LMFDB - Embedded newform 2888.1.bs.a.275.1

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			275.1
Root			$0.280931 + 0.959728i$ of defining polynomial
Character	$\chi$	$=$	2888.275
Dual form			2888.1.bs.a.2867.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.467849 + 0.883809i) q^{2} +(1.67040 + 0.216011i) q^{3} +(-0.562235 - 0.826977i) q^{4} +(-0.972408 + 1.37525i) q^{6} +(0.993931 - 0.110008i) q^{8} +(1.77648 + 0.467271i) q^{9} +O(q^{10})$	\(q+(-0.467849 + 0.883809i) q^{2} +(1.67040 + 0.216011i) q^{3} +(-0.562235 - 0.826977i) q^{4} +(-0.972408 + 1.37525i) q^{6} +(0.993931 - 0.110008i) q^{8} +(1.77648 + 0.467271i) q^{9} +(-1.33321 + 0.924424i) q^{11} +(-0.760522 - 1.50283i) q^{12} +(-0.367783 + 0.929912i) q^{16} +(1.69924 + 0.125098i) q^{17} +(-1.24410 + 1.35145i) q^{18} +(-0.531476 + 0.847073i) q^{19} +(-0.193276 - 1.61079i) q^{22} +(1.68403 + 0.0309422i) q^{24} +(0.957107 - 0.289735i) q^{25} +(1.30599 + 0.530447i) q^{27} +(-0.649797 - 0.760108i) q^{32} +(-2.42667 + 1.25617i) q^{33} +(-0.905550 + 1.44328i) q^{34} +(-0.612375 - 1.73182i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(1.65758 - 0.638034i) q^{41} +(-1.82180 - 0.338517i) q^{43} +(1.51405 + 0.582787i) q^{44} +(-0.815216 + 1.47388i) q^{48} +(0.0275543 + 0.999620i) q^{49} +(-0.191711 + 0.981451i) q^{50} +(2.81139 + 0.576019i) q^{51} +(-1.07982 + 0.906076i) q^{54} +(-1.07076 + 1.30015i) q^{57} +(-0.0652307 + 0.414313i) q^{59} +(0.975796 - 0.218681i) q^{64} +(0.0251005 - 2.73241i) q^{66} +(-0.438109 - 0.292008i) q^{67} +(-0.851919 - 1.47557i) q^{68} +(1.81710 + 0.269008i) q^{72} +(-0.812051 - 1.68060i) q^{73} +(1.66134 - 0.277228i) q^{75} +(0.999325 - 0.0367355i) q^{76} +(0.467770 + 0.264368i) q^{81} +(-0.211598 + 1.76349i) q^{82} +(1.13076 - 0.695073i) q^{83} +(1.15151 - 1.45175i) q^{86} +(-1.22342 + 1.06548i) q^{88} +(-0.0239759 + 0.0496198i) q^{89} +(-0.921231 - 1.41005i) q^{96} +(-1.56385 + 1.04234i) q^{97} +(-0.896364 - 0.443318i) q^{98} +(-2.80036 + 1.01925i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2888\mathbb{Z}\right)^\times$.

$n$	$1445$	$2167$	$2529$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{112}{171}\right)$

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 $

$2$	−0.467849	+	0.883809i	−0.467849	+	0.883809i
$2$	−0.467849	+	0.883809i	−0.467849	+	0.883809i
$3$	1.67040	+	0.216011i	1.67040	+	0.216011i	0.904357	−	0.426776i	$-0.140351\pi$
$3$	1.67040	+	0.216011i	1.67040	+	0.216011i	0.766044	+	0.642788i	$0.222222\pi$
$4$	−0.562235	−	0.826977i	−0.562235	−	0.826977i
$5$		0			0		0.989219	−	0.146447i	$-0.0467836\pi$
$5$		0			0		−0.989219	+	0.146447i	$0.953216\pi$
$6$	−0.972408	+	1.37525i	−0.972408	+	1.37525i
$7$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$7$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$8$	0.993931	−	0.110008i	0.993931	−	0.110008i
$9$	1.77648	+	0.467271i	1.77648	+	0.467271i
$10$		0			0
$11$	−1.33321	+	0.924424i	−1.33321	+	0.924424i	−0.999831	−	0.0183709i	$-0.994152\pi$
$11$	−1.33321	+	0.924424i	−1.33321	+	0.924424i	−0.333374	+	0.942795i	$0.608187\pi$
$12$	−0.760522	−	1.50283i	−0.760522	−	1.50283i
$13$		0			0		−0.0459136	−	0.998945i	$-0.514620\pi$
$13$		0			0		0.0459136	+	0.998945i	$0.485380\pi$
$14$		0			0
$15$		0			0
$16$	−0.367783	+	0.929912i	−0.367783	+	0.929912i
$17$	1.69924	+	0.125098i	1.69924	+	0.125098i	0.888069	−	0.459710i	$-0.152047\pi$
$17$	1.69924	+	0.125098i	1.69924	+	0.125098i	0.811171	+	0.584809i	$0.198830\pi$
$18$	−1.24410	+	1.35145i	−1.24410	+	1.35145i
$19$	−0.531476	+	0.847073i	−0.531476	+	0.847073i
$19$	−0.531476	+	0.847073i	−0.531476	+	0.847073i
$20$		0			0
$21$		0			0
$22$	−0.193276	−	1.61079i	−0.193276	−	1.61079i
$23$		0			0		0.384804	−	0.922998i	$-0.374269\pi$
$23$		0			0		−0.384804	+	0.922998i	$0.625731\pi$
$24$	1.68403	+	0.0309422i	1.68403	+	0.0309422i
$25$	0.957107	−	0.289735i	0.957107	−	0.289735i
$26$		0			0
$27$	1.30599	+	0.530447i	1.30599	+	0.530447i
$28$		0			0
$29$		0			0		−0.912045	−	0.410091i	$-0.865497\pi$
$29$		0			0		0.912045	+	0.410091i	$0.134503\pi$
$30$		0			0
$31$		0			0		−0.137354	−	0.990522i	$-0.543860\pi$
$31$		0			0		0.137354	+	0.990522i	$0.456140\pi$
$32$	−0.649797	−	0.760108i	−0.649797	−	0.760108i
$33$	−2.42667	+	1.25617i	−2.42667	+	1.25617i
$34$	−0.905550	+	1.44328i	−0.905550	+	1.44328i
$35$		0			0
$36$	−0.612375	−	1.73182i	−0.612375	−	1.73182i
$37$		0			0		−0.0825793	−	0.996584i	$-0.526316\pi$
$37$		0			0		0.0825793	+	0.996584i	$0.473684\pi$
$38$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$39$		0			0
$40$		0			0
$41$	1.65758	−	0.638034i	1.65758	−	0.638034i	0.663651	−	0.748042i	$-0.269006\pi$
$41$	1.65758	−	0.638034i	1.65758	−	0.638034i	0.993931	+	0.110008i	$0.0350877\pi$
$42$		0			0
$43$	−1.82180	−	0.338517i	−1.82180	−	0.338517i	−0.842155	−	0.539235i	$-0.818713\pi$
$43$	−1.82180	−	0.338517i	−1.82180	−	0.338517i	−0.979649	+	0.200718i	$0.935673\pi$
$44$	1.51405	+	0.582787i	1.51405	+	0.582787i
$45$		0			0
$46$		0			0
$47$		0			0		−0.995784	−	0.0917303i	$-0.970760\pi$
$47$		0			0		0.995784	+	0.0917303i	$0.0292398\pi$
$48$	−0.815216	+	1.47388i	−0.815216	+	1.47388i
$49$	0.0275543	+	0.999620i	0.0275543	+	0.999620i
$50$	−0.191711	+	0.981451i	−0.191711	+	0.981451i
$51$	2.81139	+	0.576019i	2.81139	+	0.576019i
$52$		0			0
$53$		0			0		−0.418451	−	0.908239i	$-0.637427\pi$
$53$		0			0		0.418451	+	0.908239i	$0.362573\pi$
$54$	−1.07982	+	0.906076i	−1.07982	+	0.906076i
$55$		0			0
$56$		0			0
$57$	−1.07076	+	1.30015i	−1.07076	+	1.30015i
$58$		0			0
$59$	−0.0652307	+	0.414313i	−0.0652307	+	0.414313i	0.933251	+	0.359225i	$0.116959\pi$
$59$	−0.0652307	+	0.414313i	−0.0652307	+	0.414313i	−0.998482	+	0.0550878i	$0.982456\pi$
$60$		0			0
$61$		0			0		−0.690683	−	0.723158i	$-0.742690\pi$
$61$		0			0		0.690683	+	0.723158i	$0.257310\pi$
$62$		0			0
$63$		0			0
$64$	0.975796	−	0.218681i	0.975796	−	0.218681i
$65$		0			0
$66$	0.0251005	−	2.73241i	0.0251005	−	2.73241i
$67$	−0.438109	−	0.292008i	−0.438109	−	0.292008i	0.315998	−	0.948760i	$-0.397661\pi$
