LMFDB - Embedded newform 672.2.bc.c.353.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [672,2,Mod(257,672)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(672, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("672.257"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			353.3
Root			$1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	672.353
Dual form			672.2.bc.c.257.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 1.50000i) q^{3} +(-1.32288 - 2.29129i) q^{5} +(-2.29129 - 1.32288i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(0.866025 + 0.500000i) q^{11} +3.46410i q^{13} -4.58258 q^{15} +(2.64575 - 4.58258i) q^{17} +(-4.58258 + 2.64575i) q^{19} +(-3.96863 + 2.29129i) q^{21} +(-1.73205 + 1.00000i) q^{23} +(-1.00000 + 1.73205i) q^{25} -5.19615 q^{27} +4.58258i q^{29} +(-6.87386 - 3.96863i) q^{31} +(1.50000 - 0.866025i) q^{33} +7.00000i q^{35} +(-3.00000 - 5.19615i) q^{37} +(5.19615 + 3.00000i) q^{39} +10.5830 q^{41} +(-3.96863 + 6.87386i) q^{45} +(-3.46410 - 6.00000i) q^{47} +(3.50000 + 6.06218i) q^{49} +(-4.58258 - 7.93725i) q^{51} +(-3.96863 - 2.29129i) q^{53} -2.64575i q^{55} +9.16515i q^{57} +(6.06218 - 10.5000i) q^{59} +(12.0000 - 6.92820i) q^{61} +7.93725i q^{63} +(7.93725 - 4.58258i) q^{65} +(-4.58258 + 7.93725i) q^{67} +3.46410i q^{69} -4.00000i q^{71} +(-6.00000 - 3.46410i) q^{73} +(1.73205 + 3.00000i) q^{75} +(-1.32288 - 2.29129i) q^{77} +(2.29129 + 3.96863i) q^{79} +(-4.50000 + 7.79423i) q^{81} -1.73205 q^{83} -14.0000 q^{85} +(6.87386 + 3.96863i) q^{87} +(-2.64575 - 4.58258i) q^{89} +(4.58258 - 7.93725i) q^{91} +(-11.9059 + 6.87386i) q^{93} +(12.1244 + 7.00000i) q^{95} -8.66025i q^{97} -3.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{9} - 8 q^{25} + 12 q^{33} - 24 q^{37} + 28 q^{49} + 96 q^{61} - 48 q^{73} - 36 q^{81} - 112 q^{85}+O(q^{100}) $ 8 * q - 12 * q^9 - 8 * q^25 + 12 * q^33 - 24 * q^37 + 28 * q^49 + 96 * q^61 - 48 * q^73 - 36 * q^81 - 112 * q^85

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$		0			0
$5$	−1.32288	−	2.29129i	−0.591608	−	1.02470i	−0.994016	−	0.109235i	$-0.965160\pi$
$5$	−1.32288	−	2.29129i	−0.591608	−	1.02470i	0.402408	−	0.915460i	$-0.368173\pi$
$6$		0			0
$7$	−2.29129	−	1.32288i	−0.866025	−	0.500000i
$7$	−2.29129	−	1.32288i	−0.866025	−	0.500000i
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i	0.624844	−	0.780750i	$-0.285163\pi$
$11$	0.866025	+	0.500000i	0.261116	+	0.150756i	−0.363727	+	0.931505i	$0.618496\pi$
$12$		0			0
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$		0			0
$15$	−4.58258			−1.18322
$16$		0			0
$17$	2.64575	−	4.58258i	0.641689	−	1.11144i	−0.343367	−	0.939201i	$-0.611567\pi$
$17$	2.64575	−	4.58258i	0.641689	−	1.11144i	0.985056	−	0.172236i	$-0.0550993\pi$
$18$		0			0
$19$	−4.58258	+	2.64575i	−1.05131	+	0.606977i	−0.923017	−	0.384759i	$-0.874285\pi$
$19$	−4.58258	+	2.64575i	−1.05131	+	0.606977i	−0.128298	+	0.991736i	$0.540951\pi$
$20$		0			0
$21$	−3.96863	+	2.29129i	−0.866025	+	0.500000i
$22$		0			0
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	−0.669588	−	0.742732i	$-0.733529\pi$
$23$	−1.73205	+	1.00000i	−0.361158	+	0.208514i	0.308431	+	0.951247i	$0.400196\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$			4.58258i			0.850963i	0.904967	+	0.425481i	$0.139895\pi$
$29$			4.58258i			0.850963i	−0.904967	+	0.425481i	$0.860105\pi$
$30$		0			0
$31$	−6.87386	−	3.96863i	−1.23458	−	0.712786i	−0.266601	−	0.963807i	$-0.585900\pi$
$31$	−6.87386	−	3.96863i	−1.23458	−	0.712786i	−0.967982	+	0.251021i	$0.919234\pi$
$32$		0			0
$33$	1.50000	−	0.866025i	0.261116	−	0.150756i
$34$		0			0
$35$			7.00000i			1.18322i
$36$		0			0
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	0.506772	−	0.862080i	$-0.330838\pi$
$37$	−3.00000	−	5.19615i	−0.493197	−	0.854242i	−0.999969	+	0.00783774i	$0.997505\pi$
$38$		0			0
$39$	5.19615	+	3.00000i	0.832050	+	0.480384i
$40$		0			0
$41$	10.5830			1.65279			0.826394	−	0.563093i	$-0.190389\pi$
$41$	10.5830			1.65279			0.826394	+	0.563093i	$0.190389\pi$
$42$		0			0
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−3.96863	+	6.87386i	−0.591608	+	1.02470i
$46$		0			0
$47$	−3.46410	−	6.00000i	−0.505291	−	0.875190i	−0.999981	−	0.00612051i	$-0.998052\pi$
$47$	−3.46410	−	6.00000i	−0.505291	−	0.875190i	0.494690	−	0.869069i	$-0.335282\pi$
$48$		0			0
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$		0			0
$51$	−4.58258	−	7.93725i	−0.641689	−	1.11144i
$52$		0			0
$53$	−3.96863	−	2.29129i	−0.545133	−	0.314733i	0.202024	−	0.979381i	$-0.435248\pi$
$53$	−3.96863	−	2.29129i	−0.545133	−	0.314733i	−0.747157	+	0.664648i	$0.768582\pi$
$54$		0			0
$55$		−	2.64575i		−	0.356753i
$56$		0			0
$57$			9.16515i			1.21395i
$58$		0			0
$59$	6.06218	−	10.5000i	0.789228	−	1.36698i	−0.137212	−	0.990542i	$-0.543814\pi$
$59$	6.06218	−	10.5000i	0.789228	−	1.36698i	0.926440	−	0.376442i	$-0.122853\pi$
$60$		0			0
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.537400	−	0.843328i	$-0.319407\pi$
$61$	12.0000	−	6.92820i	1.53644	−	0.887066i	0.999043	−	0.0437377i	$-0.0139266\pi$
$62$		0			0
$63$			7.93725i			1.00000i
$64$		0			0
$65$	7.93725	−	4.58258i	0.984495	−	0.568399i
$66$		0			0
$67$	−4.58258	+	7.93725i	−0.559851	+	0.969690i	0.437658	+	0.899142i	$0.355808\pi$
$67$	−4.58258	+	7.93725i	−0.559851	+	0.969690i	−0.997508	+	0.0705482i	$0.977525\pi$
$68$		0			0
$69$			3.46410i			0.417029i
$70$		0			0
$71$		−	4.00000i		−	0.474713i	−0.971423	−	0.237356i	$-0.923719\pi$
$71$		−	4.00000i		−	0.474713i	0.971423	−	0.237356i	$-0.0762809\pi$
$72$		0			0
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	0.105937	−	0.994373i	$-0.466216\pi$
$73$	−6.00000	−	3.46410i	−0.702247	−	0.405442i	−0.808184	+	0.588930i	$0.799549\pi$
$74$		0			0
$75$	1.73205	+	3.00000i	0.200000	+	0.346410i
$76$		0			0
$77$	−1.32288	−	2.29129i	−0.150756	−	0.261116i
$78$		0			0
$79$	2.29129	+	3.96863i	0.257790	+	0.446505i	0.965650	−	0.259848i	$-0.0836724\pi$
$79$	2.29129	+	3.96863i	0.257790	+	0.446505i	−0.707860	+	0.706353i	$0.750339\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−1.73205			−0.190117			−0.0950586	−	0.995472i	$-0.530304\pi$
$83$	−1.73205			−0.190117			−0.0950586	+	0.995472i	$0.530304\pi$
