LMFDB - Embedded newform 3784.1.em.b.1131.1

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			1131.1
Root			$-0.420357 + 0.907359i$ of defining polynomial
Character	$\chi$	$=$	3784.1131
Dual form			3784.1.em.b.1171.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.858449 + 0.512899i) q^{2} +(0.0518827 - 0.263406i) q^{3} +(0.473869 + 0.880596i) q^{4} +(0.179639 - 0.199510i) q^{6} +(-0.0448648 + 0.998993i) q^{8} +(0.858614 + 0.351893i) q^{9} +O(q^{10})$	\(q+(0.858449 + 0.512899i) q^{2} +(0.0518827 - 0.263406i) q^{3} +(0.473869 + 0.880596i) q^{4} +(0.179639 - 0.199510i) q^{6} +(-0.0448648 + 0.998993i) q^{8} +(0.858614 + 0.351893i) q^{9} +(0.193256 - 0.981148i) q^{11} +(0.256539 - 0.0791319i) q^{12} +(-0.550897 + 0.834573i) q^{16} +(-0.470291 - 0.940319i) q^{17} +(0.556590 + 0.742464i) q^{18} +(1.29262 + 1.52498i) q^{19} +(0.669131 - 0.743145i) q^{22} +(0.260813 + 0.0636481i) q^{24} +(-0.946327 + 0.323210i) q^{25} +(0.285135 - 0.431961i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(-0.248413 - 0.101809i) q^{33} +(0.0785688 - 1.04843i) q^{34} +(0.0969946 + 0.922842i) q^{36} +(0.327489 + 1.97210i) q^{38} +(0.607158 + 1.42052i) q^{41} +(0.420357 - 0.907359i) q^{43} +(0.955573 - 0.294755i) q^{44} +(0.191249 + 0.188409i) q^{48} +(0.669131 - 0.743145i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(-0.272085 + 0.0750908i) q^{51} +(0.466327 - 0.224571i) q^{54} +(0.468752 - 0.261363i) q^{57} +(-0.0890878 - 1.98369i) q^{59} +(-0.995974 - 0.0896393i) q^{64} +(-0.161032 - 0.214809i) q^{66} +(-0.0156228 - 0.208472i) q^{67} +(0.605185 - 0.859724i) q^{68} +(-0.390060 + 0.841961i) q^{72} +(-0.492178 + 1.89337i) q^{73} +(0.0360371 + 0.266037i) q^{75} +(-0.730355 + 1.86091i) q^{76} +(0.562045 + 0.553699i) q^{81} +(-0.207368 + 1.53085i) q^{82} +(-1.49955 - 0.836110i) q^{83} +(0.826239 - 0.563320i) q^{86} +(0.971490 + 0.237080i) q^{88} +(-1.46348 + 1.35791i) q^{89} +(0.0675426 + 0.259831i) q^{96} +(0.112852 + 0.833106i) q^{97} +(0.955573 - 0.294755i) q^{98} +(0.511191 - 0.774422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{16}{21}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$

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 $

$2$	0.858449	+	0.512899i	0.858449	+	0.512899i
$2$	0.858449	+	0.512899i	0.858449	+	0.512899i
$3$	0.0518827	−	0.263406i	0.0518827	−	0.263406i	−0.946327	−	0.323210i	$-0.895238\pi$
$3$	0.0518827	−	0.263406i	0.0518827	−	0.263406i	0.998210	+	0.0598042i	$0.0190476\pi$
$4$	0.473869	+	0.880596i	0.473869	+	0.880596i
$5$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$5$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$6$	0.179639	−	0.199510i	0.179639	−	0.199510i
$7$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$7$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$8$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$9$	0.858614	+	0.351893i	0.858614	+	0.351893i
$10$		0			0
$11$	0.193256	−	0.981148i	0.193256	−	0.981148i
$11$	0.193256	−	0.981148i	0.193256	−	0.981148i
$12$	0.256539	−	0.0791319i	0.256539	−	0.0791319i
$13$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$13$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$14$		0			0
$15$		0			0
$16$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$17$	−0.470291	−	0.940319i	−0.470291	−	0.940319i	−0.995974	−	0.0896393i	$-0.971429\pi$
$17$	−0.470291	−	0.940319i	−0.470291	−	0.940319i	0.525684	−	0.850680i	$-0.323810\pi$
$18$	0.556590	+	0.742464i	0.556590	+	0.742464i
$19$	1.29262	+	1.52498i	1.29262	+	1.52498i	0.669131	+	0.743145i	$0.266667\pi$
$19$	1.29262	+	1.52498i	1.29262	+	1.52498i	0.623490	+	0.781831i	$0.285714\pi$
$20$		0			0
$21$		0			0
$22$	0.669131	−	0.743145i	0.669131	−	0.743145i
$23$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$23$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$24$	0.260813	+	0.0636481i	0.260813	+	0.0636481i
$25$	−0.946327	+	0.323210i	−0.946327	+	0.323210i
$26$		0			0
$27$	0.285135	−	0.431961i	0.285135	−	0.431961i
$28$		0			0
$29$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$29$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$30$		0			0
$31$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$31$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$32$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$33$	−0.248413	−	0.101809i	−0.248413	−	0.101809i
$34$	0.0785688	−	1.04843i	0.0785688	−	1.04843i
$35$		0			0
$36$	0.0969946	+	0.922842i	0.0969946	+	0.922842i
$37$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$37$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$38$	0.327489	+	1.97210i	0.327489	+	1.97210i
$39$		0			0
$40$		0			0
$41$	0.607158	+	1.42052i	0.607158	+	1.42052i	0.887586	+	0.460642i	$0.152381\pi$
$41$	0.607158	+	1.42052i	0.607158	+	1.42052i	−0.280427	+	0.959875i	$0.590476\pi$
$42$		0			0
$43$	0.420357	−	0.907359i	0.420357	−	0.907359i
$43$	0.420357	−	0.907359i	0.420357	−	0.907359i
$44$	0.955573	−	0.294755i	0.955573	−	0.294755i
$45$		0			0
$46$		0			0
$47$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$47$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$48$	0.191249	+	0.188409i	0.191249	+	0.188409i
$49$	0.669131	−	0.743145i	0.669131	−	0.743145i
$50$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$51$	−0.272085	+	0.0750908i	−0.272085	+	0.0750908i
$52$		0			0
$53$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$53$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$54$	0.466327	−	0.224571i	0.466327	−	0.224571i
$55$		0			0
$56$		0			0
$57$	0.468752	−	0.261363i	0.468752	−	0.261363i
$58$		0			0
$59$	−0.0890878	−	1.98369i	−0.0890878	−	1.98369i	−0.163818	−	0.986491i	$-0.552381\pi$
$59$	−0.0890878	−	1.98369i	−0.0890878	−	1.98369i	0.0747301	−	0.997204i	$-0.476190\pi$
$60$		0			0
$61$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$61$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$62$		0			0
$63$		0			0
$64$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$65$		0			0