$67$	−0.438109	−	0.292008i	−0.438109	−	0.292008i	−0.754107	+	0.656752i	$0.771930\pi$
$68$	−0.851919	−	1.47557i	−0.851919	−	1.47557i
$69$		0			0
$70$		0			0
$71$		0			0		0.690683	−	0.723158i	$-0.257310\pi$
$71$		0			0		−0.690683	+	0.723158i	$0.742690\pi$
$72$	1.81710	+	0.269008i	1.81710	+	0.269008i
$73$	−0.812051	−	1.68060i	−0.812051	−	1.68060i	−0.729471	−	0.684011i	$-0.760234\pi$
$73$	−0.812051	−	1.68060i	−0.812051	−	1.68060i	−0.0825793	−	0.996584i	$-0.526316\pi$
$74$		0			0
$75$	1.66134	−	0.277228i	1.66134	−	0.277228i
$76$	0.999325	−	0.0367355i	0.999325	−	0.0367355i
$77$		0			0
$78$		0			0
$79$		0			0		0.649797	−	0.760108i	$-0.274854\pi$
$79$		0			0		−0.649797	+	0.760108i	$0.725146\pi$
$80$		0			0
$81$	0.467770	+	0.264368i	0.467770	+	0.264368i
$82$	−0.211598	+	1.76349i	−0.211598	+	1.76349i
$83$	1.13076	−	0.695073i	1.13076	−	0.695073i	0.173648	−	0.984808i	$-0.444444\pi$
$83$	1.13076	−	0.695073i	1.13076	−	0.695073i	0.957107	+	0.289735i	$0.0935673\pi$
$84$		0			0
$85$		0			0
$86$	1.15151	−	1.45175i	1.15151	−	1.45175i
$87$		0			0
$88$	−1.22342	+	1.06548i	−1.22342	+	1.06548i
$89$	−0.0239759	+	0.0496198i	−0.0239759	+	0.0496198i	−0.912045	−	0.410091i	$-0.865497\pi$
$89$	−0.0239759	+	0.0496198i	−0.0239759	+	0.0496198i	0.888069	+	0.459710i	$0.152047\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.921231	−	1.41005i	−0.921231	−	1.41005i
$97$	−1.56385	+	1.04234i	−1.56385	+	1.04234i	−0.592235	+	0.805765i	$0.701754\pi$
$97$	−1.56385	+	1.04234i	−1.56385	+	1.04234i	−0.971614	+	0.236570i	$0.923977\pi$
$98$	−0.896364	−	0.443318i	−0.896364	−	0.443318i
$99$	−2.80036	+	1.01925i	−2.80036	+	1.01925i
$100$	−0.777724	−	0.628606i	−0.777724	−	0.628606i
$101$		0			0		0.703852	−	0.710347i	$-0.251462\pi$
$101$		0			0		−0.703852	+	0.710347i	$0.748538\pi$
$102$	−1.82440	+	2.21524i	−1.82440	+	2.21524i
$103$		0			0		0.716783	−	0.697297i	$-0.245614\pi$
$103$		0			0		−0.716783	+	0.697297i	$0.754386\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.39735	−	0.567555i	1.39735	−	0.567555i	0.451533	−	0.892254i	$-0.350877\pi$
$107$	1.39735	−	0.567555i	1.39735	−	0.567555i	0.945817	+	0.324699i	$0.105263\pi$
$108$	−0.295606	−	1.37826i	−0.295606	−	1.37826i
$109$		0			0		0.418451	−	0.908239i	$-0.362573\pi$
$109$		0			0		−0.418451	+	0.908239i	$0.637427\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.490640	+	1.93749i	0.490640	+	1.93749i	0.280931	+	0.959728i	$0.409357\pi$
$113$	0.490640	+	1.93749i	0.490640	+	1.93749i	0.209708	+	0.977764i	$0.432749\pi$
$114$	−0.648130	−	1.55462i	−0.648130	−	1.55462i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.335655	−	0.251487i	−0.335655	−	0.251487i
$119$		0			0
$120$		0			0
$121$	0.572239	−	1.52838i	0.572239	−	1.52838i
$122$		0			0
$123$	2.90665	−	0.707716i	2.90665	−	0.707716i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$127$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$128$	−0.263253	+	0.964727i	−0.263253	+	0.964727i
$129$	−2.97002	−	0.958990i	−2.97002	−	0.958990i
$130$		0			0
$131$	−0.922104	−	0.833339i	−0.922104	−	0.833339i	0.0642573	−	0.997933i	$-0.479532\pi$
$131$	−0.922104	−	0.833339i	−0.922104	−	0.833339i	−0.986361	+	0.164595i	$0.947368\pi$
$132$	2.40319	+	1.30054i	2.40319	+	1.30054i
$133$		0			0
$134$	0.463048	−	0.250589i	0.463048	−	0.250589i
$135$		0			0
$136$	1.70269	−	0.0625914i	1.70269	−	0.0625914i
$137$	−0.00118051	+	0.0183337i	−0.00118051	+	0.0183337i	−0.998482	−	0.0550878i	$-0.982456\pi$
$137$	−0.00118051	+	0.0183337i	−0.00118051	+	0.0183337i	0.997301	+	0.0734214i	$0.0233918\pi$
$138$		0			0
$139$	0.392168	+	0.231247i	0.392168	+	0.231247i	0.690683	−	0.723158i	$-0.257310\pi$
$139$	0.392168	+	0.231247i	0.392168	+	0.231247i	−0.298515	+	0.954405i	$0.596491\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−1.08788	+	1.48011i	−1.08788	+	1.48011i
$145$		0			0
$146$	1.86524	+	0.0685669i	1.86524	+	0.0685669i
$147$	−0.169902	+	1.67572i	−0.169902	+	1.67572i
$148$		0			0
$149$		0			0		0.515825	−	0.856694i	$-0.327485\pi$
$149$		0			0		−0.515825	+	0.856694i	$0.672515\pi$
$150$	−0.532238	+	1.59801i	−0.532238	+	1.59801i
$151$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$151$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$152$	−0.435066	+	0.900399i	−0.435066	+	0.900399i
$153$	2.96021	+	1.01624i	2.96021	+	1.01624i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.384804	−	0.922998i	$-0.625731\pi$
$157$		0			0		0.384804	+	0.922998i	$0.374269\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.452497	+	0.289735i	−0.452497	+	0.289735i
$163$	0.252572	−	1.82142i	0.252572	−	1.82142i	−0.263253	−	0.964727i	$-0.584795\pi$
$163$	0.252572	−	1.82142i	0.252572	−	1.82142i	0.515825	−	0.856694i	$-0.327485\pi$
$164$	−1.45959	−	1.01206i	−1.45959	−	1.01206i
$165$		0			0
$166$	0.0852889	+	1.32456i	0.0852889	+	1.32456i
$167$		0			0		−0.100874	−	0.994899i	$-0.532164\pi$
$167$		0			0		0.100874	+	0.994899i	$0.467836\pi$
$168$		0			0
$169$	−0.995784	+	0.0917303i	−0.995784	+	0.0917303i
$170$		0			0
$171$	−1.33997	+	1.25646i	−1.33997	+	1.25646i
$172$	0.744337	+	1.69692i	0.744337	+	1.69692i
$173$		0			0		−0.484006	−	0.875065i	$-0.660819\pi$
$173$		0			0		0.484006	+	0.875065i	$0.339181\pi$
$174$		0			0
$175$		0			0
$176$	−0.369303	−	1.57975i	−0.369303	−	1.57975i
$177$	−0.198458	+	0.677979i	−0.198458	+	0.677979i
$178$	−0.0326373	−	0.0444047i	−0.0326373	−	0.0444047i
$179$	−0.667349	−	1.78241i	−0.667349	−	1.78241i	−0.621436	−	0.783465i	$-0.713450\pi$
$179$	−0.667349	−	1.78241i	−0.667349	−	1.78241i	−0.0459136	−	0.998945i	$-0.514620\pi$
$180$		0			0
$181$		0			0		−0.467849	−	0.883809i	$-0.654971\pi$
$181$		0			0		0.467849	+	0.883809i	$0.345029\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−2.38108	+	1.40404i	−2.38108	+	1.40404i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.401695	−	0.915773i	$-0.368421\pi$
$191$		0			0		−0.401695	+	0.915773i	$0.631579\pi$
$192$	1.67721	−	0.154502i	1.67721	−	0.154502i
