LMFDB - Embedded newform 4020.2.q.k.3781.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4020,2,Mod(841,4020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4020, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("4020.841");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4020.q (of order $3$, 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:	$32.0998616126$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} + 11 x^{12} - 8 x^{11} + 88 x^{10} - 57 x^{9} + 270 x^{8} + 17 x^{7} + 458 x^{6} + \cdots + 4 $ x^14 - x^13 + 11x^12 - 8x^11 + 88x^10 - 57x^9 + 270x^8 + 17x^7 + 458x^6 - 101x^5 + 189x^4 - 30x^3 + 54x^2 - 12x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3781.3
Root			$1.10425 + 1.91261i$ of defining polynomial
Character	$\chi$	$=$	4020.3781
Dual form			4020.2.q.k.841.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{3} +1.00000 q^{5} +(-0.952306 - 1.64944i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{3} +1.00000 q^{5} +(-0.952306 - 1.64944i) q^{7} +1.00000 q^{9} +(-1.50261 - 2.60259i) q^{11} +(2.70849 - 4.69125i) q^{13} -1.00000 q^{15} +(-2.26869 + 3.92948i) q^{17} +(1.93872 - 3.35797i) q^{19} +(0.952306 + 1.64944i) q^{21} +(1.94438 - 3.36777i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(4.12189 + 7.13932i) q^{29} +(-3.48804 - 6.04146i) q^{31} +(1.50261 + 2.60259i) q^{33} +(-0.952306 - 1.64944i) q^{35} +(0.725995 - 1.25746i) q^{37} +(-2.70849 + 4.69125i) q^{39} +(0.0559598 + 0.0969252i) q^{41} +2.08087 q^{43} +1.00000 q^{45} +(-0.778456 - 1.34832i) q^{47} +(1.68623 - 2.92063i) q^{49} +(2.26869 - 3.92948i) q^{51} -8.39503 q^{53} +(-1.50261 - 2.60259i) q^{55} +(-1.93872 + 3.35797i) q^{57} -2.69514 q^{59} +(-0.711547 + 1.23244i) q^{61} +(-0.952306 - 1.64944i) q^{63} +(2.70849 - 4.69125i) q^{65} +(-7.90197 + 2.13517i) q^{67} +(-1.94438 + 3.36777i) q^{69} +(2.11366 + 3.66096i) q^{71} +(-2.91448 + 5.04802i) q^{73} -1.00000 q^{75} +(-2.86188 + 4.95693i) q^{77} +(3.12853 + 5.41877i) q^{79} +1.00000 q^{81} +(0.214571 - 0.371649i) q^{83} +(-2.26869 + 3.92948i) q^{85} +(-4.12189 - 7.13932i) q^{87} -7.70404 q^{89} -10.3173 q^{91} +(3.48804 + 6.04146i) q^{93} +(1.93872 - 3.35797i) q^{95} +(-1.52705 + 2.64493i) q^{97} +(-1.50261 - 2.60259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	$ 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) $ 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times$.

$n$	$1141$	$2011$	$2681$	$3217$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		0			0
$2$		0			0
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		0			0
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$		0			0
$7$	−0.952306	−	1.64944i	−0.359938	−	0.623431i	0.628012	−	0.778204i	$-0.283869\pi$
$7$	−0.952306	−	1.64944i	−0.359938	−	0.623431i	−0.987950	+	0.154773i	$0.950535\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.50261	−	2.60259i	−0.453053	−	0.784710i	0.545521	−	0.838097i	$-0.316332\pi$
$11$	−1.50261	−	2.60259i	−0.453053	−	0.784710i	−0.998574	+	0.0533866i	$0.982998\pi$
$12$		0			0
$13$	2.70849	−	4.69125i	0.751201	−	1.30112i	−0.196040	−	0.980596i	$-0.562808\pi$
$13$	2.70849	−	4.69125i	0.751201	−	1.30112i	0.947241	−	0.320522i	$-0.103858\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$		0			0
$17$	−2.26869	+	3.92948i	−0.550237	+	0.953039i	0.448020	+	0.894024i	$0.352129\pi$
$17$	−2.26869	+	3.92948i	−0.550237	+	0.953039i	−0.998257	+	0.0590155i	$0.981204\pi$
$18$		0			0
$19$	1.93872	−	3.35797i	0.444773	−	0.770370i	−0.553263	−	0.833007i	$-0.686618\pi$
$19$	1.93872	−	3.35797i	0.444773	−	0.770370i	0.998036	+	0.0626366i	$0.0199509\pi$
$20$		0			0
$21$	0.952306	+	1.64944i	0.207810	+	0.359938i
$22$		0			0
$23$	1.94438	−	3.36777i	0.405432	−	0.702228i	−0.588940	−	0.808177i	$-0.700455\pi$
$23$	1.94438	−	3.36777i	0.405432	−	0.702228i	0.994372	+	0.105949i	$0.0337879\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	4.12189	+	7.13932i	0.765415	+	1.32574i	0.940027	+	0.341100i	$0.110800\pi$
$29$	4.12189	+	7.13932i	0.765415	+	1.32574i	−0.174612	+	0.984637i	$0.555867\pi$
$30$		0			0
$31$	−3.48804	−	6.04146i	−0.626470	−	1.08508i	−0.988255	−	0.152817i	$-0.951166\pi$
$31$	−3.48804	−	6.04146i	−0.626470	−	1.08508i	0.361784	−	0.932262i	$-0.382168\pi$
$32$		0			0
$33$	1.50261	+	2.60259i	0.261570	+	0.453053i
$34$		0			0
$35$	−0.952306	−	1.64944i	−0.160969	−	0.278807i
$36$		0			0
$37$	0.725995	−	1.25746i	0.119353	−	0.206725i	−0.800159	−	0.599788i	$-0.795251\pi$
$37$	0.725995	−	1.25746i	0.119353	−	0.206725i	0.919511	+	0.393063i	$0.128585\pi$
$38$		0			0
$39$	−2.70849	+	4.69125i	−0.433706	+	0.751201i
$40$		0			0
$41$	0.0559598	+	0.0969252i	0.00873945	+	0.0151372i	0.870362	−	0.492412i	$-0.163885\pi$
$41$	0.0559598	+	0.0969252i	0.00873945	+	0.0151372i	−0.861623	+	0.507549i	$0.830551\pi$
$42$		0			0
$43$	2.08087			0.317330			0.158665	−	0.987332i	$-0.449281\pi$
$43$	2.08087			0.317330			0.158665	+	0.987332i	$0.449281\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−0.778456	−	1.34832i	−0.113549	−	0.196673i	0.803650	−	0.595103i	$-0.202889\pi$
$47$	−0.778456	−	1.34832i	−0.113549	−	0.196673i	−0.917199	+	0.398429i	$0.869555\pi$
$48$		0			0
$49$	1.68623	−	2.92063i	0.240889	−	0.417233i
$50$		0			0
$51$	2.26869	−	3.92948i	0.317680	−	0.550237i
$52$		0			0
$53$	−8.39503			−1.15315			−0.576573	−	0.817046i	$-0.695610\pi$
$53$	−8.39503			−1.15315			−0.576573	+	0.817046i	$0.695610\pi$
$54$		0			0
$55$	−1.50261	−	2.60259i	−0.202611	−	0.350933i
$56$		0			0
$57$	−1.93872	+	3.35797i	−0.256790	+	0.444773i
$58$		0			0
$59$	−2.69514			−0.350877			−0.175438	−	0.984490i	$-0.556134\pi$
$59$	−2.69514			−0.350877			−0.175438	+	0.984490i	$0.556134\pi$
$60$		0			0
$61$	−0.711547	+	1.23244i	−0.0911043	+	0.157797i	−0.907976	−	0.419022i	$-0.862373\pi$
$61$	−0.711547	+	1.23244i	−0.0911043	+	0.157797i	0.816872	+	0.576819i	$0.195706\pi$
$62$		0			0
$63$	−0.952306	−	1.64944i	−0.119979	−	0.207810i
$64$		0			0
$65$	2.70849	−	4.69125i	0.335947	−	0.581878i
$66$		0			0
$67$	−7.90197	+	2.13517i	−0.965379	+	0.260852i
$67$	−7.90197	+	2.13517i	−0.965379	+	0.260852i
$68$		0			0
$69$	−1.94438	+	3.36777i	−0.234076	+	0.405432i
$70$		0			0
$71$	2.11366	+	3.66096i	0.250845	+	0.434476i	0.963759	−	0.266776i	$-0.0859582\pi$
$71$	2.11366	+	3.66096i	0.250845	+	0.434476i	−0.712914	+	0.701252i	$0.752625\pi$
$72$		0			0
$73$	−2.91448	+	5.04802i	−0.341114	+	0.590826i	−0.984640	−	0.174598i	$-0.944137\pi$
