LMFDB - Embedded newform 3784.1.em.b.1643.1

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			1643.1
Root			$-0.712376 + 0.701798i$ of defining polynomial
Character	$\chi$	$=$	3784.1643
Dual form			3784.1.em.b.2819.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0448648 - 0.998993i) q^{2} +(0.351611 - 0.703025i) q^{3} +(-0.995974 + 0.0896393i) q^{4} +(-0.718092 - 0.319715i) q^{6} +(0.134233 + 0.990950i) q^{8} +(0.229207 + 0.305751i) q^{9} +O(q^{10})$	\(q+(-0.0448648 - 0.998993i) q^{2} +(0.351611 - 0.703025i) q^{3} +(-0.995974 + 0.0896393i) q^{4} +(-0.718092 - 0.319715i) q^{6} +(0.134233 + 0.990950i) q^{8} +(0.229207 + 0.305751i) q^{9} +(-0.447313 + 0.894377i) q^{11} +(-0.287176 + 0.731713i) q^{12} +(0.983930 - 0.178557i) q^{16} +(-0.388346 + 1.08376i) q^{17} +(0.295160 - 0.242694i) q^{18} +(0.0125766 - 0.840620i) q^{19} +(0.913545 + 0.406737i) q^{22} +(0.743861 + 0.254059i) q^{24} +(0.998210 - 0.0598042i) q^{25} +(1.06896 - 0.193988i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(0.471490 + 0.628945i) q^{33} +(1.10009 + 0.339332i) q^{34} +(-0.255692 - 0.283974i) q^{36} +(-0.840338 + 0.0251504i) q^{38} +(0.984327 - 0.369424i) q^{41} +(0.712376 - 0.701798i) q^{43} +(0.365341 - 0.930874i) q^{44} +(0.220430 - 0.754510i) q^{48} +(0.913545 + 0.406737i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(0.625362 + 0.654077i) q^{51} +(-0.241751 - 1.05918i) q^{54} +(-0.586555 - 0.304413i) q^{57} +(-0.0439796 + 0.324671i) q^{59} +(-0.963963 + 0.266037i) q^{64} +(0.607158 - 0.499233i) q^{66} +(1.27881 - 0.394459i) q^{67} +(0.289635 - 1.11420i) q^{68} +(-0.272217 + 0.268175i) q^{72} +(-0.203097 + 0.0495633i) q^{73} +(0.308937 - 0.722795i) q^{75} +(0.0628267 + 0.838364i) q^{76} +(0.132321 - 0.452922i) q^{81} +(-0.413214 - 0.966762i) q^{82} +(-0.0796428 + 0.0413333i) q^{83} +(-0.733052 - 0.680173i) q^{86} +(-0.946327 - 0.323210i) q^{88} +(1.27876 + 0.192741i) q^{89} +(-0.763640 - 0.186357i) q^{96} +(-0.559963 + 1.31010i) q^{97} +(0.365341 - 0.930874i) q^{98} +(-0.375984 + 0.0682311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$2$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$3$	0.351611	−	0.703025i	0.351611	−	0.703025i	−0.646600	−	0.762830i	$-0.723810\pi$
$3$	0.351611	−	0.703025i	0.351611	−	0.703025i	0.998210	+	0.0598042i	$0.0190476\pi$
$4$	−0.995974	+	0.0896393i	−0.995974	+	0.0896393i
$5$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$5$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$6$	−0.718092	−	0.319715i	−0.718092	−	0.319715i
$7$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$7$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$8$	0.134233	+	0.990950i	0.134233	+	0.990950i
$9$	0.229207	+	0.305751i	0.229207	+	0.305751i
$10$		0			0
$11$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$11$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$12$	−0.287176	+	0.731713i	−0.287176	+	0.731713i
$13$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$13$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$14$		0			0
$15$		0			0
$16$	0.983930	−	0.178557i	0.983930	−	0.178557i
$17$	−0.388346	+	1.08376i	−0.388346	+	1.08376i	0.575617	+	0.817719i	$0.304762\pi$
$17$	−0.388346	+	1.08376i	−0.388346	+	1.08376i	−0.963963	+	0.266037i	$0.914286\pi$
$18$	0.295160	−	0.242694i	0.295160	−	0.242694i
$19$	0.0125766	−	0.840620i	0.0125766	−	0.840620i	−0.900969	−	0.433884i	$-0.857143\pi$
$19$	0.0125766	−	0.840620i	0.0125766	−	0.840620i	0.913545	−	0.406737i	$-0.133333\pi$
$20$		0			0
$21$		0			0
$22$	0.913545	+	0.406737i	0.913545	+	0.406737i
$23$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$23$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$24$	0.743861	+	0.254059i	0.743861	+	0.254059i
$25$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$26$		0			0
$27$	1.06896	−	0.193988i	1.06896	−	0.193988i
$28$		0			0
$29$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$29$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$30$		0			0
$31$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$31$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$32$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$33$	0.471490	+	0.628945i	0.471490	+	0.628945i
$34$	1.10009	+	0.339332i	1.10009	+	0.339332i
$35$		0			0
$36$	−0.255692	−	0.283974i	−0.255692	−	0.283974i
$37$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$37$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$38$	−0.840338	+	0.0251504i	−0.840338	+	0.0251504i
$39$		0			0
$40$		0			0
$41$	0.984327	−	0.369424i	0.984327	−	0.369424i	0.193256	−	0.981148i	$-0.438095\pi$
$41$	0.984327	−	0.369424i	0.984327	−	0.369424i	0.791071	+	0.611724i	$0.209524\pi$
$42$		0			0
$43$	0.712376	−	0.701798i	0.712376	−	0.701798i
$43$	0.712376	−	0.701798i	0.712376	−	0.701798i
$44$	0.365341	−	0.930874i	0.365341	−	0.930874i
$45$		0			0
$46$		0			0
$47$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$47$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$48$	0.220430	−	0.754510i	0.220430	−	0.754510i
$49$	0.913545	+	0.406737i	0.913545	+	0.406737i
$50$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$51$	0.625362	+	0.654077i	0.625362	+	0.654077i
$52$		0			0
$53$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$53$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$54$	−0.241751	−	1.05918i	−0.241751	−	1.05918i
$55$		0			0
$56$		0			0
$57$	−0.586555	−	0.304413i	−0.586555	−	0.304413i
$58$		0			0
$59$	−0.0439796	+	0.324671i	−0.0439796	+	0.324671i	0.955573	+	0.294755i	$0.0952381\pi$
$59$	−0.0439796	+	0.324671i	−0.0439796	+	0.324671i	−0.999552	+	0.0299155i	$0.990476\pi$
$60$		0			0
$61$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$61$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$62$		0			0
$63$		0			0
$64$	−0.963963	+	0.266037i	−0.963963	+	0.266037i
$65$		0			0
$66$	0.607158	−	0.499233i	0.607158	−	0.499233i
$67$	1.27881	−	0.394459i	1.27881	−	0.394459i	0.420357	−	0.907359i	$-0.361905\pi$
$67$	1.27881	−	0.394459i	1.27881	−	0.394459i	0.858449	+	0.512899i	$0.171429\pi$