$193$	−1.27307	−	1.28481i	−1.27307	−	1.28481i	−0.939693	−	0.342020i	$-0.888889\pi$
$193$	−1.27307	−	1.28481i	−1.27307	−	1.28481i	−0.333374	−	0.942795i	$-0.608187\pi$
$194$	−0.189580	−	1.86980i	−0.189580	−	1.86980i
$195$		0			0
$196$	0.811171	−	0.584809i	0.811171	−	0.584809i
$197$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$197$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$198$	0.409325	−	2.95184i	0.409325	−	2.95184i
$199$		0			0		0.842155	−	0.539235i	$-0.181287\pi$
$199$		0			0		−0.842155	+	0.539235i	$0.818713\pi$
$200$	0.919425	−	0.393266i	0.919425	−	0.393266i
$201$	−0.668741	−	0.582407i	−0.668741	−	0.582407i
$202$		0			0
$203$		0			0
$204$	−1.10431	−	2.64881i	−1.10431	−	2.64881i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.0744875	−	1.62063i	−0.0744875	−	1.62063i
$210$		0			0
$211$	0.628160	−	1.88600i	0.628160	−	1.88600i	0.209708	−	0.977764i	$-0.432749\pi$
$211$	0.628160	−	1.88600i	0.628160	−	1.88600i	0.418451	−	0.908239i	$-0.362573\pi$
$212$		0			0
$213$		0			0
$214$	−0.152139	+	1.50052i	−0.152139	+	1.50052i
$215$		0			0
$216$	1.35642	+	0.383558i	1.35642	+	0.383558i
$217$		0			0
$218$		0			0
$219$	−0.993424	−	2.98268i	−0.993424	−	2.98268i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.531476	−	0.847073i	$-0.678363\pi$
$223$		0			0		0.531476	+	0.847073i	$0.321637\pi$
$224$		0			0
$225$	1.83566	−	0.0674795i	1.83566	−	0.0674795i
$226$	−1.94192	−	0.472821i	−1.94192	−	0.472821i
$227$	−0.113025	+	0.0611662i	−0.113025	+	0.0611662i	−0.531476	−	0.847073i	$-0.678363\pi$
$227$	−0.113025	+	0.0611662i	−0.113025	+	0.0611662i	0.418451	+	0.908239i	$0.362573\pi$
$228$	1.67721	+	0.154502i	1.67721	+	0.154502i
$229$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$229$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.0914267	+	0.335046i	−0.0914267	+	0.335046i	−0.995784	−	0.0917303i	$-0.970760\pi$
$233$	−0.0914267	+	0.335046i	−0.0914267	+	0.335046i	0.904357	+	0.426776i	$0.140351\pi$
$234$		0			0
$235$		0			0
$236$	0.379303	−	0.178997i	0.379303	−	0.178997i
$237$		0			0
$238$		0			0
$239$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$239$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$240$		0			0
$241$	−0.960018	+	0.124147i	−0.960018	+	0.124147i	−0.592235	−	0.805765i	$-0.701754\pi$
$241$	−0.960018	+	0.124147i	−0.960018	+	0.124147i	−0.367783	+	0.929912i	$0.619883\pi$
$242$	1.08308	+	1.22080i	1.08308	+	1.22080i
$243$	−0.403835	−	0.302570i	−0.403835	−	0.302570i
$244$		0			0
$245$		0			0
$246$	−0.734386	+	2.90003i	−0.734386	+	2.90003i
$247$		0			0
$248$		0			0
$249$	2.03896	−	0.916795i	2.03896	−	0.916795i
$250$		0			0
$251$	0.480197	+	1.75975i	0.480197	+	1.75975i	0.635724	+	0.771917i	$0.280702\pi$
$251$	0.480197	+	1.75975i	0.480197	+	1.75975i	−0.155527	+	0.987832i	$0.549708\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.729471	−	0.684011i	−0.729471	−	0.684011i
$257$	−0.300822	−	1.91067i	−0.300822	−	1.91067i	−0.401695	−	0.915773i	$-0.631579\pi$
$257$	−0.300822	−	1.91067i	−0.300822	−	1.91067i	0.100874	−	0.994899i	$-0.467836\pi$
$258$	2.23708	−	2.17627i	2.23708	−	2.17627i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	1.16792	−	0.425087i	1.16792	−	0.425087i
$263$		0			0		−0.896364	−	0.443318i	$-0.853801\pi$
$263$		0			0		0.896364	+	0.443318i	$0.146199\pi$
$264$	−2.27376	+	1.51550i	−2.27376	+	1.51550i
$265$		0			0
$266$		0			0
$267$	−0.0507678	+	0.0777059i	−0.0507678	+	0.0777059i
$268$	0.00483638	+	0.526483i	0.00483638	+	0.526483i
$269$		0			0		0.979649	−	0.200718i	$-0.0643275\pi$
$269$		0			0		−0.979649	+	0.200718i	$0.935673\pi$
$270$		0			0
$271$		0			0		0.562235	−	0.826977i	$-0.309942\pi$
$271$		0			0		−0.562235	+	0.826977i	$0.690058\pi$
$272$	−0.741282	+	1.53413i	−0.741282	+	1.53413i
$273$		0			0
$274$	−0.0156511	−	0.00962072i	−0.0156511	−	0.00962072i
$275$	−1.00818	+	1.27105i	−1.00818	+	1.27105i
$276$		0			0
$277$		0			0		0.298515	−	0.954405i	$-0.403509\pi$
$277$		0			0		−0.298515	+	0.954405i	$0.596491\pi$
$278$	−0.387854	+	0.238413i	−0.387854	+	0.238413i
$279$		0			0
$280$		0			0
$281$	0.442348	−	1.89221i	0.442348	−	1.89221i	−0.00918581	−	0.999958i	$-0.502924\pi$
$281$	0.442348	−	1.89221i	0.442348	−	1.89221i	0.451533	−	0.892254i	$-0.350877\pi$
$282$		0			0
$283$	−1.29026	−	0.826156i	−1.29026	−	0.826156i	−0.298515	−	0.954405i	$-0.596491\pi$
$283$	−1.29026	−	0.826156i	−1.29026	−	0.826156i	−0.991742	+	0.128249i	$0.959064\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.799173	−	1.65394i	−0.799173	−	1.65394i
$289$	1.88255	+	0.278697i	1.88255	+	0.278697i
$290$		0			0
$291$	−2.83741	+	1.40331i	−2.83741	+	1.40331i
$292$	−0.933251	+	1.61644i	−0.933251	+	1.61644i
$293$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$293$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$294$	−1.40153	−	0.934144i	−1.40153	−	0.934144i
$295$		0			0
$296$		0			0
$297$	−2.23151	+	0.500093i	−2.23151	+	0.500093i
$298$		0			0
$299$		0			0
$300$	−1.16332	−	1.21802i	−1.16332	−	1.21802i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.592235	−	0.805765i	−0.592235	−	0.805765i
$305$		0			0
$306$	−2.28309	+	2.14081i	−2.28309	+	2.14081i
$307$	−1.51944	+	1.27496i	−1.51944	+	1.27496i	−0.677282	+	0.735724i	$0.736842\pi$
$307$	−1.51944	+	1.27496i	−1.51944	+	1.27496i	−0.842155	+	0.539235i	$0.818713\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.191711	−	0.981451i	$-0.438596\pi$
$311$		0			0		−0.191711	+	0.981451i	$0.561404\pi$
$312$		0			0
$313$	−0.322710	+	0.583447i	−0.322710	+	0.583447i	−0.986361	−	0.164595i	$-0.947368\pi$
$313$	−0.322710	+	0.583447i	−0.322710	+	0.583447i	0.663651	+	0.748042i	$0.269006\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.933251	−	0.359225i	$-0.883041\pi$
$317$		0			0		0.933251	+	0.359225i	$0.116959\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	2.45673	−	0.646201i	2.45673	−	0.646201i
$322$		0			0
$323$	−1.00907	+	1.37289i	−1.00907	+	1.37289i
$324$	−0.0443705	−	0.535473i	−0.0443705	−	0.535473i
$325$		0			0
