LMFDB - Embedded newform 1920.2.bl.a.289.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1920,2,Mod(289,1920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1920, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 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("1920.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1920 = 2^{7} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1920.bl (of order $4$, 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:	$15.3312771881$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			289.3
Character	$\chi$	$=$	1920.289
Dual form			1920.2.bl.a.1249.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{3} +(1.50085 + 1.65754i) q^{5} -2.58977 q^{7} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{3} +(1.50085 + 1.65754i) q^{5} -2.58977 q^{7} -1.00000i q^{9} +(-4.39624 + 4.39624i) q^{11} +(0.417468 - 0.417468i) q^{13} +(-2.23332 - 0.110799i) q^{15} -4.40417i q^{17} +(4.53682 + 4.53682i) q^{19} +(1.83125 - 1.83125i) q^{21} -0.281063 q^{23} +(-0.494901 + 4.97545i) q^{25} +(0.707107 + 0.707107i) q^{27} +(-3.73710 - 3.73710i) q^{29} -3.05233 q^{31} -6.21722i q^{33} +(-3.88686 - 4.29266i) q^{35} +(-5.26234 - 5.26234i) q^{37} +0.590389i q^{39} +5.16508i q^{41} +(-2.66933 - 2.66933i) q^{43} +(1.65754 - 1.50085i) q^{45} -7.45202i q^{47} -0.293066 q^{49} +(3.11422 + 3.11422i) q^{51} +(-2.89462 - 2.89462i) q^{53} +(-13.8850 - 0.688864i) q^{55} -6.41604 q^{57} +(4.60721 - 4.60721i) q^{59} +(0.211318 + 0.211318i) q^{61} +2.58977i q^{63} +(1.31853 + 0.0654147i) q^{65} +(-7.17140 + 7.17140i) q^{67} +(0.198741 - 0.198741i) q^{69} -15.9477i q^{71} +10.5662 q^{73} +(-3.16822 - 3.86812i) q^{75} +(11.3853 - 11.3853i) q^{77} +4.53907 q^{79} -1.00000 q^{81} +(-4.56660 + 4.56660i) q^{83} +(7.30010 - 6.61000i) q^{85} +5.28505 q^{87} +10.2745i q^{89} +(-1.08115 + 1.08115i) q^{91} +(2.15832 - 2.15832i) q^{93} +(-0.710893 + 14.3291i) q^{95} +6.78053i q^{97} +(4.39624 + 4.39624i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) $ 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times$.

$n$	$511$	$641$	$901$	$1537$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$		0			0
$5$	1.50085	+	1.65754i	0.671200	+	0.741276i
$5$	1.50085	+	1.65754i	0.671200	+	0.741276i
$6$		0			0
$7$	−2.58977			−0.978843			−0.489421	−	0.872047i	$-0.662792\pi$
$7$	−2.58977			−0.978843			−0.489421	+	0.872047i	$0.662792\pi$
$8$		0			0
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−4.39624	+	4.39624i	−1.32552	+	1.32552i	−0.416278	+	0.909237i	$0.636666\pi$
$11$	−4.39624	+	4.39624i	−1.32552	+	1.32552i	−0.909237	+	0.416278i	$0.863334\pi$
$12$		0			0
$13$	0.417468	−	0.417468i	0.115785	−	0.115785i	−0.646840	−	0.762625i	$-0.723910\pi$
$13$	0.417468	−	0.417468i	0.115785	−	0.115785i	0.762625	+	0.646840i	$0.223910\pi$
$14$		0			0
$15$	−2.23332	−	0.110799i	−0.576641	−	0.0286083i
$16$		0			0
$17$		−	4.40417i		−	1.06817i	−0.845431	−	0.534084i	$-0.820657\pi$
$17$		−	4.40417i		−	1.06817i	0.845431	−	0.534084i	$-0.179343\pi$
$18$		0			0
$19$	4.53682	+	4.53682i	1.04082	+	1.04082i	0.999131	+	0.0416882i	$0.0132736\pi$
$19$	4.53682	+	4.53682i	1.04082	+	1.04082i	0.0416882	+	0.999131i	$0.486726\pi$
$20$		0			0
$21$	1.83125	−	1.83125i	0.399611	−	0.399611i
$22$		0			0
$23$	−0.281063			−0.0586056			−0.0293028	−	0.999571i	$-0.509329\pi$
$23$	−0.281063			−0.0586056			−0.0293028	+	0.999571i	$0.509329\pi$
$24$		0			0
$25$	−0.494901	+	4.97545i	−0.0989802	+	0.995089i
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$		0			0
$29$	−3.73710	−	3.73710i	−0.693962	−	0.693962i	0.269140	−	0.963101i	$-0.413261\pi$
$29$	−3.73710	−	3.73710i	−0.693962	−	0.693962i	−0.963101	+	0.269140i	$0.913261\pi$
$30$		0			0
$31$	−3.05233			−0.548214			−0.274107	−	0.961699i	$-0.588382\pi$
$31$	−3.05233			−0.548214			−0.274107	+	0.961699i	$0.588382\pi$
$32$		0			0
$33$		−	6.21722i		−	1.08228i
$34$		0			0
$35$	−3.88686	−	4.29266i	−0.657000	−	0.725593i
$36$		0			0
$37$	−5.26234	−	5.26234i	−0.865124	−	0.865124i	0.126804	−	0.991928i	$-0.459528\pi$
$37$	−5.26234	−	5.26234i	−0.865124	−	0.865124i	−0.991928	+	0.126804i	$0.959528\pi$
$38$		0			0
$39$			0.590389i			0.0945380i
$40$		0			0
$41$			5.16508i			0.806649i	0.915057	+	0.403325i	$0.132145\pi$
$41$			5.16508i			0.806649i	−0.915057	+	0.403325i	$0.867855\pi$
$42$		0			0
$43$	−2.66933	−	2.66933i	−0.407069	−	0.407069i	0.473647	−	0.880715i	$-0.342937\pi$
$43$	−2.66933	−	2.66933i	−0.407069	−	0.407069i	−0.880715	+	0.473647i	$0.842937\pi$
$44$		0			0
$45$	1.65754	−	1.50085i	0.247092	−	0.223733i
$46$		0			0
$47$		−	7.45202i		−	1.08699i	−0.839413	−	0.543495i	$-0.817101\pi$
$47$		−	7.45202i		−	1.08699i	0.839413	−	0.543495i	$-0.182899\pi$
$48$		0			0
$49$	−0.293066			−0.0418665
$50$		0			0
$51$	3.11422	+	3.11422i	0.436078	+	0.436078i
$52$		0			0
$53$	−2.89462	−	2.89462i	−0.397606	−	0.397606i	0.479782	−	0.877388i	$-0.340716\pi$
$53$	−2.89462	−	2.89462i	−0.397606	−	0.397606i	−0.877388	+	0.479782i	$0.840716\pi$
$54$		0			0
$55$	−13.8850	−	0.688864i	−1.87226	−	0.0928863i
$56$		0			0
$57$	−6.41604			−0.849825
$58$		0			0
$59$	4.60721	−	4.60721i	0.599808	−	0.599808i	−0.340453	−	0.940261i	$-0.610580\pi$
$59$	4.60721	−	4.60721i	0.599808	−	0.599808i	0.940261	+	0.340453i	$0.110580\pi$
$60$		0			0
$61$	0.211318	+	0.211318i	0.0270564	+	0.0270564i	0.720506	−	0.693449i	$-0.243910\pi$
$61$	0.211318	+	0.211318i	0.0270564	+	0.0270564i	−0.693449	+	0.720506i	$0.743910\pi$
$62$		0			0
$63$			2.58977i			0.326281i
$64$		0			0
$65$	1.31853	+	0.0654147i	0.163543	+	0.00811370i
$66$		0			0
$67$	−7.17140	+	7.17140i	−0.876126	+	0.876126i	−0.993131	−	0.117005i	$-0.962671\pi$
$67$	−7.17140	+	7.17140i	−0.876126	+	0.876126i	0.117005	+	0.993131i	$0.462671\pi$
$68$		0			0
$69$	0.198741	−	0.198741i	0.0239257	−	0.0239257i
$70$		0			0
$71$		−	15.9477i		−	1.89265i	−0.323222	−	0.946323i	$-0.604766\pi$
$71$		−	15.9477i		−	1.89265i	0.323222	−	0.946323i	$-0.395234\pi$
$72$		0			0
$73$	10.5662			1.23668			0.618339	−	0.785912i	$-0.287806\pi$
$73$	10.5662			1.23668			0.618339	+	0.785912i	$0.287806\pi$
$74$		0			0
$75$	−3.16822	−	3.86812i	−0.365835	−	0.446652i
$76$		0			0
$77$	11.3853	−	11.3853i	1.29747	−	1.29747i
$78$		0			0
$79$	4.53907			0.510685			0.255342	−	0.966851i	$-0.417812\pi$
$79$	4.53907			0.510685			0.255342	+	0.966851i	$0.417812\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−4.56660	+	4.56660i	−0.501249	+	0.501249i	−0.911826	−	0.410577i	$-0.865327\pi$
