LMFDB - Embedded newform 1775.1.bb.b.1419.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1775,1,Mod(354,1775)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1775, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1, 5]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1775.354");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1775 = 5^{2} \cdot 71 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1775.bb (of order $10$, degree $4$, 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:	$0.885840397424$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{35})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{24} - x^{23} + x^{19} - x^{18} + x^{17} - x^{16} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} + \cdots + 1 $ x^24 - x^23 + x^19 - x^18 + x^17 - x^16 + x^14 - x^13 + x^12 - x^11 + x^10 - x^8 + x^7 - x^6 + x^5 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{70}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{70} + \cdots)$

Embedding invariants

Embedding label			1419.3
Root			$0.134233 - 0.990950i$ of defining polynomial
Character	$\chi$	$=$	1775.1419
Dual form			1775.1.bb.b.354.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.975592 + 0.316989i) q^{2} +(-0.981100 - 1.35037i) q^{3} +(0.0422814 - 0.0307192i) q^{4} +(-0.983930 - 0.178557i) q^{5} +(1.38521 + 1.00641i) q^{6} +(0.571438 - 0.786516i) q^{8} +(-0.551920 + 1.69863i) q^{9} +O(q^{10})$	\(q+(-0.975592 + 0.316989i) q^{2} +(-0.981100 - 1.35037i) q^{3} +(0.0422814 - 0.0307192i) q^{4} +(-0.983930 - 0.178557i) q^{5} +(1.38521 + 1.00641i) q^{6} +(0.571438 - 0.786516i) q^{8} +(-0.551920 + 1.69863i) q^{9} +(1.01651 - 0.137696i) q^{10} +(-0.0829645 - 0.0269568i) q^{12} +(0.724216 + 1.50385i) q^{15} +(-0.324323 + 0.998164i) q^{16} -1.83213i q^{18} +(1.21850 + 0.885289i) q^{19} +(-0.0470870 + 0.0226759i) q^{20} -1.62272 q^{24} +(0.936235 + 0.351375i) q^{25} +(1.24782 - 0.405440i) q^{27} +(-0.0725928 + 0.0527418i) q^{29} +(-1.18324 - 1.23758i) q^{30} -0.104420i q^{32} +(0.0288448 + 0.0887752i) q^{36} +(1.25147 + 0.406628i) q^{37} +(-1.46938 - 0.477431i) q^{38} +(-0.702692 + 0.671843i) q^{40} -1.44559i q^{43} +(0.846353 - 1.57279i) q^{45} +(1.66608 - 0.541343i) q^{48} -1.00000 q^{49} +(-1.02477 - 0.0460223i) q^{50} +(-1.08884 + 0.791089i) q^{54} -2.51397i q^{57} +(0.0541024 - 0.0744656i) q^{58} +(0.0768179 + 0.0413375i) q^{60} +(-0.291223 - 0.896292i) q^{64} +(0.809017 - 0.587785i) q^{71} +(1.02062 + 1.40476i) q^{72} +(-1.37484 + 0.446712i) q^{73} -1.34983 q^{74} +(-0.444054 - 1.60900i) q^{75} +0.0787151 q^{76} +(0.766736 - 0.557066i) q^{79} +(0.497340 - 0.924213i) q^{80} +(-0.326782 - 0.237421i) q^{81} +(1.14610 - 1.57747i) q^{83} +(0.458236 + 1.41031i) q^{86} +(0.142442 + 0.0462821i) q^{87} +(-0.340473 - 1.04787i) q^{89} +(-0.327139 + 1.80268i) q^{90} +(-1.04084 - 1.08863i) q^{95} +(-0.141006 + 0.102447i) q^{96} +(0.975592 - 0.316989i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 5 q^{2} + 3 q^{4} - q^{5} + 5 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q - 5 * q^2 + 3 * q^4 - q^5 + 5 * q^6 - 5 * q^8 + 8 * q^9	$ 24 q - 5 q^{2} + 3 q^{4} - q^{5} + 5 q^{6} - 5 q^{8} + 8 q^{9} - 5 q^{10} + 10 q^{12} - 11 q^{16} + 3 q^{19} + q^{20} - 4 q^{24} + q^{25} - 5 q^{27} + 3 q^{29} + 7 q^{30} - 11 q^{36} - 30 q^{38} - 5 q^{40} + 4 q^{45} + 10 q^{48} - 24 q^{49} - 10 q^{54} + 5 q^{58} - 23 q^{60} + 8 q^{64} + 6 q^{71} + 25 q^{72} - 5 q^{73} - 14 q^{74} - 7 q^{75} + 8 q^{76} + 3 q^{79} + 22 q^{80} - q^{81} - 5 q^{87} - 3 q^{89} + 12 q^{90} + 2 q^{95} - 11 q^{96} + 5 q^{98}+O(q^{100}) $ 24 * q - 5 * q^2 + 3 * q^4 - q^5 + 5 * q^6 - 5 * q^8 + 8 * q^9 - 5 * q^10 + 10 * q^12 - 11 * q^16 + 3 * q^19 + q^20 - 4 * q^24 + q^25 - 5 * q^27 + 3 * q^29 + 7 * q^30 - 11 * q^36 - 30 * q^38 - 5 * q^40 + 4 * q^45 + 10 * q^48 - 24 * q^49 - 10 * q^54 + 5 * q^58 - 23 * q^60 + 8 * q^64 + 6 * q^71 + 25 * q^72 - 5 * q^73 - 14 * q^74 - 7 * q^75 + 8 * q^76 + 3 * q^79 + 22 * q^80 - q^81 - 5 * q^87 - 3 * q^89 + 12 * q^90 + 2 * q^95 - 11 * q^96 + 5 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1775\mathbb{Z}\right)^\times$.

