LMFDB - Embedded newform 2303.1.q.b.1409.3

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			1409.3
Root			$-0.0149594 + 0.999888i$ of defining polynomial
Character	$\chi$	$=$	2303.1409
Dual form			2303.1.q.b.1033.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.10572 - 0.753869i) q^{2} +(0.0657765 - 0.0610317i) q^{3} +(0.288964 - 0.736268i) q^{4} +(0.0267207 - 0.117071i) q^{6} +(-0.280427 + 0.959875i) q^{7} +(0.0622553 + 0.272758i) q^{8} +(-0.0741284 + 0.989175i) q^{9} +O(q^{10})$	\(q+(1.10572 - 0.753869i) q^{2} +(0.0657765 - 0.0610317i) q^{3} +(0.288964 - 0.736268i) q^{4} +(0.0267207 - 0.117071i) q^{6} +(-0.280427 + 0.959875i) q^{7} +(0.0622553 + 0.272758i) q^{8} +(-0.0741284 + 0.989175i) q^{9} +(-0.0259286 - 0.0660651i) q^{12} +(0.413545 + 1.27276i) q^{14} +(0.854264 + 0.792641i) q^{16} +(-0.382195 - 0.0576066i) q^{17} +(0.663743 + 1.14964i) q^{18} +(0.0401373 + 0.0802522i) q^{21} +(0.0207418 + 0.0141415i) q^{24} +(0.826239 + 0.563320i) q^{25} +(0.111441 + 0.139742i) q^{27} +(0.625692 + 0.483839i) q^{28} +(1.26548 + 0.190740i) q^{32} +(-0.466030 + 0.224428i) q^{34} +(0.706878 + 0.340414i) q^{36} +(-0.730355 - 1.86091i) q^{37} +(0.104880 + 0.0584785i) q^{42} +(0.826239 - 0.563320i) q^{47} +0.104567 q^{48} +(-0.842721 - 0.538351i) q^{49} +1.33826 q^{50} +(-0.0286553 + 0.0195368i) q^{51} +(-0.326844 + 0.832784i) q^{53} +(0.228570 + 0.0705044i) q^{54} +(-0.279272 - 0.0167316i) q^{56} +(1.10009 - 0.339332i) q^{59} +(-0.676103 - 1.72268i) q^{61} +(-0.928697 - 0.348546i) q^{63} +(0.493117 - 0.237472i) q^{64} +(-0.152854 + 0.264752i) q^{68} +(1.10680 + 1.38789i) q^{71} +(-0.274421 + 0.0413622i) q^{72} +(-2.21046 - 1.50706i) q^{74} +(0.0887275 - 0.0133735i) q^{75} +(0.393025 - 0.680739i) q^{79} +(-0.965010 - 0.145452i) q^{81} +(-0.658322 + 0.317031i) q^{83} +(0.0706853 - 0.00636180i) q^{84} +(0.0461857 - 0.616306i) q^{89} +(0.488922 - 1.24575i) q^{94} +(0.0948800 - 0.0646881i) q^{96} -1.95630 q^{97} +(-1.33766 + 0.0400347i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/2303\mathbb{Z}\right)^\times$.

$n$	$99$	$2257$
$\chi(n)$	$-1$	$e\left(\frac{16}{21}\right)$

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 $

$2$	1.10572	−	0.753869i	1.10572	−	0.753869i	0.134233	−	0.990950i	$-0.457143\pi$
$2$	1.10572	−	0.753869i	1.10572	−	0.753869i	0.971490	+	0.237080i	$0.0761905\pi$
$3$	0.0657765	−	0.0610317i	0.0657765	−	0.0610317i	−0.646600	−	0.762830i	$-0.723810\pi$
$3$	0.0657765	−	0.0610317i	0.0657765	−	0.0610317i	0.712376	+	0.701798i	$0.247619\pi$
$4$	0.288964	−	0.736268i	0.288964	−	0.736268i
$5$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$5$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$6$	0.0267207	−	0.117071i	0.0267207	−	0.117071i
$7$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$7$	−0.280427	+	0.959875i	−0.280427	+	0.959875i
$8$	0.0622553	+	0.272758i	0.0622553	+	0.272758i
$9$	−0.0741284	+	0.989175i	−0.0741284	+	0.989175i
$10$		0			0
$11$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$11$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$12$	−0.0259286	−	0.0660651i	−0.0259286	−	0.0660651i
$13$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$13$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$14$	0.413545	+	1.27276i	0.413545	+	1.27276i
$15$		0			0
$16$	0.854264	+	0.792641i	0.854264	+	0.792641i
$17$	−0.382195	−	0.0576066i	−0.382195	−	0.0576066i	−0.0448648	−	0.998993i	$-0.514286\pi$
$17$	−0.382195	−	0.0576066i	−0.382195	−	0.0576066i	−0.337330	+	0.941386i	$0.609524\pi$
$18$	0.663743	+	1.14964i	0.663743	+	1.14964i
$19$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$19$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$20$		0			0
$21$	0.0401373	+	0.0802522i	0.0401373	+	0.0802522i
$22$		0			0
$23$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$23$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$24$	0.0207418	+	0.0141415i	0.0207418	+	0.0141415i
$25$	0.826239	+	0.563320i	0.826239	+	0.563320i
$26$		0			0
$27$	0.111441	+	0.139742i	0.111441	+	0.139742i
$28$	0.625692	+	0.483839i	0.625692	+	0.483839i
$29$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$29$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$30$		0			0
$31$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$31$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$32$	1.26548	+	0.190740i	1.26548	+	0.190740i
$33$		0			0
$34$	−0.466030	+	0.224428i	−0.466030	+	0.224428i
$35$		0			0
$36$	0.706878	+	0.340414i	0.706878	+	0.340414i
$37$	−0.730355	−	1.86091i	−0.730355	−	1.86091i	−0.393025	−	0.919528i	$-0.628571\pi$
$37$	−0.730355	−	1.86091i	−0.730355	−	1.86091i	−0.337330	−	0.941386i	$-0.609524\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$41$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$42$	0.104880	+	0.0584785i	0.104880	+	0.0584785i
$43$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$43$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.826239	−	0.563320i	0.826239	−	0.563320i
$47$	0.826239	−	0.563320i	0.826239	−	0.563320i
$48$	0.104567			0.104567
$49$	−0.842721	−	0.538351i	−0.842721	−	0.538351i
$50$	1.33826			1.33826
$51$	−0.0286553	+	0.0195368i	−0.0286553	+	0.0195368i
$52$		0			0
$53$	−0.326844	+	0.832784i	−0.326844	+	0.832784i	0.669131	+	0.743145i	$0.266667\pi$
$53$	−0.326844	+	0.832784i	−0.326844	+	0.832784i	−0.995974	+	0.0896393i	$0.971429\pi$
$54$	0.228570	+	0.0705044i	0.228570	+	0.0705044i
$55$		0			0
$56$	−0.279272	−	0.0167316i	−0.279272	−	0.0167316i
$57$		0			0
$58$		0			0
$59$	1.10009	−	0.339332i	1.10009	−	0.339332i	0.309017	−	0.951057i	$-0.400000\pi$
$59$	1.10009	−	0.339332i	1.10009	−	0.339332i	0.791071	+	0.611724i	$0.209524\pi$
$60$		0			0
$61$	−0.676103	−	1.72268i	−0.676103	−	1.72268i	−0.691063	−	0.722795i	$-0.742857\pi$
$61$	−0.676103	−	1.72268i	−0.676103	−	1.72268i	0.0149594	−	0.999888i	$-0.495238\pi$
$62$		0			0
$63$	−0.928697	−	0.348546i	−0.928697	−	0.348546i
$64$	0.493117	−	0.237472i	0.493117	−	0.237472i
$65$		0			0
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−0.152854	+	0.264752i	−0.152854	+	0.264752i