$66$	−0.161032	−	0.214809i	−0.161032	−	0.214809i
$67$	−0.0156228	−	0.208472i	−0.0156228	−	0.208472i	−0.999552	−	0.0299155i	$-0.990476\pi$
$67$	−0.0156228	−	0.208472i	−0.0156228	−	0.208472i	0.983930	−	0.178557i	$-0.0571429\pi$
$68$	0.605185	−	0.859724i	0.605185	−	0.859724i
$69$		0			0
$70$		0			0
$71$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$71$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$72$	−0.390060	+	0.841961i	−0.390060	+	0.841961i
$73$	−0.492178	+	1.89337i	−0.492178	+	1.89337i	−0.0448648	+	0.998993i	$0.514286\pi$
$73$	−0.492178	+	1.89337i	−0.492178	+	1.89337i	−0.447313	+	0.894377i	$0.647619\pi$
$74$		0			0
$75$	0.0360371	+	0.266037i	0.0360371	+	0.266037i
$76$	−0.730355	+	1.86091i	−0.730355	+	1.86091i
$77$		0			0
$78$		0			0
$79$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$79$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$80$		0			0
$81$	0.562045	+	0.553699i	0.562045	+	0.553699i
$82$	−0.207368	+	1.53085i	−0.207368	+	1.53085i
$83$	−1.49955	−	0.836110i	−1.49955	−	0.836110i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−1.49955	−	0.836110i	−1.49955	−	0.836110i	−0.999552	+	0.0299155i	$0.990476\pi$
$84$		0			0
$85$		0			0
$86$	0.826239	−	0.563320i	0.826239	−	0.563320i
$87$		0			0
$88$	0.971490	+	0.237080i	0.971490	+	0.237080i
$89$	−1.46348	+	1.35791i	−1.46348	+	1.35791i	−0.691063	+	0.722795i	$0.742857\pi$
$89$	−1.46348	+	1.35791i	−1.46348	+	1.35791i	−0.772417	+	0.635116i	$0.780952\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.0675426	+	0.259831i	0.0675426	+	0.259831i
$97$	0.112852	+	0.833106i	0.112852	+	0.833106i	0.955573	+	0.294755i	$0.0952381\pi$
$97$	0.112852	+	0.833106i	0.112852	+	0.833106i	−0.842721	+	0.538351i	$0.819048\pi$
$98$	0.955573	−	0.294755i	0.955573	−	0.294755i
$99$	0.511191	−	0.774422i	0.511191	−	0.774422i
$100$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$101$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$101$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$102$	−0.272085	−	0.0750908i	−0.272085	−	0.0750908i
$103$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$103$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.673718	−	0.588609i	−0.673718	−	0.588609i	0.251587	−	0.967835i	$-0.419048\pi$
$107$	−0.673718	−	0.588609i	−0.673718	−	0.588609i	−0.925304	+	0.379225i	$0.876190\pi$
$108$	0.515500	+	0.0463958i	0.515500	+	0.0463958i
$109$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$109$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.24660	+	0.344039i	1.24660	+	0.344039i	0.826239	−	0.563320i	$-0.190476\pi$
$113$	1.24660	+	0.344039i	1.24660	+	0.344039i	0.420357	+	0.907359i	$0.361905\pi$
$114$	0.536453	+	0.0160554i	0.536453	+	0.0160554i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.940958	−	1.74859i	0.940958	−	1.74859i
$119$		0			0
$120$		0			0
$121$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$122$		0			0
$123$	0.405673	−	0.0862285i	0.405673	−	0.0862285i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$127$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$128$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$129$	−0.217194	−	0.157801i	−0.217194	−	0.157801i
$130$		0			0
$131$	−0.317037	+	1.38903i	−0.317037	+	1.38903i	0.525684	+	0.850680i	$0.323810\pi$
$131$	−0.317037	+	1.38903i	−0.317037	+	1.38903i	−0.842721	+	0.538351i	$0.819048\pi$
$132$	−0.0280624	−	0.266996i	−0.0280624	−	0.266996i
$133$		0			0
$134$	0.0935139	−	0.186976i	0.0935139	−	0.186976i
$135$		0			0
$136$	0.960472	−	0.427630i	0.960472	−	0.427630i
$137$	−1.86493	−	0.699921i	−1.86493	−	0.699921i	−0.963963	−	0.266037i	$-0.914286\pi$
$137$	−1.86493	−	0.699921i	−1.86493	−	0.699921i	−0.900969	−	0.433884i	$-0.857143\pi$
$138$		0			0
$139$	1.66662	−	1.06468i	1.66662	−	1.06468i	0.753071	−	0.657939i	$-0.228571\pi$
$139$	1.66662	−	1.06468i	1.66662	−	1.06468i	0.913545	−	0.406737i	$-0.133333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.766688	+	0.522719i	−0.766688	+	0.522719i
$145$		0			0
$146$	−1.39362	+	1.37292i	−1.39362	+	1.37292i
$147$	−0.161032	−	0.214809i	−0.161032	−	0.214809i
$148$		0			0
$149$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$149$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$150$	−0.105514	+	0.246862i	−0.105514	+	0.246862i
$151$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$151$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$152$	−1.58143	+	1.22290i	−1.58143	+	1.22290i
$153$	−0.0729060	−	0.972863i	−0.0729060	−	0.972863i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$157$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.198495	+	0.763594i	0.198495	+	0.763594i
$163$	−1.64257	−	0.673190i	−1.64257	−	0.673190i	−0.646600	−	0.762830i	$-0.723810\pi$
$163$	−1.64257	−	0.673190i	−1.64257	−	0.673190i	−0.995974	+	0.0896393i	$0.971429\pi$
$164$	−0.963188	+	1.20780i	−0.963188	+	1.20780i
$165$		0			0
$166$	−0.858449	−	1.48688i	−0.858449	−	1.48688i
$167$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$167$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$168$		0			0
$169$	0.992847	−	0.119394i	0.992847	−	0.119394i
$170$		0			0
$171$	0.573233	+	1.76423i	0.573233	+	1.76423i
$172$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$173$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$173$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$174$		0			0
$175$		0			0
$176$	0.712376	+	0.701798i	0.712376	+	0.701798i
$177$	−0.527138	−	0.0794533i	−0.527138	−	0.0794533i
$178$	−1.95279	+	0.415079i	−1.95279	+	0.415079i
$179$	−0.207562	−	1.97482i	−0.207562	−	1.97482i	−0.222521	−	0.974928i	$-0.571429\pi$
$179$	−0.207562	−	1.97482i	−0.207562	−	1.97482i	0.0149594	−	0.999888i	$-0.495238\pi$
$180$		0			0
$181$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$181$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−1.01348	+	0.279703i	−1.01348	+	0.279703i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$191$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$192$	−0.0752854	+	0.257694i	−0.0752854	+	0.257694i