$326$	1.49162	+	1.07537i	1.49162	+	1.07537i
$327$		0			0
$328$	1.57733	−	0.816509i	1.57733	−	0.816509i
$329$		0			0
$330$		0			0
$331$	−0.809477	+	1.59957i	−0.809477	+	1.59957i	−0.00918581	+	0.999958i	$0.502924\pi$
$331$	−0.809477	+	1.59957i	−0.809477	+	1.59957i	−0.800291	+	0.599612i	$0.795322\pi$
$332$	−1.21056	−	0.544314i	−1.21056	−	0.544314i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.45870	+	0.0268020i	1.45870	+	0.0268020i	0.741914	−	0.670495i	$-0.233918\pi$
$337$	1.45870	+	0.0268020i	1.45870	+	0.0268020i	0.716783	+	0.697297i	$0.245614\pi$
$338$	0.384804	−	0.922998i	0.384804	−	0.922998i
$339$	0.401045	+	3.34237i	0.401045	+	3.34237i
$340$		0			0
$341$		0			0
$342$	−0.483570	−	1.77211i	−0.483570	−	1.77211i
$343$		0			0
$344$	−1.84799	−	0.136049i	−1.84799	−	0.136049i
$345$		0			0
$346$		0			0
$347$	−0.191987	+	0.0619907i	−0.191987	+	0.0619907i	−0.401695	−	0.915773i	$-0.631579\pi$
$347$	−0.191987	+	0.0619907i	−0.191987	+	0.0619907i	0.209708	+	0.977764i	$0.432749\pi$
$348$		0			0
$349$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$349$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$350$		0			0
$351$		0			0
$352$	1.56897	+	0.412691i	1.56897	+	0.412691i
$353$	−1.59087	+	0.176077i	−1.59087	+	0.176077i	−0.861396	−	0.507934i	$-0.830409\pi$
$353$	−1.59087	+	0.176077i	−1.59087	+	0.176077i	−0.729471	+	0.684011i	$0.760234\pi$
$354$	−0.506355	−	0.492590i	−0.506355	−	0.492590i
$355$		0			0
$356$	0.0545145	−	0.00807047i	0.0545145	−	0.00807047i
$357$		0			0
$358$	1.88753	+	0.244089i	1.88753	+	0.244089i
$359$		0			0		0.467849	−	0.883809i	$-0.345029\pi$
$359$		0			0		−0.467849	+	0.883809i	$0.654971\pi$
$360$		0			0
$361$	−0.435066	−	0.900399i	−0.435066	−	0.900399i
$362$		0			0
$363$	1.28602	−	2.42940i	1.28602	−	2.42940i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.577333	−	0.816509i	$-0.304094\pi$
$367$		0			0		−0.577333	+	0.816509i	$0.695906\pi$
$368$		0			0
$369$	3.24279	−	0.358912i	3.24279	−	0.358912i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.451533	−	0.892254i	$-0.649123\pi$
$373$		0			0		0.451533	+	0.892254i	$0.350877\pi$
$374$	−0.126915	−	2.76130i	−0.126915	−	2.76130i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.111859	−	0.121511i	0.111859	−	0.121511i	−0.677282	−	0.735724i	$-0.736842\pi$
$379$	0.111859	−	0.121511i	0.111859	−	0.121511i	0.789141	+	0.614213i	$0.210526\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.119134	−	0.992878i	$-0.538012\pi$
$383$		0			0		0.119134	+	0.992878i	$0.461988\pi$
$384$	−0.648130	+	1.55462i	−0.648130	+	1.55462i
$385$		0			0
$386$	1.73113	−	0.524048i	1.73113	−	0.524048i
$387$	−3.07821	−	1.45264i	−3.07821	−	1.45264i
$388$	1.74124	+	0.707230i	1.74124	+	0.707230i
$389$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$389$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$390$		0			0
$391$		0			0
$392$	0.137354	+	0.990522i	0.137354	+	0.990522i
$393$	−1.36027	−	1.59120i	−1.36027	−	1.59120i
$394$		0			0
$395$		0			0
$396$	2.41736	+	1.74278i	2.41736	+	1.74278i
$397$		0			0		−0.333374	−	0.942795i	$-0.608187\pi$
$397$		0			0		0.333374	+	0.942795i	$0.391813\pi$
$398$		0			0
$399$		0			0
$400$	−0.0825793	+	0.996584i	−0.0825793	+	0.996584i
$401$	−1.66612	+	0.438244i	−1.66612	+	0.438244i	−0.962268	−	0.272103i	$-0.912281\pi$
$401$	−1.66612	+	0.438244i	−1.66612	+	0.438244i	−0.703852	+	0.710347i	$0.748538\pi$
$402$	0.827606	−	0.318561i	0.827606	−	0.318561i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	2.85769	+	0.263247i	2.85769	+	0.263247i
$409$	0.271945	−	0.491666i	0.271945	−	0.491666i	−0.703852	−	0.710347i	$-0.748538\pi$
$409$	0.271945	−	0.491666i	0.271945	−	0.491666i	0.975796	+	0.218681i	$0.0701754\pi$
$410$		0			0
$411$	−0.00593220	+	0.0303696i	−0.00593220	+	0.0303696i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.605127	+	0.470989i	0.605127	+	0.470989i
$418$	1.46718	+	0.692378i	1.46718	+	0.692378i
$419$	1.13128	−	0.880514i	1.13128	−	0.880514i	0.137354	−	0.990522i	$-0.456140\pi$
$419$	1.13128	−	0.880514i	1.13128	−	0.880514i	0.993931	+	0.110008i	$0.0350877\pi$
$420$		0			0
$421$		0			0		−0.577333	−	0.816509i	$-0.695906\pi$
$421$		0			0		0.577333	+	0.816509i	$0.304094\pi$
$422$	1.37298	+	1.43754i	1.37298	+	1.43754i
$423$		0			0
$424$		0			0
$425$	1.66260	−	0.372597i	1.66260	−	0.372597i
$426$		0			0
$427$		0			0
$428$	−1.25499	−	0.836478i	−1.25499	−	0.836478i
$429$		0			0
$430$		0			0
$431$		0			0		0.896364	−	0.443318i	$-0.146199\pi$
$431$		0			0		−0.896364	+	0.443318i	$0.853801\pi$
$432$	−0.973589	+	1.01937i	−0.973589	+	1.01937i
$433$	−1.33996	−	0.198371i	−1.33996	−	0.198371i	−0.562235	−	0.826977i	$-0.690058\pi$
$433$	−1.33996	−	0.198371i	−1.33996	−	0.198371i	−0.777724	+	0.628606i	$0.783626\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	3.10089	+	0.517447i	3.10089	+	0.517447i
$439$		0			0		−0.842155	−	0.539235i	$-0.818713\pi$
$439$		0			0		0.842155	+	0.539235i	$0.181287\pi$
$440$		0			0
$441$	−0.418144	+	1.78868i	−0.418144	+	1.78868i
$442$		0			0
$443$	0.111473	−	0.929033i	0.111473	−	0.929033i	−0.821778	−	0.569808i	$-0.807018\pi$
$443$	0.111473	−	0.929033i	0.111473	−	0.929033i	0.933251	−	0.359225i	$-0.116959\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.915392	+	0.797215i	−0.915392	+	0.797215i	−0.979649	−	0.200718i	$-0.935673\pi$
$449$	−0.915392	+	0.797215i	−0.915392	+	0.797215i	0.0642573	+	0.997933i	$0.479532\pi$
$450$	−0.799173	+	1.65394i	−0.799173	+	1.65394i
$451$	−1.62008	+	2.38294i	−1.62008	+	2.38294i
$452$	1.32641	−	1.49507i	1.32641	−	1.49507i
$453$		0			0
$454$	−0.00118051	−	0.128509i	−0.00118051	−	0.128509i
$455$		0			0
$456$	−0.921231	+	1.41005i	−0.921231	+	1.41005i
$457$	0.755536	+	1.15643i	0.755536	+	1.15643i	0.983171	+	0.182687i	$0.0584795\pi$
$457$	0.755536	+	1.15643i	0.755536	+	1.15643i	−0.227635	+	0.973746i	$0.573099\pi$
$458$		0			0
$459$	2.15283	+	1.06473i	2.15283	+	1.06473i
$460$		0			0
$461$		0			0		−0.777724	−	0.628606i	$-0.783626\pi$
$461$		0			0		0.777724	+	0.628606i	$0.216374\pi$
