LMFDB - Embedded newform 420.2.bk.a.19.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(19,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 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("420.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.bk (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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.12
Character	$\chi$	$=$	420.19
Dual form			420.2.bk.a.199.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07664 - 0.916974i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.318317 + 1.97451i) q^{4} +(-1.63361 + 1.52686i) q^{5} +(1.39089 + 0.255802i) q^{6} +(0.935228 + 2.47494i) q^{7} +(1.46786 - 2.41772i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.07664 - 0.916974i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.318317 + 1.97451i) q^{4} +(-1.63361 + 1.52686i) q^{5} +(1.39089 + 0.255802i) q^{6} +(0.935228 + 2.47494i) q^{7} +(1.46786 - 2.41772i) q^{8} +(0.500000 - 0.866025i) q^{9} +(3.15891 - 0.145905i) q^{10} +(2.69840 - 1.55792i) q^{11} +(-1.26292 - 1.55081i) q^{12} -4.60611 q^{13} +(1.26255 - 3.52221i) q^{14} +(0.651318 - 2.13911i) q^{15} +(-3.79735 + 1.25704i) q^{16} +(-2.11679 - 3.66639i) q^{17} +(-1.33244 + 0.473912i) q^{18} +(-3.59444 + 6.22575i) q^{19} +(-3.53481 - 2.73955i) q^{20} +(-2.04740 - 1.67575i) q^{21} +(-4.33379 - 0.797040i) q^{22} +(-0.354512 + 0.614033i) q^{23} +(-0.0623403 + 2.82774i) q^{24} +(0.337377 - 4.98860i) q^{25} +(4.95913 + 4.22368i) q^{26} +1.00000i q^{27} +(-4.58909 + 2.63443i) q^{28} -9.36267 q^{29} +(-2.66274 + 1.70581i) q^{30} +(-0.370153 - 0.641124i) q^{31} +(5.24106 + 2.12869i) q^{32} +(-1.55792 + 2.69840i) q^{33} +(-1.08296 + 5.88844i) q^{34} +(-5.30670 - 2.61513i) q^{35} +(1.86913 + 0.711583i) q^{36} +(1.78046 + 1.02795i) q^{37} +(9.57878 - 3.40690i) q^{38} +(3.98901 - 2.30305i) q^{39} +(1.29362 + 6.19084i) q^{40} -1.97405i q^{41} +(0.667701 + 3.68160i) q^{42} +7.68301 q^{43} +(3.93508 + 4.83210i) q^{44} +(0.505496 + 2.17818i) q^{45} +(0.944736 - 0.336015i) q^{46} +(-11.0988 - 6.40788i) q^{47} +(2.66008 - 2.98730i) q^{48} +(-5.25070 + 4.62927i) q^{49} +(-4.93766 + 5.06158i) q^{50} +(3.66639 + 2.11679i) q^{51} +(-1.46620 - 9.09479i) q^{52} +(-7.63173 + 4.40618i) q^{53} +(0.916974 - 1.07664i) q^{54} +(-2.02941 + 6.66514i) q^{55} +(7.35652 + 1.37174i) q^{56} -7.18888i q^{57} +(10.0802 + 8.58533i) q^{58} +(2.91078 + 5.04162i) q^{59} +(4.43101 + 0.605118i) q^{60} +(-7.04806 - 4.06920i) q^{61} +(-0.189372 + 1.02968i) q^{62} +(2.61098 + 0.427541i) q^{63} +(-3.69078 - 7.09775i) q^{64} +(7.52460 - 7.03290i) q^{65} +(4.15169 - 1.47664i) q^{66} +(-2.85842 - 4.95093i) q^{67} +(6.56551 - 5.34669i) q^{68} -0.709025i q^{69} +(3.31541 + 7.68167i) q^{70} +9.09059i q^{71} +(-1.35988 - 2.48006i) q^{72} +(2.26326 + 3.92008i) q^{73} +(-0.974315 - 2.73937i) q^{74} +(2.20213 + 4.48895i) q^{75} +(-13.4370 - 5.11548i) q^{76} +(6.37940 + 5.22138i) q^{77} +(-6.40658 - 1.17825i) q^{78} +(-4.91560 - 2.83802i) q^{79} +(4.28407 - 7.85154i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.81016 + 2.12535i) q^{82} -1.15916i q^{83} +(2.65706 - 4.57603i) q^{84} +(9.05610 + 2.75741i) q^{85} +(-8.27186 - 7.04513i) q^{86} +(8.10831 - 4.68134i) q^{87} +(0.194243 - 8.81081i) q^{88} +(2.56797 + 1.48262i) q^{89} +(1.45310 - 2.80865i) q^{90} +(-4.30776 - 11.3999i) q^{91} +(-1.32526 - 0.504530i) q^{92} +(0.641124 + 0.370153i) q^{93} +(6.07354 + 17.0763i) q^{94} +(-3.63395 - 15.6587i) q^{95} +(-5.60323 + 0.777025i) q^{96} +10.2289 q^{97} +(9.89805 - 0.169318i) q^{98} -3.11585i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 48 q^{9}+O(q^{10}) $ 96 * q + 48 * q^9	$ 96 q + 48 q^{9} + 18 q^{10} + 4 q^{14} - 8 q^{16} + 4 q^{25} - 8 q^{30} - 30 q^{40} + 16 q^{44} + 44 q^{46} - 8 q^{49} - 48 q^{50} - 52 q^{56} + 2 q^{60} - 144 q^{64} - 36 q^{66} - 42 q^{70} - 20 q^{74} - 36 q^{80} - 48 q^{81} - 20 q^{84} - 32 q^{85} - 32 q^{86} - 36 q^{94} - 60 q^{96}+O(q^{100}) $ 96 * q + 48 * q^9 + 18 * q^10 + 4 * q^14 - 8 * q^16 + 4 * q^25 - 8 * q^30 - 30 * q^40 + 16 * q^44 + 44 * q^46 - 8 * q^49 - 48 * q^50 - 52 * q^56 + 2 * q^60 - 144 * q^64 - 36 * q^66 - 42 * q^70 - 20 * q^74 - 36 * q^80 - 48 * q^81 - 20 * q^84 - 32 * q^85 - 32 * q^86 - 36 * q^94 - 60 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.07664	−	0.916974i	−0.761301	−	0.648399i
$2$	−1.07664	−	0.916974i	−0.761301	−	0.648399i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.318317	+	1.97451i	0.159158	+	0.987253i
$5$	−1.63361	+	1.52686i	−0.730574	+	0.682834i
$5$	−1.63361	+	1.52686i	−0.730574	+	0.682834i
$6$	1.39089	+	0.255802i	0.567827	+	0.104431i
$7$	0.935228	+	2.47494i	0.353483	+	0.935441i
$7$	0.935228	+	2.47494i	0.353483	+	0.935441i
$8$	1.46786	−	2.41772i	0.518966	−	0.854795i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	3.15891	−	0.145905i	0.998935	−	0.0461392i
$11$	2.69840	−	1.55792i	0.813599	−	0.469732i	−0.0346050	−	0.999401i	$-0.511017\pi$
$11$	2.69840	−	1.55792i	0.813599	−	0.469732i	0.848204	+	0.529669i	$0.177684\pi$
$12$	−1.26292	−	1.55081i	−0.364575	−	0.447682i
$13$	−4.60611			−1.27750			−0.638752	−	0.769412i	$-0.720549\pi$
$13$	−4.60611			−1.27750			−0.638752	+	0.769412i	$0.720549\pi$
$14$	1.26255	−	3.52221i	0.337432	−	0.941350i
$15$	0.651318	−	2.13911i	0.168170	−	0.552315i
$16$	−3.79735	+	1.25704i	−0.949337	+	0.314259i
$17$	−2.11679	−	3.66639i	−0.513398	−	0.889231i	−0.999879	−	0.0155401i	$-0.995053\pi$
$17$	−2.11679	−	3.66639i	−0.513398	−	0.889231i	0.486481	−	0.873691i	$-0.338280\pi$
$18$	−1.33244	+	0.473912i	−0.314060	+	0.111702i
$19$	−3.59444	+	6.22575i	−0.824621	+	1.42829i	0.0775875	+	0.996986i	$0.475278\pi$
$19$	−3.59444	+	6.22575i	−0.824621	+	1.42829i	−0.902209	+	0.431300i	$0.858055\pi$
$20$	−3.53481	−	2.73955i	−0.790407	−	0.612582i
$21$	−2.04740	−	1.67575i	−0.446780	−	0.365679i
$22$	−4.33379	−	0.797040i	−0.923967	−	0.169929i
$23$	−0.354512	+	0.614033i	−0.0739209	+	0.128035i	−0.900617	−	0.434615i	$-0.856885\pi$
$23$	−0.354512	+	0.614033i	−0.0739209	+	0.128035i	0.826696	+	0.562649i	$0.190218\pi$
$24$	−0.0623403	+	2.82774i	−0.0127252	+	0.577210i
$25$	0.337377	−	4.98860i	0.0674754	−	0.997721i
$26$	4.95913	+	4.22368i	0.972566	+	0.828332i
$27$			1.00000i			0.192450i
$28$	−4.58909	+	2.63443i	−0.867257	+	0.497860i
$29$	−9.36267			−1.73860			−0.869302	−	0.494281i	$-0.835431\pi$
$29$	−9.36267			−1.73860			−0.869302	+	0.494281i	$0.835431\pi$
$30$	−2.66274	+	1.70581i	−0.486148	+	0.311437i
$31$	−0.370153	−	0.641124i	−0.0664815	−	0.115149i	0.830869	−	0.556468i	$-0.187844\pi$
$31$	−0.370153	−	0.641124i	−0.0664815	−	0.115149i	−0.897350	+	0.441319i	$0.854511\pi$
$32$	5.24106	+	2.12869i	0.926496	+	0.376303i
$33$	−1.55792	+	2.69840i	−0.271200	+	0.469732i
$34$	−1.08296	+	5.88844i	−0.185726	+	1.00986i
$35$	−5.30670	−	2.61513i	−0.896996	−	0.442038i
$36$	1.86913	+	0.711583i	0.311522	+	0.118597i
$37$	1.78046	+	1.02795i	0.292706	+	0.168994i	0.639161	−	0.769073i	$-0.279282\pi$
$37$	1.78046	+	1.02795i	0.292706	+	0.168994i	−0.346456	+	0.938066i	$0.612615\pi$
$38$	9.57878	−	3.40690i	1.55388	−	0.552672i
$39$	3.98901	−	2.30305i	0.638752	−	0.368784i
$40$	1.29362	+	6.19084i	0.204540	+	0.978858i
$41$		−	1.97405i		−	0.308295i	−0.988048	−	0.154148i	$-0.950737\pi$
$41$		−	1.97405i		−	0.308295i	0.988048	−	0.154148i	$-0.0492632\pi$
$42$	0.667701	+	3.68160i	0.103028	+	0.568083i
$43$	7.68301			1.17165			0.585824	−	0.810438i	$-0.300771\pi$
$43$	7.68301			1.17165			0.585824	+	0.810438i	$0.300771\pi$
$44$	3.93508	+	4.83210i	0.593235	+	0.728467i
$45$	0.505496	+	2.17818i	0.0753549	+	0.324704i
$46$	0.944736	−	0.336015i	0.139294	−	0.0495428i
$47$	−11.0988	−	6.40788i	−1.61892	−	0.934685i	−0.987200	−	0.159490i	$-0.949015\pi$
$47$	−11.0988	−	6.40788i	−1.61892	−	0.934685i	−0.631722	−	0.775195i	$-0.717652\pi$
$48$	2.66008	−	2.98730i	0.383950	−	0.431180i
$49$	−5.25070	+	4.62927i	−0.750100	+	0.661325i
$50$	−4.93766	+	5.06158i	−0.698290	+	0.715815i
$51$	3.66639	+	2.11679i	0.513398	+	0.296410i
$52$	−1.46620	−	9.09479i	−0.203325	−	1.26122i
$53$	−7.63173	+	4.40618i	−1.04830	+	0.605235i	−0.922173	−	0.386779i	$-0.873588\pi$
$53$	−7.63173	+	4.40618i	−1.04830	+	0.605235i	−0.126126	+	0.992014i	$0.540254\pi$
$54$	0.916974	−	1.07664i	0.124784	−	0.146512i
$55$	−2.02941	+	6.66514i	−0.273645	+	0.898727i
$56$	7.35652	+	1.37174i	0.983056	+	0.183307i
$57$		−	7.18888i		−	0.952190i
$58$	10.0802	+	8.58533i	1.32360	+	1.12731i
$59$	2.91078	+	5.04162i	0.378951	+	0.656363i	0.990910	−	0.134527i	$-0.0429515\pi$
$59$	2.91078	+	5.04162i	0.378951	+	0.656363i	−0.611959	+	0.790890i	$0.709618\pi$
$60$	4.43101	+	0.605118i	0.572041	+	0.0781204i
$61$	−7.04806	−	4.06920i	−0.902412	−	0.521008i	−0.0244301	−	0.999702i	$-0.507777\pi$
$61$	−7.04806	−	4.06920i	−0.902412	−	0.521008i	−0.877982	+	0.478694i	$0.841110\pi$
$62$	−0.189372	+	1.02968i	−0.0240502	+	0.130770i
$63$	2.61098	+	0.427541i	0.328952	+	0.0538651i
$64$	−3.69078	−	7.09775i	−0.461348	−	0.887219i
$65$	7.52460	−	7.03290i	0.933311	−	0.872324i
$66$	4.15169	−	1.47664i	0.511038	−	0.181762i
$67$	−2.85842	−	4.95093i	−0.349212	−	0.604852i	0.636898	−	0.770948i	$-0.280217\pi$
$67$	−2.85842	−	4.95093i	−0.349212	−	0.604852i	−0.986110	+	0.166096i	$0.946884\pi$
$68$	6.56551	−	5.34669i	0.796185	−	0.648382i