$193$	−0.382046	+	0.228262i	−0.382046	+	0.228262i	−0.691063	−	0.722795i	$-0.742857\pi$
$193$	−0.382046	+	0.228262i	−0.382046	+	0.228262i	0.309017	+	0.951057i	$0.400000\pi$
$194$	−0.330422	+	0.773060i	−0.330422	+	0.773060i
$195$		0			0
$196$	0.971490	+	0.237080i	0.971490	+	0.237080i
$197$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$197$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$198$	0.836032	−	0.402612i	0.836032	−	0.402612i
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$201$	−0.0557233	−	0.00670098i	−0.0557233	−	0.00670098i
$202$		0			0
$203$		0			0
$204$	−0.195057	−	0.204014i	−0.195057	−	0.204014i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.74603	−	0.973542i	1.74603	−	0.973542i
$210$		0			0
$211$	0.761409	−	0.796371i	0.761409	−	0.796371i	−0.222521	−	0.974928i	$-0.571429\pi$
$211$	0.761409	−	0.796371i	0.761409	−	0.796371i	0.983930	+	0.178557i	$0.0571429\pi$
$212$		0			0
$213$		0			0
$214$	−0.276455	−	0.850840i	−0.276455	−	0.850840i
$215$		0			0
$216$	0.418734	+	0.304228i	0.418734	+	0.304228i
$217$		0			0
$218$		0			0
$219$	0.473189	+	0.227876i	0.473189	+	0.227876i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$223$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$224$		0			0
$225$	−0.926265	−	0.0554938i	−0.926265	−	0.0554938i
$226$	0.893682	+	0.934718i	0.893682	+	0.934718i
$227$	1.13526	+	0.387736i	1.13526	+	0.387736i	0.826239	−	0.563320i	$-0.190476\pi$
$227$	1.13526	+	0.387736i	1.13526	+	0.387736i	0.309017	+	0.951057i	$0.400000\pi$
$228$	0.452282	+	0.288929i	0.452282	+	0.288929i
$229$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$229$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.910708	−	1.29375i	0.910708	−	1.29375i	−0.0448648	−	0.998993i	$-0.514286\pi$
$233$	0.910708	−	1.29375i	0.910708	−	1.29375i	0.955573	−	0.294755i	$-0.0952381\pi$
$234$		0			0
$235$		0			0
$236$	1.70462	−	1.01846i	1.70462	−	1.01846i
$237$		0			0
$238$		0			0
$239$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$239$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$240$		0			0
$241$	−1.48932	+	0.224479i	−1.48932	+	0.224479i	−0.842721	−	0.538351i	$-0.819048\pi$
$241$	−1.48932	+	0.224479i	−1.48932	+	0.224479i	−0.646600	+	0.762830i	$0.723810\pi$
$242$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$243$	0.602655	−	0.410883i	0.602655	−	0.410883i
$244$		0			0
$245$		0			0
$246$	0.392476	+	0.134047i	0.392476	+	0.134047i
$247$		0			0
$248$		0			0
$249$	−0.298037	+	0.351611i	−0.298037	+	0.351611i
$250$		0			0
$251$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	0.309017	−	0.951057i	$-0.400000\pi$
$251$	−0.669131	−	0.743145i	−0.669131	−	0.743145i	−0.978148	+	0.207912i	$0.933333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$257$	−1.08268	−	0.786610i	−1.08268	−	0.786610i	−0.104528	−	0.994522i	$-0.533333\pi$
$257$	−1.08268	−	0.786610i	−1.08268	−	0.786610i	−0.978148	+	0.207912i	$0.933333\pi$
$258$	−0.105514	−	0.246862i	−0.105514	−	0.246862i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.984593	+	1.02980i	−0.984593	+	1.02980i
$263$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$263$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$264$	0.112852	−	0.243595i	0.112852	−	0.243595i
$265$		0			0
$266$		0			0
$267$	0.281752	+	0.455941i	0.281752	+	0.455941i
$268$	0.176177	−	0.112546i	0.176177	−	0.112546i
$269$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$269$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$270$		0			0
$271$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$271$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$272$	1.04385	+	0.125527i	1.04385	+	0.125527i
$273$		0			0
$274$	−1.24196	−	1.55737i	−1.24196	−	1.55737i
$275$	0.134233	+	0.990950i	0.134233	+	0.990950i
$276$		0			0
$277$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$277$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$278$	1.97678	−	0.0591627i	1.97678	−	0.0591627i
$279$		0			0
$280$		0			0
$281$	0.548599	−	1.87780i	0.548599	−	1.87780i	0.0747301	−	0.997204i	$-0.476190\pi$
$281$	0.548599	−	1.87780i	0.548599	−	1.87780i	0.473869	−	0.880596i	$-0.342857\pi$
$282$		0			0
$283$	−1.56378	+	0.534097i	−1.56378	+	0.534097i	−0.963963	−	0.266037i	$-0.914286\pi$
$283$	−1.56378	+	0.534097i	−1.56378	+	0.534097i	−0.599822	+	0.800134i	$0.704762\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.926265	+	0.0554938i	−0.926265	+	0.0554938i
$289$	−0.0632055	+	0.0843130i	−0.0632055	+	0.0843130i
$290$		0			0
$291$	0.225300	+	0.0134980i	0.225300	+	0.0134980i
$292$	−1.90052	+	0.463799i	−1.90052	+	0.463799i
$293$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$293$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$294$	−0.0280624	−	0.266996i	−0.0280624	−	0.266996i
$295$		0			0
$296$		0			0
$297$	−0.368714	−	0.363239i	−0.368714	−	0.363239i
$298$		0			0
$299$		0			0
$300$	−0.217194	+	0.157801i	−0.217194	+	0.157801i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−1.98481	+	0.238682i	−1.98481	+	0.238682i
$305$		0			0
$306$	0.436395	−	0.872547i	0.436395	−	0.872547i
$307$	0.925304	+	1.60267i	0.925304	+	1.60267i	0.791071	+	0.611724i	$0.209524\pi$
$307$	0.925304	+	1.60267i	0.925304	+	1.60267i	0.134233	+	0.990950i	$0.457143\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$311$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$312$		0			0
$313$	−1.10975	−	1.57650i	−1.10975	−	1.57650i	−0.772417	−	0.635116i	$-0.780952\pi$
$313$	−1.10975	−	1.57650i	−1.10975	−	1.57650i	−0.337330	−	0.941386i	$-0.609524\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$317$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.189997	+	0.146922i	−0.189997	+	0.146922i
$322$		0			0
$323$	0.826058	−	1.93266i	0.826058	−	1.93266i
$324$	−0.221249	+	0.757315i	−0.221249	+	0.757315i
$325$		0			0
$326$	−1.06479	−	1.42037i	−1.06479	−	1.42037i
$327$		0			0
