LMFDB - Embedded newform 420.2.bb.a.289.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(109,420)]

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([0, 0, 3, 4]))

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

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

chi := DirichletCharacter("420.109");

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.bb (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} - 20 x^{13} - 12 x^{12} + 124 x^{11} - 24 x^{10} + 328 x^{9} + 1132 x^{8} + \cdots + 16 $ x^16 - 2x^15 + 2x^14 - 20x^13 - 12x^12 + 124x^11 - 24x^10 + 328x^9 + 1132x^8 - 760x^7 + 96x^6 - 640x^5 + 96x^4 + 224x^3 + 32x^2 + 32*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.6
Root			$-0.781303 - 2.91586i$ of defining polynomial
Character	$\chi$	$=$	420.289
Dual form			420.2.bb.a.109.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{3} +(0.490439 - 2.18162i) q^{5} +(2.55486 + 0.687541i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{3} +(0.490439 - 2.18162i) q^{5} +(2.55486 + 0.687541i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.90032 - 3.29145i) q^{11} +2.31204i q^{13} +(-0.666078 - 2.13456i) q^{15} +(-0.324831 + 0.187541i) q^{17} +(0.453301 - 0.785140i) q^{19} +(2.55634 - 0.681999i) q^{21} +(1.13626 + 0.656022i) q^{23} +(-4.51894 - 2.13990i) q^{25} -1.00000i q^{27} +6.15561 q^{29} +(-2.81204 - 4.87060i) q^{31} +(-3.29145 - 1.90032i) q^{33} +(2.75296 - 5.23653i) q^{35} +(4.96891 + 2.86880i) q^{37} +(1.15602 + 2.00229i) q^{39} +0.199364 q^{41} +12.4019i q^{43} +(-1.64412 - 1.51554i) q^{45} +(-9.35944 - 5.40368i) q^{47} +(6.05457 + 3.51314i) q^{49} +(-0.187541 + 0.324831i) q^{51} +(2.65267 - 1.53152i) q^{53} +(-8.11268 + 2.53152i) q^{55} -0.906602i q^{57} +(7.14756 + 12.3799i) q^{59} +(-1.08963 + 1.88729i) q^{61} +(1.87286 - 1.86880i) q^{63} +(5.04400 + 1.13392i) q^{65} +(-4.81673 + 2.78094i) q^{67} +1.31204 q^{69} -9.88296 q^{71} +(5.54422 - 3.20095i) q^{73} +(-4.98347 + 0.406258i) q^{75} +(-2.59203 - 9.71572i) q^{77} +(-7.61645 + 13.1921i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.99917i q^{83} +(0.249834 + 0.800636i) q^{85} +(5.33091 - 3.07780i) q^{87} +(-2.50512 + 4.33900i) q^{89} +(-1.58963 + 5.90694i) q^{91} +(-4.87060 - 2.81204i) q^{93} +(-1.49056 - 1.37399i) q^{95} +6.36252i q^{97} -3.80064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{5} + 8 q^{9}+O(q^{10}) $ 16 * q + 2 * q^5 + 8 * q^9	$ 16 q + 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} + 8 q^{19} - 4 q^{21} + 12 q^{25} + 24 q^{29} + 10 q^{35} - 4 q^{39} + 48 q^{41} - 2 q^{45} + 8 q^{49} + 4 q^{51} - 40 q^{55} - 28 q^{59} - 32 q^{61} - 26 q^{65} - 24 q^{69} - 56 q^{71} - 8 q^{75} - 16 q^{79} - 8 q^{81} + 32 q^{85} - 16 q^{89} - 40 q^{91} + 22 q^{95} - 16 q^{99}+O(q^{100}) $ 16 * q + 2 * q^5 + 8 * q^9 - 8 * q^11 + 4 * q^15 + 8 * q^19 - 4 * q^21 + 12 * q^25 + 24 * q^29 + 10 * q^35 - 4 * q^39 + 48 * q^41 - 2 * q^45 + 8 * q^49 + 4 * q^51 - 40 * q^55 - 28 * q^59 - 32 * q^61 - 26 * q^65 - 24 * q^69 - 56 * q^71 - 8 * q^75 - 16 * q^79 - 8 * q^81 + 32 * q^85 - 16 * q^89 - 40 * q^91 + 22 * q^95 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$		0			0
$5$	0.490439	−	2.18162i	0.219331	−	0.975650i
$5$	0.490439	−	2.18162i	0.219331	−	0.975650i
$6$		0			0
$7$	2.55486	+	0.687541i	0.965645	+	0.259866i
$7$	2.55486	+	0.687541i	0.965645	+	0.259866i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−1.90032	−	3.29145i	−0.572967	−	0.992409i	−0.996259	−	0.0864153i	$-0.972459\pi$
$11$	−1.90032	−	3.29145i	−0.572967	−	0.992409i	0.423292	−	0.905993i	$-0.360875\pi$
$12$		0			0
$13$			2.31204i			0.641246i	0.947207	+	0.320623i	$0.103892\pi$
$13$			2.31204i			0.641246i	−0.947207	+	0.320623i	$0.896108\pi$
$14$		0			0
$15$	−0.666078	−	2.13456i	−0.171981	−	0.551141i
$16$		0			0
$17$	−0.324831	+	0.187541i	−0.0787832	+	0.0454855i	−0.538874	−	0.842386i	$-0.681150\pi$
$17$	−0.324831	+	0.187541i	−0.0787832	+	0.0454855i	0.460091	+	0.887872i	$0.347817\pi$
$18$		0			0
$19$	0.453301	−	0.785140i	0.103994	−	0.180124i	−0.809333	−	0.587351i	$-0.800171\pi$
$19$	0.453301	−	0.785140i	0.103994	−	0.180124i	0.913327	+	0.407227i	$0.133504\pi$
$20$		0			0
$21$	2.55634	−	0.681999i	0.557839	−	0.148824i
$22$		0			0
$23$	1.13626	+	0.656022i	0.236927	+	0.136790i	0.613764	−	0.789490i	$-0.289655\pi$
$23$	1.13626	+	0.656022i	0.236927	+	0.136790i	−0.376836	+	0.926280i	$0.622988\pi$
$24$		0			0
$25$	−4.51894	−	2.13990i	−0.903788	−	0.427981i
$26$		0			0
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	6.15561			1.14307			0.571534	−	0.820578i	$-0.306349\pi$
$29$	6.15561			1.14307			0.571534	+	0.820578i	$0.306349\pi$
$30$		0			0
$31$	−2.81204	−	4.87060i	−0.505058	−	0.874786i	−0.999983	−	0.00585051i	$-0.998138\pi$
$31$	−2.81204	−	4.87060i	−0.505058	−	0.874786i	0.494925	−	0.868936i	$-0.335196\pi$
$32$		0			0
$33$	−3.29145	−	1.90032i	−0.572967	−	0.330803i
$34$		0			0
$35$	2.75296	−	5.23653i	0.465334	−	0.885135i
$36$		0			0
$37$	4.96891	+	2.86880i	0.816883	+	0.471628i	0.849340	−	0.527845i	$-0.177000\pi$
$37$	4.96891	+	2.86880i	0.816883	+	0.471628i	−0.0324574	+	0.999473i	$0.510333\pi$
$38$		0			0
$39$	1.15602	+	2.00229i	0.185112	+	0.320623i
$40$		0			0
$41$	0.199364			0.0311354			0.0155677	−	0.999879i	$-0.495044\pi$
$41$	0.199364			0.0311354			0.0155677	+	0.999879i	$0.495044\pi$
$42$		0			0
$43$			12.4019i			1.89127i	0.325225	+	0.945637i	$0.394560\pi$
$43$			12.4019i			1.89127i	−0.325225	+	0.945637i	$0.605440\pi$
$44$		0			0
$45$	−1.64412	−	1.51554i	−0.245091	−	0.225924i
$46$		0			0
$47$	−9.35944	−	5.40368i	−1.36521	−	0.788207i	−0.374902	−	0.927064i	$-0.622324\pi$
$47$	−9.35944	−	5.40368i	−1.36521	−	0.788207i	−0.990312	+	0.138857i	$0.955657\pi$
$48$		0			0
$49$	6.05457	+	3.51314i	0.864939	+	0.501877i
$50$		0			0
$51$	−0.187541	+	0.324831i	−0.0262611	+	0.0454855i
$52$		0			0
$53$	2.65267	−	1.53152i	0.364372	−	0.210370i	−0.306625	−	0.951830i	$-0.599200\pi$
$53$	2.65267	−	1.53152i	0.364372	−	0.210370i	0.670997	+	0.741460i	$0.265866\pi$
$54$		0			0
$55$	−8.11268	+	2.53152i	−1.09391	+	0.341350i
$56$		0			0
$57$		−	0.906602i		−	0.120082i
$58$		0			0
$59$	7.14756	+	12.3799i	0.930533	+	1.61173i	0.782412	+	0.622761i	$0.213989\pi$
$59$	7.14756	+	12.3799i	0.930533	+	1.61173i	0.148120	+	0.988969i	$0.452678\pi$
$60$		0			0
$61$	−1.08963	+	1.88729i	−0.139512	+	0.241643i	−0.927312	−	0.374289i	$-0.877887\pi$
$61$	−1.08963	+	1.88729i	−0.139512	+	0.241643i	0.787800	+	0.615931i	$0.211220\pi$
$62$		0			0
$63$	1.87286	−	1.86880i	0.235958	−	0.235447i
$64$		0			0
$65$	5.04400	+	1.13392i	0.625632	+	0.140645i
$66$		0			0
$67$	−4.81673	+	2.78094i	−0.588457	+	0.339746i	−0.764487	−	0.644639i	$-0.777008\pi$
$67$	−4.81673	+	2.78094i	−0.588457	+	0.339746i	0.176030	+	0.984385i	$0.443674\pi$
$68$		0			0
$69$	1.31204			0.157952
$70$		0			0
