LMFDB - Embedded newform 2888.1.bs.a.403.1

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			403.1
Root			$-0.467849 + 0.883809i$ of defining polynomial
Character	$\chi$	$=$	2888.403
Dual form			2888.1.bs.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.888069 - 0.459710i) q^{2} +(1.02557 - 0.461135i) q^{3} +(0.577333 - 0.816509i) q^{4} +(0.698786 - 0.880984i) q^{6} +(0.137354 - 0.990522i) q^{8} +(0.175492 - 0.197808i) q^{9} +O(q^{10})$	\(q+(0.888069 - 0.459710i) q^{2} +(1.02557 - 0.461135i) q^{3} +(0.577333 - 0.816509i) q^{4} +(0.698786 - 0.880984i) q^{6} +(0.137354 - 0.990522i) q^{8} +(0.175492 - 0.197808i) q^{9} +(0.0532959 + 1.93347i) q^{11} +(0.215573 - 1.10361i) q^{12} +(-0.333374 - 0.942795i) q^{16} +(0.532039 - 1.15478i) q^{17} +(0.0649148 - 0.256343i) q^{18} +(-0.0459136 - 0.998945i) q^{19} +(0.936169 + 1.69256i) q^{22} +(-0.315899 - 1.07919i) q^{24} +(-0.155527 - 0.987832i) q^{25} +(-0.246908 + 0.789409i) q^{27} +(-0.729471 - 0.684011i) q^{32} +(0.946251 + 1.95833i) q^{33} +(-0.0583767 - 1.27011i) q^{34} +(-0.0601946 - 0.257492i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(-0.724042 + 0.482588i) q^{41} +(-0.571421 - 0.172981i) q^{43} +(1.60947 + 1.07274i) q^{44} +(-0.776653 - 0.813169i) q^{48} +(0.350638 + 0.936511i) q^{49} +(-0.592235 - 0.805765i) q^{50} +(0.0131330 - 1.42965i) q^{51} +(0.143628 + 0.814556i) q^{54} +(-0.507736 - 1.00331i) q^{57} +(0.0780004 + 1.21137i) q^{59} +(-0.962268 - 0.272103i) q^{64} +(1.74060 + 1.30413i) q^{66} +(1.86451 + 0.602032i) q^{67} +(-0.635724 - 1.10111i) q^{68} +(-0.171829 - 0.200998i) q^{72} +(-1.65720 + 0.152659i) q^{73} +(-0.615027 - 0.941369i) q^{75} +(-0.842155 - 0.539235i) q^{76} +(0.142306 + 1.18600i) q^{81} +(-0.421149 + 0.761421i) q^{82} +(-1.09522 + 1.32985i) q^{83} +(-0.586982 + 0.109070i) q^{86} +(1.92247 + 0.212779i) q^{88} +(-0.698318 - 0.0643282i) q^{89} +(-1.06354 - 0.365115i) q^{96} +(-1.45797 + 0.470764i) q^{97} +(0.741914 + 0.670495i) q^{98} +(0.391809 + 0.328767i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{145}{171}\right)$

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 $

$2$	0.888069	−	0.459710i	0.888069	−	0.459710i
$2$	0.888069	−	0.459710i	0.888069	−	0.459710i
$3$	1.02557	−	0.461135i	1.02557	−	0.461135i	0.173648	−	0.984808i	$-0.444444\pi$
$3$	1.02557	−	0.461135i	1.02557	−	0.461135i	0.851919	+	0.523673i	$0.175439\pi$
$4$	0.577333	−	0.816509i	0.577333	−	0.816509i
$5$		0			0		0.649797	−	0.760108i	$-0.274854\pi$
$5$		0			0		−0.649797	+	0.760108i	$0.725146\pi$
$6$	0.698786	−	0.880984i	0.698786	−	0.880984i
$7$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$7$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$8$	0.137354	−	0.990522i	0.137354	−	0.990522i
$9$	0.175492	−	0.197808i	0.175492	−	0.197808i
$10$		0			0
$11$	0.0532959	+	1.93347i	0.0532959	+	1.93347i	0.280931	+	0.959728i	$0.409357\pi$
$11$	0.0532959	+	1.93347i	0.0532959	+	1.93347i	−0.227635	+	0.973746i	$0.573099\pi$
$12$	0.215573	−	1.10361i	0.215573	−	1.10361i
$13$		0			0		0.997301	−	0.0734214i	$-0.0233918\pi$
$13$		0			0		−0.997301	+	0.0734214i	$0.976608\pi$
$14$		0			0
$15$		0			0
$16$	−0.333374	−	0.942795i	−0.333374	−	0.942795i
$17$	0.532039	−	1.15478i	0.532039	−	1.15478i	−0.435066	−	0.900399i	$-0.643275\pi$
$17$	0.532039	−	1.15478i	0.532039	−	1.15478i	0.967104	−	0.254380i	$-0.0818713\pi$
$18$	0.0649148	−	0.256343i	0.0649148	−	0.256343i
$19$	−0.0459136	−	0.998945i	−0.0459136	−	0.998945i
$19$	−0.0459136	−	0.998945i	−0.0459136	−	0.998945i
$20$		0			0
$21$		0			0
$22$	0.936169	+	1.69256i	0.936169	+	1.69256i
$23$		0			0		0.811171	−	0.584809i	$-0.198830\pi$
$23$		0			0		−0.811171	+	0.584809i	$0.801170\pi$
$24$	−0.315899	−	1.07919i	−0.315899	−	1.07919i
$25$	−0.155527	−	0.987832i	−0.155527	−	0.987832i
$26$		0			0
$27$	−0.246908	+	0.789409i	−0.246908	+	0.789409i
$28$		0			0
$29$		0			0		−0.263253	−	0.964727i	$-0.584795\pi$
$29$		0			0		0.263253	+	0.964727i	$0.415205\pi$
$30$		0			0
$31$		0			0		0.975796	−	0.218681i	$-0.0701754\pi$
$31$		0			0		−0.975796	+	0.218681i	$0.929825\pi$
$32$	−0.729471	−	0.684011i	−0.729471	−	0.684011i
$33$	0.946251	+	1.95833i	0.946251	+	1.95833i
$34$	−0.0583767	−	1.27011i	−0.0583767	−	1.27011i
$35$		0			0
$36$	−0.0601946	−	0.257492i	−0.0601946	−	0.257492i
$37$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$37$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$38$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$39$		0			0
$40$		0			0
$41$	−0.724042	+	0.482588i	−0.724042	+	0.482588i	−0.861396	−	0.507934i	$-0.830409\pi$
$41$	−0.724042	+	0.482588i	−0.724042	+	0.482588i	0.137354	+	0.990522i	$0.456140\pi$
$42$		0			0
$43$	−0.571421	−	0.172981i	−0.571421	−	0.172981i	−0.00918581	−	0.999958i	$-0.502924\pi$
$43$	−0.571421	−	0.172981i	−0.571421	−	0.172981i	−0.562235	+	0.826977i	$0.690058\pi$
$44$	1.60947	+	1.07274i	1.60947	+	1.07274i
$45$		0			0
$46$		0			0
$47$		0			0		−0.989219	−	0.146447i	$-0.953216\pi$
$47$		0			0		0.989219	+	0.146447i	$0.0467836\pi$
$48$	−0.776653	−	0.813169i	−0.776653	−	0.813169i
$49$	0.350638	+	0.936511i	0.350638	+	0.936511i
$50$	−0.592235	−	0.805765i	−0.592235	−	0.805765i
$51$	0.0131330	−	1.42965i	0.0131330	−	1.42965i
$52$		0			0
$53$		0			0		−0.367783	−	0.929912i	$-0.619883\pi$
$53$		0			0		0.367783	+	0.929912i	$0.380117\pi$
$54$	0.143628	+	0.814556i	0.143628	+	0.814556i
$55$		0			0
$56$		0			0
$57$	−0.507736	−	1.00331i	−0.507736	−	1.00331i
$58$		0			0
$59$	0.0780004	+	1.21137i	0.0780004	+	1.21137i	0.832107	+	0.554615i	$0.187135\pi$
$59$	0.0780004	+	1.21137i	0.0780004	+	1.21137i	−0.754107	+	0.656752i	$0.771930\pi$
$60$		0			0
$61$		0			0		−0.999325	−	0.0367355i	$-0.988304\pi$
$61$		0			0		0.999325	+	0.0367355i	$0.0116959\pi$
$62$		0			0
$63$		0			0
$64$	−0.962268	−	0.272103i	−0.962268	−	0.272103i
$65$		0			0
$66$	1.74060	+	1.30413i	1.74060	+	1.30413i
$67$	1.86451	+	0.602032i	1.86451	+	0.602032i	0.993931	+	0.110008i	$0.0350877\pi$
