LMFDB - Embedded newform 2303.1.q.b.1362.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,1,Mod(46,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([22, 21]))

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

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

chi := DirichletCharacter("2303.46");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2303.q (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:	$1.14934672409$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$4$ over $\Q(\zeta_{42})$
Coefficient field:	$\Q(\zeta_{210})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{48} - x^{47} + x^{46} + x^{43} - x^{42} + 2 x^{41} - x^{40} + x^{39} + x^{36} - x^{35} + x^{34} + \cdots + 1 $ x^48 - x^47 + x^46 + x^43 - x^42 + 2x^41 - x^40 + x^39 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 - x^28 - x^26 - x^24 - x^22 - x^20 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 + x^9 - x^8 + 2x^7 - x^6 + x^5 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{105}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{105} - \cdots)$

Embedding invariants

Embedding label			1362.3
Root			$0.646600 - 0.762830i$ of defining polynomial
Character	$\chi$	$=$	2303.1362
Dual form			2303.1.q.b.93.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.206722 + 0.0311583i) q^{2} +(1.41857 - 0.967163i) q^{3} +(-0.913810 - 0.281873i) q^{4} +(0.323384 - 0.155734i) q^{6} +(0.712376 - 0.701798i) q^{7} +(-0.368476 - 0.177448i) q^{8} +(0.711588 - 1.81310i) q^{9} +O(q^{10})$	\(q+(0.206722 + 0.0311583i) q^{2} +(1.41857 - 0.967163i) q^{3} +(-0.913810 - 0.281873i) q^{4} +(0.323384 - 0.155734i) q^{6} +(0.712376 - 0.701798i) q^{7} +(-0.368476 - 0.177448i) q^{8} +(0.711588 - 1.81310i) q^{9} +(-1.56892 + 0.483947i) q^{12} +(0.169131 - 0.122881i) q^{14} +(0.719485 + 0.490537i) q^{16} +(0.411136 + 0.381478i) q^{17} +(0.203594 - 0.352635i) q^{18} +(0.331801 - 1.68453i) q^{21} +(-0.694329 + 0.104653i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(-0.362079 - 1.58637i) q^{27} +(-0.848794 + 0.440510i) q^{28} +(0.433250 + 0.401998i) q^{32} +(0.0731045 + 0.0916702i) q^{34} +(-1.16132 + 1.45625i) q^{36} +(-0.313080 + 0.0965724i) q^{37} +(0.121078 - 0.337891i) q^{42} +(-0.988831 - 0.149042i) q^{47} +1.49507 q^{48} +(0.0149594 - 0.999888i) q^{49} -0.209057 q^{50} +(0.952175 + 0.143517i) q^{51} +(0.369340 + 0.113926i) q^{53} +(-0.0254210 - 0.339220i) q^{54} +(-0.387026 + 0.132185i) q^{56} +(0.0785688 - 1.04843i) q^{59} +(-1.61056 + 0.496793i) q^{61} +(-0.765510 - 1.79100i) q^{63} +(-0.465895 - 0.584214i) q^{64} +(-0.268171 - 0.464486i) q^{68} +(0.388703 + 1.70302i) q^{71} +(-0.583934 + 0.541812i) q^{72} +(-0.0677295 + 0.0102086i) q^{74} +(-1.25857 + 1.16779i) q^{75} +(-0.134233 - 0.232499i) q^{79} +(-0.620120 - 0.575388i) q^{81} +(1.19158 + 1.49419i) q^{83} +(-0.778026 + 1.44582i) q^{84} +(-0.591134 + 1.50619i) q^{89} +(-0.199769 - 0.0616206i) q^{94} +(1.00339 + 0.151237i) q^{96} +1.82709 q^{97} +(0.0342473 - 0.206233i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9	$ 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 40 q^{12} - 18 q^{14} + 6 q^{16} + q^{17} - 9 q^{18} + 5 q^{21} + 8 q^{24} + 4 q^{25} - 6 q^{27} - 5 q^{32} + 2 q^{34} - 10 q^{36} + q^{37} + 7 q^{42} + 4 q^{47} + 6 q^{48} - q^{49} + 12 q^{50} + 4 q^{51} + 8 q^{53} - q^{54} - 11 q^{56} - 13 q^{59} + q^{61} - 4 q^{63} - 8 q^{64} - 5 q^{68} + 5 q^{71} - 8 q^{72} + 13 q^{74} + 5 q^{75} - 2 q^{79} + 8 q^{83} + 5 q^{84} - 2 q^{89} + q^{94} + 10 q^{96} + 12 q^{97} + q^{98}+O(q^{100}) $ 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - 40 * q^12 - 18 * q^14 + 6 * q^16 + q^17 - 9 * q^18 + 5 * q^21 + 8 * q^24 + 4 * q^25 - 6 * q^27 - 5 * q^32 + 2 * q^34 - 10 * q^36 + q^37 + 7 * q^42 + 4 * q^47 + 6 * q^48 - q^49 + 12 * q^50 + 4 * q^51 + 8 * q^53 - q^54 - 11 * q^56 - 13 * q^59 + q^61 - 4 * q^63 - 8 * q^64 - 5 * q^68 + 5 * q^71 - 8 * q^72 + 13 * q^74 + 5 * q^75 - 2 * q^79 + 8 * q^83 + 5 * q^84 - 2 * q^89 + q^94 + 10 * q^96 + 12 * q^97 + q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2303\mathbb{Z}\right)^\times$.

