LMFDB - Embedded newform 1110.2.i.k.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.i (of order $3$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{41})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 11x^{2} + 10x + 100 $ x^4 - x^3 + 11x^2 + 10x + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$1.85078 - 3.20565i$ of defining polynomial
Character	$\chi$	$=$	1110.211
Dual form			1110.2.i.k.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +2.00000 q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.20156 - 5.54527i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 - 0.866025i) q^{18} +(0.350781 - 0.607571i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.50000 + 2.59808i) q^{21} +(1.00000 + 1.73205i) q^{22} +5.40312 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +6.40312 q^{26} +1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +4.70156 q^{29} +(0.500000 - 0.866025i) q^{30} -1.70156 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(1.50000 + 2.59808i) q^{35} +1.00000 q^{36} +(-6.05234 - 0.607571i) q^{37} +0.701562 q^{38} +(3.20156 + 5.54527i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.701562 - 1.21514i) q^{41} +(-1.50000 + 2.59808i) q^{42} +3.70156 q^{43} +(-1.00000 + 1.73205i) q^{44} +1.00000 q^{45} +(2.70156 + 4.67924i) q^{46} -8.00000 q^{47} +1.00000 q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +(3.20156 + 5.54527i) q^{52} +(4.70156 + 8.14334i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(0.350781 + 0.607571i) q^{57} +(2.35078 + 4.07167i) q^{58} +(-1.00000 - 1.73205i) q^{59} +1.00000 q^{60} +(-1.70156 + 2.94719i) q^{61} +(-0.850781 - 1.47360i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(3.20156 + 5.54527i) q^{65} -2.00000 q^{66} +(2.14922 - 3.72256i) q^{67} -2.00000 q^{68} +(-2.70156 + 4.67924i) q^{69} +(-1.50000 + 2.59808i) q^{70} +(1.35078 - 2.33962i) q^{71} +(0.500000 + 0.866025i) q^{72} +11.7016 q^{73} +(-2.50000 - 5.54527i) q^{74} +1.00000 q^{75} +(0.350781 + 0.607571i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-3.20156 + 5.54527i) q^{78} +(-5.55234 + 9.61694i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +1.40312 q^{82} +(0.649219 + 1.12448i) q^{83} -3.00000 q^{84} -2.00000 q^{85} +(1.85078 + 3.20565i) q^{86} +(-2.35078 + 4.07167i) q^{87} -2.00000 q^{88} +(-5.70156 - 9.87540i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-9.60469 - 16.6358i) q^{91} +(-2.70156 + 4.67924i) q^{92} +(0.850781 - 1.47360i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(0.350781 + 0.607571i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.29844 q^{97} +(1.00000 - 1.73205i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 - 2 * q^9	$ 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{12} + 12 q^{14} - 2 q^{15} - 2 q^{16} + 4 q^{17} + 2 q^{18} - 5 q^{19} - 2 q^{20} + 6 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{27} + 6 q^{28} + 6 q^{29} + 2 q^{30} + 6 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 6 q^{35} + 4 q^{36} - 5 q^{37} - 10 q^{38} + 2 q^{40} - 10 q^{41} - 6 q^{42} + 2 q^{43} - 4 q^{44} + 4 q^{45} - 2 q^{46} - 32 q^{47} + 4 q^{48} - 4 q^{49} + 2 q^{50} - 8 q^{51} + 6 q^{53} + 2 q^{54} - 4 q^{55} - 6 q^{56} - 5 q^{57} + 3 q^{58} - 4 q^{59} + 4 q^{60} + 6 q^{61} + 3 q^{62} - 12 q^{63} + 4 q^{64} - 8 q^{66} + 15 q^{67} - 8 q^{68} + 2 q^{69} - 6 q^{70} - q^{71} + 2 q^{72} + 34 q^{73} - 10 q^{74} + 4 q^{75} - 5 q^{76} + 12 q^{77} - 3 q^{79} + 4 q^{80} - 2 q^{81} - 20 q^{82} + 9 q^{83} - 12 q^{84} - 8 q^{85} + q^{86} - 3 q^{87} - 8 q^{88} - 10 q^{89} + 2 q^{90} + 2 q^{92} - 3 q^{93} - 16 q^{94} - 5 q^{95} + 2 q^{96} - 46 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^12 + 12 * q^14 - 2 * q^15 - 2 * q^16 + 4 * q^17 + 2 * q^18 - 5 * q^19 - 2 * q^20 + 6 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^27 + 6 * q^28 + 6 * q^29 + 2 * q^30 + 6 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 + 6 * q^35 + 4 * q^36 - 5 * q^37 - 10 * q^38 + 2 * q^40 - 10 * q^41 - 6 * q^42 + 2 * q^43 - 4 * q^44 + 4 * q^45 - 2 * q^46 - 32 * q^47 + 4 * q^48 - 4 * q^49 + 2 * q^50 - 8 * q^51 + 6 * q^53 + 2 * q^54 - 4 * q^55 - 6 * q^56 - 5 * q^57 + 3 * q^58 - 4 * q^59 + 4 * q^60 + 6 * q^61 + 3 * q^62 - 12 * q^63 + 4 * q^64 - 8 * q^66 + 15 * q^67 - 8 * q^68 + 2 * q^69 - 6 * q^70 - q^71 + 2 * q^72 + 34 * q^73 - 10 * q^74 + 4 * q^75 - 5 * q^76 + 12 * q^77 - 3 * q^79 + 4 * q^80 - 2 * q^81 - 20 * q^82 + 9 * q^83 - 12 * q^84 - 8 * q^85 + q^86 - 3 * q^87 - 8 * q^88 - 10 * q^89 + 2 * q^90 + 2 * q^92 - 3 * q^93 - 16 * q^94 - 5 * q^95 + 2 * q^96 - 46 * q^97 + 4 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−1.00000			−0.408248
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	−0.429919	−	0.902867i	$-0.641458\pi$
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	0.996866	−	0.0791130i	$-0.0252088\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	3.20156	−	5.54527i	0.887954	−	1.53798i	0.0456630	−	0.998957i	$-0.485460\pi$
$13$	3.20156	−	5.54527i	0.887954	−	1.53798i	0.842291	−	0.539024i	$-0.181207\pi$
$14$	3.00000			0.801784
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	0.350781	−	0.607571i	0.0804747	−	0.139386i	−0.822979	−	0.568071i	$-0.807690\pi$
$19$	0.350781	−	0.607571i	0.0804747	−	0.139386i	0.903454	+	0.428685i	$0.141023\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	1.50000	+	2.59808i	0.327327	+	0.566947i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	5.40312			1.12663			0.563315	−	0.826242i	$-0.309526\pi$
$23$	5.40312			1.12663			0.563315	+	0.826242i	$0.309526\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	6.40312			1.25576
$27$	1.00000			0.192450
$28$	1.50000	+	2.59808i	0.283473	+	0.490990i
$29$	4.70156			0.873058			0.436529	−	0.899690i	$-0.356208\pi$
$29$	4.70156			0.873058			0.436529	+	0.899690i	$0.356208\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	−1.70156			−0.305610			−0.152805	−	0.988256i	$-0.548831\pi$
$31$	−1.70156			−0.305610			−0.152805	+	0.988256i	$0.548831\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	1.50000	+	2.59808i	0.253546	+	0.439155i
$36$	1.00000			0.166667
$37$	−6.05234	−	0.607571i	−0.994999	−	0.0998840i
$37$	−6.05234	−	0.607571i	−0.994999	−	0.0998840i
$38$	0.701562			0.113808
$39$	3.20156	+	5.54527i	0.512660	+	0.887954i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	0.701562	−	1.21514i	0.109566	−	0.189773i	−0.806029	−	0.591876i	$-0.798387\pi$
$41$	0.701562	−	1.21514i	0.109566	−	0.189773i	0.915594	+	0.402103i	$0.131721\pi$
$42$	−1.50000	+	2.59808i	−0.231455	+	0.400892i
$43$	3.70156			0.564483			0.282241	−	0.959343i	$-0.408922\pi$
$43$	3.70156			0.564483			0.282241	+	0.959343i	$0.408922\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	1.00000			0.149071
$46$	2.70156	+	4.67924i	0.398324	+	0.689917i
$47$	−8.00000			−1.16692			−0.583460	−	0.812142i	$-0.698301\pi$
$47$	−8.00000			−1.16692			−0.583460	+	0.812142i	$0.698301\pi$
$48$	1.00000			0.144338
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−2.00000			−0.280056
$52$	3.20156	+	5.54527i	0.443977	+	0.768990i
$53$	4.70156	+	8.14334i	0.645809	+	1.11857i	0.984114	+	0.177538i	$0.0568132\pi$
$53$	4.70156	+	8.14334i	0.645809	+	1.11857i	−0.338305	+	0.941037i	$0.609853\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$	0.350781	+	0.607571i	0.0464621	+	0.0804747i
$58$	2.35078	+	4.07167i	0.308673	+	0.534637i
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	0.793560	−	0.608492i	$-0.208225\pi$
$59$	−1.00000	−	1.73205i	−0.130189	−	0.225494i	−0.923749	+	0.382998i	$0.874892\pi$
$60$	1.00000			0.129099
$61$	−1.70156	+	2.94719i	−0.217863	+	0.377349i	−0.954154	−	0.299315i	$-0.903242\pi$
$61$	−1.70156	+	2.94719i	−0.217863	+	0.377349i	0.736292	+	0.676664i	$0.236575\pi$
$62$	−0.850781	−	1.47360i	−0.108049	−	0.187147i
$63$	−3.00000			−0.377964
$64$	1.00000			0.125000
$65$	3.20156	+	5.54527i	0.397105	+	0.687806i
$66$	−2.00000			−0.246183
$67$	2.14922	−	3.72256i	0.262569	−	0.454783i	−0.704355	−	0.709848i	$-0.748764\pi$
$67$	2.14922	−	3.72256i	0.262569	−	0.454783i	0.966924	+	0.255065i	$0.0820970\pi$
$68$	−2.00000			−0.242536
$69$	−2.70156	+	4.67924i	−0.325230	+	0.563315i
$70$	−1.50000	+	2.59808i	−0.179284	+	0.310530i
$71$	1.35078	−	2.33962i	0.160308	−	0.277662i	−0.774671	−	0.632364i	$-0.782085\pi$
$71$	1.35078	−	2.33962i	0.160308	−	0.277662i	0.934979	+	0.354703i	$0.115418\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	11.7016			1.36956			0.684782	−	0.728748i	$-0.259897\pi$
