LMFDB - Embedded newform 1764.2.l.j.949.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(949,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("1764.949");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.l (of order $3$, degree $2$, not 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:	$14.0856109166$
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			949.12
Character	$\chi$	$=$	1764.949
Dual form			1764.2.l.j.961.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73160 - 0.0393104i) q^{3} -2.38486 q^{5} +(2.99691 - 0.136140i) q^{9} -2.25956 q^{11} +(2.37884 - 4.12027i) q^{13} +(-4.12964 + 0.0937498i) q^{15} +(2.15202 - 3.72740i) q^{17} +(4.29815 + 7.44461i) q^{19} +1.32910 q^{23} +0.687562 q^{25} +(5.18411 - 0.353550i) q^{27} +(-3.87886 - 6.71839i) q^{29} +(-0.405320 - 0.702036i) q^{31} +(-3.91267 + 0.0888242i) q^{33} +(2.31613 + 4.01166i) q^{37} +(3.95723 - 7.22818i) q^{39} +(5.00426 - 8.66764i) q^{41} +(-1.74292 - 3.01883i) q^{43} +(-7.14721 + 0.324675i) q^{45} +(2.18338 - 3.78173i) q^{47} +(3.57992 - 6.53899i) q^{51} +(5.83934 - 10.1140i) q^{53} +5.38874 q^{55} +(7.73534 + 12.7222i) q^{57} +(2.40463 + 4.16495i) q^{59} +(0.575967 - 0.997604i) q^{61} +(-5.67319 + 9.82626i) q^{65} +(2.06381 + 3.57463i) q^{67} +(2.30148 - 0.0522474i) q^{69} -4.41593 q^{71} +(6.05590 - 10.4891i) q^{73} +(1.19059 - 0.0270283i) q^{75} +(4.23312 - 7.33198i) q^{79} +(8.96293 - 0.815999i) q^{81} +(0.817808 + 1.41648i) q^{83} +(-5.13226 + 8.88934i) q^{85} +(-6.98076 - 11.4811i) q^{87} +(3.17155 + 5.49329i) q^{89} +(-0.729452 - 1.19971i) q^{93} +(-10.2505 - 17.7543i) q^{95} +(5.98278 + 10.3625i) q^{97} +(-6.77170 + 0.307617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{9} + 8 q^{11} - 28 q^{15} + 16 q^{23} + 24 q^{25} - 32 q^{29} - 12 q^{37} + 32 q^{51} - 16 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} - 8 q^{81} + 12 q^{85} + 32 q^{95}+ \cdots - 4 q^{99}+O(q^{100}) $ 24 * q - 4 * q^9 + 8 * q^11 - 28 * q^15 + 16 * q^23 + 24 * q^25 - 32 * q^29 - 12 * q^37 + 32 * q^51 - 16 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 - 8 * q^81 + 12 * q^85 + 32 * q^95 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.73160	−	0.0393104i	0.999742	−	0.0226958i
$3$	1.73160	−	0.0393104i	0.999742	−	0.0226958i
$4$		0			0
$5$	−2.38486			−1.06654			−0.533271	−	0.845944i	$-0.679037\pi$
$5$	−2.38486			−1.06654			−0.533271	+	0.845944i	$0.679037\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	2.99691	−	0.136140i	0.998970	−	0.0453800i
$10$		0			0
$11$	−2.25956			−0.681283			−0.340642	−	0.940193i	$-0.610644\pi$
$11$	−2.25956			−0.681283			−0.340642	+	0.940193i	$0.610644\pi$
$12$		0			0
$13$	2.37884	−	4.12027i	0.659770	−	1.14276i	−0.320904	−	0.947112i	$-0.603987\pi$
$13$	2.37884	−	4.12027i	0.659770	−	1.14276i	0.980675	−	0.195644i	$-0.0626798\pi$
$14$		0			0
$15$	−4.12964	+	0.0937498i	−1.06627	+	0.0242061i
$16$		0			0
$17$	2.15202	−	3.72740i	0.521941	−	0.904028i	−0.477733	−	0.878505i	$-0.658541\pi$
$17$	2.15202	−	3.72740i	0.521941	−	0.904028i	0.999674	−	0.0255234i	$-0.00812524\pi$
$18$		0			0
$19$	4.29815	+	7.44461i	0.986062	+	1.70791i	0.637118	+	0.770766i	$0.280126\pi$
$19$	4.29815	+	7.44461i	0.986062	+	1.70791i	0.348944	+	0.937144i	$0.386540\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.32910			0.277137			0.138568	−	0.990353i	$-0.455750\pi$
$23$	1.32910			0.277137			0.138568	+	0.990353i	$0.455750\pi$
$24$		0			0
$25$	0.687562			0.137512
$26$		0			0
$27$	5.18411	−	0.353550i	0.997683	−	0.0680408i
$28$		0			0
$29$	−3.87886	−	6.71839i	−0.720287	−	1.24757i	−0.960885	−	0.276948i	$-0.910677\pi$
$29$	−3.87886	−	6.71839i	−0.720287	−	1.24757i	0.240598	−	0.970625i	$-0.422656\pi$
$30$		0			0
$31$	−0.405320	−	0.702036i	−0.0727977	−	0.126089i	0.827329	−	0.561718i	$-0.189859\pi$
$31$	−0.405320	−	0.702036i	−0.0727977	−	0.126089i	−0.900126	+	0.435629i	$0.856526\pi$
$32$		0			0
$33$	−3.91267	+	0.0888242i	−0.681108	+	0.0154623i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	2.31613	+	4.01166i	0.380770	+	0.659513i	0.991172	−	0.132579i	$-0.0423257\pi$
$37$	2.31613	+	4.01166i	0.380770	+	0.659513i	−0.610403	+	0.792091i	$0.708992\pi$
$38$		0			0
$39$	3.95723	−	7.22818i	0.633665	−	1.15744i
$40$		0			0
$41$	5.00426	−	8.66764i	0.781534	−	1.35366i	−0.149513	−	0.988760i	$-0.547771\pi$
$41$	5.00426	−	8.66764i	0.781534	−	1.35366i	0.931048	−	0.364898i	$-0.118896\pi$
$42$		0			0
$43$	−1.74292	−	3.01883i	−0.265793	−	0.460367i	0.701978	−	0.712199i	$-0.252300\pi$
$43$	−1.74292	−	3.01883i	−0.265793	−	0.460367i	−0.967771	+	0.251831i	$0.918967\pi$
$44$		0			0
$45$	−7.14721	+	0.324675i	−1.06544	+	0.0483997i
$46$		0			0
$47$	2.18338	−	3.78173i	0.318479	−	0.551622i	−0.661692	−	0.749776i	$-0.730161\pi$
$47$	2.18338	−	3.78173i	0.318479	−	0.551622i	0.980171	+	0.198154i	$0.0634946\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	3.57992	−	6.53899i	0.501289	−	0.915641i
$52$		0			0
$53$	5.83934	−	10.1140i	0.802094	−	1.38927i	−0.116141	−	0.993233i	$-0.537052\pi$
$53$	5.83934	−	10.1140i	0.802094	−	1.38927i	0.918235	−	0.396036i	$-0.129614\pi$
$54$		0			0
$55$	5.38874			0.726617
$56$		0			0
$57$	7.73534	+	12.7222i	1.02457	+	1.68509i
$58$		0			0
$59$	2.40463	+	4.16495i	0.313056	+	0.542230i	0.979022	−	0.203752i	$-0.0653137\pi$
$59$	2.40463	+	4.16495i	0.313056	+	0.542230i	−0.665966	+	0.745982i	$0.731980\pi$
$60$		0			0
$61$	0.575967	−	0.997604i	0.0737450	−	0.127730i	−0.826795	−	0.562504i	$-0.809838\pi$
$61$	0.575967	−	0.997604i	0.0737450	−	0.127730i	0.900540	+	0.434774i	$0.143172\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.67319	+	9.82626i	−0.703673	+	1.21880i
$66$		0			0
$67$	2.06381	+	3.57463i	0.252135	+	0.436710i	0.964113	−	0.265491i	$-0.0855341\pi$
$67$	2.06381	+	3.57463i	0.252135	+	0.436710i	−0.711979	+	0.702201i	$0.752201\pi$
$68$		0			0
$69$	2.30148	−	0.0522474i	0.277065	−	0.00628985i
$70$		0			0
$71$	−4.41593			−0.524074			−0.262037	−	0.965058i	$-0.584394\pi$
$71$	−4.41593			−0.524074			−0.262037	+	0.965058i	$0.584394\pi$
$72$		0			0
$73$	6.05590	−	10.4891i	0.708790	−	1.22766i	−0.256517	−	0.966540i	$-0.582575\pi$
$73$	6.05590	−	10.4891i	0.708790	−	1.22766i	0.965306	−	0.261120i	$-0.0840919\pi$
$74$		0			0
$75$	1.19059	−	0.0270283i	0.137477	−	0.00312096i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.23312	−	7.33198i	0.476263	−	0.824913i	−0.523367	−	0.852108i	$-0.675324\pi$
