LMFDB - Embedded newform 168.2.ba.c.101.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.24
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.24

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41416 - 0.0117470i) q^{2} +(-1.11142 - 1.32844i) q^{3} +(1.99972 - 0.0332243i) q^{4} +(-0.337879 + 0.195075i) q^{5} +(-1.58733 - 1.86558i) q^{6} +(1.39526 - 2.24795i) q^{7} +(2.82755 - 0.0704754i) q^{8} +(-0.529502 + 2.95290i) q^{9} +(-0.475526 + 0.279837i) q^{10} +(0.748582 - 1.29658i) q^{11} +(-2.26666 - 2.61959i) q^{12} -3.28768 q^{13} +(1.94672 - 3.19536i) q^{14} +(0.634670 + 0.232043i) q^{15} +(3.99779 - 0.132879i) q^{16} +(-1.68169 + 2.91278i) q^{17} +(-0.714115 + 4.18211i) q^{18} +(2.56203 + 4.43756i) q^{19} +(-0.669184 + 0.401321i) q^{20} +(-4.53697 + 0.644892i) q^{21} +(1.04339 - 1.84237i) q^{22} +(-4.72764 + 2.72950i) q^{23} +(-3.23621 - 3.67790i) q^{24} +(-2.42389 + 4.19830i) q^{25} +(-4.64932 + 0.0386203i) q^{26} +(4.51125 - 2.57850i) q^{27} +(2.71544 - 4.54163i) q^{28} +4.13801 q^{29} +(0.900254 + 0.320691i) q^{30} +(-3.60237 - 2.07983i) q^{31} +(5.65198 - 0.234875i) q^{32} +(-2.55442 + 0.446598i) q^{33} +(-2.34398 + 4.13891i) q^{34} +(-0.0329110 + 1.03171i) q^{35} +(-0.960750 + 5.92258i) q^{36} +(-7.46581 + 4.31038i) q^{37} +(3.67525 + 6.24534i) q^{38} +(3.65399 + 4.36748i) q^{39} +(-0.941622 + 0.575396i) q^{40} +11.1607 q^{41} +(-6.40845 + 0.965280i) q^{42} -4.79323i q^{43} +(1.45388 - 2.61768i) q^{44} +(-0.397129 - 1.10102i) q^{45} +(-6.65359 + 3.91550i) q^{46} +(-2.51067 - 4.34861i) q^{47} +(-4.61974 - 5.16314i) q^{48} +(-3.10652 - 6.27292i) q^{49} +(-3.37846 + 5.96557i) q^{50} +(5.73852 - 1.00329i) q^{51} +(-6.57445 + 0.109231i) q^{52} +(0.499243 - 0.864715i) q^{53} +(6.34936 - 3.69941i) q^{54} +0.584118i q^{55} +(3.78673 - 6.45451i) q^{56} +(3.04755 - 8.33548i) q^{57} +(5.85183 - 0.0486091i) q^{58} +(-1.36034 - 0.785391i) q^{59} +(1.27687 + 0.442935i) q^{60} +(-3.40889 - 5.90437i) q^{61} +(-5.11878 - 2.89891i) q^{62} +(5.89917 + 5.31035i) q^{63} +(7.99007 - 0.398545i) q^{64} +(1.11084 - 0.641343i) q^{65} +(-3.60712 + 0.661570i) q^{66} +(-3.05467 - 1.76361i) q^{67} +(-3.26615 + 5.88063i) q^{68} +(8.88036 + 3.24676i) q^{69} +(-0.0344221 + 1.45940i) q^{70} -14.3360i q^{71} +(-1.28909 + 8.38679i) q^{72} +(2.76107 + 1.59410i) q^{73} +(-10.5072 + 6.18329i) q^{74} +(8.27115 - 1.44608i) q^{75} +(5.27078 + 8.78877i) q^{76} +(-1.87018 - 3.49184i) q^{77} +(5.21864 + 6.13342i) q^{78} +(-0.239413 - 0.414676i) q^{79} +(-1.32485 + 0.824765i) q^{80} +(-8.43926 - 3.12713i) q^{81} +(15.7831 - 0.131105i) q^{82} +17.4548i q^{83} +(-9.05127 + 1.44034i) q^{84} -1.31222i q^{85} +(-0.0563059 - 6.77842i) q^{86} +(-4.59906 - 5.49710i) q^{87} +(2.02527 - 3.71891i) q^{88} +(2.54840 + 4.41396i) q^{89} +(-0.574539 - 1.55235i) q^{90} +(-4.58716 + 7.39053i) q^{91} +(-9.36328 + 5.61532i) q^{92} +(1.24081 + 7.09709i) q^{93} +(-3.60159 - 6.12016i) q^{94} +(-1.73131 - 0.999573i) q^{95} +(-6.59372 - 7.24726i) q^{96} -9.00074i q^{97} +(-4.46682 - 8.83445i) q^{98} +(3.43230 + 2.89703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$

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 $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.41416	−	0.0117470i	0.999966	−	0.00830636i
$2$	1.41416	−	0.0117470i	0.999966	−	0.00830636i
$3$	−1.11142	−	1.32844i	−0.641677	−	0.766975i
$3$	−1.11142	−	1.32844i	−0.641677	−	0.766975i
$4$	1.99972	−	0.0332243i	0.999862	−	0.0166122i
$5$	−0.337879	+	0.195075i	−0.151104	+	0.0872401i	−0.573646	−	0.819103i	$-0.694471\pi$
$5$	−0.337879	+	0.195075i	−0.151104	+	0.0872401i	0.422542	+	0.906344i	$0.361138\pi$
$6$	−1.58733	−	1.86558i	−0.648026	−	0.761618i
$7$	1.39526	−	2.24795i	0.527357	−	0.849644i
$7$	1.39526	−	2.24795i	0.527357	−	0.849644i
$8$	2.82755	−	0.0704754i	0.999690	−	0.0249168i
$9$	−0.529502	+	2.95290i	−0.176501	+	0.984301i
$10$	−0.475526	+	0.279837i	−0.150374	+	0.0884922i
$11$	0.748582	−	1.29658i	0.225706	−	0.390934i	−0.730825	−	0.682565i	$-0.760864\pi$
$11$	0.748582	−	1.29658i	0.225706	−	0.390934i	0.956531	+	0.291631i	$0.0941978\pi$
$12$	−2.26666	−	2.61959i	−0.654330	−	0.756209i
$13$	−3.28768			−0.911838			−0.455919	−	0.890021i	$-0.650689\pi$
$13$	−3.28768			−0.911838			−0.455919	+	0.890021i	$0.650689\pi$
$14$	1.94672	−	3.19536i	0.520282	−	0.853995i
$15$	0.634670	+	0.232043i	0.163871	+	0.0599132i
$16$	3.99779	−	0.132879i	0.999448	−	0.0332197i
$17$	−1.68169	+	2.91278i	−0.407871	+	0.706453i	−0.994651	−	0.103293i	$-0.967062\pi$
$17$	−1.68169	+	2.91278i	−0.407871	+	0.706453i	0.586780	+	0.809746i	$0.300395\pi$
$18$	−0.714115	+	4.18211i	−0.168319	+	0.985733i
$19$	2.56203	+	4.43756i	0.587769	+	1.01805i	0.994524	+	0.104509i	$0.0333270\pi$
$19$	2.56203	+	4.43756i	0.587769	+	1.01805i	−0.406755	+	0.913537i	$0.633340\pi$
$20$	−0.669184	+	0.401321i	−0.149634	+	0.0897382i
$21$	−4.53697	+	0.644892i	−0.990048	+	0.140727i
$22$	1.04339	−	1.84237i	0.222451	−	0.392795i
$23$	−4.72764	+	2.72950i	−0.985780	+	0.569141i	−0.904010	−	0.427511i	$-0.859391\pi$
$23$	−4.72764	+	2.72950i	−0.985780	+	0.569141i	−0.0817700	+	0.996651i	$0.526057\pi$
$24$	−3.23621	−	3.67790i	−0.660589	−	0.750748i
$25$	−2.42389	+	4.19830i	−0.484778	+	0.839661i
$26$	−4.64932	+	0.0386203i	−0.911807	+	0.00757406i
$27$	4.51125	−	2.57850i	0.868190	−	0.496232i
$28$	2.71544	−	4.54163i	0.513170	−	0.858287i
$29$	4.13801			0.768410			0.384205	−	0.923248i	$-0.374476\pi$
$29$	4.13801			0.768410			0.384205	+	0.923248i	$0.374476\pi$
$30$	0.900254	+	0.320691i	0.164363	+	0.0585499i
$31$	−3.60237	−	2.07983i	−0.647005	−	0.373549i	0.140303	−	0.990109i	$-0.455192\pi$
$31$	−3.60237	−	2.07983i	−0.647005	−	0.373549i	−0.787308	+	0.616560i	$0.788526\pi$
$32$	5.65198	−	0.234875i	0.999138	−	0.0415204i
$33$	−2.55442	+	0.446598i	−0.444667	+	0.0777428i
$34$	−2.34398	+	4.13891i	−0.401989	+	0.709816i
$35$	−0.0329110	+	1.03171i	−0.00556298	+	0.174391i
$36$	−0.960750	+	5.92258i	−0.160125	+	0.987097i
$37$	−7.46581	+	4.31038i	−1.22737	+	0.708623i	−0.966479	−	0.256745i	$-0.917350\pi$
$37$	−7.46581	+	4.31038i	−1.22737	+	0.708623i	−0.260892	+	0.965368i	$0.584017\pi$
$38$	3.67525	+	6.24534i	0.596205	+	1.01313i
$39$	3.65399	+	4.36748i	0.585106	+	0.699357i
$40$	−0.941622	+	0.575396i	−0.148884	+	0.0909780i
$41$	11.1607			1.74301			0.871505	−	0.490387i	$-0.163145\pi$
$41$	11.1607			1.74301			0.871505	+	0.490387i	$0.163145\pi$
$42$	−6.40845	+	0.965280i	−0.988845	+	0.148946i
$43$		−	4.79323i		−	0.730961i	−0.930819	−	0.365480i	$-0.880905\pi$
$43$		−	4.79323i		−	0.730961i	0.930819	−	0.365480i	$-0.119095\pi$
$44$	1.45388	−	2.61768i	0.219181	−	0.394630i
$45$	−0.397129	−	1.10102i	−0.0592005	−	0.164130i
$46$	−6.65359	+	3.91550i	−0.981019	+	0.577309i
$47$	−2.51067	−	4.34861i	−0.366219	−	0.634310i	0.622752	−	0.782419i	$-0.286015\pi$
$47$	−2.51067	−	4.34861i	−0.366219	−	0.634310i	−0.988971	+	0.148109i	$0.952681\pi$
$48$	−4.61974	−	5.16314i	−0.666802	−	0.745235i
$49$	−3.10652	−	6.27292i	−0.443788	−	0.896132i
$50$	−3.37846	+	5.96557i	−0.477787	+	0.843658i
$51$	5.73852	−	1.00329i	0.803553	−	0.140488i
$52$	−6.57445	+	0.109231i	−0.911712	+	0.0151476i
$53$	0.499243	−	0.864715i	0.0685763	−	0.118778i	−0.829699	−	0.558212i	$-0.811488\pi$
$53$	0.499243	−	0.864715i	0.0685763	−	0.118778i	0.898275	+	0.439434i	$0.144821\pi$
$54$	6.34936	−	3.69941i	0.864038	−	0.503426i
$55$			0.584118i			0.0787624i
$56$	3.78673	−	6.45451i	0.506023	−	0.862520i
$57$	3.04755	−	8.33548i	0.403657	−	1.10406i
$58$	5.85183	−	0.0486091i	0.768383	−	0.00638269i
$59$	−1.36034	−	0.785391i	−0.177101	−	0.102249i	0.408829	−	0.912611i	$-0.365937\pi$
$59$	−1.36034	−	0.785391i	−0.177101	−	0.102249i	−0.585930	+	0.810362i	$0.699271\pi$
$60$	1.27687	+	0.442935i	0.164844	+	0.0571827i
$61$	−3.40889	−	5.90437i	−0.436464	−	0.755977i	0.560950	−	0.827850i	$-0.310436\pi$
$61$	−3.40889	−	5.90437i	−0.436464	−	0.755977i	−0.997414	+	0.0718723i	$0.977103\pi$
$62$	−5.11878	−	2.89891i	−0.650085	−	0.368161i
$63$	5.89917	+	5.31035i	0.743226	+	0.669041i
$64$	7.99007	−	0.398545i	0.998758	−	0.0498181i
$65$	1.11084	−	0.641343i	0.137783	−	0.0795488i
$66$	−3.60712	+	0.661570i	−0.444006	+	0.0814337i
$67$	−3.05467	−	1.76361i	−0.373187	−	0.215460i	0.301663	−	0.953415i	$-0.402458\pi$
$67$	−3.05467	−	1.76361i	−0.373187	−	0.215460i	−0.674850	+	0.737955i	$0.735792\pi$
$68$	−3.26615	+	5.88063i	−0.396079	+	0.713131i
$69$	8.88036	+	3.24676i	1.06907	+	0.390864i
$70$	−0.0344221	+	1.45940i	−0.00411423	+	0.174432i
$71$		−	14.3360i		−	1.70137i	−0.525677	−	0.850684i	$-0.676188\pi$
$71$		−	14.3360i		−	1.70137i	0.525677	−	0.850684i	$-0.323812\pi$
$72$	−1.28909	+	8.38679i	−0.151920	+	0.988393i
$73$	2.76107	+	1.59410i	0.323159	+	0.186576i	0.652800	−	0.757531i	$-0.273594\pi$
$73$	2.76107	+	1.59410i	0.323159	+	0.186576i	−0.329641	+	0.944106i	$0.606928\pi$
$74$	−10.5072	+	6.18329i	−1.22144	+	0.718793i
$75$	8.27115	−	1.44608i	0.955070	−	0.166978i
$76$	5.27078	+	8.78877i	0.604600	+	1.00814i
$77$	−1.87018	−	3.49184i	−0.213127	−	0.397932i
$78$	5.21864	+	6.13342i	0.590895	+	0.694473i
$79$	−0.239413	−	0.414676i	−0.0269361	−	0.0466547i	0.852243	−	0.523146i	$-0.175242\pi$
$79$	−0.239413	−	0.414676i	−0.0269361	−	0.0466547i	−0.879179	+	0.476491i	$0.841908\pi$
