LMFDB - Embedded newform 2888.1.bs.a.283.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2888,1,Mod(35,2888)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2888, base_ring=CyclotomicField(342))

chi = DirichletCharacter(H, H._module([171, 171, 40]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("2888.35");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2888 = 2^{3} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2888.bs (of order $342$, degree $108$, 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:	$1.44129975648$
Analytic rank:	$0$
Dimension:	$108$
Coefficient field:	$\Q(\zeta_{171})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{108} - x^{105} + x^{99} - x^{96} + x^{90} - x^{87} + x^{81} - x^{78} + x^{72} - x^{69} + x^{63} + \cdots + 1 $ x^108 - x^105 + x^99 - x^96 + x^90 - x^87 + x^81 - x^78 + x^72 - x^69 + x^63 - x^60 + x^54 - x^48 + x^45 - x^39 + x^36 - x^30 + x^27 - x^21 + x^18 - x^12 + x^9 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{171}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{171} - \cdots)$

Embedding invariants

Embedding label			283.1
Root			$-0.861396 - 0.507934i$ of defining polynomial
Character	$\chi$	$=$	2888.283
Dual form			2888.1.bs.a.1643.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.919425 - 0.393266i) q^{2} +(0.903398 + 0.347734i) q^{3} +(0.690683 - 0.723158i) q^{4} +(0.967359 - 0.0355604i) q^{6} +(0.350638 - 0.936511i) q^{8} +(-0.0467056 - 0.0422095i) q^{9} +O(q^{10})$	\(q+(0.919425 - 0.393266i) q^{2} +(0.903398 + 0.347734i) q^{3} +(0.690683 - 0.723158i) q^{4} +(0.967359 - 0.0355604i) q^{6} +(0.350638 - 0.936511i) q^{8} +(-0.0467056 - 0.0422095i) q^{9} +(1.66095 - 0.674621i) q^{11} +(0.875429 - 0.413125i) q^{12} +(-0.0459136 - 0.998945i) q^{16} +(-1.89620 + 0.461689i) q^{17} +(-0.0595418 - 0.0204407i) q^{18} +(-0.800291 + 0.599612i) q^{19} +(1.26181 - 1.27346i) q^{22} +(0.642423 - 0.724114i) q^{24} +(0.577333 + 0.816509i) q^{25} +(-0.464606 - 0.918086i) q^{27} +(-0.435066 - 0.900399i) q^{32} +(1.73509 - 0.0318805i) q^{33} +(-1.56184 + 1.17020i) q^{34} +(-0.0627829 + 0.00462208i) q^{36} +(-0.500000 + 0.866025i) q^{38} +(0.735442 + 1.85951i) q^{41} +(-0.507736 - 0.746816i) q^{43} +(0.659335 - 1.66708i) q^{44} +(0.305890 - 0.918411i) q^{48} +(-0.298515 - 0.954405i) q^{49} +(0.851919 + 0.523673i) q^{50} +(-1.87356 - 0.242284i) q^{51} +(-0.788222 - 0.661397i) q^{54} +(-0.931487 + 0.263399i) q^{57} +(-1.18956 + 1.49972i) q^{59} +(-0.754107 - 0.656752i) q^{64} +(1.58275 - 0.711664i) q^{66} +(0.634492 + 1.79437i) q^{67} +(-0.975796 + 1.69013i) q^{68} +(-0.0559064 + 0.0289401i) q^{72} +(-0.206643 + 0.705943i) q^{73} +(0.237633 + 0.938391i) q^{75} +(-0.119134 + 0.992878i) q^{76} +(-0.0941235 - 0.928325i) q^{81} +(1.40747 + 1.42045i) q^{82} +(0.750981 + 0.168299i) q^{83} +(-0.760522 - 0.486965i) q^{86} +(-0.0493975 - 1.79205i) q^{88} +(-0.167724 - 0.572986i) q^{89} +(-0.0799378 - 0.964706i) q^{96} +(0.626538 - 1.77187i) q^{97} +(-0.649797 - 0.760108i) q^{98} +(-0.106051 - 0.0385995i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 108 * q + 3 * q^3 + 3 * q^6 + 3 * q^8 + 3 * q^9	$ 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{18} - 6 q^{22} + 3 q^{24} - 60 q^{27} + 3 q^{33} + 3 q^{36} - 54 q^{38} + 3 q^{41} - 6 q^{44} - 6 q^{48} + 3 q^{49} + 3 q^{50} - 3 q^{51} + 3 q^{54} + 3 q^{59} + 3 q^{64} + 3 q^{66} + 3 q^{67} - 3 q^{68} - 6 q^{72} - 6 q^{73} - 3 q^{81} + 3 q^{82} + 3 q^{97} - 3 q^{99}+O(q^{100}) $ 108 * q + 3 * q^3 + 3 * q^6 + 3 * q^8 + 3 * q^9 - 6 * q^18 - 6 * q^22 + 3 * q^24 - 60 * q^27 + 3 * q^33 + 3 * q^36 - 54 * q^38 + 3 * q^41 - 6 * q^44 - 6 * q^48 + 3 * q^49 + 3 * q^50 - 3 * q^51 + 3 * q^54 + 3 * q^59 + 3 * q^64 + 3 * q^66 + 3 * q^67 - 3 * q^68 - 6 * q^72 - 6 * q^73 - 3 * q^81 + 3 * q^82 + 3 * q^97 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{149}{171}\right)$

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 $

$2$	0.919425	−	0.393266i	0.919425	−	0.393266i
$2$	0.919425	−	0.393266i	0.919425	−	0.393266i
$3$	0.903398	+	0.347734i	0.903398	+	0.347734i	0.766044	−	0.642788i	$-0.222222\pi$
$3$	0.903398	+	0.347734i	0.903398	+	0.347734i	0.137354	+	0.990522i	$0.456140\pi$
$4$	0.690683	−	0.723158i	0.690683	−	0.723158i
$5$		0			0		−0.888069	−	0.459710i	$-0.847953\pi$
$5$		0			0		0.888069	+	0.459710i	$0.152047\pi$
$6$	0.967359	−	0.0355604i	0.967359	−	0.0355604i
$7$		0			0		0.592235	−	0.805765i	$-0.298246\pi$
$7$		0			0		−0.592235	+	0.805765i	$0.701754\pi$
$8$	0.350638	−	0.936511i	0.350638	−	0.936511i
$9$	−0.0467056	−	0.0422095i	−0.0467056	−	0.0422095i
$10$		0			0
$11$	1.66095	−	0.674621i	1.66095	−	0.674621i	0.663651	−	0.748042i	$-0.269006\pi$
$11$	1.66095	−	0.674621i	1.66095	−	0.674621i	0.997301	+	0.0734214i	$0.0233918\pi$
$12$	0.875429	−	0.413125i	0.875429	−	0.413125i
$13$		0			0		0.515825	−	0.856694i	$-0.327485\pi$
$13$		0			0		−0.515825	+	0.856694i	$0.672515\pi$
$14$		0			0
$15$		0			0
$16$	−0.0459136	−	0.998945i	−0.0459136	−	0.998945i
$17$	−1.89620	+	0.461689i	−1.89620	+	0.461689i	−0.896364	+	0.443318i	$0.853801\pi$
$17$	−1.89620	+	0.461689i	−1.89620	+	0.461689i	−0.999831	+	0.0183709i	$0.994152\pi$
$18$	−0.0595418	−	0.0204407i	−0.0595418	−	0.0204407i
$19$	−0.800291	+	0.599612i	−0.800291	+	0.599612i
$19$	−0.800291	+	0.599612i	−0.800291	+	0.599612i
$20$		0			0
$21$		0			0
$22$	1.26181	−	1.27346i	1.26181	−	1.27346i
$23$		0			0		−0.777724	−	0.628606i	$-0.783626\pi$
$23$		0			0		0.777724	+	0.628606i	$0.216374\pi$
$24$	0.642423	−	0.724114i	0.642423	−	0.724114i
$25$	0.577333	+	0.816509i	0.577333	+	0.816509i
$26$		0			0
$27$	−0.464606	−	0.918086i	−0.464606	−	0.918086i
$28$		0			0
$29$		0			0		0.832107	−	0.554615i	$-0.187135\pi$
$29$		0			0		−0.832107	+	0.554615i	$0.812865\pi$
$30$		0			0
$31$		0			0		−0.998482	−	0.0550878i	$-0.982456\pi$
$31$		0			0		0.998482	+	0.0550878i	$0.0175439\pi$
$32$	−0.435066	−	0.900399i	−0.435066	−	0.900399i
$33$	1.73509	−	0.0318805i	1.73509	−	0.0318805i
$34$	−1.56184	+	1.17020i	−1.56184	+	1.17020i
$35$		0			0
$36$	−0.0627829	+	0.00462208i	−0.0627829	+	0.00462208i
$37$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$37$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$38$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$39$		0			0
$40$		0			0
