LMFDB - Embedded newform 420.2.q.c.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(121,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("420.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.q (of order $3$, degree $2$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	420.361
Dual form			420.2.q.c.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.822876 - 1.42526i) q^{11} -2.64575 q^{13} +1.00000 q^{15} +(0.822876 - 1.42526i) q^{17} +(-4.14575 - 7.18065i) q^{19} +2.64575 q^{21} +(-0.822876 - 1.42526i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +7.64575 q^{29} +(2.14575 - 3.71655i) q^{31} +(0.822876 + 1.42526i) q^{33} +(-1.32288 + 2.29129i) q^{35} +(-0.322876 - 0.559237i) q^{37} +(1.32288 - 2.29129i) q^{39} +4.93725 q^{41} -5.93725 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(0.822876 + 1.42526i) q^{51} +(-1.64575 + 2.85052i) q^{53} -1.64575 q^{55} +8.29150 q^{57} +(-5.46863 + 9.47194i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-1.32288 + 2.29129i) q^{63} +(1.32288 + 2.29129i) q^{65} +(-0.322876 + 0.559237i) q^{67} +1.64575 q^{69} +13.6458 q^{71} +(-6.61438 + 11.4564i) q^{73} +(-0.500000 - 0.866025i) q^{75} -4.35425 q^{77} +(-1.14575 - 1.98450i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.9373 q^{83} -1.64575 q^{85} +(-3.82288 + 6.62141i) q^{87} +(7.11438 + 12.3225i) q^{89} +(3.50000 + 6.06218i) q^{91} +(2.14575 + 3.71655i) q^{93} +(-4.14575 + 7.18065i) q^{95} +8.00000 q^{97} -1.64575 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9} - 2 q^{11} + 4 q^{15} - 2 q^{17} - 6 q^{19} + 2 q^{23} - 2 q^{25} + 4 q^{27} + 20 q^{29} - 2 q^{31} - 2 q^{33} + 4 q^{37} - 12 q^{41} + 8 q^{43} - 2 q^{45} - 12 q^{47} - 14 q^{49} - 2 q^{51} + 4 q^{53} + 4 q^{55} + 12 q^{57} - 6 q^{59} - 16 q^{61} + 4 q^{67} - 4 q^{69} + 44 q^{71} - 2 q^{75} - 28 q^{77} + 6 q^{79} - 2 q^{81} - 12 q^{83} + 4 q^{85} - 10 q^{87} + 2 q^{89} + 14 q^{91} - 2 q^{93} - 6 q^{95} + 32 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9 - 2 * q^11 + 4 * q^15 - 2 * q^17 - 6 * q^19 + 2 * q^23 - 2 * q^25 + 4 * q^27 + 20 * q^29 - 2 * q^31 - 2 * q^33 + 4 * q^37 - 12 * q^41 + 8 * q^43 - 2 * q^45 - 12 * q^47 - 14 * q^49 - 2 * q^51 + 4 * q^53 + 4 * q^55 + 12 * q^57 - 6 * q^59 - 16 * q^61 + 4 * q^67 - 4 * q^69 + 44 * q^71 - 2 * q^75 - 28 * q^77 + 6 * q^79 - 2 * q^81 - 12 * q^83 + 4 * q^85 - 10 * q^87 + 2 * q^89 + 14 * q^91 - 2 * q^93 - 6 * q^95 + 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$7$	−1.32288	−	2.29129i	−0.500000	−	0.866025i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.822876	−	1.42526i	0.248106	−	0.429733i	−0.714894	−	0.699233i	$-0.753525\pi$
$11$	0.822876	−	1.42526i	0.248106	−	0.429733i	0.963000	+	0.269500i	$0.0868584\pi$
$12$		0			0
$13$	−2.64575			−0.733799			−0.366900	−	0.930261i	$-0.619581\pi$
$13$	−2.64575			−0.733799			−0.366900	+	0.930261i	$0.619581\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	0.822876	−	1.42526i	0.199577	−	0.345677i	−0.748815	−	0.662780i	$-0.769377\pi$
$17$	0.822876	−	1.42526i	0.199577	−	0.345677i	0.948391	+	0.317103i	$0.102710\pi$
$18$		0			0
$19$	−4.14575	−	7.18065i	−0.951101	−	1.64735i	−0.743049	−	0.669237i	$-0.766621\pi$
$19$	−4.14575	−	7.18065i	−0.951101	−	1.64735i	−0.208051	−	0.978118i	$-0.566712\pi$
$20$		0			0
$21$	2.64575			0.577350
$22$		0			0
$23$	−0.822876	−	1.42526i	−0.171581	−	0.297188i	0.767391	−	0.641179i	$-0.221554\pi$
$23$	−0.822876	−	1.42526i	−0.171581	−	0.297188i	−0.938973	+	0.343991i	$0.888221\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	7.64575			1.41978			0.709890	−	0.704312i	$-0.248745\pi$
$29$	7.64575			1.41978			0.709890	+	0.704312i	$0.248745\pi$
$30$		0			0
$31$	2.14575	−	3.71655i	0.385388	−	0.667512i	−0.606435	−	0.795133i	$-0.707401\pi$
$31$	2.14575	−	3.71655i	0.385388	−	0.667512i	0.991823	+	0.127621i	$0.0407342\pi$
$32$		0			0
$33$	0.822876	+	1.42526i	0.143244	+	0.248106i
$34$		0			0
$35$	−1.32288	+	2.29129i	−0.223607	+	0.387298i
$36$		0			0
$37$	−0.322876	−	0.559237i	−0.0530804	−	0.0919380i	0.838264	−	0.545264i	$-0.183571\pi$
$37$	−0.322876	−	0.559237i	−0.0530804	−	0.0919380i	−0.891345	+	0.453326i	$0.850237\pi$
$38$		0			0
$39$	1.32288	−	2.29129i	0.211830	−	0.366900i
$40$		0			0
$41$	4.93725			0.771070			0.385535	−	0.922693i	$-0.374017\pi$
$41$	4.93725			0.771070			0.385535	+	0.922693i	$0.374017\pi$
$42$		0			0
$43$	−5.93725			−0.905423			−0.452711	−	0.891657i	$-0.649543\pi$
$43$	−5.93725			−0.905423			−0.452711	+	0.891657i	$0.649543\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$		0			0
$51$	0.822876	+	1.42526i	0.115226	+	0.199577i
$52$		0			0
$53$	−1.64575	+	2.85052i	−0.226061	+	0.391550i	−0.956637	−	0.291282i	$-0.905918\pi$
$53$	−1.64575	+	2.85052i	−0.226061	+	0.391550i	0.730576	+	0.682831i	$0.239252\pi$
$54$		0			0
$55$	−1.64575			−0.221913
$56$		0			0
$57$	8.29150			1.09824
$58$		0			0
$59$	−5.46863	+	9.47194i	−0.711955	+	1.23314i	0.252168	+	0.967684i	$0.418856\pi$
$59$	−5.46863	+	9.47194i	−0.711955	+	1.23314i	−0.964122	+	0.265458i	$0.914477\pi$
$60$		0			0
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$		0			0
$63$	−1.32288	+	2.29129i	−0.166667	+	0.288675i
$64$		0			0
$65$	1.32288	+	2.29129i	0.164083	+	0.284199i
$66$		0			0
$67$	−0.322876	+	0.559237i	−0.0394455	+	0.0683217i	−0.885074	−	0.465450i	$-0.845892\pi$
$67$	−0.322876	+	0.559237i	−0.0394455	+	0.0683217i	0.845629	+	0.533772i	$0.179226\pi$
$68$		0			0
$69$	1.64575			0.198125
$70$		0			0
$71$	13.6458			1.61945			0.809726	−	0.586808i	$-0.199616\pi$
$71$	13.6458			1.61945			0.809726	+	0.586808i	$0.199616\pi$
$72$		0			0
$73$	−6.61438	+	11.4564i	−0.774154	+	1.34087i	0.161114	+	0.986936i	$0.448491\pi$
$73$	−6.61438	+	11.4564i	−0.774154	+	1.34087i	−0.935269	+	0.353939i	$0.884842\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	−4.35425			−0.496213
$78$		0			0
$79$	−1.14575	−	1.98450i	−0.128907	−	0.223274i	0.794346	−	0.607465i	$-0.207814\pi$
$79$	−1.14575	−	1.98450i	−0.128907	−	0.223274i	−0.923253	+	0.384192i	$0.874480\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−10.9373			−1.20052			−0.600260	−	0.799805i	$-0.704936\pi$
$83$	−10.9373			−1.20052			−0.600260	+	0.799805i	$0.704936\pi$
$84$		0			0
$85$	−1.64575			−0.178507
$86$		0			0
$87$	−3.82288	+	6.62141i	−0.409855	+	0.709890i
$88$		0			0