$80$	−1.32485	+	0.824765i	−0.148123	+	0.0922116i
$81$	−8.43926	−	3.12713i	−0.937695	−	0.347459i
$82$	15.7831	−	0.131105i	1.74295	−	0.0144781i
$83$			17.4548i			1.91591i	0.286911	+	0.957957i	$0.407372\pi$
$83$			17.4548i			1.91591i	−0.286911	+	0.957957i	$0.592628\pi$
$84$	−9.05127	+	1.44034i	−0.987574	+	0.157154i
$85$		−	1.31222i		−	0.142331i
$86$	−0.0563059	−	6.77842i	−0.00607163	−	0.730935i
$87$	−4.59906	−	5.49710i	−0.493071	−	0.589351i
$88$	2.02527	−	3.71891i	0.215895	−	0.396437i
$89$	2.54840	+	4.41396i	0.270130	+	0.467879i	0.968895	−	0.247473i	$-0.0796000\pi$
$89$	2.54840	+	4.41396i	0.270130	+	0.467879i	−0.698765	+	0.715351i	$0.746267\pi$
$90$	−0.574539	−	1.55235i	−0.0605617	−	0.163633i
$91$	−4.58716	+	7.39053i	−0.480865	+	0.774738i
$92$	−9.36328	+	5.61532i	−0.976190	+	0.585438i
$93$	1.24081	+	7.09709i	0.128666	+	0.735934i
$94$	−3.60159	−	6.12016i	−0.371475	−	0.631246i
$95$	−1.73131	−	0.999573i	−0.177629	−	0.102554i
$96$	−6.59372	−	7.24726i	−0.672969	−	0.739671i
$97$		−	9.00074i		−	0.913887i	−0.889496	−	0.456943i	$-0.848944\pi$
$97$		−	9.00074i		−	0.913887i	0.889496	−	0.456943i	$-0.151056\pi$
$98$	−4.46682	−	8.83445i	−0.451217	−	0.892414i
$99$	3.43230	+	2.89703i	0.344959	+	0.291163i
$100$	−4.70763	+	8.47598i	−0.470763	+	0.847598i
$101$	4.63907	+	2.67837i	0.461605	+	0.266508i	0.712719	−	0.701450i	$-0.247464\pi$
$101$	4.63907	+	2.67837i	0.461605	+	0.266508i	−0.251114	+	0.967958i	$0.580797\pi$
$102$	8.10342	−	1.48622i	0.802358	−	0.147158i
$103$	7.70831	−	4.45039i	0.759522	−	0.438510i	−0.0696021	−	0.997575i	$-0.522173\pi$
$103$	7.70831	−	4.45039i	0.759522	−	0.438510i	0.829124	+	0.559065i	$0.188840\pi$
$104$	−9.29608	+	0.231700i	−0.911555	+	0.0227201i
$105$	1.40715	−	1.10294i	0.137323	−	0.107636i
$106$	0.695854	−	1.22871i	0.0675874	−	0.119343i
$107$	−7.85256	−	13.6010i	−0.759135	−	1.31486i	−0.943292	−	0.331964i	$-0.892289\pi$
$107$	−7.85256	−	13.6010i	−0.759135	−	1.31486i	0.184157	−	0.982897i	$-0.441045\pi$
$108$	8.93558	−	5.30616i	0.859827	−	0.510586i
$109$	15.1582	+	8.75159i	1.45189	+	0.838250i	0.998589	−	0.0531069i	$-0.0169124\pi$
$109$	15.1582	+	8.75159i	1.45189	+	0.838250i	0.453303	+	0.891357i	$0.350246\pi$
$110$	0.00686161	+	0.826039i	0.000654229	+	0.0787597i
$111$	14.0237	+	5.12723i	1.33107	+	0.486655i
$112$	5.27924	−	9.17222i	0.498841	−	0.866693i
$113$		−	0.0726142i		−	0.00683097i	−0.999994	−	0.00341549i	$-0.998913\pi$
$113$		−	0.0726142i		−	0.00683097i	0.999994	−	0.00341549i	$-0.00108718\pi$
$114$	4.21182	−	11.8235i	0.394473	−	1.10738i
$115$	1.06491	−	1.84448i	0.0993037	−	0.171999i
$116$	8.27488	−	0.137483i	0.768304	−	0.0127649i
$117$	1.74083	−	9.70819i	0.160940	−	0.897523i
$118$	−1.93297	−	1.09469i	−0.177944	−	0.100775i
$119$	4.20138	+	7.84443i	0.385139	+	0.719098i
$120$	1.81091	+	0.611384i	0.165313	+	0.0558114i
$121$	4.37925	+	7.58508i	0.398114	+	0.689553i
$122$	−4.89009	−	8.30971i	−0.442728	−	0.752326i
$123$	−12.4042	−	14.8263i	−1.11845	−	1.33684i
$124$	−7.27285	−	4.03940i	−0.653121	−	0.362749i
$125$		−	3.84211i		−	0.343649i
$126$	8.40478	+	7.44041i	0.748757	+	0.662844i
$127$	−8.81577			−0.782273			−0.391137	−	0.920333i	$-0.627918\pi$
$127$	−8.81577			−0.782273			−0.391137	+	0.920333i	$0.627918\pi$
$128$	11.2946	−	0.657467i	0.998310	−	0.0581125i
$129$	−6.36751	+	5.32728i	−0.560628	+	0.469041i
$130$	1.56338	−	0.920014i	0.137117	−	0.0806906i
$131$	−4.36183	+	2.51830i	−0.381095	+	0.220025i	−0.678294	−	0.734790i	$-0.737281\pi$
$131$	−4.36183	+	2.51830i	−0.381095	+	0.220025i	0.297200	+	0.954815i	$0.403947\pi$
$132$	−5.09329	+	0.977942i	−0.443314	+	0.0851189i
$133$	13.5501	+	0.432239i	1.17494	+	0.0374799i
$134$	−4.34052	−	2.45816i	−0.374964	−	0.212352i
$135$	−1.02126	+	1.75125i	−0.0878959	+	0.150724i
$136$	−4.54979	+	8.35455i	−0.390142	+	0.716396i
$137$	−6.34787	−	3.66494i	−0.542335	−	0.313117i	0.203690	−	0.979035i	$-0.434707\pi$
$137$	−6.34787	−	3.66494i	−0.542335	−	0.313117i	−0.746025	+	0.665918i	$0.768040\pi$
$138$	12.5964	+	4.48714i	1.07228	+	0.381971i
$139$	−15.7497			−1.33587			−0.667935	−	0.744220i	$-0.732822\pi$
$139$	−15.7497			−1.33587			−0.667935	+	0.744220i	$0.732822\pi$
$140$	−0.0315350	+	2.06424i	−0.00266519	+	0.174460i
$141$	−2.98646	+	8.16840i	−0.251505	+	0.687903i
$142$	−0.168404	−	20.2735i	−0.0141322	−	1.70131i
$143$	−2.46110	+	4.26275i	−0.205807	+	0.356469i
$144$	−1.72446	+	11.8754i	−0.143705	+	0.989621i
$145$	−1.39815	+	0.807222i	−0.116110	+	0.0670361i
$146$	3.92333	+	2.22189i	0.324697	+	0.183885i
$147$	−4.88056	+	11.0987i	−0.402542	+	0.915402i
$148$	−14.7863	+	8.86763i	−1.21543	+	0.728914i
$149$	−8.98969	−	15.5706i	−0.736464	−	1.27559i	−0.954078	−	0.299559i	$-0.903161\pi$
$149$	−8.98969	−	15.5706i	−0.736464	−	1.27559i	0.217613	−	0.976035i	$-0.430173\pi$
$150$	11.6798	−	2.14215i	0.953650	−	0.174906i
$151$	−7.89149	+	13.6685i	−0.642201	+	1.11232i	0.342740	+	0.939430i	$0.388645\pi$
$151$	−7.89149	+	13.6685i	−0.642201	+	1.11232i	−0.984940	+	0.172894i	$0.944688\pi$
$152$	7.55699	+	12.3669i	0.612953	+	1.00308i
$153$	−7.71069	−	6.50820i	−0.623373	−	0.526157i
$154$	−2.68576	−	4.91606i	−0.216425	−	0.396148i
$155$	1.62289			0.130354
$156$	7.45207	+	8.61236i	0.596643	+	0.689541i
$157$	2.53274	−	4.38683i	0.202134	−	0.350107i	−0.747082	−	0.664732i	$-0.768546\pi$
$157$	2.53274	−	4.38683i	0.202134	−	0.350107i	0.949216	+	0.314625i	$0.101879\pi$
$158$	−0.343441	−	0.583608i	−0.0273227	−	0.0464294i
$159$	−1.70359	+	0.297845i	−0.135103	+	0.0236206i
$160$	−1.86387	+	1.18192i	−0.147352	+	0.0934387i
$161$	−0.460494	+	14.4358i	−0.0362920	+	1.13770i
$162$	−11.9712	−	4.32315i	−0.940549	−	0.339659i
$163$	10.8745	−	6.27840i	0.851757	−	0.491762i	−0.00948597	−	0.999955i	$-0.503020\pi$
$163$	10.8745	−	6.27840i	0.851757	−	0.491762i	0.861243	+	0.508193i	$0.169686\pi$
$164$	22.3183	−	0.370807i	1.74277	−	0.0289551i
$165$	0.775965	−	0.649199i	0.0604088	−	0.0505400i
$166$	0.205041	+	24.6840i	0.0159143	+	1.91585i
$167$	−7.43145			−0.575063			−0.287531	−	0.957771i	$-0.592835\pi$
$167$	−7.43145			−0.575063			−0.287531	+	0.957771i	$0.592835\pi$
$168$	−12.7831	+	2.14321i	−0.986235	+	0.165352i
$169$	−2.19116			−0.168551
$170$	−0.0154147	−	1.85570i	−0.00118225	−	0.142326i
$171$	−14.4603	+	5.21571i	−1.10580	+	0.398856i
$172$	−0.159252	−	9.58514i	−0.0121428	−	0.730860i
$173$	−15.2445	+	8.80144i	−1.15902	+	0.669161i	−0.951069	−	0.308978i	$-0.900013\pi$
$173$	−15.2445	+	8.80144i	−1.15902	+	0.669161i	−0.207952	+	0.978139i	$0.566680\pi$
$174$	−6.56840	−	7.71978i	−0.497949	−	0.585235i
$175$	6.05561	+	11.3065i	0.457761	+	0.854690i
$176$	2.82039	−	5.28294i	0.212595	−	0.398216i
$177$	0.468558	+	2.68002i	0.0352190	+	0.201443i
$178$	3.65571	+	6.21213i	0.274007	+	0.465619i
$179$	−8.11784	+	14.0605i	−0.606756	+	1.05093i	0.385016	+	0.922910i	$0.374196\pi$
$179$	−8.11784	+	14.0605i	−0.606756	+	1.05093i	−0.991771	+	0.128022i	$0.959137\pi$
$180$	−0.830728	−	2.18854i	−0.0619188	−	0.163124i
$181$	6.19340			0.460351			0.230176	−	0.973149i	$-0.426070\pi$
$181$	6.19340			0.460351			0.230176	+	0.973149i	$0.426070\pi$
$182$	−6.40018	+	10.5053i	−0.474413	+	0.778705i
$183$	−4.05490	+	11.0907i	−0.299747	+	0.819850i
$184$	−13.1753	+	8.05098i	−0.971293	+	0.593526i
$185$	1.68169	−	2.91278i	0.123641	−	0.214152i
$186$	1.83808	+	10.0219i	0.134775	+	0.734840i
$187$	2.51777	+	4.36091i	0.184118	+	0.318901i
$188$	−5.16513	−	8.61261i	−0.376706	−	0.628139i
$189$	0.498031	−	13.7387i	0.0362264	−	0.999344i
$190$	−2.46010	−	1.39322i	−0.178475	−	0.101075i
$191$	−7.28788	+	4.20766i	−0.527333	+	0.304456i	−0.739930	−	0.672684i	$-0.765141\pi$
$191$	−7.28788	+	4.20766i	−0.527333	+	0.304456i	0.212597	+	0.977140i	$0.431808\pi$
$192$	−9.40974	−	10.1714i	−0.679090	−	0.734055i
$193$	6.57333	−	11.3853i	0.473158	−	0.819534i	−0.526370	−	0.850256i	$-0.676447\pi$
$193$	6.57333	−	11.3853i	0.473158	−	0.819534i	0.999528	+	0.0307215i	$0.00978048\pi$
$194$	−0.105731	−	12.7285i	−0.00759108	−	0.913855i
$195$	−2.08659	−	0.762882i	−0.149424	−	0.0546311i
$196$	−6.42059	−	12.4409i	−0.458614	−	0.888636i
$197$	17.6119			1.25480			0.627398	−	0.778699i	$-0.284120\pi$
$197$	17.6119			1.25480			0.627398	+	0.778699i	$0.284120\pi$
$198$	4.88787	+	4.05656i	0.347366	+	0.288287i
$199$	17.2688	+	9.97017i	1.22416	+	0.706767i	0.965801	−	0.259284i	$-0.0834864\pi$
$199$	17.2688	+	9.97017i	1.22416	+	0.706767i	0.258354	+	0.966050i	$0.416820\pi$
$200$	−6.55780	+	12.0417i	−0.463706	+	0.851479i
$201$	1.05216	+	6.01805i	0.0742135	+	0.424480i
$202$	6.59187	+	3.73316i	0.463803	+	0.262664i
$203$	5.77359	−	9.30203i	0.405227	−	0.652874i
$204$	11.4421	−	2.19695i	0.801108	−	0.153818i
$205$	−3.77097	+	2.17717i	−0.263376	+	0.152060i
$206$	10.8485	−	6.38414i	0.755853	−	0.444804i
$207$	−5.55666	−	15.4055i	−0.386214	−	1.07076i
$208$	−13.1435	+	0.436863i	−0.911335	+	0.0302910i
$209$	7.67154			0.530652
$210$	1.97698	−	1.57627i	0.136425	−	0.108773i
$211$		−	14.5159i		−	0.999314i	−0.866223	−	0.499657i	$-0.833459\pi$
$211$		−	14.5159i		−	0.999314i	0.866223	−	0.499657i	$-0.166541\pi$
$212$	0.969619	−	1.74578i	0.0665937	−	0.119901i
$213$	−19.0445	+	15.9333i	−1.30491	+	1.09173i
$214$	−11.2646	−	19.1419i	−0.770031	−	1.30851i