$73$	11.7016			1.36956			0.684782	+	0.728748i	$0.259897\pi$
$74$	−2.50000	−	5.54527i	−0.290619	−	0.644624i
$75$	1.00000			0.115470
$76$	0.350781	+	0.607571i	0.0402373	+	0.0696931i
$77$	3.00000	−	5.19615i	0.341882	−	0.592157i
$78$	−3.20156	+	5.54527i	−0.362506	+	0.627878i
$79$	−5.55234	+	9.61694i	−0.624687	+	1.08199i	0.363914	+	0.931433i	$0.381440\pi$
$79$	−5.55234	+	9.61694i	−0.624687	+	1.08199i	−0.988601	+	0.150558i	$0.951893\pi$
$80$	1.00000			0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.40312			0.154949
$83$	0.649219	+	1.12448i	0.0712610	+	0.123428i	0.899454	−	0.437015i	$-0.143964\pi$
$83$	0.649219	+	1.12448i	0.0712610	+	0.123428i	−0.828193	+	0.560443i	$0.810631\pi$
$84$	−3.00000			−0.327327
$85$	−2.00000			−0.216930
$86$	1.85078	+	3.20565i	0.199575	+	0.345674i
$87$	−2.35078	+	4.07167i	−0.252030	+	0.436529i
$88$	−2.00000			−0.213201
$89$	−5.70156	−	9.87540i	−0.604364	−	1.04679i	−0.992152	−	0.125041i	$-0.960094\pi$
$89$	−5.70156	−	9.87540i	−0.604364	−	1.04679i	0.387787	−	0.921749i	$-0.373240\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−9.60469	−	16.6358i	−1.00684	−	1.74391i
$92$	−2.70156	+	4.67924i	−0.281657	+	0.487845i
$93$	0.850781	−	1.47360i	0.0882219	−	0.152805i
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	0.350781	+	0.607571i	0.0359894	+	0.0623354i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−8.29844			−0.842579			−0.421289	−	0.906926i	$-0.638422\pi$
$97$	−8.29844			−0.842579			−0.421289	+	0.906926i	$0.638422\pi$
$98$	1.00000	−	1.73205i	0.101015	−	0.174964i
$99$	−1.00000	−	1.73205i	−0.100504	−	0.174078i
$100$	1.00000			0.100000
$101$	16.8062			1.67228			0.836142	−	0.548513i	$-0.184806\pi$
$101$	16.8062			1.67228			0.836142	+	0.548513i	$0.184806\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	14.1047			1.38978			0.694888	−	0.719118i	$-0.255454\pi$
$103$	14.1047			1.38978			0.694888	+	0.719118i	$0.255454\pi$
$104$	−3.20156	+	5.54527i	−0.313939	+	0.543758i
$105$	−3.00000			−0.292770
$106$	−4.70156	+	8.14334i	−0.456656	+	0.790952i
$107$	−1.70156	+	2.94719i	−0.164496	+	0.284916i	−0.936476	−	0.350731i	$-0.885933\pi$
$107$	−1.70156	+	2.94719i	−0.164496	+	0.284916i	0.771980	+	0.635647i	$0.219267\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−1.55234	−	2.68874i	−0.148688	−	0.257534i	0.782055	−	0.623209i	$-0.214172\pi$
$109$	−1.55234	−	2.68874i	−0.148688	−	0.257534i	−0.930743	+	0.365675i	$0.880838\pi$
$110$	−2.00000			−0.190693
$111$	3.55234	−	4.93770i	0.337173	−	0.468666i
$112$	−3.00000			−0.283473
$113$	3.64922	+	6.32063i	0.343290	+	0.594595i	0.985042	−	0.172317i	$-0.0551254\pi$
$113$	3.64922	+	6.32063i	0.343290	+	0.594595i	−0.641752	+	0.766912i	$0.721792\pi$
$114$	−0.350781	+	0.607571i	−0.0328537	+	0.0569042i
$115$	−2.70156	+	4.67924i	−0.251922	+	0.436342i
$116$	−2.35078	+	4.07167i	−0.218265	+	0.378045i
$117$	−6.40312			−0.591969
$118$	1.00000	−	1.73205i	0.0920575	−	0.159448i
$119$	6.00000			0.550019
$120$	0.500000	+	0.866025i	0.0456435	+	0.0790569i
$121$	−7.00000			−0.636364
$122$	−3.40312			−0.308104
$123$	0.701562	+	1.21514i	0.0632577	+	0.109566i
$124$	0.850781	−	1.47360i	0.0764024	−	0.132333i
$125$	1.00000			0.0894427
$126$	−1.50000	−	2.59808i	−0.133631	−	0.231455i
$127$	6.50000	+	11.2583i	0.576782	+	0.999015i	0.995846	+	0.0910585i	$0.0290250\pi$
$127$	6.50000	+	11.2583i	0.576782	+	0.999015i	−0.419064	+	0.907957i	$0.637642\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.85078	+	3.20565i	−0.162952	+	0.282241i
$130$	−3.20156	+	5.54527i	−0.280796	+	0.486352i
$131$	−3.70156	−	6.41129i	−0.323407	−	0.560157i	0.657782	−	0.753209i	$-0.271495\pi$
$131$	−3.70156	−	6.41129i	−0.323407	−	0.560157i	−0.981189	+	0.193051i	$0.938162\pi$
$132$	−1.00000	−	1.73205i	−0.0870388	−	0.150756i
$133$	−1.05234	−	1.82271i	−0.0912497	−	0.158049i
$134$	4.29844			0.371328
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	10.1047			0.863302			0.431651	−	0.902041i	$-0.357931\pi$
$137$	10.1047			0.863302			0.431651	+	0.902041i	$0.357931\pi$
$138$	−5.40312			−0.459944
$139$	−6.25391	−	10.8321i	−0.530449	−	0.918765i	−0.999369	−	0.0355243i	$-0.988690\pi$
$139$	−6.25391	−	10.8321i	−0.530449	−	0.918765i	0.468919	−	0.883241i	$-0.344643\pi$
$140$	−3.00000			−0.253546
$141$	4.00000	−	6.92820i	0.336861	−	0.583460i
$142$	2.70156			0.226710
$143$	6.40312	−	11.0905i	0.535456	−	0.927437i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.35078	+	4.07167i	−0.195222	+	0.338134i
$146$	5.85078	+	10.1339i	0.484214	+	0.838683i
$147$	2.00000			0.164957
$148$	3.55234	−	4.93770i	0.292001	−	0.405876i
$149$	−6.10469			−0.500115			−0.250058	−	0.968231i	$-0.580450\pi$
$149$	−6.10469			−0.500115			−0.250058	+	0.968231i	$0.580450\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	9.85078	−	17.0621i	0.801645	−	1.38849i	−0.116887	−	0.993145i	$-0.537292\pi$
$151$	9.85078	−	17.0621i	0.801645	−	1.38849i	0.918533	−	0.395345i	$-0.129375\pi$
$152$	−0.350781	+	0.607571i	−0.0284521	+	0.0492805i
$153$	1.00000	−	1.73205i	0.0808452	−	0.140028i
$154$	6.00000			0.483494
$155$	0.850781	−	1.47360i	0.0683364	−	0.118362i
$156$	−6.40312			−0.512660
$157$	6.20156	+	10.7414i	0.494939	+	0.857259i	0.999983	−	0.00583464i	$-0.00185724\pi$
$157$	6.20156	+	10.7414i	0.494939	+	0.857259i	−0.505044	+	0.863093i	$0.668524\pi$
$158$	−11.1047			−0.883441
$159$	−9.40312			−0.745716
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	8.10469	−	14.0377i	0.638739	−	1.10633i
$162$	−1.00000			−0.0785674
$163$	−9.40312	−	16.2867i	−0.736510	−	1.27567i	−0.954058	−	0.299622i	$-0.903139\pi$
$163$	−9.40312	−	16.2867i	−0.736510	−	1.27567i	0.217548	−	0.976050i	$-0.430194\pi$
$164$	0.701562	+	1.21514i	0.0547828	+	0.0948866i
$165$	−1.00000	−	1.73205i	−0.0778499	−	0.134840i
$166$	−0.649219	+	1.12448i	−0.0503892	+	0.0872766i
$167$	−1.29844	+	2.24896i	−0.100476	+	0.174030i	−0.911881	−	0.410455i	$-0.865370\pi$
$167$	−1.29844	+	2.24896i	−0.100476	+	0.174030i	0.811405	+	0.584485i	$0.198703\pi$
$168$	−1.50000	−	2.59808i	−0.115728	−	0.200446i
$169$	−14.0000	−	24.2487i	−1.07692	−	1.86529i
$170$	−1.00000	−	1.73205i	−0.0766965	−	0.132842i
$171$	−0.701562			−0.0536498
$172$	−1.85078	+	3.20565i	−0.141121	+	0.244428i
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$	−4.70156			−0.356425
$175$	−3.00000			−0.226779
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	2.00000			0.150329
$178$	5.70156	−	9.87540i	0.427350	−	0.740192i
$179$	−18.2094			−1.36103			−0.680516	−	0.732733i	$-0.738244\pi$
$179$	−18.2094			−1.36103			−0.680516	+	0.732733i	$0.738244\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	−3.55234	+	6.15284i	−0.264044	+	0.457337i	−0.967313	−	0.253587i	$-0.918390\pi$
$181$	−3.55234	+	6.15284i	−0.264044	+	0.457337i	0.703269	+	0.710924i	$0.251723\pi$
$182$	9.60469	−	16.6358i	0.711947	−	1.23313i
$183$	−1.70156	−	2.94719i	−0.125783	−	0.217863i
$184$	−5.40312			−0.398324
$185$	3.55234	−	4.93770i	0.261173	−	0.363027i
$186$	1.70156			0.124765
$187$	2.00000	+	3.46410i	0.146254	+	0.253320i
$188$	4.00000	−	6.92820i	0.291730	−	0.505291i
$189$	1.50000	−	2.59808i	0.109109	−	0.188982i
$190$	−0.350781	+	0.607571i	−0.0254483	+	0.0440778i
$191$	−3.40312			−0.246241			−0.123121	−	0.992392i	$-0.539290\pi$
$191$	−3.40312			−0.246241			−0.123121	+	0.992392i	$0.539290\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	3.10469			0.223480			0.111740	−	0.993737i	$-0.464358\pi$
$193$	3.10469			0.223480			0.111740	+	0.993737i	$0.464358\pi$
$194$	−4.14922	−	7.18666i	−0.297897	−	0.515972i
$195$	−6.40312			−0.458537
$196$	2.00000			0.142857
$197$	4.40312	+	7.62643i	0.313710	+	0.543361i	0.979162	−	0.203079i	$-0.0650948\pi$
$197$	4.40312	+	7.62643i	0.313710	+	0.543361i	−0.665453	+	0.746440i	$0.731761\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	2.89531			0.205243			0.102622	−	0.994720i	$-0.467277\pi$
$199$	2.89531			0.205243			0.102622	+	0.994720i	$0.467277\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	2.14922	+	3.72256i	0.151594	+	0.262569i
$202$	8.40312	+	14.5546i	0.591242	+	1.02406i
$203$	7.05234	−	12.2150i	0.494977	−	0.857326i
$204$	1.00000	−	1.73205i	0.0700140	−	0.121268i
$205$	0.701562	+	1.21514i	0.0489992	+	0.0848691i
$206$	7.05234	+	12.2150i	0.491360	+	0.851061i
$207$	−2.70156	−	4.67924i	−0.187772	−	0.325230i
$208$	−6.40312			−0.443977
$209$	0.701562	−	1.21514i	0.0485281	−	0.0840531i
$210$	−1.50000	−	2.59808i	−0.103510	−	0.179284i
$211$	−13.2094			−0.909371			−0.454685	−	0.890652i	$-0.650248\pi$
$211$	−13.2094			−0.909371			−0.454685	+	0.890652i	$0.650248\pi$
$212$	−9.40312			−0.645809
