LMFDB - Embedded newform 1960.1.cz.a.1019.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1960,1,Mod(179,1960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1960, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 21, 21, 4]))

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

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

chi := DirichletCharacter("1960.179");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 1960 = 2^{3} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	1960.cz (of order $42$, degree $12$, 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:	$0.978167424761$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{21})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 $ x^12 - x^11 + x^9 - x^8 + x^6 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{21}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{21} + \cdots)$

Embedding invariants

Embedding label			1019.1
Root			$0.826239 + 0.563320i$ of defining polynomial
Character	$\chi$	$=$	1960.1019
Dual form			1960.1.cz.a.779.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988831 + 0.149042i) q^{2} +(0.955573 + 0.294755i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.900969 - 0.433884i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})$	\(q+(0.988831 + 0.149042i) q^{2} +(0.955573 + 0.294755i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.900969 - 0.433884i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +(0.0747301 - 0.997204i) q^{10} +(0.0546039 + 0.139129i) q^{11} +(-1.19158 + 1.49419i) q^{13} +(0.955573 - 0.294755i) q^{14} +(0.826239 + 0.563320i) q^{16} +(0.500000 - 0.866025i) q^{18} +(-0.826239 - 1.43109i) q^{19} +(0.222521 - 0.974928i) q^{20} +(0.0332580 + 0.145713i) q^{22} +(-0.733052 + 0.680173i) q^{23} +(-0.988831 + 0.149042i) q^{25} +(-1.40097 + 1.29991i) q^{26} +(0.988831 - 0.149042i) q^{28} +(0.733052 + 0.680173i) q^{32} +(-0.500000 - 0.866025i) q^{35} +(0.623490 - 0.781831i) q^{36} +(-0.698220 + 0.215372i) q^{37} +(-0.603718 - 1.53825i) q^{38} +(0.365341 - 0.930874i) q^{40} +(1.78181 + 0.858075i) q^{41} +(0.0111692 + 0.149042i) q^{44} +(-0.955573 - 0.294755i) q^{45} +(-0.826239 + 0.563320i) q^{46} +(-1.44973 - 0.218511i) q^{47} +(0.623490 - 0.781831i) q^{49} -1.00000 q^{50} +(-1.57906 + 1.07659i) q^{52} +(1.40097 + 0.432142i) q^{53} +(0.134659 - 0.0648483i) q^{55} +1.00000 q^{56} +(-0.134659 + 1.79690i) q^{59} +(-0.0747301 - 0.997204i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.57906 + 1.07659i) q^{65} +(-0.365341 - 0.930874i) q^{70} +(0.733052 - 0.680173i) q^{72} +(-0.722521 + 0.108903i) q^{74} +(-0.367711 - 1.61105i) q^{76} +(0.109562 + 0.101659i) q^{77} +(0.500000 - 0.866025i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(1.63402 + 1.11406i) q^{82} +(-0.0111692 + 0.149042i) q^{88} +(-0.162592 + 0.414278i) q^{89} +(-0.900969 - 0.433884i) q^{90} +(-0.425270 + 1.86323i) q^{91} +(-0.900969 + 0.433884i) q^{92} +(-1.40097 - 0.432142i) q^{94} +(-1.36534 + 0.930874i) q^{95} +(0.733052 - 0.680173i) q^{98} +0.149460 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} + q^{4} - q^{5} + 2 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) $ 12 * q - q^2 + q^4 - q^5 + 2 * q^7 + 2 * q^8 + q^9	$ 12 q - q^{2} + q^{4} - q^{5} + 2 q^{7} + 2 q^{8} + q^{9} + q^{10} - q^{11} - 2 q^{13} + q^{14} + q^{16} + 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{22} + q^{23} + q^{25} - 8 q^{26} - q^{28} - q^{32} - 6 q^{35} - 2 q^{36} + q^{37} + q^{38} + q^{40} + 2 q^{41} + 13 q^{44} - q^{45} - q^{46} + q^{47} - 2 q^{49} - 12 q^{50} + q^{52} + 8 q^{53} + 5 q^{55} + 12 q^{56} - 5 q^{59} - q^{63} - 2 q^{64} - q^{65} - q^{70} - q^{72} - 8 q^{74} + 2 q^{76} + q^{77} + 6 q^{80} + q^{81} + q^{82} - 13 q^{88} + 2 q^{89} - 2 q^{90} - 5 q^{91} - 2 q^{92} - 8 q^{94} - 13 q^{95} - q^{98} + 2 q^{99}+O(q^{100}) $ 12 * q - q^2 + q^4 - q^5 + 2 * q^7 + 2 * q^8 + q^9 + q^10 - q^11 - 2 * q^13 + q^14 + q^16 + 6 * q^18 - q^19 + 2 * q^20 - 2 * q^22 + q^23 + q^25 - 8 * q^26 - q^28 - q^32 - 6 * q^35 - 2 * q^36 + q^37 + q^38 + q^40 + 2 * q^41 + 13 * q^44 - q^45 - q^46 + q^47 - 2 * q^49 - 12 * q^50 + q^52 + 8 * q^53 + 5 * q^55 + 12 * q^56 - 5 * q^59 - q^63 - 2 * q^64 - q^65 - q^70 - q^72 - 8 * q^74 + 2 * q^76 + q^77 + 6 * q^80 + q^81 + q^82 - 13 * q^88 + 2 * q^89 - 2 * q^90 - 5 * q^91 - 2 * q^92 - 8 * q^94 - 13 * q^95 - q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times$.