$71$	−9.88296			−1.17289			−0.586446	−	0.809989i	$-0.699473\pi$
$71$	−9.88296			−1.17289			−0.586446	+	0.809989i	$0.699473\pi$
$72$		0			0
$73$	5.54422	−	3.20095i	0.648901	−	0.374643i	−0.139134	−	0.990274i	$-0.544432\pi$
$73$	5.54422	−	3.20095i	0.648901	−	0.374643i	0.788035	+	0.615630i	$0.211098\pi$
$74$		0			0
$75$	−4.98347	+	0.406258i	−0.575441	+	0.0469106i
$76$		0			0
$77$	−2.59203	−	9.71572i	−0.295389	−	1.10721i
$78$		0			0
$79$	−7.61645	+	13.1921i	−0.856918	+	1.48423i	0.0179364	+	0.999839i	$0.494290\pi$
$79$	−7.61645	+	13.1921i	−0.856918	+	1.48423i	−0.874854	+	0.484386i	$0.839043\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	8.99917i		−	0.987787i	−0.869522	−	0.493894i	$-0.835573\pi$
$83$		−	8.99917i		−	0.987787i	0.869522	−	0.493894i	$-0.164427\pi$
$84$		0			0
$85$	0.249834	+	0.800636i	0.0270983	+	0.0868412i
$86$		0			0
$87$	5.33091	−	3.07780i	0.571534	−	0.329975i
$88$		0			0
$89$	−2.50512	+	4.33900i	−0.265543	+	0.459933i	−0.967706	−	0.252083i	$-0.918884\pi$
$89$	−2.50512	+	4.33900i	−0.265543	+	0.459933i	0.702163	+	0.712016i	$0.252218\pi$
$90$		0			0
$91$	−1.58963	+	5.90694i	−0.166638	+	0.619216i
$92$		0			0
$93$	−4.87060	−	2.81204i	−0.505058	−	0.291595i
$94$		0			0
$95$	−1.49056	−	1.37399i	−0.152928	−	0.140969i
$96$		0			0
$97$			6.36252i			0.646016i	0.946396	+	0.323008i	$0.104694\pi$
$97$			6.36252i			0.646016i	−0.946396	+	0.323008i	$0.895306\pi$
$98$		0			0
$99$	−3.80064			−0.381978
$100$		0			0
$101$	2.94148	+	5.09479i	0.292688	+	0.506951i	0.974444	−	0.224629i	$-0.0721169\pi$
$101$	2.94148	+	5.09479i	0.292688	+	0.506951i	−0.681756	+	0.731579i	$0.738784\pi$
$102$		0			0
$103$	−10.9765	−	6.33728i	−1.08155	−	0.624431i	−0.150233	−	0.988651i	$-0.548002\pi$
$103$	−10.9765	−	6.33728i	−1.08155	−	0.624431i	−0.931313	+	0.364220i	$0.881336\pi$
$104$		0			0
$105$	−0.234135	−	5.91144i	−0.0228492	−	0.576898i
$106$		0			0
$107$	−2.18076	−	1.25906i	−0.210822	−	0.121718i	0.390871	−	0.920445i	$-0.372174\pi$
$107$	−2.18076	−	1.25906i	−0.210822	−	0.121718i	−0.601693	+	0.798727i	$0.705507\pi$
$108$		0			0
$109$	5.65938	+	9.80233i	0.542070	+	0.938893i	0.998785	+	0.0492801i	$0.0156927\pi$
$109$	5.65938	+	9.80233i	0.542070	+	0.938893i	−0.456715	+	0.889613i	$0.650974\pi$
$110$		0			0
$111$	5.73760			0.544589
$112$		0			0
$113$			15.4752i			1.45578i	0.685692	+	0.727892i	$0.259500\pi$
$113$			15.4752i			1.45578i	−0.685692	+	0.727892i	$0.740500\pi$
$114$		0			0
$115$	1.98846	−	2.15716i	0.185425	−	0.201156i
$116$		0			0
$117$	2.00229	+	1.15602i	0.185112	+	0.106874i
$118$		0			0
$119$	−0.958839	+	0.255806i	−0.0878967	+	0.0234497i
$120$		0			0
$121$	−1.72242	+	2.98332i	−0.156583	+	0.271211i
$122$		0			0
$123$	0.172654	−	0.0996818i	0.0155677	−	0.00898801i
$124$		0			0
$125$	−6.88472	+	8.80912i	−0.615788	+	0.787912i
$126$		0			0
$127$			15.1159i			1.34132i	0.741767	+	0.670658i	$0.233988\pi$
$127$			15.1159i			1.34132i	−0.741767	+	0.670658i	$0.766012\pi$
$128$		0			0
$129$	6.20095	+	10.7404i	0.545964	+	0.945637i
$130$		0			0
$131$	1.93519	−	3.35186i	0.169079	−	0.292853i	−0.769017	−	0.639228i	$-0.779254\pi$
$131$	1.93519	−	3.35186i	0.169079	−	0.292853i	0.938096	+	0.346375i	$0.112587\pi$
$132$		0			0
$133$	1.69793	−	1.69426i	0.147230	−	0.146911i
$134$		0			0
$135$	−2.18162	−	0.490439i	−0.187764	−	0.0422103i
$136$		0			0
$137$	−14.7187	+	8.49782i	−1.25750	+	0.726018i	−0.972588	−	0.232536i	$-0.925298\pi$
$137$	−14.7187	+	8.49782i	−1.25750	+	0.726018i	−0.284912	+	0.958554i	$0.591964\pi$
$138$		0			0
$139$	8.19500			0.695091			0.347546	−	0.937663i	$-0.387015\pi$
$139$	8.19500			0.695091			0.347546	+	0.937663i	$0.387015\pi$
$140$		0			0
$141$	−10.8074			−0.910143
$142$		0			0
$143$	7.60997	−	4.39362i	0.636378	−	0.367413i
$144$		0			0
$145$	3.01895	−	13.4292i	0.250710	−	1.11523i
$146$		0			0
$147$	6.99998	+	0.0151800i	0.577349	+	0.00125202i
$148$		0			0
$149$	5.97812	−	10.3544i	0.489747	−	0.848266i	−0.510184	−	0.860066i	$-0.670423\pi$
$149$	5.97812	−	10.3544i	0.489747	−	0.848266i	0.999930	+	0.0117991i	$0.00375586\pi$
$150$		0			0
$151$	−9.02305	−	15.6284i	−0.734286	−	1.27182i	−0.955036	−	0.296490i	$-0.904184\pi$
$151$	−9.02305	−	15.6284i	−0.734286	−	1.27182i	0.220750	−	0.975330i	$-0.429149\pi$
$152$		0			0
$153$			0.375083i			0.0303237i
$154$		0			0
$155$	−12.0049	+	3.74608i	−0.964261	+	0.300892i
$156$		0			0
$157$	19.4777	−	11.2455i	1.55449	−	0.897486i	0.556725	−	0.830697i	$-0.312058\pi$
$157$	19.4777	−	11.2455i	1.55449	−	0.897486i	0.997767	−	0.0667896i	$-0.0212756\pi$
$158$		0			0
$159$	1.53152	−	2.65267i	0.121457	−	0.210370i
$160$		0			0
$161$	2.45195	+	2.45727i	0.193241	+	0.193660i
$162$		0			0
$163$	−8.96461	−	5.17572i	−0.702162	−	0.405394i	0.105990	−	0.994367i	$-0.466199\pi$
$163$	−8.96461	−	5.17572i	−0.702162	−	0.405394i	−0.808152	+	0.588974i	$0.799532\pi$
$164$		0			0
$165$	−5.76003	+	6.24870i	−0.448418	+	0.486461i
$166$		0			0
$167$		−	2.08083i		−	0.161020i	−0.996754	−	0.0805098i	$-0.974345\pi$
$167$		−	2.08083i		−	0.161020i	0.996754	−	0.0805098i	$-0.0256548\pi$
$168$		0			0
$169$	7.65445			0.588804
$170$		0			0
$171$	−0.453301	−	0.785140i	−0.0346648	−	0.0600412i
$172$		0			0
$173$	−20.6724	−	11.9352i	−1.57169	−	0.907416i	−0.995962	−	0.0897753i	$-0.971385\pi$
$173$	−20.6724	−	11.9352i	−1.57169	−	0.907416i	−0.575729	−	0.817641i	$-0.695282\pi$
$174$		0			0
$175$	−10.0740	−	8.57410i	−0.761520	−	0.648141i
$176$		0			0
$177$	12.3799	+	7.14756i	0.930533	+	0.537243i
$178$		0			0
$179$	6.40544	+	11.0946i	0.478765	+	0.829246i	0.999704	−	0.0243486i	$-0.00775116\pi$
$179$	6.40544	+	11.0946i	0.478765	+	0.829246i	−0.520938	+	0.853594i	$0.674418\pi$
$180$		0			0
$181$	−3.04611			−0.226416			−0.113208	−	0.993571i	$-0.536113\pi$
$181$	−3.04611			−0.226416			−0.113208	+	0.993571i	$0.536113\pi$
$182$		0			0
$183$			2.17925i			0.161095i
$184$		0			0
$185$	8.69558	−	9.43330i	0.639312	−	0.693550i
$186$		0			0
$187$	1.23457	+	0.712777i	0.0902804	+	0.0521234i
$188$		0			0
$189$	0.687541	−	2.55486i	0.0500113	−	0.185838i
$190$		0			0
$191$	8.58116	−	14.8630i	0.620911	−	1.07545i	−0.368405	−	0.929665i	$-0.620096\pi$
$191$	8.58116	−	14.8630i	0.620911	−	1.07545i	0.989316	−	0.145784i	$-0.0465705\pi$
$192$		0			0
$193$	12.2424	−	7.06816i	0.881228	−	0.508777i	0.0101652	−	0.999948i	$-0.496764\pi$
$193$	12.2424	−	7.06816i	0.881228	−	0.508777i	0.871063	+	0.491171i	$0.163431\pi$
$194$		0			0
$195$	4.93519	−	1.54000i	0.353417	−	0.110282i
$196$		0			0
$197$		−	1.80818i		−	0.128827i	−0.997923	−	0.0644137i	$-0.979482\pi$
$197$		−	1.80818i		−	0.128827i	0.997923	−	0.0644137i	$-0.0205177\pi$
$198$		0			0
$199$	−9.11645	−	15.7902i	−0.646248	−	1.11933i	−0.984012	−	0.178104i	$-0.943004\pi$
$199$	−9.11645	−	15.7902i	−0.646248	−	1.11933i	0.337764	−	0.941231i	$-0.390330\pi$
$200$		0			0
$201$	−2.78094	+	4.81673i	−0.196152	+	0.339746i
$202$		0			0
$203$	15.7267	+	4.23224i	1.10380	+	0.297045i
