LMFDB - Embedded newform 3784.1.em.b.1027.1

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			1027.1
Root			$0.599822 - 0.800134i$ of defining polynomial
Character	$\chi$	$=$	3784.1027
Dual form			3784.1.em.b.619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.753071 - 0.657939i) q^{2} +(1.13273 - 1.60916i) q^{3} +(0.134233 - 0.990950i) q^{4} +(-0.205697 - 1.95708i) q^{6} +(-0.550897 - 0.834573i) q^{8} +(-0.968970 - 2.70410i) q^{9} +O(q^{10})$	\(q+(0.753071 - 0.657939i) q^{2} +(1.13273 - 1.60916i) q^{3} +(0.134233 - 0.990950i) q^{4} +(-0.205697 - 1.95708i) q^{6} +(-0.550897 - 0.834573i) q^{8} +(-0.968970 - 2.70410i) q^{9} +(0.575617 - 0.817719i) q^{11} +(-1.44254 - 1.33848i) q^{12} +(-0.963963 - 0.266037i) q^{16} +(0.398046 + 1.53125i) q^{17} +(-2.50884 - 1.39886i) q^{18} +(0.518961 + 1.77635i) q^{19} +(-0.104528 - 0.994522i) q^{22} +(-1.96698 - 0.0588694i) q^{24} +(0.420357 + 0.907359i) q^{25} +(-3.55197 - 0.980281i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(-0.663818 - 1.85252i) q^{33} +(1.30723 + 0.891252i) q^{34} +(-2.80970 + 0.597220i) q^{36} +(1.55955 + 0.996276i) q^{38} +(1.52389 + 0.910484i) q^{41} +(-0.599822 + 0.800134i) q^{43} +(-0.733052 - 0.680173i) q^{44} +(-1.52001 + 1.24982i) q^{48} +(-0.104528 - 0.994522i) q^{49} +(0.913545 + 0.406737i) q^{50} +(2.91490 + 1.09398i) q^{51} +(-3.31985 + 1.59876i) q^{54} +(3.44628 + 1.17704i) q^{57} +(-0.0164822 + 0.0249694i) q^{59} +(-0.393025 + 0.919528i) q^{64} +(-1.71874 - 0.958325i) q^{66} +(-1.61637 + 1.10202i) q^{67} +(1.57082 - 0.188899i) q^{68} +(-1.72297 + 2.29836i) q^{72} +(-0.299310 - 1.80241i) q^{73} +(1.93623 + 0.351375i) q^{75} +(1.82994 - 0.275819i) q^{76} +(-3.38211 + 2.78093i) q^{81} +(1.74664 - 0.316969i) q^{82} +(-1.42530 + 0.486800i) q^{83} +(0.0747301 + 0.997204i) q^{86} +(-0.999552 - 0.0299155i) q^{88} +(1.36145 + 0.419953i) q^{89} +(-0.322371 + 1.94127i) q^{96} +(-1.18037 - 0.214205i) q^{97} +(-0.733052 - 0.680173i) q^{98} +(-2.76895 - 0.764183i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

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 $

$2$	0.753071	−	0.657939i	0.753071	−	0.657939i
$2$	0.753071	−	0.657939i	0.753071	−	0.657939i
$3$	1.13273	−	1.60916i	1.13273	−	1.60916i	0.420357	−	0.907359i	$-0.361905\pi$
$3$	1.13273	−	1.60916i	1.13273	−	1.60916i	0.712376	−	0.701798i	$-0.247619\pi$
$4$	0.134233	−	0.990950i	0.134233	−	0.990950i
$5$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$5$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$6$	−0.205697	−	1.95708i	−0.205697	−	1.95708i
$7$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$7$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$8$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$9$	−0.968970	−	2.70410i	−0.968970	−	2.70410i
$10$		0			0
$11$	0.575617	−	0.817719i	0.575617	−	0.817719i
$11$	0.575617	−	0.817719i	0.575617	−	0.817719i
$12$	−1.44254	−	1.33848i	−1.44254	−	1.33848i
$13$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$13$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$14$		0			0
$15$		0			0
$16$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$17$	0.398046	+	1.53125i	0.398046	+	1.53125i	0.791071	+	0.611724i	$0.209524\pi$
$17$	0.398046	+	1.53125i	0.398046	+	1.53125i	−0.393025	+	0.919528i	$0.628571\pi$
$18$	−2.50884	−	1.39886i	−2.50884	−	1.39886i
$19$	0.518961	+	1.77635i	0.518961	+	1.77635i	0.623490	+	0.781831i	$0.285714\pi$
$19$	0.518961	+	1.77635i	0.518961	+	1.77635i	−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		0.0747301	−	0.997204i	$-0.476190\pi$
$23$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$24$	−1.96698	−	0.0588694i	−1.96698	−	0.0588694i
$25$	0.420357	+	0.907359i	0.420357	+	0.907359i
$26$		0			0
$27$	−3.55197	−	0.980281i	−3.55197	−	0.980281i
$28$		0			0
$29$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$29$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$30$		0			0
$31$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$31$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$32$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$33$	−0.663818	−	1.85252i	−0.663818	−	1.85252i
$34$	1.30723	+	0.891252i	1.30723	+	0.891252i
$35$		0			0
$36$	−2.80970	+	0.597220i	−2.80970	+	0.597220i
$37$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$37$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$38$	1.55955	+	0.996276i	1.55955	+	0.996276i
$39$		0			0
$40$		0			0
$41$	1.52389	+	0.910484i	1.52389	+	0.910484i	0.998210	+	0.0598042i	$0.0190476\pi$
$41$	1.52389	+	0.910484i	1.52389	+	0.910484i	0.525684	+	0.850680i	$0.323810\pi$
$42$		0			0
$43$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$43$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$44$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$45$		0			0
$46$		0			0
$47$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$47$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$48$	−1.52001	+	1.24982i	−1.52001	+	1.24982i
$49$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$50$	0.913545	+	0.406737i	0.913545	+	0.406737i
$51$	2.91490	+	1.09398i	2.91490	+	1.09398i
$52$		0			0
$53$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$53$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$54$	−3.31985	+	1.59876i	−3.31985	+	1.59876i
$55$		0			0
$56$		0			0
$57$	3.44628	+	1.17704i	3.44628	+	1.17704i
$58$		0			0
$59$	−0.0164822	+	0.0249694i	−0.0164822	+	0.0249694i	−0.842721	−	0.538351i	$-0.819048\pi$
$59$	−0.0164822	+	0.0249694i	−0.0164822	+	0.0249694i	0.826239	+	0.563320i	$0.190476\pi$
$60$		0			0
$61$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$61$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$62$		0			0
$63$		0			0
$64$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$65$		0			0
$66$	−1.71874	−	0.958325i	−1.71874	−	0.958325i
$67$	−1.61637	+	1.10202i	−1.61637	+	1.10202i	−0.691063	+	0.722795i	$0.742857\pi$
