LMFDB - Embedded newform 1110.2.bb.d.1099.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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, 3, 4]))

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (of order $6$, 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:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1099.10
Character	$\chi$	$=$	1110.1099
Dual form			1110.2.bb.d.1009.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.363043 - 2.20640i) q^{5} +1.00000 q^{6} +(-0.268117 - 0.154798i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.363043 - 2.20640i) q^{5} +1.00000 q^{6} +(-0.268117 - 0.154798i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.41760 - 1.72928i) q^{10} +4.57198 q^{11} +(0.866025 - 0.500000i) q^{12} +(-3.32139 - 1.91760i) q^{13} -0.309595 q^{14} +(0.788796 - 2.09232i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.86619 - 1.65480i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.688327 + 1.19222i) q^{19} +(-2.09232 - 0.788796i) q^{20} +(-0.154798 - 0.268117i) q^{21} +(3.95946 - 2.28599i) q^{22} -5.47919i q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.73640 + 1.60203i) q^{25} -3.83521 q^{26} +1.00000i q^{27} +(-0.268117 + 0.154798i) q^{28} -0.690405 q^{29} +(-0.363043 - 2.20640i) q^{30} +2.73678 q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.95946 + 2.28599i) q^{33} +(1.65480 - 2.86619i) q^{34} +(-0.244208 + 0.647772i) q^{35} +1.00000 q^{36} +(6.02425 - 0.841687i) q^{37} +1.37665i q^{38} +(-1.91760 - 3.32139i) q^{39} +(-2.20640 + 0.363043i) q^{40} +(0.175457 - 0.303900i) q^{41} +(-0.268117 - 0.154798i) q^{42} -5.04831i q^{43} +(2.28599 - 3.95946i) q^{44} +(1.72928 - 1.41760i) q^{45} +(-2.73959 - 4.74511i) q^{46} -3.77518i q^{47} -1.00000i q^{48} +(-3.45208 - 5.97917i) q^{49} +(-3.30083 + 3.75560i) q^{50} +3.30960 q^{51} +(-3.32139 + 1.91760i) q^{52} +(-11.8620 + 6.84854i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.65982 - 10.0876i) q^{55} +(-0.154798 + 0.268117i) q^{56} +(-1.19222 + 0.688327i) q^{57} +(-0.597908 + 0.345202i) q^{58} +(5.77406 + 10.0010i) q^{59} +(-1.41760 - 1.72928i) q^{60} +(2.37967 - 4.12172i) q^{61} +(2.37012 - 1.36839i) q^{62} -0.309595i q^{63} -1.00000 q^{64} +(-3.02520 + 8.02448i) q^{65} +4.57198 q^{66} +(4.13186 + 2.38553i) q^{67} -3.30960i q^{68} +(2.73959 - 4.74511i) q^{69} +(0.112396 + 0.683091i) q^{70} +(-6.67007 + 11.5529i) q^{71} +(0.866025 - 0.500000i) q^{72} +13.3833i q^{73} +(4.79631 - 3.74105i) q^{74} +(-4.90286 - 0.980798i) q^{75} +(0.688327 + 1.19222i) q^{76} +(-1.22583 - 0.707733i) q^{77} +(-3.32139 - 1.91760i) q^{78} +(7.63359 - 13.2218i) q^{79} +(-1.72928 + 1.41760i) q^{80} +(-0.500000 + 0.866025i) q^{81} -0.350914i q^{82} +(2.66210 - 1.53697i) q^{83} -0.309595 q^{84} +(-4.69170 - 5.72321i) q^{85} +(-2.52416 - 4.37197i) q^{86} +(-0.597908 - 0.345202i) q^{87} -4.57198i q^{88} +(5.47776 + 9.48775i) q^{89} +(0.788796 - 2.09232i) q^{90} +(0.593681 + 1.02829i) q^{91} +(-4.74511 - 2.73959i) q^{92} +(2.37012 + 1.36839i) q^{93} +(-1.88759 - 3.26940i) q^{94} +(2.88040 + 1.08590i) q^{95} +(-0.500000 - 0.866025i) q^{96} -0.990093i q^{97} +(-5.97917 - 3.45208i) q^{98} +(2.28599 + 3.95946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * 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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.363043	−	2.20640i	−0.162358	−	0.986732i
$5$	−0.363043	−	2.20640i	−0.162358	−	0.986732i
$6$	1.00000			0.408248
$7$	−0.268117	−	0.154798i	−0.101339	−	0.0585080i	0.448474	−	0.893796i	$-0.351968\pi$
$7$	−0.268117	−	0.154798i	−0.101339	−	0.0585080i	−0.549813	+	0.835288i	$0.685301\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.41760	−	1.72928i	−0.448286	−	0.546845i
$11$	4.57198			1.37851			0.689253	−	0.724521i	$-0.257939\pi$
$11$	4.57198			1.37851			0.689253	+	0.724521i	$0.257939\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−3.32139	−	1.91760i	−0.921187	−	0.531848i	−0.0371735	−	0.999309i	$-0.511835\pi$
$13$	−3.32139	−	1.91760i	−0.921187	−	0.531848i	−0.884014	+	0.467461i	$0.845169\pi$
$14$	−0.309595			−0.0827428
$15$	0.788796	−	2.09232i	0.203666	−	0.540235i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.86619	−	1.65480i	0.695154	−	0.401347i	−0.110386	−	0.993889i	$-0.535209\pi$
$17$	2.86619	−	1.65480i	0.695154	−	0.401347i	0.805540	+	0.592541i	$0.201875\pi$
$18$	0.866025	+	0.500000i	0.204124	+	0.117851i
$19$	−0.688327	+	1.19222i	−0.157913	+	0.273513i	−0.934116	−	0.356970i	$-0.883810\pi$
$19$	−0.688327	+	1.19222i	−0.157913	+	0.273513i	0.776203	+	0.630483i	$0.217143\pi$
$20$	−2.09232	−	0.788796i	−0.467857	−	0.176380i
$21$	−0.154798	−	0.268117i	−0.0337796	−	0.0585080i
$22$	3.95946	−	2.28599i	0.844159	−	0.487375i
$23$		−	5.47919i		−	1.14249i	−0.820780	−	0.571245i	$-0.806461\pi$
$23$		−	5.47919i		−	1.14249i	0.820780	−	0.571245i	$-0.193539\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−4.73640	+	1.60203i	−0.947280	+	0.320407i
$26$	−3.83521			−0.752146
$27$			1.00000i			0.192450i
$28$	−0.268117	+	0.154798i	−0.0506694	+	0.0292540i
$29$	−0.690405			−0.128205			−0.0641025	−	0.997943i	$-0.520418\pi$
$29$	−0.690405			−0.128205			−0.0641025	+	0.997943i	$0.520418\pi$
$30$	−0.363043	−	2.20640i	−0.0662822	−	0.402832i
$31$	2.73678			0.491540			0.245770	−	0.969328i	$-0.420959\pi$
$31$	2.73678			0.491540			0.245770	+	0.969328i	$0.420959\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	3.95946	+	2.28599i	0.689253	+	0.397940i
$34$	1.65480	−	2.86619i	0.283795	−	0.491548i
$35$	−0.244208	+	0.647772i	−0.0412786	+	0.109494i
$36$	1.00000			0.166667
$37$	6.02425	−	0.841687i	0.990380	−	0.138372i
$37$	6.02425	−	0.841687i	0.990380	−	0.138372i
$38$			1.37665i			0.223323i
$39$	−1.91760	−	3.32139i	−0.307062	−	0.531848i
$40$	−2.20640	+	0.363043i	−0.348862	+	0.0574021i
$41$	0.175457	−	0.303900i	0.0274017	−	0.0474612i	−0.851999	−	0.523543i	$-0.824610\pi$
$41$	0.175457	−	0.303900i	0.0274017	−	0.0474612i	0.879401	+	0.476082i	$0.157943\pi$
$42$	−0.268117	−	0.154798i	−0.0413714	−	0.0238858i
$43$		−	5.04831i		−	0.769860i	−0.922946	−	0.384930i	$-0.874226\pi$
$43$		−	5.04831i		−	0.769860i	0.922946	−	0.384930i	$-0.125774\pi$
$44$	2.28599	−	3.95946i	0.344626	−	0.596910i
$45$	1.72928	−	1.41760i	0.257785	−	0.211324i
$46$	−2.73959	−	4.74511i	−0.403931	−	0.699629i
$47$		−	3.77518i		−	0.550667i	−0.961349	−	0.275333i	$-0.911212\pi$
$47$		−	3.77518i		−	0.550667i	0.961349	−	0.275333i	$-0.0887882\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.45208	−	5.97917i	−0.493154	−	0.854167i
$50$	−3.30083	+	3.75560i	−0.466807	+	0.531122i
$51$	3.30960			0.463436
$52$	−3.32139	+	1.91760i	−0.460594	+	0.265924i
$53$	−11.8620	+	6.84854i	−1.62937	+	0.940720i	−0.645095	+	0.764102i	$0.723182\pi$
$53$	−11.8620	+	6.84854i	−1.62937	+	0.940720i	−0.984280	+	0.176617i	$0.943484\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−1.65982	−	10.0876i	−0.223811	−	1.36022i
$56$	−0.154798	+	0.268117i	−0.0206857	+	0.0358287i
$57$	−1.19222	+	0.688327i	−0.157913	+	0.0911711i
$58$	−0.597908	+	0.345202i	−0.0785092	+	0.0453273i
$59$	5.77406	+	10.0010i	0.751719	+	1.30202i	0.946989	+	0.321266i	$0.104108\pi$
$59$	5.77406	+	10.0010i	0.751719	+	1.30202i	−0.195270	+	0.980750i	$0.562558\pi$
$60$	−1.41760	−	1.72928i	−0.183012	−	0.223249i
$61$	2.37967	−	4.12172i	0.304686	−	0.527732i	−0.672505	−	0.740092i	$-0.734782\pi$
$61$	2.37967	−	4.12172i	0.304686	−	0.527732i	0.977191	+	0.212361i	$0.0681151\pi$
$62$	2.37012	−	1.36839i	0.301005	−	0.173786i
$63$		−	0.309595i		−	0.0390053i
$64$	−1.00000			−0.125000
$65$	−3.02520	+	8.02448i	−0.375229	+	0.995314i
$66$	4.57198			0.562772
$67$	4.13186	+	2.38553i	0.504787	+	0.291439i	0.730688	−	0.682711i	$-0.239199\pi$
$67$	4.13186	+	2.38553i	0.504787	+	0.291439i	−0.225901	+	0.974150i	$0.572533\pi$
$68$		−	3.30960i		−	0.401347i
$69$	2.73959	−	4.74511i	0.329808	−	0.571245i
$70$	0.112396	+	0.683091i	0.0134339	+	0.0816450i
$71$	−6.67007	+	11.5529i	−0.791591	+	1.37108i	0.133390	+	0.991064i	$0.457414\pi$
$71$	−6.67007	+	11.5529i	−0.791591	+	1.37108i	−0.924981	+	0.380013i	$0.875920\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			13.3833i			1.56640i	0.621769	+	0.783201i	$0.286414\pi$
$73$			13.3833i			1.56640i	−0.621769	+	0.783201i	$0.713586\pi$
$74$	4.79631	−	3.74105i	0.557560	−	0.434888i
$75$	−4.90286	−	0.980798i	−0.566133	−	0.113253i
$76$	0.688327	+	1.19222i	0.0789565	+	0.136757i
$77$	−1.22583	−	0.707733i	−0.139696	−	0.0806536i
$78$	−3.32139	−	1.91760i	−0.376073	−	0.217126i
$79$	7.63359	−	13.2218i	0.858846	−	1.48757i	−0.0141837	−	0.999899i	$-0.504515\pi$
