LMFDB - Embedded newform 117.2.f.a.61.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(61,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("117.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.f (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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	117.61
Dual form			117.2.f.a.94.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.567922 - 0.983670i) q^{2} +(-0.529547 - 1.64911i) q^{3} +(0.354929 - 0.614756i) q^{4} +(-0.0587384 - 0.101738i) q^{5} +(-1.32144 + 1.45747i) q^{6} +0.849445 q^{7} -3.07798 q^{8} +(-2.43916 + 1.74657i) q^{9} +(-0.0667177 + 0.115558i) q^{10} +(0.231971 + 0.401786i) q^{11} +(-1.20175 - 0.259777i) q^{12} +(1.54170 - 3.25932i) q^{13} +(-0.482419 - 0.835574i) q^{14} +(-0.136673 + 0.150741i) q^{15} +(1.03819 + 1.79820i) q^{16} +(-1.26296 - 2.18751i) q^{17} +(3.10330 + 1.40741i) q^{18} +(3.09113 + 5.35399i) q^{19} -0.0833920 q^{20} +(-0.449821 - 1.40083i) q^{21} +(0.263483 - 0.456366i) q^{22} +6.65773 q^{23} +(1.62993 + 5.07594i) q^{24} +(2.49310 - 4.31818i) q^{25} +(-4.08166 + 0.334515i) q^{26} +(4.17194 + 3.09756i) q^{27} +(0.301493 - 0.522201i) q^{28} +(-0.952265 - 1.64937i) q^{29} +(0.225899 + 0.0488315i) q^{30} +(0.657577 + 1.13896i) q^{31} +(-1.89875 + 3.28874i) q^{32} +(0.539751 - 0.595312i) q^{33} +(-1.43452 + 2.48467i) q^{34} +(-0.0498951 - 0.0864208i) q^{35} +(0.207983 + 2.11940i) q^{36} +(-2.01347 + 3.48743i) q^{37} +(3.51104 - 6.08129i) q^{38} +(-6.19139 - 0.816478i) q^{39} +(0.180795 + 0.313147i) q^{40} +9.68663 q^{41} +(-1.12249 + 1.23804i) q^{42} -4.20953 q^{43} +0.329333 q^{44} +(0.320965 + 0.145564i) q^{45} +(-3.78107 - 6.54901i) q^{46} +(1.34586 - 2.33109i) q^{47} +(2.41567 - 2.66433i) q^{48} -6.27844 q^{49} -5.66354 q^{50} +(-2.93865 + 3.24115i) q^{51} +(-1.45649 - 2.10460i) q^{52} -0.389682 q^{53} +(0.677644 - 5.86299i) q^{54} +(0.0272512 - 0.0472005i) q^{55} -2.61457 q^{56} +(7.19244 - 7.93281i) q^{57} +(-1.08162 + 1.87343i) q^{58} +(-5.53661 + 9.58969i) q^{59} +(0.0441600 + 0.137523i) q^{60} -7.76759 q^{61} +(0.746905 - 1.29368i) q^{62} +(-2.07193 + 1.48361i) q^{63} +8.46614 q^{64} +(-0.422153 + 0.0345978i) q^{65} +(-0.892126 - 0.192846i) q^{66} -1.02270 q^{67} -1.79304 q^{68} +(-3.52558 - 10.9794i) q^{69} +(-0.0566730 + 0.0981605i) q^{70} +(3.61012 + 6.25291i) q^{71} +(7.50768 - 5.37589i) q^{72} -3.31321 q^{73} +4.57397 q^{74} +(-8.44138 - 1.82473i) q^{75} +4.38853 q^{76} +(0.197047 + 0.341295i) q^{77} +(2.71308 + 6.55398i) q^{78} +(-4.41302 + 7.64357i) q^{79} +(0.121963 - 0.211247i) q^{80} +(2.89900 - 8.52032i) q^{81} +(-5.50125 - 9.52844i) q^{82} +(1.75800 - 3.04495i) q^{83} +(-1.02082 - 0.220667i) q^{84} +(-0.148368 + 0.256981i) q^{85} +(2.39069 + 4.14079i) q^{86} +(-2.21573 + 2.44382i) q^{87} +(-0.714002 - 1.23669i) q^{88} +(-6.62760 + 11.4793i) q^{89} +(-0.0390955 - 0.398392i) q^{90} +(1.30959 - 2.76861i) q^{91} +(2.36303 - 4.09288i) q^{92} +(1.53005 - 1.68755i) q^{93} -3.05736 q^{94} +(0.363136 - 0.628970i) q^{95} +(6.42898 + 1.38972i) q^{96} +15.7455 q^{97} +(3.56567 + 6.17591i) q^{98} +(-1.26756 - 0.574866i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.567922	−	0.983670i	−0.401581	−	0.695559i	0.592336	−	0.805691i	$-0.298206\pi$
$2$	−0.567922	−	0.983670i	−0.401581	−	0.695559i	−0.993917	+	0.110132i	$0.964873\pi$
$3$	−0.529547	−	1.64911i	−0.305734	−	0.952117i
$3$	−0.529547	−	1.64911i	−0.305734	−	0.952117i
$4$	0.354929	−	0.614756i	0.177465	−	0.307378i
$5$	−0.0587384	−	0.101738i	−0.0262686	−	0.0454986i	0.852592	−	0.522577i	$-0.175029\pi$
$5$	−0.0587384	−	0.101738i	−0.0262686	−	0.0454986i	−0.878861	+	0.477078i	$0.841696\pi$
$6$	−1.32144	+	1.45747i	−0.539477	+	0.595009i
$7$	0.849445			0.321060			0.160530	−	0.987031i	$-0.448680\pi$
$7$	0.849445			0.321060			0.160530	+	0.987031i	$0.448680\pi$
$8$	−3.07798			−1.08823
$9$	−2.43916	+	1.74657i	−0.813053	+	0.582189i
$10$	−0.0667177	+	0.115558i	−0.0210980	+	0.0365428i
$11$	0.231971	+	0.401786i	0.0699419	+	0.121143i	0.898876	−	0.438204i	$-0.144385\pi$
$11$	0.231971	+	0.401786i	0.0699419	+	0.121143i	−0.828934	+	0.559347i	$0.811052\pi$
$12$	−1.20175	−	0.259777i	−0.346917	−	0.0749912i
$13$	1.54170	−	3.25932i	0.427591	−	0.903972i
$13$	1.54170	−	3.25932i	0.427591	−	0.903972i
$14$	−0.482419	−	0.835574i	−0.128932	−	0.223316i
$15$	−0.136673	+	0.150741i	−0.0352888	+	0.0389213i
$16$	1.03819	+	1.79820i	0.259548	+	0.449550i
$17$	−1.26296	−	2.18751i	−0.306312	−	0.530548i	0.671240	−	0.741240i	$-0.265762\pi$
$17$	−1.26296	−	2.18751i	−0.306312	−	0.530548i	−0.977553	+	0.210692i	$0.932428\pi$
$18$	3.10330	+	1.40741i	0.731454	+	0.331730i
$19$	3.09113	+	5.35399i	0.709153	+	1.22829i	0.965172	+	0.261617i	$0.0842558\pi$
$19$	3.09113	+	5.35399i	0.709153	+	1.22829i	−0.256019	+	0.966672i	$0.582411\pi$
$20$	−0.0833920			−0.0186470
$21$	−0.449821	−	1.40083i	−0.0981590	−	0.305687i
$22$	0.263483	−	0.456366i	0.0561748	−	0.0972975i
$23$	6.65773			1.38823			0.694117	−	0.719862i	$-0.255795\pi$
$23$	6.65773			1.38823			0.694117	+	0.719862i	$0.255795\pi$
$24$	1.62993	+	5.07594i	0.332709	+	1.03612i
$25$	2.49310	−	4.31818i	0.498620	−	0.863635i
$26$	−4.08166	+	0.334515i	−0.800479	+	0.0656037i
$27$	4.17194	+	3.09756i	0.802890	+	0.596127i
$28$	0.301493	−	0.522201i	0.0569768	−	0.0986868i
$29$	−0.952265	−	1.64937i	−0.176831	−	0.306281i	0.763962	−	0.645261i	$-0.223251\pi$
$29$	−0.952265	−	1.64937i	−0.176831	−	0.306281i	−0.940793	+	0.338980i	$0.889918\pi$
$30$	0.225899	+	0.0488315i	0.0412434	+	0.00891537i
$31$	0.657577	+	1.13896i	0.118104	+	0.204563i	0.919016	−	0.394219i	$-0.128985\pi$
$31$	0.657577	+	1.13896i	0.118104	+	0.204563i	−0.800912	+	0.598782i	$0.795652\pi$
$32$	−1.89875	+	3.28874i	−0.335655	+	0.581372i
$33$	0.539751	−	0.595312i	0.0939586	−	0.103630i
$34$	−1.43452	+	2.48467i	−0.246019	+	0.426117i
$35$	−0.0498951	−	0.0864208i	−0.00843381	−	0.0146078i
$36$	0.207983	+	2.11940i	0.0346639	+	0.353233i
$37$	−2.01347	+	3.48743i	−0.331012	+	0.573330i	−0.982711	−	0.185148i	$-0.940723\pi$
$37$	−2.01347	+	3.48743i	−0.331012	+	0.573330i	0.651698	+	0.758478i	$0.274057\pi$
$38$	3.51104	−	6.08129i	0.569565	−	0.986516i
$39$	−6.19139	−	0.816478i	−0.991417	−	0.130741i
$40$	0.180795	+	0.313147i	0.0285863	+	0.0495129i
$41$	9.68663			1.51280			0.756399	−	0.654111i	$-0.226957\pi$
$41$	9.68663			1.51280			0.756399	+	0.654111i	$0.226957\pi$
$42$	−1.12249	+	1.23804i	−0.173204	+	0.191034i
$43$	−4.20953			−0.641948			−0.320974	−	0.947088i	$-0.604010\pi$
$43$	−4.20953			−0.641948			−0.320974	+	0.947088i	$0.604010\pi$
$44$	0.329333			0.0496489
$45$	0.320965	+	0.145564i	0.0478466	+	0.0216995i
$46$	−3.78107	−	6.54901i	−0.557489	−	0.965599i
$47$	1.34586	−	2.33109i	0.196313	−	0.340025i	−0.751017	−	0.660283i	$-0.770436\pi$
$47$	1.34586	−	2.33109i	0.196313	−	0.340025i	0.947330	+	0.320258i	$0.103770\pi$
$48$	2.41567	−	2.66433i	0.348672	−	0.384563i
$49$	−6.27844			−0.896920
$50$	−5.66354			−0.800946
$51$	−2.93865	+	3.24115i	−0.411494	+	0.453852i
$52$	−1.45649	−	2.10460i	−0.201979	−	0.291855i
$53$	−0.389682			−0.0535269			−0.0267634	−	0.999642i	$-0.508520\pi$
$53$	−0.389682			−0.0535269			−0.0267634	+	0.999642i	$0.508520\pi$
$54$	0.677644	−	5.86299i	0.0922156	−	0.797851i
$55$	0.0272512	−	0.0472005i	0.00367456	−	0.00636452i
$56$	−2.61457			−0.349387
$57$	7.19244	−	7.93281i	0.952662	−	1.05073i
$58$	−1.08162	+	1.87343i	−0.142024	+	0.245993i
$59$	−5.53661	+	9.58969i	−0.720805	+	1.24847i	0.239872	+	0.970805i	$0.422895\pi$
$59$	−5.53661	+	9.58969i	−0.720805	+	1.24847i	−0.960677	+	0.277667i	$0.910439\pi$
$60$	0.0441600	+	0.137523i	0.00570103	+	0.0177541i
$61$	−7.76759			−0.994538			−0.497269	−	0.867596i	$-0.665664\pi$
$61$	−7.76759			−0.994538			−0.497269	+	0.867596i	$0.665664\pi$
$62$	0.746905	−	1.29368i	0.0948570	−	0.164297i
$63$	−2.07193	+	1.48361i	−0.261039	+	0.186918i
$64$	8.46614			1.05827
$65$	−0.422153	+	0.0345978i	−0.0523617	+	0.00429133i
$66$	−0.892126	−	0.192846i	−0.109813	−	0.0237378i
$67$	−1.02270			−0.124943			−0.0624715	−	0.998047i	$-0.519898\pi$
$67$	−1.02270			−0.124943			−0.0624715	+	0.998047i	$0.519898\pi$
$68$	−1.79304			−0.217438
$69$	−3.52558	−	10.9794i	−0.424430	−	1.32176i
$70$	−0.0566730	+	0.0981605i	−0.00677372	+	0.0117324i
$71$	3.61012	+	6.25291i	0.428442	+	0.742083i	0.996735	−	0.0807430i	$-0.0257293\pi$
$71$	3.61012	+	6.25291i	0.428442	+	0.742083i	−0.568293	+	0.822826i	$0.692396\pi$
$72$	7.50768	−	5.37589i	0.884788	−	0.633555i
$73$	−3.31321			−0.387782			−0.193891	−	0.981023i	$-0.562111\pi$
$73$	−3.31321			−0.387782			−0.193891	+	0.981023i	$0.562111\pi$
$74$	4.57397			0.531713
$75$	−8.44138	−	1.82473i	−0.974727	−	0.210702i
$76$	4.38853			0.503398
$77$	0.197047	+	0.341295i	0.0224556	+	0.0388942i
$78$	2.71308	+	6.55398i	0.307196	+	0.742092i
