249047i
\(369\) 25.9845 2.77830i 1.35270 0.144633i
\(370\) −1.35755 10.4332i −0.0705756 0.542396i
\(371\) −2.80451 9.15508i −0.145603 0.475308i
\(372\) −19.8982 4.27356i −1.03167 0.221574i
\(373\) 29.7144i 1.53856i 0.638914 + 0.769278i \(0.279384\pi\)
−0.638914 + 0.769278i \(0.720616\pi\)
\(374\) −21.1557 8.80037i −1.09393 0.455056i
\(375\) −33.2606 + 21.6422i −1.71757 + 1.11760i
\(376\) 6.02559 7.77956i 0.310746 0.401200i
\(377\) 5.47937 0.282202
\(378\) −16.1939 + 10.7591i −0.832925 + 0.553386i
\(379\) 6.00191i 0.308298i −0.988048 0.154149i \(-0.950736\pi\)
0.988048 0.154149i \(-0.0492635\pi\)
\(380\) 13.5968 13.5150i 0.697502 0.693306i
\(381\) 10.5187 + 16.1655i 0.538888 + 0.828185i
\(382\) 6.43961 15.4805i 0.329479 0.792051i
\(383\) −30.1913 −1.54270 −0.771352 0.636409i \(-0.780419\pi\)
−0.771352 + 0.636409i \(0.780419\pi\)
\(384\) 17.7677 8.26501i 0.906702 0.421772i
\(385\) 5.40337 23.4636i 0.275381 1.19582i
\(386\) 0.516935 + 3.97281i 0.0263113 + 0.202211i
\(387\) −29.1894 + 21.2876i −1.48378 + 1.08211i
\(388\) 14.0973 14.0125i 0.715681 0.711375i
\(389\) −22.7017 −1.15102 −0.575510 0.817795i \(-0.695196\pi\)
−0.575510 + 0.817795i \(0.695196\pi\)
\(390\) −6.97998 + 1.28926i −0.353445 + 0.0652842i
\(391\) −8.47376 + 4.89233i −0.428536 + 0.247416i
\(392\) −1.27630 + 19.7578i −0.0644631 + 0.997920i
\(393\) −9.72889 + 6.33045i −0.490758 + 0.319329i
\(394\) 15.7570 12.0530i 0.793824 0.607223i
\(395\) −13.0627 + 7.54174i −0.657255 + 0.379466i
\(396\) −10.6754 8.66636i −0.536460 0.435501i
\(397\) −8.45399 + 14.6427i −0.424294 + 0.734898i −0.996354 0.0853131i \(-0.972811\pi\)
0.572060 + 0.820211i \(0.306144\pi\)
\(398\) 3.03063 7.28549i 0.151912 0.365189i
\(399\) 10.8963 + 1.90503i 0.545500 + 0.0953707i
\(400\) 37.1754 + 21.7634i 1.85877 + 1.08817i
\(401\) 0.886779i 0.0442837i 0.999755 + 0.0221418i \(0.00704854\pi\)
−0.999755 + 0.0221418i \(0.992951\pi\)
\(402\) −2.69107 3.15473i −0.134218 0.157344i
\(403\) 4.28718i 0.213560i
\(404\) −8.73074 2.36765i −0.434371 0.117795i
\(405\) −26.4735 + 24.0097i −1.31548 + 1.19305i
\(406\) 2.71959 27.9636i 0.134971 1.38781i
\(407\) 3.71819 + 2.14670i 0.184304 + 0.106408i
\(408\) 34.5180 + 2.84262i 1.70890 + 0.140731i
\(409\) 20.3540 + 11.7514i 1.00644 + 0.581067i 0.910147 0.414286i \(-0.135969\pi\)
0.0962915 + 0.995353i \(0.469302\pi\)
\(410\) 18.7889 45.1676i 0.927918 2.23067i
\(411\) −24.0804 + 15.6688i −1.18780 + 0.772884i
\(412\) −28.1834 7.64291i −1.38849 0.376539i
\(413\) 12.7939 + 11.9173i 0.629545 + 0.586411i
\(414\) −5.70920 + 1.37240i −0.280592 + 0.0674498i
\(415\) 25.2448 43.7254i 1.23922 2.14639i
\(416\) 2.48815 + 3.29376i 0.121992 + 0.161490i
\(417\) −3.03113 + 5.96216i −0.148435 + 0.291968i
\(418\) 1.00943 + 7.75780i 0.0493729 + 0.379447i
\(419\) −28.8996 + 16.6852i −1.41184 + 0.815125i −0.995561 0.0941134i \(-0.969998\pi\)
−0.416276 + 0.909238i \(0.636665\pi\)
\(420\) 3.11527 + 36.2618i 0.152010 + 1.76940i
\(421\) 14.7598 + 8.52157i 0.719349 + 0.415316i 0.814513 0.580145i \(-0.197004\pi\)
−0.0951643 + 0.995462i \(0.530338\pi\)
\(422\) −1.69922 + 4.08483i −0.0827166 + 0.198847i
\(423\) 10.3779 1.10962i 0.504593 0.0539518i
\(424\) −6.26803 + 8.09257i −0.304403 + 0.393010i
\(425\) 38.0686 + 65.9367i 1.84660 + 3.19840i
\(426\) 6.06810 17.1026i 0.294000 0.828625i
\(427\) −1.76951 5.77641i −0.0856327 0.279540i
\(428\) −20.0310 20.1522i −0.968235 0.974095i
\(429\) 1.31268 2.58200i 0.0633766 0.124660i
\(430\) 8.72626 + 67.0641i 0.420818 + 3.23412i
\(431\) −1.82346 + 1.05278i −0.0878330 + 0.0507104i −0.543273 0.839556i \(-0.682815\pi\)
0.455440 + 0.890266i \(0.349482\pi\)
\(432\) 19.3791 + 7.51327i 0.932379 + 0.361482i
\(433\) 7.31623i 0.351596i −0.984426 0.175798i \(-0.943749\pi\)
0.984426 0.175798i \(-0.0562505\pi\)
\(434\) −21.8794 2.12787i −1.05024 0.102141i
\(435\) −2.74931 51.5733i −0.131819 2.47275i
\(436\) 2.65239 + 10.0197i 0.127027 + 0.479855i
\(437\) 2.89319 + 1.67039i 0.138400 + 0.0799054i
\(438\) −2.57483 + 0.475593i −0.123030 + 0.0227247i
\(439\) −4.15397 + 2.39829i −0.198258 + 0.114464i −0.595843 0.803101i \(-0.703182\pi\)
0.397585 + 0.917565i \(0.369848\pi\)
\(440\) −23.8252 + 9.74264i −1.13582 + 0.464462i
\(441\) −16.0477 + 13.5451i −0.764177 + 0.645007i
\(442\) 0.941395 + 7.23492i 0.0447776 + 0.344130i
\(443\) 9.24510 + 16.0130i 0.439248 + 0.760799i 0.997632 0.0687833i \(-0.0219117\pi\)
−0.558384 + 0.829583i \(0.688578\pi\)
\(444\) −6.34511 1.36275i −0.301126 0.0646733i
\(445\) 14.1170 + 8.15044i 0.669209 + 0.386368i
\(446\) 10.5329 1.37053i 0.498749 0.0648963i
\(447\) −5.64680 8.67822i −0.267084 0.410466i