$79$	7.63359	−	13.2218i	0.858846	−	1.48757i	0.873030	−	0.487666i	$-0.162152\pi$
$80$	−1.72928	+	1.41760i	−0.193339	+	0.158493i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		−	0.350914i		−	0.0387519i
$83$	2.66210	−	1.53697i	0.292204	−	0.168704i	−0.346732	−	0.937964i	$-0.612708\pi$
$83$	2.66210	−	1.53697i	0.292204	−	0.168704i	0.638935	+	0.769261i	$0.279375\pi$
$84$	−0.309595			−0.0337796
$85$	−4.69170	−	5.72321i	−0.508886	−	0.620769i
$86$	−2.52416	−	4.37197i	−0.272187	−	0.471441i
$87$	−0.597908	−	0.345202i	−0.0641025	−	0.0370096i
$88$		−	4.57198i		−	0.487375i
$89$	5.47776	+	9.48775i	0.580641	+	1.00570i	0.995403	+	0.0957700i	$0.0305313\pi$
$89$	5.47776	+	9.48775i	0.580641	+	1.00570i	−0.414763	+	0.909930i	$0.636135\pi$
$90$	0.788796	−	2.09232i	0.0831464	−	0.220550i
$91$	0.593681	+	1.02829i	0.0622347	+	0.107794i
$92$	−4.74511	−	2.73959i	−0.494712	−	0.285622i
$93$	2.37012	+	1.36839i	0.245770	+	0.141895i
$94$	−1.88759	−	3.26940i	−0.194690	−	0.337213i
$95$	2.88040	+	1.08590i	0.295523	+	0.111411i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$		−	0.990093i		−	0.100529i	−0.998736	−	0.0502644i	$-0.983994\pi$
$97$		−	0.990093i		−	0.100529i	0.998736	−	0.0502644i	$-0.0160064\pi$
$98$	−5.97917	−	3.45208i	−0.603987	−	0.348712i
$99$	2.28599	+	3.95946i	0.229751	+	0.397940i
$100$	−0.980798	+	4.90286i	−0.0980798	+	0.490286i
$101$	13.4339			1.33672			0.668360	−	0.743838i	$-0.266997\pi$
$101$	13.4339			1.33672			0.668360	+	0.743838i	$0.266997\pi$
$102$	2.86619	−	1.65480i	0.283795	−	0.163849i
$103$			5.80947i			0.572424i	0.958166	+	0.286212i	$0.0923961\pi$
$103$			5.80947i			0.572424i	−0.958166	+	0.286212i	$0.907604\pi$
$104$	−1.91760	+	3.32139i	−0.188037	+	0.325689i
$105$	−0.535376	+	0.438884i	−0.0522474	+	0.0428307i
$106$	−6.84854	+	11.8620i	−0.665189	+	1.15214i
$107$	−6.31907	−	3.64832i	−0.610888	−	0.352696i	0.162425	−	0.986721i	$-0.448068\pi$
$107$	−6.31907	−	3.64832i	−0.610888	−	0.352696i	−0.773313	+	0.634025i	$0.781402\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	6.46495	+	11.1976i	0.619229	+	1.07254i	0.989627	+	0.143663i	$0.0458883\pi$
$109$	6.46495	+	11.1976i	0.619229	+	1.07254i	−0.370397	+	0.928873i	$0.620778\pi$
$110$	−6.48126	−	7.90623i	−0.617964	−	0.753829i
$111$	5.63800	+	2.28320i	0.535135	+	0.216712i
$112$			0.309595i			0.0292540i
$113$	−2.12749	+	1.22831i	−0.200138	+	0.115549i	−0.596720	−	0.802450i	$-0.703530\pi$
$113$	−2.12749	+	1.22831i	−0.200138	+	0.115549i	0.396582	+	0.917999i	$0.370196\pi$
$114$	−0.688327	+	1.19222i	−0.0644677	+	0.111661i
$115$	−12.0893	+	1.98918i	−1.12733	+	0.185492i
$116$	−0.345202	+	0.597908i	−0.0320512	+	0.0555144i
$117$		−	3.83521i		−	0.354565i
$118$	10.0010	+	5.77406i	0.920664	+	0.531546i
$119$	−1.02464			−0.0939282
$120$	−2.09232	−	0.788796i	−0.191002	−	0.0720069i
$121$	9.90305			0.900277
$122$		−	4.75935i		−	0.430891i
$123$	0.303900	−	0.175457i	0.0274017	−	0.0158204i
$124$	1.36839	−	2.37012i	0.122885	−	0.212843i
$125$	5.25424	+	9.86879i	0.469954	+	0.882691i
$126$	−0.154798	−	0.268117i	−0.0137905	−	0.0238858i
$127$	−1.18210	+	0.682488i	−0.104895	+	0.0605610i	−0.551530	−	0.834155i	$-0.685956\pi$
$127$	−1.18210	+	0.682488i	−0.104895	+	0.0605610i	0.446635	+	0.894716i	$0.352622\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.52416	−	4.37197i	0.222239	−	0.384930i
$130$	1.39234	+	8.46200i	0.122117	+	0.742167i
$131$	5.74528	+	9.95113i	0.501968	+	0.869434i	0.999997	+	0.00227379i	$0.000723771\pi$
$131$	5.74528	+	9.95113i	0.501968	+	0.869434i	−0.498030	+	0.867160i	$0.665943\pi$
$132$	3.95946	−	2.28599i	0.344626	−	0.198970i
$133$	0.369105	−	0.213103i	0.0320055	−	0.0184784i
$134$	4.77106			0.412157
$135$	2.20640	−	0.363043i	0.189897	−	0.0312457i
$136$	−1.65480	−	2.86619i	−0.141898	−	0.245774i
$137$			9.54995i			0.815908i	0.913003	+	0.407954i	$0.133758\pi$
$137$			9.54995i			0.815908i	−0.913003	+	0.407954i	$0.866242\pi$
$138$		−	5.47919i		−	0.466419i
$139$	−1.30897	−	2.26721i	−0.111026	−	0.192302i	0.805158	−	0.593060i	$-0.202080\pi$
$139$	−1.30897	−	2.26721i	−0.111026	−	0.192302i	−0.916184	+	0.400758i	$0.868747\pi$
$140$	0.438884	+	0.535376i	0.0370924	+	0.0452475i
$141$	1.88759	−	3.26940i	0.158964	−	0.275333i
$142$			13.3401i			1.11948i
$143$	−15.1853	−	8.76726i	−1.26986	−	0.733155i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	0.250646	+	1.52331i	0.0208150	+	0.126504i
$146$	6.69167	+	11.5903i	0.553806	+	0.959221i
$147$		−	6.90415i		−	0.569445i
$148$	2.28320	−	5.63800i	0.187678	−	0.463440i
$149$	−6.42401			−0.526276			−0.263138	−	0.964758i	$-0.584757\pi$
$149$	−6.42401			−0.526276			−0.263138	+	0.964758i	$0.584757\pi$
$150$	−4.73640	+	1.60203i	−0.386725	+	0.130806i
$151$	−2.44034	+	4.22679i	−0.198592	+	0.343972i	−0.948072	−	0.318055i	$-0.896970\pi$
$151$	−2.44034	+	4.22679i	−0.198592	+	0.343972i	0.749480	+	0.662027i	$0.230304\pi$
$152$	1.19222	+	0.688327i	0.0967016	+	0.0558307i
$153$	2.86619	+	1.65480i	0.231718	+	0.133782i
$154$	−1.41547			−0.114061
$155$	−0.993566	−	6.03842i	−0.0798052	−	0.485018i
$156$	−3.83521			−0.307062
$157$	8.03324	−	4.63800i	0.641123	−	0.370152i	−0.143924	−	0.989589i	$-0.545972\pi$
$157$	8.03324	−	4.63800i	0.641123	−	0.370152i	0.785047	+	0.619436i	$0.212639\pi$
$158$		−	15.2672i		−	1.21459i
$159$	−13.6971			−1.08625
$160$	−0.788796	+	2.09232i	−0.0623598	+	0.165412i
$161$	−0.848165	+	1.46907i	−0.0668448	+	0.115779i
$162$			1.00000i			0.0785674i
$163$	−11.3462	+	6.55071i	−0.888700	+	0.513091i	−0.873517	−	0.486794i	$-0.838166\pi$
$163$	−11.3462	+	6.55071i	−0.888700	+	0.513091i	−0.0151830	+	0.999885i	$0.504833\pi$
$164$	−0.175457	−	0.303900i	−0.0137009	−	0.0237306i
$165$	3.60636	−	9.56605i	0.280755	−	0.744716i
$166$	1.53697	−	2.66210i	0.119292	−	0.206619i
$167$	18.9448	+	10.9378i	1.46599	+	0.846392i	0.999277	−	0.0380142i	$-0.0121032\pi$
$167$	18.9448	+	10.9378i	1.46599	+	0.846392i	0.466717	+	0.884407i	$0.345437\pi$
$168$	−0.268117	+	0.154798i	−0.0206857	+	0.0119429i
$169$	0.854410	+	1.47988i	0.0657238	+	0.113837i
$170$	−6.92473	−	2.61060i	−0.531103	−	0.200224i
$171$	−1.37665			−0.105275
$172$	−4.37197	−	2.52416i	−0.333359	−	0.192465i
$173$	−3.66596	+	2.11655i	−0.278718	+	0.160918i	−0.632843	−	0.774280i	$-0.718112\pi$
$173$	−3.66596	+	2.11655i	−0.278718	+	0.160918i	0.354125	+	0.935198i	$0.384779\pi$
$174$	−0.690405			−0.0523394
$175$	1.51790	+	0.303651i	0.114743	+	0.0229538i
$176$	−2.28599	−	3.95946i	−0.172313	−	0.298455i
$177$			11.5481i			0.868011i
$178$	9.48775	+	5.47776i	0.711137	+	0.410575i
$179$	−18.1757			−1.35852			−0.679260	−	0.733898i	$-0.737699\pi$
$179$	−18.1757			−1.35852			−0.679260	+	0.733898i	$0.737699\pi$
$180$	−0.363043	−	2.20640i	−0.0270596	−	0.164455i
$181$	3.63216	−	6.29109i	0.269977	−	0.467613i	−0.698879	−	0.715240i	$-0.746317\pi$
$181$	3.63216	−	6.29109i	0.269977	−	0.467613i	0.968855	+	0.247627i	$0.0796507\pi$
$182$	1.02829	+	0.593681i	0.0762216	+	0.0440066i
$183$	4.12172	−	2.37967i	0.304686	−	0.175911i
$184$	−5.47919			−0.403931
$185$	−4.04416	−	12.9863i	−0.297332	−	0.954774i
$186$	2.73678			0.200670
$187$	13.1042	−	7.56571i	0.958274	−	0.553260i
$188$	−3.26940	−	1.88759i	−0.238446	−	0.137667i
$189$	0.154798	−	0.268117i	0.0112599	−	0.0195027i
$190$	3.03745	−	0.499784i	0.220360	−	0.0362581i
$191$	−3.42110			−0.247542			−0.123771	−	0.992311i	$-0.539499\pi$
$191$	−3.42110			−0.247542			−0.123771	+	0.992311i	$0.539499\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$			19.2854i			1.38819i	0.719883	+	0.694096i	$0.244195\pi$
$193$			19.2854i			1.38819i	−0.719883	+	0.694096i	$0.755805\pi$
$194$	−0.495047	−	0.857446i	−0.0355423	−	0.0615610i
$195$	−6.63214	+	5.43681i	−0.474937	+	0.389338i
$196$	−6.90415			−0.493154
$197$	−7.69610	+	4.44334i	−0.548324	+	0.316575i	−0.748446	−	0.663196i	$-0.769200\pi$
$197$	−7.69610	+	4.44334i	−0.548324	+	0.316575i	0.200122	+	0.979771i	$0.435866\pi$
$198$	3.95946	+	2.28599i	0.281386	+	0.162458i
$199$	−12.5562			−0.890082			−0.445041	−	0.895510i	$-0.646811\pi$
$199$	−12.5562			−0.890082			−0.445041	+	0.895510i	$0.646811\pi$
$200$	1.60203	+	4.73640i	0.113281	+	0.334914i
$201$	2.38553	+	4.13186i	0.168262	+	0.291439i
$202$	11.6341	−	6.71693i	0.818570	−	0.472602i
$203$	0.185110	+	0.106873i	0.0129921	+	0.00750102i
$204$	1.65480	−	2.86619i	0.115859	−	0.200674i
$205$	−0.734223	−	0.276799i	−0.0512804	−	0.0193325i
$206$	2.90473	+	5.03115i	0.202382	+	0.350537i
$207$	4.74511	−	2.73959i	0.329808	−	0.190415i
$208$			3.83521i			0.265924i
$209$	−3.14702	+	5.45080i	−0.217684	+	0.377040i
$210$	−0.244208	+	0.647772i	−0.0168519	+	0.0447005i
$211$	−19.5648			−1.34689			−0.673447	−	0.739235i	$-0.735187\pi$
$211$	−19.5648			−1.34689			−0.673447	+	0.739235i	$0.735187\pi$
