LMFDB - Embedded newform 3784.1.em.b.883.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3784,1,Mod(203,3784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3784, base_ring=CyclotomicField(210))

chi = DirichletCharacter(H, H._module([105, 105, 84, 170]))

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

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

chi := DirichletCharacter("3784.203");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 3784 = 2^{3} \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	3784.em (of order $210$, degree $48$, 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:	$1.88846200780$
Analytic rank:	$0$
Dimension:	$48$
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			883.1
Root			$0.842721 - 0.538351i$ of defining polynomial
Character	$\chi$	$=$	3784.883
Dual form			3784.1.em.b.1907.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.963963 - 0.266037i) q^{2} +(-1.16337 + 0.956575i) q^{3} +(0.858449 + 0.512899i) q^{4} +(1.37593 - 0.612604i) q^{6} +(-0.691063 - 0.722795i) q^{8} +(0.245139 - 1.24455i) q^{9} +O(q^{10})$	\(q+(-0.963963 - 0.266037i) q^{2} +(-1.16337 + 0.956575i) q^{3} +(0.858449 + 0.512899i) q^{4} +(1.37593 - 0.612604i) q^{6} +(-0.691063 - 0.722795i) q^{8} +(0.245139 - 1.24455i) q^{9} +(-0.772417 + 0.635116i) q^{11} +(-1.48932 + 0.224479i) q^{12} +(0.473869 + 0.880596i) q^{16} +(-0.918273 + 1.48598i) q^{17} +(-0.567402 + 1.13449i) q^{18} +(0.0125766 - 0.0271471i) q^{19} +(0.913545 - 0.406737i) q^{22} +(1.49537 + 0.179825i) q^{24} +(-0.163818 - 0.986491i) q^{25} +(0.191608 + 0.356068i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(0.291071 - 1.47775i) q^{33} +(1.28051 - 1.18814i) q^{34} +(0.848770 - 0.942654i) q^{36} +(-0.0193455 + 0.0228230i) q^{38} +(0.371668 - 0.563053i) q^{41} +(-0.842721 + 0.538351i) q^{43} +(-0.988831 + 0.149042i) q^{44} +(-1.39364 - 0.571168i) q^{48} +(0.913545 - 0.406737i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(-0.353162 - 2.60714i) q^{51} +(-0.0899761 - 0.394211i) q^{54} +(0.0113370 + 0.0436126i) q^{57} +(-1.37965 + 1.44300i) q^{59} +(-0.0448648 + 0.998993i) q^{64} +(-0.673718 + 1.34706i) q^{66} +(-0.981015 - 0.910249i) q^{67} +(-1.55045 + 0.804658i) q^{68} +(-1.06896 + 0.682880i) q^{72} +(-0.165379 + 0.127885i) q^{73} +(1.13423 + 0.990950i) q^{75} +(0.0247201 - 0.0168539i) q^{76} +(0.610200 + 0.250084i) q^{81} +(-0.508067 + 0.443885i) q^{82} +(-0.485041 + 1.86591i) q^{83} +(0.955573 - 0.294755i) q^{86} +(0.992847 + 0.119394i) q^{88} +(-0.730355 - 1.86091i) q^{89} +(1.19147 + 0.921344i) q^{96} +(-1.26926 - 1.10892i) q^{97} +(-0.988831 + 0.149042i) q^{98} +(0.601087 + 1.11701i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	$ 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) $ 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3784\mathbb{Z}\right)^\times$.

$n$	$89$	$1377$	$1893$	$2839$
$\chi(n)$	$e\left(\frac{8}{21}\right)$	$e\left(\frac{4}{5}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$2$	−0.963963	−	0.266037i	−0.963963	−	0.266037i
$3$	−1.16337	+	0.956575i	−1.16337	+	0.956575i	−0.999552	−	0.0299155i	$-0.990476\pi$
$3$	−1.16337	+	0.956575i	−1.16337	+	0.956575i	−0.163818	+	0.986491i	$0.552381\pi$
$4$	0.858449	+	0.512899i	0.858449	+	0.512899i
$5$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$5$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$6$	1.37593	−	0.612604i	1.37593	−	0.612604i
$7$		0			0		0.978148	−	0.207912i	$-0.0666667\pi$
$7$		0			0		−0.978148	+	0.207912i	$0.933333\pi$
$8$	−0.691063	−	0.722795i	−0.691063	−	0.722795i
$9$	0.245139	−	1.24455i	0.245139	−	1.24455i
$10$		0			0
$11$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$11$	−0.772417	+	0.635116i	−0.772417	+	0.635116i
$12$	−1.48932	+	0.224479i	−1.48932	+	0.224479i
$13$		0			0		0.999552	−	0.0299155i	$-0.00952381\pi$
$13$		0			0		−0.999552	+	0.0299155i	$0.990476\pi$
$14$		0			0
$15$		0			0
$16$	0.473869	+	0.880596i	0.473869	+	0.880596i
$17$	−0.918273	+	1.48598i	−0.918273	+	1.48598i	−0.0448648	+	0.998993i	$0.514286\pi$
$17$	−0.918273	+	1.48598i	−0.918273	+	1.48598i	−0.873408	+	0.486989i	$0.838095\pi$
$18$	−0.567402	+	1.13449i	−0.567402	+	1.13449i
$19$	0.0125766	−	0.0271471i	0.0125766	−	0.0271471i	−0.900969	−	0.433884i	$-0.857143\pi$
$19$	0.0125766	−	0.0271471i	0.0125766	−	0.0271471i	0.913545	+	0.406737i	$0.133333\pi$
$20$		0			0
$21$		0			0
$22$	0.913545	−	0.406737i	0.913545	−	0.406737i
$23$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$23$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$24$	1.49537	+	0.179825i	1.49537	+	0.179825i
$25$	−0.163818	−	0.986491i	−0.163818	−	0.986491i
$26$		0			0
$27$	0.191608	+	0.356068i	0.191608	+	0.356068i
$28$		0			0
$29$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$29$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$30$		0			0
$31$		0			0		0.712376	−	0.701798i	$-0.247619\pi$
$31$		0			0		−0.712376	+	0.701798i	$0.752381\pi$
$32$	−0.222521	−	0.974928i	−0.222521	−	0.974928i
$33$	0.291071	−	1.47775i	0.291071	−	1.47775i
$34$	1.28051	−	1.18814i	1.28051	−	1.18814i
$35$		0			0
$36$	0.848770	−	0.942654i	0.848770	−	0.942654i
$37$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$37$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$38$	−0.0193455	+	0.0228230i	−0.0193455	+	0.0228230i
$39$		0			0
$40$		0			0
$41$	0.371668	−	0.563053i	0.371668	−	0.563053i	−0.599822	−	0.800134i	$-0.704762\pi$
$41$	0.371668	−	0.563053i	0.371668	−	0.563053i	0.971490	+	0.237080i	$0.0761905\pi$
$42$		0			0
$43$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$43$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$44$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$45$		0			0
$46$		0			0
$47$		0			0		0.995974	−	0.0896393i	$-0.0285714\pi$
$47$		0			0		−0.995974	+	0.0896393i	$0.971429\pi$
$48$	−1.39364	−	0.571168i	−1.39364	−	0.571168i
$49$	0.913545	−	0.406737i	0.913545	−	0.406737i
$50$	−0.104528	+	0.994522i	−0.104528	+	0.994522i
$51$	−0.353162	−	2.60714i	−0.353162	−	2.60714i
$52$		0			0
$53$		0			0		0.337330	−	0.941386i	$-0.390476\pi$
$53$		0			0		−0.337330	+	0.941386i	$0.609524\pi$
$54$	−0.0899761	−	0.394211i	−0.0899761	−	0.394211i
$55$		0			0
$56$		0			0
$57$	0.0113370	+	0.0436126i	0.0113370	+	0.0436126i
$58$		0			0
$59$	−1.37965	+	1.44300i	−1.37965	+	1.44300i	−0.646600	+	0.762830i	$0.723810\pi$