$215$	0.935038	+	1.61953i	0.0637691	+	0.110451i
$216$	12.5741	−	7.60875i	0.855556	−	0.517710i
$217$	−9.70158	+	5.19604i	−0.658586	+	0.352730i
$218$	21.5390	+	12.1981i	1.45880	+	0.826161i
$219$	−0.951031	−	5.43963i	−0.0642647	−	0.367576i
$220$	0.0194069	+	1.16807i	0.00130841	+	0.0787515i
$221$	5.52887	−	9.57629i	0.371912	−	0.644171i
$222$	19.8921	+	7.08601i	1.33507	+	0.475582i
$223$		−	2.77897i		−	0.186093i	−0.995662	−	0.0930467i	$-0.970339\pi$
$223$		−	2.77897i		−	0.186093i	0.995662	−	0.0930467i	$-0.0296606\pi$
$224$	7.35797	−	13.0330i	0.491625	−	0.870807i
$225$	−11.1137	−	9.38052i	−0.740915	−	0.625368i
$226$	−0.000852997	−	0.102688i	−5.67405e−5	−	0.00683074i
$227$	14.0438	+	8.10819i	0.932119	+	0.538159i	0.887481	−	0.460844i	$-0.152453\pi$
$227$	14.0438	+	8.10819i	0.932119	+	0.538159i	0.0446379	+	0.999003i	$0.485787\pi$
$228$	5.81731	−	16.7699i	0.385261	−	1.11061i
$229$	−10.3150	−	17.8661i	−0.681633	−	1.18062i	−0.974482	−	0.224464i	$-0.927937\pi$
$229$	−10.3150	−	17.8661i	−0.681633	−	1.18062i	0.292849	−	0.956159i	$-0.405397\pi$
$230$	1.48430	−	2.62091i	0.0978716	−	0.172818i
$231$	−2.56014	+	6.36531i	−0.168445	+	0.418807i
$232$	11.7004	−	0.291628i	0.768171	−	0.0191463i
$233$	−1.80462	+	1.04190i	−0.118225	+	0.0682572i	−0.557946	−	0.829877i	$-0.688411\pi$
$233$	−1.80462	+	1.04190i	−0.118225	+	0.0682572i	0.439721	+	0.898134i	$0.355077\pi$
$234$	2.34778	−	13.7494i	0.153479	−	0.898829i
$235$	1.69661	+	0.979538i	0.110675	+	0.0638980i
$236$	−2.74639	−	1.52537i	−0.178775	−	0.0992931i
$237$	−0.284784	+	0.778925i	−0.0184987	+	0.0505966i
$238$	6.03359	+	11.0440i	0.391099	+	0.715874i
$239$			0.851762i			0.0550959i	0.999620	+	0.0275480i	$0.00876990\pi$
$239$			0.851762i			0.0550959i	−0.999620	+	0.0275480i	$0.991230\pi$
$240$	2.56811	+	0.843324i	0.165771	+	0.0544364i
$241$	13.0417	+	7.52961i	0.840087	+	0.485025i	0.857294	−	0.514827i	$-0.172144\pi$
$241$	13.0417	+	7.52961i	0.840087	+	0.485025i	−0.0172066	+	0.999852i	$0.505477\pi$
$242$	6.28208	+	10.6751i	0.403828	+	0.686222i
$243$	5.22533	+	14.6866i	0.335205	+	0.942145i
$244$	−7.01301	−	11.6939i	−0.448962	−	0.748622i
$245$	2.27332	+	1.51349i	0.145237	+	0.0966932i
$246$	−17.7158	−	20.8211i	−1.12952	−	1.32751i
$247$	−8.42312	−	14.5893i	−0.535950	−	0.928293i
$248$	−10.3325	−	5.62694i	−0.656112	−	0.357311i
$249$	23.1877	−	19.3996i	1.46946	−	1.22940i
$250$	−0.0451331	−	5.43337i	−0.00285447	−	0.343637i
$251$		−	11.8022i		−	0.744948i	−0.928043	−	0.372474i	$-0.878510\pi$
$251$		−	11.8022i		−	0.744948i	0.928043	−	0.372474i	$-0.121490\pi$
$252$	11.9731	+	10.4232i	0.754237	+	0.656602i
$253$			8.17302i			0.513834i
$254$	−12.4670	+	0.103559i	−0.782246	+	0.00649785i
$255$	−1.74321	+	1.45843i	−0.109164	+	0.0913304i
$256$	15.9647	−	1.06244i	0.997793	−	0.0664028i
$257$	−8.86901	−	15.3616i	−0.553233	−	0.958228i	−0.998039	−	0.0626011i	$-0.980060\pi$
$257$	−8.86901	−	15.3616i	−0.553233	−	0.958228i	0.444805	−	0.895627i	$-0.353273\pi$
$258$	−8.94213	+	7.60845i	−0.556713	+	0.473681i
$259$	−0.727204	+	22.7968i	−0.0451863	+	1.41653i
$260$	2.20006	−	1.31942i	0.136442	−	0.0818267i
$261$	−2.19109	+	12.2191i	−0.135625	+	0.756346i
$262$	−6.13876	+	3.61253i	−0.379254	+	0.223183i
$263$	6.27815	+	3.62469i	0.387128	+	0.223508i	0.680915	−	0.732363i	$-0.261582\pi$
$263$	6.27815	+	3.62469i	0.387128	+	0.223508i	−0.293787	+	0.955871i	$0.594916\pi$
$264$	−7.19127	+	1.44280i	−0.442592	+	0.0887983i
$265$			0.389559i			0.0239304i
$266$	19.1671	+	0.452085i	1.17521	+	0.0277191i
$267$	3.03134	−	8.29114i	0.185515	−	0.507410i
$268$	−6.16709	−	3.42525i	−0.376715	−	0.209230i
$269$	2.95817	+	1.70790i	0.180363	+	0.104132i	0.587463	−	0.809251i	$-0.300127\pi$
$269$	2.95817	+	1.70790i	0.180363	+	0.104132i	−0.407100	+	0.913383i	$0.633460\pi$
$270$	−1.42366	+	2.48855i	−0.0866409	+	0.151449i
$271$	3.96989	−	2.29201i	0.241153	−	0.139230i	−0.374553	−	0.927205i	$-0.622204\pi$
$271$	3.96989	−	2.29201i	0.241153	−	0.139230i	0.615707	+	0.787975i	$0.288871\pi$
$272$	−6.33602	+	11.8682i	−0.384177	+	0.719612i
$273$	14.9161	−	2.12020i	0.902764	−	0.128320i
$274$	−9.01998	−	5.10826i	−0.544917	−	0.308601i
$275$	3.62896	+	6.28555i	0.218835	+	0.379033i
$276$	17.8661	+	6.19758i	1.07541	+	0.373051i
$277$	10.6940	+	6.17421i	0.642543	+	0.370972i	0.785593	−	0.618743i	$-0.212358\pi$
$277$	10.6940	+	6.17421i	0.642543	+	0.370972i	−0.143050	+	0.989715i	$0.545691\pi$
$278$	−22.2726	+	0.185011i	−1.33582	+	0.0110962i
$279$	8.04900	−	9.53617i	0.481881	−	0.570916i
$280$	−0.0203471	+	2.91954i	−0.00121597	+	0.174476i
$281$			7.91565i			0.472208i	0.971728	+	0.236104i	$0.0758706\pi$
$281$			7.91565i			0.472208i	−0.971728	+	0.236104i	$0.924129\pi$
$282$	−4.12740	+	11.5865i	−0.245783	+	0.689969i
$283$	11.3552	−	19.6678i	0.674999	−	1.16913i	−0.301471	−	0.953475i	$-0.597478\pi$
$283$	11.3552	−	19.6678i	0.674999	−	1.16913i	0.976469	−	0.215656i	$-0.0691891\pi$
$284$	−0.476303	−	28.6680i	−0.0282634	−	1.70113i
$285$	0.596338	+	3.41089i	0.0353240	+	0.202043i
$286$	−3.43032	+	6.05714i	−0.202839	+	0.358166i
$287$	15.5720	−	25.0887i	0.919189	−	1.48094i
$288$	−2.29917	+	16.8141i	−0.135480	+	0.990780i
$289$	2.84381	+	4.92562i	0.167283	+	0.289742i
$290$	−1.96773	+	1.15797i	−0.115549	+	0.0679983i
$291$	−11.9569	+	10.0036i	−0.700928	+	0.586420i
$292$	5.57434	+	3.09603i	0.326214	+	0.181182i
$293$			12.8246i			0.749220i	0.927183	+	0.374610i	$0.122223\pi$
$293$			12.8246i			0.749220i	−0.927183	+	0.374610i	$0.877777\pi$
$294$	−6.77154	+	15.7527i	−0.394924	+	0.918714i
$295$	0.612840			0.0356809
$296$	−20.8062	+	12.7140i	−1.20933	+	0.738985i
$297$	0.0338081	−	7.77942i	0.00196175	−	0.451408i
$298$	−12.8958	−	21.9138i	−0.747035	−	1.26943i
$299$	15.5430	−	8.97373i	0.898872	−	0.518964i
$300$	16.4920	−	3.16655i	0.952164	−	0.182821i
$301$	−10.7749	−	6.68778i	−0.621056	−	0.385477i
$302$	−10.9993	+	19.4222i	−0.632939	+	1.11762i
$303$	−1.59789	−	9.13951i	−0.0917966	−	0.525051i
$304$	10.8321	+	17.4000i	0.621264	+	0.997958i
$305$	2.30359	+	1.32998i	0.131903	+	0.0761542i
$306$	−10.9806	−	9.11309i	−0.627721	−	0.520961i
$307$	12.3622			0.705549			0.352774	−	0.935708i	$-0.385238\pi$
$307$	12.3622			0.705549			0.352774	+	0.935708i	$0.385238\pi$
$308$	−3.85586	−	6.92057i	−0.219708	−	0.394336i
$309$	−14.4792	−	5.29377i	−0.823694	−	0.301152i
$310$	2.29503	−	0.0190640i	0.130349	−	0.00108276i
$311$	0.720819	−	1.24850i	0.0408739	−	0.0707957i	−0.844865	−	0.534980i	$-0.820319\pi$
$311$	0.720819	−	1.24850i	0.0408739	−	0.0707957i	0.885739	+	0.464184i	$0.153652\pi$
$312$	10.6396	+	12.0918i	0.602350	+	0.684561i
$313$	−20.8822	+	12.0564i	−1.18033	+	0.681466i	−0.956092	−	0.293067i	$-0.905324\pi$
$313$	−20.8822	+	12.0564i	−1.18033	+	0.681466i	−0.224242	+	0.974533i	$0.571991\pi$
$314$	3.53017	−	6.23345i	0.199219	−	0.351774i
$315$	−3.02912	−	0.643477i	−0.170672	−	0.0362558i
$316$	−0.492538	−	0.821284i	−0.0277074	−	0.0462008i
$317$	13.4686	+	23.3283i	0.756472	+	1.31025i	0.944639	+	0.328111i	$0.106412\pi$
$317$	13.4686	+	23.3283i	0.756472	+	1.31025i	−0.188167	+	0.982137i	$0.560255\pi$
$318$	−2.40566	+	0.441214i	−0.134903	+	0.0247420i
$319$	3.09764	−	5.36527i	0.173435	−	0.300398i
$320$	−2.62193	+	1.69332i	−0.146570	+	0.0946595i
$321$	−9.34067	+	25.5481i	−0.521345	+	1.42595i
$322$	−0.481637	+	20.4200i	−0.0268406	+	1.13796i
$323$	−17.2342			−0.958935
$324$	−16.9801	−	5.97302i	−0.943338	−	0.331834i
$325$	7.96898	−	13.8027i	0.442039	−	0.765635i
$326$	15.3046	−	9.00644i	0.847643	−	0.498820i
$327$	−5.22113	−	29.8634i	−0.288729	−	1.65145i
$328$	31.5574	−	0.786555i	1.74247	−	0.0434302i
$329$	−13.2785	−	0.423575i	−0.732066	−	0.0233524i
$330$	1.08972	−	0.927189i	0.0599869	−	0.0510401i
$331$	15.2782	−	8.82087i	0.839766	−	0.484839i	−0.0174189	−	0.999848i	$-0.505545\pi$
$331$	15.2782	−	8.82087i	0.839766	−	0.484839i	0.857185	+	0.515009i	$0.172212\pi$
$332$	0.579924	+	34.9048i	0.0318275	+	1.91565i
$333$	−8.77498	−	24.3281i	−0.480866	−	1.33317i
$334$	−10.5093	+	0.0872970i	−0.575043	+	0.00477668i
$335$	1.37615			0.0751868
$336$	−18.0522	+	3.18101i	−0.984827	+	0.173539i
$337$	11.0396			0.601365			0.300682	−	0.953724i	$-0.402786\pi$
$337$	11.0396			0.601365			0.300682	+	0.953724i	$0.402786\pi$
$338$	−3.09866	+	0.0257395i	−0.168545	+	0.00140005i
$339$	−0.0964636	+	0.0807047i	−0.00523918	+	0.00438328i
$340$	−0.0435978	−	2.62409i	−0.00236442	−	0.142311i
$341$	−5.39334	+	3.11385i	−0.292066	+	0.168624i
$342$	−20.3879	+	7.54574i	−1.10245	+	0.408027i
$343$	−18.4356	−	1.76905i	−0.995428	−	0.0955198i
$344$	−0.337805	−	13.5531i	−0.0182132	−	0.730734i
$345$	−3.63385	+	0.635319i	−0.195640	+	0.0342045i
$346$	−21.4549	+	12.6258i	−1.15342	+	0.678765i
$347$	10.8299	−	18.7579i	0.581377	−	1.00697i	−0.413940	−	0.910304i	$-0.635848\pi$
$347$	10.8299	−	18.7579i	0.581377	−	1.00697i	0.995316	−	0.0966701i	$-0.0308192\pi$
$348$	−9.37949	−	10.8399i	−0.502793	−	0.581079i
$349$	−6.46130			−0.345865			−0.172933	−	0.984934i	$-0.555324\pi$
$349$	−6.46130			−0.345865			−0.172933	+	0.984934i	$0.555324\pi$
$350$	8.69644	+	15.9181i	0.464844	+	0.850858i
$351$	−14.8315	+	8.47727i	−0.791649	+	0.452483i
$352$	3.92643	−	7.50407i	0.209280	−	0.399968i
$353$	14.9846	−	25.9541i	0.797549	−	1.38140i	−0.123659	−	0.992325i	$-0.539463\pi$
