LMFDB - Embedded newform 2352.2.bl.r.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2352,2,Mod(31,2352)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2352, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))

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

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

chi := DirichletCharacter("2352.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2352 = 2^{4} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2352.bl (of order $6$, 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:	$18.7808145554$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.339738624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 $ x^8 - 4x^6 + 14x^4 - 8*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Root			$-1.60021 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	2352.31
Dual form			2352.2.bl.r.607.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(2.78415 - 1.60743i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(2.78415 - 1.60743i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.18394 + 0.683549i) q^{11} -2.93015i q^{13} -3.21486i q^{15} +(-5.98456 - 3.45519i) q^{17} +(-3.67725 - 6.36918i) q^{19} +(-3.14171 + 1.81387i) q^{23} +(2.66765 - 4.62051i) q^{25} -1.00000 q^{27} -1.11185 q^{29} +(-4.35159 + 7.53718i) q^{31} +(1.18394 - 0.683549i) q^{33} +(-3.81896 - 6.61463i) q^{37} +(-2.53759 - 1.46508i) q^{39} -0.833147i q^{41} +4.82362i q^{43} +(-2.78415 - 1.60743i) q^{45} +(-1.47683 - 2.55795i) q^{47} +(-5.98456 + 3.45519i) q^{51} +(2.28897 - 3.96462i) q^{53} +4.39502 q^{55} -7.35449 q^{57} +(7.04923 - 12.2096i) q^{59} +(9.57981 - 5.53091i) q^{61} +(-4.71001 - 8.15797i) q^{65} +(10.5261 + 6.07723i) q^{67} +3.62774i q^{69} +12.6249i q^{71} +(5.62060 + 3.24505i) q^{73} +(-2.66765 - 4.62051i) q^{75} +(6.74952 - 3.89684i) q^{79} +(-0.500000 + 0.866025i) q^{81} +8.87502 q^{83} -22.2159 q^{85} +(-0.555927 + 0.962893i) q^{87} +(10.9246 - 6.30731i) q^{89} +(4.35159 + 7.53718i) q^{93} +(-20.4760 - 11.8218i) q^{95} +13.8811i q^{97} -1.36710i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^9	$ 8 q + 4 q^{3} - 4 q^{9} - 24 q^{23} + 12 q^{25} - 8 q^{27} + 16 q^{29} - 16 q^{31} - 8 q^{47} - 8 q^{53} + 64 q^{55} + 24 q^{59} + 48 q^{61} + 8 q^{65} + 48 q^{67} + 48 q^{73} - 12 q^{75} + 24 q^{79} - 4 q^{81} - 64 q^{85} + 8 q^{87} + 48 q^{89} + 16 q^{93} - 72 q^{95}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^9 - 24 * q^23 + 12 * q^25 - 8 * q^27 + 16 * q^29 - 16 * q^31 - 8 * q^47 - 8 * q^53 + 64 * q^55 + 24 * q^59 + 48 * q^61 + 8 * q^65 + 48 * q^67 + 48 * q^73 - 12 * q^75 + 24 * q^79 - 4 * q^81 - 64 * q^85 + 8 * q^87 + 48 * q^89 + 16 * q^93 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times$.

$n$	$785$	$1471$	$1765$	$2257$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$		0			0
$5$	2.78415	−	1.60743i	1.24511	−	0.718864i	0.274979	−	0.961450i	$-0.411329\pi$
$5$	2.78415	−	1.60743i	1.24511	−	0.718864i	0.970130	+	0.242586i	$0.0779958\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.18394	+	0.683549i	0.356972	+	0.206098i	0.667752	−	0.744384i	$-0.267257\pi$
$11$	1.18394	+	0.683549i	0.356972	+	0.206098i	−0.310780	+	0.950482i	$0.600590\pi$
$12$		0			0
$13$		−	2.93015i		−	0.812678i	−0.913722	−	0.406339i	$-0.866805\pi$
$13$		−	2.93015i		−	0.812678i	0.913722	−	0.406339i	$-0.133195\pi$
$14$		0			0
$15$		−	3.21486i		−	0.830072i
$16$		0			0
$17$	−5.98456	−	3.45519i	−1.45147	−	0.838006i	−0.452904	−	0.891559i	$-0.649612\pi$
$17$	−5.98456	−	3.45519i	−1.45147	−	0.838006i	−0.998565	+	0.0535532i	$0.982945\pi$
$18$		0			0
$19$	−3.67725	−	6.36918i	−0.843618	−	1.46119i	−0.886816	−	0.462123i	$-0.847088\pi$
$19$	−3.67725	−	6.36918i	−0.843618	−	1.46119i	0.0431974	−	0.999067i	$-0.486246\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.14171	+	1.81387i	−0.655092	+	0.378218i	−0.790405	−	0.612585i	$-0.790130\pi$
$23$	−3.14171	+	1.81387i	−0.655092	+	0.378218i	0.135312	+	0.990803i	$0.456796\pi$
$24$		0			0
$25$	2.66765	−	4.62051i	0.533530	−	0.924102i
$26$		0			0
$27$	−1.00000			−0.192450
$28$		0			0
$29$	−1.11185			−0.206466			−0.103233	−	0.994657i	$-0.532919\pi$
$29$	−1.11185			−0.206466			−0.103233	+	0.994657i	$0.532919\pi$
$30$		0			0
$31$	−4.35159	+	7.53718i	−0.781569	+	1.35372i	0.149458	+	0.988768i	$0.452247\pi$
$31$	−4.35159	+	7.53718i	−0.781569	+	1.35372i	−0.931027	+	0.364949i	$0.881086\pi$
$32$		0			0
$33$	1.18394	−	0.683549i	0.206098	−	0.118991i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−3.81896	−	6.61463i	−0.627833	−	1.08744i	−0.987986	−	0.154546i	$-0.950609\pi$
$37$	−3.81896	−	6.61463i	−0.627833	−	1.08744i	0.360152	−	0.932893i	$-0.382725\pi$
$38$		0			0
$39$	−2.53759	−	1.46508i	−0.406339	−	0.234600i
$40$		0			0
$41$		−	0.833147i		−	0.130116i	−0.997881	−	0.0650579i	$-0.979277\pi$
$41$		−	0.833147i		−	0.130116i	0.997881	−	0.0650579i	$-0.0207232\pi$
$42$		0			0
$43$			4.82362i			0.735595i	0.929906	+	0.367797i	$0.119888\pi$
$43$			4.82362i			0.735595i	−0.929906	+	0.367797i	$0.880112\pi$
$44$		0			0
$45$	−2.78415	−	1.60743i	−0.415036	−	0.239621i
$46$		0			0
$47$	−1.47683	−	2.55795i	−0.215418	−	0.373116i	0.737983	−	0.674819i	$-0.235778\pi$
$47$	−1.47683	−	2.55795i	−0.215418	−	0.373116i	−0.953402	+	0.301703i	$0.902445\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−5.98456	+	3.45519i	−0.838006	+	0.483823i
$52$		0			0
$53$	2.28897	−	3.96462i	0.314414	−	0.544582i	−0.664898	−	0.746934i	$-0.731525\pi$
$53$	2.28897	−	3.96462i	0.314414	−	0.544582i	0.979313	+	0.202352i	$0.0648585\pi$
$54$		0			0
$55$	4.39502			0.592625
$56$		0			0
$57$	−7.35449			−0.974127
$58$		0			0
$59$	7.04923	−	12.2096i	0.917732	−	1.58956i	0.114880	−	0.993379i	$-0.463352\pi$
$59$	7.04923	−	12.2096i	0.917732	−	1.58956i	0.802852	−	0.596179i	$-0.203315\pi$
$60$		0			0
$61$	9.57981	−	5.53091i	1.22657	−	0.708160i	0.260259	−	0.965539i	$-0.416192\pi$
$61$	9.57981	−	5.53091i	1.22657	−	0.708160i	0.966311	+	0.257379i	$0.0828588\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.71001	−	8.15797i	−0.584205	−	1.01187i
$66$		0			0
$67$	10.5261	+	6.07723i	1.28596	+	0.742452i	0.977932	−	0.208924i	$-0.0669963\pi$
$67$	10.5261	+	6.07723i	1.28596	+	0.742452i	0.308032	+	0.951376i	$0.400330\pi$
$68$		0			0
$69$			3.62774i			0.436728i
$70$		0			0