$68$	0.289635	−	1.11420i	0.289635	−	1.11420i
$69$		0			0
$70$		0			0
$71$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$71$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$72$	−0.272217	+	0.268175i	−0.272217	+	0.268175i
$73$	−0.203097	+	0.0495633i	−0.203097	+	0.0495633i	−0.337330	−	0.941386i	$-0.609524\pi$
$73$	−0.203097	+	0.0495633i	−0.203097	+	0.0495633i	0.134233	+	0.990950i	$0.457143\pi$
$74$		0			0
$75$	0.308937	−	0.722795i	0.308937	−	0.722795i
$76$	0.0628267	+	0.838364i	0.0628267	+	0.838364i
$77$		0			0
$78$		0			0
$79$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$79$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$80$		0			0
$81$	0.132321	−	0.452922i	0.132321	−	0.452922i
$82$	−0.413214	−	0.966762i	−0.413214	−	0.966762i
$83$	−0.0796428	+	0.0413333i	−0.0796428	+	0.0413333i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−0.0796428	+	0.0413333i	−0.0796428	+	0.0413333i	0.420357	+	0.907359i	$0.361905\pi$
$84$		0			0
$85$		0			0
$86$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$87$		0			0
$88$	−0.946327	−	0.323210i	−0.946327	−	0.323210i
$89$	1.27876	+	0.192741i	1.27876	+	0.192741i	0.753071	−	0.657939i	$-0.228571\pi$
$89$	1.27876	+	0.192741i	1.27876	+	0.192741i	0.525684	+	0.850680i	$0.323810\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.763640	−	0.186357i	−0.763640	−	0.186357i
$97$	−0.559963	+	1.31010i	−0.559963	+	1.31010i	0.365341	+	0.930874i	$0.380952\pi$
$97$	−0.559963	+	1.31010i	−0.559963	+	1.31010i	−0.925304	+	0.379225i	$0.876190\pi$
$98$	0.365341	−	0.930874i	0.365341	−	0.930874i
$99$	−0.375984	+	0.0682311i	−0.375984	+	0.0682311i
$100$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$101$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$101$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$102$	0.625362	−	0.654077i	0.625362	−	0.654077i
$103$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$103$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.371668	+	0.563053i	0.371668	+	0.563053i	0.971490	−	0.237080i	$-0.0761905\pi$
$107$	0.371668	+	0.563053i	0.371668	+	0.563053i	−0.599822	+	0.800134i	$0.704762\pi$
$108$	−1.04727	+	0.289028i	−1.04727	+	0.289028i
$109$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$109$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.0206758	+	0.0216252i	−0.0206758	+	0.0216252i	−0.733052	−	0.680173i	$-0.761905\pi$
$113$	−0.0206758	+	0.0216252i	−0.0206758	+	0.0216252i	0.712376	+	0.701798i	$0.247619\pi$
$114$	−0.277790	+	0.599622i	−0.277790	+	0.599622i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.326317	+	0.0293690i	0.326317	+	0.0293690i
$119$		0			0
$120$		0			0
$121$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$122$		0			0
$123$	0.0863852	−	0.821900i	0.0863852	−	0.821900i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$127$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$128$	0.309017	+	0.951057i	0.309017	+	0.951057i
$129$	−0.242903	−	0.747578i	−0.242903	−	0.747578i
$130$		0			0
$131$	−0.349687	−	0.438494i	−0.349687	−	0.438494i	0.575617	−	0.817719i	$-0.304762\pi$
$131$	−0.349687	−	0.438494i	−0.349687	−	0.438494i	−0.925304	+	0.379225i	$0.876190\pi$
$132$	−0.525970	−	0.584149i	−0.525970	−	0.584149i
$133$		0			0
$134$	−0.451436	−	1.25982i	−0.451436	−	1.25982i
$135$		0			0
$136$	−1.12608	−	0.239355i	−1.12608	−	0.239355i
$137$	−0.913584	+	1.69772i	−0.913584	+	1.69772i	−0.222521	+	0.974928i	$0.571429\pi$
$137$	−0.913584	+	1.69772i	−0.913584	+	1.69772i	−0.691063	+	0.722795i	$0.742857\pi$
$138$		0			0
$139$	−1.52904	+	0.626662i	−1.52904	+	0.626662i	−0.978148	−	0.207912i	$-0.933333\pi$
$139$	−1.52904	+	0.626662i	−1.52904	+	0.626662i	−0.550897	+	0.834573i	$0.685714\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.280118	+	0.259911i	0.280118	+	0.259911i
$145$		0			0
$146$	0.0586253	+	0.200669i	0.0586253	+	0.200669i
$147$	0.607158	−	0.499233i	0.607158	−	0.499233i
$148$		0			0
$149$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$149$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$150$	−0.735927	−	0.276198i	−0.735927	−	0.276198i
$151$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$151$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$152$	0.834701	−	0.100376i	0.834701	−	0.100376i
$153$	−0.420371	+	0.129667i	−0.420371	+	0.129667i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$157$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.458402	−	0.111868i	−0.458402	−	0.111868i
$163$	−0.949003	−	1.26592i	−0.949003	−	1.26592i	−0.963963	−	0.266037i	$-0.914286\pi$
$163$	−0.949003	−	1.26592i	−0.949003	−	1.26592i	0.0149594	−	0.999888i	$-0.495238\pi$
$164$	−0.947249	+	0.456171i	−0.947249	+	0.456171i
$165$		0			0
$166$	0.0448648	+	0.0777082i	0.0448648	+	0.0777082i
$167$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$167$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$168$		0			0
$169$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$170$		0			0
$171$	0.259903	−	0.188831i	0.259903	−	0.188831i
$172$	−0.646600	+	0.762830i	−0.646600	+	0.762830i
$173$		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
$176$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$177$	0.212788	+	0.145076i	0.212788	+	0.145076i
$178$	0.135176	−	1.28611i	0.135176	−	1.28611i
$179$	−0.219231	−	0.243481i	−0.219231	−	0.243481i	0.623490	−	0.781831i	$-0.285714\pi$
$179$	−0.219231	−	0.243481i	−0.219231	−	0.243481i	−0.842721	+	0.538351i	$0.819048\pi$
$180$		0			0
$181$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$181$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.795575	−	0.832106i	−0.795575	−	0.832106i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$191$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$192$	−0.151909	+	0.771232i	−0.151909	+	0.771232i
$193$	−0.0559455	+	1.24572i	−0.0559455	+	1.24572i	0.753071	+	0.657939i	$0.228571\pi$
$193$	−0.0559455	+	1.24572i	−0.0559455	+	1.24572i	−0.809017	+	0.587785i	$0.800000\pi$
$194$	1.33390	+	0.500622i	1.33390	+	0.500622i