$67$	1.86451	+	0.602032i	1.86451	+	0.602032i	0.870582	+	0.492024i	$0.163743\pi$
$68$	−0.635724	−	1.10111i	−0.635724	−	1.10111i
$69$		0			0
$70$		0			0
$71$		0			0		0.999325	−	0.0367355i	$-0.0116959\pi$
$71$		0			0		−0.999325	+	0.0367355i	$0.988304\pi$
$72$	−0.171829	−	0.200998i	−0.171829	−	0.200998i
$73$	−1.65720	+	0.152659i	−1.65720	+	0.152659i	−0.879474	−	0.475947i	$-0.842105\pi$
$73$	−1.65720	+	0.152659i	−1.65720	+	0.152659i	−0.777724	+	0.628606i	$0.783626\pi$
$74$		0			0
$75$	−0.615027	−	0.941369i	−0.615027	−	0.941369i
$76$	−0.842155	−	0.539235i	−0.842155	−	0.539235i
$77$		0			0
$78$		0			0
$79$		0			0		0.729471	−	0.684011i	$-0.239766\pi$
$79$		0			0		−0.729471	+	0.684011i	$0.760234\pi$
$80$		0			0
$81$	0.142306	+	1.18600i	0.142306	+	1.18600i
$82$	−0.421149	+	0.761421i	−0.421149	+	0.761421i
$83$	−1.09522	+	1.32985i	−1.09522	+	1.32985i	−0.155527	+	0.987832i	$0.549708\pi$
$83$	−1.09522	+	1.32985i	−1.09522	+	1.32985i	−0.939693	+	0.342020i	$0.888889\pi$
$84$		0			0
$85$		0			0
$86$	−0.586982	+	0.109070i	−0.586982	+	0.109070i
$87$		0			0
$88$	1.92247	+	0.212779i	1.92247	+	0.212779i
$89$	−0.698318	−	0.0643282i	−0.698318	−	0.0643282i	−0.263253	−	0.964727i	$-0.584795\pi$
$89$	−0.698318	−	0.0643282i	−0.698318	−	0.0643282i	−0.435066	+	0.900399i	$0.643275\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.06354	−	0.365115i	−1.06354	−	0.365115i
$97$	−1.45797	+	0.470764i	−1.45797	+	0.470764i	−0.926494	−	0.376309i	$-0.877193\pi$
$97$	−1.45797	+	0.470764i	−1.45797	+	0.470764i	−0.531476	+	0.847073i	$0.678363\pi$
$98$	0.741914	+	0.670495i	0.741914	+	0.670495i
$99$	0.391809	+	0.328767i	0.391809	+	0.328767i
$100$	−0.896364	−	0.443318i	−0.896364	−	0.443318i
$101$		0			0		−0.315998	−	0.948760i	$-0.602339\pi$
$101$		0			0		0.315998	+	0.948760i	$0.397661\pi$
$102$	−0.645560	−	1.27566i	−0.645560	−	1.27566i
$103$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$103$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.593406	−	1.89722i	−0.593406	−	1.89722i	−0.401695	−	0.915773i	$-0.631579\pi$
$107$	−0.593406	−	1.89722i	−0.593406	−	1.89722i	−0.191711	−	0.981451i	$-0.561404\pi$
$108$	0.502012	+	0.657355i	0.502012	+	0.657355i
$109$		0			0		0.367783	−	0.929912i	$-0.380117\pi$
$109$		0			0		−0.367783	+	0.929912i	$0.619883\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.139089	+	1.67856i	0.139089	+	1.67856i	0.606938	+	0.794749i	$0.292398\pi$
$113$	0.139089	+	1.67856i	0.139089	+	1.67856i	−0.467849	+	0.883809i	$0.654971\pi$
$114$	−0.912138	−	0.657600i	−0.912138	−	0.657600i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.626148	+	1.03992i	0.626148	+	1.03992i
$119$		0			0
$120$		0			0
$121$	−2.73700	+	0.151005i	−2.73700	+	0.151005i
$122$		0			0
$123$	−0.520016	+	0.828808i	−0.520016	+	0.828808i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$127$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$128$	−0.979649	+	0.200718i	−0.979649	+	0.200718i
$129$	−0.665798	+	0.0860990i	−0.665798	+	0.0860990i
$130$		0			0
$131$	0.756657	+	1.81493i	0.756657	+	1.81493i	0.546948	+	0.837166i	$0.315789\pi$
$131$	0.756657	+	1.81493i	0.756657	+	1.81493i	0.209708	+	0.977764i	$0.432749\pi$
$132$	2.14530	+	0.357987i	2.14530	+	0.357987i
$133$		0			0
$134$	1.93258	−	0.322490i	1.93258	−	0.322490i
$135$		0			0
$136$	−1.07076	−	0.685609i	−1.07076	−	0.685609i
$137$	−0.335655	−	1.56499i	−0.335655	−	1.56499i	−0.754107	−	0.656752i	$-0.771930\pi$
$137$	−0.335655	−	1.56499i	−0.335655	−	1.56499i	0.418451	−	0.908239i	$-0.362573\pi$
$138$		0			0
$139$	1.71611	−	0.734032i	1.71611	−	0.734032i	0.716783	−	0.697297i	$-0.245614\pi$
$139$	1.71611	−	0.734032i	1.71611	−	0.734032i	0.999325	−	0.0367355i	$-0.0116959\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.244997	−	0.0995091i	−0.244997	−	0.0995091i
$145$		0			0
$146$	−1.40153	+	0.897402i	−1.40153	+	0.897402i
$147$	0.791460	+	0.798764i	0.791460	+	0.798764i
$148$		0			0
$149$		0			0		−0.971614	−	0.236570i	$-0.923977\pi$
$149$		0			0		0.971614	+	0.236570i	$0.0760234\pi$
$150$	−0.978944	−	0.553266i	−0.978944	−	0.553266i
$151$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$151$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$152$	−0.995784	−	0.0917303i	−0.995784	−	0.0917303i
$153$	−0.135056	−	0.307896i	−0.135056	−	0.307896i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.811171	−	0.584809i	$-0.801170\pi$
$157$		0			0		0.811171	+	0.584809i	$0.198830\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.671595	+	0.987832i	0.671595	+	0.987832i
$163$	−1.95126	−	0.437288i	−1.95126	−	0.437288i	−0.979649	−	0.200718i	$-0.935673\pi$
$163$	−1.95126	−	0.437288i	−1.95126	−	0.437288i	−0.971614	−	0.236570i	$-0.923977\pi$
$164$	−0.0239759	+	0.869801i	−0.0239759	+	0.869801i
$165$		0			0
$166$	−0.361284	+	1.68448i	−0.361284	+	1.68448i
$167$		0			0		0.703852	−	0.710347i	$-0.251462\pi$
$167$		0			0		−0.703852	+	0.710347i	$0.748538\pi$
$168$		0			0
$169$	0.989219	−	0.146447i	0.989219	−	0.146447i
$170$		0			0
$171$	−0.205657	−	0.166225i	−0.205657	−	0.166225i
$172$	−0.471140	+	0.366703i	−0.471140	+	0.366703i
$173$		0			0		0.690683	−	0.723158i	$-0.257310\pi$
$173$		0			0		−0.690683	+	0.723158i	$0.742690\pi$
$174$		0			0
$175$		0			0
$176$	1.80510	−	0.694817i	1.80510	−	0.694817i
$177$	0.638598	+	1.20637i	0.638598	+	1.20637i
$178$	−0.649727	+	0.263896i	−0.649727	+	0.263896i
$179$	1.98047	+	0.109266i	1.98047	+	0.109266i	0.997301	−	0.0734214i	$-0.0233918\pi$
$179$	1.98047	+	0.109266i	1.98047	+	0.109266i	0.983171	+	0.182687i	$0.0584795\pi$
$180$		0			0
$181$		0			0		−0.888069	−	0.459710i	$-0.847953\pi$
$181$		0			0		0.888069	+	0.459710i	$0.152047\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.26109	+	0.967138i	2.26109	+	0.967138i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.789141	−	0.614213i	$-0.789474\pi$
$191$		0			0		0.789141	+	0.614213i	$0.210526\pi$
$192$	−1.11235	+	0.164675i	−1.11235	+	0.164675i
$193$	0.538409	−	1.61653i	0.538409	−	1.61653i	−0.227635	−	0.973746i	$-0.573099\pi$
