LMFDB - Embedded newform 3784.1.em.b.1115.1

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			1115.1
Root			$0.646600 + 0.762830i$ of defining polynomial
Character	$\chi$	$=$	3784.1115
Dual form			3784.1.em.b.2379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.473869 + 0.880596i) q^{2} +(1.78392 + 0.731119i) q^{3} +(-0.550897 + 0.834573i) q^{4} +(0.201523 + 1.91736i) q^{6} +(-0.995974 - 0.0896393i) q^{8} +(1.93545 + 1.90671i) q^{9} +O(q^{10})$	\(q+(0.473869 + 0.880596i) q^{2} +(1.78392 + 0.731119i) q^{3} +(-0.550897 + 0.834573i) q^{4} +(0.201523 + 1.91736i) q^{6} +(-0.995974 - 0.0896393i) q^{8} +(1.93545 + 1.90671i) q^{9} +(-0.925304 - 0.379225i) q^{11} +(-1.59293 + 1.08604i) q^{12} +(-0.393025 - 0.919528i) q^{16} +(0.536616 - 0.715821i) q^{17} +(-0.761892 + 2.60788i) q^{18} +(-0.327049 + 1.96945i) q^{19} +(-0.104528 - 0.994522i) q^{22} +(-1.71120 - 0.888084i) q^{24} +(0.791071 - 0.611724i) q^{25} +(1.30093 + 3.04368i) q^{27} +(0.623490 - 0.781831i) q^{32} +(-1.37341 - 1.35301i) q^{33} +(0.884634 + 0.133337i) q^{34} +(-2.65753 + 0.564875i) q^{36} +(-1.88927 + 0.645262i) q^{38} +(-0.267104 + 0.279369i) q^{41} +(-0.646600 - 0.762830i) q^{43} +(0.826239 - 0.563320i) q^{44} +(-0.0288406 - 1.92771i) q^{48} +(-0.104528 - 0.994522i) q^{49} +(0.913545 + 0.406737i) q^{50} +(1.48063 - 0.884635i) q^{51} +(-2.06378 + 2.58790i) q^{54} +(-2.02333 + 3.27423i) q^{57} +(-1.93516 + 0.174167i) q^{59} +(0.983930 + 0.178557i) q^{64} +(0.540643 - 1.85057i) q^{66} +(1.93445 - 0.291571i) q^{67} +(0.301784 + 0.842189i) q^{68} +(-1.75674 - 2.07253i) q^{72} +(-1.59580 - 0.889773i) q^{73} +(1.85845 - 0.512899i) q^{75} +(-1.46348 - 1.35791i) q^{76} +(0.0548208 + 3.66422i) q^{81} +(-0.372583 - 0.102826i) q^{82} +(0.498210 + 0.806221i) q^{83} +(0.365341 - 0.930874i) q^{86} +(0.887586 + 0.460642i) q^{88} +(0.148391 - 1.98014i) q^{89} +(1.68387 - 0.938878i) q^{96} +(1.24660 - 0.344039i) q^{97} +(0.826239 - 0.563320i) q^{98} +(-1.06781 - 2.49826i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{11}{21}\right)$	$e\left(\frac{1}{5}\right)$	$-1$	$-1$

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 $

$2$	0.473869	+	0.880596i	0.473869	+	0.880596i
$2$	0.473869	+	0.880596i	0.473869	+	0.880596i
$3$	1.78392	+	0.731119i	1.78392	+	0.731119i	0.992847	+	0.119394i	$0.0380952\pi$
$3$	1.78392	+	0.731119i	1.78392	+	0.731119i	0.791071	+	0.611724i	$0.209524\pi$
$4$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$5$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$5$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$6$	0.201523	+	1.91736i	0.201523	+	1.91736i
$7$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$7$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$8$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$9$	1.93545	+	1.90671i	1.93545	+	1.90671i
$10$		0			0
$11$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$11$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$12$	−1.59293	+	1.08604i	−1.59293	+	1.08604i
$13$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$13$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$14$		0			0
$15$		0			0
$16$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$17$	0.536616	−	0.715821i	0.536616	−	0.715821i	−0.447313	−	0.894377i	$-0.647619\pi$
$17$	0.536616	−	0.715821i	0.536616	−	0.715821i	0.983930	+	0.178557i	$0.0571429\pi$
$18$	−0.761892	+	2.60788i	−0.761892	+	2.60788i
$19$	−0.327049	+	1.96945i	−0.327049	+	1.96945i	−0.104528	+	0.994522i	$0.533333\pi$
$19$	−0.327049	+	1.96945i	−0.327049	+	1.96945i	−0.222521	+	0.974928i	$0.571429\pi$
$20$		0			0
$21$		0			0
$22$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$23$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$23$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$24$	−1.71120	−	0.888084i	−1.71120	−	0.888084i
$25$	0.791071	−	0.611724i	0.791071	−	0.611724i
$26$		0			0
$27$	1.30093	+	3.04368i	1.30093	+	3.04368i
$28$		0			0
$29$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$29$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$30$		0			0
$31$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$31$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$32$	0.623490	−	0.781831i	0.623490	−	0.781831i
$33$	−1.37341	−	1.35301i	−1.37341	−	1.35301i
$34$	0.884634	+	0.133337i	0.884634	+	0.133337i
$35$		0			0
$36$	−2.65753	+	0.564875i	−2.65753	+	0.564875i
$37$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$37$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$38$	−1.88927	+	0.645262i	−1.88927	+	0.645262i
$39$		0			0
$40$		0			0
$41$	−0.267104	+	0.279369i	−0.267104	+	0.279369i	−0.842721	−	0.538351i	$-0.819048\pi$
$41$	−0.267104	+	0.279369i	−0.267104	+	0.279369i	0.575617	+	0.817719i	$0.304762\pi$
$42$		0			0
$43$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$43$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$44$	0.826239	−	0.563320i	0.826239	−	0.563320i
$45$		0			0
$46$		0			0
$47$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$47$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$48$	−0.0288406	−	1.92771i	−0.0288406	−	1.92771i
$49$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$50$	0.913545	+	0.406737i	0.913545	+	0.406737i
$51$	1.48063	−	0.884635i	1.48063	−	0.884635i
$52$		0			0
$53$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$53$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$54$	−2.06378	+	2.58790i	−2.06378	+	2.58790i
$55$		0			0
$56$		0			0
$57$	−2.02333	+	3.27423i	−2.02333	+	3.27423i
$58$		0			0
$59$	−1.93516	+	0.174167i	−1.93516	+	0.174167i	−0.988831	−	0.149042i	$-0.952381\pi$
$59$	−1.93516	+	0.174167i	−1.93516	+	0.174167i	−0.946327	+	0.323210i	$0.895238\pi$
$60$		0			0
$61$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$61$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$62$		0			0