$83$	−4.56660	+	4.56660i	−0.501249	+	0.501249i	0.410577	+	0.911826i	$0.365327\pi$
$84$		0			0
$85$	7.30010	−	6.61000i	0.791807	−	0.716955i
$86$		0			0
$87$	5.28505			0.566617
$88$		0			0
$89$			10.2745i			1.08910i	0.838730	+	0.544548i	$0.183299\pi$
$89$			10.2745i			1.08910i	−0.838730	+	0.544548i	$0.816701\pi$
$90$		0			0
$91$	−1.08115	+	1.08115i	−0.113335	+	0.113335i
$92$		0			0
$93$	2.15832	−	2.15832i	0.223808	−	0.223808i
$94$		0			0
$95$	−0.710893	+	14.3291i	−0.0729361	+	1.47013i
$96$		0			0
$97$			6.78053i			0.688459i	0.938886	+	0.344229i	$0.111860\pi$
$97$			6.78053i			0.688459i	−0.938886	+	0.344229i	$0.888140\pi$
$98$		0			0
$99$	4.39624	+	4.39624i	0.441838	+	0.441838i
$100$		0			0
$101$	−10.0764	+	10.0764i	−1.00264	+	1.00264i	−0.00264739	+	0.999996i	$0.500843\pi$
$101$	−10.0764	+	10.0764i	−1.00264	+	1.00264i	−0.999996	+	0.00264739i	$0.999157\pi$
$102$		0			0
$103$	−4.71475			−0.464558			−0.232279	−	0.972649i	$-0.574618\pi$
$103$	−4.71475			−0.464558			−0.232279	+	0.972649i	$0.574618\pi$
$104$		0			0
$105$	5.78380	+	0.286945i	0.564441	+	0.0280030i
$106$		0			0
$107$	−12.9687	−	12.9687i	−1.25373	−	1.25373i	−0.954035	−	0.299696i	$-0.903115\pi$
$107$	−12.9687	−	12.9687i	−1.25373	−	1.25373i	−0.299696	−	0.954035i	$-0.596885\pi$
$108$		0			0
$109$	0.382902	+	0.382902i	0.0366754	+	0.0366754i	0.725207	−	0.688531i	$-0.241744\pi$
$109$	0.382902	+	0.382902i	0.0366754	+	0.0366754i	−0.688531	+	0.725207i	$0.741744\pi$
$110$		0			0
$111$	7.44208			0.706371
$112$		0			0
$113$		−	12.1861i		−	1.14637i	−0.819424	−	0.573187i	$-0.805707\pi$
$113$		−	12.1861i		−	1.14637i	0.819424	−	0.573187i	$-0.194293\pi$
$114$		0			0
$115$	−0.421833	−	0.465874i	−0.0393361	−	0.0434430i
$116$		0			0
$117$	−0.417468	−	0.417468i	−0.0385950	−	0.0385950i
$118$		0			0
$119$			11.4058i			1.04557i
$120$		0			0
$121$		−	27.6538i		−	2.51398i
$122$		0			0
$123$	−3.65226	−	3.65226i	−0.329313	−	0.329313i
$124$		0			0
$125$	−8.98979	+	6.64708i	−0.804071	+	0.594533i
$126$		0			0
$127$		−	6.75303i		−	0.599234i	−0.954060	−	0.299617i	$-0.903141\pi$
$127$		−	6.75303i		−	0.599234i	0.954060	−	0.299617i	$-0.0968589\pi$
$128$		0			0
$129$	3.77500			0.332370
$130$		0			0
$131$	−3.95303	−	3.95303i	−0.345378	−	0.345378i	0.513007	−	0.858385i	$-0.328532\pi$
$131$	−3.95303	−	3.95303i	−0.345378	−	0.345378i	−0.858385	+	0.513007i	$0.828532\pi$
$132$		0			0
$133$	−11.7494	−	11.7494i	−1.01880	−	1.01880i
$134$		0			0
$135$	−0.110799	+	2.23332i	−0.00953609	+	0.192214i
$136$		0			0
$137$	−5.19519			−0.443855			−0.221927	−	0.975063i	$-0.571235\pi$
$137$	−5.19519			−0.443855			−0.221927	+	0.975063i	$0.571235\pi$
$138$		0			0
$139$	−0.977024	+	0.977024i	−0.0828701	+	0.0828701i	−0.747327	−	0.664457i	$-0.768663\pi$
$139$	−0.977024	+	0.977024i	−0.0828701	+	0.0828701i	0.664457	+	0.747327i	$0.268663\pi$
$140$		0			0
$141$	5.26938	+	5.26938i	0.443761	+	0.443761i
$142$		0			0
$143$			3.67058i			0.306949i
$144$		0			0
$145$	0.585580	−	11.8032i	0.0486298	−	0.980204i
$146$		0			0
$147$	0.207229	−	0.207229i	0.0170919	−	0.0170919i
$148$		0			0
$149$	−11.3051	+	11.3051i	−0.926150	+	0.926150i	−0.997455	−	0.0713047i	$-0.977284\pi$
$149$	−11.3051	+	11.3051i	−0.926150	+	0.926150i	0.0713047	+	0.997455i	$0.477284\pi$
$150$		0			0
$151$			2.87287i			0.233791i	0.993144	+	0.116895i	$0.0372942\pi$
$151$			2.87287i			0.233791i	−0.993144	+	0.116895i	$0.962706\pi$
$152$		0			0
$153$	−4.40417			−0.356056
$154$		0			0
$155$	−4.58109	−	5.05937i	−0.367962	−	0.406378i
$156$		0			0
$157$	5.73516	−	5.73516i	0.457716	−	0.457716i	−0.440189	−	0.897905i	$-0.645089\pi$
$157$	5.73516	−	5.73516i	0.457716	−	0.457716i	0.897905	+	0.440189i	$0.145089\pi$
$158$		0			0
$159$	4.09361			0.324644
$160$		0			0
$161$	0.727889			0.0573657
$162$		0			0
$163$	11.9561	−	11.9561i	0.936474	−	0.936474i	−0.0616255	−	0.998099i	$-0.519628\pi$
$163$	11.9561	−	11.9561i	0.936474	−	0.936474i	0.998099	+	0.0616255i	$0.0196285\pi$
$164$		0			0
$165$	10.3053	−	9.33111i	0.802267	−	0.726426i
$166$		0			0
$167$	−9.23665			−0.714754			−0.357377	−	0.933960i	$-0.616329\pi$
$167$	−9.23665			−0.714754			−0.357377	+	0.933960i	$0.616329\pi$
$168$		0			0
$169$			12.6514i			0.973188i
$170$		0			0
$171$	4.53682	−	4.53682i	0.346940	−	0.346940i
$172$		0			0
$173$	2.36187	−	2.36187i	0.179570	−	0.179570i	−0.611598	−	0.791168i	$-0.709473\pi$
$173$	2.36187	−	2.36187i	0.179570	−	0.179570i	0.791168	+	0.611598i	$0.209473\pi$
$174$		0			0
$175$	1.28168	−	12.8853i	0.0968861	−	0.974036i
$176$		0			0
$177$			6.51559i			0.489741i
$178$		0			0
$179$	−9.27202	−	9.27202i	−0.693023	−	0.693023i	0.269873	−	0.962896i	$-0.413018\pi$
$179$	−9.27202	−	9.27202i	−0.693023	−	0.693023i	−0.962896	+	0.269873i	$0.913018\pi$
$180$		0			0
$181$	10.5707	−	10.5707i	0.785715	−	0.785715i	−0.195074	−	0.980789i	$-0.562495\pi$
$181$	10.5707	−	10.5707i	0.785715	−	0.785715i	0.980789	+	0.195074i	$0.0624946\pi$
$182$		0			0
$183$	−0.298848			−0.0220915
$184$		0			0
$185$	0.824577	−	16.6206i	0.0606241	−	1.22197i
$186$		0			0
$187$	19.3618	+	19.3618i	1.41587	+	1.41587i
$188$		0			0
$189$	−1.83125	−	1.83125i	−0.133204	−	0.133204i
$190$		0			0
$191$	−8.32988			−0.602729			−0.301364	−	0.953509i	$-0.597442\pi$
$191$	−8.32988			−0.602729			−0.301364	+	0.953509i	$0.597442\pi$
$192$		0			0
$193$		−	5.73404i		−	0.412745i	−0.978473	−	0.206373i	$-0.933834\pi$
$193$		−	5.73404i		−	0.412745i	0.978473	−	0.206373i	$-0.0661659\pi$
$194$		0			0
$195$	−0.978596	+	0.886086i	−0.0700787	+	0.0634539i
$196$		0			0
$197$	−3.23239	−	3.23239i	−0.230298	−	0.230298i	0.582519	−	0.812817i	$-0.302067\pi$
$197$	−3.23239	−	3.23239i	−0.230298	−	0.230298i	−0.812817	+	0.582519i	$0.802067\pi$
$198$		0			0
$199$			19.0599i			1.35112i	0.737303	+	0.675562i	$0.236099\pi$
$199$			19.0599i			1.35112i	−0.737303	+	0.675562i	$0.763901\pi$
$200$		0			0
$201$		−	10.1419i		−	0.715354i
$202$		0			0
$203$	9.67824	+	9.67824i	0.679279	+	0.679279i
$204$		0			0
$205$	−8.56134	+	7.75200i	−0.597950	+	0.541423i
$206$		0			0
$207$			0.281063i			0.0195352i
$208$		0			0
$209$	−39.8899			−2.75924
$210$		0			0
$211$	−4.43719	−	4.43719i	−0.305469	−	0.305469i	0.537680	−	0.843149i	$-0.319301\pi$
$211$	−4.43719	−	4.43719i	−0.305469	−	0.305469i	−0.843149	+	0.537680i	$0.819301\pi$
$212$		0			0