$73$	−2.91448	+	5.04802i	−0.341114	+	0.590826i	0.643526	+	0.765424i	$0.277471\pi$
$74$		0			0
$75$	−1.00000			−0.115470
$76$		0			0
$77$	−2.86188	+	4.95693i	−0.326142	+	0.564894i
$78$		0			0
$79$	3.12853	+	5.41877i	0.351987	+	0.609659i	0.986597	−	0.163173i	$-0.0521728\pi$
$79$	3.12853	+	5.41877i	0.351987	+	0.609659i	−0.634611	+	0.772832i	$0.718839\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	0.214571	−	0.371649i	0.0235523	−	0.0407937i	−0.854009	−	0.520258i	$-0.825836\pi$
$83$	0.214571	−	0.371649i	0.0235523	−	0.0407937i	0.877561	+	0.479464i	$0.159169\pi$
$84$		0			0
$85$	−2.26869	+	3.92948i	−0.246074	+	0.426212i
$86$		0			0
$87$	−4.12189	−	7.13932i	−0.441913	−	0.765415i
$88$		0			0
$89$	−7.70404			−0.816626			−0.408313	−	0.912842i	$-0.633883\pi$
$89$	−7.70404			−0.816626			−0.408313	+	0.912842i	$0.633883\pi$
$90$		0			0
$91$	−10.3173			−1.08154
$92$		0			0
$93$	3.48804	+	6.04146i	0.361693	+	0.626470i
$94$		0			0
$95$	1.93872	−	3.35797i	0.198909	−	0.344520i
$96$		0			0
$97$	−1.52705	+	2.64493i	−0.155048	+	0.268552i	−0.933077	−	0.359678i	$-0.882887\pi$
$97$	−1.52705	+	2.64493i	−0.155048	+	0.268552i	0.778028	+	0.628229i	$0.216220\pi$
$98$		0			0
$99$	−1.50261	−	2.60259i	−0.151018	−	0.261570i
$100$		0			0
$101$	−3.83823	−	6.64801i	−0.381918	−	0.661502i	0.609418	−	0.792849i	$-0.291403\pi$
$101$	−3.83823	−	6.64801i	−0.381918	−	0.661502i	−0.991336	+	0.131347i	$0.958070\pi$
$102$		0			0
$103$	−8.08233	−	13.9990i	−0.796376	−	1.37936i	−0.921962	−	0.387281i	$-0.873414\pi$
$103$	−8.08233	−	13.9990i	−0.796376	−	1.37936i	0.125586	−	0.992083i	$-0.459919\pi$
$104$		0			0
$105$	0.952306	+	1.64944i	0.0929356	+	0.160969i
$106$		0			0
$107$	8.41550			0.813557			0.406779	−	0.913527i	$-0.366652\pi$
$107$	8.41550			0.813557			0.406779	+	0.913527i	$0.366652\pi$
$108$		0			0
$109$	−4.00738			−0.383837			−0.191919	−	0.981411i	$-0.561471\pi$
$109$	−4.00738			−0.383837			−0.191919	+	0.981411i	$0.561471\pi$
$110$		0			0
$111$	−0.725995	+	1.25746i	−0.0689084	+	0.119353i
$112$		0			0
$113$	−0.127891	−	0.221514i	−0.0120310	−	0.0208383i	0.859947	−	0.510383i	$-0.170496\pi$
$113$	−0.127891	−	0.221514i	−0.0120310	−	0.0208383i	−0.871978	+	0.489545i	$0.837163\pi$
$114$		0			0
$115$	1.94438	−	3.36777i	0.181315	−	0.314046i
$116$		0			0
$117$	2.70849	−	4.69125i	0.250400	−	0.433706i
$118$		0			0
$119$	8.64194			0.792205
$120$		0			0
$121$	0.984349	−	1.70494i	0.0894863	−	0.154995i
$122$		0			0
$123$	−0.0559598	−	0.0969252i	−0.00504573	−	0.00873945i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−1.91787	−	3.32185i	−0.170184	−	0.294767i	0.768300	−	0.640090i	$-0.221103\pi$
$127$	−1.91787	−	3.32185i	−0.170184	−	0.294767i	−0.938484	+	0.345323i	$0.887769\pi$
$128$		0			0
$129$	−2.08087			−0.183211
$130$		0			0
$131$	20.6597			1.80504			0.902521	−	0.430645i	$-0.141714\pi$
$131$	20.6597			1.80504			0.902521	+	0.430645i	$0.141714\pi$
$132$		0			0
$133$	−7.38503			−0.640363
$134$		0			0
$135$	−1.00000			−0.0860663
$136$		0			0
$137$	−6.37529			−0.544678			−0.272339	−	0.962201i	$-0.587797\pi$
$137$	−6.37529			−0.544678			−0.272339	+	0.962201i	$0.587797\pi$
$138$		0			0
$139$	6.06502			0.514429			0.257214	−	0.966354i	$-0.417195\pi$
$139$	6.06502			0.514429			0.257214	+	0.966354i	$0.417195\pi$
$140$		0			0
$141$	0.778456	+	1.34832i	0.0655578	+	0.113549i
$142$		0			0
$143$	−16.2792			−1.36133
$144$		0			0
$145$	4.12189	+	7.13932i	0.342304	+	0.592888i
$146$		0			0
$147$	−1.68623	+	2.92063i	−0.139078	+	0.240889i
$148$		0			0
$149$	−19.0684			−1.56215			−0.781073	−	0.624440i	$-0.785327\pi$
$149$	−19.0684			−1.56215			−0.781073	+	0.624440i	$0.785327\pi$
$150$		0			0
$151$	−3.80844	+	6.59641i	−0.309926	+	0.536808i	−0.978346	−	0.206976i	$-0.933638\pi$
$151$	−3.80844	+	6.59641i	−0.309926	+	0.536808i	0.668420	+	0.743784i	$0.266971\pi$
$152$		0			0
$153$	−2.26869	+	3.92948i	−0.183412	+	0.317680i
$154$		0			0
$155$	−3.48804	−	6.04146i	−0.280166	−	0.485262i
$156$		0			0
$157$	2.20493	−	3.81905i	0.175973	−	0.304793i	−0.764525	−	0.644594i	$-0.777026\pi$
$157$	2.20493	−	3.81905i	0.175973	−	0.304793i	0.940497	+	0.339801i	$0.110360\pi$
$158$		0			0
$159$	8.39503			0.665769
$160$		0			0
$161$	−7.40659			−0.583721
$162$		0			0
$163$	−3.43242	−	5.94512i	−0.268848	−	0.465658i	0.699717	−	0.714420i	$-0.253309\pi$
$163$	−3.43242	−	5.94512i	−0.268848	−	0.465658i	−0.968564	+	0.248763i	$0.919976\pi$
$164$		0			0
$165$	1.50261	+	2.60259i	0.116978	+	0.202611i
$166$		0			0
$167$	−9.03170	−	15.6434i	−0.698894	−	1.21052i	−0.968850	−	0.247647i	$-0.920343\pi$
$167$	−9.03170	−	15.6434i	−0.698894	−	1.21052i	0.269957	−	0.962872i	$-0.412991\pi$
$168$		0			0
$169$	−8.17188	−	14.1541i	−0.628606	−	1.08878i
$170$		0			0
$171$	1.93872	−	3.35797i	0.148258	−	0.256790i
$172$		0			0
$173$	2.91255	−	5.04469i	0.221437	−	0.383541i	−0.733807	−	0.679358i	$-0.762258\pi$
$173$	2.91255	−	5.04469i	0.221437	−	0.383541i	0.955245	+	0.295817i	$0.0955918\pi$
$174$		0			0
$175$	−0.952306	−	1.64944i	−0.0719876	−	0.124686i
$176$		0			0
$177$	2.69514			0.202579
$178$		0			0
$179$	8.32860			0.622509			0.311254	−	0.950327i	$-0.399251\pi$
$179$	8.32860			0.622509			0.311254	+	0.950327i	$0.399251\pi$
$180$		0			0
$181$	4.40709	+	7.63330i	0.327576	+	0.567378i	0.982030	−	0.188723i	$-0.0604349\pi$
$181$	4.40709	+	7.63330i	0.327576	+	0.567378i	−0.654454	+	0.756102i	$0.727102\pi$
$182$		0			0
$183$	0.711547	−	1.23244i	0.0525991	−	0.0911043i
$184$		0			0
$185$	0.725995	−	1.25746i	0.0533762	−	0.0924503i
$186$		0			0
$187$	13.6358			0.997147
$188$		0			0
$189$	0.952306	+	1.64944i	0.0692701	+	0.119979i
$190$		0			0
$191$	−2.58985	+	4.48576i	−0.187395	+	0.324578i	−0.944381	−	0.328853i	$-0.893338\pi$
$191$	−2.58985	+	4.48576i	−0.187395	+	0.324578i	0.756986	+	0.653431i	$0.226671\pi$
$192$		0			0
$193$	−11.1088			−0.799629			−0.399814	−	0.916596i	$-0.630925\pi$
$193$	−11.1088			−0.799629			−0.399814	+	0.916596i	$0.630925\pi$
$194$		0			0
$195$	−2.70849	+	4.69125i	−0.193959	+	0.335947i
$196$		0			0
$197$	0.822256	+	1.42419i	0.0585833	+	0.101469i	0.893830	−	0.448407i	$-0.148008\pi$
$197$	0.822256	+	1.42419i	0.0585833	+	0.101469i	−0.835246	+	0.549876i	$0.814675\pi$
$198$		0			0
$199$	6.25750	−	10.8383i	0.443582	−	0.768307i	−0.554370	−	0.832270i	$-0.687041\pi$
$199$	6.25750	−	10.8383i	0.443582	−	0.768307i	0.997952	+	0.0639631i	$0.0203740\pi$
$200$		0			0
$201$	7.90197	−	2.13517i	0.557362	−	0.150603i
$202$		0			0
$203$	7.85060	−	13.5976i	0.551004	−	0.954367i