$63$		0			0
$64$	0.983930	+	0.178557i	0.983930	+	0.178557i
$65$		0			0
$66$	0.540643	−	1.85057i	0.540643	−	1.85057i
$67$	1.93445	−	0.291571i	1.93445	−	0.291571i	0.936235	−	0.351375i	$-0.114286\pi$
$67$	1.93445	−	0.291571i	1.93445	−	0.291571i	0.998210	+	0.0598042i	$0.0190476\pi$
$68$	0.301784	+	0.842189i	0.301784	+	0.842189i
$69$		0			0
$70$		0			0
$71$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$71$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$72$	−1.75674	−	2.07253i	−1.75674	−	2.07253i
$73$	−1.59580	−	0.889773i	−1.59580	−	0.889773i	−0.995974	−	0.0896393i	$-0.971429\pi$
$73$	−1.59580	−	0.889773i	−1.59580	−	0.889773i	−0.599822	−	0.800134i	$-0.704762\pi$
$74$		0			0
$75$	1.85845	−	0.512899i	1.85845	−	0.512899i
$76$	−1.46348	−	1.35791i	−1.46348	−	1.35791i
$77$		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
$81$	0.0548208	+	3.66422i	0.0548208	+	3.66422i
$82$	−0.372583	−	0.102826i	−0.372583	−	0.102826i
$83$	0.498210	+	0.806221i	0.498210	+	0.806221i	0.998210	−	0.0598042i	$-0.0190476\pi$
$83$	0.498210	+	0.806221i	0.498210	+	0.806221i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	0.365341	−	0.930874i	0.365341	−	0.930874i
$87$		0			0
$88$	0.887586	+	0.460642i	0.887586	+	0.460642i
$89$	0.148391	−	1.98014i	0.148391	−	1.98014i	−0.0448648	−	0.998993i	$-0.514286\pi$
$89$	0.148391	−	1.98014i	0.148391	−	1.98014i	0.193256	−	0.981148i	$-0.438095\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	1.68387	−	0.938878i	1.68387	−	0.938878i
$97$	1.24660	−	0.344039i	1.24660	−	0.344039i	0.420357	−	0.907359i	$-0.361905\pi$
$97$	1.24660	−	0.344039i	1.24660	−	0.344039i	0.826239	+	0.563320i	$0.190476\pi$
$98$	0.826239	−	0.563320i	0.826239	−	0.563320i
$99$	−1.06781	−	2.49826i	−1.06781	−	2.49826i
$100$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$101$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$101$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$102$	1.48063	+	0.884635i	1.48063	+	0.884635i
$103$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$103$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.161032	−	1.18879i	−0.161032	−	1.18879i	−0.873408	−	0.486989i	$-0.838095\pi$
$107$	−0.161032	−	1.18879i	−0.161032	−	1.18879i	0.712376	−	0.701798i	$-0.247619\pi$
$108$	−3.25686	−	0.591032i	−3.25686	−	0.591032i
$109$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$109$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.281259	−	0.168044i	−0.281259	−	0.168044i	0.365341	−	0.930874i	$-0.380952\pi$
$113$	−0.281259	−	0.168044i	−0.281259	−	0.168044i	−0.646600	+	0.762830i	$0.723810\pi$
$114$	−3.84206	−	0.230183i	−3.84206	−	0.230183i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−1.07038	−	1.62156i	−1.07038	−	1.62156i
$119$		0			0
$120$		0			0
$121$	0.712376	+	0.701798i	0.712376	+	0.701798i
$122$		0			0
$123$	−0.680743	+	0.303086i	−0.680743	+	0.303086i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$127$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$128$	0.309017	+	0.951057i	0.309017	+	0.951057i
$129$	−0.595762	−	1.83357i	−0.595762	−	1.83357i
$130$		0			0
$131$	−0.0269559	−	0.0129813i	−0.0269559	−	0.0129813i	0.420357	−	0.907359i	$-0.361905\pi$
$131$	−0.0269559	−	0.0129813i	−0.0269559	−	0.0129813i	−0.447313	+	0.894377i	$0.647619\pi$
$132$	1.88580	−	0.400838i	1.88580	−	0.400838i
$133$		0			0
$134$	1.17343	+	1.56530i	1.17343	+	1.56530i
$135$		0			0
$136$	−0.598622	+	0.664837i	−0.598622	+	0.664837i
$137$	1.48194	+	1.29473i	1.48194	+	1.29473i	0.858449	+	0.512899i	$0.171429\pi$
$137$	1.48194	+	1.29473i	1.48194	+	1.29473i	0.623490	+	0.781831i	$0.285714\pi$
$138$		0			0
$139$	0.803364	−	1.73409i	0.803364	−	1.73409i	0.134233	−	0.990950i	$-0.457143\pi$
$139$	0.803364	−	1.73409i	0.803364	−	1.73409i	0.669131	−	0.743145i	$-0.266667\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.992594	−	2.52909i	0.992594	−	2.52909i
$145$		0			0
$146$	0.0273322	−	1.82689i	0.0273322	−	1.82689i
$147$	0.540643	−	1.85057i	0.540643	−	1.85057i
$148$		0			0
$149$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$149$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$150$	1.33232	+	1.39349i	1.33232	+	1.39349i
$151$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$151$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$152$	0.502273	−	1.93220i	0.502273	−	1.93220i
$153$	2.40346	−	0.362263i	2.40346	−	0.362263i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$157$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−3.20072	+	1.78464i	−3.20072	+	1.78464i
$163$	0.820112	+	0.807934i	0.820112	+	0.807934i	0.983930	−	0.178557i	$-0.0571429\pi$
$163$	0.820112	+	0.807934i	0.820112	+	0.807934i	−0.163818	+	0.986491i	$0.552381\pi$
$164$	−0.0860070	−	0.376821i	−0.0860070	−	0.376821i
$165$		0			0
$166$	−0.473869	+	0.820765i	−0.473869	+	0.820765i
$167$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$167$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$168$		0			0
$169$	0.971490	−	0.237080i	0.971490	−	0.237080i
$170$		0			0
$171$	−4.38816	+	3.18819i	−4.38816	+	3.18819i
$172$	0.992847	−	0.119394i	0.992847	−	0.119394i
$173$		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
$176$	0.0149594	+	0.999888i	0.0149594	+	0.999888i
$177$	−3.57950	−	1.10413i	−3.57950	−	1.10413i
$178$	1.81402	−	0.807654i	1.81402	−	0.807654i
$179$	−1.90052	+	0.403968i	−1.90052	+	0.403968i	−0.999552	−	0.0299155i	$-0.990476\pi$
$179$	−1.90052	+	0.403968i	−1.90052	+	0.403968i	−0.900969	+	0.433884i	$0.857143\pi$
$180$		0			0
$181$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$181$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.767991	+	0.458853i	−0.767991	+	0.458853i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$191$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$192$	1.62470	+	1.03790i	1.62470	+	1.03790i
