LMFDB - Embedded newform 3784.1.em.b.443.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3784,1,Mod(203,3784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3784, base_ring=CyclotomicField(210))

chi = DirichletCharacter(H, H._module([105, 105, 84, 170]))

N = Newforms(chi, 1, names="a")

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

chi := DirichletCharacter("3784.203");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3784 = 2^{3} \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3784.em (of order $210$, degree $48$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.88846200780$
Analytic rank:	$0$
Dimension:	$48$
Coefficient field:	$\Q(\zeta_{210})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 $ x^48 - x^47 + x^46 + x^43 - x^42 + 2x^41 - x^40 + x^39 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 - x^28 - x^26 - x^24 - x^22 - x^20 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 + x^9 - x^8 + 2x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{105}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{105} - \cdots)$

Embedding invariants

Embedding label			443.1
Root			$-0.193256 - 0.981148i$ of defining polynomial
Character	$\chi$	$=$	3784.443
Dual form			3784.1.em.b.3579.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.393025 - 0.919528i) q^{2} +(-0.827762 - 0.461537i) q^{3} +(-0.691063 + 0.722795i) q^{4} +(-0.0990655 + 0.942546i) q^{6} +(0.936235 + 0.351375i) q^{8} +(-0.0535114 - 0.0865941i) q^{9} +O(q^{10})$	\(q+(-0.393025 - 0.919528i) q^{2} +(-0.827762 - 0.461537i) q^{3} +(-0.691063 + 0.722795i) q^{4} +(-0.0990655 + 0.942546i) q^{6} +(0.936235 + 0.351375i) q^{8} +(-0.0535114 - 0.0865941i) q^{9} +(-0.873408 - 0.486989i) q^{11} +(0.905632 - 0.279350i) q^{12} +(-0.0448648 - 0.998993i) q^{16} +(1.72456 + 0.895019i) q^{17} +(-0.0585943 + 0.0832389i) q^{18} +(0.518961 - 0.212690i) q^{19} +(-0.104528 + 0.994522i) q^{22} +(-0.612807 - 0.722962i) q^{24} +(0.0149594 + 0.999888i) q^{25} +(0.0468484 + 1.04316i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(0.498210 + 0.806221i) q^{33} +(0.145199 - 1.93755i) q^{34} +(0.0995695 + 0.0211642i) q^{36} +(-0.399540 - 0.393607i) q^{38} +(-0.501148 + 0.0451041i) q^{41} +(0.193256 + 0.981148i) q^{43} +(0.955573 - 0.294755i) q^{44} +(-0.423935 + 0.847635i) q^{48} +(-0.104528 + 0.994522i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-1.01444 - 1.53681i) q^{51} +(0.940802 - 0.453066i) q^{54} +(-0.527741 - 0.0634632i) q^{57} +(0.787106 - 0.295406i) q^{59} +(0.753071 + 0.657939i) q^{64} +(0.545534 - 0.774983i) q^{66} +(-0.146194 - 1.95083i) q^{67} +(-1.83870 + 0.627990i) q^{68} +(-0.0196723 - 0.0998750i) q^{72} +(1.82382 - 0.109268i) q^{73} +(0.449103 - 0.834573i) q^{75} +(-0.204903 + 0.522085i) q^{76} +(0.397144 - 0.794068i) q^{81} +(0.238438 + 0.443092i) q^{82} +(-0.780427 + 0.0938498i) q^{83} +(0.826239 - 0.563320i) q^{86} +(-0.646600 - 0.762830i) q^{88} +(1.23552 - 1.14639i) q^{89} +(0.946041 + 0.0566786i) q^{96} +(0.183156 - 0.340361i) q^{97} +(0.955573 - 0.294755i) q^{98} +(0.00456697 + 0.101691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-1$

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 $

$2$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$2$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$3$	−0.827762	−	0.461537i	−0.827762	−	0.461537i	0.0149594	−	0.999888i	$-0.495238\pi$
$3$	−0.827762	−	0.461537i	−0.827762	−	0.461537i	−0.842721	+	0.538351i	$0.819048\pi$
$4$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$5$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$5$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$6$	−0.0990655	+	0.942546i	−0.0990655	+	0.942546i
$7$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$7$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$8$	0.936235	+	0.351375i	0.936235	+	0.351375i
$9$	−0.0535114	−	0.0865941i	−0.0535114	−	0.0865941i
$10$		0			0
$11$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$11$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$12$	0.905632	−	0.279350i	0.905632	−	0.279350i
$13$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$13$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$14$		0			0
$15$		0			0
$16$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$17$	1.72456	+	0.895019i	1.72456	+	0.895019i	0.971490	+	0.237080i	$0.0761905\pi$
$17$	1.72456	+	0.895019i	1.72456	+	0.895019i	0.753071	+	0.657939i	$0.228571\pi$
$18$	−0.0585943	+	0.0832389i	−0.0585943	+	0.0832389i
$19$	0.518961	−	0.212690i	0.518961	−	0.212690i	−0.104528	−	0.994522i	$-0.533333\pi$
$19$	0.518961	−	0.212690i	0.518961	−	0.212690i	0.623490	+	0.781831i	$0.285714\pi$
$20$		0			0
$21$		0			0
$22$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$23$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$23$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$24$	−0.612807	−	0.722962i	−0.612807	−	0.722962i
$25$	0.0149594	+	0.999888i	0.0149594	+	0.999888i
$26$		0			0
$27$	0.0468484	+	1.04316i	0.0468484	+	1.04316i
$28$		0			0
$29$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$29$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$30$		0			0
$31$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$31$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$32$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$33$	0.498210	+	0.806221i	0.498210	+	0.806221i
$34$	0.145199	−	1.93755i	0.145199	−	1.93755i
$35$		0			0
$36$	0.0995695	+	0.0211642i	0.0995695	+	0.0211642i
$37$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$37$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$38$	−0.399540	−	0.393607i	−0.399540	−	0.393607i
$39$		0			0
$40$		0			0
$41$	−0.501148	+	0.0451041i	−0.501148	+	0.0451041i	−0.337330	−	0.941386i	$-0.609524\pi$
$41$	−0.501148	+	0.0451041i	−0.501148	+	0.0451041i	−0.163818	+	0.986491i	$0.552381\pi$
$42$		0			0
$43$	0.193256	+	0.981148i	0.193256	+	0.981148i
$43$	0.193256	+	0.981148i	0.193256	+	0.981148i
$44$	0.955573	−	0.294755i	0.955573	−	0.294755i
$45$		0			0
$46$		0			0