$89$	7.11438	+	12.3225i	0.754123	+	1.30618i	0.945809	+	0.324722i	$0.105271\pi$
$89$	7.11438	+	12.3225i	0.754123	+	1.30618i	−0.191687	+	0.981456i	$0.561396\pi$
$90$		0			0
$91$	3.50000	+	6.06218i	0.366900	+	0.635489i
$92$		0			0
$93$	2.14575	+	3.71655i	0.222504	+	0.385388i
$94$		0			0
$95$	−4.14575	+	7.18065i	−0.425345	+	0.736719i
$96$		0			0
$97$	8.00000			0.812277			0.406138	−	0.913812i	$-0.366875\pi$
$97$	8.00000			0.812277			0.406138	+	0.913812i	$0.366875\pi$
$98$		0			0
$99$	−1.64575			−0.165404
$100$		0			0
$101$	2.46863	−	4.27579i	0.245638	−	0.425457i	−0.716673	−	0.697409i	$-0.754336\pi$
$101$	2.46863	−	4.27579i	0.245638	−	0.425457i	0.962311	+	0.271953i	$0.0876694\pi$
$102$		0			0
$103$	−4.67712	−	8.10102i	−0.460851	−	0.798217i	0.538153	−	0.842847i	$-0.319122\pi$
$103$	−4.67712	−	8.10102i	−0.460851	−	0.798217i	−0.999004	+	0.0446304i	$0.985789\pi$
$104$		0			0
$105$	−1.32288	−	2.29129i	−0.129099	−	0.223607i
$106$		0			0
$107$	8.46863	+	14.6681i	0.818693	+	1.41802i	0.906645	+	0.421893i	$0.138634\pi$
$107$	8.46863	+	14.6681i	0.818693	+	1.41802i	−0.0879524	+	0.996125i	$0.528032\pi$
$108$		0			0
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	−0.366415	−	0.930451i	$-0.619415\pi$
$109$	6.50000	−	11.2583i	0.622587	−	1.07835i	0.989002	−	0.147901i	$-0.0472517\pi$
$110$		0			0
$111$	0.645751			0.0612920
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	−0.822876	+	1.42526i	−0.0767336	+	0.132906i
$116$		0			0
$117$	1.32288	+	2.29129i	0.122300	+	0.211830i
$118$		0			0
$119$	−4.35425			−0.399153
$120$		0			0
$121$	4.14575	+	7.18065i	0.376886	+	0.652787i
$122$		0			0
$123$	−2.46863	+	4.27579i	−0.222589	+	0.385535i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−2.06275			−0.183039			−0.0915196	−	0.995803i	$-0.529172\pi$
$127$	−2.06275			−0.183039			−0.0915196	+	0.995803i	$0.529172\pi$
$128$		0			0
$129$	2.96863	−	5.14181i	0.261373	−	0.452711i
$130$		0			0
$131$	−10.6458	−	18.4390i	−0.930124	−	1.61102i	−0.783107	−	0.621887i	$-0.786366\pi$
$131$	−10.6458	−	18.4390i	−0.930124	−	1.61102i	−0.147017	−	0.989134i	$-0.546967\pi$
$132$		0			0
$133$	−10.9686	+	18.9982i	−0.951101	+	1.64735i
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	10.1144	−	17.5186i	0.864130	−	1.49672i	−0.00377913	−	0.999993i	$-0.501203\pi$
$137$	10.1144	−	17.5186i	0.864130	−	1.49672i	0.867909	−	0.496724i	$-0.165464\pi$
$138$		0			0
$139$	5.00000			0.424094			0.212047	−	0.977259i	$-0.431987\pi$
$139$	5.00000			0.424094			0.212047	+	0.977259i	$0.431987\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	−2.17712	+	3.77089i	−0.182060	+	0.315338i
$144$		0			0
$145$	−3.82288	−	6.62141i	−0.317473	−	0.549879i
$146$		0			0
$147$	−3.50000	−	6.06218i	−0.288675	−	0.500000i
$148$		0			0
$149$	3.29150	+	5.70105i	0.269650	+	0.467048i	0.968772	−	0.247955i	$-0.0797585\pi$
$149$	3.29150	+	5.70105i	0.269650	+	0.467048i	−0.699121	+	0.715003i	$0.746425\pi$
$150$		0			0
$151$	2.29150	−	3.96900i	0.186480	−	0.322993i	−0.757594	−	0.652726i	$-0.773625\pi$
$151$	2.29150	−	3.96900i	0.186480	−	0.322993i	0.944074	+	0.329733i	$0.106959\pi$
$152$		0			0
$153$	−1.64575			−0.133051
$154$		0			0
$155$	−4.29150			−0.344702
$156$		0			0
$157$	0.645751	−	1.11847i	0.0515366	−	0.0892639i	−0.839106	−	0.543968i	$-0.816921\pi$
$157$	0.645751	−	1.11847i	0.0515366	−	0.0892639i	0.890643	+	0.454704i	$0.150255\pi$
$158$		0			0
$159$	−1.64575	−	2.85052i	−0.130517	−	0.226061i
$160$		0			0
$161$	−2.17712	+	3.77089i	−0.171581	+	0.297188i
$162$		0			0
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	0.988227	+	0.152992i	$0.0488907\pi$
$163$	8.00000	+	13.8564i	0.626608	+	1.08532i	−0.361619	+	0.932326i	$0.617776\pi$
$164$		0			0
$165$	0.822876	−	1.42526i	0.0640608	−	0.110957i
$166$		0			0
$167$	19.6458			1.52023			0.760117	−	0.649786i	$-0.225142\pi$
$167$	19.6458			1.52023			0.760117	+	0.649786i	$0.225142\pi$
$168$		0			0
$169$	−6.00000			−0.461538
$170$		0			0
$171$	−4.14575	+	7.18065i	−0.317034	+	0.549118i
$172$		0			0
$173$	−4.93725	−	8.55157i	−0.375372	−	0.650164i	0.615010	−	0.788519i	$-0.289152\pi$
$173$	−4.93725	−	8.55157i	−0.375372	−	0.650164i	−0.990383	+	0.138355i	$0.955819\pi$
$174$		0			0
$175$	2.64575			0.200000
$176$		0			0
$177$	−5.46863	−	9.47194i	−0.411047	−	0.711955i
$178$		0			0
$179$	−0.291503	+	0.504897i	−0.0217879	+	0.0377378i	−0.876714	−	0.481012i	$-0.840269\pi$
$179$	−0.291503	+	0.504897i	−0.0217879	+	0.0377378i	0.854926	+	0.518750i	$0.173603\pi$
$180$		0			0
$181$	−4.29150			−0.318985			−0.159492	−	0.987199i	$-0.550986\pi$
$181$	−4.29150			−0.318985			−0.159492	+	0.987199i	$0.550986\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$		0			0
$185$	−0.322876	+	0.559237i	−0.0237383	+	0.0411159i
$186$		0			0
$187$	−1.35425	−	2.34563i	−0.0990325	−	0.171529i
$188$		0			0
$189$	−1.32288	−	2.29129i	−0.0962250	−	0.166667i
$190$		0			0
$191$	−9.58301	−	16.5983i	−0.693402	−	1.20101i	−0.970716	−	0.240228i	$-0.922778\pi$
$191$	−9.58301	−	16.5983i	−0.693402	−	1.20101i	0.277315	−	0.960779i	$-0.410556\pi$
$192$		0			0
$193$	4.03137	−	6.98254i	0.290185	−	0.502614i	−0.683669	−	0.729793i	$-0.739617\pi$
$193$	4.03137	−	6.98254i	0.290185	−	0.502614i	0.973853	+	0.227178i	$0.0729500\pi$
$194$		0			0
$195$	−2.64575			−0.189466
$196$		0			0
$197$	−4.93725			−0.351765			−0.175882	−	0.984411i	$-0.556278\pi$
$197$	−4.93725			−0.351765			−0.175882	+	0.984411i	$0.556278\pi$
$198$		0			0
$199$	11.5830	−	20.0624i	0.821097	−	1.42218i	−0.0837682	−	0.996485i	$-0.526696\pi$
$199$	11.5830	−	20.0624i	0.821097	−	1.42218i	0.904866	−	0.425697i	$-0.139971\pi$
$200$		0			0
$201$	−0.322876	−	0.559237i	−0.0227739	−	0.0394455i
$202$		0			0
$203$	−10.1144	−	17.5186i	−0.709890	−	1.22957i
$204$		0			0
$205$	−2.46863	−	4.27579i	−0.172416	−	0.298634i
$206$		0			0
$207$	−0.822876	+	1.42526i	−0.0571938	+	0.0990626i
$208$		0			0
$209$	−13.6458			−0.943896
$210$		0			0
$211$	8.58301			0.590878			0.295439	−	0.955362i	$-0.404534\pi$
$211$	8.58301			0.590878			0.295439	+	0.955362i	$0.404534\pi$
$212$		0			0
$213$	−6.82288	+	11.8176i	−0.467496	+	0.809726i
$214$		0			0
$215$	2.96863	+	5.14181i	0.202459	+	0.350669i
$216$		0			0
$217$	−11.3542			−0.770777
$218$		0			0
$219$	−6.61438	−	11.4564i	−0.446958	−	0.774154i
$220$		0			0
$221$	−2.17712	+	3.77089i	−0.146449	+	0.253658i
$222$		0			0
