LMFDB - Embedded newform 3784.1.em.b.267.1

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			267.1
Root			$-0.887586 - 0.460642i$ of defining polynomial
Character	$\chi$	$=$	3784.267
Dual form			3784.1.em.b.411.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.963963 - 0.266037i) q^{2} +(-0.246733 - 1.48580i) q^{3} +(0.858449 + 0.512899i) q^{4} +(-0.157435 + 1.49789i) q^{6} +(-0.691063 - 0.722795i) q^{8} +(-1.20038 + 0.409981i) q^{9} +O(q^{10})$	\(q+(-0.963963 - 0.266037i) q^{2} +(-0.246733 - 1.48580i) q^{3} +(0.858449 + 0.512899i) q^{4} +(-0.157435 + 1.49789i) q^{6} +(-0.691063 - 0.722795i) q^{8} +(-1.20038 + 0.409981i) q^{9} +(-0.163818 - 0.986491i) q^{11} +(0.550256 - 1.40203i) q^{12} +(0.473869 + 0.880596i) q^{16} +(-0.0299054 - 0.000895035i) q^{17} +(1.26620 - 0.0758596i) q^{18} +(-1.00550 - 1.42841i) q^{19} +(-0.104528 + 0.994522i) q^{22} +(-0.903418 + 1.20512i) q^{24} +(-0.772417 + 0.635116i) q^{25} +(0.191608 + 0.356068i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(-1.42530 + 0.486800i) q^{33} +(0.0285896 + 0.00881873i) q^{34} +(-1.24075 - 0.263729i) q^{36} +(0.589254 + 1.64443i) q^{38} +(0.712420 - 1.07927i) q^{41} +(0.887586 + 0.460642i) q^{43} +(0.365341 - 0.930874i) q^{44} +(1.19147 - 0.921344i) q^{48} +(-0.104528 + 0.994522i) q^{49} +(0.913545 - 0.406737i) q^{50} +(0.00604882 + 0.0446542i) q^{51} +(-0.0899761 - 0.394211i) q^{54} +(-1.87423 + 1.84640i) q^{57} +(0.618243 - 0.646631i) q^{59} +(-0.0448648 + 0.998993i) q^{64} +(1.50345 - 0.0900736i) q^{66} +(-1.86938 + 0.576628i) q^{67} +(-0.0252132 - 0.0161068i) q^{68} +(1.12587 + 0.584310i) q^{72} +(-1.69062 - 0.692879i) q^{73} +(1.13423 + 0.990950i) q^{75} +(-0.130540 - 1.74193i) q^{76} +(-0.521679 + 0.403407i) q^{81} +(-0.973871 + 0.850846i) q^{82} +(-1.37341 - 1.35301i) q^{83} +(-0.733052 - 0.680173i) q^{86} +(-0.599822 + 0.800134i) q^{88} +(-1.03962 - 0.156698i) q^{89} +(-1.39364 + 0.571168i) q^{96} +(1.33683 + 1.16795i) q^{97} +(0.365341 - 0.930874i) q^{98} +(0.601087 + 1.11701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$2$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$3$	−0.246733	−	1.48580i	−0.246733	−	1.48580i	−0.772417	−	0.635116i	$-0.780952\pi$
$3$	−0.246733	−	1.48580i	−0.246733	−	1.48580i	0.525684	−	0.850680i	$-0.323810\pi$
$4$	0.858449	+	0.512899i	0.858449	+	0.512899i
$5$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$5$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$6$	−0.157435	+	1.49789i	−0.157435	+	1.49789i
$7$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$7$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$8$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$9$	−1.20038	+	0.409981i	−1.20038	+	0.409981i
$10$		0			0
$11$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$11$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$12$	0.550256	−	1.40203i	0.550256	−	1.40203i
$13$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$13$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$14$		0			0
$15$		0			0
$16$	0.473869	+	0.880596i	0.473869	+	0.880596i
$17$	−0.0299054		0.000895035i	−0.0299054		0.000895035i	0.0149594	−	0.999888i	$-0.495238\pi$
$17$	−0.0299054		0.000895035i	−0.0299054		0.000895035i	−0.0448648	+	0.998993i	$0.514286\pi$
$18$	1.26620	−	0.0758596i	1.26620	−	0.0758596i
$19$	−1.00550	−	1.42841i	−1.00550	−	1.42841i	−0.900969	−	0.433884i	$-0.857143\pi$
$19$	−1.00550	−	1.42841i	−1.00550	−	1.42841i	−0.104528	−	0.994522i	$-0.533333\pi$
$20$		0			0
$21$		0			0
$22$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$23$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$23$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$24$	−0.903418	+	1.20512i	−0.903418	+	1.20512i
$25$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$26$		0			0
$27$	0.191608	+	0.356068i	0.191608	+	0.356068i
$28$		0			0
$29$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$29$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$30$		0			0
$31$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$31$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$32$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$33$	−1.42530	+	0.486800i	−1.42530	+	0.486800i
$34$	0.0285896	+	0.00881873i	0.0285896	+	0.00881873i
$35$		0			0
$36$	−1.24075	−	0.263729i	−1.24075	−	0.263729i
$37$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$37$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$38$	0.589254	+	1.64443i	0.589254	+	1.64443i
$39$		0			0
$40$		0			0
$41$	0.712420	−	1.07927i	0.712420	−	1.07927i	−0.280427	−	0.959875i	$-0.590476\pi$
$41$	0.712420	−	1.07927i	0.712420	−	1.07927i	0.992847	−	0.119394i	$-0.0380952\pi$
$42$		0			0
$43$	0.887586	+	0.460642i	0.887586	+	0.460642i
$43$	0.887586	+	0.460642i	0.887586	+	0.460642i
$44$	0.365341	−	0.930874i	0.365341	−	0.930874i
$45$		0			0
$46$		0			0
$47$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$47$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$48$	1.19147	−	0.921344i	1.19147	−	0.921344i
$49$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$50$	0.913545	−	0.406737i	0.913545	−	0.406737i
$51$	0.00604882	+	0.0446542i	0.00604882	+	0.0446542i
$52$		0			0
$53$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$53$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$54$	−0.0899761	−	0.394211i	−0.0899761	−	0.394211i
$55$		0			0
$56$		0			0
$57$	−1.87423	+	1.84640i	−1.87423	+	1.84640i
$58$		0			0
$59$	0.618243	−	0.646631i	0.618243	−	0.646631i	−0.337330	−	0.941386i	$-0.609524\pi$
$59$	0.618243	−	0.646631i	0.618243	−	0.646631i	0.955573	+	0.294755i	$0.0952381\pi$
$60$		0			0
$61$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$61$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$62$		0			0
$63$		0			0
$64$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$65$		0			0