$462$		0			0
$463$		0			0		0.635724	−	0.771917i	$-0.280702\pi$
$463$		0			0		−0.635724	+	0.771917i	$0.719298\pi$
$464$		0			0
$465$		0			0
$466$	−0.253343	−	0.237555i	−0.253343	−	0.237555i
$467$	1.55309	+	0.0856861i	1.55309	+	0.0856861i	0.811171	−	0.584809i	$-0.198830\pi$
$467$	1.55309	+	0.0856861i	1.55309	+	0.0856861i	0.741914	+	0.670495i	$0.233918\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.0192569	+	0.418974i	−0.0192569	+	0.418974i
$473$	2.74177	−	1.23281i	2.74177	−	1.23281i
$474$		0			0
$475$	−0.263253	+	0.964727i	−0.263253	+	0.964727i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.800291	−	0.599612i	$-0.795322\pi$
$479$		0			0		0.800291	+	0.599612i	$0.204678\pi$
$480$		0			0
$481$		0			0
$482$	0.339421	−	0.906554i	0.339421	−	0.906554i
$483$		0			0
$484$	−1.58567	+	0.386082i	−1.58567	+	0.386082i
$485$		0			0
$486$	0.456348	−	0.215356i	0.456348	−	0.215356i
$487$		0			0		0.998482	−	0.0550878i	$-0.0175439\pi$
$487$		0			0		−0.998482	+	0.0550878i	$0.982456\pi$
$488$		0			0
$489$	0.815345	−	2.98795i	0.815345	−	2.98795i
$490$		0			0
$491$	1.21691	+	0.368383i	1.21691	+	0.368383i	0.832107	−	0.554615i	$-0.187135\pi$
$491$	1.21691	+	0.368383i	1.21691	+	0.368383i	0.384804	+	0.922998i	$0.374269\pi$
$492$	−2.21949	−	2.00583i	−2.21949	−	2.00583i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.143653	+	2.23097i	−0.143653	+	2.23097i
$499$	0.952793	+	1.51857i	0.952793	+	1.51857i	0.851919	+	0.523673i	$0.175439\pi$
$499$	0.952793	+	1.51857i	0.952793	+	1.51857i	0.100874	+	0.994899i	$0.467836\pi$
$500$		0			0
$501$		0			0
$502$	−1.77994	−	0.398894i	−1.77994	−	0.398894i
$503$		0			0		−0.315998	−	0.948760i	$-0.602339\pi$
$503$		0			0		0.315998	+	0.948760i	$0.397661\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.68317	−	0.0618740i	−1.68317	−	0.0618740i
$508$		0			0
$509$		0			0		0.777724	−	0.628606i	$-0.216374\pi$
$509$		0			0		−0.777724	+	0.628606i	$0.783626\pi$
$510$		0			0
$511$		0			0
$512$	0.945817	−	0.324699i	0.945817	−	0.324699i
$513$	−1.14343	+	0.824348i	−1.14343	+	0.824348i
$514$	1.82941	+	0.628037i	1.82941	+	0.628037i
$515$		0			0
$516$	0.876788	+	2.99532i	0.876788	+	2.99532i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.37556	+	1.19797i	1.37556	+	1.19797i	0.957107	+	0.289735i	$0.0935673\pi$
$521$	1.37556	+	1.19797i	1.37556	+	1.19797i	0.418451	+	0.908239i	$0.362573\pi$
$522$		0			0
$523$	1.48131	−	0.948486i	1.48131	−	0.948486i	0.484006	−	0.875065i	$-0.339181\pi$
$523$	1.48131	−	0.948486i	1.48131	−	0.948486i	0.997301	−	0.0734214i	$-0.0233918\pi$
$524$	−0.170713	+	1.23109i	−0.170713	+	1.23109i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.275640	−	2.71859i	−0.275640	−	2.71859i
$529$	−0.703852	−	0.710347i	−0.703852	−	0.710347i
$530$		0			0
$531$	−0.309477	+	0.705537i	−0.309477	+	0.705537i
$532$		0			0
$533$		0			0
$534$	−0.0449255	−	0.0812236i	−0.0449255	−	0.0812236i
$535$		0			0
$536$	−0.467573	−	0.242040i	−0.467573	−	0.242040i
$537$	−0.729721	−	3.12150i	−0.729721	−	3.12150i
$538$		0			0
$539$	−0.960808	−	1.30723i	−0.960808	−	1.30723i
$540$		0			0
$541$		0			0		−0.467849	−	0.883809i	$-0.654971\pi$
$541$		0			0		0.467849	+	0.883809i	$0.345029\pi$
$542$		0			0
$543$		0			0
$544$	−1.00907	−	1.37289i	−1.00907	−	1.37289i
$545$		0			0
$546$		0			0
$547$	−1.45959	−	0.755560i	−1.45959	−	0.755560i	−0.467849	−	0.883809i	$-0.654971\pi$
$547$	−1.45959	−	0.755560i	−1.45959	−	0.755560i	−0.991742	+	0.128249i	$0.959064\pi$
$548$	0.0158252	−	0.00933158i	0.0158252	−	0.00933158i
$549$		0			0
$550$	−0.651688	−	1.48570i	−0.651688	−	1.48570i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.0292545	−	0.454330i	−0.0292545	−	0.454330i
$557$		0			0		0.811171	−	0.584809i	$-0.198830\pi$
$557$		0			0		−0.811171	+	0.584809i	$0.801170\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−4.28065	+	1.83097i	−4.28065	+	1.83097i
$562$	1.46540	+	1.27622i	1.46540	+	1.27622i
$563$	−0.307963	−	0.984612i	−0.307963	−	0.984612i	−0.971614	−	0.236570i	$-0.923977\pi$
$563$	−0.307963	−	0.984612i	−0.307963	−	0.984612i	0.663651	−	0.748042i	$-0.269006\pi$
$564$		0			0
$565$		0			0
$566$	1.33381	−	0.753824i	1.33381	−	0.753824i
$567$		0			0
$568$		0			0
$569$	1.20256	+	0.412838i	1.20256	+	0.412838i	0.851919	−	0.523673i	$-0.175439\pi$
$569$	1.20256	+	0.412838i	1.20256	+	0.412838i	0.350638	+	0.936511i	$0.385965\pi$
$570$		0			0
$571$	−0.294200	+	0.100999i	−0.294200	+	0.100999i	−0.467849	−	0.883809i	$-0.654971\pi$
$571$	−0.294200	+	0.100999i	−0.294200	+	0.100999i	0.173648	+	0.984808i	$0.444444\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.83566	+	0.0674795i	1.83566	+	0.0674795i
$577$	1.90864	+	0.539713i	1.90864	+	0.539713i	0.989219	+	0.146447i	$0.0467836\pi$
$577$	1.90864	+	0.539713i	1.90864	+	0.539713i	0.919425	+	0.393266i	$0.128655\pi$
$578$	−1.12706	+	1.53342i	−1.12706	+	1.53342i
$579$	−1.84900	−	2.42115i	−1.84900	−	2.42115i
$580$		0			0
$581$		0			0
$582$	0.0872224	−	3.16427i	0.0872224	−	3.16427i
$583$		0			0
$584$	−0.992002	−	1.58106i	−0.992002	−	1.58106i
$585$		0			0
$586$		0			0
$587$	1.86991	+	0.455288i	1.86991	+	0.455288i	0.999325	−	0.0367355i	$-0.0116959\pi$
$587$	1.86991	+	0.455288i	1.86991	+	0.455288i	0.870582	+	0.492024i	$0.163743\pi$
$588$	1.48131	−	0.801643i	1.48131	−	0.801643i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.82161	−	0.588179i	−1.82161	−	0.588179i	−0.999831	−	0.0183709i	$-0.994152\pi$
$593$	−1.82161	−	0.588179i	−1.82161	−	0.588179i	−0.821778	−	0.569808i	$-0.807018\pi$
$594$	0.602022	−	2.20620i	0.602022	−	2.20620i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.971614	−	0.236570i	$-0.0760234\pi$
$599$		0			0		−0.971614	+	0.236570i	$0.923977\pi$
$600$	1.62076	−	0.458307i	1.62076	−	0.458307i
$601$	0.537208	−	1.43482i	0.537208	−	1.43482i	−0.333374	−	0.942795i	$-0.608187\pi$
$601$	0.537208	−	1.43482i	0.537208	−	1.43482i	0.870582	−	0.492024i	$-0.163743\pi$
$602$		0			0
