LMFDB - Embedded newform 4020.2.q.m.841.12

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:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			841.12
Character	$\chi$	$=$	4020.841
Dual form			4020.2.q.m.3781.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{3} +1.00000 q^{5} +(2.29305 - 3.97167i) q^{7} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{3} +1.00000 q^{5} +(2.29305 - 3.97167i) q^{7} +1.00000 q^{9} +(2.82399 - 4.89129i) q^{11} +(-2.64071 - 4.57385i) q^{13} +1.00000 q^{15} +(3.09932 + 5.36818i) q^{17} +(0.0519162 + 0.0899215i) q^{19} +(2.29305 - 3.97167i) q^{21} +(2.07475 + 3.59357i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(3.10343 - 5.37530i) q^{29} +(-2.19346 + 3.79918i) q^{31} +(2.82399 - 4.89129i) q^{33} +(2.29305 - 3.97167i) q^{35} +(-0.218836 - 0.379036i) q^{37} +(-2.64071 - 4.57385i) q^{39} +(-1.91389 + 3.31495i) q^{41} +5.08815 q^{43} +1.00000 q^{45} +(-3.13045 + 5.42210i) q^{47} +(-7.01613 - 12.1523i) q^{49} +(3.09932 + 5.36818i) q^{51} +6.60315 q^{53} +(2.82399 - 4.89129i) q^{55} +(0.0519162 + 0.0899215i) q^{57} -1.94404 q^{59} +(-1.08519 - 1.87960i) q^{61} +(2.29305 - 3.97167i) q^{63} +(-2.64071 - 4.57385i) q^{65} +(-4.91266 - 6.54719i) q^{67} +(2.07475 + 3.59357i) q^{69} +(-6.29684 + 10.9064i) q^{71} +(3.95675 + 6.85329i) q^{73} +1.00000 q^{75} +(-12.9511 - 22.4319i) q^{77} +(-1.36463 + 2.36361i) q^{79} +1.00000 q^{81} +(-5.87767 - 10.1804i) q^{83} +(3.09932 + 5.36818i) q^{85} +(3.10343 - 5.37530i) q^{87} +10.3200 q^{89} -24.2211 q^{91} +(-2.19346 + 3.79918i) q^{93} +(0.0519162 + 0.0899215i) q^{95} +(-1.26265 - 2.18697i) q^{97} +(2.82399 - 4.89129i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	$ 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) $ 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	2.29305	−	3.97167i	0.866690	−	1.50115i	0.00133152	−	0.999999i	$-0.499576\pi$
$7$	2.29305	−	3.97167i	0.866690	−	1.50115i	0.865359	−	0.501153i	$-0.167091\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	2.82399	−	4.89129i	0.851464	−	1.47478i	−0.0284225	−	0.999596i	$-0.509048\pi$
$11$	2.82399	−	4.89129i	0.851464	−	1.47478i	0.879887	−	0.475183i	$-0.157618\pi$
$12$		0			0
$13$	−2.64071	−	4.57385i	−0.732402	−	1.26856i	−0.955854	−	0.293843i	$-0.905066\pi$
$13$	−2.64071	−	4.57385i	−0.732402	−	1.26856i	0.223452	−	0.974715i	$-0.428267\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	3.09932	+	5.36818i	0.751695	+	1.30197i	0.947000	+	0.321232i	$0.104097\pi$
$17$	3.09932	+	5.36818i	0.751695	+	1.30197i	−0.195305	+	0.980743i	$0.562570\pi$
$18$		0			0
$19$	0.0519162	+	0.0899215i	0.0119104	+	0.0206294i	0.871919	−	0.489650i	$-0.162875\pi$
$19$	0.0519162	+	0.0899215i	0.0119104	+	0.0206294i	−0.860009	+	0.510279i	$0.829542\pi$
$20$		0			0
$21$	2.29305	−	3.97167i	0.500384	−	0.866690i
$22$		0			0
$23$	2.07475	+	3.59357i	0.432616	+	0.749312i	0.997098	−	0.0761332i	$-0.0242574\pi$
$23$	2.07475	+	3.59357i	0.432616	+	0.749312i	−0.564482	+	0.825445i	$0.690924\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	3.10343	−	5.37530i	0.576293	−	0.998169i	−0.419607	−	0.907706i	$-0.637832\pi$
$29$	3.10343	−	5.37530i	0.576293	−	0.998169i	0.995900	−	0.0904627i	$-0.0288346\pi$
$30$		0			0
$31$	−2.19346	+	3.79918i	−0.393956	+	0.682352i	−0.992967	−	0.118388i	$-0.962227\pi$
$31$	−2.19346	+	3.79918i	−0.393956	+	0.682352i	0.599011	+	0.800741i	$0.295561\pi$
$32$		0			0
$33$	2.82399	−	4.89129i	0.491593	−	0.851464i
$34$		0			0
$35$	2.29305	−	3.97167i	0.387596	−	0.671335i
$36$		0			0
$37$	−0.218836	−	0.379036i	−0.0359765	−	0.0623131i	0.847477	−	0.530833i	$-0.178121\pi$
$37$	−0.218836	−	0.379036i	−0.0359765	−	0.0623131i	−0.883453	+	0.468520i	$0.844787\pi$
$38$		0			0
$39$	−2.64071	−	4.57385i	−0.422853	−	0.732402i
$40$		0			0
$41$	−1.91389	+	3.31495i	−0.298899	+	0.517708i	−0.975884	−	0.218288i	$-0.929953\pi$
$41$	−1.91389	+	3.31495i	−0.298899	+	0.517708i	0.676985	+	0.735997i	$0.263286\pi$
$42$		0			0
$43$	5.08815			0.775935			0.387968	−	0.921673i	$-0.373177\pi$
$43$	5.08815			0.775935			0.387968	+	0.921673i	$0.373177\pi$
$44$		0			0
$45$	1.00000			0.149071
$46$		0			0
$47$	−3.13045	+	5.42210i	−0.456623	+	0.790895i	−0.998780	−	0.0493828i	$-0.984275\pi$
$47$	−3.13045	+	5.42210i	−0.456623	+	0.790895i	0.542157	+	0.840277i	$0.317608\pi$
$48$		0			0
$49$	−7.01613	−	12.1523i	−1.00230	−	1.73604i
$50$		0			0
$51$	3.09932	+	5.36818i	0.433992	+	0.751695i
$52$		0			0
$53$	6.60315			0.907013			0.453506	−	0.891253i	$-0.350173\pi$
$53$	6.60315			0.907013			0.453506	+	0.891253i	$0.350173\pi$
$54$		0			0
$55$	2.82399	−	4.89129i	0.380786	−	0.659541i
$56$		0			0
$57$	0.0519162	+	0.0899215i	0.00687647	+	0.0119104i
$58$		0			0
$59$	−1.94404			−0.253093			−0.126546	−	0.991961i	$-0.540389\pi$
$59$	−1.94404			−0.253093			−0.126546	+	0.991961i	$0.540389\pi$
$60$		0			0
$61$	−1.08519	−	1.87960i	−0.138944	−	0.240658i	0.788153	−	0.615479i	$-0.211037\pi$
$61$	−1.08519	−	1.87960i	−0.138944	−	0.240658i	−0.927097	+	0.374821i	$0.877704\pi$
$62$		0			0
$63$	2.29305	−	3.97167i	0.288897	−	0.500384i
$64$		0			0
$65$	−2.64071	−	4.57385i	−0.327540	−	0.567316i
$66$		0			0
$67$	−4.91266	−	6.54719i	−0.600177	−	0.799867i
$67$	−4.91266	−	6.54719i	−0.600177	−	0.799867i
$68$		0			0
$69$	2.07475	+	3.59357i	0.249771	+	0.432616i
$70$		0			0
$71$	−6.29684	+	10.9064i	−0.747297	+	1.29436i	0.201817	+	0.979423i	$0.435315\pi$
$71$	−6.29684	+	10.9064i	−0.747297	+	1.29436i	−0.949114	+	0.314933i	$0.898018\pi$
$72$		0			0
$73$	3.95675	+	6.85329i	0.463102	+	0.802117i	0.999114	−	0.0420940i	$-0.0134029\pi$
$73$	3.95675	+	6.85329i	0.463102	+	0.802117i	−0.536011	+	0.844211i	$0.680070\pi$
$74$		0			0
$75$	1.00000			0.115470
$76$		0			0
$77$	−12.9511	−	22.4319i	−1.47591	−	2.55635i
$78$		0			0
$79$	−1.36463	+	2.36361i	−0.153533	+	0.265927i	−0.932524	−	0.361108i	$-0.882399\pi$
$79$	−1.36463	+	2.36361i	−0.153533	+	0.265927i	0.778991	+	0.627035i	$0.215732\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	−5.87767	−	10.1804i	−0.645158	−	1.11745i	−0.984265	−	0.176699i	$-0.943458\pi$
$83$	−5.87767	−	10.1804i	−0.645158	−	1.11745i	0.339107	−	0.940748i	$-0.389875\pi$
$84$		0			0
$85$	3.09932	+	5.36818i	0.336168	+	0.582261i
$86$		0			0
$87$	3.10343	−	5.37530i	0.332723	−	0.576293i
$88$		0			0
$89$	10.3200			1.09392			0.546961	−	0.837158i	$-0.315785\pi$