$n$	$981$	$1081$	$1177$	$1471$
$\chi(n)$	$-1$	$e\left(\frac{17}{21}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.988831	+	0.149042i	0.988831	+	0.149042i
$2$	0.988831	+	0.149042i	0.988831	+	0.149042i
$3$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$3$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$4$	0.955573	+	0.294755i	0.955573	+	0.294755i
$5$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$5$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$6$		0			0
$7$	0.900969	−	0.433884i	0.900969	−	0.433884i
$7$	0.900969	−	0.433884i	0.900969	−	0.433884i
$8$	0.900969	+	0.433884i	0.900969	+	0.433884i
$9$	0.365341	−	0.930874i	0.365341	−	0.930874i
$10$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$11$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	0.955573	−	0.294755i	$-0.0952381\pi$
$11$	0.0546039	+	0.139129i	0.0546039	+	0.139129i	−0.900969	+	0.433884i	$0.857143\pi$
$12$		0			0
$13$	−1.19158	+	1.49419i	−1.19158	+	1.49419i	−0.365341	+	0.930874i	$0.619048\pi$
$13$	−1.19158	+	1.49419i	−1.19158	+	1.49419i	−0.826239	+	0.563320i	$0.809524\pi$
$14$	0.955573	−	0.294755i	0.955573	−	0.294755i
$15$		0			0
$16$	0.826239	+	0.563320i	0.826239	+	0.563320i
$17$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$17$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$18$	0.500000	−	0.866025i	0.500000	−	0.866025i
$19$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$19$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$20$	0.222521	−	0.974928i	0.222521	−	0.974928i
$21$		0			0
$22$	0.0332580	+	0.145713i	0.0332580	+	0.145713i
$23$	−0.733052	+	0.680173i	−0.733052	+	0.680173i	−0.955573	−	0.294755i	$-0.904762\pi$
$23$	−0.733052	+	0.680173i	−0.733052	+	0.680173i	0.222521	+	0.974928i	$0.428571\pi$
$24$		0			0
$25$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$26$	−1.40097	+	1.29991i	−1.40097	+	1.29991i
$27$		0			0
$28$	0.988831	−	0.149042i	0.988831	−	0.149042i
$29$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$29$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$30$		0			0
$31$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$31$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.733052	+	0.680173i	0.733052	+	0.680173i
$33$		0			0
$34$		0			0
$35$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$36$	0.623490	−	0.781831i	0.623490	−	0.781831i
$37$	−0.698220	+	0.215372i	−0.698220	+	0.215372i	−0.623490	−	0.781831i	$-0.714286\pi$
$37$	−0.698220	+	0.215372i	−0.698220	+	0.215372i	−0.0747301	+	0.997204i	$0.523810\pi$
$38$	−0.603718	−	1.53825i	−0.603718	−	1.53825i
$39$		0			0
$40$	0.365341	−	0.930874i	0.365341	−	0.930874i
$41$	1.78181	+	0.858075i	1.78181	+	0.858075i	0.955573	+	0.294755i	$0.0952381\pi$
$41$	1.78181	+	0.858075i	1.78181	+	0.858075i	0.826239	+	0.563320i	$0.190476\pi$
$42$		0			0
$43$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$43$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$44$	0.0111692	+	0.149042i	0.0111692	+	0.149042i
$45$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$46$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$47$	−1.44973	−	0.218511i	−1.44973	−	0.218511i	−0.623490	−	0.781831i	$-0.714286\pi$
$47$	−1.44973	−	0.218511i	−1.44973	−	0.218511i	−0.826239	+	0.563320i	$0.809524\pi$
$48$		0			0
$49$	0.623490	−	0.781831i	0.623490	−	0.781831i
$50$	−1.00000			−1.00000
$51$		0			0
$52$	−1.57906	+	1.07659i	−1.57906	+	1.07659i
$53$	1.40097	+	0.432142i	1.40097	+	0.432142i	0.900969	−	0.433884i	$-0.142857\pi$
$53$	1.40097	+	0.432142i	1.40097	+	0.432142i	0.500000	+	0.866025i	$0.333333\pi$
$54$		0			0
$55$	0.134659	−	0.0648483i	0.134659	−	0.0648483i
$56$	1.00000			1.00000
$57$		0			0
$58$		0			0
$59$	−0.134659	+	1.79690i	−0.134659	+	1.79690i	0.365341	+	0.930874i	$0.380952\pi$
$59$	−0.134659	+	1.79690i	−0.134659	+	1.79690i	−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$61$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$62$		0			0
$63$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$64$	0.623490	+	0.781831i	0.623490	+	0.781831i
$65$	1.57906	+	1.07659i	1.57906	+	1.07659i
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$		0			0
$69$		0			0
$70$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$71$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$71$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$72$	0.733052	−	0.680173i	0.733052	−	0.680173i
$73$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$73$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$74$	−0.722521	+	0.108903i	−0.722521	+	0.108903i
$75$		0			0
$76$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$77$	0.109562	+	0.101659i	0.109562	+	0.101659i
$78$		0			0
$79$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$79$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$80$	0.500000	−	0.866025i	0.500000	−	0.866025i
$81$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$82$	1.63402	+	1.11406i	1.63402	+	1.11406i
$83$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$83$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$		0			0
$88$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i
$89$	−0.162592	+	0.414278i	−0.162592	+	0.414278i	−0.988831	−	0.149042i	$-0.952381\pi$
$89$	−0.162592	+	0.414278i	−0.162592	+	0.414278i	0.826239	+	0.563320i	$0.190476\pi$
$90$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$91$	−0.425270	+	1.86323i	−0.425270	+	1.86323i
$92$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$93$		0			0
$94$	−1.40097	−	0.432142i	−1.40097	−	0.432142i
$95$	−1.36534	+	0.930874i	−1.36534	+	0.930874i
$96$		0			0
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	0.733052	−	0.680173i	0.733052	−	0.680173i
$99$	0.149460			0.149460
$100$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$101$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$101$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$102$		0			0
$103$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i	−0.826239	−	0.563320i	$-0.809524\pi$
$103$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i	0.733052	−	0.680173i	$-0.238095\pi$
$104$	−1.72188	+	0.829215i	−1.72188	+	0.829215i
$105$		0			0
$106$	1.32091	+	0.636119i	1.32091	+	0.636119i
$107$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$107$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$108$		0			0
$109$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$109$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$110$	0.142820	−	0.0440542i	0.142820	−	0.0440542i
$111$		0			0
$112$	0.988831	+	0.149042i	0.988831	+	0.149042i
$113$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$113$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$114$		0			0
$115$	0.733052	+	0.680173i	0.733052	+	0.680173i
$116$		0			0
$117$	0.955573	+	1.65510i	0.955573	+	1.65510i
$118$	−0.400969	+	1.75676i	−0.400969	+	1.75676i
$119$		0			0
$120$		0			0
$121$	0.716677	−	0.664979i	0.716677	−	0.664979i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.222521	+	0.974928i	0.222521	+	0.974928i