$223$	17.8745			1.19697			0.598483	−	0.801136i	$-0.295770\pi$
$223$	17.8745			1.19697			0.598483	+	0.801136i	$0.295770\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−9.82288	+	17.0137i	−0.651967	+	1.12924i	0.330678	+	0.943744i	$0.392723\pi$
$227$	−9.82288	+	17.0137i	−0.651967	+	1.12924i	−0.982645	+	0.185497i	$0.940611\pi$
$228$		0			0
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	0.958187	−	0.286143i	$-0.0923732\pi$
$229$	3.50000	+	6.06218i	0.231287	+	0.400600i	−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	2.17712	−	3.77089i	0.143244	−	0.248106i
$232$		0			0
$233$	−10.6458	−	18.4390i	−0.697426	−	1.20798i	−0.969356	−	0.245661i	$-0.920995\pi$
$233$	−10.6458	−	18.4390i	−0.697426	−	1.20798i	0.271930	−	0.962317i	$-0.412338\pi$
$234$		0			0
$235$	−3.00000	+	5.19615i	−0.195698	+	0.338960i
$236$		0			0
$237$	2.29150			0.148849
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	6.35425	−	11.0059i	0.409313	−	0.708951i	−0.585500	−	0.810673i	$-0.699102\pi$
$241$	6.35425	−	11.0059i	0.409313	−	0.708951i	0.994813	+	0.101721i	$0.0324350\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	7.00000			0.447214
$246$		0			0
$247$	10.9686	+	18.9982i	0.697917	+	1.20883i
$248$		0			0
$249$	5.46863	−	9.47194i	0.346560	−	0.600260i
$250$		0			0
$251$	−10.9373			−0.690353			−0.345177	−	0.938538i	$-0.612181\pi$
$251$	−10.9373			−0.690353			−0.345177	+	0.938538i	$0.612181\pi$
$252$		0			0
$253$	−2.70850			−0.170282
$254$		0			0
$255$	0.822876	−	1.42526i	0.0515305	−	0.0892534i
$256$		0			0
$257$	−2.76013	−	4.78068i	−0.172172	−	0.298211i	0.767007	−	0.641639i	$-0.221745\pi$
$257$	−2.76013	−	4.78068i	−0.172172	−	0.298211i	−0.939179	+	0.343428i	$0.888412\pi$
$258$		0			0
$259$	−0.854249	+	1.47960i	−0.0530804	+	0.0919380i
$260$		0			0
$261$	−3.82288	−	6.62141i	−0.236630	−	0.409855i
$262$		0			0
$263$	14.2288	−	24.6449i	0.877383	−	1.51967i	0.0231800	−	0.999731i	$-0.492621\pi$
$263$	14.2288	−	24.6449i	0.877383	−	1.51967i	0.854203	−	0.519940i	$-0.174046\pi$
$264$		0			0
$265$	3.29150			0.202195
$266$		0			0
$267$	−14.2288			−0.870786
$268$		0			0
$269$	−13.9373	+	24.1400i	−0.849769	+	1.47184i	0.0316446	+	0.999499i	$0.489926\pi$
$269$	−13.9373	+	24.1400i	−0.849769	+	1.47184i	−0.881414	+	0.472345i	$0.843408\pi$
$270$		0			0
$271$	−3.70850	−	6.42331i	−0.225275	−	0.390188i	0.731127	−	0.682242i	$-0.238995\pi$
$271$	−3.70850	−	6.42331i	−0.225275	−	0.390188i	−0.956402	+	0.292054i	$0.905661\pi$
$272$		0			0
$273$	−7.00000			−0.423659
$274$		0			0
$275$	0.822876	+	1.42526i	0.0496213	+	0.0859466i
$276$		0			0
$277$	10.3229	−	17.8797i	0.620241	−	1.07429i	−0.369199	−	0.929350i	$-0.620368\pi$
$277$	10.3229	−	17.8797i	0.620241	−	1.07429i	0.989441	−	0.144939i	$-0.0462987\pi$
$278$		0			0
$279$	−4.29150			−0.256926
$280$		0			0
$281$	24.0000			1.43172			0.715860	−	0.698244i	$-0.246035\pi$
$281$	24.0000			1.43172			0.715860	+	0.698244i	$0.246035\pi$
$282$		0			0
$283$	7.32288	−	12.6836i	0.435300	−	0.753961i	−0.562020	−	0.827123i	$-0.689976\pi$
$283$	7.32288	−	12.6836i	0.435300	−	0.753961i	0.997320	+	0.0731621i	$0.0233091\pi$
$284$		0			0
$285$	−4.14575	−	7.18065i	−0.245573	−	0.425345i
$286$		0			0
$287$	−6.53137	−	11.3127i	−0.385535	−	0.667766i
$288$		0			0
$289$	7.14575	+	12.3768i	0.420338	+	0.728047i
$290$		0			0
$291$	−4.00000	+	6.92820i	−0.234484	+	0.406138i
$292$		0			0
$293$		0			0			−	1.00000i	$-0.5\pi$
$293$		0			0				1.00000i	$0.5\pi$
$294$		0			0
$295$	10.9373			0.636792
$296$		0			0
$297$	0.822876	−	1.42526i	0.0477481	−	0.0827021i
$298$		0			0
$299$	2.17712	+	3.77089i	0.125906	+	0.218076i
$300$		0			0
$301$	7.85425	+	13.6040i	0.452711	+	0.784119i
$302$		0			0
$303$	2.46863	+	4.27579i	0.141819	+	0.245638i
$304$		0			0
$305$	−4.00000	+	6.92820i	−0.229039	+	0.396708i
$306$		0			0
$307$	27.9373			1.59446			0.797232	−	0.603674i	$-0.206297\pi$
$307$	27.9373			1.59446			0.797232	+	0.603674i	$0.206297\pi$
$308$		0			0
$309$	9.35425			0.532145
$310$		0			0
$311$	−6.82288	+	11.8176i	−0.386890	+	0.670113i	−0.992029	−	0.126007i	$-0.959784\pi$
$311$	−6.82288	+	11.8176i	−0.386890	+	0.670113i	0.605140	+	0.796119i	$0.293117\pi$
$312$		0			0
$313$	10.6144	+	18.3846i	0.599960	+	1.03916i	0.992826	+	0.119566i	$0.0381502\pi$
$313$	10.6144	+	18.3846i	0.599960	+	1.03916i	−0.392866	+	0.919596i	$0.628516\pi$
$314$		0			0
$315$	2.64575			0.149071
$316$		0			0
$317$	−11.7601	−	20.3691i	−0.660515	−	1.14404i	−0.980481	−	0.196616i	$-0.937005\pi$
$317$	−11.7601	−	20.3691i	−0.660515	−	1.14404i	0.319966	−	0.947429i	$-0.396329\pi$
$318$		0			0
$319$	6.29150	−	10.8972i	0.352257	−	0.610126i
$320$		0			0
$321$	−16.9373			−0.945345
$322$		0			0
$323$	−13.6458			−0.759270
$324$		0			0
$325$	1.32288	−	2.29129i	0.0733799	−	0.127098i
$326$		0			0
$327$	6.50000	+	11.2583i	0.359451	+	0.622587i
$328$		0			0
$329$	−7.93725	+	13.7477i	−0.437595	+	0.757937i
$330$		0			0
$331$	10.0830	+	17.4643i	0.554212	+	0.959923i	0.997964	+	0.0637740i	$0.0203137\pi$
$331$	10.0830	+	17.4643i	0.554212	+	0.959923i	−0.443752	+	0.896149i	$0.646353\pi$
$332$		0			0
$333$	−0.322876	+	0.559237i	−0.0176935	+	0.0306460i
$334$		0			0
$335$	0.645751			0.0352812
$336$		0			0
$337$	−33.2288			−1.81009			−0.905043	−	0.425320i	$-0.860161\pi$
$337$	−33.2288			−1.81009			−0.905043	+	0.425320i	$0.860161\pi$
$338$		0			0
$339$	−3.00000	+	5.19615i	−0.162938	+	0.282216i
$340$		0			0
$341$	−3.53137	−	6.11652i	−0.191235	−	0.331228i
$342$		0			0
$343$	18.5203			1.00000
$344$		0			0
$345$	−0.822876	−	1.42526i	−0.0443021	−	0.0767336i
$346$		0			0
$347$	−6.58301	+	11.4021i	−0.353394	+	0.612097i	−0.986842	−	0.161689i	$-0.948306\pi$
$347$	−6.58301	+	11.4021i	−0.353394	+	0.612097i	0.633448	+	0.773786i	$0.281639\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$	−2.64575			−0.141220
$352$		0			0
$353$	18.0516	−	31.2663i	0.960791	−	1.66414i	0.240271	−	0.970706i	$-0.422764\pi$
$353$	18.0516	−	31.2663i	0.960791	−	1.66414i	0.720520	−	0.693434i	$-0.243903\pi$
$354$		0			0
$355$	−6.82288	−	11.8176i	−0.362121	−	0.627211i
$356$		0			0
$357$	2.17712	−	3.77089i	0.115226	−	0.199577i
$358$		0			0
$359$	10.4059	+	18.0235i	0.549201	+	0.951245i	0.998329	+	0.0577773i	$0.0184013\pi$
$359$	10.4059	+	18.0235i	0.549201	+	0.951245i	−0.449128	+	0.893467i	$0.648265\pi$
$360$		0			0
$361$	−24.8745	+	43.0839i	−1.30918	+	2.26757i
$362$		0			0