\(448\) 18.0445 11.0633i 0.852521 0.522693i
\(449\) 26.6011i 1.25538i −0.778462 0.627692i \(-0.784000\pi\)
0.778462 0.627692i \(-0.216000\pi\)
\(450\) 10.6790 + 44.4249i 0.503415 + 2.09421i
\(451\) 9.98142 + 17.2883i 0.470007 + 0.814075i
\(452\) 1.40629 + 5.31241i 0.0661464 + 0.249875i
\(453\) 2.38605 + 3.66698i 0.112106 + 0.172290i
\(454\) −13.4768 17.6183i −0.632497 0.826866i
\(455\) −7.33053 + 2.24559i −0.343660 + 0.105275i
\(456\) −5.05221 10.6918i −0.236591 0.500689i
\(457\) −8.03420 13.9156i −0.375824 0.650946i 0.614626 0.788819i \(-0.289307\pi\)
−0.990450 + 0.137872i \(0.955974\pi\)
\(458\) −6.31531 + 4.83079i −0.295095 + 0.225728i
\(459\) 23.1955 + 28.4867i 1.08267 + 1.32964i
\(460\) −2.87694 + 10.6088i −0.134138 + 0.494636i
\(461\) −25.3072 14.6111i −1.17867 0.680508i −0.222967 0.974826i \(-0.571574\pi\)
−0.955707 + 0.294318i \(0.904907\pi\)
\(462\) −12.5256 7.98070i −0.582743 0.371296i
\(463\) 0.610326 + 1.05712i 0.0283643 + 0.0491284i 0.879859 0.475235i \(-0.157637\pi\)
−0.851495 + 0.524363i \(0.824303\pi\)
\(464\) −26.1016 + 14.8605i −1.21174 + 0.689881i
\(465\) −40.3521 + 2.15112i −1.87128 + 0.0997559i
\(466\) −32.9204 + 4.28355i −1.52501 + 0.198432i
\(467\) −10.2857 5.93844i −0.475964 0.274798i 0.242769 0.970084i \(-0.421944\pi\)
−0.718733 + 0.695286i \(0.755278\pi\)
\(468\) −0.690195 + 4.32358i −0.0319043 + 0.199858i
\(469\) −3.27729 3.05274i −0.151331 0.140963i
\(470\) 7.50409 18.0395i 0.346138 0.832098i
\(471\) 18.0640 0.962968i 0.832343 0.0443712i
\(472\) 2.52358 18.5205i 0.116157 0.852475i
\(473\) −23.9004 13.7989i −1.09894 0.634474i
\(474\) 1.68994 + 9.14925i 0.0776217 + 0.420239i
\(475\) 12.9977 22.5128i 0.596377 1.03296i
\(476\) 37.3902 1.21343i 1.71378 0.0556175i
\(477\) −10.7955 + 1.15427i −0.494292 + 0.0528504i
\(478\) 12.3774 29.7547i 0.566129 1.36095i
\(479\) −1.58663 −0.0724951 −0.0362476 0.999343i \(-0.511540\pi\)
−0.0362476 + 0.999343i \(0.511540\pi\)
\(480\) 29.7533 25.0718i 1.35805 1.14437i
\(481\) 1.36709i 0.0623340i
\(482\) 18.3510 + 23.9904i 0.835867 + 1.09273i
\(483\) −5.95667 + 2.17784i −0.271038 + 0.0990951i
\(484\) −3.00890 + 11.0954i −0.136768 + 0.504334i
\(485\) 19.7329 34.1784i 0.896024 1.55196i
\(486\) 8.49715 + 20.3420i 0.385439 + 0.922733i
\(487\) −1.55221 2.68850i −0.0703372 0.121828i 0.828712 0.559675i \(-0.189074\pi\)
−0.899049 + 0.437848i \(0.855741\pi\)
\(488\) −3.95483 + 5.10602i −0.179027 + 0.231139i
\(489\) −1.18948 22.3131i −0.0537902 1.00903i
\(490\) 7.82187 + 38.5255i 0.353356 + 1.74040i
\(491\) 1.72926 + 2.99516i 0.0780403 + 0.135170i 0.902404 0.430890i \(-0.141800\pi\)
−0.824364 + 0.566060i \(0.808467\pi\)
\(492\) −22.3818 20.2387i −1.00905 0.912432i
\(493\) −53.0862 −2.39088
\(494\) 1.97856 1.51347i 0.0890196 0.0680941i
\(495\) −24.9612 11.0597i −1.12192 0.497098i
\(496\) 11.6272 + 20.4225i 0.522076 + 0.916995i
\(497\) 4.39878 19.1013i 0.197312 0.856810i
\(498\) −20.2118 23.6943i −0.905714 1.06177i
\(499\) 4.57563i 0.204833i 0.994742 + 0.102417i \(0.0326575\pi\)
−0.994742 + 0.102417i \(0.967342\pi\)
\(500\) 44.2235 + 11.9928i 1.97773 + 0.536332i
\(501\) 9.78808 19.2529i 0.437299 0.860158i
\(502\) 3.03682 + 3.97004i 0.135540 + 0.177192i
\(503\) −11.9056 −0.530845 −0.265423 0.964132i \(-0.585511\pi\)
−0.265423 + 0.964132i \(0.585511\pi\)
\(504\) 21.7226 + 5.66830i 0.967600 + 0.252486i
\(505\) −17.9613 −0.799266
\(506\) −2.72524 3.56272i −0.121152 0.158382i
\(507\) 21.5637 1.14954i 0.957679 0.0510527i
\(508\) 5.82879 21.4937i 0.258611 0.953631i
\(509\) 25.7345i 1.14066i −0.821415 0.570331i \(-0.806815\pi\)
0.821415 0.570331i \(-0.193185\pi\)
\(510\) 67.6247 12.4908i 2.99447 0.553104i
\(511\) −2.70415 + 0.828373i −0.119624 + 0.0366451i
\(512\) −20.7855 8.94213i −0.918599 0.395190i
\(513\) 4.46332 11.7217i 0.197060 0.517525i
\(514\) 4.07400 3.11634i 0.179697 0.137456i
\(515\) −57.9801 −2.55491
\(516\) 40.7861 + 8.75970i 1.79551 + 0.385624i
\(517\) 3.98647 + 6.90477i 0.175325 + 0.303672i
\(518\) −6.97687 0.678532i −0.306546 0.0298130i
\(519\) 26.8802 + 13.6657i 1.17991 + 0.599860i
\(520\) 6.47977 + 5.01885i 0.284157 + 0.220091i
\(521\) −14.7657 25.5750i −0.646898 1.12046i −0.983860 0.178941i \(-0.942733\pi\)
0.336962 0.941518i \(-0.390601\pi\)
\(522\) −30.5481 9.03917i −1.33705 0.395634i
\(523\) −5.45309 + 9.44503i −0.238447 + 0.413002i −0.960269 0.279076i \(-0.909972\pi\)
0.721822 + 0.692079i \(0.243305\pi\)
\(524\) 12.9356 + 3.50794i 0.565093 + 0.153245i
\(525\) 16.9464 + 46.3505i 0.739601 + 2.02290i
\(526\) 2.97436 + 3.88840i 0.129688 + 0.169542i
\(527\) 41.5358i 1.80933i