$67$	−1.61637	+	1.10202i	−1.61637	+	1.10202i	−0.925304	+	0.379225i	$0.876190\pi$
$68$	1.57082	−	0.188899i	1.57082	−	0.188899i
$69$		0			0
$70$		0			0
$71$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$71$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$72$	−1.72297	+	2.29836i	−1.72297	+	2.29836i
$73$	−0.299310	−	1.80241i	−0.299310	−	1.80241i	−0.550897	−	0.834573i	$-0.685714\pi$
$73$	−0.299310	−	1.80241i	−0.299310	−	1.80241i	0.251587	−	0.967835i	$-0.419048\pi$
$74$		0			0
$75$	1.93623	+	0.351375i	1.93623	+	0.351375i
$76$	1.82994	−	0.275819i	1.82994	−	0.275819i
$77$		0			0
$78$		0			0
$79$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$79$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$80$		0			0
$81$	−3.38211	+	2.78093i	−3.38211	+	2.78093i
$82$	1.74664	−	0.316969i	1.74664	−	0.316969i
$83$	−1.42530	+	0.486800i	−1.42530	+	0.486800i	−0.925304	−	0.379225i	$-0.876190\pi$
$83$	−1.42530	+	0.486800i	−1.42530	+	0.486800i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$87$		0			0
$88$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$89$	1.36145	+	0.419953i	1.36145	+	0.419953i	0.887586	−	0.460642i	$-0.152381\pi$
$89$	1.36145	+	0.419953i	1.36145	+	0.419953i	0.473869	+	0.880596i	$0.342857\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.322371	+	1.94127i	−0.322371	+	1.94127i
$97$	−1.18037	−	0.214205i	−1.18037	−	0.214205i	−0.447313	−	0.894377i	$-0.647619\pi$
$97$	−1.18037	−	0.214205i	−1.18037	−	0.214205i	−0.733052	+	0.680173i	$0.761905\pi$
$98$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$99$	−2.76895	−	0.764183i	−2.76895	−	0.764183i
$100$	0.955573	−	0.294755i	0.955573	−	0.294755i
$101$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$101$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$102$	2.91490	−	1.09398i	2.91490	−	1.09398i
$103$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$103$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.501148	−	0.0451041i	−0.501148	−	0.0451041i	−0.163818	−	0.986491i	$-0.552381\pi$
$107$	−0.501148	−	0.0451041i	−0.501148	−	0.0451041i	−0.337330	+	0.941386i	$0.609524\pi$
$108$	−1.44820	+	3.38824i	−1.44820	+	3.38824i
$109$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$109$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.525092	+	0.197070i	−0.525092	+	0.197070i	−0.599822	−	0.800134i	$-0.704762\pi$
$113$	−0.525092	+	0.197070i	−0.525092	+	0.197070i	0.0747301	+	0.997204i	$0.476190\pi$
$114$	3.36972	−	1.38104i	3.36972	−	1.38104i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.00401610	+	0.0296480i	0.00401610	+	0.0296480i
$119$		0			0
$120$		0			0
$121$	−0.337330	−	0.941386i	−0.337330	−	0.941386i
$122$		0			0
$123$	3.19128	−	1.42085i	3.19128	−	1.42085i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$127$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$128$	0.309017	+	0.951057i	0.309017	+	0.951057i
$129$	0.608102	+	1.87155i	0.608102	+	1.87155i
$130$		0			0
$131$	0.343758	−	1.50610i	0.343758	−	1.50610i	−0.447313	−	0.894377i	$-0.647619\pi$
$131$	0.343758	−	1.50610i	0.343758	−	1.50610i	0.791071	−	0.611724i	$-0.209524\pi$
$132$	−1.92486	+	0.409141i	−1.92486	+	0.409141i
$133$		0			0
$134$	−0.492178	+	1.89337i	−0.492178	+	1.89337i
$135$		0			0
$136$	1.05866	−	1.17576i	1.05866	−	1.17576i
$137$	0.0352660	−	0.785259i	0.0352660	−	0.785259i	−0.900969	−	0.433884i	$-0.857143\pi$
$137$	0.0352660	−	0.785259i	0.0352660	−	0.785259i	0.936235	−	0.351375i	$-0.114286\pi$
$138$		0			0
$139$	−0.326844	−	0.653506i	−0.326844	−	0.653506i	0.669131	−	0.743145i	$-0.266667\pi$
$139$	−0.326844	−	0.653506i	−0.326844	−	0.653506i	−0.995974	+	0.0896393i	$0.971429\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.214660	+	2.86444i	0.214660	+	2.86444i
$145$		0			0
$146$	−1.41128	−	1.16041i	−1.41128	−	1.16041i
$147$	−1.71874	−	0.958325i	−1.71874	−	0.958325i
$148$		0			0
$149$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$149$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$150$	1.68931	−	1.00931i	1.68931	−	1.00931i
$151$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$151$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$152$	1.19660	−	1.41170i	1.19660	−	1.41170i
$153$	3.75497	−	2.56010i	3.75497	−	2.56010i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$157$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.717295	+	4.31946i	−0.717295	+	4.31946i
$163$	−0.673452	−	1.87940i	−0.673452	−	1.87940i	−0.393025	−	0.919528i	$-0.628571\pi$
$163$	−0.673452	−	1.87940i	−0.673452	−	1.87940i	−0.280427	−	0.959875i	$-0.590476\pi$
$164$	1.10680	−	1.38789i	1.10680	−	1.38789i
$165$		0			0
$166$	−0.753071	+	1.30436i	−0.753071	+	1.30436i
$167$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$167$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$168$		0			0
$169$	0.0149594	+	0.999888i	0.0149594	+	0.999888i
$170$		0			0
$171$	4.30059	−	3.12456i	4.30059	−	3.12456i
$172$	0.712376	+	0.701798i	0.712376	+	0.701798i
$173$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$173$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$174$		0			0
$175$		0			0
$176$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$177$	0.0215098	+	0.0548061i	0.0215098	+	0.0548061i
$178$	1.30158	−	0.579499i	1.30158	−	0.579499i
$179$	−0.0292650	+	0.00622047i	−0.0292650	+	0.00622047i	−0.222521	−	0.974928i	$-0.571429\pi$
$179$	−0.0292650	+	0.00622047i	−0.0292650	+	0.00622047i	0.193256	+	0.981148i	$0.438095\pi$
$180$		0			0
$181$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$181$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.48126	+	0.555925i	1.48126	+	0.555925i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$191$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$192$	1.03447	+	1.67402i	1.03447	+	1.67402i
$193$	−0.335148	−	0.292810i	−0.335148	−	0.292810i	0.473869	−	0.880596i	$-0.342857\pi$