$126$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$127$	−0.440071	+	1.92808i	−0.440071	+	1.92808i	−0.0747301	+	0.997204i	$0.523810\pi$
$127$	−0.440071	+	1.92808i	−0.440071	+	1.92808i	−0.365341	+	0.930874i	$0.619048\pi$
$128$	0.500000	+	0.866025i	0.500000	+	0.866025i
$129$		0			0
$130$	1.40097	+	1.29991i	1.40097	+	1.29991i
$131$	0.603718	+	0.411608i	0.603718	+	0.411608i	0.826239	−	0.563320i	$-0.190476\pi$
$131$	0.603718	+	0.411608i	0.603718	+	0.411608i	−0.222521	+	0.974928i	$0.571429\pi$
$132$		0			0
$133$	−1.36534	−	0.930874i	−1.36534	−	0.930874i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$137$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$138$		0			0
$139$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$139$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$140$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$141$		0			0
$142$		0			0
$143$	−0.272950	−	0.0841939i	−0.272950	−	0.0841939i
$144$	0.826239	−	0.563320i	0.826239	−	0.563320i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	−0.730682			−0.730682
$149$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$149$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$150$		0			0
$151$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$151$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$152$	−0.123490	−	1.64786i	−0.123490	−	1.64786i
$153$		0			0
$154$	0.0931869	+	0.116853i	0.0931869	+	0.116853i
$155$		0			0
$156$		0			0
$157$	0.0747301	−	0.997204i	0.0747301	−	0.997204i	−0.826239	−	0.563320i	$-0.809524\pi$
$157$	0.0747301	−	0.997204i	0.0747301	−	0.997204i	0.900969	−	0.433884i	$-0.142857\pi$
$158$		0			0
$159$		0			0
$160$	0.623490	−	0.781831i	0.623490	−	0.781831i
$161$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$162$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$163$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$163$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$164$	1.44973	+	1.34515i	1.44973	+	1.34515i
$165$		0			0
$166$		0			0
$167$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$167$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$168$		0			0
$169$	−0.590232	−	2.58597i	−0.590232	−	2.58597i
$170$		0			0
$171$	−1.63402	+	0.246289i	−1.63402	+	0.246289i
$172$		0			0
$173$	0.535628	−	0.496990i	0.535628	−	0.496990i	−0.365341	−	0.930874i	$-0.619048\pi$
$173$	0.535628	−	0.496990i	0.535628	−	0.496990i	0.900969	+	0.433884i	$0.142857\pi$
$174$		0			0
$175$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$176$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i
$177$		0			0
$178$	−0.222521	+	0.385418i	−0.222521	+	0.385418i
$179$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$179$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$180$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$181$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$181$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$182$	−0.698220	+	1.77904i	−0.698220	+	1.77904i
$183$		0			0
$184$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$185$	0.266948	+	0.680173i	0.266948	+	0.680173i
$186$		0			0
$187$		0			0
$188$	−1.32091	−	0.636119i	−1.32091	−	0.636119i
$189$		0			0
$190$	−1.48883	+	0.716983i	−1.48883	+	0.716983i
$191$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$191$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$192$		0			0
$193$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$193$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$194$		0			0
$195$		0			0
$196$	0.826239	−	0.563320i	0.826239	−	0.563320i
$197$	−1.91115			−1.91115			−0.955573	−	0.294755i	$-0.904762\pi$
$197$	−1.91115			−1.91115			−0.955573	+	0.294755i	$0.904762\pi$
$198$	0.147791	+	0.0222759i	0.147791	+	0.0222759i
$199$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$199$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$200$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$	0.722521	−	1.84095i	0.722521	−	1.84095i
$206$	0.0931869	−	1.24349i	0.0931869	−	1.24349i
$207$	0.365341	+	0.930874i	0.365341	+	0.930874i
$208$	−1.82624	+	0.563320i	−1.82624	+	0.563320i
$209$	0.153989	−	0.193096i	0.153989	−	0.193096i
$210$		0			0
$211$	−1.23305	−	1.54620i	−1.23305	−	1.54620i	−0.733052	−	0.680173i	$-0.761905\pi$
$211$	−1.23305	−	1.54620i	−1.23305	−	1.54620i	−0.500000	−	0.866025i	$-0.666667\pi$
$212$	1.21135	+	0.825886i	1.21135	+	0.825886i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$		0			0
$219$		0			0
$220$	0.147791	−	0.0222759i	0.147791	−	0.0222759i
$221$		0			0
$222$		0			0
$223$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$223$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$224$	0.955573	+	0.294755i	0.955573	+	0.294755i
$225$	−0.222521	+	0.974928i	−0.222521	+	0.974928i
$226$		0			0
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$		0			0
$229$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$229$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$230$	0.623490	+	0.781831i	0.623490	+	0.781831i
$231$		0			0
$232$		0			0
$233$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$233$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$234$	0.698220	+	1.77904i	0.698220	+	1.77904i
$235$	−0.109562	+	1.46200i	−0.109562	+	1.46200i
$236$	−0.658322	+	1.67738i	−0.658322	+	1.67738i
$237$		0			0
$238$		0			0
$239$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$239$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$240$		0			0
$241$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	0.365341	−	0.930874i	$-0.380952\pi$
$241$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	−0.222521	+	0.974928i	$0.571429\pi$
$242$	0.807782	−	0.550736i	0.807782	−	0.550736i
$243$		0			0
$244$		0			0
$245$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$246$		0			0
$247$	3.12285	+	0.470694i	3.12285	+	0.470694i
$248$		0			0
$249$		0			0
$250$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$251$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i	−0.500000	−	0.866025i	$-0.666667\pi$
$251$	−0.134659	+	0.0648483i	−0.134659	+	0.0648483i	0.365341	+	0.930874i	$0.380952\pi$
$252$	0.222521	−	0.974928i	0.222521	−	0.974928i
$253$	−0.134659	−	0.0648483i	−0.134659	−	0.0648483i
$254$	−0.722521	+	1.84095i	−0.722521	+	1.84095i
$255$		0			0
$256$	0.365341	+	0.930874i	0.365341	+	0.930874i
$257$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$257$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$258$		0			0
$259$	−0.535628	+	0.496990i	−0.535628	+	0.496990i
$260$	1.19158	+	1.49419i	1.19158	+	1.49419i
$261$		0			0
$262$	0.535628	+	0.496990i	0.535628	+	0.496990i
$263$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	−0.955573	−	0.294755i	$-0.904762\pi$
$263$	−0.222521	+	0.385418i	−0.222521	+	0.385418i	0.733052	+	0.680173i	$0.238095\pi$
$264$		0			0
$265$	0.326239	−	1.42935i	0.326239	−	1.42935i
$266$	−1.21135	−	1.12397i	−1.21135	−	1.12397i