$41$	0.735442	+	1.85951i	0.735442	+	1.85951i	0.384804	+	0.922998i	$0.374269\pi$
$41$	0.735442	+	1.85951i	0.735442	+	1.85951i	0.350638	+	0.936511i	$0.385965\pi$
$42$		0			0
$43$	−0.507736	−	0.746816i	−0.507736	−	0.746816i	0.484006	−	0.875065i	$-0.339181\pi$
$43$	−0.507736	−	0.746816i	−0.507736	−	0.746816i	−0.991742	+	0.128249i	$0.959064\pi$
$44$	0.659335	−	1.66708i	0.659335	−	1.66708i
$45$		0			0
$46$		0			0
$47$		0			0		0.467849	−	0.883809i	$-0.345029\pi$
$47$		0			0		−0.467849	+	0.883809i	$0.654971\pi$
$48$	0.305890	−	0.918411i	0.305890	−	0.918411i
$49$	−0.298515	−	0.954405i	−0.298515	−	0.954405i
$50$	0.851919	+	0.523673i	0.851919	+	0.523673i
$51$	−1.87356	−	0.242284i	−1.87356	−	0.242284i
$52$		0			0
$53$		0			0		−0.531476	−	0.847073i	$-0.678363\pi$
$53$		0			0		0.531476	+	0.847073i	$0.321637\pi$
$54$	−0.788222	−	0.661397i	−0.788222	−	0.661397i
$55$		0			0
$56$		0			0
$57$	−0.931487	+	0.263399i	−0.931487	+	0.263399i
$58$		0			0
$59$	−1.18956	+	1.49972i	−1.18956	+	1.49972i	−0.367783	+	0.929912i	$0.619883\pi$
$59$	−1.18956	+	1.49972i	−1.18956	+	1.49972i	−0.821778	+	0.569808i	$0.807018\pi$
$60$		0			0
$61$		0			0		−0.870582	−	0.492024i	$-0.836257\pi$
$61$		0			0		0.870582	+	0.492024i	$0.163743\pi$
$62$		0			0
$63$		0			0
$64$	−0.754107	−	0.656752i	−0.754107	−	0.656752i
$65$		0			0
$66$	1.58275	−	0.711664i	1.58275	−	0.711664i
$67$	0.634492	+	1.79437i	0.634492	+	1.79437i	0.606938	+	0.794749i	$0.292398\pi$
$67$	0.634492	+	1.79437i	0.634492	+	1.79437i	0.0275543	+	0.999620i	$0.491228\pi$
$68$	−0.975796	+	1.69013i	−0.975796	+	1.69013i
$69$		0			0
$70$		0			0
$71$		0			0		0.870582	−	0.492024i	$-0.163743\pi$
$71$		0			0		−0.870582	+	0.492024i	$0.836257\pi$
$72$	−0.0559064	+	0.0289401i	−0.0559064	+	0.0289401i
$73$	−0.206643	+	0.705943i	−0.206643	+	0.705943i	0.789141	+	0.614213i	$0.210526\pi$
$73$	−0.206643	+	0.705943i	−0.206643	+	0.705943i	−0.995784	+	0.0917303i	$0.970760\pi$
$74$		0			0
$75$	0.237633	+	0.938391i	0.237633	+	0.938391i
$76$	−0.119134	+	0.992878i	−0.119134	+	0.992878i
$77$		0			0
$78$		0			0
$79$		0			0		0.435066	−	0.900399i	$-0.356725\pi$
$79$		0			0		−0.435066	+	0.900399i	$0.643275\pi$
$80$		0			0
$81$	−0.0941235	−	0.928325i	−0.0941235	−	0.928325i
$82$	1.40747	+	1.42045i	1.40747	+	1.42045i
$83$	0.750981	+	0.168299i	0.750981	+	0.168299i	0.577333	−	0.816509i	$-0.304094\pi$
$83$	0.750981	+	0.168299i	0.750981	+	0.168299i	0.173648	+	0.984808i	$0.444444\pi$
$84$		0			0
$85$		0			0
$86$	−0.760522	−	0.486965i	−0.760522	−	0.486965i
$87$		0			0
$88$	−0.0493975	−	1.79205i	−0.0493975	−	1.79205i
$89$	−0.167724	−	0.572986i	−0.167724	−	0.572986i	−0.999831	−	0.0183709i	$-0.994152\pi$
$89$	−0.167724	−	0.572986i	−0.167724	−	0.572986i	0.832107	−	0.554615i	$-0.187135\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.0799378	−	0.964706i	−0.0799378	−	0.964706i
$97$	0.626538	−	1.77187i	0.626538	−	1.77187i	−0.00918581	−	0.999958i	$-0.502924\pi$
$97$	0.626538	−	1.77187i	0.626538	−	1.77187i	0.635724	−	0.771917i	$-0.280702\pi$
$98$	−0.649797	−	0.760108i	−0.649797	−	0.760108i
$99$	−0.106051	−	0.0385995i	−0.106051	−	0.0385995i
$100$	0.989219	+	0.146447i	0.989219	+	0.146447i
$101$		0			0		0.209708	−	0.977764i	$-0.432749\pi$
$101$		0			0		−0.209708	+	0.977764i	$0.567251\pi$
$102$	−1.81788	+	0.514048i	−1.81788	+	0.514048i
$103$		0			0		−0.592235	−	0.805765i	$-0.701754\pi$
$103$		0			0		0.592235	+	0.805765i	$0.298246\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.0248834	−	0.0491710i	0.0248834	−	0.0491710i	−0.879474	−	0.475947i	$-0.842105\pi$
$107$	0.0248834	−	0.0491710i	0.0248834	−	0.0491710i	0.904357	+	0.426776i	$0.140351\pi$
$108$	−0.984816	−	0.298123i	−0.984816	−	0.298123i
$109$		0			0		0.531476	−	0.847073i	$-0.321637\pi$
$109$		0			0		−0.531476	+	0.847073i	$0.678363\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.0957109	−	0.218199i	0.0957109	−	0.218199i	−0.861396	−	0.507934i	$-0.830409\pi$
$113$	0.0957109	−	0.218199i	0.0957109	−	0.218199i	0.957107	+	0.289735i	$0.0935673\pi$
$114$	−0.752846	+	0.608498i	−0.752846	+	0.608498i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.503922	+	1.84669i	−0.503922	+	1.84669i
$119$		0			0
$120$		0			0
$121$	1.58687	−	1.54373i	1.58687	−	1.54373i
$122$		0			0
$123$	0.0177810	+	1.93562i	0.0177810	+	1.93562i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.766044	−	0.642788i	$-0.222222\pi$
$127$		0			0		−0.766044	+	0.642788i	$0.777778\pi$
$128$	−0.951623	−	0.307269i	−0.951623	−	0.307269i
$129$	−0.198994	−	0.851229i	−0.198994	−	0.851229i
$130$		0			0
$131$	1.22866	+	1.15209i	1.22866	+	1.15209i	0.983171	+	0.182687i	$0.0584795\pi$
$131$	1.22866	+	1.15209i	1.22866	+	1.15209i	0.245485	+	0.969400i	$0.421053\pi$
$132$	1.17534	−	1.27676i	1.17534	−	1.27676i
$133$		0			0
$134$	1.28903	+	1.40026i	1.28903	+	1.40026i
$135$		0			0
$136$	−0.232500	+	1.93769i	−0.232500	+	1.93769i
$137$	−1.79339	−	0.333238i	−1.79339	−	0.333238i	−0.821778	−	0.569808i	$-0.807018\pi$
$137$	−1.79339	−	0.333238i	−1.79339	−	0.333238i	−0.971614	+	0.236570i	$0.923977\pi$
$138$		0			0
$139$	0.678871	+	0.489428i	0.678871	+	0.489428i	0.870582	−	0.492024i	$-0.163743\pi$
$139$	0.678871	+	0.489428i	0.678871	+	0.489428i	−0.191711	+	0.981451i	$0.561404\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.0400206	+	0.0485943i	−0.0400206	+	0.0485943i
$145$		0			0
$146$	0.0876306	+	0.730327i	0.0876306	+	0.730327i
$147$	0.0622018	−	0.966011i	0.0622018	−	0.966011i
$148$		0			0
$149$		0			0		−0.979649	−	0.200718i	$-0.935673\pi$
$149$		0			0		0.979649	+	0.200718i	$0.0643275\pi$
$150$	0.587523	+	0.769327i	0.587523	+	0.769327i
$151$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$151$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$152$	0.280931	+	0.959728i	0.280931	+	0.959728i
$153$	0.108051	+	0.0584740i	0.108051	+	0.0584740i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.777724	−	0.628606i	$-0.216374\pi$
$157$		0			0		−0.777724	+	0.628606i	$0.783626\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.451618	−	0.816509i	−0.451618	−	0.816509i
$163$	−1.93127	+	0.106551i	−1.93127	+	0.106551i	−0.979649	−	0.200718i	$-0.935673\pi$
$163$	−1.93127	+	0.106551i	−1.93127	+	0.106551i	−0.951623	+	0.307269i	$0.900585\pi$
$164$	1.85268	+	0.752492i	1.85268	+	0.752492i
$165$		0			0
$166$	0.756657	−	0.140597i	0.756657	−	0.140597i
$167$		0			0		−0.0642573	−	0.997933i	$-0.520468\pi$