$195$		0			0
$196$	−0.946327	−	0.323210i	−0.946327	−	0.323210i
$197$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$197$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$198$	0.0850309	+	0.372545i	0.0850309	+	0.372545i
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	0.193256	+	0.981148i	0.193256	+	0.981148i
$201$	0.172327	−	1.03773i	0.172327	−	1.03773i
$202$		0			0
$203$		0			0
$204$	−0.681475	−	0.595387i	−0.681475	−	0.595387i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.746206	+	0.387269i	0.746206	+	0.387269i
$210$		0			0
$211$	1.48194	−	1.29473i	1.48194	−	1.29473i	0.623490	−	0.781831i	$-0.285714\pi$
$211$	1.48194	−	1.29473i	1.48194	−	1.29473i	0.858449	−	0.512899i	$-0.171429\pi$
$212$		0			0
$213$		0			0
$214$	0.545811	−	0.396555i	0.545811	−	0.396555i
$215$		0			0
$216$	0.335722	+	1.03325i	0.335722	+	1.03325i
$217$		0			0
$218$		0			0
$219$	−0.0365667	+	0.160209i	−0.0365667	+	0.160209i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$223$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$224$		0			0
$225$	0.247082	+	0.291496i	0.247082	+	0.291496i
$226$	0.0225310	+	0.0196847i	0.0225310	+	0.0196847i
$227$	−1.54207	−	0.0923875i	−1.54207	−	0.0923875i	−0.733052	−	0.680173i	$-0.761905\pi$
$227$	−1.54207	−	0.0923875i	−1.54207	−	0.0923875i	−0.809017	+	0.587785i	$0.800000\pi$
$228$	0.611481	+	0.250609i	0.611481	+	0.250609i
$229$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$229$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.499574	−	1.92182i	0.499574	−	1.92182i	0.134233	−	0.990950i	$-0.457143\pi$
$233$	0.499574	−	1.92182i	0.499574	−	1.92182i	0.365341	−	0.930874i	$-0.380952\pi$
$234$		0			0
$235$		0			0
$236$	0.0146993	−	0.327306i	0.0146993	−	0.327306i
$237$		0			0
$238$		0			0
$239$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$239$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$240$		0			0
$241$	−0.910345	+	0.620663i	−0.910345	+	0.620663i	−0.925304	−	0.379225i	$-0.876190\pi$
$241$	−0.910345	+	0.620663i	−0.910345	+	0.620663i	0.0149594	+	0.999888i	$0.495238\pi$
$242$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$243$	0.524512	+	0.486676i	0.524512	+	0.486676i
$244$		0			0
$245$		0			0
$246$	−0.824948	−	0.0494238i	−0.824948	−	0.0494238i
$247$		0			0
$248$		0			0
$249$	0.00105512	+	0.0705241i	0.00105512	+	0.0705241i
$250$		0			0
$251$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.809017	−	0.587785i	$-0.800000\pi$
$251$	−0.913545	+	0.406737i	−0.913545	+	0.406737i	−0.104528	+	0.994522i	$0.533333\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.936235	−	0.351375i	0.936235	−	0.351375i
$257$	0.564602	+	1.73767i	0.564602	+	1.73767i	0.669131	+	0.743145i	$0.266667\pi$
$257$	0.564602	+	1.73767i	0.564602	+	1.73767i	−0.104528	+	0.994522i	$0.533333\pi$
$258$	−0.735927	+	0.276198i	−0.735927	+	0.276198i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.422364	+	0.369008i	−0.422364	+	0.369008i
$263$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$263$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$264$	−0.559963	+	0.551648i	−0.559963	+	0.551648i
$265$		0			0
$266$		0			0
$267$	0.585126	−	0.831228i	0.585126	−	0.831228i
$268$	−1.23830	+	0.507503i	−1.23830	+	0.507503i
$269$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$269$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$270$		0			0
$271$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$271$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$272$	−0.188593	+	1.13568i	−0.188593	+	1.13568i
$273$		0			0
$274$	1.73700	+	0.836496i	1.73700	+	0.836496i
$275$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$276$		0			0
$277$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$277$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$278$	0.694631	+	1.49939i	0.694631	+	1.49939i
$279$		0			0
$280$		0			0
$281$	−0.0404015	+	0.205116i	−0.0404015	+	0.205116i	−0.995974	−	0.0896393i	$-0.971429\pi$
$281$	−0.0404015	+	0.205116i	−0.0404015	+	0.205116i	0.955573	+	0.294755i	$0.0952381\pi$
$282$		0			0
$283$	−1.46348	+	0.0876791i	−1.46348	+	0.0876791i	−0.772417	−	0.635116i	$-0.780952\pi$
$283$	−1.46348	+	0.0876791i	−1.46348	+	0.0876791i	−0.691063	+	0.722795i	$0.742857\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.247082	−	0.291496i	0.247082	−	0.291496i
$289$	−0.251298	−	0.206629i	−0.251298	−	0.206629i
$290$		0			0
$291$	0.724144	+	0.854313i	0.724144	+	0.854313i
$292$	0.197836	−	0.0675692i	0.197836	−	0.0675692i
$293$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$293$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$294$	−0.525970	−	0.584149i	−0.525970	−	0.584149i
$295$		0			0
$296$		0			0
$297$	−0.304662	+	1.04283i	−0.304662	+	1.04283i
$298$		0			0
$299$		0			0
$300$	−0.242903	+	0.747578i	−0.242903	+	0.747578i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.137724	−	0.829357i	−0.137724	−	0.829357i
$305$		0			0
$306$	0.148397	+	0.414131i	0.148397	+	0.414131i
$307$	0.599822	+	1.03892i	0.599822	+	1.03892i	0.992847	+	0.119394i	$0.0380952\pi$
$307$	0.599822	+	1.03892i	0.599822	+	1.03892i	−0.393025	+	0.919528i	$0.628571\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$311$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$312$		0			0
$313$	−0.347724	−	1.33767i	−0.347724	−	1.33767i	−0.873408	−	0.486989i	$-0.838095\pi$
$313$	−0.347724	−	1.33767i	−0.347724	−	1.33767i	0.525684	−	0.850680i	$-0.323810\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$317$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	0.526523	−	0.0633167i	0.526523	−	0.0633167i
$322$		0			0
$323$	0.906144	+	0.340081i	0.906144	+	0.340081i
$324$	−0.0911888	+	0.462960i	−0.0911888	+	0.462960i
$325$		0			0
$326$	−1.22207	+	1.00484i	−1.22207	+	1.00484i
$327$		0			0
$328$	0.498210	+	0.925830i	0.498210	+	0.925830i
$329$		0			0
$330$		0			0
$331$	0.132659	−	1.77021i	0.132659	−	1.77021i	−0.393025	−	0.919528i	$-0.628571\pi$
$331$	0.132659	−	1.77021i	0.132659	−	1.77021i	0.525684	−	0.850680i	$-0.323810\pi$