$47$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$47$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$48$	−0.423935	+	0.847635i	−0.423935	+	0.847635i
$49$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$50$	0.913545	−	0.406737i	0.913545	−	0.406737i
$51$	−1.01444	−	1.53681i	−1.01444	−	1.53681i
$52$		0			0
$53$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$53$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$54$	0.940802	−	0.453066i	0.940802	−	0.453066i
$55$		0			0
$56$		0			0
$57$	−0.527741	−	0.0634632i	−0.527741	−	0.0634632i
$58$		0			0
$59$	0.787106	−	0.295406i	0.787106	−	0.295406i	0.0747301	−	0.997204i	$-0.476190\pi$
$59$	0.787106	−	0.295406i	0.787106	−	0.295406i	0.712376	+	0.701798i	$0.247619\pi$
$60$		0			0
$61$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$61$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$62$		0			0
$63$		0			0
$64$	0.753071	+	0.657939i	0.753071	+	0.657939i
$65$		0			0
$66$	0.545534	−	0.774983i	0.545534	−	0.774983i
$67$	−0.146194	−	1.95083i	−0.146194	−	1.95083i	−0.280427	−	0.959875i	$-0.590476\pi$
$67$	−0.146194	−	1.95083i	−0.146194	−	1.95083i	0.134233	−	0.990950i	$-0.457143\pi$
$68$	−1.83870	+	0.627990i	−1.83870	+	0.627990i
$69$		0			0
$70$		0			0
$71$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$71$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$72$	−0.0196723	−	0.0998750i	−0.0196723	−	0.0998750i
$73$	1.82382	−	0.109268i	1.82382	−	0.109268i	0.887586	−	0.460642i	$-0.152381\pi$
$73$	1.82382	−	0.109268i	1.82382	−	0.109268i	0.936235	+	0.351375i	$0.114286\pi$
$74$		0			0
$75$	0.449103	−	0.834573i	0.449103	−	0.834573i
$76$	−0.204903	+	0.522085i	−0.204903	+	0.522085i
$77$		0			0
$78$		0			0
$79$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$79$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$80$		0			0
$81$	0.397144	−	0.794068i	0.397144	−	0.794068i
$82$	0.238438	+	0.443092i	0.238438	+	0.443092i
$83$	−0.780427	+	0.0938498i	−0.780427	+	0.0938498i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−0.780427	+	0.0938498i	−0.780427	+	0.0938498i	−0.280427	+	0.959875i	$0.590476\pi$
$84$		0			0
$85$		0			0
$86$	0.826239	−	0.563320i	0.826239	−	0.563320i
$87$		0			0
$88$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$89$	1.23552	−	1.14639i	1.23552	−	1.14639i	0.251587	−	0.967835i	$-0.419048\pi$
$89$	1.23552	−	1.14639i	1.23552	−	1.14639i	0.983930	−	0.178557i	$-0.0571429\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.946041	+	0.0566786i	0.946041	+	0.0566786i
$97$	0.183156	−	0.340361i	0.183156	−	0.340361i	−0.772417	−	0.635116i	$-0.780952\pi$
$97$	0.183156	−	0.340361i	0.183156	−	0.340361i	0.955573	+	0.294755i	$0.0952381\pi$
$98$	0.955573	−	0.294755i	0.955573	−	0.294755i
$99$	0.00456697	+	0.101691i	0.00456697	+	0.101691i
$100$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$101$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$101$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$102$	−1.01444	+	1.53681i	−1.01444	+	1.53681i
$103$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$103$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.52389	−	0.910484i	1.52389	−	0.910484i	0.525684	−	0.850680i	$-0.323810\pi$
$107$	1.52389	−	0.910484i	1.52389	−	0.910484i	0.998210	−	0.0598042i	$-0.0190476\pi$
$108$	−0.786366	−	0.687027i	−0.786366	−	0.687027i
$109$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$109$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.01949	−	1.54447i	1.01949	−	1.54447i	0.193256	−	0.981148i	$-0.438095\pi$
$113$	1.01949	−	1.54447i	1.01949	−	1.54447i	0.826239	−	0.563320i	$-0.190476\pi$
$114$	0.149059	+	0.510215i	0.149059	+	0.510215i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.580986	−	0.607664i	−0.580986	−	0.607664i
$119$		0			0
$120$		0			0
$121$	0.525684	+	0.850680i	0.525684	+	0.850680i
$122$		0			0
$123$	0.435648	+	0.193963i	0.435648	+	0.193963i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$127$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$128$	0.309017	−	0.951057i	0.309017	−	0.951057i
$129$	0.292867	−	0.901352i	0.292867	−	0.901352i
$130$		0			0
$131$	0.199073	−	0.872196i	0.199073	−	0.872196i	−0.772417	−	0.635116i	$-0.780952\pi$
$131$	0.199073	−	0.872196i	0.199073	−	0.872196i	0.971490	−	0.237080i	$-0.0761905\pi$
$132$	−0.927027	−	0.197046i	−0.927027	−	0.197046i
$133$		0			0
$134$	−1.73638	+	0.901153i	−1.73638	+	0.901153i
$135$		0			0
$136$	1.30011	+	1.44392i	1.30011	+	1.44392i
$137$	−1.45187	+	0.400690i	−1.45187	+	0.400690i	−0.900969	−	0.433884i	$-0.857143\pi$
$137$	−1.45187	+	0.400690i	−1.45187	+	0.400690i	−0.550897	+	0.834573i	$0.685714\pi$
$138$		0			0
$139$	1.52758	+	1.25604i	1.52758	+	1.25604i	0.858449	+	0.512899i	$0.171429\pi$
$139$	1.52758	+	1.25604i	1.52758	+	1.25604i	0.669131	+	0.743145i	$0.266667\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.0841061	+	0.0573426i	−0.0841061	+	0.0573426i
$145$		0			0
$146$	−0.817282	−	1.63411i	−0.817282	−	1.63411i
$147$	0.545534	−	0.774983i	0.545534	−	0.774983i
$148$		0			0
$149$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$149$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$150$	−0.943922	−	0.0849545i	−0.943922	−	0.0849545i
$151$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$151$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$152$	0.560604	−	0.0167782i	0.560604	−	0.0167782i
$153$	−0.0147804	−	0.197231i	−0.0147804	−	0.197231i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$157$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.886255	−	0.0530968i	−0.886255	−	0.0530968i
$163$	−0.172233	−	0.278713i	−0.172233	−	0.278713i	0.753071	−	0.657939i	$-0.228571\pi$
$163$	−0.172233	−	0.278713i	−0.172233	−	0.278713i	−0.925304	+	0.379225i	$0.876190\pi$
$164$	0.313724	−	0.393397i	0.313724	−	0.393397i
$165$		0			0
$166$	0.393025	+	0.680739i	0.393025	+	0.680739i
$167$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$167$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$168$		0			0
$169$	0.420357	+	0.907359i	0.420357	+	0.907359i
$170$		0			0
$171$	−0.0461881	−	0.0335576i	−0.0461881	−	0.0335576i