$212$			13.6971i			0.940720i
$213$	−11.5529	+	6.67007i	−0.791591	+	0.457025i
$214$	−7.29664			−0.498788
$215$	−11.1386	+	1.83275i	−0.759646	+	0.124993i
$216$	1.00000			0.0680414
$217$	−0.733778	−	0.423647i	−0.0498121	−	0.0287590i
$218$	11.1976	+	6.46495i	0.758398	+	0.437861i
$219$	−6.69167	+	11.5903i	−0.452181	+	0.783201i
$220$	−9.56605	−	3.60636i	−0.644943	−	0.243141i
$221$	−12.6930			−0.853823
$222$	6.02425	−	0.841687i	0.404321	−	0.0564903i
$223$		−	3.99326i		−	0.267408i	−0.991021	−	0.133704i	$-0.957313\pi$
$223$		−	3.99326i		−	0.267408i	0.991021	−	0.133704i	$-0.0426872\pi$
$224$	0.154798	+	0.268117i	0.0103429	+	0.0179144i
$225$	−3.75560	−	3.30083i	−0.250373	−	0.220055i
$226$	−1.22831	+	2.12749i	−0.0817058	+	0.141519i
$227$	23.6856	+	13.6749i	1.57207	+	0.907633i	0.995916	+	0.0902890i	$0.0287791\pi$
$227$	23.6856	+	13.6749i	1.57207	+	0.907633i	0.576150	+	0.817344i	$0.304554\pi$
$228$			1.37665i			0.0911711i
$229$	11.8978	−	20.6075i	0.786226	−	1.36178i	−0.142038	−	0.989861i	$-0.545365\pi$
$229$	11.8978	−	20.6075i	0.786226	−	1.36178i	0.928264	−	0.371922i	$-0.121301\pi$
$230$	−9.47503	+	7.76732i	−0.624765	+	0.512162i
$231$	−0.707733	−	1.22583i	−0.0465654	−	0.0806536i
$232$			0.690405i			0.0453273i
$233$			25.6377i			1.67958i	0.542910	+	0.839791i	$0.317322\pi$
$233$			25.6377i			1.67958i	−0.542910	+	0.839791i	$0.682678\pi$
$234$	−1.91760	−	3.32139i	−0.125358	−	0.217126i
$235$	−8.32956	+	1.37055i	−0.543360	+	0.0894049i
$236$	11.5481			0.751719
$237$	13.2218	−	7.63359i	0.858846	−	0.495855i
$238$	−0.887360	+	0.512318i	−0.0575190	+	0.0332086i
$239$	−3.08398	−	5.34161i	−0.199486	−	0.345520i	0.748876	−	0.662710i	$-0.230594\pi$
$239$	−3.08398	−	5.34161i	−0.199486	−	0.345520i	−0.948362	+	0.317190i	$0.897261\pi$
$240$	−2.20640	+	0.363043i	−0.142422	+	0.0234343i
$241$	2.00641	−	3.47521i	0.129244	−	0.223858i	−0.794140	−	0.607735i	$-0.792078\pi$
$241$	2.00641	−	3.47521i	0.129244	−	0.223858i	0.923384	+	0.383878i	$0.125412\pi$
$242$	8.57629	−	4.95152i	0.551305	−	0.318296i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−2.37967	−	4.12172i	−0.152343	−	0.263866i
$245$	−11.9392	+	9.78735i	−0.762767	+	0.625291i
$246$	0.175457	−	0.303900i	0.0111867	−	0.0193760i
$247$	4.57240	−	2.63988i	0.290935	−	0.167971i
$248$		−	2.73678i		−	0.173786i
$249$	3.07393			0.194803
$250$	9.48470	+	5.91950i	0.599865	+	0.374382i
$251$	16.7469			1.05706			0.528528	−	0.848916i	$-0.322744\pi$
$251$	16.7469			1.05706			0.528528	+	0.848916i	$0.322744\pi$
$252$	−0.268117	−	0.154798i	−0.0168898	−	0.00975134i
$253$		−	25.0508i		−	1.57493i
$254$	−0.682488	+	1.18210i	−0.0428231	+	0.0741718i
$255$	−1.20152	−	7.30229i	−0.0752423	−	0.457287i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.60041	−	0.923995i	0.0998306	−	0.0576372i	−0.449253	−	0.893404i	$-0.648310\pi$
$257$	1.60041	−	0.923995i	0.0998306	−	0.0576372i	0.549084	+	0.835767i	$0.314977\pi$
$258$		−	5.04831i		−	0.314294i
$259$	−1.74550	−	0.706869i	−0.108460	−	0.0439227i
$260$	5.43681	+	6.63214i	0.337176	+	0.411308i
$261$	−0.345202	−	0.597908i	−0.0213675	−	0.0370096i
$262$	9.95113	+	5.74528i	0.614783	+	0.354945i
$263$	−6.35247	−	3.66760i	−0.391710	−	0.226154i	0.291191	−	0.956665i	$-0.405949\pi$
$263$	−6.35247	−	3.66760i	−0.391710	−	0.226154i	−0.682901	+	0.730511i	$0.739282\pi$
$264$	2.28599	−	3.95946i	0.140693	−	0.243688i
$265$	19.4170	+	23.6861i	1.19278	+	1.45502i
$266$	0.213103	−	0.369105i	0.0130662	−	0.0226313i
$267$			10.9555i			0.670466i
$268$	4.13186	−	2.38553i	0.252394	−	0.145720i
$269$	−16.3744			−0.998363			−0.499181	−	0.866498i	$-0.666366\pi$
$269$	−16.3744			−0.998363			−0.499181	+	0.866498i	$0.666366\pi$
$270$	1.72928	−	1.41760i	0.105240	−	0.0862726i
$271$	−4.72672	−	8.18692i	−0.287128	−	0.497320i	0.685995	−	0.727606i	$-0.259367\pi$
$271$	−4.72672	−	8.18692i	−0.287128	−	0.497320i	−0.973123	+	0.230286i	$0.926034\pi$
$272$	−2.86619	−	1.65480i	−0.173789	−	0.100337i
$273$			1.18736i			0.0718625i
$274$	4.77498	+	8.27050i	0.288467	+	0.499639i
$275$	−21.6548	+	7.32447i	−1.30583	+	0.441682i
$276$	−2.73959	−	4.74511i	−0.164904	−	0.285622i
$277$	7.62602	+	4.40289i	0.458203	+	0.264544i	0.711289	−	0.702900i	$-0.248112\pi$
$277$	7.62602	+	4.40289i	0.458203	+	0.264544i	−0.253085	+	0.967444i	$0.581445\pi$
$278$	−2.26721	−	1.30897i	−0.135978	−	0.0785071i
$279$	1.36839	+	2.37012i	0.0819233	+	0.141895i
$280$	0.647772	+	0.244208i	0.0387118	+	0.0145942i
$281$	−1.60303	−	2.77653i	−0.0956286	−	0.165634i	0.814242	−	0.580525i	$-0.197153\pi$
$281$	−1.60303	−	2.77653i	−0.0956286	−	0.165634i	−0.909871	+	0.414892i	$0.863819\pi$
$282$		−	3.77518i		−	0.224809i
$283$	−17.6209	−	10.1734i	−1.04745	−	0.604748i	−0.125519	−	0.992091i	$-0.540059\pi$
$283$	−17.6209	−	10.1734i	−1.04745	−	0.604748i	−0.921936	+	0.387343i	$0.873393\pi$
$284$	6.67007	+	11.5529i	0.395796	+	0.685538i
$285$	1.95155	+	2.38062i	0.115600	+	0.141016i
$286$	−17.5345			−1.03684
$287$	−0.0940861	+	0.0543206i	−0.00555372	+	0.00320644i
$288$		−	1.00000i		−	0.0589256i
$289$	−3.02329	+	5.23649i	−0.177841	+	0.308029i
$290$	0.978720	+	1.19390i	0.0574724	+	0.0701083i
$291$	0.495047	−	0.857446i	0.0290201	−	0.0502644i
$292$	11.5903	+	6.69167i	0.678272	+	0.391600i
$293$	−16.0621	−	9.27344i	−0.938357	−	0.541760i	−0.0489118	−	0.998803i	$-0.515575\pi$
$293$	−16.0621	−	9.27344i	−0.938357	−	0.541760i	−0.889445	+	0.457043i	$0.848909\pi$
$294$	−3.45208	−	5.97917i	−0.201329	−	0.348712i
$295$	19.9699	−	16.3707i	1.16269	−	0.953137i
$296$	−0.841687	−	6.02425i	−0.0489220	−	0.350152i
$297$			4.57198i			0.265293i
$298$	−5.56336	+	3.21201i	−0.322277	+	0.186067i
$299$	−10.5069	+	18.1985i	−0.607630	+	1.05245i
$300$	−3.30083	+	3.75560i	−0.190573	+	0.216830i
$301$	−0.781467	+	1.35354i	−0.0450430	+	0.0780168i
$302$			4.88068i			0.280852i
$303$	11.6341	+	6.71693i	0.668360	+	0.385878i
$304$	1.37665			0.0789565
$305$	−9.95808	−	3.75415i	−0.570198	−	0.214962i
$306$	3.30960			0.189197
$307$			2.00272i			0.114301i	0.998366	+	0.0571506i	$0.0182015\pi$
$307$			2.00272i			0.114301i	−0.998366	+	0.0571506i	$0.981798\pi$
$308$	−1.22583	+	0.707733i	−0.0698481	+	0.0403268i
$309$	−2.90473	+	5.03115i	−0.165245	+	0.286212i
$310$	−3.87967	−	4.73265i	−0.220350	−	0.268796i
$311$	12.6672	+	21.9402i	0.718290	+	1.24411i	0.961677	+	0.274185i	$0.0884082\pi$
$311$	12.6672	+	21.9402i	0.718290	+	1.24411i	−0.243387	+	0.969929i	$0.578259\pi$
$312$	−3.32139	+	1.91760i	−0.188037	+	0.108563i
$313$	29.0006	−	16.7435i	1.63921	−	0.946398i	0.658103	−	0.752928i	$-0.271359\pi$
$313$	29.0006	−	16.7435i	1.63921	−	0.946398i	0.981106	−	0.193470i	$-0.0619742\pi$
$314$	4.63800	−	8.03324i	0.261737	−	0.453342i
$315$	−0.683091	+	0.112396i	−0.0384878	+	0.00633281i
$316$	−7.63359	−	13.2218i	−0.429423	−	0.743783i
$317$	26.9267	−	15.5461i	1.51235	−	0.873158i	0.512458	−	0.858712i	$-0.328735\pi$
$317$	26.9267	−	15.5461i	1.51235	−	0.873158i	0.999896	−	0.0144452i	$-0.00459822\pi$
$318$	−11.8620	+	6.84854i	−0.665189	+	0.384047i
$319$	−3.15652			−0.176731
$320$	0.363043	+	2.20640i	0.0202947	+	0.123341i
$321$	−3.64832	−	6.31907i	−0.203629	−	0.352696i
$322$			1.69633i			0.0945328i
$323$			4.55617i			0.253512i
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	18.8035	+	3.76156i	1.04303	+	0.208654i
$326$	−6.55071	+	11.3462i	−0.362810	+	0.628406i
$327$			12.9299i			0.715025i
$328$	−0.303900	−	0.175457i	−0.0167801	−	0.00968798i
$329$	−0.584389	+	1.01219i	−0.0322184	+	0.0558039i
$330$	−1.65982	−	10.0876i	−0.0913704	−	0.555306i
$331$	−15.1793	−	26.2913i	−0.834328	−	1.44510i	−0.894576	−	0.446915i	$-0.852523\pi$
$331$	−15.1793	−	26.2913i	−0.834328	−	1.44510i	0.0602485	−	0.998183i	$-0.480811\pi$
$332$		−	3.07393i		−	0.168704i
$333$	3.74105	+	4.79631i	0.205008	+	0.262836i
$334$	21.8756			1.19698
$335$	3.76340	−	9.98259i	0.205616	−	0.545407i
$336$	−0.154798	+	0.268117i	−0.00844491	+	0.0146270i
$337$	10.2584	+	5.92268i	0.558809	+	0.322629i	0.752668	−	0.658401i	$-0.228767\pi$
$337$	10.2584	+	5.92268i	0.558809	+	0.322629i	−0.193858	+	0.981030i	$0.562100\pi$
$338$	1.47988	+	0.854410i	0.0804949	+	0.0464738i
$339$	−2.45662			−0.133425
$340$	−7.30229	+	1.20152i	−0.396022	+	0.0651618i
$341$	12.5125			0.677590
$342$	−1.19222	+	0.688327i	−0.0644677	+	0.0372205i
$343$			4.30466i			0.232430i
$344$	−5.04831			−0.272187
$345$	−11.4642	−	4.32196i	−0.617212	−	0.232686i
$346$	−2.11655	+	3.66596i	−0.113786	+	0.197083i
$347$			1.18913i			0.0638360i	0.999490	+	0.0319180i	$0.0101615\pi$
$347$			1.18913i			0.0638360i	−0.999490	+	0.0319180i	$0.989838\pi$
$348$	−0.597908	+	0.345202i	−0.0320512	+	0.0185048i
$349$	−3.71744	−	6.43879i	−0.198990	−	0.344660i	0.749211	−	0.662331i	$-0.230433\pi$