$332$	0.0756171	−	0.0483060i	0.0756171	−	0.0483060i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.95279	−	0.415079i	−1.95279	−	0.415079i	−0.988831	−	0.149042i	$-0.952381\pi$
$337$	−1.95279	−	0.415079i	−1.95279	−	0.415079i	−0.963963	−	0.266037i	$-0.914286\pi$
$338$	−0.978148	+	0.207912i	−0.978148	+	0.207912i
$339$	0.00793322	+	0.0221392i	0.00793322	+	0.0221392i
$340$		0			0
$341$		0			0
$342$	−0.200301	−	0.251170i	−0.200301	−	0.251170i
$343$		0			0
$344$	0.791071	+	0.611724i	0.791071	+	0.611724i
$345$		0			0
$346$		0			0
$347$	0.0265555	−	0.0137819i	0.0265555	−	0.0137819i	−0.447313	−	0.894377i	$-0.647619\pi$
$347$	0.0265555	−	0.0137819i	0.0265555	−	0.0137819i	0.473869	+	0.880596i	$0.342857\pi$
$348$		0			0
$349$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$349$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$350$		0			0
$351$		0			0
$352$	0.971490	+	0.237080i	0.971490	+	0.237080i
$353$	1.51185	+	0.466345i	1.51185	+	0.466345i	0.936235	−	0.351375i	$-0.114286\pi$
$353$	1.51185	+	0.466345i	1.51185	+	0.466345i	0.575617	+	0.817719i	$0.304762\pi$
$354$	0.135384	−	0.219083i	0.135384	−	0.219083i
$355$		0			0
$356$	−1.29088	−	0.0773387i	−1.29088	−	0.0773387i
$357$		0			0
$358$	−0.233400	+	0.229934i	−0.233400	+	0.229934i
$359$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$359$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$360$		0			0
$361$	0.293068	+	0.00877119i	0.293068	+	0.00877119i
$362$		0			0
$363$	−0.773418	+	0.140355i	−0.773418	+	0.140355i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$367$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$368$		0			0
$369$	0.338567	+	0.216285i	0.338567	+	0.216285i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$373$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$374$	−0.795575	+	0.832106i	−0.795575	+	0.832106i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.841198	−	1.56321i	0.841198	−	1.56321i	0.0149594	−	0.999888i	$-0.495238\pi$
$379$	0.841198	−	1.56321i	0.841198	−	1.56321i	0.826239	−	0.563320i	$-0.190476\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$383$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$384$	0.777271	+	0.117155i	0.777271	+	0.117155i
$385$		0			0
$386$	1.24698			1.24698
$387$	0.377857	+	0.0569528i	0.377857	+	0.0569528i
$388$	0.440273	−	1.35502i	0.440273	−	1.35502i
$389$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$389$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$390$		0			0
$391$		0			0
$392$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$393$	−0.431226	+	0.0916599i	−0.431226	+	0.0916599i
$394$		0			0
$395$		0			0
$396$	0.368355	−	0.101659i	0.368355	−	0.101659i
$397$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$397$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$398$		0			0
$399$		0			0
$400$	0.971490	−	0.237080i	0.971490	−	0.237080i
$401$	−1.37341	+	1.35301i	−1.37341	+	1.35301i	−0.500000	+	0.866025i	$0.666667\pi$
$401$	−1.37341	+	1.35301i	−1.37341	+	1.35301i	−0.873408	+	0.486989i	$0.838095\pi$
$402$	−1.04442	−	0.125596i	−1.04442	−	0.125596i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.564213	+	0.707501i	−0.564213	+	0.707501i
$409$	−0.144074	+	0.0397619i	−0.144074	+	0.0397619i	−0.337330	−	0.941386i	$-0.609524\pi$
$409$	−0.144074	+	0.0397619i	−0.144074	+	0.0397619i	0.193256	+	0.981148i	$0.438095\pi$
$410$		0			0
$411$	0.872317	+	1.23921i	0.872317	+	1.23921i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.0970692	+	1.29530i	−0.0970692	+	1.29530i
$418$	0.353400	−	0.762830i	0.353400	−	0.762830i
$419$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	−0.963963	−	0.266037i	$-0.914286\pi$
$419$	−0.210891	−	0.923976i	−0.210891	−	0.923976i	0.753071	−	0.657939i	$-0.228571\pi$
$420$		0			0
$421$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$421$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$422$	−1.35991	−	1.42236i	−1.35991	−	1.42236i
$423$		0			0
$424$		0			0
$425$	−0.322838	+	1.10504i	−0.322838	+	1.10504i
$426$		0			0
$427$		0			0
$428$	−0.420644	−	0.527470i	−0.420644	−	0.527470i
$429$		0			0
$430$		0			0
$431$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$431$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$432$	1.01714	−	0.381741i	1.01714	−	0.381741i
$433$	−0.0439796	−	0.264840i	−0.0439796	−	0.264840i	0.955573	−	0.294755i	$-0.0952381\pi$
$433$	−0.0439796	−	0.264840i	−0.0439796	−	0.264840i	−0.999552	+	0.0299155i	$0.990476\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	0.161688	+	0.0293421i	0.161688	+	0.0293421i
$439$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$439$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$440$		0			0
$441$	0.0850309	+	0.372545i	0.0850309	+	0.372545i
$442$		0			0
$443$	−0.876945	−	0.359406i	−0.876945	−	0.359406i	−0.104528	−	0.994522i	$-0.533333\pi$
$443$	−0.876945	−	0.359406i	−0.876945	−	0.359406i	−0.772417	+	0.635116i	$0.780952\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.846609	+	0.289152i	0.846609	+	0.289152i	0.712376	−	0.701798i	$-0.247619\pi$
$449$	0.846609	+	0.289152i	0.846609	+	0.289152i	0.134233	+	0.990950i	$0.457143\pi$
$450$	0.280118	−	0.259911i	0.280118	−	0.259911i
$451$	−0.109898	+	1.04561i	−0.109898	+	1.04561i
$452$	0.0186541	−	0.0233915i	0.0186541	−	0.0233915i
$453$		0			0
$454$	−0.0231098	+	1.54466i	−0.0231098	+	1.54466i
$455$		0			0
$456$	0.222922	−	0.622109i	0.222922	−	0.622109i
$457$	−1.96698	+	0.356954i	−1.96698	+	0.356954i	−0.978148	+	0.207912i	$0.933333\pi$
$457$	−1.96698	+	0.356954i	−1.96698	+	0.356954i	−0.988831	+	0.149042i	$0.952381\pi$
$458$		0			0
$459$	−0.204891	+	1.23383i	−0.204891	+	1.23383i
$460$		0			0
$461$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$461$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$462$		0			0
$463$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$463$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$464$		0			0
$465$		0			0
$466$	−1.94230	−	0.412849i	−1.94230	−	0.412849i
$467$	0.136539	+	0.0607909i	0.136539	+	0.0607909i	0.473869	−	0.880596i	$-0.342857\pi$