$79$	−4.41302	+	7.64357i	−0.496503	+	0.859969i	−0.999992	−	0.00403289i	$-0.998716\pi$
$79$	−4.41302	+	7.64357i	−0.496503	+	0.859969i	0.503489	+	0.864002i	$0.332050\pi$
$80$	0.121963	−	0.211247i	0.0136359	−	0.0236181i
$81$	2.89900	−	8.52032i	0.322111	−	0.946702i
$82$	−5.50125	−	9.52844i	−0.607511	−	1.05224i
$83$	1.75800	−	3.04495i	0.192966	−	0.334227i	−0.753266	−	0.657716i	$-0.771523\pi$
$83$	1.75800	−	3.04495i	0.192966	−	0.334227i	0.946232	+	0.323489i	$0.104856\pi$
$84$	−1.02082	−	0.220667i	−0.111381	−	0.0240767i
$85$	−0.148368	+	0.256981i	−0.0160928	+	0.0278735i
$86$	2.39069	+	4.14079i	0.257794	+	0.446513i
$87$	−2.21573	+	2.44382i	−0.237552	+	0.262004i
$88$	−0.714002	−	1.23669i	−0.0761128	−	0.131831i
$89$	−6.62760	+	11.4793i	−0.702525	+	1.21681i	0.265053	+	0.964234i	$0.414611\pi$
$89$	−6.62760	+	11.4793i	−0.702525	+	1.21681i	−0.967577	+	0.252574i	$0.918723\pi$
$90$	−0.0390955	−	0.398392i	−0.00412103	−	0.0419942i
$91$	1.30959	−	2.76861i	0.137282	−	0.290230i
$92$	2.36303	−	4.09288i	0.246362	−	0.426712i
$93$	1.53005	−	1.68755i	0.158659	−	0.174991i
$94$	−3.05736			−0.315343
$95$	0.363136	−	0.628970i	0.0372569	−	0.0645309i
$96$	6.42898	+	1.38972i	0.656155	+	0.141838i
$97$	15.7455			1.59871			0.799354	−	0.600860i	$-0.205175\pi$
$97$	15.7455			1.59871			0.799354	+	0.600860i	$0.205175\pi$
$98$	3.56567	+	6.17591i	0.360187	+	0.623861i
$99$	−1.26756	−	0.574866i	−0.127395	−	0.0577762i
$100$	−1.76975	−	3.06529i	−0.176975	−	0.306529i
$101$	7.81909	+	13.5431i	0.778028	+	1.34758i	0.933077	+	0.359677i	$0.117113\pi$
$101$	7.81909	+	13.5431i	0.778028	+	1.34758i	−0.155049	+	0.987907i	$0.549553\pi$
$102$	4.85715	+	1.04994i	0.480929	+	0.103960i
$103$	7.23270	+	12.5274i	0.712659	+	1.23436i	0.963855	+	0.266426i	$0.0858428\pi$
$103$	7.23270	+	12.5274i	0.712659	+	1.23436i	−0.251196	+	0.967936i	$0.580824\pi$
$104$	−4.74532	+	10.0321i	−0.465317	+	0.983729i
$105$	−0.116096	+	0.128047i	−0.0113298	+	0.0124961i
$106$	0.221309	+	0.383318i	0.0214954	+	0.0372311i
$107$	3.13817	−	5.43546i	0.303378	−	0.525466i	−0.673521	−	0.739168i	$-0.735219\pi$
$107$	3.13817	−	5.43546i	0.303378	−	0.525466i	0.976899	+	0.213702i	$0.0685522\pi$
$108$	3.38499	−	1.46531i	0.325721	−	0.140999i
$109$	−17.5426			−1.68028			−0.840138	−	0.542373i	$-0.817526\pi$
$109$	−17.5426			−1.68028			−0.840138	+	0.542373i	$0.817526\pi$
$110$	−0.0619063			−0.00590253
$111$	6.81740	+	1.47368i	0.647079	+	0.139876i
$112$	0.881887	+	1.52747i	0.0833305	+	0.144333i
$113$	6.57492	−	11.3881i	0.618516	−	1.07130i	−0.371240	−	0.928537i	$-0.621067\pi$
$113$	6.57492	−	11.3881i	0.618516	−	1.07130i	0.989757	−	0.142765i	$-0.0455993\pi$
$114$	−11.8880	−	2.56977i	−1.11341	−	0.240681i
$115$	−0.391065	−	0.677344i	−0.0364670	−	0.0631627i
$116$	−1.35195			−0.125525
$117$	1.93217	+	10.6427i	0.178629	+	0.983917i
$118$	12.5775			1.15785
$119$	−1.07281	−	1.85817i	−0.0983446	−	0.170338i
$120$	0.420676	−	0.463979i	0.0384023	−	0.0423553i
$121$	5.39238	−	9.33987i	0.490216	−	0.849079i
$122$	4.41139	+	7.64075i	0.399388	+	0.691761i
$123$	−5.12953	−	15.9744i	−0.462514	−	1.44036i
$124$	0.933573			0.0838374
$125$	−1.17315			−0.104929
$126$	2.63608	+	1.19552i	0.234841	+	0.106505i
$127$	−4.75121	+	8.22934i	−0.421602	+	0.730236i	−0.996096	−	0.0882724i	$-0.971865\pi$
$127$	−4.75121	+	8.22934i	−0.421602	+	0.730236i	0.574494	+	0.818509i	$0.305199\pi$
$128$	−1.01060	−	1.75041i	−0.0893254	−	0.154716i
$129$	2.22915	+	6.94200i	0.196265	+	0.611209i
$130$	0.273783	+	0.395611i	0.0240124	+	0.0346973i
$131$	−8.21488	−	14.2286i	−0.717738	−	1.24316i	−0.961894	−	0.273422i	$-0.911844\pi$
$131$	−8.21488	−	14.2286i	−0.717738	−	1.24316i	0.244157	−	0.969736i	$-0.421489\pi$
$132$	−0.174398	−	0.543109i	−0.0151794	−	0.0472715i
$133$	2.62574	+	4.54792i	0.227681	+	0.394355i
$134$	0.580815	+	1.00600i	0.0501748	+	0.0869052i
$135$	0.0700866	−	0.606391i	0.00603209	−	0.0521898i
$136$	3.88735	+	6.73309i	0.333338	+	0.577358i
$137$	−19.4310			−1.66010			−0.830050	−	0.557689i	$-0.811688\pi$
$137$	−19.4310			−1.66010			−0.830050	+	0.557689i	$0.811688\pi$
$138$	−8.79782	+	9.70343i	−0.748920	+	0.826011i
$139$	−7.53640	+	13.0534i	−0.639229	+	1.10718i	0.346373	+	0.938097i	$0.387413\pi$
$139$	−7.53640	+	13.0534i	−0.639229	+	1.10718i	−0.985602	+	0.169081i	$0.945920\pi$
$140$	−0.0708369			−0.00598681
$141$	−4.55693	−	0.985049i	−0.383763	−	0.0829561i
$142$	4.10053	−	7.10232i	0.344109	−	0.596014i
$143$	1.66718	−	0.136635i	0.139416	−	0.0114260i
$144$	−5.67299	−	2.57283i	−0.472750	−	0.214402i
$145$	−0.111869	+	0.193763i	−0.00929023	+	0.0160911i
$146$	1.88164	+	3.25910i	0.155726	+	0.269725i
$147$	3.32473	+	10.3539i	0.274219	+	0.853973i
$148$	1.42928	+	2.47558i	0.117486	+	0.203492i
$149$	7.05071	−	12.2122i	0.577616	−	1.00046i	−0.418136	−	0.908385i	$-0.637316\pi$
$149$	7.05071	−	12.2122i	0.577616	−	1.00046i	0.995752	−	0.0920762i	$-0.0293503\pi$
$150$	2.99911	+	9.33983i	0.244877	+	0.762594i
$151$	3.33115	−	5.76972i	0.271085	−	0.469534i	−0.698055	−	0.716044i	$-0.745951\pi$
$151$	3.33115	−	5.76972i	0.271085	−	0.469534i	0.969140	+	0.246511i	$0.0792841\pi$
$152$	−9.51441	−	16.4794i	−0.771721	−	1.33666i
$153$	6.90118	+	3.12984i	0.557928	+	0.253032i
$154$	0.223814	−	0.387658i	0.0180355	−	0.0312384i
$155$	0.0772501	−	0.133801i	0.00620487	−	0.0107472i
$156$	−2.69944	+	3.51640i	−0.216128	+	0.281538i
$157$	−5.87578	−	10.1771i	−0.468938	−	0.812224i	0.530432	−	0.847728i	$-0.322030\pi$
$157$	−5.87578	−	10.1771i	−0.468938	−	0.812224i	−0.999370	+	0.0355033i	$0.988697\pi$
$158$	10.0250			0.797546
$159$	0.206355	+	0.642630i	0.0163650	+	0.0509639i
$160$	0.446119			0.0352688
$161$	5.65538			0.445706
$162$	−10.0276	+	1.98722i	−0.787841	+	0.156130i
$163$	−7.13612	−	12.3601i	−0.558944	−	0.968119i	−0.997585	−	0.0694568i	$-0.977873\pi$
$163$	−7.13612	−	12.3601i	−0.558944	−	0.968119i	0.438641	−	0.898662i	$-0.355460\pi$
$164$	3.43807	−	5.95491i	0.268468	−	0.465000i
$165$	−0.0922699	−	0.0199455i	−0.00718320	−	0.00155276i
$166$	−3.99363			−0.309966
$167$	−11.1708			−0.864419			−0.432210	−	0.901773i	$-0.642266\pi$
$167$	−11.1708			−0.864419			−0.432210	+	0.901773i	$0.642266\pi$
$168$	1.38454	+	4.31173i	0.106820	+	0.332657i
$169$	−8.24632	−	10.0498i	−0.634332	−	0.773061i
$170$	0.337046			0.0258503
$171$	−16.8909	−	7.66037i	−1.29168	−	0.585803i
$172$	−1.49409	+	2.58783i	−0.113923	+	0.197320i
$173$	−12.3831			−0.941467			−0.470734	−	0.882275i	$-0.656011\pi$
$173$	−12.3831			−0.941467			−0.470734	+	0.882275i	$0.656011\pi$
$174$	3.66227	+	0.791655i	0.277636	+	0.0600152i
$175$	2.11775	−	3.66805i	0.160087	−	0.277279i
$176$	−0.481661	+	0.834261i	−0.0363066	+	0.0628848i
$177$	18.7464	+	4.05232i	1.40907	+	0.304591i
$178$	15.0558			1.12848
$179$	12.0175	−	20.8149i	0.898230	−	1.55578i	0.0684753	−	0.997653i	$-0.478187\pi$
$179$	12.0175	−	20.8149i	0.898230	−	1.55578i	0.829755	−	0.558128i	$-0.188480\pi$
$180$	0.203406	−	0.145650i	0.0151610	−	0.0108561i
$181$	21.6433			1.60873			0.804366	−	0.594135i	$-0.202505\pi$
$181$	21.6433			1.60873			0.804366	+	0.594135i	$0.202505\pi$
$182$	−3.46715	+	0.284152i	−0.257002	+	0.0210627i
$183$	4.11331	+	12.8097i	0.304064	+	0.946917i
$184$	−20.4923			−1.51072
$185$	0.473072			0.0347809
$186$	−2.52894	−	0.546669i	−0.185431	−	0.0400837i
$187$	0.585939	−	1.01488i	0.0428481	−	0.0742151i
$188$	−0.955368	−	1.65475i	−0.0696773	−	0.120685i
$189$	3.54384	+	2.63121i	0.257776	+	0.191392i
$190$	−0.824931			−0.0598468
$191$	5.49494			0.397600			0.198800	−	0.980040i	$-0.436296\pi$
$191$	5.49494			0.397600			0.198800	+	0.980040i	$0.436296\pi$
$192$	−4.48322	−	13.9616i	−0.323549	−	1.00759i
$193$	0.128719			0.00926538			0.00463269	−	0.999989i	$-0.498525\pi$
$193$	0.128719			0.00926538			0.00463269	+	0.999989i	$0.498525\pi$
$194$	−8.94219	−	15.4883i	−0.642012	−	1.11200i
$195$	0.280606	+	0.677858i	0.0200946	+	0.0485424i
$196$	−2.22840	+	3.85971i	−0.159172	+	0.275693i
$197$	−1.80122	+	3.11981i	−0.128332	+	0.222277i	−0.923030	−	0.384727i	$-0.874296\pi$
$197$	−1.80122	+	3.11981i	−0.128332	+	0.222277i	0.794699	+	0.607004i	$0.207629\pi$
$198$	0.154397	+	1.57334i	0.0109725	+	0.111812i
$199$	10.2188	+	17.6995i	0.724394	+	1.25469i	0.959223	+	0.282650i	$0.0912135\pi$
$199$	10.2188	+	17.6995i	0.724394	+	1.25469i	−0.234829	+	0.972037i	$0.575453\pi$
$200$	−7.67370	+	13.2912i	−0.542613	+	0.939833i
$201$	0.541569	+	1.68655i	0.0381993	+	0.118960i
$202$	8.88126	−	15.3828i	0.624883	−	1.08233i
$203$	−0.808897	−	1.40105i	−0.0567735	−	0.0983345i
$204$	0.949500	+	2.95693i	0.0664783	+	0.207027i
$205$	−0.568977	−	0.985498i	−0.0397391	−	0.0688301i
$206$	8.21522	−	14.2292i	0.572382	−	0.991394i
$207$	−16.2393	+	11.6282i	−1.12871	+	0.808215i
$208$	7.46149	−	0.611511i	0.517361	−	0.0424006i
$209$	−1.43410	+	2.48394i	−0.0991990	+	0.171818i
$210$	0.191889	+	0.0414797i	0.0132416	+	0.00286237i