$n$	$427$	$1001$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$

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 $

$2$	−0.975592	+	0.316989i	−0.975592	+	0.316989i	−0.753071	−	0.657939i	$-0.771429\pi$
$2$	−0.975592	+	0.316989i	−0.975592	+	0.316989i	−0.222521	+	0.974928i	$0.571429\pi$
$3$	−0.981100	−	1.35037i	−0.981100	−	1.35037i	−0.936235	−	0.351375i	$-0.885714\pi$
$3$	−0.981100	−	1.35037i	−0.981100	−	1.35037i	−0.0448648	−	0.998993i	$-0.514286\pi$
$4$	0.0422814	−	0.0307192i	0.0422814	−	0.0307192i
$5$	−0.983930	−	0.178557i	−0.983930	−	0.178557i
$5$	−0.983930	−	0.178557i	−0.983930	−	0.178557i
$6$	1.38521	+	1.00641i	1.38521	+	1.00641i
$7$		0			0			−	1.00000i	$-0.5\pi$
$7$		0			0				1.00000i	$0.5\pi$
$8$	0.571438	−	0.786516i	0.571438	−	0.786516i
$9$	−0.551920	+	1.69863i	−0.551920	+	1.69863i
$10$	1.01651	−	0.137696i	1.01651	−	0.137696i
$11$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$11$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$12$	−0.0829645	−	0.0269568i	−0.0829645	−	0.0269568i
$13$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$13$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$14$		0			0
$15$	0.724216	+	1.50385i	0.724216	+	1.50385i
$16$	−0.324323	+	0.998164i	−0.324323	+	0.998164i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$		−	1.83213i		−	1.83213i
$19$	1.21850	+	0.885289i	1.21850	+	0.885289i	0.995974	−	0.0896393i	$-0.0285714\pi$
$19$	1.21850	+	0.885289i	1.21850	+	0.885289i	0.222521	+	0.974928i	$0.428571\pi$
$20$	−0.0470870	+	0.0226759i	−0.0470870	+	0.0226759i
$21$		0			0
$22$		0			0
$23$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$23$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$24$	−1.62272			−1.62272
$25$	0.936235	+	0.351375i	0.936235	+	0.351375i
$26$		0			0
$27$	1.24782	−	0.405440i	1.24782	−	0.405440i
$28$		0			0
$29$	−0.0725928	+	0.0527418i	−0.0725928	+	0.0527418i	−0.623490	−	0.781831i	$-0.714286\pi$
$29$	−0.0725928	+	0.0527418i	−0.0725928	+	0.0527418i	0.550897	+	0.834573i	$0.314286\pi$
$30$	−1.18324	−	1.23758i	−1.18324	−	1.23758i
$31$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$31$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$32$		−	0.104420i		−	0.104420i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.0288448	+	0.0887752i	0.0288448	+	0.0887752i
$37$	1.25147	+	0.406628i	1.25147	+	0.406628i	0.858449	−	0.512899i	$-0.171429\pi$
$37$	1.25147	+	0.406628i	1.25147	+	0.406628i	0.393025	+	0.919528i	$0.371429\pi$
$38$	−1.46938	−	0.477431i	−1.46938	−	0.477431i
$39$		0			0
$40$	−0.702692	+	0.671843i	−0.702692	+	0.671843i
$41$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$41$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$42$		0			0
$43$		−	1.44559i		−	1.44559i	−0.691063	−	0.722795i	$-0.742857\pi$
$43$		−	1.44559i		−	1.44559i	0.691063	−	0.722795i	$-0.257143\pi$
$44$		0			0
$45$	0.846353	−	1.57279i	0.846353	−	1.57279i
$46$		0			0
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$	1.66608	−	0.541343i	1.66608	−	0.541343i
$49$	−1.00000			−1.00000
$50$	−1.02477	−	0.0460223i	−1.02477	−	0.0460223i
$51$		0			0
$52$		0			0
$53$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$53$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$54$	−1.08884	+	0.791089i	−1.08884	+	0.791089i
$55$		0			0
$56$		0			0
$57$		−	2.51397i		−	2.51397i
$58$	0.0541024	−	0.0744656i	0.0541024	−	0.0744656i
$59$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$59$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$60$	0.0768179	+	0.0413375i	0.0768179	+	0.0413375i
$61$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$61$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$62$		0			0
$63$		0			0
$64$	−0.291223	−	0.896292i	−0.291223	−	0.896292i
$65$		0			0
$66$		0			0
$67$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$67$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.809017	−	0.587785i	0.809017	−	0.587785i
$71$	0.809017	−	0.587785i	0.809017	−	0.587785i
$72$	1.02062	+	1.40476i	1.02062	+	1.40476i
$73$	−1.37484	+	0.446712i	−1.37484	+	0.446712i	−0.900969	−	0.433884i	$-0.857143\pi$
$73$	−1.37484	+	0.446712i	−1.37484	+	0.446712i	−0.473869	+	0.880596i	$0.657143\pi$
$74$	−1.34983			−1.34983
$75$	−0.444054	−	1.60900i	−0.444054	−	1.60900i
$76$	0.0787151			0.0787151
$77$		0			0
$78$		0			0
$79$	0.766736	−	0.557066i	0.766736	−	0.557066i	−0.134233	−	0.990950i	$-0.542857\pi$
$79$	0.766736	−	0.557066i	0.766736	−	0.557066i	0.900969	+	0.433884i	$0.142857\pi$
$80$	0.497340	−	0.924213i	0.497340	−	0.924213i
$81$	−0.326782	−	0.237421i	−0.326782	−	0.237421i
$82$		0			0
$83$	1.14610	−	1.57747i	1.14610	−	1.57747i	0.393025	−	0.919528i	$-0.371429\pi$
$83$	1.14610	−	1.57747i	1.14610	−	1.57747i	0.753071	−	0.657939i	$-0.228571\pi$
$84$		0			0
$85$		0			0
$86$	0.458236	+	1.41031i	0.458236	+	1.41031i
$87$	0.142442	+	0.0462821i	0.142442	+	0.0462821i
$88$		0			0
$89$	−0.340473	−	1.04787i	−0.340473	−	1.04787i	−0.963963	−	0.266037i	$-0.914286\pi$
$89$	−0.340473	−	1.04787i	−0.340473	−	1.04787i	0.623490	−	0.781831i	$-0.285714\pi$
$90$	−0.327139	+	1.80268i	−0.327139	+	1.80268i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.04084	−	1.08863i	−1.04084	−	1.08863i
$96$	−0.141006	+	0.102447i	−0.141006	+	0.102447i
$97$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$97$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$98$	0.975592	−	0.316989i	0.975592	−	0.316989i
$99$		0			0
$100$	0.0503793	−	0.0139038i	0.0503793	−	0.0139038i
$101$	−0.786050			−0.786050			−0.393025	−	0.919528i	$-0.628571\pi$
$101$	−0.786050			−0.786050			−0.393025	+	0.919528i	$0.628571\pi$
$102$		0			0
$103$	0.919098	+	1.26503i	0.919098	+	1.26503i	0.963963	+	0.266037i	$0.0857143\pi$
$103$	0.919098	+	1.26503i	0.919098	+	1.26503i	−0.0448648	+	0.998993i	$0.514286\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$107$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$108$	0.0403046	−	0.0554746i	0.0403046	−	0.0554746i
$109$	0.385338	−	1.18595i	0.385338	−	1.18595i	−0.550897	−	0.834573i	$-0.685714\pi$
$109$	0.385338	−	1.18595i	0.385338	−	1.18595i	0.936235	−	0.351375i	$-0.114286\pi$
$110$		0			0
$111$	−0.678723	−	2.08889i	−0.678723	−	2.08889i
$112$		0			0
$113$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$113$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$114$	0.796902	+	2.45261i	0.796902	+	2.45261i
$115$		0			0
$116$	−0.00144914	+	0.00445999i	−0.00144914	+	0.00445999i
$117$		0			0