$467$	0.136539	+	0.0607909i	0.136539	+	0.0607909i	−0.337330	+	0.941386i	$0.609524\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.327636			−0.327636
$473$	0.309017	+	0.951057i	0.309017	+	0.951057i
$474$		0			0
$475$	−0.0377185	−	0.839868i	−0.0377185	−	0.839868i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$479$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$480$		0			0
$481$		0			0
$482$	0.660880	+	0.881582i	0.660880	+	0.881582i
$483$		0			0
$484$	0.669131	+	0.743145i	0.669131	+	0.743145i
$485$		0			0
$486$	0.462654	−	0.545818i	0.462654	−	0.545818i
$487$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$487$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$488$		0			0
$489$	−1.22366	+	0.222061i	−1.22366	+	0.222061i
$490$		0			0
$491$	0.926625	−	0.761913i	0.926625	−	0.761913i	−0.0448648	−	0.998993i	$-0.514286\pi$
$491$	0.926625	−	0.761913i	0.926625	−	0.761913i	0.971490	+	0.237080i	$0.0761905\pi$
$492$	−0.0123629	+	0.826335i	−0.0123629	+	0.826335i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0704058	−	0.00421811i	0.0704058	−	0.00421811i
$499$	1.12708	+	0.871556i	1.12708	+	0.871556i	0.992847	−	0.119394i	$-0.0380952\pi$
$499$	1.12708	+	0.871556i	1.12708	+	0.871556i	0.134233	+	0.990950i	$0.457143\pi$
$500$		0			0
$501$		0			0
$502$	0.447313	+	0.894377i	0.447313	+	0.894377i
$503$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$503$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.751128	−	0.231692i	−0.751128	−	0.231692i
$508$		0			0
$509$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$509$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$510$		0			0
$511$		0			0
$512$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$513$	−0.149626	−	0.901030i	−0.149626	−	0.901030i
$514$	1.71059	−	0.641994i	1.71059	−	0.641994i
$515$		0			0
$516$	0.308937	+	0.722795i	0.308937	+	0.722795i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.157279	−	0.538351i	0.157279	−	0.538351i	−0.842721	−	0.538351i	$-0.819048\pi$
$521$	0.157279	−	0.538351i	0.157279	−	0.538351i	1.00000			$0$
$522$		0			0
$523$	−0.203097	−	1.93234i	−0.203097	−	1.93234i	−0.337330	−	0.941386i	$-0.609524\pi$
$523$	−0.203097	−	1.93234i	−0.203097	−	1.93234i	0.134233	−	0.990950i	$-0.457143\pi$
$524$	0.387586	+	0.405383i	0.387586	+	0.405383i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.576215	+	0.534650i	0.576215	+	0.534650i
$529$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$530$		0			0
$531$	−0.109349	+	0.0609700i	−0.109349	+	0.0609700i
$532$		0			0
$533$		0			0
$534$	−0.856642	−	0.547244i	−0.856642	−	0.547244i
$535$		0			0
$536$	0.562548	+	1.21428i	0.562548	+	1.21428i
$537$	−0.248257	+	0.0685146i	−0.248257	+	0.0685146i
$538$		0			0
$539$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$540$		0			0
$541$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$541$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$542$		0			0
$543$		0			0
$544$	1.14300	+	0.137451i	1.14300	+	0.137451i
$545$		0			0
$546$		0			0
$547$	−0.207368	−	0.170507i	−0.207368	−	0.170507i	0.525684	−	0.850680i	$-0.323810\pi$
$547$	−0.207368	−	0.170507i	−0.207368	−	0.170507i	−0.733052	+	0.680173i	$0.761905\pi$
$548$	0.757723	−	1.77278i	0.757723	−	1.77278i
$549$		0			0
$550$	0.936235	+	0.351375i	0.936235	+	0.351375i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	1.46672	−	0.761201i	1.46672	−	0.761201i
$557$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$557$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.864724	+	0.266732i	−0.864724	+	0.266732i
$562$	0.206722	+	0.0311583i	0.206722	+	0.0311583i
$563$	0.713714	−	0.623553i	0.713714	−	0.623553i	−0.222521	−	0.974928i	$-0.571429\pi$
$563$	0.713714	−	0.623553i	0.713714	−	0.623553i	0.936235	+	0.351375i	$0.114286\pi$
$564$		0			0
$565$		0			0
$566$	0.153250	+	1.45807i	0.153250	+	1.45807i
$567$		0			0
$568$		0			0
$569$	−0.869121	−	0.212098i	−0.869121	−	0.212098i	−0.222521	−	0.974928i	$-0.571429\pi$
$569$	−0.869121	−	0.212098i	−0.869121	−	0.212098i	−0.646600	+	0.762830i	$0.723810\pi$
$570$		0			0
$571$	0.455573	−	1.16078i	0.455573	−	1.16078i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	0.455573	−	1.16078i	0.455573	−	1.16078i	0.955573	−	0.294755i	$-0.0952381\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.302288	−	0.233755i	−0.302288	−	0.233755i
$577$	0.928505	+	0.593151i	0.928505	+	0.593151i	0.913545	−	0.406737i	$-0.133333\pi$
$577$	0.928505	+	0.593151i	0.928505	+	0.593151i	0.0149594	+	0.999888i	$0.495238\pi$
$578$	−0.195146	+	0.260315i	−0.195146	+	0.260315i
$579$	0.856105	+	0.477341i	0.856105	+	0.477341i
$580$		0			0
$581$		0			0
$582$	0.820964	−	0.761744i	0.820964	−	0.761744i
$583$		0			0
$584$	−0.0763771	−	0.194606i	−0.0763771	−	0.194606i
$585$		0			0
$586$		0			0
$587$	−0.649382	+	1.40172i	−0.649382	+	1.40172i	0.251587	+	0.967835i	$0.419048\pi$
$587$	−0.649382	+	1.40172i	−0.649382	+	1.40172i	−0.900969	+	0.433884i	$0.857143\pi$
$588$	−0.559963	+	0.551648i	−0.559963	+	0.551648i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.66921	−	0.514883i	−1.66921	−	0.514883i	−0.691063	−	0.722795i	$-0.742857\pi$
$593$	−1.66921	−	0.514883i	−1.66921	−	0.514883i	−0.978148	+	0.207912i	$0.933333\pi$
$594$	1.05545	+	0.257569i	1.05545	+	0.257569i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$599$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$600$	0.757723	+	0.209118i	0.757723	+	0.209118i
$601$	0.548558	+	1.68829i	0.548558	+	1.68829i	0.712376	+	0.701798i	$0.247619\pi$
$601$	0.548558	+	1.68829i	0.548558	+	1.68829i	−0.163818	+	0.986491i	$0.552381\pi$
$602$		0			0
$603$	0.413718	+	0.300584i	0.413718	+	0.300584i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$607$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$608$	−0.822343	+	0.174794i	−0.822343	+	0.174794i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.407056	−	0.166827i	0.407056	−	0.166827i