$69$		−	0.709025i		−	0.0853565i
$70$	3.31541	+	7.68167i	0.396267	+	0.918135i
$71$			9.09059i			1.07885i	0.842032	+	0.539427i	$0.181359\pi$
$71$			9.09059i			1.07885i	−0.842032	+	0.539427i	$0.818641\pi$
$72$	−1.35988	−	2.48006i	−0.160264	−	0.292278i
$73$	2.26326	+	3.92008i	0.264895	+	0.458811i	0.967536	−	0.252733i	$-0.0813294\pi$
$73$	2.26326	+	3.92008i	0.264895	+	0.458811i	−0.702641	+	0.711544i	$0.747996\pi$
$74$	−0.974315	−	2.73937i	−0.113262	−	0.318445i
$75$	2.20213	+	4.48895i	0.254280	+	0.518339i
$76$	−13.4370	−	5.11548i	−1.54132	−	0.586786i
$77$	6.37940	+	5.22138i	0.727000	+	0.595032i
$78$	−6.40658	−	1.17825i	−0.725402	−	0.133411i
$79$	−4.91560	−	2.83802i	−0.553048	−	0.319302i	0.197302	−	0.980343i	$-0.436782\pi$
$79$	−4.91560	−	2.83802i	−0.553048	−	0.319302i	−0.750350	+	0.661040i	$0.770115\pi$
$80$	4.28407	−	7.85154i	0.478974	−	0.877829i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.81016	+	2.12535i	−0.199898	+	0.234706i
$83$		−	1.15916i		−	0.127235i	−0.997974	−	0.0636173i	$-0.979736\pi$
$83$		−	1.15916i		−	0.127235i	0.997974	−	0.0636173i	$-0.0202637\pi$
$84$	2.65706	−	4.57603i	0.289909	−	0.499286i
$85$	9.05610	+	2.75741i	0.982272	+	0.299083i
$86$	−8.27186	−	7.04513i	−0.891977	−	0.759696i
$87$	8.10831	−	4.68134i	0.869302	−	0.501892i
$88$	0.194243	−	8.81081i	0.0207064	−	0.939235i
$89$	2.56797	+	1.48262i	0.272204	+	0.157157i	0.629889	−	0.776685i	$-0.283100\pi$
$89$	2.56797	+	1.48262i	0.272204	+	0.157157i	−0.357685	+	0.933842i	$0.616434\pi$
$90$	1.45310	−	2.80865i	0.153170	−	0.296058i
$91$	−4.30776	−	11.3999i	−0.451576	−	1.19503i
$92$	−1.32526	−	0.504530i	−0.138168	−	0.0526009i
$93$	0.641124	+	0.370153i	0.0664815	+	0.0383831i
$94$	6.07354	+	17.0763i	0.626438	+	1.76128i
$95$	−3.63395	−	15.6587i	−0.372836	−	1.60655i
$96$	−5.60323	+	0.777025i	−0.571878	+	0.0793048i
$97$	10.2289			1.03859			0.519295	−	0.854595i	$-0.326194\pi$
$97$	10.2289			1.03859			0.519295	+	0.854595i	$0.326194\pi$
$98$	9.89805	−	0.169318i	0.999854	−	0.0171037i
$99$		−	3.11585i		−	0.313154i
$100$	9.95742	−	0.921802i	0.995742	−	0.0921802i
$101$	11.5961	−	6.69503i	1.15386	−	0.666180i	0.204033	−	0.978964i	$-0.434595\pi$
$101$	11.5961	−	6.69503i	1.15386	−	0.666180i	0.949824	+	0.312784i	$0.101262\pi$
$102$	−2.00635	−	5.64102i	−0.198658	−	0.558544i
$103$	−2.07982	−	1.20078i	−0.204931	−	0.118317i	0.394023	−	0.919101i	$-0.371083\pi$
$103$	−2.07982	−	1.20078i	−0.204931	−	0.118317i	−0.598953	+	0.800784i	$0.704416\pi$
$104$	−6.76112	+	11.1363i	−0.662982	+	1.09200i
$105$	5.90330	−	0.388578i	0.576104	−	0.0379214i
$106$	12.2570	+	2.25422i	1.19050	+	0.218949i
$107$	−6.48146	+	11.2262i	−0.626587	+	1.08528i	0.361645	+	0.932316i	$0.382215\pi$
$107$	−6.48146	+	11.2262i	−0.626587	+	1.08528i	−0.988232	+	0.152964i	$0.951118\pi$
$108$	−1.97451	+	0.318317i	−0.189997	+	0.0306300i
$109$	3.31365	+	5.73942i	0.317391	+	0.549737i	0.979943	−	0.199279i	$-0.0638600\pi$
$109$	3.31365	+	5.73942i	0.317391	+	0.549737i	−0.662552	+	0.749016i	$0.730527\pi$
$110$	8.29670	−	5.31505i	0.791060	−	0.506770i
$111$	−2.05590			−0.195137
$112$	−6.66248	−	8.22261i	−0.629545	−	0.776964i
$113$		−	4.32878i		−	0.407217i	−0.979052	−	0.203609i	$-0.934733\pi$
$113$		−	4.32878i		−	0.407217i	0.979052	−	0.203609i	$-0.0652670\pi$
$114$	−6.59202	+	7.73985i	−0.617399	+	0.724903i
$115$	−0.358409	−	1.54438i	−0.0334218	−	0.144015i
$116$	−2.98029	−	18.4867i	−0.276713	−	1.71644i
$117$	−2.30305	+	3.98901i	−0.212917	+	0.368784i
$118$	1.48917	−	8.09713i	0.137089	−	0.745401i
$119$	7.09443	−	8.66786i	0.650346	−	0.794581i
$120$	−4.21573	−	4.71462i	−0.384842	−	0.430384i
$121$	−0.645746	+	1.11847i	−0.0587042	+	0.101679i
$122$	3.85689	+	10.8440i	0.349186	+	0.981767i
$123$	0.987027	+	1.70958i	0.0889972	+	0.154148i
$124$	1.14808	−	0.934950i	0.103100	−	0.0839610i
$125$	7.06577	+	8.66457i	0.631982	+	0.774983i
$126$	−2.41905	−	2.85451i	−0.215506	−	0.254300i
$127$	19.4705			1.72773			0.863866	−	0.503722i	$-0.168037\pi$
$127$	19.4705			1.72773			0.863866	+	0.503722i	$0.168037\pi$
$128$	−2.53480	+	11.0261i	−0.224047	+	0.974578i
$129$	−6.65369	+	3.84151i	−0.585824	+	0.338226i
$130$	−14.5503	+	0.672055i	−1.27614	+	0.0589431i
$131$	−3.24344	+	5.61779i	−0.283380	+	0.490829i	−0.972215	−	0.234089i	$-0.924789\pi$
$131$	−3.24344	+	5.61779i	−0.283380	+	0.490829i	0.688835	+	0.724918i	$0.258123\pi$
$132$	−5.82393	−	2.21718i	−0.506908	−	0.192981i
$133$	−18.7700	−	3.07354i	−1.62757	−	0.266510i
$134$	−1.46238	+	7.95148i	−0.126330	+	0.686903i
$135$	−1.52686	−	1.63361i	−0.131411	−	0.140599i
$136$	−11.9715	−	0.263923i	−1.02655	−	0.0226312i
$137$	10.1785	−	5.87654i	0.869606	−	0.502067i	0.00238847	−	0.999997i	$-0.499240\pi$
$137$	10.1785	−	5.87654i	0.869606	−	0.502067i	0.867217	+	0.497930i	$0.165906\pi$
$138$	−0.650157	+	0.763366i	−0.0553451	+	0.0649820i
$139$	−2.76292			−0.234348			−0.117174	−	0.993111i	$-0.537383\pi$
$139$	−2.76292			−0.234348			−0.117174	+	0.993111i	$0.537383\pi$
$140$	3.47439	−	11.3106i	0.293639	−	0.955916i
$141$	12.8158			1.07928
$142$	8.33584	−	9.78732i	0.699528	−	0.821333i
$143$	−12.4291	+	7.17597i	−1.03938	+	0.600085i
$144$	−0.810050	+	3.91712i	−0.0675041	+	0.326427i
$145$	15.2950	−	14.2955i	1.27018	−	1.18718i
$146$	1.15789	−	6.29588i	0.0958280	−	0.521051i
$147$	2.23260	−	6.63442i	0.184142	−	0.547198i
$148$	−1.46294	+	3.84274i	−0.120253	+	0.315871i
$149$	−3.90602	+	6.76543i	−0.319994	+	0.554246i	−0.980486	−	0.196587i	$-0.937014\pi$
$149$	−3.90602	+	6.76543i	−0.319994	+	0.554246i	0.660493	+	0.750833i	$0.270348\pi$
$150$	1.74535	−	6.85228i	0.142507	−	0.559486i
$151$	3.66936	−	2.11851i	0.298608	−	0.172402i	−0.343209	−	0.939259i	$-0.611514\pi$
$151$	3.66936	−	2.11851i	0.298608	−	0.172402i	0.641818	+	0.766857i	$0.278181\pi$
$152$	9.77603	+	17.8289i	0.792940	+	1.44611i
$153$	−4.23359			−0.342265
$154$	−2.08045	−	11.4713i	−0.167648	−	0.924384i
$155$	1.58360	+	0.482175i	0.127198	+	0.0387292i
$156$	5.81716	+	7.14322i	0.465746	+	0.571915i
$157$	−1.64193	−	2.84391i	−0.131040	−	0.226969i	0.793038	−	0.609173i	$-0.208498\pi$
$157$	−1.64193	−	2.84391i	−0.131040	−	0.226969i	−0.924078	+	0.382204i	$0.875165\pi$
$158$	2.68995	+	7.56301i	0.214001	+	0.601681i
$159$	4.40618	−	7.63173i	0.349433	−	0.605235i
$160$	−11.8121	+	4.52492i	−0.933827	+	0.357726i
$161$	−1.85125	−	0.303137i	−0.145899	−	0.0238905i
$162$	−0.255802	+	1.39089i	−0.0200977	+	0.109278i
$163$	−7.86075	+	13.6152i	−0.615702	+	1.06643i	0.374559	+	0.927203i	$0.377794\pi$
$163$	−7.86075	+	13.6152i	−0.615702	+	1.06643i	−0.990261	+	0.139224i	$0.955539\pi$
$164$	3.89778	−	0.628374i	0.304366	−	0.0490677i
$165$	−1.57505	−	6.78688i	−0.122617	−	0.528358i
$166$	−1.06292	+	1.24800i	−0.0824988	+	0.0968638i
$167$			21.1913i			1.63983i	0.572482	+	0.819917i	$0.305981\pi$
$167$			21.1913i			1.63983i	−0.572482	+	0.819917i	$0.694019\pi$
$168$	−7.05680	+	2.49029i	−0.544444	+	0.192130i
$169$	8.21624			0.632019
$170$	−7.22170	−	11.2730i	−0.553879	−	0.864596i
$171$	3.59444	+	6.22575i	0.274874	+	0.476095i
$172$	2.44563	+	15.1702i	0.186478	+	1.15671i
$173$	−7.82442	+	13.5523i	−0.594879	+	1.03036i	0.398684	+	0.917088i	$0.369467\pi$
$173$	−7.82442	+	13.5523i	−0.594879	+	1.03036i	−0.993564	+	0.113273i	$0.963866\pi$
$174$	−13.0224	−	2.39499i	−0.987227	−	0.181564i
$175$	12.6620	−	3.83049i	0.957160	−	0.289558i
$176$	−8.28841	+	9.30797i	−0.624763	+	0.701615i
$177$	−5.04162	−	2.91078i	−0.378951	−	0.218788i
$178$	−1.40526	−	3.95101i	−0.105329	−	0.296141i
$179$	−3.67305	+	2.12064i	−0.274537	+	0.158504i	−0.630948	−	0.775825i	$-0.717334\pi$
$179$	−3.67305	+	2.12064i	−0.274537	+	0.158504i	0.356411	+	0.934329i	$0.384000\pi$
$180$	−4.13992	+	1.69146i	−0.308572	+	0.126074i
$181$			7.53922i			0.560386i	0.959944	+	0.280193i	$0.0903985\pi$
$181$			7.53922i			0.560386i	−0.959944	+	0.280193i	$0.909602\pi$
$182$	−5.81546	+	16.2237i	−0.431071	+	1.20258i
$183$	8.13840			0.601608
$184$	0.964190	+	1.75843i	0.0710810	+	0.129633i
$185$	−4.47812	+	1.03925i	−0.329238	+	0.0764071i
$186$	−0.350840	−	0.986417i	−0.0257249	−	0.0723276i
$187$	−11.4239	−	6.59561i	−0.835400	−	0.482318i
$188$	9.11947	−	23.9543i	0.665106	−	1.74705i
$189$	−2.47494	+	0.935228i	−0.180026	+	0.0680278i
$190$	−10.4461	+	20.1910i	−0.757843	+	1.46481i
$191$	2.83230	+	1.63523i	0.204938	+	0.118321i	0.598957	−	0.800781i	$-0.295582\pi$
$191$	2.83230	+	1.63523i	0.204938	+	0.118321i	−0.394019	+	0.919102i	$0.628915\pi$
$192$	6.74519	+	4.30144i	0.486792	+	0.310430i
$193$	−5.38729	+	3.11035i	−0.387785	+	0.223888i	−0.681200	−	0.732097i	$-0.738542\pi$
$193$	−5.38729	+	3.11035i	−0.387785	+	0.223888i	0.293415	+	0.955985i	$0.405208\pi$
$194$	−11.0129	−	9.37967i	−0.790680	−	0.673421i
$195$	−3.00004	+	9.85297i	−0.214837	+	0.705586i
$196$	−10.8119	−	8.89396i	−0.772280	−	0.635283i
$197$			8.05847i			0.574142i	0.957909	+	0.287071i	$0.0926816\pi$
$197$			8.05847i			0.574142i	−0.957909	+	0.287071i	$0.907318\pi$
$198$	−2.85715	+	3.35465i	−0.203049	+	0.238405i
$199$	13.9067	+	24.0871i	0.985819	+	1.70749i	0.638240	+	0.769838i	$0.279663\pi$
$199$	13.9067	+	24.0871i	0.985819	+	1.70749i	0.347579	+	0.937651i	$0.387004\pi$
$200$	−11.5658	−	8.13825i	−0.817829	−	0.575461i
$201$	4.95093	+	2.85842i	0.349212	+	0.201617i
$202$	−18.6240	−	3.42520i	−1.31038	−	0.240996i