$79$	4.23312	−	7.33198i	0.476263	−	0.824913i	0.999630	+	0.0271950i	$0.00865752\pi$
$80$		0			0
$81$	8.96293	−	0.815999i	0.995881	−	0.0906665i
$82$		0			0
$83$	0.817808	+	1.41648i	0.0897661	+	0.155479i	0.907412	−	0.420242i	$-0.138055\pi$
$83$	0.817808	+	1.41648i	0.0897661	+	0.155479i	−0.817646	+	0.575721i	$0.804721\pi$
$84$		0			0
$85$	−5.13226	+	8.88934i	−0.556672	+	0.964184i
$86$		0			0
$87$	−6.98076	−	11.4811i	−0.748416	−	1.23090i
$88$		0			0
$89$	3.17155	+	5.49329i	0.336184	+	0.582287i	0.983711	−	0.179755i	$-0.0575304\pi$
$89$	3.17155	+	5.49329i	0.336184	+	0.582287i	−0.647528	+	0.762042i	$0.724197\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−0.729452	−	1.19971i	−0.0756407	−	0.124405i
$94$		0			0
$95$	−10.2505	−	17.7543i	−1.05168	−	1.82156i
$96$		0			0
$97$	5.98278	+	10.3625i	0.607459	+	1.05215i	0.991658	+	0.128900i	$0.0411445\pi$
$97$	5.98278	+	10.3625i	0.607459	+	1.05215i	−0.384198	+	0.923251i	$0.625522\pi$
$98$		0			0
$99$	−6.77170	+	0.307617i	−0.680581	+	0.0309166i
$100$		0			0
$101$	10.8470			1.07931			0.539656	−	0.841885i	$-0.318554\pi$
$101$	10.8470			1.07931			0.539656	+	0.841885i	$0.318554\pi$
$102$		0			0
$103$	18.3445			1.80754			0.903769	−	0.428020i	$-0.140789\pi$
$103$	18.3445			1.80754			0.903769	+	0.428020i	$0.140789\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.91706	−	3.32044i	−0.185329	−	0.321000i	0.758358	−	0.651838i	$-0.226002\pi$
$107$	−1.91706	−	3.32044i	−0.185329	−	0.321000i	−0.943687	+	0.330838i	$0.892668\pi$
$108$		0			0
$109$	−1.32248	+	2.29060i	−0.126671	+	0.219400i	−0.922385	−	0.386272i	$-0.873762\pi$
$109$	−1.32248	+	2.29060i	−0.126671	+	0.219400i	0.795714	+	0.605672i	$0.207096\pi$
$110$		0			0
$111$	4.16832	+	6.85556i	0.395640	+	0.650701i
$112$		0			0
$113$	−2.64275	+	4.57738i	−0.248609	+	0.430603i	−0.963140	−	0.269000i	$-0.913307\pi$
$113$	−2.64275	+	4.57738i	−0.248609	+	0.430603i	0.714531	+	0.699604i	$0.246640\pi$
$114$		0			0
$115$	−3.16972			−0.295578
$116$		0			0
$117$	6.56822	−	12.6719i	0.607232	−	1.17152i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.89438			−0.535853
$122$		0			0
$123$	8.32468	−	15.2056i	0.750611	−	1.37105i
$124$		0			0
$125$	10.2846			0.919880
$126$		0			0
$127$	−7.67115			−0.680704			−0.340352	−	0.940298i	$-0.610546\pi$
$127$	−7.67115			−0.680704			−0.340352	+	0.940298i	$0.610546\pi$
$128$		0			0
$129$	−3.13672	−	5.15890i	−0.276173	−	0.454216i
$130$		0			0
$131$	−19.3801			−1.69325			−0.846625	−	0.532189i	$-0.821369\pi$
$131$	−19.3801			−1.69325			−0.846625	+	0.532189i	$0.821369\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−12.3634	+	0.843168i	−1.06407	+	0.0725684i
$136$		0			0
$137$	−9.68997			−0.827870			−0.413935	−	0.910306i	$-0.635846\pi$
$137$	−9.68997			−0.827870			−0.413935	+	0.910306i	$0.635846\pi$
$138$		0			0
$139$	3.81197	−	6.60252i	0.323327	−	0.560018i	−0.657846	−	0.753153i	$-0.728532\pi$
$139$	3.81197	−	6.60252i	0.323327	−	0.560018i	0.981172	+	0.193135i	$0.0618654\pi$
$140$		0			0
$141$	3.63210	−	6.63429i	0.305878	−	0.558708i
$142$		0			0
$143$	−5.37513	+	9.30999i	−0.449491	+	0.778541i
$144$		0			0
$145$	9.25055	+	16.0224i	0.768216	+	1.33059i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.09179			−0.744829			−0.372414	−	0.928067i	$-0.621470\pi$
$149$	−9.09179			−0.744829			−0.372414	+	0.928067i	$0.621470\pi$
$150$		0			0
$151$	−20.2582			−1.64859			−0.824294	−	0.566162i	$-0.808428\pi$
$151$	−20.2582			−1.64859			−0.824294	+	0.566162i	$0.808428\pi$
$152$		0			0
$153$	5.94195	−	11.4637i	0.480379	−	0.926783i
$154$		0			0
$155$	0.966633	+	1.67426i	0.0776418	+	0.134480i
$156$		0			0
$157$	−4.18075	−	7.24127i	−0.333660	−	0.577917i	0.649566	−	0.760305i	$-0.274951\pi$
$157$	−4.18075	−	7.24127i	−0.333660	−	0.577917i	−0.983227	+	0.182388i	$0.941617\pi$
$158$		0			0
$159$	9.71383	−	17.7430i	0.770357	−	1.40711i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	9.69195	+	16.7869i	0.759132	+	1.31486i	0.943294	+	0.331959i	$0.107710\pi$
$163$	9.69195	+	16.7869i	0.759132	+	1.31486i	−0.184162	+	0.982896i	$0.558957\pi$
$164$		0			0
$165$	9.33117	−	0.211833i	0.726430	−	0.0164912i
$166$		0			0
$167$	−8.84158	+	15.3141i	−0.684182	+	1.18504i	0.289511	+	0.957175i	$0.406507\pi$
$167$	−8.84158	+	15.3141i	−0.684182	+	1.18504i	−0.973693	+	0.227864i	$0.926826\pi$
$168$		0			0
$169$	−4.81772	−	8.34454i	−0.370594	−	0.641888i
$170$		0			0
$171$	13.8947	+	21.7257i	1.06255	+	1.66140i
$172$		0			0
$173$	−10.5928	+	18.3473i	−0.805356	+	1.39492i	0.110695	+	0.993854i	$0.464692\pi$
$173$	−10.5928	+	18.3473i	−0.805356	+	1.39492i	−0.916051	+	0.401063i	$0.868641\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.32760	+	7.11751i	0.325282	+	0.534985i
$178$		0			0
$179$	−6.49389	+	11.2478i	−0.485376	+	0.840697i	−0.999859	−	0.0168043i	$-0.994651\pi$
$179$	−6.49389	+	11.2478i	−0.485376	+	0.840697i	0.514482	+	0.857501i	$0.327984\pi$
$180$		0			0
$181$	−16.8238			−1.25050			−0.625251	−	0.780423i	$-0.715004\pi$
$181$	−16.8238			−1.25050			−0.625251	+	0.780423i	$0.715004\pi$
$182$		0			0
$183$	0.958131	−	1.75010i	0.0708271	−	0.129371i
$184$		0			0
$185$	−5.52365	−	9.56725i	−0.406107	−	0.703398i
$186$		0			0
$187$	−4.86262	+	8.42230i	−0.355590	+	0.615899i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.58561	+	7.94251i	−0.331803	+	0.574700i	−0.982865	−	0.184324i	$-0.940990\pi$
$191$	−4.58561	+	7.94251i	−0.331803	+	0.574700i	0.651062	+	0.759024i	$0.274324\pi$
$192$		0			0
$193$	12.8153	+	22.1968i	0.922466	+	1.59776i	0.795586	+	0.605840i	$0.207163\pi$
$193$	12.8153	+	22.1968i	0.922466	+	1.59776i	0.126880	+	0.991918i	$0.459504\pi$
$194$		0			0
$195$	−9.43745	+	17.2382i	−0.675830	+	1.23445i
$196$		0			0
$197$	16.1036			1.14734			0.573668	−	0.819088i	$-0.305520\pi$
$197$	16.1036			1.14734			0.573668	+	0.819088i	$0.305520\pi$
$198$		0			0
$199$	9.61411	−	16.6521i	0.681526	−	1.18044i	−0.292989	−	0.956116i	$-0.594650\pi$
$199$	9.61411	−	16.6521i	0.681526	−	1.18044i	0.974515	−	0.224322i	$-0.0720168\pi$
$200$		0			0
$201$	3.71423	+	6.10871i	0.261981	+	0.430875i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−11.9345	+	20.6711i	−0.833540	+	1.44373i
$206$		0			0
$207$	3.98319	−	0.180944i	0.276851	−	0.0125765i
$208$		0			0
$209$	−9.71192	−	16.8215i	−0.671788	−	1.16357i
$210$		0			0
$211$	−12.3251	+	21.3477i	−0.848496	+	1.46964i	0.0340549	+	0.999420i	$0.489158\pi$
$211$	−12.3251	+	21.3477i	−0.848496	+	1.46964i	−0.882551	+	0.470218i	$0.844175\pi$
$212$		0			0
