LMFDB - Embedded newform 2888.1.bs.a.435.1

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			435.1
Root			$-0.991742 + 0.128249i$ of defining polynomial
Character	$\chi$	$=$	2888.435
Dual form			2888.1.bs.a.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.912045 - 0.410091i) q^{2} +(1.11668 - 1.57930i) q^{3} +(0.663651 + 0.748042i) q^{4} +(-1.66612 + 0.982450i) q^{6} +(-0.298515 - 0.954405i) q^{8} +(-0.913832 - 2.58435i) q^{9} +O(q^{10})$	\(q+(-0.912045 - 0.410091i) q^{2} +(1.11668 - 1.57930i) q^{3} +(0.663651 + 0.748042i) q^{4} +(-1.66612 + 0.982450i) q^{6} +(-0.298515 - 0.954405i) q^{8} +(-0.913832 - 2.58435i) q^{9} +(-0.467617 + 0.567795i) q^{11} +(1.92247 - 0.212779i) q^{12} +(-0.119134 + 0.992878i) q^{16} +(-0.631036 - 1.89464i) q^{17} +(-0.226363 + 2.73180i) q^{18} +(0.100874 - 0.994899i) q^{19} +(0.659335 - 0.326090i) q^{22} +(-1.84064 - 0.594323i) q^{24} +(0.280931 + 0.959728i) q^{25} +(-3.24070 - 0.916383i) q^{27} +(0.515825 - 0.856694i) q^{32} +(0.374540 + 1.37255i) q^{33} +(-0.201441 + 1.98678i) q^{34} +(1.32674 - 2.39870i) q^{36} +(-0.500000 + 0.866025i) q^{38} +(-0.526150 - 0.0193414i) q^{41} +(1.92421 - 0.0353554i) q^{43} +(-0.735069 + 0.0270214i) q^{44} +(1.43502 + 1.29688i) q^{48} +(0.451533 + 0.892254i) q^{49} +(0.137354 - 0.990522i) q^{50} +(-3.69687 - 1.11911i) q^{51} +(2.57986 + 2.16476i) q^{54} +(-1.45860 - 1.27030i) q^{57} +(0.407090 + 0.769030i) q^{59} +(-0.821778 + 0.569808i) q^{64} +(0.221274 - 1.40543i) q^{66} +(-1.65597 - 1.06032i) q^{67} +(0.998482 - 1.72942i) q^{68} +(-2.19373 + 1.64363i) q^{72} +(-1.95798 - 0.401165i) q^{73} +(1.82941 + 0.628037i) q^{75} +(0.811171 - 0.584809i) q^{76} +(-2.93421 + 2.37161i) q^{81} +(0.471941 + 0.233410i) q^{82} +(0.454579 + 0.0250798i) q^{83} +(-1.76947 - 0.756855i) q^{86} +(0.681497 + 0.276800i) q^{88} +(-0.884688 + 0.181262i) q^{89} +(-0.776963 - 1.77130i) q^{96} +(1.58273 - 1.01343i) q^{97} +(-0.0459136 - 0.998945i) q^{98} +(1.89471 + 0.689617i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{23}{171}\right)$

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 $

$2$	−0.912045	−	0.410091i	−0.912045	−	0.410091i
$2$	−0.912045	−	0.410091i	−0.912045	−	0.410091i
$3$	1.11668	−	1.57930i	1.11668	−	1.57930i	0.350638	−	0.936511i	$-0.385965\pi$
$3$	1.11668	−	1.57930i	1.11668	−	1.57930i	0.766044	−	0.642788i	$-0.222222\pi$
$4$	0.663651	+	0.748042i	0.663651	+	0.748042i
$5$		0			0		−0.800291	−	0.599612i	$-0.795322\pi$
$5$		0			0		0.800291	+	0.599612i	$0.204678\pi$
$6$	−1.66612	+	0.982450i	−1.66612	+	0.982450i
$7$		0			0		−0.851919	−	0.523673i	$-0.824561\pi$
$7$		0			0		0.851919	+	0.523673i	$0.175439\pi$
$8$	−0.298515	−	0.954405i	−0.298515	−	0.954405i
$9$	−0.913832	−	2.58435i	−0.913832	−	2.58435i
$10$		0			0
$11$	−0.467617	+	0.567795i	−0.467617	+	0.567795i	−0.951623	−	0.307269i	$-0.900585\pi$
$11$	−0.467617	+	0.567795i	−0.467617	+	0.567795i	0.484006	+	0.875065i	$0.339181\pi$
$12$	1.92247	−	0.212779i	1.92247	−	0.212779i
$13$		0			0		−0.703852	−	0.710347i	$-0.748538\pi$
$13$		0			0		0.703852	+	0.710347i	$0.251462\pi$
$14$		0			0
$15$		0			0
$16$	−0.119134	+	0.992878i	−0.119134	+	0.992878i
$17$	−0.631036	−	1.89464i	−0.631036	−	1.89464i	−0.367783	−	0.929912i	$-0.619883\pi$
$17$	−0.631036	−	1.89464i	−0.631036	−	1.89464i	−0.263253	−	0.964727i	$-0.584795\pi$
$18$	−0.226363	+	2.73180i	−0.226363	+	2.73180i
$19$	0.100874	−	0.994899i	0.100874	−	0.994899i
$19$	0.100874	−	0.994899i	0.100874	−	0.994899i
$20$		0			0
$21$		0			0
$22$	0.659335	−	0.326090i	0.659335	−	0.326090i
$23$		0			0		0.418451	−	0.908239i	$-0.362573\pi$
$23$		0			0		−0.418451	+	0.908239i	$0.637427\pi$
$24$	−1.84064	−	0.594323i	−1.84064	−	0.594323i
$25$	0.280931	+	0.959728i	0.280931	+	0.959728i
$26$		0			0
$27$	−3.24070	−	0.916383i	−3.24070	−	0.916383i
$28$		0			0
$29$		0			0		−0.621436	−	0.783465i	$-0.713450\pi$
$29$		0			0		0.621436	+	0.783465i	$0.286550\pi$
$30$		0			0
$31$		0			0		0.716783	−	0.697297i	$-0.245614\pi$
$31$		0			0		−0.716783	+	0.697297i	$0.754386\pi$
$32$	0.515825	−	0.856694i	0.515825	−	0.856694i
$33$	0.374540	+	1.37255i	0.374540	+	1.37255i
$34$	−0.201441	+	1.98678i	−0.201441	+	1.98678i
$35$		0			0
$36$	1.32674	−	2.39870i	1.32674	−	2.39870i
$37$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$37$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$38$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$39$		0			0
$40$		0			0
$41$	−0.526150	−	0.0193414i	−0.526150	−	0.0193414i	−0.227635	−	0.973746i	$-0.573099\pi$
$41$	−0.526150	−	0.0193414i	−0.526150	−	0.0193414i	−0.298515	+	0.954405i	$0.596491\pi$
$42$		0			0
$43$	1.92421	−	0.0353554i	1.92421	−	0.0353554i	0.957107	−	0.289735i	$-0.0935673\pi$
$43$	1.92421	−	0.0353554i	1.92421	−	0.0353554i	0.967104	+	0.254380i	$0.0818713\pi$
$44$	−0.735069	+	0.0270214i	−0.735069	+	0.0270214i
$45$		0			0
$46$		0			0
$47$		0			0		−0.00918581	−	0.999958i	$-0.502924\pi$
$47$		0			0		0.00918581	+	0.999958i	$0.497076\pi$
$48$	1.43502	+	1.29688i	1.43502	+	1.29688i
$49$	0.451533	+	0.892254i	0.451533	+	0.892254i
$50$	0.137354	−	0.990522i	0.137354	−	0.990522i
$51$	−3.69687	−	1.11911i	−3.69687	−	1.11911i
$52$		0			0
$53$		0			0		−0.870582	−	0.492024i	$-0.836257\pi$
$53$		0			0		0.870582	+	0.492024i	$0.163743\pi$
$54$	2.57986	+	2.16476i	2.57986	+	2.16476i
$55$		0			0
$56$		0			0
$57$	−1.45860	−	1.27030i	−1.45860	−	1.27030i
$58$		0			0
$59$	0.407090	+	0.769030i	0.407090	+	0.769030i	0.999325	−	0.0367355i	$-0.0116959\pi$
$59$	0.407090	+	0.769030i	0.407090	+	0.769030i	−0.592235	+	0.805765i	$0.701754\pi$
$60$		0			0
$61$		0			0		−0.384804	−	0.922998i	$-0.625731\pi$
$61$		0			0		0.384804	+	0.922998i	$0.374269\pi$
$62$		0			0
$63$		0			0
$64$	−0.821778	+	0.569808i	−0.821778	+	0.569808i
$65$		0			0
$66$	0.221274	−	1.40543i	0.221274	−	1.40543i
$67$	−1.65597	−	1.06032i	−1.65597	−	1.06032i	−0.926494	−	0.376309i	$-0.877193\pi$