$172$	−0.842721	−	0.538351i	−0.842721	−	0.538351i
$173$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$173$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$174$		0			0
$175$		0			0
$176$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$177$	−0.787877	−	0.118753i	−0.787877	−	0.118753i
$178$	−1.53973	−	0.685531i	−1.53973	−	0.685531i
$179$	−0.822343	−	0.174794i	−0.822343	−	0.174794i	−0.222521	−	0.974928i	$-0.571429\pi$
$179$	−0.822343	−	0.174794i	−0.822343	−	0.174794i	−0.599822	+	0.800134i	$0.704762\pi$
$180$		0			0
$181$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$181$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.07038	−	1.62156i	−1.07038	−	1.62156i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$191$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$192$	−0.319700	−	0.892187i	−0.319700	−	0.892187i
$193$	0.174913	−	0.409228i	0.174913	−	0.409228i	−0.809017	−	0.587785i	$-0.800000\pi$
$193$	0.174913	−	0.409228i	0.174913	−	0.409228i	0.983930	+	0.178557i	$0.0571429\pi$
$194$	−0.384956	−	0.0346467i	−0.384956	−	0.0346467i
$195$		0			0
$196$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$197$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$197$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$198$	0.0917132	−	0.0441667i	0.0917132	−	0.0441667i
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	−0.337330	+	0.941386i	−0.337330	+	0.941386i
$201$	−0.779365	+	1.68229i	−0.779365	+	1.68229i
$202$		0			0
$203$		0			0
$204$	1.81184	+	0.328801i	1.81184	+	0.328801i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−0.556843	−	0.0669628i	−0.556843	−	0.0669628i
$210$		0			0
$211$	−0.0882877	+	0.0160218i	−0.0882877	+	0.0160218i	−0.222521	−	0.974928i	$-0.571429\pi$
$211$	−0.0882877	+	0.0160218i	−0.0882877	+	0.0160218i	0.134233	+	0.990950i	$0.457143\pi$
$212$		0			0
$213$		0			0
$214$	−1.43614	−	1.04342i	−1.43614	−	1.04342i
$215$		0			0
$216$	−0.322679	+	0.993104i	−0.322679	+	0.993104i
$217$		0			0
$218$		0			0
$219$	−1.56012	−	0.751314i	−1.56012	−	0.751314i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$223$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$224$		0			0
$225$	0.0857839	−	0.0548008i	0.0857839	−	0.0548008i
$226$	−1.82087	−	0.330439i	−1.82087	−	0.330439i
$227$	0.0172218	−	1.15111i	0.0172218	−	1.15111i	−0.809017	−	0.587785i	$-0.800000\pi$
$227$	0.0172218	−	1.15111i	0.0172218	−	1.15111i	0.826239	−	0.563320i	$-0.190476\pi$
$228$	0.410573	−	0.337591i	0.410573	−	0.337591i
$229$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$229$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.89181	−	0.646130i	1.89181	−	0.646130i	0.936235	−	0.351375i	$-0.114286\pi$
$233$	1.89181	−	0.646130i	1.89181	−	0.646130i	0.955573	−	0.294755i	$-0.0952381\pi$
$234$		0			0
$235$		0			0
$236$	−0.330422	+	0.773060i	−0.330422	+	0.773060i
$237$		0			0
$238$		0			0
$239$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$239$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$240$		0			0
$241$	−1.69772	+	0.255890i	−1.69772	+	0.255890i	−0.925304	−	0.379225i	$-0.876190\pi$
$241$	−1.69772	+	0.255890i	−1.69772	+	0.255890i	−0.772417	+	0.635116i	$0.780952\pi$
$242$	0.575617	−	0.817719i	0.575617	−	0.817719i
$243$	0.167535	−	0.114223i	0.167535	−	0.114223i
$244$		0			0
$245$		0			0
$246$	0.00713379	−	0.476823i	0.00713379	−	0.476823i
$247$		0			0
$248$		0			0
$249$	0.689323	+	0.282511i	0.689323	+	0.282511i
$250$		0			0
$251$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$251$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$257$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i	−0.978148	−	0.207912i	$-0.933333\pi$
$257$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i	0.913545	+	0.406737i	$0.133333\pi$
$258$	−0.943922	+	0.0849545i	−0.943922	+	0.0849545i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.880249	+	0.159742i	−0.880249	+	0.159742i
$263$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$263$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$264$	0.183156	+	0.929871i	0.183156	+	0.929871i
$265$		0			0
$266$		0			0
$267$	−1.55182	+	0.378702i	−1.55182	+	0.378702i
$268$	1.51108	+	1.24247i	1.51108	+	1.24247i
$269$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$269$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$270$		0			0
$271$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$271$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$272$	0.816746	−	1.76298i	0.816746	−	1.76298i
$273$		0			0
$274$	0.939065	+	1.17755i	0.939065	+	1.17755i
$275$	0.473869	−	0.880596i	0.473869	−	0.880596i
$276$		0			0
$277$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$277$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$278$	0.554590	−	1.89831i	0.554590	−	1.89831i
$279$		0			0
$280$		0			0
$281$	−0.616333	−	1.72000i	−0.616333	−	1.72000i	−0.691063	−	0.722795i	$-0.742857\pi$
$281$	−0.616333	−	1.72000i	−0.616333	−	1.72000i	0.0747301	−	0.997204i	$-0.476190\pi$
$282$		0			0
$283$	0.0247201	+	1.65229i	0.0247201	+	1.65229i	0.575617	+	0.817719i	$0.304762\pi$
$283$	0.0247201	+	1.65229i	0.0247201	+	1.65229i	−0.550897	+	0.834573i	$0.685714\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.0857839	+	0.0548008i	0.0857839	+	0.0548008i
$289$	1.59744	+	2.26931i	1.59744	+	2.26931i
$290$		0			0
$291$	−0.308699	+	0.197204i	−0.308699	+	0.197204i
$292$	−1.18140	+	1.39376i	−1.18140	+	1.39376i
$293$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$293$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$294$	−0.927027	−	0.197046i	−0.927027	−	0.197046i
$295$		0			0
$296$		0			0
$297$	0.467089	−	0.933919i	0.467089	−	0.933919i
$298$		0			0
$299$		0			0
$300$	0.292867	+	0.901352i	0.292867	+	0.901352i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.235759	−	0.508896i	−0.235759	−	0.508896i
$305$		0			0
$306$	−0.175550	+	0.0911075i	−0.175550	+	0.0911075i
$307$	−0.525684	−	0.910511i	−0.525684	−	0.910511i	−0.999552	−	0.0299155i	$-0.990476\pi$