$69$		0			0
$70$		0			0
$71$	1.10680	+	1.38789i	1.10680	+	1.38789i	0.913545	+	0.406737i	$0.133333\pi$
$71$	1.10680	+	1.38789i	1.10680	+	1.38789i	0.193256	+	0.981148i	$0.438095\pi$
$72$	−0.274421	+	0.0413622i	−0.274421	+	0.0413622i
$73$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$73$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$74$	−2.21046	−	1.50706i	−2.21046	−	1.50706i
$75$	0.0887275	−	0.0133735i	0.0887275	−	0.0133735i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	0.393025	−	0.680739i	0.393025	−	0.680739i	−0.599822	−	0.800134i	$-0.704762\pi$
$79$	0.393025	−	0.680739i	0.393025	−	0.680739i	0.992847	+	0.119394i	$0.0380952\pi$
$80$		0			0
$81$	−0.965010	−	0.145452i	−0.965010	−	0.145452i
$82$		0			0
$83$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	−0.733052	−	0.680173i	$-0.761905\pi$
$83$	−0.658322	+	0.317031i	−0.658322	+	0.317031i	0.0747301	+	0.997204i	$0.476190\pi$
$84$	0.0706853	−	0.00636180i	0.0706853	−	0.00636180i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	0.0461857	−	0.616306i	0.0461857	−	0.616306i	−0.925304	−	0.379225i	$-0.876190\pi$
$89$	0.0461857	−	0.616306i	0.0461857	−	0.616306i	0.971490	−	0.237080i	$-0.0761905\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$	0.488922	−	1.24575i	0.488922	−	1.24575i
$95$		0			0
$96$	0.0948800	−	0.0646881i	0.0948800	−	0.0646881i
$97$	−1.95630			−1.95630			−0.978148	−	0.207912i	$-0.933333\pi$
$97$	−1.95630			−1.95630			−0.978148	+	0.207912i	$0.933333\pi$
$98$	−1.33766	+	0.0400347i	−1.33766	+	0.0400347i
$99$		0			0
$100$	0.653508	−	0.445554i	0.653508	−	0.445554i
$101$	1.38741	−	1.28733i	1.38741	−	1.28733i	0.473869	−	0.880596i	$-0.342857\pi$
$101$	1.38741	−	1.28733i	1.38741	−	1.28733i	0.913545	−	0.406737i	$-0.133333\pi$
$102$	−0.0169566	+	0.0432047i	−0.0169566	+	0.0432047i
$103$	1.00466	+	0.309896i	1.00466	+	0.309896i	0.753071	−	0.657939i	$-0.228571\pi$
$103$	1.00466	+	0.309896i	1.00466	+	0.309896i	0.251587	+	0.967835i	$0.419048\pi$
$104$		0			0
$105$		0			0
$106$	0.266412	+	1.16723i	0.266412	+	1.16723i
$107$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$107$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$108$	0.135090	−	0.0416697i	0.135090	−	0.0416697i
$109$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$109$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$110$		0			0
$111$	−0.161615	−	0.0778296i	−0.161615	−	0.0778296i
$112$	−1.00040	+	0.597708i	−1.00040	+	0.597708i
$113$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$113$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$		0			0
$118$	0.960581	−	1.20453i	0.960581	−	1.20453i
$119$	0.162473	−	0.350705i	0.162473	−	0.350705i
$120$		0			0
$121$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$122$	−2.04626	−	1.39512i	−2.04626	−	1.39512i
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−1.28964	+	0.314721i	−1.28964	+	0.314721i
$127$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$127$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$128$	−0.273659	+	0.473991i	−0.273659	+	0.473991i
$129$		0			0
$130$		0			0
$131$	−1.15979	−	1.07613i	−1.15979	−	1.07613i	−0.995974	−	0.0896393i	$-0.971429\pi$
$131$	−1.15979	−	1.07613i	−1.15979	−	1.07613i	−0.163818	−	0.986491i	$-0.552381\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.00808098	−	0.107833i	−0.00808098	−	0.107833i
$137$		0			0		0.955573	−	0.294755i	$-0.0952381\pi$
$137$		0			0		−0.955573	+	0.294755i	$0.904762\pi$
$138$		0			0
$139$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$139$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$140$		0			0
$141$	0.0199667	−	0.0874800i	0.0199667	−	0.0874800i
$142$	2.27010	+	0.700233i	2.27010	+	0.700233i
$143$		0			0
$144$	−0.847386	+	0.786259i	−0.847386	+	0.786259i
$145$		0			0
$146$		0			0
$147$	−0.0882877	+	0.0160218i	−0.0882877	+	0.0160218i
$148$	−1.58118			−1.58118
$149$	1.17719	−	0.802591i	1.17719	−	0.802591i	0.193256	−	0.981148i	$-0.438095\pi$
$149$	1.17719	−	0.802591i	1.17719	−	0.802591i	0.983930	+	0.178557i	$0.0571429\pi$
$150$	0.0880261	−	0.0816763i	0.0880261	−	0.0816763i
$151$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$151$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$152$		0			0
$153$	0.0853145	−	0.373787i	0.0853145	−	0.373787i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−1.32072	+	0.407389i	−1.32072	+	0.407389i	−0.873408	−	0.486989i	$-0.838095\pi$
$157$	−1.32072	+	0.407389i	−1.32072	+	0.407389i	−0.447313	+	0.894377i	$0.647619\pi$
$158$	−0.0786116	−	1.04900i	−0.0786116	−	1.04900i
$159$	0.0293276	+	0.0747254i	0.0293276	+	0.0747254i
$160$		0			0
$161$		0			0
$162$	−1.17669	+	0.566662i	−1.17669	+	0.566662i
$163$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$163$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$164$		0			0
$165$		0			0
$166$	−0.488922	+	0.846837i	−0.488922	+	0.846837i
$167$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$167$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$168$	−0.0193907	+	0.0159439i	−0.0193907	+	0.0159439i
$169$	0.623490	+	0.781831i	0.623490	+	0.781831i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.884634	−	0.133337i	0.884634	−	0.133337i	0.309017	−	0.951057i	$-0.400000\pi$
$173$	0.884634	−	0.133337i	0.884634	−	0.133337i	0.575617	+	0.817719i	$0.304762\pi$
$174$		0			0
$175$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$176$		0			0
$177$	0.0516499	−	0.0894603i	0.0516499	−	0.0894603i
$178$	−0.413545	−	0.716282i	−0.413545	−	0.716282i
$179$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$179$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$180$		0			0
$181$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$181$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$182$		0			0
$183$	−0.149610	−	0.0720483i	−0.149610	−	0.0720483i
$184$		0			0
$185$		0			0
$186$		0			0
$187$		0			0
$188$	−0.176001	−	0.771112i	−0.176001	−	0.771112i
$189$	−0.165386	+	0.0677816i	−0.165386	+	0.0677816i
$190$		0			0
$191$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	0.365341	−	0.930874i	$-0.380952\pi$