$67$	−1.65597	−	1.06032i	−1.65597	−	1.06032i	−0.729471	−	0.684011i	$-0.760234\pi$
$68$	0.998482	−	1.72942i	0.998482	−	1.72942i
$69$		0			0
$70$		0			0
$71$		0			0		0.384804	−	0.922998i	$-0.374269\pi$
$71$		0			0		−0.384804	+	0.922998i	$0.625731\pi$
$72$	−2.19373	+	1.64363i	−2.19373	+	1.64363i
$73$	−1.95798	−	0.401165i	−1.95798	−	0.401165i	−0.986361	−	0.164595i	$-0.947368\pi$
$73$	−1.95798	−	0.401165i	−1.95798	−	0.401165i	−0.971614	−	0.236570i	$-0.923977\pi$
$74$		0			0
$75$	1.82941	+	0.628037i	1.82941	+	0.628037i
$76$	0.811171	−	0.584809i	0.811171	−	0.584809i
$77$		0			0
$78$		0			0
$79$		0			0		−0.515825	−	0.856694i	$-0.672515\pi$
$79$		0			0		0.515825	+	0.856694i	$0.327485\pi$
$80$		0			0
$81$	−2.93421	+	2.37161i	−2.93421	+	2.37161i
$82$	0.471941	+	0.233410i	0.471941	+	0.233410i
$83$	0.454579	+	0.0250798i	0.454579	+	0.0250798i	0.280931	−	0.959728i	$-0.409357\pi$
$83$	0.454579	+	0.0250798i	0.454579	+	0.0250798i	0.173648	+	0.984808i	$0.444444\pi$
$84$		0			0
$85$		0			0
$86$	−1.76947	−	0.756855i	−1.76947	−	0.756855i
$87$		0			0
$88$	0.681497	+	0.276800i	0.681497	+	0.276800i
$89$	−0.884688	+	0.181262i	−0.884688	+	0.181262i	−0.621436	−	0.783465i	$-0.713450\pi$
$89$	−0.884688	+	0.181262i	−0.884688	+	0.181262i	−0.263253	+	0.964727i	$0.584795\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.776963	−	1.77130i	−0.776963	−	1.77130i
$97$	1.58273	−	1.01343i	1.58273	−	1.01343i	0.606938	−	0.794749i	$-0.292398\pi$
$97$	1.58273	−	1.01343i	1.58273	−	1.01343i	0.975796	−	0.218681i	$-0.0701754\pi$
$98$	−0.0459136	−	0.998945i	−0.0459136	−	0.998945i
$99$	1.89471	+	0.689617i	1.89471	+	0.689617i
$100$	−0.531476	+	0.847073i	−0.531476	+	0.847073i
$101$		0			0		0.649797	−	0.760108i	$-0.274854\pi$
$101$		0			0		−0.649797	+	0.760108i	$0.725146\pi$
$102$	2.91277	+	2.53673i	2.91277	+	2.53673i
$103$		0			0		0.851919	−	0.523673i	$-0.175439\pi$
$103$		0			0		−0.851919	+	0.523673i	$0.824561\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.78307	−	0.504204i	1.78307	−	0.504204i	0.789141	−	0.614213i	$-0.210526\pi$
$107$	1.78307	−	0.504204i	1.78307	−	0.504204i	0.993931	+	0.110008i	$0.0350877\pi$
$108$	−1.46520	−	3.03234i	−1.46520	−	3.03234i
$109$		0			0		0.870582	−	0.492024i	$-0.163743\pi$
$109$		0			0		−0.870582	+	0.492024i	$0.836257\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.42681	−	0.772150i	−1.42681	−	0.772150i	−0.435066	−	0.900399i	$-0.643275\pi$
$113$	−1.42681	−	0.772150i	−1.42681	−	0.772150i	−0.991742	+	0.128249i	$0.959064\pi$
$114$	0.809372	+	1.75672i	0.809372	+	1.75672i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.0559123	−	0.868333i	−0.0559123	−	0.868333i
$119$		0			0
$120$		0			0
$121$	0.0879842	+	0.450430i	0.0879842	+	0.450430i
$122$		0			0
$123$	−0.618088	+	0.809350i	−0.618088	+	0.809350i
$124$		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	$0.777778\pi$
$128$	0.983171	−	0.182687i	0.983171	−	0.182687i
$129$	2.09290	−	3.07839i	2.09290	−	3.07839i
$130$		0			0
$131$	1.83389	−	0.135011i	1.83389	−	0.135011i	0.888069	−	0.459710i	$-0.152047\pi$
$131$	1.83389	−	0.135011i	1.83389	−	0.135011i	0.945817	+	0.324699i	$0.105263\pi$
$132$	−0.778164	+	1.19107i	−0.778164	+	1.19107i
$133$		0			0
$134$	1.07549	+	1.64616i	1.07549	+	1.64616i
$135$		0			0
$136$	−1.61988	+	1.16784i	−1.61988	+	1.16784i
$137$	−0.276238	+	0.142995i	−0.276238	+	0.142995i	−0.592235	−	0.805765i	$-0.701754\pi$
$137$	−0.276238	+	0.142995i	−0.276238	+	0.142995i	0.315998	+	0.948760i	$0.397661\pi$
$138$		0			0
$139$	1.28916	−	0.496222i	1.28916	−	0.496222i	0.384804	−	0.922998i	$-0.374269\pi$
$139$	1.28916	−	0.496222i	1.28916	−	0.496222i	0.904357	+	0.426776i	$0.140351\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	2.67482	−	0.599441i	2.67482	−	0.599441i
$145$		0			0
$146$	1.62125	+	1.16883i	1.62125	+	1.16883i
$147$	1.91336	+	0.283258i	1.91336	+	0.283258i
$148$		0			0
$149$		0			0		−0.209708	−	0.977764i	$-0.567251\pi$
$149$		0			0		0.209708	+	0.977764i	$0.432749\pi$
$150$	−1.41095	−	1.32302i	−1.41095	−	1.32302i
$151$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$151$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$152$	−0.979649	+	0.200718i	−0.979649	+	0.200718i
$153$	−4.31976	+	3.36220i	−4.31976	+	3.36220i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.418451	−	0.908239i	$-0.637427\pi$
$157$		0			0		0.418451	+	0.908239i	$0.362573\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	3.64870	−	0.959728i	3.64870	−	0.959728i
$163$	1.19288	+	1.16045i	1.19288	+	1.16045i	0.983171	+	0.182687i	$0.0584795\pi$
$163$	1.19288	+	1.16045i	1.19288	+	1.16045i	0.209708	+	0.977764i	$0.432749\pi$
$164$	−0.334712	−	0.406418i	−0.334712	−	0.406418i
$165$		0			0
$166$	−0.404312	−	0.209293i	−0.404312	−	0.209293i
$167$		0			0		0.989219	−	0.146447i	$-0.0467836\pi$
$167$		0			0		−0.989219	+	0.146447i	$0.953216\pi$
$168$		0			0
$169$	−0.00918581	+	0.999958i	−0.00918581	+	0.999958i
$170$		0			0
$171$	−2.66335	+	0.648478i	−2.66335	+	0.648478i
$172$	1.30345	+	1.41593i	1.30345	+	1.41593i
$173$		0			0		0.741914	−	0.670495i	$-0.233918\pi$
$173$		0			0		−0.741914	+	0.670495i	$0.766082\pi$
$174$		0			0
$175$		0			0
$176$	−0.508043	−	0.531930i	−0.508043	−	0.531930i
$177$	1.66912	+	0.215845i	1.66912	+	0.215845i
$178$	0.881209	+	0.197484i	0.881209	+	0.197484i
$179$	0.215573	−	1.10361i	0.215573	−	1.10361i	−0.703852	−	0.710347i	$-0.748538\pi$
$179$	0.215573	−	1.10361i	0.215573	−	1.10361i	0.919425	−	0.393266i	$-0.128655\pi$
$180$		0			0
$181$		0			0		0.912045	−	0.410091i	$-0.134503\pi$
$181$		0			0		−0.912045	+	0.410091i	$0.865497\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.37085	+	0.527665i	1.37085	+	0.527665i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.677282	−	0.735724i	$-0.263158\pi$
$191$		0			0		−0.677282	+	0.735724i	$0.736842\pi$
$192$	−0.0177673	+	1.93413i	−0.0177673	+	1.93413i
$193$	−0.455687	−	0.533045i	−0.455687	−	0.533045i	0.484006	−	0.875065i	$-0.339181\pi$