$71$			12.6249i			1.49830i	0.662402	+	0.749148i	$0.269537\pi$
$71$			12.6249i			1.49830i	−0.662402	+	0.749148i	$0.730463\pi$
$72$		0			0
$73$	5.62060	+	3.24505i	0.657841	+	0.379805i	0.791454	−	0.611229i	$-0.209324\pi$
$73$	5.62060	+	3.24505i	0.657841	+	0.379805i	−0.133613	+	0.991034i	$0.542658\pi$
$74$		0			0
$75$	−2.66765	−	4.62051i	−0.308034	−	0.533530i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	6.74952	−	3.89684i	0.759380	−	0.438428i	−0.0696931	−	0.997568i	$-0.522202\pi$
$79$	6.74952	−	3.89684i	0.759380	−	0.438428i	0.829073	+	0.559140i	$0.188869\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	8.87502			0.974159			0.487080	−	0.873358i	$-0.338062\pi$
$83$	8.87502			0.974159			0.487080	+	0.873358i	$0.338062\pi$
$84$		0			0
$85$	−22.2159			−2.40965
$86$		0			0
$87$	−0.555927	+	0.962893i	−0.0596016	+	0.103233i
$88$		0			0
$89$	10.9246	−	6.30731i	1.15800	−	0.668574i	0.207179	−	0.978303i	$-0.433572\pi$
$89$	10.9246	−	6.30731i	1.15800	−	0.668574i	0.950825	+	0.309729i	$0.100238\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	4.35159	+	7.53718i	0.451239	+	0.781569i
$94$		0			0
$95$	−20.4760	−	11.8218i	−2.10079	−	1.21289i
$96$		0			0
$97$			13.8811i			1.40942i	0.709497	+	0.704708i	$0.248922\pi$
$97$			13.8811i			1.40942i	−0.709497	+	0.704708i	$0.751078\pi$
$98$		0			0
$99$		−	1.36710i		−	0.137398i
$100$		0			0
$101$	1.43666	+	0.829455i	0.142953	+	0.0825338i	0.569771	−	0.821804i	$-0.307032\pi$
$101$	1.43666	+	0.829455i	0.142953	+	0.0825338i	−0.426818	+	0.904338i	$0.640365\pi$
$102$		0			0
$103$	−0.653953	−	1.13268i	−0.0644359	−	0.111606i	0.832008	−	0.554764i	$-0.187191\pi$
$103$	−0.653953	−	1.13268i	−0.0644359	−	0.111606i	−0.896444	+	0.443158i	$0.853858\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−6.19385	+	3.57602i	−0.598782	+	0.345707i	−0.768562	−	0.639775i	$-0.779027\pi$
$107$	−6.19385	+	3.57602i	−0.598782	+	0.345707i	0.169780	+	0.985482i	$0.445694\pi$
$108$		0			0
$109$	7.52215	−	13.0287i	0.720491	−	1.24793i	−0.240312	−	0.970696i	$-0.577250\pi$
$109$	7.52215	−	13.0287i	0.720491	−	1.24793i	0.960803	−	0.277231i	$-0.0894168\pi$
$110$		0			0
$111$	−7.63792			−0.724959
$112$		0			0
$113$	−15.4530			−1.45369			−0.726846	−	0.686800i	$-0.759015\pi$
$113$	−15.4530			−1.45369			−0.726846	+	0.686800i	$0.759015\pi$
$114$		0			0
$115$	−5.83133	+	10.1002i	−0.543774	+	0.941845i
$116$		0			0
$117$	−2.53759	+	1.46508i	−0.234600	+	0.135446i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−4.56552	−	7.90772i	−0.415047	−	0.718883i
$122$		0			0
$123$	−0.721527	−	0.416574i	−0.0650579	−	0.0375612i
$124$		0			0
$125$		−	1.07795i		−	0.0964149i
$126$		0			0
$127$			2.16478i			0.192094i	0.995377	+	0.0960468i	$0.0306198\pi$
$127$			2.16478i			0.192094i	−0.995377	+	0.0960468i	$0.969380\pi$
$128$		0			0
$129$	4.17738	+	2.41181i	0.367797	+	0.212348i
$130$		0			0
$131$	2.48938	+	4.31174i	0.217499	+	0.376718i	0.954043	−	0.299671i	$-0.0968769\pi$
$131$	2.48938	+	4.31174i	0.217499	+	0.376718i	−0.736544	+	0.676390i	$0.763544\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.78415	+	1.60743i	−0.239621	+	0.138345i
$136$		0			0
$137$	1.84490	−	3.19546i	0.157620	−	0.273006i	−0.776390	−	0.630253i	$-0.782951\pi$
$137$	1.84490	−	3.19546i	0.157620	−	0.273006i	0.934010	+	0.357247i	$0.116284\pi$
$138$		0			0
$139$	−12.0577			−1.02272			−0.511360	−	0.859367i	$-0.670858\pi$
$139$	−12.0577			−1.02272			−0.511360	+	0.859367i	$0.670858\pi$
$140$		0			0
$141$	−2.95367			−0.248744
$142$		0			0
$143$	2.00290	−	3.46913i	0.167491	−	0.290103i
$144$		0			0
$145$	−3.09556	+	1.78722i	−0.257073	+	0.148421i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.65131	−	2.86015i	−0.135280	−	0.234313i	0.790424	−	0.612560i	$-0.209860\pi$
$149$	−1.65131	−	2.86015i	−0.135280	−	0.234313i	−0.925705	+	0.378247i	$0.876527\pi$
$150$		0			0
$151$	−16.4122	−	9.47557i	−1.33560	−	0.771111i	−0.349452	−	0.936954i	$-0.613632\pi$
$151$	−16.4122	−	9.47557i	−1.33560	−	0.771111i	−0.986152	+	0.165843i	$0.946965\pi$
$152$		0			0
$153$			6.91037i			0.558671i
$154$		0			0
$155$			27.9795i			2.24737i
$156$		0			0
$157$	−0.767676	−	0.443218i	−0.0612672	−	0.0353726i	0.469053	−	0.883170i	$-0.344595\pi$
$157$	−0.767676	−	0.443218i	−0.0612672	−	0.0353726i	−0.530321	+	0.847797i	$0.677928\pi$
$158$		0			0
$159$	−2.28897	−	3.96462i	−0.181527	−	0.314414i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−16.7609	+	9.67689i	−1.31281	+	0.757953i	−0.982561	−	0.185941i	$-0.940467\pi$
$163$	−16.7609	+	9.67689i	−1.31281	+	0.757953i	−0.330251	+	0.943893i	$0.607133\pi$
$164$		0			0
$165$	2.19751	−	3.80620i	0.171076	−	0.296312i
$166$		0			0
$167$	25.4855			1.97213			0.986065	−	0.166360i	$-0.0532014\pi$
$167$	25.4855			1.97213			0.986065	+	0.166360i	$0.0532014\pi$
$168$		0			0
$169$	4.41421			0.339555
$170$		0			0
$171$	−3.67725	+	6.36918i	−0.281206	+	0.487063i
$172$		0			0
$173$	18.7862	−	10.8462i	1.42829	−	0.824623i	0.431303	−	0.902207i	$-0.358054\pi$
$173$	18.7862	−	10.8462i	1.42829	−	0.824623i	0.996986	+	0.0775839i	$0.0247206\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−7.04923	−	12.2096i	−0.529853	−	0.917732i
$178$		0			0
$179$	10.6369	+	6.14122i	0.795039	+	0.459016i	0.841734	−	0.539893i	$-0.181535\pi$
$179$	10.6369	+	6.14122i	0.795039	+	0.459016i	−0.0466943	+	0.998909i	$0.514869\pi$
$180$		0			0
$181$			2.74444i			0.203993i	0.994785	+	0.101996i	$0.0325230\pi$
$181$			2.74444i			0.203993i	−0.994785	+	0.101996i	$0.967477\pi$
$182$		0			0
$183$		−	11.0618i		−	0.817713i
$184$		0			0
$185$	−21.2651	−	12.2774i	−1.56344	−	0.902653i
$186$		0			0
$187$	−4.72358	−	8.18148i	−0.345422	−	0.598289i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	19.8196	−	11.4428i	1.43409	−	0.827974i	0.436664	−	0.899625i	$-0.356160\pi$
$191$	19.8196	−	11.4428i	1.43409	−	0.827974i	0.997430	+	0.0716507i	$0.0228267\pi$
$192$		0			0
$193$	−7.30816	+	12.6581i	−0.526053	+	0.911151i	0.473486	+	0.880801i	$0.342995\pi$
$193$	−7.30816	+	12.6581i	−0.526053	+	0.911151i	−0.999539	+	0.0303495i	$0.990338\pi$
$194$		0			0
$195$	−9.42002			−0.674581
$196$		0			0
$197$	24.5430			1.74861			0.874307	−	0.485374i	$-0.161316\pi$
$197$	24.5430			1.74861			0.874307	+	0.485374i	$0.161316\pi$
$198$		0			0
$199$	−3.02329	+	5.23650i	−0.214316	+	0.371206i	−0.953061	−	0.302779i	$-0.902085\pi$