$204$		0			0
$205$	0.0559598	+	0.0969252i	0.00390840	+	0.00676955i
$206$		0			0
$207$	1.94438	−	3.36777i	0.135144	−	0.234076i
$208$		0			0
$209$	−11.6525			−0.806023
$210$		0			0
$211$	−6.16577	+	10.6794i	−0.424469	+	0.735202i	−0.996371	−	0.0851205i	$-0.972872\pi$
$211$	−6.16577	+	10.6794i	−0.424469	+	0.735202i	0.571902	+	0.820322i	$0.306206\pi$
$212$		0			0
$213$	−2.11366	−	3.66096i	−0.144825	−	0.250845i
$214$		0			0
$215$	2.08087			0.141914
$216$		0			0
$217$	−6.64337	+	11.5066i	−0.450981	+	0.781122i
$218$		0			0
$219$	2.91448	−	5.04802i	0.196942	−	0.341114i
$220$		0			0
$221$	12.2894	+	21.2860i	0.826678	+	1.43185i
$222$		0			0
$223$	−14.1142			−0.945159			−0.472579	−	0.881288i	$-0.656677\pi$
$223$	−14.1142			−0.945159			−0.472579	+	0.881288i	$0.656677\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−9.17609	−	15.8935i	−0.609039	−	1.05489i	−0.991399	−	0.130873i	$-0.958222\pi$
$227$	−9.17609	−	15.8935i	−0.609039	−	1.05489i	0.382361	−	0.924013i	$-0.375111\pi$
$228$		0			0
$229$	11.3960	−	19.7385i	0.753071	−	1.30436i	−0.193256	−	0.981148i	$-0.561905\pi$
$229$	11.3960	−	19.7385i	0.753071	−	1.30436i	0.946327	−	0.323210i	$-0.104762\pi$
$230$		0			0
$231$	2.86188	−	4.95693i	0.188298	−	0.326142i
$232$		0			0
$233$	−8.00903	−	13.8721i	−0.524689	−	0.908789i	−0.999587	−	0.0287474i	$-0.990848\pi$
$233$	−8.00903	−	13.8721i	−0.524689	−	0.908789i	0.474897	−	0.880041i	$-0.342485\pi$
$234$		0			0
$235$	−0.778456	−	1.34832i	−0.0507808	−	0.0879550i
$236$		0			0
$237$	−3.12853	−	5.41877i	−0.203220	−	0.351987i
$238$		0			0
$239$	−10.3235	−	17.8809i	−0.667774	−	1.15662i	−0.978525	−	0.206127i	$-0.933914\pi$
$239$	−10.3235	−	17.8809i	−0.667774	−	1.15662i	0.310752	−	0.950491i	$-0.399419\pi$
$240$		0			0
$241$	3.17862			0.204753			0.102376	−	0.994746i	$-0.467355\pi$
$241$	3.17862			0.204753			0.102376	+	0.994746i	$0.467355\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	1.68623	−	2.92063i	0.107729	−	0.186592i
$246$		0			0
$247$	−10.5020	−	18.1901i	−0.668228	−	1.15741i
$248$		0			0
$249$	−0.214571	+	0.371649i	−0.0135979	+	0.0235523i
$250$		0			0
$251$	−5.34236	+	9.25324i	−0.337207	+	0.584059i	−0.983906	−	0.178686i	$-0.942815\pi$
$251$	−5.34236	+	9.25324i	−0.337207	+	0.584059i	0.646699	+	0.762745i	$0.276149\pi$
$252$		0			0
$253$	−11.6866			−0.734728
$254$		0			0
$255$	2.26869	−	3.92948i	0.142071	−	0.246074i
$256$		0			0
$257$	8.37861	+	14.5122i	0.522643	+	0.905244i	0.999653	+	0.0263465i	$0.00838731\pi$
$257$	8.37861	+	14.5122i	0.522643	+	0.905244i	−0.477010	+	0.878898i	$0.658279\pi$
$258$		0			0
$259$	−2.76548			−0.171838
$260$		0			0
$261$	4.12189	+	7.13932i	0.255138	+	0.441913i
$262$		0			0
$263$	−8.51186			−0.524864			−0.262432	−	0.964951i	$-0.584525\pi$
$263$	−8.51186			−0.524864			−0.262432	+	0.964951i	$0.584525\pi$
$264$		0			0
$265$	−8.39503			−0.515703
$266$		0			0
$267$	7.70404			0.471479
$268$		0			0
$269$	−5.08990			−0.310337			−0.155168	−	0.987888i	$-0.549592\pi$
$269$	−5.08990			−0.310337			−0.155168	+	0.987888i	$0.549592\pi$
$270$		0			0
$271$	6.32399			0.384155			0.192078	−	0.981380i	$-0.438477\pi$
$271$	6.32399			0.384155			0.192078	+	0.981380i	$0.438477\pi$
$272$		0			0
$273$	10.3173			0.624429
$274$		0			0
$275$	−1.50261	−	2.60259i	−0.0906106	−	0.156942i
$276$		0			0
$277$	−21.2318			−1.27569			−0.637847	−	0.770163i	$-0.720175\pi$
$277$	−21.2318			−1.27569			−0.637847	+	0.770163i	$0.720175\pi$
$278$		0			0
$279$	−3.48804	−	6.04146i	−0.208823	−	0.361693i
$280$		0			0
$281$	−5.94374	+	10.2949i	−0.354574	+	0.614139i	−0.987045	−	0.160444i	$-0.948707\pi$
$281$	−5.94374	+	10.2949i	−0.354574	+	0.614139i	0.632471	+	0.774584i	$0.282041\pi$
$282$		0			0
$283$	−17.9152			−1.06495			−0.532473	−	0.846447i	$-0.678737\pi$
$283$	−17.9152			−1.06495			−0.532473	+	0.846447i	$0.678737\pi$
$284$		0			0
$285$	−1.93872	+	3.35797i	−0.114840	+	0.198909i
$286$		0			0
$287$	0.106582	−	0.184605i	0.00629132	−	0.0108969i
$288$		0			0
$289$	−1.79388	−	3.10710i	−0.105523	−	0.182770i
$290$		0			0
$291$	1.52705	−	2.64493i	0.0895172	−	0.155048i
$292$		0			0
$293$	8.98886			0.525135			0.262567	−	0.964914i	$-0.415431\pi$
$293$	8.98886			0.525135			0.262567	+	0.964914i	$0.415431\pi$
$294$		0			0
$295$	−2.69514			−0.156917
$296$		0			0
$297$	1.50261	+	2.60259i	0.0871901	+	0.151018i
$298$		0			0
$299$	−10.5327	−	18.2432i	−0.609121	−	1.05503i
$300$		0			0
$301$	−1.98163	−	3.43228i	−0.114219	−	0.197833i
$302$		0			0
$303$	3.83823	+	6.64801i	0.220501	+	0.381918i
$304$		0			0
$305$	−0.711547	+	1.23244i	−0.0407431	+	0.0705691i
$306$		0			0
$307$	−8.11191	+	14.0502i	−0.462971	+	0.801890i	−0.999107	−	0.0422417i	$-0.986550\pi$
$307$	−8.11191	+	14.0502i	−0.462971	+	0.801890i	0.536136	+	0.844132i	$0.319883\pi$
$308$		0			0
$309$	8.08233	+	13.9990i	0.459788	+	0.796376i
$310$		0			0
$311$	−7.88048			−0.446861			−0.223430	−	0.974720i	$-0.571726\pi$
$311$	−7.88048			−0.446861			−0.223430	+	0.974720i	$0.571726\pi$
$312$		0			0
$313$	20.1030			1.13629			0.568143	−	0.822930i	$-0.307662\pi$
$313$	20.1030			1.13629			0.568143	+	0.822930i	$0.307662\pi$
$314$		0			0
$315$	−0.952306	−	1.64944i	−0.0536564	−	0.0929356i
$316$		0			0
$317$	3.36681	−	5.83149i	0.189099	−	0.327529i	−0.755851	−	0.654744i	$-0.772777\pi$
$317$	3.36681	−	5.83149i	0.189099	−	0.327529i	0.944950	+	0.327214i	$0.106110\pi$
$318$		0			0
$319$	12.3871	−	21.4552i	0.693547	−	1.20126i
$320$		0			0
$321$	−8.41550			−0.469708
$322$		0			0
$323$	8.79671	+	15.2363i	0.489462	+	0.847773i
$324$		0			0
$325$	2.70849	−	4.69125i	0.150240	−	0.260224i
$326$		0			0
$327$	4.00738			0.221609
$328$		0			0
$329$	−1.48266	+	2.56804i	−0.0817415	+	0.141580i
$330$		0			0
$331$	−8.62257	−	14.9347i	−0.473939	−	0.820887i	0.525616	−	0.850722i	$-0.323835\pi$
$331$	−8.62257	−	14.9347i	−0.473939	−	0.820887i	−0.999555	+	0.0298355i	$0.990502\pi$
$332$		0			0
$333$	0.725995	−	1.25746i	0.0397843	−	0.0689084i
$334$		0			0
$335$	−7.90197	+	2.13517i	−0.431731	+	0.116657i
$336$		0			0
$337$	−3.60167	+	6.23828i	−0.196196	+	0.339821i	−0.947292	−	0.320372i	$-0.896192\pi$
$337$	−3.60167	+	6.23828i	−0.196196	+	0.339821i	0.751096	+	0.660193i	$0.229525\pi$
$338$		0			0
$339$	0.127891	+	0.221514i	0.00694610	+	0.0120310i
$340$		0			0
$341$	−10.4823	+	18.1559i	−0.567648	+	0.983196i
$342$		0			0
$343$	−19.7555			−1.06670
$344$		0			0
$345$	−1.94438	+	3.36777i	−0.104682	+	0.181315i
$346$		0			0
$347$	11.3596	+	19.6754i	0.609815	+	1.05623i	0.991270	+	0.131844i	$0.0420898\pi$