$59$	−1.37965	+	1.44300i	−1.37965	+	1.44300i	−0.733052	+	0.680173i	$0.761905\pi$
$60$		0			0
$61$		0			0		−0.712376	−	0.701798i	$-0.752381\pi$
$61$		0			0		0.712376	+	0.701798i	$0.247619\pi$
$62$		0			0
$63$		0			0
$64$	−0.0448648	+	0.998993i	−0.0448648	+	0.998993i
$65$		0			0
$66$	−0.673718	+	1.34706i	−0.673718	+	1.34706i
$67$	−0.981015	−	0.910249i	−0.981015	−	0.910249i	0.0149594	−	0.999888i	$-0.495238\pi$
$67$	−0.981015	−	0.910249i	−0.981015	−	0.910249i	−0.995974	+	0.0896393i	$0.971429\pi$
$68$	−1.55045	+	0.804658i	−1.55045	+	0.804658i
$69$		0			0
$70$		0			0
$71$		0			0		−0.946327	−	0.323210i	$-0.895238\pi$
$71$		0			0		0.946327	+	0.323210i	$0.104762\pi$
$72$	−1.06896	+	0.682880i	−1.06896	+	0.682880i
$73$	−0.165379	+	0.127885i	−0.165379	+	0.127885i	−0.691063	−	0.722795i	$-0.742857\pi$
$73$	−0.165379	+	0.127885i	−0.165379	+	0.127885i	0.525684	+	0.850680i	$0.323810\pi$
$74$		0			0
$75$	1.13423	+	0.990950i	1.13423	+	0.990950i
$76$	0.0247201	−	0.0168539i	0.0247201	−	0.0168539i
$77$		0			0
$78$		0			0
$79$		0			0		−0.913545	−	0.406737i	$-0.866667\pi$
$79$		0			0		0.913545	+	0.406737i	$0.133333\pi$
$80$		0			0
$81$	0.610200	+	0.250084i	0.610200	+	0.250084i
$82$	−0.508067	+	0.443885i	−0.508067	+	0.443885i
$83$	−0.485041	+	1.86591i	−0.485041	+	1.86591i	0.0149594	+	0.999888i	$0.495238\pi$
$83$	−0.485041	+	1.86591i	−0.485041	+	1.86591i	−0.500000	+	0.866025i	$0.666667\pi$
$84$		0			0
$85$		0			0
$86$	0.955573	−	0.294755i	0.955573	−	0.294755i
$87$		0			0
$88$	0.992847	+	0.119394i	0.992847	+	0.119394i
$89$	−0.730355	−	1.86091i	−0.730355	−	1.86091i	−0.393025	−	0.919528i	$-0.628571\pi$
$89$	−0.730355	−	1.86091i	−0.730355	−	1.86091i	−0.337330	−	0.941386i	$-0.609524\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$	1.19147	+	0.921344i	1.19147	+	0.921344i
$97$	−1.26926	−	1.10892i	−1.26926	−	1.10892i	−0.988831	−	0.149042i	$-0.952381\pi$
$97$	−1.26926	−	1.10892i	−1.26926	−	1.10892i	−0.280427	−	0.959875i	$-0.590476\pi$
$98$	−0.988831	+	0.149042i	−0.988831	+	0.149042i
$99$	0.601087	+	1.11701i	0.601087	+	1.11701i
$100$	0.365341	−	0.930874i	0.365341	−	0.930874i
$101$		0			0		0.599822	−	0.800134i	$-0.295238\pi$
$101$		0			0		−0.599822	+	0.800134i	$0.704762\pi$
$102$	−0.353162	+	2.60714i	−0.353162	+	2.60714i
$103$		0			0		−0.971490	−	0.237080i	$-0.923810\pi$
$103$		0			0		0.971490	+	0.237080i	$0.0761905\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.984327	+	0.369424i	0.984327	+	0.369424i	0.791071	−	0.611724i	$-0.209524\pi$
$107$	0.984327	+	0.369424i	0.984327	+	0.369424i	0.193256	+	0.981148i	$0.438095\pi$
$108$	−0.0181410	+	0.403942i	−0.0181410	+	0.403942i
$109$		0			0		−0.955573	−	0.294755i	$-0.904762\pi$
$109$		0			0		0.955573	+	0.294755i	$0.0952381\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.112852	−	0.833106i	0.112852	−	0.833106i	−0.842721	−	0.538351i	$-0.819048\pi$
$113$	0.112852	−	0.833106i	0.112852	−	0.833106i	0.955573	−	0.294755i	$-0.0952381\pi$
$114$	0.000674101	−	0.0450570i	0.000674101	−	0.0450570i
$115$		0			0
$116$		0			0
$117$		0			0
$118$	1.71382	−	1.02396i	1.71382	−	1.02396i
$119$		0			0
$120$		0			0
$121$	0.193256	−	0.981148i	0.193256	−	0.981148i
$122$		0			0
$123$	0.106215	+	1.01057i	0.106215	+	1.01057i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		0			0		−0.0448648	−	0.998993i	$-0.514286\pi$
$127$		0			0		0.0448648	+	0.998993i	$0.485714\pi$
$128$	0.309017	−	0.951057i	0.309017	−	0.951057i
$129$	0.465424	−	1.43243i	0.465424	−	1.43243i
$130$		0			0
$131$	−1.15384	−	1.44686i	−1.15384	−	1.44686i	−0.873408	−	0.486989i	$-0.838095\pi$
$131$	−1.15384	−	1.44686i	−1.15384	−	1.44686i	−0.280427	−	0.959875i	$-0.590476\pi$
$132$	1.00781	−	1.11928i	1.00781	−	1.11928i
$133$		0			0
$134$	0.703502	+	1.13843i	0.703502	+	1.13843i
$135$		0			0
$136$	1.70864	−	0.363184i	1.70864	−	0.363184i
$137$	−0.0882877	−	0.0160218i	−0.0882877	−	0.0160218i	0.134233	−	0.990950i	$-0.457143\pi$
$137$	−0.0882877	−	0.0160218i	−0.0882877	−	0.0160218i	−0.222521	+	0.974928i	$0.571429\pi$
$138$		0			0
$139$	−0.0419127	−	0.143463i	−0.0419127	−	0.143463i	0.936235	−	0.351375i	$-0.114286\pi$
$139$	−0.0419127	−	0.143463i	−0.0419127	−	0.143463i	−0.978148	+	0.207912i	$0.933333\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	1.21211	−	0.373887i	1.21211	−	0.373887i
$145$		0			0
$146$	0.193441	−	0.0792797i	0.193441	−	0.0792797i
$147$	−0.673718	+	1.34706i	−0.673718	+	1.34706i
$148$		0			0
$149$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$149$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$150$	−0.829730	−	1.25699i	−0.829730	−	1.25699i
$151$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$151$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$152$	−0.0283130	+	0.00967005i	−0.0283130	+	0.00967005i
$153$	1.62428	+	1.50711i	1.62428	+	1.50711i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		0			0		−0.575617	−	0.817719i	$-0.695238\pi$
$157$		0			0		0.575617	+	0.817719i	$0.304762\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		0			0
$162$	−0.521679	−	0.403407i	−0.521679	−	0.403407i
$163$	0.375492	−	1.90635i	0.375492	−	1.90635i	−0.0448648	−	0.998993i	$-0.514286\pi$
$163$	0.375492	−	1.90635i	0.375492	−	1.90635i	0.420357	−	0.907359i	$-0.361905\pi$
$164$	0.607848	−	0.292724i	0.607848	−	0.292724i
$165$		0			0
$166$	0.963963	−	1.66963i	0.963963	−	1.66963i
$167$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$167$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$168$		0			0
$169$	0.998210	−	0.0598042i	0.998210	−	0.0598042i
$170$		0			0
$171$	−0.0307030	−	0.0223070i	−0.0307030	−	0.0223070i
$172$	−0.999552	+	0.0299155i	−0.999552	+	0.0299155i
$173$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$173$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$174$		0			0
$175$		0			0
$176$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$177$	0.224705	−	2.99849i	0.224705	−	2.99849i
$178$	0.208963	+	1.98815i	0.208963	+	1.98815i
$179$	1.33587	−	1.48363i	1.33587	−	1.48363i	0.623490	−	0.781831i	$-0.285714\pi$
$179$	1.33587	−	1.48363i	1.33587	−	1.48363i	0.712376	−	0.701798i	$-0.247619\pi$
$180$		0			0
$181$		0			0		0.992847	−	0.119394i	$-0.0380952\pi$
$181$		0			0		−0.992847	+	0.119394i	$0.961905\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−0.234481	−	1.73101i	−0.234481	−	1.73101i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		0.873408	−	0.486989i	$-0.161905\pi$