$89$	10.3200			1.09392			0.546961	+	0.837158i	$0.315785\pi$
$90$		0			0
$91$	−24.2211			−2.53906
$92$		0			0
$93$	−2.19346	+	3.79918i	−0.227451	+	0.393956i
$94$		0			0
$95$	0.0519162	+	0.0899215i	0.00532649	+	0.00922575i
$96$		0			0
$97$	−1.26265	−	2.18697i	−0.128202	−	0.222053i	0.794778	−	0.606901i	$-0.207587\pi$
$97$	−1.26265	−	2.18697i	−0.128202	−	0.222053i	−0.922980	+	0.384847i	$0.874254\pi$
$98$		0			0
$99$	2.82399	−	4.89129i	0.283821	−	0.491593i
$100$		0			0
$101$	2.10598	−	3.64766i	0.209553	−	0.362956i	−0.742021	−	0.670377i	$-0.766133\pi$
$101$	2.10598	−	3.64766i	0.209553	−	0.362956i	0.951574	+	0.307421i	$0.0994659\pi$
$102$		0			0
$103$	−3.70019	+	6.40891i	−0.364590	+	0.631489i	−0.988710	−	0.149840i	$-0.952124\pi$
$103$	−3.70019	+	6.40891i	−0.364590	+	0.631489i	0.624120	+	0.781329i	$0.285458\pi$
$104$		0			0
$105$	2.29305	−	3.97167i	0.223778	−	0.387596i
$106$		0			0
$107$	−12.0227			−1.16228			−0.581138	−	0.813805i	$-0.697392\pi$
$107$	−12.0227			−1.16228			−0.581138	+	0.813805i	$0.697392\pi$
$108$		0			0
$109$	−18.6064			−1.78217			−0.891084	−	0.453839i	$-0.850054\pi$
$109$	−18.6064			−1.78217			−0.891084	+	0.453839i	$0.850054\pi$
$110$		0			0
$111$	−0.218836	−	0.379036i	−0.0207710	−	0.0359765i
$112$		0			0
$113$	8.23549	−	14.2643i	0.774730	−	1.34187i	−0.160216	−	0.987082i	$-0.551219\pi$
$113$	8.23549	−	14.2643i	0.774730	−	1.34187i	0.934946	−	0.354790i	$-0.115448\pi$
$114$		0			0
$115$	2.07475	+	3.59357i	0.193472	+	0.335103i
$116$		0			0
$117$	−2.64071	−	4.57385i	−0.244134	−	0.422853i
$118$		0			0
$119$	28.4275			2.60595
$120$		0			0
$121$	−10.4498	−	18.0996i	−0.949983	−	1.64542i
$122$		0			0
$123$	−1.91389	+	3.31495i	−0.172569	+	0.298899i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−11.1095	+	19.2423i	−0.985812	+	1.70748i	−0.347539	+	0.937665i	$0.612983\pi$
$127$	−11.1095	+	19.2423i	−0.985812	+	1.70748i	−0.638272	+	0.769811i	$0.720351\pi$
$128$		0			0
$129$	5.08815			0.447986
$130$		0			0
$131$	−11.3992			−0.995952			−0.497976	−	0.867191i	$-0.665923\pi$
$131$	−11.3992			−0.995952			−0.497976	+	0.867191i	$0.665923\pi$
$132$		0			0
$133$	0.476185			0.0412905
$134$		0			0
$135$	1.00000			0.0860663
$136$		0			0
$137$	−1.41176			−0.120615			−0.0603073	−	0.998180i	$-0.519208\pi$
$137$	−1.41176			−0.120615			−0.0603073	+	0.998180i	$0.519208\pi$
$138$		0			0
$139$	8.39852			0.712353			0.356177	−	0.934419i	$-0.384080\pi$
$139$	8.39852			0.712353			0.356177	+	0.934419i	$0.384080\pi$
$140$		0			0
$141$	−3.13045	+	5.42210i	−0.263632	+	0.456623i
$142$		0			0
$143$	−29.8294			−2.49446
$144$		0			0
$145$	3.10343	−	5.37530i	0.257726	−	0.446395i
$146$		0			0
$147$	−7.01613	−	12.1523i	−0.578681	−	1.00230i
$148$		0			0
$149$	5.89131			0.482635			0.241317	−	0.970446i	$-0.422420\pi$
$149$	5.89131			0.482635			0.241317	+	0.970446i	$0.422420\pi$
$150$		0			0
$151$	10.2566	+	17.7649i	0.834669	+	1.44569i	0.894300	+	0.447469i	$0.147674\pi$
$151$	10.2566	+	17.7649i	0.834669	+	1.44569i	−0.0596306	+	0.998221i	$0.518992\pi$
$152$		0			0
$153$	3.09932	+	5.36818i	0.250565	+	0.433992i
$154$		0			0
$155$	−2.19346	+	3.79918i	−0.176183	+	0.305157i
$156$		0			0
$157$	5.78246	+	10.0155i	0.461490	+	0.799325i	0.999035	−	0.0439101i	$-0.0139815\pi$
$157$	5.78246	+	10.0155i	0.461490	+	0.799325i	−0.537545	+	0.843235i	$0.680648\pi$
$158$		0			0
$159$	6.60315			0.523664
$160$		0			0
$161$	19.0300			1.49977
$162$		0			0
$163$	9.83178	−	17.0291i	0.770085	−	1.33383i	−0.167431	−	0.985884i	$-0.553547\pi$
$163$	9.83178	−	17.0291i	0.770085	−	1.33383i	0.937516	−	0.347942i	$-0.113119\pi$
$164$		0			0
$165$	2.82399	−	4.89129i	0.219847	−	0.380786i
$166$		0			0
$167$	−2.41393	+	4.18105i	−0.186796	+	0.323540i	−0.944180	−	0.329430i	$-0.893144\pi$
$167$	−2.41393	+	4.18105i	−0.186796	+	0.323540i	0.757384	+	0.652969i	$0.226477\pi$
$168$		0			0
$169$	−7.44673	+	12.8981i	−0.572825	+	0.992163i
$170$		0			0
$171$	0.0519162	+	0.0899215i	0.00397013	+	0.00687647i
$172$		0			0
$173$	−6.55432	−	11.3524i	−0.498316	−	0.863109i	0.501682	−	0.865052i	$-0.332715\pi$
$173$	−6.55432	−	11.3524i	−0.498316	−	0.863109i	−0.999998	+	0.00194338i	$0.999381\pi$
$174$		0			0
$175$	2.29305	−	3.97167i	0.173338	−	0.300230i
$176$		0			0
$177$	−1.94404			−0.146123
$178$		0			0
$179$	17.3353			1.29570			0.647851	−	0.761767i	$-0.275668\pi$
$179$	17.3353			1.29570			0.647851	+	0.761767i	$0.275668\pi$
$180$		0			0
$181$	2.76902	−	4.79608i	0.205819	−	0.356490i	−0.744574	−	0.667540i	$-0.767347\pi$
$181$	2.76902	−	4.79608i	0.205819	−	0.356490i	0.950394	+	0.311050i	$0.100681\pi$
$182$		0			0
$183$	−1.08519	−	1.87960i	−0.0802194	−	0.138944i
$184$		0			0
$185$	−0.218836	−	0.379036i	−0.0160892	−	0.0278673i
$186$		0			0
$187$	35.0098			2.56017
$188$		0			0
$189$	2.29305	−	3.97167i	0.166795	−	0.288897i
$190$		0			0
$191$	8.48169	+	14.6907i	0.613714	+	1.06298i	0.990609	+	0.136727i	$0.0436583\pi$
$191$	8.48169	+	14.6907i	0.613714	+	1.06298i	−0.376895	+	0.926256i	$0.623008\pi$
$192$		0			0
$193$	4.79613			0.345233			0.172616	−	0.984989i	$-0.444778\pi$
$193$	4.79613			0.345233			0.172616	+	0.984989i	$0.444778\pi$
$194$		0			0
$195$	−2.64071	−	4.57385i	−0.189105	−	0.327540i
$196$		0			0
$197$	−9.61418	+	16.6522i	−0.684982	+	1.18642i	0.288460	+	0.957492i	$0.406857\pi$
$197$	−9.61418	+	16.6522i	−0.684982	+	1.18642i	−0.973442	+	0.228932i	$0.926477\pi$
$198$		0			0
$199$	−10.1390	−	17.5613i	−0.718735	−	1.24489i	−0.961501	−	0.274801i	$-0.911388\pi$
$199$	−10.1390	−	17.5613i	−0.718735	−	1.24489i	0.242766	−	0.970085i	$-0.421945\pi$
$200$		0			0
$201$	−4.91266	−	6.54719i	−0.346513	−	0.461803i
$202$		0			0
$203$	−14.2326	−	24.6516i	−0.998935	−	1.73021i
$204$		0			0
$205$	−1.91389	+	3.31495i	−0.133672	+	0.231526i
$206$		0			0
$207$	2.07475	+	3.59357i	0.144205	+	0.249771i
$208$		0			0
$209$	0.586443			0.0405651
$210$		0			0
$211$	9.52081	+	16.4905i	0.655439	+	1.13525i	0.981783	+	0.190003i	$0.0608499\pi$
$211$	9.52081	+	16.4905i	0.655439	+	1.13525i	−0.326344	+	0.945251i	$0.605817\pi$
$212$		0			0
$213$	−6.29684	+	10.9064i	−0.431452	+	0.747297i
$214$		0			0
$215$	5.08815			0.347009
$216$		0			0
$217$	10.0594	+	17.4234i	0.682876	+	1.18278i
$218$		0			0
$219$	3.95675	+	6.85329i	0.267372	+	0.463102i
$220$		0			0
$221$	16.3688	−	28.3516i	1.10109	−	1.90714i
$222$		0			0