$118$		0			0
$119$		0			0
$120$	1.59665	+	0.289748i	1.59665	+	0.289748i
$121$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.858449	−	0.512899i	−0.858449	−	0.512899i
$126$		0			0
$127$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$127$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$128$	0.629606	+	0.866579i	0.629606	+	0.866579i
$129$	−1.95208	+	1.41827i	−1.95208	+	1.41827i
$130$		0			0
$131$	−0.217194	−	0.157801i	−0.217194	−	0.157801i	0.473869	−	0.880596i	$-0.342857\pi$
$131$	−0.217194	−	0.157801i	−0.217194	−	0.157801i	−0.691063	+	0.722795i	$0.742857\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−1.30016	+	0.176118i	−1.30016	+	0.176118i
$136$		0			0
$137$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$137$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$138$		0			0
$139$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$139$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$140$		0			0
$141$		0			0
$142$	−0.602949	+	0.829888i	−0.602949	+	0.829888i
$143$		0			0
$144$	−1.51651	−	1.10181i	−1.51651	−	1.10181i
$145$	0.0808436	−	0.0389322i	0.0808436	−	0.0389322i
$146$	1.19968	−	0.871617i	1.19968	−	0.871617i
$147$	0.981100	+	1.35037i	0.981100	+	1.35037i
$148$	0.0654054	−	0.0212515i	0.0654054	−	0.0212515i
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	0.943250	+	1.42896i	0.943250	+	1.42896i
$151$	1.92793			1.92793			0.963963	−	0.266037i	$-0.0857143\pi$
$151$	1.92793			1.92793			0.963963	+	0.266037i	$0.0857143\pi$
$152$	1.39259	−	0.452479i	1.39259	−	0.452479i
$153$		0			0
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	0.702750i		−	0.702750i	−0.936235	−	0.351375i	$-0.885714\pi$
$157$		−	0.702750i		−	0.702750i	0.936235	−	0.351375i	$-0.114286\pi$
$158$	−0.571438	+	0.786516i	−0.571438	+	0.786516i
$159$		0			0
$160$	−0.0186449	+	0.102742i	−0.0186449	+	0.102742i
$161$		0			0
$162$	0.394066	+	0.128040i	0.394066	+	0.128040i
$163$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$163$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$164$		0			0
$165$		0			0
$166$	−0.618083	+	1.90226i	−0.618083	+	1.90226i
$167$	−0.510061	+	0.702039i	−0.510061	+	0.702039i	−0.983930	−	0.178557i	$-0.942857\pi$
$167$	−0.510061	+	0.702039i	−0.510061	+	0.702039i	0.473869	+	0.880596i	$0.342857\pi$
$168$		0			0
$169$	0.809017	+	0.587785i	0.809017	+	0.587785i
$170$		0			0
$171$	−2.17629	+	1.58117i	−2.17629	+	1.58117i
$172$	−0.0444074	−	0.0611215i	−0.0444074	−	0.0611215i
$173$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$173$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$174$	−0.153636			−0.153636
$175$		0			0
$176$		0			0
$177$		0			0
$178$	0.664326	+	0.914366i	0.664326	+	0.914366i
$179$	1.11816	−	0.812393i	1.11816	−	0.812393i	0.134233	−	0.990950i	$-0.457143\pi$
$179$	1.11816	−	0.812393i	1.11816	−	0.812393i	0.983930	+	0.178557i	$0.0571429\pi$
$180$	−0.0125298	−	0.0924990i	−0.0125298	−	0.0924990i
$181$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$181$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.15876	−	0.623553i	−1.15876	−	0.623553i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$	1.36052	+	0.732127i	1.36052	+	0.732127i
$191$	−0.578625	+	1.78082i	−0.578625	+	1.78082i	0.0448648	+	0.998993i	$0.485714\pi$
$191$	−0.578625	+	1.78082i	−0.578625	+	1.78082i	−0.623490	+	0.781831i	$0.714286\pi$
$192$	−0.924605	+	1.27261i	−0.924605	+	1.27261i
$193$		0			0			−	1.00000i	$-0.5\pi$
$193$		0			0				1.00000i	$0.5\pi$
$194$		0			0
$195$		0			0
$196$	−0.0422814	+	0.0307192i	−0.0422814	+	0.0307192i
$197$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$197$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$198$		0			0
$199$	1.71690			1.71690			0.858449	−	0.512899i	$-0.171429\pi$
$199$	1.71690			1.71690			0.858449	+	0.512899i	$0.171429\pi$
$200$	0.811362	−	0.535575i	0.811362	−	0.535575i
$201$		0			0
$202$	0.766864	−	0.249169i	0.766864	−	0.249169i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	−1.29767	−	0.942809i	−1.29767	−	0.942809i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$		0			0
$213$	−1.58745	−	0.515795i	−1.58745	−	0.515795i
$214$	0.602949	+	1.85569i	0.602949	+	1.85569i
$215$	−0.258120	+	1.42236i	−0.258120	+	1.42236i
$216$	0.394164	−	1.21311i	0.394164	−	1.21311i
$217$		0			0
$218$			1.27915i			1.27915i
$219$	1.95208	+	1.41827i	1.95208	+	1.41827i
$220$		0			0
$221$		0			0
$222$	1.32431	+	1.82276i	1.32431	+	1.82276i
$223$	−1.25147	+	0.406628i	−1.25147	+	0.406628i	−0.858449	−	0.512899i	$-0.828571\pi$
$223$	−1.25147	+	0.406628i	−1.25147	+	0.406628i	−0.393025	+	0.919528i	$0.628571\pi$
$224$		0			0
$225$	−1.11358	+	1.39639i	−1.11358	+	1.39639i
$226$		0			0
$227$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$227$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$228$	−0.0772273	−	0.106294i	−0.0772273	−	0.106294i
$229$	1.59203	−	1.15668i	1.59203	−	1.15668i	0.691063	−	0.722795i	$-0.257143\pi$
$229$	1.59203	−	1.15668i	1.59203	−	1.15668i	0.900969	−	0.433884i	$-0.142857\pi$
$230$		0			0
$231$		0			0
$232$			0.0872341i			0.0872341i
$233$	−1.08097	+	1.48783i	−1.08097	+	1.48783i	−0.222521	+	0.974928i	$0.571429\pi$
$233$	−1.08097	+	1.48783i	−1.08097	+	1.48783i	−0.858449	+	0.512899i	$0.828571\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.50449	−	0.488838i	−1.50449	−	0.488838i
$238$		0			0
$239$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$239$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$240$	−1.73597	+	0.235153i	−1.73597	+	0.235153i
$241$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$241$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$242$	0.602949	−	0.829888i	0.602949	−	0.829888i
$243$		−	0.637823i		−	0.637823i
$244$		0			0
$245$	0.983930	+	0.178557i	0.983930	+	0.178557i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−3.25460			−3.25460
$250$	1.00008	+	0.228262i	1.00008	+	0.228262i
$251$	1.99195			1.99195			0.995974	−	0.0896393i	$-0.0285714\pi$
$251$	1.99195			1.99195			0.995974	+	0.0896393i	$0.0285714\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.126504	−	0.0919104i	−0.126504	−	0.0919104i
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$	1.45486	−	2.00244i	1.45486	−	2.00244i
$259$		0			0
$260$		0			0
$261$	−0.0495236	−	0.152418i	−0.0495236	−	0.152418i
$262$	0.261914	+	0.0851010i	0.261914	+	0.0851010i
$263$	1.67499	+	0.544238i	1.67499	+	0.544238i	0.983930	−	0.178557i	$-0.0571429\pi$
