LMFDB - Embedded newform 2695.1.ck.b.1374.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2695,1,Mod(109,2695)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2695, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 40, 21]))

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

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

chi := DirichletCharacter("2695.109");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2695 = 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2695.ck (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:	$1.34498020905$
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:	$\Z[a_1, \ldots, a_{4}]$
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			1374.1
Root			$0.0747301 + 0.997204i$ of defining polynomial
Character	$\chi$	$=$	2695.1374
Dual form			2695.1.ck.b.2034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.57906 - 0.487076i) q^{2} +(1.42996 + 0.974928i) q^{4} +(-0.988831 + 0.149042i) q^{5} +(0.222521 - 0.974928i) q^{7} +(-0.752824 - 0.944011i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(1.63402 + 0.246289i) q^{10} +(-0.733052 + 0.680173i) q^{11} +(-0.326239 - 1.42935i) q^{13} +(-0.826239 + 1.43109i) q^{14} +(0.0966613 + 0.246289i) q^{16} +(-0.0931869 - 1.24349i) q^{17} +(0.826239 + 1.43109i) q^{18} +(-1.55929 - 0.750915i) q^{20} +(1.48883 - 0.716983i) q^{22} +(0.955573 - 0.294755i) q^{25} +(-0.181049 + 2.41593i) q^{26} +(1.26868 - 1.17716i) q^{28} +(0.500000 + 0.866025i) q^{31} +(0.0575591 + 0.768072i) q^{32} +(-0.458528 + 2.00894i) q^{34} +(-0.0747301 + 0.997204i) q^{35} +(-0.385113 - 1.68729i) q^{36} +(0.885113 + 0.821265i) q^{40} +(-1.19158 + 1.49419i) q^{43} +(-1.71135 + 0.257945i) q^{44} +(0.826239 + 0.563320i) q^{45} +(-0.900969 - 0.433884i) q^{49} -1.65248 q^{50} +(0.927001 - 2.36196i) q^{52} +(0.623490 - 0.781831i) q^{55} +(-1.08786 + 0.523887i) q^{56} +(1.44973 + 0.218511i) q^{59} +(-0.367711 - 1.61105i) q^{62} +(-0.826239 + 0.563320i) q^{63} +(0.342095 - 1.49881i) q^{64} +(0.535628 + 1.36476i) q^{65} +(1.07906 - 1.86899i) q^{68} +(0.603718 - 1.53825i) q^{70} +(-1.48883 + 0.716983i) q^{71} +(-0.0902318 + 1.20406i) q^{72} +(-0.698220 + 0.215372i) q^{73} +(0.500000 + 0.866025i) q^{77} +(-0.132289 - 0.229132i) q^{80} +(0.0747301 + 0.997204i) q^{81} +(-0.222521 + 0.974928i) q^{83} +(0.277479 + 1.21572i) q^{85} +(2.60937 - 1.77904i) q^{86} +(1.19395 + 0.179959i) q^{88} +(-1.40097 - 1.29991i) q^{89} +(-1.03030 - 1.29196i) q^{90} -1.46610 q^{91} +(1.21135 + 1.12397i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} + q^{5} + 2 q^{7} + 2 q^{8} + q^{9} + q^{10} + q^{11} + 5 q^{13} - q^{14} + 13 q^{16} - 2 q^{17} + q^{18} + 5 q^{22} + q^{25} + q^{26} + 6 q^{31} + 7 q^{32} - 3 q^{34} - q^{35} + 6 q^{40}+ \cdots + 12 q^{99}+O(q^{100}) $ 12 * q + q^2 + q^5 + 2 * q^7 + 2 * q^8 + q^9 + q^10 + q^11 + 5 * q^13 - q^14 + 13 * q^16 - 2 * q^17 + q^18 + 5 * q^22 + q^25 + q^26 + 6 * q^31 + 7 * q^32 - 3 * q^34 - q^35 + 6 * q^40 - 2 * q^43 - 7 * q^44 + q^45 - 2 * q^49 - 2 * q^50 - 14 * q^52 - 2 * q^55 - 9 * q^56 - q^59 + 2 * q^62 - q^63 - 9 * q^64 + q^65 - 7 * q^68 - q^70 - 5 * q^71 + 6 * q^72 + q^73 + 6 * q^77 - 8 * q^80 + q^81 - 2 * q^83 + 4 * q^85 + q^86 - q^88 - 8 * q^89 - 2 * q^90 + 2 * q^91 + q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2695\mathbb{Z}\right)^\times$.

$n$	$981$	$1816$	$2157$
$\chi(n)$	$-1$	$e\left(\frac{13}{21}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.57906	−	0.487076i	−1.57906	−	0.487076i	−0.623490	−	0.781831i	$-0.714286\pi$
$2$	−1.57906	−	0.487076i	−1.57906	−	0.487076i	−0.955573	+	0.294755i	$0.904762\pi$
$3$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$3$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$4$	1.42996	+	0.974928i	1.42996	+	0.974928i
$5$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$5$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$6$		0			0
$7$	0.222521	−	0.974928i	0.222521	−	0.974928i
$7$	0.222521	−	0.974928i	0.222521	−	0.974928i
$8$	−0.752824	−	0.944011i	−0.752824	−	0.944011i
$9$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$10$	1.63402	+	0.246289i	1.63402	+	0.246289i
$11$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$11$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$12$		0			0
$13$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	−0.826239	−	0.563320i	$-0.809524\pi$
$13$	−0.326239	−	1.42935i	−0.326239	−	1.42935i	0.500000	−	0.866025i	$-0.333333\pi$
$14$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$15$		0			0
$16$	0.0966613	+	0.246289i	0.0966613	+	0.246289i
$17$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i	−0.826239	−	0.563320i	$-0.809524\pi$
$17$	−0.0931869	−	1.24349i	−0.0931869	−	1.24349i	0.733052	−	0.680173i	$-0.238095\pi$
$18$	0.826239	+	1.43109i	0.826239	+	1.43109i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$	−1.55929	−	0.750915i	−1.55929	−	0.750915i
$21$		0			0
$22$	1.48883	−	0.716983i	1.48883	−	0.716983i
$23$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$23$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$24$		0			0
$25$	0.955573	−	0.294755i	0.955573	−	0.294755i
$26$	−0.181049	+	2.41593i	−0.181049	+	2.41593i
$27$		0			0
$28$	1.26868	−	1.17716i	1.26868	−	1.17716i
$29$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$29$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.500000	+	0.866025i	1.00000			$0$
$31$	0.500000	+	0.866025i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$32$	0.0575591	+	0.768072i	0.0575591	+	0.768072i
$33$		0			0
$34$	−0.458528	+	2.00894i	−0.458528	+	2.00894i
$35$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i
$36$	−0.385113	−	1.68729i	−0.385113	−	1.68729i
$37$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$37$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$38$		0			0
$39$		0			0
$40$	0.885113	+	0.821265i	0.885113	+	0.821265i
$41$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$41$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$42$		0			0
$43$	−1.19158	+	1.49419i	−1.19158	+	1.49419i	−0.365341	+	0.930874i	$0.619048\pi$
$43$	−1.19158	+	1.49419i	−1.19158	+	1.49419i	−0.826239	+	0.563320i	$0.809524\pi$
$44$	−1.71135	+	0.257945i	−1.71135	+	0.257945i
$45$	0.826239	+	0.563320i	0.826239	+	0.563320i
$46$		0			0