$204$		0			0
$205$	0.0977757	−	0.434936i	0.00682895	−	0.0303772i
$206$		0			0
$207$	1.13626	−	0.656022i	0.0789758	−	0.0455967i
$208$		0			0
$209$	−3.44566			−0.238342
$210$		0			0
$211$	16.1927			1.11475			0.557375	−	0.830261i	$-0.311809\pi$
$211$	16.1927			1.11475			0.557375	+	0.830261i	$0.311809\pi$
$212$		0			0
$213$	−8.55889	+	4.94148i	−0.586446	+	0.338585i
$214$		0			0
$215$	27.0563	+	6.08238i	1.84522	+	0.414815i
$216$		0			0
$217$	−3.83563	−	14.3771i	−0.260379	−	0.975980i
$218$		0			0
$219$	3.20095	−	5.54422i	0.216300	−	0.374643i
$220$		0			0
$221$	−0.433604	−	0.751024i	−0.0291674	−	0.0505194i
$222$		0			0
$223$		−	9.91415i		−	0.663900i	−0.943297	−	0.331950i	$-0.892293\pi$
$223$		−	9.91415i		−	0.663900i	0.943297	−	0.331950i	$-0.107707\pi$
$224$		0			0
$225$	−4.11268	+	2.84356i	−0.274179	+	0.189571i
$226$		0			0
$227$	−11.7950	+	6.80986i	−0.782864	+	0.451987i	−0.837444	−	0.546523i	$-0.815951\pi$
$227$	−11.7950	+	6.80986i	−0.782864	+	0.451987i	0.0545806	+	0.998509i	$0.482618\pi$
$228$		0			0
$229$	11.5268	−	19.9650i	0.761714	−	1.31933i	−0.180252	−	0.983620i	$-0.557691\pi$
$229$	11.5268	−	19.9650i	0.761714	−	1.31933i	0.941966	−	0.335707i	$-0.108975\pi$
$230$		0			0
$231$	−7.10263	−	7.11804i	−0.467318	−	0.468333i
$232$		0			0
$233$	26.2589	+	15.1606i	1.72027	+	0.993201i	0.918343	+	0.395786i	$0.129528\pi$
$233$	26.2589	+	15.1606i	1.72027	+	0.993201i	0.801932	+	0.597416i	$0.203806\pi$
$234$		0			0
$235$	−16.3790	+	17.7686i	−1.06845	+	1.15909i
$236$		0			0
$237$			15.2329i			0.989484i
$238$		0			0
$239$	−11.0327			−0.713647			−0.356823	−	0.934172i	$-0.616140\pi$
$239$	−11.0327			−0.713647			−0.356823	+	0.934172i	$0.616140\pi$
$240$		0			0
$241$	−3.16021	−	5.47364i	−0.203567	−	0.352588i	0.746108	−	0.665825i	$-0.231920\pi$
$241$	−3.16021	−	5.47364i	−0.203567	−	0.352588i	−0.949675	+	0.313236i	$0.898587\pi$
$242$		0			0
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$		0			0
$245$	10.6337	−	11.4858i	0.679364	−	0.733801i
$246$		0			0
$247$	1.81528	+	1.04805i	0.115503	+	0.0666860i
$248$		0			0
$249$	−4.49959	−	7.79351i	−0.285150	−	0.493894i
$250$		0			0
$251$	19.3161			1.21922			0.609609	−	0.792702i	$-0.291326\pi$
$251$	19.3161			1.21922			0.609609	+	0.792702i	$0.291326\pi$
$252$		0			0
$253$		−	4.98660i		−	0.313505i
$254$		0			0
$255$	0.616681	+	0.568454i	0.0386181	+	0.0355980i
$256$		0			0
$257$	−12.4229	−	7.17238i	−0.774921	−	0.447401i	0.0597064	−	0.998216i	$-0.480984\pi$
$257$	−12.4229	−	7.17238i	−0.774921	−	0.447401i	−0.834627	+	0.550815i	$0.814317\pi$
$258$		0			0
$259$	10.7224	+	10.7457i	0.666259	+	0.667705i
$260$		0			0
$261$	3.07780	−	5.33091i	0.190511	−	0.329975i
$262$		0			0
$263$	7.85188	−	4.53329i	0.484168	−	0.279534i	−0.237984	−	0.971269i	$-0.576487\pi$
$263$	7.85188	−	4.53329i	0.484168	−	0.279534i	0.722152	+	0.691735i	$0.243153\pi$
$264$		0			0
$265$	−2.04022	−	6.53823i	−0.125330	−	0.401641i
$266$		0			0
$267$			5.01025i			0.306622i
$268$		0			0
$269$	−5.33309	−	9.23719i	−0.325165	−	0.563201i	0.656381	−	0.754429i	$-0.272086\pi$
$269$	−5.33309	−	9.23719i	−0.325165	−	0.563201i	−0.981546	+	0.191228i	$0.938753\pi$
$270$		0			0
$271$	10.2721	−	17.7917i	0.623983	−	1.08077i	−0.364753	−	0.931104i	$-0.618847\pi$
$271$	10.2721	−	17.7917i	0.623983	−	1.08077i	0.988737	−	0.149667i	$-0.0478200\pi$
$272$		0			0
$273$	1.57681	+	5.91037i	0.0954331	+	0.357712i
$274$		0			0
$275$	1.54404	+	18.9403i	0.0931090	+	1.14215i
$276$		0			0
$277$	11.3552	−	6.55593i	0.682268	−	0.393907i	−0.118441	−	0.992961i	$-0.537790\pi$
$277$	11.3552	−	6.55593i	0.682268	−	0.393907i	0.800709	+	0.599054i	$0.204456\pi$
$278$		0			0
$279$	−5.62409			−0.336705
$280$		0			0
$281$	−12.3701			−0.737936			−0.368968	−	0.929442i	$-0.620289\pi$
$281$	−12.3701			−0.737936			−0.368968	+	0.929442i	$0.620289\pi$
$282$		0			0
$283$	−16.7131	+	9.64932i	−0.993492	+	0.573593i	−0.906316	−	0.422600i	$-0.861117\pi$
$283$	−16.7131	+	9.64932i	−0.993492	+	0.573593i	−0.0871757	+	0.996193i	$0.527784\pi$
$284$		0			0
$285$	−1.97786	−	0.444633i	−0.117158	−	0.0263378i
$286$		0			0
$287$	0.509345	+	0.137071i	0.0300657	+	0.00809103i
$288$		0			0
$289$	−8.42966	+	14.6006i	−0.495862	+	0.858858i
$290$		0			0
$291$	3.18126	+	5.51010i	0.186489	+	0.323008i
$292$		0			0
$293$			18.6340i			1.08861i	0.838888	+	0.544305i	$0.183206\pi$
$293$			18.6340i			1.08861i	−0.838888	+	0.544305i	$0.816794\pi$
$294$		0			0
$295$	30.5138	−	9.52166i	1.77658	−	0.554372i
$296$		0			0
$297$	−3.29145	+	1.90032i	−0.190989	+	0.110268i
$298$		0			0
$299$	−1.51675	+	2.62709i	−0.0877161	+	0.151929i
$300$		0			0
$301$	−8.52683	+	31.6851i	−0.491478	+	1.82630i
$302$		0			0
$303$	5.09479	+	2.94148i	0.292688	+	0.168984i
$304$		0			0
$305$	3.58295	+	3.30275i	0.205159	+	0.189115i
$306$		0			0
$307$		−	17.3278i		−	0.988949i	−0.869192	−	0.494475i	$-0.835360\pi$
$307$		−	17.3278i		−	0.988949i	0.869192	−	0.494475i	$-0.164640\pi$
$308$		0			0
$309$	−12.6746			−0.721031
$310$		0			0
$311$	0.484075	+	0.838442i	0.0274494	+	0.0475437i	0.879424	−	0.476040i	$-0.157928\pi$
$311$	0.484075	+	0.838442i	0.0274494	+	0.0475437i	−0.851974	+	0.523583i	$0.824595\pi$
$312$		0			0
$313$	−23.1008	−	13.3373i	−1.30574	−	0.753868i	−0.324355	−	0.945935i	$-0.605147\pi$
$313$	−23.1008	−	13.3373i	−1.30574	−	0.753868i	−0.981382	+	0.192068i	$0.938481\pi$
$314$		0			0
$315$	−3.15849	−	5.00239i	−0.177961	−	0.281853i
$316$		0			0
$317$	−27.7435	−	16.0177i	−1.55823	−	0.899644i	−0.997427	−	0.0716949i	$-0.977159\pi$
$317$	−27.7435	−	16.0177i	−1.55823	−	0.899644i	−0.560803	−	0.827949i	$-0.689507\pi$
$318$		0			0
$319$	−11.6976	−	20.2609i	−0.654941	−	1.13439i
$320$		0			0
$321$	−2.51812			−0.140548
$322$		0			0
$323$			0.340051i			0.0189209i
$324$		0			0
$325$	4.94755	−	10.4480i	0.274441	−	0.579550i
$326$		0			0
$327$	9.80233	+	5.65938i	0.542070	+	0.312964i
$328$		0			0
$329$	−20.1968	−	20.2406i	−1.11348	−	1.11590i
$330$		0			0
$331$	0.343564	−	0.595070i	0.0188840	−	0.0327080i	−0.856429	−	0.516265i	$-0.827322\pi$
$331$	0.343564	−	0.595070i	0.0188840	−	0.0327080i	0.875313	+	0.483557i	$0.160655\pi$
$332$		0			0
$333$	4.96891	−	2.86880i	0.272294	−	0.157209i
$334$		0			0
$335$	3.70464	+	11.8722i	0.202406	+	0.648645i
$336$		0			0
$337$		−	15.0220i		−	0.818300i	−0.912467	−	0.409150i	$-0.865825\pi$
$337$		−	15.0220i		−	0.818300i	0.912467	−	0.409150i	$-0.134175\pi$
$338$		0			0
$339$	7.73760	+	13.4019i	0.420249	+	0.727892i
$340$		0			0
$341$	−10.6876	+	18.5114i	−0.578764	+	1.00245i
$342$		0			0
$343$	13.0531	+	13.1383i	0.704803	+	0.709403i
$344$		0			0
$345$	0.643478	−	2.86238i	0.0346437	−	0.154106i
$346$		0			0
$347$	−21.5203	+	12.4247i	−1.15527	+	0.666994i	−0.950165	−	0.311746i	$-0.899086\pi$
$347$	−21.5203	+	12.4247i	−1.15527	+	0.666994i	−0.205102	+	0.978740i	$0.565753\pi$
$348$		0			0
$349$	−25.4530			−1.36247			−0.681235	−	0.732065i	$-0.738557\pi$