$193$	0.538409	−	1.61653i	0.538409	−	1.61653i	0.766044	−	0.642788i	$-0.222222\pi$
$194$	−1.07836	+	1.08831i	−1.07836	+	1.08831i
$195$		0			0
$196$	0.967104	+	0.254380i	0.967104	+	0.254380i
$197$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$197$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$198$	0.499092	+	0.111849i	0.499092	+	0.111849i
$199$		0			0		−0.562235	−	0.826977i	$-0.690058\pi$
$199$		0			0		0.562235	+	0.826977i	$0.309942\pi$
$200$	−0.999831	+	0.0183709i	−0.999831	+	0.0183709i
$201$	2.18980	−	0.242367i	2.18980	−	0.242367i
$202$		0			0
$203$		0			0
$204$	−1.15974	−	0.836104i	−1.15974	−	0.836104i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.92899	−	0.142012i	1.92899	−	0.142012i
$210$		0			0
$211$	0.239155	+	0.135162i	0.239155	+	0.135162i	0.606938	−	0.794749i	$-0.292398\pi$
$211$	0.239155	+	0.135162i	0.239155	+	0.135162i	−0.367783	+	0.929912i	$0.619883\pi$
$212$		0			0
$213$		0			0
$214$	−1.39916	−	1.41207i	−1.39916	−	1.41207i
$215$		0			0
$216$	0.748014	+	0.352996i	0.748014	+	0.352996i
$217$		0			0
$218$		0			0
$219$	−1.62917	+	0.920753i	−1.62917	+	0.920753i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.0459136	−	0.998945i	$-0.485380\pi$
$223$		0			0		−0.0459136	+	0.998945i	$0.514620\pi$
$224$		0			0
$225$	−0.222695	−	0.142592i	−0.222695	−	0.142592i
$226$	0.895171	+	1.42673i	0.895171	+	1.42673i
$227$	−0.413696	+	0.0690337i	−0.413696	+	0.0690337i	−0.367783	−	0.929912i	$-0.619883\pi$
$227$	−0.413696	+	0.0690337i	−0.413696	+	0.0690337i	−0.0459136	+	0.998945i	$0.514620\pi$
$228$	−1.11235	−	0.164675i	−1.11235	−	0.164675i
$229$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$229$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.84114	−	0.377226i	1.84114	−	0.377226i	0.851919	−	0.523673i	$-0.175439\pi$
$233$	1.84114	−	0.377226i	1.84114	−	0.377226i	0.989219	+	0.146447i	$0.0467836\pi$
$234$		0			0
$235$		0			0
$236$	1.03412	+	0.635674i	1.03412	+	0.635674i
$237$		0			0
$238$		0			0
$239$		0			0		0.904357	−	0.426776i	$-0.140351\pi$
$239$		0			0		−0.904357	+	0.426776i	$0.859649\pi$
$240$		0			0
$241$	−1.25987	−	0.566485i	−1.25987	−	0.566485i	−0.333374	−	0.942795i	$-0.608187\pi$
$241$	−1.25987	−	0.566485i	−1.25987	−	0.566485i	−0.926494	+	0.376309i	$0.877193\pi$
$242$	−2.36123	+	1.39233i	−2.36123	+	1.39233i
$243$	0.266201	+	0.442112i	0.266201	+	0.442112i
$244$		0			0
$245$		0			0
$246$	−0.0807987	+	0.975095i	−0.0807987	+	0.975095i
$247$		0			0
$248$		0			0
$249$	−0.509981	+	1.86890i	−0.509981	+	1.86890i
$250$		0			0
$251$	0.515791	+	0.105679i	0.515791	+	0.105679i	0.451533	−	0.892254i	$-0.350877\pi$
$251$	0.515791	+	0.105679i	0.515791	+	0.105679i	0.0642573	+	0.997933i	$0.479532\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.777724	+	0.628606i	−0.777724	+	0.628606i
$257$	0.0852889	−	1.32456i	0.0852889	−	1.32456i	−0.703852	−	0.710347i	$-0.748538\pi$
$257$	0.0852889	−	1.32456i	0.0852889	−	1.32456i	0.789141	−	0.614213i	$-0.210526\pi$
$258$	−0.551694	+	0.382536i	−0.551694	+	0.382536i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.50631	+	1.26394i	1.50631	+	1.26394i
$263$		0			0		−0.741914	−	0.670495i	$-0.766082\pi$
$263$		0			0		0.741914	+	0.670495i	$0.233918\pi$
$264$	2.06974	−	0.668299i	2.06974	−	0.668299i
$265$		0			0
$266$		0			0
$267$	−0.745837	+	0.256046i	−0.745837	+	0.256046i
$268$	1.56801	−	1.17482i	1.56801	−	1.17482i
$269$		0			0		−0.00918581	−	0.999958i	$-0.502924\pi$
$269$		0			0		0.00918581	+	0.999958i	$0.497076\pi$
$270$		0			0
$271$		0			0		−0.577333	−	0.816509i	$-0.695906\pi$
$271$		0			0		0.577333	+	0.816509i	$0.304094\pi$
$272$	−1.26609	−	0.116630i	−1.26609	−	0.116630i
$273$		0			0
$274$	−1.01753	−	1.23552i	−1.01753	−	1.23552i
$275$	1.90166	−	0.353355i	1.90166	−	0.353355i
$276$		0			0
$277$		0			0		0.716783	−	0.697297i	$-0.245614\pi$
$277$		0			0		−0.716783	+	0.697297i	$0.754386\pi$
$278$	1.18658	−	1.44078i	1.18658	−	1.44078i
$279$		0			0
$280$		0			0
$281$	−0.992002	−	0.381840i	−0.992002	−	0.381840i	−0.191711	−	0.981451i	$-0.561404\pi$
$281$	−0.992002	−	0.381840i	−0.992002	−	0.381840i	−0.800291	+	0.599612i	$0.795322\pi$
$282$		0			0
$283$	−0.195262	+	0.287206i	−0.195262	+	0.287206i	−0.912045	−	0.410091i	$-0.865497\pi$
$283$	−0.195262	+	0.287206i	−0.195262	+	0.287206i	0.716783	+	0.697297i	$0.245614\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.263319	+	0.0242566i	−0.263319	+	0.0242566i
$289$	−0.400651	−	0.468666i	−0.400651	−	0.468666i
$290$		0			0
$291$	−1.27816	+	1.15512i	−1.27816	+	1.15512i
$292$	−0.832107	+	1.44125i	−0.832107	+	1.44125i
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	1.07007	+	0.345515i	1.07007	+	0.345515i
$295$		0			0
$296$		0			0
$297$	−1.53946	−	0.435318i	−1.53946	−	0.435318i
$298$		0			0
$299$		0			0
$300$	−1.12371	−	0.0413080i	−1.12371	−	0.0413080i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.926494	+	0.376309i	−0.926494	+	0.376309i
$305$		0			0
$306$	−0.261482	−	0.211346i	−0.261482	−	0.211346i
$307$	−0.316750	−	1.79638i	−0.316750	−	1.79638i	−0.562235	−	0.826977i	$-0.690058\pi$
$307$	−0.316750	−	1.79638i	−0.316750	−	1.79638i	0.245485	−	0.969400i	$-0.421053\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.592235	−	0.805765i	$-0.701754\pi$
$311$		0			0		0.592235	+	0.805765i	$0.298246\pi$
$312$		0			0
$313$	−0.314448	−	0.329232i	−0.314448	−	0.329232i	0.546948	−	0.837166i	$-0.315789\pi$
$313$	−0.314448	−	0.329232i	−0.314448	−	0.329232i	−0.861396	+	0.507934i	$0.830409\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.832107	−	0.554615i	$-0.812865\pi$
$317$		0			0		0.832107	+	0.554615i	$0.187135\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.48345	−	1.67209i	−1.48345	−	1.67209i
$322$		0			0
$323$	−1.17799	−	0.478458i	−1.17799	−	0.478458i
$324$	1.05054	+	0.568523i	1.05054	+	0.568523i
$325$		0			0
$326$	−1.93388	+	0.508674i	−1.93388	+	0.508674i
$327$		0			0
$328$	0.378564	+	0.783465i	0.378564	+	0.783465i
$329$		0			0
$330$		0			0