$167$		0			0		0.0642573	+	0.997933i	$0.479532\pi$
$168$		0			0
$169$	−0.467849	−	0.883809i	−0.467849	−	0.883809i
$170$		0			0
$171$	0.0626874	+	0.00577468i	0.0626874	+	0.00577468i
$172$	−0.890750	−	0.148640i	−0.890750	−	0.148640i
$173$		0			0		−0.315998	−	0.948760i	$-0.602339\pi$
$173$		0			0		0.315998	+	0.948760i	$0.397661\pi$
$174$		0			0
$175$		0			0
$176$	−0.750169	−	1.62823i	−0.750169	−	1.62823i
$177$	−1.59615	+	0.941193i	−1.59615	+	0.941193i
$178$	−0.379546	−	0.460857i	−0.379546	−	0.460857i
$179$	−0.326330	−	0.317459i	−0.326330	−	0.317459i	0.515825	−	0.856694i	$-0.327485\pi$
$179$	−0.326330	−	0.317459i	−0.326330	−	0.317459i	−0.842155	+	0.539235i	$0.818713\pi$
$180$		0			0
$181$		0			0		−0.919425	−	0.393266i	$-0.871345\pi$
$181$		0			0		0.919425	+	0.393266i	$0.128655\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.83803	+	2.04606i	−2.83803	+	2.04606i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$191$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$192$	−0.452883	−	0.855537i	−0.452883	−	0.855537i
$193$	0.0576084	+	0.268599i	0.0576084	+	0.268599i	0.997301	−	0.0734214i	$-0.0233918\pi$
$193$	0.0576084	+	0.268599i	0.0576084	+	0.268599i	−0.939693	+	0.342020i	$0.888889\pi$
$194$	−0.120764	−	1.87550i	−0.120764	−	1.87550i
$195$		0			0
$196$	−0.896364	−	0.443318i	−0.896364	−	0.443318i
$197$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$197$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$198$	−0.112686	+	0.00621705i	−0.112686	+	0.00621705i
$199$		0			0		−0.484006	−	0.875065i	$-0.660819\pi$
$199$		0			0		0.484006	+	0.875065i	$0.339181\pi$
$200$	0.967104	−	0.254380i	0.967104	−	0.254380i
$201$	−0.0507651	+	1.84166i	−0.0507651	+	1.84166i
$202$		0			0
$203$		0			0
$204$	−1.46925	+	1.18754i	−1.46925	+	1.18754i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.924735	+	1.53582i	−0.924735	+	1.53582i
$210$		0			0
$211$	0.425630	+	0.557338i	0.425630	+	0.557338i	0.957107	−	0.289735i	$-0.0935673\pi$
$211$	0.425630	+	0.557338i	0.425630	+	0.557338i	−0.531476	+	0.847073i	$0.678363\pi$
$212$		0			0
$213$		0			0
$214$	0.00354114	−	0.0549948i	0.00354114	−	0.0549948i
$215$		0			0
$216$	−1.02271	+	0.113193i	−1.02271	+	0.113193i
$217$		0			0
$218$		0			0
$219$	−0.432162	+	0.565890i	−0.432162	+	0.565890i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.800291	−	0.599612i	$-0.795322\pi$
$223$		0			0		0.800291	+	0.599612i	$0.204678\pi$
$224$		0			0
$225$	0.00749979	−	0.0625045i	0.00749979	−	0.0625045i
$226$	0.00218868	−	0.238257i	0.00218868	−	0.238257i
$227$	−1.33177	−	1.44668i	−1.33177	−	1.44668i	−0.800291	−	0.599612i	$-0.795322\pi$
$227$	−1.33177	−	1.44668i	−1.33177	−	1.44668i	−0.531476	−	0.847073i	$-0.678363\pi$
$228$	−0.452883	+	0.855537i	−0.452883	+	0.855537i
$229$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$229$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.330495	−	0.106713i	−0.330495	−	0.106713i	0.137354	−	0.990522i	$-0.456140\pi$
$233$	−0.330495	−	0.106713i	−0.330495	−	0.106713i	−0.467849	+	0.883809i	$0.654971\pi$
$234$		0			0
$235$		0			0
$236$	0.262924	+	1.89607i	0.262924	+	1.89607i
$237$		0			0
$238$		0			0
$239$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$239$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$240$		0			0
$241$	0.589810	−	0.227029i	0.589810	−	0.227029i	−0.0459136	−	0.998945i	$-0.514620\pi$
$241$	0.589810	−	0.227029i	0.589810	−	0.227029i	0.635724	+	0.771917i	$0.280702\pi$
$242$	0.851908	−	2.04340i	0.851908	−	2.04340i
$243$	−0.0330947	+	0.121280i	−0.0330947	+	0.121280i
$244$		0			0
$245$		0			0
$246$	0.777561	+	1.77266i	0.777561	+	1.77266i
$247$		0			0
$248$		0			0
$249$	0.619911	+	0.413183i	0.619911	+	0.413183i
$250$		0			0
$251$	−1.58370	+	0.511362i	−1.58370	+	0.511362i	−0.962268	−	0.272103i	$-0.912281\pi$
$251$	−1.58370	+	0.511362i	−1.58370	+	0.511362i	−0.621436	+	0.783465i	$0.713450\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.995784	+	0.0917303i	−0.995784	+	0.0917303i
$257$	−0.922104	−	1.16253i	−0.922104	−	1.16253i	−0.986361	−	0.164595i	$-0.947368\pi$
$257$	−0.922104	−	1.16253i	−0.922104	−	1.16253i	0.0642573	−	0.997933i	$-0.479532\pi$
$258$	−0.517720	−	0.704383i	−0.517720	−	0.704383i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.58273	+	0.576068i	1.58273	+	0.576068i
$263$		0			0		−0.649797	−	0.760108i	$-0.725146\pi$
$263$		0			0		0.649797	+	0.760108i	$0.274854\pi$
$264$	0.578531	−	1.63611i	0.578531	−	1.63611i
$265$		0			0
$266$		0			0
$267$	0.0477252	−	0.575958i	0.0477252	−	0.575958i
$268$	1.73584	+	0.780503i	1.73584	+	0.780503i
$269$		0			0		0.991742	−	0.128249i	$-0.0409357\pi$
$269$		0			0		−0.991742	+	0.128249i	$0.959064\pi$
$270$		0			0
$271$		0			0		−0.690683	−	0.723158i	$-0.742690\pi$
$271$		0			0		0.690683	+	0.723158i	$0.257310\pi$
$272$	0.548263	+	1.87300i	0.548263	+	1.87300i
$273$		0			0
$274$	−1.77994	+	0.398894i	−1.77994	+	0.398894i
$275$	1.50976	+	0.966702i	1.50976	+	0.966702i
$276$		0			0
$277$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$277$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$278$	0.816646	+	0.183015i	0.816646	+	0.183015i
$279$		0			0
$280$		0			0
$281$	−0.00768763	+	0.0166858i	−0.00768763	+	0.0166858i	−0.912045	−	0.410091i	$-0.865497\pi$
$281$	−0.00768763	+	0.0166858i	−0.00768763	+	0.0166858i	0.904357	+	0.426776i	$0.140351\pi$
$282$		0			0
$283$	0.741540	−	1.34068i	0.741540	−	1.34068i	−0.191711	−	0.981451i	$-0.561404\pi$
$283$	0.741540	−	1.34068i	0.741540	−	1.34068i	0.933251	−	0.359225i	$-0.116959\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0176854	+	0.0604175i	−0.0176854	+	0.0604175i
$289$	2.49433	−	1.29120i	2.49433	−	1.29120i
$290$		0			0
$291$	1.18215	−	1.38284i	1.18215	−	1.38284i
$292$	0.367783	+	0.637019i	0.367783	+	0.637019i
$293$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$293$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$294$	−0.322710	−	0.912637i	−0.322710	−	0.912637i
$295$		0			0
$296$		0			0
$297$	−1.39105	−	1.21146i	−1.39105	−	1.21146i
$298$		0			0
$299$		0			0
$300$	0.842734	+	0.476285i	0.842734	+	0.476285i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.635724	+	0.771917i	0.635724	+	0.771917i
$305$		0			0
$306$	0.122340	+	0.0112698i	0.122340	+	0.0112698i
$307$	1.42982	+	1.19976i	1.42982	+	1.19976i	0.945817	+	0.324699i	$0.105263\pi$