$193$	−0.335148	−	0.292810i	−0.335148	−	0.292810i	−0.809017	+	0.587785i	$0.800000\pi$
$194$	−1.02983	+	0.615296i	−1.02983	+	0.615296i
$195$		0			0
$196$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$197$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$197$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$198$	−2.58801	+	1.24632i	−2.58801	+	1.24632i
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	0.525684	−	0.850680i	0.525684	−	0.850680i
$201$	−0.0575894	+	3.84928i	−0.0575894	+	3.84928i
$202$		0			0
$203$		0			0
$204$	1.47536	−	2.74168i	1.47536	−	2.74168i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.75128	+	0.598135i	1.75128	+	0.598135i
$210$		0			0
$211$	−0.913584	−	1.69772i	−0.913584	−	1.69772i	−0.691063	−	0.722795i	$-0.742857\pi$
$211$	−0.913584	−	1.69772i	−0.913584	−	1.69772i	−0.222521	−	0.974928i	$-0.571429\pi$
$212$		0			0
$213$		0			0
$214$	−0.407076	+	0.295758i	−0.407076	+	0.295758i
$215$		0			0
$216$	1.13865	+	3.50441i	1.13865	+	3.50441i
$217$		0			0
$218$		0			0
$219$	−3.23940	−	1.56001i	−3.23940	−	1.56001i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$223$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$224$		0			0
$225$	2.04628	−	2.01589i	2.04628	−	2.01589i
$226$	−0.265772	+	0.493886i	−0.265772	+	0.493886i
$227$	−0.734287	+	1.58499i	−0.734287	+	1.58499i	0.0747301	+	0.997204i	$0.476190\pi$
$227$	−0.734287	+	1.58499i	−0.734287	+	1.58499i	−0.809017	+	0.587785i	$0.800000\pi$
$228$	1.62900	−	3.25709i	1.62900	−	3.25709i
$229$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$229$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.28395	+	0.154401i	−1.28395	+	0.154401i	−0.733052	−	0.680173i	$-0.761905\pi$
$233$	−1.28395	+	0.154401i	−1.28395	+	0.154401i	−0.550897	+	0.834573i	$0.685714\pi$
$234$		0			0
$235$		0			0
$236$	0.0225310	+	0.0196847i	0.0225310	+	0.0196847i
$237$		0			0
$238$		0			0
$239$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$239$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$240$		0			0
$241$	−0.727741	+	1.85425i	−0.727741	+	1.85425i	−0.280427	+	0.959875i	$0.590476\pi$
$241$	−0.727741	+	1.85425i	−0.727741	+	1.85425i	−0.447313	+	0.894377i	$0.647619\pi$
$242$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$243$	0.368549	+	4.91795i	0.368549	+	4.91795i
$244$		0			0
$245$		0			0
$246$	1.46843	−	3.16966i	1.46843	−	3.16966i
$247$		0			0
$248$		0			0
$249$	−0.831152	+	2.84495i	−0.831152	+	2.84495i
$250$		0			0
$251$	0.104528	−	0.994522i	0.104528	−	0.994522i	−0.809017	−	0.587785i	$-0.800000\pi$
$251$	0.104528	−	0.994522i	0.104528	−	0.994522i	0.913545	−	0.406737i	$-0.133333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.858449	+	0.512899i	0.858449	+	0.512899i
$257$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	0.913545	−	0.406737i	$-0.133333\pi$
$257$	−0.0646021	−	0.198825i	−0.0646021	−	0.198825i	−0.978148	+	0.207912i	$0.933333\pi$
$258$	1.68931	+	1.00931i	1.68931	+	1.00931i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.732048	−	1.36037i	−0.732048	−	1.36037i
$263$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$263$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$264$	−1.18037	+	1.57455i	−1.18037	+	1.57455i
$265$		0			0
$266$		0			0
$267$	2.21794	−	1.71510i	2.21794	−	1.71510i
$268$	0.875077	+	1.74967i	0.875077	+	1.74967i
$269$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$269$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$270$		0			0
$271$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$271$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$272$	0.0236679	−	1.58197i	0.0236679	−	1.58197i
$273$		0			0
$274$	−0.490094	−	0.614559i	−0.490094	−	0.614559i
$275$	0.983930	+	0.178557i	0.983930	+	0.178557i
$276$		0			0
$277$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$277$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$278$	−0.676103	−	0.277093i	−0.676103	−	0.277093i
$279$		0			0
$280$		0			0
$281$	0.960472	+	1.55427i	0.960472	+	1.55427i	0.826239	+	0.563320i	$0.190476\pi$
$281$	0.960472	+	1.55427i	0.960472	+	1.55427i	0.134233	+	0.990950i	$0.457143\pi$
$282$		0			0
$283$	0.0628267	+	0.135614i	0.0628267	+	0.135614i	0.936235	−	0.351375i	$-0.114286\pi$
$283$	0.0628267	+	0.135614i	0.0628267	+	0.135614i	−0.873408	+	0.486989i	$0.838095\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.04628	+	2.01589i	2.04628	+	2.01589i
$289$	−1.31288	+	0.732029i	−1.31288	+	0.732029i
$290$		0			0
$291$	−1.68173	+	1.65676i	−1.68173	+	1.65676i
$292$	−1.82627	+	0.0546583i	−1.82627	+	0.0546583i
$293$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$293$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$294$	−1.92486	+	0.409141i	−1.92486	+	0.409141i
$295$		0			0
$296$		0			0
$297$	−2.84617	+	2.34025i	−2.84617	+	2.34025i
$298$		0			0
$299$		0			0
$300$	0.608102	−	1.87155i	0.608102	−	1.87155i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.0276840	−	1.85040i	−0.0276840	−	1.85040i
$305$		0			0
$306$	1.14338	−	4.39848i	1.14338	−	4.39848i
$307$	0.337330	−	0.584273i	0.337330	−	0.584273i	−0.646600	−	0.762830i	$-0.723810\pi$
$307$	0.337330	−	0.584273i	0.337330	−	0.584273i	0.983930	+	0.178557i	$0.0571429\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$311$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$312$		0			0
$313$	1.85908	+	0.223562i	1.85908	+	0.223562i	0.971490	−	0.237080i	$-0.0761905\pi$
$313$	1.85908	+	0.223562i	1.85908	+	0.223562i	0.887586	+	0.460642i	$0.152381\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$317$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.640247	+	0.755334i	−0.640247	+	0.755334i
$322$		0			0
$323$	−2.51347	+	1.50173i	−2.51347	+	1.50173i
$324$	2.30177	+	3.72480i	2.30177	+	3.72480i
$325$		0			0
$326$	−1.74369	−	0.972234i	−1.74369	−	0.972234i
$327$		0			0
$328$	−0.0796428	−	1.77338i	−0.0796428	−	1.77338i
$329$		0			0
$330$		0			0