$349$	−3.71744	−	6.43879i	−0.198990	−	0.344660i	−0.948201	+	0.317671i	$0.897099\pi$
$350$	1.46637	−	0.495982i	0.0783806	−	0.0265114i
$351$	1.91760	−	3.32139i	0.102354	−	0.177283i
$352$	−3.95946	−	2.28599i	−0.211040	−	0.121844i
$353$	12.2088	−	7.04878i	0.649811	−	0.375169i	−0.138573	−	0.990352i	$-0.544251\pi$
$353$	12.2088	−	7.04878i	0.649811	−	0.375169i	0.788384	+	0.615184i	$0.210918\pi$
$354$	5.77406	+	10.0010i	0.306888	+	0.531546i
$355$	27.9118	+	10.5226i	1.48141	+	0.558484i
$356$	10.9555			0.580641
$357$	−0.887360	−	0.512318i	−0.0469641	−	0.0271147i
$358$	−15.7407	+	9.08787i	−0.831920	+	0.480309i
$359$	1.41624			0.0747465			0.0373733	−	0.999301i	$-0.488101\pi$
$359$	1.41624			0.0747465			0.0373733	+	0.999301i	$0.488101\pi$
$360$	−1.41760	−	1.72928i	−0.0747143	−	0.0911409i
$361$	8.55241	+	14.8132i	0.450127	+	0.779643i
$362$		−	7.26433i		−	0.381805i
$363$	8.57629	+	4.95152i	0.450138	+	0.259888i
$364$	1.18736			0.0622347
$365$	29.5290	−	4.85872i	1.54562	−	0.254317i
$366$	2.37967	−	4.12172i	0.124388	−	0.215446i
$367$	−16.3472	−	9.43807i	−0.853318	−	0.492663i	0.00845116	−	0.999964i	$-0.497310\pi$
$367$	−16.3472	−	9.43807i	−0.853318	−	0.492663i	−0.861769	+	0.507301i	$0.830643\pi$
$368$	−4.74511	+	2.73959i	−0.247356	+	0.142811i
$369$	0.350914			0.0182678
$370$	−9.99551	−	9.22442i	−0.519642	−	0.479555i
$371$	4.24055			0.220159
$372$	2.37012	−	1.36839i	0.122885	−	0.0709476i
$373$	19.4504	+	11.2297i	1.00710	+	0.581451i	0.910342	−	0.413857i	$-0.135819\pi$
$373$	19.4504	+	11.2297i	1.00710	+	0.581451i	0.0967600	+	0.995308i	$0.469152\pi$
$374$	7.56571	−	13.1042i	0.391214	−	0.677602i
$375$	−0.384086	+	11.1737i	−0.0198341	+	0.577009i
$376$	−3.77518			−0.194690
$377$	2.29310	+	1.32392i	0.118101	+	0.0681855i
$378$		−	0.309595i		−	0.0159239i
$379$	17.5279	+	30.3592i	0.900347	+	1.55945i	0.827044	+	0.562137i	$0.190021\pi$
$379$	17.5279	+	30.3592i	0.900347	+	1.55945i	0.0733034	+	0.997310i	$0.476646\pi$
$380$	2.38062	−	1.95155i	0.122123	−	0.100112i
$381$	−1.36498			−0.0699298
$382$	−2.96276	+	1.71055i	−0.151588	+	0.0875193i
$383$	−10.7629	−	6.21395i	−0.549957	−	0.317518i	0.199148	−	0.979969i	$-0.436183\pi$
$383$	−10.7629	−	6.21395i	−0.549957	−	0.317518i	−0.749105	+	0.662452i	$0.769516\pi$
$384$	−1.00000			−0.0510310
$385$	−1.11651	+	2.96161i	−0.0569028	+	0.150937i
$386$	9.64268	+	16.7016i	0.490800	+	0.850090i
$387$	4.37197	−	2.52416i	0.222239	−	0.128310i
$388$	−0.857446	−	0.495047i	−0.0435302	−	0.0251322i
$389$	−12.6077	+	21.8372i	−0.639235	+	1.10719i	0.346366	+	0.938100i	$0.387416\pi$
$389$	−12.6077	+	21.8372i	−0.639235	+	1.10719i	−0.985601	+	0.169088i	$0.945918\pi$
$390$	−3.02520	+	8.02448i	−0.153187	+	0.406335i
$391$	−9.06694	−	15.7044i	−0.458535	−	0.794206i
$392$	−5.97917	+	3.45208i	−0.301994	+	0.174356i
$393$			11.4906i			0.579623i
$394$	−4.44334	+	7.69610i	−0.223852	+	0.387724i
$395$	−31.9438	−	12.0427i	−1.60727	−	0.605934i
$396$	4.57198			0.229751
$397$		−	6.79635i		−	0.341099i	−0.985349	−	0.170550i	$-0.945446\pi$
$397$		−	6.79635i		−	0.341099i	0.985349	−	0.170550i	$-0.0545543\pi$
$398$	−10.8739	+	6.27808i	−0.545062	+	0.314692i
$399$	0.426206			0.0213370
$400$	3.75560	+	3.30083i	0.187780	+	0.165041i
$401$	−4.27501			−0.213484			−0.106742	−	0.994287i	$-0.534042\pi$
$401$	−4.27501			−0.213484			−0.106742	+	0.994287i	$0.534042\pi$
$402$	4.13186	+	2.38553i	0.206079	+	0.118980i
$403$	−9.08990	−	5.24805i	−0.452800	−	0.261424i
$404$	6.71693	−	11.6341i	0.334180	−	0.578817i
$405$	2.09232	+	0.788796i	0.103968	+	0.0391956i
$406$	0.213746			0.0106080
$407$	27.5428	−	3.84818i	1.36524	−	0.190747i
$408$		−	3.30960i		−	0.163849i
$409$	4.25865	+	7.37620i	0.210577	+	0.364730i	0.951895	−	0.306424i	$-0.0991325\pi$
$409$	4.25865	+	7.37620i	0.210577	+	0.364730i	−0.741318	+	0.671153i	$0.765799\pi$
$410$	−0.774256	+	0.127397i	−0.0382378	+	0.00629167i
$411$	−4.77498	+	8.27050i	−0.235532	+	0.407954i
$412$	5.03115	+	2.90473i	0.247867	+	0.143106i
$413$		−	3.57525i		−	0.175926i
$414$	2.73959	−	4.74511i	0.134644	−	0.233210i
$415$	−4.35762	−	5.31568i	−0.213907	−	0.260936i
$416$	1.91760	+	3.32139i	0.0940183	+	0.162844i
$417$		−	2.61795i		−	0.128202i
$418$			6.29404i			0.307852i
$419$	−8.64775	−	14.9783i	−0.422470	−	0.731740i	0.573710	−	0.819058i	$-0.305504\pi$
$419$	−8.64775	−	14.9783i	−0.422470	−	0.731740i	−0.996180	+	0.0873184i	$0.972170\pi$
$420$	0.112396	+	0.683091i	0.00548438	+	0.0333314i
$421$	−14.3686			−0.700282			−0.350141	−	0.936697i	$-0.613866\pi$
$421$	−14.3686			−0.700282			−0.350141	+	0.936697i	$0.613866\pi$
$422$	−16.9436	+	9.78239i	−0.824801	+	0.476199i
$423$	3.26940	−	1.88759i	0.158964	−	0.0917778i
$424$	6.84854	+	11.8620i	0.332595	+	0.576071i
$425$	−10.9244	+	12.4295i	−0.529911	+	0.602920i
$426$	−6.67007	+	11.5529i	−0.323166	+	0.559740i
$427$	−1.27606	+	0.736736i	−0.0617531	+	0.0356532i
$428$	−6.31907	+	3.64832i	−0.305444	+	0.176348i
$429$	−8.76726	−	15.1853i	−0.423287	−	0.733155i
$430$	−8.72993	+	7.15651i	−0.420995	+	0.345117i
$431$	11.6582	−	20.1926i	0.561557	−	0.972645i	−0.435804	−	0.900042i	$-0.643536\pi$
$431$	11.6582	−	20.1926i	0.561557	−	0.972645i	0.997361	−	0.0726036i	$-0.0231308\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$		−	30.7382i		−	1.47718i	−0.674154	−	0.738591i	$-0.735491\pi$
$433$		−	30.7382i		−	1.47718i	0.674154	−	0.738591i	$-0.264509\pi$
$434$	−0.847293			−0.0406714
$435$	−0.544588	+	1.44455i	−0.0261110	+	0.0692607i
$436$	12.9299			0.619229
$437$	6.53238	+	3.77147i	0.312486	+	0.180414i
$438$			13.3833i			0.639481i
$439$	−18.6368	+	32.2798i	−0.889484	+	1.54063i	−0.0489981	+	0.998799i	$0.515603\pi$
$439$	−18.6368	+	32.2798i	−0.889484	+	1.54063i	−0.840486	+	0.541833i	$0.817731\pi$
$440$	−10.0876	+	1.65982i	−0.480909	+	0.0791290i
$441$	3.45208	−	5.97917i	0.164385	−	0.284722i
$442$	−10.9924	+	6.34649i	−0.522857	+	0.301872i
$443$		−	15.5587i		−	0.739218i	−0.929187	−	0.369609i	$-0.879492\pi$
$443$		−	15.5587i		−	0.739218i	0.929187	−	0.369609i	$-0.120508\pi$
$444$	4.79631	−	3.74105i	0.227623	−	0.177542i
$445$	18.9451	−	15.5306i	0.898085	−	0.736220i
$446$	−1.99663	−	3.45826i	−0.0945431	−	0.163753i
$447$	−5.56336	−	3.21201i	−0.263138	−	0.151923i
$448$	0.268117	+	0.154798i	0.0126674	+	0.00731350i
$449$	0.541729	−	0.938301i	0.0255658	−	0.0442812i	−0.852959	−	0.521977i	$-0.825195\pi$
$449$	0.541729	−	0.938301i	0.0255658	−	0.0442812i	0.878525	+	0.477696i	$0.158528\pi$
$450$	−4.90286	−	0.980798i	−0.231123	−	0.0462353i
$451$	0.802186	−	1.38943i	0.0377735	−	0.0654255i
$452$			2.45662i			0.115549i
$453$	−4.22679	+	2.44034i	−0.198592	+	0.114657i
$454$	27.3497			1.28359
$455$	2.05328	−	1.68321i	0.0962592	−	0.0789101i
$456$	0.688327	+	1.19222i	0.0322339	+	0.0558307i
$457$	−21.6972	−	12.5269i	−1.01495	−	0.585984i	−0.102316	−	0.994752i	$-0.532625\pi$
$457$	−21.6972	−	12.5269i	−1.01495	−	0.585984i	−0.912638	+	0.408768i	$0.865958\pi$
$458$		−	23.7955i		−	1.11189i
$459$	1.65480	+	2.86619i	0.0772393	+	0.133782i
$460$	−4.32196	+	11.4642i	−0.201512	+	0.534521i
$461$	−5.11582	−	8.86086i	−0.238267	−	0.412691i	0.721950	−	0.691945i	$-0.243246\pi$
$461$	−5.11582	−	8.86086i	−0.238267	−	0.412691i	−0.960217	+	0.279254i	$0.909913\pi$
$462$	−1.22583	−	0.707733i	−0.0570307	−	0.0329267i
$463$	−14.3453	−	8.28227i	−0.666683	−	0.384910i	0.128135	−	0.991757i	$-0.459101\pi$
$463$	−14.3453	−	8.28227i	−0.666683	−	0.384910i	−0.794819	+	0.606847i	$0.792434\pi$
$464$	0.345202	+	0.597908i	0.0160256	+	0.0277572i
$465$	2.15876	−	5.72621i	0.100110	−	0.265547i
$466$	12.8189	+	22.2029i	0.593822	+	1.02853i
$467$			26.1213i			1.20875i	0.796699	+	0.604376i	$0.206577\pi$
$467$			26.1213i			1.20875i	−0.796699	+	0.604376i	$0.793423\pi$
$468$	−3.32139	−	1.91760i	−0.153531	−	0.0886413i
$469$	−0.738550	−	1.27921i	−0.0341031	−	0.0590682i
$470$	−6.52833	+	5.35171i	−0.301130	+	0.246856i
$471$	9.27599			0.427415
$472$	10.0010	−	5.77406i	0.460332	−	0.265773i
$473$		−	23.0808i		−	1.06126i
$474$	7.63359	−	13.2218i	0.350623	−	0.607296i
$475$	1.35022	−	6.74954i	0.0619523	−	0.309690i
$476$	−0.512318	+	0.887360i	−0.0234820	+	0.0406721i
$477$	−11.8620	−	6.84854i	−0.543125	−	0.313573i
$478$	−5.34161	−	3.08398i	−0.244319	−	0.141058i
$479$	2.17164	+	3.76140i	0.0992250	+	0.171863i	0.911364	−	0.411601i	$-0.135030\pi$
$479$	2.17164	+	3.76140i	0.0992250	+	0.171863i	−0.812139	+	0.583464i	$0.801697\pi$
$480$	−1.72928	+	1.41760i	−0.0789303	+	0.0647045i
$481$	−21.6229	−	8.75655i	−0.985919	−	0.399265i
$482$		−	4.01282i		−	0.182779i
$483$	−1.46907	+	0.848165i	−0.0668448	+	0.0385929i
$484$	4.95152	−	8.57629i	0.225069	−	0.389831i