$211$	7.10204			0.488925			0.244462	−	0.969659i	$-0.421389\pi$
$211$	7.10204			0.488925			0.244462	+	0.969659i	$0.421389\pi$
$212$	−0.138309	+	0.239559i	−0.00949913	+	0.0164530i
$213$	8.40003	−	9.26470i	0.575561	−	0.634807i
$214$	−7.12893			−0.487324
$215$	0.247261	+	0.428269i	0.0168631	+	0.0292077i
$216$	−12.8411	−	9.53423i	−0.873729	−	0.648722i
$217$	0.558576	+	0.967481i	0.0379186	+	0.0656769i
$218$	9.96282	+	17.2561i	0.674768	+	1.16873i
$219$	1.75450	+	5.46386i	0.118558	+	0.369213i
$220$	−0.0193445	−	0.0335057i	−0.00130421	−	0.00225895i
$221$	−9.07688	+	0.743901i	−0.610577	+	0.0500402i
$222$	−2.42213	−	7.54300i	−0.162563	−	0.506253i
$223$	7.01317	+	12.1472i	0.469636	+	0.813434i	0.999397	−	0.0347129i	$-0.0110517\pi$
$223$	7.01317	+	12.1472i	0.469636	+	0.813434i	−0.529761	+	0.848147i	$0.677718\pi$
$224$	−1.61289	+	2.79360i	−0.107766	+	0.186655i
$225$	1.46092	+	14.8871i	0.0973945	+	0.992472i
$226$	−14.9362			−0.993539
$227$	−13.9373			−0.925054			−0.462527	−	0.886605i	$-0.653057\pi$
$227$	−13.9373			−0.925054			−0.462527	+	0.886605i	$0.653057\pi$
$228$	−2.32393	−	7.23718i	−0.153906	−	0.479294i
$229$	−1.62150	−	2.80852i	−0.107152	−	0.185593i	0.807463	−	0.589918i	$-0.200840\pi$
$229$	−1.62150	−	2.80852i	−0.107152	−	0.185593i	−0.914615	+	0.404325i	$0.867506\pi$
$230$	−0.444189	+	0.769357i	−0.0292889	+	0.0507299i
$231$	0.458489	−	0.505685i	0.0301664	−	0.0332716i
$232$	2.93105	+	5.07673i	0.192433	+	0.333304i
$233$	−9.70153			−0.635568			−0.317784	−	0.948163i	$-0.602939\pi$
$233$	−9.70153			−0.635568			−0.317784	+	0.948163i	$0.602939\pi$
$234$	9.37156	−	7.94483i	0.612638	−	0.519370i
$235$	−0.316214			−0.0206275
$236$	3.93021	+	6.80733i	0.255835	+	0.443119i
$237$	14.9420	+	3.22994i	0.970589	+	0.209807i
$238$	−1.21855	+	2.11059i	−0.0789867	+	0.136809i
$239$	−4.81288	−	8.33616i	−0.311319	−	0.539221i	0.667329	−	0.744763i	$-0.267438\pi$
$239$	−4.81288	−	8.33616i	−0.311319	−	0.539221i	−0.978648	+	0.205542i	$0.934104\pi$
$240$	−0.412956	−	0.0892666i	−0.0266562	−	0.00576213i
$241$	−0.286300			−0.0184422			−0.00922111	−	0.999957i	$-0.502935\pi$
$241$	−0.286300			−0.0184422			−0.00922111	+	0.999957i	$0.502935\pi$
$242$	−12.2498			−0.787447
$243$	−15.5861	−	0.268877i	−0.999851	−	0.0172485i
$244$	−2.75695	+	4.77517i	−0.176495	+	0.305699i
$245$	0.368786	+	0.638756i	0.0235609	+	0.0408086i
$246$	−12.8003	+	14.1180i	−0.816119	+	0.900128i
$247$	22.2159	−	1.82072i	1.41357	−	0.115850i
$248$	−2.02401	−	3.50568i	−0.128525	−	0.222611i
$249$	−5.95241	−	1.28670i	−0.377219	−	0.0815415i
$250$	0.666256	+	1.15399i	0.0421377	+	0.0729847i
$251$	12.2860	+	21.2800i	0.775488	+	1.34318i	0.934520	+	0.355911i	$0.115829\pi$
$251$	12.2860	+	21.2800i	0.775488	+	1.34318i	−0.159032	+	0.987273i	$0.550837\pi$
$252$	0.176670	+	1.80031i	0.0111292	+	0.113409i
$253$	1.54440	+	2.67498i	0.0970957	+	0.168175i
$254$	10.7933			0.677230
$255$	0.502360	+	0.108593i	0.0314590	+	0.00680033i
$256$	7.31825	−	12.6756i	0.457391	−	0.792224i
$257$	1.29510			0.0807861			0.0403930	−	0.999184i	$-0.487139\pi$
$257$	1.29510			0.0807861			0.0403930	+	0.999184i	$0.487139\pi$
$258$	5.56266	−	6.13526i	0.346316	−	0.381965i
$259$	−1.71033	+	2.96238i	−0.106275	+	0.184073i
$260$	−0.128565	+	0.271801i	−0.00797329	+	0.0168564i
$261$	5.20347	+	2.35989i	0.322087	+	0.146073i
$262$	−9.33082	+	16.1615i	−0.576460	+	0.998458i
$263$	5.86423	+	10.1571i	0.361604	+	0.626316i	0.988225	−	0.153008i	$-0.0488959\pi$
$263$	5.86423	+	10.1571i	0.361604	+	0.626316i	−0.626621	+	0.779324i	$0.715563\pi$
$264$	−1.66134	+	1.83235i	−0.102249	+	0.112774i
$265$	0.0228893	+	0.0396454i	0.00140608	+	0.00243540i
$266$	2.98243	−	5.16573i	0.182865	−	0.316731i
$267$	22.4404	+	4.85083i	1.37333	+	0.296866i
$268$	−0.362987	+	0.628712i	−0.0221730	+	0.0384047i
$269$	13.4278	+	23.2576i	0.818705	+	1.41804i	0.906637	+	0.421912i	$0.138641\pi$
$269$	13.4278	+	23.2576i	0.818705	+	1.41804i	−0.0879319	+	0.996126i	$0.528026\pi$
$270$	−0.636292	+	0.275441i	−0.0387235	+	0.0167628i
$271$	14.1476	−	24.5044i	0.859408	−	1.48854i	−0.0130858	−	0.999914i	$-0.504165\pi$
$271$	14.1476	−	24.5044i	0.859408	−	1.48854i	0.872494	−	0.488625i	$-0.162501\pi$
$272$	2.62238	−	4.54210i	0.159005	−	0.275405i
$273$	−5.25925	−	0.693554i	−0.318304	−	0.0419758i
$274$	11.0353	+	19.1137i	0.666666	+	1.15470i
$275$	2.31331			0.139498
$276$	−8.00096	−	1.72953i	−0.481601	−	0.104105i
$277$	−16.6176			−0.998454			−0.499227	−	0.866471i	$-0.666383\pi$
$277$	−16.6176			−0.998454			−0.499227	+	0.866471i	$0.666383\pi$
$278$	17.1204			1.02681
$279$	−3.59320	−	1.62959i	−0.215119	−	0.0975613i
$280$	0.153576	+	0.266001i	0.00917791	+	0.0158966i
$281$	−0.612801	+	1.06140i	−0.0365567	+	0.0633180i	−0.883725	−	0.468007i	$-0.844972\pi$
$281$	−0.612801	+	1.06140i	−0.0365567	+	0.0633180i	0.847168	+	0.531325i	$0.178306\pi$
$282$	1.61902	+	5.04195i	0.0964112	+	0.300243i
$283$	3.04077			0.180755			0.0903776	−	0.995908i	$-0.471193\pi$
$283$	3.04077			0.180755			0.0903776	+	0.995908i	$0.471193\pi$
$284$	5.12535			0.304133
$285$	−1.22954	−	0.265784i	−0.0728317	−	0.0157437i
$286$	−1.08123	−	1.56235i	−0.0639345	−	0.0923840i
$287$	8.22826			0.485699
$288$	−1.11264	−	11.3381i	−0.0655629	−	0.668101i
$289$	5.30988	−	9.19698i	0.312346	−	0.540999i
$290$	0.254132			0.0149231
$291$	−8.33796	−	25.9661i	−0.488780	−	1.52216i
$292$	−1.17595	+	2.03681i	−0.0688175	+	0.119195i
$293$	−13.8021	+	23.9059i	−0.806325	+	1.39660i	0.109068	+	0.994034i	$0.465213\pi$
$293$	−13.8021	+	23.9059i	−0.806325	+	1.39660i	−0.915393	+	0.402561i	$0.868120\pi$
$294$	8.29660	−	9.15063i	0.483868	−	0.533676i
$295$	1.30085			0.0757383
$296$	6.19741	−	10.7342i	0.360217	−	0.623914i
$297$	−0.276788	+	2.39477i	−0.0160608	+	0.138959i
$298$	−16.0170			−0.927840
$299$	10.2642	−	21.6997i	0.593596	−	1.25492i
$300$	−4.11786	+	4.54174i	−0.237745	+	0.262217i
$301$	−3.57577			−0.206104
$302$	−7.56734			−0.435451
$303$	18.1935	−	20.0663i	1.04519	−	1.15278i
$304$	−6.41836	+	11.1169i	−0.368118	+	0.637600i
$305$	0.456256	+	0.790259i	0.0261252	+	0.0452501i
$306$	−0.840608	−	8.56599i	−0.0480544	−	0.489685i
$307$	7.74191			0.441854			0.220927	−	0.975290i	$-0.429092\pi$
$307$	7.74191			0.441854			0.220927	+	0.975290i	$0.429092\pi$
$308$	0.279751			0.0159403
$309$	16.8291	−	18.5614i	0.957373	−	1.05592i
$310$	−0.175488			−0.00996705
$311$	−4.70886	−	8.15598i	−0.267015	−	0.462483i	0.701075	−	0.713088i	$-0.252704\pi$
$311$	−4.70886	−	8.15598i	−0.267015	−	0.462483i	−0.968090	+	0.250605i	$0.919371\pi$
$312$	19.0570	+	2.51310i	1.07889	+	0.142276i
$313$	6.58566	−	11.4067i	0.372243	−	0.644744i	−0.617667	−	0.786440i	$-0.711922\pi$
$313$	6.58566	−	11.4067i	0.372243	−	0.644744i	0.989910	+	0.141695i	$0.0452554\pi$
$314$	−6.67396	+	11.5596i	−0.376634	+	0.652349i
$315$	0.272642	+	0.123649i	0.0153616	+	0.00696683i
$316$	3.13262	+	5.42586i	0.176224	+	0.305228i
$317$	−12.5673	+	21.7671i	−0.705848	+	1.22256i	0.260537	+	0.965464i	$0.416100\pi$
$317$	−12.5673	+	21.7671i	−0.705848	+	1.22256i	−0.966385	+	0.257100i	$0.917233\pi$
$318$	0.514942	−	0.567948i	0.0288765	−	0.0318490i
$319$	0.441796	−	0.765213i	0.0247358	−	0.0428437i
$320$	−0.497288	−	0.861328i	−0.0277992	−	0.0481497i
$321$	−10.6255	−	2.29686i	−0.593058	−	0.128198i
$322$	−3.21181	−	5.56303i	−0.178987	−	0.310015i
$323$	7.80792	−	13.5237i	0.434444	−	0.752480i
$324$	−4.20897	−	4.80629i	−0.233832	−	0.267016i
$325$	−10.2307	−	14.7831i	−0.567497	−	0.820021i
$326$	−8.10551	+	14.0392i	−0.448923	+	0.777557i
$327$	9.28963	+	28.9298i	0.513718	+	1.59982i
$328$	−29.8152			−1.64627
$329$	1.14323	−	1.98013i	0.0630284	−	0.109168i
$330$	0.0327823	+	0.102091i	0.00180461	+	0.00561990i
$331$	−29.1108			−1.60007			−0.800036	−	0.599952i	$-0.795186\pi$
$331$	−29.1108			−1.60007			−0.800036	+	0.599952i	$0.795186\pi$
$332$	−1.24793	−	2.16148i	−0.0684892	−	0.118627i
$333$	−1.17986	−	12.0231i	−0.0646560	−	0.658859i
$334$	6.34412	+	10.9883i	0.347135	+	0.601255i
$335$	0.0600719	+	0.104048i	0.00328208	+	0.00568473i
$336$	2.05198	−	2.26320i	0.111945	−	0.123468i
$337$	−7.69878	−	13.3347i	−0.419379	−	0.726386i	0.576498	−	0.817099i	$-0.304419\pi$
$337$	−7.69878	−	13.3347i	−0.419379	−	0.726386i	−0.995877	+	0.0907124i	$0.971086\pi$
$338$	−5.20241	+	13.8191i	−0.282974	+	0.751663i
$339$	−22.2620	−	4.81227i	−1.20911	−	0.261366i
$340$	0.105320	+	0.182420i	0.00571180	+	0.00989314i
$341$	−0.305078	+	0.528410i	−0.0165209	+	0.0286150i
$342$	2.05741	+	20.9655i	0.111252	+	1.13369i
$343$	−11.2793			−0.609026
$344$	12.9568			0.698586
$345$	−0.909931	+	1.00360i	−0.0489890	+	0.0540318i
$346$	7.03262	+	12.1808i	0.378076	+	0.654847i
$347$	−5.21428	+	9.03139i	−0.279917	+	0.484831i	−0.971364	−	0.237597i	$-0.923640\pi$
$347$	−5.21428	+	9.03139i	−0.279917	+	0.484831i	0.691447	+	0.722427i	$0.256974\pi$
$348$	0.715920	+	2.22952i	0.0383773	+	0.119515i
