LMFDB - Embedded newform 3784.1.em.b.971.1

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			971.1
Root			$0.999552 + 0.0299155i$ of defining polynomial
Character	$\chi$	$=$	3784.971
Dual form			3784.1.em.b.2611.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.983930 - 0.178557i) q^{2} +(0.0251627 - 0.0861293i) q^{3} +(0.936235 - 0.351375i) q^{4} +(0.00937930 - 0.0892381i) q^{6} +(0.858449 - 0.512899i) q^{8} +(0.835936 + 0.534016i) q^{9} +O(q^{10})$	\(q+(0.983930 - 0.178557i) q^{2} +(0.0251627 - 0.0861293i) q^{3} +(0.936235 - 0.351375i) q^{4} +(0.00937930 - 0.0892381i) q^{6} +(0.858449 - 0.512899i) q^{8} +(0.835936 + 0.534016i) q^{9} +(-0.280427 + 0.959875i) q^{11} +(-0.00670551 - 0.0894788i) q^{12} +(0.753071 - 0.657939i) q^{16} +(-0.298548 - 1.51571i) q^{17} +(0.917854 + 0.376172i) q^{18} +(-0.327049 - 0.0195940i) q^{19} +(-0.104528 + 0.994522i) q^{22} +(-0.0225748 - 0.0868435i) q^{24} +(0.971490 - 0.237080i) q^{25} +(0.134602 - 0.117598i) q^{27} +(0.623490 - 0.781831i) q^{32} +(0.0756171 + 0.0483060i) q^{33} +(-0.564391 - 1.43805i) q^{34} +(0.970272 + 0.206238i) q^{36} +(-0.325292 + 0.0391178i) q^{38} +(-0.161032 + 1.18879i) q^{41} +(-0.999552 - 0.0299155i) q^{43} +(0.0747301 + 0.997204i) q^{44} +(-0.0377185 - 0.0814170i) q^{48} +(-0.104528 + 0.994522i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-0.138059 - 0.0124256i) q^{51} +(0.111441 - 0.139742i) q^{54} +(-0.00991705 + 0.0276755i) q^{57} +(1.35819 + 0.811480i) q^{59} +(0.473869 - 0.880596i) q^{64} +(0.0830272 + 0.0340278i) q^{66} +(-0.714715 + 1.82106i) q^{67} +(-0.812094 - 1.31416i) q^{68} +(0.991505 + 0.0296746i) q^{72} +(1.05170 - 1.49405i) q^{73} +(0.00402571 - 0.0896393i) q^{75} +(-0.313080 + 0.0965724i) q^{76} +(0.410231 + 0.885501i) q^{81} +(0.0538218 + 1.19844i) q^{82} +(-0.663818 - 1.85252i) q^{83} +(-0.988831 + 0.149042i) q^{86} +(0.251587 + 0.967835i) q^{88} +(-1.56378 - 1.06617i) q^{89} +(-0.0516499 - 0.0733737i) q^{96} +(0.0896895 - 1.99709i) q^{97} +(0.0747301 + 0.997204i) q^{98} +(-0.747008 + 0.652641i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{4}{21}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-1$

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 $

$2$	0.983930	−	0.178557i	0.983930	−	0.178557i
$2$	0.983930	−	0.178557i	0.983930	−	0.178557i
$3$	0.0251627	−	0.0861293i	0.0251627	−	0.0861293i	−0.946327	−	0.323210i	$-0.895238\pi$
$3$	0.0251627	−	0.0861293i	0.0251627	−	0.0861293i	0.971490	+	0.237080i	$0.0761905\pi$
$4$	0.936235	−	0.351375i	0.936235	−	0.351375i
$5$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$5$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$6$	0.00937930	−	0.0892381i	0.00937930	−	0.0892381i
$7$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$7$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$8$	0.858449	−	0.512899i	0.858449	−	0.512899i
$9$	0.835936	+	0.534016i	0.835936	+	0.534016i
$10$		0			0
$11$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$11$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$12$	−0.00670551	−	0.0894788i	−0.00670551	−	0.0894788i
$13$		0			0		0.946327	−	0.323210i	$-0.104762\pi$
$13$		0			0		−0.946327	+	0.323210i	$0.895238\pi$
$14$		0			0
$15$		0			0
$16$	0.753071	−	0.657939i	0.753071	−	0.657939i
$17$	−0.298548	−	1.51571i	−0.298548	−	1.51571i	−0.772417	−	0.635116i	$-0.780952\pi$
$17$	−0.298548	−	1.51571i	−0.298548	−	1.51571i	0.473869	−	0.880596i	$-0.342857\pi$
$18$	0.917854	+	0.376172i	0.917854	+	0.376172i
$19$	−0.327049	−	0.0195940i	−0.327049	−	0.0195940i	−0.104528	−	0.994522i	$-0.533333\pi$
$19$	−0.327049	−	0.0195940i	−0.327049	−	0.0195940i	−0.222521	+	0.974928i	$0.571429\pi$
$20$		0			0
$21$		0			0
$22$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$23$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$23$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$24$	−0.0225748	−	0.0868435i	−0.0225748	−	0.0868435i
$25$	0.971490	−	0.237080i	0.971490	−	0.237080i
$26$		0			0
$27$	0.134602	−	0.117598i	0.134602	−	0.117598i
$28$		0			0
$29$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$29$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$30$		0			0
$31$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$31$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$32$	0.623490	−	0.781831i	0.623490	−	0.781831i
$33$	0.0756171	+	0.0483060i	0.0756171	+	0.0483060i
$34$	−0.564391	−	1.43805i	−0.564391	−	1.43805i
$35$		0			0
$36$	0.970272	+	0.206238i	0.970272	+	0.206238i
$37$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$37$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$38$	−0.325292	+	0.0391178i	−0.325292	+	0.0391178i
$39$		0			0
$40$		0			0
$41$	−0.161032	+	1.18879i	−0.161032	+	1.18879i	0.712376	+	0.701798i	$0.247619\pi$
$41$	−0.161032	+	1.18879i	−0.161032	+	1.18879i	−0.873408	+	0.486989i	$0.838095\pi$
$42$		0			0
$43$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$43$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$44$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$45$		0			0
$46$		0			0
$47$		0			0		0.550897	−	0.834573i	$-0.314286\pi$
$47$		0			0		−0.550897	+	0.834573i	$0.685714\pi$
$48$	−0.0377185	−	0.0814170i	−0.0377185	−	0.0814170i
$49$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$50$	0.913545	−	0.406737i	0.913545	−	0.406737i
$51$	−0.138059	−	0.0124256i	−0.138059	−	0.0124256i
$52$		0			0
$53$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$53$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$54$	0.111441	−	0.139742i	0.111441	−	0.139742i
$55$		0			0
$56$		0			0
$57$	−0.00991705	+	0.0276755i	−0.00991705	+	0.0276755i
$58$		0			0
$59$	1.35819	+	0.811480i	1.35819	+	0.811480i	0.992847	−	0.119394i	$-0.0380952\pi$
$59$	1.35819	+	0.811480i	1.35819	+	0.811480i	0.365341	+	0.930874i	$0.380952\pi$
$60$		0			0
$61$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$61$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$62$		0			0
$63$		0			0
$64$	0.473869	−	0.880596i	0.473869	−	0.880596i
$65$		0			0