$203$	−8.75623	−	23.1721i	−0.614567	−	1.62636i
$204$	−3.01255	+	7.91313i	−0.210921	+	0.554030i
$205$	3.01411	+	3.22484i	0.210515	+	0.225232i
$206$	1.13813	+	3.19995i	0.0792974	+	0.222951i
$207$	0.354512	+	0.614033i	0.0246403	+	0.0426783i
$208$	17.4910	−	5.79004i	1.21278	−	0.401467i
$209$			22.3995i			1.54940i
$210$	−6.71206	−	4.99482i	−0.463176	−	0.344675i
$211$		−	13.8146i		−	0.951037i	−0.879706	−	0.475519i	$-0.842260\pi$
$211$		−	13.8146i		−	0.951037i	0.879706	−	0.475519i	$-0.157740\pi$
$212$	−11.1293	−	13.6663i	−0.764366	−	0.938608i
$213$	−4.54530	−	7.87268i	−0.311439	−	0.539427i
$214$	17.2724	−	6.14329i	1.18071	−	0.419947i
$215$	−12.5511	+	11.7309i	−0.855976	+	0.800042i
$216$	2.41772	+	1.46786i	0.164505	+	0.0998751i
$217$	1.24057	−	1.51571i	0.0842153	−	0.102893i
$218$	1.69528	−	9.21784i	0.114819	−	0.624311i
$219$	−3.92008	−	2.26326i	−0.264895	−	0.152937i
$220$	−13.8063	−	1.88546i	−0.930824	−	0.127117i
$221$	9.75018	+	16.8878i	0.655868	+	1.13600i
$222$	2.21347	+	1.88521i	0.148558	+	0.126527i
$223$			12.1377i			0.812803i	0.913695	+	0.406402i	$0.133217\pi$
$223$			12.1377i			0.812803i	−0.913695	+	0.406402i	$0.866783\pi$
$224$	−0.366816	+	14.9621i	−0.0245089	+	0.999700i
$225$	−4.15157	−	2.78648i	−0.276771	−	0.185765i
$226$	−3.96938	+	4.66055i	−0.264039	+	0.310015i
$227$	−3.61577	+	2.08757i	−0.239987	+	0.138557i	−0.615171	−	0.788394i	$-0.710913\pi$
$227$	−3.61577	+	2.08757i	−0.239987	+	0.138557i	0.375184	+	0.926951i	$0.377580\pi$
$228$	14.1945	−	2.28834i	0.940053	−	0.151549i
$229$	−1.82163	−	1.05172i	−0.120376	−	0.0694994i	0.438603	−	0.898681i	$-0.355474\pi$
$229$	−1.82163	−	1.05172i	−0.120376	−	0.0694994i	−0.558979	+	0.829182i	$0.688807\pi$
$230$	−1.03028	+	1.99140i	−0.0679348	+	0.131309i
$231$	−8.13541	−	1.33215i	−0.535271	−	0.0876492i
$232$	−13.7431	+	22.6364i	−0.902277	+	1.48615i
$233$	−13.0248	−	7.51987i	−0.853282	−	0.492643i	0.00847469	−	0.999964i	$-0.497302\pi$
$233$	−13.0248	−	7.51987i	−0.853282	−	0.492643i	−0.861757	+	0.507321i	$0.830636\pi$
$234$	6.13738	−	2.18289i	0.401213	−	0.142700i
$235$	27.9150	−	6.47832i	1.82098	−	0.422599i
$236$	−9.02816	+	7.35218i	−0.587683	+	0.478586i
$237$	5.67604			0.368699
$238$	−15.5864	+	2.82677i	−1.01031	+	0.183232i
$239$		−	10.0923i		−	0.652819i	−0.945228	−	0.326410i	$-0.894161\pi$
$239$		−	10.0923i		−	0.652819i	0.945228	−	0.326410i	$-0.105839\pi$
$240$	0.215654	+	8.94167i	0.0139204	+	0.577182i
$241$	4.55972	−	2.63255i	0.293717	−	0.169578i	−0.345900	−	0.938271i	$-0.612426\pi$
$241$	4.55972	−	2.63255i	0.293717	−	0.169578i	0.639617	+	0.768694i	$0.279093\pi$
$242$	1.72084	−	0.612054i	0.110620	−	0.0393443i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	5.79115	−	15.2117i	0.370740	−	0.973832i
$245$	1.50933	−	15.5795i	0.0964278	−	0.995340i
$246$	0.504967	−	2.74568i	0.0321955	−	0.175058i
$247$	16.5564	−	28.6765i	1.05346	−	1.82464i
$248$	−2.09339	−	0.0461510i	−0.132931	−	0.00293059i
$249$	0.579581	+	1.00386i	0.0367295	+	0.0636173i
$250$	0.337882	−	15.8078i	0.0213695	−	0.999772i
$251$	−7.74554			−0.488894			−0.244447	−	0.969663i	$-0.578606\pi$
$251$	−7.74554			−0.488894			−0.244447	+	0.969663i	$0.578606\pi$
$252$	−0.0130645	+	5.29149i	−0.000822987	+	0.333332i
$253$			2.20921i			0.138892i
$254$	−20.9628	−	17.8540i	−1.31532	−	1.12026i
$255$	−9.22152	+	2.14006i	−0.577474	+	0.134016i
$256$	12.8397	−	9.54681i	0.802483	−	0.596675i
$257$	−1.71375	+	2.96829i	−0.106901	+	0.185157i	−0.914513	−	0.404556i	$-0.867426\pi$
$257$	−1.71375	+	2.96829i	−0.106901	+	0.185157i	0.807613	+	0.589713i	$0.200759\pi$
$258$	10.6862	+	1.96533i	0.665294	+	0.122356i
$259$	−0.878980	+	5.36791i	−0.0546172	+	0.333545i
$260$	16.2817	+	12.6187i	1.00975	+	0.782577i
$261$	−4.68134	+	8.10831i	−0.289767	+	0.501892i
$262$	8.64339	−	3.07421i	0.533991	−	0.189925i
$263$	−1.28700	−	2.22915i	−0.0793598	−	0.137455i	0.823614	−	0.567151i	$-0.191954\pi$
$263$	−1.28700	−	2.22915i	−0.0793598	−	0.137455i	−0.902974	+	0.429695i	$0.858621\pi$
$264$	4.23718	+	7.72750i	0.260781	+	0.475595i
$265$	5.73965	−	18.8506i	0.352584	−	1.15798i
$266$	17.3902	+	20.5207i	1.06626	+	1.25821i
$267$	−2.96524			−0.181470
$268$	8.86576	−	7.21993i	0.541563	−	0.441028i
$269$	24.8309	−	14.3361i	1.51397	−	0.874089i	0.514100	−	0.857730i	$-0.328126\pi$
$269$	24.8309	−	14.3361i	1.51397	−	0.874089i	0.999866	−	0.0163587i	$-0.00520736\pi$
$270$	0.145905	+	3.15891i	0.00887950	+	0.192245i
$271$	7.12103	−	12.3340i	0.432572	−	0.749236i	−0.564522	−	0.825418i	$-0.690940\pi$
$271$	7.12103	−	12.3340i	0.432572	−	0.749236i	0.997094	+	0.0761816i	$0.0242729\pi$
$272$	12.6470	+	11.2617i	0.766836	+	0.682840i
$273$	9.43056	+	7.71869i	0.570764	+	0.467156i
$274$	−16.3472	−	3.00646i	−0.987571	−	0.181627i
$275$	−6.86149	−	13.9869i	−0.413763	−	0.843440i
$276$	1.39997	−	0.225694i	0.0842685	−	0.0135852i
$277$	−24.7318	+	14.2789i	−1.48599	+	0.857937i	−0.999873	−	0.0159562i	$-0.994921\pi$
$277$	−24.7318	+	14.2789i	−1.48599	+	0.857937i	−0.486118	+	0.873893i	$0.661587\pi$
$278$	2.97468	+	2.53353i	0.178409	+	0.151951i
$279$	−0.740307			−0.0443210
$280$	−14.1122	+	8.99150i	−0.843363	+	0.537345i
$281$	−23.8188			−1.42091			−0.710454	−	0.703743i	$-0.751511\pi$
$281$	−23.8188			−1.42091			−0.710454	+	0.703743i	$0.751511\pi$
$282$	−13.7980	−	11.7517i	−0.821658	−	0.699805i
$283$	10.7778	−	6.22256i	0.640673	−	0.369893i	−0.144200	−	0.989548i	$-0.546061\pi$
$283$	10.7778	−	6.22256i	0.640673	−	0.369893i	0.784874	+	0.619656i	$0.212728\pi$
$284$	−17.9494	+	2.89369i	−1.06510	+	0.171709i
$285$	10.9764	+	11.7438i	0.650188	+	0.695645i
$286$	19.9619	+	3.67125i	1.18037	+	0.217086i
$287$	4.88567	−	1.84619i	0.288392	−	0.108977i
$288$	4.46403	−	3.47454i	0.263046	−	0.204739i
$289$	−0.461627	+	0.799562i	−0.0271546	+	0.0470331i
$290$	−29.5758	+	1.36606i	−1.73675	+	0.0802179i
$291$	−8.85852	+	5.11447i	−0.519295	+	0.299815i
$292$	−7.01980	+	5.71665i	−0.410803	+	0.334542i
$293$	−18.4199			−1.07610			−0.538051	−	0.842912i	$-0.680839\pi$
$293$	−18.4199			−1.07610			−0.538051	+	0.842912i	$0.680839\pi$
$294$	−8.48730	+	5.09566i	−0.494989	+	0.297185i
$295$	−12.4529	−	3.79169i	−0.725038	−	0.220760i
$296$	5.09876	−	2.79578i	0.296359	−	0.162501i
$297$	1.55792	+	2.69840i	0.0903999	+	0.156577i
$298$	10.4091	−	3.70222i	0.602984	−	0.214464i
$299$	1.63292	−	2.82830i	0.0944343	−	0.163565i
$300$	−8.16248	+	5.77702i	−0.471261	+	0.333536i
$301$	7.18537	+	19.0150i	0.414158	+	1.09601i
$302$	−5.89321	−	1.08384i	−0.339116	−	0.0623678i
$303$	−6.69503	+	11.5961i	−0.384619	+	0.666180i
$304$	5.82335	−	28.1597i	0.333992	−	1.61507i
$305$	17.7269	−	4.11393i	1.01504	−	0.235563i
$306$	4.55806	+	3.88209i	0.260567	+	0.221924i
$307$			16.3428i			0.932733i	0.884592	+	0.466367i	$0.154437\pi$
$307$			16.3428i			0.932733i	−0.884592	+	0.466367i	$0.845563\pi$
$308$	−8.27899	+	14.2582i	−0.471739	+	0.812437i
$309$	2.40157			0.136620
$310$	−1.26282	−	1.97125i	−0.0717236	−	0.111959i
$311$	1.16241	+	2.01336i	0.0659145	+	0.114167i	0.897099	−	0.441829i	$-0.145670\pi$
$311$	1.16241	+	2.01336i	0.0659145	+	0.114167i	−0.831185	+	0.555996i	$0.812337\pi$
$312$	0.287146	−	13.0249i	0.0162565	−	0.737389i
$313$	3.09996	−	5.36930i	0.175220	−	0.303491i	−0.765017	−	0.644010i	$-0.777270\pi$
$313$	3.09996	−	5.36930i	0.175220	−	0.303491i	0.940238	+	0.340519i	$0.110603\pi$
$314$	−0.840018	+	4.56748i	−0.0474050	+	0.257758i
$315$	−4.91812	+	3.28817i	−0.277105	+	0.185267i
$316$	4.03898	−	10.6093i	0.227210	−	0.596818i
$317$	−0.779600	−	0.450102i	−0.0437867	−	0.0252803i	0.477947	−	0.878389i	$-0.341381\pi$
$317$	−0.779600	−	0.450102i	−0.0437867	−	0.0252803i	−0.521734	+	0.853108i	$0.674714\pi$
$318$	−11.7420	+	4.17629i	−0.658457	+	0.234195i
$319$	−25.2643	+	14.5863i	−1.41453	+	0.816678i
$320$	16.8666	+	5.95966i	0.942872	+	0.333155i
$321$		−	12.9629i		−	0.723520i
$322$	1.71516	+	2.02392i	0.0955823	+	0.112788i
$323$	30.4347			1.69343
$324$	1.55081	−	1.26292i	0.0861563	−	0.0701624i
$325$	−1.55400	+	22.9781i	−0.0862002	+	1.27459i
$326$	20.9480	−	7.45062i	1.16020	−	0.412651i
$327$	−5.73942	−	3.31365i	−0.317391	−	0.183246i
$328$	−4.77272	−	2.89763i	−0.263529	−	0.159995i
$329$	5.47926	−	33.4617i	0.302081	−	1.84480i
$330$	−4.52763	+	8.75132i	−0.249238	+	0.481744i
$331$	19.5002	+	11.2584i	1.07183	+	0.618819i	0.928680	−	0.370883i	$-0.120945\pi$
$331$	19.5002	+	11.2584i	1.07183	+	0.618819i	0.143146	+	0.989702i	$0.454278\pi$
$332$	2.28877	−	0.368981i	0.125613	−	0.0202504i
$333$	1.78046	−	1.02795i	0.0975686	−	0.0563313i
$334$	19.4319	−	22.8155i	1.06327	−	1.24841i
$335$	12.2289	+	3.72348i	0.668139	+	0.203436i
$336$	9.88118	+	3.78975i	0.539063	+	0.206748i
$337$		−	9.29942i		−	0.506572i	−0.967391	−	0.253286i	$-0.918489\pi$
$337$		−	9.29942i		−	0.506572i	0.967391	−	0.253286i	$-0.0815113\pi$
$338$	−8.84595	−	7.53408i	−0.481156	−	0.409800i
$339$	2.16439	+	3.74883i	0.117554	+	0.203609i
$340$	−2.56182	+	18.7591i	−0.138934	+	1.01735i
$341$	−1.99765	−	1.15334i	−0.108179	−	0.0624569i
$342$	1.83893	−	9.99892i	0.0994379	−	0.540679i
$343$	−16.3678	−	8.66576i	−0.883778	−	0.467907i
$344$	11.2776	−	18.5754i	0.608046	−	1.00152i
$345$	1.08258	+	1.15827i	0.0582843	+	0.0623592i
$346$	20.8512	−	7.41618i	1.12097	−	0.398696i
$347$	5.47992	+	9.49151i	0.294178	+	0.509531i	0.974793	−	0.223110i	$-0.0716209\pi$