$347$	11.3596	+	19.6754i	0.609815	+	1.05623i	−0.381455	+	0.924387i	$0.624577\pi$
$348$		0			0
$349$	−4.33225			−0.231900			−0.115950	−	0.993255i	$-0.536991\pi$
$349$	−4.33225			−0.231900			−0.115950	+	0.993255i	$0.536991\pi$
$350$		0			0
$351$	−2.70849	+	4.69125i	−0.144569	+	0.250400i
$352$		0			0
$353$	11.7645	−	20.3768i	0.626163	−	1.08455i	−0.362151	−	0.932119i	$-0.617958\pi$
$353$	11.7645	−	20.3768i	0.626163	−	1.08455i	0.988315	−	0.152427i	$-0.0487090\pi$
$354$		0			0
$355$	2.11366	+	3.66096i	0.112181	+	0.194304i
$356$		0			0
$357$	−8.64194			−0.457380
$358$		0			0
$359$	16.6177			0.877048			0.438524	−	0.898719i	$-0.355501\pi$
$359$	16.6177			0.877048			0.438524	+	0.898719i	$0.355501\pi$
$360$		0			0
$361$	1.98271	+	3.43416i	0.104353	+	0.180745i
$362$		0			0
$363$	−0.984349	+	1.70494i	−0.0516649	+	0.0894863i
$364$		0			0
$365$	−2.91448	+	5.04802i	−0.152551	+	0.264226i
$366$		0			0
$367$	−16.6017	−	28.7549i	−0.866600	−	1.50100i	−0.865449	−	0.500996i	$-0.832967\pi$
$367$	−16.6017	−	28.7549i	−0.866600	−	1.50100i	−0.00115093	−	0.999999i	$-0.500366\pi$
$368$		0			0
$369$	0.0559598	+	0.0969252i	0.00291315	+	0.00504573i
$370$		0			0
$371$	7.99464	+	13.8471i	0.415061	+	0.718907i
$372$		0			0
$373$	−14.4803	−	25.0807i	−0.749763	−	1.29863i	−0.947936	−	0.318461i	$-0.896834\pi$
$373$	−14.4803	−	25.0807i	−0.749763	−	1.29863i	0.198173	−	0.980167i	$-0.436499\pi$
$374$		0			0
$375$	−1.00000			−0.0516398
$376$		0			0
$377$	44.6564			2.29992
$378$		0			0
$379$	1.44016	−	2.49444i	0.0739763	−	0.128131i	−0.826664	−	0.562695i	$-0.809764\pi$
$379$	1.44016	−	2.49444i	0.0739763	−	0.128131i	0.900641	+	0.434565i	$0.143098\pi$
$380$		0			0
$381$	1.91787	+	3.32185i	0.0982556	+	0.170184i
$382$		0			0
$383$	−5.91934	+	10.2526i	−0.302464	+	0.523883i	−0.976694	−	0.214639i	$-0.931143\pi$
$383$	−5.91934	+	10.2526i	−0.302464	+	0.523883i	0.674229	+	0.738522i	$0.264476\pi$
$384$		0			0
$385$	−2.86188	+	4.95693i	−0.145855	+	0.252628i
$386$		0			0
$387$	2.08087			0.105777
$388$		0			0
$389$	−14.4580	+	25.0421i	−0.733051	+	1.26968i	0.222521	+	0.974928i	$0.428571\pi$
$389$	−14.4580	+	25.0421i	−0.733051	+	1.26968i	−0.955573	+	0.294755i	$0.904762\pi$
$390$		0			0
$391$	8.82239	+	15.2808i	0.446167	+	0.772785i
$392$		0			0
$393$	−20.6597			−1.04214
$394$		0			0
$395$	3.12853	+	5.41877i	0.157413	+	0.272648i
$396$		0			0
$397$	−27.7710			−1.39379			−0.696894	−	0.717174i	$-0.745435\pi$
$397$	−27.7710			−1.39379			−0.696894	+	0.717174i	$0.745435\pi$
$398$		0			0
$399$	7.38503			0.369714
$400$		0			0
$401$	31.0164			1.54889			0.774443	−	0.632644i	$-0.218030\pi$
$401$	31.0164			1.54889			0.774443	+	0.632644i	$0.218030\pi$
$402$		0			0
$403$	−37.7893			−1.88242
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−4.36354			−0.216292
$408$		0			0
$409$	−12.7849	−	22.1442i	−0.632174	−	1.09496i	−0.987106	−	0.160066i	$-0.948829\pi$
$409$	−12.7849	−	22.1442i	−0.632174	−	1.09496i	0.354932	−	0.934892i	$-0.384504\pi$
$410$		0			0
$411$	6.37529			0.314470
$412$		0			0
$413$	2.56660	+	4.44548i	0.126294	+	0.218748i
$414$		0			0
$415$	0.214571	−	0.371649i	0.0105329	−	0.0182435i
$416$		0			0
$417$	−6.06502			−0.297005
$418$		0			0
$419$	13.1209	−	22.7261i	0.641000	−	1.11024i	−0.344210	−	0.938893i	$-0.611853\pi$
$419$	13.1209	−	22.7261i	0.641000	−	1.11024i	0.985210	−	0.171352i	$-0.0548135\pi$
$420$		0			0
$421$	13.0050	−	22.5253i	0.633823	−	1.09781i	−0.352940	−	0.935646i	$-0.614818\pi$
$421$	13.0050	−	22.5253i	0.633823	−	1.09781i	0.986763	−	0.162168i	$-0.0518486\pi$
$422$		0			0
$423$	−0.778456	−	1.34832i	−0.0378498	−	0.0655578i
$424$		0			0
$425$	−2.26869	+	3.92948i	−0.110047	+	0.190608i
$426$		0			0
$427$	2.71044			0.131168
$428$		0			0
$429$	16.2792			0.785967
$430$		0			0
$431$	4.02725	+	6.97541i	0.193986	+	0.335993i	0.946568	−	0.322505i	$-0.104525\pi$
$431$	4.02725	+	6.97541i	0.193986	+	0.335993i	−0.752582	+	0.658499i	$0.771192\pi$
$432$		0			0
$433$	−7.04054	−	12.1946i	−0.338347	−	0.586034i	0.645775	−	0.763528i	$-0.276534\pi$
$433$	−7.04054	−	12.1946i	−0.338347	−	0.586034i	−0.984122	+	0.177494i	$0.943201\pi$
$434$		0			0
$435$	−4.12189	−	7.13932i	−0.197629	−	0.342304i
$436$		0			0
$437$	−7.53923	−	13.0583i	−0.360650	−	0.624665i
$438$		0			0
$439$	−16.5384	+	28.6453i	−0.789333	+	1.36717i	0.137042	+	0.990565i	$0.456240\pi$
$439$	−16.5384	+	28.6453i	−0.789333	+	1.36717i	−0.926376	+	0.376600i	$0.877093\pi$
$440$		0			0
$441$	1.68623	−	2.92063i	0.0802964	−	0.139078i
$442$		0			0
$443$	−2.08553	−	3.61225i	−0.0990867	−	0.171623i	0.812220	−	0.583351i	$-0.198259\pi$
$443$	−2.08553	−	3.61225i	−0.0990867	−	0.171623i	−0.911307	+	0.411728i	$0.864925\pi$
$444$		0			0
$445$	−7.70404			−0.365206
$446$		0			0
$447$	19.0684			0.901905
$448$		0			0
$449$	4.90893	+	8.50251i	0.231667	+	0.401258i	0.958299	−	0.285769i	$-0.0922488\pi$
$449$	4.90893	+	8.50251i	0.231667	+	0.401258i	−0.726632	+	0.687027i	$0.758916\pi$
$450$		0			0
$451$	0.168171	−	0.291281i	0.00791887	−	0.0137159i
$452$		0			0
$453$	3.80844	−	6.59641i	0.178936	−	0.309926i
$454$		0			0
$455$	−10.3173			−0.483681
$456$		0			0
$457$	0.154702	+	0.267953i	0.00723668	+	0.0125343i	0.869621	−	0.493720i	$-0.164363\pi$
$457$	0.154702	+	0.267953i	0.00723668	+	0.0125343i	−0.862384	+	0.506254i	$0.831030\pi$
$458$		0			0
$459$	2.26869	−	3.92948i	0.105893	−	0.183412i
$460$		0			0
$461$	14.0077			0.652403			0.326202	−	0.945300i	$-0.394231\pi$
$461$	14.0077			0.652403			0.326202	+	0.945300i	$0.394231\pi$
$462$		0			0
$463$	14.5872	−	25.2657i	0.677923	−	1.17420i	−0.297682	−	0.954665i	$-0.596214\pi$
$463$	14.5872	−	25.2657i	0.677923	−	1.17420i	0.975605	−	0.219532i	$-0.0704530\pi$
$464$		0			0
$465$	3.48804	+	6.04146i	0.161754	+	0.280166i
$466$		0			0
$467$	−3.69351	+	6.39735i	−0.170915	+	0.296034i	−0.938740	−	0.344626i	$-0.888006\pi$
$467$	−3.69351	+	6.39735i	−0.170915	+	0.296034i	0.767825	+	0.640660i	$0.221339\pi$
$468$		0			0
$469$	11.0469	+	11.0005i	0.510100	+	0.507956i
$470$		0			0
$471$	−2.20493	+	3.81905i	−0.101598	+	0.175973i
$472$		0			0
$473$	−3.12673	−	5.41566i	−0.143767	−	0.249012i
$474$		0			0
$475$	1.93872	−	3.35797i	0.0889547	−	0.154074i
$476$		0			0
$477$	−8.39503			−0.384382
$478$		0			0
$479$	−17.1665	+	29.7333i	−0.784359	+	1.35855i	0.145023	+	0.989428i	$0.453675\pi$
$479$	−17.1665	+	29.7333i	−0.784359	+	1.35855i	−0.929381	+	0.369121i	$0.879659\pi$
$480$		0			0
$481$	−3.93270	−	6.81164i	−0.179316	−	0.310584i