$213$	−7.64664	+	0.173592i	−0.523939	+	0.0118943i
$214$		0			0
$215$	4.15663	+	7.19949i	0.283480	+	0.491001i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	10.0741	−	18.4011i	0.680744	−	1.24343i
$220$		0			0
$221$	−10.2386	−	17.7338i	−0.688723	−	1.19290i
$222$		0			0
$223$	−7.41074	−	12.8358i	−0.496260	−	0.859547i	0.503731	−	0.863861i	$-0.331960\pi$
$223$	−7.41074	−	12.8358i	−0.496260	−	0.859547i	−0.999991	+	0.00431335i	$0.998627\pi$
$224$		0			0
$225$	2.06056	−	0.0936047i	0.137371	−	0.00624031i
$226$		0			0
$227$	18.1550			1.20499			0.602496	−	0.798122i	$-0.294173\pi$
$227$	18.1550			1.20499			0.602496	+	0.798122i	$0.294173\pi$
$228$		0			0
$229$	−9.50691			−0.628235			−0.314117	−	0.949384i	$-0.601709\pi$
$229$	−9.50691			−0.628235			−0.314117	+	0.949384i	$0.601709\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−10.1715	−	17.6176i	−0.666360	−	1.15417i	−0.978915	−	0.204270i	$-0.934518\pi$
$233$	−10.1715	−	17.6176i	−0.666360	−	1.15417i	0.312554	−	0.949900i	$-0.398815\pi$
$234$		0			0
$235$	−5.20707	+	9.01890i	−0.339671	+	0.588328i
$236$		0			0
$237$	7.04187	−	12.8625i	0.457419	−	0.835509i
$238$		0			0
$239$	8.90544	−	15.4247i	0.576045	−	0.997739i	−0.419882	−	0.907579i	$-0.637929\pi$
$239$	8.90544	−	15.4247i	0.576045	−	0.997739i	0.995927	−	0.0901607i	$-0.0287381\pi$
$240$		0			0
$241$	−6.28873			−0.405093			−0.202546	−	0.979273i	$-0.564922\pi$
$241$	−6.28873			−0.405093			−0.202546	+	0.979273i	$0.564922\pi$
$242$		0			0
$243$	15.4882	−	1.76532i	0.993567	−	0.113246i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	40.8983			2.60230
$248$		0			0
$249$	1.47180	+	2.42064i	0.0932717	+	0.153402i
$250$		0			0
$251$	25.1868			1.58978			0.794889	−	0.606755i	$-0.207529\pi$
$251$	25.1868			1.58978			0.794889	+	0.606755i	$0.207529\pi$
$252$		0			0
$253$	−3.00318			−0.188809
$254$		0			0
$255$	−8.53761	+	15.5946i	−0.534646	+	0.976570i
$256$		0			0
$257$	−28.6803			−1.78903			−0.894514	−	0.447040i	$-0.852478\pi$
$257$	−28.6803			−1.78903			−0.894514	+	0.447040i	$0.852478\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−12.5392	−	19.6063i	−0.776160	−	1.21360i
$262$		0			0
$263$	−14.4168			−0.888977			−0.444489	−	0.895784i	$-0.646615\pi$
$263$	−14.4168			−0.888977			−0.444489	+	0.895784i	$0.646615\pi$
$264$		0			0
$265$	−13.9260	+	24.1205i	−0.855468	+	1.48171i
$266$		0			0
$267$	5.70782	+	9.38753i	0.349313	+	0.574507i
$268$		0			0
$269$	−6.44997	+	11.1717i	−0.393262	+	0.681150i	−0.992878	−	0.119138i	$-0.961987\pi$
$269$	−6.44997	+	11.1717i	−0.393262	+	0.681150i	0.599616	+	0.800288i	$0.295320\pi$
$270$		0			0
$271$	−9.73110	−	16.8548i	−0.591122	−	1.02385i	−0.994082	−	0.108636i	$-0.965352\pi$
$271$	−9.73110	−	16.8548i	−0.591122	−	1.02385i	0.402959	−	0.915218i	$-0.367982\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.55359			−0.0936849
$276$		0			0
$277$	15.9124			0.956084			0.478042	−	0.878337i	$-0.341347\pi$
$277$	15.9124			0.956084			0.478042	+	0.878337i	$0.341347\pi$
$278$		0			0
$279$	−1.31028	−	2.04876i	−0.0784446	−	0.122656i
$280$		0			0
$281$	−13.9998	−	24.2484i	−0.835158	−	1.44654i	−0.893901	−	0.448263i	$-0.852043\pi$
$281$	−13.9998	−	24.2484i	−0.835158	−	1.44654i	0.0587432	−	0.998273i	$-0.481291\pi$
$282$		0			0
$283$	2.62345	+	4.54394i	0.155948	+	0.270109i	0.933404	−	0.358828i	$-0.116824\pi$
$283$	2.62345	+	4.54394i	0.155948	+	0.270109i	−0.777456	+	0.628937i	$0.783490\pi$
$284$		0			0
$285$	−18.4477	−	30.3406i	−1.09275	−	1.79722i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	−0.762363	−	1.32045i	−0.0448449	−	0.0776736i
$290$		0			0
$291$	10.7672	+	17.7085i	0.631182	+	1.03809i
$292$		0			0
$293$	−1.65939	+	2.87415i	−0.0969428	+	0.167910i	−0.910418	−	0.413690i	$-0.864240\pi$
$293$	−1.65939	+	2.87415i	−0.0969428	+	0.167910i	0.813475	+	0.581600i	$0.197573\pi$
$294$		0			0
$295$	−5.73471	−	9.93282i	−0.333888	−	0.578311i
$296$		0			0
$297$	−11.7138	+	0.798868i	−0.679704	+	0.0463551i
$298$		0			0
$299$	3.16171	−	5.47625i	0.182847	−	0.316700i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	18.7826	−	0.426398i	1.07903	−	0.0244959i
$304$		0			0
$305$	−1.37360	+	2.37915i	−0.0786521	+	0.136230i
$306$		0			0
$307$	−12.4703			−0.711715			−0.355857	−	0.934540i	$-0.615811\pi$
$307$	−12.4703			−0.711715			−0.355857	+	0.934540i	$0.615811\pi$
$308$		0			0
$309$	31.7654	−	0.721130i	1.80707	−	0.0410236i
$310$		0			0
$311$	11.3383	+	19.6385i	0.642936	+	1.11360i	0.984774	+	0.173840i	$0.0556174\pi$
$311$	11.3383	+	19.6385i	0.642936	+	1.11360i	−0.341838	+	0.939759i	$0.611049\pi$
$312$		0			0
$313$	3.16108	−	5.47515i	0.178675	−	0.309474i	−0.762752	−	0.646691i	$-0.776152\pi$
$313$	3.16108	−	5.47515i	0.178675	−	0.309474i	0.941427	+	0.337217i	$0.109486\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.79041	−	13.4934i	0.437553	−	0.757864i	−0.559947	−	0.828528i	$-0.689179\pi$
$317$	7.79041	−	13.4934i	0.437553	−	0.757864i	0.997500	+	0.0706643i	$0.0225119\pi$
$318$		0			0
$319$	8.76453	+	15.1806i	0.490719	+	0.849951i
$320$		0			0
$321$	−3.45012	−	5.67434i	−0.192567	−	0.316711i
$322$		0			0
$323$	36.9987			2.05867
$324$		0			0
$325$	1.63560	−	2.83294i	0.0907266	−	0.157143i
$326$		0			0
$327$	−2.19997	+	4.01841i	−0.121659	+	0.222219i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	10.8634	−	18.8159i	0.597104	−	1.03422i	−0.396142	−	0.918189i	$-0.629651\pi$
$331$	10.8634	−	18.8159i	0.597104	−	1.03422i	0.993246	−	0.116026i	$-0.0370155\pi$
$332$		0			0
$333$	7.48738	+	11.7073i	0.410306	+	0.641554i
$334$		0			0
$335$	−4.92190	−	8.52499i	−0.268912	−	0.465770i
$336$		0			0
$337$	4.04329	−	7.00319i	0.220252	−	0.381488i	−0.734632	−	0.678465i	$-0.762645\pi$
$337$	4.04329	−	7.00319i	0.220252	−	0.381488i	0.954884	+	0.296977i	$0.0959786\pi$
$338$		0			0
$339$	−4.39626	+	8.03009i	−0.238772	+	0.436135i
$340$		0			0
$341$	0.915846	+	1.58629i	0.0495959	+	0.0859026i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−5.48870	+	0.124603i	−0.295502	+	0.00670839i
$346$		0			0
$347$	0.466877	+	0.808654i	0.0250632	+	0.0434108i	0.878285	−	0.478138i	$-0.158688\pi$
$347$	0.466877	+	0.808654i	0.0250632	+	0.0434108i	−0.853222	+	0.521548i	$0.825355\pi$
$348$		0			0
$349$	−1.90264	−	3.29548i	−0.101846	−	0.176403i	0.810599	−	0.585601i	$-0.199142\pi$
$349$	−1.90264	−	3.29548i	−0.101846	−	0.176403i	−0.912445	+	0.409199i	$0.865808\pi$
$350$		0			0
$351$	10.8754	−	22.2009i	0.580487	−	1.18500i
$352$		0			0