$331$	−0.284466	−	1.45631i	−0.284466	−	1.45631i	−0.800291	−	0.599612i	$-0.795322\pi$
$331$	−0.284466	−	1.45631i	−0.284466	−	1.45631i	0.515825	−	0.856694i	$-0.327485\pi$
$332$	0.453530	+	1.66202i	0.453530	+	1.66202i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.436974	−	1.49281i	−0.436974	−	1.49281i	−0.821778	−	0.569808i	$-0.807018\pi$
$337$	−0.436974	−	1.49281i	−0.436974	−	1.49281i	0.384804	−	0.922998i	$-0.374269\pi$
$338$	0.811171	−	0.584809i	0.811171	−	0.584809i
$339$	0.916687	+	1.65734i	0.916687	+	1.65734i
$340$		0			0
$341$		0			0
$342$	−0.259053	−	0.0530767i	−0.259053	−	0.0530767i
$343$		0			0
$344$	−0.249828	+	0.542246i	−0.249828	+	0.542246i
$345$		0			0
$346$		0			0
$347$	1.39608	+	0.180537i	1.39608	+	0.180537i	0.789141	−	0.614213i	$-0.210526\pi$
$347$	1.39608	+	0.180537i	1.39608	+	0.180537i	0.606938	+	0.794749i	$0.292398\pi$
$348$		0			0
$349$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$349$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$350$		0			0
$351$		0			0
$352$	1.28364	−	1.44687i	1.28364	−	1.44687i
$353$	0.141701	−	1.02187i	0.141701	−	1.02187i	−0.777724	−	0.628606i	$-0.783626\pi$
$353$	0.141701	−	1.02187i	0.141701	−	1.02187i	0.919425	−	0.393266i	$-0.128655\pi$
$354$	1.12170	+	0.777770i	1.12170	+	0.777770i
$355$		0			0
$356$	−0.455687	+	0.533045i	−0.455687	+	0.533045i
$357$		0			0
$358$	1.80903	−	0.813408i	1.80903	−	0.813408i
$359$		0			0		0.888069	−	0.459710i	$-0.152047\pi$
$359$		0			0		−0.888069	+	0.459710i	$0.847953\pi$
$360$		0			0
$361$	−0.995784	+	0.0917303i	−0.995784	+	0.0917303i
$362$		0			0
$363$	−2.73735	+	1.41699i	−2.73735	+	1.41699i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.621436	−	0.783465i	$-0.286550\pi$
$367$		0			0		−0.621436	+	0.783465i	$0.713450\pi$
$368$		0			0
$369$	−0.0316040	+	0.227912i	−0.0316040	+	0.227912i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$373$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$374$	2.45261	−	0.180561i	2.45261	−	0.180561i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	0.245485	+	0.969400i	$0.421053\pi$
$379$	−0.431796	+	1.70512i	−0.431796	+	1.70512i	−0.677282	+	0.735724i	$0.736842\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.484006	−	0.875065i	$-0.660819\pi$
$383$		0			0		0.484006	+	0.875065i	$0.339181\pi$
$384$	−0.912138	+	0.657600i	−0.912138	+	0.657600i
$385$		0			0
$386$	−0.264993	−	1.68311i	−0.264993	−	1.68311i
$387$	−0.134497	+	0.0826749i	−0.134497	+	0.0826749i
$388$	−0.457351	+	1.46223i	−0.457351	+	1.46223i
$389$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$389$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$390$		0			0
$391$		0			0
$392$	0.975796	−	0.218681i	0.975796	−	0.218681i
$393$	1.61293	+	1.51241i	1.61293	+	1.51241i
$394$		0			0
$395$		0			0
$396$	0.494646	−	0.130108i	0.494646	−	0.130108i
$397$		0			0		−0.227635	−	0.973746i	$-0.573099\pi$
$397$		0			0		0.227635	+	0.973746i	$0.426901\pi$
$398$		0			0
$399$		0			0
$400$	−0.879474	+	0.475947i	−0.879474	+	0.475947i
$401$	1.22035	+	1.37554i	1.22035	+	1.37554i	0.904357	+	0.426776i	$0.140351\pi$
$401$	1.22035	+	1.37554i	1.22035	+	1.37554i	0.315998	+	0.948760i	$0.397661\pi$
$402$	1.83328	−	1.22191i	1.83328	−	1.22191i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.41429	−	0.209375i	−1.41429	−	0.209375i
$409$	−0.646270	−	0.676657i	−0.646270	−	0.676657i	0.315998	−	0.948760i	$-0.397661\pi$
$409$	−0.646270	−	0.676657i	−0.646270	−	0.676657i	−0.962268	+	0.272103i	$0.912281\pi$
$410$		0			0
$411$	−1.06591	−	1.45022i	−1.06591	−	1.45022i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	1.42150	−	1.54416i	1.42150	−	1.54416i
$418$	1.64779	−	1.01289i	1.64779	−	1.01289i
$419$	1.11315	+	1.20920i	1.11315	+	1.20920i	0.975796	+	0.218681i	$0.0701754\pi$
$419$	1.11315	+	1.20920i	1.11315	+	1.20920i	0.137354	+	0.990522i	$0.456140\pi$
$420$		0			0
$421$		0			0		−0.621436	−	0.783465i	$-0.713450\pi$
$421$		0			0		0.621436	+	0.783465i	$0.286550\pi$
$422$	0.274522	+	0.0100915i	0.274522	+	0.0100915i
$423$		0			0
$424$		0			0
$425$	−1.22347	−	0.345965i	−1.22347	−	0.345965i
$426$		0			0
$427$		0			0
$428$	−1.89169	−	0.610809i	−1.89169	−	0.610809i
$429$		0			0
$430$		0			0
$431$		0			0		0.741914	−	0.670495i	$-0.233918\pi$
$431$		0			0		−0.741914	+	0.670495i	$0.766082\pi$
$432$	0.826564	−	0.0303848i	0.826564	−	0.0303848i
$433$	−0.319032	−	0.373191i	−0.319032	−	0.373191i	0.577333	−	0.816509i	$-0.304094\pi$
$433$	−0.319032	−	0.373191i	−0.319032	−	0.373191i	−0.896364	+	0.443318i	$0.853801\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−1.02354	+	1.56664i	−1.02354	+	1.56664i
$439$		0			0		0.562235	−	0.826977i	$-0.309942\pi$
$439$		0			0		−0.562235	+	0.826977i	$0.690058\pi$
$440$		0			0
$441$	0.246783	+	0.0949915i	0.246783	+	0.0949915i
$442$		0			0
$443$	0.859661	−	1.55424i	0.859661	−	1.55424i	0.0275543	−	0.999620i	$-0.491228\pi$
$443$	0.859661	−	1.55424i	0.859661	−	1.55424i	0.832107	−	0.554615i	$-0.187135\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.200523	+	0.0221938i	0.200523	+	0.0221938i	0.209708	−	0.977764i	$-0.432749\pi$
$449$	0.200523	+	0.0221938i	0.200523	+	0.0221938i	−0.00918581	+	0.999958i	$0.502924\pi$
$450$	−0.263319	−	0.0242566i	−0.263319	−	0.0242566i
$451$	−0.971660	−	1.37420i	−0.971660	−	1.37420i
$452$	1.45086	+	0.855519i	1.45086	+	0.855519i
$453$		0			0
$454$	−0.335655	+	0.251487i	−0.335655	+	0.251487i
$455$		0			0
$456$	−1.06354	+	0.365115i	−1.06354	+	0.365115i
$457$	1.89036	+	0.648961i	1.89036	+	0.648961i	0.957107	+	0.289735i	$0.0935673\pi$
$457$	1.89036	+	0.648961i	1.89036	+	0.648961i	0.933251	+	0.359225i	$0.116959\pi$
$458$		0			0
$459$	0.780228	+	0.705121i	0.780228	+	0.705121i
$460$		0			0
$461$		0			0		−0.896364	−	0.443318i	$-0.853801\pi$
$461$		0			0		0.896364	+	0.443318i	$0.146199\pi$
$462$		0			0
$463$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$463$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$464$		0			0
$465$		0			0
$466$	1.46164	−	1.18139i	1.46164	−	1.18139i