$213$	1.35078	+	2.33962i	0.0925540	+	0.160308i
$214$	−3.40312			−0.232633
$215$	−1.85078	+	3.20565i	−0.126222	+	0.218623i
$216$	−1.00000			−0.0680414
$217$	−2.55234	+	4.42079i	−0.173264	+	0.300103i
$218$	1.55234	−	2.68874i	0.105138	−	0.182104i
$219$	−5.85078	+	10.1339i	−0.395359	+	0.684782i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	12.8062			0.861441
$222$	6.05234	+	0.607571i	0.406207	+	0.0407775i
$223$	−24.5078			−1.64116			−0.820582	−	0.571529i	$-0.806351\pi$
$223$	−24.5078			−1.64116			−0.820582	+	0.571529i	$0.806351\pi$
$224$	−1.50000	−	2.59808i	−0.100223	−	0.173591i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−3.64922	+	6.32063i	−0.242742	+	0.420442i
$227$	8.75391	−	15.1622i	0.581017	−	1.00635i	−0.414342	−	0.910121i	$-0.635988\pi$
$227$	8.75391	−	15.1622i	0.581017	−	1.00635i	0.995359	−	0.0962299i	$-0.0306784\pi$
$228$	−0.701562			−0.0464621
$229$	−2.25391	+	3.90388i	−0.148942	+	0.257976i	−0.930837	−	0.365435i	$-0.880920\pi$
$229$	−2.25391	+	3.90388i	−0.148942	+	0.257976i	0.781895	+	0.623411i	$0.214254\pi$
$230$	−5.40312			−0.356271
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$	−4.70156			−0.308673
$233$	17.5078			1.14697			0.573487	−	0.819214i	$-0.305590\pi$
$233$	17.5078			1.14697			0.573487	+	0.819214i	$0.305590\pi$
$234$	−3.20156	−	5.54527i	−0.209293	−	0.362506i
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	2.00000			0.130189
$237$	−5.55234	−	9.61694i	−0.360663	−	0.624687i
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$	5.05234	+	8.75092i	0.326809	+	0.566050i	0.981877	−	0.189520i	$-0.0606933\pi$
$239$	5.05234	+	8.75092i	0.326809	+	0.566050i	−0.655068	+	0.755570i	$0.727360\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−7.55234	+	13.0810i	−0.486489	+	0.842624i	−0.999879	−	0.0155313i	$-0.995056\pi$
$241$	−7.55234	+	13.0810i	−0.486489	+	0.842624i	0.513390	+	0.858155i	$0.328389\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−1.70156	−	2.94719i	−0.108931	−	0.188675i
$245$	2.00000			0.127775
$246$	−0.701562	+	1.21514i	−0.0447300	+	0.0774746i
$247$	−2.24609	−	3.89035i	−0.142916	−	0.247537i
$248$	1.70156			0.108049
$249$	−1.29844			−0.0822852
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−4.80625			−0.303368			−0.151684	−	0.988429i	$-0.548470\pi$
$251$	−4.80625			−0.303368			−0.151684	+	0.988429i	$0.548470\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$	10.8062			0.679383
$254$	−6.50000	+	11.2583i	−0.407846	+	0.706410i
$255$	1.00000	−	1.73205i	0.0626224	−	0.108465i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	9.64922	+	16.7129i	0.601902	+	1.04252i	0.992533	+	0.121977i	$0.0389235\pi$
$257$	9.64922	+	16.7129i	0.601902	+	1.04252i	−0.390631	+	0.920547i	$0.627743\pi$
$258$	−3.70156			−0.230449
$259$	−10.6570	+	14.8131i	−0.662196	+	0.920441i
$260$	−6.40312			−0.397105
$261$	−2.35078	−	4.07167i	−0.145510	−	0.252030i
$262$	3.70156	−	6.41129i	0.228683	−	0.396091i
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	−0.895209	−	0.445647i	$-0.852974\pi$
$263$	−1.00000	+	1.73205i	−0.0616626	+	0.106803i	0.833546	+	0.552450i	$0.186307\pi$
$264$	1.00000	−	1.73205i	0.0615457	−	0.106600i
$265$	−9.40312			−0.577629
$266$	1.05234	−	1.82271i	0.0645233	−	0.111758i
$267$	11.4031			0.697860
$268$	2.14922	+	3.72256i	0.131284	+	0.227391i
$269$	−28.7016			−1.74997			−0.874983	−	0.484154i	$-0.839127\pi$
$269$	−28.7016			−1.74997			−0.874983	+	0.484154i	$0.839127\pi$
$270$	−1.00000			−0.0608581
$271$	−15.6570	−	27.1188i	−0.951097	−	1.64735i	−0.743058	−	0.669228i	$-0.766625\pi$
$271$	−15.6570	−	27.1188i	−0.951097	−	1.64735i	−0.208039	−	0.978120i	$-0.566708\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$	19.2094			1.16260
$274$	5.05234	+	8.75092i	0.305223	+	0.528662i
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$	−2.70156	−	4.67924i	−0.162615	−	0.281657i
$277$	−12.0523	+	20.8753i	−0.724155	+	1.25427i	0.235166	+	0.971955i	$0.424437\pi$
$277$	−12.0523	+	20.8753i	−0.724155	+	1.25427i	−0.959321	+	0.282318i	$0.908897\pi$
$278$	6.25391	−	10.8321i	0.375084	−	0.649665i
$279$	0.850781	+	1.47360i	0.0509349	+	0.0882219i
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	15.1047	+	26.1621i	0.901070	+	1.56070i	0.826107	+	0.563513i	$0.190550\pi$
$281$	15.1047	+	26.1621i	0.901070	+	1.56070i	0.0749627	+	0.997186i	$0.476116\pi$
$282$	8.00000			0.476393
$283$	7.25391	−	12.5641i	0.431200	−	0.746860i	−0.565777	−	0.824558i	$-0.691424\pi$
$283$	7.25391	−	12.5641i	0.431200	−	0.746860i	0.996977	+	0.0776981i	$0.0247570\pi$
$284$	1.35078	+	2.33962i	0.0801541	+	0.138831i
$285$	−0.701562			−0.0415570
$286$	12.8062			0.757249
$287$	−2.10469	−	3.64542i	−0.124236	−	0.215183i
$288$	−1.00000			−0.0589256
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−4.70156			−0.276085
$291$	4.14922	−	7.18666i	0.243232	−	0.421289i
$292$	−5.85078	+	10.1339i	−0.342391	+	0.593039i
$293$	−0.701562	+	1.21514i	−0.0409857	+	0.0709893i	−0.885791	−	0.464085i	$-0.846383\pi$
$293$	−0.701562	+	1.21514i	−0.0409857	+	0.0709893i	0.844805	+	0.535075i	$0.179716\pi$
$294$	1.00000	+	1.73205i	0.0583212	+	0.101015i
$295$	2.00000			0.116445
$296$	6.05234	+	0.607571i	0.351785	+	0.0353143i
$297$	2.00000			0.116052
$298$	−3.05234	−	5.28681i	−0.176817	−	0.306257i
$299$	17.2984	−	29.9618i	1.00039	−	1.73273i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	5.55234	−	9.61694i	0.320032	−	0.554311i
$302$	19.7016			1.13370
$303$	−8.40312	+	14.5546i	−0.482747	+	0.836142i
$304$	−0.701562			−0.0402373
$305$	−1.70156	−	2.94719i	−0.0974312	−	0.168756i
$306$	2.00000			0.114332
$307$	−29.1047			−1.66109			−0.830546	−	0.556950i	$-0.811972\pi$
$307$	−29.1047			−1.66109			−0.830546	+	0.556950i	$0.811972\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	−7.05234	+	12.2150i	−0.401194	+	0.694888i
$310$	1.70156			0.0966422
$311$	−10.0000	−	17.3205i	−0.567048	−	0.982156i	−0.996856	−	0.0792356i	$-0.974752\pi$
$311$	−10.0000	−	17.3205i	−0.567048	−	0.982156i	0.429808	−	0.902920i	$-0.358581\pi$
$312$	−3.20156	−	5.54527i	−0.181253	−	0.313939i
$313$	6.55234	+	11.3490i	0.370360	+	0.641483i	0.989621	−	0.143703i	$-0.0459009\pi$
$313$	6.55234	+	11.3490i	0.370360	+	0.641483i	−0.619261	+	0.785186i	$0.712568\pi$
$314$	−6.20156	+	10.7414i	−0.349974	+	0.606173i
$315$	1.50000	−	2.59808i	0.0845154	−	0.146385i
$316$	−5.55234	−	9.61694i	−0.312344	−	0.540995i
$317$	−14.4031	−	24.9469i	−0.808960	−	1.40116i	−0.913585	−	0.406648i	$-0.866698\pi$
$317$	−14.4031	−	24.9469i	−0.808960	−	1.40116i	0.104625	−	0.994512i	$-0.466636\pi$
$318$	−4.70156	−	8.14334i	−0.263651	−	0.456656i
$319$	9.40312			0.526474
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	−1.70156	−	2.94719i	−0.0949719	−	0.164496i
$322$	16.2094			0.903313
$323$	1.40312			0.0780719
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−6.40312			−0.355181
$326$	9.40312	−	16.2867i	0.520791	−	0.902036i
$327$	3.10469			0.171690
$328$	−0.701562	+	1.21514i	−0.0387373	+	0.0670950i
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$	1.00000	−	1.73205i	0.0550482	−	0.0953463i
$331$	−9.90312	−	17.1527i	−0.544325	−	0.942798i	−0.998649	−	0.0519620i	$-0.983453\pi$
$331$	−9.90312	−	17.1527i	−0.544325	−	0.942798i	0.454324	−	0.890836i	$-0.349881\pi$
$332$	−1.29844			−0.0712610
$333$	2.50000	+	5.54527i	0.136999	+	0.303879i
$334$	−2.59688			−0.142095
$335$	2.14922	+	3.72256i	0.117424	+	0.203385i
$336$	1.50000	−	2.59808i	0.0818317	−	0.141737i
$337$	−3.25391	+	5.63593i	−0.177252	+	0.307009i	−0.940938	−	0.338578i	$-0.890054\pi$
$337$	−3.25391	+	5.63593i	−0.177252	+	0.307009i	0.763687	+	0.645587i	$0.223387\pi$
$338$	14.0000	−	24.2487i	0.761500	−	1.31896i
$339$	−7.29844			−0.396397
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$	−3.40312			−0.184290
$342$	−0.350781	−	0.607571i	−0.0189681	−	0.0328537i
$343$	15.0000			0.809924
$344$	−3.70156			−0.199575
$345$	−2.70156	−	4.67924i	−0.145447	−	0.251922i
$346$	−2.00000	+	3.46410i	−0.107521	+	0.186231i
$347$	3.29844			0.177069			0.0885347	−	0.996073i	$-0.471782\pi$
$347$	3.29844			0.177069			0.0885347	+	0.996073i	$0.471782\pi$
$348$	−2.35078	−	4.07167i	−0.126015	−	0.218265i
$349$	−3.70156	−	6.41129i	−0.198140	−	0.343189i	0.749785	−	0.661681i	$-0.230157\pi$
$349$	−3.70156	−	6.41129i	−0.198140	−	0.343189i	−0.947925	+	0.318493i	$0.896823\pi$
$350$	−1.50000	−	2.59808i	−0.0801784	−	0.138873i
$351$	3.20156	−	5.54527i	0.170887	−	0.295985i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	6.35078	+	10.9999i	0.338018	+	0.585464i	0.984060	−	0.177838i	$-0.0569102\pi$