$267$		0			0
$268$		0			0
$269$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$269$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$270$		0			0
$271$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$271$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.0747301	−	0.129436i	−0.0747301	−	0.129436i
$276$		0			0
$277$	−0.326239	−	0.302705i	−0.326239	−	0.302705i	0.500000	−	0.866025i	$-0.333333\pi$
$277$	−0.326239	−	0.302705i	−0.326239	−	0.302705i	−0.826239	+	0.563320i	$0.809524\pi$
$278$	−1.03030	−	0.702449i	−1.03030	−	0.702449i
$279$		0			0
$280$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$281$	−0.914101	+	1.14625i	−0.914101	+	1.14625i	0.0747301	+	0.997204i	$0.476190\pi$
$281$	−0.914101	+	1.14625i	−0.914101	+	1.14625i	−0.988831	+	0.149042i	$0.952381\pi$
$282$		0			0
$283$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$283$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$284$		0			0
$285$		0			0
$286$	−0.257353	−	0.123935i	−0.257353	−	0.123935i
$287$	1.97766			1.97766
$288$	0.900969	−	0.433884i	0.900969	−	0.433884i
$289$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.97766			1.97766			0.988831	−	0.149042i	$-0.0476190\pi$
$293$	1.97766			1.97766			0.988831	+	0.149042i	$0.0476190\pi$
$294$		0			0
$295$	1.80194			1.80194
$296$	−0.722521	−	0.108903i	−0.722521	−	0.108903i
$297$		0			0
$298$		0			0
$299$	−0.142820	−	1.90580i	−0.142820	−	1.90580i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.123490	−	1.64786i	0.123490	−	1.64786i
$305$		0			0
$306$		0			0
$307$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$307$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$308$	0.0747301	+	0.129436i	0.0747301	+	0.129436i
$309$		0			0
$310$		0			0
$311$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$311$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$312$		0			0
$313$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$313$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$314$	0.222521	−	0.974928i	0.222521	−	0.974928i
$315$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$316$		0			0
$317$	0.914101	−	0.848162i	0.914101	−	0.848162i	−0.0747301	−	0.997204i	$-0.523810\pi$
$317$	0.914101	−	0.848162i	0.914101	−	0.848162i	0.988831	+	0.149042i	$0.0476190\pi$
$318$		0			0
$319$		0			0
$320$	0.733052	−	0.680173i	0.733052	−	0.680173i
$321$		0			0
$322$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$325$	0.955573	−	1.65510i	0.955573	−	1.65510i
$326$		0			0
$327$		0			0
$328$	1.23305	+	1.54620i	1.23305	+	1.54620i
$329$	−1.40097	+	0.432142i	−1.40097	+	0.432142i
$330$		0			0
$331$	0.698220	−	0.215372i	0.698220	−	0.215372i	0.0747301	−	0.997204i	$-0.476190\pi$
$331$	0.698220	−	0.215372i	0.698220	−	0.215372i	0.623490	+	0.781831i	$0.285714\pi$
$332$		0			0
$333$	−0.0546039	+	0.728639i	−0.0546039	+	0.728639i
$334$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$335$		0			0
$336$		0			0
$337$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$337$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$338$	−0.198220	−	2.64506i	−0.198220	−	2.64506i
$339$		0			0
$340$		0			0
$341$		0			0
$342$	−1.65248			−1.65248
$343$	0.222521	−	0.974928i	0.222521	−	0.974928i
$344$		0			0
$345$		0			0
$346$	0.603718	−	0.411608i	0.603718	−	0.411608i
$347$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$347$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$348$		0			0
$349$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$349$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$350$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$351$		0			0
$352$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i
$353$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$353$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$354$		0			0
$355$		0			0
$356$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$357$		0			0
$358$	−1.03030	−	1.29196i	−1.03030	−	1.29196i
$359$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$359$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$360$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$361$	−0.865341	+	1.49881i	−0.865341	+	1.49881i
$362$		0			0
$363$		0			0
$364$	−0.955573	+	1.65510i	−0.955573	+	1.65510i
$365$		0			0
$366$		0			0
$367$	−1.95557	+	0.294755i	−1.95557	+	0.294755i	−0.955573	+	0.294755i	$0.904762\pi$
$367$	−1.95557	+	0.294755i	−1.95557	+	0.294755i	−1.00000			$1.00000\pi$
$368$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$369$	1.44973	−	1.34515i	1.44973	−	1.34515i
$370$	0.162592	+	0.712362i	0.162592	+	0.712362i
$371$	1.44973	−	0.218511i	1.44973	−	0.218511i
$372$		0			0
$373$	0.623490	+	1.07992i	0.623490	+	1.07992i	0.988831	+	0.149042i	$0.0476190\pi$
$373$	0.623490	+	1.07992i	0.623490	+	1.07992i	−0.365341	+	0.930874i	$0.619048\pi$
$374$		0			0
$375$		0			0
$376$	−1.21135	−	0.825886i	−1.21135	−	0.825886i
$377$		0			0
$378$		0			0
$379$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.365341	−	0.930874i	$-0.380952\pi$
$379$	1.19158	−	1.49419i	1.19158	−	1.49419i	0.826239	−	0.563320i	$-0.190476\pi$
$380$	−1.57906	+	0.487076i	−1.57906	+	0.487076i
$381$		0			0
$382$		0			0
$383$	0.722521	−	1.84095i	0.722521	−	1.84095i	0.222521	−	0.974928i	$-0.428571\pi$
$383$	0.722521	−	1.84095i	0.722521	−	1.84095i	0.500000	−	0.866025i	$-0.333333\pi$
$384$		0			0
$385$	0.0931869	−	0.116853i	0.0931869	−	0.116853i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$389$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$390$		0			0
$391$		0			0
$392$	0.900969	−	0.433884i	0.900969	−	0.433884i
$393$		0			0
$394$	−1.88980	−	0.284841i	−1.88980	−	0.284841i
$395$		0			0
$396$	0.142820	+	0.0440542i	0.142820	+	0.0440542i
$397$	0.0332580	+	0.443797i	0.0332580	+	0.443797i	0.988831	+	0.149042i	$0.0476190\pi$
$397$	0.0332580	+	0.443797i	0.0332580	+	0.443797i	−0.955573	+	0.294755i	$0.904762\pi$
$398$		0			0
$399$		0			0
$400$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$401$	−0.535628	+	1.36476i	−0.535628	+	1.36476i	0.365341	+	0.930874i	$0.380952\pi$
$401$	−0.535628	+	1.36476i	−0.535628	+	1.36476i	−0.900969	+	0.433884i	$0.857143\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$406$		0			0
$407$	−0.0680900	−	0.0853822i	−0.0680900	−	0.0853822i
$408$		0			0
$409$	1.32091	+	1.22563i	1.32091	+	1.22563i	0.955573	+	0.294755i	$0.0952381\pi$
$409$	1.32091	+	1.22563i	1.32091	+	1.22563i	0.365341	+	0.930874i	$0.380952\pi$
$410$	0.988831	−	1.71271i	0.988831	−	1.71271i
$411$		0			0
$412$	0.277479	−	1.21572i	0.277479	−	1.21572i
$413$	0.658322	+	1.67738i	0.658322	+	1.67738i
$414$	0.222521	+	0.974928i	0.222521	+	0.974928i
$415$		0			0
$416$	−1.88980	+	0.284841i	−1.88980	+	0.284841i
$417$		0			0
$418$	0.181049	−	0.167989i	0.181049	−	0.167989i
$419$	0.326239	+	1.42935i	0.326239	+	1.42935i	0.826239	+	0.563320i	$0.190476\pi$
$419$	0.326239	+	1.42935i	0.326239	+	1.42935i	−0.500000	+	0.866025i	$0.666667\pi$
$420$		0			0