$193$	−0.455687	−	0.533045i	−0.455687	−	0.533045i	−0.939693	+	0.342020i	$0.888889\pi$
$194$	−1.85912	+	0.275229i	−1.85912	+	0.275229i
$195$		0			0
$196$	−0.367783	+	0.929912i	−0.367783	+	0.929912i
$197$		0			0		−0.635724	−	0.771917i	$-0.719298\pi$
$197$		0			0		0.635724	+	0.771917i	$0.280702\pi$
$198$	−1.44525	−	1.40596i	−1.44525	−	1.40596i
$199$		0			0		0.967104	−	0.254380i	$-0.0818713\pi$
$199$		0			0		−0.967104	+	0.254380i	$0.918129\pi$
$200$	0.832107	−	0.554615i	0.832107	−	0.554615i
$201$	−3.52375	+	1.43122i	−3.52375	+	1.43122i
$202$		0			0
$203$		0			0
$204$	−1.61629	−	3.50811i	−1.61629	−	3.50811i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.517729	+	0.522507i	0.517729	+	0.522507i
$210$		0			0
$211$	0.435516	+	0.408375i	0.435516	+	0.408375i	0.870582	−	0.492024i	$-0.163743\pi$
$211$	0.435516	+	0.408375i	0.435516	+	0.408375i	−0.435066	+	0.900399i	$0.643275\pi$
$212$		0			0
$213$		0			0
$214$	−1.83301	−	0.271364i	−1.83301	−	0.271364i
$215$		0			0
$216$	0.0927968	+	3.36650i	0.0927968	+	3.36650i
$217$		0			0
$218$		0			0
$219$	−2.82000	+	2.64425i	−2.82000	+	2.64425i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.100874	−	0.994899i	$-0.532164\pi$
$223$		0			0		0.100874	+	0.994899i	$0.467836\pi$
$224$		0			0
$225$	2.22355	−	1.60306i	2.22355	−	1.60306i
$226$	0.984661	+	1.28936i	0.984661	+	1.28936i
$227$	0.971455	+	1.48692i	0.971455	+	1.48692i	0.870582	+	0.492024i	$0.163743\pi$
$227$	0.971455	+	1.48692i	0.971455	+	1.48692i	0.100874	+	0.994899i	$0.467836\pi$
$228$	−0.0177673	−	1.93413i	−0.0177673	−	1.93413i
$229$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$229$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.341452	−	0.0634466i	0.341452	−	0.0634466i	−0.00918581	−	0.999958i	$-0.502924\pi$
$233$	0.341452	−	0.0634466i	0.341452	−	0.0634466i	0.350638	+	0.936511i	$0.385965\pi$
$234$		0			0
$235$		0			0
$236$	−0.305101	+	0.814888i	−0.305101	+	0.814888i
$237$		0			0
$238$		0			0
$239$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$239$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$240$		0			0
$241$	0.856663	+	1.21156i	0.856663	+	1.21156i	0.975796	+	0.218681i	$0.0701754\pi$
$241$	0.856663	+	1.21156i	0.856663	+	1.21156i	−0.119134	+	0.992878i	$0.538012\pi$
$242$	0.104472	−	0.446894i	0.104472	−	0.446894i
$243$	0.252508	+	3.92152i	0.252508	+	3.92152i
$244$		0			0
$245$		0			0
$246$	0.895631	−	0.484691i	0.895631	−	0.484691i
$247$		0			0
$248$		0			0
$249$	0.547229	−	0.689910i	0.547229	−	0.689910i
$250$		0			0
$251$	−1.22196	−	0.227057i	−1.22196	−	0.227057i	−0.467849	−	0.883809i	$-0.654971\pi$
$251$	−1.22196	−	0.227057i	−1.22196	−	0.227057i	−0.754107	+	0.656752i	$0.771930\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.971614	−	0.236570i	−0.971614	−	0.236570i
$257$	0.311937	−	0.589277i	0.311937	−	0.589277i	−0.677282	−	0.735724i	$-0.736842\pi$
$257$	0.311937	−	0.589277i	0.311937	−	0.589277i	0.989219	+	0.146447i	$0.0467836\pi$
$258$	−3.17123	+	1.94935i	−3.17123	+	1.94935i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−1.72795	−	0.628923i	−1.72795	−	0.628923i
$263$		0			0		−0.0459136	−	0.998945i	$-0.514620\pi$
$263$		0			0		0.0459136	+	0.998945i	$0.485380\pi$
$264$	1.19817	−	0.767190i	1.19817	−	0.767190i
$265$		0			0
$266$		0			0
$267$	−0.701649	+	1.59960i	−0.701649	+	1.59960i
$268$	−0.305820	−	1.94242i	−0.305820	−	1.94242i
$269$		0			0		0.957107	−	0.289735i	$-0.0935673\pi$
$269$		0			0		−0.957107	+	0.289735i	$0.906433\pi$
$270$		0			0
$271$		0			0		0.663651	−	0.748042i	$-0.269006\pi$
$271$		0			0		−0.663651	+	0.748042i	$0.730994\pi$
$272$	1.95632	−	0.400826i	1.95632	−	0.400826i
$273$		0			0
$274$	0.310582	−	0.0171353i	0.310582	−	0.0171353i
$275$	−0.676297	−	0.289273i	−0.676297	−	0.289273i
$276$		0			0
$277$		0			0		−0.904357	−	0.426776i	$-0.859649\pi$
$277$		0			0		0.904357	+	0.426776i	$0.140351\pi$
$278$	−1.37927	−	0.0760964i	−1.37927	−	0.0760964i
$279$		0			0
$280$		0			0
$281$	0.838404	−	0.877823i	0.838404	−	0.877823i	−0.155527	−	0.987832i	$-0.549708\pi$
$281$	0.838404	−	0.877823i	0.838404	−	0.877823i	0.993931	+	0.110008i	$0.0350877\pi$
$282$		0			0
$283$	1.48169	+	0.389733i	1.48169	+	0.389733i	0.904357	−	0.426776i	$-0.140351\pi$
$283$	1.48169	+	0.389733i	1.48169	+	0.389733i	0.577333	+	0.816509i	$0.304094\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−2.68538	−	0.550201i	−2.68538	−	0.550201i
$289$	−2.39116	+	1.79156i	−2.39116	+	1.79156i
$290$		0			0
$291$	0.166901	−	3.63129i	0.166901	−	3.63129i
$292$	−0.999325	−	1.73088i	−0.999325	−	1.73088i
$293$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$293$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$294$	−1.62890	−	1.04299i	−1.62890	−	1.04299i
$295$		0			0
$296$		0			0
$297$	2.03572	−	1.41154i	2.03572	−	1.41154i
$298$		0			0
$299$		0			0
$300$	0.744291	+	1.78527i	0.744291	+	1.78527i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.975796	+	0.218681i	0.975796	+	0.218681i
$305$		0			0
$306$	5.31862	−	1.29499i	5.31862	−	1.29499i
$307$	0.884525	+	0.742205i	0.884525	+	0.742205i	0.967104	−	0.254380i	$-0.0818713\pi$
$307$	0.884525	+	0.742205i	0.884525	+	0.742205i	−0.0825793	+	0.996584i	$0.526316\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$311$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$312$		0			0
$313$	0.718182	+	0.649047i	0.718182	+	0.649047i	0.945817	−	0.324699i	$-0.105263\pi$
$313$	0.718182	+	0.649047i	0.718182	+	0.649047i	−0.227635	+	0.973746i	$0.573099\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.999325	−	0.0367355i	$-0.0116959\pi$
$317$		0			0		−0.999325	+	0.0367355i	$0.988304\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	1.19483	−	3.37904i	1.19483	−	3.37904i
$322$		0			0
$323$	−1.94863	+	0.436698i	−1.94863	+	0.436698i
$324$	−3.72136	−	0.620985i	−3.72136	−	0.620985i
$325$		0			0
$326$	−0.612069	−	1.54757i	−0.612069	−	1.54757i
$327$		0			0
$328$	0.138604	+	0.507934i	0.138604	+	0.507934i