$353$	6.35078	+	10.9999i	0.338018	+	0.585464i	−0.646042	+	0.763302i	$0.723577\pi$
$354$	1.00000	+	1.73205i	0.0531494	+	0.0920575i
$355$	1.35078	+	2.33962i	0.0716920	+	0.124174i
$356$	11.4031			0.604364
$357$	−3.00000	+	5.19615i	−0.158777	+	0.275010i
$358$	−9.10469	−	15.7698i	−0.481198	−	0.833459i
$359$	−2.70156			−0.142583			−0.0712915	−	0.997456i	$-0.522712\pi$
$359$	−2.70156			−0.142583			−0.0712915	+	0.997456i	$0.522712\pi$
$360$	−1.00000			−0.0527046
$361$	9.25391	+	16.0282i	0.487048	+	0.843591i
$362$	−7.10469			−0.373414
$363$	3.50000	−	6.06218i	0.183702	−	0.318182i
$364$	19.2094			1.00684
$365$	−5.85078	+	10.1339i	−0.306244	+	0.530430i
$366$	1.70156	−	2.94719i	0.0889421	−	0.154052i
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	−0.724345	−	0.689438i	$-0.757858\pi$
$367$	4.50000	−	7.79423i	0.234898	−	0.406855i	0.959243	+	0.282582i	$0.0911910\pi$
$368$	−2.70156	−	4.67924i	−0.140829	−	0.243922i
$369$	−1.40312			−0.0730437
$370$	6.05234	+	0.607571i	0.314646	+	0.0315861i
$371$	28.2094			1.46456
$372$	0.850781	+	1.47360i	0.0441109	+	0.0764024i
$373$	−7.79844	+	13.5073i	−0.403788	+	0.699381i	−0.994180	−	0.107736i	$-0.965640\pi$
$373$	−7.79844	+	13.5073i	−0.403788	+	0.699381i	0.590392	+	0.807117i	$0.298973\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	8.00000			0.412568
$377$	15.0523	−	26.0714i	0.775235	−	1.34275i
$378$	3.00000			0.154303
$379$	−9.64922	−	16.7129i	−0.495647	−	0.858486i	0.504340	−	0.863505i	$-0.331736\pi$
$379$	−9.64922	−	16.7129i	−0.495647	−	0.858486i	−0.999987	+	0.00501904i	$0.998402\pi$
$380$	−0.701562			−0.0359894
$381$	−13.0000			−0.666010
$382$	−1.70156	−	2.94719i	−0.0870595	−	0.150791i
$383$	−4.10469	+	7.10953i	−0.209740	+	0.363280i	−0.951632	−	0.307239i	$-0.900595\pi$
$383$	−4.10469	+	7.10953i	−0.209740	+	0.363280i	0.741893	+	0.670519i	$0.233928\pi$
$384$	−1.00000			−0.0510310
$385$	3.00000	+	5.19615i	0.152894	+	0.264820i
$386$	1.55234	+	2.68874i	0.0790122	+	0.136853i
$387$	−1.85078	−	3.20565i	−0.0940805	−	0.162952i
$388$	4.14922	−	7.18666i	0.210645	−	0.364847i
$389$	−14.3508	+	24.8563i	−0.727613	+	1.26026i	0.230276	+	0.973125i	$0.426037\pi$
$389$	−14.3508	+	24.8563i	−0.727613	+	1.26026i	−0.957889	+	0.287138i	$0.907296\pi$
$390$	−3.20156	−	5.54527i	−0.162117	−	0.280796i
$391$	5.40312	+	9.35849i	0.273248	+	0.473279i
$392$	1.00000	+	1.73205i	0.0505076	+	0.0874818i
$393$	7.40312			0.373438
$394$	−4.40312	+	7.62643i	−0.221826	+	0.384214i
$395$	−5.55234	−	9.61694i	−0.279369	−	0.483881i
$396$	2.00000			0.100504
$397$	−11.7016			−0.587285			−0.293642	−	0.955915i	$-0.594867\pi$
$397$	−11.7016			−0.587285			−0.293642	+	0.955915i	$0.594867\pi$
$398$	1.44766	+	2.50742i	0.0725645	+	0.125685i
$399$	2.10469			0.105366
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$	−2.14922	+	3.72256i	−0.107193	+	0.185664i
$403$	−5.44766	+	9.43562i	−0.271367	+	0.470022i
$404$	−8.40312	+	14.5546i	−0.418071	+	0.724120i
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	14.1047			0.700004
$407$	−12.1047	−	1.21514i	−0.600007	−	0.0602323i
$408$	2.00000			0.0990148
$409$	10.7984	+	18.7034i	0.533948	+	0.924826i	0.999213	+	0.0396543i	$0.0126257\pi$
$409$	10.7984	+	18.7034i	0.533948	+	0.924826i	−0.465265	+	0.885171i	$0.654041\pi$
$410$	−0.701562	+	1.21514i	−0.0346477	+	0.0600115i
$411$	−5.05234	+	8.75092i	−0.249214	+	0.431651i
$412$	−7.05234	+	12.2150i	−0.347444	+	0.601791i
$413$	−6.00000			−0.295241
$414$	2.70156	−	4.67924i	0.132775	−	0.229972i
$415$	−1.29844			−0.0637378
$416$	−3.20156	−	5.54527i	−0.156969	−	0.271879i
$417$	12.5078			0.612510
$418$	1.40312			0.0686290
$419$	9.10469	+	15.7698i	0.444793	+	0.770404i	0.998038	−	0.0626146i	$-0.0199439\pi$
$419$	9.10469	+	15.7698i	0.444793	+	0.770404i	−0.553245	+	0.833019i	$0.686611\pi$
$420$	1.50000	−	2.59808i	0.0731925	−	0.126773i
$421$	12.5969			0.613934			0.306967	−	0.951720i	$-0.400686\pi$
$421$	12.5969			0.613934			0.306967	+	0.951720i	$0.400686\pi$
$422$	−6.60469	−	11.4397i	−0.321511	−	0.556874i
$423$	4.00000	+	6.92820i	0.194487	+	0.336861i
$424$	−4.70156	−	8.14334i	−0.228328	−	0.395476i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$	−1.35078	+	2.33962i	−0.0654456	+	0.113355i
$427$	5.10469	+	8.84158i	0.247033	+	0.427874i
$428$	−1.70156	−	2.94719i	−0.0822481	−	0.142458i
$429$	6.40312	+	11.0905i	0.309146	+	0.535456i
$430$	−3.70156			−0.178505
$431$	−19.0523	+	32.9996i	−0.917719	+	1.58954i	−0.114848	+	0.993383i	$0.536638\pi$
$431$	−19.0523	+	32.9996i	−0.917719	+	1.58954i	−0.802871	+	0.596153i	$0.796695\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	19.4031			0.932455			0.466227	−	0.884665i	$-0.345613\pi$
$433$	19.4031			0.932455			0.466227	+	0.884665i	$0.345613\pi$
$434$	−5.10469			−0.245033
$435$	−2.35078	−	4.07167i	−0.112711	−	0.195222i
$436$	3.10469			0.148688
$437$	1.89531	−	3.28278i	0.0906651	−	0.157037i
$438$	−11.7016			−0.559122
$439$	−1.44766	+	2.50742i	−0.0690929	+	0.119672i	−0.898502	−	0.438969i	$-0.855344\pi$
$439$	−1.44766	+	2.50742i	−0.0690929	+	0.119672i	0.829409	+	0.558641i	$0.188677\pi$
$440$	1.00000	−	1.73205i	0.0476731	−	0.0825723i
$441$	−1.00000	+	1.73205i	−0.0476190	+	0.0824786i
$442$	6.40312	+	11.0905i	0.304566	+	0.527523i
$443$	−17.5078			−0.831821			−0.415911	−	0.909406i	$-0.636537\pi$
$443$	−17.5078			−0.831821			−0.415911	+	0.909406i	$0.636537\pi$
$444$	2.50000	+	5.54527i	0.118645	+	0.263167i
$445$	11.4031			0.540560
$446$	−12.2539	−	21.2244i	−0.580239	−	1.00500i
$447$	3.05234	−	5.28681i	0.144371	−	0.250058i
$448$	1.50000	−	2.59808i	0.0708683	−	0.122748i
$449$	8.00000	−	13.8564i	0.377543	−	0.653924i	−0.613161	−	0.789958i	$-0.710102\pi$
$449$	8.00000	−	13.8564i	0.377543	−	0.653924i	0.990704	+	0.136034i	$0.0434356\pi$
$450$	−1.00000			−0.0471405
$451$	1.40312	−	2.43028i	0.0660705	−	0.114438i
$452$	−7.29844			−0.343290
$453$	9.85078	+	17.0621i	0.462830	+	0.801645i
$454$	17.5078			0.821682
$455$	19.2094			0.900549
$456$	−0.350781	−	0.607571i	−0.0164268	−	0.0284521i
$457$	−9.80625	+	16.9849i	−0.458717	+	0.794521i	−0.998893	−	0.0470307i	$-0.985024\pi$
$457$	−9.80625	+	16.9849i	−0.458717	+	0.794521i	0.540176	+	0.841552i	$0.318357\pi$
$458$	−4.50781			−0.210636
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$	−2.70156	−	4.67924i	−0.125961	−	0.218171i
$461$	3.35078	+	5.80372i	0.156061	+	0.270306i	0.933445	−	0.358721i	$-0.116787\pi$
$461$	3.35078	+	5.80372i	0.156061	+	0.270306i	−0.777384	+	0.629027i	$0.783454\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	−10.2016	+	17.6696i	−0.474107	+	0.821177i	−0.999560	−	0.0296451i	$-0.990562\pi$
$463$	−10.2016	+	17.6696i	−0.474107	+	0.821177i	0.525454	+	0.850822i	$0.323896\pi$
$464$	−2.35078	−	4.07167i	−0.109132	−	0.189023i
$465$	0.850781	+	1.47360i	0.0394540	+	0.0683364i
$466$	8.75391	+	15.1622i	0.405517	+	0.702376i
$467$	−22.9109			−1.06019			−0.530096	−	0.847938i	$-0.677844\pi$
$467$	−22.9109			−1.06019			−0.530096	+	0.847938i	$0.677844\pi$
$468$	3.20156	−	5.54527i	0.147992	−	0.256330i
$469$	−6.44766	−	11.1677i	−0.297725	−	0.515675i
$470$	8.00000			0.369012
$471$	−12.4031			−0.571506
$472$	1.00000	+	1.73205i	0.0460287	+	0.0797241i
$473$	7.40312			0.340396
$474$	5.55234	−	9.61694i	0.255028	−	0.441721i
$475$	−0.701562			−0.0321899
$476$	−3.00000	+	5.19615i	−0.137505	+	0.238165i
$477$	4.70156	−	8.14334i	0.215270	−	0.372858i
$478$	−5.05234	+	8.75092i	−0.231089	+	0.400258i
$479$	3.40312	+	5.89438i	0.155493	+	0.269321i	0.933238	−	0.359258i	$-0.116970\pi$
$479$	3.40312	+	5.89438i	0.155493	+	0.269321i	−0.777746	+	0.628579i	$0.783637\pi$
$480$	−1.00000			−0.0456435
$481$	−22.7461	+	31.6167i	−1.03713	+	1.44160i
$482$	−15.1047			−0.688000
$483$	8.10469	+	14.0377i	0.368776	+	0.638739i
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	4.14922	−	7.18666i	0.188406	−	0.326329i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	26.3141			1.19240			0.596202	−	0.802835i	$-0.296676\pi$
$487$	26.3141			1.19240			0.596202	+	0.802835i	$0.296676\pi$
$488$	1.70156	−	2.94719i	0.0770261	−	0.133413i
$489$	18.8062			0.850448
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	−33.4031			−1.50746			−0.753731	−	0.657183i	$-0.771748\pi$
$491$	−33.4031			−1.50746			−0.753731	+	0.657183i	$0.771748\pi$
$492$	−1.40312			−0.0632577
$493$	4.70156	+	8.14334i	0.211748	+	0.366758i
$494$	2.24609	−	3.89035i	0.101057	−	0.175035i
$495$	2.00000			0.0898933
$496$	0.850781	+	1.47360i	0.0382012	+	0.0661664i
$497$	−4.05234	−	7.01886i	−0.181772	−	0.314839i
$498$	−0.649219	−	1.12448i	−0.0290922	−	0.0503892i