$331$	1.87152	+	0.282086i	1.87152	+	0.282086i	0.983930	−	0.178557i	$-0.0571429\pi$
$331$	1.87152	+	0.282086i	1.87152	+	0.282086i	0.887586	+	0.460642i	$0.152381\pi$
$332$	0.291071	+	1.47775i	0.291071	+	1.47775i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.562548	−	0.624773i	0.562548	−	0.624773i	−0.393025	−	0.919528i	$-0.628571\pi$
$337$	0.562548	−	0.624773i	0.562548	−	0.624773i	0.955573	+	0.294755i	$0.0952381\pi$
$338$	0.669131	+	0.743145i	0.669131	+	0.743145i
$339$	−0.277672	+	1.06818i	−0.277672	+	1.06818i
$340$		0			0
$341$		0			0
$342$	1.18288	−	5.18254i	1.18288	−	5.18254i
$343$		0			0
$344$	0.998210	+	0.0598042i	0.998210	+	0.0598042i
$345$		0			0
$346$		0			0
$347$	0.530752	−	0.181274i	0.530752	−	0.181274i	−0.0448648	−	0.998993i	$-0.514286\pi$
$347$	0.530752	−	0.181274i	0.530752	−	0.181274i	0.575617	+	0.817719i	$0.304762\pi$
$348$		0			0
$349$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$349$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$350$		0			0
$351$		0			0
$352$	−0.163818	+	0.986491i	−0.163818	+	0.986491i
$353$	1.64952	+	1.12462i	1.64952	+	1.12462i	0.858449	+	0.512899i	$0.171429\pi$
$353$	1.64952	+	1.12462i	1.64952	+	1.12462i	0.791071	+	0.611724i	$0.209524\pi$
$354$	0.0522575	+	0.0271208i	0.0522575	+	0.0271208i
$355$		0			0
$356$	0.598905	−	1.29276i	0.598905	−	1.29276i
$357$		0			0
$358$	−0.0179460	+	0.0239390i	−0.0179460	+	0.0239390i
$359$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$359$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$360$		0			0
$361$	−2.04339	+	1.30537i	−2.04339	+	1.30537i
$362$		0			0
$363$	−1.89694	−	0.523523i	−1.89694	−	0.523523i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$367$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$368$		0			0
$369$	0.985436	−	5.00300i	0.985436	−	5.00300i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$373$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$374$	1.48126	−	0.555925i	1.48126	−	0.555925i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0849136	−	1.89075i	0.0849136	−	1.89075i	−0.280427	−	0.959875i	$-0.590476\pi$
$379$	0.0849136	−	1.89075i	0.0849136	−	1.89075i	0.365341	−	0.930874i	$-0.380952\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$383$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$384$	1.88043	+	0.580037i	1.88043	+	0.580037i
$385$		0			0
$386$	−0.445042			−0.445042
$387$	2.74485	+	0.846675i	2.74485	+	0.846675i
$388$	−0.370710	+	1.14093i	−0.370710	+	1.14093i
$389$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$389$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$390$		0			0
$391$		0			0
$392$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$393$	−2.03417	−	2.25917i	−2.03417	−	2.25917i
$394$		0			0
$395$		0			0
$396$	−1.12895	+	2.64132i	−1.12895	+	2.64132i
$397$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$397$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$398$		0			0
$399$		0			0
$400$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$401$	0.471490	−	0.628945i	0.471490	−	0.628945i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.471490	−	0.628945i	0.471490	−	0.628945i	0.971490	+	0.237080i	$0.0761905\pi$
$402$	2.48922	+	2.93668i	2.48922	+	2.93668i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.692804	−	3.03537i	−0.692804	−	3.03537i
$409$	0.777271	−	1.81851i	0.777271	−	1.81851i	0.251587	−	0.967835i	$-0.419048\pi$
$409$	0.777271	−	1.81851i	0.777271	−	1.81851i	0.525684	−	0.850680i	$-0.323810\pi$
$410$		0			0
$411$	−1.22366	−	0.946237i	−1.22366	−	0.946237i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.42182	−	0.214305i	−1.42182	−	0.214305i
$418$	1.71238	−	0.701798i	1.71238	−	0.701798i
$419$	0.0808436	−	0.0389322i	0.0808436	−	0.0389322i	−0.393025	−	0.919528i	$-0.628571\pi$
$419$	0.0808436	−	0.0389322i	0.0808436	−	0.0389322i	0.473869	+	0.880596i	$0.342857\pi$
$420$		0			0
$421$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$421$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$422$	−1.80499	−	0.677425i	−1.80499	−	0.677425i
$423$		0			0
$424$		0			0
$425$	−1.22207	+	1.00484i	−1.22207	+	1.00484i
$426$		0			0
$427$		0			0
$428$	−0.111967	+	0.490558i	−0.111967	+	0.490558i
$429$		0			0
$430$		0			0
$431$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$431$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$432$	3.16317	+	1.88991i	3.16317	+	1.88991i
$433$	−0.0164822	−	1.10167i	−0.0164822	−	1.10167i	−0.842721	−	0.538351i	$-0.819048\pi$
$433$	−0.0164822	−	1.10167i	−0.0164822	−	1.10167i	0.826239	−	0.563320i	$-0.190476\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−3.46589	+	0.956524i	−3.46589	+	0.956524i
$439$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$439$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$440$		0			0
$441$	−2.58801	+	1.24632i	−2.58801	+	1.24632i
$442$		0			0
$443$	0.0401373	−	0.0802522i	0.0401373	−	0.0802522i	−0.873408	−	0.486989i	$-0.838095\pi$
$443$	0.0401373	−	0.0802522i	0.0401373	−	0.0802522i	0.913545	+	0.406737i	$0.133333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.15072	−	0.0344397i	−1.15072	−	0.0344397i	−0.550897	−	0.834573i	$-0.685714\pi$
$449$	−1.15072	−	0.0344397i	−1.15072	−	0.0344397i	−0.599822	+	0.800134i	$0.704762\pi$
$450$	0.214660	−	2.86444i	0.214660	−	2.86444i
$451$	1.62170	−	0.722027i	1.62170	−	0.722027i
$452$	0.124802	+	0.546793i	0.124802	+	0.546793i
$453$		0			0
$454$	0.489855	+	1.67673i	0.489855	+	1.67673i
$455$		0			0
$456$	−0.916213	−	3.52460i	−0.916213	−	3.52460i
$457$	1.62470	+	0.448390i	1.62470	+	0.448390i	0.955573	−	0.294755i	$-0.0952381\pi$
$457$	1.62470	+	0.448390i	1.62470	+	0.448390i	0.669131	+	0.743145i	$0.266667\pi$
$458$		0			0
$459$	0.0872105	−	5.82916i	0.0872105	−	5.82916i
$460$		0			0
$461$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$461$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$462$		0			0