$603$	−0.641843	−	0.723461i	−0.641843	−	0.723461i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$607$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$608$	0.989219	−	0.146447i	0.989219	−	0.146447i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.823925	−	3.01939i	−0.823925	−	3.01939i
$613$		0			0		0.418451	−	0.908239i	$-0.362573\pi$
$613$		0			0		−0.418451	+	0.908239i	$0.637427\pi$
$614$	−0.415953	−	1.93938i	−0.415953	−	1.93938i
$615$		0			0
$616$		0			0
$617$	1.42925	+	1.34018i	1.42925	+	1.34018i	0.851919	+	0.523673i	$0.175439\pi$
$617$	1.42925	+	1.34018i	1.42925	+	1.34018i	0.577333	+	0.816509i	$0.304094\pi$
$618$		0			0
$619$	1.42486	−	1.38613i	1.42486	−	1.38613i	0.635724	−	0.771917i	$-0.280702\pi$
$619$	1.42486	−	1.38613i	1.42486	−	1.38613i	0.789141	−	0.614213i	$-0.210526\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.832107	−	0.554615i	0.832107	−	0.554615i
$626$	−0.364676	−	0.558179i	−0.364676	−	0.558179i
$627$	0.225650	−	2.72320i	0.225650	−	2.72320i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.663651	−	0.748042i	$-0.269006\pi$
$631$		0			0		−0.663651	+	0.748042i	$0.730994\pi$
$632$		0			0
$633$	1.45668	−	3.01469i	1.45668	−	3.01469i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.925387	−	0.522998i	−0.925387	−	0.522998i	−0.0459136	−	0.998945i	$-0.514620\pi$
$641$	−0.925387	−	0.522998i	−0.925387	−	0.522998i	−0.879474	+	0.475947i	$0.842105\pi$
$642$	−0.578262	+	2.47361i	−0.578262	+	2.47361i
$643$	−0.629012	+	0.735793i	−0.629012	+	0.735793i	−0.979649	−	0.200718i	$-0.935673\pi$
$643$	−0.629012	+	0.735793i	−0.629012	+	0.735793i	0.350638	+	0.936511i	$0.385965\pi$
$644$		0			0
$645$		0			0
$646$	−0.741282	−	1.53413i	−0.741282	−	1.53413i
$647$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$647$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$648$	0.494014	+	0.211305i	0.494014	+	0.211305i
$649$	−0.296035	−	0.612665i	−0.296035	−	0.612665i
$650$		0			0
$651$		0			0
$652$	−1.64828	+	0.815195i	−1.64828	+	0.815195i
$653$		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
$656$	−0.0163153	+	1.77606i	−0.0163153	+	1.77606i
$657$	−0.657295	−	3.36499i	−0.657295	−	3.36499i
$658$		0			0
$659$	0.739469	+	1.22813i	0.739469	+	1.22813i	0.967104	+	0.254380i	$0.0818713\pi$
$659$	0.739469	+	1.22813i	0.739469	+	1.22813i	−0.227635	+	0.973746i	$0.573099\pi$
$660$		0			0
$661$		0			0		−0.690683	−	0.723158i	$-0.742690\pi$
$661$		0			0		0.690683	+	0.723158i	$0.257310\pi$
$662$	−1.03500	−	1.46378i	−1.03500	−	1.46378i
$663$		0			0
$664$	1.04743	−	0.815246i	1.04743	−	0.815246i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.0537749	+	1.95085i	0.0537749	+	1.95085i	0.245485	+	0.969400i	$0.421053\pi$
$673$	0.0537749	+	1.95085i	0.0537749	+	1.95085i	−0.191711	+	0.981451i	$0.561404\pi$
$674$	−0.706137	+	1.27667i	−0.706137	+	1.27667i
$675$	1.40366	+	0.129303i	1.40366	+	0.129303i
$676$	0.635724	+	0.771917i	0.635724	+	0.771917i
$677$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$677$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$678$	−3.14165	−	1.20928i	−3.14165	−	1.20928i
$679$		0			0
$680$		0			0
$681$	−0.202010	+	0.0777574i	−0.202010	+	0.0777574i
$682$		0			0
$683$	0.0493023	−	0.594990i	0.0493023	−	0.594990i	−0.926494	−	0.376309i	$-0.877193\pi$
$683$	0.0493023	−	0.594990i	0.0493023	−	0.594990i	0.975796	−	0.218681i	$-0.0701754\pi$
$684$	1.79244	+	0.401696i	1.79244	+	0.401696i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.984819	−	1.56962i	0.984819	−	1.56962i
$689$		0			0
$690$		0			0
$691$	0.248433	+	1.79157i	0.248433	+	1.79157i	0.546948	+	0.837166i	$0.315789\pi$
$691$	0.248433	+	1.79157i	0.248433	+	1.79157i	−0.298515	+	0.954405i	$0.596491\pi$
$692$		0			0
$693$		0			0
$694$	0.0350330	−	0.198682i	0.0350330	−	0.198682i
$695$		0			0
$696$		0			0
$697$	2.89645	−	0.876812i	2.89645	−	0.876812i
$698$		0			0
$699$	−0.225093	+	0.539912i	−0.225093	+	0.539912i
$700$		0			0
$701$		0			0		−0.621436	−	0.783465i	$-0.713450\pi$
$701$		0			0		0.621436	+	0.783465i	$0.286550\pi$
$702$		0			0
$703$		0			0
$704$	−1.09878	+	1.19360i	−1.09878	+	1.19360i
$705$		0			0
$706$	0.588667	−	1.48840i	0.588667	−	1.48840i
$707$		0			0
$708$	0.672253	−	0.217064i	0.672253	−	0.217064i
$709$		0			0		−0.0459136	−	0.998945i	$-0.514620\pi$
$709$		0			0		0.0459136	+	0.998945i	$0.485380\pi$
$710$		0			0
$711$		0			0
$712$	−0.0183718	+	0.0519562i	−0.0183718	+	0.0519562i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.09881	+	1.55402i	−1.09881	+	1.55402i
$717$		0			0
$718$		0			0
$719$		0			0		−0.991742	−	0.128249i	$-0.959064\pi$
$719$		0			0		0.991742	+	0.128249i	$0.0409357\pi$
$720$		0			0
$721$		0			0
$722$	0.999325	+	0.0367355i	0.999325	+	0.0367355i
$723$	−1.63043			−1.63043
$724$		0			0
$725$		0			0
$726$	1.54547	+	2.27318i	1.54547	+	2.27318i
$727$		0			0		0.989219	−	0.146447i	$-0.0467836\pi$
$727$		0			0		−0.989219	+	0.146447i	$0.953216\pi$
$728$		0			0
$729$	−0.994341	−	0.967310i	−0.994341	−	0.967310i
$730$		0			0
$731$	−3.05334	−	0.803126i	−3.05334	−	0.803126i
$732$		0			0
$733$		0			0		0.821778	−	0.569808i	$-0.192982\pi$
$733$		0			0		−0.821778	+	0.569808i	$0.807018\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.854028	−	0.0156919i	0.854028	−	0.0156919i
$738$	−1.19993	+	3.03392i	−1.19993	+	3.03392i
$739$	−1.59626	−	0.117517i	−1.59626	−	0.117517i	−0.754107	−	0.656752i	$-0.771930\pi$
$739$	−1.59626	−	0.117517i	−1.59626	−	0.117517i	−0.842155	+	0.539235i	$0.818713\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.621436	−	0.783465i	$-0.713450\pi$
$743$		0			0		0.621436	+	0.783465i	$0.286550\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.33355	−	0.706411i	2.33355	−	0.706411i
$748$	2.49983	+	1.17970i	2.49983	+	1.17970i
$749$		0			0
$750$		0			0
$751$		0			0		−0.912045	−	0.410091i	$-0.865497\pi$
$751$		0			0		0.912045	+	0.410091i	$0.134503\pi$
$752$		0			0
$753$	0.421996	+	3.04321i	0.421996	+	3.04321i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.811171	−	0.584809i	$-0.801170\pi$
$757$		0			0		0.811171	+	0.584809i	$0.198830\pi$