$307$	1.42982	+	1.19976i	1.42982	+	1.19976i	0.484006	+	0.875065i	$0.339181\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$311$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$312$		0			0
$313$	0.630290	−	1.89240i	0.630290	−	1.89240i	0.245485	−	0.969400i	$-0.421053\pi$
$313$	0.630290	−	1.89240i	0.630290	−	1.89240i	0.384804	−	0.922998i	$-0.374269\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.367783	−	0.929912i	$-0.380117\pi$
$317$		0			0		−0.367783	+	0.929912i	$0.619883\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.0395781	−	0.0357681i	0.0395781	−	0.0357681i
$322$		0			0
$323$	1.24067	−	1.50647i	1.24067	−	1.50647i
$324$	−0.736335	−	0.573112i	−0.736335	−	0.573112i
$325$		0			0
$326$	−1.73376	+	0.857470i	−1.73376	+	0.857470i
$327$		0			0
$328$	1.99933	−	0.0367355i	1.99933	−	0.0367355i
$329$		0			0
$330$		0			0
$331$	−1.17530	−	0.554636i	−1.17530	−	0.554636i	−0.263253	−	0.964727i	$-0.584795\pi$
$331$	−1.17530	−	0.554636i	−1.17530	−	0.554636i	−0.912045	+	0.410091i	$0.865497\pi$
$332$	0.640396	−	0.426836i	0.640396	−	0.426836i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.32171	+	1.48978i	−1.32171	+	1.48978i	−0.592235	+	0.805765i	$0.701754\pi$
$337$	−1.32171	+	1.48978i	−1.32171	+	1.48978i	−0.729471	+	0.684011i	$0.760234\pi$
$338$	−0.777724	−	0.628606i	−0.777724	−	0.628606i
$339$	0.162340	−	0.163838i	0.162340	−	0.163838i
$340$		0			0
$341$		0			0
$342$	0.0599073	−	0.0193435i	0.0599073	−	0.0193435i
$343$		0			0
$344$	−0.877433	+	0.213639i	−0.877433	+	0.213639i
$345$		0			0
$346$		0			0
$347$	−0.0292545	+	0.125141i	−0.0292545	+	0.125141i	−0.986361	−	0.164595i	$-0.947368\pi$
$347$	−0.0292545	+	0.125141i	−0.0292545	+	0.125141i	0.957107	+	0.289735i	$0.0935673\pi$
$348$		0			0
$349$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$349$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$350$		0			0
$351$		0			0
$352$	−1.33005	−	1.20202i	−1.33005	−	1.20202i
$353$	−0.184613	+	0.493078i	−0.184613	+	0.493078i	−0.995784	−	0.0917303i	$-0.970760\pi$
$353$	−0.184613	+	0.493078i	−0.184613	+	0.493078i	0.811171	+	0.584809i	$0.198830\pi$
$354$	−1.09740	+	1.49307i	−1.09740	+	1.49307i
$355$		0			0
$356$	−0.530203	−	0.274461i	−0.530203	−	0.274461i
$357$		0			0
$358$	−0.424882	−	0.163545i	−0.424882	−	0.163545i
$359$		0			0		0.919425	−	0.393266i	$-0.128655\pi$
$359$		0			0		−0.919425	+	0.393266i	$0.871345\pi$
$360$		0			0
$361$	0.280931	−	0.959728i	0.280931	−	0.959728i
$362$		0			0
$363$	1.97038	−	0.842793i	1.97038	−	0.842793i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.999325	−	0.0367355i	$-0.0116959\pi$
$367$		0			0		−0.999325	+	0.0367355i	$0.988304\pi$
$368$		0			0
$369$	0.0441398	−	0.117892i	0.0441398	−	0.117892i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$373$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$374$	−1.80471	+	2.99729i	−1.80471	+	2.99729i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.49277	+	0.512467i	1.49277	+	0.512467i	0.945817	−	0.324699i	$-0.105263\pi$
$379$	1.49277	+	0.512467i	1.49277	+	0.512467i	0.546948	+	0.837166i	$0.315789\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.703852	−	0.710347i	$-0.251462\pi$
$383$		0			0		−0.703852	+	0.710347i	$0.748538\pi$
$384$	−0.752846	−	0.608498i	−0.752846	−	0.608498i
$385$		0			0
$386$	0.158597	+	0.224301i	0.158597	+	0.224301i
$387$	−0.00780863	+	0.0563117i	−0.00780863	+	0.0563117i
$388$	−0.848605	−	1.67689i	−0.848605	−	1.67689i
$389$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$389$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$390$		0			0
$391$		0			0
$392$	−0.998482	−	0.0550878i	−0.998482	−	0.0550878i
$393$	0.709345	+	1.46804i	0.709345	+	1.46804i
$394$		0			0
$395$		0			0
$396$	−0.101161	+	0.0500317i	−0.101161	+	0.0500317i
$397$		0			0		0.997301	−	0.0734214i	$-0.0233918\pi$
$397$		0			0		−0.997301	+	0.0734214i	$0.976608\pi$
$398$		0			0
$399$		0			0
$400$	0.789141	−	0.614213i	0.789141	−	0.614213i
$401$	1.20364	−	1.08777i	1.20364	−	1.08777i	0.209708	−	0.977764i	$-0.432749\pi$
$401$	1.20364	−	1.08777i	1.20364	−	1.08777i	0.993931	−	0.110008i	$-0.0350877\pi$
$402$	0.677590	+	1.71324i	0.677590	+	1.71324i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.883843	+	1.66966i	−0.883843	+	1.66966i
$409$	−0.544398	+	1.63452i	−0.544398	+	1.63452i	0.209708	+	0.977764i	$0.432749\pi$
$409$	−0.544398	+	1.63452i	−0.544398	+	1.63452i	−0.754107	+	0.656752i	$0.771930\pi$
$410$		0			0
$411$	−1.50427	−	0.924671i	−1.50427	−	0.924671i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.443100	+	0.678215i	0.443100	+	0.678215i
$418$	−0.246238	+	1.77574i	−0.246238	+	1.77574i
$419$	−0.647844	+	0.991599i	−0.647844	+	0.991599i	0.350638	+	0.936511i	$0.385965\pi$
$419$	−0.647844	+	0.991599i	−0.647844	+	0.991599i	−0.998482	+	0.0550878i	$0.982456\pi$
$420$		0			0
$421$		0			0		−0.999325	−	0.0367355i	$-0.988304\pi$
$421$		0			0		0.999325	+	0.0367355i	$0.0116959\pi$
$422$	0.610517	+	0.345044i	0.610517	+	0.345044i
$423$		0			0
$424$		0			0
$425$	−1.47171	−	1.28171i	−1.47171	−	1.28171i
$426$		0			0
$427$		0			0
$428$	−0.0183718	−	0.0519562i	−0.0183718	−	0.0519562i
$429$		0			0
$430$		0			0
$431$		0			0		0.649797	−	0.760108i	$-0.274854\pi$
$431$		0			0		−0.649797	+	0.760108i	$0.725146\pi$
$432$	−0.895786	+	0.506268i	−0.895786	+	0.506268i
$433$	1.67990	−	0.869604i	1.67990	−	0.869604i	0.690683	−	0.723158i	$-0.257310\pi$
$433$	1.67990	−	0.869604i	1.67990	−	0.869604i	0.989219	−	0.146447i	$-0.0467836\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.174795	+	0.690248i	−0.174795	+	0.690248i
$439$		0			0		0.484006	−	0.875065i	$-0.339181\pi$
$439$		0			0		−0.484006	+	0.875065i	$0.660819\pi$
$440$		0			0
$441$	−0.0263427	+	0.0571762i	−0.0263427	+	0.0571762i
$442$		0			0
$443$	−1.29428	−	1.30622i	−1.29428	−	1.30622i	−0.926494	−	0.376309i	$-0.877193\pi$
$443$	−1.29428	−	1.30622i	−1.29428	−	1.30622i	−0.367783	−	0.929912i	$-0.619883\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.00857089	−	0.310936i	−0.00857089	−	0.310936i	−0.991742	−	0.128249i	$-0.959064\pi$
$449$	−0.00857089	−	0.310936i	−0.00857089	−	0.310936i	0.983171	−	0.182687i	$-0.0584795\pi$
$450$	−0.0176854	−	0.0604175i	−0.0176854	−	0.0604175i
$451$	2.47600	+	2.59241i	2.47600	+	2.59241i
$452$	−0.0916862	−	0.219920i	−0.0916862	−	0.219920i
$453$		0			0
$454$	−1.79339	−	0.806378i	−1.79339	−	0.806378i