$307$	−0.525684	−	0.910511i	−0.525684	−	0.910511i	0.473869	−	0.880596i	$-0.342857\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$311$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$312$		0			0
$313$	1.04266	+	0.356110i	1.04266	+	0.356110i	0.791071	−	0.611724i	$-0.209524\pi$
$313$	1.04266	+	0.356110i	1.04266	+	0.356110i	0.251587	+	0.967835i	$0.419048\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$317$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.68164	+	0.0503297i	−1.68164	+	0.0503297i
$322$		0			0
$323$	1.08534	+	0.0976826i	1.08534	+	0.0976826i
$324$	0.299496	+	0.835804i	0.299496	+	0.835804i
$325$		0			0
$326$	−0.188593	+	0.267914i	−0.188593	+	0.267914i
$327$		0			0
$328$	−0.485041	−	0.133863i	−0.485041	−	0.133863i
$329$		0			0
$330$		0			0
$331$	0.725455	+	1.84843i	0.725455	+	1.84843i	0.473869	+	0.880596i	$0.342857\pi$
$331$	0.725455	+	1.84843i	0.725455	+	1.84843i	0.251587	+	0.967835i	$0.419048\pi$
$332$	0.471490	−	0.628945i	0.471490	−	0.628945i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0200196	+	0.0222340i	0.0200196	+	0.0222340i	0.753071	−	0.657939i	$-0.228571\pi$
$337$	0.0200196	+	0.0222340i	0.0200196	+	0.0222340i	−0.733052	+	0.680173i	$0.761905\pi$
$338$	0.669131	−	0.743145i	0.669131	−	0.743145i
$339$	−1.55673	+	0.807917i	−1.55673	+	0.807917i
$340$		0			0
$341$		0			0
$342$	−0.0127041	+	0.0556602i	−0.0127041	+	0.0556602i
$343$		0			0
$344$	−0.163818	+	0.986491i	−0.163818	+	0.986491i
$345$		0			0
$346$		0			0
$347$	−1.83737	+	0.220952i	−1.83737	+	0.220952i	−0.963963	−	0.266037i	$-0.914286\pi$
$347$	−1.83737	+	0.220952i	−1.83737	+	0.220952i	−0.873408	+	0.486989i	$0.838095\pi$
$348$		0			0
$349$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$349$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$350$		0			0
$351$		0			0
$352$	0.998210	+	0.0598042i	0.998210	+	0.0598042i
$353$	−0.0244843	+	0.326720i	−0.0244843	+	0.326720i	0.971490	+	0.237080i	$0.0761905\pi$
$353$	−0.0244843	+	0.326720i	−0.0244843	+	0.326720i	−0.995974	+	0.0896393i	$0.971429\pi$
$354$	0.200458	+	0.771148i	0.200458	+	0.771148i
$355$		0			0
$356$	−0.0252132	+	1.68525i	−0.0252132	+	1.68525i
$357$		0			0
$358$	0.162473	+	0.824866i	0.162473	+	0.824866i
$359$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$359$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$360$		0			0
$361$	−0.488292	+	0.481042i	−0.488292	+	0.481042i
$362$		0			0
$363$	−0.0425201	−	0.946783i	−0.0425201	−	0.946783i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$367$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$368$		0			0
$369$	0.0307229	+	0.0409829i	0.0307229	+	0.0409829i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$373$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$374$	−1.07038	+	1.62156i	−1.07038	+	1.62156i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.91414	+	0.528268i	−1.91414	+	0.528268i	−0.925304	+	0.379225i	$0.876190\pi$
$379$	−1.91414	+	0.528268i	−1.91414	+	0.528268i	−0.988831	+	0.149042i	$0.952381\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$383$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$384$	−0.694741	+	0.644625i	−0.694741	+	0.644625i
$385$		0			0
$386$	−0.445042			−0.445042
$387$	0.0746203	−	0.0692375i	0.0746203	−	0.0692375i
$388$	0.119439	+	0.367595i	0.119439	+	0.367595i
$389$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$389$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$390$		0			0
$391$		0			0
$392$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$393$	−0.567336	+	0.630091i	−0.567336	+	0.630091i
$394$		0			0
$395$		0			0
$396$	−0.0766581	−	0.0669742i	−0.0766581	−	0.0669742i
$397$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$397$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$398$		0			0
$399$		0			0
$400$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$401$	0.291071	+	1.47775i	0.291071	+	1.47775i	0.791071	+	0.611724i	$0.209524\pi$
$401$	0.291071	+	1.47775i	0.291071	+	1.47775i	−0.500000	+	0.866025i	$0.666667\pi$
$402$	1.85322	+	0.0554649i	1.85322	+	0.0554649i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.409758	−	1.79527i	−0.409758	−	1.79527i
$409$	0.550256	+	0.480744i	0.550256	+	0.480744i	0.887586	−	0.460642i	$-0.152381\pi$
$409$	0.550256	+	0.480744i	0.550256	+	0.480744i	−0.337330	+	0.941386i	$0.609524\pi$
$410$		0			0
$411$	1.38673	+	0.338415i	1.38673	+	0.338415i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.684760	−	1.74474i	−0.684760	−	1.74474i
$418$	0.157279	+	0.538351i	0.157279	+	0.538351i
$419$	1.73700	−	0.836496i	1.73700	−	0.836496i	0.753071	−	0.657939i	$-0.228571\pi$
$419$	1.73700	−	0.836496i	1.73700	−	0.836496i	0.983930	−	0.178557i	$-0.0571429\pi$
$420$		0			0
$421$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$421$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$422$	0.0494318	+	0.0748860i	0.0494318	+	0.0748860i
$423$		0			0
$424$		0			0
$425$	−0.869121	+	1.73776i	−0.869121	+	1.73776i
$426$		0			0
$427$		0			0
$428$	−0.395013	+	1.73066i	−0.395013	+	1.73066i
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	1.04001	−	0.0936024i	1.04001	−	0.0936024i
$433$	0.787106	+	1.69900i	0.787106	+	1.69900i	0.712376	+	0.701798i	$0.247619\pi$
$433$	0.787106	+	1.69900i	0.787106	+	1.69900i	0.0747301	+	0.997204i	$0.476190\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.0776880	+	1.72986i	−0.0776880	+	1.72986i
$439$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$439$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$440$		0			0
$441$	0.0917132	−	0.0441667i	0.0917132	−	0.0441667i
$442$		0			0
$443$	1.48916	−	1.22446i	1.48916	−	1.22446i	0.575617	−	0.817719i	$-0.304762\pi$
$443$	1.48916	−	1.22446i	1.48916	−	1.22446i	0.913545	−	0.406737i	$-0.133333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.12949	+	1.33252i	1.12949	+	1.33252i	0.936235	+	0.351375i	$0.114286\pi$
$449$	1.12949	+	1.33252i	1.12949	+	1.33252i	0.193256	+	0.981148i	$0.438095\pi$
$450$	−0.0841061	−	0.0573426i	−0.0841061	−	0.0573426i
$451$	0.459672	+	0.204659i	0.459672	+	0.204659i
$452$	0.411799	+	1.80421i	0.411799	+	1.80421i
$453$		0			0
$454$	−1.06524	+	0.436577i	−1.06524	+	0.436577i
