LMFDB - Embedded newform 1575.2.m.c.1457.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1575,2,Mod(1268,1575)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1575.1268"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1575, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1575 = 3^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1575.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.5764383184$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 $ x^12 + 18x^10 + 107x^8 + 240x^6 + 151x^4 + 30*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 315)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1457.5
Root			$0.699479i$ of defining polynomial
Character	$\chi$	$=$	1575.1457
Dual form			1575.2.m.c.1268.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.62044 - 1.62044i) q^{2} -3.25168i q^{4} +(0.707107 + 0.707107i) q^{7} +(-2.02827 - 2.02827i) q^{8} -3.03260i q^{11} +(2.54141 - 2.54141i) q^{13} +2.29165 q^{14} -0.0700407 q^{16} +(-2.70395 + 2.70395i) q^{17} -6.63081i q^{19} +(-4.91416 - 4.91416i) q^{22} +(2.99113 + 2.99113i) q^{23} -8.23642i q^{26} +(2.29928 - 2.29928i) q^{28} +5.10191 q^{29} -3.28427 q^{31} +(3.94304 - 3.94304i) q^{32} +8.76319i q^{34} +(-6.68770 - 6.68770i) q^{37} +(-10.7449 - 10.7449i) q^{38} -7.36835i q^{41} +(-1.74832 + 1.74832i) q^{43} -9.86103 q^{44} +9.69392 q^{46} +(-0.173326 + 0.173326i) q^{47} +1.00000i q^{49} +(-8.26384 - 8.26384i) q^{52} +(8.45145 + 8.45145i) q^{53} -2.86841i q^{56} +(8.26736 - 8.26736i) q^{58} -4.60104 q^{59} -10.5309 q^{61} +(-5.32198 + 5.32198i) q^{62} -12.9190i q^{64} +(8.00655 + 8.00655i) q^{67} +(8.79236 + 8.79236i) q^{68} +5.47459i q^{71} +(5.58444 - 5.58444i) q^{73} -21.6741 q^{74} -21.5612 q^{76} +(2.14437 - 2.14437i) q^{77} -16.1081i q^{79} +(-11.9400 - 11.9400i) q^{82} +(-0.998247 - 0.998247i) q^{83} +5.66612i q^{86} +(-6.15093 + 6.15093i) q^{88} -3.00035 q^{89} +3.59409 q^{91} +(9.72619 - 9.72619i) q^{92} +0.561731i q^{94} +(8.52367 + 8.52367i) q^{97} +(1.62044 + 1.62044i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 24 q^{8} + 4 q^{13} - 4 q^{14} - 20 q^{16} - 8 q^{17} + 8 q^{22} - 8 q^{23} - 32 q^{29} - 48 q^{32} - 4 q^{37} - 24 q^{38} - 40 q^{43} - 64 q^{44} + 16 q^{46} - 24 q^{47} - 36 q^{52} + 40 q^{53}+ \cdots - 12 q^{97}+O(q^{100}) $ 12 * q - 24 * q^8 + 4 * q^13 - 4 * q^14 - 20 * q^16 - 8 * q^17 + 8 * q^22 - 8 * q^23 - 32 * q^29 - 48 * q^32 - 4 * q^37 - 24 * q^38 - 40 * q^43 - 64 * q^44 + 16 * q^46 - 24 * q^47 - 36 * q^52 + 40 * q^53 + 28 * q^58 - 80 * q^59 - 32 * q^61 - 16 * q^62 + 48 * q^67 - 32 * q^68 + 20 * q^73 - 64 * q^74 + 16 * q^76 - 20 * q^82 - 24 * q^83 - 56 * q^89 - 8 * q^92 - 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$1226$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.62044	−	1.62044i	1.14583	−	1.14583i	0.158462	−	0.987365i	$-0.449347\pi$
$2$	1.62044	−	1.62044i	1.14583	−	1.14583i	0.987365	−	0.158462i	$-0.0506534\pi$
$3$		0			0
$3$		0			0
$4$		−	3.25168i		−	1.62584i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$	−2.02827	−	2.02827i	−0.717101	−	0.717101i
$9$		0			0
$10$		0			0
$11$		−	3.03260i		−	0.914363i	−0.889373	−	0.457181i	$-0.848859\pi$
$11$		−	3.03260i		−	0.914363i	0.889373	−	0.457181i	$-0.151141\pi$
$12$		0			0
$13$	2.54141	−	2.54141i	0.704860	−	0.704860i	−0.260590	−	0.965450i	$-0.583917\pi$
$13$	2.54141	−	2.54141i	0.704860	−	0.704860i	0.965450	+	0.260590i	$0.0839170\pi$
$14$	2.29165			0.612470
$15$		0			0
$16$	−0.0700407			−0.0175102
$17$	−2.70395	+	2.70395i	−0.655803	+	0.655803i	−0.954384	−	0.298581i	$-0.903487\pi$
$17$	−2.70395	+	2.70395i	−0.655803	+	0.655803i	0.298581	+	0.954384i	$0.403487\pi$
$18$		0			0
$19$		−	6.63081i		−	1.52121i	−0.649214	−	0.760606i	$-0.724902\pi$
$19$		−	6.63081i		−	1.52121i	0.649214	−	0.760606i	$-0.275098\pi$
$20$		0			0
$21$		0			0
$22$	−4.91416	−	4.91416i	−1.04770	−	1.04770i
$23$	2.99113	+	2.99113i	0.623694	+	0.623694i	0.946474	−	0.322780i	$-0.104617\pi$
$23$	2.99113	+	2.99113i	0.623694	+	0.623694i	−0.322780	+	0.946474i	$0.604617\pi$
$24$		0			0
$25$		0			0
$26$		−	8.23642i		−	1.61529i
$27$		0			0
$28$	2.29928	−	2.29928i	0.434523	−	0.434523i
$29$	5.10191			0.947401			0.473701	−	0.880686i	$-0.342918\pi$
$29$	5.10191			0.947401			0.473701	+	0.880686i	$0.342918\pi$
$30$		0			0
$31$	−3.28427			−0.589873			−0.294937	−	0.955517i	$-0.595298\pi$
$31$	−3.28427			−0.589873			−0.294937	+	0.955517i	$0.595298\pi$
$32$	3.94304	−	3.94304i	0.697038	−	0.697038i
$33$		0			0
$34$			8.76319i			1.50287i
$35$		0			0
$36$		0			0
$37$	−6.68770	−	6.68770i	−1.09945	−	1.09945i	−0.994475	−	0.104976i	$-0.966523\pi$
$37$	−6.68770	−	6.68770i	−1.09945	−	1.09945i	−0.104976	−	0.994475i	$-0.533477\pi$
$38$	−10.7449	−	10.7449i	−1.74305	−	1.74305i
$39$		0			0
$40$		0			0
$41$		−	7.36835i		−	1.15074i	−0.817892	−	0.575371i	$-0.804858\pi$
$41$		−	7.36835i		−	1.15074i	0.817892	−	0.575371i	$-0.195142\pi$
$42$		0			0
$43$	−1.74832	+	1.74832i	−0.266617	+	0.266617i	−0.827736	−	0.561118i	$-0.810371\pi$
$43$	−1.74832	+	1.74832i	−0.266617	+	0.266617i	0.561118	+	0.827736i	$0.310371\pi$
$44$	−9.86103			−1.48661
$45$		0			0
$46$	9.69392			1.42929
$47$	−0.173326	+	0.173326i	−0.0252822	+	0.0252822i	−0.719635	−	0.694353i	$-0.755691\pi$
$47$	−0.173326	+	0.173326i	−0.0252822	+	0.0252822i	0.694353	+	0.719635i	$0.255691\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$		0			0
$52$	−8.26384	−	8.26384i	−1.14599	−	1.14599i
$53$	8.45145	+	8.45145i	1.16090	+	1.16090i	0.984280	+	0.176616i	$0.0565150\pi$
$53$	8.45145	+	8.45145i	1.16090	+	1.16090i	0.176616	+	0.984280i	$0.443485\pi$
$54$		0			0
$55$		0			0
$56$		−	2.86841i		−	0.383307i
$57$		0			0
$58$	8.26736	−	8.26736i	1.08556	−	1.08556i
$59$	−4.60104			−0.599005			−0.299502	−	0.954096i	$-0.596821\pi$
$59$	−4.60104			−0.599005			−0.299502	+	0.954096i	$0.596821\pi$
$60$		0			0
$61$	−10.5309			−1.34834			−0.674171	−	0.738575i	$-0.735499\pi$
$61$	−10.5309			−1.34834			−0.674171	+	0.738575i	$0.735499\pi$
$62$	−5.32198	+	5.32198i	−0.675892	+	0.675892i
$63$		0			0
$64$		−	12.9190i		−	1.61488i
$65$		0			0
$66$		0			0
$67$	8.00655	+	8.00655i	0.978156	+	0.978156i	0.999766	−	0.0216101i	$-0.00687926\pi$
$67$	8.00655	+	8.00655i	0.978156	+	0.978156i	−0.0216101	+	0.999766i	$0.506879\pi$
$68$	8.79236	+	8.79236i	1.06623	+	1.06623i