$263$	1.67499	+	0.544238i	1.67499	+	0.544238i	0.691063	+	0.722795i	$0.257143\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−1.08097	+	1.48783i	−1.08097	+	1.48783i
$268$		0			0
$269$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$269$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$270$	1.21260	−	0.583956i	1.21260	−	0.583956i
$271$	−1.51486	+	1.10061i	−1.51486	+	1.10061i	−0.550897	+	0.834573i	$0.685714\pi$
$271$	−1.51486	+	1.10061i	−1.51486	+	1.10061i	−0.963963	+	0.266037i	$0.914286\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	1.74905	−	0.568299i	1.74905	−	0.568299i	0.753071	−	0.657939i	$-0.228571\pi$
$277$	1.74905	−	0.568299i	1.74905	−	0.568299i	0.995974	+	0.0896393i	$0.0285714\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$281$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$282$		0			0
$283$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$283$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$284$	0.0161501	−	0.0497048i	0.0161501	−	0.0497048i
$285$	−0.448887	+	2.47357i	−0.448887	+	2.47357i
$286$		0			0
$287$		0			0
$288$	0.177372	+	0.0576315i	0.177372	+	0.0576315i
$289$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$290$	−0.0665293	+	0.0636086i	−0.0665293	+	0.0636086i
$291$		0			0
$292$	−0.0444074	+	0.0611215i	−0.0444074	+	0.0611215i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−1.38521	−	1.00641i	−1.38521	−	1.00641i
$295$		0			0
$296$	1.03496	−	0.751942i	1.03496	−	0.751942i
$297$		0			0
$298$		0			0
$299$		0			0
$300$	−0.0682023	−	0.0543895i	−0.0682023	−	0.0543895i
$301$		0			0
$302$	−1.88087	+	0.611132i	−1.88087	+	0.611132i
$303$	0.771193	+	1.06146i	0.771193	+	1.06146i
$304$	−1.27885	+	0.929138i	−1.27885	+	0.929138i
$305$		0			0
$306$		0			0
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$		0			0
$309$	0.806529	−	2.48224i	0.806529	−	2.48224i
$310$		0			0
$311$	−0.465424	−	1.43243i	−0.465424	−	1.43243i	−0.858449	−	0.512899i	$-0.828571\pi$
$311$	−0.465424	−	1.43243i	−0.465424	−	1.43243i	0.393025	−	0.919528i	$-0.371429\pi$
$312$		0			0
$313$	−1.85442	−	0.602539i	−1.85442	−	0.602539i	−0.995974	−	0.0896393i	$-0.971429\pi$
$313$	−1.85442	−	0.602539i	−1.85442	−	0.602539i	−0.858449	−	0.512899i	$-0.828571\pi$
$314$	0.222764	+	0.685597i	0.222764	+	0.685597i
$315$		0			0
$316$	0.0153060	−	0.0471071i	0.0153060	−	0.0471071i
$317$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$317$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$318$		0			0
$319$		0			0
$320$	0.126504	+	0.933888i	0.126504	+	0.933888i
$321$	−2.56855	+	1.86616i	−2.56855	+	1.86616i
$322$		0			0
$323$		0			0
$324$	−0.0211102			−0.0211102
$325$		0			0
$326$		0			0
$327$	−1.97952	+	0.643185i	−1.97952	+	0.643185i
$328$		0			0
$329$		0			0
$330$		0			0
$331$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$331$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$332$		−	0.101905i		−	0.101905i
$333$	−1.38143	+	1.90137i	−1.38143	+	1.90137i
$334$	0.275073	−	0.846587i	0.275073	−	0.846587i
$335$		0			0
$336$		0			0
$337$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$337$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$338$	−0.975592	−	0.316989i	−0.975592	−	0.316989i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	1.62196	−	2.23244i	1.62196	−	2.23244i
$343$		0			0
$344$	−1.13698	−	0.826064i	−1.13698	−	0.826064i
$345$		0			0
$346$		0			0
$347$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$347$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$348$	0.00744438	−	0.00241883i	0.00744438	−	0.00241883i
$349$		0			0		1.00000			$0$
$349$		0			0		−1.00000			$\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$353$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$354$		0			0
$355$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$356$	−0.0465854	−	0.0338463i	−0.0465854	−	0.0338463i
$357$		0			0
$358$	−0.833351	+	1.14701i	−0.833351	+	1.14701i
$359$	0.608102	−	1.87155i	0.608102	−	1.87155i	0.134233	−	0.990950i	$-0.457143\pi$
$359$	0.608102	−	1.87155i	0.608102	−	1.87155i	0.473869	−	0.880596i	$-0.342857\pi$
$360$	−0.753385	−	1.56442i	−0.753385	−	1.56442i
$361$	0.391978	+	1.20638i	0.391978	+	1.20638i
$362$		0			0
$363$	1.58745	+	0.515795i	1.58745	+	0.515795i
$364$		0			0
$365$	1.43251	−	0.194046i	1.43251	−	0.194046i
$366$		0			0
$367$	0.510061	−	0.702039i	0.510061	−	0.702039i	−0.473869	−	0.880596i	$-0.657143\pi$
$367$	0.510061	−	0.702039i	0.510061	−	0.702039i	0.983930	+	0.178557i	$0.0571429\pi$
$368$		0			0
$369$		0			0
$370$	1.32813	+	0.241021i	1.32813	+	0.241021i
$371$		0			0
$372$		0			0
$373$	−0.339635	+	0.110354i	−0.339635	+	0.110354i	−0.473869	−	0.880596i	$-0.657143\pi$
$373$	−0.339635	+	0.110354i	−0.339635	+	0.110354i	0.134233	+	0.990950i	$0.457143\pi$
$374$		0			0
$375$	0.149621	+	1.66243i	0.149621	+	1.66243i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.00883	−	0.732956i	1.00883	−	0.732956i	0.0448648	−	0.998993i	$-0.485714\pi$
$379$	1.00883	−	0.732956i	1.00883	−	0.732956i	0.963963	+	0.266037i	$0.0857143\pi$
$380$	−0.0774501	−	0.0140551i	−0.0774501	−	0.0140551i
$381$		0			0
$382$		−	1.92078i		−	1.92078i
$383$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$383$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$384$	0.552494	−	1.70040i	0.552494	−	1.70040i
$385$		0			0
$386$		0			0
$387$	2.45553	+	0.797850i	2.45553	+	0.797850i
$388$		0			0
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$		0			0
$391$		0			0
$392$	−0.571438	+	0.786516i	−0.571438	+	0.786516i
$393$			0.448110i			0.448110i
$394$		0			0
$395$	−0.853882	+	0.411208i	−0.853882	+	0.411208i
$396$		0			0
$397$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$397$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$398$	−1.67499	+	0.544238i	−1.67499	+	0.544238i
$399$		0			0
$400$	−0.654372	+	0.820557i	−0.654372	+	0.820557i
$401$		0			0		1.00000			$0$
$401$		0			0		−1.00000			$\pi$
$402$		0			0
$403$		0			0
$404$	−0.0332353	+	0.0241469i	−0.0332353	+	0.0241469i
$405$	0.279137	+	0.291955i	0.279137	+	0.291955i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	0.595762	−	1.83357i	0.595762	−	1.83357i	0.0448648	−	0.998993i	$-0.485714\pi$
$409$	0.595762	−	1.83357i	0.595762	−	1.83357i	0.550897	−	0.834573i	$-0.314286\pi$
$410$		0			0
$411$		0			0
$412$	0.0777215	+	0.0252532i	0.0777215	+	0.0252532i
$413$		0			0
$414$		0			0
$415$	−1.40935	+	1.34747i	−1.40935	+	1.34747i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.00883	−	0.732956i	−1.00883	−	0.732956i	−0.0448648	−	0.998993i	$-0.514286\pi$