$199$	−3.02329	+	5.23650i	−0.214316	+	0.371206i	0.738745	+	0.673985i	$0.235419\pi$
$200$		0			0
$201$	10.5261	−	6.07723i	0.742452	−	0.428655i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−1.33922	−	2.31960i	−0.0935355	−	0.162008i
$206$		0			0
$207$	3.14171	+	1.81387i	0.218364	+	0.126073i
$208$		0			0
$209$		−	10.0543i		−	0.695471i
$210$		0			0
$211$		−	9.33513i		−	0.642657i	−0.946968	−	0.321328i	$-0.895871\pi$
$211$		−	9.33513i		−	0.642657i	0.946968	−	0.321328i	$-0.104129\pi$
$212$		0			0
$213$	10.9335	+	6.31243i	0.749148	+	0.432521i
$214$		0			0
$215$	7.75362	+	13.4297i	0.528792	+	0.915895i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	5.62060	−	3.24505i	0.379805	−	0.219280i
$220$		0			0
$221$	−10.1242	+	17.5357i	−0.681029	+	1.17958i
$222$		0			0
$223$	−5.48794			−0.367500			−0.183750	−	0.982973i	$-0.558824\pi$
$223$	−5.48794			−0.367500			−0.183750	+	0.982973i	$0.558824\pi$
$224$		0			0
$225$	−5.33530			−0.355687
$226$		0			0
$227$	−0.519063	+	0.899043i	−0.0344514	+	0.0596716i	−0.882737	−	0.469867i	$-0.844302\pi$
$227$	−0.519063	+	0.899043i	−0.0344514	+	0.0596716i	0.848286	+	0.529539i	$0.177635\pi$
$228$		0			0
$229$	13.5133	−	7.80193i	0.892987	−	0.515566i	0.0180687	−	0.999837i	$-0.494248\pi$
$229$	13.5133	−	7.80193i	0.892987	−	0.515566i	0.874918	+	0.484270i	$0.160915\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.60780	−	7.98095i	−0.301867	−	0.522849i	0.674692	−	0.738100i	$-0.264277\pi$
$233$	−4.60780	−	7.98095i	−0.301867	−	0.522849i	−0.976559	+	0.215250i	$0.930943\pi$
$234$		0			0
$235$	−8.22345	−	4.74781i	−0.536439	−	0.309713i
$236$		0			0
$237$		−	7.79367i		−	0.506253i
$238$		0			0
$239$		−	1.54809i		−	0.100137i	−0.998746	−	0.0500687i	$-0.984056\pi$
$239$		−	1.54809i		−	0.100137i	0.998746	−	0.0500687i	$-0.0159440\pi$
$240$		0			0
$241$	−3.19154	−	1.84264i	−0.205585	−	0.118695i	0.393673	−	0.919251i	$-0.371204\pi$
$241$	−3.19154	−	1.84264i	−0.205585	−	0.118695i	−0.599258	+	0.800556i	$0.704538\pi$
$242$		0			0
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−18.6627	+	10.7749i	−1.18748	+	0.685590i
$248$		0			0
$249$	4.43751	−	7.68599i	0.281216	−	0.487080i
$250$		0			0
$251$	−26.1940			−1.65335			−0.826676	−	0.562679i	$-0.809771\pi$
$251$	−26.1940			−1.65335			−0.826676	+	0.562679i	$0.809771\pi$
$252$		0			0
$253$	−4.95947			−0.311799
$254$		0			0
$255$	−11.1079	+	19.2395i	−0.695606	+	1.20482i
$256$		0			0
$257$	0.721527	−	0.416574i	0.0450076	−	0.0259851i	−0.477327	−	0.878726i	$-0.658394\pi$
$257$	0.721527	−	0.416574i	0.0450076	−	0.0259851i	0.522335	+	0.852740i	$0.325061\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	0.555927	+	0.962893i	0.0344110	+	0.0596016i
$262$		0			0
$263$	4.36661	+	2.52106i	0.269256	+	0.155455i	0.628550	−	0.777769i	$-0.283649\pi$
$263$	4.36661	+	2.52106i	0.269256	+	0.155455i	−0.359293	+	0.933225i	$0.616982\pi$
$264$		0			0
$265$		−	14.7174i		−	0.904085i
$266$		0			0
$267$		−	12.6146i		−	0.772002i
$268$		0			0
$269$	−4.20537	−	2.42797i	−0.256406	−	0.148036i	0.366288	−	0.930501i	$-0.380628\pi$
$269$	−4.20537	−	2.42797i	−0.256406	−	0.148036i	−0.622694	+	0.782466i	$0.713962\pi$
$270$		0			0
$271$	−11.1244	−	19.2680i	−0.675759	−	1.17045i	−0.976246	−	0.216664i	$-0.930483\pi$
$271$	−11.1244	−	19.2680i	−0.675759	−	1.17045i	0.300487	−	0.953786i	$-0.402851\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.31669	−	3.64694i	0.380910	−	0.219919i
$276$		0			0
$277$	−0.335303	+	0.580762i	−0.0201464	+	0.0348946i	−0.875923	−	0.482451i	$-0.839747\pi$
$277$	−0.335303	+	0.580762i	−0.0201464	+	0.0348946i	0.855776	+	0.517346i	$0.173080\pi$
$278$		0			0
$279$	8.70319			0.521046
$280$		0			0
$281$	25.5971			1.52700			0.763499	−	0.645810i	$-0.223480\pi$
$281$	25.5971			1.52700			0.763499	+	0.645810i	$0.223480\pi$
$282$		0			0
$283$	5.55574	−	9.62283i	0.330255	−	0.572018i	−0.652307	−	0.757955i	$-0.726199\pi$
$283$	5.55574	−	9.62283i	0.330255	−	0.572018i	0.982562	+	0.185937i	$0.0595320\pi$
$284$		0			0
$285$	−20.4760	+	11.8218i	−1.21289	+	0.700264i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	15.3766	+	26.6331i	0.904508	+	1.56665i
$290$		0			0
$291$	12.0214	+	6.94057i	0.704708	+	0.406864i
$292$		0			0
$293$		−	19.2818i		−	1.12645i	−0.826303	−	0.563226i	$-0.809560\pi$
$293$		−	19.2818i		−	1.12645i	0.826303	−	0.563226i	$-0.190440\pi$
$294$		0			0
$295$		−	45.3245i		−	2.63890i
$296$		0			0
$297$	−1.18394	−	0.683549i	−0.0686992	−	0.0396635i
$298$		0			0
$299$	5.31491	+	9.20569i	0.307369	+	0.532379i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	1.43666	−	0.829455i	0.0825338	−	0.0476509i
$304$		0			0
$305$	17.7811	−	30.7977i	1.01814	−	1.76347i
$306$		0			0
$307$	−26.0058			−1.48423			−0.742115	−	0.670273i	$-0.766177\pi$
$307$	−26.0058			−1.48423			−0.742115	+	0.670273i	$0.766177\pi$
$308$		0			0
$309$	−1.30791			−0.0744042
$310$		0			0
$311$	9.53862	−	16.5214i	0.540885	−	0.936841i	−0.457968	−	0.888969i	$-0.651423\pi$
$311$	9.53862	−	16.5214i	0.540885	−	0.936841i	0.998853	−	0.0478723i	$-0.0152440\pi$
$312$		0			0
$313$	−18.4968	+	10.6791i	−1.04550	+	0.603620i	−0.921386	−	0.388648i	$-0.872942\pi$
$313$	−18.4968	+	10.6791i	−1.04550	+	0.603620i	−0.124114	+	0.992268i	$0.539609\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.87066	−	6.70417i	−0.217398	−	0.376544i	0.736614	−	0.676313i	$-0.236424\pi$
$317$	−3.87066	−	6.70417i	−0.217398	−	0.376544i	−0.954012	+	0.299770i	$0.903090\pi$
$318$		0			0
$319$	−1.31637	−	0.760006i	−0.0737025	−	0.0425522i
$320$		0			0
$321$			7.15204i			0.399188i
$322$		0			0
$323$			50.8223i			2.82783i
$324$		0			0
$325$	−13.5388	−	7.81662i	−0.750997	−	0.433588i
$326$		0			0
$327$	−7.52215	−	13.0287i	−0.415976	−	0.720491i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.585423	−	0.337994i	0.0321778	−	0.0185778i	−0.483825	−	0.875165i	$-0.660753\pi$
$331$	0.585423	−	0.337994i	0.0321778	−	0.0185778i	0.516003	+	0.856587i	$0.327419\pi$
$332$		0			0
$333$	−3.81896	+	6.61463i	−0.209278	+	0.362480i
$334$		0			0
$335$	39.0748			2.13489
$336$		0			0
$337$	−0.176755			−0.00962847			−0.00481423	−	0.999988i	$-0.501532\pi$
$337$	−0.176755			−0.00962847			−0.00481423	+	0.999988i	$0.501532\pi$
$338$		0			0
$339$	−7.72648	+	13.3827i	−0.419645	+	0.726846i
$340$		0			0
$341$	−10.3041	+	5.94905i	−0.557996	+	0.322159i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	5.83133	+	10.1002i	0.313948	+	0.543774i