$47$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$47$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$48$		0			0
$49$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$50$	−1.65248			−1.65248
$51$		0			0
$52$	0.927001	−	2.36196i	0.927001	−	2.36196i
$53$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$53$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$54$		0			0
$55$	0.623490	−	0.781831i	0.623490	−	0.781831i
$56$	−1.08786	+	0.523887i	−1.08786	+	0.523887i
$57$		0			0
$58$		0			0
$59$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.826239	−	0.563320i	$-0.190476\pi$
$59$	1.44973	+	0.218511i	1.44973	+	0.218511i	0.623490	+	0.781831i	$0.285714\pi$
$60$		0			0
$61$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$61$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$62$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$63$	−0.826239	+	0.563320i	−0.826239	+	0.563320i
$64$	0.342095	−	1.49881i	0.342095	−	1.49881i
$65$	0.535628	+	1.36476i	0.535628	+	1.36476i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	1.07906	−	1.86899i	1.07906	−	1.86899i
$69$		0			0
$70$	0.603718	−	1.53825i	0.603718	−	1.53825i
$71$	−1.48883	+	0.716983i	−1.48883	+	0.716983i	−0.988831	−	0.149042i	$-0.952381\pi$
$71$	−1.48883	+	0.716983i	−1.48883	+	0.716983i	−0.500000	+	0.866025i	$0.666667\pi$
$72$	−0.0902318	+	1.20406i	−0.0902318	+	1.20406i
$73$	−0.698220	+	0.215372i	−0.698220	+	0.215372i	−0.623490	−	0.781831i	$-0.714286\pi$
$73$	−0.698220	+	0.215372i	−0.698220	+	0.215372i	−0.0747301	+	0.997204i	$0.523810\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.500000	+	0.866025i	0.500000	+	0.866025i
$78$		0			0
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$	−0.132289	−	0.229132i	−0.132289	−	0.229132i
$81$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$82$		0			0
$83$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	0.733052	+	0.680173i	$0.238095\pi$
$83$	−0.222521	+	0.974928i	−0.222521	+	0.974928i	−0.955573	+	0.294755i	$0.904762\pi$
$84$		0			0
$85$	0.277479	+	1.21572i	0.277479	+	1.21572i
$86$	2.60937	−	1.77904i	2.60937	−	1.77904i
$87$		0			0
$88$	1.19395	+	0.179959i	1.19395	+	0.179959i
$89$	−1.40097	−	1.29991i	−1.40097	−	1.29991i	−0.900969	−	0.433884i	$-0.857143\pi$
$89$	−1.40097	−	1.29991i	−1.40097	−	1.29991i	−0.500000	−	0.866025i	$-0.666667\pi$
$90$	−1.03030	−	1.29196i	−1.03030	−	1.29196i
$91$	−1.46610			−1.46610
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	1.21135	+	1.12397i	1.21135	+	1.12397i
$99$	1.00000			1.00000
$100$	1.65379	+	0.510127i	1.65379	+	0.510127i
$101$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$101$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$102$		0			0
$103$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$103$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$104$	−1.10372	+	1.38402i	−1.10372	+	1.38402i
$105$		0			0
$106$		0			0
$107$	−1.32091	−	1.22563i	−1.32091	−	1.22563i	−0.955573	−	0.294755i	$-0.904762\pi$
$107$	−1.32091	−	1.22563i	−1.32091	−	1.22563i	−0.365341	−	0.930874i	$-0.619048\pi$
$108$		0			0
$109$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$109$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$110$	−1.36534	+	0.930874i	−1.36534	+	0.930874i
$111$		0			0
$112$	0.261623	−	0.0394334i	0.261623	−	0.0394334i
$113$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$113$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−0.733052	+	1.26968i	−0.733052	+	1.26968i
$118$	−2.18278	−	1.05117i	−2.18278	−	1.05117i
$119$	−1.23305	−	0.185853i	−1.23305	−	0.185853i
$120$		0			0
$121$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$122$		0			0
$123$		0			0
$124$	−0.129334	+	1.72584i	−0.129334	+	1.72584i
$125$	−0.900969	+	0.433884i	−0.900969	+	0.433884i
$126$	1.57906	−	0.487076i	1.57906	−	0.487076i
$127$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$127$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$128$	−0.885113	+	1.53306i	−0.885113	+	1.53306i
$129$		0			0
$130$	−0.181049	−	2.41593i	−0.181049	−	2.41593i
$131$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$131$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−1.10372	+	1.02410i	−1.10372	+	1.02410i
$137$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$137$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$138$		0			0
$139$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$139$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$140$	−1.07906	+	1.35310i	−1.07906	+	1.35310i
$141$		0			0
$142$	2.70018	−	0.406987i	2.70018	−	0.406987i
$143$	1.21135	+	0.825886i	1.21135	+	0.825886i
$144$	0.0966613	−	0.246289i	0.0966613	−	0.246289i
$145$		0			0
$146$	1.20744			1.20744
$147$		0			0
$148$		0			0
$149$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$149$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$150$		0			0
$151$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$151$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$152$		0			0
$153$	−0.777479	+	0.974928i	−0.777479	+	0.974928i
$154$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$155$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$156$		0			0
$157$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$157$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$158$		0			0
$159$		0			0
$160$	−0.171391	−	0.750915i	−0.171391	−	0.750915i
$161$		0			0
$162$	0.367711	−	1.61105i	0.367711	−	1.61105i
$163$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$163$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$164$		0			0
$165$		0			0
$166$	0.826239	−	1.43109i	0.826239	−	1.43109i
$167$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$167$	1.80194	+	0.867767i	1.80194	+	0.867767i	0.900969	+	0.433884i	$0.142857\pi$
$168$		0			0
$169$	−1.03563	+	0.498732i	−1.03563	+	0.498732i
$170$	0.153989	−	2.05484i	0.153989	−	2.05484i
$171$		0			0
$172$	−3.16064	+	0.974928i	−3.16064	+	0.974928i
$173$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i	0.988831	+	0.149042i	$0.0476190\pi$
$173$	−0.0111692	+	0.149042i	−0.0111692	+	0.149042i	−1.00000			$\pi$
$174$		0			0
$175$	−0.0747301	−	0.997204i	−0.0747301	−	0.997204i
$176$	−0.238377	−	0.114796i	−0.238377	−	0.114796i
$177$		0			0
$178$	1.57906	+	2.73502i	1.57906	+	2.73502i
$179$	0.123490	+	1.64786i	0.123490	+	1.64786i	0.623490	+	0.781831i	$0.285714\pi$