$353$	−13.1195			−0.698280			−0.349140	−	0.937071i	$-0.613526\pi$
$353$	−13.1195			−0.698280			−0.349140	+	0.937071i	$0.613526\pi$
$354$		0			0
$355$	10.5314			0.558947
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.7829	+	18.6765i	0.569100	+	0.985710i	0.996655	+	0.0817206i	$0.0260415\pi$
$359$	10.7829	+	18.6765i	0.569100	+	0.985710i	−0.427556	+	0.903989i	$0.640625\pi$
$360$		0			0
$361$	−27.4481	+	47.5415i	−1.44464	+	2.50218i
$362$		0			0
$363$	−10.2067	+	0.231710i	−0.535715	+	0.0121616i
$364$		0			0
$365$	−14.4425	+	25.0151i	−0.755954	+	1.30935i
$366$		0			0
$367$	18.6619			0.974143			0.487072	−	0.873362i	$-0.338065\pi$
$367$	18.6619			0.974143			0.487072	+	0.873362i	$0.338065\pi$
$368$		0			0
$369$	13.8173	−	26.6574i	0.719300	−	1.38773i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−20.1707			−1.04440			−0.522201	−	0.852823i	$-0.674889\pi$
$373$	−20.1707			−1.04440			−0.522201	+	0.852823i	$0.674889\pi$
$374$		0			0
$375$	17.8088	−	0.404290i	0.919643	−	0.0208774i
$376$		0			0
$377$	−36.9087			−1.90090
$378$		0			0
$379$	18.2436			0.937110			0.468555	−	0.883434i	$-0.344775\pi$
$379$	18.2436			0.937110			0.468555	+	0.883434i	$0.344775\pi$
$380$		0			0
$381$	−13.2834	+	0.301556i	−0.680529	+	0.0154492i
$382$		0			0
$383$	−22.8563			−1.16790			−0.583952	−	0.811788i	$-0.698494\pi$
$383$	−22.8563			−1.16790			−0.583952	+	0.811788i	$0.698494\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−5.63436	−	8.80988i	−0.286411	−	0.447831i
$388$		0			0
$389$	12.3429			0.625811			0.312905	−	0.949784i	$-0.398698\pi$
$389$	12.3429			0.625811			0.312905	+	0.949784i	$0.398698\pi$
$390$		0			0
$391$	2.86025	−	4.95410i	0.144649	−	0.250539i
$392$		0			0
$393$	−33.5587	+	0.761840i	−1.69281	+	0.0384298i
$394$		0			0
$395$	−10.0954	+	17.4858i	−0.507955	+	0.879804i
$396$		0			0
$397$	13.1016	+	22.6927i	0.657551	+	1.13891i	0.981248	+	0.192751i	$0.0617410\pi$
$397$	13.1016	+	22.6927i	0.657551	+	1.13891i	−0.323696	+	0.946161i	$0.604926\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.91118			0.195315			0.0976575	−	0.995220i	$-0.468865\pi$
$401$	3.91118			0.195315			0.0976575	+	0.995220i	$0.468865\pi$
$402$		0			0
$403$	−3.85676			−0.192119
$404$		0			0
$405$	−21.3753	+	1.94604i	−1.06215	+	0.0966997i
$406$		0			0
$407$	−5.23344	−	9.06459i	−0.259412	−	0.449315i
$408$		0			0
$409$	−1.05065	−	1.81978i	−0.0519513	−	0.0899823i	0.838880	−	0.544316i	$-0.183211\pi$
$409$	−1.05065	−	1.81978i	−0.0519513	−	0.0899823i	−0.890832	+	0.454334i	$0.849877\pi$
$410$		0			0
$411$	−16.7792	+	0.380916i	−0.827657	+	0.0187892i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−1.95036	−	3.37812i	−0.0957393	−	0.165825i
$416$		0			0
$417$	6.34127	−	11.5828i	0.310533	−	0.567212i
$418$		0			0
$419$	−11.7017	+	20.2679i	−0.571664	+	0.990150i	0.424732	+	0.905319i	$0.360368\pi$
$419$	−11.7017	+	20.2679i	−0.571664	+	0.990150i	−0.996395	+	0.0848311i	$0.972965\pi$
$420$		0			0
$421$	9.78341	+	16.9454i	0.476814	+	0.825866i	0.999647	−	0.0265688i	$-0.00845812\pi$
$421$	9.78341	+	16.9454i	0.476814	+	0.825866i	−0.522833	+	0.852435i	$0.675125\pi$
$422$		0			0
$423$	6.02856	−	11.6307i	0.293118	−	0.565506i
$424$		0			0
$425$	1.47965	−	2.56282i	0.0717733	−	0.124315i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−8.94161	+	16.3325i	−0.431705	+	0.788542i
$430$		0			0
$431$	−3.35438	+	5.80996i	−0.161575	+	0.279856i	−0.935434	−	0.353502i	$-0.884991\pi$
$431$	−3.35438	+	5.80996i	−0.161575	+	0.279856i	0.773859	+	0.633358i	$0.218324\pi$
$432$		0			0
$433$	9.46607			0.454910			0.227455	−	0.973789i	$-0.426959\pi$
$433$	9.46607			0.454910			0.227455	+	0.973789i	$0.426959\pi$
$434$		0			0
$435$	16.6481	+	27.3809i	0.798217	+	1.31281i
$436$		0			0
$437$	5.71267	+	9.89463i	0.273274	+	0.473324i
$438$		0			0
$439$	−3.82386	+	6.62312i	−0.182503	+	0.316104i	−0.942732	−	0.333550i	$-0.891753\pi$
$439$	−3.82386	+	6.62312i	−0.182503	+	0.316104i	0.760229	+	0.649655i	$0.225087\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−18.0763	+	31.3091i	−0.858833	+	1.48754i	0.0142102	+	0.999899i	$0.495477\pi$
$443$	−18.0763	+	31.3091i	−0.858833	+	1.48754i	−0.873043	+	0.487643i	$0.837857\pi$
$444$		0			0
$445$	−7.56371	−	13.1007i	−0.358554	−	0.621034i
$446$		0			0
$447$	−15.7434	+	0.357402i	−0.744637	+	0.0169045i
$448$		0			0
$449$	13.7337			0.648132			0.324066	−	0.946034i	$-0.394950\pi$
$449$	13.7337			0.648132			0.324066	+	0.946034i	$0.394950\pi$
$450$		0			0
$451$	−11.3074	+	19.5851i	−0.532446	+	0.922224i
$452$		0			0
$453$	−35.0792	+	0.796357i	−1.64816	+	0.0374161i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.213109	−	0.369115i	0.00996881	−	0.0172665i	−0.860998	−	0.508608i	$-0.830160\pi$
$457$	0.213109	−	0.369115i	0.00996881	−	0.0172665i	0.870967	+	0.491342i	$0.163493\pi$
$458$		0			0
$459$	9.83847	−	20.0841i	0.459221	−	0.937447i
$460$		0			0
$461$	−2.26453	−	3.92228i	−0.105470	−	0.182679i	0.808460	−	0.588551i	$-0.200301\pi$
$461$	−2.26453	−	3.92228i	−0.105470	−	0.182679i	−0.913930	+	0.405872i	$0.866968\pi$
$462$		0			0
$463$	16.5598	−	28.6825i	0.769600	−	1.33299i	−0.168179	−	0.985756i	$-0.553789\pi$
$463$	16.5598	−	28.6825i	0.769600	−	1.33299i	0.937780	−	0.347230i	$-0.112878\pi$
$464$		0			0
$465$	1.73964	+	2.86115i	0.0806740	+	0.132683i
$466$		0			0
$467$	0.756660	+	1.31057i	0.0350140	+	0.0606461i	0.883001	−	0.469370i	$-0.155519\pi$
$467$	0.756660	+	1.31057i	0.0350140	+	0.0606461i	−0.847987	+	0.530016i	$0.822186\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−7.52407	−	12.3747i	−0.346691	−	0.570195i
$472$		0			0
$473$	3.93824	+	6.82123i	0.181080	+	0.313640i
$474$		0			0
$475$	2.95524	+	5.11863i	0.135596	+	0.234859i
$476$		0			0
$477$	16.1230	−	31.1058i	0.738223	−	1.42424i
$478$		0			0
$479$	22.2926			1.01858			0.509288	−	0.860596i	$-0.329909\pi$
$479$	22.2926			1.01858			0.509288	+	0.860596i	$0.329909\pi$
$480$		0			0
$481$	22.0388			1.00488
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−14.2681	−	24.7131i	−0.647881	−	1.12216i
$486$		0			0
$487$	−2.31676	+	4.01275i	−0.104983	+	0.181835i	−0.913731	−	0.406319i	$-0.866812\pi$
$487$	−2.31676	+	4.01275i	−0.104983	+	0.181835i	0.808749	+	0.588155i	$0.200145\pi$
$488$		0			0
$489$	17.4425	+	28.6874i	0.788778	+	1.29729i
$490$		0			0
$491$	−12.5858	+	21.7993i	−0.567990	+	0.983788i	0.428774	+	0.903412i	$0.358946\pi$
$491$	−12.5858	+	21.7993i	−0.567990	+	0.983788i	−0.996765	+	0.0803766i	$0.974388\pi$
$492$		0			0