$191$		0			0		−0.873408	+	0.486989i	$0.838095\pi$
$192$	−0.903418	−	1.20512i	−0.903418	−	1.20512i
$193$	−1.20204	+	0.331743i	−1.20204	+	0.331743i	−0.809017	−	0.587785i	$-0.800000\pi$
$193$	−1.20204	+	0.331743i	−1.20204	+	0.331743i	−0.393025	+	0.919528i	$0.628571\pi$
$194$	0.928505	+	1.40662i	0.928505	+	1.40662i
$195$		0			0
$196$	0.992847	+	0.119394i	0.992847	+	0.119394i
$197$		0			0		−0.988831	−	0.149042i	$-0.952381\pi$
$197$		0			0		0.988831	+	0.149042i	$0.0476190\pi$
$198$	−0.282260	−	1.23666i	−0.282260	−	1.23666i
$199$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$199$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$200$	−0.599822	+	0.800134i	−0.599822	+	0.800134i
$201$	2.01200	+	0.120542i	2.01200	+	0.120542i
$202$		0			0
$203$		0			0
$204$	1.03403	−	2.41924i	1.03403	−	2.41924i
$205$		0			0
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.00752718	+	0.0289565i	0.00752718	+	0.0289565i
$210$		0			0
$211$	−0.372484	−	0.871471i	−0.372484	−	0.871471i	−0.995974	−	0.0896393i	$-0.971429\pi$
$211$	−0.372484	−	0.871471i	−0.372484	−	0.871471i	0.623490	−	0.781831i	$-0.285714\pi$
$212$		0			0
$213$		0			0
$214$	−0.850574	−	0.617978i	−0.850574	−	0.617978i
$215$		0			0
$216$	0.124951	−	0.384559i	0.124951	−	0.384559i
$217$		0			0
$218$		0			0
$219$	0.0700651	−	0.306975i	0.0700651	−	0.306975i
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.691063	−	0.722795i	$-0.742857\pi$
$223$		0			0		0.691063	+	0.722795i	$0.257143\pi$
$224$		0			0
$225$	−1.26790	−	0.0379468i	−1.26790	−	0.0379468i
$226$	−0.330422	+	0.773060i	−0.330422	+	0.773060i
$227$	0.146556	−	0.882540i	0.146556	−	0.882540i	−0.809017	−	0.587785i	$-0.800000\pi$
$227$	0.146556	−	0.882540i	0.146556	−	0.882540i	0.955573	−	0.294755i	$-0.0952381\pi$
$228$	−0.0126366	+	0.0432539i	−0.0126366	+	0.0432539i
$229$		0			0		−0.251587	−	0.967835i	$-0.580952\pi$
$229$		0			0		0.251587	+	0.967835i	$0.419048\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.67989	+	0.871837i	−1.67989	+	0.871837i	−0.691063	+	0.722795i	$0.742857\pi$
$233$	−1.67989	+	0.871837i	−1.67989	+	0.871837i	−0.988831	+	0.149042i	$0.952381\pi$
$234$		0			0
$235$		0			0
$236$	−1.92447	+	0.531121i	−1.92447	+	0.531121i
$237$		0			0
$238$		0			0
$239$		0			0		0.420357	−	0.907359i	$-0.361905\pi$
$239$		0			0		−0.420357	+	0.907359i	$0.638095\pi$
$240$		0			0
$241$	0.139930	+	1.86723i	0.139930	+	1.86723i	0.420357	+	0.907359i	$0.361905\pi$
$241$	0.139930	+	1.86723i	0.139930	+	1.86723i	−0.280427	+	0.959875i	$0.590476\pi$
$242$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$243$	−1.33550	+	0.411947i	−1.33550	+	0.411947i
$244$		0			0
$245$		0			0
$246$	0.166461	−	1.00241i	0.166461	−	1.00241i
$247$		0			0
$248$		0			0
$249$	−1.22060	−	2.63473i	−1.22060	−	2.63473i
$250$		0			0
$251$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.104528	−	0.994522i	$-0.533333\pi$
$251$	−0.913545	−	0.406737i	−0.913545	−	0.406737i	−0.809017	+	0.587785i	$0.800000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$257$	0.564602	−	1.73767i	0.564602	−	1.73767i	−0.104528	−	0.994522i	$-0.533333\pi$
$257$	0.564602	−	1.73767i	0.564602	−	1.73767i	0.669131	−	0.743145i	$-0.266667\pi$
$258$	−0.829730	+	1.25699i	−0.829730	+	1.25699i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	0.727336	+	1.70169i	0.727336	+	1.70169i
$263$		0			0		0.0747301	−	0.997204i	$-0.476190\pi$
$263$		0			0		−0.0747301	+	0.997204i	$0.523810\pi$
$264$	−1.26926	+	0.810833i	−1.26926	+	0.810833i
$265$		0			0
$266$		0			0
$267$	2.62978	+	1.46629i	2.62978	+	1.46629i
$268$	−0.375285	−	1.28456i	−0.375285	−	1.28456i
$269$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$269$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$270$		0			0
$271$		0			0		0.791071	−	0.611724i	$-0.209524\pi$
$271$		0			0		−0.791071	+	0.611724i	$0.790476\pi$
$272$	−1.74369	−	0.104467i	−1.74369	−	0.104467i
$273$		0			0
$274$	0.0808436	+	0.0389322i	0.0808436	+	0.0389322i
$275$	0.753071	+	0.657939i	0.753071	+	0.657939i
$276$		0			0
$277$		0			0		−0.992847	−	0.119394i	$-0.961905\pi$
$277$		0			0		0.992847	+	0.119394i	$0.0380952\pi$
$278$	0.00223584	+	0.149443i	0.00223584	+	0.149443i
$279$		0			0
$280$		0			0
$281$	0.125397	+	0.167273i	0.125397	+	0.167273i	0.858449	−	0.512899i	$-0.171429\pi$
$281$	0.125397	+	0.167273i	0.125397	+	0.167273i	−0.733052	+	0.680173i	$0.761905\pi$
$282$		0			0
$283$	−0.313080	−	1.88533i	−0.313080	−	1.88533i	−0.447313	−	0.894377i	$-0.647619\pi$
$283$	−0.313080	−	1.88533i	−0.313080	−	1.88533i	0.134233	−	0.990950i	$-0.457143\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−1.26790	+	0.0379468i	−1.26790	+	0.0379468i
$289$	−0.917604	−	1.83470i	−0.917604	−	1.83470i
$290$		0			0
$291$	2.53738	+	0.0759409i	2.53738	+	0.0759409i
$292$	−0.207562	+	0.0249602i	−0.207562	+	0.0249602i
$293$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$293$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$294$	1.00781	−	1.11928i	1.00781	−	1.11928i
$295$		0			0
$296$		0			0
$297$	−0.374146	−	0.153339i	−0.374146	−	0.153339i
$298$		0			0
$299$		0			0
$300$	0.465424	+	1.43243i	0.465424	+	1.43243i
$301$		0			0
$302$		0			0
$303$		0			0
$304$	0.0298653	−	0.00178927i	0.0298653	−	0.00178927i
$305$		0			0
$306$	−1.16480	−	1.88492i	−1.16480	−	1.88492i
$307$	−0.193256	+	0.334729i	−0.193256	+	0.334729i	−0.946327	−	0.323210i	$-0.895238\pi$
$307$	−0.193256	+	0.334729i	−0.193256	+	0.334729i	0.753071	+	0.657939i	$0.228571\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.791071	−	0.611724i	$-0.790476\pi$
$311$		0			0		0.791071	+	0.611724i	$0.209524\pi$
$312$		0			0
$313$	0.238287	+	0.123667i	0.238287	+	0.123667i	0.575617	−	0.817719i	$-0.304762\pi$
$313$	0.238287	+	0.123667i	0.238287	+	0.123667i	−0.337330	+	0.941386i	$0.609524\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		0			0		0.983930	−	0.178557i	$-0.0571429\pi$
$317$		0			0		−0.983930	+	0.178557i	$0.942857\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$	−1.49852	+	0.511806i	−1.49852	+	0.511806i
$322$		0			0
$323$	0.0287913	+	0.0436170i	0.0287913	+	0.0436170i
$324$	0.395558	+	0.527655i	0.395558	+	0.527655i
$325$		0			0
$326$	−0.869121	+	1.73776i	−0.869121	+	1.73776i
$327$		0			0
$328$	−0.663818	+	0.120465i	−0.663818	+	0.120465i