$329$		0			0
$330$		0			0
$331$	−0.0912698	−	0.0101017i	−0.0912698	−	0.0101017i	0.0642573	−	0.997933i	$-0.479532\pi$
$331$	−0.0912698	−	0.0101017i	−0.0912698	−	0.0101017i	−0.155527	+	0.987832i	$0.549708\pi$
$332$	0.282921	+	0.356689i	0.282921	+	0.356689i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.84922	+	0.597094i	1.84922	+	0.597094i	0.997301	+	0.0734214i	$0.0233918\pi$
$337$	1.84922	+	0.597094i	1.84922	+	0.597094i	0.851919	+	0.523673i	$0.175439\pi$
$338$	0.418451	−	0.908239i	0.418451	−	0.908239i
$339$	−2.81275	+	1.39111i	−2.81275	+	1.39111i
$340$		0			0
$341$		0			0
$342$	2.69503	+	0.500775i	2.69503	+	0.500775i
$343$		0			0
$344$	−0.608149	−	1.82592i	−0.608149	−	1.82592i
$345$		0			0
$346$		0			0
$347$	−1.11235	−	1.63612i	−1.11235	−	1.63612i	−0.677282	−	0.735724i	$-0.736842\pi$
$347$	−1.11235	−	1.63612i	−1.11235	−	1.63612i	−0.435066	−	0.900399i	$-0.643275\pi$
$348$		0			0
$349$		0			0		0.993931	−	0.110008i	$-0.0350877\pi$
$349$		0			0		−0.993931	+	0.110008i	$0.964912\pi$
$350$		0			0
$351$		0			0
$352$	0.245218	+	0.693488i	0.245218	+	0.693488i
$353$	−0.0383635	−	0.122655i	−0.0383635	−	0.122655i	0.933251	−	0.359225i	$-0.116959\pi$
$353$	−0.0383635	−	0.122655i	−0.0383635	−	0.122655i	−0.971614	+	0.236570i	$0.923977\pi$
$354$	−1.43379	−	0.881350i	−1.43379	−	0.881350i
$355$		0			0
$356$	−0.722716	−	0.541490i	−0.722716	−	0.541490i
$357$		0			0
$358$	−0.649194	+	0.918140i	−0.649194	+	0.918140i
$359$		0			0		−0.912045	−	0.410091i	$-0.865497\pi$
$359$		0			0		0.912045	+	0.410091i	$0.134503\pi$
$360$		0			0
$361$	−0.979649	−	0.200718i	−0.979649	−	0.200718i
$362$		0			0
$363$	0.809614	+	0.364034i	0.809614	+	0.364034i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.861396	−	0.507934i	$-0.169591\pi$
$367$		0			0		−0.861396	+	0.507934i	$0.830409\pi$
$368$		0			0
$369$	0.430828	+	1.37743i	0.430828	+	1.37743i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.993931	−	0.110008i	$-0.0350877\pi$
$373$		0			0		−0.993931	+	0.110008i	$0.964912\pi$
$374$	−1.03389	−	1.04343i	−1.03389	−	1.04343i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.162906	−	1.96598i	0.162906	−	1.96598i	−0.0825793	−	0.996584i	$-0.526316\pi$
$379$	0.162906	−	1.96598i	0.162906	−	1.96598i	0.245485	−	0.969400i	$-0.421053\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.896364	−	0.443318i	$-0.146199\pi$
$383$		0			0		−0.896364	+	0.443318i	$0.853801\pi$
$384$	0.809372	−	1.75672i	0.809372	−	1.75672i
$385$		0			0
$386$	0.197010	+	0.673033i	0.197010	+	0.673033i
$387$	−1.84978	−	4.94054i	−1.84978	−	4.94054i
$388$	1.80847	+	0.511387i	1.80847	+	0.511387i
$389$		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
$392$	0.716783	−	0.697297i	0.716783	−	0.697297i
$393$	1.83465	−	3.04702i	1.83465	−	3.04702i
$394$		0			0
$395$		0			0
$396$	0.741563	+	1.87499i	0.741563	+	1.87499i
$397$		0			0		0.484006	−	0.875065i	$-0.339181\pi$
$397$		0			0		−0.484006	+	0.875065i	$0.660819\pi$
$398$		0			0
$399$		0			0
$400$	−0.986361	+	0.164595i	−0.986361	+	0.164595i
$401$	−0.622243	+	1.75973i	−0.622243	+	1.75973i	0.0275543	+	0.999620i	$0.491228\pi$
$401$	−0.622243	+	1.75973i	−0.622243	+	1.75973i	−0.649797	+	0.760108i	$0.725146\pi$
$402$	3.80075	+	0.139717i	3.80075	+	0.139717i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.0354806	+	3.86238i	0.0354806	+	3.86238i
$409$	−1.47158	−	1.32992i	−1.47158	−	1.32992i	−0.821778	−	0.569808i	$-0.807018\pi$
$409$	−1.47158	−	1.32992i	−1.47158	−	1.32992i	−0.649797	−	0.760108i	$-0.725146\pi$
$410$		0			0
$411$	−0.0826379	+	0.595941i	−0.0826379	+	0.595941i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.655901	−	2.59009i	0.655901	−	2.59009i
$418$	−0.257917	−	0.688866i	−0.257917	−	0.688866i
$419$	0.418268	+	1.65170i	0.418268	+	1.65170i	0.716783	+	0.697297i	$0.245614\pi$
$419$	0.418268	+	1.65170i	0.418268	+	1.65170i	−0.298515	+	0.954405i	$0.596491\pi$
$420$		0			0
$421$		0			0		−0.861396	−	0.507934i	$-0.830409\pi$
$421$		0			0		0.861396	+	0.507934i	$0.169591\pi$
$422$	−0.229739	−	0.551057i	−0.229739	−	0.551057i
$423$		0			0
$424$		0			0
$425$	1.64106	−	1.13789i	1.64106	−	1.13789i
$426$		0			0
$427$		0			0
$428$	1.56050	+	0.999196i	1.56050	+	0.999196i
$429$		0			0
$430$		0			0
$431$		0			0		0.0459136	−	0.998945i	$-0.485380\pi$
$431$		0			0		−0.0459136	+	0.998945i	$0.514620\pi$
$432$	1.29593	−	3.10845i	1.29593	−	3.10845i
$433$	0.132175	−	0.0990311i	0.132175	−	0.0990311i	−0.531476	−	0.847073i	$-0.678363\pi$
$433$	0.132175	−	0.0990311i	0.132175	−	0.0990311i	0.663651	+	0.748042i	$0.269006\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	3.65635	−	1.25523i	3.65635	−	1.25523i
$439$		0			0		−0.967104	−	0.254380i	$-0.918129\pi$
$439$		0			0		0.967104	+	0.254380i	$0.0818713\pi$
$440$		0			0
$441$	1.89328	−	1.98229i	1.89328	−	1.98229i
$442$		0			0
$443$	1.63505	+	0.808652i	1.63505	+	0.808652i	0.999325	+	0.0367355i	$0.0116959\pi$
$443$	1.63505	+	0.808652i	1.63505	+	0.808652i	0.635724	+	0.771917i	$0.280702\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.84518	+	0.749446i	1.84518	+	0.749446i	0.957107	+	0.289735i	$0.0935673\pi$
$449$	1.84518	+	0.749446i	1.84518	+	0.749446i	0.888069	+	0.459710i	$0.152047\pi$
$450$	−2.68538	+	0.550201i	−2.68538	+	0.550201i
$451$	0.257019	−	0.289701i	0.257019	−	0.289701i
$452$	−0.369303	−	1.57975i	−0.369303	−	1.57975i
$453$		0			0
$454$	−0.276238	−	1.75453i	−0.276238	−	1.75453i
$455$		0			0
$456$	−0.776963	+	1.77130i	−0.776963	+	1.77130i
$457$	−0.309148	−	0.704787i	−0.309148	−	0.704787i	0.690683	−	0.723158i	$-0.257310\pi$
$457$	−0.309148	−	0.704787i	−0.309148	−	0.704787i	−0.999831	+	0.0183709i	$0.994152\pi$
$458$		0			0
$459$	0.308783	+	6.71823i	0.308783	+	6.71823i
$460$		0			0
$461$		0			0		0.531476	−	0.847073i	$-0.321637\pi$
$461$		0			0		−0.531476	+	0.847073i	$0.678363\pi$
$462$		0			0
$463$		0			0		−0.754107	−	0.656752i	$-0.771930\pi$
$463$		0			0		0.754107	+	0.656752i	$0.228070\pi$
$464$		0			0