$213$	11.2767	+	11.2767i	0.772670	+	0.772670i
$214$		0			0
$215$	0.418267	−	8.43078i	0.0285256	−	0.574975i
$216$		0			0
$217$	7.90485			0.536616
$218$		0			0
$219$	−7.47142	+	7.47142i	−0.504871	+	0.504871i
$220$		0			0
$221$	−1.83860	−	1.83860i	−0.123678	−	0.123678i
$222$		0			0
$223$			5.10536i			0.341880i	0.985281	+	0.170940i	$0.0546805\pi$
$223$			5.10536i			0.341880i	−0.985281	+	0.170940i	$0.945320\pi$
$224$		0			0
$225$	4.97545	+	0.494901i	0.331696	+	0.0329934i
$226$		0			0
$227$	−15.0563	+	15.0563i	−0.999320	+	0.999320i	−1.00000		0.000680242i	$-0.999783\pi$
$227$	−15.0563	+	15.0563i	−0.999320	+	0.999320i	0.000680242		1.00000i	$0.499783\pi$
$228$		0			0
$229$	−17.5250	+	17.5250i	−1.15809	+	1.15809i	−0.173200	+	0.984887i	$0.555411\pi$
$229$	−17.5250	+	17.5250i	−1.15809	+	1.15809i	−0.984887	+	0.173200i	$0.944589\pi$
$230$		0			0
$231$			16.1012i			1.05938i
$232$		0			0
$233$	−9.15254			−0.599603			−0.299802	−	0.954002i	$-0.596920\pi$
$233$	−9.15254			−0.599603			−0.299802	+	0.954002i	$0.596920\pi$
$234$		0			0
$235$	12.3521	−	11.1844i	0.805759	−	0.729588i
$236$		0			0
$237$	−3.20960	+	3.20960i	−0.208486	+	0.208486i
$238$		0			0
$239$	−12.9198			−0.835713			−0.417857	−	0.908513i	$-0.637219\pi$
$239$	−12.9198			−0.835713			−0.417857	+	0.908513i	$0.637219\pi$
$240$		0			0
$241$	10.7071			0.689703			0.344851	−	0.938657i	$-0.387929\pi$
$241$	10.7071			0.689703			0.344851	+	0.938657i	$0.387929\pi$
$242$		0			0
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		0			0
$245$	−0.439847	−	0.485769i	−0.0281008	−	0.0310346i
$246$		0			0
$247$	3.78796			0.241022
$248$		0			0
$249$		−	6.45814i		−	0.409268i
$250$		0			0
$251$	4.48257	−	4.48257i	0.282937	−	0.282937i	−0.551342	−	0.834279i	$-0.685884\pi$
$251$	4.48257	−	4.48257i	0.282937	−	0.282937i	0.834279	+	0.551342i	$0.185884\pi$
$252$		0			0
$253$	1.23562	−	1.23562i	0.0776827	−	0.0776827i
$254$		0			0
$255$	−0.487979	+	9.83593i	−0.0305584	+	0.615950i
$256$		0			0
$257$			16.9307i			1.05610i	0.849212	+	0.528052i	$0.177078\pi$
$257$			16.9307i			1.05610i	−0.849212	+	0.528052i	$0.822922\pi$
$258$		0			0
$259$	13.6283	+	13.6283i	0.846821	+	0.846821i
$260$		0			0
$261$	−3.73710	+	3.73710i	−0.231321	+	0.231321i
$262$		0			0
$263$	2.07893			0.128192			0.0640962	−	0.997944i	$-0.479584\pi$
$263$	2.07893			0.128192			0.0640962	+	0.997944i	$0.479584\pi$
$264$		0			0
$265$	0.453569	−	9.14234i	0.0278625	−	0.561609i
$266$		0			0
$267$	−7.26517	−	7.26517i	−0.444621	−	0.444621i
$268$		0			0
$269$	16.0709	+	16.0709i	0.979860	+	0.979860i	0.999801	−	0.0199408i	$-0.00634778\pi$
$269$	16.0709	+	16.0709i	0.979860	+	0.979860i	−0.0199408	+	0.999801i	$0.506348\pi$
$270$		0			0
$271$	4.18571			0.254264			0.127132	−	0.991886i	$-0.459423\pi$
$271$	4.18571			0.254264			0.127132	+	0.991886i	$0.459423\pi$
$272$		0			0
$273$		−	1.52898i		−	0.0925378i
$274$		0			0
$275$	−19.6975	−	24.0489i	−1.18781	−	1.45021i
$276$		0			0
$277$	15.8235	+	15.8235i	0.950744	+	0.950744i	0.998843	−	0.0480985i	$-0.0153161\pi$
$277$	15.8235	+	15.8235i	0.950744	+	0.950744i	−0.0480985	+	0.998843i	$0.515316\pi$
$278$		0			0
$279$			3.05233i			0.182738i
$280$		0			0
$281$			12.6546i			0.754911i	0.926028	+	0.377455i	$0.123201\pi$
$281$			12.6546i			0.754911i	−0.926028	+	0.377455i	$0.876799\pi$
$282$		0			0
$283$	−1.54865	−	1.54865i	−0.0920579	−	0.0920579i	0.659578	−	0.751636i	$-0.270735\pi$
$283$	−1.54865	−	1.54865i	−0.0920579	−	0.0920579i	−0.751636	+	0.659578i	$0.770735\pi$
$284$		0			0
$285$	−9.62951	−	10.6349i	−0.570403	−	0.629955i
$286$		0			0
$287$		−	13.3764i		−	0.789583i
$288$		0			0
$289$	−2.39672			−0.140983
$290$		0			0
$291$	−4.79456	−	4.79456i	−0.281062	−	0.281062i
$292$		0			0
$293$	21.2881	+	21.2881i	1.24366	+	1.24366i	0.958470	+	0.285194i	$0.0920582\pi$
$293$	21.2881	+	21.2881i	1.24366	+	1.24366i	0.285194	+	0.958470i	$0.407942\pi$
$294$		0			0
$295$	14.5514	+	0.721922i	0.847215	+	0.0420319i
$296$		0			0
$297$	−6.21722			−0.360760
$298$		0			0
$299$	−0.117335	+	0.117335i	−0.00678565	+	0.00678565i
$300$		0			0
$301$	6.91296	+	6.91296i	0.398456	+	0.398456i
$302$		0			0
$303$		−	14.2502i		−	0.818655i
$304$		0			0
$305$	−0.0331122	+	0.667424i	−0.00189600	+	0.0382166i
$306$		0			0
$307$	−12.2344	+	12.2344i	−0.698255	+	0.698255i	−0.964034	−	0.265779i	$-0.914371\pi$
$307$	−12.2344	+	12.2344i	−0.698255	+	0.698255i	0.265779	+	0.964034i	$0.414371\pi$
$308$		0			0
$309$	3.33383	−	3.33383i	0.189655	−	0.189655i
$310$		0			0
$311$		−	19.4874i		−	1.10503i	−0.833503	−	0.552515i	$-0.813668\pi$
$311$		−	19.4874i		−	1.10503i	0.833503	−	0.552515i	$-0.186332\pi$
$312$		0			0
$313$	−9.73432			−0.550217			−0.275108	−	0.961413i	$-0.588714\pi$
$313$	−9.73432			−0.550217			−0.275108	+	0.961413i	$0.588714\pi$
$314$		0			0
$315$	−4.29266	+	3.88686i	−0.241864	+	0.219000i
$316$		0			0
$317$	−8.46658	+	8.46658i	−0.475530	+	0.475530i	−0.903699	−	0.428168i	$-0.859159\pi$
$317$	−8.46658	+	8.46658i	−0.475530	+	0.475530i	0.428168	+	0.903699i	$0.359159\pi$
$318$		0			0
$319$	32.8583			1.83971
$320$		0			0
$321$	18.3405			1.02367
$322$		0			0
$323$	19.9809	−	19.9809i	1.11177	−	1.11177i
$324$		0			0
$325$	1.87049	+	2.28370i	0.103756	+	0.126677i
$326$		0			0
$327$	−0.541505			−0.0299453
$328$		0			0
$329$			19.2991i			1.06399i
$330$		0			0
$331$	−7.11555	+	7.11555i	−0.391106	+	0.391106i	−0.875082	−	0.483975i	$-0.839192\pi$
$331$	−7.11555	+	7.11555i	−0.391106	+	0.391106i	0.483975	+	0.875082i	$0.339192\pi$
$332$		0			0
$333$	−5.26234	+	5.26234i	−0.288375	+	0.288375i
$334$		0			0
$335$	−22.6501	−	1.12371i	−1.23751	−	0.0613951i
$336$		0			0
$337$			15.8355i			0.862613i	0.902205	+	0.431307i	$0.141947\pi$
$337$			15.8355i			0.862613i	−0.902205	+	0.431307i	$0.858053\pi$
$338$		0			0
$339$	8.61689	+	8.61689i	0.468005	+	0.468005i
$340$		0			0
$341$	13.4188	−	13.4188i	0.726667	−	0.726667i
$342$		0			0
$343$	18.8874			1.01982
$344$		0			0
$345$	0.627703	+	0.0311416i	0.0337944	+	0.00167661i
$346$		0			0
$347$	9.38020	+	9.38020i	0.503555	+	0.503555i	0.912541	−	0.408986i	$-0.134117\pi$
$347$	9.38020	+	9.38020i	0.503555	+	0.503555i	−0.408986	+	0.912541i	$0.634117\pi$
$348$		0			0
$349$	−0.479184	−	0.479184i	−0.0256501	−	0.0256501i	0.694165	−	0.719816i	$-0.255774\pi$
$349$	−0.479184	−	0.479184i	−0.0256501	−	0.0256501i	−0.719816	+	0.694165i	$0.755774\pi$
$350$		0			0
$351$	0.590389			0.0315127
$352$		0			0