$455$		0			0
$456$	−0.0799378	+	0.964706i	−0.0799378	+	0.964706i
$457$	−0.143784	−	1.73522i	−0.143784	−	1.73522i	−0.562235	−	0.826977i	$-0.690058\pi$
$457$	−0.143784	−	1.73522i	−0.143784	−	1.73522i	0.418451	−	0.908239i	$-0.362573\pi$
$458$		0			0
$459$	1.30485	+	1.52637i	1.30485	+	1.52637i
$460$		0			0
$461$		0			0		−0.989219	−	0.146447i	$-0.953216\pi$
$461$		0			0		0.989219	+	0.146447i	$0.0467836\pi$
$462$		0			0
$463$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$463$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$464$		0			0
$465$		0			0
$466$	−0.345832	+	0.0318576i	−0.345832	+	0.0318576i
$467$	−1.62584	−	1.12733i	−1.62584	−	1.12733i	−0.896364	−	0.443318i	$-0.853801\pi$
$467$	−1.62584	−	1.12733i	−1.62584	−	1.12733i	−0.729471	−	0.684011i	$-0.760234\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.987400	+	1.63990i	0.987400	+	1.63990i
$473$	−1.34714	−	0.897896i	−1.34714	−	0.897896i
$474$		0			0
$475$	−0.951623	−	0.307269i	−0.951623	−	0.307269i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.263253	−	0.964727i	$-0.415205\pi$
$479$		0			0		−0.263253	+	0.964727i	$0.584795\pi$
$480$		0			0
$481$		0			0
$482$	0.453003	−	0.440688i	0.453003	−	0.440688i
$483$		0			0
$484$	−0.0203363	−	2.21378i	−0.0203363	−	2.21378i
$485$		0			0
$486$	0.0172673	+	0.124523i	0.0172673	+	0.124523i
$487$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$487$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$488$		0			0
$489$	−1.78176	−	0.575312i	−1.78176	−	0.575312i
$490$		0			0
$491$	−1.11110	+	1.57140i	−1.11110	+	1.57140i	−0.333374	+	0.942795i	$0.608187\pi$
$491$	−1.11110	+	1.57140i	−1.11110	+	1.57140i	−0.777724	+	0.628606i	$0.783626\pi$
$492$	1.41204	+	1.32404i	1.41204	+	1.32404i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.732453	+	0.136100i	0.732453	+	0.136100i
$499$	1.04005	+	0.779252i	1.04005	+	0.779252i	0.975796	−	0.218681i	$-0.0701754\pi$
$499$	1.04005	+	0.779252i	1.04005	+	0.779252i	0.0642573	+	0.997933i	$0.479532\pi$
$500$		0			0
$501$		0			0
$502$	−1.25499	+	1.09298i	−1.25499	+	1.09298i
$503$		0			0		0.606938	−	0.794749i	$-0.292398\pi$
$503$		0			0		−0.606938	+	0.794749i	$0.707602\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.115323	−	0.961118i	−0.115323	−	0.961118i
$508$		0			0
$509$		0			0		0.989219	−	0.146447i	$-0.0467836\pi$
$509$		0			0		−0.989219	+	0.146447i	$0.953216\pi$
$510$		0			0
$511$		0			0
$512$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$513$	0.922315	+	0.456153i	0.922315	+	0.456153i
$514$	−1.30499	−	0.706224i	−1.30499	−	0.706224i
$515$		0			0
$516$	−0.753015	−	0.444025i	−0.753015	−	0.444025i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.0458563	−	1.66358i	0.0458563	−	1.66358i	−0.531476	−	0.847073i	$-0.678363\pi$
$521$	0.0458563	−	1.66358i	0.0458563	−	1.66358i	0.577333	−	0.816509i	$-0.304094\pi$
$522$		0			0
$523$	−0.655617	−	1.18533i	−0.655617	−	1.18533i	−0.971614	−	0.236570i	$-0.923977\pi$
$523$	−0.655617	−	1.18533i	−0.655617	−	1.18533i	0.315998	−	0.948760i	$-0.397661\pi$
$524$	1.68175	−	0.0927849i	1.68175	−	0.0927849i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.111511	−	1.73180i	−0.111511	−	1.73180i
$529$	0.209708	+	0.977764i	0.209708	+	0.977764i
$530$		0			0
$531$	0.118862	−	0.0198345i	0.118862	−	0.0198345i
$532$		0			0
$533$		0			0
$534$	−0.182625	−	0.548319i	−0.182625	−	0.548319i
$535$		0			0
$536$	1.90292	+	0.0349642i	1.90292	+	0.0349642i
$537$	−0.184415	−	0.400268i	−0.184415	−	0.400268i
$538$		0			0
$539$	−1.13968	−	1.38384i	−1.13968	−	1.38384i
$540$		0			0
$541$		0			0		−0.919425	−	0.393266i	$-0.871345\pi$
$541$		0			0		0.919425	+	0.393266i	$0.128655\pi$
$542$		0			0
$543$		0			0
$544$	1.24067	+	1.50647i	1.24067	+	1.50647i
$545$		0			0
$546$		0			0
$547$	1.85268	+	0.0340410i	1.85268	+	0.0340410i	0.933251	−	0.359225i	$-0.116959\pi$
$547$	1.85268	+	0.0340410i	1.85268	+	0.0340410i	0.919425	+	0.393266i	$0.128655\pi$
$548$	−1.47965	+	1.06674i	−1.47965	+	1.06674i
$549$		0			0
$550$	1.76828	+	0.295073i	1.76828	+	0.295073i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.822818	−	0.152891i	0.822818	−	0.152891i
$557$		0			0		−0.896364	−	0.443318i	$-0.853801\pi$
$557$		0			0		0.896364	+	0.443318i	$0.146199\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−3.27535	+	0.861524i	−3.27535	+	0.861524i
$562$	−0.000506218		0.0183647i	−0.000506218		0.0183647i
$563$	0.375618	+	1.92296i	0.375618	+	1.92296i	0.384804	+	0.922998i	$0.374269\pi$
$563$	0.375618	+	1.92296i	0.375618	+	1.92296i	−0.00918581	+	0.999958i	$0.502924\pi$
$564$		0			0
$565$		0			0
$566$	0.154547	−	1.52427i	0.154547	−	1.52427i
$567$		0			0
$568$		0			0
$569$	1.69258	+	0.915978i	1.69258	+	0.915978i	0.975796	+	0.218681i	$0.0701754\pi$
$569$	1.69258	+	0.915978i	1.69258	+	0.915978i	0.716783	+	0.697297i	$0.245614\pi$
$570$		0			0
$571$	1.09307	−	0.591541i	1.09307	−	0.591541i	0.173648	−	0.984808i	$-0.444444\pi$
$571$	1.09307	−	0.591541i	1.09307	−	0.591541i	0.919425	+	0.393266i	$0.128655\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.00749979	+	0.0625045i	0.00749979	+	0.0625045i
$577$	1.85517	−	0.205331i	1.85517	−	0.205331i	0.888069	−	0.459710i	$-0.152047\pi$
$577$	1.85517	−	0.205331i	1.85517	−	0.205331i	0.967104	+	0.254380i	$0.0818713\pi$
$578$	1.78557	−	2.16809i	1.78557	−	2.16809i
$579$	−0.0413577	+	0.262684i	−0.0413577	+	0.262684i
$580$		0			0
$581$		0			0
$582$	0.543078	−	1.73632i	0.543078	−	1.73632i
$583$		0			0
$584$	0.588667	+	0.441054i	0.588667	+	0.441054i
$585$		0			0
$586$		0			0
$587$	−0.0182601	+	1.98778i	−0.0182601	+	1.98778i	0.100874	+	0.994899i	$0.467836\pi$
$587$	−0.0182601	+	1.98778i	−0.0182601	+	1.98778i	−0.119134	+	0.992878i	$0.538012\pi$
$588$	−0.655617	−	0.712190i	−0.655617	−	0.712190i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.262843	−	1.12435i	−0.262843	−	1.12435i	−0.926494	−	0.376309i	$-0.877193\pi$
$593$	−0.262843	−	1.12435i	−0.262843	−	1.12435i	0.663651	−	0.748042i	$-0.269006\pi$
$594$	−1.75539	−	0.566798i	−1.75539	−	0.566798i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.00918581	−	0.999958i	$-0.502924\pi$
$599$		0			0		0.00918581	+	0.999958i	$0.497076\pi$
$600$	0.962137	+	0.106489i	0.962137	+	0.106489i
$601$	1.09817	−	1.06832i	1.09817	−	1.06832i	0.100874	−	0.994899i	$-0.467836\pi$
$601$	1.09817	−	1.06832i	1.09817	−	1.06832i	0.997301	−	0.0734214i	$-0.0233918\pi$