$485$	−2.18454	+	0.359446i	−0.0991949	+	0.0163216i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$		−	13.9410i		−	0.631728i	−0.948804	−	0.315864i	$-0.897706\pi$
$487$		−	13.9410i		−	0.631728i	0.948804	−	0.315864i	$-0.102294\pi$
$488$	−4.12172	−	2.37967i	−0.186581	−	0.107723i
$489$	−13.1014			−0.592467
$490$	−5.44597	+	14.4457i	−0.246024	+	0.652590i
$491$	−28.8479			−1.30189			−0.650943	−	0.759127i	$-0.725626\pi$
$491$	−28.8479			−1.30189			−0.650943	+	0.759127i	$0.725626\pi$
$492$		−	0.350914i		−	0.0158204i
$493$	−1.97883	+	1.14248i	−0.0891222	+	0.0514547i
$494$	2.63988	−	4.57240i	0.118774	−	0.205722i
$495$	7.90623	−	6.48126i	0.355359	−	0.291311i
$496$	−1.36839	−	2.37012i	−0.0614425	−	0.106421i
$497$	3.57672	−	2.06502i	0.160438	−	0.0926289i
$498$	2.66210	−	1.53697i	0.119292	−	0.0688731i
$499$	16.1947	−	28.0501i	0.724976	−	1.25570i	−0.234007	−	0.972235i	$-0.575184\pi$
$499$	16.1947	−	28.0501i	0.724976	−	1.25570i	0.958984	−	0.283461i	$-0.0914827\pi$
$500$	11.1737	+	0.384086i	0.499705	+	0.0171768i
$501$	10.9378	+	18.9448i	0.488665	+	0.846392i
$502$	14.5033	−	8.37346i	0.647312	−	0.373726i
$503$	−6.88500	+	3.97506i	−0.306987	+	0.177239i	−0.645577	−	0.763695i	$-0.723383\pi$
$503$	−6.88500	+	3.97506i	−0.306987	+	0.177239i	0.338590	+	0.940934i	$0.390050\pi$
$504$	−0.309595			−0.0137905
$505$	−4.87706	−	29.6405i	−0.217027	−	1.31898i
$506$	−12.5254	−	21.6946i	−0.556821	−	0.964442i
$507$			1.70882i			0.0758913i
$508$			1.36498i			0.0605610i
$509$	−18.3769	−	31.8297i	−0.814541	−	1.41083i	−0.909657	−	0.415361i	$-0.863655\pi$
$509$	−18.3769	−	31.8297i	−0.814541	−	1.41083i	0.0951156	−	0.995466i	$-0.469678\pi$
$510$	−4.69170	−	5.72321i	−0.207752	−	0.253428i
$511$	2.07171	−	3.58831i	0.0916470	−	0.158737i
$512$			1.00000i			0.0441942i
$513$	−1.19222	−	0.688327i	−0.0526377	−	0.0303904i
$514$	0.923995	−	1.60041i	0.0407557	−	0.0705909i
$515$	12.8180	−	2.10908i	0.564829	−	0.0929373i
$516$	−2.52416	−	4.37197i	−0.111120	−	0.192465i
$517$		−	17.2601i		−	0.759097i
$518$	−1.86508	+	0.260582i	−0.0819469	+	0.0114493i
$519$	−4.23309			−0.185812
$520$	8.02448	+	3.02520i	0.351897	+	0.132664i
$521$	10.8737	−	18.8338i	0.476386	−	0.825125i	−0.523248	−	0.852181i	$-0.675280\pi$
$521$	10.8737	−	18.8338i	0.476386	−	0.825125i	0.999634	+	0.0270553i	$0.00861303\pi$
$522$	−0.597908	−	0.345202i	−0.0261697	−	0.0151091i
$523$	28.0959	+	16.2211i	1.22855	+	0.709301i	0.966726	−	0.255815i	$-0.0823439\pi$
$523$	28.0959	+	16.2211i	1.22855	+	0.709301i	0.261820	+	0.965117i	$0.415677\pi$
$524$	11.4906			0.501968
$525$	1.16272	+	1.02192i	0.0507451	+	0.0446003i
$526$	−7.33520			−0.319830
$527$	7.84413	−	4.52881i	0.341696	−	0.197278i
$528$		−	4.57198i		−	0.198970i
$529$	−7.02148			−0.305282
$530$	28.6587	+	10.8042i	1.24485	+	0.469305i
$531$	−5.77406	+	10.0010i	−0.250573	+	0.434005i
$532$		−	0.426206i		−	0.0184784i
$533$	−1.16552	+	0.672913i	−0.0504843	+	0.0291471i
$534$	5.47776	+	9.48775i	0.237046	+	0.410575i
$535$	−5.75556	+	15.2669i	−0.248834	+	0.660046i
$536$	2.38553	−	4.13186i	0.103039	−	0.178469i
$537$	−15.7407	−	9.08787i	−0.679260	−	0.392171i
$538$	−14.1806	+	8.18718i	−0.611370	+	0.352975i
$539$	−15.7828	−	27.3367i	−0.679815	−	1.17747i
$540$	0.788796	−	2.09232i	0.0339444	−	0.0900391i
$541$	1.49631			0.0643316			0.0321658	−	0.999483i	$-0.489760\pi$
$541$	1.49631			0.0643316			0.0321658	+	0.999483i	$0.489760\pi$
$542$	−8.18692	−	4.72672i	−0.351659	−	0.203030i
$543$	6.29109	−	3.63216i	0.269977	−	0.155871i
$544$	−3.30960			−0.141898
$545$	22.3594	−	18.3295i	0.957770	−	0.785148i
$546$	0.593681	+	1.02829i	0.0254072	+	0.0440066i
$547$		−	18.3785i		−	0.785806i	−0.919580	−	0.392903i	$-0.871471\pi$
$547$		−	18.3785i		−	0.785806i	0.919580	−	0.392903i	$-0.128529\pi$
$548$	8.27050	+	4.77498i	0.353298	+	0.203977i
$549$	4.75935			0.203124
$550$	−15.0913	+	17.1706i	−0.643496	+	0.732155i
$551$	0.475224	−	0.823112i	0.0202452	−	0.0350658i
$552$	−4.74511	−	2.73959i	−0.201965	−	0.116605i
$553$	−4.09340	+	2.36333i	−0.174069	+	0.100499i
$554$	8.80577			0.374121
$555$	2.99082	−	13.2686i	0.126953	−	0.563219i
$556$	−2.61795			−0.111026
$557$	−6.04437	+	3.48972i	−0.256108	+	0.147864i	−0.622558	−	0.782574i	$-0.713906\pi$
$557$	−6.04437	+	3.48972i	−0.256108	+	0.147864i	0.366450	+	0.930438i	$0.380573\pi$
$558$	2.37012	+	1.36839i	0.100335	+	0.0579285i
$559$	−9.68066	+	16.7674i	−0.409448	+	0.709185i
$560$	0.683091	−	0.112396i	0.0288659	−	0.00474961i
$561$	15.1314			0.638849
$562$	−2.77653	−	1.60303i	−0.117121	−	0.0676197i
$563$		−	41.0519i		−	1.73013i	−0.501660	−	0.865065i	$-0.667277\pi$
$563$		−	41.0519i		−	1.73013i	0.501660	−	0.865065i	$-0.332723\pi$
$564$	−1.88759	−	3.26940i	−0.0794819	−	0.137667i
$565$	3.48251	+	4.24817i	0.146510	+	0.178722i
$566$	−20.3469			−0.855243
$567$	0.268117	−	0.154798i	0.0112599	−	0.00650089i
$568$	11.5529	+	6.67007i	0.484749	+	0.279870i
$569$	2.75954			0.115686			0.0578429	−	0.998326i	$-0.481578\pi$
$569$	2.75954			0.115686			0.0578429	+	0.998326i	$0.481578\pi$
$570$	2.88040	+	1.08590i	0.120647	+	0.0454833i
$571$	−11.4590	−	19.8475i	−0.479544	−	0.830594i	0.520181	−	0.854056i	$-0.325864\pi$
$571$	−11.4590	−	19.8475i	−0.479544	−	0.830594i	−0.999725	+	0.0234621i	$0.992531\pi$
$572$	−15.1853	+	8.76726i	−0.634931	+	0.366577i
$573$	−2.96276	−	1.71055i	−0.123771	−	0.0714592i
$574$	−0.0543206	+	0.0940861i	−0.00226730	+	0.00392708i
$575$	8.77784	+	25.9516i	0.366061	+	1.08226i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	9.23858	−	5.33389i	0.384607	−	0.222053i	−0.295214	−	0.955431i	$-0.595391\pi$
$577$	9.23858	−	5.33389i	0.384607	−	0.222053i	0.679821	+	0.733378i	$0.262058\pi$
$578$			6.04658i			0.251505i
$579$	−9.64268	+	16.7016i	−0.400736	+	0.694096i
$580$	1.44455	+	0.544588i	0.0599816	+	0.0226128i
$581$	−0.951675			−0.0394821
$582$		−	0.990093i		−	0.0410407i
$583$	−54.2330	+	31.3114i	−2.24610	+	1.29679i
$584$	13.3833			0.553806
$585$	−8.46200	+	1.39234i	−0.349861	+	0.0575663i
$586$	−18.5469			−0.766165
$587$	−21.0853	−	12.1736i	−0.870284	−	0.502459i	−0.00284149	−	0.999996i	$-0.500904\pi$
$587$	−21.0853	−	12.1736i	−0.870284	−	0.502459i	−0.867443	+	0.497537i	$0.834238\pi$
$588$	−5.97917	−	3.45208i	−0.246577	−	0.142361i
$589$	−1.88380	+	3.26283i	−0.0776205	+	0.134443i
$590$	9.10912	−	24.1624i	0.375016	−	0.994749i
$591$	−8.88669			−0.365550
$592$	−3.74105	−	4.79631i	−0.153756	−	0.197127i
$593$			21.9586i			0.901733i	0.892591	+	0.450867i	$0.148885\pi$
$593$			21.9586i			0.901733i	−0.892591	+	0.450867i	$0.851115\pi$
$594$	2.28599	+	3.95946i	0.0937954	+	0.162458i
$595$	0.371986	+	2.26076i	0.0152499	+	0.0926819i
$596$	−3.21201	+	5.56336i	−0.131569	+	0.227884i
$597$	−10.8739	−	6.27808i	−0.445041	−	0.256945i
$598$			21.0138i			0.859319i
$599$	−22.2901	+	38.6075i	−0.910747	+	1.57746i	−0.0977352	+	0.995212i	$0.531160\pi$
$599$	−22.2901	+	38.6075i	−0.910747	+	1.57746i	−0.813012	+	0.582247i	$0.802173\pi$
$600$	−0.980798	+	4.90286i	−0.0400409	+	0.200158i
$601$	10.9231	+	18.9193i	0.445562	+	0.771736i	0.998091	−	0.0617578i	$-0.0196706\pi$
$601$	10.9231	+	18.9193i	0.445562	+	0.771736i	−0.552529	+	0.833493i	$0.686337\pi$
$602$			1.56293i			0.0637004i
$603$			4.77106i			0.194293i
$604$	2.44034	+	4.22679i	0.0992961	+	0.171986i
$605$	−3.59523	−	21.8501i	−0.146167	−	0.888332i
$606$	13.4339			0.545713
$607$	−21.2315	+	12.2580i	−0.861762	+	0.497539i	−0.864602	−	0.502457i	$-0.832429\pi$
$607$	−21.2315	+	12.2580i	−0.861762	+	0.497539i	0.00283994	+	0.999996i	$0.499096\pi$
$608$	1.19222	−	0.688327i	0.0483508	−	0.0279153i
$609$	0.106873	+	0.185110i	0.00433071	+	0.00750102i
$610$	−10.5010	+	1.72785i	−0.425174	+	0.0699584i
$611$	−7.23930	+	12.5388i	−0.292871	+	0.507267i
$612$	2.86619	−	1.65480i	0.115859	−	0.0668912i
$613$	15.8847	−	9.17104i	0.641577	−	0.370415i	−0.143645	−	0.989629i	$-0.545882\pi$
$613$	15.8847	−	9.17104i	0.641577	−	0.370415i	0.785222	+	0.619215i	$0.212549\pi$
$614$	1.00136	+	1.73440i	0.0404116	+	0.0699949i
$615$	−0.497457	−	0.606827i	−0.0200594	−	0.0244696i
$616$	−0.707733	+	1.22583i	−0.0285154	+	0.0493901i
$617$	24.8079	−	14.3229i	0.998730	−	0.576617i	0.0908575	−	0.995864i	$-0.471039\pi$
$617$	24.8079	−	14.3229i	0.998730	−	0.576617i	0.907872	+	0.419247i	$0.137706\pi$
$618$			5.80947i			0.233691i
$619$	−11.1758			−0.449193			−0.224596	−	0.974452i	$-0.572106\pi$
$619$	−11.1758			−0.449193			−0.224596	+	0.974452i	$0.572106\pi$
$620$	−5.72621	−	2.15876i	−0.229970	−	0.0866978i
$621$	5.47919			0.219872
$622$	21.9402	+	12.6672i	0.879722	+	0.507908i
$623$		−	3.39178i		−	0.135889i
$624$	−1.91760	+	3.32139i	−0.0767656	+	0.132962i
$625$	19.8670	−	15.1757i	0.794679	−	0.607030i
$626$	16.7435	−	29.0006i	0.669204	−	1.15910i