$482$		0			0
$483$	7.40659			0.337011
$484$		0			0
$485$	−1.52705	+	2.64493i	−0.0693397	+	0.120100i
$486$		0			0
$487$	20.3592	−	35.2631i	0.922562	−	1.59792i	0.127126	−	0.991887i	$-0.459425\pi$
$487$	20.3592	−	35.2631i	0.922562	−	1.59792i	0.795436	−	0.606038i	$-0.207242\pi$
$488$		0			0
$489$	3.43242	+	5.94512i	0.155219	+	0.268848i
$490$		0			0
$491$	10.0579			0.453909			0.226954	−	0.973905i	$-0.427123\pi$
$491$	10.0579			0.453909			0.226954	+	0.973905i	$0.427123\pi$
$492$		0			0
$493$	−37.4051			−1.68464
$494$		0			0
$495$	−1.50261	−	2.60259i	−0.0675371	−	0.116978i
$496$		0			0
$497$	4.02570	−	6.97271i	0.180577	−	0.312769i
$498$		0			0
$499$	−7.55005	+	13.0771i	−0.337987	+	0.585410i	−0.984054	−	0.177870i	$-0.943079\pi$
$499$	−7.55005	+	13.0771i	−0.337987	+	0.585410i	0.646067	+	0.763281i	$0.276413\pi$
$500$		0			0
$501$	9.03170	+	15.6434i	0.403506	+	0.698894i
$502$		0			0
$503$	−9.62438	−	16.6699i	−0.429130	−	0.743274i	0.567666	−	0.823259i	$-0.307846\pi$
$503$	−9.62438	−	16.6699i	−0.429130	−	0.743274i	−0.996796	+	0.0799842i	$0.974513\pi$
$504$		0			0
$505$	−3.83823	−	6.64801i	−0.170799	−	0.295833i
$506$		0			0
$507$	8.17188	+	14.1541i	0.362926	+	0.628606i
$508$		0			0
$509$	−28.0604			−1.24376			−0.621878	−	0.783114i	$-0.713630\pi$
$509$	−28.0604			−1.24376			−0.621878	+	0.783114i	$0.713630\pi$
$510$		0			0
$511$	11.1019			0.491119
$512$		0			0
$513$	−1.93872	+	3.35797i	−0.0855967	+	0.148258i
$514$		0			0
$515$	−8.08233	−	13.9990i	−0.356150	−	0.616870i
$516$		0			0
$517$	−2.33942	+	4.05200i	−0.102888	+	0.178207i
$518$		0			0
$519$	−2.91255	+	5.04469i	−0.127847	+	0.221437i
$520$		0			0
$521$	33.9781			1.48861			0.744303	−	0.667842i	$-0.232782\pi$
$521$	33.9781			1.48861			0.744303	+	0.667842i	$0.232782\pi$
$522$		0			0
$523$	−2.30814	+	3.99781i	−0.100928	+	0.174812i	−0.912067	−	0.410041i	$-0.865514\pi$
$523$	−2.30814	+	3.99781i	−0.100928	+	0.174812i	0.811139	+	0.584853i	$0.198848\pi$
$524$		0			0
$525$	0.952306	+	1.64944i	0.0415621	+	0.0719876i
$526$		0			0
$527$	31.6531			1.37883
$528$		0			0
$529$	3.93876	+	6.82213i	0.171250	+	0.296614i
$530$		0			0
$531$	−2.69514			−0.116959
$532$		0			0
$533$	0.606267			0.0262603
$534$		0			0
$535$	8.41550			0.363834
$536$		0			0
$537$	−8.32860			−0.359406
$538$		0			0
$539$	−10.1349			−0.436542
$540$		0			0
$541$	45.1210			1.93990			0.969952	−	0.243295i	$-0.0782284\pi$
$541$	45.1210			1.93990			0.969952	+	0.243295i	$0.0782284\pi$
$542$		0			0
$543$	−4.40709	−	7.63330i	−0.189126	−	0.327576i
$544$		0			0
$545$	−4.00738			−0.171657
$546$		0			0
$547$	−9.41013	−	16.2988i	−0.402348	−	0.696887i	0.591661	−	0.806187i	$-0.298472\pi$
$547$	−9.41013	−	16.2988i	−0.402348	−	0.696887i	−0.994009	+	0.109300i	$0.965139\pi$
$548$		0			0
$549$	−0.711547	+	1.23244i	−0.0303681	+	0.0525991i
$550$		0			0
$551$	31.9648			1.36174
$552$		0			0
$553$	5.95863	−	10.3207i	0.253387	−	0.438879i
$554$		0			0
$555$	−0.725995	+	1.25746i	−0.0308168	+	0.0533762i
$556$		0			0
$557$	10.2456	+	17.7459i	0.434121	+	0.751919i	0.997223	−	0.0744679i	$-0.0237258\pi$
$557$	10.2456	+	17.7459i	0.434121	+	0.751919i	−0.563103	+	0.826387i	$0.690392\pi$
$558$		0			0
$559$	5.63603	−	9.76189i	0.238379	−	0.412884i
$560$		0			0
$561$	−13.6358			−0.575703
$562$		0			0
$563$	14.3876			0.606366			0.303183	−	0.952932i	$-0.401951\pi$
$563$	14.3876			0.606366			0.303183	+	0.952932i	$0.401951\pi$
$564$		0			0
$565$	−0.127891	−	0.221514i	−0.00538043	−	0.00931917i
$566$		0			0
$567$	−0.952306	−	1.64944i	−0.0399931	−	0.0692701i
$568$		0			0
$569$	−15.0338	−	26.0393i	−0.630249	−	1.09162i	−0.987501	−	0.157615i	$-0.949620\pi$
$569$	−15.0338	−	26.0393i	−0.630249	−	1.09162i	0.357252	−	0.934008i	$-0.383714\pi$
$570$		0			0
$571$	−7.25219	−	12.5612i	−0.303495	−	0.525668i	0.673430	−	0.739251i	$-0.264820\pi$
$571$	−7.25219	−	12.5612i	−0.303495	−	0.525668i	−0.976925	+	0.213582i	$0.931487\pi$
$572$		0			0
$573$	2.58985	−	4.48576i	0.108193	−	0.187395i
$574$		0			0
$575$	1.94438	−	3.36777i	0.0810863	−	0.140446i
$576$		0			0
$577$	1.32727	+	2.29889i	0.0552548	+	0.0957041i	0.892330	−	0.451384i	$-0.149070\pi$
$577$	1.32727	+	2.29889i	0.0552548	+	0.0957041i	−0.837075	+	0.547088i	$0.815736\pi$
$578$		0			0
$579$	11.1088			0.461666
$580$		0			0
$581$	−0.817351			−0.0339094
$582$		0			0
$583$	12.6144	+	21.8488i	0.522436	+	0.904886i
$584$		0			0
$585$	2.70849	−	4.69125i	0.111982	−	0.193959i
$586$		0			0
$587$	0.111235	−	0.192665i	0.00459117	−	0.00795214i	−0.863721	−	0.503971i	$-0.831872\pi$
$587$	0.111235	−	0.192665i	0.00459117	−	0.00795214i	0.868312	+	0.496019i	$0.165205\pi$
$588$		0			0
$589$	−27.0494			−1.11455
$590$		0			0
$591$	−0.822256	−	1.42419i	−0.0338231	−	0.0585833i
$592$		0			0
$593$	−11.7261	+	20.3103i	−0.481535	+	0.834043i	−0.999775	−	0.0211918i	$-0.993254\pi$
$593$	−11.7261	+	20.3103i	−0.481535	+	0.834043i	0.518240	+	0.855235i	$0.326587\pi$
$594$		0			0
$595$	8.64194			0.354285
$596$		0			0
$597$	−6.25750	+	10.8383i	−0.256102	+	0.443582i
$598$		0			0
$599$	18.6959	+	32.3823i	0.763895	+	1.32310i	0.940829	+	0.338882i	$0.110049\pi$
$599$	18.6959	+	32.3823i	0.763895	+	1.32310i	−0.176934	+	0.984223i	$0.556618\pi$
$600$		0			0
$601$	0.570375	−	0.987919i	0.0232661	−	0.0402980i	−0.854158	−	0.520014i	$-0.825927\pi$
$601$	0.570375	−	0.987919i	0.0232661	−	0.0402980i	0.877424	+	0.479716i	$0.159260\pi$
$602$		0			0
$603$	−7.90197	+	2.13517i	−0.321793	+	0.0869507i
$604$		0			0
$605$	0.984349	−	1.70494i	0.0400195	−	0.0693158i
$606$		0			0
$607$	16.2178	+	28.0901i	0.658262	+	1.14014i	0.981065	+	0.193677i	$0.0620413\pi$
$607$	16.2178	+	28.0901i	0.658262	+	1.14014i	−0.322804	+	0.946466i	$0.604625\pi$
$608$		0			0
$609$	−7.85060	+	13.5976i	−0.318122	+	0.551004i
$610$		0			0
$611$	−8.43377			−0.341194
$612$		0			0
$613$	−3.20790	+	5.55625i	−0.129566	+	0.224415i	−0.923508	−	0.383578i	$-0.874692\pi$
$613$	−3.20790	+	5.55625i	−0.129566	+	0.224415i	0.793943	+	0.607993i	$0.208025\pi$
$614$		0			0
$615$	−0.0559598	−	0.0969252i	−0.00225652	−	0.00390840i
$616$		0			0
$617$	22.0259			0.886730			0.443365	−	0.896341i	$-0.353785\pi$
$617$	22.0259			0.886730			0.443365	+	0.896341i	$0.353785\pi$
$618$		0			0
$619$	−20.7749	+	35.9831i	−0.835012	+	1.44628i	0.0590084	+	0.998257i	$0.481206\pi$
$619$	−20.7749	+	35.9831i	−0.835012	+	1.44628i	−0.894021	+	0.448026i	$0.852127\pi$
$620$		0			0
$621$	−1.94438	+	3.36777i	−0.0780254	+	0.135144i
$622$		0			0