$463$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$463$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$464$		0			0
$465$		0			0
$466$	−0.865319	+	0.961034i	−0.865319	+	0.961034i
$467$	0.206722	+	1.96683i	0.206722	+	1.96683i	0.251587	+	0.967835i	$0.419048\pi$
$467$	0.206722	+	1.96683i	0.206722	+	1.96683i	−0.0448648	+	0.998993i	$0.514286\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	0.0299188			0.0299188
$473$	0.309017	+	0.951057i	0.309017	+	0.951057i
$474$		0			0
$475$	−1.39364	+	1.21759i	−1.39364	+	1.21759i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$479$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$480$		0			0
$481$		0			0
$482$	0.671944	+	1.87519i	0.671944	+	1.87519i
$483$		0			0
$484$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$485$		0			0
$486$	3.51325	+	3.46108i	3.51325	+	3.46108i
$487$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$487$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$488$		0			0
$489$	−3.78710	−	1.04517i	−3.78710	−	1.04517i
$490$		0			0
$491$	0.589254	+	0.328552i	0.589254	+	0.328552i	0.753071	−	0.657939i	$-0.228571\pi$
$491$	0.589254	+	0.328552i	0.589254	+	0.328552i	−0.163818	+	0.986491i	$0.552381\pi$
$492$	−0.979614	−	3.35312i	−0.979614	−	3.35312i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	1.24589	+	2.68930i	1.24589	+	2.68930i
$499$	−1.19750	−	0.0717437i	−1.19750	−	0.0717437i	−0.550897	−	0.834573i	$-0.685714\pi$
$499$	−1.19750	−	0.0717437i	−1.19750	−	0.0717437i	−0.646600	+	0.762830i	$0.723810\pi$
$500$		0			0
$501$		0			0
$502$	−0.575617	−	0.817719i	−0.575617	−	0.817719i
$503$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$503$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.62592	+	1.10853i	1.62592	+	1.10853i
$508$		0			0
$509$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$509$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$510$		0			0
$511$		0			0
$512$	0.983930	−	0.178557i	0.983930	−	0.178557i
$513$	−0.102009	−	6.81828i	−0.102009	−	6.81828i
$514$	−0.179465	−	0.107225i	−0.179465	−	0.107225i
$515$		0			0
$516$	1.93623	−	0.351375i	1.93623	−	0.351375i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.19326	−	0.981148i	1.19326	−	0.981148i	0.193256	−	0.981148i	$-0.438095\pi$
$521$	1.19326	−	0.981148i	1.19326	−	0.981148i	1.00000			$0$
$522$		0			0
$523$	−0.299310	−	0.133261i	−0.299310	−	0.133261i	0.251587	−	0.967835i	$-0.419048\pi$
$523$	−0.299310	−	0.133261i	−0.299310	−	0.133261i	−0.550897	+	0.834573i	$0.685714\pi$
$524$	−1.44633	−	0.542816i	−1.44633	−	0.542816i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.147058	+	1.96236i	0.147058	+	1.96236i
$529$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$530$		0			0
$531$	0.0834907	+	0.0203749i	0.0834907	+	0.0203749i
$532$		0			0
$533$		0			0
$534$	0.541834	−	2.75086i	0.541834	−	2.75086i
$535$		0			0
$536$	1.81017	+	0.741877i	1.81017	+	0.741877i
$537$	−0.0231397	+	0.0541381i	−0.0231397	+	0.0541381i
$538$		0			0
$539$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$540$		0			0
$541$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$541$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$542$		0			0
$543$		0			0
$544$	−1.02301	−	1.20690i	−1.02301	−	1.20690i
$545$		0			0
$546$		0			0
$547$	0.962316	−	0.536561i	0.962316	−	0.536561i	0.0747301	−	0.997204i	$-0.476190\pi$
$547$	0.962316	−	0.536561i	0.962316	−	0.536561i	0.887586	+	0.460642i	$0.152381\pi$
$548$	−0.773418	−	0.140355i	−0.773418	−	0.140355i
$549$		0			0
$550$	0.858449	−	0.512899i	0.858449	−	0.512899i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	−0.691464	+	0.236163i	−0.691464	+	0.236163i
$557$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$557$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	2.57244	−	1.75386i	2.57244	−	1.75386i
$562$	1.74592	+	0.538545i	1.74592	+	0.538545i
$563$	−0.0425201	−	0.0790155i	−0.0425201	−	0.0790155i	0.858449	−	0.512899i	$-0.171429\pi$
$563$	−0.0425201	−	0.0790155i	−0.0425201	−	0.0790155i	−0.900969	+	0.433884i	$0.857143\pi$
$564$		0			0
$565$		0			0
$566$	0.136539	+	0.0607909i	0.136539	+	0.0607909i
$567$		0			0
$568$		0			0
$569$	−0.188593	+	1.13568i	−0.188593	+	1.13568i	0.712376	+	0.701798i	$0.247619\pi$
$569$	−0.188593	+	1.13568i	−0.188593	+	1.13568i	−0.900969	+	0.433884i	$0.857143\pi$
$570$		0			0
$571$	0.326239	+	0.302705i	0.326239	+	0.302705i	0.826239	−	0.563320i	$-0.190476\pi$
$571$	0.326239	+	0.302705i	0.326239	+	0.302705i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	2.86733	+	0.171786i	2.86733	+	0.171786i
$577$	−0.384956	+	1.95440i	−0.384956	+	1.95440i	−0.104528	+	0.994522i	$0.533333\pi$
$577$	−0.384956	+	1.95440i	−0.384956	+	1.95440i	−0.280427	+	0.959875i	$0.590476\pi$
$578$	−0.507066	+	1.41507i	−0.507066	+	1.41507i
$579$	−0.850811	+	0.207630i	−0.850811	+	0.207630i
$580$		0			0
$581$		0			0
$582$	−0.176418	+	2.35413i	−0.176418	+	2.35413i
$583$		0			0
$584$	−1.33935	+	1.24274i	−1.33935	+	1.24274i
$585$		0			0
$586$		0			0
$587$	1.61634	−	0.662437i	1.61634	−	0.662437i	0.623490	−	0.781831i	$-0.285714\pi$
$587$	1.61634	−	0.662437i	1.61634	−	0.662437i	0.992847	+	0.119394i	$0.0380952\pi$
$588$	−1.18037	+	1.57455i	−1.18037	+	1.57455i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.60537	+	1.09452i	1.60537	+	1.09452i	0.936235	+	0.351375i	$0.114286\pi$
$593$	1.60537	+	1.09452i	1.60537	+	1.09452i	0.669131	+	0.743145i	$0.266667\pi$
$594$	−0.603629	+	3.63498i	−0.603629	+	3.63498i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$599$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$600$	−0.773418	−	1.80950i	−0.773418	−	1.80950i
$601$	−0.584862	−	1.80002i	−0.584862	−	1.80002i	−0.599822	−	0.800134i	$-0.704762\pi$
$601$	−0.584862	−	1.80002i	−0.584862	−	1.80002i	0.0149594	−	0.999888i	$-0.495238\pi$
$602$		0			0