$455$		0			0
$456$	−0.471790	−	0.244851i	−0.471790	−	0.244851i
$457$	−0.0639213	−	1.42332i	−0.0639213	−	1.42332i	−0.733052	−	0.680173i	$-0.761905\pi$
$457$	−0.0639213	−	1.42332i	−0.0639213	−	1.42332i	0.669131	−	0.743145i	$-0.266667\pi$
$458$		0			0
$459$	−0.852855	+	1.84092i	−0.852855	+	1.84092i
$460$		0			0
$461$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$461$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$462$		0			0
$463$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$463$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$464$		0			0
$465$		0			0
$466$	−1.33766	−	1.48562i	−1.33766	−	1.48562i
$467$	−0.0763771	+	0.726679i	−0.0763771	+	0.726679i	0.887586	+	0.460642i	$0.152381\pi$
$467$	−0.0763771	+	0.726679i	−0.0763771	+	0.726679i	−0.963963	+	0.266037i	$0.914286\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.840714			0.840714
$473$	0.309017	−	0.951057i	0.309017	−	0.951057i
$474$		0			0
$475$	0.220430	+	0.515722i	0.220430	+	0.515722i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$479$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$480$		0			0
$481$		0			0
$482$	0.902545	+	1.46053i	0.902545	+	1.46053i
$483$		0			0
$484$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$485$		0			0
$486$	−0.170877	−	0.109160i	−0.170877	−	0.109160i
$487$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$487$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$488$		0			0
$489$	0.0139311	+	0.310200i	0.0139311	+	0.310200i
$490$		0			0
$491$	0.605185	−	0.859724i	0.605185	−	0.859724i	−0.393025	−	0.919528i	$-0.628571\pi$
$491$	0.605185	−	0.859724i	0.605185	−	0.859724i	0.998210	+	0.0598042i	$0.0190476\pi$
$492$	−0.441256	+	0.180844i	−0.441256	+	0.180844i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.0111443	−	0.744886i	−0.0111443	−	0.744886i
$499$	−0.0633176	+	0.381290i	−0.0633176	+	0.381290i	0.936235	+	0.351375i	$0.114286\pi$
$499$	−0.0633176	+	0.381290i	−0.0633176	+	0.381290i	−0.999552	+	0.0299155i	$0.990476\pi$
$500$		0			0
$501$		0			0
$502$	0.873408	−	0.486989i	0.873408	−	0.486989i
$503$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$503$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.0708245	−	0.945087i	0.0708245	−	0.945087i
$508$		0			0
$509$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$509$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$510$		0			0
$511$		0			0
$512$	0.473869	+	0.880596i	0.473869	+	0.880596i
$513$	0.246183	+	0.531395i	0.246183	+	0.531395i
$514$	0.208215	−	0.0187397i	0.208215	−	0.0187397i
$515$		0			0
$516$	0.449103	+	0.834573i	0.449103	+	0.834573i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.400178	−	0.800134i	0.400178	−	0.800134i	−0.599822	−	0.800134i	$-0.704762\pi$
$521$	0.400178	−	0.800134i	0.400178	−	0.800134i	1.00000			$0$
$522$		0			0
$523$	1.82382	−	0.812017i	1.82382	−	0.812017i	0.887586	−	0.460642i	$-0.152381\pi$
$523$	1.82382	−	0.812017i	1.82382	−	0.812017i	0.936235	−	0.351375i	$-0.114286\pi$
$524$	0.492847	+	0.746631i	0.492847	+	0.746631i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.783057	−	0.533879i	0.783057	−	0.533879i
$529$	0.365341	+	0.930874i	0.365341	+	0.930874i
$530$		0			0
$531$	−0.0676996	−	0.0523512i	−0.0676996	−	0.0523512i
$532$		0			0
$533$		0			0
$534$	0.958129	+	1.27810i	0.958129	+	1.27810i
$535$		0			0
$536$	0.548599	−	1.87780i	0.548599	−	1.87780i
$537$	0.600030	+	0.524230i	0.600030	+	0.524230i
$538$		0			0
$539$	0.575617	−	0.817719i	0.575617	−	0.817719i
$540$		0			0
$541$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$541$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$542$		0			0
$543$		0			0
$544$	−1.94211	−	0.0581252i	−1.94211	−	0.0581252i
$545$		0			0
$546$		0			0
$547$	1.07783	+	1.53115i	1.07783	+	1.53115i	0.826239	+	0.563320i	$0.190476\pi$
$547$	1.07783	+	1.53115i	1.07783	+	1.53115i	0.251587	+	0.967835i	$0.419048\pi$
$548$	0.713714	−	1.32630i	0.713714	−	1.32630i
$549$		0			0
$550$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−1.96352	+	0.236121i	−1.96352	+	0.236121i
$557$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$557$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.137611	+	1.83629i	0.137611	+	1.83629i
$562$	−1.33935	+	1.24274i	−1.33935	+	1.24274i
$563$	−1.89694	+	0.344244i	−1.89694	+	0.344244i	−0.995974	−	0.0896393i	$-0.971429\pi$
$563$	−1.89694	+	0.344244i	−1.89694	+	0.344244i	−0.900969	+	0.433884i	$0.857143\pi$
$564$		0			0
$565$		0			0
$566$	1.50961	−	0.672123i	1.50961	−	0.672123i
$567$		0			0
$568$		0			0
$569$	−1.74369	−	0.104467i	−1.74369	−	0.104467i	−0.842721	−	0.538351i	$-0.819048\pi$
$569$	−1.74369	−	0.104467i	−1.74369	−	0.104467i	−0.900969	+	0.433884i	$0.857143\pi$
$570$		0			0
$571$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	0.0747301	+	0.997204i	$0.476190\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.0166757	−	0.100419i	0.0166757	−	0.100419i
$577$	−1.02983	−	1.37375i	−1.02983	−	1.37375i	−0.925304	−	0.379225i	$-0.876190\pi$
$577$	−1.02983	−	1.37375i	−1.02983	−	1.37375i	−0.104528	−	0.994522i	$-0.533333\pi$
$578$	1.45886	−	2.36078i	1.45886	−	2.36078i
$579$	−0.333660	+	0.258015i	−0.333660	+	0.258015i
$580$		0			0
$581$		0			0
$582$	0.302661	+	0.206351i	0.302661	+	0.206351i
$583$		0			0
$584$	1.74592	+	0.538545i	1.74592	+	0.538545i
$585$		0			0
$586$		0			0
$587$	−0.322838	−	1.10504i	−0.322838	−	1.10504i	−0.946327	−	0.323210i	$-0.895238\pi$
$587$	−0.322838	−	1.10504i	−0.322838	−	1.10504i	0.623490	−	0.781831i	$-0.285714\pi$
$588$	0.183156	+	0.929871i	0.183156	+	0.929871i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.118234	−	1.57772i	0.118234	−	1.57772i	−0.550897	−	0.834573i	$-0.685714\pi$
$593$	0.118234	−	1.57772i	0.118234	−	1.57772i	0.669131	−	0.743145i	$-0.266667\pi$
$594$	−1.04234	−	0.0624482i	−1.04234	−	0.0624482i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$599$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$600$	0.713714	−	0.623553i	0.713714	−	0.623553i
$601$	0.613613	−	1.88851i	0.613613	−	1.88851i	0.193256	−	0.981148i	$-0.438095\pi$