$84$		0			0
$85$	−14.0000			−1.51851
$86$		0			0
$87$	6.87386	+	3.96863i	0.736956	+	0.425481i
$88$		0			0
$89$	−2.64575	−	4.58258i	−0.280449	−	0.485752i	0.691046	−	0.722810i	$-0.257150\pi$
$89$	−2.64575	−	4.58258i	−0.280449	−	0.485752i	−0.971495	+	0.237058i	$0.923817\pi$
$90$		0			0
$91$	4.58258	−	7.93725i	0.480384	−	0.832050i
$92$		0			0
$93$	−11.9059	+	6.87386i	−1.23458	+	0.712786i
$94$		0			0
$95$	12.1244	+	7.00000i	1.24393	+	0.718185i
$96$		0			0
$97$		−	8.66025i		−	0.879316i	−0.898165	−	0.439658i	$-0.855100\pi$
$97$		−	8.66025i		−	0.879316i	0.898165	−	0.439658i	$-0.144900\pi$
$98$		0			0
$99$		−	3.00000i		−	0.301511i
$100$		0			0
$101$	5.29150	−	9.16515i	0.526524	−	0.911967i	−0.472998	−	0.881063i	$-0.656828\pi$
$101$	5.29150	−	9.16515i	0.526524	−	0.911967i	0.999522	−	0.0309033i	$-0.00983838\pi$
$102$		0			0
$103$	13.7477	−	7.93725i	1.35460	−	0.782081i	0.365713	−	0.930728i	$-0.380825\pi$
$103$	13.7477	−	7.93725i	1.35460	−	0.782081i	0.988890	+	0.148647i	$0.0474917\pi$
$104$		0			0
$105$	10.5000	+	6.06218i	1.02470	+	0.591608i
$106$		0			0
$107$	−4.33013	+	2.50000i	−0.418609	+	0.241684i	−0.694482	−	0.719510i	$-0.744366\pi$
$107$	−4.33013	+	2.50000i	−0.418609	+	0.241684i	0.275873	+	0.961194i	$0.411033\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$		0			0
$111$	−10.3923			−0.986394
$112$		0			0
$113$		−	18.3303i		−	1.72437i	−0.506594	−	0.862185i	$-0.669096\pi$
$113$		−	18.3303i		−	1.72437i	0.506594	−	0.862185i	$-0.330904\pi$
$114$		0			0
$115$	4.58258	+	2.64575i	0.427327	+	0.246718i
$116$		0			0
$117$	9.00000	−	5.19615i	0.832050	−	0.480384i
$118$		0			0
$119$	−12.1244	+	7.00000i	−1.11144	+	0.641689i
$120$		0			0
$121$	−5.00000	−	8.66025i	−0.454545	−	0.787296i
$122$		0			0
$123$	9.16515	−	15.8745i	0.826394	−	1.43136i
$124$		0			0
$125$	−7.93725			−0.709930
$126$		0			0
$127$	13.7477			1.21991			0.609957	−	0.792435i	$-0.291187\pi$
$127$	13.7477			1.21991			0.609957	+	0.792435i	$0.291187\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	0.729921	−	0.683531i	$-0.239557\pi$
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	−0.956916	+	0.290365i	$0.906223\pi$
$132$		0			0
$133$	14.0000			1.21395
$134$		0			0
$135$	6.87386	+	11.9059i	0.591608	+	1.02470i
$136$		0			0
$137$	7.93725	+	4.58258i	0.678125	+	0.391516i	0.799148	−	0.601134i	$-0.205284\pi$
$137$	7.93725	+	4.58258i	0.678125	+	0.391516i	−0.121023	+	0.992650i	$0.538617\pi$
$138$		0			0
$139$			15.8745i			1.34646i	0.739434	+	0.673229i	$0.235093\pi$
$139$			15.8745i			1.34646i	−0.739434	+	0.673229i	$0.764907\pi$
$140$		0			0
$141$	−12.0000			−1.01058
$142$		0			0
$143$	−1.73205	+	3.00000i	−0.144841	+	0.250873i
$144$		0			0
$145$	10.5000	−	6.06218i	0.871978	−	0.503436i
$146$		0			0
$147$	12.1244			1.00000
$148$		0			0
$149$	7.93725	−	4.58258i	0.650245	−	0.375419i	−0.138305	−	0.990390i	$-0.544165\pi$
$149$	7.93725	−	4.58258i	0.650245	−	0.375419i	0.788550	+	0.614970i	$0.210832\pi$
$150$		0			0
$151$	2.29129	−	3.96863i	0.186462	−	0.322962i	−0.757606	−	0.652712i	$-0.773631\pi$
$151$	2.29129	−	3.96863i	0.186462	−	0.322962i	0.944068	+	0.329750i	$0.106964\pi$
$152$		0			0
$153$	−15.8745			−1.28338
$154$		0			0
$155$			21.0000i			1.68676i
$156$		0			0
$157$	6.00000	+	3.46410i	0.478852	+	0.276465i	0.719938	−	0.694038i	$-0.244170\pi$
$157$	6.00000	+	3.46410i	0.478852	+	0.276465i	−0.241086	+	0.970504i	$0.577504\pi$
$158$		0			0
$159$	−6.87386	+	3.96863i	−0.545133	+	0.314733i
$160$		0			0
$161$	5.29150			0.417029
$162$		0			0
$163$	4.58258	+	7.93725i	0.358935	+	0.621694i	0.987783	−	0.155834i	$-0.0498066\pi$
$163$	4.58258	+	7.93725i	0.358935	+	0.621694i	−0.628848	+	0.777528i	$0.716473\pi$
$164$		0			0
$165$	−3.96863	−	2.29129i	−0.308957	−	0.178377i
$166$		0			0
$167$	10.3923			0.804181			0.402090	−	0.915600i	$-0.368284\pi$
$167$	10.3923			0.804181			0.402090	+	0.915600i	$0.368284\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	13.7477	+	7.93725i	1.05131	+	0.606977i
$172$		0			0
$173$	5.29150	+	9.16515i	0.402305	+	0.696814i	0.994004	−	0.109346i	$-0.0348756\pi$
$173$	5.29150	+	9.16515i	0.402305	+	0.696814i	−0.591698	+	0.806160i	$0.701542\pi$
$174$		0			0
$175$	4.58258	−	2.64575i	0.346410	−	0.200000i
$176$		0			0
$177$	−10.5000	−	18.1865i	−0.789228	−	1.36698i
$178$		0			0
$179$	−17.3205	−	10.0000i	−1.29460	−	0.747435i	−0.315130	−	0.949048i	$-0.602048\pi$
$179$	−17.3205	−	10.0000i	−1.29460	−	0.747435i	−0.979465	+	0.201613i	$0.935382\pi$
$180$		0			0
$181$			20.7846i			1.54491i	0.635071	+	0.772454i	$0.280971\pi$
$181$			20.7846i			1.54491i	−0.635071	+	0.772454i	$0.719029\pi$
$182$		0			0
$183$		−	24.0000i		−	1.77413i
$184$		0			0
$185$	−7.93725	+	13.7477i	−0.583559	+	1.01075i
$186$		0			0
$187$	4.58258	−	2.64575i	0.335111	−	0.193476i
$188$		0			0
$189$	11.9059	+	6.87386i	0.866025	+	0.500000i
$190$		0			0
$191$	13.8564	−	8.00000i	1.00261	−	0.578860i	0.0935936	−	0.995610i	$-0.470165\pi$
$191$	13.8564	−	8.00000i	1.00261	−	0.578860i	0.909021	+	0.416751i	$0.136831\pi$
$192$		0			0
$193$	−10.5000	+	18.1865i	−0.755807	+	1.30910i	0.189166	+	0.981945i	$0.439422\pi$
$193$	−10.5000	+	18.1865i	−0.755807	+	1.30910i	−0.944972	+	0.327150i	$0.893912\pi$
$194$		0			0
$195$		−	15.8745i		−	1.13680i
$196$		0			0
$197$		−	9.16515i		−	0.652990i	−0.945199	−	0.326495i	$-0.894132\pi$
$197$		−	9.16515i		−	0.652990i	0.945199	−	0.326495i	$-0.105868\pi$
$198$		0			0
$199$	−4.58258	−	2.64575i	−0.324850	−	0.187552i	0.328702	−	0.944434i	$-0.393389\pi$
$199$	−4.58258	−	2.64575i	−0.324850	−	0.187552i	−0.653552	+	0.756881i	$0.726722\pi$
$200$		0			0
$201$	7.93725	+	13.7477i	0.559851	+	0.969690i
$202$		0			0
$203$	6.06218	−	10.5000i	0.425481	−	0.736956i
$204$		0			0
$205$	−14.0000	−	24.2487i	−0.977802	−	1.69360i
$206$		0			0
$207$	5.19615	+	3.00000i	0.361158	+	0.208514i
$208$		0			0
$209$	−5.29150			−0.366021
$210$		0			0
$211$	18.3303			1.26191			0.630955	−	0.775819i	$-0.282663\pi$
$211$	18.3303			1.26191			0.630955	+	0.775819i	$0.282663\pi$
$212$		0			0
$213$	−6.00000	−	3.46410i	−0.411113	−	0.237356i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	10.5000	+	18.1865i	0.712786	+	1.23458i
$218$		0			0