$465$		0			0
$466$	−0.337438	−	0.0821600i	−0.337438	−	0.0821600i
$467$	0.629518	+	0.856490i	0.629518	+	0.856490i	0.997301	−	0.0734214i	$-0.0233918\pi$
$467$	0.629518	+	0.856490i	0.629518	+	0.856490i	−0.367783	+	0.929912i	$0.619883\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.612443	−	0.618095i	0.612443	−	0.618095i
$473$	−0.879719	+	1.10909i	−0.879719	+	1.10909i
$474$		0			0
$475$	0.983171	−	0.182687i	0.983171	−	0.182687i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.0642573	−	0.997933i	$-0.520468\pi$
$479$		0			0		0.0642573	+	0.997933i	$0.479532\pi$
$480$		0			0
$481$		0			0
$482$	−0.284466	−	1.45631i	−0.284466	−	1.45631i
$483$		0			0
$484$	−0.278550	+	0.364745i	−0.278550	+	0.364745i
$485$		0			0
$486$	1.37788	−	3.68015i	1.37788	−	3.68015i
$487$		0			0		0.592235	−	0.805765i	$-0.298246\pi$
$487$		0			0		−0.592235	+	0.805765i	$0.701754\pi$
$488$		0			0
$489$	3.16477	−	0.588058i	3.16477	−	0.588058i
$490$		0			0
$491$	−0.423704	+	1.44747i	−0.423704	+	1.44747i	0.418451	+	0.908239i	$0.362573\pi$
$491$	−0.423704	+	1.44747i	−0.423704	+	1.44747i	−0.842155	+	0.539235i	$0.818713\pi$
$492$	−1.01562	+	0.0747703i	−1.01562	+	0.0747703i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.782023	+	0.404816i	−0.782023	+	0.404816i
$499$	−0.00926293	−	0.0913588i	−0.00926293	−	0.0913588i	0.989219	−	0.146447i	$-0.0467836\pi$
$499$	−0.00926293	−	0.0913588i	−0.00926293	−	0.0913588i	−0.998482	+	0.0550878i	$0.982456\pi$
$500$		0			0
$501$		0			0
$502$	1.02136	+	0.708198i	1.02136	+	0.708198i
$503$		0			0		0.729471	−	0.684011i	$-0.239766\pi$
$503$		0			0		−0.729471	+	0.684011i	$0.760234\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.56897	+	1.13114i	1.56897	+	1.13114i
$508$		0			0
$509$		0			0		−0.531476	−	0.847073i	$-0.678363\pi$
$509$		0			0		0.531476	+	0.847073i	$0.321637\pi$
$510$		0			0
$511$		0			0
$512$	0.789141	+	0.614213i	0.789141	+	0.614213i
$513$	−1.23861	+	3.13173i	−1.23861	+	3.13173i
$514$	−0.526158	+	0.409525i	−0.526158	+	0.409525i
$515$		0			0
$516$	3.69171	−	0.477401i	3.69171	−	0.477401i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.15151	−	0.467704i	1.15151	−	0.467704i	0.280931	−	0.959728i	$-0.409357\pi$
$521$	1.15151	−	0.467704i	1.15151	−	0.467704i	0.870582	+	0.492024i	$0.163743\pi$
$522$		0			0
$523$	1.05791	−	0.278265i	1.05791	−	0.278265i	0.315998	−	0.948760i	$-0.397661\pi$
$523$	1.05791	−	0.278265i	1.05791	−	0.278265i	0.741914	+	0.670495i	$0.233918\pi$
$524$	1.31805	+	1.28222i	1.31805	+	1.28222i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.40740	+	0.208355i	−1.40740	+	0.208355i
$529$	−0.649797	−	0.760108i	−0.649797	−	0.760108i
$530$		0			0
$531$	1.61543	−	1.75483i	1.61543	−	1.75483i
$532$		0			0
$533$		0			0
$534$	1.29592	−	1.17117i	1.29592	−	1.17117i
$535$		0			0
$536$	−0.517645	+	1.89698i	−0.517645	+	1.89698i
$537$	−1.50221	−	1.57284i	−1.50221	−	1.57284i
$538$		0			0
$539$	−0.717762	−	0.160854i	−0.717762	−	0.160854i
$540$		0			0
$541$		0			0		0.912045	−	0.410091i	$-0.134503\pi$
$541$		0			0		−0.912045	+	0.410091i	$0.865497\pi$
$542$		0			0
$543$		0			0
$544$	−1.94863	−	0.436698i	−1.94863	−	0.436698i
$545$		0			0
$546$		0			0
$547$	−0.334712	+	1.22660i	−0.334712	+	1.22660i	0.577333	+	0.816509i	$0.304094\pi$
$547$	−0.334712	+	1.22660i	−0.334712	+	1.22660i	−0.912045	+	0.410091i	$0.865497\pi$
$548$	−0.290292	−	0.111739i	−0.290292	−	0.111739i
$549$		0			0
$550$	0.498185	+	0.541173i	0.498185	+	0.541173i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.22675	+	0.635028i	1.22675	+	0.635028i
$557$		0			0		0.367783	−	0.929912i	$-0.380117\pi$
$557$		0			0		−0.367783	+	0.929912i	$0.619883\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	2.36414	−	1.57575i	2.36414	−	1.57575i
$562$	−1.12465	+	0.456793i	−1.12465	+	0.456793i
$563$	0.379303	−	0.178997i	0.379303	−	0.178997i	−0.227635	−	0.973746i	$-0.573099\pi$
$563$	0.379303	−	0.178997i	0.379303	−	0.178997i	0.606938	+	0.794749i	$0.292398\pi$
$564$		0			0
$565$		0			0
$566$	−1.19154	−	0.963081i	−1.19154	−	0.963081i
$567$		0			0
$568$		0			0
$569$	−1.19019	+	0.926364i	−1.19019	+	0.926364i	−0.998482	−	0.0550878i	$-0.982456\pi$
$569$	−1.19019	+	0.926364i	−1.19019	+	0.926364i	−0.191711	+	0.981451i	$0.561404\pi$
$570$		0			0
$571$	−0.738397	−	0.574717i	−0.738397	−	0.574717i	0.173648	−	0.984808i	$-0.444444\pi$
$571$	−0.738397	−	0.574717i	−0.738397	−	0.574717i	−0.912045	+	0.410091i	$0.865497\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	2.22355	+	1.60306i	2.22355	+	1.60306i
$577$	0.0318160	+	1.15423i	0.0318160	+	1.15423i	0.832107	+	0.554615i	$0.187135\pi$
$577$	0.0318160	+	1.15423i	0.0318160	+	1.15423i	−0.800291	+	0.599612i	$0.795322\pi$
$578$	2.91554	−	0.653389i	2.91554	−	0.653389i
$579$	−1.35069	+	0.124424i	−1.35069	+	0.124424i
$580$		0			0
$581$		0			0
$582$	−1.64138	+	3.24345i	−1.64138	+	3.24345i
$583$		0			0
$584$	0.201611	+	1.98846i	0.201611	+	1.98846i
$585$		0			0
$586$		0			0
$587$	0.0334475	+	0.0437976i	0.0334475	+	0.0437976i	0.811171	−	0.584809i	$-0.198830\pi$
$587$	0.0334475	+	0.0437976i	0.0334475	+	0.0437976i	−0.777724	+	0.628606i	$0.783626\pi$
$588$	1.05791	+	1.61925i	1.05791	+	1.61925i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.315899	+	0.464647i	−0.315899	+	0.464647i	−0.951623	−	0.307269i	$-0.900585\pi$
$593$	−0.315899	+	0.464647i	−0.315899	+	0.464647i	0.635724	+	0.771917i	$0.280702\pi$
$594$	−2.43553	+	0.452556i	−2.43553	+	0.452556i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.606938	−	0.794749i	$-0.292398\pi$
$599$		0			0		−0.606938	+	0.794749i	$0.707602\pi$
$600$	0.0532959	−	1.93347i	0.0532959	−	1.93347i
$601$	−0.293718	−	1.50367i	−0.293718	−	1.50367i	−0.777724	−	0.628606i	$-0.783626\pi$
$601$	−0.293718	−	1.50367i	−0.293718	−	1.50367i	0.484006	−	0.875065i	$-0.339181\pi$
$602$		0			0
$603$	−1.22697	+	5.24856i	−1.22697	+	5.24856i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.879474	−	0.475947i	$-0.157895\pi$
