LMFDB - Embedded newform 3784.1.em.b.339.1

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			339.1
Root			$-0.575617 - 0.817719i$ of defining polynomial
Character	$\chi$	$=$	3784.339
Dual form			3784.1.em.b.3371.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.858449 + 0.512899i) q^{2} +(-0.254057 + 0.0867710i) q^{3} +(0.473869 + 0.880596i) q^{4} +(-0.262600 - 0.0558173i) q^{6} +(-0.0448648 + 0.998993i) q^{8} +(-0.734055 + 0.567635i) q^{9} +O(q^{10})$	\(q+(0.858449 + 0.512899i) q^{2} +(-0.254057 + 0.0867710i) q^{3} +(0.473869 + 0.880596i) q^{4} +(-0.262600 - 0.0558173i) q^{6} +(-0.0448648 + 0.998993i) q^{8} +(-0.734055 + 0.567635i) q^{9} +(-0.946327 + 0.323210i) q^{11} +(-0.196800 - 0.182604i) q^{12} +(-0.550897 + 0.834573i) q^{16} +(-1.99553 - 0.119555i) q^{17} +(-0.921288 + 0.110789i) q^{18} +(-0.354658 + 0.989743i) q^{19} +(-0.978148 - 0.207912i) q^{22} +(-0.0752854 - 0.257694i) q^{24} +(0.193256 - 0.981148i) q^{25} +(0.285135 - 0.431961i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(0.212376 - 0.164228i) q^{33} +(-1.65174 - 1.12614i) q^{34} +(-0.847702 - 0.377421i) q^{36} +(-0.812094 + 0.667740i) q^{38} +(0.128769 + 0.301270i) q^{41} +(0.575617 + 0.817719i) q^{43} +(-0.733052 - 0.680173i) q^{44} +(0.0675426 - 0.259831i) q^{48} +(-0.978148 - 0.207912i) q^{49} +(0.669131 - 0.743145i) q^{50} +(0.517352 - 0.142780i) q^{51} +(0.466327 - 0.224571i) q^{54} +(0.00422240 - 0.282225i) q^{57} +(0.0538218 + 1.19844i) q^{59} +(-0.995974 - 0.0896393i) q^{64} +(0.266546 - 0.0320534i) q^{66} +(1.50961 - 1.02924i) q^{67} +(-0.840338 - 1.81391i) q^{68} +(-0.534130 - 0.758783i) q^{72} +(0.953345 + 0.939189i) q^{73} +(0.0360371 + 0.266037i) q^{75} +(-1.03962 + 0.156698i) q^{76} +(0.198495 - 0.763594i) q^{81} +(-0.0439796 + 0.324671i) q^{82} +(0.0256838 + 1.71671i) q^{83} +(0.0747301 + 0.997204i) q^{86} +(-0.280427 - 0.959875i) q^{88} +(-0.854881 - 0.263696i) q^{89} +(0.191249 - 0.188409i) q^{96} +(0.154534 + 1.14082i) q^{97} +(-0.733052 - 0.680173i) q^{98} +(0.511191 - 0.774422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{2}{21}\right)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.858449	+	0.512899i	0.858449	+	0.512899i
$2$	0.858449	+	0.512899i	0.858449	+	0.512899i
$3$	−0.254057	+	0.0867710i	−0.254057	+	0.0867710i	−0.447313	−	0.894377i	$-0.647619\pi$
$3$	−0.254057	+	0.0867710i	−0.254057	+	0.0867710i	0.193256	+	0.981148i	$0.438095\pi$
$4$	0.473869	+	0.880596i	0.473869	+	0.880596i
$5$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$5$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$6$	−0.262600	−	0.0558173i	−0.262600	−	0.0558173i
$7$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$7$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$8$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$9$	−0.734055	+	0.567635i	−0.734055	+	0.567635i
$10$		0			0
$11$	−0.946327	+	0.323210i	−0.946327	+	0.323210i
$11$	−0.946327	+	0.323210i	−0.946327	+	0.323210i
$12$	−0.196800	−	0.182604i	−0.196800	−	0.182604i
$13$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$13$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$14$		0			0
$15$		0			0
$16$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$17$	−1.99553	−	0.119555i	−1.99553	−	0.119555i	−0.999552	−	0.0299155i	$-0.990476\pi$
$17$	−1.99553	−	0.119555i	−1.99553	−	0.119555i	−0.995974	−	0.0896393i	$-0.971429\pi$
$18$	−0.921288	+	0.110789i	−0.921288	+	0.110789i
$19$	−0.354658	+	0.989743i	−0.354658	+	0.989743i	0.623490	+	0.781831i	$0.285714\pi$
$19$	−0.354658	+	0.989743i	−0.354658	+	0.989743i	−0.978148	+	0.207912i	$0.933333\pi$
$20$		0			0
$21$		0			0
$22$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$23$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$23$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$24$	−0.0752854	−	0.257694i	−0.0752854	−	0.257694i
$25$	0.193256	−	0.981148i	0.193256	−	0.981148i
$26$		0			0
$27$	0.285135	−	0.431961i	0.285135	−	0.431961i
$28$		0			0
$29$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$29$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$30$		0			0
$31$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$31$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$32$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$33$	0.212376	−	0.164228i	0.212376	−	0.164228i
$34$	−1.65174	−	1.12614i	−1.65174	−	1.12614i
$35$		0			0
$36$	−0.847702	−	0.377421i	−0.847702	−	0.377421i
$37$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$37$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$38$	−0.812094	+	0.667740i	−0.812094	+	0.667740i
$39$		0			0
$40$		0			0
$41$	0.128769	+	0.301270i	0.128769	+	0.301270i	0.971490	−	0.237080i	$-0.0761905\pi$
$41$	0.128769	+	0.301270i	0.128769	+	0.301270i	−0.842721	+	0.538351i	$0.819048\pi$
$42$		0			0
$43$	0.575617	+	0.817719i	0.575617	+	0.817719i
$43$	0.575617	+	0.817719i	0.575617	+	0.817719i
$44$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$45$		0			0
$46$		0			0
$47$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$47$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$48$	0.0675426	−	0.259831i	0.0675426	−	0.259831i
$49$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$50$	0.669131	−	0.743145i	0.669131	−	0.743145i
$51$	0.517352	−	0.142780i	0.517352	−	0.142780i
$52$		0			0
$53$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$53$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$54$	0.466327	−	0.224571i	0.466327	−	0.224571i
$55$		0			0
$56$		0			0
$57$	0.00422240	−	0.282225i	0.00422240	−	0.282225i
$58$		0			0
$59$	0.0538218	+	1.19844i	0.0538218	+	1.19844i	0.826239	+	0.563320i	$0.190476\pi$
$59$	0.0538218	+	1.19844i	0.0538218	+	1.19844i	−0.772417	+	0.635116i	$0.780952\pi$
$60$		0			0
$61$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$61$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$62$		0			0
$63$		0			0
$64$	−0.995974	−	0.0896393i	−0.995974	−	0.0896393i
$65$		0			0
$66$	0.266546	−	0.0320534i	0.266546	−	0.0320534i