$219$	−10.3923	+	6.00000i	−0.702247	+	0.405442i
$220$		0			0
$221$	15.8745	+	9.16515i	1.06783	+	0.616515i
$222$		0			0
$223$		−	13.2288i		−	0.885863i	−0.896555	−	0.442932i	$-0.853938\pi$
$223$		−	13.2288i		−	0.885863i	0.896555	−	0.442932i	$-0.146062\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$		0			0
$227$	6.06218	−	10.5000i	0.402361	−	0.696909i	−0.591649	−	0.806195i	$-0.701523\pi$
$227$	6.06218	−	10.5000i	0.402361	−	0.696909i	0.994010	+	0.109286i	$0.0348564\pi$
$228$		0			0
$229$	12.0000	−	6.92820i	0.792982	−	0.457829i	−0.0480291	−	0.998846i	$-0.515294\pi$
$229$	12.0000	−	6.92820i	0.792982	−	0.457829i	0.841011	+	0.541017i	$0.181961\pi$
$230$		0			0
$231$	−4.58258			−0.301511
$232$		0			0
$233$	−23.8118	+	13.7477i	−1.55996	+	0.900644i	−0.562701	+	0.826661i	$0.690238\pi$
$233$	−23.8118	+	13.7477i	−1.55996	+	0.900644i	−0.997260	+	0.0739830i	$0.976429\pi$
$234$		0			0
$235$	−9.16515	+	15.8745i	−0.597869	+	1.03554i
$236$		0			0
$237$	7.93725			0.515580
$238$		0			0
$239$			10.0000i			0.646846i	0.946254	+	0.323423i	$0.104834\pi$
$239$			10.0000i			0.646846i	−0.946254	+	0.323423i	$0.895166\pi$
$240$		0			0
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	0.348013	−	0.937490i	$-0.386857\pi$
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	−0.637883	+	0.770133i	$0.720190\pi$
$242$		0			0
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$		0			0
$245$	9.26013	−	16.0390i	0.591608	−	1.02470i
$246$		0			0
$247$	−9.16515	−	15.8745i	−0.583165	−	1.01007i
$248$		0			0
$249$	−1.50000	+	2.59808i	−0.0950586	+	0.164646i
$250$		0			0
$251$	12.1244			0.765283			0.382641	−	0.923897i	$-0.375015\pi$
$251$	12.1244			0.765283			0.382641	+	0.923897i	$0.375015\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$		0			0
$255$	−12.1244	+	21.0000i	−0.759257	+	1.31507i
$256$		0			0
$257$	2.64575	+	4.58258i	0.165037	+	0.285853i	0.936669	−	0.350217i	$-0.113892\pi$
$257$	2.64575	+	4.58258i	0.165037	+	0.285853i	−0.771631	+	0.636070i	$0.780559\pi$
$258$		0			0
$259$			15.8745i			0.986394i
$260$		0			0
$261$	11.9059	−	6.87386i	0.736956	−	0.425481i
$262$		0			0
$263$	−6.92820	−	4.00000i	−0.427211	−	0.246651i	0.270947	−	0.962594i	$-0.412663\pi$
$263$	−6.92820	−	4.00000i	−0.427211	−	0.246651i	−0.698158	+	0.715944i	$0.745997\pi$
$264$		0			0
$265$			12.1244i			0.744793i
$266$		0			0
$267$	−9.16515			−0.560898
$268$		0			0
$269$	−6.61438	+	11.4564i	−0.403286	+	0.698511i	−0.994120	−	0.108281i	$-0.965465\pi$
$269$	−6.61438	+	11.4564i	−0.403286	+	0.698511i	0.590835	+	0.806793i	$0.298799\pi$
$270$		0			0
$271$	−6.87386	+	3.96863i	−0.417557	+	0.241077i	−0.694032	−	0.719944i	$-0.744167\pi$
$271$	−6.87386	+	3.96863i	−0.417557	+	0.241077i	0.276474	+	0.961021i	$0.410834\pi$
$272$		0			0
$273$	−7.93725	−	13.7477i	−0.480384	−	0.832050i
$274$		0			0
$275$	−1.73205	+	1.00000i	−0.104447	+	0.0603023i
$276$		0			0
$277$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$277$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$278$		0			0
$279$			23.8118i			1.42557i
$280$		0			0
$281$			9.16515i			0.546747i	0.961908	+	0.273374i	$0.0881395\pi$
$281$			9.16515i			0.546747i	−0.961908	+	0.273374i	$0.911860\pi$
$282$		0			0
$283$	−18.3303	−	10.5830i	−1.08962	−	0.629094i	−0.156147	−	0.987734i	$-0.549907\pi$
$283$	−18.3303	−	10.5830i	−1.08962	−	0.629094i	−0.933476	+	0.358639i	$0.883241\pi$
$284$		0			0
$285$	21.0000	−	12.1244i	1.24393	−	0.718185i
$286$		0			0
$287$	−24.2487	−	14.0000i	−1.43136	−	0.826394i
$288$		0			0
$289$	−5.50000	−	9.52628i	−0.323529	−	0.560369i
$290$		0			0
$291$	−12.9904	−	7.50000i	−0.761510	−	0.439658i
$292$		0			0
$293$	−2.64575			−0.154566			−0.0772832	−	0.997009i	$-0.524625\pi$
$293$	−2.64575			−0.154566			−0.0772832	+	0.997009i	$0.524625\pi$
$294$		0			0
$295$	−32.0780			−1.86766
$296$		0			0
$297$	−4.50000	−	2.59808i	−0.261116	−	0.150756i
$298$		0			0
$299$	−3.46410	−	6.00000i	−0.200334	−	0.346989i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−9.16515	−	15.8745i	−0.526524	−	0.911967i
$304$		0			0
$305$	−31.7490	−	18.3303i	−1.81794	−	1.04959i
$306$		0			0
$307$		−	5.29150i		−	0.302002i	−0.988534	−	0.151001i	$-0.951750\pi$
$307$		−	5.29150i		−	0.302002i	0.988534	−	0.151001i	$-0.0482497\pi$
$308$		0			0
$309$		−	27.4955i		−	1.56416i
$310$		0			0
$311$	−13.8564	+	24.0000i	−0.785725	+	1.36092i	0.142840	+	0.989746i	$0.454376\pi$
$311$	−13.8564	+	24.0000i	−0.785725	+	1.36092i	−0.928565	+	0.371169i	$0.878957\pi$
$312$		0			0
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.165406	−	0.986226i	$-0.447107\pi$
$313$	19.5000	−	11.2583i	1.10221	−	0.636358i	0.936799	+	0.349867i	$0.113773\pi$
$314$		0			0
$315$	18.1865	−	10.5000i	1.02470	−	0.591608i
$316$		0			0
$317$	11.9059	−	6.87386i	0.668701	−	0.386075i	−0.126883	−	0.991918i	$-0.540497\pi$
$317$	11.9059	−	6.87386i	0.668701	−	0.386075i	0.795584	+	0.605843i	$0.207164\pi$
$318$		0			0
$319$	−2.29129	+	3.96863i	−0.128287	+	0.222200i
$320$		0			0
$321$			8.66025i			0.483368i
$322$		0			0
$323$			28.0000i			1.55796i
$324$		0			0
$325$	−6.00000	−	3.46410i	−0.332820	−	0.192154i
$326$		0			0
$327$	12.1244	+	21.0000i	0.670478	+	1.16130i
$328$		0			0
$329$			18.3303i			1.01058i
$330$		0			0
$331$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$331$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$332$		0			0
$333$	−9.00000	+	15.5885i	−0.493197	+	0.854242i
$334$		0			0
$335$	24.2487			1.32485
$336$		0			0
$337$	−7.00000			−0.381314			−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000			−0.381314			−0.190657	+	0.981657i	$0.561062\pi$
$338$		0			0
$339$	−27.4955	−	15.8745i	−1.49335	−	0.862185i
$340$		0			0
$341$	−3.96863	−	6.87386i	−0.214913	−	0.372241i
$342$		0			0
$343$		−	18.5203i		−	1.00000i
$344$		0			0
$345$	7.93725	−	4.58258i	0.427327	−	0.246718i
$346$		0			0
$347$	−17.3205	−	10.0000i	−0.929814	−	0.536828i	−0.0430610	−	0.999072i	$-0.513711\pi$
$347$	−17.3205	−	10.0000i	−0.929814	−	0.536828i	−0.886753	+	0.462244i	$0.847044\pi$
$348$		0			0
$349$		−	3.46410i		−	0.185429i	−0.995693	−	0.0927146i	$-0.970446\pi$
$349$		−	3.46410i		−	0.185429i	0.995693	−	0.0927146i	$-0.0295544\pi$
$350$		0			0
$351$		−	18.0000i		−	0.960769i