$223$	7.95466			0.532683			0.266342	−	0.963879i	$-0.414185\pi$
$223$	7.95466			0.532683			0.266342	+	0.963879i	$0.414185\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	4.54589	−	7.87371i	0.301721	−	0.522597i	−0.674805	−	0.737996i	$-0.735772\pi$
$227$	4.54589	−	7.87371i	0.301721	−	0.522597i	0.976526	+	0.215400i	$0.0691055\pi$
$228$		0			0
$229$	10.5542	+	18.2804i	0.697439	+	1.20800i	0.969352	+	0.245678i	$0.0790105\pi$
$229$	10.5542	+	18.2804i	0.697439	+	1.20800i	−0.271913	+	0.962322i	$0.587656\pi$
$230$		0			0
$231$	−12.9511	−	22.4319i	−0.852118	−	1.47591i
$232$		0			0
$233$	5.33809	−	9.24584i	0.349710	−	0.605715i	−0.636488	−	0.771287i	$-0.719613\pi$
$233$	5.33809	−	9.24584i	0.349710	−	0.605715i	0.986198	+	0.165571i	$0.0529468\pi$
$234$		0			0
$235$	−3.13045	+	5.42210i	−0.204208	+	0.353699i
$236$		0			0
$237$	−1.36463	+	2.36361i	−0.0886424	+	0.153533i
$238$		0			0
$239$	3.06585	−	5.31021i	0.198313	−	0.343489i	−0.749668	−	0.661814i	$-0.769787\pi$
$239$	3.06585	−	5.31021i	0.198313	−	0.343489i	0.947982	+	0.318325i	$0.103120\pi$
$240$		0			0
$241$	11.5321			0.742850			0.371425	−	0.928463i	$-0.378869\pi$
$241$	11.5321			0.742850			0.371425	+	0.928463i	$0.378869\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−7.01613	−	12.1523i	−0.448244	−	0.776382i
$246$		0			0
$247$	0.274192	−	0.474914i	0.0174464	−	0.0302180i
$248$		0			0
$249$	−5.87767	−	10.1804i	−0.372482	−	0.645158i
$250$		0			0
$251$	−12.5236	−	21.6915i	−0.790481	−	1.36915i	−0.925670	−	0.378333i	$-0.876497\pi$
$251$	−12.5236	−	21.6915i	−0.790481	−	1.36915i	0.135189	−	0.990820i	$-0.456836\pi$
$252$		0			0
$253$	23.4363			1.47343
$254$		0			0
$255$	3.09932	+	5.36818i	0.194087	+	0.336168i
$256$		0			0
$257$	1.19085	−	2.06262i	0.0742834	−	0.128663i	−0.826491	−	0.562950i	$-0.809666\pi$
$257$	1.19085	−	2.06262i	0.0742834	−	0.128663i	0.900774	+	0.434287i	$0.143000\pi$
$258$		0			0
$259$	−2.00721			−0.124722
$260$		0			0
$261$	3.10343	−	5.37530i	0.192098	−	0.332723i
$262$		0			0
$263$	−3.79222			−0.233838			−0.116919	−	0.993141i	$-0.537302\pi$
$263$	−3.79222			−0.233838			−0.116919	+	0.993141i	$0.537302\pi$
$264$		0			0
$265$	6.60315			0.405628
$266$		0			0
$267$	10.3200			0.631576
$268$		0			0
$269$	−25.9778			−1.58390			−0.791948	−	0.610588i	$-0.790933\pi$
$269$	−25.9778			−1.58390			−0.791948	+	0.610588i	$0.790933\pi$
$270$		0			0
$271$	−20.3268			−1.23476			−0.617382	−	0.786663i	$-0.711807\pi$
$271$	−20.3268			−1.23476			−0.617382	+	0.786663i	$0.711807\pi$
$272$		0			0
$273$	−24.2211			−1.46593
$274$		0			0
$275$	2.82399	−	4.89129i	0.170293	−	0.294956i
$276$		0			0
$277$	2.09984			0.126167			0.0630835	−	0.998008i	$-0.479907\pi$
$277$	2.09984			0.126167			0.0630835	+	0.998008i	$0.479907\pi$
$278$		0			0
$279$	−2.19346	+	3.79918i	−0.131319	+	0.227451i
$280$		0			0
$281$	15.6035	+	27.0261i	0.930827	+	1.61224i	0.781912	+	0.623389i	$0.214245\pi$
$281$	15.6035	+	27.0261i	0.930827	+	1.61224i	0.148915	+	0.988850i	$0.452422\pi$
$282$		0			0
$283$	−16.5494			−0.983762			−0.491881	−	0.870662i	$-0.663691\pi$
$283$	−16.5494			−0.983762			−0.491881	+	0.870662i	$0.663691\pi$
$284$		0			0
$285$	0.0519162	+	0.0899215i	0.00307525	+	0.00532649i
$286$		0			0
$287$	8.77727	+	15.2027i	0.518106	+	0.897386i
$288$		0			0
$289$	−10.7116	+	18.5530i	−0.630092	+	1.09135i
$290$		0			0
$291$	−1.26265	−	2.18697i	−0.0740177	−	0.128202i
$292$		0			0
$293$	22.0233			1.28662			0.643308	−	0.765607i	$-0.277561\pi$
$293$	22.0233			1.28662			0.643308	+	0.765607i	$0.277561\pi$
$294$		0			0
$295$	−1.94404			−0.113186
$296$		0			0
$297$	2.82399	−	4.89129i	0.163864	−	0.283821i
$298$		0			0
$299$	10.9576	−	18.9792i	0.633697	−	1.09760i
$300$		0			0
$301$	11.6674	−	20.2085i	0.672495	−	1.16480i
$302$		0			0
$303$	2.10598	−	3.64766i	0.120985	−	0.209553i
$304$		0			0
$305$	−1.08519	−	1.87960i	−0.0621377	−	0.107626i
$306$		0			0
$307$	−9.10474	−	15.7699i	−0.519635	−	0.900034i	−0.999740	−	0.0228228i	$-0.992735\pi$
$307$	−9.10474	−	15.7699i	−0.519635	−	0.900034i	0.480105	−	0.877211i	$-0.340599\pi$
$308$		0			0
$309$	−3.70019	+	6.40891i	−0.210496	+	0.364590i
$310$		0			0
$311$	−5.83479			−0.330860			−0.165430	−	0.986221i	$-0.552901\pi$
$311$	−5.83479			−0.330860			−0.165430	+	0.986221i	$0.552901\pi$
$312$		0			0
$313$	−23.0399			−1.30229			−0.651145	−	0.758953i	$-0.725711\pi$
$313$	−23.0399			−1.30229			−0.651145	+	0.758953i	$0.725711\pi$
$314$		0			0
$315$	2.29305	−	3.97167i	0.129199	−	0.223778i
$316$		0			0
$317$	6.08784	+	10.5444i	0.341927	+	0.592235i	0.984791	−	0.173746i	$-0.0555871\pi$
$317$	6.08784	+	10.5444i	0.341927	+	0.592235i	−0.642864	+	0.765981i	$0.722254\pi$
$318$		0			0
$319$	−17.5281	−	30.3596i	−0.981386	−	1.69981i
$320$		0			0
$321$	−12.0227			−0.671040
$322$		0			0
$323$	−0.321810	+	0.557391i	−0.0179060	+	0.0310141i
$324$		0			0
$325$	−2.64071	−	4.57385i	−0.146480	−	0.253712i
$326$		0			0
$327$	−18.6064			−1.02893
$328$		0			0
$329$	14.3565	+	24.8663i	0.791502	+	1.37092i
$330$		0			0
$331$	7.31878	−	12.6765i	0.402276	−	0.696763i	−0.591724	−	0.806141i	$-0.701552\pi$
$331$	7.31878	−	12.6765i	0.402276	−	0.696763i	0.994000	+	0.109378i	$0.0348858\pi$
$332$		0			0
$333$	−0.218836	−	0.379036i	−0.0119922	−	0.0207710i
$334$		0			0
$335$	−4.91266	−	6.54719i	−0.268407	−	0.357711i
$336$		0			0
$337$	13.0809	+	22.6568i	0.712563	+	1.23420i	0.963892	+	0.266293i	$0.0857990\pi$
$337$	13.0809	+	22.6568i	0.712563	+	1.23420i	−0.251329	+	0.967902i	$0.580868\pi$
$338$		0			0
$339$	8.23549	−	14.2643i	0.447291	−	0.774730i
$340$		0			0
$341$	12.3886	+	21.4577i	0.670879	+	1.16200i
$342$		0			0
$343$	−32.2506			−1.74137
$344$		0			0
$345$	2.07475	+	3.59357i	0.111701	+	0.193472i
$346$		0			0
$347$	4.67865	−	8.10366i	0.251163	−	0.435027i	−0.712683	−	0.701486i	$-0.752520\pi$
$347$	4.67865	−	8.10366i	0.251163	−	0.435027i	0.963846	+	0.266459i	$0.0858536\pi$
$348$		0			0
$349$	15.0690			0.806623			0.403312	−	0.915063i	$-0.367859\pi$
$349$	15.0690			0.806623			0.403312	+	0.915063i	$0.367859\pi$
$350$		0			0
$351$	−2.64071	−	4.57385i	−0.140951	−	0.244134i
$352$		0			0
$353$	−11.2072	−	19.4114i	−0.596499	−	1.03317i	−0.993333	−	0.115277i	$-0.963225\pi$
$353$	−11.2072	−	19.4114i	−0.596499	−	1.03317i	0.396834	−	0.917890i	$-0.370109\pi$
$354$		0			0
$355$	−6.29684	+	10.9064i	−0.334201	+	0.578854i