$67$	1.50961	−	1.02924i	1.50961	−	1.02924i	0.525684	−	0.850680i	$-0.323810\pi$
$67$	1.50961	−	1.02924i	1.50961	−	1.02924i	0.983930	−	0.178557i	$-0.0571429\pi$
$68$	−0.840338	−	1.81391i	−0.840338	−	1.81391i
$69$		0			0
$70$		0			0
$71$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$71$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$72$	−0.534130	−	0.758783i	−0.534130	−	0.758783i
$73$	0.953345	+	0.939189i	0.953345	+	0.939189i	0.998210	−	0.0598042i	$-0.0190476\pi$
$73$	0.953345	+	0.939189i	0.953345	+	0.939189i	−0.0448648	+	0.998993i	$0.514286\pi$
$74$		0			0
$75$	0.0360371	+	0.266037i	0.0360371	+	0.266037i
$76$	−1.03962	+	0.156698i	−1.03962	+	0.156698i
$77$		0			0
$78$		0			0
$79$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$79$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$80$		0			0
$81$	0.198495	−	0.763594i	0.198495	−	0.763594i
$82$	−0.0439796	+	0.324671i	−0.0439796	+	0.324671i
$83$	0.0256838	+	1.71671i	0.0256838	+	1.71671i	0.525684	+	0.850680i	$0.323810\pi$
$83$	0.0256838	+	1.71671i	0.0256838	+	1.71671i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$87$		0			0
$88$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$89$	−0.854881	−	0.263696i	−0.854881	−	0.263696i	−0.163818	−	0.986491i	$-0.552381\pi$
$89$	−0.854881	−	0.263696i	−0.854881	−	0.263696i	−0.691063	+	0.722795i	$0.742857\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.191249	−	0.188409i	0.191249	−	0.188409i
$97$	0.154534	+	1.14082i	0.154534	+	1.14082i	0.887586	+	0.460642i	$0.152381\pi$
$97$	0.154534	+	1.14082i	0.154534	+	1.14082i	−0.733052	+	0.680173i	$0.761905\pi$
$98$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$99$	0.511191	−	0.774422i	0.511191	−	0.774422i
$100$	0.955573	−	0.294755i	0.955573	−	0.294755i
$101$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$101$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$102$	0.517352	+	0.142780i	0.517352	+	0.142780i
$103$		0			0		0.842721	−	0.538351i	$-0.180952\pi$
$103$		0			0		−0.842721	+	0.538351i	$0.819048\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.50345	+	1.31352i	1.50345	+	1.31352i	0.791071	+	0.611724i	$0.209524\pi$
$107$	1.50345	+	1.31352i	1.50345	+	1.31352i	0.712376	+	0.701798i	$0.247619\pi$
$108$	0.515500	+	0.0463958i	0.515500	+	0.0463958i
$109$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$109$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.650347	+	0.179484i	0.650347	+	0.179484i	0.575617	−	0.817719i	$-0.304762\pi$
$113$	0.650347	+	0.179484i	0.650347	+	0.179484i	0.0747301	+	0.997204i	$0.476190\pi$
$114$	0.148378	−	0.240110i	0.148378	−	0.240110i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	−0.568474	+	1.05640i	−0.568474	+	1.05640i
$119$		0			0
$120$		0			0
$121$	0.791071	−	0.611724i	0.791071	−	0.611724i
$122$		0			0
$123$	−0.0588562	−	0.0653665i	−0.0588562	−	0.0653665i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$127$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$128$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$129$	−0.217194	−	0.157801i	−0.217194	−	0.157801i
$130$		0			0
$131$	−0.111967	+	0.490558i	−0.111967	+	0.490558i	0.887586	+	0.460642i	$0.152381\pi$
$131$	−0.111967	+	0.490558i	−0.111967	+	0.490558i	−0.999552	+	0.0299155i	$0.990476\pi$
$132$	0.245256	+	0.109195i	0.245256	+	0.109195i
$133$		0			0
$134$	1.82382	−	0.109268i	1.82382	−	0.109268i
$135$		0			0
$136$	0.208963	−	1.98815i	0.208963	−	1.98815i
$137$	−1.86493	−	0.699921i	−1.86493	−	0.699921i	−0.963963	−	0.266037i	$-0.914286\pi$
$137$	−1.86493	−	0.699921i	−1.86493	−	0.699921i	−0.900969	−	0.433884i	$-0.857143\pi$
$138$		0			0
$139$	0.648543	+	0.336583i	0.648543	+	0.336583i	0.753071	−	0.657939i	$-0.228571\pi$
$139$	0.648543	+	0.336583i	0.648543	+	0.336583i	−0.104528	+	0.994522i	$0.533333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−0.0693440	−	0.925331i	−0.0693440	−	0.925331i
$145$		0			0
$146$	0.336689	+	1.29522i	0.336689	+	1.29522i
$147$	0.266546	−	0.0320534i	0.266546	−	0.0320534i
$148$		0			0
$149$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$149$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$150$	−0.105514	+	0.246862i	−0.105514	+	0.246862i
$151$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$151$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$152$	−0.972835	−	0.398705i	−0.972835	−	0.398705i
$153$	1.53269	−	1.04497i	1.53269	−	1.04497i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$157$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.562045	−	0.553699i	0.562045	−	0.553699i
$163$	−1.33330	+	1.03103i	−1.33330	+	1.03103i	−0.337330	+	0.941386i	$0.609524\pi$
$163$	−1.33330	+	1.03103i	−1.33330	+	1.03103i	−0.995974	+	0.0896393i	$0.971429\pi$
$164$	−0.204278	+	0.256156i	−0.204278	+	0.256156i
$165$		0			0
$166$	−0.858449	+	1.48688i	−0.858449	+	1.48688i
$167$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$167$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$168$		0			0
$169$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$170$		0			0
$171$	−0.301474	−	0.927842i	−0.301474	−	0.927842i
$172$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$173$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$173$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$174$		0			0
$175$		0			0
$176$	0.251587	−	0.967835i	0.251587	−	0.967835i
$177$	−0.117663	−	0.299801i	−0.117663	−	0.299801i
$178$	−0.598622	−	0.664837i	−0.598622	−	0.664837i
$179$	−1.09593	−	0.487939i	−1.09593	−	0.487939i	−0.222521	−	0.974928i	$-0.571429\pi$
$179$	−1.09593	−	0.487939i	−1.09593	−	0.487939i	−0.873408	+	0.486989i	$0.838095\pi$
$180$		0			0
$181$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$181$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.92706	−	0.531836i	1.92706	−	0.531836i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.999552	−	0.0299155i	$-0.990476\pi$
$191$		0			0		0.999552	+	0.0299155i	$0.00952381\pi$
$192$	0.260813	−	0.0636481i	0.260813	−	0.0636481i
$193$	−0.382046	+	0.228262i	−0.382046	+	0.228262i	−0.691063	−	0.722795i	$-0.742857\pi$