$467$	1.35191	+	1.17738i	1.35191	+	1.17738i	0.967104	+	0.254380i	$0.0818713\pi$
$467$	1.35191	+	1.17738i	1.35191	+	1.17738i	0.384804	+	0.922998i	$0.374269\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.21060	+	0.0891245i	1.21060	+	0.0891245i
$473$	0.303999	−	1.11405i	0.303999	−	1.11405i
$474$		0			0
$475$	−0.979649	+	0.200718i	−0.979649	+	0.200718i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.515825	−	0.856694i	$-0.672515\pi$
$479$		0			0		0.515825	+	0.856694i	$0.327485\pi$
$480$		0			0
$481$		0			0
$482$	−1.37927	+	0.0760964i	−1.37927	+	0.0760964i
$483$		0			0
$484$	−1.45686	+	2.32197i	−1.45686	+	2.32197i
$485$		0			0
$486$	0.439648	+	0.270251i	0.439648	+	0.270251i
$487$		0			0		0.754107	−	0.656752i	$-0.228070\pi$
$487$		0			0		−0.754107	+	0.656752i	$0.771930\pi$
$488$		0			0
$489$	−2.20280	+	0.451327i	−2.20280	+	0.451327i
$490$		0			0
$491$	−0.140451	+	0.892078i	−0.140451	+	0.892078i	0.811171	+	0.584809i	$0.198830\pi$
$491$	−0.140451	+	0.892078i	−0.140451	+	0.892078i	−0.951623	+	0.307269i	$0.900585\pi$
$492$	0.376507	+	0.903096i	0.376507	+	0.903096i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.406253	+	1.89415i	0.406253	+	1.89415i
$499$	−0.0681279	+	1.48226i	−0.0681279	+	1.48226i	0.635724	+	0.771917i	$0.280702\pi$
$499$	−0.0681279	+	1.48226i	−0.0681279	+	1.48226i	−0.703852	+	0.710347i	$0.748538\pi$
$500$		0			0
$501$		0			0
$502$	0.506639	−	0.143264i	0.506639	−	0.143264i
$503$		0			0		0.870582	−	0.492024i	$-0.163743\pi$
$503$		0			0		−0.870582	+	0.492024i	$0.836257\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.946979	−	0.606354i	0.946979	−	0.606354i
$508$		0			0
$509$		0			0		0.896364	−	0.443318i	$-0.146199\pi$
$509$		0			0		−0.896364	+	0.443318i	$0.853801\pi$
$510$		0			0
$511$		0			0
$512$	−0.401695	+	0.915773i	−0.401695	+	0.915773i
$513$	0.799913	+	0.210403i	0.799913	+	0.210403i
$514$	−0.533171	−	1.21551i	−0.533171	−	1.21551i
$515$		0			0
$516$	−0.314087	+	0.593338i	−0.314087	+	0.593338i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.523310	+	0.0579199i	−0.523310	+	0.0579199i	−0.367783	−	0.929912i	$-0.619883\pi$
$521$	−0.523310	+	0.0579199i	−0.523310	+	0.0579199i	−0.155527	+	0.987832i	$0.549708\pi$
$522$		0			0
$523$	1.10913	+	1.63140i	1.10913	+	1.63140i	0.690683	+	0.723158i	$0.257310\pi$
$523$	1.10913	+	1.63140i	1.10913	+	1.63140i	0.418451	+	0.908239i	$0.362573\pi$
$524$	1.91875	+	0.430002i	1.91875	+	0.430002i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.53085	−	1.54498i	1.53085	−	1.54498i
$529$	0.315998	−	0.948760i	0.315998	−	0.948760i
$530$		0			0
$531$	0.253306	+	0.197156i	0.253306	+	0.197156i
$532$		0			0
$533$		0			0
$534$	−0.544647	+	0.570255i	−0.544647	+	0.570255i
$535$		0			0
$536$	0.852423	−	1.76415i	0.852423	−	1.76415i
$537$	2.08149	−	0.801205i	2.08149	−	0.801205i
$538$		0			0
$539$	−1.79203	+	0.727861i	−1.79203	+	0.727861i
$540$		0			0
$541$		0			0		−0.888069	−	0.459710i	$-0.847953\pi$
$541$		0			0		0.888069	+	0.459710i	$0.152047\pi$
$542$		0			0
$543$		0			0
$544$	−1.17799	+	0.478458i	−1.17799	+	0.478458i
$545$		0			0
$546$		0			0
$547$	−0.0239759	+	0.0496198i	−0.0239759	+	0.0496198i	−0.912045	−	0.410091i	$-0.865497\pi$
$547$	−0.0239759	+	0.0496198i	−0.0239759	+	0.0496198i	0.888069	+	0.459710i	$0.152047\pi$
$548$	−1.47161	−	0.629455i	−1.47161	−	0.629455i
$549$		0			0
$550$	1.52636	−	1.18802i	1.52636	−	1.18802i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.391421	−	1.82500i	0.391421	−	1.82500i
$557$		0			0		−0.967104	−	0.254380i	$-0.918129\pi$
$557$		0			0		0.967104	+	0.254380i	$0.0818713\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	2.76488	−	0.0508018i	2.76488	−	0.0508018i
$562$	−1.05650	+	0.116934i	−1.05650	+	0.116934i
$563$	−1.39287	−	1.35501i	−1.39287	−	1.35501i	−0.861396	−	0.507934i	$-0.830409\pi$
$563$	−1.39287	−	1.35501i	−1.39287	−	1.35501i	−0.531476	−	0.847073i	$-0.678363\pi$
$564$		0			0
$565$		0			0
$566$	−0.0413747	+	0.344823i	−0.0413747	+	0.344823i
$567$		0			0
$568$		0			0
$569$	−0.362758	−	0.827004i	−0.362758	−	0.827004i	−0.998482	−	0.0550878i	$-0.982456\pi$
$569$	−0.362758	−	0.827004i	−0.362758	−	0.827004i	0.635724	−	0.771917i	$-0.280702\pi$
$570$		0			0
$571$	−0.0516237	+	0.117690i	−0.0516237	+	0.117690i	−0.939693	−	0.342020i	$-0.888889\pi$
$571$	−0.0516237	+	0.117690i	−0.0516237	+	0.117690i	0.888069	+	0.459710i	$0.152047\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.222695	+	0.142592i	−0.222695	+	0.142592i
$577$	−1.64963	−	0.778478i	−1.64963	−	0.778478i	−0.999831	−	0.0183709i	$-0.994152\pi$
$577$	−1.64963	−	0.778478i	−1.64963	−	0.778478i	−0.649797	−	0.760108i	$-0.725146\pi$
$578$	−0.571257	−	0.232024i	−0.571257	−	0.232024i
$579$	−0.193265	−	1.90614i	−0.193265	−	1.90614i
$580$		0			0
$581$		0			0
$582$	−0.604075	+	1.61341i	−0.604075	+	1.61341i
$583$		0			0
$584$	−0.0764100	+	1.66246i	−0.0764100	+	1.66246i
$585$		0			0
$586$		0			0
$587$	−0.961289	−	1.53211i	−0.961289	−	1.53211i	−0.842155	−	0.539235i	$-0.818713\pi$
$587$	−0.961289	−	1.53211i	−0.961289	−	1.53211i	−0.119134	−	0.992878i	$-0.538012\pi$
$588$	1.10913	−	0.185082i	1.10913	−	0.185082i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.308486	−	0.0398924i	0.308486	−	0.0398924i	0.0275543	−	0.999620i	$-0.491228\pi$
$593$	0.308486	−	0.0398924i	0.308486	−	0.0398924i	0.280931	+	0.959728i	$0.409357\pi$
$594$	−1.56727	+	0.321114i	−1.56727	+	0.321114i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.531476	−	0.847073i	$-0.321637\pi$
$599$		0			0		−0.531476	+	0.847073i	$0.678363\pi$
$600$	−1.01692	+	0.479898i	−1.01692	+	0.479898i
$601$	−0.346769	+	0.0191318i	−0.346769	+	0.0191318i	−0.227635	−	0.973746i	$-0.573099\pi$
$601$	−0.346769	+	0.0191318i	−0.346769	+	0.0191318i	−0.119134	+	0.992878i	$0.538012\pi$
$602$		0			0
$603$	0.446294	−	0.263163i	0.446294	−	0.263163i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.0825793	−	0.996584i	$-0.473684\pi$
$607$		0			0		−0.0825793	+	0.996584i	$0.526316\pi$