$n$	$99$	$2257$
$\chi(n)$	$-1$	$e\left(\frac{17}{21}\right)$

Coefficient data

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

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

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

$2$	0.206722	+	0.0311583i	0.206722	+	0.0311583i	0.251587	−	0.967835i	$-0.419048\pi$
$2$	0.206722	+	0.0311583i	0.206722	+	0.0311583i	−0.0448648	+	0.998993i	$0.514286\pi$
$3$	1.41857	−	0.967163i	1.41857	−	0.967163i	0.420357	−	0.907359i	$-0.361905\pi$
$3$	1.41857	−	0.967163i	1.41857	−	0.967163i	0.998210	−	0.0598042i	$-0.0190476\pi$
$4$	−0.913810	−	0.281873i	−0.913810	−	0.281873i
$5$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$5$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$6$	0.323384	−	0.155734i	0.323384	−	0.155734i
$7$	0.712376	−	0.701798i	0.712376	−	0.701798i
$7$	0.712376	−	0.701798i	0.712376	−	0.701798i
$8$	−0.368476	−	0.177448i	−0.368476	−	0.177448i
$9$	0.711588	−	1.81310i	0.711588	−	1.81310i
$10$		0			0
$11$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$11$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$12$	−1.56892	+	0.483947i	−1.56892	+	0.483947i
$13$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$13$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$14$	0.169131	−	0.122881i	0.169131	−	0.122881i
$15$		0			0
$16$	0.719485	+	0.490537i	0.719485	+	0.490537i
$17$	0.411136	+	0.381478i	0.411136	+	0.381478i	0.858449	−	0.512899i	$-0.171429\pi$
$17$	0.411136	+	0.381478i	0.411136	+	0.381478i	−0.447313	+	0.894377i	$0.647619\pi$
$18$	0.203594	−	0.352635i	0.203594	−	0.352635i
$19$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$19$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$20$		0			0
$21$	0.331801	−	1.68453i	0.331801	−	1.68453i
$22$		0			0
$23$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$23$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$24$	−0.694329	+	0.104653i	−0.694329	+	0.104653i
$25$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$26$		0			0
$27$	−0.362079	−	1.58637i	−0.362079	−	1.58637i
$28$	−0.848794	+	0.440510i	−0.848794	+	0.440510i
$29$		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	$0.666667\pi$
$32$	0.433250	+	0.401998i	0.433250	+	0.401998i
$33$		0			0
$34$	0.0731045	+	0.0916702i	0.0731045	+	0.0916702i
$35$		0			0
$36$	−1.16132	+	1.45625i	−1.16132	+	1.45625i
$37$	−0.313080	+	0.0965724i	−0.313080	+	0.0965724i	−0.447313	−	0.894377i	$-0.647619\pi$
$37$	−0.313080	+	0.0965724i	−0.313080	+	0.0965724i	0.134233	+	0.990950i	$0.457143\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$41$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$42$	0.121078	−	0.337891i	0.121078	−	0.337891i
$43$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$43$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$47$	−0.988831	−	0.149042i	−0.988831	−	0.149042i
$48$	1.49507			1.49507
$49$	0.0149594	−	0.999888i	0.0149594	−	0.999888i
$50$	−0.209057			−0.209057
$51$	0.952175	+	0.143517i	0.952175	+	0.143517i
$52$		0			0
$53$	0.369340	+	0.113926i	0.369340	+	0.113926i	0.473869	−	0.880596i	$-0.342857\pi$
$53$	0.369340	+	0.113926i	0.369340	+	0.113926i	−0.104528	+	0.994522i	$0.533333\pi$
$54$	−0.0254210	−	0.339220i	−0.0254210	−	0.339220i
$55$		0			0
$56$	−0.387026	+	0.132185i	−0.387026	+	0.132185i
$57$		0			0
$58$		0			0
$59$	0.0785688	−	1.04843i	0.0785688	−	1.04843i	−0.809017	−	0.587785i	$-0.800000\pi$
$59$	0.0785688	−	1.04843i	0.0785688	−	1.04843i	0.887586	−	0.460642i	$-0.152381\pi$
$60$		0			0
$61$	−1.61056	+	0.496793i	−1.61056	+	0.496793i	−0.963963	−	0.266037i	$-0.914286\pi$
$61$	−1.61056	+	0.496793i	−1.61056	+	0.496793i	−0.646600	+	0.762830i	$0.723810\pi$
$62$		0			0
$63$	−0.765510	−	1.79100i	−0.765510	−	1.79100i
$64$	−0.465895	−	0.584214i	−0.465895	−	0.584214i
$65$		0			0
$66$		0			0
$67$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$67$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$68$	−0.268171	−	0.464486i	−0.268171	−	0.464486i
$69$		0			0
$70$		0			0
$71$	0.388703	+	1.70302i	0.388703	+	1.70302i	0.669131	+	0.743145i	$0.266667\pi$
$71$	0.388703	+	1.70302i	0.388703	+	1.70302i	−0.280427	+	0.959875i	$0.590476\pi$
$72$	−0.583934	+	0.541812i	−0.583934	+	0.541812i
$73$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$73$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$74$	−0.0677295	+	0.0102086i	−0.0677295	+	0.0102086i
$75$	−1.25857	+	1.16779i	−1.25857	+	1.16779i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−0.134233	−	0.232499i	−0.134233	−	0.232499i	0.791071	−	0.611724i	$-0.209524\pi$
$79$	−0.134233	−	0.232499i	−0.134233	−	0.232499i	−0.925304	+	0.379225i	$0.876190\pi$
$80$		0			0
$81$	−0.620120	−	0.575388i	−0.620120	−	0.575388i
$82$		0			0
$83$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.826239	+	0.563320i	$0.190476\pi$
$83$	1.19158	+	1.49419i	1.19158	+	1.49419i	0.365341	+	0.930874i	$0.380952\pi$
$84$	−0.778026	+	1.44582i	−0.778026	+	1.44582i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.591134	+	1.50619i	−0.591134	+	1.50619i	0.251587	+	0.967835i	$0.419048\pi$
$89$	−0.591134	+	1.50619i	−0.591134	+	1.50619i	−0.842721	+	0.538351i	$0.819048\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−0.199769	−	0.0616206i	−0.199769	−	0.0616206i
$95$		0			0
$96$	1.00339	+	0.151237i	1.00339	+	0.151237i
$97$	1.82709			1.82709			0.913545	−	0.406737i	$-0.133333\pi$
$97$	1.82709			1.82709			0.913545	+	0.406737i	$0.133333\pi$
$98$	0.0342473	−	0.206233i	0.0342473	−	0.206233i
$99$		0			0
$100$	0.945614	+	0.142528i	0.945614	+	0.142528i
$101$	1.60537	−	1.09452i	1.60537	−	1.09452i	0.669131	−	0.743145i	$-0.266667\pi$
$101$	1.60537	−	1.09452i	1.60537	−	1.09452i	0.936235	−	0.351375i	$-0.114286\pi$
$102$	0.192364	+	0.0593363i	0.192364	+	0.0593363i
$103$	−0.115446	−	1.54051i	−0.115446	−	1.54051i	−0.691063	−	0.722795i	$-0.742857\pi$
$103$	−0.115446	−	1.54051i	−0.115446	−	1.54051i	0.575617	−	0.817719i	$-0.304762\pi$
$104$		0			0
$105$		0			0
$106$	0.0728010	+	0.0350591i	0.0728010	+	0.0350591i
$107$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$107$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$108$	−0.116284	+	1.55170i	−0.116284	+	1.55170i
$109$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$109$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$110$		0			0
$111$	−0.350724	+	0.439794i	−0.350724	+	0.439794i
$112$	0.856802	−	0.155487i	0.856802	−	0.155487i
$113$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$113$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.0489091	−	0.214285i	0.0489091	−	0.214285i