$349$	−7.06904	−	12.2439i	−0.378397	−	0.655403i	0.612432	−	0.790523i	$-0.290191\pi$
$349$	−7.06904	−	12.2439i	−0.378397	−	0.655403i	−0.990829	+	0.135120i	$0.956858\pi$
$350$	−4.81087			−0.257152
$351$	16.5278	−	8.82217i	0.882191	−	0.470893i
$352$	−1.76182			−0.0939055
$353$	−7.37735	−	12.7779i	−0.392657	−	0.680102i	0.600142	−	0.799893i	$-0.295111\pi$
$353$	−7.37735	−	12.7779i	−0.392657	−	0.680102i	−0.992799	+	0.119792i	$0.961777\pi$
$354$	−6.66035	−	20.7417i	−0.353994	−	1.10241i
$355$	0.424105	−	0.734572i	0.0225092	−	0.0389870i
$356$	4.70466	+	8.14871i	0.249347	+	0.431881i
$357$	−2.49623	+	2.75318i	−0.132114	+	0.145714i
$358$	−27.3000			−1.44285
$359$	−0.0643609			−0.00339684			−0.00169842	−	0.999999i	$-0.500541\pi$
$359$	−0.0643609			−0.00339684			−0.00169842	+	0.999999i	$0.500541\pi$
$360$	−0.987922	−	0.448044i	−0.0520680	−	0.0236140i
$361$	−9.61012	+	16.6452i	−0.505796	+	0.876064i
$362$	−12.2917	−	21.2898i	−0.646037	−	1.11897i
$363$	−18.2580	−	3.94675i	−0.958299	−	0.207151i
$364$	−1.23721	−	1.78774i	−0.0648473	−	0.0937030i
$365$	0.194613	+	0.337079i	0.0101865	+	0.0176435i
$366$	10.2644	−	11.3210i	0.536530	−	0.591759i
$367$	3.57378	+	6.18997i	0.186550	+	0.323114i	0.944098	−	0.329666i	$-0.106936\pi$
$367$	3.57378	+	6.18997i	0.186550	+	0.323114i	−0.757548	+	0.652780i	$0.773603\pi$
$368$	6.91200	+	11.9719i	0.360313	+	0.624081i
$369$	−23.6272	+	16.9184i	−1.22998	+	0.880734i
$370$	−0.268668	−	0.465346i	−0.0139674	−	0.0241922i
$371$	−0.331013			−0.0171853
$372$	−0.494371	−	1.53957i	−0.0256319	−	0.0798230i
$373$	−9.89911	+	17.1458i	−0.512557	+	0.887774i	0.487337	+	0.873214i	$0.337968\pi$
$373$	−9.89911	+	17.1458i	−0.512557	+	0.887774i	−0.999894	+	0.0145604i	$0.995365\pi$
$374$	−1.33107			−0.0688280
$375$	0.621237	+	1.93465i	0.0320805	+	0.0999051i
$376$	−4.14251	+	7.17504i	−0.213634	+	0.370025i
$377$	−6.84394	+	0.560899i	−0.352481	+	0.0288878i
$378$	0.575621	−	4.98029i	0.0296068	−	0.256158i
$379$	10.8356	−	18.7679i	0.556589	−	0.964041i	−0.441189	−	0.897414i	$-0.645443\pi$
$379$	10.8356	−	18.7679i	0.556589	−	0.964041i	0.997778	−	0.0666264i	$-0.0212236\pi$
$380$	−0.257775	−	0.446480i	−0.0132236	−	0.0229039i
$381$	16.0871	+	3.47747i	0.824168	+	0.178156i
$382$	−3.12070	−	5.40520i	−0.159669	−	0.276554i
$383$	11.3679	−	19.6898i	0.580874	−	1.00610i	−0.414502	−	0.910048i	$-0.636044\pi$
$383$	11.3679	−	19.6898i	0.580874	−	1.00610i	0.995376	−	0.0960544i	$-0.0306223\pi$
$384$	−2.35147	+	2.59352i	−0.119998	+	0.132350i
$385$	0.0231484	−	0.0400943i	0.00117975	−	0.00204339i
$386$	−0.0731022	−	0.126617i	−0.00372080	−	0.00644462i
$387$	10.2677	−	7.35223i	0.521938	−	0.373735i
$388$	5.58852	−	9.67961i	0.283714	−	0.491408i
$389$	6.49522	−	11.2501i	0.329321	−	0.570400i	−0.653057	−	0.757309i	$-0.726514\pi$
$389$	6.49522	−	11.2501i	0.329321	−	0.570400i	0.982377	+	0.186909i	$0.0598469\pi$
$390$	0.507426	−	0.660994i	0.0256945	−	0.0334707i
$391$	−8.40843	−	14.5638i	−0.425233	−	0.736525i
$392$	19.3249			0.976055
$393$	−19.1144	+	21.0820i	−0.964195	+	1.06345i
$394$	4.09182			0.206143
$395$	1.03685			0.0521698
$396$	−0.803297	+	0.575203i	−0.0403672	+	0.0289050i
$397$	−6.19600	−	10.7318i	−0.310968	−	0.538613i	0.667604	−	0.744517i	$-0.267320\pi$
$397$	−6.19600	−	10.7318i	−0.310968	−	0.538613i	−0.978572	+	0.205904i	$0.933987\pi$
$398$	11.6070	−	20.1039i	0.581806	−	1.00772i
$399$	6.10959	−	6.73849i	0.305862	−	0.337346i
$400$	10.3533			0.517663
$401$	8.24798			0.411884			0.205942	−	0.978564i	$-0.433974\pi$
$401$	8.24798			0.411884			0.205942	+	0.978564i	$0.433974\pi$
$402$	1.35144	−	1.49056i	0.0674038	−	0.0743421i
$403$	4.72601	−	0.387323i	0.235419	−	0.0192939i
$404$	11.1009			0.552290
$405$	−1.03712	+	0.205532i	−0.0515350	+	0.0102129i
$406$	−0.918781	+	1.59138i	−0.0455983	+	0.0789786i
$407$	−1.86827			−0.0926065
$408$	9.04511	−	9.97618i	0.447799	−	0.493894i
$409$	−4.64304	+	8.04198i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$409$	−4.64304	+	8.04198i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$410$	−0.646269	+	1.11937i	−0.0319170	+	0.0552818i
$411$	10.2896	+	32.0439i	0.507549	+	1.58061i
$412$	10.2684			0.505887
$413$	−4.70305	+	8.14592i	−0.231422	+	0.400834i
$414$	20.6609	+	9.37018i	1.01543	+	0.460519i
$415$	−0.413049			−0.0202758
$416$	7.79173	+	11.2589i	0.382021	+	0.552012i
$417$	25.5175	+	5.51599i	1.24960	+	0.270119i
$418$	3.25784			0.159346
$419$	−0.305711			−0.0149349			−0.00746747	−	0.999972i	$-0.502377\pi$
$419$	−0.305711			−0.0149349			−0.00746747	+	0.999972i	$0.502377\pi$
$420$	0.0375115	+	0.116818i	0.00183037	+	0.00570014i
$421$	10.2975	−	17.8358i	0.501869	−	0.869262i	−0.498129	−	0.867103i	$-0.665979\pi$
$421$	10.2975	−	17.8358i	0.501869	−	0.869262i	0.999998	−	0.00215912i	$-0.000687270\pi$
$422$	−4.03341	−	6.98607i	−0.196343	−	0.340076i
$423$	0.788651	+	8.03653i	0.0383455	+	0.390750i
$424$	1.19943			0.0582495
$425$	−12.5947			−0.610933
$426$	−13.8840	−	3.00123i	−0.672681	−	0.145410i
$427$	−6.59814			−0.319307
$428$	−2.22765	−	3.85841i	−0.107678	−	0.186503i
$429$	−1.10818	−	2.67701i	−0.0535032	−	0.129247i
$430$	0.280850	−	0.486447i	0.0135438	−	0.0234586i
$431$	−1.90600	+	3.30129i	−0.0918088	+	0.159017i	−0.908272	−	0.418380i	$-0.862598\pi$
$431$	−1.90600	+	3.30129i	−0.0918088	+	0.159017i	0.816463	+	0.577397i	$0.195932\pi$
$432$	−1.23877	+	10.7179i	−0.0596003	+	0.515663i
$433$	7.23683	+	12.5346i	0.347780	+	0.602373i	0.985855	−	0.167602i	$-0.0536023\pi$
$433$	7.23683	+	12.5346i	0.347780	+	0.602373i	−0.638075	+	0.769974i	$0.720269\pi$
$434$	0.634455	−	1.09891i	0.0304548	−	0.0527493i
$435$	0.378777	+	0.0818784i	0.0181610	+	0.00392577i
$436$	−6.22638	+	10.7844i	−0.298190	+	0.516479i
$437$	20.5799	+	35.6454i	0.984470	+	1.70515i
$438$	4.37821	−	4.82889i	0.209199	−	0.230733i
$439$	4.49736	+	7.78966i	0.214647	+	0.371780i	0.953163	−	0.302456i	$-0.0978064\pi$
$439$	4.49736	+	7.78966i	0.214647	+	0.371780i	−0.738516	+	0.674236i	$0.764473\pi$
$440$	−0.0838787	+	0.145282i	−0.00399876	+	0.00692605i
$441$	15.3141	−	10.9657i	0.729244	−	0.522177i
$442$	5.88671	+	8.50617i	0.280002	+	0.404597i
$443$	−0.560007	+	0.969961i	−0.0266068	+	0.0460842i	−0.879022	−	0.476781i	$-0.841804\pi$
$443$	−0.560007	+	0.969961i	−0.0266068	+	0.0460842i	0.852415	+	0.522865i	$0.175137\pi$
$444$	3.32565	−	3.66798i	0.157828	−	0.174075i
$445$	1.55718			0.0738174
$446$	7.96586	−	13.7973i	0.377195	−	0.653320i
$447$	−23.8730	−	5.16050i	−1.12915	−	0.244083i
$448$	7.19152			0.339768
$449$	−7.92893	−	13.7333i	−0.374189	−	0.648115i	0.616016	−	0.787734i	$-0.288746\pi$
$449$	−7.92893	−	13.7333i	−0.374189	−	0.648115i	−0.990205	+	0.139619i	$0.955412\pi$
$450$	13.8143	−	9.89176i	0.651212	−	0.466302i
$451$	2.24702	+	3.89195i	0.105808	+	0.183265i
$452$	−4.66726	−	8.08394i	−0.219530	−	0.380236i
$453$	−11.2789	−	2.43811i	−0.529931	−	0.114552i
$454$	7.91532	+	13.7097i	0.371484	+	0.643430i
$455$	−0.358596	+	0.0293890i	−0.0168113	+	0.00137778i
$456$	−22.1382	+	24.4170i	−1.03671	+	1.14343i
$457$	17.0421	+	29.5178i	0.797196	+	1.38078i	0.921435	+	0.388531i	$0.127017\pi$
$457$	17.0421	+	29.5178i	0.797196	+	1.38078i	−0.124240	+	0.992252i	$0.539649\pi$
$458$	−1.84177	+	3.19005i	−0.0860604	+	0.149061i
$459$	1.50696	−	13.0382i	0.0703388	−	0.608573i
$460$	−0.555202			−0.0258864
$461$	−5.12256			−0.238582			−0.119291	−	0.992859i	$-0.538062\pi$
$461$	−5.12256			−0.238582			−0.119291	+	0.992859i	$0.538062\pi$
$462$	−0.757813	−	0.163813i	−0.0352566	−	0.00762125i
$463$	3.59883	+	6.23335i	0.167252	+	0.289688i	0.937453	−	0.348113i	$-0.113177\pi$
$463$	3.59883	+	6.23335i	0.167252	+	0.289688i	−0.770201	+	0.637801i	$0.779844\pi$
$464$	1.97727	−	3.42473i	0.0917924	−	0.158989i
$465$	−0.261561	−	0.0565403i	−0.0121296	−	0.00262199i
$466$	5.50971	+	9.54310i	0.255232	+	0.442076i
$467$	−31.2424			−1.44573			−0.722863	−	0.690992i	$-0.757174\pi$
$467$	−31.2424			−1.44573			−0.722863	+	0.690992i	$0.757174\pi$
$468$	7.22843	+	2.58959i	0.334134	+	0.119704i
$469$	−0.868729			−0.0401142
$470$	0.179585	+	0.311050i	0.00828363	+	0.0143477i
$471$	−13.6718	+	15.0791i	−0.629962	+	0.694809i
$472$	17.0416	−	29.5168i	0.784401	−	1.35862i
$473$	−0.976490	−	1.69133i	−0.0448991	−	0.0777675i
$474$	−5.30871	−	16.5324i	−0.243837	−	0.759357i
$475$	30.8259			1.41439
$476$	−1.52309			−0.0698108
$477$	0.950496	−	0.680605i	0.0435202	−	0.0311628i
$478$	−5.46668	+	9.46857i	−0.250040	+	0.433082i
$479$	15.2329	+	26.3841i	0.696008	+	1.20552i	0.969840	+	0.243744i	$0.0783755\pi$
$479$	15.2329	+	26.3841i	0.696008	+	1.20552i	−0.273832	+	0.961778i	$0.588291\pi$
$480$	−0.236241	−	0.735701i	−0.0107829	−	0.0335800i
$481$	8.26248	+	11.9391i	0.376737	+	0.544376i
$482$	0.162596	+	0.281625i	0.00740606	+	0.0128277i
$483$	−2.99479	−	9.32637i	−0.136268	−	0.424365i
$484$	−3.82783	−	6.62999i	−0.173992	−	0.301363i