$191$	0.142820	+	0.0440542i	0.142820	+	0.0440542i	−0.222521	+	0.974928i	$0.571429\pi$
$192$	0.0179421	−	0.0457158i	0.0179421	−	0.0457158i
$193$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$193$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$194$	−2.16312	+	1.47479i	−2.16312	+	1.47479i
$195$		0			0
$196$	−0.639886	+	0.464905i	−0.639886	+	0.464905i
$197$	1.91115			1.91115			0.955573	−	0.294755i	$-0.0952381\pi$
$197$	1.91115			1.91115			0.955573	+	0.294755i	$0.0952381\pi$
$198$		0			0
$199$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$199$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$200$	−0.102212	+	0.260433i	−0.102212	+	0.260433i
$201$		0			0
$202$	0.563616	−	2.46936i	0.563616	−	2.46936i
$203$		0			0
$204$	0.00610401	+	0.0267434i	0.00610401	+	0.0267434i
$205$		0			0
$206$	1.34450	−	0.414722i	1.34450	−	0.414722i
$207$		0			0
$208$		0			0
$209$		0			0
$210$		0			0
$211$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$211$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$212$	0.518706	+	0.481289i	0.518706	+	0.481289i
$213$	0.157506	+	0.0237403i	0.157506	+	0.0237403i
$214$		0			0
$215$		0			0
$216$	−0.0311781	+	0.0390960i	−0.0311781	+	0.0390960i
$217$		0			0
$218$		0			0
$219$		0			0
$220$		0			0
$221$		0			0
$222$	−0.237375	+	0.0357785i	−0.237375	+	0.0357785i
$223$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$223$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$224$	−0.537962	+	1.16121i	−0.537962	+	1.16121i
$225$	−0.618470	+	0.775537i	−0.618470	+	0.775537i
$226$		0			0
$227$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$227$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$228$		0			0
$229$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$229$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$233$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$234$		0			0
$235$		0			0
$236$	0.0680463	−	0.908015i	0.0680463	−	0.908015i
$237$	−0.0156948	−	0.0687636i	−0.0156948	−	0.0687636i
$238$	−0.0847354	−	0.510266i	−0.0847354	−	0.510266i
$239$	−0.233951	+	1.02501i	−0.233951	+	1.02501i	0.712376	+	0.701798i	$0.247619\pi$
$239$	−0.233951	+	1.02501i	−0.233951	+	1.02501i	−0.946327	+	0.323210i	$0.895238\pi$
$240$		0			0
$241$	−0.246481	+	0.628023i	−0.246481	+	0.628023i	−0.999552	−	0.0299155i	$-0.990476\pi$
$241$	−0.246481	+	0.628023i	−0.246481	+	0.628023i	0.753071	+	0.657939i	$0.228571\pi$
$242$	−0.981015	+	0.910249i	−0.981015	+	0.910249i
$243$	−0.220032	+	0.150015i	−0.220032	+	0.150015i
$244$	−1.46373			−1.46373
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$	−0.0239532	+	0.0610317i	−0.0239532	+	0.0610317i
$250$		0			0
$251$	−0.441858	+	1.93591i	−0.441858	+	1.93591i	−0.104528	+	0.994522i	$0.533333\pi$
$251$	−0.441858	+	1.93591i	−0.441858	+	1.93591i	−0.337330	+	0.941386i	$0.609524\pi$
$252$	−0.524983	+	0.583053i	−0.524983	+	0.583053i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.0956375	+	1.27619i	0.0956375	+	1.27619i
$257$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$257$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$258$		0			0
$259$	1.99106	−	0.179198i	1.99106	−	0.179198i
$260$		0			0
$261$		0			0
$262$	−2.09367	−	0.315570i	−2.09367	−	0.315570i
$263$	−0.134233	−	0.232499i	−0.134233	−	0.232499i	0.791071	−	0.611724i	$-0.209524\pi$
$263$	−0.134233	−	0.232499i	−0.134233	−	0.232499i	−0.925304	+	0.379225i	$0.876190\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−0.0345762	−	0.0433572i	−0.0345762	−	0.0433572i
$268$		0			0
$269$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.222521	−	0.974928i	$-0.571429\pi$
$269$	−1.21135	−	0.825886i	−1.21135	−	0.825886i	−0.988831	+	0.149042i	$0.952381\pi$
$270$		0			0
$271$	1.97678	−	0.297951i	1.97678	−	0.297951i	0.983930	−	0.178557i	$-0.0571429\pi$
$271$	1.97678	−	0.297951i	1.97678	−	0.297951i	0.992847	−	0.119394i	$-0.0380952\pi$
$272$	−0.280834	−	0.352154i	−0.280834	−	0.352154i
$273$		0			0
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−0.937152	−	0.141253i	−0.937152	−	0.141253i	−0.337330	−	0.941386i	$-0.609524\pi$
$277$	−0.937152	−	0.141253i	−0.937152	−	0.141253i	−0.599822	+	0.800134i	$0.704762\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$281$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$282$	−0.0438708	−	0.111781i	−0.0438708	−	0.111781i
$283$	0.145199	+	1.93755i	0.145199	+	1.93755i	0.309017	+	0.951057i	$0.400000\pi$
$283$	0.145199	+	1.93755i	0.145199	+	1.93755i	−0.163818	+	0.986491i	$0.552381\pi$
$284$	1.34168	−	0.413854i	1.34168	−	0.413854i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.282483	+	1.23764i	−0.282483	+	1.23764i
$289$	−0.812818	−	0.250721i	−0.812818	−	0.250721i
$290$		0			0
$291$	−0.128678	+	0.119396i	−0.128678	+	0.119396i
$292$		0			0
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$	−0.0855434	+	0.0842731i	−0.0855434	+	0.0842731i
$295$		0			0
$296$	0.462111	−	0.315062i	0.462111	−	0.315062i
$297$		0			0
$298$	0.696592	−	1.77489i	0.696592	−	1.77489i
$299$		0			0
$300$	0.0157925	−	0.0691917i	0.0157925	−	0.0691917i
$301$		0			0
$302$		0			0
$303$	0.0126912	−	0.169352i	0.0126912	−	0.169352i
$304$		0			0
$305$		0			0
$306$	−0.187453	−	0.477621i	−0.187453	−	0.477621i
$307$	−1.59937	−	0.770218i	−1.59937	−	0.770218i	−0.599822	−	0.800134i	$-0.704762\pi$
$307$	−1.59937	−	0.770218i	−1.59937	−	0.770218i	−0.999552	+	0.0299155i	$0.990476\pi$
$308$		0			0
$309$	0.0849964	−	0.0409321i	0.0849964	−	0.0409321i
$310$		0			0
$311$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$311$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$312$		0			0
$313$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$313$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$314$	−1.15323	+	1.44611i	−1.15323	+	1.44611i
$315$		0			0
$316$	−0.387637	−	0.486081i	−0.387637	−	0.486081i
$317$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$317$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$318$	0.0887614	+	0.0605165i	0.0887614	+	0.0605165i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.385945	+	0.668476i	−0.385945	+	0.668476i