\(528\) 0.749531 + 15.8598i 0.0326192 + 0.690207i
\(529\) 21.0845 0.916719
\(530\) −7.80602 + 18.7653i −0.339072 + 0.815112i
\(531\) 16.0182 11.6819i 0.695129 0.506952i
\(532\) −6.74187 10.8487i −0.292297 0.470349i
\(533\) 3.17825 5.50490i 0.137665 0.238443i
\(534\) 7.64983 6.52550i 0.331040 0.282386i
\(535\) −48.8584 28.2084i −2.11233 1.21956i
\(536\) −0.646443 + 4.74423i −0.0279221 + 0.204919i
\(537\) 1.74103 3.42457i 0.0751311 0.147781i
\(538\) −6.98640 + 16.7950i −0.301205 + 0.724083i
\(539\) −14.4262 7.01643i −0.621381 0.302219i
\(540\) 41.0410 + 4.32692i 1.76612 + 0.186201i
\(541\) −12.1063 6.98956i −0.520489 0.300505i 0.216645 0.976250i \(-0.430488\pi\)
−0.737135 + 0.675746i \(0.763822\pi\)
\(542\) −24.9583 + 3.24754i −1.07205 + 0.139494i
\(543\) −5.75194 8.83982i −0.246840 0.379353i
\(544\) −24.1061 31.9112i −1.03354 1.36818i
\(545\) 10.2898 + 17.8225i 0.440767 + 0.763431i
\(546\) −0.206556 + 4.72462i −0.00883976 + 0.202195i
\(547\) −4.75243 2.74382i −0.203199 0.117317i 0.394948 0.918704i \(-0.370763\pi\)
−0.598147 + 0.801386i \(0.704096\pi\)
\(548\) 32.0174 + 8.68265i 1.36772 + 0.370904i
\(549\) −6.81144 + 0.728289i −0.290705 + 0.0310826i
\(550\) −27.7225 + 21.2059i −1.18209 + 0.904222i
\(551\) 9.06260 + 15.6969i 0.386080 + 0.668710i
\(552\) 5.57379 + 3.86059i 0.237236 + 0.164318i
\(553\) 2.94349 + 9.60875i 0.125170 + 0.408606i
\(554\) 22.0055 + 28.7678i 0.934923 + 1.22223i
\(555\) −12.8674 + 0.685948i −0.546192 + 0.0291169i
\(556\) 7.46597 1.97638i 0.316628 0.0838171i
\(557\) −12.8261 22.2154i −0.543458 0.941296i −0.998702 0.0509299i \(-0.983781\pi\)
0.455245 0.890366i \(-0.349552\pi\)
\(558\) −7.07245 + 23.9015i −0.299400 + 1.01183i
\(559\) 8.78761i 0.371676i
\(560\) 28.8296 30.5781i 1.21827 1.29216i
\(561\) −12.7177 + 25.0154i −0.536942 + 1.05615i
\(562\) 24.1295 3.13969i 1.01784 0.132440i
\(563\) 22.1839 + 12.8079i 0.934940 + 0.539788i 0.888371 0.459127i \(-0.151838\pi\)
0.0465696 + 0.998915i \(0.485171\pi\)
\(564\) −8.93907 8.08313i −0.376403 0.340361i
\(565\) 5.45564 + 9.44944i 0.229520 + 0.397541i
\(566\) 5.12091 + 39.3558i 0.215248 + 1.65425i
\(567\) 11.6304 + 20.7782i 0.488432 + 0.872602i
\(568\) −19.3956 + 7.93129i −0.813822 + 0.332790i
\(569\) 32.2440 18.6161i 1.35174 0.780428i 0.363247 0.931693i \(-0.381668\pi\)
0.988493 + 0.151265i \(0.0483346\pi\)
\(570\) −15.2379 17.8634i −0.638246 0.748214i
\(571\) 20.7354 + 11.9716i 0.867749 + 0.500995i 0.866599 0.499005i \(-0.166301\pi\)
0.00114912 + 0.999999i \(0.499634\pi\)
\(572\) −3.23325 + 0.855902i −0.135189 + 0.0357870i
\(573\) −18.3049 9.30609i −0.764697 0.388768i
\(574\) −26.5164 18.9523i −1.10678 0.791053i
\(575\) 14.9048i 0.621574i
\(576\) −8.43809 22.4677i −0.351587 0.936155i
\(577\) 12.6598 7.30912i 0.527033 0.304283i −0.212774 0.977101i \(-0.568250\pi\)
0.739807 + 0.672819i \(0.234917\pi\)
\(578\) −6.01849 46.2540i −0.250336 1.92391i
\(579\) 4.89974 0.261199i 0.203626 0.0108551i
\(580\) −42.2962 + 42.0418i −1.75626 + 1.74569i
\(581\) −24.6148 22.9283i −1.02119 0.951225i
\(582\) −15.7988 18.5209i −0.654881 0.767714i
\(583\) −4.14687 7.18259i −0.171746 0.297472i
\(584\) 2.39031 + 1.85140i 0.0989119 + 0.0766114i
\(585\) 0.924232 + 8.64403i 0.0382123 + 0.357387i
\(586\) −13.9453 + 33.5238i −0.576074 + 1.38485i
\(587\) 3.04268 + 1.75669i 0.125585 + 0.0725065i 0.561476 0.827493i \(-0.310234\pi\)
−0.435891 + 0.899999i \(0.643567\pi\)
\(588\) 24.0093 + 3.39913i 0.990126 + 0.140178i
\(589\) 12.2816 7.09078i 0.506054 0.292171i
\(590\) −4.78869 36.8026i −0.197147 1.51514i
\(591\) −13.2513 20.3651i −0.545086 0.837710i
\(592\) 3.70767 + 6.51229i 0.152384 + 0.267654i
\(593\) 10.5178 18.2173i 0.431914 0.748096i −0.565125 0.825006i \(-0.691172\pi\)
0.997038 + 0.0769094i \(0.0245052\pi\)
\(594\) −11.5778 + 12.2295i −0.475042 + 0.501782i
\(595\) 71.0209 21.7562i 2.91157 0.891915i
\(596\) −3.12910 + 11.5386i −0.128173 + 0.472639i
\(597\) −8.61470 4.37967i −0.352576 0.179248i
\(598\) −0.548564 + 1.31872i −0.0224324 + 0.0539265i
\(599\) −28.9493 16.7139i −1.18284 0.682912i −0.226168 0.974088i \(-0.572620\pi\)
−0.956669 + 0.291177i \(0.905953\pi\)
\(600\) 30.0404 43.3712i 1.22639 1.77062i
\(601\) 5.05174 + 2.91662i 0.206065 + 0.118972i 0.599481 0.800389i \(-0.295374\pi\)
−0.393416 + 0.919360i \(0.628707\pi\)
\(602\) 44.8470 + 4.36157i 1.82783 + 0.177765i
\(603\) −4.10323 + 2.99245i −0.167096 + 0.121862i
\(604\) 1.32220 4.87563i 0.0537995 0.198387i
\(605\) 22.8259i 0.928003i
\(606\) −3.70466 + 10.4414i −0.150492 + 0.424153i
\(607\) 19.1187i 0.776004i −0.921659 0.388002i \(-0.873165\pi\)
