LMFDB - Embedded newform 1400.1.cc.a.69.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,1,Mod(69,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 9, 5]))

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

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

chi := DirichletCharacter("1400.69");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1400.cc (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:	$0.698691017686$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{40})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} + x^{8} - x^{4} + 1 $ x^16 - x^12 + x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{20}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{20} - \cdots)$

Embedding invariants

Embedding label			69.2
Root			$-0.891007 - 0.453990i$ of defining polynomial
Character	$\chi$	$=$	1400.69
Dual form			1400.1.cc.a.629.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(1.16110 + 1.59811i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(-1.59811 - 1.16110i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.896802 + 2.76007i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(1.16110 + 1.59811i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(-1.59811 - 1.16110i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.896802 + 2.76007i) q^{9} +(0.156434 - 0.987688i) q^{10} +(1.87869 + 0.610425i) q^{12} +(0.297556 + 0.0966818i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.95106 + 0.309017i) q^{15} +(0.309017 - 0.951057i) q^{16} -2.90211i q^{18} +(1.14412 + 0.831254i) q^{19} +(0.156434 + 0.987688i) q^{20} +(1.59811 - 1.16110i) q^{21} +(-1.11803 + 0.363271i) q^{23} -1.97538 q^{24} +(-0.587785 - 0.809017i) q^{25} -0.312869 q^{26} +(-3.57349 + 1.16110i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(1.76007 - 0.896802i) q^{30} +1.00000i q^{32} +(0.891007 + 0.453990i) q^{35} +(0.896802 + 2.76007i) q^{36} +(-1.34500 - 0.437016i) q^{38} +(0.190983 + 0.587785i) q^{39} +(-0.453990 - 0.891007i) q^{40} +(-1.16110 + 1.59811i) q^{42} +(-2.05210 - 2.05210i) q^{45} +(0.951057 - 0.690983i) q^{46} +(1.87869 - 0.610425i) q^{48} -1.00000 q^{49} +(0.809017 + 0.587785i) q^{50} +(0.297556 - 0.0966818i) q^{52} +(3.03979 - 2.20854i) q^{54} +(0.809017 + 0.587785i) q^{56} +2.79360i q^{57} +(0.550672 - 1.69480i) q^{59} +(-1.39680 + 1.39680i) q^{60} +(0.280582 + 0.863541i) q^{61} +(2.76007 + 0.896802i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.221232 + 0.221232i) q^{65} +(-1.87869 - 1.36495i) q^{69} +(-0.987688 - 0.156434i) q^{70} +(1.53884 - 1.11803i) q^{71} +(-1.70582 - 2.34786i) q^{72} +(0.610425 - 1.87869i) q^{75} +1.41421 q^{76} +(-0.363271 - 0.500000i) q^{78} +(0.951057 - 0.690983i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-3.65688 - 2.65688i) q^{81} +(0.533698 - 0.734572i) q^{83} +(0.610425 - 1.87869i) q^{84} +(2.58580 + 1.31753i) q^{90} +(0.0966818 - 0.297556i) q^{91} +(-0.690983 + 0.951057i) q^{92} +(-1.26007 + 0.642040i) q^{95} +(-1.59811 + 1.16110i) q^{96} +(0.951057 - 0.309017i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 4 * q^9	$ 16 q + 4 q^{4} + 4 q^{9} - 4 q^{14} - 16 q^{15} - 4 q^{16} + 4 q^{30} - 4 q^{36} + 12 q^{39} - 16 q^{49} + 4 q^{50} + 4 q^{56} - 4 q^{60} + 20 q^{63} + 4 q^{64} - 4 q^{65} - 16 q^{81} - 20 q^{92} + 4 q^{95}+O(q^{100}) $ 16 * q + 4 * q^4 + 4 * q^9 - 4 * q^14 - 16 * q^15 - 4 * q^16 + 4 * q^30 - 4 * q^36 + 12 * q^39 - 16 * q^49 + 4 * q^50 + 4 * q^56 - 4 * q^60 + 20 * q^63 + 4 * q^64 - 4 * q^65 - 16 * q^81 - 20 * q^92 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$2$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$3$	1.16110	+	1.59811i	1.16110	+	1.59811i	0.707107	+	0.707107i	$0.250000\pi$
$3$	1.16110	+	1.59811i	1.16110	+	1.59811i	0.453990	+	0.891007i	$0.350000\pi$
$4$	0.809017	−	0.587785i	0.809017	−	0.587785i
$5$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$5$	−0.453990	+	0.891007i	−0.453990	+	0.891007i
$6$	−1.59811	−	1.16110i	−1.59811	−	1.16110i
$7$		−	1.00000i		−	1.00000i
$7$		−	1.00000i		−	1.00000i
$8$	−0.587785	+	0.809017i	−0.587785	+	0.809017i
$9$	−0.896802	+	2.76007i	−0.896802	+	2.76007i
$10$	0.156434	−	0.987688i	0.156434	−	0.987688i
$11$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$11$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$12$	1.87869	+	0.610425i	1.87869	+	0.610425i
$13$	0.297556	+	0.0966818i	0.297556	+	0.0966818i	0.453990	−	0.891007i	$-0.350000\pi$
$13$	0.297556	+	0.0966818i	0.297556	+	0.0966818i	−0.156434	+	0.987688i	$0.550000\pi$
$14$	0.309017	+	0.951057i	0.309017	+	0.951057i
$15$	−1.95106	+	0.309017i	−1.95106	+	0.309017i
$16$	0.309017	−	0.951057i	0.309017	−	0.951057i
$17$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$17$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$18$		−	2.90211i		−	2.90211i
$19$	1.14412	+	0.831254i	1.14412	+	0.831254i	0.987688	−	0.156434i	$-0.0500000\pi$
$19$	1.14412	+	0.831254i	1.14412	+	0.831254i	0.156434	+	0.987688i	$0.450000\pi$
$20$	0.156434	+	0.987688i	0.156434	+	0.987688i
$21$	1.59811	−	1.16110i	1.59811	−	1.16110i
$22$		0			0
$23$	−1.11803	+	0.363271i	−1.11803	+	0.363271i	−0.809017	−	0.587785i	$-0.800000\pi$
$23$	−1.11803	+	0.363271i	−1.11803	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$24$	−1.97538			−1.97538
$25$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$26$	−0.312869			−0.312869
$27$	−3.57349	+	1.16110i	−3.57349	+	1.16110i
$28$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$29$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$29$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$30$	1.76007	−	0.896802i	1.76007	−	0.896802i
$31$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$31$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$32$			1.00000i			1.00000i
$33$		0			0
$34$		0			0
$35$	0.891007	+	0.453990i	0.891007	+	0.453990i
$36$	0.896802	+	2.76007i	0.896802	+	2.76007i
$37$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$37$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$38$	−1.34500	−	0.437016i	−1.34500	−	0.437016i
$39$	0.190983	+	0.587785i	0.190983	+	0.587785i
$40$	−0.453990	−	0.891007i	−0.453990	−	0.891007i
$41$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$41$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$42$	−1.16110	+	1.59811i	−1.16110	+	1.59811i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−2.05210	−	2.05210i	−2.05210	−	2.05210i