$353$	14.9846	−	25.9541i	0.797549	−	1.38140i	0.921208	−	0.389071i	$-0.127204\pi$
$354$	0.694101	+	3.78449i	0.0368910	+	0.201143i
$355$	2.79659	+	4.84383i	0.148428	+	0.257084i
$356$	5.24275	+	8.74203i	0.277865	+	0.463327i
$357$	5.75137	−	14.2997i	0.304395	−	0.756821i
$358$	−11.3148	+	19.9792i	−0.598005	+	1.05594i
$359$	9.44412	−	5.45257i	0.498442	−	0.287775i	−0.229628	−	0.973278i	$-0.573751\pi$
$359$	9.44412	−	5.45257i	0.498442	−	0.287775i	0.728070	+	0.685503i	$0.240418\pi$
$360$	−1.20050	−	3.08519i	−0.0632717	−	0.162604i
$361$	−3.62795	+	6.28380i	−0.190945	+	0.330726i
$362$	8.75848	−	0.0727537i	0.460336	−	0.00382385i
$363$	5.20915	−	14.2478i	0.273409	−	0.747814i
$364$	−8.92750	+	14.9314i	−0.467928	+	0.782619i
$365$	−1.24388			−0.0651075
$366$	−5.60401	+	15.7317i	−0.292926	+	0.822312i
$367$	−2.43552	−	1.40615i	−0.127133	−	0.0734002i	0.435085	−	0.900389i	$-0.356718\pi$
$367$	−2.43552	−	1.40615i	−0.127133	−	0.0734002i	−0.562218	+	0.826989i	$0.690052\pi$
$368$	−18.5374	+	11.5402i	−0.966330	+	0.601574i
$369$	−5.90961	+	32.9565i	−0.307642	+	1.71564i
$370$	2.34398	−	4.13891i	0.121858	−	0.215171i
$371$	−1.24726	−	2.32877i	−0.0647545	−	0.120904i
$372$	2.71708	+	14.1510i	0.140874	+	0.733695i
$373$	−26.9266	+	15.5461i	−1.39421	+	0.804947i	−0.993778	−	0.111380i	$-0.964473\pi$
$373$	−26.9266	+	15.5461i	−1.39421	+	0.804947i	−0.400431	+	0.916327i	$0.631140\pi$
$374$	3.61177	+	6.13747i	0.186760	+	0.317361i
$375$	−5.10401	+	4.27019i	−0.263570	+	0.220511i
$376$	−7.40552	−	12.1190i	−0.381911	−	0.624988i
$377$	−13.6045			−0.700665
$378$	0.542910	−	19.4346i	0.0279243	−	0.999610i
$379$			17.6950i			0.908931i	0.890764	+	0.454465i	$0.150170\pi$
$379$			17.6950i			0.908931i	−0.890764	+	0.454465i	$0.849830\pi$
$380$	−3.49535	−	1.94135i	−0.179308	−	0.0995891i
$381$	9.79800	+	11.7112i	0.501967	+	0.599984i
$382$	−10.2568	+	6.03594i	−0.524786	+	0.308825i
$383$	17.4953	+	30.3028i	0.893968	+	1.54840i	0.835076	+	0.550134i	$0.185423\pi$
$383$	17.4953	+	30.3028i	0.893968	+	1.54840i	0.0588917	+	0.998264i	$0.481243\pi$
$384$	−13.4264	−	14.2735i	−0.685164	−	0.728389i
$385$	1.31306	+	0.814994i	0.0669200	+	0.0415359i
$386$	9.16202	−	16.1780i	0.466335	−	0.823436i
$387$	14.1539	+	2.53802i	0.719485	+	0.129015i
$388$	−0.299044	−	17.9990i	−0.0151816	−	0.913761i
$389$	−10.4422	+	18.0864i	−0.529439	+	0.917015i	0.469971	+	0.882682i	$0.344264\pi$
$389$	−10.4422	+	18.0864i	−0.529439	+	0.917015i	−0.999410	+	0.0343338i	$0.989069\pi$
$390$	−2.95975	−	1.05433i	−0.149873	−	0.0533881i
$391$		−	18.3608i		−	0.928543i
$392$	−9.22592	−	17.5181i	−0.465979	−	0.884796i
$393$	8.19322	+	2.99554i	0.413293	+	0.151105i
$394$	24.9061	−	0.206886i	1.25475	−	0.0104228i
$395$	0.161786	+	0.0934070i	0.00814032	+	0.00469982i
$396$	6.95991	+	5.67923i	0.349749	+	0.285392i
$397$	−2.44443	−	4.23387i	−0.122682	−	0.212492i	0.798142	−	0.602469i	$-0.205816\pi$
$397$	−2.44443	−	4.23387i	−0.122682	−	0.212492i	−0.920825	+	0.389977i	$0.872483\pi$
$398$	24.5381	+	13.8966i	1.22998	+	0.696574i
$399$	−14.4856	−	18.4808i	−0.725186	−	0.925200i
$400$	−9.13235	+	17.1060i	−0.456617	+	0.855301i
$401$	6.62355	−	3.82411i	0.330764	−	0.190967i	−0.325416	−	0.945571i	$-0.605504\pi$
$401$	6.62355	−	3.82411i	0.330764	−	0.190967i	0.656180	+	0.754604i	$0.272171\pi$
$402$	1.55862	+	8.49815i	0.0777368	+	0.423849i
$403$	11.8434	+	6.83782i	0.589964	+	0.340616i
$404$	9.36585	+	5.20187i	0.465968	+	0.258803i
$405$	3.46148	−	0.589691i	0.172002	−	0.0293020i
$406$	8.05554	−	13.2224i	0.399790	−	0.656218i
$407$			12.9067i			0.639762i
$408$	16.1552	−	3.24126i	0.799803	−	0.160467i
$409$	−6.66584	−	3.84852i	−0.329604	−	0.190297i	0.326061	−	0.945349i	$-0.394279\pi$
$409$	−6.66584	−	3.84852i	−0.329604	−	0.190297i	−0.655666	+	0.755051i	$0.727612\pi$
$410$	−5.30720	+	3.12318i	−0.262104	+	0.154243i
$411$	2.18648	+	12.5060i	0.107851	+	0.616877i
$412$	15.2666	−	9.15566i	0.752133	−	0.451067i
$413$	−3.66354	+	1.96214i	−0.180271	+	0.0965507i
$414$	−8.03900	−	21.7207i	−0.395095	−	1.06751i
$415$	−3.40499	−	5.89762i	−0.167145	−	0.289503i
$416$	−18.5819	+	0.772193i	−0.911052	+	0.0378599i
$417$	17.5045	+	20.9225i	0.857197	+	1.02458i
$418$	10.8488	−	0.0901174i	0.530634	−	0.00440779i
$419$			4.38235i			0.214092i	0.994254	+	0.107046i	$0.0341392\pi$
$419$			4.38235i			0.214092i	−0.994254	+	0.107046i	$0.965861\pi$
$420$	2.77726	−	2.25234i	0.135516	−	0.109903i
$421$			11.9400i			0.581921i	0.956735	+	0.290961i	$0.0939749\pi$
$421$			11.9400i			0.581921i	−0.956735	+	0.290961i	$0.906025\pi$
$422$	−0.170518	−	20.5278i	−0.00830067	−	0.999280i
$423$	14.1704	−	5.11117i	0.688990	−	0.248514i
$424$	1.35069	−	2.48021i	0.0655955	−	0.120450i
$425$	−8.15249	−	14.1205i	−0.395454	−	0.684946i
$426$	−26.7449	+	22.7560i	−1.29579	+	1.10253i
$427$	−18.0290	−	0.575113i	−0.872484	−	0.0278317i
$428$	−16.1548	−	26.9374i	−0.780873	−	1.30207i
$429$	8.39811	−	1.46827i	0.405464	−	0.0708888i
$430$	1.34132	+	2.27930i	0.0646843	+	0.109918i
$431$	−0.588922	−	0.340014i	−0.0283674	−	0.0163779i	0.485749	−	0.874098i	$-0.338547\pi$
$431$	−0.588922	−	0.340014i	−0.0283674	−	0.0163779i	−0.514117	+	0.857720i	$0.671880\pi$
$432$	17.6924	−	10.9077i	0.851226	−	0.524799i
$433$		−	0.238499i		−	0.0114615i	−0.999984	−	0.00573077i	$-0.998176\pi$
$433$		−	0.238499i		−	0.0114615i	0.999984	−	0.00573077i	$-0.00182417\pi$
$434$	−13.6586	+	7.46202i	−0.655633	+	0.358188i
$435$	2.62627	+	0.960196i	0.125920	+	0.0460379i
$436$	30.6030	+	16.9971i	1.46562	+	0.814015i
$437$	−24.2247	−	13.9861i	−1.15882	−	0.669046i
$438$	−1.40881	−	7.68136i	−0.0673157	−	0.367030i
$439$	3.29894	−	1.90465i	0.157450	−	0.0909038i	−0.419205	−	0.907892i	$-0.637691\pi$
$439$	3.29894	−	1.90465i	0.157450	−	0.0909038i	0.576655	+	0.816988i	$0.304358\pi$
$440$	0.0411659	+	1.65162i	0.00196251	+	0.0787380i
$441$	20.1682	−	5.85172i	0.960392	−	0.278653i
$442$	7.70624	−	13.6074i	0.366549	−	0.647238i
$443$	−3.02001	−	5.23080i	−0.143485	−	0.248523i	0.785322	−	0.619088i	$-0.212497\pi$
$443$	−3.02001	−	5.23080i	−0.143485	−	0.248523i	−0.928807	+	0.370565i	$0.879164\pi$
$444$	28.2139	+	9.78712i	1.33897	+	0.464476i
$445$	−1.72210	−	0.994257i	−0.0816355	−	0.0471323i
$446$	−0.0326445	−	3.92992i	−0.00154576	−	0.186087i
$447$	−10.6933	+	29.2477i	−0.505776	+	1.38337i
$448$	10.2523	−	18.5173i	0.484375	−	0.874861i
$449$			28.1482i			1.32839i	0.747558	+	0.664197i	$0.231226\pi$
$449$			28.1482i			1.32839i	−0.747558	+	0.664197i	$0.768774\pi$
$450$	−15.8268	−	13.1351i	−0.746084	−	0.619192i
$451$	8.35470	−	14.4708i	0.393408	−	0.681402i
$452$	−0.00241256	−	0.145208i	−0.000113477	−	0.00683003i
$453$	26.9285	−	4.70801i	1.26521	−	0.221201i
$454$	19.9555	+	11.3013i	0.936557	+	0.530398i
$455$	0.108201	−	3.39194i	0.00507254	−	0.159017i
$456$	8.02964	−	23.7837i	0.376022	−	1.11378i
$457$	−6.23304	−	10.7959i	−0.291569	−	0.505013i	0.682612	−	0.730781i	$-0.260844\pi$
$457$	−6.23304	−	10.7959i	−0.291569	−	0.505013i	−0.974181	+	0.225768i	$0.927511\pi$
$458$	−14.7970	−	25.1444i	−0.691416	−	1.17492i
$459$	−0.0759502	+	17.4765i	−0.00354505	+	0.815734i
$460$	2.06825	−	3.72384i	0.0964327	−	0.173625i
$461$		−	31.6209i		−	1.47273i	−0.676583	−	0.736367i	$-0.736540\pi$
$461$		−	31.6209i		−	1.47273i	0.676583	−	0.736367i	$-0.263460\pi$
$462$	−3.54569	+	9.03167i	−0.164960	+	0.420191i
$463$	23.5095			1.09258			0.546290	−	0.837596i	$-0.316040\pi$
$463$	23.5095			1.09258			0.546290	+	0.837596i	$0.316040\pi$
$464$	16.5429	−	0.549855i	0.767986	−	0.0255264i
$465$	−1.80371	−	2.15591i	−0.0836449	−	0.0999779i
$466$	−2.53980	+	1.49462i	−0.117654	+	0.0692368i
$467$	12.7642	−	7.36942i	0.590657	−	0.341016i	−0.174700	−	0.984622i	$-0.555896\pi$
$467$	12.7642	−	7.36942i	0.590657	−	0.341016i	0.765357	+	0.643606i	$0.222562\pi$
$468$	3.15864	−	19.4715i	0.146008	−	0.900073i
$469$	−8.22655	+	4.40603i	−0.379867	+	0.203452i
$470$	2.41079	+	1.36530i	0.111201	+	0.0629765i
$471$	−8.64256	+	1.51101i	−0.398228	+	0.0696237i
$472$	−3.90177	−	2.12486i	−0.179594	−	0.0978047i
$473$	−6.21481	−	3.58812i	−0.285757	−	0.164982i
$474$	−0.393581	+	1.10487i	−0.0180778	+	0.0507485i
$475$	−24.8403			−1.13975
$476$	8.66222	+	15.5471i	0.397032	+	0.712601i
$477$	2.28907	+	1.93208i	0.104809	+	0.0884641i
$478$	0.0100056	+	1.20453i	0.000457647	+	0.0550940i
$479$	−17.3034	+	29.9703i	−0.790611	+	1.36938i	0.134979	+	0.990848i	$0.456903\pi$
$479$	−17.3034	+	29.9703i	−0.790611	+	1.36938i	−0.925589	+	0.378529i	$0.876430\pi$
$480$	3.64164	+	1.16243i	0.166217	+	0.0530575i
$481$	24.5452	−	14.1712i	1.11916	−	0.646150i
$482$	18.5315	+	10.4949i	0.844087	+	0.478030i
$483$	19.6889	−	15.4325i	0.895877	−	0.702203i
$484$	9.00930	+	15.0226i	0.409514	+	0.682844i
$485$	1.75582	+	3.04117i	0.0797276	+	0.138092i
$486$	7.56200	+	20.7079i	0.343019	+	0.939328i
$487$	−12.0284	+	20.8338i	−0.545058	+	0.944068i	0.453545	+	0.891233i	$0.350159\pi$
$487$	−12.0284	+	20.8338i	−0.545058	+	0.944068i	−0.998603	+	0.0528351i	$0.983174\pi$
$488$	−10.0549	−	16.4547i	−0.455165	−	0.744867i
$489$	−20.4266	−	7.46820i	−0.923723	−	0.337724i
$490$	3.23262	+	2.11362i	0.146035	+	0.0954834i
$491$	−15.3708			−0.693675			−0.346837	−	0.937925i	$-0.612744\pi$