$193$	−0.382046	+	0.228262i	−0.382046	+	0.228262i	0.309017	+	0.951057i	$0.400000\pi$
$194$	−0.452464	+	1.05859i	−0.452464	+	1.05859i
$195$		0			0
$196$	−0.280427	−	0.959875i	−0.280427	−	0.959875i
$197$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$197$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$198$	0.836032	−	0.402612i	0.836032	−	0.402612i
$199$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$199$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$200$	0.971490	+	0.237080i	0.971490	+	0.237080i
$201$	−0.294220	+	0.392476i	−0.294220	+	0.392476i
$202$		0			0
$203$		0			0
$204$	0.370888	+	0.387919i	0.370888	+	0.387919i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.0157278	−	1.05125i	0.0157278	−	1.05125i
$210$		0			0
$211$	0.761409	−	0.796371i	0.761409	−	0.796371i	−0.222521	−	0.974928i	$-0.571429\pi$
$211$	0.761409	−	0.796371i	0.761409	−	0.796371i	0.983930	+	0.178557i	$0.0571429\pi$
$212$		0			0
$213$		0			0
$214$	0.616928	+	1.89871i	0.616928	+	1.89871i
$215$		0			0
$216$	0.418734	+	0.304228i	0.418734	+	0.304228i
$217$		0			0
$218$		0			0
$219$	−0.323699	−	0.155885i	−0.323699	−	0.155885i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.0448648	−	0.998993i	$-0.485714\pi$
$223$		0			0		−0.0448648	+	0.998993i	$0.514286\pi$
$224$		0			0
$225$	0.415073	+	0.829916i	0.415073	+	0.829916i
$226$	0.466232	+	0.487641i	0.466232	+	0.487641i
$227$	0.383747	+	1.94826i	0.383747	+	1.94826i	0.309017	+	0.951057i	$0.400000\pi$
$227$	0.383747	+	1.94826i	0.383747	+	1.94826i	0.0747301	+	0.997204i	$0.476190\pi$
$228$	0.250527	−	0.130020i	0.250527	−	0.130020i
$229$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$229$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.777917	−	1.67917i	−0.777917	−	1.67917i	−0.733052	−	0.680173i	$-0.761905\pi$
$233$	−0.777917	−	1.67917i	−0.777917	−	1.67917i	−0.0448648	−	0.998993i	$-0.514286\pi$
$234$		0			0
$235$		0			0
$236$	−1.02983	+	0.615296i	−1.02983	+	0.615296i
$237$		0			0
$238$		0			0
$239$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$239$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$240$		0			0
$241$	0.550256	−	1.40203i	0.550256	−	1.40203i	−0.337330	−	0.941386i	$-0.609524\pi$
$241$	0.550256	−	1.40203i	0.550256	−	1.40203i	0.887586	−	0.460642i	$-0.152381\pi$
$242$	0.992847	−	0.119394i	0.992847	−	0.119394i
$243$	0.0545078	+	0.727357i	0.0545078	+	0.727357i
$244$		0			0
$245$		0			0
$246$	−0.0169986	−	0.0863011i	−0.0169986	−	0.0863011i
$247$		0			0
$248$		0			0
$249$	−0.155485	−	0.433913i	−0.155485	−	0.433913i
$250$		0			0
$251$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.309017	−	0.951057i	$-0.400000\pi$
$251$	0.978148	−	0.207912i	0.978148	−	0.207912i	0.669131	+	0.743145i	$0.266667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$257$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.913545	+	0.406737i	$0.133333\pi$
$257$	1.58268	+	1.14988i	1.58268	+	1.14988i	0.669131	+	0.743145i	$0.266667\pi$
$258$	−0.105514	−	0.246862i	−0.105514	−	0.246862i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.347724	+	0.363691i	−0.347724	+	0.363691i
$263$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$263$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$264$	0.154534	+	0.219530i	0.154534	+	0.219530i
$265$		0			0
$266$		0			0
$267$	0.240070	−	0.00718501i	0.240070	−	0.00718501i
$268$	1.62170	+	0.841636i	1.62170	+	0.841636i
$269$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$269$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$270$		0			0
$271$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$271$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$272$	1.19911	−	1.59955i	1.19911	−	1.59955i
$273$		0			0
$274$	−1.24196	−	1.55737i	−1.24196	−	1.55737i
$275$	0.134233	+	0.990950i	0.134233	+	0.990950i
$276$		0			0
$277$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$277$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$278$	0.384108	+	0.621577i	0.384108	+	0.621577i
$279$		0			0
$280$		0			0
$281$	1.30011	−	0.317275i	1.30011	−	0.317275i	0.473869	−	0.880596i	$-0.342857\pi$
$281$	1.30011	−	0.317275i	1.30011	−	0.317275i	0.826239	+	0.563320i	$0.190476\pi$
$282$		0			0
$283$	0.0288841	−	0.146643i	0.0288841	−	0.146643i	−0.963963	−	0.266037i	$-0.914286\pi$
$283$	0.0288841	−	0.146643i	0.0288841	−	0.146643i	0.992847	+	0.119394i	$0.0380952\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.415073	−	0.829916i	0.415073	−	0.829916i
$289$	2.97499	+	0.357755i	2.97499	+	0.357755i
$290$		0			0
$291$	−0.138250	−	0.276423i	−0.138250	−	0.276423i
$292$	−0.375285	+	1.28456i	−0.375285	+	1.28456i
$293$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$293$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$294$	0.245256	+	0.109195i	0.245256	+	0.109195i
$295$		0			0
$296$		0			0
$297$	−0.130217	+	0.500935i	−0.130217	+	0.500935i
$298$		0			0
$299$		0			0
$300$	−0.217194	+	0.157801i	−0.217194	+	0.157801i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.630633	−	0.841234i	−0.630633	−	0.841234i
$305$		0			0
$306$	1.85170	−	0.110938i	1.85170	−	0.110938i
$307$	−0.791071	+	1.37018i	−0.791071	+	1.37018i	0.134233	+	0.990950i	$0.457143\pi$
$307$	−0.791071	+	1.37018i	−0.791071	+	1.37018i	−0.925304	+	0.379225i	$0.876190\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$311$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$312$		0			0
$313$	−0.810418	+	1.74932i	−0.810418	+	1.74932i	−0.163818	+	0.986491i	$0.552381\pi$
$313$	−0.810418	+	1.74932i	−0.810418	+	1.74932i	−0.646600	+	0.762830i	$0.723810\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$317$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.495937	−	0.203254i	−0.495937	−	0.203254i
$322$		0			0
$323$	0.826058	−	1.93266i	0.826058	−	1.93266i
$324$	0.766478	−	0.187050i	0.766478	−	0.187050i
$325$		0			0
$326$	−1.67339	+	0.201232i	−1.67339	+	0.201232i
$327$		0			0
$328$	−0.306744	+	0.115123i	−0.306744	+	0.115123i
$329$		0			0
$330$		0			0
$331$	−0.0295846	−	0.00445917i	−0.0295846	−	0.00445917i	0.134233	−	0.990950i	$-0.457143\pi$