$627$	−5.45080	+	3.14702i	−0.217684	+	0.125680i
$628$		−	9.27599i		−	0.370152i
$629$	15.8738	−	12.3813i	0.632931	−	0.493677i
$630$	−0.535376	+	0.438884i	−0.0213299	+	0.0174855i
$631$	−18.1519	−	31.4400i	−0.722615	−	1.25161i	−0.959948	−	0.280178i	$-0.909607\pi$
$631$	−18.1519	−	31.4400i	−0.722615	−	1.25161i	0.237333	−	0.971428i	$-0.423727\pi$
$632$	−13.2218	−	7.63359i	−0.525934	−	0.303648i
$633$	−16.9436	−	9.78239i	−0.673447	−	0.388815i
$634$	15.5461	−	26.9267i	0.617416	−	1.06940i
$635$	1.93500	+	2.36042i	0.0767879	+	0.0936705i
$636$	−6.84854	+	11.8620i	−0.271562	+	0.470360i
$637$			26.4789i			1.04913i
$638$	−2.73363	+	1.57826i	−0.108225	+	0.0624839i
$639$	−13.3401			−0.527728
$640$	1.41760	+	1.72928i	0.0560357	+	0.0683557i
$641$	20.8852	+	36.1742i	0.824916	+	1.42880i	0.901984	+	0.431770i	$0.142111\pi$
$641$	20.8852	+	36.1742i	0.824916	+	1.42880i	−0.0770677	+	0.997026i	$0.524556\pi$
$642$	−6.31907	−	3.64832i	−0.249394	−	0.143988i
$643$		−	9.18122i		−	0.362072i	−0.983476	−	0.181036i	$-0.942055\pi$
$643$		−	9.18122i		−	0.362072i	0.983476	−	0.181036i	$-0.0579451\pi$
$644$	0.848165	+	1.46907i	0.0334224	+	0.0578893i
$645$	−10.5627	−	3.98209i	−0.415905	−	0.156795i
$646$	2.27808	+	3.94576i	0.0896300	+	0.155244i
$647$	2.25144	+	1.29987i	0.0885133	+	0.0511032i	0.543603	−	0.839342i	$-0.317060\pi$
$647$	2.25144	+	1.29987i	0.0885133	+	0.0511032i	−0.455090	+	0.890445i	$0.650393\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	26.3989	+	45.7243i	1.03625	+	1.79484i
$650$	18.1651	−	6.14413i	0.712493	−	0.240993i
$651$	−0.423647	−	0.733778i	−0.0166040	−	0.0287590i
$652$			13.1014i			0.513091i
$653$	16.7712	+	9.68287i	0.656309	+	0.378920i	0.790869	−	0.611985i	$-0.209629\pi$
$653$	16.7712	+	9.68287i	0.656309	+	0.378920i	−0.134560	+	0.990905i	$0.542962\pi$
$654$	6.46495	+	11.1976i	0.252799	+	0.437861i
$655$	19.8704	−	16.2891i	0.776400	−	0.636467i
$656$	−0.350914			−0.0137009
$657$	−11.5903	+	6.69167i	−0.452181	+	0.261067i
$658$			1.16878i			0.0455637i
$659$	3.00412	−	5.20328i	0.117024	−	0.202691i	−0.801563	−	0.597910i	$-0.795998\pi$
$659$	3.00412	−	5.20328i	0.117024	−	0.202691i	0.918587	+	0.395219i	$0.129331\pi$
$660$	−6.48126	−	7.90623i	−0.252283	−	0.307750i
$661$	17.0665	−	29.5601i	0.663811	−	1.14975i	−0.315796	−	0.948827i	$-0.602271\pi$
$661$	17.0665	−	29.5601i	0.663811	−	1.14975i	0.979606	−	0.200927i	$-0.0643953\pi$
$662$	−26.2913	−	15.1793i	−1.02184	−	0.589959i
$663$	−10.9924	−	6.34649i	−0.426911	−	0.246477i
$664$	−1.53697	−	2.66210i	−0.0596458	−	0.103310i
$665$	−0.604191	−	0.737028i	−0.0234295	−	0.0285807i
$666$	5.63800	+	2.28320i	0.218468	+	0.0884723i
$667$			3.78286i			0.146473i
$668$	18.9448	−	10.9378i	0.732997	−	0.423196i
$669$	1.99663	−	3.45826i	0.0771941	−	0.133704i
$670$	−1.73210	−	10.5269i	−0.0669168	−	0.406689i
$671$	10.8798	−	18.8444i	0.420011	−	0.727481i
$672$			0.309595i			0.0119429i
$673$	−5.77448	−	3.33389i	−0.222590	−	0.128512i	0.384559	−	0.923100i	$-0.374353\pi$
$673$	−5.77448	−	3.33389i	−0.222590	−	0.128512i	−0.607149	+	0.794588i	$0.707687\pi$
$674$	11.8454			0.456266
$675$	−1.60203	−	4.73640i	−0.0616623	−	0.182304i
$676$	1.70882			0.0657238
$677$			8.18243i			0.314476i	0.987561	+	0.157238i	$0.0502590\pi$
$677$			8.18243i			0.314476i	−0.987561	+	0.157238i	$0.949741\pi$
$678$	−2.12749	+	1.22831i	−0.0817058	+	0.0471729i
$679$	−0.153264	+	0.265461i	−0.00588174	+	0.0101875i
$680$	−5.72321	+	4.69170i	−0.219475	+	0.179918i
$681$	13.6749	+	23.6856i	0.524022	+	0.907633i
$682$	10.8361	−	6.25625i	0.414937	−	0.239564i
$683$	26.9900	−	15.5827i	1.03274	−	0.596254i	0.114974	−	0.993369i	$-0.463322\pi$
$683$	26.9900	−	15.5827i	1.03274	−	0.596254i	0.917769	+	0.397114i	$0.129988\pi$
$684$	−0.688327	+	1.19222i	−0.0263188	+	0.0455856i
$685$	21.0710	−	3.46704i	0.805082	−	0.132469i
$686$	2.15233	+	3.72795i	0.0821764	+	0.142334i
$687$	20.6075	−	11.8978i	0.786226	−	0.453928i
$688$	−4.37197	+	2.52416i	−0.166680	+	0.0962325i
$689$	52.5312			2.00128
$690$	−12.0893	+	1.98918i	−0.460231	+	0.0757267i
$691$	−20.8249	−	36.0698i	−0.792218	−	1.37216i	−0.924591	−	0.380962i	$-0.875593\pi$
$691$	−20.8249	−	36.0698i	−0.792218	−	1.37216i	0.132373	−	0.991200i	$-0.457740\pi$
$692$			4.23309i			0.160918i
$693$		−	1.41547i		−	0.0537691i
$694$	0.594567	+	1.02982i	0.0225694	+	0.0390914i
$695$	−4.52716	+	3.71122i	−0.171725	+	0.140774i
$696$	−0.345202	+	0.597908i	−0.0130849	+	0.0226636i
$697$		−	1.16138i		−	0.0439905i
$698$	−6.43879	−	3.71744i	−0.243712	−	0.140707i
$699$	−12.8189	+	22.2029i	−0.484854	+	0.839791i
$700$	1.02192	−	1.16272i	0.0386250	−	0.0439466i
$701$	−24.5191	−	42.4683i	−0.926073	−	1.60400i	−0.789827	−	0.613330i	$-0.789830\pi$
$701$	−24.5191	−	42.4683i	−0.926073	−	1.60400i	−0.136246	−	0.990675i	$-0.543504\pi$
$702$		−	3.83521i		−	0.144751i
$703$	−3.14318	+	7.76157i	−0.118547	+	0.292733i
$704$	−4.57198			−0.172313
$705$	−7.89888	−	2.97785i	−0.297489	−	0.112152i
$706$	7.04878	−	12.2088i	0.265284	−	0.459486i
$707$	−3.60185	−	2.07953i	−0.135462	−	0.0782088i
$708$	10.0010	+	5.77406i	0.375860	+	0.217003i
$709$	−16.7309			−0.628343			−0.314171	−	0.949366i	$-0.601727\pi$
$709$	−16.7309			−0.628343			−0.314171	+	0.949366i	$0.601727\pi$
$710$	29.4337	−	4.84304i	1.10463	−	0.181756i
$711$	15.2672			0.572564
$712$	9.48775	−	5.47776i	0.355569	−	0.205288i
$713$		−	14.9953i		−	0.561579i
$714$	−1.02464			−0.0383460
$715$	−13.8312	+	36.6878i	−0.517256	+	1.37205i
$716$	−9.08787	+	15.7407i	−0.339630	+	0.588256i
$717$		−	6.16796i		−	0.230347i
$718$	1.22650	−	0.708122i	0.0457727	−	0.0264269i
$719$	−14.7645	−	25.5728i	−0.550622	−	0.953705i	−0.998230	−	0.0594751i	$-0.981057\pi$
$719$	−14.7645	−	25.5728i	−0.550622	−	0.953705i	0.447608	−	0.894230i	$-0.352276\pi$
$720$	−2.09232	−	0.788796i	−0.0779761	−	0.0293967i
$721$	0.899292	−	1.55762i	0.0334914	−	0.0580088i
$722$	14.8132	+	8.55241i	0.551291	+	0.318288i
$723$	3.47521	−	2.00641i	0.129244	−	0.0746192i
$724$	−3.63216	−	6.29109i	−0.134988	−	0.233807i
$725$	3.27003	−	1.10605i	0.121446	−	0.0410777i
$726$	9.90305			0.367537
$727$	−33.7503	−	19.4857i	−1.25173	−	0.722685i	−0.280275	−	0.959920i	$-0.590426\pi$
$727$	−33.7503	−	19.4857i	−1.25173	−	0.722685i	−0.971452	+	0.237234i	$0.923759\pi$
$728$	1.02829	−	0.593681i	0.0381108	−	0.0220033i
$729$	−1.00000			−0.0370370
$730$	23.1435	−	18.9723i	0.856579	−	0.702195i
$731$	−8.35393	−	14.4694i	−0.308981	−	0.535171i
$732$		−	4.75935i		−	0.175911i
$733$	29.8567	+	17.2377i	1.10278	+	0.636691i	0.936950	−	0.349463i	$-0.113636\pi$
$733$	29.8567	+	17.2377i	1.10278	+	0.636691i	0.165831	+	0.986154i	$0.446969\pi$
$734$	−18.8761			−0.696731
$735$	−15.2333	+	2.50650i	−0.561889	+	0.0924537i
$736$	−2.73959	+	4.74511i	−0.100983	+	0.174907i
$737$	18.8908	+	10.9066i	0.695852	+	0.401750i
$738$	0.303900	−	0.175457i	0.0111867	−	0.00645865i
$739$	−9.23484			−0.339709			−0.169855	−	0.985469i	$-0.554330\pi$
$739$	−9.23484			−0.339709			−0.169855	+	0.985469i	$0.554330\pi$
$740$	−13.2686	−	2.99082i	−0.487762	−	0.109945i
$741$	5.27975			0.193957
$742$	3.67243	−	2.12028i	0.134819	−	0.0778378i
$743$	−24.7745	−	14.3036i	−0.908889	−	0.524747i	−0.0288154	−	0.999585i	$-0.509173\pi$
$743$	−24.7745	−	14.3036i	−0.908889	−	0.524747i	−0.880073	+	0.474838i	$0.842507\pi$
$744$	1.36839	−	2.37012i	0.0501676	−	0.0868928i
$745$	2.33219	+	14.1739i	0.0854448	+	0.519293i
$746$	22.4593			0.822295
$747$	2.66210	+	1.53697i	0.0974013	+	0.0562346i
$748$		−	15.1314i		−	0.553260i
$749$	1.12950	+	1.95636i	0.0412711	+	0.0714837i
$750$	5.25424	+	9.86879i	0.191858	+	0.360357i
$751$	13.7813			0.502886			0.251443	−	0.967872i	$-0.419095\pi$
$751$	13.7813			0.502886			0.251443	+	0.967872i	$0.419095\pi$
$752$	−3.26940	+	1.88759i	−0.119223	+	0.0688333i
$753$	14.5033	+	8.37346i	0.528528	+	0.305146i
$754$	2.64785			0.0964288
$755$	10.2119	+	3.84986i	0.371651	+	0.140111i
$756$	−0.154798	−	0.268117i	−0.00562994	−	0.00975134i
$757$	−11.6427	+	6.72193i	−0.423162	+	0.244313i	−0.696429	−	0.717625i	$-0.745229\pi$
$757$	−11.6427	+	6.72193i	−0.423162	+	0.244313i	0.273267	+	0.961938i	$0.411896\pi$
$758$	30.3592	+	17.5279i	1.10270	+	0.636642i
$759$	12.5254	−	21.6946i	0.454642	−	0.787464i
$760$	1.08590	−	2.88040i	0.0393897	−	0.104483i
$761$	15.8359	+	27.4286i	0.574051	+	0.994286i	0.996144	+	0.0877334i	$0.0279624\pi$
$761$	15.8359	+	27.4286i	0.574051	+	0.994286i	−0.422093	+	0.906553i	$0.638704\pi$
$762$	−1.18210	+	0.682488i	−0.0428231	+	0.0247239i
$763$		−	4.00303i		−	0.144920i
$764$	−1.71055	+	2.96276i	−0.0618855	+	0.107189i
$765$	2.61060	−	6.92473i	0.0943863	−	0.250364i
$766$	−12.4279			−0.449038
$767$		−	44.2895i		−	1.59920i