$325$		0			0
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.309017	+	0.951057i	0.309017	+	0.951057i
$330$		0			0
$331$	−0.402531	−	1.02563i	−0.402531	−	1.02563i	−0.978148	−	0.207912i	$-0.933333\pi$
$331$	−0.402531	−	1.02563i	−0.402531	−	1.02563i	0.575617	−	0.817719i	$-0.304762\pi$
$332$	0.0431886	+	0.576312i	0.0431886	+	0.576312i
$333$	1.89491	−	0.584502i	1.89491	−	0.584502i
$334$		0			0
$335$		0			0
$336$	−0.0293234	+	0.100371i	−0.0293234	+	0.100371i
$337$	0.343758	−	1.50610i	0.343758	−	1.50610i	−0.447313	−	0.894377i	$-0.647619\pi$
$337$	0.343758	−	1.50610i	0.343758	−	1.50610i	0.791071	−	0.611724i	$-0.209524\pi$
$338$	1.27881	+	0.394459i	1.27881	+	0.394459i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.753071	−	0.657939i	0.753071	−	0.657939i
$344$		0			0
$345$		0			0
$346$	0.877642	−	0.814333i	0.877642	−	0.814333i
$347$	0.725455	−	1.84843i	0.725455	−	1.84843i	0.251587	−	0.967835i	$-0.419048\pi$
$347$	0.725455	−	1.84843i	0.725455	−	1.84843i	0.473869	−	0.880596i	$-0.342857\pi$
$348$		0			0
$349$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$349$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$350$	−0.375285	+	1.28456i	−0.375285	+	1.28456i
$351$		0			0
$352$		0			0
$353$	1.27881	−	0.394459i	1.27881	−	0.394459i	0.420357	−	0.907359i	$-0.361905\pi$
$353$	1.27881	−	0.394459i	1.27881	−	0.394459i	0.858449	+	0.512899i	$0.171429\pi$
$354$	−0.0103309	−	0.137856i	−0.0103309	−	0.137856i
$355$		0			0
$356$	−0.440420	−	0.212095i	−0.440420	−	0.212095i
$357$	−0.0107172	−	0.0329841i	−0.0107172	−	0.0329841i
$358$		0			0
$359$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$359$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$360$		0			0
$361$	−0.500000	−	0.866025i	−0.500000	−	0.866025i
$362$		0			0
$363$	−0.0559455	+	0.0701535i	−0.0559455	+	0.0701535i
$364$		0			0
$365$		0			0
$366$	−0.219742	+	0.0331208i	−0.219742	+	0.0331208i
$367$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$367$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.707713	−	0.547265i	−0.707713	−	0.547265i
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$		0			0
$375$		0			0
$376$	0.205088	+	0.190294i	0.205088	+	0.190294i
$377$		0			0
$378$	−0.131773	+	0.199627i	−0.131773	+	0.199627i
$379$	−1.03723	−	0.499502i	−1.03723	−	0.499502i	−0.163818	−	0.986491i	$-0.552381\pi$
$379$	−1.03723	−	0.499502i	−1.03723	−	0.499502i	−0.873408	+	0.486989i	$0.838095\pi$
$380$		0			0
$381$		0			0
$382$	0.191131	−	0.0589560i	0.191131	−	0.0589560i
$383$	−0.125953	+	1.68073i	−0.125953	+	1.68073i	0.473869	+	0.880596i	$0.342857\pi$
$383$	−0.125953	+	1.68073i	−0.125953	+	1.68073i	−0.599822	+	0.800134i	$0.704762\pi$
$384$	0.0109282	+	0.0478794i	0.0109282	+	0.0478794i
$385$		0			0
$386$		0			0
$387$		0			0
$388$	−0.565299	+	1.44036i	−0.565299	+	1.44036i
$389$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$389$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$390$		0			0
$391$		0			0
$392$	0.0943757	−	0.263374i	0.0943757	−	0.263374i
$393$	−0.141965			−0.141965
$394$	2.11320	−	1.44075i	2.11320	−	1.44075i
$395$		0			0
$396$		0			0
$397$	−1.61056	−	0.496793i	−1.61056	−	0.496793i	−0.646600	−	0.762830i	$-0.723810\pi$
$397$	−1.61056	−	0.496793i	−1.61056	−	0.496793i	−0.963963	+	0.266037i	$0.914286\pi$
$398$		0			0
$399$		0			0
$400$	0.259315	+	1.13613i	0.259315	+	1.13613i
$401$	0.0376022	−	0.501767i	0.0376022	−	0.501767i	−0.946327	−	0.323210i	$-0.895238\pi$
$401$	0.0376022	−	0.501767i	0.0376022	−	0.501767i	0.983930	−	0.178557i	$-0.0571429\pi$
$402$		0			0
$403$		0			0
$404$	−0.546909	−	1.39350i	−0.546909	−	1.39350i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−0.00711277	−	0.00659969i	−0.00711277	−	0.00659969i
$409$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$409$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$410$		0			0
$411$		0			0
$412$	0.518477	−	0.650149i	0.518477	−	0.650149i
$413$	0.0172218	+	1.15111i	0.0172218	+	1.15111i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$419$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$420$		0			0
$421$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$421$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$422$		0			0
$423$	0.495974	+	0.859053i	0.495974	+	0.859053i
$424$	−0.247497	−	0.0373041i	−0.247497	−	0.0373041i
$425$	−0.283333	−	0.262895i	−0.283333	−	0.262895i
$426$	0.192056	−	0.0924891i	0.192056	−	0.0924891i
$427$	1.84316	−	0.165887i	1.84316	−	0.165887i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.47620	+	0.455348i	−1.47620	+	0.455348i	−0.925304	−	0.379225i	$-0.876190\pi$
$431$	−1.47620	+	0.455348i	−1.47620	+	0.455348i	−0.550897	+	0.834573i	$0.685714\pi$
$432$	−0.0155656	+	0.207709i	−0.0155656	+	0.207709i
$433$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$433$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$		0			0
$439$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.623490	−	0.781831i	$-0.285714\pi$
$439$	1.57906	−	1.07659i	1.57906	−	1.07659i	0.955573	−	0.294755i	$-0.0952381\pi$
$440$		0			0
$441$	0.594992	−	0.793691i	0.594992	−	0.793691i
$442$		0			0
$443$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$443$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$444$	−0.104004	+	0.0965019i	−0.104004	+	0.0965019i
$445$		0			0
$446$		0			0
$447$	0.0284476	−	0.124637i	0.0284476	−	0.124637i
$448$	0.0896605	+	0.539924i	0.0896605	+	0.539924i
$449$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$449$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$450$	−0.0992032	+	1.32377i	−0.0992032	+	1.32377i
$451$		0			0
$452$		0			0
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.10408	−	1.02444i	−1.10408	−	1.02444i	−0.999552	−	0.0299155i	$-0.990476\pi$
$457$	−1.10408	−	1.02444i	−1.10408	−	1.02444i	−0.104528	−	0.994522i	$-0.533333\pi$
$458$		0			0
$459$	−0.0345420	−	0.0598284i	−0.0345420	−	0.0598284i
$460$		0			0
$461$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$461$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$462$		0			0