$603$	4.54619	+	3.30300i	4.54619	+	3.30300i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$607$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$608$	−1.23830	−	1.37527i	−1.23830	−	1.37527i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−2.03288	−	4.06464i	−2.03288	−	4.06464i
$613$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$613$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$614$	−0.130382	−	0.661942i	−0.130382	−	0.661942i
$615$		0			0
$616$		0			0
$617$	−0.103286	−	1.37826i	−0.103286	−	1.37826i	−0.772417	−	0.635116i	$-0.780952\pi$
$617$	−0.103286	−	1.37826i	−0.103286	−	1.37826i	0.669131	−	0.743145i	$-0.266667\pi$
$618$		0			0
$619$	−0.207368	−	0.170507i	−0.207368	−	0.170507i	0.525684	−	0.850680i	$-0.323810\pi$
$619$	−0.207368	−	0.170507i	−0.207368	−	0.170507i	−0.733052	+	0.680173i	$0.761905\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.646600	+	0.762830i	−0.646600	+	0.762830i
$626$	1.54711	−	1.05480i	1.54711	−	1.05480i
$627$	2.94623	−	2.14056i	2.94623	−	2.14056i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$631$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$632$		0			0
$633$	−3.76675	−	0.452968i	−3.76675	−	0.452968i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.37224	+	1.43525i	−1.37224	+	1.43525i	−0.599822	+	0.800134i	$0.704762\pi$
$641$	−1.37224	+	1.43525i	−1.37224	+	1.43525i	−0.772417	+	0.635116i	$0.780952\pi$
$642$	0.0148124	+	0.990064i	0.0148124	+	0.990064i
$643$	−0.413214	−	0.966762i	−0.413214	−	0.966762i	−0.988831	−	0.149042i	$-0.952381\pi$
$643$	−0.413214	−	0.966762i	−0.413214	−	0.966762i	0.575617	−	0.817719i	$-0.304762\pi$
$644$		0			0
$645$		0			0
$646$	−0.904779	+	2.78462i	−0.904779	+	2.78462i
$647$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$647$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$648$	4.18408	+	1.29062i	4.18408	+	1.29062i
$649$	0.0109306	+	0.0278506i	0.0109306	+	0.0278506i
$650$		0			0
$651$		0			0
$652$	−1.95279	+	0.415079i	−1.95279	+	0.415079i
$653$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$653$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$654$		0			0
$655$		0			0
$656$	−1.22675	−	1.28308i	−1.22675	−	1.28308i
$657$	−4.58388	+	2.55585i	−4.58388	+	2.55585i
$658$		0			0
$659$	0.256539	−	0.0791319i	0.256539	−	0.0791319i	−0.163818	−	0.986491i	$-0.552381\pi$
$659$	0.256539	−	0.0791319i	0.256539	−	0.0791319i	0.420357	+	0.907359i	$0.361905\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	1.59498	−	1.01891i	1.59498	−	1.01891i
$663$		0			0
$664$	1.19147	+	0.921344i	1.19147	+	0.921344i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.470291	+	0.761041i	−0.470291	+	0.761041i	−0.995974	−	0.0896393i	$-0.971429\pi$
$673$	−0.470291	+	0.761041i	−0.470291	+	0.761041i	0.525684	+	0.850680i	$0.323810\pi$
$674$	0.0125766	−	0.840620i	0.0125766	−	0.840620i
$675$	−0.603629	−	3.63498i	−0.603629	−	3.63498i
$676$	0.992847	+	0.119394i	0.992847	+	0.119394i
$677$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$677$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$678$	0.493692	+	0.987109i	0.493692	+	0.987109i
$679$		0			0
$680$		0			0
$681$	1.71874	+	2.97695i	1.71874	+	2.97695i
$682$		0			0
$683$	−0.658322	−	1.67738i	−0.658322	−	1.67738i	−0.733052	−	0.680173i	$-0.761905\pi$
$683$	−0.658322	−	1.67738i	−0.658322	−	1.67738i	0.0747301	−	0.997204i	$-0.476190\pi$
$684$	−2.51900	−	4.68108i	−2.51900	−	4.68108i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.791071	−	0.611724i	0.791071	−	0.611724i
$689$		0			0
$690$		0			0
$691$	−0.802718	−	1.07079i	−0.802718	−	1.07079i	−0.995974	−	0.0896393i	$-0.971429\pi$
$691$	−0.802718	−	1.07079i	−0.802718	−	1.07079i	0.193256	−	0.981148i	$-0.438095\pi$
$692$		0			0
$693$		0			0
$694$	0.280427	−	0.485714i	0.280427	−	0.485714i
$695$		0			0
$696$		0			0
$697$	−0.787601	+	2.69588i	−0.787601	+	2.69588i
$698$		0			0
$699$	−1.20592	+	2.24097i	−1.20592	+	2.24097i
$700$		0			0
$701$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$701$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$702$		0			0
$703$		0			0
$704$	0.525684	+	0.850680i	0.525684	+	0.850680i
$705$		0			0
$706$	1.98214	−	0.238361i	1.98214	−	0.238361i
$707$		0			0
$708$	0.0571975	−	0.0139583i	0.0571975	−	0.0139583i
$709$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$709$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$710$		0			0
$711$		0			0
$712$	−0.399540	−	1.36758i	−0.399540	−	1.36758i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.00223584	+	0.0298352i	0.00223584	+	0.0298352i
$717$		0			0
$718$		0			0
$719$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$719$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$720$		0			0
$721$		0			0
$722$	−0.679967	+	2.32746i	−0.679967	+	2.32746i
$723$	2.15945	+	3.27142i	2.15945	+	3.27142i
$724$		0			0
$725$		0			0
$726$	−1.77298	+	0.853822i	−1.77298	+	0.853822i
$727$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$727$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$728$		0			0
$729$	4.57240	+	2.73188i	4.57240	+	2.73188i
$730$		0			0
$731$	−1.46396	−	0.599989i	−1.46396	−	0.599989i
$732$		0			0
$733$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$733$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.0292650	+	1.95608i	−0.0292650	+	1.95608i
$738$	−2.54956	−	4.41597i	−2.54956	−	4.41597i
$739$	1.06209	−	0.293118i	1.06209	−	0.293118i	0.309017	−	0.951057i	$-0.400000\pi$
$739$	1.06209	−	0.293118i	1.06209	−	0.293118i	0.753071	+	0.657939i	$0.228571\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$743$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.69744	+	3.38248i	2.69744	+	3.38248i
$748$	0.749728	−	1.39323i	0.749728	−	1.39323i
$749$		0			0
$750$		0			0
$751$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$751$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$752$		0			0
$753$	−1.48194	−	1.29473i	−1.48194	−	1.29473i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$757$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$758$	−1.18005	−	1.47974i	−1.18005	−	1.47974i