$602$		0			0
$603$	0.0461051	−	0.110589i	0.0461051	−	0.110589i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$607$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$608$	0.888069	+	0.459710i	0.888069	+	0.459710i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.116915	−	0.0377505i	0.116915	−	0.0377505i
$613$		0			0		0.531476	−	0.847073i	$-0.321637\pi$
$613$		0			0		−0.531476	+	0.847073i	$0.678363\pi$
$614$	1.78644	+	0.540791i	1.78644	+	0.540791i
$615$		0			0
$616$		0			0
$617$	1.97512	−	0.181946i	1.97512	−	0.181946i	0.975796	−	0.218681i	$-0.0701754\pi$
$617$	1.97512	−	0.181946i	1.97512	−	0.181946i	0.999325	+	0.0367355i	$0.0116959\pi$
$618$		0			0
$619$	−0.415320	−	0.565063i	−0.415320	−	0.565063i	0.546948	−	0.837166i	$-0.315789\pi$
$619$	−0.415320	−	0.565063i	−0.415320	−	0.565063i	−0.962268	+	0.272103i	$0.912281\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.333374	+	0.942795i	−0.333374	+	0.942795i
$626$	−0.164713	−	1.98779i	−0.164713	−	1.98779i
$627$	−1.36946	+	1.06589i	−1.36946	+	1.06589i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.384804	−	0.922998i	$-0.625731\pi$
$631$		0			0		0.384804	+	0.922998i	$0.374269\pi$
$632$		0			0
$633$	0.190708	+	0.651504i	0.190708	+	0.651504i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.161456	−	1.59242i	−0.161456	−	1.59242i	−0.677282	−	0.735724i	$-0.736842\pi$
$641$	−0.161456	−	1.59242i	−0.161456	−	1.59242i	0.515825	−	0.856694i	$-0.327485\pi$
$642$	0.0223226	−	0.0484508i	0.0223226	−	0.0484508i
$643$	−0.274959	+	0.569048i	−0.274959	+	0.569048i	−0.991742	−	0.128249i	$-0.959064\pi$
$643$	−0.274959	+	0.569048i	−0.274959	+	0.569048i	0.716783	+	0.697297i	$0.245614\pi$
$644$		0			0
$645$		0			0
$646$	0.548263	−	1.87300i	0.548263	−	1.87300i
$647$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$647$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$648$	−0.902390	−	0.237358i	−0.902390	−	0.237358i
$649$	−0.964062	+	3.29347i	−0.964062	+	3.29347i
$650$		0			0
$651$		0			0
$652$	−1.25684	+	1.47021i	−1.25684	+	1.47021i
$653$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$653$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$654$		0			0
$655$		0			0
$656$	1.82378	−	0.820043i	1.82378	−	0.820043i
$657$	0.0394489	−	0.0242492i	0.0394489	−	0.0242492i
$658$		0			0
$659$	1.16037	−	0.237745i	1.16037	−	0.237745i	0.418451	−	0.908239i	$-0.362573\pi$
$659$	1.16037	−	0.237745i	1.16037	−	0.237745i	0.741914	+	0.670495i	$0.233918\pi$
$660$		0			0
$661$		0			0		−0.870582	−	0.492024i	$-0.836257\pi$
$661$		0			0		0.870582	+	0.492024i	$0.163743\pi$
$662$	−1.29872	−	0.0477413i	−1.29872	−	0.0477413i
$663$		0			0
$664$	0.420936	−	0.644290i	0.420936	−	0.644290i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.450224	+	1.43945i	0.450224	+	1.43945i	0.851919	+	0.523673i	$0.175439\pi$
$673$	0.450224	+	1.43945i	0.450224	+	1.43945i	−0.401695	+	0.915773i	$0.631579\pi$
$674$	−0.629331	+	1.88952i	−0.629331	+	1.88952i
$675$	0.481393	−	0.909396i	0.481393	−	0.909396i
$676$	−0.962268	−	0.272103i	−0.962268	−	0.272103i
$677$		0			0		−0.350638	−	0.936511i	$-0.614035\pi$
$677$		0			0		0.350638	+	0.936511i	$0.385965\pi$
$678$	0.0848275	−	0.214480i	0.0848275	−	0.214480i
$679$		0			0
$680$		0			0
$681$	−0.700054	−	1.77003i	−0.700054	−	1.77003i
$682$		0			0
$683$	−0.302573	+	0.235502i	−0.302573	+	0.235502i	−0.754107	−	0.656752i	$-0.771930\pi$
$683$	−0.302573	+	0.235502i	−0.302573	+	0.235502i	0.451533	+	0.892254i	$0.350877\pi$
$684$	0.0474731	−	0.0413444i	0.0474731	−	0.0413444i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.722716	+	0.541490i	−0.722716	+	0.541490i
$689$		0			0
$690$		0			0
$691$	−0.274290	−	0.0151330i	−0.274290	−	0.0151330i	−0.0825793	−	0.996584i	$-0.526316\pi$
$691$	−0.274290	−	0.0151330i	−0.274290	−	0.0151330i	−0.191711	+	0.981451i	$0.561404\pi$
$692$		0			0
$693$		0			0
$694$	0.0223163	+	0.126562i	0.0223163	+	0.126562i
$695$		0			0
$696$		0			0
$697$	−2.25306	−	3.18645i	−2.25306	−	3.18645i
$698$		0			0
$699$	−0.261461	−	0.211329i	−0.261461	−	0.211329i
$700$		0			0
$701$		0			0		0.842155	−	0.539235i	$-0.181287\pi$
$701$		0			0		−0.842155	+	0.539235i	$0.818713\pi$
$702$		0			0
$703$		0			0
$704$	−1.69559	−	0.582098i	−1.69559	−	0.582098i
$705$		0			0
$706$	0.0241737	+	0.525950i	0.0241737	+	0.525950i
$707$		0			0
$708$	−0.421804	+	1.80433i	−0.421804	+	1.80433i
$709$		0			0		0.515825	−	0.856694i	$-0.327485\pi$
$709$		0			0		−0.515825	+	0.856694i	$0.672515\pi$
$710$		0			0
$711$		0			0
$712$	−0.595418	−	0.0438348i	−0.595418	−	0.0438348i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.454963	+	0.0167246i	−0.454963	+	0.0167246i
$717$		0			0
$718$		0			0
$719$		0			0		−0.933251	−	0.359225i	$-0.883041\pi$
$719$		0			0		0.933251	+	0.359225i	$0.116959\pi$
$720$		0			0
$721$		0			0
$722$	−0.119134	−	0.992878i	−0.119134	−	0.992878i
$723$	0.611779			0.611779
$724$		0			0
$725$		0			0
$726$	1.48017	−	1.54977i	1.48017	−	1.54977i
$727$		0			0		−0.888069	−	0.459710i	$-0.847953\pi$
$727$		0			0		0.888069	+	0.459710i	$0.152047\pi$
$728$		0			0
$729$	−0.624676	+	0.849903i	−0.624676	+	0.849903i
$730$		0			0
$731$	1.30756	+	1.18169i	1.30756	+	1.18169i
$732$		0			0
$733$		0			0		0.926494	−	0.376309i	$-0.122807\pi$
$733$		0			0		−0.926494	+	0.376309i	$0.877193\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.26438	+	2.55232i	2.26438	+	2.55232i
$738$	−0.00577980	−	0.125752i	−0.00577980	−	0.125752i
$739$	0.511560	−	0.124556i	0.511560	−	0.124556i	0.0275543	−	0.999620i	$-0.491228\pi$
$739$	0.511560	−	0.124556i	0.511560	−	0.124556i	0.484006	+	0.875065i	$0.339181\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.842155	−	0.539235i	$-0.181287\pi$
$743$		0			0		−0.842155	+	0.539235i	$0.818713\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0279712	−	0.0395590i	−0.0279712	−	0.0395590i
$748$	−0.480556	+	3.46552i	−0.480556	+	3.46552i
$749$		0			0
$750$		0			0
$751$		0			0		0.832107	−	0.554615i	$-0.187135\pi$
$751$		0			0		−0.832107	+	0.554615i	$0.812865\pi$
$752$		0			0
$753$	−1.60853	−	0.0887452i	−1.60853	−	0.0887452i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.896364	−	0.443318i	$-0.146199\pi$
$757$		0			0		−0.896364	+	0.443318i	$0.853801\pi$
$758$	1.57402	−	0.115880i	1.57402	−	0.115880i
$759$		0			0
$760$		0			0