$346$		0			0
$347$	−5.39220	−	3.11319i	−0.289468	−	0.167125i	0.348234	−	0.937408i	$-0.386782\pi$
$347$	−5.39220	−	3.11319i	−0.289468	−	0.167125i	−0.637702	+	0.770283i	$0.720115\pi$
$348$		0			0
$349$			17.4414i			0.933616i	0.884359	+	0.466808i	$0.154596\pi$
$349$			17.4414i			0.933616i	−0.884359	+	0.466808i	$0.845404\pi$
$350$		0			0
$351$			2.93015i			0.156400i
$352$		0			0
$353$	7.53631	+	4.35109i	0.401117	+	0.231585i	0.686966	−	0.726690i	$-0.258942\pi$
$353$	7.53631	+	4.35109i	0.401117	+	0.231585i	−0.285849	+	0.958275i	$0.592275\pi$
$354$		0			0
$355$	20.2936	+	35.1495i	1.07707	+	1.86554i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−0.661871	+	0.382131i	−0.0349322	+	0.0201681i	−0.517364	−	0.855765i	$-0.673087\pi$
$359$	−0.661871	+	0.382131i	−0.0349322	+	0.0201681i	0.482432	+	0.875933i	$0.339753\pi$
$360$		0			0
$361$	−17.5443	+	30.3876i	−0.923384	+	1.59935i
$362$		0			0
$363$	−9.13104			−0.479256
$364$		0			0
$365$	20.8648			1.09211
$366$		0			0
$367$	13.2581	−	22.9637i	0.692067	−	1.19869i	−0.279093	−	0.960264i	$-0.590034\pi$
$367$	13.2581	−	22.9637i	0.692067	−	1.19869i	0.971160	−	0.238431i	$-0.0766330\pi$
$368$		0			0
$369$	−0.721527	+	0.416574i	−0.0375612	+	0.0216860i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	10.0655	+	17.4340i	0.521173	+	0.902698i	0.999697	+	0.0246235i	$0.00783870\pi$
$373$	10.0655	+	17.4340i	0.521173	+	0.902698i	−0.478524	+	0.878075i	$0.658828\pi$
$374$		0			0
$375$	−0.933533	−	0.538976i	−0.0482074	−	0.0278326i
$376$		0			0
$377$			3.25790i			0.167790i
$378$		0			0
$379$		−	10.2608i		−	0.527061i	−0.964651	−	0.263531i	$-0.915113\pi$
$379$		−	10.2608i		−	0.527061i	0.964651	−	0.263531i	$-0.0848870\pi$
$380$		0			0
$381$	1.87476	+	1.08239i	0.0960468	+	0.0554526i
$382$		0			0
$383$	−1.17157	−	2.02922i	−0.0598646	−	0.103688i	0.834540	−	0.550947i	$-0.185734\pi$
$383$	−1.17157	−	2.02922i	−0.0598646	−	0.103688i	−0.894404	+	0.447259i	$0.852400\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	4.17738	−	2.41181i	0.212348	−	0.122599i
$388$		0			0
$389$	−12.0220	+	20.8227i	−0.609540	+	1.05576i	0.381776	+	0.924255i	$0.375313\pi$
$389$	−12.0220	+	20.8227i	−0.609540	+	1.05576i	−0.991316	+	0.131500i	$0.958021\pi$
$390$		0			0
$391$	25.0690			1.26780
$392$		0			0
$393$	4.97877			0.251146
$394$		0			0
$395$	12.5278	−	21.6987i	0.630340	−	1.09178i
$396$		0			0
$397$	−15.8938	+	9.17628i	−0.797686	+	0.460544i	−0.842661	−	0.538444i	$-0.819012\pi$
$397$	−15.8938	+	9.17628i	−0.797686	+	0.460544i	0.0449754	+	0.998988i	$0.485679\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.48486	+	2.57185i	0.0741503	+	0.128432i	0.900716	−	0.434407i	$-0.143042\pi$
$401$	1.48486	+	2.57185i	0.0741503	+	0.128432i	−0.826566	+	0.562840i	$0.809709\pi$
$402$		0			0
$403$	22.0851	+	12.7508i	1.10014	+	0.635164i
$404$		0			0
$405$			3.21486i			0.159748i
$406$		0			0
$407$		−	10.4418i		−	0.517580i
$408$		0			0
$409$	20.7415	+	11.9751i	1.02560	+	0.592131i	0.915721	−	0.401814i	$-0.131620\pi$
$409$	20.7415	+	11.9751i	1.02560	+	0.592131i	0.109880	+	0.993945i	$0.464953\pi$
$410$		0			0
$411$	−1.84490	−	3.19546i	−0.0910021	−	0.157620i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	24.7094	−	14.2660i	1.21293	−	0.700288i
$416$		0			0
$417$	−6.02884	+	10.4423i	−0.295234	+	0.511360i
$418$		0			0
$419$	36.3065			1.77369			0.886844	−	0.462069i	$-0.152893\pi$
$419$	36.3065			1.77369			0.886844	+	0.462069i	$0.152893\pi$
$420$		0			0
$421$	−22.6274			−1.10279			−0.551396	−	0.834243i	$-0.685905\pi$
$421$	−22.6274			−1.10279			−0.551396	+	0.834243i	$0.685905\pi$
$422$		0			0
$423$	−1.47683	+	2.55795i	−0.0718061	+	0.124372i
$424$		0			0
$425$	−31.9294	+	18.4345i	−1.54881	+	0.894203i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−2.00290	−	3.46913i	−0.0967010	−	0.167491i
$430$		0			0
$431$	26.5038	+	15.3020i	1.27664	+	0.737071i	0.976230	−	0.216738i	$-0.0695418\pi$
$431$	26.5038	+	15.3020i	1.27664	+	0.737071i	0.300414	+	0.953809i	$0.402875\pi$
$432$		0			0
$433$			14.4650i			0.695146i	0.937653	+	0.347573i	$0.112994\pi$
$433$			14.4650i			0.695146i	−0.937653	+	0.347573i	$0.887006\pi$
$434$		0			0
$435$			3.57445i			0.171382i
$436$		0			0
$437$	23.1057	+	13.3401i	1.10530	+	0.638143i
$438$		0			0
$439$	−4.55491	−	7.88933i	−0.217394	−	0.376537i	0.736617	−	0.676311i	$-0.236422\pi$
$439$	−4.55491	−	7.88933i	−0.217394	−	0.376537i	−0.954010	+	0.299773i	$0.903089\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.45362	−	1.41660i	0.116575	−	0.0673045i	−0.440579	−	0.897714i	$-0.645227\pi$
$443$	2.45362	−	1.41660i	0.116575	−	0.0673045i	0.557154	+	0.830409i	$0.311893\pi$
$444$		0			0
$445$	20.2771	−	35.1210i	0.961227	−	1.66489i
$446$		0			0
$447$	−3.30262			−0.156208
$448$		0			0
$449$	10.3630			0.489058			0.244529	−	0.969642i	$-0.421367\pi$
$449$	10.3630			0.489058			0.244529	+	0.969642i	$0.421367\pi$
$450$		0			0
$451$	0.569497	−	0.986397i	0.0268166	−	0.0464476i
$452$		0			0
$453$	−16.4122	+	9.47557i	−0.771111	+	0.445201i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	3.32976	+	5.76731i	0.155759	+	0.269783i	0.933335	−	0.359006i	$-0.116884\pi$
$457$	3.32976	+	5.76731i	0.155759	+	0.269783i	−0.777576	+	0.628789i	$0.783551\pi$
$458$		0			0
$459$	5.98456	+	3.45519i	0.279335	+	0.161274i
$460$		0			0
$461$			1.71311i			0.0797873i	0.999204	+	0.0398936i	$0.0127019\pi$
$461$			1.71311i			0.0797873i	−0.999204	+	0.0398936i	$0.987298\pi$
$462$		0			0
$463$		−	24.1733i		−	1.12343i	−0.827331	−	0.561715i	$-0.810142\pi$
$463$		−	24.1733i		−	1.12343i	0.827331	−	0.561715i	$-0.189858\pi$
$464$		0			0
$465$	24.2310	+	13.9897i	1.12368	+	0.648759i
$466$		0			0
$467$	18.6327	+	32.2728i	0.862220	+	1.49341i	0.869782	+	0.493437i	$0.164260\pi$
$467$	18.6327	+	32.2728i	0.862220	+	1.49341i	−0.00756221	+	0.999971i	$0.502407\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.767676	+	0.443218i	−0.0353726	+	0.0204224i
$472$		0			0
$473$	−3.29718	+	5.71088i	−0.151604	+	0.262587i
$474$		0			0
$475$	−39.2385			−1.80038
$476$		0			0
$477$	−4.57794			−0.209610
$478$		0			0
$479$	10.9298	−	18.9310i	0.499395	−	0.864978i	−0.500605	−	0.865676i	$-0.666889\pi$
$479$	10.9298	−	18.9310i	0.499395	−	0.864978i	1.00000		0.000698448i	$0.000222323\pi$
$480$		0			0