$356$		0			0
$357$	28.4275			1.50455
$358$		0			0
$359$	34.2252			1.80634			0.903169	−	0.429286i	$-0.141235\pi$
$359$	34.2252			1.80634			0.903169	+	0.429286i	$0.141235\pi$
$360$		0			0
$361$	9.49461	−	16.4451i	0.499716	−	0.865534i
$362$		0			0
$363$	−10.4498	−	18.0996i	−0.548473	−	0.949983i
$364$		0			0
$365$	3.95675	+	6.85329i	0.207106	+	0.358718i
$366$		0			0
$367$	3.64037	−	6.30530i	0.190026	−	0.329134i	−0.755233	−	0.655457i	$-0.772476\pi$
$367$	3.64037	−	6.30530i	0.190026	−	0.329134i	0.945258	+	0.326323i	$0.105810\pi$
$368$		0			0
$369$	−1.91389	+	3.31495i	−0.0996330	+	0.172569i
$370$		0			0
$371$	15.1413	−	26.2256i	0.786099	−	1.36156i
$372$		0			0
$373$	1.90581	−	3.30096i	0.0986791	−	0.170917i	−0.812459	−	0.583018i	$-0.801872\pi$
$373$	1.90581	−	3.30096i	0.0986791	−	0.170917i	0.911138	+	0.412101i	$0.135205\pi$
$374$		0			0
$375$	1.00000			0.0516398
$376$		0			0
$377$	−32.7811			−1.68831
$378$		0			0
$379$	14.5335	+	25.1727i	0.746535	+	1.29304i	0.949474	+	0.313845i	$0.101617\pi$
$379$	14.5335	+	25.1727i	0.746535	+	1.29304i	−0.202939	+	0.979191i	$0.565049\pi$
$380$		0			0
$381$	−11.1095	+	19.2423i	−0.569159	+	0.985812i
$382$		0			0
$383$	5.07037	+	8.78214i	0.259084	+	0.448746i	0.965997	−	0.258554i	$-0.0832461\pi$
$383$	5.07037	+	8.78214i	0.259084	+	0.448746i	−0.706913	+	0.707301i	$0.749913\pi$
$384$		0			0
$385$	−12.9511	−	22.4319i	−0.660048	−	1.14324i
$386$		0			0
$387$	5.08815			0.258645
$388$		0			0
$389$	4.68706	+	8.11823i	0.237643	+	0.411611i	0.960038	−	0.279871i	$-0.0902917\pi$
$389$	4.68706	+	8.11823i	0.237643	+	0.411611i	−0.722394	+	0.691481i	$0.756958\pi$
$390$		0			0
$391$	−12.8606	+	22.2753i	−0.650390	+	1.12651i
$392$		0			0
$393$	−11.3992			−0.575013
$394$		0			0
$395$	−1.36463	+	2.36361i	−0.0686621	+	0.118926i
$396$		0			0
$397$	−7.59795			−0.381330			−0.190665	−	0.981655i	$-0.561064\pi$
$397$	−7.59795			−0.381330			−0.190665	+	0.981655i	$0.561064\pi$
$398$		0			0
$399$	0.476185			0.0238391
$400$		0			0
$401$	−26.9737			−1.34700			−0.673500	−	0.739187i	$-0.735210\pi$
$401$	−26.9737			−1.34700			−0.673500	+	0.739187i	$0.735210\pi$
$402$		0			0
$403$	23.1692			1.15414
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−2.47197			−0.122531
$408$		0			0
$409$	−15.1098	+	26.1709i	−0.747131	+	1.29407i	0.202062	+	0.979373i	$0.435236\pi$
$409$	−15.1098	+	26.1709i	−0.747131	+	1.29407i	−0.949193	+	0.314695i	$0.898098\pi$
$410$		0			0
$411$	−1.41176			−0.0696368
$412$		0			0
$413$	−4.45778	+	7.72110i	−0.219353	+	0.379930i
$414$		0			0
$415$	−5.87767	−	10.1804i	−0.288524	−	0.499737i
$416$		0			0
$417$	8.39852			0.411277
$418$		0			0
$419$	−0.478024	−	0.827962i	−0.0233530	−	0.0404486i	0.854113	−	0.520088i	$-0.174101\pi$
$419$	−0.478024	−	0.827962i	−0.0233530	−	0.0404486i	−0.877466	+	0.479639i	$0.840768\pi$
$420$		0			0
$421$	6.12793	+	10.6139i	0.298657	+	0.517289i	0.975829	−	0.218536i	$-0.0701280\pi$
$421$	6.12793	+	10.6139i	0.298657	+	0.517289i	−0.677172	+	0.735825i	$0.736795\pi$
$422$		0			0
$423$	−3.13045	+	5.42210i	−0.152208	+	0.263632i
$424$		0			0
$425$	3.09932	+	5.36818i	0.150339	+	0.260395i
$426$		0			0
$427$	−9.95355			−0.481686
$428$		0			0
$429$	−29.8294			−1.44018
$430$		0			0
$431$	5.76878	−	9.99183i	0.277873	−	0.481289i	−0.692983	−	0.720954i	$-0.743704\pi$
$431$	5.76878	−	9.99183i	0.277873	−	0.481289i	0.970856	+	0.239664i	$0.0770374\pi$
$432$		0			0
$433$	−5.43953	+	9.42154i	−0.261407	+	0.452770i	−0.966616	−	0.256229i	$-0.917520\pi$
$433$	−5.43953	+	9.42154i	−0.261407	+	0.452770i	0.705209	+	0.709000i	$0.250853\pi$
$434$		0			0
$435$	3.10343	−	5.37530i	0.148798	−	0.257726i
$436$		0			0
$437$	−0.215426	+	0.373129i	−0.0103052	+	0.0178492i
$438$		0			0
$439$	12.4867	+	21.6276i	0.595957	+	1.03223i	0.993411	+	0.114605i	$0.0365603\pi$
$439$	12.4867	+	21.6276i	0.595957	+	1.03223i	−0.397455	+	0.917622i	$0.630106\pi$
$440$		0			0
$441$	−7.01613	−	12.1523i	−0.334101	−	0.578681i
$442$		0			0
$443$	12.6218	−	21.8617i	0.599682	−	1.03868i	−0.393186	−	0.919459i	$-0.628627\pi$
$443$	12.6218	−	21.8617i	0.599682	−	1.03868i	0.992868	−	0.119220i	$-0.0380395\pi$
$444$		0			0
$445$	10.3200			0.489216
$446$		0			0
$447$	5.89131			0.278649
$448$		0			0
$449$	0.679946	−	1.17770i	0.0320886	−	0.0555791i	−0.849535	−	0.527532i	$-0.823117\pi$
$449$	0.679946	−	1.17770i	0.0320886	−	0.0555791i	0.881624	+	0.471953i	$0.156451\pi$
$450$		0			0
$451$	10.8096	+	18.7228i	0.509004	+	0.881621i
$452$		0			0
$453$	10.2566	+	17.7649i	0.481896	+	0.834669i
$454$		0			0
$455$	−24.2211			−1.13550
$456$		0			0
$457$	1.92897	−	3.34107i	0.0902332	−	0.156289i	−0.817376	−	0.576105i	$-0.804572\pi$
$457$	1.92897	−	3.34107i	0.0902332	−	0.156289i	0.907609	+	0.419816i	$0.137905\pi$
$458$		0			0
$459$	3.09932	+	5.36818i	0.144664	+	0.250565i
$460$		0			0
$461$	−15.6684			−0.729751			−0.364876	−	0.931056i	$-0.618888\pi$
$461$	−15.6684			−0.729751			−0.364876	+	0.931056i	$0.618888\pi$
$462$		0			0
$463$	−7.05627	−	12.2218i	−0.327932	−	0.567996i	0.654169	−	0.756348i	$-0.273019\pi$
$463$	−7.05627	−	12.2218i	−0.327932	−	0.567996i	−0.982101	+	0.188353i	$0.939685\pi$
$464$		0			0
$465$	−2.19346	+	3.79918i	−0.101719	+	0.176183i
$466$		0			0
$467$	−9.66160	−	16.7344i	−0.447085	−	0.774375i	0.551109	−	0.834433i	$-0.314205\pi$
$467$	−9.66160	−	16.7344i	−0.447085	−	0.774375i	−0.998195	+	0.0600583i	$0.980871\pi$
$468$		0			0
$469$	−37.2683	+	4.49848i	−1.72089	+	0.207720i
$470$		0			0
$471$	5.78246	+	10.0155i	0.266442	+	0.461490i
$472$		0			0
$473$	14.3689	−	24.8876i	0.660681	−	1.14433i
$474$		0			0
$475$	0.0519162	+	0.0899215i	0.00238208	+	0.00412588i
$476$		0			0
$477$	6.60315			0.302338
$478$		0			0
$479$	0.0791092	+	0.137021i	0.00361459	+	0.00626065i	0.867827	−	0.496866i	$-0.165516\pi$
$479$	0.0791092	+	0.137021i	0.00361459	+	0.00626065i	−0.864212	+	0.503127i	$0.832183\pi$
$480$		0			0
$481$	−1.15577	+	2.00185i	−0.0526985	+	0.0912765i
$482$		0			0
$483$	19.0300			0.865895
$484$		0			0
$485$	−1.26265	−	2.18697i	−0.0573339	−	0.0993052i
$486$		0			0
$487$	2.53420	+	4.38936i	0.114835	+	0.198901i	0.917714	−	0.397242i	$-0.130033\pi$
$487$	2.53420	+	4.38936i	0.114835	+	0.198901i	−0.802879	+	0.596143i	$0.796699\pi$
$488$		0			0
$489$	9.83178	−	17.0291i	0.444609	−	0.770085i
$490$		0			0
$491$	−34.4177			−1.55325			−0.776625	−	0.629963i	$-0.783070\pi$