$66$	0.0830272	+	0.0340278i	0.0830272	+	0.0340278i
$67$	−0.714715	+	1.82106i	−0.714715	+	1.82106i	−0.163818	+	0.986491i	$0.552381\pi$
$67$	−0.714715	+	1.82106i	−0.714715	+	1.82106i	−0.550897	+	0.834573i	$0.685714\pi$
$68$	−0.812094	−	1.31416i	−0.812094	−	1.31416i
$69$		0			0
$70$		0			0
$71$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$71$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$72$	0.991505	+	0.0296746i	0.991505	+	0.0296746i
$73$	1.05170	−	1.49405i	1.05170	−	1.49405i	0.193256	−	0.981148i	$-0.438095\pi$
$73$	1.05170	−	1.49405i	1.05170	−	1.49405i	0.858449	−	0.512899i	$-0.171429\pi$
$74$		0			0
$75$	0.00402571	−	0.0896393i	0.00402571	−	0.0896393i
$76$	−0.313080	+	0.0965724i	−0.313080	+	0.0965724i
$77$		0			0
$78$		0			0
$79$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$79$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$80$		0			0
$81$	0.410231	+	0.885501i	0.410231	+	0.885501i
$82$	0.0538218	+	1.19844i	0.0538218	+	1.19844i
$83$	−0.663818	−	1.85252i	−0.663818	−	1.85252i	−0.500000	−	0.866025i	$-0.666667\pi$
$83$	−0.663818	−	1.85252i	−0.663818	−	1.85252i	−0.163818	−	0.986491i	$-0.552381\pi$
$84$		0			0
$85$		0			0
$86$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$87$		0			0
$88$	0.251587	+	0.967835i	0.251587	+	0.967835i
$89$	−1.56378	−	1.06617i	−1.56378	−	1.06617i	−0.963963	−	0.266037i	$-0.914286\pi$
$89$	−1.56378	−	1.06617i	−1.56378	−	1.06617i	−0.599822	−	0.800134i	$-0.704762\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	−0.0516499	−	0.0733737i	−0.0516499	−	0.0733737i
$97$	0.0896895	−	1.99709i	0.0896895	−	1.99709i	0.0149594	−	0.999888i	$-0.495238\pi$
$97$	0.0896895	−	1.99709i	0.0896895	−	1.99709i	0.0747301	−	0.997204i	$-0.476190\pi$
$98$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$99$	−0.747008	+	0.652641i	−0.747008	+	0.652641i
$100$	0.826239	−	0.563320i	0.826239	−	0.563320i
$101$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$101$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$102$	−0.138059	+	0.0124256i	−0.138059	+	0.0124256i
$103$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$103$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.267104	−	0.279369i	−0.267104	−	0.279369i	0.575617	−	0.817719i	$-0.304762\pi$
$107$	−0.267104	−	0.279369i	−0.267104	−	0.279369i	−0.842721	+	0.538351i	$0.819048\pi$
$108$	0.0846978	−	0.157395i	0.0846978	−	0.157395i
$109$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$109$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.98838	+	0.178958i	−1.98838	+	0.178958i	−0.988831	+	0.149042i	$0.952381\pi$
$113$	−1.98838	+	0.178958i	−1.98838	+	0.178958i	−0.999552	+	0.0299155i	$0.990476\pi$
$114$	−0.00481603	+	0.0290015i	−0.00481603	+	0.0290015i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.48126	+	0.555925i	1.48126	+	0.555925i
$119$		0			0
$120$		0			0
$121$	−0.842721	−	0.538351i	−0.842721	−	0.538351i
$122$		0			0
$123$	0.0983373	+	0.0437826i	0.0983373	+	0.0437826i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$127$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$128$	0.309017	−	0.951057i	0.309017	−	0.951057i
$129$	−0.0277280	+	0.0853380i	−0.0277280	+	0.0853380i
$130$		0			0
$131$	−0.757458	−	0.364772i	−0.757458	−	0.364772i	0.0149594	−	0.999888i	$-0.495238\pi$
$131$	−0.757458	−	0.364772i	−0.757458	−	0.364772i	−0.772417	+	0.635116i	$0.780952\pi$
$132$	0.0877689	+	0.0186558i	0.0877689	+	0.0186558i
$133$		0			0
$134$	−0.378066	+	1.91942i	−0.378066	+	1.91942i
$135$		0			0
$136$	−1.03370	−	1.14804i	−1.03370	−	1.14804i
$137$	−0.372484	+	0.871471i	−0.372484	+	0.871471i	0.623490	+	0.781831i	$0.285714\pi$
$137$	−0.372484	+	0.871471i	−0.372484	+	0.871471i	−0.995974	+	0.0896393i	$0.971429\pi$
$138$		0			0
$139$	−0.0219320	+	1.46594i	−0.0219320	+	1.46594i	0.669131	+	0.743145i	$0.266667\pi$
$139$	−0.0219320	+	1.46594i	−0.0219320	+	1.46594i	−0.691063	+	0.722795i	$0.742857\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.980869	−	0.147842i	0.980869	−	0.147842i
$145$		0			0
$146$	0.768031	−	1.65783i	0.768031	−	1.65783i
$147$	0.0830272	+	0.0340278i	0.0830272	+	0.0340278i
$148$		0			0
$149$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$149$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$150$	−0.0120447	−	0.0889176i	−0.0120447	−	0.0889176i
$151$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$151$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$152$	−0.290805	+	0.150923i	−0.290805	+	0.150923i
$153$	0.559847	−	1.42647i	0.559847	−	1.42647i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.447313	−	0.894377i	$-0.647619\pi$
$157$		0			0		0.447313	+	0.894377i	$0.352381\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	0.561751	+	0.798021i	0.561751	+	0.798021i
$163$	1.47208	+	0.940400i	1.47208	+	0.940400i	0.998210	+	0.0598042i	$0.0190476\pi$
$163$	1.47208	+	0.940400i	1.47208	+	0.940400i	0.473869	+	0.880596i	$0.342857\pi$
$164$	0.266946	+	1.16957i	0.266946	+	1.16957i
$165$		0			0
$166$	−0.983930	−	1.70422i	−0.983930	−	1.70422i
$167$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$167$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$168$		0			0
$169$	0.791071	−	0.611724i	0.791071	−	0.611724i
$170$		0			0
$171$	−0.262929	−	0.191029i	−0.262929	−	0.191029i
$172$	−0.946327	+	0.323210i	−0.946327	+	0.323210i
$173$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$173$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$174$		0			0
$175$		0			0
$176$	0.420357	+	0.907359i	0.420357	+	0.907359i
$177$	0.104068	−	0.0965608i	0.104068	−	0.0965608i
$178$	−1.72903	−	0.769812i	−1.72903	−	0.769812i
$179$	−1.54757	−	0.328946i	−1.54757	−	0.328946i	−0.646600	−	0.762830i	$-0.723810\pi$
$179$	−1.54757	−	0.328946i	−1.54757	−	0.328946i	−0.900969	+	0.433884i	$0.857143\pi$
$180$		0			0
$181$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$181$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.53861	+	0.138478i	1.53861	+	0.138478i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$191$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$192$	−0.0639213	−	0.0629721i	−0.0639213	−	0.0629721i