$352$		0			0
$353$	5.29150	−	9.16515i	0.281638	−	0.487812i	−0.690150	−	0.723666i	$-0.742456\pi$
$353$	5.29150	−	9.16515i	0.281638	−	0.487812i	0.971788	+	0.235854i	$0.0757889\pi$
$354$		0			0
$355$	−9.16515	+	5.29150i	−0.486436	+	0.280844i
$356$		0			0
$357$			24.2487i			1.28338i
$358$		0			0
$359$	22.5167	−	13.0000i	1.18838	−	0.686114i	0.230445	−	0.973085i	$-0.425982\pi$
$359$	22.5167	−	13.0000i	1.18838	−	0.686114i	0.957939	+	0.286972i	$0.0926486\pi$
$360$		0			0
$361$	4.50000	−	7.79423i	0.236842	−	0.410223i
$362$		0			0
$363$	−17.3205			−0.909091
$364$		0			0
$365$			18.3303i			0.959452i
$366$		0			0
$367$	11.4564	+	6.61438i	0.598021	+	0.345268i	0.768263	−	0.640135i	$-0.221121\pi$
$367$	11.4564	+	6.61438i	0.598021	+	0.345268i	−0.170241	+	0.985402i	$0.554455\pi$
$368$		0			0
$369$	−15.8745	−	27.4955i	−0.826394	−	1.43136i
$370$		0			0
$371$	6.06218	+	10.5000i	0.314733	+	0.545133i
$372$		0			0
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	0.743691	−	0.668523i	$-0.233073\pi$
$373$	−4.00000	−	6.92820i	−0.207112	−	0.358729i	−0.950804	+	0.309794i	$0.899740\pi$
$374$		0			0
$375$	−6.87386	+	11.9059i	−0.354965	+	0.614817i
$376$		0			0
$377$	−15.8745			−0.817579
$378$		0			0
$379$	−36.6606			−1.88313			−0.941564	−	0.336833i	$-0.890644\pi$
$379$	−36.6606			−1.88313			−0.941564	+	0.336833i	$0.890644\pi$
$380$		0			0
$381$	11.9059	−	20.6216i	0.609957	−	1.05648i
$382$		0			0
$383$	−12.1244	−	21.0000i	−0.619526	−	1.07305i	−0.989572	−	0.144037i	$-0.953992\pi$
$383$	−12.1244	−	21.0000i	−0.619526	−	1.07305i	0.370047	−	0.929013i	$-0.379342\pi$
$384$		0			0
$385$	−3.50000	+	6.06218i	−0.178377	+	0.308957i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.93725	+	4.58258i	0.402435	+	0.232346i	0.687534	−	0.726152i	$-0.258693\pi$
$389$	7.93725	+	4.58258i	0.402435	+	0.232346i	−0.285099	+	0.958498i	$0.592027\pi$
$390$		0			0
$391$			10.5830i			0.535206i
$392$		0			0
$393$	−9.00000			−0.453990
$394$		0			0
$395$	6.06218	−	10.5000i	0.305021	−	0.528312i
$396$		0			0
$397$	−12.0000	+	6.92820i	−0.602263	+	0.347717i	−0.769931	−	0.638127i	$-0.779710\pi$
$397$	−12.0000	+	6.92820i	−0.602263	+	0.347717i	0.167668	+	0.985843i	$0.446376\pi$
$398$		0			0
$399$	12.1244	−	21.0000i	0.606977	−	1.05131i
$400$		0			0
$401$	−15.8745	+	9.16515i	−0.792735	+	0.457686i	−0.840925	−	0.541152i	$-0.817988\pi$
$401$	−15.8745	+	9.16515i	−0.792735	+	0.457686i	0.0481894	+	0.998838i	$0.484655\pi$
$402$		0			0
$403$	13.7477	−	23.8118i	0.684823	−	1.18615i
$404$		0			0
$405$	23.8118			1.18322
$406$		0			0
$407$		−	6.00000i		−	0.297409i
$408$		0			0
$409$	−16.5000	−	9.52628i	−0.815872	−	0.471044i	0.0331186	−	0.999451i	$-0.489456\pi$
$409$	−16.5000	−	9.52628i	−0.815872	−	0.471044i	−0.848991	+	0.528407i	$0.822789\pi$
$410$		0			0
$411$	13.7477	−	7.93725i	0.678125	−	0.391516i
$412$		0			0
$413$	−27.7804	+	16.0390i	−1.36698	+	0.789228i
$414$		0			0
$415$	2.29129	+	3.96863i	0.112475	+	0.194812i
$416$		0			0
$417$	23.8118	+	13.7477i	1.16607	+	0.673229i
$418$		0			0
$419$	24.2487			1.18463			0.592314	−	0.805708i	$-0.298215\pi$
$419$	24.2487			1.18463			0.592314	+	0.805708i	$0.298215\pi$
$420$		0			0
$421$		0			0			−	1.00000i	$-0.5\pi$
$421$		0			0				1.00000i	$0.5\pi$
$422$		0			0
$423$	−10.3923	+	18.0000i	−0.505291	+	0.875190i
$424$		0			0
$425$	5.29150	+	9.16515i	0.256676	+	0.444575i
$426$		0			0
$427$	−36.6606			−1.77413
$428$		0			0
$429$	3.00000	+	5.19615i	0.144841	+	0.250873i
$430$		0			0
$431$	6.92820	+	4.00000i	0.333720	+	0.192673i	0.657491	−	0.753462i	$-0.271618\pi$
$431$	6.92820	+	4.00000i	0.333720	+	0.192673i	−0.323772	+	0.946135i	$0.604951\pi$
$432$		0			0
$433$		−	20.7846i		−	0.998845i	−0.866359	−	0.499422i	$-0.833546\pi$
$433$		−	20.7846i		−	0.998845i	0.866359	−	0.499422i	$-0.166454\pi$
$434$		0			0
$435$		−	21.0000i		−	1.00687i
$436$		0			0
$437$	5.29150	−	9.16515i	0.253127	−	0.438429i
$438$		0			0
$439$	−29.7867	+	17.1974i	−1.42164	+	0.820786i	−0.996439	−	0.0843111i	$-0.973131\pi$
$439$	−29.7867	+	17.1974i	−1.42164	+	0.820786i	−0.425204	+	0.905097i	$0.639798\pi$
$440$		0			0
$441$	10.5000	−	18.1865i	0.500000	−	0.866025i
$442$		0			0
$443$	−4.33013	+	2.50000i	−0.205731	+	0.118779i	−0.599326	−	0.800505i	$-0.704565\pi$
$443$	−4.33013	+	2.50000i	−0.205731	+	0.118779i	0.393595	+	0.919284i	$0.371231\pi$
$444$		0			0
$445$	−7.00000	+	12.1244i	−0.331832	+	0.574750i
$446$		0			0
$447$		−	15.8745i		−	0.750838i
$448$		0			0
$449$			27.4955i			1.29759i	0.760963	+	0.648795i	$0.224727\pi$
$449$			27.4955i			1.29759i	−0.760963	+	0.648795i	$0.775273\pi$
$450$		0			0
$451$	9.16515	+	5.29150i	0.431570	+	0.249167i
$452$		0			0
$453$	−3.96863	−	6.87386i	−0.186462	−	0.322962i
$454$		0			0
$455$	−24.2487			−1.13680
$456$		0			0
$457$	6.50000	+	11.2583i	0.304057	+	0.526642i	0.977051	−	0.213006i	$-0.0683253\pi$
$457$	6.50000	+	11.2583i	0.304057	+	0.526642i	−0.672994	+	0.739648i	$0.734992\pi$
$458$		0			0
$459$	−13.7477	+	23.8118i	−0.641689	+	1.11144i
$460$		0			0
$461$	10.5830			0.492900			0.246450	−	0.969156i	$-0.420736\pi$
$461$	10.5830			0.492900			0.246450	+	0.969156i	$0.420736\pi$
$462$		0			0
$463$	36.6606			1.70376			0.851881	−	0.523735i	$-0.175462\pi$
$463$	36.6606			1.70376			0.851881	+	0.523735i	$0.175462\pi$
$464$		0			0
$465$	31.5000	+	18.1865i	1.46078	+	0.843380i
$466$		0			0
$467$	12.1244	+	21.0000i	0.561048	+	0.971764i	0.997405	+	0.0719905i	$0.0229351\pi$
$467$	12.1244	+	21.0000i	0.561048	+	0.971764i	−0.436357	+	0.899774i	$0.643732\pi$
$468$		0			0
$469$	21.0000	−	12.1244i	0.969690	−	0.559851i
$470$		0			0
$471$	10.3923	−	6.00000i	0.478852	−	0.276465i
$472$		0			0
$473$		0			0
$474$		0			0
$475$		−	10.5830i		−	0.485582i
$476$		0			0
$477$			13.7477i			0.629465i
$478$		0			0
$479$	−10.3923	+	18.0000i	−0.474837	+	0.822441i	−0.999585	−	0.0288165i	$-0.990826\pi$
$479$	−10.3923	+	18.0000i	−0.474837	+	0.822441i	0.524748	+	0.851258i	$0.324159\pi$
$480$		0			0
$481$	18.0000	−	10.3923i	0.820729	−	0.473848i
$482$		0			0
$483$	4.58258	−	7.93725i	0.208514	−	0.361158i
$484$		0			0
$485$	−19.8431	+	11.4564i	−0.901030	+	0.520210i
$486$		0			0
$487$	6.87386	−	11.9059i	0.311484	−	0.539507i	−0.667199	−	0.744879i	$-0.732507\pi$