$463$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$463$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$467$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−0.0620088	+	0.107402i	−0.0620088	+	0.107402i
$472$	0.161042	+	0.278933i	0.161042	+	0.278933i
$473$		0			0
$474$	−0.0691929	−	0.0642017i	−0.0691929	−	0.0642017i
$475$		0			0
$476$	−0.211264	−	0.220965i	−0.211264	−	0.220965i
$477$	−0.799541	−	0.385039i	−0.799541	−	0.385039i
$478$	0.514036	+	1.30974i	0.514036	+	1.30974i
$479$	0.139930	+	1.86723i	0.139930	+	1.86723i	0.420357	+	0.907359i	$0.361905\pi$
$479$	0.139930	+	1.86723i	0.139930	+	1.86723i	−0.280427	+	0.959875i	$0.590476\pi$
$480$		0			0
$481$		0			0
$482$	0.200908	+	0.880234i	0.200908	+	0.880234i
$483$		0			0
$484$	−0.176001	+	0.771112i	−0.176001	+	0.771112i
$485$		0			0
$486$	−0.130202	+	0.331750i	−0.130202	+	0.331750i
$487$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.222521	+	0.974928i	$0.571429\pi$
$487$	−1.21135	+	1.12397i	−1.21135	+	1.12397i	−0.988831	+	0.149042i	$0.952381\pi$
$488$	0.427785	−	0.291659i	0.427785	−	0.291659i
$489$		0			0
$490$		0			0
$491$	1.71690			1.71690			0.858449	−	0.512899i	$-0.171429\pi$
$491$	1.71690			1.71690			0.858449	+	0.512899i	$0.171429\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.64257	+	0.673190i	−1.64257	+	0.673190i
$498$	0.0195243	+	0.0855417i	0.0195243	+	0.0855417i
$499$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$499$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$500$		0			0
$501$		0			0
$502$	0.970849	+	2.47368i	0.970849	+	2.47368i
$503$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$503$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$504$	0.0372524	−	0.275009i	0.0372524	−	0.275009i
$505$		0			0
$506$		0			0
$507$	0.0887275	+	0.0133735i	0.0887275	+	0.0133735i
$508$		0			0
$509$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$509$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$510$		0			0
$511$		0			0
$512$	0.726585	+	0.911109i	0.726585	+	0.911109i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	2.06647	−	1.69914i	2.06647	−	1.69914i
$519$	0.0500503	−	0.0627611i	0.0500503	−	0.0627611i
$520$		0			0
$521$	−0.971490	−	1.68267i	−0.971490	−	1.68267i	−0.691063	−	0.722795i	$-0.742857\pi$
$521$	−0.971490	−	1.68267i	−0.971490	−	1.68267i	−0.280427	−	0.959875i	$-0.590476\pi$
$522$		0			0
$523$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$523$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$524$	−1.12746	+	0.542955i	−1.12746	+	0.542955i
$525$	−0.0120447	+	0.0889176i	−0.0120447	+	0.0889176i
$526$	−0.323699	−	0.155885i	−0.323699	−	0.155885i
$527$		0			0
$528$		0			0
$529$	0.955573	−	0.294755i	0.955573	−	0.294755i
$530$		0			0
$531$	0.254111	+	1.11333i	0.254111	+	1.11333i
$532$		0			0
$533$		0			0
$534$	−0.0709174	−	0.0218751i	−0.0709174	−	0.0218751i
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.96203			−1.96203
$539$		0			0
$540$		0			0
$541$	−0.463400	+	0.315941i	−0.463400	+	0.315941i	−0.772417	−	0.635116i	$-0.780952\pi$
$541$	−0.463400	+	0.315941i	−0.463400	+	0.315941i	0.309017	+	0.951057i	$0.400000\pi$
$542$	1.96115	−	1.81968i	1.96115	−	1.81968i
$543$		0			0
$544$	−0.472672	−	0.145800i	−0.472672	−	0.145800i
$545$		0			0
$546$		0			0
$547$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$547$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$548$		0			0
$549$	1.75415	−	0.541085i	1.75415	−	0.541085i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	0.543210	+	0.568153i	0.543210	+	0.568153i
$554$	−1.14272	+	0.550303i	−1.14272	+	0.550303i
$555$		0			0
$556$		0			0
$557$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$557$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$		0			0
$563$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$563$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$564$	−0.0586390	−	0.0399794i	−0.0586390	−	0.0399794i
$565$		0			0
$566$	1.62121	+	2.03293i	1.62121	+	2.03293i
$567$	0.410231	−	0.885501i	0.410231	−	0.885501i
$568$	−0.309653	+	0.388292i	−0.309653	+	0.388292i
$569$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$569$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$570$		0			0
$571$	1.27876	+	0.192741i	1.27876	+	0.192741i	0.753071	−	0.657939i	$-0.228571\pi$
$571$	1.27876	+	0.192741i	1.27876	+	0.192741i	0.525684	+	0.850680i	$0.323810\pi$
$572$		0			0
$573$	0.0120829	−	0.00581882i	0.0120829	−	0.00581882i
$574$		0			0
$575$		0			0
$576$	0.198348	+	0.505382i	0.198348	+	0.505382i
$577$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$577$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$578$	−1.08776	+	0.335531i	−1.08776	+	0.335531i
$579$		0			0
$580$		0			0
$581$	−0.119699	−	0.720811i	−0.119699	−	0.720811i
$582$	−0.0522736	+	0.229025i	−0.0522736	+	0.229025i
$583$		0			0
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$	−0.0137156	+	0.0696331i	−0.0137156	+	0.0696331i
$589$		0			0
$590$		0			0
$591$	0.125708	−	0.116640i	0.125708	−	0.116640i
$592$	0.851121	−	2.16862i	0.851121	−	2.16862i
$593$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$593$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$594$		0			0
$595$		0			0
$596$	−0.250758	−	1.09864i	−0.250758	−	1.09864i
$597$		0			0
$598$		0			0
$599$		0			0		−0.0747301	−	0.997204i	$-0.523810\pi$
$599$		0			0		0.0747301	+	0.997204i	$0.476190\pi$
$600$	0.00917149	+	0.0233686i	0.00917149	+	0.0233686i
$601$	1.79468	+	0.864274i	1.79468	+	0.864274i	0.936235	+	0.351375i	$0.114286\pi$
$601$	1.79468	+	0.864274i	1.79468	+	0.864274i	0.858449	+	0.512899i	$0.171429\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		0			0
$606$	−0.113637	−	0.196824i	−0.113637	−	0.196824i
$607$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$607$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−0.250555	−	0.170825i	−0.250555	−	0.170825i
$613$	−0.270705	−	0.184564i	−0.270705	−	0.184564i	0.420357	−	0.907359i	$-0.361905\pi$
$613$	−0.270705	−	0.184564i	−0.270705	−	0.184564i	−0.691063	+	0.722795i	$0.742857\pi$
$614$	−2.34911	+	0.354071i	−2.34911	+	0.354071i
$615$		0			0
$616$		0			0