$349$	−25.4530			−1.36247			−0.681235	+	0.732065i	$0.738557\pi$
$350$		0			0
$351$	2.31204			0.123408
$352$		0			0
$353$	−12.6953	+	7.32964i	−0.675703	+	0.390118i	−0.798234	−	0.602347i	$-0.794232\pi$
$353$	−12.6953	+	7.32964i	−0.675703	+	0.390118i	0.122531	+	0.992465i	$0.460899\pi$
$354$		0			0
$355$	−4.84699	+	21.5609i	−0.257251	+	1.14433i
$356$		0			0
$357$	−0.702476	+	0.700954i	−0.0371790	+	0.0370984i
$358$		0			0
$359$	−2.96430	+	5.13431i	−0.156450	+	0.270979i	−0.933586	−	0.358354i	$-0.883338\pi$
$359$	−2.96430	+	5.13431i	−0.156450	+	0.270979i	0.777136	+	0.629332i	$0.216672\pi$
$360$		0			0
$361$	9.08904	+	15.7427i	0.478370	+	0.828562i
$362$		0			0
$363$			3.44484i			0.180807i
$364$		0			0
$365$	−4.26417	−	13.6652i	−0.223197	−	0.715272i
$366$		0			0
$367$	4.41884	−	2.55122i	0.230661	−	0.133172i	−0.380216	−	0.924898i	$-0.624150\pi$
$367$	4.41884	−	2.55122i	0.230661	−	0.133172i	0.610877	+	0.791725i	$0.290817\pi$
$368$		0			0
$369$	0.0996818	−	0.172654i	0.00518923	−	0.00898801i
$370$		0			0
$371$	7.83017	−	2.08899i	0.406522	−	0.108455i
$372$		0			0
$373$	−4.12611	−	2.38221i	−0.213642	−	0.123346i	0.389361	−	0.921085i	$-0.372696\pi$
$373$	−4.12611	−	2.38221i	−0.213642	−	0.123346i	−0.603003	+	0.797739i	$0.706029\pi$
$374$		0			0
$375$	−1.55779	+	11.0713i	−0.0804438	+	0.571719i
$376$		0			0
$377$			14.2320i			0.732987i
$378$		0			0
$379$	14.6147			0.750707			0.375353	−	0.926882i	$-0.377521\pi$
$379$	14.6147			0.750707			0.375353	+	0.926882i	$0.377521\pi$
$380$		0			0
$381$	7.55793	+	13.0907i	0.387205	+	0.670658i
$382$		0			0
$383$	1.74368	+	1.00672i	0.0890980	+	0.0514408i	0.543887	−	0.839158i	$-0.316952\pi$
$383$	1.74368	+	1.00672i	0.0890980	+	0.0514408i	−0.454789	+	0.890599i	$0.650285\pi$
$384$		0			0
$385$	−22.4673	+	0.889861i	−1.14504	+	0.0453515i
$386$		0			0
$387$	10.7404	+	6.20095i	0.545964	+	0.315212i
$388$		0			0
$389$	−0.264600	−	0.458301i	−0.0134158	−	0.0232368i	0.859240	−	0.511573i	$-0.170937\pi$
$389$	−0.264600	−	0.458301i	−0.0134158	−	0.0232368i	−0.872655	+	0.488337i	$0.837604\pi$
$390$		0			0
$391$	−0.492125			−0.0248879
$392$		0			0
$393$		−	3.87039i		−	0.195235i
$394$		0			0
$395$	25.0447	+	23.0861i	1.26014	+	1.16159i
$396$		0			0
$397$	24.7394	+	14.2833i	1.24163	+	0.716857i	0.969427	−	0.245382i	$-0.0789133\pi$
$397$	24.7394	+	14.2833i	1.24163	+	0.716857i	0.272206	+	0.962239i	$0.412247\pi$
$398$		0			0
$399$	0.623326	−	2.31624i	0.0312053	−	0.115957i
$400$		0			0
$401$	−16.4945	+	28.5693i	−0.823695	+	1.42668i	0.0792176	+	0.996857i	$0.474758\pi$
$401$	−16.4945	+	28.5693i	−0.823695	+	1.42668i	−0.902913	+	0.429824i	$0.858576\pi$
$402$		0			0
$403$	11.2611	−	6.50157i	0.560953	−	0.323866i
$404$		0			0
$405$	−2.13456	+	0.666078i	−0.106067	+	0.0330977i
$406$		0			0
$407$		−	21.8065i		−	1.08091i
$408$		0			0
$409$	−9.10799	−	15.7755i	−0.450361	−	0.780048i	0.548047	−	0.836447i	$-0.315371\pi$
$409$	−9.10799	−	15.7755i	−0.450361	−	0.780048i	−0.998408	+	0.0563992i	$0.982038\pi$
$410$		0			0
$411$	−8.49782	+	14.7187i	−0.419167	+	0.726018i
$412$		0			0
$413$	9.74926	+	36.5432i	0.479730	+	1.79817i
$414$		0			0
$415$	−19.6328	−	4.41355i	−0.963735	−	0.216652i
$416$		0			0
$417$	7.09708	−	4.09750i	0.347546	−	0.200655i
$418$		0			0
$419$	14.3665			0.701851			0.350925	−	0.936403i	$-0.385867\pi$
$419$	14.3665			0.701851			0.350925	+	0.936403i	$0.385867\pi$
$420$		0			0
$421$	15.9374			0.776743			0.388372	−	0.921503i	$-0.373038\pi$
$421$	15.9374			0.776743			0.388372	+	0.921503i	$0.373038\pi$
$422$		0			0
$423$	−9.35944	+	5.40368i	−0.455072	+	0.262736i
$424$		0			0
$425$	1.86921	−	0.152380i	0.0906702	−	0.00739153i
$426$		0			0
$427$	−4.08143	+	4.07259i	−0.197514	+	0.197086i
$428$		0			0
$429$	4.39362	−	7.60997i	0.212126	−	0.367413i
$430$		0			0
$431$	−5.10420	−	8.84073i	−0.245861	−	0.425843i	0.716513	−	0.697574i	$-0.245737\pi$
$431$	−5.10420	−	8.84073i	−0.245861	−	0.425843i	−0.962373	+	0.271731i	$0.912404\pi$
$432$		0			0
$433$		−	32.6618i		−	1.56963i	−0.619732	−	0.784814i	$-0.712759\pi$
$433$		−	32.6618i		−	1.56963i	0.619732	−	0.784814i	$-0.287241\pi$
$434$		0			0
$435$	−4.10011	−	13.1395i	−0.196585	−	0.629991i
$436$		0			0
$437$	1.03014	−	0.594751i	0.0492782	−	0.0284508i
$438$		0			0
$439$	−5.26181	+	9.11373i	−0.251133	+	0.434974i	−0.963838	−	0.266489i	$-0.914136\pi$
$439$	−5.26181	+	9.11373i	−0.251133	+	0.434974i	0.712705	+	0.701464i	$0.247470\pi$
$440$		0			0
$441$	6.06975	−	3.48685i	0.289036	−	0.166040i
$442$		0			0
$443$	−30.4879	−	17.6022i	−1.44853	−	0.836306i	−0.450131	−	0.892962i	$-0.648623\pi$
$443$	−30.4879	−	17.6022i	−1.44853	−	0.836306i	−0.998394	+	0.0566561i	$0.981956\pi$
$444$		0			0
$445$	8.23745	+	7.59325i	0.390493	+	0.359955i
$446$		0			0
$447$		−	11.9562i		−	0.565511i
$448$		0			0
$449$	2.85276			0.134630			0.0673151	−	0.997732i	$-0.478557\pi$
$449$	2.85276			0.134630			0.0673151	+	0.997732i	$0.478557\pi$
$450$		0			0
$451$	−0.378854	−	0.656195i	−0.0178396	−	0.0308990i
$452$		0			0
$453$	−15.6284	−	9.02305i	−0.734286	−	0.423940i
$454$		0			0
$455$	12.1071	+	6.36496i	0.567589	+	0.298394i
$456$		0			0
$457$	0.161053	+	0.0929842i	0.00753376	+	0.00434962i	0.503762	−	0.863842i	$-0.331949\pi$
$457$	0.161053	+	0.0929842i	0.00753376	+	0.00434962i	−0.496228	+	0.868192i	$0.665282\pi$
$458$		0			0
$459$	0.187541	+	0.324831i	0.00875368	+	0.0151618i
$460$		0			0
$461$	−7.00484			−0.326248			−0.163124	−	0.986606i	$-0.552157\pi$
$461$	−7.00484			−0.326248			−0.163124	+	0.986606i	$0.552157\pi$
$462$		0			0
$463$			38.3435i			1.78198i	0.454027	+	0.890988i	$0.349987\pi$
$463$			38.3435i			1.78198i	−0.454027	+	0.890988i	$0.650013\pi$
$464$		0			0
$465$	−8.52355	+	9.24668i	−0.395270	+	0.428804i
$466$		0			0
$467$	16.0546	+	9.26912i	0.742917	+	0.428924i	0.823129	−	0.567854i	$-0.192226\pi$
$467$	16.0546	+	9.26912i	0.742917	+	0.428924i	−0.0802117	+	0.996778i	$0.525560\pi$
$468$		0			0
$469$	−14.2181	+	3.79320i	−0.656529	+	0.175154i
$470$		0			0
$471$	11.2455	−	19.4777i	0.518164	−	0.897486i
$472$		0			0
$473$	40.8202	−	23.5676i	1.87692	−	1.08364i
$474$		0			0
$475$	−3.72856	+	2.57798i	−0.171078	+	0.118286i
$476$		0			0
$477$		−	3.06304i		−	0.140247i
$478$		0			0
$479$	−17.0983	−	29.6152i	−0.781243	−	1.35315i	−0.931218	−	0.364463i	$-0.881252\pi$
$479$	−17.0983	−	29.6152i	−0.781243	−	1.35315i	0.149974	−	0.988690i	$-0.452081\pi$
$480$		0			0
$481$	−6.63279	+	11.4883i	−0.302429	+	0.523823i
$482$		0			0
$483$	3.35208	+	0.902085i	0.152525	+	0.0410463i
$484$		0			0
$485$	13.8806	+	3.12043i	0.630285	+	0.141691i
$486$		0			0
$487$	−12.8143	+	7.39831i	−0.580669	+	0.335250i	−0.761399	−	0.648283i	$-0.775487\pi$
$487$	−12.8143	+	7.39831i	−0.580669	+	0.335250i	0.180730	+	0.983533i	$0.442154\pi$
$488$		0			0
$489$	−10.3514			−0.468108
$490$		0			0
$491$	−5.47873			−0.247252			−0.123626	−	0.992329i	$-0.539452\pi$