$487$	6.87386	−	11.9059i	0.311484	−	0.539507i	0.978684	+	0.205372i	$0.0658405\pi$
$488$		0			0
$489$	15.8745			0.717870
$490$		0			0
$491$			31.0000i			1.39901i	0.714628	+	0.699505i	$0.246596\pi$
$491$			31.0000i			1.39901i	−0.714628	+	0.699505i	$0.753404\pi$
$492$		0			0
$493$	21.0000	+	12.1244i	0.945792	+	0.546054i
$494$		0			0
$495$	−6.87386	+	3.96863i	−0.308957	+	0.178377i
$496$		0			0
$497$	−5.29150	+	9.16515i	−0.237356	+	0.411113i
$498$		0			0
$499$	4.58258	+	7.93725i	0.205144	+	0.355320i	0.950179	−	0.311706i	$-0.100900\pi$
$499$	4.58258	+	7.93725i	0.205144	+	0.355320i	−0.745034	+	0.667026i	$0.767567\pi$
$500$		0			0
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$		0			0
$503$	24.2487			1.08120			0.540598	−	0.841281i	$-0.318198\pi$
$503$	24.2487			1.08120			0.540598	+	0.841281i	$0.318198\pi$
$504$		0			0
$505$	−28.0000			−1.24598
$506$		0			0
$507$	0.866025	−	1.50000i	0.0384615	−	0.0666173i
$508$		0			0
$509$	1.32288	+	2.29129i	0.0586354	+	0.101560i	0.893853	−	0.448360i	$-0.147992\pi$
$509$	1.32288	+	2.29129i	0.0586354	+	0.101560i	−0.835218	+	0.549920i	$0.814658\pi$
$510$		0			0
$511$	9.16515	+	15.8745i	0.405442	+	0.702247i
$512$		0			0
$513$	23.8118	−	13.7477i	1.05131	−	0.606977i
$514$		0			0
$515$	−36.3731	−	21.0000i	−1.60279	−	0.925371i
$516$		0			0
$517$		−	6.92820i		−	0.304702i
$518$		0			0
$519$	18.3303			0.804611
$520$		0			0
$521$	−10.5830	+	18.3303i	−0.463650	+	0.803065i	−0.999139	−	0.0414767i	$-0.986794\pi$
$521$	−10.5830	+	18.3303i	−0.463650	+	0.803065i	0.535490	+	0.844542i	$0.320127\pi$
$522$		0			0
$523$	13.7477	−	7.93725i	0.601146	−	0.347072i	−0.168346	−	0.985728i	$-0.553843\pi$
$523$	13.7477	−	7.93725i	0.601146	−	0.347072i	0.769492	+	0.638656i	$0.220509\pi$
$524$		0			0
$525$		−	9.16515i		−	0.400000i
$526$		0			0
$527$	−36.3731	+	21.0000i	−1.58444	+	0.914774i
$528$		0			0
$529$	−9.50000	+	16.4545i	−0.413043	+	0.715412i
$530$		0			0
$531$	−36.3731			−1.57846
$532$		0			0
$533$			36.6606i			1.58795i
$534$		0			0
$535$	11.4564	+	6.61438i	0.495305	+	0.285965i
$536$		0			0
$537$	−30.0000	+	17.3205i	−1.29460	+	0.747435i
$538$		0			0
$539$			7.00000i			0.301511i
$540$		0			0
$541$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$541$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$542$		0			0
$543$	31.1769	+	18.0000i	1.33793	+	0.772454i
$544$		0			0
$545$	37.0405			1.58664
$546$		0			0
$547$	9.16515			0.391874			0.195937	−	0.980617i	$-0.437225\pi$
$547$	9.16515			0.391874			0.195937	+	0.980617i	$0.437225\pi$
$548$		0			0
$549$	−36.0000	−	20.7846i	−1.53644	−	0.887066i
$550$		0			0
$551$	−12.1244	−	21.0000i	−0.516515	−	0.894630i
$552$		0			0
$553$		−	12.1244i		−	0.515580i
$554$		0			0
$555$	13.7477	+	23.8118i	0.583559	+	1.01075i
$556$		0			0
$557$	−27.7804	−	16.0390i	−1.17709	−	0.679595i	−0.221753	−	0.975103i	$-0.571178\pi$
$557$	−27.7804	−	16.0390i	−1.17709	−	0.679595i	−0.955340	+	0.295508i	$0.904511\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		−	9.16515i		−	0.386953i
$562$		0			0
$563$	18.1865	−	31.5000i	0.766471	−	1.32757i	−0.172994	−	0.984923i	$-0.555344\pi$
$563$	18.1865	−	31.5000i	0.766471	−	1.32757i	0.939465	−	0.342644i	$-0.111322\pi$
$564$		0			0
$565$	−42.0000	+	24.2487i	−1.76695	+	1.02015i
$566$		0			0
$567$	20.6216	−	11.9059i	0.866025	−	0.500000i
$568$		0			0
$569$	23.8118	−	13.7477i	0.998241	−	0.576335i	0.0905136	−	0.995895i	$-0.471149\pi$
$569$	23.8118	−	13.7477i	0.998241	−	0.576335i	0.907727	+	0.419561i	$0.137816\pi$
$570$		0			0
$571$	18.3303	−	31.7490i	0.767099	−	1.32865i	−0.172030	−	0.985092i	$-0.555033\pi$
$571$	18.3303	−	31.7490i	0.767099	−	1.32865i	0.939130	−	0.343563i	$-0.111634\pi$
$572$		0			0
$573$		−	27.7128i		−	1.15772i
$574$		0			0
$575$		−	4.00000i		−	0.166812i
$576$		0			0
$577$	16.5000	+	9.52628i	0.686904	+	0.396584i	0.802451	−	0.596718i	$-0.203529\pi$
$577$	16.5000	+	9.52628i	0.686904	+	0.396584i	−0.115547	+	0.993302i	$0.536862\pi$
$578$		0			0
$579$	18.1865	+	31.5000i	0.755807	+	1.30910i
$580$		0			0
$581$	3.96863	+	2.29129i	0.164646	+	0.0950586i
$582$		0			0
$583$	−2.29129	−	3.96863i	−0.0948954	−	0.164364i
$584$		0			0
$585$	−23.8118	−	13.7477i	−0.984495	−	0.568399i
$586$		0			0
$587$	12.1244			0.500426			0.250213	−	0.968191i	$-0.419499\pi$
$587$	12.1244			0.500426			0.250213	+	0.968191i	$0.419499\pi$
$588$		0			0
$589$	42.0000			1.73058
$590$		0			0
$591$	−13.7477	−	7.93725i	−0.565506	−	0.326495i
$592$		0			0
$593$	−13.2288	−	22.9129i	−0.543240	−	0.940919i	−0.998715	−	0.0506708i	$-0.983864\pi$
$593$	−13.2288	−	22.9129i	−0.543240	−	0.940919i	0.455475	−	0.890248i	$-0.349469\pi$
$594$		0			0
$595$	32.0780	+	18.5203i	1.31507	+	0.759257i
$596$		0			0
$597$	−7.93725	+	4.58258i	−0.324850	+	0.187552i
$598$		0			0
$599$	19.0526	+	11.0000i	0.778466	+	0.449448i	0.835887	−	0.548902i	$-0.184954\pi$
$599$	19.0526	+	11.0000i	0.778466	+	0.449448i	−0.0574201	+	0.998350i	$0.518287\pi$
$600$		0			0
$601$			32.9090i			1.34238i	0.741283	+	0.671192i	$0.234218\pi$
$601$			32.9090i			1.34238i	−0.741283	+	0.671192i	$0.765782\pi$
$602$		0			0
$603$	27.4955			1.11970
$604$		0			0
$605$	−13.2288	+	22.9129i	−0.537825	+	0.931541i
$606$		0			0
$607$	16.0390	−	9.26013i	0.651004	−	0.375857i	−0.137837	−	0.990455i	$-0.544015\pi$
$607$	16.0390	−	9.26013i	0.651004	−	0.375857i	0.788841	+	0.614598i	$0.210682\pi$
$608$		0			0
$609$	−10.5000	−	18.1865i	−0.425481	−	0.736956i
$610$		0			0
$611$	20.7846	−	12.0000i	0.840855	−	0.485468i
$612$		0			0
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	−0.689328	−	0.724449i	$-0.742094\pi$
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	0.972056	+	0.234751i	$0.0754275\pi$
$614$		0			0
$615$	−48.4974			−1.95560
$616$		0			0
$617$		−	18.3303i		−	0.737950i	−0.929439	−	0.368975i	$-0.879709\pi$
$617$		−	18.3303i		−	0.737950i	0.929439	−	0.368975i	$-0.120291\pi$
$618$		0			0
$619$	27.4955	+	15.8745i	1.10514	+	0.638050i	0.937565	−	0.347810i	$-0.113074\pi$
$619$	27.4955	+	15.8745i	1.10514	+	0.638050i	0.167570	+	0.985860i	$0.446408\pi$
$620$		0			0
$621$	9.00000	−	5.19615i	0.361158	−	0.208514i
$622$		0			0
$623$			14.0000i			0.560898i