$485$	−0.924863	−	1.60191i	−0.0419959	−	0.0727390i
$486$	8.58722	+	15.4843i	0.389524	+	0.702383i
$487$	−10.3039	−	17.8469i	−0.466914	−	0.808719i	0.532371	−	0.846511i	$-0.321301\pi$
$487$	−10.3039	−	17.8469i	−0.466914	−	0.808719i	−0.999286	+	0.0377916i	$0.987968\pi$
$488$	23.9085			1.08229
$489$	−16.6043	+	18.3135i	−0.750874	+	0.828167i
$490$	0.418883	−	0.725527i	0.0189232	−	0.0327760i
$491$	−42.9735			−1.93936			−0.969682	−	0.244369i	$-0.921419\pi$
$491$	−42.9735			−1.93936			−0.969682	+	0.244369i	$0.921419\pi$
$492$	−11.6410	−	2.51637i	−0.524815	−	0.113447i
$493$	−2.40534	+	4.16617i	−0.108331	+	0.187635i
$494$	−14.4079	−	20.8191i	−0.648242	−	0.936697i
$495$	0.0159688	+	0.162726i	0.000717744	+	0.00731398i
$496$	−1.36538	+	2.36491i	−0.0613074	+	0.106188i
$497$	3.06660	+	5.31150i	0.137556	+	0.238253i
$498$	2.11482	+	6.58596i	0.0947672	+	0.295124i
$499$	−2.11925	−	3.67064i	−0.0948705	−	0.164321i	0.814684	−	0.579905i	$-0.196910\pi$
$499$	−2.11925	−	3.67064i	−0.0948705	−	0.164321i	−0.909555	+	0.415585i	$0.863577\pi$
$500$	−0.416384	+	0.721199i	−0.0186213	+	0.0322530i
$501$	5.91544	+	18.4219i	0.264283	+	0.823028i
$502$	13.9550	−	24.1708i	0.622843	−	1.07880i
$503$	1.12652	+	1.95120i	0.0502292	+	0.0869995i	0.890047	−	0.455869i	$-0.150671\pi$
$503$	1.12652	+	1.95120i	0.0502292	+	0.0869995i	−0.839818	+	0.542869i	$0.817338\pi$
$504$	6.37736	−	4.56653i	0.284070	−	0.203409i
$505$	0.918562	−	1.59100i	0.0408755	−	0.0707984i
$506$	1.75420	−	3.03836i	0.0779837	−	0.135072i
$507$	−12.2064	+	18.9210i	−0.542107	+	0.840309i
$508$	3.37269	+	5.84167i	0.149639	+	0.259182i
$509$	14.1124			0.625522			0.312761	−	0.949832i	$-0.398746\pi$
$509$	14.1124			0.625522			0.312761	+	0.949832i	$0.398746\pi$
$510$	−0.178482	−	0.555828i	−0.00790331	−	0.0246125i
$511$	−2.81439			−0.124501
$512$	−20.6672			−0.913370
$513$	−3.68833	+	31.9115i	−0.162844	+	1.40893i
$514$	−0.735515	−	1.27395i	−0.0324422	−	0.0561915i
$515$	0.849675	−	1.47168i	0.0374412	−	0.0648500i
$516$	5.05882	+	1.09354i	0.222702	+	0.0481404i
$517$	1.24880			0.0549221
$518$	3.88534			0.170712
$519$	6.55742	+	20.4211i	0.287839	+	0.896387i
$520$	1.29938	−	0.106491i	0.0569815	−	0.00466995i
$521$	−17.6305			−0.772405			−0.386202	−	0.922414i	$-0.626213\pi$
$521$	−17.6305			−0.772405			−0.386202	+	0.922414i	$0.626213\pi$
$522$	−0.633815	−	6.45872i	−0.0277413	−	0.282691i
$523$	0.106583	−	0.184608i	0.00466057	−	0.00807234i	−0.863686	−	0.504031i	$-0.831850\pi$
$523$	0.106583	−	0.184608i	0.00466057	−	0.00807234i	0.868346	+	0.495958i	$0.165183\pi$
$524$	−11.6628			−0.509492
$525$	−7.17049	−	1.55001i	−0.312946	−	0.0676479i
$526$	6.66085	−	11.5369i	0.290427	−	0.503034i
$527$	1.66098	−	2.87691i	0.0723536	−	0.125320i
$528$	1.63085	+	0.352534i	0.0709738	+	0.0153421i
$529$	21.3254			0.927192
$530$	0.0259987	−	0.0450310i	0.00112931	−	0.00195602i
$531$	−3.24437	−	33.0609i	−0.140794	−	1.43472i
$532$	3.72781			0.161621
$533$	14.9339	−	31.5718i	0.646858	−	1.36753i
$534$	−7.97278	−	24.8288i	−0.345016	−	1.07445i
$535$	−0.737324			−0.0318773
$536$	3.14785			0.135967
$537$	−40.6900	−	8.79576i	−1.75590	−	0.379565i
$538$	15.2518	−	26.4170i	0.657553	−	1.13892i
$539$	−1.45642	−	2.52259i	−0.0627323	−	0.108656i
$540$	−0.347906	−	0.258312i	−0.0149715	−	0.0111160i
$541$	−20.0920			−0.863821			−0.431910	−	0.901917i	$-0.642160\pi$
$541$	−20.0920			−0.863821			−0.431910	+	0.901917i	$0.642160\pi$
$542$	−32.1390			−1.38049
$543$	−11.4611	−	35.6922i	−0.491844	−	1.53170i
$544$	9.59217			0.411261
$545$	1.03042	+	1.78475i	0.0441385	+	0.0764502i
$546$	2.30462	+	5.56725i	0.0986285	+	0.238256i
$547$	3.84585	−	6.66121i	0.164437	−	0.284813i	−0.772018	−	0.635600i	$-0.780753\pi$
$547$	3.84585	−	6.66121i	0.164437	−	0.284813i	0.936455	+	0.350787i	$0.114086\pi$
$548$	−6.89662	+	11.9453i	−0.294609	+	0.510278i
$549$	18.9464	−	13.5666i	0.808613	−	0.579010i
$550$	−1.31378	−	2.27553i	−0.0560197	−	0.0970290i
$551$	5.88714	−	10.1968i	0.250801	−	0.434400i
$552$	10.8517	+	33.7942i	0.461877	+	1.43838i
$553$	−3.74862	+	6.49280i	−0.159407	+	0.276102i
$554$	9.43749	+	16.3462i	0.400960	+	0.694484i
$555$	−0.250514	−	0.780150i	−0.0106337	−	0.0331155i
$556$	5.34978	+	9.26609i	0.226881	+	0.392970i
$557$	−13.4015	+	23.2121i	−0.567841	+	0.983529i	0.428938	+	0.903334i	$0.358888\pi$
$557$	−13.4015	+	23.2121i	−0.567841	+	0.983529i	−0.996779	+	0.0801952i	$0.974446\pi$
$558$	0.437675	+	4.46000i	0.0185282	+	0.188807i
$559$	−6.48984	+	13.7202i	−0.274491	+	0.580303i
$560$	0.103601	−	0.179443i	0.00437795	−	0.00758284i
$561$	−1.98393	−	0.428856i	−0.0837616	−	0.0181063i
$562$	1.39209			0.0587219
$563$	8.81327	−	15.2650i	0.371435	−	0.643344i	−0.618352	−	0.785902i	$-0.712199\pi$
$563$	8.81327	−	15.2650i	0.371435	−	0.643344i	0.989787	+	0.142557i	$0.0455326\pi$
$564$	−2.22295	+	2.45178i	−0.0936032	+	0.103238i
$565$	−1.54480			−0.0649903
$566$	−1.72692	−	2.99112i	−0.0725879	−	0.125726i
$567$	2.46254	−	7.23754i	0.103417	−	0.303948i
$568$	−11.1119	−	19.2463i	−0.466243	−	0.807557i
$569$	4.51133	+	7.81385i	0.189125	+	0.327573i	0.944959	−	0.327190i	$-0.106102\pi$
$569$	4.51133	+	7.81385i	0.189125	+	0.327573i	−0.755834	+	0.654763i	$0.772768\pi$
$570$	0.436840	+	1.36041i	0.0182972	+	0.0569811i
$571$	−0.221208	−	0.383144i	−0.00925727	−	0.0160341i	0.861360	−	0.507996i	$-0.169613\pi$
$571$	−0.221208	−	0.383144i	−0.00925727	−	0.0160341i	−0.870617	+	0.491962i	$0.836280\pi$
$572$	0.507734	−	1.07340i	0.0212294	−	0.0448812i
$573$	−2.90983	−	9.06178i	−0.121560	−	0.378561i
$574$	−4.67301	−	8.09389i	−0.195048	−	0.337832i
$575$	16.5984	−	28.7493i	0.692201	−	1.19893i
$576$	−20.6503	+	14.7867i	−0.860428	+	0.616112i
$577$	26.2964			1.09474			0.547368	−	0.836892i	$-0.315630\pi$
$577$	26.2964			1.09474			0.547368	+	0.836892i	$0.315630\pi$
$578$	−12.0624			−0.501729
$579$	−0.0681626	−	0.212272i	−0.00283274	−	0.00882172i
$580$	0.0794113	+	0.137544i	0.00329737	+	0.00571122i
$581$	1.49333	−	2.58652i	0.0619536	−	0.107307i
$582$	−20.8067	+	22.9485i	−0.862466	+	0.951246i
$583$	−0.0903949	−	0.156569i	−0.00374377	−	0.00648441i
$584$	10.1980			0.421995
$585$	0.969272	−	0.821709i	0.0400745	−	0.0339735i
$586$	31.3540			1.29522
$587$	−15.2058	−	26.3372i	−0.627610	−	1.08705i	−0.988030	−	0.154263i	$-0.950700\pi$
$587$	−15.2058	−	26.3372i	−0.627610	−	1.08705i	0.360420	−	0.932790i	$-0.382634\pi$
$588$	7.54515	+	1.63100i	0.311157	+	0.0672612i
$589$	−4.06531	+	7.04132i	−0.167508	+	0.290132i
$590$	−0.738780	−	1.27960i	−0.0304151	−	0.0526805i
$591$	6.09876	+	1.31834i	0.250869	+	0.0542292i
$592$	−8.36146			−0.343654
$593$	−29.4682			−1.21011			−0.605056	−	0.796183i	$-0.706849\pi$
$593$	−29.4682			−1.21011			−0.605056	+	0.796183i	$0.706849\pi$
$594$	2.51286	−	1.08778i	0.103104	−	0.0446320i
$595$	−0.126031	+	0.218292i	−0.00516675	+	0.00894908i
$596$	−5.00500	−	8.66892i	−0.205013	−	0.355093i
$597$	23.7772	−	26.2248i	0.973137	−	1.07331i
$598$	−27.1746	+	2.22711i	−1.11125	+	0.0910733i
$599$	17.9709	+	31.1266i	0.734273	+	1.27180i	0.955042	+	0.296472i	$0.0958102\pi$
$599$	17.9709	+	31.1266i	0.734273	+	1.27180i	−0.220768	+	0.975326i	$0.570857\pi$
$600$	25.9824	+	5.61648i	1.06073	+	0.229292i
$601$	−1.53954	−	2.66656i	−0.0627992	−	0.108771i	0.832916	−	0.553399i	$-0.186669\pi$
$601$	−1.53954	−	2.66656i	−0.0627992	−	0.108771i	−0.895716	+	0.444627i	$0.853336\pi$
$602$	2.03076	+	3.51737i	0.0827675	+	0.143357i
$603$	2.49453	−	1.78622i	0.101585	−	0.0727404i
$604$	−2.36465	−	4.09569i	−0.0962161	−	0.166651i
$605$	−1.26696			−0.0515092
$606$	−30.0710	−	6.50031i	−1.22155	−	0.264057i
$607$	−3.45276	+	5.98036i	−0.140143	+	0.242735i	−0.927550	−	0.373698i	$-0.878090\pi$
$607$	−3.45276	+	5.98036i	−0.140143	+	0.242735i	0.787407	+	0.616433i	$0.211423\pi$
$608$	−23.4771			−0.952124
$609$	−1.88215	+	2.07589i	−0.0762684	+	0.0841192i
$610$	0.518236	−	0.897611i	0.0209828	−	0.0363432i
$611$	−5.52286	−	7.98042i	−0.223431	−	0.322853i
$612$	4.37352	−	3.13167i	0.176789	−	0.126590i
$613$	4.37980	−	7.58604i	0.176899	−	0.306397i	−0.763918	−	0.645313i	$-0.776727\pi$
$613$	4.37980	−	7.58604i	0.176899	−	0.306397i	0.940817	+	0.338916i	$0.110060\pi$
$614$	−4.39680	−	7.61548i	−0.177440	−	0.307336i
$615$	−1.32390	+	1.46018i	−0.0533847	+	0.0588800i
$616$	−0.606505	−	1.05050i	−0.0244368	−	0.0423258i
$617$	9.94309	−	17.2219i	0.400294	−	0.693329i	−0.593467	−	0.804858i	$-0.702241\pi$
$617$	9.94309	−	17.2219i	0.400294	−	0.693329i	0.993761	+	0.111529i	$0.0355747\pi$
$618$	−27.8159	−	6.01282i	−1.11892	−	0.241871i
$619$	−1.74906	+	3.02947i	−0.0703008	+	0.121765i	−0.899033	−	0.437881i	$-0.855729\pi$
$619$	−1.74906	+	3.02947i	−0.0703008	+	0.121765i	0.828732	+	0.559645i	$0.189063\pi$
$620$	−0.0548366	−	0.0949798i	−0.00220229	−	0.00381448i
$621$	27.7757	+	20.6228i	1.11460	+	0.827563i
$622$	−5.34852	+	9.26392i	−0.214456	+	0.371449i