$491$	−5.47873			−0.247252			−0.123626	+	0.992329i	$0.539452\pi$
$492$		0			0
$493$	−1.99953	+	1.15443i	−0.0900545	+	0.0519930i
$494$		0			0
$495$	−1.86398	+	8.29155i	−0.0837797	+	0.372677i
$496$		0			0
$497$	−25.2495	−	6.79494i	−1.13260	−	0.304795i
$498$		0			0
$499$	3.21395	−	5.56673i	0.143876	−	0.249201i	−0.785077	−	0.619398i	$-0.787377\pi$
$499$	3.21395	−	5.56673i	0.143876	−	0.249201i	0.928953	+	0.370197i	$0.120710\pi$
$500$		0			0
$501$	−1.04042	−	1.80205i	−0.0464823	−	0.0805098i
$502$		0			0
$503$		−	33.5288i		−	1.49498i	−0.664274	−	0.747489i	$-0.731259\pi$
$503$		−	33.5288i		−	1.49498i	0.664274	−	0.747489i	$-0.268741\pi$
$504$		0			0
$505$	12.5575	−	3.91851i	0.558802	−	0.174371i
$506$		0			0
$507$	6.62895	−	3.82722i	0.294402	−	0.169973i
$508$		0			0
$509$	−16.5079	+	28.5925i	−0.731699	+	1.26734i	0.224458	+	0.974484i	$0.427939\pi$
$509$	−16.5079	+	28.5925i	−0.731699	+	1.26734i	−0.956157	+	0.292856i	$0.905395\pi$
$510$		0			0
$511$	16.3655	−	4.36610i	0.723965	−	0.193145i
$512$		0			0
$513$	−0.785140	−	0.453301i	−0.0346648	−	0.0200137i
$514$		0			0
$515$	−19.2088	+	20.8385i	−0.846443	+	0.918254i
$516$		0			0
$517$			41.0748i			1.80647i
$518$		0			0
$519$	−23.8704			−1.04779
$520$		0			0
$521$	7.49884	+	12.9884i	0.328530	+	0.569031i	0.982220	−	0.187731i	$-0.0601134\pi$
$521$	7.49884	+	12.9884i	0.328530	+	0.569031i	−0.653690	+	0.756762i	$0.726780\pi$
$522$		0			0
$523$	17.6140	+	10.1695i	0.770207	+	0.444679i	0.832948	−	0.553351i	$-0.186651\pi$
$523$	17.6140	+	10.1695i	0.770207	+	0.444679i	−0.0627415	+	0.998030i	$0.519984\pi$
$524$		0			0
$525$	−13.0114	−	2.38841i	−0.567862	−	0.104239i
$526$		0			0
$527$	1.82688	+	1.05475i	0.0795801	+	0.0459456i
$528$		0			0
$529$	−10.6393	−	18.4278i	−0.462577	−	0.801207i
$530$		0			0
$531$	14.2951			0.620355
$532$		0			0
$533$			0.460938i			0.0199654i
$534$		0			0
$535$	−3.81633	+	4.14010i	−0.164994	+	0.178992i
$536$		0			0
$537$	11.0946	+	6.40544i	0.478765	+	0.276415i
$538$		0			0
$539$	0.0576935	−	26.6044i	0.00248504	−	1.14593i
$540$		0			0
$541$	−8.38064	+	14.5157i	−0.360312	+	0.624078i	−0.988012	−	0.154377i	$-0.950663\pi$
$541$	−8.38064	+	14.5157i	−0.360312	+	0.624078i	0.627700	+	0.778455i	$0.283996\pi$
$542$		0			0
$543$	−2.63801	+	1.52305i	−0.113208	+	0.0653605i
$544$		0			0
$545$	24.1606	−	7.53917i	1.03492	−	0.322943i
$546$		0			0
$547$		−	4.58552i		−	0.196063i	−0.995183	−	0.0980314i	$-0.968745\pi$
$547$		−	4.58552i		−	0.196063i	0.995183	−	0.0980314i	$-0.0312546\pi$
$548$		0			0
$549$	1.08963	+	1.88729i	0.0465041	+	0.0805475i
$550$		0			0
$551$	2.79034	−	4.83302i	0.118873	−	0.205893i
$552$		0			0
$553$	−28.5290	+	28.4672i	−1.21318	+	1.21055i
$554$		0			0
$555$	2.81394	−	12.5173i	0.119445	−	0.531328i
$556$		0			0
$557$	19.8726	−	11.4734i	0.842028	−	0.486145i	−0.0159254	−	0.999873i	$-0.505069\pi$
$557$	19.8726	−	11.4734i	0.842028	−	0.486145i	0.857953	+	0.513728i	$0.171736\pi$
$558$		0			0
$559$	−28.6738			−1.21277
$560$		0			0
$561$	1.42555			0.0601869
$562$		0			0
$563$	−19.0116	+	10.9764i	−0.801244	+	0.462598i	−0.843906	−	0.536491i	$-0.819749\pi$
$563$	−19.0116	+	10.9764i	−0.801244	+	0.462598i	0.0426622	+	0.999090i	$0.486416\pi$
$564$		0			0
$565$	33.7610	+	7.58964i	1.42034	+	0.319299i
$566$		0			0
$567$	−0.681999	−	2.55634i	−0.0286413	−	0.107356i
$568$		0			0
$569$	19.3554	−	33.5245i	0.811421	−	1.40542i	−0.100449	−	0.994942i	$-0.532028\pi$
$569$	19.3554	−	33.5245i	0.811421	−	1.40542i	0.911870	−	0.410480i	$-0.134639\pi$
$570$		0			0
$571$	−10.9478	−	18.9621i	−0.458150	−	0.793540i	0.540713	−	0.841207i	$-0.318155\pi$
$571$	−10.9478	−	18.9621i	−0.458150	−	0.793540i	−0.998863	+	0.0476675i	$0.984821\pi$
$572$		0			0
$573$		−	17.1623i		−	0.716966i
$574$		0			0
$575$	−3.73088	−	5.39602i	−0.155589	−	0.225030i
$576$		0			0
$577$	−29.6175	+	17.0997i	−1.23299	+	0.711870i	−0.967653	−	0.252285i	$-0.918818\pi$
$577$	−29.6175	+	17.0997i	−1.23299	+	0.711870i	−0.265342	+	0.964154i	$0.585485\pi$
$578$		0			0
$579$	7.06816	−	12.2424i	0.293743	−	0.508777i
$580$		0			0
$581$	6.18730	−	22.9916i	0.256693	−	0.953852i
$582$		0			0
$583$	−10.0818	−	5.82075i	−0.417547	−	0.241071i
$584$		0			0
$585$	3.50400	−	3.80128i	0.144873	−	0.157163i
$586$		0			0
$587$		−	24.2455i		−	1.00072i	−0.865818	−	0.500359i	$-0.833201\pi$
$587$		−	24.2455i		−	1.00072i	0.865818	−	0.500359i	$-0.166799\pi$
$588$		0			0
$589$	−5.09881			−0.210093
$590$		0			0
$591$	−0.904090	−	1.56593i	−0.0371893	−	0.0644137i
$592$		0			0
$593$	12.4229	+	7.17238i	0.510148	+	0.294534i	0.732895	−	0.680342i	$-0.238169\pi$
$593$	12.4229	+	7.17238i	0.510148	+	0.294534i	−0.222746	+	0.974876i	$0.571502\pi$
$594$		0			0
$595$	0.0878200	+	2.21728i	0.00360027	+	0.0908997i
$596$		0			0
$597$	−15.7902	−	9.11645i	−0.646248	−	0.373112i
$598$		0			0
$599$	−5.35992	−	9.28365i	−0.219000	−	0.379320i	0.735502	−	0.677522i	$-0.236946\pi$
$599$	−5.35992	−	9.28365i	−0.219000	−	0.379320i	−0.954503	+	0.298202i	$0.903613\pi$
$600$		0			0
$601$	12.4069			0.506089			0.253045	−	0.967455i	$-0.418568\pi$
$601$	12.4069			0.506089			0.253045	+	0.967455i	$0.418568\pi$
$602$		0			0
$603$			5.56188i			0.226497i
$604$		0			0
$605$	5.66372	+	5.22080i	0.230263	+	0.212256i
$606$		0			0
$607$	29.8127	+	17.2124i	1.21006	+	0.698629i	0.962773	−	0.270313i	$-0.0871272\pi$
$607$	29.8127	+	17.2124i	1.21006	+	0.698629i	0.247288	+	0.968942i	$0.420461\pi$
$608$		0			0
$609$	15.7358	−	4.19812i	0.637648	−	0.170116i
$610$		0			0
$611$	12.4935	−	21.6394i	0.505435	−	0.875438i
$612$		0			0
$613$	42.1774	−	24.3511i	1.70353	−	0.983533i	0.761399	−	0.648284i	$-0.224513\pi$
$613$	42.1774	−	24.3511i	1.70353	−	0.983533i	0.942130	−	0.335249i	$-0.108821\pi$
$614$		0			0
$615$	−0.132792	−	0.425553i	−0.00535468	−	0.0171600i
$616$		0			0
$617$		−	21.6164i		−	0.870242i	−0.900372	−	0.435121i	$-0.856706\pi$
$617$		−	21.6164i		−	0.870242i	0.900372	−	0.435121i	$-0.143294\pi$
$618$		0			0
$619$	−1.89437	−	3.28114i	−0.0761410	−	0.131880i	0.825441	−	0.564489i	$-0.190927\pi$
$619$	−1.89437	−	3.28114i	−0.0761410	−	0.131880i	−0.901582	+	0.432609i	$0.857593\pi$
$620$		0			0
$621$	0.656022	−	1.13626i	0.0263253	−	0.0455967i
$622$		0			0
$623$	−9.38348	+	9.36315i	−0.375941	+	0.375127i
$624$		0			0
$625$	15.8416	+	19.3402i	0.633665	+	0.773608i
$626$		0			0
$627$	−2.98403	+	1.72283i	−0.119171	+	0.0688033i
$628$		0			0
$629$	−2.15207			−0.0858088
$630$		0			0
$631$	31.2160			1.24269			0.621344	−	0.783538i	$-0.286587\pi$
$631$	31.2160			1.24269			0.621344	+	0.783538i	$0.286587\pi$
$632$		0			0
$633$	14.0233	−	8.09634i	0.557375	−	0.321801i
$634$		0			0
$635$	32.9771	+	7.41341i	1.30866	+	0.294192i
$636$		0			0
$637$	−8.12253	+	13.9984i	−0.321826	+	0.554639i
$638$		0			0
$639$	−4.94148	+	8.55889i	−0.195482	+	0.338585i
$640$		0			0
$641$	12.0953	+	20.9497i	0.477736	+	0.827464i	0.999674	−	0.0255197i	$-0.00812406\pi$