$69$		0			0
$70$		0			0
$71$			5.47459i			0.649714i	0.945763	+	0.324857i	$0.105316\pi$
$71$			5.47459i			0.649714i	−0.945763	+	0.324857i	$0.894684\pi$
$72$		0			0
$73$	5.58444	−	5.58444i	0.653610	−	0.653610i	−0.300251	−	0.953860i	$-0.597070\pi$
$73$	5.58444	−	5.58444i	0.653610	−	0.653610i	0.953860	+	0.300251i	$0.0970703\pi$
$74$	−21.6741			−2.51956
$75$		0			0
$76$	−21.5612			−2.47324
$77$	2.14437	−	2.14437i	0.244374	−	0.244374i
$78$		0			0
$79$		−	16.1081i		−	1.81230i	−0.422951	−	0.906152i	$-0.639006\pi$
$79$		−	16.1081i		−	1.81230i	0.422951	−	0.906152i	$-0.360994\pi$
$80$		0			0
$81$		0			0
$82$	−11.9400	−	11.9400i	−1.31855	−	1.31855i
$83$	−0.998247	−	0.998247i	−0.109572	−	0.109572i	0.650195	−	0.759767i	$-0.274687\pi$
$83$	−0.998247	−	0.998247i	−0.109572	−	0.109572i	−0.759767	+	0.650195i	$0.774687\pi$
$84$		0			0
$85$		0			0
$86$			5.66612i			0.610994i
$87$		0			0
$88$	−6.15093	+	6.15093i	−0.655691	+	0.655691i
$89$	−3.00035			−0.318037			−0.159018	−	0.987276i	$-0.550833\pi$
$89$	−3.00035			−0.318037			−0.159018	+	0.987276i	$0.550833\pi$
$90$		0			0
$91$	3.59409			0.376763
$92$	9.72619	−	9.72619i	1.01403	−	1.01403i
$93$		0			0
$94$			0.561731i			0.0579381i
$95$		0			0
$96$		0			0
$97$	8.52367	+	8.52367i	0.865448	+	0.865448i	0.991964	−	0.126517i	$-0.0403797\pi$
$97$	8.52367	+	8.52367i	0.865448	+	0.865448i	−0.126517	+	0.991964i	$0.540380\pi$
$98$	1.62044	+	1.62044i	0.163690	+	0.163690i
$99$		0			0
$100$		0			0
$101$			16.8630i			1.67793i	0.544183	+	0.838966i	$0.316840\pi$
$101$			16.8630i			1.67793i	−0.544183	+	0.838966i	$0.683160\pi$
$102$		0			0
$103$	1.24992	−	1.24992i	0.123158	−	0.123158i	−0.642841	−	0.766000i	$-0.722244\pi$
$103$	1.24992	−	1.24992i	0.123158	−	0.123158i	0.766000	+	0.642841i	$0.222244\pi$
$104$	−10.3093			−1.01091
$105$		0			0
$106$	27.3902			2.66037
$107$	−14.1755	+	14.1755i	−1.37040	+	1.37040i	−0.510544	+	0.859852i	$0.670556\pi$
$107$	−14.1755	+	14.1755i	−1.37040	+	1.37040i	−0.859852	+	0.510544i	$0.829444\pi$
$108$		0			0
$109$			0.574370i			0.0550146i	0.999622	+	0.0275073i	$0.00875696\pi$
$109$			0.574370i			0.0550146i	−0.999622	+	0.0275073i	$0.991243\pi$
$110$		0			0
$111$		0			0
$112$	−0.0495262	−	0.0495262i	−0.00467979	−	0.00467979i
$113$	6.98481	+	6.98481i	0.657076	+	0.657076i	0.954687	−	0.297611i	$-0.0961899\pi$
$113$	6.98481	+	6.98481i	0.657076	+	0.657076i	−0.297611	+	0.954687i	$0.596190\pi$
$114$		0			0
$115$		0			0
$116$		−	16.5898i		−	1.54032i
$117$		0			0
$118$	−7.45573	+	7.45573i	−0.686356	+	0.686356i
$119$	−3.82396			−0.350542
$120$		0			0
$121$	1.80334			0.163940
$122$	−17.0647	+	17.0647i	−1.54497	+	1.54497i
$123$		0			0
$124$			10.6794i			0.959038i
$125$		0			0
$126$		0			0
$127$	3.96367	+	3.96367i	0.351718	+	0.351718i	0.860749	−	0.509030i	$-0.169996\pi$
$127$	3.96367	+	3.96367i	0.351718	+	0.351718i	−0.509030	+	0.860749i	$0.669996\pi$
$128$	−13.0485	−	13.0485i	−1.15333	−	1.15333i
$129$		0			0
$130$		0			0
$131$			19.0779i			1.66684i	0.552640	+	0.833420i	$0.313620\pi$
$131$			19.0779i			1.66684i	−0.552640	+	0.833420i	$0.686380\pi$
$132$		0			0
$133$	4.68869	−	4.68869i	0.406561	−	0.406561i
$134$	25.9483			2.24160
$135$		0			0
$136$	10.9687			0.940555
$137$	−0.370993	+	0.370993i	−0.0316961	+	0.0316961i	−0.722777	−	0.691081i	$-0.757135\pi$
$137$	−0.370993	+	0.370993i	−0.0316961	+	0.0316961i	0.691081	+	0.722777i	$0.257135\pi$
$138$		0			0
$139$			16.3127i			1.38363i	0.722076	+	0.691814i	$0.243188\pi$
$139$			16.3127i			1.38363i	−0.722076	+	0.691814i	$0.756812\pi$
$140$		0			0
$141$		0			0
$142$	8.87127	+	8.87127i	0.744460	+	0.744460i
$143$	−7.70707	−	7.70707i	−0.644498	−	0.644498i
$144$		0			0
$145$		0			0
$146$		−	18.0986i		−	1.49785i
$147$		0			0
$148$	−21.7462	+	21.7462i	−1.78753	+	1.78753i
$149$	11.9577			0.979611			0.489806	−	0.871832i	$-0.337068\pi$
$149$	11.9577			0.979611			0.489806	+	0.871832i	$0.337068\pi$
$150$		0			0
$151$	−1.85059			−0.150599			−0.0752994	−	0.997161i	$-0.523991\pi$
$151$	−1.85059			−0.150599			−0.0752994	+	0.997161i	$0.523991\pi$
$152$	−13.4491	+	13.4491i	−1.09086	+	1.09086i
$153$		0			0
$154$		−	6.94967i		−	0.560020i
$155$		0			0
$156$		0			0
$157$	−2.71202	−	2.71202i	−0.216443	−	0.216443i	0.590555	−	0.806998i	$-0.298909\pi$
$157$	−2.71202	−	2.71202i	−0.216443	−	0.216443i	−0.806998	+	0.590555i	$0.798909\pi$
$158$	−26.1023	−	26.1023i	−2.07659	−	2.07659i
$159$		0			0
$160$		0			0
$161$			4.23010i			0.333379i
$162$		0			0
$163$	5.24571	−	5.24571i	0.410876	−	0.410876i	−0.471168	−	0.882043i	$-0.656167\pi$
$163$	5.24571	−	5.24571i	0.410876	−	0.410876i	0.882043	+	0.471168i	$0.156167\pi$
$164$	−23.9595			−1.87092
$165$		0			0
$166$	−3.23520			−0.251101
$167$	−8.01311	+	8.01311i	−0.620073	+	0.620073i	−0.945550	−	0.325477i	$-0.894475\pi$
$167$	−8.01311	+	8.01311i	−0.620073	+	0.620073i	0.325477	+	0.945550i	$0.394475\pi$
$168$		0			0
$169$			0.0824845i			0.00634496i
$170$		0			0
$171$		0			0
$172$	5.68498	+	5.68498i	0.433476	+	0.433476i
$173$	−0.181459	−	0.181459i	−0.0137961	−	0.0137961i	0.700175	−	0.713971i	$-0.253105\pi$
$173$	−0.181459	−	0.181459i	−0.0137961	−	0.0137961i	−0.713971	+	0.700175i	$0.753105\pi$
$174$		0			0
$175$		0			0
$176$			0.212405i			0.0160106i
$177$		0			0
$178$	−4.86190	+	4.86190i	−0.364415	+	0.364415i
$179$	12.4629			0.931523			0.465762	−	0.884910i	$-0.345780\pi$
$179$	12.4629			0.931523			0.465762	+	0.884910i	$0.345780\pi$
$180$		0			0
$181$	14.2000			1.05548			0.527738	−	0.849407i	$-0.323040\pi$
$181$	14.2000			1.05548			0.527738	+	0.849407i	$0.323040\pi$
$182$	5.82403	−	5.82403i	0.431706	−	0.431706i
$183$		0			0
$184$		−	12.1336i		−	0.894504i
$185$		0			0
$186$		0			0
$187$	8.19999	+	8.19999i	0.599642	+	0.599642i
$188$	0.563601	+	0.563601i	0.0411048	+	0.0411048i
$189$		0			0
$190$		0			0
$191$		−	10.3158i		−	0.746425i	−0.927746	−	0.373212i	$-0.878256\pi$
$191$		−	10.3158i		−	0.746425i	0.927746	−	0.373212i	$-0.121744\pi$
$192$		0			0
$193$	−0.266580	+	0.266580i	−0.0191888	+	0.0191888i	−0.716636	−	0.697447i	$-0.754319\pi$
$193$	−0.266580	+	0.266580i	−0.0191888	+	0.0191888i	0.697447	+	0.716636i	$0.254319\pi$
$194$	27.6243			1.98331
$195$		0			0
$196$	3.25168			0.232263
$197$	6.98481	−	6.98481i	0.497647	−	0.497647i	−0.413058	−	0.910705i	$-0.635539\pi$
$197$	6.98481	−	6.98481i	0.497647	−	0.497647i	0.910705	+	0.413058i	$0.135539\pi$