$481$	−19.3819	+	11.1901i	−0.883737	+	0.510226i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	22.3129	+	38.6472i	1.01318	+	1.75488i
$486$		0			0
$487$	2.92083	+	1.68634i	0.132356	+	0.0764155i	0.564716	−	0.825285i	$-0.308986\pi$
$487$	2.92083	+	1.68634i	0.132356	+	0.0764155i	−0.432360	+	0.901701i	$0.642319\pi$
$488$		0			0
$489$			19.3538i			0.875208i
$490$		0			0
$491$		−	9.68824i		−	0.437224i	−0.975812	−	0.218612i	$-0.929847\pi$
$491$		−	9.68824i		−	0.437224i	0.975812	−	0.218612i	$-0.0701529\pi$
$492$		0			0
$493$	6.65395	+	3.84166i	0.299679	+	0.173020i
$494$		0			0
$495$	−2.19751	−	3.80620i	−0.0987708	−	0.171076i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−11.8992	+	6.87003i	−0.532683	+	0.307545i	−0.742108	−	0.670280i	$-0.766174\pi$
$499$	−11.8992	+	6.87003i	−0.532683	+	0.307545i	0.209425	+	0.977825i	$0.432841\pi$
$500$		0			0
$501$	12.7428	−	22.0711i	0.569305	−	0.986065i
$502$		0			0
$503$	1.92715			0.0859273			0.0429637	−	0.999077i	$-0.486320\pi$
$503$	1.92715			0.0859273			0.0429637	+	0.999077i	$0.486320\pi$
$504$		0			0
$505$	5.33316			0.237322
$506$		0			0
$507$	2.20711	−	3.82282i	0.0980211	−	0.169777i
$508$		0			0
$509$	−12.2647	+	7.08104i	−0.543624	+	0.313862i	−0.746546	−	0.665333i	$-0.768289\pi$
$509$	−12.2647	+	7.08104i	−0.543624	+	0.313862i	0.202922	+	0.979195i	$0.434956\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	3.67725	+	6.36918i	0.162354	+	0.281206i
$514$		0			0
$515$	−3.64140	−	2.10236i	−0.160459	−	0.0926413i
$516$		0			0
$517$		−	4.03795i		−	0.177589i
$518$		0			0
$519$		−	21.6924i		−	0.952193i
$520$		0			0
$521$	−18.7084	−	10.8013i	−0.819630	−	0.473213i	0.0306591	−	0.999530i	$-0.490239\pi$
$521$	−18.7084	−	10.8013i	−0.819630	−	0.473213i	−0.850289	+	0.526316i	$0.823573\pi$
$522$		0			0
$523$	6.98251	+	12.0941i	0.305324	+	0.528836i	0.977333	−	0.211706i	$-0.0679020\pi$
$523$	6.98251	+	12.0941i	0.305324	+	0.528836i	−0.672010	+	0.740542i	$0.734569\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	52.0847	−	30.0711i	2.26885	−	1.30992i
$528$		0			0
$529$	−4.91976	+	8.52127i	−0.213903	+	0.370490i
$530$		0			0
$531$	−14.0985			−0.611821
$532$		0			0
$533$	−2.44125			−0.105742
$534$		0			0
$535$	−11.4964	+	19.9123i	−0.497032	+	0.860885i
$536$		0			0
$537$	10.6369	−	6.14122i	0.459016	−	0.265013i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−1.94002	−	3.36022i	−0.0834081	−	0.144467i	0.821304	−	0.570491i	$-0.193247\pi$
$541$	−1.94002	−	3.36022i	−0.0834081	−	0.144467i	−0.904712	+	0.426024i	$0.859914\pi$
$542$		0			0
$543$	2.37676	+	1.37222i	0.101996	+	0.0588876i
$544$		0			0
$545$		−	48.3652i		−	2.07174i
$546$		0			0
$547$			35.1640i			1.50351i	0.659445	+	0.751753i	$0.270791\pi$
$547$			35.1640i			1.50351i	−0.659445	+	0.751753i	$0.729209\pi$
$548$		0			0
$549$	−9.57981	−	5.53091i	−0.408856	−	0.236053i
$550$		0			0
$551$	4.08856	+	7.08159i	0.174178	+	0.301686i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−21.2651	+	12.2774i	−0.902653	+	0.521147i
$556$		0			0
$557$	−21.2173	+	36.7495i	−0.899006	+	1.55712i	−0.0702393	+	0.997530i	$0.522376\pi$
$557$	−21.2173	+	36.7495i	−0.899006	+	1.55712i	−0.828767	+	0.559594i	$0.810957\pi$
$558$		0			0
$559$	14.1339			0.597802
$560$		0			0
$561$	−9.44716			−0.398859
$562$		0			0
$563$	−8.27438	+	14.3316i	−0.348724	+	0.604007i	−0.986023	−	0.166609i	$-0.946718\pi$
$563$	−8.27438	+	14.3316i	−0.348724	+	0.604007i	0.637299	+	0.770616i	$0.280051\pi$
$564$		0			0
$565$	−43.0233	+	24.8395i	−1.81000	+	1.04501i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	12.1283	+	21.0069i	0.508446	+	0.880654i	0.999952	+	0.00978001i	$0.00311312\pi$
$569$	12.1283	+	21.0069i	0.508446	+	0.880654i	−0.491506	+	0.870874i	$0.663554\pi$
$570$		0			0
$571$	4.00591	+	2.31281i	0.167642	+	0.0967882i	0.581474	−	0.813565i	$-0.302476\pi$
$571$	4.00591	+	2.31281i	0.167642	+	0.0967882i	−0.413831	+	0.910354i	$0.635810\pi$
$572$		0			0
$573$		−	22.8857i		−	0.956062i
$574$		0			0
$575$			19.3551i			0.807163i
$576$		0			0
$577$	23.2014	+	13.3954i	0.965889	+	0.557656i	0.897980	−	0.440035i	$-0.145034\pi$
$577$	23.2014	+	13.3954i	0.965889	+	0.557656i	0.0679083	+	0.997692i	$0.478367\pi$
$578$		0			0
$579$	7.30816	+	12.6581i	0.303717	+	0.526053i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	5.42002	−	3.12925i	0.224474	−	0.129600i
$584$		0			0
$585$	−4.71001	+	8.15797i	−0.194735	+	0.337291i
$586$		0			0
$587$	−27.8591			−1.14987			−0.574933	−	0.818200i	$-0.694972\pi$
$587$	−27.8591			−1.14987			−0.574933	+	0.818200i	$0.694972\pi$
$588$		0			0
$589$	64.0075			2.63738
$590$		0			0
$591$	12.2715	−	21.2548i	0.504781	−	0.874307i
$592$		0			0
$593$	1.35884	−	0.784528i	0.0558010	−	0.0322167i	−0.471840	−	0.881684i	$-0.656410\pi$
$593$	1.35884	−	0.784528i	0.0558010	−	0.0322167i	0.527641	+	0.849468i	$0.323077\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3.02329	+	5.23650i	0.123735	+	0.214316i
$598$		0			0
$599$	−34.7412	−	20.0578i	−1.41949	−	0.819540i	−0.423232	−	0.906021i	$-0.639105\pi$
$599$	−34.7412	−	20.0578i	−1.41949	−	0.819540i	−0.996254	+	0.0864809i	$0.972438\pi$
$600$		0			0
$601$		−	24.7827i		−	1.01091i	−0.862854	−	0.505453i	$-0.831325\pi$
$601$		−	24.7827i		−	1.01091i	0.862854	−	0.505453i	$-0.168675\pi$
$602$		0			0
$603$		−	12.1545i		−	0.494968i
$604$		0			0
$605$	−25.4222	−	14.6775i	−1.03356	−	0.596725i
$606$		0			0
$607$	−2.33120	−	4.03776i	−0.0946205	−	0.163887i	0.814830	−	0.579700i	$-0.196830\pi$
$607$	−2.33120	−	4.03776i	−0.0946205	−	0.163887i	−0.909450	+	0.415813i	$0.863497\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.49519	+	4.32735i	−0.303223	+	0.175066i
$612$		0			0
$613$	−14.2909	+	24.7525i	−0.577202	+	0.999743i	0.418596	+	0.908172i	$0.362522\pi$
$613$	−14.2909	+	24.7525i	−0.577202	+	0.999743i	−0.995799	+	0.0915710i	$0.970811\pi$
$614$		0			0
$615$	−2.67845			−0.108005
$616$		0			0
$617$	10.1524			0.408720			0.204360	−	0.978896i	$-0.434489\pi$
$617$	10.1524			0.408720			0.204360	+	0.978896i	$0.434489\pi$
$618$		0			0
$619$	−4.32011	+	7.48265i	−0.173640	+	0.300753i	−0.939690	−	0.342028i	$-0.888886\pi$
$619$	−4.32011	+	7.48265i	−0.173640	+	0.300753i	0.766050	+	0.642781i	$0.222220\pi$
$620$		0			0
$621$	3.14171	−	1.81387i	0.126073	−	0.0727881i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	11.6055	+	20.1014i	0.464221	+	0.804055i
$626$		0			0
$627$	−8.70729	−	5.02716i	−0.347736	−	0.200765i