$193$	−0.853882	+	1.58678i	−0.853882	+	1.58678i	−0.0448648	+	0.998993i	$0.514286\pi$
$193$	−0.853882	+	1.58678i	−0.853882	+	1.58678i	−0.809017	+	0.587785i	$0.800000\pi$
$194$	0.893682	+	0.934718i	0.893682	+	0.934718i
$195$		0			0
$196$	0.887586	+	0.460642i	0.887586	+	0.460642i
$197$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$197$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$198$	1.69396	−	2.12416i	1.69396	−	2.12416i
$199$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$199$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$200$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$201$	3.66406	+	0.894170i	3.66406	+	0.894170i
$202$		0			0
$203$		0			0
$204$	−0.0773817	+	1.72304i	−0.0773817	+	1.72304i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.04949	−	1.69831i	1.04949	−	1.69831i
$210$		0			0
$211$	0.0352660	+	0.785259i	0.0352660	+	0.785259i	0.936235	+	0.351375i	$0.114286\pi$
$211$	0.0352660	+	0.785259i	0.0352660	+	0.785259i	−0.900969	+	0.433884i	$0.857143\pi$
$212$		0			0
$213$		0			0
$214$	0.970532	−	0.705133i	0.970532	−	0.705133i
$215$		0			0
$216$	−1.02286	−	3.14805i	−1.02286	−	3.14805i
$217$		0			0
$218$		0			0
$219$	−2.19624	−	2.75400i	−2.19624	−	2.75400i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$223$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$224$		0			0
$225$	2.69746	+	0.324382i	2.69746	+	0.324382i
$226$	0.0146993	−	0.327306i	0.0146993	−	0.327306i
$227$	−0.443676	−	0.343088i	−0.443676	−	0.343088i	0.365341	−	0.930874i	$-0.380952\pi$
$227$	−0.443676	−	0.343088i	−0.443676	−	0.343088i	−0.809017	+	0.587785i	$0.800000\pi$
$228$	−1.61793	−	3.49238i	−1.61793	−	3.49238i
$229$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$229$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.169736	−	0.473681i	−0.169736	−	0.473681i	0.826239	−	0.563320i	$-0.190476\pi$
$233$	−0.169736	−	0.473681i	−0.169736	−	0.473681i	−0.995974	+	0.0896393i	$0.971429\pi$
$234$		0			0
$235$		0			0
$236$	0.920717	−	1.71098i	0.920717	−	1.71098i
$237$		0			0
$238$		0			0
$239$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$239$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$240$		0			0
$241$	0.256539	−	0.0791319i	0.256539	−	0.0791319i	−0.163818	−	0.986491i	$-0.552381\pi$
$241$	0.256539	−	0.0791319i	0.256539	−	0.0791319i	0.420357	+	0.907359i	$0.361905\pi$
$242$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$243$	−1.37189	+	3.49552i	−1.37189	+	3.49552i
$244$		0			0
$245$		0			0
$246$	−0.589479	−	0.455836i	−0.589479	−	0.455836i
$247$		0			0
$248$		0			0
$249$	0.299323	+	1.80248i	0.299323	+	1.80248i
$250$		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
$256$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$257$	−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	$0.933333\pi$
$258$	1.33232	−	1.39349i	1.33232	−	1.39349i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.00134230	−	0.0298887i	−0.00134230	−	0.0298887i
$263$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$263$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$264$	1.24660	+	1.47068i	1.24660	+	1.47068i
$265$		0			0
$266$		0			0
$267$	1.71244	−	3.42392i	1.71244	−	3.42392i
$268$	−0.822343	+	1.77506i	−0.822343	+	1.77506i
$269$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$269$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$270$		0			0
$271$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$271$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$272$	−0.869121	−	0.212098i	−0.869121	−	0.212098i
$273$		0			0
$274$	−0.437890	+	1.91852i	−0.437890	+	1.91852i
$275$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$276$		0			0
$277$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$277$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$278$	1.90772	−	0.114294i	1.90772	−	0.114294i
$279$		0			0
$280$		0			0
$281$	−1.53973	−	0.983616i	−1.53973	−	0.983616i	−0.988831	−	0.149042i	$-0.952381\pi$
$281$	−1.53973	−	0.983616i	−1.53973	−	0.983616i	−0.550897	−	0.834573i	$-0.685714\pi$
$282$		0			0
$283$	0.578021	−	0.446976i	0.578021	−	0.446976i	−0.280427	−	0.959875i	$-0.590476\pi$
$283$	0.578021	−	0.446976i	0.578021	−	0.446976i	0.858449	+	0.512899i	$0.171429\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	2.69746	−	0.324382i	2.69746	−	0.324382i
$289$	0.0559856	+	0.191633i	0.0559856	+	0.191633i
$290$		0			0
$291$	2.47536	+	0.297673i	2.47536	+	0.297673i
$292$	1.62170	−	0.841636i	1.62170	−	0.841636i
$293$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$293$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$294$	1.88580	−	0.400838i	1.88580	−	0.400838i
$295$		0			0
$296$		0			0
$297$	−0.0495164	−	3.30968i	−0.0495164	−	3.30968i
$298$		0			0
$299$		0			0
$300$	−0.595762	+	1.83357i	−0.595762	+	1.83357i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	1.93950	−	0.473312i	1.93950	−	0.473312i
$305$		0			0
$306$	1.45793	+	1.94481i	1.45793	+	1.94481i
$307$	−0.712376	+	1.23387i	−0.712376	+	1.23387i	0.251587	+	0.967835i	$0.419048\pi$
$307$	−0.712376	+	1.23387i	−0.712376	+	1.23387i	−0.963963	+	0.266037i	$0.914286\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$311$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$312$		0			0
$313$	−0.579161	+	1.61626i	−0.579161	+	1.61626i	0.193256	+	0.981148i	$0.438095\pi$
$313$	−0.579161	+	1.61626i	−0.579161	+	1.61626i	−0.772417	+	0.635116i	$0.780952\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$317$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.581876	−	2.23843i	0.581876	−	2.23843i
$322$		0			0
$323$	1.23427	+	1.29095i	1.23427	+	1.29095i
$324$	−3.08826	−	1.97286i	−3.08826	−	1.97286i
$325$		0			0
$326$	−0.322838	+	1.10504i	−0.322838	+	1.10504i
$327$		0			0
$328$	0.291071	−	0.254301i	0.291071	−	0.254301i
$329$		0			0
$330$		0			0