$198$		0			0
$199$		−	16.7701i		−	1.18880i	−0.804168	−	0.594402i	$-0.797389\pi$
$199$		−	16.7701i		−	1.18880i	0.804168	−	0.594402i	$-0.202611\pi$
$200$		0			0
$201$		0			0
$202$	27.3256	+	27.3256i	1.92262	+	1.92262i
$203$	3.60760	+	3.60760i	0.253204	+	0.253204i
$204$		0			0
$205$		0			0
$206$		−	4.05086i		−	0.282236i
$207$		0			0
$208$	−0.178002	+	0.178002i	−0.0123422	+	0.0123422i
$209$	−20.1086			−1.39094
$210$		0			0
$211$	16.9651			1.16793			0.583963	−	0.811780i	$-0.301501\pi$
$211$	16.9651			1.16793			0.583963	+	0.811780i	$0.301501\pi$
$212$	27.4814	−	27.4814i	1.88743	−	1.88743i
$213$		0			0
$214$			45.9411i			3.14047i
$215$		0			0
$216$		0			0
$217$	−2.32233	−	2.32233i	−0.157650	−	0.157650i
$218$	0.930734	+	0.930734i	0.0630372	+	0.0630372i
$219$		0			0
$220$		0			0
$221$			13.7437i			0.924499i
$222$		0			0
$223$	−13.3495	+	13.3495i	−0.893947	+	0.893947i	−0.994892	−	0.100945i	$-0.967813\pi$
$223$	−13.3495	+	13.3495i	−0.893947	+	0.893947i	0.100945	+	0.994892i	$0.467813\pi$
$224$	5.57630			0.372582
$225$		0			0
$226$	22.6370			1.50579
$227$	11.9255	−	11.9255i	0.791525	−	0.791525i	−0.190217	−	0.981742i	$-0.560919\pi$
$227$	11.9255	−	11.9255i	0.791525	−	0.791525i	0.981742	+	0.190217i	$0.0609193\pi$
$228$		0			0
$229$		−	8.42386i		−	0.556665i	−0.960485	−	0.278332i	$-0.910218\pi$
$229$		−	8.42386i		−	0.556665i	0.960485	−	0.278332i	$-0.0897816\pi$
$230$		0			0
$231$		0			0
$232$	−10.3481	−	10.3481i	−0.679383	−	0.679383i
$233$	0.822128	+	0.822128i	0.0538594	+	0.0538594i	0.733524	−	0.679664i	$-0.237874\pi$
$233$	0.822128	+	0.822128i	0.0538594	+	0.0538594i	−0.679664	+	0.733524i	$0.737874\pi$
$234$		0			0
$235$		0			0
$236$			14.9611i			0.973884i
$237$		0			0
$238$	−6.19651	+	6.19651i	−0.401660	+	0.401660i
$239$	−11.4492			−0.740586			−0.370293	−	0.928915i	$-0.620743\pi$
$239$	−11.4492			−0.740586			−0.370293	+	0.928915i	$0.620743\pi$
$240$		0			0
$241$	−22.9679			−1.47949			−0.739747	−	0.672885i	$-0.765055\pi$
$241$	−22.9679			−1.47949			−0.739747	+	0.672885i	$0.765055\pi$
$242$	2.92222	−	2.92222i	0.187847	−	0.187847i
$243$		0			0
$244$			34.2430i			2.19218i
$245$		0			0
$246$		0			0
$247$	−16.8516	−	16.8516i	−1.07224	−	1.07224i
$248$	6.66139	+	6.66139i	0.422999	+	0.422999i
$249$		0			0
$250$		0			0
$251$		−	3.83285i		−	0.241928i	−0.992657	−	0.120964i	$-0.961402\pi$
$251$		−	3.83285i		−	0.241928i	0.992657	−	0.120964i	$-0.0385985\pi$
$252$		0			0
$253$	9.07090	−	9.07090i	0.570283	−	0.570283i
$254$	12.8458			0.806017
$255$		0			0
$256$	−16.4506			−1.02816
$257$	−14.4687	+	14.4687i	−0.902532	+	0.902532i	−0.995655	−	0.0931230i	$-0.970315\pi$
$257$	−14.4687	+	14.4687i	−0.902532	+	0.902532i	0.0931230	+	0.995655i	$0.470315\pi$
$258$		0			0
$259$		−	9.45784i		−	0.587681i
$260$		0			0
$261$		0			0
$262$	30.9146	+	30.9146i	1.90991	+	1.90991i
$263$	−14.4785	−	14.4785i	−0.892783	−	0.892783i	0.102002	−	0.994784i	$-0.467475\pi$
$263$	−14.4785	−	14.4785i	−0.892783	−	0.892783i	−0.994784	+	0.102002i	$0.967475\pi$
$264$		0			0
$265$		0			0
$266$		−	15.1955i		−	0.931697i
$267$		0			0
$268$	26.0347	−	26.0347i	1.59032	−	1.59032i
$269$	−6.60739			−0.402860			−0.201430	−	0.979503i	$-0.564559\pi$
$269$	−6.60739			−0.402860			−0.201430	+	0.979503i	$0.564559\pi$
$270$		0			0
$271$	22.9409			1.39356			0.696780	−	0.717285i	$-0.254615\pi$
$271$	22.9409			1.39356			0.696780	+	0.717285i	$0.254615\pi$
$272$	0.189386	−	0.189386i	0.0114832	−	0.0114832i
$273$		0			0
$274$			1.20235i			0.0726365i
$275$		0			0
$276$		0			0
$277$	13.9239	+	13.9239i	0.836605	+	0.836605i	0.988410	−	0.151806i	$-0.0485088\pi$
$277$	13.9239	+	13.9239i	0.836605	+	0.836605i	−0.151806	+	0.988410i	$0.548509\pi$
$278$	26.4339	+	26.4339i	1.58540	+	1.58540i
$279$		0			0
$280$		0			0
$281$			14.7206i			0.878156i	0.898449	+	0.439078i	$0.144695\pi$
$281$			14.7206i			0.878156i	−0.898449	+	0.439078i	$0.855305\pi$
$282$		0			0
$283$	−8.42004	+	8.42004i	−0.500520	+	0.500520i	−0.911599	−	0.411080i	$-0.865152\pi$
$283$	−8.42004	+	8.42004i	−0.500520	+	0.500520i	0.411080	+	0.911599i	$0.365152\pi$
$284$	17.8016			1.05633
$285$		0			0
$286$	−24.9778			−1.47697
$287$	5.21021	−	5.21021i	0.307549	−	0.307549i
$288$		0			0
$289$			2.37734i			0.139844i
$290$		0			0
$291$		0			0
$292$	−18.1588	−	18.1588i	−1.06266	−	1.06266i
$293$	21.6859	+	21.6859i	1.26690	+	1.26690i	0.947680	+	0.319221i	$0.103421\pi$
$293$	21.6859	+	21.6859i	1.26690	+	1.26690i	0.319221	+	0.947680i	$0.396579\pi$
$294$		0			0
$295$		0			0
$296$			27.1289i			1.57684i
$297$		0			0
$298$	19.3767	−	19.3767i	1.12246	−	1.12246i
$299$	15.2034			0.879234
$300$		0			0
$301$	−2.47250			−0.142513
$302$	−2.99878	+	2.99878i	−0.172560	+	0.172560i
$303$		0			0
$304$			0.464426i			0.0266367i
$305$		0			0
$306$		0			0
$307$	−8.85014	−	8.85014i	−0.505104	−	0.505104i	0.407915	−	0.913020i	$-0.366256\pi$
$307$	−8.85014	−	8.85014i	−0.505104	−	0.505104i	−0.913020	+	0.407915i	$0.866256\pi$
$308$	−6.97280	−	6.97280i	−0.397312	−	0.397312i
$309$		0			0
$310$		0			0
$311$		−	12.8964i		−	0.731286i	−0.930755	−	0.365643i	$-0.880849\pi$
$311$		−	12.8964i		−	0.731286i	0.930755	−	0.365643i	$-0.119151\pi$
$312$		0			0
$313$	1.54078	−	1.54078i	0.0870900	−	0.0870900i	−0.662220	−	0.749310i	$-0.730385\pi$
$313$	1.54078	−	1.54078i	0.0870900	−	0.0870900i	0.749310	+	0.662220i	$0.230385\pi$
$314$	−8.78935			−0.496012
$315$		0			0
$316$	−52.3784			−2.94651
$317$	1.84855	−	1.84855i	0.103825	−	0.103825i	−0.653286	−	0.757111i	$-0.726610\pi$
$317$	1.84855	−	1.84855i	0.103825	−	0.103825i	0.757111	+	0.653286i	$0.226610\pi$
$318$		0			0
$319$		−	15.4721i		−	0.866269i
$320$		0			0
$321$		0			0
$322$	6.85464	+	6.85464i	0.381994	+	0.381994i
$323$	17.9294	+	17.9294i	0.997616	+	0.997616i
$324$		0			0
$325$		0			0
$326$		−	17.0007i		−	0.941584i
$327$		0			0
$328$	−14.9450	+	14.9450i	−0.825199	+	0.825199i
$329$	−0.245120			−0.0135139
$330$		0			0
$331$	−9.39910			−0.516621			−0.258310	−	0.966062i	$-0.583166\pi$
$331$	−9.39910			−0.516621			−0.258310	+	0.966062i	$0.583166\pi$
$332$	−3.24597	+	3.24597i	−0.178146	+	0.178146i
$333$		0			0
$334$			25.9696i			1.42099i
$335$		0			0
$336$		0			0
$337$	−18.1546	−	18.1546i	−0.988942	−	0.988942i	0.0109971	−	0.999940i	$-0.496499\pi$
$337$	−18.1546	−	18.1546i	−0.988942	−	0.988942i	−0.999940	+	0.0109971i	$0.996499\pi$