$328$	−1.44633	+	0.542816i	−1.44633	+	0.542816i
$329$		0			0
$330$		0			0
$331$	−0.638184	−	1.62607i	−0.638184	−	1.62607i	−0.772417	−	0.635116i	$-0.780952\pi$
$331$	−0.638184	−	1.62607i	−0.638184	−	1.62607i	0.134233	−	0.990950i	$-0.457143\pi$
$332$	0.0256838	−	1.71671i	0.0256838	−	1.71671i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.72903	+	0.769812i	−1.72903	+	0.769812i	−0.733052	+	0.680173i	$0.761905\pi$
$337$	−1.72903	+	0.769812i	−1.72903	+	0.769812i	−0.995974	+	0.0896393i	$0.971429\pi$
$338$	0.913545	+	0.406737i	0.913545	+	0.406737i
$339$	0.155298	−	0.310511i	0.155298	−	0.310511i
$340$		0			0
$341$		0			0
$342$	−0.412781	+	1.80851i	−0.412781	+	1.80851i
$343$		0			0
$344$	0.887586	+	0.460642i	0.887586	+	0.460642i
$345$		0			0
$346$		0			0
$347$	1.12949	+	0.629774i	1.12949	+	0.629774i	0.936235	−	0.351375i	$-0.114286\pi$
$347$	1.12949	+	0.629774i	1.12949	+	0.629774i	0.193256	+	0.981148i	$0.438095\pi$
$348$		0			0
$349$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$349$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$350$		0			0
$351$		0			0
$352$	0.251587	+	0.967835i	0.251587	+	0.967835i
$353$	0.132659	−	1.77021i	0.132659	−	1.77021i	−0.393025	−	0.919528i	$-0.628571\pi$
$353$	0.132659	−	1.77021i	0.132659	−	1.77021i	0.525684	−	0.850680i	$-0.323810\pi$
$354$	−0.411770	−	0.338575i	−0.411770	−	0.338575i
$355$		0			0
$356$	−1.88927	−	0.645262i	−1.88927	−	0.645262i
$357$		0			0
$358$	0.834701	−	1.80174i	0.834701	−	1.80174i
$359$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$359$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$360$		0			0
$361$	−0.490867	+	2.95594i	−0.490867	+	2.95594i
$362$		0			0
$363$	−0.147897	+	0.224055i	−0.147897	+	0.224055i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$367$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$368$		0			0
$369$	0.0214442	+	1.43333i	0.0214442	+	1.43333i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$373$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$374$	−1.01348	−	0.279703i	−1.01348	−	0.279703i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−1.63543	−	0.613787i	−1.63543	−	0.613787i	−0.646600	−	0.762830i	$-0.723810\pi$
$379$	−1.63543	−	0.613787i	−1.63543	−	0.613787i	−0.988831	+	0.149042i	$0.952381\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$383$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$384$	−0.196800	+	0.182604i	−0.196800	+	0.182604i
$385$		0			0
$386$	−0.445042			−0.445042
$387$	0.680218	−	0.631150i	0.680218	−	0.631150i
$388$	−0.680152	+	0.494160i	−0.680152	+	0.494160i
$389$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$389$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$390$		0			0
$391$		0			0
$392$	0.712376	+	0.701798i	0.712376	+	0.701798i
$393$	0.349430	+	0.155576i	0.349430	+	0.155576i
$394$		0			0
$395$		0			0
$396$	0.924190	+	0.0831786i	0.924190	+	0.0831786i
$397$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$397$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$398$		0			0
$399$		0			0
$400$	0.251587	−	0.967835i	0.251587	−	0.967835i
$401$	−0.837330	+	1.80741i	−0.837330	+	1.80741i	−0.337330	+	0.941386i	$0.609524\pi$
$401$	−0.837330	+	1.80741i	−0.837330	+	1.80741i	−0.500000	+	0.866025i	$0.666667\pi$
$402$	−0.0443987	−	0.0343329i	−0.0443987	−	0.0343329i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.0628081	−	0.275180i	−0.0628081	−	0.275180i
$409$	−0.727741	−	0.0654978i	−0.727741	−	0.0654978i	−0.280427	−	0.959875i	$-0.590476\pi$
$409$	−0.727741	−	0.0654978i	−0.727741	−	0.0654978i	−0.447313	+	0.894377i	$0.647619\pi$
$410$		0			0
$411$	−0.281121	+	0.454919i	−0.281121	+	0.454919i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.193973	−	0.494234i	−0.193973	−	0.494234i
$418$	1.99821	+	0.0598042i	1.99821	+	0.0598042i
$419$	−1.68704	+	0.812434i	−1.68704	+	0.812434i	−0.691063	+	0.722795i	$0.742857\pi$
$419$	−1.68704	+	0.812434i	−1.68704	+	0.812434i	−0.995974	+	0.0896393i	$0.971429\pi$
$420$		0			0
$421$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$421$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$422$	1.06209	−	0.293118i	1.06209	−	0.293118i
$423$		0			0
$424$		0			0
$425$	0.748969	+	0.737848i	0.748969	+	0.737848i
$426$		0			0
$427$		0			0
$428$	0.199073	−	0.872196i	0.199073	−	0.872196i
$429$		0			0
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$	0.203423	+	0.475932i	0.203423	+	0.475932i
$433$	−0.0890878	+	0.0107132i	−0.0890878	+	0.0107132i	−0.163818	−	0.986491i	$-0.552381\pi$
$433$	−0.0890878	+	0.0107132i	−0.0890878	+	0.0107132i	0.0747301	+	0.997204i	$0.476190\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.289331	+	0.438318i	0.289331	+	0.438318i
$439$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$439$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$440$		0			0
$441$	0.836032	−	0.402612i	0.836032	−	0.402612i
$442$		0			0
$443$	−1.57797	−	1.00805i	−1.57797	−	1.00805i	−0.978148	−	0.207912i	$-0.933333\pi$
$443$	−1.57797	−	1.00805i	−1.57797	−	1.00805i	−0.599822	−	0.800134i	$-0.704762\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.375492	+	0.0916344i	0.375492	+	0.0916344i	0.420357	−	0.907359i	$-0.361905\pi$
$449$	0.375492	+	0.0916344i	0.375492	+	0.0916344i	−0.0448648	+	0.998993i	$0.514286\pi$
$450$	−0.766688	−	0.522719i	−0.766688	−	0.522719i
$451$	1.51108	−	0.321189i	1.51108	−	0.321189i
$452$	0.287764	+	1.26078i	0.287764	+	1.26078i
$453$		0			0
$454$	0.775689	+	0.915124i	0.775689	+	0.915124i
$455$		0			0
$456$	0.240070	+	0.480006i	0.240070	+	0.480006i
$457$	0.180494	−	0.273436i	0.180494	−	0.273436i	−0.733052	−	0.680173i	$-0.761905\pi$
$457$	0.180494	−	0.273436i	0.180494	−	0.273436i	0.913545	+	0.406737i	$0.133333\pi$
$458$		0			0
$459$	−0.540278	−	0.0649708i	−0.540278	−	0.0649708i
$460$		0			0
$461$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$461$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$462$		0			0
$463$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$463$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$464$		0			0