$46$	0.951057	−	0.690983i	0.951057	−	0.690983i
$47$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$47$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$48$	1.87869	−	0.610425i	1.87869	−	0.610425i
$49$	−1.00000			−1.00000
$50$	0.809017	+	0.587785i	0.809017	+	0.587785i
$51$		0			0
$52$	0.297556	−	0.0966818i	0.297556	−	0.0966818i
$53$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$53$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$54$	3.03979	−	2.20854i	3.03979	−	2.20854i
$55$		0			0
$56$	0.809017	+	0.587785i	0.809017	+	0.587785i
$57$			2.79360i			2.79360i
$58$		0			0
$59$	0.550672	−	1.69480i	0.550672	−	1.69480i	−0.156434	−	0.987688i	$-0.550000\pi$
$59$	0.550672	−	1.69480i	0.550672	−	1.69480i	0.707107	−	0.707107i	$-0.250000\pi$
$60$	−1.39680	+	1.39680i	−1.39680	+	1.39680i
$61$	0.280582	+	0.863541i	0.280582	+	0.863541i	0.987688	+	0.156434i	$0.0500000\pi$
$61$	0.280582	+	0.863541i	0.280582	+	0.863541i	−0.707107	+	0.707107i	$0.750000\pi$
$62$		0			0
$63$	2.76007	+	0.896802i	2.76007	+	0.896802i
$64$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$65$	−0.221232	+	0.221232i	−0.221232	+	0.221232i
$66$		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
$69$	−1.87869	−	1.36495i	−1.87869	−	1.36495i
$70$	−0.987688	−	0.156434i	−0.987688	−	0.156434i
$71$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.587785	−	0.809017i	$-0.300000\pi$
$71$	1.53884	−	1.11803i	1.53884	−	1.11803i	0.951057	−	0.309017i	$-0.100000\pi$
$72$	−1.70582	−	2.34786i	−1.70582	−	2.34786i
$73$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$73$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$74$		0			0
$75$	0.610425	−	1.87869i	0.610425	−	1.87869i
$76$	1.41421			1.41421
$77$		0			0
$78$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$79$	0.951057	−	0.690983i	0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$79$	0.951057	−	0.690983i	0.951057	−	0.690983i	0.951057	+	0.309017i	$0.100000\pi$
$80$	0.707107	+	0.707107i	0.707107	+	0.707107i
$81$	−3.65688	−	2.65688i	−3.65688	−	2.65688i
$82$		0			0
$83$	0.533698	−	0.734572i	0.533698	−	0.734572i	−0.453990	−	0.891007i	$-0.650000\pi$
$83$	0.533698	−	0.734572i	0.533698	−	0.734572i	0.987688	+	0.156434i	$0.0500000\pi$
$84$	0.610425	−	1.87869i	0.610425	−	1.87869i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$89$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$90$	2.58580	+	1.31753i	2.58580	+	1.31753i
$91$	0.0966818	−	0.297556i	0.0966818	−	0.297556i
$92$	−0.690983	+	0.951057i	−0.690983	+	0.951057i
$93$		0			0
$94$		0			0
$95$	−1.26007	+	0.642040i	−1.26007	+	0.642040i
$96$	−1.59811	+	1.16110i	−1.59811	+	1.16110i
$97$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$97$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$98$	0.951057	−	0.309017i	0.951057	−	0.309017i
$99$		0			0
$100$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$101$	0.312869			0.312869			0.156434	−	0.987688i	$-0.450000\pi$
$101$	0.312869			0.312869			0.156434	+	0.987688i	$0.450000\pi$
$102$		0			0
$103$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$103$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$104$	−0.253116	+	0.183900i	−0.253116	+	0.183900i
$105$	0.309017	+	1.95106i	0.309017	+	1.95106i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$	−2.20854	+	3.03979i	−2.20854	+	3.03979i
$109$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$109$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$110$		0			0
$111$		0			0
$112$	−0.951057	−	0.309017i	−0.951057	−	0.309017i
$113$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$113$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$114$	−0.863271	−	2.65688i	−0.863271	−	2.65688i
$115$	0.183900	−	1.16110i	0.183900	−	1.16110i
$116$		0			0
$117$	−0.533698	+	0.734572i	−0.533698	+	0.734572i
$118$			1.78201i			1.78201i
$119$		0			0
$120$	0.896802	−	1.76007i	0.896802	−	1.76007i
$121$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$122$	−0.533698	−	0.734572i	−0.533698	−	0.734572i
$123$		0			0
$124$		0			0
$125$	0.987688	−	0.156434i	0.987688	−	0.156434i
$126$	−2.90211			−2.90211
$127$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$127$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$128$	0.587785	+	0.809017i	0.587785	+	0.809017i
$129$		0			0
$130$	0.142040	−	0.278768i	0.142040	−	0.278768i
$131$	0.734572	+	0.533698i	0.734572	+	0.533698i	0.891007	−	0.453990i	$-0.150000\pi$
$131$	0.734572	+	0.533698i	0.734572	+	0.533698i	−0.156434	+	0.987688i	$0.550000\pi$
$132$		0			0
$133$	0.831254	−	1.14412i	0.831254	−	1.14412i
$134$		0			0
$135$	0.587785	−	3.71113i	0.587785	−	3.71113i
$136$		0			0
$137$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$137$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$138$	2.20854	+	0.717598i	2.20854	+	0.717598i
$139$	0.437016	+	1.34500i	0.437016	+	1.34500i	0.891007	+	0.453990i	$0.150000\pi$
$139$	0.437016	+	1.34500i	0.437016	+	1.34500i	−0.453990	+	0.891007i	$0.650000\pi$
$140$	0.987688	−	0.156434i	0.987688	−	0.156434i
$141$		0			0
$142$	−1.11803	+	1.53884i	−1.11803	+	1.53884i
$143$		0			0
$144$	2.34786	+	1.70582i	2.34786	+	1.70582i
$145$		0			0
$146$		0			0
$147$	−1.16110	−	1.59811i	−1.16110	−	1.59811i
$148$		0			0
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$			1.97538i			1.97538i
$151$	1.61803			1.61803			0.809017	−	0.587785i	$-0.200000\pi$
$151$	1.61803			1.61803			0.809017	+	0.587785i	$0.200000\pi$
$152$	−1.34500	+	0.437016i	−1.34500	+	0.437016i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	0.500000	+	0.363271i	0.500000	+	0.363271i
$157$			0.907981i			0.907981i	0.891007	+	0.453990i	$0.150000\pi$
$157$			0.907981i			0.907981i	−0.891007	+	0.453990i	$0.850000\pi$
$158$	−0.690983	+	0.951057i	−0.690983	+	0.951057i
$159$		0			0
$160$	−0.891007	−	0.453990i	−0.891007	−	0.453990i
$161$	0.363271	+	1.11803i	0.363271	+	1.11803i
$162$	4.29892	+	1.39680i	4.29892	+	1.39680i
$163$		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
$166$	−0.280582	+	0.863541i	−0.280582	+	0.863541i
$167$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$167$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$168$			1.97538i			1.97538i
$169$	−0.729825	−	0.530249i	−0.729825	−	0.530249i
$170$		0			0
$171$	−3.32037	+	2.41239i	−3.32037	+	2.41239i
$172$		0			0
$173$	−1.69480	+	0.550672i	−1.69480	+	0.550672i	−0.987688	−	0.156434i	$-0.950000\pi$