$338$	0.133661	+	0.133661i	0.00727022	+	0.00727022i
$339$		0			0
$340$		0			0
$341$			9.95988i			0.539358i
$342$		0			0
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	7.09215			0.382383
$345$		0			0
$346$	−0.588089			−0.0316158
$347$	−6.52324	+	6.52324i	−0.350186	+	0.350186i	−0.860179	−	0.509993i	$-0.829648\pi$
$347$	−6.52324	+	6.52324i	−0.350186	+	0.350186i	0.509993	+	0.860179i	$0.329648\pi$
$348$		0			0
$349$			28.6246i			1.53224i	0.642697	+	0.766121i	$0.277816\pi$
$349$			28.6246i			1.53224i	−0.642697	+	0.766121i	$0.722184\pi$
$350$		0			0
$351$		0			0
$352$	−11.9577	−	11.9577i	−0.637345	−	0.637345i
$353$	7.79446	+	7.79446i	0.414857	+	0.414857i	0.883427	−	0.468570i	$-0.155230\pi$
$353$	7.79446	+	7.79446i	0.414857	+	0.414857i	−0.468570	+	0.883427i	$0.655230\pi$
$354$		0			0
$355$		0			0
$356$			9.75617i			0.517076i
$357$		0			0
$358$	20.1955	−	20.1955i	1.06736	−	1.06736i
$359$	−0.715285			−0.0377513			−0.0188756	−	0.999822i	$-0.506009\pi$
$359$	−0.715285			−0.0377513			−0.0188756	+	0.999822i	$0.506009\pi$
$360$		0			0
$361$	−24.9676			−1.31409
$362$	23.0103	−	23.0103i	1.20939	−	1.20939i
$363$		0			0
$364$		−	11.6868i		−	0.612556i
$365$		0			0
$366$		0			0
$367$	−13.6098	−	13.6098i	−0.710427	−	0.710427i	0.256198	−	0.966624i	$-0.417530\pi$
$367$	−13.6098	−	13.6098i	−0.710427	−	0.710427i	−0.966624	+	0.256198i	$0.917530\pi$
$368$	−0.209501	−	0.209501i	−0.0109210	−	0.0109210i
$369$		0			0
$370$		0			0
$371$			11.9522i			0.620525i
$372$		0			0
$373$	−22.2558	+	22.2558i	−1.15236	+	1.15236i	−0.166284	+	0.986078i	$0.553177\pi$
$373$	−22.2558	+	22.2558i	−1.15236	+	1.15236i	−0.986078	+	0.166284i	$0.946823\pi$
$374$	26.5752			1.37417
$375$		0			0
$376$	0.703105			0.0362599
$377$	12.9660	−	12.9660i	0.667785	−	0.667785i
$378$		0			0
$379$			0.695620i			0.0357316i	0.999840	+	0.0178658i	$0.00568717\pi$
$379$			0.695620i			0.0357316i	−0.999840	+	0.0178658i	$0.994313\pi$
$380$		0			0
$381$		0			0
$382$	−16.7162	−	16.7162i	−0.855273	−	0.855273i
$383$	7.23025	+	7.23025i	0.369448	+	0.369448i	0.867276	−	0.497828i	$-0.165869\pi$
$383$	7.23025	+	7.23025i	0.369448	+	0.369448i	−0.497828	+	0.867276i	$0.665869\pi$
$384$		0			0
$385$		0			0
$386$			0.863955i			0.0439741i
$387$		0			0
$388$	27.7162	−	27.7162i	1.40708	−	1.40708i
$389$	−20.5075			−1.03977			−0.519885	−	0.854236i	$-0.674025\pi$
$389$	−20.5075			−1.03977			−0.519885	+	0.854236i	$0.674025\pi$
$390$		0			0
$391$	−16.1757			−0.818042
$392$	2.02827	−	2.02827i	0.102443	−	0.102443i
$393$		0			0
$394$		−	22.6370i		−	1.14044i
$395$		0			0
$396$		0			0
$397$	−8.69971	−	8.69971i	−0.436626	−	0.436626i	0.454249	−	0.890875i	$-0.349908\pi$
$397$	−8.69971	−	8.69971i	−0.436626	−	0.436626i	−0.890875	+	0.454249i	$0.849908\pi$
$398$	−27.1751	−	27.1751i	−1.36216	−	1.36216i
$399$		0			0
$400$		0			0
$401$		−	1.07299i		−	0.0535826i	−0.999641	−	0.0267913i	$-0.991471\pi$
$401$		−	1.07299i		−	0.0535826i	0.999641	−	0.0267913i	$-0.00852896\pi$
$402$		0			0
$403$	−8.34668	+	8.34668i	−0.415778	+	0.415778i
$404$	54.8330			2.72805
$405$		0			0
$406$	11.6918			0.580255
$407$	−20.2811	+	20.2811i	−1.00530	+	1.00530i
$408$		0			0
$409$			17.9019i			0.885193i	0.896721	+	0.442596i	$0.145943\pi$
$409$			17.9019i			0.885193i	−0.896721	+	0.442596i	$0.854057\pi$
$410$		0			0
$411$		0			0
$412$	−4.06434	−	4.06434i	−0.200236	−	0.200236i
$413$	−3.25343	−	3.25343i	−0.160091	−	0.160091i
$414$		0			0
$415$		0			0
$416$		−	20.0418i		−	0.982628i
$417$		0			0
$418$	−32.5848	+	32.5848i	−1.59378	+	1.59378i
$419$	−14.8415			−0.725057			−0.362528	−	0.931973i	$-0.618086\pi$
$419$	−14.8415			−0.725057			−0.362528	+	0.931973i	$0.618086\pi$
$420$		0			0
$421$	17.4595			0.850925			0.425463	−	0.904976i	$-0.360111\pi$
$421$	17.4595			0.850925			0.425463	+	0.904976i	$0.360111\pi$
$422$	27.4910	−	27.4910i	1.33824	−	1.33824i
$423$		0			0
$424$		−	34.2836i		−	1.66496i
$425$		0			0
$426$		0			0
$427$	−7.44646	−	7.44646i	−0.360359	−	0.360359i
$428$	46.0941	+	46.0941i	2.22804	+	2.22804i
$429$		0			0
$430$		0			0
$431$		−	2.29829i		−	0.110705i	−0.998467	−	0.0553524i	$-0.982372\pi$
$431$		−	2.29829i		−	0.110705i	0.998467	−	0.0553524i	$-0.0176282\pi$
$432$		0			0
$433$	−2.80323	+	2.80323i	−0.134715	+	0.134715i	−0.771249	−	0.636534i	$-0.780367\pi$
$433$	−2.80323	+	2.80323i	−0.134715	+	0.134715i	0.636534	+	0.771249i	$0.280367\pi$
$434$	−7.52642			−0.361280
$435$		0			0
$436$	1.86766			0.0894449
$437$	19.8336	−	19.8336i	0.948771	−	0.948771i
$438$		0			0
$439$		−	15.5162i		−	0.740548i	−0.928923	−	0.370274i	$-0.879264\pi$
$439$		−	15.5162i		−	0.740548i	0.928923	−	0.370274i	$-0.120736\pi$
$440$		0			0
$441$		0			0
$442$	22.2708	+	22.2708i	1.05932	+	1.05932i
$443$	−6.66424	−	6.66424i	−0.316628	−	0.316628i	0.530843	−	0.847470i	$-0.321876\pi$
$443$	−6.66424	−	6.66424i	−0.316628	−	0.316628i	−0.847470	+	0.530843i	$0.821876\pi$
$444$		0			0
$445$		0			0
$446$			43.2641i			2.04862i
$447$		0			0
$448$	9.13514	−	9.13514i	0.431595	−	0.431595i
$449$	16.4469			0.776178			0.388089	−	0.921622i	$-0.373135\pi$
$449$	16.4469			0.776178			0.388089	+	0.921622i	$0.373135\pi$
$450$		0			0
$451$	−22.3452			−1.05220
$452$	22.7123	−	22.7123i	1.06830	−	1.06830i
$453$		0			0
$454$		−	38.6493i		−	1.81390i
$455$		0			0
$456$		0			0
$457$	12.2198	+	12.2198i	0.571619	+	0.571619i	0.932581	−	0.360961i	$-0.117551\pi$
$457$	12.2198	+	12.2198i	0.571619	+	0.571619i	−0.360961	+	0.932581i	$0.617551\pi$
$458$	−13.6504	−	13.6504i	−0.637841	−	0.637841i
$459$		0			0
$460$		0			0
$461$			10.3252i			0.480891i	0.970663	+	0.240446i	$0.0772936\pi$
$461$			10.3252i			0.480891i	−0.970663	+	0.240446i	$0.922706\pi$
$462$		0			0
$463$	13.2678	−	13.2678i	0.616605	−	0.616605i	−0.328054	−	0.944659i	$-0.606393\pi$
$463$	13.2678	−	13.2678i	0.616605	−	0.616605i	0.944659	+	0.328054i	$0.106393\pi$
$464$	−0.357341			−0.0165892
$465$		0			0
$466$	2.66443			0.123427
$467$	9.71989	−	9.71989i	0.449783	−	0.449783i	−0.445499	−	0.895282i	$-0.646974\pi$
$467$	9.71989	−	9.71989i	0.449783	−	0.449783i	0.895282	+	0.445499i	$0.146974\pi$
$468$		0			0
$469$			11.3230i			0.522847i
$470$		0			0
$471$		0			0
$472$	9.33215	+	9.33215i	0.429547	+	0.429547i
$473$	5.30197	+	5.30197i	0.243785	+	0.243785i
$474$		0			0
$475$		0			0
$476$			12.4343i			0.569924i
$477$		0			0
$478$	−18.5527	+	18.5527i	−0.848583	+	0.848583i