$499$	1.05234	−	1.82271i	0.0471094	−	0.0815958i	−0.841509	−	0.540243i	$-0.818332\pi$
$499$	1.05234	−	1.82271i	0.0471094	−	0.0815958i	0.888619	+	0.458647i	$0.151666\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	−1.29844	−	2.24896i	−0.0580099	−	0.100476i
$502$	−2.40312	−	4.16233i	−0.107257	−	0.185774i
$503$	7.80625	+	13.5208i	0.348063	+	0.602864i	0.985905	−	0.167304i	$-0.0535061\pi$
$503$	7.80625	+	13.5208i	0.348063	+	0.602864i	−0.637842	+	0.770167i	$0.720173\pi$
$504$	3.00000			0.133631
$505$	−8.40312	+	14.5546i	−0.373934	+	0.647673i
$506$	5.40312	+	9.35849i	0.240198	+	0.416035i
$507$	28.0000			1.24352
$508$	−13.0000			−0.576782
$509$	13.0523	+	22.6073i	0.578535	+	1.00205i	0.995648	+	0.0931972i	$0.0297087\pi$
$509$	13.0523	+	22.6073i	0.578535	+	1.00205i	−0.417113	+	0.908855i	$0.636958\pi$
$510$	2.00000			0.0885615
$511$	17.5523	−	30.4016i	0.776470	−	1.34489i
$512$	−1.00000			−0.0441942
$513$	0.350781	−	0.607571i	0.0154874	−	0.0268249i
$514$	−9.64922	+	16.7129i	−0.425609	+	0.737176i
$515$	−7.05234	+	12.2150i	−0.310763	+	0.538258i
$516$	−1.85078	−	3.20565i	−0.0814761	−	0.141121i
$517$	−16.0000			−0.703679
$518$	−18.1570	−	1.82271i	−0.797774	−	0.0800854i
$519$	−4.00000			−0.175581
$520$	−3.20156	−	5.54527i	−0.140398	−	0.243176i
$521$	4.29844	−	7.44511i	0.188318	−	0.326176i	−0.756372	−	0.654142i	$-0.773030\pi$
$521$	4.29844	−	7.44511i	0.188318	−	0.326176i	0.944690	+	0.327966i	$0.106363\pi$
$522$	2.35078	−	4.07167i	0.102891	−	0.178212i
$523$	8.85078	−	15.3300i	0.387018	−	0.670334i	−0.605029	−	0.796203i	$-0.706839\pi$
$523$	8.85078	−	15.3300i	0.387018	−	0.670334i	0.992047	+	0.125869i	$0.0401719\pi$
$524$	7.40312			0.323407
$525$	1.50000	−	2.59808i	0.0654654	−	0.113389i
$526$	−2.00000			−0.0872041
$527$	−1.70156	−	2.94719i	−0.0741212	−	0.128382i
$528$	2.00000			0.0870388
$529$	6.19375			0.269294
$530$	−4.70156	−	8.14334i	−0.204223	−	0.353724i
$531$	−1.00000	+	1.73205i	−0.0433963	+	0.0751646i
$532$	2.10469			0.0912497
$533$	−4.49219	−	7.78070i	−0.194578	−	0.337020i
$534$	5.70156	+	9.87540i	0.246731	+	0.427350i
$535$	−1.70156	−	2.94719i	−0.0735649	−	0.127418i
$536$	−2.14922	+	3.72256i	−0.0928321	+	0.160790i
$537$	9.10469	−	15.7698i	0.392896	−	0.680516i
$538$	−14.3508	−	24.8563i	−0.618706	−	1.07163i
$539$	−2.00000	−	3.46410i	−0.0861461	−	0.149209i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	20.5078			0.881700			0.440850	−	0.897581i	$-0.354677\pi$
$541$	20.5078			0.881700			0.440850	+	0.897581i	$0.354677\pi$
$542$	15.6570	−	27.1188i	0.672527	−	1.16485i
$543$	−3.55234	−	6.15284i	−0.152446	−	0.264044i
$544$	2.00000			0.0857493
$545$	3.10469			0.132990
$546$	9.60469	+	16.6358i	0.411043	+	0.711947i
$547$	−13.1047			−0.560316			−0.280158	−	0.959954i	$-0.590387\pi$
$547$	−13.1047			−0.560316			−0.280158	+	0.959954i	$0.590387\pi$
$548$	−5.05234	+	8.75092i	−0.215825	+	0.373821i
$549$	3.40312			0.145242
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	1.64922	−	2.85653i	0.0702591	−	0.121692i
$552$	2.70156	−	4.67924i	0.114986	−	0.199162i
$553$	16.6570	+	28.8508i	0.708329	+	1.22686i
$554$	−24.1047			−1.02411
$555$	2.50000	+	5.54527i	0.106119	+	0.235384i
$556$	12.5078			0.530449
$557$	−11.8062	−	20.4490i	−0.500247	−	0.866453i	−1.00000		0.000285007i	$-0.999909\pi$
$557$	−11.8062	−	20.4490i	−0.500247	−	0.866453i	0.499753	−	0.866168i	$-0.333424\pi$
$558$	−0.850781	+	1.47360i	−0.0360164	+	0.0623823i
$559$	11.8508	−	20.5262i	0.501235	−	0.868164i
$560$	1.50000	−	2.59808i	0.0633866	−	0.109789i
$561$	−4.00000			−0.168880
$562$	−15.1047	+	26.1621i	−0.637153	+	1.10358i
$563$	−14.1047			−0.594442			−0.297221	−	0.954809i	$-0.596060\pi$
$563$	−14.1047			−0.594442			−0.297221	+	0.954809i	$0.596060\pi$
$564$	4.00000	+	6.92820i	0.168430	+	0.291730i
$565$	−7.29844			−0.307048
$566$	14.5078			0.609809
$567$	1.50000	+	2.59808i	0.0629941	+	0.109109i
$568$	−1.35078	+	2.33962i	−0.0566775	+	0.0981683i
$569$	16.8062			0.704555			0.352277	−	0.935896i	$-0.385407\pi$
$569$	16.8062			0.704555			0.352277	+	0.935896i	$0.385407\pi$
$570$	−0.350781	−	0.607571i	−0.0146926	−	0.0254483i
$571$	22.2016	+	38.4542i	0.929106	+	1.60926i	0.784820	+	0.619724i	$0.212755\pi$
$571$	22.2016	+	38.4542i	0.929106	+	1.60926i	0.144286	+	0.989536i	$0.453911\pi$
$572$	6.40312	+	11.0905i	0.267728	+	0.463719i
$573$	1.70156	−	2.94719i	0.0710838	−	0.123121i
$574$	2.10469	−	3.64542i	0.0878479	−	0.152157i
$575$	−2.70156	−	4.67924i	−0.112663	−	0.195138i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−3.10469	−	5.37747i	−0.129250	−	0.223867i	0.794136	−	0.607740i	$-0.207924\pi$
$577$	−3.10469	−	5.37747i	−0.129250	−	0.223867i	−0.923386	+	0.383872i	$0.874590\pi$
$578$	13.0000			0.540729
$579$	−1.55234	+	2.68874i	−0.0645132	+	0.111740i
$580$	−2.35078	−	4.07167i	−0.0976109	−	0.169067i
$581$	3.89531			0.161605
$582$	8.29844			0.343981
$583$	9.40312	+	16.2867i	0.389438	+	0.674526i
$584$	−11.7016			−0.484214
$585$	3.20156	−	5.54527i	0.132368	−	0.229269i
$586$	−1.40312			−0.0579625
$587$	15.4555	−	26.7697i	0.637915	−	1.10490i	−0.347974	−	0.937504i	$-0.613130\pi$
$587$	15.4555	−	26.7697i	0.637915	−	1.10490i	0.985889	−	0.167398i	$-0.0535364\pi$
$588$	−1.00000	+	1.73205i	−0.0412393	+	0.0714286i
$589$	−0.596876	+	1.03382i	−0.0245938	+	0.0425978i
$590$	1.00000	+	1.73205i	0.0411693	+	0.0713074i
$591$	−8.80625			−0.362241
$592$	2.50000	+	5.54527i	0.102749	+	0.227909i
$593$	−26.5969			−1.09220			−0.546101	−	0.837719i	$-0.683889\pi$
$593$	−26.5969			−1.09220			−0.546101	+	0.837719i	$0.683889\pi$
$594$	1.00000	+	1.73205i	0.0410305	+	0.0710669i
$595$	−3.00000	+	5.19615i	−0.122988	+	0.213021i
$596$	3.05234	−	5.28681i	0.125029	−	0.216556i
$597$	−1.44766	+	2.50742i	−0.0592486	+	0.102622i
$598$	34.5969			1.41477
$599$	−9.05234	+	15.6791i	−0.369869	+	0.640631i	−0.989545	−	0.144226i	$-0.953931\pi$
$599$	−9.05234	+	15.6791i	−0.369869	+	0.640631i	0.619676	+	0.784858i	$0.287264\pi$
$600$	−1.00000			−0.0408248
$601$	−20.0602	−	34.7452i	−0.818271	−	1.41729i	−0.906955	−	0.421227i	$-0.861600\pi$
$601$	−20.0602	−	34.7452i	−0.818271	−	1.41729i	0.0886846	−	0.996060i	$-0.471734\pi$
$602$	11.1047			0.452593
$603$	−4.29844			−0.175046
$604$	9.85078	+	17.0621i	0.400823	+	0.694245i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$	−16.8062			−0.682707
$607$	19.7539	+	34.2148i	0.801786	+	1.38873i	0.918439	+	0.395562i	$0.129450\pi$
$607$	19.7539	+	34.2148i	0.801786	+	1.38873i	−0.116653	+	0.993173i	$0.537217\pi$
$608$	−0.350781	−	0.607571i	−0.0142261	−	0.0246402i
$609$	7.05234	+	12.2150i	0.285775	+	0.494977i
$610$	1.70156	−	2.94719i	0.0688942	−	0.119328i
$611$	−25.6125	+	44.3621i	−1.03617	+	1.79470i
$612$	1.00000	+	1.73205i	0.0404226	+	0.0700140i
$613$	−22.7539	−	39.4109i	−0.919022	−	1.59179i	−0.800904	−	0.598792i	$-0.795647\pi$
$613$	−22.7539	−	39.4109i	−0.919022	−	1.59179i	−0.118117	−	0.993000i	$-0.537686\pi$
$614$	−14.5523	−	25.2054i	−0.587285	−	1.01721i
$615$	−1.40312			−0.0565794
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	21.1570	+	36.6451i	0.851750	+	1.47527i	0.879628	+	0.475663i	$0.157792\pi$
$617$	21.1570	+	36.6451i	0.851750	+	1.47527i	−0.0278778	+	0.999611i	$0.508875\pi$
$618$	−14.1047			−0.567374
$619$	−43.3141			−1.74094			−0.870470	−	0.492222i	$-0.836185\pi$
$619$	−43.3141			−1.74094			−0.870470	+	0.492222i	$0.836185\pi$
$620$	0.850781	+	1.47360i	0.0341682	+	0.0591810i
$621$	5.40312			0.216820
$622$	10.0000	−	17.3205i	0.400963	−	0.694489i
$623$	−34.2094			−1.37057
$624$	3.20156	−	5.54527i	0.128165	−	0.221988i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−6.55234	+	11.3490i	−0.261884	+	0.453597i
$627$	0.701562	+	1.21514i	0.0280177	+	0.0485281i
$628$	−12.4031			−0.494939
$629$	−5.00000	−	11.0905i	−0.199363	−	0.442209i
$630$	3.00000			0.119523
$631$	6.95547	+	12.0472i	0.276893	+	0.479592i	0.970611	−	0.240654i	$-0.0773620\pi$
$631$	6.95547	+	12.0472i	0.276893	+	0.479592i	−0.693718	+	0.720247i	$0.744029\pi$
$632$	5.55234	−	9.61694i	0.220860	−	0.382541i
$633$	6.60469	−	11.4397i	0.262513	−	0.454685i
$634$	14.4031	−	24.9469i	0.572021	−	0.990770i
$635$	−13.0000			−0.515889
$636$	4.70156	−	8.14334i	0.186429	−	0.322905i
$637$	−12.8062			−0.507402
$638$	4.70156	+	8.14334i	0.186137	+	0.322398i
$639$	−2.70156			−0.106872
$640$	−1.00000			−0.0395285
$641$	20.0000	+	34.6410i	0.789953	+	1.36824i	0.925995	+	0.377535i	$0.123228\pi$
$641$	20.0000	+	34.6410i	0.789953	+	1.36824i	−0.136043	+	0.990703i	$0.543438\pi$
$642$	1.70156	−	2.94719i	0.0671553	−	0.116316i
$643$	37.1047			1.46327			0.731633	−	0.681699i	$-0.238759\pi$