$329$		0			0
$330$		0			0
$331$	0.415741	+	0.283448i	0.415741	+	0.283448i	0.753071	−	0.657939i	$-0.228571\pi$
$331$	0.415741	+	0.283448i	0.415741	+	0.283448i	−0.337330	+	0.941386i	$0.609524\pi$
$332$	−1.37341	+	1.35301i	−1.37341	+	1.35301i
$333$		0			0
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.320476	−	0.0681193i	0.320476	−	0.0681193i	−0.0448648	−	0.998993i	$-0.514286\pi$
$337$	0.320476	−	0.0681193i	0.320476	−	0.0681193i	0.365341	+	0.930874i	$0.380952\pi$
$338$	−0.978148	−	0.207912i	−0.978148	−	0.207912i
$339$	0.665640	+	1.07716i	0.665640	+	1.07716i
$340$		0			0
$341$		0			0
$342$	0.0236621	+	0.0296713i	0.0236621	+	0.0296713i
$343$		0			0
$344$	0.971490	+	0.237080i	0.971490	+	0.237080i
$345$		0			0
$346$		0			0
$347$	0.211513	−	0.813673i	0.211513	−	0.813673i	−0.772417	−	0.635116i	$-0.780952\pi$
$347$	0.211513	−	0.813673i	0.211513	−	0.813673i	0.983930	−	0.178557i	$-0.0571429\pi$
$348$		0			0
$349$		0			0		0.971490	−	0.237080i	$-0.0761905\pi$
$349$		0			0		−0.971490	+	0.237080i	$0.923810\pi$
$350$		0			0
$351$		0			0
$352$	0.791071	+	0.611724i	0.791071	+	0.611724i
$353$	−1.42431	+	1.32156i	−1.42431	+	1.32156i	−0.550897	+	0.834573i	$0.685714\pi$
$353$	−1.42431	+	1.32156i	−1.42431	+	1.32156i	−0.873408	+	0.486989i	$0.838095\pi$
$354$	−1.01432	+	2.83065i	−1.01432	+	2.83065i
$355$		0			0
$356$	0.327489	−	1.97210i	0.327489	−	1.97210i
$357$		0			0
$358$	−1.68243	+	1.07477i	−1.68243	+	1.07477i
$359$		0			0		0.0149594	−	0.999888i	$-0.495238\pi$
$359$		0			0		−0.0149594	+	0.999888i	$0.504762\pi$
$360$		0			0
$361$	0.646021	+	0.762147i	0.646021	+	0.762147i
$362$		0			0
$363$	0.713714	+	1.32630i	0.713714	+	1.32630i
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.575617	−	0.817719i	$-0.304762\pi$
$367$		0			0		−0.575617	+	0.817719i	$0.695238\pi$
$368$		0			0
$369$	−0.609640	−	0.600587i	−0.609640	−	0.600587i
$370$		0			0
$371$		0			0
$372$		0			0
$373$		0			0		0.365341	−	0.930874i	$-0.380952\pi$
$373$		0			0		−0.365341	+	0.930874i	$0.619048\pi$
$374$	−0.234481	+	1.73101i	−0.234481	+	1.73101i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	0.495087	+	0.0898451i	0.495087	+	0.0898451i	0.420357	−	0.907359i	$-0.361905\pi$
$379$	0.495087	+	0.0898451i	0.495087	+	0.0898451i	0.0747301	+	0.997204i	$0.476190\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.393025	−	0.919528i	$-0.628571\pi$
$383$		0			0		0.393025	+	0.919528i	$0.371429\pi$
$384$	0.550256	+	1.40203i	0.550256	+	1.40203i
$385$		0			0
$386$	1.24698			1.24698
$387$	0.463423	+	1.18078i	0.463423	+	1.18078i
$388$	−0.520830	−	1.60295i	−0.520830	−	1.60295i
$389$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$389$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$390$		0			0
$391$		0			0
$392$	−0.925304	−	0.379225i	−0.925304	−	0.379225i
$393$	2.72637	+	0.579508i	2.72637	+	0.579508i
$394$		0			0
$395$		0			0
$396$	−0.0569095	+	1.26719i	−0.0569095	+	1.26719i
$397$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$397$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$398$		0			0
$399$		0			0
$400$	0.791071	−	0.611724i	0.791071	−	0.611724i
$401$	0.0756171	−	0.0483060i	0.0756171	−	0.0483060i	−0.500000	−	0.866025i	$-0.666667\pi$
$401$	0.0756171	−	0.0483060i	0.0756171	−	0.0483060i	0.575617	+	0.817719i	$0.304762\pi$
$402$	−1.90743	−	0.651465i	−1.90743	−	0.651465i
$403$		0			0
$404$		0			0
$405$		0			0
$406$		0			0
$407$		0			0
$408$	−1.64037	+	2.05696i	−1.64037	+	2.05696i
$409$	−0.0741381	+	1.65081i	−0.0741381	+	1.65081i	0.525684	+	0.850680i	$0.323810\pi$
$409$	−0.0741381	+	1.65081i	−0.0741381	+	1.65081i	−0.599822	+	0.800134i	$0.704762\pi$
$410$		0			0
$411$	0.118037	−	0.0658144i	0.118037	−	0.0658144i
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$		0			0
$417$	0.185993	+	0.126808i	0.185993	+	0.126808i
$418$	0.000447568	−	0.0299155i	0.000447568	−	0.0299155i
$419$	−0.437890	−	1.91852i	−0.437890	−	1.91852i	−0.393025	−	0.919528i	$-0.628571\pi$
$419$	−0.437890	−	1.91852i	−0.437890	−	1.91852i	−0.0448648	−	0.998993i	$-0.514286\pi$
$420$		0			0
$421$		0			0		−0.873408	−	0.486989i	$-0.838095\pi$
$421$		0			0		0.873408	+	0.486989i	$0.161905\pi$
$422$	0.127218	+	0.939160i	0.127218	+	0.939160i
$423$		0			0
$424$		0			0
$425$	1.61634	+	0.662437i	1.61634	+	0.662437i
$426$		0			0
$427$		0			0
$428$	0.655517	+	0.821992i	0.655517	+	0.821992i
$429$		0			0
$430$		0			0
$431$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$431$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$432$	−0.222755	+	0.337459i	−0.222755	+	0.337459i
$433$	−1.37965	+	0.0826568i	−1.37965	+	0.0826568i	−0.733052	−	0.680173i	$-0.761905\pi$
$433$	−1.37965	+	0.0826568i	−1.37965	+	0.0826568i	−0.646600	+	0.762830i	$0.723810\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		0			0
$438$	−0.149207	+	0.277273i	−0.149207	+	0.277273i
$439$		0			0		0.733052	−	0.680173i	$-0.238095\pi$
$439$		0			0		−0.733052	+	0.680173i	$0.761905\pi$
$440$		0			0
$441$	−0.282260	−	1.23666i	−0.282260	−	1.23666i
$442$		0			0
$443$	−0.551842	+	1.88890i	−0.551842	+	1.88890i	−0.104528	+	0.994522i	$0.533333\pi$
$443$	−0.551842	+	1.88890i	−0.551842	+	1.88890i	−0.447313	+	0.894377i	$0.647619\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.53378	−	0.184444i	−1.53378	−	0.184444i	−0.691063	−	0.722795i	$-0.742857\pi$
$449$	−1.53378	−	0.184444i	−1.53378	−	0.184444i	−0.842721	+	0.538351i	$0.819048\pi$
$450$	1.21211	+	0.373887i	1.21211	+	0.373887i
$451$	0.0705212	+	0.670964i	0.0705212	+	0.670964i
$452$	0.524177	−	0.657297i	0.524177	−	0.657297i
$453$		0			0
$454$	−0.376063	+	0.811747i	−0.376063	+	0.811747i
$455$		0			0
$456$	0.0236884	−	0.0383334i	0.0236884	−	0.0383334i
$457$	−0.612807	−	1.13879i	−0.612807	−	1.13879i	−0.978148	−	0.207912i	$-0.933333\pi$
$457$	−0.612807	−	1.13879i	−0.612807	−	1.13879i	0.365341	−	0.930874i	$-0.380952\pi$
$458$		0			0
$459$	−0.705059	−	0.0422411i	−0.705059	−	0.0422411i
$460$		0			0
$461$		0			0		0.988831	−	0.149042i	$-0.0476190\pi$
$461$		0			0		−0.988831	+	0.149042i	$0.952381\pi$
$462$		0			0
$463$		0			0		0.826239	−	0.563320i	$-0.190476\pi$
$463$		0			0		−0.826239	+	0.563320i	$0.809524\pi$
$464$		0			0
$465$		0			0
$466$	1.85130	−	0.393505i	1.85130	−	0.393505i
$467$	1.50961	−	0.672123i	1.50961	−	0.672123i	0.525684	−	0.850680i	$-0.323810\pi$