$768$	−0.866025	+	0.500000i	−0.0312500	+	0.0180422i
$769$	−8.70963			−0.314077			−0.157039	−	0.987592i	$-0.550195\pi$
$769$	−8.70963			−0.314077			−0.157039	+	0.987592i	$0.550195\pi$
$770$	0.513874	+	3.12308i	0.0185187	+	0.112548i
$771$	1.84799			0.0665538
$772$	16.7016	+	9.64268i	0.601104	+	0.347048i
$773$	2.32166	+	1.34041i	0.0835044	+	0.0482113i	0.541171	−	0.840913i	$-0.317981\pi$
$773$	2.32166	+	1.34041i	0.0835044	+	0.0482113i	−0.457666	+	0.889124i	$0.651315\pi$
$774$	2.52416	−	4.37197i	0.0907289	−	0.157147i
$775$	−12.9625	+	4.38441i	−0.465626	+	0.157493i
$776$	−0.990093			−0.0355423
$777$	−1.15821	−	1.48491i	−0.0415506	−	0.0532710i
$778$			25.2154i			0.904015i
$779$	0.241543	+	0.418365i	0.00865419	+	0.0149895i
$780$	1.39234	+	8.46200i	0.0498539	+	0.302988i
$781$	−30.4954	+	52.8197i	−1.09121	+	1.89004i
$782$	−15.7044	−	9.06694i	−0.561589	−	0.324233i
$783$		−	0.690405i		−	0.0246730i
$784$	−3.45208	+	5.97917i	−0.123288	+	0.213542i
$785$	−13.1497	−	16.0408i	−0.469332	−	0.572519i
$786$	5.74528	+	9.95113i	0.204928	+	0.354945i
$787$			3.44647i			0.122853i	0.998112	+	0.0614266i	$0.0195650\pi$
$787$			3.44647i			0.122853i	−0.998112	+	0.0614266i	$0.980435\pi$
$788$			8.88669i			0.316575i
$789$	−3.66760	−	6.35247i	−0.130570	−	0.226154i
$790$	−33.6855	+	5.54264i	−1.19848	+	0.197198i
$791$	0.760557			0.0270423
$792$	3.95946	−	2.28599i	0.140693	−	0.0812292i
$793$	−15.8076	+	9.12654i	−0.561346	+	0.324093i
$794$	−3.39818	−	5.88581i	−0.120597	−	0.208880i
$795$	4.97263	+	30.2213i	0.176361	+	1.07184i
$796$	−6.27808	+	10.8739i	−0.222520	+	0.385417i
$797$	25.2225	−	14.5622i	0.893426	−	0.515820i	0.0183643	−	0.999831i	$-0.494154\pi$
$797$	25.2225	−	14.5622i	0.893426	−	0.515820i	0.875062	+	0.484012i	$0.160821\pi$
$798$	0.369105	−	0.213103i	0.0130662	−	0.00754376i
$799$	−6.24716	−	10.8204i	−0.221009	−	0.382798i
$800$	4.90286	+	0.980798i	0.173342	+	0.0346764i
$801$	−5.47776	+	9.48775i	−0.193547	+	0.335233i
$802$	−3.70227	+	2.13751i	−0.130732	+	0.0754780i
$803$			61.1884i			2.15929i
$804$	4.77106			0.168262
$805$	3.54927	+	1.33806i	0.125095	+	0.0471604i
$806$	−10.4961			−0.369710
$807$	−14.1806	−	8.18718i	−0.499181	−	0.288203i
$808$		−	13.4339i		−	0.472602i
$809$	20.7139	−	35.8775i	0.728262	−	1.26139i	−0.229355	−	0.973343i	$-0.573662\pi$
$809$	20.7139	−	35.8775i	0.728262	−	1.26139i	0.957617	−	0.288044i	$-0.0930049\pi$
$810$	2.20640	−	0.363043i	0.0775250	−	0.0127560i
$811$	−1.58024	+	2.73706i	−0.0554897	+	0.0961110i	−0.892436	−	0.451174i	$-0.851005\pi$
$811$	−1.58024	+	2.73706i	−0.0554897	+	0.0961110i	0.836946	+	0.547285i	$0.184339\pi$
$812$	0.185110	−	0.106873i	0.00649607	−	0.00375051i
$813$		−	9.45345i		−	0.331547i
$814$	21.9286	−	17.1040i	0.768599	−	0.599495i
$815$	18.5726	+	22.6560i	0.650571	+	0.793605i
$816$	−1.65480	−	2.86619i	−0.0579295	−	0.100337i
$817$	6.01868	+	3.47489i	0.210567	+	0.121571i
$818$	7.37620	+	4.25865i	0.257903	+	0.148900i
$819$	−0.593681	+	1.02829i	−0.0207449	+	0.0359312i
$820$	−0.606827	+	0.497457i	−0.0211913	+	0.0173719i
$821$	15.2576	−	26.4270i	0.532495	−	0.922308i	−0.466785	−	0.884371i	$-0.654588\pi$
$821$	15.2576	−	26.4270i	0.532495	−	0.922308i	0.999280	−	0.0379377i	$-0.0120788\pi$
$822$			9.54995i			0.333093i
$823$	−8.61740	+	4.97526i	−0.300384	+	0.173427i	−0.642615	−	0.766189i	$-0.722151\pi$
$823$	−8.61740	+	4.97526i	−0.300384	+	0.173427i	0.342232	+	0.939616i	$0.388817\pi$
$824$	5.80947			0.202382
$825$	−22.4158	−	4.48419i	−0.780418	−	0.156120i
$826$	−1.78762	−	3.09625i	−0.0621994	−	0.107732i
$827$	4.71088	+	2.71983i	0.163813	+	0.0945777i	0.579665	−	0.814855i	$-0.303183\pi$
$827$	4.71088	+	2.71983i	0.163813	+	0.0945777i	−0.415852	+	0.909432i	$0.636517\pi$
$828$		−	5.47919i		−	0.190415i
$829$	14.9584	+	25.9088i	0.519528	+	0.899849i	0.999742	+	0.0226976i	$0.00722549\pi$
$829$	14.9584	+	25.9088i	0.519528	+	0.899849i	−0.480214	+	0.877151i	$0.659441\pi$
$830$	−6.43165	−	2.42470i	−0.223246	−	0.0841627i
$831$	4.40289	+	7.62602i	0.152734	+	0.264544i
$832$	3.32139	+	1.91760i	0.115148	+	0.0664810i
$833$	−19.7886	−	11.4250i	−0.685635	−	0.395852i
$834$	−1.30897	−	2.26721i	−0.0453261	−	0.0785071i
$835$	17.2554	−	45.7707i	0.597147	−	1.58396i
$836$	3.14702	+	5.45080i	0.108842	+	0.188520i
$837$			2.73678i			0.0945969i
$838$	−14.9783	−	8.64775i	−0.517418	−	0.298732i
$839$	15.6157	+	27.0471i	0.539113	+	0.933771i	0.998952	+	0.0457688i	$0.0145738\pi$
$839$	15.6157	+	27.0471i	0.539113	+	0.933771i	−0.459839	+	0.888002i	$0.652093\pi$
$840$	0.438884	+	0.535376i	0.0151429	+	0.0184722i
$841$	−28.5233			−0.983563
$842$	−12.4436	+	7.18429i	−0.428833	+	0.247587i
$843$		−	3.20606i		−	0.110422i
$844$	−9.78239	+	16.9436i	−0.336724	+	0.583223i
$845$	2.95502	−	2.42243i	0.101656	−	0.0833341i
$846$	1.88759	−	3.26940i	0.0648967	−	0.112404i
$847$	−2.65518	−	1.53297i	−0.0912330	−	0.0526734i
$848$	11.8620	+	6.84854i	0.407344	+	0.235180i
$849$	−10.1734	−	17.6209i	−0.349151	−	0.604748i
$850$	−3.24604	+	16.2265i	−0.111338	+	0.556564i
$851$	−4.61176	−	33.0080i	−0.158089	−	1.13150i
$852$			13.3401i			0.457025i
$853$	3.38454	−	1.95407i	0.115885	−	0.0669060i	−0.440937	−	0.897538i	$-0.645354\pi$
$853$	3.38454	−	1.95407i	0.115885	−	0.0669060i	0.556822	+	0.830632i	$0.312021\pi$
$854$	−0.736736	+	1.27606i	−0.0252106	+	0.0436660i
$855$	0.499784	+	3.03745i	0.0170922	+	0.103879i
$856$	−3.64832	+	6.31907i	−0.124697	+	0.215981i
$857$			40.0174i			1.36697i	0.729965	+	0.683484i	$0.239536\pi$
$857$			40.0174i			1.36697i	−0.729965	+	0.683484i	$0.760464\pi$
$858$	−15.1853	−	8.76726i	−0.518419	−	0.299309i
$859$	25.6649			0.875677			0.437838	−	0.899054i	$-0.355744\pi$
$859$	25.6649			0.875677			0.437838	+	0.899054i	$0.355744\pi$
$860$	−3.98209	+	10.5627i	−0.135788	+	0.360184i
$861$	−0.108641			−0.00370248
$862$		−	23.3165i		−	0.794161i
$863$	27.5998	−	15.9347i	0.939508	−	0.542425i	0.0497019	−	0.998764i	$-0.484173\pi$
$863$	27.5998	−	15.9347i	0.939508	−	0.542425i	0.889806	+	0.456339i	$0.150840\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	6.00085	+	7.32019i	0.204035	+	0.248894i
$866$	−15.3691	−	26.6200i	−0.522263	−	0.904586i
$867$	−5.23649	+	3.02329i	−0.177841	+	0.102676i
$868$	−0.733778	+	0.423647i	−0.0249060	+	0.0143795i
$869$	34.9007	−	60.4497i	1.18392	−	2.05062i
$870$	0.250646	+	1.52331i	0.00849770	+	0.0516450i
$871$	−9.14901	−	15.8466i	−0.310002	−	0.536940i
$872$	11.1976	−	6.46495i	0.379199	−	0.218931i
$873$	0.857446	−	0.495047i	0.0290201	−	0.0167548i
$874$	7.54294			0.255144
$875$	0.118911	−	3.45934i	0.00401993	−	0.116947i
$876$	6.69167	+	11.5903i	0.226091	+	0.391600i
$877$			39.3230i			1.32784i	0.747802	+	0.663922i	$0.231109\pi$
$877$			39.3230i			1.32784i	−0.747802	+	0.663922i	$0.768891\pi$
$878$			37.2735i			1.25792i
$879$	−9.27344	−	16.0621i	−0.312786	−	0.541760i
$880$	−7.90623	+	6.48126i	−0.266519	+	0.218483i
$881$	3.70381	−	6.41518i	0.124784	−	0.216133i	−0.796864	−	0.604158i	$-0.793509\pi$
$881$	3.70381	−	6.41518i	0.124784	−	0.216133i	0.921649	+	0.388026i	$0.126843\pi$
$882$		−	6.90415i		−	0.232475i
$883$	24.5241	+	14.1590i	0.825302	+	0.476488i	0.852241	−	0.523149i	$-0.175243\pi$
$883$	24.5241	+	14.1590i	0.825302	+	0.476488i	−0.0269392	+	0.999637i	$0.508576\pi$
$884$	−6.34649	+	10.9924i	−0.213456	+	0.369716i
$885$	25.4798	−	4.19246i	0.856494	−	0.140928i
$886$	−7.77937	−	13.4743i	−0.261353	−	0.452677i
$887$			46.0973i			1.54780i	0.633311	+	0.773898i	$0.281695\pi$
$887$			46.0973i			1.54780i	−0.633311	+	0.773898i	$0.718305\pi$
$888$	2.28320	−	5.63800i	0.0766192	−	0.189199i
$889$	0.422590			0.0141732
$890$	8.64166	−	22.9224i	0.289669	−	0.768362i
$891$	−2.28599	+	3.95946i	−0.0765836	+	0.132647i
$892$	−3.45826	−	1.99663i	−0.115791	−	0.0668521i
$893$	4.50084	+	2.59856i	0.150615	+	0.0869574i
$894$	−6.42401			−0.214851
$895$	6.59857	+	40.1030i	0.220566	+	1.34049i
$896$	0.309595			0.0103429
$897$	−18.1985	+	10.5069i	−0.607630	+	0.350815i
$898$		−	1.08346i		−	0.0361554i
$899$	−1.88948			−0.0630178
$900$	−4.73640	+	1.60203i	−0.157880	+	0.0534011i
$901$	−22.6659	+	39.2585i	−0.755111	+	1.30789i
$902$		−	1.60437i		−	0.0534197i
$903$	−1.35354	+	0.781467i	−0.0450430	+	0.0260056i
$904$	1.22831	+	2.12749i	0.0408529	+	0.0707593i
$905$	−15.1993	−	5.73007i	−0.505242	−	0.190474i
$906$	−2.44034	+	4.22679i	−0.0810749	+	0.140426i
$907$	−25.7386	−	14.8602i	−0.854635	−	0.493424i	0.00757682	−	0.999971i	$-0.497588\pi$
$907$	−25.7386	−	14.8602i	−0.854635	−	0.493424i	−0.862212	+	0.506547i	$0.830922\pi$
$908$	23.6856	−	13.6749i	0.786033	−	0.453816i
$909$	6.71693	+	11.6341i	0.222787	+	0.385878i
$910$	0.936587	−	2.48434i	0.0310475	−	0.0823551i