$491$	−15.3708			−0.693675			−0.346837	+	0.937925i	$0.612744\pi$
$492$	−25.2976	−	29.2364i	−1.14050	−	1.31808i
$493$	−6.95887	+	12.0531i	−0.313412	+	0.542845i
$494$	−12.0831	−	20.5327i	−0.543643	−	0.923809i
$495$	−1.72484	−	0.309291i	−0.0775259	−	0.0139016i
$496$	−14.6779	−	7.83605i	−0.659057	−	0.351849i
$497$	−32.2265	−	20.0024i	−1.44556	−	0.897229i
$498$	32.5633	−	27.7066i	1.45920	−	1.24156i
$499$	−22.8684	+	13.2031i	−1.02373	+	0.591051i	−0.915182	−	0.403040i	$-0.867953\pi$
$499$	−22.8684	+	13.2031i	−1.02373	+	0.591051i	−0.108548	+	0.994091i	$0.534620\pi$
$500$	−0.127651	−	7.68315i	−0.00570874	−	0.343601i
$501$	8.25944	+	9.87223i	0.369005	+	0.441059i
$502$	−0.138640	−	16.6902i	−0.00618781	−	0.744922i
$503$	−28.3616			−1.26458			−0.632291	−	0.774731i	$-0.717885\pi$
$503$	−28.3616			−1.26458			−0.632291	+	0.774731i	$0.717885\pi$
$504$	17.0544	+	14.5995i	0.759665	+	0.650314i
$505$	−2.08993			−0.0930006
$506$	0.0960083	+	11.5580i	0.00426809	+	0.513816i
$507$	2.43530	+	2.91083i	0.108155	+	0.129274i
$508$	−17.6291	+	0.292898i	−0.782165	+	0.0129952i
$509$	−18.3731	+	10.6077i	−0.814373	+	0.470179i	−0.848472	−	0.529240i	$-0.822477\pi$
$509$	−18.3731	+	10.6077i	−0.814373	+	0.470179i	0.0340991	+	0.999418i	$0.489144\pi$
$510$	−2.44805	+	2.08294i	−0.108402	+	0.0922340i
$511$	7.43586	−	3.98255i	0.328943	−	0.176178i
$512$	22.5642	−	1.69001i	0.997207	−	0.0746885i
$513$	23.0002	+	13.4128i	1.01548	+	0.592188i
$514$	−12.7227	−	21.6196i	−0.561174	−	0.953600i
$515$	−1.73632	+	3.00739i	−0.0765113	+	0.132522i
$516$	−12.5563	+	10.8646i	−0.552759	+	0.478289i
$517$	−7.51778			−0.330631
$518$	−0.760593	+	32.2470i	−0.0334185	+	1.41685i
$519$	28.6352	+	10.4694i	1.25695	+	0.459554i
$520$	3.09575	−	1.89172i	0.135758	−	0.0829572i
$521$	−5.91179	+	10.2395i	−0.259000	+	0.448601i	−0.965974	−	0.258638i	$-0.916726\pi$
$521$	−5.91179	+	10.2395i	−0.259000	+	0.448601i	0.706974	+	0.707239i	$0.250060\pi$
$522$	−2.95502	+	17.3056i	−0.129338	+	0.757447i
$523$	−3.37960	−	5.85364i	−0.147780	−	0.255962i	0.782627	−	0.622491i	$-0.213879\pi$
$523$	−3.37960	−	5.85364i	−0.147780	−	0.255962i	−0.930407	+	0.366529i	$0.880546\pi$
$524$	−8.63878	+	5.18083i	−0.377387	+	0.226326i
$525$	8.28967	−	20.6107i	0.361791	−	0.899526i
$526$	8.92092	+	5.05217i	0.388971	+	0.220285i
$527$	12.1162	−	6.99528i	0.527789	−	0.304719i
$528$	−10.1527	+	2.12484i	−0.441839	+	0.0924716i
$529$	3.40036	−	5.88960i	0.147842	−	0.256070i
$530$	0.00457614	+	0.550901i	0.000198775	+	0.0239296i
$531$	3.03948	−	3.60108i	0.131902	−	0.156273i
$532$	27.1108	+	0.414166i	1.17540	+	0.0179564i
$533$	−36.6928			−1.58934
$534$	4.18942	−	11.7607i	0.181294	−	0.508933i
$535$	5.30643	+	3.06367i	0.229417	+	0.132454i
$536$	−8.76151	−	4.77142i	−0.378440	−	0.206094i
$537$	27.7008	−	4.84304i	1.19538	−	0.208993i
$538$	4.20340	+	2.38050i	0.181221	+	0.102631i
$539$	−10.4588	−	0.667940i	−0.450494	−	0.0287702i
$540$	−1.98405	+	3.53595i	−0.0853799	+	0.152163i
$541$	15.3128	−	8.84087i	0.658351	−	0.380099i	−0.133298	−	0.991076i	$-0.542557\pi$
$541$	15.3128	−	8.84087i	0.658351	−	0.380099i	0.791648	+	0.610977i	$0.209223\pi$
$542$	5.58715	−	3.28792i	0.239989	−	0.141228i
$543$	−6.88345	−	8.22755i	−0.295397	−	0.353078i
$544$	−8.82076	+	16.8580i	−0.378187	+	0.722779i
$545$	−6.82885			−0.292516
$546$	21.0689	−	3.17353i	0.901667	−	0.135815i
$547$			1.49834i			0.0640644i	0.999487	+	0.0320322i	$0.0101979\pi$
$547$			1.49834i			0.0640644i	−0.999487	+	0.0320322i	$0.989802\pi$
$548$	−12.8157	−	7.11797i	−0.547461	−	0.304065i
$549$	19.2400	−	6.93974i	0.821145	−	0.296181i
$550$	5.20579	+	8.84617i	0.221976	+	0.377202i
$551$	10.6017	+	18.3627i	0.451647	+	0.782276i
$552$	25.3385	+	8.55453i	1.07848	+	0.364105i
$553$	−1.26621	−	0.0403914i	−0.0538448	−	0.00171762i
$554$	15.1957	+	8.60573i	0.645602	+	0.365622i
$555$	−5.73852	+	1.00329i	−0.243586	+	0.0425871i
$556$	−31.4950	+	0.523272i	−1.33569	+	0.0221917i
$557$	1.46808	−	2.54278i	0.0622044	−	0.107741i	−0.833246	−	0.552902i	$-0.813520\pi$
$557$	1.46808	−	2.54278i	0.0622044	−	0.107741i	0.895450	+	0.445161i	$0.146854\pi$
$558$	11.2706	−	13.5803i	0.477122	−	0.574899i
$559$			15.7586i			0.666518i
$560$	0.00552159	+	4.12895i	0.000233330	+	0.174480i
$561$	2.99491	−	8.19150i	0.126445	−	0.345845i
$562$	0.0929850	+	11.1940i	0.00392233	+	0.472192i
$563$	−14.3950	−	8.31096i	−0.606677	−	0.350265i	0.164987	−	0.986296i	$-0.447242\pi$
$563$	−14.3950	−	8.31096i	−0.606677	−	0.350265i	−0.771664	+	0.636031i	$0.780575\pi$
$564$	−5.70071	+	16.4338i	−0.240043	+	0.691987i
$565$	0.0141652	+	0.0245348i	0.000595934	+	0.00103219i
$566$	15.8271	−	27.9470i	0.665264	−	1.17470i
$567$	−18.8046	+	14.6078i	−0.789717	+	0.613471i
$568$	−1.01033	−	40.5357i	−0.0423927	−	1.70084i
$569$	19.2204	−	11.0969i	0.805763	−	0.465207i	−0.0397194	−	0.999211i	$-0.512646\pi$
$569$	19.2204	−	11.0969i	0.805763	−	0.465207i	0.845482	+	0.534003i	$0.179313\pi$
$570$	0.883387	+	4.81655i	0.0370010	+	0.201743i
$571$	−5.22532	−	3.01684i	−0.218673	−	0.126251i	0.386663	−	0.922221i	$-0.373628\pi$
$571$	−5.22532	−	3.01684i	−0.218673	−	0.126251i	−0.605336	+	0.795970i	$0.706961\pi$
$572$	−4.77989	+	8.60608i	−0.199857	+	0.359838i
$573$	13.6895	+	5.00504i	0.571887	+	0.209089i
$574$	21.7267	−	35.6624i	0.906856	−	1.48852i
$575$		−	26.4641i		−	1.10363i
$576$	−3.05389	+	23.8049i	−0.127245	+	0.991871i
$577$	−17.4549	−	10.0776i	−0.726659	−	0.419537i	0.0905396	−	0.995893i	$-0.471141\pi$
$577$	−17.4549	−	10.0776i	−0.726659	−	0.419537i	−0.817199	+	0.576356i	$0.804474\pi$
$578$	4.07947	+	6.93223i	0.169684	+	0.288343i
$579$	−22.4304	+	3.92160i	−0.932177	+	0.162976i
$580$	−2.76909	+	1.66067i	−0.114980	+	0.0689557i
$581$	39.2375	+	24.3539i	1.62784	+	1.01037i
$582$	−16.7916	+	14.2872i	−0.696033	+	0.592222i
$583$	−0.747449	−	1.29462i	−0.0309562	−	0.0536177i
$584$	7.91941	+	4.31282i	0.327707	+	0.178466i
$585$	1.30563	+	3.61979i	0.0539812	+	0.149660i
$586$	0.150650	+	18.1361i	0.00622329	+	0.749194i
$587$			0.369829i			0.0152645i	0.999971	+	0.00763224i	$0.00242944\pi$
$587$			0.369829i			0.0152645i	−0.999971	+	0.00763224i	$0.997571\pi$
$588$	−9.39102	+	22.3564i	−0.387279	+	0.921962i
$589$		−	21.3143i		−	0.878241i
$590$	0.866656	−	0.00719901i	0.0356797	−	0.000296379i
$591$	−19.5742	−	23.3963i	−0.805174	−	0.962396i
$592$	−29.2740	+	18.2241i	−1.20315	+	0.749005i
$593$	4.89233	+	8.47376i	0.200904	+	0.347976i	0.948820	−	0.315818i	$-0.102279\pi$
$593$	4.89233	+	8.47376i	0.200904	+	0.347976i	−0.747916	+	0.663793i	$0.768945\pi$
$594$	−0.0435743	−	11.0018i	−0.00178788	−	0.451408i
$595$	−2.94981	−	1.83089i	−0.120930	−	0.0750592i
$596$	−18.4942	−	30.8382i	−0.757553	−	1.26318i
$597$	−5.94813	−	34.0216i	−0.243441	−	1.39241i
$598$	21.8749	−	12.8729i	0.894531	−	0.526413i
$599$	31.2524	+	18.0436i	1.27694	+	0.737240i	0.976284	−	0.216494i	$-0.0694621\pi$
$599$	31.2524	+	18.0436i	1.27694	+	0.737240i	0.300653	+	0.953734i	$0.402795\pi$
$600$	23.2852	−	4.67176i	0.950613	−	0.190724i
$601$			9.75944i			0.398096i	0.979990	+	0.199048i	$0.0637849\pi$
$601$			9.75944i			0.398096i	−0.979990	+	0.199048i	$0.936215\pi$
$602$	−15.3161	−	9.33106i	−0.624236	−	0.380305i
$603$	6.82523	−	8.08629i	0.277945	−	0.329299i
$604$	−15.3267	+	27.5954i	−0.623634	+	1.12284i
$605$	−2.95932	−	1.70856i	−0.120313	−	0.0694629i
$606$	−2.36705	−	12.9060i	−0.0961547	−	0.524271i
$607$	−7.33740	+	4.23625i	−0.297816	+	0.171944i	−0.641461	−	0.767155i	$-0.721672\pi$
$607$	−7.33740	+	4.23625i	−0.297816	+	0.171944i	0.343645	+	0.939099i	$0.388338\pi$
$608$	15.5228	+	24.4792i	0.629532	+	0.992764i
$609$	−18.7741	+	2.66857i	−0.760763	+	0.108136i
$610$	3.27328	+	1.85375i	0.132531	+	0.0750560i
$611$	8.25429	+	14.2968i	0.333933	+	0.578388i
$612$	−15.6355	−	12.7584i	−0.632027	−	0.515729i
$613$	10.1968	+	5.88712i	0.411844	+	0.237779i	0.691582	−	0.722298i	$-0.256914\pi$
$613$	10.1968	+	5.88712i	0.411844	+	0.237779i	−0.279737	+	0.960077i	$0.590247\pi$
$614$	17.4822	−	0.145219i	0.705525	−	0.00586055i
$615$	7.08336	+	2.58976i	0.285629	+	0.104429i
$616$	−5.53412	−	9.74153i	−0.222976	−	0.392498i
$617$			17.5244i			0.705506i	0.935717	+	0.352753i	$0.114754\pi$
$617$			17.5244i			0.705506i	−0.935717	+	0.352753i	$0.885246\pi$
$618$	−20.5382	−	7.31618i	−0.826167	−	0.294300i
$619$	−12.8081	+	22.1843i	−0.514801	+	0.891661i	0.485052	+	0.874485i	$0.338801\pi$
$619$	−12.8081	+	22.1843i	−0.514801	+	0.891661i	−0.999852	+	0.0171755i	$0.994533\pi$
$620$	3.24533	−	0.0539194i	0.130336	−	0.00216545i
$621$	−14.2895	+	24.5037i	−0.573419	+	0.983298i
$622$	1.00469	−	1.77405i	0.0402844	−	0.0711328i
$623$	13.4780	+	0.429940i	0.539985	+	0.0172252i
$624$	15.1882	+	16.9748i	0.608015	+	0.679534i
$625$	−11.3700	−	19.6933i	−0.454798	−	0.787734i
$626$	−29.3893	+	17.2950i	−1.17463	+	0.691247i
$627$	−8.52629	−	10.1912i	−0.340507	−	0.406997i
$628$	4.91902	−	8.85659i	0.196290	−	0.353416i
$629$		−	28.9950i		−	1.15611i
$630$	−4.29124	−	0.874400i	−0.170967	−	0.0348369i
$631$	−7.24555			−0.288441			−0.144220	−	0.989546i	$-0.546067\pi$
$631$	−7.24555			−0.288441			−0.144220	+	0.989546i	$0.546067\pi$
$632$	−0.706178	−	1.15564i	−0.0280902	−	0.0459691i
$633$	−19.2835	+	16.1332i	−0.766449	+	0.641237i
$634$	19.3209	+	32.8319i	0.767330	+	1.30392i