$491$	−34.4177			−1.55325			−0.776625	+	0.629963i	$0.783070\pi$
$492$		0			0
$493$	38.4741			1.73279
$494$		0			0
$495$	2.82399	−	4.89129i	0.126929	−	0.219847i
$496$		0			0
$497$	28.8779	+	50.0180i	1.29535	+	2.24361i
$498$		0			0
$499$	7.71898	+	13.3697i	0.345549	+	0.598509i	0.985453	−	0.169946i	$-0.0543593\pi$
$499$	7.71898	+	13.3697i	0.345549	+	0.598509i	−0.639904	+	0.768455i	$0.721026\pi$
$500$		0			0
$501$	−2.41393	+	4.18105i	−0.107847	+	0.186796i
$502$		0			0
$503$	3.29601	−	5.70885i	0.146962	−	0.254545i	−0.783141	−	0.621844i	$-0.786384\pi$
$503$	3.29601	−	5.70885i	0.146962	−	0.254545i	0.930103	+	0.367299i	$0.119717\pi$
$504$		0			0
$505$	2.10598	−	3.64766i	0.0937148	−	0.162319i
$506$		0			0
$507$	−7.44673	+	12.8981i	−0.330721	+	0.572825i
$508$		0			0
$509$	0.585719			0.0259615			0.0129808	−	0.999916i	$-0.495868\pi$
$509$	0.585719			0.0259615			0.0129808	+	0.999916i	$0.495868\pi$
$510$		0			0
$511$	36.2920			1.60547
$512$		0			0
$513$	0.0519162	+	0.0899215i	0.00229216	+	0.00397013i
$514$		0			0
$515$	−3.70019	+	6.40891i	−0.163050	+	0.282410i
$516$		0			0
$517$	17.6807	+	30.6239i	0.777597	+	1.34684i
$518$		0			0
$519$	−6.55432	−	11.3524i	−0.287703	−	0.498316i
$520$		0			0
$521$	33.7833			1.48007			0.740037	−	0.672567i	$-0.234808\pi$
$521$	33.7833			1.48007			0.740037	+	0.672567i	$0.234808\pi$
$522$		0			0
$523$	2.69188	+	4.66248i	0.117708	+	0.203876i	0.918859	−	0.394586i	$-0.129112\pi$
$523$	2.69188	+	4.66248i	0.117708	+	0.203876i	−0.801151	+	0.598462i	$0.795779\pi$
$524$		0			0
$525$	2.29305	−	3.97167i	0.100077	−	0.173338i
$526$		0			0
$527$	−27.1929			−1.18454
$528$		0			0
$529$	2.89082	−	5.00704i	0.125688	−	0.217697i
$530$		0			0
$531$	−1.94404			−0.0843642
$532$		0			0
$533$	20.2161			0.875657
$534$		0			0
$535$	−12.0227			−0.519786
$536$		0			0
$537$	17.3353			0.748074
$538$		0			0
$539$	−79.2539			−3.41371
$540$		0			0
$541$	−2.99645			−0.128828			−0.0644138	−	0.997923i	$-0.520518\pi$
$541$	−2.99645			−0.128828			−0.0644138	+	0.997923i	$0.520518\pi$
$542$		0			0
$543$	2.76902	−	4.79608i	0.118830	−	0.205819i
$544$		0			0
$545$	−18.6064			−0.797010
$546$		0			0
$547$	−10.4626	+	18.1218i	−0.447351	+	0.774834i	−0.998213	−	0.0597624i	$-0.980966\pi$
$547$	−10.4626	+	18.1218i	−0.447351	+	0.774834i	0.550862	+	0.834596i	$0.314299\pi$
$548$		0			0
$549$	−1.08519	−	1.87960i	−0.0463147	−	0.0802194i
$550$		0			0
$551$	0.644474			0.0274555
$552$		0			0
$553$	6.25833	+	10.8398i	0.266131	+	0.460953i
$554$		0			0
$555$	−0.218836	−	0.379036i	−0.00928909	−	0.0160892i
$556$		0			0
$557$	−15.4472	+	26.7554i	−0.654519	+	1.13366i	0.327495	+	0.944853i	$0.393796\pi$
$557$	−15.4472	+	26.7554i	−0.654519	+	1.13366i	−0.982014	+	0.188808i	$0.939538\pi$
$558$		0			0
$559$	−13.4363	−	23.2724i	−0.568296	−	0.984318i
$560$		0			0
$561$	35.0098			1.47811
$562$		0			0
$563$	39.6777			1.67222			0.836109	−	0.548564i	$-0.184825\pi$
$563$	39.6777			1.67222			0.836109	+	0.548564i	$0.184825\pi$
$564$		0			0
$565$	8.23549	−	14.2643i	0.346470	−	0.600103i
$566$		0			0
$567$	2.29305	−	3.97167i	0.0962989	−	0.166795i
$568$		0			0
$569$	4.09742	−	7.09694i	0.171773	−	0.297519i	−0.767267	−	0.641328i	$-0.778384\pi$
$569$	4.09742	−	7.09694i	0.171773	−	0.297519i	0.939040	+	0.343809i	$0.111717\pi$
$570$		0			0
$571$	−13.0832	+	22.6609i	−0.547517	+	0.948327i	0.450927	+	0.892561i	$0.351094\pi$
$571$	−13.0832	+	22.6609i	−0.547517	+	0.948327i	−0.998444	+	0.0557663i	$0.982240\pi$
$572$		0			0
$573$	8.48169	+	14.6907i	0.354328	+	0.613714i
$574$		0			0
$575$	2.07475	+	3.59357i	0.0865231	+	0.149862i
$576$		0			0
$577$	4.80811	−	8.32788i	0.200164	−	0.346694i	−0.748417	−	0.663228i	$-0.769186\pi$
$577$	4.80811	−	8.32788i	0.200164	−	0.346694i	0.948581	+	0.316534i	$0.102519\pi$
$578$		0			0
$579$	4.79613			0.199320
$580$		0			0
$581$	−53.9111			−2.23661
$582$		0			0
$583$	18.6472	−	32.2979i	0.772289	−	1.33764i
$584$		0			0
$585$	−2.64071	−	4.57385i	−0.109180	−	0.189105i
$586$		0			0
$587$	−1.25990	−	2.18221i	−0.0520016	−	0.0900693i	0.838853	−	0.544358i	$-0.183227\pi$
$587$	−1.25990	−	2.18221i	−0.0520016	−	0.0900693i	−0.890854	+	0.454289i	$0.849893\pi$
$588$		0			0
$589$	−0.455504			−0.0187687
$590$		0			0
$591$	−9.61418	+	16.6522i	−0.395475	+	0.684982i
$592$		0			0
$593$	−21.0258	−	36.4178i	−0.863426	−	1.49550i	−0.868601	−	0.495512i	$-0.834981\pi$
$593$	−21.0258	−	36.4178i	−0.863426	−	1.49550i	0.00517488	−	0.999987i	$-0.498353\pi$
$594$		0			0
$595$	28.4275			1.16542
$596$		0			0
$597$	−10.1390	−	17.5613i	−0.414962	−	0.718735i
$598$		0			0
$599$	−12.0306	+	20.8376i	−0.491557	+	0.851402i	−0.999953	−	0.00972158i	$-0.996905\pi$
$599$	−12.0306	+	20.8376i	−0.491557	+	0.851402i	0.508396	+	0.861124i	$0.330239\pi$
$600$		0			0
$601$	−0.0577179	−	0.0999704i	−0.00235436	−	0.00407788i	0.864846	−	0.502038i	$-0.167416\pi$
$601$	−0.0577179	−	0.0999704i	−0.00235436	−	0.00407788i	−0.867200	+	0.497960i	$0.834083\pi$
$602$		0			0
$603$	−4.91266	−	6.54719i	−0.200059	−	0.266622i
$604$		0			0
$605$	−10.4498	−	18.0996i	−0.424845	−	0.735854i
$606$		0			0
$607$	0.269147	−	0.466177i	0.0109243	−	0.0189215i	−0.860512	−	0.509431i	$-0.829856\pi$
$607$	0.269147	−	0.466177i	0.0109243	−	0.0189215i	0.871436	+	0.490509i	$0.163189\pi$
$608$		0			0
$609$	−14.2326	−	24.6516i	−0.576735	−	0.998935i
$610$		0			0
$611$	33.0665			1.33773
$612$		0			0
$613$	8.94547	+	15.4940i	0.361304	+	0.625797i	0.988176	−	0.153325i	$-0.0489983\pi$
$613$	8.94547	+	15.4940i	0.361304	+	0.625797i	−0.626872	+	0.779123i	$0.715665\pi$
$614$		0			0
$615$	−1.91389	+	3.31495i	−0.0771754	+	0.133672i
$616$		0			0
$617$	−6.68853			−0.269270			−0.134635	−	0.990895i	$-0.542986\pi$
$617$	−6.68853			−0.269270			−0.134635	+	0.990895i	$0.542986\pi$
$618$		0			0
$619$	−16.5105	−	28.5970i	−0.663613	−	1.14941i	−0.979659	−	0.200668i	$-0.935689\pi$
$619$	−16.5105	−	28.5970i	−0.663613	−	1.14941i	0.316046	−	0.948744i	$-0.397644\pi$
$620$		0			0
$621$	2.07475	+	3.59357i	0.0832569	+	0.144205i
$622$		0			0
$623$	23.6643	−	40.9878i	0.948091	−	1.64214i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	0.586443			0.0234203
$628$		0			0
$629$	1.35649	−	2.34951i	0.0540867	−	0.0936810i
$630$		0			0
$631$	18.4417	+	31.9420i	0.734154	+	1.27159i	0.955094	+	0.296304i	$0.0957541\pi$