$363$	−8.29150			−0.435191
$364$		0			0
$365$	13.2288			0.692425
$366$		0			0
$367$	−3.61438	+	6.26029i	−0.188669	+	0.326784i	−0.944807	−	0.327628i	$-0.893751\pi$
$367$	−3.61438	+	6.26029i	−0.188669	+	0.326784i	0.756138	+	0.654413i	$0.227084\pi$
$368$		0			0
$369$	−2.46863	−	4.27579i	−0.128512	−	0.222589i
$370$		0			0
$371$	8.70850			0.452123
$372$		0			0
$373$	−0.0313730	−	0.0543397i	−0.00162443	−	0.00281360i	0.865212	−	0.501406i	$-0.167184\pi$
$373$	−0.0313730	−	0.0543397i	−0.00162443	−	0.00281360i	−0.866836	+	0.498593i	$0.833850\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	−20.2288			−1.04183
$378$		0			0
$379$	−15.7085			−0.806891			−0.403446	−	0.915004i	$-0.632188\pi$
$379$	−15.7085			−0.806891			−0.403446	+	0.915004i	$0.632188\pi$
$380$		0			0
$381$	1.03137	−	1.78639i	0.0528388	−	0.0915196i
$382$		0			0
$383$	13.6458	+	23.6351i	0.697265	+	1.20770i	0.969411	+	0.245443i	$0.0789334\pi$
$383$	13.6458	+	23.6351i	0.697265	+	1.20770i	−0.272146	+	0.962256i	$0.587733\pi$
$384$		0			0
$385$	2.17712	+	3.77089i	0.110957	+	0.192182i
$386$		0			0
$387$	2.96863	+	5.14181i	0.150904	+	0.261373i
$388$		0			0
$389$	0.239870	−	0.415468i	0.0121619	−	0.0210651i	−0.859880	−	0.510496i	$-0.829462\pi$
$389$	0.239870	−	0.415468i	0.0121619	−	0.0210651i	0.872042	+	0.489430i	$0.162795\pi$
$390$		0			0
$391$	−2.70850			−0.136975
$392$		0			0
$393$	21.2915			1.07401
$394$		0			0
$395$	−1.14575	+	1.98450i	−0.0576490	+	0.0998510i
$396$		0			0
$397$	5.67712	+	9.83307i	0.284927	+	0.493508i	0.972591	−	0.232521i	$-0.0746974\pi$
$397$	5.67712	+	9.83307i	0.284927	+	0.493508i	−0.687665	+	0.726028i	$0.741364\pi$
$398$		0			0
$399$	−10.9686	−	18.9982i	−0.549118	−	0.951101i
$400$		0			0
$401$	−4.35425	−	7.54178i	−0.217441	−	0.376619i	0.736584	−	0.676346i	$-0.236438\pi$
$401$	−4.35425	−	7.54178i	−0.217441	−	0.376619i	−0.954025	+	0.299727i	$0.903104\pi$
$402$		0			0
$403$	−5.67712	+	9.83307i	−0.282798	+	0.489820i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	−1.06275			−0.0526784
$408$		0			0
$409$	−3.08301	+	5.33992i	−0.152445	+	0.264042i	−0.932126	−	0.362135i	$-0.882048\pi$
$409$	−3.08301	+	5.33992i	−0.152445	+	0.264042i	0.779681	+	0.626177i	$0.215381\pi$
$410$		0			0
$411$	10.1144	+	17.5186i	0.498905	+	0.864130i
$412$		0			0
$413$	28.9373			1.42391
$414$		0			0
$415$	5.46863	+	9.47194i	0.268444	+	0.464959i
$416$		0			0
$417$	−2.50000	+	4.33013i	−0.122426	+	0.212047i
$418$		0			0
$419$	21.2915			1.04016			0.520079	−	0.854118i	$-0.325903\pi$
$419$	21.2915			1.04016			0.520079	+	0.854118i	$0.325903\pi$
$420$		0			0
$421$	−19.5830			−0.954417			−0.477209	−	0.878790i	$-0.658351\pi$
$421$	−19.5830			−0.954417			−0.477209	+	0.878790i	$0.658351\pi$
$422$		0			0
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$		0			0
$425$	0.822876	+	1.42526i	0.0399153	+	0.0691354i
$426$		0			0
$427$	−10.5830	+	18.3303i	−0.512148	+	0.887066i
$428$		0			0
$429$	−2.17712	−	3.77089i	−0.105113	−	0.182060i
$430$		0			0
$431$	−19.9373	+	34.5323i	−0.960344	+	1.66336i	−0.238708	+	0.971091i	$0.576724\pi$
$431$	−19.9373	+	34.5323i	−0.960344	+	1.66336i	−0.721636	+	0.692273i	$0.756610\pi$
$432$		0			0
$433$	3.35425			0.161195			0.0805975	−	0.996747i	$-0.474317\pi$
$433$	3.35425			0.161195			0.0805975	+	0.996747i	$0.474317\pi$
$434$		0			0
$435$	7.64575			0.366586
$436$		0			0
$437$	−6.82288	+	11.8176i	−0.326382	+	0.565311i
$438$		0			0
$439$	−2.64575	−	4.58258i	−0.126275	−	0.218714i	0.795956	−	0.605355i	$-0.206969\pi$
$439$	−2.64575	−	4.58258i	−0.126275	−	0.218714i	−0.922231	+	0.386640i	$0.873635\pi$
$440$		0			0
$441$	7.00000			0.333333
$442$		0			0
$443$	−4.93725	−	8.55157i	−0.234576	−	0.406298i	0.724573	−	0.689198i	$-0.242037\pi$
$443$	−4.93725	−	8.55157i	−0.234576	−	0.406298i	−0.959149	+	0.282900i	$0.908704\pi$
$444$		0			0
$445$	7.11438	−	12.3225i	0.337254	−	0.584141i
$446$		0			0
$447$	−6.58301			−0.311365
$448$		0			0
$449$	−12.5830			−0.593829			−0.296914	−	0.954904i	$-0.595958\pi$
$449$	−12.5830			−0.593829			−0.296914	+	0.954904i	$0.595958\pi$
$450$		0			0
$451$	4.06275	−	7.03688i	0.191307	−	0.331354i
$452$		0			0
$453$	2.29150	+	3.96900i	0.107664	+	0.186480i
$454$		0			0
$455$	3.50000	−	6.06218i	0.164083	−	0.284199i
$456$		0			0
$457$	7.32288	+	12.6836i	0.342550	+	0.593313i	0.984905	−	0.173093i	$-0.0553762\pi$
$457$	7.32288	+	12.6836i	0.342550	+	0.593313i	−0.642356	+	0.766407i	$0.722043\pi$
$458$		0			0
$459$	0.822876	−	1.42526i	0.0384085	−	0.0665256i
$460$		0			0
$461$	−19.6458			−0.914994			−0.457497	−	0.889211i	$-0.651254\pi$
$461$	−19.6458			−0.914994			−0.457497	+	0.889211i	$0.651254\pi$
$462$		0			0
$463$	10.5203			0.488918			0.244459	−	0.969660i	$-0.421390\pi$
$463$	10.5203			0.488918			0.244459	+	0.969660i	$0.421390\pi$
$464$		0			0
$465$	2.14575	−	3.71655i	0.0995068	−	0.172351i
$466$		0			0
$467$	18.8745	+	32.6916i	0.873408	+	1.51279i	0.858449	+	0.512899i	$0.171428\pi$
$467$	18.8745	+	32.6916i	0.873408	+	1.51279i	0.0149591	+	0.999888i	$0.495238\pi$
$468$		0			0
$469$	1.70850			0.0788911
$470$		0			0
$471$	0.645751	+	1.11847i	0.0297546	+	0.0515366i
$472$		0			0
$473$	−4.88562	+	8.46215i	−0.224641	+	0.389090i
$474$		0			0
$475$	8.29150			0.380440
$476$		0			0
$477$	3.29150			0.150708
$478$		0			0
$479$	3.29150	−	5.70105i	0.150393	−	0.260488i	−0.780979	−	0.624557i	$-0.785280\pi$
$479$	3.29150	−	5.70105i	0.150393	−	0.260488i	0.931372	+	0.364069i	$0.118613\pi$
$480$		0			0
$481$	0.854249	+	1.47960i	0.0389504	+	0.0674641i
$482$		0			0
$483$	−2.17712	−	3.77089i	−0.0990626	−	0.171581i
$484$		0			0
$485$	−4.00000	−	6.92820i	−0.181631	−	0.314594i
$486$		0			0
$487$	1.32288	−	2.29129i	0.0599452	−	0.103828i	−0.834495	−	0.551015i	$-0.814241\pi$
$487$	1.32288	−	2.29129i	0.0599452	−	0.103828i	0.894441	+	0.447187i	$0.147574\pi$
$488$		0			0
$489$	−16.0000			−0.723545
$490$		0			0
$491$	2.12549			0.0959221			0.0479611	−	0.998849i	$-0.484728\pi$
$491$	2.12549			0.0959221			0.0479611	+	0.998849i	$0.484728\pi$
$492$		0			0
$493$	6.29150	−	10.8972i	0.283355	−	0.490785i
$494$		0			0
$495$	0.822876	+	1.42526i	0.0369855	+	0.0640608i
$496$		0			0
$497$	−18.0516	−	31.2663i	−0.809726	−	1.40249i
$498$		0			0
$499$	−13.7288	−	23.7789i	−0.614584	−	1.06449i	−0.990457	−	0.137819i	$-0.955991\pi$
$499$	−13.7288	−	23.7789i	−0.614584	−	1.06449i	0.375874	−	0.926671i	$-0.377343\pi$