$635$	2.97867	−	1.71973i	0.118205	−	0.0682456i
$636$	−3.39681	+	0.652208i	−0.134692	+	0.0258617i
$637$	10.2132	+	20.6234i	0.404663	+	0.817127i
$638$	4.31755	−	7.62377i	0.170933	−	0.301828i
$639$	42.3328	+	7.59093i	1.67466	+	0.300293i
$640$	−3.68795	+	2.42543i	−0.145779	+	0.0958737i
$641$	−11.9401	−	6.89362i	−0.471606	−	0.272282i	0.245306	−	0.969446i	$-0.421112\pi$
$641$	−11.9401	−	6.89362i	−0.471606	−	0.272282i	−0.716912	+	0.697164i	$0.754445\pi$
$642$	−12.9091	+	36.2389i	−0.509483	+	1.43024i
$643$	−20.7470			−0.818184			−0.409092	−	0.912493i	$-0.634154\pi$
$643$	−20.7470			−0.818184			−0.409092	+	0.912493i	$0.634154\pi$
$644$	−0.441240	+	28.8830i	−0.0173873	+	1.13815i
$645$	1.11223	−	3.04212i	0.0437942	−	0.119783i
$646$	−24.3720	+	0.202449i	−0.958902	+	0.00796527i
$647$	16.1242	−	27.9279i	0.633907	−	1.09796i	−0.352838	−	0.935684i	$-0.614783\pi$
$647$	16.1242	−	27.9279i	0.633907	−	1.09796i	0.986746	−	0.162275i	$-0.0518832\pi$
$648$	−24.0828	−	8.24737i	−0.946061	−	0.323987i
$649$	−2.03665	+	1.17586i	−0.0799454	+	0.0461565i
$650$	11.1073	−	19.6129i	0.435665	−	0.769280i
$651$	17.6851	+	7.11299i	0.693135	+	0.278780i
$652$	21.5374	−	12.9164i	0.843471	−	0.505844i
$653$	9.95455	+	17.2418i	0.389552	+	0.674723i	0.992389	−	0.123141i	$-0.0392966\pi$
$653$	9.95455	+	17.2418i	0.389552	+	0.674723i	−0.602838	+	0.797864i	$0.705963\pi$
$654$	−7.73434	−	42.1704i	−0.302437	−	1.64899i
$655$	0.982514	−	1.70176i	0.0383900	−	0.0664934i
$656$	44.6182	−	1.48302i	1.74205	−	0.0579023i
$657$	−6.16923	+	7.30909i	−0.240684	+	0.285155i
$658$	−18.7829	−	0.443023i	−0.732235	−	0.0172708i
$659$	11.4275			0.445153			0.222576	−	0.974915i	$-0.428553\pi$
$659$	11.4275			0.445153			0.222576	+	0.974915i	$0.428553\pi$
$660$	1.53015	−	1.32400i	0.0595609	−	0.0515366i
$661$	2.31268	−	4.00568i	0.0899529	−	0.155803i	−0.817538	−	0.575875i	$-0.804662\pi$
$661$	2.31268	−	4.00568i	0.0899529	−	0.155803i	0.907491	+	0.420071i	$0.137995\pi$
$662$	21.5023	−	12.6536i	0.835709	−	0.491798i
$663$	−18.8664	+	3.29848i	−0.732710	+	0.128102i
$664$	1.23013	+	49.3543i	0.0477385	+	1.91532i
$665$	−4.66261	+	2.49723i	−0.180808	+	0.0968385i
$666$	−12.6951	−	34.3009i	−0.491923	−	1.32913i
$667$	−19.5630	+	11.2947i	−0.757483	+	0.437333i
$668$	−14.8608	+	0.246905i	−0.574983	+	0.00955303i
$669$	−3.69169	+	3.08859i	−0.142729	+	0.119412i
$670$	1.94610	−	0.0161655i	0.0751842	−	0.000624529i
$671$	−10.2073			−0.394050
$672$	−25.4914	+	4.71054i	−0.983352	+	0.181713i
$673$	19.2606			0.742441			0.371220	−	0.928545i	$-0.378939\pi$
$673$	19.2606			0.742441			0.371220	+	0.928545i	$0.378939\pi$
$674$	15.6118	−	0.129682i	0.601344	−	0.00499516i
$675$	−0.109470	+	25.1896i	−0.00421350	+	0.969548i
$676$	−4.38172	+	0.0727998i	−0.168528	+	0.00279999i
$677$	36.2236	−	20.9137i	1.39219	−	0.803780i	0.398630	−	0.917112i	$-0.369486\pi$
$677$	36.2236	−	20.9137i	1.39219	−	0.803780i	0.993557	+	0.113332i	$0.0361524\pi$
$678$	−0.135467	+	0.115263i	−0.00520259	+	0.00442665i
$679$	−20.2332	−	12.5583i	−0.776478	−	0.481945i
$680$	−0.0924795	−	3.71038i	−0.00354643	−	0.142287i
$681$	−4.83728	−	27.6679i	−0.185365	−	1.06024i
$682$	−7.59049	+	4.46685i	−0.290655	+	0.171044i
$683$	−6.73357	+	11.6629i	−0.257653	+	0.446268i	−0.965613	−	0.259985i	$-0.916282\pi$
$683$	−6.73357	+	11.6629i	−0.257653	+	0.446268i	0.707960	+	0.706253i	$0.249616\pi$
$684$	−28.7433	+	10.9104i	−1.09903	+	0.417170i
$685$	2.85975			0.109265
$686$	−26.0917	−	2.28517i	−0.996187	−	0.0872481i
$687$	−12.2697	+	33.5595i	−0.468120	+	1.28037i
$688$	−0.636919	−	19.1623i	−0.0242823	−	0.730557i
$689$	−1.64135	+	2.84291i	−0.0625305	+	0.108306i
$690$	−5.13140	+	0.941133i	−0.195349	+	0.0358283i
$691$	−15.2232	−	26.3674i	−0.579118	−	1.00306i	−0.995581	−	0.0939090i	$-0.970064\pi$
$691$	−15.2232	−	26.3674i	−0.579118	−	1.00306i	0.416463	−	0.909153i	$-0.363270\pi$
$692$	−30.1925	+	18.1069i	−1.14774	+	0.688323i
$693$	11.3013	−	3.67353i	0.429301	−	0.139546i
$694$	15.0948	−	26.6539i	0.572993	−	1.01177i
$695$	5.32149	−	3.07236i	0.201856	−	0.116541i
$696$	−13.3915	−	15.2192i	−0.507603	−	0.576882i
$697$	−18.7689	+	32.5087i	−0.710923	+	1.23135i
$698$	−9.13734	+	0.0759007i	−0.345853	+	0.00287288i
$699$	3.38979	+	1.23935i	0.128214	+	0.0468764i
$700$	12.4852	+	22.4087i	0.471896	+	0.846968i
$701$	37.2839			1.40819			0.704096	−	0.710105i	$-0.251353\pi$
$701$	37.2839			1.40819			0.704096	+	0.710105i	$0.251353\pi$
$702$	−20.8747	+	12.1625i	−0.787863	+	0.459043i
$703$	−38.2552	−	22.0866i	−1.44282	−	0.833013i
$704$	5.46447	−	10.6581i	0.205950	−	0.401693i
$705$	−0.584385	−	3.34252i	−0.0220092	−	0.125886i
$706$	20.8858	−	36.8793i	0.786047	−	1.38797i
$707$	12.4935	−	6.69137i	0.469867	−	0.251655i
$708$	1.02603	+	5.34374i	0.0385605	+	0.200830i
$709$	39.5076	−	22.8097i	1.48374	−	0.856637i	0.483910	−	0.875118i	$-0.339216\pi$
$709$	39.5076	−	22.8097i	1.48374	−	0.856637i	0.999829	+	0.0184810i	$0.00588302\pi$
$710$	4.01174	+	6.81713i	0.150558	+	0.255842i
$711$	1.35127	−	0.487392i	0.0506765	−	0.0182786i
$712$	7.51680	+	12.3011i	0.281704	+	0.461003i
$713$	22.7076			0.850406
$714$	7.96541	−	20.2897i	0.298098	−	0.759323i
$715$		−	1.92039i		−	0.0718186i
$716$	−15.7663	+	28.3868i	−0.589214	+	1.06087i
$717$	1.13151	−	0.946663i	0.0422572	−	0.0353538i
$718$	13.2915	−	7.82177i	0.496034	−	0.291906i
$719$	−8.37315	−	14.5027i	−0.312266	−	0.540860i	0.666587	−	0.745428i	$-0.267755\pi$
$719$	−8.37315	−	14.5027i	−0.312266	−	0.540860i	−0.978853	+	0.204567i	$0.934421\pi$
$720$	−1.73394	−	4.34887i	−0.0646201	−	0.162073i
$721$	0.750825	−	23.5373i	0.0279622	−	0.876575i
$722$	−5.05671	+	8.92895i	−0.188191	+	0.332301i
$723$	−4.49211	−	25.6936i	−0.167063	−	0.955555i
$724$	12.3851	−	0.205771i	0.460288	−	0.00764743i
$725$	−10.0301	+	17.3726i	−0.372508	+	0.645204i
$726$	7.19923	−	20.2099i	0.267188	−	0.750059i
$727$			14.7144i			0.545726i	0.962053	+	0.272863i	$0.0879705\pi$
$727$			14.7144i			0.545726i	−0.962053	+	0.272863i	$0.912029\pi$
$728$	−12.4496	+	21.2204i	−0.461411	+	0.786479i
$729$	13.7027	−	23.2645i	0.507508	−	0.861647i
$730$	−1.75905	+	0.0146118i	−0.0651053	+	0.000540807i
$731$	13.9616	+	8.06075i	0.516389	+	0.298137i
$732$	−7.74020	+	22.3131i	−0.286086	+	0.824716i
$733$	17.1186	+	29.6503i	0.632290	+	1.09516i	0.987082	+	0.160213i	$0.0512181\pi$
$733$	17.1186	+	29.6503i	0.632290	+	1.09516i	−0.354793	+	0.934945i	$0.615449\pi$
$734$	−3.46074	−	1.95991i	−0.127738	−	0.0723417i
$735$	−0.516028	−	4.70208i	−0.0190340	−	0.173439i
$736$	−26.0794	+	16.5375i	−0.961299	+	0.609580i
$737$	−4.57334	+	2.64042i	−0.168461	+	0.0972610i
$738$	−7.97003	+	46.6753i	−0.293381	+	1.71814i
$739$	−1.92964	−	1.11408i	−0.0709829	−	0.0409820i	0.464089	−	0.885789i	$-0.346382\pi$
$739$	−1.92964	−	1.11408i	−0.0709829	−	0.0409820i	−0.535071	+	0.844807i	$0.679715\pi$
$740$	3.26615	−	5.88063i	0.120066	−	0.216176i
$741$	−10.0194	+	27.4044i	−0.368070	+	1.00673i
$742$	−1.79119	−	3.27861i	−0.0657565	−	0.120362i
$743$		−	14.7964i		−	0.542829i	−0.962463	−	0.271414i	$-0.912509\pi$
$743$		−	14.7964i		−	0.542829i	0.962463	−	0.271414i	$-0.0874914\pi$
$744$	4.00862	+	19.9799i	0.146963	+	0.732500i
$745$	6.07486	+	3.50732i	0.222566	+	0.128498i
$746$	−37.8961	+	22.3011i	−1.38747	+	0.816500i
$747$	−51.5423	−	9.24236i	−1.88584	−	0.338160i
$748$	5.17974	+	8.63696i	0.189390	+	0.315799i
$749$	−41.5307	−	1.32480i	−1.51750	−	0.0484073i
$750$	−7.16774	+	6.09870i	−0.261729	+	0.222693i
$751$	18.2439	+	31.5994i	0.665729	+	1.15308i	0.979087	+	0.203442i	$0.0652128\pi$
$751$	18.2439	+	31.5994i	0.665729	+	1.15308i	−0.313358	+	0.949635i	$0.601454\pi$
$752$	−10.6150	−	17.0512i	−0.387089	−	0.621795i
$753$	−15.6785	+	13.1172i	−0.571356	+	0.478016i
$754$	−19.2390	+	0.159811i	−0.700641	+	0.00581998i
$755$		−	6.15772i		−	0.224103i
$756$	0.539466	−	27.4902i	0.0196202	−	0.999808i
$757$			19.9557i			0.725302i	0.931925	+	0.362651i	$0.118128\pi$
$757$			19.9557i			0.725302i	−0.931925	+	0.362651i	$0.881872\pi$
$758$	0.207863	+	25.0236i	0.00754991	+	0.908899i
$759$	10.8574	−	9.08364i	0.394097	−	0.329715i
$760$	−4.96581	−	2.70433i	−0.180129	−	0.0980962i
$761$	−18.2013	−	31.5257i	−0.659798	−	1.14280i	−0.980668	−	0.195681i	$-0.937308\pi$
$761$	−18.2013	−	31.5257i	−0.659798	−	1.14280i	0.320869	−	0.947124i	$-0.396025\pi$
$762$	13.9936	+	16.4465i	0.506933	+	0.595794i
$763$	40.8227	−	21.8641i	1.47788	−	0.791533i
$764$	−14.4340	+	8.65630i	−0.522202	+	0.313174i
$765$	3.87487	+	0.694825i	0.140096	+	0.0251215i
$766$	25.0972	+	42.6476i	0.906799	+	1.54092i
$767$	4.47235	+	2.58211i	0.161487	+	0.0932347i
$768$	−19.1548	−	20.0273i	−0.691190	−	0.722673i
$769$		−	33.7570i		−	1.21731i	−0.793436	−	0.608654i	$-0.791710\pi$
$769$		−	33.7570i		−	1.21731i	0.793436	−	0.608654i	$-0.208290\pi$
$770$	1.86646	+	1.13711i	0.0672627	+	0.0409786i
$771$	−10.5497	+	28.8551i	−0.379940	+	1.03919i
$772$	12.7666	−	22.9859i	0.459479	−	0.827282i
$773$	35.3297	+	20.3976i	1.27072	+	0.733651i	0.975124	−	0.221662i	$-0.0711481\pi$
$773$	35.3297	+	20.3976i	1.27072	+	0.733651i	0.295597	+	0.955313i	$0.404481\pi$
$774$	20.0458	+	3.42292i	0.720532	+	0.123034i
$775$	17.4635	−	10.0826i	0.627308	−	0.362176i
$776$	−0.634331	−	25.4500i	−0.0227711	−	0.913603i