$193$	−1.77298	−	0.321748i	−1.77298	−	0.321748i	−0.809017	−	0.587785i	$-0.800000\pi$
$193$	−1.77298	−	0.321748i	−1.77298	−	0.321748i	−0.963963	+	0.266037i	$0.914286\pi$
$194$	−0.268346	−	1.98101i	−0.268346	−	1.98101i
$195$		0			0
$196$	0.251587	+	0.967835i	0.251587	+	0.967835i
$197$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$197$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$198$	−0.618470	+	0.775537i	−0.618470	+	0.775537i
$199$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$199$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$200$	0.712376	−	0.701798i	0.712376	−	0.701798i
$201$	0.138863	+	0.107381i	0.138863	+	0.107381i
$202$		0			0
$203$		0			0
$204$	−0.133622	+	0.0368773i	−0.133622	+	0.0368773i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.110521	−	0.308432i	0.110521	−	0.308432i
$210$		0			0
$211$	−1.45187	−	0.400690i	−1.45187	−	0.400690i	−0.550897	−	0.834573i	$-0.685714\pi$
$211$	−1.45187	−	0.400690i	−1.45187	−	0.400690i	−0.900969	+	0.433884i	$0.857143\pi$
$212$		0			0
$213$		0			0
$214$	−0.312695	−	0.227186i	−0.312695	−	0.227186i
$215$		0			0
$216$	0.0552327	−	0.169989i	0.0552327	−	0.169989i
$217$		0			0
$218$		0			0
$219$	−0.102218	−	0.128177i	−0.102218	−	0.128177i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$223$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$224$		0			0
$225$	0.938708	+	0.320607i	0.938708	+	0.320607i
$226$	−1.92447	+	0.531121i	−1.92447	+	0.531121i
$227$	−1.79785	−	0.438743i	−1.79785	−	0.438743i	−0.809017	−	0.587785i	$-0.800000\pi$
$227$	−1.79785	−	0.438743i	−1.79785	−	0.438743i	−0.988831	+	0.149042i	$0.952381\pi$
$228$	0.000439786		0.0293954i	0.000439786		0.0293954i
$229$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$229$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.933179	+	1.51010i	0.933179	+	1.51010i	0.858449	+	0.512899i	$0.171429\pi$
$233$	0.933179	+	1.51010i	0.933179	+	1.51010i	0.0747301	+	0.997204i	$0.476190\pi$
$234$		0			0
$235$		0			0
$236$	1.55672	+	0.282502i	1.55672	+	0.282502i
$237$		0			0
$238$		0			0
$239$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$239$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$240$		0			0
$241$	1.01317	+	0.940084i	1.01317	+	0.940084i	0.998210	−	0.0598042i	$-0.0190476\pi$
$241$	1.01317	+	0.940084i	1.01317	+	0.940084i	0.0149594	+	0.999888i	$0.495238\pi$
$242$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$243$	0.263331	−	0.0396907i	0.263331	−	0.0396907i
$244$		0			0
$245$		0			0
$246$	0.104575	+	0.0255202i	0.104575	+	0.0255202i
$247$		0			0
$248$		0			0
$249$	−0.176259	+	0.0105599i	−0.176259	+	0.0105599i
$250$		0			0
$251$	0.104528	+	0.994522i	0.104528	+	0.994522i	0.913545	+	0.406737i	$0.133333\pi$
$251$	0.104528	+	0.994522i	0.104528	+	0.994522i	−0.809017	+	0.587785i	$0.800000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.134233	−	0.990950i	0.134233	−	0.990950i
$257$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i	−0.978148	−	0.207912i	$-0.933333\pi$
$257$	−0.0646021	+	0.198825i	−0.0646021	+	0.198825i	0.913545	+	0.406737i	$0.133333\pi$
$258$	−0.0120447	+	0.0889176i	−0.0120447	+	0.0889176i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−0.810418	−	0.223661i	−0.810418	−	0.223661i
$263$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$263$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$264$	0.0896895	+	0.00268430i	0.0896895	+	0.00268430i
$265$		0			0
$266$		0			0
$267$	−0.131177	+	0.107860i	−0.131177	+	0.107860i
$268$	−0.0292650	+	1.95608i	−0.0292650	+	1.95608i
$269$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$269$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$270$		0			0
$271$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$271$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$272$	−1.22207	−	0.945012i	−1.22207	−	0.945012i
$273$		0			0
$274$	−0.210891	+	0.923976i	−0.210891	+	0.923976i
$275$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$276$		0			0
$277$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$277$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$278$	0.240174	+	1.44630i	0.240174	+	1.44630i
$279$		0			0
$280$		0			0
$281$	1.30158	+	1.28225i	1.30158	+	1.28225i	0.936235	+	0.351375i	$0.114286\pi$
$281$	1.30158	+	1.28225i	1.30158	+	1.28225i	0.365341	+	0.930874i	$0.380952\pi$
$282$		0			0
$283$	−1.92128	+	0.468865i	−1.92128	+	0.468865i	−0.925304	+	0.379225i	$0.876190\pi$
$283$	−1.92128	+	0.468865i	−1.92128	+	0.468865i	−0.995974	+	0.0896393i	$0.971429\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	0.938708	−	0.320607i	0.938708	−	0.320607i
$289$	−1.28295	+	0.525801i	−1.28295	+	0.525801i
$290$		0			0
$291$	−0.169751	−	0.0579770i	−0.169751	−	0.0579770i
$292$	0.459672	−	1.76832i	0.459672	−	1.76832i
$293$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$293$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$294$	0.0877689	+	0.0186558i	0.0877689	+	0.0186558i
$295$		0			0
$296$		0			0
$297$	0.0751333	+	0.162178i	0.0751333	+	0.162178i
$298$		0			0
$299$		0			0
$300$	−0.0277280	−	0.0853380i	−0.0277280	−	0.0853380i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−0.259183	+	0.200423i	−0.259183	+	0.200423i
$305$		0			0
$306$	0.296145	−	1.50351i	0.296145	−	1.50351i
$307$	0.842721	+	1.45964i	0.842721	+	1.45964i	0.887586	+	0.460642i	$0.152381\pi$
$307$	0.842721	+	1.45964i	0.842721	+	1.45964i	−0.0448648	+	0.998993i	$0.514286\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$311$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$312$		0			0
$313$	−1.04714	+	1.69451i	−1.04714	+	1.69451i	−0.447313	+	0.894377i	$0.647619\pi$
$313$	−1.04714	+	1.69451i	−1.04714	+	1.69451i	−0.599822	+	0.800134i	$0.704762\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$317$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−0.0307829	+	0.0159758i	−0.0307829	+	0.0159758i
$322$		0			0
$323$	0.0679412	+	0.501562i	0.0679412	+	0.501562i