$331$	−0.0295846	−	0.00445917i	−0.0295846	−	0.00445917i	−0.163818	+	0.986491i	$0.552381\pi$
$332$	−1.49955	+	0.836110i	−1.49955	+	0.836110i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−0.0404015	+	0.384394i	−0.0404015	+	0.384394i	0.955573	+	0.294755i	$0.0952381\pi$
$337$	−0.0404015	+	0.384394i	−0.0404015	+	0.384394i	−0.995974	+	0.0896393i	$0.971429\pi$
$338$	−0.104528	−	0.994522i	−0.104528	−	0.994522i
$339$	−0.180799	+	0.0108319i	−0.180799	+	0.0108319i
$340$		0			0
$341$		0			0
$342$	0.217089	−	0.951131i	0.217089	−	0.951131i
$343$		0			0
$344$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$345$		0			0
$346$		0			0
$347$	−0.0100925	−	0.674584i	−0.0100925	−	0.674584i	−0.946327	−	0.323210i	$-0.895238\pi$
$347$	−0.0100925	−	0.674584i	−0.0100925	−	0.674584i	0.936235	−	0.351375i	$-0.114286\pi$
$348$		0			0
$349$		0			0		−0.842721	−	0.538351i	$-0.819048\pi$
$349$		0			0		0.842721	+	0.538351i	$0.180952\pi$
$350$		0			0
$351$		0			0
$352$	0.712376	−	0.701798i	0.712376	−	0.701798i
$353$	−1.39258	−	0.949443i	−1.39258	−	0.949443i	−0.999552	−	0.0299155i	$-0.990476\pi$
$353$	−1.39258	−	0.949443i	−1.39258	−	0.949443i	−0.393025	−	0.919528i	$-0.628571\pi$
$354$	0.0527599	−	0.317713i	0.0527599	−	0.317713i
$355$		0			0
$356$	−0.172892	−	0.877761i	−0.172892	−	0.877761i
$357$		0			0
$358$	−0.690535	−	0.980972i	−0.690535	−	0.980972i
$359$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$359$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$360$		0			0
$361$	−0.0813924	−	0.0669245i	−0.0813924	−	0.0669245i
$362$		0			0
$363$	−0.147897	+	0.224055i	−0.147897	+	0.224055i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$367$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$368$		0			0
$369$	−0.265535	−	0.148055i	−0.265535	−	0.148055i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$373$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$374$	1.92706	+	0.531836i	1.92706	+	0.531836i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.0280110	+	0.0105127i	0.0280110	+	0.0105127i	0.365341	−	0.930874i	$-0.380952\pi$
$379$	0.0280110	+	0.0105127i	0.0280110	+	0.0105127i	−0.337330	+	0.941386i	$0.609524\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$383$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$384$	0.256539	+	0.0791319i	0.256539	+	0.0791319i
$385$		0			0
$386$	−0.445042			−0.445042
$387$	−0.886701	−	0.273511i	−0.886701	−	0.273511i
$388$	−0.931368	+	0.676678i	−0.931368	+	0.676678i
$389$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$389$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$390$		0			0
$391$		0			0
$392$	0.251587	−	0.967835i	0.251587	−	0.967835i
$393$	−0.0141203	−	0.134345i	−0.0141203	−	0.134345i
$394$		0			0
$395$		0			0
$396$	0.924190	+	0.0831786i	0.924190	+	0.0831786i
$397$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$397$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$398$		0			0
$399$		0			0
$400$	0.712376	+	0.701798i	0.712376	+	0.701798i
$401$	−1.14660	−	1.62885i	−1.14660	−	1.62885i	−0.646600	−	0.762830i	$-0.723810\pi$
$401$	−1.14660	−	1.62885i	−1.14660	−	1.62885i	−0.500000	−	0.866025i	$-0.666667\pi$
$402$	−0.453874	+	0.186015i	−0.453874	+	0.186015i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	0.119425	+	0.523237i	0.119425	+	0.523237i
$409$	1.96970	+	0.177276i	1.96970	+	0.177276i	0.998210	−	0.0598042i	$-0.0190476\pi$
$409$	1.96970	+	0.177276i	1.96970	+	0.177276i	0.971490	+	0.237080i	$0.0761905\pi$
$410$		0			0
$411$	0.534532	+	0.0159979i	0.534532	+	0.0159979i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−0.193973	−	0.0292367i	−0.193973	−	0.0292367i
$418$	0.552687	−	0.894377i	0.552687	−	0.894377i
$419$	−1.68704	+	0.812434i	−1.68704	+	0.812434i	−0.691063	+	0.722795i	$0.742857\pi$
$419$	−1.68704	+	0.812434i	−1.68704	+	0.812434i	−0.995974	+	0.0896393i	$0.971429\pi$
$420$		0			0
$421$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$421$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$422$	1.06209	−	0.293118i	1.06209	−	0.293118i
$423$		0			0
$424$		0			0
$425$	−0.502948	+	1.93480i	−0.502948	+	1.93480i
$426$		0			0
$427$		0			0
$428$	−0.444245	+	1.94637i	−0.444245	+	1.94637i
$429$		0			0
$430$		0			0
$431$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$431$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$432$	0.203423	+	0.475932i	0.203423	+	0.475932i
$433$	0.0538218	+	0.0717957i	0.0538218	+	0.0717957i	0.826239	−	0.563320i	$-0.190476\pi$
$433$	0.0538218	+	0.0717957i	0.0538218	+	0.0717957i	−0.772417	+	0.635116i	$0.780952\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.197925	−	0.299844i	−0.197925	−	0.299844i
$439$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$439$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$440$		0			0
$441$	0.836032	−	0.402612i	0.836032	−	0.402612i
$442$		0			0
$443$	1.66198	−	0.862539i	1.66198	−	0.862539i	0.669131	−	0.743145i	$-0.266667\pi$
$443$	1.66198	−	0.862539i	1.66198	−	0.862539i	0.992847	−	0.119394i	$-0.0380952\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	0.530752	+	1.81671i	0.530752	+	1.81671i	0.575617	+	0.817719i	$0.304762\pi$
$449$	0.530752	+	1.81671i	0.530752	+	1.81671i	−0.0448648	+	0.998993i	$0.514286\pi$
$450$	−0.0693440	+	0.925331i	−0.0693440	+	0.925331i
$451$	−0.219231	−	0.243481i	−0.219231	−	0.243481i
$452$	0.150126	+	0.657745i	0.150126	+	0.657745i
$453$		0			0
$454$	−0.669834	+	1.86931i	−0.669834	+	1.86931i
$455$		0			0
$456$	0.281752	+	0.0168801i	0.281752	+	0.0168801i
$457$	0.851044	−	1.28928i	0.851044	−	1.28928i	−0.104528	−	0.994522i	$-0.533333\pi$
$457$	0.851044	−	1.28928i	0.851044	−	1.28928i	0.955573	−	0.294755i	$-0.0952381\pi$
$458$		0			0
$459$	−0.620638	+	0.827901i	−0.620638	+	0.827901i
$460$		0			0
$461$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$461$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$462$		0			0
$463$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$463$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$464$		0			0