$631$	18.4417	+	31.9420i	0.734154	+	1.27159i	−0.220940	+	0.975287i	$0.570913\pi$
$632$		0			0
$633$	9.52081	+	16.4905i	0.378418	+	0.655439i
$634$		0			0
$635$	−11.1095	+	19.2423i	−0.440868	+	0.763606i
$636$		0			0
$637$	−37.0552	+	64.1815i	−1.46818	+	2.54296i
$638$		0			0
$639$	−6.29684	+	10.9064i	−0.249099	+	0.431452i
$640$		0			0
$641$	4.59243	−	7.95433i	0.181390	−	0.314177i	−0.760964	−	0.648794i	$-0.775274\pi$
$641$	4.59243	−	7.95433i	0.181390	−	0.314177i	0.942354	+	0.334617i	$0.108607\pi$
$642$		0			0
$643$	−46.5719			−1.83662			−0.918308	−	0.395867i	$-0.870444\pi$
$643$	−46.5719			−1.83662			−0.918308	+	0.395867i	$0.870444\pi$
$644$		0			0
$645$	5.08815			0.200346
$646$		0			0
$647$	1.60229	+	2.77525i	0.0629925	+	0.109106i	0.895802	−	0.444454i	$-0.146602\pi$
$647$	1.60229	+	2.77525i	0.0629925	+	0.109106i	−0.832809	+	0.553560i	$0.813269\pi$
$648$		0			0
$649$	−5.48995	+	9.50887i	−0.215499	+	0.373256i
$650$		0			0
$651$	10.0594	+	17.4234i	0.394259	+	0.682876i
$652$		0			0
$653$	20.1890	+	34.9683i	0.790056	+	1.36842i	0.925932	+	0.377691i	$0.123282\pi$
$653$	20.1890	+	34.9683i	0.790056	+	1.36842i	−0.135876	+	0.990726i	$0.543385\pi$
$654$		0			0
$655$	−11.3992			−0.445403
$656$		0			0
$657$	3.95675	+	6.85329i	0.154367	+	0.267372i
$658$		0			0
$659$	−23.9741	+	41.5243i	−0.933896	+	1.61756i	−0.157306	+	0.987550i	$0.550281\pi$
$659$	−23.9741	+	41.5243i	−0.933896	+	1.61756i	−0.776590	+	0.630006i	$0.783052\pi$
$660$		0			0
$661$	−50.7634			−1.97447			−0.987233	−	0.159282i	$-0.949082\pi$
$661$	−50.7634			−1.97447			−0.987233	+	0.159282i	$0.949082\pi$
$662$		0			0
$663$	16.3688	−	28.3516i	0.635713	−	1.10109i
$664$		0			0
$665$	0.476185			0.0184657
$666$		0			0
$667$	25.7554			0.997253
$668$		0			0
$669$	7.95466			0.307545
$670$		0			0
$671$	−12.2582			−0.473224
$672$		0			0
$673$	35.3405			1.36228			0.681138	−	0.732155i	$-0.261486\pi$
$673$	35.3405			1.36228			0.681138	+	0.732155i	$0.261486\pi$
$674$		0			0
$675$	1.00000			0.0384900
$676$		0			0
$677$	24.1963	−	41.9091i	0.929938	−	1.61070i	0.146516	−	0.989208i	$-0.453194\pi$
$677$	24.1963	−	41.9091i	0.929938	−	1.61070i	0.783421	−	0.621491i	$-0.213473\pi$
$678$		0			0
$679$	−11.5812			−0.444447
$680$		0			0
$681$	4.54589	−	7.87371i	0.174199	−	0.301721i
$682$		0			0
$683$	−8.21194	−	14.2235i	−0.314221	−	0.544247i	0.665051	−	0.746798i	$-0.268410\pi$
$683$	−8.21194	−	14.2235i	−0.314221	−	0.544247i	−0.979272	+	0.202552i	$0.935077\pi$
$684$		0			0
$685$	−1.41176			−0.0539405
$686$		0			0
$687$	10.5542	+	18.2804i	0.402667	+	0.697439i
$688$		0			0
$689$	−17.4370	−	30.2018i	−0.664298	−	1.15060i
$690$		0			0
$691$	−4.17794	+	7.23641i	−0.158936	+	0.275286i	−0.934485	−	0.356001i	$-0.884140\pi$
$691$	−4.17794	+	7.23641i	−0.158936	+	0.275286i	0.775549	+	0.631287i	$0.217473\pi$
$692$		0			0
$693$	−12.9511	−	22.4319i	−0.491971	−	0.852118i
$694$		0			0
$695$	8.39852			0.318574
$696$		0			0
$697$	−23.7270			−0.898724
$698$		0			0
$699$	5.33809	−	9.24584i	0.201905	−	0.349710i
$700$		0			0
$701$	−12.7014	+	21.9995i	−0.479726	+	0.830911i	−0.999730	−	0.0232538i	$-0.992597\pi$
$701$	−12.7014	+	21.9995i	−0.479726	+	0.830911i	0.520003	+	0.854164i	$0.325931\pi$
$702$		0			0
$703$	0.0227223	−	0.0393562i	0.000856988	−	0.00148435i
$704$		0			0
$705$	−3.13045	+	5.42210i	−0.117900	+	0.204208i
$706$		0			0
$707$	−9.65821	−	16.7285i	−0.363234	−	0.629141i
$708$		0			0
$709$	−16.1060	−	27.8965i	−0.604875	−	1.04767i	−0.992071	−	0.125676i	$-0.959890\pi$
$709$	−16.1060	−	27.8965i	−0.604875	−	1.04767i	0.387197	−	0.921997i	$-0.373443\pi$
$710$		0			0
$711$	−1.36463	+	2.36361i	−0.0511777	+	0.0886424i
$712$		0			0
$713$	−18.2035			−0.681726
$714$		0			0
$715$	−29.8294			−1.11555
$716$		0			0
$717$	3.06585	−	5.31021i	0.114496	−	0.198313i
$718$		0			0
$719$	−8.03895	−	13.9239i	−0.299802	−	0.519273i	0.676288	−	0.736637i	$-0.263587\pi$
$719$	−8.03895	−	13.9239i	−0.299802	−	0.519273i	−0.976091	+	0.217364i	$0.930254\pi$
$720$		0			0
$721$	16.9694	+	29.3919i	0.631974	+	1.09461i
$722$		0			0
$723$	11.5321			0.428885
$724$		0			0
$725$	3.10343	−	5.37530i	0.115259	−	0.199634i
$726$		0			0
$727$	−17.9767	−	31.1365i	−0.666718	−	1.15479i	−0.978816	−	0.204740i	$-0.934365\pi$
$727$	−17.9767	−	31.1365i	−0.666718	−	1.15479i	0.312098	−	0.950050i	$-0.398968\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	15.7698	+	27.3141i	0.583267	+	1.01025i
$732$		0			0
$733$	20.0382	−	34.7072i	0.740128	−	1.28194i	−0.212309	−	0.977203i	$-0.568098\pi$
$733$	20.0382	−	34.7072i	0.740128	−	1.28194i	0.952437	−	0.304736i	$-0.0985683\pi$
$734$		0			0
$735$	−7.01613	−	12.1523i	−0.258794	−	0.448244i
$736$		0			0
$737$	−45.8975	+	5.54007i	−1.69066	+	0.204071i
$738$		0			0
$739$	6.38770	+	11.0638i	0.234975	+	0.406989i	0.959266	−	0.282506i	$-0.0911657\pi$
$739$	6.38770	+	11.0638i	0.234975	+	0.406989i	−0.724290	+	0.689495i	$0.757832\pi$
$740$		0			0
$741$	0.274192	−	0.474914i	0.0100727	−	0.0174464i
$742$		0			0
$743$	−12.1109	−	20.9767i	−0.444306	−	0.769560i	0.553698	−	0.832718i	$-0.313216\pi$
$743$	−12.1109	−	20.9767i	−0.444306	−	0.769560i	−0.998004	+	0.0631577i	$0.979883\pi$
$744$		0			0
$745$	5.89131			0.215841
$746$		0			0
$747$	−5.87767	−	10.1804i	−0.215053	−	0.372482i
$748$		0			0
$749$	−27.5686	+	47.7501i	−1.00733	+	1.74475i
$750$		0			0
$751$	11.3415			0.413857			0.206929	−	0.978356i	$-0.433653\pi$
$751$	11.3415			0.413857			0.206929	+	0.978356i	$0.433653\pi$
$752$		0			0
$753$	−12.5236	−	21.6915i	−0.456384	−	0.790481i
$754$		0			0
$755$	10.2566	+	17.7649i	0.373275	+	0.646532i
$756$		0			0
$757$	15.5212	−	26.8835i	0.564128	−	0.977098i	−0.433003	−	0.901393i	$-0.642546\pi$
$757$	15.5212	−	26.8835i	0.564128	−	0.977098i	0.997130	−	0.0757049i	$-0.0241207\pi$
$758$		0			0
$759$	23.4363			0.850683
$760$		0			0
$761$	25.3754			0.919857			0.459929	−	0.887956i	$-0.347875\pi$
$761$	25.3754			0.919857			0.459929	+	0.887956i	$0.347875\pi$
$762$		0			0
$763$	−42.6653	+	73.8985i	−1.54459	+	2.67530i
$764$		0			0
$765$	3.09932	+	5.36818i	0.112056	+	0.194087i
$766$		0			0
$767$	5.13366	+	8.89175i	0.185366	+	0.321063i
$768$		0			0
$769$	−11.3766	+	19.7048i	−0.410250	+	0.710574i	−0.994917	−	0.100699i	$-0.967892\pi$
$769$	−11.3766	+	19.7048i	−0.410250	+	0.710574i	0.584667	+	0.811274i	$0.301225\pi$
$770$		0			0
$771$	1.19085	−	2.06262i	0.0428875	−	0.0742834i
$772$		0			0