$479$	1.57498			0.0719627			0.0359814	−	0.999352i	$-0.488544\pi$
$479$	1.57498			0.0719627			0.0359814	+	0.999352i	$0.488544\pi$
$480$		0			0
$481$	−33.9924			−1.54992
$482$	−37.2182	+	37.2182i	−1.69524	+	1.69524i
$483$		0			0
$484$		−	5.86389i		−	0.266540i
$485$		0			0
$486$		0			0
$487$	14.0684	+	14.0684i	0.637502	+	0.637502i	0.949939	−	0.312437i	$-0.101145\pi$
$487$	14.0684	+	14.0684i	0.637502	+	0.637502i	−0.312437	+	0.949939i	$0.601145\pi$
$488$	21.3595	+	21.3595i	0.966898	+	0.966898i
$489$		0			0
$490$		0			0
$491$			22.6169i			1.02069i	0.859971	+	0.510344i	$0.170482\pi$
$491$			22.6169i			1.02069i	−0.859971	+	0.510344i	$0.829518\pi$
$492$		0			0
$493$	−13.7953	+	13.7953i	−0.621309	+	0.621309i
$494$	−54.6141			−2.45721
$495$		0			0
$496$	0.230033			0.0103288
$497$	−3.87112	+	3.87112i	−0.173643	+	0.173643i
$498$		0			0
$499$		−	35.1641i		−	1.57416i	−0.616851	−	0.787080i	$-0.711592\pi$
$499$		−	35.1641i		−	1.57416i	0.616851	−	0.787080i	$-0.288408\pi$
$500$		0			0
$501$		0			0
$502$	−6.21092	−	6.21092i	−0.277207	−	0.277207i
$503$	3.09215	+	3.09215i	0.137872	+	0.137872i	0.772674	−	0.634802i	$-0.218919\pi$
$503$	3.09215	+	3.09215i	0.137872	+	0.137872i	−0.634802	+	0.772674i	$0.718919\pi$
$504$		0			0
$505$		0			0
$506$		−	29.3978i		−	1.30689i
$507$		0			0
$508$	12.8886	−	12.8886i	0.571837	−	0.571837i
$509$	−7.39653			−0.327845			−0.163923	−	0.986473i	$-0.552415\pi$
$509$	−7.39653			−0.327845			−0.163923	+	0.986473i	$0.552415\pi$
$510$		0			0
$511$	7.89760			0.349369
$512$	−0.560296	+	0.560296i	−0.0247618	+	0.0247618i
$513$		0			0
$514$			46.8914i			2.06829i
$515$		0			0
$516$		0			0
$517$	0.525629	+	0.525629i	0.0231171	+	0.0231171i
$518$	−15.3259	−	15.3259i	−0.673381	−	0.673381i
$519$		0			0
$520$		0			0
$521$		−	40.5578i		−	1.77687i	−0.459002	−	0.888435i	$-0.651793\pi$
$521$		−	40.5578i		−	1.77687i	0.459002	−	0.888435i	$-0.348207\pi$
$522$		0			0
$523$	−21.0323	+	21.0323i	−0.919680	+	0.919680i	−0.997006	−	0.0773260i	$-0.975362\pi$
$523$	−21.0323	+	21.0323i	−0.919680	+	0.919680i	0.0773260	+	0.997006i	$0.475362\pi$
$524$	62.0350			2.71001
$525$		0			0
$526$	−46.9232			−2.04595
$527$	8.88050	−	8.88050i	0.386841	−	0.386841i
$528$		0			0
$529$		−	5.10626i		−	0.222011i
$530$		0			0
$531$		0			0
$532$	−15.2461	−	15.2461i	−0.661002	−	0.661002i
$533$	−18.7260	−	18.7260i	−0.811112	−	0.811112i
$534$		0			0
$535$		0			0
$536$		−	32.4789i		−	1.40287i
$537$		0			0
$538$	−10.7069	+	10.7069i	−0.461607	+	0.461607i
$539$	3.03260			0.130623
$540$		0			0
$541$	12.2534			0.526813			0.263406	−	0.964685i	$-0.415154\pi$
$541$	12.2534			0.526813			0.263406	+	0.964685i	$0.415154\pi$
$542$	37.1744	−	37.1744i	1.59678	−	1.59678i
$543$		0			0
$544$			21.3235i			0.914240i
$545$		0			0
$546$		0			0
$547$	−9.49738	−	9.49738i	−0.406079	−	0.406079i	0.474290	−	0.880369i	$-0.342705\pi$
$547$	−9.49738	−	9.49738i	−0.406079	−	0.406079i	−0.880369	+	0.474290i	$0.842705\pi$
$548$	1.20635	+	1.20635i	0.0515327	+	0.0515327i
$549$		0			0
$550$		0			0
$551$		−	33.8298i		−	1.44120i
$552$		0			0
$553$	11.3902	−	11.3902i	0.484359	−	0.484359i
$554$	45.1257			1.91721
$555$		0			0
$556$	53.0437			2.24955
$557$	−5.20644	+	5.20644i	−0.220604	+	0.220604i	−0.808753	−	0.588149i	$-0.799857\pi$
$557$	−5.20644	+	5.20644i	−0.220604	+	0.220604i	0.588149	+	0.808753i	$0.299857\pi$
$558$		0			0
$559$			8.88642i			0.375855i
$560$		0			0
$561$		0			0
$562$	23.8539	+	23.8539i	1.00621	+	1.00621i
$563$	−11.2865	−	11.2865i	−0.475670	−	0.475670i	0.428074	−	0.903744i	$-0.359192\pi$
$563$	−11.2865	−	11.2865i	−0.475670	−	0.475670i	−0.903744	+	0.428074i	$0.859192\pi$
$564$		0			0
$565$		0			0
$566$			27.2884i			1.14702i
$567$		0			0
$568$	11.1039	−	11.1039i	0.465911	−	0.465911i
$569$	16.7669			0.702903			0.351452	−	0.936206i	$-0.385688\pi$
$569$	16.7669			0.702903			0.351452	+	0.936206i	$0.385688\pi$
$570$		0			0
$571$	35.3888			1.48097			0.740487	−	0.672070i	$-0.234595\pi$
$571$	35.3888			1.48097			0.740487	+	0.672070i	$0.234595\pi$
$572$	−25.0609	+	25.0609i	−1.04785	+	1.04785i
$573$		0			0
$574$		−	16.8857i		−	0.704795i
$575$		0			0
$576$		0			0
$577$	11.4351	+	11.4351i	0.476048	+	0.476048i	0.903865	−	0.427817i	$-0.140717\pi$
$577$	11.4351	+	11.4351i	0.476048	+	0.476048i	−0.427817	+	0.903865i	$0.640717\pi$
$578$	3.85235	+	3.85235i	0.160236	+	0.160236i
$579$		0			0
$580$		0			0
$581$		−	1.41173i		−	0.0585686i
$582$		0			0
$583$	25.6298	−	25.6298i	1.06148	−	1.06148i
$584$	−22.6535			−0.937409
$585$		0			0
$586$	70.2814			2.90330
$587$	−13.2944	+	13.2944i	−0.548721	+	0.548721i	−0.926071	−	0.377350i	$-0.876835\pi$
$587$	−13.2944	+	13.2944i	−0.548721	+	0.548721i	0.377350	+	0.926071i	$0.376835\pi$
$588$		0			0
$589$			21.7774i			0.897322i
$590$		0			0
$591$		0			0
$592$	0.468411	+	0.468411i	0.0192516	+	0.0192516i
$593$	−15.2944	−	15.2944i	−0.628066	−	0.628066i	0.319515	−	0.947581i	$-0.396480\pi$
$593$	−15.2944	−	15.2944i	−0.628066	−	0.628066i	−0.947581	+	0.319515i	$0.896480\pi$
$594$		0			0
$595$		0			0
$596$		−	38.8825i		−	1.59269i
$597$		0			0
$598$	24.6362	−	24.6362i	1.00745	−	1.00745i
$599$	−27.3235			−1.11641			−0.558203	−	0.829704i	$-0.688509\pi$
$599$	−27.3235			−1.11641			−0.558203	+	0.829704i	$0.688509\pi$
$600$		0			0
$601$	1.42918			0.0582974			0.0291487	−	0.999575i	$-0.490720\pi$
$601$	1.42918			0.0582974			0.0291487	+	0.999575i	$0.490720\pi$
$602$	−4.00655	+	4.00655i	−0.163295	+	0.163295i
$603$		0			0
$604$			6.01752i			0.244849i
$605$		0			0
$606$		0			0
$607$	−8.27456	−	8.27456i	−0.335854	−	0.335854i	0.518950	−	0.854804i	$-0.326323\pi$
$607$	−8.27456	−	8.27456i	−0.335854	−	0.335854i	−0.854804	+	0.518950i	$0.826323\pi$
$608$	−26.1456	−	26.1456i	−1.06034	−	1.06034i
$609$		0			0
$610$		0			0
$611$			0.880986i			0.0356409i
$612$		0			0
$613$	15.7991	−	15.7991i	0.638122	−	0.638122i	−0.311970	−	0.950092i	$-0.600989\pi$
$613$	15.7991	−	15.7991i	0.638122	−	0.638122i	0.950092	+	0.311970i	$0.100989\pi$
$614$	−28.6823			−1.15752
$615$		0			0
$616$	−8.69872			−0.350482
$617$	−8.74842	+	8.74842i	−0.352198	+	0.352198i	−0.860927	−	0.508729i	$-0.830116\pi$
$617$	−8.74842	+	8.74842i	−0.352198	+	0.352198i	0.508729	+	0.860927i	$0.330116\pi$
$618$		0			0
$619$			15.7537i			0.633195i	0.948560	+	0.316597i	$0.102540\pi$
$619$			15.7537i			0.633195i	−0.948560	+	0.316597i	$0.897460\pi$