$465$		0			0
$466$	1.44536	−	0.643515i	1.44536	−	0.643515i
$467$	0.488922	−	0.543003i	0.488922	−	0.543003i	−0.447313	−	0.894377i	$-0.647619\pi$
$467$	0.488922	−	0.543003i	0.488922	−	0.543003i	0.936235	+	0.351375i	$0.114286\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.98569			1.98569
$473$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$474$		0			0
$475$	−1.71613	−	1.02534i	−1.71613	−	1.02534i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$479$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$480$		0			0
$481$		0			0
$482$	−1.39364	−	0.571168i	−1.39364	−	0.571168i
$483$		0			0
$484$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$485$		0			0
$486$	0.728091	−	0.0436209i	0.728091	−	0.0436209i
$487$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$487$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$488$		0			0
$489$	−0.262543	+	0.397736i	−0.262543	+	0.397736i
$490$		0			0
$491$	1.11004	+	1.48073i	1.11004	+	1.48073i	0.858449	+	0.512899i	$0.171429\pi$
$491$	1.11004	+	1.48073i	1.11004	+	1.48073i	0.251587	+	0.967835i	$0.419048\pi$
$492$	0.268168	+	0.316373i	0.268168	+	0.316373i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.436190	+	0.148977i	−0.436190	+	0.148977i
$499$	0.746206	+	0.387269i	0.746206	+	0.387269i	0.791071	−	0.611724i	$-0.209524\pi$
$499$	0.746206	+	0.387269i	0.746206	+	0.387269i	−0.0448648	+	0.998993i	$0.514286\pi$
$500$		0			0
$501$		0			0
$502$	−0.193256	−	0.981148i	−0.193256	−	0.981148i
$503$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$503$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.0200625	−	0.267716i	0.0200625	−	0.267716i
$508$		0			0
$509$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$509$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$510$		0			0
$511$		0			0
$512$	0.134233	−	0.990950i	0.134233	−	0.990950i
$513$	1.02730	−	0.123538i	1.02730	−	0.123538i
$514$	−0.525970	−	1.23057i	−0.525970	−	1.23057i
$515$		0			0
$516$	0.0360371	−	0.266037i	0.0360371	−	0.266037i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.01496	+	0.999888i	1.01496	+	0.999888i	1.00000			$0$
$521$	1.01496	+	0.999888i	1.01496	+	0.999888i	0.0149594	+	0.999888i	$0.495238\pi$
$522$		0			0
$523$	−0.492178	−	0.104616i	−0.492178	−	0.104616i	−0.0448648	−	0.998993i	$-0.514286\pi$
$523$	−0.492178	−	0.104616i	−0.492178	−	0.104616i	−0.447313	+	0.894377i	$0.647619\pi$
$524$	−1.37341	+	0.379037i	−1.37341	+	0.379037i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.221817	−	0.151233i	0.221817	−	0.151233i
$529$	0.365341	+	0.930874i	0.365341	+	0.930874i
$530$		0			0
$531$	0.621556	−	1.73458i	0.621556	−	1.73458i
$532$		0			0
$533$		0			0
$534$	0.00801782	+	0.535912i	0.00801782	+	0.535912i
$535$		0			0
$536$	0.208963	−	0.00625404i	0.208963	−	0.00625404i
$537$	−0.530946	−	0.0477860i	−0.530946	−	0.0477860i
$538$		0			0
$539$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$540$		0			0
$541$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$541$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$542$		0			0
$543$		0			0
$544$	0.831706	+	0.643147i	0.831706	+	0.643147i
$545$		0			0
$546$		0			0
$547$	0.0538218	−	0.0717957i	0.0538218	−	0.0717957i	−0.772417	−	0.635116i	$-0.780952\pi$
$547$	0.0538218	−	0.0717957i	0.0538218	−	0.0717957i	0.826239	+	0.563320i	$0.190476\pi$
$548$	−0.267386	−	1.97392i	−0.267386	−	1.97392i
$549$		0			0
$550$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.72731	+	0.963099i	1.72731	+	0.963099i
$557$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$557$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.0210931	+	0.281468i	0.0210931	+	0.281468i
$562$	1.43407	−	1.33062i	1.43407	−	1.33062i
$563$	−1.29399	+	1.35341i	−1.29399	+	1.35341i	−0.393025	+	0.919528i	$0.628571\pi$
$563$	−1.29399	+	1.35341i	−1.29399	+	1.35341i	−0.900969	+	0.433884i	$0.857143\pi$
$564$		0			0
$565$		0			0
$566$	−1.61637	−	0.343569i	−1.61637	−	0.343569i
$567$		0			0
$568$		0			0
$569$	0.0972413	+	0.374080i	0.0972413	+	0.374080i	0.998210	−	0.0598042i	$-0.0190476\pi$
$569$	0.0972413	+	0.374080i	0.0972413	+	0.374080i	−0.900969	+	0.433884i	$0.857143\pi$
$570$		0			0
$571$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−0.425270	+	0.131178i	−0.425270	+	0.131178i	0.0747301	+	0.997204i	$0.476190\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.823614	−	0.427442i	−0.823614	−	0.427442i
$577$	0.0225310	+	1.50597i	0.0225310	+	1.50597i	0.669131	+	0.743145i	$0.266667\pi$
$577$	0.0225310	+	1.50597i	0.0225310	+	1.50597i	−0.646600	+	0.762830i	$0.723810\pi$
$578$	−0.0975027	+	0.0399604i	−0.0975027	+	0.0399604i
$579$	0.0403038	+	0.112476i	0.0403038	+	0.112476i
$580$		0			0
$581$		0			0
$582$	0.186485	+	0.127143i	0.186485	+	0.127143i
$583$		0			0
$584$	−1.86938	−	0.576628i	−1.86938	−	0.576628i
$585$		0			0
$586$		0			0
$587$	1.19911	+	0.0358879i	1.19911	+	0.0358879i	0.623490	−	0.781831i	$-0.285714\pi$
$587$	1.19911	+	0.0358879i	1.19911	+	0.0358879i	0.575617	+	0.817719i	$0.304762\pi$
$588$	0.112852	−	0.243595i	0.112852	−	0.243595i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.0504174	+	0.672773i	−0.0504174	+	0.672773i	0.913545	+	0.406737i	$0.133333\pi$
$593$	−0.0504174	+	0.672773i	−0.0504174	+	0.672773i	−0.963963	+	0.266037i	$0.914286\pi$
$594$	−0.130217	−	0.500935i	−0.130217	−	0.500935i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$599$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$600$	−0.267386	+	0.0240652i	−0.267386	+	0.0240652i
$601$	1.41320	+	1.02675i	1.41320	+	1.02675i	0.992847	+	0.119394i	$0.0380952\pi$
$601$	1.41320	+	1.02675i	1.41320	+	1.02675i	0.420357	+	0.907359i	$0.361905\pi$
$602$		0			0
$603$	0.0599460	−	0.184495i	0.0599460	−	0.184495i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$607$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$608$	−1.82627	−	0.813109i	−1.82627	−	0.813109i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.822151	−	0.525210i	0.822151	−	0.525210i