$465$		0			0
$466$	0.193441	−	1.84047i	0.193441	−	1.84047i
$467$	1.93445	+	0.411179i	1.93445	+	0.411179i	0.998210	+	0.0598042i	$0.0190476\pi$
$467$	1.93445	+	0.411179i	1.93445	+	0.411179i	0.936235	+	0.351375i	$0.114286\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−1.19964			−1.19964
$473$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$474$		0			0
$475$	0.902545	+	0.539246i	0.902545	+	0.539246i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$479$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$480$		0			0
$481$		0			0
$482$	1.19147	−	0.921344i	1.19147	−	0.921344i
$483$		0			0
$484$	0.913545	+	0.406737i	0.913545	+	0.406737i
$485$		0			0
$486$	−0.326268	+	0.652355i	−0.326268	+	0.652355i
$487$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$487$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$488$		0			0
$489$	0.249272	−	0.377632i	0.249272	−	0.377632i
$490$		0			0
$491$	1.57082	−	0.188899i	1.57082	−	0.188899i	0.712376	−	0.701798i	$-0.247619\pi$
$491$	1.57082	−	0.188899i	1.57082	−	0.188899i	0.858449	+	0.512899i	$0.171429\pi$
$492$	0.0296713	−	0.0828037i	0.0296713	−	0.0828037i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.0890774	−	0.452240i	0.0890774	−	0.452240i
$499$	−0.970169	+	0.619768i	−0.970169	+	0.619768i	−0.925304	−	0.379225i	$-0.876190\pi$
$499$	−0.970169	+	0.619768i	−0.970169	+	0.619768i	−0.0448648	+	0.998993i	$0.514286\pi$
$500$		0			0
$501$		0			0
$502$	0.946327	+	0.323210i	0.946327	+	0.323210i
$503$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$503$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.221817	+	0.151233i	0.221817	+	0.151233i
$508$		0			0
$509$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$509$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$510$		0			0
$511$		0			0
$512$	0.134233	−	0.990950i	0.134233	−	0.990950i
$513$	0.326405	+	0.435409i	0.326405	+	0.435409i
$514$	0.768873	+	1.79887i	0.768873	+	1.79887i
$515$		0			0
$516$	0.0360371	−	0.266037i	0.0360371	−	0.266037i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.126592	−	0.486989i	0.126592	−	0.486989i	−0.873408	−	0.486989i	$-0.838095\pi$
$521$	0.126592	−	0.486989i	0.126592	−	0.486989i	1.00000			$0$
$522$		0			0
$523$	0.953345	−	1.05880i	0.953345	−	1.05880i	−0.0448648	−	0.998993i	$-0.514286\pi$
$523$	0.953345	−	1.05880i	0.953345	−	1.05880i	0.998210	−	0.0598042i	$-0.0190476\pi$
$524$	−0.485041	+	0.133863i	−0.485041	+	0.133863i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.0200625	+	0.267716i	0.0200625	+	0.267716i
$529$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$530$		0			0
$531$	−0.719782	−	0.849167i	−0.719782	−	0.849167i
$532$		0			0
$533$		0			0
$534$	0.209773	+	0.116964i	0.209773	+	0.116964i
$535$		0			0
$536$	0.960472	+	1.55427i	0.960472	+	1.55427i
$537$	0.320768	+	0.0288696i	0.320768	+	0.0288696i
$538$		0			0
$539$	0.992847	−	0.119394i	0.992847	−	0.119394i
$540$		0			0
$541$		0			0		−0.420357	−	0.907359i	$-0.638095\pi$
$541$		0			0		0.420357	+	0.907359i	$0.361905\pi$
$542$		0			0
$543$		0			0
$544$	1.84978	−	0.758111i	1.84978	−	0.758111i
$545$		0			0
$546$		0			0
$547$	−0.0890878	−	0.0107132i	−0.0890878	−	0.0107132i	0.0747301	−	0.997204i	$-0.476190\pi$
$547$	−0.0890878	−	0.0107132i	−0.0890878	−	0.0107132i	−0.163818	+	0.986491i	$0.552381\pi$
$548$	−0.267386	−	1.97392i	−0.267386	−	1.97392i
$549$		0			0
$550$	−0.393025	+	0.919528i	−0.393025	+	0.919528i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.0109306	+	0.730600i	0.0109306	+	0.730600i
$557$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$557$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	−0.443436	+	0.302330i	−0.443436	+	0.302330i
$562$	1.27881	+	0.394459i	1.27881	+	0.394459i
$563$	−1.29399	+	1.35341i	−1.29399	+	1.35341i	−0.393025	+	0.919528i	$0.628571\pi$
$563$	−1.29399	+	1.35341i	−1.29399	+	1.35341i	−0.900969	+	0.433884i	$0.857143\pi$
$564$		0			0
$565$		0			0
$566$	0.100008	−	0.111071i	0.100008	−	0.111071i
$567$		0			0
$568$		0			0
$569$	−1.34828	+	1.32826i	−1.34828	+	1.32826i	−0.447313	+	0.894377i	$0.647619\pi$
$569$	−1.34828	+	1.32826i	−1.34828	+	1.32826i	−0.900969	+	0.433884i	$0.857143\pi$
$570$		0			0
$571$	0.326239	+	0.302705i	0.326239	+	0.302705i	0.826239	−	0.563320i	$-0.190476\pi$
$571$	0.326239	+	0.302705i	0.326239	+	0.302705i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.781982	−	0.499549i	0.781982	−	0.499549i
$577$	−1.31548	−	0.733475i	−1.31548	−	0.733475i	−0.337330	−	0.941386i	$-0.609524\pi$
$577$	−1.31548	−	0.733475i	−1.31548	−	0.733475i	−0.978148	+	0.207912i	$0.933333\pi$
$578$	2.37038	+	1.83298i	2.37038	+	1.83298i
$579$	0.0772550	−	0.0911420i	0.0772550	−	0.0911420i
$580$		0			0
$581$		0			0
$582$	0.0230967	−	0.308204i	0.0230967	−	0.308204i
$583$		0			0
$584$	−0.981015	+	0.910249i	−0.981015	+	0.910249i
$585$		0			0
$586$		0			0
$587$	1.04385	−	1.68919i	1.04385	−	1.68919i	0.420357	−	0.907359i	$-0.361905\pi$
$587$	1.04385	−	1.68919i	1.04385	−	1.68919i	0.623490	−	0.781831i	$-0.285714\pi$
$588$	0.154534	+	0.219530i	0.154534	+	0.219530i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.06849	−	0.728485i	−1.06849	−	0.728485i	−0.104528	−	0.994522i	$-0.533333\pi$
$593$	−1.06849	−	0.728485i	−1.06849	−	0.728485i	−0.963963	+	0.266037i	$0.914286\pi$
$594$	−0.368714	+	0.363239i	−0.368714	+	0.363239i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$599$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$600$	−0.267386	+	0.0240652i	−0.267386	+	0.0240652i
$601$	−0.0242048	−	0.0175858i	−0.0242048	−	0.0175858i	0.575617	−	0.817719i	$-0.304762\pi$
$601$	−0.0242048	−	0.0175858i	−0.0242048	−	0.0175858i	−0.599822	+	0.800134i	$0.704762\pi$
$602$		0			0
$603$	−0.523909	+	1.61243i	−0.523909	+	1.61243i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.998210	−	0.0598042i	$-0.0190476\pi$
$607$		0			0		−0.998210	+	0.0598042i	$0.980952\pi$
$608$	−0.109898	−	1.04561i	−0.109898	−	1.04561i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	1.64649	+	0.854501i	1.64649	+	0.854501i