$623$	7.33660	+	12.7074i	0.293935	+	0.509110i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	11.6525			0.465358
$628$		0			0
$629$	3.29411	+	5.70556i	0.131345	+	0.227496i
$630$		0			0
$631$	8.33335	−	14.4338i	0.331745	−	0.574600i	−0.651109	−	0.758984i	$-0.725696\pi$
$631$	8.33335	−	14.4338i	0.331745	−	0.574600i	0.982854	+	0.184385i	$0.0590292\pi$
$632$		0			0
$633$	6.16577	−	10.6794i	0.245067	−	0.424469i
$634$		0			0
$635$	−1.91787	−	3.32185i	−0.0761084	−	0.131824i
$636$		0			0
$637$	−9.13426	−	15.8210i	−0.361913	−	0.626851i
$638$		0			0
$639$	2.11366	+	3.66096i	0.0836150	+	0.144825i
$640$		0			0
$641$	19.4494	+	33.6874i	0.768206	+	1.33057i	0.938535	+	0.345184i	$0.112184\pi$
$641$	19.4494	+	33.6874i	0.768206	+	1.33057i	−0.170329	+	0.985387i	$0.554483\pi$
$642$		0			0
$643$	14.0504			0.554092			0.277046	−	0.960857i	$-0.410644\pi$
$643$	14.0504			0.554092			0.277046	+	0.960857i	$0.410644\pi$
$644$		0			0
$645$	−2.08087			−0.0819342
$646$		0			0
$647$	17.7320	−	30.7127i	0.697116	−	1.20744i	−0.272345	−	0.962200i	$-0.587799\pi$
$647$	17.7320	−	30.7127i	0.697116	−	1.20744i	0.969462	−	0.245242i	$-0.0788673\pi$
$648$		0			0
$649$	4.04973	+	7.01434i	0.158966	+	0.275337i
$650$		0			0
$651$	6.64337	−	11.5066i	0.260374	−	0.450981i
$652$		0			0
$653$	9.25399	−	16.0284i	0.362137	−	0.627239i	−0.626176	−	0.779682i	$-0.715381\pi$
$653$	9.25399	−	16.0284i	0.362137	−	0.627239i	0.988312	+	0.152443i	$0.0487140\pi$
$654$		0			0
$655$	20.6597			0.807240
$656$		0			0
$657$	−2.91448	+	5.04802i	−0.113705	+	0.196942i
$658$		0			0
$659$	−5.16040	−	8.93807i	−0.201021	−	0.348178i	0.747837	−	0.663882i	$-0.231092\pi$
$659$	−5.16040	−	8.93807i	−0.201021	−	0.348178i	−0.948858	+	0.315705i	$0.897759\pi$
$660$		0			0
$661$	−21.1457			−0.822471			−0.411235	−	0.911529i	$-0.634903\pi$
$661$	−21.1457			−0.822471			−0.411235	+	0.911529i	$0.634903\pi$
$662$		0			0
$663$	−12.2894	−	21.2860i	−0.477283	−	0.826678i
$664$		0			0
$665$	−7.38503			−0.286379
$666$		0			0
$667$	32.0581			1.24129
$668$		0			0
$669$	14.1142			0.545688
$670$		0			0
$671$	4.27670			0.165100
$672$		0			0
$673$	−28.5294			−1.09973			−0.549864	−	0.835254i	$-0.685321\pi$
$673$	−28.5294			−1.09973			−0.549864	+	0.835254i	$0.685321\pi$
$674$		0			0
$675$	−1.00000			−0.0384900
$676$		0			0
$677$	15.2026	+	26.3317i	0.584285	+	1.01201i	0.994964	+	0.100231i	$0.0319581\pi$
$677$	15.2026	+	26.3317i	0.584285	+	1.01201i	−0.410680	+	0.911780i	$0.634709\pi$
$678$		0			0
$679$	5.81688			0.223231
$680$		0			0
$681$	9.17609	+	15.8935i	0.351629	+	0.609039i
$682$		0			0
$683$	−10.0436	+	17.3960i	−0.384307	+	0.665639i	−0.991673	−	0.128783i	$-0.958893\pi$
$683$	−10.0436	+	17.3960i	−0.384307	+	0.665639i	0.607366	+	0.794422i	$0.292226\pi$
$684$		0			0
$685$	−6.37529			−0.243587
$686$		0			0
$687$	−11.3960	+	19.7385i	−0.434786	+	0.753071i
$688$		0			0
$689$	−22.7379	+	39.3832i	−0.866245	+	1.50038i
$690$		0			0
$691$	0.382534	+	0.662568i	0.0145523	+	0.0252053i	0.873210	−	0.487344i	$-0.162034\pi$
$691$	0.382534	+	0.662568i	0.0145523	+	0.0252053i	−0.858658	+	0.512550i	$0.828701\pi$
$692$		0			0
$693$	−2.86188	+	4.95693i	−0.108714	+	0.188298i
$694$		0			0
$695$	6.06502			0.230059
$696$		0			0
$697$	−0.507821			−0.0192351
$698$		0			0
$699$	8.00903	+	13.8721i	0.302930	+	0.524689i
$700$		0			0
$701$	11.1887	+	19.3794i	0.422592	+	0.731951i	0.996192	−	0.0871843i	$-0.0277869\pi$
$701$	11.1887	+	19.3794i	0.422592	+	0.731951i	−0.573600	+	0.819136i	$0.694454\pi$
$702$		0			0
$703$	−2.81500	−	4.87573i	−0.106170	−	0.183892i
$704$		0			0
$705$	0.778456	+	1.34832i	0.0293183	+	0.0507808i
$706$		0			0
$707$	−7.31034	+	12.6619i	−0.274934	+	0.476199i
$708$		0			0
$709$	−13.7785	+	23.8651i	−0.517462	+	0.896271i	0.482332	+	0.875988i	$0.339790\pi$
$709$	−13.7785	+	23.8651i	−0.517462	+	0.896271i	−0.999794	+	0.0202824i	$0.993543\pi$
$710$		0			0
$711$	3.12853	+	5.41877i	0.117329	+	0.203220i
$712$		0			0
$713$	−27.1283			−1.01596
$714$		0			0
$715$	−16.2792			−0.608807
$716$		0			0
$717$	10.3235	+	17.8809i	0.385539	+	0.667774i
$718$		0			0
$719$	17.9605	−	31.1085i	0.669813	−	1.16015i	−0.308143	−	0.951340i	$-0.599707\pi$
$719$	17.9605	−	31.1085i	0.669813	−	1.16015i	0.977956	−	0.208811i	$-0.0669593\pi$
$720$		0			0
$721$	−15.3937	+	26.6627i	−0.573292	+	0.992971i
$722$		0			0
$723$	−3.17862			−0.118214
$724$		0			0
$725$	4.12189	+	7.13932i	0.153083	+	0.265148i
$726$		0			0
$727$	−8.61887	+	14.9283i	−0.319656	+	0.553661i	−0.980416	−	0.196937i	$-0.936901\pi$
$727$	−8.61887	+	14.9283i	−0.319656	+	0.553661i	0.660760	+	0.750597i	$0.270234\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.72085	+	8.17675i	−0.174607	+	0.302428i
$732$		0			0
$733$	10.1070	+	17.5058i	0.373311	+	0.646593i	0.990073	−	0.140557i	$-0.0448892\pi$
$733$	10.1070	+	17.5058i	0.373311	+	0.646593i	−0.616762	+	0.787150i	$0.711556\pi$
$734$		0			0
$735$	−1.68623	+	2.92063i	−0.0621974	+	0.107729i
$736$		0			0
$737$	17.4305	+	17.3573i	0.642061	+	0.639363i
$738$		0			0
$739$	−2.29101	+	3.96814i	−0.0842760	+	0.145970i	−0.905082	−	0.425236i	$-0.860191\pi$
$739$	−2.29101	+	3.96814i	−0.0842760	+	0.145970i	0.820806	+	0.571206i	$0.193524\pi$
$740$		0			0
$741$	10.5020	+	18.1901i	0.385802	+	0.668228i
$742$		0			0
$743$	14.5208	−	25.1508i	0.532717	−	0.922693i	−0.466553	−	0.884493i	$-0.654504\pi$
$743$	14.5208	−	25.1508i	0.532717	−	0.922693i	0.999270	−	0.0382000i	$-0.0121624\pi$
$744$		0			0
$745$	−19.0684			−0.698613
$746$		0			0
$747$	0.214571	−	0.371649i	0.00785076	−	0.0135979i
$748$		0			0
$749$	−8.01414	−	13.8809i	−0.292830	−	0.507197i
$750$		0			0
$751$	32.5475			1.18767			0.593837	−	0.804586i	$-0.297613\pi$
$751$	32.5475			1.18767			0.593837	+	0.804586i	$0.297613\pi$
$752$		0			0
$753$	5.34236	−	9.25324i	0.194686	−	0.337207i
$754$		0			0
$755$	−3.80844	+	6.59641i	−0.138603	+	0.240068i
$756$		0			0
$757$	15.9972	+	27.7080i	0.581428	+	1.00706i	0.995310	+	0.0967327i	$0.0308392\pi$
$757$	15.9972	+	27.7080i	0.581428	+	1.00706i	−0.413882	+	0.910330i	$0.635827\pi$
$758$		0			0
$759$	11.6866			0.424195
$760$		0			0
$761$	21.4269			0.776726			0.388363	−	0.921507i	$-0.373041\pi$
$761$	21.4269			0.776726			0.388363	+	0.921507i	$0.373041\pi$
$762$		0			0
$763$	3.81625	+	6.60995i	0.138158	+	0.239296i
$764$		0			0
$765$	−2.26869	+	3.92948i	−0.0820246	+	0.142071i
$766$		0			0
$767$	−7.29976	+	12.6436i	−0.263579	+	0.456532i
$768$		0			0
$769$	20.6011	+	35.6821i	0.742893	+	1.28673i	0.951173	+	0.308659i	$0.0998802\pi$