$419$	−1.00883	−	0.732956i	−1.00883	−	0.732956i	−0.963963	+	0.266037i	$0.914286\pi$
$420$		0			0
$421$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$421$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$		0			0
$426$	1.71221			1.71221
$427$		0			0
$428$	−0.0584314	−	0.0804240i	−0.0584314	−	0.0804240i
$429$		0			0
$430$	−0.199052	−	1.46946i	−0.199052	−	1.46946i
$431$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.858449	+	0.512899i	$0.171429\pi$
$431$	1.61152	+	1.17084i	1.61152	+	1.17084i	0.753071	+	0.657939i	$0.228571\pi$
$432$			1.37702i			1.37702i
$433$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$433$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$434$		0			0
$435$	−0.131889	−	0.0709722i	−0.131889	−	0.0709722i
$436$	−0.0201388	−	0.0619808i	−0.0201388	−	0.0619808i
$437$		0			0
$438$	−2.35401	−	0.764864i	−2.35401	−	0.764864i
$439$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$439$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$440$		0			0
$441$	0.551920	−	1.69863i	0.551920	−	1.69863i
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$	−0.0928665	−	0.0674715i	−0.0928665	−	0.0674715i
$445$	0.147897	+	1.09182i	0.147897	+	1.09182i
$446$	1.09203	−	0.793407i	1.09203	−	0.793407i
$447$		0			0
$448$		0			0
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$	0.643764	−	1.71530i	0.643764	−	1.71530i
$451$		0			0
$452$		0			0
$453$	−1.89149	−	2.60341i	−1.89149	−	2.60341i
$454$		0			0
$455$		0			0
$456$	−1.97728	−	1.43658i	−1.97728	−	1.43658i
$457$		0			0			−	1.00000i	$-0.5\pi$
$457$		0			0				1.00000i	$0.5\pi$
$458$	−1.18652	+	1.63310i	−1.18652	+	1.63310i
$459$		0			0
$460$		0			0
$461$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$461$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$462$		0			0
$463$	−1.74905	−	0.568299i	−1.74905	−	0.568299i	−0.753071	−	0.657939i	$-0.771429\pi$
$463$	−1.74905	−	0.568299i	−1.74905	−	0.568299i	−0.995974	+	0.0896393i	$0.971429\pi$
$464$	−0.0291014	−	0.0895649i	−0.0291014	−	0.0895649i
$465$		0			0
$466$	0.582961	−	1.79417i	0.582961	−	1.79417i
$467$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$467$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.948971	+	0.689467i	−0.948971	+	0.689467i
$472$		0			0
$473$		0			0
$474$	1.62272			1.62272
$475$	0.829730	+	1.25699i	0.829730	+	1.25699i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$479$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$480$	0.157032	−	0.0756227i	0.157032	−	0.0756227i
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−0.0161501	+	0.0497048i	−0.0161501	+	0.0497048i
$485$		0			0
$486$	0.202183	+	0.622255i	0.202183	+	0.622255i
$487$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$487$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$488$		0			0
$489$		0			0
$490$	−1.01651	+	0.137696i	−1.01651	+	0.137696i
$491$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$491$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	3.17516	−	1.03167i	3.17516	−	1.03167i
$499$	−1.10179			−1.10179			−0.550897	−	0.834573i	$-0.685714\pi$
$499$	−1.10179			−1.10179			−0.550897	+	0.834573i	$0.685714\pi$
$500$	−0.0520523	+	0.00468479i	−0.0520523	+	0.00468479i
$501$	1.44843			1.44843
$502$	−1.94333	+	0.631426i	−1.94333	+	0.631426i
$503$	−0.413066	−	0.568536i	−0.413066	−	0.568536i	0.550897	−	0.834573i	$-0.314286\pi$
$503$	−0.413066	−	0.568536i	−0.413066	−	0.568536i	−0.963963	+	0.266037i	$0.914286\pi$
$504$		0			0
$505$	0.773418	+	0.140355i	0.773418	+	0.140355i
$506$		0			0
$507$		−	1.66915i		−	1.66915i
$508$		0			0
$509$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	0.309017	+	0.951057i	$0.400000\pi$
$509$	−0.500000	+	1.53884i	−0.500000	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$510$		0			0
$511$		0			0
$512$	−0.866174	−	0.281437i	−0.866174	−	0.281437i
$513$	1.87939	+	0.610651i	1.87939	+	0.610651i
$514$		0			0
$515$	−0.678448	−	1.40881i	−0.678448	−	1.40881i
$516$	−0.0389685	+	0.119933i	−0.0389685	+	0.119933i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	0.217194	−	0.157801i	0.217194	−	0.157801i	−0.473869	−	0.880596i	$-0.657143\pi$
$521$	0.217194	−	0.157801i	0.217194	−	0.157801i	0.691063	+	0.722795i	$0.257143\pi$
$522$	0.0966297	+	0.132999i	0.0966297	+	0.132999i
$523$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$523$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$524$	−0.0140308			−0.0140308
$525$		0			0
$526$	−1.80663			−1.80663
$527$		0			0
$528$		0			0
$529$	0.809017	−	0.587785i	0.809017	−	0.587785i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$	0.582961	−	1.79417i	0.582961	−	1.79417i
$535$	−0.339635	+	1.87155i	−0.339635	+	1.87155i
$536$		0			0
$537$	−2.19406	−	0.712893i	−2.19406	−	0.712893i
$538$		0			0
$539$		0			0
$540$	−0.0495623	+	0.0473864i	−0.0495623	+	0.0473864i
$541$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$541$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$542$	1.12900	−	1.55394i	1.12900	−	1.55394i
$543$		0			0
$544$		0			0
$545$	−0.590905	+	1.09808i	−0.590905	+	1.09808i
$546$		0			0
$547$	−0.105377	−	0.145039i	−0.105377	−	0.145039i	0.753071	−	0.657939i	$-0.228571\pi$
$547$	−0.105377	−	0.145039i	−0.105377	−	0.145039i	−0.858449	+	0.512899i	$0.828571\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.135146			−0.135146
$552$		0			0
$553$		0			0
$554$	−1.52621	+	1.10886i	−1.52621	+	1.10886i
$555$	0.294829	+	2.17651i	0.294829	+	2.17651i
$556$		0			0
$557$			1.56366i			1.56366i	0.623490	+	0.781831i	$0.285714\pi$
$557$			1.56366i			1.56366i	−0.623490	+	0.781831i	$0.714286\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$563$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		−	0.972188i		−	0.972188i
$569$	0.766736	+	0.557066i	0.766736	+	0.557066i	0.900969	−	0.433884i	$-0.142857\pi$
$569$	0.766736	+	0.557066i	0.766736	+	0.557066i	−0.134233	+	0.990950i	$0.542857\pi$
$570$	−0.346165	−	2.55549i	−0.346165	−	2.55549i
$571$	1.21850	−	0.885289i	1.21850	−	0.885289i	0.222521	−	0.974928i	$-0.428571\pi$
$571$	1.21850	−	0.885289i	1.21850	−	0.885289i	0.995974	+	0.0896393i	$0.0285714\pi$
$572$		0			0
$573$	2.97246	−	0.965810i	2.97246	−	0.965810i
$574$		0			0
$575$		0			0
$576$	1.68320			1.68320
$577$	0.825296	−	0.268155i	0.825296	−	0.268155i	0.134233	−	0.990950i	$-0.457143\pi$
$577$	0.825296	−	0.268155i	0.825296	−	0.268155i	0.691063	+	0.722795i	$0.257143\pi$