$608$	−0.649797	+	0.760108i	−0.649797	+	0.760108i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.329372	−	0.0674842i	−0.329372	−	0.0674842i
$613$		0			0		0.367783	−	0.929912i	$-0.380117\pi$
$613$		0			0		−0.367783	+	0.929912i	$0.619883\pi$
$614$	−1.10711	−	1.44969i	−1.10711	−	1.44969i
$615$		0			0
$616$		0			0
$617$	0.0142881	−	0.0115485i	0.0142881	−	0.0115485i	−0.621436	−	0.783465i	$-0.713450\pi$
$617$	0.0142881	−	0.0115485i	0.0142881	−	0.0115485i	0.635724	+	0.771917i	$0.280702\pi$
$618$		0			0
$619$	−0.225748	+	0.156530i	−0.225748	+	0.156530i	−0.677282	−	0.735724i	$-0.736842\pi$
$619$	−0.225748	+	0.156530i	−0.225748	+	0.156530i	0.451533	+	0.892254i	$0.350877\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.951623	+	0.307269i	−0.951623	+	0.307269i
$626$	−0.430603	−	0.147826i	−0.430603	−	0.147826i
$627$	1.91282	−	1.03517i	1.91282	−	1.03517i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.861396	−	0.507934i	$-0.830409\pi$
$631$		0			0		0.861396	+	0.507934i	$0.169591\pi$
$632$		0			0
$633$	0.307598	+	0.0283355i	0.307598	+	0.0283355i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.0109397	+	0.0911732i	0.0109397	+	0.0911732i	0.997301	−	0.0734214i	$-0.0233918\pi$
$641$	0.0109397	+	0.0911732i	0.0109397	+	0.0911732i	−0.986361	+	0.164595i	$0.947368\pi$
$642$	−2.08609	−	0.802974i	−2.08609	−	0.802974i
$643$	−1.00767	+	0.944870i	−1.00767	+	0.944870i	−0.998482	−	0.0550878i	$-0.982456\pi$
$643$	−1.00767	+	0.944870i	−1.00767	+	0.944870i	−0.00918581	+	0.999958i	$0.502924\pi$
$644$		0			0
$645$		0			0
$646$	−1.26609	+	0.116630i	−1.26609	+	0.116630i
$647$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$647$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$648$	1.19431	+	0.0219441i	1.19431	+	0.0219441i
$649$	−2.33799	+	0.215373i	−2.33799	+	0.215373i
$650$		0			0
$651$		0			0
$652$	−1.48358	+	1.34076i	−1.48358	+	1.34076i
$653$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$653$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$654$		0			0
$655$		0			0
$656$	0.696358	+	0.521741i	0.696358	+	0.521741i
$657$	−0.260628	+	0.354597i	−0.260628	+	0.354597i
$658$		0			0
$659$	1.59690	−	0.388817i	1.59690	−	0.388817i	0.663651	−	0.748042i	$-0.269006\pi$
$659$	1.59690	−	0.388817i	1.59690	−	0.388817i	0.933251	+	0.359225i	$0.116959\pi$
$660$		0			0
$661$		0			0		−0.999325	−	0.0367355i	$-0.988304\pi$
$661$		0			0		0.999325	+	0.0367355i	$0.0116959\pi$
$662$	−0.922104	−	1.16253i	−0.922104	−	1.16253i
$663$		0			0
$664$	1.16682	+	1.26750i	1.16682	+	1.26750i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.674815	−	1.80235i	−0.674815	−	1.80235i	−0.592235	−	0.805765i	$-0.701754\pi$
$673$	−0.674815	−	1.80235i	−0.674815	−	1.80235i	−0.0825793	−	0.996584i	$-0.526316\pi$
$674$	−1.07432	−	1.12483i	−1.07432	−	1.12483i
$675$	0.818205	+	0.121129i	0.818205	+	0.121129i
$676$	0.451533	−	0.892254i	0.451533	−	0.892254i
$677$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$677$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$678$	1.57598	+	1.05042i	1.57598	+	1.05042i
$679$		0			0
$680$		0			0
$681$	−0.392440	+	0.261569i	−0.392440	+	0.261569i
$682$		0			0
$683$	−1.26078	+	0.682302i	−1.26078	+	0.682302i	−0.962268	−	0.272103i	$-0.912281\pi$
$683$	−1.26078	+	0.682302i	−1.26078	+	0.682302i	−0.298515	+	0.954405i	$0.596491\pi$
$684$	−0.254457	+	0.0719535i	−0.254457	+	0.0719535i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.0274118	+	0.596400i	0.0274118	+	0.596400i
$689$		0			0
$690$		0			0
$691$	1.66260	−	0.372597i	1.66260	−	0.372597i	0.716783	−	0.697297i	$-0.245614\pi$
$691$	1.66260	−	0.372597i	1.66260	−	0.372597i	0.945817	+	0.324699i	$0.105263\pi$
$692$		0			0
$693$		0			0
$694$	1.32281	−	0.481463i	1.32281	−	0.481463i
$695$		0			0
$696$		0			0
$697$	0.172064	+	1.09286i	0.172064	+	1.09286i
$698$		0			0
$699$	1.71426	−	1.23588i	1.71426	−	1.23588i
$700$		0			0
$701$		0			0		−0.983171	−	0.182687i	$-0.941520\pi$
$701$		0			0		0.983171	+	0.182687i	$0.0584795\pi$
$702$		0			0
$703$		0			0
$704$	0.474820	−	1.87502i	0.474820	−	1.87502i
$705$		0			0
$706$	−0.343925	−	0.972635i	−0.343925	−	0.972635i
$707$		0			0
$708$	1.35370	+	0.175056i	1.35370	+	0.175056i
$709$		0			0		0.997301	−	0.0734214i	$-0.0233918\pi$
$709$		0			0		−0.997301	+	0.0734214i	$0.976608\pi$
$710$		0			0
$711$		0			0
$712$	−0.159635	+	0.682864i	−0.159635	+	0.682864i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.23261	−	1.55399i	1.23261	−	1.55399i
$717$		0			0
$718$		0			0
$719$		0			0		0.912045	−	0.410091i	$-0.134503\pi$
$719$		0			0		−0.912045	+	0.410091i	$0.865497\pi$
$720$		0			0
$721$		0			0
$722$	−0.842155	+	0.539235i	−0.842155	+	0.539235i
$723$	−1.55331			−1.55331
$724$		0			0
$725$		0			0
$726$	−1.77955	+	2.51677i	−1.77955	+	2.51677i
$727$		0			0		0.649797	−	0.760108i	$-0.274854\pi$
$727$		0			0		−0.649797	+	0.760108i	$0.725146\pi$
$728$		0			0
$729$	−0.504741	−	0.349979i	−0.504741	−	0.349979i
$730$		0			0
$731$	−0.503772	+	0.567833i	−0.503772	+	0.567833i
$732$		0			0
$733$		0			0		−0.0275543	−	0.999620i	$-0.508772\pi$
$733$		0			0		0.0275543	+	0.999620i	$0.491228\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.06464	+	3.63707i	−1.06464	+	3.63707i
$738$	0.0767068	+	0.216930i	0.0767068	+	0.216930i
$739$	0.431695	−	0.936986i	0.431695	−	0.936986i	−0.562235	−	0.826977i	$-0.690058\pi$
$739$	0.431695	−	0.936986i	0.431695	−	0.936986i	0.993931	−	0.110008i	$-0.0350877\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.983171	−	0.182687i	$-0.941520\pi$
$743$		0			0		0.983171	+	0.182687i	$0.0584795\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0708527	+	0.450022i	0.0708527	+	0.450022i
$748$	2.09508	−	1.28784i	2.09508	−	1.28784i
$749$		0			0
$750$		0			0
$751$		0			0		−0.263253	−	0.964727i	$-0.584795\pi$
$751$		0			0		0.263253	+	0.964727i	$0.415205\pi$
$752$		0			0
$753$	0.577711	−	0.129468i	0.577711	−	0.129468i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.967104	−	0.254380i	$-0.0818713\pi$