$421$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$421$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$422$	−0.988831	−	1.71271i	−0.988831	−	1.71271i
$423$	−0.733052	+	1.26968i	−0.733052	+	1.26968i
$424$	1.07473	+	0.997204i	1.07473	+	0.997204i
$425$		0			0
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$431$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$432$		0			0
$433$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$433$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.57906	+	0.487076i	1.57906	+	0.487076i
$438$		0			0
$439$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$439$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$440$	0.149460			0.149460
$441$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$442$		0			0
$443$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$443$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$444$		0			0
$445$	0.425270	+	0.131178i	0.425270	+	0.131178i
$446$	−0.134659	−	1.79690i	−0.134659	−	1.79690i
$447$		0			0
$448$	0.900969	+	0.433884i	0.900969	+	0.433884i
$449$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	0.0747301	−	0.997204i	$-0.476190\pi$
$449$	−0.658322	−	0.317031i	−0.658322	−	0.317031i	−0.733052	+	0.680173i	$0.761905\pi$
$450$	−0.365341	+	0.930874i	−0.365341	+	0.930874i
$451$	−0.0220888	+	0.294755i	−0.0220888	+	0.294755i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.88980	+	0.284841i	1.88980	+	0.284841i
$456$		0			0
$457$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$457$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$458$		0			0
$459$		0			0
$460$	0.500000	+	0.866025i	0.500000	+	0.866025i
$461$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$461$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$462$		0			0
$463$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	−0.826239	−	0.563320i	$-0.809524\pi$
$463$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	0.500000	−	0.866025i	$-0.333333\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$467$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$468$	0.425270	+	1.86323i	0.425270	+	1.86323i
$469$		0			0
$470$	−0.326239	+	1.42935i	−0.326239	+	1.42935i
$471$		0			0
$472$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$473$		0			0
$474$		0			0
$475$	1.03030	+	1.29196i	1.03030	+	1.29196i
$476$		0			0
$477$	0.914101	−	1.14625i	0.914101	−	1.14625i
$478$		0			0
$479$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$479$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$480$		0			0
$481$	0.510177	−	1.29991i	0.510177	−	1.29991i
$482$	0.134659	+	0.0648483i	0.134659	+	0.0648483i
$483$		0			0
$484$	0.880843	−	0.424191i	0.880843	−	0.424191i
$485$		0			0
$486$		0			0
$487$	0.367711	−	0.250701i	0.367711	−	0.250701i	−0.365341	−	0.930874i	$-0.619048\pi$
$487$	0.367711	−	0.250701i	0.367711	−	0.250701i	0.733052	+	0.680173i	$0.238095\pi$
$488$		0			0
$489$		0			0
$490$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$491$	−0.445042			−0.445042			−0.222521	−	0.974928i	$-0.571429\pi$
$491$	−0.445042			−0.445042			−0.222521	+	0.974928i	$0.571429\pi$
$492$		0			0
$493$		0			0
$494$	3.01782	+	0.930874i	3.01782	+	0.930874i
$495$	−0.0111692	−	0.149042i	−0.0111692	−	0.149042i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−0.658322	+	1.67738i	−0.658322	+	1.67738i	0.0747301	+	0.997204i	$0.476190\pi$
$499$	−0.658322	+	1.67738i	−0.658322	+	1.67738i	−0.733052	+	0.680173i	$0.761905\pi$
$500$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$501$		0			0
$502$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i
$503$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$503$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$504$	0.365341	−	0.930874i	0.365341	−	0.930874i
$505$		0			0
$506$	−0.123490	−	0.0841939i	−0.123490	−	0.0841939i
$507$		0			0
$508$	−0.988831	+	1.71271i	−0.988831	+	1.71271i
$509$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$509$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$510$		0			0
$511$		0			0
$512$	0.222521	+	0.974928i	0.222521	+	0.974928i
$513$		0			0
$514$		0			0
$515$	−1.23305	+	0.185853i	−1.23305	+	0.185853i
$516$		0			0
$517$	−0.0487597	−	0.213630i	−0.0487597	−	0.213630i
$518$	−0.603718	+	0.411608i	−0.603718	+	0.411608i
$519$		0			0
$520$	0.955573	+	1.65510i	0.955573	+	1.65510i
$521$	0.733052	−	1.26968i	0.733052	−	1.26968i	−0.222521	−	0.974928i	$-0.571429\pi$
$521$	0.733052	−	1.26968i	0.733052	−	1.26968i	0.955573	−	0.294755i	$-0.0952381\pi$
$522$		0			0
$523$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$523$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$524$	0.455573	+	0.571270i	0.455573	+	0.571270i
$525$		0			0
$526$	−0.277479	+	0.347948i	−0.277479	+	0.347948i
$527$		0			0
$528$		0			0
$529$		0			0
$530$	0.535628	−	1.36476i	0.535628	−	1.36476i
$531$	1.62349	+	0.781831i	1.62349	+	0.781831i
$532$	−1.03030	−	1.29196i	−1.03030	−	1.29196i
$533$	−3.40530	+	1.63991i	−3.40530	+	1.63991i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.142820	+	0.0440542i	0.142820	+	0.0440542i
$540$		0			0
$541$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$541$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$547$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$548$		0			0
$549$		0			0
$550$	−0.0546039	−	0.139129i	−0.0546039	−	0.139129i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.277479	−	0.347948i	−0.277479	−	0.347948i
$555$		0			0
$556$	−0.914101	−	0.848162i	−0.914101	−	0.848162i
$557$	0.955573	−	1.65510i	0.955573	−	1.65510i	0.222521	−	0.974928i	$-0.428571\pi$
$557$	0.955573	−	1.65510i	0.955573	−	1.65510i	0.733052	−	0.680173i	$-0.238095\pi$
$558$		0			0
$559$		0			0
$560$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$561$		0			0
$562$	−1.07473	+	0.997204i	−1.07473	+	0.997204i
$563$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$563$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$568$		0			0
$569$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$569$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$570$		0			0
$571$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	0.0747301	−	0.997204i	$-0.476190\pi$
$571$	−0.914101	−	0.848162i	−0.914101	−	0.848162i	−0.988831	+	0.149042i	$0.952381\pi$
$572$	−0.236007	−	0.160907i	−0.236007	−	0.160907i
$573$		0			0
$574$	1.95557	+	0.294755i	1.95557	+	0.294755i
$575$	0.623490	−	0.781831i	0.623490	−	0.781831i
$576$	0.955573	−	0.294755i	0.955573	−	0.294755i
$577$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$577$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$578$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	0.0163752	+	0.218511i	0.0163752	+	0.218511i
$584$		0			0
$585$	1.57906	−	1.07659i	1.57906	−	1.07659i
$586$	1.95557	+	0.294755i	1.95557	+	0.294755i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	1.78181	+	0.268565i	1.78181	+	0.268565i
$591$		0			0
$592$	−0.698220	−	0.215372i	−0.698220	−	0.215372i