$613$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$613$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$614$	1.01096	−	0.645829i	1.01096	−	0.645829i
$615$		0			0
$616$		0			0
$617$	−1.25857	−	1.16779i	−1.25857	−	1.16779i	−0.978148	−	0.207912i	$-0.933333\pi$
$617$	−1.25857	−	1.16779i	−1.25857	−	1.16779i	−0.280427	−	0.959875i	$-0.590476\pi$
$618$		0			0
$619$	0.558597	+	1.91202i	0.558597	+	1.91202i	0.365341	+	0.930874i	$0.380952\pi$
$619$	0.558597	+	1.91202i	0.558597	+	1.91202i	0.193256	+	0.981148i	$0.438095\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.992847	−	0.119394i	0.992847	−	0.119394i
$626$	−1.32072	+	0.407389i	−1.32072	+	0.407389i
$627$	0.534634	−	0.388434i	0.534634	−	0.388434i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$631$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$632$		0			0
$633$	−0.389163	−	1.49708i	−0.389163	−	1.49708i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.431949	+	0.258077i	0.431949	+	0.258077i	0.712376	−	0.701798i	$-0.247619\pi$
$641$	0.431949	+	0.258077i	0.431949	+	0.258077i	−0.280427	+	0.959875i	$0.590476\pi$
$642$	−0.0868753	−	0.523152i	−0.0868753	−	0.523152i
$643$	−0.372583	−	0.102826i	−0.372583	−	0.102826i	0.0747301	−	0.997204i	$-0.476190\pi$
$643$	−0.372583	−	0.102826i	−0.372583	−	0.102826i	−0.447313	+	0.894377i	$0.647619\pi$
$644$		0			0
$645$		0			0
$646$	0.299085	−	0.920489i	0.299085	−	0.920489i
$647$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$647$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$648$	0.466585	+	0.0703263i	0.466585	+	0.0703263i
$649$	−0.270705	−	0.184564i	−0.270705	−	0.184564i
$650$		0			0
$651$		0			0
$652$	1.05866	+	1.17576i	1.05866	+	1.17576i
$653$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$653$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$654$		0			0
$655$		0			0
$656$	0.902545	−	0.539246i	0.902545	−	0.539246i
$657$	−0.0617053	−	0.0507368i	−0.0617053	−	0.0507368i
$658$		0			0
$659$	1.96970	−	0.296885i	1.96970	−	0.296885i	0.971490	−	0.237080i	$-0.0761905\pi$
$659$	1.96970	−	0.296885i	1.96970	−	0.296885i	0.998210	−	0.0598042i	$-0.0190476\pi$
$660$		0			0
$661$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$661$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$662$	−1.77438	−	0.0531051i	−1.77438	−	0.0531051i
$663$		0			0
$664$	−0.0516499	−	0.0733737i	−0.0516499	−	0.0733737i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.357641	−	1.81572i	−0.357641	−	1.81572i	−0.550897	−	0.834573i	$-0.685714\pi$
$673$	−0.357641	−	1.81572i	−0.357641	−	1.81572i	0.193256	−	0.981148i	$-0.438095\pi$
$674$	−0.327049	+	1.96945i	−0.327049	+	1.96945i
$675$	1.05545	−	0.257569i	1.05545	−	0.257569i
$676$	0.251587	+	0.967835i	0.251587	+	0.967835i
$677$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$677$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$678$	0.0217610	−	0.00891851i	0.0217610	−	0.00891851i
$679$		0			0
$680$		0			0
$681$	−0.607158	+	1.05163i	−0.607158	+	1.05163i
$682$		0			0
$683$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	0.365341	−	0.930874i	$-0.380952\pi$
$683$	−0.367711	−	0.250701i	−0.367711	−	0.250701i	−0.733052	+	0.680173i	$0.761905\pi$
$684$	−0.241930	+	0.211368i	−0.241930	+	0.211368i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	0.575617	−	0.817719i	0.575617	−	0.817719i
$689$		0			0
$690$		0			0
$691$	−1.39362	−	1.37292i	−1.39362	−	1.37292i	−0.842721	−	0.538351i	$-0.819048\pi$
$691$	−1.39362	−	1.37292i	−1.39362	−	1.37292i	−0.550897	−	0.834573i	$-0.685714\pi$
$692$		0			0
$693$		0			0
$694$	−0.0149594	−	0.0259105i	−0.0149594	−	0.0259105i
$695$		0			0
$696$		0			0
$697$	0.0181064	+	1.21023i	0.0181064	+	1.21023i
$698$		0			0
$699$	−1.17544	−	1.02695i	−1.17544	−	1.02695i
$700$		0			0
$701$		0			0		−0.925304	−	0.379225i	$-0.876190\pi$
$701$		0			0		0.925304	+	0.379225i	$0.123810\pi$
$702$		0			0
$703$		0			0
$704$	0.193256	−	0.981148i	0.193256	−	0.981148i
$705$		0			0
$706$	0.398046	−	1.53125i	0.398046	−	1.53125i
$707$		0			0
$708$	−0.224936	−	0.125418i	−0.224936	−	0.125418i
$709$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$709$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$710$		0			0
$711$		0			0
$712$	−0.0193455	+	1.29305i	−0.0193455	+	1.29305i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.240174	+	0.222849i	0.240174	+	0.222849i
$717$		0			0
$718$		0			0
$719$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$719$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$720$		0			0
$721$		0			0
$722$	−0.00438609	−	0.293166i	−0.00438609	−	0.293166i
$723$	0.116255	+	0.858227i	0.116255	+	0.858227i
$724$		0			0
$725$		0			0
$726$	0.174913	+	0.766342i	0.174913	+	0.766342i
$727$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$727$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$728$		0			0
$729$	0.968336	−	0.363423i	0.968336	−	0.363423i
$730$		0			0
$731$	0.483930	+	1.04458i	0.483930	+	1.04458i
$732$		0			0
$733$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$733$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−0.219231	+	1.32018i	−0.219231	+	1.32018i
$738$	0.200877	−	0.347929i	0.200877	−	0.347929i
$739$	0.264152	+	0.0479366i	0.264152	+	0.0479366i	0.309017	−	0.951057i	$-0.400000\pi$
$739$	0.264152	+	0.0479366i	0.264152	+	0.0479366i	−0.0448648	+	0.998993i	$0.514286\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$743$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.0308924	−	0.0148770i	−0.0308924	−	0.0148770i
$748$	0.866962	+	0.757442i	0.866962	+	0.757442i
$749$		0			0
$750$		0			0
$751$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$751$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$752$		0			0
$753$	−0.0352660	+	0.785259i	−0.0352660	+	0.785259i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$757$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$758$	−1.59937	−	0.770218i	−1.59937	−	0.770218i
$759$		0			0
$760$		0			0
$761$	−0.173590	+	0.204794i	−0.173590	+	0.204794i	−0.842721	−	0.538351i	$-0.819048\pi$