$773$	−17.4651	+	30.2504i	−0.628174	+	1.08803i	0.359743	+	0.933051i	$0.382864\pi$
$773$	−17.4651	+	30.2504i	−0.628174	+	1.08803i	−0.987918	+	0.154979i	$0.950469\pi$
$774$		0			0
$775$	−2.19346	+	3.79918i	−0.0787913	+	0.136470i
$776$		0			0
$777$	−2.00721			−0.0720082
$778$		0			0
$779$	−0.397447			−0.0142400
$780$		0			0
$781$	35.5644	+	61.5993i	1.27259	+	2.20420i
$782$		0			0
$783$	3.10343	−	5.37530i	0.110908	−	0.192098i
$784$		0			0
$785$	5.78246	+	10.0155i	0.206385	+	0.357469i
$786$		0			0
$787$	7.75236	+	13.4275i	0.276342	+	0.478638i	0.970473	−	0.241211i	$-0.0775445\pi$
$787$	7.75236	+	13.4275i	0.276342	+	0.478638i	−0.694131	+	0.719849i	$0.744211\pi$
$788$		0			0
$789$	−3.79222			−0.135006
$790$		0			0
$791$	−37.7688	−	65.4174i	−1.34290	−	2.32597i
$792$		0			0
$793$	−5.73134	+	9.92697i	−0.203526	+	0.352517i
$794$		0			0
$795$	6.60315			0.234190
$796$		0			0
$797$	12.4074	−	21.4902i	0.439492	−	0.761223i	−0.558158	−	0.829735i	$-0.688492\pi$
$797$	12.4074	−	21.4902i	0.439492	−	0.761223i	0.997650	+	0.0685115i	$0.0218250\pi$
$798$		0			0
$799$	−38.8091			−1.37297
$800$		0			0
$801$	10.3200			0.364640
$802$		0			0
$803$	44.6952			1.57726
$804$		0			0
$805$	19.0300			0.670720
$806$		0			0
$807$	−25.9778			−0.914463
$808$		0			0
$809$	42.3458			1.48880			0.744400	−	0.667734i	$-0.232736\pi$
$809$	42.3458			1.48880			0.744400	+	0.667734i	$0.232736\pi$
$810$		0			0
$811$	−20.5942	+	35.6702i	−0.723160	+	1.25255i	0.236567	+	0.971615i	$0.423978\pi$
$811$	−20.5942	+	35.6702i	−0.723160	+	1.25255i	−0.959727	+	0.280934i	$0.909356\pi$
$812$		0			0
$813$	−20.3268			−0.712891
$814$		0			0
$815$	9.83178	−	17.0291i	0.344392	−	0.596505i
$816$		0			0
$817$	0.264157	+	0.457534i	0.00924169	+	0.0160071i
$818$		0			0
$819$	−24.2211			−0.846354
$820$		0			0
$821$	5.81351	+	10.0693i	0.202893	+	0.351421i	0.949459	−	0.313890i	$-0.101632\pi$
$821$	5.81351	+	10.0693i	0.202893	+	0.351421i	−0.746566	+	0.665311i	$0.768299\pi$
$822$		0			0
$823$	−23.3905	−	40.5135i	−0.815340	−	1.41221i	−0.909084	−	0.416614i	$-0.863217\pi$
$823$	−23.3905	−	40.5135i	−0.815340	−	1.41221i	0.0937436	−	0.995596i	$-0.470117\pi$
$824$		0			0
$825$	2.82399	−	4.89129i	0.0983186	−	0.170293i
$826$		0			0
$827$	6.44153	+	11.1570i	0.223994	+	0.387969i	0.956017	−	0.293311i	$-0.0947571\pi$
$827$	6.44153	+	11.1570i	0.223994	+	0.387969i	−0.732023	+	0.681280i	$0.761424\pi$
$828$		0			0
$829$	12.3217			0.427950			0.213975	−	0.976839i	$-0.431359\pi$
$829$	12.3217			0.427950			0.213975	+	0.976839i	$0.431359\pi$
$830$		0			0
$831$	2.09984			0.0728426
$832$		0			0
$833$	43.4905	−	75.3277i	1.50686	−	2.60995i
$834$		0			0
$835$	−2.41393	+	4.18105i	−0.0835376	+	0.144691i
$836$		0			0
$837$	−2.19346	+	3.79918i	−0.0758169	+	0.131319i
$838$		0			0
$839$	18.0232	−	31.2171i	0.622229	−	1.07773i	−0.366840	−	0.930284i	$-0.619560\pi$
$839$	18.0232	−	31.2171i	0.622229	−	1.07773i	0.989070	−	0.147449i	$-0.0471062\pi$
$840$		0			0
$841$	−4.76258	−	8.24904i	−0.164227	−	0.284450i
$842$		0			0
$843$	15.6035	+	27.0261i	0.537413	+	0.930827i
$844$		0			0
$845$	−7.44673	+	12.8981i	−0.256175	+	0.443709i
$846$		0			0
$847$	−95.8476			−3.29336
$848$		0			0
$849$	−16.5494			−0.567975
$850$		0			0
$851$	0.908062	−	1.57281i	0.0311280	−	0.0539152i
$852$		0			0
$853$	29.0873	+	50.3807i	0.995930	+	1.72500i	0.576016	+	0.817439i	$0.304607\pi$
$853$	29.0873	+	50.3807i	0.995930	+	1.72500i	0.419915	+	0.907564i	$0.362060\pi$
$854$		0			0
$855$	0.0519162	+	0.0899215i	0.00177550	+	0.00307525i
$856$		0			0
$857$	11.9651			0.408719			0.204359	−	0.978896i	$-0.434489\pi$
$857$	11.9651			0.408719			0.204359	+	0.978896i	$0.434489\pi$
$858$		0			0
$859$	−20.7475	+	35.9358i	−0.707897	+	1.22611i	0.257739	+	0.966215i	$0.417023\pi$
$859$	−20.7475	+	35.9358i	−0.707897	+	1.22611i	−0.965636	+	0.259899i	$0.916311\pi$
$860$		0			0
$861$	8.77727	+	15.2027i	0.299129	+	0.518106i
$862$		0			0
$863$	48.5251			1.65181			0.825907	−	0.563806i	$-0.190664\pi$
$863$	48.5251			1.65181			0.825907	+	0.563806i	$0.190664\pi$
$864$		0			0
$865$	−6.55432	−	11.3524i	−0.222854	−	0.385994i
$866$		0			0
$867$	−10.7116	+	18.5530i	−0.363784	+	0.630092i
$868$		0			0
$869$	7.70741	+	13.3496i	0.261456	+	0.452855i
$870$		0			0
$871$	−16.9729	+	39.7590i	−0.575106	+	1.34718i
$872$		0			0
$873$	−1.26265	−	2.18697i	−0.0427341	−	0.0740177i
$874$		0			0
$875$	2.29305	−	3.97167i	0.0775191	−	0.134267i
$876$		0			0
$877$	20.1266	+	34.8602i	0.679625	+	1.17715i	0.975094	+	0.221793i	$0.0711910\pi$
$877$	20.1266	+	34.8602i	0.679625	+	1.17715i	−0.295468	+	0.955353i	$0.595476\pi$
$878$		0			0
$879$	22.0233			0.742828
$880$		0			0
$881$	−0.763458	−	1.32235i	−0.0257216	−	0.0445510i	0.852878	−	0.522110i	$-0.174855\pi$
$881$	−0.763458	−	1.32235i	−0.0257216	−	0.0445510i	−0.878600	+	0.477559i	$0.841522\pi$
$882$		0			0
$883$	10.6006	−	18.3607i	0.356738	−	0.617888i	−0.630676	−	0.776046i	$-0.717222\pi$
$883$	10.6006	−	18.3607i	0.356738	−	0.617888i	0.987414	+	0.158158i	$0.0505557\pi$
$884$		0			0
$885$	−1.94404			−0.0653482
$886$		0			0
$887$	11.2796	+	19.5369i	0.378732	+	0.655983i	0.990878	−	0.134762i	$-0.0430268\pi$
$887$	11.2796	+	19.5369i	0.378732	+	0.655983i	−0.612146	+	0.790745i	$0.709693\pi$
$888$		0			0
$889$	50.9494	+	88.2469i	1.70879	+	2.95971i
$890$		0			0
$891$	2.82399	−	4.89129i	0.0946071	−	0.163864i
$892$		0			0
$893$	−0.650084			−0.0217542
$894$		0			0
$895$	17.3353			0.579455
$896$		0			0
$897$	10.9576	−	18.9792i	0.365865	−	0.633697i
$898$		0			0
$899$	13.6145	+	23.5810i	0.454068	+	0.786470i
$900$		0			0
$901$	20.4653	+	35.4469i	0.681797	+	1.18091i
$902$		0			0
$903$	11.6674	−	20.2085i	0.388265	−	0.672495i
$904$		0			0
$905$	2.76902	−	4.79608i	0.0920452	−	0.159427i
$906$		0			0
$907$	14.2235	−	24.6357i	0.472282	−	0.818017i	−0.527215	−	0.849732i	$-0.676764\pi$
$907$	14.2235	−	24.6357i	0.472282	−	0.818017i	0.999497	+	0.0317155i	$0.0100970\pi$
$908$		0			0
$909$	2.10598	−	3.64766i	0.0698509	−	0.120985i
$910$		0			0
$911$	52.4573			1.73799			0.868994	−	0.494823i	$-0.164767\pi$
$911$	52.4573			1.73799			0.868994	+	0.494823i	$0.164767\pi$
$912$		0			0
$913$	−66.3939			−2.19732
$914$		0			0
$915$	−1.08519	−	1.87960i	−0.0358752	−	0.0621377i
$916$		0			0
$917$	−26.1389	+	45.2739i	−0.863182	+	1.49508i
$918$		0			0