$769$	20.6011	+	35.6821i	0.742893	+	1.28673i	−0.208280	+	0.978069i	$0.566786\pi$
$770$		0			0
$771$	−8.37861	−	14.5122i	−0.301748	−	0.522643i
$772$		0			0
$773$	13.9889	+	24.2295i	0.503147	+	0.871476i	0.999993	+	0.00363766i	$0.00115790\pi$
$773$	13.9889	+	24.2295i	0.503147	+	0.871476i	−0.496846	+	0.867839i	$0.665509\pi$
$774$		0			0
$775$	−3.48804	−	6.04146i	−0.125294	−	0.217016i
$776$		0			0
$777$	2.76548			0.0992109
$778$		0			0
$779$	0.433962			0.0155483
$780$		0			0
$781$	6.35199	−	11.0020i	0.227292	−	0.393681i
$782$		0			0
$783$	−4.12189	−	7.13932i	−0.147304	−	0.255138i
$784$		0			0
$785$	2.20493	−	3.81905i	0.0786973	−	0.136308i
$786$		0			0
$787$	−9.55242	+	16.5453i	−0.340507	+	0.589776i	−0.984527	−	0.175233i	$-0.943932\pi$
$787$	−9.55242	+	16.5453i	−0.340507	+	0.589776i	0.644020	+	0.765009i	$0.277265\pi$
$788$		0			0
$789$	8.51186			0.303030
$790$		0			0
$791$	−0.243583	+	0.421899i	−0.00866083	+	0.0150010i
$792$		0			0
$793$	3.85444	+	6.67609i	0.136875	+	0.237075i
$794$		0			0
$795$	8.39503			0.297741
$796$		0			0
$797$	9.83180	+	17.0292i	0.348260	+	0.603204i	0.985940	−	0.167097i	$-0.0534393\pi$
$797$	9.83180	+	17.0292i	0.348260	+	0.603204i	−0.637680	+	0.770301i	$0.720106\pi$
$798$		0			0
$799$	7.06429			0.249917
$800$		0			0
$801$	−7.70404			−0.272209
$802$		0			0
$803$	17.5172			0.618170
$804$		0			0
$805$	−7.40659			−0.261048
$806$		0			0
$807$	5.08990			0.179173
$808$		0			0
$809$	19.6838			0.692045			0.346022	−	0.938226i	$-0.387532\pi$
$809$	19.6838			0.692045			0.346022	+	0.938226i	$0.387532\pi$
$810$		0			0
$811$	−2.82112	−	4.88633i	−0.0990630	−	0.171582i	0.812234	−	0.583332i	$-0.198251\pi$
$811$	−2.82112	−	4.88633i	−0.0990630	−	0.171582i	−0.911297	+	0.411749i	$0.864918\pi$
$812$		0			0
$813$	−6.32399			−0.221792
$814$		0			0
$815$	−3.43242	−	5.94512i	−0.120232	−	0.208248i
$816$		0			0
$817$	4.03423	−	6.98749i	0.141140	−	0.244461i
$818$		0			0
$819$	−10.3173			−0.360514
$820$		0			0
$821$	4.40512	−	7.62990i	0.153740	−	0.266285i	−0.778860	−	0.627198i	$-0.784202\pi$
$821$	4.40512	−	7.62990i	0.153740	−	0.266285i	0.932599	+	0.360913i	$0.117535\pi$
$822$		0			0
$823$	16.6375	−	28.8169i	0.579946	−	1.00450i	−0.415539	−	0.909575i	$-0.636407\pi$
$823$	16.6375	−	28.8169i	0.579946	−	1.00450i	0.995485	−	0.0949199i	$-0.0302595\pi$
$824$		0			0
$825$	1.50261	+	2.60259i	0.0523140	+	0.0906106i
$826$		0			0
$827$	−1.79121	+	3.10247i	−0.0622865	+	0.107883i	−0.895487	−	0.445087i	$-0.853173\pi$
$827$	−1.79121	+	3.10247i	−0.0622865	+	0.107883i	0.833201	+	0.552971i	$0.186506\pi$
$828$		0			0
$829$	31.1861			1.08314			0.541570	−	0.840656i	$-0.317830\pi$
$829$	31.1861			1.08314			0.541570	+	0.840656i	$0.317830\pi$
$830$		0			0
$831$	21.2318			0.736523
$832$		0			0
$833$	7.65104	+	13.2520i	0.265093	+	0.459154i
$834$		0			0
$835$	−9.03170	−	15.6434i	−0.312555	−	0.541361i
$836$		0			0
$837$	3.48804	+	6.04146i	0.120564	+	0.208823i
$838$		0			0
$839$	5.35033	+	9.26705i	0.184714	+	0.319934i	0.943480	−	0.331429i	$-0.107531\pi$
$839$	5.35033	+	9.26705i	0.184714	+	0.319934i	−0.758766	+	0.651363i	$0.774197\pi$
$840$		0			0
$841$	−19.4799	+	33.7402i	−0.671720	+	1.16345i
$842$		0			0
$843$	5.94374	−	10.2949i	0.204713	−	0.354574i
$844$		0			0
$845$	−8.17188	−	14.1541i	−0.281121	−	0.486916i
$846$		0			0
$847$	−3.74961			−0.128838
$848$		0			0
$849$	17.9152			0.614846
$850$		0			0
$851$	−2.82322	−	4.88996i	−0.0967788	−	0.167626i
$852$		0			0
$853$	21.3954	−	37.0579i	0.732564	−	1.26884i	−0.223220	−	0.974768i	$-0.571657\pi$
$853$	21.3954	−	37.0579i	0.732564	−	1.26884i	0.955784	−	0.294069i	$-0.0950097\pi$
$854$		0			0
$855$	1.93872	−	3.35797i	0.0663029	−	0.114840i
$856$		0			0
$857$	17.8449			0.609571			0.304786	−	0.952421i	$-0.401415\pi$
$857$	17.8449			0.609571			0.304786	+	0.952421i	$0.401415\pi$
$858$		0			0
$859$	−8.54386	−	14.7984i	−0.291513	−	0.504915i	0.682655	−	0.730741i	$-0.260825\pi$
$859$	−8.54386	−	14.7984i	−0.291513	−	0.504915i	−0.974168	+	0.225826i	$0.927492\pi$
$860$		0			0
$861$	−0.106582	+	0.184605i	−0.00363230	+	0.00629132i
$862$		0			0
$863$	14.1803			0.482704			0.241352	−	0.970438i	$-0.422409\pi$
$863$	14.1803			0.482704			0.241352	+	0.970438i	$0.422409\pi$
$864$		0			0
$865$	2.91255	−	5.04469i	0.0990298	−	0.171525i
$866$		0			0
$867$	1.79388	+	3.10710i	0.0609235	+	0.105523i
$868$		0			0
$869$	9.40189	−	16.2846i	0.318937	−	0.552416i
$870$		0			0
$871$	−11.3858	+	42.8532i	−0.385794	+	1.45202i
$872$		0			0
$873$	−1.52705	+	2.64493i	−0.0516828	+	0.0895172i
$874$		0			0
$875$	−0.952306	−	1.64944i	−0.0321938	−	0.0557614i
$876$		0			0
$877$	6.96197	−	12.0585i	0.235089	−	0.407186i	−0.724209	−	0.689580i	$-0.757795\pi$
$877$	6.96197	−	12.0585i	0.235089	−	0.407186i	0.959299	+	0.282394i	$0.0911285\pi$
$878$		0			0
$879$	−8.98886			−0.303187
$880$		0			0
$881$	15.7274	−	27.2406i	0.529869	−	0.917759i	−0.469524	−	0.882919i	$-0.655575\pi$
$881$	15.7274	−	27.2406i	0.529869	−	0.917759i	0.999393	−	0.0348397i	$-0.0110921\pi$
$882$		0			0
$883$	−15.6082	−	27.0343i	−0.525259	−	0.909776i	−0.999567	−	0.0294167i	$-0.990635\pi$
$883$	−15.6082	−	27.0343i	−0.525259	−	0.909776i	0.474308	−	0.880359i	$-0.342698\pi$
$884$		0			0
$885$	2.69514			0.0905960
$886$		0			0
$887$	1.99034	−	3.44737i	0.0668291	−	0.115751i	−0.830675	−	0.556758i	$-0.812045\pi$
$887$	1.99034	−	3.44737i	0.0668291	−	0.115751i	0.897504	+	0.441006i	$0.145378\pi$
$888$		0			0
$889$	−3.65280	+	6.32684i	−0.122511	+	0.212195i
$890$		0			0
$891$	−1.50261	−	2.60259i	−0.0503392	−	0.0871901i
$892$		0			0
$893$	−6.03684			−0.202015
$894$		0			0
$895$	8.32860			0.278394
$896$		0			0
$897$	10.5327	+	18.2432i	0.351676	+	0.609121i
$898$		0			0
$899$	28.7546	−	49.8044i	0.959020	−	1.66107i
$900$		0			0
$901$	19.0457	−	32.9881i	0.634504	−	1.09899i
$902$		0			0
$903$	1.98163	+	3.43228i	0.0659444	+	0.114219i
$904$		0			0
$905$	4.40709	+	7.63330i	0.146496	+	0.253739i
$906$		0			0
$907$	10.2302	+	17.7193i	0.339690	+	0.588360i	0.984374	−	0.176089i	$-0.0563446\pi$
$907$	10.2302	+	17.7193i	0.339690	+	0.588360i	−0.644685	+	0.764449i	$0.723011\pi$
$908$		0			0
$909$	−3.83823	−	6.64801i	−0.127306	−	0.220501i
$910$		0			0
$911$	−7.25478			−0.240361			−0.120181	−	0.992752i	$-0.538347\pi$
$911$	−7.25478			−0.240361			−0.120181	+	0.992752i	$0.538347\pi$
$912$		0			0
$913$	−1.28967			−0.0426817
$914$		0			0
$915$	0.711547	−	1.23244i	0.0235230	−	0.0407431i
$916$		0			0