$331$	−0.770707	+	0.715112i	−0.770707	+	0.715112i	−0.963963	−	0.266037i	$-0.914286\pi$
$331$	−0.770707	+	0.715112i	−0.770707	+	0.715112i	0.193256	+	0.981148i	$0.438095\pi$
$332$	−0.947313	−	0.0283520i	−0.947313	−	0.0283520i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.05866	−	1.17576i	1.05866	−	1.17576i	0.0747301	−	0.997204i	$-0.476190\pi$
$337$	1.05866	−	1.17576i	1.05866	−	1.17576i	0.983930	−	0.178557i	$-0.0571429\pi$
$338$	0.669131	+	0.743145i	0.669131	+	0.743145i
$339$	−0.378882	−	0.505410i	−0.378882	−	0.505410i
$340$		0			0
$341$		0			0
$342$	−4.88692	−	2.35342i	−4.88692	−	2.35342i
$343$		0			0
$344$	0.575617	+	0.817719i	0.575617	+	0.817719i
$345$		0			0
$346$		0			0
$347$	−0.172233	−	0.278713i	−0.172233	−	0.278713i	0.753071	−	0.657939i	$-0.228571\pi$
$347$	−0.172233	−	0.278713i	−0.172233	−	0.278713i	−0.925304	+	0.379225i	$0.876190\pi$
$348$		0			0
$349$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$349$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$350$		0			0
$351$		0			0
$352$	−0.873408	+	0.486989i	−0.873408	+	0.486989i
$353$	−1.13838	−	0.171583i	−1.13838	−	0.171583i	−0.447313	−	0.894377i	$-0.647619\pi$
$353$	−1.13838	−	0.171583i	−1.13838	−	0.171583i	−0.691063	+	0.722795i	$0.742857\pi$
$354$	−0.723921	−	3.67530i	−0.723921	−	3.67530i
$355$		0			0
$356$	1.57082	+	1.21470i	1.57082	+	1.21470i
$357$		0			0
$358$	−1.25633	−	1.48216i	−1.25633	−	1.48216i
$359$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$359$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$360$		0			0
$361$	−2.82544	−	0.965005i	−2.82544	−	0.965005i
$362$		0			0
$363$	0.757723	+	1.77278i	0.757723	+	1.77278i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$367$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$368$		0			0
$369$	−1.04964	+	0.0314146i	−1.04964	+	0.0314146i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$373$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$374$	−0.767991	−	0.458853i	−0.767991	−	0.458853i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.791755	+	0.691735i	0.791755	+	0.691735i	0.955573	−	0.294755i	$-0.0952381\pi$
$379$	0.791755	+	0.691735i	0.791755	+	0.691735i	−0.163818	+	0.986491i	$0.552381\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$383$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$384$	−0.144074	+	1.92253i	−0.144074	+	1.92253i
$385$		0			0
$386$	−1.80194			−1.80194
$387$	0.203034	−	2.70930i	0.203034	−	2.70930i
$388$	−0.399621	+	1.22991i	−0.399621	+	1.22991i
$389$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$389$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$390$		0			0
$391$		0			0
$392$	0.0149594	+	0.999888i	0.0149594	+	0.999888i
$393$	−0.0385963	−	0.0428655i	−0.0385963	−	0.0428655i
$394$		0			0
$395$		0			0
$396$	2.67324	+	0.485121i	2.67324	+	0.485121i
$397$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$397$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$398$		0			0
$399$		0			0
$400$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$401$	−1.27242	−	1.50114i	−1.27242	−	1.50114i	−0.772417	−	0.635116i	$-0.780952\pi$
$401$	−1.27242	−	1.50114i	−1.27242	−	1.50114i	−0.500000	−	0.866025i	$-0.666667\pi$
$402$	0.948883	+	3.65028i	0.948883	+	3.65028i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.55397	+	0.748351i	−1.55397	+	0.748351i
$409$	−1.44254	−	0.261783i	−1.44254	−	0.261783i	−0.599822	−	0.800134i	$-0.704762\pi$
$409$	−1.44254	−	0.261783i	−1.44254	−	0.261783i	−0.842721	+	0.538351i	$0.819048\pi$
$410$		0			0
$411$	1.69706	+	3.39317i	1.69706	+	3.39317i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.70096	−	2.50613i	2.70096	−	2.50613i
$418$	1.99285	+	0.119394i	1.99285	+	0.119394i
$419$	0.939065	−	1.17755i	0.939065	−	1.17755i	−0.0448648	−	0.998993i	$-0.514286\pi$
$419$	0.939065	−	1.17755i	0.939065	−	1.17755i	0.983930	−	0.178557i	$-0.0571429\pi$
$420$		0			0
$421$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$421$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$422$	−0.674784	+	0.403165i	−0.674784	+	0.403165i
$423$		0			0
$424$		0			0
$425$	−0.0133831	−	0.894526i	−0.0133831	−	0.894526i
$426$		0			0
$427$		0			0
$428$	1.08084	+	0.520506i	1.08084	+	0.520506i
$429$		0			0
$430$		0			0
$431$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$431$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$432$	2.28745	−	2.39249i	2.28745	−	2.39249i
$433$	−1.93516	+	0.472252i	−1.93516	+	0.472252i	−0.946327	+	0.323210i	$0.895238\pi$
$433$	−1.93516	+	0.472252i	−1.93516	+	0.472252i	−0.988831	+	0.149042i	$0.952381\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	1.38443	−	3.23903i	1.38443	−	3.23903i
$439$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$439$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$440$		0			0
$441$	1.69396	−	2.12416i	1.69396	−	2.12416i
$442$		0			0
$443$	0.633118	+	1.36661i	0.633118	+	1.36661i	0.913545	+	0.406737i	$0.133333\pi$
$443$	0.633118	+	1.36661i	0.633118	+	1.36661i	−0.280427	+	0.959875i	$0.590476\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.64257	−	0.852469i	−1.64257	−	0.852469i	−0.995974	−	0.0896393i	$-0.971429\pi$
$449$	−1.64257	−	0.852469i	−1.64257	−	0.852469i	−0.646600	−	0.762830i	$-0.723810\pi$
$450$	0.992594	+	2.52909i	0.992594	+	2.52909i
$451$	0.353096	−	0.157209i	0.353096	−	0.157209i
$452$	0.295190	−	0.142156i	0.295190	−	0.142156i
$453$		0			0
$454$	0.0918781	−	0.553278i	0.0918781	−	0.553278i
$455$		0			0
$456$	2.30868	−	3.07967i	2.30868	−	3.07967i
$457$	0.743861	+	1.74035i	0.743861	+	1.74035i	0.669131	+	0.743145i	$0.266667\pi$
$457$	0.743861	+	1.74035i	0.743861	+	1.74035i	0.0747301	+	0.997204i	$0.476190\pi$
$458$		0			0
$459$	2.87683	+	0.702056i	2.87683	+	0.702056i
$460$		0			0
$461$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$461$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$462$		0			0