$601$	0.613613	−	1.88851i	0.613613	−	1.88851i	0.420357	−	0.907359i	$-0.361905\pi$
$602$		0			0
$603$	−0.161107	+	0.117051i	−0.161107	+	0.117051i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$607$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$608$	−0.375285	+	0.416796i	−0.375285	+	0.416796i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.152771	+	0.125616i	0.152771	+	0.125616i
$613$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$613$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$614$	−0.630633	+	0.841234i	−0.630633	+	0.841234i
$615$		0			0
$616$		0			0
$617$	0.221817	−	0.151233i	0.221817	−	0.151233i	−0.447313	−	0.894377i	$-0.647619\pi$
$617$	0.221817	−	0.151233i	0.221817	−	0.151233i	0.669131	+	0.743145i	$0.266667\pi$
$618$		0			0
$619$	0.618243	+	1.23614i	0.618243	+	1.23614i	0.955573	+	0.294755i	$0.0952381\pi$
$619$	0.618243	+	1.23614i	0.618243	+	1.23614i	−0.337330	+	0.941386i	$0.609524\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$626$	−0.0823372	−	1.09871i	−0.0823372	−	1.09871i
$627$	0.430027	+	0.312433i	0.430027	+	0.312433i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$631$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$632$		0			0
$633$	0.0804758	+	0.0274858i	0.0804758	+	0.0274858i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.254057	+	1.87553i	−0.254057	+	1.87553i	0.193256	+	0.981148i	$0.438095\pi$
$641$	−0.254057	+	1.87553i	−0.254057	+	1.87553i	−0.447313	+	0.894377i	$0.647619\pi$
$642$	0.707207	+	1.52654i	0.707207	+	1.52654i
$643$	−0.508067	+	0.443885i	−0.508067	+	0.443885i	−0.873408	−	0.486989i	$-0.838095\pi$
$643$	−0.508067	+	0.443885i	−0.508067	+	0.443885i	0.365341	+	0.930874i	$0.380952\pi$
$644$		0			0
$645$		0			0
$646$	−0.336745	−	1.03639i	−0.336745	−	1.03639i
$647$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$647$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$648$	0.650836	−	0.603887i	0.650836	−	0.603887i
$649$	−0.831324	−	0.125302i	−0.831324	−	0.125302i
$650$		0			0
$651$		0			0
$652$	0.320476	+	0.0681193i	0.320476	+	0.0681193i
$653$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$653$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$654$		0			0
$655$		0			0
$656$	0.0675426	+	0.498620i	0.0675426	+	0.498620i
$657$	−0.107057	−	0.152085i	−0.107057	−	0.152085i
$658$		0			0
$659$	1.01317	+	0.940084i	1.01317	+	0.940084i	0.998210	−	0.0598042i	$-0.0190476\pi$
$659$	1.01317	+	0.940084i	1.01317	+	0.940084i	0.0149594	+	0.999888i	$0.495238\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	1.41456	−	1.39356i	1.41456	−	1.39356i
$663$		0			0
$664$	−0.763640	−	0.186357i	−0.763640	−	0.186357i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.521119	−	1.45429i	0.521119	−	1.45429i	−0.337330	−	0.941386i	$-0.609524\pi$
$673$	0.521119	−	1.45429i	0.521119	−	1.45429i	0.858449	−	0.512899i	$-0.171429\pi$
$674$	0.0125766	−	0.0271471i	0.0125766	−	0.0271471i
$675$	−1.04234	+	0.0624482i	−1.04234	+	0.0624482i
$676$	−0.946327	−	0.323210i	−0.946327	−	0.323210i
$677$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$677$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$678$	1.35474	+	1.11392i	1.35474	+	1.11392i
$679$		0			0
$680$		0			0
$681$	−0.545534	+	0.944892i	−0.545534	+	0.944892i
$682$		0			0
$683$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$683$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$684$	0.0561741	−	0.0101941i	0.0561741	−	0.0101941i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.971490	−	0.237080i	0.971490	−	0.237080i
$689$		0			0
$690$		0			0
$691$	0.258627	−	1.31303i	0.258627	−	1.31303i	−0.599822	−	0.800134i	$-0.704762\pi$
$691$	0.258627	−	1.31303i	0.258627	−	1.31303i	0.858449	−	0.512899i	$-0.171429\pi$
$692$		0			0
$693$		0			0
$694$	0.925304	+	1.60267i	0.925304	+	1.60267i
$695$		0			0
$696$		0			0
$697$	−0.904629	−	0.370752i	−0.904629	−	0.370752i
$698$		0			0
$699$	−1.86418	−	0.338299i	−1.86418	−	0.338299i
$700$		0			0
$701$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$701$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$702$		0			0
$703$		0			0
$704$	−0.337330	−	0.941386i	−0.337330	−	0.941386i
$705$		0			0
$706$	0.310051	−	0.105895i	0.310051	−	0.105895i
$707$		0			0
$708$	0.630307	−	0.487408i	0.630307	−	0.487408i
$709$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$709$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$710$		0			0
$711$		0			0
$712$	1.55955	−	0.639162i	1.55955	−	0.639162i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.694631	−	0.473591i	0.694631	−	0.473591i
$717$		0			0
$718$		0			0
$719$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$719$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$720$		0			0
$721$		0			0
$722$	0.634242	+	0.259937i	0.634242	+	0.259937i
$723$	1.52341	+	0.571746i	1.52341	+	0.571746i
$724$		0			0
$725$		0			0
$726$	−0.853882	+	0.411208i	−0.853882	+	0.411208i
$727$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$727$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$728$		0			0
$729$	−1.07567	+	0.0968118i	−1.07567	+	0.0968118i
$730$		0			0
$731$	−0.544865	+	1.86502i	−0.544865	+	1.86502i
$732$		0			0
$733$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$733$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.822343	+	1.77506i	−0.822343	+	1.77506i
$738$	0.0256100	−	0.0443578i	0.0256100	−	0.0443578i
$739$	−0.0840080	+	1.87058i	−0.0840080	+	1.87058i	0.309017	+	0.951057i	$0.400000\pi$
$739$	−0.0840080	+	1.87058i	−0.0840080	+	1.87058i	−0.393025	+	0.919528i	$0.628571\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$743$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.0498886	+	0.0625584i	0.0498886	+	0.0625584i
$748$	1.91176	+	0.346932i	1.91176	+	0.346932i
$749$		0			0
$750$		0			0
$751$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$751$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$752$		0			0
$753$	0.372484	−	0.871471i	0.372484	−	0.871471i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$757$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$758$	1.23806	+	1.55248i	1.23806	+	1.55248i