$761$	−0.173590	+	0.204794i	−0.173590	+	0.204794i	0.669131	+	0.743145i	$0.266667\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.0821646	−	0.781744i	0.0821646	−	0.781744i
$769$	0.603718	+	0.411608i	0.603718	+	0.411608i	0.826239	−	0.563320i	$-0.190476\pi$
$769$	0.603718	+	0.411608i	0.603718	+	0.411608i	−0.222521	+	0.974928i	$0.571429\pi$
$770$		0			0
$771$	1.42014	+	0.214052i	1.42014	+	0.214052i
$772$	−0.0559455	−	1.24572i	−0.0559455	−	1.24572i
$773$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$773$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$774$	0.0399430	−	0.380032i	0.0399430	−	0.380032i
$775$		0			0
$776$	−1.37341	−	0.379037i	−1.37341	−	0.379037i
$777$		0			0
$778$		0			0
$779$	−0.298166	−	0.832091i	−0.298166	−	0.832091i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.971490	+	0.237080i	0.971490	+	0.237080i
$785$		0			0
$786$	0.110915	+	0.426680i	0.110915	+	0.426680i
$787$	0.902545	+	1.46053i	0.902545	+	1.46053i	0.887586	+	0.460642i	$0.152381\pi$
$787$	0.902545	+	1.46053i	0.902545	+	1.46053i	0.0149594	+	0.999888i	$0.495238\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.118083	−	0.363423i	−0.118083	−	0.363423i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$797$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$798$		0			0
$799$		0			0
$800$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$801$	0.234169	+	0.435159i	0.234169	+	0.435159i
$802$	1.41327	+	1.31132i	1.41327	+	1.31132i
$803$	0.0465195	−	0.203815i	0.0465195	−	0.203815i
$804$	−0.0786116	+	1.04900i	−0.0786116	+	1.04900i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.813584	−	1.51189i	0.813584	−	1.51189i	−0.0448648	−	0.998993i	$-0.514286\pi$
$809$	0.813584	−	1.51189i	0.813584	−	1.51189i	0.858449	−	0.512899i	$-0.171429\pi$
$810$		0			0
$811$	−1.78716	+	0.379874i	−1.78716	+	0.379874i	−0.978148	−	0.207912i	$-0.933333\pi$
$811$	−1.78716	+	0.379874i	−1.78716	+	0.379874i	−0.809017	+	0.587785i	$0.800000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	0.732102	+	0.531903i	0.732102	+	0.531903i
$817$	−0.580986	−	0.607664i	−0.580986	−	0.607664i
$818$	0.0461857	+	0.142145i	0.0461857	+	0.142145i
$819$		0			0
$820$		0			0
$821$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$821$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$822$	1.19883	−	0.927035i	1.19883	−	0.927035i
$823$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$823$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$824$		0			0
$825$	0.508260	+	0.599622i	0.508260	+	0.599622i
$826$		0			0
$827$	−0.972835	+	1.57428i	−0.972835	+	1.57428i	−0.163818	+	0.986491i	$0.552381\pi$
$827$	−0.972835	+	1.57428i	−0.972835	+	1.57428i	−0.809017	+	0.587785i	$0.800000\pi$
$828$		0			0
$829$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$829$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.795575	+	0.832106i	−0.795575	+	0.832106i
$834$	1.29835	+	0.0388581i	1.29835	+	0.0388581i
$835$		0			0
$836$	−0.777917	−	0.318820i	−0.777917	−	0.318820i
$837$		0			0
$838$	−0.913584	+	0.252133i	−0.913584	+	0.252133i
$839$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$839$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$840$		0			0
$841$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$842$		0			0
$843$	0.129996	+	0.100524i	0.129996	+	0.100524i
$844$	−1.35991	+	1.42236i	−1.35991	+	1.42236i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.452934	+	1.05969i	−0.452934	+	1.05969i
$850$	1.11841	+	0.272935i	1.11841	+	0.272935i
$851$		0			0
$852$		0			0
$853$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$853$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$854$		0			0
$855$		0			0
$856$	−0.508067	+	0.443885i	−0.508067	+	0.443885i
$857$	−1.48932	−	0.224479i	−1.48932	−	0.224479i	−0.646600	−	0.762830i	$-0.723810\pi$
$857$	−1.48932	−	0.224479i	−1.48932	−	0.224479i	−0.842721	+	0.538351i	$0.819048\pi$
$858$		0			0
$859$	−0.560855			−0.560855			−0.280427	−	0.959875i	$-0.590476\pi$
$859$	−0.560855			−0.560855			−0.280427	+	0.959875i	$0.590476\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$863$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$864$	−0.426990	−	0.998993i	−0.426990	−	0.998993i
$865$		0			0
$866$	−0.262600	+	0.0558173i	−0.262600	+	0.0558173i
$867$	−0.233624	+	0.104016i	−0.233624	+	0.104016i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.528912	+	0.129075i	−0.528912	+	0.129075i
$874$		0			0
$875$		0			0
$876$	0.0220584	−	0.162842i	0.0220584	−	0.162842i
$877$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$877$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.240986	−	0.302187i	0.240986	−	0.302187i	−0.646600	−	0.762830i	$-0.723810\pi$
$881$	0.240986	−	0.302187i	0.240986	−	0.302187i	0.887586	+	0.460642i	$0.152381\pi$
$882$	0.368355	−	0.101659i	0.368355	−	0.101659i
$883$	0.633118	+	1.36661i	0.633118	+	1.36661i	0.913545	+	0.406737i	$0.133333\pi$
$883$	0.633118	+	1.36661i	0.633118	+	1.36661i	−0.280427	+	0.959875i	$0.590476\pi$
$884$		0			0
$885$		0			0
$886$	−0.319700	+	0.892187i	−0.319700	+	0.892187i
$887$		0			0		0.134233	−	0.990950i	$-0.457143\pi$
$887$		0			0		−0.134233	+	0.990950i	$0.542857\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.345894	+	0.320943i	0.345894	+	0.320943i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	0.250878	−	0.858730i	0.250878	−	0.858730i
$899$		0			0
$900$	−0.272217	−	0.268175i	−0.272217	−	0.268175i
$901$		0			0
$902$	1.04949	+	0.0628761i	1.04949	+	0.0628761i
$903$		0			0
$904$	−0.0242048	−	0.0175858i	−0.0242048	−	0.0175858i
$905$		0			0
$906$		0			0
$907$	−0.763640	−	1.78662i	−0.763640	−	1.78662i	−0.599822	−	0.800134i	$-0.704762\pi$
$907$	−0.763640	−	1.78662i	−0.763640	−	1.78662i	−0.163818	−	0.986491i	$-0.552381\pi$
$908$	1.54414	−	0.0462144i	1.54414	−	0.0462144i
$909$		0			0
$910$		0			0
$911$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$911$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$912$	−0.631484	−	0.194787i	−0.631484	−	0.194787i
$913$	−0.00134230	−	0.0897196i	−0.00134230	−	0.0897196i