$467$	1.50961	−	0.672123i	1.50961	−	0.672123i	0.983930	+	0.178557i	$0.0571429\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$		0			0
$472$	1.99642			1.99642
$473$	0.309017	−	0.951057i	0.309017	−	0.951057i
$474$		0			0
$475$	−0.0288406	−	0.00795951i	−0.0288406	−	0.00795951i
$476$		0			0
$477$		0			0
$478$		0			0
$479$		0			0		0.913545	−	0.406737i	$-0.133333\pi$
$479$		0			0		−0.913545	+	0.406737i	$0.866667\pi$
$480$		0			0
$481$		0			0
$482$	0.361866	−	1.83717i	0.361866	−	1.83717i
$483$		0			0
$484$	0.669131	−	0.743145i	0.669131	−	0.743145i
$485$		0			0
$486$	1.39696	−	0.0418095i	1.39696	−	0.0418095i
$487$		0			0		−0.998210	−	0.0598042i	$-0.980952\pi$
$487$		0			0		0.998210	+	0.0598042i	$0.0190476\pi$
$488$		0			0
$489$	1.38673	+	2.57698i	1.38673	+	2.57698i
$490$		0			0
$491$	−0.172892	+	0.345687i	−0.172892	+	0.345687i	−0.963963	−	0.266037i	$-0.914286\pi$
$491$	−0.172892	+	0.345687i	−0.172892	+	0.345687i	0.791071	+	0.611724i	$0.209524\pi$
$492$	−0.427139	+	0.921998i	−0.427139	+	0.921998i
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$	0.475683	+	2.86450i	0.475683	+	2.86450i
$499$	−1.63739	−	0.399585i	−1.63739	−	0.399585i	−0.691063	−	0.722795i	$-0.742857\pi$
$499$	−1.63739	−	0.399585i	−1.63739	−	0.399585i	−0.946327	+	0.323210i	$0.895238\pi$
$500$		0			0
$501$		0			0
$502$	0.772417	+	0.635116i	0.772417	+	0.635116i
$503$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$503$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−1.10408	+	1.02444i	−1.10408	+	1.02444i
$508$		0			0
$509$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$509$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$510$		0			0
$511$		0			0
$512$	0.753071	−	0.657939i	0.753071	−	0.657939i
$513$	0.0120760		0.000723489i	0.0120760		0.000723489i
$514$	−1.00654	+	1.52484i	−1.00654	+	1.52484i
$515$		0			0
$516$	1.13423	−	0.990950i	1.13423	−	0.990950i
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.71238	+	0.701798i	1.71238	+	0.701798i	1.00000			$0$
$521$	1.71238	+	0.701798i	1.71238	+	0.701798i	0.712376	+	0.701798i	$0.247619\pi$
$522$		0			0
$523$	−0.165379	+	1.57347i	−0.165379	+	1.57347i	0.525684	+	0.850680i	$0.323810\pi$
$523$	−0.165379	+	1.57347i	−0.165379	+	1.57347i	−0.691063	+	0.722795i	$0.742857\pi$
$524$	−0.248413	−	1.83386i	−0.248413	−	1.83386i
$525$		0			0
$526$		0			0
$527$		0			0
$528$	1.43923	−	0.443943i	1.43923	−	0.443943i
$529$	0.826239	+	0.563320i	0.826239	+	0.563320i
$530$		0			0
$531$	1.45769	+	2.07079i	1.45769	+	2.07079i
$532$		0			0
$533$		0			0
$534$	−2.14492	−	2.11307i	−2.14492	−	2.11307i
$535$		0			0
$536$	0.0200196	+	1.33811i	0.0200196	+	1.33811i
$537$	−0.134904	+	3.00387i	−0.134904	+	3.00387i
$538$		0			0
$539$	−0.447313	+	0.894377i	−0.447313	+	0.894377i
$540$		0			0
$541$		0			0		0.887586	−	0.460642i	$-0.152381\pi$
$541$		0			0		−0.887586	+	0.460642i	$0.847619\pi$
$542$		0			0
$543$		0			0
$544$	1.65306	+	0.564588i	1.65306	+	0.564588i
$545$		0			0
$546$		0			0
$547$	0.618243	+	1.23614i	0.618243	+	1.23614i	0.955573	+	0.294755i	$0.0952381\pi$
$547$	0.618243	+	1.23614i	0.618243	+	1.23614i	−0.337330	+	0.941386i	$0.609524\pi$
$548$	−0.0675728	−	0.0590366i	−0.0675728	−	0.0590366i
$549$		0			0
$550$	−0.550897	−	0.834573i	−0.550897	−	0.834573i
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$		0			0
$556$	0.0376022	−	0.144653i	0.0376022	−	0.144653i
$557$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$557$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	1.92863	+	1.78950i	1.92863	+	1.78950i
$562$	−0.0763771	−	0.194606i	−0.0763771	−	0.194606i
$563$	−0.773418	−	1.80950i	−0.773418	−	1.80950i	−0.550897	−	0.834573i	$-0.685714\pi$
$563$	−0.773418	−	1.80950i	−0.773418	−	1.80950i	−0.222521	−	0.974928i	$-0.571429\pi$
$564$		0			0
$565$		0			0
$566$	−0.199769	+	1.90068i	−0.199769	+	1.90068i
$567$		0			0
$568$		0			0
$569$	−1.22207	−	0.945012i	−1.22207	−	0.945012i	−0.222521	−	0.974928i	$-0.571429\pi$
$569$	−1.22207	−	0.945012i	−1.22207	−	0.945012i	−0.999552	+	0.0299155i	$0.990476\pi$
$570$		0			0
$571$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.733052	−	0.680173i	$-0.761905\pi$
$571$	−1.23305	+	0.185853i	−1.23305	+	0.185853i	−0.500000	+	0.866025i	$0.666667\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.23230	+	0.300729i	1.23230	+	0.300729i
$577$	1.33390	+	1.31410i	1.33390	+	1.31410i	0.913545	+	0.406737i	$0.133333\pi$
$577$	1.33390	+	1.31410i	1.33390	+	1.31410i	0.420357	+	0.907359i	$0.361905\pi$
$578$	0.396439	+	2.01270i	0.396439	+	2.01270i
$579$	1.08108	−	1.53578i	1.08108	−	1.53578i
$580$		0			0
$581$		0			0
$582$	−2.42574	−	0.748241i	−2.42574	−	0.748241i
$583$		0			0
$584$	0.206722	+	0.0311583i	0.206722	+	0.0311583i
$585$		0			0
$586$		0			0
$587$	−0.0133831	+	0.894526i	−0.0133831	+	0.894526i	0.887586	+	0.460642i	$0.152381\pi$
$587$	−0.0133831	+	0.894526i	−0.0133831	+	0.894526i	−0.900969	+	0.433884i	$0.857143\pi$
$588$	−1.26926	+	0.810833i	−1.26926	+	0.810833i
$589$		0			0
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.843914	+	0.783038i	−0.843914	+	0.783038i	−0.978148	−	0.207912i	$-0.933333\pi$
$593$	−0.843914	+	0.783038i	−0.843914	+	0.783038i	0.134233	+	0.990950i	$0.457143\pi$
$594$	0.319869	+	0.247350i	0.319869	+	0.247350i
$595$		0			0
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$599$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$600$	−0.0675728	−	1.50463i	−0.0675728	−	1.50463i
$601$	0.155489	−	0.478546i	0.155489	−	0.478546i	−0.842721	−	0.538351i	$-0.819048\pi$
$601$	0.155489	−	0.478546i	0.155489	−	0.478546i	0.998210	+	0.0598042i	$0.0190476\pi$
$602$		0			0
$603$	−1.37334	+	0.997789i	−1.37334	+	0.997789i
$604$		0			0
$605$		0			0
$606$		0			0
$607$		0			0		−0.525684	−	0.850680i	$-0.676190\pi$
$607$		0			0		0.525684	+	0.850680i	$0.323810\pi$
$608$	−0.0292650	−	0.00622047i	−0.0292650	−	0.00622047i
$609$		0			0
$610$		0			0
$611$		0			0
$612$	0.621365	+	2.12687i	0.621365	+	2.12687i
$613$		0			0		0.858449	−	0.512899i	$-0.171429\pi$
$613$		0			0		−0.858449	+	0.512899i	$0.828571\pi$
$614$	0.275342	−	0.271253i	0.275342	−	0.271253i
$615$		0			0
$616$		0			0
$617$	−1.90345	+	0.587137i	−1.90345	+	0.587137i	−0.925304	+	0.379225i	$0.876190\pi$
$617$	−1.90345	+	0.587137i	−1.90345	+	0.587137i	−0.978148	+	0.207912i	$0.933333\pi$
$618$		0			0
$619$	−1.58865	+	0.651091i	−1.58865	+	0.651091i	−0.988831	−	0.149042i	$-0.952381\pi$