$759$		0			0
$760$		0			0
$761$	−1.57797	−	1.00805i	−1.57797	−	1.00805i	−0.978148	−	0.207912i	$-0.933333\pi$
$761$	−1.57797	−	1.00805i	−1.57797	−	1.00805i	−0.599822	−	0.800134i	$-0.704762\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.865801	+	0.385479i	0.865801	+	0.385479i
$769$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.900969	−	0.433884i	$-0.857143\pi$
$769$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.988831	+	0.149042i	$0.952381\pi$
$770$		0			0
$771$	0.145240	−	0.134763i	0.145240	−	0.134763i
$772$	0.174913	+	0.409228i	0.174913	+	0.409228i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	−0.0929934	−	0.0414033i	−0.0929934	−	0.0414033i
$775$		0			0
$776$	0.291071	−	0.254301i	0.291071	−	0.254301i
$777$		0			0
$778$		0			0
$779$	−0.250483	+	0.129997i	−0.250483	+	0.129997i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.998210	+	0.0598042i	0.998210	+	0.0598042i
$785$		0			0
$786$	0.802363	+	0.274040i	0.802363	+	0.274040i
$787$	0.0675426	−	0.259831i	0.0675426	−	0.259831i	−0.925304	−	0.379225i	$-0.876190\pi$
$787$	0.0675426	−	0.259831i	0.0675426	−	0.259831i	0.992847	+	0.119394i	$0.0380952\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.0314561	+	0.0968118i	−0.0314561	+	0.0968118i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$797$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$798$		0			0
$799$		0			0
$800$	−0.447313	−	0.894377i	−0.447313	−	0.894377i
$801$	−0.165385	−	0.0456434i	−0.165385	−	0.0456434i
$802$	1.24443	−	0.848441i	1.24443	−	0.848441i
$803$	−1.64615	−	0.792745i	−1.64615	−	0.792745i
$804$	−0.677362	−	1.72589i	−0.677362	−	1.72589i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−0.258792	+	0.0714220i	−0.258792	+	0.0714220i	−0.393025	−	0.919528i	$-0.628571\pi$
$809$	−0.258792	+	0.0714220i	−0.258792	+	0.0714220i	0.134233	+	0.990950i	$0.457143\pi$
$810$		0			0
$811$	−0.139886	+	0.155360i	−0.139886	+	0.155360i	−0.809017	−	0.587785i	$-0.800000\pi$
$811$	−0.139886	+	0.155360i	−0.139886	+	0.155360i	0.669131	+	0.743145i	$0.266667\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−1.48975	+	1.08237i	−1.48975	+	1.08237i
$817$	0.308973	+	0.468074i	0.308973	+	0.468074i
$818$	0.225793	−	0.694920i	0.225793	−	0.694920i
$819$		0			0
$820$		0			0
$821$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$821$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$822$	−0.233838	−	1.40814i	−0.233838	−	1.40814i
$823$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$823$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$824$		0			0
$825$	−0.798678	+	0.510215i	−0.798678	+	0.510215i
$826$		0			0
$827$	−0.388660	−	1.49514i	−0.388660	−	1.49514i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	−0.388660	−	1.49514i	−0.388660	−	1.49514i	0.420357	−	0.907359i	$-0.361905\pi$
$828$		0			0
$829$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$829$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.07038	+	1.62156i	−1.07038	+	1.62156i
$834$	−1.33521	+	1.31538i	−1.33521	+	1.31538i
$835$		0			0
$836$	0.433214	−	0.356208i	0.433214	−	0.356208i
$837$		0			0
$838$	−1.45187	−	1.26846i	−1.45187	−	1.26846i
$839$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$839$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$840$		0			0
$841$	0.525684	−	0.850680i	0.525684	−	0.850680i
$842$		0			0
$843$	−0.283667	+	1.70821i	−0.283667	+	1.70821i
$844$	0.0494318	−	0.0748860i	0.0494318	−	0.0748860i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.742133	−	1.37911i	0.742133	−	1.37911i
$850$	1.93950	+	0.116198i	1.93950	+	0.116198i
$851$		0			0
$852$		0			0
$853$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$853$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$854$		0			0
$855$		0			0
$856$	1.74664	−	0.316969i	1.74664	−	0.316969i
$857$	−1.44254	+	1.33848i	−1.44254	+	1.33848i	−0.599822	+	0.800134i	$0.704762\pi$
$857$	−1.44254	+	1.33848i	−1.44254	+	1.33848i	−0.842721	+	0.538351i	$0.819048\pi$
$858$		0			0
$859$	−0.894626			−0.894626			−0.447313	−	0.894377i	$-0.647619\pi$
$859$	−0.894626			−0.894626			−0.447313	+	0.894377i	$0.647619\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$863$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$864$	−0.494819	−	0.919528i	−0.494819	−	0.919528i
$865$		0			0
$866$	1.25293	−	1.39152i	1.25293	−	1.39152i
$867$	−0.274924	−	2.61573i	−0.274924	−	2.61573i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.0392741	+	0.00235297i	−0.0392741	+	0.00235297i
$874$		0			0
$875$		0			0
$876$	1.62119	−	0.608441i	1.62119	−	0.608441i
$877$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$877$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.150126	+	0.657745i	0.150126	+	0.657745i	0.992847	+	0.119394i	$0.0380952\pi$
$881$	0.150126	+	0.657745i	0.150126	+	0.657745i	−0.842721	+	0.538351i	$0.819048\pi$
$882$	−0.0766581	−	0.0669742i	−0.0766581	−	0.0669742i
$883$	−0.551842	+	1.88890i	−0.551842	+	1.88890i	−0.104528	+	0.994522i	$0.533333\pi$
$883$	−0.551842	+	1.88890i	−0.551842	+	1.88890i	−0.447313	+	0.894377i	$0.647619\pi$
$884$		0			0
$885$		0			0
$886$	−1.71120	−	0.888084i	−1.71120	−	0.888084i
$887$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$887$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.733571	+	0.500140i	−0.733571	+	0.500140i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.781374	−	1.56231i	0.781374	−	1.56231i
$899$		0			0
$900$	−0.0196723	+	0.0998750i	−0.0196723	+	0.0998750i
$901$		0			0
$902$	0.00752718	−	0.503117i	0.00752718	−	0.503117i
$903$		0			0
$904$	1.49717	−	1.08776i	1.49717	−	1.08776i
$905$		0			0
$906$		0			0
$907$	0.946041	+	1.75804i	0.946041	+	1.75804i	0.525684	+	0.850680i	$0.323810\pi$
$907$	0.946041	+	1.75804i	0.946041	+	1.75804i	0.420357	+	0.907359i	$0.361905\pi$
$908$	0.820112	+	0.807934i	0.820112	+	0.807934i
$909$		0			0
$910$		0			0
$911$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$911$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$912$	−0.0397223	+	0.530057i	−0.0397223	+	0.530057i
$913$	0.727336	+	0.298090i	0.727336	+	0.298090i