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$		0			0
$627$	−4.58258	+	7.93725i	−0.183010	+	0.316983i
$628$		0			0
$629$	−31.7490			−1.26592
$630$		0			0
$631$	−13.7477			−0.547288			−0.273644	−	0.961831i	$-0.588229\pi$
$631$	−13.7477			−0.547288			−0.273644	+	0.961831i	$0.588229\pi$
$632$		0			0
$633$	15.8745	−	27.4955i	0.630955	−	1.09285i
$634$		0			0
$635$	−18.1865	−	31.5000i	−0.721711	−	1.25004i
$636$		0			0
$637$	−21.0000	+	12.1244i	−0.832050	+	0.480384i
$638$		0			0
$639$	−10.3923	+	6.00000i	−0.411113	+	0.237356i
$640$		0			0
$641$	31.7490	+	18.3303i	1.25401	+	0.724003i	0.971904	−	0.235379i	$-0.0756333\pi$
$641$	31.7490	+	18.3303i	1.25401	+	0.724003i	0.282107	+	0.959383i	$0.408967\pi$
$642$		0			0
$643$			5.29150i			0.208676i	0.994542	+	0.104338i	$0.0332725\pi$
$643$			5.29150i			0.208676i	−0.994542	+	0.104338i	$0.966728\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	13.8564	−	24.0000i	0.544752	−	0.943537i	−0.453871	−	0.891067i	$-0.649957\pi$
$647$	13.8564	−	24.0000i	0.544752	−	0.943537i	0.998623	−	0.0524699i	$-0.0167094\pi$
$648$		0			0
$649$	10.5000	−	6.06218i	0.412161	−	0.237961i
$650$		0			0
$651$	36.3731			1.42557
$652$		0			0
$653$	−3.96863	+	2.29129i	−0.155304	+	0.0896650i	−0.575638	−	0.817705i	$-0.695246\pi$
$653$	−3.96863	+	2.29129i	−0.155304	+	0.0896650i	0.420334	+	0.907370i	$0.361913\pi$
$654$		0			0
$655$	−6.87386	+	11.9059i	−0.268584	+	0.465201i
$656$		0			0
$657$			20.7846i			0.810885i
$658$		0			0
$659$			4.00000i			0.155818i	0.996960	+	0.0779089i	$0.0248243\pi$
$659$			4.00000i			0.155818i	−0.996960	+	0.0779089i	$0.975176\pi$
$660$		0			0
$661$	6.00000	+	3.46410i	0.233373	+	0.134738i	0.612127	−	0.790759i	$-0.290314\pi$
$661$	6.00000	+	3.46410i	0.233373	+	0.134738i	−0.378754	+	0.925497i	$0.623647\pi$
$662$		0			0
$663$	27.4955	−	15.8745i	1.06783	−	0.616515i
$664$		0			0
$665$	−18.5203	−	32.0780i	−0.718185	−	1.24393i
$666$		0			0
$667$	−4.58258	−	7.93725i	−0.177438	−	0.307332i
$668$		0			0
$669$	−19.8431	−	11.4564i	−0.767180	−	0.442932i
$670$		0			0
$671$	13.8564			0.534921
$672$		0			0
$673$	−9.00000			−0.346925			−0.173462	−	0.984841i	$-0.555495\pi$
$673$	−9.00000			−0.346925			−0.173462	+	0.984841i	$0.555495\pi$
$674$		0			0
$675$	5.19615	−	9.00000i	0.200000	−	0.346410i
$676$		0			0
$677$	−1.32288	−	2.29129i	−0.0508422	−	0.0880613i	0.839484	−	0.543384i	$-0.182857\pi$
$677$	−1.32288	−	2.29129i	−0.0508422	−	0.0880613i	−0.890326	+	0.455323i	$0.849524\pi$
$678$		0			0
$679$	−11.4564	+	19.8431i	−0.439658	+	0.761510i
$680$		0			0
$681$	−10.5000	−	18.1865i	−0.402361	−	0.696909i
$682$		0			0
$683$	−0.866025	−	0.500000i	−0.0331375	−	0.0191320i	0.483340	−	0.875433i	$-0.339424\pi$
$683$	−0.866025	−	0.500000i	−0.0331375	−	0.0191320i	−0.516477	+	0.856301i	$0.672757\pi$
$684$		0			0
$685$		−	24.2487i		−	0.926496i
$686$		0			0
$687$		−	24.0000i		−	0.915657i
$688$		0			0
$689$	7.93725	−	13.7477i	0.302385	−	0.523747i
$690$		0			0
$691$	27.4955	−	15.8745i	1.04598	−	0.603895i	0.124456	−	0.992225i	$-0.460281\pi$
$691$	27.4955	−	15.8745i	1.04598	−	0.603895i	0.921520	+	0.388330i	$0.126948\pi$
$692$		0			0
$693$	−3.96863	+	6.87386i	−0.150756	+	0.261116i
$694$		0			0
$695$	36.3731	−	21.0000i	1.37971	−	0.796575i
$696$		0			0
$697$	28.0000	−	48.4974i	1.06058	−	1.83697i
$698$		0			0
$699$			47.6235i			1.80129i
$700$		0			0
$701$		−	41.2432i		−	1.55773i	−0.627189	−	0.778867i	$-0.715795\pi$
$701$		−	41.2432i		−	1.55773i	0.627189	−	0.778867i	$-0.284205\pi$
$702$		0			0
$703$	27.4955	+	15.8745i	1.03701	+	0.598718i
$704$		0			0
$705$	15.8745	+	27.4955i	0.597869	+	1.03554i
$706$		0			0
$707$	−24.2487	+	14.0000i	−0.911967	+	0.526524i
$708$		0			0
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	0.967009	−	0.254743i	$-0.0819909\pi$
$709$	7.00000	+	12.1244i	0.262891	+	0.455340i	−0.704118	+	0.710083i	$0.748658\pi$
$710$		0			0
$711$	6.87386	−	11.9059i	0.257790	−	0.446505i
$712$		0			0
$713$	15.8745			0.594505
$714$		0			0
$715$	9.16515			0.342757
$716$		0			0
$717$	15.0000	+	8.66025i	0.560185	+	0.323423i
$718$		0			0
$719$	−12.1244	−	21.0000i	−0.452162	−	0.783168i	0.546358	−	0.837552i	$-0.316014\pi$
$719$	−12.1244	−	21.0000i	−0.452162	−	0.783168i	−0.998520	+	0.0543839i	$0.982681\pi$
$720$		0			0
$721$	−42.0000			−1.56416
$722$		0			0
$723$	−7.79423	+	4.50000i	−0.289870	+	0.167357i
$724$		0			0
$725$	−7.93725	−	4.58258i	−0.294782	−	0.170193i
$726$		0			0
$727$			7.93725i			0.294376i	0.989109	+	0.147188i	$0.0470223\pi$
$727$			7.93725i			0.294376i	−0.989109	+	0.147188i	$0.952978\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$		0			0
$732$		0			0
$733$	−30.0000	+	17.3205i	−1.10808	+	0.639748i	−0.938330	−	0.345740i	$-0.887628\pi$
$733$	−30.0000	+	17.3205i	−1.10808	+	0.639748i	−0.169745	+	0.985488i	$0.554294\pi$
$734$		0			0
$735$	−16.0390	−	27.7804i	−0.591608	−	1.02470i
$736$		0			0
$737$	−7.93725	+	4.58258i	−0.292373	+	0.168801i
$738$		0			0
$739$	−13.7477	+	23.8118i	−0.505718	+	0.875930i	0.494260	+	0.869314i	$0.335439\pi$
$739$	−13.7477	+	23.8118i	−0.505718	+	0.875930i	−0.999978	+	0.00661558i	$0.997894\pi$
$740$		0			0
$741$	−31.7490			−1.16633
$742$		0			0
$743$			10.0000i			0.366864i	0.983032	+	0.183432i	$0.0587208\pi$
$743$			10.0000i			0.366864i	−0.983032	+	0.183432i	$0.941279\pi$
$744$		0			0
$745$	−21.0000	−	12.1244i	−0.769380	−	0.444202i
$746$		0			0
$747$	2.59808	+	4.50000i	0.0950586	+	0.164646i
$748$		0			0
$749$	13.2288			0.483368
$750$		0			0
$751$	−2.29129	−	3.96863i	−0.0836103	−	0.144817i	0.821188	−	0.570658i	$-0.193312\pi$
$751$	−2.29129	−	3.96863i	−0.0836103	−	0.144817i	−0.904798	+	0.425841i	$0.859978\pi$
$752$		0			0
$753$	10.5000	−	18.1865i	0.382641	−	0.662754i
$754$		0			0
$755$	−12.1244			−0.441250
$756$		0			0
$757$	28.0000			1.01768			0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000			1.01768			0.508839	+	0.860862i	$0.330075\pi$
$758$		0			0
$759$	−1.73205	+	3.00000i	−0.0628695	+	0.108893i
$760$		0			0
$761$	2.64575	+	4.58258i	0.0959084	+	0.166118i	0.909987	−	0.414636i	$-0.136091\pi$
$761$	2.64575	+	4.58258i	0.0959084	+	0.166118i	−0.814079	+	0.580754i	$0.802758\pi$
$762$		0			0
$763$	32.0780	−	18.5203i	1.16130	−	0.670478i
$764$		0			0