$179$	0.123490	+	1.64786i	0.123490	+	1.64786i	−0.500000	+	0.866025i	$0.666667\pi$
$180$	0.632289	+	1.61105i	0.632289	+	1.61105i
$181$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	0.826239	+	0.563320i	$0.190476\pi$
$181$	−0.162592	+	0.712362i	−0.162592	+	0.712362i	−0.988831	+	0.149042i	$0.952381\pi$
$182$	2.31507	+	0.714104i	2.31507	+	0.714104i
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	0.914101	+	0.848162i	0.914101	+	0.848162i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.988831	−	0.149042i	0.988831	−	0.149042i	0.365341	−	0.930874i	$-0.380952\pi$
$191$	0.988831	−	0.149042i	0.988831	−	0.149042i	0.623490	+	0.781831i	$0.285714\pi$
$192$		0			0
$193$	−0.455573	+	1.16078i	−0.455573	+	1.16078i	0.500000	+	0.866025i	$0.333333\pi$
$193$	−0.455573	+	1.16078i	−0.455573	+	1.16078i	−0.955573	+	0.294755i	$0.904762\pi$
$194$		0			0
$195$		0			0
$196$	−0.865341	−	1.49881i	−0.865341	−	1.49881i
$197$	−0.149460			−0.149460			−0.0747301	−	0.997204i	$-0.523810\pi$
$197$	−0.149460			−0.149460			−0.0747301	+	0.997204i	$0.523810\pi$
$198$	−1.57906	−	0.487076i	−1.57906	−	0.487076i
$199$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	−0.900969	−	0.433884i	$-0.857143\pi$
$199$	0.0546039	−	0.139129i	0.0546039	−	0.139129i	0.955573	+	0.294755i	$0.0952381\pi$
$200$	−0.997630	−	0.680173i	−0.997630	−	0.680173i
$201$		0			0
$202$		0			0
$203$		0			0
$204$		0			0
$205$		0			0
$206$		0			0
$207$		0			0
$208$	0.320497	−	0.218511i	0.320497	−	0.218511i
$209$		0			0
$210$		0			0
$211$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$211$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$212$		0			0
$213$		0			0
$214$	1.48883	+	2.57873i	1.48883	+	2.57873i
$215$	0.955573	−	1.65510i	0.955573	−	1.65510i
$216$		0			0
$217$	0.955573	−	0.294755i	0.955573	−	0.294755i
$218$		0			0
$219$		0			0
$220$	1.65379	−	0.510127i	1.65379	−	0.510127i
$221$	−1.74698	+	0.538872i	−1.74698	+	0.538872i
$222$		0			0
$223$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$223$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$224$	0.761623	+	0.114796i	0.761623	+	0.114796i
$225$	−0.900969	−	0.433884i	−0.900969	−	0.433884i
$226$		0			0
$227$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.623490	−	0.781831i	$-0.714286\pi$
$227$	−0.988831	−	1.71271i	−0.988831	−	1.71271i	−0.365341	−	0.930874i	$-0.619048\pi$
$228$		0			0
$229$	0.603718	+	1.53825i	0.603718	+	1.53825i	0.826239	+	0.563320i	$0.190476\pi$
$229$	0.603718	+	1.53825i	0.603718	+	1.53825i	−0.222521	+	0.974928i	$0.571429\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.65248	+	1.12664i	−1.65248	+	1.12664i	−0.826239	+	0.563320i	$0.809524\pi$
$233$	−1.65248	+	1.12664i	−1.65248	+	1.12664i	−0.826239	+	0.563320i	$0.809524\pi$
$234$	1.77597	−	1.64786i	1.77597	−	1.64786i
$235$		0			0
$236$	1.86002	+	1.72584i	1.86002	+	1.72584i
$237$		0			0
$238$	1.85654	+	0.894063i	1.85654	+	0.894063i
$239$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$239$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$240$		0			0
$241$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$241$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$242$	−0.603718	+	1.53825i	−0.603718	+	1.53825i
$243$		0			0
$244$		0			0
$245$	0.955573	+	0.294755i	0.955573	+	0.294755i
$246$		0			0
$247$		0			0
$248$	0.441126	−	1.12397i	0.441126	−	1.12397i
$249$		0			0
$250$	1.63402	−	0.246289i	1.63402	−	0.246289i
$251$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.222521	+	0.974928i	$0.571429\pi$
$251$	−1.12349	+	1.40881i	−1.12349	+	1.40881i	−0.900969	+	0.433884i	$0.857143\pi$
$252$	−1.73068			−1.73068
$253$		0			0
$254$	2.18278	+	2.02532i	2.18278	+	2.02532i
$255$		0			0
$256$	1.01740	−	0.944011i	1.01740	−	0.944011i
$257$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$257$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$258$		0			0
$259$		0			0
$260$	−0.564616	+	2.47374i	−0.564616	+	2.47374i
$261$		0			0
$262$		0			0
$263$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$263$	−0.500000	−	0.866025i	−0.500000	−	0.866025i	−1.00000			$\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.19158	−	0.367554i	1.19158	−	0.367554i	0.365341	−	0.930874i	$-0.380952\pi$
$269$	1.19158	−	0.367554i	1.19158	−	0.367554i	0.826239	+	0.563320i	$0.190476\pi$
$270$		0			0
$271$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$271$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$272$	0.297251	−	0.143149i	0.297251	−	0.143149i
$273$		0			0
$274$		0			0
$275$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$276$		0			0
$277$	−0.0546039	−	0.728639i	−0.0546039	−	0.728639i	−0.955573	−	0.294755i	$-0.904762\pi$
$277$	−0.0546039	−	0.728639i	−0.0546039	−	0.728639i	0.900969	−	0.433884i	$-0.142857\pi$
$278$		0			0
$279$	0.222521	−	0.974928i	0.222521	−	0.974928i
$280$	0.997630	−	0.680173i	0.997630	−	0.680173i
$281$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$281$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$282$		0			0
$283$	−0.326239	+	0.302705i	−0.326239	+	0.302705i	−0.826239	−	0.563320i	$-0.809524\pi$
$283$	−0.326239	+	0.302705i	−0.326239	+	0.302705i	0.500000	+	0.866025i	$0.333333\pi$
$284$	−2.82797	−	0.426248i	−2.82797	−	0.426248i
$285$		0			0
$286$	−1.51053	−	1.89415i	−1.51053	−	1.89415i
$287$		0			0
$288$	0.480228	−	0.602187i	0.480228	−	0.602187i
$289$	−0.548760	+	0.0827122i	−0.548760	+	0.0827122i
$290$		0			0
$291$		0			0
$292$	−1.20840	−	0.372741i	−1.20840	−	0.372741i
$293$	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
$295$	−1.46610			−1.46610
$296$		0			0
$297$		0			0
$298$		0			0
$299$		0			0
$300$		0			0
$301$	1.19158	+	1.49419i	1.19158	+	1.49419i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$	1.70255	−	1.16078i	1.70255	−	1.16078i
$307$	0.367711	+	1.61105i	0.367711	+	1.61105i	0.733052	+	0.680173i	$0.238095\pi$
$307$	0.367711	+	1.61105i	0.367711	+	1.61105i	−0.365341	+	0.930874i	$0.619048\pi$
$308$	−0.129334	+	1.72584i	−0.129334	+	1.72584i
$309$		0			0
$310$	0.603718	+	1.53825i	0.603718	+	1.53825i
$311$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	−0.222521	−	0.974928i	$-0.571429\pi$
$311$	−0.147791	−	1.97213i	−0.147791	−	1.97213i	0.0747301	−	0.997204i	$-0.476190\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$		0			0
$315$	0.733052	−	0.680173i	0.733052	−	0.680173i
$316$		0			0