$353$			8.95345i			0.476544i	0.971198	+	0.238272i	$0.0765810\pi$
$353$			8.95345i			0.476544i	−0.971198	+	0.238272i	$0.923419\pi$
$354$		0			0
$355$	26.4340	−	23.9351i	1.40297	−	1.27034i
$356$		0			0
$357$	−8.06513	−	8.06513i	−0.426852	−	0.426852i
$358$		0			0
$359$		−	3.47704i		−	0.183511i	−0.995782	−	0.0917556i	$-0.970752\pi$
$359$		−	3.47704i		−	0.183511i	0.995782	−	0.0917556i	$-0.0292478\pi$
$360$		0			0
$361$			22.1655i			1.16661i
$362$		0			0
$363$	19.5542	+	19.5542i	1.02633	+	1.02633i
$364$		0			0
$365$	15.8582	+	17.5139i	0.830058	+	0.916719i
$366$		0			0
$367$			15.1190i			0.789206i	0.918852	+	0.394603i	$0.129118\pi$
$367$			15.1190i			0.789206i	−0.918852	+	0.394603i	$0.870882\pi$
$368$		0			0
$369$	5.16508			0.268883
$370$		0			0
$371$	7.49640	+	7.49640i	0.389194	+	0.389194i
$372$		0			0
$373$	−19.0505	−	19.0505i	−0.986398	−	0.986398i	0.0135107	−	0.999909i	$-0.495699\pi$
$373$	−19.0505	−	19.0505i	−0.986398	−	0.986398i	−0.999909	+	0.0135107i	$0.995699\pi$
$374$		0			0
$375$	1.65655	−	11.0569i	0.0855438	−	0.570978i
$376$		0			0
$377$	−3.12024			−0.160701
$378$		0			0
$379$	−3.52823	+	3.52823i	−0.181233	+	0.181233i	−0.791893	−	0.610660i	$-0.790904\pi$
$379$	−3.52823	+	3.52823i	−0.181233	+	0.181233i	0.610660	+	0.791893i	$0.290904\pi$
$380$		0			0
$381$	4.77511	+	4.77511i	0.244636	+	0.244636i
$382$		0			0
$383$			3.20268i			0.163649i	0.996647	+	0.0818246i	$0.0260747\pi$
$383$			3.20268i			0.163649i	−0.996647	+	0.0818246i	$0.973925\pi$
$384$		0			0
$385$	35.9591	+	1.78400i	1.83265	+	0.0909211i
$386$		0			0
$387$	−2.66933	+	2.66933i	−0.135690	+	0.135690i
$388$		0			0
$389$	−16.9595	+	16.9595i	−0.859882	+	0.859882i	−0.991324	−	0.131441i	$-0.958039\pi$
$389$	−16.9595	+	16.9595i	−0.859882	+	0.859882i	0.131441	+	0.991324i	$0.458039\pi$
$390$		0			0
$391$			1.23785i			0.0626007i
$392$		0			0
$393$	5.59043			0.282000
$394$		0			0
$395$	6.81246	+	7.52370i	0.342772	+	0.378558i
$396$		0			0
$397$	15.8392	−	15.8392i	0.794946	−	0.794946i	−0.187348	−	0.982294i	$-0.559989\pi$
$397$	15.8392	−	15.8392i	0.794946	−	0.794946i	0.982294	+	0.187348i	$0.0599891\pi$
$398$		0			0
$399$	16.6161			0.831845
$400$		0			0
$401$	−10.8608			−0.542364			−0.271182	−	0.962528i	$-0.587414\pi$
$401$	−10.8608			−0.542364			−0.271182	+	0.962528i	$0.587414\pi$
$402$		0			0
$403$	−1.27425	+	1.27425i	−0.0634750	+	0.0634750i
$404$		0			0
$405$	−1.50085	−	1.65754i	−0.0745778	−	0.0823640i
$406$		0			0
$407$	46.2690			2.29347
$408$		0			0
$409$		−	12.5363i		−	0.619880i	−0.950756	−	0.309940i	$-0.899691\pi$
$409$		−	12.5363i		−	0.619880i	0.950756	−	0.309940i	$-0.100309\pi$
$410$		0			0
$411$	3.67355	−	3.67355i	0.181203	−	0.181203i
$412$		0			0
$413$	−11.9316	+	11.9316i	−0.587118	+	0.587118i
$414$		0			0
$415$	−14.4231	−	0.715558i	−0.708002	−	0.0351253i
$416$		0			0
$417$		−	1.38172i		−	0.0676631i
$418$		0			0
$419$	21.6745	+	21.6745i	1.05887	+	1.05887i	0.998155	+	0.0607123i	$0.0193372\pi$
$419$	21.6745	+	21.6745i	1.05887	+	1.05887i	0.0607123	+	0.998155i	$0.480663\pi$
$420$		0			0
$421$	9.02933	−	9.02933i	0.440063	−	0.440063i	−0.451970	−	0.892033i	$-0.649279\pi$
$421$	9.02933	−	9.02933i	0.440063	−	0.440063i	0.892033	+	0.451970i	$0.149279\pi$
$422$		0			0
$423$	−7.45202			−0.362330
$424$		0			0
$425$	21.9127	+	2.17963i	1.06292	+	0.105727i
$426$		0			0
$427$	−0.547265	−	0.547265i	−0.0264840	−	0.0264840i
$428$		0			0
$429$	−2.59549	−	2.59549i	−0.125312	−	0.125312i
$430$		0			0
$431$	−22.1994			−1.06931			−0.534653	−	0.845072i	$-0.679558\pi$
$431$	−22.1994			−1.06931			−0.534653	+	0.845072i	$0.679558\pi$
$432$		0			0
$433$			31.1117i			1.49513i	0.664187	+	0.747566i	$0.268778\pi$
$433$			31.1117i			1.49513i	−0.664187	+	0.747566i	$0.731222\pi$
$434$		0			0
$435$	7.93207	+	8.76021i	0.380314	+	0.420020i
$436$		0			0
$437$	−1.27513	−	1.27513i	−0.0609979	−	0.0609979i
$438$		0			0
$439$			0.460911i			0.0219981i	0.999940	+	0.0109990i	$0.00350117\pi$
$439$			0.460911i			0.0219981i	−0.999940	+	0.0109990i	$0.996499\pi$
$440$		0			0
$441$			0.293066i			0.0139555i
$442$		0			0
$443$	−2.88482	−	2.88482i	−0.137062	−	0.137062i	0.635247	−	0.772309i	$-0.280898\pi$
$443$	−2.88482	−	2.88482i	−0.137062	−	0.137062i	−0.772309	+	0.635247i	$0.780898\pi$
$444$		0			0
$445$	−17.0304	+	15.4205i	−0.807321	+	0.731001i
$446$		0			0
$447$		−	15.9878i		−	0.756198i
$448$		0			0
$449$	3.02196			0.142615			0.0713075	−	0.997454i	$-0.477283\pi$
$449$	3.02196			0.142615			0.0713075	+	0.997454i	$0.477283\pi$
$450$		0			0
$451$	−22.7069	−	22.7069i	−1.06923	−	1.06923i
$452$		0			0
$453$	−2.03143	−	2.03143i	−0.0954447	−	0.0954447i
$454$		0			0
$455$	−3.41469	−	0.169409i	−0.160083	−	0.00794204i
$456$		0			0
$457$	4.69013			0.219395			0.109698	−	0.993965i	$-0.465012\pi$
$457$	4.69013			0.219395			0.109698	+	0.993965i	$0.465012\pi$
$458$		0			0
$459$	3.11422	−	3.11422i	0.145359	−	0.145359i
$460$		0			0
$461$	−20.9304	−	20.9304i	−0.974824	−	0.974824i	0.0248664	−	0.999691i	$-0.492084\pi$
$461$	−20.9304	−	20.9304i	−0.974824	−	0.974824i	−0.999691	+	0.0248664i	$0.992084\pi$
$462$		0			0
$463$			25.5190i			1.18597i	0.805215	+	0.592983i	$0.202050\pi$
$463$			25.5190i			1.18597i	−0.805215	+	0.592983i	$0.797950\pi$
$464$		0			0
$465$	6.81683	+	0.338196i	0.316123	+	0.0156835i
$466$		0			0
$467$	20.6018	−	20.6018i	0.953336	−	0.953336i	−0.0456227	−	0.998959i	$-0.514527\pi$
$467$	20.6018	−	20.6018i	0.953336	−	0.953336i	0.998959	+	0.0456227i	$0.0145272\pi$
$468$		0			0
$469$	18.5723	−	18.5723i	0.857590	−	0.857590i
$470$		0			0
$471$			8.11074i			0.373723i
$472$		0			0
$473$	23.4700			1.07915
$474$		0			0
$475$	−24.8180	+	20.3275i	−1.13873	+	0.932687i
$476$		0			0
$477$	−2.89462	+	2.89462i	−0.132535	+	0.132535i
$478$		0			0
$479$	30.6830			1.40194			0.700972	−	0.713189i	$-0.252750\pi$
$479$	30.6830			1.40194			0.700972	+	0.713189i	$0.252750\pi$
$480$		0			0
$481$	−4.39372			−0.200337
$482$		0			0
$483$	−0.514696	+	0.514696i	−0.0234195	+	0.0234195i
$484$		0			0
$485$	−11.2390	+	10.1766i	−0.510338	+	0.462094i
$486$		0			0
$487$	4.53105			0.205322			0.102661	−	0.994716i	$-0.467264\pi$
$487$	4.53105			0.205322			0.102661	+	0.994716i	$0.467264\pi$
$488$		0			0
$489$			16.9085i			0.764628i
$490$		0			0
$491$	−2.06787	+	2.06787i	−0.0933215	+	0.0933215i	−0.752226	−	0.658905i	$-0.771020\pi$
$491$	−2.06787	+	2.06787i	−0.0933215	+	0.0933215i	0.658905	+	0.752226i	$0.271020\pi$