$173$	−1.69480	+	0.550672i	−1.69480	+	0.550672i	−0.707107	+	0.707107i	$0.750000\pi$
$174$		0			0
$175$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$176$		0			0
$177$	3.34786	−	1.08779i	3.34786	−	1.08779i
$178$		0			0
$179$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$179$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$180$	−2.86638	−	0.453990i	−2.86638	−	0.453990i
$181$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.987688	−	0.156434i	$-0.950000\pi$
$181$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.453990	−	0.891007i	$-0.650000\pi$
$182$			0.312869i			0.312869i
$183$	−1.05425	+	1.45106i	−1.05425	+	1.45106i
$184$	0.363271	−	1.11803i	0.363271	−	1.11803i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$	1.16110	+	3.57349i	1.16110	+	3.57349i
$190$	1.00000	−	1.00000i	1.00000	−	1.00000i
$191$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$191$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$192$	1.16110	−	1.59811i	1.16110	−	1.59811i
$193$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$193$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$194$		0			0
$195$	−0.610425	−	0.0966818i	−0.610425	−	0.0966818i
$196$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$197$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$197$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	1.00000			1.00000
$201$		0			0
$202$	−0.297556	+	0.0966818i	−0.297556	+	0.0966818i
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	3.41164i		−	3.41164i
$208$	0.183900	−	0.253116i	0.183900	−	0.253116i
$209$		0			0
$210$	−0.896802	−	1.76007i	−0.896802	−	1.76007i
$211$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$211$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$212$		0			0
$213$	3.57349	+	1.16110i	3.57349	+	1.16110i
$214$		0			0
$215$		0			0
$216$	1.16110	−	3.57349i	1.16110	−	3.57349i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$223$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$224$	1.00000			1.00000
$225$	2.76007	−	0.896802i	2.76007	−	0.896802i
$226$	−0.618034			−0.618034
$227$	1.87869	−	0.610425i	1.87869	−	0.610425i	0.891007	−	0.453990i	$-0.150000\pi$
$227$	1.87869	−	0.610425i	1.87869	−	0.610425i	0.987688	−	0.156434i	$-0.0500000\pi$
$228$	1.64204	+	2.26007i	1.64204	+	2.26007i
$229$	−1.44168	+	1.04744i	−1.44168	+	1.04744i	−0.453990	+	0.891007i	$0.650000\pi$
$229$	−1.44168	+	1.04744i	−1.44168	+	1.04744i	−0.987688	+	0.156434i	$0.950000\pi$
$230$	0.183900	+	1.16110i	0.183900	+	1.16110i
$231$		0			0
$232$		0			0
$233$	1.11803	−	1.53884i	1.11803	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$233$	1.11803	−	1.53884i	1.11803	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$234$	0.280582	−	0.863541i	0.280582	−	0.863541i
$235$		0			0
$236$	−0.550672	−	1.69480i	−0.550672	−	1.69480i
$237$	2.20854	+	0.717598i	2.20854	+	0.717598i
$238$		0			0
$239$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	−0.809017	−	0.587785i	$-0.800000\pi$
$239$	−0.500000	−	1.53884i	−0.500000	−	1.53884i	0.309017	−	0.951057i	$-0.400000\pi$
$240$	−0.309017	+	1.95106i	−0.309017	+	1.95106i
$241$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$241$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$242$	0.587785	−	0.809017i	0.587785	−	0.809017i
$243$		−	5.17160i		−	5.17160i
$244$	0.734572	+	0.533698i	0.734572	+	0.533698i
$245$	0.453990	−	0.891007i	0.453990	−	0.891007i
$246$		0			0
$247$	0.260074	+	0.357960i	0.260074	+	0.357960i
$248$		0			0
$249$	1.79360			1.79360
$250$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$251$	0.907981			0.907981			0.453990	−	0.891007i	$-0.350000\pi$
$251$	0.907981			0.907981			0.453990	+	0.891007i	$0.350000\pi$
$252$	2.76007	−	0.896802i	2.76007	−	0.896802i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.809017	−	0.587785i	−0.809017	−	0.587785i
$257$		0			0			−	1.00000i	$-0.5\pi$
$257$		0			0				1.00000i	$0.5\pi$
$258$		0			0
$259$		0			0
$260$	−0.0489435	+	0.309017i	−0.0489435	+	0.309017i
$261$		0			0
$262$	−0.863541	−	0.280582i	−0.863541	−	0.280582i
$263$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$263$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$264$		0			0
$265$		0			0
$266$	−0.437016	+	1.34500i	−0.437016	+	1.34500i
$267$		0			0
$268$		0			0
$269$	1.44168	+	1.04744i	1.44168	+	1.04744i	0.987688	+	0.156434i	$0.0500000\pi$
$269$	1.44168	+	1.04744i	1.44168	+	1.04744i	0.453990	+	0.891007i	$0.350000\pi$
$270$	0.587785	+	3.71113i	0.587785	+	3.71113i
$271$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$271$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$272$		0			0
$273$	0.587785	−	0.190983i	0.587785	−	0.190983i
$274$		0			0
$275$		0			0
$276$	−2.32219			−2.32219
$277$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$277$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$278$	−0.831254	−	1.14412i	−0.831254	−	1.14412i
$279$		0			0
$280$	−0.891007	+	0.453990i	−0.891007	+	0.453990i
$281$	0.500000	+	0.363271i	0.500000	+	0.363271i	0.809017	−	0.587785i	$-0.200000\pi$
$281$	0.500000	+	0.363271i	0.500000	+	0.363271i	−0.309017	+	0.951057i	$0.600000\pi$
$282$		0			0
$283$	1.16110	−	1.59811i	1.16110	−	1.59811i	0.453990	−	0.891007i	$-0.350000\pi$
$283$	1.16110	−	1.59811i	1.16110	−	1.59811i	0.707107	−	0.707107i	$-0.250000\pi$
$284$	0.587785	−	1.80902i	0.587785	−	1.80902i
$285$	−2.48912	−	1.26827i	−2.48912	−	1.26827i
$286$		0			0
$287$		0			0
$288$	−2.76007	−	0.896802i	−2.76007	−	0.896802i
$289$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$293$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$294$	1.59811	+	1.16110i	1.59811	+	1.16110i
$295$	1.26007	+	1.26007i	1.26007	+	1.26007i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.367799			−0.367799
$300$	−0.610425	−	1.87869i	−0.610425	−	1.87869i
$301$		0			0
$302$	−1.53884	+	0.500000i	−1.53884	+	0.500000i
$303$	0.363271	+	0.500000i	0.363271	+	0.500000i
$304$	1.14412	−	0.831254i	1.14412	−	0.831254i
$305$	−0.896802	−	0.142040i	−0.896802	−	0.142040i
$306$		0			0
$307$			1.41421i			1.41421i	0.707107	+	0.707107i	$0.250000\pi$
$307$			1.41421i			1.41421i	−0.707107	+	0.707107i	$0.750000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$311$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$312$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$313$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$313$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$314$	−0.280582	−	0.863541i	−0.280582	−	0.863541i