$919$	22.4345	+	38.8576i	0.740044	+	1.28179i	0.952475	+	0.304618i	$0.0985289\pi$
$919$	22.4345	+	38.8576i	0.740044	+	1.28179i	−0.212430	+	0.977176i	$0.568138\pi$
$920$		0			0
$921$	−9.10474	−	15.7699i	−0.300011	−	0.519635i
$922$		0			0
$923$	66.5125			2.18929
$924$		0			0
$925$	−0.218836	−	0.379036i	−0.00719530	−	0.0124626i
$926$		0			0
$927$	−3.70019	+	6.40891i	−0.121530	+	0.210496i
$928$		0			0
$929$	−22.9127			−0.751742			−0.375871	−	0.926672i	$-0.622656\pi$
$929$	−22.9127			−0.751742			−0.375871	+	0.926672i	$0.622656\pi$
$930$		0			0
$931$	0.728502	−	1.26180i	0.0238757	−	0.0413539i
$932$		0			0
$933$	−5.83479			−0.191022
$934$		0			0
$935$	35.0098			1.14494
$936$		0			0
$937$	12.3658			0.403972			0.201986	−	0.979388i	$-0.435261\pi$
$937$	12.3658			0.403972			0.201986	+	0.979388i	$0.435261\pi$
$938$		0			0
$939$	−23.0399			−0.751878
$940$		0			0
$941$	44.1852			1.44040			0.720198	−	0.693769i	$-0.244051\pi$
$941$	44.1852			1.44040			0.720198	+	0.693769i	$0.244051\pi$
$942$		0			0
$943$	−15.8834			−0.517234
$944$		0			0
$945$	2.29305	−	3.97167i	0.0745928	−	0.129199i
$946$		0			0
$947$	−10.3616			−0.336706			−0.168353	−	0.985727i	$-0.553845\pi$
$947$	−10.3616			−0.336706			−0.168353	+	0.985727i	$0.553845\pi$
$948$		0			0
$949$	20.8973	−	36.1951i	0.678354	−	1.17494i
$950$		0			0
$951$	6.08784	+	10.5444i	0.197412	+	0.341927i
$952$		0			0
$953$	17.0011			0.550721			0.275360	−	0.961341i	$-0.411203\pi$
$953$	17.0011			0.550721			0.275360	+	0.961341i	$0.411203\pi$
$954$		0			0
$955$	8.48169	+	14.6907i	0.274461	+	0.475380i
$956$		0			0
$957$	−17.5281	−	30.3596i	−0.566603	−	0.981386i
$958$		0			0
$959$	−3.23723	+	5.60704i	−0.104535	+	0.181061i
$960$		0			0
$961$	5.87750	+	10.1801i	0.189597	+	0.328391i
$962$		0			0
$963$	−12.0227			−0.387425
$964$		0			0
$965$	4.79613			0.154393
$966$		0			0
$967$	12.0173	−	20.8145i	0.386449	−	0.669349i	−0.605520	−	0.795830i	$-0.707035\pi$
$967$	12.0173	−	20.8145i	0.386449	−	0.669349i	0.991969	+	0.126481i	$0.0403682\pi$
$968$		0			0
$969$	−0.321810	+	0.557391i	−0.0103380	+	0.0179060i
$970$		0			0
$971$	2.51269	−	4.35210i	0.0806360	−	0.139666i	−0.822887	−	0.568205i	$-0.807638\pi$
$971$	2.51269	−	4.35210i	0.0806360	−	0.139666i	0.903523	+	0.428539i	$0.140972\pi$
$972$		0			0
$973$	19.2582	−	33.3562i	0.617390	−	1.06935i
$974$		0			0
$975$	−2.64071	−	4.57385i	−0.0845705	−	0.146480i
$976$		0			0
$977$	12.0451	+	20.8628i	0.385358	+	0.667459i	0.991819	−	0.127654i	$-0.0407448\pi$
$977$	12.0451	+	20.8628i	0.385358	+	0.667459i	−0.606461	+	0.795113i	$0.707411\pi$
$978$		0			0
$979$	29.1436	−	50.4783i	0.931435	−	1.61329i
$980$		0			0
$981$	−18.6064			−0.594056
$982$		0			0
$983$	−28.4239			−0.906581			−0.453291	−	0.891363i	$-0.649750\pi$
$983$	−28.4239			−0.906581			−0.453291	+	0.891363i	$0.649750\pi$
$984$		0			0
$985$	−9.61418	+	16.6522i	−0.306333	+	0.530585i
$986$		0			0
$987$	14.3565	+	24.8663i	0.456974	+	0.791502i
$988$		0			0
$989$	10.5566	+	18.2846i	0.335682	+	0.581417i
$990$		0			0
$991$	−57.3631			−1.82220			−0.911099	−	0.412187i	$-0.864765\pi$
$991$	−57.3631			−1.82220			−0.911099	+	0.412187i	$0.864765\pi$
$992$		0			0
$993$	7.31878	−	12.6765i	0.232254	−	0.402276i
$994$		0			0
$995$	−10.1390	−	17.5613i	−0.321428	−	0.556730i
$996$		0			0
$997$	−58.0624			−1.83885			−0.919427	−	0.393261i	$-0.871347\pi$
$997$	−58.0624			−1.83885			−0.919427	+	0.393261i	$0.871347\pi$
$998$		0			0
$999$	−0.218836	−	0.379036i	−0.00692368	−	0.0119922i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4020.2.q.m.841.12	✓	24
67.29	even	3	inner	4020.2.q.m.3781.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4020.2.q.m.841.12	✓	24	1.1	even	1	trivial
4020.2.q.m.3781.12	yes	24	67.29	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(2.29305 - 3.97167i) q^{7} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{3} +1.00000 q^{5} +(2.29305 - 3.97167i) q^{7} +1.00000 q^{9} +(2.82399 - 4.89129i) q^{11} +(-2.64071 - 4.57385i) q^{13} +1.00000 q^{15} +(3.09932 + 5.36818i) q^{17} +(0.0519162 + 0.0899215i) q^{19} +(2.29305 - 3.97167i) q^{21} +(2.07475 + 3.59357i) q^{23} +1.00000 q^{25} +1.00000 q^{27} +(3.10343 - 5.37530i) q^{29} +(-2.19346 + 3.79918i) q^{31} +(2.82399 - 4.89129i) q^{33} +(2.29305 - 3.97167i) q^{35} +(-0.218836 - 0.379036i) q^{37} +(-2.64071 - 4.57385i) q^{39} +(-1.91389 + 3.31495i) q^{41} +5.08815 q^{43} +1.00000 q^{45} +(-3.13045 + 5.42210i) q^{47} +(-7.01613 - 12.1523i) q^{49} +(3.09932 + 5.36818i) q^{51} +6.60315 q^{53} +(2.82399 - 4.89129i) q^{55} +(0.0519162 + 0.0899215i) q^{57} -1.94404 q^{59} +(-1.08519 - 1.87960i) q^{61} +(2.29305 - 3.97167i) q^{63} +(-2.64071 - 4.57385i) q^{65} +(-4.91266 - 6.54719i) q^{67} +(2.07475 + 3.59357i) q^{69} +(-6.29684 + 10.9064i) q^{71} +(3.95675 + 6.85329i) q^{73} +1.00000 q^{75} +(-12.9511 - 22.4319i) q^{77} +(-1.36463 + 2.36361i) q^{79} +1.00000 q^{81} +(-5.87767 - 10.1804i) q^{83} +(3.09932 + 5.36818i) q^{85} +(3.10343 - 5.37530i) q^{87} +10.3200 q^{89} -24.2211 q^{91} +(-2.19346 + 3.79918i) q^{93} +(0.0519162 + 0.0899215i) q^{95} +(-1.26265 - 2.18697i) q^{97} +(2.82399 - 4.89129i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9}+O(q^{10}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9	\( 24 q + 24 q^{3} + 24 q^{5} - 3 q^{7} + 24 q^{9} - 2 q^{13} + 24 q^{15} - 6 q^{19} - 3 q^{21} + 2 q^{23} + 24 q^{25} + 24 q^{27} + 7 q^{29} - 8 q^{31} - 3 q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 28 q^{43} + 24 q^{45} - 3 q^{47} - 17 q^{49} + 36 q^{53} - 6 q^{57} - 10 q^{59} + 9 q^{61} - 3 q^{63} - 2 q^{65} - 46 q^{67} + 2 q^{69} - 12 q^{71} + 6 q^{73} + 24 q^{75} - 5 q^{77} + 2 q^{79} + 24 q^{81} + 11 q^{83} + 7 q^{87} + 52 q^{89} - 22 q^{91} - 8 q^{93} - 6 q^{95} + 3 q^{97}+O(q^{100}) \) 24 * q + 24 * q^3 + 24 * q^5 - 3 * q^7 + 24 * q^9 - 2 * q^13 + 24 * q^15 - 6 * q^19 - 3 * q^21 + 2 * q^23 + 24 * q^25 + 24 * q^27 + 7 * q^29 - 8 * q^31 - 3 * q^35 - 10 * q^37 - 2 * q^39 + 2 * q^41 + 28 * q^43 + 24 * q^45 - 3 * q^47 - 17 * q^49 + 36 * q^53 - 6 * q^57 - 10 * q^59 + 9 * q^61 - 3 * q^63 - 2 * q^65 - 46 * q^67 + 2 * q^69 - 12 * q^71 + 6 * q^73 + 24 * q^75 - 5 * q^77 + 2 * q^79 + 24 * q^81 + 11 * q^83 + 7 * q^87 + 52 * q^89 - 22 * q^91 - 8 * q^93 - 6 * q^95 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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