$623$	−5.62979	+	9.75108i	−0.225553	+	0.390669i
$624$	−4.95966	−	11.9810i	−0.198545	−	0.479625i
$625$	−12.3966	−	21.4715i	−0.495864	−	0.858861i
$626$	−14.9606			−0.597944
$627$	4.85573	+	1.04964i	0.193919	+	0.0419185i
$628$	−8.34194			−0.332880
$629$	10.1717			0.405572
$630$	−0.0332095	−	0.338413i	−0.00132310	−	0.0134827i
$631$	14.5446	+	25.1919i	0.579010	+	1.00287i	0.995593	+	0.0937767i	$0.0298940\pi$
$631$	14.5446	+	25.1919i	0.579010	+	1.00287i	−0.416584	+	0.909097i	$0.636773\pi$
$632$	13.5832	−	23.5267i	0.540309	−	0.935843i
$633$	−3.76087	−	11.7121i	−0.149481	−	0.465514i
$634$	28.5489			1.13382
$635$	1.11632			0.0442996
$636$	0.468302	+	0.101230i	0.0185694	+	0.00401405i
$637$	−9.67948	+	20.4634i	−0.383515	+	0.810791i
$638$	−1.00362			−0.0397338
$639$	−19.7268	−	8.94652i	−0.780379	−	0.353919i
$640$	−0.118722	+	0.205633i	−0.00469291	+	0.00812836i
$641$	−11.2937			−0.446074			−0.223037	−	0.974810i	$-0.571597\pi$
$641$	−11.2937			−0.446074			−0.223037	+	0.974810i	$0.571597\pi$
$642$	3.77510	+	11.7564i	0.148992	+	0.463989i
$643$	−3.84277	+	6.65588i	−0.151544	+	0.262482i	−0.931795	−	0.362984i	$-0.881758\pi$
$643$	−3.84277	+	6.65588i	−0.151544	+	0.262482i	0.780251	+	0.625466i	$0.215091\pi$
$644$	2.00726	−	3.47668i	0.0790972	−	0.137000i
$645$	0.575329	−	0.634551i	0.0226535	−	0.0249854i
$646$	−17.7372			−0.697859
$647$	10.5548	−	18.2815i	0.414952	−	0.718718i	−0.580471	−	0.814281i	$-0.697132\pi$
$647$	10.5548	−	18.2815i	0.414952	−	0.718718i	0.995423	+	0.0955626i	$0.0304650\pi$
$648$	−8.92306	+	26.2253i	−0.350531	+	1.03023i
$649$	−5.13734			−0.201658
$650$	−8.73149	+	18.4593i	−0.342477	+	0.724033i
$651$	1.29970	−	1.43348i	0.0509391	−	0.0561826i
$652$	−10.1313			−0.396771
$653$	22.4240			0.877521			0.438760	−	0.898604i	$-0.355418\pi$
$653$	22.4240			0.877521			0.438760	+	0.898604i	$0.355418\pi$
$654$	23.1815	−	25.5678i	0.906470	−	0.999779i
$655$	−0.965058	+	1.67153i	−0.0377080	+	0.0653121i
$656$	10.0566	+	17.4185i	0.392643	+	0.680078i
$657$	8.08144	−	5.78674i	0.315287	−	0.225762i
$658$	−2.59706			−0.101244
$659$	49.2418			1.91819			0.959095	−	0.283086i	$-0.0913582\pi$
$659$	49.2418			1.91819			0.959095	+	0.283086i	$0.0913582\pi$
$660$	−0.0450109	+	0.0496442i	−0.00175205	+	0.00193240i
$661$	−13.3963			−0.521057			−0.260528	−	0.965466i	$-0.583897\pi$
$661$	−13.3963			−0.521057			−0.260528	+	0.965466i	$0.583897\pi$
$662$	16.5326	+	28.6354i	0.642559	+	1.11295i
$663$	6.03341	+	14.5749i	0.234318	+	0.566042i
$664$	−5.41109	+	9.37228i	−0.209991	+	0.363715i
$665$	0.308464	−	0.534275i	0.0119617	−	0.0207183i
$666$	−11.1566	+	7.98875i	−0.432311	+	0.309558i
$667$	−6.33993	−	10.9811i	−0.245483	−	0.425189i
$668$	−3.96483	+	6.86729i	−0.153404	+	0.265703i
$669$	16.3183	−	17.9980i	0.630900	−	0.695843i
$670$	0.0682323	−	0.118182i	0.00263604	−	0.00456576i
$671$	−1.80186	−	3.12091i	−0.0695599	−	0.120481i
$672$	5.46107	+	1.18049i	0.210665	+	0.0455385i
$673$	5.42836	+	9.40220i	0.209248	+	0.362428i	0.951478	−	0.307717i	$-0.0995651\pi$
$673$	5.42836	+	9.40220i	0.209248	+	0.362428i	−0.742230	+	0.670145i	$0.766232\pi$
$674$	−8.74461	+	15.1461i	−0.336830	+	0.583407i
$675$	23.7769	−	10.2926i	0.915173	−	0.396164i
$676$	−9.10502	+	1.50251i	−0.350193	+	0.0577887i
$677$	13.6699	−	23.6769i	0.525377	−	0.909979i	−0.474186	−	0.880424i	$-0.657258\pi$
$677$	13.6699	−	23.6769i	0.525377	−	0.909979i	0.999563	−	0.0295547i	$-0.00940891\pi$
$678$	7.90940	+	24.6315i	0.303759	+	0.945965i
$679$	13.3749			0.513282
$680$	0.456674	−	0.790982i	0.0175126	−	0.0303328i
$681$	7.38048	+	22.9843i	0.282821	+	0.880759i
$682$	0.693041			0.0265379
$683$	−14.9448	−	25.8851i	−0.571846	−	0.990466i	−0.996376	−	0.0850523i	$-0.972894\pi$
$683$	−14.9448	−	25.8851i	−0.571846	−	0.990466i	0.424531	−	0.905414i	$-0.360439\pi$
$684$	−10.7043	+	7.66486i	−0.409290	+	0.293073i
$685$	1.14135	+	1.97687i	0.0436086	+	0.0755322i
$686$	6.40577	+	11.0951i	0.244573	+	0.423613i
$687$	−3.77292	+	4.16129i	−0.143946	+	0.158763i
$688$	−4.37030	−	7.56958i	−0.166616	−	0.288588i
$689$	−0.600772	+	1.27010i	−0.0228876	+	0.0483868i
$690$	1.50398	+	0.325107i	0.0572554	+	0.0123766i
$691$	−11.3956	−	19.7378i	−0.433510	−	0.750861i	0.563663	−	0.826005i	$-0.309392\pi$
$691$	−11.3956	−	19.7378i	−0.433510	−	0.750861i	−0.997173	+	0.0751436i	$0.976058\pi$
$692$	−4.39511	+	7.61256i	−0.167077	+	0.289386i
$693$	−1.07672	−	0.488318i	−0.0409013	−	0.0185496i
$694$	11.8452			0.449638
$695$	1.77071			0.0671667
$696$	6.81998	−	7.52201i	0.258511	−	0.285121i
$697$	−12.2338	−	21.1896i	−0.463388	−	0.802612i
$698$	−8.02933	+	13.9072i	−0.303914	+	0.526395i
$699$	5.13742	+	15.9989i	0.194315	+	0.605135i
$700$	−1.50330	−	2.60380i	−0.0568196	−	0.0984144i
$701$	36.2555			1.36935			0.684675	−	0.728848i	$-0.259944\pi$
$701$	36.2555			1.36935			0.684675	+	0.728848i	$0.259944\pi$
$702$	−18.0646	−	11.2476i	−0.681805	−	0.424514i
$703$	−24.8955			−0.938953
$704$	1.96390	+	3.40157i	0.0740173	+	0.128202i
$705$	0.167450	+	0.521473i	0.00630654	+	0.0196398i
$706$	−8.37952	+	14.5138i	−0.315367	+	0.546232i
$707$	6.64189	+	11.5041i	0.249794	+	0.432656i
$708$	9.14483	−	10.0862i	0.343684	−	0.379062i
$709$	−19.8795			−0.746590			−0.373295	−	0.927713i	$-0.621772\pi$
$709$	−19.8795			−0.746590			−0.373295	+	0.927713i	$0.621772\pi$
$710$	−0.963434			−0.0361570
$711$	−2.58596	−	26.3515i	−0.0969811	−	0.988260i
$712$	20.3996	−	35.3332i	0.764508	−	1.32417i
$713$	4.37797	+	7.58287i	0.163956	+	0.283981i
$714$	4.12588	+	0.891871i	0.154407	+	0.0333774i
$715$	−0.111828	−	0.161590i	−0.00418214	−	0.00604311i
$716$	−8.53073	−	14.7757i	−0.318808	−	0.552192i
$717$	−11.1986	+	12.3514i	−0.418221	+	0.461271i
$718$	0.0365519	+	0.0633098i	0.00136411	+	0.00236270i
$719$	4.26020	+	7.37888i	0.158879	+	0.275186i	0.934465	−	0.356056i	$-0.115879\pi$
$719$	4.26020	+	7.37888i	0.158879	+	0.275186i	−0.775586	+	0.631242i	$0.782545\pi$
$720$	0.0714687	+	0.728283i	0.00266348	+	0.0271415i
$721$	6.14378	+	10.6413i	0.228806	+	0.396304i
$722$	21.8312			0.812473
$723$	0.151610	+	0.472142i	0.00563842	+	0.0175592i
$724$	7.68183	−	13.3053i	0.285493	−	0.494488i
$725$	−9.49637			−0.352686
$726$	6.48685	+	20.2013i	0.240749	+	0.749742i
$727$	−7.74562	+	13.4158i	−0.287269	+	0.497565i	−0.973157	−	0.230143i	$-0.926081\pi$
$727$	−7.74562	+	13.4158i	−0.287269	+	0.497565i	0.685888	+	0.727707i	$0.259414\pi$
$728$	−4.03089	+	8.52173i	−0.149395	+	0.315836i
$729$	7.81018	+	25.8457i	0.289266	+	0.957249i
$730$	0.221050	−	0.382869i	0.00818141	−	0.0141706i
$731$	5.31646	+	9.20838i	0.196636	+	0.340584i
$732$	9.33474	+	2.01784i	0.345022	+	0.0745816i
$733$	16.9965	+	29.4388i	0.627779	+	1.08735i	0.987996	+	0.154477i	$0.0493694\pi$
$733$	16.9965	+	29.4388i	0.627779	+	1.08735i	−0.360217	+	0.932869i	$0.617297\pi$
$734$	4.05926	−	7.03084i	0.149830	−	0.259513i
$735$	0.858092	−	0.946421i	0.0316512	−	0.0349093i
$736$	−12.6414	+	21.8955i	−0.465968	+	0.807080i
$737$	−0.237237	−	0.410907i	−0.00873875	−	0.0151360i
$738$	30.0605	+	13.6331i	1.10654	+	0.501841i
$739$	−24.2722	+	42.0407i	−0.892867	+	1.54649i	−0.0564440	+	0.998406i	$0.517976\pi$
$739$	−24.2722	+	42.0407i	−0.892867	+	1.54649i	−0.836423	+	0.548085i	$0.815357\pi$
$740$	0.167907	−	0.290824i	0.00617239	−	0.0106909i
$741$	−14.7670	−	35.6725i	−0.542478	−	1.31046i
$742$	0.187990	+	0.325608i	0.00690132	+	0.0119534i
$743$	−34.0986			−1.25096			−0.625478	−	0.780241i	$-0.715096\pi$
$743$	−34.0986			−1.25096			−0.625478	+	0.780241i	$0.715096\pi$
$744$	−4.70947	+	5.19424i	−0.172657	+	0.190430i
$745$	−1.65659			−0.0606927
$746$	22.4877			0.823333
$747$	1.03016	+	10.4976i	0.0376917	+	0.384087i
$748$	−0.415934	−	0.720419i	−0.0152081	−	0.0263411i
$749$	2.66570	−	4.61713i	0.0974025	−	0.168706i
$750$	1.55025	−	1.70982i	0.0566070	−	0.0624340i
$751$	−22.9688			−0.838143			−0.419072	−	0.907953i	$-0.637644\pi$
$751$	−22.9688			−0.838143			−0.419072	+	0.907953i	$0.637644\pi$
$752$	5.58903			0.203811
$753$	28.5872	−	31.5299i	1.04178	−	1.14901i
$754$	4.43856	+	6.41363i	0.161643	+	0.233571i
$755$	−0.782666			−0.0284841
$756$	2.87536	−	1.24470i	0.104576	−	0.0452693i
$757$	4.65491	−	8.06254i	0.169186	−	0.293038i	−0.768948	−	0.639311i	$-0.779220\pi$
$757$	4.65491	−	8.06254i	0.169186	−	0.293038i	0.938134	+	0.346273i	$0.112553\pi$
$758$	−24.6152			−0.894063
$759$	3.59352	−	3.96343i	0.130437	−	0.143863i
$760$	−1.11772	+	1.93595i	−0.0405441	+	0.0702244i
$761$	12.1360	−	21.0202i	0.439931	−	0.761983i	−0.557753	−	0.830007i	$-0.688336\pi$
$761$	12.1360	−	21.0202i	0.439931	−	0.761983i	0.997684	+	0.0680245i	$0.0216696\pi$
$762$	−5.71555	−	17.7993i	−0.207052	−	0.644802i
$763$	−14.9015			−0.539470
$764$	1.95031	−	3.37804i	0.0705599	−	0.122213i
$765$	−0.0869415	−	0.885954i	−0.00314338	−	0.0320317i
$766$	−25.8244			−0.933072
$767$	22.7201	+	32.8300i	0.820374	+	1.18542i