$347$	5.47992	+	9.49151i	0.294178	+	0.509531i	−0.680616	+	0.732641i	$0.738288\pi$
$348$	11.8243	+	14.5198i	0.633851	+	0.778341i
$349$		−	19.6471i		−	1.05169i	−0.850582	−	0.525843i	$-0.823750\pi$
$349$		−	19.6471i		−	1.05169i	0.850582	−	0.525843i	$-0.176250\pi$
$350$	−17.1450	−	7.48670i	−0.916436	−	0.400181i
$351$		−	4.60611i		−	0.245856i
$352$	17.4588	−	2.42109i	0.930558	−	0.129045i
$353$	−1.13259	−	1.96170i	−0.0602815	−	0.104411i	0.834310	−	0.551296i	$-0.185867\pi$
$353$	−1.13259	−	1.96170i	−0.0602815	−	0.104411i	−0.894591	+	0.446885i	$0.852533\pi$
$354$	2.75891	+	7.75690i	0.146634	+	0.412275i
$355$	−13.8801	−	14.8505i	−0.736679	−	0.788183i
$356$	−2.11001	+	5.54242i	−0.111830	+	0.293747i
$357$	−1.81003	+	11.0538i	−0.0957970	+	0.585029i
$358$	5.89913	+	1.08493i	0.311779	+	0.0573402i
$359$	−11.1493	−	6.43708i	−0.588440	−	0.339736i	0.176041	−	0.984383i	$-0.443671\pi$
$359$	−11.1493	−	6.43708i	−0.588440	−	0.339736i	−0.764480	+	0.644647i	$0.777004\pi$
$360$	6.00824	+	1.97511i	0.316662	+	0.104097i
$361$	−16.3400	−	28.3017i	−0.860000	−	1.48956i
$362$	6.91327	−	8.11705i	0.363354	−	0.426622i
$363$		−	1.29149i		−	0.0677858i
$364$	21.1379	−	12.1345i	1.10793	−	0.636019i
$365$	−9.68273	−	2.94821i	−0.506817	−	0.154316i
$366$	−8.76215	−	7.46271i	−0.458005	−	0.390082i
$367$	−27.5936	+	15.9312i	−1.44038	+	0.831602i	−0.997874	−	0.0651656i	$-0.979242\pi$
$367$	−27.5936	+	15.9312i	−1.44038	+	0.831602i	−0.442502	+	0.896767i	$0.645909\pi$
$368$	0.574345	−	2.77733i	0.0299398	−	0.144779i
$369$	−1.70958	−	0.987027i	−0.0889972	−	0.0513826i
$370$	5.77429	+	2.98742i	0.300191	+	0.155309i
$371$	−18.0425	−	14.7673i	−0.936718	−	0.766681i
$372$	−0.526790	+	1.38373i	−0.0273128	+	0.0717431i
$373$	6.62525	+	3.82509i	0.343042	+	0.198056i	0.661617	−	0.749842i	$-0.269871\pi$
$373$	6.62525	+	3.82509i	0.343042	+	0.198056i	−0.318574	+	0.947898i	$0.603204\pi$
$374$	6.25148	+	17.5766i	0.323256	+	0.908862i
$375$	−10.4514	−	3.97085i	−0.539709	−	0.205054i
$376$	−31.7839	+	17.4279i	−1.63913	+	0.898776i
$377$	43.1255			2.22108
$378$	3.52221	+	1.26255i	0.181163	+	0.0649388i
$379$		−	14.2552i		−	0.732240i	−0.930568	−	0.366120i	$-0.880686\pi$
$379$		−	14.2552i		−	0.732240i	0.930568	−	0.366120i	$-0.119314\pi$
$380$	29.7614	−	12.1597i	1.52673	−	0.623778i
$381$	−16.8620	+	9.73527i	−0.863866	+	0.498753i
$382$	−1.54991	−	4.35770i	−0.0793003	−	0.222959i
$383$	10.6824	+	6.16751i	0.545847	+	0.315145i	0.747445	−	0.664323i	$-0.231280\pi$
$383$	10.6824	+	6.16751i	0.545847	+	0.315145i	−0.201598	+	0.979468i	$0.564614\pi$
$384$	−3.31784	−	10.8163i	−0.169313	−	0.551966i
$385$	−18.3938	+	1.21075i	−0.937435	+	0.0617056i
$386$	8.65229	+	1.59127i	0.440390	+	0.0809934i
$387$	3.84151	−	6.65369i	0.195275	−	0.338226i
$388$	3.25604	+	20.1971i	0.165300	+	1.02535i
$389$	−7.85606	−	13.6071i	−0.398318	−	0.689907i	0.595201	−	0.803577i	$-0.297073\pi$
$389$	−7.85606	−	13.6071i	−0.398318	−	0.689907i	−0.993519	+	0.113670i	$0.963739\pi$
$390$	12.2649	−	7.85716i	0.621057	−	0.397863i
$391$	3.00172			0.151803
$392$	3.48503	+	19.4899i	0.176021	+	0.984386i
$393$		−	6.48687i		−	0.327219i
$394$	7.38941	−	8.67608i	0.372273	−	0.437095i
$395$	12.3635	−	2.86922i	0.622073	−	0.144366i
$396$	6.15226	−	0.991826i	0.309163	−	0.0498411i
$397$	13.4814	−	23.3504i	0.676611	−	1.17192i	−0.299384	−	0.954133i	$-0.596781\pi$
$397$	13.4814	−	23.3504i	0.676611	−	1.17192i	0.975995	−	0.217792i	$-0.0698855\pi$
$398$	7.11471	−	38.6852i	0.356628	−	1.93912i
$399$	17.7921	−	6.72324i	0.890718	−	0.336583i
$400$	4.98972	+	19.3676i	0.249486	+	0.968378i
$401$	−1.45224	+	2.51535i	−0.0725214	+	0.125611i	−0.900006	−	0.435878i	$-0.856438\pi$
$401$	−1.45224	+	2.51535i	−0.0725214	+	0.125611i	0.827484	+	0.561489i	$0.189771\pi$
$402$	−2.70928	−	7.61737i	−0.135127	−	0.379920i
$403$	1.70497	+	2.95309i	0.0849304	+	0.147104i
$404$	16.9106	+	20.7655i	0.841334	+	1.03312i
$405$	2.13911	+	0.651318i	0.106293	+	0.0323643i
$406$	−11.8209	+	32.9773i	−0.586660	+	1.63664i
$407$	6.40586			0.317527
$408$	10.4996	−	5.75718i	0.519806	−	0.285023i
$409$	−3.89199	+	2.24704i	−0.192446	+	0.111109i	−0.593127	−	0.805109i	$-0.702107\pi$
$409$	−3.89199	+	2.24704i	−0.192446	+	0.111109i	0.400681	+	0.916218i	$0.368774\pi$
$410$	−0.288024	−	6.23586i	−0.0142245	−	0.307967i
$411$	−5.87654	+	10.1785i	−0.289869	+	0.502067i
$412$	1.70891	−	4.48884i	0.0841922	−	0.221149i
$413$	−9.75548	+	11.9191i	−0.480036	+	0.586499i
$414$	0.181370	−	0.986173i	0.00891384	−	0.0484677i
$415$	1.76988	+	1.89362i	0.0868801	+	0.0929542i
$416$	−24.1409	−	9.80500i	−1.18360	−	0.480729i
$417$	2.39276	−	1.38146i	0.117174	−	0.0676504i
$418$	20.5397	−	24.1162i	1.00463	−	1.17956i
$419$	38.7751			1.89429			0.947145	−	0.320807i	$-0.103954\pi$
$419$	38.7751			1.89429			0.947145	+	0.320807i	$0.103954\pi$
$420$	2.64637	+	11.5324i	0.129130	+	0.562725i
$421$	−1.51063			−0.0736237			−0.0368118	−	0.999322i	$-0.511720\pi$
$421$	−1.51063			−0.0736237			−0.0368118	+	0.999322i	$0.511720\pi$
$422$	−12.6676	+	14.8734i	−0.616651	+	0.724025i
$423$	−11.0988	+	6.40788i	−0.539641	+	0.311562i
$424$	−0.549365	+	24.9191i	−0.0266795	+	1.21018i
$425$	−19.0043	+	9.32289i	−0.921846	+	0.452226i
$426$	−2.32539	+	12.6440i	−0.112666	+	0.612603i
$427$	3.47950	−	21.2492i	0.168385	−	1.02832i
$428$	−24.2294	−	9.22420i	−1.17117	−	0.445868i
$429$	7.17597	−	12.4291i	0.346459	−	0.600085i
$430$	24.2700	−	1.12099i	1.17040	−	0.0540590i
$431$	−22.2616	+	12.8527i	−1.07230	+	0.619093i	−0.928809	−	0.370558i	$-0.879166\pi$
$431$	−22.2616	+	12.8527i	−1.07230	+	0.619093i	−0.143492	+	0.989651i	$0.545833\pi$
$432$	−1.25704	−	3.79735i	−0.0604792	−	0.182700i
$433$	−11.3336			−0.544656			−0.272328	−	0.962205i	$-0.587794\pi$
$433$	−11.3336			−0.544656			−0.272328	+	0.962205i	$0.587794\pi$
$434$	−2.72551	+	0.494303i	−0.130829	+	0.0237273i
$435$	−6.09808	+	20.0278i	−0.292380	+	0.960258i
$436$	−10.2777	+	8.36978i	−0.492214	+	0.400840i
$437$	−2.54855	−	4.41421i	−0.121914	−	0.211160i
$438$	2.14518	+	6.03134i	0.102500	+	0.288189i
$439$	−17.4426	+	30.2115i	−0.832491	+	1.44192i	0.0635656	+	0.997978i	$0.479753\pi$
$439$	−17.4426	+	30.2115i	−0.832491	+	1.44192i	−0.896057	+	0.443939i	$0.853581\pi$
$440$	13.1356	+	14.6900i	0.626214	+	0.700319i
$441$	1.38372	+	6.86187i	0.0658915	+	0.326756i
$442$	4.98823	−	27.1228i	0.237266	−	1.29010i
$443$	0.0799173	−	0.138421i	0.00379699	−	0.00657658i	−0.864121	−	0.503285i	$-0.832125\pi$
$443$	0.0799173	−	0.138421i	0.00379699	−	0.00657658i	0.867918	+	0.496708i	$0.165458\pi$
$444$	−0.654426	−	4.05938i	−0.0310577	−	0.192650i
$445$	−6.45882	+	1.49892i	−0.306178	+	0.0710554i
$446$	11.1300	−	13.0680i	0.527020	−	0.618788i
$447$		−	7.81205i		−	0.369497i
$448$	14.1148	−	15.7725i	0.666863	−	0.745181i
$449$	−14.9152			−0.703892			−0.351946	−	0.936020i	$-0.614480\pi$
$449$	−14.9152			−0.703892			−0.351946	+	0.936020i	$0.614480\pi$
$450$	1.91462	+	6.80692i	0.0902563	+	0.320881i
$451$	−3.07542	−	5.32679i	−0.144816	−	0.250829i
$452$	8.54720	−	1.37792i	0.402027	−	0.0648120i
$453$	−2.11851	+	3.66936i	−0.0995362	+	0.172402i
$454$	5.80714	+	1.06801i	0.272543	+	0.0501241i
$455$	24.4432	+	12.0456i	1.14592	+	0.564706i
$456$	−17.3807	−	10.5523i	−0.813927	−	0.494155i
$457$	24.2021	+	13.9731i	1.13212	+	0.653633i	0.944468	−	0.328602i	$-0.106578\pi$
$457$	24.2021	+	13.9731i	1.13212	+	0.653633i	0.187656	+	0.982235i	$0.439911\pi$
$458$	0.996843	+	2.80271i	0.0465794	+	0.130962i
$459$	3.66639	−	2.11679i	0.171133	−	0.0988034i
$460$	2.93531	−	1.19928i	0.136859	−	0.0559169i
$461$		−	14.2305i		−	0.662780i	−0.943494	−	0.331390i	$-0.892482\pi$
$461$		−	14.2305i		−	0.662780i	0.943494	−	0.331390i	$-0.107518\pi$
$462$	7.53738	+	8.89421i	0.350671	+	0.413796i
$463$	36.9235			1.71598			0.857990	−	0.513666i	$-0.171713\pi$
$463$	36.9235			1.71598			0.857990	+	0.513666i	$0.171713\pi$
$464$	35.5533	−	11.7692i	1.65052	−	0.546372i
$465$	−1.61252	+	0.374222i	−0.0747789	+	0.0173541i
$466$	7.12751	+	20.0396i	0.330176	+	0.928317i
$467$	15.8517	+	9.15196i	0.733527	+	0.423502i	0.819711	−	0.572777i	$-0.194134\pi$
$467$	15.8517	+	9.15196i	0.733527	+	0.423502i	−0.0861839	+	0.996279i	$0.527467\pi$
$468$	−8.60942	−	3.27763i	−0.397971	−	0.151508i
$469$	9.58000	−	11.7047i	0.442363	−	0.540472i
$470$	−35.9950	−	18.6225i	−1.66032	−	0.858994i
$471$	2.84391	+	1.64193i	0.131040	+	0.0756562i
$472$	16.4619	+	0.362918i	0.757718	+	0.0167046i
$473$	20.7319	−	11.9696i	0.953253	−	0.550361i
$474$	−6.11107	−	5.20479i	−0.280691	−	0.239064i
$475$	29.8451	+	20.0317i	1.36939	+	0.919116i
$476$	19.3730	+	11.2489i	0.887961	+	0.515592i
$477$			8.81236i			0.403490i
$478$	−9.25441	+	10.8658i	−0.423287	+	0.496992i
$479$	−11.0819	−	19.1944i	−0.506345	−	0.877015i	−0.999973	−	0.00734170i	$-0.997663\pi$
$479$	−11.0819	−	19.1944i	−0.506345	−	0.877015i	0.493628	−	0.869673i	$-0.335670\pi$
$480$	7.96710	−	9.82473i	0.363647	−	0.448436i
$481$	−8.20099	−	4.73484i	−0.373933	−	0.215890i
$482$	−7.32317	−	1.34682i	−0.333561	−	0.0613462i
$483$	1.75480	−	0.663100i	0.0798460	−	0.0301721i
$484$	−2.41397	−	0.919004i	−0.109726	−	0.0417729i
$485$	−16.7101	+	15.6182i	−0.758767	+	0.709185i
$486$	−0.473912	−	1.33244i	−0.0214971	−	0.0604409i
$487$	−0.742553	−	1.28614i	−0.0336483	−	0.0582805i	0.848711	−	0.528857i	$-0.177379\pi$