$619$	−1.58865	+	0.651091i	−1.58865	+	0.651091i	−0.599822	+	0.800134i	$0.704762\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.946327	+	0.323210i	−0.946327	+	0.323210i
$626$	−0.196800	−	0.182604i	−0.196800	−	0.182604i
$627$	−0.0364559	−	0.0264868i	−0.0364559	−	0.0264868i
$628$		0			0
$629$		0			0
$630$		0			0
$631$		0			0		−0.772417	−	0.635116i	$-0.780952\pi$
$631$		0			0		0.772417	+	0.635116i	$0.219048\pi$
$632$		0			0
$633$	1.26696	+	0.657534i	1.26696	+	0.657534i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.76803	+	0.159125i	−1.76803	+	0.159125i	−0.925304	−	0.379225i	$-0.876190\pi$
$641$	−1.76803	+	0.159125i	−1.76803	+	0.159125i	−0.842721	+	0.538351i	$0.819048\pi$
$642$	1.58068	−	0.0947005i	1.58068	−	0.0947005i
$643$	0.0538218	+	1.19844i	0.0538218	+	1.19844i	0.826239	+	0.563320i	$0.190476\pi$
$643$	0.0538218	+	1.19844i	0.0538218	+	1.19844i	−0.772417	+	0.635116i	$0.780952\pi$
$644$		0			0
$645$		0			0
$646$	−0.0161501	−	0.0497048i	−0.0161501	−	0.0497048i
$647$		0			0		−0.963963	−	0.266037i	$-0.914286\pi$
$647$		0			0		0.963963	+	0.266037i	$0.0857143\pi$
$648$	−0.240927	−	0.613873i	−0.240927	−	0.613873i
$649$	0.149193	−	1.99084i	0.149193	−	1.99084i
$650$		0			0
$651$		0			0
$652$	1.30011	−	1.44392i	1.30011	−	1.44392i
$653$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$653$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$654$		0			0
$655$		0			0
$656$	0.671944	+	0.0604761i	0.671944	+	0.0604761i
$657$	0.118619	+	0.237173i	0.118619	+	0.237173i
$658$		0			0
$659$	0.627253	−	1.59821i	0.627253	−	1.59821i	−0.163818	−	0.986491i	$-0.552381\pi$
$659$	0.627253	−	1.59821i	0.627253	−	1.59821i	0.791071	−	0.611724i	$-0.209524\pi$
$660$		0			0
$661$		0			0		−0.900969	−	0.433884i	$-0.857143\pi$
$661$		0			0		0.900969	+	0.433884i	$0.142857\pi$
$662$	−0.325352	−	0.383836i	−0.325352	−	0.383836i
$663$		0			0
$664$	1.68387	−	0.938878i	1.68387	−	0.938878i
$665$		0			0
$666$		0			0
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	0.336413	−	0.448759i	0.336413	−	0.448759i	−0.599822	−	0.800134i	$-0.704762\pi$
$673$	0.336413	−	0.448759i	0.336413	−	0.448759i	0.936235	+	0.351375i	$0.114286\pi$
$674$	−0.327049	−	0.0195940i	−0.327049	−	0.0195940i
$675$	0.319869	−	0.247350i	0.319869	−	0.247350i
$676$	0.887586	+	0.460642i	0.887586	+	0.460642i
$677$		0			0		0.393025	−	0.919528i	$-0.371429\pi$
$677$		0			0		−0.393025	+	0.919528i	$0.628571\pi$
$678$	−0.355087	−	1.21543i	−0.355087	−	1.21543i
$679$		0			0
$680$		0			0
$681$	0.673718	+	1.16691i	0.673718	+	1.16691i
$682$		0			0
$683$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	0.955573	+	0.294755i	$0.0952381\pi$
$683$	−0.0332580	+	0.443797i	−0.0332580	+	0.443797i	−0.988831	+	0.149042i	$0.952381\pi$
$684$	−0.0149157	−	0.0348970i	−0.0149157	−	0.0348970i
$685$		0			0
$686$		0			0
$687$		0			0
$688$	−0.873408	−	0.486989i	−0.873408	−	0.486989i
$689$		0			0
$690$		0			0
$691$	1.64861	+	1.05317i	1.64861	+	1.05317i	0.936235	+	0.351375i	$0.114286\pi$
$691$	1.64861	+	1.05317i	1.64861	+	1.05317i	0.712376	+	0.701798i	$0.247619\pi$
$692$		0			0
$693$		0			0
$694$	−0.420357	+	0.728080i	−0.420357	+	0.728080i
$695$		0			0
$696$		0			0
$697$	0.495394	+	1.06933i	0.495394	+	1.06933i
$698$		0			0
$699$	1.12036	−	2.62121i	1.12036	−	2.62121i
$700$		0			0
$701$		0			0		0.280427	−	0.959875i	$-0.409524\pi$
$701$		0			0		−0.280427	+	0.959875i	$0.590476\pi$
$702$		0			0
$703$		0			0
$704$	−0.599822	−	0.800134i	−0.599822	−	0.800134i
$705$		0			0
$706$	1.72456	−	0.895019i	1.72456	−	0.895019i
$707$		0			0
$708$	1.73082	−	2.45880i	1.73082	−	2.45880i
$709$		0			0		0.963963	−	0.266037i	$-0.0857143\pi$
$709$		0			0		−0.963963	+	0.266037i	$0.914286\pi$
$710$		0			0
$711$		0			0
$712$	−0.840338	+	1.81391i	−0.840338	+	1.81391i
$713$		0			0
$714$		0			0
$715$		0			0
$716$	1.90772	−	0.588455i	1.90772	−	0.588455i
$717$		0			0
$718$		0			0
$719$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$719$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$720$		0			0
$721$		0			0
$722$	−0.419981	−	0.906546i	−0.419981	−	0.906546i
$723$	−1.94894	−	2.03843i	−1.94894	−	2.03843i
$724$		0			0
$725$		0			0
$726$	−0.335148	−	1.46838i	−0.335148	−	1.46838i
$727$		0			0		0.222521	−	0.974928i	$-0.428571\pi$
$727$		0			0		−0.222521	+	0.974928i	$0.571429\pi$
$728$		0			0
$729$	0.796327	−	1.20638i	0.796327	−	1.20638i
$730$		0			0
$731$	−0.0261313	−	1.74662i	−0.0261313	−	1.74662i
$732$		0			0
$733$		0			0		0.936235	−	0.351375i	$-0.114286\pi$
$733$		0			0		−0.936235	+	0.351375i	$0.885714\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.33587	+	0.0800336i	1.33587	+	0.0800336i
$738$	0.427892	+	0.741130i	0.427892	+	0.741130i
$739$	−0.654946	+	1.21709i	−0.654946	+	1.21709i	0.309017	+	0.951057i	$0.400000\pi$
$739$	−0.654946	+	1.21709i	−0.654946	+	1.21709i	−0.963963	+	0.266037i	$0.914286\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		0			0		−0.887586	−	0.460642i	$-0.847619\pi$
$743$		0			0		0.887586	+	0.460642i	$0.152381\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2.20333	+	1.06107i	2.20333	+	1.06107i
$748$	0.686543	−	1.60625i	0.686543	−	1.60625i
$749$		0			0
$750$		0			0
$751$		0			0		−0.0149594	−	0.999888i	$-0.504762\pi$
$751$		0			0		0.0149594	+	0.999888i	$0.495238\pi$
$752$		0			0
$753$	1.45187	−	0.400690i	1.45187	−	0.400690i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		0			0		−0.646600	−	0.762830i	$-0.723810\pi$
$757$		0			0		0.646600	+	0.762830i	$0.276190\pi$
$758$	−0.453344	−	0.218319i	−0.453344	−	0.218319i
$759$		0			0
$760$		0			0
$761$	1.38151	−	0.0413469i	1.38151	−	0.0413469i	0.669131	−	0.743145i	$-0.266667\pi$
$761$	1.38151	−	0.0413469i	1.38151	−	0.0413469i	0.712376	+	0.701798i	$0.247619\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$	−0.157435	−	1.49789i	−0.157435	−	1.49789i
$769$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	0.0747301	+	0.997204i	$0.476190\pi$
$769$	−0.147791	+	1.97213i	−0.147791	+	1.97213i	−0.222521	+	0.974928i	$0.571429\pi$
$770$		0			0
$771$	1.00537	+	2.56163i	1.00537	+	2.56163i
$772$	−1.20204	−	0.331743i	−1.20204	−	0.331743i
$773$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$773$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$774$	−0.132591	−	1.26152i	−0.132591	−	1.26152i
$775$		0			0
$776$	0.0756171	+	1.68374i	0.0756171	+	1.68374i