$641$	12.0953	+	20.9497i	0.477736	+	0.827464i	−0.521938	+	0.852983i	$0.674791\pi$
$642$		0			0
$643$			6.83519i			0.269554i	0.990876	+	0.134777i	$0.0430318\pi$
$643$			6.83519i			0.269554i	−0.990876	+	0.134777i	$0.956968\pi$
$644$		0			0
$645$	26.4726	−	8.26063i	1.04236	−	0.325262i
$646$		0			0
$647$	−3.72927	+	2.15310i	−0.146613	+	0.0846469i	−0.571512	−	0.820594i	$-0.693643\pi$
$647$	−3.72927	+	2.15310i	−0.146613	+	0.0846469i	0.424899	+	0.905241i	$0.360310\pi$
$648$		0			0
$649$	27.1653	−	47.0516i	1.06633	−	1.84694i
$650$		0			0
$651$	−10.5103	−	10.5331i	−0.411931	−	0.412825i
$652$		0			0
$653$	−20.4305	−	11.7955i	−0.799506	−	0.461595i	0.0437927	−	0.999041i	$-0.486056\pi$
$653$	−20.4305	−	11.7955i	−0.799506	−	0.461595i	−0.843298	+	0.537446i	$0.819389\pi$
$654$		0			0
$655$	−6.36338	−	5.86574i	−0.248638	−	0.229194i
$656$		0			0
$657$		−	6.40191i		−	0.249762i
$658$		0			0
$659$	12.5231			0.487833			0.243916	−	0.969796i	$-0.421568\pi$
$659$	12.5231			0.487833			0.243916	+	0.969796i	$0.421568\pi$
$660$		0			0
$661$	−21.2598	−	36.8231i	−0.826911	−	1.43225i	−0.900450	−	0.434960i	$-0.856762\pi$
$661$	−21.2598	−	36.8231i	−0.826911	−	1.43225i	0.0735384	−	0.997292i	$-0.476571\pi$
$662$		0			0
$663$	−0.751024	−	0.433604i	−0.0291674	−	0.0168398i
$664$		0			0
$665$	−2.86349	−	4.53518i	−0.111041	−	0.175867i
$666$		0			0
$667$	6.99440	+	4.03822i	0.270824	+	0.156360i
$668$		0			0
$669$	−4.95707	−	8.58590i	−0.191651	−	0.331950i
$670$		0			0
$671$	8.28255			0.319744
$672$		0			0
$673$			15.8140i			0.609586i	0.952419	+	0.304793i	$0.0985873\pi$
$673$			15.8140i			0.609586i	−0.952419	+	0.304793i	$0.901413\pi$
$674$		0			0
$675$	−2.13990	+	4.51894i	−0.0823650	+	0.173934i
$676$		0			0
$677$	−3.96635	−	2.28997i	−0.152439	−	0.0880108i	0.421840	−	0.906670i	$-0.361384\pi$
$677$	−3.96635	−	2.28997i	−0.152439	−	0.0880108i	−0.574279	+	0.818659i	$0.694718\pi$
$678$		0			0
$679$	−4.37449	+	16.2553i	−0.167878	+	0.623821i
$680$		0			0
$681$	−6.80986	+	11.7950i	−0.260955	+	0.451987i
$682$		0			0
$683$	36.6034	−	21.1330i	1.40059	−	0.808631i	0.406137	−	0.913812i	$-0.366875\pi$
$683$	36.6034	−	21.1330i	1.40059	−	0.808631i	0.994453	+	0.105181i	$0.0335422\pi$
$684$		0			0
$685$	11.3204	+	36.2782i	0.432531	+	1.38612i
$686$		0			0
$687$		−	23.0537i		−	0.879552i
$688$		0			0
$689$	3.54094	+	6.13309i	0.134899	+	0.233652i
$690$		0			0
$691$	−12.0575	+	20.8842i	−0.458690	+	0.794474i	−0.998892	−	0.0470615i	$-0.985014\pi$
$691$	−12.0575	+	20.8842i	−0.458690	+	0.794474i	0.540202	+	0.841535i	$0.318348\pi$
$692$		0			0
$693$	−9.71008	−	2.61309i	−0.368855	−	0.0992633i
$694$		0			0
$695$	4.01915	−	17.8784i	0.152455	−	0.678166i
$696$		0			0
$697$	−0.0647596	+	0.0373889i	−0.00245294	+	0.00141621i
$698$		0			0
$699$	30.3211			1.14685
$700$		0			0
$701$	−7.28290			−0.275071			−0.137536	−	0.990497i	$-0.543918\pi$
$701$	−7.28290			−0.275071			−0.137536	+	0.990497i	$0.543918\pi$
$702$		0			0
$703$	4.50482	−	2.60086i	0.169902	−	0.0980932i
$704$		0			0
$705$	−5.30035	+	23.5775i	−0.199623	+	0.887982i
$706$		0			0
$707$	4.01217	+	15.0388i	0.150893	+	0.565594i
$708$		0			0
$709$	3.25510	−	5.63799i	0.122248	−	0.211739i	−0.798406	−	0.602119i	$-0.794323\pi$
$709$	3.25510	−	5.63799i	0.122248	−	0.211739i	0.920654	+	0.390380i	$0.127656\pi$
$710$		0			0
$711$	7.61645	+	13.1921i	0.285639	+	0.494742i
$712$		0			0
$713$		−	7.37906i		−	0.276348i
$714$		0			0
$715$	−5.85299	−	18.7569i	−0.218889	−	0.701468i
$716$		0			0
$717$	−9.55461	+	5.51636i	−0.356823	+	0.206012i
$718$		0			0
$719$	−22.3725	+	38.7503i	−0.834353	+	1.44514i	0.0602031	+	0.998186i	$0.480825\pi$
$719$	−22.3725	+	38.7503i	−0.834353	+	1.44514i	−0.894556	+	0.446956i	$0.852508\pi$
$720$		0			0
$721$	−23.6862	−	23.7376i	−0.882120	−	0.884035i
$722$		0			0
$723$	−5.47364	−	3.16021i	−0.203567	−	0.117529i
$724$		0			0
$725$	−27.8168	−	13.1724i	−1.03309	−	0.489211i
$726$		0			0
$727$		−	23.7510i		−	0.880877i	−0.897783	−	0.440438i	$-0.854823\pi$
$727$		−	23.7510i		−	0.880877i	0.897783	−	0.440438i	$-0.145177\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−2.32587	−	4.02853i	−0.0860255	−	0.149000i
$732$		0			0
$733$	−12.6702	−	7.31516i	−0.467986	−	0.270192i	0.247410	−	0.968911i	$-0.420420\pi$
$733$	−12.6702	−	7.31516i	−0.467986	−	0.270192i	−0.715396	+	0.698719i	$0.753754\pi$
$734$		0			0
$735$	3.46618	−	15.2639i	0.127852	−	0.563016i
$736$		0			0
$737$	18.3066	+	10.5693i	0.674334	+	0.389327i
$738$		0			0
$739$	−0.403658	−	0.699156i	−0.0148488	−	0.0257189i	0.858506	−	0.512804i	$-0.171393\pi$
$739$	−0.403658	−	0.699156i	−0.0148488	−	0.0257189i	−0.873354	+	0.487085i	$0.838060\pi$
$740$		0			0
$741$	2.09610			0.0770023
$742$		0			0
$743$		−	2.34476i		−	0.0860208i	−0.999075	−	0.0430104i	$-0.986305\pi$
$743$		−	2.34476i		−	0.0860208i	0.999075	−	0.0430104i	$-0.0136949\pi$
$744$		0			0
$745$	−19.6575	−	18.1202i	−0.720195	−	0.663873i
$746$		0			0
$747$	−7.79351	−	4.49959i	−0.285150	−	0.164631i
$748$		0			0
$749$	−4.70587	−	4.71608i	−0.171949	−	0.172322i
$750$		0			0
$751$	−10.1746	+	17.6229i	−0.371275	+	0.643067i	−0.989762	−	0.142728i	$-0.954413\pi$
$751$	−10.1746	+	17.6229i	−0.371275	+	0.643067i	0.618487	+	0.785795i	$0.287746\pi$
$752$		0			0
$753$	16.7282	−	9.65803i	0.609609	−	0.351958i
$754$		0			0
$755$	−38.5205	+	12.0201i	−1.40190	+	0.437457i
$756$		0			0
$757$			4.83602i			0.175768i	0.996131	+	0.0878841i	$0.0280105\pi$
$757$			4.83602i			0.175768i	−0.996131	+	0.0878841i	$0.971989\pi$
$758$		0			0
$759$	−2.49330	−	4.31853i	−0.0905011	−	0.156753i
$760$		0			0
$761$	20.7725	−	35.9790i	0.753002	−	1.30424i	−0.193360	−	0.981128i	$-0.561939\pi$
$761$	20.7725	−	35.9790i	0.753002	−	1.30424i	0.946362	−	0.323109i	$-0.104728\pi$
$762$		0			0
$763$	7.71939	+	28.9346i	0.279461	+	1.04750i
$764$		0			0
$765$	0.818289	+	0.183955i	0.0295853	+	0.00665092i
$766$		0			0
$767$	−28.6230	+	16.5255i	−1.03352	+	0.596700i
$768$		0			0
$769$	15.9814			0.576305			0.288152	−	0.957585i	$-0.406959\pi$
$769$	15.9814			0.576305			0.288152	+	0.957585i	$0.406959\pi$
$770$		0			0
$771$	−14.3448			−0.516614
$772$		0			0
$773$	−8.40834	+	4.85456i	−0.302427	+	0.174606i	−0.643533	−	0.765419i	$-0.722532\pi$
$773$	−8.40834	+	4.85456i	−0.302427	+	0.174606i	0.341106	+	0.940025i	$0.389199\pi$
$774$		0			0
$775$	2.28483	+	28.0275i	0.0820736	+	1.00678i
$776$		0			0
$777$	14.6587	+	3.94484i	0.525879	+	0.141520i
$778$		0			0
$779$	0.0903717	−	0.156528i	0.00323790	−	0.00560821i
$780$		0			0
$781$	18.7808	+	32.5292i	0.672029	+	1.16399i
$782$		0			0
$783$		−	6.15561i		−	0.219983i
$784$		0			0
$785$	−14.9807	−	48.0082i	−0.534685	−	1.71349i
$786$		0			0
$787$	23.2523	−	13.4247i	0.828855	−	0.478540i	−0.0246053	−	0.999697i	$-0.507833\pi$
$787$	23.2523	−	13.4247i	0.828855	−	0.478540i	0.853461	+	0.521157i	$0.174500\pi$
$788$		0			0