$66$	1.50345	−	0.0900736i	1.50345	−	0.0900736i
$67$	−1.86938	+	0.576628i	−1.86938	+	0.576628i	−0.873408	+	0.486989i	$0.838095\pi$
$67$	−1.86938	+	0.576628i	−1.86938	+	0.576628i	−0.995974	+	0.0896393i	$0.971429\pi$
$68$	−0.0252132	−	0.0161068i	−0.0252132	−	0.0161068i
$69$		0			0
$70$		0			0
$71$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$71$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$72$	1.12587	+	0.584310i	1.12587	+	0.584310i
$73$	−1.69062	−	0.692879i	−1.69062	−	0.692879i	−0.691063	−	0.722795i	$-0.742857\pi$
$73$	−1.69062	−	0.692879i	−1.69062	−	0.692879i	−0.999552	+	0.0299155i	$0.990476\pi$
$74$		0			0
$75$	1.13423	+	0.990950i	1.13423	+	0.990950i
$76$	−0.130540	−	1.74193i	−0.130540	−	1.74193i
$77$		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
$81$	−0.521679	+	0.403407i	−0.521679	+	0.403407i
$82$	−0.973871	+	0.850846i	−0.973871	+	0.850846i
$83$	−1.37341	−	1.35301i	−1.37341	−	1.35301i	−0.873408	−	0.486989i	$-0.838095\pi$
$83$	−1.37341	−	1.35301i	−1.37341	−	1.35301i	−0.500000	−	0.866025i	$-0.666667\pi$
$84$		0			0
$85$		0			0
$86$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$87$		0			0
$88$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$89$	−1.03962	−	0.156698i	−1.03962	−	0.156698i	−0.393025	−	0.919528i	$-0.628571\pi$
$89$	−1.03962	−	0.156698i	−1.03962	−	0.156698i	−0.646600	+	0.762830i	$0.723810\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−1.39364	+	0.571168i	−1.39364	+	0.571168i
$97$	1.33683	+	1.16795i	1.33683	+	1.16795i	0.971490	+	0.237080i	$0.0761905\pi$
$97$	1.33683	+	1.16795i	1.33683	+	1.16795i	0.365341	+	0.930874i	$0.380952\pi$
$98$	0.365341	−	0.930874i	0.365341	−	0.930874i
$99$	0.601087	+	1.11701i	0.601087	+	1.11701i
$100$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$101$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$101$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$102$	0.00604882	−	0.0446542i	0.00604882	−	0.0446542i
$103$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$103$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.87163	−	0.702435i	−1.87163	−	0.702435i	−0.946327	−	0.323210i	$-0.895238\pi$
$107$	−1.87163	−	0.702435i	−1.87163	−	0.702435i	−0.925304	−	0.379225i	$-0.876190\pi$
$108$	−0.0181410	+	0.403942i	−0.0181410	+	0.403942i
$109$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$109$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.154534	−	1.14082i	0.154534	−	1.14082i	−0.733052	−	0.680173i	$-0.761905\pi$
$113$	0.154534	−	1.14082i	0.154534	−	1.14082i	0.887586	−	0.460642i	$-0.152381\pi$
$114$	2.29790	−	1.28125i	2.29790	−	1.28125i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.767991	+	0.458853i	−0.767991	+	0.458853i
$119$		0			0
$120$		0			0
$121$	−0.946327	+	0.323210i	−0.946327	+	0.323210i
$122$		0			0
$123$	−1.77935	−	0.792218i	−1.77935	−	0.792218i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$127$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$128$	0.309017	−	0.951057i	0.309017	−	0.951057i
$129$	0.465424	−	1.43243i	0.465424	−	1.43243i
$130$		0			0
$131$	0.986449	+	1.23697i	0.986449	+	1.23697i	0.971490	+	0.237080i	$0.0761905\pi$
$131$	0.986449	+	1.23697i	0.986449	+	1.23697i	0.0149594	+	0.999888i	$0.495238\pi$
$132$	−1.47323	−	0.313145i	−1.47323	−	0.313145i
$133$		0			0
$134$	1.95542	−	0.0585235i	1.95542	−	0.0585235i
$135$		0			0
$136$	0.0200196	+	0.0222340i	0.0200196	+	0.0222340i
$137$	−0.0882877	−	0.0160218i	−0.0882877	−	0.0160218i	0.134233	−	0.990950i	$-0.457143\pi$
$137$	−0.0882877	−	0.0160218i	−0.0882877	−	0.0160218i	−0.222521	+	0.974928i	$0.571429\pi$
$138$		0			0
$139$	1.60537	+	0.391770i	1.60537	+	0.391770i	0.936235	−	0.351375i	$-0.114286\pi$
$139$	1.60537	+	0.391770i	1.60537	+	0.391770i	0.669131	+	0.743145i	$0.266667\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.929852	−	0.862776i	−0.929852	−	0.862776i
$145$		0			0
$146$	1.44536	+	1.11768i	1.44536	+	1.11768i
$147$	1.50345	−	0.0900736i	1.50345	−	0.0900736i
$148$		0			0
$149$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$149$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$150$	−0.829730	−	1.25699i	−0.829730	−	1.25699i
$151$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$151$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$152$	−0.337583	+	1.71389i	−0.337583	+	1.71389i
$153$	0.0362650	−	0.0111863i	0.0362650	−	0.0111863i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$157$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.610200	−	0.250084i	0.610200	−	0.250084i
$163$	0.530752	−	0.181274i	0.530752	−	0.181274i	−0.0448648	−	0.998993i	$-0.514286\pi$
$163$	0.530752	−	0.181274i	0.530752	−	0.181274i	0.575617	+	0.817719i	$0.304762\pi$
$164$	1.16513	−	0.561098i	1.16513	−	0.561098i
$165$		0			0
$166$	0.963963	+	1.66963i	0.963963	+	1.66963i
$167$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$167$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$168$		0			0
$169$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$170$		0			0
$171$	1.79260	+	1.30240i	1.79260	+	1.30240i
$172$	0.525684	+	0.850680i	0.525684	+	0.850680i
$173$		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
$176$	0.791071	−	0.611724i	0.791071	−	0.611724i
$177$	−1.11330	−	0.759037i	−1.11330	−	0.759037i
$178$	0.960472	+	0.427630i	0.960472	+	0.427630i
$179$	0.875077	+	0.186003i	0.875077	+	0.186003i	0.623490	−	0.781831i	$-0.285714\pi$
$179$	0.875077	+	0.186003i	0.875077	+	0.186003i	0.251587	+	0.967835i	$0.419048\pi$
$180$		0			0
$181$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$181$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.00401610	+	0.0296480i	0.00401610	+	0.0296480i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$191$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$192$	1.49537	−	0.179825i	1.49537	−	0.179825i