$324$	0.695215	+	0.684892i	0.695215	+	0.684892i
$325$		0			0
$326$	1.61634	+	0.662437i	1.61634	+	0.662437i
$327$		0			0
$328$	0.471490	+	1.10311i	0.471490	+	1.10311i
$329$		0			0
$330$		0			0
$331$	−0.644687	−	0.198860i	−0.644687	−	0.198860i	−0.0448648	−	0.998993i	$-0.514286\pi$
$331$	−0.644687	−	0.198860i	−0.644687	−	0.198860i	−0.599822	+	0.800134i	$0.704762\pi$
$332$	−1.27242	−	1.50114i	−1.27242	−	1.50114i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	1.30011	+	1.44392i	1.30011	+	1.44392i	0.826239	+	0.563320i	$0.190476\pi$
$337$	1.30011	+	1.44392i	1.30011	+	1.44392i	0.473869	+	0.880596i	$0.342857\pi$
$338$	0.669131	−	0.743145i	0.669131	−	0.743145i
$339$	−0.0346195	+	0.175761i	−0.0346195	+	0.175761i
$340$		0			0
$341$		0			0
$342$	−0.292813	−	0.141011i	−0.292813	−	0.141011i
$343$		0			0
$344$	−0.873408	+	0.486989i	−0.873408	+	0.486989i
$345$		0			0
$346$		0			0
$347$	−0.673452	−	1.87940i	−0.673452	−	1.87940i	−0.393025	−	0.919528i	$-0.628571\pi$
$347$	−0.673452	−	1.87940i	−0.673452	−	1.87940i	−0.280427	−	0.959875i	$-0.590476\pi$
$348$		0			0
$349$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$349$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$350$		0			0
$351$		0			0
$352$	0.575617	+	0.817719i	0.575617	+	0.817719i
$353$	−0.638184	−	1.62607i	−0.638184	−	1.62607i	−0.772417	−	0.635116i	$-0.780952\pi$
$353$	−0.638184	−	1.62607i	−0.638184	−	1.62607i	0.134233	−	0.990950i	$-0.457143\pi$
$354$	0.0851538	−	0.113591i	0.0851538	−	0.113591i
$355$		0			0
$356$	−1.83870	−	0.448711i	−1.83870	−	0.448711i
$357$		0			0
$358$	−1.58143	−	0.0473305i	−1.58143	−	0.0473305i
$359$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$359$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$360$		0			0
$361$	−0.886270	−	0.106578i	−0.886270	−	0.106578i
$362$		0			0
$363$	−0.0675728	+	0.0590366i	−0.0675728	+	0.0590366i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.447313	−	0.894377i	$-0.352381\pi$
$367$		0			0		−0.447313	+	0.894377i	$0.647619\pi$
$368$		0			0
$369$	−0.769444	+	0.907756i	−0.769444	+	0.907756i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$373$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$374$	1.53861	−	0.138478i	1.53861	−	0.138478i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.265158	−	0.620369i	0.265158	−	0.620369i	−0.733052	−	0.680173i	$-0.761905\pi$
$379$	0.265158	−	0.620369i	0.265158	−	0.620369i	0.998210	+	0.0598042i	$0.0190476\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$383$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$384$	−0.0741381	−	0.0505465i	−0.0741381	−	0.0505465i
$385$		0			0
$386$	−1.80194			−1.80194
$387$	−0.819586	−	0.558785i	−0.819586	−	0.558785i
$388$	−0.617757	−	1.90126i	−0.617757	−	1.90126i
$389$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$389$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$390$		0			0
$391$		0			0
$392$	0.420357	+	0.907359i	0.420357	+	0.907359i
$393$	−0.0504772	+	0.0560606i	−0.0504772	+	0.0560606i
$394$		0			0
$395$		0			0
$396$	−0.470053	+	0.873505i	−0.470053	+	0.873505i
$397$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$397$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$398$		0			0
$399$		0			0
$400$	0.575617	−	0.817719i	0.575617	−	0.817719i
$401$	−0.947313	−	0.0283520i	−0.947313	−	0.0283520i	−0.447313	−	0.894377i	$-0.647619\pi$
$401$	−0.947313	−	0.0283520i	−0.947313	−	0.0283520i	−0.500000	+	0.866025i	$0.666667\pi$
$402$	0.155805	+	0.0808601i	0.155805	+	0.0808601i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.124890	+	0.0601438i	−0.124890	+	0.0601438i
$409$	0.905632	−	1.68295i	0.905632	−	1.68295i	0.193256	−	0.981148i	$-0.438095\pi$
$409$	0.905632	−	1.68295i	0.905632	−	1.68295i	0.712376	−	0.701798i	$-0.247619\pi$
$410$		0			0
$411$	0.0656865	+	0.0540103i	0.0656865	+	0.0540103i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.125708	+	0.0387759i	0.125708	+	0.0387759i
$418$	0.0536726	−	0.323210i	0.0536726	−	0.323210i
$419$	−0.490094	+	0.614559i	−0.490094	+	0.614559i	−0.963963	−	0.266037i	$-0.914286\pi$
$419$	−0.490094	+	0.614559i	−0.490094	+	0.614559i	0.473869	+	0.880596i	$0.342857\pi$
$420$		0			0
$421$		0			0		0.772417	−	0.635116i	$-0.219048\pi$
$421$		0			0		−0.772417	+	0.635116i	$0.780952\pi$
$422$	−1.50008	−	0.135010i	−1.50008	−	0.135010i
$423$		0			0
$424$		0			0
$425$	−0.649382	−	1.40172i	−0.649382	−	1.40172i
$426$		0			0
$427$		0			0
$428$	−0.348235	−	0.167701i	−0.348235	−	0.167701i
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	0.0239924	−	0.177119i	0.0239924	−	0.177119i
$433$	1.35819	−	1.05027i	1.35819	−	1.05027i	0.365341	−	0.930874i	$-0.380952\pi$
$433$	1.35819	−	1.05027i	1.35819	−	1.05027i	0.992847	−	0.119394i	$-0.0380952\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.123462	−	0.107865i	−0.123462	−	0.107865i
$439$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$439$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$440$		0			0
$441$	−0.618470	+	0.775537i	−0.618470	+	0.775537i
$442$		0			0
$443$	−0.0117588	−	0.785962i	−0.0117588	−	0.785962i	−0.925304	−	0.379225i	$-0.876190\pi$
$443$	−0.0117588	−	0.785962i	−0.0117588	−	0.785962i	0.913545	−	0.406737i	$-0.133333\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.141104	−	0.542815i	−0.141104	−	0.542815i	−0.999552	−	0.0299155i	$-0.990476\pi$
$449$	−0.141104	−	0.542815i	−0.141104	−	0.542815i	0.858449	−	0.512899i	$-0.171429\pi$
$450$	0.980869	+	0.147842i	0.980869	+	0.147842i
$451$	−1.09593	−	0.487939i	−1.09593	−	0.487939i
$452$	−1.79871	+	0.866214i	−1.79871	+	0.866214i
$453$		0			0
$454$	−1.84730	−	0.110674i	−1.84730	−	0.110674i
$455$		0			0
$456$	0.00568146	+	0.0288444i	0.00568146	+	0.0288444i
$457$	1.49537	−	1.30646i	1.49537	−	1.30646i	0.669131	−	0.743145i	$-0.266667\pi$
$457$	1.49537	−	1.30646i	1.49537	−	1.30646i	0.826239	−	0.563320i	$-0.190476\pi$
$458$		0			0
$459$	−0.218430	−	0.168909i	−0.218430	−	0.168909i
$460$		0			0
$461$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$461$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$462$		0			0