$317$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$317$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$318$		0			0
$319$		0			0
$320$	−0.114887	+	1.53306i	−0.114887	+	1.53306i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.865341	+	1.49881i	−0.865341	+	1.49881i
$325$	−0.733052	−	1.26968i	−0.733052	−	1.26968i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.623490	−	0.781831i	$-0.285714\pi$
$331$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.955573	−	0.294755i	$-0.0952381\pi$
$332$	−1.26868	+	1.17716i	−1.26868	+	1.17716i
$333$		0			0
$334$	−2.42270	−	2.24794i	−2.42270	−	2.24794i
$335$		0			0
$336$		0			0
$337$	0.914101	−	1.14625i	0.914101	−	1.14625i	−0.0747301	−	0.997204i	$-0.523810\pi$
$337$	0.914101	−	1.14625i	0.914101	−	1.14625i	0.988831	−	0.149042i	$-0.0476190\pi$
$338$	1.87824	−	0.283099i	1.87824	−	0.283099i
$339$		0			0
$340$	−0.788452	+	2.00894i	−0.788452	+	2.00894i
$341$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$342$		0			0
$343$	−0.623490	+	0.781831i	−0.623490	+	0.781831i
$344$	2.30759			2.30759
$345$		0			0
$346$	0.0902318	−	0.229907i	0.0902318	−	0.229907i
$347$	−0.123490	−	0.0841939i	−0.123490	−	0.0841939i	0.500000	−	0.866025i	$-0.333333\pi$
$347$	−0.123490	−	0.0841939i	−0.123490	−	0.0841939i	−0.623490	+	0.781831i	$0.714286\pi$
$348$		0			0
$349$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$349$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$350$	−0.367711	+	1.61105i	−0.367711	+	1.61105i
$351$		0			0
$352$	−0.564616	−	0.523887i	−0.564616	−	0.523887i
$353$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$353$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$354$		0			0
$355$	1.36534	−	0.930874i	1.36534	−	0.930874i
$356$	−0.736007	−	3.22466i	−0.736007	−	3.22466i
$357$		0			0
$358$	0.607634	−	2.66222i	0.607634	−	2.66222i
$359$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$359$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$360$	−0.0902318	−	1.20406i	−0.0902318	−	1.20406i
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$	0.603718	−	1.04567i	0.603718	−	1.04567i
$363$		0			0
$364$	−2.09646	−	1.42935i	−2.09646	−	1.42935i
$365$	0.658322	−	0.317031i	0.658322	−	0.317031i
$366$		0			0
$367$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$367$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−0.988831	+	1.71271i	−0.988831	+	1.71271i	−0.365341	+	0.930874i	$0.619048\pi$
$373$	−0.988831	+	1.71271i	−0.988831	+	1.71271i	−0.623490	+	0.781831i	$0.714286\pi$
$374$	−1.03030	−	1.78454i	−1.03030	−	1.78454i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.440071	+	1.92808i	0.440071	+	1.92808i	0.365341	+	0.930874i	$0.380952\pi$
$379$	0.440071	+	1.92808i	0.440071	+	1.92808i	0.0747301	+	0.997204i	$0.476190\pi$
$380$		0			0
$381$		0			0
$382$	−1.63402	−	0.246289i	−1.63402	−	0.246289i
$383$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$383$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$384$		0			0
$385$	−0.623490	−	0.781831i	−0.623490	−	0.781831i
$386$	1.28477	−	1.61105i	1.28477	−	1.61105i
$387$	1.88980	−	0.284841i	1.88980	−	0.284841i
$388$		0			0
$389$	−0.722521	+	1.84095i	−0.722521	+	1.84095i	−0.222521	+	0.974928i	$0.571429\pi$
$389$	−0.722521	+	1.84095i	−0.722521	+	1.84095i	−0.500000	+	0.866025i	$0.666667\pi$
$390$		0			0
$391$		0			0
$392$	0.268680	+	1.17716i	0.268680	+	1.17716i
$393$		0			0
$394$	0.236007	+	0.0727985i	0.236007	+	0.0727985i
$395$		0			0
$396$	1.42996	+	0.974928i	1.42996	+	0.974928i
$397$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$397$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$398$	−0.153989	+	0.193096i	−0.153989	+	0.193096i
$399$		0			0
$400$	0.164962	+	0.206856i	0.164962	+	0.206856i
$401$	−1.40097	−	1.29991i	−1.40097	−	1.29991i	−0.900969	−	0.433884i	$-0.857143\pi$
$401$	−1.40097	−	1.29991i	−1.40097	−	1.29991i	−0.500000	−	0.866025i	$-0.666667\pi$
$402$		0			0
$403$	1.07473	−	0.997204i	1.07473	−	0.997204i
$404$		0			0
$405$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$406$		0			0
$407$		0			0
$408$		0			0
$409$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$409$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.535628	−	1.36476i	0.535628	−	1.36476i
$414$		0			0
$415$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$416$	1.07906	−	0.332847i	1.07906	−	0.332847i
$417$		0			0
$418$		0			0
$419$	1.32091	−	0.636119i	1.32091	−	0.636119i	0.365341	−	0.930874i	$-0.380952\pi$
$419$	1.32091	−	0.636119i	1.32091	−	0.636119i	0.955573	+	0.294755i	$0.0952381\pi$
$420$		0			0
$421$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.222521	−	0.974928i	$-0.571429\pi$
$421$	−1.12349	−	0.541044i	−1.12349	−	0.541044i	−0.900969	+	0.433884i	$0.857143\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.455573	−	1.16078i	−0.455573	−	1.16078i
$426$		0			0
$427$		0			0
$428$	−0.693950	−	3.04039i	−0.693950	−	3.04039i
$429$		0			0
$430$	−2.31507	+	2.14807i	−2.31507	+	2.14807i
$431$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$431$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$432$		0			0
$433$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$433$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$434$	−1.65248			−1.65248
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$439$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$440$	−1.20744			−1.20744
$441$	0.365341	+	0.930874i	0.365341	+	0.930874i
$442$	3.02106			3.02106
$443$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$443$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$444$		0			0
$445$	1.57906	+	1.07659i	1.57906	+	1.07659i
$446$		0			0
$447$		0			0
$448$	−1.38511	−	0.667035i	−1.38511	−	0.667035i
$449$	−0.914101	−	1.14625i	−0.914101	−	1.14625i	−0.988831	−	0.149042i	$-0.952381\pi$
$449$	−0.914101	−	1.14625i	−0.914101	−	1.14625i	0.0747301	−	0.997204i	$-0.476190\pi$
$450$	1.21135	+	1.12397i	1.21135	+	1.12397i
$451$		0			0
$452$		0			0
$453$		0			0
$454$	0.727208	+	3.18610i	0.727208	+	3.18610i
$455$	1.44973	−	0.218511i	1.44973	−	0.218511i
$456$		0			0
$457$	0.365341	+	0.930874i	0.365341	+	0.930874i	0.988831	+	0.149042i	$0.0476190\pi$
$457$	0.365341	+	0.930874i	0.365341	+	0.930874i	−0.623490	+	0.781831i	$0.714286\pi$
$458$	−0.204064	−	2.72305i	−0.204064	−	2.72305i
$459$		0			0
$460$		0			0
$461$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$461$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$462$		0			0