0.921659 0.388002i \(-0.126835\pi\)
\(608\) −5.32045 + 12.5756i −0.215773 + 0.510007i
\(609\) −33.8958 5.92606i −1.37353 0.240136i
\(610\) −4.92522 + 11.8400i −0.199416 + 0.479387i
\(611\) 1.26936 2.19860i 0.0513528 0.0889457i
\(612\) 6.68687 41.8885i 0.270301 1.69324i
\(613\) 17.8761 10.3208i 0.722010 0.416853i −0.0934820 0.995621i \(-0.529800\pi\)
0.815492 + 0.578768i \(0.196466\pi\)
\(614\) −3.36881 + 2.57692i −0.135954 + 0.103996i
\(615\) −53.4083 27.1525i −2.15363 1.09489i
\(616\) 2.76328 + 16.9255i 0.111336 + 0.681949i
\(617\) 31.8887 18.4110i 1.28379 0.741198i 0.306253 0.951950i \(-0.400925\pi\)
0.977540 + 0.210752i \(0.0675913\pi\)
\(618\) −11.9589 + 33.7055i −0.481057 + 1.35583i
\(619\) −0.243563 −0.00978961 −0.00489480 0.999988i \(-0.501558\pi\)
−0.00489480 + 0.999988i \(0.501558\pi\)
\(620\) 32.8944 + 33.0935i 1.32107 + 1.32907i
\(621\) 1.14414 + 7.09990i 0.0459128 + 0.284909i
\(622\) 5.05195 + 38.8259i 0.202565 + 1.55677i
\(623\) 7.40252 7.94702i 0.296576 0.318391i
\(624\) 4.25411 2.73170i 0.170301 0.109355i
\(625\) 37.1319 1.48528
\(626\) 7.22710 17.3736i 0.288853 0.694389i
\(627\) 9.56784 0.510050i 0.382103 0.0203694i
\(628\) −14.7255 14.8146i −0.587610 0.591167i
\(629\) 13.2449i 0.528109i
\(630\) 44.5730 0.426452i 1.77583 0.0169903i
\(631\) −32.4980 −1.29373 −0.646863 0.762606i \(-0.723919\pi\)
−0.646863 + 0.762606i \(0.723919\pi\)
\(632\) 6.57864 8.49359i 0.261684 0.337857i
\(633\) 4.83010 + 2.45560i 0.191979 + 0.0976011i
\(634\) −23.4629 9.76015i −0.931832 0.387625i
\(635\) 44.2179i 1.75473i
\(636\) 9.29874 + 8.40835i 0.368719 + 0.333413i
\(637\) 0.361944 + 5.09520i 0.0143407 + 0.201879i
\(638\) −3.14009 24.1326i −0.124317 0.955417i
\(639\) −20.3204 9.00351i −0.803863 0.356173i
\(640\) −44.4787 6.33419i −1.75817 0.250381i
\(641\) 17.9350i 0.708391i 0.935171 + 0.354196i \(0.115245\pi\)
−0.935171 + 0.354196i \(0.884755\pi\)
\(642\) −26.4758 + 22.5846i −1.04492 + 0.891342i
\(643\) −13.4583 23.3105i −0.530745 0.919277i −0.999356 0.0358726i \(-0.988579\pi\)
0.468612 0.883404i \(-0.344754\pi\)
\(644\) 6.45774 + 3.45409i 0.254471 + 0.136110i
\(645\) 82.7113 4.40924i 3.25676 0.173614i
\(646\) −19.1690 + 14.6630i −0.754196 + 0.576910i
\(647\) 9.67192 + 16.7523i 0.380242 + 0.658599i 0.991097 0.133144i \(-0.0425072\pi\)
−0.610854 + 0.791743i \(0.709174\pi\)
\(648\) 10.9804 22.9659i 0.431351 0.902184i
\(649\) 13.1157 + 7.57238i 0.514838 + 0.297242i
\(650\) 10.2613 + 4.26853i 0.402483 + 0.167425i
\(651\) −4.63668 + 26.5208i −0.181726 + 1.03943i
\(652\) −18.2994 + 18.1893i −0.716658 + 0.712347i
\(653\) −4.50823 −0.176421 −0.0882104 0.996102i \(-0.528115\pi\)
−0.0882104 + 0.996102i \(0.528115\pi\)
\(654\) 12.4831 2.30573i 0.488127 0.0901611i
\(655\) 26.6116 1.03980
\(656\) −0.210230 + 34.8429i −0.00820810 + 1.36039i
\(657\) 0.340938 + 3.18868i 0.0133013 + 0.124402i
\(658\) −10.5904 7.56934i −0.412856 0.295084i
\(659\) −19.6047 + 33.9563i −0.763689 + 1.32275i 0.177248 + 0.984166i \(0.443281\pi\)
−0.940937 + 0.338582i \(0.890053\pi\)
\(660\) 9.67828 + 30.0028i 0.376727 + 1.16786i
\(661\) 4.80431 8.32131i 0.186866 0.323661i −0.757338 0.653023i \(-0.773500\pi\)
0.944204 + 0.329362i \(0.106834\pi\)
\(662\) 2.97222 7.14506i 0.115518 0.277701i
\(663\) 8.92296 0.475672i 0.346539 0.0184736i
\(664\) −4.85525 + 35.6325i −0.188420 + 1.38281i
\(665\) −18.5573 17.2859i −0.719623 0.670317i
\(666\) −2.25526 + 7.62169i −0.0873894 + 0.295335i
\(667\) −8.99999 5.19615i −0.348481 0.201196i
\(668\) −24.1090 + 6.38210i −0.932806 + 0.246931i
\(669\) −0.692505 12.9905i −0.0267738 0.502240i
\(670\) 1.22667 + 9.42738i 0.0473906 + 0.364211i
\(671\) −2.61647 4.53187i −0.101008 0.174951i
\(672\) −11.8296 23.0664i −0.456337 0.889807i
\(673\) 19.7167 34.1503i 0.760023 1.31640i −0.182816 0.983147i \(-0.558521\pi\)
0.942838 0.333251i \(-0.108146\pi\)
\(674\) −5.54756 2.30768i −0.213684 0.0888886i
\(675\) 55.2464 8.90288i 2.12643 0.342672i
\(676\) −17.5784 17.6848i −0.676094 0.680186i
\(677\) −2.72325 + 1.57227i −0.104663 + 0.0604272i −0.551418 0.834229i \(-0.685913\pi\)
0.446755 + 0.894656i \(0.352580\pi\)
\(678\) 6.61850 1.22249i 0.254182 0.0469495i
\(679\) −19.2404 17.9221i −0.738378 0.687787i
\(680\) −62.7785 48.6246i −2.40745 1.86467i
\(681\) −22.7708 + 14.8166i −0.872578 + 0.567774i
\(682\) −18.8819 + 2.45687i −0.723023 + 0.0940786i
\(683\) 6.94387 + 12.0271i 0.265700 + 0.460205i 0.967747 0.251925i \(-0.0810637\pi\)
−0.702047 + 0.712131i \(0.747730\pi\)
\(684\) −13.5274 + 5.17377i −0.517234 + 0.197824i
\(685\) 65.8677 2.51668
\(686\) 26.1827 + 0.681756i 0.999661 + 0.0260296i