$492$		0			0
$493$	−16.4588	+	16.4588i	−0.741268	+	0.741268i
$494$		0			0
$495$	−0.688864	+	13.8850i	−0.0309621	+	0.624086i
$496$		0			0
$497$			41.3010i			1.85260i
$498$		0			0
$499$	27.0618	+	27.0618i	1.21145	+	1.21145i	0.970549	+	0.240906i	$0.0774444\pi$
$499$	27.0618	+	27.0618i	1.21145	+	1.21145i	0.240906	+	0.970549i	$0.422556\pi$
$500$		0			0
$501$	6.53130	−	6.53130i	0.291797	−	0.291797i
$502$		0			0
$503$	−8.42170			−0.375505			−0.187753	−	0.982216i	$-0.560120\pi$
$503$	−8.42170			−0.375505			−0.187753	+	0.982216i	$0.560120\pi$
$504$		0			0
$505$	−31.8254	−	1.57892i	−1.41621	−	0.0702609i
$506$		0			0
$507$	−8.94592	−	8.94592i	−0.397302	−	0.397302i
$508$		0			0
$509$	−22.5863	−	22.5863i	−1.00112	−	1.00112i	−0.999999	−	0.00112047i	$-0.999643\pi$
$509$	−22.5863	−	22.5863i	−1.00112	−	1.00112i	−0.00112047	−	0.999999i	$-0.500357\pi$
$510$		0			0
$511$	−27.3640			−1.21051
$512$		0			0
$513$			6.41604i			0.283275i
$514$		0			0
$515$	−7.07612	−	7.81490i	−0.311811	−	0.344365i
$516$		0			0
$517$	32.7609	+	32.7609i	1.44082	+	1.44082i
$518$		0			0
$519$			3.34020i			0.146618i
$520$		0			0
$521$			30.9260i			1.35489i	0.735572	+	0.677447i	$0.236914\pi$
$521$			30.9260i			1.35489i	−0.735572	+	0.677447i	$0.763086\pi$
$522$		0			0
$523$	−26.4425	−	26.4425i	−1.15625	−	1.15625i	−0.985276	−	0.170974i	$-0.945309\pi$
$523$	−26.4425	−	26.4425i	−1.15625	−	1.15625i	−0.170974	−	0.985276i	$-0.554691\pi$
$524$		0			0
$525$	8.20499	+	10.0176i	0.358095	+	0.437202i
$526$		0			0
$527$			13.4430i			0.585585i
$528$		0			0
$529$	−22.9210			−0.996565
$530$		0			0
$531$	−4.60721	−	4.60721i	−0.199936	−	0.199936i
$532$		0			0
$533$	2.15626	+	2.15626i	0.0933978	+	0.0933978i
$534$		0			0
$535$	2.03211	−	40.9602i	0.0878560	−	1.77086i
$536$		0			0
$537$	13.1126			0.565851
$538$		0			0
$539$	1.28839	−	1.28839i	0.0554947	−	0.0554947i
$540$		0			0
$541$	−21.6730	−	21.6730i	−0.931794	−	0.931794i	0.0660242	−	0.997818i	$-0.478969\pi$
$541$	−21.6730	−	21.6730i	−0.931794	−	0.931794i	−0.997818	+	0.0660242i	$0.978969\pi$
$542$		0			0
$543$			14.9492i			0.641533i
$544$		0			0
$545$	−0.0599984	+	1.20935i	−0.00257005	+	0.0518031i
$546$		0			0
$547$	2.92159	−	2.92159i	0.124918	−	0.124918i	−0.641884	−	0.766802i	$-0.721847\pi$
$547$	2.92159	−	2.92159i	0.124918	−	0.124918i	0.766802	+	0.641884i	$0.221847\pi$
$548$		0			0
$549$	0.211318	−	0.211318i	0.00901881	−	0.00901881i
$550$		0			0
$551$		−	33.9091i		−	1.44458i
$552$		0			0
$553$	−11.7552			−0.499880
$554$		0			0
$555$	11.1694	+	12.3356i	0.474116	+	0.523616i
$556$		0			0
$557$	−25.5453	+	25.5453i	−1.08239	+	1.08239i	−0.0861022	+	0.996286i	$0.527441\pi$
$557$	−25.5453	+	25.5453i	−1.08239	+	1.08239i	−0.996286	+	0.0861022i	$0.972559\pi$
$558$		0			0
$559$	−2.22872			−0.0942648
$560$		0			0
$561$	−27.3817			−1.15606
$562$		0			0
$563$	−11.6203	+	11.6203i	−0.489736	+	0.489736i	−0.908223	−	0.418487i	$-0.862561\pi$
$563$	−11.6203	+	11.6203i	−0.489736	+	0.489736i	0.418487	+	0.908223i	$0.362561\pi$
$564$		0			0
$565$	20.1990	−	18.2895i	0.849780	−	0.769447i
$566$		0			0
$567$	2.58977			0.108760
$568$		0			0
$569$		−	13.3498i		−	0.559654i	−0.960050	−	0.279827i	$-0.909723\pi$
$569$		−	13.3498i		−	0.559654i	0.960050	−	0.279827i	$-0.0902771\pi$
$570$		0			0
$571$	23.5430	−	23.5430i	0.985244	−	0.985244i	−0.0146492	−	0.999893i	$-0.504663\pi$
$571$	23.5430	−	23.5430i	0.985244	−	0.985244i	0.999893	+	0.0146492i	$0.00466314\pi$
$572$		0			0
$573$	5.89011	−	5.89011i	0.246063	−	0.246063i
$574$		0			0
$575$	0.139098	−	1.39841i	0.00580080	−	0.0583179i
$576$		0			0
$577$		−	34.7117i		−	1.44507i	−0.691335	−	0.722534i	$-0.742977\pi$
$577$		−	34.7117i		−	1.44507i	0.691335	−	0.722534i	$-0.257023\pi$
$578$		0			0
$579$	4.05458	+	4.05458i	0.168503	+	0.168503i
$580$		0			0
$581$	11.8265	−	11.8265i	0.490644	−	0.490644i
$582$		0			0
$583$	25.4508			1.05407
$584$		0			0
$585$	0.0654147	−	1.31853i	0.00270457	−	0.0545145i
$586$		0			0
$587$	26.8949	+	26.8949i	1.11007	+	1.11007i	0.993140	+	0.116931i	$0.0373057\pi$
$587$	26.8949	+	26.8949i	1.11007	+	1.11007i	0.116931	+	0.993140i	$0.462694\pi$
$588$		0			0
$589$	−13.8479	−	13.8479i	−0.570592	−	0.570592i
$590$		0			0
$591$	4.57128			0.188037
$592$		0			0
$593$		−	8.25028i		−	0.338798i	−0.985548	−	0.169399i	$-0.945817\pi$
$593$		−	8.25028i		−	0.338798i	0.985548	−	0.169399i	$-0.0541827\pi$
$594$		0			0
$595$	−18.9056	+	17.1184i	−0.775055	+	0.701786i
$596$		0			0
$597$	−13.4774	−	13.4774i	−0.551594	−	0.551594i
$598$		0			0
$599$			19.6734i			0.803832i	0.915677	+	0.401916i	$0.131656\pi$
$599$			19.6734i			0.803832i	−0.915677	+	0.401916i	$0.868344\pi$
$600$		0			0
$601$		−	30.0313i		−	1.22500i	−0.790470	−	0.612501i	$-0.790164\pi$
$601$		−	30.0313i		−	1.22500i	0.790470	−	0.612501i	$-0.209836\pi$
$602$		0			0
$603$	7.17140	+	7.17140i	0.292042	+	0.292042i
$604$		0			0
$605$	45.8374	−	41.5042i	1.86355	−	1.68739i
$606$		0			0
$607$			5.52944i			0.224433i	0.993684	+	0.112217i	$0.0357950\pi$
$607$			5.52944i			0.224433i	−0.993684	+	0.112217i	$0.964205\pi$
$608$		0			0
$609$	−13.6871			−0.554629
$610$		0			0
$611$	−3.11098	−	3.11098i	−0.125857	−	0.125857i
$612$		0			0
$613$	28.9851	+	28.9851i	1.17070	+	1.17070i	0.982044	+	0.188653i	$0.0604122\pi$
$613$	28.9851	+	28.9851i	1.17070	+	1.17070i	0.188653	+	0.982044i	$0.439588\pi$
$614$		0			0
$615$	0.572287	−	11.5353i	0.0230768	−	0.465147i
$616$		0			0
$617$	−26.5578			−1.06918			−0.534588	−	0.845113i	$-0.679533\pi$
$617$	−26.5578			−1.06918			−0.534588	+	0.845113i	$0.679533\pi$
$618$		0			0
$619$	−5.91235	+	5.91235i	−0.237638	+	0.237638i	−0.815871	−	0.578234i	$-0.803742\pi$
$619$	−5.91235	+	5.91235i	−0.237638	+	0.237638i	0.578234	+	0.815871i	$0.303742\pi$
$620$		0			0
$621$	−0.198741	−	0.198741i	−0.00797522	−	0.00797522i
$622$		0			0
$623$		−	26.6087i		−	1.06605i
$624$		0			0
$625$	−24.5101	−	4.92471i	−0.980406	−	0.196988i
$626$		0			0
$627$	28.2064	−	28.2064i	1.12646	−	1.12646i
$628$		0			0
$629$	−23.1763	+	23.1763i	−0.924098	+	0.924098i
$630$		0			0
$631$			37.6881i			1.50034i	0.661246	+	0.750169i	$0.270028\pi$
$631$			37.6881i			1.50034i	−0.661246	+	0.750169i	$0.729972\pi$
$632$		0			0
$633$	6.27514			0.249414
$634$		0			0
$635$	11.1934	−	10.1353i	0.444198	−	0.402206i
$636$		0			0
$637$	−0.122346	+	0.122346i	−0.00484751	+	0.00484751i
$638$		0			0
$639$	−15.9477			−0.630882
$640$		0			0