$643$	37.1047			1.46327			0.731633	+	0.681699i	$0.238759\pi$
$644$	8.10469	+	14.0377i	0.319369	+	0.553164i
$645$	−1.85078	−	3.20565i	−0.0728744	−	0.126222i
$646$	0.701562	+	1.21514i	0.0276026	+	0.0478091i
$647$	−0.403124	+	0.698232i	−0.0158484	+	0.0274503i	−0.873841	−	0.486212i	$-0.838378\pi$
$647$	−0.403124	+	0.698232i	−0.0158484	+	0.0274503i	0.857992	+	0.513662i	$0.171712\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−2.00000	−	3.46410i	−0.0785069	−	0.135978i
$650$	−3.20156	−	5.54527i	−0.125576	−	0.217503i
$651$	−2.55234	−	4.42079i	−0.100034	−	0.173264i
$652$	18.8062			0.736510
$653$	−17.0000	+	29.4449i	−0.665261	+	1.15227i	0.313953	+	0.949439i	$0.398347\pi$
$653$	−17.0000	+	29.4449i	−0.665261	+	1.15227i	−0.979214	+	0.202828i	$0.934987\pi$
$654$	1.55234	+	2.68874i	0.0607014	+	0.105138i
$655$	7.40312			0.289264
$656$	−1.40312			−0.0547828
$657$	−5.85078	−	10.1339i	−0.228261	−	0.395359i
$658$	−24.0000			−0.935617
$659$	−22.4031	+	38.8033i	−0.872702	+	1.51156i	−0.0135109	+	0.999909i	$0.504301\pi$
$659$	−22.4031	+	38.8033i	−0.872702	+	1.51156i	−0.859191	+	0.511655i	$0.829033\pi$
$660$	2.00000			0.0778499
$661$	12.1492	−	21.0431i	0.472550	−	0.818480i	−0.526957	−	0.849892i	$-0.676667\pi$
$661$	12.1492	−	21.0431i	0.472550	−	0.818480i	0.999507	+	0.0314118i	$0.0100003\pi$
$662$	9.90312	−	17.1527i	0.384896	−	0.666659i
$663$	−6.40312	+	11.0905i	−0.248677	+	0.430721i
$664$	−0.649219	−	1.12448i	−0.0251946	−	0.0436383i
$665$	2.10469			0.0816162
$666$	−3.55234	+	4.93770i	−0.137651	+	0.191332i
$667$	25.4031			0.983613
$668$	−1.29844	−	2.24896i	−0.0502381	−	0.0870149i
$669$	12.2539	−	21.2244i	0.473763	−	0.820582i
$670$	−2.14922	+	3.72256i	−0.0830316	+	0.143815i
$671$	−3.40312	+	5.89438i	−0.131376	+	0.227550i
$672$	3.00000			0.115728
$673$	25.8062	−	44.6977i	0.994758	−	1.72297i	0.408820	−	0.912615i	$-0.365940\pi$
$673$	25.8062	−	44.6977i	0.994758	−	1.72297i	0.585938	−	0.810356i	$-0.300726\pi$
$674$	−6.50781			−0.250671
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	28.0000			1.07692
$677$	−35.4031			−1.36065			−0.680326	−	0.732909i	$-0.738162\pi$
$677$	−35.4031			−1.36065			−0.680326	+	0.732909i	$0.738162\pi$
$678$	−3.64922	−	6.32063i	−0.140147	−	0.242742i
$679$	−12.4477	+	21.5600i	−0.477697	+	0.827396i
$680$	2.00000			0.0766965
$681$	8.75391	+	15.1622i	0.335450	+	0.581017i
$682$	−1.70156	−	2.94719i	−0.0651562	−	0.112854i
$683$	20.0000	+	34.6410i	0.765279	+	1.32550i	0.940099	+	0.340901i	$0.110732\pi$
$683$	20.0000	+	34.6410i	0.765279	+	1.32550i	−0.174820	+	0.984600i	$0.555934\pi$
$684$	0.350781	−	0.607571i	0.0134124	−	0.0232310i
$685$	−5.05234	+	8.75092i	−0.193040	+	0.334355i
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$	−2.25391	−	3.90388i	−0.0859919	−	0.148942i
$688$	−1.85078	−	3.20565i	−0.0705604	−	0.122214i
$689$	60.2094			2.29379
$690$	2.70156	−	4.67924i	0.102847	−	0.178136i
$691$	−6.20156	−	10.7414i	−0.235919	−	0.408623i	0.723621	−	0.690198i	$-0.242477\pi$
$691$	−6.20156	−	10.7414i	−0.235919	−	0.408623i	−0.959539	+	0.281575i	$0.909143\pi$
$692$	−4.00000			−0.152057
$693$	−6.00000			−0.227921
$694$	1.64922	+	2.85653i	0.0626035	+	0.108432i
$695$	12.5078			0.474448
$696$	2.35078	−	4.07167i	0.0891061	−	0.154336i
$697$	2.80625			0.106294
$698$	3.70156	−	6.41129i	0.140106	−	0.242671i
$699$	−8.75391	+	15.1622i	−0.331103	+	0.573487i
$700$	1.50000	−	2.59808i	0.0566947	−	0.0981981i
$701$	5.80625	+	10.0567i	0.219299	+	0.379837i	0.954594	−	0.297910i	$-0.0962897\pi$
$701$	5.80625	+	10.0567i	0.219299	+	0.379837i	−0.735295	+	0.677747i	$0.762956\pi$
$702$	6.40312			0.241670
$703$	−2.49219	+	3.46410i	−0.0939947	+	0.130651i
$704$	2.00000			0.0753778
$705$	4.00000	+	6.92820i	0.150649	+	0.260931i
$706$	−6.35078	+	10.9999i	−0.239015	+	0.413986i
$707$	25.2094	−	43.6639i	0.948096	−	1.64215i
$708$	−1.00000	+	1.73205i	−0.0375823	+	0.0650945i
$709$	−22.5078			−0.845299			−0.422649	−	0.906293i	$-0.638900\pi$
$709$	−22.5078			−0.845299			−0.422649	+	0.906293i	$0.638900\pi$
$710$	−1.35078	+	2.33962i	−0.0506939	+	0.0878044i
$711$	11.1047			0.416458
$712$	5.70156	+	9.87540i	0.213675	+	0.370096i
$713$	−9.19375			−0.344309
$714$	−6.00000			−0.224544
$715$	6.40312	+	11.0905i	0.239463	+	0.414763i
$716$	9.10469	−	15.7698i	0.340258	−	0.589344i
$717$	−10.1047			−0.377366
$718$	−1.35078	−	2.33962i	−0.0504107	−	0.0873139i
$719$	−6.94766	−	12.0337i	−0.259104	−	0.448781i	0.706898	−	0.707315i	$-0.250094\pi$
$719$	−6.94766	−	12.0337i	−0.259104	−	0.448781i	−0.966002	+	0.258534i	$0.916761\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$	21.1570	−	36.6451i	0.787929	−	1.36473i
$722$	−9.25391	+	16.0282i	−0.344395	+	0.596509i
$723$	−7.55234	−	13.0810i	−0.280875	−	0.486489i
$724$	−3.55234	−	6.15284i	−0.132022	−	0.228668i
$725$	−2.35078	−	4.07167i	−0.0873058	−	0.151218i
$726$	7.00000			0.259794
$727$	6.60469	−	11.4397i	0.244954	−	0.424273i	−0.717164	−	0.696904i	$-0.754560\pi$
$727$	6.60469	−	11.4397i	0.244954	−	0.424273i	0.962119	+	0.272631i	$0.0878937\pi$
$728$	9.60469	+	16.6358i	0.355973	+	0.616564i
$729$	1.00000			0.0370370
$730$	−11.7016			−0.433094
$731$	3.70156	+	6.41129i	0.136907	+	0.237130i
$732$	3.40312			0.125783
$733$	13.5523	−	23.4733i	0.500567	−	0.867008i	−0.499433	−	0.866353i	$-0.666458\pi$
$733$	13.5523	−	23.4733i	0.500567	−	0.867008i	1.00000		0.000655089i	$-0.000208521\pi$
$734$	9.00000			0.332196
$735$	−1.00000	+	1.73205i	−0.0368856	+	0.0638877i
$736$	2.70156	−	4.67924i	0.0995809	−	0.172479i
$737$	4.29844	−	7.44511i	0.158335	−	0.274244i
$738$	−0.701562	−	1.21514i	−0.0258249	−	0.0447300i
$739$	−31.2984			−1.15133			−0.575666	−	0.817685i	$-0.695257\pi$
$739$	−31.2984			−1.15133			−0.575666	+	0.817685i	$0.695257\pi$
$740$	2.50000	+	5.54527i	0.0919018	+	0.203848i
$741$	4.49219			0.165025
$742$	14.1047	+	24.4300i	0.517799	+	0.896855i
$743$	−9.10469	+	15.7698i	−0.334019	+	0.578537i	−0.983296	−	0.182015i	$-0.941738\pi$
$743$	−9.10469	+	15.7698i	−0.334019	+	0.578537i	0.649277	+	0.760552i	$0.275071\pi$
$744$	−0.850781	+	1.47360i	−0.0311911	+	0.0540247i
$745$	3.05234	−	5.28681i	0.111829	−	0.193694i
$746$	−15.5969			−0.571042
$747$	0.649219	−	1.12448i	0.0237537	−	0.0411426i
$748$	−4.00000			−0.146254
$749$	5.10469	+	8.84158i	0.186521	+	0.323064i
$750$	−1.00000			−0.0365148
$751$	19.3141			0.704780			0.352390	−	0.935853i	$-0.385369\pi$
$751$	19.3141			0.704780			0.352390	+	0.935853i	$0.385369\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$	2.40312	−	4.16233i	0.0875747	−	0.151684i
$754$	30.1047			1.09635
$755$	9.85078	+	17.0621i	0.358507	+	0.620952i
$756$	1.50000	+	2.59808i	0.0545545	+	0.0944911i
$757$	3.90312	+	6.76041i	0.141861	+	0.245711i	0.928198	−	0.372088i	$-0.121358\pi$
$757$	3.90312	+	6.76041i	0.141861	+	0.245711i	−0.786336	+	0.617799i	$0.788025\pi$
$758$	9.64922	−	16.7129i	0.350475	−	0.607041i
$759$	−5.40312	+	9.35849i	−0.196121	+	0.339692i
$760$	−0.350781	−	0.607571i	−0.0127242	−	0.0220389i
$761$	−3.59688	−	6.22997i	−0.130387	−	0.225836i	0.793439	−	0.608650i	$-0.208289\pi$
$761$	−3.59688	−	6.22997i	−0.130387	−	0.225836i	−0.923826	+	0.382813i	$0.874955\pi$
$762$	−6.50000	−	11.2583i	−0.235470	−	0.407846i
$763$	−9.31406			−0.337192
$764$	1.70156	−	2.94719i	0.0615604	−	0.106626i
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$	−8.20937			−0.296617
$767$	−12.8062			−0.462407
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	0.193752			0.00698686			0.00349343	−	0.999994i	$-0.498888\pi$
$769$	0.193752			0.00698686			0.00349343	+	0.999994i	$0.498888\pi$
$770$	−3.00000	+	5.19615i	−0.108112	+	0.187256i
$771$	−19.2984			−0.695016
$772$	−1.55234	+	2.68874i	−0.0558701	+	0.0967698i
$773$	−15.4031	+	26.6790i	−0.554012	+	0.959577i	0.443968	+	0.896043i	$0.353570\pi$
$773$	−15.4031	+	26.6790i	−0.554012	+	0.959577i	−0.997980	+	0.0635340i	$0.979763\pi$
$774$	1.85078	−	3.20565i	0.0665250	−	0.115225i
$775$	0.850781	+	1.47360i	0.0305610	+	0.0529331i
$776$	8.29844			0.297897
$777$	−7.50000	−	16.6358i	−0.269061	−	0.596806i
$778$	−28.7016			−1.02900
$779$	−0.492189	−	0.852497i	−0.0176345	−	0.0305439i
$780$	3.20156	−	5.54527i	0.114634	−	0.198552i
$781$	2.70156	−	4.67924i	0.0966695	−	0.167436i
$782$	−5.40312	+	9.35849i	−0.193215	+	0.334659i
$783$	4.70156			0.168020
$784$	−1.00000	+	1.73205i	−0.0357143	+	0.0618590i
$785$	−12.4031			−0.442686
$786$	3.70156	+	6.41129i	0.132030	+	0.228683i
$787$	−5.49219			−0.195775			−0.0978877	−	0.995197i	$-0.531209\pi$
$787$	−5.49219			−0.195775			−0.0978877	+	0.995197i	$0.531209\pi$
$788$	−8.80625			−0.313710
$789$	−1.00000	−	1.73205i	−0.0356009	−	0.0616626i