$613$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$613$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$614$	−0.0276840	+	1.85040i	−0.0276840	+	1.85040i
$615$		0			0
$616$		0			0
$617$	1.62592	−	1.10853i	1.62592	−	1.10853i	0.712376	−	0.701798i	$-0.247619\pi$
$617$	1.62592	−	1.10853i	1.62592	−	1.10853i	0.913545	−	0.406737i	$-0.133333\pi$
$618$		0			0
$619$	0.675145	−	0.665120i	0.675145	−	0.665120i	−0.280427	−	0.959875i	$-0.590476\pi$
$619$	0.675145	−	0.665120i	0.675145	−	0.665120i	0.955573	+	0.294755i	$0.0952381\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.791071	−	0.611724i	0.791071	−	0.611724i
$626$	−0.144074	−	1.92253i	−0.144074	−	1.92253i
$627$	−0.165847	−	0.510425i	−0.165847	−	0.510425i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$631$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$632$		0			0
$633$	−0.170265	−	0.241877i	−0.170265	−	0.241877i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.13273	−	0.205561i	1.13273	−	0.205561i	0.420357	−	0.907359i	$-0.361905\pi$
$641$	1.13273	−	0.205561i	1.13273	−	0.205561i	0.712376	+	0.701798i	$0.247619\pi$
$642$	−0.238459	+	0.0286758i	−0.238459	+	0.0286758i
$643$	0.558597	−	0.0502746i	0.558597	−	0.0502746i	0.193256	−	0.981148i	$-0.438095\pi$
$643$	0.558597	−	0.0502746i	0.558597	−	0.0502746i	0.365341	+	0.930874i	$0.380952\pi$
$644$		0			0
$645$		0			0
$646$	1.70039	−	1.23540i	1.70039	−	1.23540i
$647$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$647$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$648$	−0.578357	+	0.536637i	−0.578357	+	0.536637i
$649$	−1.96352	−	0.295952i	−1.96352	−	0.295952i
$650$		0			0
$651$		0			0
$652$	−0.185556	−	1.76545i	−0.185556	−	1.76545i
$653$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$653$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$654$		0			0
$655$		0			0
$656$	−1.52001	−	0.275841i	−1.52001	−	0.275841i
$657$	−1.08885	+	1.45248i	−1.08885	+	1.45248i
$658$		0			0
$659$	−0.694741	−	0.644625i	−0.694741	−	0.644625i	0.251587	−	0.967835i	$-0.419048\pi$
$659$	−0.694741	−	0.644625i	−0.694741	−	0.644625i	−0.946327	+	0.323210i	$0.895238\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	0.286160	−	1.72322i	0.286160	−	1.72322i
$663$		0			0
$664$	0.902545	−	1.46053i	0.902545	−	1.46053i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.472644	+	1.61781i	0.472644	+	1.61781i	0.753071	+	0.657939i	$0.228571\pi$
$673$	0.472644	+	1.61781i	0.472644	+	1.61781i	−0.280427	+	0.959875i	$0.590476\pi$
$674$	−1.87912	−	0.225972i	−1.87912	−	0.225972i
$675$	−0.130217	+	0.500935i	−0.130217	+	0.500935i
$676$	0.575617	+	0.817719i	0.575617	+	0.817719i
$677$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$677$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$678$	0.292576	−	0.186905i	0.292576	−	0.186905i
$679$		0			0
$680$		0			0
$681$	0.161032	−	0.278916i	0.161032	−	0.278916i
$682$		0			0
$683$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.955573	−	0.294755i	$-0.0952381\pi$
$683$	1.78181	+	0.268565i	1.78181	+	0.268565i	0.826239	+	0.563320i	$0.190476\pi$
$684$	−1.28194	+	1.34080i	−1.28194	+	1.34080i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.525684	+	0.850680i	0.525684	+	0.850680i
$689$		0			0
$690$		0			0
$691$	0.768031	+	1.65783i	0.768031	+	1.65783i	0.753071	+	0.657939i	$0.228571\pi$
$691$	0.768031	+	1.65783i	0.768031	+	1.65783i	0.0149594	+	0.999888i	$0.495238\pi$
$692$		0			0
$693$		0			0
$694$	0.646600	+	1.11994i	0.646600	+	1.11994i
$695$		0			0
$696$		0			0
$697$	1.05020	−	1.23898i	1.05020	−	1.23898i
$698$		0			0
$699$	−0.293530	−	0.307009i	−0.293530	−	0.307009i
$700$		0			0
$701$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$701$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$702$		0			0
$703$		0			0
$704$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$705$		0			0
$706$	1.02182	−	1.45159i	1.02182	−	1.45159i
$707$		0			0
$708$	−0.179828	−	0.501846i	−0.179828	−	0.501846i
$709$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$709$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$710$		0			0
$711$		0			0
$712$	−1.29088	−	1.52293i	−1.29088	−	1.52293i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.64066	−	1.11858i	1.64066	−	1.11858i
$717$		0			0
$718$		0			0
$719$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$719$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$720$		0			0
$721$		0			0
$722$	−1.93748	+	2.28576i	−1.93748	+	2.28576i
$723$	−0.0181410	+	0.403942i	−0.0181410	+	0.403942i
$724$		0			0
$725$		0			0
$726$	−0.241880	+	0.116483i	−0.241880	+	0.116483i
$727$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$727$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$728$		0			0
$729$	0.233124	+	0.545421i	0.233124	+	0.545421i
$730$		0			0
$731$	−1.05090	+	0.0314522i	−1.05090	+	0.0314522i
$732$		0			0
$733$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$733$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.207562	−	0.0249602i	−0.207562	−	0.0249602i
$738$	−0.716746	+	1.24144i	−0.716746	+	1.24144i
$739$	0.0494318	+	0.0748860i	0.0494318	+	0.0748860i	0.858449	−	0.512899i	$-0.171429\pi$
$739$	0.0494318	+	0.0748860i	0.0494318	+	0.0748860i	−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$743$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.993315	−	1.24558i	−0.993315	−	1.24558i
$748$	−0.726561	−	0.759923i	−0.726561	−	0.759923i
$749$		0			0
$750$		0			0
$751$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$751$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$752$		0			0
$753$	−0.230465	+	0.137696i	−0.230465	+	0.137696i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$757$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$758$	−1.08912	−	1.36572i	−1.08912	−	1.36572i
$759$		0			0
$760$		0			0
$761$	−0.0895691	+	0.00536621i	−0.0895691	+	0.00536621i	−0.104528	−	0.994522i	$-0.533333\pi$