$914$	0.444843	+	1.94898i	0.444843	+	1.94898i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	1.24178	+	0.149329i	1.24178	+	0.149329i
$919$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$919$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$920$		0			0
$921$	0.941292	−	0.0563941i	0.941292	−	0.0563941i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.659917	−	1.84163i	0.659917	−	1.84163i	0.134233	−	0.990950i	$-0.457143\pi$
$929$	0.659917	−	1.84163i	0.659917	−	1.84163i	0.525684	−	0.850680i	$-0.323810\pi$
$930$		0			0
$931$	0.353400	−	0.762830i	0.353400	−	0.762830i
$932$	−0.325292	+	1.95887i	−0.325292	+	1.95887i
$933$		0			0
$934$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$935$		0			0
$936$		0			0
$937$	0.536616	+	0.715821i	0.536616	+	0.715821i	0.983930	−	0.178557i	$-0.0571429\pi$
$937$	0.536616	+	0.715821i	0.536616	+	0.715821i	−0.447313	+	0.894377i	$0.647619\pi$
$938$		0			0
$939$	−1.06268	−	0.225879i	−1.06268	−	0.225879i
$940$		0			0
$941$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$941$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$942$		0			0
$943$		0			0
$944$	0.0146993	+	0.327306i	0.0146993	+	0.327306i
$945$		0			0
$946$	0.936235	−	0.351375i	0.936235	−	0.351375i
$947$	−1.74682			−1.74682			−0.873408	−	0.486989i	$-0.838095\pi$
$947$	−1.74682			−1.74682			−0.873408	+	0.486989i	$0.838095\pi$
$948$		0			0
$949$		0			0
$950$	−0.837330	+	0.0753611i	−0.837330	+	0.0753611i
$951$		0			0
$952$		0			0
$953$	−0.927027	−	0.197046i	−0.927027	−	0.197046i	−0.280427	−	0.959875i	$-0.590476\pi$
$953$	−0.927027	−	0.197046i	−0.927027	−	0.197046i	−0.646600	+	0.762830i	$0.723810\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.420357	−	0.907359i	0.420357	−	0.907359i
$962$		0			0
$963$	−0.0869652	+	0.242694i	−0.0869652	+	0.242694i
$964$	0.851044	−	0.699767i	0.851044	−	0.699767i
$965$		0			0
$966$		0			0
$967$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$967$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$968$	0.712376	−	0.701798i	0.712376	−	0.701798i
$969$	0.557695	−	0.517466i	0.557695	−	0.517466i
$970$		0			0
$971$	−1.79871	+	0.107763i	−1.79871	+	0.107763i	−0.925304	−	0.379225i	$-0.876190\pi$
$971$	−1.79871	+	0.107763i	−1.79871	+	0.107763i	−0.873408	+	0.486989i	$0.838095\pi$
$972$	−0.566026	−	0.437700i	−0.566026	−	0.437700i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.23552	−	0.789278i	1.23552	−	0.789278i	0.251587	−	0.967835i	$-0.419048\pi$
$977$	1.23552	−	0.789278i	1.23552	−	0.789278i	0.983930	+	0.178557i	$0.0571429\pi$
$978$	0.276737	+	1.21246i	0.276737	+	1.21246i
$979$	−0.744388	+	1.05747i	−0.744388	+	1.05747i
$980$		0			0
$981$		0			0
$982$	−0.802718	−	0.891509i	−0.802718	−	0.891509i
$983$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$983$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$984$	0.826058	−	0.0247230i	0.826058	−	0.0247230i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$991$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$992$		0			0
$993$	−1.19786	−	0.715686i	−1.19786	−	0.715686i
$994$		0			0
$995$		0			0
$996$	−0.00737260	−	0.0701456i	−0.00737260	−	0.0701456i
$997$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$997$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$998$	0.820112	−	1.16505i	0.820112	−	1.16505i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.1643.1	yes	48
8.3	odd	2	CM	3784.1.em.b.1643.1	yes	48
11.3	even	5		3784.1.em.a.267.1	✓	48
43.24	even	21		3784.1.em.a.411.1	yes	48
88.3	odd	10		3784.1.em.a.267.1	✓	48
344.67	odd	42		3784.1.em.a.411.1	yes	48
473.454	even	105	inner	3784.1.em.b.2819.1	yes	48
3784.2819	odd	210	inner	3784.1.em.b.2819.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.267.1	✓	48	11.3	even	5
3784.1.em.a.267.1	✓	48	88.3	odd	10
3784.1.em.a.411.1	yes	48	43.24	even	21
3784.1.em.a.411.1	yes	48	344.67	odd	42
3784.1.em.b.1643.1	yes	48	1.1	even	1	trivial
3784.1.em.b.1643.1	yes	48	8.3	odd	2	CM
3784.1.em.b.2819.1	yes	48	473.454	even	105	inner
3784.1.em.b.2819.1	yes	48	3784.2819	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)

\(f(q)\)	\(=\)	\(q+(-0.0448648 - 0.998993i) q^{2} +(0.351611 - 0.703025i) q^{3} +(-0.995974 + 0.0896393i) q^{4} +(-0.718092 - 0.319715i) q^{6} +(0.134233 + 0.990950i) q^{8} +(0.229207 + 0.305751i) q^{9} +O(q^{10})\)	\(q+(-0.0448648 - 0.998993i) q^{2} +(0.351611 - 0.703025i) q^{3} +(-0.995974 + 0.0896393i) q^{4} +(-0.718092 - 0.319715i) q^{6} +(0.134233 + 0.990950i) q^{8} +(0.229207 + 0.305751i) q^{9} +(-0.447313 + 0.894377i) q^{11} +(-0.287176 + 0.731713i) q^{12} +(0.983930 - 0.178557i) q^{16} +(-0.388346 + 1.08376i) q^{17} +(0.295160 - 0.242694i) q^{18} +(0.0125766 - 0.840620i) q^{19} +(0.913545 + 0.406737i) q^{22} +(0.743861 + 0.254059i) q^{24} +(0.998210 - 0.0598042i) q^{25} +(1.06896 - 0.193988i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(0.471490 + 0.628945i) q^{33} +(1.10009 + 0.339332i) q^{34} +(-0.255692 - 0.283974i) q^{36} +(-0.840338 + 0.0251504i) q^{38} +(0.984327 - 0.369424i) q^{41} +(0.712376 - 0.701798i) q^{43} +(0.365341 - 0.930874i) q^{44} +(0.220430 - 0.754510i) q^{48} +(0.913545 + 0.406737i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(0.625362 + 0.654077i) q^{51} +(-0.241751 - 1.05918i) q^{54} +(-0.586555 - 0.304413i) q^{57} +(-0.0439796 + 0.324671i) q^{59} +(-0.963963 + 0.266037i) q^{64} +(0.607158 - 0.499233i) q^{66} +(1.27881 - 0.394459i) q^{67} +(0.289635 - 1.11420i) q^{68} +(-0.272217 + 0.268175i) q^{72} +(-0.203097 + 0.0495633i) q^{73} +(0.308937 - 0.722795i) q^{75} +(0.0628267 + 0.838364i) q^{76} +(0.132321 - 0.452922i) q^{81} +(-0.413214 - 0.966762i) q^{82} +(-0.0796428 + 0.0413333i) q^{83} +(-0.733052 - 0.680173i) q^{86} +(-0.946327 - 0.323210i) q^{88} +(1.27876 + 0.192741i) q^{89} +(-0.763640 - 0.186357i) q^{96} +(-0.559963 + 1.31010i) q^{97} +(0.365341 - 0.930874i) q^{98} +(-0.375984 + 0.0682311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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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