$493$	−33.3895			−1.50379
$494$		0			0
$495$	16.1496	−	0.733623i	0.725869	−	0.0329739i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−2.27455			−0.101823			−0.0509114	−	0.998703i	$-0.516213\pi$
$499$	−2.27455			−0.101823			−0.0509114	+	0.998703i	$0.516213\pi$
$500$		0			0
$501$	−14.7081	+	26.8655i	−0.657111	+	1.20026i
$502$		0			0
$503$	−8.94793			−0.398968			−0.199484	−	0.979901i	$-0.563927\pi$
$503$	−8.94793			−0.398968			−0.199484	+	0.979901i	$0.563927\pi$
$504$		0			0
$505$	−25.8685			−1.15113
$506$		0			0
$507$	−8.67042	−	14.2601i	−0.385067	−	0.633312i
$508$		0			0
$509$	−33.2687			−1.47461			−0.737304	−	0.675561i	$-0.763901\pi$
$509$	−33.2687			−1.47461			−0.737304	+	0.675561i	$0.763901\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	24.9141	+	37.0740i	1.09998	+	1.63686i
$514$		0			0
$515$	−43.7491			−1.92782
$516$		0			0
$517$	−4.93349	+	8.54505i	−0.216975	+	0.375811i
$518$		0			0
$519$	−17.6213	+	32.1866i	−0.773490	+	1.41284i
$520$		0			0
$521$	7.57396	−	13.1185i	0.331821	−	0.574731i	−0.651048	−	0.759037i	$-0.725670\pi$
$521$	7.57396	−	13.1185i	0.331821	−	0.574731i	0.982869	+	0.184306i	$0.0590036\pi$
$522$		0			0
$523$	5.23952	+	9.07512i	0.229108	+	0.396827i	0.957544	−	0.288287i	$-0.0930856\pi$
$523$	5.23952	+	9.07512i	0.229108	+	0.396827i	−0.728436	+	0.685114i	$0.759752\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−3.48903			−0.151984
$528$		0			0
$529$	−21.2335			−0.923195
$530$		0			0
$531$	7.77348	+	12.1546i	0.337340	+	0.527465i
$532$		0			0
$533$	−23.8086	−	41.2378i	−1.03127	−	1.78621i
$534$		0			0
$535$	4.57192	+	7.91880i	0.197661	+	0.342360i
$536$		0			0
$537$	−10.8027	+	19.7319i	−0.466171	+	0.851496i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−2.43874	−	4.22402i	−0.104850	−	0.181605i	0.808827	−	0.588047i	$-0.200103\pi$
$541$	−2.43874	−	4.22402i	−0.104850	−	0.181605i	−0.913677	+	0.406442i	$0.866769\pi$
$542$		0			0
$543$	−29.1322	+	0.661349i	−1.25018	+	0.0283812i
$544$		0			0
$545$	3.15393	−	5.46277i	0.135100	−	0.234000i
$546$		0			0
$547$	9.62179	+	16.6654i	0.411398	+	0.712562i	0.995043	−	0.0994468i	$-0.0317073\pi$
$547$	9.62179	+	16.6654i	0.411398	+	0.712562i	−0.583645	+	0.812009i	$0.698374\pi$
$548$		0			0
$549$	1.59031	−	3.06814i	0.0678726	−	0.130945i
$550$		0			0
$551$	33.3438	−	57.7532i	1.42049	−	2.46037i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−9.94087	−	16.3496i	−0.421967	−	0.694000i
$556$		0			0
$557$	−7.32388	+	12.6853i	−0.310323	+	0.537495i	−0.978432	−	0.206568i	$-0.933771\pi$
$557$	−7.32388	+	12.6853i	−0.310323	+	0.537495i	0.668109	+	0.744063i	$0.267104\pi$
$558$		0			0
$559$	−16.5845			−0.701450
$560$		0			0
$561$	−8.08905	+	14.7752i	−0.341520	+	0.623811i
$562$		0			0
$563$	−1.85335	−	3.21010i	−0.0781095	−	0.135290i	0.824325	−	0.566117i	$-0.191555\pi$
$563$	−1.85335	−	3.21010i	−0.0781095	−	0.135290i	−0.902434	+	0.430828i	$0.858222\pi$
$564$		0			0
$565$	6.30259	−	10.9164i	0.265152	−	0.459257i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−15.1768	+	26.2871i	−0.636246	+	1.10201i	0.350004	+	0.936748i	$0.386180\pi$
$569$	−15.1768	+	26.2871i	−0.636246	+	1.10201i	−0.986250	+	0.165262i	$0.947153\pi$
$570$		0			0
$571$	5.88458	+	10.1924i	0.246262	+	0.426539i	0.962486	−	0.271332i	$-0.0874642\pi$
$571$	5.88458	+	10.1924i	0.246262	+	0.426539i	−0.716224	+	0.697871i	$0.754131\pi$
$572$		0			0
$573$	−7.62825	+	13.9336i	−0.318675	+	0.582083i
$574$		0			0
$575$	0.913839			0.0381097
$576$		0			0
$577$	1.79640	−	3.11146i	0.0747852	−	0.129532i	−0.826208	−	0.563366i	$-0.809506\pi$
$577$	1.79640	−	3.11146i	0.0747852	−	0.129532i	0.900993	+	0.433834i	$0.142840\pi$
$578$		0			0
$579$	23.0636	+	37.9323i	0.958491	+	1.57641i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−13.1943	+	22.8533i	−0.546454	+	0.946485i
$584$		0			0
$585$	−15.6643	+	30.2208i	−0.647639	+	1.24947i
$586$		0			0
$587$	−4.62298	−	8.00724i	−0.190811	−	0.330494i	0.754708	−	0.656060i	$-0.227778\pi$
$587$	−4.62298	−	8.00724i	−0.190811	−	0.330494i	−0.945519	+	0.325566i	$0.894445\pi$
$588$		0			0
$589$	3.48425	−	6.03490i	0.143566	−	0.248664i
$590$		0			0
$591$	27.8851	−	0.633039i	1.14704	−	0.0260398i
$592$		0			0
$593$	17.0396	+	29.5135i	0.699735	+	1.21198i	0.968558	+	0.248786i	$0.0800317\pi$
$593$	17.0396	+	29.5135i	0.699735	+	1.21198i	−0.268824	+	0.963189i	$0.586635\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	15.9932	−	29.2128i	0.654560	−	1.19560i
$598$		0			0
$599$	3.51340	+	6.08539i	0.143554	+	0.248642i	0.928832	−	0.370500i	$-0.120814\pi$
$599$	3.51340	+	6.08539i	0.143554	+	0.248642i	−0.785279	+	0.619142i	$0.787480\pi$
$600$		0			0
$601$	2.31218	+	4.00481i	0.0943158	+	0.163360i	0.909323	−	0.416091i	$-0.136600\pi$
$601$	2.31218	+	4.00481i	0.0943158	+	0.163360i	−0.815007	+	0.579451i	$0.803267\pi$
$602$		0			0
$603$	6.67171	+	10.4319i	0.271693	+	0.424818i
$604$		0			0
$605$	14.0573			0.571510
$606$		0			0
$607$	−20.2081			−0.820222			−0.410111	−	0.912036i	$-0.634510\pi$
$607$	−20.2081			−0.820222			−0.410111	+	0.912036i	$0.634510\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−10.3878	−	17.9922i	−0.420246	−	0.727888i
$612$		0			0
$613$	8.91037	−	15.4332i	0.359887	−	0.623342i	−0.628055	−	0.778169i	$-0.716149\pi$
$613$	8.91037	−	15.4332i	0.359887	−	0.623342i	0.987942	+	0.154827i	$0.0494820\pi$
$614$		0			0
$615$	−19.8532	+	36.2633i	−0.800558	+	1.46228i
$616$		0			0
$617$	15.0671	−	26.0969i	0.606577	−	1.05062i	−0.385223	−	0.922824i	$-0.625875\pi$
$617$	15.0671	−	26.0969i	0.606577	−	1.05062i	0.991800	−	0.127799i	$-0.0407913\pi$
$618$		0			0
$619$	31.9116			1.28264			0.641318	−	0.767275i	$-0.278388\pi$
$619$	31.9116			1.28264			0.641318	+	0.767275i	$0.278388\pi$
$620$		0			0
$621$	6.89020	−	0.469904i	0.276494	−	0.0188566i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−27.9651			−1.11860
$626$		0			0
$627$	−17.4785	−	28.7465i	−0.698023	−	1.14802i
$628$		0			0
$629$	19.9374			0.794957
$630$		0			0
$631$	−10.1430			−0.403788			−0.201894	−	0.979407i	$-0.564710\pi$
$631$	−10.1430			−0.403788			−0.201894	+	0.979407i	$0.564710\pi$
$632$		0			0
$633$	−20.5030	+	37.4503i	−0.814922	+	1.48852i
$634$		0			0
$635$	18.2946			0.726000
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−13.2341	+	0.601184i	−0.523534	+	0.0237825i
$640$		0			0
$641$	43.8512			1.73202			0.866009	−	0.500028i	$-0.166677\pi$
$641$	43.8512			1.73202			0.866009	+	0.500028i	$0.166677\pi$
$642$		0			0