$463$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$463$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$464$		0			0
$465$		0			0
$466$	0.336689	−	0.373931i	0.336689	−	0.373931i
$467$	0.153250	+	1.45807i	0.153250	+	1.45807i	0.753071	+	0.657939i	$0.228571\pi$
$467$	0.153250	+	1.45807i	0.153250	+	1.45807i	−0.599822	+	0.800134i	$0.704762\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.94298			1.94298
$473$	0.309017	+	0.951057i	0.309017	+	0.951057i
$474$		0			0
$475$	0.946041	+	1.75804i	0.946041	+	1.75804i
$476$		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
$482$	0.191249	+	0.188409i	0.191249	+	0.188409i
$483$		0			0
$484$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$485$		0			0
$486$	−3.72823	+	0.448336i	−3.72823	+	0.448336i
$487$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$487$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$488$		0			0
$489$	0.872317	+	2.04089i	0.872317	+	2.04089i
$490$		0			0
$491$	−0.399540	+	1.36758i	−0.399540	+	1.36758i	0.473869	+	0.880596i	$0.342857\pi$
$491$	−0.399540	+	1.36758i	−0.399540	+	1.36758i	−0.873408	+	0.486989i	$0.838095\pi$
$492$	0.122072	−	0.735099i	0.122072	−	0.735099i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−1.44542	+	1.11772i	−1.44542	+	1.11772i
$499$	−0.744388	−	1.05747i	−0.744388	−	1.05747i	−0.995974	−	0.0896393i	$-0.971429\pi$
$499$	−0.744388	−	1.05747i	−0.744388	−	1.05747i	0.251587	−	0.967835i	$-0.419048\pi$
$500$		0			0
$501$		0			0
$502$	0.925304	−	0.379225i	0.925304	−	0.379225i
$503$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$503$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	1.90639	+	0.287342i	1.90639	+	0.287342i
$508$		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
$512$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$513$	−6.41985	+	1.56669i	−6.41985	+	1.56669i
$514$	0.144471	−	0.151105i	0.144471	−	0.151105i
$515$		0			0
$516$	1.85845	+	0.512899i	1.85845	+	0.512899i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.000447568		0.0299155i	0.000447568		0.0299155i	1.00000			$0$
$521$	0.000447568		0.0299155i	0.000447568		0.0299155i	−0.999552	+	0.0299155i	$0.990476\pi$
$522$		0			0
$523$	−1.59580	−	0.710494i	−1.59580	−	0.710494i	−0.599822	−	0.800134i	$-0.704762\pi$
$523$	−1.59580	−	0.710494i	−1.59580	−	0.710494i	−0.995974	+	0.0896393i	$0.971429\pi$
$524$	0.0256838	−	0.0153453i	0.0256838	−	0.0153453i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	−0.704350	+	1.79466i	−0.704350	+	1.79466i
$529$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$530$		0			0
$531$	−4.07749	−	3.35270i	−4.07749	−	3.35270i
$532$		0			0
$533$		0			0
$534$	3.82656	−	0.114524i	3.82656	−	0.114524i
$535$		0			0
$536$	−1.95279	+	0.116995i	−1.95279	+	0.116995i
$537$	−3.68572	−	0.668860i	−3.68572	−	0.668860i
$538$		0			0
$539$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$540$		0			0
$541$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$541$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$542$		0			0
$543$		0			0
$544$	−0.225076	−	0.865850i	−0.225076	−	0.865850i
$545$		0			0
$546$		0			0
$547$	0.558597	+	1.91202i	0.558597	+	1.91202i	0.365341	+	0.930874i	$0.380952\pi$
$547$	0.558597	+	1.91202i	0.558597	+	1.91202i	0.193256	+	0.981148i	$0.438095\pi$
$548$	−1.89694	+	0.523523i	−1.89694	+	0.523523i
$549$		0			0
$550$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.00466	+	1.62577i	1.00466	+	1.62577i
$557$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$557$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−1.70551	+	0.257064i	−1.70551	+	0.257064i
$562$	0.136539	−	1.82198i	0.136539	−	1.82198i
$563$	−0.0675728	−	1.50463i	−0.0675728	−	1.50463i	−0.691063	−	0.722795i	$-0.742857\pi$
$563$	−0.0675728	−	1.50463i	−0.0675728	−	1.50463i	0.623490	−	0.781831i	$-0.285714\pi$
$564$		0			0
$565$		0			0
$566$	0.667511	+	0.297195i	0.667511	+	0.297195i
$567$		0			0
$568$		0			0
$569$	1.61634	−	0.901226i	1.61634	−	0.901226i	0.623490	−	0.781831i	$-0.285714\pi$
$569$	1.61634	−	0.901226i	1.61634	−	0.901226i	0.992847	−	0.119394i	$-0.0380952\pi$
$570$		0			0
$571$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.500000	+	0.866025i	$0.666667\pi$
$571$	−1.48883	+	1.01507i	−1.48883	+	1.01507i	−0.988831	+	0.149042i	$0.952381\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.56389	+	2.22166i	1.56389	+	2.22166i
$577$	−0.268346	+	0.00803130i	−0.268346	+	0.00803130i	−0.163818	−	0.986491i	$-0.552381\pi$
$577$	−0.268346	+	0.00803130i	−0.268346	+	0.00803130i	−0.104528	+	0.994522i	$0.533333\pi$
$578$	−0.142221	+	0.140110i	−0.142221	+	0.140110i
$579$	−2.68338	+	2.20639i	−2.68338	+	2.20639i
$580$		0			0
$581$		0			0
$582$	0.910865	+	2.32085i	0.910865	+	2.32085i
$583$		0			0
$584$	1.50961	+	1.02924i	1.50961	+	1.02924i
$585$		0			0
$586$		0			0
$587$	−0.559851	−	0.0335414i	−0.559851	−	0.0335414i	−0.222521	−	0.974928i	$-0.571429\pi$
$587$	−0.559851	−	0.0335414i	−0.559851	−	0.0335414i	−0.337330	+	0.941386i	$0.609524\pi$
$588$	1.24660	+	1.47068i	1.24660	+	1.47068i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.52758	+	0.230246i	1.52758	+	0.230246i	0.858449	−	0.512899i	$-0.171429\pi$
$593$	1.52758	+	0.230246i	1.52758	+	0.230246i	0.669131	+	0.743145i	$0.266667\pi$
$594$	2.89103	−	1.61196i	2.89103	−	1.61196i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$599$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$600$	−1.89694	+	0.344244i	−1.89694	+	0.344244i
$601$	0.324890	+	0.999910i	0.324890	+	0.999910i	0.971490	+	0.237080i	$0.0761905\pi$
$601$	0.324890	+	0.999910i	0.324890	+	0.999910i	−0.646600	+	0.762830i	$0.723810\pi$
$602$		0			0
$603$	4.29997	+	3.12411i	4.29997	+	3.12411i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$607$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$608$	1.33587	+	1.48363i	1.33587	+	1.48363i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.02172	+	2.20543i	−1.02172	+	2.20543i