$463$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$463$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$464$		0			0
$465$		0			0
$466$	1.18782	+	1.31921i	1.18782	+	1.31921i
$467$	−0.199769	+	1.90068i	−0.199769	+	1.90068i	0.193256	+	0.981148i	$0.438095\pi$
$467$	−0.199769	+	1.90068i	−0.199769	+	1.90068i	−0.393025	+	0.919528i	$0.628571\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.58214			1.58214
$473$	0.309017	−	0.951057i	0.309017	−	0.951057i
$474$		0			0
$475$	−0.322371	+	0.0585016i	−0.322371	+	0.0585016i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$479$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$480$		0			0
$481$		0			0
$482$	1.16475	+	0.744068i	1.16475	+	0.744068i
$483$		0			0
$484$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$485$		0			0
$486$	0.252012	−	0.0860723i	0.252012	−	0.0860723i
$487$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$487$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$488$		0			0
$489$	0.118037	−	0.103126i	0.118037	−	0.103126i
$490$		0			0
$491$	1.55955	+	0.639162i	1.55955	+	0.639162i	0.983930	−	0.178557i	$-0.0571429\pi$
$491$	1.55955	+	0.639162i	1.55955	+	0.639162i	0.575617	+	0.817719i	$0.304762\pi$
$492$	0.107451	+	0.00643754i	0.107451	+	0.00643754i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	−0.171541	+	0.0418625i	−0.171541	+	0.0418625i
$499$	1.74603	−	0.973542i	1.74603	−	0.973542i	0.858449	−	0.512899i	$-0.171429\pi$
$499$	1.74603	−	0.973542i	1.74603	−	0.973542i	0.887586	−	0.460642i	$-0.152381\pi$
$500$		0			0
$501$		0			0
$502$	0.280427	+	0.959875i	0.280427	+	0.959875i
$503$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$503$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−0.0327819	−	0.0835270i	−0.0327819	−	0.0835270i
$508$		0			0
$509$		0			0		−0.978148	−	0.207912i	$-0.933333\pi$
$509$		0			0		0.978148	+	0.207912i	$0.0666667\pi$
$510$		0			0
$511$		0			0
$512$	−0.0448648	−	0.998993i	−0.0448648	−	0.998993i
$513$	−0.0463256	+	0.0358229i	−0.0463256	+	0.0358229i
$514$	−0.0280624	+	0.207165i	−0.0280624	+	0.207165i
$515$		0			0
$516$	0.00402571	+	0.0896393i	0.00402571	+	0.0896393i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.353400	+	0.762830i	0.353400	+	0.762830i	1.00000			$0$
$521$	0.353400	+	0.762830i	0.353400	+	0.762830i	−0.646600	+	0.762830i	$0.723810\pi$
$522$		0			0
$523$	1.05170	−	0.468249i	1.05170	−	0.468249i	0.193256	−	0.981148i	$-0.438095\pi$
$523$	1.05170	−	0.468249i	1.05170	−	0.468249i	0.858449	+	0.512899i	$0.171429\pi$
$524$	−0.837330	−	0.0753611i	−0.837330	−	0.0753611i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	0.0887275	−	0.0133735i	0.0887275	−	0.0133735i
$529$	0.955573	+	0.294755i	0.955573	+	0.294755i
$530$		0			0
$531$	0.702015	+	1.40364i	0.702015	+	1.40364i
$532$		0			0
$533$		0			0
$534$	−0.109810	+	0.129549i	−0.109810	+	0.129549i
$535$		0			0
$536$	0.320476	+	1.92987i	0.320476	+	1.92987i
$537$	−0.0672728	+	0.125014i	−0.0672728	+	0.125014i
$538$		0			0
$539$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$540$		0			0
$541$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$541$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$542$		0			0
$543$		0			0
$544$	−1.37117	−	0.711616i	−1.37117	−	0.711616i
$545$		0			0
$546$		0			0
$547$	−1.58865	+	0.651091i	−1.58865	+	0.651091i	−0.988831	−	0.149042i	$-0.952381\pi$
$547$	−1.58865	+	0.651091i	−1.58865	+	0.651091i	−0.599822	+	0.800134i	$0.704762\pi$
$548$	−0.0425201	+	0.946783i	−0.0425201	+	0.946783i
$549$		0			0
$550$	0.134233	+	0.990950i	0.134233	+	0.990950i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.494561	+	1.38017i	0.494561	+	1.38017i
$557$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$557$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	0.0506426	−	0.129035i	0.0506426	−	0.129035i
$562$	1.50961	+	1.02924i	1.50961	+	1.02924i
$563$	0.757723	+	0.209118i	0.757723	+	0.209118i	0.623490	−	0.781831i	$-0.285714\pi$
$563$	0.757723	+	0.209118i	0.757723	+	0.209118i	0.134233	+	0.990950i	$0.457143\pi$
$564$		0			0
$565$		0			0
$566$	−1.80668	+	0.804387i	−1.80668	+	0.804387i
$567$		0			0
$568$		0			0
$569$	−0.322838	−	0.458622i	−0.322838	−	0.458622i	0.623490	−	0.781831i	$-0.285714\pi$
$569$	−0.322838	−	0.458622i	−0.322838	−	0.458622i	−0.946327	+	0.323210i	$0.895238\pi$
$570$		0			0
$571$	−0.134659	−	1.79690i	−0.134659	−	1.79690i	−0.500000	−	0.866025i	$-0.666667\pi$
$571$	−0.134659	−	1.79690i	−0.134659	−	1.79690i	0.365341	−	0.930874i	$-0.380952\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	0.866376	−	0.483068i	0.866376	−	0.483068i
$577$	0.893682	−	1.05433i	0.893682	−	1.05433i	−0.104528	−	0.994522i	$-0.533333\pi$
$577$	0.893682	−	1.05433i	0.893682	−	1.05433i	0.998210	−	0.0598042i	$-0.0190476\pi$
$578$	−1.16844	+	0.746430i	−1.16844	+	0.746430i
$579$	−0.0723248	+	0.144609i	−0.0723248	+	0.144609i
$580$		0			0
$581$		0			0
$582$	−0.177375	−	0.0267351i	−0.177375	−	0.0267351i
$583$		0			0
$584$	0.136539	−	1.82198i	0.136539	−	1.82198i
$585$		0			0
$586$		0			0
$587$	0.303163	−	1.82561i	0.303163	−	1.82561i	−0.222521	−	0.974928i	$-0.571429\pi$
$587$	0.303163	−	1.82561i	0.303163	−	1.82561i	0.525684	−	0.850680i	$-0.323810\pi$
$588$	0.0896895	+	0.00268430i	0.0896895	+	0.00268430i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.326844	−	0.832784i	−0.326844	−	0.832784i	−0.995974	−	0.0896393i	$-0.971429\pi$
$593$	−0.326844	−	0.832784i	−0.326844	−	0.832784i	0.669131	−	0.743145i	$-0.266667\pi$
$594$	0.102884	+	0.146157i	0.102884	+	0.146157i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$599$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$600$	−0.0425201	−	0.0790155i	−0.0425201	−	0.0790155i
$601$	−0.208481	+	0.641640i	−0.208481	+	0.641640i	0.791071	+	0.611724i	$0.209524\pi$
$601$	−0.208481	+	0.641640i	−0.208481	+	0.641640i	−0.999552	+	0.0299155i	$0.990476\pi$
$602$		0			0
$603$	−1.56993	+	1.14062i	−1.56993	+	1.14062i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		0.193256	−	0.981148i	$-0.438095\pi$