$607$		0			0		−0.879474	+	0.475947i	$0.842105\pi$
$608$	−0.800291	−	0.599612i	−0.800291	−	0.599612i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−5.38188	−	1.00003i	−5.38188	−	1.00003i
$613$		0			0		0.870582	−	0.492024i	$-0.163743\pi$
$613$		0			0		−0.870582	+	0.492024i	$0.836257\pi$
$614$	−0.502355	−	1.03966i	−0.502355	−	1.03966i
$615$		0			0
$616$		0			0
$617$	−1.85988	−	0.452846i	−1.85988	−	0.452846i	−0.861396	−	0.507934i	$-0.830409\pi$
$617$	−1.85988	−	0.452846i	−1.85988	−	0.452846i	−0.998482	+	0.0550878i	$0.982456\pi$
$618$		0			0
$619$	−0.508621	+	0.312648i	−0.508621	+	0.312648i	−0.754107	−	0.656752i	$-0.771930\pi$
$619$	−0.508621	+	0.312648i	−0.508621	+	0.312648i	0.245485	+	0.969400i	$0.421053\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.842155	+	0.539235i	−0.842155	+	0.539235i
$626$	−0.388846	−	0.886480i	−0.388846	−	0.886480i
$627$	1.40333	−	0.234175i	1.40333	−	0.234175i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.227635	−	0.973746i	$-0.573099\pi$
$631$		0			0		0.227635	+	0.973746i	$0.426901\pi$
$632$		0			0
$633$	1.13128	−	0.231785i	1.13128	−	0.231785i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.156903	+	0.126819i	−0.156903	+	0.126819i	−0.703852	−	0.710347i	$-0.748538\pi$
$641$	−0.156903	+	0.126819i	−0.156903	+	0.126819i	0.546948	+	0.837166i	$0.315789\pi$
$642$	−2.47545	+	2.59184i	−2.47545	+	2.59184i
$643$	0.765396	+	1.27119i	0.765396	+	1.27119i	0.957107	+	0.289735i	$0.0935673\pi$
$643$	0.765396	+	1.27119i	0.765396	+	1.27119i	−0.191711	+	0.981451i	$0.561404\pi$
$644$		0			0
$645$		0			0
$646$	1.95632	+	0.400826i	1.95632	+	0.400826i
$647$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$647$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$648$	3.13938	+	2.09246i	3.13938	+	2.09246i
$649$	−0.627013	−	0.128467i	−0.627013	−	0.128467i
$650$		0			0
$651$		0			0
$652$	−0.0764100	+	1.66246i	−0.0764100	+	1.66246i
$653$		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
$656$	0.0818859	−	0.520099i	0.0818859	−	0.520099i
$657$	0.752509	+	5.42670i	0.752509	+	5.42670i
$658$		0			0
$659$	0.357309	−	1.66595i	0.357309	−	1.66595i	−0.333374	−	0.942795i	$-0.608187\pi$
$659$	0.357309	−	1.66595i	0.357309	−	1.66595i	0.690683	−	0.723158i	$-0.257310\pi$
$660$		0			0
$661$		0			0		−0.384804	−	0.922998i	$-0.625731\pi$
$661$		0			0		0.384804	+	0.922998i	$0.374269\pi$
$662$	0.0790995	+	0.0466421i	0.0790995	+	0.0466421i
$663$		0			0
$664$	−0.111762	−	0.441340i	−0.111762	−	0.441340i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.742120	−	1.46647i	−0.742120	−	1.46647i	−0.879474	−	0.475947i	$-0.842105\pi$
$673$	−0.742120	−	1.46647i	−0.742120	−	1.46647i	0.137354	−	0.990522i	$-0.456140\pi$
$674$	−1.44171	−	1.30292i	−1.44171	−	1.30292i
$675$	−0.0309357	−	3.36763i	−0.0309357	−	3.36763i
$676$	−0.754107	+	0.656752i	−0.754107	+	0.656752i
$677$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$677$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$678$	3.13583	−	0.115274i	3.13583	−	0.115274i
$679$		0			0
$680$		0			0
$681$	3.43310	+	0.126202i	3.43310	+	0.126202i
$682$		0			0
$683$	−1.78405	+	0.297705i	−1.78405	+	0.297705i	−0.962268	−	0.272103i	$-0.912281\pi$
$683$	−1.78405	+	0.297705i	−1.78405	+	0.297705i	−0.821778	+	0.569808i	$0.807018\pi$
$684$	−2.25263	−	1.56194i	−2.25263	−	1.56194i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.194135	+	1.91472i	−0.194135	+	1.91472i
$689$		0			0
$690$		0			0
$691$	0.502662	−	0.488997i	0.502662	−	0.488997i	−0.401695	−	0.915773i	$-0.631579\pi$
$691$	0.502662	−	0.488997i	0.502662	−	0.488997i	0.904357	+	0.426776i	$0.140351\pi$
$692$		0			0
$693$		0			0
$694$	0.343552	+	1.94838i	0.343552	+	1.94838i
$695$		0			0
$696$		0			0
$697$	0.295374	+	1.00907i	0.295374	+	1.00907i
$698$		0			0
$699$	0.281092	−	0.610104i	0.281092	−	0.610104i
$700$		0			0
$701$		0			0		0.919425	−	0.393266i	$-0.128655\pi$
$701$		0			0		−0.919425	+	0.393266i	$0.871345\pi$
$702$		0			0
$703$		0			0
$704$	0.0607425	−	0.733053i	0.0607425	−	0.733053i
$705$		0			0
$706$	−0.0153104	+	0.127599i	−0.0153104	+	0.127599i
$707$		0			0
$708$	0.946251	+	1.39182i	0.946251	+	1.39182i
$709$		0			0		−0.703852	−	0.710347i	$-0.748538\pi$
$709$		0			0		0.703852	+	0.710347i	$0.251462\pi$
$710$		0			0
$711$		0			0
$712$	0.437090	+	0.790242i	0.437090	+	0.790242i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.968614	−	0.571157i	0.968614	−	0.571157i
$717$		0			0
$718$		0			0
$719$		0			0		0.577333	−	0.816509i	$-0.304094\pi$
$719$		0			0		−0.577333	+	0.816509i	$0.695906\pi$
$720$		0			0
$721$		0			0
$722$	0.811171	+	0.584809i	0.811171	+	0.584809i
$723$	2.87003			2.87003
$724$		0			0
$725$		0			0
$726$	−0.589118	−	0.664031i	−0.589118	−	0.664031i
$727$		0			0		−0.800291	−	0.599612i	$-0.795322\pi$
$727$		0			0		0.800291	+	0.599612i	$0.204678\pi$
$728$		0			0
$729$	3.26108	+	2.00458i	3.26108	+	2.00458i
$730$		0			0
$731$	−1.28123	−	3.62337i	−1.28123	−	3.62337i
$732$		0			0
$733$		0			0		0.635724	−	0.771917i	$-0.280702\pi$
$733$		0			0		−0.635724	+	0.771917i	$0.719298\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.37640	−	0.444426i	1.37640	−	0.444426i
$738$	0.171938	−	1.43296i	0.171938	−	1.43296i
$739$	0.0406103	+	0.121930i	0.0406103	+	0.121930i	0.967104	−	0.254380i	$-0.0818713\pi$
$739$	0.0406103	+	0.121930i	0.0406103	+	0.121930i	−0.926494	+	0.376309i	$0.877193\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.919425	−	0.393266i	$-0.128655\pi$
$743$		0			0		−0.919425	+	0.393266i	$0.871345\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.350594	−	1.19771i	−0.350594	−	1.19771i
$748$	0.515051	+	1.37564i	0.515051	+	1.37564i
$749$		0			0
$750$		0			0
$751$		0			0		−0.621436	−	0.783465i	$-0.713450\pi$
$751$		0			0		0.621436	+	0.783465i	$0.286550\pi$
$752$		0			0
$753$	−1.72313	+	1.67628i	−1.72313	+	1.67628i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.367783	−	0.929912i	$-0.619883\pi$