$790$	5.55234	−	9.61694i	0.197544	−	0.342155i
$791$	21.8953			0.778508
$792$	1.00000	+	1.73205i	0.0355335	+	0.0615457i
$793$	10.8953	+	18.8712i	0.386904	+	0.670137i
$794$	−5.85078	−	10.1339i	−0.207636	−	0.359637i
$795$	4.70156	−	8.14334i	0.166747	−	0.288815i
$796$	−1.44766	+	2.50742i	−0.0513108	+	0.0888730i
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	0.980237	−	0.197826i	$-0.0633881\pi$
$797$	9.00000	+	15.5885i	0.318796	+	0.552171i	−0.661441	+	0.749997i	$0.730055\pi$
$798$	1.05234	+	1.82271i	0.0372525	+	0.0645233i
$799$	−8.00000	−	13.8564i	−0.283020	−	0.490204i
$800$	−1.00000			−0.0353553
$801$	−5.70156	+	9.87540i	−0.201455	+	0.348930i
$802$	−9.00000	−	15.5885i	−0.317801	−	0.550448i
$803$	23.4031			0.825878
$804$	−4.29844			−0.151594
$805$	8.10469	+	14.0377i	0.285653	+	0.494765i
$806$	−10.8953			−0.383771
$807$	14.3508	−	24.8563i	0.505171	−	0.874983i
$808$	−16.8062			−0.591242
$809$	15.4031	−	26.6790i	0.541545	−	0.937983i	−0.457271	−	0.889328i	$-0.651173\pi$
$809$	15.4031	−	26.6790i	0.541545	−	0.937983i	0.998816	−	0.0486559i	$-0.0154938\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	2.00000	−	3.46410i	0.0702295	−	0.121641i	−0.828772	−	0.559586i	$-0.810960\pi$
$811$	2.00000	−	3.46410i	0.0702295	−	0.121641i	0.899002	+	0.437945i	$0.144294\pi$
$812$	7.05234	+	12.2150i	0.247489	+	0.428663i
$813$	31.3141			1.09823
$814$	−5.00000	−	11.0905i	−0.175250	−	0.388723i
$815$	18.8062			0.658754
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	1.29844	−	2.24896i	0.0454266	−	0.0786812i
$818$	−10.7984	+	18.7034i	−0.377559	+	0.653951i
$819$	−9.60469	+	16.6358i	−0.335615	+	0.581302i
$820$	−1.40312			−0.0489992
$821$	0.753905	−	1.30580i	0.0263115	−	0.0455728i	−0.852570	−	0.522613i	$-0.824957\pi$
$821$	0.753905	−	1.30580i	0.0263115	−	0.0455728i	0.878881	+	0.477040i	$0.158290\pi$
$822$	−10.1047			−0.352441
$823$	15.3062	+	26.5112i	0.533542	+	0.924122i	0.999232	+	0.0391745i	$0.0124728\pi$
$823$	15.3062	+	26.5112i	0.533542	+	0.924122i	−0.465690	+	0.884948i	$0.654194\pi$
$824$	−14.1047			−0.491360
$825$	2.00000			0.0696311
$826$	−3.00000	−	5.19615i	−0.104383	−	0.180797i
$827$	−20.7539	+	35.9468i	−0.721684	+	1.24999i	0.238640	+	0.971108i	$0.423298\pi$
$827$	−20.7539	+	35.9468i	−0.721684	+	1.24999i	−0.960324	+	0.278885i	$0.910035\pi$
$828$	5.40312			0.187772
$829$	11.7461	+	20.3448i	0.407959	+	0.706605i	0.994661	−	0.103198i	$-0.0329074\pi$
$829$	11.7461	+	20.3448i	0.407959	+	0.706605i	−0.586702	+	0.809803i	$0.699574\pi$
$830$	−0.649219	−	1.12448i	−0.0225347	−	0.0390313i
$831$	−12.0523	−	20.8753i	−0.418091	−	0.724155i
$832$	3.20156	−	5.54527i	0.110994	−	0.192248i
$833$	2.00000	−	3.46410i	0.0692959	−	0.120024i
$834$	6.25391	+	10.8321i	0.216555	+	0.375084i
$835$	−1.29844	−	2.24896i	−0.0449343	−	0.0778285i
$836$	0.701562	+	1.21514i	0.0242640	+	0.0420265i
$837$	−1.70156			−0.0588146
$838$	−9.10469	+	15.7698i	−0.314516	+	0.544758i
$839$	−10.2094	−	17.6832i	−0.352467	−	0.610490i	0.634214	−	0.773157i	$-0.281324\pi$
$839$	−10.2094	−	17.6832i	−0.352467	−	0.610490i	−0.986681	+	0.162667i	$0.947990\pi$
$840$	3.00000			0.103510
$841$	−6.89531			−0.237769
$842$	6.29844	+	10.9092i	0.217059	+	0.375956i
$843$	−30.2094			−1.04047
$844$	6.60469	−	11.4397i	0.227343	−	0.393769i
$845$	28.0000			0.963229
$846$	−4.00000	+	6.92820i	−0.137523	+	0.238197i
$847$	−10.5000	+	18.1865i	−0.360784	+	0.624897i
$848$	4.70156	−	8.14334i	0.161452	−	0.279644i
$849$	7.25391	+	12.5641i	0.248953	+	0.431200i
$850$	2.00000			0.0685994
$851$	−32.7016	−	3.28278i	−1.12100	−	0.112532i
$852$	−2.70156			−0.0925540
$853$	−3.59688	−	6.22997i	−0.123155	−	0.213310i	0.797855	−	0.602849i	$-0.205968\pi$
$853$	−3.59688	−	6.22997i	−0.123155	−	0.213310i	−0.921010	+	0.389539i	$0.872634\pi$
$854$	−5.10469	+	8.84158i	−0.174679	+	0.302553i
$855$	0.350781	−	0.607571i	0.0119965	−	0.0207785i
$856$	1.70156	−	2.94719i	0.0581582	−	0.100733i
$857$	25.2984			0.864178			0.432089	−	0.901831i	$-0.357777\pi$
$857$	25.2984			0.864178			0.432089	+	0.901831i	$0.357777\pi$
$858$	−6.40312	+	11.0905i	−0.218599	+	0.378625i
$859$	33.2094			1.13309			0.566545	−	0.824031i	$-0.308280\pi$
$859$	33.2094			1.13309			0.566545	+	0.824031i	$0.308280\pi$
$860$	−1.85078	−	3.20565i	−0.0631111	−	0.109312i
$861$	4.20937			0.143455
$862$	−38.1047			−1.29785
$863$	−3.10469	−	5.37747i	−0.105685	−	0.183051i	0.808333	−	0.588726i	$-0.200370\pi$
$863$	−3.10469	−	5.37747i	−0.105685	−	0.183051i	−0.914018	+	0.405674i	$0.867037\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−4.00000			−0.136004
$866$	9.70156	+	16.8036i	0.329673	+	0.571010i
$867$	6.50000	+	11.2583i	0.220752	+	0.382353i
$868$	−2.55234	−	4.42079i	−0.0866322	−	0.150051i
$869$	−11.1047	+	19.2339i	−0.376701	+	0.652465i
$870$	2.35078	−	4.07167i	0.0796989	−	0.138043i
$871$	−13.7617	−	23.8360i	−0.466298	−	0.807652i
$872$	1.55234	+	2.68874i	0.0525690	+	0.0910521i
$873$	4.14922	+	7.18666i	0.140430	+	0.243232i
$874$	3.79063			0.128220
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$	−5.85078	−	10.1339i	−0.197680	−	0.342391i
$877$	−30.0156			−1.01356			−0.506778	−	0.862077i	$-0.669164\pi$
$877$	−30.0156			−1.01356			−0.506778	+	0.862077i	$0.669164\pi$
$878$	−2.89531			−0.0977121
$879$	−0.701562	−	1.21514i	−0.0236631	−	0.0409857i
$880$	2.00000			0.0674200
$881$	17.8062	−	30.8413i	0.599908	−	1.03907i	−0.392926	−	0.919570i	$-0.628537\pi$
$881$	17.8062	−	30.8413i	0.599908	−	1.03907i	0.992834	−	0.119501i	$-0.0381294\pi$
$882$	−2.00000			−0.0673435
$883$	22.2094	−	38.4678i	0.747405	−	1.29454i	−0.201658	−	0.979456i	$-0.564633\pi$
$883$	22.2094	−	38.4678i	0.747405	−	1.29454i	0.949063	−	0.315087i	$-0.102034\pi$
$884$	−6.40312	+	11.0905i	−0.215360	+	0.373015i
$885$	−1.00000	+	1.73205i	−0.0336146	+	0.0582223i
$886$	−8.75391	−	15.1622i	−0.294093	−	0.509384i
$887$	−21.0156			−0.705635			−0.352818	−	0.935692i	$-0.614776\pi$
$887$	−21.0156			−0.705635			−0.352818	+	0.935692i	$0.614776\pi$
$888$	−3.55234	+	4.93770i	−0.119209	+	0.165698i
$889$	39.0000			1.30802
$890$	5.70156	+	9.87540i	0.191117	+	0.331024i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	12.2539	−	21.2244i	0.410291	−	0.710645i
$893$	−2.80625	+	4.86056i	−0.0939075	+	0.162653i
$894$	6.10469			0.204171
$895$	9.10469	−	15.7698i	0.304336	−	0.527126i
$896$	3.00000			0.100223
$897$	17.2984	+	29.9618i	0.577578	+	1.00039i
$898$	16.0000			0.533927
$899$	−8.00000			−0.266815
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	−9.40312	+	16.2867i	−0.313263	+	0.542588i
$902$	2.80625			0.0934379
$903$	5.55234	+	9.61694i	0.184770	+	0.320032i
$904$	−3.64922	−	6.32063i	−0.121371	−	0.210221i
$905$	−3.55234	−	6.15284i	−0.118084	−	0.204527i
$906$	−9.85078	+	17.0621i	−0.327270	+	0.566849i
$907$	27.3586	−	47.3865i	0.908427	−	1.57344i	0.0921775	−	0.995743i	$-0.470617\pi$
$907$	27.3586	−	47.3865i	0.908427	−	1.57344i	0.816250	−	0.577699i	$-0.196049\pi$
$908$	8.75391	+	15.1622i	0.290509	+	0.503176i
$909$	−8.40312	−	14.5546i	−0.278714	−	0.482747i
$910$	9.60469	+	16.6358i	0.318392	+	0.551472i
$911$	−55.1203			−1.82622			−0.913109	−	0.407716i	$-0.866325\pi$
$911$	−55.1203			−1.82622			−0.913109	+	0.407716i	$0.866325\pi$
$912$	0.350781	−	0.607571i	0.0116155	−	0.0201187i
$913$	1.29844	+	2.24896i	0.0429720	+	0.0744297i
$914$	−19.6125			−0.648724
$915$	3.40312			0.112504
$916$	−2.25391	−	3.90388i	−0.0744711	−	0.128988i
$917$	−22.2094			−0.733418
$918$	−1.00000	+	1.73205i	−0.0330049	+	0.0571662i
$919$	29.1047			0.960075			0.480038	−	0.877248i	$-0.340623\pi$
$919$	29.1047			0.960075			0.480038	+	0.877248i	$0.340623\pi$
$920$	2.70156	−	4.67924i	0.0890679	−	0.154270i
$921$	14.5523	−	25.2054i	0.479516	−	0.830546i
$922$	−3.35078	+	5.80372i	−0.110352	+	0.191135i
$923$	−8.64922	−	14.9809i	−0.284693	−	0.493102i
$924$	−6.00000			−0.197386
$925$	2.50000	+	5.54527i	0.0821995	+	0.182327i
$926$	−20.4031			−0.670488
$927$	−7.05234	−	12.2150i	−0.231629	−	0.401194i
$928$	2.35078	−	4.07167i	0.0771682	−	0.133659i
$929$	−5.89531	+	10.2110i	−0.193419	+	0.335011i	−0.946381	−	0.323052i	$-0.895291\pi$
$929$	−5.89531	+	10.2110i	−0.193419	+	0.335011i	0.752962	+	0.658064i	$0.228624\pi$
$930$	−0.850781	+	1.47360i	−0.0278982	+	0.0483211i
$931$	−1.40312			−0.0459855
$932$	−8.75391	+	15.1622i	−0.286744	+	0.496655i
$933$	20.0000			0.654771
$934$	−11.4555	−	19.8415i	−0.374834	−	0.649232i
$935$	−4.00000			−0.130814
$936$	6.40312			0.209293
$937$	13.9555	+	24.1716i	0.455905	+	0.789651i	0.998740	−	0.0501886i	$-0.0159823\pi$
$937$	13.9555	+	24.1716i	0.455905	+	0.789651i	−0.542835	+	0.839840i	$0.682649\pi$