$757$		0			0		−0.967104	+	0.254380i	$0.918129\pi$
$758$	0.400399	+	1.71277i	0.400399	+	1.71277i
$759$		0			0
$760$		0			0
$761$	−0.113025	+	0.0611662i	−0.113025	+	0.0611662i	−0.531476	−	0.847073i	$-0.678363\pi$
$761$	−0.113025	+	0.0611662i	−0.113025	+	0.0611662i	0.418451	+	0.908239i	$0.362573\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.507736	+	1.00331i	−0.507736	+	1.00331i
$769$	0.0545145	+	0.00807047i	0.0545145	+	0.00807047i	0.173648	−	0.984808i	$-0.444444\pi$
$769$	0.0545145	+	0.00807047i	0.0545145	+	0.00807047i	−0.119134	+	0.992878i	$0.538012\pi$
$770$		0			0
$771$	−0.523331	−	1.39776i	−0.523331	−	1.39776i
$772$	−1.00907	−	1.37289i	−1.00907	−	1.37289i
$773$		0			0		0.00918581	−	0.999958i	$-0.497076\pi$
$773$		0			0		−0.00918581	+	0.999958i	$0.502924\pi$
$774$	−0.0814359	+	0.135251i	−0.0814359	+	0.135251i
$775$		0			0
$776$	0.266044	+	1.50881i	0.266044	+	1.50881i
$777$		0			0
$778$		0			0
$779$	0.515322	+	0.701121i	0.515322	+	0.701121i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.766044	−	0.642788i	0.766044	−	0.642788i
$785$		0			0
$786$	2.12767	+	0.601646i	2.12767	+	0.601646i
$787$	−0.374290	+	0.509240i	−0.374290	+	0.509240i	−0.951623	−	0.307269i	$-0.900585\pi$
$787$	−0.374290	+	0.509240i	−0.374290	+	0.509240i	0.577333	+	0.816509i	$0.304094\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.379468	−	0.342939i	0.379468	−	0.342939i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.546948	−	0.837166i	$-0.684211\pi$
$797$		0			0		0.546948	+	0.837166i	$0.315789\pi$
$798$		0			0
$799$		0			0
$800$	−0.562235	+	0.826977i	−0.562235	+	0.826977i
$801$	−0.135274	+	0.126844i	−0.135274	+	0.126844i
$802$	1.71611	+	0.660561i	1.71611	+	0.660561i
$803$	−0.383484	−	3.19601i	−0.383484	−	3.19601i
$804$	1.06635	−	1.92792i	1.06635	−	1.92792i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.26802	+	1.53967i	1.26802	+	1.53967i	0.690683	+	0.723158i	$0.257310\pi$
$809$	1.26802	+	1.53967i	1.26802	+	1.53967i	0.577333	+	0.816509i	$0.304094\pi$
$810$		0			0
$811$	0.800004	+	0.0736953i	0.800004	+	0.0736953i	0.484006	−	0.875065i	$-0.339181\pi$
$811$	0.800004	+	0.0736953i	0.800004	+	0.0736953i	0.315998	+	0.948760i	$0.397661\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.35224	+	0.464225i	−1.35224	+	0.464225i
$817$	−0.146562	+	0.578761i	−0.146562	+	0.578761i
$818$	−0.884999	−	0.303820i	−0.884999	−	0.303820i
$819$		0			0
$820$		0			0
$821$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$821$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$822$	−1.61328	−	0.797887i	−1.61328	−	0.797887i
$823$		0			0		−0.315998	−	0.948760i	$-0.602339\pi$
$823$		0			0		0.315998	+	0.948760i	$0.397661\pi$
$824$		0			0
$825$	1.78733	−	1.23931i	1.78733	−	1.23931i
$826$		0			0
$827$	−1.55125	+	1.25382i	−1.55125	+	1.25382i	−0.729471	+	0.684011i	$0.760234\pi$
$827$	−1.55125	+	1.25382i	−1.55125	+	1.25382i	−0.821778	+	0.569808i	$0.807018\pi$
$828$		0			0
$829$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$829$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.26802	+	0.0933515i	1.26802	+	0.0933515i
$834$	0.552522	−	2.02479i	0.552522	−	2.02479i
$835$		0			0
$836$	0.997714	−	1.65702i	0.997714	−	1.65702i
$837$		0			0
$838$	1.54444	+	0.562129i	1.54444	+	0.562129i
$839$		0			0		0.606938	−	0.794749i	$-0.292398\pi$
$839$		0			0		−0.606938	+	0.794749i	$0.707602\pi$
$840$		0			0
$841$	−0.861396	+	0.507934i	−0.861396	+	0.507934i
$842$		0			0
$843$	−1.19344	+	0.0658442i	−1.19344	+	0.0658442i
$844$	0.248433	−	0.117239i	0.248433	−	0.117239i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.0678139	+	0.384592i	−0.0678139	+	0.384592i
$850$	−1.24557	+	0.255202i	−1.24557	+	0.255202i
$851$		0			0
$852$		0			0
$853$		0			0		−0.384804	−	0.922998i	$-0.625731\pi$
$853$		0			0		0.384804	+	0.922998i	$0.374269\pi$
$854$		0			0
$855$		0			0
$856$	−1.96075	+	0.327191i	−1.96075	+	0.327191i
$857$	1.01153	+	1.61219i	1.01153	+	1.61219i	0.766044	+	0.642788i	$0.222222\pi$
$857$	1.01153	+	1.61219i	1.01153	+	1.61219i	0.245485	+	0.969400i	$0.421053\pi$
$858$		0			0
$859$	−0.00385268	−	0.0179631i	−0.00385268	−	0.0179631i	0.975796	−	0.218681i	$-0.0701754\pi$
$859$	−0.00385268	−	0.0179631i	−0.00385268	−	0.0179631i	−0.979649	+	0.200718i	$0.935673\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$863$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$864$	0.720077	−	0.406964i	0.720077	−	0.406964i
$865$		0			0
$866$	−0.454882	−	0.184757i	−0.454882	−	0.184757i
$867$	−0.627013	−	0.295895i	−0.627013	−	0.295895i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.162742	+	0.371013i	−0.162742	+	0.371013i
$874$		0			0
$875$		0			0
$876$	−0.188771	+	1.86181i	−0.188771	+	1.86181i
$877$		0			0		0.467849	−	0.883809i	$-0.345029\pi$
$877$		0			0		−0.467849	+	0.883809i	$0.654971\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.42173	−	1.38308i	−1.42173	−	1.38308i	−0.800291	−	0.599612i	$-0.795322\pi$
$881$	−1.42173	−	1.38308i	−1.42173	−	1.38308i	−0.621436	−	0.783465i	$-0.713450\pi$
$882$	0.262829	−	0.0290899i	0.262829	−	0.0290899i
$883$	1.29938	−	0.0238747i	1.29938	−	0.0238747i	0.635724	−	0.771917i	$-0.280702\pi$
$883$	1.29938	−	0.0238747i	1.29938	−	0.0238747i	0.663651	+	0.748042i	$0.269006\pi$
$884$		0			0
$885$		0			0
$886$	0.0489403	−	1.77546i	0.0489403	−	1.77546i
$887$		0			0		−0.967104	−	0.254380i	$-0.918129\pi$
$887$		0			0		0.967104	+	0.254380i	$0.0818713\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−2.28552	+	0.338354i	−2.28552	+	0.338354i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.188281	−	0.0724727i	0.188281	−	0.0724727i
$899$		0			0
$900$	−0.244997	+	0.0995091i	−0.244997	+	0.0995091i
$901$		0			0
$902$	−1.49463	−	0.773700i	−1.49463	−	0.773700i
$903$		0			0
$904$	1.68175	+	0.0927849i	1.68175	+	0.0927849i
$905$		0			0
$906$		0			0
$907$	0.903398	−	0.347734i	0.903398	−	0.347734i	0.137354	−	0.990522i	$-0.456140\pi$
$907$	0.903398	−	0.347734i	0.903398	−	0.347734i	0.766044	+	0.642788i	$0.222222\pi$