$315$	−2.05210	+	2.05210i	−2.05210	+	2.05210i
$316$	0.363271	−	1.11803i	0.363271	−	1.11803i
$317$		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
$320$	0.987688	+	0.156434i	0.987688	+	0.156434i
$321$		0			0
$322$	−0.690983	−	0.951057i	−0.690983	−	0.951057i
$323$		0			0
$324$	−4.52015			−4.52015
$325$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i
$326$		0			0
$327$		0			0
$328$		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	$0.200000\pi$
$332$		−	0.907981i		−	0.907981i
$333$		0			0
$334$		0			0
$335$		0			0
$336$	−0.610425	−	1.87869i	−0.610425	−	1.87869i
$337$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.587785	−	0.809017i	$-0.700000\pi$
$337$	−1.53884	−	0.500000i	−1.53884	−	0.500000i	−0.951057	+	0.309017i	$0.900000\pi$
$338$	0.857960	+	0.278768i	0.857960	+	0.278768i
$339$	0.377263	+	1.16110i	0.377263	+	1.16110i
$340$		0			0
$341$		0			0
$342$	2.41239	−	3.32037i	2.41239	−	3.32037i
$343$			1.00000i			1.00000i
$344$		0			0
$345$	2.06909	−	1.05425i	2.06909	−	1.05425i
$346$	1.44168	−	1.04744i	1.44168	−	1.04744i
$347$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$347$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$348$		0			0
$349$	0.312869			0.312869			0.156434	−	0.987688i	$-0.450000\pi$
$349$	0.312869			0.312869			0.156434	+	0.987688i	$0.450000\pi$
$350$	0.587785	−	0.809017i	0.587785	−	0.809017i
$351$	−1.17557			−1.17557
$352$		0			0
$353$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$353$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$354$	−2.84786	+	2.06909i	−2.84786	+	2.06909i
$355$	0.297556	+	1.87869i	0.297556	+	1.87869i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	0.500000	−	1.53884i	0.500000	−	1.53884i	−0.309017	−	0.951057i	$-0.600000\pi$
$359$	0.500000	−	1.53884i	0.500000	−	1.53884i	0.809017	−	0.587785i	$-0.200000\pi$
$360$	2.86638	−	0.453990i	2.86638	−	0.453990i
$361$	0.309017	+	0.951057i	0.309017	+	0.951057i
$362$	1.69480	+	0.550672i	1.69480	+	0.550672i
$363$	−1.87869	−	0.610425i	−1.87869	−	0.610425i
$364$	−0.0966818	−	0.297556i	−0.0966818	−	0.297556i
$365$		0			0
$366$	0.554254	−	1.70582i	0.554254	−	1.70582i
$367$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$367$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$368$			1.17557i			1.17557i
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$373$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$374$		0			0
$375$	1.39680	+	1.39680i	1.39680	+	1.39680i
$376$		0			0
$377$		0			0
$378$	−2.20854	−	3.03979i	−2.20854	−	3.03979i
$379$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$379$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$380$	−0.642040	+	1.26007i	−0.642040	+	1.26007i
$381$		0			0
$382$		−	1.17557i		−	1.17557i
$383$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$383$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$384$	−0.610425	+	1.87869i	−0.610425	+	1.87869i
$385$		0			0
$386$	0.190983	+	0.587785i	0.190983	+	0.587785i
$387$		0			0
$388$		0			0
$389$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$389$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$390$	0.610425	−	0.0966818i	0.610425	−	0.0966818i
$391$		0			0
$392$	0.587785	−	0.809017i	0.587785	−	0.809017i
$393$			1.79360i			1.79360i
$394$		0			0
$395$	0.183900	+	1.16110i	0.183900	+	1.16110i
$396$		0			0
$397$	−0.183900	−	0.253116i	−0.183900	−	0.253116i	0.707107	−	0.707107i	$-0.250000\pi$
$397$	−0.183900	−	0.253116i	−0.183900	−	0.253116i	−0.891007	+	0.453990i	$0.850000\pi$
$398$		0			0
$399$	2.79360			2.79360
$400$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$401$		0			0			−	1.00000i	$-0.5\pi$
$401$		0			0				1.00000i	$0.5\pi$
$402$		0			0
$403$		0			0
$404$	0.253116	−	0.183900i	0.253116	−	0.183900i
$405$	4.02748	−	2.05210i	4.02748	−	2.05210i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$409$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.69480	−	0.550672i	−1.69480	−	0.550672i
$414$	1.05425	+	3.24466i	1.05425	+	3.24466i
$415$	0.412215	+	0.809017i	0.412215	+	0.809017i
$416$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i
$417$	−1.64204	+	2.26007i	−1.64204	+	2.26007i
$418$		0			0
$419$	−1.59811	−	1.16110i	−1.59811	−	1.16110i	−0.891007	−	0.453990i	$-0.850000\pi$
$419$	−1.59811	−	1.16110i	−1.59811	−	1.16110i	−0.707107	−	0.707107i	$-0.750000\pi$
$420$	1.39680	+	1.39680i	1.39680	+	1.39680i
$421$		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
$426$	−3.75739			−3.75739
$427$	0.863541	−	0.280582i	0.863541	−	0.280582i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	0.309017	−	0.951057i	$-0.400000\pi$
$431$	−0.500000	−	0.363271i	−0.500000	−	0.363271i	−0.809017	+	0.587785i	$0.800000\pi$
$432$			3.75739i			3.75739i
$433$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$433$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.58114	−	0.513743i	−1.58114	−	0.513743i
$438$		0			0
$439$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$439$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$440$		0			0
$441$	0.896802	−	2.76007i	0.896802	−	2.76007i
$442$		0			0
$443$		0			0			−	1.00000i	$-0.5\pi$
$443$		0			0				1.00000i	$0.5\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.951057	+	0.309017i	−0.951057	+	0.309017i
$449$	−1.61803			−1.61803			−0.809017	−	0.587785i	$-0.800000\pi$
$449$	−1.61803			−1.61803			−0.809017	+	0.587785i	$0.800000\pi$
$450$	−2.34786	+	1.70582i	−2.34786	+	1.70582i
$451$		0			0
$452$	0.587785	−	0.190983i	0.587785	−	0.190983i
$453$	1.87869	+	2.58580i	1.87869	+	2.58580i
$454$	−1.59811	+	1.16110i	−1.59811	+	1.16110i
$455$	0.221232	+	0.221232i	0.221232	+	0.221232i
$456$	−2.26007	−	1.64204i	−2.26007	−	1.64204i
$457$		−	0.618034i		−	0.618034i	−0.951057	−	0.309017i	$-0.900000\pi$
$457$		−	0.618034i		−	0.618034i	0.951057	−	0.309017i	$-0.100000\pi$
$458$	1.04744	−	1.44168i	1.04744	−	1.44168i
$459$		0			0
$460$	−0.533698	−	1.04744i	−0.533698	−	1.04744i
$461$	0.437016	+	1.34500i	0.437016	+	1.34500i	0.891007	+	0.453990i	$0.150000\pi$
$461$	0.437016	+	1.34500i	0.437016	+	1.34500i	−0.453990	+	0.891007i	$0.650000\pi$
$462$		0			0
$463$	−0.587785	−	0.190983i	−0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$463$	−0.587785	−	0.190983i	−0.587785	−	0.190983i	−0.587785	+	0.809017i	$0.700000\pi$
$464$		0			0
$465$		0			0
$466$	−0.587785	+	1.80902i	−0.587785	+	1.80902i