$119$	0.560604	−	0.0167782i	0.560604	−	0.0167782i
$120$		0			0
$121$	−0.733052	+	0.680173i	−0.733052	+	0.680173i
$122$	−0.348418	+	0.0525155i	−0.348418	+	0.0525155i
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.102443	−	0.394091i	−0.102443	−	0.394091i
$127$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$127$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$128$	−0.373619	−	0.647127i	−0.373619	−	0.647127i
$129$		0			0
$130$		0			0
$131$	1.46672	+	0.999990i	1.46672	+	0.999990i	0.992847	+	0.119394i	$0.0380952\pi$
$131$	1.46672	+	0.999990i	1.46672	+	0.999990i	0.473869	+	0.880596i	$0.342857\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.0838007	−	0.213521i	−0.0838007	−	0.213521i
$137$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$137$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$138$		0			0
$139$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$139$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$140$		0			0
$141$	−1.54687	+	0.744934i	−1.54687	+	0.744934i
$142$	0.0272902	+	0.364163i	0.0272902	+	0.364163i
$143$		0			0
$144$	1.40137	−	0.955437i	1.40137	−	0.955437i
$145$		0			0
$146$		0			0
$147$	−0.945834	−	1.43288i	−0.945834	−	1.43288i
$148$	0.313317			0.313317
$149$	−0.831324	−	0.125302i	−0.831324	−	0.125302i	−0.280427	−	0.959875i	$-0.590476\pi$
$149$	−0.831324	−	0.125302i	−0.831324	−	0.125302i	−0.550897	+	0.834573i	$0.685714\pi$
$150$	−0.296561	+	0.202192i	−0.296561	+	0.202192i
$151$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$151$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$152$		0			0
$153$	0.984216	−	0.473974i	0.984216	−	0.473974i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.144074	+	1.92253i	−0.144074	+	1.92253i	0.193256	+	0.981148i	$0.438095\pi$
$157$	−0.144074	+	1.92253i	−0.144074	+	1.92253i	−0.337330	+	0.941386i	$0.609524\pi$
$158$	−0.0205047	−	0.0522451i	−0.0205047	−	0.0522451i
$159$	0.634119	−	0.195600i	0.634119	−	0.195600i
$160$		0			0
$161$		0			0
$162$	−0.110264	−	0.138267i	−0.110264	−	0.138267i
$163$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$163$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$164$		0			0
$165$		0			0
$166$	0.199769	+	0.346010i	0.199769	+	0.346010i
$167$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$167$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$168$	−0.421178	+	0.561831i	−0.421178	+	0.561831i
$169$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.283333	+	0.262895i	−0.283333	+	0.262895i	−0.809017	−	0.587785i	$-0.800000\pi$
$173$	−0.283333	+	0.262895i	−0.283333	+	0.262895i	0.525684	+	0.850680i	$0.323810\pi$
$174$		0			0
$175$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$176$		0			0
$177$	−0.902545	−	1.56325i	−0.902545	−	1.56325i
$178$	−0.169131	+	0.292943i	−0.169131	+	0.292943i
$179$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$179$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$180$		0			0
$181$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$181$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$182$		0			0
$183$	−1.80421	+	2.26241i	−1.80421	+	2.26241i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	0.861592	+	0.414921i	0.861592	+	0.414921i
$189$	−1.37125	−	0.875987i	−1.37125	−	0.875987i
$190$		0			0
$191$	0.0546039	+	0.728639i	0.0546039	+	0.728639i	0.955573	+	0.294755i	$0.0952381\pi$
$191$	0.0546039	+	0.728639i	0.0546039	+	0.728639i	−0.900969	+	0.433884i	$0.857143\pi$
$192$	−1.22593	−	0.378151i	−1.22593	−	0.378151i
$193$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$193$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$194$	0.377700	+	0.0569291i	0.377700	+	0.0569291i
$195$		0			0
$196$	−0.295511	+	0.909491i	−0.295511	+	0.909491i
$197$	0.149460			0.149460			0.0747301	−	0.997204i	$-0.476190\pi$
$197$	0.149460			0.149460			0.0747301	+	0.997204i	$0.476190\pi$
$198$		0			0
$199$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$199$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$200$	0.390807	+	0.120548i	0.390807	+	0.120548i
$201$		0			0
$202$	0.365968	−	0.176241i	0.365968	−	0.176241i
$203$		0			0
$204$	−0.829653	−	0.399540i	−0.829653	−	0.399540i
$205$		0			0
$206$	0.0241347	−	0.322055i	0.0241347	−	0.322055i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$211$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$212$	−0.305394	−	0.208214i	−0.305394	−	0.208214i
$213$	2.19850	+	2.03991i	2.19850	+	2.03991i
$214$		0			0
$215$		0			0
$216$	−0.148082	+	0.648790i	−0.148082	+	0.648790i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−0.0862055	+	0.0799870i	−0.0862055	+	0.0799870i
$223$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$223$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$224$	0.590758	−	0.0176807i	0.590758	−	0.0176807i
$225$	−0.433412	+	1.89890i	−0.433412	+	1.89890i
$226$		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			0
$231$		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			0
$235$		0			0
$236$	−0.367320	+	0.935917i	−0.367320	+	0.935917i
$237$	−0.415283	−	0.199990i	−0.415283	−	0.199990i
$238$	0.116412	+	0.0139990i	0.116412	+	0.0139990i
$239$	1.39185	−	0.670278i	1.39185	−	0.670278i	0.420357	−	0.907359i	$-0.361905\pi$
$239$	1.39185	−	0.670278i	1.39185	−	0.670278i	0.971490	+	0.237080i	$0.0761905\pi$
$240$		0			0
$241$	−0.854881	−	0.263696i	−0.854881	−	0.263696i	−0.163818	−	0.986491i	$-0.552381\pi$
$241$	−0.854881	−	0.263696i	−0.854881	−	0.263696i	−0.691063	+	0.722795i	$0.742857\pi$
$242$	−0.172731	+	0.117766i	−0.172731	+	0.117766i
$243$	0.172818	+	0.0260481i	0.172818	+	0.0260481i
$244$	1.61178			1.61178
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	3.13546	+	0.967163i	3.13546	+	0.967163i
$250$		0			0
$251$	−1.42546	+	0.686466i	−1.42546	+	0.686466i	−0.978148	−	0.207912i	$-0.933333\pi$
$251$	−1.42546	+	0.686466i	−1.42546	+	0.686466i	−0.447313	+	0.894377i	$0.647619\pi$
$252$	0.194696	+	1.85241i	0.194696	+	1.85241i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.215925	+	0.550168i	0.215925	+	0.550168i
$257$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$257$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$258$		0			0
$259$	−0.155256	+	0.288515i	−0.155256	+	0.288515i
$260$		0			0
$261$		0			0
$262$	0.272044	+	0.252420i	0.272044	+	0.252420i
$263$	0.0448648	−	0.0777082i	0.0448648	−	0.0777082i	−0.842721	−	0.538351i	$-0.819048\pi$