$914$	−1.28366	+	0.618177i	−1.28366	+	0.618177i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	2.02797	+	0.0606949i	2.02797	+	0.0606949i
$919$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$919$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$920$		0			0
$921$	0.0149059	+	0.996309i	0.0149059	+	0.996309i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.18782	+	0.616460i	1.18782	+	0.616460i	0.936235	−	0.351375i	$-0.114286\pi$
$929$	1.18782	+	0.616460i	1.18782	+	0.616460i	0.251587	+	0.967835i	$0.419048\pi$
$930$		0			0
$931$	0.157279	+	0.538351i	0.157279	+	0.538351i
$932$	−0.840338	+	1.81391i	−0.840338	+	1.81391i
$933$		0			0
$934$	0.698220	−	0.215372i	0.698220	−	0.215372i
$935$		0			0
$936$		0			0
$937$	−0.918273	−	1.48598i	−0.918273	−	1.48598i	−0.873408	−	0.486989i	$-0.838095\pi$
$937$	−0.918273	−	1.48598i	−0.918273	−	1.48598i	−0.0448648	−	0.998993i	$-0.514286\pi$
$938$		0			0
$939$	−0.698714	−	0.776000i	−0.698714	−	0.776000i
$940$		0			0
$941$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$941$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$942$		0			0
$943$		0			0
$944$	−0.330422	−	0.773060i	−0.330422	−	0.773060i
$945$		0			0
$946$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$947$	1.58214			1.58214			0.791071	−	0.611724i	$-0.209524\pi$
$947$	1.58214			1.58214			0.791071	+	0.611724i	$0.209524\pi$
$948$		0			0
$949$		0			0
$950$	0.387586	−	0.405383i	0.387586	−	0.405383i
$951$		0			0
$952$		0			0
$953$	−1.29003	−	1.43273i	−1.29003	−	1.43273i	−0.842721	−	0.538351i	$-0.819048\pi$
$953$	−1.29003	−	1.43273i	−1.29003	−	1.43273i	−0.447313	−	0.894377i	$-0.647619\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$962$		0			0
$963$	−0.160388	−	0.0832389i	−0.160388	−	0.0832389i
$964$	0.988276	−	1.40394i	0.988276	−	1.40394i
$965$		0			0
$966$		0			0
$967$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$967$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$968$	0.193256	+	0.981148i	0.193256	+	0.981148i
$969$	−0.853321	−	0.581784i	−0.853321	−	0.581784i
$970$		0			0
$971$	0.0186541	+	1.24684i	0.0186541	+	1.24684i	0.791071	+	0.611724i	$0.209524\pi$
$971$	0.0186541	+	1.24684i	0.0186541	+	1.24684i	−0.772417	+	0.635116i	$0.780952\pi$
$972$	−0.0332171	+	0.200029i	−0.0332171	+	0.200029i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.991192	+	1.32220i	−0.991192	+	1.32220i	−0.0448648	+	0.998993i	$0.514286\pi$
$977$	−0.991192	+	1.32220i	−0.991192	+	1.32220i	−0.946327	+	0.323210i	$0.895238\pi$
$978$	0.279762	−	0.134726i	0.279762	−	0.134726i
$979$	−1.63739	+	0.399585i	−1.63739	+	0.399585i
$980$		0			0
$981$		0			0
$982$	−1.02839	−	0.218592i	−1.02839	−	0.218592i
$983$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$983$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$984$	0.339715	+	0.334671i	0.339715	+	0.334671i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$991$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$992$		0			0
$993$	0.252616	−	1.86488i	0.252616	−	1.86488i
$994$		0			0
$995$		0			0
$996$	−0.680563	+	0.303006i	−0.680563	+	0.303006i
$997$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$997$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$998$	0.375492	−	0.0916344i	0.375492	−	0.0916344i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.443.1	yes	48
8.3	odd	2	CM	3784.1.em.b.443.1	yes	48
11.4	even	5		3784.1.em.a.1819.1	✓	48
43.10	even	21		3784.1.em.a.2203.1	yes	48
88.59	odd	10		3784.1.em.a.1819.1	✓	48
344.139	odd	42		3784.1.em.a.2203.1	yes	48
473.268	even	105	inner	3784.1.em.b.3579.1	yes	48
3784.3579	odd	210	inner	3784.1.em.b.3579.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.1819.1	✓	48	11.4	even	5
3784.1.em.a.1819.1	✓	48	88.59	odd	10
3784.1.em.a.2203.1	yes	48	43.10	even	21
3784.1.em.a.2203.1	yes	48	344.139	odd	42
3784.1.em.b.443.1	yes	48	1.1	even	1	trivial
3784.1.em.b.443.1	yes	48	8.3	odd	2	CM
3784.1.em.b.3579.1	yes	48	473.268	even	105	inner
3784.1.em.b.3579.1	yes	48	3784.3579	odd	210	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3784 = 2^{3} \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3784.em (of order \(210\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.393025 - 0.919528i) q^{2} +(-0.827762 - 0.461537i) q^{3} +(-0.691063 + 0.722795i) q^{4} +(-0.0990655 + 0.942546i) q^{6} +(0.936235 + 0.351375i) q^{8} +(-0.0535114 - 0.0865941i) q^{9} +O(q^{10})\)	\(q+(-0.393025 - 0.919528i) q^{2} +(-0.827762 - 0.461537i) q^{3} +(-0.691063 + 0.722795i) q^{4} +(-0.0990655 + 0.942546i) q^{6} +(0.936235 + 0.351375i) q^{8} +(-0.0535114 - 0.0865941i) q^{9} +(-0.873408 - 0.486989i) q^{11} +(0.905632 - 0.279350i) q^{12} +(-0.0448648 - 0.998993i) q^{16} +(1.72456 + 0.895019i) q^{17} +(-0.0585943 + 0.0832389i) q^{18} +(0.518961 - 0.212690i) q^{19} +(-0.104528 + 0.994522i) q^{22} +(-0.612807 - 0.722962i) q^{24} +(0.0149594 + 0.999888i) q^{25} +(0.0468484 + 1.04316i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(0.498210 + 0.806221i) q^{33} +(0.145199 - 1.93755i) q^{34} +(0.0995695 + 0.0211642i) q^{36} +(-0.399540 - 0.393607i) q^{38} +(-0.501148 + 0.0451041i) q^{41} +(0.193256 + 0.981148i) q^{43} +(0.955573 - 0.294755i) q^{44} +(-0.423935 + 0.847635i) q^{48} +(-0.104528 + 0.994522i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-1.01444 - 1.53681i) q^{51} +(0.940802 - 0.453066i) q^{54} +(-0.527741 - 0.0634632i) q^{57} +(0.787106 - 0.295406i) q^{59} +(0.753071 + 0.657939i) q^{64} +(0.545534 - 0.774983i) q^{66} +(-0.146194 - 1.95083i) q^{67} +(-1.83870 + 0.627990i) q^{68} +(-0.0196723 - 0.0998750i) q^{72} +(1.82382 - 0.109268i) q^{73} +(0.449103 - 0.834573i) q^{75} +(-0.204903 + 0.522085i) q^{76} +(0.397144 - 0.794068i) q^{81} +(0.238438 + 0.443092i) q^{82} +(-0.780427 + 0.0938498i) q^{83} +(0.826239 - 0.563320i) q^{86} +(-0.646600 - 0.762830i) q^{88} +(1.23552 - 1.14639i) q^{89} +(0.946041 + 0.0566786i) q^{96} +(0.183156 - 0.340361i) q^{97} +(0.955573 - 0.294755i) q^{98} +(0.00456697 + 0.101691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

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