$463$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$463$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$464$		0			0
$465$		0			0
$466$	3.15813	−	0.974153i	3.15813	−	0.974153i
$467$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$467$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$468$	−2.28608	+	1.10092i	−2.28608	+	1.10092i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	−0.885113	−	1.53306i	−0.885113	−	1.53306i
$473$	−0.142820	−	1.90580i	−0.142820	−	1.90580i
$474$		0			0
$475$		0			0
$476$	−1.58202	−	1.46790i	−1.58202	−	1.46790i
$477$		0			0
$478$		0			0
$479$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$479$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	1.07906	−	1.35310i	1.07906	−	1.35310i
$485$		0			0
$486$		0			0
$487$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$487$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$488$		0			0
$489$		0			0
$490$	−1.36534	−	0.930874i	−1.36534	−	0.930874i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$496$	−0.164962	+	0.206856i	−0.164962	+	0.206856i
$497$	0.367711	+	1.61105i	0.367711	+	1.61105i
$498$		0			0
$499$	−1.40097	−	1.29991i	−1.40097	−	1.29991i	−0.900969	−	0.433884i	$-0.857143\pi$
$499$	−1.40097	−	1.29991i	−1.40097	−	1.29991i	−0.500000	−	0.866025i	$-0.666667\pi$
$500$	−1.71135	−	0.257945i	−1.71135	−	0.257945i
$501$		0			0
$502$	2.46026	−	1.67738i	2.46026	−	1.67738i
$503$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	−0.955573	−	0.294755i	$-0.904762\pi$
$503$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	0.733052	−	0.680173i	$-0.238095\pi$
$504$	1.15379	+	0.355898i	1.15379	+	0.355898i
$505$		0			0
$506$		0			0
$507$		0			0
$508$	−1.55929	−	2.70077i	−1.55929	−	2.70077i
$509$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.365341	−	0.930874i	$-0.380952\pi$
$509$	0.988831	−	1.71271i	0.988831	−	1.71271i	0.623490	−	0.781831i	$-0.285714\pi$
$510$		0			0
$511$	0.0546039	+	0.728639i	0.0546039	+	0.728639i
$512$	−0.471429	+	0.227028i	−0.471429	+	0.227028i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.885113	−	1.53306i	0.885113	−	1.53306i
$521$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	−0.900969	−	0.433884i	$-0.857143\pi$
$521$	−0.826239	−	1.43109i	−0.826239	−	1.43109i	0.0747301	−	0.997204i	$-0.476190\pi$
$522$		0			0
$523$	−0.698220	−	1.77904i	−0.698220	−	1.77904i	−0.623490	−	0.781831i	$-0.714286\pi$
$523$	−0.698220	−	1.77904i	−0.698220	−	1.77904i	−0.0747301	−	0.997204i	$-0.523810\pi$
$524$		0			0
$525$		0			0
$526$	0.367711	+	1.61105i	0.367711	+	1.61105i
$527$	1.03030	−	0.702449i	1.03030	−	0.702449i
$528$		0			0
$529$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$530$		0			0
$531$	−0.914101	−	1.14625i	−0.914101	−	1.14625i
$532$		0			0
$533$		0			0
$534$		0			0
$535$	1.48883	+	1.01507i	1.48883	+	1.01507i
$536$		0			0
$537$		0			0
$538$	−2.06061			−2.06061
$539$	0.955573	−	0.294755i	0.955573	−	0.294755i
$540$		0			0
$541$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$541$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$542$		0			0
$543$		0			0
$544$	0.949729	−	0.143149i	0.949729	−	0.143149i
$545$		0			0
$546$		0			0
$547$	−0.455573	−	0.571270i	−0.455573	−	0.571270i	0.500000	−	0.866025i	$-0.333333\pi$
$547$	−0.455573	−	0.571270i	−0.455573	−	0.571270i	−0.955573	+	0.294755i	$0.904762\pi$
$548$		0			0
$549$		0			0
$550$	1.21135	−	1.12397i	1.21135	−	1.12397i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−0.268680	+	1.17716i	−0.268680	+	1.17716i
$555$		0			0
$556$		0			0
$557$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	0.733052	−	0.680173i	$-0.238095\pi$
$557$	−0.222521	−	0.385418i	−0.222521	−	0.385418i	−0.955573	+	0.294755i	$0.904762\pi$
$558$	−0.826239	+	1.43109i	−0.826239	+	1.43109i
$559$	2.52446	+	1.21572i	2.52446	+	1.21572i
$560$	−0.252824	+	0.0779858i	−0.252824	+	0.0779858i
$561$		0			0
$562$		0			0
$563$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i	−0.365341	−	0.930874i	$-0.619048\pi$
$563$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i	0.222521	+	0.974928i	$0.428571\pi$
$564$		0			0
$565$		0			0
$566$	0.662592	−	0.319088i	0.662592	−	0.319088i
$567$	0.988831	+	0.149042i	0.988831	+	0.149042i
$568$	1.79767	+	0.865711i	1.79767	+	0.865711i
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$571$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$572$	0.927001	+	2.36196i	0.927001	+	2.36196i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−1.27023	+	0.866025i	−1.27023	+	0.866025i
$577$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$577$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$578$	0.906813	+	0.136680i	0.906813	+	0.136680i
$579$		0			0
$580$		0			0
$581$	0.900969	+	0.433884i	0.900969	+	0.433884i
$582$		0			0
$583$		0			0
$584$	0.728950	+	0.496990i	0.728950	+	0.496990i
$585$	0.535628	−	1.36476i	0.535628	−	1.36476i
$586$	−3.12285	−	0.963272i	−3.12285	−	0.963272i
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$		0			0
$589$		0			0
$590$	2.31507	+	0.714104i	2.31507	+	0.714104i
$591$		0			0
$592$		0			0
$593$	1.88980	−	0.284841i	1.88980	−	0.284841i	0.900969	−	0.433884i	$-0.142857\pi$
$593$	1.88980	−	0.284841i	1.88980	−	0.284841i	0.988831	+	0.149042i	$0.0476190\pi$
$594$		0			0
$595$	1.24698			1.24698
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.623490	−	0.781831i	$-0.285714\pi$
$599$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$600$		0			0
$601$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$601$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$602$	−1.15379	−	2.93982i	−1.15379	−	2.93982i
$603$		0			0
$604$		0			0
$605$	0.0747301	+	0.997204i	0.0747301	+	0.997204i
$606$		0			0
$607$	−0.988831	+	1.71271i	−0.988831	+	1.71271i	−0.365341	+	0.930874i	$0.619048\pi$
$607$	−0.988831	+	1.71271i	−0.988831	+	1.71271i	−0.623490	+	0.781831i	$0.714286\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−2.06225	+	0.636119i	−2.06225	+	0.636119i
$613$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i	−0.365341	−	0.930874i	$-0.619048\pi$
$613$	−0.142820	+	0.0440542i	−0.142820	+	0.0440542i	0.222521	+	0.974928i	$0.428571\pi$
$614$	0.204064	−	2.72305i	0.204064	−	2.72305i
$615$		0			0
$616$	0.441126	−	1.12397i	0.441126	−	1.12397i