$761$	−0.980800	+	0.763387i	−0.980800	+	0.763387i	−0.971614	−	0.236570i	$-0.923977\pi$
$761$	−0.980800	+	0.763387i	−0.980800	+	0.763387i	−0.00918581	+	0.999958i	$0.502924\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.931487	−	0.263399i	−0.931487	−	0.263399i
$769$	0.866918	−	1.63769i	0.866918	−	1.63769i	0.100874	−	0.994899i	$-0.467836\pi$
$769$	0.866918	−	1.63769i	0.866918	−	1.63769i	0.766044	−	0.642788i	$-0.222222\pi$
$770$		0			0
$771$	−0.428776	−	1.37087i	−0.428776	−	1.37087i
$772$	0.234028	+	0.143857i	0.234028	+	0.143857i
$773$		0			0		−0.991742	−	0.128249i	$-0.959064\pi$
$773$		0			0		0.991742	+	0.128249i	$0.0409357\pi$
$774$	0.0149661	+	0.0548453i	0.0149661	+	0.0548453i
$775$		0			0
$776$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$777$		0			0
$778$		0			0
$779$	−1.70355	−	1.04717i	−1.70355	−	1.04717i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$785$		0			0
$786$	1.22952	+	1.07079i	1.22952	+	1.07079i
$787$	0.357309	−	0.219637i	0.357309	−	0.219637i	−0.333374	−	0.942795i	$-0.608187\pi$
$787$	0.357309	−	0.219637i	0.357309	−	0.219637i	0.690683	+	0.723158i	$0.257310\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.0733343	+	0.0857837i	−0.0733343	+	0.0857837i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.245485	−	0.969400i	$-0.578947\pi$
$797$		0			0		0.245485	+	0.969400i	$0.421053\pi$
$798$		0			0
$799$		0			0
$800$	0.484006	−	0.875065i	0.484006	−	0.875065i
$801$	−0.0163518	+	0.0338412i	−0.0163518	+	0.0338412i
$802$	0.678871	−	1.47348i	0.678871	−	1.47348i
$803$	0.133019	+	1.31194i	0.133019	+	1.31194i
$804$	1.29675	+	1.30872i	1.29675	+	1.30872i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.00668	−	0.225602i	1.00668	−	0.225602i	0.315998	−	0.948760i	$-0.397661\pi$
$809$	1.00668	−	0.225602i	1.00668	−	0.225602i	0.690683	+	0.723158i	$0.257310\pi$
$810$		0			0
$811$	−0.494143	−	1.68811i	−0.494143	−	1.68811i	−0.703852	−	0.710347i	$-0.748538\pi$
$811$	−0.494143	−	1.68811i	−0.494143	−	1.68811i	0.209708	−	0.977764i	$-0.432749\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.156006	+	1.88271i	−0.156006	+	1.88271i
$817$	0.854136	+	0.293225i	0.854136	+	0.293225i
$818$	0.142267	+	1.71691i	0.142267	+	1.71691i
$819$		0			0
$820$		0			0
$821$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$821$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$822$	−1.74670	−	0.258587i	−1.74670	−	0.258587i
$823$		0			0		0.209708	−	0.977764i	$-0.432749\pi$
$823$		0			0		−0.209708	+	0.977764i	$0.567251\pi$
$824$		0			0
$825$	1.02775	+	1.39831i	1.02775	+	1.39831i
$826$		0			0
$827$	−1.02730	+	0.0946336i	−1.02730	+	0.0946336i	−0.592235	−	0.805765i	$-0.701754\pi$
$827$	−1.02730	+	0.0946336i	−1.02730	+	0.0946336i	−0.435066	+	0.900399i	$0.643275\pi$
$828$		0			0
$829$		0			0		0.451533	−	0.892254i	$-0.350877\pi$
$829$		0			0		−0.451533	+	0.892254i	$0.649123\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.00668	+	1.67192i	1.00668	+	1.67192i
$834$	0.674116	+	0.449311i	0.674116	+	0.449311i
$835$		0			0
$836$	0.471941	+	1.72949i	0.471941	+	1.72949i
$837$		0			0
$838$	−0.205681	+	1.16648i	−0.205681	+	1.16648i
$839$		0			0		0.957107	−	0.289735i	$-0.0935673\pi$
$839$		0			0		−0.957107	+	0.289735i	$0.906433\pi$
$840$		0			0
$841$	0.384804	−	0.922998i	0.384804	−	0.922998i
$842$		0			0
$843$	−0.0127472	+	0.0124007i	−0.0127472	+	0.0124007i
$844$	0.697019	+	0.0771460i	0.697019	+	0.0771460i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.13611	−	0.953306i	1.13611	−	0.953306i
$850$	−1.85718	−	0.599664i	−1.85718	−	0.599664i
$851$		0			0
$852$		0			0
$853$		0			0		−0.729471	−	0.684011i	$-0.760234\pi$
$853$		0			0		0.729471	+	0.684011i	$0.239766\pi$
$854$		0			0
$855$		0			0
$856$	−0.0373241	−	0.0405448i	−0.0373241	−	0.0405448i
$857$	0.00612462	−	0.666720i	0.00612462	−	0.666720i	−0.939693	−	0.342020i	$-0.888889\pi$
$857$	0.00612462	−	0.666720i	0.00612462	−	0.666720i	0.945817	−	0.324699i	$-0.105263\pi$
$858$		0			0
$859$	−1.95010	−	0.362357i	−1.95010	−	0.362357i	−0.998482	−	0.0550878i	$-0.982456\pi$
$859$	−1.95010	−	0.362357i	−1.95010	−	0.362357i	−0.951623	−	0.307269i	$-0.900585\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$863$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$864$	−0.624509	+	0.817758i	−0.624509	+	0.817758i
$865$		0			0
$866$	1.20256	−	1.46018i	1.20256	−	1.46018i
$867$	2.70237	−	0.299098i	2.70237	−	0.299098i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.104053	+	0.0563105i	−0.104053	+	0.0563105i
$874$		0			0
$875$		0			0
$876$	0.110741	+	0.703372i	0.110741	+	0.703372i
$877$		0			0		−0.861396	−	0.507934i	$-0.830409\pi$
$877$		0			0		0.861396	+	0.507934i	$0.169591\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.0872802	+	0.446826i	0.0872802	+	0.446826i	0.999325	+	0.0367355i	$0.0116959\pi$
$881$	0.0872802	+	0.446826i	0.0872802	+	0.446826i	−0.912045	+	0.410091i	$0.865497\pi$
$882$	−0.00173462	+	0.0629289i	−0.00173462	+	0.0629289i
$883$	1.71771	−	0.451814i	1.71771	−	0.451814i	0.741914	−	0.670495i	$-0.233918\pi$
$883$	1.71771	−	0.451814i	1.71771	−	0.451814i	0.975796	+	0.218681i	$0.0701754\pi$
$884$		0			0
$885$		0			0
$886$	−1.70368	−	0.691976i	−1.70368	−	0.691976i
$887$		0			0		−0.896364	−	0.443318i	$-0.853801\pi$
$887$		0			0		0.896364	+	0.443318i	$0.146199\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.782602	−	1.47841i	−0.782602	−	1.47841i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.130161	−	0.282512i	−0.130161	−	0.282512i
$899$		0			0
$900$	−0.0400206	−	0.0485943i	−0.0400206	−	0.0485943i
$901$		0			0
$902$	3.29600	+	1.40980i	3.29600	+	1.40980i
$903$		0			0
$904$	−0.170786	−	0.166143i	−0.170786	−	0.166143i
$905$		0			0
$906$		0			0
$907$	−0.589055	−	1.27853i	−0.589055	−	1.27853i	−0.939693	−	0.342020i	$-0.888889\pi$
$907$	−0.589055	−	1.27853i	−0.589055	−	1.27853i	0.350638	−	0.936511i	$-0.385965\pi$
$908$	−1.96601	−	0.0361234i	−1.96601	−	0.0361234i
$909$		0			0
$910$		0			0
$911$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$911$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$912$	0.305890	+	0.918411i	0.305890	+	0.918411i
$913$	1.36088	−	0.227091i	1.36088	−	0.227091i
$914$	−0.814601	−	1.53886i	−0.814601	−	1.53886i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.79998	+	0.890224i	1.79998	+	0.890224i
$919$		0			0		−0.926494	−	0.376309i	$-0.877193\pi$