$620$		0			0
$621$		0			0
$622$	−20.8978	−	20.8978i	−0.837927	−	0.837927i
$623$	−2.12157	−	2.12157i	−0.0849989	−	0.0849989i
$624$		0			0
$625$		0			0
$626$		−	4.99349i		−	0.199580i
$627$		0			0
$628$	−8.81861	+	8.81861i	−0.351901	+	0.351901i
$629$	36.1664			1.44205
$630$		0			0
$631$	−31.6048			−1.25817			−0.629083	−	0.777338i	$-0.716569\pi$
$631$	−31.6048			−1.25817			−0.629083	+	0.777338i	$0.716569\pi$
$632$	−32.6716	+	32.6716i	−1.29961	+	1.29961i
$633$		0			0
$634$		−	5.99093i		−	0.237930i
$635$		0			0
$636$		0			0
$637$	2.54141	+	2.54141i	0.100694	+	0.100694i
$638$	−25.0716	−	25.0716i	−0.992594	−	0.992594i
$639$		0			0
$640$		0			0
$641$			2.19982i			0.0868877i	0.999056	+	0.0434439i	$0.0138330\pi$
$641$			2.19982i			0.0868877i	−0.999056	+	0.0434439i	$0.986167\pi$
$642$		0			0
$643$	31.0585	−	31.0585i	1.22483	−	1.22483i	0.258934	−	0.965895i	$-0.416629\pi$
$643$	31.0585	−	31.0585i	1.22483	−	1.22483i	0.965895	−	0.258934i	$-0.0833712\pi$
$644$	13.7549			0.542019
$645$		0			0
$646$	58.1070			2.28619
$647$	4.31046	−	4.31046i	0.169462	−	0.169462i	−0.617281	−	0.786743i	$-0.711766\pi$
$647$	4.31046	−	4.31046i	0.169462	−	0.169462i	0.786743	+	0.617281i	$0.211766\pi$
$648$		0			0
$649$			13.9531i			0.547708i
$650$		0			0
$651$		0			0
$652$	−17.0573	−	17.0573i	−0.668017	−	0.668017i
$653$	−13.3336	−	13.3336i	−0.521784	−	0.521784i	0.396326	−	0.918110i	$-0.370285\pi$
$653$	−13.3336	−	13.3336i	−0.521784	−	0.521784i	−0.918110	+	0.396326i	$0.870285\pi$
$654$		0			0
$655$		0			0
$656$			0.516084i			0.0201497i
$657$		0			0
$658$	−0.397204	+	0.397204i	−0.0154846	+	0.0154846i
$659$	−42.9189			−1.67188			−0.835941	−	0.548819i	$-0.815077\pi$
$659$	−42.9189			−1.67188			−0.835941	+	0.548819i	$0.815077\pi$
$660$		0			0
$661$	−14.5564			−0.566180			−0.283090	−	0.959093i	$-0.591359\pi$
$661$	−14.5564			−0.566180			−0.283090	+	0.959093i	$0.591359\pi$
$662$	−15.2307	+	15.2307i	−0.591958	+	0.591958i
$663$		0			0
$664$			4.04942i			0.157148i
$665$		0			0
$666$		0			0
$667$	15.2605	+	15.2605i	0.590889	+	0.590889i
$668$	26.0560	+	26.0560i	1.00814	+	1.00814i
$669$		0			0
$670$		0			0
$671$			31.9360i			1.23287i
$672$		0			0
$673$	0.0675877	−	0.0675877i	0.00260531	−	0.00260531i	−0.705803	−	0.708408i	$-0.749414\pi$
$673$	0.0675877	−	0.0675877i	0.00260531	−	0.00260531i	0.708408	+	0.705803i	$0.249414\pi$
$674$	−58.8369			−2.26631
$675$		0			0
$676$	0.268213			0.0103159
$677$	6.34254	−	6.34254i	0.243763	−	0.243763i	−0.574642	−	0.818405i	$-0.694859\pi$
$677$	6.34254	−	6.34254i	0.243763	−	0.243763i	0.818405	+	0.574642i	$0.194859\pi$
$678$		0			0
$679$			12.0543i			0.462601i
$680$		0			0
$681$		0			0
$682$	16.1394	+	16.1394i	0.618011	+	0.618011i
$683$	1.00502	+	1.00502i	0.0384559	+	0.0384559i	0.726073	−	0.687617i	$-0.241343\pi$
$683$	1.00502	+	1.00502i	0.0384559	+	0.0384559i	−0.687617	+	0.726073i	$0.741343\pi$
$684$		0			0
$685$		0			0
$686$			2.29165i			0.0874957i
$687$		0			0
$688$	0.122454	−	0.122454i	0.00466851	−	0.00466851i
$689$	42.9572			1.63654
$690$		0			0
$691$	−22.1726			−0.843487			−0.421744	−	0.906715i	$-0.638582\pi$
$691$	−22.1726			−0.843487			−0.421744	+	0.906715i	$0.638582\pi$
$692$	−0.590046	+	0.590046i	−0.0224302	+	0.0224302i
$693$		0			0
$694$			21.1411i			0.802505i
$695$		0			0
$696$		0			0
$697$	19.9236	+	19.9236i	0.754661	+	0.754661i
$698$	46.3846	+	46.3846i	1.75568	+	1.75568i
$699$		0			0
$700$		0			0
$701$			5.69755i			0.215194i	0.994195	+	0.107597i	$0.0343155\pi$
$701$			5.69755i			0.215194i	−0.994195	+	0.107597i	$0.965684\pi$
$702$		0			0
$703$	−44.3449	+	44.3449i	−1.67250	+	1.67250i
$704$	−39.1782			−1.47659
$705$		0			0
$706$	25.2610			0.950709
$707$	−11.9240	+	11.9240i	−0.448446	+	0.448446i
$708$		0			0
$709$			14.5892i			0.547908i	0.961743	+	0.273954i	$0.0883317\pi$
$709$			14.5892i			0.547908i	−0.961743	+	0.273954i	$0.911668\pi$
$710$		0			0
$711$		0			0
$712$	6.08552	+	6.08552i	0.228065	+	0.228065i
$713$	−9.82370	−	9.82370i	−0.367900	−	0.367900i
$714$		0			0
$715$		0			0
$716$		−	40.5254i		−	1.51451i
$717$		0			0
$718$	−1.15908	+	1.15908i	−0.0432564	+	0.0432564i
$719$	7.14831			0.266587			0.133293	−	0.991077i	$-0.457445\pi$
$719$	7.14831			0.266587			0.133293	+	0.991077i	$0.457445\pi$
$720$		0			0
$721$	1.76766			0.0658310
$722$	−40.4587	+	40.4587i	−1.50572	+	1.50572i
$723$		0			0
$724$		−	46.1737i		−	1.71603i
$725$		0			0
$726$		0			0
$727$	−8.29940	−	8.29940i	−0.307808	−	0.307808i	0.536251	−	0.844059i	$-0.319840\pi$
$727$	−8.29940	−	8.29940i	−0.307808	−	0.307808i	−0.844059	+	0.536251i	$0.819840\pi$
$728$	−7.28979	−	7.28979i	−0.270178	−	0.270178i
$729$		0			0
$730$		0			0
$731$		−	9.45476i		−	0.349697i
$732$		0			0
$733$	−22.8769	+	22.8769i	−0.844978	+	0.844978i	−0.989501	−	0.144523i	$-0.953835\pi$
$733$	−22.8769	+	22.8769i	−0.844978	+	0.844978i	0.144523	+	0.989501i	$0.453835\pi$
$734$	−44.1079			−1.62805
$735$		0			0
$736$	23.5883			0.869477
$737$	24.2807	−	24.2807i	0.894390	−	0.894390i
$738$		0			0
$739$			21.9271i			0.806601i	0.915068	+	0.403301i	$0.132137\pi$
$739$			21.9271i			0.806601i	−0.915068	+	0.403301i	$0.867863\pi$
$740$		0			0
$741$		0			0
$742$	19.3678	+	19.3678i	0.711014	+	0.711014i
$743$	−14.6434	−	14.6434i	−0.537213	−	0.537213i	0.385496	−	0.922709i	$-0.374030\pi$
$743$	−14.6434	−	14.6434i	−0.537213	−	0.537213i	−0.922709	+	0.385496i	$0.874030\pi$
$744$		0			0
$745$		0			0
$746$			72.1285i			2.64081i
$747$		0			0
$748$	26.6637	−	26.6637i	0.974921	−	0.974921i
$749$	−20.0472			−0.732507
$750$		0			0
$751$	−46.6877			−1.70366			−0.851829	−	0.523820i	$-0.824506\pi$
$751$	−46.6877			−1.70366			−0.851829	+	0.523820i	$0.824506\pi$
$752$	0.0121399	−	0.0121399i	0.000442696	−	0.000442696i
$753$		0			0
$754$		−	42.0215i		−	1.53033i
$755$		0			0
$756$		0			0
$757$	−4.34878	−	4.34878i	−0.158059	−	0.158059i	0.623647	−	0.781706i	$-0.285650\pi$
$757$	−4.34878	−	4.34878i	−0.158059	−	0.158059i	−0.781706	+	0.623647i	$0.785650\pi$
$758$	1.12721	+	1.12721i	0.0409422	+	0.0409422i
$759$		0			0
$760$		0			0
$761$		−	20.3466i		−	0.737562i	−0.929516	−	0.368781i	$-0.879775\pi$
$761$		−	20.3466i		−	0.737562i	0.929516	−	0.368781i	$-0.120225\pi$
$762$		0			0
$763$	−0.406141	+	0.406141i	−0.0147033	+	0.0147033i
$764$	−33.5436			−1.21357
$765$		0			0
$766$	23.4324			0.846647