$617$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$617$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$618$		0			0
$619$	0.222521	+	0.385418i	0.222521	+	0.385418i	0.955573	−	0.294755i	$-0.0952381\pi$
$619$	0.222521	+	0.385418i	0.222521	+	0.385418i	−0.733052	+	0.680173i	$0.761905\pi$
$620$	−0.129334	−	1.72584i	−0.129334	−	1.72584i
$621$		0			0
$622$	−0.727208	+	3.18610i	−0.727208	+	3.18610i
$623$	−1.57906	+	1.07659i	−1.57906	+	1.07659i
$624$		0			0
$625$	0.826239	−	0.563320i	0.826239	−	0.563320i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$	−1.48883	+	0.716983i	−1.48883	+	0.716983i
$631$	0.0931869	−	0.116853i	0.0931869	−	0.116853i	−0.733052	−	0.680173i	$-0.761905\pi$
$631$	0.0931869	−	0.116853i	0.0931869	−	0.116853i	0.826239	+	0.563320i	$0.190476\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.72188	+	0.531130i	1.72188	+	0.531130i
$636$		0			0
$637$	−0.326239	+	1.42935i	−0.326239	+	1.42935i
$638$		0			0
$639$	1.57906	+	0.487076i	1.57906	+	0.487076i
$640$	0.646736	−	1.64786i	0.646736	−	1.64786i
$641$	−1.48883	−	1.01507i	−1.48883	−	1.01507i	−0.988831	−	0.149042i	$-0.952381\pi$
$641$	−1.48883	−	1.01507i	−1.48883	−	1.01507i	−0.500000	−	0.866025i	$-0.666667\pi$
$642$		0			0
$643$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$643$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$647$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$648$	0.885113	−	0.821265i	0.885113	−	0.821265i
$649$	−1.21135	+	0.825886i	−1.21135	+	0.825886i
$650$	0.539102	+	2.36196i	0.539102	+	2.36196i
$651$		0			0
$652$		0			0
$653$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$653$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	0.658322	+	0.317031i	0.658322	+	0.317031i
$658$		0			0
$659$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$659$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$660$		0			0
$661$	−1.72188	+	0.531130i	−1.72188	+	0.531130i	−0.988831	−	0.149042i	$-0.952381\pi$
$661$	−1.72188	+	0.531130i	−1.72188	+	0.531130i	−0.733052	+	0.680173i	$0.761905\pi$
$662$	−3.01782	+	0.930874i	−3.01782	+	0.930874i
$663$		0			0
$664$	1.08786	−	0.523887i	1.08786	−	0.523887i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	1.73068	+	2.99763i	1.73068	+	2.99763i
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	−0.955573	−	0.294755i	$-0.904762\pi$
$673$	−0.222521	−	0.974928i	−0.222521	−	0.974928i	0.733052	−	0.680173i	$-0.238095\pi$
$674$	−2.00173	+	1.36476i	−2.00173	+	1.36476i
$675$		0			0
$676$	−1.96713	−	0.296497i	−1.96713	−	0.296497i
$677$	−0.326239	−	0.302705i	−0.326239	−	0.302705i	0.500000	−	0.866025i	$-0.333333\pi$
$677$	−0.326239	−	0.302705i	−0.326239	−	0.302705i	−0.826239	+	0.563320i	$0.809524\pi$
$678$		0			0
$679$		0			0
$680$	0.938756	−	1.17716i	0.938756	−	1.17716i
$681$		0			0
$682$	1.36534	+	0.930874i	1.36534	+	0.930874i
$683$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$683$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$684$		0			0
$685$		0			0
$686$	1.36534	−	0.930874i	1.36534	−	0.930874i
$687$		0			0
$688$	−0.483183	−	0.149042i	−0.483183	−	0.149042i
$689$		0			0
$690$		0			0
$691$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.733052	−	0.680173i	$-0.761905\pi$
$691$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.500000	+	0.866025i	$0.666667\pi$
$692$	−0.161277	+	0.202235i	−0.161277	+	0.202235i
$693$	0.222521	−	0.974928i	0.222521	−	0.974928i
$694$	0.153989	+	0.193096i	0.153989	+	0.193096i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.865341	−	1.49881i	0.865341	−	1.49881i
$701$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$701$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$702$		0			0
$703$		0			0
$704$	0.768680	+	1.33139i	0.768680	+	1.33139i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	0.826239	+	0.563320i	$0.190476\pi$
$709$	−0.0747301	+	0.997204i	−0.0747301	+	0.997204i	−0.900969	+	0.433884i	$0.857143\pi$
$710$	−2.60937	+	0.804883i	−2.60937	+	0.804883i
$711$		0			0
$712$	−0.172446	+	2.30113i	−0.172446	+	2.30113i
$713$		0			0
$714$		0			0
$715$	−1.32091	−	0.636119i	−1.32091	−	0.636119i
$716$	−1.42996	+	2.47676i	−1.42996	+	2.47676i
$717$		0			0
$718$		0			0
$719$	0.455573	+	1.16078i	0.455573	+	1.16078i	0.955573	+	0.294755i	$0.0952381\pi$
$719$	0.455573	+	1.16078i	0.455573	+	1.16078i	−0.500000	+	0.866025i	$0.666667\pi$
$720$	−0.0588742	+	0.257945i	−0.0588742	+	0.257945i
$721$		0			0
$722$	0.367711	+	1.61105i	0.367711	+	1.61105i
$723$		0			0
$724$	−0.927001	+	0.860132i	−0.927001	+	0.860132i
$725$		0			0
$726$		0			0
$727$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$727$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$728$	1.10372	+	1.38402i	1.10372	+	1.38402i
$729$	0.623490	−	0.781831i	0.623490	−	0.781831i
$730$	−1.19395	+	0.179959i	−1.19395	+	0.179959i
$731$	1.96906	+	1.34248i	1.96906	+	1.34248i
$732$		0			0
$733$	1.72188	+	0.531130i	1.72188	+	0.531130i	0.988831	−	0.149042i	$-0.0476190\pi$
$733$	1.72188	+	0.531130i	1.72188	+	0.531130i	0.733052	+	0.680173i	$0.238095\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$739$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	0.914101	+	1.14625i	0.914101	+	1.14625i	0.988831	+	0.149042i	$0.0476190\pi$
$743$	0.914101	+	1.14625i	0.914101	+	1.14625i	−0.0747301	+	0.997204i	$0.523810\pi$
$744$		0			0
$745$		0			0
$746$	2.39564	−	2.22283i	2.39564	−	2.22283i
$747$	0.826239	−	0.563320i	0.826239	−	0.563320i
$748$	0.480228	+	2.10402i	0.480228	+	2.10402i
$749$	−1.48883	+	1.01507i	−1.48883	+	1.01507i
$750$		0			0
$751$	0.266948	+	0.680173i	0.266948	+	0.680173i	1.00000			$0$
$751$	0.266948	+	0.680173i	0.266948	+	0.680173i	−0.733052	+	0.680173i	$0.761905\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$757$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$758$	0.244221	−	3.25890i	0.244221	−	3.25890i
$759$		0			0
$760$		0			0
$761$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$761$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$762$		0			0
$763$		0			0
$764$	1.55929	+	0.750915i	1.55929	+	0.750915i
$765$	0.623490	−	1.07992i	0.623490	−	1.07992i
$766$		0			0
$767$	−0.160629	−	2.14345i	−0.160629	−	2.14345i
$768$		0			0
$769$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$769$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$770$	0.603718	+	1.53825i	0.603718	+	1.53825i
$771$		0			0