$613$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$613$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$614$	−1.38186	+	0.770486i	−1.38186	+	0.770486i
$615$		0			0
$616$		0			0
$617$	0.147058	+	1.96236i	0.147058	+	1.96236i	0.251587	+	0.967835i	$0.419048\pi$
$617$	0.147058	+	1.96236i	0.147058	+	1.96236i	−0.104528	+	0.994522i	$0.533333\pi$
$618$		0			0
$619$	0.238438	+	0.917253i	0.238438	+	0.917253i	0.971490	+	0.237080i	$0.0761905\pi$
$619$	0.238438	+	0.917253i	0.238438	+	0.917253i	−0.733052	+	0.680173i	$0.761905\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$626$	−1.59293	+	1.08604i	−1.59293	+	1.08604i
$627$	0.0872222	+	0.268442i	0.0872222	+	0.268442i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$631$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$632$		0			0
$633$	−0.124339	+	0.268392i	−0.124339	+	0.268392i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	0.827204	−	0.150115i	0.827204	−	0.150115i	0.251587	−	0.967835i	$-0.419048\pi$
$641$	0.827204	−	0.150115i	0.827204	−	0.150115i	0.575617	+	0.817719i	$0.304762\pi$
$642$	−0.321488	−	0.428849i	−0.321488	−	0.428849i
$643$	−1.93516	+	0.174167i	−1.93516	+	0.174167i	−0.988831	−	0.149042i	$-0.952381\pi$
$643$	−1.93516	+	0.174167i	−1.93516	+	0.174167i	−0.946327	+	0.323210i	$0.895238\pi$
$644$		0			0
$645$		0			0
$646$	1.70039	−	1.23540i	1.70039	−	1.23540i
$647$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$647$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$648$	0.753920	+	0.232554i	0.753920	+	0.232554i
$649$	−0.438279	−	1.11672i	−0.438279	−	1.11672i
$650$		0			0
$651$		0			0
$652$	−1.53973	−	0.685531i	−1.53973	−	0.685531i
$653$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$653$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$654$		0			0
$655$		0			0
$656$	−0.322371	−	0.0585016i	−0.322371	−	0.0585016i
$657$	−1.23292	−	0.148265i	−1.23292	−	0.148265i
$658$		0			0
$659$	0.905632	−	0.279350i	0.905632	−	0.279350i	0.193256	−	0.981148i	$-0.438095\pi$
$659$	0.905632	−	0.279350i	0.905632	−	0.279350i	0.712376	+	0.701798i	$0.247619\pi$
$660$		0			0
$661$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$661$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$662$	−0.0231098	−	0.0190019i	−0.0231098	−	0.0190019i
$663$		0			0
$664$	−1.71613	−	0.0513618i	−1.71613	−	0.0513618i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	1.72456	+	0.420858i	1.72456	+	0.420858i	0.971490	−	0.237080i	$-0.0761905\pi$
$673$	1.72456	+	0.420858i	1.72456	+	0.420858i	0.753071	+	0.657939i	$0.228571\pi$
$674$	−0.231838	+	0.309261i	−0.231838	+	0.309261i
$675$	−0.368714	−	0.363239i	−0.368714	−	0.363239i
$676$	0.420357	−	0.907359i	0.420357	−	0.907359i
$677$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$677$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$678$	−0.160763	−	0.0834332i	−0.160763	−	0.0834332i
$679$		0			0
$680$		0			0
$681$	−0.266546	−	0.461672i	−0.266546	−	0.461672i
$682$		0			0
$683$	−0.658322	−	1.67738i	−0.658322	−	1.67738i	−0.733052	−	0.680173i	$-0.761905\pi$
$683$	−0.658322	−	1.67738i	−0.658322	−	1.67738i	0.0747301	−	0.997204i	$-0.476190\pi$
$684$	0.674194	−	0.705152i	0.674194	−	0.705152i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$689$		0			0
$690$		0			0
$691$	−0.120337	+	0.170950i	−0.120337	+	0.170950i	−0.873408	−	0.486989i	$-0.838095\pi$
$691$	−0.120337	+	0.170950i	−0.120337	+	0.170950i	0.753071	+	0.657939i	$0.228571\pi$
$692$		0			0
$693$		0			0
$694$	0.337330	−	0.584273i	0.337330	−	0.584273i
$695$		0			0
$696$		0			0
$697$	−0.220944	−	0.616588i	−0.220944	−	0.616588i
$698$		0			0
$699$	0.343338	+	0.359104i	0.343338	+	0.359104i
$700$		0			0
$701$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$701$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$702$		0			0
$703$		0			0
$704$	0.971490	−	0.237080i	0.971490	−	0.237080i
$705$		0			0
$706$	−0.708488	−	1.52930i	−0.708488	−	1.52930i
$707$		0			0
$708$	0.208247	−	0.245680i	0.208247	−	0.245680i
$709$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$709$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$710$		0			0
$711$		0			0
$712$	0.301784	−	0.842189i	0.301784	−	0.842189i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−0.0896495	−	1.19629i	−0.0896495	−	1.19629i
$717$		0			0
$718$		0			0
$719$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$719$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$720$		0			0
$721$		0			0
$722$	−0.0355457	−	0.0991974i	−0.0355457	−	0.0991974i
$723$	−0.0181410	+	0.403942i	−0.0181410	+	0.403942i
$724$		0			0
$725$		0			0
$726$	−0.241880	+	0.116483i	−0.241880	+	0.116483i
$727$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$727$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$728$		0			0
$729$	0.233124	+	0.545421i	0.233124	+	0.545421i
$730$		0			0
$731$	−1.05090	−	1.70060i	−1.05090	−	1.70060i
$732$		0			0
$733$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$733$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.09593	+	1.46192i	−1.09593	+	1.46192i
$738$	−0.152011	−	0.263291i	−0.152011	−	0.263291i
$739$	0.0494318	+	0.0748860i	0.0494318	+	0.0748860i	0.858449	−	0.512899i	$-0.171429\pi$
$739$	0.0494318	+	0.0748860i	0.0494318	+	0.0748860i	−0.809017	+	0.587785i	$0.800000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$743$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.993315	−	1.24558i	−0.993315	−	1.24558i
$748$	1.38151	+	1.44494i	1.38151	+	1.44494i
$749$		0			0
$750$		0			0
$751$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$751$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$752$		0			0
$753$	−0.230465	+	0.137696i	−0.230465	+	0.137696i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$757$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$758$	0.0186541	+	0.0233915i	0.0186541	+	0.0233915i
$759$		0			0
$760$		0			0
$761$	0.0401373	−	0.0802522i	0.0401373	−	0.0802522i	−0.873408	−	0.486989i	$-0.838095\pi$