$767$	−11.6931	+	11.6931i	−0.422214	+	0.422214i
$768$		0			0
$769$		−	10.6781i		−	0.385063i	−0.981291	−	0.192532i	$-0.938330\pi$
$769$		−	10.6781i		−	0.385063i	0.981291	−	0.192532i	$-0.0616698\pi$
$770$		0			0
$771$		0			0
$772$	0.866831	+	0.866831i	0.0311979	+	0.0311979i
$773$	16.1983	+	16.1983i	0.582611	+	0.582611i	0.935620	−	0.353009i	$-0.114841\pi$
$773$	16.1983	+	16.1983i	0.582611	+	0.582611i	−0.353009	+	0.935620i	$0.614841\pi$
$774$		0			0
$775$		0			0
$776$		−	34.5766i		−	1.24123i
$777$		0			0
$778$	−33.2312	+	33.2312i	−1.19140	+	1.19140i
$779$	−48.8581			−1.75052
$780$		0			0
$781$	16.6022			0.594075
$782$	−26.2119	+	26.2119i	−0.937334	+	0.937334i
$783$		0			0
$784$		−	0.0700407i		−	0.00250145i
$785$		0			0
$786$		0			0
$787$	−3.85920	−	3.85920i	−0.137566	−	0.137566i	0.634971	−	0.772536i	$-0.281012\pi$
$787$	−3.85920	−	3.85920i	−0.137566	−	0.137566i	−0.772536	+	0.634971i	$0.781012\pi$
$788$	−22.7123	−	22.7123i	−0.809094	−	0.809094i
$789$		0			0
$790$		0			0
$791$			9.87802i			0.351222i
$792$		0			0
$793$	−26.7633	+	26.7633i	−0.950392	+	0.950392i
$794$	−28.1948			−1.00060
$795$		0			0
$796$	−54.5311			−1.93280
$797$	31.4439	−	31.4439i	1.11380	−	1.11380i	0.121168	−	0.992632i	$-0.461336\pi$
$797$	31.4439	−	31.4439i	1.11380	−	1.11380i	0.992632	−	0.121168i	$-0.0386640\pi$
$798$		0			0
$799$		−	0.937330i		−	0.0331604i
$800$		0			0
$801$		0			0
$802$	−1.73872	−	1.73872i	−0.0613964	−	0.0613964i
$803$	−16.9354	−	16.9354i	−0.597636	−	0.597636i
$804$		0			0
$805$		0			0
$806$			27.0507i			0.952819i
$807$		0			0
$808$	34.2027	−	34.2027i	1.20325	−	1.20325i
$809$	29.8706			1.05019			0.525097	−	0.851043i	$-0.324029\pi$
$809$	29.8706			1.05019			0.525097	+	0.851043i	$0.324029\pi$
$810$		0			0
$811$	41.5858			1.46028			0.730138	−	0.683300i	$-0.239456\pi$
$811$	41.5858			1.46028			0.730138	+	0.683300i	$0.239456\pi$
$812$	11.7307	−	11.7307i	0.411668	−	0.411668i
$813$		0			0
$814$			65.7288i			2.30379i
$815$		0			0
$816$		0			0
$817$	11.5928	+	11.5928i	0.405581	+	0.405581i
$818$	29.0090	+	29.0090i	1.01428	+	1.01428i
$819$		0			0
$820$		0			0
$821$			49.6249i			1.73192i	0.500114	+	0.865960i	$0.333292\pi$
$821$			49.6249i			1.73192i	−0.500114	+	0.865960i	$0.666708\pi$
$822$		0			0
$823$	−11.9691	+	11.9691i	−0.417216	+	0.417216i	−0.884243	−	0.467027i	$-0.845325\pi$
$823$	−11.9691	+	11.9691i	−0.417216	+	0.417216i	0.467027	+	0.884243i	$0.345325\pi$
$824$	−5.07035			−0.176634
$825$		0			0
$826$	−10.5440			−0.366873
$827$	−24.1358	+	24.1358i	−0.839285	+	0.839285i	−0.988765	−	0.149480i	$-0.952240\pi$
$827$	−24.1358	+	24.1358i	−0.839285	+	0.839285i	0.149480	+	0.988765i	$0.452240\pi$
$828$		0			0
$829$		−	24.8211i		−	0.862071i	−0.902335	−	0.431035i	$-0.858148\pi$
$829$		−	24.8211i		−	0.862071i	0.902335	−	0.431035i	$-0.141852\pi$
$830$		0			0
$831$		0			0
$832$	−32.8325	−	32.8325i	−1.13826	−	1.13826i
$833$	−2.70395	−	2.70395i	−0.0936862	−	0.0936862i
$834$		0			0
$835$		0			0
$836$			65.3866i			2.26144i
$837$		0			0
$838$	−24.0499	+	24.0499i	−0.830789	+	0.830789i
$839$	−31.3907			−1.08373			−0.541863	−	0.840467i	$-0.682281\pi$
$839$	−31.3907			−1.08373			−0.541863	+	0.840467i	$0.682281\pi$
$840$		0			0
$841$	−2.97048			−0.102430
$842$	28.2922	−	28.2922i	0.975013	−	0.975013i
$843$		0			0
$844$		−	55.1650i		−	1.89886i
$845$		0			0
$846$		0			0
$847$	1.27516	+	1.27516i	0.0438149	+	0.0438149i
$848$	−0.591945	−	0.591945i	−0.0203275	−	0.0203275i
$849$		0			0
$850$		0			0
$851$		−	40.0076i		−	1.37144i
$852$		0			0
$853$	−38.4133	+	38.4133i	−1.31525	+	1.31525i	−0.397755	+	0.917491i	$0.630211\pi$
$853$	−38.4133	+	38.4133i	−1.31525	+	1.31525i	−0.917491	+	0.397755i	$0.869789\pi$
$854$	−24.1331			−0.825819
$855$		0			0
$856$	57.5034			1.96542
$857$	−16.0449	+	16.0449i	−0.548084	+	0.548084i	−0.925886	−	0.377802i	$-0.876680\pi$
$857$	−16.0449	+	16.0449i	−0.548084	+	0.548084i	0.377802	+	0.925886i	$0.376680\pi$
$858$		0			0
$859$		−	27.9426i		−	0.953389i	−0.879069	−	0.476695i	$-0.841835\pi$
$859$		−	27.9426i		−	0.953389i	0.879069	−	0.476695i	$-0.158165\pi$
$860$		0			0
$861$		0			0
$862$	−3.72425	−	3.72425i	−0.126849	−	0.126849i
$863$	−6.65308	−	6.65308i	−0.226474	−	0.226474i	0.584744	−	0.811218i	$-0.301195\pi$
$863$	−6.65308	−	6.65308i	−0.226474	−	0.226474i	−0.811218	+	0.584744i	$0.801195\pi$
$864$		0			0
$865$		0			0
$866$			9.08495i			0.308719i
$867$		0			0
$868$	−7.55147	+	7.55147i	−0.256314	+	0.256314i
$869$	−48.8495			−1.65710
$870$		0			0
$871$	40.6959			1.37893
$872$	1.16498	−	1.16498i	0.0394511	−	0.0394511i
$873$		0			0
$874$		−	64.2786i		−	2.17425i
$875$		0			0
$876$		0			0
$877$	−17.2572	−	17.2572i	−0.582734	−	0.582734i	0.352920	−	0.935654i	$-0.385189\pi$
$877$	−17.2572	−	17.2572i	−0.582734	−	0.582734i	−0.935654	+	0.352920i	$0.885189\pi$
$878$	−25.1431	−	25.1431i	−0.848540	−	0.848540i
$879$		0			0
$880$		0			0
$881$		−	10.6210i		−	0.357830i	−0.983865	−	0.178915i	$-0.942741\pi$
$881$		−	10.6210i		−	0.357830i	0.983865	−	0.178915i	$-0.0572587\pi$
$882$		0			0
$883$	11.4145	−	11.4145i	0.384130	−	0.384130i	−0.488458	−	0.872588i	$-0.662440\pi$
$883$	11.4145	−	11.4145i	0.384130	−	0.384130i	0.872588	+	0.488458i	$0.162440\pi$
$884$	44.6899			1.50309
$885$		0			0
$886$	−21.5981			−0.725601
$887$	−18.4290	+	18.4290i	−0.618786	+	0.618786i	−0.945220	−	0.326434i	$-0.894153\pi$
$887$	−18.4290	+	18.4290i	−0.618786	+	0.618786i	0.326434	+	0.945220i	$0.394153\pi$
$888$		0			0
$889$			5.60547i			0.188001i
$890$		0			0
$891$		0			0
$892$	43.4081	+	43.4081i	1.45341	+	1.45341i
$893$	1.14929	+	1.14929i	0.0384597	+	0.0384597i
$894$		0			0
$895$		0			0
$896$		−	18.4533i		−	0.616483i
$897$		0			0
$898$	26.6513	−	26.6513i	0.889366	−	0.889366i
$899$	−16.7561			−0.558847
$900$		0			0
$901$	−45.7045			−1.52264
$902$	−36.2092	+	36.2092i	−1.20563	+	1.20563i
$903$		0			0
$904$		−	28.3342i		−	0.942380i
$905$		0			0
$906$		0			0
$907$	−39.8245	−	39.8245i	−1.32235	−	1.32235i	−0.911868	−	0.410483i	$-0.865360\pi$
$907$	−39.8245	−	39.8245i	−1.32235	−	1.32235i	−0.410483	−	0.911868i	$-0.634640\pi$
$908$	−38.7779	−	38.7779i	−1.28689	−	1.28689i
$909$		0			0
$910$		0			0
$911$			1.26894i			0.0420419i	0.999779	+	0.0210210i	$0.00669167\pi$
$911$			1.26894i			0.0420419i	−0.999779	+	0.0210210i	$0.993308\pi$
$912$		0			0
$913$	−3.02728	+	3.02728i	−0.100188	+	0.100188i