$487$	−0.742553	−	1.28614i	−0.0336483	−	0.0582805i	−0.882359	+	0.470577i	$0.844046\pi$
$488$	−20.1838	+	11.0673i	−0.913676	+	0.500992i
$489$		−	15.7215i		−	0.710951i
$490$	−15.9110	+	15.3896i	−0.718788	+	0.695230i
$491$			22.0995i			0.997336i	0.866793	+	0.498668i	$0.166177\pi$
$491$			22.0995i			0.997336i	−0.866793	+	0.498668i	$0.833823\pi$
$492$	−3.06139	+	2.49308i	−0.138018	+	0.112397i
$493$	19.8188	+	34.3272i	0.892596	+	1.54602i
$494$	−44.1209	+	15.6925i	−1.98509	+	0.706041i
$495$	4.75747	+	5.09009i	0.213833	+	0.228782i
$496$	2.21152	+	1.96928i	0.0993001	+	0.0884231i
$497$	−22.4987	+	8.50178i	−1.00921	+	0.381357i
$498$	0.296516	−	1.61226i	0.0132872	−	0.0722473i
$499$	−16.8812	−	9.74638i	−0.755708	−	0.436308i	0.0720449	−	0.997401i	$-0.477048\pi$
$499$	−16.8812	−	9.74638i	−0.755708	−	0.436308i	−0.827753	+	0.561093i	$0.810381\pi$
$500$	−14.8591	+	16.7095i	−0.664519	+	0.747271i
$501$	−10.5957	−	18.3522i	−0.473379	−	0.819917i
$502$	8.33918	+	7.10246i	0.372196	+	0.316998i
$503$		−	7.53881i		−	0.336139i	−0.985775	−	0.168069i	$-0.946247\pi$
$503$		−	7.53881i		−	0.336139i	0.985775	−	0.168069i	$-0.0537533\pi$
$504$	4.86622	−	5.68506i	0.216759	−	0.253233i
$505$	−8.72118	+	28.6428i	−0.388087	+	1.27459i
$506$	2.02579	−	2.37853i	0.0900574	−	0.105739i
$507$	−7.11547	+	4.10812i	−0.316009	+	0.182448i
$508$	6.19780	+	38.4447i	0.274983	+	1.70571i
$509$	−3.96461	−	2.28897i	−0.175728	−	0.101457i	0.409556	−	0.912285i	$-0.365684\pi$
$509$	−3.96461	−	2.28897i	−0.175728	−	0.101457i	−0.585284	+	0.810828i	$0.699017\pi$
$510$	11.8907	+	6.15181i	0.526527	+	0.272407i
$511$	−7.58533	+	9.26762i	−0.335555	+	0.409975i
$512$	−22.5780	−	1.49520i	−0.997814	−	0.0660791i
$513$	−6.22575	−	3.59444i	−0.274874	−	0.158698i
$514$	4.56694	−	1.62433i	0.201439	−	0.0716461i
$515$	5.23105	−	1.21398i	0.230508	−	0.0534945i
$516$	−9.70306	−	11.9149i	−0.427153	−	0.524526i
$517$	−39.9319			−1.75620
$518$	5.86858	−	4.97331i	0.257851	−	0.218515i
$519$		−	15.6488i		−	0.686908i
$520$	−5.95857	−	28.5157i	−0.261301	−	1.25050i
$521$	−2.52195	+	1.45605i	−0.110489	+	0.0637906i	−0.554226	−	0.832366i	$-0.686986\pi$
$521$	−2.52195	+	1.45605i	−0.110489	+	0.0637906i	0.443737	+	0.896157i	$0.353652\pi$
$522$	12.4752	−	4.43708i	0.546026	−	0.194206i
$523$	−23.0806	−	13.3256i	−1.00924	−	0.582688i	−0.0982743	−	0.995159i	$-0.531332\pi$
$523$	−23.0806	−	13.3256i	−1.00924	−	0.582688i	−0.910970	+	0.412472i	$0.864666\pi$
$524$	−12.1248	−	4.61595i	−0.529675	−	0.201649i
$525$	−9.05040	+	9.64833i	−0.394992	+	0.421087i
$526$	−0.658434	+	3.58014i	−0.0287091	+	0.156102i
$527$	−1.56708	+	2.71426i	−0.0682629	+	0.118235i
$528$	2.52399	−	12.2051i	0.109843	−	0.531161i
$529$	11.2486	+	19.4832i	0.489071	+	0.847097i
$530$	−23.4651	+	15.0322i	−1.01926	+	0.652959i
$531$	5.82156			0.252634
$532$	0.0939192	−	38.0399i	0.00407191	−	1.64924i
$533$			9.09270i			0.393849i
$534$	3.19250	+	2.71905i	0.138153	+	0.117665i
$535$	−6.55271	−	28.2356i	−0.283298	−	1.22073i
$536$	−16.1657	−	0.356390i	−0.698254	−	0.0153937i
$537$	2.12064	−	3.67305i	0.0915123	−	0.158504i
$538$	−39.8798	−	7.33442i	−1.71934	−	0.316209i
$539$	−6.95644	+	20.6718i	−0.299635	+	0.890399i
$540$	2.73955	−	3.53481i	0.117892	−	0.152114i
$541$	15.7055	−	27.2026i	0.675230	−	1.16953i	−0.301171	−	0.953570i	$-0.597378\pi$
$541$	15.7055	−	27.2026i	0.675230	−	1.16953i	0.976402	−	0.215963i	$-0.0692891\pi$
$542$	−18.9767	+	6.74949i	−0.815121	+	0.289915i
$543$	−3.76961	−	6.52916i	−0.161770	−	0.280193i
$544$	−3.28960	−	23.7218i	−0.141041	−	1.01706i
$545$	−14.1765	−	4.31649i	−0.607256	−	0.184898i
$546$	−3.07550	−	16.9578i	−0.131619	−	0.725729i
$547$	−40.5136			−1.73223			−0.866117	−	0.499841i	$-0.833392\pi$
$547$	−40.5136			−1.73223			−0.866117	+	0.499841i	$0.833392\pi$
$548$	14.8432	+	18.2269i	0.634072	+	0.778613i
$549$	−7.04806	+	4.06920i	−0.300804	+	0.173669i
$550$	−5.43824	+	21.3507i	−0.231887	+	0.910395i
$551$	33.6536	−	58.2897i	1.43369	−	2.48322i
$552$	−1.71423	−	1.04075i	−0.0729623	−	0.0442972i
$553$	2.42674	−	14.8200i	0.103196	−	0.630212i
$554$	39.7207	+	7.30515i	1.68757	+	0.310366i
$555$	3.35854	−	3.13907i	0.142562	−	0.133246i
$556$	−0.879483	−	5.45540i	−0.0372984	−	0.231361i
$557$	−7.89267	+	4.55683i	−0.334423	+	0.193079i	−0.657803	−	0.753190i	$-0.728514\pi$
$557$	−7.89267	+	4.55683i	−0.334423	+	0.193079i	0.323380	+	0.946269i	$0.395181\pi$
$558$	0.797045	+	0.678842i	0.0337416	+	0.0287377i
$559$	−35.3888			−1.49679
$560$	23.4387	+	3.25986i	0.990466	+	0.137754i
$561$	13.1912			0.556933
$562$	25.6443	+	21.8412i	1.08174	+	0.921315i
$563$	−9.85118	+	5.68758i	−0.415178	+	0.239703i	−0.693012	−	0.720926i	$-0.743717\pi$
$563$	−9.85118	+	5.68758i	−0.415178	+	0.239703i	0.277834	+	0.960629i	$0.410383\pi$
$564$	4.07947	+	25.3048i	0.171777	+	1.06552i
$565$	6.60946	+	7.07155i	0.278062	+	0.297502i
$566$	−17.3098	−	3.18349i	−0.727583	−	0.133812i
$567$	1.67575	−	2.04740i	0.0703749	−	0.0859829i
$568$	21.9785	+	13.3437i	0.922199	+	0.559889i
$569$	−11.9775	+	20.7457i	−0.502125	+	0.869705i	0.497872	+	0.867250i	$0.334115\pi$
$569$	−11.9775	+	20.7457i	−0.502125	+	0.869705i	−0.999997	+	0.00245502i	$0.999219\pi$
$570$	−1.04889	−	22.7090i	−0.0439333	−	0.951176i
$571$	−18.3790	+	10.6111i	−0.769138	+	0.444062i	−0.832567	−	0.553925i	$-0.813130\pi$
$571$	−18.3790	+	10.6111i	−0.769138	+	0.444062i	0.0634293	+	0.997986i	$0.479796\pi$
$572$	−18.1254	−	22.2572i	−0.757861	−	0.930620i
$573$	−3.27046			−0.136625
$574$	−6.95303	−	2.49235i	−0.290214	−	0.104029i
$575$	2.94357	+	1.97568i	0.122755	+	0.0823917i
$576$	−7.99223	−	0.352564i	−0.333009	−	0.0146902i
$577$	−14.6683	−	25.4063i	−0.610650	−	1.05768i	−0.991131	−	0.132888i	$-0.957575\pi$
$577$	−14.6683	−	25.4063i	−0.610650	−	1.05768i	0.380481	−	0.924789i	$-0.375759\pi$
$578$	1.23019	−	0.437542i	0.0511690	−	0.0181993i
$579$	3.11035	−	5.38729i	0.129262	−	0.223888i
$580$	33.0952	+	25.6495i	1.37420	+	1.06504i
$581$	2.86886	−	1.08408i	0.119020	−	0.0449753i
$582$	14.2273	+	2.61658i	0.589740	+	0.108461i
$583$	−13.7290	+	23.7793i	−0.568597	+	0.984838i
$584$	12.7998	+	0.282185i	0.529661	+	0.0116769i
$585$	−2.32837	−	10.0329i	−0.0962663	−	0.414811i
$586$	19.8317	+	16.8906i	0.819238	+	0.697744i
$587$			7.91128i			0.326533i	0.986582	+	0.163267i	$0.0522031\pi$
$587$			7.91128i			0.326533i	−0.986582	+	0.163267i	$0.947797\pi$
$588$	13.8104	+	2.29644i	0.569530	+	0.0947035i
$589$	5.32198			0.219288
$590$	9.93049	+	15.5013i	0.408832	+	0.638179i
$591$	−4.02923	−	6.97884i	−0.165741	−	0.287071i
$592$	−8.05320	−	1.66538i	−0.330984	−	0.0684467i
$593$	9.28290	−	16.0785i	0.381203	−	0.660263i	−0.610031	−	0.792377i	$-0.708843\pi$
$593$	9.28290	−	16.0785i	0.381203	−	0.660263i	0.991235	+	0.132114i	$0.0421765\pi$
$594$	0.797040	−	4.33379i	0.0327029	−	0.177818i
$595$	1.64508	+	24.9922i	0.0674417	+	1.02458i
$596$	−14.6017	−	5.55892i	−0.598110	−	0.227702i
$597$	−24.0871	−	13.9067i	−0.985819	−	0.569163i
$598$	−4.35156	+	1.54772i	−0.177948	+	0.0632911i
$599$	20.3164	−	11.7297i	0.830104	−	0.479261i	−0.0237846	−	0.999717i	$-0.507572\pi$
$599$	20.3164	−	11.7297i	0.830104	−	0.479261i	0.853888	+	0.520457i	$0.174238\pi$
$600$	14.0854	+	1.26501i	0.575036	+	0.0516437i
$601$			26.1512i			1.06673i	0.845886	+	0.533364i	$0.179072\pi$
$601$			26.1512i			1.06673i	−0.845886	+	0.533364i	$0.820928\pi$
$602$	9.70022	−	27.0612i	0.395352	−	1.10293i
$603$	−5.71684			−0.232808
$604$	5.35102	+	6.57082i	0.217730	+	0.267363i
$605$	−0.652845	−	2.81311i	−0.0265419	−	0.114369i
$606$	17.8415	−	6.34571i	0.724761	−	0.257777i
$607$	13.8062	+	7.97102i	0.560377	+	0.323534i	0.753297	−	0.657681i	$-0.228462\pi$
$607$	13.8062	+	7.97102i	0.560377	+	0.323534i	−0.192920	+	0.981215i	$0.561796\pi$
$608$	−32.0914	+	24.9781i	−1.30148	+	1.01299i
$609$	19.1692	+	15.6895i	0.776774	+	0.635771i
$610$	−22.8579	−	11.8259i	−0.925490	−	0.478816i
$611$	51.1221	+	29.5154i	2.06818	+	1.19406i
$612$	−1.34762	−	8.35924i	−0.0544743	−	0.337902i
$613$	−13.9443	+	8.05072i	−0.563203	+	0.325166i	−0.754430	−	0.656380i	$-0.772087\pi$
$613$	−13.9443	+	8.05072i	−0.563203	+	0.325166i	0.191227	+	0.981546i	$0.438753\pi$
$614$	14.9859	−	17.5954i	0.604783	−	0.710091i
$615$	−4.22271	−	1.28574i	−0.170276	−	0.0518459i
$616$	21.9879	−	7.75937i	0.885918	−	0.312634i
$617$		−	25.1649i		−	1.01310i	−0.862210	−	0.506551i	$-0.830920\pi$
$617$		−	25.1649i		−	1.01310i	0.862210	−	0.506551i	$-0.169080\pi$
$618$	−2.58563	−	2.20218i	−0.104009	−	0.0885845i
$619$	−12.6655	−	21.9372i	−0.509068	−	0.881732i	−0.999945	−	0.0105028i	$-0.996657\pi$
$619$	−12.6655	−	21.9372i	−0.509068	−	0.881732i	0.490877	−	0.871229i	$-0.336677\pi$
$620$	−0.447973	+	3.28030i	−0.0179910	+	0.131740i
$621$	−0.614033	−	0.354512i	−0.0246403	−	0.0142261i
$622$	0.594696	−	3.23357i	0.0238451	−	0.129655i
$623$	−1.26776	+	7.74217i	−0.0507917	+	0.310183i
$624$	−12.2526	+	13.7598i	−0.490498	+	0.550834i
$625$	−24.7724	−	3.36608i	−0.990894	−	0.134643i
$626$	−8.26106	+	2.93822i	−0.330178	+	0.117435i
$627$	−11.1997	−	19.3985i	−0.447274	−	0.774701i
$628$	5.09266	−	4.14727i	0.203219	−	0.165494i
$629$		−	8.70382i		−	0.347044i
$630$	8.31023	+	0.969608i	0.331087	+	0.0386301i
$631$			42.2033i			1.68009i	0.542520	+	0.840043i	$0.317470\pi$
$631$			42.2033i			1.68009i	−0.542520	+	0.840043i	$0.682530\pi$
$632$	−14.0770	+	7.71875i	−0.559951	+	0.307035i