$500$		0			0
$501$	−9.82288	+	17.0137i	−0.438854	+	0.760117i
$502$		0			0
$503$	22.4575			1.00133			0.500666	−	0.865641i	$-0.333089\pi$
$503$	22.4575			1.00133			0.500666	+	0.865641i	$0.333089\pi$
$504$		0			0
$505$	−4.93725			−0.219705
$506$		0			0
$507$	3.00000	−	5.19615i	0.133235	−	0.230769i
$508$		0			0
$509$	13.9373	+	24.1400i	0.617758	+	1.06999i	0.989894	+	0.141810i	$0.0452922\pi$
$509$	13.9373	+	24.1400i	0.617758	+	1.06999i	−0.372136	+	0.928178i	$0.621374\pi$
$510$		0			0
$511$	35.0000			1.54831
$512$		0			0
$513$	−4.14575	−	7.18065i	−0.183039	−	0.317034i
$514$		0			0
$515$	−4.67712	+	8.10102i	−0.206099	+	0.356973i
$516$		0			0
$517$	−9.87451			−0.434280
$518$		0			0
$519$	9.87451			0.433443
$520$		0			0
$521$	1.06275	−	1.84073i	0.0465598	−	0.0806439i	−0.841806	−	0.539780i	$-0.818508\pi$
$521$	1.06275	−	1.84073i	0.0465598	−	0.0806439i	0.888366	+	0.459136i	$0.151841\pi$
$522$		0			0
$523$	−15.6144	−	27.0449i	−0.682769	−	1.18259i	−0.974132	−	0.225978i	$-0.927442\pi$
$523$	−15.6144	−	27.0449i	−0.682769	−	1.18259i	0.291363	−	0.956612i	$-0.405891\pi$
$524$		0			0
$525$	−1.32288	+	2.29129i	−0.0577350	+	0.100000i
$526$		0			0
$527$	−3.53137	−	6.11652i	−0.153829	−	0.266440i
$528$		0			0
$529$	10.1458	−	17.5730i	0.441120	−	0.764042i
$530$		0			0
$531$	10.9373			0.474636
$532$		0			0
$533$	−13.0627			−0.565810
$534$		0			0
$535$	8.46863	−	14.6681i	0.366131	−	0.634157i
$536$		0			0
$537$	−0.291503	−	0.504897i	−0.0125793	−	0.0217879i
$538$		0			0
$539$	5.76013	+	9.97684i	0.248106	+	0.429733i
$540$		0			0
$541$	−18.3745	−	31.8256i	−0.789982	−	1.36829i	−0.925977	−	0.377579i	$-0.876757\pi$
$541$	−18.3745	−	31.8256i	−0.789982	−	1.36829i	0.135996	−	0.990709i	$-0.456577\pi$
$542$		0			0
$543$	2.14575	−	3.71655i	0.0920830	−	0.159492i
$544$		0			0
$545$	−13.0000			−0.556859
$546$		0			0
$547$	−43.2915			−1.85101			−0.925505	−	0.378734i	$-0.876359\pi$
$547$	−43.2915			−1.85101			−0.925505	+	0.378734i	$0.876359\pi$
$548$		0			0
$549$	−4.00000	+	6.92820i	−0.170716	+	0.295689i
$550$		0			0
$551$	−31.6974	−	54.9015i	−1.35035	−	2.33888i
$552$		0			0
$553$	−3.03137	+	5.25049i	−0.128907	+	0.223274i
$554$		0			0
$555$	−0.322876	−	0.559237i	−0.0137053	−	0.0237383i
$556$		0			0
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	−0.609912	−	0.792469i	$-0.708795\pi$
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	0.991254	+	0.131965i	$0.0421286\pi$
$558$		0			0
$559$	15.7085			0.664399
$560$		0			0
$561$	2.70850			0.114353
$562$		0			0
$563$	18.2915	−	31.6818i	0.770895	−	1.33523i	−0.166178	−	0.986096i	$-0.553143\pi$
$563$	18.2915	−	31.6818i	0.770895	−	1.33523i	0.937073	−	0.349133i	$-0.113524\pi$
$564$		0			0
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$		0			0
$567$	2.64575			0.111111
$568$		0			0
$569$	1.88562	+	3.26599i	0.0790494	+	0.136918i	0.902840	−	0.429977i	$-0.141478\pi$
$569$	1.88562	+	3.26599i	0.0790494	+	0.136918i	−0.823791	+	0.566894i	$0.808145\pi$
$570$		0			0
$571$	−22.1458	+	38.3576i	−0.926771	+	1.60521i	−0.138083	+	0.990421i	$0.544094\pi$
$571$	−22.1458	+	38.3576i	−0.926771	+	1.60521i	−0.788688	+	0.614793i	$0.789239\pi$
$572$		0			0
$573$	19.1660			0.800672
$574$		0			0
$575$	1.64575			0.0686326
$576$		0			0
$577$	21.2601	−	36.8236i	0.885071	−	1.53299i	0.0394383	−	0.999222i	$-0.487443\pi$
$577$	21.2601	−	36.8236i	0.885071	−	1.53299i	0.845633	−	0.533766i	$-0.179224\pi$
$578$		0			0
$579$	4.03137	+	6.98254i	0.167538	+	0.290185i
$580$		0			0
$581$	14.4686	+	25.0604i	0.600260	+	1.03968i
$582$		0			0
$583$	2.70850	+	4.69126i	0.112174	+	0.194292i
$584$		0			0
$585$	1.32288	−	2.29129i	0.0546942	−	0.0947331i
$586$		0			0
$587$	16.9373			0.699075			0.349538	−	0.936922i	$-0.386339\pi$
$587$	16.9373			0.699075			0.349538	+	0.936922i	$0.386339\pi$
$588$		0			0
$589$	−35.5830			−1.46617
$590$		0			0
$591$	2.46863	−	4.27579i	0.101546	−	0.175882i
$592$		0			0
$593$	12.5314	+	21.7050i	0.514602	+	0.891316i	0.999856	+	0.0169436i	$0.00539357\pi$
$593$	12.5314	+	21.7050i	0.514602	+	0.891316i	−0.485255	+	0.874373i	$0.661273\pi$
$594$		0			0
$595$	2.17712	+	3.77089i	0.0892534	+	0.154591i
$596$		0			0
$597$	11.5830	+	20.0624i	0.474061	+	0.821097i
$598$		0			0
$599$	−1.06275	+	1.84073i	−0.0434226	+	0.0752102i	−0.886920	−	0.461923i	$-0.847160\pi$
$599$	−1.06275	+	1.84073i	−0.0434226	+	0.0752102i	0.843497	+	0.537133i	$0.180493\pi$
$600$		0			0
$601$	−37.5830			−1.53304			−0.766521	−	0.642219i	$-0.778014\pi$
$601$	−37.5830			−1.53304			−0.766521	+	0.642219i	$0.778014\pi$
$602$		0			0
$603$	0.645751			0.0262970
$604$		0			0
$605$	4.14575	−	7.18065i	0.168549	−	0.291935i
$606$		0			0
$607$	8.38562	+	14.5243i	0.340362	+	0.589524i	0.984500	−	0.175385i	$-0.0561171\pi$
$607$	8.38562	+	14.5243i	0.340362	+	0.589524i	−0.644138	+	0.764909i	$0.722784\pi$
$608$		0			0
$609$	20.2288			0.819711
$610$		0			0
$611$	7.93725	+	13.7477i	0.321107	+	0.556174i
$612$		0			0
$613$	20.5830	−	35.6508i	0.831340	−	1.43992i	−0.0656363	−	0.997844i	$-0.520908\pi$
$613$	20.5830	−	35.6508i	0.831340	−	1.43992i	0.896976	−	0.442079i	$-0.145759\pi$
$614$		0			0
$615$	4.93725			0.199089
$616$		0			0
$617$	9.29150			0.374062			0.187031	−	0.982354i	$-0.440114\pi$
$617$	9.29150			0.374062			0.187031	+	0.982354i	$0.440114\pi$
$618$		0			0
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	−0.609488	−	0.792796i	$-0.708625\pi$
$619$	9.50000	−	16.4545i	0.381837	−	0.661361i	0.991325	+	0.131434i	$0.0419582\pi$
$620$		0			0
$621$	−0.822876	−	1.42526i	−0.0330209	−	0.0571938i
$622$		0			0
$623$	18.8229	−	32.6022i	0.754123	−	1.30618i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	6.82288	−	11.8176i	0.272479	−	0.471948i
$628$		0			0
$629$	−1.06275			−0.0423745
$630$		0			0
$631$	−35.7490			−1.42315			−0.711573	−	0.702612i	$-0.752017\pi$
$631$	−35.7490			−1.42315			−0.711573	+	0.702612i	$0.752017\pi$
$632$		0			0
$633$	−4.29150	+	7.43310i	−0.170572	+	0.295439i
$634$		0			0
$635$	1.03137	+	1.78639i	0.0409288	+	0.0708907i
$636$		0			0
$637$	9.26013	−	16.0390i	0.366900	−	0.635489i
$638$		0			0
$639$	−6.82288	−	11.8176i	−0.269909	−	0.467496i
$640$		0			0
$641$	6.05163	−	10.4817i	0.239025	−	0.414004i	−0.721410	−	0.692509i	$-0.756506\pi$
$641$	6.05163	−	10.4817i	0.239025	−	0.414004i	0.960435	+	0.278505i	$0.0898388\pi$
$642$		0			0