$578$	0.602949	+	0.829888i	0.602949	+	0.829888i
$579$		0			0
$580$	0.00222221	−	0.00412956i	0.00222221	−	0.00412956i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−0.434288	+	1.33660i	−0.434288	+	1.33660i
$585$		0			0
$586$		0			0
$587$	1.58745	+	0.515795i	1.58745	+	0.515795i	0.963963	−	0.266037i	$-0.0857143\pi$
$587$	1.58745	+	0.515795i	1.58745	+	0.515795i	0.623490	+	0.781831i	$0.285714\pi$
$588$	0.0829645	+	0.0269568i	0.0829645	+	0.0269568i
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.811764	+	1.11730i	−0.811764	+	1.11730i
$593$		−	0.532074i		−	0.532074i	−0.963963	−	0.266037i	$-0.914286\pi$
$593$		−	0.532074i		−	0.532074i	0.963963	−	0.266037i	$-0.0857143\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−1.68445	−	2.31844i	−1.68445	−	2.31844i
$598$		0			0
$599$		0			0		1.00000			$0$
$599$		0			0		−1.00000			$\pi$
$600$	−1.51925	−	0.570184i	−1.51925	−	0.570184i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	0.0815154	−	0.0592244i	0.0815154	−	0.0592244i
$605$	0.900969	−	0.433884i	0.900969	−	0.433884i
$606$	−1.08884	−	0.791089i	−1.08884	−	0.791089i
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	0.0924419	−	0.127235i	0.0924419	−	0.127235i
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	1.48713	+	0.483198i	1.48713	+	0.483198i	0.936235	−	0.351375i	$-0.114286\pi$
$613$	1.48713	+	0.483198i	1.48713	+	0.483198i	0.550897	+	0.834573i	$0.314286\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.16493	−	1.60339i	1.16493	−	1.60339i	0.473869	−	0.880596i	$-0.342857\pi$
$617$	1.16493	−	1.60339i	1.16493	−	1.60339i	0.691063	−	0.722795i	$-0.257143\pi$
$618$			2.67732i			2.67732i
$619$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$619$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$620$		0			0
$621$		0			0
$622$	0.908128	+	1.24993i	0.908128	+	1.24993i
$623$		0			0
$624$		0			0
$625$	0.753071	+	0.657939i	0.753071	+	0.657939i
$626$	2.00016			2.00016
$627$		0			0
$628$	−0.0215879	−	0.0297132i	−0.0215879	−	0.0297132i
$629$		0			0
$630$		0			0
$631$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$631$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$632$		−	0.921378i		−	0.921378i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$	0.551920	+	1.69863i	0.551920	+	1.69863i
$640$	−0.464755	−	0.965073i	−0.464755	−	0.965073i
$641$	0.530551	−	1.63287i	0.530551	−	1.63287i	−0.222521	−	0.974928i	$-0.571429\pi$
$641$	0.530551	−	1.63287i	0.530551	−	1.63287i	0.753071	−	0.657939i	$-0.228571\pi$
$642$	1.91431	−	2.63482i	1.91431	−	2.63482i
$643$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$643$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$644$		0			0
$645$	2.17395	−	1.04692i	2.17395	−	1.04692i
$646$		0			0
$647$	0.690983	+	0.951057i	0.690983	+	0.951057i	1.00000			$0$
$647$	0.690983	+	0.951057i	0.690983	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$648$	−0.373471	+	0.121348i	−0.373471	+	0.121348i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$653$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$654$	1.72732	−	1.25497i	1.72732	−	1.25497i
$655$	0.185527	+	0.194046i	0.185527	+	0.194046i
$656$		0			0
$657$		−	2.58190i		−	2.58190i
$658$		0			0
$659$	−0.578625	+	1.78082i	−0.578625	+	1.78082i	0.0448648	+	0.998993i	$0.485714\pi$
$659$	−0.578625	+	1.78082i	−0.578625	+	1.78082i	−0.623490	+	0.781831i	$0.714286\pi$
$660$		0			0
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$		0			0
$663$		0			0
$664$	−0.585781	−	1.80285i	−0.585781	−	1.80285i
$665$		0			0
$666$	0.744995	−	2.29286i	0.744995	−	2.29286i
$667$		0			0
$668$			0.0453518i			0.0453518i
$669$	1.77692	+	1.29101i	1.77692	+	1.29101i
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$673$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$674$		0			0
$675$	1.31071	+	0.0588641i	1.31071	+	0.0588641i
$676$	0.0522627			0.0522627
$677$	−0.668355	+	0.217162i	−0.668355	+	0.217162i	−0.623490	−	0.781831i	$-0.714286\pi$
$677$	−0.668355	+	0.217162i	−0.668355	+	0.217162i	−0.0448648	+	0.998993i	$0.514286\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$683$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$684$	−0.0434444	+	0.133708i	−0.0434444	+	0.133708i
$685$		0			0
$686$		0			0
$687$	−3.12388	−	1.01501i	−3.12388	−	1.01501i
$688$	1.44294	+	0.468838i	1.44294	+	0.468838i
$689$		0			0
$690$		0			0
$691$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$691$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$		0			0
$696$	0.117798	−	0.0855853i	0.117798	−	0.0855853i
$697$		0			0
$698$		0			0
$699$	3.06965			3.06965
$700$		0			0
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$		0			0
$703$	1.16493	+	1.60339i	1.16493	+	1.60339i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$	0.741442	−	0.708891i	0.741442	−	0.708891i
$711$	0.523075	+	1.60986i	0.523075	+	1.60986i
$712$	−1.01872	−	0.331004i	−1.01872	−	0.331004i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	0.0223214	−	0.0686982i	0.0223214	−	0.0686982i
$717$		0			0
$718$			2.01863i			2.01863i
$719$	1.38900	+	1.00917i	1.38900	+	1.00917i	0.995974	+	0.0896393i	$0.0285714\pi$
$719$	1.38900	+	1.00917i	1.38900	+	1.00917i	0.393025	+	0.919528i	$0.371429\pi$
$720$	1.29541	+	1.35489i	1.29541	+	1.35489i
$721$		0			0
$722$	−0.764821	−	1.05269i	−0.764821	−	1.05269i
$723$		0			0
$724$		0			0
$725$	−0.0864961	+	0.0238714i	−0.0864961	+	0.0238714i
$726$	−1.71221			−1.71221
$727$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$727$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$728$		0			0
$729$	−1.18808	+	0.863189i	−1.18808	+	0.863189i
$730$	−1.33603	+	0.643399i	−1.33603	+	0.643399i
$731$		0			0
$732$		0			0
$733$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$733$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$734$	−0.275073	+	0.846587i	−0.275073	+	0.846587i
$735$	−0.724216	−	1.50385i	−0.724216	−	1.50385i
$736$		0			0
$737$		0			0
$738$		0			0
$739$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$739$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$740$	−0.0681489	+	0.00923139i	−0.0681489	+	0.00923139i
$741$		0			0
$742$		0			0
$743$		0			0			−	1.00000i	$-0.5\pi$
$743$		0			0				1.00000i	$0.5\pi$
$744$		0			0
$745$		0			0
$746$	0.296365	−	0.215321i	0.296365	−	0.215321i
$747$	2.04699	+	2.81743i	2.04699	+	2.81743i
$748$		0			0
$749$		0			0
$750$	−0.672941	−	1.57442i	−0.672941	−	1.57442i
$751$		0			0		1.00000			$0$