$193$	−1.20204	+	0.331743i	−1.20204	+	0.331743i	−0.809017	−	0.587785i	$-0.800000\pi$
$193$	−1.20204	+	0.331743i	−1.20204	+	0.331743i	−0.393025	+	0.919528i	$0.628571\pi$
$194$	−0.977937	−	1.48151i	−0.977937	−	1.48151i
$195$		0			0
$196$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$197$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$197$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$198$	−0.282260	−	1.23666i	−0.282260	−	1.23666i
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	0.992847	+	0.119394i	0.992847	+	0.119394i
$201$	1.31799	+	2.63525i	1.31799	+	2.63525i
$202$		0			0
$203$		0			0
$204$	−0.0177105	+	0.0414358i	−0.0177105	+	0.0414358i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.24439	+	1.22591i	−1.24439	+	1.22591i
$210$		0			0
$211$	−0.372484	−	0.871471i	−0.372484	−	0.871471i	−0.995974	−	0.0896393i	$-0.971429\pi$
$211$	−0.372484	−	0.871471i	−0.372484	−	0.871471i	0.623490	−	0.781831i	$-0.285714\pi$
$212$		0			0
$213$		0			0
$214$	1.61731	+	1.17504i	1.61731	+	1.17504i
$215$		0			0
$216$	0.124951	−	0.384559i	0.124951	−	0.384559i
$217$		0			0
$218$		0			0
$219$	−0.612346	+	2.68287i	−0.612346	+	2.68287i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$223$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$224$		0			0
$225$	0.666812	−	1.07906i	0.666812	−	1.07906i
$226$	−0.452464	+	1.05859i	−0.452464	+	1.05859i
$227$	−1.54207	−	1.26796i	−1.54207	−	1.26796i	−0.809017	−	0.587785i	$-0.800000\pi$
$227$	−1.54207	−	1.26796i	−1.54207	−	1.26796i	−0.733052	−	0.680173i	$-0.761905\pi$
$228$	−2.55595	+	0.623748i	−2.55595	+	0.623748i
$229$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$229$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.325722	−	0.208079i	−0.325722	−	0.208079i	0.365341	−	0.930874i	$-0.380952\pi$
$233$	−0.325722	−	0.208079i	−0.325722	−	0.208079i	−0.691063	+	0.722795i	$0.742857\pi$
$234$		0			0
$235$		0			0
$236$	0.862387	−	0.238004i	0.862387	−	0.238004i
$237$		0			0
$238$		0			0
$239$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$239$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$240$		0			0
$241$	1.54711	−	1.05480i	1.54711	−	1.05480i	0.575617	−	0.817719i	$-0.304762\pi$
$241$	1.54711	−	1.05480i	1.54711	−	1.05480i	0.971490	−	0.237080i	$-0.0761905\pi$
$242$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$243$	1.02451	+	0.950602i	1.02451	+	0.950602i
$244$		0			0
$245$		0			0
$246$	1.50447	+	1.23704i	1.50447	+	1.23704i
$247$		0			0
$248$		0			0
$249$	−1.67144	+	2.37444i	−1.67144	+	2.37444i
$250$		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
$256$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$257$	−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	$0.133333\pi$
$258$	−0.829730	+	1.25699i	−0.829730	+	1.25699i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.621821	−	1.45482i	−0.621821	−	1.45482i
$263$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$263$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$264$	1.33683	+	0.693793i	1.33683	+	0.693793i
$265$		0			0
$266$		0			0
$267$	0.0236884	+	1.58333i	0.0236884	+	1.58333i
$268$	−1.90052	−	0.463799i	−1.90052	−	0.463799i
$269$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$269$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$270$		0			0
$271$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$271$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$272$	−0.0133831	−	0.0267587i	−0.0133831	−	0.0267587i
$273$		0			0
$274$	0.0808436	+	0.0389322i	0.0808436	+	0.0389322i
$275$	0.753071	+	0.657939i	0.753071	+	0.657939i
$276$		0			0
$277$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$277$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$278$	−1.44329	−	0.804738i	−1.44329	−	0.804738i
$279$		0			0
$280$		0			0
$281$	1.81402	−	0.218144i	1.81402	−	0.218144i	0.858449	−	0.512899i	$-0.171429\pi$
$281$	1.81402	−	0.218144i	1.81402	−	0.218144i	0.955573	+	0.294755i	$0.0952381\pi$
$282$		0			0
$283$	1.13244	−	0.931146i	1.13244	−	0.931146i	0.134233	−	0.990950i	$-0.457143\pi$
$283$	1.13244	−	0.931146i	1.13244	−	0.931146i	0.998210	+	0.0598042i	$0.0190476\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.666812	+	1.07906i	0.666812	+	1.07906i
$289$	−0.997317	−	0.0597506i	−0.997317	−	0.0597506i
$290$		0			0
$291$	1.40550	−	2.27443i	1.40550	−	2.27443i
$292$	−1.09593	−	1.46192i	−1.09593	−	1.46192i
$293$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$293$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$294$	−1.47323	−	0.313145i	−1.47323	−	0.313145i
$295$		0			0
$296$		0			0
$297$	0.319869	−	0.247350i	0.319869	−	0.247350i
$298$		0			0
$299$		0			0
$300$	0.465424	+	1.43243i	0.465424	+	1.43243i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.781374	−	1.56231i	0.781374	−	1.56231i
$305$		0			0
$306$	−0.0379340	+	0.00113532i	−0.0379340	+	0.00113532i
$307$	0.946327	+	1.63909i	0.946327	+	1.63909i	0.753071	+	0.657939i	$0.228571\pi$
$307$	0.946327	+	1.63909i	0.946327	+	1.63909i	0.193256	+	0.981148i	$0.438095\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$311$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$312$		0			0
$313$	−0.226242	+	0.144529i	−0.226242	+	0.144529i	−0.646600	−	0.762830i	$-0.723810\pi$
$313$	−0.226242	+	0.144529i	−0.226242	+	0.144529i	0.420357	+	0.907359i	$0.361905\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$317$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.581882	+	2.95418i	−0.581882	+	2.95418i
$322$		0			0
$323$	0.0287913	+	0.0436170i	0.0287913	+	0.0436170i
$324$	−0.654742	+	0.0787356i	−0.654742	+	0.0787356i
$325$		0			0
$326$	−0.559851	+	0.0335414i	−0.559851	+	0.0335414i
$327$		0			0
$328$	−1.27242	+	0.230910i	−1.27242	+	0.230910i
$329$		0			0
$330$		0			0
$331$	0.106472	−	1.42077i	0.106472	−	1.42077i	−0.646600	−	0.762830i	$-0.723810\pi$
$331$	0.106472	−	1.42077i	0.106472	−	1.42077i	0.753071	−	0.657939i	$-0.228571\pi$