$643$	−21.8118			−0.860172			−0.430086	−	0.902788i	$-0.641517\pi$
$643$	−21.8118			−0.860172			−0.430086	+	0.902788i	$0.641517\pi$
$644$		0			0
$645$	−5.93725			−0.233779
$646$		0			0
$647$	−11.4686	+	19.8642i	−0.450878	+	0.780944i	−0.998441	−	0.0558207i	$-0.982222\pi$
$647$	−11.4686	+	19.8642i	−0.450878	+	0.780944i	0.547563	+	0.836765i	$0.315556\pi$
$648$		0			0
$649$	9.00000	+	15.5885i	0.353281	+	0.611900i
$650$		0			0
$651$	5.67712	−	9.83307i	0.222504	−	0.385388i
$652$		0			0
$653$	−14.1771	−	24.5555i	−0.554794	−	0.960931i	−0.997920	−	0.0644715i	$-0.979464\pi$
$653$	−14.1771	−	24.5555i	−0.554794	−	0.960931i	0.443126	−	0.896459i	$-0.353869\pi$
$654$		0			0
$655$	−10.6458	+	18.4390i	−0.415964	+	0.720471i
$656$		0			0
$657$	13.2288			0.516103
$658$		0			0
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$		0			0
$661$	20.4373	−	35.3984i	0.794917	−	1.37684i	−0.127975	−	0.991777i	$-0.540848\pi$
$661$	20.4373	−	35.3984i	0.794917	−	1.37684i	0.922892	−	0.385059i	$-0.125819\pi$
$662$		0			0
$663$	−2.17712	−	3.77089i	−0.0845525	−	0.146449i
$664$		0			0
$665$	21.9373			0.850690
$666$		0			0
$667$	−6.29150	−	10.8972i	−0.243608	−	0.421941i
$668$		0			0
$669$	−8.93725	+	15.4798i	−0.345534	+	0.598483i
$670$		0			0
$671$	−13.1660			−0.508268
$672$		0			0
$673$	−5.35425			−0.206391			−0.103196	−	0.994661i	$-0.532907\pi$
$673$	−5.35425			−0.206391			−0.103196	+	0.994661i	$0.532907\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	11.1771	+	19.3593i	0.429572	+	0.744040i	0.996835	−	0.0794963i	$-0.0253312\pi$
$677$	11.1771	+	19.3593i	0.429572	+	0.744040i	−0.567263	+	0.823536i	$0.691998\pi$
$678$		0			0
$679$	−10.5830	−	18.3303i	−0.406138	−	0.703452i
$680$		0			0
$681$	−9.82288	−	17.0137i	−0.376413	−	0.651967i
$682$		0			0
$683$	−2.46863	+	4.27579i	−0.0944594	+	0.163608i	−0.909383	−	0.415960i	$-0.863446\pi$
$683$	−2.46863	+	4.27579i	−0.0944594	+	0.163608i	0.814923	+	0.579569i	$0.196779\pi$
$684$		0			0
$685$	−20.2288			−0.772901
$686$		0			0
$687$	−7.00000			−0.267067
$688$		0			0
$689$	4.35425	−	7.54178i	0.165884	−	0.287319i
$690$		0			0
$691$	−11.7915	−	20.4235i	−0.448570	−	0.776946i	0.549723	−	0.835347i	$-0.314733\pi$
$691$	−11.7915	−	20.4235i	−0.448570	−	0.776946i	−0.998293	+	0.0584009i	$0.981400\pi$
$692$		0			0
$693$	2.17712	+	3.77089i	0.0827021	+	0.143244i
$694$		0			0
$695$	−2.50000	−	4.33013i	−0.0948304	−	0.164251i
$696$		0			0
$697$	4.06275	−	7.03688i	0.153887	−	0.266541i
$698$		0			0
$699$	21.2915			0.805319
$700$		0			0
$701$	34.9373			1.31956			0.659781	−	0.751458i	$-0.270649\pi$
$701$	34.9373			1.31956			0.659781	+	0.751458i	$0.270649\pi$
$702$		0			0
$703$	−2.67712	+	4.63692i	−0.100970	+	0.174885i
$704$		0			0
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$		0			0
$707$	−13.0627			−0.491275
$708$		0			0
$709$	11.2915	+	19.5575i	0.424061	+	0.734496i	0.996332	−	0.0855689i	$-0.0272708\pi$
$709$	11.2915	+	19.5575i	0.424061	+	0.734496i	−0.572271	+	0.820065i	$0.693937\pi$
$710$		0			0
$711$	−1.14575	+	1.98450i	−0.0429690	+	0.0744245i
$712$		0			0
$713$	−7.06275			−0.264502
$714$		0			0
$715$	4.35425			0.162840
$716$		0			0
$717$	−3.00000	+	5.19615i	−0.112037	+	0.194054i
$718$		0			0
$719$	7.35425	+	12.7379i	0.274267	+	0.475045i	0.969950	−	0.243304i	$-0.0782314\pi$
$719$	7.35425	+	12.7379i	0.274267	+	0.475045i	−0.695683	+	0.718349i	$0.744898\pi$
$720$		0			0
$721$	−12.3745	+	21.4333i	−0.460851	+	0.798217i
$722$		0			0
$723$	6.35425	+	11.0059i	0.236317	+	0.409313i
$724$		0			0
$725$	−3.82288	+	6.62141i	−0.141978	+	0.245913i
$726$		0			0
$727$	−33.8118			−1.25401			−0.627004	−	0.779016i	$-0.715719\pi$
$727$	−33.8118			−1.25401			−0.627004	+	0.779016i	$0.715719\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.88562	+	8.46215i	−0.180701	+	0.312984i
$732$		0			0
$733$	−3.61438	−	6.26029i	−0.133500	−	0.231229i	0.791523	−	0.611139i	$-0.209288\pi$
$733$	−3.61438	−	6.26029i	−0.133500	−	0.231229i	−0.925023	+	0.379910i	$0.875955\pi$
$734$		0			0
$735$	−3.50000	+	6.06218i	−0.129099	+	0.223607i
$736$		0			0
$737$	0.531373	+	0.920365i	0.0195734	+	0.0339021i
$738$		0			0
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	0.465848	+	0.884865i	$0.345749\pi$
$739$	−14.5000	+	25.1147i	−0.533391	+	0.923861i	−0.999239	+	0.0389959i	$0.987584\pi$
$740$		0			0
$741$	−21.9373			−0.805885
$742$		0			0
$743$	−13.0627			−0.479226			−0.239613	−	0.970869i	$-0.577021\pi$
$743$	−13.0627			−0.479226			−0.239613	+	0.970869i	$0.577021\pi$
$744$		0			0
$745$	3.29150	−	5.70105i	0.120591	−	0.208870i
$746$		0			0
$747$	5.46863	+	9.47194i	0.200087	+	0.346560i
$748$		0			0
$749$	22.4059	−	38.8081i	0.818693	−	1.41802i
$750$		0			0
$751$	−12.0830	−	20.9284i	−0.440915	−	0.763687i	0.556843	−	0.830618i	$-0.312013\pi$
$751$	−12.0830	−	20.9284i	−0.440915	−	0.763687i	−0.997758	+	0.0669307i	$0.978679\pi$
$752$		0			0
$753$	5.46863	−	9.47194i	0.199288	−	0.345177i
$754$		0			0
$755$	−4.58301			−0.166793
$756$		0			0
$757$	−8.83399			−0.321077			−0.160538	−	0.987030i	$-0.551323\pi$
$757$	−8.83399			−0.321077			−0.160538	+	0.987030i	$0.551323\pi$
$758$		0			0
$759$	1.35425	−	2.34563i	0.0491561	−	0.0851409i
$760$		0			0
$761$	6.05163	+	10.4817i	0.219371	+	0.379963i	0.954616	−	0.297839i	$-0.0962660\pi$
$761$	6.05163	+	10.4817i	0.219371	+	0.379963i	−0.735244	+	0.677802i	$0.762933\pi$
$762$		0			0
$763$	−34.3948			−1.24517
$764$		0			0
$765$	0.822876	+	1.42526i	0.0297511	+	0.0515305i
$766$		0			0
$767$	14.4686	−	25.0604i	0.522432	−	0.904878i
$768$		0			0
$769$	−3.70850			−0.133732			−0.0668659	−	0.997762i	$-0.521300\pi$
$769$	−3.70850			−0.133732			−0.0668659	+	0.997762i	$0.521300\pi$
$770$		0			0
$771$	5.52026			0.198807
$772$		0			0
$773$	−13.6974	+	23.7246i	−0.492661	+	0.853313i	−0.999964	−	0.00845413i	$-0.997309\pi$
$773$	−13.6974	+	23.7246i	−0.492661	+	0.853313i	0.507304	+	0.861767i	$0.330642\pi$
$774$		0			0
$775$	2.14575	+	3.71655i	0.0770777	+	0.133502i
$776$		0			0
$777$	−0.854249	−	1.47960i	−0.0306460	−	0.0530804i
$778$		0			0
$779$	−20.4686	−	35.4527i	−0.733365	−	1.27022i
$780$		0			0
$781$	11.2288	−	19.4488i	0.401796	−	0.695932i
$782$		0			0
$783$	7.64575			0.273237
$784$		0			0
$785$	−1.29150			−0.0460957
$786$		0			0
$787$	−2.93725	+	5.08747i	−0.104702	+	0.181349i	−0.913616	−	0.406577i	$-0.866722\pi$