$613$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$613$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$614$	−1.42411	−	0.0426221i	−1.42411	−	0.0426221i
$615$		0			0
$616$		0			0
$617$	0.684090	−	1.74303i	0.684090	−	1.74303i	0.0149594	−	0.999888i	$-0.495238\pi$
$617$	0.684090	−	1.74303i	0.684090	−	1.74303i	0.669131	−	0.743145i	$-0.266667\pi$
$618$		0			0
$619$	−0.0164822	+	1.10167i	−0.0164822	+	1.10167i	0.826239	+	0.563320i	$0.190476\pi$
$619$	−0.0164822	+	1.10167i	−0.0164822	+	1.10167i	−0.842721	+	0.538351i	$0.819048\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.251587	−	0.967835i	0.251587	−	0.967835i
$626$	−1.69772	+	0.255890i	−1.69772	+	0.255890i
$627$	3.11387	−	2.26236i	3.11387	−	2.26236i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$631$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$632$		0			0
$633$	−0.511205	+	1.42662i	−0.511205	+	1.42662i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.631640	+	0.237059i	−0.631640	+	0.237059i	−0.646600	−	0.762830i	$-0.723810\pi$
$641$	−0.631640	+	0.237059i	−0.631640	+	0.237059i	0.0149594	+	0.999888i	$0.495238\pi$
$642$	2.24689	−	0.548325i	2.24689	−	0.548325i
$643$	−1.65836	+	0.300947i	−1.65836	+	0.300947i	−0.925304	−	0.379225i	$-0.876190\pi$
$643$	−1.65836	+	0.300947i	−1.65836	+	0.300947i	−0.733052	+	0.680173i	$0.761905\pi$
$644$		0			0
$645$		0			0
$646$	−0.551920	+	1.69863i	−0.551920	+	1.69863i
$647$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$647$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$648$	0.273859	−	3.65439i	0.273859	−	3.65439i
$649$	1.85666	+	0.572703i	1.85666	+	0.572703i
$650$		0			0
$651$		0			0
$652$	−1.12608	+	0.239355i	−1.12608	+	0.239355i
$653$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$653$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$654$		0			0
$655$		0			0
$656$	0.361866	+	0.135811i	0.361866	+	0.135811i
$657$	−1.39205	−	4.76484i	−1.39205	−	4.76484i
$658$		0			0
$659$	−0.0823372	−	1.09871i	−0.0823372	−	1.09871i	−0.873408	−	0.486989i	$-0.838095\pi$
$659$	−0.0823372	−	1.09871i	−0.0823372	−	1.09871i	0.791071	−	0.611724i	$-0.209524\pi$
$660$		0			0
$661$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$661$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$662$	−0.994938	−	0.339812i	−0.994938	−	0.339812i
$663$		0			0
$664$	−0.423935	−	0.847635i	−0.423935	−	0.847635i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.708488	+	0.452599i	−0.708488	+	0.452599i	−0.842721	−	0.538351i	$-0.819048\pi$
$673$	−0.708488	+	0.452599i	−0.708488	+	0.452599i	0.134233	+	0.990950i	$0.457143\pi$
$674$	1.53704	+	0.375095i	1.53704	+	0.375095i
$675$	2.89103	+	1.61196i	2.89103	+	1.61196i
$676$	−0.337330	+	0.941386i	−0.337330	+	0.941386i
$677$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$677$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$678$	0.265522	−	0.573140i	0.265522	−	0.573140i
$679$		0			0
$680$		0			0
$681$	−0.540643	−	0.936421i	−0.540643	−	0.936421i
$682$		0			0
$683$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.826239	−	0.563320i	$-0.190476\pi$
$683$	1.19158	+	0.367554i	1.19158	+	0.367554i	0.365341	+	0.930874i	$0.380952\pi$
$684$	−0.243350	−	5.41861i	−0.243350	−	5.41861i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$689$		0			0
$690$		0			0
$691$	−0.865319	+	1.02087i	−0.865319	+	1.02087i	0.134233	+	0.990950i	$0.457143\pi$
$691$	−0.865319	+	1.02087i	−0.865319	+	1.02087i	−0.999552	+	0.0299155i	$0.990476\pi$
$692$		0			0
$693$		0			0
$694$	0.163818	−	0.283741i	0.163818	−	0.283741i
$695$		0			0
$696$		0			0
$697$	0.0566456	+	0.341112i	0.0566456	+	0.341112i
$698$		0			0
$699$	0.0435225	−	0.969104i	0.0435225	−	0.969104i
$700$		0			0
$701$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$701$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$702$		0			0
$703$		0			0
$704$	−0.842721	−	0.538351i	−0.842721	−	0.538351i
$705$		0			0
$706$	−0.388346	−	1.08376i	−0.388346	−	1.08376i
$707$		0			0
$708$	2.89341	−	2.37909i	2.89341	−	2.37909i
$709$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$709$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$710$		0			0
$711$		0			0
$712$	−0.325292	+	1.95887i	−0.325292	+	1.95887i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.709850	−	1.80867i	0.709850	−	1.80867i
$717$		0			0
$718$		0			0
$719$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$719$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$720$		0			0
$721$		0			0
$722$	−0.489110	−	2.94536i	−0.489110	−	2.94536i
$723$	0.515500	+	0.0463958i	0.515500	+	0.0463958i
$724$		0			0
$725$		0			0
$726$	−1.20204	+	1.50731i	−1.20204	+	1.50731i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$		0			0
$729$	−2.47048	+	2.58392i	−2.47048	+	2.58392i
$730$		0			0
$731$	−0.893025	+	0.0535024i	−0.893025	+	0.0535024i
$732$		0			0
$733$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$733$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.90052	−	0.463799i	−1.90052	−	0.463799i
$738$	−0.525057	−	0.909425i	−0.525057	−	0.909425i
$739$	0.782886	−	1.83165i	0.782886	−	1.83165i	0.309017	−	0.951057i	$-0.400000\pi$
$739$	0.782886	−	1.83165i	0.782886	−	1.83165i	0.473869	−	0.880596i	$-0.342857\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$743$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.572970	+	2.51035i	−0.572970	+	2.51035i
$748$	0.0401373	−	0.893725i	0.0401373	−	0.893725i
$749$		0			0
$750$		0			0
$751$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$751$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$752$		0			0
$753$	0.913584	−	1.69772i	0.913584	−	1.69772i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$757$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$758$	−0.233951	+	1.02501i	−0.233951	+	1.02501i