$789$	4.53329	−	7.85188i	0.161389	−	0.279534i
$790$		0			0
$791$	−10.6398	+	39.5369i	−0.378309	+	1.40577i
$792$		0			0
$793$	−4.36350	−	2.51927i	−0.154952	−	0.0894617i
$794$		0			0
$795$	−5.03600	−	4.64217i	−0.178609	−	0.164641i
$796$		0			0
$797$			17.6365i			0.624716i	0.949964	+	0.312358i	$0.101119\pi$
$797$			17.6365i			0.624716i	−0.949964	+	0.312358i	$0.898881\pi$
$798$		0			0
$799$	4.05365			0.143408
$800$		0			0
$801$	2.50512	+	4.33900i	0.0885142	+	0.153311i
$802$		0			0
$803$	−21.0715	−	12.1657i	−0.743599	−	0.429317i
$804$		0			0
$805$	6.56336	−	4.14408i	0.231328	−	0.146060i
$806$		0			0
$807$	−9.23719	−	5.33309i	−0.325165	−	0.187734i
$808$		0			0
$809$	14.0251	+	24.2921i	0.493095	+	0.854065i	0.999968	−	0.00795514i	$-0.00253223\pi$
$809$	14.0251	+	24.2921i	0.493095	+	0.854065i	−0.506874	+	0.862020i	$0.669199\pi$
$810$		0			0
$811$	−41.3801			−1.45305			−0.726527	−	0.687138i	$-0.758867\pi$
$811$	−41.3801			−1.45305			−0.726527	+	0.687138i	$0.758867\pi$
$812$		0			0
$813$		−	20.5441i		−	0.720514i
$814$		0			0
$815$	−15.6881	+	17.0190i	−0.549528	+	0.596150i
$816$		0			0
$817$	9.73724	+	5.62180i	0.340663	+	0.196682i
$818$		0			0
$819$	4.32075	+	4.33013i	0.150979	+	0.151307i
$820$		0			0
$821$	9.42516	−	16.3249i	0.328940	−	0.569741i	−0.653362	−	0.757046i	$-0.726642\pi$
$821$	9.42516	−	16.3249i	0.328940	−	0.569741i	0.982302	+	0.187305i	$0.0599752\pi$
$822$		0			0
$823$	8.47726	−	4.89435i	0.295499	−	0.170606i	−0.344920	−	0.938632i	$-0.612094\pi$
$823$	8.47726	−	4.89435i	0.295499	−	0.170606i	0.640419	+	0.768026i	$0.278761\pi$
$824$		0			0
$825$	10.8074	+	15.6308i	0.376264	+	0.544195i
$826$		0			0
$827$		−	18.6206i		−	0.647500i	−0.946143	−	0.323750i	$-0.895056\pi$
$827$		−	18.6206i		−	0.647500i	0.946143	−	0.323750i	$-0.104944\pi$
$828$		0			0
$829$	22.6558	+	39.2411i	0.786870	+	1.36290i	0.927876	+	0.372890i	$0.121633\pi$
$829$	22.6558	+	39.2411i	0.786870	+	1.36290i	−0.141005	+	0.990009i	$0.545034\pi$
$830$		0			0
$831$	6.55593	−	11.3552i	0.227423	−	0.393907i
$832$		0			0
$833$	−2.62557	−	0.00569375i	−0.0909707	−	0.000197277i
$834$		0			0
$835$	−4.53958	−	1.02052i	−0.157099	−	0.0353166i
$836$		0			0
$837$	−4.87060	+	2.81204i	−0.168353	+	0.0971985i
$838$		0			0
$839$	−2.31727			−0.0800010			−0.0400005	−	0.999200i	$-0.512736\pi$
$839$	−2.31727			−0.0800010			−0.0400005	+	0.999200i	$0.512736\pi$
$840$		0			0
$841$	8.89152			0.306604
$842$		0			0
$843$	−10.7128	+	6.18503i	−0.368968	+	0.213024i
$844$		0			0
$845$	3.75404	−	16.6991i	0.129143	−	0.574467i
$846$		0			0
$847$	−6.45168	+	6.43771i	−0.221682	+	0.221202i
$848$		0			0
$849$	−9.64932	+	16.7131i	−0.331164	+	0.573593i
$850$		0			0
$851$	3.76399	+	6.51943i	0.129028	+	0.223483i
$852$		0			0
$853$			12.6273i			0.432350i	0.976355	+	0.216175i	$0.0693581\pi$
$853$			12.6273i			0.432350i	−0.976355	+	0.216175i	$0.930642\pi$
$854$		0			0
$855$	−1.93519	+	0.603867i	−0.0661823	+	0.0206518i
$856$		0			0
$857$	−15.6919	+	9.05970i	−0.536024	+	0.309473i	−0.743466	−	0.668774i	$-0.766819\pi$
$857$	−15.6919	+	9.05970i	−0.536024	+	0.309473i	0.207442	+	0.978247i	$0.433486\pi$
$858$		0			0
$859$	−8.92380	+	15.4565i	−0.304476	+	0.527368i	−0.977145	−	0.212576i	$-0.931815\pi$
$859$	−8.92380	+	15.4565i	−0.304476	+	0.527368i	0.672668	+	0.739944i	$0.265148\pi$
$860$		0			0
$861$	0.509641	−	0.135966i	0.0173685	−	0.00463371i
$862$		0			0
$863$	−11.2928	−	6.51989i	−0.384411	−	0.221940i	0.295325	−	0.955397i	$-0.404572\pi$
$863$	−11.2928	−	6.51989i	−0.384411	−	0.221940i	−0.679736	+	0.733457i	$0.737905\pi$
$864$		0			0
$865$	−36.1766	+	39.2458i	−1.23004	+	1.33440i
$866$		0			0
$867$			16.8593i			0.572572i
$868$		0			0
$869$	57.8947			1.96394
$870$		0			0
$871$	−6.42966	−	11.1365i	−0.217861	−	0.377346i
$872$		0			0
$873$	5.51010	+	3.18126i	0.186489	+	0.107669i
$874$		0			0
$875$	−23.6461	+	17.7725i	−0.799384	+	0.600820i
$876$		0			0
$877$	−19.5187	−	11.2691i	−0.659099	−	0.380531i	0.132835	−	0.991138i	$-0.457592\pi$
$877$	−19.5187	−	11.2691i	−0.659099	−	0.380531i	−0.791934	+	0.610607i	$0.790925\pi$
$878$		0			0
$879$	9.31699	+	16.1375i	0.314254	+	0.544305i
$880$		0			0
$881$	−25.3761			−0.854944			−0.427472	−	0.904029i	$-0.640596\pi$
$881$	−25.3761			−0.854944			−0.427472	+	0.904029i	$0.640596\pi$
$882$		0			0
$883$		−	15.1504i		−	0.509852i	−0.966961	−	0.254926i	$-0.917949\pi$
$883$		−	15.1504i		−	0.509852i	0.966961	−	0.254926i	$-0.0820511\pi$
$884$		0			0
$885$	21.6649	−	23.5029i	0.728256	−	0.790041i
$886$		0			0
$887$	35.7054	+	20.6145i	1.19887	+	0.692167i	0.960303	−	0.278959i	$-0.0899893\pi$
$887$	35.7054	+	20.6145i	1.19887	+	0.692167i	0.238566	+	0.971126i	$0.423323\pi$
$888$		0			0
$889$	−10.3928	+	38.6188i	−0.348563	+	1.29523i
$890$		0			0
$891$	−1.90032	+	3.29145i	−0.0636631	+	0.110268i
$892$		0			0
$893$	−8.48529	+	4.89898i	−0.283949	+	0.163938i
$894$		0			0
$895$	27.3456	−	8.53305i	0.914062	−	0.285228i
$896$		0			0
$897$			3.03351i			0.101286i
$898$		0			0
$899$	−17.3098	−	29.9815i	−0.577316	−	0.999940i
$900$		0			0
$901$	−0.574447	+	0.994971i	−0.0191376	+	0.0331473i
$902$		0			0
$903$	8.45809	+	31.7035i	0.281468	+	1.05503i
$904$		0			0
$905$	−1.49393	+	6.64545i	−0.0496599	+	0.220902i
$906$		0			0
$907$	−6.07450	+	3.50711i	−0.201700	+	0.116452i	−0.597448	−	0.801907i	$-0.703819\pi$
$907$	−6.07450	+	3.50711i	−0.201700	+	0.116452i	0.395748	+	0.918359i	$0.370485\pi$
$908$		0			0
$909$	5.88296			0.195125
$910$		0			0
$911$	−3.78721			−0.125476			−0.0627379	−	0.998030i	$-0.519983\pi$
$911$	−3.78721			−0.125476			−0.0627379	+	0.998030i	$0.519983\pi$
$912$		0			0
$913$	−29.6203	+	17.1013i	−0.980289	+	0.565970i
$914$		0			0
$915$	4.75430	+	1.06879i	0.157172	+	0.0353331i
$916$		0			0
$917$	7.24868	−	7.23298i	0.239373	−	0.238854i
$918$		0			0
$919$	−12.6119	+	21.8444i	−0.416027	+	0.720579i	−0.995536	−	0.0943866i	$-0.969911\pi$
$919$	−12.6119	+	21.8444i	−0.416027	+	0.720579i	0.579509	+	0.814966i	$0.303244\pi$
$920$		0			0
$921$	−8.66390	−	15.0063i	−0.285485	−	0.494475i
$922$		0			0
$923$		−	22.8498i		−	0.752112i
$924$		0			0
$925$	−16.3152	−	23.5969i	−0.536441	−	0.775862i
$926$		0			0
$927$	−10.9765	+	6.33728i	−0.360515	+	0.208144i
$928$		0			0
$929$	−23.6884	+	41.0295i	−0.777191	+	1.34613i	0.156364	+	0.987699i	$0.450023\pi$
$929$	−23.6884	+	41.0295i	−0.777191	+	1.34613i	−0.933555	+	0.358434i	$0.883311\pi$
$930$		0			0
$931$	5.50285	−	3.16118i	0.180349	−	0.103604i
$932$		0			0
$933$	0.838442	+	0.484075i	0.0274494	+	0.0158479i
$934$		0			0
$935$	2.16049	−	2.34378i	0.0706555	−	0.0766498i
$936$		0			0
$937$			9.59102i			0.313325i	0.987652	+	0.156663i	$0.0500735\pi$
$937$			9.59102i			0.313325i	−0.987652	+	0.156663i	$0.949926\pi$
$938$		0			0
$939$	−26.6746			−0.870491
$940$		0			0
$941$	24.8312	+	43.0088i	0.809472	+	1.40205i	0.913230	+	0.407445i	$0.133580\pi$