$777$	31.0924	−	24.3707i	1.11543	−	0.874295i
$778$	−14.5545	+	25.6998i	−0.521804	+	0.921382i
$779$	28.5940	+	49.5263i	1.02449	+	1.77446i
$780$	−4.19795	−	1.45623i	−0.150311	−	0.0521413i
$781$	−18.5878	−	10.7317i	−0.665123	−	0.384009i
$782$	−0.215683	−	25.9651i	−0.00771282	−	0.928511i
$783$	18.6676	−	10.6698i	0.667126	−	0.381309i
$784$	−13.2528	−	24.6650i	−0.473313	−	0.880895i
$785$			1.97629i			0.0705368i
$786$	11.6218	+	4.13994i	0.414534	+	0.147667i
$787$	−5.80545	+	10.0553i	−0.206942	+	0.358434i	−0.950750	−	0.309960i	$-0.899684\pi$
$787$	−5.80545	+	10.0553i	−0.206942	+	0.358434i	0.743808	+	0.668394i	$0.233018\pi$
$788$	35.2189	−	0.585143i	1.25462	−	0.0208449i
$789$	−2.16246	−	12.3687i	−0.0769858	−	0.440337i
$790$	0.229889	+	0.130192i	0.00817908	+	0.00463204i
$791$	−0.163233	−	0.101315i	−0.00580389	−	0.00360236i
$792$	9.90917	+	7.94960i	0.352107	+	0.282477i
$793$	11.2073	+	19.4117i	0.397984	+	0.689329i
$794$	−3.50656	−	5.95868i	−0.124443	−	0.211466i
$795$	0.517505	−	0.432963i	0.0183540	−	0.0153556i
$796$	34.8642	+	19.3638i	1.23573	+	0.686333i
$797$			9.90792i			0.350956i	0.984483	+	0.175478i	$0.0561472\pi$
$797$			9.90792i			0.350956i	−0.984483	+	0.175478i	$0.943853\pi$
$798$	−20.7021	−	25.9648i	−0.732846	−	0.919144i
$799$	16.8887			0.597481
$800$	−12.7137	+	24.2980i	−0.449497	+	0.859065i
$801$	−14.3834	+	5.18797i	−0.508211	+	0.183308i
$802$	9.32187	−	5.48573i	0.329167	−	0.193708i
$803$	4.13377	−	2.38664i	0.145878	−	0.0842225i
$804$	2.30397	+	11.9995i	0.0812548	+	0.423189i
$805$	−2.66047	−	4.96740i	−0.0937694	−	0.175078i
$806$	16.8289	+	9.53067i	0.592773	+	0.335704i
$807$	−1.01892	−	5.82793i	−0.0358677	−	0.205153i
$808$	13.3060	+	7.24628i	0.468102	+	0.254923i
$809$	14.3590	+	8.29016i	0.504835	+	0.291466i	0.730708	−	0.682690i	$-0.239190\pi$
$809$	14.3590	+	8.29016i	0.504835	+	0.291466i	−0.225873	+	0.974157i	$0.572523\pi$
$810$	4.88817	−	0.874583i	0.171753	−	0.0307297i
$811$	49.5706			1.74066			0.870330	−	0.492470i	$-0.163906\pi$
$811$	49.5706			1.74066			0.870330	+	0.492470i	$0.163906\pi$
$812$	11.2365	−	18.7933i	0.394325	−	0.659516i
$813$	−7.45700	−	2.72637i	−0.261528	−	0.0956179i
$814$	0.151615	+	18.2522i	0.00531409	+	0.639739i
$815$	−2.44952	+	4.24268i	−0.0858028	+	0.148615i
$816$	22.8081	−	4.77346i	0.798442	−	0.167104i
$817$	21.2702	−	12.2804i	0.744151	−	0.429636i
$818$	−9.47180	−	5.36414i	−0.331174	−	0.187553i
$819$	−19.3946	−	17.4587i	−0.677702	−	0.610057i
$820$	−7.46857	+	4.47903i	−0.260814	+	0.156415i
$821$	−26.4055	−	45.7357i	−0.921559	−	1.59619i	−0.797004	−	0.603973i	$-0.793583\pi$
$821$	−26.4055	−	45.7357i	−0.921559	−	1.59619i	−0.124554	−	0.992213i	$-0.539750\pi$
$822$	3.23895	+	17.6599i	0.112971	+	0.615960i
$823$	12.3351	−	21.3650i	0.429975	−	0.744739i	−0.566896	−	0.823790i	$-0.691856\pi$
$823$	12.3351	−	21.3650i	0.429975	−	0.744739i	0.996871	+	0.0790510i	$0.0251890\pi$
$824$	21.4820	−	13.1269i	0.748360	−	0.457299i
$825$	4.31668	−	11.8067i	0.150287	−	0.411057i
$826$	−5.15779	+	2.81783i	−0.179463	+	0.0980447i
$827$	−23.0662			−0.802091			−0.401045	−	0.916058i	$-0.631353\pi$
$827$	−23.0662			−0.802091			−0.401045	+	0.916058i	$0.631353\pi$
$828$	−11.6236	−	30.6222i	−0.403949	−	1.06419i
$829$	12.2068	−	21.1429i	0.423961	−	0.734322i	−0.572362	−	0.820001i	$-0.693973\pi$
$829$	12.2068	−	21.1429i	0.423961	−	0.734322i	0.996323	+	0.0856795i	$0.0273061\pi$
$830$	−4.88450	−	8.30021i	−0.169543	−	0.288104i
$831$	−3.68349	−	21.0685i	−0.127779	−	0.730859i
$832$	−26.2688	+	1.31029i	−0.910706	+	0.0454261i
$833$	23.4959	+	1.50053i	0.814083	+	0.0519904i
$834$	25.0000	+	29.3822i	0.865678	+	1.01742i
$835$	2.51093	−	1.44969i	0.0868944	−	0.0501685i
$836$	15.3410	−	0.254882i	0.530579	−	0.00881527i
$837$	−21.6140	−	0.0939312i	−0.747090	−	0.00324674i
$838$	0.0514793	+	6.19736i	0.00177832	+	0.214084i
$839$	−48.3464			−1.66910			−0.834551	−	0.550931i	$-0.814273\pi$
$839$	−48.3464			−1.66910			−0.834551	+	0.550931i	$0.814273\pi$
$840$	3.90105	−	3.21780i	0.134599	−	0.111025i
$841$	−11.8768			−0.409546
$842$	0.140259	+	16.8852i	0.00483365	+	0.581901i
$843$	10.5155	−	8.79760i	0.362172	−	0.303005i
$844$	−0.482280	−	29.0278i	−0.0166008	−	0.999176i
$845$	0.740348	−	0.427440i	0.0254688	−	0.0147044i
$846$	19.9793	−	7.39450i	0.686902	−	0.254228i
$847$	23.1610	+	0.738822i	0.795823	+	0.0253862i
$848$	1.88097	−	3.52329i	0.0645927	−	0.120990i
$849$	−38.7479	+	6.77445i	−1.32983	+	0.232498i
$850$	−11.6948	−	19.8730i	−0.401130	−	0.681638i
$851$	23.5304	−	40.7559i	0.806612	−	1.39709i
$852$	−37.5544	+	32.4949i	−1.28659	+	1.11326i
$853$	−34.6867			−1.18765			−0.593825	−	0.804595i	$-0.702383\pi$
$853$	−34.6867			−1.18765			−0.593825	+	0.804595i	$0.702383\pi$
$854$	−25.5027	−	0.601519i	−0.872685	−	0.0205835i
$855$	3.86837	−	4.58312i	0.132296	−	0.156739i
$856$	−23.1620	−	37.9042i	−0.791662	−	1.29554i
$857$	10.7545	−	18.6273i	0.367366	−	0.636297i	−0.621786	−	0.783187i	$-0.713593\pi$
$857$	10.7545	−	18.6273i	0.367366	−	0.636297i	0.989153	+	0.146889i	$0.0469262\pi$
$858$	11.8591	−	2.17503i	0.404862	−	0.0742543i
$859$	0.332259	+	0.575490i	0.0113365	+	0.0196355i	0.871638	−	0.490150i	$-0.163058\pi$
$859$	0.332259	+	0.575490i	0.0113365	+	0.0196355i	−0.860301	+	0.509786i	$0.829725\pi$
$860$	1.92363	+	3.20755i	0.0655951	+	0.109377i
$861$	−50.6358	+	7.19745i	−1.72566	+	0.245289i
$862$	−0.836827	−	0.473918i	−0.0285025	−	0.0161417i
$863$	−14.2150	+	8.20702i	−0.483883	+	0.279370i	−0.722033	−	0.691858i	$-0.756792\pi$
$863$	−14.2150	+	8.20702i	−0.483883	+	0.279370i	0.238150	+	0.971228i	$0.423459\pi$
$864$	24.8918	−	15.6332i	0.846838	−	0.531851i
$865$	3.43388	−	5.94765i	0.116755	−	0.202226i
$866$	−0.00280165	−	0.337277i	−9.52038e−5	−	0.0114612i
$867$	3.38273	−	9.25225i	0.114884	−	0.314223i
$868$	−19.2278	+	10.7130i	−0.652635	+	0.363622i
$869$	−0.716882			−0.0243186
$870$	3.72526	+	1.32702i	0.126298	+	0.0449903i
$871$	10.0428	+	5.79819i	0.340286	+	0.196464i
$872$	43.4773	+	23.6773i	1.47233	+	0.801813i
$873$	26.5783	+	4.76591i	0.899539	+	0.161302i
$874$	−34.4219	−	19.4941i	−1.16434	−	0.659398i
$875$	−8.63685	−	5.36073i	−0.291979	−	0.181226i
$876$	−2.08253	−	10.8462i	−0.0703621	−	0.366458i
$877$	11.1473	−	6.43591i	0.376419	−	0.217325i	−0.299840	−	0.953989i	$-0.596933\pi$
$877$	11.1473	−	6.43591i	0.376419	−	0.217325i	0.676259	+	0.736664i	$0.263600\pi$
$878$	4.64288	−	2.73224i	0.156690	−	0.0922085i
$879$	17.0367	−	14.2535i	0.574633	−	0.480757i
$880$	0.0776169	+	2.33518i	0.00261647	+	0.0787189i
$881$	42.1373			1.41964			0.709821	−	0.704382i	$-0.248776\pi$
$881$	42.1373			1.41964			0.709821	+	0.704382i	$0.248776\pi$
$882$	28.4525	−	8.51221i	0.958044	−	0.286621i
$883$			14.3108i			0.481596i	0.970575	+	0.240798i	$0.0774091\pi$
$883$			14.3108i			0.481596i	−0.970575	+	0.240798i	$0.922591\pi$
$884$	10.7381	−	19.3336i	0.361160	−	0.650260i
$885$	−0.681121	−	0.814120i	−0.0228956	−	0.0273664i
$886$	−4.33223	−	7.36174i	−0.145544	−	0.247323i
$887$	−3.93855	−	6.82176i	−0.132243	−	0.229052i	0.792298	−	0.610135i	$-0.208885\pi$
$887$	−3.93855	−	6.82176i	−0.132243	−	0.229052i	−0.924541	+	0.381082i	$0.875551\pi$
$888$	40.0141	+	13.5092i	1.34278	+	0.453338i
$889$	−12.3003	+	19.8174i	−0.412538	+	0.664653i
$890$	−2.44702	−	1.38581i	−0.0820242	−	0.0464526i
$891$	−10.3721	+	8.60127i	−0.347477	+	0.288153i
$892$	−0.0923293	−	5.55717i	−0.00309141	−	0.186068i
$893$	12.8648	−	22.2825i	0.430505	−	0.745656i
$894$	−14.7785	+	41.4867i	−0.494268	+	1.38752i
$895$		−	6.33434i		−	0.211734i
$896$	14.2809	−	26.3070i	0.477091	−	0.878854i
$897$	−29.1958	−	10.6743i	−0.974818	−	0.356405i
$898$	0.330656	+	39.8061i	0.0110341	+	1.32835i
$899$	−14.9067	−	8.60636i	−0.497165	−	0.287038i
$900$	−22.5360	−	18.3892i	−0.751201	−	0.612974i
$901$	1.67915	+	2.90837i	0.0559406	+	0.0968919i
$902$	11.6449	−	20.5622i	0.387734	−	0.684646i
$903$	3.09112	+	21.7467i	0.102866	+	0.723686i
$904$	−0.00511751	−	0.205320i	−0.000170206	−	0.00682885i
$905$	−2.09262	+	1.20818i	−0.0695611	+	0.0401611i
$906$	38.0260	−	6.97422i	1.26333	−	0.231703i
$907$	24.8886	+	14.3694i	0.826413	+	0.477130i	0.852623	−	0.522527i	$-0.175011\pi$
$907$	24.8886	+	14.3694i	0.826413	+	0.477130i	−0.0262101	+	0.999656i	$0.508344\pi$
$908$	28.3531	+	15.7475i	0.940930	+	0.522600i
$909$	−10.3654	+	12.2805i	−0.343797	+	0.407319i
$910$	0.113169	−	4.79804i	0.00375151	−	0.159053i
$911$			4.32207i			0.143197i	0.997434	+	0.0715983i	$0.0228100\pi$
$911$			4.32207i			0.143197i	−0.997434	+	0.0715983i	$0.977190\pi$
$912$	11.0759	−	33.7285i	0.366758	−	1.11686i
$913$	22.6316	+	13.0664i	0.748996	+	0.432433i
$914$	−8.94137	−	15.1940i	−0.295754	−	0.502574i
$915$	−0.793454	−	4.53834i	−0.0262308	−	0.150033i
$916$	−21.2207	−	35.3845i	−0.701152	−	1.16914i
$917$	−0.424862	+	13.3188i	−0.0140302	+	0.439826i
$918$	0.0978901	+	24.7156i	0.00323085	+	0.815735i
$919$	18.1008	+	31.3515i	0.597089	+	1.03419i	0.993248	+	0.116007i	$0.0370095\pi$
$919$	18.1008	+	31.3515i	0.597089	+	1.03419i	−0.396159	+	0.918182i	$0.629657\pi$
$920$	2.88111	−	5.29042i	0.0949872	−	0.174420i
$921$	−13.7396	−	16.4225i	−0.452735	−	0.541138i
$922$	−0.371450	−	44.7172i	−0.0122331	−	1.47268i
$923$			47.1321i			1.55137i
$924$	−4.90809	+	12.8139i	−0.161464	+	0.421547i