$777$		0			0
$778$		0			0
$779$	−0.0106109	−	0.0171710i	−0.0106109	−	0.0171710i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	0.791071	+	0.611724i	0.791071	+	0.611724i
$785$		0			0
$786$	−2.47395	−	1.28394i	−2.47395	−	1.28394i
$787$	0.671944	+	1.87519i	0.671944	+	1.87519i	0.420357	+	0.907359i	$0.361905\pi$
$787$	0.671944	+	1.87519i	0.671944	+	1.87519i	0.251587	+	0.967835i	$0.419048\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		0			0
$792$	0.391978	−	1.20638i	0.391978	−	1.20638i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.599822	−	0.800134i	$-0.704762\pi$
$797$		0			0		0.599822	+	0.800134i	$0.295238\pi$
$798$		0			0
$799$		0			0
$800$	−0.925304	+	0.379225i	−0.925304	+	0.379225i
$801$	−2.49505	+	0.452784i	−2.49505	+	0.452784i
$802$	−0.0857432	+	0.0264483i	−0.0857432	+	0.0264483i
$803$	0.0465195	−	0.203815i	0.0465195	−	0.203815i
$804$	1.66538	+	1.13544i	1.66538	+	1.13544i
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.95994	−	0.355676i	−1.95994	−	0.355676i	−0.995974	−	0.0896393i	$-0.971429\pi$
$809$	−1.95994	−	0.355676i	−1.95994	−	0.355676i	−0.963963	−	0.266037i	$-0.914286\pi$
$810$		0			0
$811$	−1.78716	−	0.379874i	−1.78716	−	0.379874i	−0.809017	−	0.587785i	$-0.800000\pi$
$811$	−1.78716	−	0.379874i	−1.78716	−	0.379874i	−0.978148	+	0.207912i	$0.933333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$	2.12849	−	1.54644i	2.12849	−	1.54644i
$817$	0.00401610	+	0.0296480i	0.00401610	+	0.0296480i
$818$	0.510644	−	1.57160i	0.510644	−	1.57160i
$819$		0			0
$820$		0			0
$821$		0			0		−0.858449	−	0.512899i	$-0.828571\pi$
$821$		0			0		0.858449	+	0.512899i	$0.171429\pi$
$822$	−0.131293	+	0.0320404i	−0.131293	+	0.0320404i
$823$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$823$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$824$		0			0
$825$	−1.50547	−	0.0450570i	−1.50547	−	0.0450570i
$826$		0			0
$827$	0.189193	−	0.527981i	0.189193	−	0.527981i	−0.809017	−	0.587785i	$-0.800000\pi$
$827$	0.189193	−	0.527981i	0.189193	−	0.527981i	0.998210	+	0.0598042i	$0.0190476\pi$
$828$		0			0
$829$		0			0		0.163818	−	0.986491i	$-0.447619\pi$
$829$		0			0		−0.163818	+	0.986491i	$0.552381\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.234481	+	1.73101i	−0.234481	+	1.73101i
$834$	−0.145555	−	0.171719i	−0.145555	−	0.171719i
$835$		0			0
$836$	−0.00839005	+	0.0287183i	−0.00839005	+	0.0287183i
$837$		0			0
$838$	−0.0882877	+	1.96588i	−0.0882877	+	1.96588i
$839$		0			0		−0.936235	−	0.351375i	$-0.885714\pi$
$839$		0			0		0.936235	+	0.351375i	$0.114286\pi$
$840$		0			0
$841$	0.193256	+	0.981148i	0.193256	+	0.981148i
$842$		0			0
$843$	−0.305893	−	0.0746494i	−0.305893	−	0.0746494i
$844$	0.127218	−	0.939160i	0.127218	−	0.939160i
$845$		0			0
$846$		0			0
$847$		0			0
$848$		0			0
$849$	2.16768	+	1.89385i	2.16768	+	1.89385i
$850$	−1.38186	−	1.06857i	−1.38186	−	1.06857i
$851$		0			0
$852$		0			0
$853$		0			0		0.104528	−	0.994522i	$-0.466667\pi$
$853$		0			0		−0.104528	+	0.994522i	$0.533333\pi$
$854$		0			0
$855$		0			0
$856$	−0.413214	−	0.966762i	−0.413214	−	0.966762i
$857$	−0.287176	−	0.731713i	−0.287176	−	0.731713i	−0.999552	−	0.0299155i	$-0.990476\pi$
$857$	−0.287176	−	0.731713i	−0.287176	−	0.731713i	0.712376	−	0.701798i	$-0.247619\pi$
$858$		0			0
$859$	−1.85061			−1.85061			−0.925304	−	0.379225i	$-0.876190\pi$
$859$	−1.85061			−1.85061			−0.925304	+	0.379225i	$0.876190\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		0.251587	−	0.967835i	$-0.419048\pi$
$863$		0			0		−0.251587	+	0.967835i	$0.580952\pi$
$864$	0.304504	−	0.266037i	0.304504	−	0.266037i
$865$		0			0
$866$	1.35192	+	0.287360i	1.35192	+	0.287360i
$867$	2.82254	+	1.25667i	2.82254	+	1.25667i
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−1.69125	+	1.30782i	−1.69125	+	1.30782i
$874$		0			0
$875$		0			0
$876$	0.217595	−	0.227586i	0.217595	−	0.227586i
$877$		0			0		0.925304	−	0.379225i	$-0.123810\pi$
$877$		0			0		−0.925304	+	0.379225i	$0.876190\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.747966	+	0.937919i	−0.747966	+	0.937919i	−0.999552	−	0.0299155i	$-0.990476\pi$
$881$	−0.747966	+	0.937919i	−0.747966	+	0.937919i	0.251587	+	0.967835i	$0.419048\pi$
$882$	−0.0569095	+	1.26719i	−0.0569095	+	1.26719i
$883$	−0.0117588	−	0.785962i	−0.0117588	−	0.785962i	−0.925304	−	0.379225i	$-0.876190\pi$
$883$	−0.0117588	−	0.785962i	−0.0117588	−	0.785962i	0.913545	−	0.406737i	$-0.133333\pi$
$884$		0			0
$885$		0			0
$886$	1.03447	−	1.67402i	1.03447	−	1.67402i
$887$		0			0		0.691063	−	0.722795i	$-0.257143\pi$
$887$		0			0		−0.691063	+	0.722795i	$0.742857\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−0.630161	+	0.194379i	−0.630161	+	0.194379i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.42944	+	0.585840i	1.42944	+	0.585840i
$899$		0			0
$900$	−1.06896	−	0.682880i	−1.06896	−	0.682880i
$901$		0			0
$902$	0.110521	−	0.665546i	0.110521	−	0.665546i
$903$		0			0
$904$	−0.680152	+	0.494160i	−0.680152	+	0.494160i
$905$		0			0
$906$		0			0
$907$	1.19147	−	1.04095i	1.19147	−	1.04095i	0.193256	−	0.981148i	$-0.438095\pi$
$907$	1.19147	−	1.04095i	1.19147	−	1.04095i	0.998210	−	0.0598042i	$-0.0190476\pi$
$908$	0.578465	−	0.682447i	0.578465	−	0.682447i
$909$		0			0
$910$		0			0
$911$		0			0		0.473869	−	0.880596i	$-0.342857\pi$
$911$		0			0		−0.473869	+	0.880596i	$0.657143\pi$
$912$	−0.0330328	+	0.0306500i	−0.0330328	+	0.0306500i
$913$	−0.810418	−	1.74932i	−0.810418	−	1.74932i
$914$	0.287764	+	1.26078i	0.287764	+	1.26078i
$915$		0			0
$916$		0			0
$917$		0			0
$918$	0.668413	+	0.228291i	0.668413	+	0.228291i
$919$		0			0		−0.473869	−	0.880596i	$-0.657143\pi$
$919$		0			0		0.473869	+	0.880596i	$0.342857\pi$
$920$		0			0
$921$	−0.0953653	−	0.574278i	−0.0953653	−	0.574278i
$922$		0			0
$923$		0			0
$924$		0			0
$925$		0			0
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.02839	+	1.66418i	−1.02839	+	1.66418i	−0.337330	+	0.941386i	$0.609524\pi$
$929$	−1.02839	+	1.66418i	−1.02839	+	1.66418i	−0.691063	+	0.722795i	$0.742857\pi$
$930$		0			0
$931$	0.000447568	−	0.0299155i	0.000447568	−	0.0299155i
$932$	−1.88927	−	0.113189i	−1.88927	−	0.113189i
$933$		0			0
$934$	−1.63402	+	0.246289i	−1.63402	+	0.246289i
$935$		0			0
$936$		0			0
$937$	−0.298548	+	1.51571i	−0.298548	+	1.51571i	0.473869	+	0.880596i	$0.342857\pi$