$643$	−1.10737	+	1.91802i	−0.0436704	+	0.0756394i	−0.887034	−	0.461703i	$-0.847238\pi$
$643$	−1.10737	+	1.91802i	−0.0436704	+	0.0756394i	0.843364	+	0.537343i	$0.180572\pi$
$644$		0			0
$645$	7.48065	+	12.3033i	0.294550	+	0.484441i
$646$		0			0
$647$	10.4633	−	18.1230i	0.411355	−	0.712488i	−0.583683	−	0.811981i	$-0.698389\pi$
$647$	10.4633	−	18.1230i	0.411355	−	0.712488i	0.995038	+	0.0994938i	$0.0317224\pi$
$648$		0			0
$649$	−5.43341	−	9.41095i	−0.213280	−	0.369412i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.02883			0.314193			0.157096	−	0.987583i	$-0.449787\pi$
$653$	8.02883			0.314193			0.157096	+	0.987583i	$0.449787\pi$
$654$		0			0
$655$	46.2189			1.80592
$656$		0			0
$657$	16.7210	−	32.2594i	0.652348	−	1.25856i
$658$		0			0
$659$	9.25793	+	16.0352i	0.360638	+	0.624643i	0.988066	−	0.154031i	$-0.0492257\pi$
$659$	9.25793	+	16.0352i	0.360638	+	0.624643i	−0.627428	+	0.778675i	$0.715892\pi$
$660$		0			0
$661$	−10.4273	−	18.0606i	−0.405574	−	0.702474i	0.588814	−	0.808268i	$-0.299595\pi$
$661$	−10.4273	−	18.0606i	−0.405574	−	0.702474i	−0.994388	+	0.105794i	$0.966262\pi$
$662$		0			0
$663$	−18.4263	−	30.3054i	−0.715619	−	1.17696i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−5.15540	−	8.92941i	−0.199618	−	0.345748i
$668$		0			0
$669$	−13.3371	−	21.9352i	−0.515640	−	0.848063i
$670$		0			0
$671$	−1.30143	+	2.25415i	−0.0502412	+	0.0870204i
$672$		0			0
$673$	11.4484	+	19.8292i	0.441303	+	0.764360i	0.997786	−	0.0664992i	$-0.0211830\pi$
$673$	11.4484	+	19.8292i	0.441303	+	0.764360i	−0.556483	+	0.830859i	$0.687850\pi$
$674$		0			0
$675$	3.56440	−	0.243088i	0.137194	−	0.00935645i
$676$		0			0
$677$	23.3119	−	40.3774i	0.895948	−	1.55183i	0.0633218	−	0.997993i	$-0.479831\pi$
$677$	23.3119	−	40.3774i	0.895948	−	1.55183i	0.832627	−	0.553835i	$-0.186836\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	31.4373	−	0.713681i	1.20468	−	0.0273483i
$682$		0			0
$683$	18.3102	−	31.7141i	0.700618	−	1.21351i	−0.267631	−	0.963521i	$-0.586241\pi$
$683$	18.3102	−	31.7141i	0.700618	−	1.21351i	0.968250	−	0.249985i	$-0.0804258\pi$
$684$		0			0
$685$	23.1092			0.882958
$686$		0			0
$687$	−16.4622	+	0.373720i	−0.628073	+	0.0142583i
$688$		0			0
$689$	−27.7816	−	48.1192i	−1.05840	−	1.83320i
$690$		0			0
$691$	−13.2586	+	22.9645i	−0.504380	+	0.873611i	0.495607	+	0.868547i	$0.334945\pi$
$691$	−13.2586	+	22.9645i	−0.504380	+	0.873611i	−0.999987	+	0.00506472i	$0.998388\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−9.09101	+	15.7461i	−0.344842	+	0.597283i
$696$		0			0
$697$	−21.5385	−	37.3058i	−0.815830	−	1.41306i
$698$		0			0
$699$	−18.3057	−	30.1069i	−0.692383	−	1.13875i
$700$		0			0
$701$	−29.9931			−1.13282			−0.566411	−	0.824123i	$-0.691669\pi$
$701$	−29.9931			−1.13282			−0.566411	+	0.824123i	$0.691669\pi$
$702$		0			0
$703$	−19.9101	+	34.4854i	−0.750925	+	1.30064i
$704$		0			0
$705$	−8.66204	+	15.8219i	−0.326231	+	0.595886i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−5.48805	+	9.50558i	−0.206108	+	0.356990i	−0.950485	−	0.310770i	$-0.899413\pi$
$709$	−5.48805	+	9.50558i	−0.206108	+	0.356990i	0.744377	+	0.667759i	$0.232746\pi$
$710$		0			0
$711$	11.6881	−	22.5496i	0.438338	−	0.845676i
$712$		0			0
$713$	−0.538712	−	0.933076i	−0.0201749	−	0.0349440i
$714$		0			0
$715$	12.8189	−	22.2030i	0.479401	−	0.830346i
$716$		0			0
$717$	14.8144	−	27.0595i	0.553252	−	1.01056i
$718$		0			0
$719$	6.55211	+	11.3486i	0.244352	+	0.423231i	0.961949	−	0.273228i	$-0.0880913\pi$
$719$	6.55211	+	11.3486i	0.244352	+	0.423231i	−0.717597	+	0.696459i	$0.754758\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−10.8896	+	0.247212i	−0.404988	+	0.00919392i
$724$		0			0
$725$	−2.66696	−	4.61931i	−0.0990483	−	0.171557i
$726$		0			0
$727$	−8.96026	−	15.5196i	−0.332318	−	0.575591i	0.650648	−	0.759379i	$-0.274497\pi$
$727$	−8.96026	−	15.5196i	−0.332318	−	0.575591i	−0.982966	+	0.183788i	$0.941164\pi$
$728$		0			0
$729$	26.7500	−	3.66569i	0.990741	−	0.135766i
$730$		0			0
$731$	−15.0032			−0.554913
$732$		0			0
$733$	5.91320			0.218409			0.109204	−	0.994019i	$-0.465170\pi$
$733$	5.91320			0.218409			0.109204	+	0.994019i	$0.465170\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.66331	−	8.07709i	−0.171775	−	0.297523i
$738$		0			0
$739$	14.5887	−	25.2683i	0.536653	−	0.929511i	−0.462428	−	0.886657i	$-0.653022\pi$
$739$	14.5887	−	25.2683i	0.536653	−	0.929511i	0.999081	−	0.0428538i	$-0.0136450\pi$
$740$		0			0
$741$	70.8197	−	1.60773i	2.60163	−	0.0590614i
$742$		0			0
$743$	−18.8512	+	32.6513i	−0.691584	+	1.19786i	0.279735	+	0.960077i	$0.409753\pi$
$743$	−18.8512	+	32.6513i	−0.691584	+	1.19786i	−0.971319	+	0.237781i	$0.923580\pi$
$744$		0			0
$745$	21.6827			0.794391
$746$		0			0
$747$	2.64374	+	4.13374i	0.0967292	+	0.151246i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	40.6553			1.48353			0.741767	−	0.670658i	$-0.233988\pi$
$751$	40.6553			1.48353			0.741767	+	0.670658i	$0.233988\pi$
$752$		0			0
$753$	43.6136	−	0.990103i	1.58937	−	0.0360814i
$754$		0			0
$755$	48.3130			1.75829
$756$		0			0
$757$	17.6704			0.642241			0.321120	−	0.947038i	$-0.395941\pi$
$757$	17.6704			0.642241			0.321120	+	0.947038i	$0.395941\pi$
$758$		0			0
$759$	−5.20033	+	0.118056i	−0.188760	+	0.00428517i
$760$		0			0
$761$	−1.28837			−0.0467033			−0.0233516	−	0.999727i	$-0.507434\pi$
$761$	−1.28837			−0.0467033			−0.0233516	+	0.999727i	$0.507434\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−14.1707	+	27.3393i	−0.512344	+	0.988453i
$766$		0			0
$767$	22.8809			0.826182
$768$		0			0
$769$	4.19275	−	7.26205i	0.151194	−	0.261876i	−0.780472	−	0.625190i	$-0.785021\pi$
$769$	4.19275	−	7.26205i	0.151194	−	0.261876i	0.931667	+	0.363314i	$0.118355\pi$
$770$		0			0
$771$	−49.6629	+	1.12743i	−1.78857	+	0.0406035i
$772$		0			0
$773$	−25.1530	+	43.5663i	−0.904691	+	1.56697i	−0.0833598	+	0.996520i	$0.526565\pi$
$773$	−25.1530	+	43.5663i	−0.904691	+	1.56697i	−0.821331	+	0.570451i	$0.806768\pi$
$774$		0			0
$775$	−0.278683	−	0.482693i	−0.0100106	−	0.0173388i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	86.0362			3.08257
$780$		0			0
$781$	9.97806			0.357043
$782$		0			0
$783$	−22.4837	−	33.4575i	−0.803503	−	1.19567i
$784$		0			0
$785$	9.97051	+	17.2694i	0.355863	+	0.616373i
$786$		0			0
$787$	−11.1922	−	19.3855i	−0.398960	−	0.691020i	0.594638	−	0.803994i	$-0.297296\pi$
$787$	−11.1922	−	19.3855i	−0.398960	−	0.691020i	−0.993598	+	0.112974i	$0.963962\pi$