$751$		0			0		−1.00000			$\pi$
$752$		0			0
$753$	−1.95430	−	2.68986i	−1.95430	−	2.68986i
$754$		0			0
$755$	−1.89694	−	0.344244i	−1.89694	−	0.344244i
$756$		0			0
$757$		0			0			−	1.00000i	$-0.5\pi$
$757$		0			0				1.00000i	$0.5\pi$
$758$	−0.751865	+	1.03485i	−0.751865	+	1.03485i
$759$		0			0
$760$	−1.45100	+	0.196552i	−1.45100	+	0.196552i
$761$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$761$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$762$		0			0
$763$		0			0
$764$	0.0302405	+	0.0930707i	0.0302405	+	0.0930707i
$765$		0			0
$766$		0			0
$767$		0			0
$768$			0.261000i			0.261000i
$769$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$769$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$773$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$774$	−2.64850			−2.64850
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$	−0.0691989	+	0.0952442i	−0.0691989	+	0.0952442i
$784$	0.324323	−	0.998164i	0.324323	−	0.998164i
$785$	−0.125481	+	0.691456i	−0.125481	+	0.691456i
$786$	−0.142046	−	0.437173i	−0.142046	−	0.437173i
$787$	−0.506032	−	0.164420i	−0.506032	−	0.164420i	0.0448648	−	0.998993i	$-0.485714\pi$
$787$	−0.506032	−	0.164420i	−0.506032	−	0.164420i	−0.550897	+	0.834573i	$0.685714\pi$
$788$		0			0
$789$	−0.908413	−	2.79581i	−0.908413	−	2.79581i
$790$	0.702692	−	0.671843i	0.702692	−	0.671843i
$791$		0			0
$792$		0			0
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.0725928	−	0.0527418i	0.0725928	−	0.0527418i
$797$	0.602949	+	0.829888i	0.602949	+	0.829888i	0.995974	−	0.0896393i	$-0.0285714\pi$
$797$	0.602949	+	0.829888i	0.602949	+	0.829888i	−0.393025	+	0.919528i	$0.628571\pi$
$798$		0			0
$799$		0			0
$800$	0.0366906	−	0.0977617i	0.0366906	−	0.0977617i
$801$	1.96786			1.96786
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−0.449178	+	0.618241i	−0.449178	+	0.618241i
$809$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$809$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$810$	−0.364871	−	0.196345i	−0.364871	−	0.196345i
$811$	−0.427100	−	1.31448i	−0.427100	−	1.31448i	−0.900969	−	0.433884i	$-0.857143\pi$
$811$	−0.427100	−	1.31448i	−0.427100	−	1.31448i	0.473869	−	0.880596i	$-0.342857\pi$
$812$		0			0
$813$	2.97246	+	0.965810i	2.97246	+	0.965810i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	1.27976	−	1.76144i	1.27976	−	1.76144i
$818$			1.97766i			1.97766i
$819$		0			0
$820$		0			0
$821$	−0.360046	+	0.261589i	−0.360046	+	0.261589i	−0.753071	−	0.657939i	$-0.771429\pi$
$821$	−0.360046	+	0.261589i	−0.360046	+	0.261589i	0.393025	+	0.919528i	$0.371429\pi$
$822$		0			0
$823$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$823$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$824$	1.52017			1.52017
$825$		0			0
$826$		0			0
$827$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$827$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$828$		0			0
$829$	−1.21850	+	0.885289i	−1.21850	+	0.885289i	−0.995974	−	0.0896393i	$-0.971429\pi$
$829$	−1.21850	+	0.885289i	−1.21850	+	0.885289i	−0.222521	+	0.974928i	$0.571429\pi$
$830$	0.947813	−	1.76133i	0.947813	−	1.76133i
$831$	−2.48340	−	1.80430i	−2.48340	−	1.80430i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	0.627218	−	0.599682i	0.627218	−	0.599682i
$836$		0			0
$837$		0			0
$838$	1.21654	+	0.395279i	1.21654	+	0.395279i
$839$	−0.137526	−	0.423260i	−0.137526	−	0.423260i	0.858449	−	0.512899i	$-0.171429\pi$
$839$	−0.137526	−	0.423260i	−0.137526	−	0.423260i	−0.995974	+	0.0896393i	$0.971429\pi$
$840$		0			0
$841$	−0.306529	+	0.943399i	−0.306529	+	0.943399i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$		0			0
$851$		0			0
$852$	−0.0829645	+	0.0269568i	−0.0829645	+	0.0269568i
$853$	0.312745	+	0.430457i	0.312745	+	0.430457i	0.936235	−	0.351375i	$-0.114286\pi$
$853$	0.312745	+	0.430457i	0.312745	+	0.430457i	−0.623490	+	0.781831i	$0.714286\pi$
$854$		0			0
$855$	2.42365	−	1.16717i	2.42365	−	1.16717i
$856$	−1.49604	−	1.08694i	−1.49604	−	1.08694i
$857$			1.66915i			1.66915i	0.550897	+	0.834573i	$0.314286\pi$
$857$			1.66915i			1.66915i	−0.550897	+	0.834573i	$0.685714\pi$
$858$		0			0
$859$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$859$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$860$	0.0327801	+	0.0680685i	0.0327801	+	0.0680685i
$861$		0			0
$862$	−1.94333	−	0.631426i	−1.94333	−	0.631426i
$863$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$863$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$864$	−0.0423361	−	0.130297i	−0.0423361	−	0.130297i
$865$		0			0
$866$		0			0
$867$	−0.981100	+	1.35037i	−0.981100	+	1.35037i
$868$		0			0
$869$		0			0
$870$	0.151167	+	0.0274327i	0.151167	+	0.0274327i
$871$		0			0
$872$	−0.712571	−	0.980770i	−0.712571	−	0.980770i
$873$		0			0
$874$		0			0
$875$		0			0
$876$	0.126105			0.126105
$877$	−1.88490	+	0.612441i	−1.88490	+	0.612441i	−0.900969	+	0.433884i	$0.857143\pi$
$877$	−1.88490	+	0.612441i	−1.88490	+	0.612441i	−0.983930	+	0.178557i	$0.942857\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.45780	−	1.05915i	−1.45780	−	1.05915i	−0.983930	−	0.178557i	$-0.942857\pi$
$881$	−1.45780	−	1.05915i	−1.45780	−	1.05915i	−0.473869	−	0.880596i	$-0.657143\pi$
$882$			1.83213i			1.83213i
$883$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$883$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$	−2.03080	−	0.659846i	−2.03080	−	0.659846i
$889$		0			0
$890$	−0.490383	−	1.01829i	−0.490383	−	1.01829i
$891$		0			0
$892$	−0.0404227	+	0.0556371i	−0.0404227	+	0.0556371i
$893$		0			0
$894$		0			0
$895$	−1.24525	+	0.599682i	−1.24525	+	0.599682i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$	−0.00418785	+	0.0932498i	−0.00418785	+	0.0932498i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$	2.67057	+	1.94028i	2.67057	+	1.94028i
$907$		0			0			−	1.00000i	$-0.5\pi$
$907$		0			0				1.00000i	$0.5\pi$
$908$		0			0
$909$	0.433837	−	1.33521i	0.433837	−	1.33521i
$910$		0			0
$911$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$911$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$912$	2.50936	+	0.815339i	2.50936	+	0.815339i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	0.0317810	−	0.0978120i	0.0317810	−	0.0978120i
$917$		0			0
$918$		0			0
$919$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$919$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	1.02879	+	0.820436i	1.02879	+	0.820436i
$926$	1.88650			1.88650
$927$	−2.65609	+	0.863017i	−2.65609	+	0.863017i