$937$	−0.298548	+	1.51571i	−0.298548	+	1.51571i	−0.772417	+	0.635116i	$0.780952\pi$
$938$		0			0
$939$	−0.395513	+	0.0840689i	−0.395513	+	0.0840689i
$940$		0			0
$941$		0			0		0.646600	−	0.762830i	$-0.276190\pi$
$941$		0			0		−0.646600	+	0.762830i	$0.723810\pi$
$942$		0			0
$943$		0			0
$944$	−1.92447	−	0.531121i	−1.92447	−	0.531121i
$945$		0			0
$946$	−0.550897	+	0.834573i	−0.550897	+	0.834573i
$947$	1.15123			1.15123			0.575617	−	0.817719i	$-0.304762\pi$
$947$	1.15123			1.15123			0.575617	+	0.817719i	$0.304762\pi$
$948$		0			0
$949$		0			0
$950$	0.0256838	+	0.0153453i	0.0256838	+	0.0153453i
$951$		0			0
$952$		0			0
$953$	−1.92486	+	0.409141i	−1.92486	+	0.409141i	−0.925304	+	0.379225i	$0.876190\pi$
$953$	−1.92486	+	0.409141i	−1.92486	+	0.409141i	−0.999552	+	0.0299155i	$0.990476\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	0.0149594	−	0.999888i	0.0149594	−	0.999888i
$962$		0			0
$963$	0.701065	−	1.13449i	0.701065	−	1.13449i
$964$	−0.837580	+	1.67469i	−0.837580	+	1.67469i
$965$		0			0
$966$		0			0
$967$		0			0		0.623490	−	0.781831i	$-0.285714\pi$
$967$		0			0		−0.623490	+	0.781831i	$0.714286\pi$
$968$	−0.842721	+	0.538351i	−0.842721	+	0.538351i
$969$	−0.0752180	−	0.0232017i	−0.0752180	−	0.0232017i
$970$		0			0
$971$	0.295190	+	1.77759i	0.295190	+	1.77759i	0.575617	+	0.817719i	$0.304762\pi$
$971$	0.295190	+	1.77759i	0.295190	+	1.77759i	−0.280427	+	0.959875i	$0.590476\pi$
$972$	−1.35774	−	0.331341i	−1.35774	−	0.331341i
$973$		0			0
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.36145	−	1.34124i	1.36145	−	1.34124i	0.473869	−	0.880596i	$-0.342857\pi$
$977$	1.36145	−	1.34124i	1.36145	−	1.34124i	0.887586	−	0.460642i	$-0.152381\pi$
$978$	−0.651187	−	2.85303i	−0.651187	−	2.85303i
$979$	1.74603	+	0.973542i	1.74603	+	0.973542i
$980$		0			0
$981$		0			0
$982$	0.258627	−	0.287234i	0.258627	−	0.287234i
$983$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$983$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$984$	0.657032	−	0.775137i	0.657032	−	0.775137i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.623490	−	0.781831i	$-0.714286\pi$
$991$		0			0		0.623490	+	0.781831i	$0.285714\pi$
$992$		0			0
$993$	−0.754800	+	0.0679333i	−0.754800	+	0.0679333i
$994$		0			0
$995$		0			0
$996$	0.303523	−	2.88782i	0.303523	−	2.88782i
$997$		0			0		−0.134233	−	0.990950i	$-0.542857\pi$
$997$		0			0		0.134233	+	0.990950i	$0.457143\pi$
$998$	1.47208	+	0.820791i	1.47208	+	0.820791i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3784.1.em.b.883.1	yes	48
8.3	odd	2	CM	3784.1.em.b.883.1	yes	48
11.4	even	5		3784.1.em.a.2259.1	yes	48
43.15	even	21		3784.1.em.a.531.1	✓	48
88.59	odd	10		3784.1.em.a.2259.1	yes	48
344.187	odd	42		3784.1.em.a.531.1	✓	48
473.15	even	105	inner	3784.1.em.b.1907.1	yes	48
3784.1907	odd	210	inner	3784.1.em.b.1907.1	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3784.1.em.a.531.1	✓	48	43.15	even	21
3784.1.em.a.531.1	✓	48	344.187	odd	42
3784.1.em.a.2259.1	yes	48	11.4	even	5
3784.1.em.a.2259.1	yes	48	88.59	odd	10
3784.1.em.b.883.1	yes	48	1.1	even	1	trivial
3784.1.em.b.883.1	yes	48	8.3	odd	2	CM
3784.1.em.b.1907.1	yes	48	473.15	even	105	inner
3784.1.em.b.1907.1	yes	48	3784.1907	odd	210	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3784 = 2^{3} \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3784.em (of order \(210\), degree \(48\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.963963 - 0.266037i) q^{2} +(-1.16337 + 0.956575i) q^{3} +(0.858449 + 0.512899i) q^{4} +(1.37593 - 0.612604i) q^{6} +(-0.691063 - 0.722795i) q^{8} +(0.245139 - 1.24455i) q^{9} +O(q^{10})\)	\(q+(-0.963963 - 0.266037i) q^{2} +(-1.16337 + 0.956575i) q^{3} +(0.858449 + 0.512899i) q^{4} +(1.37593 - 0.612604i) q^{6} +(-0.691063 - 0.722795i) q^{8} +(0.245139 - 1.24455i) q^{9} +(-0.772417 + 0.635116i) q^{11} +(-1.48932 + 0.224479i) q^{12} +(0.473869 + 0.880596i) q^{16} +(-0.918273 + 1.48598i) q^{17} +(-0.567402 + 1.13449i) q^{18} +(0.0125766 - 0.0271471i) q^{19} +(0.913545 - 0.406737i) q^{22} +(1.49537 + 0.179825i) q^{24} +(-0.163818 - 0.986491i) q^{25} +(0.191608 + 0.356068i) q^{27} +(-0.222521 - 0.974928i) q^{32} +(0.291071 - 1.47775i) q^{33} +(1.28051 - 1.18814i) q^{34} +(0.848770 - 0.942654i) q^{36} +(-0.0193455 + 0.0228230i) q^{38} +(0.371668 - 0.563053i) q^{41} +(-0.842721 + 0.538351i) q^{43} +(-0.988831 + 0.149042i) q^{44} +(-1.39364 - 0.571168i) q^{48} +(0.913545 - 0.406737i) q^{49} +(-0.104528 + 0.994522i) q^{50} +(-0.353162 - 2.60714i) q^{51} +(-0.0899761 - 0.394211i) q^{54} +(0.0113370 + 0.0436126i) q^{57} +(-1.37965 + 1.44300i) q^{59} +(-0.0448648 + 0.998993i) q^{64} +(-0.673718 + 1.34706i) q^{66} +(-0.981015 - 0.910249i) q^{67} +(-1.55045 + 0.804658i) q^{68} +(-1.06896 + 0.682880i) q^{72} +(-0.165379 + 0.127885i) q^{73} +(1.13423 + 0.990950i) q^{75} +(0.0247201 - 0.0168539i) q^{76} +(0.610200 + 0.250084i) q^{81} +(-0.508067 + 0.443885i) q^{82} +(-0.485041 + 1.86591i) q^{83} +(0.955573 - 0.294755i) q^{86} +(0.992847 + 0.119394i) q^{88} +(-0.730355 - 1.86091i) q^{89} +(1.19147 + 0.921344i) q^{96} +(-1.26926 - 1.10892i) q^{97} +(-0.988831 + 0.149042i) q^{98} +(0.601087 + 1.11701i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9	\( 48 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 3 q^{6} + 2 q^{8} - 3 q^{9} - q^{11} - 2 q^{12} + 2 q^{16} + q^{17} + 2 q^{18} - 2 q^{19} + 6 q^{22} + 10 q^{24} - q^{25} - 2 q^{27} - 8 q^{32} - 25 q^{33} - 13 q^{34} + 9 q^{36} + q^{38} - 2 q^{41} - q^{43} + 4 q^{44} - 2 q^{48} + 6 q^{49} + 6 q^{50} + 8 q^{51} - 6 q^{54} - 8 q^{57} + 3 q^{59} + 2 q^{64} - 2 q^{66} + q^{67} + q^{68} - 3 q^{72} + q^{73} + 50 q^{75} + q^{76} - 28 q^{81} + 3 q^{82} - 25 q^{83} + 4 q^{86} - q^{88} + q^{89} - 2 q^{96} + 3 q^{97} + 4 q^{98} - 8 q^{99}+O(q^{100}) \) 48 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 3 * q^6 + 2 * q^8 - 3 * q^9 - q^11 - 2 * q^12 + 2 * q^16 + q^17 + 2 * q^18 - 2 * q^19 + 6 * q^22 + 10 * q^24 - q^25 - 2 * q^27 - 8 * q^32 - 25 * q^33 - 13 * q^34 + 9 * q^36 + q^38 - 2 * q^41 - q^43 + 4 * q^44 - 2 * q^48 + 6 * q^49 + 6 * q^50 + 8 * q^51 - 6 * q^54 - 8 * q^57 + 3 * q^59 + 2 * q^64 - 2 * q^66 + q^67 + q^68 - 3 * q^72 + q^73 + 50 * q^75 + q^76 - 28 * q^81 + 3 * q^82 - 25 * q^83 + 4 * q^86 - q^88 + q^89 - 2 * q^96 + 3 * q^97 + 4 * q^98 - 8 * q^99

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