$641$	36.5113			1.44211			0.721055	−	0.692878i	$-0.243657\pi$
$641$	36.5113			1.44211			0.721055	+	0.692878i	$0.243657\pi$
$642$		0			0
$643$	−12.1973	+	12.1973i	−0.481014	+	0.481014i	−0.905455	−	0.424441i	$-0.860471\pi$
$643$	−12.1973	+	12.1973i	−0.481014	+	0.481014i	0.424441	+	0.905455i	$0.360471\pi$
$644$		0			0
$645$	5.66570	+	6.25722i	0.223087	+	0.246378i
$646$		0			0
$647$	−16.5371			−0.650142			−0.325071	−	0.945690i	$-0.605388\pi$
$647$	−16.5371			−0.650142			−0.325071	+	0.945690i	$0.605388\pi$
$648$		0			0
$649$			40.5088i			1.59011i
$650$		0			0
$651$	−5.58957	+	5.58957i	−0.219073	+	0.219073i
$652$		0			0
$653$	−2.73228	+	2.73228i	−0.106923	+	0.106923i	−0.758544	−	0.651622i	$-0.774089\pi$
$653$	−2.73228	+	2.73228i	−0.106923	+	0.106923i	0.651622	+	0.758544i	$0.274089\pi$
$654$		0			0
$655$	0.619416	−	12.4852i	0.0242026	−	0.487838i
$656$		0			0
$657$		−	10.5662i		−	0.412226i
$658$		0			0
$659$	−14.1442	−	14.1442i	−0.550982	−	0.550982i	0.375743	−	0.926724i	$-0.377388\pi$
$659$	−14.1442	−	14.1442i	−0.550982	−	0.550982i	−0.926724	+	0.375743i	$0.877388\pi$
$660$		0			0
$661$	−14.2173	+	14.2173i	−0.552991	+	0.552991i	−0.927303	−	0.374312i	$-0.877879\pi$
$661$	−14.2173	+	14.2173i	−0.552991	+	0.552991i	0.374312	+	0.927303i	$0.377879\pi$
$662$		0			0
$663$	2.60018			0.100982
$664$		0			0
$665$	1.84105	−	37.1091i	0.0713929	−	1.43903i
$666$		0			0
$667$	1.05036	+	1.05036i	0.0406701	+	0.0406701i
$668$		0			0
$669$	−3.61003	−	3.61003i	−0.139572	−	0.139572i
$670$		0			0
$671$	−1.85800			−0.0717274
$672$		0			0
$673$			17.6236i			0.679341i	0.940545	+	0.339670i	$0.110316\pi$
$673$			17.6236i			0.679341i	−0.940545	+	0.339670i	$0.889684\pi$
$674$		0			0
$675$	−3.86812	+	3.16822i	−0.148884	+	0.121945i
$676$		0			0
$677$	−33.4900	−	33.4900i	−1.28713	−	1.28713i	−0.936525	−	0.350601i	$-0.885977\pi$
$677$	−33.4900	−	33.4900i	−1.28713	−	1.28713i	−0.350601	−	0.936525i	$-0.614023\pi$
$678$		0			0
$679$		−	17.5601i		−	0.673893i
$680$		0			0
$681$		−	21.2928i		−	0.815941i
$682$		0			0
$683$	−0.602993	−	0.602993i	−0.0230729	−	0.0230729i	0.695476	−	0.718549i	$-0.255193\pi$
$683$	−0.602993	−	0.602993i	−0.0230729	−	0.0230729i	−0.718549	+	0.695476i	$0.755193\pi$
$684$		0			0
$685$	−7.79720	−	8.61125i	−0.297916	−	0.329019i
$686$		0			0
$687$		−	24.7841i		−	0.945574i
$688$		0			0
$689$	−2.41682			−0.0920736
$690$		0			0
$691$	14.0957	+	14.0957i	0.536226	+	0.536226i	0.922418	−	0.386192i	$-0.126210\pi$
$691$	14.0957	+	14.0957i	0.536226	+	0.536226i	−0.386192	+	0.922418i	$0.626210\pi$
$692$		0			0
$693$	−11.3853	−	11.3853i	−0.432490	−	0.432490i
$694$		0			0
$695$	−3.08582	−	0.153094i	−0.117052	−	0.00580717i
$696$		0			0
$697$	22.7479			0.861637
$698$		0			0
$699$	6.47183	−	6.47183i	0.244787	−	0.244787i
$700$		0			0
$701$	−23.9043	−	23.9043i	−0.902854	−	0.902854i	0.0928282	−	0.995682i	$-0.470409\pi$
$701$	−23.9043	−	23.9043i	−0.902854	−	0.902854i	−0.995682	+	0.0928282i	$0.970409\pi$
$702$		0			0
$703$		−	47.7487i		−	1.80087i
$704$		0			0
$705$	−0.825679	+	16.6428i	−0.0310969	+	0.626803i
$706$		0			0
$707$	26.0957	−	26.0957i	0.981431	−	0.981431i
$708$		0			0
$709$	−30.0855	+	30.0855i	−1.12989	+	1.12989i	−0.139691	+	0.990195i	$0.544611\pi$
$709$	−30.0855	+	30.0855i	−1.12989	+	1.12989i	−0.990195	+	0.139691i	$0.955389\pi$
$710$		0			0
$711$		−	4.53907i		−	0.170228i
$712$		0			0
$713$	0.857896			0.0321285
$714$		0			0
$715$	−6.08415	+	5.50899i	−0.227534	+	0.206024i
$716$		0			0
$717$	9.13569	−	9.13569i	0.341178	−	0.341178i
$718$		0			0
$719$	20.9727			0.782148			0.391074	−	0.920359i	$-0.372104\pi$
$719$	20.9727			0.782148			0.391074	+	0.920359i	$0.372104\pi$
$720$		0			0
$721$	12.2101			0.454729
$722$		0			0
$723$	−7.57104	+	7.57104i	−0.281570	+	0.281570i
$724$		0			0
$725$	20.4432	−	16.7442i	0.759242	−	0.621865i
$726$		0			0
$727$	−19.5823			−0.726269			−0.363134	−	0.931737i	$-0.618293\pi$
$727$	−19.5823			−0.726269			−0.363134	+	0.931737i	$0.618293\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	−11.7562	+	11.7562i	−0.434818	+	0.434818i
$732$		0			0
$733$	−3.95752	+	3.95752i	−0.146174	+	0.146174i	−0.776407	−	0.630232i	$-0.782960\pi$
$733$	−3.95752	+	3.95752i	−0.146174	+	0.146174i	0.630232	+	0.776407i	$0.282960\pi$
$734$		0			0
$735$	0.654510	+	0.0324715i	0.0241420	+	0.00119773i
$736$		0			0
$737$		−	63.0544i		−	2.32264i
$738$		0			0
$739$	1.94684	+	1.94684i	0.0716155	+	0.0716155i	0.742007	−	0.670392i	$-0.233874\pi$
$739$	1.94684	+	1.94684i	0.0716155	+	0.0716155i	−0.670392	+	0.742007i	$0.733874\pi$
$740$		0			0
$741$	−2.67849	+	2.67849i	−0.0983969	+	0.0983969i
$742$		0			0
$743$	−10.5553			−0.387238			−0.193619	−	0.981077i	$-0.562023\pi$
$743$	−10.5553			−0.387238			−0.193619	+	0.981077i	$0.562023\pi$
$744$		0			0
$745$	−35.7060	−	1.77144i	−1.30816	−	0.0649006i
$746$		0			0
$747$	4.56660	+	4.56660i	0.167083	+	0.167083i
$748$		0			0
$749$	33.5860	+	33.5860i	1.22721	+	1.22721i
$750$		0			0
$751$	49.4390			1.80405			0.902027	−	0.431680i	$-0.142079\pi$
$751$	49.4390			1.80405			0.902027	+	0.431680i	$0.142079\pi$
$752$		0			0
$753$			6.33931i			0.231017i
$754$		0			0
$755$	−4.76191	+	4.31174i	−0.173304	+	0.156920i
$756$		0			0
$757$	4.11693	+	4.11693i	0.149632	+	0.149632i	0.777954	−	0.628321i	$-0.216258\pi$
$757$	4.11693	+	4.11693i	0.149632	+	0.149632i	−0.628321	+	0.777954i	$0.716258\pi$
$758$		0			0
$759$			1.74743i			0.0634276i
$760$		0			0
$761$			14.6496i			0.531049i	0.964104	+	0.265525i	$0.0855452\pi$
$761$			14.6496i			0.531049i	−0.964104	+	0.265525i	$0.914455\pi$
$762$		0			0
$763$	−0.991630	−	0.991630i	−0.0358994	−	0.0358994i
$764$		0			0
$765$	−6.61000	−	7.30010i	−0.238985	−	0.263936i
$766$		0			0
$767$		−	3.84673i		−	0.138897i
$768$		0			0
$769$	2.44453			0.0881520			0.0440760	−	0.999028i	$-0.485966\pi$
$769$	2.44453			0.0881520			0.0440760	+	0.999028i	$0.485966\pi$
$770$		0			0
$771$	−11.9718	−	11.9718i	−0.431153	−	0.431153i
$772$		0			0
$773$	−12.2398	−	12.2398i	−0.440234	−	0.440234i	0.451857	−	0.892091i	$-0.350762\pi$
$773$	−12.2398	−	12.2398i	−0.440234	−	0.440234i	−0.892091	+	0.451857i	$0.850762\pi$
$774$		0			0
$775$	1.51060	−	15.1867i	0.0542624	−	0.545522i
$776$		0			0
$777$	−19.2733			−0.691426
$778$		0			0
$779$	−23.4330	+	23.4330i	−0.839576	+	0.839576i
$780$		0			0
$781$	70.1100	+	70.1100i	2.50873	+	2.50873i
$782$		0			0
$783$		−	5.28505i		−	0.188872i