$263$	0.0448648	−	0.0777082i	0.0448648	−	0.0777082i	0.887586	+	0.460642i	$0.152381\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	0.618163	+	2.70835i	0.618163	+	2.70835i
$268$		0			0
$269$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.900969	−	0.433884i	$-0.857143\pi$
$269$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.733052	+	0.680173i	$0.761905\pi$
$270$		0			0
$271$	0.240174	−	0.222849i	0.240174	−	0.222849i	−0.550897	−	0.834573i	$-0.685714\pi$
$271$	0.240174	−	0.222849i	0.240174	−	0.222849i	0.791071	+	0.611724i	$0.209524\pi$
$272$	0.108677	+	0.476145i	0.108677	+	0.476145i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−1.37262	−	1.27360i	−1.37262	−	1.27360i	−0.925304	−	0.379225i	$-0.876190\pi$
$277$	−1.37262	−	1.27360i	−1.37262	−	1.27360i	−0.447313	−	0.894377i	$-0.647619\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$281$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$282$	−0.342983	+	0.105796i	−0.342983	+	0.105796i
$283$	0.183830	+	0.468391i	0.183830	+	0.468391i	0.992847	−	0.119394i	$-0.0380952\pi$
$283$	0.183830	+	0.468391i	0.183830	+	0.468391i	−0.809017	+	0.587785i	$0.800000\pi$
$284$	0.124835	−	1.66580i	0.124835	−	1.66580i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	1.03716	−	0.499468i	1.03716	−	0.499468i
$289$	−0.0512231	−	0.683525i	−0.0512231	−	0.683525i
$290$		0			0
$291$	2.59185	−	1.76709i	2.59185	−	1.76709i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−0.150879	−	0.325678i	−0.150879	−	0.325678i
$295$		0			0
$296$	0.132499	+	0.0199710i	0.132499	+	0.0199710i
$297$		0			0
$298$	−0.167949	−	0.0518053i	−0.167949	−	0.0518053i
$299$		0			0
$300$	1.47927	−	0.712377i	1.47927	−	0.712377i
$301$		0			0
$302$		0			0
$303$	1.21874	−	3.10530i	1.21874	−	3.10530i
$304$		0			0
$305$		0			0
$306$	0.218227	−	0.0673142i	0.218227	−	0.0673142i
$307$	−1.08912	+	1.36572i	−1.08912	+	1.36572i	−0.163818	+	0.986491i	$0.552381\pi$
$307$	−1.08912	+	1.36572i	−1.08912	+	1.36572i	−0.925304	+	0.379225i	$0.876190\pi$
$308$		0			0
$309$	−1.65370	−	2.07367i	−1.65370	−	2.07367i
$310$		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	$0.333333\pi$
$314$	−0.0896862	+	0.392941i	−0.0896862	+	0.392941i
$315$		0			0
$316$	0.0571285	+	0.250296i	0.0571285	+	0.250296i
$317$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$317$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$318$	0.137181	−	0.0206767i	0.137181	−	0.0206767i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	0.404486	+	0.700590i	0.404486	+	0.700590i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.809017	+	0.587785i	−0.809017	+	0.587785i
$330$		0			0
$331$	1.43923	−	0.443943i	1.43923	−	0.443943i	0.525684	−	0.850680i	$-0.323810\pi$
$331$	1.43923	−	0.443943i	1.43923	−	0.443943i	0.913545	+	0.406737i	$0.133333\pi$
$332$	−0.667704	−	1.70128i	−0.667704	−	1.70128i
$333$	−0.0476889	+	0.636364i	−0.0476889	+	0.636364i
$334$		0			0
$335$		0			0
$336$	1.06505	−	1.04923i	1.06505	−	1.04923i
$337$	1.08084	−	0.520506i	1.08084	−	0.520506i	0.193256	−	0.981148i	$-0.438095\pi$
$337$	1.08084	−	0.520506i	1.08084	−	0.520506i	0.887586	+	0.460642i	$0.152381\pi$
$338$	−0.0156228	−	0.208472i	−0.0156228	−	0.208472i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$344$		0			0
$345$		0			0
$346$	−0.0667626	+	0.0455179i	−0.0667626	+	0.0455179i
$347$	1.51185	+	0.466345i	1.51185	+	0.466345i	0.936235	−	0.351375i	$-0.114286\pi$
$347$	1.51185	+	0.466345i	1.51185	+	0.466345i	0.575617	+	0.817719i	$0.304762\pi$
$348$		0			0
$349$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$349$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$350$	−0.148927	+	0.146716i	−0.148927	+	0.146716i
$351$		0			0
$352$		0			0
$353$	−0.0156228	+	0.208472i	−0.0156228	+	0.208472i	0.983930	+	0.178557i	$0.0571429\pi$
$353$	−0.0156228	+	0.208472i	−0.0156228	+	0.208472i	−0.999552	+	0.0299155i	$0.990476\pi$
$354$	−0.137868	−	0.351281i	−0.137868	−	0.351281i
$355$		0			0
$356$	0.964737	−	1.20974i	0.964737	−	1.20974i
$357$	0.779027	−	0.565996i	0.779027	−	0.565996i
$358$		0			0
$359$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$359$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$362$		0			0
$363$	−0.382046	+	1.67385i	−0.382046	+	1.67385i
$364$		0			0
$365$		0			0
$366$	−0.443463	+	0.411474i	−0.443463	+	0.411474i
$367$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$367$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.343062	−	0.178044i	0.343062	−	0.178044i
$372$		0			0
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$		0			0
$376$	0.337913	+	0.230385i	0.337913	+	0.230385i
$377$		0			0
$378$	−0.256173	−	0.223811i	−0.256173	−	0.223811i
$379$	0.655517	−	0.821992i	0.655517	−	0.821992i	−0.337330	−	0.941386i	$-0.609524\pi$
$379$	0.655517	−	0.821992i	0.655517	−	0.821992i	0.992847	+	0.119394i	$0.0380952\pi$
$380$		0			0
$381$		0			0
$382$	−0.0114153	+	0.152327i	−0.0114153	+	0.152327i
$383$	0.0109306	−	0.0278506i	0.0109306	−	0.0278506i	−0.925304	−	0.379225i	$-0.876190\pi$
$383$	0.0109306	−	0.0278506i	0.0109306	−	0.0278506i	0.936235	+	0.351375i	$0.114286\pi$
$384$	−1.15588	−	0.556643i	−1.15588	−	0.556643i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−1.66961	−	0.515008i	−1.66961	−	0.515008i
$389$		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
$392$	−0.182941	+	0.365780i	−0.182941	+	0.365780i
$393$	3.04779			3.04779
$394$	0.0308967	+	0.00465693i	0.0308967	+	0.00465693i
$395$		0			0
$396$		0			0
$397$	0.00223584	+	0.0298352i	0.00223584	+	0.0298352i	0.998210	−	0.0598042i	$-0.0190476\pi$
$397$	0.00223584	+	0.0298352i	0.00223584	+	0.0298352i	−0.995974	+	0.0896393i	$0.971429\pi$
$398$		0			0
$399$		0			0
$400$	−0.784560	−	0.377824i	−0.784560	−	0.377824i
$401$	0.420593	−	1.07165i	0.420593	−	1.07165i	−0.550897	−	0.834573i	$-0.685714\pi$
$401$	0.420593	−	1.07165i	0.420593	−	1.07165i	0.971490	−	0.237080i	$-0.0761905\pi$
$402$		0			0
$403$		0			0
$404$	−1.77551	+	0.547674i	−1.77551	+	0.547674i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.325386	−	0.221845i	−0.325386	−	0.221845i
$409$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$409$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$410$		0			0
$411$		0			0
$412$	−0.328734	+	1.44028i	−0.328734	+	1.44028i
$413$	−0.679814	−	0.802014i	−0.679814	−	0.802014i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$419$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$420$		0			0
$421$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$421$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$422$		0			0
$423$	−0.973869	+	1.68679i	−0.973869	+	1.68679i