$908$	−0.182474	+	0.377642i	−0.182474	+	0.377642i
$909$		0			0
$910$		0			0
$911$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$911$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$912$	−0.776653	+	0.813169i	−0.776653	+	0.813169i
$913$	−2.62960	−	2.04670i	−2.62960	−	2.04670i
$914$	1.97710	−	0.292695i	1.97710	−	0.292695i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.01705	+	0.267517i	1.01705	+	0.267517i
$919$		0			0		0.0275543	−	0.999620i	$-0.491228\pi$
$919$		0			0		−0.0275543	+	0.999620i	$0.508772\pi$
$920$		0			0
$921$	−1.15322	−	1.69624i	−1.15322	−	1.69624i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.185491	−	1.82947i	0.185491	−	1.82947i	−0.298515	−	0.954405i	$-0.596491\pi$
$929$	0.185491	−	1.82947i	0.185491	−	1.82947i	0.484006	−	0.875065i	$-0.339181\pi$
$930$		0			0
$931$	0.919425	−	0.393266i	0.919425	−	0.393266i
$932$	0.754940	−	1.72109i	0.754940	−	1.72109i
$933$		0			0
$934$	1.74184	+	0.424107i	1.74184	+	0.424107i
$935$		0			0
$936$		0			0
$937$	−1.49578	+	0.957756i	−1.49578	+	0.957756i	−0.500000	+	0.866025i	$0.666667\pi$
$937$	−1.49578	+	0.957756i	−1.49578	+	0.957756i	−0.995784	+	0.0917303i	$0.970760\pi$
$938$		0			0
$939$	−0.474308	−	0.192647i	−0.474308	−	0.192647i
$940$		0			0
$941$		0			0		0.870582	−	0.492024i	$-0.163743\pi$
$941$		0			0		−0.870582	+	0.492024i	$0.836257\pi$
$942$		0			0
$943$		0			0
$944$	1.11607	−	0.477377i	1.11607	−	0.477377i
$945$		0			0
$946$	−0.242167	−	1.12910i	−0.242167	−	1.12910i
$947$	1.14075	+	0.730428i	1.14075	+	0.730428i	0.967104	−	0.254380i	$-0.0818713\pi$
$947$	1.14075	+	0.730428i	1.14075	+	0.730428i	0.173648	+	0.984808i	$0.444444\pi$
$948$		0			0
$949$		0			0
$950$	−0.777724	+	0.628606i	−0.777724	+	0.628606i
$951$		0			0
$952$		0			0
$953$	−0.150552	+	0.956233i	−0.150552	+	0.956233i	0.789141	+	0.614213i	$0.210526\pi$
$953$	−0.150552	+	0.956233i	−0.150552	+	0.956233i	−0.939693	+	0.342020i	$0.888889\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.904357	−	0.426776i	0.904357	−	0.426776i
$962$		0			0
$963$	−0.479424	−	0.215568i	−0.479424	−	0.215568i
$964$	−1.18990	+	0.701643i	−1.18990	+	0.701643i
$965$		0			0
$966$		0			0
$967$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$967$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$968$	−0.226363	+	2.73180i	−0.226363	+	2.73180i
$969$	−1.42874	+	0.0525210i	−1.42874	+	0.0525210i
$970$		0			0
$971$	0.494753	−	1.81309i	0.494753	−	1.81309i	−0.0825793	−	0.996584i	$-0.526316\pi$
$971$	0.494753	−	1.81309i	0.494753	−	1.81309i	0.577333	−	0.816509i	$-0.304094\pi$
$972$	0.514675	+	0.0378904i	0.514675	+	0.0378904i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.20701	+	1.05119i	1.20701	+	1.05119i	0.997301	+	0.0734214i	$0.0233918\pi$
$977$	1.20701	+	1.05119i	1.20701	+	1.05119i	0.209708	+	0.977764i	$0.432749\pi$
$978$	−1.74876	+	1.41346i	−1.74876	+	1.41346i
$979$	0.0871594	−	1.35361i	0.0871594	−	1.35361i
$980$		0			0
$981$		0			0
$982$	0.285367	+	0.856794i	0.285367	+	0.856794i
$983$		0			0		−0.896364	−	0.443318i	$-0.853801\pi$
$983$		0			0		0.896364	+	0.443318i	$0.146199\pi$
$984$	0.749526	+	0.628927i	0.749526	+	0.628927i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.00918581	−	0.999958i	$-0.502924\pi$
$991$		0			0		0.00918581	+	0.999958i	$0.497076\pi$
$992$		0			0
$993$	−0.963292	−	1.36236i	−0.963292	−	1.36236i
$994$		0			0
$995$		0			0
$996$	1.23154	+	1.49538i	1.23154	+	1.49538i
$997$		0			0		0.983171	−	0.182687i	$-0.0584795\pi$
$997$		0			0		−0.983171	+	0.182687i	$0.941520\pi$
$998$	0.620910	+	1.34767i	0.620910	+	1.34767i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bs.a.403.1	yes	108
8.3	odd	2	CM	2888.1.bs.a.403.1	yes	108
361.43	even	171	inner	2888.1.bs.a.43.1	✓	108
2888.43	odd	342	inner	2888.1.bs.a.43.1	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bs.a.43.1	✓	108	361.43	even	171	inner
2888.1.bs.a.43.1	✓	108	2888.43	odd	342	inner
2888.1.bs.a.403.1	yes	108	1.1	even	1	trivial
2888.1.bs.a.403.1	yes	108	8.3	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(0.888069 - 0.459710i) q^{2} +(1.02557 - 0.461135i) q^{3} +(0.577333 - 0.816509i) q^{4} +(0.698786 - 0.880984i) q^{6} +(0.137354 - 0.990522i) q^{8} +(0.175492 - 0.197808i) q^{9} +O(q^{10})\)	\(q+(0.888069 - 0.459710i) q^{2} +(1.02557 - 0.461135i) q^{3} +(0.577333 - 0.816509i) q^{4} +(0.698786 - 0.880984i) q^{6} +(0.137354 - 0.990522i) q^{8} +(0.175492 - 0.197808i) q^{9} +(0.0532959 + 1.93347i) q^{11} +(0.215573 - 1.10361i) q^{12} +(-0.333374 - 0.942795i) q^{16} +(0.532039 - 1.15478i) q^{17} +(0.0649148 - 0.256343i) q^{18} +(-0.0459136 - 0.998945i) q^{19} +(0.936169 + 1.69256i) q^{22} +(-0.315899 - 1.07919i) q^{24} +(-0.155527 - 0.987832i) q^{25} +(-0.246908 + 0.789409i) q^{27} +(-0.729471 - 0.684011i) q^{32} +(0.946251 + 1.95833i) q^{33} +(-0.0583767 - 1.27011i) q^{34} +(-0.0601946 - 0.257492i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(-0.724042 + 0.482588i) q^{41} +(-0.571421 - 0.172981i) q^{43} +(1.60947 + 1.07274i) q^{44} +(-0.776653 - 0.813169i) q^{48} +(0.350638 + 0.936511i) q^{49} +(-0.592235 - 0.805765i) q^{50} +(0.0131330 - 1.42965i) q^{51} +(0.143628 + 0.814556i) q^{54} +(-0.507736 - 1.00331i) q^{57} +(0.0780004 + 1.21137i) q^{59} +(-0.962268 - 0.272103i) q^{64} +(1.74060 + 1.30413i) q^{66} +(1.86451 + 0.602032i) q^{67} +(-0.635724 - 1.10111i) q^{68} +(-0.171829 - 0.200998i) q^{72} +(-1.65720 + 0.152659i) q^{73} +(-0.615027 - 0.941369i) q^{75} +(-0.842155 - 0.539235i) q^{76} +(0.142306 + 1.18600i) q^{81} +(-0.421149 + 0.761421i) q^{82} +(-1.09522 + 1.32985i) q^{83} +(-0.586982 + 0.109070i) q^{86} +(1.92247 + 0.212779i) q^{88} +(-0.698318 - 0.0643282i) q^{89} +(-1.06354 - 0.365115i) q^{96} +(-1.45797 + 0.470764i) q^{97} +(0.741914 + 0.670495i) q^{98} +(0.391809 + 0.328767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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

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