$628$		0			0
$629$			52.7809i			2.10451i
$630$		0			0
$631$		−	5.46211i		−	0.217443i	−0.994072	−	0.108722i	$-0.965324\pi$
$631$		−	5.46211i		−	0.217443i	0.994072	−	0.108722i	$-0.0346757\pi$
$632$		0			0
$633$	−8.08446	−	4.66756i	−0.321328	−	0.185519i
$634$		0			0
$635$	3.47974	+	6.02708i	0.138089	+	0.239177i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	10.9335	−	6.31243i	0.432521	−	0.249716i
$640$		0			0
$641$	−0.714111	+	1.23688i	−0.0282057	+	0.0488537i	−0.879784	−	0.475374i	$-0.842313\pi$
$641$	−0.714111	+	1.23688i	−0.0282057	+	0.0488537i	0.851578	+	0.524228i	$0.175646\pi$
$642$		0			0
$643$	24.6036			0.970270			0.485135	−	0.874439i	$-0.338771\pi$
$643$	24.6036			0.970270			0.485135	+	0.874439i	$0.338771\pi$
$644$		0			0
$645$	15.5072			0.610597
$646$		0			0
$647$	10.1392	−	17.5617i	0.398614	−	0.690420i	−0.594941	−	0.803770i	$-0.702825\pi$
$647$	10.1392	−	17.5617i	0.398614	−	0.690420i	0.993555	+	0.113349i	$0.0361578\pi$
$648$		0			0
$649$	16.6918	−	9.63699i	0.655209	−	0.378285i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.4420	−	37.1387i	−0.839092	−	1.45335i	−0.890655	−	0.454680i	$-0.849754\pi$
$653$	−21.4420	−	37.1387i	−0.839092	−	1.45335i	0.0515635	−	0.998670i	$-0.483580\pi$
$654$		0			0
$655$	13.8616	+	8.00301i	0.541619	+	0.312704i
$656$		0			0
$657$		−	6.49011i		−	0.253203i
$658$		0			0
$659$		−	31.4717i		−	1.22596i	−0.790098	−	0.612981i	$-0.789970\pi$
$659$		−	31.4717i		−	1.22596i	0.790098	−	0.612981i	$-0.210030\pi$
$660$		0			0
$661$	10.6655	+	6.15771i	0.414839	+	0.239507i	0.692867	−	0.721066i	$-0.256347\pi$
$661$	10.6655	+	6.15771i	0.414839	+	0.239507i	−0.278028	+	0.960573i	$0.589681\pi$
$662$		0			0
$663$	10.1242	+	17.5357i	0.393192	+	0.681029i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	3.49312	−	2.01676i	0.135254	−	0.0780891i
$668$		0			0
$669$	−2.74397	+	4.75270i	−0.106088	+	0.183750i
$670$		0			0
$671$	15.1226			0.583801
$672$		0			0
$673$	37.1864			1.43343			0.716716	−	0.697365i	$-0.245645\pi$
$673$	37.1864			1.43343			0.716716	+	0.697365i	$0.245645\pi$
$674$		0			0
$675$	−2.66765	+	4.62051i	−0.102678	+	0.177843i
$676$		0			0
$677$	30.8345	−	17.8023i	1.18507	−	0.684198i	0.227885	−	0.973688i	$-0.426819\pi$
$677$	30.8345	−	17.8023i	1.18507	−	0.684198i	0.957181	+	0.289490i	$0.0934857\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	0.519063	+	0.899043i	0.0198905	+	0.0344514i
$682$		0			0
$683$	27.8909	+	16.1028i	1.06722	+	0.616157i	0.927419	−	0.374023i	$-0.122022\pi$
$683$	27.8909	+	16.1028i	1.06722	+	0.616157i	0.139796	+	0.990180i	$0.455355\pi$
$684$		0			0
$685$		−	11.8622i		−	0.453230i
$686$		0			0
$687$		−	15.6039i		−	0.595325i
$688$		0			0
$689$	−11.6169	−	6.70703i	−0.442570	−	0.255518i
$690$		0			0
$691$	−19.3084	−	33.4432i	−0.734527	−	1.27224i	−0.954931	−	0.296829i	$-0.904071\pi$
$691$	−19.3084	−	33.4432i	−0.734527	−	1.27224i	0.220404	−	0.975409i	$-0.429263\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−33.5704	+	19.3819i	−1.27340	+	0.735196i
$696$		0			0
$697$	−2.87868	+	4.98602i	−0.109038	+	0.188859i
$698$		0			0
$699$	−9.21561			−0.348566
$700$		0			0
$701$	30.8725			1.16604			0.583018	−	0.812459i	$-0.301872\pi$
$701$	30.8725			1.16604			0.583018	+	0.812459i	$0.301872\pi$
$702$		0			0
$703$	−28.0865	+	48.6473i	−1.05930	+	1.83477i
$704$		0			0
$705$	−8.22345	+	4.74781i	−0.309713	+	0.178813i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−19.9226	−	34.5070i	−0.748209	−	1.29594i	−0.948680	−	0.316237i	$-0.897581\pi$
$709$	−19.9226	−	34.5070i	−0.748209	−	1.29594i	0.200471	−	0.979700i	$-0.435753\pi$
$710$		0			0
$711$	−6.74952	−	3.89684i	−0.253127	−	0.146143i
$712$		0			0
$713$		−	31.5729i		−	1.18241i
$714$		0			0
$715$		−	12.8781i		−	0.481613i
$716$		0			0
$717$	−1.34068	−	0.774044i	−0.0500687	−	0.0289072i
$718$		0			0
$719$	1.04633	+	1.81230i	0.0390216	+	0.0675873i	0.884877	−	0.465826i	$-0.154243\pi$
$719$	1.04633	+	1.81230i	0.0390216	+	0.0675873i	−0.845855	+	0.533413i	$0.820909\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−3.19154	+	1.84264i	−0.118695	+	0.0685284i
$724$		0			0
$725$	−2.96604	+	5.13733i	−0.110156	+	0.190796i
$726$		0			0
$727$	−21.5164			−0.798001			−0.399000	−	0.916951i	$-0.630643\pi$
$727$	−21.5164			−0.798001			−0.399000	+	0.916951i	$0.630643\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	16.6665	−	28.8672i	0.616433	−	1.06769i
$732$		0			0
$733$	6.69313	−	3.86428i	0.247216	−	0.142730i	−0.371273	−	0.928524i	$-0.621078\pi$
$733$	6.69313	−	3.86428i	0.247216	−	0.142730i	0.618489	+	0.785794i	$0.287745\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.30816	+	14.3902i	0.306035	+	0.530068i
$738$		0			0
$739$	13.9485	+	8.05316i	0.513103	+	0.296240i	0.734108	−	0.679032i	$-0.237600\pi$
$739$	13.9485	+	8.05316i	0.513103	+	0.296240i	−0.221005	+	0.975273i	$0.570934\pi$
$740$		0			0
$741$			21.5498i			0.791651i
$742$		0			0
$743$		−	29.3296i		−	1.07600i	−0.842945	−	0.537999i	$-0.819180\pi$
$743$		−	29.3296i		−	1.07600i	0.842945	−	0.537999i	$-0.180820\pi$
$744$		0			0
$745$	−9.19497	−	5.30872i	−0.336878	−	0.194496i
$746$		0			0
$747$	−4.43751	−	7.68599i	−0.162360	−	0.281216i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	11.7772	−	6.79955i	0.429755	−	0.248119i	−0.269487	−	0.963004i	$-0.586854\pi$
$751$	11.7772	−	6.79955i	0.429755	−	0.248119i	0.699242	+	0.714885i	$0.253521\pi$
$752$		0			0
$753$	−13.0970	+	22.6847i	−0.477281	+	0.826676i
$754$		0			0
$755$	−60.9252			−2.21730
$756$		0			0
$757$	−2.59688			−0.0943851			−0.0471926	−	0.998886i	$-0.515027\pi$
$757$	−2.59688			−0.0943851			−0.0471926	+	0.998886i	$0.515027\pi$
$758$		0			0
$759$	−2.47974	+	4.29503i	−0.0900087	+	0.155900i
$760$		0			0
$761$	−14.9753	+	8.64598i	−0.542853	+	0.313416i	−0.746235	−	0.665683i	$-0.768140\pi$
$761$	−14.9753	+	8.64598i	−0.542853	+	0.313416i	0.203381	+	0.979100i	$0.434807\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	11.1079	+	19.2395i	0.401608	+	0.695606i
$766$		0			0
$767$	−35.7761	−	20.6553i	−1.29180	−	0.745820i
$768$		0			0
$769$			41.4025i			1.49301i	0.665378	+	0.746507i	$0.268270\pi$
$769$			41.4025i			1.49301i	−0.665378	+	0.746507i	$0.731730\pi$
$770$		0			0
$771$		−	0.833147i		−	0.0300051i
$772$		0			0
$773$	25.5191	+	14.7335i	0.917858	+	0.529925i	0.882951	−	0.469465i	$-0.155553\pi$