$787$	−2.93725	+	5.08747i	−0.104702	+	0.181349i	0.808915	+	0.587926i	$0.200055\pi$
$788$		0			0
$789$	14.2288	+	24.6449i	0.506557	+	0.877383i
$790$		0			0
$791$	−7.93725	−	13.7477i	−0.282216	−	0.488813i
$792$		0			0
$793$	10.5830	+	18.3303i	0.375814	+	0.650928i
$794$		0			0
$795$	−1.64575	+	2.85052i	−0.0583688	+	0.101098i
$796$		0			0
$797$	4.93725			0.174887			0.0874433	−	0.996170i	$-0.472130\pi$
$797$	4.93725			0.174887			0.0874433	+	0.996170i	$0.472130\pi$
$798$		0			0
$799$	−9.87451			−0.349335
$800$		0			0
$801$	7.11438	−	12.3225i	0.251374	−	0.435393i
$802$		0			0
$803$	10.8856	+	18.8544i	0.384145	+	0.665359i
$804$		0			0
$805$	4.35425			0.153467
$806$		0			0
$807$	−13.9373	−	24.1400i	−0.490615	−	0.849769i
$808$		0			0
$809$	−9.58301	+	16.5983i	−0.336921	+	0.583563i	−0.983852	−	0.178985i	$-0.942719\pi$
$809$	−9.58301	+	16.5983i	−0.336921	+	0.583563i	0.646931	+	0.762548i	$0.276052\pi$
$810$		0			0
$811$	17.2915			0.607187			0.303593	−	0.952802i	$-0.401814\pi$
$811$	17.2915			0.607187			0.303593	+	0.952802i	$0.401814\pi$
$812$		0			0
$813$	7.41699			0.260125
$814$		0			0
$815$	8.00000	−	13.8564i	0.280228	−	0.485369i
$816$		0			0
$817$	24.6144	+	42.6334i	0.861148	+	1.49155i
$818$		0			0
$819$	3.50000	−	6.06218i	0.122300	−	0.211830i
$820$		0			0
$821$	25.9889	+	45.0141i	0.907018	+	1.57100i	0.818185	+	0.574955i	$0.194981\pi$
$821$	25.9889	+	45.0141i	0.907018	+	1.57100i	0.0888337	+	0.996046i	$0.471686\pi$
$822$		0			0
$823$	−9.22876	+	15.9847i	−0.321694	+	0.557191i	−0.980838	−	0.194826i	$-0.937586\pi$
$823$	−9.22876	+	15.9847i	−0.321694	+	0.557191i	0.659144	+	0.752017i	$0.270919\pi$
$824$		0			0
$825$	−1.64575			−0.0572977
$826$		0			0
$827$	22.4575			0.780924			0.390462	−	0.920619i	$-0.372315\pi$
$827$	22.4575			0.780924			0.390462	+	0.920619i	$0.372315\pi$
$828$		0			0
$829$	−9.85425	+	17.0681i	−0.342252	+	0.592798i	−0.984851	−	0.173405i	$-0.944523\pi$
$829$	−9.85425	+	17.0681i	−0.342252	+	0.592798i	0.642598	+	0.766203i	$0.277856\pi$
$830$		0			0
$831$	10.3229	+	17.8797i	0.358097	+	0.620241i
$832$		0			0
$833$	5.76013	+	9.97684i	0.199577	+	0.345677i
$834$		0			0
$835$	−9.82288	−	17.0137i	−0.339935	−	0.588784i
$836$		0			0
$837$	2.14575	−	3.71655i	0.0741680	−	0.128463i
$838$		0			0
$839$	16.3542			0.564611			0.282306	−	0.959325i	$-0.408901\pi$
$839$	16.3542			0.564611			0.282306	+	0.959325i	$0.408901\pi$
$840$		0			0
$841$	29.4575			1.01578
$842$		0			0
$843$	−12.0000	+	20.7846i	−0.413302	+	0.715860i
$844$		0			0
$845$	3.00000	+	5.19615i	0.103203	+	0.178753i
$846$		0			0
$847$	10.9686	−	18.9982i	0.376886	−	0.652787i
$848$		0			0
$849$	7.32288	+	12.6836i	0.251320	+	0.435300i
$850$		0			0
$851$	−0.531373	+	0.920365i	−0.0182152	+	0.0315497i
$852$		0			0
$853$	43.2288			1.48012			0.740062	−	0.672538i	$-0.234796\pi$
$853$	43.2288			1.48012			0.740062	+	0.672538i	$0.234796\pi$
$854$		0			0
$855$	8.29150			0.283563
$856$		0			0
$857$	6.82288	−	11.8176i	0.233065	−	0.403680i	−0.725644	−	0.688071i	$-0.758458\pi$
$857$	6.82288	−	11.8176i	0.233065	−	0.403680i	0.958709	+	0.284390i	$0.0917912\pi$
$858$		0			0
$859$	13.2288	+	22.9129i	0.451359	+	0.781777i	0.998471	−	0.0552825i	$-0.0176059\pi$
$859$	13.2288	+	22.9129i	0.451359	+	0.781777i	−0.547111	+	0.837060i	$0.684273\pi$
$860$		0			0
$861$	13.0627			0.445177
$862$		0			0
$863$	17.2288	+	29.8411i	0.586474	+	1.01580i	0.994690	+	0.102917i	$0.0328176\pi$
$863$	17.2288	+	29.8411i	0.586474	+	1.01580i	−0.408216	+	0.912885i	$0.633849\pi$
$864$		0			0
$865$	−4.93725	+	8.55157i	−0.167872	+	0.290762i
$866$		0			0
$867$	−14.2915			−0.485365
$868$		0			0
$869$	−3.77124			−0.127931
$870$		0			0
$871$	0.854249	−	1.47960i	0.0289451	−	0.0501344i
$872$		0			0
$873$	−4.00000	−	6.92820i	−0.135379	−	0.234484i
$874$		0			0
$875$	−1.32288	−	2.29129i	−0.0447214	−	0.0774597i
$876$		0			0
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.16601			0.0392839			0.0196419	−	0.999807i	$-0.493747\pi$
$881$	1.16601			0.0392839			0.0196419	+	0.999807i	$0.493747\pi$
$882$		0			0
$883$	−21.8118			−0.734024			−0.367012	−	0.930216i	$-0.619619\pi$
$883$	−21.8118			−0.734024			−0.367012	+	0.930216i	$0.619619\pi$
$884$		0			0
$885$	−5.46863	+	9.47194i	−0.183826	+	0.318396i
$886$		0			0
$887$	9.82288	+	17.0137i	0.329820	+	0.571265i	0.982476	−	0.186390i	$-0.0596786\pi$
$887$	9.82288	+	17.0137i	0.329820	+	0.571265i	−0.652656	+	0.757654i	$0.726345\pi$
$888$		0			0
$889$	2.72876	+	4.72634i	0.0915196	+	0.158517i
$890$		0			0
$891$	0.822876	+	1.42526i	0.0275674	+	0.0477481i
$892$		0			0
$893$	−24.8745	+	43.0839i	−0.832394	+	1.44175i
$894$		0			0
$895$	0.583005			0.0194877
$896$		0			0
$897$	−4.35425			−0.145384
$898$		0			0
$899$	16.4059	−	28.4158i	0.547167	−	0.947721i
$900$		0			0
$901$	2.70850	+	4.69126i	0.0902331	+	0.156288i
$902$		0			0
$903$	−15.7085			−0.522746
$904$		0			0
$905$	2.14575	+	3.71655i	0.0713272	+	0.123542i
$906$		0			0
$907$	10.3229	−	17.8797i	0.342765	−	0.593687i	−0.642180	−	0.766554i	$-0.721970\pi$
$907$	10.3229	−	17.8797i	0.342765	−	0.593687i	0.984945	+	0.172867i	$0.0553031\pi$
$908$		0			0
$909$	−4.93725			−0.163758
$910$		0			0
$911$	−5.52026			−0.182894			−0.0914472	−	0.995810i	$-0.529149\pi$
$911$	−5.52026			−0.182894			−0.0914472	+	0.995810i	$0.529149\pi$
$912$		0			0
$913$	−9.00000	+	15.5885i	−0.297857	+	0.515903i
$914$		0			0
$915$	−4.00000	−	6.92820i	−0.132236	−	0.229039i
$916$		0			0
$917$	−28.1660	+	48.7850i	−0.930124	+	1.61102i
$918$		0			0
$919$	−5.20850	−	9.02138i	−0.171812	−	0.297588i	0.767241	−	0.641359i	$-0.221629\pi$
$919$	−5.20850	−	9.02138i	−0.171812	−	0.297588i	−0.939054	+	0.343771i	$0.888296\pi$
$920$		0			0
$921$	−13.9686	+	24.1944i	−0.460282	+	0.797232i
$922$		0			0
$923$	−36.1033			−1.18835
$924$		0			0
$925$	0.645751			0.0212322
$926$		0			0
$927$	−4.67712	+	8.10102i	−0.153617	+	0.266072i
$928$		0			0
$929$	−17.7601	−	30.7614i	−0.582691	−	1.00925i	−0.995159	−	0.0982783i	$-0.968666\pi$
$929$	−17.7601	−	30.7614i	−0.582691	−	1.00925i	0.412468	−	0.910972i	$-0.364667\pi$
$930$		0			0
$931$	58.0405			1.90220
$932$		0			0
$933$	−6.82288	−	11.8176i	−0.223371	−	0.386890i
$934$		0			0
$935$	−1.35425	+	2.34563i	−0.0442887	+	0.0767102i
$936$		0			0
$937$	38.9778			1.27335			0.636674	−	0.771133i	$-0.280310\pi$
$937$	38.9778			1.27335			0.636674	+	0.771133i	$0.280310\pi$
$938$		0			0