$757$		0			0		0.367783	+	0.929912i	$0.380117\pi$
$758$	−0.954810	+	1.72626i	−0.954810	+	1.72626i
$759$		0			0
$760$		0			0
$761$	0.922936	−	0.154011i	0.922936	−	0.154011i	0.315998	−	0.948760i	$-0.397661\pi$
$761$	0.922936	−	0.154011i	0.922936	−	0.154011i	0.606938	+	0.794749i	$0.292398\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.45860	+	1.27030i	−1.45860	+	1.27030i
$769$	−0.0116793	−	1.27139i	−0.0116793	−	1.27139i	−0.777724	−	0.628606i	$-0.783626\pi$
$769$	−0.0116793	−	1.27139i	−0.0116793	−	1.27139i	0.766044	−	0.642788i	$-0.222222\pi$
$770$		0			0
$771$	−0.582311	−	1.15068i	−0.582311	−	1.15068i
$772$	0.0963226	−	0.694628i	0.0963226	−	0.694628i
$773$		0			0		−0.957107	−	0.289735i	$-0.906433\pi$
$773$		0			0		0.957107	+	0.289735i	$0.0935673\pi$
$774$	−0.338987	+	5.26457i	−0.338987	+	5.26457i
$775$		0			0
$776$	−1.43969	−	1.20805i	−1.43969	−	1.20805i
$777$		0			0
$778$		0			0
$779$	−0.0723174	+	0.521515i	−0.0723174	+	0.521515i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.939693	+	0.342020i	−0.939693	+	0.342020i
$785$		0			0
$786$	−2.92283	+	2.02665i	−2.92283	+	2.02665i
$787$	−0.178504	−	1.28728i	−0.178504	−	1.28728i	−0.842155	−	0.539235i	$-0.818713\pi$
$787$	−0.178504	−	1.28728i	−0.178504	−	1.28728i	0.663651	−	0.748042i	$-0.269006\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.0925758	−	2.01418i	0.0925758	−	2.01418i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.945817	−	0.324699i	$-0.894737\pi$
$797$		0			0		0.945817	+	0.324699i	$0.105263\pi$
$798$		0			0
$799$		0			0
$800$	0.967104	+	0.254380i	0.967104	+	0.254380i
$801$	1.27690	+	2.12071i	1.27690	+	2.12071i
$802$	1.28916	−	1.34977i	1.28916	−	1.34977i
$803$	1.14336	−	0.924138i	1.14336	−	0.924138i
$804$	−3.40916	−	1.68608i	−3.40916	−	1.68608i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.40557	−	0.0775472i	1.40557	−	0.0775472i	0.663651	−	0.748042i	$-0.269006\pi$
$809$	1.40557	−	0.0775472i	1.40557	−	0.0775472i	0.741914	+	0.670495i	$0.233918\pi$
$810$		0			0
$811$	−1.54616	+	0.316789i	−1.54616	+	0.316789i	−0.896364	−	0.443318i	$-0.853801\pi$
$811$	−1.54616	+	0.316789i	−1.54616	+	0.316789i	−0.649797	+	0.760108i	$0.725146\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	1.55157	−	3.53721i	1.55157	−	3.53721i
$817$	0.158927	−	1.91796i	0.158927	−	1.91796i
$818$	0.796756	+	1.81642i	0.796756	+	1.81642i
$819$		0			0
$820$		0			0
$821$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$821$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$822$	0.319759	−	0.509636i	0.319759	−	0.509636i
$823$		0			0		0.649797	−	0.760108i	$-0.274854\pi$
$823$		0			0		−0.649797	+	0.760108i	$0.725146\pi$
$824$		0			0
$825$	−1.21206	+	0.745049i	−1.21206	+	0.745049i
$826$		0			0
$827$	1.36774	+	0.333021i	1.36774	+	0.333021i	0.851919	−	0.523673i	$-0.175439\pi$
$827$	1.36774	+	0.333021i	1.36774	+	0.333021i	0.515825	+	0.856694i	$0.327485\pi$
$828$		0			0
$829$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$829$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.40557	−	1.41854i	1.40557	−	1.41854i
$834$	−1.66038	+	2.09330i	−1.66038	+	2.09330i
$835$		0			0
$836$	−0.0472655	+	0.734046i	−0.0472655	+	0.734046i
$837$		0			0
$838$	0.295869	−	1.67795i	0.295869	−	1.67795i
$839$		0			0		0.435066	−	0.900399i	$-0.356725\pi$
$839$		0			0		−0.435066	+	0.900399i	$0.643275\pi$
$840$		0			0
$841$	−0.227635	+	0.973746i	−0.227635	+	0.973746i
$842$		0			0
$843$	−0.450115	−	2.30434i	−0.450115	−	2.30434i
$844$	−0.0164508	+	0.596803i	−0.0164508	+	0.596803i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2.27008	−	1.90482i	2.27008	−	1.90482i
$850$	−1.96336	+	0.364819i	−1.96336	+	0.364819i
$851$		0			0
$852$		0			0
$853$		0			0		0.997301	−	0.0734214i	$-0.0233918\pi$
$853$		0			0		−0.997301	+	0.0734214i	$0.976608\pi$
$854$		0			0
$855$		0			0
$856$	−1.01349	−	1.55126i	−1.01349	−	1.55126i
$857$	−1.02227	−	1.33860i	−1.02227	−	1.33860i	−0.939693	−	0.342020i	$-0.888889\pi$
$857$	−1.02227	−	1.33860i	−1.02227	−	1.33860i	−0.0825793	−	0.996584i	$-0.526316\pi$
$858$		0			0
$859$	1.69995	−	0.879984i	1.69995	−	0.879984i	0.716783	−	0.697297i	$-0.245614\pi$
$859$	1.69995	−	0.879984i	1.69995	−	0.879984i	0.983171	−	0.182687i	$-0.0584795\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$863$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$864$	−2.45669	+	2.30360i	−2.45669	+	2.30360i
$865$		0			0
$866$	−0.161161	+	0.0361171i	−0.161161	+	0.0361171i
$867$	0.159241	+	5.77695i	0.159241	+	5.77695i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−4.06542	−	3.16424i	−4.06542	−	3.16424i
$874$		0			0
$875$		0			0
$876$	−3.84951	−	0.354612i	−3.84951	−	0.354612i
$877$		0			0		0.991742	−	0.128249i	$-0.0409357\pi$
$877$		0			0		−0.991742	+	0.128249i	$0.959064\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.01692	+	0.479898i	−1.01692	+	0.479898i	−0.861396	−	0.507934i	$-0.830409\pi$
$881$	−1.01692	+	0.479898i	−1.01692	+	0.479898i	−0.155527	+	0.987832i	$0.549708\pi$
$882$	−2.53967	+	1.03153i	−2.53967	+	1.03153i
$883$	−1.33186	+	0.887707i	−1.33186	+	0.887707i	−0.998482	−	0.0550878i	$-0.982456\pi$
$883$	−1.33186	+	0.887707i	−1.33186	+	0.887707i	−0.333374	+	0.942795i	$0.608187\pi$
$884$		0			0
$885$		0			0
$886$	−1.15962	−	1.40805i	−1.15962	−	1.40805i
$887$		0			0		0.367783	−	0.929912i	$-0.380117\pi$
$887$		0			0		−0.367783	+	0.929912i	$0.619883\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.0254920	−	2.77504i	0.0254920	−	2.77504i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−1.37554	−	1.44022i	−1.37554	−	1.44022i
$899$		0			0
$900$	2.67482	+	0.599441i	2.67482	+	0.599441i
$901$		0			0
$902$	−0.353216	+	0.158820i	−0.353216	+	0.158820i
$903$		0			0
$904$	−0.311020	+	1.59225i	−0.311020	+	1.59225i
$905$		0			0
$906$		0			0
$907$	−1.23821	−	1.29643i	−1.23821	−	1.29643i	−0.939693	−	0.342020i	$-0.888889\pi$
$907$	−1.23821	−	1.29643i	−1.23821	−	1.29643i	−0.298515	−	0.954405i	$-0.596491\pi$