$772$	−1.78313	+	1.21572i	−1.78313	+	1.21572i
$773$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$773$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$774$	−3.12285	−	0.470694i	−3.12285	−	0.470694i
$775$	0.733052	+	0.680173i	0.733052	+	0.680173i
$776$		0			0
$777$		0			0
$778$	2.03759	−	2.55506i	2.03759	−	2.55506i
$779$		0			0
$780$		0			0
$781$	0.603718	−	1.53825i	0.603718	−	1.53825i
$782$		0			0
$783$		0			0
$784$	0.0197720	−	0.263838i	0.0197720	−	0.263838i
$785$		0			0
$786$		0			0
$787$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	−0.955573	−	0.294755i	$-0.904762\pi$
$787$	−0.0546039	+	0.139129i	−0.0546039	+	0.139129i	0.900969	+	0.433884i	$0.142857\pi$
$788$	−0.213722	−	0.145713i	−0.213722	−	0.145713i
$789$		0			0
$790$		0			0
$791$		0			0
$792$	−0.752824	−	0.944011i	−0.752824	−	0.944011i
$793$		0			0
$794$		0			0
$795$		0			0
$796$	0.213722	−	0.145713i	0.213722	−	0.145713i
$797$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$797$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$798$		0			0
$799$		0			0
$800$	0.281395	+	0.716983i	0.281395	+	0.716983i
$801$	0.142820	+	1.90580i	0.142820	+	1.90580i
$802$	1.57906	+	2.73502i	1.57906	+	2.73502i
$803$	0.365341	−	0.632789i	0.365341	−	0.632789i
$804$		0			0
$805$		0			0
$806$	−2.18278	+	1.05117i	−2.18278	+	1.05117i
$807$		0			0
$808$		0			0
$809$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$809$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$810$	−0.123490	+	1.64786i	−0.123490	+	1.64786i
$811$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$811$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$	1.07473	+	0.997204i	1.07473	+	0.997204i
$820$		0			0
$821$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$821$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$822$		0			0
$823$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$823$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$824$		0			0
$825$		0			0
$826$	−1.51053	+	1.89415i	−1.51053	+	1.89415i
$827$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	0.222521	+	0.974928i	$0.428571\pi$
$827$	−0.777479	+	0.974928i	−0.777479	+	0.974928i	−1.00000			$\pi$
$828$		0			0
$829$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.222521	−	0.974928i	$-0.571429\pi$
$829$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.988831	+	0.149042i	$0.952381\pi$
$830$	−0.603718	+	1.53825i	−0.603718	+	1.53825i
$831$		0			0
$832$	−2.25393			−2.25393
$833$	−0.455573	+	1.16078i	−0.455573	+	1.16078i
$834$		0			0
$835$	−1.91115	−	0.589510i	−1.91115	−	0.589510i
$836$		0			0
$837$		0			0
$838$	−2.39564	+	0.361085i	−2.39564	+	0.361085i
$839$	0.777479	−	0.974928i	0.777479	−	0.974928i	−0.222521	−	0.974928i	$-0.571429\pi$
$839$	0.777479	−	0.974928i	0.777479	−	0.974928i	1.00000			$0$
$840$		0			0
$841$	0.623490	+	0.781831i	0.623490	+	0.781831i
$842$	1.51053	+	1.40157i	1.51053	+	1.40157i
$843$		0			0
$844$		0			0
$845$	0.949729	−	0.647514i	0.949729	−	0.647514i
$846$		0			0
$847$	−0.955573	−	0.294755i	−0.955573	−	0.294755i
$848$		0			0
$849$		0			0
$850$	0.153989	+	2.05484i	0.153989	+	2.05484i
$851$		0			0
$852$		0			0
$853$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−0.623490	−	0.781831i	$-0.714286\pi$
$853$	−1.62349	−	0.781831i	−1.62349	−	0.781831i	−1.00000			$\pi$
$854$		0			0
$855$		0			0
$856$	−0.162592	+	2.16964i	−0.162592	+	2.16964i
$857$	−1.57906	+	0.487076i	−1.57906	+	0.487076i	−0.955573	−	0.294755i	$-0.904762\pi$
$857$	−1.57906	+	0.487076i	−1.57906	+	0.487076i	−0.623490	+	0.781831i	$0.714286\pi$
$858$		0			0
$859$	0.0931869	−	1.24349i	0.0931869	−	1.24349i	−0.733052	−	0.680173i	$-0.761905\pi$
$859$	0.0931869	−	1.24349i	0.0931869	−	1.24349i	0.826239	−	0.563320i	$-0.190476\pi$
$860$	2.98003	−	1.43511i	2.98003	−	1.43511i
$861$		0			0
$862$		0			0
$863$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$863$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$864$		0			0
$865$	−0.0111692	−	0.149042i	−0.0111692	−	0.149042i
$866$		0			0
$867$		0			0
$868$	1.65379	+	0.510127i	1.65379	+	0.510127i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$		0			0
$874$		0			0
$875$	0.222521	+	0.974928i	0.222521	+	0.974928i
$876$		0			0
$877$	−0.988831	+	0.149042i	−0.988831	+	0.149042i	−0.623490	−	0.781831i	$-0.714286\pi$
$877$	−0.988831	+	0.149042i	−0.988831	+	0.149042i	−0.365341	+	0.930874i	$0.619048\pi$
$878$		0			0
$879$		0			0
$880$	0.252824	+	0.0779858i	0.252824	+	0.0779858i
$881$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$881$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$882$	−0.123490	−	1.64786i	−0.123490	−	1.64786i
$883$		0			0		1.00000			$0$
$883$		0			0		−1.00000			$\pi$
$884$	−3.02347	−	0.932616i	−3.02347	−	0.932616i
$885$		0			0
$886$		0			0
$887$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.222521	−	0.974928i	$-0.428571\pi$
$887$	0.722521	−	0.108903i	0.722521	−	0.108903i	0.500000	+	0.866025i	$0.333333\pi$
$888$		0			0
$889$	−1.12349	+	1.40881i	−1.12349	+	1.40881i
$890$	−1.96906	−	2.46912i	−1.96906	−	2.46912i
$891$	−0.733052	−	0.680173i	−0.733052	−	0.680173i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−0.367711	−	1.61105i	−0.367711	−	1.61105i
$896$	1.29767	+	1.20406i	1.29767	+	1.20406i
$897$		0			0
$898$	0.885113	+	2.25523i	0.885113	+	2.25523i
$899$		0			0
$900$	−0.865341	−	1.49881i	−0.865341	−	1.49881i
$901$		0			0
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.0546039	−	0.728639i	0.0546039	−	0.728639i
$906$		0			0
$907$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$907$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$908$	0.255779	−	3.41313i	0.255779	−	3.41313i
$909$		0			0
$910$	−2.39564	−	0.361085i	−2.39564	−	0.361085i
$911$	−0.134659	−	0.0648483i	−0.134659	−	0.0648483i	0.365341	−	0.930874i	$-0.380952\pi$
$911$	−0.134659	−	0.0648483i	−0.134659	−	0.0648483i	−0.500000	+	0.866025i	$0.666667\pi$
$912$		0			0
$913$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$914$	−0.123490	−	1.64786i	−0.123490	−	1.64786i
$915$		0			0
$916$	−0.636391	+	2.78821i	−0.636391	+	2.78821i
$917$		0			0
$918$		0			0
$919$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$919$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.51053	+	1.89415i	1.51053	+	1.89415i
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.72188	−	0.531130i	−1.72188	−	0.531130i	−0.733052	−	0.680173i	$-0.761905\pi$