$607$		0			0		−0.193256	+	0.981148i	$0.561905\pi$
$608$	−0.219231	+	0.243481i	−0.219231	+	0.243481i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.0229237	−	1.53222i	0.0229237	−	1.53222i
$613$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$613$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$614$	1.08981	+	1.28570i	1.08981	+	1.28570i
$615$		0			0
$616$		0			0
$617$	1.08949	−	0.164214i	1.08949	−	0.164214i	0.420357	−	0.907359i	$-0.361905\pi$
$617$	1.08949	−	0.164214i	1.08949	−	0.164214i	0.669131	+	0.743145i	$0.266667\pi$
$618$		0			0
$619$	0.787106	−	1.69900i	0.787106	−	1.69900i	0.0747301	−	0.997204i	$-0.476190\pi$
$619$	0.787106	−	1.69900i	0.787106	−	1.69900i	0.712376	−	0.701798i	$-0.247619\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.887586	−	0.460642i	0.887586	−	0.460642i
$626$	−0.727741	+	1.85425i	−0.727741	+	1.85425i
$627$	−0.0237840	−	0.0172801i	−0.0237840	−	0.0172801i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.280427	−	0.959875i	$-0.590476\pi$
$631$		0			0		0.280427	+	0.959875i	$0.409524\pi$
$632$		0			0
$633$	−0.0710439	+	0.114966i	−0.0710439	+	0.114966i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.579195	+	0.877443i	−0.579195	+	0.877443i	−0.999552	−	0.0299155i	$-0.990476\pi$
$641$	−0.579195	+	0.877443i	−0.579195	+	0.877443i	0.420357	+	0.907359i	$0.361905\pi$
$642$	−0.0274356	+	0.0212156i	−0.0274356	+	0.0212156i
$643$	0.675145	+	1.25463i	0.675145	+	1.25463i	0.955573	+	0.294755i	$0.0952381\pi$
$643$	0.675145	+	1.25463i	0.675145	+	1.25463i	−0.280427	+	0.959875i	$0.590476\pi$
$644$		0			0
$645$		0			0
$646$	0.156407	+	0.481371i	0.156407	+	0.481371i
$647$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$647$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$648$	0.806335	+	0.549750i	0.806335	+	0.549750i
$649$	−1.15979	+	1.07613i	−1.15979	+	1.07613i
$650$		0			0
$651$		0			0
$652$	1.70864	+	0.363184i	1.70864	+	0.363184i
$653$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$653$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$654$		0			0
$655$		0			0
$656$	0.660880	+	1.00119i	0.660880	+	1.00119i
$657$	1.67700	−	0.687301i	1.67700	−	0.687301i
$658$		0			0
$659$	1.54711	−	1.05480i	1.54711	−	1.05480i	0.575617	−	0.817719i	$-0.304762\pi$
$659$	1.54711	−	1.05480i	1.54711	−	1.05480i	0.971490	−	0.237080i	$-0.0761905\pi$
$660$		0			0
$661$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$661$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$662$	−0.669834	−	0.0805505i	−0.669834	−	0.0805505i
$663$		0			0
$664$	−1.52001	−	1.24982i	−1.52001	−	1.24982i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.0213134	−	0.0209970i	0.0213134	−	0.0209970i	−0.691063	−	0.722795i	$-0.742857\pi$
$673$	0.0213134	−	0.0209970i	0.0213134	−	0.0209970i	0.712376	+	0.701798i	$0.247619\pi$
$674$	1.53704	+	1.18857i	1.53704	+	1.18857i
$675$	0.102884	−	0.146157i	0.102884	−	0.146157i
$676$	0.525684	−	0.850680i	0.525684	−	0.850680i
$677$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$677$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$678$	−0.00267980	+	0.179118i	−0.00267980	+	0.179118i
$679$		0			0
$680$		0			0
$681$	−0.0830272	+	0.143807i	−0.0830272	+	0.143807i
$682$		0			0
$683$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$683$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$684$	−0.313286	−	0.0864614i	−0.313286	−	0.0864614i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$689$		0			0
$690$		0			0
$691$	−1.33766	+	0.0400347i	−1.33766	+	0.0400347i	−0.691063	−	0.722795i	$-0.742857\pi$
$691$	−1.33766	+	0.0400347i	−1.33766	+	0.0400347i	−0.646600	+	0.762830i	$0.723810\pi$
$692$		0			0
$693$		0			0
$694$	−0.998210	−	1.72895i	−0.998210	−	1.72895i
$695$		0			0
$696$		0			0
$697$	1.84993	−	0.110832i	1.84993	−	0.110832i
$698$		0			0
$699$	0.153545	−	0.0423758i	0.153545	−	0.0423758i
$700$		0			0
$701$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$701$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$702$		0			0
$703$		0			0
$704$	0.712376	+	0.701798i	0.712376	+	0.701798i
$705$		0			0
$706$	−0.918273	−	1.48598i	−0.918273	−	1.48598i
$707$		0			0
$708$	0.0635028	−	0.126970i	0.0635028	−	0.126970i
$709$		0			0		−0.983930	−	0.178557i	$-0.942857\pi$
$709$		0			0		0.983930	+	0.178557i	$0.0571429\pi$
$710$		0			0
$711$		0			0
$712$	−1.88927	−	0.113189i	−1.88927	−	0.113189i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−1.56447	+	0.235806i	−1.56447	+	0.235806i
$717$		0			0
$718$		0			0
$719$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$719$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$720$		0			0
$721$		0			0
$722$	−0.891057	+	0.0533845i	−0.891057	+	0.0533845i
$723$	0.106463	−	0.0636086i	0.106463	−	0.0636086i
$724$		0			0
$725$		0			0
$726$	−0.0559455	+	0.0701535i	−0.0559455	+	0.0701535i
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$		0			0
$729$	−0.127792	+	0.943399i	−0.127792	+	0.943399i
$730$		0			0
$731$	0.253071	+	1.52396i	0.253071	+	1.52396i
$732$		0			0
$733$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$733$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.54757	−	1.19671i	−1.54757	−	1.19671i
$738$	−0.594992	+	1.03056i	−0.594992	+	1.03056i
$739$	1.29295	+	1.12961i	1.29295	+	1.12961i	0.983930	+	0.178557i	$0.0571429\pi$
$739$	1.29295	+	1.12961i	1.29295	+	1.12961i	0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		0.525684	−	0.850680i	$-0.323810\pi$
$743$		0			0		−0.525684	+	0.850680i	$0.676190\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.434364	−	1.90307i	0.434364	−	1.90307i
$748$	1.48916	−	0.410983i	1.48916	−	0.410983i
$749$		0			0
$750$		0			0
$751$		0			0		−0.163818	−	0.986491i	$-0.552381\pi$
$751$		0			0		0.163818	+	0.986491i	$0.447619\pi$
$752$		0			0
$753$	0.0882877	+	0.0160218i	0.0882877	+	0.0160218i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$757$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$758$	0.150126	−	0.657745i	0.150126	−	0.657745i