$332$	−0.485041	−	1.86591i	−0.485041	−	1.86591i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.03370	−	1.14804i	−1.03370	−	1.14804i	−0.988831	−	0.149042i	$-0.952381\pi$
$337$	−1.03370	−	1.14804i	−1.03370	−	1.14804i	−0.0448648	−	0.998993i	$-0.514286\pi$
$338$	0.669131	−	0.743145i	0.669131	−	0.743145i
$339$	−1.73315	+	0.0518711i	−1.73315	+	0.0518711i
$340$		0			0
$341$		0			0
$342$	−1.38152	−	1.73237i	−1.38152	−	1.73237i
$343$		0			0
$344$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$345$		0			0
$346$		0			0
$347$	0.820112	+	0.807934i	0.820112	+	0.807934i	0.983930	−	0.178557i	$-0.0571429\pi$
$347$	0.820112	+	0.807934i	0.820112	+	0.807934i	−0.163818	+	0.986491i	$0.552381\pi$
$348$		0			0
$349$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$349$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$350$		0			0
$351$		0			0
$352$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$353$	−0.535938	−	0.165315i	−0.535938	−	0.165315i	0.0149594	−	0.999888i	$-0.495238\pi$
$353$	−0.535938	−	0.165315i	−0.535938	−	0.165315i	−0.550897	+	0.834573i	$0.685714\pi$
$354$	0.871251	+	1.02786i	0.871251	+	1.02786i
$355$		0			0
$356$	−0.812094	−	0.667740i	−0.812094	−	0.667740i
$357$		0			0
$358$	−0.794058	−	0.412103i	−0.794058	−	0.412103i
$359$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$359$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$360$		0			0
$361$	−0.691988	+	1.93113i	−0.691988	+	1.93113i
$362$		0			0
$363$	0.713714	+	1.32630i	0.713714	+	1.32630i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$367$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$368$		0			0
$369$	−0.412698	+	1.58762i	−0.412698	+	1.58762i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$373$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$374$	0.00401610	−	0.0296480i	0.00401610	−	0.0296480i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.40186	+	0.254399i	1.40186	+	0.254399i	0.826239	−	0.563320i	$-0.190476\pi$
$379$	1.40186	+	0.254399i	1.40186	+	0.254399i	0.575617	+	0.817719i	$0.304762\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$383$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$384$	−1.48932	−	0.224479i	−1.48932	−	0.224479i
$385$		0			0
$386$	1.24698			1.24698
$387$	−1.25430	−	0.189055i	−1.25430	−	0.189055i
$388$	0.548558	+	1.68829i	0.548558	+	1.68829i
$389$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$389$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$390$		0			0
$391$		0			0
$392$	0.791071	−	0.611724i	0.791071	−	0.611724i
$393$	1.59449	−	1.77086i	1.59449	−	1.77086i
$394$		0			0
$395$		0			0
$396$	−0.0569095	+	1.26719i	−0.0569095	+	1.26719i
$397$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$397$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$398$		0			0
$399$		0			0
$400$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$401$	−0.0796428	−	0.0413333i	−0.0796428	−	0.0413333i	0.420357	−	0.907359i	$-0.361905\pi$
$401$	−0.0796428	−	0.0413333i	−0.0796428	−	0.0413333i	−0.500000	+	0.866025i	$0.666667\pi$
$402$	−0.569421	−	2.89091i	−0.569421	−	2.89091i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.0280957	−	0.0352309i	0.0280957	−	0.0352309i
$409$	−0.00670551	+	0.149310i	−0.00670551	+	0.149310i	0.992847	+	0.119394i	$0.0380952\pi$
$409$	−0.00670551	+	0.149310i	−0.00670551	+	0.149310i	−0.999552	+	0.0299155i	$0.990476\pi$
$410$		0			0
$411$	−0.00202170	+	0.135131i	−0.00202170	+	0.135131i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.185993	−	2.48191i	0.185993	−	2.48191i
$418$	1.52568	−	0.850680i	1.52568	−	0.850680i
$419$	−0.437890	−	1.91852i	−0.437890	−	1.91852i	−0.393025	−	0.919528i	$-0.628571\pi$
$419$	−0.437890	−	1.91852i	−0.437890	−	1.91852i	−0.0448648	−	0.998993i	$-0.514286\pi$
$420$		0			0
$421$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$421$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$422$	0.127218	+	0.939160i	0.127218	+	0.939160i
$423$		0			0
$424$		0			0
$425$	0.0236679	−	0.0183021i	0.0236679	−	0.0183021i
$426$		0			0
$427$		0			0
$428$	−1.24642	−	1.56296i	−1.24642	−	1.56296i
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	−0.222755	+	0.337459i	−0.222755	+	0.337459i
$433$	0.618243	−	1.23614i	0.618243	−	1.23614i	−0.337330	−	0.941386i	$-0.609524\pi$
$433$	0.618243	−	1.23614i	0.618243	−	1.23614i	0.955573	−	0.294755i	$-0.0952381\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.30402	−	2.42328i	1.30402	−	2.42328i
$439$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$439$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$440$		0			0
$441$	−0.282260	−	1.23666i	−0.282260	−	1.23666i
$442$		0			0
$443$	1.91176	−	0.466541i	1.91176	−	0.466541i	0.913545	−	0.406737i	$-0.133333\pi$
$443$	1.91176	−	0.466541i	1.91176	−	0.466541i	0.998210	−	0.0598042i	$-0.0190476\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.196523	−	0.262152i	0.196523	−	0.262152i	−0.691063	−	0.722795i	$-0.742857\pi$
$449$	0.196523	−	0.262152i	0.196523	−	0.262152i	0.887586	+	0.460642i	$0.152381\pi$
$450$	−0.929852	+	0.862776i	−0.929852	+	0.862776i
$451$	−1.18140	−	0.525992i	−1.18140	−	0.525992i
$452$	0.717783	−	0.900071i	0.717783	−	0.900071i
$453$		0			0
$454$	1.14917	+	1.63251i	1.14917	+	1.63251i
$455$		0			0
$456$	2.62978	+	0.0787063i	2.62978	+	0.0787063i
$457$	−0.319700	−	0.594103i	−0.319700	−	0.594103i	0.669131	−	0.743145i	$-0.266667\pi$
$457$	−0.319700	−	0.594103i	−0.319700	−	0.594103i	−0.988831	+	0.149042i	$0.952381\pi$
$458$		0			0
$459$	−0.00541143	−	0.0108199i	−0.00541143	−	0.0108199i
$460$		0			0
$461$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$461$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$462$		0			0
$463$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$463$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$464$		0			0