$759$		0			0
$760$		0			0
$761$	−0.784892	−	0.773237i	−0.784892	−	0.773237i	0.193256	−	0.981148i	$-0.438095\pi$
$761$	−0.784892	−	0.773237i	−0.784892	−	0.773237i	−0.978148	+	0.207912i	$0.933333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	1.79773	−	0.800400i	1.79773	−	0.800400i
$769$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$769$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$770$		0			0
$771$	−0.393117	−	0.121261i	−0.393117	−	0.121261i
$772$	−0.335148	+	0.292810i	−0.335148	+	0.292810i
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$	2.62413	−	1.16834i	2.62413	−	1.16834i
$775$		0			0
$776$	0.471490	+	1.10311i	0.471490	+	1.10311i
$777$		0			0
$778$		0			0
$779$	−0.826500	+	3.17948i	−0.826500	+	3.17948i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.163818	+	0.986491i	−0.163818	+	0.986491i
$785$		0			0
$786$	−3.01827	−	0.362960i	−3.01827	−	0.362960i
$787$	−1.22675	+	0.636666i	−1.22675	+	0.636666i	−0.946327	−	0.323210i	$-0.895238\pi$
$787$	−1.22675	+	0.636666i	−1.22675	+	0.636666i	−0.280427	+	0.959875i	$0.590476\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.887642	+	2.73188i	0.887642	+	2.73188i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$797$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$798$		0			0
$799$		0			0
$800$	−0.772417	−	0.635116i	−0.772417	−	0.635116i
$801$	−0.183612	−	4.08844i	−0.183612	−	4.08844i
$802$	−0.0587416	−	0.783852i	−0.0587416	−	0.783852i
$803$	−1.64615	−	0.792745i	−1.64615	−	0.792745i
$804$	3.80672	+	0.573770i	3.80672	+	0.573770i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.0620088	−	1.38073i	0.0620088	−	1.38073i	−0.691063	−	0.722795i	$-0.742857\pi$
$809$	0.0620088	−	1.38073i	0.0620088	−	1.38073i	0.753071	−	0.657939i	$-0.228571\pi$
$810$		0			0
$811$	−0.139886	−	0.155360i	−0.139886	−	0.155360i	0.669131	−	0.743145i	$-0.266667\pi$
$811$	−0.139886	−	0.155360i	−0.139886	−	0.155360i	−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−2.51882	−	1.83003i	−2.51882	−	1.83003i
$817$	−1.73260	−	0.650257i	−1.73260	−	0.650257i
$818$	−0.611131	−	1.88087i	−0.611131	−	1.88087i
$819$		0			0
$820$		0			0
$821$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$821$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$822$	−1.54407	+	0.0925072i	−1.54407	+	0.0925072i
$823$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$823$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$824$		0			0
$825$	1.40186	−	1.38104i	1.40186	−	1.38104i
$826$		0			0
$827$	−0.794058	−	0.412103i	−0.794058	−	0.412103i	0.0149594	−	0.999888i	$-0.495238\pi$
$827$	−0.794058	−	0.412103i	−0.794058	−	0.412103i	−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$829$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.48126	−	0.555925i	1.48126	−	0.555925i
$834$	−1.21173	+	0.774083i	−1.21173	+	0.774083i
$835$		0			0
$836$	0.827802	−	1.65514i	0.827802	−	1.65514i
$837$		0			0
$838$	0.0352660	−	0.0825089i	0.0352660	−	0.0825089i
$839$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$839$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$840$		0			0
$841$	−0.337330	+	0.941386i	−0.337330	+	0.941386i
$842$		0			0
$843$	3.58902	+	0.215023i	3.58902	+	0.215023i
$844$	−1.80499	+	0.677425i	−1.80499	+	0.677425i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.289390	+	0.0525165i	0.289390	+	0.0525165i
$850$	−0.259183	+	1.56077i	−0.259183	+	1.56077i
$851$		0			0
$852$		0			0
$853$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$853$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$854$		0			0
$855$		0			0
$856$	0.238438	+	0.443092i	0.238438	+	0.443092i
$857$	0.905632	+	0.279350i	0.905632	+	0.279350i	0.712376	−	0.701798i	$-0.247619\pi$
$857$	0.905632	+	0.279350i	0.905632	+	0.279350i	0.193256	+	0.981148i	$0.438095\pi$
$858$		0			0
$859$	−1.54483			−1.54483			−0.772417	−	0.635116i	$-0.780952\pi$
$859$	−1.54483			−1.54483			−0.772417	+	0.635116i	$0.780952\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$863$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$864$	3.62554	−	0.657939i	3.62554	−	0.657939i
$865$		0			0
$866$	−0.737244	−	0.818792i	−0.737244	−	0.818792i
$867$	−0.309199	+	2.94183i	−0.309199	+	2.94183i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.564507	+	3.39939i	0.564507	+	3.39939i
$874$		0			0
$875$		0			0
$876$	−1.98073	+	3.00067i	−1.98073	+	3.00067i
$877$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$877$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.233951	−	1.02501i	−0.233951	−	1.02501i	−0.946327	−	0.323210i	$-0.895238\pi$
$881$	−0.233951	−	1.02501i	−0.233951	−	1.02501i	0.712376	−	0.701798i	$-0.247619\pi$
$882$	−1.12895	+	2.64132i	−1.12895	+	2.64132i
$883$	−0.876945	−	0.359406i	−0.876945	−	0.359406i	−0.104528	−	0.994522i	$-0.533333\pi$
$883$	−0.876945	−	0.359406i	−0.876945	−	0.359406i	−0.772417	+	0.635116i	$0.780952\pi$
$884$		0			0
$885$		0			0
$886$	−0.0225748	−	0.0868435i	−0.0225748	−	0.0868435i
$887$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$887$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.327214	+	4.36637i	0.327214	+	4.36637i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.889233	+	0.731167i	−0.889233	+	0.731167i
$899$		0			0
$900$	−1.72297	−	2.29836i	−1.72297	−	2.29836i
$901$		0			0
$902$	0.746206	−	1.61072i	0.746206	−	1.61072i
$903$		0			0
$904$	0.453741	+	0.329662i	0.453741	+	0.329662i
$905$		0			0
$906$		0			0
$907$	−0.322371	+	0.0585016i	−0.322371	+	0.0585016i	−0.337330	−	0.941386i	$-0.609524\pi$
$907$	−0.322371	+	0.0585016i	−0.322371	+	0.0585016i	0.0149594	+	0.999888i	$0.495238\pi$
$908$	1.47208	+	0.940400i	1.47208	+	0.940400i
$909$		0			0
$910$		0			0
$911$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$911$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$912$	−3.00894	−	2.05146i	−3.00894	−	2.05146i
$913$	−0.422364	+	1.44571i	−0.422364	+	1.44571i