$617$	−0.420644	+	0.527470i	−0.420644	+	0.527470i	−0.946327	−	0.323210i	$-0.895238\pi$
$617$	−0.420644	+	0.527470i	−0.420644	+	0.527470i	0.525684	+	0.850680i	$0.323810\pi$
$618$	0.0631250	−	0.109336i	0.0631250	−	0.109336i
$619$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.826239	+	0.563320i	$0.190476\pi$
$619$	0.900969	+	1.56052i	0.900969	+	1.56052i	0.0747301	+	0.997204i	$0.476190\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.578625	+	0.217162i	0.578625	+	0.217162i
$624$		0			0
$625$	0.365341	+	0.930874i	0.365341	+	0.930874i
$626$		0			0
$627$		0			0
$628$	−0.0816936	+	1.09013i	−0.0816936	+	1.09013i
$629$	0.171937	+	0.753305i	0.171937	+	0.753305i
$630$		0			0
$631$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$631$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$632$	0.210145	+	0.0648212i	0.210145	+	0.0648212i
$633$		0			0
$634$		0			0
$635$		0			0
$636$	0.0634926			0.0634926
$637$		0			0
$638$		0			0
$639$	−1.45491	+	0.991938i	−1.45491	+	0.991938i
$640$		0			0
$641$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$641$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$642$		0			0
$643$	0.0729058	−	0.319421i	0.0729058	−	0.319421i	−0.925304	−	0.379225i	$-0.876190\pi$
$643$	0.0729058	−	0.319421i	0.0729058	−	0.319421i	0.998210	+	0.0598042i	$0.0190476\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.803364	−	0.247805i	0.803364	−	0.247805i	0.134233	−	0.990950i	$-0.457143\pi$
$647$	0.803364	−	0.247805i	0.803364	−	0.247805i	0.669131	+	0.743145i	$0.266667\pi$
$648$	−0.0204038	−	0.272270i	−0.0204038	−	0.272270i
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.41327	+	1.31132i	1.41327	+	1.31132i	0.887586	+	0.460642i	$0.152381\pi$
$653$	1.41327	+	1.31132i	1.41327	+	1.31132i	0.525684	+	0.850680i	$0.323810\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$	1.05866	+	0.818647i	1.05866	+	0.818647i
$659$	0.590905	+	0.740971i	0.590905	+	0.740971i	0.983930	−	0.178557i	$-0.0571429\pi$
$659$	0.590905	+	0.740971i	0.590905	+	0.740971i	−0.393025	+	0.919528i	$0.628571\pi$
$660$		0			0
$661$	−1.06849	−	0.728485i	−1.06849	−	0.728485i	−0.104528	−	0.994522i	$-0.533333\pi$
$661$	−1.06849	−	0.728485i	−1.06849	−	0.728485i	−0.963963	+	0.266037i	$0.914286\pi$
$662$	−1.21828	−	0.830609i	−1.21828	−	0.830609i
$663$		0			0
$664$	−0.127457	−	0.159826i	−0.127457	−	0.159826i
$665$		0			0
$666$	1.65461	−	2.07481i	1.65461	−	2.07481i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$	0.0354855	+	0.109213i	0.0354855	+	0.109213i
$673$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$673$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$674$	−0.755303	−	1.92448i	−0.755303	−	1.92448i
$675$	0.0133570	+	0.178237i	0.0133570	+	0.178237i
$676$	0.755804	−	0.233135i	0.755804	−	0.233135i
$677$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$677$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$678$		0			0
$679$	0.548599	−	1.87780i	0.548599	−	1.87780i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−0.453051	+	0.420370i	−0.453051	+	0.420370i	−0.873408	−	0.486989i	$-0.838095\pi$
$683$	−0.453051	+	0.420370i	−0.453051	+	0.420370i	0.420357	+	0.907359i	$0.361905\pi$
$684$		0			0
$685$		0			0
$686$	0.336689	−	1.29522i	0.336689	−	1.29522i
$687$		0			0
$688$		0			0
$689$		0			0
$690$		0			0
$691$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$691$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$692$	0.157455	−	0.689858i	0.157455	−	0.689858i
$693$		0			0
$694$	−0.591322	−	2.59075i	−0.591322	−	2.59075i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	0.244415	+	0.752232i	0.244415	+	0.752232i
$701$		0			0		0.900969	−	0.433884i	$-0.142857\pi$
$701$		0			0		−0.900969	+	0.433884i	$0.857143\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	1.11663	−	1.40022i	1.11663	−	1.40022i
$707$	0.846609	+	1.69275i	0.846609	+	1.69275i
$708$	−0.0509418	−	0.0638790i	−0.0509418	−	0.0638790i
$709$	−0.831324	+	0.125302i	−0.831324	+	0.125302i	−0.550897	−	0.834573i	$-0.685714\pi$
$709$	−0.831324	+	0.125302i	−0.831324	+	0.125302i	−0.280427	+	0.959875i	$0.590476\pi$
$710$		0			0
$711$	0.644236	+	0.439233i	0.644236	+	0.439233i
$712$	0.170978	−	0.0257708i	0.170978	−	0.0257708i
$713$		0			0
$714$	−0.0367160	−	0.0283920i	−0.0367160	−	0.0283920i
$715$		0			0
$716$		0			0
$717$	0.0471694	+	0.0816998i	0.0471694	+	0.0816998i
$718$		0			0
$719$	1.01317	+	0.940084i	1.01317	+	0.940084i	0.998210	−	0.0598042i	$-0.0190476\pi$
$719$	1.01317	+	0.940084i	1.01317	+	0.940084i	0.0149594	+	0.999888i	$0.495238\pi$
$720$		0			0
$721$	−0.579195	+	0.877443i	−0.579195	+	0.877443i
$722$	−1.20573	−	0.580650i	−1.20573	−	0.580650i
$723$	0.0221167	+	0.0563523i	0.0221167	+	0.0563523i
$724$		0			0
$725$		0			0
$726$	−0.00897372	+	0.119746i	−0.00897372	+	0.119746i
$727$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$727$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$728$		0			0
$729$	0.211843	−	0.928146i	0.211843	−	0.928146i
$730$		0			0
$731$		0			0
$732$	−0.0962788	+	0.0893336i	−0.0962788	+	0.0893336i
$733$	0.415741	−	0.283448i	0.415741	−	0.283448i	−0.337330	−	0.941386i	$-0.609524\pi$
$733$	0.415741	−	0.283448i	0.415741	−	0.283448i	0.753071	+	0.657939i	$0.228571\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	0.578021	−	1.47277i	0.578021	−	1.47277i	−0.280427	−	0.959875i	$-0.590476\pi$
$739$	0.578021	−	1.47277i	0.578021	−	1.47277i	0.858449	−	0.512899i	$-0.171429\pi$
$740$		0			0
$741$		0			0
$742$	−1.19510	−	0.0716001i	−1.19510	−	0.0716001i
$743$		0			0		−0.222521	−	0.974928i	$-0.571429\pi$
$743$		0			0		0.222521	+	0.974928i	$0.428571\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−0.264799	−	0.674696i	−0.264799	−	0.674696i
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.733052	−	0.680173i	$-0.761905\pi$
$751$		0			0		0.733052	+	0.680173i	$0.238095\pi$
$752$	1.15234	+	0.173687i	1.15234	+	0.173687i
$753$	0.0890878	+	0.154305i	0.0890878	+	0.154305i
$754$		0			0
$755$		0			0
$756$	0.00211482	+	0.141355i	0.00211482	+	0.141355i