$593$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$593$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$		0			0
$598$	0.142820	−	1.90580i	0.142820	−	1.90580i
$599$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$599$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$600$		0			0
$601$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$601$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.716677	−	0.664979i	−0.716677	−	0.664979i
$606$		0			0
$607$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$607$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$608$	0.367711	−	1.61105i	0.367711	−	1.61105i
$609$		0			0
$610$		0			0
$611$	2.05397	−	1.90580i	2.05397	−	1.90580i
$612$		0			0
$613$	1.63402	−	0.246289i	1.63402	−	0.246289i	0.733052	−	0.680173i	$-0.238095\pi$
$613$	1.63402	−	0.246289i	1.63402	−	0.246289i	0.900969	+	0.433884i	$0.142857\pi$
$614$		0			0
$615$		0			0
$616$	0.0546039	+	0.139129i	0.0546039	+	0.139129i
$617$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$617$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$618$		0			0
$619$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.365341	−	0.930874i	$-0.380952\pi$
$619$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.623490	−	0.781831i	$-0.285714\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.0332580	+	0.443797i	0.0332580	+	0.443797i
$624$		0			0
$625$	0.955573	−	0.294755i	0.955573	−	0.294755i
$626$		0			0
$627$		0			0
$628$	0.365341	−	0.930874i	0.365341	−	0.930874i
$629$		0			0
$630$	−1.00000			−1.00000
$631$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$631$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$632$		0			0
$633$		0			0
$634$	1.03030	−	0.702449i	1.03030	−	0.702449i
$635$	1.95557	+	0.294755i	1.95557	+	0.294755i
$636$		0			0
$637$	0.425270	+	1.86323i	0.425270	+	1.86323i
$638$		0			0
$639$		0			0
$640$	0.826239	−	0.563320i	0.826239	−	0.563320i
$641$	−0.955573	−	0.294755i	−0.955573	−	0.294755i	−0.222521	−	0.974928i	$-0.571429\pi$
$641$	−0.955573	−	0.294755i	−0.955573	−	0.294755i	−0.733052	+	0.680173i	$0.761905\pi$
$642$		0			0
$643$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$643$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$644$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$645$		0			0
$646$		0			0
$647$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	0.500000	+	0.866025i	$0.333333\pi$
$647$	−0.123490	+	1.64786i	−0.123490	+	1.64786i	−0.623490	+	0.781831i	$0.714286\pi$
$648$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$649$	−0.257353	+	0.0793829i	−0.257353	+	0.0793829i
$650$	1.19158	−	1.49419i	1.19158	−	1.49419i
$651$		0			0
$652$		0			0
$653$	−1.36534	−	0.930874i	−1.36534	−	0.930874i	−0.365341	−	0.930874i	$-0.619048\pi$
$653$	−1.36534	−	0.930874i	−1.36534	−	0.930874i	−1.00000			$\pi$
$654$		0			0
$655$	0.365341	−	0.632789i	0.365341	−	0.632789i
$656$	0.988831	+	1.71271i	0.988831	+	1.71271i
$657$		0			0
$658$	−1.44973	+	0.218511i	−1.44973	+	0.218511i
$659$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	1.00000			$0$
$659$	0.0990311	+	0.433884i	0.0990311	+	0.433884i	−0.900969	+	0.433884i	$0.857143\pi$
$660$		0			0
$661$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$661$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$662$	0.722521	−	0.108903i	0.722521	−	0.108903i
$663$		0			0
$664$		0			0
$665$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$666$	−0.162592	+	0.712362i	−0.162592	+	0.712362i
$667$		0			0
$668$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$673$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$674$		0			0
$675$		0			0
$676$	0.198220	−	2.64506i	0.198220	−	2.64506i
$677$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	−0.955573	−	0.294755i	$-0.904762\pi$
$677$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	0.900969	+	0.433884i	$0.142857\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$683$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$684$	−1.63402	−	0.246289i	−1.63402	−	0.246289i
$685$		0			0
$686$	0.365341	−	0.930874i	0.365341	−	0.930874i
$687$		0			0
$688$		0			0
$689$	−2.31507	+	1.57839i	−2.31507	+	1.57839i
$690$		0			0
$691$	0.0931869	+	1.24349i	0.0931869	+	1.24349i	0.826239	+	0.563320i	$0.190476\pi$
$691$	0.0931869	+	1.24349i	0.0931869	+	1.24349i	−0.733052	+	0.680173i	$0.761905\pi$
$692$	0.658322	−	0.317031i	0.658322	−	0.317031i
$693$	0.134659	−	0.0648483i	0.134659	−	0.0648483i
$694$		0			0
$695$	−0.455573	+	1.16078i	−0.455573	+	1.16078i
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$701$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$701$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$702$		0			0
$703$	0.885113	+	0.821265i	0.885113	+	0.821265i
$704$	−0.0747301	+	0.129436i	−0.0747301	+	0.129436i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$709$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$710$		0			0
$711$		0			0
$712$	−0.326239	+	0.302705i	−0.326239	+	0.302705i
$713$		0			0
$714$		0			0
$715$	−0.0635609	+	0.278479i	−0.0635609	+	0.278479i
$716$	−0.826239	−	1.43109i	−0.826239	−	1.43109i
$717$		0			0
$718$		0			0
$719$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$719$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$720$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$721$	−0.623490	−	1.07992i	−0.623490	−	1.07992i
$722$	−1.07906	+	1.35310i	−1.07906	+	1.35310i
$723$		0			0
$724$		0			0
$725$		0			0
$726$		0			0
$727$	0.658322	+	0.317031i	0.658322	+	0.317031i	0.733052	−	0.680173i	$-0.238095\pi$
$727$	0.658322	+	0.317031i	0.658322	+	0.317031i	−0.0747301	+	0.997204i	$0.523810\pi$
$728$	−1.19158	+	1.49419i	−1.19158	+	1.49419i
$729$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$730$		0			0
$731$		0			0
$732$		0			0
$733$	1.63402	+	0.246289i	1.63402	+	0.246289i	0.900969	−	0.433884i	$-0.142857\pi$
$733$	1.63402	+	0.246289i	1.63402	+	0.246289i	0.733052	+	0.680173i	$0.238095\pi$
$734$	−1.97766			−1.97766
$735$		0			0
$736$	−1.00000			−1.00000
$737$		0			0
$738$	1.63402	−	1.11406i	1.63402	−	1.11406i
$739$	1.82624	+	0.563320i	1.82624	+	0.563320i	1.00000			$0$
$739$	1.82624	+	0.563320i	1.82624	+	0.563320i	0.826239	+	0.563320i	$0.190476\pi$
$740$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$741$		0			0
$742$	1.46610			1.46610
$743$	0.658322	+	0.317031i	0.658322	+	0.317031i	0.733052	−	0.680173i	$-0.238095\pi$
$743$	0.658322	+	0.317031i	0.658322	+	0.317031i	−0.0747301	+	0.997204i	$0.523810\pi$
$744$		0			0
$745$		0			0
$746$	0.455573	+	1.16078i	0.455573	+	1.16078i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$751$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$752$	−1.07473	−	0.997204i	−1.07473	−	0.997204i
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	−0.623490	−	0.781831i	$-0.714286\pi$
$757$	−0.400969	−	1.75676i	−0.400969	−	1.75676i	0.222521	−	0.974928i	$-0.428571\pi$
$758$	1.40097	−	1.29991i	1.40097	−	1.29991i
$759$		0			0