$928$	0.00550730	+	0.00758015i	0.00550730	+	0.00758015i
$929$	−1.61152	+	1.17084i	−1.61152	+	1.17084i	−0.753071	+	0.657939i	$0.771429\pi$
$929$	−1.61152	+	1.17084i	−1.61152	+	1.17084i	−0.858449	+	0.512899i	$0.828571\pi$
$930$		0			0
$931$	−1.21850	−	0.885289i	−1.21850	−	0.885289i
$932$			0.0961140i			0.0961140i
$933$	−1.47768	+	2.03385i	−1.47768	+	2.03385i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$937$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$938$		0			0
$939$	1.00573	+	3.09530i	1.00573	+	3.09530i
$940$		0			0
$941$	−0.530551	+	1.63287i	−0.530551	+	1.63287i	0.222521	+	0.974928i	$0.428571\pi$
$941$	−0.530551	+	1.63287i	−0.530551	+	1.63287i	−0.753071	+	0.657939i	$0.771429\pi$
$942$	0.707255	−	0.973453i	0.707255	−	0.973453i
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.16493	+	1.60339i	1.16493	+	1.60339i	0.691063	+	0.722795i	$0.257143\pi$
$947$	1.16493	+	1.60339i	1.16493	+	1.60339i	0.473869	+	0.880596i	$0.342857\pi$
$948$	−0.0786286	+	0.0255480i	−0.0786286	+	0.0255480i
$949$		0			0
$950$	−1.20793	−	0.963291i	−1.20793	−	0.963291i
$951$		0			0
$952$		0			0
$953$	1.03520	+	1.42483i	1.03520	+	1.42483i	0.900969	+	0.433884i	$0.142857\pi$
$953$	1.03520	+	1.42483i	1.03520	+	1.42483i	0.134233	+	0.990950i	$0.457143\pi$
$954$		0			0
$955$	0.887305	−	1.64889i	0.887305	−	1.64889i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$	1.13698	−	1.08706i	1.13698	−	1.08706i
$961$	0.309017	+	0.951057i	0.309017	+	0.951057i
$962$		0			0
$963$	3.23099	+	1.04981i	3.23099	+	1.04981i
$964$		0			0
$965$		0			0
$966$		0			0
$967$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$967$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$968$			0.972188i			0.972188i
$969$		0			0
$970$		0			0
$971$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$971$	−1.30902	+	0.951057i	−1.30902	+	0.951057i	−1.00000			$\pi$
$972$	−0.0195934	−	0.0269680i	−0.0195934	−	0.0269680i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.90020	+	0.617412i	−1.90020	+	0.617412i	−0.936235	+	0.351375i	$0.885714\pi$
$977$	−1.90020	+	0.617412i	−1.90020	+	0.617412i	−0.963963	+	0.266037i	$0.914286\pi$
$978$		0			0
$979$		0			0
$980$	0.0470870	−	0.0226759i	0.0470870	−	0.0226759i
$981$	1.80182	+	1.30910i	1.80182	+	1.30910i
$982$		0			0
$983$	0.105377	−	0.145039i	0.105377	−	0.145039i	−0.753071	−	0.657939i	$-0.771429\pi$
$983$	0.105377	−	0.145039i	0.105377	−	0.145039i	0.858449	+	0.512899i	$0.171429\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$991$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.68931	−	0.306564i	−1.68931	−	0.306564i
$996$	−0.137609	+	0.0999787i	−0.137609	+	0.0999787i
$997$	−1.03520	−	1.42483i	−1.03520	−	1.42483i	−0.900969	−	0.433884i	$-0.857143\pi$
$997$	−1.03520	−	1.42483i	−1.03520	−	1.42483i	−0.134233	−	0.990950i	$-0.542857\pi$
$998$	1.07490	−	0.349257i	1.07490	−	0.349257i
$999$	1.72647			1.72647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1775.1.bb.b.1419.3	yes	24
25.4	even	10	inner	1775.1.bb.b.354.3	✓	24
71.70	odd	2	CM	1775.1.bb.b.1419.3	yes	24
1775.354	odd	10	inner	1775.1.bb.b.354.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1775.1.bb.b.354.3	✓	24	25.4	even	10	inner
1775.1.bb.b.354.3	✓	24	1775.354	odd	10	inner
1775.1.bb.b.1419.3	yes	24	1.1	even	1	trivial
1775.1.bb.b.1419.3	yes	24	71.70	odd	2	CM

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:	\( N \)	\(=\)	\( 1775 = 5^{2} \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1775.bb (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.975592 + 0.316989i) q^{2} +(-0.981100 - 1.35037i) q^{3} +(0.0422814 - 0.0307192i) q^{4} +(-0.983930 - 0.178557i) q^{5} +(1.38521 + 1.00641i) q^{6} +(0.571438 - 0.786516i) q^{8} +(-0.551920 + 1.69863i) q^{9} +O(q^{10})\)	\(q+(-0.975592 + 0.316989i) q^{2} +(-0.981100 - 1.35037i) q^{3} +(0.0422814 - 0.0307192i) q^{4} +(-0.983930 - 0.178557i) q^{5} +(1.38521 + 1.00641i) q^{6} +(0.571438 - 0.786516i) q^{8} +(-0.551920 + 1.69863i) q^{9} +(1.01651 - 0.137696i) q^{10} +(-0.0829645 - 0.0269568i) q^{12} +(0.724216 + 1.50385i) q^{15} +(-0.324323 + 0.998164i) q^{16} -1.83213i q^{18} +(1.21850 + 0.885289i) q^{19} +(-0.0470870 + 0.0226759i) q^{20} -1.62272 q^{24} +(0.936235 + 0.351375i) q^{25} +(1.24782 - 0.405440i) q^{27} +(-0.0725928 + 0.0527418i) q^{29} +(-1.18324 - 1.23758i) q^{30} -0.104420i q^{32} +(0.0288448 + 0.0887752i) q^{36} +(1.25147 + 0.406628i) q^{37} +(-1.46938 - 0.477431i) q^{38} +(-0.702692 + 0.671843i) q^{40} -1.44559i q^{43} +(0.846353 - 1.57279i) q^{45} +(1.66608 - 0.541343i) q^{48} -1.00000 q^{49} +(-1.02477 - 0.0460223i) q^{50} +(-1.08884 + 0.791089i) q^{54} -2.51397i q^{57} +(0.0541024 - 0.0744656i) q^{58} +(0.0768179 + 0.0413375i) q^{60} +(-0.291223 - 0.896292i) q^{64} +(0.809017 - 0.587785i) q^{71} +(1.02062 + 1.40476i) q^{72} +(-1.37484 + 0.446712i) q^{73} -1.34983 q^{74} +(-0.444054 - 1.60900i) q^{75} +0.0787151 q^{76} +(0.766736 - 0.557066i) q^{79} +(0.497340 - 0.924213i) q^{80} +(-0.326782 - 0.237421i) q^{81} +(1.14610 - 1.57747i) q^{83} +(0.458236 + 1.41031i) q^{86} +(0.142442 + 0.0462821i) q^{87} +(-0.340473 - 1.04787i) q^{89} +(-0.327139 + 1.80268i) q^{90} +(-1.04084 - 1.08863i) q^{95} +(-0.141006 + 0.102447i) q^{96} +(0.975592 - 0.316989i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 5 q^{2} + 3 q^{4} - q^{5} + 5 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q - 5 * q^2 + 3 * q^4 - q^5 + 5 * q^6 - 5 * q^8 + 8 * q^9	\( 24 q - 5 q^{2} + 3 q^{4} - q^{5} + 5 q^{6} - 5 q^{8} + 8 q^{9} - 5 q^{10} + 10 q^{12} - 11 q^{16} + 3 q^{19} + q^{20} - 4 q^{24} + q^{25} - 5 q^{27} + 3 q^{29} + 7 q^{30} - 11 q^{36} - 30 q^{38} - 5 q^{40} + 4 q^{45} + 10 q^{48} - 24 q^{49} - 10 q^{54} + 5 q^{58} - 23 q^{60} + 8 q^{64} + 6 q^{71} + 25 q^{72} - 5 q^{73} - 14 q^{74} - 7 q^{75} + 8 q^{76} + 3 q^{79} + 22 q^{80} - q^{81} - 5 q^{87} - 3 q^{89} + 12 q^{90} + 2 q^{95} - 11 q^{96} + 5 q^{98}+O(q^{100}) \) 24 * q - 5 * q^2 + 3 * q^4 - q^5 + 5 * q^6 - 5 * q^8 + 8 * q^9 - 5 * q^10 + 10 * q^12 - 11 * q^16 + 3 * q^19 + q^20 - 4 * q^24 + q^25 - 5 * q^27 + 3 * q^29 + 7 * q^30 - 11 * q^36 - 30 * q^38 - 5 * q^40 + 4 * q^45 + 10 * q^48 - 24 * q^49 - 10 * q^54 + 5 * q^58 - 23 * q^60 + 8 * q^64 + 6 * q^71 + 25 * q^72 - 5 * q^73 - 14 * q^74 - 7 * q^75 + 8 * q^76 + 3 * q^79 + 22 * q^80 - q^81 - 5 * q^87 - 3 * q^89 + 12 * q^90 + 2 * q^95 - 11 * q^96 + 5 * q^98

Introduction

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