$633$	6.90731	+	11.9638i	0.274541	+	0.475519i
$634$	0.426618	+	1.19947i	0.0169432	+	0.0476371i
$635$	−31.8073	+	29.7289i	−1.26223	+	1.17975i
$636$	16.4715	+	6.27073i	0.653136	+	0.248650i
$637$	24.1853	−	21.3229i	0.958256	−	0.844846i
$638$	40.5759	+	7.46242i	1.60641	+	0.295440i
$639$	7.87268	+	4.54530i	0.311439	+	0.179809i
$640$	−12.6945	−	21.8827i	−0.501792	−	0.864988i
$641$	13.1174	+	22.7200i	0.518107	+	0.897387i	0.999779	+	0.0210356i	$0.00669635\pi$
$641$	13.1174	+	22.7200i	0.518107	+	0.897387i	−0.481672	+	0.876352i	$0.659970\pi$
$642$	−11.8867	+	13.9564i	−0.469129	+	0.550816i
$643$		−	46.1413i		−	1.81964i	−0.415007	−	0.909818i	$-0.636221\pi$
$643$		−	46.1413i		−	1.81964i	0.415007	−	0.909818i	$-0.363779\pi$
$644$	0.00926306	−	3.75179i	0.000365016	−	0.147841i
$645$	5.00409	−	16.4348i	0.197036	−	0.647120i
$646$	−32.7673	−	27.9079i	−1.28921	−	1.09802i
$647$	0.544511	−	0.314373i	0.0214069	−	0.0123593i	−0.489258	−	0.872139i	$-0.662732\pi$
$647$	0.544511	−	0.314373i	0.0214069	−	0.0123593i	0.510665	+	0.859780i	$0.329399\pi$
$648$	−2.82774	−	0.0623403i	−0.111084	−	0.00244896i
$649$	15.7089	+	9.06954i	0.616629	+	0.356011i
$650$	22.7434	−	23.3142i	0.892069	−	0.914457i
$651$	−0.316511	+	1.93292i	−0.0124051	+	0.0757573i
$652$	−29.3856	−	11.1872i	−1.15083	−	0.438123i
$653$	34.0898	+	19.6818i	1.33404	+	0.770207i	0.985916	−	0.167243i	$-0.0534863\pi$
$653$	34.0898	+	19.6818i	1.33404	+	0.770207i	0.348122	+	0.937449i	$0.386820\pi$
$654$	3.14076	+	8.83052i	0.122814	+	0.345301i
$655$	−3.27909	−	14.1296i	−0.128125	−	0.552088i
$656$	2.48146	+	7.49617i	0.0968846	+	0.292676i
$657$	4.52652			0.176597
$658$	−36.5827	+	31.0019i	−1.42614	+	1.20858i
$659$		−	38.0895i		−	1.48376i	−0.670534	−	0.741879i	$-0.733935\pi$
$659$		−	38.0895i		−	1.48376i	0.670534	−	0.741879i	$-0.266065\pi$
$660$	12.8994	−	5.27032i	0.502107	−	0.205147i
$661$	−35.2333	+	20.3420i	−1.37042	+	0.791210i	−0.990980	−	0.134008i	$-0.957215\pi$
$661$	−35.2333	+	20.3420i	−1.37042	+	0.791210i	−0.379436	+	0.925218i	$0.623882\pi$
$662$	−10.6710	−	30.0024i	−0.414741	−	1.16608i
$663$	−16.8878	−	9.75018i	−0.655868	−	0.378666i
$664$	−2.80254	−	1.70149i	−0.108759	−	0.0660305i
$665$	35.3558	−	23.6383i	1.37104	−	0.916653i
$666$	−2.85952	−	0.525903i	−0.110804	−	0.0203783i
$667$	3.31918	−	5.74899i	0.128519	−	0.222602i
$668$	−41.8424	+	6.74555i	−1.61893	+	0.260993i
$669$	−6.06887	−	10.5116i	−0.234636	−	0.406402i
$670$	−9.75186	−	15.2225i	−0.376747	−	0.588096i
$671$	−25.3580			−0.978936
$672$	−7.16339	−	13.1410i	−0.276334	−	0.506925i
$673$		−	43.8931i		−	1.69196i	−0.533217	−	0.845978i	$-0.679017\pi$
$673$		−	43.8931i		−	1.69196i	0.533217	−	0.845978i	$-0.320983\pi$
$674$	−8.52733	+	10.0122i	−0.328461	+	0.385654i
$675$	4.98860	+	0.337377i	0.192011	+	0.0129857i
$676$	2.61537	+	16.2230i	0.100591	+	0.623962i
$677$	1.43240	−	2.48099i	0.0550516	−	0.0953522i	−0.837186	−	0.546918i	$-0.815801\pi$
$677$	1.43240	−	2.48099i	0.0550516	−	0.0953522i	0.892238	+	0.451566i	$0.149134\pi$
$678$	1.10731	−	6.02084i	0.0425260	−	0.231229i
$679$	9.56639	+	25.3160i	0.367124	+	0.971541i
$680$	19.9597	−	17.8477i	0.765421	−	0.684427i
$681$	2.08757	−	3.61577i	0.0799958	−	0.138557i
$682$	1.09317	+	3.07353i	0.0418595	+	0.117691i
$683$	7.48982	+	12.9728i	0.286590	+	0.496389i	0.972994	−	0.230832i	$-0.0741449\pi$
$683$	7.48982	+	12.9728i	0.286590	+	0.496389i	−0.686403	+	0.727221i	$0.740812\pi$
$684$	−11.1486	+	9.07900i	−0.426278	+	0.347144i
$685$	−7.65500	+	25.1411i	−0.292482	+	0.960593i
$686$	9.67598	+	24.3388i	0.369431	+	0.929258i
$687$	2.10343			0.0802510
$688$	−29.1751	+	9.65782i	−1.11229	+	0.368201i
$689$	35.1526	−	20.2953i	1.33921	−	0.773191i
$690$	−0.103450	−	2.23974i	−0.00393828	−	0.0852656i
$691$	11.3906	−	19.7291i	0.433319	−	0.750531i	−0.563838	−	0.825886i	$-0.690676\pi$
$691$	11.3906	−	19.7291i	0.433319	−	0.750531i	0.997157	+	0.0753548i	$0.0240089\pi$
$692$	−29.2497	−	11.1354i	−1.11191	−	0.423306i
$693$	7.71155	−	2.91403i	0.292938	−	0.110695i
$694$	2.80355	−	15.2439i	0.106421	−	0.578651i
$695$	4.51354	−	4.21860i	0.171208	−	0.160021i
$696$	0.583672	−	26.4752i	0.0221240	−	1.00354i
$697$	−7.23766	+	4.17866i	−0.274146	+	0.158278i
$698$	−18.0159	+	21.1529i	−0.681912	+	0.800650i
$699$	15.0397			0.568855
$700$	11.5939	+	23.7820i	0.438207	+	0.898874i
$701$	2.82673			0.106764			0.0533821	−	0.998574i	$-0.483000\pi$
$701$	2.82673			0.106764			0.0533821	+	0.998574i	$0.483000\pi$
$702$	−4.22368	+	4.95913i	−0.159413	+	0.187170i
$703$	−12.7995	+	7.38980i	−0.482743	+	0.278712i
$704$	−21.0170	−	13.4026i	−0.792107	−	0.505131i
$705$	−20.9360	+	19.5679i	−0.788494	+	0.736970i
$706$	−0.579436	+	3.15060i	−0.0218074	+	0.118574i
$707$	27.4148	+	22.4384i	1.03104	+	0.843882i
$708$	4.14252	−	10.8813i	0.155685	−	0.408943i
$709$	13.9578	−	24.1757i	0.524198	−	0.907937i	−0.475405	−	0.879767i	$-0.657699\pi$
$709$	13.9578	−	24.1757i	0.524198	−	0.907937i	0.999603	−	0.0281702i	$-0.00896804\pi$
$710$	1.32636	+	28.7164i	0.0497775	+	1.07771i
$711$	−4.91560	+	2.83802i	−0.184349	+	0.106434i
$712$	7.35398	−	4.03237i	0.275602	−	0.151120i
$713$	0.524896			0.0196575
$714$	12.0848	−	10.2412i	0.452263	−	0.383269i
$715$	9.34767	−	30.7003i	0.349583	−	1.14813i
$716$	−5.35641	−	6.57743i	−0.200178	−	0.245810i
$717$	5.04617	+	8.74022i	0.188453	+	0.326410i
$718$	6.10122	+	17.1541i	0.227695	+	0.640185i
$719$	8.80110	−	15.2440i	0.328226	−	0.568504i	−0.653934	−	0.756551i	$-0.726883\pi$
$719$	8.80110	−	15.2440i	0.328226	−	0.568504i	0.982160	+	0.188048i	$0.0602160\pi$
$720$	−4.65760	−	7.63589i	−0.173578	−	0.284573i
$721$	1.02677	−	6.27044i	0.0382389	−	0.233523i
$722$	−8.35960	+	45.4542i	−0.311112	+	1.69163i
$723$	−2.63255	+	4.55972i	−0.0979057	+	0.169578i
$724$	−14.8862	+	2.39986i	−0.553243	+	0.0891901i
$725$	−3.15875	+	46.7067i	−0.117313	+	1.73464i
$726$	−1.18427	+	1.39048i	−0.0439522	+	0.0516054i
$727$			6.20044i			0.229962i	0.993368	+	0.114981i	$0.0366807\pi$
$727$			6.20044i			0.229962i	−0.993368	+	0.114981i	$0.963319\pi$
$728$	−33.8849	−	6.31840i	−1.25586	−	0.234176i
$729$	−1.00000			−0.0370370
$730$	7.72140	+	12.0530i	0.285782	+	0.446101i
$731$	−16.2634	−	28.1690i	−0.601522	−	1.04187i
$732$	2.59059	+	16.0693i	0.0957509	+	0.593939i
$733$	3.13605	−	5.43181i	0.115833	−	0.200628i	−0.802280	−	0.596949i	$-0.796380\pi$
$733$	3.13605	−	5.43181i	0.115833	−	0.200628i	0.918112	+	0.396320i	$0.129713\pi$
$734$	44.3170	+	8.15046i	1.63577	+	0.300839i
$735$	6.48265	+	14.2469i	0.239116	+	0.525506i
$736$	−3.16511	+	2.46353i	−0.116667	+	0.0908071i
$737$	−15.4263	−	8.90640i	−0.568237	−	0.328072i
$738$	0.935528	+	2.63032i	0.0344373	+	0.0968233i
$739$	−15.9997	+	9.23744i	−0.588559	+	0.339805i	−0.764528	−	0.644591i	$-0.777028\pi$
$739$	−15.9997	+	9.23744i	−0.588559	+	0.339805i	0.175968	+	0.984396i	$0.443694\pi$
$740$	−3.47746	−	8.51126i	−0.127834	−	0.312880i
$741$			33.1128i			1.21643i
$742$	5.88402	+	32.4436i	0.216009	+	1.19104i
$743$	25.9711			0.952787			0.476394	−	0.879232i	$-0.341944\pi$
$743$	25.9711			0.952787			0.476394	+	0.879232i	$0.341944\pi$
$744$	1.83601	−	1.00673i	0.0673113	−	0.0369085i
$745$	−3.94896	−	17.0161i	−0.144679	−	0.623420i
$746$	−3.62551	−	10.1934i	−0.132740	−	0.373208i
$747$	−1.00386	−	0.579581i	−0.0367295	−	0.0212058i
$748$	9.38664	−	24.6561i	0.343210	−	0.901516i
$749$	−33.8459	−	5.54218i	−1.23670	−	0.202507i
$750$	7.61127	+	13.8589i	0.277924	+	0.506055i
$751$	19.2348	+	11.1052i	0.701888	+	0.405235i	0.808050	−	0.589113i	$-0.200523\pi$
$751$	19.2348	+	11.1052i	0.701888	+	0.405235i	−0.106162	+	0.994349i	$0.533856\pi$
$752$	50.2008	+	10.3814i	1.83064	+	0.378571i
$753$	6.70783	−	3.87277i	0.244447	−	0.141132i
$754$	−46.4307	−	39.5450i	−1.69091	−	1.44014i
$755$	−2.75964	+	9.06343i	−0.100434	+	0.329852i
$756$	−2.63443	−	4.58909i	−0.0958133	−	0.166904i
$757$			22.6272i			0.822400i	0.911545	+	0.411200i	$0.134890\pi$
$757$			22.6272i			0.822400i	−0.911545	+	0.411200i	$0.865110\pi$
$758$	−13.0716	+	15.3477i	−0.474783	+	0.557455i
$759$	−1.10461	−	1.91323i	−0.0400947	−	0.0694460i
$760$	−43.1925	−	14.1988i	−1.56676	−	0.515046i
$761$	−6.14427	−	3.54740i	−0.222730	−	0.128593i	0.384484	−	0.923132i	$-0.374379\pi$
$761$	−6.14427	−	3.54740i	−0.222730	−	0.128593i	−0.607214	+	0.794539i	$0.707713\pi$
$762$	27.0813	+	4.98060i	0.981053	+	0.180428i
$763$	−11.1057	+	13.5688i	−0.402054	+	0.491223i
$764$	−2.32720	+	6.11291i	−0.0841952	+	0.221157i
$765$	6.91604	−	6.46411i	0.250050	−	0.233710i
$766$	−5.84571	−	16.4357i	−0.211214	−	0.593847i
$767$	−13.4074	−	23.2222i	−0.484112	−	0.838506i
$768$	−6.34612	+	14.6876i	−0.228996	+	0.529995i
$769$			8.40173i			0.302974i	0.988459	+	0.151487i	$0.0484062\pi$
$769$			8.40173i			0.302974i	−0.988459	+	0.151487i	$0.951594\pi$
$770$	20.9138	+	15.5631i	0.753680	+	0.560855i
$771$		−	3.42749i		−	0.123438i
$772$	−7.85627	−	9.64716i	−0.282753	−	0.347209i
$773$	−23.7462	−	41.1297i	−0.854093	−	1.47933i	−0.877484	−	0.479606i	$-0.840780\pi$
$773$	−23.7462	−	41.1297i	−0.854093	−	1.47933i	0.0233915	−	0.999726i	$-0.492554\pi$
$774$	−10.2372	+	3.64108i	−0.367968	+	0.130876i
$775$	−3.32320	+	1.63025i	−0.119373	+	0.0585602i
$776$	15.0146	−	24.7307i	0.538994	−	0.887782i
$777$	−1.92273	−	5.08823i	−0.0689777	−	0.182539i
$778$	−4.01919	+	21.8538i	−0.144095	+	0.783495i