$914$	1.51853	−	0.731286i	1.51853	−	0.731286i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−3.76955	−	4.44715i	−3.76955	−	4.44715i
$919$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$919$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$920$		0			0
$921$	−0.558081	−	1.20464i	−0.558081	−	1.20464i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.336689	+	1.29522i	0.336689	+	1.29522i	0.887586	+	0.460642i	$0.152381\pi$
$929$	0.336689	+	1.29522i	0.336689	+	1.29522i	−0.550897	+	0.834573i	$0.685714\pi$
$930$		0			0
$931$	1.71238	−	0.701798i	1.71238	−	0.701798i
$932$	−0.0193455	+	1.29305i	−0.0193455	+	1.29305i
$933$		0			0
$934$	1.44973	+	1.34515i	1.44973	+	1.34515i
$935$		0			0
$936$		0			0
$937$	−0.388346	−	1.08376i	−0.388346	−	1.08376i	−0.963963	−	0.266037i	$-0.914286\pi$
$937$	−0.388346	−	1.08376i	−0.388346	−	1.08376i	0.575617	−	0.817719i	$-0.304762\pi$
$938$		0			0
$939$	2.46558	−	2.73831i	2.46558	−	2.73831i
$940$		0			0
$941$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$941$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$942$		0			0
$943$		0			0
$944$	0.0225310	−	0.0196847i	0.0225310	−	0.0196847i
$945$		0			0
$946$	0.858449	+	0.512899i	0.858449	+	0.512899i
$947$	1.94298			1.94298			0.971490	−	0.237080i	$-0.0761905\pi$
$947$	1.94298			1.94298			0.971490	+	0.237080i	$0.0761905\pi$
$948$		0			0
$949$		0			0
$950$	−0.248413	+	1.83386i	−0.248413	+	1.83386i
$951$		0			0
$952$		0			0
$953$	−0.0600409	+	0.0666821i	−0.0600409	+	0.0666821i	−0.772417	−	0.635116i	$-0.780952\pi$
$953$	−0.0600409	+	0.0666821i	−0.0600409	+	0.0666821i	0.712376	+	0.701798i	$0.247619\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$962$		0			0
$963$	0.363631	+	1.39886i	0.363631	+	1.39886i
$964$	1.73978	+	0.970057i	1.73978	+	0.970057i
$965$		0			0
$966$		0			0
$967$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$967$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$968$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$969$	−0.430576	+	5.74563i	−0.430576	+	5.74563i
$970$		0			0
$971$	0.524177	+	1.13146i	0.524177	+	1.13146i	0.971490	+	0.237080i	$0.0761905\pi$
$971$	0.524177	+	1.13146i	0.524177	+	1.13146i	−0.447313	+	0.894377i	$0.647619\pi$
$972$	4.92291	+	0.294938i	4.92291	+	0.294938i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.0288841	+	0.146643i	0.0288841	+	0.146643i	0.992847	−	0.119394i	$-0.0380952\pi$
$977$	0.0288841	+	0.146643i	0.0288841	+	0.146643i	−0.963963	+	0.266037i	$0.914286\pi$
$978$	−3.53961	+	1.70459i	−3.53961	+	1.70459i
$979$	1.12708	−	0.871556i	1.12708	−	0.871556i
$980$		0			0
$981$		0			0
$982$	0.659917	−	0.140270i	0.659917	−	0.140270i
$983$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$983$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$984$	−2.94387	−	1.88061i	−2.94387	−	1.88061i
$985$		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
$993$	2.57385	−	2.69203i	2.57385	−	2.69203i
$994$		0			0
$995$		0			0
$996$	2.70764	+	1.20552i	2.70764	+	1.20552i
$997$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$997$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$998$	−0.949003	+	0.733851i	−0.949003	+	0.733851i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.1027.1	yes	48
8.3	odd	2	CM	3784.1.em.b.1027.1	yes	48
11.3	even	5		3784.1.em.a.3435.1	yes	48
43.17	even	21		3784.1.em.a.1995.1	✓	48
88.3	odd	10		3784.1.em.a.3435.1	yes	48
344.275	odd	42		3784.1.em.a.1995.1	✓	48
473.146	even	105	inner	3784.1.em.b.619.1	yes	48
3784.619	odd	210	inner	3784.1.em.b.619.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.1995.1	✓	48	43.17	even	21
3784.1.em.a.1995.1	✓	48	344.275	odd	42
3784.1.em.a.3435.1	yes	48	11.3	even	5
3784.1.em.a.3435.1	yes	48	88.3	odd	10
3784.1.em.b.619.1	yes	48	473.146	even	105	inner
3784.1.em.b.619.1	yes	48	3784.619	odd	210	inner
3784.1.em.b.1027.1	yes	48	1.1	even	1	trivial
3784.1.em.b.1027.1	yes	48	8.3	odd	2	CM

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)

\(f(q)\)	\(=\)	\(q+(0.753071 - 0.657939i) q^{2} +(1.13273 - 1.60916i) q^{3} +(0.134233 - 0.990950i) q^{4} +(-0.205697 - 1.95708i) q^{6} +(-0.550897 - 0.834573i) q^{8} +(-0.968970 - 2.70410i) q^{9} +O(q^{10})\)	\(q+(0.753071 - 0.657939i) q^{2} +(1.13273 - 1.60916i) q^{3} +(0.134233 - 0.990950i) q^{4} +(-0.205697 - 1.95708i) q^{6} +(-0.550897 - 0.834573i) q^{8} +(-0.968970 - 2.70410i) q^{9} +(0.575617 - 0.817719i) q^{11} +(-1.44254 - 1.33848i) q^{12} +(-0.963963 - 0.266037i) q^{16} +(0.398046 + 1.53125i) q^{17} +(-2.50884 - 1.39886i) q^{18} +(0.518961 + 1.77635i) q^{19} +(-0.104528 - 0.994522i) q^{22} +(-1.96698 - 0.0588694i) q^{24} +(0.420357 + 0.907359i) q^{25} +(-3.55197 - 0.980281i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(-0.663818 - 1.85252i) q^{33} +(1.30723 + 0.891252i) q^{34} +(-2.80970 + 0.597220i) q^{36} +(1.55955 + 0.996276i) q^{38} +(1.52389 + 0.910484i) q^{41} +(-0.599822 + 0.800134i) q^{43} +(-0.733052 - 0.680173i) q^{44} +(-1.52001 + 1.24982i) q^{48} +(-0.104528 - 0.994522i) q^{49} +(0.913545 + 0.406737i) q^{50} +(2.91490 + 1.09398i) q^{51} +(-3.31985 + 1.59876i) q^{54} +(3.44628 + 1.17704i) q^{57} +(-0.0164822 + 0.0249694i) q^{59} +(-0.393025 + 0.919528i) q^{64} +(-1.71874 - 0.958325i) q^{66} +(-1.61637 + 1.10202i) q^{67} +(1.57082 - 0.188899i) q^{68} +(-1.72297 + 2.29836i) q^{72} +(-0.299310 - 1.80241i) q^{73} +(1.93623 + 0.351375i) q^{75} +(1.82994 - 0.275819i) q^{76} +(-3.38211 + 2.78093i) q^{81} +(1.74664 - 0.316969i) q^{82} +(-1.42530 + 0.486800i) q^{83} +(0.0747301 + 0.997204i) q^{86} +(-0.999552 - 0.0299155i) q^{88} +(1.36145 + 0.419953i) q^{89} +(-0.322371 + 1.94127i) q^{96} +(-1.18037 - 0.214205i) q^{97} +(-0.733052 - 0.680173i) q^{98} +(-2.76895 - 0.764183i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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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