$759$		0			0
$760$		0			0
$761$	−1.62475	+	0.554918i	−1.62475	+	0.554918i	−0.978148	−	0.207912i	$-0.933333\pi$
$761$	−1.62475	+	0.554918i	−1.62475	+	0.554918i	−0.646600	+	0.762830i	$0.723810\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.0819721	−	0.0364963i	−0.0819721	−	0.0364963i
$769$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	−0.733052	−	0.680173i	$-0.761905\pi$
$769$	−0.109562	+	0.101659i	−0.109562	+	0.101659i	0.623490	+	0.781831i	$0.285714\pi$
$770$		0			0
$771$	0.0154991	+	0.0105671i	0.0154991	+	0.0105671i
$772$	−1.77298	+	0.321748i	−1.77298	+	0.321748i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	−0.906190	−	0.403462i	−0.906190	−	0.403462i
$775$		0			0
$776$	−0.947313	−	1.76040i	−0.947313	−	1.76040i
$777$		0			0
$778$		0			0
$779$	0.0759585	−	0.385637i	0.0759585	−	0.385637i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.575617	+	0.817719i	0.575617	+	0.817719i
$785$		0			0
$786$	−0.0396560	+	0.0641728i	−0.0396560	+	0.0641728i
$787$	0.660880	+	0.881582i	0.660880	+	0.881582i	0.998210	−	0.0598042i	$-0.0190476\pi$
$787$	0.660880	+	0.881582i	0.660880	+	0.881582i	−0.337330	+	0.941386i	$0.609524\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.306529	+	0.943399i	−0.306529	+	0.943399i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$797$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$798$		0			0
$799$		0			0
$800$	0.420357	−	0.907359i	0.420357	−	0.907359i
$801$	−0.737872	−	1.72634i	−0.737872	−	1.72634i
$802$	−0.937152	+	0.141253i	−0.937152	+	0.141253i
$803$	1.13917	+	1.42848i	1.13917	+	1.42848i
$804$	0.167739	+	0.0517406i	0.167739	+	0.0517406i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.433033	−	1.01313i	0.433033	−	1.01313i	−0.550897	−	0.834573i	$-0.685714\pi$
$809$	0.433033	−	1.01313i	0.433033	−	1.01313i	0.983930	−	0.178557i	$-0.0571429\pi$
$810$		0			0
$811$	−0.139886	+	0.155360i	−0.139886	+	0.155360i	−0.809017	−	0.587785i	$-0.800000\pi$
$811$	−0.139886	+	0.155360i	−0.139886	+	0.155360i	0.669131	+	0.743145i	$0.266667\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	−0.112144	+	0.0814773i	−0.112144	+	0.0814773i
$817$	0.326317	+	0.0293690i	0.326317	+	0.0293690i
$818$	0.590576	−	1.81761i	0.590576	−	1.81761i
$819$		0			0
$820$		0			0
$821$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$821$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$822$	0.0742748	+	0.0414136i	0.0742748	+	0.0414136i
$823$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$823$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$824$		0			0
$825$	0.0849136	+	0.0290015i	0.0849136	+	0.0290015i
$826$		0			0
$827$	−0.0179460	+	0.0239390i	−0.0179460	+	0.0239390i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	−0.0179460	+	0.0239390i	−0.0179460	+	0.0239390i	0.791071	+	0.611724i	$0.209524\pi$
$828$		0			0
$829$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$829$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.53861	−	0.138478i	1.53861	−	0.138478i
$834$	0.130612	+	0.0157067i	0.130612	+	0.0157067i
$835$		0			0
$836$	−0.00490124	−	0.327599i	−0.00490124	−	0.327599i
$837$		0			0
$838$	−0.372484	+	0.692192i	−0.372484	+	0.692192i
$839$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$839$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$840$		0			0
$841$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$842$		0			0
$843$	0.143190	−	0.0798390i	0.143190	−	0.0798390i
$844$	−1.50008	+	0.135010i	−1.50008	+	0.135010i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−0.00796148	+	0.177276i	−0.00796148	+	0.177276i
$850$	−0.889233	−	1.26324i	−0.889233	−	1.26324i
$851$		0			0
$852$		0			0
$853$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$853$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$854$		0			0
$855$		0			0
$856$	−0.372583	−	0.102826i	−0.372583	−	0.102826i
$857$	−1.59293	−	1.08604i	−1.59293	−	1.08604i	−0.946327	−	0.323210i	$-0.895238\pi$
$857$	−1.59293	−	1.08604i	−1.59293	−	1.08604i	−0.646600	−	0.762830i	$-0.723810\pi$
$858$		0			0
$859$	0.840714			0.840714			0.420357	−	0.907359i	$-0.361905\pi$
$859$	0.840714			0.840714			0.420357	+	0.907359i	$0.361905\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.337330	−	0.941386i	$-0.609524\pi$
$863$		0			0		0.337330	+	0.941386i	$0.390476\pi$
$864$	−0.00801900	−	0.178557i	−0.00801900	−	0.178557i
$865$		0			0
$866$	1.14883	−	1.27590i	1.14883	−	1.27590i
$867$	0.0130045	+	0.123730i	0.0130045	+	0.123730i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.14145	−	1.62155i	1.14145	−	1.62155i
$874$		0			0
$875$		0			0
$876$	−0.140738	−	0.0840869i	−0.140738	−	0.0840869i
$877$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$877$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.28366	+	0.618177i	−1.28366	+	0.618177i	−0.946327	−	0.323210i	$-0.895238\pi$
$881$	−1.28366	+	0.618177i	−1.28366	+	0.618177i	−0.337330	+	0.941386i	$0.609524\pi$
$882$	−0.470053	+	0.873505i	−0.470053	+	0.873505i
$883$	0.315829	+	1.90188i	0.315829	+	1.90188i	0.420357	+	0.907359i	$0.361905\pi$
$883$	0.315829	+	1.90188i	0.315829	+	1.90188i	−0.104528	+	0.994522i	$0.533333\pi$
$884$		0			0
$885$		0			0
$886$	−0.151909	−	0.771232i	−0.151909	−	0.771232i
$887$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$887$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.965010	+	0.145452i	−0.965010	+	0.145452i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	−0.235759	−	0.508896i	−0.235759	−	0.508896i
$899$		0			0
$900$	0.991505	−	0.0296746i	0.991505	−	0.0296746i
$901$		0			0
$902$	−1.16544	−	0.284412i	−1.16544	−	0.284412i
$903$		0			0
$904$	−1.61514	+	1.17347i	−1.61514	+	1.17347i
$905$		0			0
$906$		0			0
$907$	−0.0516499	−	1.15007i	−0.0516499	−	1.15007i	−0.842721	−	0.538351i	$-0.819048\pi$
$907$	−0.0516499	−	1.15007i	−0.0516499	−	1.15007i	0.791071	−	0.611724i	$-0.209524\pi$
$908$	−1.83737	+	0.220952i	−1.83737	+	0.220952i
$909$		0			0
$910$		0			0
$911$		0			0		−0.753071	−	0.657939i	$-0.771429\pi$
$911$		0			0		0.753071	+	0.657939i	$0.228571\pi$