$759$		0			0
$760$		0			0
$761$	−1.97770	+	0.237827i	−1.97770	+	0.237827i	−0.978148	+	0.207912i	$0.933333\pi$
$761$	−1.97770	+	0.237827i	−1.97770	+	0.237827i	−0.999552	+	0.0299155i	$0.990476\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−1.76125	+	0.784158i	−1.76125	+	0.784158i
$769$	1.57906	+	0.487076i	1.57906	+	0.487076i	0.955573	−	0.294755i	$-0.0952381\pi$
$769$	1.57906	+	0.487076i	1.57906	+	0.487076i	0.623490	+	0.781831i	$0.285714\pi$
$770$		0			0
$771$	0.0301197	−	0.401919i	0.0301197	−	0.401919i
$772$	−0.853882	−	1.58678i	−0.853882	−	1.58678i
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$	2.48201	−	1.10506i	2.48201	−	1.10506i
$775$		0			0
$776$	−1.27242	+	0.230910i	−1.27242	+	0.230910i
$777$		0			0
$778$		0			0
$779$	−0.462847	−	0.617415i	−0.462847	−	0.617415i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.873408	+	0.486989i	−0.873408	+	0.486989i
$785$		0			0
$786$	0.0194576	−	0.0543003i	0.0194576	−	0.0543003i
$787$	0.361866	−	1.83717i	0.361866	−	1.83717i	−0.163818	−	0.986491i	$-0.552381\pi$
$787$	0.361866	−	1.83717i	0.361866	−	1.83717i	0.525684	−	0.850680i	$-0.323810\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.839568	+	2.58392i	0.839568	+	2.58392i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$797$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$798$		0			0
$799$		0			0
$800$	0.0149594	−	0.999888i	0.0149594	−	0.999888i
$801$	4.06277	−	3.54953i	4.06277	−	3.54953i
$802$	0.718940	−	1.83183i	0.718940	−	1.83183i
$803$	1.13917	+	1.42848i	1.13917	+	1.42848i
$804$	−2.76477	+	2.56533i	−2.76477	+	2.56533i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.41010	+	1.23197i	1.41010	+	1.23197i	0.936235	+	0.351375i	$0.114286\pi$
$809$	1.41010	+	1.23197i	1.41010	+	1.23197i	0.473869	+	0.880596i	$0.342857\pi$
$810$		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
$816$	−1.39537	−	1.01380i	−1.39537	−	1.01380i
$817$	1.71382	−	1.02396i	1.71382	−	1.02396i
$818$	−0.453051	−	1.39435i	−0.453051	−	1.39435i
$819$		0			0
$820$		0			0
$821$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$821$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$822$	−2.18383	+	3.10233i	−2.18383	+	3.10233i
$823$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$823$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$824$		0			0
$825$	−1.91414	−	0.230183i	−1.91414	−	0.230183i
$826$		0			0
$827$	0.162473	+	0.824866i	0.162473	+	0.824866i	0.971490	+	0.237080i	$0.0761905\pi$
$827$	0.162473	+	0.824866i	0.162473	+	0.824866i	−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$829$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.767991	−	0.458853i	−0.767991	−	0.458853i
$834$	3.48679	+	1.19088i	3.48679	+	1.19088i
$835$		0			0
$836$	0.839210	+	1.81147i	0.839210	+	1.81147i
$837$		0			0
$838$	1.48194	+	0.268932i	1.48194	+	0.268932i
$839$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$839$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$840$		0			0
$841$	0.712376	−	0.701798i	0.712376	−	0.701798i
$842$		0			0
$843$	−2.02761	−	2.88041i	−2.02761	−	2.88041i
$844$	−0.674784	−	0.403165i	−0.674784	−	0.403165i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	1.35794	−	0.374766i	1.35794	−	0.374766i
$850$	0.781374	−	0.435673i	0.781374	−	0.435673i
$851$		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
$856$	0.0538218	+	1.19844i	0.0538218	+	1.19844i
$857$	−0.00670551	+	0.0894788i	−0.00670551	+	0.0894788i	−0.999552	−	0.0299155i	$-0.990476\pi$
$857$	−0.00670551	+	0.0894788i	−0.00670551	+	0.0894788i	0.992847	+	0.119394i	$0.0380952\pi$
$858$		0			0
$859$	0.0299188			0.0299188			0.0149594	−	0.999888i	$-0.495238\pi$
$859$	0.0299188			0.0299188			0.0149594	+	0.999888i	$0.495238\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$863$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$864$	3.19077	+	0.880596i	3.19077	+	0.880596i
$865$		0			0
$866$	−1.33287	−	1.48031i	−1.33287	−	1.48031i
$867$	−0.0402328	+	0.382790i	−0.0402328	+	0.382790i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	3.06871	+	1.71103i	3.06871	+	1.71103i
$874$		0			0
$875$		0			0
$876$	3.50832	−	0.315754i	3.50832	−	0.315754i
$877$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$877$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.51853	−	0.731286i	1.51853	−	0.731286i	0.525684	−	0.850680i	$-0.323810\pi$
$881$	1.51853	−	0.731286i	1.51853	−	0.731286i	0.992847	+	0.119394i	$0.0380952\pi$
$882$	2.67324	+	0.485121i	2.67324	+	0.485121i
$883$	−0.0895691	+	0.00536621i	−0.0895691	+	0.00536621i	−0.104528	−	0.994522i	$-0.533333\pi$
$883$	−0.0895691	+	0.00536621i	−0.0895691	+	0.00536621i	0.0149594	+	0.999888i	$0.495238\pi$
$884$		0			0
$885$		0			0
$886$	−0.903418	+	1.20512i	−0.903418	+	1.20512i
$887$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$887$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.33884	−	3.41131i	1.33884	−	3.41131i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.0276840	−	1.85040i	−0.0276840	−	1.85040i
$899$		0			0
$900$	−1.75674	+	2.07253i	−1.75674	+	2.07253i
$901$		0			0
$902$	0.305758	+	0.236439i	0.305758	+	0.236439i
$903$		0			0
$904$	0.265063	+	0.192580i	0.265063	+	0.192580i
$905$		0			0
$906$		0			0
$907$	1.68387	+	0.464718i	1.68387	+	0.464718i	0.971490	−	0.237080i	$-0.0761905\pi$
$907$	1.68387	+	0.464718i	1.68387	+	0.464718i	0.712376	+	0.701798i	$0.247619\pi$
$908$	0.530752	−	0.181274i	0.530752	−	0.181274i
$909$		0			0
$910$		0			0
$911$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$911$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$912$	3.80596	+	0.573656i	3.80596	+	0.573656i
$913$	−0.155256	−	0.934934i	−0.155256	−	0.934934i
$914$	−1.18005	+	1.47974i	−1.18005	+	1.47974i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.745013	+	2.86601i	0.745013	+	2.86601i