$941$	24.8312	+	43.0088i	0.809472	+	1.40205i	−0.103757	+	0.994603i	$0.533087\pi$
$942$		0			0
$943$	0.226530	+	0.130787i	0.00737682	+	0.00425901i
$944$		0			0
$945$	−5.23653	−	2.75296i	−0.170344	−	0.0895537i
$946$		0			0
$947$	41.3941	+	23.8989i	1.34513	+	0.776610i	0.987555	−	0.157275i	$-0.0502710\pi$
$947$	41.3941	+	23.8989i	1.34513	+	0.776610i	0.357573	+	0.933885i	$0.383604\pi$
$948$		0			0
$949$	7.40075	+	12.8185i	0.240239	+	0.416105i
$950$		0			0
$951$	−32.0354			−1.03882
$952$		0			0
$953$			47.3018i			1.53226i	0.642688	+	0.766128i	$0.277819\pi$
$953$			47.3018i			1.53226i	−0.642688	+	0.766128i	$0.722181\pi$
$954$		0			0
$955$	−28.2169	−	26.0102i	−0.913078	−	0.841672i
$956$		0			0
$957$	−20.2609	−	11.6976i	−0.654941	−	0.378130i
$958$		0			0
$959$	−43.4466	+	11.5910i	−1.40297	+	0.374293i
$960$		0			0
$961$	−0.315191	+	0.545926i	−0.0101674	+	0.0176105i
$962$		0			0
$963$	−2.18076	+	1.25906i	−0.0702740	+	0.0405727i
$964$		0			0
$965$	−9.41589	−	30.1748i	−0.303108	−	0.971362i
$966$		0			0
$967$		−	37.9613i		−	1.22075i	−0.792111	−	0.610377i	$-0.791018\pi$
$967$		−	37.9613i		−	1.22075i	0.792111	−	0.610377i	$-0.208982\pi$
$968$		0			0
$969$	0.170025	+	0.294493i	0.00546200	+	0.00946047i
$970$		0			0
$971$	6.51989	−	11.2928i	0.209233	−	0.362403i	−0.742240	−	0.670134i	$-0.766237\pi$
$971$	6.51989	−	11.2928i	0.209233	−	0.362403i	0.951473	+	0.307732i	$0.0995699\pi$
$972$		0			0
$973$	20.9370	+	5.63440i	0.671211	+	0.180631i
$974$		0			0
$975$	−0.939287	−	11.5220i	−0.0300812	−	0.368999i
$976$		0			0
$977$	41.0472	−	23.6986i	1.31322	−	0.758185i	0.330588	−	0.943775i	$-0.392753\pi$
$977$	41.0472	−	23.6986i	1.31322	−	0.758185i	0.982627	+	0.185590i	$0.0594196\pi$
$978$		0			0
$979$	19.0421			0.608589
$980$		0			0
$981$	11.3188			0.361380
$982$		0			0
$983$	−15.8815	+	9.16920i	−0.506542	+	0.292452i	−0.731411	−	0.681937i	$-0.761138\pi$
$983$	−15.8815	+	9.16920i	−0.506542	+	0.292452i	0.224869	+	0.974389i	$0.427805\pi$
$984$		0			0
$985$	−3.94476	−	0.886802i	−0.125691	−	0.0282559i
$986$		0			0
$987$	−27.6112	−	7.43050i	−0.878875	−	0.236515i
$988$		0			0
$989$	−8.13593	+	14.0918i	−0.258708	+	0.448095i
$990$		0			0
$991$	3.31968	+	5.74986i	0.105453	+	0.182650i	0.913923	−	0.405887i	$-0.133037\pi$
$991$	3.31968	+	5.74986i	0.105453	+	0.182650i	−0.808470	+	0.588537i	$0.799704\pi$
$992$		0			0
$993$		−	0.687128i		−	0.0218053i
$994$		0			0
$995$	−38.9192	+	12.1445i	−1.23382	+	0.385008i
$996$		0			0
$997$	0.240312	−	0.138744i	0.00761075	−	0.00439407i	−0.496190	−	0.868214i	$-0.665268\pi$
$997$	0.240312	−	0.138744i	0.00761075	−	0.00439407i	0.503801	+	0.863820i	$0.331935\pi$
$998$		0			0
$999$	2.86880	−	4.96891i	0.0907648	−	0.157209i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.bb.a.289.6	yes	16
3.2	odd	2		1260.2.bm.c.289.5		16
4.3	odd	2		1680.2.di.e.289.2		16
5.2	odd	4		2100.2.q.l.1801.2		8
5.3	odd	4		2100.2.q.m.1801.3		8
5.4	even	2	inner	420.2.bb.a.289.3	yes	16
7.2	even	3		2940.2.k.f.589.5		8
7.3	odd	6		2940.2.bb.i.949.6		16
7.4	even	3	inner	420.2.bb.a.109.3	✓	16
7.5	odd	6		2940.2.k.g.589.4		8
7.6	odd	2		2940.2.bb.i.1549.3		16
15.14	odd	2		1260.2.bm.c.289.3		16
20.19	odd	2		1680.2.di.e.289.7		16
21.11	odd	6		1260.2.bm.c.109.3		16
28.11	odd	6		1680.2.di.e.529.7		16
35.4	even	6	inner	420.2.bb.a.109.6	yes	16
35.9	even	6		2940.2.k.f.589.1		8
35.18	odd	12		2100.2.q.m.1201.3		8
35.19	odd	6		2940.2.k.g.589.8		8
35.24	odd	6		2940.2.bb.i.949.3		16
35.32	odd	12		2100.2.q.l.1201.2		8
35.34	odd	2		2940.2.bb.i.1549.6		16
105.74	odd	6		1260.2.bm.c.109.5		16
140.39	odd	6		1680.2.di.e.529.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.bb.a.109.3	✓	16	7.4	even	3	inner
420.2.bb.a.109.6	yes	16	35.4	even	6	inner
420.2.bb.a.289.3	yes	16	5.4	even	2	inner
420.2.bb.a.289.6	yes	16	1.1	even	1	trivial
1260.2.bm.c.109.3		16	21.11	odd	6
1260.2.bm.c.109.5		16	105.74	odd	6
1260.2.bm.c.289.3		16	15.14	odd	2
1260.2.bm.c.289.5		16	3.2	odd	2
1680.2.di.e.289.2		16	4.3	odd	2
1680.2.di.e.289.7		16	20.19	odd	2
1680.2.di.e.529.2		16	140.39	odd	6
1680.2.di.e.529.7		16	28.11	odd	6
2100.2.q.l.1201.2		8	35.32	odd	12
2100.2.q.l.1801.2		8	5.2	odd	4
2100.2.q.m.1201.3		8	35.18	odd	12
2100.2.q.m.1801.3		8	5.3	odd	4
2940.2.k.f.589.1		8	35.9	even	6
2940.2.k.f.589.5		8	7.2	even	3
2940.2.k.g.589.4		8	7.5	odd	6
2940.2.k.g.589.8		8	35.19	odd	6
2940.2.bb.i.949.3		16	35.24	odd	6
2940.2.bb.i.949.6		16	7.3	odd	6
2940.2.bb.i.1549.3		16	7.6	odd	2
2940.2.bb.i.1549.6		16	35.34	odd	2

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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{3} +(0.490439 - 2.18162i) q^{5} +(2.55486 + 0.687541i) q^{7} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{3} +(0.490439 - 2.18162i) q^{5} +(2.55486 + 0.687541i) q^{7} +(0.500000 - 0.866025i) q^{9} +(-1.90032 - 3.29145i) q^{11} +2.31204i q^{13} +(-0.666078 - 2.13456i) q^{15} +(-0.324831 + 0.187541i) q^{17} +(0.453301 - 0.785140i) q^{19} +(2.55634 - 0.681999i) q^{21} +(1.13626 + 0.656022i) q^{23} +(-4.51894 - 2.13990i) q^{25} -1.00000i q^{27} +6.15561 q^{29} +(-2.81204 - 4.87060i) q^{31} +(-3.29145 - 1.90032i) q^{33} +(2.75296 - 5.23653i) q^{35} +(4.96891 + 2.86880i) q^{37} +(1.15602 + 2.00229i) q^{39} +0.199364 q^{41} +12.4019i q^{43} +(-1.64412 - 1.51554i) q^{45} +(-9.35944 - 5.40368i) q^{47} +(6.05457 + 3.51314i) q^{49} +(-0.187541 + 0.324831i) q^{51} +(2.65267 - 1.53152i) q^{53} +(-8.11268 + 2.53152i) q^{55} -0.906602i q^{57} +(7.14756 + 12.3799i) q^{59} +(-1.08963 + 1.88729i) q^{61} +(1.87286 - 1.86880i) q^{63} +(5.04400 + 1.13392i) q^{65} +(-4.81673 + 2.78094i) q^{67} +1.31204 q^{69} -9.88296 q^{71} +(5.54422 - 3.20095i) q^{73} +(-4.98347 + 0.406258i) q^{75} +(-2.59203 - 9.71572i) q^{77} +(-7.61645 + 13.1921i) q^{79} +(-0.500000 - 0.866025i) q^{81} -8.99917i q^{83} +(0.249834 + 0.800636i) q^{85} +(5.33091 - 3.07780i) q^{87} +(-2.50512 + 4.33900i) q^{89} +(-1.58963 + 5.90694i) q^{91} +(-4.87060 - 2.81204i) q^{93} +(-1.49056 - 1.37399i) q^{95} +6.36252i q^{97} -3.80064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{5} + 8 q^{9}+O(q^{10}) \) 16 * q + 2 * q^5 + 8 * q^9	\( 16 q + 2 q^{5} + 8 q^{9} - 8 q^{11} + 4 q^{15} + 8 q^{19} - 4 q^{21} + 12 q^{25} + 24 q^{29} + 10 q^{35} - 4 q^{39} + 48 q^{41} - 2 q^{45} + 8 q^{49} + 4 q^{51} - 40 q^{55} - 28 q^{59} - 32 q^{61} - 26 q^{65} - 24 q^{69} - 56 q^{71} - 8 q^{75} - 16 q^{79} - 8 q^{81} + 32 q^{85} - 16 q^{89} - 40 q^{91} + 22 q^{95} - 16 q^{99}+O(q^{100}) \) 16 * q + 2 * q^5 + 8 * q^9 - 8 * q^11 + 4 * q^15 + 8 * q^19 - 4 * q^21 + 12 * q^25 + 24 * q^29 + 10 * q^35 - 4 * q^39 + 48 * q^41 - 2 * q^45 + 8 * q^49 + 4 * q^51 - 40 * q^55 - 28 * q^59 - 32 * q^61 - 26 * q^65 - 24 * q^69 - 56 * q^71 - 8 * q^75 - 16 * q^79 - 8 * q^81 + 32 * q^85 - 16 * q^89 - 40 * q^91 + 22 * q^95 - 16 * q^99

Introduction

L-functions

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