$424$	−0.115877	−	0.107518i	−0.115877	−	0.107518i
$425$	−0.463400	−	0.315941i	−0.463400	−	0.315941i
$426$	0.390918	+	0.490196i	0.390918	+	0.490196i
$427$	−0.798678	+	1.48419i	−0.798678	+	1.48419i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.0896495	+	1.19629i	−0.0896495	+	1.19629i	0.753071	+	0.657939i	$0.228571\pi$
$431$	−0.0896495	+	1.19629i	−0.0896495	+	1.19629i	−0.842721	+	0.538351i	$0.819048\pi$
$432$	0.517663	−	1.31898i	0.517663	−	1.31898i
$433$		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
$437$		0			0
$438$		0			0
$439$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i	0.0747301	−	0.997204i	$-0.476190\pi$
$439$	−0.147791	−	0.0222759i	−0.147791	−	0.0222759i	−0.222521	+	0.974928i	$0.571429\pi$
$440$		0			0
$441$	−1.80225	−	0.738632i	−1.80225	−	0.738632i
$442$		0			0
$443$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$443$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$444$	0.444461	−	0.303028i	0.444461	−	0.303028i
$445$		0			0
$446$		0			0
$447$	−1.30048	+	0.626277i	−1.30048	+	0.626277i
$448$	−0.741893	−	0.0892159i	−0.741893	−	0.0892159i
$449$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$449$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$450$	−0.148762	+	0.379041i	−0.148762	+	0.379041i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.14197	−	0.778579i	−1.14197	−	0.778579i	−0.163818	−	0.986491i	$-0.552381\pi$
$457$	−1.14197	−	0.778579i	−1.14197	−	0.778579i	−0.978148	+	0.207912i	$0.933333\pi$
$458$		0			0
$459$	0.456302	−	0.790339i	0.456302	−	0.790339i
$460$		0			0
$461$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$461$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$462$		0			0
$463$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$463$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$464$		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			0
$469$		0			0
$470$		0			0
$471$	1.65503	+	2.86659i	1.65503	+	2.86659i
$472$	−0.214993	+	0.372378i	−0.214993	+	0.372378i
$473$		0			0
$474$	−0.0796168	−	0.0542818i	−0.0796168	−	0.0542818i
$475$		0			0
$476$	−0.517014	−	0.142687i	−0.517014	−	0.142687i
$477$	0.469378	−	0.588581i	0.469378	−	0.588581i
$478$	0.308610	−	0.0951936i	0.308610	−	0.0951936i
$479$	−0.287176	−	0.731713i	−0.287176	−	0.731713i	−0.999552	−	0.0299155i	$-0.990476\pi$
$479$	−0.287176	−	0.731713i	−0.287176	−	0.731713i	0.712376	−	0.701798i	$-0.247619\pi$
$480$		0			0
$481$		0			0
$482$	−0.168506	−	0.0811483i	−0.168506	−	0.0811483i
$483$		0			0
$484$	0.861592	−	0.414921i	0.861592	−	0.414921i
$485$		0			0
$486$	0.0349136	+	0.0107694i	0.0349136	+	0.0107694i
$487$	−1.63402	+	1.11406i	−1.63402	+	1.11406i	−0.733052	+	0.680173i	$0.761905\pi$
$487$	−1.63402	+	1.11406i	−1.63402	+	1.11406i	−0.900969	+	0.433884i	$0.857143\pi$
$488$	0.681608	+	0.102736i	0.681608	+	0.102736i
$489$		0			0
$490$		0			0
$491$	1.96786			1.96786			0.983930	−	0.178557i	$-0.0571429\pi$
$491$	1.96786			1.96786			0.983930	+	0.178557i	$0.0571429\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.47208	+	0.940400i	1.47208	+	0.940400i
$498$	0.618034	+	0.297630i	0.618034	+	0.297630i
$499$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$499$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$500$		0			0
$501$		0			0
$502$	−0.316063	+	0.0974926i	−0.316063	+	0.0974926i
$503$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$503$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$504$	−0.0357384	+	0.795778i	−0.0357384	+	0.795778i
$505$		0			0
$506$		0			0
$507$	−1.25857	−	1.16779i	−1.25857	−	1.16779i
$508$		0			0
$509$		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
$512$	0.193770	+	0.848963i	0.193770	+	0.848963i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−0.0410845	+	0.0548048i	−0.0410845	+	0.0548048i
$519$	−0.147665	+	0.646963i	−0.147665	+	0.646963i
$520$		0			0
$521$	−0.251587	+	0.435761i	−0.251587	+	0.435761i	−0.963963	−	0.266037i	$-0.914286\pi$
$521$	−0.251587	+	0.435761i	−0.251587	+	0.435761i	0.712376	+	0.701798i	$0.247619\pi$
$522$		0			0
$523$	−1.63402	−	1.11406i	−1.63402	−	1.11406i	−0.900969	−	0.433884i	$-0.857143\pi$
$523$	−1.63402	−	1.11406i	−1.63402	−	1.11406i	−0.733052	−	0.680173i	$-0.761905\pi$
$524$	−1.05843	−	1.32723i	−1.05843	−	1.32723i
$525$	−0.0770283	+	1.71517i	−0.0770283	+	1.71517i
$526$	0.0116958	−	0.0146661i	0.0116958	−	0.0146661i
$527$		0			0
$528$		0			0
$529$	0.0747301	−	0.997204i	0.0747301	−	0.997204i
$530$		0			0
$531$	−1.84499	−	0.888502i	−1.84499	−	0.888502i
$532$		0			0
$533$		0			0
$534$	0.0434002	+	0.579136i	0.0434002	+	0.579136i
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−0.345462			−0.345462
$539$		0			0
$540$		0			0
$541$	−1.40884	−	0.212348i	−1.40884	−	0.212348i	−0.599822	−	0.800134i	$-0.704762\pi$
$541$	−1.40884	−	0.212348i	−1.40884	−	0.212348i	−0.809017	+	0.587785i	$0.800000\pi$
$542$	0.0565928	−	0.0385843i	0.0565928	−	0.0385843i
$543$		0			0
$544$	0.0247714	+	0.330551i	0.0247714	+	0.330551i
$545$		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
$549$	−0.245324	+	3.27362i	−0.245324	+	3.27362i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−0.258792	−	0.0714220i	−0.258792	−	0.0714220i
$554$	−0.244067	−	0.306050i	−0.244067	−	0.306050i
$555$		0			0
$556$		0			0
$557$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$557$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$563$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$564$	1.62352	−	0.244707i	1.62352	−	0.244707i
$565$		0			0
$566$	0.0234074	+	0.102555i	0.0234074	+	0.102555i
$567$	−0.845565	+	0.0253068i	−0.845565	+	0.0253068i
$568$	0.158971	−	0.696496i	0.158971	−	0.696496i
$569$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$569$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$570$		0			0
$571$	−1.46348	−	1.35791i	−1.46348	−	1.35791i	−0.772417	−	0.635116i	$-0.780952\pi$
$571$	−1.46348	−	1.35791i	−1.46348	−	1.35791i	−0.691063	−	0.722795i	$-0.742857\pi$
$572$		0			0
$573$	0.782172	+	0.980812i	0.782172	+	0.980812i
$574$		0			0
$575$		0			0
$576$	−1.39076	+	0.428994i	−1.39076	+	0.428994i
$577$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$577$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$578$	0.0107086	−	0.142896i	0.0107086	−	0.142896i
$579$		0			0
$580$		0			0
$581$	1.89748	+	0.228180i	1.89748	+	0.228180i
$582$	0.590852	−	0.284539i	0.590852	−	0.284539i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	0.460423	+	1.57598i	0.460423	+	1.57598i
$589$		0			0
$590$		0			0