$925$		−	41.7916i		−	1.37410i
$926$	33.2463	−	0.276166i	1.09254	−	0.00907537i
$927$	9.06001	+	25.1184i	0.297570	+	0.824995i
$928$	23.3880	−	0.971914i	0.767747	−	0.0319047i
$929$	−0.370626	−	0.641943i	−0.0121598	−	0.0210615i	0.859881	−	0.510494i	$-0.170537\pi$
$929$	−0.370626	−	0.641943i	−0.0121598	−	0.0210615i	−0.872041	+	0.489432i	$0.837204\pi$
$930$	−2.57607	−	3.02762i	−0.0844725	−	0.0992797i
$931$	19.8775	−	29.8567i	0.651458	−	0.978515i
$932$	−3.57413	+	2.14347i	−0.117075	+	0.0702117i
$933$	−2.45968	+	0.430035i	−0.0805264	+	0.0140787i
$934$	17.9641	−	10.5715i	0.587804	−	0.345910i
$935$	−1.70141	−	0.982307i	−0.0556419	−	0.0321249i
$936$	4.23810	−	27.5731i	0.138527	−	0.901254i
$937$			49.0746i			1.60320i	0.597863	+	0.801598i	$0.296017\pi$
$937$			49.0746i			1.60320i	−0.597863	+	0.801598i	$0.703983\pi$
$938$	−11.5819	+	6.32749i	−0.378164	+	0.206600i
$939$	39.2250	+	14.3411i	1.28006	+	0.468005i
$940$	3.42529	+	1.90244i	0.111721	+	0.0620506i
$941$	−26.9660	−	15.5688i	−0.879065	−	0.507529i	−0.00871528	−	0.999962i	$-0.502774\pi$
$941$	−26.9660	−	15.5688i	−0.879065	−	0.507529i	−0.870350	+	0.492433i	$0.836108\pi$
$942$	−12.2043	+	2.23834i	−0.397636	+	0.0729291i
$943$	−52.7638	+	30.4632i	−1.71822	+	0.992017i
$944$	−5.54271	−	2.95907i	−0.180400	−	0.0963095i
$945$	2.51180	+	4.73918i	0.0817088	+	0.154165i
$946$	−8.83092	−	5.00119i	−0.287118	−	0.162603i
$947$	−11.6780	−	20.2270i	−0.379485	−	0.657288i	0.611502	−	0.791243i	$-0.290566\pi$
$947$	−11.6780	−	20.2270i	−0.379485	−	0.657288i	−0.990987	+	0.133955i	$0.957232\pi$
$948$	−0.543610	+	1.56710i	−0.0176556	+	0.0508969i
$949$	−9.07751	−	5.24090i	−0.294669	−	0.170127i
$950$	−35.1283	+	0.291798i	−1.13971	+	0.00946719i
$951$	16.0210	−	43.8197i	0.519517	−	1.42095i
$952$	12.4324	+	21.8844i	0.402938	+	0.709278i
$953$			37.3593i			1.21019i	0.796155	+	0.605093i	$0.206864\pi$
$953$			37.3593i			1.21019i	−0.796155	+	0.605093i	$0.793136\pi$
$954$	3.25981	+	2.70540i	0.105540	+	0.0875904i
$955$	1.64162	−	2.84336i	0.0531215	−	0.0920091i
$956$	0.0282992	+	1.70329i	0.000915262	+	0.0550883i
$957$	−10.5702	+	1.84803i	−0.341686	+	0.0597383i
$958$	−24.1177	+	42.5862i	−0.779209	+	1.37590i
$959$	−17.0955	+	9.15612i	−0.552042	+	0.295667i
$960$	5.16353	+	1.60109i	0.166652	+	0.0516750i
$961$	−6.84861	−	11.8621i	−0.220923	−	0.382650i
$962$	34.5445	−	20.3287i	1.11376	−	0.655423i
$963$	44.3204	−	15.9861i	1.42821	−	0.515144i
$964$	26.3299	+	14.6238i	0.848029	+	0.471002i
$965$			5.12916i			0.165114i
$966$	27.6621	−	22.0554i	0.890013	−	0.709620i
$967$	−32.9761			−1.06044			−0.530220	−	0.847860i	$-0.677891\pi$
$967$	−32.9761			−1.06044			−0.530220	+	0.847860i	$0.677891\pi$
$968$	12.9171	+	21.1386i	0.415172	+	0.679419i
$969$	19.1544	+	22.8946i	0.615327	+	0.735479i
$970$	2.51874	+	4.28008i	0.0808719	+	0.137425i
$971$	−14.3859	+	8.30570i	−0.461665	+	0.266543i	−0.712744	−	0.701424i	$-0.752548\pi$
$971$	−14.3859	+	8.30570i	−0.461665	+	0.266543i	0.251079	+	0.967967i	$0.419215\pi$
$972$	10.9372	+	29.1955i	0.350810	+	0.936447i
$973$	−21.9748	+	35.4044i	−0.704481	+	1.13501i
$974$	−16.7654	+	29.6037i	−0.537198	+	0.948563i
$975$	−27.1929	+	4.75423i	−0.870869	+	0.152257i
$976$	−14.4126	−	23.1515i	−0.461336	−	0.741061i
$977$	−0.641595	−	0.370425i	−0.0205264	−	0.0118509i	0.489702	−	0.871890i	$-0.337106\pi$
$977$	−0.641595	−	0.370425i	−0.0205264	−	0.0118509i	−0.510228	+	0.860039i	$0.670439\pi$
$978$	−28.9743	−	10.3213i	−0.926496	−	0.330039i
$979$	7.63074			0.243880
$980$	4.59629	+	2.95103i	0.146823	+	0.0942671i
$981$	−33.8689	+	40.1267i	−1.08135	+	1.28115i
$982$	−21.7369	+	0.180560i	−0.693651	+	0.00576192i
$983$	−5.11340	+	8.85666i	−0.163092	+	0.282484i	−0.935976	−	0.352064i	$-0.885480\pi$
$983$	−5.11340	+	8.85666i	−0.163092	+	0.282484i	0.772884	+	0.634547i	$0.218813\pi$
$984$	−36.1184	−	41.0480i	−1.15141	−	1.30856i
$985$	−5.95069	+	3.43563i	−0.189605	+	0.109468i
$986$	−9.69941	+	17.1268i	−0.308892	+	0.545430i
$987$	14.1952	+	18.1104i	0.451839	+	0.576461i
$988$	−17.3286	−	28.8947i	−0.551297	−	0.919262i
$989$	13.0831	+	22.6606i	0.416019	+	0.720567i
$990$	−2.44284	−	0.417127i	−0.0776387	−	0.0132572i
$991$	22.7297	−	39.3690i	0.722032	−	1.25060i	−0.238152	−	0.971228i	$-0.576541\pi$
$991$	22.7297	−	39.3690i	0.722032	−	1.25060i	0.960184	−	0.279369i	$-0.0901252\pi$
$992$	−20.8490	−	10.9090i	−0.661957	−	0.346362i
$993$	−28.6984	−	10.4925i	−0.910718	−	0.332969i
$994$	−45.8086	−	27.9081i	−1.45296	−	0.885191i
$995$	−7.77971			−0.246633
$996$	45.7244	−	39.5642i	1.44883	−	1.25364i
$997$	−13.6051	+	23.5647i	−0.430877	+	0.746300i	−0.996949	−	0.0780552i	$-0.975129\pi$
$997$	−13.6051	+	23.5647i	−0.430877	+	0.746300i	0.566072	+	0.824356i	$0.308462\pi$
$998$	−32.1846	+	18.9400i	−1.01879	+	0.599534i
$999$	−22.5658	+	38.6958i	−0.713950	+	1.22428i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.101.24	yes	48
3.2	odd	2	inner	168.2.ba.c.101.1	yes	48
4.3	odd	2		672.2.bi.c.17.19		48
7.5	odd	6	inner	168.2.ba.c.5.9	yes	48
8.3	odd	2		672.2.bi.c.17.6		48
8.5	even	2	inner	168.2.ba.c.101.16	yes	48
12.11	even	2		672.2.bi.c.17.2		48
21.5	even	6	inner	168.2.ba.c.5.16	yes	48
24.5	odd	2	inner	168.2.ba.c.101.9	yes	48
24.11	even	2		672.2.bi.c.17.23		48
28.19	even	6		672.2.bi.c.593.23		48
56.5	odd	6	inner	168.2.ba.c.5.1	✓	48
56.19	even	6		672.2.bi.c.593.2		48
84.47	odd	6		672.2.bi.c.593.6		48
168.5	even	6	inner	168.2.ba.c.5.24	yes	48
168.131	odd	6		672.2.bi.c.593.19		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.1	✓	48	56.5	odd	6	inner
168.2.ba.c.5.9	yes	48	7.5	odd	6	inner
168.2.ba.c.5.16	yes	48	21.5	even	6	inner
168.2.ba.c.5.24	yes	48	168.5	even	6	inner
168.2.ba.c.101.1	yes	48	3.2	odd	2	inner
168.2.ba.c.101.9	yes	48	24.5	odd	2	inner
168.2.ba.c.101.16	yes	48	8.5	even	2	inner
168.2.ba.c.101.24	yes	48	1.1	even	1	trivial
672.2.bi.c.17.2		48	12.11	even	2
672.2.bi.c.17.6		48	8.3	odd	2
672.2.bi.c.17.19		48	4.3	odd	2
672.2.bi.c.17.23		48	24.11	even	2
672.2.bi.c.593.2		48	56.19	even	6
672.2.bi.c.593.6		48	84.47	odd	6
672.2.bi.c.593.19		48	168.131	odd	6
672.2.bi.c.593.23		48	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41416 - 0.0117470i) q^{2} +(-1.11142 - 1.32844i) q^{3} +(1.99972 - 0.0332243i) q^{4} +(-0.337879 + 0.195075i) q^{5} +(-1.58733 - 1.86558i) q^{6} +(1.39526 - 2.24795i) q^{7} +(2.82755 - 0.0704754i) q^{8} +(-0.529502 + 2.95290i) q^{9} +(-0.475526 + 0.279837i) q^{10} +(0.748582 - 1.29658i) q^{11} +(-2.26666 - 2.61959i) q^{12} -3.28768 q^{13} +(1.94672 - 3.19536i) q^{14} +(0.634670 + 0.232043i) q^{15} +(3.99779 - 0.132879i) q^{16} +(-1.68169 + 2.91278i) q^{17} +(-0.714115 + 4.18211i) q^{18} +(2.56203 + 4.43756i) q^{19} +(-0.669184 + 0.401321i) q^{20} +(-4.53697 + 0.644892i) q^{21} +(1.04339 - 1.84237i) q^{22} +(-4.72764 + 2.72950i) q^{23} +(-3.23621 - 3.67790i) q^{24} +(-2.42389 + 4.19830i) q^{25} +(-4.64932 + 0.0386203i) q^{26} +(4.51125 - 2.57850i) q^{27} +(2.71544 - 4.54163i) q^{28} +4.13801 q^{29} +(0.900254 + 0.320691i) q^{30} +(-3.60237 - 2.07983i) q^{31} +(5.65198 - 0.234875i) q^{32} +(-2.55442 + 0.446598i) q^{33} +(-2.34398 + 4.13891i) q^{34} +(-0.0329110 + 1.03171i) q^{35} +(-0.960750 + 5.92258i) q^{36} +(-7.46581 + 4.31038i) q^{37} +(3.67525 + 6.24534i) q^{38} +(3.65399 + 4.36748i) q^{39} +(-0.941622 + 0.575396i) q^{40} +11.1607 q^{41} +(-6.40845 + 0.965280i) q^{42} -4.79323i q^{43} +(1.45388 - 2.61768i) q^{44} +(-0.397129 - 1.10102i) q^{45} +(-6.65359 + 3.91550i) q^{46} +(-2.51067 - 4.34861i) q^{47} +(-4.61974 - 5.16314i) q^{48} +(-3.10652 - 6.27292i) q^{49} +(-3.37846 + 5.96557i) q^{50} +(5.73852 - 1.00329i) q^{51} +(-6.57445 + 0.109231i) q^{52} +(0.499243 - 0.864715i) q^{53} +(6.34936 - 3.69941i) q^{54} +0.584118i q^{55} +(3.78673 - 6.45451i) q^{56} +(3.04755 - 8.33548i) q^{57} +(5.85183 - 0.0486091i) q^{58} +(-1.36034 - 0.785391i) q^{59} +(1.27687 + 0.442935i) q^{60} +(-3.40889 - 5.90437i) q^{61} +(-5.11878 - 2.89891i) q^{62} +(5.89917 + 5.31035i) q^{63} +(7.99007 - 0.398545i) q^{64} +(1.11084 - 0.641343i) q^{65} +(-3.60712 + 0.661570i) q^{66} +(-3.05467 - 1.76361i) q^{67} +(-3.26615 + 5.88063i) q^{68} +(8.88036 + 3.24676i) q^{69} +(-0.0344221 + 1.45940i) q^{70} -14.3360i q^{71} +(-1.28909 + 8.38679i) q^{72} +(2.76107 + 1.59410i) q^{73} +(-10.5072 + 6.18329i) q^{74} +(8.27115 - 1.44608i) q^{75} +(5.27078 + 8.78877i) q^{76} +(-1.87018 - 3.49184i) q^{77} +(5.21864 + 6.13342i) q^{78} +(-0.239413 - 0.414676i) q^{79} +(-1.32485 + 0.824765i) q^{80} +(-8.43926 - 3.12713i) q^{81} +(15.7831 - 0.131105i) q^{82} +17.4548i q^{83} +(-9.05127 + 1.44034i) q^{84} -1.31222i q^{85} +(-0.0563059 - 6.77842i) q^{86} +(-4.59906 - 5.49710i) q^{87} +(2.02527 - 3.71891i) q^{88} +(2.54840 + 4.41396i) q^{89} +(-0.574539 - 1.55235i) q^{90} +(-4.58716 + 7.39053i) q^{91} +(-9.36328 + 5.61532i) q^{92} +(1.24081 + 7.09709i) q^{93} +(-3.60159 - 6.12016i) q^{94} +(-1.73131 - 0.999573i) q^{95} +(-6.59372 - 7.24726i) q^{96} -9.00074i q^{97} +(-4.46682 - 8.83445i) q^{98} +(3.43230 + 2.89703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42}+ \cdots + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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