$779$	12.2900	+	7.09562i	0.440334	+	0.254227i
$780$	−20.4097	−	2.78724i	−0.730785	−	0.0997992i
$781$	14.1625	+	24.5301i	0.506772	+	0.877755i
$782$	−3.23178	−	2.75250i	−0.115568	−	0.0984291i
$783$		−	9.36267i		−	0.334595i
$784$	14.1196	−	24.1793i	0.504270	−	0.863546i
$785$	7.02454	+	2.13884i	0.250716	+	0.0763384i
$786$	−5.94829	+	6.98404i	−0.212169	+	0.249112i
$787$	26.6167	−	15.3672i	0.948783	−	0.547780i	0.0560803	−	0.998426i	$-0.482140\pi$
$787$	26.6167	−	15.3672i	0.948783	−	0.547780i	0.892703	+	0.450646i	$0.148806\pi$
$788$	−15.9115	+	2.56514i	−0.566823	+	0.0913794i
$789$	2.22915	+	1.28700i	0.0793598	+	0.0458184i
$790$	−15.9420	−	8.24785i	−0.567191	−	0.293445i
$791$	10.7135	−	4.04840i	0.380928	−	0.143944i
$792$	−7.53326	−	4.57362i	−0.267683	−	0.162517i
$793$	32.4641	+	18.7432i	1.15284	+	0.665590i
$794$	−35.9264	+	12.7780i	−1.27498	+	0.453474i
$795$	4.45462	+	19.1949i	0.157989	+	0.680774i
$796$	−43.1334	+	35.1262i	−1.52882	+	1.24501i
$797$	−0.198198			−0.00702052			−0.00351026	−	0.999994i	$-0.501117\pi$
$797$	−0.198198			−0.00702052			−0.00351026	+	0.999994i	$0.501117\pi$
$798$	−25.3207	−	9.07635i	−0.896344	−	0.321299i
$799$			54.2566i			1.91946i
$800$	12.3874	−	25.4274i	0.437962	−	0.898994i
$801$	2.56797	−	1.48262i	0.0907348	−	0.0523857i
$802$	3.87005	−	1.37647i	0.136656	−	0.0486048i
$803$	12.2144	+	7.05198i	0.431036	+	0.248859i
$804$	−4.06801	+	10.6855i	−0.143468	+	0.376849i
$805$	3.48707	−	2.33139i	0.122903	−	0.0821709i
$806$	0.872267	−	4.74283i	0.0307243	−	0.167059i
$807$	−14.3361	+	24.8309i	−0.504655	+	0.874089i
$808$	0.834740	−	37.8636i	0.0293661	−	1.33204i
$809$	27.0306	+	46.8184i	0.950346	+	1.64605i	0.744677	+	0.667426i	$0.232604\pi$
$809$	27.0306	+	46.8184i	0.950346	+	1.64605i	0.205669	+	0.978622i	$0.434063\pi$
$810$	−1.70581	−	2.66274i	−0.0599361	−	0.0935593i
$811$	45.1487			1.58538			0.792692	−	0.609622i	$-0.208679\pi$
$811$	45.1487			1.58538			0.792692	+	0.609622i	$0.208679\pi$
$812$	42.9662	−	24.6653i	1.50782	−	0.865582i
$813$			14.2421i			0.499491i
$814$	−6.89682	−	5.87401i	−0.241734	−	0.205884i
$815$	−7.94716	−	34.2443i	−0.278377	−	1.19953i
$816$	−16.5835	−	3.42942i	−0.580537	−	0.120054i
$817$	−27.6161	+	47.8325i	−0.966166	+	1.67345i
$818$	6.25075	+	1.14959i	0.218552	+	0.0401946i
$819$	−12.0265	−	1.96930i	−0.420238	−	0.0688129i
$820$	−5.40802	+	6.97790i	−0.188856	+	0.243679i
$821$	−9.49127	+	16.4394i	−0.331247	+	0.573737i	−0.982757	−	0.184903i	$-0.940803\pi$
$821$	−9.49127	+	16.4394i	−0.331247	+	0.573737i	0.651509	+	0.758641i	$0.274136\pi$
$822$	15.6603	−	5.56993i	0.546217	−	0.194274i
$823$	15.8455	+	27.4452i	0.552339	+	0.956679i	0.998105	+	0.0615297i	$0.0195979\pi$
$823$	15.8455	+	27.4452i	0.552339	+	0.956679i	−0.445766	+	0.895149i	$0.647069\pi$
$824$	−5.95604	+	3.26585i	−0.207489	+	0.113771i
$825$	12.9357	+	8.68225i	0.450362	+	0.302277i
$826$	21.4326	−	3.88706i	0.745737	−	0.135248i
$827$	−5.52546			−0.192139			−0.0960695	−	0.995375i	$-0.530627\pi$
$827$	−5.52546			−0.192139			−0.0960695	+	0.995375i	$0.530627\pi$
$828$	−1.09957	+	0.895444i	−0.0382125	+	0.0311188i
$829$	−28.9137	+	16.6933i	−1.00421	+	0.579783i	−0.909492	−	0.415721i	$-0.863529\pi$
$829$	−28.9137	+	16.6933i	−1.00421	+	0.579783i	−0.0947208	+	0.995504i	$0.530196\pi$
$830$	−0.169128	−	3.66169i	−0.00587051	−	0.127099i
$831$	14.2789	−	24.7318i	0.495330	−	0.857937i
$832$	17.0002	+	32.6930i	0.589374	+	1.13343i
$833$	28.0874	+	9.45191i	0.973170	+	0.327489i
$834$	−3.84291	−	0.706760i	−0.133069	−	0.0244731i
$835$	−32.3563	−	34.6184i	−1.11973	−	1.19802i
$836$	−44.2279	+	7.13012i	−1.52965	+	0.246600i
$837$	0.641124	−	0.370153i	0.0221605	−	0.0127944i
$838$	−41.7469	−	35.5558i	−1.44212	−	1.22825i
$839$	−11.3973			−0.393480			−0.196740	−	0.980456i	$-0.563035\pi$
$839$	−11.3973			−0.393480			−0.196740	+	0.980456i	$0.563035\pi$
$840$	7.72574	−	14.8429i	0.266563	−	0.512130i
$841$	58.6596			2.02274
$842$	1.62641	+	1.38521i	0.0560498	+	0.0477375i
$843$	20.6277	−	11.9094i	0.710454	−	0.410181i
$844$	27.2770	−	4.39742i	0.938914	−	0.151365i
$845$	−13.4222	+	12.5451i	−0.461736	+	0.431564i
$846$	17.8253	+	3.27829i	0.612845	+	0.112710i
$847$	−3.37206	−	0.552166i	−0.115865	−	0.0189726i
$848$	23.4416	−	26.3252i	0.804988	−	0.904010i
$849$	−6.22256	+	10.7778i	−0.213558	+	0.369893i
$850$	29.0097	+	7.38908i	0.995025	+	0.253443i
$851$	−1.26239	+	0.728841i	−0.0432742	+	0.0249844i
$852$	14.0978	−	11.4807i	0.482983	−	0.393323i
$853$	55.1181			1.88721			0.943604	−	0.331075i	$-0.107411\pi$
$853$	55.1181			1.88721			0.943604	+	0.331075i	$0.107411\pi$
$854$	−23.2311	+	19.6872i	−0.794953	+	0.673681i
$855$	−15.3778	−	4.68225i	−0.525909	−	0.160129i
$856$	17.6280	+	32.1489i	0.602514	+	1.09883i
$857$	6.35075	+	10.9998i	0.216937	+	0.375747i	0.953870	−	0.300219i	$-0.0970599\pi$
$857$	6.35075	+	10.9998i	0.216937	+	0.375747i	−0.736933	+	0.675966i	$0.763727\pi$
$858$	−19.1231	+	6.80156i	−0.652854	+	0.232201i
$859$	−5.30662	+	9.19133i	−0.181059	+	0.313604i	−0.942242	−	0.334934i	$-0.891286\pi$
$859$	−5.30662	+	9.19133i	−0.181059	+	0.313604i	0.761182	+	0.648538i	$0.224619\pi$
$860$	−27.1580	−	21.0480i	−0.926079	−	0.717731i
$861$	−3.30802	+	4.04168i	−0.112737	+	0.137740i
$862$	35.7533	+	6.57550i	1.21776	+	0.223962i
$863$	−0.570921	+	0.988865i	−0.0194344	+	0.0336614i	−0.875579	−	0.483075i	$-0.839520\pi$
$863$	−0.570921	+	0.988865i	−0.0194344	+	0.0336614i	0.856145	+	0.516736i	$0.172853\pi$
$864$	−2.12869	+	5.24106i	−0.0724196	+	0.178304i
$865$	−7.91043	−	34.0860i	−0.268963	−	1.15896i
$866$	12.2022	+	10.3926i	0.414647	+	0.353154i
$867$		−	0.923255i		−	0.0313554i
$868$	3.38766	+	1.96704i	0.114985	+	0.0667656i
$869$	−17.6857			−0.599946
$870$	24.9304	−	15.9710i	0.845219	−	0.541466i
$871$	13.1662	+	22.8045i	0.446120	+	0.772702i
$872$	18.7403	+	0.413149i	0.634627	+	0.0139910i
$873$	5.11447	−	8.85852i	0.173098	−	0.299815i
$874$	−1.30385	+	7.08948i	−0.0441033	+	0.239805i
$875$	−14.8362	+	25.5907i	−0.501556	+	0.865125i
$876$	3.22100	−	8.46067i	0.108827	−	0.285859i
$877$	46.3424	+	26.7558i	1.56487	+	0.903480i	0.996752	+	0.0805350i	$0.0256629\pi$
$877$	46.3424	+	26.7558i	1.56487	+	0.903480i	0.568121	+	0.822945i	$0.307670\pi$
$878$	46.4827	−	16.5326i	1.56871	−	0.557947i
$879$	15.9521	−	9.20996i	0.538051	−	0.310644i
$880$	−0.671945	−	27.8609i	−0.0226513	−	0.939190i
$881$		−	28.8502i		−	0.971986i	−0.873963	−	0.485993i	$-0.838458\pi$
$881$		−	28.8502i		−	0.971986i	0.873963	−	0.485993i	$-0.161542\pi$
$882$	4.80239	−	8.65662i	0.161705	−	0.291484i
$883$	−22.8029			−0.767377			−0.383689	−	0.923463i	$-0.625346\pi$
$883$	−22.8029			−0.767377			−0.383689	+	0.923463i	$0.625346\pi$
$884$	−30.2414	+	24.6275i	−1.01713	+	0.828311i
$885$	12.6804	−	2.94278i	0.426247	−	0.0989203i
$886$	−0.212971	+	0.0757476i	−0.00715489	+	0.00254479i
$887$	−14.2356	−	8.21891i	−0.477984	−	0.275964i	0.241592	−	0.970378i	$-0.422330\pi$
$887$	−14.2356	−	8.21891i	−0.477984	−	0.275964i	−0.719576	+	0.694414i	$0.755664\pi$
$888$	−3.01777	+	4.97059i	−0.101270	+	0.166802i
$889$	18.2094	+	48.1885i	0.610724	+	1.61619i
$890$	8.32831	+	4.30878i	0.279166	+	0.144431i
$891$	−2.69840	−	1.55792i	−0.0903999	−	0.0521924i
$892$	−23.9660	+	3.86364i	−0.802442	+	0.129364i
$893$	79.7877	−	46.0655i	2.66999	−	1.54152i
$894$	−7.16344	+	8.41078i	−0.239581	+	0.281298i
$895$	2.76242	−	9.07255i	0.0923375	−	0.303262i
$896$	−29.6596	+	4.03841i	−0.990857	+	0.134914i
$897$			3.26584i			0.109043i
$898$	16.0583	+	13.6769i	0.535873	+	0.456402i
$899$	3.46562	+	6.00264i	0.115585	+	0.200199i
$900$	4.18041	−	9.08428i	0.139347	−	0.302809i
$901$	32.3096	+	18.6539i	1.07639	+	0.621453i
$902$	−1.57340	+	8.55513i	−0.0523885	+	0.284855i
$903$	−15.7302	−	12.8748i	−0.523469	−	0.428447i
$904$	−10.4658	−	6.35404i	−0.348087	−	0.211332i
$905$	−11.5114	−	12.3162i	−0.382651	−	0.409403i
$906$	5.64558	−	2.00797i	0.187562	−	0.0667104i
$907$	16.0002	+	27.7132i	0.531278	+	0.920200i	0.999334	+	0.0365014i	$0.0116213\pi$
$907$	16.0002	+	27.7132i	0.531278	+	0.920200i	−0.468056	+	0.883699i	$0.655045\pi$
$908$	−5.27288	−	6.47486i	−0.174987	−	0.214876i
$909$		−	13.3901i		−	0.444120i
$910$	−15.2711	−	35.3826i	−0.506233	−	1.17292i
$911$			10.7731i			0.356929i	0.983946	+	0.178464i	$0.0571129\pi$
$911$			10.7731i			0.356929i	−0.983946	+	0.178464i	$0.942887\pi$
$912$	9.03668	+	27.2987i	0.299234	+	0.903950i
$913$	−1.80589	−	3.12789i	−0.0597661	−	0.103518i
$914$	−13.2440	−	37.2367i	−0.438073	−	1.23168i
$915$	−13.2950	+	12.4262i	−0.439519	+	0.410798i
$916$	1.49677	−	3.93159i	0.0494546	−	0.129903i
$917$	−16.9371	−	2.77340i	−0.559312	−	0.0915858i
$918$	−5.88844	−	1.08296i	−0.194347	−	0.0357430i
$919$	−17.6254	−	10.1760i	−0.581408	−	0.335676i	0.180285	−	0.983614i	$-0.442298\pi$
$919$	−17.6254	−	10.1760i	−0.581408	−	0.335676i	−0.761693	+	0.647939i	$0.775631\pi$
$920$	−4.25999	−	1.40040i	−0.140448	−	0.0461699i
$921$	−8.17140	−	14.1533i	−0.269257	−	0.466367i
$922$	−13.0490	+	15.3211i	−0.429746	+	0.504575i
$923$		−	41.8723i		−	1.37824i
$924$	0.0407070	−	16.4875i	0.00133916	−	0.542398i
$925$	5.72872	−	8.53520i	0.188359	−	0.280636i
$926$	−39.7534	−	33.8579i	−1.30638	−	1.11264i
$927$	−2.07982	+	1.20078i	−0.0683102	+	0.0394389i
$928$	−49.0703	−	19.9303i	−1.61081	−	0.654243i