$465$		0			0
$466$	0.258627	+	0.287234i	0.258627	+	0.287234i
$467$	−0.0156228	+	0.148641i	−0.0156228	+	0.148641i	−0.999552	−	0.0299155i	$-0.990476\pi$
$467$	−0.0156228	+	0.148641i	−0.0156228	+	0.148641i	0.983930	+	0.178557i	$0.0571429\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.894626			−0.894626
$473$	0.309017	−	0.951057i	0.309017	−	0.951057i
$474$		0			0
$475$	1.68387	+	0.464718i	1.68387	+	0.464718i
$476$		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
$482$	−1.77197	+	0.605200i	−1.77197	+	0.605200i
$483$		0			0
$484$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$485$		0			0
$486$	−0.734690	−	1.18890i	−0.734690	−	1.18890i
$487$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$487$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$488$		0			0
$489$	−0.400290	−	0.743863i	−0.400290	−	0.743863i
$490$		0			0
$491$	−1.88927	+	0.113189i	−1.88927	+	0.113189i	−0.963963	−	0.266037i	$-0.914286\pi$
$491$	−1.88927	+	0.113189i	−1.88927	+	0.113189i	−0.925304	+	0.379225i	$0.876190\pi$
$492$	−1.12115	−	1.59271i	−1.12115	−	1.59271i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	2.24289	−	1.84421i	2.24289	−	1.84421i
$499$	−0.497807	−	1.70394i	−0.497807	−	1.70394i	−0.691063	−	0.722795i	$-0.742857\pi$
$499$	−0.497807	−	1.70394i	−0.497807	−	1.70394i	0.193256	−	0.981148i	$-0.438095\pi$
$500$		0			0
$501$		0			0
$502$	0.163818	−	0.986491i	0.163818	−	0.986491i
$503$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$503$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.43923	+	0.443943i	1.43923	+	0.443943i
$508$		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
$512$	0.753071	−	0.657939i	0.753071	−	0.657939i
$513$	0.315948	−	0.631720i	0.315948	−	0.631720i
$514$	0.115169	−	0.174473i	0.115169	−	0.174473i
$515$		0			0
$516$	1.13423	−	0.990950i	1.13423	−	0.990950i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.25159	−	0.967835i	1.25159	−	0.967835i	0.251587	−	0.967835i	$-0.419048\pi$
$521$	1.25159	−	0.967835i	1.25159	−	0.967835i	1.00000			$0$
$522$		0			0
$523$	−1.69062	+	0.752710i	−1.69062	+	0.752710i	−0.691063	+	0.722795i	$0.742857\pi$
$523$	−1.69062	+	0.752710i	−1.69062	+	0.752710i	−0.999552	+	0.0299155i	$0.990476\pi$
$524$	0.212376	+	1.56782i	0.212376	+	1.56782i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−1.10408	−	1.02444i	−1.10408	−	1.02444i
$529$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$530$		0			0
$531$	−0.477023	+	1.02967i	−0.477023	+	1.02967i
$532$		0			0
$533$		0			0
$534$	0.398390	−	1.53258i	0.398390	−	1.53258i
$535$		0			0
$536$	1.70864	+	0.952694i	1.70864	+	0.952694i
$537$	0.0604524	−	1.34608i	0.0604524	−	1.34608i
$538$		0			0
$539$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$540$		0			0
$541$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$541$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$542$		0			0
$543$		0			0
$544$	0.00578199	+	0.0293548i	0.00578199	+	0.0293548i
$545$		0			0
$546$		0			0
$547$	−1.37965	−	0.0826568i	−1.37965	−	0.0826568i	−0.646600	−	0.762830i	$-0.723810\pi$
$547$	−1.37965	−	0.0826568i	−1.37965	−	0.0826568i	−0.733052	+	0.680173i	$0.761905\pi$
$548$	−0.0675728	−	0.0590366i	−0.0675728	−	0.0590366i
$549$		0			0
$550$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.17719	+	1.15971i	1.17719	+	1.15971i
$557$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$557$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.0430600	−	0.0132823i	0.0430600	−	0.0132823i
$562$	−1.80668	−	0.272314i	−1.80668	−	0.272314i
$563$	−0.773418	−	1.80950i	−0.773418	−	1.80950i	−0.550897	−	0.834573i	$-0.685714\pi$
$563$	−0.773418	−	1.80950i	−0.773418	−	1.80950i	−0.222521	−	0.974928i	$-0.571429\pi$
$564$		0			0
$565$		0			0
$566$	−1.33935	+	0.596318i	−1.33935	+	0.596318i
$567$		0			0
$568$		0			0
$569$	0.303163	−	0.124248i	0.303163	−	0.124248i	−0.222521	−	0.974928i	$-0.571429\pi$
$569$	0.303163	−	0.124248i	0.303163	−	0.124248i	0.525684	+	0.850680i	$0.323810\pi$
$570$		0			0
$571$	0.455573	−	1.16078i	0.455573	−	1.16078i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	0.455573	−	1.16078i	0.455573	−	1.16078i	0.955573	−	0.294755i	$-0.0952381\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.355713	−	1.21757i	−0.355713	−	1.21757i
$577$	0.471089	−	1.81224i	0.471089	−	1.81224i	−0.104528	−	0.994522i	$-0.533333\pi$
$577$	0.471089	−	1.81224i	0.471089	−	1.81224i	0.575617	−	0.817719i	$-0.304762\pi$
$578$	0.945480	+	0.322920i	0.945480	+	0.322920i
$579$	0.789485	+	1.70414i	0.789485	+	1.70414i
$580$		0			0
$581$		0			0
$582$	−1.95993	+	1.81855i	−1.95993	+	1.81855i
$583$		0			0
$584$	0.667511	+	1.70079i	0.667511	+	1.70079i
$585$		0			0
$586$		0			0
$587$	−1.74369	+	0.972234i	−1.74369	+	0.972234i	−0.842721	+	0.538351i	$0.819048\pi$
$587$	−1.74369	+	0.972234i	−1.74369	+	0.972234i	−0.900969	+	0.433884i	$0.857143\pi$
$588$	1.33683	+	0.693793i	1.33683	+	0.693793i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	0.803364	+	0.247805i	0.803364	+	0.247805i	0.669131	−	0.743145i	$-0.266667\pi$
$593$	0.803364	+	0.247805i	0.803364	+	0.247805i	0.134233	+	0.990950i	$0.457143\pi$
$594$	−0.374146	+	0.153339i	−0.374146	+	0.153339i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$599$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$600$	−0.0675728	−	1.50463i	−0.0675728	−	1.50463i
$601$	0.440273	−	1.35502i	0.440273	−	1.35502i	−0.447313	−	0.894377i	$-0.647619\pi$
$601$	0.440273	−	1.35502i	0.440273	−	1.35502i	0.887586	−	0.460642i	$-0.152381\pi$
$602$		0			0
$603$	2.00757	−	1.45859i	2.00757	−	1.45859i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$607$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$608$	−1.16885	+	1.29814i	−1.16885	+	1.29814i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.0368690	+	0.00899744i	0.0368690	+	0.00899744i