$768$	−24.7789	−	5.35632i	−0.894130	−	0.193280i
$769$	31.8364			1.14805			0.574026	−	0.818837i	$-0.305381\pi$
$769$	31.8364			1.14805			0.574026	+	0.818837i	$0.305381\pi$
$770$	−0.0525860			−0.00189507
$771$	−0.685816	−	2.13577i	−0.0246991	−	0.0769178i
$772$	0.0456861	−	0.0791306i	0.00164428	−	0.00284797i
$773$	25.7735	+	44.6410i	0.927007	+	1.60562i	0.788301	+	0.615290i	$0.210961\pi$
$773$	25.7735	+	44.6410i	0.927007	+	1.60562i	0.138707	+	0.990334i	$0.455705\pi$
$774$	−13.0634	−	5.92455i	−0.469555	−	0.212954i
$775$	6.55762			0.235557
$776$	−48.4641			−1.73976
$777$	5.79101	+	1.25181i	0.207751	+	0.0449085i
$778$	−14.7551			−0.528996
$779$	29.9426	+	51.8621i	1.07280	+	1.85815i
$780$	0.516313	+	0.0680877i	0.0184870	+	0.00243793i
$781$	−1.67489	+	2.90099i	−0.0599321	+	0.103805i
$782$	−9.55067	+	16.5422i	−0.341531	+	0.591549i
$783$	1.13624	−	9.83079i	0.0406060	−	0.351324i
$784$	−6.51823	−	11.2899i	−0.232794	−	0.403211i
$785$	−0.690268	+	1.19558i	−0.0246367	+	0.0426720i
$786$	31.5932	+	6.82935i	1.12689	+	0.243595i
$787$	4.03765	−	6.99341i	0.143927	−	0.249288i	−0.785045	−	0.619438i	$-0.787360\pi$
$787$	4.03765	−	6.99341i	0.143927	−	0.249288i	0.928972	+	0.370150i	$0.120694\pi$
$788$	1.27861	+	2.21463i	0.0455488	+	0.0788928i
$789$	13.6449	−	15.0495i	0.485772	−	0.535776i
$790$	−0.588853	−	1.01992i	−0.0209504	−	0.0362872i
$791$	5.58503	−	9.67356i	0.198581	−	0.343952i
$792$	3.90152	+	1.76943i	0.138635	+	0.0628738i
$793$	−11.9753	+	25.3171i	−0.425255	+	0.899035i
$794$	−7.03769	+	12.1896i	−0.249758	+	0.432594i
$795$	0.0532589	−	0.0587412i	0.00188890	−	0.00208333i
$796$	14.5079			0.514217
$797$	2.89799	−	5.01947i	0.102652	−	0.177799i	−0.810124	−	0.586258i	$-0.800600\pi$
$797$	2.89799	−	5.01947i	0.102652	−	0.177799i	0.912777	+	0.408459i	$0.133934\pi$
$798$	−10.0982	−	2.18288i	−0.357473	−	0.0772731i
$799$	−6.79903			−0.240533
$800$	9.46756	+	16.3983i	0.334729	+	0.579767i
$801$	−3.88367	−	39.5755i	−0.137223	−	1.39833i
$802$	−4.68421	−	8.11329i	−0.165405	−	0.286490i
$803$	−0.768569	−	1.33120i	−0.0271222	−	0.0469770i
$804$	1.22904	+	0.265675i	0.0433448	+	0.00936962i
$805$	−0.332188	−	0.575367i	−0.0117081	−	0.0202790i
$806$	−3.06500	−	4.42886i	−0.107960	−	0.156000i
$807$	31.2438	−	34.4599i	1.09983	−	1.21305i
$808$	−24.0670	−	41.6852i	−0.846673	−	1.46648i
$809$	0.705053	−	1.22119i	0.0247884	−	0.0429347i	−0.853365	−	0.521314i	$-0.825442\pi$
$809$	0.705053	−	1.22119i	0.0247884	−	0.0429347i	0.878153	+	0.478379i	$0.158775\pi$
$810$	0.791180	+	0.903460i	0.0277992	+	0.0317443i
$811$	30.4340			1.06868			0.534341	−	0.845269i	$-0.320560\pi$
$811$	30.4340			1.06868			0.534341	+	0.845269i	$0.320560\pi$
$812$	−1.14841			−0.0403011
$813$	−47.9025	−	10.3548i	−1.68001	−	0.363160i
$814$	1.06103	+	1.83776i	0.0371891	+	0.0644133i
$815$	−0.838329	+	1.45203i	−0.0293654	+	0.0508623i
$816$	−8.87912	−	1.91935i	−0.310831	−	0.0671909i
$817$	−13.0122	−	22.5378i	−0.455239	−	0.788497i
$818$	10.5475			0.368786
$819$	1.64127	+	9.04038i	0.0573506	+	0.315896i
$820$	−0.807787			−0.0282091
$821$	−14.5866	−	25.2647i	−0.509076	−	0.881746i	−0.999945	−	0.0105120i	$-0.996654\pi$
$821$	−14.5866	−	25.2647i	−0.509076	−	0.881746i	0.490869	−	0.871234i	$-0.336679\pi$
$822$	25.6769	−	28.3200i	0.895586	−	0.987774i
$823$	−11.0375	+	19.1175i	−0.384743	+	0.666395i	−0.991734	−	0.128315i	$-0.959043\pi$
$823$	−11.0375	+	19.1175i	−0.384743	+	0.666395i	0.606990	+	0.794709i	$0.292377\pi$
$824$	−22.2621	−	38.5591i	−0.775537	−	1.34327i
$825$	−1.22501	−	3.81491i	−0.0426492	−	0.132818i
$826$	10.6839			0.371739
$827$	−46.3762			−1.61266			−0.806329	−	0.591467i	$-0.798549\pi$
$827$	−46.3762			−1.61266			−0.806329	+	0.591467i	$0.798549\pi$
$828$	1.38470	+	14.1104i	0.0481215	+	0.490369i
$829$	7.67652	−	13.2961i	0.266616	−	0.461793i	−0.701369	−	0.712798i	$-0.747428\pi$
$829$	7.67652	−	13.2961i	0.266616	−	0.461793i	0.967986	+	0.251005i	$0.0807610\pi$
$830$	0.234580	+	0.406304i	0.00814238	+	0.0141030i
$831$	8.79979	+	27.4043i	0.305261	+	0.950645i
$832$	13.0523	−	27.5938i	0.452505	−	0.956645i
$833$	7.92940	+	13.7341i	0.274738	+	0.475859i
$834$	−9.06603	−	28.2334i	−0.313931	−	0.977644i
$835$	0.656153	+	1.13649i	0.0227071	+	0.0393299i
$836$	1.01801	+	1.76325i	0.0352087	+	0.0609832i
$837$	−0.784620	+	6.78855i	−0.0271204	+	0.234647i
$838$	0.173620	+	0.300718i	0.00599759	+	0.0103881i
$839$	21.0376			0.726299			0.363149	−	0.931731i	$-0.381701\pi$
$839$	21.0376			0.726299			0.363149	+	0.931731i	$0.381701\pi$
$840$	0.357341	−	0.394124i	0.0123294	−	0.0135986i
$841$	12.6864	−	21.9735i	0.437461	−	0.757705i
$842$	−23.3927			−0.806165
$843$	2.07488	+	0.448517i	0.0714628	+	0.0154477i
$844$	2.52072	−	4.36602i	0.0867669	−	0.150285i
$845$	−0.538069	+	1.42927i	−0.0185101	+	0.0491685i
$846$	7.45740	−	5.33990i	0.256391	−	0.183589i
$847$	4.58053	−	7.93371i	0.157389	−	0.272606i
$848$	−0.404564	−	0.700726i	−0.0138928	−	0.0240630i
$849$	−1.61023	−	5.01458i	−0.0552630	−	0.172100i
$850$	7.15281	+	12.3890i	0.245339	+	0.424940i
$851$	−13.4051	+	23.2184i	−0.459522	+	0.795916i
$852$	−2.71411	−	8.45228i	−0.0929839	−	0.289570i
$853$	−16.5578	+	28.6789i	−0.566928	+	0.981947i	0.429940	+	0.902858i	$0.358535\pi$
$853$	−16.5578	+	28.6789i	−0.566928	+	0.981947i	−0.996867	+	0.0790899i	$0.974799\pi$
$854$	3.74723	+	6.49039i	0.128228	+	0.222097i
$855$	0.212792	+	2.16840i	0.00727733	+	0.0741577i
$856$	−9.65920	+	16.7302i	−0.330145	+	0.571827i
$857$	10.2603	−	17.7714i	0.350486	−	0.607060i	−0.635848	−	0.771814i	$-0.719350\pi$
$857$	10.2603	−	17.7714i	0.350486	−	0.607060i	0.986335	+	0.164754i	$0.0526830\pi$
$858$	−2.00394	+	2.61041i	−0.0684134	+	0.0891180i
$859$	3.24826	+	5.62615i	0.110829	+	0.191962i	0.916105	−	0.400939i	$-0.131316\pi$
$859$	3.24826	+	5.62615i	0.110829	+	0.191962i	−0.805276	+	0.592901i	$0.797983\pi$
$860$	0.351041			0.0119704
$861$	−4.35725	−	13.5693i	−0.148495	−	0.462442i
$862$	4.32984			0.147475
$863$	23.8577			0.812124			0.406062	−	0.913845i	$-0.366902\pi$
$863$	23.8577			0.812124			0.406062	+	0.913845i	$0.366902\pi$
$864$	−18.1086	+	7.83890i	−0.616066	+	0.266685i
$865$	0.727362	+	1.25983i	0.0247310	+	0.0428354i
$866$	8.21991	−	14.2373i	0.279324	−	0.483803i
$867$	−17.9787	−	3.88637i	−0.610589	−	0.131988i
$868$	0.793019			0.0269168
$869$	−4.09477			−0.138906
$870$	−0.134575	−	0.419092i	−0.00456251	−	0.0142086i
$871$	−1.57670	+	3.33331i	−0.0534244	+	0.112945i
$872$	53.9957			1.82852
$873$	−38.4057	+	27.5005i	−1.29984	+	0.930751i
$874$	23.3755	−	40.4876i	0.790690	−	1.36951i
$875$	−0.996524			−0.0336887
$876$	3.98166	+	0.860696i	0.134528	+	0.0290802i
$877$	7.14487	−	12.3753i	0.241265	−	0.417883i	−0.719810	−	0.694171i	$-0.755771\pi$
$877$	7.14487	−	12.3753i	0.241265	−	0.417883i	0.961075	+	0.276288i	$0.0891044\pi$
$878$	5.10830	−	8.84784i	0.172397	−	0.298600i
$879$	46.7324	+	10.1019i	1.57624	+	0.340729i
$880$	0.113168			0.00381489
$881$	2.05178	−	3.55379i	0.0691263	−	0.119730i	−0.829391	−	0.558669i	$-0.811312\pi$
$881$	2.05178	−	3.55379i	0.0691263	−	0.119730i	0.898517	+	0.438939i	$0.144646\pi$
$882$	−19.4839	−	8.83636i	−0.656056	−	0.297536i
$883$	−4.59858			−0.154755			−0.0773773	−	0.997002i	$-0.524655\pi$
$883$	−4.59858			−0.154755			−0.0773773	+	0.997002i	$0.524655\pi$
$884$	−2.76433	+	5.84410i	−0.0929746	+	0.196558i
$885$	−0.688860	−	2.14525i	−0.0231558	−	0.0721117i
$886$	1.27216			0.0427391
$887$	−58.1282			−1.95175			−0.975877	−	0.218323i	$-0.929941\pi$
$887$	−58.1282			−1.95175			−0.975877	+	0.218323i	$0.929941\pi$
$888$	−20.9838	−	4.53596i	−0.704170	−	0.152217i
$889$	−4.03590	+	6.99038i	−0.135360	+	0.234450i
$890$	−0.884357	−	1.53175i	−0.0296437	−	0.0513444i
$891$	4.09583	−	0.811690i	0.137215	−	0.0271926i
$892$	9.95671			0.333375
$893$	16.6408			0.556865
$894$	8.48176	+	26.4139i	0.283672	+	0.883412i
$895$	−2.82356			−0.0943811
$896$	−0.858450	−	1.48688i	−0.0286788	−	0.0496732i
$897$	−41.2207	−	5.43590i	−1.37632	−	0.181499i
$898$	−9.00603	+	15.5989i	−0.300535	+	0.520542i
$899$	1.25238	−	2.16918i	0.0417691	−	0.0723461i
$900$	9.67044	+	4.38576i	0.322348	+	0.146192i
$901$	0.492151	+	0.852431i	0.0163959	+	0.0283986i
$902$	2.55226	−	4.42065i	0.0849810	−	0.147191i
$903$	1.89354	+	5.89685i	0.0630130	+	0.196235i
$904$	−20.2374	+	35.0523i	−0.673087	+	1.16582i
$905$	−1.27129	−	2.20194i	−0.0422592	−	0.0731950i
$906$	4.00726	+	12.4794i	0.133132	+	0.414601i
$907$	−15.4165	−	26.7022i	−0.511898	−	0.886633i	−0.999905	−	0.0137936i	$-0.995609\pi$
$907$	−15.4165	−	26.7022i	−0.511898	−	0.886633i	0.488007	−	0.872840i	$-0.337724\pi$
$908$	−4.94677	+	8.56806i	−0.164164	+	0.284341i
$909$	−42.7259	−	19.3771i	−1.41713	−	0.642698i
$910$	0.232564	+	0.336050i	0.00770941	+	0.0111399i
$911$	−25.0010	+	43.3031i	−0.828322	+	1.43470i	0.0710324	+	0.997474i	$0.477371\pi$
$911$	−25.0010	+	43.3031i	−0.828322	+	1.43470i	−0.899354	+	0.437221i	$0.855963\pi$