$758$	0.0550596	+	0.155711i	0.0550596	+	0.155711i
$759$		0			0
$760$		0			0
$761$	0.0256867	−	0.309992i	0.0256867	−	0.309992i	−0.971614	−	0.236570i	$-0.923977\pi$
$761$	0.0256867	−	0.309992i	0.0256867	−	0.309992i	0.997301	−	0.0734214i	$-0.0233918\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.07076	−	1.30015i	−1.07076	−	1.30015i
$769$	1.63663	+	0.150764i	1.63663	+	0.150764i	0.870582	−	0.492024i	$-0.163743\pi$
$769$	1.63663	+	0.150764i	1.63663	+	0.150764i	0.766044	+	0.642788i	$0.222222\pi$
$770$		0			0
$771$	−0.0897668	−	3.25657i	−0.0897668	−	3.25657i
$772$	−0.346750	+	1.77517i	−0.346750	+	1.77517i
$773$		0			0		−0.979649	−	0.200718i	$-0.935673\pi$
$773$		0			0		0.979649	+	0.200718i	$0.0643275\pi$
$774$	2.72400	−	2.04093i	2.72400	−	2.04093i
$775$		0			0
$776$	−1.43969	+	1.20805i	−1.43969	+	1.20805i
$777$		0			0
$778$		0			0
$779$	−0.340504	+	1.74319i	−0.340504	+	1.74319i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.939693	−	0.342020i	−0.939693	−	0.342020i
$785$		0			0
$786$	2.04271	−	0.457783i	2.04271	−	0.457783i
$787$	0.269872	+	1.38159i	0.269872	+	1.38159i	0.832107	+	0.554615i	$0.187135\pi$
$787$	0.269872	+	1.38159i	0.269872	+	1.38159i	−0.562235	+	0.826977i	$0.690058\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−2.67124	+	1.32113i	−2.67124	+	1.32113i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$797$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$798$		0			0
$799$		0			0
$800$	−0.842155	−	0.539235i	−0.842155	−	0.539235i
$801$	−0.0657785	+	0.0769451i	−0.0657785	+	0.0769451i
$802$	0.392168	−	1.67756i	0.392168	−	1.67756i
$803$	2.63621	+	1.48990i	2.63621	+	1.48990i
$804$	−0.105648	+	0.880483i	−0.105648	+	0.880483i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.0782293	−	0.0480874i	−0.0782293	−	0.0480874i	0.484006	−	0.875065i	$-0.339181\pi$
$809$	−0.0782293	−	0.0480874i	−0.0782293	−	0.0480874i	−0.562235	+	0.826977i	$0.690058\pi$
$810$		0			0
$811$	−0.822985	+	1.70323i	−0.822985	+	1.70323i	−0.119134	+	0.992878i	$0.538012\pi$
$811$	−0.822985	+	1.70323i	−0.822985	+	1.70323i	−0.703852	+	0.710347i	$0.748538\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.56963	+	2.40250i	−1.56963	+	2.40250i
$817$	1.25499	−	1.36329i	1.25499	−	1.36329i
$818$	0.307310	+	0.470372i	0.307310	+	0.470372i
$819$		0			0
$820$		0			0
$821$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$821$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$822$	−0.0240655	−	0.0194513i	−0.0240655	−	0.0194513i
$823$		0			0		0.703852	−	0.710347i	$-0.251462\pi$
$823$		0			0		−0.703852	+	0.710347i	$0.748538\pi$
$824$		0			0
$825$	−1.95863	+	1.90538i	−1.95863	+	1.90538i
$826$		0			0
$827$	0.0669853	+	0.0628108i	0.0669853	+	0.0628108i	0.716783	−	0.697297i	$-0.245614\pi$
$827$	0.0669853	+	0.0628108i	0.0669853	+	0.0628108i	−0.649797	+	0.760108i	$0.725146\pi$
$828$		0			0
$829$		0			0		0.926494	−	0.376309i	$-0.122807\pi$
$829$		0			0		−0.926494	+	0.376309i	$0.877193\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.0782293	+	1.70204i	−0.0782293	+	1.70204i
$834$	−0.699372	+	0.314465i	−0.699372	+	0.314465i
$835$		0			0
$836$	−1.29835	+	0.972776i	−1.29835	+	0.972776i
$837$		0			0
$838$	0.248936	+	1.41179i	0.248936	+	1.41179i
$839$		0			0		0.209708	−	0.977764i	$-0.432749\pi$
$839$		0			0		−0.209708	+	0.977764i	$0.567251\pi$
$840$		0			0
$841$	0.663651	+	0.748042i	0.663651	+	0.748042i
$842$		0			0
$843$	1.14764	−	3.06520i	1.14764	−	3.06520i
$844$	−1.91286	+	0.540904i	−1.91286	+	0.540904i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.97679	−	1.65872i	−1.97679	−	1.65872i
$850$	−0.448540	+	1.64374i	−0.448540	+	1.64374i
$851$		0			0
$852$		0			0
$853$		0			0		−0.741914	−	0.670495i	$-0.766082\pi$
$853$		0			0		0.741914	+	0.670495i	$0.233918\pi$
$854$		0			0
$855$		0			0
$856$	1.32643	−	0.717830i	1.32643	−	0.717830i
$857$	−1.61697	−	0.393704i	−1.61697	−	0.393704i	−0.677282	−	0.735724i	$-0.736842\pi$
$857$	−1.61697	−	0.393704i	−1.61697	−	0.393704i	−0.939693	+	0.342020i	$0.888889\pi$
$858$		0			0
$859$	−0.125899	+	1.95525i	−0.125899	+	1.95525i	0.137354	+	0.990522i	$0.456140\pi$
$859$	−0.125899	+	1.95525i	−0.125899	+	1.95525i	−0.263253	+	0.964727i	$0.584795\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.975796	−	0.218681i	$-0.929825\pi$
$863$		0			0		0.975796	+	0.218681i	$0.0701754\pi$
$864$	−0.445431	−	1.33738i	−0.445431	−	1.33738i
$865$		0			0
$866$	0.802220	−	1.09146i	0.802220	−	1.09146i
$867$	3.08441	+	0.872188i	3.08441	+	0.872188i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−3.26519	+	1.12094i	−3.26519	+	1.12094i
$874$		0			0
$875$		0			0
$876$	−1.90807	+	2.49851i	−1.90807	+	2.49851i
$877$		0			0		−0.280931	−	0.959728i	$-0.590643\pi$
$877$		0			0		0.280931	+	0.959728i	$0.409357\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.568147	+	1.81647i	0.568147	+	1.81647i	0.577333	+	0.816509i	$0.304094\pi$
$881$	0.568147	+	1.81647i	0.568147	+	1.81647i	−0.00918581	+	0.999958i	$0.502924\pi$
$882$	−1.38522	−	1.20639i	−1.38522	−	1.20639i
$883$	1.81902	−	0.778053i	1.81902	−	0.778053i	0.851919	−	0.523673i	$-0.175439\pi$
$883$	1.81902	−	0.778053i	1.81902	−	0.778053i	0.967104	−	0.254380i	$-0.0818713\pi$
$884$		0			0
$885$		0			0
$886$	0.768935	+	0.533168i	0.768935	+	0.533168i
$887$		0			0		0.811171	−	0.584809i	$-0.198830\pi$
$887$		0			0		−0.811171	+	0.584809i	$0.801170\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.868022	+	0.0799611i	−0.868022	+	0.0799611i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.276321	−	1.18201i	−0.276321	−	1.18201i
$899$		0			0
$900$	−1.08788	−	1.48011i	−1.08788	−	1.48011i
$901$		0			0
$902$	−1.34811	−	2.54670i	−1.34811	−	2.54670i
$903$		0			0
$904$	0.700802	+	1.87176i	0.700802	+	1.87176i
$905$		0			0
$906$		0			0
$907$	0.0542381	+	0.232012i	0.0542381	+	0.232012i	0.993931	−	0.110008i	$-0.0350877\pi$
$907$	0.0542381	+	0.232012i	0.0542381	+	0.232012i	−0.939693	+	0.342020i	$0.888889\pi$
$908$	0.114130	+	0.0590795i	0.114130	+	0.0590795i