$784$		0			0
$785$	18.1139	+	0.898665i	0.646512	+	0.0320747i
$786$		0			0
$787$	−18.2070	+	18.2070i	−0.649009	+	0.649009i	−0.952753	−	0.303745i	$-0.901763\pi$
$787$	−18.2070	+	18.2070i	−0.649009	+	0.649009i	0.303745	+	0.952753i	$0.401763\pi$
$788$		0			0
$789$	−1.47003	+	1.47003i	−0.0523343	+	0.0523343i
$790$		0			0
$791$			31.5593i			1.12212i
$792$		0			0
$793$	0.176437			0.00626545
$794$		0			0
$795$	6.14389	+	6.78533i	0.217901	+	0.240651i
$796$		0			0
$797$	−5.02164	+	5.02164i	−0.177876	+	0.177876i	−0.790429	−	0.612553i	$-0.790142\pi$
$797$	−5.02164	+	5.02164i	−0.177876	+	0.177876i	0.612553	+	0.790429i	$0.290142\pi$
$798$		0			0
$799$	−32.8200			−1.16109
$800$		0			0
$801$	10.2745			0.363032
$802$		0			0
$803$	−46.4514	+	46.4514i	−1.63923	+	1.63923i
$804$		0			0
$805$	1.09245	+	1.20651i	0.0385039	+	0.0425238i
$806$		0			0
$807$	−22.7277			−0.800053
$808$		0			0
$809$		−	23.6476i		−	0.831404i	−0.909501	−	0.415702i	$-0.863536\pi$
$809$		−	23.6476i		−	0.831404i	0.909501	−	0.415702i	$-0.136464\pi$
$810$		0			0
$811$	24.2614	−	24.2614i	0.851934	−	0.851934i	−0.138438	−	0.990371i	$-0.544208\pi$
$811$	24.2614	−	24.2614i	0.851934	−	0.851934i	0.990371	+	0.138438i	$0.0442080\pi$
$812$		0			0
$813$	−2.95975	+	2.95975i	−0.103803	+	0.103803i
$814$		0			0
$815$	37.7621	+	1.87345i	1.32275	+	0.0656240i
$816$		0			0
$817$		−	24.2205i		−	0.847369i
$818$		0			0
$819$	1.08115	+	1.08115i	0.0377784	+	0.0377784i
$820$		0			0
$821$	38.9257	−	38.9257i	1.35852	−	1.35852i	0.482771	−	0.875746i	$-0.339630\pi$
$821$	38.9257	−	38.9257i	1.35852	−	1.35852i	0.875746	−	0.482771i	$-0.160370\pi$
$822$		0			0
$823$	−38.6799			−1.34830			−0.674148	−	0.738596i	$-0.735489\pi$
$823$	−38.6799			−1.34830			−0.674148	+	0.738596i	$0.735489\pi$
$824$		0			0
$825$	30.9334	+	3.07691i	1.07696	+	0.107124i
$826$		0			0
$827$	−25.6217	−	25.6217i	−0.890955	−	0.890955i	0.103658	−	0.994613i	$-0.466945\pi$
$827$	−25.6217	−	25.6217i	−0.890955	−	0.890955i	−0.994613	+	0.103658i	$0.966945\pi$
$828$		0			0
$829$	14.8962	+	14.8962i	0.517367	+	0.517367i	0.916774	−	0.399407i	$-0.130784\pi$
$829$	14.8962	+	14.8962i	0.517367	+	0.517367i	−0.399407	+	0.916774i	$0.630784\pi$
$830$		0			0
$831$	−22.3779			−0.776279
$832$		0			0
$833$			1.29071i			0.0447205i
$834$		0			0
$835$	−13.8628	−	15.3102i	−0.479743	−	0.529830i
$836$		0			0
$837$	−2.15832	−	2.15832i	−0.0746025	−	0.0746025i
$838$		0			0
$839$			14.5709i			0.503045i	0.967851	+	0.251522i	$0.0809312\pi$
$839$			14.5709i			0.503045i	−0.967851	+	0.251522i	$0.919069\pi$
$840$		0			0
$841$		−	1.06820i		−	0.0368344i
$842$		0			0
$843$	−8.94816	−	8.94816i	−0.308191	−	0.308191i
$844$		0			0
$845$	−20.9703	+	18.9879i	−0.721401	+	0.653204i
$846$		0			0
$847$			71.6171i			2.46079i
$848$		0			0
$849$	2.19013			0.0751650
$850$		0			0
$851$	1.47905	+	1.47905i	0.0507011	+	0.0507011i
$852$		0			0
$853$	11.9474	+	11.9474i	0.409070	+	0.409070i	0.881414	−	0.472344i	$-0.156592\pi$
$853$	11.9474	+	11.9474i	0.409070	+	0.409070i	−0.472344	+	0.881414i	$0.656592\pi$
$854$		0			0
$855$	14.3291	+	0.710893i	0.490044	+	0.0243120i
$856$		0			0
$857$	−18.3405			−0.626498			−0.313249	−	0.949671i	$-0.601417\pi$
$857$	−18.3405			−0.626498			−0.313249	+	0.949671i	$0.601417\pi$
$858$		0			0
$859$	17.4227	−	17.4227i	0.594455	−	0.594455i	−0.344377	−	0.938832i	$-0.611910\pi$
$859$	17.4227	−	17.4227i	0.594455	−	0.594455i	0.938832	+	0.344377i	$0.111910\pi$
$860$		0			0
$861$	9.45853	+	9.45853i	0.322346	+	0.322346i
$862$		0			0
$863$			40.5444i			1.38015i	0.723740	+	0.690073i	$0.242422\pi$
$863$			40.5444i			1.38015i	−0.723740	+	0.690073i	$0.757578\pi$
$864$		0			0
$865$	7.45973	+	0.370091i	0.253638	+	0.0125835i
$866$		0			0
$867$	1.69474	−	1.69474i	0.0575562	−	0.0575562i
$868$		0			0
$869$	−19.9548	+	19.9548i	−0.676921	+	0.676921i
$870$		0			0
$871$			5.98767i			0.202884i
$872$		0			0
$873$	6.78053			0.229486
$874$		0			0
$875$	23.2815	−	17.2144i	0.787060	−	0.581954i
$876$		0			0
$877$	31.0594	−	31.0594i	1.04880	−	1.04880i	0.0500546	−	0.998746i	$-0.484060\pi$
$877$	31.0594	−	31.0594i	1.04880	−	1.04880i	0.998746	−	0.0500546i	$-0.0159395\pi$
$878$		0			0
$879$	−30.1059			−1.01545
$880$		0			0
$881$	−18.0615			−0.608506			−0.304253	−	0.952591i	$-0.598407\pi$
$881$	−18.0615			−0.608506			−0.304253	+	0.952591i	$0.598407\pi$
$882$		0			0
$883$	18.0110	−	18.0110i	0.606117	−	0.606117i	−0.335812	−	0.941929i	$-0.609011\pi$
$883$	18.0110	−	18.0110i	0.606117	−	0.606117i	0.941929	+	0.335812i	$0.109011\pi$
$884$		0			0
$885$	−10.7999	+	9.77891i	−0.363034	+	0.328715i
$886$		0			0
$887$	−37.8699			−1.27155			−0.635774	−	0.771876i	$-0.719319\pi$
$887$	−37.8699			−1.27155			−0.635774	+	0.771876i	$0.719319\pi$
$888$		0			0
$889$			17.4888i			0.586556i
$890$		0			0
$891$	4.39624	−	4.39624i	0.147279	−	0.147279i
$892$		0			0
$893$	33.8085	−	33.8085i	1.13136	−	1.13136i
$894$		0			0
$895$	1.45287	−	29.2847i	0.0485641	−	0.978879i
$896$		0			0
$897$		−	0.165936i		−	0.00554046i
$898$		0			0
$899$	11.4069	+	11.4069i	0.380440	+	0.380440i
$900$		0			0
$901$	−12.7484	+	12.7484i	−0.424710	+	0.424710i
$902$		0			0
$903$	−9.77640			−0.325338
$904$		0			0
$905$	33.3865	+	1.65637i	1.10980	+	0.0550595i
$906$		0			0
$907$	−13.1614	−	13.1614i	−0.437018	−	0.437018i	0.453989	−	0.891007i	$-0.350001\pi$
$907$	−13.1614	−	13.1614i	−0.437018	−	0.437018i	−0.891007	+	0.453989i	$0.850001\pi$
$908$		0			0
$909$	10.0764	+	10.0764i	0.334215	+	0.334215i
$910$		0			0
$911$	4.85931			0.160996			0.0804981	−	0.996755i	$-0.474349\pi$
$911$	4.85931			0.160996			0.0804981	+	0.996755i	$0.474349\pi$
$912$		0			0
$913$		−	40.1517i		−	1.32883i
$914$		0			0
$915$	−0.448526	−	0.495354i	−0.0148278	−	0.0163759i
$916$		0			0
$917$	10.2375	+	10.2375i	0.338071	+	0.338071i
$918$		0			0
$919$			37.6319i			1.24136i	0.784063	+	0.620681i	$0.213144\pi$
$919$			37.6319i			1.24136i	−0.784063	+	0.620681i	$0.786856\pi$
$920$		0			0
$921$		−	17.3021i		−	0.570123i
$922$		0			0
$923$	−6.65767	−	6.65767i	−0.219140	−	0.219140i
$924$		0			0
$925$	28.7869	−	23.5782i	0.946506	−	0.775246i
$926$		0			0
$927$			4.71475i			0.154853i
$928$		0			0
$929$	37.6717			1.23597			0.617984	−	0.786191i	$-0.287950\pi$
$929$	37.6717			1.23597			0.617984	+	0.786191i	$0.287950\pi$
$930$		0			0
$931$	−1.32959	−	1.32959i	−0.0435755	−	0.0435755i
$932$		0			0
$933$	13.7797	+	13.7797i	0.451126	+	0.451126i