$912$	21.7319	+	4.69768i	0.719616	+	0.155556i
$913$	1.63122			0.0539856
$914$	19.3572	−	33.5276i	0.640278	−	1.10899i
$915$	1.06162	−	1.17090i	0.0350960	−	0.0387087i
$916$	−2.30208			−0.0760627
$917$	−6.97809	−	12.0864i	−0.230437	−	0.399128i
$918$	−13.6812	+	5.92235i	−0.451545	+	0.195467i
$919$	−8.08276	−	13.9998i	−0.266626	−	0.461809i	0.701363	−	0.712805i	$-0.252575\pi$
$919$	−8.08276	−	13.9998i	−0.266626	−	0.461809i	−0.967988	+	0.250995i	$0.919242\pi$
$920$	1.20369	+	2.08485i	0.0396844	+	0.0687354i
$921$	−4.09971	−	12.7673i	−0.135090	−	0.420697i
$922$	2.90922	+	5.03891i	0.0958099	+	0.165948i
$923$	25.9459	−	2.12641i	0.854021	−	0.0699918i
$924$	−0.148141	−	0.461341i	−0.00487349	−	0.0151770i
$925$	10.0396	+	17.3890i	0.330098	+	0.571747i
$926$	4.08770	−	7.08011i	0.134330	−	0.232667i
$927$	−39.5217	−	17.9239i	−1.29806	−	0.588700i
$928$	7.23247			0.237417
$929$	−38.2892			−1.25623			−0.628114	−	0.778122i	$-0.716173\pi$
$929$	−38.2892			−1.25623			−0.628114	+	0.778122i	$0.716173\pi$
$930$	0.0929292	+	0.289400i	0.00304727	+	0.00948980i
$931$	−19.4075	−	33.6147i	−0.636054	−	1.10168i
$932$	−3.44336	+	5.96407i	−0.112791	+	0.195360i
$933$	−10.9566	+	12.0844i	−0.358702	+	0.395626i
$934$	17.7432	+	30.7322i	0.580577	+	1.00559i
$935$	−0.137669			−0.00450224
$936$	−5.94717	−	32.7579i	−0.194389	−	1.07073i
$937$	−3.73973			−0.122172			−0.0610858	−	0.998133i	$-0.519456\pi$
$937$	−3.73973			−0.122172			−0.0610858	+	0.998133i	$0.519456\pi$
$938$	0.493370	+	0.854543i	0.0161091	+	0.0279018i
$939$	−22.2984	−	4.82012i	−0.727679	−	0.157299i
$940$	−0.112234	+	0.194394i	−0.00366066	+	0.00634044i
$941$	−27.4352	−	47.5192i	−0.894363	−	1.54908i	−0.834591	−	0.550871i	$-0.814296\pi$
$941$	−27.4352	−	47.5192i	−0.894363	−	1.54908i	−0.0597725	−	0.998212i	$-0.519038\pi$
$942$	22.5974	+	4.88476i	0.736262	+	0.159154i
$943$	64.4910			2.10012
$944$	−22.9923			−0.748334
$945$	0.0595347	−	0.515096i	0.00193667	−	0.0167561i
$946$	−1.10914	+	1.92109i	−0.0360613	+	0.0624599i
$947$	18.8507	+	32.6503i	0.612565	+	1.06099i	0.990807	+	0.135286i	$0.0431954\pi$
$947$	18.8507	+	32.6503i	0.612565	+	1.06099i	−0.378242	+	0.925707i	$0.623471\pi$
$948$	7.28899	−	8.03930i	0.236735	−	0.261104i
$949$	−5.10797	+	10.7988i	−0.165812	+	0.350544i
$950$	−17.5067	−	30.3225i	−0.567993	−	0.983793i
$951$	42.5515	+	9.19814i	1.37983	+	0.298270i
$952$	3.30209	+	5.71939i	0.107021	+	0.185367i
$953$	−19.3375	−	33.4935i	−0.626402	−	1.08496i	−0.988268	−	0.152730i	$-0.951194\pi$
$953$	−19.3375	−	33.4935i	−0.626402	−	1.08496i	0.361866	−	0.932230i	$-0.382140\pi$
$954$	−1.20930	−	0.548443i	−0.0391525	−	0.0177565i
$955$	−0.322764	−	0.559044i	−0.0104444	−	0.0180902i
$956$	−6.83293			−0.220993
$957$	−1.49588	−	0.323356i	−0.0483548	−	0.0104526i
$958$	17.3022	−	29.9682i	0.559008	−	0.968230i
$959$	−16.5056			−0.532992
$960$	−1.15709	+	1.27620i	−0.0373449	+	0.0411891i
$961$	14.6352	−	25.3489i	0.472103	−	0.817706i
$962$	7.05169	−	14.9080i	0.227356	−	0.480654i
$963$	1.83892	+	18.7390i	0.0592583	+	0.603855i
$964$	−0.101616	+	0.176005i	−0.00327284	+	0.00566873i
$965$	−0.00756074	−	0.0130956i	−0.000243389	−	0.000421562i
$966$	−7.47326	+	8.24254i	−0.240448	+	0.265199i
$967$	3.01037	+	5.21412i	0.0968070	+	0.167675i	0.910361	−	0.413814i	$-0.135804\pi$
$967$	3.01037	+	5.21412i	0.0968070	+	0.167675i	−0.813554	+	0.581489i	$0.802470\pi$
$968$	−16.5976	+	28.7479i	−0.533468	+	0.923993i
$969$	−26.4368	−	5.71471i	−0.849273	−	0.183583i
$970$	−1.05050	+	1.81952i	−0.0337295	+	0.0584213i
$971$	9.27919	+	16.0720i	0.297783	+	0.515776i	0.975629	−	0.219429i	$-0.0704194\pi$
$971$	9.27919	+	16.0720i	0.297783	+	0.515776i	−0.677845	+	0.735205i	$0.737086\pi$
$972$	−5.69727	+	9.48623i	−0.182740	+	0.304271i
$973$	−6.40176	+	11.0882i	−0.205231	+	0.355471i
$974$	−11.7036	+	20.2713i	−0.375008	+	0.649533i
$975$	−18.9615	+	24.7000i	−0.607253	+	0.791032i
$976$	−8.06425	−	13.9677i	−0.258130	−	0.447095i
$977$	30.9608			0.990524			0.495262	−	0.868744i	$-0.335072\pi$
$977$	30.9608			0.990524			0.495262	+	0.868744i	$0.335072\pi$
$978$	27.4444	+	5.93253i	0.877577	+	0.189701i
$979$	−6.14965			−0.196544
$980$	0.523572			0.0167249
$981$	42.7892	−	30.6393i	1.36615	−	0.978238i
$982$	24.4056	+	42.2717i	0.778813	+	1.34894i
$983$	−20.2634	+	35.0972i	−0.646301	+	1.11943i	0.337699	+	0.941254i	$0.390351\pi$
$983$	−20.2634	+	35.0972i	−0.646301	+	1.11943i	−0.983999	+	0.178171i	$0.942982\pi$
$984$	15.7886	+	49.1687i	0.503321	+	1.56744i
$985$	0.423204			0.0134844
$986$	5.46418			0.174015
$987$	−3.87086	−	0.836745i	−0.123211	−	0.0266339i
$988$	6.76579	−	14.3036i	0.215249	−	0.455058i
$989$	−28.0260			−0.891173
$990$	0.150999	−	0.108124i	0.00479907	−	0.00343639i
$991$	−21.8458	+	37.8381i	−0.693955	+	1.20197i	0.276577	+	0.960992i	$0.410800\pi$
$991$	−21.8458	+	37.8381i	−0.693955	+	1.20197i	−0.970532	+	0.240973i	$0.922533\pi$
$992$	−4.99430			−0.158569
$993$	15.4155	+	48.0070i	0.489197	+	1.52346i
$994$	3.48317	−	6.03304i	0.110480	−	0.191356i
$995$	1.20048	−	2.07929i	0.0380576	−	0.0659178i
$996$	−2.90369	+	3.20259i	−0.0920071	+	0.101478i
$997$	−26.8912			−0.851654			−0.425827	−	0.904805i	$-0.640017\pi$
$997$	−26.8912			−0.851654			−0.425827	+	0.904805i	$0.640017\pi$
$998$	−2.40713	+	4.16928i	−0.0761965	+	0.131976i
$999$	−19.2026	+	8.31250i	−0.607544	+	0.262996i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.f.a.61.4	✓	24
3.2	odd	2		351.2.f.a.100.9		24
9.4	even	3		117.2.h.a.22.9	yes	24
9.5	odd	6		351.2.h.a.334.4		24
13.3	even	3		117.2.h.a.16.9	yes	24
39.29	odd	6		351.2.h.a.289.4		24
117.68	odd	6		351.2.f.a.172.9		24
117.94	even	3	inner	117.2.f.a.94.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.4	✓	24	1.1	even	1	trivial
117.2.f.a.94.4	yes	24	117.94	even	3	inner
117.2.h.a.16.9	yes	24	13.3	even	3
117.2.h.a.22.9	yes	24	9.4	even	3
351.2.f.a.100.9		24	3.2	odd	2
351.2.f.a.172.9		24	117.68	odd	6
351.2.h.a.289.4		24	39.29	odd	6
351.2.h.a.334.4		24	9.5	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.567922 - 0.983670i) q^{2} +(-0.529547 - 1.64911i) q^{3} +(0.354929 - 0.614756i) q^{4} +(-0.0587384 - 0.101738i) q^{5} +(-1.32144 + 1.45747i) q^{6} +0.849445 q^{7} -3.07798 q^{8} +(-2.43916 + 1.74657i) q^{9} +(-0.0667177 + 0.115558i) q^{10} +(0.231971 + 0.401786i) q^{11} +(-1.20175 - 0.259777i) q^{12} +(1.54170 - 3.25932i) q^{13} +(-0.482419 - 0.835574i) q^{14} +(-0.136673 + 0.150741i) q^{15} +(1.03819 + 1.79820i) q^{16} +(-1.26296 - 2.18751i) q^{17} +(3.10330 + 1.40741i) q^{18} +(3.09113 + 5.35399i) q^{19} -0.0833920 q^{20} +(-0.449821 - 1.40083i) q^{21} +(0.263483 - 0.456366i) q^{22} +6.65773 q^{23} +(1.62993 + 5.07594i) q^{24} +(2.49310 - 4.31818i) q^{25} +(-4.08166 + 0.334515i) q^{26} +(4.17194 + 3.09756i) q^{27} +(0.301493 - 0.522201i) q^{28} +(-0.952265 - 1.64937i) q^{29} +(0.225899 + 0.0488315i) q^{30} +(0.657577 + 1.13896i) q^{31} +(-1.89875 + 3.28874i) q^{32} +(0.539751 - 0.595312i) q^{33} +(-1.43452 + 2.48467i) q^{34} +(-0.0498951 - 0.0864208i) q^{35} +(0.207983 + 2.11940i) q^{36} +(-2.01347 + 3.48743i) q^{37} +(3.51104 - 6.08129i) q^{38} +(-6.19139 - 0.816478i) q^{39} +(0.180795 + 0.313147i) q^{40} +9.68663 q^{41} +(-1.12249 + 1.23804i) q^{42} -4.20953 q^{43} +0.329333 q^{44} +(0.320965 + 0.145564i) q^{45} +(-3.78107 - 6.54901i) q^{46} +(1.34586 - 2.33109i) q^{47} +(2.41567 - 2.66433i) q^{48} -6.27844 q^{49} -5.66354 q^{50} +(-2.93865 + 3.24115i) q^{51} +(-1.45649 - 2.10460i) q^{52} -0.389682 q^{53} +(0.677644 - 5.86299i) q^{54} +(0.0272512 - 0.0472005i) q^{55} -2.61457 q^{56} +(7.19244 - 7.93281i) q^{57} +(-1.08162 + 1.87343i) q^{58} +(-5.53661 + 9.58969i) q^{59} +(0.0441600 + 0.137523i) q^{60} -7.76759 q^{61} +(0.746905 - 1.29368i) q^{62} +(-2.07193 + 1.48361i) q^{63} +8.46614 q^{64} +(-0.422153 + 0.0345978i) q^{65} +(-0.892126 - 0.192846i) q^{66} -1.02270 q^{67} -1.79304 q^{68} +(-3.52558 - 10.9794i) q^{69} +(-0.0566730 + 0.0981605i) q^{70} +(3.61012 + 6.25291i) q^{71} +(7.50768 - 5.37589i) q^{72} -3.31321 q^{73} +4.57397 q^{74} +(-8.44138 - 1.82473i) q^{75} +4.38853 q^{76} +(0.197047 + 0.341295i) q^{77} +(2.71308 + 6.55398i) q^{78} +(-4.41302 + 7.64357i) q^{79} +(0.121963 - 0.211247i) q^{80} +(2.89900 - 8.52032i) q^{81} +(-5.50125 - 9.52844i) q^{82} +(1.75800 - 3.04495i) q^{83} +(-1.02082 - 0.220667i) q^{84} +(-0.148368 + 0.256981i) q^{85} +(2.39069 + 4.14079i) q^{86} +(-2.21573 + 2.44382i) q^{87} +(-0.714002 - 1.23669i) q^{88} +(-6.62760 + 11.4793i) q^{89} +(-0.0390955 - 0.398392i) q^{90} +(1.30959 - 2.76861i) q^{91} +(2.36303 - 4.09288i) q^{92} +(1.53005 - 1.68755i) q^{93} -3.05736 q^{94} +(0.363136 - 0.628970i) q^{95} +(6.42898 + 1.38972i) q^{96} +15.7455 q^{97} +(3.56567 + 6.17591i) q^{98} +(-1.26756 - 0.574866i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more