$788$		0			0
$789$	−24.9642	+	0.566729i	−0.888748	+	0.0201761i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−2.74026	−	4.74627i	−0.0973095	−	0.168545i
$794$		0			0
$795$	−23.1661	+	42.3147i	−0.821618	+	1.50075i
$796$		0			0
$797$	−0.706182	+	1.22314i	−0.0250143	+	0.0433260i	−0.878262	−	0.478181i	$-0.841296\pi$
$797$	−0.706182	+	1.22314i	−0.0250143	+	0.0433260i	0.853247	+	0.521507i	$0.174630\pi$
$798$		0			0
$799$	−9.39736	−	16.2767i	−0.332455	−	0.575828i
$800$		0			0
$801$	10.2527	+	16.0311i	0.362262	+	0.566431i
$802$		0			0
$803$	−13.6837	+	23.7008i	−0.482887	+	0.836384i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−10.7296	+	19.5985i	−0.377701	+	0.689900i
$808$		0			0
$809$	−10.0424	+	17.3939i	−0.353071	+	0.611537i	−0.986786	−	0.162030i	$-0.948196\pi$
$809$	−10.0424	+	17.3939i	−0.353071	+	0.611537i	0.633715	+	0.773567i	$0.281529\pi$
$810$		0			0
$811$	55.7821			1.95878			0.979388	−	0.201988i	$-0.0647401\pi$
$811$	55.7821			1.95878			0.979388	+	0.201988i	$0.0647401\pi$
$812$		0			0
$813$	−17.5130	−	28.8033i	−0.614207	−	1.01017i
$814$		0			0
$815$	−23.1140	−	40.0345i	−0.809646	−	1.40235i
$816$		0			0
$817$	14.9827	−	25.9507i	0.524177	−	0.907901i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	24.4346	−	42.3219i	0.852772	−	1.47704i	−0.0259249	−	0.999664i	$-0.508253\pi$
$821$	24.4346	−	42.3219i	0.852772	−	1.47704i	0.878697	−	0.477380i	$-0.158414\pi$
$822$		0			0
$823$	0.266319	+	0.461277i	0.00928328	+	0.0160791i	0.870630	−	0.491939i	$-0.163712\pi$
$823$	0.266319	+	0.461277i	0.00928328	+	0.0160791i	−0.861346	+	0.508018i	$0.830378\pi$
$824$		0			0
$825$	−2.69020	+	0.0610721i	−0.0936607	+	0.00212626i
$826$		0			0
$827$	10.1951			0.354518			0.177259	−	0.984164i	$-0.443277\pi$
$827$	10.1951			0.354518			0.177259	+	0.984164i	$0.443277\pi$
$828$		0			0
$829$	−10.6346	+	18.4197i	−0.369355	+	0.639742i	−0.989465	−	0.144773i	$-0.953755\pi$
$829$	−10.6346	+	18.4197i	−0.369355	+	0.639742i	0.620110	+	0.784515i	$0.287088\pi$
$830$		0			0
$831$	27.5540	−	0.625522i	0.955837	−	0.0216991i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	21.0859	−	36.5219i	0.729709	−	1.26389i
$836$		0			0
$837$	−2.34943	−	3.49613i	−0.0812082	−	0.120844i
$838$		0			0
$839$	9.47717	+	16.4149i	0.327188	+	0.566707i	0.981953	−	0.189126i	$-0.0605655\pi$
$839$	9.47717	+	16.4149i	0.327188	+	0.566707i	−0.654765	+	0.755833i	$0.727232\pi$
$840$		0			0
$841$	−15.5912	+	27.0047i	−0.537626	+	0.931196i
$842$		0			0
$843$	−25.1953	−	41.4383i	−0.867774	−	1.42721i
$844$		0			0
$845$	11.4896	+	19.9006i	0.395254	+	0.684601i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	4.72140	+	7.76518i	0.162038	+	0.266500i
$850$		0			0
$851$	3.07837	+	5.33190i	0.105525	+	0.182775i
$852$		0			0
$853$	−2.75811	−	4.77718i	−0.0944358	−	0.163568i	0.814937	−	0.579549i	$-0.196771\pi$
$853$	−2.75811	−	4.77718i	−0.0944358	−	0.163568i	−0.909373	+	0.415982i	$0.863438\pi$
$854$		0			0
$855$	−33.1368	−	51.8127i	−1.13326	−	1.77196i
$856$		0			0
$857$	15.8494			0.541406			0.270703	−	0.962663i	$-0.412744\pi$
$857$	15.8494			0.541406			0.270703	+	0.962663i	$0.412744\pi$
$858$		0			0
$859$	−21.4009			−0.730189			−0.365095	−	0.930970i	$-0.618963\pi$
$859$	−21.4009			−0.730189			−0.365095	+	0.930970i	$0.618963\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.01860	+	3.49632i	0.0687140	+	0.119016i	0.898335	−	0.439310i	$-0.144777\pi$
$863$	2.01860	+	3.49632i	0.0687140	+	0.119016i	−0.829621	+	0.558326i	$0.811444\pi$
$864$		0			0
$865$	25.2624	−	43.7557i	0.858946	−	1.48774i
$866$		0			0
$867$	−1.37202	−	2.25653i	−0.0465962	−	0.0766358i
$868$		0			0
$869$	−9.56500	+	16.5671i	−0.324470	+	0.561999i
$870$		0			0
$871$	19.6379			0.665404
$872$		0			0
$873$	19.3406	+	30.2409i	0.654580	+	1.02350i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−25.3810			−0.857057			−0.428529	−	0.903528i	$-0.640968\pi$
$877$	−25.3810			−0.857057			−0.428529	+	0.903528i	$0.640968\pi$
$878$		0			0
$879$	−2.76043	+	5.04213i	−0.0931070	+	0.170067i
$880$		0			0
$881$	−18.7755			−0.632561			−0.316281	−	0.948666i	$-0.602434\pi$
$881$	−18.7755			−0.632561			−0.316281	+	0.948666i	$0.602434\pi$
$882$		0			0
$883$	8.52167			0.286777			0.143388	−	0.989666i	$-0.454200\pi$
$883$	8.52167			0.286777			0.143388	+	0.989666i	$0.454200\pi$
$884$		0			0
$885$	−10.3207	−	16.9743i	−0.346927	−	0.570584i
$886$		0			0
$887$	−10.1008			−0.339152			−0.169576	−	0.985517i	$-0.554240\pi$
$887$	−10.1008			−0.339152			−0.169576	+	0.985517i	$0.554240\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−20.2523	+	1.84380i	−0.678477	+	0.0617696i
$892$		0			0
$893$	37.5380			1.25616
$894$		0			0
$895$	15.4870	−	26.8243i	0.517674	−	0.896638i
$896$		0			0
$897$	5.25956	−	9.60698i	0.175612	−	0.320768i
$898$		0			0
$899$	−3.14437	+	5.44620i	−0.104870	+	0.181641i
$900$		0			0
$901$	−25.1327	−	43.5311i	−0.837292	−	1.45023i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	40.1224			1.33371
$906$		0			0
$907$	−21.2176			−0.704519			−0.352260	−	0.935902i	$-0.614587\pi$
$907$	−21.2176			−0.704519			−0.352260	+	0.935902i	$0.614587\pi$
$908$		0			0
$909$	32.5073	−	1.47670i	1.07820	−	0.0489792i
$910$		0			0
$911$	−4.46609	−	7.73550i	−0.147968	−	0.256289i	0.782508	−	0.622640i	$-0.213940\pi$
$911$	−4.46609	−	7.73550i	−0.147968	−	0.256289i	−0.930476	+	0.366352i	$0.880607\pi$
$912$		0			0
$913$	−1.84789	−	3.20063i	−0.0611561	−	0.105925i
$914$		0			0
$915$	−2.28501	+	4.17374i	−0.0755400	+	0.137980i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−17.4564	−	30.2354i	−0.575834	−	0.997374i	−0.995950	−	0.0899041i	$-0.971344\pi$
$919$	−17.4564	−	30.2354i	−0.575834	−	0.997374i	0.420116	−	0.907470i	$-0.361989\pi$
$920$		0			0
$921$	−21.5935	+	0.490210i	−0.711532	+	0.0161530i
$922$		0			0
$923$	−10.5048	+	18.1948i	−0.345769	+	0.598889i
$924$		0			0
$925$	1.59248	+	2.75826i	0.0523605	+	0.0906911i
$926$		0			0
$927$	54.9768	−	2.49742i	1.80568	−	0.0820261i
$928$		0			0
$929$	−5.51692	+	9.55559i	−0.181004	+	0.313509i	−0.942223	−	0.334987i	$-0.891268\pi$
$929$	−5.51692	+	9.55559i	−0.181004	+	0.313509i	0.761218	+	0.648496i	$0.224601\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	20.4055	+	33.5604i	0.668045	+	1.09872i
$934$		0			0
$935$	11.5967	−	20.0860i	0.379251	−	0.656883i
$936$		0			0
$937$	13.6426			0.445686			0.222843	−	0.974854i	$-0.428466\pi$
$937$	13.6426			0.445686			0.222843	+	0.974854i	$0.428466\pi$