$909$		0			0
$910$		0			0
$911$		0			0		−0.401695	−	0.915773i	$-0.631579\pi$
$911$		0			0		0.401695	+	0.915773i	$0.368421\pi$
$912$	−0.815216	−	1.47388i	−0.815216	−	1.47388i
$913$	−0.864987	+	1.97197i	−0.864987	+	1.97197i
$914$	−1.37554	+	0.126713i	−1.37554	+	0.126713i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−1.94822	+	1.40456i	−1.94822	+	1.40456i
$919$		0			0		−0.821778	−	0.569808i	$-0.807018\pi$
$919$		0			0		0.821778	+	0.569808i	$0.192982\pi$
$920$		0			0
$921$	−2.81348	+	1.80148i	−2.81348	+	1.80148i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.04563	+	1.36919i	−1.04563	+	1.36919i	−0.119134	+	0.992878i	$0.538012\pi$
$929$	−1.04563	+	1.36919i	−1.04563	+	1.36919i	−0.926494	+	0.376309i	$0.877193\pi$
$930$		0			0
$931$	−0.861396	−	0.507934i	−0.861396	−	0.507934i
$932$	0.328479	−	0.112767i	0.328479	−	0.112767i
$933$		0			0
$934$	−0.802339	+	1.33254i	−0.802339	+	1.33254i
$935$		0			0
$936$		0			0
$937$	−0.935066	−	0.0343733i	−0.935066	−	0.0343733i	−0.435066	−	0.900399i	$-0.643275\pi$
$937$	−0.935066	−	0.0343733i	−0.935066	−	0.0343733i	−0.500000	+	0.866025i	$0.666667\pi$
$938$		0			0
$939$	−0.665086	+	0.904883i	−0.665086	+	0.904883i
$940$		0			0
$941$		0			0		−0.315998	−	0.948760i	$-0.602339\pi$
$941$		0			0		0.315998	+	0.948760i	$0.397661\pi$
$942$		0			0
$943$		0			0
$944$	−0.361284	−	0.213036i	−0.361284	−	0.213036i
$945$		0			0
$946$	−0.193169	+	2.99997i	−0.193169	+	2.99997i
$947$	1.57722	−	0.0579790i	1.57722	−	0.0579790i	0.766044	−	0.642788i	$-0.222222\pi$
$947$	1.57722	−	0.0579790i	1.57722	−	0.0579790i	0.811171	+	0.584809i	$0.198830\pi$
$948$		0			0
$949$		0			0
$950$	−0.729471	−	0.684011i	−0.729471	−	0.684011i
$951$		0			0
$952$		0			0
$953$	−0.228047	−	0.0690344i	−0.228047	−	0.0690344i	0.173648	−	0.984808i	$-0.444444\pi$
$953$	−0.228047	−	0.0690344i	−0.228047	−	0.0690344i	−0.401695	+	0.915773i	$0.631579\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.962268	+	0.272103i	−0.962268	+	0.272103i
$962$		0			0
$963$	2.74756	−	0.355306i	2.74756	−	0.355306i
$964$	0.642423	+	0.724114i	0.642423	+	0.724114i
$965$		0			0
$966$		0			0
$967$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$967$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$968$	0.400631	−	1.58206i	0.400631	−	1.58206i
$969$	−1.98212	+	2.07531i	−1.98212	+	2.07531i
$970$		0			0
$971$	−0.316750	+	0.142423i	−0.316750	+	0.142423i	−0.562235	−	0.826977i	$-0.690058\pi$
$971$	−0.316750	+	0.142423i	−0.316750	+	0.142423i	0.245485	+	0.969400i	$0.421053\pi$
$972$	−0.0231685	+	0.504078i	−0.0231685	+	0.504078i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.0183437	+	0.00101205i	0.0183437	+	0.00101205i	0.0642573	−	0.997933i	$-0.479532\pi$
$977$	0.0183437	+	0.00101205i	0.0183437	+	0.00101205i	−0.0459136	+	0.998945i	$0.514620\pi$
$978$	2.25931	+	2.11851i	2.25931	+	2.11851i
$979$	−0.0139049	−	0.0883172i	−0.0139049	−	0.0883172i
$980$		0			0
$981$		0			0
$982$	−0.894910	+	0.903169i	−0.894910	+	0.903169i
$983$		0			0		−0.777724	−	0.628606i	$-0.783626\pi$
$983$		0			0		0.777724	+	0.628606i	$0.216374\pi$
$984$	2.81115	−	1.02318i	2.81115	−	1.02318i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.979649	−	0.200718i	$-0.0643275\pi$
$991$		0			0		−0.979649	+	0.200718i	$0.935673\pi$
$992$		0			0
$993$	−1.69768	+	2.49707i	−1.69768	+	2.49707i
$994$		0			0
$995$		0			0
$996$	−1.90454	−	1.17072i	−1.90454	−	1.17072i
$997$		0			0		0.621436	−	0.783465i	$-0.286550\pi$
$997$		0			0		−0.621436	+	0.783465i	$0.713450\pi$
$998$	−1.78789	+	0.131625i	−1.78789	+	0.131625i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2888.1.bs.a.275.1	✓	108
8.3	odd	2	CM	2888.1.bs.a.275.1	✓	108
361.340	even	171	inner	2888.1.bs.a.2867.1	yes	108
2888.2867	odd	342	inner	2888.1.bs.a.2867.1	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2888.1.bs.a.275.1	✓	108	1.1	even	1	trivial
2888.1.bs.a.275.1	✓	108	8.3	odd	2	CM
2888.1.bs.a.2867.1	yes	108	361.340	even	171	inner
2888.1.bs.a.2867.1	yes	108	2888.2867	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)

\(f(q)\)	\(=\)	\(q+(-0.467849 + 0.883809i) q^{2} +(1.67040 + 0.216011i) q^{3} +(-0.562235 - 0.826977i) q^{4} +(-0.972408 + 1.37525i) q^{6} +(0.993931 - 0.110008i) q^{8} +(1.77648 + 0.467271i) q^{9} +O(q^{10})\)	\(q+(-0.467849 + 0.883809i) q^{2} +(1.67040 + 0.216011i) q^{3} +(-0.562235 - 0.826977i) q^{4} +(-0.972408 + 1.37525i) q^{6} +(0.993931 - 0.110008i) q^{8} +(1.77648 + 0.467271i) q^{9} +(-1.33321 + 0.924424i) q^{11} +(-0.760522 - 1.50283i) q^{12} +(-0.367783 + 0.929912i) q^{16} +(1.69924 + 0.125098i) q^{17} +(-1.24410 + 1.35145i) q^{18} +(-0.531476 + 0.847073i) q^{19} +(-0.193276 - 1.61079i) q^{22} +(1.68403 + 0.0309422i) q^{24} +(0.957107 - 0.289735i) q^{25} +(1.30599 + 0.530447i) q^{27} +(-0.649797 - 0.760108i) q^{32} +(-2.42667 + 1.25617i) q^{33} +(-0.905550 + 1.44328i) q^{34} +(-0.612375 - 1.73182i) q^{36} +(-0.500000 - 0.866025i) q^{38} +(1.65758 - 0.638034i) q^{41} +(-1.82180 - 0.338517i) q^{43} +(1.51405 + 0.582787i) q^{44} +(-0.815216 + 1.47388i) q^{48} +(0.0275543 + 0.999620i) q^{49} +(-0.191711 + 0.981451i) q^{50} +(2.81139 + 0.576019i) q^{51} +(-1.07982 + 0.906076i) q^{54} +(-1.07076 + 1.30015i) q^{57} +(-0.0652307 + 0.414313i) q^{59} +(0.975796 - 0.218681i) q^{64} +(0.0251005 - 2.73241i) q^{66} +(-0.438109 - 0.292008i) q^{67} +(-0.851919 - 1.47557i) q^{68} +(1.81710 + 0.269008i) q^{72} +(-0.812051 - 1.68060i) q^{73} +(1.66134 - 0.277228i) q^{75} +(0.999325 - 0.0367355i) q^{76} +(0.467770 + 0.264368i) q^{81} +(-0.211598 + 1.76349i) q^{82} +(1.13076 - 0.695073i) q^{83} +(1.15151 - 1.45175i) q^{86} +(-1.22342 + 1.06548i) q^{88} +(-0.0239759 + 0.0496198i) q^{89} +(-0.921231 - 1.41005i) q^{96} +(-1.56385 + 1.04234i) q^{97} +(-0.896364 - 0.443318i) q^{98} +(-2.80036 + 1.01925i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 3 q^{3} + 3 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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