$938$	6.44766	−	11.1677i	0.210523	−	0.364637i
$939$	−13.1047			−0.427655
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	−22.5602	−	39.0753i	−0.735440	−	1.27382i	−0.954530	−	0.298115i	$-0.903642\pi$
$941$	−22.5602	−	39.0753i	−0.735440	−	1.27382i	0.219090	−	0.975705i	$-0.429691\pi$
$942$	−6.20156	−	10.7414i	−0.202058	−	0.349974i
$943$	3.79063	−	6.56556i	0.123440	−	0.213804i
$944$	−1.00000	+	1.73205i	−0.0325472	+	0.0563735i
$945$	1.50000	+	2.59808i	0.0487950	+	0.0845154i
$946$	3.70156	+	6.41129i	0.120348	+	0.208449i
$947$	−28.1570	−	48.7694i	−0.914981	−	1.58479i	−0.806930	−	0.590647i	$-0.798872\pi$
$947$	−28.1570	−	48.7694i	−0.914981	−	1.58479i	−0.108051	−	0.994145i	$-0.534461\pi$
$948$	11.1047			0.360663
$949$	37.4633	−	64.8883i	1.21611	−	2.10636i
$950$	−0.350781	−	0.607571i	−0.0113808	−	0.0197122i
$951$	28.8062			0.934107
$952$	−6.00000			−0.194461
$953$	8.94766	+	15.4978i	0.289843	+	0.502023i	0.973772	−	0.227526i	$-0.0730636\pi$
$953$	8.94766	+	15.4978i	0.289843	+	0.502023i	−0.683929	+	0.729549i	$0.739730\pi$
$954$	9.40312			0.304437
$955$	1.70156	−	2.94719i	0.0550613	−	0.0953689i
$956$	−10.1047			−0.326809
$957$	−4.70156	+	8.14334i	−0.151980	+	0.263237i
$958$	−3.40312	+	5.89438i	−0.109950	+	0.190439i
$959$	15.1570	−	26.2527i	0.489446	−	0.847745i
$960$	−0.500000	−	0.866025i	−0.0161374	−	0.0279508i
$961$	−28.1047			−0.906603
$962$	−38.7539	−	3.89035i	−1.24948	−	0.125430i
$963$	3.40312			0.109664
$964$	−7.55234	−	13.0810i	−0.243245	−	0.421312i
$965$	−1.55234	+	2.68874i	−0.0499717	+	0.0865535i
$966$	−8.10469	+	14.0377i	−0.260764	+	0.451657i
$967$	−5.79844	+	10.0432i	−0.186465	+	0.322967i	−0.944069	−	0.329747i	$-0.893036\pi$
$967$	−5.79844	+	10.0432i	−0.186465	+	0.322967i	0.757604	+	0.652714i	$0.226370\pi$
$968$	7.00000			0.224989
$969$	−0.701562	+	1.21514i	−0.0225374	+	0.0390360i
$970$	8.29844			0.266447
$971$	−16.5969	−	28.7466i	−0.532619	−	0.922523i	−0.999275	−	0.0380841i	$-0.987875\pi$
$971$	−16.5969	−	28.7466i	−0.532619	−	0.922523i	0.466655	−	0.884439i	$-0.345459\pi$
$972$	1.00000			0.0320750
$973$	−37.5234			−1.20295
$974$	13.1570	+	22.7886i	0.421578	+	0.730195i
$975$	3.20156	−	5.54527i	0.102532	−	0.177591i
$976$	3.40312			0.108931
$977$	−10.9477	−	18.9619i	−0.350247	−	0.606645i	0.636046	−	0.771651i	$-0.280569\pi$
$977$	−10.9477	−	18.9619i	−0.350247	−	0.606645i	−0.986293	+	0.165006i	$0.947236\pi$
$978$	9.40312	+	16.2867i	0.300679	+	0.520791i
$979$	−11.4031	−	19.7508i	−0.364445	−	0.631238i
$980$	−1.00000	+	1.73205i	−0.0319438	+	0.0553283i
$981$	−1.55234	+	2.68874i	−0.0495625	+	0.0858448i
$982$	−16.7016	−	28.9280i	−0.532968	−	0.923128i
$983$	−22.0000	−	38.1051i	−0.701691	−	1.21536i	−0.967872	−	0.251442i	$-0.919095\pi$
$983$	−22.0000	−	38.1051i	−0.701691	−	1.21536i	0.266181	−	0.963923i	$-0.414238\pi$
$984$	−0.701562	−	1.21514i	−0.0223650	−	0.0387373i
$985$	−8.80625			−0.280590
$986$	−4.70156	+	8.14334i	−0.149728	+	0.259337i
$987$	−12.0000	−	20.7846i	−0.381964	−	0.661581i
$988$	4.49219			0.142916
$989$	20.0000			0.635963
$990$	1.00000	+	1.73205i	0.0317821	+	0.0550482i
$991$	4.20937			0.133715			0.0668576	−	0.997763i	$-0.478703\pi$
$991$	4.20937			0.133715			0.0668576	+	0.997763i	$0.478703\pi$
$992$	−0.850781	+	1.47360i	−0.0270123	+	0.0467867i
$993$	19.8062			0.628532
$994$	4.05234	−	7.01886i	0.128533	−	0.222625i
$995$	−1.44766	+	2.50742i	−0.0458938	+	0.0794904i
$996$	0.649219	−	1.12448i	0.0205713	−	0.0356305i
$997$	−19.4555	−	33.6979i	−0.616161	−	1.06722i	−0.990180	−	0.139801i	$-0.955354\pi$
$997$	−19.4555	−	33.6979i	−0.616161	−	1.06722i	0.374019	−	0.927421i	$-0.377980\pi$
$998$	2.10469			0.0666227
$999$	−6.05234	−	0.607571i	−0.191488	−	0.0192227i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.k.211.2	yes	4
37.10	even	3	inner	1110.2.i.k.121.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.k.121.2	✓	4	37.10	even	3	inner
1110.2.i.k.211.2	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} -1.00000 q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} +2.00000 q^{11} +(-0.500000 - 0.866025i) q^{12} +(3.20156 - 5.54527i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 - 0.866025i) q^{18} +(0.350781 - 0.607571i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(1.50000 + 2.59808i) q^{21} +(1.00000 + 1.73205i) q^{22} +5.40312 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +6.40312 q^{26} +1.00000 q^{27} +(1.50000 + 2.59808i) q^{28} +4.70156 q^{29} +(0.500000 - 0.866025i) q^{30} -1.70156 q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(1.50000 + 2.59808i) q^{35} +1.00000 q^{36} +(-6.05234 - 0.607571i) q^{37} +0.701562 q^{38} +(3.20156 + 5.54527i) q^{39} +(0.500000 - 0.866025i) q^{40} +(0.701562 - 1.21514i) q^{41} +(-1.50000 + 2.59808i) q^{42} +3.70156 q^{43} +(-1.00000 + 1.73205i) q^{44} +1.00000 q^{45} +(2.70156 + 4.67924i) q^{46} -8.00000 q^{47} +1.00000 q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} -2.00000 q^{51} +(3.20156 + 5.54527i) q^{52} +(4.70156 + 8.14334i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.00000 + 1.73205i) q^{55} +(-1.50000 + 2.59808i) q^{56} +(0.350781 + 0.607571i) q^{57} +(2.35078 + 4.07167i) q^{58} +(-1.00000 - 1.73205i) q^{59} +1.00000 q^{60} +(-1.70156 + 2.94719i) q^{61} +(-0.850781 - 1.47360i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(3.20156 + 5.54527i) q^{65} -2.00000 q^{66} +(2.14922 - 3.72256i) q^{67} -2.00000 q^{68} +(-2.70156 + 4.67924i) q^{69} +(-1.50000 + 2.59808i) q^{70} +(1.35078 - 2.33962i) q^{71} +(0.500000 + 0.866025i) q^{72} +11.7016 q^{73} +(-2.50000 - 5.54527i) q^{74} +1.00000 q^{75} +(0.350781 + 0.607571i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-3.20156 + 5.54527i) q^{78} +(-5.55234 + 9.61694i) q^{79} +1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} +1.40312 q^{82} +(0.649219 + 1.12448i) q^{83} -3.00000 q^{84} -2.00000 q^{85} +(1.85078 + 3.20565i) q^{86} +(-2.35078 + 4.07167i) q^{87} -2.00000 q^{88} +(-5.70156 - 9.87540i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-9.60469 - 16.6358i) q^{91} +(-2.70156 + 4.67924i) q^{92} +(0.850781 - 1.47360i) q^{93} +(-4.00000 - 6.92820i) q^{94} +(0.350781 + 0.607571i) q^{95} +(0.500000 + 0.866025i) q^{96} -8.29844 q^{97} +(1.00000 - 1.73205i) q^{98} +(-1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 - 2 * q^9	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{5} - 4 q^{6} + 6 q^{7} - 4 q^{8} - 2 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{12} + 12 q^{14} - 2 q^{15} - 2 q^{16} + 4 q^{17} + 2 q^{18} - 5 q^{19} - 2 q^{20} + 6 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} - 2 q^{25} + 4 q^{27} + 6 q^{28} + 6 q^{29} + 2 q^{30} + 6 q^{31} + 2 q^{32} - 4 q^{33} - 4 q^{34} + 6 q^{35} + 4 q^{36} - 5 q^{37} - 10 q^{38} + 2 q^{40} - 10 q^{41} - 6 q^{42} + 2 q^{43} - 4 q^{44} + 4 q^{45} - 2 q^{46} - 32 q^{47} + 4 q^{48} - 4 q^{49} + 2 q^{50} - 8 q^{51} + 6 q^{53} + 2 q^{54} - 4 q^{55} - 6 q^{56} - 5 q^{57} + 3 q^{58} - 4 q^{59} + 4 q^{60} + 6 q^{61} + 3 q^{62} - 12 q^{63} + 4 q^{64} - 8 q^{66} + 15 q^{67} - 8 q^{68} + 2 q^{69} - 6 q^{70} - q^{71} + 2 q^{72} + 34 q^{73} - 10 q^{74} + 4 q^{75} - 5 q^{76} + 12 q^{77} - 3 q^{79} + 4 q^{80} - 2 q^{81} - 20 q^{82} + 9 q^{83} - 12 q^{84} - 8 q^{85} + q^{86} - 3 q^{87} - 8 q^{88} - 10 q^{89} + 2 q^{90} + 2 q^{92} - 3 q^{93} - 16 q^{94} - 5 q^{95} + 2 q^{96} - 46 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^5 - 4 * q^6 + 6 * q^7 - 4 * q^8 - 2 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^12 + 12 * q^14 - 2 * q^15 - 2 * q^16 + 4 * q^17 + 2 * q^18 - 5 * q^19 - 2 * q^20 + 6 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 - 2 * q^25 + 4 * q^27 + 6 * q^28 + 6 * q^29 + 2 * q^30 + 6 * q^31 + 2 * q^32 - 4 * q^33 - 4 * q^34 + 6 * q^35 + 4 * q^36 - 5 * q^37 - 10 * q^38 + 2 * q^40 - 10 * q^41 - 6 * q^42 + 2 * q^43 - 4 * q^44 + 4 * q^45 - 2 * q^46 - 32 * q^47 + 4 * q^48 - 4 * q^49 + 2 * q^50 - 8 * q^51 + 6 * q^53 + 2 * q^54 - 4 * q^55 - 6 * q^56 - 5 * q^57 + 3 * q^58 - 4 * q^59 + 4 * q^60 + 6 * q^61 + 3 * q^62 - 12 * q^63 + 4 * q^64 - 8 * q^66 + 15 * q^67 - 8 * q^68 + 2 * q^69 - 6 * q^70 - q^71 + 2 * q^72 + 34 * q^73 - 10 * q^74 + 4 * q^75 - 5 * q^76 + 12 * q^77 - 3 * q^79 + 4 * q^80 - 2 * q^81 - 20 * q^82 + 9 * q^83 - 12 * q^84 - 8 * q^85 + q^86 - 3 * q^87 - 8 * q^88 - 10 * q^89 + 2 * q^90 + 2 * q^92 - 3 * q^93 - 16 * q^94 - 5 * q^95 + 2 * q^96 - 46 * q^97 + 4 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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