\(687\) 5.31105 + 8.16224i 0.202629 + 0.311409i
\(688\) −23.8327 41.8607i −0.908614 1.59593i
\(689\) −1.32043 + 2.28706i −0.0503045 + 0.0871300i
\(690\) 12.6874 + 4.50155i 0.483001 + 0.171371i
\(691\) −7.04505 12.2024i −0.268006 0.464201i 0.700341 0.713809i \(-0.253031\pi\)
−0.968347 + 0.249608i \(0.919698\pi\)
\(692\) −8.91045 33.6601i −0.338724 1.27957i
\(693\) −10.9128 + 14.5528i −0.414543 + 0.552815i
\(694\) 4.33598 + 33.3234i 0.164592 + 1.26494i
\(695\) 13.2801 7.66726i 0.503742 0.290836i
\(696\) 15.7162 + 33.2595i 0.595719 + 1.26070i
\(697\) −30.7921 + 53.3335i −1.16633 + 2.02015i
\(698\) 5.90140 + 45.3542i 0.223371 + 1.71668i
\(699\) 2.16441 + 40.6013i 0.0818655 + 1.53568i
\(700\) 26.8772 50.2495i 1.01586 1.89925i
\(701\) −13.5350 −0.511211 −0.255606 0.966781i \(-0.582275\pi\)
−0.255606 + 0.966781i \(0.582275\pi\)
\(702\) 5.21565 + 1.24562i 0.196852 + 0.0470129i
\(703\) 3.91634 2.26110i 0.147708 0.0852791i
\(704\) 13.0807 12.8460i 0.492997 0.484153i
\(705\) −21.3307 10.8444i −0.803361 0.408424i
\(706\) 6.79847 5.20037i 0.255864 0.195719i
\(707\) −2.68552 + 11.6616i −0.100999 + 0.438580i
\(708\) −22.3821 4.80704i −0.841170 0.180659i
\(709\) 39.2743 22.6750i 1.47498 0.851578i 0.475374 0.879784i \(-0.342313\pi\)
0.999602 + 0.0282058i \(0.00897939\pi\)
\(710\) −33.0464 + 25.2783i −1.24021 + 0.948678i
\(711\) 11.3305 1.21147i 0.424926 0.0454337i
\(712\) −11.5042 1.56754i −0.431136 0.0587462i
\(713\) −4.06558 + 7.04179i −0.152257 + 0.263717i
\(714\) 2.00119 45.7739i 0.0748926 1.71304i
\(715\) −5.75114 + 3.32042i −0.215081 + 0.124177i
\(716\) −4.28834 + 1.13520i −0.160263 + 0.0424245i
\(717\) −35.1833 17.8870i −1.31394 0.668002i
\(718\) 31.9143 4.15263i 1.19103 0.154975i
\(719\) 14.2665 24.7102i 0.532049 0.921536i −0.467251 0.884125i \(-0.654755\pi\)
0.999300 0.0374114i \(-0.0119112\pi\)
\(720\) −27.8460 38.6702i −1.03776 1.44115i
\(721\) −8.66901 + 37.6444i −0.322851 + 1.40195i
\(722\) −17.2010 7.15532i −0.640157 0.266294i
\(723\) 31.0065 20.1755i 1.15314 0.750333i
\(724\) −3.18736 + 11.7535i −0.118457 + 0.436814i
\(725\) −40.4327 + 70.0315i −1.50163 + 2.60090i
\(726\) 13.2693 + 4.70802i 0.492471 + 0.174731i
\(727\) 10.4643 + 6.04157i 0.388099 + 0.224069i 0.681336 0.731970i \(-0.261399\pi\)
−0.293237 + 0.956040i \(0.594732\pi\)
\(728\) 4.22740 3.45668i 0.156678 0.128113i
\(729\) 25.6332 8.48177i 0.949377 0.314140i
\(730\) 5.54273 + 2.30567i 0.205145 + 0.0853368i
\(731\) 85.1377i 3.14893i
\(732\) 5.86705 + 5.30527i 0.216853 + 0.196088i
\(733\) −37.8424 −1.39774 −0.698871 0.715247i \(-0.746314\pi\)
−0.698871 + 0.715247i \(0.746314\pi\)
\(734\) −19.9779 26.1171i −0.737397 0.964001i
\(735\) 47.7758 5.96327i 1.76224 0.219958i
\(736\) −0.963334 7.76962i −0.0355090 0.286392i
\(737\) −3.35974 1.93975i −0.123758 0.0714515i
\(738\) −26.8004 + 25.4473i −0.986536 + 0.936729i
\(739\) −24.8702 + 14.3588i −0.914866 + 0.528198i −0.881993 0.471262i \(-0.843799\pi\)
−0.0328721 + 0.999460i \(0.510465\pi\)
\(740\) 10.4893 + 10.5528i 0.385596 + 0.387930i
\(741\) −1.66393 2.55720i −0.0611261 0.0939410i
\(742\) 11.0165 + 7.87390i 0.404428 + 0.289060i
\(743\) 21.1666 12.2205i 0.776527 0.448328i −0.0586709 0.998277i \(-0.518686\pi\)
0.835198 + 0.549949i \(0.185353\pi\)
\(744\) 26.0230 12.2967i 0.954048 0.450818i
\(745\) 23.7377i 0.869683i
\(746\) −25.5314 33.3773i −0.934771 1.22203i
\(747\) −30.8182 + 22.4754i −1.12758 + 0.822333i
\(748\) 31.3250 8.29230i 1.14535 0.303196i
\(749\) −25.6199 + 27.5044i −0.936130 + 1.00499i
\(750\) 18.7651 52.8884i 0.685204 1.93121i
\(751\) −25.9021 −0.945183 −0.472591 0.881282i \(-0.656681\pi\)
−0.472591 + 0.881282i \(0.656681\pi\)
\(752\) −0.0839636 + 13.9159i −0.00306184 + 0.507460i
\(753\) 5.13109 3.33873i 0.186987 0.121670i
\(754\) −6.15480 + 4.70801i −0.224145 + 0.171456i
\(755\) 10.0304i 0.365042i
\(756\) 8.94565 25.9995i 0.325350 0.945594i
\(757\) 10.2462i 0.372404i 0.982511 + 0.186202i \(0.0596179\pi\)
−0.982511 + 0.186202i \(0.940382\pi\)
\(758\) 5.15700 + 6.74176i 0.187310 + 0.244872i
\(759\) −4.60465 + 2.99618i −0.167138 + 0.108754i
\(760\) −3.66042 + 26.8637i −0.132777 + 0.974449i
\(761\) −48.7071 −1.76563 −0.882816 0.469719i \(-0.844355\pi\)
−0.882816 + 0.469719i \(0.844355\pi\)
\(762\) −25.7051 9.12031i −0.931199 0.330394i
\(763\) 13.1100 4.01604i 0.474614 0.145391i
\(764\) 6.06783 + 22.9218i 0.219526 + 0.829283i
\(765\) −8.95431 83.7466i −0.323744 3.02787i
\(766\) 33.9129 25.9411i 1.22532 0.937291i
\(767\) 4.82235i 0.174125i
\(768\) −12.8563 + 24.5502i −0.463913 + 0.885881i
\(769\) 33.6265 19.4142i 1.21260 0.700096i 0.249276 0.968432i \(-0.419807\pi\)