$939$	−21.2288			−0.692774
$940$		0			0
$941$	5.46863	−	9.47194i	0.178272	−	0.308776i	−0.763017	−	0.646379i	$-0.776283\pi$
$941$	5.46863	−	9.47194i	0.178272	−	0.308776i	0.941289	+	0.337602i	$0.109616\pi$
$942$		0			0
$943$	−4.06275	−	7.03688i	−0.132301	−	0.229152i
$944$		0			0
$945$	−1.32288	+	2.29129i	−0.0430331	+	0.0745356i
$946$		0			0
$947$	20.1771	+	34.9478i	0.655668	+	1.13565i	0.981726	+	0.190301i	$0.0609464\pi$
$947$	20.1771	+	34.9478i	0.655668	+	1.13565i	−0.326057	+	0.945350i	$0.605720\pi$
$948$		0			0
$949$	17.5000	−	30.3109i	0.568074	−	0.983933i
$950$		0			0
$951$	23.5203			0.762697
$952$		0			0
$953$	−52.4575			−1.69927			−0.849633	−	0.527375i	$-0.823176\pi$
$953$	−52.4575			−1.69927			−0.849633	+	0.527375i	$0.823176\pi$
$954$		0			0
$955$	−9.58301	+	16.5983i	−0.310099	+	0.537107i
$956$		0			0
$957$	6.29150	+	10.8972i	0.203375	+	0.352257i
$958$		0			0
$959$	−53.5203			−1.72826
$960$		0			0
$961$	6.29150	+	10.8972i	0.202952	+	0.351523i
$962$		0			0
$963$	8.46863	−	14.6681i	0.272898	−	0.472673i
$964$		0			0
$965$	−8.06275			−0.259549
$966$		0			0
$967$	−28.3948			−0.913114			−0.456557	−	0.889694i	$-0.650918\pi$
$967$	−28.3948			−0.913114			−0.456557	+	0.889694i	$0.650918\pi$
$968$		0			0
$969$	6.82288	−	11.8176i	0.219182	−	0.379635i
$970$		0			0
$971$	−5.41699	−	9.38251i	−0.173840	−	0.301099i	0.765919	−	0.642937i	$-0.222284\pi$
$971$	−5.41699	−	9.38251i	−0.173840	−	0.301099i	−0.939759	+	0.341837i	$0.888951\pi$
$972$		0			0
$973$	−6.61438	−	11.4564i	−0.212047	−	0.367277i
$974$		0			0
$975$	1.32288	+	2.29129i	0.0423659	+	0.0733799i
$976$		0			0
$977$	12.5314	−	21.7050i	0.400914	−	0.694404i	−0.592922	−	0.805260i	$-0.702026\pi$
$977$	12.5314	−	21.7050i	0.400914	−	0.694404i	0.993836	+	0.110856i	$0.0353592\pi$
$978$		0			0
$979$	23.4170			0.748410
$980$		0			0
$981$	−13.0000			−0.415058
$982$		0			0
$983$	−12.3431	+	21.3789i	−0.393685	+	0.681882i	−0.992932	−	0.118682i	$-0.962133\pi$
$983$	−12.3431	+	21.3789i	−0.393685	+	0.681882i	0.599247	+	0.800564i	$0.295467\pi$
$984$		0			0
$985$	2.46863	+	4.27579i	0.0786570	+	0.136238i
$986$		0			0
$987$	−7.93725	−	13.7477i	−0.252646	−	0.437595i
$988$		0			0
$989$	4.88562	+	8.46215i	0.155354	+	0.269081i
$990$		0			0
$991$	−22.1458	+	38.3576i	−0.703483	+	1.21847i	0.263753	+	0.964590i	$0.415040\pi$
$991$	−22.1458	+	38.3576i	−0.703483	+	1.21847i	−0.967236	+	0.253878i	$0.918294\pi$
$992$		0			0
$993$	−20.1660			−0.639949
$994$		0			0
$995$	−23.1660			−0.734412
$996$		0			0
$997$	−21.6144	+	37.4372i	−0.684534	+	1.18565i	0.289049	+	0.957314i	$0.406661\pi$
$997$	−21.6144	+	37.4372i	−0.684534	+	1.18565i	−0.973583	+	0.228334i	$0.926672\pi$
$998$		0			0
$999$	−0.322876	−	0.559237i	−0.0102153	−	0.0176935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.q.c.361.1	yes	4
3.2	odd	2		1260.2.s.f.361.1		4
4.3	odd	2		1680.2.bg.q.1201.2		4
5.2	odd	4		2100.2.bc.e.949.4		8
5.3	odd	4		2100.2.bc.e.949.1		8
5.4	even	2		2100.2.q.h.1201.2		4
7.2	even	3	inner	420.2.q.c.121.1	✓	4
7.3	odd	6		2940.2.a.m.1.1		2
7.4	even	3		2940.2.a.s.1.1		2
7.5	odd	6		2940.2.q.t.961.2		4
7.6	odd	2		2940.2.q.t.361.2		4
21.2	odd	6		1260.2.s.f.541.1		4
21.11	odd	6		8820.2.a.be.1.2		2
21.17	even	6		8820.2.a.bj.1.2		2
28.23	odd	6		1680.2.bg.q.961.2		4
35.2	odd	12		2100.2.bc.e.1549.1		8
35.9	even	6		2100.2.q.h.1801.2		4
35.23	odd	12		2100.2.bc.e.1549.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.q.c.121.1	✓	4	7.2	even	3	inner
420.2.q.c.361.1	yes	4	1.1	even	1	trivial
1260.2.s.f.361.1		4	3.2	odd	2
1260.2.s.f.541.1		4	21.2	odd	6
1680.2.bg.q.961.2		4	28.23	odd	6
1680.2.bg.q.1201.2		4	4.3	odd	2
2100.2.q.h.1201.2		4	5.4	even	2
2100.2.q.h.1801.2		4	35.9	even	6
2100.2.bc.e.949.1		8	5.3	odd	4
2100.2.bc.e.949.4		8	5.2	odd	4
2100.2.bc.e.1549.1		8	35.2	odd	12
2100.2.bc.e.1549.4		8	35.23	odd	12
2940.2.a.m.1.1		2	7.3	odd	6
2940.2.a.s.1.1		2	7.4	even	3
2940.2.q.t.361.2		4	7.6	odd	2
2940.2.q.t.961.2		4	7.5	odd	6
8820.2.a.be.1.2		2	21.11	odd	6
8820.2.a.bj.1.2		2	21.17	even	6

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-1.32288 - 2.29129i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(0.822876 - 1.42526i) q^{11} -2.64575 q^{13} +1.00000 q^{15} +(0.822876 - 1.42526i) q^{17} +(-4.14575 - 7.18065i) q^{19} +2.64575 q^{21} +(-0.822876 - 1.42526i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +7.64575 q^{29} +(2.14575 - 3.71655i) q^{31} +(0.822876 + 1.42526i) q^{33} +(-1.32288 + 2.29129i) q^{35} +(-0.322876 - 0.559237i) q^{37} +(1.32288 - 2.29129i) q^{39} +4.93725 q^{41} -5.93725 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-3.00000 - 5.19615i) q^{47} +(-3.50000 + 6.06218i) q^{49} +(0.822876 + 1.42526i) q^{51} +(-1.64575 + 2.85052i) q^{53} -1.64575 q^{55} +8.29150 q^{57} +(-5.46863 + 9.47194i) q^{59} +(-4.00000 - 6.92820i) q^{61} +(-1.32288 + 2.29129i) q^{63} +(1.32288 + 2.29129i) q^{65} +(-0.322876 + 0.559237i) q^{67} +1.64575 q^{69} +13.6458 q^{71} +(-6.61438 + 11.4564i) q^{73} +(-0.500000 - 0.866025i) q^{75} -4.35425 q^{77} +(-1.14575 - 1.98450i) q^{79} +(-0.500000 + 0.866025i) q^{81} -10.9373 q^{83} -1.64575 q^{85} +(-3.82288 + 6.62141i) q^{87} +(7.11438 + 12.3225i) q^{89} +(3.50000 + 6.06218i) q^{91} +(2.14575 + 3.71655i) q^{93} +(-4.14575 + 7.18065i) q^{95} +8.00000 q^{97} -1.64575 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9} - 2 q^{11} + 4 q^{15} - 2 q^{17} - 6 q^{19} + 2 q^{23} - 2 q^{25} + 4 q^{27} + 20 q^{29} - 2 q^{31} - 2 q^{33} + 4 q^{37} - 12 q^{41} + 8 q^{43} - 2 q^{45} - 12 q^{47} - 14 q^{49} - 2 q^{51} + 4 q^{53} + 4 q^{55} + 12 q^{57} - 6 q^{59} - 16 q^{61} + 4 q^{67} - 4 q^{69} + 44 q^{71} - 2 q^{75} - 28 q^{77} + 6 q^{79} - 2 q^{81} - 12 q^{83} + 4 q^{85} - 10 q^{87} + 2 q^{89} + 14 q^{91} - 2 q^{93} - 6 q^{95} + 32 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9 - 2 * q^11 + 4 * q^15 - 2 * q^17 - 6 * q^19 + 2 * q^23 - 2 * q^25 + 4 * q^27 + 20 * q^29 - 2 * q^31 - 2 * q^33 + 4 * q^37 - 12 * q^41 + 8 * q^43 - 2 * q^45 - 12 * q^47 - 14 * q^49 - 2 * q^51 + 4 * q^53 + 4 * q^55 + 12 * q^57 - 6 * q^59 - 16 * q^61 + 4 * q^67 - 4 * q^69 + 44 * q^71 - 2 * q^75 - 28 * q^77 + 6 * q^79 - 2 * q^81 - 12 * q^83 + 4 * q^85 - 10 * q^87 + 2 * q^89 + 14 * q^91 - 2 * q^93 - 6 * q^95 + 32 * q^97 + 4 * q^99

Introduction

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