$760$	−1.63402	+	0.246289i	−1.63402	+	0.246289i
$761$	1.07473	−	0.997204i	1.07473	−	0.997204i	0.0747301	−	0.997204i	$-0.476190\pi$
$761$	1.07473	−	0.997204i	1.07473	−	0.997204i	1.00000			$0$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$	0.988831	−	1.71271i	0.988831	−	1.71271i
$767$	−2.52446	−	2.34236i	−2.52446	−	2.34236i
$768$		0			0
$769$	0.455573	+	0.571270i	0.455573	+	0.571270i	0.955573	−	0.294755i	$-0.0952381\pi$
$769$	0.455573	+	0.571270i	0.455573	+	0.571270i	−0.500000	+	0.866025i	$0.666667\pi$
$770$	0.109562	−	0.101659i	0.109562	−	0.101659i
$771$		0			0
$772$		0			0
$773$	0.535628	+	1.36476i	0.535628	+	1.36476i	0.900969	+	0.433884i	$0.142857\pi$
$773$	0.535628	+	1.36476i	0.535628	+	1.36476i	−0.365341	+	0.930874i	$0.619048\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−0.244221	−	3.25890i	−0.244221	−	3.25890i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.955573	−	0.294755i	0.955573	−	0.294755i
$785$	−1.00000			−1.00000
$786$		0			0
$787$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$787$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$788$	−1.82624	−	0.563320i	−1.82624	−	0.563320i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.134659	+	0.0648483i	0.134659	+	0.0648483i
$793$		0			0
$794$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i
$795$		0			0
$796$		0			0
$797$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$797$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$798$		0			0
$799$		0			0
$800$	−0.826239	−	0.563320i	−0.826239	−	0.563320i
$801$	0.326239	+	0.302705i	0.326239	+	0.302705i
$802$	−0.733052	+	1.26968i	−0.733052	+	1.26968i
$803$		0			0
$804$		0			0
$805$	0.955573	+	0.294755i	0.955573	+	0.294755i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.95557	−	0.294755i	1.95557	−	0.294755i	0.955573	−	0.294755i	$-0.0952381\pi$
$809$	1.95557	−	0.294755i	1.95557	−	0.294755i	1.00000			$0$
$810$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$811$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	−0.988831	−	0.149042i	$-0.952381\pi$
$811$	−0.162592	−	0.712362i	−0.162592	−	0.712362i	0.826239	−	0.563320i	$-0.190476\pi$
$812$		0			0
$813$		0			0
$814$	−0.0546039	−	0.0945768i	−0.0546039	−	0.0945768i
$815$		0			0
$816$		0			0
$817$		0			0
$818$	1.12349	+	1.40881i	1.12349	+	1.40881i
$819$	1.57906	+	1.07659i	1.57906	+	1.07659i
$820$	1.23305	−	1.54620i	1.23305	−	1.54620i
$821$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$821$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$822$		0			0
$823$	0.0332580	−	0.443797i	0.0332580	−	0.443797i	−0.955573	−	0.294755i	$-0.904762\pi$
$823$	0.0332580	−	0.443797i	0.0332580	−	0.443797i	0.988831	−	0.149042i	$-0.0476190\pi$
$824$	0.455573	−	1.16078i	0.455573	−	1.16078i
$825$		0			0
$826$	0.400969	+	1.75676i	0.400969	+	1.75676i
$827$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$827$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$828$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$829$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$829$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$830$		0			0
$831$		0			0
$832$	−1.91115			−1.91115
$833$		0			0
$834$		0			0
$835$	0.988831	+	0.149042i	0.988831	+	0.149042i
$836$	0.204064	−	0.139129i	0.204064	−	0.139129i
$837$		0			0
$838$	0.109562	+	1.46200i	0.109562	+	1.46200i
$839$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$839$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$840$		0			0
$841$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$842$		0			0
$843$		0			0
$844$	−0.722521	−	1.84095i	−0.722521	−	1.84095i
$845$	−2.53464	+	0.781831i	−2.53464	+	0.781831i
$846$	−0.914101	+	1.14625i	−0.914101	+	1.14625i
$847$	0.357180	−	0.910080i	0.357180	−	0.910080i
$848$	0.914101	+	1.14625i	0.914101	+	1.14625i
$849$		0			0
$850$		0			0
$851$	0.365341	−	0.632789i	0.365341	−	0.632789i
$852$		0			0
$853$	0.162592	−	0.712362i	0.162592	−	0.712362i	−0.826239	−	0.563320i	$-0.809524\pi$
$853$	0.162592	−	0.712362i	0.162592	−	0.712362i	0.988831	−	0.149042i	$-0.0476190\pi$
$854$		0			0
$855$	0.367711	+	1.61105i	0.367711	+	1.61105i
$856$		0			0
$857$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$857$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$858$		0			0
$859$	0.326239	−	0.302705i	0.326239	−	0.302705i	−0.500000	−	0.866025i	$-0.666667\pi$
$859$	0.326239	−	0.302705i	0.326239	−	0.302705i	0.826239	+	0.563320i	$0.190476\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	0.365341	+	0.632789i	0.365341	+	0.632789i	0.988831	−	0.149042i	$-0.0476190\pi$
$863$	0.365341	+	0.632789i	0.365341	+	0.632789i	−0.623490	+	0.781831i	$0.714286\pi$
$864$		0			0
$865$	−0.535628	−	0.496990i	−0.535628	−	0.496990i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$	1.48883	+	0.716983i	1.48883	+	0.716983i
$875$	0.623490	+	0.781831i	0.623490	+	0.781831i
$876$		0			0
$877$	−0.142820	−	1.90580i	−0.142820	−	1.90580i	−0.365341	−	0.930874i	$-0.619048\pi$
$877$	−0.142820	−	1.90580i	−0.142820	−	1.90580i	0.222521	−	0.974928i	$-0.428571\pi$
$878$		0			0
$879$		0			0
$880$	0.147791	+	0.0222759i	0.147791	+	0.0222759i
$881$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$881$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$882$	−0.365341	−	0.930874i	−0.365341	−	0.930874i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.134659	+	1.79690i	0.134659	+	1.79690i	0.500000	+	0.866025i	$0.333333\pi$
$887$	0.134659	+	1.79690i	0.134659	+	1.79690i	−0.365341	+	0.930874i	$0.619048\pi$
$888$		0			0
$889$	0.440071	+	1.92808i	0.440071	+	1.92808i
$890$	0.400969	+	0.193096i	0.400969	+	0.193096i
$891$	0.0546039	−	0.139129i	0.0546039	−	0.139129i
$892$	0.134659	−	1.79690i	0.134659	−	1.79690i
$893$	0.885113	+	2.25523i	0.885113	+	2.25523i
$894$		0			0
$895$	−1.03030	+	1.29196i	−1.03030	+	1.29196i
$896$	0.826239	+	0.563320i	0.826239	+	0.563320i
$897$		0			0
$898$	−0.603718	−	0.411608i	−0.603718	−	0.411608i
$899$		0			0
$900$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$901$		0			0
$902$	−0.0657731	+	0.288171i	−0.0657731	+	0.288171i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$907$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$908$		0			0
$909$		0			0
$910$	1.82624	+	0.563320i	1.82624	+	0.563320i
$911$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$911$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.722521	+	0.108903i	0.722521	+	0.108903i
$918$		0			0
$919$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$919$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$920$	0.365341	+	0.930874i	0.365341	+	0.930874i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.658322	−	0.317031i	0.658322	−	0.317031i
$926$	−0.109562	−	1.46200i	−0.109562	−	1.46200i
$927$	−1.19158	−	0.367554i	−1.19158	−	0.367554i
$928$		0			0
$929$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.900969	−	0.433884i	$-0.857143\pi$
$929$	−1.88980	−	0.284841i	−1.88980	−	0.284841i	−0.988831	+	0.149042i	$0.952381\pi$