$757$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$757$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$758$	−1.52344	+	0.229622i	−1.52344	+	0.229622i
$759$		0			0
$760$		0			0
$761$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.900969	−	0.433884i	$-0.857143\pi$
$761$	−1.63402	+	0.246289i	−1.63402	+	0.246289i	−0.733052	+	0.680173i	$0.761905\pi$
$762$		0			0
$763$		0			0
$764$	0.0737055	−	0.0924238i	0.0737055	−	0.0924238i
$765$		0			0
$766$	1.12778	+	1.95337i	1.12778	+	1.95337i
$767$		0			0
$768$	0.0841790	+	0.0781067i	0.0841790	+	0.0781067i
$769$	−1.35699	+	0.653491i	−1.35699	+	0.653491i	−0.963963	−	0.266037i	$-0.914286\pi$
$769$	−1.35699	+	0.653491i	−1.35699	+	0.653491i	−0.393025	+	0.919528i	$0.628571\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.0708245	+	0.945087i	0.0708245	+	0.945087i	0.913545	+	0.406737i	$0.133333\pi$
$773$	0.0708245	+	0.945087i	0.0708245	+	0.945087i	−0.842721	+	0.538351i	$0.819048\pi$
$774$		0			0
$775$		0			0
$776$	−0.121790	−	0.533596i	−0.121790	−	0.533596i
$777$	0.120028	−	0.133305i	0.120028	−	0.133305i
$778$		0			0
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.293187	−	1.12787i	−0.293187	−	1.12787i
$785$		0			0
$786$	−0.156974	+	0.107023i	−0.156974	+	0.107023i
$787$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$787$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$788$	0.552252	−	1.40712i	0.552252	−	1.40712i
$789$	−0.0230192	−	0.00710048i	−0.0230192	−	0.00710048i
$790$		0			0
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−2.15535	+	0.664838i	−2.15535	+	0.664838i
$795$		0			0
$796$		0			0
$797$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$797$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$798$		0			0
$799$	−0.348235	+	0.167701i	−0.348235	+	0.167701i
$800$	0.938140	+	0.870467i	0.938140	+	0.870467i
$801$	0.606211	+	0.0913715i	0.606211	+	0.0913715i
$802$	−0.336689	−	0.583162i	−0.336689	−	0.583162i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−0.130084	+	0.0196070i	−0.130084	+	0.0196070i
$808$	0.437504	+	0.298285i	0.437504	+	0.298285i
$809$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$809$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$810$		0			0
$811$	−0.130345	−	0.163447i	−0.130345	−	0.163447i	0.712376	−	0.701798i	$-0.247619\pi$
$811$	−0.130345	−	0.163447i	−0.130345	−	0.163447i	−0.842721	+	0.538351i	$0.819048\pi$
$812$		0			0
$813$	0.111841	−	0.140244i	0.111841	−	0.140244i
$814$		0			0
$815$		0			0
$816$	−0.0399648	−	0.00602373i	−0.0399648	−	0.00602373i
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$821$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$822$		0			0
$823$	1.82624	−	0.563320i	1.82624	−	0.563320i	0.826239	−	0.563320i	$-0.190476\pi$
$823$	1.82624	−	0.563320i	1.82624	−	0.563320i	1.00000			$0$
$824$	−0.0219814	+	0.293322i	−0.0219814	+	0.293322i
$825$		0			0
$826$	0.886826	+	1.25982i	0.886826	+	1.25982i
$827$	−0.00665756	+	0.0291687i	−0.00665756	+	0.0291687i	−0.978148	−	0.207912i	$-0.933333\pi$
$827$	−0.00665756	+	0.0291687i	−0.00665756	+	0.0291687i	0.971490	+	0.237080i	$0.0761905\pi$
$828$		0			0
$829$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$829$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$830$		0			0
$831$	−0.0702635	+	0.0479048i	−0.0702635	+	0.0479048i
$832$		0			0
$833$	0.291071	+	0.254301i	0.291071	+	0.254301i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$839$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$840$		0			0
$841$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		0			0
$846$	1.19602	+	0.575975i	1.19602	+	0.575975i
$847$	0.134233	−	0.990950i	0.134233	−	0.990950i
$848$	−0.939309	+	0.452348i	−0.939309	+	0.452348i
$849$	0.127802	+	0.118583i	0.127802	+	0.118583i
$850$	−0.511477	−	0.0770927i	−0.511477	−	0.0770927i
$851$		0			0
$852$	0.0629929	−	0.109107i	0.0629929	−	0.109107i
$853$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.0448648	+	0.998993i	$0.514286\pi$
$853$	−1.00883	+	1.26503i	−1.00883	+	1.26503i	−0.963963	+	0.266037i	$0.914286\pi$
$854$	1.91297	−	1.57293i	1.91297	−	1.57293i
$855$		0			0
$856$		0			0
$857$		0			0		−0.826239	−	0.563320i	$-0.809524\pi$
$857$		0			0		0.826239	+	0.563320i	$0.190476\pi$
$858$		0			0
$859$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$859$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$860$		0			0
$861$		0			0
$862$	−1.28900	+	1.61635i	−1.28900	+	1.61635i
$863$	0.0448648	−	0.0777082i	0.0448648	−	0.0777082i	−0.842721	−	0.538351i	$-0.819048\pi$
$863$	0.0448648	−	0.0777082i	0.0448648	−	0.0777082i	0.887586	+	0.460642i	$0.152381\pi$
$864$	0.114371	+	0.198097i	0.114371	+	0.198097i
$865$		0			0
$866$		0			0
$867$	−0.0687663	+	0.0331161i	−0.0687663	+	0.0331161i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	0.145017	−	1.93512i	0.145017	−	1.93512i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$877$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$878$	0.934401	−	2.38081i	0.934401	−	2.38081i
$879$		0			0
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	0.0595574	−	1.32615i	0.0595574	−	1.32615i
$883$	−1.74682			−1.74682			−0.873408	−	0.486989i	$-0.838095\pi$
$883$	−1.74682			−1.74682			−0.873408	+	0.486989i	$0.838095\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$887$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$888$	0.0111673	−	0.0489271i	0.0111673	−	0.0489271i
$889$		0			0
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$	−0.0625050	−	0.159260i	−0.0625050	−	0.159260i
$895$		0			0
$896$	−0.378231	−	0.395599i	−0.378231	−	0.395599i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.392287	+	0.679462i	0.392287	+	0.679462i
$901$	0.172892	−	0.299457i	0.172892	−	0.299457i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−0.826239	−	0.563320i	−0.826239	−	0.563320i	0.0747301	−	0.997204i	$-0.476190\pi$
$907$	−0.826239	−	0.563320i	−0.826239	−	0.563320i	−0.900969	+	0.433884i	$0.857143\pi$
$908$		0			0
$909$	1.17055	+	1.46782i	1.17055	+	1.46782i
$910$		0			0
$911$	0.986449	−	1.23697i	0.986449	−	1.23697i	0.0149594	−	0.999888i	$-0.495238\pi$