$765$	21.0000	+	36.3731i	0.759257	+	1.31507i
$766$		0			0
$767$	36.3731	+	21.0000i	1.31336	+	0.758266i
$768$		0			0
$769$		−	15.5885i		−	0.562134i	−0.959688	−	0.281067i	$-0.909312\pi$
$769$		−	15.5885i		−	0.562134i	0.959688	−	0.281067i	$-0.0906883\pi$
$770$		0			0
$771$	9.16515			0.330075
$772$		0			0
$773$	−5.29150	+	9.16515i	−0.190322	+	0.329648i	−0.945357	−	0.326037i	$-0.894287\pi$
$773$	−5.29150	+	9.16515i	−0.190322	+	0.329648i	0.755035	+	0.655685i	$0.227620\pi$
$774$		0			0
$775$	13.7477	−	7.93725i	0.493833	−	0.285115i
$776$		0			0
$777$	23.8118	+	13.7477i	0.854242	+	0.493197i
$778$		0			0
$779$	−48.4974	+	28.0000i	−1.73760	+	1.00320i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$		−	23.8118i		−	0.850963i
$784$		0			0
$785$		−	18.3303i		−	0.654237i
$786$		0			0
$787$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$787$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$788$		0			0
$789$	−12.0000	+	6.92820i	−0.427211	+	0.246651i
$790$		0			0
$791$	−24.2487	+	42.0000i	−0.862185	+	1.49335i
$792$		0			0
$793$	24.0000	+	41.5692i	0.852265	+	1.47617i
$794$		0			0
$795$	18.1865	+	10.5000i	0.645010	+	0.372397i
$796$		0			0
$797$	−13.2288			−0.468587			−0.234293	−	0.972166i	$-0.575278\pi$
$797$	−13.2288			−0.468587			−0.234293	+	0.972166i	$0.575278\pi$
$798$		0			0
$799$	−36.6606			−1.29696
$800$		0			0
$801$	−7.93725	+	13.7477i	−0.280449	+	0.485752i
$802$		0			0
$803$	−3.46410	−	6.00000i	−0.122245	−	0.211735i
$804$		0			0
$805$	−7.00000	−	12.1244i	−0.246718	−	0.427327i
$806$		0			0
$807$	11.4564	+	19.8431i	0.403286	+	0.698511i
$808$		0			0
$809$	31.7490	+	18.3303i	1.11624	+	0.644459i	0.940437	−	0.339967i	$-0.110416\pi$
$809$	31.7490	+	18.3303i	1.11624	+	0.644459i	0.175799	+	0.984426i	$0.443749\pi$
$810$		0			0
$811$		−	47.6235i		−	1.67229i	−0.548510	−	0.836144i	$-0.684805\pi$
$811$		−	47.6235i		−	1.67229i	0.548510	−	0.836144i	$-0.315195\pi$
$812$		0			0
$813$			13.7477i			0.482154i
$814$		0			0
$815$	12.1244	−	21.0000i	0.424698	−	0.735598i
$816$		0			0
$817$		0			0
$818$		0			0
$819$	−27.4955			−0.960769
$820$		0			0
$821$	−11.9059	+	6.87386i	−0.415518	+	0.239899i	−0.693158	−	0.720786i	$-0.743781\pi$
$821$	−11.9059	+	6.87386i	−0.415518	+	0.239899i	0.277640	+	0.960685i	$0.410448\pi$
$822$		0			0
$823$	9.16515	−	15.8745i	0.319477	−	0.553351i	−0.660902	−	0.750472i	$-0.729826\pi$
$823$	9.16515	−	15.8745i	0.319477	−	0.553351i	0.980379	+	0.197122i	$0.0631594\pi$
$824$		0			0
$825$			3.46410i			0.120605i
$826$		0			0
$827$			17.0000i			0.591148i	0.955320	+	0.295574i	$0.0955109\pi$
$827$			17.0000i			0.591148i	−0.955320	+	0.295574i	$0.904489\pi$
$828$		0			0
$829$	−15.0000	−	8.66025i	−0.520972	−	0.300783i	0.216361	−	0.976314i	$-0.430581\pi$
$829$	−15.0000	−	8.66025i	−0.520972	−	0.300783i	−0.737332	+	0.675530i	$0.763915\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	37.0405			1.28338
$834$		0			0
$835$	−13.7477	−	23.8118i	−0.475760	−	0.824040i
$836$		0			0
$837$	35.7176	+	20.6216i	1.23458	+	0.712786i
$838$		0			0
$839$	−38.1051			−1.31553			−0.657767	−	0.753221i	$-0.728499\pi$
$839$	−38.1051			−1.31553			−0.657767	+	0.753221i	$0.728499\pi$
$840$		0			0
$841$	8.00000			0.275862
$842$		0			0
$843$	13.7477	+	7.93725i	0.473497	+	0.273374i
$844$		0			0
$845$	−1.32288	−	2.29129i	−0.0455083	−	0.0788227i
$846$		0			0
$847$			26.4575i			0.909091i
$848$		0			0
$849$	−31.7490	+	18.3303i	−1.08962	+	0.629094i
$850$		0			0
$851$	10.3923	+	6.00000i	0.356244	+	0.205677i
$852$		0			0
$853$			3.46410i			0.118609i	0.998240	+	0.0593043i	$0.0188882\pi$
$853$			3.46410i			0.118609i	−0.998240	+	0.0593043i	$0.981112\pi$
$854$		0			0
$855$		−	42.0000i		−	1.43637i
$856$		0			0
$857$	10.5830	−	18.3303i	0.361509	−	0.626151i	−0.626701	−	0.779260i	$-0.715595\pi$
$857$	10.5830	−	18.3303i	0.361509	−	0.626151i	0.988209	+	0.153109i	$0.0489285\pi$
$858$		0			0
$859$	−45.8258	+	26.4575i	−1.56355	+	0.902719i	−0.566662	+	0.823951i	$0.691765\pi$
$859$	−45.8258	+	26.4575i	−1.56355	+	0.902719i	−0.996893	+	0.0787681i	$0.974901\pi$
$860$		0			0
$861$	−42.0000	+	24.2487i	−1.43136	+	0.826394i
$862$		0			0
$863$	−22.5167	+	13.0000i	−0.766476	+	0.442525i	−0.831616	−	0.555351i	$-0.812584\pi$
$863$	−22.5167	+	13.0000i	−0.766476	+	0.442525i	0.0651400	+	0.997876i	$0.479251\pi$
$864$		0			0
$865$	14.0000	−	24.2487i	0.476014	−	0.824481i
$866$		0			0
$867$	−19.0526			−0.647059
$868$		0			0
$869$			4.58258i			0.155453i
$870$		0			0
$871$	−27.4955	−	15.8745i	−0.931648	−	0.537887i
$872$		0			0
$873$	−22.5000	+	12.9904i	−0.761510	+	0.439658i
$874$		0			0
$875$	18.1865	+	10.5000i	0.614817	+	0.354965i
$876$		0			0
$877$	−14.0000	−	24.2487i	−0.472746	−	0.818821i	0.526767	−	0.850010i	$-0.323404\pi$
$877$	−14.0000	−	24.2487i	−0.472746	−	0.818821i	−0.999514	+	0.0311889i	$0.990071\pi$
$878$		0			0
$879$	−2.29129	+	3.96863i	−0.0772832	+	0.133858i
$880$		0			0
$881$	−58.2065			−1.96103			−0.980514	−	0.196450i	$-0.937059\pi$
$881$	−58.2065			−1.96103			−0.980514	+	0.196450i	$0.937059\pi$
$882$		0			0
$883$	−18.3303			−0.616864			−0.308432	−	0.951246i	$-0.599804\pi$
$883$	−18.3303			−0.616864			−0.308432	+	0.951246i	$0.599804\pi$
$884$		0			0
$885$	−27.7804	+	48.1170i	−0.933828	+	1.61744i
$886$		0			0
$887$	15.5885	+	27.0000i	0.523409	+	0.906571i	0.999629	+	0.0272449i	$0.00867339\pi$
$887$	15.5885	+	27.0000i	0.523409	+	0.906571i	−0.476220	+	0.879326i	$0.657993\pi$
$888$		0			0
$889$	−31.5000	−	18.1865i	−1.05648	−	0.609957i
$890$		0			0
$891$	−7.79423	+	4.50000i	−0.261116	+	0.150756i
$892$		0			0
$893$	31.7490	+	18.3303i	1.06244	+	0.613400i
$894$		0			0
$895$			52.9150i			1.76875i
$896$		0			0
$897$	−12.0000			−0.400668
$898$		0			0
$899$	18.1865	−	31.5000i	0.606555	−	1.05058i
$900$		0			0
$901$	−21.0000	+	12.1244i	−0.699611	+	0.403921i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	47.6235	−	27.4955i	1.58306	−	0.913980i
$906$		0			0
$907$	4.58258	−	7.93725i	0.152162	−	0.263552i	−0.779860	−	0.625954i	$-0.784710\pi$
$907$	4.58258	−	7.93725i	0.152162	−	0.263552i	0.932022	+	0.362402i	$0.118043\pi$
$908$		0			0
$909$	−31.7490			−1.05305
$910$		0			0
$911$			32.0000i			1.06021i	0.847933	+	0.530104i	$0.177847\pi$