$761$	0.0401373	−	0.0802522i	0.0401373	−	0.0802522i	0.913545	+	0.406737i	$0.133333\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	0.179639	+	0.199510i	0.179639	+	0.199510i
$769$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	−0.900969	−	0.433884i	$-0.857143\pi$
$769$	−0.535628	−	1.36476i	−0.535628	−	1.36476i	0.365341	−	0.930874i	$-0.380952\pi$
$770$		0			0
$771$	−0.501867	−	0.154805i	−0.501867	−	0.154805i
$772$	−0.382046	−	0.228262i	−0.382046	−	0.228262i
$773$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$773$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$774$	−0.620904	−	0.689583i	−0.620904	−	0.689583i
$775$		0			0
$776$	−1.14660	+	0.103196i	−1.14660	+	0.103196i
$777$		0			0
$778$		0			0
$779$	−0.343849	+	0.0206005i	−0.343849	+	0.0206005i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.712376	−	0.701798i	0.712376	−	0.701798i
$785$		0			0
$786$	0.0567841	−	0.122571i	0.0567841	−	0.122571i
$787$	−0.322371	−	1.94127i	−0.322371	−	1.94127i	−0.337330	−	0.941386i	$-0.609524\pi$
$787$	−0.322371	−	1.94127i	−0.322371	−	1.94127i	0.0149594	−	0.999888i	$-0.495238\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.750708	+	0.545421i	0.750708	+	0.545421i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$797$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$798$		0			0
$799$		0			0
$800$	0.251587	+	0.967835i	0.251587	+	0.967835i
$801$	0.777212	−	0.291693i	0.777212	−	0.291693i
$802$	−0.148859	−	1.98638i	−0.148859	−	1.98638i
$803$	−1.20573	−	0.580650i	−1.20573	−	0.580650i
$804$	−0.485034	−	0.0731071i	−0.485034	−	0.0731071i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.84238	+	0.691456i	1.84238	+	0.691456i	0.983930	+	0.178557i	$0.0571429\pi$
$809$	1.84238	+	0.691456i	1.84238	+	0.691456i	0.858449	+	0.512899i	$0.171429\pi$
$810$		0			0
$811$	0.204489	+	1.94558i	0.204489	+	1.94558i	0.309017	+	0.951057i	$0.400000\pi$
$811$	0.204489	+	1.94558i	0.204489	+	1.94558i	−0.104528	+	0.994522i	$0.533333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.165847	+	0.510425i	−0.165847	+	0.510425i
$817$	−1.01348	+	0.279703i	−1.01348	+	0.279703i
$818$	1.59996	+	1.16244i	1.59996	+	1.16244i
$819$		0			0
$820$		0			0
$821$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$821$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$822$	0.450663	+	0.287895i	0.450663	+	0.287895i
$823$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$823$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$824$		0			0
$825$	−0.120089	−	0.240110i	−0.120089	−	0.240110i
$826$		0			0
$827$	−0.290805	+	1.75119i	−0.290805	+	1.75119i	0.309017	+	0.951057i	$0.400000\pi$
$827$	−0.290805	+	1.75119i	−0.290805	+	1.75119i	−0.599822	+	0.800134i	$0.704762\pi$
$828$		0			0
$829$		0			0		−0.193256	−	0.981148i	$-0.561905\pi$
$829$		0			0		0.193256	+	0.981148i	$0.438095\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.92706	+	0.531836i	1.92706	+	0.531836i
$834$	−0.151520	−	0.124587i	−0.151520	−	0.124587i
$835$		0			0
$836$	0.933179	−	0.484305i	0.933179	−	0.484305i
$837$		0			0
$838$	−1.86493	−	0.167847i	−1.86493	−	0.167847i
$839$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$839$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$840$		0			0
$841$	0.791071	+	0.611724i	0.791071	+	0.611724i
$842$		0			0
$843$	−0.302771	+	0.193418i	−0.302771	+	0.193418i
$844$	1.06209	+	0.293118i	1.06209	+	0.293118i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	0.00538612	+	0.0397619i	0.00538612	+	0.0397619i
$850$	−1.42411	+	1.40297i	−1.42411	+	1.40297i
$851$		0			0
$852$		0			0
$853$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$853$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$854$		0			0
$855$		0			0
$856$	−1.37965	+	1.44300i	−1.37965	+	1.44300i
$857$	−1.32072	−	0.407389i	−1.32072	−	0.407389i	−0.447313	−	0.894377i	$-0.647619\pi$
$857$	−1.32072	−	0.407389i	−1.32072	−	0.407389i	−0.873408	+	0.486989i	$0.838095\pi$
$858$		0			0
$859$	0.503174			0.503174			0.251587	−	0.967835i	$-0.419048\pi$
$859$	0.503174			0.503174			0.251587	+	0.967835i	$0.419048\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$863$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$864$	−0.0694769	+	0.512899i	−0.0694769	+	0.512899i
$865$		0			0
$866$	0.00937930	+	0.0892381i	0.00937930	+	0.0892381i
$867$	−0.786860	+	0.167252i	−0.786860	+	0.167252i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−0.761003	−	0.749702i	−0.761003	−	0.749702i
$874$		0			0
$875$		0			0
$876$	−0.0161190	−	0.358917i	−0.0161190	−	0.358917i
$877$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$877$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.432354	−	1.89427i	−0.432354	−	1.89427i	−0.447313	−	0.894377i	$-0.647619\pi$
$881$	−0.432354	−	1.89427i	−0.432354	−	1.89427i	0.0149594	−	0.999888i	$-0.495238\pi$
$882$	0.924190	+	0.0831786i	0.924190	+	0.0831786i
$883$	−0.726561	−	1.17575i	−0.726561	−	1.17575i	−0.978148	−	0.207912i	$-0.933333\pi$
$883$	−0.726561	−	1.17575i	−0.726561	−	1.17575i	0.251587	−	0.967835i	$-0.419048\pi$
$884$		0			0
$885$		0			0
$886$	1.86912	+	0.111981i	1.86912	+	0.111981i
$887$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$887$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	0.0589599	+	0.786766i	0.0589599	+	0.786766i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.476167	+	1.83178i	−0.476167	+	1.83178i
$899$		0			0
$900$	−0.534130	+	0.758783i	−0.534130	+	0.758783i
$901$		0			0
$902$	−0.0633176	−	0.321459i	−0.0633176	−	0.321459i
$903$		0			0
$904$	−0.208481	+	0.641640i	−0.208481	+	0.641640i
$905$		0			0
$906$		0			0
$907$	0.191249	−	1.41186i	0.191249	−	1.41186i	−0.599822	−	0.800134i	$-0.704762\pi$
$907$	0.191249	−	1.41186i	0.191249	−	1.41186i	0.791071	−	0.611724i	$-0.209524\pi$
$908$	−1.53378	+	1.26115i	−1.53378	+	1.26115i
$909$		0			0
$910$		0			0
$911$		0			0		−0.550897	−	0.834573i	$-0.685714\pi$
$911$		0			0		0.550897	+	0.834573i	$0.314286\pi$
$912$	0.233212	+	0.159001i	0.233212	+	0.159001i
$913$	−0.579161	−	1.61626i	−0.579161	−	1.61626i
$914$	1.39185	−	0.670278i	1.39185	−	0.670278i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.957416	+	0.392386i	−0.957416	+	0.392386i