$591$	0.212019	−	0.144552i	0.212019	−	0.144552i
$592$	−0.272629	−	0.0840948i	−0.272629	−	0.0840948i
$593$		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
$596$	0.724353	+	0.348830i	0.724353	+	0.348830i
$597$		0			0
$598$		0			0
$599$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$599$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$600$	0.670976	−	0.206969i	0.670976	−	0.206969i
$601$	0.590905	−	0.740971i	0.590905	−	0.740971i	−0.393025	−	0.919528i	$-0.628571\pi$
$601$	0.590905	−	0.740971i	0.590905	−	0.740971i	0.983930	+	0.178557i	$0.0571429\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	0.348696	−	0.603960i	0.348696	−	0.603960i
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−1.03299	+	0.155698i	−1.03299	+	0.155698i
$613$	−1.96352	+	0.295952i	−1.96352	+	0.295952i	−0.963963	+	0.266037i	$0.914286\pi$
$613$	−1.96352	+	0.295952i	−1.96352	+	0.295952i	−0.999552	+	0.0299155i	$0.990476\pi$
$614$	−0.267699	+	0.248388i	−0.267699	+	0.248388i
$615$		0			0
$616$		0			0
$617$	0.199073	−	0.872196i	0.199073	−	0.872196i	−0.772417	−	0.635116i	$-0.780952\pi$
$617$	0.199073	−	0.872196i	0.199073	−	0.872196i	0.971490	−	0.237080i	$-0.0761905\pi$
$618$	−0.277243	−	0.480199i	−0.277243	−	0.480199i
$619$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	0.365341	+	0.930874i	$0.380952\pi$
$619$	−0.623490	+	1.07992i	−0.623490	+	1.07992i	−0.988831	+	0.149042i	$0.952381\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.635928	+	1.48783i	0.635928	+	1.48783i
$624$		0			0
$625$	0.955573	−	0.294755i	0.955573	−	0.294755i
$626$		0			0
$627$		0			0
$628$	0.673567	−	1.71622i	0.673567	−	1.71622i
$629$	−0.165559	−	0.0797288i	−0.165559	−	0.0797288i
$630$		0			0
$631$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$631$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$632$	0.00820511	+	0.109490i	0.00820511	+	0.109490i
$633$		0			0
$634$		0			0
$635$		0			0
$636$	−0.634599			−0.634599
$637$		0			0
$638$		0			0
$639$	3.36434	+	0.507092i	3.36434	+	0.507092i
$640$		0			0
$641$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$641$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$642$		0			0
$643$	−1.78905	+	0.861560i	−1.78905	+	0.861560i	−0.842721	+	0.538351i	$0.819048\pi$
$643$	−1.78905	+	0.861560i	−1.78905	+	0.861560i	−0.946327	+	0.323210i	$0.895238\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.149393	+	1.99351i	−0.149393	+	1.99351i	−0.0448648	+	0.998993i	$0.514286\pi$
$647$	−0.149393	+	1.99351i	−0.149393	+	1.99351i	−0.104528	+	0.994522i	$0.533333\pi$
$648$	0.126398	+	0.322056i	0.126398	+	0.322056i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.64583	−	1.12210i	−1.64583	−	1.12210i	−0.873408	−	0.486989i	$-0.838095\pi$
$653$	−1.64583	−	1.12210i	−1.64583	−	1.12210i	−0.772417	−	0.635116i	$-0.780952\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	−0.185556	+	0.0963005i	−0.185556	+	0.0963005i
$659$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	−0.550897	−	0.834573i	$-0.685714\pi$
$659$	−0.416664	−	1.82552i	−0.416664	−	1.82552i	0.134233	−	0.990950i	$-0.457143\pi$
$660$		0			0
$661$	−1.97412	+	0.297551i	−1.97412	+	0.297551i	−0.978148	+	0.207912i	$0.933333\pi$
$661$	−1.97412	+	0.297551i	−1.97412	+	0.297551i	−0.995974	+	0.0896393i	$0.971429\pi$
$662$	0.311353	−	0.0469289i	0.311353	−	0.0469289i
$663$		0			0
$664$	−0.173926	−	0.762018i	−0.173926	−	0.762018i
$665$		0			0
$666$	−0.0296864	+	0.130065i	−0.0296864	+	0.130065i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.820930	−	0.596441i	0.820930	−	0.596441i
$673$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$673$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$674$	0.239652	−	0.0739228i	0.239652	−	0.0739228i
$675$	0.594471	+	1.51469i	0.594471	+	1.51469i
$676$	−0.0714640	+	0.953621i	−0.0714640	+	0.953621i
$677$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$677$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$678$		0			0
$679$	1.30158	−	1.28225i	1.30158	−	1.28225i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.33688	+	0.911471i	−1.33688	+	0.911471i	−0.999552	−	0.0299155i	$-0.990476\pi$
$683$	−1.33688	+	0.911471i	−1.33688	+	0.911471i	−0.337330	+	0.941386i	$0.609524\pi$
$684$		0			0
$685$		0			0
$686$	−0.120337	−	0.170950i	−0.120337	−	0.170950i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$691$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$692$	0.333016	−	0.160372i	0.333016	−	0.160372i
$693$		0			0
$694$	0.298002	+	0.143510i	0.298002	+	0.143510i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.773659	−	0.562096i	0.773659	−	0.562096i
$701$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$701$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−0.00972523	+	0.0426090i	−0.00972523	+	0.0426090i
$707$	0.375492	−	1.90635i	0.375492	−	1.90635i
$708$	0.384115	+	1.68292i	0.384115	+	1.68292i
$709$	1.46545	−	1.35974i	1.46545	−	1.35974i	0.712376	−	0.701798i	$-0.247619\pi$
$709$	1.46545	−	1.35974i	1.46545	−	1.35974i	0.753071	−	0.657939i	$-0.228571\pi$
$710$		0			0
$711$	−0.517062	+	0.0779345i	−0.517062	+	0.0779345i
$712$	0.485089	−	0.450097i	0.485089	−	0.450097i
$713$		0			0
$714$	0.178677	−	0.0927307i	0.178677	−	0.0927307i
$715$		0			0
$716$		0			0
$717$	1.32616	−	2.29698i	1.32616	−	2.29698i
$718$		0			0
$719$	−1.59293	−	1.08604i	−1.59293	−	1.08604i	−0.946327	−	0.323210i	$-0.895238\pi$
$719$	−1.59293	−	1.08604i	−1.59293	−	1.08604i	−0.646600	−	0.762830i	$-0.723810\pi$
$720$		0			0
$721$	−1.16337	−	1.01641i	−1.16337	−	1.01641i
$722$	−0.130345	+	0.163447i	−0.130345	+	0.163447i
$723$	−1.46774	+	0.452739i	−1.46774	+	0.452739i
$724$		0			0
$725$		0			0
$726$	−0.131132	+	0.334118i	−0.131132	+	0.334118i
$727$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$727$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$728$		0			0
$729$	1.03252	−	0.497233i	1.03252	−	0.497233i
$730$		0			0
$731$		0			0
$732$	2.28642	−	1.55885i	2.28642	−	1.55885i
$733$	−1.13838	−	0.171583i	−1.13838	−	0.171583i	−0.447313	−	0.894377i	$-0.647619\pi$
$733$	−1.13838	−	0.171583i	−1.13838	−	0.171583i	−0.691063	+	0.722795i	$0.742857\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	1.69631	+	0.523241i	1.69631	+	0.523241i	0.983930	−	0.178557i	$-0.0571429\pi$
$739$	1.69631	+	0.523241i	1.69631	+	0.523241i	0.712376	+	0.701798i	$0.247619\pi$
$740$		0			0
$741$		0			0
$742$	0.0764661	−	0.0261163i	0.0764661	−	0.0261163i
$743$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$743$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	3.55703	−	1.09720i	3.55703	−	1.09720i