$773$	25.5191	+	14.7335i	0.917858	+	0.529925i	0.0349068	+	0.999391i	$0.488887\pi$
$774$		0			0
$775$	23.2171	+	40.2131i	0.833982	+	1.44450i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.30646	+	3.06369i	−0.190124	+	0.109768i
$780$		0			0
$781$	−8.62971	+	14.9471i	−0.308795	+	0.534849i
$782$		0			0
$783$	1.11185			0.0397344
$784$		0			0
$785$	−2.84976			−0.101712
$786$		0			0
$787$	−27.0921	+	46.9248i	−0.965728	+	1.67269i	−0.258081	+	0.966123i	$0.583090\pi$
$787$	−27.0921	+	46.9248i	−0.965728	+	1.67269i	−0.707647	+	0.706566i	$0.750243\pi$
$788$		0			0
$789$	4.36661	−	2.52106i	0.155455	−	0.0897521i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−16.2064	−	28.0703i	−0.575506	−	0.996806i
$794$		0			0
$795$	−12.7457	−	7.35872i	−0.452042	−	0.260987i
$796$		0			0
$797$		−	0.512549i		−	0.0181554i	−0.999959	−	0.00907771i	$-0.997110\pi$
$797$		−	0.512549i		−	0.0181554i	0.999959	−	0.00907771i	$-0.00288956\pi$
$798$		0			0
$799$			20.4110i			0.722088i
$800$		0			0
$801$	−10.9246	−	6.30731i	−0.386001	−	0.222858i
$802$		0			0
$803$	4.43631	+	7.68391i	0.156554	+	0.271159i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−4.20537	+	2.42797i	−0.148036	+	0.0854686i
$808$		0			0
$809$	26.5704	−	46.0212i	0.934164	−	1.61802i	0.158046	−	0.987432i	$-0.449481\pi$
$809$	26.5704	−	46.0212i	0.934164	−	1.61802i	0.776118	−	0.630588i	$-0.217186\pi$
$810$		0			0
$811$	−10.8127			−0.379687			−0.189843	−	0.981814i	$-0.560798\pi$
$811$	−10.8127			−0.379687			−0.189843	+	0.981814i	$0.560798\pi$
$812$		0			0
$813$	−22.2488			−0.780300
$814$		0			0
$815$	−31.1098	+	53.8838i	−1.08973	+	1.88747i
$816$		0			0
$817$	30.7225	−	17.7376i	1.07484	−	0.620561i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.35039	+	2.33895i	0.0471290	+	0.0816298i	0.888628	−	0.458630i	$-0.151659\pi$
$821$	1.35039	+	2.33895i	0.0471290	+	0.0816298i	−0.841499	+	0.540259i	$0.818326\pi$
$822$		0			0
$823$	−10.9234	−	6.30662i	−0.380765	−	0.219835i	0.297386	−	0.954757i	$-0.403885\pi$
$823$	−10.9234	−	6.30662i	−0.380765	−	0.219835i	−0.678151	+	0.734922i	$0.737219\pi$
$824$		0			0
$825$		−	7.29388i		−	0.253940i
$826$		0			0
$827$			2.95803i			0.102861i	0.998677	+	0.0514304i	$0.0163780\pi$
$827$			2.95803i			0.102861i	−0.998677	+	0.0514304i	$0.983622\pi$
$828$		0			0
$829$	−13.6919	−	7.90504i	−0.475540	−	0.274553i	0.243016	−	0.970022i	$-0.421863\pi$
$829$	−13.6919	−	7.90504i	−0.475540	−	0.274553i	−0.718556	+	0.695469i	$0.755197\pi$
$830$		0			0
$831$	0.335303	+	0.580762i	0.0116315	+	0.0201464i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	70.9555	−	40.9662i	2.45552	−	1.41769i
$836$		0			0
$837$	4.35159	−	7.53718i	0.150413	−	0.260523i
$838$		0			0
$839$	−5.13130			−0.177152			−0.0885761	−	0.996069i	$-0.528232\pi$
$839$	−5.13130			−0.177152			−0.0885761	+	0.996069i	$0.528232\pi$
$840$		0			0
$841$	−27.7638			−0.957372
$842$		0			0
$843$	12.7986	−	22.1678i	0.440806	−	0.763499i
$844$		0			0
$845$	12.2898	−	7.09553i	0.422783	−	0.244094i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−5.55574	−	9.62283i	−0.190673	−	0.330255i
$850$		0			0
$851$	23.9962	+	13.8542i	0.822578	+	0.474915i
$852$		0			0
$853$		−	45.1627i		−	1.54634i	−0.634198	−	0.773170i	$-0.718670\pi$
$853$		−	45.1627i		−	1.54634i	0.634198	−	0.773170i	$-0.281330\pi$
$854$		0			0
$855$			23.6436i			0.808596i
$856$		0			0
$857$	−1.27933	−	0.738624i	−0.0437012	−	0.0252309i	0.477990	−	0.878365i	$-0.341365\pi$
$857$	−1.27933	−	0.738624i	−0.0437012	−	0.0252309i	−0.521691	+	0.853134i	$0.674699\pi$
$858$		0			0
$859$	1.54091	+	2.66894i	0.0525753	+	0.0910631i	0.891115	−	0.453777i	$-0.149924\pi$
$859$	1.54091	+	2.66894i	0.0525753	+	0.0910631i	−0.838540	+	0.544840i	$0.816590\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−40.1836	+	23.2000i	−1.36787	+	0.789738i	−0.990655	−	0.136390i	$-0.956450\pi$
$863$	−40.1836	+	23.2000i	−1.36787	+	0.789738i	−0.377210	+	0.926128i	$0.623117\pi$
$864$		0			0
$865$	34.8691	−	60.3950i	1.18558	−	2.05349i
$866$		0			0
$867$	30.7533			1.04444
$868$		0			0
$869$	10.6547			0.361436
$870$		0			0
$871$	17.8072	−	30.8430i	0.603374	−	1.04507i
$872$		0			0
$873$	12.0214	−	6.94057i	0.406864	−	0.234903i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	25.2387	+	43.7147i	0.852251	+	1.47614i	0.879172	+	0.476504i	$0.158096\pi$
$877$	25.2387	+	43.7147i	0.852251	+	1.47614i	−0.0269211	+	0.999638i	$0.508570\pi$
$878$		0			0
$879$	−16.6985	−	9.64088i	−0.563226	−	0.325179i
$880$		0			0
$881$			3.66920i			0.123619i	0.998088	+	0.0618093i	$0.0196870\pi$
$881$			3.66920i			0.123619i	−0.998088	+	0.0618093i	$0.980313\pi$
$882$		0			0
$883$			18.0393i			0.607071i	0.952820	+	0.303535i	$0.0981671\pi$
$883$			18.0393i			0.607071i	−0.952820	+	0.303535i	$0.901833\pi$
$884$		0			0
$885$	−39.2522	−	22.6623i	−1.31945	−	0.761784i
$886$		0			0
$887$	−6.44980	−	11.1714i	−0.216563	−	0.375098i	0.737192	−	0.675683i	$-0.236151\pi$
$887$	−6.44980	−	11.1714i	−0.216563	−	0.375098i	−0.953755	+	0.300585i	$0.902818\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.18394	+	0.683549i	−0.0396635	+	0.0228997i
$892$		0			0
$893$	−10.8614	+	18.8124i	−0.363462	+	0.629534i
$894$		0			0
$895$	39.4863			1.31988
$896$		0			0
$897$	10.6298			0.354919
$898$		0			0
$899$	4.83833	−	8.38024i	0.161367	−	0.279497i
$900$		0			0
$901$	−27.3970	+	15.8177i	−0.912726	+	0.526962i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.41149	+	7.64093i	0.146643	+	0.253993i
$906$		0			0
$907$	−0.662657	−	0.382585i	−0.0220032	−	0.0127035i	0.488958	−	0.872307i	$-0.337377\pi$
$907$	−0.662657	−	0.382585i	−0.0220032	−	0.0127035i	−0.510961	+	0.859604i	$0.670710\pi$
$908$		0			0
$909$		−	1.65891i		−	0.0550226i
$910$		0			0
$911$			18.7415i			0.620934i	0.950584	+	0.310467i	$0.100485\pi$
$911$			18.7415i			0.620934i	−0.950584	+	0.310467i	$0.899515\pi$
$912$		0			0
$913$	10.5075	+	6.06651i	0.347747	+	0.200772i
$914$		0			0
$915$	−17.7811	−	30.7977i	−0.587824	−	1.01814i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	18.2263	−	10.5230i	0.601231	−	0.347121i	−0.168295	−	0.985737i	$-0.553826\pi$
$919$	18.2263	−	10.5230i	0.601231	−	0.347121i	0.769526	+	0.638616i	$0.220493\pi$
$920$		0			0
$921$	−13.0029	+	22.5217i	−0.428460	+	0.742115i
$922$		0			0
$923$	36.9928			1.21763
$924$		0			0
$925$	−40.7506			−1.33987
$926$		0			0
$927$	−0.653953	+	1.13268i	−0.0214786	+	0.0372021i