$919$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$919$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$920$		0			0
$921$	0.0820859	−	0.416745i	0.0820859	−	0.416745i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−0.208683	−	0.0125025i	−0.208683	−	0.0125025i	−0.0448648	−	0.998993i	$-0.514286\pi$
$929$	−0.208683	−	0.0125025i	−0.208683	−	0.0125025i	−0.163818	+	0.986491i	$0.552381\pi$
$930$		0			0
$931$	0.552687	−	0.894377i	0.552687	−	0.894377i
$932$	1.11004	−	1.48073i	1.11004	−	1.48073i
$933$		0			0
$934$	1.44973	+	1.34515i	1.44973	+	1.34515i
$935$		0			0
$936$		0			0
$937$	−1.49722	+	1.15778i	−1.49722	+	1.15778i	−0.550897	+	0.834573i	$0.685714\pi$
$937$	−1.49722	+	1.15778i	−1.49722	+	1.15778i	−0.946327	+	0.323210i	$0.895238\pi$
$938$		0			0
$939$	0.0541022	−	0.514748i	0.0541022	−	0.514748i
$940$		0			0
$941$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$941$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$942$		0			0
$943$		0			0
$944$	−1.02983	−	0.615296i	−1.02983	−	0.615296i
$945$		0			0
$946$	−0.393025	−	0.919528i	−0.393025	−	0.919528i
$947$	−1.29320			−1.29320			−0.646600	−	0.762830i	$-0.723810\pi$
$947$	−1.29320			−1.29320			−0.646600	+	0.762830i	$0.723810\pi$
$948$		0			0
$949$		0			0
$950$	0.498210	+	0.925830i	0.498210	+	0.925830i
$951$		0			0
$952$		0			0
$953$	−0.195726	+	1.86221i	−0.195726	+	1.86221i	0.251587	+	0.967835i	$0.419048\pi$
$953$	−0.195726	+	1.86221i	−0.195726	+	1.86221i	−0.447313	+	0.894377i	$0.647619\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.525684	−	0.850680i	0.525684	−	0.850680i
$962$		0			0
$963$	−1.84921	−	0.110789i	−1.84921	−	0.110789i
$964$	1.49537	−	0.179825i	1.49537	−	0.179825i
$965$		0			0
$966$		0			0
$967$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$967$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$968$	0.575617	+	0.817719i	0.575617	+	0.817719i
$969$	−0.0421673	+	0.562684i	−0.0421673	+	0.562684i
$970$		0			0
$971$	0.240986	−	1.22347i	0.240986	−	1.22347i	−0.646600	−	0.762830i	$-0.723810\pi$
$971$	0.240986	−	1.22347i	0.240986	−	1.22347i	0.887586	−	0.460642i	$-0.152381\pi$
$972$	−0.614677	+	0.392671i	−0.614677	+	0.392671i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.130540	+	0.0727854i	−0.130540	+	0.0727854i	−0.550897	−	0.834573i	$-0.685714\pi$
$977$	−0.130540	+	0.0727854i	−0.130540	+	0.0727854i	0.420357	+	0.907359i	$0.361905\pi$
$978$	0.407675	−	0.196326i	0.407675	−	0.196326i
$979$	0.894226	−	0.0267632i	0.894226	−	0.0267632i
$980$		0			0
$981$		0			0
$982$	1.44536	+	0.643515i	1.44536	+	0.643515i
$983$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$983$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$984$	0.0679412	−	0.0558643i	0.0679412	−	0.0558643i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$991$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$992$		0			0
$993$	0.00790312	−	0.00143420i	0.00790312	−	0.00143420i
$994$		0			0
$995$		0			0
$996$	0.308422	−	0.342537i	0.308422	−	0.342537i
$997$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$997$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$998$	−1.15072	+	0.0344397i	−1.15072	+	0.0344397i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.339.1	yes	48
8.3	odd	2	CM	3784.1.em.b.339.1	yes	48
11.5	even	5		3784.1.em.a.2403.1	yes	48
43.17	even	21		3784.1.em.a.1307.1	✓	48
88.27	odd	10		3784.1.em.a.2403.1	yes	48
344.275	odd	42		3784.1.em.a.1307.1	✓	48
473.60	even	105	inner	3784.1.em.b.3371.1	yes	48
3784.3371	odd	210	inner	3784.1.em.b.3371.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.1307.1	✓	48	43.17	even	21
3784.1.em.a.1307.1	✓	48	344.275	odd	42
3784.1.em.a.2403.1	yes	48	11.5	even	5
3784.1.em.a.2403.1	yes	48	88.27	odd	10
3784.1.em.b.339.1	yes	48	1.1	even	1	trivial
3784.1.em.b.339.1	yes	48	8.3	odd	2	CM
3784.1.em.b.3371.1	yes	48	473.60	even	105	inner
3784.1.em.b.3371.1	yes	48	3784.3371	odd	210	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3784 = 2^{3} \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3784.em (of order \(210\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(0.858449 + 0.512899i) q^{2} +(-0.254057 + 0.0867710i) q^{3} +(0.473869 + 0.880596i) q^{4} +(-0.262600 - 0.0558173i) q^{6} +(-0.0448648 + 0.998993i) q^{8} +(-0.734055 + 0.567635i) q^{9} +O(q^{10})\)	\(q+(0.858449 + 0.512899i) q^{2} +(-0.254057 + 0.0867710i) q^{3} +(0.473869 + 0.880596i) q^{4} +(-0.262600 - 0.0558173i) q^{6} +(-0.0448648 + 0.998993i) q^{8} +(-0.734055 + 0.567635i) q^{9} +(-0.946327 + 0.323210i) q^{11} +(-0.196800 - 0.182604i) q^{12} +(-0.550897 + 0.834573i) q^{16} +(-1.99553 - 0.119555i) q^{17} +(-0.921288 + 0.110789i) q^{18} +(-0.354658 + 0.989743i) q^{19} +(-0.978148 - 0.207912i) q^{22} +(-0.0752854 - 0.257694i) q^{24} +(0.193256 - 0.981148i) q^{25} +(0.285135 - 0.431961i) q^{27} +(-0.900969 + 0.433884i) q^{32} +(0.212376 - 0.164228i) q^{33} +(-1.65174 - 1.12614i) q^{34} +(-0.847702 - 0.377421i) q^{36} +(-0.812094 + 0.667740i) q^{38} +(0.128769 + 0.301270i) q^{41} +(0.575617 + 0.817719i) q^{43} +(-0.733052 - 0.680173i) q^{44} +(0.0675426 - 0.259831i) q^{48} +(-0.978148 - 0.207912i) q^{49} +(0.669131 - 0.743145i) q^{50} +(0.517352 - 0.142780i) q^{51} +(0.466327 - 0.224571i) q^{54} +(0.00422240 - 0.282225i) q^{57} +(0.0538218 + 1.19844i) q^{59} +(-0.995974 - 0.0896393i) q^{64} +(0.266546 - 0.0320534i) q^{66} +(1.50961 - 1.02924i) q^{67} +(-0.840338 - 1.81391i) q^{68} +(-0.534130 - 0.758783i) q^{72} +(0.953345 + 0.939189i) q^{73} +(0.0360371 + 0.266037i) q^{75} +(-1.03962 + 0.156698i) q^{76} +(0.198495 - 0.763594i) q^{81} +(-0.0439796 + 0.324671i) q^{82} +(0.0256838 + 1.71671i) q^{83} +(0.0747301 + 0.997204i) q^{86} +(-0.280427 - 0.959875i) q^{88} +(-0.854881 - 0.263696i) q^{89} +(0.191249 - 0.188409i) q^{96} +(0.154534 + 1.14082i) q^{97} +(-0.733052 - 0.680173i) q^{98} +(0.511191 - 0.774422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

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