$917$	−19.6743	−	34.0769i	−0.649703	−	1.12532i
$918$		0			0
$919$	5.98927	−	10.3737i	0.197568	−	0.342198i	−0.750171	−	0.661243i	$-0.770029\pi$
$919$	5.98927	−	10.3737i	0.197568	−	0.342198i	0.947739	+	0.319046i	$0.103362\pi$
$920$		0			0
$921$	8.11191	−	14.0502i	0.267297	−	0.462971i
$922$		0			0
$923$	22.8993			0.753740
$924$		0			0
$925$	0.725995	−	1.25746i	0.0238706	−	0.0413450i
$926$		0			0
$927$	−8.08233	−	13.9990i	−0.265459	−	0.459788i
$928$		0			0
$929$	6.70214			0.219890			0.109945	−	0.993938i	$-0.464933\pi$
$929$	6.70214			0.219890			0.109945	+	0.993938i	$0.464933\pi$
$930$		0			0
$931$	−6.53824	−	11.3246i	−0.214282	−	0.371148i
$932$		0			0
$933$	7.88048			0.257995
$934$		0			0
$935$	13.6358			0.445937
$936$		0			0
$937$	33.0798			1.08067			0.540335	−	0.841450i	$-0.318298\pi$
$937$	33.0798			1.08067			0.540335	+	0.841450i	$0.318298\pi$
$938$		0			0
$939$	−20.1030			−0.656035
$940$		0			0
$941$	−11.0151			−0.359081			−0.179540	−	0.983751i	$-0.557461\pi$
$941$	−11.0151			−0.359081			−0.179540	+	0.983751i	$0.557461\pi$
$942$		0			0
$943$	0.435229			0.0141730
$944$		0			0
$945$	0.952306	+	1.64944i	0.0309785	+	0.0536564i
$946$		0			0
$947$	−36.9084			−1.19936			−0.599681	−	0.800239i	$-0.704706\pi$
$947$	−36.9084			−1.19936			−0.599681	+	0.800239i	$0.704706\pi$
$948$		0			0
$949$	15.7877	+	27.3451i	0.512490	+	0.887659i
$950$		0			0
$951$	−3.36681	+	5.83149i	−0.109176	+	0.189099i
$952$		0			0
$953$	21.1751			0.685928			0.342964	−	0.939349i	$-0.388569\pi$
$953$	21.1751			0.685928			0.342964	+	0.939349i	$0.388569\pi$
$954$		0			0
$955$	−2.58985	+	4.48576i	−0.0838057	+	0.145156i
$956$		0			0
$957$	−12.3871	+	21.4552i	−0.400419	+	0.693547i
$958$		0			0
$959$	6.07123	+	10.5157i	0.196050	+	0.339569i
$960$		0			0
$961$	−8.83284	+	15.2989i	−0.284930	+	0.493514i
$962$		0			0
$963$	8.41550			0.271186
$964$		0			0
$965$	−11.1088			−0.357605
$966$		0			0
$967$	12.2858	+	21.2796i	0.395084	+	0.684305i	0.993112	−	0.117170i	$-0.0373822\pi$
$967$	12.2858	+	21.2796i	0.395084	+	0.684305i	−0.598028	+	0.801475i	$0.704049\pi$
$968$		0			0
$969$	−8.79671	−	15.2363i	−0.282591	−	0.489462i
$970$		0			0
$971$	−11.5014	−	19.9211i	−0.369098	−	0.639297i	0.620327	−	0.784344i	$-0.287000\pi$
$971$	−11.5014	−	19.9211i	−0.369098	−	0.639297i	−0.989425	+	0.145047i	$0.953667\pi$
$972$		0			0
$973$	−5.77576	−	10.0039i	−0.185162	−	0.320711i
$974$		0			0
$975$	−2.70849	+	4.69125i	−0.0867412	+	0.150240i
$976$		0			0
$977$	−24.9723	+	43.2532i	−0.798933	+	1.38379i	0.121378	+	0.992606i	$0.461269\pi$
$977$	−24.9723	+	43.2532i	−0.798933	+	1.38379i	−0.920311	+	0.391187i	$0.872065\pi$
$978$		0			0
$979$	11.5761	+	20.0505i	0.369975	+	0.640815i
$980$		0			0
$981$	−4.00738			−0.127946
$982$		0			0
$983$	−22.0654			−0.703778			−0.351889	−	0.936042i	$-0.614461\pi$
$983$	−22.0654			−0.703778			−0.351889	+	0.936042i	$0.614461\pi$
$984$		0			0
$985$	0.822256	+	1.42419i	0.0261992	+	0.0453784i
$986$		0			0
$987$	1.48266	−	2.56804i	0.0471935	−	0.0817415i
$988$		0			0
$989$	4.04601	−	7.00789i	0.128656	−	0.222838i
$990$		0			0
$991$	3.96913			0.126084			0.0630418	−	0.998011i	$-0.479920\pi$
$991$	3.96913			0.126084			0.0630418	+	0.998011i	$0.479920\pi$
$992$		0			0
$993$	8.62257	+	14.9347i	0.273629	+	0.473939i
$994$		0			0
$995$	6.25750	−	10.8383i	0.198376	−	0.343598i
$996$		0			0
$997$	−2.98418			−0.0945099			−0.0472550	−	0.998883i	$-0.515047\pi$
$997$	−2.98418			−0.0945099			−0.0472550	+	0.998883i	$0.515047\pi$
$998$		0			0
$999$	−0.725995	+	1.25746i	−0.0229695	+	0.0397843i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.k.3781.3	yes	14
67.37	even	3	inner	4020.2.q.k.841.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.k.841.3	✓	14	67.37	even	3	inner
4020.2.q.k.3781.3	yes	14	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4020.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(-0.952306 - 1.64944i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{3} +1.00000 q^{5} +(-0.952306 - 1.64944i) q^{7} +1.00000 q^{9} +(-1.50261 - 2.60259i) q^{11} +(2.70849 - 4.69125i) q^{13} -1.00000 q^{15} +(-2.26869 + 3.92948i) q^{17} +(1.93872 - 3.35797i) q^{19} +(0.952306 + 1.64944i) q^{21} +(1.94438 - 3.36777i) q^{23} +1.00000 q^{25} -1.00000 q^{27} +(4.12189 + 7.13932i) q^{29} +(-3.48804 - 6.04146i) q^{31} +(1.50261 + 2.60259i) q^{33} +(-0.952306 - 1.64944i) q^{35} +(0.725995 - 1.25746i) q^{37} +(-2.70849 + 4.69125i) q^{39} +(0.0559598 + 0.0969252i) q^{41} +2.08087 q^{43} +1.00000 q^{45} +(-0.778456 - 1.34832i) q^{47} +(1.68623 - 2.92063i) q^{49} +(2.26869 - 3.92948i) q^{51} -8.39503 q^{53} +(-1.50261 - 2.60259i) q^{55} +(-1.93872 + 3.35797i) q^{57} -2.69514 q^{59} +(-0.711547 + 1.23244i) q^{61} +(-0.952306 - 1.64944i) q^{63} +(2.70849 - 4.69125i) q^{65} +(-7.90197 + 2.13517i) q^{67} +(-1.94438 + 3.36777i) q^{69} +(2.11366 + 3.66096i) q^{71} +(-2.91448 + 5.04802i) q^{73} -1.00000 q^{75} +(-2.86188 + 4.95693i) q^{77} +(3.12853 + 5.41877i) q^{79} +1.00000 q^{81} +(0.214571 - 0.371649i) q^{83} +(-2.26869 + 3.92948i) q^{85} +(-4.12189 - 7.13932i) q^{87} -7.70404 q^{89} -10.3173 q^{91} +(3.48804 + 6.04146i) q^{93} +(1.93872 - 3.35797i) q^{95} +(-1.52705 + 2.64493i) q^{97} +(-1.50261 - 2.60259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9	\( 14 q - 14 q^{3} + 14 q^{5} + 3 q^{7} + 14 q^{9} + 6 q^{11} + 9 q^{13} - 14 q^{15} - 12 q^{17} + 14 q^{19} - 3 q^{21} + 6 q^{23} + 14 q^{25} - 14 q^{27} - q^{29} + 7 q^{31} - 6 q^{33} + 3 q^{35} - 2 q^{37} - 9 q^{39} - 18 q^{41} - 6 q^{43} + 14 q^{45} + 7 q^{47} + 12 q^{51} - 12 q^{53} + 6 q^{55} - 14 q^{57} - 2 q^{59} + 3 q^{63} + 9 q^{65} + 25 q^{67} - 6 q^{69} + 22 q^{71} - 15 q^{73} - 14 q^{75} + q^{77} + 9 q^{79} + 14 q^{81} - q^{83} - 12 q^{85} + q^{87} - 12 q^{89} - 38 q^{91} - 7 q^{93} + 14 q^{95} + 16 q^{97} + 6 q^{99}+O(q^{100}) \) 14 * q - 14 * q^3 + 14 * q^5 + 3 * q^7 + 14 * q^9 + 6 * q^11 + 9 * q^13 - 14 * q^15 - 12 * q^17 + 14 * q^19 - 3 * q^21 + 6 * q^23 + 14 * q^25 - 14 * q^27 - q^29 + 7 * q^31 - 6 * q^33 + 3 * q^35 - 2 * q^37 - 9 * q^39 - 18 * q^41 - 6 * q^43 + 14 * q^45 + 7 * q^47 + 12 * q^51 - 12 * q^53 + 6 * q^55 - 14 * q^57 - 2 * q^59 + 3 * q^63 + 9 * q^65 + 25 * q^67 - 6 * q^69 + 22 * q^71 - 15 * q^73 - 14 * q^75 + q^77 + 9 * q^79 + 14 * q^81 - q^83 - 12 * q^85 + q^87 - 12 * q^89 - 38 * q^91 - 7 * q^93 + 14 * q^95 + 16 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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