$761$	−0.0895691	+	0.00536621i	−0.0895691	+	0.00536621i	0.0149594	+	0.999888i	$0.495238\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.262600	+	0.0558173i	−0.262600	+	0.0558173i
$769$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.900969	−	0.433884i	$-0.857143\pi$
$769$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.988831	+	0.149042i	$0.952381\pi$
$770$		0			0
$771$	−0.263370	+	0.244371i	−0.263370	+	0.244371i
$772$	−0.382046	−	0.228262i	−0.382046	−	0.228262i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	0.907648	−	0.192927i	0.907648	−	0.192927i
$775$		0			0
$776$	−0.837330	+	0.0753611i	−0.837330	+	0.0753611i
$777$		0			0
$778$		0			0
$779$	−1.38143	+	2.76209i	−1.38143	+	2.76209i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.251587	+	0.967835i	0.251587	+	0.967835i
$785$		0			0
$786$	0.220173	+	0.312776i	0.220173	+	0.312776i
$787$	−1.52001	+	1.24982i	−1.52001	+	1.24982i	−0.646600	+	0.762830i	$0.723810\pi$
$787$	−1.52001	+	1.24982i	−1.52001	+	1.24982i	−0.873408	+	0.486989i	$0.838095\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.750708	+	0.545421i	0.750708	+	0.545421i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$797$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$798$		0			0
$799$		0			0
$800$	0.712376	−	0.701798i	0.712376	−	0.701798i
$801$	−1.73440	+	0.650932i	−1.73440	+	0.650932i
$802$	−1.64583	+	1.12210i	−1.64583	+	1.12210i
$803$	1.76256	+	0.848805i	1.76256	+	0.848805i
$804$	−0.0205047	−	0.0522451i	−0.0205047	−	0.0522451i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.84238	+	0.691456i	1.84238	+	0.691456i	0.983930	+	0.178557i	$0.0571429\pi$
$809$	1.84238	+	0.691456i	1.84238	+	0.691456i	0.858449	+	0.512899i	$0.171429\pi$
$810$		0			0
$811$	1.22256	+	0.544320i	1.22256	+	0.544320i	0.913545	−	0.406737i	$-0.133333\pi$
$811$	1.22256	+	0.544320i	1.22256	+	0.544320i	0.309017	+	0.951057i	$0.400000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.0872222	−	0.268442i	0.0872222	−	0.268442i
$817$	1.92706	−	0.531836i	1.92706	−	0.531836i
$818$	−0.591134	−	0.429484i	−0.591134	−	0.429484i
$819$		0			0
$820$		0			0
$821$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$821$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$822$	−0.474656	+	0.246338i	−0.474656	+	0.246338i
$823$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$823$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$824$		0			0
$825$	0.267986	+	0.0160554i	0.267986	+	0.0160554i
$826$		0			0
$827$	1.30186	+	1.07045i	1.30186	+	1.07045i	0.992847	+	0.119394i	$0.0380952\pi$
$827$	1.30186	+	1.07045i	1.30186	+	1.07045i	0.309017	+	0.951057i	$0.400000\pi$
$828$		0			0
$829$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$829$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.01348	−	0.279703i	−1.01348	−	0.279703i
$834$	0.0869768	−	0.523763i	0.0869768	−	0.523763i
$835$		0			0
$836$	1.68469	+	1.07622i	1.68469	+	1.07622i
$837$		0			0
$838$	−1.86493	−	0.167847i	−1.86493	−	0.167847i
$839$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$839$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$840$		0			0
$841$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$842$		0			0
$843$	−0.466160	−	0.241929i	−0.466160	−	0.241929i
$844$	1.06209	+	0.293118i	1.06209	+	0.293118i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.0595506	+	0.439620i	0.0595506	+	0.439620i
$850$	0.264510	+	1.01755i	0.264510	+	1.01755i
$851$		0			0
$852$		0			0
$853$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$853$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$854$		0			0
$855$		0			0
$856$	0.618243	−	0.646631i	0.618243	−	0.646631i
$857$	1.01317	−	0.940084i	1.01317	−	0.940084i	0.0149594	−	0.999888i	$-0.495238\pi$
$857$	1.01317	−	0.940084i	1.01317	−	0.940084i	0.998210	+	0.0598042i	$0.0190476\pi$
$858$		0			0
$859$	1.42475			1.42475			0.712376	−	0.701798i	$-0.247619\pi$
$859$	1.42475			1.42475			0.712376	+	0.701798i	$0.247619\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$863$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$864$	−0.0694769	+	0.512899i	−0.0694769	+	0.512899i
$865$		0			0
$866$	−0.0819721	−	0.0364963i	−0.0819721	−	0.0364963i
$867$	0.0189292	+	0.0210231i	0.0189292	+	0.0210231i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.196268	+	0.755028i	−0.196268	+	0.755028i
$874$		0			0
$875$		0			0
$876$	0.0235630	+	0.524671i	0.0235630	+	0.524671i
$877$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$877$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.124802	+	0.546793i	0.124802	+	0.546793i	0.998210	+	0.0598042i	$0.0190476\pi$
$881$	0.124802	+	0.546793i	0.124802	+	0.546793i	−0.873408	+	0.486989i	$0.838095\pi$
$882$	0.924190	+	0.0831786i	0.924190	+	0.0831786i
$883$	1.38151	−	0.0413469i	1.38151	−	0.0413469i	0.669131	−	0.743145i	$-0.266667\pi$
$883$	1.38151	−	0.0413469i	1.38151	−	0.0413469i	0.712376	+	0.701798i	$0.247619\pi$
$884$		0			0
$885$		0			0
$886$	−0.837580	−	1.67469i	−0.837580	−	1.67469i
$887$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$887$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.651879	−	0.444444i	0.651879	−	0.444444i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.275342	+	0.271253i	0.275342	+	0.271253i
$899$		0			0
$900$	−0.390060	−	0.841961i	−0.390060	−	0.841961i
$901$		0			0
$902$	1.46192	+	0.499305i	1.46192	+	0.499305i
$903$		0			0
$904$	−0.399621	+	1.22991i	−0.399621	+	1.22991i
$905$		0			0
$906$		0			0
$907$	0.0675426	−	0.498620i	0.0675426	−	0.498620i	−0.925304	−	0.379225i	$-0.876190\pi$
$907$	0.0675426	−	0.498620i	0.0675426	−	0.498620i	0.992847	−	0.119394i	$-0.0380952\pi$
$908$	0.196523	+	1.18344i	0.196523	+	1.18344i
$909$		0			0
$910$		0			0
$911$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$911$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$912$	−0.0401071	+	0.535192i	−0.0401071	+	0.535192i
$913$	−1.11015	+	1.30970i	−1.11015	+	1.30970i