$919$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$919$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$920$		0			0
$921$	−2.17293	+	1.68029i	−2.17293	+	1.68029i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.802718	+	1.07079i	−0.802718	+	1.07079i	0.193256	+	0.981148i	$0.438095\pi$
$929$	−0.802718	+	1.07079i	−0.802718	+	1.07079i	−0.995974	+	0.0896393i	$0.971429\pi$
$930$		0			0
$931$	1.99285	+	0.119394i	1.99285	+	0.119394i
$932$	0.488828	+	0.119293i	0.488828	+	0.119293i
$933$		0			0
$934$	−1.21135	+	0.825886i	−1.21135	+	0.825886i
$935$		0			0
$936$		0			0
$937$	−1.31833	−	1.29875i	−1.31833	−	1.29875i	−0.925304	−	0.379225i	$-0.876190\pi$
$937$	−1.31833	−	1.29875i	−1.31833	−	1.29875i	−0.393025	−	0.919528i	$-0.628571\pi$
$938$		0			0
$939$	−2.21486	+	2.45985i	−2.21486	+	2.45985i
$940$		0			0
$941$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$941$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$942$		0			0
$943$		0			0
$944$	0.920717	+	1.71098i	0.920717	+	1.71098i
$945$		0			0
$946$	−0.691063	+	0.722795i	−0.691063	+	0.722795i
$947$	−1.54483			−1.54483			−0.772417	−	0.635116i	$-0.780952\pi$
$947$	−1.54483			−1.54483			−0.772417	+	0.635116i	$0.780952\pi$
$948$		0			0
$949$		0			0
$950$	−1.09982	+	1.66616i	−1.09982	+	1.66616i
$951$		0			0
$952$		0			0
$953$	1.00781	−	1.11928i	1.00781	−	1.11928i	0.0149594	−	0.999888i	$-0.495238\pi$
$953$	1.00781	−	1.11928i	1.00781	−	1.11928i	0.992847	−	0.119394i	$-0.0380952\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.998210	+	0.0598042i	0.998210	+	0.0598042i
$962$		0			0
$963$	1.95501	−	2.60788i	1.95501	−	2.60788i
$964$	−0.0752854	+	0.257694i	−0.0752854	+	0.257694i
$965$		0			0
$966$		0			0
$967$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$967$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$968$	−0.646600	−	0.762830i	−0.646600	−	0.762830i
$969$	1.25801	+	3.20534i	1.25801	+	3.20534i
$970$		0			0
$971$	−0.352060	+	0.272243i	−0.352060	+	0.272243i	−0.772417	−	0.635116i	$-0.780952\pi$
$971$	−0.352060	+	0.272243i	−0.352060	+	0.272243i	0.420357	+	0.907359i	$0.361905\pi$
$972$	−2.16150	−	3.07061i	−2.16150	−	3.07061i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.730355	−	0.0218587i	−0.730355	−	0.0218587i	−0.337330	−	0.941386i	$-0.609524\pi$
$977$	−0.730355	−	0.0218587i	−0.730355	−	0.0218587i	−0.393025	+	0.919528i	$0.628571\pi$
$978$	−1.38383	+	1.73527i	−1.38383	+	1.73527i
$979$	−0.888227	+	1.77596i	−0.888227	+	1.77596i
$980$		0			0
$981$		0			0
$982$	−1.39362	+	0.296223i	−1.39362	+	0.296223i
$983$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$983$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$984$	0.705171	−	0.240845i	0.705171	−	0.240845i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$991$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$992$		0			0
$993$	−1.89771	+	0.712222i	−1.89771	+	0.712222i
$994$		0			0
$995$		0			0
$996$	−1.66920	−	0.743176i	−1.66920	−	0.743176i
$997$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$997$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$998$	0.578465	−	1.15661i	0.578465	−	1.15661i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.1115.1	yes	48
8.3	odd	2	CM	3784.1.em.b.1115.1	yes	48
11.3	even	5		3784.1.em.a.3523.1	✓	48
43.14	even	21		3784.1.em.a.3755.1	yes	48
88.3	odd	10		3784.1.em.a.3523.1	✓	48
344.315	odd	42		3784.1.em.a.3755.1	yes	48
473.14	even	105	inner	3784.1.em.b.2379.1	yes	48
3784.2379	odd	210	inner	3784.1.em.b.2379.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.3523.1	✓	48	11.3	even	5
3784.1.em.a.3523.1	✓	48	88.3	odd	10
3784.1.em.a.3755.1	yes	48	43.14	even	21
3784.1.em.a.3755.1	yes	48	344.315	odd	42
3784.1.em.b.1115.1	yes	48	1.1	even	1	trivial
3784.1.em.b.1115.1	yes	48	8.3	odd	2	CM
3784.1.em.b.2379.1	yes	48	473.14	even	105	inner
3784.1.em.b.2379.1	yes	48	3784.2379	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)

\(f(q)\)	\(=\)	\(q+(0.473869 + 0.880596i) q^{2} +(1.78392 + 0.731119i) q^{3} +(-0.550897 + 0.834573i) q^{4} +(0.201523 + 1.91736i) q^{6} +(-0.995974 - 0.0896393i) q^{8} +(1.93545 + 1.90671i) q^{9} +O(q^{10})\)	\(q+(0.473869 + 0.880596i) q^{2} +(1.78392 + 0.731119i) q^{3} +(-0.550897 + 0.834573i) q^{4} +(0.201523 + 1.91736i) q^{6} +(-0.995974 - 0.0896393i) q^{8} +(1.93545 + 1.90671i) q^{9} +(-0.925304 - 0.379225i) q^{11} +(-1.59293 + 1.08604i) q^{12} +(-0.393025 - 0.919528i) q^{16} +(0.536616 - 0.715821i) q^{17} +(-0.761892 + 2.60788i) q^{18} +(-0.327049 + 1.96945i) q^{19} +(-0.104528 - 0.994522i) q^{22} +(-1.71120 - 0.888084i) q^{24} +(0.791071 - 0.611724i) q^{25} +(1.30093 + 3.04368i) q^{27} +(0.623490 - 0.781831i) q^{32} +(-1.37341 - 1.35301i) q^{33} +(0.884634 + 0.133337i) q^{34} +(-2.65753 + 0.564875i) q^{36} +(-1.88927 + 0.645262i) q^{38} +(-0.267104 + 0.279369i) q^{41} +(-0.646600 - 0.762830i) q^{43} +(0.826239 - 0.563320i) q^{44} +(-0.0288406 - 1.92771i) q^{48} +(-0.104528 - 0.994522i) q^{49} +(0.913545 + 0.406737i) q^{50} +(1.48063 - 0.884635i) q^{51} +(-2.06378 + 2.58790i) q^{54} +(-2.02333 + 3.27423i) q^{57} +(-1.93516 + 0.174167i) q^{59} +(0.983930 + 0.178557i) q^{64} +(0.540643 - 1.85057i) q^{66} +(1.93445 - 0.291571i) q^{67} +(0.301784 + 0.842189i) q^{68} +(-1.75674 - 2.07253i) q^{72} +(-1.59580 - 0.889773i) q^{73} +(1.85845 - 0.512899i) q^{75} +(-1.46348 - 1.35791i) q^{76} +(0.0548208 + 3.66422i) q^{81} +(-0.372583 - 0.102826i) q^{82} +(0.498210 + 0.806221i) q^{83} +(0.365341 - 0.930874i) q^{86} +(0.887586 + 0.460642i) q^{88} +(0.148391 - 1.98014i) q^{89} +(1.68387 - 0.938878i) q^{96} +(1.24660 - 0.344039i) q^{97} +(0.826239 - 0.563320i) q^{98} +(-1.06781 - 2.49826i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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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