$929$	−1.72188	−	0.531130i	−1.72188	−	0.531130i	−0.988831	+	0.149042i	$0.952381\pi$
$930$		0			0
$931$		0			0
$932$	−3.46136			−3.46136
$933$		0			0
$934$		0			0
$935$	−1.03030	−	0.702449i	−1.03030	−	0.702449i
$936$	1.75045	−	0.263838i	1.75045	−	0.263838i
$937$	0.914101	−	1.14625i	0.914101	−	1.14625i	−0.0747301	−	0.997204i	$-0.523810\pi$
$937$	0.914101	−	1.14625i	0.914101	−	1.14625i	0.988831	−	0.149042i	$-0.0476190\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$941$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$942$		0			0
$943$		0			0
$944$	0.0863157	+	0.378174i	0.0863157	+	0.378174i
$945$		0			0
$946$	−0.702749	+	3.07894i	−0.702749	+	3.07894i
$947$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$947$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$948$		0			0
$949$	0.535628	+	0.927735i	0.535628	+	0.927735i
$950$		0			0
$951$		0			0
$952$	0.752824	+	1.30393i	0.752824	+	1.30393i
$953$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	−0.623490	−	0.781831i	$-0.714286\pi$
$953$	−0.400969	+	0.193096i	−0.400969	+	0.193096i	0.222521	+	0.974928i	$0.428571\pi$
$954$		0			0
$955$	−0.955573	+	0.294755i	−0.955573	+	0.294755i
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$		0			0
$962$		0			0
$963$	0.134659	+	1.79690i	0.134659	+	1.79690i
$964$		0			0
$965$	0.277479	−	1.21572i	0.277479	−	1.21572i
$966$		0			0
$967$	0.162592	+	0.712362i	0.162592	+	0.712362i	0.988831	+	0.149042i	$0.0476190\pi$
$967$	0.162592	+	0.712362i	0.162592	+	0.712362i	−0.826239	+	0.563320i	$0.809524\pi$
$968$	−0.997630	+	0.680173i	−0.997630	+	0.680173i
$969$		0			0
$970$		0			0
$971$	−0.109562	−	0.101659i	−0.109562	−	0.101659i	0.623490	−	0.781831i	$-0.285714\pi$
$971$	−0.109562	−	0.101659i	−0.109562	−	0.101659i	−0.733052	+	0.680173i	$0.761905\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$977$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$978$		0			0
$979$	1.91115			1.91115
$980$	1.07906	+	1.35310i	1.07906	+	1.35310i
$981$		0			0
$982$		0			0
$983$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$983$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$984$		0			0
$985$	0.147791	−	0.0222759i	0.147791	−	0.0222759i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$	1.63402	+	0.246289i	1.63402	+	0.246289i
$991$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	−0.988831	−	0.149042i	$-0.952381\pi$
$991$	−0.914101	+	0.848162i	−0.914101	+	0.848162i	0.0747301	+	0.997204i	$0.476190\pi$
$992$	−0.636391	+	0.433884i	−0.636391	+	0.433884i
$993$		0			0
$994$	0.204064	−	2.72305i	0.204064	−	2.72305i
$995$	−0.0332580	+	0.145713i	−0.0332580	+	0.145713i
$996$		0			0
$997$	−0.142820	−	1.90580i	−0.142820	−	1.90580i	−0.365341	−	0.930874i	$-0.619048\pi$
$997$	−0.142820	−	1.90580i	−0.142820	−	1.90580i	0.222521	−	0.974928i	$-0.428571\pi$
$998$	1.57906	+	2.73502i	1.57906	+	2.73502i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2695.1.ck.b.1374.1	yes	12
5.4	even	2		2695.1.ck.a.1374.1	✓	12
11.10	odd	2		2695.1.ck.a.1374.1	✓	12
49.25	even	21	inner	2695.1.ck.b.2034.1	yes	12
55.54	odd	2	CM	2695.1.ck.b.1374.1	yes	12
245.74	even	42		2695.1.ck.a.2034.1	yes	12
539.417	odd	42		2695.1.ck.a.2034.1	yes	12
2695.2034	odd	42	inner	2695.1.ck.b.2034.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2695.1.ck.a.1374.1	✓	12	5.4	even	2
2695.1.ck.a.1374.1	✓	12	11.10	odd	2
2695.1.ck.a.2034.1	yes	12	245.74	even	42
2695.1.ck.a.2034.1	yes	12	539.417	odd	42
2695.1.ck.b.1374.1	yes	12	1.1	even	1	trivial
2695.1.ck.b.1374.1	yes	12	55.54	odd	2	CM
2695.1.ck.b.2034.1	yes	12	49.25	even	21	inner
2695.1.ck.b.2034.1	yes	12	2695.2034	odd	42	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:	\( N \)	\(=\)	\( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2695.ck (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.57906 - 0.487076i) q^{2} +(1.42996 + 0.974928i) q^{4} +(-0.988831 + 0.149042i) q^{5} +(0.222521 - 0.974928i) q^{7} +(-0.752824 - 0.944011i) q^{8} +(-0.733052 - 0.680173i) q^{9} +(1.63402 + 0.246289i) q^{10} +(-0.733052 + 0.680173i) q^{11} +(-0.326239 - 1.42935i) q^{13} +(-0.826239 + 1.43109i) q^{14} +(0.0966613 + 0.246289i) q^{16} +(-0.0931869 - 1.24349i) q^{17} +(0.826239 + 1.43109i) q^{18} +(-1.55929 - 0.750915i) q^{20} +(1.48883 - 0.716983i) q^{22} +(0.955573 - 0.294755i) q^{25} +(-0.181049 + 2.41593i) q^{26} +(1.26868 - 1.17716i) q^{28} +(0.500000 + 0.866025i) q^{31} +(0.0575591 + 0.768072i) q^{32} +(-0.458528 + 2.00894i) q^{34} +(-0.0747301 + 0.997204i) q^{35} +(-0.385113 - 1.68729i) q^{36} +(0.885113 + 0.821265i) q^{40} +(-1.19158 + 1.49419i) q^{43} +(-1.71135 + 0.257945i) q^{44} +(0.826239 + 0.563320i) q^{45} +(-0.900969 - 0.433884i) q^{49} -1.65248 q^{50} +(0.927001 - 2.36196i) q^{52} +(0.623490 - 0.781831i) q^{55} +(-1.08786 + 0.523887i) q^{56} +(1.44973 + 0.218511i) q^{59} +(-0.367711 - 1.61105i) q^{62} +(-0.826239 + 0.563320i) q^{63} +(0.342095 - 1.49881i) q^{64} +(0.535628 + 1.36476i) q^{65} +(1.07906 - 1.86899i) q^{68} +(0.603718 - 1.53825i) q^{70} +(-1.48883 + 0.716983i) q^{71} +(-0.0902318 + 1.20406i) q^{72} +(-0.698220 + 0.215372i) q^{73} +(0.500000 + 0.866025i) q^{77} +(-0.132289 - 0.229132i) q^{80} +(0.0747301 + 0.997204i) q^{81} +(-0.222521 + 0.974928i) q^{83} +(0.277479 + 1.21572i) q^{85} +(2.60937 - 1.77904i) q^{86} +(1.19395 + 0.179959i) q^{88} +(-1.40097 - 1.29991i) q^{89} +(-1.03030 - 1.29196i) q^{90} -1.46610 q^{91} +(1.21135 + 1.12397i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} + q^{5} + 2 q^{7} + 2 q^{8} + q^{9} + q^{10} + q^{11} + 5 q^{13} - q^{14} + 13 q^{16} - 2 q^{17} + q^{18} + 5 q^{22} + q^{25} + q^{26} + 6 q^{31} + 7 q^{32} - 3 q^{34} - q^{35} + 6 q^{40}+ \cdots + 12 q^{99}+O(q^{100}) \) 12 * q + q^2 + q^5 + 2 * q^7 + 2 * q^8 + q^9 + q^10 + q^11 + 5 * q^13 - q^14 + 13 * q^16 - 2 * q^17 + q^18 + 5 * q^22 + q^25 + q^26 + 6 * q^31 + 7 * q^32 - 3 * q^34 - q^35 + 6 * q^40 - 2 * q^43 - 7 * q^44 + q^45 - 2 * q^49 - 2 * q^50 - 14 * q^52 - 2 * q^55 - 9 * q^56 - q^59 + 2 * q^62 - q^63 - 9 * q^64 + q^65 - 7 * q^68 - q^70 - 5 * q^71 + 6 * q^72 + q^73 + 6 * q^77 - 8 * q^80 + q^81 - 2 * q^83 + 4 * q^85 + q^86 - q^88 - 8 * q^89 - 2 * q^90 + 2 * q^91 + q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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