$613$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$613$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$614$	−0.476167	−	1.83178i	−0.476167	−	1.83178i
$615$		0			0
$616$		0			0
$617$	1.46020	+	1.35487i	1.46020	+	1.35487i	0.791071	+	0.611724i	$0.209524\pi$
$617$	1.46020	+	1.35487i	1.46020	+	1.35487i	0.669131	+	0.743145i	$0.266667\pi$
$618$		0			0
$619$	1.35819	+	1.05027i	1.35819	+	1.05027i	0.992847	+	0.119394i	$0.0380952\pi$
$619$	1.35819	+	1.05027i	1.35819	+	1.05027i	0.365341	+	0.930874i	$0.380952\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.193256	−	0.981148i	0.193256	−	0.981148i
$626$	0.256539	−	0.0791319i	0.256539	−	0.0791319i
$627$	2.12849	+	1.54644i	2.12849	+	1.54644i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$631$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$632$		0			0
$633$	−1.20292	+	0.768457i	−1.20292	+	0.768457i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.67866	−	0.151082i	1.67866	−	0.151082i	0.791071	−	0.611724i	$-0.209524\pi$
$641$	1.67866	−	0.151082i	1.67866	−	0.151082i	0.887586	+	0.460642i	$0.152381\pi$
$642$	1.34683	−	2.69291i	1.34683	−	2.69291i
$643$	−0.0890878	−	1.98369i	−0.0890878	−	1.98369i	−0.163818	−	0.986491i	$-0.552381\pi$
$643$	−0.0890878	−	1.98369i	−0.0890878	−	1.98369i	0.0747301	−	0.997204i	$-0.476190\pi$
$644$		0			0
$645$		0			0
$646$	−0.0161501	−	0.0497048i	−0.0161501	−	0.0497048i
$647$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$647$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$648$	0.652094	+	0.0982873i	0.652094	+	0.0982873i
$649$	−0.739175	−	0.503961i	−0.739175	−	0.503961i
$650$		0			0
$651$		0			0
$652$	0.548599	+	0.116608i	0.548599	+	0.116608i
$653$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$653$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$654$		0			0
$655$		0			0
$656$	1.28799	+	0.115921i	1.28799	+	0.115921i
$657$	2.31346	+	0.138602i	2.31346	+	0.138602i
$658$		0			0
$659$	−1.69772	+	0.255890i	−1.69772	+	0.255890i	−0.925304	−	0.379225i	$-0.876190\pi$
$659$	−1.69772	+	0.255890i	−1.69772	+	0.255890i	−0.772417	+	0.635116i	$0.780952\pi$
$660$		0			0
$661$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$661$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$662$	−0.480612	+	1.34124i	−0.480612	+	1.34124i
$663$		0			0
$664$	−0.0288406	+	1.92771i	−0.0288406	+	1.92771i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.92908	+	0.231981i	1.92908	+	0.231981i	0.992847	−	0.119394i	$-0.0380952\pi$
$673$	1.92908	+	0.231981i	1.92908	+	0.231981i	0.936235	+	0.351375i	$0.114286\pi$
$674$	0.691025	+	1.38166i	0.691025	+	1.38166i
$675$	−0.374146	−	0.153339i	−0.374146	−	0.153339i
$676$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$677$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$677$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$678$	1.68449	+	0.411079i	1.68449	+	0.411079i
$679$		0			0
$680$		0			0
$681$	−1.50345	+	2.60405i	−1.50345	+	2.60405i
$682$		0			0
$683$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	0.365341	−	0.930874i	$-0.380952\pi$
$683$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	−0.733052	+	0.680173i	$0.761905\pi$
$684$	0.870856	+	2.03747i	0.870856	+	2.03747i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.0149594	+	0.999888i	0.0149594	+	0.999888i
$689$		0			0
$690$		0			0
$691$	1.18782	−	0.616460i	1.18782	−	0.616460i	0.251587	−	0.967835i	$-0.419048\pi$
$691$	1.18782	−	0.616460i	1.18782	−	0.616460i	0.936235	+	0.351375i	$0.114286\pi$
$692$		0			0
$693$		0			0
$694$	−0.575617	−	0.996998i	−0.575617	−	0.996998i
$695$		0			0
$696$		0			0
$697$	−0.0222712	+	0.0316384i	−0.0222712	+	0.0316384i
$698$		0			0
$699$	−0.228796	+	0.535296i	−0.228796	+	0.535296i
$700$		0			0
$701$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$701$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$702$		0			0
$703$		0			0
$704$	0.992847	−	0.119394i	0.992847	−	0.119394i
$705$		0			0
$706$	0.472644	+	0.301937i	0.472644	+	0.301937i
$707$		0			0
$708$	−0.566404	−	1.22261i	−0.566404	−	1.22261i
$709$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$709$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$710$		0			0
$711$		0			0
$712$	0.605185	+	0.859724i	0.605185	+	0.859724i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.655807	+	0.608500i	0.655807	+	0.608500i
$717$		0			0
$718$		0			0
$719$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$719$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$720$		0			0
$721$		0			0
$722$	1.18080	−	1.67744i	1.18080	−	1.67744i
$723$	−1.94894	−	2.03843i	−1.94894	−	2.03843i
$724$		0			0
$725$		0			0
$726$	−0.335148	−	1.46838i	−0.335148	−	1.46838i
$727$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$727$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$728$		0			0
$729$	0.796327	−	1.20638i	0.796327	−	1.20638i
$730$		0			0
$731$	−0.0261313	−	0.0145701i	−0.0261313	−	0.0145701i
$732$		0			0
$733$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$733$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	0.875077	+	1.74967i	0.875077	+	1.74967i
$738$	0.820190	−	1.42061i	0.820190	−	1.42061i
$739$	−0.654946	+	1.21709i	−0.654946	+	1.21709i	0.309017	+	0.951057i	$0.400000\pi$
$739$	−0.654946	+	1.21709i	−0.654946	+	1.21709i	−0.963963	+	0.266037i	$0.914286\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$743$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.20333	+	1.06107i	2.20333	+	1.06107i
$748$	−0.0117588	+	0.0275112i	−0.0117588	+	0.0275112i
$749$		0			0
$750$		0			0
$751$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$751$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$752$		0			0
$753$	1.45187	−	0.400690i	1.45187	−	0.400690i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$757$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$758$	−1.28366	−	0.618177i	−1.28366	−	0.618177i