$908$	−0.467573	+	1.71349i	−0.467573	+	1.71349i
$909$		0			0
$910$		0			0
$911$		0			0		−0.677282	−	0.735724i	$-0.736842\pi$
$911$		0			0		0.677282	+	0.735724i	$0.263158\pi$
$912$	1.43502	−	1.29688i	1.43502	−	1.29688i
$913$	−0.226809	+	0.246380i	−0.226809	+	0.246380i
$914$	−0.00706948	+	0.769576i	−0.00706948	+	0.769576i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	2.47346	−	6.25395i	2.47346	−	6.25395i
$919$		0			0		−0.635724	−	0.771917i	$-0.719298\pi$
$919$		0			0		0.635724	+	0.771917i	$0.280702\pi$
$920$		0			0
$921$	2.15990	−	0.568123i	2.15990	−	0.568123i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.85863	−	0.171215i	−1.85863	−	0.171215i	−0.896364	−	0.443318i	$-0.853801\pi$
$929$	−1.85863	−	0.171215i	−1.85863	−	0.171215i	−0.962268	+	0.272103i	$0.912281\pi$
$930$		0			0
$931$	0.933251	−	0.359225i	0.933251	−	0.359225i
$932$	0.274066	+	0.213314i	0.274066	+	0.213314i
$933$		0			0
$934$	−0.222910	−	1.03932i	−0.222910	−	1.03932i
$935$		0			0
$936$		0			0
$937$	−1.47965	−	1.06674i	−1.47965	−	1.06674i	−0.979649	−	0.200718i	$-0.935673\pi$
$937$	−1.47965	−	1.06674i	−1.47965	−	1.06674i	−0.500000	−	0.866025i	$-0.666667\pi$
$938$		0			0
$939$	1.82702	−	0.409445i	1.82702	−	0.409445i
$940$		0			0
$941$		0			0		0.729471	−	0.684011i	$-0.239766\pi$
$941$		0			0		−0.729471	+	0.684011i	$0.760234\pi$
$942$		0			0
$943$		0			0
$944$	−0.812051	+	0.312573i	−0.812051	+	0.312573i
$945$		0			0
$946$	1.25717	−	0.650777i	1.25717	−	0.650777i
$947$	0.398262	−	0.287124i	0.398262	−	0.287124i	−0.367783	−	0.929912i	$-0.619883\pi$
$947$	0.398262	−	0.287124i	0.398262	−	0.287124i	0.766044	+	0.642788i	$0.222222\pi$
$948$		0			0
$949$		0			0
$950$	−0.971614	−	0.236570i	−0.971614	−	0.236570i
$951$		0			0
$952$		0			0
$953$	−0.503633	+	1.72053i	−0.503633	+	1.72053i	0.173648	+	0.984808i	$0.444444\pi$
$953$	−0.503633	+	1.72053i	−0.503633	+	1.72053i	−0.677282	+	0.735724i	$0.736842\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.0275543	−	0.999620i	0.0275543	−	0.999620i
$962$		0			0
$963$	−2.93247	−	4.14733i	−2.93247	−	4.14733i
$964$	−0.337772	+	1.44487i	−0.337772	+	1.44487i
$965$		0			0
$966$		0			0
$967$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$967$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$968$	0.403628	−	0.218433i	0.403628	−	0.218433i
$969$	−1.48632	+	3.56512i	−1.48632	+	3.56512i
$970$		0			0
$971$	−0.215822	+	0.272095i	−0.215822	+	0.272095i	−0.879474	−	0.475947i	$-0.842105\pi$
$971$	−0.215822	+	0.272095i	−0.215822	+	0.272095i	0.663651	+	0.748042i	$0.269006\pi$
$972$	−2.76588	+	2.79141i	−2.76588	+	2.79141i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.184217	+	0.250637i	0.184217	+	0.250637i	0.888069	−	0.459710i	$-0.152047\pi$
$977$	0.184217	+	0.250637i	0.184217	+	0.250637i	−0.703852	+	0.710347i	$0.748538\pi$
$978$	−3.12757	−	0.761505i	−3.12757	−	0.761505i
$979$	0.310775	−	0.587083i	0.310775	−	0.587083i
$980$		0			0
$981$		0			0
$982$	0.980033	−	1.14640i	0.980033	−	1.14640i
$983$		0			0		0.531476	−	0.847073i	$-0.321637\pi$
$983$		0			0		−0.531476	+	0.847073i	$0.678363\pi$
$984$	0.956956	+	0.348304i	0.956956	+	0.348304i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.957107	−	0.289735i	$-0.0935673\pi$
$991$		0			0		−0.957107	+	0.289735i	$0.906433\pi$
$992$		0			0
$993$	−0.117873	+	0.132862i	−0.117873	+	0.132862i
$994$		0			0
$995$		0			0
$996$	0.879251	−	0.0485097i	0.879251	−	0.0485097i
$997$		0			0		−0.919425	−	0.393266i	$-0.871345\pi$
$997$		0			0		0.919425	+	0.393266i	$0.128655\pi$
$998$	−0.0290172	+	0.0871219i	−0.0290172	+	0.0871219i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bs.a.435.1	✓	108
8.3	odd	2	CM	2888.1.bs.a.435.1	✓	108
361.161	even	171	inner	2888.1.bs.a.883.1	yes	108
2888.883	odd	342	inner	2888.1.bs.a.883.1	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bs.a.435.1	✓	108	1.1	even	1	trivial
2888.1.bs.a.435.1	✓	108	8.3	odd	2	CM
2888.1.bs.a.883.1	yes	108	361.161	even	171	inner
2888.1.bs.a.883.1	yes	108	2888.883	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)

\(f(q)\)	\(=\)	\(q+(-0.912045 - 0.410091i) q^{2} +(1.11668 - 1.57930i) q^{3} +(0.663651 + 0.748042i) q^{4} +(-1.66612 + 0.982450i) q^{6} +(-0.298515 - 0.954405i) q^{8} +(-0.913832 - 2.58435i) q^{9} +O(q^{10})\)	\(q+(-0.912045 - 0.410091i) q^{2} +(1.11668 - 1.57930i) q^{3} +(0.663651 + 0.748042i) q^{4} +(-1.66612 + 0.982450i) q^{6} +(-0.298515 - 0.954405i) q^{8} +(-0.913832 - 2.58435i) q^{9} +(-0.467617 + 0.567795i) q^{11} +(1.92247 - 0.212779i) q^{12} +(-0.119134 + 0.992878i) q^{16} +(-0.631036 - 1.89464i) q^{17} +(-0.226363 + 2.73180i) q^{18} +(0.100874 - 0.994899i) q^{19} +(0.659335 - 0.326090i) q^{22} +(-1.84064 - 0.594323i) q^{24} +(0.280931 + 0.959728i) q^{25} +(-3.24070 - 0.916383i) q^{27} +(0.515825 - 0.856694i) q^{32} +(0.374540 + 1.37255i) q^{33} +(-0.201441 + 1.98678i) q^{34} +(1.32674 - 2.39870i) q^{36} +(-0.500000 + 0.866025i) q^{38} +(-0.526150 - 0.0193414i) q^{41} +(1.92421 - 0.0353554i) q^{43} +(-0.735069 + 0.0270214i) q^{44} +(1.43502 + 1.29688i) q^{48} +(0.451533 + 0.892254i) q^{49} +(0.137354 - 0.990522i) q^{50} +(-3.69687 - 1.11911i) q^{51} +(2.57986 + 2.16476i) q^{54} +(-1.45860 - 1.27030i) q^{57} +(0.407090 + 0.769030i) q^{59} +(-0.821778 + 0.569808i) q^{64} +(0.221274 - 1.40543i) q^{66} +(-1.65597 - 1.06032i) q^{67} +(0.998482 - 1.72942i) q^{68} +(-2.19373 + 1.64363i) q^{72} +(-1.95798 - 0.401165i) q^{73} +(1.82941 + 0.628037i) q^{75} +(0.811171 - 0.584809i) q^{76} +(-2.93421 + 2.37161i) q^{81} +(0.471941 + 0.233410i) q^{82} +(0.454579 + 0.0250798i) q^{83} +(-1.76947 - 0.756855i) q^{86} +(0.681497 + 0.276800i) q^{88} +(-0.884688 + 0.181262i) q^{89} +(-0.776963 - 1.77130i) q^{96} +(1.58273 - 1.01343i) q^{97} +(-0.0459136 - 0.998945i) q^{98} +(1.89471 + 0.689617i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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