$929$	12.3330	+	7.12045i	0.404632	+	0.233614i	0.688481	−	0.725255i	$-0.258278\pi$
$929$	12.3330	+	7.12045i	0.404632	+	0.233614i	−0.283849	+	0.958869i	$0.591611\pi$
$930$	2.07926	+	1.07574i	0.0681817	+	0.0352748i
$931$	−9.94740	−	49.3292i	−0.326013	−	1.61670i
$932$	10.7020	−	28.1112i	0.350556	−	0.920814i
$933$	−2.01336	−	1.16241i	−0.0659145	−	0.0380558i
$934$	−8.67445	−	24.3889i	−0.283837	−	0.798031i
$935$	28.7328	−	6.66811i	0.939665	−	0.218070i
$936$	6.26376	+	11.4234i	0.204738	+	0.373387i
$937$	−1.26038			−0.0411748			−0.0205874	−	0.999788i	$-0.506554\pi$
$937$	−1.26038			−0.0411748			−0.0205874	+	0.999788i	$0.506554\pi$
$938$	−21.0471	+	3.81714i	−0.687213	+	0.124634i
$939$			6.19993i			0.202327i
$940$	21.6773	+	53.0563i	0.707035	+	1.73050i
$941$	20.7652	−	11.9888i	0.676928	−	0.390824i	−0.121769	−	0.992558i	$-0.538857\pi$
$941$	20.7652	−	11.9888i	0.676928	−	0.390824i	0.798696	+	0.601734i	$0.205523\pi$
$942$	−1.55626	−	4.37556i	−0.0507058	−	0.142564i
$943$	1.21213	+	0.699826i	0.0394725	+	0.0227895i
$944$	−17.3907	−	15.4858i	−0.566020	−	0.504021i
$945$	2.61513	−	5.30670i	0.0850703	−	0.172627i
$946$	−33.2966	−	6.12367i	−1.08257	−	0.199098i
$947$	3.59385	−	6.22472i	0.116784	−	0.202276i	−0.801707	−	0.597717i	$-0.796075\pi$
$947$	3.59385	−	6.22472i	0.116784	−	0.202276i	0.918492	+	0.395440i	$0.129408\pi$
$948$	1.80678	+	11.2074i	0.0586814	+	0.363999i
$949$	−10.4248	−	18.0563i	−0.338404	−	0.586134i
$950$	−13.7640	−	48.9342i	−0.446563	−	1.58763i
$951$	0.900205			0.0291911
$952$	−10.5429	−	29.8756i	−0.341696	−	0.968273i
$953$			29.4360i			0.953525i	0.879032	+	0.476763i	$0.158190\pi$
$953$			29.4360i			0.953525i	−0.879032	+	0.476763i	$0.841810\pi$
$954$	8.08071	−	9.48776i	0.261623	−	0.307178i
$955$	−7.12365	+	1.65320i	−0.230516	+	0.0534964i
$956$	19.9274	−	3.21256i	0.644498	−	0.103902i
$957$	14.5863	−	25.2643i	0.471509	−	0.816678i
$958$	−5.66954	+	30.8273i	−0.183174	+	0.995985i
$959$	24.0633	+	19.6952i	0.777045	+	0.635993i
$960$	−17.5867	+	3.27209i	−0.567610	+	0.105606i
$961$	15.2260	−	26.3722i	0.491160	−	0.850715i
$962$	4.48780	+	12.6178i	0.144693	+	0.406815i
$963$	6.48146	+	11.2262i	0.208862	+	0.361760i
$964$	6.64943	+	8.16520i	0.214164	+	0.262984i
$965$	4.05166	−	13.3068i	0.130427	−	0.428360i
$966$	−2.49733	−	0.895182i	−0.0803504	−	0.0288020i
$967$	−7.70333			−0.247722			−0.123861	−	0.992300i	$-0.539528\pi$
$967$	−7.70333			−0.247722			−0.123861	+	0.992300i	$0.539528\pi$
$968$	1.75628	+	3.20299i	0.0564489	+	0.102948i
$969$	−26.3573	+	15.2174i	−0.846717	+	0.488852i
$970$	32.3123	−	1.49245i	1.03748	−	0.0479198i
$971$	−12.6974	+	21.9926i	−0.407480	+	0.705776i	−0.994607	−	0.103719i	$-0.966926\pi$
$971$	−12.6974	+	21.9926i	−0.407480	+	0.705776i	0.587127	+	0.809495i	$0.300259\pi$
$972$	−0.711583	+	1.86913i	−0.0228240	+	0.0599524i
$973$	−2.58396	−	6.83807i	−0.0828380	−	0.219219i
$974$	−0.379893	+	2.06561i	−0.0121726	+	0.0661865i
$975$	−10.1432	−	20.6766i	−0.324843	−	0.662181i
$976$	31.8791	+	6.59251i	1.02042	+	0.211021i
$977$	−32.0954	+	18.5303i	−1.02682	+	0.592837i	−0.916073	−	0.401011i	$-0.868659\pi$
$977$	−32.0954	+	18.5303i	−1.02682	+	0.592837i	−0.110751	+	0.993848i	$0.535326\pi$
$978$	−14.4162	+	16.9264i	−0.460980	+	0.541248i
$979$	9.23923			0.295287
$980$	31.2423	−	1.97903i	0.998000	−	0.0632179i
$981$	6.62731			0.211594
$982$	20.2647	−	23.7932i	0.646671	−	0.759273i
$983$	6.80263	−	3.92750i	0.216970	−	0.125268i	−0.387576	−	0.921838i	$-0.626688\pi$
$983$	6.80263	−	3.92750i	0.216970	−	0.125268i	0.604547	+	0.796570i	$0.293354\pi$
$984$	5.58211	+	0.123063i	0.177951	+	0.00392311i
$985$	−12.3042	−	13.1644i	−0.392044	−	0.419453i
$986$	10.1394	−	55.1315i	0.322904	−	1.75574i
$987$	11.9857	+	31.7183i	0.381508	+	1.00960i
$988$	61.8921	+	23.5625i	1.96905	+	0.749622i
$989$	−2.72372	+	4.71763i	−0.0866094	+	0.150012i
$990$	−0.454618	−	9.84268i	−0.0144487	−	0.312821i
$991$	−41.3258	+	23.8595i	−1.31276	+	0.757921i	−0.982552	−	0.185989i	$-0.940451\pi$
$991$	−41.3258	+	23.8595i	−1.31276	+	0.757921i	−0.330205	+	0.943909i	$0.607118\pi$
$992$	−0.575237	−	4.14811i	−0.0182638	−	0.131703i
$993$	−22.5168			−0.714550
$994$	32.0190	+	11.4774i	1.01558	+	0.364040i
$995$	−59.4958	−	18.1153i	−1.88614	−	0.574295i
$996$	−1.79765	+	1.46393i	−0.0569606	+	0.0463865i
$997$	−8.49992	−	14.7223i	−0.269195	−	0.466260i	0.699459	−	0.714673i	$-0.253424\pi$
$997$	−8.49992	−	14.7223i	−0.269195	−	0.466260i	−0.968654	+	0.248413i	$0.920091\pi$
$998$	9.23786	+	25.9730i	0.292419	+	0.822162i
$999$	−1.02795	+	1.78046i	−0.0325229	+	0.0563313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bk.a.19.12	yes	96
4.3	odd	2	inner	420.2.bk.a.19.5	✓	96
5.4	even	2	inner	420.2.bk.a.19.37	yes	96
7.3	odd	6	inner	420.2.bk.a.199.44	yes	96
20.19	odd	2	inner	420.2.bk.a.19.44	yes	96
28.3	even	6	inner	420.2.bk.a.199.37	yes	96
35.24	odd	6	inner	420.2.bk.a.199.5	yes	96
140.59	even	6	inner	420.2.bk.a.199.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bk.a.19.5	✓	96	4.3	odd	2	inner
420.2.bk.a.19.12	yes	96	1.1	even	1	trivial
420.2.bk.a.19.37	yes	96	5.4	even	2	inner
420.2.bk.a.19.44	yes	96	20.19	odd	2	inner
420.2.bk.a.199.5	yes	96	35.24	odd	6	inner
420.2.bk.a.199.12	yes	96	140.59	even	6	inner
420.2.bk.a.199.37	yes	96	28.3	even	6	inner
420.2.bk.a.199.44	yes	96	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.bk (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07664 - 0.916974i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.318317 + 1.97451i) q^{4} +(-1.63361 + 1.52686i) q^{5} +(1.39089 + 0.255802i) q^{6} +(0.935228 + 2.47494i) q^{7} +(1.46786 - 2.41772i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.07664 - 0.916974i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.318317 + 1.97451i) q^{4} +(-1.63361 + 1.52686i) q^{5} +(1.39089 + 0.255802i) q^{6} +(0.935228 + 2.47494i) q^{7} +(1.46786 - 2.41772i) q^{8} +(0.500000 - 0.866025i) q^{9} +(3.15891 - 0.145905i) q^{10} +(2.69840 - 1.55792i) q^{11} +(-1.26292 - 1.55081i) q^{12} -4.60611 q^{13} +(1.26255 - 3.52221i) q^{14} +(0.651318 - 2.13911i) q^{15} +(-3.79735 + 1.25704i) q^{16} +(-2.11679 - 3.66639i) q^{17} +(-1.33244 + 0.473912i) q^{18} +(-3.59444 + 6.22575i) q^{19} +(-3.53481 - 2.73955i) q^{20} +(-2.04740 - 1.67575i) q^{21} +(-4.33379 - 0.797040i) q^{22} +(-0.354512 + 0.614033i) q^{23} +(-0.0623403 + 2.82774i) q^{24} +(0.337377 - 4.98860i) q^{25} +(4.95913 + 4.22368i) q^{26} +1.00000i q^{27} +(-4.58909 + 2.63443i) q^{28} -9.36267 q^{29} +(-2.66274 + 1.70581i) q^{30} +(-0.370153 - 0.641124i) q^{31} +(5.24106 + 2.12869i) q^{32} +(-1.55792 + 2.69840i) q^{33} +(-1.08296 + 5.88844i) q^{34} +(-5.30670 - 2.61513i) q^{35} +(1.86913 + 0.711583i) q^{36} +(1.78046 + 1.02795i) q^{37} +(9.57878 - 3.40690i) q^{38} +(3.98901 - 2.30305i) q^{39} +(1.29362 + 6.19084i) q^{40} -1.97405i q^{41} +(0.667701 + 3.68160i) q^{42} +7.68301 q^{43} +(3.93508 + 4.83210i) q^{44} +(0.505496 + 2.17818i) q^{45} +(0.944736 - 0.336015i) q^{46} +(-11.0988 - 6.40788i) q^{47} +(2.66008 - 2.98730i) q^{48} +(-5.25070 + 4.62927i) q^{49} +(-4.93766 + 5.06158i) q^{50} +(3.66639 + 2.11679i) q^{51} +(-1.46620 - 9.09479i) q^{52} +(-7.63173 + 4.40618i) q^{53} +(0.916974 - 1.07664i) q^{54} +(-2.02941 + 6.66514i) q^{55} +(7.35652 + 1.37174i) q^{56} -7.18888i q^{57} +(10.0802 + 8.58533i) q^{58} +(2.91078 + 5.04162i) q^{59} +(4.43101 + 0.605118i) q^{60} +(-7.04806 - 4.06920i) q^{61} +(-0.189372 + 1.02968i) q^{62} +(2.61098 + 0.427541i) q^{63} +(-3.69078 - 7.09775i) q^{64} +(7.52460 - 7.03290i) q^{65} +(4.15169 - 1.47664i) q^{66} +(-2.85842 - 4.95093i) q^{67} +(6.56551 - 5.34669i) q^{68} -0.709025i q^{69} +(3.31541 + 7.68167i) q^{70} +9.09059i q^{71} +(-1.35988 - 2.48006i) q^{72} +(2.26326 + 3.92008i) q^{73} +(-0.974315 - 2.73937i) q^{74} +(2.20213 + 4.48895i) q^{75} +(-13.4370 - 5.11548i) q^{76} +(6.37940 + 5.22138i) q^{77} +(-6.40658 - 1.17825i) q^{78} +(-4.91560 - 2.83802i) q^{79} +(4.28407 - 7.85154i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.81016 + 2.12535i) q^{82} -1.15916i q^{83} +(2.65706 - 4.57603i) q^{84} +(9.05610 + 2.75741i) q^{85} +(-8.27186 - 7.04513i) q^{86} +(8.10831 - 4.68134i) q^{87} +(0.194243 - 8.81081i) q^{88} +(2.56797 + 1.48262i) q^{89} +(1.45310 - 2.80865i) q^{90} +(-4.30776 - 11.3999i) q^{91} +(-1.32526 - 0.504530i) q^{92} +(0.641124 + 0.370153i) q^{93} +(6.07354 + 17.0763i) q^{94} +(-3.63395 - 15.6587i) q^{95} +(-5.60323 + 0.777025i) q^{96} +10.2289 q^{97} +(9.89805 - 0.169318i) q^{98} -3.11585i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 48 q^{9}+O(q^{10}) \) 96 * q + 48 * q^9	\( 96 q + 48 q^{9} + 18 q^{10} + 4 q^{14} - 8 q^{16} + 4 q^{25} - 8 q^{30} - 30 q^{40} + 16 q^{44} + 44 q^{46} - 8 q^{49} - 48 q^{50} - 52 q^{56} + 2 q^{60} - 144 q^{64} - 36 q^{66} - 42 q^{70} - 20 q^{74} - 36 q^{80} - 48 q^{81} - 20 q^{84} - 32 q^{85} - 32 q^{86} - 36 q^{94} - 60 q^{96}+O(q^{100}) \) 96 * q + 48 * q^9 + 18 * q^10 + 4 * q^14 - 8 * q^16 + 4 * q^25 - 8 * q^30 - 30 * q^40 + 16 * q^44 + 44 * q^46 - 8 * q^49 - 48 * q^50 - 52 * q^56 + 2 * q^60 - 144 * q^64 - 36 * q^66 - 42 * q^70 - 20 * q^74 - 36 * q^80 - 48 * q^81 - 20 * q^84 - 32 * q^85 - 32 * q^86 - 36 * q^94 - 60 * q^96

Introduction

L-functions

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