$748$		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	$0.190476\pi$
$752$	−0.638338	−	0.592292i	−0.638338	−	0.592292i
$753$	−1.35819	+	2.35245i	−1.35819	+	2.35245i
$754$		0			0
$755$		0			0
$756$	1.00614	+	1.18700i	1.00614	+	1.18700i
$757$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$757$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$758$	0.161122	−	0.149499i	0.161122	−	0.149499i
$759$		0			0
$760$		0			0
$761$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.623490	−	0.781831i	$-0.285714\pi$
$761$	1.44973	−	1.34515i	1.44973	−	1.34515i	0.826239	−	0.563320i	$-0.190476\pi$
$762$		0			0
$763$		0			0
$764$	0.155486	−	0.681229i	0.155486	−	0.681229i
$765$		0			0
$766$	0.00312737	−	0.00541676i	0.00312737	−	0.00541676i
$767$		0			0
$768$	0.838406	+	0.571615i	0.838406	+	0.571615i
$769$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	−0.995974	−	0.0896393i	$-0.971429\pi$
$769$	−0.861741	−	1.08059i	−0.861741	−	1.08059i	0.134233	−	0.990950i	$-0.457143\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.684090	+	1.74303i	0.684090	+	1.74303i	0.669131	+	0.743145i	$0.266667\pi$
$773$	0.684090	+	1.74303i	0.684090	+	1.74303i	0.0149594	+	0.999888i	$0.495238\pi$
$774$		0			0
$775$		0			0
$776$	−0.673238	−	0.324215i	−0.673238	−	0.324215i
$777$	0.0587991	+	0.559436i	0.0587991	+	0.559436i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.501245	−	0.712067i	0.501245	−	0.712067i
$785$		0			0
$786$	0.630045	+	0.0949639i	0.630045	+	0.0949639i
$787$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$787$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$788$	−0.136578	−	0.0421288i	−0.136578	−	0.0421288i
$789$	−0.0115127	−	0.153626i	−0.0115127	−	0.153626i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−0.000467417		0.00623725i	−0.000467417		0.00623725i
$795$		0			0
$796$		0			0
$797$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$797$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$798$		0			0
$799$	−0.349687	−	0.438494i	−0.349687	−	0.438494i
$800$	−0.488326	−	0.332935i	−0.488326	−	0.332935i
$801$	2.31022	+	2.14357i	2.31022	+	2.14357i
$802$	0.120337	−	0.208429i	0.120337	−	0.208429i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−2.07977	+	1.92974i	−2.07977	+	1.92974i
$808$	−0.785759	+	0.118434i	−0.785759	+	0.118434i
$809$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$809$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$810$		0			0
$811$	0.435317	+	1.90725i	0.435317	+	1.90725i	0.420357	+	0.907359i	$0.361905\pi$
$811$	0.435317	+	1.90725i	0.435317	+	1.90725i	0.0149594	+	0.999888i	$0.495238\pi$
$812$		0			0
$813$	0.125172	−	0.548414i	0.125172	−	0.548414i
$814$		0			0
$815$		0			0
$816$	0.614675	+	0.570335i	0.614675	+	0.570335i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$821$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$822$		0			0
$823$	0.0111692	−	0.149042i	0.0111692	−	0.149042i	−0.988831	−	0.149042i	$-0.952381\pi$
$823$	0.0111692	−	0.149042i	0.0111692	−	0.149042i	1.00000			$0$
$824$	−0.230823	+	0.588128i	−0.230823	+	0.588128i
$825$		0			0
$826$	−0.115543	−	0.186976i	−0.115543	−	0.186976i
$827$	1.16513	−	0.561098i	1.16513	−	0.561098i	0.251587	−	0.967835i	$-0.419048\pi$
$827$	1.16513	−	0.561098i	1.16513	−	0.561098i	0.913545	+	0.406737i	$0.133333\pi$
$828$		0			0
$829$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$829$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$830$		0			0
$831$	−3.17893	−	0.479147i	−3.17893	−	0.479147i
$832$		0			0
$833$	0.387586	−	0.405383i	0.387586	−	0.405383i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		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			0
$845$		0			0
$846$	−0.253878	+	0.318352i	−0.253878	+	0.318352i
$847$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$848$	0.209850	+	0.263143i	0.209850	+	0.263143i
$849$	0.713786	+	0.486651i	0.713786	+	0.486651i
$850$	−0.0859508	−	0.0797506i	−0.0859508	−	0.0797506i
$851$		0			0
$852$	−1.43401	−	2.48379i	−1.43401	−	2.48379i
$853$	−0.137526	+	0.602539i	−0.137526	+	0.602539i	0.858449	+	0.512899i	$0.171429\pi$
$853$	−0.137526	+	0.602539i	−0.137526	+	0.602539i	−0.995974	+	0.0896393i	$0.971429\pi$
$854$	−0.211349	+	0.281930i	−0.211349	+	0.281930i
$855$		0			0
$856$		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			0		0.733052	−	0.680173i	$-0.238095\pi$
$859$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$860$		0			0
$861$		0			0
$862$	−0.0558069	+	0.244506i	−0.0558069	+	0.244506i
$863$	−0.858449	−	1.48688i	−0.858449	−	1.48688i	−0.873408	−	0.486989i	$-0.838095\pi$
$863$	−0.858449	−	1.48688i	−0.858449	−	1.48688i	0.0149594	−	0.999888i	$-0.495238\pi$
$864$	0.480847	−	0.832851i	0.480847	−	0.832851i
$865$		0			0
$866$		0			0
$867$	−0.733744	−	0.920086i	−0.733744	−	0.920086i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	1.30014	−	3.31269i	1.30014	−	3.31269i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$877$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$878$	−0.0298575	−	0.00920983i	−0.0298575	−	0.00920983i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−0.349550	−	0.208846i	−0.349550	−	0.208846i
$883$	−0.674660			−0.674660			−0.337330	−	0.941386i	$-0.609524\pi$
$883$	−0.674660			−0.674660			−0.337330	+	0.941386i	$0.609524\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$887$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$888$	0.207274	−	0.0998178i	0.207274	−	0.0998178i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	−0.288351	+	0.0889445i	−0.288351	+	0.0889445i
$895$		0			0
$896$	−0.720310	−	0.198793i	−0.720310	−	0.198793i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.931306	−	1.61307i	0.931306	−	1.61307i
$901$	0.108389	+	0.187734i	0.108389	+	0.187734i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	0.988831	−	0.149042i	0.988831	−	0.149042i	0.365341	−	0.930874i	$-0.380952\pi$
$907$	0.988831	−	0.149042i	0.988831	−	0.149042i	0.623490	+	0.781831i	$0.285714\pi$
$908$		0			0
$909$	−0.842112	−	3.68953i	−0.842112	−	3.68953i
$910$		0			0
$911$	−0.395013	+	1.73066i	−0.395013	+	1.73066i	0.251587	+	0.967835i	$0.419048\pi$
$911$	−0.395013	+	1.73066i	−0.395013	+	1.73066i	−0.646600	+	0.762830i	$0.723810\pi$
$912$		0			0
$913$		0			0
$914$	−0.211810	−	0.196531i	−0.211810	−	0.196531i
$915$		0			0
$916$		0			0
$917$	1.74664	−	0.316969i	1.74664	−	0.316969i
$918$	0.118953	−	0.149163i	0.118953	−	0.149163i