$467$	−0.831254	+	1.14412i	−0.831254	+	1.14412i	0.156434	+	0.987688i	$0.450000\pi$
$467$	−0.831254	+	1.14412i	−0.831254	+	1.14412i	−0.987688	+	0.156434i	$0.950000\pi$
$468$			0.907981i			0.907981i
$469$		0			0
$470$		0			0
$471$	−1.45106	+	1.05425i	−1.45106	+	1.05425i
$472$	1.04744	+	1.44168i	1.04744	+	1.44168i
$473$		0			0
$474$	−2.32219			−2.32219
$475$		−	1.41421i		−	1.41421i
$476$		0			0
$477$		0			0
$478$	0.951057	+	1.30902i	0.951057	+	1.30902i
$479$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$479$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$480$	−0.309017	−	1.95106i	−0.309017	−	1.95106i
$481$		0			0
$482$		0			0
$483$	−1.36495	+	1.87869i	−1.36495	+	1.87869i
$484$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$485$		0			0
$486$	1.59811	+	4.91849i	1.59811	+	4.91849i
$487$	1.80902	+	0.587785i	1.80902	+	0.587785i	1.00000			$0$
$487$	1.80902	+	0.587785i	1.80902	+	0.587785i	0.809017	+	0.587785i	$0.200000\pi$
$488$	−0.863541	−	0.280582i	−0.863541	−	0.280582i
$489$		0			0
$490$	−0.156434	+	0.987688i	−0.156434	+	0.987688i
$491$		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
$494$	−0.357960	−	0.260074i	−0.357960	−	0.260074i
$495$		0			0
$496$		0			0
$497$	−1.11803	−	1.53884i	−1.11803	−	1.53884i
$498$	−1.70582	+	0.554254i	−1.70582	+	0.554254i
$499$		0			0		1.00000			$0$
$499$		0			0		−1.00000			$\pi$
$500$	0.707107	−	0.707107i	0.707107	−	0.707107i
$501$		0			0
$502$	−0.863541	+	0.280582i	−0.863541	+	0.280582i
$503$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$503$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$504$	−2.34786	+	1.70582i	−2.34786	+	1.70582i
$505$	−0.142040	+	0.278768i	−0.142040	+	0.278768i
$506$		0			0
$507$		−	1.78201i		−	1.78201i
$508$		0			0
$509$	0.437016	−	1.34500i	0.437016	−	1.34500i	−0.453990	−	0.891007i	$-0.650000\pi$
$509$	0.437016	−	1.34500i	0.437016	−	1.34500i	0.891007	−	0.453990i	$-0.150000\pi$
$510$		0			0
$511$		0			0
$512$	0.951057	+	0.309017i	0.951057	+	0.309017i
$513$	−5.05368	−	1.64204i	−5.05368	−	1.64204i
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$	−2.84786	−	2.06909i	−2.84786	−	2.06909i
$520$	−0.0489435	−	0.309017i	−0.0489435	−	0.309017i
$521$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$521$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$522$		0			0
$523$	0.297556	−	0.0966818i	0.297556	−	0.0966818i	−0.156434	−	0.987688i	$-0.550000\pi$
$523$	0.297556	−	0.0966818i	0.297556	−	0.0966818i	0.453990	+	0.891007i	$0.350000\pi$
$524$	0.907981			0.907981
$525$	−1.87869	−	0.610425i	−1.87869	−	0.610425i
$526$	1.61803			1.61803
$527$		0			0
$528$		0			0
$529$	0.309017	−	0.224514i	0.309017	−	0.224514i
$530$		0			0
$531$	4.18391	+	3.03979i	4.18391	+	3.03979i
$532$		−	1.41421i		−	1.41421i
$533$		0			0
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.69480	−	0.550672i	−1.69480	−	0.550672i
$539$		0			0
$540$	−1.70582	−	3.34786i	−1.70582	−	3.34786i
$541$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$541$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$542$		0			0
$543$		−	3.52015i		−	3.52015i
$544$		0			0
$545$		0			0
$546$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$547$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$547$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$548$		0			0
$549$	−2.63506			−2.63506
$550$		0			0
$551$		0			0
$552$	2.20854	−	0.717598i	2.20854	−	0.717598i
$553$	−0.690983	−	0.951057i	−0.690983	−	0.951057i
$554$		0			0
$555$		0			0
$556$	1.14412	+	0.831254i	1.14412	+	0.831254i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$		0			0
$559$		0			0
$560$	0.707107	−	0.707107i	0.707107	−	0.707107i
$561$		0			0
$562$	−0.587785	−	0.190983i	−0.587785	−	0.190983i
$563$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i	0.156434	−	0.987688i	$-0.450000\pi$
$563$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i	−0.453990	+	0.891007i	$0.650000\pi$
$564$		0			0
$565$	−0.437016	+	0.437016i	−0.437016	+	0.437016i
$566$	−0.610425	+	1.87869i	−0.610425	+	1.87869i
$567$	−2.65688	+	3.65688i	−2.65688	+	3.65688i
$568$			1.90211i			1.90211i
$569$	−0.951057	−	0.690983i	−0.951057	−	0.690983i		−	1.00000i	$-0.5\pi$
$569$	−0.951057	−	0.690983i	−0.951057	−	0.690983i	−0.951057	+	0.309017i	$0.900000\pi$
$570$	2.75921	+	0.437016i	2.75921	+	0.437016i
$571$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$571$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$572$		0			0
$573$	−2.20854	+	0.717598i	−2.20854	+	0.717598i
$574$		0			0
$575$	0.951057	+	0.690983i	0.951057	+	0.690983i
$576$	2.90211			2.90211
$577$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$577$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$578$	0.587785	+	0.809017i	0.587785	+	0.809017i
$579$	0.987688	−	0.717598i	0.987688	−	0.717598i
$580$		0			0
$581$	−0.734572	−	0.533698i	−0.734572	−	0.533698i
$582$		0			0
$583$		0			0
$584$		0			0
$585$	−0.412215	−	0.809017i	−0.412215	−	0.809017i
$586$	−0.437016	−	1.34500i	−0.437016	−	1.34500i
$587$	−1.69480	−	0.550672i	−1.69480	−	0.550672i	−0.707107	−	0.707107i	$-0.750000\pi$
$587$	−1.69480	−	0.550672i	−1.69480	−	0.550672i	−0.987688	+	0.156434i	$0.950000\pi$
$588$	−1.87869	−	0.610425i	−1.87869	−	0.610425i
$589$		0			0
$590$	−1.58779	−	0.809017i	−1.58779	−	0.809017i
$591$		0			0
$592$		0			0
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.349798	−	0.113656i	0.349798	−	0.113656i
$599$	−1.17557			−1.17557			−0.587785	−	0.809017i	$-0.700000\pi$
$599$	−1.17557			−1.17557			−0.587785	+	0.809017i	$0.700000\pi$
$600$	1.16110	+	1.59811i	1.16110	+	1.59811i
$601$		0			0		1.00000			$0$
$601$		0			0		−1.00000			$\pi$
$602$		0			0
$603$		0			0
$604$	1.30902	−	0.951057i	1.30902	−	0.951057i
$605$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$606$	−0.500000	−	0.363271i	−0.500000	−	0.363271i
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	−0.831254	+	1.14412i	−0.831254	+	1.14412i
$609$		0			0
$610$	0.896802	−	0.142040i	0.896802	−	0.142040i
$611$		0			0
$612$		0			0
$613$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$613$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$614$	−0.437016	−	1.34500i	−0.437016	−	1.34500i
$615$		0			0
$616$		0			0
$617$	0.951057	−	1.30902i	0.951057	−	1.30902i		−	1.00000i	$-0.5\pi$
$617$	0.951057	−	1.30902i	0.951057	−	1.30902i	0.951057	−	0.309017i	$-0.100000\pi$
$618$		0			0
$619$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.987688	−	0.156434i	$-0.950000\pi$