0.963325 + 0.268337i \(0.0864740\pi\)
\(770\) 14.0911 + 30.9987i 0.507809 + 1.11711i
\(771\) −3.42616 5.26546i −0.123390 0.189631i
\(772\) −3.99419 4.01837i −0.143754 0.144624i
\(773\) 31.7959 18.3574i 1.14362 0.660270i 0.196296 0.980545i \(-0.437109\pi\)
0.947325 + 0.320275i \(0.103775\pi\)
\(774\) 14.4967 48.9919i 0.521072 1.76098i
\(775\) 54.7942 + 31.6354i 1.96826 + 1.13638i
\(776\) −3.79515 + 27.8525i −0.136238 + 0.999847i
\(777\) −1.47854 + 8.45693i −0.0530423 + 0.303391i
\(778\) 25.5001 19.5059i 0.914222 0.699319i
\(779\) 21.0267 0.753359
\(780\) 6.73262 7.44556i 0.241067 0.266594i
\(781\) 16.9783i 0.607532i
\(782\) 5.31469 12.7763i 0.190053 0.456878i
\(783\) −13.8843 + 36.4632i −0.496183 + 1.30309i
\(784\) −15.5428 23.2900i −0.555099 0.831784i
\(785\) −35.9175 20.7370i −1.28195 0.740134i
\(786\) 5.48887 15.4701i 0.195782 0.551800i
\(787\) −22.8555 + 39.5869i −0.814711 + 1.41112i 0.0948248 + 0.995494i \(0.469771\pi\)
−0.909535 + 0.415626i \(0.863562\pi\)
\(788\) −7.34304 + 27.0776i −0.261585 + 0.964598i
\(789\) 5.02557 3.27007i 0.178915 0.116417i
\(790\) 8.19284 19.6952i 0.291488 0.700723i
\(791\) 6.95089 2.12930i 0.247145 0.0757091i
\(792\) 19.4377 + 0.562064i 0.690689 + 0.0199721i
\(793\) −0.833130 + 1.44302i −0.0295853 + 0.0512433i
\(794\) −3.08531 23.7116i −0.109494 0.841494i
\(795\) 22.1889 + 11.2807i 0.786961 + 0.400086i
\(796\) 2.85566 + 10.7876i 0.101216 + 0.382355i
\(797\) −40.7020 + 23.4993i −1.44174 + 0.832388i −0.997966 0.0637514i \(-0.979694\pi\)
−0.443773 + 0.896139i \(0.646360\pi\)
\(798\) −13.8764 + 7.22256i −0.491218 + 0.255676i
\(799\) −12.2980 + 21.3008i −0.435074 + 0.753570i
\(800\) −60.4576 + 7.49598i −2.13750 + 0.265023i
\(801\) −7.25632 9.94982i −0.256389 0.351560i
\(802\) −0.761943 0.996091i −0.0269052 0.0351732i
\(803\) −2.12153 + 1.22487i −0.0748672 + 0.0432246i
\(804\) 5.73342 + 1.23137i 0.202202 + 0.0434272i
\(805\) 14.1701 + 3.26319i 0.499430 + 0.115012i
\(806\) 3.68365 + 4.81565i 0.129751 + 0.169624i
\(807\) 19.8592 + 10.0963i 0.699076 + 0.355406i
\(808\) 11.8413 4.84217i 0.416576 0.170347i
\(809\) −6.52111 + 3.76496i −0.229270 + 0.132369i −0.610235 0.792220i \(-0.708925\pi\)
0.380965 + 0.924589i \(0.375592\pi\)
\(810\) 9.10713 49.7161i 0.319992 1.74685i
\(811\) 18.9342 0.664869 0.332435 0.943126i \(-0.392130\pi\)
0.332435 + 0.943126i \(0.392130\pi\)
\(812\) 20.9722 + 33.7474i 0.735981 + 1.18430i
\(813\) 1.64093 + 30.7816i 0.0575499 + 1.07956i
\(814\) −6.02103 + 0.783446i −0.211037 + 0.0274598i
\(815\) −25.6148 + 44.3662i −0.897248 + 1.55408i
\(816\) −41.2154 + 26.4657i −1.44283 + 0.926485i
\(817\) −25.1741 + 14.5343i −0.880730 + 0.508490i
\(818\) −32.9600 + 4.28870i −1.15242 + 0.149951i
\(819\) 5.75045 + 0.692359i 0.200937 + 0.0241930i
\(820\) 17.7042 + 66.8792i 0.618256 + 2.33552i
\(821\) 24.8209 + 42.9911i 0.866257 + 1.50040i 0.865794 + 0.500401i \(0.166814\pi\)
0.000462541 1.00000i \(0.499853\pi\)
\(822\) 13.5858 38.2908i 0.473858 1.33554i
\(823\) −0.163058 + 0.282425i −0.00568384 + 0.00984471i −0.868853 0.495070i \(-0.835143\pi\)
0.863169 + 0.504914i \(0.168476\pi\)
\(824\) 38.2245 15.6308i 1.33161 0.544525i
\(825\) 23.3141 + 35.8301i 0.811693 + 1.24744i
\(826\) −24.6106 2.39349i −0.856312 0.0832801i
\(827\) −20.1060 −0.699154 −0.349577 0.936908i \(-0.613675\pi\)
−0.349577 + 0.936908i \(0.613675\pi\)
\(828\) 5.23376 6.44706i 0.181886 0.224051i
\(829\) 8.72452 + 15.1113i 0.303015 + 0.524837i 0.976817 0.214074i \(-0.0686734\pi\)
−0.673802 + 0.738912i \(0.735340\pi\)
\(830\) 9.21320 + 70.8063i 0.319795 + 2.45772i
\(831\) 37.1811 24.1932i 1.28980 0.839252i
\(832\) −5.62494 1.56190i −0.195010 0.0541490i
\(833\) −3.50665 49.3643i −0.121498 1.71037i
\(834\) −1.71807 9.30152i −0.0594918 0.322085i
\(835\) −42.8839 + 24.7590i −1.48406 + 0.856821i
\(836\) −7.79956 7.84677i −0.269754 0.271386i
\(837\) 28.5296 + 10.8634i 0.986128 + 0.375492i
\(838\) 18.1257 43.5732i 0.626141 1.50521i
\(839\) −7.57991 + 13.1288i −0.261688 + 0.453256i −0.966690 0.255948i \(-0.917612\pi\)
0.705003 + 0.709204i \(0.250946\pi\)
\(840\) −34.6564 38.0550i −1.19576 1.31302i
\(841\) −13.6915 23.7143i −0.472120 0.817735i
\(842\) −23.9012 + 3.10998i −0.823689 + 0.107177i
\(843\) −1.58644 29.7594i −0.0546398 1.02497i
\(844\) −1.60112 6.04838i −0.0551127 0.208194i
\(845\) −42.8763 24.7546i −1.47499 0.851585i
\(846\) −10.7038 + 10.1634i −0.368004 + 0.349425i
\(847\) 14.8200 + 3.41286i 0.509222 + 0.117267i
\(848\) 0.0873419 14.4758i 0.00299933 0.497100i
\(849\) 48.5383 2.58752i 1.66583 0.0888033i