$919$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$919$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$920$		0			0
$921$	−0.224123	+	2.99072i	−0.224123	+	2.99072i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.295190	−	0.142156i	0.295190	−	0.142156i
$926$		0			0
$927$	−2.87525	−	0.886898i	−2.87525	−	0.886898i
$928$		0			0
$929$	1.96970	+	0.296885i	1.96970	+	0.296885i	0.998210	+	0.0598042i	$0.0190476\pi$
$929$	1.96970	+	0.296885i	1.96970	+	0.296885i	0.971490	+	0.237080i	$0.0761905\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		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			0
$941$	0.147058	−	1.96236i	0.147058	−	1.96236i	−0.104528	−	0.994522i	$-0.533333\pi$
$941$	0.147058	−	1.96236i	0.147058	−	1.96236i	0.251587	−	0.967835i	$-0.419048\pi$
$942$	0.252812	+	0.644154i	0.252812	+	0.644154i
$943$		0			0
$944$	0.570821	−	0.715787i	0.570821	−	0.715787i
$945$		0			0
$946$		0			0
$947$	−1.63402	−	1.11406i	−1.63402	−	1.11406i	−0.900969	−	0.433884i	$-0.857143\pi$
$947$	−1.63402	−	1.11406i	−1.63402	−	1.11406i	−0.733052	−	0.680173i	$-0.761905\pi$
$948$	0.323118	+	0.299810i	0.323118	+	0.299810i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	−0.209546	−	0.0932959i	−0.209546	−	0.0932959i
$953$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$953$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$954$	0.115370	−	0.107048i	0.115370	−	0.107048i
$955$		0			0
$956$	−1.46082	+	0.220183i	−1.46082	+	0.220183i
$957$		0			0
$958$	−0.0365667	−	0.160209i	−0.0365667	−	0.160209i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$962$		0			0
$963$		0			0
$964$	0.706869	+	0.481935i	0.706869	+	0.481935i
$965$		0			0
$966$		0			0
$967$	1.22694	−	1.53853i	1.22694	−	1.53853i	0.473869	−	0.880596i	$-0.342857\pi$
$967$	1.22694	−	1.53853i	1.22694	−	1.53853i	0.753071	−	0.657939i	$-0.228571\pi$
$968$	0.390807	−	0.120548i	0.390807	−	0.120548i
$969$		0			0
$970$		0			0
$971$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$971$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$972$	−0.150580	−	0.0725157i	−0.150580	−	0.0725157i
$973$		0			0
$974$	−0.372500	+	0.179387i	−0.372500	+	0.179387i
$975$		0			0
$976$	−1.40247	−	0.432605i	−1.40247	−	0.432605i
$977$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.623490	−	0.781831i	$-0.285714\pi$
$977$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.955573	−	0.294755i	$-0.0952381\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	0.406800	+	0.0613152i	0.406800	+	0.0613152i
$983$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$983$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−0.579161	+	1.61626i	−0.579161	+	1.61626i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	−0.691464	−	1.76182i	−0.691464	−	1.76182i	−0.646600	−	0.762830i	$-0.723810\pi$
$991$	−0.691464	−	1.76182i	−0.691464	−	1.76182i	−0.0448648	−	0.998993i	$-0.514286\pi$
$992$		0			0
$993$	1.61228	−	2.02173i	1.61228	−	2.02173i
$994$	0.275010	+	0.240269i	0.275010	+	0.240269i
$995$		0			0
$996$	−2.59260	−	1.76761i	−2.59260	−	1.76761i
$997$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$997$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$998$		0			0
$999$	0.266559	+	0.461694i	0.266559	+	0.461694i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.1.q.b.1362.3	yes	48
47.46	odd	2	CM	2303.1.q.b.1362.3	yes	48
49.44	even	21	inner	2303.1.q.b.93.3	✓	48
2303.93	odd	42	inner	2303.1.q.b.93.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.1.q.b.93.3	✓	48	49.44	even	21	inner
2303.1.q.b.93.3	✓	48	2303.93	odd	42	inner
2303.1.q.b.1362.3	yes	48	1.1	even	1	trivial
2303.1.q.b.1362.3	yes	48	47.46	odd	2	CM

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2303.q (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.206722 + 0.0311583i) q^{2} +(1.41857 - 0.967163i) q^{3} +(-0.913810 - 0.281873i) q^{4} +(0.323384 - 0.155734i) q^{6} +(0.712376 - 0.701798i) q^{7} +(-0.368476 - 0.177448i) q^{8} +(0.711588 - 1.81310i) q^{9} +O(q^{10})\)	\(q+(0.206722 + 0.0311583i) q^{2} +(1.41857 - 0.967163i) q^{3} +(-0.913810 - 0.281873i) q^{4} +(0.323384 - 0.155734i) q^{6} +(0.712376 - 0.701798i) q^{7} +(-0.368476 - 0.177448i) q^{8} +(0.711588 - 1.81310i) q^{9} +(-1.56892 + 0.483947i) q^{12} +(0.169131 - 0.122881i) q^{14} +(0.719485 + 0.490537i) q^{16} +(0.411136 + 0.381478i) q^{17} +(0.203594 - 0.352635i) q^{18} +(0.331801 - 1.68453i) q^{21} +(-0.694329 + 0.104653i) q^{24} +(-0.988831 + 0.149042i) q^{25} +(-0.362079 - 1.58637i) q^{27} +(-0.848794 + 0.440510i) q^{28} +(0.433250 + 0.401998i) q^{32} +(0.0731045 + 0.0916702i) q^{34} +(-1.16132 + 1.45625i) q^{36} +(-0.313080 + 0.0965724i) q^{37} +(0.121078 - 0.337891i) q^{42} +(-0.988831 - 0.149042i) q^{47} +1.49507 q^{48} +(0.0149594 - 0.999888i) q^{49} -0.209057 q^{50} +(0.952175 + 0.143517i) q^{51} +(0.369340 + 0.113926i) q^{53} +(-0.0254210 - 0.339220i) q^{54} +(-0.387026 + 0.132185i) q^{56} +(0.0785688 - 1.04843i) q^{59} +(-1.61056 + 0.496793i) q^{61} +(-0.765510 - 1.79100i) q^{63} +(-0.465895 - 0.584214i) q^{64} +(-0.268171 - 0.464486i) q^{68} +(0.388703 + 1.70302i) q^{71} +(-0.583934 + 0.541812i) q^{72} +(-0.0677295 + 0.0102086i) q^{74} +(-1.25857 + 1.16779i) q^{75} +(-0.134233 - 0.232499i) q^{79} +(-0.620120 - 0.575388i) q^{81} +(1.19158 + 1.49419i) q^{83} +(-0.778026 + 1.44582i) q^{84} +(-0.591134 + 1.50619i) q^{89} +(-0.199769 - 0.0616206i) q^{94} +(1.00339 + 0.151237i) q^{96} +1.82709 q^{97} +(0.0342473 - 0.206233i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9	\( 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 40 q^{12} - 18 q^{14} + 6 q^{16} + q^{17} - 9 q^{18} + 5 q^{21} + 8 q^{24} + 4 q^{25} - 6 q^{27} - 5 q^{32} + 2 q^{34} - 10 q^{36} + q^{37} + 7 q^{42} + 4 q^{47} + 6 q^{48} - q^{49} + 12 q^{50} + 4 q^{51} + 8 q^{53} - q^{54} - 11 q^{56} - 13 q^{59} + q^{61} - 4 q^{63} - 8 q^{64} - 5 q^{68} + 5 q^{71} - 8 q^{72} + 13 q^{74} + 5 q^{75} - 2 q^{79} + 8 q^{83} + 5 q^{84} - 2 q^{89} + q^{94} + 10 q^{96} + 12 q^{97} + q^{98}+O(q^{100}) \) 48 * q + q^2 - 2 * q^3 + 5 * q^4 - 4 * q^6 - q^7 + 2 * q^8 + 2 * q^9 - 40 * q^12 - 18 * q^14 + 6 * q^16 + q^17 - 9 * q^18 + 5 * q^21 + 8 * q^24 + 4 * q^25 - 6 * q^27 - 5 * q^32 + 2 * q^34 - 10 * q^36 + q^37 + 7 * q^42 + 4 * q^47 + 6 * q^48 - q^49 + 12 * q^50 + 4 * q^51 + 8 * q^53 - q^54 - 11 * q^56 - 13 * q^59 + q^61 - 4 * q^63 - 8 * q^64 - 5 * q^68 + 5 * q^71 - 8 * q^72 + 13 * q^74 + 5 * q^75 - 2 * q^79 + 8 * q^83 + 5 * q^84 - 2 * q^89 + q^94 + 10 * q^96 + 12 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more