$938$		0			0
$939$	5.25851	−	9.60506i	0.171605	−	0.313449i
$940$		0			0
$941$	12.0278	+	20.8328i	0.392095	+	0.679129i	0.992726	−	0.120398i	$-0.0384170\pi$
$941$	12.0278	+	20.8328i	0.392095	+	0.679129i	−0.600630	+	0.799527i	$0.705084\pi$
$942$		0			0
$943$	6.65117	−	11.5202i	0.216592	−	0.375148i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−6.69602	+	11.5978i	−0.217591	+	0.376879i	−0.954071	−	0.299580i	$-0.903153\pi$
$947$	−6.69602	+	11.5978i	−0.217591	+	0.376879i	0.736480	+	0.676460i	$0.236487\pi$
$948$		0			0
$949$	−28.8120	−	49.9038i	−0.935277	−	1.61995i
$950$		0			0
$951$	12.9595	−	23.6715i	0.420240	−	0.767600i
$952$		0			0
$953$	36.3444			1.17731			0.588655	−	0.808384i	$-0.299658\pi$
$953$	36.3444			1.17731			0.588655	+	0.808384i	$0.299658\pi$
$954$		0			0
$955$	10.9360	−	18.9418i	0.353882	−	0.612942i
$956$		0			0
$957$	15.7735	+	25.9423i	0.509883	+	0.838595i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	15.1714	−	26.2777i	0.489401	−	0.847667i
$962$		0			0
$963$	−6.19730	−	9.69008i	−0.199705	−	0.312259i
$964$		0			0
$965$	−30.5627	−	52.9362i	−0.983849	−	1.70408i
$966$		0			0
$967$	4.82455	−	8.35637i	0.155147	−	0.268723i	−0.777965	−	0.628307i	$-0.783748\pi$
$967$	4.82455	−	8.35637i	0.155147	−	0.268723i	0.933113	+	0.359584i	$0.117082\pi$
$968$		0			0
$969$	64.0672	−	1.45443i	2.05813	−	0.0467232i
$970$		0			0
$971$	21.6888	+	37.5660i	0.696025	+	1.20555i	0.969834	+	0.243767i	$0.0783832\pi$
$971$	21.6888	+	37.5660i	0.696025	+	1.20555i	−0.273809	+	0.961784i	$0.588283\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	2.72084	−	4.96982i	0.0871367	−	0.159162i
$976$		0			0
$977$	−2.60004	−	4.50340i	−0.0831826	−	0.144076i	0.821433	−	0.570305i	$-0.193175\pi$
$977$	−2.60004	−	4.50340i	−0.0831826	−	0.144076i	−0.904615	+	0.426229i	$0.859842\pi$
$978$		0			0
$979$	−7.16631	−	12.4124i	−0.229036	−	0.396703i
$980$		0			0
$981$	−3.65151	+	7.04478i	−0.116584	+	0.224922i
$982$		0			0
$983$	−23.2697			−0.742190			−0.371095	−	0.928595i	$-0.621018\pi$
$983$	−23.2697			−0.742190			−0.371095	+	0.928595i	$0.621018\pi$
$984$		0			0
$985$	−38.4049			−1.22368
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.31652	−	4.01233i	−0.0736610	−	0.127585i
$990$		0			0
$991$	19.5191	−	33.8080i	0.620044	−	1.07395i	−0.369433	−	0.929257i	$-0.620448\pi$
$991$	19.5191	−	33.8080i	0.620044	−	1.07395i	0.989477	−	0.144691i	$-0.0462187\pi$
$992$		0			0
$993$	18.0714	−	33.0087i	0.573478	−	1.04750i
$994$		0			0
$995$	−22.9283	+	39.7130i	−0.726877	+	1.25899i
$996$		0			0
$997$	24.1809			0.765818			0.382909	−	0.923786i	$-0.374922\pi$
$997$	24.1809			0.765818			0.382909	+	0.923786i	$0.374922\pi$
$998$		0			0
$999$	13.4254	+	19.9780i	0.424761	+	0.632076i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.l.j.949.12		24
3.2	odd	2		5292.2.l.j.361.10		24
7.2	even	3		1764.2.i.j.373.5		24
7.3	odd	6		1764.2.j.i.589.8	yes	24
7.4	even	3		1764.2.j.i.589.5	✓	24
7.5	odd	6		1764.2.i.j.373.8		24
7.6	odd	2	inner	1764.2.l.j.949.1		24
9.2	odd	6		5292.2.i.j.2125.3		24
9.7	even	3		1764.2.i.j.1537.5		24
21.2	odd	6		5292.2.i.j.1549.3		24
21.5	even	6		5292.2.i.j.1549.10		24
21.11	odd	6		5292.2.j.i.1765.3		24
21.17	even	6		5292.2.j.i.1765.10		24
21.20	even	2		5292.2.l.j.361.3		24
63.2	odd	6		5292.2.l.j.3313.10		24
63.11	odd	6		5292.2.j.i.3529.3		24
63.16	even	3	inner	1764.2.l.j.961.12		24
63.20	even	6		5292.2.i.j.2125.10		24
63.25	even	3		1764.2.j.i.1177.5	yes	24
63.34	odd	6		1764.2.i.j.1537.8		24
63.38	even	6		5292.2.j.i.3529.10		24
63.47	even	6		5292.2.l.j.3313.3		24
63.52	odd	6		1764.2.j.i.1177.8	yes	24
63.61	odd	6	inner	1764.2.l.j.961.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1764.2.i.j.373.5		24	7.2	even	3
1764.2.i.j.373.8		24	7.5	odd	6
1764.2.i.j.1537.5		24	9.7	even	3
1764.2.i.j.1537.8		24	63.34	odd	6
1764.2.j.i.589.5	✓	24	7.4	even	3
1764.2.j.i.589.8	yes	24	7.3	odd	6
1764.2.j.i.1177.5	yes	24	63.25	even	3
1764.2.j.i.1177.8	yes	24	63.52	odd	6
1764.2.l.j.949.1		24	7.6	odd	2	inner
1764.2.l.j.949.12		24	1.1	even	1	trivial
1764.2.l.j.961.1		24	63.61	odd	6	inner
1764.2.l.j.961.12		24	63.16	even	3	inner
5292.2.i.j.1549.3		24	21.2	odd	6
5292.2.i.j.1549.10		24	21.5	even	6
5292.2.i.j.2125.3		24	9.2	odd	6
5292.2.i.j.2125.10		24	63.20	even	6
5292.2.j.i.1765.3		24	21.11	odd	6
5292.2.j.i.1765.10		24	21.17	even	6
5292.2.j.i.3529.3		24	63.11	odd	6
5292.2.j.i.3529.10		24	63.38	even	6
5292.2.l.j.361.3		24	21.20	even	2
5292.2.l.j.361.10		24	3.2	odd	2
5292.2.l.j.3313.3		24	63.47	even	6
5292.2.l.j.3313.10		24	63.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.l (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73160 - 0.0393104i) q^{3} -2.38486 q^{5} +(2.99691 - 0.136140i) q^{9} -2.25956 q^{11} +(2.37884 - 4.12027i) q^{13} +(-4.12964 + 0.0937498i) q^{15} +(2.15202 - 3.72740i) q^{17} +(4.29815 + 7.44461i) q^{19} +1.32910 q^{23} +0.687562 q^{25} +(5.18411 - 0.353550i) q^{27} +(-3.87886 - 6.71839i) q^{29} +(-0.405320 - 0.702036i) q^{31} +(-3.91267 + 0.0888242i) q^{33} +(2.31613 + 4.01166i) q^{37} +(3.95723 - 7.22818i) q^{39} +(5.00426 - 8.66764i) q^{41} +(-1.74292 - 3.01883i) q^{43} +(-7.14721 + 0.324675i) q^{45} +(2.18338 - 3.78173i) q^{47} +(3.57992 - 6.53899i) q^{51} +(5.83934 - 10.1140i) q^{53} +5.38874 q^{55} +(7.73534 + 12.7222i) q^{57} +(2.40463 + 4.16495i) q^{59} +(0.575967 - 0.997604i) q^{61} +(-5.67319 + 9.82626i) q^{65} +(2.06381 + 3.57463i) q^{67} +(2.30148 - 0.0522474i) q^{69} -4.41593 q^{71} +(6.05590 - 10.4891i) q^{73} +(1.19059 - 0.0270283i) q^{75} +(4.23312 - 7.33198i) q^{79} +(8.96293 - 0.815999i) q^{81} +(0.817808 + 1.41648i) q^{83} +(-5.13226 + 8.88934i) q^{85} +(-6.98076 - 11.4811i) q^{87} +(3.17155 + 5.49329i) q^{89} +(-0.729452 - 1.19971i) q^{93} +(-10.2505 - 17.7543i) q^{95} +(5.98278 + 10.3625i) q^{97} +(-6.77170 + 0.307617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{9} + 8 q^{11} - 28 q^{15} + 16 q^{23} + 24 q^{25} - 32 q^{29} - 12 q^{37} + 32 q^{51} - 16 q^{53} + 52 q^{57} - 36 q^{65} + 12 q^{67} + 48 q^{71} + 12 q^{79} - 8 q^{81} + 12 q^{85} + 32 q^{95}+ \cdots - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^9 + 8 * q^11 - 28 * q^15 + 16 * q^23 + 24 * q^25 - 32 * q^29 - 12 * q^37 + 32 * q^51 - 16 * q^53 + 52 * q^57 - 36 * q^65 + 12 * q^67 + 48 * q^71 + 12 * q^79 - 8 * q^81 + 12 * q^85 + 32 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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