$911$	−15.4077			−0.510479			−0.255239	−	0.966878i	$-0.582154\pi$
$911$	−15.4077			−0.510479			−0.255239	+	0.966878i	$0.582154\pi$
$912$	1.19222	+	0.688327i	0.0394783	+	0.0227928i
$913$	12.1711	−	7.02698i	0.402804	−	0.232559i
$914$	−25.0538			−0.828706
$915$	−6.74687	−	8.23023i	−0.223045	−	0.272083i
$916$	−11.8978	−	20.6075i	−0.393113	−	0.680892i
$917$		−	3.55743i		−	0.117477i
$918$	2.86619	+	1.65480i	0.0945985	+	0.0546165i
$919$	−15.5228			−0.512048			−0.256024	−	0.966670i	$-0.582413\pi$
$919$	−15.5228			−0.512048			−0.256024	+	0.966670i	$0.582413\pi$
$920$	1.98918	+	12.0893i	0.0655812	+	0.398572i
$921$	−1.00136	+	1.73440i	−0.0329959	+	0.0571506i
$922$	−8.86086	−	5.11582i	−0.291817	−	0.168481i
$923$	44.3078	−	25.5811i	1.45841	−	0.842012i
$924$	−1.41547			−0.0465654
$925$	−27.1848	+	13.6376i	−0.893832	+	0.448402i
$926$	−16.5645			−0.544345
$927$	−5.03115	+	2.90473i	−0.165245	+	0.0954040i
$928$	0.597908	+	0.345202i	0.0196273	+	0.0113318i
$929$	−13.6062	+	23.5666i	−0.446405	+	0.773196i	−0.998149	−	0.0608178i	$-0.980629\pi$
$929$	−13.6062	+	23.5666i	−0.446405	+	0.773196i	0.551744	+	0.834013i	$0.313962\pi$
$930$	−0.993566	−	6.03842i	−0.0325803	−	0.198008i
$931$	9.50463			0.311502
$932$	22.2029	+	12.8189i	0.727280	+	0.419895i
$933$			25.3344i			0.829410i
$934$	13.0607	+	22.6217i	0.427358	+	0.740206i
$935$	−21.4504	−	26.1664i	−0.701502	−	0.855733i
$936$	−3.83521			−0.125358
$937$	−30.3829	+	17.5416i	−0.992565	+	0.573058i	−0.906040	−	0.423192i	$-0.860910\pi$
$937$	−30.3829	+	17.5416i	−0.992565	+	0.573058i	−0.0865251	+	0.996250i	$0.527576\pi$
$938$	−1.27921	−	0.738550i	−0.0417675	−	0.0241145i
$939$	33.4870			1.09281
$940$	−2.97785	+	7.89888i	−0.0971267	+	0.257633i
$941$	22.3408	+	38.6954i	0.728290	+	1.26144i	0.957605	+	0.288083i	$0.0930180\pi$
$941$	22.3408	+	38.6954i	0.728290	+	1.26144i	−0.229315	+	0.973352i	$0.573649\pi$
$942$	8.03324	−	4.63800i	0.261737	−	0.151114i
$943$	−1.66513	−	0.961360i	−0.0542239	−	0.0313062i
$944$	5.77406	−	10.0010i	0.187930	−	0.325504i
$945$	−0.647772	−	0.244208i	−0.0210720	−	0.00794407i
$946$	−11.5404	−	19.9886i	−0.375211	−	0.649884i
$947$	23.2795	−	13.4404i	0.756483	−	0.436756i	−0.0715483	−	0.997437i	$-0.522794\pi$
$947$	23.2795	−	13.4404i	0.756483	−	0.436756i	0.828032	+	0.560681i	$0.189461\pi$
$948$		−	15.2672i		−	0.495855i
$949$	25.6639	−	44.4512i	0.833087	−	1.44295i
$950$	−2.20545	−	6.52038i	−0.0715541	−	0.211549i
$951$	31.0923			1.00824
$952$			1.02464i			0.0332086i
$953$	−32.4670	+	18.7448i	−1.05171	+	0.607205i	−0.923127	−	0.384494i	$-0.874376\pi$
$953$	−32.4670	+	18.7448i	−1.05171	+	0.607205i	−0.128582	+	0.991699i	$0.541043\pi$
$954$	−13.6971			−0.443460
$955$	1.24200	+	7.54831i	0.0401903	+	0.244258i
$956$	−6.16796			−0.199486
$957$	−2.73363	−	1.57826i	−0.0883656	−	0.0510179i
$958$	3.76140	+	2.17164i	0.121525	+	0.0701626i
$959$	1.47831	−	2.56051i	0.0477371	−	0.0826832i
$960$	−0.788796	+	2.09232i	−0.0254583	+	0.0675293i
$961$	−23.5101			−0.758389
$962$	−23.1042	+	3.22804i	−0.744911	+	0.104076i
$963$		−	7.29664i		−	0.235131i
$964$	−2.00641	−	3.47521i	−0.0646221	−	0.111929i
$965$	42.5512	−	7.00141i	1.36977	−	0.225383i
$966$	−0.848165	+	1.46907i	−0.0272893	+	0.0472664i
$967$	−21.8076	−	12.5906i	−0.701285	−	0.404887i	0.106541	−	0.994308i	$-0.466023\pi$
$967$	−21.8076	−	12.5906i	−0.701285	−	0.404887i	−0.807826	+	0.589421i	$0.799356\pi$
$968$		−	9.90305i		−	0.318296i
$969$	−2.27808	+	3.94576i	−0.0731826	+	0.126756i
$970$	−1.71215	+	1.40356i	−0.0549737	+	0.0450656i
$971$	−4.24551	−	7.35344i	−0.136245	−	0.235983i	0.789827	−	0.613329i	$-0.210170\pi$
$971$	−4.24551	−	7.35344i	−0.136245	−	0.235983i	−0.926072	+	0.377346i	$0.876837\pi$
$972$			1.00000i			0.0320750i
$973$			0.810505i			0.0259836i
$974$	−6.97051	−	12.0733i	−0.223350	−	0.386853i
$975$	14.4035	+	12.6594i	0.461282	+	0.405424i
$976$	−4.75935			−0.152343
$977$	−21.3821	+	12.3450i	−0.684075	+	0.394951i	−0.801389	−	0.598144i	$-0.795905\pi$
$977$	−21.3821	+	12.3450i	−0.684075	+	0.394951i	0.117314	+	0.993095i	$0.462572\pi$
$978$	−11.3462	+	6.55071i	−0.362810	+	0.209469i
$979$	25.0442	+	43.3779i	0.800417	+	1.38636i
$980$	2.50650	+	15.2333i	0.0800672	+	0.486610i
$981$	−6.46495	+	11.1976i	−0.206410	+	0.357512i
$982$	−24.9830	+	14.4239i	−0.797239	+	0.460286i
$983$	34.3314	−	19.8212i	1.09500	−	0.632199i	0.160097	−	0.987101i	$-0.448819\pi$
$983$	34.3314	−	19.8212i	1.09500	−	0.632199i	0.934903	+	0.354903i	$0.115486\pi$
$984$	−0.175457	−	0.303900i	−0.00559336	−	0.00968798i
$985$	12.5978	+	15.3675i	0.401399	+	0.489651i
$986$	−1.14248	+	1.97883i	−0.0363840	+	0.0630189i
$987$	−1.01219	+	0.584389i	−0.0322184	+	0.0186013i
$988$		−	5.27975i		−	0.167971i
$989$	−27.6606			−0.879557
$990$	3.60636	−	9.56605i	0.114618	−	0.304029i
$991$	−38.4167			−1.22035			−0.610173	−	0.792268i	$-0.708900\pi$
$991$	−38.4167			−1.22035			−0.610173	+	0.792268i	$0.708900\pi$
$992$	−2.37012	−	1.36839i	−0.0752513	−	0.0434464i
$993$		−	30.3585i		−	0.963399i
$994$	2.06502	−	3.57672i	0.0654985	−	0.113447i
$995$	4.55842	+	27.7039i	0.144512	+	0.878272i
$996$	1.53697	−	2.66210i	0.0487006	−	0.0843520i
$997$	−16.0040	+	9.23989i	−0.506850	+	0.292630i	−0.731538	−	0.681801i	$-0.761197\pi$
$997$	−16.0040	+	9.23989i	−0.506850	+	0.292630i	0.224688	+	0.974431i	$0.427864\pi$
$998$		−	32.3895i		−	1.02527i
$999$	0.841687	+	6.02425i	0.0266298	+	0.190599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.d.1099.10	yes	28
5.4	even	2	inner	1110.2.bb.d.1099.5	yes	28
37.10	even	3	inner	1110.2.bb.d.1009.5	✓	28
185.84	even	6	inner	1110.2.bb.d.1009.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.5	✓	28	37.10	even	3	inner
1110.2.bb.d.1009.10	yes	28	185.84	even	6	inner
1110.2.bb.d.1099.5	yes	28	5.4	even	2	inner
1110.2.bb.d.1099.10	yes	28	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.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.363043 - 2.20640i) q^{5} +1.00000 q^{6} +(-0.268117 - 0.154798i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.363043 - 2.20640i) q^{5} +1.00000 q^{6} +(-0.268117 - 0.154798i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.41760 - 1.72928i) q^{10} +4.57198 q^{11} +(0.866025 - 0.500000i) q^{12} +(-3.32139 - 1.91760i) q^{13} -0.309595 q^{14} +(0.788796 - 2.09232i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.86619 - 1.65480i) q^{17} +(0.866025 + 0.500000i) q^{18} +(-0.688327 + 1.19222i) q^{19} +(-2.09232 - 0.788796i) q^{20} +(-0.154798 - 0.268117i) q^{21} +(3.95946 - 2.28599i) q^{22} -5.47919i q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.73640 + 1.60203i) q^{25} -3.83521 q^{26} +1.00000i q^{27} +(-0.268117 + 0.154798i) q^{28} -0.690405 q^{29} +(-0.363043 - 2.20640i) q^{30} +2.73678 q^{31} +(-0.866025 - 0.500000i) q^{32} +(3.95946 + 2.28599i) q^{33} +(1.65480 - 2.86619i) q^{34} +(-0.244208 + 0.647772i) q^{35} +1.00000 q^{36} +(6.02425 - 0.841687i) q^{37} +1.37665i q^{38} +(-1.91760 - 3.32139i) q^{39} +(-2.20640 + 0.363043i) q^{40} +(0.175457 - 0.303900i) q^{41} +(-0.268117 - 0.154798i) q^{42} -5.04831i q^{43} +(2.28599 - 3.95946i) q^{44} +(1.72928 - 1.41760i) q^{45} +(-2.73959 - 4.74511i) q^{46} -3.77518i q^{47} -1.00000i q^{48} +(-3.45208 - 5.97917i) q^{49} +(-3.30083 + 3.75560i) q^{50} +3.30960 q^{51} +(-3.32139 + 1.91760i) q^{52} +(-11.8620 + 6.84854i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.65982 - 10.0876i) q^{55} +(-0.154798 + 0.268117i) q^{56} +(-1.19222 + 0.688327i) q^{57} +(-0.597908 + 0.345202i) q^{58} +(5.77406 + 10.0010i) q^{59} +(-1.41760 - 1.72928i) q^{60} +(2.37967 - 4.12172i) q^{61} +(2.37012 - 1.36839i) q^{62} -0.309595i q^{63} -1.00000 q^{64} +(-3.02520 + 8.02448i) q^{65} +4.57198 q^{66} +(4.13186 + 2.38553i) q^{67} -3.30960i q^{68} +(2.73959 - 4.74511i) q^{69} +(0.112396 + 0.683091i) q^{70} +(-6.67007 + 11.5529i) q^{71} +(0.866025 - 0.500000i) q^{72} +13.3833i q^{73} +(4.79631 - 3.74105i) q^{74} +(-4.90286 - 0.980798i) q^{75} +(0.688327 + 1.19222i) q^{76} +(-1.22583 - 0.707733i) q^{77} +(-3.32139 - 1.91760i) q^{78} +(7.63359 - 13.2218i) q^{79} +(-1.72928 + 1.41760i) q^{80} +(-0.500000 + 0.866025i) q^{81} -0.350914i q^{82} +(2.66210 - 1.53697i) q^{83} -0.309595 q^{84} +(-4.69170 - 5.72321i) q^{85} +(-2.52416 - 4.37197i) q^{86} +(-0.597908 - 0.345202i) q^{87} -4.57198i q^{88} +(5.47776 + 9.48775i) q^{89} +(0.788796 - 2.09232i) q^{90} +(0.593681 + 1.02829i) q^{91} +(-4.74511 - 2.73959i) q^{92} +(2.37012 + 1.36839i) q^{93} +(-1.88759 - 3.26940i) q^{94} +(2.88040 + 1.08590i) q^{95} +(-0.500000 - 0.866025i) q^{96} -0.990093i q^{97} +(-5.97917 - 3.45208i) q^{98} +(2.28599 + 3.95946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more