$759$		0			0
$760$		0			0
$761$	−0.726561	−	1.17575i	−0.726561	−	1.17575i	−0.978148	−	0.207912i	$-0.933333\pi$
$761$	−0.726561	−	1.17575i	−0.726561	−	1.17575i	0.251587	−	0.967835i	$-0.419048\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.37593	+	0.612604i	1.37593	+	0.612604i
$769$	0.603718	+	0.411608i	0.603718	+	0.411608i	0.826239	−	0.563320i	$-0.190476\pi$
$769$	0.603718	+	0.411608i	0.603718	+	0.411608i	−0.222521	+	0.974928i	$0.571429\pi$
$770$		0			0
$771$	0.311353	+	0.0469289i	0.311353	+	0.0469289i
$772$	−1.20204	−	0.331743i	−1.20204	−	0.331743i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	1.15880	+	0.515932i	1.15880	+	0.515932i
$775$		0			0
$776$	−0.0796428	−	1.77338i	−0.0796428	−	1.77338i
$777$		0			0
$778$		0			0
$779$	−2.25797	+	0.0675785i	−2.25797	+	0.0675785i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$785$		0			0
$786$	−2.00815	+	1.28285i	−2.00815	+	1.28285i
$787$	1.28799	−	1.51952i	1.28799	−	1.51952i	0.575617	−	0.817719i	$-0.304762\pi$
$787$	1.28799	−	1.51952i	1.28799	−	1.51952i	0.712376	−	0.701798i	$-0.247619\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.391978	−	1.20638i	0.391978	−	1.20638i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$797$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$798$		0			0
$799$		0			0
$800$	0.791071	+	0.611724i	0.791071	+	0.611724i
$801$	1.31219	−	0.238128i	1.31219	−	0.238128i
$802$	0.0657765	+	0.0610317i	0.0657765	+	0.0610317i
$803$	−0.406566	+	1.78128i	−0.406566	+	1.78128i
$804$	−0.220189	+	2.93822i	−0.220189	+	2.93822i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.95994	−	0.355676i	−1.95994	−	0.355676i	−0.995974	−	0.0896393i	$-0.971429\pi$
$809$	−1.95994	−	0.355676i	−1.95994	−	0.355676i	−0.963963	−	0.266037i	$-0.914286\pi$
$810$		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
$816$	−0.0364559	+	0.0264868i	−0.0364559	+	0.0264868i
$817$	−0.234481	−	1.73101i	−0.234481	−	1.73101i
$818$	0.0461857	−	0.142145i	0.0461857	−	0.142145i
$819$		0			0
$820$		0			0
$821$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$821$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$822$	0.0378986	−	0.129723i	0.0378986	−	0.129723i
$823$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$823$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$824$		0			0
$825$	0.791755	−	1.28125i	0.791755	−	1.28125i
$826$		0			0
$827$	−1.25633	−	1.48216i	−1.25633	−	1.48216i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	−1.25633	−	1.48216i	−1.25633	−	1.48216i	−0.447313	−	0.894377i	$-0.647619\pi$
$828$		0			0
$829$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$829$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.00401610	−	0.0296480i	0.00401610	−	0.0296480i
$834$	−0.839570	+	2.34299i	−0.839570	+	2.34299i
$835$		0			0
$836$	−1.69701	+	0.414136i	−1.69701	+	0.414136i
$837$		0			0
$838$	−0.0882877	+	1.96588i	−0.0882877	+	1.96588i
$839$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$839$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$840$		0			0
$841$	−0.946327	−	0.323210i	−0.946327	−	0.323210i
$842$		0			0
$843$	−0.771697	−	2.64144i	−0.771697	−	2.64144i
$844$	0.127218	−	0.939160i	0.127218	−	0.939160i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.66290	−	1.45284i	−1.66290	−	1.45284i
$850$	−0.0276840	+	0.0113460i	−0.0276840	+	0.0113460i
$851$		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
$856$	0.785698	+	1.83823i	0.785698	+	1.83823i
$857$	0.777271	+	0.117155i	0.777271	+	0.117155i	0.525684	−	0.850680i	$-0.323810\pi$
$857$	0.777271	+	0.117155i	0.777271	+	0.117155i	0.251587	+	0.967835i	$0.419048\pi$
$858$		0			0
$859$	1.58214			1.58214			0.791071	−	0.611724i	$-0.209524\pi$
$859$	1.58214			1.58214			0.791071	+	0.611724i	$0.209524\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$863$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$864$	0.304504	−	0.266037i	0.304504	−	0.266037i
$865$		0			0
$866$	−0.924822	+	1.02712i	−0.924822	+	1.02712i
$867$	0.157294	+	1.49655i	0.157294	+	1.49655i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−2.08355	−	0.853919i	−2.08355	−	0.853919i
$874$		0			0
$875$		0			0
$876$	−1.90171	+	1.98903i	−1.90171	+	1.98903i
$877$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$877$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.23806	−	1.55248i	1.23806	−	1.55248i	0.525684	−	0.850680i	$-0.323810\pi$
$881$	1.23806	−	1.55248i	1.23806	−	1.55248i	0.712376	−	0.701798i	$-0.247619\pi$
$882$	−0.0569095	+	1.26719i	−0.0569095	+	1.26719i
$883$	0.686543	+	0.382798i	0.686543	+	0.382798i	0.791071	−	0.611724i	$-0.209524\pi$
$883$	0.686543	+	0.382798i	0.686543	+	0.382798i	−0.104528	+	0.994522i	$0.533333\pi$
$884$		0			0
$885$		0			0
$886$	−1.96698	−	0.0588694i	−1.96698	−	0.0588694i
$887$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$887$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.483418	+	0.448546i	0.483418	+	0.448546i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.259183	+	0.200423i	−0.259183	+	0.200423i
$899$		0			0
$900$	1.12587	−	0.584310i	1.12587	−	0.584310i
$901$		0			0
$902$	0.998889	+	0.821331i	0.998889	+	0.821331i
$903$		0			0
$904$	−0.931368	+	0.676678i	−0.931368	+	0.676678i
$905$		0			0
$906$		0			0
$907$	−1.39364	+	1.21759i	−1.39364	+	1.21759i	−0.447313	+	0.894377i	$0.647619\pi$
$907$	−1.39364	+	1.21759i	−1.39364	+	1.21759i	−0.946327	+	0.323210i	$0.895238\pi$
$908$	−0.673452	−	1.87940i	−0.673452	−	1.87940i
$909$		0			0
$910$		0			0
$911$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$911$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$912$	−2.51407	−	0.775488i	−2.51407	−	0.775488i
$913$	−1.10975	+	1.57650i	−1.10975	+	1.57650i
$914$	0.150126	+	0.657745i	0.150126	+	0.657745i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.00233794	+	0.0118696i	0.00233794	+	0.0118696i