\(850\) −99.4157 41.3551i −3.40993 1.41847i
\(851\) −1.29643 + 2.24548i −0.0444410 + 0.0769741i
\(852\) 7.87890 + 24.4247i 0.269927 + 0.836776i
\(853\) −7.82600 + 13.5550i −0.267957 + 0.464116i −0.968334 0.249658i \(-0.919682\pi\)
0.700377 + 0.713773i \(0.253015\pi\)
\(854\) 6.95088 + 4.96805i 0.237854 + 0.170003i
\(855\) −23.2341 + 16.9445i −0.794591 + 0.579489i
\(856\) 39.8155 + 5.42522i 1.36087 + 0.185430i
\(857\) −19.7927 −0.676107 −0.338054 0.941127i \(-0.609769\pi\)
−0.338054 + 0.941127i \(0.609769\pi\)
\(858\) 0.744036 + 4.02817i 0.0254010 + 0.137519i
\(859\) 16.2819 0.555531 0.277765 0.960649i \(-0.410406\pi\)
0.277765 + 0.960649i \(0.410406\pi\)
\(860\) −67.4251 67.8331i −2.29918 2.31309i
\(861\) −25.6146 + 30.6163i −0.872942 + 1.04340i
\(862\) 1.14366 2.74931i 0.0389534 0.0936419i
\(863\) −17.2522 9.96055i −0.587271 0.339061i 0.176747 0.984256i \(-0.443443\pi\)
−0.764018 + 0.645195i \(0.776776\pi\)
\(864\) −28.2236 + 8.21163i −0.960185 + 0.279365i
\(865\) −34.5676 59.8729i −1.17533 2.03574i
\(866\) 6.28629 + 8.21810i 0.213617 + 0.279262i
\(867\) −57.0459 + 3.04105i −1.93738 + 0.103279i
\(868\) 26.4047 16.4091i 0.896234 0.556963i
\(869\) 4.35236 + 7.53852i 0.147644 + 0.255727i
\(870\) 47.4013 + 55.5684i 1.60705 + 1.88394i
\(871\) 1.23530i 0.0418565i
\(872\) −11.5885 8.97578i −0.392436 0.303958i
\(873\) −24.0893 + 17.5681i −0.815300 + 0.594592i
\(874\) −4.68507 + 0.609613i −0.158475 + 0.0206205i
\(875\) 13.6028 59.0691i 0.459860 1.99690i
\(876\) 2.48359 2.74658i 0.0839126 0.0927983i
\(877\) 23.4804i 0.792876i 0.918062 + 0.396438i \(0.129754\pi\)
−0.918062 + 0.396438i \(0.870246\pi\)
\(878\) 2.60535 6.26312i 0.0879261 0.211370i
\(879\) 39.6401 + 20.1528i 1.33703 + 0.679737i
\(880\) 18.3910 31.4148i 0.619959 1.05899i
\(881\) 34.2467 1.15380 0.576901 0.816814i \(-0.304262\pi\)
0.576901 + 0.816814i \(0.304262\pi\)
\(882\) 6.38755 29.0034i 0.215080 0.976596i
\(883\) 53.3983i 1.79699i −0.438979 0.898497i \(-0.644660\pi\)
0.438979 0.898497i \(-0.355340\pi\)
\(884\) −7.27387 7.31789i −0.244647 0.246127i
\(885\) −45.3893 + 2.41965i −1.52574 + 0.0813356i
\(886\) −24.1435 10.0432i −0.811116 0.337410i
\(887\) 20.2679 0.680529 0.340264 0.940330i \(-0.389483\pi\)
0.340264 + 0.940330i \(0.389483\pi\)
\(888\) 8.29818 3.92115i 0.278469 0.131585i
\(889\) −28.7091 6.61133i −0.962873 0.221737i
\(890\) −22.8602 + 2.97453i −0.766276 + 0.0997065i
\(891\) 13.8561 + 15.2780i 0.464197 + 0.511831i
\(892\) −10.6537 + 10.5896i −0.356713 + 0.354567i
\(893\) 8.39784 0.281023
\(894\) 13.7994 + 4.89610i 0.461521 + 0.163750i
\(895\) −7.62787 + 4.40395i −0.254972 + 0.147208i
\(896\) −10.7629 + 27.9313i −0.359563 + 0.933121i
\(897\) 1.55932 + 0.792748i 0.0520641 + 0.0264691i
\(898\) 22.8564 + 29.8802i 0.762726 + 0.997115i
\(899\) −38.2049 + 22.0576i −1.27421 + 0.735663i
\(900\) −50.1664 40.7254i −1.67221 1.35751i
\(901\) 12.7929 22.1579i 0.426192 0.738186i
\(902\) −26.0664 10.8431i −0.867915 0.361037i
\(903\) 9.50399 54.3608i 0.316273 1.80901i
\(904\) −6.14420 4.75894i −0.204353 0.158280i
\(905\) 24.1797i 0.803762i
\(906\) −5.83094 2.06885i −0.193720 0.0687328i
\(907\) 19.8218i 0.658171i −0.944300 0.329085i \(-0.893260\pi\)
0.944300 0.329085i \(-0.106740\pi\)
\(908\) 30.2761 + 8.21043i 1.00475 + 0.272473i
\(909\) 12.4059 + 5.49677i 0.411478 + 0.182316i
\(910\) 6.30468 8.82098i 0.208998 0.292413i
\(911\) 19.7999 + 11.4315i 0.656001 + 0.378743i 0.790752 0.612137i \(-0.209690\pi\)
−0.134750 + 0.990880i \(0.543023\pi\)
\(912\) 14.8617 + 7.66877i 0.492119 + 0.253938i
\(913\) −25.2341 14.5689i −0.835125 0.482160i
\(914\) 20.9812 + 8.72781i 0.693997 + 0.288690i
\(915\) 14.0002 + 7.11760i 0.462831 + 0.235301i
\(916\) 2.94305 10.8525i 0.0972411 0.358578i
\(917\) 3.97890 17.2780i 0.131395 0.570570i
\(918\) −50.5312 12.0680i −1.66778 0.398305i
\(919\) 9.63211 16.6833i 0.317734 0.550331i −0.662281 0.749256i \(-0.730411\pi\)
0.980015 + 0.198924i \(0.0637448\pi\)
\(920\) −5.88374 14.3884i −0.193981 0.474373i
\(921\) 2.83311 + 4.35403i 0.0933540 + 0.143470i
\(922\) 40.9810 5.33238i 1.34964 0.175613i
\(923\) −4.68189 + 2.70309i −0.154106 + 0.0889734i
\(924\) 20.9268 1.79783i 0.688442 0.0591444i
\(925\) 17.4727 + 10.0879i 0.574499 + 0.331687i
\(926\) −1.59386 0.663017i −0.0523775 0.0217881i
\(927\) 40.0470 + 17.7439i 1.31532 + 0.582787i
\(928\) 16.5506 39.1195i 0.543299 1.28416i
\(929\) −13.8247 23.9451i −0.453574 0.785613i 0.545031 0.838416i \(-0.316518\pi\)
−0.998605 + 0.0528026i \(0.983185\pi\)
\(930\) 43.4779 37.0878i 1.42570 1.21616i
\(931\) −13.9977 + 9.46409i −0.458757 + 0.310173i