$619$	−1.44168	−	1.04744i	−1.44168	−	1.04744i	−0.453990	−	0.891007i	$-0.650000\pi$
$620$		0			0
$621$	3.57349	−	2.59629i	3.57349	−	2.59629i
$622$		0			0
$623$		0			0
$624$	0.618034			0.618034
$625$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$626$		0			0
$627$		0			0
$628$	0.533698	+	0.734572i	0.533698	+	0.734572i
$629$		0			0
$630$	1.31753	−	2.58580i	1.31753	−	2.58580i
$631$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.951057	+	0.309017i	$0.100000\pi$
$631$	1.53884	+	1.11803i	1.53884	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$632$			1.17557i			1.17557i
$633$		0			0
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−0.297556	−	0.0966818i	−0.297556	−	0.0966818i
$638$		0			0
$639$	1.70582	+	5.24997i	1.70582	+	5.24997i
$640$	−0.987688	+	0.156434i	−0.987688	+	0.156434i
$641$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	0.587785	+	0.809017i	$0.300000\pi$
$641$	−0.363271	+	1.11803i	−0.363271	+	1.11803i	−0.951057	+	0.309017i	$0.900000\pi$
$642$		0			0
$643$		−	0.907981i		−	0.907981i	−0.891007	−	0.453990i	$-0.850000\pi$
$643$		−	0.907981i		−	0.907981i	0.891007	−	0.453990i	$-0.150000\pi$
$644$	0.951057	+	0.690983i	0.951057	+	0.690983i
$645$		0			0
$646$		0			0
$647$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$647$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$648$	4.29892	−	1.39680i	4.29892	−	1.39680i
$649$		0			0
$650$	0.183900	+	0.253116i	0.183900	+	0.253116i
$651$		0			0
$652$		0			0
$653$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$653$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$654$		0			0
$655$	−0.809017	+	0.412215i	−0.809017	+	0.412215i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$659$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$660$		0			0
$661$	−0.280582	−	0.863541i	−0.280582	−	0.863541i	−0.987688	−	0.156434i	$-0.950000\pi$
$661$	−0.280582	−	0.863541i	−0.280582	−	0.863541i	0.707107	−	0.707107i	$-0.250000\pi$
$662$		0			0
$663$		0			0
$664$	0.280582	+	0.863541i	0.280582	+	0.863541i
$665$	0.642040	+	1.26007i	0.642040	+	1.26007i
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	1.16110	+	1.59811i	1.16110	+	1.59811i
$673$	1.80902	−	0.587785i	1.80902	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$673$	1.80902	−	0.587785i	1.80902	−	0.587785i	1.00000			$0$
$674$	1.61803			1.61803
$675$	3.03979	+	2.20854i	3.03979	+	2.20854i
$676$	−0.902113			−0.902113
$677$	−0.863541	+	0.280582i	−0.863541	+	0.280582i	−0.707107	−	0.707107i	$-0.750000\pi$
$677$	−0.863541	+	0.280582i	−0.863541	+	0.280582i	−0.156434	+	0.987688i	$0.550000\pi$
$678$	−0.717598	−	0.987688i	−0.717598	−	0.987688i
$679$		0			0
$680$		0			0
$681$	3.15688	+	2.29360i	3.15688	+	2.29360i
$682$		0			0
$683$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$683$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$684$	−1.26827	+	3.90333i	−1.26827	+	3.90333i
$685$		0			0
$686$	−0.309017	−	0.951057i	−0.309017	−	0.951057i
$687$	−3.34786	−	1.08779i	−3.34786	−	1.08779i
$688$		0			0
$689$		0			0
$690$	−1.64204	+	1.64204i	−1.64204	+	1.64204i
$691$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i	−0.987688	−	0.156434i	$-0.950000\pi$
$691$	−0.0966818	+	0.297556i	−0.0966818	+	0.297556i	0.891007	+	0.453990i	$0.150000\pi$
$692$	−1.04744	+	1.44168i	−1.04744	+	1.44168i
$693$		0			0
$694$		0			0
$695$	−1.39680	−	0.221232i	−1.39680	−	0.221232i
$696$		0			0
$697$		0			0
$698$	−0.297556	+	0.0966818i	−0.297556	+	0.0966818i
$699$	3.75739			3.75739
$700$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$701$		0			0		1.00000			$0$
$701$		0			0		−1.00000			$\pi$
$702$	1.11803	−	0.363271i	1.11803	−	0.363271i
$703$		0			0
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	0.312869i		−	0.312869i
$708$	2.06909	−	2.84786i	2.06909	−	2.84786i
$709$		0			0		0.309017	−	0.951057i	$-0.400000\pi$
$709$		0			0		−0.309017	+	0.951057i	$0.600000\pi$
$710$	−0.863541	−	1.69480i	−0.863541	−	1.69480i
$711$	1.05425	+	3.24466i	1.05425	+	3.24466i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$	1.87869	−	2.58580i	1.87869	−	2.58580i
$718$			1.61803i			1.61803i
$719$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$719$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$720$	−2.58580	+	1.31753i	−2.58580	+	1.31753i
$721$		0			0
$722$	−0.587785	−	0.809017i	−0.587785	−	0.809017i
$723$		0			0
$724$	−1.78201			−1.78201
$725$		0			0
$726$	1.97538			1.97538
$727$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$727$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$728$	0.183900	+	0.253116i	0.183900	+	0.253116i
$729$	4.60793	−	3.34786i	4.60793	−	3.34786i
$730$		0			0
$731$		0			0
$732$			1.79360i			1.79360i
$733$	1.04744	−	1.44168i	1.04744	−	1.44168i	0.156434	−	0.987688i	$-0.450000\pi$
$733$	1.04744	−	1.44168i	1.04744	−	1.44168i	0.891007	−	0.453990i	$-0.150000\pi$
$734$		0			0
$735$	1.95106	−	0.309017i	1.95106	−	0.309017i
$736$	−0.363271	−	1.11803i	−0.363271	−	1.11803i
$737$		0			0
$738$		0			0
$739$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$739$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$740$		0			0
$741$	−0.270091	+	0.831254i	−0.270091	+	0.831254i
$742$		0			0
$743$		−	1.90211i		−	1.90211i	−0.309017	−	0.951057i	$-0.600000\pi$
$743$		−	1.90211i		−	1.90211i	0.309017	−	0.951057i	$-0.400000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	1.54885	+	2.13181i	1.54885	+	2.13181i
$748$		0			0
$749$		0			0
$750$	−1.76007	−	0.896802i	−1.76007	−	0.896802i
$751$	−2.00000			−2.00000			−1.00000			$\pi$
$751$	−2.00000			−2.00000			−1.00000			$\pi$
$752$		0			0
$753$	1.05425	+	1.45106i	1.05425	+	1.45106i
$754$		0			0
$755$	−0.734572	+	1.44168i	−0.734572	+	1.44168i
$756$	3.03979	+	2.20854i	3.03979	+	2.20854i
$757$		0			0			−	1.00000i	$-0.5\pi$
$757$		0			0				1.00000i	$0.5\pi$
$758$		0			0
$759$		0			0
$760$	0.221232	−	1.39680i	0.221232	−	1.39680i
$761$		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
$764$	0.363271	+	1.11803i	0.363271	+	1.11803i
$765$		0			0
$766$		0			0
$767$	0.327712	−	0.451057i	0.327712	−	0.451057i
$768$		−	1.97538i		−	1.97538i
$769$		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
$772$	−0.363271	−	0.500000i	−0.363271	−	0.500000i
$773$	−1.87869	+	0.610425i	−1.87869	+	0.610425i	−0.891007	+	0.453990i	$0.850000\pi$
$773$	−1.87869	+	0.610425i	−1.87869	+	0.610425i	−0.987688	+	0.156434i	$0.950000\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$		0			0