$919$		0			0		0.926494	+	0.376309i	$0.122807\pi$
$920$		0			0
$921$	0.874500	+	1.58106i	0.874500	+	1.58106i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.252318	−	1.60260i	−0.252318	−	1.60260i	−0.703852	−	0.710347i	$-0.748538\pi$
$929$	−0.252318	−	1.60260i	−0.252318	−	1.60260i	0.451533	−	0.892254i	$-0.350877\pi$
$930$		0			0
$931$	0.811171	+	0.584809i	0.811171	+	0.584809i
$932$	−0.305438	+	0.165295i	−0.305438	+	0.165295i
$933$		0			0
$934$	−1.93817	−	0.397108i	−1.93817	−	0.397108i
$935$		0			0
$936$		0			0
$937$	−0.219069	−	1.82575i	−0.219069	−	1.82575i	−0.500000	−	0.866025i	$-0.666667\pi$
$937$	−0.219069	−	1.82575i	−0.219069	−	1.82575i	0.280931	−	0.959728i	$-0.409357\pi$
$938$		0			0
$939$	1.22745	−	1.49042i	1.22745	−	1.49042i
$940$		0			0
$941$		0			0		0.606938	−	0.794749i	$-0.292398\pi$
$941$		0			0		−0.606938	+	0.794749i	$0.707602\pi$
$942$		0			0
$943$		0			0
$944$	1.55276	+	1.11945i	1.55276	+	1.11945i
$945$		0			0
$946$	−1.59171	−	0.295762i	−1.59171	−	0.295762i
$947$	−0.130320	+	1.08611i	−0.130320	+	1.08611i	0.766044	+	0.642788i	$0.222222\pi$
$947$	−0.130320	+	1.08611i	−0.130320	+	1.08611i	−0.896364	+	0.443318i	$0.853801\pi$
$948$		0			0
$949$		0			0
$950$	−0.995784	+	0.0917303i	−0.995784	+	0.0917303i
$951$		0			0
$952$		0			0
$953$	−0.812713	+	1.14940i	−0.812713	+	1.14940i	0.173648	+	0.984808i	$0.444444\pi$
$953$	−0.812713	+	1.14940i	−0.812713	+	1.14940i	−0.986361	+	0.164595i	$0.947368\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.993931	+	0.110008i	0.993931	+	0.110008i
$962$		0			0
$963$	−0.00323768	+	0.00124624i	−0.00323768	+	0.00124624i
$964$	0.243194	−	0.583331i	0.243194	−	0.583331i
$965$		0			0
$966$		0			0
$967$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$967$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$968$	−0.889304	−	2.02741i	−0.889304	−	2.02741i
$969$	1.64467	−	0.929514i	1.64467	−	0.929514i
$970$		0			0
$971$	0.288988	+	0.192616i	0.288988	+	0.192616i	0.690683	−	0.723158i	$-0.257310\pi$
$971$	0.288988	+	0.192616i	0.288988	+	0.192616i	−0.401695	+	0.915773i	$0.631579\pi$
$972$	0.0648467	+	0.107699i	0.0648467	+	0.107699i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.49900	+	1.03938i	1.49900	+	1.03938i	0.983171	+	0.182687i	$0.0584795\pi$
$977$	1.49900	+	1.03938i	1.49900	+	1.03938i	0.515825	+	0.856694i	$0.327485\pi$
$978$	−1.86444	+	0.171750i	−1.86444	+	0.171750i
$979$	−0.665130	−	0.838552i	−0.665130	−	0.838552i
$980$		0			0
$981$		0			0
$982$	−0.403591	+	1.88174i	−0.403591	+	1.88174i
$983$		0			0		−0.989219	−	0.146447i	$-0.953216\pi$
$983$		0			0		0.989219	+	0.146447i	$0.0467836\pi$
$984$	1.81896	+	0.662047i	1.81896	+	0.662047i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.991742	−	0.128249i	$-0.0409357\pi$
$991$		0			0		−0.991742	+	0.128249i	$0.959064\pi$
$992$		0			0
$993$	−0.868895	−	0.909749i	−0.868895	−	0.909749i
$994$		0			0
$995$		0			0
$996$	0.726959	−	0.162915i	0.726959	−	0.162915i
$997$		0			0		−0.842155	−	0.539235i	$-0.818713\pi$
$997$		0			0		0.842155	+	0.539235i	$0.181287\pi$
$998$	1.26270	+	0.307446i	1.26270	+	0.307446i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bs.a.283.1	✓	108
8.3	odd	2	CM	2888.1.bs.a.283.1	✓	108
361.199	even	171	inner	2888.1.bs.a.1643.1	yes	108
2888.1643	odd	342	inner	2888.1.bs.a.1643.1	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bs.a.283.1	✓	108	1.1	even	1	trivial
2888.1.bs.a.283.1	✓	108	8.3	odd	2	CM
2888.1.bs.a.1643.1	yes	108	361.199	even	171	inner
2888.1.bs.a.1643.1	yes	108	2888.1643	odd	342	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2888 = 2^{3} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2888.bs (of order \(342\), degree \(108\), minimal)

\(f(q)\)	\(=\)	\(q+(0.919425 - 0.393266i) q^{2} +(0.903398 + 0.347734i) q^{3} +(0.690683 - 0.723158i) q^{4} +(0.967359 - 0.0355604i) q^{6} +(0.350638 - 0.936511i) q^{8} +(-0.0467056 - 0.0422095i) q^{9} +O(q^{10})\)	\(q+(0.919425 - 0.393266i) q^{2} +(0.903398 + 0.347734i) q^{3} +(0.690683 - 0.723158i) q^{4} +(0.967359 - 0.0355604i) q^{6} +(0.350638 - 0.936511i) q^{8} +(-0.0467056 - 0.0422095i) q^{9} +(1.66095 - 0.674621i) q^{11} +(0.875429 - 0.413125i) q^{12} +(-0.0459136 - 0.998945i) q^{16} +(-1.89620 + 0.461689i) q^{17} +(-0.0595418 - 0.0204407i) q^{18} +(-0.800291 + 0.599612i) q^{19} +(1.26181 - 1.27346i) q^{22} +(0.642423 - 0.724114i) q^{24} +(0.577333 + 0.816509i) q^{25} +(-0.464606 - 0.918086i) q^{27} +(-0.435066 - 0.900399i) q^{32} +(1.73509 - 0.0318805i) q^{33} +(-1.56184 + 1.17020i) q^{34} +(-0.0627829 + 0.00462208i) q^{36} +(-0.500000 + 0.866025i) q^{38} +(0.735442 + 1.85951i) q^{41} +(-0.507736 - 0.746816i) q^{43} +(0.659335 - 1.66708i) q^{44} +(0.305890 - 0.918411i) q^{48} +(-0.298515 - 0.954405i) q^{49} +(0.851919 + 0.523673i) q^{50} +(-1.87356 - 0.242284i) q^{51} +(-0.788222 - 0.661397i) q^{54} +(-0.931487 + 0.263399i) q^{57} +(-1.18956 + 1.49972i) q^{59} +(-0.754107 - 0.656752i) q^{64} +(1.58275 - 0.711664i) q^{66} +(0.634492 + 1.79437i) q^{67} +(-0.975796 + 1.69013i) q^{68} +(-0.0559064 + 0.0289401i) q^{72} +(-0.206643 + 0.705943i) q^{73} +(0.237633 + 0.938391i) q^{75} +(-0.119134 + 0.992878i) q^{76} +(-0.0941235 - 0.928325i) q^{81} +(1.40747 + 1.42045i) q^{82} +(0.750981 + 0.168299i) q^{83} +(-0.760522 - 0.486965i) q^{86} +(-0.0493975 - 1.79205i) q^{88} +(-0.167724 - 0.572986i) q^{89} +(-0.0799378 - 0.964706i) q^{96} +(0.626538 - 1.77187i) q^{97} +(-0.649797 - 0.760108i) q^{98} +(-0.106051 - 0.0385995i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 108 * q + 3 * q^3 + 3 * q^6 + 3 * q^8 + 3 * q^9	\( 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{18} - 6 q^{22} + 3 q^{24} - 60 q^{27} + 3 q^{33} + 3 q^{36} - 54 q^{38} + 3 q^{41} - 6 q^{44} - 6 q^{48} + 3 q^{49} + 3 q^{50} - 3 q^{51} + 3 q^{54} + 3 q^{59} + 3 q^{64} + 3 q^{66} + 3 q^{67} - 3 q^{68} - 6 q^{72} - 6 q^{73} - 3 q^{81} + 3 q^{82} + 3 q^{97} - 3 q^{99}+O(q^{100}) \) 108 * q + 3 * q^3 + 3 * q^6 + 3 * q^8 + 3 * q^9 - 6 * q^18 - 6 * q^22 + 3 * q^24 - 60 * q^27 + 3 * q^33 + 3 * q^36 - 54 * q^38 + 3 * q^41 - 6 * q^44 - 6 * q^48 + 3 * q^49 + 3 * q^50 - 3 * q^51 + 3 * q^54 + 3 * q^59 + 3 * q^64 + 3 * q^66 + 3 * q^67 - 3 * q^68 - 6 * q^72 - 6 * q^73 - 3 * q^81 + 3 * q^82 + 3 * q^97 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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