$928$		0			0
$929$	−28.3438	+	16.3643i	−0.929929	+	0.536895i	−0.886789	−	0.462174i	$-0.847069\pi$
$929$	−28.3438	+	16.3643i	−0.929929	+	0.536895i	−0.0431400	+	0.999069i	$0.513736\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−9.53862	−	16.5214i	−0.312280	−	0.540885i
$934$		0			0
$935$	−26.3023	−	15.1856i	−0.860176	−	0.496623i
$936$		0			0
$937$		−	2.53824i		−	0.0829207i	−0.999140	−	0.0414603i	$-0.986799\pi$
$937$		−	2.53824i		−	0.0829207i	0.999140	−	0.0414603i	$-0.0132010\pi$
$938$		0			0
$939$			21.3583i			0.697001i
$940$		0			0
$941$	39.9880	+	23.0871i	1.30357	+	0.752617i	0.981015	−	0.193933i	$-0.0621246\pi$
$941$	39.9880	+	23.0871i	1.30357	+	0.752617i	0.322556	+	0.946550i	$0.395458\pi$
$942$		0			0
$943$	1.51122	+	2.61751i	0.0492121	+	0.0852378i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.31063	+	0.756690i	−0.0425896	+	0.0245891i	−0.521144	−	0.853469i	$-0.674494\pi$
$947$	−1.31063	+	0.756690i	−0.0425896	+	0.0245891i	0.478554	+	0.878058i	$0.341161\pi$
$948$		0			0
$949$	9.50850	−	16.4692i	0.308659	−	0.534613i
$950$		0			0
$951$	−7.74131			−0.251029
$952$		0			0
$953$	−43.1132			−1.39657			−0.698287	−	0.715818i	$-0.746054\pi$
$953$	−43.1132			−1.39657			−0.698287	+	0.715818i	$0.746054\pi$
$954$		0			0
$955$	36.7871	−	63.7171i	1.19040	−	2.06184i
$956$		0			0
$957$	−1.31637	+	0.760006i	−0.0425522	+	0.0245675i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−22.3727	−	38.7507i	−0.721701	−	1.25002i
$962$		0			0
$963$	6.19385	+	3.57602i	0.199594	+	0.115236i
$964$		0			0
$965$			46.9894i			1.51264i
$966$		0			0
$967$			22.5218i			0.724253i	0.932129	+	0.362127i	$0.117949\pi$
$967$			22.5218i			0.724253i	−0.932129	+	0.362127i	$0.882051\pi$
$968$		0			0
$969$	44.0134	+	25.4112i	1.41391	+	0.816324i
$970$		0			0
$971$	−12.2447	−	21.2084i	−0.392951	−	0.680612i	0.599886	−	0.800085i	$-0.295213\pi$
$971$	−12.2447	−	21.2084i	−0.392951	−	0.680612i	−0.992837	+	0.119474i	$0.961879\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−13.5388	+	7.81662i	−0.433588	+	0.250332i
$976$		0			0
$977$	−8.31909	+	14.4091i	−0.266151	+	0.460987i	−0.967865	−	0.251472i	$-0.919085\pi$
$977$	−8.31909	+	14.4091i	−0.266151	+	0.460987i	0.701713	+	0.712459i	$0.252419\pi$
$978$		0			0
$979$	17.2454			0.551166
$980$		0			0
$981$	−15.0443			−0.480327
$982$		0			0
$983$	2.67809	−	4.63858i	0.0854177	−	0.147948i	−0.820151	−	0.572146i	$-0.806111\pi$
$983$	2.67809	−	4.63858i	0.0854177	−	0.147948i	0.905569	+	0.424199i	$0.139444\pi$
$984$		0			0
$985$	68.3312	−	39.4510i	2.17721	−	1.25701i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.74941	−	15.1544i	−0.278215	−	0.481883i
$990$		0			0
$991$	−4.04958	−	2.33803i	−0.128639	−	0.0742698i	0.434300	−	0.900769i	$-0.356996\pi$
$991$	−4.04958	−	2.33803i	−0.128639	−	0.0742698i	−0.562939	+	0.826499i	$0.690329\pi$
$992$		0			0
$993$		−	0.675988i		−	0.0214518i
$994$		0			0
$995$			19.4389i			0.616255i
$996$		0			0
$997$	0.785425	+	0.453465i	0.0248746	+	0.0143614i	0.512386	−	0.858755i	$-0.328762\pi$
$997$	0.785425	+	0.453465i	0.0248746	+	0.0143614i	−0.487511	+	0.873117i	$0.662095\pi$
$998$		0			0
$999$	3.81896	+	6.61463i	0.120827	+	0.209278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2352.2.bl.r.31.4		8
4.3	odd	2		2352.2.bl.q.31.4		8
7.2	even	3		2352.2.bl.t.607.1		8
7.3	odd	6		2352.2.b.l.1567.2	yes	8
7.4	even	3		2352.2.b.k.1567.7	yes	8
7.5	odd	6		2352.2.bl.q.607.4		8
7.6	odd	2		2352.2.bl.o.31.1		8
21.11	odd	6		7056.2.b.x.1567.2		8
21.17	even	6		7056.2.b.w.1567.7		8
28.3	even	6		2352.2.b.k.1567.2	✓	8
28.11	odd	6		2352.2.b.l.1567.7	yes	8
28.19	even	6	inner	2352.2.bl.r.607.4		8
28.23	odd	6		2352.2.bl.o.607.1		8
28.27	even	2		2352.2.bl.t.31.1		8
84.11	even	6		7056.2.b.w.1567.2		8
84.59	odd	6		7056.2.b.x.1567.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2352.2.b.k.1567.2	✓	8	28.3	even	6
2352.2.b.k.1567.7	yes	8	7.4	even	3
2352.2.b.l.1567.2	yes	8	7.3	odd	6
2352.2.b.l.1567.7	yes	8	28.11	odd	6
2352.2.bl.o.31.1		8	7.6	odd	2
2352.2.bl.o.607.1		8	28.23	odd	6
2352.2.bl.q.31.4		8	4.3	odd	2
2352.2.bl.q.607.4		8	7.5	odd	6
2352.2.bl.r.31.4		8	1.1	even	1	trivial
2352.2.bl.r.607.4		8	28.19	even	6	inner
2352.2.bl.t.31.1		8	28.27	even	2
2352.2.bl.t.607.1		8	7.2	even	3
7056.2.b.w.1567.2		8	84.11	even	6
7056.2.b.w.1567.7		8	21.17	even	6
7056.2.b.x.1567.2		8	21.11	odd	6
7056.2.b.x.1567.7		8	84.59	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2352.bl (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(2.78415 - 1.60743i) q^{5} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(2.78415 - 1.60743i) q^{5} +(-0.500000 - 0.866025i) q^{9} +(1.18394 + 0.683549i) q^{11} -2.93015i q^{13} -3.21486i q^{15} +(-5.98456 - 3.45519i) q^{17} +(-3.67725 - 6.36918i) q^{19} +(-3.14171 + 1.81387i) q^{23} +(2.66765 - 4.62051i) q^{25} -1.00000 q^{27} -1.11185 q^{29} +(-4.35159 + 7.53718i) q^{31} +(1.18394 - 0.683549i) q^{33} +(-3.81896 - 6.61463i) q^{37} +(-2.53759 - 1.46508i) q^{39} -0.833147i q^{41} +4.82362i q^{43} +(-2.78415 - 1.60743i) q^{45} +(-1.47683 - 2.55795i) q^{47} +(-5.98456 + 3.45519i) q^{51} +(2.28897 - 3.96462i) q^{53} +4.39502 q^{55} -7.35449 q^{57} +(7.04923 - 12.2096i) q^{59} +(9.57981 - 5.53091i) q^{61} +(-4.71001 - 8.15797i) q^{65} +(10.5261 + 6.07723i) q^{67} +3.62774i q^{69} +12.6249i q^{71} +(5.62060 + 3.24505i) q^{73} +(-2.66765 - 4.62051i) q^{75} +(6.74952 - 3.89684i) q^{79} +(-0.500000 + 0.866025i) q^{81} +8.87502 q^{83} -22.2159 q^{85} +(-0.555927 + 0.962893i) q^{87} +(10.9246 - 6.30731i) q^{89} +(4.35159 + 7.53718i) q^{93} +(-20.4760 - 11.8218i) q^{95} +13.8811i q^{97} -1.36710i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^9	\( 8 q + 4 q^{3} - 4 q^{9} - 24 q^{23} + 12 q^{25} - 8 q^{27} + 16 q^{29} - 16 q^{31} - 8 q^{47} - 8 q^{53} + 64 q^{55} + 24 q^{59} + 48 q^{61} + 8 q^{65} + 48 q^{67} + 48 q^{73} - 12 q^{75} + 24 q^{79} - 4 q^{81} - 64 q^{85} + 8 q^{87} + 48 q^{89} + 16 q^{93} - 72 q^{95}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^9 - 24 * q^23 + 12 * q^25 - 8 * q^27 + 16 * q^29 - 16 * q^31 - 8 * q^47 - 8 * q^53 + 64 * q^55 + 24 * q^59 + 48 * q^61 + 8 * q^65 + 48 * q^67 + 48 * q^73 - 12 * q^75 + 24 * q^79 - 4 * q^81 - 64 * q^85 + 8 * q^87 + 48 * q^89 + 16 * q^93 - 72 * q^95

Introduction

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