$934$		0			0
$935$	−3.03387	+	61.1521i	−0.0992182	+	1.99989i
$936$		0			0
$937$	22.1390			0.723251			0.361625	−	0.932323i	$-0.382222\pi$
$937$	22.1390			0.723251			0.361625	+	0.932323i	$0.382222\pi$
$938$		0			0
$939$	6.88321	−	6.88321i	0.224625	−	0.224625i
$940$		0			0
$941$	6.24976	+	6.24976i	0.203736	+	0.203736i	0.801599	−	0.597862i	$-0.203983\pi$
$941$	6.24976	+	6.24976i	0.203736	+	0.203736i	−0.597862	+	0.801599i	$0.703983\pi$
$942$		0			0
$943$		−	1.45171i		−	0.0472742i
$944$		0			0
$945$	0.286945	−	5.78380i	0.00933433	−	0.188147i
$946$		0			0
$947$	−4.23108	+	4.23108i	−0.137492	+	0.137492i	−0.772503	−	0.635011i	$-0.780995\pi$
$947$	−4.23108	+	4.23108i	−0.137492	+	0.137492i	0.635011	+	0.772503i	$0.280995\pi$
$948$		0			0
$949$	4.41104	−	4.41104i	0.143189	−	0.143189i
$950$		0			0
$951$		−	11.9736i		−	0.388269i
$952$		0			0
$953$	0.585699			0.0189726			0.00948632	−	0.999955i	$-0.496980\pi$
$953$	0.585699			0.0189726			0.00948632	+	0.999955i	$0.496980\pi$
$954$		0			0
$955$	−12.5019	−	13.8071i	−0.404552	−	0.446789i
$956$		0			0
$957$	−23.2344	+	23.2344i	−0.751060	+	0.751060i
$958$		0			0
$959$	13.4544			0.434464
$960$		0			0
$961$	−21.6833			−0.699461
$962$		0			0
$963$	−12.9687	+	12.9687i	−0.417910	+	0.417910i
$964$		0			0
$965$	9.50443	−	8.60594i	0.305958	−	0.277035i
$966$		0			0
$967$	41.5832			1.33722			0.668612	−	0.743611i	$-0.266889\pi$
$967$	41.5832			1.33722			0.668612	+	0.743611i	$0.266889\pi$
$968$		0			0
$969$			28.2573i			0.907756i
$970$		0			0
$971$	−18.8728	+	18.8728i	−0.605656	+	0.605656i	−0.941808	−	0.336152i	$-0.890874\pi$
$971$	−18.8728	+	18.8728i	−0.605656	+	0.605656i	0.336152	+	0.941808i	$0.390874\pi$
$972$		0			0
$973$	2.53027	−	2.53027i	0.0811168	−	0.0811168i
$974$		0			0
$975$	−2.93745	−	0.292184i	−0.0940737	−	0.00935739i
$976$		0			0
$977$		−	17.3929i		−	0.556448i	−0.960516	−	0.278224i	$-0.910254\pi$
$977$		−	17.3929i		−	0.556448i	0.960516	−	0.278224i	$-0.0897457\pi$
$978$		0			0
$979$	−45.1692	−	45.1692i	−1.44361	−	1.44361i
$980$		0			0
$981$	0.382902	−	0.382902i	0.0122251	−	0.0122251i
$982$		0			0
$983$	−28.6927			−0.915154			−0.457577	−	0.889170i	$-0.651283\pi$
$983$	−28.6927			−0.915154			−0.457577	+	0.889170i	$0.651283\pi$
$984$		0			0
$985$	0.506495	−	10.2091i	0.0161383	−	0.325290i
$986$		0			0
$987$	−13.6465	−	13.6465i	−0.434373	−	0.434373i
$988$		0			0
$989$	0.750248	+	0.750248i	0.0238565	+	0.0238565i
$990$		0			0
$991$	5.67944			0.180413			0.0902066	−	0.995923i	$-0.471247\pi$
$991$	5.67944			0.180413			0.0902066	+	0.995923i	$0.471247\pi$
$992$		0			0
$993$		−	10.0629i		−	0.319337i
$994$		0			0
$995$	−31.5927	+	28.6061i	−1.00156	+	0.906875i
$996$		0			0
$997$	−25.4723	−	25.4723i	−0.806717	−	0.806717i	0.177419	−	0.984135i	$-0.443225\pi$
$997$	−25.4723	−	25.4723i	−0.806717	−	0.806717i	−0.984135	+	0.177419i	$0.943225\pi$
$998$		0			0
$999$		−	7.44208i		−	0.235457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1920.2.bl.a.289.3		48
4.3	odd	2		1920.2.bl.b.289.22		48
5.4	even	2	inner	1920.2.bl.a.289.22		48
8.3	odd	2		960.2.bl.a.529.4		48
8.5	even	2		240.2.bl.a.109.10	✓	48
16.3	odd	4		960.2.bl.a.49.22		48
16.5	even	4	inner	1920.2.bl.a.1249.22		48
16.11	odd	4		1920.2.bl.b.1249.3		48
16.13	even	4		240.2.bl.a.229.15	yes	48
20.19	odd	2		1920.2.bl.b.289.3		48
24.5	odd	2		720.2.bm.h.109.15		48
40.19	odd	2		960.2.bl.a.529.22		48
40.29	even	2		240.2.bl.a.109.15	yes	48
48.29	odd	4		720.2.bm.h.469.10		48
80.19	odd	4		960.2.bl.a.49.4		48
80.29	even	4		240.2.bl.a.229.10	yes	48
80.59	odd	4		1920.2.bl.b.1249.22		48
80.69	even	4	inner	1920.2.bl.a.1249.3		48
120.29	odd	2		720.2.bm.h.109.10		48
240.29	odd	4		720.2.bm.h.469.15		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.10	✓	48	8.5	even	2
240.2.bl.a.109.15	yes	48	40.29	even	2
240.2.bl.a.229.10	yes	48	80.29	even	4
240.2.bl.a.229.15	yes	48	16.13	even	4
720.2.bm.h.109.10		48	120.29	odd	2
720.2.bm.h.109.15		48	24.5	odd	2
720.2.bm.h.469.10		48	48.29	odd	4
720.2.bm.h.469.15		48	240.29	odd	4
960.2.bl.a.49.4		48	80.19	odd	4
960.2.bl.a.49.22		48	16.3	odd	4
960.2.bl.a.529.4		48	8.3	odd	2
960.2.bl.a.529.22		48	40.19	odd	2
1920.2.bl.a.289.3		48	1.1	even	1	trivial
1920.2.bl.a.289.22		48	5.4	even	2	inner
1920.2.bl.a.1249.3		48	80.69	even	4	inner
1920.2.bl.a.1249.22		48	16.5	even	4	inner
1920.2.bl.b.289.3		48	20.19	odd	2
1920.2.bl.b.289.22		48	4.3	odd	2
1920.2.bl.b.1249.3		48	16.11	odd	4
1920.2.bl.b.1249.22		48	80.59	odd	4

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:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.bl (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.50085 + 1.65754i) q^{5} -2.58977 q^{7} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{3} +(1.50085 + 1.65754i) q^{5} -2.58977 q^{7} -1.00000i q^{9} +(-4.39624 + 4.39624i) q^{11} +(0.417468 - 0.417468i) q^{13} +(-2.23332 - 0.110799i) q^{15} -4.40417i q^{17} +(4.53682 + 4.53682i) q^{19} +(1.83125 - 1.83125i) q^{21} -0.281063 q^{23} +(-0.494901 + 4.97545i) q^{25} +(0.707107 + 0.707107i) q^{27} +(-3.73710 - 3.73710i) q^{29} -3.05233 q^{31} -6.21722i q^{33} +(-3.88686 - 4.29266i) q^{35} +(-5.26234 - 5.26234i) q^{37} +0.590389i q^{39} +5.16508i q^{41} +(-2.66933 - 2.66933i) q^{43} +(1.65754 - 1.50085i) q^{45} -7.45202i q^{47} -0.293066 q^{49} +(3.11422 + 3.11422i) q^{51} +(-2.89462 - 2.89462i) q^{53} +(-13.8850 - 0.688864i) q^{55} -6.41604 q^{57} +(4.60721 - 4.60721i) q^{59} +(0.211318 + 0.211318i) q^{61} +2.58977i q^{63} +(1.31853 + 0.0654147i) q^{65} +(-7.17140 + 7.17140i) q^{67} +(0.198741 - 0.198741i) q^{69} -15.9477i q^{71} +10.5662 q^{73} +(-3.16822 - 3.86812i) q^{75} +(11.3853 - 11.3853i) q^{77} +4.53907 q^{79} -1.00000 q^{81} +(-4.56660 + 4.56660i) q^{83} +(7.30010 - 6.61000i) q^{85} +5.28505 q^{87} +10.2745i q^{89} +(-1.08115 + 1.08115i) q^{91} +(2.15832 - 2.15832i) q^{93} +(-0.710893 + 14.3291i) q^{95} +6.78053i q^{97} +(4.39624 + 4.39624i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{19} - 48 q^{31} - 24 q^{35} + 48 q^{49} - 8 q^{51} + 32 q^{59} - 16 q^{61} + 16 q^{65} + 16 q^{69} + 16 q^{75} - 96 q^{79} - 48 q^{81} + 32 q^{91} - 48 q^{95}+O(q^{100}) \) 48 * q - 8 * q^19 - 48 * q^31 - 24 * q^35 + 48 * q^49 - 8 * q^51 + 32 * q^59 - 16 * q^61 + 16 * q^65 + 16 * q^69 + 16 * q^75 - 96 * q^79 - 48 * q^81 + 32 * q^91 - 48 * q^95

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