$912$	0.0107405	+	0.0273664i	0.0107405	+	0.0273664i
$913$	1.96434	−	0.117686i	1.96434	−	0.117686i
$914$	1.23806	−	1.55248i	1.23806	−	1.55248i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	−0.245079	−	0.127192i	−0.245079	−	0.127192i
$919$		0			0		0.753071	−	0.657939i	$-0.228571\pi$
$919$		0			0		−0.753071	+	0.657939i	$0.771429\pi$
$920$		0			0
$921$	0.146922	−	0.0358546i	0.146922	−	0.0358546i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	0.258627	+	1.31303i	0.258627	+	1.31303i	0.858449	+	0.512899i	$0.171429\pi$
$929$	0.258627	+	1.31303i	0.258627	+	1.31303i	−0.599822	+	0.800134i	$0.704762\pi$
$930$		0			0
$931$	0.0536726	−	0.323210i	0.0536726	−	0.323210i
$932$	1.40429	+	1.08592i	1.40429	+	1.08592i
$933$		0			0
$934$	0.142820	+	1.90580i	0.142820	+	1.90580i
$935$		0			0
$936$		0			0
$937$	0.472644	+	0.301937i	0.472644	+	0.301937i	0.753071	−	0.657939i	$-0.228571\pi$
$937$	0.472644	+	0.301937i	0.472644	+	0.301937i	−0.280427	+	0.959875i	$0.590476\pi$
$938$		0			0
$939$	0.119598	+	0.132827i	0.119598	+	0.132827i
$940$		0			0
$941$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$941$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$942$		0			0
$943$		0			0
$944$	1.55672	−	0.282502i	1.55672	−	0.282502i
$945$		0			0
$946$	0.134233	−	0.990950i	0.134233	−	0.990950i
$947$	−0.894626			−0.894626			−0.447313	−	0.894377i	$-0.647619\pi$
$947$	−0.894626			−0.894626			−0.447313	+	0.894377i	$0.647619\pi$
$948$		0			0
$949$		0			0
$950$	−0.306744	+	0.115123i	−0.306744	+	0.115123i
$951$		0			0
$952$		0			0
$953$	−0.525970	−	0.584149i	−0.525970	−	0.584149i	0.420357	−	0.907359i	$-0.361905\pi$
$953$	−0.525970	−	0.584149i	−0.525970	−	0.584149i	−0.946327	+	0.323210i	$0.895238\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.163818	+	0.986491i	−0.163818	+	0.986491i
$962$		0			0
$963$	−0.0740943	−	0.376172i	−0.0740943	−	0.376172i
$964$	1.27889	+	0.524137i	1.27889	+	0.524137i
$965$		0			0
$966$		0			0
$967$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$967$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$968$	−0.999552	−	0.0299155i	−0.999552	−	0.0299155i
$969$	0.0449088	+	0.00676891i	0.0449088	+	0.00676891i
$970$		0			0
$971$	−0.432354	+	0.105511i	−0.432354	+	0.105511i	−0.447313	−	0.894377i	$-0.647619\pi$
$971$	−0.432354	+	0.105511i	−0.432354	+	0.105511i	0.0149594	+	0.999888i	$0.495238\pi$
$972$	0.232593	−	0.129688i	0.232593	−	0.129688i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.27876	+	1.50862i	1.27876	+	1.50862i	0.753071	+	0.657939i	$0.228571\pi$
$977$	1.27876	+	1.50862i	1.27876	+	1.50862i	0.525684	+	0.850680i	$0.323810\pi$
$978$	0.0977266	−	0.122545i	0.0977266	−	0.122545i
$979$	1.46192	−	1.20205i	1.46192	−	1.20205i
$980$		0			0
$981$		0			0
$982$	1.64861	+	0.350423i	1.64861	+	0.350423i
$983$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$983$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$984$	0.106874	−	0.0128520i	0.106874	−	0.0128520i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$991$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$992$		0			0
$993$	−0.0333497	+	0.0505226i	−0.0333497	+	0.0505226i
$994$		0			0
$995$		0			0
$996$	−0.161310	+	0.0718197i	−0.161310	+	0.0718197i
$997$		0			0		−0.995974	−	0.0896393i	$-0.971429\pi$
$997$		0			0		0.995974	+	0.0896393i	$0.0285714\pi$
$998$	1.54414	−	1.26966i	1.54414	−	1.26966i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.971.1	yes	48
8.3	odd	2	CM	3784.1.em.b.971.1	yes	48
11.4	even	5		3784.1.em.a.2347.1	yes	48
43.31	even	21		3784.1.em.a.1235.1	✓	48
88.59	odd	10		3784.1.em.a.2347.1	yes	48
344.203	odd	42		3784.1.em.a.1235.1	✓	48
473.246	even	105	inner	3784.1.em.b.2611.1	yes	48
3784.2611	odd	210	inner	3784.1.em.b.2611.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.1235.1	✓	48	43.31	even	21
3784.1.em.a.1235.1	✓	48	344.203	odd	42
3784.1.em.a.2347.1	yes	48	11.4	even	5
3784.1.em.a.2347.1	yes	48	88.59	odd	10
3784.1.em.b.971.1	yes	48	1.1	even	1	trivial
3784.1.em.b.971.1	yes	48	8.3	odd	2	CM
3784.1.em.b.2611.1	yes	48	473.246	even	105	inner
3784.1.em.b.2611.1	yes	48	3784.2611	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)

\(f(q)\)	\(=\)	\(q+(0.983930 - 0.178557i) q^{2} +(0.0251627 - 0.0861293i) q^{3} +(0.936235 - 0.351375i) q^{4} +(0.00937930 - 0.0892381i) q^{6} +(0.858449 - 0.512899i) q^{8} +(0.835936 + 0.534016i) q^{9} +O(q^{10})\)	\(q+(0.983930 - 0.178557i) q^{2} +(0.0251627 - 0.0861293i) q^{3} +(0.936235 - 0.351375i) q^{4} +(0.00937930 - 0.0892381i) q^{6} +(0.858449 - 0.512899i) q^{8} +(0.835936 + 0.534016i) q^{9} +(-0.280427 + 0.959875i) q^{11} +(-0.00670551 - 0.0894788i) q^{12} +(0.753071 - 0.657939i) q^{16} +(-0.298548 - 1.51571i) q^{17} +(0.917854 + 0.376172i) q^{18} +(-0.327049 - 0.0195940i) q^{19} +(-0.104528 + 0.994522i) q^{22} +(-0.0225748 - 0.0868435i) q^{24} +(0.971490 - 0.237080i) q^{25} +(0.134602 - 0.117598i) q^{27} +(0.623490 - 0.781831i) q^{32} +(0.0756171 + 0.0483060i) q^{33} +(-0.564391 - 1.43805i) q^{34} +(0.970272 + 0.206238i) q^{36} +(-0.325292 + 0.0391178i) q^{38} +(-0.161032 + 1.18879i) q^{41} +(-0.999552 - 0.0299155i) q^{43} +(0.0747301 + 0.997204i) q^{44} +(-0.0377185 - 0.0814170i) q^{48} +(-0.104528 + 0.994522i) q^{49} +(0.913545 - 0.406737i) q^{50} +(-0.138059 - 0.0124256i) q^{51} +(0.111441 - 0.139742i) q^{54} +(-0.00991705 + 0.0276755i) q^{57} +(1.35819 + 0.811480i) q^{59} +(0.473869 - 0.880596i) q^{64} +(0.0830272 + 0.0340278i) q^{66} +(-0.714715 + 1.82106i) q^{67} +(-0.812094 - 1.31416i) q^{68} +(0.991505 + 0.0296746i) q^{72} +(1.05170 - 1.49405i) q^{73} +(0.00402571 - 0.0896393i) q^{75} +(-0.313080 + 0.0965724i) q^{76} +(0.410231 + 0.885501i) q^{81} +(0.0538218 + 1.19844i) q^{82} +(-0.663818 - 1.85252i) q^{83} +(-0.988831 + 0.149042i) q^{86} +(0.251587 + 0.967835i) q^{88} +(-1.56378 - 1.06617i) q^{89} +(-0.0516499 - 0.0733737i) q^{96} +(0.0896895 - 1.99709i) q^{97} +(0.0747301 + 0.997204i) q^{98} +(-0.747008 + 0.652641i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more