\(932\) 33.2979 33.0976i 1.09071 1.08415i
\(933\) 47.8846 2.55267i 1.56767 0.0835707i
\(934\) 16.6560 2.16725i 0.545002 0.0709147i
\(935\) 55.7193 32.1695i 1.82221 1.05206i
\(936\) −2.93966 5.44957i −0.0960856 0.178125i
\(937\) 22.2046i 0.725392i 0.931908 + 0.362696i \(0.118144\pi\)
−0.931908 + 0.362696i \(0.881856\pi\)
\(938\) 6.30427 + 0.613118i 0.205842 + 0.0200190i
\(939\) −20.5434 10.4441i −0.670407 0.340831i
\(940\) 7.07086 + 26.7109i 0.230626 + 0.871212i
\(941\) 1.27292 + 0.734922i 0.0414961 + 0.0239578i 0.520605 0.853798i \(-0.325707\pi\)
−0.479108 + 0.877756i \(0.659040\pi\)
\(942\) −19.4633 + 16.6027i −0.634147 + 0.540945i
\(943\) −10.4407 + 6.02795i −0.339996 + 0.196297i
\(944\) 13.0786 + 22.9718i 0.425673 + 0.747669i
\(945\) 3.63134 54.4722i 0.118128 1.77198i
\(946\) 38.7029 5.03596i 1.25834 0.163733i
\(947\) −13.3870 23.1870i −0.435019 0.753475i 0.562278 0.826948i \(-0.309925\pi\)
−0.997297 + 0.0734728i \(0.976592\pi\)
\(948\) −9.75953 8.82503i −0.316975 0.286624i
\(949\) 0.675531 + 0.390018i 0.0219287 + 0.0126605i
\(950\) 4.74357 + 36.4559i 0.153902 + 1.18278i
\(951\) −14.1047 + 27.7437i −0.457377 + 0.899650i
\(952\) −40.9567 + 33.4896i −1.32741 + 1.08541i
\(953\) 1.83030i 0.0592893i 0.999561 + 0.0296446i \(0.00943756\pi\)
−0.999561 + 0.0296446i \(0.990562\pi\)
\(954\) 11.1345 10.5723i 0.360492 0.342292i
\(955\) 23.5398 + 40.7722i 0.761731 + 1.31936i
\(956\) 11.6628 + 44.0574i 0.377202 + 1.42492i
\(957\) −29.7631 + 1.58664i −0.962105 + 0.0512887i
\(958\) 1.78222 1.36328i 0.0575808 0.0440454i
\(959\) 9.84834 42.7655i 0.318020 1.38097i
\(960\) −11.8786 + 53.7272i −0.383381 + 1.73404i
\(961\) 1.75837 + 3.04559i 0.0567217 + 0.0982449i
\(962\) 1.17464 + 1.53561i 0.0378719 + 0.0495101i
\(963\) 25.1139 + 34.4360i 0.809284 + 1.10968i
\(964\) −41.2263 11.1800i −1.32781 0.360082i
\(965\) −9.74239 5.62477i −0.313619 0.181068i
\(966\) 4.81968 7.56442i 0.155071 0.243381i
\(967\) 3.23033 + 5.59510i 0.103881 + 0.179926i 0.913280 0.407332i \(-0.133541\pi\)
−0.809400 + 0.587258i \(0.800207\pi\)
\(968\) −6.15361 15.0484i −0.197785 0.483673i
\(969\) 16.1208 + 24.7751i 0.517875 + 0.795891i
\(970\) 7.20159 + 55.3465i 0.231229 + 1.77707i
\(971\) 39.6908 + 22.9155i 1.27374 + 0.735393i 0.975689 0.219158i \(-0.0703309\pi\)
0.298049 + 0.954551i \(0.403664\pi\)
\(972\) −27.0230 15.5486i −0.866762 0.498721i
\(973\) −2.99248 9.76867i −0.0959344 0.313169i
\(974\) 4.05357 + 1.68621i 0.129885 + 0.0540297i
\(975\) 6.16859 12.1335i 0.197553 0.388583i
\(976\) 0.0551085 9.13352i 0.00176398 0.292357i
\(977\) −23.2405 13.4179i −0.743529 0.429277i 0.0798221 0.996809i \(-0.474565\pi\)
−0.823351 + 0.567533i \(0.807898\pi\)
\(978\) 20.5080 + 24.0415i 0.655775 + 0.768763i
\(979\) 4.70365 8.14696i 0.150329 0.260378i
\(980\) −41.8881 36.5537i −1.33807 1.16767i
\(981\) −1.65291 15.4591i −0.0527733 0.493570i
\(982\) −4.51594 1.87855i −0.144109 0.0599469i
\(983\) −13.3525 −0.425879 −0.212940 0.977065i \(-0.568304\pi\)
−0.212940 + 0.977065i \(0.568304\pi\)
\(984\) 42.5304 + 3.50246i 1.35582 + 0.111654i
\(985\) 55.7052i 1.77492i
\(986\) 59.6301 45.6130i 1.89901 1.45261i
\(987\) −10.2302 + 12.2278i −0.325631 + 0.389217i
\(988\) −0.922045 + 3.40006i −0.0293342 + 0.108170i
\(989\) 8.33339 14.4339i 0.264986 0.458970i
\(990\) 37.5409 9.02423i 1.19313 0.286809i
\(991\) −8.15321 14.1218i −0.258995 0.448593i 0.706978 0.707236i \(-0.250058\pi\)
−0.965973 + 0.258643i \(0.916725\pi\)
\(992\) −30.6079 12.9495i −0.971803 0.411148i
\(993\) −8.44866 4.29525i −0.268110 0.136306i
\(994\) 11.4713 + 25.2354i 0.363848 + 0.800418i
\(995\) 11.0784 + 19.1883i 0.351209 + 0.608311i
\(996\) 43.0620 + 9.24850i 1.36447 + 0.293050i
\(997\) 19.1554 0.606656 0.303328 0.952886i \(-0.401902\pi\)
0.303328 + 0.952886i \(0.401902\pi\)
\(998\) −3.93150 5.13966i −0.124449 0.162693i
\(999\) 9.09750 + 3.46410i 0.287832 + 0.109599i
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 504.2.y.a.173.20 yes 184
7.3 odd 6 504.2.ca.a.101.43 yes 184
8.5 even 2 inner 504.2.y.a.173.13 184
9.5 odd 6 504.2.ca.a.5.50 yes 184
56.45 odd 6 504.2.ca.a.101.50 yes 184
63.59 even 6 inner 504.2.y.a.437.13 yes 184
72.5 odd 6 504.2.ca.a.5.43 yes 184
504.437 even 6 inner 504.2.y.a.437.20 yes 184
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.y.a.173.13 184 8.5 even 2 inner
504.2.y.a.173.20 yes 184 1.1 even 1 trivial
504.2.y.a.437.13 yes 184 63.59 even 6 inner
504.2.y.a.437.20 yes 184 504.437 even 6 inner
504.2.ca.a.5.43 yes 184 72.5 odd 6
504.2.ca.a.5.50 yes 184 9.5 odd 6
504.2.ca.a.101.43 yes 184 7.3 odd 6
504.2.ca.a.101.50 yes 184 56.45 odd 6