$911$	0.986449	−	1.23697i	0.986449	−	1.23697i	0.971490	−	0.237080i	$-0.0761905\pi$
$912$		0			0
$913$		0			0
$914$	−1.99310	−	0.300411i	−1.99310	−	0.300411i
$915$		0			0
$916$		0			0
$917$	1.35819	−	0.811480i	1.35819	−	0.811480i
$918$	−0.0832967	−	0.0401136i	−0.0832967	−	0.0401136i
$919$		0			0		−0.365341	−	0.930874i	$-0.619048\pi$
$919$		0			0		0.365341	+	0.930874i	$0.380952\pi$
$920$		0			0
$921$	−0.152209	+	0.0469502i	−0.152209	+	0.0469502i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.444843	−	1.94898i	0.444843	−	1.94898i
$926$		0			0
$927$	−0.381015	+	0.970811i	−0.381015	+	0.970811i
$928$		0			0
$929$	−1.59293	+	1.08604i	−1.59293	+	1.08604i	−0.646600	+	0.762830i	$0.723810\pi$
$929$	−1.59293	+	1.08604i	−1.59293	+	1.08604i	−0.946327	+	0.323210i	$0.895238\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$937$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.64062	−	0.506064i	1.64062	−	0.506064i	0.669131	−	0.743145i	$-0.266667\pi$
$941$	1.64062	−	0.506064i	1.64062	−	0.506064i	0.971490	+	0.237080i	$0.0761905\pi$
$942$	0.0124028	+	0.165504i	0.0124028	+	0.165504i
$943$		0			0
$944$	1.20873	+	0.582095i	1.20873	+	0.582095i
$945$		0			0
$946$		0			0
$947$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.988831	−	0.149042i	$-0.952381\pi$
$947$	−1.21135	−	1.12397i	−1.21135	−	1.12397i	−0.222521	−	0.974928i	$-0.571429\pi$
$948$	−0.0551637	−	0.00831459i	−0.0551637	−	0.00831459i
$949$		0			0
$950$		0			0
$951$		0			0
$952$	0.105772	+	0.0224826i	0.105772	+	0.0224826i
$953$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$953$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$954$	−1.17434	+	0.177003i	−1.17434	+	0.177003i
$955$		0			0
$956$	0.687077	+	0.468441i	0.687077	+	0.468441i
$957$		0			0
$958$	1.56237	+	1.95916i	1.56237	+	1.95916i
$959$		0			0
$960$		0			0
$961$	−0.500000	+	0.866025i	−0.500000	+	0.866025i
$962$		0			0
$963$		0			0
$964$	0.391169	+	0.362952i	0.391169	+	0.362952i
$965$		0			0
$966$		0			0
$967$	−1.54687	−	0.744934i	−1.54687	−	0.744934i	−0.550897	−	0.834573i	$-0.685714\pi$
$967$	−1.54687	−	0.744934i	−1.54687	−	0.744934i	−0.995974	+	0.0896393i	$0.971429\pi$
$968$	−0.102212	−	0.260433i	−0.102212	−	0.260433i
$969$		0			0
$970$		0			0
$971$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$971$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$972$	0.0468701	+	0.205351i	0.0468701	+	0.205351i
$973$		0			0
$974$	−0.492093	+	2.15600i	−0.492093	+	2.15600i
$975$		0			0
$976$	0.787898	−	2.00753i	0.787898	−	2.00753i
$977$	−0.535628	+	0.496990i	−0.535628	+	0.496990i	−0.900969	−	0.433884i	$-0.857143\pi$
$977$	−0.535628	+	0.496990i	−0.535628	+	0.496990i	0.365341	+	0.930874i	$0.380952\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	1.89841	−	1.29432i	1.89841	−	1.29432i
$983$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$983$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	0.0783706	+	0.0436973i	0.0783706	+	0.0436973i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	0.149193	+	1.99084i	0.149193	+	1.99084i	0.134233	+	0.990950i	$0.457143\pi$
$991$	0.149193	+	1.99084i	0.149193	+	1.99084i	0.0149594	+	0.999888i	$0.495238\pi$
$992$		0			0
$993$	−0.0890730	−	0.0428953i	−0.0890730	−	0.0428953i
$994$	−1.30873	+	1.98265i	−1.30873	+	1.98265i
$995$		0			0
$996$	0.0380141	+	0.0352719i	0.0380141	+	0.0352719i
$997$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$997$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$998$		0			0
$999$	0.178657	−	0.309443i	0.178657	−	0.309443i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.1.q.b.1409.3	yes	48
47.46	odd	2	CM	2303.1.q.b.1409.3	yes	48
49.4	even	21	inner	2303.1.q.b.1033.3	✓	48
2303.1033	odd	42	inner	2303.1.q.b.1033.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.1.q.b.1033.3	✓	48	49.4	even	21	inner
2303.1.q.b.1033.3	✓	48	2303.1033	odd	42	inner
2303.1.q.b.1409.3	yes	48	1.1	even	1	trivial
2303.1.q.b.1409.3	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)

\(f(q)\)	\(=\)	\(q+(1.10572 - 0.753869i) q^{2} +(0.0657765 - 0.0610317i) q^{3} +(0.288964 - 0.736268i) q^{4} +(0.0267207 - 0.117071i) q^{6} +(-0.280427 + 0.959875i) q^{7} +(0.0622553 + 0.272758i) q^{8} +(-0.0741284 + 0.989175i) q^{9} +O(q^{10})\)	\(q+(1.10572 - 0.753869i) q^{2} +(0.0657765 - 0.0610317i) q^{3} +(0.288964 - 0.736268i) q^{4} +(0.0267207 - 0.117071i) q^{6} +(-0.280427 + 0.959875i) q^{7} +(0.0622553 + 0.272758i) q^{8} +(-0.0741284 + 0.989175i) q^{9} +(-0.0259286 - 0.0660651i) q^{12} +(0.413545 + 1.27276i) q^{14} +(0.854264 + 0.792641i) q^{16} +(-0.382195 - 0.0576066i) q^{17} +(0.663743 + 1.14964i) q^{18} +(0.0401373 + 0.0802522i) q^{21} +(0.0207418 + 0.0141415i) q^{24} +(0.826239 + 0.563320i) q^{25} +(0.111441 + 0.139742i) q^{27} +(0.625692 + 0.483839i) q^{28} +(1.26548 + 0.190740i) q^{32} +(-0.466030 + 0.224428i) q^{34} +(0.706878 + 0.340414i) q^{36} +(-0.730355 - 1.86091i) q^{37} +(0.104880 + 0.0584785i) q^{42} +(0.826239 - 0.563320i) q^{47} +0.104567 q^{48} +(-0.842721 - 0.538351i) q^{49} +1.33826 q^{50} +(-0.0286553 + 0.0195368i) q^{51} +(-0.326844 + 0.832784i) q^{53} +(0.228570 + 0.0705044i) q^{54} +(-0.279272 - 0.0167316i) q^{56} +(1.10009 - 0.339332i) q^{59} +(-0.676103 - 1.72268i) q^{61} +(-0.928697 - 0.348546i) q^{63} +(0.493117 - 0.237472i) q^{64} +(-0.152854 + 0.264752i) q^{68} +(1.10680 + 1.38789i) q^{71} +(-0.274421 + 0.0413622i) q^{72} +(-2.21046 - 1.50706i) q^{74} +(0.0887275 - 0.0133735i) q^{75} +(0.393025 - 0.680739i) q^{79} +(-0.965010 - 0.145452i) q^{81} +(-0.658322 + 0.317031i) q^{83} +(0.0706853 - 0.00636180i) q^{84} +(0.0461857 - 0.616306i) q^{89} +(0.488922 - 1.24575i) q^{94} +(0.0948800 - 0.0646881i) q^{96} -1.95630 q^{97} +(-1.33766 + 0.0400347i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 2 q^{3} + 5 q^{4} - 4 q^{6} - q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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

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Representations

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Database

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