$914$	0.295190	−	0.142156i	0.295190	−	0.142156i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.430478	−	0.332882i	−0.430478	−	0.332882i
$919$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$919$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$920$		0			0
$921$	0.470160	−	0.160579i	0.470160	−	0.160579i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.817282	−	1.63411i	−0.817282	−	1.63411i	−0.772417	−	0.635116i	$-0.780952\pi$
$929$	−0.817282	−	1.63411i	−0.817282	−	1.63411i	−0.0448648	−	0.998993i	$-0.514286\pi$
$930$		0			0
$931$	1.99821	+	0.0598042i	1.99821	+	0.0598042i
$932$	1.57082	+	0.188899i	1.57082	+	0.188899i
$933$		0			0
$934$	0.698220	−	0.215372i	0.698220	−	0.215372i
$935$		0			0
$936$		0			0
$937$	−0.357641	−	0.146575i	−0.357641	−	0.146575i	0.193256	−	0.981148i	$-0.438095\pi$
$937$	−0.357641	−	0.146575i	−0.357641	−	0.146575i	−0.550897	+	0.834573i	$0.685714\pi$
$938$		0			0
$939$	−0.472836	+	0.210520i	−0.472836	+	0.210520i
$940$		0			0
$941$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$941$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$942$		0			0
$943$		0			0
$944$	1.70462	+	1.01846i	1.70462	+	1.01846i
$945$		0			0
$946$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$947$	−0.674660			−0.674660			−0.337330	−	0.941386i	$-0.609524\pi$
$947$	−0.674660			−0.674660			−0.337330	+	0.941386i	$0.609524\pi$
$948$		0			0
$949$		0			0
$950$	−0.947313	−	1.76040i	−0.947313	−	1.76040i
$951$		0			0
$952$		0			0
$953$	1.71059	−	0.761602i	1.71059	−	0.761602i	0.712376	−	0.701798i	$-0.247619\pi$
$953$	1.71059	−	0.761602i	1.71059	−	0.761602i	0.998210	−	0.0598042i	$-0.0190476\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$962$		0			0
$963$	−0.371336	−	0.742464i	−0.371336	−	0.742464i
$964$	−0.903418	−	1.20512i	−0.903418	−	1.20512i
$965$		0			0
$966$		0			0
$967$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$967$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$968$	0.420357	−	0.907359i	0.420357	−	0.907359i
$969$	−0.466215	−	0.317860i	−0.466215	−	0.317860i
$970$		0			0
$971$	−1.18005	+	0.403036i	−1.18005	+	0.403036i	−0.842721	−	0.538351i	$-0.819048\pi$
$971$	−1.18005	+	0.403036i	−1.18005	+	0.403036i	−0.337330	+	0.941386i	$0.609524\pi$
$972$	0.647402	+	0.335991i	0.647402	+	0.335991i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	0.0247201	−	1.65229i	0.0247201	−	1.65229i	−0.550897	−	0.834573i	$-0.685714\pi$
$977$	0.0247201	−	1.65229i	0.0247201	−	1.65229i	0.575617	−	0.817719i	$-0.304762\pi$
$978$	−0.429378	+	0.206778i	−0.429378	+	0.206778i
$979$	1.04949	+	1.69831i	1.04949	+	1.69831i
$980$		0			0
$981$		0			0
$982$	0.193441	+	1.84047i	0.193441	+	1.84047i
$983$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$983$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$984$	0.0679412	+	0.409133i	0.0679412	+	0.409133i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$991$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$992$		0			0
$993$	−0.461425	+	0.0837364i	−0.461425	+	0.0837364i
$994$		0			0
$995$		0			0
$996$	−0.450857	−	0.0958326i	−0.450857	−	0.0958326i
$997$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$997$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$998$	0.441950	+	0.715179i	0.441950	+	0.715179i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.1131.1	yes	48
8.3	odd	2	CM	3784.1.em.b.1131.1	yes	48
11.5	even	5		3784.1.em.a.3195.1	yes	48
43.10	even	21		3784.1.em.a.2891.1	✓	48
88.27	odd	10		3784.1.em.a.3195.1	yes	48
344.139	odd	42		3784.1.em.a.2891.1	✓	48
473.225	even	105	inner	3784.1.em.b.1171.1	yes	48
3784.1171	odd	210	inner	3784.1.em.b.1171.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.2891.1	✓	48	43.10	even	21
3784.1.em.a.2891.1	✓	48	344.139	odd	42
3784.1.em.a.3195.1	yes	48	11.5	even	5
3784.1.em.a.3195.1	yes	48	88.27	odd	10
3784.1.em.b.1131.1	yes	48	1.1	even	1	trivial
3784.1.em.b.1131.1	yes	48	8.3	odd	2	CM
3784.1.em.b.1171.1	yes	48	473.225	even	105	inner
3784.1.em.b.1171.1	yes	48	3784.1171	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)

\(f(q)\)	\(=\)	\(q+(0.858449 + 0.512899i) q^{2} +(0.0518827 - 0.263406i) q^{3} +(0.473869 + 0.880596i) q^{4} +(0.179639 - 0.199510i) q^{6} +(-0.0448648 + 0.998993i) q^{8} +(0.858614 + 0.351893i) q^{9} +O(q^{10})\)	\(q+(0.858449 + 0.512899i) q^{2} +(0.0518827 - 0.263406i) q^{3} +(0.473869 + 0.880596i) q^{4} +(0.179639 - 0.199510i) q^{6} +(-0.0448648 + 0.998993i) q^{8} +(0.858614 + 0.351893i) q^{9} +(0.193256 - 0.981148i) q^{11} +(0.256539 - 0.0791319i) q^{12} +(-0.550897 + 0.834573i) q^{16} +(-0.470291 - 0.940319i) q^{17} +(0.556590 + 0.742464i) q^{18} +(1.29262 + 1.52498i) q^{19} +(0.669131 - 0.743145i) q^{22} +(0.260813 + 0.0636481i) q^{24} +(-0.946327 + 0.323210i) q^{25} +(0.285135 - 0.431961i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(-0.248413 - 0.101809i) q^{33} +(0.0785688 - 1.04843i) q^{34} +(0.0969946 + 0.922842i) q^{36} +(0.327489 + 1.97210i) q^{38} +(0.607158 + 1.42052i) q^{41} +(0.420357 - 0.907359i) q^{43} +(0.955573 - 0.294755i) q^{44} +(0.191249 + 0.188409i) q^{48} +(0.669131 - 0.743145i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(-0.272085 + 0.0750908i) q^{51} +(0.466327 - 0.224571i) q^{54} +(0.468752 - 0.261363i) q^{57} +(-0.0890878 - 1.98369i) q^{59} +(-0.995974 - 0.0896393i) q^{64} +(-0.161032 - 0.214809i) q^{66} +(-0.0156228 - 0.208472i) q^{67} +(0.605185 - 0.859724i) q^{68} +(-0.390060 + 0.841961i) q^{72} +(-0.492178 + 1.89337i) q^{73} +(0.0360371 + 0.266037i) q^{75} +(-0.730355 + 1.86091i) q^{76} +(0.562045 + 0.553699i) q^{81} +(-0.207368 + 1.53085i) q^{82} +(-1.49955 - 0.836110i) q^{83} +(0.826239 - 0.563320i) q^{86} +(0.971490 + 0.237080i) q^{88} +(-1.46348 + 1.35791i) q^{89} +(0.0675426 + 0.259831i) q^{96} +(0.112852 + 0.833106i) q^{97} +(0.955573 - 0.294755i) q^{98} +(0.511191 - 0.774422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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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