$911$			32.0000i			1.06021i	−0.847933	+	0.530104i	$0.822153\pi$
$912$		0			0
$913$	−1.50000	−	0.866025i	−0.0496428	−	0.0286613i
$914$		0			0
$915$	−54.9909	+	31.7490i	−1.81794	+	1.04959i
$916$		0			0
$917$			13.7477i			0.453990i
$918$		0			0
$919$	18.3303	+	31.7490i	0.604661	+	1.04730i	0.992105	+	0.125410i	$0.0400247\pi$
$919$	18.3303	+	31.7490i	0.604661	+	1.04730i	−0.387444	+	0.921893i	$0.626642\pi$
$920$		0			0
$921$	−7.93725	−	4.58258i	−0.261541	−	0.151001i
$922$		0			0
$923$	13.8564			0.456089
$924$		0			0
$925$	12.0000			0.394558
$926$		0			0
$927$	−41.2432	−	23.8118i	−1.35460	−	0.782081i
$928$		0			0
$929$	26.4575	+	45.8258i	0.868043	+	1.50349i	0.863994	+	0.503503i	$0.167956\pi$
$929$	26.4575	+	45.8258i	0.868043	+	1.50349i	0.00404909	+	0.999992i	$0.498711\pi$
$930$		0			0
$931$	−32.0780	−	18.5203i	−1.05131	−	0.606977i
$932$		0			0
$933$	24.0000	+	41.5692i	0.785725	+	1.36092i
$934$		0			0
$935$	−12.1244	−	7.00000i	−0.396509	−	0.228924i
$936$		0			0
$937$			8.66025i			0.282918i	0.989944	+	0.141459i	$0.0451794\pi$
$937$			8.66025i			0.282918i	−0.989944	+	0.141459i	$0.954821\pi$
$938$		0			0
$939$		−	39.0000i		−	1.27272i
$940$		0			0
$941$	14.5516	−	25.2042i	0.474370	−	0.821632i	−0.525200	−	0.850979i	$-0.676009\pi$
$941$	14.5516	−	25.2042i	0.474370	−	0.821632i	0.999569	+	0.0293467i	$0.00934269\pi$
$942$		0			0
$943$	−18.3303	+	10.5830i	−0.596917	+	0.344630i
$944$		0			0
$945$		−	36.3731i		−	1.18322i
$946$		0			0
$947$	38.1051	−	22.0000i	1.23825	−	0.714904i	0.269514	−	0.962997i	$-0.413137\pi$
$947$	38.1051	−	22.0000i	1.23825	−	0.714904i	0.968736	+	0.248093i	$0.0798037\pi$
$948$		0			0
$949$	12.0000	−	20.7846i	0.389536	−	0.674697i
$950$		0			0
$951$		−	23.8118i		−	0.772149i
$952$		0			0
$953$		−	36.6606i		−	1.18755i	−0.804630	−	0.593777i	$-0.797636\pi$
$953$		−	36.6606i		−	1.18755i	0.804630	−	0.593777i	$-0.202364\pi$
$954$		0			0
$955$	−36.6606	−	21.1660i	−1.18631	−	0.684916i
$956$		0			0
$957$	3.96863	+	6.87386i	0.128287	+	0.222200i
$958$		0			0
$959$	−12.1244	−	21.0000i	−0.391516	−	0.678125i
$960$		0			0
$961$	16.0000	+	27.7128i	0.516129	+	0.893962i
$962$		0			0
$963$	12.9904	+	7.50000i	0.418609	+	0.241684i
$964$		0			0
$965$	55.5608			1.78856
$966$		0			0
$967$	22.9129			0.736828			0.368414	−	0.929662i	$-0.379901\pi$
$967$	22.9129			0.736828			0.368414	+	0.929662i	$0.379901\pi$
$968$		0			0
$969$	42.0000	+	24.2487i	1.34923	+	0.778981i
$970$		0			0
$971$	−26.8468	−	46.5000i	−0.861554	−	1.49226i	−0.870428	−	0.492295i	$-0.836158\pi$
$971$	−26.8468	−	46.5000i	−0.861554	−	1.49226i	0.00887379	−	0.999961i	$-0.497175\pi$
$972$		0			0
$973$	21.0000	−	36.3731i	0.673229	−	1.16607i
$974$		0			0
$975$	−10.3923	+	6.00000i	−0.332820	+	0.192154i
$976$		0			0
$977$	−31.7490	−	18.3303i	−1.01574	−	0.586438i	−0.102874	−	0.994694i	$-0.532804\pi$
$977$	−31.7490	−	18.3303i	−1.01574	−	0.586438i	−0.912867	+	0.408256i	$0.866137\pi$
$978$		0			0
$979$		−	5.29150i		−	0.169117i
$980$		0			0
$981$	42.0000			1.34096
$982$		0			0
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$		0			0
$985$	−21.0000	+	12.1244i	−0.669116	+	0.386314i
$986$		0			0
$987$	27.4955	+	15.8745i	0.875190	+	0.505291i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−2.29129	+	3.96863i	−0.0727852	+	0.126068i	−0.900121	−	0.435640i	$-0.856522\pi$
$991$	−2.29129	+	3.96863i	−0.0727852	+	0.126068i	0.827336	+	0.561708i	$0.189855\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			14.0000i			0.443830i
$996$		0			0
$997$	15.0000	+	8.66025i	0.475055	+	0.274273i	0.718353	−	0.695678i	$-0.244896\pi$
$997$	15.0000	+	8.66025i	0.475055	+	0.274273i	−0.243299	+	0.969951i	$0.578229\pi$
$998$		0			0
$999$	15.5885	+	27.0000i	0.493197	+	0.854242i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bc.c.353.3	yes	8
3.2	odd	2	inner	672.2.bc.c.353.2	yes	8
4.3	odd	2	inner	672.2.bc.c.353.1	yes	8
7.5	odd	6	inner	672.2.bc.c.257.2	yes	8
12.11	even	2	inner	672.2.bc.c.353.4	yes	8
21.5	even	6	inner	672.2.bc.c.257.3	yes	8
28.19	even	6	inner	672.2.bc.c.257.4	yes	8
84.47	odd	6	inner	672.2.bc.c.257.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bc.c.257.1	✓	8	84.47	odd	6	inner
672.2.bc.c.257.2	yes	8	7.5	odd	6	inner
672.2.bc.c.257.3	yes	8	21.5	even	6	inner
672.2.bc.c.257.4	yes	8	28.19	even	6	inner
672.2.bc.c.353.1	yes	8	4.3	odd	2	inner
672.2.bc.c.353.2	yes	8	3.2	odd	2	inner
672.2.bc.c.353.3	yes	8	1.1	even	1	trivial
672.2.bc.c.353.4	yes	8	12.11	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{3} +(-1.32288 - 2.29129i) q^{5} +(-2.29129 - 1.32288i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(0.866025 + 0.500000i) q^{11} +3.46410i q^{13} -4.58258 q^{15} +(2.64575 - 4.58258i) q^{17} +(-4.58258 + 2.64575i) q^{19} +(-3.96863 + 2.29129i) q^{21} +(-1.73205 + 1.00000i) q^{23} +(-1.00000 + 1.73205i) q^{25} -5.19615 q^{27} +4.58258i q^{29} +(-6.87386 - 3.96863i) q^{31} +(1.50000 - 0.866025i) q^{33} +7.00000i q^{35} +(-3.00000 - 5.19615i) q^{37} +(5.19615 + 3.00000i) q^{39} +10.5830 q^{41} +(-3.96863 + 6.87386i) q^{45} +(-3.46410 - 6.00000i) q^{47} +(3.50000 + 6.06218i) q^{49} +(-4.58258 - 7.93725i) q^{51} +(-3.96863 - 2.29129i) q^{53} -2.64575i q^{55} +9.16515i q^{57} +(6.06218 - 10.5000i) q^{59} +(12.0000 - 6.92820i) q^{61} +7.93725i q^{63} +(7.93725 - 4.58258i) q^{65} +(-4.58258 + 7.93725i) q^{67} +3.46410i q^{69} -4.00000i q^{71} +(-6.00000 - 3.46410i) q^{73} +(1.73205 + 3.00000i) q^{75} +(-1.32288 - 2.29129i) q^{77} +(2.29129 + 3.96863i) q^{79} +(-4.50000 + 7.79423i) q^{81} -1.73205 q^{83} -14.0000 q^{85} +(6.87386 + 3.96863i) q^{87} +(-2.64575 - 4.58258i) q^{89} +(4.58258 - 7.93725i) q^{91} +(-11.9059 + 6.87386i) q^{93} +(12.1244 + 7.00000i) q^{95} -8.66025i q^{97} -3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{9} - 8 q^{25} + 12 q^{33} - 24 q^{37} + 28 q^{49} + 96 q^{61} - 48 q^{73} - 36 q^{81} - 112 q^{85}+O(q^{100}) \) 8 * q - 12 * q^9 - 8 * q^25 + 12 * q^33 - 24 * q^37 + 28 * q^49 + 96 * q^61 - 48 * q^73 - 36 * q^81 - 112 * q^85

Introduction

L-functions

Modular forms

Varieties

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Database

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