$780$	−0.550672	+	0.280582i	−0.550672	+	0.280582i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.309017	+	0.951057i	−0.309017	+	0.951057i
$785$	−0.809017	−	0.412215i	−0.809017	−	0.412215i
$786$	−0.554254	−	1.70582i	−0.554254	−	1.70582i
$787$	−1.34500	−	0.437016i	−1.34500	−	0.437016i	−0.453990	−	0.891007i	$-0.650000\pi$
$787$	−1.34500	−	0.437016i	−1.34500	−	0.437016i	−0.891007	+	0.453990i	$0.850000\pi$
$788$		0			0
$789$	−0.987688	−	3.03979i	−0.987688	−	3.03979i
$790$	−0.533698	−	1.04744i	−0.533698	−	1.04744i
$791$	0.190983	−	0.587785i	0.190983	−	0.587785i
$792$		0			0
$793$			0.284079i			0.284079i
$794$	0.253116	+	0.183900i	0.253116	+	0.183900i
$795$		0			0
$796$		0			0
$797$	−1.04744	−	1.44168i	−1.04744	−	1.44168i	−0.891007	−	0.453990i	$-0.850000\pi$
$797$	−1.04744	−	1.44168i	−1.04744	−	1.44168i	−0.156434	−	0.987688i	$-0.550000\pi$
$798$	−2.65688	+	0.863271i	−2.65688	+	0.863271i
$799$		0			0
$800$	0.809017	−	0.587785i	0.809017	−	0.587785i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$	−1.16110	−	0.183900i	−1.16110	−	0.183900i
$806$		0			0
$807$			3.52015i			3.52015i
$808$	−0.183900	+	0.253116i	−0.183900	+	0.253116i
$809$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$809$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$810$	−3.19623	+	3.19623i	−3.19623	+	3.19623i
$811$	−0.610425	−	1.87869i	−0.610425	−	1.87869i	−0.453990	−	0.891007i	$-0.650000\pi$
$811$	−0.610425	−	1.87869i	−0.610425	−	1.87869i	−0.156434	−	0.987688i	$-0.550000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	0.734572	+	0.533698i	0.734572	+	0.533698i
$820$		0			0
$821$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$821$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$822$		0			0
$823$	0.587785	−	0.190983i	0.587785	−	0.190983i		−	1.00000i	$-0.5\pi$
$823$	0.587785	−	0.190983i	0.587785	−	0.190983i	0.587785	+	0.809017i	$0.300000\pi$
$824$		0			0
$825$		0			0
$826$	1.78201			1.78201
$827$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$827$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$828$	−2.00531	−	2.76007i	−2.00531	−	2.76007i
$829$	−1.14412	+	0.831254i	−1.14412	+	0.831254i	−0.987688	−	0.156434i	$-0.950000\pi$
$829$	−1.14412	+	0.831254i	−1.14412	+	0.831254i	−0.156434	+	0.987688i	$0.550000\pi$
$830$	−0.642040	−	0.642040i	−0.642040	−	0.642040i
$831$		0			0
$832$		−	0.312869i		−	0.312869i
$833$		0			0
$834$	0.863271	−	2.65688i	0.863271	−	2.65688i
$835$		0			0
$836$		0			0
$837$		0			0
$838$	1.87869	+	0.610425i	1.87869	+	0.610425i
$839$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$839$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$840$	−1.76007	−	0.896802i	−1.76007	−	0.896802i
$841$	0.309017	−	0.951057i	0.309017	−	0.951057i
$842$		0			0
$843$			1.22085i			1.22085i
$844$		0			0
$845$	0.803789	−	0.409551i	0.803789	−	0.409551i
$846$		0			0
$847$	0.587785	+	0.809017i	0.587785	+	0.809017i
$848$		0			0
$849$	3.90211			3.90211
$850$		0			0
$851$		0			0
$852$	3.57349	−	1.16110i	3.57349	−	1.16110i
$853$	−1.04744	−	1.44168i	−1.04744	−	1.44168i	−0.891007	−	0.453990i	$-0.850000\pi$
$853$	−1.04744	−	1.44168i	−1.04744	−	1.44168i	−0.156434	−	0.987688i	$-0.550000\pi$
$854$	−0.734572	+	0.533698i	−0.734572	+	0.533698i
$855$	−0.642040	−	4.05368i	−0.642040	−	4.05368i
$856$		0			0
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$	−0.550672	+	1.69480i	−0.550672	+	1.69480i	0.156434	+	0.987688i	$0.450000\pi$
$859$	−0.550672	+	1.69480i	−0.550672	+	1.69480i	−0.707107	+	0.707107i	$0.750000\pi$
$860$		0			0
$861$		0			0
$862$	0.587785	+	0.190983i	0.587785	+	0.190983i
$863$	0.587785	+	0.190983i	0.587785	+	0.190983i	0.587785	−	0.809017i	$-0.300000\pi$
$863$	0.587785	+	0.190983i	0.587785	+	0.190983i			1.00000i	$0.5\pi$
$864$	−1.16110	−	3.57349i	−1.16110	−	3.57349i
$865$	0.278768	−	1.76007i	0.278768	−	1.76007i
$866$		0			0
$867$	1.16110	−	1.59811i	1.16110	−	1.59811i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	1.66251			1.66251
$875$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$876$		0			0
$877$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$877$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$878$		0			0
$879$	−2.26007	+	1.64204i	−2.26007	+	1.64204i
$880$		0			0
$881$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$881$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$882$			2.90211i			2.90211i
$883$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$883$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$884$		0			0
$885$	−0.550672	+	3.47681i	−0.550672	+	3.47681i
$886$		0			0
$887$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$887$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	0.809017	−	0.587785i	0.809017	−	0.587785i
$897$	−0.427051	−	0.587785i	−0.427051	−	0.587785i
$898$	1.53884	−	0.500000i	1.53884	−	0.500000i
$899$		0			0
$900$	1.70582	−	2.34786i	1.70582	−	2.34786i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	−0.500000	+	0.363271i	−0.500000	+	0.363271i
$905$	1.58779	−	0.809017i	1.58779	−	0.809017i
$906$	−2.58580	−	1.87869i	−2.58580	−	1.87869i
$907$		0			0			−	1.00000i	$-0.5\pi$
$907$		0			0				1.00000i	$0.5\pi$
$908$	1.16110	−	1.59811i	1.16110	−	1.59811i
$909$	−0.280582	+	0.863541i	−0.280582	+	0.863541i
$910$	−0.278768	−	0.142040i	−0.278768	−	0.142040i
$911$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	0.809017	−	0.587785i	$-0.200000\pi$
$911$	−0.190983	−	0.587785i	−0.190983	−	0.587785i	−1.00000			$\pi$
$912$	2.65688	+	0.863271i	2.65688	+	0.863271i
$913$		0			0
$914$	0.190983	+	0.587785i	0.190983	+	0.587785i
$915$	−0.814279	−	1.59811i	−0.814279	−	1.59811i
$916$	−0.550672	+	1.69480i	−0.550672	+	1.69480i
$917$	0.533698	−	0.734572i	0.533698	−	0.734572i
$918$		0			0
$919$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$919$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$920$	0.831254	+	0.831254i	0.831254	+	0.831254i
$921$	−2.26007	+	1.64204i	−2.26007	+	1.64204i
$922$	−0.831254	−	1.14412i	−0.831254	−	1.14412i
$923$	0.565985	−	0.183900i	0.565985	−	0.183900i
$924$		0			0
$925$		0			0
$926$	0.618034			0.618034
$927$		0			0
$928$		0			0
$929$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$929$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$930$		0			0
$931$	−1.14412	−	0.831254i	−1.14412	−	0.831254i
$932$		−	1.90211i		−	1.90211i
$933$		0			0