$914$	39.6031			1.30995
$915$		0			0
$916$	−27.3917			−0.905046
$917$	−13.4901	+	13.4901i	−0.445482	+	0.445482i
$918$		0			0
$919$			41.5356i			1.37013i	0.728481	+	0.685066i	$0.240227\pi$
$919$			41.5356i			1.37013i	−0.728481	+	0.685066i	$0.759773\pi$
$920$		0			0
$921$		0			0
$922$	16.7314	+	16.7314i	0.551018	+	0.551018i
$923$	13.9132	+	13.9132i	0.457958	+	0.457958i
$924$		0			0
$925$		0			0
$926$		−	42.9993i		−	1.41304i
$927$		0			0
$928$	20.1171	−	20.1171i	0.660375	−	0.660375i
$929$	41.6802			1.36748			0.683741	−	0.729725i	$-0.260352\pi$
$929$	41.6802			1.36748			0.683741	+	0.729725i	$0.260352\pi$
$930$		0			0
$931$	6.63081			0.217316
$932$	2.67329	−	2.67329i	0.0875667	−	0.0875667i
$933$		0			0
$934$		−	31.5011i		−	1.03075i
$935$		0			0
$936$		0			0
$937$	41.7653	+	41.7653i	1.36441	+	1.36441i	0.868203	+	0.496210i	$0.165275\pi$
$937$	41.7653	+	41.7653i	1.36441	+	1.36441i	0.496210	+	0.868203i	$0.334725\pi$
$938$	18.3482	+	18.3482i	0.599092	+	0.599092i
$939$		0			0
$940$		0			0
$941$		−	51.7350i		−	1.68651i	−0.537511	−	0.843257i	$-0.680635\pi$
$941$		−	51.7350i		−	1.68651i	0.537511	−	0.843257i	$-0.319365\pi$
$942$		0			0
$943$	22.0397	−	22.0397i	0.717711	−	0.717711i
$944$	0.322260			0.0104887
$945$		0			0
$946$	17.1831			0.558670
$947$	−25.5564	+	25.5564i	−0.830472	+	0.830472i	−0.987581	−	0.157109i	$-0.949783\pi$
$947$	−25.5564	+	25.5564i	−0.830472	+	0.830472i	0.157109	+	0.987581i	$0.449783\pi$
$948$		0			0
$949$		−	28.3847i		−	0.921407i
$950$		0			0
$951$		0			0
$952$	7.75602	+	7.75602i	0.251374	+	0.251374i
$953$	11.2847	+	11.2847i	0.365546	+	0.365546i	0.865850	−	0.500304i	$-0.166778\pi$
$953$	11.2847	+	11.2847i	0.365546	+	0.365546i	−0.500304	+	0.865850i	$0.666778\pi$
$954$		0			0
$955$		0			0
$956$			37.2290i			1.20407i
$957$		0			0
$958$	2.55217	−	2.55217i	0.0824568	−	0.0824568i
$959$	−0.524664			−0.0169423
$960$		0			0
$961$	−20.2135			−0.652050
$962$	−55.0827	+	55.0827i	−1.77594	+	1.77594i
$963$		0			0
$964$			74.6842i			2.40542i
$965$		0			0
$966$		0			0
$967$	11.3331	+	11.3331i	0.364447	+	0.364447i	0.865447	−	0.501000i	$-0.167034\pi$
$967$	11.3331	+	11.3331i	0.364447	+	0.364447i	−0.501000	+	0.865447i	$0.667034\pi$
$968$	−3.65767	−	3.65767i	−0.117562	−	0.117562i
$969$		0			0
$970$		0			0
$971$		−	30.7436i		−	0.986609i	−0.869857	−	0.493304i	$-0.835789\pi$
$971$		−	30.7436i		−	0.986609i	0.869857	−	0.493304i	$-0.164211\pi$
$972$		0			0
$973$	−11.5348	+	11.5348i	−0.369790	+	0.369790i
$974$	45.5942			1.46093
$975$		0			0
$976$	0.737590			0.0236097
$977$	−6.76461	+	6.76461i	−0.216419	+	0.216419i	−0.806988	−	0.590568i	$-0.798904\pi$
$977$	−6.76461	+	6.76461i	−0.216419	+	0.216419i	0.590568	+	0.806988i	$0.298904\pi$
$978$		0			0
$979$			9.09886i			0.290801i
$980$		0			0
$981$		0			0
$982$	36.6494	+	36.6494i	1.16953	+	1.16953i
$983$	−15.0257	−	15.0257i	−0.479247	−	0.479247i	0.425644	−	0.904891i	$-0.360048\pi$
$983$	−15.0257	−	15.0257i	−0.479247	−	0.479247i	−0.904891	+	0.425644i	$0.860048\pi$
$984$		0			0
$985$		0			0
$986$			44.7090i			1.42383i
$987$		0			0
$988$	−54.7959	+	54.7959i	−1.74329	+	1.74329i
$989$	−10.4589			−0.332575
$990$		0			0
$991$	37.5534			1.19292			0.596461	−	0.802642i	$-0.296573\pi$
$991$	37.5534			1.19292			0.596461	+	0.802642i	$0.296573\pi$
$992$	−12.9500	+	12.9500i	−0.411164	+	0.411164i
$993$		0			0
$994$			12.5459i			0.397931i
$995$		0			0
$996$		0			0
$997$	−36.6256	−	36.6256i	−1.15995	−	1.15995i	−0.984487	−	0.175459i	$-0.943859\pi$
$997$	−36.6256	−	36.6256i	−1.15995	−	1.15995i	−0.175459	−	0.984487i	$-0.556141\pi$
$998$	−56.9814	−	56.9814i	−1.80371	−	1.80371i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1575.2.m.c.1457.5		12
3.2	odd	2		1575.2.m.d.1457.2		12
5.2	odd	4		315.2.m.b.8.5	yes	12
5.3	odd	4		1575.2.m.d.1268.2		12
5.4	even	2		315.2.m.a.197.2	yes	12
15.2	even	4		315.2.m.a.8.2	✓	12
15.8	even	4	inner	1575.2.m.c.1268.5		12
15.14	odd	2		315.2.m.b.197.5	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.m.a.8.2	✓	12	15.2	even	4
315.2.m.a.197.2	yes	12	5.4	even	2
315.2.m.b.8.5	yes	12	5.2	odd	4
315.2.m.b.197.5	yes	12	15.14	odd	2
1575.2.m.c.1268.5		12	15.8	even	4	inner
1575.2.m.c.1457.5		12	1.1	even	1	trivial
1575.2.m.d.1268.2		12	5.3	odd	4
1575.2.m.d.1457.2		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1575.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.62044 - 1.62044i) q^{2} -3.25168i q^{4} +(0.707107 + 0.707107i) q^{7} +(-2.02827 - 2.02827i) q^{8} -3.03260i q^{11} +(2.54141 - 2.54141i) q^{13} +2.29165 q^{14} -0.0700407 q^{16} +(-2.70395 + 2.70395i) q^{17} -6.63081i q^{19} +(-4.91416 - 4.91416i) q^{22} +(2.99113 + 2.99113i) q^{23} -8.23642i q^{26} +(2.29928 - 2.29928i) q^{28} +5.10191 q^{29} -3.28427 q^{31} +(3.94304 - 3.94304i) q^{32} +8.76319i q^{34} +(-6.68770 - 6.68770i) q^{37} +(-10.7449 - 10.7449i) q^{38} -7.36835i q^{41} +(-1.74832 + 1.74832i) q^{43} -9.86103 q^{44} +9.69392 q^{46} +(-0.173326 + 0.173326i) q^{47} +1.00000i q^{49} +(-8.26384 - 8.26384i) q^{52} +(8.45145 + 8.45145i) q^{53} -2.86841i q^{56} +(8.26736 - 8.26736i) q^{58} -4.60104 q^{59} -10.5309 q^{61} +(-5.32198 + 5.32198i) q^{62} -12.9190i q^{64} +(8.00655 + 8.00655i) q^{67} +(8.79236 + 8.79236i) q^{68} +5.47459i q^{71} +(5.58444 - 5.58444i) q^{73} -21.6741 q^{74} -21.5612 q^{76} +(2.14437 - 2.14437i) q^{77} -16.1081i q^{79} +(-11.9400 - 11.9400i) q^{82} +(-0.998247 - 0.998247i) q^{83} +5.66612i q^{86} +(-6.15093 + 6.15093i) q^{88} -3.00035 q^{89} +3.59409 q^{91} +(9.72619 - 9.72619i) q^{92} +0.561731i q^{94} +(8.52367 + 8.52367i) q^{97} +(1.62044 + 1.62044i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 24 q^{8} + 4 q^{13} - 4 q^{14} - 20 q^{16} - 8 q^{17} + 8 q^{22} - 8 q^{23} - 32 q^{29} - 48 q^{32} - 4 q^{37} - 24 q^{38} - 40 q^{43} - 64 q^{44} + 16 q^{46} - 24 q^{47} - 36 q^{52} + 40 q^{53}+ \cdots - 12 q^{97}+O(q^{100}) \) 12 * q - 24 * q^8 + 4 * q^13 - 4 * q^14 - 20 * q^16 - 8 * q^17 + 8 * q^22 - 8 * q^23 - 32 * q^29 - 48 * q^32 - 4 * q^37 - 24 * q^38 - 40 * q^43 - 64 * q^44 + 16 * q^46 - 24 * q^47 - 36 * q^52 + 40 * q^53 + 28 * q^58 - 80 * q^59 - 32 * q^61 - 16 * q^62 + 48 * q^67 - 32 * q^68 + 20 * q^73 - 64 * q^74 + 16 * q^76 - 20 * q^82 - 24 * q^83 - 56 * q^89 - 8 * q^92 - 12 * q^97

Introduction

L-functions

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