$919$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$919$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$920$		0			0
$921$	2.20186	−	1.81047i	2.20186	−	1.81047i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.33766	−	0.0400347i	−1.33766	−	0.0400347i	−0.646600	−	0.762830i	$-0.723810\pi$
$929$	−1.33766	−	0.0400347i	−1.33766	−	0.0400347i	−0.691063	+	0.722795i	$0.742857\pi$
$930$		0			0
$931$	1.52568	−	0.850680i	1.52568	−	0.850680i
$932$	−0.172892	−	0.345687i	−0.172892	−	0.345687i
$933$		0			0
$934$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$935$		0			0
$936$		0			0
$937$	0.310051	−	0.105895i	0.310051	−	0.105895i	−0.163818	−	0.986491i	$-0.552381\pi$
$937$	0.310051	−	0.105895i	0.310051	−	0.105895i	0.473869	+	0.880596i	$0.342857\pi$
$938$		0			0
$939$	0.270562	+	0.300490i	0.270562	+	0.300490i
$940$		0			0
$941$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$941$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$942$		0			0
$943$		0			0
$944$	0.862387	+	0.238004i	0.862387	+	0.238004i
$945$		0			0
$946$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$947$	0.840714			0.840714			0.420357	−	0.907359i	$-0.361905\pi$
$947$	0.840714			0.840714			0.420357	+	0.907359i	$0.361905\pi$
$948$		0			0
$949$		0			0
$950$	−1.49955	−	0.895941i	−1.49955	−	0.895941i
$951$		0			0
$952$		0			0
$953$	1.31675	+	1.46240i	1.31675	+	1.46240i	0.791071	+	0.611724i	$0.209524\pi$
$953$	1.31675	+	1.46240i	1.31675	+	1.46240i	0.525684	+	0.850680i	$0.323810\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.873408	+	0.486989i	−0.873408	+	0.486989i
$962$		0			0
$963$	2.53466	+	0.0758596i	2.53466	+	0.0758596i
$964$	1.86912	−	0.111981i	1.86912	−	0.111981i
$965$		0			0
$966$		0			0
$967$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$967$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$968$	0.887586	+	0.460642i	0.887586	+	0.460642i
$969$	0.0577022	−	0.0535398i	0.0577022	−	0.0535398i
$970$		0			0
$971$	1.39185	−	1.14444i	1.39185	−	1.14444i	0.420357	−	0.907359i	$-0.361905\pi$
$971$	1.39185	−	1.14444i	1.39185	−	1.14444i	0.971490	−	0.237080i	$-0.0761905\pi$
$972$	0.391922	+	1.34151i	0.391922	+	1.34151i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.368852	−	1.41895i	−0.368852	−	1.41895i	−0.842721	−	0.538351i	$-0.819048\pi$
$977$	−0.368852	−	1.41895i	−0.368852	−	1.41895i	0.473869	−	0.880596i	$-0.342857\pi$
$978$	0.187970	+	0.823548i	0.187970	+	0.823548i
$979$	0.0157278	+	1.05125i	0.0157278	+	1.05125i
$980$		0			0
$981$		0			0
$982$	1.85130	+	0.393505i	1.85130	+	0.393505i
$983$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$983$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$984$	0.657032	+	1.83358i	0.657032	+	1.83358i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$991$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$992$		0			0
$993$	−2.13724	+	0.192355i	−2.13724	+	0.192355i
$994$		0			0
$995$		0			0
$996$	−2.65269	+	1.18105i	−2.65269	+	1.18105i
$997$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$997$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$998$	0.0265555	+	1.77497i	0.0265555	+	1.77497i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.267.1	yes	48
8.3	odd	2	CM	3784.1.em.b.267.1	yes	48
11.4	even	5		3784.1.em.a.1643.1	✓	48
43.24	even	21		3784.1.em.a.2819.1	yes	48
88.59	odd	10		3784.1.em.a.1643.1	✓	48
344.67	odd	42		3784.1.em.a.2819.1	yes	48
473.411	even	105	inner	3784.1.em.b.411.1	yes	48
3784.411	odd	210	inner	3784.1.em.b.411.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.1643.1	✓	48	11.4	even	5
3784.1.em.a.1643.1	✓	48	88.59	odd	10
3784.1.em.a.2819.1	yes	48	43.24	even	21
3784.1.em.a.2819.1	yes	48	344.67	odd	42
3784.1.em.b.267.1	yes	48	1.1	even	1	trivial
3784.1.em.b.267.1	yes	48	8.3	odd	2	CM
3784.1.em.b.411.1	yes	48	473.411	even	105	inner
3784.1.em.b.411.1	yes	48	3784.411	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)

\(f(q)\)	\(=\)	\(q+(-0.963963 - 0.266037i) q^{2} +(-0.246733 - 1.48580i) q^{3} +(0.858449 + 0.512899i) q^{4} +(-0.157435 + 1.49789i) q^{6} +(-0.691063 - 0.722795i) q^{8} +(-1.20038 + 0.409981i) q^{9} +O(q^{10})\)	\(q+(-0.963963 - 0.266037i) q^{2} +(-0.246733 - 1.48580i) q^{3} +(0.858449 + 0.512899i) q^{4} +(-0.157435 + 1.49789i) q^{6} +(-0.691063 - 0.722795i) q^{8} +(-1.20038 + 0.409981i) q^{9} +(-0.163818 - 0.986491i) q^{11} +(0.550256 - 1.40203i) q^{12} +(0.473869 + 0.880596i) q^{16} +(-0.0299054 - 0.000895035i) q^{17} +(1.26620 - 0.0758596i) q^{18} +(-1.00550 - 1.42841i) q^{19} +(-0.104528 + 0.994522i) q^{22} +(-0.903418 + 1.20512i) q^{24} +(-0.772417 + 0.635116i) q^{25} +(0.191608 + 0.356068i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(-1.42530 + 0.486800i) q^{33} +(0.0285896 + 0.00881873i) q^{34} +(-1.24075 - 0.263729i) q^{36} +(0.589254 + 1.64443i) q^{38} +(0.712420 - 1.07927i) q^{41} +(0.887586 + 0.460642i) q^{43} +(0.365341 - 0.930874i) q^{44} +(1.19147 - 0.921344i) q^{48} +(-0.104528 + 0.994522i) q^{49} +(0.913545 - 0.406737i) q^{50} +(0.00604882 + 0.0446542i) q^{51} +(-0.0899761 - 0.394211i) q^{54} +(-1.87423 + 1.84640i) q^{57} +(0.618243 - 0.646631i) q^{59} +(-0.0448648 + 0.998993i) q^{64} +(1.50345 - 0.0900736i) q^{66} +(-1.86938 + 0.576628i) q^{67} +(-0.0252132 - 0.0161068i) q^{68} +(1.12587 + 0.584310i) q^{72} +(-1.69062 - 0.692879i) q^{73} +(1.13423 + 0.990950i) q^{75} +(-0.130540 - 1.74193i) q^{76} +(-0.521679 + 0.403407i) q^{81} +(-0.973871 + 0.850846i) q^{82} +(-1.37341 - 1.35301i) q^{83} +(-0.733052 - 0.680173i) q^{86} +(-0.599822 + 0.800134i) q^{88} +(-1.03962 - 0.156698i) q^{89} +(-1.39364 + 0.571168i) q^{96} +(1.33683 + 1.16795i) q^{97} +(0.365341 - 0.930874i) q^{98} +(0.601087 + 1.11701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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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