$934$	0.437016	−	1.34500i	0.437016	−	1.34500i
$935$		0			0
$936$	−0.280582	−	0.863541i	−0.280582	−	0.863541i
$937$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$937$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−0.280582	+	0.863541i	−0.280582	+	0.863541i	0.707107	+	0.707107i	$0.250000\pi$
$941$	−0.280582	+	0.863541i	−0.280582	+	0.863541i	−0.987688	+	0.156434i	$0.950000\pi$
$942$	1.05425	−	1.45106i	1.05425	−	1.45106i
$943$		0			0
$944$	−1.44168	−	1.04744i	−1.44168	−	1.04744i
$945$	−3.71113	−	0.587785i	−3.71113	−	0.587785i
$946$		0			0
$947$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$947$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$948$	2.20854	−	0.717598i	2.20854	−	0.717598i
$949$		0			0
$950$	0.437016	+	1.34500i	0.437016	+	1.34500i
$951$		0			0
$952$		0			0
$953$	0.690983	+	0.951057i	0.690983	+	0.951057i	1.00000			$0$
$953$	0.690983	+	0.951057i	0.690983	+	0.951057i	−0.309017	+	0.951057i	$0.600000\pi$
$954$		0			0
$955$	−0.831254	−	0.831254i	−0.831254	−	0.831254i
$956$	−1.30902	−	0.951057i	−1.30902	−	0.951057i
$957$		0			0
$958$		0			0
$959$		0			0
$960$	0.896802	+	1.76007i	0.896802	+	1.76007i
$961$	0.309017	+	0.951057i	0.309017	+	0.951057i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.550672	+	0.280582i	0.550672	+	0.280582i
$966$	0.717598	−	2.20854i	0.717598	−	2.20854i
$967$	−1.11803	+	1.53884i	−1.11803	+	1.53884i	−0.309017	+	0.951057i	$0.600000\pi$
$967$	−1.11803	+	1.53884i	−1.11803	+	1.53884i	−0.809017	+	0.587785i	$0.800000\pi$
$968$		−	1.00000i		−	1.00000i
$969$		0			0
$970$		0			0
$971$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	−0.707107	−	0.707107i	$-0.750000\pi$
$971$	−0.253116	+	0.183900i	−0.253116	+	0.183900i	0.453990	+	0.891007i	$0.350000\pi$
$972$	−3.03979	−	4.18391i	−3.03979	−	4.18391i
$973$	1.34500	−	0.437016i	1.34500	−	0.437016i
$974$	−1.90211			−1.90211
$975$	0.363271	−	0.500000i	0.363271	−	0.500000i
$976$	0.907981			0.907981
$977$	−1.80902	+	0.587785i	−1.80902	+	0.587785i	−0.809017	+	0.587785i	$0.800000\pi$
$977$	−1.80902	+	0.587785i	−1.80902	+	0.587785i	−1.00000			$\pi$
$978$		0			0
$979$		0			0
$980$	−0.156434	−	0.987688i	−0.156434	−	0.987688i
$981$		0			0
$982$		0			0
$983$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$983$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	0.420808	+	0.136729i	0.420808	+	0.136729i
$989$		0			0
$990$		0			0
$991$	0.587785	−	1.80902i	0.587785	−	1.80902i		−	1.00000i	$-0.5\pi$
$991$	0.587785	−	1.80902i	0.587785	−	1.80902i	0.587785	−	0.809017i	$-0.300000\pi$
$992$		0			0
$993$		0			0
$994$	1.53884	+	1.11803i	1.53884	+	1.11803i
$995$		0			0
$996$	1.45106	−	1.05425i	1.45106	−	1.05425i
$997$	1.16110	+	1.59811i	1.16110	+	1.59811i	0.707107	+	0.707107i	$0.250000\pi$
$997$	1.16110	+	1.59811i	1.16110	+	1.59811i	0.453990	+	0.891007i	$0.350000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.1.cc.a.69.2	yes	16
7.6	odd	2	inner	1400.1.cc.a.69.1	✓	16
8.5	even	2	inner	1400.1.cc.a.69.1	✓	16
25.4	even	10	inner	1400.1.cc.a.629.2	yes	16
56.13	odd	2	CM	1400.1.cc.a.69.2	yes	16
175.104	odd	10	inner	1400.1.cc.a.629.1	yes	16
200.29	even	10	inner	1400.1.cc.a.629.1	yes	16
1400.629	odd	10	inner	1400.1.cc.a.629.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1400.1.cc.a.69.1	✓	16	7.6	odd	2	inner
1400.1.cc.a.69.1	✓	16	8.5	even	2	inner
1400.1.cc.a.69.2	yes	16	1.1	even	1	trivial
1400.1.cc.a.69.2	yes	16	56.13	odd	2	CM
1400.1.cc.a.629.1	yes	16	175.104	odd	10	inner
1400.1.cc.a.629.1	yes	16	200.29	even	10	inner
1400.1.cc.a.629.2	yes	16	25.4	even	10	inner
1400.1.cc.a.629.2	yes	16	1400.629	odd	10	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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1400.cc (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.16110 + 1.59811i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(-1.59811 - 1.16110i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.896802 + 2.76007i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(1.16110 + 1.59811i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.453990 + 0.891007i) q^{5} +(-1.59811 - 1.16110i) q^{6} -1.00000i q^{7} +(-0.587785 + 0.809017i) q^{8} +(-0.896802 + 2.76007i) q^{9} +(0.156434 - 0.987688i) q^{10} +(1.87869 + 0.610425i) q^{12} +(0.297556 + 0.0966818i) q^{13} +(0.309017 + 0.951057i) q^{14} +(-1.95106 + 0.309017i) q^{15} +(0.309017 - 0.951057i) q^{16} -2.90211i q^{18} +(1.14412 + 0.831254i) q^{19} +(0.156434 + 0.987688i) q^{20} +(1.59811 - 1.16110i) q^{21} +(-1.11803 + 0.363271i) q^{23} -1.97538 q^{24} +(-0.587785 - 0.809017i) q^{25} -0.312869 q^{26} +(-3.57349 + 1.16110i) q^{27} +(-0.587785 - 0.809017i) q^{28} +(1.76007 - 0.896802i) q^{30} +1.00000i q^{32} +(0.891007 + 0.453990i) q^{35} +(0.896802 + 2.76007i) q^{36} +(-1.34500 - 0.437016i) q^{38} +(0.190983 + 0.587785i) q^{39} +(-0.453990 - 0.891007i) q^{40} +(-1.16110 + 1.59811i) q^{42} +(-2.05210 - 2.05210i) q^{45} +(0.951057 - 0.690983i) q^{46} +(1.87869 - 0.610425i) q^{48} -1.00000 q^{49} +(0.809017 + 0.587785i) q^{50} +(0.297556 - 0.0966818i) q^{52} +(3.03979 - 2.20854i) q^{54} +(0.809017 + 0.587785i) q^{56} +2.79360i q^{57} +(0.550672 - 1.69480i) q^{59} +(-1.39680 + 1.39680i) q^{60} +(0.280582 + 0.863541i) q^{61} +(2.76007 + 0.896802i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-0.221232 + 0.221232i) q^{65} +(-1.87869 - 1.36495i) q^{69} +(-0.987688 - 0.156434i) q^{70} +(1.53884 - 1.11803i) q^{71} +(-1.70582 - 2.34786i) q^{72} +(0.610425 - 1.87869i) q^{75} +1.41421 q^{76} +(-0.363271 - 0.500000i) q^{78} +(0.951057 - 0.690983i) q^{79} +(0.707107 + 0.707107i) q^{80} +(-3.65688 - 2.65688i) q^{81} +(0.533698 - 0.734572i) q^{83} +(0.610425 - 1.87869i) q^{84} +(2.58580 + 1.31753i) q^{90} +(0.0966818 - 0.297556i) q^{91} +(-0.690983 + 0.951057i) q^{92} +(-1.26007 + 0.642040i) q^{95} +(-1.59811 + 1.16110i) q^{96} +(0.951057 - 0.309017i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 4 * q^9	\( 16 q + 4 q^{4} + 4 q^{9} - 4 q^{14} - 16 q^{15} - 4 q^{16} + 4 q^{30} - 4 q^{36} + 12 q^{39} - 16 q^{49} + 4 q^{50} + 4 q^{56} - 4 q^{60} + 20 q^{63} + 4 q^{64} - 4 q^{65} - 16 q^{81} - 20 q^{92} + 4 q^{95}+O(q^{100}) \) 16 * q + 4 * q^4 + 4 * q^9 - 4 * q^14 - 16 * q^15 - 4 * q^16 + 4 * q^30 - 4 * q^36 + 12 * q^39 - 16 * q^49 + 4 * q^50 + 4 * q^56 - 4 * q^60 + 20 * q^63 + 4 * q^64 - 4 * q^65 - 16 * q^81 - 20 * q^92 + 4 * q^95

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