$930$		0			0
$931$	−1.63402	−	0.246289i	−1.63402	−	0.246289i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$	0.142820	+	1.90580i	0.142820	+	1.90580i
$937$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$937$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$938$		0			0
$939$		0			0
$940$	−0.535628	+	1.36476i	−0.535628	+	1.36476i
$941$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$941$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$942$		0			0
$943$	−1.88980	+	0.582926i	−1.88980	+	0.582926i
$944$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$945$		0			0
$946$		0			0
$947$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$947$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$948$		0			0
$949$		0			0
$950$	0.826239	+	1.43109i	0.826239	+	1.43109i
$951$		0			0
$952$		0			0
$953$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$953$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$954$	1.07473	−	0.997204i	1.07473	−	0.997204i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$	0.698220	−	1.20935i	0.698220	−	1.20935i
$963$		0			0
$964$	0.123490	+	0.0841939i	0.123490	+	0.0841939i
$965$		0			0
$966$		0			0
$967$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.222521	−	0.974928i	$-0.428571\pi$
$967$	1.12349	−	1.40881i	1.12349	−	1.40881i	0.900969	−	0.433884i	$-0.142857\pi$
$968$	0.934227	−	0.288171i	0.934227	−	0.288171i
$969$		0			0
$970$		0			0
$971$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	0.623490	+	0.781831i	$0.285714\pi$
$971$	−0.365341	+	0.930874i	−0.365341	+	0.930874i	−0.988831	+	0.149042i	$0.952381\pi$
$972$		0			0
$973$	−1.24698			−1.24698
$974$	0.400969	−	0.193096i	0.400969	−	0.193096i
$975$		0			0
$976$		0			0
$977$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$977$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$978$		0			0
$979$	−0.0665160			−0.0665160
$980$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$981$		0			0
$982$	−0.440071	−	0.0663300i	−0.440071	−	0.0663300i
$983$	0.826239	−	0.563320i	0.826239	−	0.563320i	−0.0747301	−	0.997204i	$-0.523810\pi$
$983$	0.826239	−	0.563320i	0.826239	−	0.563320i	0.900969	+	0.433884i	$0.142857\pi$
$984$		0			0
$985$	0.142820	+	1.90580i	0.142820	+	1.90580i
$986$		0			0
$987$		0			0
$988$	2.84537	+	1.37026i	2.84537	+	1.37026i
$989$		0			0
$990$	0.0111692	−	0.149042i	0.0111692	−	0.149042i
$991$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$991$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1.32091	−	1.22563i	−1.32091	−	1.22563i	−0.955573	−	0.294755i	$-0.904762\pi$
$997$	−1.32091	−	1.22563i	−1.32091	−	1.22563i	−0.365341	−	0.930874i	$-0.619048\pi$
$998$	−0.900969	+	1.56052i	−0.900969	+	1.56052i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1960.1.cz.a.1019.1	yes	12
5.4	even	2		1960.1.cz.b.1019.1	yes	12
8.3	odd	2		1960.1.cz.b.1019.1	yes	12
40.19	odd	2	CM	1960.1.cz.a.1019.1	yes	12
49.44	even	21	inner	1960.1.cz.a.779.1	✓	12
245.44	even	42		1960.1.cz.b.779.1	yes	12
392.387	odd	42		1960.1.cz.b.779.1	yes	12
1960.779	odd	42	inner	1960.1.cz.a.779.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1960.1.cz.a.779.1	✓	12	49.44	even	21	inner
1960.1.cz.a.779.1	✓	12	1960.779	odd	42	inner
1960.1.cz.a.1019.1	yes	12	1.1	even	1	trivial
1960.1.cz.a.1019.1	yes	12	40.19	odd	2	CM
1960.1.cz.b.779.1	yes	12	245.44	even	42
1960.1.cz.b.779.1	yes	12	392.387	odd	42
1960.1.cz.b.1019.1	yes	12	5.4	even	2
1960.1.cz.b.1019.1	yes	12	8.3	odd	2

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:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1960.cz (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988831 + 0.149042i) q^{2} +(0.955573 + 0.294755i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.900969 - 0.433884i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +O(q^{10})\)	\(q+(0.988831 + 0.149042i) q^{2} +(0.955573 + 0.294755i) q^{4} +(-0.0747301 - 0.997204i) q^{5} +(0.900969 - 0.433884i) q^{7} +(0.900969 + 0.433884i) q^{8} +(0.365341 - 0.930874i) q^{9} +(0.0747301 - 0.997204i) q^{10} +(0.0546039 + 0.139129i) q^{11} +(-1.19158 + 1.49419i) q^{13} +(0.955573 - 0.294755i) q^{14} +(0.826239 + 0.563320i) q^{16} +(0.500000 - 0.866025i) q^{18} +(-0.826239 - 1.43109i) q^{19} +(0.222521 - 0.974928i) q^{20} +(0.0332580 + 0.145713i) q^{22} +(-0.733052 + 0.680173i) q^{23} +(-0.988831 + 0.149042i) q^{25} +(-1.40097 + 1.29991i) q^{26} +(0.988831 - 0.149042i) q^{28} +(0.733052 + 0.680173i) q^{32} +(-0.500000 - 0.866025i) q^{35} +(0.623490 - 0.781831i) q^{36} +(-0.698220 + 0.215372i) q^{37} +(-0.603718 - 1.53825i) q^{38} +(0.365341 - 0.930874i) q^{40} +(1.78181 + 0.858075i) q^{41} +(0.0111692 + 0.149042i) q^{44} +(-0.955573 - 0.294755i) q^{45} +(-0.826239 + 0.563320i) q^{46} +(-1.44973 - 0.218511i) q^{47} +(0.623490 - 0.781831i) q^{49} -1.00000 q^{50} +(-1.57906 + 1.07659i) q^{52} +(1.40097 + 0.432142i) q^{53} +(0.134659 - 0.0648483i) q^{55} +1.00000 q^{56} +(-0.134659 + 1.79690i) q^{59} +(-0.0747301 - 0.997204i) q^{63} +(0.623490 + 0.781831i) q^{64} +(1.57906 + 1.07659i) q^{65} +(-0.365341 - 0.930874i) q^{70} +(0.733052 - 0.680173i) q^{72} +(-0.722521 + 0.108903i) q^{74} +(-0.367711 - 1.61105i) q^{76} +(0.109562 + 0.101659i) q^{77} +(0.500000 - 0.866025i) q^{80} +(-0.733052 - 0.680173i) q^{81} +(1.63402 + 1.11406i) q^{82} +(-0.0111692 + 0.149042i) q^{88} +(-0.162592 + 0.414278i) q^{89} +(-0.900969 - 0.433884i) q^{90} +(-0.425270 + 1.86323i) q^{91} +(-0.900969 + 0.433884i) q^{92} +(-1.40097 - 0.432142i) q^{94} +(-1.36534 + 0.930874i) q^{95} +(0.733052 - 0.680173i) q^{98} +0.149460 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} + q^{4} - q^{5} + 2 q^{7} + 2 q^{8} + q^{9}+O(q^{10}) \) 12 * q - q^2 + q^4 - q^5 + 2 * q^7 + 2 * q^8 + q^9	\( 12 q - q^{2} + q^{4} - q^{5} + 2 q^{7} + 2 q^{8} + q^{9} + q^{10} - q^{11} - 2 q^{13} + q^{14} + q^{16} + 6 q^{18} - q^{19} + 2 q^{20} - 2 q^{22} + q^{23} + q^{25} - 8 q^{26} - q^{28} - q^{32} - 6 q^{35} - 2 q^{36} + q^{37} + q^{38} + q^{40} + 2 q^{41} + 13 q^{44} - q^{45} - q^{46} + q^{47} - 2 q^{49} - 12 q^{50} + q^{52} + 8 q^{53} + 5 q^{55} + 12 q^{56} - 5 q^{59} - q^{63} - 2 q^{64} - q^{65} - q^{70} - q^{72} - 8 q^{74} + 2 q^{76} + q^{77} + 6 q^{80} + q^{81} + q^{82} - 13 q^{88} + 2 q^{89} - 2 q^{90} - 5 q^{91} - 2 q^{92} - 8 q^{94} - 13 q^{95} - q^{98} + 2 q^{99}+O(q^{100}) \) 12 * q - q^2 + q^4 - q^5 + 2 * q^7 + 2 * q^8 + q^9 + q^10 - q^11 - 2 * q^13 + q^14 + q^16 + 6 * q^18 - q^19 + 2 * q^20 - 2 * q^22 + q^23 + q^25 - 8 * q^26 - q^28 - q^32 - 6 * q^35 - 2 * q^36 + q^37 + q^38 + q^40 + 2 * q^41 + 13 * q^44 - q^45 - q^46 + q^47 - 2 * q^49 - 12 * q^50 + q^52 + 8 * q^53 + 5 * q^55 + 12 * q^56 - 5 * q^59 - q^63 - 2 * q^64 - q^65 - q^70 - q^72 - 8 * q^74 + 2 * q^76 + q^77 + 6 * q^80 + q^81 + q^82 - 13 * q^88 + 2 * q^89 - 2 * q^90 - 5 * q^91 - 2 * q^92 - 8 * q^94 - 13 * q^95 - q^98 + 2 * q^99

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